TSTP Solution File: SEU239+1 by Bliksem---1.12
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%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SEU239+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n003.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 : Tue Jul 19 07:11:47 EDT 2022
% Result : Theorem 0.75s 1.33s
% Output : Refutation 0.75s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU239+1 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.13 % Command : bliksem %s
% 0.13/0.34 % Computer : n003.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 : Sun Jun 19 23:48:29 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.75/1.33 *** allocated 10000 integers for termspace/termends
% 0.75/1.33 *** allocated 10000 integers for clauses
% 0.75/1.33 *** allocated 10000 integers for justifications
% 0.75/1.33 Bliksem 1.12
% 0.75/1.33
% 0.75/1.33
% 0.75/1.33 Automatic Strategy Selection
% 0.75/1.33
% 0.75/1.33
% 0.75/1.33 Clauses:
% 0.75/1.33
% 0.75/1.33 { ! in( X, Y ), ! in( Y, X ) }.
% 0.75/1.33 { ! empty( X ), function( X ) }.
% 0.75/1.33 { ! relation( X ), ! empty( X ), ! function( X ), relation( X ) }.
% 0.75/1.33 { ! relation( X ), ! empty( X ), ! function( X ), function( X ) }.
% 0.75/1.33 { ! relation( X ), ! empty( X ), ! function( X ), one_to_one( X ) }.
% 0.75/1.33 { unordered_pair( X, Y ) = unordered_pair( Y, X ) }.
% 0.75/1.33 { set_union2( X, Y ) = set_union2( Y, X ) }.
% 0.75/1.33 { ! relation( X ), ! is_reflexive_in( X, Y ), ! in( Z, Y ), in(
% 0.75/1.33 ordered_pair( Z, Z ), X ) }.
% 0.75/1.33 { ! relation( X ), in( skol1( Z, Y ), Y ), is_reflexive_in( X, Y ) }.
% 0.75/1.33 { ! relation( X ), ! in( ordered_pair( skol1( X, Y ), skol1( X, Y ) ), X )
% 0.75/1.33 , is_reflexive_in( X, Y ) }.
% 0.75/1.33 { ordered_pair( X, Y ) = unordered_pair( unordered_pair( X, Y ), singleton
% 0.75/1.33 ( X ) ) }.
% 0.75/1.33 { ! relation( X ), relation_field( X ) = set_union2( relation_dom( X ),
% 0.75/1.33 relation_rng( X ) ) }.
% 0.75/1.33 { ! relation( X ), ! reflexive( X ), is_reflexive_in( X, relation_field( X
% 0.75/1.33 ) ) }.
% 0.75/1.33 { ! relation( X ), ! is_reflexive_in( X, relation_field( X ) ), reflexive(
% 0.75/1.33 X ) }.
% 0.75/1.33 { && }.
% 0.75/1.33 { && }.
% 0.75/1.33 { && }.
% 0.75/1.33 { && }.
% 0.75/1.33 { && }.
% 0.75/1.33 { && }.
% 0.75/1.33 { && }.
% 0.75/1.33 { && }.
% 0.75/1.33 { && }.
% 0.75/1.33 { element( skol2( X ), X ) }.
% 0.75/1.33 { empty( empty_set ) }.
% 0.75/1.33 { ! empty( ordered_pair( X, Y ) ) }.
% 0.75/1.33 { empty( X ), ! empty( set_union2( X, Y ) ) }.
% 0.75/1.33 { empty( X ), ! empty( set_union2( Y, X ) ) }.
% 0.75/1.33 { set_union2( X, X ) = X }.
% 0.75/1.33 { relation( skol3 ) }.
% 0.75/1.33 { alpha1( skol3 ), ! in( X, relation_field( skol3 ) ), in( ordered_pair( X
% 0.75/1.33 , X ), skol3 ) }.
% 0.75/1.33 { alpha1( skol3 ), ! reflexive( skol3 ) }.
% 0.75/1.33 { ! alpha1( X ), reflexive( X ) }.
% 0.75/1.33 { ! alpha1( X ), in( skol4( X ), relation_field( X ) ) }.
% 0.75/1.33 { ! alpha1( X ), ! in( ordered_pair( skol4( X ), skol4( X ) ), X ) }.
% 0.75/1.33 { ! reflexive( X ), ! in( Y, relation_field( X ) ), in( ordered_pair( Y, Y
% 0.75/1.33 ), X ), alpha1( X ) }.
% 0.75/1.33 { relation( skol5 ) }.
% 0.75/1.33 { function( skol5 ) }.
% 0.75/1.33 { empty( skol6 ) }.
% 0.75/1.33 { relation( skol7 ) }.
% 0.75/1.33 { empty( skol7 ) }.
% 0.75/1.33 { function( skol7 ) }.
% 0.75/1.33 { ! empty( skol8 ) }.
% 0.75/1.33 { relation( skol9 ) }.
% 0.75/1.33 { function( skol9 ) }.
% 0.75/1.33 { one_to_one( skol9 ) }.
% 0.75/1.33 { set_union2( X, empty_set ) = X }.
% 0.75/1.33 { ! in( X, Y ), element( X, Y ) }.
% 0.75/1.33 { ! element( X, Y ), empty( Y ), in( X, Y ) }.
% 0.75/1.33 { ! empty( X ), X = empty_set }.
% 0.75/1.33 { ! in( X, Y ), ! empty( Y ) }.
% 0.75/1.33 { ! empty( X ), X = Y, ! empty( Y ) }.
% 0.75/1.33
% 0.75/1.33 percentage equality = 0.103896, percentage horn = 0.904762
% 0.75/1.33 This is a problem with some equality
% 0.75/1.33
% 0.75/1.33
% 0.75/1.33
% 0.75/1.33 Options Used:
% 0.75/1.33
% 0.75/1.33 useres = 1
% 0.75/1.33 useparamod = 1
% 0.75/1.33 useeqrefl = 1
% 0.75/1.33 useeqfact = 1
% 0.75/1.33 usefactor = 1
% 0.75/1.33 usesimpsplitting = 0
% 0.75/1.33 usesimpdemod = 5
% 0.75/1.33 usesimpres = 3
% 0.75/1.33
% 0.75/1.33 resimpinuse = 1000
% 0.75/1.33 resimpclauses = 20000
% 0.75/1.33 substype = eqrewr
% 0.75/1.33 backwardsubs = 1
% 0.75/1.33 selectoldest = 5
% 0.75/1.33
% 0.75/1.33 litorderings [0] = split
% 0.75/1.33 litorderings [1] = extend the termordering, first sorting on arguments
% 0.75/1.33
% 0.75/1.33 termordering = kbo
% 0.75/1.33
% 0.75/1.33 litapriori = 0
% 0.75/1.33 termapriori = 1
% 0.75/1.33 litaposteriori = 0
% 0.75/1.33 termaposteriori = 0
% 0.75/1.33 demodaposteriori = 0
% 0.75/1.33 ordereqreflfact = 0
% 0.75/1.33
% 0.75/1.33 litselect = negord
% 0.75/1.33
% 0.75/1.33 maxweight = 15
% 0.75/1.33 maxdepth = 30000
% 0.75/1.33 maxlength = 115
% 0.75/1.33 maxnrvars = 195
% 0.75/1.33 excuselevel = 1
% 0.75/1.33 increasemaxweight = 1
% 0.75/1.33
% 0.75/1.33 maxselected = 10000000
% 0.75/1.33 maxnrclauses = 10000000
% 0.75/1.33
% 0.75/1.33 showgenerated = 0
% 0.75/1.33 showkept = 0
% 0.75/1.33 showselected = 0
% 0.75/1.33 showdeleted = 0
% 0.75/1.33 showresimp = 1
% 0.75/1.33 showstatus = 2000
% 0.75/1.33
% 0.75/1.33 prologoutput = 0
% 0.75/1.33 nrgoals = 5000000
% 0.75/1.33 totalproof = 1
% 0.75/1.33
% 0.75/1.33 Symbols occurring in the translation:
% 0.75/1.33
% 0.75/1.33 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.75/1.33 . [1, 2] (w:1, o:33, a:1, s:1, b:0),
% 0.75/1.33 && [3, 0] (w:1, o:4, a:1, s:1, b:0),
% 0.75/1.33 ! [4, 1] (w:0, o:16, a:1, s:1, b:0),
% 0.75/1.33 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.75/1.33 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.75/1.33 in [37, 2] (w:1, o:57, a:1, s:1, b:0),
% 0.75/1.33 empty [38, 1] (w:1, o:21, a:1, s:1, b:0),
% 0.75/1.33 function [39, 1] (w:1, o:22, a:1, s:1, b:0),
% 0.75/1.33 relation [40, 1] (w:1, o:23, a:1, s:1, b:0),
% 0.75/1.33 one_to_one [41, 1] (w:1, o:24, a:1, s:1, b:0),
% 0.75/1.33 unordered_pair [42, 2] (w:1, o:58, a:1, s:1, b:0),
% 0.75/1.33 set_union2 [43, 2] (w:1, o:59, a:1, s:1, b:0),
% 0.75/1.33 is_reflexive_in [44, 2] (w:1, o:60, a:1, s:1, b:0),
% 0.75/1.33 ordered_pair [46, 2] (w:1, o:61, a:1, s:1, b:0),
% 0.75/1.33 singleton [47, 1] (w:1, o:29, a:1, s:1, b:0),
% 0.75/1.33 relation_field [48, 1] (w:1, o:25, a:1, s:1, b:0),
% 0.75/1.33 relation_dom [49, 1] (w:1, o:26, a:1, s:1, b:0),
% 0.75/1.33 relation_rng [50, 1] (w:1, o:27, a:1, s:1, b:0),
% 0.75/1.33 reflexive [51, 1] (w:1, o:28, a:1, s:1, b:0),
% 0.75/1.33 element [52, 2] (w:1, o:62, a:1, s:1, b:0),
% 0.75/1.33 empty_set [53, 0] (w:1, o:9, a:1, s:1, b:0),
% 0.75/1.33 alpha1 [54, 1] (w:1, o:30, a:1, s:1, b:1),
% 0.75/1.33 skol1 [55, 2] (w:1, o:63, a:1, s:1, b:1),
% 0.75/1.33 skol2 [56, 1] (w:1, o:31, a:1, s:1, b:1),
% 0.75/1.33 skol3 [57, 0] (w:1, o:10, a:1, s:1, b:1),
% 0.75/1.33 skol4 [58, 1] (w:1, o:32, a:1, s:1, b:1),
% 0.75/1.33 skol5 [59, 0] (w:1, o:11, a:1, s:1, b:1),
% 0.75/1.33 skol6 [60, 0] (w:1, o:12, a:1, s:1, b:1),
% 0.75/1.33 skol7 [61, 0] (w:1, o:13, a:1, s:1, b:1),
% 0.75/1.33 skol8 [62, 0] (w:1, o:14, a:1, s:1, b:1),
% 0.75/1.33 skol9 [63, 0] (w:1, o:15, a:1, s:1, b:1).
% 0.75/1.33
% 0.75/1.33
% 0.75/1.33 Starting Search:
% 0.75/1.33
% 0.75/1.33 *** allocated 15000 integers for clauses
% 0.75/1.33 *** allocated 22500 integers for clauses
% 0.75/1.33 *** allocated 33750 integers for clauses
% 0.75/1.33 *** allocated 50625 integers for clauses
% 0.75/1.33 *** allocated 15000 integers for termspace/termends
% 0.75/1.33 Resimplifying inuse:
% 0.75/1.33 Done
% 0.75/1.33
% 0.75/1.33 *** allocated 75937 integers for clauses
% 0.75/1.33 *** allocated 22500 integers for termspace/termends
% 0.75/1.33 *** allocated 113905 integers for clauses
% 0.75/1.33
% 0.75/1.33 Intermediate Status:
% 0.75/1.33 Generated: 8266
% 0.75/1.33 Kept: 2008
% 0.75/1.33 Inuse: 306
% 0.75/1.33 Deleted: 97
% 0.75/1.33 Deletedinuse: 51
% 0.75/1.33
% 0.75/1.33 Resimplifying inuse:
% 0.75/1.33 Done
% 0.75/1.33
% 0.75/1.33 *** allocated 33750 integers for termspace/termends
% 0.75/1.33 *** allocated 170857 integers for clauses
% 0.75/1.33 *** allocated 50625 integers for termspace/termends
% 0.75/1.33 Resimplifying inuse:
% 0.75/1.33 Done
% 0.75/1.33
% 0.75/1.33 *** allocated 256285 integers for clauses
% 0.75/1.33
% 0.75/1.33 Intermediate Status:
% 0.75/1.33 Generated: 18431
% 0.75/1.33 Kept: 4016
% 0.75/1.33 Inuse: 415
% 0.75/1.33 Deleted: 178
% 0.75/1.33 Deletedinuse: 101
% 0.75/1.33
% 0.75/1.33 Resimplifying inuse:
% 0.75/1.33 Done
% 0.75/1.33
% 0.75/1.33 *** allocated 75937 integers for termspace/termends
% 0.75/1.33
% 0.75/1.33 Bliksems!, er is een bewijs:
% 0.75/1.33 % SZS status Theorem
% 0.75/1.33 % SZS output start Refutation
% 0.75/1.33
% 0.75/1.33 (5) {G0,W13,D3,L4,V3,M4} I { ! relation( X ), ! is_reflexive_in( X, Y ), !
% 0.75/1.33 in( Z, Y ), in( ordered_pair( Z, Z ), X ) }.
% 0.75/1.33 (6) {G0,W10,D3,L3,V3,M3} I { ! relation( X ), in( skol1( Z, Y ), Y ),
% 0.75/1.33 is_reflexive_in( X, Y ) }.
% 0.75/1.33 (7) {G0,W14,D4,L3,V2,M3} I { ! relation( X ), ! in( ordered_pair( skol1( X
% 0.75/1.33 , Y ), skol1( X, Y ) ), X ), is_reflexive_in( X, Y ) }.
% 0.75/1.33 (10) {G0,W8,D3,L3,V1,M3} I { ! relation( X ), ! reflexive( X ),
% 0.75/1.33 is_reflexive_in( X, relation_field( X ) ) }.
% 0.75/1.33 (11) {G0,W8,D3,L3,V1,M3} I { ! relation( X ), ! is_reflexive_in( X,
% 0.75/1.33 relation_field( X ) ), reflexive( X ) }.
% 0.75/1.33 (19) {G0,W2,D2,L1,V0,M1} I { relation( skol3 ) }.
% 0.75/1.33 (20) {G0,W11,D3,L3,V1,M3} I { alpha1( skol3 ), ! in( X, relation_field(
% 0.75/1.33 skol3 ) ), in( ordered_pair( X, X ), skol3 ) }.
% 0.75/1.33 (21) {G0,W4,D2,L2,V0,M2} I { alpha1( skol3 ), ! reflexive( skol3 ) }.
% 0.75/1.33 (22) {G0,W4,D2,L2,V1,M2} I { ! alpha1( X ), reflexive( X ) }.
% 0.75/1.33 (23) {G0,W7,D3,L2,V1,M2} I { ! alpha1( X ), in( skol4( X ), relation_field
% 0.75/1.33 ( X ) ) }.
% 0.75/1.33 (24) {G0,W9,D4,L2,V1,M2} I { ! alpha1( X ), ! in( ordered_pair( skol4( X )
% 0.75/1.33 , skol4( X ) ), X ) }.
% 0.75/1.33 (71) {G1,W8,D3,L2,V2,M2} R(6,19) { in( skol1( X, Y ), Y ), is_reflexive_in
% 0.75/1.33 ( skol3, Y ) }.
% 0.75/1.33 (82) {G1,W12,D4,L2,V1,M2} R(7,19) { ! in( ordered_pair( skol1( skol3, X ),
% 0.75/1.33 skol1( skol3, X ) ), skol3 ), is_reflexive_in( skol3, X ) }.
% 0.75/1.33 (126) {G1,W8,D3,L3,V1,M3} R(10,22) { ! relation( X ), is_reflexive_in( X,
% 0.75/1.33 relation_field( X ) ), ! alpha1( X ) }.
% 0.75/1.33 (139) {G1,W6,D3,L2,V0,M2} R(11,21);r(19) { ! is_reflexive_in( skol3,
% 0.75/1.33 relation_field( skol3 ) ), alpha1( skol3 ) }.
% 0.75/1.33 (212) {G1,W15,D4,L4,V2,M4} R(23,5) { ! alpha1( X ), ! relation( Y ), !
% 0.75/1.33 is_reflexive_in( Y, relation_field( X ) ), in( ordered_pair( skol4( X ),
% 0.75/1.33 skol4( X ) ), Y ) }.
% 0.75/1.33 (664) {G2,W13,D5,L2,V1,M2} R(71,20);r(139) { alpha1( skol3 ), in(
% 0.75/1.33 ordered_pair( skol1( X, relation_field( skol3 ) ), skol1( X,
% 0.75/1.33 relation_field( skol3 ) ) ), skol3 ) }.
% 0.75/1.33 (1484) {G3,W2,D2,L1,V0,M1} R(139,82);r(664) { alpha1( skol3 ) }.
% 0.75/1.33 (4414) {G2,W4,D2,L2,V1,M2} R(212,126);f;f;r(24) { ! alpha1( X ), ! relation
% 0.75/1.33 ( X ) }.
% 0.75/1.33 (4418) {G4,W0,D0,L0,V0,M0} R(4414,1484);r(19) { }.
% 0.75/1.33
% 0.75/1.33
% 0.75/1.33 % SZS output end Refutation
% 0.75/1.33 found a proof!
% 0.75/1.33
% 0.75/1.33
% 0.75/1.33 Unprocessed initial clauses:
% 0.75/1.33
% 0.75/1.33 (4420) {G0,W6,D2,L2,V2,M2} { ! in( X, Y ), ! in( Y, X ) }.
% 0.75/1.33 (4421) {G0,W4,D2,L2,V1,M2} { ! empty( X ), function( X ) }.
% 0.75/1.33 (4422) {G0,W8,D2,L4,V1,M4} { ! relation( X ), ! empty( X ), ! function( X
% 0.75/1.33 ), relation( X ) }.
% 0.75/1.33 (4423) {G0,W8,D2,L4,V1,M4} { ! relation( X ), ! empty( X ), ! function( X
% 0.75/1.33 ), function( X ) }.
% 0.75/1.33 (4424) {G0,W8,D2,L4,V1,M4} { ! relation( X ), ! empty( X ), ! function( X
% 0.75/1.33 ), one_to_one( X ) }.
% 0.75/1.33 (4425) {G0,W7,D3,L1,V2,M1} { unordered_pair( X, Y ) = unordered_pair( Y, X
% 0.75/1.33 ) }.
% 0.75/1.33 (4426) {G0,W7,D3,L1,V2,M1} { set_union2( X, Y ) = set_union2( Y, X ) }.
% 0.75/1.33 (4427) {G0,W13,D3,L4,V3,M4} { ! relation( X ), ! is_reflexive_in( X, Y ),
% 0.75/1.33 ! in( Z, Y ), in( ordered_pair( Z, Z ), X ) }.
% 0.75/1.33 (4428) {G0,W10,D3,L3,V3,M3} { ! relation( X ), in( skol1( Z, Y ), Y ),
% 0.75/1.33 is_reflexive_in( X, Y ) }.
% 0.75/1.33 (4429) {G0,W14,D4,L3,V2,M3} { ! relation( X ), ! in( ordered_pair( skol1(
% 0.75/1.33 X, Y ), skol1( X, Y ) ), X ), is_reflexive_in( X, Y ) }.
% 0.75/1.33 (4430) {G0,W10,D4,L1,V2,M1} { ordered_pair( X, Y ) = unordered_pair(
% 0.75/1.33 unordered_pair( X, Y ), singleton( X ) ) }.
% 0.75/1.33 (4431) {G0,W10,D4,L2,V1,M2} { ! relation( X ), relation_field( X ) =
% 0.75/1.33 set_union2( relation_dom( X ), relation_rng( X ) ) }.
% 0.75/1.33 (4432) {G0,W8,D3,L3,V1,M3} { ! relation( X ), ! reflexive( X ),
% 0.75/1.33 is_reflexive_in( X, relation_field( X ) ) }.
% 0.75/1.33 (4433) {G0,W8,D3,L3,V1,M3} { ! relation( X ), ! is_reflexive_in( X,
% 0.75/1.33 relation_field( X ) ), reflexive( X ) }.
% 0.75/1.33 (4434) {G0,W1,D1,L1,V0,M1} { && }.
% 0.75/1.33 (4435) {G0,W1,D1,L1,V0,M1} { && }.
% 0.75/1.33 (4436) {G0,W1,D1,L1,V0,M1} { && }.
% 0.75/1.33 (4437) {G0,W1,D1,L1,V0,M1} { && }.
% 0.75/1.33 (4438) {G0,W1,D1,L1,V0,M1} { && }.
% 0.75/1.33 (4439) {G0,W1,D1,L1,V0,M1} { && }.
% 0.75/1.33 (4440) {G0,W1,D1,L1,V0,M1} { && }.
% 0.75/1.33 (4441) {G0,W1,D1,L1,V0,M1} { && }.
% 0.75/1.33 (4442) {G0,W1,D1,L1,V0,M1} { && }.
% 0.75/1.33 (4443) {G0,W4,D3,L1,V1,M1} { element( skol2( X ), X ) }.
% 0.75/1.33 (4444) {G0,W2,D2,L1,V0,M1} { empty( empty_set ) }.
% 0.75/1.33 (4445) {G0,W4,D3,L1,V2,M1} { ! empty( ordered_pair( X, Y ) ) }.
% 0.75/1.33 (4446) {G0,W6,D3,L2,V2,M2} { empty( X ), ! empty( set_union2( X, Y ) ) }.
% 0.75/1.33 (4447) {G0,W6,D3,L2,V2,M2} { empty( X ), ! empty( set_union2( Y, X ) ) }.
% 0.75/1.33 (4448) {G0,W5,D3,L1,V1,M1} { set_union2( X, X ) = X }.
% 0.75/1.33 (4449) {G0,W2,D2,L1,V0,M1} { relation( skol3 ) }.
% 0.75/1.33 (4450) {G0,W11,D3,L3,V1,M3} { alpha1( skol3 ), ! in( X, relation_field(
% 0.75/1.33 skol3 ) ), in( ordered_pair( X, X ), skol3 ) }.
% 0.75/1.33 (4451) {G0,W4,D2,L2,V0,M2} { alpha1( skol3 ), ! reflexive( skol3 ) }.
% 0.75/1.33 (4452) {G0,W4,D2,L2,V1,M2} { ! alpha1( X ), reflexive( X ) }.
% 0.75/1.33 (4453) {G0,W7,D3,L2,V1,M2} { ! alpha1( X ), in( skol4( X ), relation_field
% 0.75/1.33 ( X ) ) }.
% 0.75/1.33 (4454) {G0,W9,D4,L2,V1,M2} { ! alpha1( X ), ! in( ordered_pair( skol4( X )
% 0.75/1.33 , skol4( X ) ), X ) }.
% 0.75/1.33 (4455) {G0,W13,D3,L4,V2,M4} { ! reflexive( X ), ! in( Y, relation_field( X
% 0.75/1.33 ) ), in( ordered_pair( Y, Y ), X ), alpha1( X ) }.
% 0.75/1.33 (4456) {G0,W2,D2,L1,V0,M1} { relation( skol5 ) }.
% 0.75/1.33 (4457) {G0,W2,D2,L1,V0,M1} { function( skol5 ) }.
% 0.75/1.33 (4458) {G0,W2,D2,L1,V0,M1} { empty( skol6 ) }.
% 0.75/1.33 (4459) {G0,W2,D2,L1,V0,M1} { relation( skol7 ) }.
% 0.75/1.33 (4460) {G0,W2,D2,L1,V0,M1} { empty( skol7 ) }.
% 0.75/1.33 (4461) {G0,W2,D2,L1,V0,M1} { function( skol7 ) }.
% 0.75/1.33 (4462) {G0,W2,D2,L1,V0,M1} { ! empty( skol8 ) }.
% 0.75/1.33 (4463) {G0,W2,D2,L1,V0,M1} { relation( skol9 ) }.
% 0.75/1.33 (4464) {G0,W2,D2,L1,V0,M1} { function( skol9 ) }.
% 0.75/1.33 (4465) {G0,W2,D2,L1,V0,M1} { one_to_one( skol9 ) }.
% 0.75/1.33 (4466) {G0,W5,D3,L1,V1,M1} { set_union2( X, empty_set ) = X }.
% 0.75/1.33 (4467) {G0,W6,D2,L2,V2,M2} { ! in( X, Y ), element( X, Y ) }.
% 0.75/1.33 (4468) {G0,W8,D2,L3,V2,M3} { ! element( X, Y ), empty( Y ), in( X, Y ) }.
% 0.75/1.33 (4469) {G0,W5,D2,L2,V1,M2} { ! empty( X ), X = empty_set }.
% 0.75/1.33 (4470) {G0,W5,D2,L2,V2,M2} { ! in( X, Y ), ! empty( Y ) }.
% 0.75/1.33 (4471) {G0,W7,D2,L3,V2,M3} { ! empty( X ), X = Y, ! empty( Y ) }.
% 0.75/1.33
% 0.75/1.33
% 0.75/1.33 Total Proof:
% 0.75/1.33
% 0.75/1.33 subsumption: (5) {G0,W13,D3,L4,V3,M4} I { ! relation( X ), !
% 0.75/1.33 is_reflexive_in( X, Y ), ! in( Z, Y ), in( ordered_pair( Z, Z ), X ) }.
% 0.75/1.33 parent0: (4427) {G0,W13,D3,L4,V3,M4} { ! relation( X ), ! is_reflexive_in
% 0.75/1.33 ( X, Y ), ! in( Z, Y ), in( ordered_pair( Z, Z ), X ) }.
% 0.75/1.33 substitution0:
% 0.75/1.33 X := X
% 0.75/1.33 Y := Y
% 0.75/1.33 Z := Z
% 0.75/1.33 end
% 0.75/1.33 permutation0:
% 0.75/1.33 0 ==> 0
% 0.75/1.33 1 ==> 1
% 0.75/1.33 2 ==> 2
% 0.75/1.33 3 ==> 3
% 0.75/1.33 end
% 0.75/1.33
% 0.75/1.33 subsumption: (6) {G0,W10,D3,L3,V3,M3} I { ! relation( X ), in( skol1( Z, Y
% 0.75/1.33 ), Y ), is_reflexive_in( X, Y ) }.
% 0.75/1.33 parent0: (4428) {G0,W10,D3,L3,V3,M3} { ! relation( X ), in( skol1( Z, Y )
% 0.75/1.33 , Y ), is_reflexive_in( X, Y ) }.
% 0.75/1.33 substitution0:
% 0.75/1.33 X := X
% 0.75/1.33 Y := Y
% 0.75/1.33 Z := Z
% 0.75/1.33 end
% 0.75/1.33 permutation0:
% 0.75/1.33 0 ==> 0
% 0.75/1.33 1 ==> 1
% 0.75/1.33 2 ==> 2
% 0.75/1.33 end
% 0.75/1.33
% 0.75/1.33 subsumption: (7) {G0,W14,D4,L3,V2,M3} I { ! relation( X ), ! in(
% 0.75/1.33 ordered_pair( skol1( X, Y ), skol1( X, Y ) ), X ), is_reflexive_in( X, Y
% 0.75/1.33 ) }.
% 0.75/1.33 parent0: (4429) {G0,W14,D4,L3,V2,M3} { ! relation( X ), ! in( ordered_pair
% 0.75/1.33 ( skol1( X, Y ), skol1( X, Y ) ), X ), is_reflexive_in( X, Y ) }.
% 0.75/1.33 substitution0:
% 0.75/1.33 X := X
% 0.75/1.33 Y := Y
% 0.75/1.33 end
% 0.75/1.33 permutation0:
% 0.75/1.33 0 ==> 0
% 0.75/1.33 1 ==> 1
% 0.75/1.33 2 ==> 2
% 0.75/1.33 end
% 0.75/1.33
% 0.75/1.33 subsumption: (10) {G0,W8,D3,L3,V1,M3} I { ! relation( X ), ! reflexive( X )
% 0.75/1.33 , is_reflexive_in( X, relation_field( X ) ) }.
% 0.75/1.33 parent0: (4432) {G0,W8,D3,L3,V1,M3} { ! relation( X ), ! reflexive( X ),
% 0.75/1.33 is_reflexive_in( X, relation_field( X ) ) }.
% 0.75/1.33 substitution0:
% 0.75/1.33 X := X
% 0.75/1.33 end
% 0.75/1.33 permutation0:
% 0.75/1.33 0 ==> 0
% 0.75/1.33 1 ==> 1
% 0.75/1.33 2 ==> 2
% 0.75/1.33 end
% 0.75/1.33
% 0.75/1.33 subsumption: (11) {G0,W8,D3,L3,V1,M3} I { ! relation( X ), !
% 0.75/1.33 is_reflexive_in( X, relation_field( X ) ), reflexive( X ) }.
% 0.75/1.33 parent0: (4433) {G0,W8,D3,L3,V1,M3} { ! relation( X ), ! is_reflexive_in(
% 0.75/1.33 X, relation_field( X ) ), reflexive( X ) }.
% 0.75/1.33 substitution0:
% 0.75/1.33 X := X
% 0.75/1.33 end
% 0.75/1.33 permutation0:
% 0.75/1.33 0 ==> 0
% 0.75/1.33 1 ==> 1
% 0.75/1.33 2 ==> 2
% 0.75/1.33 end
% 0.75/1.33
% 0.75/1.33 subsumption: (19) {G0,W2,D2,L1,V0,M1} I { relation( skol3 ) }.
% 0.75/1.33 parent0: (4449) {G0,W2,D2,L1,V0,M1} { relation( skol3 ) }.
% 0.75/1.33 substitution0:
% 0.75/1.33 end
% 0.75/1.33 permutation0:
% 0.75/1.33 0 ==> 0
% 0.75/1.33 end
% 0.75/1.33
% 0.75/1.33 subsumption: (20) {G0,W11,D3,L3,V1,M3} I { alpha1( skol3 ), ! in( X,
% 0.75/1.33 relation_field( skol3 ) ), in( ordered_pair( X, X ), skol3 ) }.
% 0.75/1.33 parent0: (4450) {G0,W11,D3,L3,V1,M3} { alpha1( skol3 ), ! in( X,
% 0.75/1.33 relation_field( skol3 ) ), in( ordered_pair( X, X ), skol3 ) }.
% 0.75/1.33 substitution0:
% 0.75/1.33 X := X
% 0.75/1.33 end
% 0.75/1.33 permutation0:
% 0.75/1.33 0 ==> 0
% 0.75/1.33 1 ==> 1
% 0.75/1.33 2 ==> 2
% 0.75/1.33 end
% 0.75/1.33
% 0.75/1.33 subsumption: (21) {G0,W4,D2,L2,V0,M2} I { alpha1( skol3 ), ! reflexive(
% 0.75/1.33 skol3 ) }.
% 0.75/1.33 parent0: (4451) {G0,W4,D2,L2,V0,M2} { alpha1( skol3 ), ! reflexive( skol3
% 0.75/1.33 ) }.
% 0.75/1.33 substitution0:
% 0.75/1.33 end
% 0.75/1.33 permutation0:
% 0.75/1.33 0 ==> 0
% 0.75/1.33 1 ==> 1
% 0.75/1.33 end
% 0.75/1.33
% 0.75/1.33 subsumption: (22) {G0,W4,D2,L2,V1,M2} I { ! alpha1( X ), reflexive( X ) }.
% 0.75/1.33 parent0: (4452) {G0,W4,D2,L2,V1,M2} { ! alpha1( X ), reflexive( X ) }.
% 0.75/1.33 substitution0:
% 0.75/1.33 X := X
% 0.75/1.33 end
% 0.75/1.33 permutation0:
% 0.75/1.33 0 ==> 0
% 0.75/1.33 1 ==> 1
% 0.75/1.33 end
% 0.75/1.33
% 0.75/1.33 subsumption: (23) {G0,W7,D3,L2,V1,M2} I { ! alpha1( X ), in( skol4( X ),
% 0.75/1.33 relation_field( X ) ) }.
% 0.75/1.33 parent0: (4453) {G0,W7,D3,L2,V1,M2} { ! alpha1( X ), in( skol4( X ),
% 0.75/1.33 relation_field( X ) ) }.
% 0.75/1.33 substitution0:
% 0.75/1.33 X := X
% 0.75/1.33 end
% 0.75/1.33 permutation0:
% 0.75/1.33 0 ==> 0
% 0.75/1.33 1 ==> 1
% 0.75/1.33 end
% 0.75/1.33
% 0.75/1.33 subsumption: (24) {G0,W9,D4,L2,V1,M2} I { ! alpha1( X ), ! in( ordered_pair
% 0.75/1.33 ( skol4( X ), skol4( X ) ), X ) }.
% 0.75/1.33 parent0: (4454) {G0,W9,D4,L2,V1,M2} { ! alpha1( X ), ! in( ordered_pair(
% 0.75/1.33 skol4( X ), skol4( X ) ), X ) }.
% 0.75/1.33 substitution0:
% 0.75/1.33 X := X
% 0.75/1.33 end
% 0.75/1.33 permutation0:
% 0.75/1.33 0 ==> 0
% 0.75/1.33 1 ==> 1
% 0.75/1.33 end
% 0.75/1.33
% 0.75/1.33 resolution: (4505) {G1,W8,D3,L2,V2,M2} { in( skol1( X, Y ), Y ),
% 0.75/1.33 is_reflexive_in( skol3, Y ) }.
% 0.75/1.33 parent0[0]: (6) {G0,W10,D3,L3,V3,M3} I { ! relation( X ), in( skol1( Z, Y )
% 0.75/1.33 , Y ), is_reflexive_in( X, Y ) }.
% 0.75/1.33 parent1[0]: (19) {G0,W2,D2,L1,V0,M1} I { relation( skol3 ) }.
% 0.75/1.33 substitution0:
% 0.75/1.33 X := skol3
% 0.75/1.33 Y := Y
% 0.75/1.33 Z := X
% 0.75/1.33 end
% 0.75/1.33 substitution1:
% 0.75/1.33 end
% 0.75/1.33
% 0.75/1.33 subsumption: (71) {G1,W8,D3,L2,V2,M2} R(6,19) { in( skol1( X, Y ), Y ),
% 0.75/1.33 is_reflexive_in( skol3, Y ) }.
% 0.75/1.33 parent0: (4505) {G1,W8,D3,L2,V2,M2} { in( skol1( X, Y ), Y ),
% 0.75/1.33 is_reflexive_in( skol3, Y ) }.
% 0.75/1.33 substitution0:
% 0.75/1.33 X := X
% 0.75/1.33 Y := Y
% 0.75/1.33 end
% 0.75/1.33 permutation0:
% 0.75/1.33 0 ==> 0
% 0.75/1.33 1 ==> 1
% 0.75/1.33 end
% 0.75/1.33
% 0.75/1.33 resolution: (4506) {G1,W12,D4,L2,V1,M2} { ! in( ordered_pair( skol1( skol3
% 0.75/1.33 , X ), skol1( skol3, X ) ), skol3 ), is_reflexive_in( skol3, X ) }.
% 0.75/1.33 parent0[0]: (7) {G0,W14,D4,L3,V2,M3} I { ! relation( X ), ! in(
% 0.75/1.33 ordered_pair( skol1( X, Y ), skol1( X, Y ) ), X ), is_reflexive_in( X, Y
% 0.75/1.33 ) }.
% 0.75/1.33 parent1[0]: (19) {G0,W2,D2,L1,V0,M1} I { relation( skol3 ) }.
% 0.75/1.33 substitution0:
% 0.75/1.33 X := skol3
% 0.75/1.33 Y := X
% 0.75/1.33 end
% 0.75/1.33 substitution1:
% 0.75/1.33 end
% 0.75/1.33
% 0.75/1.33 subsumption: (82) {G1,W12,D4,L2,V1,M2} R(7,19) { ! in( ordered_pair( skol1
% 0.75/1.33 ( skol3, X ), skol1( skol3, X ) ), skol3 ), is_reflexive_in( skol3, X )
% 0.75/1.33 }.
% 0.75/1.33 parent0: (4506) {G1,W12,D4,L2,V1,M2} { ! in( ordered_pair( skol1( skol3, X
% 0.75/1.33 ), skol1( skol3, X ) ), skol3 ), is_reflexive_in( skol3, X ) }.
% 0.75/1.33 substitution0:
% 0.75/1.33 X := X
% 0.75/1.33 end
% 0.75/1.33 permutation0:
% 0.75/1.33 0 ==> 0
% 0.75/1.33 1 ==> 1
% 0.75/1.33 end
% 0.75/1.33
% 0.75/1.33 resolution: (4507) {G1,W8,D3,L3,V1,M3} { ! relation( X ), is_reflexive_in
% 0.75/1.33 ( X, relation_field( X ) ), ! alpha1( X ) }.
% 0.75/1.33 parent0[1]: (10) {G0,W8,D3,L3,V1,M3} I { ! relation( X ), ! reflexive( X )
% 0.75/1.33 , is_reflexive_in( X, relation_field( X ) ) }.
% 0.75/1.33 parent1[1]: (22) {G0,W4,D2,L2,V1,M2} I { ! alpha1( X ), reflexive( X ) }.
% 0.75/1.33 substitution0:
% 0.75/1.33 X := X
% 0.75/1.33 end
% 0.75/1.33 substitution1:
% 0.75/1.33 X := X
% 0.75/1.33 end
% 0.75/1.33
% 0.75/1.33 subsumption: (126) {G1,W8,D3,L3,V1,M3} R(10,22) { ! relation( X ),
% 0.75/1.33 is_reflexive_in( X, relation_field( X ) ), ! alpha1( X ) }.
% 0.75/1.33 parent0: (4507) {G1,W8,D3,L3,V1,M3} { ! relation( X ), is_reflexive_in( X
% 0.75/1.33 , relation_field( X ) ), ! alpha1( X ) }.
% 0.75/1.33 substitution0:
% 0.75/1.33 X := X
% 0.75/1.33 end
% 0.75/1.33 permutation0:
% 0.75/1.33 0 ==> 0
% 0.75/1.33 1 ==> 1
% 0.75/1.33 2 ==> 2
% 0.75/1.33 end
% 0.75/1.33
% 0.75/1.33 resolution: (4508) {G1,W8,D3,L3,V0,M3} { alpha1( skol3 ), ! relation(
% 0.75/1.33 skol3 ), ! is_reflexive_in( skol3, relation_field( skol3 ) ) }.
% 0.75/1.33 parent0[1]: (21) {G0,W4,D2,L2,V0,M2} I { alpha1( skol3 ), ! reflexive(
% 0.75/1.33 skol3 ) }.
% 0.75/1.33 parent1[2]: (11) {G0,W8,D3,L3,V1,M3} I { ! relation( X ), ! is_reflexive_in
% 0.75/1.33 ( X, relation_field( X ) ), reflexive( X ) }.
% 0.75/1.33 substitution0:
% 0.75/1.33 end
% 0.75/1.33 substitution1:
% 0.75/1.33 X := skol3
% 0.75/1.33 end
% 0.75/1.33
% 0.75/1.33 resolution: (4509) {G1,W6,D3,L2,V0,M2} { alpha1( skol3 ), !
% 0.75/1.33 is_reflexive_in( skol3, relation_field( skol3 ) ) }.
% 0.75/1.33 parent0[1]: (4508) {G1,W8,D3,L3,V0,M3} { alpha1( skol3 ), ! relation(
% 0.75/1.33 skol3 ), ! is_reflexive_in( skol3, relation_field( skol3 ) ) }.
% 0.75/1.33 parent1[0]: (19) {G0,W2,D2,L1,V0,M1} I { relation( skol3 ) }.
% 0.75/1.33 substitution0:
% 0.75/1.33 end
% 0.75/1.33 substitution1:
% 0.75/1.33 end
% 0.75/1.33
% 0.75/1.33 subsumption: (139) {G1,W6,D3,L2,V0,M2} R(11,21);r(19) { ! is_reflexive_in(
% 0.75/1.33 skol3, relation_field( skol3 ) ), alpha1( skol3 ) }.
% 0.75/1.33 parent0: (4509) {G1,W6,D3,L2,V0,M2} { alpha1( skol3 ), ! is_reflexive_in(
% 0.75/1.33 skol3, relation_field( skol3 ) ) }.
% 0.75/1.33 substitution0:
% 0.75/1.33 end
% 0.75/1.33 permutation0:
% 0.75/1.33 0 ==> 1
% 0.75/1.33 1 ==> 0
% 0.75/1.33 end
% 0.75/1.33
% 0.75/1.33 resolution: (4510) {G1,W15,D4,L4,V2,M4} { ! relation( X ), !
% 0.75/1.33 is_reflexive_in( X, relation_field( Y ) ), in( ordered_pair( skol4( Y ),
% 0.75/1.33 skol4( Y ) ), X ), ! alpha1( Y ) }.
% 0.75/1.33 parent0[2]: (5) {G0,W13,D3,L4,V3,M4} I { ! relation( X ), ! is_reflexive_in
% 0.75/1.33 ( X, Y ), ! in( Z, Y ), in( ordered_pair( Z, Z ), X ) }.
% 0.75/1.33 parent1[1]: (23) {G0,W7,D3,L2,V1,M2} I { ! alpha1( X ), in( skol4( X ),
% 0.75/1.33 relation_field( X ) ) }.
% 0.75/1.33 substitution0:
% 0.75/1.33 X := X
% 0.75/1.33 Y := relation_field( Y )
% 0.75/1.33 Z := skol4( Y )
% 0.75/1.33 end
% 0.75/1.33 substitution1:
% 0.75/1.33 X := Y
% 0.75/1.33 end
% 0.75/1.33
% 0.75/1.33 subsumption: (212) {G1,W15,D4,L4,V2,M4} R(23,5) { ! alpha1( X ), ! relation
% 0.75/1.33 ( Y ), ! is_reflexive_in( Y, relation_field( X ) ), in( ordered_pair(
% 0.75/1.33 skol4( X ), skol4( X ) ), Y ) }.
% 0.75/1.33 parent0: (4510) {G1,W15,D4,L4,V2,M4} { ! relation( X ), ! is_reflexive_in
% 0.75/1.33 ( X, relation_field( Y ) ), in( ordered_pair( skol4( Y ), skol4( Y ) ), X
% 0.75/1.33 ), ! alpha1( Y ) }.
% 0.75/1.33 substitution0:
% 0.75/1.33 X := Y
% 0.75/1.33 Y := X
% 0.75/1.33 end
% 0.75/1.33 permutation0:
% 0.75/1.33 0 ==> 1
% 0.75/1.33 1 ==> 2
% 0.75/1.33 2 ==> 3
% 0.75/1.33 3 ==> 0
% 0.75/1.33 end
% 0.75/1.33
% 0.75/1.33 resolution: (4511) {G1,W17,D5,L3,V1,M3} { alpha1( skol3 ), in(
% 0.75/1.33 ordered_pair( skol1( X, relation_field( skol3 ) ), skol1( X,
% 0.75/1.33 relation_field( skol3 ) ) ), skol3 ), is_reflexive_in( skol3,
% 0.75/1.33 relation_field( skol3 ) ) }.
% 0.75/1.33 parent0[1]: (20) {G0,W11,D3,L3,V1,M3} I { alpha1( skol3 ), ! in( X,
% 0.75/1.33 relation_field( skol3 ) ), in( ordered_pair( X, X ), skol3 ) }.
% 0.75/1.33 parent1[0]: (71) {G1,W8,D3,L2,V2,M2} R(6,19) { in( skol1( X, Y ), Y ),
% 0.75/1.33 is_reflexive_in( skol3, Y ) }.
% 0.75/1.33 substitution0:
% 0.75/1.33 X := skol1( X, relation_field( skol3 ) )
% 0.75/1.33 end
% 0.75/1.33 substitution1:
% 0.75/1.33 X := X
% 0.75/1.33 Y := relation_field( skol3 )
% 0.75/1.33 end
% 0.75/1.33
% 0.75/1.33 resolution: (4512) {G2,W15,D5,L3,V1,M3} { alpha1( skol3 ), alpha1( skol3 )
% 0.75/1.33 , in( ordered_pair( skol1( X, relation_field( skol3 ) ), skol1( X,
% 0.75/1.33 relation_field( skol3 ) ) ), skol3 ) }.
% 0.75/1.33 parent0[0]: (139) {G1,W6,D3,L2,V0,M2} R(11,21);r(19) { ! is_reflexive_in(
% 0.75/1.33 skol3, relation_field( skol3 ) ), alpha1( skol3 ) }.
% 0.75/1.33 parent1[2]: (4511) {G1,W17,D5,L3,V1,M3} { alpha1( skol3 ), in(
% 0.75/1.33 ordered_pair( skol1( X, relation_field( skol3 ) ), skol1( X,
% 0.75/1.33 relation_field( skol3 ) ) ), skol3 ), is_reflexive_in( skol3,
% 0.75/1.33 relation_field( skol3 ) ) }.
% 0.75/1.33 substitution0:
% 0.75/1.33 end
% 0.75/1.33 substitution1:
% 0.75/1.33 X := X
% 0.75/1.33 end
% 0.75/1.33
% 0.75/1.33 factor: (4513) {G2,W13,D5,L2,V1,M2} { alpha1( skol3 ), in( ordered_pair(
% 0.75/1.33 skol1( X, relation_field( skol3 ) ), skol1( X, relation_field( skol3 ) )
% 0.75/1.33 ), skol3 ) }.
% 0.75/1.33 parent0[0, 1]: (4512) {G2,W15,D5,L3,V1,M3} { alpha1( skol3 ), alpha1(
% 0.75/1.33 skol3 ), in( ordered_pair( skol1( X, relation_field( skol3 ) ), skol1( X
% 0.75/1.33 , relation_field( skol3 ) ) ), skol3 ) }.
% 0.75/1.33 substitution0:
% 0.75/1.33 X := X
% 0.75/1.33 end
% 0.75/1.33
% 0.75/1.33 subsumption: (664) {G2,W13,D5,L2,V1,M2} R(71,20);r(139) { alpha1( skol3 ),
% 0.75/1.33 in( ordered_pair( skol1( X, relation_field( skol3 ) ), skol1( X,
% 0.75/1.33 relation_field( skol3 ) ) ), skol3 ) }.
% 0.75/1.33 parent0: (4513) {G2,W13,D5,L2,V1,M2} { alpha1( skol3 ), in( ordered_pair(
% 0.75/1.33 skol1( X, relation_field( skol3 ) ), skol1( X, relation_field( skol3 ) )
% 0.75/1.33 ), skol3 ) }.
% 0.75/1.33 substitution0:
% 0.75/1.33 X := X
% 0.75/1.33 end
% 0.75/1.33 permutation0:
% 0.75/1.33 0 ==> 0
% 0.75/1.33 1 ==> 1
% 0.75/1.33 end
% 0.75/1.33
% 0.75/1.33 resolution: (4514) {G2,W13,D5,L2,V0,M2} { alpha1( skol3 ), ! in(
% 0.75/1.33 ordered_pair( skol1( skol3, relation_field( skol3 ) ), skol1( skol3,
% 0.75/1.33 relation_field( skol3 ) ) ), skol3 ) }.
% 0.75/1.33 parent0[0]: (139) {G1,W6,D3,L2,V0,M2} R(11,21);r(19) { ! is_reflexive_in(
% 0.75/1.33 skol3, relation_field( skol3 ) ), alpha1( skol3 ) }.
% 0.75/1.33 parent1[1]: (82) {G1,W12,D4,L2,V1,M2} R(7,19) { ! in( ordered_pair( skol1(
% 0.75/1.33 skol3, X ), skol1( skol3, X ) ), skol3 ), is_reflexive_in( skol3, X ) }.
% 0.75/1.33 substitution0:
% 0.75/1.33 end
% 0.75/1.33 substitution1:
% 0.75/1.33 X := relation_field( skol3 )
% 0.75/1.33 end
% 0.75/1.33
% 0.75/1.33 resolution: (4515) {G3,W4,D2,L2,V0,M2} { alpha1( skol3 ), alpha1( skol3 )
% 0.75/1.33 }.
% 0.75/1.33 parent0[1]: (4514) {G2,W13,D5,L2,V0,M2} { alpha1( skol3 ), ! in(
% 0.75/1.33 ordered_pair( skol1( skol3, relation_field( skol3 ) ), skol1( skol3,
% 0.75/1.33 relation_field( skol3 ) ) ), skol3 ) }.
% 0.75/1.33 parent1[1]: (664) {G2,W13,D5,L2,V1,M2} R(71,20);r(139) { alpha1( skol3 ),
% 0.75/1.33 in( ordered_pair( skol1( X, relation_field( skol3 ) ), skol1( X,
% 0.75/1.33 relation_field( skol3 ) ) ), skol3 ) }.
% 0.75/1.33 substitution0:
% 0.75/1.33 end
% 0.75/1.33 substitution1:
% 0.75/1.33 X := skol3
% 0.75/1.33 end
% 0.75/1.33
% 0.75/1.33 factor: (4516) {G3,W2,D2,L1,V0,M1} { alpha1( skol3 ) }.
% 0.75/1.33 parent0[0, 1]: (4515) {G3,W4,D2,L2,V0,M2} { alpha1( skol3 ), alpha1( skol3
% 0.75/1.33 ) }.
% 0.75/1.33 substitution0:
% 0.75/1.33 end
% 0.75/1.33
% 0.75/1.33 subsumption: (1484) {G3,W2,D2,L1,V0,M1} R(139,82);r(664) { alpha1( skol3 )
% 0.75/1.33 }.
% 0.75/1.33 parent0: (4516) {G3,W2,D2,L1,V0,M1} { alpha1( skol3 ) }.
% 0.75/1.33 substitution0:
% 0.75/1.33 end
% 0.75/1.33 permutation0:
% 0.75/1.33 0 ==> 0
% 0.75/1.33 end
% 0.75/1.33
% 0.75/1.33 resolution: (4517) {G2,W15,D4,L5,V1,M5} { ! alpha1( X ), ! relation( X ),
% 0.75/1.33 in( ordered_pair( skol4( X ), skol4( X ) ), X ), ! relation( X ), !
% 0.75/1.33 alpha1( X ) }.
% 0.75/1.33 parent0[2]: (212) {G1,W15,D4,L4,V2,M4} R(23,5) { ! alpha1( X ), ! relation
% 0.75/1.33 ( Y ), ! is_reflexive_in( Y, relation_field( X ) ), in( ordered_pair(
% 0.75/1.33 skol4( X ), skol4( X ) ), Y ) }.
% 0.75/1.33 parent1[1]: (126) {G1,W8,D3,L3,V1,M3} R(10,22) { ! relation( X ),
% 0.75/1.33 is_reflexive_in( X, relation_field( X ) ), ! alpha1( X ) }.
% 0.75/1.33 substitution0:
% 0.75/1.33 X := X
% 0.75/1.33 Y := X
% 0.75/1.33 end
% 0.75/1.33 substitution1:
% 0.75/1.33 X := X
% 0.75/1.33 end
% 0.75/1.33
% 0.75/1.33 factor: (4518) {G2,W13,D4,L4,V1,M4} { ! alpha1( X ), ! relation( X ), in(
% 0.75/1.33 ordered_pair( skol4( X ), skol4( X ) ), X ), ! relation( X ) }.
% 0.75/1.33 parent0[0, 4]: (4517) {G2,W15,D4,L5,V1,M5} { ! alpha1( X ), ! relation( X
% 0.75/1.33 ), in( ordered_pair( skol4( X ), skol4( X ) ), X ), ! relation( X ), !
% 0.75/1.33 alpha1( X ) }.
% 0.75/1.33 substitution0:
% 0.75/1.33 X := X
% 0.75/1.33 end
% 0.75/1.33
% 0.75/1.33 factor: (4519) {G2,W11,D4,L3,V1,M3} { ! alpha1( X ), ! relation( X ), in(
% 0.75/1.33 ordered_pair( skol4( X ), skol4( X ) ), X ) }.
% 0.75/1.33 parent0[1, 3]: (4518) {G2,W13,D4,L4,V1,M4} { ! alpha1( X ), ! relation( X
% 0.75/1.33 ), in( ordered_pair( skol4( X ), skol4( X ) ), X ), ! relation( X ) }.
% 0.75/1.33 substitution0:
% 0.75/1.33 X := X
% 0.75/1.33 end
% 0.75/1.33
% 0.75/1.33 resolution: (4520) {G1,W6,D2,L3,V1,M3} { ! alpha1( X ), ! alpha1( X ), !
% 0.75/1.33 relation( X ) }.
% 0.75/1.33 parent0[1]: (24) {G0,W9,D4,L2,V1,M2} I { ! alpha1( X ), ! in( ordered_pair
% 0.75/1.33 ( skol4( X ), skol4( X ) ), X ) }.
% 0.75/1.33 parent1[2]: (4519) {G2,W11,D4,L3,V1,M3} { ! alpha1( X ), ! relation( X ),
% 0.75/1.33 in( ordered_pair( skol4( X ), skol4( X ) ), X ) }.
% 0.75/1.33 substitution0:
% 0.75/1.33 X := X
% 0.75/1.33 end
% 0.75/1.33 substitution1:
% 0.75/1.33 X := X
% 0.75/1.33 end
% 0.75/1.33
% 0.75/1.33 factor: (4521) {G1,W4,D2,L2,V1,M2} { ! alpha1( X ), ! relation( X ) }.
% 0.75/1.33 parent0[0, 1]: (4520) {G1,W6,D2,L3,V1,M3} { ! alpha1( X ), ! alpha1( X ),
% 0.75/1.33 ! relation( X ) }.
% 0.75/1.33 substitution0:
% 0.75/1.33 X := X
% 0.75/1.33 end
% 0.75/1.33
% 0.75/1.33 subsumption: (4414) {G2,W4,D2,L2,V1,M2} R(212,126);f;f;r(24) { ! alpha1( X
% 0.75/1.33 ), ! relation( X ) }.
% 0.75/1.33 parent0: (4521) {G1,W4,D2,L2,V1,M2} { ! alpha1( X ), ! relation( X ) }.
% 0.75/1.33 substitution0:
% 0.75/1.33 X := X
% 0.75/1.33 end
% 0.75/1.33 permutation0:
% 0.75/1.33 0 ==> 0
% 0.75/1.33 1 ==> 1
% 0.75/1.33 end
% 0.75/1.33
% 0.75/1.33 resolution: (4522) {G3,W2,D2,L1,V0,M1} { ! relation( skol3 ) }.
% 0.75/1.33 parent0[0]: (4414) {G2,W4,D2,L2,V1,M2} R(212,126);f;f;r(24) { ! alpha1( X )
% 0.75/1.33 , ! relation( X ) }.
% 0.75/1.33 parent1[0]: (1484) {G3,W2,D2,L1,V0,M1} R(139,82);r(664) { alpha1( skol3 )
% 0.75/1.33 }.
% 0.75/1.33 substitution0:
% 0.75/1.33 X := skol3
% 0.75/1.33 end
% 0.75/1.33 substitution1:
% 0.75/1.33 end
% 0.75/1.33
% 0.75/1.33 resolution: (4523) {G1,W0,D0,L0,V0,M0} { }.
% 0.75/1.33 parent0[0]: (4522) {G3,W2,D2,L1,V0,M1} { ! relation( skol3 ) }.
% 0.75/1.33 parent1[0]: (19) {G0,W2,D2,L1,V0,M1} I { relation( skol3 ) }.
% 0.75/1.33 substitution0:
% 0.75/1.33 end
% 0.75/1.33 substitution1:
% 0.75/1.33 end
% 0.75/1.33
% 0.75/1.33 subsumption: (4418) {G4,W0,D0,L0,V0,M0} R(4414,1484);r(19) { }.
% 0.75/1.33 parent0: (4523) {G1,W0,D0,L0,V0,M0} { }.
% 0.75/1.33 substitution0:
% 0.75/1.33 end
% 0.75/1.33 permutation0:
% 0.75/1.33 end
% 0.75/1.33
% 0.75/1.33 Proof check complete!
% 0.75/1.33
% 0.75/1.33 Memory use:
% 0.75/1.33
% 0.75/1.33 space for terms: 51629
% 0.75/1.33 space for clauses: 208245
% 0.75/1.33
% 0.75/1.33
% 0.75/1.33 clauses generated: 20702
% 0.75/1.33 clauses kept: 4419
% 0.75/1.33 clauses selected: 437
% 0.75/1.33 clauses deleted: 206
% 0.75/1.33 clauses inuse deleted: 101
% 0.75/1.33
% 0.75/1.33 subsentry: 55947
% 0.75/1.33 literals s-matched: 41694
% 0.75/1.33 literals matched: 38692
% 0.75/1.33 full subsumption: 4824
% 0.75/1.33
% 0.75/1.33 checksum: -1396841603
% 0.75/1.33
% 0.75/1.33
% 0.75/1.33 Bliksem ended
%------------------------------------------------------------------------------