%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET128-6 : 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 : n019.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 05:07:24 PM UTC 2026
% Result : Unsatisfiable 10.47s 7.19s
% Output : CNFRefutation 10.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 16
% Syntax : Number of clauses : 91 ( 32 unt; 27 nHn; 45 RR)
% Number of literals : 164 ( 65 equ; 54 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 11 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 5 con; 0-2 aty)
% Number of variables : 157 ( 13 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(intersection2,axiom,
( member(X1,X3)
| ~ member(X1,intersection(X2,X3)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',intersection2) ).
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(regularity1,axiom,
( X1 = null_class
| member(regular(X1),X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',regularity1) ).
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(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(complement1,axiom,
( ~ member(X1,complement(X2))
| ~ member(X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',complement1) ).
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(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(complement2,axiom,
( member(X1,complement(X2))
| member(X1,X2)
| ~ member(X1,universal_class) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',complement2) ).
cnf(definition_of_set_builder,axiom,
union(singleton(X1),X2) = set_builder(X1,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',definition_of_set_builder) ).
cnf(singleton_set,axiom,
unordered_pair(X1,X1) = singleton(X1),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',singleton_set) ).
cnf(prove_building_a_triple_1,negated_conjecture,
union(singleton(x),union(singleton(y),singleton(z))) != set_builder(x,set_builder(y,set_builder(z,null_class))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_building_a_triple_1) ).
cnf(union,axiom,
complement(intersection(complement(X1),complement(X2))) = union(X1,X2),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',union) ).
cnf(c_0_16,axiom,
( member(X1,X3)
| ~ member(X1,intersection(X2,X3)) ),
intersection2 ).
cnf(c_0_17,axiom,
( member(not_subclass_element(X1,X2),X1)
| subclass(X1,X2) ),
not_subclass_members1 ).
cnf(c_0_18,axiom,
( X1 = X2
| X1 = X3
| ~ member(X1,unordered_pair(X2,X3)) ),
unordered_pair_member ).
cnf(c_0_19,axiom,
( X1 = null_class
| member(regular(X1),X1) ),
regularity1 ).
cnf(c_0_20,axiom,
( member(X3,X2)
| ~ subclass(X1,X2)
| ~ member(X3,X1) ),
subclass_members ).
cnf(c_0_21,axiom,
subclass(X1,universal_class),
class_elements_are_sets ).
cnf(c_0_22,axiom,
( subclass(X1,X2)
| ~ member(not_subclass_element(X1,X2),X2) ),
not_subclass_members2 ).
cnf(c_0_23,plain,
( member(not_subclass_element(intersection(X1,X2),X3),X2)
| subclass(intersection(X1,X2),X3) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_24,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_18,c_0_17]) ).
cnf(c_0_25,plain,
( intersection(X1,X2) = null_class
| member(regular(intersection(X1,X2)),X2) ),
inference(spm,[status(thm)],[c_0_16,c_0_19]) ).
cnf(c_0_26,axiom,
( ~ member(X1,complement(X2))
| ~ member(X1,X2) ),
complement1 ).
cnf(c_0_27,plain,
( member(X1,universal_class)
| ~ member(X1,X2) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_28,axiom,
( X1 = X2
| ~ subclass(X1,X2)
| ~ subclass(X2,X1) ),
subclass_implies_equal ).
cnf(c_0_29,plain,
subclass(intersection(X1,X2),X2),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
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_24])]) ).
cnf(c_0_31,plain,
( regular(intersection(X1,unordered_pair(X2,X3))) = X2
| regular(intersection(X1,unordered_pair(X2,X3))) = X3
| intersection(X1,unordered_pair(X2,X3)) = null_class ),
inference(spm,[status(thm)],[c_0_18,c_0_25]) ).
cnf(c_0_32,axiom,
( member(X1,intersection(X2,X3))
| ~ member(X1,X2)
| ~ member(X1,X3) ),
intersection3 ).
cnf(c_0_33,axiom,
( member(X1,X2)
| ~ member(X1,intersection(X2,X3)) ),
intersection1 ).
cnf(c_0_34,plain,
( complement(X1) = null_class
| ~ member(regular(complement(X1)),X1) ),
inference(spm,[status(thm)],[c_0_26,c_0_19]) ).
cnf(c_0_35,plain,
( X1 = null_class
| member(regular(X1),universal_class) ),
inference(spm,[status(thm)],[c_0_27,c_0_19]) ).
cnf(c_0_36,axiom,
( member(X1,complement(X2))
| member(X1,X2)
| ~ member(X1,universal_class) ),
complement2 ).
cnf(c_0_37,plain,
( intersection(X1,X2) = X2
| ~ subclass(X2,intersection(X1,X2)) ),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_38,plain,
( subclass(unordered_pair(X1,X1),X2)
| ~ member(X1,X2) ),
inference(spm,[status(thm)],[c_0_22,c_0_30]) ).
cnf(c_0_39,plain,
( regular(intersection(X1,unordered_pair(X2,X2))) = X2
| intersection(X1,unordered_pair(X2,X2)) = null_class ),
inference(er,[status(thm)],[inference(ef,[status(thm)],[c_0_31])]) ).
cnf(c_0_40,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_22,c_0_32]) ).
cnf(c_0_41,plain,
( member(not_subclass_element(intersection(X1,X2),X3),X1)
| subclass(intersection(X1,X2),X3) ),
inference(spm,[status(thm)],[c_0_33,c_0_17]) ).
cnf(c_0_42,plain,
complement(universal_class) = null_class,
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_43,plain,
( member(not_subclass_element(X1,complement(X2)),X2)
| subclass(X1,complement(X2))
| ~ member(not_subclass_element(X1,complement(X2)),universal_class) ),
inference(spm,[status(thm)],[c_0_22,c_0_36]) ).
cnf(c_0_44,plain,
( intersection(X1,unordered_pair(X2,X2)) = unordered_pair(X2,X2)
| ~ member(X2,intersection(X1,unordered_pair(X2,X2))) ),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_45,plain,
( intersection(X1,unordered_pair(X2,X2)) = null_class
| member(X2,intersection(X1,unordered_pair(X2,X2))) ),
inference(spm,[status(thm)],[c_0_19,c_0_39]) ).
cnf(c_0_46,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_40,c_0_41]) ).
cnf(c_0_47,plain,
( subclass(complement(X1),X2)
| ~ member(not_subclass_element(complement(X1),X2),X1) ),
inference(spm,[status(thm)],[c_0_26,c_0_17]) ).
cnf(c_0_48,plain,
( member(not_subclass_element(X1,X2),universal_class)
| subclass(X1,X2) ),
inference(spm,[status(thm)],[c_0_27,c_0_17]) ).
cnf(c_0_49,plain,
( intersection(X1,X2) = null_class
| member(regular(intersection(X1,X2)),X1) ),
inference(spm,[status(thm)],[c_0_33,c_0_19]) ).
cnf(c_0_50,axiom,
union(singleton(X1),X2) = set_builder(X1,X2),
definition_of_set_builder ).
cnf(c_0_51,axiom,
unordered_pair(X1,X1) = singleton(X1),
singleton_set ).
cnf(c_0_52,plain,
~ member(X1,null_class),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_42]),c_0_27]) ).
cnf(c_0_53,plain,
( member(not_subclass_element(universal_class,complement(X1)),X1)
| subclass(universal_class,complement(X1)) ),
inference(spm,[status(thm)],[c_0_43,c_0_17]) ).
cnf(c_0_54,plain,
( intersection(X1,unordered_pair(X2,X2)) = unordered_pair(X2,X2)
| intersection(X1,unordered_pair(X2,X2)) = null_class ),
inference(spm,[status(thm)],[c_0_44,c_0_45]) ).
cnf(c_0_55,plain,
subclass(intersection(X1,X2),intersection(X2,X1)),
inference(spm,[status(thm)],[c_0_46,c_0_23]) ).
cnf(c_0_56,plain,
( subclass(X1,intersection(X2,X1))
| ~ member(not_subclass_element(X1,intersection(X2,X1)),X2) ),
inference(spm,[status(thm)],[c_0_40,c_0_17]) ).
cnf(c_0_57,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_47,c_0_36]),c_0_48]) ).
cnf(c_0_58,plain,
( intersection(complement(X1),X2) = null_class
| ~ member(regular(intersection(complement(X1),X2)),X1) ),
inference(spm,[status(thm)],[c_0_26,c_0_49]) ).
cnf(c_0_59,plain,
( intersection(X1,intersection(X2,X3)) = null_class
| member(regular(intersection(X1,intersection(X2,X3))),X2) ),
inference(spm,[status(thm)],[c_0_33,c_0_25]) ).
cnf(c_0_60,negated_conjecture,
union(singleton(x),union(singleton(y),singleton(z))) != set_builder(x,set_builder(y,set_builder(z,null_class))),
prove_building_a_triple_1 ).
cnf(c_0_61,plain,
union(unordered_pair(X1,X1),X2) = set_builder(X1,X2),
inference(rw,[status(thm)],[c_0_50,c_0_51]) ).
cnf(c_0_62,axiom,
complement(intersection(complement(X1),complement(X2))) = union(X1,X2),
union ).
cnf(c_0_63,plain,
subclass(universal_class,complement(null_class)),
inference(spm,[status(thm)],[c_0_52,c_0_53]) ).
cnf(c_0_64,plain,
( intersection(X1,unordered_pair(X2,X2)) = null_class
| unordered_pair(X2,X2) != null_class ),
inference(ef,[status(thm)],[c_0_54]) ).
cnf(c_0_65,plain,
intersection(X1,X2) = intersection(X2,X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_55]),c_0_55])]) ).
cnf(c_0_66,plain,
subclass(complement(complement(X1)),intersection(X1,complement(complement(X1)))),
inference(spm,[status(thm)],[c_0_56,c_0_57]) ).
cnf(c_0_67,plain,
intersection(complement(X1),intersection(X1,X2)) = null_class,
inference(spm,[status(thm)],[c_0_58,c_0_59]) ).
cnf(c_0_68,negated_conjecture,
complement(intersection(complement(unordered_pair(x,x)),complement(complement(intersection(complement(unordered_pair(y,y)),complement(unordered_pair(z,z))))))) != complement(intersection(complement(unordered_pair(x,x)),complement(complement(intersection(complement(unordered_pair(y,y)),complement(complement(intersection(complement(unordered_pair(z,z)),complement(null_class))))))))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_60,c_0_51]),c_0_51]),c_0_51]),c_0_61]),c_0_61]),c_0_61]),c_0_62]),c_0_62]),c_0_62]),c_0_62]),c_0_62]) ).
cnf(c_0_69,plain,
complement(null_class) = universal_class,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_63]),c_0_21])]) ).
cnf(c_0_70,plain,
subclass(X1,intersection(universal_class,X1)),
inference(spm,[status(thm)],[c_0_56,c_0_48]) ).
cnf(c_0_71,plain,
subclass(complement(complement(X1)),X1),
inference(spm,[status(thm)],[c_0_22,c_0_57]) ).
cnf(c_0_72,plain,
( intersection(unordered_pair(X1,X1),X2) = null_class
| unordered_pair(X1,X1) != null_class ),
inference(spm,[status(thm)],[c_0_64,c_0_65]) ).
cnf(c_0_73,plain,
intersection(X1,complement(complement(X1))) = complement(complement(X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_66]),c_0_29])]) ).
cnf(c_0_74,plain,
( ~ member(X1,intersection(X2,X3))
| ~ member(X1,complement(X2)) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_67]),c_0_52]) ).
cnf(c_0_75,plain,
( intersection(X1,complement(X2)) = null_class
| ~ member(regular(intersection(X1,complement(X2))),X2) ),
inference(spm,[status(thm)],[c_0_26,c_0_25]) ).
cnf(c_0_76,negated_conjecture,
complement(intersection(complement(unordered_pair(x,x)),complement(complement(intersection(complement(unordered_pair(y,y)),complement(complement(intersection(complement(unordered_pair(z,z)),universal_class)))))))) != complement(intersection(complement(unordered_pair(x,x)),complement(complement(intersection(complement(unordered_pair(y,y)),complement(unordered_pair(z,z))))))),
inference(rw,[status(thm)],[c_0_68,c_0_69]) ).
cnf(c_0_77,plain,
intersection(universal_class,X1) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_70]),c_0_29])]) ).
cnf(c_0_78,plain,
( intersection(unordered_pair(X1,X1),X2) = unordered_pair(X1,X1)
| intersection(unordered_pair(X1,X1),X2) = null_class ),
inference(spm,[status(thm)],[c_0_54,c_0_65]) ).
cnf(c_0_79,plain,
( complement(complement(X1)) = X1
| ~ subclass(X1,complement(complement(X1))) ),
inference(spm,[status(thm)],[c_0_28,c_0_71]) ).
cnf(c_0_80,plain,
( complement(complement(unordered_pair(X1,X1))) = null_class
| unordered_pair(X1,X1) != null_class ),
inference(spm,[status(thm)],[c_0_72,c_0_73]) ).
cnf(c_0_81,plain,
( intersection(X1,X2) = null_class
| ~ member(regular(intersection(X1,X2)),complement(X1)) ),
inference(spm,[status(thm)],[c_0_74,c_0_19]) ).
cnf(c_0_82,plain,
( intersection(X1,complement(complement(X2))) = null_class
| member(regular(intersection(X1,complement(complement(X2)))),X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_36]),c_0_35]) ).
cnf(c_0_83,negated_conjecture,
complement(intersection(complement(unordered_pair(x,x)),complement(complement(intersection(complement(unordered_pair(y,y)),complement(complement(complement(unordered_pair(z,z))))))))) != complement(intersection(complement(unordered_pair(x,x)),complement(complement(intersection(complement(unordered_pair(y,y)),complement(unordered_pair(z,z))))))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_76,c_0_65]),c_0_77]) ).
cnf(c_0_84,plain,
( complement(complement(unordered_pair(X1,X1))) = unordered_pair(X1,X1)
| complement(complement(unordered_pair(X1,X1))) = null_class ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_78]),c_0_73]) ).
cnf(c_0_85,plain,
( complement(unordered_pair(X1,X1)) = universal_class
| unordered_pair(X1,X1) != null_class ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_80]),c_0_69]),c_0_69]),c_0_21])]) ).
cnf(c_0_86,plain,
intersection(X1,universal_class) = X1,
inference(spm,[status(thm)],[c_0_77,c_0_65]) ).
cnf(c_0_87,plain,
intersection(X1,complement(complement(complement(X1)))) = null_class,
inference(spm,[status(thm)],[c_0_81,c_0_82]) ).
cnf(c_0_88,negated_conjecture,
complement(complement(unordered_pair(z,z))) = null_class,
inference(spm,[status(thm)],[c_0_83,c_0_84]) ).
cnf(c_0_89,negated_conjecture,
unordered_pair(z,z) != null_class,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_85]),c_0_42]),c_0_69]),c_0_86]),c_0_86])]) ).
cnf(c_0_90,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_88]),c_0_69]),c_0_86]),c_0_89]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET128-6 : 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 : n019.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 02:13:14 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 10.47/7.19 % Version : CSE_E---1.7
% 10.47/7.19 % Problem : theBenchmark.p
% 10.47/7.19 % SZS status Unsatisfiable for theBenchmark.p
% 10.47/7.19 % SZS output start CNFRefutation
% See solution above
% 10.54/7.22 % Total time : 5.369s
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