%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SET040-3 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n010.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 02:13:14 PM UTC 2026
% Result : Unsatisfiable 79.84s 15.90s
% Output : CNFRefutation 79.84s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 31
% Syntax : Number of clauses : 135 ( 33 unt; 13 nHn; 103 RR)
% Number of literals : 302 ( 66 equ; 162 neg)
% Maximal clause size : 6 ( 2 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 18 ( 18 usr; 6 con; 0-3 aty)
% Number of variables : 243 ( 32 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(disjoint1,axiom,
( ~ member(X3,X2)
| ~ member(X3,X1)
| ~ disjoint(X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET003-0.ax',disjoint1) ).
cnf(prove_apply_for_composition2,negated_conjecture,
~ subset(apply(compose(another_function,a_function),element),apply(another_function,apply(a_function,element))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_apply_for_composition2) ).
cnf(disjoint2,axiom,
( member(f23(X1,X2),X1)
| disjoint(X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET003-0.ax',disjoint2) ).
cnf(subset2,axiom,
( member(f17(X1,X2),X1)
| subset(X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET003-0.ax',subset2) ).
cnf(first_component_is_small,axiom,
( ~ ordered_pair_predicate(X1)
| little_set(first(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',first_component_is_small) ).
cnf(apply1,axiom,
( ~ member(X1,apply(X2,X3))
| ordered_pair_predicate(f28(X1,X2,X3)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET003-0.ax',apply1) ).
cnf(apply3,axiom,
( ~ member(X1,apply(X2,X3))
| first(f28(X1,X2,X3)) = X3 ),
file('/export/starexec/sandbox/benchmark/Axioms/SET003-0.ax',apply3) ).
cnf(ordered_pair_predicate4,axiom,
( X1 != ordered_pair(X2,X3)
| ~ little_set(X3)
| ~ little_set(X2)
| ordered_pair_predicate(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET003-0.ax',ordered_pair_predicate4) ).
cnf(ordered_pair,axiom,
ordered_pair(X1,X2) = non_ordered_pair(singleton_set(X1),non_ordered_pair(X1,X2)),
file('/export/starexec/sandbox/benchmark/Axioms/SET003-0.ax',ordered_pair) ).
cnf(singleton_set,axiom,
singleton_set(X1) = non_ordered_pair(X1,X1),
file('/export/starexec/sandbox/benchmark/Axioms/SET003-0.ax',singleton_set) ).
cnf(property_of_first,axiom,
( ~ little_set(X2)
| ~ little_set(X1)
| first(ordered_pair(X1,X2)) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',property_of_first) ).
cnf(property_of_second,axiom,
( ~ little_set(X2)
| ~ little_set(X1)
| second(ordered_pair(X1,X2)) = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',property_of_second) ).
cnf(relation1,axiom,
( ~ member(X2,X1)
| ~ relation(X1)
| ordered_pair_predicate(X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET003-0.ax',relation1) ).
cnf(identity_relation3,axiom,
( first(X1) != second(X1)
| ~ ordered_pair_predicate(X1)
| ~ little_set(X1)
| member(X1,identity_relation) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET003-0.ax',identity_relation3) ).
cnf(ordered_pairs_are_small2,axiom,
( ~ ordered_pair_predicate(X1)
| little_set(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ordered_pairs_are_small2) ).
cnf(composition_is_a_relation,axiom,
relation(compose(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',composition_is_a_relation) ).
cnf(image_and_substitution5,axiom,
( second(X4) != X1
| ~ member(first(X4),X2)
| ~ member(X4,X3)
| ~ ordered_pair_predicate(X4)
| ~ little_set(X1)
| member(X1,image(X2,X3)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET003-0.ax',image_and_substitution5) ).
cnf(second_component_is_small,axiom,
( ~ ordered_pair_predicate(X1)
| little_set(second(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',second_component_is_small) ).
cnf(non_ordered_pair2,axiom,
( X1 != X2
| ~ little_set(X1)
| member(X1,non_ordered_pair(X2,X3)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET003-0.ax',non_ordered_pair2) ).
cnf(universal_set,axiom,
( ~ little_set(X1)
| member(X1,universal_set) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET003-0.ax',universal_set) ).
cnf(subset1,axiom,
( ~ member(X3,X1)
| ~ subset(X1,X2)
| member(X3,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET003-0.ax',subset1) ).
cnf(image_and_apply2,axiom,
subset(image(singleton_set(X1),X2),apply(X2,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',image_and_apply2) ).
cnf(a2,axiom,
( ~ member(X1,X2)
| little_set(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET003-0.ax',a2) ).
cnf(apply2,axiom,
( ~ member(X1,apply(X2,X3))
| member(f28(X1,X2,X3),X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET003-0.ax',apply2) ).
cnf(non_ordered_pair1,axiom,
( ~ member(X1,non_ordered_pair(X2,X3))
| X1 = X3
| X1 = X2 ),
file('/export/starexec/sandbox/benchmark/Axioms/SET003-0.ax',non_ordered_pair1) ).
cnf(regularity1,axiom,
( member(f24(X1),X1)
| X1 = empty_set ),
file('/export/starexec/sandbox/benchmark/Axioms/SET003-0.ax',regularity1) ).
cnf(regularity2,axiom,
( disjoint(f24(X1),X1)
| X1 = empty_set ),
file('/export/starexec/sandbox/benchmark/Axioms/SET003-0.ax',regularity2) ).
cnf(identity_relation2,axiom,
( ~ member(X1,identity_relation)
| first(X1) = second(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET003-0.ax',identity_relation2) ).
cnf(non_ordered_pair3,axiom,
( X1 != X3
| ~ little_set(X1)
| member(X1,non_ordered_pair(X2,X3)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET003-0.ax',non_ordered_pair3) ).
cnf(apply4,axiom,
( ~ member(X1,apply(X2,X3))
| member(X1,second(f28(X1,X2,X3))) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET003-0.ax',apply4) ).
cnf(empty_set,axiom,
~ member(X1,empty_set),
file('/export/starexec/sandbox/benchmark/Axioms/SET003-0.ax',empty_set) ).
cnf(c_0_31,plain,
( ~ member(X3,X2)
| ~ member(X3,X1)
| ~ disjoint(X1,X2) ),
inference(fof_simplification,[status(thm)],[disjoint1]) ).
cnf(c_0_32,negated_conjecture,
~ subset(apply(compose(another_function,a_function),element),apply(another_function,apply(a_function,element))),
inference(fof_simplification,[status(thm)],[prove_apply_for_composition2]) ).
cnf(c_0_33,plain,
( ~ member(X3,X2)
| ~ member(X3,X1)
| ~ disjoint(X1,X2) ),
c_0_31 ).
cnf(c_0_34,axiom,
( member(f23(X1,X2),X1)
| disjoint(X1,X2) ),
disjoint2 ).
cnf(c_0_35,negated_conjecture,
~ subset(apply(compose(another_function,a_function),element),apply(another_function,apply(a_function,element))),
c_0_32 ).
cnf(c_0_36,axiom,
( member(f17(X1,X2),X1)
| subset(X1,X2) ),
subset2 ).
cnf(c_0_37,plain,
( ~ member(X3,X1)
| ~ member(X3,X2)
| member(f23(X1,X2),X1) ),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_38,negated_conjecture,
member(f17(apply(compose(another_function,a_function),element),apply(another_function,apply(a_function,element))),apply(compose(another_function,a_function),element)),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_39,plain,
( ~ ordered_pair_predicate(X1)
| little_set(first(X1)) ),
inference(fof_simplification,[status(thm)],[first_component_is_small]) ).
cnf(c_0_40,plain,
( ~ member(X1,apply(X2,X3))
| ordered_pair_predicate(f28(X1,X2,X3)) ),
inference(fof_simplification,[status(thm)],[apply1]) ).
cnf(c_0_41,plain,
( ~ member(X1,apply(X2,X3))
| first(f28(X1,X2,X3)) = X3 ),
inference(fof_simplification,[status(thm)],[apply3]) ).
cnf(c_0_42,negated_conjecture,
( ~ member(f17(apply(compose(another_function,a_function),element),apply(another_function,apply(a_function,element))),X1)
| member(f23(X1,apply(compose(another_function,a_function),element)),X1) ),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_43,plain,
( X1 != ordered_pair(X2,X3)
| ~ little_set(X3)
| ~ little_set(X2)
| ordered_pair_predicate(X1) ),
inference(fof_simplification,[status(thm)],[ordered_pair_predicate4]) ).
cnf(c_0_44,axiom,
ordered_pair(X1,X2) = non_ordered_pair(singleton_set(X1),non_ordered_pair(X1,X2)),
ordered_pair ).
cnf(c_0_45,axiom,
singleton_set(X1) = non_ordered_pair(X1,X1),
singleton_set ).
cnf(c_0_46,plain,
( ~ little_set(X2)
| ~ little_set(X1)
| first(ordered_pair(X1,X2)) = X1 ),
inference(fof_simplification,[status(thm)],[property_of_first]) ).
cnf(c_0_47,plain,
( ~ ordered_pair_predicate(X1)
| little_set(first(X1)) ),
c_0_39 ).
cnf(c_0_48,plain,
( ~ member(X1,apply(X2,X3))
| ordered_pair_predicate(f28(X1,X2,X3)) ),
c_0_40 ).
cnf(c_0_49,plain,
( ~ member(X1,apply(X2,X3))
| first(f28(X1,X2,X3)) = X3 ),
c_0_41 ).
cnf(c_0_50,negated_conjecture,
member(f23(apply(compose(another_function,a_function),element),apply(compose(another_function,a_function),element)),apply(compose(another_function,a_function),element)),
inference(spm,[status(thm)],[c_0_42,c_0_38]) ).
cnf(c_0_51,plain,
( ~ little_set(X2)
| ~ little_set(X1)
| second(ordered_pair(X1,X2)) = X2 ),
inference(fof_simplification,[status(thm)],[property_of_second]) ).
cnf(c_0_52,plain,
( ~ member(X2,X1)
| ~ relation(X1)
| ordered_pair_predicate(X2) ),
inference(fof_simplification,[status(thm)],[relation1]) ).
cnf(c_0_53,plain,
( first(X1) != second(X1)
| ~ ordered_pair_predicate(X1)
| ~ little_set(X1)
| member(X1,identity_relation) ),
inference(fof_simplification,[status(thm)],[identity_relation3]) ).
cnf(c_0_54,plain,
( ~ ordered_pair_predicate(X1)
| little_set(X1) ),
inference(fof_simplification,[status(thm)],[ordered_pairs_are_small2]) ).
cnf(c_0_55,plain,
( X1 != ordered_pair(X2,X3)
| ~ little_set(X3)
| ~ little_set(X2)
| ordered_pair_predicate(X1) ),
c_0_43 ).
cnf(c_0_56,plain,
ordered_pair(X1,X2) = non_ordered_pair(non_ordered_pair(X1,X1),non_ordered_pair(X1,X2)),
inference(rw,[status(thm)],[c_0_44,c_0_45]) ).
cnf(c_0_57,plain,
( ~ little_set(X2)
| ~ little_set(X1)
| first(ordered_pair(X1,X2)) = X1 ),
c_0_46 ).
cnf(c_0_58,plain,
( ~ member(X1,apply(X2,X3))
| little_set(first(f28(X1,X2,X3))) ),
inference(spm,[status(thm)],[c_0_47,c_0_48]) ).
cnf(c_0_59,negated_conjecture,
first(f28(f23(apply(compose(another_function,a_function),element),apply(compose(another_function,a_function),element)),compose(another_function,a_function),element)) = element,
inference(spm,[status(thm)],[c_0_49,c_0_50]) ).
cnf(c_0_60,plain,
( ~ little_set(X2)
| ~ little_set(X1)
| second(ordered_pair(X1,X2)) = X2 ),
c_0_51 ).
cnf(c_0_61,plain,
( ~ member(X2,X1)
| ~ relation(X1)
| ordered_pair_predicate(X2) ),
c_0_52 ).
cnf(c_0_62,axiom,
relation(compose(X1,X2)),
composition_is_a_relation ).
cnf(c_0_63,plain,
( second(X4) != X1
| ~ member(first(X4),X2)
| ~ member(X4,X3)
| ~ ordered_pair_predicate(X4)
| ~ little_set(X1)
| member(X1,image(X2,X3)) ),
inference(fof_simplification,[status(thm)],[image_and_substitution5]) ).
cnf(c_0_64,plain,
( ~ ordered_pair_predicate(X1)
| little_set(second(X1)) ),
inference(fof_simplification,[status(thm)],[second_component_is_small]) ).
cnf(c_0_65,plain,
( first(X1) != second(X1)
| ~ ordered_pair_predicate(X1)
| ~ little_set(X1)
| member(X1,identity_relation) ),
c_0_53 ).
cnf(c_0_66,plain,
( ~ ordered_pair_predicate(X1)
| little_set(X1) ),
c_0_54 ).
cnf(c_0_67,plain,
( ~ little_set(X2)
| ~ little_set(X3)
| X1 != non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,X3))
| ordered_pair_predicate(X1) ),
inference(rw,[status(thm)],[c_0_55,c_0_56]) ).
cnf(c_0_68,plain,
( ~ little_set(X1)
| ~ little_set(X2)
| first(non_ordered_pair(non_ordered_pair(X1,X1),non_ordered_pair(X1,X2))) = X1 ),
inference(rw,[status(thm)],[c_0_57,c_0_56]) ).
cnf(c_0_69,negated_conjecture,
little_set(element),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_59]),c_0_50])]) ).
cnf(c_0_70,plain,
( ~ little_set(X1)
| ~ little_set(X2)
| second(non_ordered_pair(non_ordered_pair(X1,X1),non_ordered_pair(X1,X2))) = X2 ),
inference(rw,[status(thm)],[c_0_60,c_0_56]) ).
cnf(c_0_71,plain,
( ~ member(X1,compose(X2,X3))
| ordered_pair_predicate(X1) ),
inference(spm,[status(thm)],[c_0_61,c_0_62]) ).
cnf(c_0_72,plain,
( second(X4) != X1
| ~ member(first(X4),X2)
| ~ member(X4,X3)
| ~ ordered_pair_predicate(X4)
| ~ little_set(X1)
| member(X1,image(X2,X3)) ),
c_0_63 ).
cnf(c_0_73,plain,
( ~ ordered_pair_predicate(X1)
| little_set(second(X1)) ),
c_0_64 ).
cnf(c_0_74,plain,
( ~ ordered_pair_predicate(X1)
| first(X1) != second(X1)
| member(X1,identity_relation) ),
inference(csr,[status(thm)],[c_0_65,c_0_66]) ).
cnf(c_0_75,plain,
( ~ little_set(X1)
| ~ little_set(X2)
| ordered_pair_predicate(non_ordered_pair(non_ordered_pair(X1,X1),non_ordered_pair(X1,X2))) ),
inference(er,[status(thm)],[c_0_67]) ).
cnf(c_0_76,negated_conjecture,
( ~ little_set(X1)
| first(non_ordered_pair(non_ordered_pair(element,element),non_ordered_pair(element,X1))) = element ),
inference(spm,[status(thm)],[c_0_68,c_0_69]) ).
cnf(c_0_77,negated_conjecture,
( ~ little_set(X1)
| second(non_ordered_pair(non_ordered_pair(element,element),non_ordered_pair(element,X1))) = X1 ),
inference(spm,[status(thm)],[c_0_70,c_0_69]) ).
cnf(c_0_78,plain,
( X1 != X2
| ~ little_set(X1)
| member(X1,non_ordered_pair(X2,X3)) ),
inference(fof_simplification,[status(thm)],[non_ordered_pair2]) ).
cnf(c_0_79,plain,
( ~ little_set(X1)
| member(X1,universal_set) ),
inference(fof_simplification,[status(thm)],[universal_set]) ).
cnf(c_0_80,plain,
( ~ member(X1,compose(X2,X3))
| little_set(first(X1)) ),
inference(spm,[status(thm)],[c_0_47,c_0_71]) ).
cnf(c_0_81,negated_conjecture,
first(f28(f17(apply(compose(another_function,a_function),element),apply(another_function,apply(a_function,element))),compose(another_function,a_function),element)) = element,
inference(spm,[status(thm)],[c_0_49,c_0_38]) ).
cnf(c_0_82,plain,
( ~ member(X3,X1)
| ~ subset(X1,X2)
| member(X3,X2) ),
inference(fof_simplification,[status(thm)],[subset1]) ).
cnf(c_0_83,axiom,
subset(image(singleton_set(X1),X2),apply(X2,X1)),
image_and_apply2 ).
cnf(c_0_84,plain,
( ~ member(X1,X3)
| ~ member(first(X1),X2)
| ~ ordered_pair_predicate(X1)
| member(second(X1),image(X2,X3)) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_72]),c_0_73]) ).
cnf(c_0_85,plain,
( ~ little_set(X1)
| ~ little_set(X2)
| first(non_ordered_pair(non_ordered_pair(X1,X1),non_ordered_pair(X1,X2))) != second(non_ordered_pair(non_ordered_pair(X1,X1),non_ordered_pair(X1,X2)))
| member(non_ordered_pair(non_ordered_pair(X1,X1),non_ordered_pair(X1,X2)),identity_relation) ),
inference(spm,[status(thm)],[c_0_74,c_0_75]) ).
cnf(c_0_86,negated_conjecture,
first(non_ordered_pair(non_ordered_pair(element,element),non_ordered_pair(element,element))) = element,
inference(spm,[status(thm)],[c_0_76,c_0_69]) ).
cnf(c_0_87,negated_conjecture,
second(non_ordered_pair(non_ordered_pair(element,element),non_ordered_pair(element,element))) = element,
inference(spm,[status(thm)],[c_0_77,c_0_69]) ).
cnf(c_0_88,plain,
( X1 != X2
| ~ little_set(X1)
| member(X1,non_ordered_pair(X2,X3)) ),
c_0_78 ).
cnf(c_0_89,plain,
( ~ member(X1,X2)
| little_set(X1) ),
inference(fof_simplification,[status(thm)],[a2]) ).
cnf(c_0_90,plain,
( ~ little_set(X1)
| member(X1,universal_set) ),
c_0_79 ).
cnf(c_0_91,negated_conjecture,
( ~ member(f28(f17(apply(compose(another_function,a_function),element),apply(another_function,apply(a_function,element))),compose(another_function,a_function),element),compose(X1,X2))
| little_set(element) ),
inference(spm,[status(thm)],[c_0_80,c_0_81]) ).
cnf(c_0_92,plain,
( ~ member(X1,apply(X2,X3))
| member(f28(X1,X2,X3),X2) ),
inference(fof_simplification,[status(thm)],[apply2]) ).
cnf(c_0_93,plain,
( ~ member(X1,non_ordered_pair(X2,X3))
| X1 = X3
| X1 = X2 ),
inference(fof_simplification,[status(thm)],[non_ordered_pair1]) ).
cnf(c_0_94,plain,
( ~ member(X3,X1)
| ~ subset(X1,X2)
| member(X3,X2) ),
c_0_82 ).
cnf(c_0_95,plain,
subset(image(non_ordered_pair(X1,X1),X2),apply(X2,X1)),
inference(rw,[status(thm)],[c_0_83,c_0_45]) ).
cnf(c_0_96,plain,
( ~ member(non_ordered_pair(non_ordered_pair(X1,X1),non_ordered_pair(X1,X2)),X4)
| ~ member(first(non_ordered_pair(non_ordered_pair(X1,X1),non_ordered_pair(X1,X2))),X3)
| ~ little_set(X1)
| ~ little_set(X2)
| member(second(non_ordered_pair(non_ordered_pair(X1,X1),non_ordered_pair(X1,X2))),image(X3,X4)) ),
inference(spm,[status(thm)],[c_0_84,c_0_75]) ).
cnf(c_0_97,negated_conjecture,
member(non_ordered_pair(non_ordered_pair(element,element),non_ordered_pair(element,element)),identity_relation),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_86]),c_0_87]),c_0_69])]) ).
cnf(c_0_98,plain,
( ~ little_set(X1)
| member(X1,non_ordered_pair(X1,X2)) ),
inference(er,[status(thm)],[c_0_88]) ).
cnf(c_0_99,plain,
( ~ member(X1,X2)
| little_set(X1) ),
c_0_89 ).
cnf(c_0_100,negated_conjecture,
( ~ member(f28(f17(apply(compose(another_function,a_function),element),apply(another_function,apply(a_function,element))),compose(another_function,a_function),element),compose(X1,X2))
| member(element,universal_set) ),
inference(spm,[status(thm)],[c_0_90,c_0_91]) ).
cnf(c_0_101,plain,
( ~ member(X1,apply(X2,X3))
| member(f28(X1,X2,X3),X2) ),
c_0_92 ).
cnf(c_0_102,plain,
( ~ member(X1,non_ordered_pair(X2,X3))
| X1 = X3
| X1 = X2 ),
c_0_93 ).
cnf(c_0_103,axiom,
( member(f24(X1),X1)
| X1 = empty_set ),
regularity1 ).
cnf(c_0_104,plain,
( ~ member(X1,image(non_ordered_pair(X3,X3),X2))
| member(X1,apply(X2,X3)) ),
inference(spm,[status(thm)],[c_0_94,c_0_95]) ).
cnf(c_0_105,negated_conjecture,
( ~ member(element,X1)
| member(element,image(X1,identity_relation)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_96,c_0_97]),c_0_87]),c_0_69]),c_0_86])]) ).
cnf(c_0_106,plain,
( ~ member(X1,X3)
| member(X1,non_ordered_pair(X1,X2)) ),
inference(spm,[status(thm)],[c_0_98,c_0_99]) ).
cnf(c_0_107,negated_conjecture,
member(element,universal_set),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_100,c_0_101]),c_0_38])]) ).
cnf(c_0_108,axiom,
( disjoint(f24(X1),X1)
| X1 = empty_set ),
regularity2 ).
cnf(c_0_109,plain,
( non_ordered_pair(X1,X2) = empty_set
| f24(non_ordered_pair(X1,X2)) = X2
| f24(non_ordered_pair(X1,X2)) = X1 ),
inference(spm,[status(thm)],[c_0_102,c_0_103]) ).
cnf(c_0_110,plain,
( ~ member(X1,identity_relation)
| first(X1) = second(X1) ),
inference(fof_simplification,[status(thm)],[identity_relation2]) ).
cnf(c_0_111,negated_conjecture,
( ~ member(element,non_ordered_pair(X1,X1))
| member(element,apply(identity_relation,X1)) ),
inference(spm,[status(thm)],[c_0_104,c_0_105]) ).
cnf(c_0_112,negated_conjecture,
member(element,non_ordered_pair(element,X1)),
inference(spm,[status(thm)],[c_0_106,c_0_107]) ).
cnf(c_0_113,plain,
( X1 != X3
| ~ little_set(X1)
| member(X1,non_ordered_pair(X2,X3)) ),
inference(fof_simplification,[status(thm)],[non_ordered_pair3]) ).
cnf(c_0_114,plain,
( ~ member(X2,X1)
| ~ member(X2,f24(X1))
| X1 = empty_set ),
inference(spm,[status(thm)],[c_0_33,c_0_108]) ).
cnf(c_0_115,plain,
( non_ordered_pair(X1,X1) = empty_set
| f24(non_ordered_pair(X1,X1)) = X1 ),
inference(er,[status(thm)],[inference(ef,[status(thm)],[c_0_109])]) ).
cnf(c_0_116,plain,
( ~ member(X1,identity_relation)
| first(X1) = second(X1) ),
c_0_110 ).
cnf(c_0_117,negated_conjecture,
member(element,apply(identity_relation,element)),
inference(spm,[status(thm)],[c_0_111,c_0_112]) ).
cnf(c_0_118,plain,
( X1 != X3
| ~ little_set(X1)
| member(X1,non_ordered_pair(X2,X3)) ),
c_0_113 ).
cnf(c_0_119,plain,
( ~ member(X2,X1)
| ~ member(X2,non_ordered_pair(X1,X1))
| non_ordered_pair(X1,X1) = empty_set ),
inference(spm,[status(thm)],[c_0_114,c_0_115]) ).
cnf(c_0_120,plain,
( ~ member(X1,apply(X2,X3))
| member(X1,second(f28(X1,X2,X3))) ),
inference(fof_simplification,[status(thm)],[apply4]) ).
cnf(c_0_121,plain,
( ~ member(X1,apply(identity_relation,X2))
| first(f28(X1,identity_relation,X2)) = second(f28(X1,identity_relation,X2)) ),
inference(spm,[status(thm)],[c_0_116,c_0_101]) ).
cnf(c_0_122,negated_conjecture,
first(f28(element,identity_relation,element)) = element,
inference(spm,[status(thm)],[c_0_49,c_0_117]) ).
cnf(c_0_123,plain,
( ~ little_set(X1)
| member(X1,non_ordered_pair(X2,X1)) ),
inference(er,[status(thm)],[c_0_118]) ).
cnf(c_0_124,plain,
( ~ member(f24(non_ordered_pair(X1,X1)),X1)
| non_ordered_pair(X1,X1) = empty_set ),
inference(spm,[status(thm)],[c_0_119,c_0_103]) ).
cnf(c_0_125,plain,
( ~ member(X1,apply(X2,X3))
| member(X1,second(f28(X1,X2,X3))) ),
c_0_120 ).
cnf(c_0_126,negated_conjecture,
second(f28(element,identity_relation,element)) = element,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_121,c_0_117]),c_0_122]) ).
cnf(c_0_127,plain,
( ~ member(X1,X3)
| member(X1,non_ordered_pair(X2,X1)) ),
inference(spm,[status(thm)],[c_0_123,c_0_99]) ).
cnf(c_0_128,plain,
( ~ member(X1,X1)
| non_ordered_pair(X1,X1) = empty_set ),
inference(spm,[status(thm)],[c_0_124,c_0_115]) ).
cnf(c_0_129,negated_conjecture,
member(element,element),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_125,c_0_126]),c_0_117])]) ).
cnf(c_0_130,plain,
~ member(X1,empty_set),
inference(fof_simplification,[status(thm)],[empty_set]) ).
cnf(c_0_131,negated_conjecture,
member(element,non_ordered_pair(X1,element)),
inference(spm,[status(thm)],[c_0_127,c_0_107]) ).
cnf(c_0_132,negated_conjecture,
non_ordered_pair(element,element) = empty_set,
inference(spm,[status(thm)],[c_0_128,c_0_129]) ).
cnf(c_0_133,plain,
~ member(X1,empty_set),
c_0_130 ).
cnf(c_0_134,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_131,c_0_132]),c_0_133]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SET040-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.07 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.18/5.67 % Computer : n010.cluster.edu
% 0.18/5.67 % Model : x86_64 x86_64
% 0.18/5.67 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/5.67 % Memory : 8046.5625MB
% 0.18/5.67 % OS : Linux 6.8.0-71-generic
% 0.18/5.67 % CPULimit : 300
% 0.18/5.67 % WCLimit : 300
% 0.18/5.67 % DateTime : Mon Sep 21 04:47:32 UTC 2026
% 0.18/5.68 % CPUTime :
% 0.18/5.68 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.22/5.73 Running first-order theorem proving
% 0.22/5.73 Running: /export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p
% 79.84/15.90 % Version: 3.5.1
% 79.84/15.90 % Preprocessing class: FSLSSMSMSSSNFFN.
% 79.84/15.90 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 79.84/15.90 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 79.84/15.90 % Starting new_bool_3 with 300s (1) cores
% 79.84/15.90 % Starting new_bool_1 with 300s (1) cores
% 79.84/15.90 % Starting sh5l with 300s (1) cores
% 79.84/15.90 % C07_19_nc_SOS_SAT001_MinMin_p005000_rr with pid 49463 completed with status 0
% 79.84/15.90 % Result found by C07_19_nc_SOS_SAT001_MinMin_p005000_rr
% 79.84/15.90 % Preprocessing class: FSLSSMSMSSSNFFN.
% 79.84/15.90 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 79.84/15.90 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 79.84/15.90 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 79.84/15.90 % No SInE strategy applied
% 79.84/15.90 % Search class: FGHSM-FSLS31-MFFFFFNN
% 79.84/15.90 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 79.84/15.90 % Starting SubtermCWHack with 136s (1) cores
% 79.84/15.90 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 151s (1) cores
% 79.84/15.90 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y with 244s (1) cores
% 79.84/15.90 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S06DI with 136s (1) cores
% 79.84/15.90 % Starting U----_100_C09_12_F1_SE_CS_SP_PS_S5PRR_RG_ND_S04AN with 136s (1) cores
% 79.84/15.90 % G-E--_208_C18_F1_SE_CS_SP_PS_S06DI with pid 49473 completed with status 0
% 79.84/15.90 % Result found by G-E--_208_C18_F1_SE_CS_SP_PS_S06DI
% 79.84/15.90 % Preprocessing class: FSLSSMSMSSSNFFN.
% 79.84/15.90 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 79.84/15.90 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 79.84/15.90 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 79.84/15.90 % No SInE strategy applied
% 79.84/15.90 % Search class: FGHSM-FSLS31-MFFFFFNN
% 79.84/15.90 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 79.84/15.90 % Starting SubtermCWHack with 136s (1) cores
% 79.84/15.90 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 151s (1) cores
% 79.84/15.90 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y with 244s (1) cores
% 79.84/15.90 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S06DI with 136s (1) cores
% 79.84/15.90 % Preprocessing time : 0.005 s
% 79.84/15.90 % Presaturation interreduction done
% 79.84/15.90
% 79.84/15.90 % Proof found!
% 79.84/15.90 % SZS status Unsatisfiable
% 79.84/15.90 % SZS output start CNFRefutation
% See solution above
% 79.84/15.90 % Parsed axioms : 167
% 79.84/15.90 % Removed by relevancy pruning/SinE : 0
% 79.84/15.90 % Initial clauses : 167
% 79.84/15.90 % Removed in clause preprocessing : 6
% 79.84/15.90 % Initial clauses in saturation : 161
% 79.84/15.90 % Processed clauses : 22308
% 79.84/15.90 % ...of these trivial : 960
% 79.84/15.90 % ...subsumed : 14765
% 79.84/15.90 % ...remaining for further processing : 6583
% 79.84/15.90 % Other redundant clauses eliminated : 21
% 79.84/15.90 % Clauses deleted for lack of memory : 0
% 79.84/15.90 % Backward-subsumed : 101
% 79.84/15.90 % Backward-rewritten : 297
% 79.84/15.90 % Generated clauses : 505569
% 79.84/15.90 % ...of the previous two non-redundant : 488542
% 79.84/15.90 % ...aggressively subsumed : 0
% 79.84/15.90 % Contextual simplify-reflections : 19
% 79.84/15.90 % Paramodulations : 505505
% 79.84/15.90 % Factorizations : 40
% 79.84/15.90 % NegExts : 0
% 79.84/15.90 % Equation resolutions : 24
% 79.84/15.90 % Disequality decompositions : 0
% 79.84/15.90 % Total rewrite steps : 39080
% 79.84/15.90 % ...of those cached : 37547
% 79.84/15.90 % Propositional unsat checks : 0
% 79.84/15.90 % Propositional check models : 0
% 79.84/15.90 % Propositional check unsatisfiable : 0
% 79.84/15.90 % Propositional clauses : 0
% 79.84/15.90 % Propositional clauses after purity: 0
% 79.84/15.90 % Propositional unsat core size : 0
% 79.84/15.90 % Propositional preprocessing time : 0.000
% 79.84/15.90 % Propositional encoding time : 0.000
% 79.84/15.90 % Propositional solver time : 0.000
% 79.84/15.90 % Success case prop preproc time : 0.000
% 79.84/15.90 % Success case prop encoding time : 0.000
% 79.84/15.90 % Success case prop solver time : 0.000
% 79.84/15.90 % Current number of processed clauses : 6011
% 79.84/15.90 % Positive orientable unit clauses : 837
% 79.84/15.90 % Positive unorientable unit clauses: 0
% 79.84/15.90 % Negative unit clauses : 16
% 79.84/15.90 % Non-unit-clauses : 5158
% 79.84/15.90 % Current number of unprocessed clauses: 466038
% 79.84/15.90 % ...number of literals in the above : 1195437
% 79.84/15.90 % Current number of archived formulas : 0
% 79.84/15.90 % Current number of archived clauses : 563
% 79.84/15.90 % Clause-clause subsumption calls (NU) : 3647968
% 79.84/15.90 % Rec. Clause-clause subsumption calls : 2853991
% 79.84/15.90 % Non-unit clause-clause subsumptions : 7569
% 79.84/15.90 % Unit Clause-clause subsumption calls : 323380
% 79.84/15.90 % Rewrite failures with RHS unbound : 0
% 79.84/15.90 % BW rewrite match attempts : 15327
% 79.84/15.90 % BW rewrite match successes : 55
% 79.84/15.90 % Condensation attempts : 0
% 79.84/15.90 % Condensation successes : 0
% 79.84/15.90 % Termbank termtop insertions : 7200607
% 79.84/15.90 % Search garbage collected termcells : 375
% 79.84/15.90
% 79.84/15.90 % -------------------------------------------------
% 79.84/15.90 % User time : 9.473 s
% 79.84/15.90 % System time : 0.444 s
% 79.84/15.90 % Total time : 9.918 s
% 79.84/15.90 % Maximum resident set size: 3528 pages
% 79.84/15.90
% 79.84/15.90 % -------------------------------------------------
% 79.84/15.90 % User time : 47.246 s
% 79.84/15.90 % System time : 1.986 s
% 79.84/15.90 % Total time : 49.232 s
% 79.84/15.90 % Maximum resident set size: 4608 pages
% 79.84/15.90 % E exiting
%------------------------------------------------------------------------------