TSTP Solution File: NUM012-1 by CSE_E---1.5
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- Process Solution
%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : NUM012-1 : TPTP v8.1.2. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% Computer : n022.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 10:26:08 EDT 2023
% Result : Unsatisfiable 126.79s 126.81s
% Output : CNFRefutation 126.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 138
% Syntax : Number of formulae : 258 ( 44 unt; 112 typ; 0 def)
% Number of atoms : 290 ( 80 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 237 ( 93 ~; 144 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 183 ( 98 >; 85 *; 0 +; 0 <<)
% Number of predicates : 21 ( 19 usr; 1 prp; 0-5 aty)
% Number of functors : 93 ( 93 usr; 14 con; 0-5 aty)
% Number of variables : 261 ( 41 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,
associative: ( $i * $i ) > $o ).
tff(decl_95,type,
f34: ( $i * $i ) > $i ).
tff(decl_96,type,
f35: ( $i * $i ) > $i ).
tff(decl_97,type,
f36: ( $i * $i ) > $i ).
tff(decl_98,type,
identity: ( $i * $i * $i ) > $o ).
tff(decl_99,type,
f37: ( $i * $i * $i ) > $i ).
tff(decl_100,type,
inverse: ( $i * $i * $i * $i ) > $o ).
tff(decl_101,type,
f38: ( $i * $i * $i * $i ) > $i ).
tff(decl_102,type,
group: ( $i * $i ) > $o ).
tff(decl_103,type,
f39: ( $i * $i ) > $i ).
tff(decl_104,type,
f40: ( $i * $i ) > $i ).
tff(decl_105,type,
commutes: ( $i * $i ) > $o ).
tff(decl_106,type,
f41: ( $i * $i ) > $i ).
tff(decl_107,type,
f42: ( $i * $i ) > $i ).
tff(decl_108,type,
natural_numbers: $i ).
tff(decl_109,type,
f43: ( $i * $i ) > $i ).
tff(decl_110,type,
f44: $i > $i ).
tff(decl_111,type,
plus: $i ).
tff(decl_112,type,
f45: ( $i * $i ) > $i ).
tff(decl_113,type,
f46: ( $i * $i ) > $i ).
tff(decl_114,type,
f47: ( $i * $i ) > $i ).
tff(decl_115,type,
f48: ( $i * $i ) > $i ).
tff(decl_116,type,
f49: $i > $i ).
tff(decl_117,type,
times: $i ).
tff(decl_118,type,
f50: ( $i * $i ) > $i ).
tff(decl_119,type,
f51: ( $i * $i ) > $i ).
tff(decl_120,type,
f52: ( $i * $i ) > $i ).
tff(decl_121,type,
f53: ( $i * $i ) > $i ).
tff(decl_122,type,
f54: $i > $i ).
tff(decl_123,type,
prime_numbers: $i ).
tff(decl_124,type,
f55: $i > $i ).
tff(decl_125,type,
f56: $i > $i ).
tff(decl_126,type,
finite: $i > $o ).
tff(decl_127,type,
f57: $i > $i ).
tff(decl_128,type,
f58: $i > $i ).
tff(decl_129,type,
twin_prime_numbers: $i ).
tff(decl_130,type,
even_numbers: $i ).
tff(decl_131,type,
f59: $i > $i ).
tff(decl_132,type,
f76: $i ).
tff(decl_133,type,
f77: $i ).
cnf(non_ordered_pair1,axiom,
( X1 = X2
| X1 = X3
| ~ member(X1,non_ordered_pair(X2,X3)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET003-0.ax',non_ordered_pair1) ).
cnf(disjoint3,axiom,
( disjoint(X1,X2)
| member(f23(X1,X2),X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET003-0.ax',disjoint3) ).
cnf(disjoint2,axiom,
( disjoint(X1,X2)
| member(f23(X1,X2),X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET003-0.ax',disjoint2) ).
cnf(disjoint1,axiom,
( ~ disjoint(X1,X2)
| ~ member(X3,X1)
| ~ member(X3,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET003-0.ax',disjoint1) ).
cnf(non_ordered_pair2,axiom,
( member(X1,non_ordered_pair(X2,X3))
| ~ little_set(X1)
| X1 != X2 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET003-0.ax',non_ordered_pair2) ).
cnf(intersection1,axiom,
( member(X1,X2)
| ~ member(X1,intersection(X2,X3)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET003-0.ax',intersection1) ).
cnf(regularity1,axiom,
( X1 = empty_set
| member(f24(X1),X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET003-0.ax',regularity1) ).
cnf(a2,axiom,
( little_set(X1)
| ~ member(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET003-0.ax',a2) ).
cnf(intersection2,axiom,
( member(X1,X3)
| ~ member(X1,intersection(X2,X3)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET003-0.ax',intersection2) ).
cnf(intersection3,axiom,
( member(X1,intersection(X2,X3))
| ~ member(X1,X2)
| ~ member(X1,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET003-0.ax',intersection3) ).
cnf(another_natural_number,hypothesis,
member(f77,natural_numbers),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',another_natural_number) ).
cnf(complement1,axiom,
( ~ member(X1,complement(X2))
| ~ member(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET003-0.ax',complement1) ).
cnf(a_natural_number,hypothesis,
member(f76,natural_numbers),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_natural_number) ).
cnf(complement2,axiom,
( member(X1,complement(X2))
| member(X1,X2)
| ~ little_set(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET003-0.ax',complement2) ).
cnf(successor,axiom,
successor(X1) = union(X1,singleton_set(X1)),
file('/export/starexec/sandbox2/benchmark/Axioms/SET003-0.ax',successor) ).
cnf(singleton_set,axiom,
singleton_set(X1) = non_ordered_pair(X1,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/SET003-0.ax',singleton_set) ).
cnf(successors_are_equal,hypothesis,
successor(f76) = successor(f77),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',successors_are_equal) ).
cnf(union,axiom,
union(X1,X2) = complement(intersection(complement(X1),complement(X2))),
file('/export/starexec/sandbox2/benchmark/Axioms/SET003-0.ax',union) ).
cnf(empty_set,axiom,
~ member(X1,empty_set),
file('/export/starexec/sandbox2/benchmark/Axioms/SET003-0.ax',empty_set) ).
cnf(non_ordered_pair3,axiom,
( member(X1,non_ordered_pair(X2,X3))
| ~ little_set(X1)
| X1 != X3 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET003-0.ax',non_ordered_pair3) ).
cnf(prove_well_definedness_of_successor,negated_conjecture,
f76 != f77,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_well_definedness_of_successor) ).
cnf(regularity2,axiom,
( X1 = empty_set
| disjoint(f24(X1),X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET003-0.ax',regularity2) ).
cnf(subset2,axiom,
( subset(X1,X2)
| member(f17(X1,X2),X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET003-0.ax',subset2) ).
cnf(subset3,axiom,
( subset(X1,X2)
| ~ member(f17(X1,X2),X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET003-0.ax',subset3) ).
cnf(subset1,axiom,
( member(X3,X2)
| ~ subset(X1,X2)
| ~ member(X3,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET003-0.ax',subset1) ).
cnf(powerset2,axiom,
( member(X1,powerset(X2))
| ~ little_set(X1)
| ~ subset(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET003-0.ax',powerset2) ).
cnf(c_0_26,axiom,
( X1 = X2
| X1 = X3
| ~ member(X1,non_ordered_pair(X2,X3)) ),
non_ordered_pair1 ).
cnf(c_0_27,axiom,
( disjoint(X1,X2)
| member(f23(X1,X2),X2) ),
disjoint3 ).
cnf(c_0_28,axiom,
( disjoint(X1,X2)
| member(f23(X1,X2),X1) ),
disjoint2 ).
cnf(c_0_29,plain,
( f23(X1,non_ordered_pair(X2,X3)) = X2
| f23(X1,non_ordered_pair(X2,X3)) = X3
| disjoint(X1,non_ordered_pair(X2,X3)) ),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_30,plain,
( f23(non_ordered_pair(X1,X2),X3) = X1
| f23(non_ordered_pair(X1,X2),X3) = X2
| disjoint(non_ordered_pair(X1,X2),X3) ),
inference(spm,[status(thm)],[c_0_26,c_0_28]) ).
cnf(c_0_31,plain,
( f23(X1,non_ordered_pair(X2,X2)) = X2
| disjoint(X1,non_ordered_pair(X2,X2)) ),
inference(er,[status(thm)],[inference(ef,[status(thm)],[c_0_29])]) ).
cnf(c_0_32,plain,
( f23(non_ordered_pair(X1,X1),X2) = X1
| disjoint(non_ordered_pair(X1,X1),X2) ),
inference(er,[status(thm)],[inference(ef,[status(thm)],[c_0_30])]) ).
cnf(c_0_33,axiom,
( ~ disjoint(X1,X2)
| ~ member(X3,X1)
| ~ member(X3,X2) ),
disjoint1 ).
cnf(c_0_34,plain,
( X1 = X2
| disjoint(non_ordered_pair(X1,X1),non_ordered_pair(X2,X2)) ),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_35,axiom,
( member(X1,non_ordered_pair(X2,X3))
| ~ little_set(X1)
| X1 != X2 ),
non_ordered_pair2 ).
cnf(c_0_36,axiom,
( member(X1,X2)
| ~ member(X1,intersection(X2,X3)) ),
intersection1 ).
cnf(c_0_37,axiom,
( X1 = empty_set
| member(f24(X1),X1) ),
regularity1 ).
cnf(c_0_38,plain,
( X1 = X2
| ~ member(X3,non_ordered_pair(X2,X2))
| ~ member(X3,non_ordered_pair(X1,X1)) ),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_39,plain,
( member(X1,non_ordered_pair(X1,X2))
| ~ little_set(X1) ),
inference(er,[status(thm)],[c_0_35]) ).
cnf(c_0_40,axiom,
( little_set(X1)
| ~ member(X1,X2) ),
a2 ).
cnf(c_0_41,axiom,
( member(X1,X3)
| ~ member(X1,intersection(X2,X3)) ),
intersection2 ).
cnf(c_0_42,axiom,
( member(X1,intersection(X2,X3))
| ~ member(X1,X2)
| ~ member(X1,X3) ),
intersection3 ).
cnf(c_0_43,plain,
( intersection(X1,X2) = empty_set
| member(f24(intersection(X1,X2)),X1) ),
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_44,plain,
( X1 = X2
| ~ member(X2,non_ordered_pair(X1,X1)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_40]) ).
cnf(c_0_45,plain,
( intersection(X1,X2) = empty_set
| member(f24(intersection(X1,X2)),X2) ),
inference(spm,[status(thm)],[c_0_41,c_0_37]) ).
cnf(c_0_46,hypothesis,
member(f77,natural_numbers),
another_natural_number ).
cnf(c_0_47,plain,
( X1 = X2
| X1 = X3
| disjoint(non_ordered_pair(X1,X1),non_ordered_pair(X3,X2)) ),
inference(spm,[status(thm)],[c_0_29,c_0_32]) ).
cnf(c_0_48,axiom,
( ~ member(X1,complement(X2))
| ~ member(X1,X2) ),
complement1 ).
cnf(c_0_49,plain,
( disjoint(X1,intersection(X2,X3))
| member(f23(X1,intersection(X2,X3)),X3) ),
inference(spm,[status(thm)],[c_0_41,c_0_27]) ).
cnf(c_0_50,hypothesis,
member(f76,natural_numbers),
a_natural_number ).
cnf(c_0_51,plain,
( intersection(X1,X2) = empty_set
| member(f24(intersection(X1,X2)),intersection(X3,X1))
| ~ member(f24(intersection(X1,X2)),X3) ),
inference(spm,[status(thm)],[c_0_42,c_0_43]) ).
cnf(c_0_52,plain,
( f24(intersection(X1,non_ordered_pair(X2,X2))) = X2
| intersection(X1,non_ordered_pair(X2,X2)) = empty_set ),
inference(spm,[status(thm)],[c_0_44,c_0_45]) ).
cnf(c_0_53,hypothesis,
little_set(f77),
inference(spm,[status(thm)],[c_0_40,c_0_46]) ).
cnf(c_0_54,plain,
( X1 = X2
| X1 = X3
| ~ member(X4,non_ordered_pair(X2,X3))
| ~ member(X4,non_ordered_pair(X1,X1)) ),
inference(spm,[status(thm)],[c_0_33,c_0_47]) ).
cnf(c_0_55,hypothesis,
( member(f77,intersection(X1,natural_numbers))
| ~ member(f77,X1) ),
inference(spm,[status(thm)],[c_0_42,c_0_46]) ).
cnf(c_0_56,axiom,
( member(X1,complement(X2))
| member(X1,X2)
| ~ little_set(X1) ),
complement2 ).
cnf(c_0_57,axiom,
successor(X1) = union(X1,singleton_set(X1)),
successor ).
cnf(c_0_58,axiom,
singleton_set(X1) = non_ordered_pair(X1,X1),
singleton_set ).
cnf(c_0_59,plain,
( disjoint(X1,intersection(X2,complement(X3)))
| ~ member(f23(X1,intersection(X2,complement(X3))),X3) ),
inference(spm,[status(thm)],[c_0_48,c_0_49]) ).
cnf(c_0_60,plain,
( disjoint(intersection(X1,X2),X3)
| member(f23(intersection(X1,X2),X3),X1) ),
inference(spm,[status(thm)],[c_0_36,c_0_28]) ).
cnf(c_0_61,hypothesis,
little_set(f76),
inference(spm,[status(thm)],[c_0_40,c_0_50]) ).
cnf(c_0_62,plain,
( intersection(X1,non_ordered_pair(X2,X2)) = empty_set
| member(X2,intersection(X3,X1))
| ~ member(X2,X3) ),
inference(spm,[status(thm)],[c_0_51,c_0_52]) ).
cnf(c_0_63,hypothesis,
member(f77,non_ordered_pair(f77,X1)),
inference(spm,[status(thm)],[c_0_39,c_0_53]) ).
cnf(c_0_64,plain,
( intersection(X1,non_ordered_pair(X2,X3)) = empty_set
| X4 = X3
| X4 = X2
| ~ member(f24(intersection(X1,non_ordered_pair(X2,X3))),non_ordered_pair(X4,X4)) ),
inference(spm,[status(thm)],[c_0_54,c_0_45]) ).
cnf(c_0_65,hypothesis,
( member(f77,intersection(complement(X1),natural_numbers))
| member(f77,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_56]),c_0_53])]) ).
cnf(c_0_66,hypothesis,
successor(f76) = successor(f77),
successors_are_equal ).
cnf(c_0_67,plain,
successor(X1) = union(X1,non_ordered_pair(X1,X1)),
inference(rw,[status(thm)],[c_0_57,c_0_58]) ).
cnf(c_0_68,axiom,
union(X1,X2) = complement(intersection(complement(X1),complement(X2))),
union ).
cnf(c_0_69,plain,
disjoint(intersection(X1,X2),intersection(X3,complement(X1))),
inference(spm,[status(thm)],[c_0_59,c_0_60]) ).
cnf(c_0_70,hypothesis,
member(f76,non_ordered_pair(f76,X1)),
inference(spm,[status(thm)],[c_0_39,c_0_61]) ).
cnf(c_0_71,hypothesis,
( intersection(X1,non_ordered_pair(f77,f77)) = empty_set
| member(f77,intersection(non_ordered_pair(f77,X2),X1)) ),
inference(spm,[status(thm)],[c_0_62,c_0_63]) ).
cnf(c_0_72,plain,
( intersection(non_ordered_pair(X1,X1),non_ordered_pair(X2,X3)) = empty_set
| X1 = X2
| X1 = X3 ),
inference(spm,[status(thm)],[c_0_64,c_0_43]) ).
cnf(c_0_73,axiom,
~ member(X1,empty_set),
empty_set ).
cnf(c_0_74,axiom,
( member(X1,non_ordered_pair(X2,X3))
| ~ little_set(X1)
| X1 != X3 ),
non_ordered_pair3 ).
cnf(c_0_75,hypothesis,
( member(f77,complement(X1))
| member(f77,X1) ),
inference(spm,[status(thm)],[c_0_36,c_0_65]) ).
cnf(c_0_76,hypothesis,
complement(intersection(complement(f77),complement(non_ordered_pair(f77,f77)))) = complement(intersection(complement(f76),complement(non_ordered_pair(f76,f76)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_66,c_0_67]),c_0_67]),c_0_68]),c_0_68]) ).
cnf(c_0_77,plain,
( ~ member(X1,intersection(X2,complement(X3)))
| ~ member(X1,intersection(X3,X4)) ),
inference(spm,[status(thm)],[c_0_33,c_0_69]) ).
cnf(c_0_78,hypothesis,
member(f77,intersection(non_ordered_pair(f77,X1),natural_numbers)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_39]),c_0_53])]) ).
cnf(c_0_79,hypothesis,
( intersection(X1,non_ordered_pair(f76,f76)) = empty_set
| member(f76,intersection(non_ordered_pair(f76,X2),X1)) ),
inference(spm,[status(thm)],[c_0_62,c_0_70]) ).
cnf(c_0_80,hypothesis,
( intersection(non_ordered_pair(X1,X2),non_ordered_pair(f77,f77)) = empty_set
| f77 = X2
| f77 = X1 ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_72]),c_0_73]) ).
cnf(c_0_81,negated_conjecture,
f76 != f77,
prove_well_definedness_of_successor ).
cnf(c_0_82,plain,
( member(X1,non_ordered_pair(X2,X1))
| ~ little_set(X1) ),
inference(er,[status(thm)],[c_0_74]) ).
cnf(c_0_83,hypothesis,
( member(f77,complement(intersection(complement(f76),complement(non_ordered_pair(f76,f76)))))
| member(f77,intersection(complement(f77),complement(non_ordered_pair(f77,f77)))) ),
inference(spm,[status(thm)],[c_0_75,c_0_76]) ).
cnf(c_0_84,hypothesis,
~ member(f77,intersection(X1,complement(non_ordered_pair(f77,X2)))),
inference(spm,[status(thm)],[c_0_77,c_0_78]) ).
cnf(c_0_85,plain,
( disjoint(X1,X2)
| member(f23(X1,X2),intersection(X3,X1))
| ~ member(f23(X1,X2),X3) ),
inference(spm,[status(thm)],[c_0_42,c_0_28]) ).
cnf(c_0_86,plain,
( disjoint(X1,intersection(X2,X3))
| member(f23(X1,intersection(X2,X3)),X2) ),
inference(spm,[status(thm)],[c_0_36,c_0_27]) ).
cnf(c_0_87,plain,
( disjoint(X1,X2)
| member(f23(X1,X2),intersection(X3,X2))
| ~ member(f23(X1,X2),X3) ),
inference(spm,[status(thm)],[c_0_42,c_0_27]) ).
cnf(c_0_88,hypothesis,
( intersection(non_ordered_pair(f77,f77),non_ordered_pair(f76,f76)) = empty_set
| f77 = X1 ),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_80]),c_0_73]),c_0_81]) ).
cnf(c_0_89,plain,
( member(X1,intersection(X2,non_ordered_pair(X3,X1)))
| ~ member(X1,X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_82]),c_0_40]) ).
cnf(c_0_90,axiom,
( X1 = empty_set
| disjoint(f24(X1),X1) ),
regularity2 ).
cnf(c_0_91,axiom,
( subset(X1,X2)
| member(f17(X1,X2),X1) ),
subset2 ).
cnf(c_0_92,hypothesis,
member(f77,complement(intersection(complement(f76),complement(non_ordered_pair(f76,f76))))),
inference(sr,[status(thm)],[c_0_83,c_0_84]) ).
cnf(c_0_93,plain,
( member(X1,intersection(X2,complement(X3)))
| member(X1,X3)
| ~ member(X1,X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_56]),c_0_40]) ).
cnf(c_0_94,plain,
( disjoint(X1,intersection(X2,X3))
| member(f23(X1,intersection(X2,X3)),intersection(X2,X1)) ),
inference(spm,[status(thm)],[c_0_85,c_0_86]) ).
cnf(c_0_95,plain,
( disjoint(X1,X2)
| member(f23(X1,X2),intersection(X1,X2)) ),
inference(spm,[status(thm)],[c_0_87,c_0_28]) ).
cnf(c_0_96,hypothesis,
intersection(non_ordered_pair(f77,f77),non_ordered_pair(f76,f76)) = empty_set,
inference(csr,[status(thm)],[inference(ef,[status(thm)],[c_0_88]),c_0_88]) ).
cnf(c_0_97,plain,
( intersection(X1,X2) = empty_set
| member(f24(intersection(X1,X2)),intersection(X2,non_ordered_pair(X3,f24(intersection(X1,X2))))) ),
inference(spm,[status(thm)],[c_0_89,c_0_45]) ).
cnf(c_0_98,plain,
( f24(intersection(non_ordered_pair(X1,X1),X2)) = X1
| intersection(non_ordered_pair(X1,X1),X2) = empty_set ),
inference(spm,[status(thm)],[c_0_44,c_0_43]) ).
cnf(c_0_99,plain,
( intersection(complement(X1),X2) = empty_set
| ~ member(f24(intersection(complement(X1),X2)),X1) ),
inference(spm,[status(thm)],[c_0_48,c_0_43]) ).
cnf(c_0_100,plain,
( X1 = empty_set
| ~ member(X2,f24(X1))
| ~ member(X2,X1) ),
inference(spm,[status(thm)],[c_0_33,c_0_90]) ).
cnf(c_0_101,axiom,
( subset(X1,X2)
| ~ member(f17(X1,X2),X2) ),
subset3 ).
cnf(c_0_102,plain,
( subset(X1,X2)
| little_set(f17(X1,X2)) ),
inference(spm,[status(thm)],[c_0_40,c_0_91]) ).
cnf(c_0_103,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_26,c_0_37]) ).
cnf(c_0_104,hypothesis,
~ member(f77,intersection(complement(f76),complement(non_ordered_pair(f76,f76)))),
inference(spm,[status(thm)],[c_0_48,c_0_92]) ).
cnf(c_0_105,hypothesis,
( member(f77,intersection(complement(X1),complement(X2)))
| member(f77,X1)
| member(f77,X2) ),
inference(spm,[status(thm)],[c_0_93,c_0_75]) ).
cnf(c_0_106,plain,
disjoint(X1,intersection(X2,complement(intersection(X2,X1)))),
inference(spm,[status(thm)],[c_0_59,c_0_94]) ).
cnf(c_0_107,hypothesis,
( member(f76,intersection(X1,natural_numbers))
| ~ member(f76,X1) ),
inference(spm,[status(thm)],[c_0_42,c_0_50]) ).
cnf(c_0_108,hypothesis,
disjoint(non_ordered_pair(f77,f77),non_ordered_pair(f76,f76)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_96]),c_0_73]) ).
cnf(c_0_109,plain,
( intersection(non_ordered_pair(X1,X1),X2) = empty_set
| member(X1,intersection(X2,non_ordered_pair(X3,X1))) ),
inference(spm,[status(thm)],[c_0_97,c_0_98]) ).
cnf(c_0_110,plain,
intersection(complement(X1),X1) = empty_set,
inference(spm,[status(thm)],[c_0_99,c_0_45]) ).
cnf(c_0_111,plain,
( X1 = empty_set
| subset(f24(X1),X2)
| ~ member(f17(f24(X1),X2),X1) ),
inference(spm,[status(thm)],[c_0_100,c_0_91]) ).
cnf(c_0_112,plain,
( subset(X1,complement(X2))
| member(f17(X1,complement(X2)),X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_101,c_0_56]),c_0_102]) ).
cnf(c_0_113,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_100,c_0_103]) ).
cnf(c_0_114,hypothesis,
( member(f77,non_ordered_pair(f76,f76))
| member(f77,f76) ),
inference(spm,[status(thm)],[c_0_104,c_0_105]) ).
cnf(c_0_115,plain,
( ~ member(X1,intersection(X2,complement(intersection(X2,X3))))
| ~ member(X1,X3) ),
inference(spm,[status(thm)],[c_0_33,c_0_106]) ).
cnf(c_0_116,hypothesis,
( member(f76,intersection(complement(X1),natural_numbers))
| member(f76,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_107,c_0_56]),c_0_61])]) ).
cnf(c_0_117,hypothesis,
( ~ member(X1,non_ordered_pair(f76,f76))
| ~ member(X1,non_ordered_pair(f77,f77)) ),
inference(spm,[status(thm)],[c_0_33,c_0_108]) ).
cnf(c_0_118,hypothesis,
member(f76,non_ordered_pair(X1,f76)),
inference(spm,[status(thm)],[c_0_82,c_0_61]) ).
cnf(c_0_119,plain,
( member(X1,intersection(X2,non_ordered_pair(X1,X3)))
| ~ member(X1,X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_39]),c_0_40]) ).
cnf(c_0_120,plain,
intersection(non_ordered_pair(X1,X1),complement(non_ordered_pair(X2,X1))) = empty_set,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_109,c_0_110]),c_0_73]) ).
cnf(c_0_121,axiom,
( member(X3,X2)
| ~ subset(X1,X2)
| ~ member(X3,X1) ),
subset1 ).
cnf(c_0_122,plain,
( X1 = empty_set
| subset(f24(X1),complement(X1)) ),
inference(spm,[status(thm)],[c_0_111,c_0_112]) ).
cnf(c_0_123,hypothesis,
( f24(non_ordered_pair(f77,X1)) = f77
| non_ordered_pair(f77,X1) = empty_set
| ~ member(f77,X1) ),
inference(spm,[status(thm)],[c_0_113,c_0_63]) ).
cnf(c_0_124,hypothesis,
member(f77,f76),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_114]),c_0_81]) ).
cnf(c_0_125,hypothesis,
( ~ member(X1,intersection(complement(f77),complement(intersection(complement(f76),complement(non_ordered_pair(f76,f76))))))
| ~ member(X1,complement(non_ordered_pair(f77,f77))) ),
inference(spm,[status(thm)],[c_0_115,c_0_76]) ).
cnf(c_0_126,hypothesis,
( member(f76,complement(X1))
| member(f76,X1) ),
inference(spm,[status(thm)],[c_0_36,c_0_116]) ).
cnf(c_0_127,hypothesis,
~ member(f76,non_ordered_pair(f77,f77)),
inference(spm,[status(thm)],[c_0_117,c_0_118]) ).
cnf(c_0_128,plain,
( member(X1,intersection(non_ordered_pair(X1,X2),non_ordered_pair(X1,X3)))
| ~ little_set(X1) ),
inference(spm,[status(thm)],[c_0_119,c_0_39]) ).
cnf(c_0_129,plain,
disjoint(non_ordered_pair(X1,X1),complement(non_ordered_pair(X2,X1))),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_120]),c_0_73]) ).
cnf(c_0_130,axiom,
( member(X1,powerset(X2))
| ~ little_set(X1)
| ~ subset(X1,X2) ),
powerset2 ).
cnf(c_0_131,plain,
subset(X1,X1),
inference(spm,[status(thm)],[c_0_101,c_0_91]) ).
cnf(c_0_132,plain,
( X1 = empty_set
| member(X2,complement(X1))
| ~ member(X2,f24(X1)) ),
inference(spm,[status(thm)],[c_0_121,c_0_122]) ).
cnf(c_0_133,hypothesis,
( f24(non_ordered_pair(f77,f76)) = f77
| non_ordered_pair(f77,f76) = empty_set ),
inference(spm,[status(thm)],[c_0_123,c_0_124]) ).
cnf(c_0_134,hypothesis,
~ member(f76,intersection(complement(f77),complement(intersection(complement(f76),complement(non_ordered_pair(f76,f76)))))),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_125,c_0_126]),c_0_127]) ).
cnf(c_0_135,plain,
( member(X1,intersection(complement(X2),complement(X3)))
| member(X1,X2)
| member(X1,X3)
| ~ little_set(X1) ),
inference(spm,[status(thm)],[c_0_93,c_0_56]) ).
cnf(c_0_136,plain,
~ member(X1,intersection(X2,complement(non_ordered_pair(X1,X3)))),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_128]),c_0_40]) ).
cnf(c_0_137,plain,
( ~ member(X1,complement(non_ordered_pair(X2,X3)))
| ~ member(X1,non_ordered_pair(X3,X3)) ),
inference(spm,[status(thm)],[c_0_33,c_0_129]) ).
cnf(c_0_138,plain,
( member(X1,powerset(X1))
| ~ little_set(X1) ),
inference(spm,[status(thm)],[c_0_130,c_0_131]) ).
cnf(c_0_139,hypothesis,
( non_ordered_pair(f77,f76) = empty_set
| member(X1,complement(non_ordered_pair(f77,f76)))
| ~ member(X1,f77) ),
inference(spm,[status(thm)],[c_0_132,c_0_133]) ).
cnf(c_0_140,hypothesis,
member(f76,f77),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_134,c_0_135]),c_0_61])]),c_0_136]) ).
cnf(c_0_141,plain,
~ member(X1,complement(non_ordered_pair(X2,X1))),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_137,c_0_39]),c_0_40]) ).
cnf(c_0_142,plain,
( member(X1,intersection(powerset(X1),non_ordered_pair(X1,X2)))
| ~ little_set(X1) ),
inference(spm,[status(thm)],[c_0_119,c_0_138]) ).
cnf(c_0_143,hypothesis,
non_ordered_pair(f77,f76) = empty_set,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_139,c_0_140]),c_0_141]) ).
cnf(c_0_144,plain,
intersection(X1,empty_set) = empty_set,
inference(spm,[status(thm)],[c_0_73,c_0_45]) ).
cnf(c_0_145,hypothesis,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_142,c_0_143]),c_0_144]),c_0_53])]),c_0_73]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : NUM012-1 : TPTP v8.1.2. Bugfixed v1.2.1.
% 0.00/0.14 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.14/0.36 % Computer : n022.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Fri Aug 25 14:48:40 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.21/0.59 start to proof: theBenchmark
% 126.79/126.81 % Version : CSE_E---1.5
% 126.79/126.81 % Problem : theBenchmark.p
% 126.79/126.81 % Proof found
% 126.79/126.81 % SZS status Theorem for theBenchmark.p
% 126.79/126.81 % SZS output start Proof
% See solution above
% 126.79/126.82 % Total time : 126.195000 s
% 126.79/126.82 % SZS output end Proof
% 126.79/126.82 % Total time : 126.208000 s
%------------------------------------------------------------------------------