E use the current version of the new TSTP output format, documented in [SSCG2006]. Initial clauses and formulas are renamed, but sourced to their input file and original name. The following rule names are defined for the main proof search:
Additionally, the clausification will use additional rule names:
The first proof uses most inferences, although it uses some in fairly trivial ways. The second is the required CASC proof for SYN075-1, and contains examples for "ef" and "csr". The final proof is for SYN075+1, and also contains the clausification steps.
ALL_RULES
# SZS status Theorem # SZS output start CNFRefutation. fof(c_0_0, axiom, (((d=c|d=c)<=>h(i(e))=h(i(a)))), file('ALL_RULES.p', guarded_eq)). fof(c_0_1, conjecture, ((?[X3]:?[X4]:?[X1]:?[X2]:?[X5]:(k(a,b)=k(X3,X3)&f(f(g(X2,X5),X1),f(X4,X3))=f(f(X3,X4),f(X1,g(X2,X5))))&![X6]:p(X6))), file('ALL_RULES.p', conj)). cnf(c_0_2, axiom, (c=b|X1!=X2|X3!=X4|d!=c), file('ALL_RULES.p', split_or_condense)). cnf(c_0_3, axiom, (i(X1)=i(X2)), file('ALL_RULES.p', identity)). cnf(c_0_4, axiom, (p(X1)), file('ALL_RULES.p', p_holds)). cnf(c_0_5, axiom, (f(X1,X2)=f(X2,X1)), file('ALL_RULES.p', comm_f)). cnf(c_0_6, axiom, (g(X1,X2)=g(X2,X1)), file('ALL_RULES.p', comm_g)). cnf(c_0_7, axiom, (f(f(X1,X2),X3)=f(X1,f(X2,X3))), file('ALL_RULES.p', ass_f)). cnf(c_0_8, axiom, (a=b|c=a|e=a), file('ALL_RULES.p', consts1)). cnf(c_0_9, axiom, (a=b|c=a|e!=a), file('ALL_RULES.p', consts2)). fof(c_0_10, plain, ((~epred2_0<=>![X2]:![X1]:X1!=X2)), introduced(definition)). cnf(c_0_11, plain, (epred2_0|X1!=X2), inference(split_equiv,[status(thm)],[c_0_10])). fof(c_0_12, plain, ((~epred1_0<=>![X4]:![X3]:((c=b|X3!=X4)|d!=c))), introduced(definition)). cnf(c_0_13, plain, (epred2_0), inference(er,[status(thm)],[c_0_11])). fof(c_0_14, plain, ((d=c<=>h(i(e))=h(i(a)))), inference(fof_simplification,[status(thm)],[c_0_0])). fof(c_0_15, negated_conjecture, (~((?[X3]:?[X4]:?[X1]:?[X2]:?[X5]:(k(a,b)=k(X3,X3)&f(f(g(X2,X5),X1),f(X4,X3))=f(f(X3,X4),f(X1,g(X2,X5))))&![X6]:p(X6)))), inference(assume_negation,[status(cth)],[c_0_1])). cnf(c_0_16, plain, (~epred1_0), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_2, c_0_12]), c_0_10]), c_0_13])])). fof(c_0_17, plain, (((d!=c|h(i(e))=h(i(a)))&(h(i(e))!=h(i(a))|d=c))), inference(fof_nnf,[status(thm)],[c_0_14])). fof(c_0_18, negated_conjecture, (![X7]:![X8]:![X9]:![X10]:![X11]:((k(a,b)!=k(X7,X7)|f(f(g(X10,X11),X9),f(X8,X7))!=f(f(X7,X8),f(X9,g(X10,X11))))|~p(esk1_0))), inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_15])])])])])). cnf(c_0_19, plain, (c=b|d!=c|X1!=X2), inference(sr,[status(thm)],[inference(split_equiv,[status(thm)],[c_0_12]), c_0_16])). cnf(c_0_20, plain, (d=c|h(i(e))!=h(i(a))), inference(split_conjunct,[status(thm)],[c_0_17])). cnf(c_0_21, negated_conjecture, (~p(esk1_0)|f(f(g(X1,X2),X3),f(X4,X5))!=f(f(X5,X4),f(X3,g(X1,X2)))|k(a,b)!=k(X5,X5)), inference(split_conjunct,[status(thm)],[c_0_18])). cnf(c_0_22, plain, (c=b|d!=c), inference(er,[status(thm)],[c_0_19])). cnf(c_0_23, plain, (d=c), inference(sr,[status(thm)],[c_0_20, c_0_3])). cnf(c_0_24, negated_conjecture, (k(a,b)!=k(X5,X5)|f(f(g(X1,X2),X3),f(X4,X5))!=f(f(X5,X4),f(X3,g(X1,X2)))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_21, c_0_4])])). cnf(c_0_25, plain, (f(X1,X2)=f(X2,X1)), c_0_5). cnf(c_0_26, plain, (g(X1,X2)=g(X2,X1)), c_0_6). cnf(c_0_27, plain, (f(f(X1,X2),X3)=f(X1,f(X2,X3))), c_0_7). cnf(c_0_28, plain, (c=a|a=b), inference(csr,[status(thm)],[c_0_8, c_0_9])). cnf(c_0_29, plain, (c=b), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_22, c_0_23])])). cnf(c_0_30, negated_conjecture, (k(a,b)!=k(X1,X1)), inference(ar,[status(thm)],[c_0_24, c_0_25, c_0_26, c_0_27])). cnf(c_0_31, plain, (a=b), inference(pm,[status(thm)],[c_0_28, c_0_29])). cnf(c_0_32, negated_conjecture, (k(b,b)!=k(X1,X1)), inference(rw,[status(thm)],[c_0_30, c_0_31])). cnf(c_0_33, negated_conjecture, ($false), inference(er,[status(thm)],[c_0_32]), ['proof']). # SZS output end CNFRefutation.
SYN075-1
# SZS status Unsatisfiable # SZS output start CNFRefutation. cnf(c_0_0, negated_conjecture, (big_f(X1,f(X2))|f(X2)=X2|X1!=g(X2)), file('/Users/schulz/EPROVER/TPTP_6.0.0_FLAT/SYN075-1.p', clause_6)). cnf(c_0_1, negated_conjecture, (f(X2)=X2|~big_f(X1,f(X2))|X1!=g(X2)), file('/Users/schulz/EPROVER/TPTP_6.0.0_FLAT/SYN075-1.p', clause_4)). cnf(c_0_2, negated_conjecture, (big_f(h(X1,X2),f(X1))|h(X1,X2)=X2|f(X1)!=X1), file('/Users/schulz/EPROVER/TPTP_6.0.0_FLAT/SYN075-1.p', clause_9)). cnf(c_0_3, axiom, (X1=a|~big_f(X1,X2)), file('/Users/schulz/EPROVER/TPTP_6.0.0_FLAT/SYN075-1.p', clause_1)). cnf(c_0_4, negated_conjecture, (f(X1)!=X1|h(X1,X2)!=X2|~big_f(h(X1,X2),f(X1))), file('/Users/schulz/EPROVER/TPTP_6.0.0_FLAT/SYN075-1.p', clause_10)). cnf(c_0_5, axiom, (big_f(X1,X2)|X1!=a|X2!=b), file('/Users/schulz/EPROVER/TPTP_6.0.0_FLAT/SYN075-1.p', clause_3)). cnf(c_0_6, negated_conjecture, (f(X1)=X1|g(X1)!=X2), inference(csr,[status(thm)],[c_0_0, c_0_1])). cnf(c_0_7, negated_conjecture, (f(X1)=X1), inference(er,[status(thm)],[c_0_6])). cnf(c_0_8, negated_conjecture, (h(X1,X2)=X2|big_f(h(X1,X2),X1)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_2, c_0_7]), c_0_7])])). cnf(c_0_9, negated_conjecture, (h(X1,X2)=a|h(X1,X2)=X2), inference(pm,[status(thm)],[c_0_3, c_0_8])). cnf(c_0_10, negated_conjecture, (h(X1,X2)!=X2|~big_f(h(X1,X2),X1)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_4, c_0_7]), c_0_7])])). cnf(c_0_11, negated_conjecture, (h(X1,X2)=X2|a!=X2), inference(ef,[status(thm)],[c_0_9])). fof(c_0_12, plain, ((~epred1_0<=>![X2]:a!=X2)), introduced(definition)). cnf(c_0_13, negated_conjecture, (h(X1,X2)!=X2|~big_f(X2,X1)), inference(csr,[status(thm)],[inference(pm,[status(thm)],[c_0_10, c_0_11]), c_0_3])). cnf(c_0_14, negated_conjecture, (h(X1,X2)=X2|big_f(a,X1)), inference(pm,[status(thm)],[c_0_8, c_0_9])). cnf(c_0_15, negated_conjecture, (epred1_0|a!=X1), inference(split_equiv,[status(thm)],[c_0_12])). fof(c_0_16, plain, ((~epred2_0<=>![X1]:b!=X1)), introduced(definition)). cnf(c_0_17, negated_conjecture, (big_f(a,X1)|~big_f(X2,X1)), inference(pm,[status(thm)],[c_0_13, c_0_14])). cnf(c_0_18, negated_conjecture, (~big_f(X1,X2)), inference(csr,[status(thm)],[inference(pm,[status(thm)],[c_0_13, c_0_11]), c_0_3])). cnf(c_0_19, negated_conjecture, (epred1_0), inference(er,[status(thm)],[c_0_15])). cnf(c_0_20, negated_conjecture, (~epred2_0), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(sr,[status(thm)],[inference(pm,[status(thm)],[c_0_17, c_0_5]), c_0_18]), c_0_12]), c_0_16]), c_0_19])])). cnf(c_0_21, negated_conjecture, (b!=X1), inference(sr,[status(thm)],[inference(split_equiv,[status(thm)],[c_0_16]), c_0_20])). cnf(c_0_22, negated_conjecture, ($false), inference(er,[status(thm)],[c_0_21]), ['proof']). # SZS output end CNFRefutation.
SYN075+1
fof(c_0_0, conjecture, (?[X2]:![X4]:(?[X1]:![X3]:(big_f(X3,X4)<=>X3=X1)<=>X4=X2)), file('/Users/schulz/EPROVER/TPTP_6.0.0_FLAT/SYN075+1.p', pel52)). fof(c_0_1, axiom, (?[X1]:?[X2]:![X3]:![X4]:(big_f(X3,X4)<=>(X3=X1&X4=X2))), file('/Users/schulz/EPROVER/TPTP_6.0.0_FLAT/SYN075+1.p', pel52_1)). fof(c_0_2, negated_conjecture, (~(?[X2]:![X4]:(?[X1]:![X3]:(big_f(X3,X4)<=>X3=X1)<=>X4=X2))), inference(assume_negation,[status(cth)],[c_0_0])). fof(c_0_3, plain, (![X7]:![X8]:![X9]:![X10]:(((X7=esk1_0|~big_f(X7,X8))&(X8=esk2_0|~big_f(X7,X8)))&((X9!=esk1_0|X10!=esk2_0)|big_f(X9,X10)))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1])])])])])])). fof(c_0_4, negated_conjecture, (![X5]:![X7]:![X10]:![X11]:((((~big_f(esk4_2(X5,X7),esk3_1(X5))|esk4_2(X5,X7)!=X7)|esk3_1(X5)!=X5)&((big_f(esk4_2(X5,X7),esk3_1(X5))|esk4_2(X5,X7)=X7)|esk3_1(X5)!=X5))&(((~big_f(X10,esk3_1(X5))|X10=esk5_1(X5))|esk3_1(X5)=X5)&((X11!=esk5_1(X5)|big_f(X11,esk3_1(X5)))|esk3_1(X5)=X5)))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2])])])])])])). cnf(c_0_5, plain, (X2=esk2_0|~big_f(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_3])). cnf(c_0_6, negated_conjecture, (esk3_1(X1)=X1|big_f(X2,esk3_1(X1))|X2!=esk5_1(X1)), inference(split_conjunct,[status(thm)],[c_0_4])). cnf(c_0_7, negated_conjecture, (esk3_1(X1)=esk2_0|esk3_1(X1)=X1|esk5_1(X1)!=X2), inference(pm,[status(thm)],[c_0_5, c_0_6])). cnf(c_0_8, negated_conjecture, (esk3_1(X1)=esk2_0|esk3_1(X1)=X1), inference(er,[status(thm)],[c_0_7])). cnf(c_0_9, plain, (X1=esk1_0|~big_f(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_3])). cnf(c_0_10, negated_conjecture, (esk4_2(X1,X2)=X2|big_f(esk4_2(X1,X2),esk3_1(X1))|esk3_1(X1)!=X1), inference(split_conjunct,[status(thm)],[c_0_4])). cnf(c_0_11, negated_conjecture, (esk3_1(X1)!=X1|esk4_2(X1,X2)!=X2|~big_f(esk4_2(X1,X2),esk3_1(X1))), inference(split_conjunct,[status(thm)],[c_0_4])). cnf(c_0_12, negated_conjecture, (esk3_1(X1)=X1|esk2_0!=X1), inference(ef,[status(thm)],[c_0_8])). cnf(c_0_13, negated_conjecture, (esk4_2(X1,X2)=esk1_0|esk4_2(X1,X2)=X2|esk3_1(X1)!=X1), inference(pm,[status(thm)],[c_0_9, c_0_10])). cnf(c_0_14, negated_conjecture, (esk4_2(X1,X2)!=X2|esk3_1(X1)!=X1|~big_f(esk4_2(X1,X2),X1)), inference(csr,[status(thm)],[inference(pm,[status(thm)],[c_0_11, c_0_12]), c_0_5])). cnf(c_0_15, negated_conjecture, (esk4_2(X1,X2)=X2|esk3_1(X1)!=X1|esk1_0!=X2), inference(ef,[status(thm)],[c_0_13])). cnf(c_0_16, negated_conjecture, (esk4_2(X1,X2)!=X2|esk3_1(X1)!=X1|~big_f(X2,X1)), inference(csr,[status(thm)],[inference(pm,[status(thm)],[c_0_14, c_0_15]), c_0_9])). cnf(c_0_17, negated_conjecture, (esk4_2(X1,X2)=X2|esk3_1(X1)=esk2_0), inference(csr,[status(thm)],[inference(pm,[status(thm)],[c_0_5, c_0_10]), c_0_8])). cnf(c_0_18, negated_conjecture, (esk3_1(X1)=X1|big_f(X2,esk2_0)|esk5_1(X1)!=X2), inference(pm,[status(thm)],[c_0_6, c_0_8])). cnf(c_0_19, negated_conjecture, (esk3_1(X1)=esk2_0|~big_f(X2,X1)), inference(csr,[status(thm)],[inference(pm,[status(thm)],[c_0_16, c_0_17]), c_0_8])). cnf(c_0_20, negated_conjecture, (esk3_1(X1)=X1|big_f(esk5_1(X1),esk2_0)), inference(er,[status(thm)],[c_0_18])). cnf(c_0_21, negated_conjecture, (esk4_2(X1,X2)=esk1_0|esk3_1(X1)!=X1|X2!=esk1_0), inference(ef,[status(thm)],[c_0_13])). cnf(c_0_22, negated_conjecture, (esk3_1(esk2_0)=esk2_0|esk3_1(X1)=X1), inference(pm,[status(thm)],[c_0_19, c_0_20])). cnf(c_0_23, negated_conjecture, (esk3_1(X1)!=X1|~big_f(X2,X1)), inference(csr,[status(thm)],[inference(pm,[status(thm)],[c_0_16, c_0_21]), c_0_9])). cnf(c_0_24, negated_conjecture, (esk3_1(esk2_0)=esk2_0), inference(ef,[status(thm)],[c_0_22])). fof(c_0_25, plain, ((~epred11_0<=>![X1]:esk1_0!=X1)), introduced(definition)). cnf(c_0_26, negated_conjecture, (esk3_1(X1)=X1), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(pm,[status(thm)],[c_0_23, c_0_20]), c_0_24])])). cnf(c_0_27, negated_conjecture, (epred11_0|esk1_0!=X1), inference(split_equiv,[status(thm)],[c_0_25])). fof(c_0_28, plain, ((~epred12_0<=>![X2]:esk2_0!=X2)), introduced(definition)). cnf(c_0_29, negated_conjecture, (~big_f(X1,X2)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_23, c_0_26])])). cnf(c_0_30, plain, (big_f(X1,X2)|X2!=esk2_0|X1!=esk1_0), inference(split_conjunct,[status(thm)],[c_0_3])). cnf(c_0_31, negated_conjecture, (epred11_0), inference(er,[status(thm)],[c_0_27])). cnf(c_0_32, negated_conjecture, (epred12_0|esk2_0!=X1), inference(split_equiv,[status(thm)],[c_0_28])). cnf(c_0_33, negated_conjecture, (~epred12_0), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(pm,[status(thm)],[c_0_29, c_0_30]), c_0_25]), c_0_28]), c_0_31])])). cnf(c_0_34, negated_conjecture, ($false), inference(sr,[status(thm)],[inference(er,[status(thm)],[c_0_32]), c_0_33]), ['proof']). # SZS output end CNFRefutation.