TSTP Solution File: SET040-3 by CSE_E---1.5
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- Process Solution
%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SET040-3 : TPTP v8.1.2. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% Computer : n005.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 14:32:26 EDT 2023
% Result : Unsatisfiable 192.09s 192.32s
% Output : CNFRefutation 192.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 106
% Syntax : Number of formulae : 187 ( 31 unt; 75 typ; 0 def)
% Number of atoms : 242 ( 55 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 253 ( 123 ~; 130 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 122 ( 66 >; 56 *; 0 +; 0 <<)
% Number of predicates : 15 ( 13 usr; 1 prp; 0-5 aty)
% Number of functors : 62 ( 62 usr; 9 con; 0-5 aty)
% Number of variables : 194 ( 28 sgn; 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
member: ( $i * $i ) > $o ).
tff(decl_23,type,
little_set: $i > $o ).
tff(decl_24,type,
f1: ( $i * $i ) > $i ).
tff(decl_25,type,
non_ordered_pair: ( $i * $i ) > $i ).
tff(decl_26,type,
singleton_set: $i > $i ).
tff(decl_27,type,
ordered_pair: ( $i * $i ) > $i ).
tff(decl_28,type,
ordered_pair_predicate: $i > $o ).
tff(decl_29,type,
f2: $i > $i ).
tff(decl_30,type,
f3: $i > $i ).
tff(decl_31,type,
first: $i > $i ).
tff(decl_32,type,
f4: ( $i * $i ) > $i ).
tff(decl_33,type,
f5: ( $i * $i ) > $i ).
tff(decl_34,type,
second: $i > $i ).
tff(decl_35,type,
f6: ( $i * $i ) > $i ).
tff(decl_36,type,
f7: ( $i * $i ) > $i ).
tff(decl_37,type,
estin: $i ).
tff(decl_38,type,
intersection: ( $i * $i ) > $i ).
tff(decl_39,type,
complement: $i > $i ).
tff(decl_40,type,
union: ( $i * $i ) > $i ).
tff(decl_41,type,
domain_of: $i > $i ).
tff(decl_42,type,
f8: ( $i * $i ) > $i ).
tff(decl_43,type,
cross_product: ( $i * $i ) > $i ).
tff(decl_44,type,
converse: $i > $i ).
tff(decl_45,type,
rotate_right: $i > $i ).
tff(decl_46,type,
f9: ( $i * $i ) > $i ).
tff(decl_47,type,
f10: ( $i * $i ) > $i ).
tff(decl_48,type,
f11: ( $i * $i ) > $i ).
tff(decl_49,type,
flip_range_of: $i > $i ).
tff(decl_50,type,
f12: ( $i * $i ) > $i ).
tff(decl_51,type,
f13: ( $i * $i ) > $i ).
tff(decl_52,type,
f14: ( $i * $i ) > $i ).
tff(decl_53,type,
successor: $i > $i ).
tff(decl_54,type,
empty_set: $i ).
tff(decl_55,type,
universal_set: $i ).
tff(decl_56,type,
infinity: $i ).
tff(decl_57,type,
sigma: $i > $i ).
tff(decl_58,type,
f16: ( $i * $i ) > $i ).
tff(decl_59,type,
subset: ( $i * $i ) > $o ).
tff(decl_60,type,
f17: ( $i * $i ) > $i ).
tff(decl_61,type,
proper_subset: ( $i * $i ) > $o ).
tff(decl_62,type,
powerset: $i > $i ).
tff(decl_63,type,
relation: $i > $o ).
tff(decl_64,type,
f18: $i > $i ).
tff(decl_65,type,
single_valued_set: $i > $o ).
tff(decl_66,type,
f19: $i > $i ).
tff(decl_67,type,
f20: $i > $i ).
tff(decl_68,type,
f21: $i > $i ).
tff(decl_69,type,
function: $i > $o ).
tff(decl_70,type,
image: ( $i * $i ) > $i ).
tff(decl_71,type,
f22: ( $i * $i * $i ) > $i ).
tff(decl_72,type,
disjoint: ( $i * $i ) > $o ).
tff(decl_73,type,
f23: ( $i * $i ) > $i ).
tff(decl_74,type,
f24: $i > $i ).
tff(decl_75,type,
f25: $i ).
tff(decl_76,type,
f26: $i > $i ).
tff(decl_77,type,
range_of: $i > $i ).
tff(decl_78,type,
f27: ( $i * $i ) > $i ).
tff(decl_79,type,
identity_relation: $i ).
tff(decl_80,type,
restrict: ( $i * $i ) > $i ).
tff(decl_81,type,
one_to_one_function: $i > $o ).
tff(decl_82,type,
apply: ( $i * $i ) > $i ).
tff(decl_83,type,
f28: ( $i * $i * $i ) > $i ).
tff(decl_84,type,
apply_to_two_arguments: ( $i * $i * $i ) > $i ).
tff(decl_85,type,
maps: ( $i * $i * $i ) > $o ).
tff(decl_86,type,
closed: ( $i * $i ) > $o ).
tff(decl_87,type,
compose: ( $i * $i ) > $i ).
tff(decl_88,type,
f29: ( $i * $i * $i ) > $i ).
tff(decl_89,type,
f30: ( $i * $i * $i ) > $i ).
tff(decl_90,type,
f31: ( $i * $i * $i ) > $i ).
tff(decl_91,type,
homomorphism: ( $i * $i * $i * $i * $i ) > $o ).
tff(decl_92,type,
f32: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_93,type,
f33: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_94,type,
a_function: $i ).
tff(decl_95,type,
another_function: $i ).
tff(decl_96,type,
element: $i ).
cnf(disjoint1,axiom,
( ~ disjoint(X1,X2)
| ~ member(X3,X1)
| ~ member(X3,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET003-0.ax',disjoint1) ).
cnf(disjoint2,axiom,
( disjoint(X1,X2)
| member(f23(X1,X2),X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET003-0.ax',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/sandbox/benchmark/theBenchmark.p',prove_apply_for_composition2) ).
cnf(subset2,axiom,
( subset(X1,X2)
| member(f17(X1,X2),X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET003-0.ax',subset2) ).
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(first_component_is_small,axiom,
( little_set(first(X1))
| ~ ordered_pair_predicate(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',first_component_is_small) ).
cnf(apply1,axiom,
( ordered_pair_predicate(f28(X1,X2,X3))
| ~ member(X1,apply(X2,X3)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET003-0.ax',apply1) ).
cnf(apply3,axiom,
( first(f28(X1,X2,X3)) = X3
| ~ member(X1,apply(X2,X3)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET003-0.ax',apply3) ).
cnf(ordered_pair_predicate4,axiom,
( ordered_pair_predicate(X1)
| ~ little_set(X2)
| ~ little_set(X3)
| X1 != ordered_pair(X2,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET003-0.ax',ordered_pair_predicate4) ).
cnf(property_of_first,axiom,
( first(ordered_pair(X1,X2)) = X1
| ~ little_set(X1)
| ~ little_set(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',property_of_first) ).
cnf(property_of_second,axiom,
( second(ordered_pair(X1,X2)) = X2
| ~ little_set(X1)
| ~ little_set(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',property_of_second) ).
cnf(relation1,axiom,
( ordered_pair_predicate(X2)
| ~ relation(X1)
| ~ member(X2,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET003-0.ax',relation1) ).
cnf(composition_is_a_relation,axiom,
relation(compose(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.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/sandbox/benchmark/Axioms/SET003-0.ax',identity_relation3) ).
cnf(ordered_pairs_are_small2,axiom,
( little_set(X1)
| ~ ordered_pair_predicate(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.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/sandbox/benchmark/Axioms/SET003-0.ax',image_and_substitution5) ).
cnf(second_component_is_small,axiom,
( little_set(second(X1))
| ~ ordered_pair_predicate(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',second_component_is_small) ).
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(non_ordered_pair2,axiom,
( member(X1,non_ordered_pair(X2,X3))
| ~ little_set(X1)
| X1 != X2 ),
file('/export/starexec/sandbox/benchmark/Axioms/SET003-0.ax',non_ordered_pair2) ).
cnf(universal_set,axiom,
( member(X1,universal_set)
| ~ little_set(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET003-0.ax',universal_set) ).
cnf(subset1,axiom,
( member(X3,X2)
| ~ subset(X1,X2)
| ~ member(X3,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET003-0.ax',subset1) ).
cnf(a2,axiom,
( little_set(X1)
| ~ member(X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET003-0.ax',a2) ).
cnf(apply2,axiom,
( member(f28(X1,X2,X3),X2)
| ~ member(X1,apply(X2,X3)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET003-0.ax',apply2) ).
cnf(non_ordered_pair1,axiom,
( X1 = X2
| X1 = X3
| ~ member(X1,non_ordered_pair(X2,X3)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET003-0.ax',non_ordered_pair1) ).
cnf(regularity1,axiom,
( X1 = empty_set
| member(f24(X1),X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET003-0.ax',regularity1) ).
cnf(regularity2,axiom,
( X1 = empty_set
| disjoint(f24(X1),X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET003-0.ax',regularity2) ).
cnf(identity_relation2,axiom,
( first(X1) = second(X1)
| ~ member(X1,identity_relation) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET003-0.ax',identity_relation2) ).
cnf(non_ordered_pair3,axiom,
( member(X1,non_ordered_pair(X2,X3))
| ~ little_set(X1)
| X1 != X3 ),
file('/export/starexec/sandbox/benchmark/Axioms/SET003-0.ax',non_ordered_pair3) ).
cnf(apply4,axiom,
( member(X1,second(f28(X1,X2,X3)))
| ~ member(X1,apply(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,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
% 0.09/0.10 % Problem : SET040-3 : TPTP v8.1.2. Released v1.0.0.
% 0.09/0.10 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.10/0.31 % Computer : n005.cluster.edu
% 0.10/0.31 % Model : x86_64 x86_64
% 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31 % Memory : 8042.1875MB
% 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31 % CPULimit : 300
% 0.10/0.31 % WCLimit : 300
% 0.10/0.31 % DateTime : Sat Aug 26 08:20:38 EDT 2023
% 0.10/0.31 % CPUTime :
% 0.16/0.54 start to proof: theBenchmark
% 192.09/192.32 % Version : CSE_E---1.5
% 192.09/192.32 % Problem : theBenchmark.p
% 192.09/192.32 % Proof found
% 192.09/192.32 % SZS status Theorem for theBenchmark.p
% 192.09/192.32 % SZS output start Proof
% See solution above
% 192.09/192.32 % Total time : 191.680000 s
% 192.09/192.33 % SZS output end Proof
% 192.09/192.33 % Total time : 191.692000 s
%------------------------------------------------------------------------------