TSTP Solution File: NUM387+1 by Bliksem---1.12
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%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : NUM387+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %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 : 0s
% DateTime : Mon Jul 18 06:21:52 EDT 2022
% Result : Theorem 0.75s 1.15s
% Output : Refutation 0.75s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13 % Problem : NUM387+1 : TPTP v8.1.0. Released v3.2.0.
% 0.11/0.14 % Command : bliksem %s
% 0.14/0.35 % Computer : n013.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % DateTime : Tue Jul 5 11:49:59 EDT 2022
% 0.14/0.36 % CPUTime :
% 0.75/1.15 *** allocated 10000 integers for termspace/termends
% 0.75/1.15 *** allocated 10000 integers for clauses
% 0.75/1.15 *** allocated 10000 integers for justifications
% 0.75/1.15 Bliksem 1.12
% 0.75/1.15
% 0.75/1.15
% 0.75/1.15 Automatic Strategy Selection
% 0.75/1.15
% 0.75/1.15
% 0.75/1.15 Clauses:
% 0.75/1.15
% 0.75/1.15 { ! in( X, Y ), ! in( Y, X ) }.
% 0.75/1.15 { ! empty( X ), function( X ) }.
% 0.75/1.15 { ! empty( X ), relation( X ) }.
% 0.75/1.15 { ! relation( X ), ! empty( X ), ! function( X ), relation( X ) }.
% 0.75/1.15 { ! relation( X ), ! empty( X ), ! function( X ), function( X ) }.
% 0.75/1.15 { ! relation( X ), ! empty( X ), ! function( X ), one_to_one( X ) }.
% 0.75/1.15 { set_union2( X, Y ) = set_union2( Y, X ) }.
% 0.75/1.15 { succ( X ) = set_union2( X, singleton( X ) ) }.
% 0.75/1.15 { element( skol1( X ), X ) }.
% 0.75/1.15 { empty( empty_set ) }.
% 0.75/1.15 { relation( empty_set ) }.
% 0.75/1.15 { relation_empty_yielding( empty_set ) }.
% 0.75/1.15 { ! empty( succ( X ) ) }.
% 0.75/1.15 { empty( empty_set ) }.
% 0.75/1.15 { ! relation( X ), ! relation( Y ), relation( set_union2( X, Y ) ) }.
% 0.75/1.15 { empty( X ), ! empty( set_union2( X, Y ) ) }.
% 0.75/1.15 { empty( X ), ! empty( set_union2( Y, X ) ) }.
% 0.75/1.15 { empty( empty_set ) }.
% 0.75/1.15 { relation( empty_set ) }.
% 0.75/1.15 { set_union2( X, X ) = X }.
% 0.75/1.15 { relation( skol2 ) }.
% 0.75/1.15 { function( skol2 ) }.
% 0.75/1.15 { empty( skol3 ) }.
% 0.75/1.15 { relation( skol3 ) }.
% 0.75/1.15 { empty( skol4 ) }.
% 0.75/1.15 { relation( skol5 ) }.
% 0.75/1.15 { empty( skol5 ) }.
% 0.75/1.15 { function( skol5 ) }.
% 0.75/1.15 { ! empty( skol6 ) }.
% 0.75/1.15 { relation( skol6 ) }.
% 0.75/1.15 { ! empty( skol7 ) }.
% 0.75/1.15 { relation( skol8 ) }.
% 0.75/1.15 { function( skol8 ) }.
% 0.75/1.15 { one_to_one( skol8 ) }.
% 0.75/1.15 { relation( skol9 ) }.
% 0.75/1.15 { relation_empty_yielding( skol9 ) }.
% 0.75/1.15 { relation( skol10 ) }.
% 0.75/1.15 { relation_empty_yielding( skol10 ) }.
% 0.75/1.15 { function( skol10 ) }.
% 0.75/1.15 { relation( skol11 ) }.
% 0.75/1.15 { relation_non_empty( skol11 ) }.
% 0.75/1.15 { function( skol11 ) }.
% 0.75/1.15 { in( X, succ( X ) ) }.
% 0.75/1.15 { skol12 = succ( skol12 ) }.
% 0.75/1.15 { set_union2( X, empty_set ) = X }.
% 0.75/1.15 { ! in( X, Y ), element( X, Y ) }.
% 0.75/1.15 { ! element( X, Y ), empty( Y ), in( X, Y ) }.
% 0.75/1.15 { ! empty( X ), X = empty_set }.
% 0.75/1.15 { ! in( X, Y ), ! empty( Y ) }.
% 0.75/1.15 { ! empty( X ), X = Y, ! empty( Y ) }.
% 0.75/1.15
% 0.75/1.15 percentage equality = 0.112903, percentage horn = 0.977778
% 0.75/1.15 This is a problem with some equality
% 0.75/1.15
% 0.75/1.15
% 0.75/1.15
% 0.75/1.15 Options Used:
% 0.75/1.15
% 0.75/1.15 useres = 1
% 0.75/1.15 useparamod = 1
% 0.75/1.15 useeqrefl = 1
% 0.75/1.15 useeqfact = 1
% 0.75/1.15 usefactor = 1
% 0.75/1.15 usesimpsplitting = 0
% 0.75/1.15 usesimpdemod = 5
% 0.75/1.15 usesimpres = 3
% 0.75/1.15
% 0.75/1.15 resimpinuse = 1000
% 0.75/1.15 resimpclauses = 20000
% 0.75/1.15 substype = eqrewr
% 0.75/1.15 backwardsubs = 1
% 0.75/1.15 selectoldest = 5
% 0.75/1.15
% 0.75/1.15 litorderings [0] = split
% 0.75/1.15 litorderings [1] = extend the termordering, first sorting on arguments
% 0.75/1.15
% 0.75/1.15 termordering = kbo
% 0.75/1.15
% 0.75/1.15 litapriori = 0
% 0.75/1.15 termapriori = 1
% 0.75/1.15 litaposteriori = 0
% 0.75/1.15 termaposteriori = 0
% 0.75/1.15 demodaposteriori = 0
% 0.75/1.15 ordereqreflfact = 0
% 0.75/1.15
% 0.75/1.15 litselect = negord
% 0.75/1.15
% 0.75/1.15 maxweight = 15
% 0.75/1.15 maxdepth = 30000
% 0.75/1.15 maxlength = 115
% 0.75/1.15 maxnrvars = 195
% 0.75/1.15 excuselevel = 1
% 0.75/1.15 increasemaxweight = 1
% 0.75/1.15
% 0.75/1.15 maxselected = 10000000
% 0.75/1.15 maxnrclauses = 10000000
% 0.75/1.15
% 0.75/1.15 showgenerated = 0
% 0.75/1.15 showkept = 0
% 0.75/1.15 showselected = 0
% 0.75/1.15 showdeleted = 0
% 0.75/1.15 showresimp = 1
% 0.75/1.15 showstatus = 2000
% 0.75/1.15
% 0.75/1.15 prologoutput = 0
% 0.75/1.15 nrgoals = 5000000
% 0.75/1.15 totalproof = 1
% 0.75/1.15
% 0.75/1.15 Symbols occurring in the translation:
% 0.75/1.15
% 0.75/1.15 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.75/1.15 . [1, 2] (w:1, o:34, a:1, s:1, b:0),
% 0.75/1.15 ! [4, 1] (w:0, o:20, a:1, s:1, b:0),
% 0.75/1.15 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.75/1.15 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.75/1.15 in [37, 2] (w:1, o:58, a:1, s:1, b:0),
% 0.75/1.15 empty [38, 1] (w:1, o:25, a:1, s:1, b:0),
% 0.75/1.15 function [39, 1] (w:1, o:26, a:1, s:1, b:0),
% 0.75/1.15 relation [40, 1] (w:1, o:27, a:1, s:1, b:0),
% 0.75/1.15 one_to_one [41, 1] (w:1, o:28, a:1, s:1, b:0),
% 0.75/1.15 set_union2 [42, 2] (w:1, o:59, a:1, s:1, b:0),
% 0.75/1.15 succ [43, 1] (w:1, o:31, a:1, s:1, b:0),
% 0.75/1.15 singleton [44, 1] (w:1, o:32, a:1, s:1, b:0),
% 0.75/1.15 element [45, 2] (w:1, o:60, a:1, s:1, b:0),
% 0.75/1.15 empty_set [46, 0] (w:1, o:8, a:1, s:1, b:0),
% 0.75/1.15 relation_empty_yielding [47, 1] (w:1, o:29, a:1, s:1, b:0),
% 0.75/1.15 relation_non_empty [48, 1] (w:1, o:30, a:1, s:1, b:0),
% 0.75/1.15 skol1 [49, 1] (w:1, o:33, a:1, s:1, b:1),
% 0.75/1.15 skol2 [50, 0] (w:1, o:12, a:1, s:1, b:1),
% 0.75/1.15 skol3 [51, 0] (w:1, o:13, a:1, s:1, b:1),
% 0.75/1.15 skol4 [52, 0] (w:1, o:14, a:1, s:1, b:1),
% 0.75/1.15 skol5 [53, 0] (w:1, o:15, a:1, s:1, b:1),
% 0.75/1.15 skol6 [54, 0] (w:1, o:16, a:1, s:1, b:1),
% 0.75/1.15 skol7 [55, 0] (w:1, o:17, a:1, s:1, b:1),
% 0.75/1.15 skol8 [56, 0] (w:1, o:18, a:1, s:1, b:1),
% 0.75/1.15 skol9 [57, 0] (w:1, o:19, a:1, s:1, b:1),
% 0.75/1.15 skol10 [58, 0] (w:1, o:9, a:1, s:1, b:1),
% 0.75/1.15 skol11 [59, 0] (w:1, o:10, a:1, s:1, b:1),
% 0.75/1.15 skol12 [60, 0] (w:1, o:11, a:1, s:1, b:1).
% 0.75/1.15
% 0.75/1.15
% 0.75/1.15 Starting Search:
% 0.75/1.15
% 0.75/1.15
% 0.75/1.15 Bliksems!, er is een bewijs:
% 0.75/1.15 % SZS status Theorem
% 0.75/1.15 % SZS output start Refutation
% 0.75/1.15
% 0.75/1.15 (0) {G0,W6,D2,L2,V2,M2} I { ! in( X, Y ), ! in( Y, X ) }.
% 0.75/1.15 (37) {G0,W4,D3,L1,V1,M1} I { in( X, succ( X ) ) }.
% 0.75/1.15 (38) {G0,W4,D3,L1,V0,M1} I { succ( skol12 ) ==> skol12 }.
% 0.75/1.15 (45) {G1,W3,D2,L1,V1,M1} F(0) { ! in( X, X ) }.
% 0.75/1.15 (109) {G2,W0,D0,L0,V0,M0} P(38,37);r(45) { }.
% 0.75/1.15
% 0.75/1.15
% 0.75/1.15 % SZS output end Refutation
% 0.75/1.15 found a proof!
% 0.75/1.15
% 0.75/1.15
% 0.75/1.15 Unprocessed initial clauses:
% 0.75/1.15
% 0.75/1.15 (111) {G0,W6,D2,L2,V2,M2} { ! in( X, Y ), ! in( Y, X ) }.
% 0.75/1.15 (112) {G0,W4,D2,L2,V1,M2} { ! empty( X ), function( X ) }.
% 0.75/1.15 (113) {G0,W4,D2,L2,V1,M2} { ! empty( X ), relation( X ) }.
% 0.75/1.15 (114) {G0,W8,D2,L4,V1,M4} { ! relation( X ), ! empty( X ), ! function( X )
% 0.75/1.15 , relation( X ) }.
% 0.75/1.15 (115) {G0,W8,D2,L4,V1,M4} { ! relation( X ), ! empty( X ), ! function( X )
% 0.75/1.15 , function( X ) }.
% 0.75/1.15 (116) {G0,W8,D2,L4,V1,M4} { ! relation( X ), ! empty( X ), ! function( X )
% 0.75/1.15 , one_to_one( X ) }.
% 0.75/1.15 (117) {G0,W7,D3,L1,V2,M1} { set_union2( X, Y ) = set_union2( Y, X ) }.
% 0.75/1.15 (118) {G0,W7,D4,L1,V1,M1} { succ( X ) = set_union2( X, singleton( X ) )
% 0.75/1.15 }.
% 0.75/1.15 (119) {G0,W4,D3,L1,V1,M1} { element( skol1( X ), X ) }.
% 0.75/1.15 (120) {G0,W2,D2,L1,V0,M1} { empty( empty_set ) }.
% 0.75/1.15 (121) {G0,W2,D2,L1,V0,M1} { relation( empty_set ) }.
% 0.75/1.15 (122) {G0,W2,D2,L1,V0,M1} { relation_empty_yielding( empty_set ) }.
% 0.75/1.15 (123) {G0,W3,D3,L1,V1,M1} { ! empty( succ( X ) ) }.
% 0.75/1.15 (124) {G0,W2,D2,L1,V0,M1} { empty( empty_set ) }.
% 0.75/1.15 (125) {G0,W8,D3,L3,V2,M3} { ! relation( X ), ! relation( Y ), relation(
% 0.75/1.15 set_union2( X, Y ) ) }.
% 0.75/1.15 (126) {G0,W6,D3,L2,V2,M2} { empty( X ), ! empty( set_union2( X, Y ) ) }.
% 0.75/1.15 (127) {G0,W6,D3,L2,V2,M2} { empty( X ), ! empty( set_union2( Y, X ) ) }.
% 0.75/1.15 (128) {G0,W2,D2,L1,V0,M1} { empty( empty_set ) }.
% 0.75/1.15 (129) {G0,W2,D2,L1,V0,M1} { relation( empty_set ) }.
% 0.75/1.15 (130) {G0,W5,D3,L1,V1,M1} { set_union2( X, X ) = X }.
% 0.75/1.15 (131) {G0,W2,D2,L1,V0,M1} { relation( skol2 ) }.
% 0.75/1.15 (132) {G0,W2,D2,L1,V0,M1} { function( skol2 ) }.
% 0.75/1.15 (133) {G0,W2,D2,L1,V0,M1} { empty( skol3 ) }.
% 0.75/1.15 (134) {G0,W2,D2,L1,V0,M1} { relation( skol3 ) }.
% 0.75/1.15 (135) {G0,W2,D2,L1,V0,M1} { empty( skol4 ) }.
% 0.75/1.15 (136) {G0,W2,D2,L1,V0,M1} { relation( skol5 ) }.
% 0.75/1.15 (137) {G0,W2,D2,L1,V0,M1} { empty( skol5 ) }.
% 0.75/1.15 (138) {G0,W2,D2,L1,V0,M1} { function( skol5 ) }.
% 0.75/1.15 (139) {G0,W2,D2,L1,V0,M1} { ! empty( skol6 ) }.
% 0.75/1.15 (140) {G0,W2,D2,L1,V0,M1} { relation( skol6 ) }.
% 0.75/1.15 (141) {G0,W2,D2,L1,V0,M1} { ! empty( skol7 ) }.
% 0.75/1.15 (142) {G0,W2,D2,L1,V0,M1} { relation( skol8 ) }.
% 0.75/1.15 (143) {G0,W2,D2,L1,V0,M1} { function( skol8 ) }.
% 0.75/1.15 (144) {G0,W2,D2,L1,V0,M1} { one_to_one( skol8 ) }.
% 0.75/1.15 (145) {G0,W2,D2,L1,V0,M1} { relation( skol9 ) }.
% 0.75/1.15 (146) {G0,W2,D2,L1,V0,M1} { relation_empty_yielding( skol9 ) }.
% 0.75/1.15 (147) {G0,W2,D2,L1,V0,M1} { relation( skol10 ) }.
% 0.75/1.15 (148) {G0,W2,D2,L1,V0,M1} { relation_empty_yielding( skol10 ) }.
% 0.75/1.15 (149) {G0,W2,D2,L1,V0,M1} { function( skol10 ) }.
% 0.75/1.15 (150) {G0,W2,D2,L1,V0,M1} { relation( skol11 ) }.
% 0.75/1.15 (151) {G0,W2,D2,L1,V0,M1} { relation_non_empty( skol11 ) }.
% 0.75/1.15 (152) {G0,W2,D2,L1,V0,M1} { function( skol11 ) }.
% 0.75/1.15 (153) {G0,W4,D3,L1,V1,M1} { in( X, succ( X ) ) }.
% 0.75/1.15 (154) {G0,W4,D3,L1,V0,M1} { skol12 = succ( skol12 ) }.
% 0.75/1.15 (155) {G0,W5,D3,L1,V1,M1} { set_union2( X, empty_set ) = X }.
% 0.75/1.15 (156) {G0,W6,D2,L2,V2,M2} { ! in( X, Y ), element( X, Y ) }.
% 0.75/1.15 (157) {G0,W8,D2,L3,V2,M3} { ! element( X, Y ), empty( Y ), in( X, Y ) }.
% 0.75/1.15 (158) {G0,W5,D2,L2,V1,M2} { ! empty( X ), X = empty_set }.
% 0.75/1.15 (159) {G0,W5,D2,L2,V2,M2} { ! in( X, Y ), ! empty( Y ) }.
% 0.75/1.15 (160) {G0,W7,D2,L3,V2,M3} { ! empty( X ), X = Y, ! empty( Y ) }.
% 0.75/1.15
% 0.75/1.15
% 0.75/1.15 Total Proof:
% 0.75/1.15
% 0.75/1.15 subsumption: (0) {G0,W6,D2,L2,V2,M2} I { ! in( X, Y ), ! in( Y, X ) }.
% 0.75/1.15 parent0: (111) {G0,W6,D2,L2,V2,M2} { ! in( X, Y ), ! in( Y, X ) }.
% 0.75/1.15 substitution0:
% 0.75/1.15 X := X
% 0.75/1.15 Y := Y
% 0.75/1.15 end
% 0.75/1.15 permutation0:
% 0.75/1.15 0 ==> 0
% 0.75/1.15 1 ==> 1
% 0.75/1.15 end
% 0.75/1.15
% 0.75/1.15 subsumption: (37) {G0,W4,D3,L1,V1,M1} I { in( X, succ( X ) ) }.
% 0.75/1.15 parent0: (153) {G0,W4,D3,L1,V1,M1} { in( X, succ( X ) ) }.
% 0.75/1.15 substitution0:
% 0.75/1.15 X := X
% 0.75/1.15 end
% 0.75/1.15 permutation0:
% 0.75/1.15 0 ==> 0
% 0.75/1.15 end
% 0.75/1.15
% 0.75/1.15 eqswap: (170) {G0,W4,D3,L1,V0,M1} { succ( skol12 ) = skol12 }.
% 0.75/1.15 parent0[0]: (154) {G0,W4,D3,L1,V0,M1} { skol12 = succ( skol12 ) }.
% 0.75/1.15 substitution0:
% 0.75/1.15 end
% 0.75/1.15
% 0.75/1.15 subsumption: (38) {G0,W4,D3,L1,V0,M1} I { succ( skol12 ) ==> skol12 }.
% 0.75/1.15 parent0: (170) {G0,W4,D3,L1,V0,M1} { succ( skol12 ) = skol12 }.
% 0.75/1.15 substitution0:
% 0.75/1.15 end
% 0.75/1.15 permutation0:
% 0.75/1.15 0 ==> 0
% 0.75/1.15 end
% 0.75/1.15
% 0.75/1.15 factor: (171) {G0,W3,D2,L1,V1,M1} { ! in( X, X ) }.
% 0.75/1.15 parent0[0, 1]: (0) {G0,W6,D2,L2,V2,M2} I { ! in( X, Y ), ! in( Y, X ) }.
% 0.75/1.15 substitution0:
% 0.75/1.15 X := X
% 0.75/1.15 Y := X
% 0.75/1.15 end
% 0.75/1.15
% 0.75/1.15 subsumption: (45) {G1,W3,D2,L1,V1,M1} F(0) { ! in( X, X ) }.
% 0.75/1.15 parent0: (171) {G0,W3,D2,L1,V1,M1} { ! in( X, X ) }.
% 0.75/1.15 substitution0:
% 0.75/1.15 X := X
% 0.75/1.15 end
% 0.75/1.15 permutation0:
% 0.75/1.15 0 ==> 0
% 0.75/1.15 end
% 0.75/1.15
% 0.75/1.15 paramod: (173) {G1,W3,D2,L1,V0,M1} { in( skol12, skol12 ) }.
% 0.75/1.15 parent0[0]: (38) {G0,W4,D3,L1,V0,M1} I { succ( skol12 ) ==> skol12 }.
% 0.75/1.15 parent1[0; 2]: (37) {G0,W4,D3,L1,V1,M1} I { in( X, succ( X ) ) }.
% 0.75/1.15 substitution0:
% 0.75/1.15 end
% 0.75/1.15 substitution1:
% 0.75/1.15 X := skol12
% 0.75/1.15 end
% 0.75/1.15
% 0.75/1.15 resolution: (174) {G2,W0,D0,L0,V0,M0} { }.
% 0.75/1.15 parent0[0]: (45) {G1,W3,D2,L1,V1,M1} F(0) { ! in( X, X ) }.
% 0.75/1.15 parent1[0]: (173) {G1,W3,D2,L1,V0,M1} { in( skol12, skol12 ) }.
% 0.75/1.15 substitution0:
% 0.75/1.15 X := skol12
% 0.75/1.15 end
% 0.75/1.15 substitution1:
% 0.75/1.15 end
% 0.75/1.15
% 0.75/1.15 subsumption: (109) {G2,W0,D0,L0,V0,M0} P(38,37);r(45) { }.
% 0.75/1.15 parent0: (174) {G2,W0,D0,L0,V0,M0} { }.
% 0.75/1.15 substitution0:
% 0.75/1.15 end
% 0.75/1.15 permutation0:
% 0.75/1.15 end
% 0.75/1.15
% 0.75/1.15 Proof check complete!
% 0.75/1.15
% 0.75/1.15 Memory use:
% 0.75/1.15
% 0.75/1.15 space for terms: 1259
% 0.75/1.15 space for clauses: 5494
% 0.75/1.15
% 0.75/1.15
% 0.75/1.15 clauses generated: 167
% 0.75/1.15 clauses kept: 110
% 0.75/1.15 clauses selected: 52
% 0.75/1.15 clauses deleted: 1
% 0.75/1.15 clauses inuse deleted: 0
% 0.75/1.15
% 0.75/1.15 subsentry: 142
% 0.75/1.15 literals s-matched: 95
% 0.75/1.15 literals matched: 95
% 0.75/1.15 full subsumption: 14
% 0.75/1.15
% 0.75/1.15 checksum: -1649628019
% 0.75/1.15
% 0.75/1.15
% 0.75/1.15 Bliksem ended
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