%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SET020-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n013.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 02:13:08 PM UTC 2026
% Result : Unsatisfiable 0.49s 0.54s
% Output : CNFRefutation 0.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 24
% Syntax : Number of clauses : 116 ( 36 unt; 22 nHn; 79 RR)
% Number of literals : 224 ( 50 equ; 104 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 16 ( 16 usr; 4 con; 0-3 aty)
% Number of variables : 222 ( 48 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(subclass_members,axiom,
( ~ member(X3,X1)
| ~ subclass(X1,X2)
| member(X3,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',subclass_members) ).
cnf(complement1,axiom,
( ~ member(X1,X2)
| ~ member(X1,complement(X2)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',complement1) ).
cnf(class_elements_are_sets,axiom,
subclass(X1,universal_class),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',class_elements_are_sets) ).
cnf(not_subclass_members2,axiom,
( ~ member(not_subclass_element(X1,X2),X2)
| subclass(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',not_subclass_members2) ).
cnf(intersection3,axiom,
( ~ member(X1,X3)
| ~ member(X1,X2)
| member(X1,intersection(X2,X3)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',intersection3) ).
cnf(not_subclass_members1,axiom,
( subclass(X1,X2)
| member(not_subclass_element(X1,X2),X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',not_subclass_members1) ).
cnf(intersection1,axiom,
( ~ member(X1,intersection(X2,X3))
| member(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',intersection1) ).
cnf(intersection2,axiom,
( ~ member(X1,intersection(X2,X3))
| member(X1,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',intersection2) ).
cnf(domain1,axiom,
( ~ member(X2,domain_of(X1))
| restrict(X1,singleton(X2),universal_class) != null_class ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',domain1) ).
cnf(regularity1,axiom,
( member(regular(X1),X1)
| X1 = null_class ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',regularity1) ).
cnf(subclass_implies_equal,axiom,
( ~ subclass(X2,X1)
| ~ subclass(X1,X2)
| X1 = X2 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',subclass_implies_equal) ).
cnf(cartesian_product4,axiom,
( ~ member(X1,cross_product(X2,X3))
| ordered_pair(first(X1),second(X1)) = X1 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',cartesian_product4) ).
cnf(ordered_pair,axiom,
unordered_pair(singleton(X1),unordered_pair(X1,singleton(X2))) = ordered_pair(X1,X2),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',ordered_pair) ).
cnf(singleton_set,axiom,
unordered_pair(X1,X1) = singleton(X1),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',singleton_set) ).
cnf(domain2,axiom,
( ~ member(X1,universal_class)
| member(X1,domain_of(X2))
| restrict(X2,singleton(X1),universal_class) = null_class ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',domain2) ).
cnf(restriction1,axiom,
intersection(X1,cross_product(X2,X3)) = restrict(X1,X2,X3),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',restriction1) ).
cnf(cartesian_product1,axiom,
( ~ member(ordered_pair(X1,X2),cross_product(X3,X4))
| member(X1,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',cartesian_product1) ).
cnf(prove_unique_1st_and_2nd_in_pair_of_sets1_1,negated_conjecture,
member(ordered_pair(u,v),cross_product(universal_class,universal_class)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_unique_1st_and_2nd_in_pair_of_sets1_1) ).
cnf(cartesian_product3,axiom,
( ~ member(X3,X4)
| ~ member(X1,X2)
| member(ordered_pair(X1,X3),cross_product(X2,X4)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',cartesian_product3) ).
cnf(cartesian_product2,axiom,
( ~ member(ordered_pair(X1,X2),cross_product(X3,X4))
| member(X2,X4) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',cartesian_product2) ).
cnf(unordered_pair2,axiom,
( ~ member(X1,universal_class)
| member(X1,unordered_pair(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',unordered_pair2) ).
cnf(complement2,axiom,
( ~ member(X1,universal_class)
| member(X1,X2)
| member(X1,complement(X2)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',complement2) ).
cnf(prove_unique_1st_and_2nd_in_pair_of_sets1_2,negated_conjecture,
first(ordered_pair(u,v)) != u,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_unique_1st_and_2nd_in_pair_of_sets1_2) ).
cnf(unordered_pair_member,axiom,
( ~ member(X1,unordered_pair(X2,X3))
| X1 = X3
| X1 = X2 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',unordered_pair_member) ).
cnf(c_0_24,plain,
( ~ member(X3,X1)
| ~ subclass(X1,X2)
| member(X3,X2) ),
inference(fof_simplification,[status(thm)],[subclass_members]) ).
cnf(c_0_25,plain,
( ~ member(X1,X2)
| ~ member(X1,complement(X2)) ),
inference(fof_simplification,[status(thm)],[complement1]) ).
cnf(c_0_26,plain,
( ~ member(X3,X1)
| ~ subclass(X1,X2)
| member(X3,X2) ),
c_0_24 ).
cnf(c_0_27,axiom,
subclass(X1,universal_class),
class_elements_are_sets ).
cnf(c_0_28,plain,
( ~ member(not_subclass_element(X1,X2),X2)
| subclass(X1,X2) ),
inference(fof_simplification,[status(thm)],[not_subclass_members2]) ).
cnf(c_0_29,plain,
( ~ member(X1,X3)
| ~ member(X1,X2)
| member(X1,intersection(X2,X3)) ),
inference(fof_simplification,[status(thm)],[intersection3]) ).
cnf(c_0_30,plain,
( ~ member(X1,X2)
| ~ member(X1,complement(X2)) ),
c_0_25 ).
cnf(c_0_31,axiom,
( subclass(X1,X2)
| member(not_subclass_element(X1,X2),X1) ),
not_subclass_members1 ).
cnf(c_0_32,plain,
( ~ member(X1,X2)
| member(X1,universal_class) ),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_33,plain,
( ~ member(X1,intersection(X2,X3))
| member(X1,X2) ),
inference(fof_simplification,[status(thm)],[intersection1]) ).
cnf(c_0_34,plain,
( ~ member(not_subclass_element(X1,X2),X2)
| subclass(X1,X2) ),
c_0_28 ).
cnf(c_0_35,plain,
( ~ member(X1,X3)
| ~ member(X1,X2)
| member(X1,intersection(X2,X3)) ),
c_0_29 ).
cnf(c_0_36,plain,
( ~ member(X1,intersection(X2,X3))
| member(X1,X3) ),
inference(fof_simplification,[status(thm)],[intersection2]) ).
cnf(c_0_37,plain,
( ~ member(X2,domain_of(X1))
| restrict(X1,singleton(X2),universal_class) != null_class ),
inference(fof_simplification,[status(thm)],[domain1]) ).
cnf(c_0_38,axiom,
( member(regular(X1),X1)
| X1 = null_class ),
regularity1 ).
cnf(c_0_39,plain,
( ~ subclass(X2,X1)
| ~ subclass(X1,X2)
| X1 = X2 ),
inference(fof_simplification,[status(thm)],[subclass_implies_equal]) ).
cnf(c_0_40,plain,
( ~ member(not_subclass_element(complement(X1),X2),X1)
| subclass(complement(X1),X2) ),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_41,plain,
( subclass(X1,X2)
| member(not_subclass_element(X1,X2),universal_class) ),
inference(spm,[status(thm)],[c_0_32,c_0_31]) ).
cnf(c_0_42,plain,
( ~ member(X1,intersection(X2,X3))
| member(X1,X2) ),
c_0_33 ).
cnf(c_0_43,plain,
( ~ member(X1,cross_product(X2,X3))
| ordered_pair(first(X1),second(X1)) = X1 ),
inference(fof_simplification,[status(thm)],[cartesian_product4]) ).
cnf(c_0_44,axiom,
unordered_pair(singleton(X1),unordered_pair(X1,singleton(X2))) = ordered_pair(X1,X2),
ordered_pair ).
cnf(c_0_45,axiom,
unordered_pair(X1,X1) = singleton(X1),
singleton_set ).
cnf(c_0_46,plain,
( ~ member(X1,universal_class)
| member(X1,domain_of(X2))
| restrict(X2,singleton(X1),universal_class) = null_class ),
inference(fof_simplification,[status(thm)],[domain2]) ).
cnf(c_0_47,plain,
( ~ member(not_subclass_element(X1,intersection(X2,X3)),X2)
| ~ member(not_subclass_element(X1,intersection(X2,X3)),X3)
| subclass(X1,intersection(X2,X3)) ),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_48,plain,
( ~ member(X1,intersection(X2,X3))
| member(X1,X3) ),
c_0_36 ).
cnf(c_0_49,plain,
( ~ member(X2,domain_of(X1))
| restrict(X1,singleton(X2),universal_class) != null_class ),
c_0_37 ).
cnf(c_0_50,axiom,
intersection(X1,cross_product(X2,X3)) = restrict(X1,X2,X3),
restriction1 ).
cnf(c_0_51,plain,
( ~ member(regular(complement(X1)),X1)
| complement(X1) = null_class ),
inference(spm,[status(thm)],[c_0_30,c_0_38]) ).
cnf(c_0_52,plain,
( member(regular(X1),universal_class)
| X1 = null_class ),
inference(spm,[status(thm)],[c_0_32,c_0_38]) ).
cnf(c_0_53,plain,
( ~ subclass(X2,X1)
| ~ subclass(X1,X2)
| X1 = X2 ),
c_0_39 ).
cnf(c_0_54,plain,
subclass(complement(universal_class),X1),
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_55,plain,
( subclass(intersection(X1,X2),X3)
| member(not_subclass_element(intersection(X1,X2),X3),X1) ),
inference(spm,[status(thm)],[c_0_42,c_0_31]) ).
cnf(c_0_56,plain,
( ~ member(ordered_pair(X1,X2),cross_product(X3,X4))
| member(X1,X3) ),
inference(fof_simplification,[status(thm)],[cartesian_product1]) ).
cnf(c_0_57,plain,
( ~ member(X1,cross_product(X2,X3))
| ordered_pair(first(X1),second(X1)) = X1 ),
c_0_43 ).
cnf(c_0_58,plain,
unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))) = ordered_pair(X1,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_44,c_0_45]),c_0_45]) ).
cnf(c_0_59,negated_conjecture,
member(ordered_pair(u,v),cross_product(universal_class,universal_class)),
prove_unique_1st_and_2nd_in_pair_of_sets1_1 ).
cnf(c_0_60,plain,
( ~ member(X1,universal_class)
| member(X1,domain_of(X2))
| restrict(X2,singleton(X1),universal_class) = null_class ),
c_0_46 ).
cnf(c_0_61,plain,
( ~ member(not_subclass_element(X1,intersection(X2,X1)),X2)
| subclass(X1,intersection(X2,X1)) ),
inference(spm,[status(thm)],[c_0_47,c_0_31]) ).
cnf(c_0_62,plain,
( subclass(intersection(X1,X2),X3)
| member(not_subclass_element(intersection(X1,X2),X3),X2) ),
inference(spm,[status(thm)],[c_0_48,c_0_31]) ).
cnf(c_0_63,plain,
( ~ member(X2,domain_of(X1))
| intersection(X1,cross_product(unordered_pair(X2,X2),universal_class)) != null_class ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_49,c_0_45]),c_0_50]) ).
cnf(c_0_64,plain,
null_class = complement(universal_class),
inference(spm,[status(thm)],[c_0_51,c_0_52]) ).
cnf(c_0_65,plain,
( ~ subclass(X1,complement(universal_class))
| X1 = complement(universal_class) ),
inference(spm,[status(thm)],[c_0_53,c_0_54]) ).
cnf(c_0_66,plain,
subclass(intersection(X1,X2),X1),
inference(spm,[status(thm)],[c_0_34,c_0_55]) ).
cnf(c_0_67,plain,
( ~ member(ordered_pair(X1,X2),cross_product(X3,X4))
| member(X1,X3) ),
c_0_56 ).
cnf(c_0_68,plain,
( ~ member(X1,cross_product(X2,X3))
| unordered_pair(unordered_pair(first(X1),first(X1)),unordered_pair(first(X1),unordered_pair(second(X1),second(X1)))) = X1 ),
inference(rw,[status(thm)],[c_0_57,c_0_58]) ).
cnf(c_0_69,negated_conjecture,
member(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v))),cross_product(universal_class,universal_class)),
inference(rw,[status(thm)],[c_0_59,c_0_58]) ).
cnf(c_0_70,plain,
( ~ member(X3,X4)
| ~ member(X1,X2)
| member(ordered_pair(X1,X3),cross_product(X2,X4)) ),
inference(fof_simplification,[status(thm)],[cartesian_product3]) ).
cnf(c_0_71,plain,
( ~ member(ordered_pair(X1,X2),cross_product(X3,X4))
| member(X2,X4) ),
inference(fof_simplification,[status(thm)],[cartesian_product2]) ).
cnf(c_0_72,plain,
( ~ member(X1,universal_class)
| member(X1,domain_of(X2))
| intersection(X2,cross_product(unordered_pair(X1,X1),universal_class)) = null_class ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_60,c_0_45]),c_0_50]) ).
cnf(c_0_73,plain,
subclass(X1,intersection(universal_class,X1)),
inference(spm,[status(thm)],[c_0_61,c_0_41]) ).
cnf(c_0_74,plain,
subclass(intersection(X1,X2),X2),
inference(spm,[status(thm)],[c_0_34,c_0_62]) ).
cnf(c_0_75,plain,
( ~ member(X2,domain_of(X1))
| intersection(X1,cross_product(unordered_pair(X2,X2),universal_class)) != complement(universal_class) ),
inference(rw,[status(thm)],[c_0_63,c_0_64]) ).
cnf(c_0_76,plain,
intersection(complement(universal_class),X1) = complement(universal_class),
inference(spm,[status(thm)],[c_0_65,c_0_66]) ).
cnf(c_0_77,plain,
( ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),cross_product(X3,X4))
| member(X1,X3) ),
inference(rw,[status(thm)],[c_0_67,c_0_58]) ).
cnf(c_0_78,negated_conjecture,
unordered_pair(unordered_pair(first(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v)))),first(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v))))),unordered_pair(first(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v)))),unordered_pair(second(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v)))),second(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v))))))) = unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v))),
inference(spm,[status(thm)],[c_0_68,c_0_69]) ).
cnf(c_0_79,plain,
( ~ member(X3,X4)
| ~ member(X1,X2)
| member(ordered_pair(X1,X3),cross_product(X2,X4)) ),
c_0_70 ).
cnf(c_0_80,plain,
( ~ member(ordered_pair(X1,X2),cross_product(X3,X4))
| member(X2,X4) ),
c_0_71 ).
cnf(c_0_81,plain,
( ~ member(X2,universal_class)
| member(X2,domain_of(X1))
| intersection(X1,cross_product(unordered_pair(X2,X2),universal_class)) = complement(universal_class) ),
inference(rw,[status(thm)],[c_0_72,c_0_64]) ).
cnf(c_0_82,plain,
intersection(universal_class,X1) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_73]),c_0_74])]) ).
cnf(c_0_83,plain,
~ member(X1,domain_of(complement(universal_class))),
inference(spm,[status(thm)],[c_0_75,c_0_76]) ).
cnf(c_0_84,plain,
( member(regular(X1),X1)
| X1 = complement(universal_class) ),
inference(rw,[status(thm)],[c_0_38,c_0_64]) ).
cnf(c_0_85,negated_conjecture,
( ~ member(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v))),cross_product(X1,X2))
| member(first(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v)))),X1) ),
inference(spm,[status(thm)],[c_0_77,c_0_78]) ).
cnf(c_0_86,plain,
( ~ member(X1,X2)
| ~ member(X3,X4)
| member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X3,X3))),cross_product(X2,X4)) ),
inference(rw,[status(thm)],[c_0_79,c_0_58]) ).
cnf(c_0_87,plain,
( ~ member(X1,universal_class)
| member(X1,unordered_pair(X1,X2)) ),
inference(fof_simplification,[status(thm)],[unordered_pair2]) ).
cnf(c_0_88,plain,
( ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),cross_product(X3,X4))
| member(X2,X4) ),
inference(rw,[status(thm)],[c_0_80,c_0_58]) ).
cnf(c_0_89,plain,
( ~ member(X1,universal_class)
| member(X1,domain_of(universal_class))
| cross_product(unordered_pair(X1,X1),universal_class) = complement(universal_class) ),
inference(spm,[status(thm)],[c_0_81,c_0_82]) ).
cnf(c_0_90,negated_conjecture,
member(u,universal_class),
inference(spm,[status(thm)],[c_0_77,c_0_69]) ).
cnf(c_0_91,plain,
domain_of(complement(universal_class)) = complement(universal_class),
inference(spm,[status(thm)],[c_0_83,c_0_84]) ).
cnf(c_0_92,negated_conjecture,
( ~ member(u,X1)
| ~ member(v,X2)
| member(first(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v)))),X1) ),
inference(spm,[status(thm)],[c_0_85,c_0_86]) ).
cnf(c_0_93,plain,
( ~ member(X1,universal_class)
| member(X1,unordered_pair(X1,X2)) ),
c_0_87 ).
cnf(c_0_94,negated_conjecture,
member(v,universal_class),
inference(spm,[status(thm)],[c_0_88,c_0_69]) ).
cnf(c_0_95,negated_conjecture,
( member(u,domain_of(universal_class))
| cross_product(unordered_pair(u,u),universal_class) = complement(universal_class) ),
inference(spm,[status(thm)],[c_0_89,c_0_90]) ).
cnf(c_0_96,plain,
~ member(X1,complement(universal_class)),
inference(rw,[status(thm)],[c_0_83,c_0_91]) ).
cnf(c_0_97,negated_conjecture,
( ~ member(u,X1)
| member(first(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v)))),X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_92,c_0_93]),c_0_94])]) ).
cnf(c_0_98,negated_conjecture,
( ~ member(X2,universal_class)
| ~ member(X1,unordered_pair(u,u))
| member(u,domain_of(universal_class)) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_95]),c_0_96]) ).
cnf(c_0_99,negated_conjecture,
( ~ member(u,complement(X1))
| ~ member(first(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v)))),X1) ),
inference(spm,[status(thm)],[c_0_30,c_0_97]) ).
cnf(c_0_100,negated_conjecture,
member(first(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v)))),universal_class),
inference(spm,[status(thm)],[c_0_85,c_0_69]) ).
cnf(c_0_101,plain,
( ~ member(X1,universal_class)
| member(X1,X2)
| member(X1,complement(X2)) ),
inference(fof_simplification,[status(thm)],[complement2]) ).
cnf(c_0_102,negated_conjecture,
first(ordered_pair(u,v)) != u,
inference(fof_simplification,[status(thm)],[prove_unique_1st_and_2nd_in_pair_of_sets1_2]) ).
cnf(c_0_103,negated_conjecture,
( ~ member(X1,universal_class)
| member(u,domain_of(universal_class)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_98,c_0_93]),c_0_90])]) ).
cnf(c_0_104,plain,
( ~ member(X1,unordered_pair(X2,X3))
| X1 = X3
| X1 = X2 ),
inference(fof_simplification,[status(thm)],[unordered_pair_member]) ).
cnf(c_0_105,negated_conjecture,
~ member(u,complement(unordered_pair(first(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v)))),X1))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_99,c_0_93]),c_0_100])]) ).
cnf(c_0_106,plain,
( ~ member(X1,universal_class)
| member(X1,X2)
| member(X1,complement(X2)) ),
c_0_101 ).
cnf(c_0_107,negated_conjecture,
first(ordered_pair(u,v)) != u,
c_0_102 ).
cnf(c_0_108,plain,
( ~ member(X1,domain_of(universal_class))
| cross_product(unordered_pair(X1,X1),universal_class) != complement(universal_class) ),
inference(spm,[status(thm)],[c_0_75,c_0_82]) ).
cnf(c_0_109,negated_conjecture,
member(u,domain_of(universal_class)),
inference(spm,[status(thm)],[c_0_103,c_0_94]) ).
cnf(c_0_110,plain,
( ~ member(X1,unordered_pair(X2,X3))
| X1 = X3
| X1 = X2 ),
c_0_104 ).
cnf(c_0_111,negated_conjecture,
member(u,unordered_pair(first(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v)))),X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_105,c_0_106]),c_0_90])]) ).
cnf(c_0_112,negated_conjecture,
first(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v)))) != u,
inference(rw,[status(thm)],[c_0_107,c_0_58]) ).
cnf(c_0_113,negated_conjecture,
cross_product(unordered_pair(first(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v)))),first(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v))))),universal_class) != complement(universal_class),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_108,c_0_97]),c_0_109])]) ).
cnf(c_0_114,negated_conjecture,
u = X1,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_110,c_0_111]),c_0_112]) ).
cnf(c_0_115,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_113,c_0_114]),c_0_114]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET020-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.36 % Computer : n013.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Mon Sep 21 04:42:51 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.41 Running first-order theorem proving
% 0.13/0.41 Running: /export/starexec/sandbox2/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.49/0.54 % Version: 3.5.1
% 0.49/0.54 % Preprocessing class: FSLSSMSMSSSNFFN.
% 0.49/0.54 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.49/0.54 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.49/0.54 % Starting new_bool_3 with 300s (1) cores
% 0.49/0.54 % Starting new_bool_1 with 300s (1) cores
% 0.49/0.54 % Starting sh5l with 300s (1) cores
% 0.49/0.54 % C07_19_nc_SOS_SAT001_MinMin_p005000_rr with pid 4158385 completed with status 0
% 0.49/0.54 % Result found by C07_19_nc_SOS_SAT001_MinMin_p005000_rr
% 0.49/0.54 % Preprocessing class: FSLSSMSMSSSNFFN.
% 0.49/0.54 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.49/0.54 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.49/0.54 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.49/0.54 % No SInE strategy applied
% 0.49/0.54 % Search class: FGHSM-FFLM31-DFFFFFNN
% 0.49/0.54 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.49/0.54 % Starting SubtermCWHack with 136s (1) cores
% 0.49/0.54 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 151s (1) cores
% 0.49/0.54 % Starting new_bool_3 with 311s (1) cores
% 0.49/0.54 % Starting new_bool_1 with 308s (1) cores
% 0.49/0.54 % Starting sh5l with 304s (1) cores
% 0.49/0.54 % C07_19_nc_SOS_SAT001_MinMin_p005000_rr with pid 4158393 completed with status 0
% 0.49/0.54 % Result found by C07_19_nc_SOS_SAT001_MinMin_p005000_rr
% 0.49/0.54 % Preprocessing class: FSLSSMSMSSSNFFN.
% 0.49/0.54 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.49/0.54 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.49/0.54 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.49/0.54 % No SInE strategy applied
% 0.49/0.54 % Search class: FGHSM-FFLM31-DFFFFFNN
% 0.49/0.54 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.49/0.54 % Starting SubtermCWHack with 136s (1) cores
% 0.49/0.54 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 151s (1) cores
% 0.49/0.54 % Preprocessing time : 0.002 s
% 0.49/0.54 % Presaturation interreduction done
% 0.49/0.54
% 0.49/0.54 % Proof found!
% 0.49/0.54 % SZS status Unsatisfiable
% 0.49/0.54 % SZS output start CNFRefutation
% See solution above
% 0.49/0.54 % Parsed axioms : 93
% 0.49/0.54 % Removed by relevancy pruning/SinE : 0
% 0.49/0.54 % Initial clauses : 93
% 0.49/0.54 % Removed in clause preprocessing : 15
% 0.49/0.54 % Initial clauses in saturation : 78
% 0.49/0.54 % Processed clauses : 1158
% 0.49/0.54 % ...of these trivial : 5
% 0.49/0.54 % ...subsumed : 542
% 0.49/0.54 % ...remaining for further processing : 611
% 0.49/0.54 % Other redundant clauses eliminated : 5
% 0.49/0.54 % Clauses deleted for lack of memory : 0
% 0.49/0.54 % Backward-subsumed : 95
% 0.49/0.54 % Backward-rewritten : 346
% 0.49/0.54 % Generated clauses : 3879
% 0.49/0.54 % ...of the previous two non-redundant : 3447
% 0.49/0.54 % ...aggressively subsumed : 0
% 0.49/0.54 % Contextual simplify-reflections : 15
% 0.49/0.54 % Paramodulations : 3872
% 0.49/0.54 % Factorizations : 2
% 0.49/0.54 % NegExts : 0
% 0.49/0.54 % Equation resolutions : 5
% 0.49/0.54 % Disequality decompositions : 0
% 0.49/0.54 % Total rewrite steps : 1061
% 0.49/0.54 % ...of those cached : 726
% 0.49/0.54 % Propositional unsat checks : 0
% 0.49/0.54 % Propositional check models : 0
% 0.49/0.54 % Propositional check unsatisfiable : 0
% 0.49/0.54 % Propositional clauses : 0
% 0.49/0.54 % Propositional clauses after purity: 0
% 0.49/0.54 % Propositional unsat core size : 0
% 0.49/0.54 % Propositional preprocessing time : 0.000
% 0.49/0.54 % Propositional encoding time : 0.000
% 0.49/0.54 % Propositional solver time : 0.000
% 0.49/0.54 % Success case prop preproc time : 0.000
% 0.49/0.54 % Success case prop encoding time : 0.000
% 0.49/0.54 % Success case prop solver time : 0.000
% 0.49/0.54 % Current number of processed clauses : 90
% 0.49/0.54 % Positive orientable unit clauses : 17
% 0.49/0.54 % Positive unorientable unit clauses: 2
% 0.49/0.54 % Negative unit clauses : 3
% 0.49/0.54 % Non-unit-clauses : 68
% 0.49/0.54 % Current number of unprocessed clauses: 2206
% 0.49/0.54 % ...number of literals in the above : 7643
% 0.49/0.54 % Current number of archived formulas : 0
% 0.49/0.54 % Current number of archived clauses : 533
% 0.49/0.54 % Clause-clause subsumption calls (NU) : 21339
% 0.49/0.54 % Rec. Clause-clause subsumption calls : 16037
% 0.49/0.54 % Non-unit clause-clause subsumptions : 486
% 0.49/0.54 % Unit Clause-clause subsumption calls : 1160
% 0.49/0.54 % Rewrite failures with RHS unbound : 3
% 0.49/0.54 % BW rewrite match attempts : 695
% 0.49/0.54 % BW rewrite match successes : 260
% 0.49/0.54 % Condensation attempts : 0
% 0.49/0.54 % Condensation successes : 0
% 0.49/0.54 % Termbank termtop insertions : 204478
% 0.49/0.54 % Search garbage collected termcells : 156
% 0.49/0.54
% 0.49/0.54 % -------------------------------------------------
% 0.49/0.54 % User time : 0.099 s
% 0.49/0.54 % System time : 0.008 s
% 0.49/0.54 % Total time : 0.107 s
% 0.49/0.54 % Maximum resident set size: 3720 pages
% 0.49/0.54
% 0.49/0.54 % -------------------------------------------------
% 0.49/0.54 % User time : 0.429 s
% 0.49/0.54 % System time : 0.039 s
% 0.49/0.54 % Total time : 0.467 s
% 0.49/0.54 % Maximum resident set size: 4608 pages
% 0.49/0.54 % E exiting
%------------------------------------------------------------------------------