TSTP Solution File: NUM405+1 by Bliksem---1.12
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%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : NUM405+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n020.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 06:21:58 EDT 2022
% Result : Theorem 0.69s 1.16s
% Output : Refutation 0.69s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : NUM405+1 : TPTP v8.1.0. Released v3.2.0.
% 0.07/0.13 % Command : bliksem %s
% 0.13/0.34 % Computer : n020.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % DateTime : Wed Jul 6 12:30:44 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.69/1.15 *** allocated 10000 integers for termspace/termends
% 0.69/1.15 *** allocated 10000 integers for clauses
% 0.69/1.15 *** allocated 10000 integers for justifications
% 0.69/1.15 Bliksem 1.12
% 0.69/1.15
% 0.69/1.15
% 0.69/1.15 Automatic Strategy Selection
% 0.69/1.15
% 0.69/1.15
% 0.69/1.15 Clauses:
% 0.69/1.15
% 0.69/1.15 { ! in( X, Y ), ! in( Y, X ) }.
% 0.69/1.15 { ! empty( X ), function( X ) }.
% 0.69/1.15 { ! ordinal( X ), epsilon_transitive( X ) }.
% 0.69/1.15 { ! ordinal( X ), epsilon_connected( X ) }.
% 0.69/1.15 { ! empty( X ), relation( X ) }.
% 0.69/1.15 { ! relation( X ), ! empty( X ), ! function( X ), relation( X ) }.
% 0.69/1.15 { ! relation( X ), ! empty( X ), ! function( X ), function( X ) }.
% 0.69/1.15 { ! relation( X ), ! empty( X ), ! function( X ), one_to_one( X ) }.
% 0.69/1.15 { ! epsilon_transitive( X ), ! epsilon_connected( X ), ordinal( X ) }.
% 0.69/1.15 { ! empty( X ), epsilon_transitive( X ) }.
% 0.69/1.15 { ! empty( X ), epsilon_connected( X ) }.
% 0.69/1.15 { ! empty( X ), ordinal( X ) }.
% 0.69/1.15 { element( skol1( X ), X ) }.
% 0.69/1.15 { empty( empty_set ) }.
% 0.69/1.15 { relation( empty_set ) }.
% 0.69/1.15 { relation_empty_yielding( empty_set ) }.
% 0.69/1.15 { empty( empty_set ) }.
% 0.69/1.15 { relation( empty_set ) }.
% 0.69/1.15 { relation_empty_yielding( empty_set ) }.
% 0.69/1.15 { function( empty_set ) }.
% 0.69/1.15 { one_to_one( empty_set ) }.
% 0.69/1.15 { empty( empty_set ) }.
% 0.69/1.15 { epsilon_transitive( empty_set ) }.
% 0.69/1.15 { epsilon_connected( empty_set ) }.
% 0.69/1.15 { ordinal( empty_set ) }.
% 0.69/1.15 { empty( empty_set ) }.
% 0.69/1.15 { relation( empty_set ) }.
% 0.69/1.15 { relation( skol2 ) }.
% 0.69/1.15 { function( skol2 ) }.
% 0.69/1.15 { epsilon_transitive( skol3 ) }.
% 0.69/1.15 { epsilon_connected( skol3 ) }.
% 0.69/1.15 { ordinal( skol3 ) }.
% 0.69/1.15 { empty( skol4 ) }.
% 0.69/1.15 { relation( skol4 ) }.
% 0.69/1.15 { empty( skol5 ) }.
% 0.69/1.15 { relation( skol6 ) }.
% 0.69/1.15 { empty( skol6 ) }.
% 0.69/1.15 { function( skol6 ) }.
% 0.69/1.15 { relation( skol7 ) }.
% 0.69/1.15 { function( skol7 ) }.
% 0.69/1.15 { one_to_one( skol7 ) }.
% 0.69/1.15 { empty( skol7 ) }.
% 0.69/1.15 { epsilon_transitive( skol7 ) }.
% 0.69/1.15 { epsilon_connected( skol7 ) }.
% 0.69/1.15 { ordinal( skol7 ) }.
% 0.69/1.15 { ! empty( skol8 ) }.
% 0.69/1.15 { relation( skol8 ) }.
% 0.69/1.15 { ! empty( skol9 ) }.
% 0.69/1.15 { relation( skol10 ) }.
% 0.69/1.15 { function( skol10 ) }.
% 0.69/1.15 { one_to_one( skol10 ) }.
% 0.69/1.15 { ! empty( skol11 ) }.
% 0.69/1.15 { epsilon_transitive( skol11 ) }.
% 0.69/1.15 { epsilon_connected( skol11 ) }.
% 0.69/1.15 { ordinal( skol11 ) }.
% 0.69/1.15 { relation( skol12 ) }.
% 0.69/1.15 { relation_empty_yielding( skol12 ) }.
% 0.69/1.15 { relation( skol13 ) }.
% 0.69/1.15 { relation_empty_yielding( skol13 ) }.
% 0.69/1.15 { function( skol13 ) }.
% 0.69/1.15 { relation( skol14 ) }.
% 0.69/1.15 { relation_non_empty( skol14 ) }.
% 0.69/1.15 { function( skol14 ) }.
% 0.69/1.15 { ! in( Y, skol15( X ) ), in( Y, X ) }.
% 0.69/1.15 { ! in( Y, skol15( X ) ), ordinal( Y ) }.
% 0.69/1.15 { ! in( Y, X ), ! ordinal( Y ), in( Y, skol15( X ) ) }.
% 0.69/1.15 { ! in( X, Y ), element( X, Y ) }.
% 0.69/1.15 { ! element( X, Y ), empty( Y ), in( X, Y ) }.
% 0.69/1.15 { alpha1( X, skol16( X ) ), ordinal( skol16( X ) ) }.
% 0.69/1.15 { alpha1( X, skol16( X ) ), ! in( skol16( X ), X ) }.
% 0.69/1.15 { ! alpha1( X, Y ), in( Y, X ) }.
% 0.69/1.15 { ! alpha1( X, Y ), ! ordinal( Y ) }.
% 0.69/1.15 { ! in( Y, X ), ordinal( Y ), alpha1( X, Y ) }.
% 0.69/1.15 { ! ordinal( X ), in( X, skol17 ) }.
% 0.69/1.15 { ! empty( X ), X = empty_set }.
% 0.69/1.15 { ! in( X, Y ), ! empty( Y ) }.
% 0.69/1.15 { ! empty( X ), X = Y, ! empty( Y ) }.
% 0.69/1.15
% 0.69/1.15 percentage equality = 0.020000, percentage horn = 0.956522
% 0.69/1.15 This is a problem with some equality
% 0.69/1.15
% 0.69/1.15
% 0.69/1.15
% 0.69/1.15 Options Used:
% 0.69/1.15
% 0.69/1.15 useres = 1
% 0.69/1.15 useparamod = 1
% 0.69/1.15 useeqrefl = 1
% 0.69/1.15 useeqfact = 1
% 0.69/1.15 usefactor = 1
% 0.69/1.15 usesimpsplitting = 0
% 0.69/1.15 usesimpdemod = 5
% 0.69/1.15 usesimpres = 3
% 0.69/1.15
% 0.69/1.15 resimpinuse = 1000
% 0.69/1.15 resimpclauses = 20000
% 0.69/1.15 substype = eqrewr
% 0.69/1.15 backwardsubs = 1
% 0.69/1.15 selectoldest = 5
% 0.69/1.15
% 0.69/1.15 litorderings [0] = split
% 0.69/1.15 litorderings [1] = extend the termordering, first sorting on arguments
% 0.69/1.15
% 0.69/1.15 termordering = kbo
% 0.69/1.15
% 0.69/1.15 litapriori = 0
% 0.69/1.15 termapriori = 1
% 0.69/1.15 litaposteriori = 0
% 0.69/1.15 termaposteriori = 0
% 0.69/1.15 demodaposteriori = 0
% 0.69/1.15 ordereqreflfact = 0
% 0.69/1.15
% 0.69/1.15 litselect = negord
% 0.69/1.15
% 0.69/1.15 maxweight = 15
% 0.69/1.15 maxdepth = 30000
% 0.69/1.15 maxlength = 115
% 0.69/1.15 maxnrvars = 195
% 0.69/1.15 excuselevel = 1
% 0.69/1.15 increasemaxweight = 1
% 0.69/1.15
% 0.69/1.15 maxselected = 10000000
% 0.69/1.15 maxnrclauses = 10000000
% 0.69/1.15
% 0.69/1.15 showgenerated = 0
% 0.69/1.15 showkept = 0
% 0.69/1.15 showselected = 0
% 0.69/1.15 showdeleted = 0
% 0.69/1.15 showresimp = 1
% 0.69/1.15 showstatus = 2000
% 0.69/1.15
% 0.69/1.15 prologoutput = 0
% 0.69/1.15 nrgoals = 5000000
% 0.69/1.15 totalproof = 1
% 0.69/1.15
% 0.69/1.15 Symbols occurring in the translation:
% 0.69/1.15
% 0.69/1.15 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.69/1.15 . [1, 2] (w:1, o:41, a:1, s:1, b:0),
% 0.69/1.15 ! [4, 1] (w:0, o:24, a:1, s:1, b:0),
% 0.69/1.15 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.69/1.15 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.69/1.16 in [37, 2] (w:1, o:65, a:1, s:1, b:0),
% 0.69/1.16 empty [38, 1] (w:1, o:29, a:1, s:1, b:0),
% 0.69/1.16 function [39, 1] (w:1, o:32, a:1, s:1, b:0),
% 0.69/1.16 ordinal [40, 1] (w:1, o:33, a:1, s:1, b:0),
% 0.69/1.16 epsilon_transitive [41, 1] (w:1, o:30, a:1, s:1, b:0),
% 0.69/1.16 epsilon_connected [42, 1] (w:1, o:31, a:1, s:1, b:0),
% 0.69/1.16 relation [43, 1] (w:1, o:34, a:1, s:1, b:0),
% 0.69/1.16 one_to_one [44, 1] (w:1, o:35, a:1, s:1, b:0),
% 0.69/1.16 element [45, 2] (w:1, o:66, a:1, s:1, b:0),
% 0.69/1.16 empty_set [46, 0] (w:1, o:8, a:1, s:1, b:0),
% 0.69/1.16 relation_empty_yielding [47, 1] (w:1, o:36, a:1, s:1, b:0),
% 0.69/1.16 relation_non_empty [48, 1] (w:1, o:37, a:1, s:1, b:0),
% 0.69/1.16 alpha1 [50, 2] (w:1, o:67, a:1, s:1, b:1),
% 0.69/1.16 skol1 [51, 1] (w:1, o:38, a:1, s:1, b:1),
% 0.69/1.16 skol2 [52, 0] (w:1, o:16, a:1, s:1, b:1),
% 0.69/1.16 skol3 [53, 0] (w:1, o:17, a:1, s:1, b:1),
% 0.69/1.16 skol4 [54, 0] (w:1, o:18, a:1, s:1, b:1),
% 0.69/1.16 skol5 [55, 0] (w:1, o:19, a:1, s:1, b:1),
% 0.69/1.16 skol6 [56, 0] (w:1, o:20, a:1, s:1, b:1),
% 0.69/1.16 skol7 [57, 0] (w:1, o:21, a:1, s:1, b:1),
% 0.69/1.16 skol8 [58, 0] (w:1, o:22, a:1, s:1, b:1),
% 0.69/1.16 skol9 [59, 0] (w:1, o:23, a:1, s:1, b:1),
% 0.69/1.16 skol10 [60, 0] (w:1, o:10, a:1, s:1, b:1),
% 0.69/1.16 skol11 [61, 0] (w:1, o:11, a:1, s:1, b:1),
% 0.69/1.16 skol12 [62, 0] (w:1, o:12, a:1, s:1, b:1),
% 0.69/1.16 skol13 [63, 0] (w:1, o:13, a:1, s:1, b:1),
% 0.69/1.16 skol14 [64, 0] (w:1, o:14, a:1, s:1, b:1),
% 0.69/1.16 skol15 [65, 1] (w:1, o:39, a:1, s:1, b:1),
% 0.69/1.16 skol16 [66, 1] (w:1, o:40, a:1, s:1, b:1),
% 0.69/1.16 skol17 [67, 0] (w:1, o:15, a:1, s:1, b:1).
% 0.69/1.16
% 0.69/1.16
% 0.69/1.16 Starting Search:
% 0.69/1.16
% 0.69/1.16 *** allocated 15000 integers for clauses
% 0.69/1.16 *** allocated 22500 integers for clauses
% 0.69/1.16 *** allocated 33750 integers for clauses
% 0.69/1.16 *** allocated 50625 integers for clauses
% 0.69/1.16 Resimplifying inuse:
% 0.69/1.16 *** allocated 15000 integers for termspace/termends
% 0.69/1.16 Done
% 0.69/1.16
% 0.69/1.16 *** allocated 75937 integers for clauses
% 0.69/1.16
% 0.69/1.16 Bliksems!, er is een bewijs:
% 0.69/1.16 % SZS status Theorem
% 0.69/1.16 % SZS output start Refutation
% 0.69/1.16
% 0.69/1.16 (0) {G0,W6,D2,L2,V2,M2} I { ! in( X, Y ), ! in( Y, X ) }.
% 0.69/1.16 (9) {G0,W4,D2,L2,V1,M2} I { ! empty( X ), ordinal( X ) }.
% 0.69/1.16 (56) {G0,W6,D3,L2,V2,M2} I { ! in( Y, skol15( X ) ), ordinal( Y ) }.
% 0.69/1.16 (57) {G0,W9,D3,L3,V2,M3} I { ! in( Y, X ), ! ordinal( Y ), in( Y, skol15( X
% 0.69/1.16 ) ) }.
% 0.69/1.16 (58) {G0,W6,D2,L2,V2,M2} I { ! in( X, Y ), element( X, Y ) }.
% 0.69/1.16 (59) {G0,W8,D2,L3,V2,M3} I { ! element( X, Y ), empty( Y ), in( X, Y ) }.
% 0.69/1.16 (60) {G0,W7,D3,L2,V1,M2} I { alpha1( X, skol16( X ) ), ordinal( skol16( X )
% 0.69/1.16 ) }.
% 0.69/1.16 (61) {G0,W8,D3,L2,V1,M2} I { alpha1( X, skol16( X ) ), ! in( skol16( X ), X
% 0.69/1.16 ) }.
% 0.69/1.16 (62) {G0,W6,D2,L2,V2,M2} I { ! alpha1( X, Y ), in( Y, X ) }.
% 0.69/1.16 (63) {G0,W5,D2,L2,V2,M2} I { ! alpha1( X, Y ), ! ordinal( Y ) }.
% 0.69/1.16 (65) {G0,W5,D2,L2,V1,M2} I { ! ordinal( X ), in( X, skol17 ) }.
% 0.69/1.16 (67) {G0,W5,D2,L2,V2,M2} I { ! in( X, Y ), ! empty( Y ) }.
% 0.69/1.16 (69) {G1,W3,D2,L1,V1,M1} F(0) { ! in( X, X ) }.
% 0.69/1.16 (134) {G1,W9,D3,L3,V2,M3} R(59,56) { ! element( X, skol15( Y ) ), empty(
% 0.69/1.16 skol15( Y ) ), ordinal( X ) }.
% 0.69/1.16 (161) {G1,W13,D3,L3,V2,M3} R(60,57) { alpha1( X, skol16( X ) ), ! in(
% 0.69/1.16 skol16( X ), Y ), in( skol16( X ), skol15( Y ) ) }.
% 0.69/1.16 (187) {G1,W6,D2,L2,V2,M2} R(62,58) { ! alpha1( X, Y ), element( Y, X ) }.
% 0.69/1.16 (193) {G1,W5,D2,L2,V2,M2} R(62,67) { ! alpha1( X, Y ), ! empty( X ) }.
% 0.69/1.16 (213) {G1,W5,D2,L2,V1,M2} R(65,58) { ! ordinal( X ), element( X, skol17 )
% 0.69/1.16 }.
% 0.69/1.16 (217) {G2,W2,D2,L1,V0,M1} R(65,69) { ! ordinal( skol17 ) }.
% 0.69/1.16 (230) {G3,W2,D2,L1,V0,M1} R(217,9) { ! empty( skol17 ) }.
% 0.69/1.16 (233) {G4,W6,D2,L2,V1,M2} R(230,59) { ! element( X, skol17 ), in( X, skol17
% 0.69/1.16 ) }.
% 0.69/1.16 (433) {G2,W5,D3,L2,V1,M2} R(193,60) { ! empty( X ), ordinal( skol16( X ) )
% 0.69/1.16 }.
% 0.69/1.16 (682) {G2,W7,D3,L2,V1,M2} R(187,60) { element( skol16( X ), X ), ordinal(
% 0.69/1.16 skol16( X ) ) }.
% 0.69/1.16 (729) {G3,W10,D4,L3,V2,M3} R(134,433) { ! element( X, skol15( Y ) ),
% 0.69/1.16 ordinal( X ), ordinal( skol16( skol15( Y ) ) ) }.
% 0.69/1.16 (759) {G4,W4,D4,L1,V1,M1} F(729);r(682) { ordinal( skol16( skol15( X ) ) )
% 0.69/1.16 }.
% 0.69/1.16 (765) {G5,W5,D4,L1,V1,M1} R(759,213) { element( skol16( skol15( X ) ),
% 0.69/1.16 skol17 ) }.
% 0.69/1.16 (769) {G5,W5,D4,L1,V2,M1} R(759,63) { ! alpha1( X, skol16( skol15( Y ) ) )
% 0.69/1.16 }.
% 0.69/1.16 (1453) {G6,W5,D4,L1,V1,M1} R(161,61);f;r(769) { ! in( skol16( skol15( X ) )
% 0.69/1.16 , X ) }.
% 0.69/1.16 (1463) {G7,W0,D0,L0,V0,M0} R(1453,233);r(765) { }.
% 0.69/1.16
% 0.69/1.16
% 0.69/1.16 % SZS output end Refutation
% 0.69/1.16 found a proof!
% 0.69/1.16
% 0.69/1.16 *** allocated 22500 integers for termspace/termends
% 0.69/1.16
% 0.69/1.16 Unprocessed initial clauses:
% 0.69/1.16
% 0.69/1.16 (1465) {G0,W6,D2,L2,V2,M2} { ! in( X, Y ), ! in( Y, X ) }.
% 0.69/1.16 (1466) {G0,W4,D2,L2,V1,M2} { ! empty( X ), function( X ) }.
% 0.69/1.16 (1467) {G0,W4,D2,L2,V1,M2} { ! ordinal( X ), epsilon_transitive( X ) }.
% 0.69/1.16 (1468) {G0,W4,D2,L2,V1,M2} { ! ordinal( X ), epsilon_connected( X ) }.
% 0.69/1.16 (1469) {G0,W4,D2,L2,V1,M2} { ! empty( X ), relation( X ) }.
% 0.69/1.16 (1470) {G0,W8,D2,L4,V1,M4} { ! relation( X ), ! empty( X ), ! function( X
% 0.69/1.16 ), relation( X ) }.
% 0.69/1.16 (1471) {G0,W8,D2,L4,V1,M4} { ! relation( X ), ! empty( X ), ! function( X
% 0.69/1.16 ), function( X ) }.
% 0.69/1.16 (1472) {G0,W8,D2,L4,V1,M4} { ! relation( X ), ! empty( X ), ! function( X
% 0.69/1.16 ), one_to_one( X ) }.
% 0.69/1.16 (1473) {G0,W6,D2,L3,V1,M3} { ! epsilon_transitive( X ), !
% 0.69/1.16 epsilon_connected( X ), ordinal( X ) }.
% 0.69/1.16 (1474) {G0,W4,D2,L2,V1,M2} { ! empty( X ), epsilon_transitive( X ) }.
% 0.69/1.16 (1475) {G0,W4,D2,L2,V1,M2} { ! empty( X ), epsilon_connected( X ) }.
% 0.69/1.16 (1476) {G0,W4,D2,L2,V1,M2} { ! empty( X ), ordinal( X ) }.
% 0.69/1.16 (1477) {G0,W4,D3,L1,V1,M1} { element( skol1( X ), X ) }.
% 0.69/1.16 (1478) {G0,W2,D2,L1,V0,M1} { empty( empty_set ) }.
% 0.69/1.16 (1479) {G0,W2,D2,L1,V0,M1} { relation( empty_set ) }.
% 0.69/1.16 (1480) {G0,W2,D2,L1,V0,M1} { relation_empty_yielding( empty_set ) }.
% 0.69/1.16 (1481) {G0,W2,D2,L1,V0,M1} { empty( empty_set ) }.
% 0.69/1.16 (1482) {G0,W2,D2,L1,V0,M1} { relation( empty_set ) }.
% 0.69/1.16 (1483) {G0,W2,D2,L1,V0,M1} { relation_empty_yielding( empty_set ) }.
% 0.69/1.16 (1484) {G0,W2,D2,L1,V0,M1} { function( empty_set ) }.
% 0.69/1.16 (1485) {G0,W2,D2,L1,V0,M1} { one_to_one( empty_set ) }.
% 0.69/1.16 (1486) {G0,W2,D2,L1,V0,M1} { empty( empty_set ) }.
% 0.69/1.16 (1487) {G0,W2,D2,L1,V0,M1} { epsilon_transitive( empty_set ) }.
% 0.69/1.16 (1488) {G0,W2,D2,L1,V0,M1} { epsilon_connected( empty_set ) }.
% 0.69/1.16 (1489) {G0,W2,D2,L1,V0,M1} { ordinal( empty_set ) }.
% 0.69/1.16 (1490) {G0,W2,D2,L1,V0,M1} { empty( empty_set ) }.
% 0.69/1.16 (1491) {G0,W2,D2,L1,V0,M1} { relation( empty_set ) }.
% 0.69/1.16 (1492) {G0,W2,D2,L1,V0,M1} { relation( skol2 ) }.
% 0.69/1.16 (1493) {G0,W2,D2,L1,V0,M1} { function( skol2 ) }.
% 0.69/1.16 (1494) {G0,W2,D2,L1,V0,M1} { epsilon_transitive( skol3 ) }.
% 0.69/1.16 (1495) {G0,W2,D2,L1,V0,M1} { epsilon_connected( skol3 ) }.
% 0.69/1.16 (1496) {G0,W2,D2,L1,V0,M1} { ordinal( skol3 ) }.
% 0.69/1.16 (1497) {G0,W2,D2,L1,V0,M1} { empty( skol4 ) }.
% 0.69/1.16 (1498) {G0,W2,D2,L1,V0,M1} { relation( skol4 ) }.
% 0.69/1.16 (1499) {G0,W2,D2,L1,V0,M1} { empty( skol5 ) }.
% 0.69/1.16 (1500) {G0,W2,D2,L1,V0,M1} { relation( skol6 ) }.
% 0.69/1.16 (1501) {G0,W2,D2,L1,V0,M1} { empty( skol6 ) }.
% 0.69/1.16 (1502) {G0,W2,D2,L1,V0,M1} { function( skol6 ) }.
% 0.69/1.16 (1503) {G0,W2,D2,L1,V0,M1} { relation( skol7 ) }.
% 0.69/1.16 (1504) {G0,W2,D2,L1,V0,M1} { function( skol7 ) }.
% 0.69/1.16 (1505) {G0,W2,D2,L1,V0,M1} { one_to_one( skol7 ) }.
% 0.69/1.16 (1506) {G0,W2,D2,L1,V0,M1} { empty( skol7 ) }.
% 0.69/1.16 (1507) {G0,W2,D2,L1,V0,M1} { epsilon_transitive( skol7 ) }.
% 0.69/1.16 (1508) {G0,W2,D2,L1,V0,M1} { epsilon_connected( skol7 ) }.
% 0.69/1.16 (1509) {G0,W2,D2,L1,V0,M1} { ordinal( skol7 ) }.
% 0.69/1.16 (1510) {G0,W2,D2,L1,V0,M1} { ! empty( skol8 ) }.
% 0.69/1.16 (1511) {G0,W2,D2,L1,V0,M1} { relation( skol8 ) }.
% 0.69/1.16 (1512) {G0,W2,D2,L1,V0,M1} { ! empty( skol9 ) }.
% 0.69/1.16 (1513) {G0,W2,D2,L1,V0,M1} { relation( skol10 ) }.
% 0.69/1.16 (1514) {G0,W2,D2,L1,V0,M1} { function( skol10 ) }.
% 0.69/1.16 (1515) {G0,W2,D2,L1,V0,M1} { one_to_one( skol10 ) }.
% 0.69/1.16 (1516) {G0,W2,D2,L1,V0,M1} { ! empty( skol11 ) }.
% 0.69/1.16 (1517) {G0,W2,D2,L1,V0,M1} { epsilon_transitive( skol11 ) }.
% 0.69/1.16 (1518) {G0,W2,D2,L1,V0,M1} { epsilon_connected( skol11 ) }.
% 0.69/1.16 (1519) {G0,W2,D2,L1,V0,M1} { ordinal( skol11 ) }.
% 0.69/1.16 (1520) {G0,W2,D2,L1,V0,M1} { relation( skol12 ) }.
% 0.69/1.16 (1521) {G0,W2,D2,L1,V0,M1} { relation_empty_yielding( skol12 ) }.
% 0.69/1.16 (1522) {G0,W2,D2,L1,V0,M1} { relation( skol13 ) }.
% 0.69/1.16 (1523) {G0,W2,D2,L1,V0,M1} { relation_empty_yielding( skol13 ) }.
% 0.69/1.16 (1524) {G0,W2,D2,L1,V0,M1} { function( skol13 ) }.
% 0.69/1.16 (1525) {G0,W2,D2,L1,V0,M1} { relation( skol14 ) }.
% 0.69/1.16 (1526) {G0,W2,D2,L1,V0,M1} { relation_non_empty( skol14 ) }.
% 0.69/1.16 (1527) {G0,W2,D2,L1,V0,M1} { function( skol14 ) }.
% 0.69/1.16 (1528) {G0,W7,D3,L2,V2,M2} { ! in( Y, skol15( X ) ), in( Y, X ) }.
% 0.69/1.16 (1529) {G0,W6,D3,L2,V2,M2} { ! in( Y, skol15( X ) ), ordinal( Y ) }.
% 0.69/1.16 (1530) {G0,W9,D3,L3,V2,M3} { ! in( Y, X ), ! ordinal( Y ), in( Y, skol15(
% 0.69/1.16 X ) ) }.
% 0.69/1.16 (1531) {G0,W6,D2,L2,V2,M2} { ! in( X, Y ), element( X, Y ) }.
% 0.69/1.16 (1532) {G0,W8,D2,L3,V2,M3} { ! element( X, Y ), empty( Y ), in( X, Y ) }.
% 0.69/1.16 (1533) {G0,W7,D3,L2,V1,M2} { alpha1( X, skol16( X ) ), ordinal( skol16( X
% 0.69/1.16 ) ) }.
% 0.69/1.16 (1534) {G0,W8,D3,L2,V1,M2} { alpha1( X, skol16( X ) ), ! in( skol16( X ),
% 0.69/1.16 X ) }.
% 0.69/1.16 (1535) {G0,W6,D2,L2,V2,M2} { ! alpha1( X, Y ), in( Y, X ) }.
% 0.69/1.16 (1536) {G0,W5,D2,L2,V2,M2} { ! alpha1( X, Y ), ! ordinal( Y ) }.
% 0.69/1.16 (1537) {G0,W8,D2,L3,V2,M3} { ! in( Y, X ), ordinal( Y ), alpha1( X, Y )
% 0.69/1.16 }.
% 0.69/1.16 (1538) {G0,W5,D2,L2,V1,M2} { ! ordinal( X ), in( X, skol17 ) }.
% 0.69/1.16 (1539) {G0,W5,D2,L2,V1,M2} { ! empty( X ), X = empty_set }.
% 0.69/1.16 (1540) {G0,W5,D2,L2,V2,M2} { ! in( X, Y ), ! empty( Y ) }.
% 0.69/1.16 (1541) {G0,W7,D2,L3,V2,M3} { ! empty( X ), X = Y, ! empty( Y ) }.
% 0.69/1.16
% 0.69/1.16
% 0.69/1.16 Total Proof:
% 0.69/1.16
% 0.69/1.16 subsumption: (0) {G0,W6,D2,L2,V2,M2} I { ! in( X, Y ), ! in( Y, X ) }.
% 0.69/1.16 parent0: (1465) {G0,W6,D2,L2,V2,M2} { ! in( X, Y ), ! in( Y, X ) }.
% 0.69/1.16 substitution0:
% 0.69/1.16 X := X
% 0.69/1.16 Y := Y
% 0.69/1.16 end
% 0.69/1.16 permutation0:
% 0.69/1.16 0 ==> 0
% 0.69/1.16 1 ==> 1
% 0.69/1.16 end
% 0.69/1.16
% 0.69/1.16 subsumption: (9) {G0,W4,D2,L2,V1,M2} I { ! empty( X ), ordinal( X ) }.
% 0.69/1.16 parent0: (1476) {G0,W4,D2,L2,V1,M2} { ! empty( X ), ordinal( X ) }.
% 0.69/1.16 substitution0:
% 0.69/1.16 X := X
% 0.69/1.16 end
% 0.69/1.16 permutation0:
% 0.69/1.16 0 ==> 0
% 0.69/1.16 1 ==> 1
% 0.69/1.16 end
% 0.69/1.16
% 0.69/1.16 subsumption: (56) {G0,W6,D3,L2,V2,M2} I { ! in( Y, skol15( X ) ), ordinal(
% 0.69/1.16 Y ) }.
% 0.69/1.16 parent0: (1529) {G0,W6,D3,L2,V2,M2} { ! in( Y, skol15( X ) ), ordinal( Y )
% 0.69/1.16 }.
% 0.69/1.16 substitution0:
% 0.69/1.16 X := X
% 0.69/1.16 Y := Y
% 0.69/1.16 end
% 0.69/1.16 permutation0:
% 0.69/1.16 0 ==> 0
% 0.69/1.16 1 ==> 1
% 0.69/1.16 end
% 0.69/1.16
% 0.69/1.16 subsumption: (57) {G0,W9,D3,L3,V2,M3} I { ! in( Y, X ), ! ordinal( Y ), in
% 0.69/1.16 ( Y, skol15( X ) ) }.
% 0.69/1.16 parent0: (1530) {G0,W9,D3,L3,V2,M3} { ! in( Y, X ), ! ordinal( Y ), in( Y
% 0.69/1.16 , skol15( X ) ) }.
% 0.69/1.16 substitution0:
% 0.69/1.16 X := X
% 0.69/1.16 Y := Y
% 0.69/1.16 end
% 0.69/1.16 permutation0:
% 0.69/1.16 0 ==> 0
% 0.69/1.16 1 ==> 1
% 0.69/1.16 2 ==> 2
% 0.69/1.16 end
% 0.69/1.16
% 0.69/1.16 subsumption: (58) {G0,W6,D2,L2,V2,M2} I { ! in( X, Y ), element( X, Y ) }.
% 0.69/1.16 parent0: (1531) {G0,W6,D2,L2,V2,M2} { ! in( X, Y ), element( X, Y ) }.
% 0.69/1.16 substitution0:
% 0.69/1.16 X := X
% 0.69/1.16 Y := Y
% 0.69/1.16 end
% 0.69/1.16 permutation0:
% 0.69/1.16 0 ==> 0
% 0.69/1.16 1 ==> 1
% 0.69/1.16 end
% 0.69/1.16
% 0.69/1.16 subsumption: (59) {G0,W8,D2,L3,V2,M3} I { ! element( X, Y ), empty( Y ), in
% 0.69/1.16 ( X, Y ) }.
% 0.69/1.16 parent0: (1532) {G0,W8,D2,L3,V2,M3} { ! element( X, Y ), empty( Y ), in( X
% 0.69/1.16 , Y ) }.
% 0.69/1.16 substitution0:
% 0.69/1.16 X := X
% 0.69/1.16 Y := Y
% 0.69/1.16 end
% 0.69/1.16 permutation0:
% 0.69/1.16 0 ==> 0
% 0.69/1.16 1 ==> 1
% 0.69/1.16 2 ==> 2
% 0.69/1.16 end
% 0.69/1.16
% 0.69/1.16 subsumption: (60) {G0,W7,D3,L2,V1,M2} I { alpha1( X, skol16( X ) ), ordinal
% 0.69/1.16 ( skol16( X ) ) }.
% 0.69/1.16 parent0: (1533) {G0,W7,D3,L2,V1,M2} { alpha1( X, skol16( X ) ), ordinal(
% 0.69/1.16 skol16( X ) ) }.
% 0.69/1.16 substitution0:
% 0.69/1.16 X := X
% 0.69/1.16 end
% 0.69/1.16 permutation0:
% 0.69/1.16 0 ==> 0
% 0.69/1.16 1 ==> 1
% 0.69/1.16 end
% 0.69/1.16
% 0.69/1.16 subsumption: (61) {G0,W8,D3,L2,V1,M2} I { alpha1( X, skol16( X ) ), ! in(
% 0.69/1.16 skol16( X ), X ) }.
% 0.69/1.16 parent0: (1534) {G0,W8,D3,L2,V1,M2} { alpha1( X, skol16( X ) ), ! in(
% 0.69/1.16 skol16( X ), X ) }.
% 0.69/1.16 substitution0:
% 0.69/1.16 X := X
% 0.69/1.16 end
% 0.69/1.16 permutation0:
% 0.69/1.16 0 ==> 0
% 0.69/1.16 1 ==> 1
% 0.69/1.16 end
% 0.69/1.16
% 0.69/1.16 subsumption: (62) {G0,W6,D2,L2,V2,M2} I { ! alpha1( X, Y ), in( Y, X ) }.
% 0.69/1.16 parent0: (1535) {G0,W6,D2,L2,V2,M2} { ! alpha1( X, Y ), in( Y, X ) }.
% 0.69/1.16 substitution0:
% 0.69/1.16 X := X
% 0.69/1.16 Y := Y
% 0.69/1.16 end
% 0.69/1.16 permutation0:
% 0.69/1.16 0 ==> 0
% 0.69/1.16 1 ==> 1
% 0.69/1.16 end
% 0.69/1.16
% 0.69/1.16 subsumption: (63) {G0,W5,D2,L2,V2,M2} I { ! alpha1( X, Y ), ! ordinal( Y )
% 0.69/1.16 }.
% 0.69/1.16 parent0: (1536) {G0,W5,D2,L2,V2,M2} { ! alpha1( X, Y ), ! ordinal( Y ) }.
% 0.69/1.16 substitution0:
% 0.69/1.16 X := X
% 0.69/1.16 Y := Y
% 0.69/1.16 end
% 0.69/1.16 permutation0:
% 0.69/1.16 0 ==> 0
% 0.69/1.16 1 ==> 1
% 0.69/1.16 end
% 0.69/1.16
% 0.69/1.16 subsumption: (65) {G0,W5,D2,L2,V1,M2} I { ! ordinal( X ), in( X, skol17 )
% 0.69/1.16 }.
% 0.69/1.16 parent0: (1538) {G0,W5,D2,L2,V1,M2} { ! ordinal( X ), in( X, skol17 ) }.
% 0.69/1.16 substitution0:
% 0.69/1.16 X := X
% 0.69/1.16 end
% 0.69/1.16 permutation0:
% 0.69/1.16 0 ==> 0
% 0.69/1.16 1 ==> 1
% 0.69/1.16 end
% 0.69/1.16
% 0.69/1.16 subsumption: (67) {G0,W5,D2,L2,V2,M2} I { ! in( X, Y ), ! empty( Y ) }.
% 0.69/1.16 parent0: (1540) {G0,W5,D2,L2,V2,M2} { ! in( X, Y ), ! empty( Y ) }.
% 0.69/1.16 substitution0:
% 0.69/1.16 X := X
% 0.69/1.16 Y := Y
% 0.69/1.16 end
% 0.69/1.16 permutation0:
% 0.69/1.16 0 ==> 0
% 0.69/1.16 1 ==> 1
% 0.69/1.16 end
% 0.69/1.16
% 0.69/1.16 factor: (1555) {G0,W3,D2,L1,V1,M1} { ! in( X, X ) }.
% 0.69/1.16 parent0[0, 1]: (0) {G0,W6,D2,L2,V2,M2} I { ! in( X, Y ), ! in( Y, X ) }.
% 0.69/1.16 substitution0:
% 0.69/1.16 X := X
% 0.69/1.16 Y := X
% 0.69/1.16 end
% 0.69/1.16
% 0.69/1.16 subsumption: (69) {G1,W3,D2,L1,V1,M1} F(0) { ! in( X, X ) }.
% 0.69/1.16 parent0: (1555) {G0,W3,D2,L1,V1,M1} { ! in( X, X ) }.
% 0.69/1.16 substitution0:
% 0.69/1.16 X := X
% 0.69/1.16 end
% 0.69/1.16 permutation0:
% 0.69/1.16 0 ==> 0
% 0.69/1.16 end
% 0.69/1.16
% 0.69/1.16 resolution: (1556) {G1,W9,D3,L3,V2,M3} { ordinal( X ), ! element( X,
% 0.69/1.16 skol15( Y ) ), empty( skol15( Y ) ) }.
% 0.69/1.16 parent0[0]: (56) {G0,W6,D3,L2,V2,M2} I { ! in( Y, skol15( X ) ), ordinal( Y
% 0.69/1.16 ) }.
% 0.69/1.16 parent1[2]: (59) {G0,W8,D2,L3,V2,M3} I { ! element( X, Y ), empty( Y ), in
% 0.69/1.16 ( X, Y ) }.
% 0.69/1.16 substitution0:
% 0.69/1.16 X := Y
% 0.69/1.16 Y := X
% 0.69/1.16 end
% 0.69/1.16 substitution1:
% 0.69/1.16 X := X
% 0.69/1.16 Y := skol15( Y )
% 0.69/1.16 end
% 0.69/1.16
% 0.69/1.16 subsumption: (134) {G1,W9,D3,L3,V2,M3} R(59,56) { ! element( X, skol15( Y )
% 0.69/1.16 ), empty( skol15( Y ) ), ordinal( X ) }.
% 0.69/1.16 parent0: (1556) {G1,W9,D3,L3,V2,M3} { ordinal( X ), ! element( X, skol15(
% 0.69/1.16 Y ) ), empty( skol15( Y ) ) }.
% 0.69/1.16 substitution0:
% 0.69/1.16 X := X
% 0.69/1.16 Y := Y
% 0.69/1.16 end
% 0.69/1.16 permutation0:
% 0.69/1.16 0 ==> 2
% 0.69/1.16 1 ==> 0
% 0.69/1.16 2 ==> 1
% 0.69/1.16 end
% 0.69/1.16
% 0.69/1.16 resolution: (1557) {G1,W13,D3,L3,V2,M3} { ! in( skol16( X ), Y ), in(
% 0.69/1.16 skol16( X ), skol15( Y ) ), alpha1( X, skol16( X ) ) }.
% 0.69/1.16 parent0[1]: (57) {G0,W9,D3,L3,V2,M3} I { ! in( Y, X ), ! ordinal( Y ), in(
% 0.69/1.16 Y, skol15( X ) ) }.
% 0.69/1.16 parent1[1]: (60) {G0,W7,D3,L2,V1,M2} I { alpha1( X, skol16( X ) ), ordinal
% 0.69/1.16 ( skol16( X ) ) }.
% 0.69/1.16 substitution0:
% 0.69/1.16 X := Y
% 0.69/1.16 Y := skol16( X )
% 0.69/1.16 end
% 0.69/1.16 substitution1:
% 0.69/1.16 X := X
% 0.69/1.16 end
% 0.69/1.16
% 0.69/1.16 subsumption: (161) {G1,W13,D3,L3,V2,M3} R(60,57) { alpha1( X, skol16( X ) )
% 0.69/1.16 , ! in( skol16( X ), Y ), in( skol16( X ), skol15( Y ) ) }.
% 0.69/1.16 parent0: (1557) {G1,W13,D3,L3,V2,M3} { ! in( skol16( X ), Y ), in( skol16
% 0.69/1.16 ( X ), skol15( Y ) ), alpha1( X, skol16( X ) ) }.
% 0.69/1.16 substitution0:
% 0.69/1.16 X := X
% 0.69/1.16 Y := Y
% 0.69/1.16 end
% 0.69/1.16 permutation0:
% 0.69/1.16 0 ==> 1
% 0.69/1.16 1 ==> 2
% 0.69/1.16 2 ==> 0
% 0.69/1.16 end
% 0.69/1.16
% 0.69/1.16 resolution: (1558) {G1,W6,D2,L2,V2,M2} { element( X, Y ), ! alpha1( Y, X )
% 0.69/1.16 }.
% 0.69/1.16 parent0[0]: (58) {G0,W6,D2,L2,V2,M2} I { ! in( X, Y ), element( X, Y ) }.
% 0.69/1.16 parent1[1]: (62) {G0,W6,D2,L2,V2,M2} I { ! alpha1( X, Y ), in( Y, X ) }.
% 0.69/1.16 substitution0:
% 0.69/1.16 X := X
% 0.69/1.16 Y := Y
% 0.69/1.16 end
% 0.69/1.16 substitution1:
% 0.69/1.16 X := Y
% 0.69/1.16 Y := X
% 0.69/1.16 end
% 0.69/1.16
% 0.69/1.16 subsumption: (187) {G1,W6,D2,L2,V2,M2} R(62,58) { ! alpha1( X, Y ), element
% 0.69/1.16 ( Y, X ) }.
% 0.69/1.16 parent0: (1558) {G1,W6,D2,L2,V2,M2} { element( X, Y ), ! alpha1( Y, X )
% 0.69/1.16 }.
% 0.69/1.16 substitution0:
% 0.69/1.16 X := Y
% 0.69/1.16 Y := X
% 0.69/1.16 end
% 0.69/1.16 permutation0:
% 0.69/1.16 0 ==> 1
% 0.69/1.16 1 ==> 0
% 0.69/1.16 end
% 0.69/1.16
% 0.69/1.16 resolution: (1559) {G1,W5,D2,L2,V2,M2} { ! empty( Y ), ! alpha1( Y, X )
% 0.69/1.16 }.
% 0.69/1.16 parent0[0]: (67) {G0,W5,D2,L2,V2,M2} I { ! in( X, Y ), ! empty( Y ) }.
% 0.69/1.16 parent1[1]: (62) {G0,W6,D2,L2,V2,M2} I { ! alpha1( X, Y ), in( Y, X ) }.
% 0.69/1.16 substitution0:
% 0.69/1.16 X := X
% 0.69/1.16 Y := Y
% 0.69/1.16 end
% 0.69/1.16 substitution1:
% 0.69/1.16 X := Y
% 0.69/1.16 Y := X
% 0.69/1.16 end
% 0.69/1.16
% 0.69/1.16 subsumption: (193) {G1,W5,D2,L2,V2,M2} R(62,67) { ! alpha1( X, Y ), ! empty
% 0.69/1.16 ( X ) }.
% 0.69/1.16 parent0: (1559) {G1,W5,D2,L2,V2,M2} { ! empty( Y ), ! alpha1( Y, X ) }.
% 0.69/1.16 substitution0:
% 0.69/1.16 X := Y
% 0.69/1.16 Y := X
% 0.69/1.16 end
% 0.69/1.16 permutation0:
% 0.69/1.16 0 ==> 1
% 0.69/1.16 1 ==> 0
% 0.69/1.16 end
% 0.69/1.16
% 0.69/1.16 resolution: (1560) {G1,W5,D2,L2,V1,M2} { element( X, skol17 ), ! ordinal(
% 0.69/1.16 X ) }.
% 0.69/1.16 parent0[0]: (58) {G0,W6,D2,L2,V2,M2} I { ! in( X, Y ), element( X, Y ) }.
% 0.69/1.16 parent1[1]: (65) {G0,W5,D2,L2,V1,M2} I { ! ordinal( X ), in( X, skol17 )
% 0.69/1.16 }.
% 0.69/1.16 substitution0:
% 0.69/1.16 X := X
% 0.69/1.16 Y := skol17
% 0.69/1.16 end
% 0.69/1.16 substitution1:
% 0.69/1.16 X := X
% 0.69/1.16 end
% 0.69/1.16
% 0.69/1.16 subsumption: (213) {G1,W5,D2,L2,V1,M2} R(65,58) { ! ordinal( X ), element(
% 0.69/1.16 X, skol17 ) }.
% 0.69/1.16 parent0: (1560) {G1,W5,D2,L2,V1,M2} { element( X, skol17 ), ! ordinal( X )
% 0.69/1.16 }.
% 0.69/1.16 substitution0:
% 0.69/1.16 X := X
% 0.69/1.16 end
% 0.69/1.16 permutation0:
% 0.69/1.16 0 ==> 1
% 0.69/1.16 1 ==> 0
% 0.69/1.16 end
% 0.69/1.16
% 0.69/1.16 resolution: (1561) {G1,W2,D2,L1,V0,M1} { ! ordinal( skol17 ) }.
% 0.69/1.16 parent0[0]: (69) {G1,W3,D2,L1,V1,M1} F(0) { ! in( X, X ) }.
% 0.69/1.16 parent1[1]: (65) {G0,W5,D2,L2,V1,M2} I { ! ordinal( X ), in( X, skol17 )
% 0.69/1.16 }.
% 0.69/1.16 substitution0:
% 0.69/1.16 X := skol17
% 0.69/1.16 end
% 0.69/1.16 substitution1:
% 0.69/1.16 X := skol17
% 0.69/1.16 end
% 0.69/1.16
% 0.69/1.16 subsumption: (217) {G2,W2,D2,L1,V0,M1} R(65,69) { ! ordinal( skol17 ) }.
% 0.69/1.16 parent0: (1561) {G1,W2,D2,L1,V0,M1} { ! ordinal( skol17 ) }.
% 0.69/1.16 substitution0:
% 0.69/1.16 end
% 0.69/1.16 permutation0:
% 0.69/1.16 0 ==> 0
% 0.69/1.16 end
% 0.69/1.16
% 0.69/1.16 resolution: (1562) {G1,W2,D2,L1,V0,M1} { ! empty( skol17 ) }.
% 0.69/1.16 parent0[0]: (217) {G2,W2,D2,L1,V0,M1} R(65,69) { ! ordinal( skol17 ) }.
% 0.69/1.16 parent1[1]: (9) {G0,W4,D2,L2,V1,M2} I { ! empty( X ), ordinal( X ) }.
% 0.69/1.16 substitution0:
% 0.69/1.16 end
% 0.69/1.16 substitution1:
% 0.69/1.16 X := skol17
% 0.69/1.16 end
% 0.69/1.16
% 0.69/1.16 subsumption: (230) {G3,W2,D2,L1,V0,M1} R(217,9) { ! empty( skol17 ) }.
% 0.69/1.16 parent0: (1562) {G1,W2,D2,L1,V0,M1} { ! empty( skol17 ) }.
% 0.69/1.16 substitution0:
% 0.69/1.16 end
% 0.69/1.16 permutation0:
% 0.69/1.16 0 ==> 0
% 0.69/1.16 end
% 0.69/1.16
% 0.69/1.16 resolution: (1563) {G1,W6,D2,L2,V1,M2} { ! element( X, skol17 ), in( X,
% 0.69/1.16 skol17 ) }.
% 0.69/1.16 parent0[0]: (230) {G3,W2,D2,L1,V0,M1} R(217,9) { ! empty( skol17 ) }.
% 0.69/1.16 parent1[1]: (59) {G0,W8,D2,L3,V2,M3} I { ! element( X, Y ), empty( Y ), in
% 0.69/1.16 ( X, Y ) }.
% 0.69/1.16 substitution0:
% 0.69/1.16 end
% 0.69/1.16 substitution1:
% 0.69/1.16 X := X
% 0.69/1.16 Y := skol17
% 0.69/1.16 end
% 0.69/1.16
% 0.69/1.16 subsumption: (233) {G4,W6,D2,L2,V1,M2} R(230,59) { ! element( X, skol17 ),
% 0.69/1.16 in( X, skol17 ) }.
% 0.69/1.16 parent0: (1563) {G1,W6,D2,L2,V1,M2} { ! element( X, skol17 ), in( X,
% 0.69/1.16 skol17 ) }.
% 0.69/1.16 substitution0:
% 0.69/1.16 X := X
% 0.69/1.16 end
% 0.69/1.16 permutation0:
% 0.69/1.16 0 ==> 0
% 0.69/1.16 1 ==> 1
% 0.69/1.16 end
% 0.69/1.16
% 0.69/1.16 resolution: (1564) {G1,W5,D3,L2,V1,M2} { ! empty( X ), ordinal( skol16( X
% 0.69/1.16 ) ) }.
% 0.69/1.16 parent0[0]: (193) {G1,W5,D2,L2,V2,M2} R(62,67) { ! alpha1( X, Y ), ! empty
% 0.69/1.16 ( X ) }.
% 0.69/1.16 parent1[0]: (60) {G0,W7,D3,L2,V1,M2} I { alpha1( X, skol16( X ) ), ordinal
% 0.69/1.16 ( skol16( X ) ) }.
% 0.69/1.16 substitution0:
% 0.69/1.16 X := X
% 0.69/1.16 Y := skol16( X )
% 0.69/1.16 end
% 0.69/1.16 substitution1:
% 0.69/1.16 X := X
% 0.69/1.16 end
% 0.69/1.16
% 0.69/1.16 subsumption: (433) {G2,W5,D3,L2,V1,M2} R(193,60) { ! empty( X ), ordinal(
% 0.69/1.16 skol16( X ) ) }.
% 0.69/1.16 parent0: (1564) {G1,W5,D3,L2,V1,M2} { ! empty( X ), ordinal( skol16( X ) )
% 0.69/1.16 }.
% 0.69/1.16 substitution0:
% 0.69/1.16 X := X
% 0.69/1.16 end
% 0.69/1.16 permutation0:
% 0.69/1.16 0 ==> 0
% 0.69/1.16 1 ==> 1
% 0.69/1.16 end
% 0.69/1.16
% 0.69/1.16 resolution: (1565) {G1,W7,D3,L2,V1,M2} { element( skol16( X ), X ),
% 0.69/1.16 ordinal( skol16( X ) ) }.
% 0.69/1.16 parent0[0]: (187) {G1,W6,D2,L2,V2,M2} R(62,58) { ! alpha1( X, Y ), element
% 0.69/1.16 ( Y, X ) }.
% 0.69/1.16 parent1[0]: (60) {G0,W7,D3,L2,V1,M2} I { alpha1( X, skol16( X ) ), ordinal
% 0.69/1.16 ( skol16( X ) ) }.
% 0.69/1.16 substitution0:
% 0.69/1.16 X := X
% 0.69/1.16 Y := skol16( X )
% 0.69/1.16 end
% 0.69/1.16 substitution1:
% 0.69/1.16 X := X
% 0.69/1.16 end
% 0.69/1.16
% 0.69/1.16 subsumption: (682) {G2,W7,D3,L2,V1,M2} R(187,60) { element( skol16( X ), X
% 0.69/1.16 ), ordinal( skol16( X ) ) }.
% 0.69/1.16 parent0: (1565) {G1,W7,D3,L2,V1,M2} { element( skol16( X ), X ), ordinal(
% 0.69/1.16 skol16( X ) ) }.
% 0.69/1.16 substitution0:
% 0.69/1.16 X := X
% 0.69/1.16 end
% 0.69/1.16 permutation0:
% 0.69/1.16 0 ==> 0
% 0.69/1.16 1 ==> 1
% 0.69/1.16 end
% 0.69/1.16
% 0.69/1.16 resolution: (1566) {G2,W10,D4,L3,V2,M3} { ordinal( skol16( skol15( X ) ) )
% 0.69/1.16 , ! element( Y, skol15( X ) ), ordinal( Y ) }.
% 0.69/1.16 parent0[0]: (433) {G2,W5,D3,L2,V1,M2} R(193,60) { ! empty( X ), ordinal(
% 0.69/1.16 skol16( X ) ) }.
% 0.69/1.16 parent1[1]: (134) {G1,W9,D3,L3,V2,M3} R(59,56) { ! element( X, skol15( Y )
% 0.69/1.16 ), empty( skol15( Y ) ), ordinal( X ) }.
% 0.69/1.16 substitution0:
% 0.69/1.16 X := skol15( X )
% 0.69/1.16 end
% 0.69/1.16 substitution1:
% 0.69/1.16 X := Y
% 0.69/1.16 Y := X
% 0.69/1.16 end
% 0.69/1.16
% 0.69/1.16 subsumption: (729) {G3,W10,D4,L3,V2,M3} R(134,433) { ! element( X, skol15(
% 0.69/1.16 Y ) ), ordinal( X ), ordinal( skol16( skol15( Y ) ) ) }.
% 0.69/1.16 parent0: (1566) {G2,W10,D4,L3,V2,M3} { ordinal( skol16( skol15( X ) ) ), !
% 0.69/1.16 element( Y, skol15( X ) ), ordinal( Y ) }.
% 0.69/1.16 substitution0:
% 0.69/1.16 X := Y
% 0.69/1.16 Y := X
% 0.69/1.16 end
% 0.69/1.16 permutation0:
% 0.69/1.16 0 ==> 2
% 0.69/1.16 1 ==> 0
% 0.69/1.16 2 ==> 1
% 0.69/1.16 end
% 0.69/1.16
% 0.69/1.16 factor: (1568) {G3,W10,D4,L2,V1,M2} { ! element( skol16( skol15( X ) ),
% 0.69/1.16 skol15( X ) ), ordinal( skol16( skol15( X ) ) ) }.
% 0.69/1.16 parent0[1, 2]: (729) {G3,W10,D4,L3,V2,M3} R(134,433) { ! element( X, skol15
% 0.69/1.16 ( Y ) ), ordinal( X ), ordinal( skol16( skol15( Y ) ) ) }.
% 0.69/1.16 substitution0:
% 0.69/1.16 X := skol16( skol15( X ) )
% 0.69/1.16 Y := X
% 0.69/1.16 end
% 0.69/1.16
% 0.69/1.16 resolution: (1569) {G3,W8,D4,L2,V1,M2} { ordinal( skol16( skol15( X ) ) )
% 0.69/1.16 , ordinal( skol16( skol15( X ) ) ) }.
% 0.69/1.16 parent0[0]: (1568) {G3,W10,D4,L2,V1,M2} { ! element( skol16( skol15( X ) )
% 0.69/1.16 , skol15( X ) ), ordinal( skol16( skol15( X ) ) ) }.
% 0.69/1.16 parent1[0]: (682) {G2,W7,D3,L2,V1,M2} R(187,60) { element( skol16( X ), X )
% 0.69/1.16 , ordinal( skol16( X ) ) }.
% 0.69/1.16 substitution0:
% 0.69/1.16 X := X
% 0.69/1.16 end
% 0.69/1.16 substitution1:
% 0.69/1.16 X := skol15( X )
% 0.69/1.16 end
% 0.69/1.16
% 0.69/1.16 factor: (1570) {G3,W4,D4,L1,V1,M1} { ordinal( skol16( skol15( X ) ) ) }.
% 0.69/1.16 parent0[0, 1]: (1569) {G3,W8,D4,L2,V1,M2} { ordinal( skol16( skol15( X ) )
% 0.69/1.16 ), ordinal( skol16( skol15( X ) ) ) }.
% 0.69/1.16 substitution0:
% 0.69/1.16 X := X
% 0.69/1.16 end
% 0.69/1.16
% 0.69/1.16 subsumption: (759) {G4,W4,D4,L1,V1,M1} F(729);r(682) { ordinal( skol16(
% 0.69/1.16 skol15( X ) ) ) }.
% 0.69/1.16 parent0: (1570) {G3,W4,D4,L1,V1,M1} { ordinal( skol16( skol15( X ) ) ) }.
% 0.69/1.16 substitution0:
% 0.69/1.16 X := X
% 0.69/1.16 end
% 0.69/1.16 permutation0:
% 0.69/1.16 0 ==> 0
% 0.69/1.16 end
% 0.69/1.16
% 0.69/1.16 resolution: (1571) {G2,W5,D4,L1,V1,M1} { element( skol16( skol15( X ) ),
% 0.69/1.16 skol17 ) }.
% 0.69/1.16 parent0[0]: (213) {G1,W5,D2,L2,V1,M2} R(65,58) { ! ordinal( X ), element( X
% 0.69/1.16 , skol17 ) }.
% 0.69/1.16 parent1[0]: (759) {G4,W4,D4,L1,V1,M1} F(729);r(682) { ordinal( skol16(
% 0.69/1.16 skol15( X ) ) ) }.
% 0.69/1.16 substitution0:
% 0.69/1.16 X := skol16( skol15( X ) )
% 0.69/1.16 end
% 0.69/1.16 substitution1:
% 0.69/1.16 X := X
% 0.69/1.16 end
% 0.69/1.16
% 0.69/1.16 subsumption: (765) {G5,W5,D4,L1,V1,M1} R(759,213) { element( skol16( skol15
% 0.69/1.16 ( X ) ), skol17 ) }.
% 0.69/1.16 parent0: (1571) {G2,W5,D4,L1,V1,M1} { element( skol16( skol15( X ) ),
% 0.69/1.16 skol17 ) }.
% 0.69/1.16 substitution0:
% 0.69/1.16 X := X
% 0.69/1.16 end
% 0.69/1.16 permutation0:
% 0.69/1.16 0 ==> 0
% 0.69/1.16 end
% 0.69/1.16
% 0.69/1.16 resolution: (1572) {G1,W5,D4,L1,V2,M1} { ! alpha1( X, skol16( skol15( Y )
% 0.69/1.16 ) ) }.
% 0.69/1.16 parent0[1]: (63) {G0,W5,D2,L2,V2,M2} I { ! alpha1( X, Y ), ! ordinal( Y )
% 0.69/1.16 }.
% 0.69/1.16 parent1[0]: (759) {G4,W4,D4,L1,V1,M1} F(729);r(682) { ordinal( skol16(
% 0.69/1.16 skol15( X ) ) ) }.
% 0.69/1.16 substitution0:
% 0.69/1.16 X := X
% 0.69/1.16 Y := skol16( skol15( Y ) )
% 0.69/1.16 end
% 0.69/1.16 substitution1:
% 0.69/1.16 X := Y
% 0.69/1.16 end
% 0.69/1.16
% 0.69/1.16 subsumption: (769) {G5,W5,D4,L1,V2,M1} R(759,63) { ! alpha1( X, skol16(
% 0.69/1.16 skol15( Y ) ) ) }.
% 0.69/1.16 parent0: (1572) {G1,W5,D4,L1,V2,M1} { ! alpha1( X, skol16( skol15( Y ) ) )
% 0.69/1.16 }.
% 0.69/1.16 substitution0:
% 0.69/1.16 X := X
% 0.69/1.16 Y := Y
% 0.69/1.16 end
% 0.69/1.16 permutation0:
% 0.69/1.16 0 ==> 0
% 0.69/1.16 end
% 0.69/1.16
% 0.69/1.16 resolution: (1573) {G1,W17,D4,L3,V1,M3} { alpha1( skol15( X ), skol16(
% 0.69/1.16 skol15( X ) ) ), alpha1( skol15( X ), skol16( skol15( X ) ) ), ! in(
% 0.69/1.16 skol16( skol15( X ) ), X ) }.
% 0.69/1.16 parent0[1]: (61) {G0,W8,D3,L2,V1,M2} I { alpha1( X, skol16( X ) ), ! in(
% 0.69/1.16 skol16( X ), X ) }.
% 0.69/1.16 parent1[2]: (161) {G1,W13,D3,L3,V2,M3} R(60,57) { alpha1( X, skol16( X ) )
% 0.69/1.16 , ! in( skol16( X ), Y ), in( skol16( X ), skol15( Y ) ) }.
% 0.69/1.16 substitution0:
% 0.69/1.16 X := skol15( X )
% 0.69/1.16 end
% 0.69/1.16 substitution1:
% 0.69/1.16 X := skol15( X )
% 0.69/1.16 Y := X
% 0.69/1.16 end
% 0.69/1.16
% 0.69/1.16 factor: (1574) {G1,W11,D4,L2,V1,M2} { alpha1( skol15( X ), skol16( skol15
% 0.69/1.16 ( X ) ) ), ! in( skol16( skol15( X ) ), X ) }.
% 0.69/1.16 parent0[0, 1]: (1573) {G1,W17,D4,L3,V1,M3} { alpha1( skol15( X ), skol16(
% 0.69/1.16 skol15( X ) ) ), alpha1( skol15( X ), skol16( skol15( X ) ) ), ! in(
% 0.69/1.16 skol16( skol15( X ) ), X ) }.
% 0.69/1.16 substitution0:
% 0.69/1.16 X := X
% 0.69/1.16 end
% 0.69/1.16
% 0.69/1.16 resolution: (1576) {G2,W5,D4,L1,V1,M1} { ! in( skol16( skol15( X ) ), X )
% 0.69/1.16 }.
% 0.69/1.16 parent0[0]: (769) {G5,W5,D4,L1,V2,M1} R(759,63) { ! alpha1( X, skol16(
% 0.69/1.16 skol15( Y ) ) ) }.
% 0.69/1.16 parent1[0]: (1574) {G1,W11,D4,L2,V1,M2} { alpha1( skol15( X ), skol16(
% 0.69/1.16 skol15( X ) ) ), ! in( skol16( skol15( X ) ), X ) }.
% 0.69/1.16 substitution0:
% 0.69/1.16 X := skol15( X )
% 0.69/1.16 Y := X
% 0.69/1.16 end
% 0.69/1.16 substitution1:
% 0.69/1.16 X := X
% 0.69/1.16 end
% 0.69/1.16
% 0.69/1.16 subsumption: (1453) {G6,W5,D4,L1,V1,M1} R(161,61);f;r(769) { ! in( skol16(
% 0.69/1.16 skol15( X ) ), X ) }.
% 0.69/1.16 parent0: (1576) {G2,W5,D4,L1,V1,M1} { ! in( skol16( skol15( X ) ), X ) }.
% 0.69/1.16 substitution0:
% 0.69/1.16 X := X
% 0.69/1.16 end
% 0.69/1.16 permutation0:
% 0.69/1.16 0 ==> 0
% 0.69/1.16 end
% 0.69/1.16
% 0.69/1.16 resolution: (1577) {G5,W5,D4,L1,V0,M1} { ! element( skol16( skol15( skol17
% 0.69/1.16 ) ), skol17 ) }.
% 0.69/1.16 parent0[0]: (1453) {G6,W5,D4,L1,V1,M1} R(161,61);f;r(769) { ! in( skol16(
% 0.69/1.16 skol15( X ) ), X ) }.
% 0.69/1.16 parent1[1]: (233) {G4,W6,D2,L2,V1,M2} R(230,59) { ! element( X, skol17 ),
% 0.69/1.16 in( X, skol17 ) }.
% 0.69/1.16 substitution0:
% 0.69/1.16 X := skol17
% 0.69/1.16 end
% 0.69/1.16 substitution1:
% 0.69/1.16 X := skol16( skol15( skol17 ) )
% 0.69/1.16 end
% 0.69/1.16
% 0.69/1.16 resolution: (1578) {G6,W0,D0,L0,V0,M0} { }.
% 0.69/1.16 parent0[0]: (1577) {G5,W5,D4,L1,V0,M1} { ! element( skol16( skol15( skol17
% 0.69/1.16 ) ), skol17 ) }.
% 0.69/1.16 parent1[0]: (765) {G5,W5,D4,L1,V1,M1} R(759,213) { element( skol16( skol15
% 0.69/1.16 ( X ) ), skol17 ) }.
% 0.69/1.16 substitution0:
% 0.69/1.16 end
% 0.69/1.16 substitution1:
% 0.69/1.16 X := skol17
% 0.69/1.16 end
% 0.69/1.16
% 0.69/1.16 subsumption: (1463) {G7,W0,D0,L0,V0,M0} R(1453,233);r(765) { }.
% 0.69/1.16 parent0: (1578) {G6,W0,D0,L0,V0,M0} { }.
% 0.69/1.16 substitution0:
% 0.69/1.16 end
% 0.69/1.16 permutation0:
% 0.69/1.16 end
% 0.69/1.16
% 0.69/1.16 Proof check complete!
% 0.69/1.16
% 0.69/1.16 Memory use:
% 0.69/1.16
% 0.69/1.16 space for terms: 14730
% 0.69/1.16 space for clauses: 67022
% 0.69/1.16
% 0.69/1.16
% 0.69/1.16 clauses generated: 5615
% 0.69/1.16 clauses kept: 1464
% 0.69/1.16 clauses selected: 325
% 0.69/1.16 clauses deleted: 109
% 0.69/1.16 clauses inuse deleted: 62
% 0.69/1.16
% 0.69/1.16 subsentry: 11747
% 0.69/1.16 literals s-matched: 8716
% 0.69/1.16 literals matched: 8571
% 0.69/1.16 full subsumption: 1046
% 0.69/1.16
% 0.69/1.16 checksum: 335382134
% 0.69/1.16
% 0.69/1.16
% 0.69/1.16 Bliksem ended
%------------------------------------------------------------------------------