TSTP Solution File: NUM012-1 by E---3.1
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : E---3.1
% Problem : NUM012-1 : TPTP v8.1.2. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n019.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 18:45:45 EDT 2023
% Result : Unsatisfiable 874.71s 189.61s
% Output : CNFRefutation 874.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 26
% Syntax : Number of clauses : 146 ( 44 unt; 61 nHn; 72 RR)
% Number of literals : 290 ( 80 equ; 93 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 4 con; 0-2 aty)
% Number of variables : 261 ( 41 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(non_ordered_pair1,axiom,
( X1 = X2
| X1 = X3
| ~ member(X1,non_ordered_pair(X2,X3)) ),
file('/export/starexec/sandbox/tmp/tmp.IYPFPaStVy/E---3.1_18151.p',non_ordered_pair1) ).
cnf(disjoint3,axiom,
( disjoint(X1,X2)
| member(f23(X1,X2),X2) ),
file('/export/starexec/sandbox/tmp/tmp.IYPFPaStVy/E---3.1_18151.p',disjoint3) ).
cnf(disjoint2,axiom,
( disjoint(X1,X2)
| member(f23(X1,X2),X1) ),
file('/export/starexec/sandbox/tmp/tmp.IYPFPaStVy/E---3.1_18151.p',disjoint2) ).
cnf(disjoint1,axiom,
( ~ disjoint(X1,X2)
| ~ member(X3,X1)
| ~ member(X3,X2) ),
file('/export/starexec/sandbox/tmp/tmp.IYPFPaStVy/E---3.1_18151.p',disjoint1) ).
cnf(non_ordered_pair2,axiom,
( member(X1,non_ordered_pair(X2,X3))
| ~ little_set(X1)
| X1 != X2 ),
file('/export/starexec/sandbox/tmp/tmp.IYPFPaStVy/E---3.1_18151.p',non_ordered_pair2) ).
cnf(intersection1,axiom,
( member(X1,X2)
| ~ member(X1,intersection(X2,X3)) ),
file('/export/starexec/sandbox/tmp/tmp.IYPFPaStVy/E---3.1_18151.p',intersection1) ).
cnf(regularity1,axiom,
( X1 = empty_set
| member(f24(X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.IYPFPaStVy/E---3.1_18151.p',regularity1) ).
cnf(a2,axiom,
( little_set(X1)
| ~ member(X1,X2) ),
file('/export/starexec/sandbox/tmp/tmp.IYPFPaStVy/E---3.1_18151.p',a2) ).
cnf(intersection2,axiom,
( member(X1,X3)
| ~ member(X1,intersection(X2,X3)) ),
file('/export/starexec/sandbox/tmp/tmp.IYPFPaStVy/E---3.1_18151.p',intersection2) ).
cnf(intersection3,axiom,
( member(X1,intersection(X2,X3))
| ~ member(X1,X2)
| ~ member(X1,X3) ),
file('/export/starexec/sandbox/tmp/tmp.IYPFPaStVy/E---3.1_18151.p',intersection3) ).
cnf(another_natural_number,hypothesis,
member(f77,natural_numbers),
file('/export/starexec/sandbox/tmp/tmp.IYPFPaStVy/E---3.1_18151.p',another_natural_number) ).
cnf(complement1,axiom,
( ~ member(X1,complement(X2))
| ~ member(X1,X2) ),
file('/export/starexec/sandbox/tmp/tmp.IYPFPaStVy/E---3.1_18151.p',complement1) ).
cnf(a_natural_number,hypothesis,
member(f76,natural_numbers),
file('/export/starexec/sandbox/tmp/tmp.IYPFPaStVy/E---3.1_18151.p',a_natural_number) ).
cnf(complement2,axiom,
( member(X1,complement(X2))
| member(X1,X2)
| ~ little_set(X1) ),
file('/export/starexec/sandbox/tmp/tmp.IYPFPaStVy/E---3.1_18151.p',complement2) ).
cnf(successor,axiom,
successor(X1) = union(X1,singleton_set(X1)),
file('/export/starexec/sandbox/tmp/tmp.IYPFPaStVy/E---3.1_18151.p',successor) ).
cnf(singleton_set,axiom,
singleton_set(X1) = non_ordered_pair(X1,X1),
file('/export/starexec/sandbox/tmp/tmp.IYPFPaStVy/E---3.1_18151.p',singleton_set) ).
cnf(successors_are_equal,hypothesis,
successor(f76) = successor(f77),
file('/export/starexec/sandbox/tmp/tmp.IYPFPaStVy/E---3.1_18151.p',successors_are_equal) ).
cnf(union,axiom,
union(X1,X2) = complement(intersection(complement(X1),complement(X2))),
file('/export/starexec/sandbox/tmp/tmp.IYPFPaStVy/E---3.1_18151.p',union) ).
cnf(empty_set,axiom,
~ member(X1,empty_set),
file('/export/starexec/sandbox/tmp/tmp.IYPFPaStVy/E---3.1_18151.p',empty_set) ).
cnf(non_ordered_pair3,axiom,
( member(X1,non_ordered_pair(X2,X3))
| ~ little_set(X1)
| X1 != X3 ),
file('/export/starexec/sandbox/tmp/tmp.IYPFPaStVy/E---3.1_18151.p',non_ordered_pair3) ).
cnf(prove_well_definedness_of_successor,negated_conjecture,
f76 != f77,
file('/export/starexec/sandbox/tmp/tmp.IYPFPaStVy/E---3.1_18151.p',prove_well_definedness_of_successor) ).
cnf(regularity2,axiom,
( X1 = empty_set
| disjoint(f24(X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.IYPFPaStVy/E---3.1_18151.p',regularity2) ).
cnf(subset2,axiom,
( subset(X1,X2)
| member(f17(X1,X2),X1) ),
file('/export/starexec/sandbox/tmp/tmp.IYPFPaStVy/E---3.1_18151.p',subset2) ).
cnf(subset3,axiom,
( subset(X1,X2)
| ~ member(f17(X1,X2),X2) ),
file('/export/starexec/sandbox/tmp/tmp.IYPFPaStVy/E---3.1_18151.p',subset3) ).
cnf(subset1,axiom,
( member(X3,X2)
| ~ subset(X1,X2)
| ~ member(X3,X1) ),
file('/export/starexec/sandbox/tmp/tmp.IYPFPaStVy/E---3.1_18151.p',subset1) ).
cnf(powerset2,axiom,
( member(X1,powerset(X2))
| ~ little_set(X1)
| ~ subset(X1,X2) ),
file('/export/starexec/sandbox/tmp/tmp.IYPFPaStVy/E---3.1_18151.p',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
% 0.13/0.14 % Problem : NUM012-1 : TPTP v8.1.2. Bugfixed v1.2.1.
% 0.13/0.16 % Command : run_E %s %d THM
% 0.15/0.37 % Computer : n019.cluster.edu
% 0.15/0.37 % Model : x86_64 x86_64
% 0.15/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37 % Memory : 8042.1875MB
% 0.15/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37 % CPULimit : 2400
% 0.15/0.37 % WCLimit : 300
% 0.15/0.37 % DateTime : Mon Oct 2 14:31:21 EDT 2023
% 0.15/0.37 % CPUTime :
% 0.22/0.52 Running first-order theorem proving
% 0.22/0.52 Running: /export/starexec/sandbox/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/tmp/tmp.IYPFPaStVy/E---3.1_18151.p
% 874.71/189.61 # Version: 3.1pre001
% 874.71/189.61 # Preprocessing class: FSLMSMSMSSSNFFN.
% 874.71/189.61 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 874.71/189.61 # Starting G-E--_207_C18_F1_AE_CS_SP_PI_PS_S2S with 1200s (4) cores
% 874.71/189.61 # Starting new_bool_3 with 600s (2) cores
% 874.71/189.61 # Starting new_bool_1 with 300s (1) cores
% 874.71/189.61 # Starting sh5l with 300s (1) cores
% 874.71/189.61 # new_bool_3 with pid 18294 completed with status 8
% 874.71/189.61 # new_bool_1 with pid 18295 completed with status 8
% 874.71/189.61 # G-E--_207_C18_F1_AE_CS_SP_PI_PS_S2S with pid 18293 completed with status 0
% 874.71/189.61 # Result found by G-E--_207_C18_F1_AE_CS_SP_PI_PS_S2S
% 874.71/189.61 # Preprocessing class: FSLMSMSMSSSNFFN.
% 874.71/189.61 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 874.71/189.61 # Starting G-E--_207_C18_F1_AE_CS_SP_PI_PS_S2S with 1200s (4) cores
% 874.71/189.61 # No SInE strategy applied
% 874.71/189.61 # Search class: FGHSF-FSLM31-DFFFFFNN
% 874.71/189.61 # partial match(1): FGHSF-FSLM31-MFFFFFNN
% 874.71/189.61 # Scheduled 6 strats onto 4 cores with 1200 seconds (1200 total)
% 874.71/189.61 # Starting G-E--_110_C45_F1_PI_AE_Q4_CS_SP_PS_S4S with 649s (1) cores
% 874.71/189.61 # Starting G-E--_207_C18_F1_AE_CS_SP_PI_PS_S2S with 121s (1) cores
% 874.71/189.61 # Starting SAT001_MinMin_p005000_rr_RG with 109s (1) cores
% 874.71/189.61 # Starting G-E--_301_C18_F1_URBAN_S5PRR_RG_S070I with 109s (1) cores
% 874.71/189.61 # G-E--_301_C18_F1_URBAN_S5PRR_RG_S070I with pid 18314 completed with status 7
% 874.71/189.61 # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_RG_S2S with 109s (1) cores
% 874.71/189.61 # SAT001_MinMin_p005000_rr_RG with pid 18313 completed with status 7
% 874.71/189.61 # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y with 103s (1) cores
% 874.71/189.61 # G-E--_207_C18_F1_AE_CS_SP_PI_PS_S2S with pid 18311 completed with status 7
% 874.71/189.61 # G-E--_110_C45_F1_PI_AE_Q4_CS_SP_PS_S4S with pid 18310 completed with status 0
% 874.71/189.61 # Result found by G-E--_110_C45_F1_PI_AE_Q4_CS_SP_PS_S4S
% 874.71/189.61 # Preprocessing class: FSLMSMSMSSSNFFN.
% 874.71/189.61 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 874.71/189.61 # Starting G-E--_207_C18_F1_AE_CS_SP_PI_PS_S2S with 1200s (4) cores
% 874.71/189.61 # No SInE strategy applied
% 874.71/189.61 # Search class: FGHSF-FSLM31-DFFFFFNN
% 874.71/189.61 # partial match(1): FGHSF-FSLM31-MFFFFFNN
% 874.71/189.61 # Scheduled 6 strats onto 4 cores with 1200 seconds (1200 total)
% 874.71/189.61 # Starting G-E--_110_C45_F1_PI_AE_Q4_CS_SP_PS_S4S with 649s (1) cores
% 874.71/189.61 # Preprocessing time : 0.006 s
% 874.71/189.61 # Presaturation interreduction done
% 874.71/189.61
% 874.71/189.61 # Proof found!
% 874.71/189.61 # SZS status Unsatisfiable
% 874.71/189.61 # SZS output start CNFRefutation
% See solution above
% 874.71/189.61 # Parsed axioms : 223
% 874.71/189.61 # Removed by relevancy pruning/SinE : 0
% 874.71/189.61 # Initial clauses : 223
% 874.71/189.61 # Removed in clause preprocessing : 6
% 874.71/189.61 # Initial clauses in saturation : 217
% 874.71/189.61 # Processed clauses : 191014
% 874.71/189.61 # ...of these trivial : 3830
% 874.71/189.61 # ...subsumed : 158991
% 874.71/189.61 # ...remaining for further processing : 28193
% 874.71/189.61 # Other redundant clauses eliminated : 734
% 874.71/189.61 # Clauses deleted for lack of memory : 223547
% 874.71/189.61 # Backward-subsumed : 862
% 874.71/189.61 # Backward-rewritten : 619
% 874.71/189.61 # Generated clauses : 8282487
% 874.71/189.61 # ...of the previous two non-redundant : 7101009
% 874.71/189.61 # ...aggressively subsumed : 0
% 874.71/189.61 # Contextual simplify-reflections : 373
% 874.71/189.61 # Paramodulations : 8281294
% 874.71/189.61 # Factorizations : 385
% 874.71/189.61 # NegExts : 0
% 874.71/189.61 # Equation resolutions : 778
% 874.71/189.61 # Total rewrite steps : 2613438
% 874.71/189.61 # Propositional unsat checks : 0
% 874.71/189.61 # Propositional check models : 0
% 874.71/189.61 # Propositional check unsatisfiable : 0
% 874.71/189.61 # Propositional clauses : 0
% 874.71/189.61 # Propositional clauses after purity: 0
% 874.71/189.61 # Propositional unsat core size : 0
% 874.71/189.61 # Propositional preprocessing time : 0.000
% 874.71/189.61 # Propositional encoding time : 0.000
% 874.71/189.61 # Propositional solver time : 0.000
% 874.71/189.61 # Success case prop preproc time : 0.000
% 874.71/189.61 # Success case prop encoding time : 0.000
% 874.71/189.61 # Success case prop solver time : 0.000
% 874.71/189.61 # Current number of processed clauses : 26462
% 874.71/189.61 # Positive orientable unit clauses : 7174
% 874.71/189.61 # Positive unorientable unit clauses: 0
% 874.71/189.61 # Negative unit clauses : 1588
% 874.71/189.61 # Non-unit-clauses : 17700
% 874.71/189.61 # Current number of unprocessed clauses: 1619180
% 874.71/189.61 # ...number of literals in the above : 3953681
% 874.71/189.61 # Current number of archived formulas : 0
% 874.71/189.61 # Current number of archived clauses : 1734
% 874.71/189.61 # Clause-clause subsumption calls (NU) : 69054467
% 874.71/189.61 # Rec. Clause-clause subsumption calls : 22962011
% 874.71/189.61 # Non-unit clause-clause subsumptions : 63189
% 874.71/189.61 # Unit Clause-clause subsumption calls : 4109088
% 874.71/189.61 # Rewrite failures with RHS unbound : 0
% 874.71/189.61 # BW rewrite match attempts : 1911578
% 874.71/189.61 # BW rewrite match successes : 337
% 874.71/189.61 # Condensation attempts : 0
% 874.71/189.61 # Condensation successes : 0
% 874.71/189.61 # Termbank termtop insertions : 281459085
% 874.71/189.61
% 874.71/189.61 # -------------------------------------------------
% 874.71/189.61 # User time : 519.430 s
% 874.71/189.61 # System time : 8.083 s
% 874.71/189.61 # Total time : 527.513 s
% 874.71/189.61 # Maximum resident set size: 2372 pages
% 874.71/189.61
% 874.71/189.61 # -------------------------------------------------
% 874.71/189.61 # User time : 674.653 s
% 874.71/189.61 # System time : 11.435 s
% 874.71/189.61 # Total time : 686.088 s
% 874.71/189.61 # Maximum resident set size: 1884 pages
% 874.71/189.61 % E---3.1 exiting
% 874.71/189.61 % E---3.1 exiting
%------------------------------------------------------------------------------