%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : NUM411+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n011.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 06:22:00 EDT 2022
% Result : Theorem 0.78s 1.27s
% Output : Refutation 0.78s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : NUM411+1 : TPTP v8.1.0. Released v3.2.0.
% 0.03/0.13 % Command : bliksem %s
% 0.13/0.34 % Computer : n011.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 : Tue Jul 5 05:26:07 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.78/1.27 *** allocated 10000 integers for termspace/termends
% 0.78/1.27 *** allocated 10000 integers for clauses
% 0.78/1.27 *** allocated 10000 integers for justifications
% 0.78/1.27 Bliksem 1.12
% 0.78/1.27
% 0.78/1.27
% 0.78/1.27 Automatic Strategy Selection
% 0.78/1.27
% 0.78/1.27
% 0.78/1.27 Clauses:
% 0.78/1.27
% 0.78/1.27 { ! in( X, Y ), ! in( Y, X ) }.
% 0.78/1.27 { ! empty( X ), function( X ) }.
% 0.78/1.27 { ! ordinal( X ), epsilon_transitive( X ) }.
% 0.78/1.27 { ! ordinal( X ), epsilon_connected( X ) }.
% 0.78/1.27 { ! empty( X ), relation( X ) }.
% 0.78/1.27 { ! relation( X ), ! empty( X ), ! function( X ), relation( X ) }.
% 0.78/1.27 { ! relation( X ), ! empty( X ), ! function( X ), function( X ) }.
% 0.78/1.27 { ! relation( X ), ! empty( X ), ! function( X ), one_to_one( X ) }.
% 0.78/1.27 { ! epsilon_transitive( X ), ! epsilon_connected( X ), ordinal( X ) }.
% 0.78/1.27 { ! empty( X ), epsilon_transitive( X ) }.
% 0.78/1.27 { ! empty( X ), epsilon_connected( X ) }.
% 0.78/1.27 { ! empty( X ), ordinal( X ) }.
% 0.78/1.27 { ! relation( X ), ! function( X ), ! transfinite_sequence( X ), !
% 0.78/1.27 transfinite_sequence_of( X, Y ), subset( relation_rng( X ), Y ) }.
% 0.78/1.27 { ! relation( X ), ! function( X ), ! transfinite_sequence( X ), ! subset(
% 0.78/1.27 relation_rng( X ), Y ), transfinite_sequence_of( X, Y ) }.
% 0.78/1.27 { ! transfinite_sequence_of( X, Y ), relation( X ) }.
% 0.78/1.27 { ! transfinite_sequence_of( X, Y ), function( X ) }.
% 0.78/1.27 { ! transfinite_sequence_of( X, Y ), transfinite_sequence( X ) }.
% 0.78/1.27 { transfinite_sequence_of( skol1( X ), X ) }.
% 0.78/1.27 { element( skol2( X ), X ) }.
% 0.78/1.27 { empty( empty_set ) }.
% 0.78/1.27 { relation( empty_set ) }.
% 0.78/1.27 { relation_empty_yielding( empty_set ) }.
% 0.78/1.27 { empty( empty_set ) }.
% 0.78/1.27 { relation( empty_set ) }.
% 0.78/1.27 { relation_empty_yielding( empty_set ) }.
% 0.78/1.27 { function( empty_set ) }.
% 0.78/1.27 { one_to_one( empty_set ) }.
% 0.78/1.27 { empty( empty_set ) }.
% 0.78/1.27 { epsilon_transitive( empty_set ) }.
% 0.78/1.27 { epsilon_connected( empty_set ) }.
% 0.78/1.27 { ordinal( empty_set ) }.
% 0.78/1.27 { empty( empty_set ) }.
% 0.78/1.27 { relation( empty_set ) }.
% 0.78/1.27 { ! relation( X ), ! relation_non_empty( X ), ! function( X ),
% 0.78/1.27 with_non_empty_elements( relation_rng( X ) ) }.
% 0.78/1.27 { empty( X ), ! relation( X ), ! empty( relation_rng( X ) ) }.
% 0.78/1.27 { ! empty( X ), empty( relation_rng( X ) ) }.
% 0.78/1.27 { ! empty( X ), relation( relation_rng( X ) ) }.
% 0.78/1.27 { relation( skol3 ) }.
% 0.78/1.27 { function( skol3 ) }.
% 0.78/1.27 { epsilon_transitive( skol4 ) }.
% 0.78/1.27 { epsilon_connected( skol4 ) }.
% 0.78/1.27 { ordinal( skol4 ) }.
% 0.78/1.27 { empty( skol5 ) }.
% 0.78/1.27 { relation( skol5 ) }.
% 0.78/1.27 { empty( skol6 ) }.
% 0.78/1.27 { relation( skol7 ) }.
% 0.78/1.27 { empty( skol7 ) }.
% 0.78/1.27 { function( skol7 ) }.
% 0.78/1.27 { relation( skol8 ) }.
% 0.78/1.27 { function( skol8 ) }.
% 0.78/1.27 { one_to_one( skol8 ) }.
% 0.78/1.27 { empty( skol8 ) }.
% 0.78/1.27 { epsilon_transitive( skol8 ) }.
% 0.78/1.27 { epsilon_connected( skol8 ) }.
% 0.78/1.27 { ordinal( skol8 ) }.
% 0.78/1.27 { ! empty( skol9 ) }.
% 0.78/1.27 { relation( skol9 ) }.
% 0.78/1.27 { ! empty( skol10 ) }.
% 0.78/1.27 { relation( skol11 ) }.
% 0.78/1.27 { function( skol11 ) }.
% 0.78/1.27 { one_to_one( skol11 ) }.
% 0.78/1.27 { ! empty( skol12 ) }.
% 0.78/1.27 { epsilon_transitive( skol12 ) }.
% 0.78/1.27 { epsilon_connected( skol12 ) }.
% 0.78/1.27 { ordinal( skol12 ) }.
% 0.78/1.27 { relation( skol13 ) }.
% 0.78/1.27 { relation_empty_yielding( skol13 ) }.
% 0.78/1.27 { relation( skol14 ) }.
% 0.78/1.27 { relation_empty_yielding( skol14 ) }.
% 0.78/1.27 { function( skol14 ) }.
% 0.78/1.27 { relation( skol15 ) }.
% 0.78/1.27 { function( skol15 ) }.
% 0.78/1.27 { transfinite_sequence( skol15 ) }.
% 0.78/1.27 { relation( skol16 ) }.
% 0.78/1.27 { relation_non_empty( skol16 ) }.
% 0.78/1.27 { function( skol16 ) }.
% 0.78/1.27 { subset( X, X ) }.
% 0.78/1.27 { ! in( X, Y ), element( X, Y ) }.
% 0.78/1.27 { ! subset( X, Z ), ! subset( Z, Y ), subset( X, Y ) }.
% 0.78/1.27 { ! element( X, Y ), empty( Y ), in( X, Y ) }.
% 0.78/1.27 { ! element( X, powerset( Y ) ), subset( X, Y ) }.
% 0.78/1.27 { ! subset( X, Y ), element( X, powerset( Y ) ) }.
% 0.78/1.27 { subset( skol17, skol18 ) }.
% 0.78/1.27 { transfinite_sequence_of( skol19, skol17 ) }.
% 0.78/1.27 { ! transfinite_sequence_of( skol19, skol18 ) }.
% 0.78/1.27 { ! in( X, Z ), ! element( Z, powerset( Y ) ), element( X, Y ) }.
% 0.78/1.27 { ! in( X, Y ), ! element( Y, powerset( Z ) ), ! empty( Z ) }.
% 0.78/1.27 { ! empty( X ), X = empty_set }.
% 0.78/1.27 { ! in( X, Y ), ! empty( Y ) }.
% 0.78/1.27 { ! empty( X ), X = Y, ! empty( Y ) }.
% 0.78/1.27
% 0.78/1.27 percentage equality = 0.015625, percentage horn = 0.987805
% 0.78/1.27 This is a problem with some equality
% 0.78/1.27
% 0.78/1.27
% 0.78/1.27
% 0.78/1.27 Options Used:
% 0.78/1.27
% 0.78/1.27 useres = 1
% 0.78/1.27 useparamod = 1
% 0.78/1.27 useeqrefl = 1
% 0.78/1.27 useeqfact = 1
% 0.78/1.27 usefactor = 1
% 0.78/1.27 usesimpsplitting = 0
% 0.78/1.27 usesimpdemod = 5
% 0.78/1.27 usesimpres = 3
% 0.78/1.27
% 0.78/1.27 resimpinuse = 1000
% 0.78/1.27 resimpclauses = 20000
% 0.78/1.27 substype = eqrewr
% 0.78/1.27 backwardsubs = 1
% 0.78/1.27 selectoldest = 5
% 0.78/1.27
% 0.78/1.27 litorderings [0] = split
% 0.78/1.27 litorderings [1] = extend the termordering, first sorting on arguments
% 0.78/1.27
% 0.78/1.27 termordering = kbo
% 0.78/1.27
% 0.78/1.27 litapriori = 0
% 0.78/1.27 termapriori = 1
% 0.78/1.27 litaposteriori = 0
% 0.78/1.27 termaposteriori = 0
% 0.78/1.27 demodaposteriori = 0
% 0.78/1.27 ordereqreflfact = 0
% 0.78/1.27
% 0.78/1.27 litselect = negord
% 0.78/1.27
% 0.78/1.27 maxweight = 15
% 0.78/1.27 maxdepth = 30000
% 0.78/1.27 maxlength = 115
% 0.78/1.27 maxnrvars = 195
% 0.78/1.27 excuselevel = 1
% 0.78/1.27 increasemaxweight = 1
% 0.78/1.27
% 0.78/1.27 maxselected = 10000000
% 0.78/1.27 maxnrclauses = 10000000
% 0.78/1.27
% 0.78/1.27 showgenerated = 0
% 0.78/1.27 showkept = 0
% 0.78/1.27 showselected = 0
% 0.78/1.27 showdeleted = 0
% 0.78/1.27 showresimp = 1
% 0.78/1.27 showstatus = 2000
% 0.78/1.27
% 0.78/1.27 prologoutput = 0
% 0.78/1.27 nrgoals = 5000000
% 0.78/1.27 totalproof = 1
% 0.78/1.27
% 0.78/1.27 Symbols occurring in the translation:
% 0.78/1.27
% 0.78/1.27 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.78/1.27 . [1, 2] (w:1, o:47, a:1, s:1, b:0),
% 0.78/1.27 ! [4, 1] (w:0, o:27, a:1, s:1, b:0),
% 0.78/1.27 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.78/1.27 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.78/1.27 in [37, 2] (w:1, o:71, a:1, s:1, b:0),
% 0.78/1.27 empty [38, 1] (w:1, o:32, a:1, s:1, b:0),
% 0.78/1.27 function [39, 1] (w:1, o:35, a:1, s:1, b:0),
% 0.78/1.27 ordinal [40, 1] (w:1, o:36, a:1, s:1, b:0),
% 0.78/1.27 epsilon_transitive [41, 1] (w:1, o:33, a:1, s:1, b:0),
% 0.78/1.27 epsilon_connected [42, 1] (w:1, o:34, a:1, s:1, b:0),
% 0.78/1.27 relation [43, 1] (w:1, o:37, a:1, s:1, b:0),
% 0.78/1.27 one_to_one [44, 1] (w:1, o:38, a:1, s:1, b:0),
% 0.78/1.27 transfinite_sequence [45, 1] (w:1, o:41, a:1, s:1, b:0),
% 0.78/1.27 transfinite_sequence_of [46, 2] (w:1, o:73, a:1, s:1, b:0),
% 0.78/1.27 relation_rng [47, 1] (w:1, o:42, a:1, s:1, b:0),
% 0.78/1.27 subset [48, 2] (w:1, o:72, a:1, s:1, b:0),
% 0.78/1.27 element [49, 2] (w:1, o:74, a:1, s:1, b:0),
% 0.78/1.27 empty_set [50, 0] (w:1, o:8, a:1, s:1, b:0),
% 0.78/1.27 relation_empty_yielding [51, 1] (w:1, o:43, a:1, s:1, b:0),
% 0.78/1.27 relation_non_empty [52, 1] (w:1, o:44, a:1, s:1, b:0),
% 0.78/1.27 with_non_empty_elements [53, 1] (w:1, o:45, a:1, s:1, b:0),
% 0.78/1.27 powerset [55, 1] (w:1, o:46, a:1, s:1, b:0),
% 0.78/1.27 skol1 [56, 1] (w:1, o:39, a:1, s:1, b:1),
% 0.78/1.27 skol2 [57, 1] (w:1, o:40, a:1, s:1, b:1),
% 0.78/1.27 skol3 [58, 0] (w:1, o:10, a:1, s:1, b:1),
% 0.78/1.27 skol4 [59, 0] (w:1, o:11, a:1, s:1, b:1),
% 0.78/1.27 skol5 [60, 0] (w:1, o:12, a:1, s:1, b:1),
% 0.78/1.27 skol6 [61, 0] (w:1, o:13, a:1, s:1, b:1),
% 0.78/1.27 skol7 [62, 0] (w:1, o:14, a:1, s:1, b:1),
% 0.78/1.27 skol8 [63, 0] (w:1, o:15, a:1, s:1, b:1),
% 0.78/1.27 skol9 [64, 0] (w:1, o:16, a:1, s:1, b:1),
% 0.78/1.27 skol10 [65, 0] (w:1, o:17, a:1, s:1, b:1),
% 0.78/1.27 skol11 [66, 0] (w:1, o:18, a:1, s:1, b:1),
% 0.78/1.27 skol12 [67, 0] (w:1, o:19, a:1, s:1, b:1),
% 0.78/1.27 skol13 [68, 0] (w:1, o:20, a:1, s:1, b:1),
% 0.78/1.27 skol14 [69, 0] (w:1, o:21, a:1, s:1, b:1),
% 0.78/1.27 skol15 [70, 0] (w:1, o:22, a:1, s:1, b:1),
% 0.78/1.27 skol16 [71, 0] (w:1, o:23, a:1, s:1, b:1),
% 0.78/1.27 skol17 [72, 0] (w:1, o:24, a:1, s:1, b:1),
% 0.78/1.27 skol18 [73, 0] (w:1, o:25, a:1, s:1, b:1),
% 0.78/1.27 skol19 [74, 0] (w:1, o:26, a:1, s:1, b:1).
% 0.78/1.27
% 0.78/1.27
% 0.78/1.27 Starting Search:
% 0.78/1.27
% 0.78/1.27 *** allocated 15000 integers for clauses
% 0.78/1.27 *** allocated 22500 integers for clauses
% 0.78/1.27 *** allocated 33750 integers for clauses
% 0.78/1.27 *** allocated 50625 integers for clauses
% 0.78/1.27 *** allocated 15000 integers for termspace/termends
% 0.78/1.27 Resimplifying inuse:
% 0.78/1.27 Done
% 0.78/1.27
% 0.78/1.27 *** allocated 75937 integers for clauses
% 0.78/1.27 *** allocated 22500 integers for termspace/termends
% 0.78/1.27 *** allocated 113905 integers for clauses
% 0.78/1.27
% 0.78/1.27 Intermediate Status:
% 0.78/1.27 Generated: 7259
% 0.78/1.27 Kept: 2002
% 0.78/1.27 Inuse: 419
% 0.78/1.27 Deleted: 189
% 0.78/1.27 Deletedinuse: 89
% 0.78/1.27
% 0.78/1.27 Resimplifying inuse:
% 0.78/1.27 Done
% 0.78/1.27
% 0.78/1.27 *** allocated 33750 integers for termspace/termends
% 0.78/1.27 *** allocated 170857 integers for clauses
% 0.78/1.27
% 0.78/1.27 Bliksems!, er is een bewijs:
% 0.78/1.27 % SZS status Theorem
% 0.78/1.27 % SZS output start Refutation
% 0.78/1.27
% 0.78/1.27 (10) {G0,W13,D3,L5,V2,M5} I { ! relation( X ), ! function( X ), !
% 0.78/1.27 transfinite_sequence( X ), ! transfinite_sequence_of( X, Y ), subset(
% 0.78/1.27 relation_rng( X ), Y ) }.
% 0.78/1.27 (11) {G0,W13,D3,L5,V2,M5} I { ! relation( X ), ! function( X ), !
% 0.78/1.27 transfinite_sequence( X ), ! subset( relation_rng( X ), Y ),
% 0.78/1.27 transfinite_sequence_of( X, Y ) }.
% 0.78/1.27 (12) {G0,W5,D2,L2,V2,M2} I { ! transfinite_sequence_of( X, Y ), relation( X
% 0.78/1.27 ) }.
% 0.78/1.27 (13) {G0,W5,D2,L2,V2,M2} I { ! transfinite_sequence_of( X, Y ), function( X
% 0.78/1.27 ) }.
% 0.78/1.27 (14) {G0,W5,D2,L2,V2,M2} I { ! transfinite_sequence_of( X, Y ),
% 0.78/1.27 transfinite_sequence( X ) }.
% 0.78/1.27 (70) {G0,W9,D2,L3,V3,M3} I { ! subset( X, Z ), ! subset( Z, Y ), subset( X
% 0.78/1.27 , Y ) }.
% 0.78/1.27 (74) {G0,W3,D2,L1,V0,M1} I { subset( skol17, skol18 ) }.
% 0.78/1.27 (75) {G0,W3,D2,L1,V0,M1} I { transfinite_sequence_of( skol19, skol17 ) }.
% 0.78/1.27 (76) {G0,W3,D2,L1,V0,M1} I { ! transfinite_sequence_of( skol19, skol18 )
% 0.78/1.27 }.
% 0.78/1.27 (125) {G1,W14,D3,L5,V3,M5} R(12,10) { ! transfinite_sequence_of( X, Y ), !
% 0.78/1.27 function( X ), ! transfinite_sequence( X ), ! transfinite_sequence_of( X
% 0.78/1.27 , Z ), subset( relation_rng( X ), Z ) }.
% 0.78/1.27 (126) {G2,W11,D3,L4,V2,M4} F(125) { ! transfinite_sequence_of( X, Y ), !
% 0.78/1.27 function( X ), ! transfinite_sequence( X ), subset( relation_rng( X ), Y
% 0.78/1.27 ) }.
% 0.78/1.27 (136) {G1,W10,D3,L4,V0,M4} R(76,11) { ! relation( skol19 ), ! function(
% 0.78/1.27 skol19 ), ! transfinite_sequence( skol19 ), ! subset( relation_rng(
% 0.78/1.27 skol19 ), skol18 ) }.
% 0.78/1.27 (137) {G1,W2,D2,L1,V0,M1} R(75,14) { transfinite_sequence( skol19 ) }.
% 0.78/1.27 (138) {G1,W2,D2,L1,V0,M1} R(75,13) { function( skol19 ) }.
% 0.78/1.27 (139) {G1,W2,D2,L1,V0,M1} R(75,12) { relation( skol19 ) }.
% 0.78/1.27 (240) {G1,W6,D2,L2,V1,M2} R(70,74) { ! subset( X, skol17 ), subset( X,
% 0.78/1.27 skol18 ) }.
% 0.78/1.27 (849) {G3,W6,D3,L2,V0,M2} R(126,75);r(138) { ! transfinite_sequence( skol19
% 0.78/1.27 ), subset( relation_rng( skol19 ), skol17 ) }.
% 0.78/1.27 (1024) {G2,W4,D3,L1,V0,M1} S(136);r(139);r(138);r(137) { ! subset(
% 0.78/1.27 relation_rng( skol19 ), skol18 ) }.
% 0.78/1.27 (1025) {G3,W4,D3,L1,V0,M1} R(1024,240) { ! subset( relation_rng( skol19 ),
% 0.78/1.27 skol17 ) }.
% 0.78/1.27 (2969) {G4,W0,D0,L0,V0,M0} S(849);r(137);r(1025) { }.
% 0.78/1.27
% 0.78/1.27
% 0.78/1.27 % SZS output end Refutation
% 0.78/1.27 found a proof!
% 0.78/1.27
% 0.78/1.27
% 0.78/1.27 Unprocessed initial clauses:
% 0.78/1.27
% 0.78/1.27 (2971) {G0,W6,D2,L2,V2,M2} { ! in( X, Y ), ! in( Y, X ) }.
% 0.78/1.27 (2972) {G0,W4,D2,L2,V1,M2} { ! empty( X ), function( X ) }.
% 0.78/1.27 (2973) {G0,W4,D2,L2,V1,M2} { ! ordinal( X ), epsilon_transitive( X ) }.
% 0.78/1.27 (2974) {G0,W4,D2,L2,V1,M2} { ! ordinal( X ), epsilon_connected( X ) }.
% 0.78/1.27 (2975) {G0,W4,D2,L2,V1,M2} { ! empty( X ), relation( X ) }.
% 0.78/1.27 (2976) {G0,W8,D2,L4,V1,M4} { ! relation( X ), ! empty( X ), ! function( X
% 0.78/1.27 ), relation( X ) }.
% 0.78/1.27 (2977) {G0,W8,D2,L4,V1,M4} { ! relation( X ), ! empty( X ), ! function( X
% 0.78/1.27 ), function( X ) }.
% 0.78/1.27 (2978) {G0,W8,D2,L4,V1,M4} { ! relation( X ), ! empty( X ), ! function( X
% 0.78/1.27 ), one_to_one( X ) }.
% 0.78/1.27 (2979) {G0,W6,D2,L3,V1,M3} { ! epsilon_transitive( X ), !
% 0.78/1.27 epsilon_connected( X ), ordinal( X ) }.
% 0.78/1.27 (2980) {G0,W4,D2,L2,V1,M2} { ! empty( X ), epsilon_transitive( X ) }.
% 0.78/1.27 (2981) {G0,W4,D2,L2,V1,M2} { ! empty( X ), epsilon_connected( X ) }.
% 0.78/1.27 (2982) {G0,W4,D2,L2,V1,M2} { ! empty( X ), ordinal( X ) }.
% 0.78/1.27 (2983) {G0,W13,D3,L5,V2,M5} { ! relation( X ), ! function( X ), !
% 0.78/1.27 transfinite_sequence( X ), ! transfinite_sequence_of( X, Y ), subset(
% 0.78/1.27 relation_rng( X ), Y ) }.
% 0.78/1.27 (2984) {G0,W13,D3,L5,V2,M5} { ! relation( X ), ! function( X ), !
% 0.78/1.27 transfinite_sequence( X ), ! subset( relation_rng( X ), Y ),
% 0.78/1.27 transfinite_sequence_of( X, Y ) }.
% 0.78/1.27 (2985) {G0,W5,D2,L2,V2,M2} { ! transfinite_sequence_of( X, Y ), relation(
% 0.78/1.27 X ) }.
% 0.78/1.27 (2986) {G0,W5,D2,L2,V2,M2} { ! transfinite_sequence_of( X, Y ), function(
% 0.78/1.27 X ) }.
% 0.78/1.27 (2987) {G0,W5,D2,L2,V2,M2} { ! transfinite_sequence_of( X, Y ),
% 0.78/1.27 transfinite_sequence( X ) }.
% 0.78/1.27 (2988) {G0,W4,D3,L1,V1,M1} { transfinite_sequence_of( skol1( X ), X ) }.
% 0.78/1.27 (2989) {G0,W4,D3,L1,V1,M1} { element( skol2( X ), X ) }.
% 0.78/1.27 (2990) {G0,W2,D2,L1,V0,M1} { empty( empty_set ) }.
% 0.78/1.27 (2991) {G0,W2,D2,L1,V0,M1} { relation( empty_set ) }.
% 0.78/1.27 (2992) {G0,W2,D2,L1,V0,M1} { relation_empty_yielding( empty_set ) }.
% 0.78/1.27 (2993) {G0,W2,D2,L1,V0,M1} { empty( empty_set ) }.
% 0.78/1.27 (2994) {G0,W2,D2,L1,V0,M1} { relation( empty_set ) }.
% 0.78/1.27 (2995) {G0,W2,D2,L1,V0,M1} { relation_empty_yielding( empty_set ) }.
% 0.78/1.27 (2996) {G0,W2,D2,L1,V0,M1} { function( empty_set ) }.
% 0.78/1.27 (2997) {G0,W2,D2,L1,V0,M1} { one_to_one( empty_set ) }.
% 0.78/1.27 (2998) {G0,W2,D2,L1,V0,M1} { empty( empty_set ) }.
% 0.78/1.27 (2999) {G0,W2,D2,L1,V0,M1} { epsilon_transitive( empty_set ) }.
% 0.78/1.27 (3000) {G0,W2,D2,L1,V0,M1} { epsilon_connected( empty_set ) }.
% 0.78/1.27 (3001) {G0,W2,D2,L1,V0,M1} { ordinal( empty_set ) }.
% 0.78/1.27 (3002) {G0,W2,D2,L1,V0,M1} { empty( empty_set ) }.
% 0.78/1.27 (3003) {G0,W2,D2,L1,V0,M1} { relation( empty_set ) }.
% 0.78/1.27 (3004) {G0,W9,D3,L4,V1,M4} { ! relation( X ), ! relation_non_empty( X ), !
% 0.78/1.27 function( X ), with_non_empty_elements( relation_rng( X ) ) }.
% 0.78/1.27 (3005) {G0,W7,D3,L3,V1,M3} { empty( X ), ! relation( X ), ! empty(
% 0.78/1.27 relation_rng( X ) ) }.
% 0.78/1.27 (3006) {G0,W5,D3,L2,V1,M2} { ! empty( X ), empty( relation_rng( X ) ) }.
% 0.78/1.27 (3007) {G0,W5,D3,L2,V1,M2} { ! empty( X ), relation( relation_rng( X ) )
% 0.78/1.27 }.
% 0.78/1.27 (3008) {G0,W2,D2,L1,V0,M1} { relation( skol3 ) }.
% 0.78/1.27 (3009) {G0,W2,D2,L1,V0,M1} { function( skol3 ) }.
% 0.78/1.27 (3010) {G0,W2,D2,L1,V0,M1} { epsilon_transitive( skol4 ) }.
% 0.78/1.27 (3011) {G0,W2,D2,L1,V0,M1} { epsilon_connected( skol4 ) }.
% 0.78/1.27 (3012) {G0,W2,D2,L1,V0,M1} { ordinal( skol4 ) }.
% 0.78/1.27 (3013) {G0,W2,D2,L1,V0,M1} { empty( skol5 ) }.
% 0.78/1.27 (3014) {G0,W2,D2,L1,V0,M1} { relation( skol5 ) }.
% 0.78/1.27 (3015) {G0,W2,D2,L1,V0,M1} { empty( skol6 ) }.
% 0.78/1.27 (3016) {G0,W2,D2,L1,V0,M1} { relation( skol7 ) }.
% 0.78/1.27 (3017) {G0,W2,D2,L1,V0,M1} { empty( skol7 ) }.
% 0.78/1.27 (3018) {G0,W2,D2,L1,V0,M1} { function( skol7 ) }.
% 0.78/1.27 (3019) {G0,W2,D2,L1,V0,M1} { relation( skol8 ) }.
% 0.78/1.27 (3020) {G0,W2,D2,L1,V0,M1} { function( skol8 ) }.
% 0.78/1.27 (3021) {G0,W2,D2,L1,V0,M1} { one_to_one( skol8 ) }.
% 0.78/1.27 (3022) {G0,W2,D2,L1,V0,M1} { empty( skol8 ) }.
% 0.78/1.27 (3023) {G0,W2,D2,L1,V0,M1} { epsilon_transitive( skol8 ) }.
% 0.78/1.27 (3024) {G0,W2,D2,L1,V0,M1} { epsilon_connected( skol8 ) }.
% 0.78/1.27 (3025) {G0,W2,D2,L1,V0,M1} { ordinal( skol8 ) }.
% 0.78/1.27 (3026) {G0,W2,D2,L1,V0,M1} { ! empty( skol9 ) }.
% 0.78/1.27 (3027) {G0,W2,D2,L1,V0,M1} { relation( skol9 ) }.
% 0.78/1.27 (3028) {G0,W2,D2,L1,V0,M1} { ! empty( skol10 ) }.
% 0.78/1.27 (3029) {G0,W2,D2,L1,V0,M1} { relation( skol11 ) }.
% 0.78/1.27 (3030) {G0,W2,D2,L1,V0,M1} { function( skol11 ) }.
% 0.78/1.27 (3031) {G0,W2,D2,L1,V0,M1} { one_to_one( skol11 ) }.
% 0.78/1.27 (3032) {G0,W2,D2,L1,V0,M1} { ! empty( skol12 ) }.
% 0.78/1.27 (3033) {G0,W2,D2,L1,V0,M1} { epsilon_transitive( skol12 ) }.
% 0.78/1.27 (3034) {G0,W2,D2,L1,V0,M1} { epsilon_connected( skol12 ) }.
% 0.78/1.27 (3035) {G0,W2,D2,L1,V0,M1} { ordinal( skol12 ) }.
% 0.78/1.27 (3036) {G0,W2,D2,L1,V0,M1} { relation( skol13 ) }.
% 0.78/1.27 (3037) {G0,W2,D2,L1,V0,M1} { relation_empty_yielding( skol13 ) }.
% 0.78/1.27 (3038) {G0,W2,D2,L1,V0,M1} { relation( skol14 ) }.
% 0.78/1.27 (3039) {G0,W2,D2,L1,V0,M1} { relation_empty_yielding( skol14 ) }.
% 0.78/1.27 (3040) {G0,W2,D2,L1,V0,M1} { function( skol14 ) }.
% 0.78/1.27 (3041) {G0,W2,D2,L1,V0,M1} { relation( skol15 ) }.
% 0.78/1.27 (3042) {G0,W2,D2,L1,V0,M1} { function( skol15 ) }.
% 0.78/1.27 (3043) {G0,W2,D2,L1,V0,M1} { transfinite_sequence( skol15 ) }.
% 0.78/1.27 (3044) {G0,W2,D2,L1,V0,M1} { relation( skol16 ) }.
% 0.78/1.27 (3045) {G0,W2,D2,L1,V0,M1} { relation_non_empty( skol16 ) }.
% 0.78/1.27 (3046) {G0,W2,D2,L1,V0,M1} { function( skol16 ) }.
% 0.78/1.27 (3047) {G0,W3,D2,L1,V1,M1} { subset( X, X ) }.
% 0.78/1.27 (3048) {G0,W6,D2,L2,V2,M2} { ! in( X, Y ), element( X, Y ) }.
% 0.78/1.27 (3049) {G0,W9,D2,L3,V3,M3} { ! subset( X, Z ), ! subset( Z, Y ), subset( X
% 0.78/1.27 , Y ) }.
% 0.78/1.27 (3050) {G0,W8,D2,L3,V2,M3} { ! element( X, Y ), empty( Y ), in( X, Y ) }.
% 0.78/1.27 (3051) {G0,W7,D3,L2,V2,M2} { ! element( X, powerset( Y ) ), subset( X, Y )
% 0.78/1.27 }.
% 0.78/1.27 (3052) {G0,W7,D3,L2,V2,M2} { ! subset( X, Y ), element( X, powerset( Y ) )
% 0.78/1.27 }.
% 0.78/1.27 (3053) {G0,W3,D2,L1,V0,M1} { subset( skol17, skol18 ) }.
% 0.78/1.27 (3054) {G0,W3,D2,L1,V0,M1} { transfinite_sequence_of( skol19, skol17 ) }.
% 0.78/1.27 (3055) {G0,W3,D2,L1,V0,M1} { ! transfinite_sequence_of( skol19, skol18 )
% 0.78/1.27 }.
% 0.78/1.27 (3056) {G0,W10,D3,L3,V3,M3} { ! in( X, Z ), ! element( Z, powerset( Y ) )
% 0.78/1.27 , element( X, Y ) }.
% 0.78/1.27 (3057) {G0,W9,D3,L3,V3,M3} { ! in( X, Y ), ! element( Y, powerset( Z ) ),
% 0.78/1.27 ! empty( Z ) }.
% 0.78/1.27 (3058) {G0,W5,D2,L2,V1,M2} { ! empty( X ), X = empty_set }.
% 0.78/1.27 (3059) {G0,W5,D2,L2,V2,M2} { ! in( X, Y ), ! empty( Y ) }.
% 0.78/1.27 (3060) {G0,W7,D2,L3,V2,M3} { ! empty( X ), X = Y, ! empty( Y ) }.
% 0.78/1.27
% 0.78/1.27
% 0.78/1.27 Total Proof:
% 0.78/1.27
% 0.78/1.27 subsumption: (10) {G0,W13,D3,L5,V2,M5} I { ! relation( X ), ! function( X )
% 0.78/1.27 , ! transfinite_sequence( X ), ! transfinite_sequence_of( X, Y ), subset
% 0.78/1.27 ( relation_rng( X ), Y ) }.
% 0.78/1.27 parent0: (2983) {G0,W13,D3,L5,V2,M5} { ! relation( X ), ! function( X ), !
% 0.78/1.27 transfinite_sequence( X ), ! transfinite_sequence_of( X, Y ), subset(
% 0.78/1.27 relation_rng( X ), Y ) }.
% 0.78/1.27 substitution0:
% 0.78/1.27 X := X
% 0.78/1.27 Y := Y
% 0.78/1.27 end
% 0.78/1.27 permutation0:
% 0.78/1.27 0 ==> 0
% 0.78/1.27 1 ==> 1
% 0.78/1.27 2 ==> 2
% 0.78/1.27 3 ==> 3
% 0.78/1.27 4 ==> 4
% 0.78/1.27 end
% 0.78/1.27
% 0.78/1.27 subsumption: (11) {G0,W13,D3,L5,V2,M5} I { ! relation( X ), ! function( X )
% 0.78/1.27 , ! transfinite_sequence( X ), ! subset( relation_rng( X ), Y ),
% 0.78/1.27 transfinite_sequence_of( X, Y ) }.
% 0.78/1.27 parent0: (2984) {G0,W13,D3,L5,V2,M5} { ! relation( X ), ! function( X ), !
% 0.78/1.27 transfinite_sequence( X ), ! subset( relation_rng( X ), Y ),
% 0.78/1.27 transfinite_sequence_of( X, Y ) }.
% 0.78/1.27 substitution0:
% 0.78/1.27 X := X
% 0.78/1.27 Y := Y
% 0.78/1.27 end
% 0.78/1.27 permutation0:
% 0.78/1.27 0 ==> 0
% 0.78/1.27 1 ==> 1
% 0.78/1.27 2 ==> 2
% 0.78/1.27 3 ==> 3
% 0.78/1.27 4 ==> 4
% 0.78/1.27 end
% 0.78/1.27
% 0.78/1.27 subsumption: (12) {G0,W5,D2,L2,V2,M2} I { ! transfinite_sequence_of( X, Y )
% 0.78/1.27 , relation( X ) }.
% 0.78/1.27 parent0: (2985) {G0,W5,D2,L2,V2,M2} { ! transfinite_sequence_of( X, Y ),
% 0.78/1.27 relation( X ) }.
% 0.78/1.27 substitution0:
% 0.78/1.27 X := X
% 0.78/1.27 Y := Y
% 0.78/1.27 end
% 0.78/1.27 permutation0:
% 0.78/1.27 0 ==> 0
% 0.78/1.27 1 ==> 1
% 0.78/1.27 end
% 0.78/1.27
% 0.78/1.27 subsumption: (13) {G0,W5,D2,L2,V2,M2} I { ! transfinite_sequence_of( X, Y )
% 0.78/1.27 , function( X ) }.
% 0.78/1.27 parent0: (2986) {G0,W5,D2,L2,V2,M2} { ! transfinite_sequence_of( X, Y ),
% 0.78/1.27 function( X ) }.
% 0.78/1.27 substitution0:
% 0.78/1.27 X := X
% 0.78/1.27 Y := Y
% 0.78/1.27 end
% 0.78/1.27 permutation0:
% 0.78/1.27 0 ==> 0
% 0.78/1.27 1 ==> 1
% 0.78/1.27 end
% 0.78/1.27
% 0.78/1.27 subsumption: (14) {G0,W5,D2,L2,V2,M2} I { ! transfinite_sequence_of( X, Y )
% 0.78/1.27 , transfinite_sequence( X ) }.
% 0.78/1.27 parent0: (2987) {G0,W5,D2,L2,V2,M2} { ! transfinite_sequence_of( X, Y ),
% 0.78/1.27 transfinite_sequence( X ) }.
% 0.78/1.27 substitution0:
% 0.78/1.27 X := X
% 0.78/1.27 Y := Y
% 0.78/1.27 end
% 0.78/1.27 permutation0:
% 0.78/1.27 0 ==> 0
% 0.78/1.27 1 ==> 1
% 0.78/1.27 end
% 0.78/1.27
% 0.78/1.27 subsumption: (70) {G0,W9,D2,L3,V3,M3} I { ! subset( X, Z ), ! subset( Z, Y
% 0.78/1.27 ), subset( X, Y ) }.
% 0.78/1.27 parent0: (3049) {G0,W9,D2,L3,V3,M3} { ! subset( X, Z ), ! subset( Z, Y ),
% 0.78/1.27 subset( X, Y ) }.
% 0.78/1.27 substitution0:
% 0.78/1.27 X := X
% 0.78/1.27 Y := Y
% 0.78/1.27 Z := Z
% 0.78/1.27 end
% 0.78/1.27 permutation0:
% 0.78/1.27 0 ==> 0
% 0.78/1.27 1 ==> 1
% 0.78/1.27 2 ==> 2
% 0.78/1.27 end
% 0.78/1.27
% 0.78/1.27 subsumption: (74) {G0,W3,D2,L1,V0,M1} I { subset( skol17, skol18 ) }.
% 0.78/1.27 parent0: (3053) {G0,W3,D2,L1,V0,M1} { subset( skol17, skol18 ) }.
% 0.78/1.27 substitution0:
% 0.78/1.27 end
% 0.78/1.27 permutation0:
% 0.78/1.27 0 ==> 0
% 0.78/1.27 end
% 0.78/1.27
% 0.78/1.27 subsumption: (75) {G0,W3,D2,L1,V0,M1} I { transfinite_sequence_of( skol19,
% 0.78/1.27 skol17 ) }.
% 0.78/1.27 parent0: (3054) {G0,W3,D2,L1,V0,M1} { transfinite_sequence_of( skol19,
% 0.78/1.27 skol17 ) }.
% 0.78/1.27 substitution0:
% 0.78/1.27 end
% 0.78/1.27 permutation0:
% 0.78/1.27 0 ==> 0
% 0.78/1.27 end
% 0.78/1.27
% 0.78/1.27 subsumption: (76) {G0,W3,D2,L1,V0,M1} I { ! transfinite_sequence_of( skol19
% 0.78/1.27 , skol18 ) }.
% 0.78/1.27 parent0: (3055) {G0,W3,D2,L1,V0,M1} { ! transfinite_sequence_of( skol19,
% 0.78/1.27 skol18 ) }.
% 0.78/1.27 substitution0:
% 0.78/1.27 end
% 0.78/1.27 permutation0:
% 0.78/1.27 0 ==> 0
% 0.78/1.27 end
% 0.78/1.27
% 0.78/1.27 resolution: (3074) {G1,W14,D3,L5,V3,M5} { ! function( X ), !
% 0.78/1.27 transfinite_sequence( X ), ! transfinite_sequence_of( X, Y ), subset(
% 0.78/1.27 relation_rng( X ), Y ), ! transfinite_sequence_of( X, Z ) }.
% 0.78/1.27 parent0[0]: (10) {G0,W13,D3,L5,V2,M5} I { ! relation( X ), ! function( X )
% 0.78/1.27 , ! transfinite_sequence( X ), ! transfinite_sequence_of( X, Y ), subset
% 0.78/1.27 ( relation_rng( X ), Y ) }.
% 0.78/1.27 parent1[1]: (12) {G0,W5,D2,L2,V2,M2} I { ! transfinite_sequence_of( X, Y )
% 0.78/1.27 , relation( X ) }.
% 0.78/1.27 substitution0:
% 0.78/1.27 X := X
% 0.78/1.27 Y := Y
% 0.78/1.27 end
% 0.78/1.27 substitution1:
% 0.78/1.27 X := X
% 0.78/1.27 Y := Z
% 0.78/1.27 end
% 0.78/1.27
% 0.78/1.27 subsumption: (125) {G1,W14,D3,L5,V3,M5} R(12,10) { !
% 0.78/1.27 transfinite_sequence_of( X, Y ), ! function( X ), ! transfinite_sequence
% 0.78/1.27 ( X ), ! transfinite_sequence_of( X, Z ), subset( relation_rng( X ), Z )
% 0.78/1.27 }.
% 0.78/1.27 parent0: (3074) {G1,W14,D3,L5,V3,M5} { ! function( X ), !
% 0.78/1.27 transfinite_sequence( X ), ! transfinite_sequence_of( X, Y ), subset(
% 0.78/1.27 relation_rng( X ), Y ), ! transfinite_sequence_of( X, Z ) }.
% 0.78/1.27 substitution0:
% 0.78/1.27 X := X
% 0.78/1.27 Y := Z
% 0.78/1.27 Z := Y
% 0.78/1.27 end
% 0.78/1.27 permutation0:
% 0.78/1.27 0 ==> 1
% 0.78/1.27 1 ==> 2
% 0.78/1.27 2 ==> 3
% 0.78/1.27 3 ==> 4
% 0.78/1.27 4 ==> 0
% 0.78/1.27 end
% 0.78/1.27
% 0.78/1.27 factor: (3076) {G1,W11,D3,L4,V2,M4} { ! transfinite_sequence_of( X, Y ), !
% 0.78/1.27 function( X ), ! transfinite_sequence( X ), subset( relation_rng( X ), Y
% 0.78/1.27 ) }.
% 0.78/1.27 parent0[0, 3]: (125) {G1,W14,D3,L5,V3,M5} R(12,10) { !
% 0.78/1.27 transfinite_sequence_of( X, Y ), ! function( X ), ! transfinite_sequence
% 0.78/1.27 ( X ), ! transfinite_sequence_of( X, Z ), subset( relation_rng( X ), Z )
% 0.78/1.27 }.
% 0.78/1.27 substitution0:
% 0.78/1.27 X := X
% 0.78/1.27 Y := Y
% 0.78/1.27 Z := Y
% 0.78/1.27 end
% 0.78/1.27
% 0.78/1.27 subsumption: (126) {G2,W11,D3,L4,V2,M4} F(125) { ! transfinite_sequence_of
% 0.78/1.27 ( X, Y ), ! function( X ), ! transfinite_sequence( X ), subset(
% 0.78/1.27 relation_rng( X ), Y ) }.
% 0.78/1.27 parent0: (3076) {G1,W11,D3,L4,V2,M4} { ! transfinite_sequence_of( X, Y ),
% 0.78/1.27 ! function( X ), ! transfinite_sequence( X ), subset( relation_rng( X ),
% 0.78/1.27 Y ) }.
% 0.78/1.27 substitution0:
% 0.78/1.27 X := X
% 0.78/1.27 Y := Y
% 0.78/1.27 end
% 0.78/1.27 permutation0:
% 0.78/1.27 0 ==> 0
% 0.78/1.27 1 ==> 1
% 0.78/1.27 2 ==> 2
% 0.78/1.27 3 ==> 3
% 0.78/1.27 end
% 0.78/1.27
% 0.78/1.27 resolution: (3077) {G1,W10,D3,L4,V0,M4} { ! relation( skol19 ), ! function
% 0.78/1.27 ( skol19 ), ! transfinite_sequence( skol19 ), ! subset( relation_rng(
% 0.78/1.27 skol19 ), skol18 ) }.
% 0.78/1.27 parent0[0]: (76) {G0,W3,D2,L1,V0,M1} I { ! transfinite_sequence_of( skol19
% 0.78/1.27 , skol18 ) }.
% 0.78/1.27 parent1[4]: (11) {G0,W13,D3,L5,V2,M5} I { ! relation( X ), ! function( X )
% 0.78/1.27 , ! transfinite_sequence( X ), ! subset( relation_rng( X ), Y ),
% 0.78/1.27 transfinite_sequence_of( X, Y ) }.
% 0.78/1.27 substitution0:
% 0.78/1.27 end
% 0.78/1.27 substitution1:
% 0.78/1.27 X := skol19
% 0.78/1.27 Y := skol18
% 0.78/1.27 end
% 0.78/1.27
% 0.78/1.27 subsumption: (136) {G1,W10,D3,L4,V0,M4} R(76,11) { ! relation( skol19 ), !
% 0.78/1.27 function( skol19 ), ! transfinite_sequence( skol19 ), ! subset(
% 0.78/1.27 relation_rng( skol19 ), skol18 ) }.
% 0.78/1.27 parent0: (3077) {G1,W10,D3,L4,V0,M4} { ! relation( skol19 ), ! function(
% 0.78/1.27 skol19 ), ! transfinite_sequence( skol19 ), ! subset( relation_rng(
% 0.78/1.27 skol19 ), skol18 ) }.
% 0.78/1.27 substitution0:
% 0.78/1.27 end
% 0.78/1.27 permutation0:
% 0.78/1.27 0 ==> 0
% 0.78/1.27 1 ==> 1
% 0.78/1.27 2 ==> 2
% 0.78/1.27 3 ==> 3
% 0.78/1.27 end
% 0.78/1.27
% 0.78/1.27 resolution: (3078) {G1,W2,D2,L1,V0,M1} { transfinite_sequence( skol19 )
% 0.78/1.27 }.
% 0.78/1.27 parent0[0]: (14) {G0,W5,D2,L2,V2,M2} I { ! transfinite_sequence_of( X, Y )
% 0.78/1.27 , transfinite_sequence( X ) }.
% 0.78/1.27 parent1[0]: (75) {G0,W3,D2,L1,V0,M1} I { transfinite_sequence_of( skol19,
% 0.78/1.27 skol17 ) }.
% 0.78/1.27 substitution0:
% 0.78/1.27 X := skol19
% 0.78/1.27 Y := skol17
% 0.78/1.27 end
% 0.78/1.27 substitution1:
% 0.78/1.27 end
% 0.78/1.27
% 0.78/1.27 subsumption: (137) {G1,W2,D2,L1,V0,M1} R(75,14) { transfinite_sequence(
% 0.78/1.27 skol19 ) }.
% 0.78/1.27 parent0: (3078) {G1,W2,D2,L1,V0,M1} { transfinite_sequence( skol19 ) }.
% 0.78/1.27 substitution0:
% 0.78/1.27 end
% 0.78/1.27 permutation0:
% 0.78/1.27 0 ==> 0
% 0.78/1.27 end
% 0.78/1.27
% 0.78/1.27 resolution: (3079) {G1,W2,D2,L1,V0,M1} { function( skol19 ) }.
% 0.78/1.27 parent0[0]: (13) {G0,W5,D2,L2,V2,M2} I { ! transfinite_sequence_of( X, Y )
% 0.78/1.27 , function( X ) }.
% 0.78/1.27 parent1[0]: (75) {G0,W3,D2,L1,V0,M1} I { transfinite_sequence_of( skol19,
% 0.78/1.27 skol17 ) }.
% 0.78/1.27 substitution0:
% 0.78/1.27 X := skol19
% 0.78/1.27 Y := skol17
% 0.78/1.27 end
% 0.78/1.27 substitution1:
% 0.78/1.27 end
% 0.78/1.27
% 0.78/1.27 subsumption: (138) {G1,W2,D2,L1,V0,M1} R(75,13) { function( skol19 ) }.
% 0.78/1.27 parent0: (3079) {G1,W2,D2,L1,V0,M1} { function( skol19 ) }.
% 0.78/1.27 substitution0:
% 0.78/1.27 end
% 0.78/1.27 permutation0:
% 0.78/1.27 0 ==> 0
% 0.78/1.27 end
% 0.78/1.27
% 0.78/1.27 resolution: (3080) {G1,W2,D2,L1,V0,M1} { relation( skol19 ) }.
% 0.78/1.27 parent0[0]: (12) {G0,W5,D2,L2,V2,M2} I { ! transfinite_sequence_of( X, Y )
% 0.78/1.27 , relation( X ) }.
% 0.78/1.27 parent1[0]: (75) {G0,W3,D2,L1,V0,M1} I { transfinite_sequence_of( skol19,
% 0.78/1.27 skol17 ) }.
% 0.78/1.27 substitution0:
% 0.78/1.27 X := skol19
% 0.78/1.27 Y := skol17
% 0.78/1.27 end
% 0.78/1.27 substitution1:
% 0.78/1.27 end
% 0.78/1.27
% 0.78/1.27 subsumption: (139) {G1,W2,D2,L1,V0,M1} R(75,12) { relation( skol19 ) }.
% 0.78/1.27 parent0: (3080) {G1,W2,D2,L1,V0,M1} { relation( skol19 ) }.
% 0.78/1.27 substitution0:
% 0.78/1.27 end
% 0.78/1.27 permutation0:
% 0.78/1.27 0 ==> 0
% 0.78/1.27 end
% 0.78/1.27
% 0.78/1.27 resolution: (3082) {G1,W6,D2,L2,V1,M2} { ! subset( X, skol17 ), subset( X
% 0.78/1.27 , skol18 ) }.
% 0.78/1.27 parent0[1]: (70) {G0,W9,D2,L3,V3,M3} I { ! subset( X, Z ), ! subset( Z, Y )
% 0.78/1.27 , subset( X, Y ) }.
% 0.78/1.27 parent1[0]: (74) {G0,W3,D2,L1,V0,M1} I { subset( skol17, skol18 ) }.
% 0.78/1.27 substitution0:
% 0.78/1.27 X := X
% 0.78/1.27 Y := skol18
% 0.78/1.27 Z := skol17
% 0.78/1.27 end
% 0.78/1.27 substitution1:
% 0.78/1.27 end
% 0.78/1.27
% 0.78/1.27 subsumption: (240) {G1,W6,D2,L2,V1,M2} R(70,74) { ! subset( X, skol17 ),
% 0.78/1.27 subset( X, skol18 ) }.
% 0.78/1.27 parent0: (3082) {G1,W6,D2,L2,V1,M2} { ! subset( X, skol17 ), subset( X,
% 0.78/1.27 skol18 ) }.
% 0.78/1.27 substitution0:
% 0.78/1.27 X := X
% 0.78/1.27 end
% 0.78/1.27 permutation0:
% 0.78/1.27 0 ==> 0
% 0.78/1.27 1 ==> 1
% 0.78/1.27 end
% 0.78/1.27
% 0.78/1.27 resolution: (3083) {G1,W8,D3,L3,V0,M3} { ! function( skol19 ), !
% 0.78/1.27 transfinite_sequence( skol19 ), subset( relation_rng( skol19 ), skol17 )
% 0.78/1.27 }.
% 0.78/1.27 parent0[0]: (126) {G2,W11,D3,L4,V2,M4} F(125) { ! transfinite_sequence_of(
% 0.78/1.27 X, Y ), ! function( X ), ! transfinite_sequence( X ), subset(
% 0.78/1.27 relation_rng( X ), Y ) }.
% 0.78/1.27 parent1[0]: (75) {G0,W3,D2,L1,V0,M1} I { transfinite_sequence_of( skol19,
% 0.78/1.27 skol17 ) }.
% 0.78/1.27 substitution0:
% 0.78/1.27 X := skol19
% 0.78/1.27 Y := skol17
% 0.78/1.27 end
% 0.78/1.27 substitution1:
% 0.78/1.27 end
% 0.78/1.27
% 0.78/1.27 resolution: (3084) {G2,W6,D3,L2,V0,M2} { ! transfinite_sequence( skol19 )
% 0.78/1.27 , subset( relation_rng( skol19 ), skol17 ) }.
% 0.78/1.27 parent0[0]: (3083) {G1,W8,D3,L3,V0,M3} { ! function( skol19 ), !
% 0.78/1.27 transfinite_sequence( skol19 ), subset( relation_rng( skol19 ), skol17 )
% 0.78/1.27 }.
% 0.78/1.27 parent1[0]: (138) {G1,W2,D2,L1,V0,M1} R(75,13) { function( skol19 ) }.
% 0.78/1.27 substitution0:
% 0.78/1.27 end
% 0.78/1.27 substitution1:
% 0.78/1.27 end
% 0.78/1.27
% 0.78/1.27 subsumption: (849) {G3,W6,D3,L2,V0,M2} R(126,75);r(138) { !
% 0.78/1.27 transfinite_sequence( skol19 ), subset( relation_rng( skol19 ), skol17 )
% 0.78/1.27 }.
% 0.78/1.27 parent0: (3084) {G2,W6,D3,L2,V0,M2} { ! transfinite_sequence( skol19 ),
% 0.78/1.27 subset( relation_rng( skol19 ), skol17 ) }.
% 0.78/1.27 substitution0:
% 0.78/1.27 end
% 0.78/1.27 permutation0:
% 0.78/1.27 0 ==> 0
% 0.78/1.27 1 ==> 1
% 0.78/1.27 end
% 0.78/1.27
% 0.78/1.27 resolution: (3085) {G2,W8,D3,L3,V0,M3} { ! function( skol19 ), !
% 0.78/1.27 transfinite_sequence( skol19 ), ! subset( relation_rng( skol19 ), skol18
% 0.78/1.27 ) }.
% 0.78/1.27 parent0[0]: (136) {G1,W10,D3,L4,V0,M4} R(76,11) { ! relation( skol19 ), !
% 0.78/1.27 function( skol19 ), ! transfinite_sequence( skol19 ), ! subset(
% 0.78/1.27 relation_rng( skol19 ), skol18 ) }.
% 0.78/1.27 parent1[0]: (139) {G1,W2,D2,L1,V0,M1} R(75,12) { relation( skol19 ) }.
% 0.78/1.27 substitution0:
% 0.78/1.27 end
% 0.78/1.27 substitution1:
% 0.78/1.27 end
% 0.78/1.27
% 0.78/1.27 resolution: (3086) {G2,W6,D3,L2,V0,M2} { ! transfinite_sequence( skol19 )
% 0.78/1.27 , ! subset( relation_rng( skol19 ), skol18 ) }.
% 0.78/1.27 parent0[0]: (3085) {G2,W8,D3,L3,V0,M3} { ! function( skol19 ), !
% 0.78/1.27 transfinite_sequence( skol19 ), ! subset( relation_rng( skol19 ), skol18
% 0.78/1.27 ) }.
% 0.78/1.27 parent1[0]: (138) {G1,W2,D2,L1,V0,M1} R(75,13) { function( skol19 ) }.
% 0.78/1.27 substitution0:
% 0.78/1.27 end
% 0.78/1.27 substitution1:
% 0.78/1.27 end
% 0.78/1.27
% 0.78/1.27 resolution: (3087) {G2,W4,D3,L1,V0,M1} { ! subset( relation_rng( skol19 )
% 0.78/1.27 , skol18 ) }.
% 0.78/1.27 parent0[0]: (3086) {G2,W6,D3,L2,V0,M2} { ! transfinite_sequence( skol19 )
% 0.78/1.27 , ! subset( relation_rng( skol19 ), skol18 ) }.
% 0.78/1.27 parent1[0]: (137) {G1,W2,D2,L1,V0,M1} R(75,14) { transfinite_sequence(
% 0.78/1.27 skol19 ) }.
% 0.78/1.27 substitution0:
% 0.78/1.27 end
% 0.78/1.27 substitution1:
% 0.78/1.27 end
% 0.78/1.27
% 0.78/1.27 subsumption: (1024) {G2,W4,D3,L1,V0,M1} S(136);r(139);r(138);r(137) { !
% 0.78/1.27 subset( relation_rng( skol19 ), skol18 ) }.
% 0.78/1.27 parent0: (3087) {G2,W4,D3,L1,V0,M1} { ! subset( relation_rng( skol19 ),
% 0.78/1.27 skol18 ) }.
% 0.78/1.27 substitution0:
% 0.78/1.27 end
% 0.78/1.27 permutation0:
% 0.78/1.27 0 ==> 0
% 0.78/1.27 end
% 0.78/1.27
% 0.78/1.27 resolution: (3088) {G2,W4,D3,L1,V0,M1} { ! subset( relation_rng( skol19 )
% 0.78/1.27 , skol17 ) }.
% 0.78/1.27 parent0[0]: (1024) {G2,W4,D3,L1,V0,M1} S(136);r(139);r(138);r(137) { !
% 0.78/1.27 subset( relation_rng( skol19 ), skol18 ) }.
% 0.78/1.27 parent1[1]: (240) {G1,W6,D2,L2,V1,M2} R(70,74) { ! subset( X, skol17 ),
% 0.78/1.27 subset( X, skol18 ) }.
% 0.78/1.27 substitution0:
% 0.78/1.27 end
% 0.78/1.27 substitution1:
% 0.78/1.27 X := relation_rng( skol19 )
% 0.78/1.27 end
% 0.78/1.27
% 0.78/1.27 subsumption: (1025) {G3,W4,D3,L1,V0,M1} R(1024,240) { ! subset(
% 0.78/1.27 relation_rng( skol19 ), skol17 ) }.
% 0.78/1.27 parent0: (3088) {G2,W4,D3,L1,V0,M1} { ! subset( relation_rng( skol19 ),
% 0.78/1.27 skol17 ) }.
% 0.78/1.27 substitution0:
% 0.78/1.27 end
% 0.78/1.27 permutation0:
% 0.78/1.27 0 ==> 0
% 0.78/1.27 end
% 0.78/1.27
% 0.78/1.27 resolution: (3089) {G2,W4,D3,L1,V0,M1} { subset( relation_rng( skol19 ),
% 0.78/1.27 skol17 ) }.
% 0.78/1.27 parent0[0]: (849) {G3,W6,D3,L2,V0,M2} R(126,75);r(138) { !
% 0.78/1.27 transfinite_sequence( skol19 ), subset( relation_rng( skol19 ), skol17 )
% 0.78/1.27 }.
% 0.78/1.27 parent1[0]: (137) {G1,W2,D2,L1,V0,M1} R(75,14) { transfinite_sequence(
% 0.78/1.27 skol19 ) }.
% 0.78/1.27 substitution0:
% 0.78/1.27 end
% 0.78/1.27 substitution1:
% 0.78/1.27 end
% 0.78/1.27
% 0.78/1.27 resolution: (3090) {G3,W0,D0,L0,V0,M0} { }.
% 0.78/1.27 parent0[0]: (1025) {G3,W4,D3,L1,V0,M1} R(1024,240) { ! subset( relation_rng
% 0.78/1.27 ( skol19 ), skol17 ) }.
% 0.78/1.27 parent1[0]: (3089) {G2,W4,D3,L1,V0,M1} { subset( relation_rng( skol19 ),
% 0.78/1.27 skol17 ) }.
% 0.78/1.27 substitution0:
% 0.78/1.27 end
% 0.78/1.27 substitution1:
% 0.78/1.27 end
% 0.78/1.27
% 0.78/1.27 subsumption: (2969) {G4,W0,D0,L0,V0,M0} S(849);r(137);r(1025) { }.
% 0.78/1.27 parent0: (3090) {G3,W0,D0,L0,V0,M0} { }.
% 0.78/1.27 substitution0:
% 0.78/1.27 end
% 0.78/1.27 permutation0:
% 0.78/1.27 end
% 0.78/1.27
% 0.78/1.27 Proof check complete!
% 0.78/1.27
% 0.78/1.27 Memory use:
% 0.78/1.27
% 0.78/1.27 space for terms: 32847
% 0.78/1.27 space for clauses: 129136
% 0.78/1.27
% 0.78/1.27
% 0.78/1.27 clauses generated: 10064
% 0.78/1.27 clauses kept: 2970
% 0.78/1.27 clauses selected: 484
% 0.78/1.27 clauses deleted: 213
% 0.78/1.27 clauses inuse deleted: 99
% 0.78/1.27
% 0.78/1.27 subsentry: 19195
% 0.78/1.27 literals s-matched: 12775
% 0.78/1.27 literals matched: 12341
% 0.78/1.27 full subsumption: 1702
% 0.78/1.27
% 0.78/1.27 checksum: -1938487194
% 0.78/1.27
% 0.78/1.27
% 0.78/1.27 Bliksem ended
%------------------------------------------------------------------------------