%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET518-6 : TPTP v9.2.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n022.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 5 05:07:57 PM UTC 2026
% Result : Unsatisfiable 242.67s 180.62s
% Output : CNFRefutation 243.87s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 17
% Syntax : Number of clauses : 95 ( 22 unt; 34 nHn; 53 RR)
% Number of literals : 195 ( 39 equ; 64 neg)
% Maximal clause size : 3 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-2 aty)
% Number of variables : 168 ( 14 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(subclass_members,axiom,
( member(X3,X2)
| ~ subclass(X1,X2)
| ~ member(X3,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',subclass_members) ).
cnf(class_elements_are_sets,axiom,
subclass(X1,universal_class),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',class_elements_are_sets) ).
cnf(complement1,axiom,
( ~ member(X1,complement(X2))
| ~ member(X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',complement1) ).
cnf(not_subclass_members1,axiom,
( member(not_subclass_element(X1,X2),X1)
| subclass(X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',not_subclass_members1) ).
cnf(unordered_pair_member,axiom,
( X1 = X2
| X1 = X3
| ~ member(X1,unordered_pair(X2,X3)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',unordered_pair_member) ).
cnf(complement2,axiom,
( member(X1,complement(X2))
| member(X1,X2)
| ~ member(X1,universal_class) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',complement2) ).
cnf(not_subclass_members2,axiom,
( subclass(X1,X2)
| ~ member(not_subclass_element(X1,X2),X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',not_subclass_members2) ).
cnf(subclass_implies_equal,axiom,
( X1 = X2
| ~ subclass(X1,X2)
| ~ subclass(X2,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',subclass_implies_equal) ).
cnf(prove_no_cycles_length_2_2,negated_conjecture,
member(y,x),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_no_cycles_length_2_2) ).
cnf(unordered_pair2,axiom,
( member(X1,unordered_pair(X1,X2))
| ~ member(X1,universal_class) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',unordered_pair2) ).
cnf(intersection3,axiom,
( member(X1,intersection(X2,X3))
| ~ member(X1,X2)
| ~ member(X1,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',intersection3) ).
cnf(intersection1,axiom,
( member(X1,X2)
| ~ member(X1,intersection(X2,X3)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',intersection1) ).
cnf(intersection2,axiom,
( member(X1,X3)
| ~ member(X1,intersection(X2,X3)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',intersection2) ).
cnf(regularity1,axiom,
( X1 = null_class
| member(regular(X1),X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',regularity1) ).
cnf(regularity2,axiom,
( X1 = null_class
| intersection(X1,regular(X1)) = null_class ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',regularity2) ).
cnf(unordered_pair3,axiom,
( member(X1,unordered_pair(X2,X1))
| ~ member(X1,universal_class) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',unordered_pair3) ).
cnf(prove_no_cycles_length_2_1,negated_conjecture,
member(x,y),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_no_cycles_length_2_1) ).
cnf(c_0_17,axiom,
( member(X3,X2)
| ~ subclass(X1,X2)
| ~ member(X3,X1) ),
subclass_members ).
cnf(c_0_18,axiom,
subclass(X1,universal_class),
class_elements_are_sets ).
cnf(c_0_19,axiom,
( ~ member(X1,complement(X2))
| ~ member(X1,X2) ),
complement1 ).
cnf(c_0_20,axiom,
( member(not_subclass_element(X1,X2),X1)
| subclass(X1,X2) ),
not_subclass_members1 ).
cnf(c_0_21,plain,
( member(X1,universal_class)
| ~ member(X1,X2) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_22,axiom,
( X1 = X2
| X1 = X3
| ~ member(X1,unordered_pair(X2,X3)) ),
unordered_pair_member ).
cnf(c_0_23,plain,
( subclass(complement(X1),X2)
| ~ member(not_subclass_element(complement(X1),X2),X1) ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_24,axiom,
( member(X1,complement(X2))
| member(X1,X2)
| ~ member(X1,universal_class) ),
complement2 ).
cnf(c_0_25,plain,
( member(not_subclass_element(X1,X2),universal_class)
| subclass(X1,X2) ),
inference(spm,[status(thm)],[c_0_21,c_0_20]) ).
cnf(c_0_26,axiom,
( subclass(X1,X2)
| ~ member(not_subclass_element(X1,X2),X2) ),
not_subclass_members2 ).
cnf(c_0_27,plain,
( not_subclass_element(unordered_pair(X1,X2),X3) = X1
| not_subclass_element(unordered_pair(X1,X2),X3) = X2
| subclass(unordered_pair(X1,X2),X3) ),
inference(spm,[status(thm)],[c_0_22,c_0_20]) ).
cnf(c_0_28,plain,
( member(not_subclass_element(complement(complement(X1)),X2),X1)
| subclass(complement(complement(X1)),X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_25]) ).
cnf(c_0_29,plain,
( member(not_subclass_element(X1,complement(X2)),X2)
| subclass(X1,complement(X2)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_24]),c_0_25]) ).
cnf(c_0_30,plain,
( not_subclass_element(unordered_pair(X1,X1),X2) = X1
| subclass(unordered_pair(X1,X1),X2) ),
inference(er,[status(thm)],[inference(ef,[status(thm)],[c_0_27])]) ).
cnf(c_0_31,axiom,
( X1 = X2
| ~ subclass(X1,X2)
| ~ subclass(X2,X1) ),
subclass_implies_equal ).
cnf(c_0_32,plain,
subclass(complement(complement(X1)),X1),
inference(spm,[status(thm)],[c_0_26,c_0_28]) ).
cnf(c_0_33,plain,
( subclass(X1,complement(complement(X2)))
| ~ member(not_subclass_element(X1,complement(complement(X2))),X2) ),
inference(spm,[status(thm)],[c_0_19,c_0_29]) ).
cnf(c_0_34,plain,
( member(X1,X2)
| subclass(unordered_pair(X1,X1),complement(X2)) ),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_35,plain,
( complement(complement(X1)) = X1
| ~ subclass(X1,complement(complement(X1))) ),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_36,plain,
subclass(X1,complement(complement(X1))),
inference(spm,[status(thm)],[c_0_33,c_0_20]) ).
cnf(c_0_37,plain,
( subclass(unordered_pair(X1,X1),X2)
| ~ member(X1,X2) ),
inference(spm,[status(thm)],[c_0_26,c_0_30]) ).
cnf(c_0_38,plain,
( member(X1,complement(X2))
| member(X3,X2)
| ~ member(X1,unordered_pair(X3,X3)) ),
inference(spm,[status(thm)],[c_0_17,c_0_34]) ).
cnf(c_0_39,plain,
complement(complement(X1)) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_35,c_0_36])]) ).
cnf(c_0_40,plain,
( member(X1,X2)
| ~ member(X1,unordered_pair(X3,X3))
| ~ member(X3,X2) ),
inference(spm,[status(thm)],[c_0_17,c_0_37]) ).
cnf(c_0_41,plain,
( member(not_subclass_element(X1,complement(unordered_pair(X2,X2))),complement(X3))
| member(X2,X3)
| subclass(X1,complement(unordered_pair(X2,X2))) ),
inference(spm,[status(thm)],[c_0_38,c_0_29]) ).
cnf(c_0_42,plain,
( subclass(X1,X2)
| ~ member(not_subclass_element(X1,X2),complement(X1)) ),
inference(spm,[status(thm)],[c_0_23,c_0_39]) ).
cnf(c_0_43,plain,
( member(not_subclass_element(X1,complement(unordered_pair(X2,X2))),X3)
| subclass(X1,complement(unordered_pair(X2,X2)))
| ~ member(X2,X3) ),
inference(spm,[status(thm)],[c_0_40,c_0_29]) ).
cnf(c_0_44,plain,
( member(X1,X2)
| subclass(X2,complement(unordered_pair(X1,X1))) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_41]),c_0_39]) ).
cnf(c_0_45,plain,
( subclass(X1,complement(unordered_pair(X2,X2)))
| ~ member(X2,complement(X1)) ),
inference(spm,[status(thm)],[c_0_42,c_0_43]) ).
cnf(c_0_46,plain,
( member(X1,complement(unordered_pair(X2,X2)))
| member(X2,X3)
| ~ member(X1,X3) ),
inference(spm,[status(thm)],[c_0_17,c_0_44]) ).
cnf(c_0_47,negated_conjecture,
member(y,x),
prove_no_cycles_length_2_2 ).
cnf(c_0_48,plain,
( member(X1,complement(unordered_pair(X2,X2)))
| ~ member(X2,complement(X3))
| ~ member(X1,X3) ),
inference(spm,[status(thm)],[c_0_17,c_0_45]) ).
cnf(c_0_49,negated_conjecture,
( member(y,complement(unordered_pair(X1,X1)))
| member(X1,x) ),
inference(spm,[status(thm)],[c_0_46,c_0_47]) ).
cnf(c_0_50,negated_conjecture,
( member(X1,complement(unordered_pair(y,y)))
| member(X2,x)
| ~ member(X1,unordered_pair(X2,X2)) ),
inference(spm,[status(thm)],[c_0_48,c_0_49]) ).
cnf(c_0_51,axiom,
( member(X1,unordered_pair(X1,X2))
| ~ member(X1,universal_class) ),
unordered_pair2 ).
cnf(c_0_52,axiom,
( member(X1,intersection(X2,X3))
| ~ member(X1,X2)
| ~ member(X1,X3) ),
intersection3 ).
cnf(c_0_53,negated_conjecture,
( member(X1,complement(unordered_pair(y,y)))
| member(X1,x)
| ~ member(X1,universal_class) ),
inference(spm,[status(thm)],[c_0_50,c_0_51]) ).
cnf(c_0_54,axiom,
( member(X1,X2)
| ~ member(X1,intersection(X2,X3)) ),
intersection1 ).
cnf(c_0_55,axiom,
( member(X1,X3)
| ~ member(X1,intersection(X2,X3)) ),
intersection2 ).
cnf(c_0_56,plain,
( subclass(X1,intersection(X2,X3))
| ~ member(not_subclass_element(X1,intersection(X2,X3)),X3)
| ~ member(not_subclass_element(X1,intersection(X2,X3)),X2) ),
inference(spm,[status(thm)],[c_0_26,c_0_52]) ).
cnf(c_0_57,negated_conjecture,
( member(X1,x)
| ~ member(X1,unordered_pair(y,y)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_53]),c_0_21]) ).
cnf(c_0_58,plain,
( member(not_subclass_element(intersection(X1,X2),X3),X1)
| subclass(intersection(X1,X2),X3) ),
inference(spm,[status(thm)],[c_0_54,c_0_20]) ).
cnf(c_0_59,plain,
( member(not_subclass_element(intersection(X1,X2),X3),X2)
| subclass(intersection(X1,X2),X3) ),
inference(spm,[status(thm)],[c_0_55,c_0_20]) ).
cnf(c_0_60,plain,
( subclass(X1,intersection(X2,X1))
| ~ member(not_subclass_element(X1,intersection(X2,X1)),X2) ),
inference(spm,[status(thm)],[c_0_56,c_0_20]) ).
cnf(c_0_61,negated_conjecture,
( member(not_subclass_element(unordered_pair(y,y),X1),x)
| subclass(unordered_pair(y,y),X1) ),
inference(spm,[status(thm)],[c_0_57,c_0_20]) ).
cnf(c_0_62,plain,
( subclass(intersection(X1,X2),intersection(X3,X1))
| ~ member(not_subclass_element(intersection(X1,X2),intersection(X3,X1)),X3) ),
inference(spm,[status(thm)],[c_0_56,c_0_58]) ).
cnf(c_0_63,plain,
( member(not_subclass_element(intersection(X1,intersection(X2,X3)),X4),X2)
| subclass(intersection(X1,intersection(X2,X3)),X4) ),
inference(spm,[status(thm)],[c_0_54,c_0_59]) ).
cnf(c_0_64,negated_conjecture,
subclass(unordered_pair(y,y),intersection(x,unordered_pair(y,y))),
inference(spm,[status(thm)],[c_0_60,c_0_61]) ).
cnf(c_0_65,plain,
subclass(intersection(X1,X2),X2),
inference(spm,[status(thm)],[c_0_26,c_0_59]) ).
cnf(c_0_66,plain,
subclass(intersection(X1,intersection(X2,X3)),intersection(X2,X1)),
inference(spm,[status(thm)],[c_0_62,c_0_63]) ).
cnf(c_0_67,negated_conjecture,
intersection(x,unordered_pair(y,y)) = unordered_pair(y,y),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_64]),c_0_65])]) ).
cnf(c_0_68,plain,
( subclass(unordered_pair(X1,X1),intersection(X2,unordered_pair(X1,X1)))
| ~ member(X1,X2) ),
inference(spm,[status(thm)],[c_0_60,c_0_30]) ).
cnf(c_0_69,negated_conjecture,
subclass(intersection(X1,unordered_pair(y,y)),intersection(x,X1)),
inference(spm,[status(thm)],[c_0_66,c_0_67]) ).
cnf(c_0_70,plain,
( intersection(X1,unordered_pair(X2,X2)) = unordered_pair(X2,X2)
| ~ member(X2,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_68]),c_0_65])]) ).
cnf(c_0_71,axiom,
( X1 = null_class
| member(regular(X1),X1) ),
regularity1 ).
cnf(c_0_72,negated_conjecture,
( subclass(unordered_pair(y,y),intersection(x,X1))
| ~ member(y,X1) ),
inference(spm,[status(thm)],[c_0_69,c_0_70]) ).
cnf(c_0_73,axiom,
( X1 = null_class
| intersection(X1,regular(X1)) = null_class ),
regularity2 ).
cnf(c_0_74,plain,
( regular(unordered_pair(X1,X2)) = X1
| regular(unordered_pair(X1,X2)) = X2
| unordered_pair(X1,X2) = null_class ),
inference(spm,[status(thm)],[c_0_22,c_0_71]) ).
cnf(c_0_75,plain,
subclass(intersection(X1,X2),intersection(X2,X1)),
inference(spm,[status(thm)],[c_0_62,c_0_59]) ).
cnf(c_0_76,plain,
( complement(X1) = null_class
| ~ member(regular(complement(X1)),X1) ),
inference(spm,[status(thm)],[c_0_19,c_0_71]) ).
cnf(c_0_77,plain,
( X1 = null_class
| member(regular(X1),universal_class) ),
inference(spm,[status(thm)],[c_0_21,c_0_71]) ).
cnf(c_0_78,negated_conjecture,
( member(X1,intersection(x,X2))
| ~ member(X1,unordered_pair(y,y))
| ~ member(y,X2) ),
inference(spm,[status(thm)],[c_0_17,c_0_72]) ).
cnf(c_0_79,negated_conjecture,
member(y,universal_class),
inference(spm,[status(thm)],[c_0_21,c_0_47]) ).
cnf(c_0_80,plain,
( intersection(unordered_pair(X1,X2),X1) = null_class
| regular(unordered_pair(X1,X2)) = X2
| unordered_pair(X1,X2) = null_class ),
inference(spm,[status(thm)],[c_0_73,c_0_74]) ).
cnf(c_0_81,plain,
intersection(X1,X2) = intersection(X2,X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_75]),c_0_75])]) ).
cnf(c_0_82,plain,
complement(universal_class) = null_class,
inference(spm,[status(thm)],[c_0_76,c_0_77]) ).
cnf(c_0_83,negated_conjecture,
( member(y,intersection(x,X1))
| ~ member(y,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_51]),c_0_79])]) ).
cnf(c_0_84,plain,
( intersection(X1,unordered_pair(X1,X2)) = null_class
| regular(unordered_pair(X1,X2)) = X2
| unordered_pair(X1,X2) = null_class ),
inference(rw,[status(thm)],[c_0_80,c_0_81]) ).
cnf(c_0_85,plain,
~ member(X1,null_class),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_82]),c_0_21]) ).
cnf(c_0_86,negated_conjecture,
( regular(unordered_pair(x,X1)) = X1
| unordered_pair(x,X1) = null_class
| ~ member(y,unordered_pair(x,X1)) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_84]),c_0_85]) ).
cnf(c_0_87,axiom,
( member(X1,unordered_pair(X2,X1))
| ~ member(X1,universal_class) ),
unordered_pair3 ).
cnf(c_0_88,plain,
( X1 = null_class
| ~ member(X2,regular(X1))
| ~ member(X2,X1) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_73]),c_0_85]) ).
cnf(c_0_89,negated_conjecture,
( regular(unordered_pair(x,y)) = y
| unordered_pair(x,y) = null_class ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_87]),c_0_79])]) ).
cnf(c_0_90,negated_conjecture,
member(x,y),
prove_no_cycles_length_2_1 ).
cnf(c_0_91,negated_conjecture,
( unordered_pair(x,y) = null_class
| ~ member(X1,unordered_pair(x,y))
| ~ member(X1,y) ),
inference(spm,[status(thm)],[c_0_88,c_0_89]) ).
cnf(c_0_92,negated_conjecture,
member(x,universal_class),
inference(spm,[status(thm)],[c_0_21,c_0_90]) ).
cnf(c_0_93,negated_conjecture,
unordered_pair(x,y) = null_class,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_51]),c_0_90]),c_0_92])]) ).
cnf(c_0_94,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_93]),c_0_92])]),c_0_85]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET518-6 : TPTP v9.2.1. Bugfixed v2.1.0.
% 0.00/0.12 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.16/0.33 % Computer : n022.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Tue May 5 02:25:36 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 242.67/180.62 % Version : CSE_E---1.7
% 242.67/180.62 % Problem : theBenchmark.p
% 242.67/180.62 % SZS status Unsatisfiable for theBenchmark.p
% 242.67/180.62 % SZS output start CNFRefutation
% See solution above
% 243.87/181.83 % Total time : 127.556s
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