%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET135-6 : TPTP v9.2.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n027.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 05:07:25 PM UTC 2026
% Result : Unsatisfiable 20.90s 13.03s
% Output : CNFRefutation 20.90s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 17
% Syntax : Number of clauses : 75 ( 30 unt; 12 nHn; 43 RR)
% Number of literals : 129 ( 23 equ; 47 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 : 125 ( 19 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(subclass_members,axiom,
( member(X3,X2)
| ~ subclass(X1,X2)
| ~ member(X3,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',subclass_members) ).
cnf(class_elements_are_sets,axiom,
subclass(X1,universal_class),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',class_elements_are_sets) ).
cnf(complement1,axiom,
( ~ member(X1,complement(X2))
| ~ member(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',complement1) ).
cnf(regularity1,axiom,
( X1 = null_class
| member(regular(X1),X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',regularity1) ).
cnf(definition_of_set_builder,axiom,
union(singleton(X1),X2) = set_builder(X1,X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',definition_of_set_builder) ).
cnf(singleton_set,axiom,
unordered_pair(X1,X1) = singleton(X1),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',singleton_set) ).
cnf(prove_corollary_3_to_member_of_triple_2,negated_conjecture,
set_builder(x,set_builder(u,set_builder(z,null_class))) = null_class,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_corollary_3_to_member_of_triple_2) ).
cnf(union,axiom,
complement(intersection(complement(X1),complement(X2))) = union(X1,X2),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',union) ).
cnf(complement2,axiom,
( member(X1,complement(X2))
| member(X1,X2)
| ~ member(X1,universal_class) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',complement2) ).
cnf(intersection1,axiom,
( member(X1,X2)
| ~ member(X1,intersection(X2,X3)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',intersection1) ).
cnf(not_subclass_members1,axiom,
( member(not_subclass_element(X1,X2),X1)
| subclass(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',not_subclass_members1) ).
cnf(not_subclass_members2,axiom,
( subclass(X1,X2)
| ~ member(not_subclass_element(X1,X2),X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',not_subclass_members2) ).
cnf(intersection3,axiom,
( member(X1,intersection(X2,X3))
| ~ member(X1,X2)
| ~ member(X1,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',intersection3) ).
cnf(subclass_implies_equal,axiom,
( X1 = X2
| ~ subclass(X1,X2)
| ~ subclass(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',subclass_implies_equal) ).
cnf(intersection2,axiom,
( member(X1,X3)
| ~ member(X1,intersection(X2,X3)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',intersection2) ).
cnf(unordered_pair2,axiom,
( member(X1,unordered_pair(X1,X2))
| ~ member(X1,universal_class) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',unordered_pair2) ).
cnf(prove_corollary_3_to_member_of_triple_1,negated_conjecture,
member(u,universal_class),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_corollary_3_to_member_of_triple_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,
( X1 = null_class
| member(regular(X1),X1) ),
regularity1 ).
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,
union(singleton(X1),X2) = set_builder(X1,X2),
definition_of_set_builder ).
cnf(c_0_23,axiom,
unordered_pair(X1,X1) = singleton(X1),
singleton_set ).
cnf(c_0_24,plain,
( complement(X1) = null_class
| ~ member(regular(complement(X1)),X1) ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_25,plain,
( X1 = null_class
| member(regular(X1),universal_class) ),
inference(spm,[status(thm)],[c_0_21,c_0_20]) ).
cnf(c_0_26,negated_conjecture,
set_builder(x,set_builder(u,set_builder(z,null_class))) = null_class,
prove_corollary_3_to_member_of_triple_2 ).
cnf(c_0_27,plain,
union(unordered_pair(X1,X1),X2) = set_builder(X1,X2),
inference(rw,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_28,axiom,
complement(intersection(complement(X1),complement(X2))) = union(X1,X2),
union ).
cnf(c_0_29,plain,
complement(universal_class) = null_class,
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_30,axiom,
( member(X1,complement(X2))
| member(X1,X2)
| ~ member(X1,universal_class) ),
complement2 ).
cnf(c_0_31,negated_conjecture,
complement(intersection(complement(unordered_pair(x,x)),complement(complement(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(z,z)),complement(null_class))))))))) = 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)],[c_0_26,c_0_27]),c_0_27]),c_0_27]),c_0_28]),c_0_28]),c_0_28]) ).
cnf(c_0_32,plain,
~ member(X1,null_class),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_29]),c_0_21]) ).
cnf(c_0_33,axiom,
( member(X1,X2)
| ~ member(X1,intersection(X2,X3)) ),
intersection1 ).
cnf(c_0_34,negated_conjecture,
( member(X1,intersection(complement(unordered_pair(x,x)),complement(complement(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(z,z)),complement(null_class)))))))))
| ~ member(X1,universal_class) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_32]) ).
cnf(c_0_35,negated_conjecture,
( member(X1,complement(unordered_pair(x,x)))
| ~ member(X1,universal_class) ),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_36,negated_conjecture,
~ member(X1,unordered_pair(x,x)),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_35]),c_0_21]) ).
cnf(c_0_37,negated_conjecture,
unordered_pair(x,x) = null_class,
inference(spm,[status(thm)],[c_0_36,c_0_20]) ).
cnf(c_0_38,axiom,
( member(not_subclass_element(X1,X2),X1)
| subclass(X1,X2) ),
not_subclass_members1 ).
cnf(c_0_39,axiom,
( subclass(X1,X2)
| ~ member(not_subclass_element(X1,X2),X2) ),
not_subclass_members2 ).
cnf(c_0_40,axiom,
( member(X1,intersection(X2,X3))
| ~ member(X1,X2)
| ~ member(X1,X3) ),
intersection3 ).
cnf(c_0_41,axiom,
( X1 = X2
| ~ subclass(X1,X2)
| ~ subclass(X2,X1) ),
subclass_implies_equal ).
cnf(c_0_42,negated_conjecture,
( member(X1,complement(null_class))
| ~ member(X1,universal_class) ),
inference(rw,[status(thm)],[c_0_35,c_0_37]) ).
cnf(c_0_43,plain,
( member(not_subclass_element(X1,X2),universal_class)
| subclass(X1,X2) ),
inference(spm,[status(thm)],[c_0_21,c_0_38]) ).
cnf(c_0_44,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_39,c_0_40]) ).
cnf(c_0_45,axiom,
( member(X1,X3)
| ~ member(X1,intersection(X2,X3)) ),
intersection2 ).
cnf(c_0_46,plain,
( member(not_subclass_element(intersection(X1,X2),X3),X1)
| subclass(intersection(X1,X2),X3) ),
inference(spm,[status(thm)],[c_0_33,c_0_38]) ).
cnf(c_0_47,plain,
( subclass(complement(X1),X2)
| ~ member(not_subclass_element(complement(X1),X2),X1) ),
inference(spm,[status(thm)],[c_0_19,c_0_38]) ).
cnf(c_0_48,plain,
( universal_class = X1
| ~ subclass(universal_class,X1) ),
inference(spm,[status(thm)],[c_0_41,c_0_18]) ).
cnf(c_0_49,negated_conjecture,
subclass(X1,complement(null_class)),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_42]),c_0_43]) ).
cnf(c_0_50,plain,
( subclass(X1,intersection(X2,X1))
| ~ member(not_subclass_element(X1,intersection(X2,X1)),X2) ),
inference(spm,[status(thm)],[c_0_44,c_0_38]) ).
cnf(c_0_51,plain,
( member(not_subclass_element(intersection(X1,X2),X3),X2)
| subclass(intersection(X1,X2),X3) ),
inference(spm,[status(thm)],[c_0_45,c_0_38]) ).
cnf(c_0_52,plain,
( member(not_subclass_element(intersection(intersection(X1,X2),X3),X4),X1)
| subclass(intersection(intersection(X1,X2),X3),X4) ),
inference(spm,[status(thm)],[c_0_33,c_0_46]) ).
cnf(c_0_53,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_30]),c_0_43]) ).
cnf(c_0_54,negated_conjecture,
( member(X1,intersection(complement(null_class),complement(complement(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(z,z)),complement(null_class)))))))))
| ~ member(X1,universal_class) ),
inference(rw,[status(thm)],[c_0_34,c_0_37]) ).
cnf(c_0_55,negated_conjecture,
complement(null_class) = universal_class,
inference(spm,[status(thm)],[c_0_48,c_0_49]) ).
cnf(c_0_56,plain,
subclass(X1,intersection(universal_class,X1)),
inference(spm,[status(thm)],[c_0_50,c_0_43]) ).
cnf(c_0_57,plain,
subclass(intersection(X1,X2),X2),
inference(spm,[status(thm)],[c_0_39,c_0_51]) ).
cnf(c_0_58,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_44,c_0_46]) ).
cnf(c_0_59,plain,
subclass(intersection(intersection(X1,X2),X3),X1),
inference(spm,[status(thm)],[c_0_39,c_0_52]) ).
cnf(c_0_60,plain,
subclass(complement(complement(X1)),intersection(X1,complement(complement(X1)))),
inference(spm,[status(thm)],[c_0_50,c_0_53]) ).
cnf(c_0_61,negated_conjecture,
( member(X1,intersection(universal_class,complement(complement(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(z,z)),universal_class))))))))
| ~ member(X1,universal_class) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_54,c_0_55]),c_0_55]) ).
cnf(c_0_62,plain,
intersection(universal_class,X1) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_56]),c_0_57])]) ).
cnf(c_0_63,plain,
subclass(intersection(X1,X2),intersection(X2,X1)),
inference(spm,[status(thm)],[c_0_58,c_0_51]) ).
cnf(c_0_64,plain,
( member(X1,X2)
| ~ member(X1,intersection(intersection(X2,X3),X4)) ),
inference(spm,[status(thm)],[c_0_17,c_0_59]) ).
cnf(c_0_65,plain,
intersection(X1,complement(complement(X1))) = complement(complement(X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_60]),c_0_57])]) ).
cnf(c_0_66,negated_conjecture,
( member(X1,complement(complement(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(z,z)),universal_class)))))))
| ~ member(X1,universal_class) ),
inference(rw,[status(thm)],[c_0_61,c_0_62]) ).
cnf(c_0_67,plain,
intersection(X1,X2) = intersection(X2,X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_63]),c_0_63])]) ).
cnf(c_0_68,plain,
( member(X1,X2)
| ~ member(X1,complement(complement(intersection(X2,X3)))) ),
inference(spm,[status(thm)],[c_0_64,c_0_65]) ).
cnf(c_0_69,negated_conjecture,
( member(X1,complement(complement(intersection(complement(unordered_pair(u,u)),complement(complement(complement(unordered_pair(z,z))))))))
| ~ member(X1,universal_class) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_66,c_0_67]),c_0_62]) ).
cnf(c_0_70,negated_conjecture,
( member(X1,complement(unordered_pair(u,u)))
| ~ member(X1,universal_class) ),
inference(spm,[status(thm)],[c_0_68,c_0_69]) ).
cnf(c_0_71,negated_conjecture,
~ member(X1,unordered_pair(u,u)),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_70]),c_0_21]) ).
cnf(c_0_72,axiom,
( member(X1,unordered_pair(X1,X2))
| ~ member(X1,universal_class) ),
unordered_pair2 ).
cnf(c_0_73,negated_conjecture,
member(u,universal_class),
prove_corollary_3_to_member_of_triple_1 ).
cnf(c_0_74,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_72]),c_0_73])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SET135-6 : TPTP v9.2.1. Bugfixed v2.1.0.
% 0.00/0.11 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.15/0.32 % Computer : n027.cluster.edu
% 0.15/0.32 % Model : x86_64 x86_64
% 0.15/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.32 % Memory : 8042.1875MB
% 0.15/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.32 % CPULimit : 300
% 0.15/0.32 % WCLimit : 300
% 0.15/0.32 % DateTime : Tue May 5 02:13:05 EDT 2026
% 0.15/0.32 % CPUTime :
% 0.15/0.33 % start to proof: theBenchmark
% 20.90/13.03 % Version : CSE_E---1.7
% 20.90/13.03 % Problem : theBenchmark.p
% 20.90/13.03 % SZS status Unsatisfiable for theBenchmark.p
% 20.90/13.03 % SZS output start CNFRefutation
% See solution above
% 20.90/13.11 % Total time : 9.384s
%------------------------------------------------------------------------------