TSTP Solution File: SET040-3 by E-SAT---3.1
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- Process Solution
%------------------------------------------------------------------------------
% File : E-SAT---3.1
% Problem : SET040-3 : TPTP v8.1.2. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n001.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 : 2400s
% WCLimit : 300s
% DateTime : Tue Oct 10 19:21:46 EDT 2023
% Result : Unsatisfiable 62.67s 8.57s
% Output : CNFRefutation 62.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 31
% Syntax : Number of clauses : 112 ( 31 unt; 12 nHn; 82 RR)
% Number of literals : 242 ( 55 equ; 123 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 : 194 ( 28 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(disjoint1,axiom,
( ~ disjoint(X1,X2)
| ~ member(X3,X1)
| ~ member(X3,X2) ),
file('/export/starexec/sandbox2/tmp/tmp.hD9HLXQuL4/E---3.1_9400.p',disjoint1) ).
cnf(disjoint2,axiom,
( disjoint(X1,X2)
| member(f23(X1,X2),X1) ),
file('/export/starexec/sandbox2/tmp/tmp.hD9HLXQuL4/E---3.1_9400.p',disjoint2) ).
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/sandbox2/tmp/tmp.hD9HLXQuL4/E---3.1_9400.p',prove_apply_for_composition2) ).
cnf(subset2,axiom,
( subset(X1,X2)
| member(f17(X1,X2),X1) ),
file('/export/starexec/sandbox2/tmp/tmp.hD9HLXQuL4/E---3.1_9400.p',subset2) ).
cnf(ordered_pair,axiom,
ordered_pair(X1,X2) = non_ordered_pair(singleton_set(X1),non_ordered_pair(X1,X2)),
file('/export/starexec/sandbox2/tmp/tmp.hD9HLXQuL4/E---3.1_9400.p',ordered_pair) ).
cnf(singleton_set,axiom,
singleton_set(X1) = non_ordered_pair(X1,X1),
file('/export/starexec/sandbox2/tmp/tmp.hD9HLXQuL4/E---3.1_9400.p',singleton_set) ).
cnf(first_component_is_small,axiom,
( little_set(first(X1))
| ~ ordered_pair_predicate(X1) ),
file('/export/starexec/sandbox2/tmp/tmp.hD9HLXQuL4/E---3.1_9400.p',first_component_is_small) ).
cnf(apply1,axiom,
( ordered_pair_predicate(f28(X1,X2,X3))
| ~ member(X1,apply(X2,X3)) ),
file('/export/starexec/sandbox2/tmp/tmp.hD9HLXQuL4/E---3.1_9400.p',apply1) ).
cnf(apply3,axiom,
( first(f28(X1,X2,X3)) = X3
| ~ member(X1,apply(X2,X3)) ),
file('/export/starexec/sandbox2/tmp/tmp.hD9HLXQuL4/E---3.1_9400.p',apply3) ).
cnf(ordered_pair_predicate4,axiom,
( ordered_pair_predicate(X1)
| ~ little_set(X2)
| ~ little_set(X3)
| X1 != ordered_pair(X2,X3) ),
file('/export/starexec/sandbox2/tmp/tmp.hD9HLXQuL4/E---3.1_9400.p',ordered_pair_predicate4) ).
cnf(property_of_first,axiom,
( first(ordered_pair(X1,X2)) = X1
| ~ little_set(X1)
| ~ little_set(X2) ),
file('/export/starexec/sandbox2/tmp/tmp.hD9HLXQuL4/E---3.1_9400.p',property_of_first) ).
cnf(property_of_second,axiom,
( second(ordered_pair(X1,X2)) = X2
| ~ little_set(X1)
| ~ little_set(X2) ),
file('/export/starexec/sandbox2/tmp/tmp.hD9HLXQuL4/E---3.1_9400.p',property_of_second) ).
cnf(relation1,axiom,
( ordered_pair_predicate(X2)
| ~ relation(X1)
| ~ member(X2,X1) ),
file('/export/starexec/sandbox2/tmp/tmp.hD9HLXQuL4/E---3.1_9400.p',relation1) ).
cnf(composition_is_a_relation,axiom,
relation(compose(X1,X2)),
file('/export/starexec/sandbox2/tmp/tmp.hD9HLXQuL4/E---3.1_9400.p',composition_is_a_relation) ).
cnf(identity_relation3,axiom,
( member(X1,identity_relation)
| ~ little_set(X1)
| ~ ordered_pair_predicate(X1)
| first(X1) != second(X1) ),
file('/export/starexec/sandbox2/tmp/tmp.hD9HLXQuL4/E---3.1_9400.p',identity_relation3) ).
cnf(ordered_pairs_are_small2,axiom,
( little_set(X1)
| ~ ordered_pair_predicate(X1) ),
file('/export/starexec/sandbox2/tmp/tmp.hD9HLXQuL4/E---3.1_9400.p',ordered_pairs_are_small2) ).
cnf(image_and_substitution5,axiom,
( member(X1,image(X2,X3))
| ~ little_set(X1)
| ~ ordered_pair_predicate(X4)
| ~ member(X4,X3)
| ~ member(first(X4),X2)
| second(X4) != X1 ),
file('/export/starexec/sandbox2/tmp/tmp.hD9HLXQuL4/E---3.1_9400.p',image_and_substitution5) ).
cnf(second_component_is_small,axiom,
( little_set(second(X1))
| ~ ordered_pair_predicate(X1) ),
file('/export/starexec/sandbox2/tmp/tmp.hD9HLXQuL4/E---3.1_9400.p',second_component_is_small) ).
cnf(image_and_apply2,axiom,
subset(image(singleton_set(X1),X2),apply(X2,X1)),
file('/export/starexec/sandbox2/tmp/tmp.hD9HLXQuL4/E---3.1_9400.p',image_and_apply2) ).
cnf(non_ordered_pair2,axiom,
( member(X1,non_ordered_pair(X2,X3))
| ~ little_set(X1)
| X1 != X2 ),
file('/export/starexec/sandbox2/tmp/tmp.hD9HLXQuL4/E---3.1_9400.p',non_ordered_pair2) ).
cnf(universal_set,axiom,
( member(X1,universal_set)
| ~ little_set(X1) ),
file('/export/starexec/sandbox2/tmp/tmp.hD9HLXQuL4/E---3.1_9400.p',universal_set) ).
cnf(subset1,axiom,
( member(X3,X2)
| ~ subset(X1,X2)
| ~ member(X3,X1) ),
file('/export/starexec/sandbox2/tmp/tmp.hD9HLXQuL4/E---3.1_9400.p',subset1) ).
cnf(a2,axiom,
( little_set(X1)
| ~ member(X1,X2) ),
file('/export/starexec/sandbox2/tmp/tmp.hD9HLXQuL4/E---3.1_9400.p',a2) ).
cnf(apply2,axiom,
( member(f28(X1,X2,X3),X2)
| ~ member(X1,apply(X2,X3)) ),
file('/export/starexec/sandbox2/tmp/tmp.hD9HLXQuL4/E---3.1_9400.p',apply2) ).
cnf(non_ordered_pair1,axiom,
( X1 = X2
| X1 = X3
| ~ member(X1,non_ordered_pair(X2,X3)) ),
file('/export/starexec/sandbox2/tmp/tmp.hD9HLXQuL4/E---3.1_9400.p',non_ordered_pair1) ).
cnf(regularity1,axiom,
( X1 = empty_set
| member(f24(X1),X1) ),
file('/export/starexec/sandbox2/tmp/tmp.hD9HLXQuL4/E---3.1_9400.p',regularity1) ).
cnf(regularity2,axiom,
( X1 = empty_set
| disjoint(f24(X1),X1) ),
file('/export/starexec/sandbox2/tmp/tmp.hD9HLXQuL4/E---3.1_9400.p',regularity2) ).
cnf(identity_relation2,axiom,
( first(X1) = second(X1)
| ~ member(X1,identity_relation) ),
file('/export/starexec/sandbox2/tmp/tmp.hD9HLXQuL4/E---3.1_9400.p',identity_relation2) ).
cnf(non_ordered_pair3,axiom,
( member(X1,non_ordered_pair(X2,X3))
| ~ little_set(X1)
| X1 != X3 ),
file('/export/starexec/sandbox2/tmp/tmp.hD9HLXQuL4/E---3.1_9400.p',non_ordered_pair3) ).
cnf(apply4,axiom,
( member(X1,second(f28(X1,X2,X3)))
| ~ member(X1,apply(X2,X3)) ),
file('/export/starexec/sandbox2/tmp/tmp.hD9HLXQuL4/E---3.1_9400.p',apply4) ).
cnf(empty_set,axiom,
~ member(X1,empty_set),
file('/export/starexec/sandbox2/tmp/tmp.hD9HLXQuL4/E---3.1_9400.p',empty_set) ).
cnf(c_0_31,axiom,
( ~ disjoint(X1,X2)
| ~ member(X3,X1)
| ~ member(X3,X2) ),
disjoint1 ).
cnf(c_0_32,axiom,
( disjoint(X1,X2)
| member(f23(X1,X2),X1) ),
disjoint2 ).
cnf(c_0_33,negated_conjecture,
~ subset(apply(compose(another_function,a_function),element),apply(another_function,apply(a_function,element))),
prove_apply_for_composition2 ).
cnf(c_0_34,axiom,
( subset(X1,X2)
| member(f17(X1,X2),X1) ),
subset2 ).
cnf(c_0_35,plain,
( member(f23(X1,X2),X1)
| ~ member(X3,X2)
| ~ member(X3,X1) ),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_36,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_33,c_0_34]) ).
cnf(c_0_37,negated_conjecture,
( member(f23(X1,apply(compose(another_function,a_function),element)),X1)
| ~ member(f17(apply(compose(another_function,a_function),element),apply(another_function,apply(a_function,element))),X1) ),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_38,axiom,
ordered_pair(X1,X2) = non_ordered_pair(singleton_set(X1),non_ordered_pair(X1,X2)),
ordered_pair ).
cnf(c_0_39,axiom,
singleton_set(X1) = non_ordered_pair(X1,X1),
singleton_set ).
cnf(c_0_40,axiom,
( little_set(first(X1))
| ~ ordered_pair_predicate(X1) ),
first_component_is_small ).
cnf(c_0_41,axiom,
( ordered_pair_predicate(f28(X1,X2,X3))
| ~ member(X1,apply(X2,X3)) ),
apply1 ).
cnf(c_0_42,axiom,
( first(f28(X1,X2,X3)) = X3
| ~ member(X1,apply(X2,X3)) ),
apply3 ).
cnf(c_0_43,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_37,c_0_36]) ).
cnf(c_0_44,axiom,
( ordered_pair_predicate(X1)
| ~ little_set(X2)
| ~ little_set(X3)
| X1 != ordered_pair(X2,X3) ),
ordered_pair_predicate4 ).
cnf(c_0_45,plain,
ordered_pair(X1,X2) = non_ordered_pair(non_ordered_pair(X1,X1),non_ordered_pair(X1,X2)),
inference(rw,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_46,axiom,
( first(ordered_pair(X1,X2)) = X1
| ~ little_set(X1)
| ~ little_set(X2) ),
property_of_first ).
cnf(c_0_47,plain,
( little_set(first(f28(X1,X2,X3)))
| ~ member(X1,apply(X2,X3)) ),
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_48,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_42,c_0_43]) ).
cnf(c_0_49,axiom,
( second(ordered_pair(X1,X2)) = X2
| ~ little_set(X1)
| ~ little_set(X2) ),
property_of_second ).
cnf(c_0_50,axiom,
( ordered_pair_predicate(X2)
| ~ relation(X1)
| ~ member(X2,X1) ),
relation1 ).
cnf(c_0_51,axiom,
relation(compose(X1,X2)),
composition_is_a_relation ).
cnf(c_0_52,axiom,
( member(X1,identity_relation)
| ~ little_set(X1)
| ~ ordered_pair_predicate(X1)
| first(X1) != second(X1) ),
identity_relation3 ).
cnf(c_0_53,axiom,
( little_set(X1)
| ~ ordered_pair_predicate(X1) ),
ordered_pairs_are_small2 ).
cnf(c_0_54,plain,
( ordered_pair_predicate(X1)
| X1 != non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,X3))
| ~ little_set(X3)
| ~ little_set(X2) ),
inference(rw,[status(thm)],[c_0_44,c_0_45]) ).
cnf(c_0_55,plain,
( first(non_ordered_pair(non_ordered_pair(X1,X1),non_ordered_pair(X1,X2))) = X1
| ~ little_set(X2)
| ~ little_set(X1) ),
inference(rw,[status(thm)],[c_0_46,c_0_45]) ).
cnf(c_0_56,negated_conjecture,
little_set(element),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_43])]) ).
cnf(c_0_57,plain,
( second(non_ordered_pair(non_ordered_pair(X1,X1),non_ordered_pair(X1,X2))) = X2
| ~ little_set(X2)
| ~ little_set(X1) ),
inference(rw,[status(thm)],[c_0_49,c_0_45]) ).
cnf(c_0_58,plain,
( ordered_pair_predicate(X1)
| ~ member(X1,compose(X2,X3)) ),
inference(spm,[status(thm)],[c_0_50,c_0_51]) ).
cnf(c_0_59,axiom,
( member(X1,image(X2,X3))
| ~ little_set(X1)
| ~ ordered_pair_predicate(X4)
| ~ member(X4,X3)
| ~ member(first(X4),X2)
| second(X4) != X1 ),
image_and_substitution5 ).
cnf(c_0_60,axiom,
( little_set(second(X1))
| ~ ordered_pair_predicate(X1) ),
second_component_is_small ).
cnf(c_0_61,plain,
( member(X1,identity_relation)
| first(X1) != second(X1)
| ~ ordered_pair_predicate(X1) ),
inference(csr,[status(thm)],[c_0_52,c_0_53]) ).
cnf(c_0_62,plain,
( ordered_pair_predicate(non_ordered_pair(non_ordered_pair(X1,X1),non_ordered_pair(X1,X2)))
| ~ little_set(X2)
| ~ little_set(X1) ),
inference(er,[status(thm)],[c_0_54]) ).
cnf(c_0_63,negated_conjecture,
( first(non_ordered_pair(non_ordered_pair(element,element),non_ordered_pair(element,X1))) = element
| ~ little_set(X1) ),
inference(spm,[status(thm)],[c_0_55,c_0_56]) ).
cnf(c_0_64,negated_conjecture,
( second(non_ordered_pair(non_ordered_pair(element,element),non_ordered_pair(element,X1))) = X1
| ~ little_set(X1) ),
inference(spm,[status(thm)],[c_0_57,c_0_56]) ).
cnf(c_0_65,plain,
( little_set(first(X1))
| ~ member(X1,compose(X2,X3)) ),
inference(spm,[status(thm)],[c_0_40,c_0_58]) ).
cnf(c_0_66,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_42,c_0_36]) ).
cnf(c_0_67,axiom,
subset(image(singleton_set(X1),X2),apply(X2,X1)),
image_and_apply2 ).
cnf(c_0_68,plain,
( member(second(X1),image(X2,X3))
| ~ ordered_pair_predicate(X1)
| ~ member(first(X1),X2)
| ~ member(X1,X3) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_59]),c_0_60]) ).
cnf(c_0_69,plain,
( member(non_ordered_pair(non_ordered_pair(X1,X1),non_ordered_pair(X1,X2)),identity_relation)
| 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)))
| ~ little_set(X2)
| ~ little_set(X1) ),
inference(spm,[status(thm)],[c_0_61,c_0_62]) ).
cnf(c_0_70,negated_conjecture,
first(non_ordered_pair(non_ordered_pair(element,element),non_ordered_pair(element,element))) = element,
inference(spm,[status(thm)],[c_0_63,c_0_56]) ).
cnf(c_0_71,negated_conjecture,
second(non_ordered_pair(non_ordered_pair(element,element),non_ordered_pair(element,element))) = element,
inference(spm,[status(thm)],[c_0_64,c_0_56]) ).
cnf(c_0_72,axiom,
( member(X1,non_ordered_pair(X2,X3))
| ~ little_set(X1)
| X1 != X2 ),
non_ordered_pair2 ).
cnf(c_0_73,axiom,
( member(X1,universal_set)
| ~ little_set(X1) ),
universal_set ).
cnf(c_0_74,negated_conjecture,
( little_set(element)
| ~ 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)) ),
inference(spm,[status(thm)],[c_0_65,c_0_66]) ).
cnf(c_0_75,axiom,
( member(X3,X2)
| ~ subset(X1,X2)
| ~ member(X3,X1) ),
subset1 ).
cnf(c_0_76,plain,
subset(image(non_ordered_pair(X1,X1),X2),apply(X2,X1)),
inference(rw,[status(thm)],[c_0_67,c_0_39]) ).
cnf(c_0_77,plain,
( member(second(non_ordered_pair(non_ordered_pair(X1,X1),non_ordered_pair(X1,X2))),image(X3,X4))
| ~ little_set(X2)
| ~ little_set(X1)
| ~ member(first(non_ordered_pair(non_ordered_pair(X1,X1),non_ordered_pair(X1,X2))),X3)
| ~ member(non_ordered_pair(non_ordered_pair(X1,X1),non_ordered_pair(X1,X2)),X4) ),
inference(spm,[status(thm)],[c_0_68,c_0_62]) ).
cnf(c_0_78,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_69,c_0_70]),c_0_71]),c_0_56])]) ).
cnf(c_0_79,plain,
( member(X1,non_ordered_pair(X1,X2))
| ~ little_set(X1) ),
inference(er,[status(thm)],[c_0_72]) ).
cnf(c_0_80,axiom,
( little_set(X1)
| ~ member(X1,X2) ),
a2 ).
cnf(c_0_81,negated_conjecture,
( member(element,universal_set)
| ~ 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)) ),
inference(spm,[status(thm)],[c_0_73,c_0_74]) ).
cnf(c_0_82,axiom,
( member(f28(X1,X2,X3),X2)
| ~ member(X1,apply(X2,X3)) ),
apply2 ).
cnf(c_0_83,axiom,
( X1 = X2
| X1 = X3
| ~ member(X1,non_ordered_pair(X2,X3)) ),
non_ordered_pair1 ).
cnf(c_0_84,axiom,
( X1 = empty_set
| member(f24(X1),X1) ),
regularity1 ).
cnf(c_0_85,plain,
( member(X1,apply(X2,X3))
| ~ member(X1,image(non_ordered_pair(X3,X3),X2)) ),
inference(spm,[status(thm)],[c_0_75,c_0_76]) ).
cnf(c_0_86,negated_conjecture,
( member(element,image(X1,identity_relation))
| ~ member(element,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_78]),c_0_71]),c_0_56]),c_0_70])]) ).
cnf(c_0_87,plain,
( member(X1,non_ordered_pair(X1,X2))
| ~ member(X1,X3) ),
inference(spm,[status(thm)],[c_0_79,c_0_80]) ).
cnf(c_0_88,negated_conjecture,
member(element,universal_set),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_82]),c_0_36])]) ).
cnf(c_0_89,axiom,
( X1 = empty_set
| disjoint(f24(X1),X1) ),
regularity2 ).
cnf(c_0_90,plain,
( f24(non_ordered_pair(X1,X2)) = X1
| f24(non_ordered_pair(X1,X2)) = X2
| non_ordered_pair(X1,X2) = empty_set ),
inference(spm,[status(thm)],[c_0_83,c_0_84]) ).
cnf(c_0_91,negated_conjecture,
( member(element,apply(identity_relation,X1))
| ~ member(element,non_ordered_pair(X1,X1)) ),
inference(spm,[status(thm)],[c_0_85,c_0_86]) ).
cnf(c_0_92,negated_conjecture,
member(element,non_ordered_pair(element,X1)),
inference(spm,[status(thm)],[c_0_87,c_0_88]) ).
cnf(c_0_93,plain,
( X1 = empty_set
| ~ member(X2,f24(X1))
| ~ member(X2,X1) ),
inference(spm,[status(thm)],[c_0_31,c_0_89]) ).
cnf(c_0_94,plain,
( f24(non_ordered_pair(X1,X1)) = X1
| non_ordered_pair(X1,X1) = empty_set ),
inference(er,[status(thm)],[inference(ef,[status(thm)],[c_0_90])]) ).
cnf(c_0_95,axiom,
( first(X1) = second(X1)
| ~ member(X1,identity_relation) ),
identity_relation2 ).
cnf(c_0_96,negated_conjecture,
member(element,apply(identity_relation,element)),
inference(spm,[status(thm)],[c_0_91,c_0_92]) ).
cnf(c_0_97,axiom,
( member(X1,non_ordered_pair(X2,X3))
| ~ little_set(X1)
| X1 != X3 ),
non_ordered_pair3 ).
cnf(c_0_98,plain,
( non_ordered_pair(X1,X1) = empty_set
| ~ member(X2,non_ordered_pair(X1,X1))
| ~ member(X2,X1) ),
inference(spm,[status(thm)],[c_0_93,c_0_94]) ).
cnf(c_0_99,plain,
( first(f28(X1,identity_relation,X2)) = second(f28(X1,identity_relation,X2))
| ~ member(X1,apply(identity_relation,X2)) ),
inference(spm,[status(thm)],[c_0_95,c_0_82]) ).
cnf(c_0_100,negated_conjecture,
first(f28(element,identity_relation,element)) = element,
inference(spm,[status(thm)],[c_0_42,c_0_96]) ).
cnf(c_0_101,plain,
( member(X1,non_ordered_pair(X2,X1))
| ~ little_set(X1) ),
inference(er,[status(thm)],[c_0_97]) ).
cnf(c_0_102,plain,
( non_ordered_pair(X1,X1) = empty_set
| ~ member(f24(non_ordered_pair(X1,X1)),X1) ),
inference(spm,[status(thm)],[c_0_98,c_0_84]) ).
cnf(c_0_103,axiom,
( member(X1,second(f28(X1,X2,X3)))
| ~ member(X1,apply(X2,X3)) ),
apply4 ).
cnf(c_0_104,negated_conjecture,
second(f28(element,identity_relation,element)) = element,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_99,c_0_96]),c_0_100]) ).
cnf(c_0_105,plain,
( member(X1,non_ordered_pair(X2,X1))
| ~ member(X1,X3) ),
inference(spm,[status(thm)],[c_0_101,c_0_80]) ).
cnf(c_0_106,plain,
( non_ordered_pair(X1,X1) = empty_set
| ~ member(X1,X1) ),
inference(spm,[status(thm)],[c_0_102,c_0_94]) ).
cnf(c_0_107,negated_conjecture,
member(element,element),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_103,c_0_104]),c_0_96])]) ).
cnf(c_0_108,negated_conjecture,
member(element,non_ordered_pair(X1,element)),
inference(spm,[status(thm)],[c_0_105,c_0_88]) ).
cnf(c_0_109,negated_conjecture,
non_ordered_pair(element,element) = empty_set,
inference(spm,[status(thm)],[c_0_106,c_0_107]) ).
cnf(c_0_110,axiom,
~ member(X1,empty_set),
empty_set ).
cnf(c_0_111,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_108,c_0_109]),c_0_110]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SET040-3 : TPTP v8.1.2. Released v1.0.0.
% 0.06/0.13 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n001.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 2400
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon Oct 2 16:57:37 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.46 Running first-order model finding
% 0.19/0.46 Running: /export/starexec/sandbox2/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --satauto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/tmp/tmp.hD9HLXQuL4/E---3.1_9400.p
% 62.67/8.57 # Version: 3.1pre001
% 62.67/8.57 # Preprocessing class: FSLSSMSMSSSNFFN.
% 62.67/8.57 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 62.67/8.57 # Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 62.67/8.57 # Starting new_bool_3 with 300s (1) cores
% 62.67/8.57 # Starting new_bool_1 with 300s (1) cores
% 62.67/8.57 # Starting sh5l with 300s (1) cores
% 62.67/8.57 # C07_19_nc_SOS_SAT001_MinMin_p005000_rr with pid 9477 completed with status 0
% 62.67/8.57 # Result found by C07_19_nc_SOS_SAT001_MinMin_p005000_rr
% 62.67/8.57 # Preprocessing class: FSLSSMSMSSSNFFN.
% 62.67/8.57 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 62.67/8.57 # Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 62.67/8.57 # No SInE strategy applied
% 62.67/8.57 # Search class: FGHSM-FSLS31-MFFFFFNN
% 62.67/8.57 # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 62.67/8.57 # Starting G-E--_042_C45_F1_PI_AE_Q4_CS_SP_PS_S4S with 784s (1) cores
% 62.67/8.57 # Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 151s (1) cores
% 62.67/8.57 # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S06DI with 136s (1) cores
% 62.67/8.57 # Starting U----_100_C09_12_F1_SE_CS_SP_PS_S5PRR_RG_ND_S04AN with 136s (1) cores
% 62.67/8.57 # Starting SAT001_MinMin_p005000_rr_RG with 136s (1) cores
% 62.67/8.57 # G-E--_208_C18_F1_SE_CS_SP_PS_S06DI with pid 9486 completed with status 0
% 62.67/8.57 # Result found by G-E--_208_C18_F1_SE_CS_SP_PS_S06DI
% 62.67/8.57 # Preprocessing class: FSLSSMSMSSSNFFN.
% 62.67/8.57 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 62.67/8.57 # Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 62.67/8.57 # No SInE strategy applied
% 62.67/8.57 # Search class: FGHSM-FSLS31-MFFFFFNN
% 62.67/8.57 # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 62.67/8.57 # Starting G-E--_042_C45_F1_PI_AE_Q4_CS_SP_PS_S4S with 784s (1) cores
% 62.67/8.57 # Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 151s (1) cores
% 62.67/8.57 # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S06DI with 136s (1) cores
% 62.67/8.57 # Preprocessing time : 0.003 s
% 62.67/8.57 # Presaturation interreduction done
% 62.67/8.57
% 62.67/8.57 # Proof found!
% 62.67/8.57 # SZS status Unsatisfiable
% 62.67/8.57 # SZS output start CNFRefutation
% See solution above
% 62.67/8.57 # Parsed axioms : 167
% 62.67/8.57 # Removed by relevancy pruning/SinE : 0
% 62.67/8.57 # Initial clauses : 167
% 62.67/8.57 # Removed in clause preprocessing : 6
% 62.67/8.57 # Initial clauses in saturation : 161
% 62.67/8.57 # Processed clauses : 22308
% 62.67/8.57 # ...of these trivial : 958
% 62.67/8.57 # ...subsumed : 14733
% 62.67/8.57 # ...remaining for further processing : 6617
% 62.67/8.57 # Other redundant clauses eliminated : 21
% 62.67/8.57 # Clauses deleted for lack of memory : 0
% 62.67/8.57 # Backward-subsumed : 101
% 62.67/8.57 # Backward-rewritten : 304
% 62.67/8.57 # Generated clauses : 508697
% 62.67/8.57 # ...of the previous two non-redundant : 491521
% 62.67/8.57 # ...aggressively subsumed : 0
% 62.67/8.57 # Contextual simplify-reflections : 20
% 62.67/8.57 # Paramodulations : 508633
% 62.67/8.57 # Factorizations : 40
% 62.67/8.57 # NegExts : 0
% 62.67/8.57 # Equation resolutions : 24
% 62.67/8.57 # Total rewrite steps : 39242
% 62.67/8.57 # Propositional unsat checks : 0
% 62.67/8.57 # Propositional check models : 0
% 62.67/8.57 # Propositional check unsatisfiable : 0
% 62.67/8.57 # Propositional clauses : 0
% 62.67/8.57 # Propositional clauses after purity: 0
% 62.67/8.57 # Propositional unsat core size : 0
% 62.67/8.57 # Propositional preprocessing time : 0.000
% 62.67/8.57 # Propositional encoding time : 0.000
% 62.67/8.57 # Propositional solver time : 0.000
% 62.67/8.57 # Success case prop preproc time : 0.000
% 62.67/8.57 # Success case prop encoding time : 0.000
% 62.67/8.57 # Success case prop solver time : 0.000
% 62.67/8.57 # Current number of processed clauses : 6038
% 62.67/8.57 # Positive orientable unit clauses : 839
% 62.67/8.57 # Positive unorientable unit clauses: 0
% 62.67/8.57 # Negative unit clauses : 17
% 62.67/8.57 # Non-unit-clauses : 5182
% 62.67/8.57 # Current number of unprocessed clauses: 469015
% 62.67/8.57 # ...number of literals in the above : 1203399
% 62.67/8.57 # Current number of archived formulas : 0
% 62.67/8.57 # Current number of archived clauses : 570
% 62.67/8.57 # Clause-clause subsumption calls (NU) : 3438800
% 62.67/8.57 # Rec. Clause-clause subsumption calls : 2708789
% 62.67/8.57 # Non-unit clause-clause subsumptions : 7587
% 62.67/8.57 # Unit Clause-clause subsumption calls : 264816
% 62.67/8.57 # Rewrite failures with RHS unbound : 0
% 62.67/8.57 # BW rewrite match attempts : 15398
% 62.67/8.57 # BW rewrite match successes : 55
% 62.67/8.57 # Condensation attempts : 0
% 62.67/8.57 # Condensation successes : 0
% 62.67/8.57 # Termbank termtop insertions : 7270166
% 62.67/8.57
% 62.67/8.57 # -------------------------------------------------
% 62.67/8.57 # User time : 7.514 s
% 62.67/8.57 # System time : 0.372 s
% 62.67/8.57 # Total time : 7.886 s
% 62.67/8.57 # Maximum resident set size: 2080 pages
% 62.67/8.57
% 62.67/8.57 # -------------------------------------------------
% 62.67/8.57 # User time : 37.663 s
% 62.67/8.57 # System time : 1.560 s
% 62.67/8.57 # Total time : 39.223 s
% 62.67/8.57 # Maximum resident set size: 1824 pages
% 62.67/8.57 % E---3.1 exiting
%------------------------------------------------------------------------------