TSTP Solution File: SET042-3 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SET042-3 : 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 : n013.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 14:32:27 EDT 2023
% Result : Unsatisfiable 100.53s 100.77s
% Output : CNFRefutation 100.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 34
% Number of leaves : 121
% Syntax : Number of formulae : 246 ( 49 unt; 76 typ; 0 def)
% Number of atoms : 367 ( 69 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 372 ( 175 ~; 197 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 5 ( 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 : 63 ( 63 usr; 10 con; 0-5 aty)
% Number of variables : 282 ( 44 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: $i ).
tff(decl_95,type,
set_a: $i ).
tff(decl_96,type,
b: $i ).
tff(decl_97,type,
set_b: $i ).
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(subset2,axiom,
( subset(X1,X2)
| member(f17(X1,X2),X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET003-0.ax',subset2) ).
cnf(subset3,axiom,
( subset(X1,X2)
| ~ member(f17(X1,X2),X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET003-0.ax',subset3) ).
cnf(member_of_set_b,hypothesis,
member(b,set_b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',member_of_set_b) ).
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(a2,axiom,
( little_set(X1)
| ~ member(X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET003-0.ax',a2) ).
cnf(intersection3,axiom,
( member(X1,intersection(X2,X3))
| ~ member(X1,X2)
| ~ member(X1,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET003-0.ax',intersection3) ).
cnf(powerset2,axiom,
( member(X1,powerset(X2))
| ~ little_set(X1)
| ~ subset(X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET003-0.ax',powerset2) ).
cnf(non_ordered_pair4,axiom,
little_set(non_ordered_pair(X1,X2)),
file('/export/starexec/sandbox/benchmark/Axioms/SET003-0.ax',non_ordered_pair4) ).
cnf(universal_set,axiom,
( member(X1,universal_set)
| ~ little_set(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET003-0.ax',universal_set) ).
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(subset1,axiom,
( member(X3,X2)
| ~ subset(X1,X2)
| ~ member(X3,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET003-0.ax',subset1) ).
cnf(regularity1,axiom,
( X1 = empty_set
| member(f24(X1),X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET003-0.ax',regularity1) ).
cnf(sigma3,axiom,
( member(X1,sigma(X2))
| ~ member(X3,X2)
| ~ member(X1,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET003-0.ax',sigma3) ).
cnf(intersection2,axiom,
( member(X1,X3)
| ~ member(X1,intersection(X2,X3)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET003-0.ax',intersection2) ).
cnf(sigma1,axiom,
( member(f16(X1,X2),X2)
| ~ member(X1,sigma(X2)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET003-0.ax',sigma1) ).
cnf(empty_set,axiom,
~ member(X1,empty_set),
file('/export/starexec/sandbox/benchmark/Axioms/SET003-0.ax',empty_set) ).
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(range_of4,axiom,
( member(X1,range_of(X2))
| ~ little_set(X1)
| ~ ordered_pair_predicate(X3)
| ~ member(X3,X2)
| X1 != second(X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET003-0.ax',range_of4) ).
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(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(cross_product4,axiom,
( member(X1,cross_product(X2,X3))
| ~ little_set(X1)
| ~ ordered_pair_predicate(X1)
| ~ member(first(X1),X2)
| ~ member(second(X1),X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET003-0.ax',cross_product4) ).
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(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(cross_product1,axiom,
( ordered_pair_predicate(X1)
| ~ member(X1,cross_product(X2,X3)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET003-0.ax',cross_product1) ).
cnf(relation2,axiom,
( relation(X1)
| member(f18(X1),X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET003-0.ax',relation2) ).
cnf(relation3,axiom,
( relation(X1)
| ~ ordered_pair_predicate(f18(X1)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET003-0.ax',relation3) ).
cnf(cross_product2,axiom,
( member(first(X1),X2)
| ~ member(X1,cross_product(X2,X3)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET003-0.ax',cross_product2) ).
cnf(relation1,axiom,
( ordered_pair_predicate(X2)
| ~ relation(X1)
| ~ member(X2,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET003-0.ax',relation1) ).
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(cross_product3,axiom,
( member(second(X1),X3)
| ~ member(X1,cross_product(X2,X3)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET003-0.ax',cross_product3) ).
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(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(two_sets_equal,axiom,
( X1 = X2
| ~ subset(X1,X2)
| ~ subset(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',two_sets_equal) ).
cnf(powerset1,axiom,
( subset(X1,X2)
| ~ member(X1,powerset(X2)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET003-0.ax',powerset1) ).
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(identity_relation2,axiom,
( first(X1) = second(X1)
| ~ member(X1,identity_relation) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET003-0.ax',identity_relation2) ).
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(disjoint1,axiom,
( ~ disjoint(X1,X2)
| ~ member(X3,X1)
| ~ member(X3,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET003-0.ax',disjoint1) ).
cnf(regularity2,axiom,
( X1 = empty_set
| disjoint(f24(X1),X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET003-0.ax',regularity2) ).
cnf(intersection1,axiom,
( member(X1,X2)
| ~ member(X1,intersection(X2,X3)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET003-0.ax',intersection1) ).
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(apply3,axiom,
( first(f28(X1,X2,X3)) = X3
| ~ member(X1,apply(X2,X3)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET003-0.ax',apply3) ).
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(c_0_45,axiom,
( X1 = X2
| X1 = X3
| ~ member(X1,non_ordered_pair(X2,X3)) ),
non_ordered_pair1 ).
cnf(c_0_46,axiom,
( subset(X1,X2)
| member(f17(X1,X2),X1) ),
subset2 ).
cnf(c_0_47,axiom,
( subset(X1,X2)
| ~ member(f17(X1,X2),X2) ),
subset3 ).
cnf(c_0_48,plain,
( f17(non_ordered_pair(X1,X2),X3) = X1
| f17(non_ordered_pair(X1,X2),X3) = X2
| subset(non_ordered_pair(X1,X2),X3) ),
inference(spm,[status(thm)],[c_0_45,c_0_46]) ).
cnf(c_0_49,plain,
( f17(non_ordered_pair(X1,X2),X3) = X1
| subset(non_ordered_pair(X1,X2),X3)
| ~ member(X2,X3) ),
inference(spm,[status(thm)],[c_0_47,c_0_48]) ).
cnf(c_0_50,hypothesis,
member(b,set_b),
member_of_set_b ).
cnf(c_0_51,hypothesis,
( f17(non_ordered_pair(X1,b),set_b) = X1
| subset(non_ordered_pair(X1,b),set_b) ),
inference(spm,[status(thm)],[c_0_49,c_0_50]) ).
cnf(c_0_52,axiom,
( member(X1,non_ordered_pair(X2,X3))
| ~ little_set(X1)
| X1 != X3 ),
non_ordered_pair3 ).
cnf(c_0_53,hypothesis,
( subset(non_ordered_pair(X1,b),set_b)
| ~ member(X1,set_b) ),
inference(spm,[status(thm)],[c_0_47,c_0_51]) ).
cnf(c_0_54,axiom,
( little_set(X1)
| ~ member(X1,X2) ),
a2 ).
cnf(c_0_55,axiom,
( member(X1,intersection(X2,X3))
| ~ member(X1,X2)
| ~ member(X1,X3) ),
intersection3 ).
cnf(c_0_56,plain,
( member(X1,non_ordered_pair(X2,X1))
| ~ little_set(X1) ),
inference(er,[status(thm)],[c_0_52]) ).
cnf(c_0_57,axiom,
( member(X1,powerset(X2))
| ~ little_set(X1)
| ~ subset(X1,X2) ),
powerset2 ).
cnf(c_0_58,hypothesis,
subset(non_ordered_pair(b,b),set_b),
inference(spm,[status(thm)],[c_0_53,c_0_50]) ).
cnf(c_0_59,axiom,
little_set(non_ordered_pair(X1,X2)),
non_ordered_pair4 ).
cnf(c_0_60,axiom,
( member(X1,universal_set)
| ~ little_set(X1) ),
universal_set ).
cnf(c_0_61,plain,
( subset(X1,X2)
| little_set(f17(X1,X2)) ),
inference(spm,[status(thm)],[c_0_54,c_0_46]) ).
cnf(c_0_62,axiom,
( member(X1,non_ordered_pair(X2,X3))
| ~ little_set(X1)
| X1 != X2 ),
non_ordered_pair2 ).
cnf(c_0_63,plain,
( member(X1,intersection(X2,non_ordered_pair(X3,X1)))
| ~ member(X1,X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_56]),c_0_54]) ).
cnf(c_0_64,hypothesis,
member(non_ordered_pair(b,b),powerset(set_b)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_58]),c_0_59])]) ).
cnf(c_0_65,axiom,
( member(X3,X2)
| ~ subset(X1,X2)
| ~ member(X3,X1) ),
subset1 ).
cnf(c_0_66,plain,
subset(X1,universal_set),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_60]),c_0_61]) ).
cnf(c_0_67,axiom,
( X1 = empty_set
| member(f24(X1),X1) ),
regularity1 ).
cnf(c_0_68,axiom,
( member(X1,sigma(X2))
| ~ member(X3,X2)
| ~ member(X1,X3) ),
sigma3 ).
cnf(c_0_69,plain,
( member(X1,non_ordered_pair(X1,X2))
| ~ little_set(X1) ),
inference(er,[status(thm)],[c_0_62]) ).
cnf(c_0_70,axiom,
( member(X1,X3)
| ~ member(X1,intersection(X2,X3)) ),
intersection2 ).
cnf(c_0_71,hypothesis,
member(non_ordered_pair(b,b),intersection(powerset(set_b),non_ordered_pair(X1,non_ordered_pair(b,b)))),
inference(spm,[status(thm)],[c_0_63,c_0_64]) ).
cnf(c_0_72,plain,
( member(X1,universal_set)
| ~ member(X1,X2) ),
inference(spm,[status(thm)],[c_0_65,c_0_66]) ).
cnf(c_0_73,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_45,c_0_67]) ).
cnf(c_0_74,axiom,
( member(f16(X1,X2),X2)
| ~ member(X1,sigma(X2)) ),
sigma1 ).
cnf(c_0_75,plain,
( member(X1,sigma(non_ordered_pair(X2,X3)))
| ~ little_set(X2)
| ~ member(X1,X2) ),
inference(spm,[status(thm)],[c_0_68,c_0_69]) ).
cnf(c_0_76,hypothesis,
member(non_ordered_pair(b,b),non_ordered_pair(X1,non_ordered_pair(b,b))),
inference(spm,[status(thm)],[c_0_70,c_0_71]) ).
cnf(c_0_77,plain,
( X1 = empty_set
| member(f24(X1),universal_set) ),
inference(spm,[status(thm)],[c_0_72,c_0_67]) ).
cnf(c_0_78,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_73])]) ).
cnf(c_0_79,axiom,
~ member(X1,empty_set),
empty_set ).
cnf(c_0_80,plain,
( sigma(X1) = empty_set
| member(f16(f24(sigma(X1)),X1),X1) ),
inference(spm,[status(thm)],[c_0_74,c_0_67]) ).
cnf(c_0_81,axiom,
ordered_pair(X1,X2) = non_ordered_pair(singleton_set(X1),non_ordered_pair(X1,X2)),
ordered_pair ).
cnf(c_0_82,axiom,
singleton_set(X1) = non_ordered_pair(X1,X1),
singleton_set ).
cnf(c_0_83,axiom,
( member(X1,range_of(X2))
| ~ little_set(X1)
| ~ ordered_pair_predicate(X3)
| ~ member(X3,X2)
| X1 != second(X3) ),
range_of4 ).
cnf(c_0_84,axiom,
( little_set(second(X1))
| ~ ordered_pair_predicate(X1) ),
second_component_is_small ).
cnf(c_0_85,hypothesis,
member(non_ordered_pair(b,b),sigma(non_ordered_pair(non_ordered_pair(X1,non_ordered_pair(b,b)),X2))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_76]),c_0_59])]) ).
cnf(c_0_86,plain,
( non_ordered_pair(X1,X1) = empty_set
| member(X1,universal_set) ),
inference(spm,[status(thm)],[c_0_77,c_0_78]) ).
cnf(c_0_87,plain,
sigma(empty_set) = empty_set,
inference(spm,[status(thm)],[c_0_79,c_0_80]) ).
cnf(c_0_88,axiom,
( ordered_pair_predicate(X1)
| ~ little_set(X2)
| ~ little_set(X3)
| X1 != ordered_pair(X2,X3) ),
ordered_pair_predicate4 ).
cnf(c_0_89,plain,
ordered_pair(X1,X2) = non_ordered_pair(non_ordered_pair(X1,X1),non_ordered_pair(X1,X2)),
inference(rw,[status(thm)],[c_0_81,c_0_82]) ).
cnf(c_0_90,plain,
( member(second(X1),range_of(X2))
| ~ ordered_pair_predicate(X1)
| ~ member(X1,X2) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_83]),c_0_84]) ).
cnf(c_0_91,hypothesis,
member(non_ordered_pair(X1,non_ordered_pair(b,b)),universal_set),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_86]),c_0_87]),c_0_79]) ).
cnf(c_0_92,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_88,c_0_89]) ).
cnf(c_0_93,axiom,
( member(X1,cross_product(X2,X3))
| ~ little_set(X1)
| ~ ordered_pair_predicate(X1)
| ~ member(first(X1),X2)
| ~ member(second(X1),X3) ),
cross_product4 ).
cnf(c_0_94,axiom,
( little_set(X1)
| ~ ordered_pair_predicate(X1) ),
ordered_pairs_are_small2 ).
cnf(c_0_95,hypothesis,
( member(second(non_ordered_pair(X1,non_ordered_pair(b,b))),range_of(universal_set))
| ~ ordered_pair_predicate(non_ordered_pair(X1,non_ordered_pair(b,b))) ),
inference(spm,[status(thm)],[c_0_90,c_0_91]) ).
cnf(c_0_96,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_92]) ).
cnf(c_0_97,hypothesis,
little_set(b),
inference(spm,[status(thm)],[c_0_54,c_0_50]) ).
cnf(c_0_98,plain,
( member(X1,cross_product(X2,X3))
| ~ ordered_pair_predicate(X1)
| ~ member(first(X1),X2)
| ~ member(second(X1),X3) ),
inference(csr,[status(thm)],[c_0_93,c_0_94]) ).
cnf(c_0_99,axiom,
( little_set(first(X1))
| ~ ordered_pair_predicate(X1) ),
first_component_is_small ).
cnf(c_0_100,hypothesis,
member(second(non_ordered_pair(non_ordered_pair(b,b),non_ordered_pair(b,b))),range_of(universal_set)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_96]),c_0_97])]) ).
cnf(c_0_101,plain,
( member(X1,cross_product(universal_set,X2))
| ~ ordered_pair_predicate(X1)
| ~ member(second(X1),X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_98,c_0_60]),c_0_99]) ).
cnf(c_0_102,hypothesis,
member(second(non_ordered_pair(non_ordered_pair(b,b),non_ordered_pair(b,b))),universal_set),
inference(spm,[status(thm)],[c_0_72,c_0_100]) ).
cnf(c_0_103,hypothesis,
( member(non_ordered_pair(non_ordered_pair(b,b),non_ordered_pair(b,b)),cross_product(universal_set,universal_set))
| ~ ordered_pair_predicate(non_ordered_pair(non_ordered_pair(b,b),non_ordered_pair(b,b))) ),
inference(spm,[status(thm)],[c_0_101,c_0_102]) ).
cnf(c_0_104,axiom,
( ordered_pair_predicate(X1)
| ~ member(X1,cross_product(X2,X3)) ),
cross_product1 ).
cnf(c_0_105,axiom,
( relation(X1)
| member(f18(X1),X1) ),
relation2 ).
cnf(c_0_106,axiom,
( relation(X1)
| ~ ordered_pair_predicate(f18(X1)) ),
relation3 ).
cnf(c_0_107,axiom,
( member(first(X1),X2)
| ~ member(X1,cross_product(X2,X3)) ),
cross_product2 ).
cnf(c_0_108,hypothesis,
member(non_ordered_pair(non_ordered_pair(b,b),non_ordered_pair(b,b)),cross_product(universal_set,universal_set)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_103,c_0_96]),c_0_97])]) ).
cnf(c_0_109,axiom,
( ordered_pair_predicate(X2)
| ~ relation(X1)
| ~ member(X2,X1) ),
relation1 ).
cnf(c_0_110,plain,
relation(cross_product(X1,X2)),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_104,c_0_105]),c_0_106]) ).
cnf(c_0_111,hypothesis,
member(first(non_ordered_pair(non_ordered_pair(b,b),non_ordered_pair(b,b))),universal_set),
inference(spm,[status(thm)],[c_0_107,c_0_108]) ).
cnf(c_0_112,hypothesis,
ordered_pair_predicate(non_ordered_pair(non_ordered_pair(b,b),non_ordered_pair(b,b))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_109,c_0_108]),c_0_110])]) ).
cnf(c_0_113,axiom,
( second(ordered_pair(X1,X2)) = X2
| ~ little_set(X1)
| ~ little_set(X2) ),
property_of_second ).
cnf(c_0_114,hypothesis,
( member(non_ordered_pair(non_ordered_pair(b,b),non_ordered_pair(b,b)),cross_product(universal_set,X1))
| ~ member(second(non_ordered_pair(non_ordered_pair(b,b),non_ordered_pair(b,b))),X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_98,c_0_111]),c_0_112])]) ).
cnf(c_0_115,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_113,c_0_89]) ).
cnf(c_0_116,plain,
subset(X1,X1),
inference(spm,[status(thm)],[c_0_47,c_0_46]) ).
cnf(c_0_117,hypothesis,
( member(X1,sigma(set_b))
| ~ member(X1,b) ),
inference(spm,[status(thm)],[c_0_68,c_0_50]) ).
cnf(c_0_118,hypothesis,
( member(non_ordered_pair(non_ordered_pair(b,b),non_ordered_pair(b,b)),cross_product(universal_set,X1))
| ~ member(b,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_114,c_0_115]),c_0_97])]) ).
cnf(c_0_119,plain,
( member(X1,powerset(X1))
| ~ little_set(X1) ),
inference(spm,[status(thm)],[c_0_57,c_0_116]) ).
cnf(c_0_120,hypothesis,
( subset(b,X1)
| member(f17(b,X1),sigma(set_b)) ),
inference(spm,[status(thm)],[c_0_117,c_0_46]) ).
cnf(c_0_121,axiom,
( member(second(X1),X3)
| ~ member(X1,cross_product(X2,X3)) ),
cross_product3 ).
cnf(c_0_122,hypothesis,
member(non_ordered_pair(non_ordered_pair(b,b),non_ordered_pair(b,b)),cross_product(universal_set,non_ordered_pair(X1,b))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_118,c_0_56]),c_0_97])]) ).
cnf(c_0_123,hypothesis,
member(non_ordered_pair(non_ordered_pair(b,b),non_ordered_pair(b,b)),cross_product(universal_set,powerset(b))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_118,c_0_119]),c_0_97])]) ).
cnf(c_0_124,axiom,
( member(X1,identity_relation)
| ~ little_set(X1)
| ~ ordered_pair_predicate(X1)
| first(X1) != second(X1) ),
identity_relation3 ).
cnf(c_0_125,axiom,
( first(ordered_pair(X1,X2)) = X1
| ~ little_set(X1)
| ~ little_set(X2) ),
property_of_first ).
cnf(c_0_126,axiom,
( X1 = X2
| ~ subset(X1,X2)
| ~ subset(X2,X1) ),
two_sets_equal ).
cnf(c_0_127,hypothesis,
subset(b,sigma(set_b)),
inference(spm,[status(thm)],[c_0_47,c_0_120]) ).
cnf(c_0_128,hypothesis,
member(second(non_ordered_pair(non_ordered_pair(b,b),non_ordered_pair(b,b))),non_ordered_pair(X1,b)),
inference(spm,[status(thm)],[c_0_121,c_0_122]) ).
cnf(c_0_129,axiom,
( subset(X1,X2)
| ~ member(X1,powerset(X2)) ),
powerset1 ).
cnf(c_0_130,hypothesis,
member(second(non_ordered_pair(non_ordered_pair(b,b),non_ordered_pair(b,b))),powerset(b)),
inference(spm,[status(thm)],[c_0_121,c_0_123]) ).
cnf(c_0_131,plain,
( member(X1,identity_relation)
| first(X1) != second(X1)
| ~ ordered_pair_predicate(X1) ),
inference(csr,[status(thm)],[c_0_124,c_0_94]) ).
cnf(c_0_132,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_125,c_0_89]) ).
cnf(c_0_133,hypothesis,
( sigma(set_b) = b
| ~ subset(sigma(set_b),b) ),
inference(spm,[status(thm)],[c_0_126,c_0_127]) ).
cnf(c_0_134,hypothesis,
( second(non_ordered_pair(non_ordered_pair(b,b),non_ordered_pair(b,b))) = b
| second(non_ordered_pair(non_ordered_pair(b,b),non_ordered_pair(b,b))) = X1 ),
inference(spm,[status(thm)],[c_0_45,c_0_128]) ).
cnf(c_0_135,hypothesis,
subset(second(non_ordered_pair(non_ordered_pair(b,b),non_ordered_pair(b,b))),b),
inference(spm,[status(thm)],[c_0_129,c_0_130]) ).
cnf(c_0_136,plain,
( member(non_ordered_pair(non_ordered_pair(X1,X1),non_ordered_pair(X1,X2)),identity_relation)
| second(non_ordered_pair(non_ordered_pair(X1,X1),non_ordered_pair(X1,X2))) != X1
| ~ little_set(X2)
| ~ little_set(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_131,c_0_132]),c_0_96]) ).
cnf(c_0_137,hypothesis,
second(non_ordered_pair(non_ordered_pair(b,b),non_ordered_pair(b,b))) = b,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_133,c_0_134]),c_0_135])]) ).
cnf(c_0_138,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_139,axiom,
( first(X1) = second(X1)
| ~ member(X1,identity_relation) ),
identity_relation2 ).
cnf(c_0_140,hypothesis,
member(non_ordered_pair(non_ordered_pair(b,b),non_ordered_pair(b,b)),identity_relation),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_136,c_0_137]),c_0_97])]) ).
cnf(c_0_141,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_138]),c_0_84]) ).
cnf(c_0_142,hypothesis,
first(non_ordered_pair(non_ordered_pair(b,b),non_ordered_pair(b,b))) = b,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_139,c_0_140]),c_0_137]) ).
cnf(c_0_143,axiom,
subset(image(singleton_set(X1),X2),apply(X2,X1)),
image_and_apply2 ).
cnf(c_0_144,hypothesis,
( member(b,image(X1,X2))
| ~ member(non_ordered_pair(non_ordered_pair(b,b),non_ordered_pair(b,b)),X2)
| ~ member(b,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_141,c_0_142]),c_0_137]),c_0_112])]) ).
cnf(c_0_145,axiom,
( ~ disjoint(X1,X2)
| ~ member(X3,X1)
| ~ member(X3,X2) ),
disjoint1 ).
cnf(c_0_146,axiom,
( X1 = empty_set
| disjoint(f24(X1),X1) ),
regularity2 ).
cnf(c_0_147,hypothesis,
( member(b,intersection(X1,set_b))
| ~ member(b,X1) ),
inference(spm,[status(thm)],[c_0_55,c_0_50]) ).
cnf(c_0_148,plain,
subset(image(non_ordered_pair(X1,X1),X2),apply(X2,X1)),
inference(rw,[status(thm)],[c_0_143,c_0_82]) ).
cnf(c_0_149,hypothesis,
( member(b,image(non_ordered_pair(X1,b),X2))
| ~ member(non_ordered_pair(non_ordered_pair(b,b),non_ordered_pair(b,b)),X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_144,c_0_56]),c_0_97])]) ).
cnf(c_0_150,plain,
( X1 = empty_set
| ~ member(X2,f24(X1))
| ~ member(X2,X1) ),
inference(spm,[status(thm)],[c_0_145,c_0_146]) ).
cnf(c_0_151,axiom,
( member(X1,X2)
| ~ member(X1,intersection(X2,X3)) ),
intersection1 ).
cnf(c_0_152,hypothesis,
member(b,intersection(non_ordered_pair(b,X1),set_b)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_147,c_0_69]),c_0_97])]) ).
cnf(c_0_153,plain,
( member(X1,apply(X2,X3))
| ~ member(X1,image(non_ordered_pair(X3,X3),X2)) ),
inference(spm,[status(thm)],[c_0_65,c_0_148]) ).
cnf(c_0_154,hypothesis,
member(b,image(non_ordered_pair(X1,b),identity_relation)),
inference(spm,[status(thm)],[c_0_149,c_0_140]) ).
cnf(c_0_155,plain,
( f24(non_ordered_pair(X1,X2)) = X1
| non_ordered_pair(X1,X2) = empty_set
| ~ member(X3,non_ordered_pair(X1,X2))
| ~ member(X3,X2) ),
inference(spm,[status(thm)],[c_0_150,c_0_73]) ).
cnf(c_0_156,hypothesis,
member(b,non_ordered_pair(b,X1)),
inference(spm,[status(thm)],[c_0_151,c_0_152]) ).
cnf(c_0_157,axiom,
( member(f28(X1,X2,X3),X2)
| ~ member(X1,apply(X2,X3)) ),
apply2 ).
cnf(c_0_158,hypothesis,
member(b,apply(identity_relation,b)),
inference(spm,[status(thm)],[c_0_153,c_0_154]) ).
cnf(c_0_159,axiom,
( first(f28(X1,X2,X3)) = X3
| ~ member(X1,apply(X2,X3)) ),
apply3 ).
cnf(c_0_160,hypothesis,
( f24(non_ordered_pair(b,X1)) = b
| non_ordered_pair(b,X1) = empty_set
| ~ member(b,X1) ),
inference(spm,[status(thm)],[c_0_155,c_0_156]) ).
cnf(c_0_161,hypothesis,
member(f28(b,identity_relation,b),identity_relation),
inference(spm,[status(thm)],[c_0_157,c_0_158]) ).
cnf(c_0_162,hypothesis,
first(f28(b,identity_relation,b)) = b,
inference(spm,[status(thm)],[c_0_159,c_0_158]) ).
cnf(c_0_163,hypothesis,
( f24(non_ordered_pair(b,set_b)) = b
| non_ordered_pair(b,set_b) = empty_set ),
inference(spm,[status(thm)],[c_0_160,c_0_50]) ).
cnf(c_0_164,axiom,
( member(X1,second(f28(X1,X2,X3)))
| ~ member(X1,apply(X2,X3)) ),
apply4 ).
cnf(c_0_165,hypothesis,
second(f28(b,identity_relation,b)) = b,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_139,c_0_161]),c_0_162]) ).
cnf(c_0_166,hypothesis,
( non_ordered_pair(b,set_b) = empty_set
| ~ member(X1,non_ordered_pair(b,set_b))
| ~ member(X1,b) ),
inference(spm,[status(thm)],[c_0_150,c_0_163]) ).
cnf(c_0_167,hypothesis,
member(b,b),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_164,c_0_158]),c_0_165]) ).
cnf(c_0_168,hypothesis,
non_ordered_pair(b,set_b) = empty_set,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_166,c_0_167]),c_0_156])]) ).
cnf(c_0_169,hypothesis,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_168]),c_0_97])]),c_0_79]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET042-3 : TPTP v8.1.2. Released v1.0.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.35 % Computer : n013.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Sat Aug 26 11:01:32 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.56 start to proof: theBenchmark
% 100.53/100.77 % Version : CSE_E---1.5
% 100.53/100.77 % Problem : theBenchmark.p
% 100.53/100.77 % Proof found
% 100.53/100.77 % SZS status Theorem for theBenchmark.p
% 100.53/100.77 % SZS output start Proof
% See solution above
% 100.53/100.79 % Total time : 100.019000 s
% 100.53/100.79 % SZS output end Proof
% 100.53/100.79 % Total time : 100.029000 s
%------------------------------------------------------------------------------