%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : SET039-3 : 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 : n004.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 02:16:12 PM UTC 2026
% Result : Unsatisfiable 108.07s 16.30s
% Output : CNFRefutation 124.01s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 30
% Syntax : Number of clauses : 125 ( 28 unt; 9 nHn; 99 RR)
% Number of literals : 287 ( 66 equ; 158 neg)
% Maximal clause size : 6 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 4 con; 0-3 aty)
% Number of variables : 217 ( 15 sgn)
% Comments :
%------------------------------------------------------------------------------
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(domain1,axiom,
( ~ member(X1,domain_of(X2))
| ordered_pair_predicate(f8(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET003-0.ax',domain1) ).
cnf(domain3,axiom,
( ~ member(X1,domain_of(X2))
| X1 = first(f8(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET003-0.ax',domain3) ).
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(member_of_domain,hypothesis,
member(a,domain_of(a_function)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',member_of_domain) ).
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(function1,axiom,
( ~ function(X1)
| relation(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET003-0.ax',function1) ).
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(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(a_function,hypothesis,
function(a_function),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_function) ).
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(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(domain2,axiom,
( ~ member(X1,domain_of(X2))
| member(f8(X1,X2),X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET003-0.ax',domain2) ).
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(identity_relation2,axiom,
( ~ member(X1,identity_relation)
| first(X1) = second(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET003-0.ax',identity_relation2) ).
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(apply3,axiom,
( ~ member(X1,apply(X2,X3))
| first(f28(X1,X2,X3)) = X3 ),
file('/export/starexec/sandbox/benchmark/Axioms/SET003-0.ax',apply3) ).
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(disjoint1,axiom,
( ~ member(X3,X2)
| ~ member(X3,X1)
| ~ disjoint(X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET003-0.ax',disjoint1) ).
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(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_30,plain,
( ~ ordered_pair_predicate(X1)
| little_set(first(X1)) ),
inference(fof_simplification,[status(thm)],[first_component_is_small]) ).
cnf(c_0_31,plain,
( ~ member(X1,domain_of(X2))
| ordered_pair_predicate(f8(X1,X2)) ),
inference(fof_simplification,[status(thm)],[domain1]) ).
cnf(c_0_32,plain,
( ~ member(X1,domain_of(X2))
| X1 = first(f8(X1,X2)) ),
inference(fof_simplification,[status(thm)],[domain3]) ).
cnf(c_0_33,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_34,axiom,
ordered_pair(X1,X2) = non_ordered_pair(singleton_set(X1),non_ordered_pair(X1,X2)),
ordered_pair ).
cnf(c_0_35,axiom,
singleton_set(X1) = non_ordered_pair(X1,X1),
singleton_set ).
cnf(c_0_36,plain,
( ~ little_set(X2)
| ~ little_set(X1)
| first(ordered_pair(X1,X2)) = X1 ),
inference(fof_simplification,[status(thm)],[property_of_first]) ).
cnf(c_0_37,plain,
( ~ ordered_pair_predicate(X1)
| little_set(first(X1)) ),
c_0_30 ).
cnf(c_0_38,plain,
( ~ member(X1,domain_of(X2))
| ordered_pair_predicate(f8(X1,X2)) ),
c_0_31 ).
cnf(c_0_39,plain,
( ~ member(X1,domain_of(X2))
| X1 = first(f8(X1,X2)) ),
c_0_32 ).
cnf(c_0_40,hypothesis,
member(a,domain_of(a_function)),
member_of_domain ).
cnf(c_0_41,plain,
( ~ little_set(X2)
| ~ little_set(X1)
| second(ordered_pair(X1,X2)) = X2 ),
inference(fof_simplification,[status(thm)],[property_of_second]) ).
cnf(c_0_42,plain,
( ~ member(X2,X1)
| ~ relation(X1)
| ordered_pair_predicate(X2) ),
inference(fof_simplification,[status(thm)],[relation1]) ).
cnf(c_0_43,plain,
( ~ function(X1)
| relation(X1) ),
inference(fof_simplification,[status(thm)],[function1]) ).
cnf(c_0_44,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_45,plain,
( ~ ordered_pair_predicate(X1)
| little_set(X1) ),
inference(fof_simplification,[status(thm)],[ordered_pairs_are_small2]) ).
cnf(c_0_46,plain,
( X1 != ordered_pair(X2,X3)
| ~ little_set(X3)
| ~ little_set(X2)
| ordered_pair_predicate(X1) ),
c_0_33 ).
cnf(c_0_47,plain,
ordered_pair(X1,X2) = non_ordered_pair(non_ordered_pair(X1,X1),non_ordered_pair(X1,X2)),
inference(rw,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_48,plain,
( ~ little_set(X2)
| ~ little_set(X1)
| first(ordered_pair(X1,X2)) = X1 ),
c_0_36 ).
cnf(c_0_49,plain,
( ~ member(X1,domain_of(X2))
| little_set(first(f8(X1,X2))) ),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_50,hypothesis,
first(f8(a,a_function)) = a,
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_51,plain,
( ~ little_set(X2)
| ~ little_set(X1)
| second(ordered_pair(X1,X2)) = X2 ),
c_0_41 ).
cnf(c_0_52,plain,
( ~ member(X2,X1)
| ~ relation(X1)
| ordered_pair_predicate(X2) ),
c_0_42 ).
cnf(c_0_53,plain,
( ~ function(X1)
| relation(X1) ),
c_0_43 ).
cnf(c_0_54,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_55,plain,
( ~ ordered_pair_predicate(X1)
| little_set(second(X1)) ),
inference(fof_simplification,[status(thm)],[second_component_is_small]) ).
cnf(c_0_56,plain,
( first(X1) != second(X1)
| ~ ordered_pair_predicate(X1)
| ~ little_set(X1)
| member(X1,identity_relation) ),
c_0_44 ).
cnf(c_0_57,plain,
( ~ ordered_pair_predicate(X1)
| little_set(X1) ),
c_0_45 ).
cnf(c_0_58,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_46,c_0_47]) ).
cnf(c_0_59,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_48,c_0_47]) ).
cnf(c_0_60,hypothesis,
little_set(a),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_50]),c_0_40])]) ).
cnf(c_0_61,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_51,c_0_47]) ).
cnf(c_0_62,plain,
( ~ member(X1,X2)
| ~ function(X2)
| ordered_pair_predicate(X1) ),
inference(spm,[status(thm)],[c_0_52,c_0_53]) ).
cnf(c_0_63,hypothesis,
function(a_function),
a_function ).
cnf(c_0_64,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_54 ).
cnf(c_0_65,plain,
( ~ ordered_pair_predicate(X1)
| little_set(second(X1)) ),
c_0_55 ).
cnf(c_0_66,plain,
( ~ ordered_pair_predicate(X1)
| first(X1) != second(X1)
| member(X1,identity_relation) ),
inference(csr,[status(thm)],[c_0_56,c_0_57]) ).
cnf(c_0_67,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_58]) ).
cnf(c_0_68,hypothesis,
( ~ little_set(X1)
| first(non_ordered_pair(non_ordered_pair(a,a),non_ordered_pair(a,X1))) = a ),
inference(spm,[status(thm)],[c_0_59,c_0_60]) ).
cnf(c_0_69,hypothesis,
( ~ little_set(X1)
| second(non_ordered_pair(non_ordered_pair(a,a),non_ordered_pair(a,X1))) = X1 ),
inference(spm,[status(thm)],[c_0_61,c_0_60]) ).
cnf(c_0_70,plain,
( X1 != X2
| ~ little_set(X1)
| member(X1,non_ordered_pair(X2,X3)) ),
inference(fof_simplification,[status(thm)],[non_ordered_pair2]) ).
cnf(c_0_71,hypothesis,
( ~ member(X1,a_function)
| ordered_pair_predicate(X1) ),
inference(spm,[status(thm)],[c_0_62,c_0_63]) ).
cnf(c_0_72,plain,
( ~ member(X3,X1)
| ~ subset(X1,X2)
| member(X3,X2) ),
inference(fof_simplification,[status(thm)],[subset1]) ).
cnf(c_0_73,axiom,
subset(image(singleton_set(X1),X2),apply(X2,X1)),
image_and_apply2 ).
cnf(c_0_74,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_64]),c_0_65]) ).
cnf(c_0_75,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_66,c_0_67]) ).
cnf(c_0_76,hypothesis,
first(non_ordered_pair(non_ordered_pair(a,a),non_ordered_pair(a,a))) = a,
inference(spm,[status(thm)],[c_0_68,c_0_60]) ).
cnf(c_0_77,hypothesis,
second(non_ordered_pair(non_ordered_pair(a,a),non_ordered_pair(a,a))) = a,
inference(spm,[status(thm)],[c_0_69,c_0_60]) ).
cnf(c_0_78,plain,
( X1 != X2
| ~ little_set(X1)
| member(X1,non_ordered_pair(X2,X3)) ),
c_0_70 ).
cnf(c_0_79,hypothesis,
( ~ member(X1,a_function)
| little_set(first(X1)) ),
inference(spm,[status(thm)],[c_0_37,c_0_71]) ).
cnf(c_0_80,plain,
( ~ member(X3,X1)
| ~ subset(X1,X2)
| member(X3,X2) ),
c_0_72 ).
cnf(c_0_81,plain,
subset(image(non_ordered_pair(X1,X1),X2),apply(X2,X1)),
inference(rw,[status(thm)],[c_0_73,c_0_35]) ).
cnf(c_0_82,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_74,c_0_67]) ).
cnf(c_0_83,hypothesis,
member(non_ordered_pair(non_ordered_pair(a,a),non_ordered_pair(a,a)),identity_relation),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_76]),c_0_77]),c_0_60])]) ).
cnf(c_0_84,plain,
( ~ little_set(X1)
| member(X1,non_ordered_pair(X1,X2)) ),
inference(er,[status(thm)],[c_0_78]) ).
cnf(c_0_85,hypothesis,
( ~ member(f8(a,a_function),a_function)
| little_set(a) ),
inference(spm,[status(thm)],[c_0_79,c_0_50]) ).
cnf(c_0_86,plain,
( ~ member(X1,domain_of(X2))
| member(f8(X1,X2),X2) ),
inference(fof_simplification,[status(thm)],[domain2]) ).
cnf(c_0_87,plain,
( ~ member(X1,image(non_ordered_pair(X3,X3),X2))
| member(X1,apply(X2,X3)) ),
inference(spm,[status(thm)],[c_0_80,c_0_81]) ).
cnf(c_0_88,hypothesis,
( ~ member(a,X1)
| member(a,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_82,c_0_83]),c_0_77]),c_0_60]),c_0_76])]) ).
cnf(c_0_89,hypothesis,
( ~ member(f8(a,a_function),a_function)
| member(a,non_ordered_pair(a,X1)) ),
inference(spm,[status(thm)],[c_0_84,c_0_85]) ).
cnf(c_0_90,plain,
( ~ member(X1,domain_of(X2))
| member(f8(X1,X2),X2) ),
c_0_86 ).
cnf(c_0_91,plain,
( ~ member(X1,non_ordered_pair(X2,X3))
| X1 = X3
| X1 = X2 ),
inference(fof_simplification,[status(thm)],[non_ordered_pair1]) ).
cnf(c_0_92,plain,
( ~ member(X1,identity_relation)
| first(X1) = second(X1) ),
inference(fof_simplification,[status(thm)],[identity_relation2]) ).
cnf(c_0_93,plain,
( ~ member(X1,apply(X2,X3))
| member(f28(X1,X2,X3),X2) ),
inference(fof_simplification,[status(thm)],[apply2]) ).
cnf(c_0_94,plain,
( ~ member(X1,apply(X2,X3))
| first(f28(X1,X2,X3)) = X3 ),
inference(fof_simplification,[status(thm)],[apply3]) ).
cnf(c_0_95,hypothesis,
( ~ member(a,non_ordered_pair(X1,X1))
| member(a,apply(identity_relation,X1)) ),
inference(spm,[status(thm)],[c_0_87,c_0_88]) ).
cnf(c_0_96,hypothesis,
member(a,non_ordered_pair(a,X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_90]),c_0_40])]) ).
cnf(c_0_97,plain,
( X1 != X3
| ~ little_set(X1)
| member(X1,non_ordered_pair(X2,X3)) ),
inference(fof_simplification,[status(thm)],[non_ordered_pair3]) ).
cnf(c_0_98,plain,
( ~ member(X3,X2)
| ~ member(X3,X1)
| ~ disjoint(X1,X2) ),
inference(fof_simplification,[status(thm)],[disjoint1]) ).
cnf(c_0_99,plain,
( ~ member(X1,non_ordered_pair(X2,X3))
| X1 = X3
| X1 = X2 ),
c_0_91 ).
cnf(c_0_100,axiom,
( member(f24(X1),X1)
| X1 = empty_set ),
regularity1 ).
cnf(c_0_101,plain,
( ~ member(X1,identity_relation)
| first(X1) = second(X1) ),
c_0_92 ).
cnf(c_0_102,plain,
( ~ member(X1,apply(X2,X3))
| member(f28(X1,X2,X3),X2) ),
c_0_93 ).
cnf(c_0_103,plain,
( ~ member(X1,apply(X2,X3))
| first(f28(X1,X2,X3)) = X3 ),
c_0_94 ).
cnf(c_0_104,hypothesis,
member(a,apply(identity_relation,a)),
inference(spm,[status(thm)],[c_0_95,c_0_96]) ).
cnf(c_0_105,plain,
( X1 != X3
| ~ little_set(X1)
| member(X1,non_ordered_pair(X2,X3)) ),
c_0_97 ).
cnf(c_0_106,plain,
( ~ member(X3,X2)
| ~ member(X3,X1)
| ~ disjoint(X1,X2) ),
c_0_98 ).
cnf(c_0_107,axiom,
( disjoint(f24(X1),X1)
| X1 = empty_set ),
regularity2 ).
cnf(c_0_108,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_99,c_0_100]) ).
cnf(c_0_109,plain,
( ~ member(X1,apply(X2,X3))
| member(X1,second(f28(X1,X2,X3))) ),
inference(fof_simplification,[status(thm)],[apply4]) ).
cnf(c_0_110,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_101,c_0_102]) ).
cnf(c_0_111,hypothesis,
first(f28(a,identity_relation,a)) = a,
inference(spm,[status(thm)],[c_0_103,c_0_104]) ).
cnf(c_0_112,plain,
( ~ little_set(X1)
| member(X1,non_ordered_pair(X2,X1)) ),
inference(er,[status(thm)],[c_0_105]) ).
cnf(c_0_113,plain,
( ~ member(X2,X1)
| ~ member(X2,f24(X1))
| X1 = empty_set ),
inference(spm,[status(thm)],[c_0_106,c_0_107]) ).
cnf(c_0_114,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_108])]) ).
cnf(c_0_115,plain,
( ~ member(X1,apply(X2,X3))
| member(X1,second(f28(X1,X2,X3))) ),
c_0_109 ).
cnf(c_0_116,hypothesis,
second(f28(a,identity_relation,a)) = a,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_110,c_0_104]),c_0_111]) ).
cnf(c_0_117,hypothesis,
( ~ member(f8(a,a_function),a_function)
| member(a,non_ordered_pair(X1,a)) ),
inference(spm,[status(thm)],[c_0_112,c_0_85]) ).
cnf(c_0_118,plain,
( ~ member(X2,X1)
| ~ member(X2,non_ordered_pair(X1,X1))
| non_ordered_pair(X1,X1) = empty_set ),
inference(spm,[status(thm)],[c_0_113,c_0_114]) ).
cnf(c_0_119,hypothesis,
member(a,a),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_115,c_0_116]),c_0_104])]) ).
cnf(c_0_120,plain,
~ member(X1,empty_set),
inference(fof_simplification,[status(thm)],[empty_set]) ).
cnf(c_0_121,hypothesis,
member(a,non_ordered_pair(X1,a)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_117,c_0_90]),c_0_40])]) ).
cnf(c_0_122,hypothesis,
non_ordered_pair(a,a) = empty_set,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_118,c_0_96]),c_0_119])]) ).
cnf(c_0_123,plain,
~ member(X1,empty_set),
c_0_120 ).
cnf(c_0_124,hypothesis,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_121,c_0_122]),c_0_123]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET039-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n004.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Mon Sep 21 04:46:05 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.15/0.42 Running first-order theorem proving
% 0.15/0.42 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
% 108.07/16.30 % Version: 3.5.1
% 108.07/16.30 % Preprocessing class: FSLSSMSMSSSNFFN.
% 108.07/16.30 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 108.07/16.30 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 108.07/16.30 % Starting new_bool_3 with 300s (1) cores
% 108.07/16.30 % Starting new_bool_1 with 300s (1) cores
% 108.07/16.30 % Starting sh5l with 300s (1) cores
% 108.07/16.30 % C07_19_nc_SOS_SAT001_MinMin_p005000_rr with pid 2273915 completed with status 0
% 108.07/16.30 % Result found by C07_19_nc_SOS_SAT001_MinMin_p005000_rr
% 108.07/16.30 % Preprocessing class: FSLSSMSMSSSNFFN.
% 108.07/16.30 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 108.07/16.30 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 108.07/16.30 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 108.07/16.30 % No SInE strategy applied
% 108.07/16.30 % Search class: FGHSM-FSLS31-MFFFFFNN
% 108.07/16.30 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 108.07/16.30 % Starting SubtermCWHack with 136s (1) cores
% 108.07/16.30 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 151s (1) cores
% 108.07/16.30 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y with 244s (1) cores
% 108.07/16.30 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S06DI with 136s (1) cores
% 108.07/16.30 % Starting U----_100_C09_12_F1_SE_CS_SP_PS_S5PRR_RG_ND_S04AN with 136s (1) cores
% 108.07/16.30 % G-E--_208_C18_F1_SE_CS_SP_PS_S06DI with pid 2273934 completed with status 0
% 108.07/16.30 % Result found by G-E--_208_C18_F1_SE_CS_SP_PS_S06DI
% 108.07/16.30 % Preprocessing class: FSLSSMSMSSSNFFN.
% 108.07/16.30 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 108.07/16.30 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 108.07/16.30 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 108.07/16.30 % No SInE strategy applied
% 108.07/16.30 % Search class: FGHSM-FSLS31-MFFFFFNN
% 108.07/16.30 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 108.07/16.30 % Starting SubtermCWHack with 136s (1) cores
% 108.07/16.30 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 151s (1) cores
% 108.07/16.30 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y with 244s (1) cores
% 108.07/16.30 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S06DI with 136s (1) cores
% 108.07/16.30 % Preprocessing time : 0.005 s
% 108.07/16.30 % Presaturation interreduction done
% 108.07/16.30
% 108.07/16.30 % Proof found!
% 108.07/16.30 % SZS status Unsatisfiable
% 108.07/16.30 % SZS output start CNFRefutation
% See solution above
% 124.01/16.30 % Parsed axioms : 167
% 124.01/16.30 % Removed by relevancy pruning/SinE : 0
% 124.01/16.30 % Initial clauses : 167
% 124.01/16.30 % Removed in clause preprocessing : 6
% 124.01/16.30 % Initial clauses in saturation : 161
% 124.01/16.30 % Processed clauses : 22537
% 124.01/16.30 % ...of these trivial : 918
% 124.01/16.30 % ...subsumed : 14940
% 124.01/16.30 % ...remaining for further processing : 6679
% 124.01/16.30 % Other redundant clauses eliminated : 17
% 124.01/16.30 % Clauses deleted for lack of memory : 0
% 124.01/16.30 % Backward-subsumed : 146
% 124.01/16.30 % Backward-rewritten : 148
% 124.01/16.30 % Generated clauses : 520929
% 124.01/16.30 % ...of the previous two non-redundant : 502415
% 124.01/16.30 % ...aggressively subsumed : 0
% 124.01/16.30 % Contextual simplify-reflections : 57
% 124.01/16.30 % Paramodulations : 520849
% 124.01/16.30 % Factorizations : 60
% 124.01/16.30 % NegExts : 0
% 124.01/16.30 % Equation resolutions : 20
% 124.01/16.30 % Disequality decompositions : 0
% 124.01/16.30 % Total rewrite steps : 40744
% 124.01/16.30 % ...of those cached : 39128
% 124.01/16.30 % Propositional unsat checks : 0
% 124.01/16.30 % Propositional check models : 0
% 124.01/16.30 % Propositional check unsatisfiable : 0
% 124.01/16.30 % Propositional clauses : 0
% 124.01/16.30 % Propositional clauses after purity: 0
% 124.01/16.30 % Propositional unsat core size : 0
% 124.01/16.30 % Propositional preprocessing time : 0.000
% 124.01/16.30 % Propositional encoding time : 0.000
% 124.01/16.30 % Propositional solver time : 0.000
% 124.01/16.30 % Success case prop preproc time : 0.000
% 124.01/16.30 % Success case prop encoding time : 0.000
% 124.01/16.30 % Success case prop solver time : 0.000
% 124.01/16.30 % Current number of processed clauses : 6211
% 124.01/16.30 % Positive orientable unit clauses : 968
% 124.01/16.30 % Positive unorientable unit clauses: 0
% 124.01/16.30 % Negative unit clauses : 35
% 124.01/16.30 % Non-unit-clauses : 5208
% 124.01/16.30 % Current number of unprocessed clauses: 479609
% 124.01/16.30 % ...number of literals in the above : 1261094
% 124.01/16.30 % Current number of archived formulas : 0
% 124.01/16.30 % Current number of archived clauses : 459
% 124.01/16.30 % Clause-clause subsumption calls (NU) : 3572444
% 124.01/16.30 % Rec. Clause-clause subsumption calls : 2779303
% 124.01/16.30 % Non-unit clause-clause subsumptions : 8113
% 124.01/16.30 % Unit Clause-clause subsumption calls : 419769
% 124.01/16.30 % Rewrite failures with RHS unbound : 0
% 124.01/16.30 % BW rewrite match attempts : 12545
% 124.01/16.30 % BW rewrite match successes : 101
% 124.01/16.30 % Condensation attempts : 0
% 124.01/16.30 % Condensation successes : 0
% 124.01/16.30 % Termbank termtop insertions : 7637579
% 124.01/16.30 % Search garbage collected termcells : 373
% 124.01/16.30
% 124.01/16.30 % -------------------------------------------------
% 124.01/16.30 % User time : 14.771 s
% 124.01/16.30 % System time : 0.617 s
% 124.01/16.30 % Total time : 15.388 s
% 124.01/16.30 % Maximum resident set size: 4040 pages
% 124.01/16.30
% 124.01/16.30 % -------------------------------------------------
% 124.01/16.30 % User time : 73.638 s
% 124.01/16.30 % System time : 2.785 s
% 124.01/16.30 % Total time : 76.423 s
% 124.01/16.30 % Maximum resident set size: 4608 pages
% 124.01/16.30 % E exiting
%------------------------------------------------------------------------------