TSTP Solution File: NUM410+1 by Bliksem---1.12
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : NUM410+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n009.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 0.71s 1.13s
% Output : Refutation 0.71s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : NUM410+1 : TPTP v8.1.0. Released v3.2.0.
% 0.11/0.12 % Command : bliksem %s
% 0.12/0.33 % Computer : n009.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % DateTime : Tue Jul 5 15:04:37 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.71/1.13 *** allocated 10000 integers for termspace/termends
% 0.71/1.13 *** allocated 10000 integers for clauses
% 0.71/1.13 *** allocated 10000 integers for justifications
% 0.71/1.13 Bliksem 1.12
% 0.71/1.13
% 0.71/1.13
% 0.71/1.13 Automatic Strategy Selection
% 0.71/1.13
% 0.71/1.13
% 0.71/1.13 Clauses:
% 0.71/1.13
% 0.71/1.13 { ! in( X, Y ), ! in( Y, X ) }.
% 0.71/1.13 { ! empty( X ), function( X ) }.
% 0.71/1.13 { ! ordinal( X ), epsilon_transitive( X ) }.
% 0.71/1.13 { ! ordinal( X ), epsilon_connected( X ) }.
% 0.71/1.13 { ! empty( X ), relation( X ) }.
% 0.71/1.13 { ! relation( X ), ! empty( X ), ! function( X ), relation( X ) }.
% 0.71/1.13 { ! relation( X ), ! empty( X ), ! function( X ), function( X ) }.
% 0.71/1.13 { ! relation( X ), ! empty( X ), ! function( X ), one_to_one( X ) }.
% 0.71/1.13 { ! epsilon_transitive( X ), ! epsilon_connected( X ), ordinal( X ) }.
% 0.71/1.13 { ! empty( X ), epsilon_transitive( X ) }.
% 0.71/1.13 { ! empty( X ), epsilon_connected( X ) }.
% 0.71/1.13 { ! empty( X ), ordinal( X ) }.
% 0.71/1.13 { ! relation( X ), ! function( X ), ! transfinite_sequence( X ), ordinal(
% 0.71/1.13 relation_dom( X ) ) }.
% 0.71/1.13 { ! relation( X ), ! function( X ), ! ordinal( relation_dom( X ) ),
% 0.71/1.13 transfinite_sequence( X ) }.
% 0.71/1.13 { ! relation( X ), ! function( X ), ! transfinite_sequence( X ), !
% 0.71/1.13 transfinite_sequence_of( X, Y ), subset( relation_rng( X ), Y ) }.
% 0.71/1.13 { ! relation( X ), ! function( X ), ! transfinite_sequence( X ), ! subset(
% 0.71/1.13 relation_rng( X ), Y ), transfinite_sequence_of( X, Y ) }.
% 0.71/1.13 { ! transfinite_sequence_of( X, Y ), relation( X ) }.
% 0.71/1.13 { ! transfinite_sequence_of( X, Y ), function( X ) }.
% 0.71/1.13 { ! transfinite_sequence_of( X, Y ), transfinite_sequence( X ) }.
% 0.71/1.13 { transfinite_sequence_of( skol1( X ), X ) }.
% 0.71/1.13 { element( skol2( X ), X ) }.
% 0.71/1.13 { empty( empty_set ) }.
% 0.71/1.13 { relation( empty_set ) }.
% 0.71/1.13 { relation_empty_yielding( empty_set ) }.
% 0.71/1.13 { empty( empty_set ) }.
% 0.71/1.13 { relation( empty_set ) }.
% 0.71/1.13 { relation_empty_yielding( empty_set ) }.
% 0.71/1.13 { function( empty_set ) }.
% 0.71/1.13 { one_to_one( empty_set ) }.
% 0.71/1.13 { empty( empty_set ) }.
% 0.71/1.13 { epsilon_transitive( empty_set ) }.
% 0.71/1.13 { epsilon_connected( empty_set ) }.
% 0.71/1.13 { ordinal( empty_set ) }.
% 0.71/1.13 { empty( empty_set ) }.
% 0.71/1.13 { relation( empty_set ) }.
% 0.71/1.13 { empty( X ), ! relation( X ), ! empty( relation_dom( X ) ) }.
% 0.71/1.13 { ! relation( X ), ! relation_non_empty( X ), ! function( X ),
% 0.71/1.13 with_non_empty_elements( relation_rng( X ) ) }.
% 0.71/1.13 { empty( X ), ! relation( X ), ! empty( relation_rng( X ) ) }.
% 0.71/1.13 { ! empty( X ), empty( relation_dom( X ) ) }.
% 0.71/1.13 { ! empty( X ), relation( relation_dom( X ) ) }.
% 0.71/1.13 { ! empty( X ), empty( relation_rng( X ) ) }.
% 0.71/1.13 { ! empty( X ), relation( relation_rng( X ) ) }.
% 0.71/1.13 { relation( skol3 ) }.
% 0.71/1.13 { function( skol3 ) }.
% 0.71/1.13 { epsilon_transitive( skol4 ) }.
% 0.71/1.13 { epsilon_connected( skol4 ) }.
% 0.71/1.13 { ordinal( skol4 ) }.
% 0.71/1.13 { empty( skol5 ) }.
% 0.71/1.13 { relation( skol5 ) }.
% 0.71/1.13 { empty( skol6 ) }.
% 0.71/1.13 { relation( skol7 ) }.
% 0.71/1.13 { empty( skol7 ) }.
% 0.71/1.13 { function( skol7 ) }.
% 0.71/1.13 { relation( skol8 ) }.
% 0.71/1.13 { function( skol8 ) }.
% 0.71/1.13 { one_to_one( skol8 ) }.
% 0.71/1.13 { empty( skol8 ) }.
% 0.71/1.13 { epsilon_transitive( skol8 ) }.
% 0.71/1.13 { epsilon_connected( skol8 ) }.
% 0.71/1.13 { ordinal( skol8 ) }.
% 0.71/1.13 { ! empty( skol9 ) }.
% 0.71/1.13 { relation( skol9 ) }.
% 0.71/1.13 { ! empty( skol10 ) }.
% 0.71/1.13 { relation( skol11 ) }.
% 0.71/1.13 { function( skol11 ) }.
% 0.71/1.13 { one_to_one( skol11 ) }.
% 0.71/1.13 { ! empty( skol12 ) }.
% 0.71/1.13 { epsilon_transitive( skol12 ) }.
% 0.71/1.13 { epsilon_connected( skol12 ) }.
% 0.71/1.13 { ordinal( skol12 ) }.
% 0.71/1.13 { relation( skol13 ) }.
% 0.71/1.13 { relation_empty_yielding( skol13 ) }.
% 0.71/1.13 { relation( skol14 ) }.
% 0.71/1.13 { relation_empty_yielding( skol14 ) }.
% 0.71/1.13 { function( skol14 ) }.
% 0.71/1.13 { relation( skol15 ) }.
% 0.71/1.13 { function( skol15 ) }.
% 0.71/1.13 { transfinite_sequence( skol15 ) }.
% 0.71/1.13 { relation( skol16 ) }.
% 0.71/1.13 { relation_non_empty( skol16 ) }.
% 0.71/1.13 { function( skol16 ) }.
% 0.71/1.13 { subset( X, X ) }.
% 0.71/1.13 { ! in( X, Y ), element( X, Y ) }.
% 0.71/1.13 { ! element( X, Y ), empty( Y ), in( X, Y ) }.
% 0.71/1.13 { ! element( X, powerset( Y ) ), subset( X, Y ) }.
% 0.71/1.13 { ! subset( X, Y ), element( X, powerset( Y ) ) }.
% 0.71/1.13 { relation( skol17 ) }.
% 0.71/1.13 { function( skol17 ) }.
% 0.71/1.13 { ordinal( relation_dom( skol17 ) ) }.
% 0.71/1.13 { ! transfinite_sequence_of( skol17, relation_rng( skol17 ) ) }.
% 0.71/1.13 { ! in( X, Z ), ! element( Z, powerset( Y ) ), element( X, Y ) }.
% 0.71/1.13 { ! in( X, Y ), ! element( Y, powerset( Z ) ), ! empty( Z ) }.
% 0.71/1.13 { ! empty( X ), X = empty_set }.
% 0.71/1.13 { ! in( X, Y ), ! empty( Y ) }.
% 0.71/1.13 { ! empty( X ), X = Y, ! empty( Y ) }.
% 0.71/1.13
% 0.71/1.13 percentage equality = 0.014184, percentage horn = 0.988506
% 0.71/1.13 This is a problem with some equality
% 0.71/1.13
% 0.71/1.13
% 0.71/1.13
% 0.71/1.13 Options Used:
% 0.71/1.13
% 0.71/1.13 useres = 1
% 0.71/1.13 useparamod = 1
% 0.71/1.13 useeqrefl = 1
% 0.71/1.13 useeqfact = 1
% 0.71/1.13 usefactor = 1
% 0.71/1.13 usesimpsplitting = 0
% 0.71/1.13 usesimpdemod = 5
% 0.71/1.13 usesimpres = 3
% 0.71/1.13
% 0.71/1.13 resimpinuse = 1000
% 0.71/1.13 resimpclauses = 20000
% 0.71/1.13 substype = eqrewr
% 0.71/1.13 backwardsubs = 1
% 0.71/1.13 selectoldest = 5
% 0.71/1.13
% 0.71/1.13 litorderings [0] = split
% 0.71/1.13 litorderings [1] = extend the termordering, first sorting on arguments
% 0.71/1.13
% 0.71/1.13 termordering = kbo
% 0.71/1.13
% 0.71/1.13 litapriori = 0
% 0.71/1.13 termapriori = 1
% 0.71/1.13 litaposteriori = 0
% 0.71/1.13 termaposteriori = 0
% 0.71/1.13 demodaposteriori = 0
% 0.71/1.13 ordereqreflfact = 0
% 0.71/1.13
% 0.71/1.13 litselect = negord
% 0.71/1.13
% 0.71/1.13 maxweight = 15
% 0.71/1.13 maxdepth = 30000
% 0.71/1.13 maxlength = 115
% 0.71/1.13 maxnrvars = 195
% 0.71/1.13 excuselevel = 1
% 0.71/1.13 increasemaxweight = 1
% 0.71/1.13
% 0.71/1.13 maxselected = 10000000
% 0.71/1.13 maxnrclauses = 10000000
% 0.71/1.13
% 0.71/1.13 showgenerated = 0
% 0.71/1.13 showkept = 0
% 0.71/1.13 showselected = 0
% 0.71/1.13 showdeleted = 0
% 0.71/1.13 showresimp = 1
% 0.71/1.13 showstatus = 2000
% 0.71/1.13
% 0.71/1.13 prologoutput = 0
% 0.71/1.13 nrgoals = 5000000
% 0.71/1.13 totalproof = 1
% 0.71/1.13
% 0.71/1.13 Symbols occurring in the translation:
% 0.71/1.13
% 0.71/1.13 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.71/1.13 . [1, 2] (w:1, o:46, a:1, s:1, b:0),
% 0.71/1.13 ! [4, 1] (w:0, o:25, a:1, s:1, b:0),
% 0.71/1.13 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.71/1.13 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.71/1.13 in [37, 2] (w:1, o:70, a:1, s:1, b:0),
% 0.71/1.13 empty [38, 1] (w:1, o:30, a:1, s:1, b:0),
% 0.71/1.13 function [39, 1] (w:1, o:33, a:1, s:1, b:0),
% 0.71/1.13 ordinal [40, 1] (w:1, o:34, a:1, s:1, b:0),
% 0.71/1.13 epsilon_transitive [41, 1] (w:1, o:31, a:1, s:1, b:0),
% 0.71/1.13 epsilon_connected [42, 1] (w:1, o:32, a:1, s:1, b:0),
% 0.71/1.13 relation [43, 1] (w:1, o:35, a:1, s:1, b:0),
% 0.71/1.13 one_to_one [44, 1] (w:1, o:36, a:1, s:1, b:0),
% 0.71/1.13 transfinite_sequence [45, 1] (w:1, o:39, a:1, s:1, b:0),
% 0.71/1.13 relation_dom [46, 1] (w:1, o:40, a:1, s:1, b:0),
% 0.71/1.13 transfinite_sequence_of [47, 2] (w:1, o:72, a:1, s:1, b:0),
% 0.71/1.13 relation_rng [48, 1] (w:1, o:41, a:1, s:1, b:0),
% 0.71/1.13 subset [49, 2] (w:1, o:71, a:1, s:1, b:0),
% 0.71/1.13 element [50, 2] (w:1, o:73, a:1, s:1, b:0),
% 0.71/1.13 empty_set [51, 0] (w:1, o:8, a:1, s:1, b:0),
% 0.71/1.13 relation_empty_yielding [52, 1] (w:1, o:42, a:1, s:1, b:0),
% 0.71/1.13 relation_non_empty [53, 1] (w:1, o:43, a:1, s:1, b:0),
% 0.71/1.13 with_non_empty_elements [54, 1] (w:1, o:44, a:1, s:1, b:0),
% 0.71/1.13 powerset [55, 1] (w:1, o:45, a:1, s:1, b:0),
% 0.71/1.13 skol1 [57, 1] (w:1, o:37, a:1, s:1, b:1),
% 0.71/1.13 skol2 [58, 1] (w:1, o:38, a:1, s:1, b:1),
% 0.71/1.13 skol3 [59, 0] (w:1, o:10, a:1, s:1, b:1),
% 0.71/1.13 skol4 [60, 0] (w:1, o:11, a:1, s:1, b:1),
% 0.71/1.13 skol5 [61, 0] (w:1, o:12, a:1, s:1, b:1),
% 0.71/1.13 skol6 [62, 0] (w:1, o:13, a:1, s:1, b:1),
% 0.71/1.13 skol7 [63, 0] (w:1, o:14, a:1, s:1, b:1),
% 0.71/1.13 skol8 [64, 0] (w:1, o:15, a:1, s:1, b:1),
% 0.71/1.13 skol9 [65, 0] (w:1, o:16, a:1, s:1, b:1),
% 0.71/1.13 skol10 [66, 0] (w:1, o:17, a:1, s:1, b:1),
% 0.71/1.13 skol11 [67, 0] (w:1, o:18, a:1, s:1, b:1),
% 0.71/1.13 skol12 [68, 0] (w:1, o:19, a:1, s:1, b:1),
% 0.71/1.13 skol13 [69, 0] (w:1, o:20, a:1, s:1, b:1),
% 0.71/1.13 skol14 [70, 0] (w:1, o:21, a:1, s:1, b:1),
% 0.71/1.13 skol15 [71, 0] (w:1, o:22, a:1, s:1, b:1),
% 0.71/1.13 skol16 [72, 0] (w:1, o:23, a:1, s:1, b:1),
% 0.71/1.13 skol17 [73, 0] (w:1, o:24, a:1, s:1, b:1).
% 0.71/1.13
% 0.71/1.13
% 0.71/1.13 Starting Search:
% 0.71/1.13
% 0.71/1.13 *** allocated 15000 integers for clauses
% 0.71/1.13 *** allocated 22500 integers for clauses
% 0.71/1.13 *** allocated 33750 integers for clauses
% 0.71/1.13 *** allocated 50625 integers for clauses
% 0.71/1.13 *** allocated 15000 integers for termspace/termends
% 0.71/1.13 Resimplifying inuse:
% 0.71/1.13 Done
% 0.71/1.13
% 0.71/1.13 *** allocated 75937 integers for clauses
% 0.71/1.13 *** allocated 22500 integers for termspace/termends
% 0.71/1.13 *** allocated 113905 integers for clauses
% 0.71/1.13
% 0.71/1.13 Bliksems!, er is een bewijs:
% 0.71/1.13 % SZS status Theorem
% 0.71/1.13 % SZS output start Refutation
% 0.71/1.13
% 0.71/1.13 (11) {G0,W9,D3,L4,V1,M4} I { ! relation( X ), ! function( X ), ! ordinal(
% 0.71/1.13 relation_dom( X ) ), transfinite_sequence( X ) }.
% 0.71/1.13 (13) {G0,W13,D3,L5,V2,M5} I { ! relation( X ), ! function( X ), !
% 0.71/1.13 transfinite_sequence( X ), ! subset( relation_rng( X ), Y ),
% 0.71/1.13 transfinite_sequence_of( X, Y ) }.
% 0.71/1.13 (73) {G0,W3,D2,L1,V1,M1} I { subset( X, X ) }.
% 0.71/1.13 (78) {G0,W2,D2,L1,V0,M1} I { relation( skol17 ) }.
% 0.71/1.13 (79) {G0,W2,D2,L1,V0,M1} I { function( skol17 ) }.
% 0.71/1.13 (80) {G0,W3,D3,L1,V0,M1} I { ordinal( relation_dom( skol17 ) ) }.
% 0.71/1.13 (81) {G0,W4,D3,L1,V0,M1} I { ! transfinite_sequence_of( skol17,
% 0.71/1.13 relation_rng( skol17 ) ) }.
% 0.71/1.13 (170) {G1,W10,D3,L4,V1,M4} R(73,13) { ! relation( X ), ! function( X ), !
% 0.71/1.13 transfinite_sequence( X ), transfinite_sequence_of( X, relation_rng( X )
% 0.71/1.13 ) }.
% 0.71/1.13 (171) {G1,W4,D2,L2,V0,M2} R(80,11);r(78) { ! function( skol17 ),
% 0.71/1.13 transfinite_sequence( skol17 ) }.
% 0.71/1.13 (185) {G2,W2,D2,L1,V0,M1} S(171);r(79) { transfinite_sequence( skol17 ) }.
% 0.71/1.13 (1818) {G2,W4,D2,L2,V0,M2} R(170,81);r(78) { ! function( skol17 ), !
% 0.71/1.13 transfinite_sequence( skol17 ) }.
% 0.71/1.13 (1831) {G3,W0,D0,L0,V0,M0} S(1818);r(79);r(185) { }.
% 0.71/1.13
% 0.71/1.13
% 0.71/1.13 % SZS output end Refutation
% 0.71/1.13 found a proof!
% 0.71/1.13
% 0.71/1.13
% 0.71/1.13 Unprocessed initial clauses:
% 0.71/1.13
% 0.71/1.13 (1833) {G0,W6,D2,L2,V2,M2} { ! in( X, Y ), ! in( Y, X ) }.
% 0.71/1.13 (1834) {G0,W4,D2,L2,V1,M2} { ! empty( X ), function( X ) }.
% 0.71/1.13 (1835) {G0,W4,D2,L2,V1,M2} { ! ordinal( X ), epsilon_transitive( X ) }.
% 0.71/1.13 (1836) {G0,W4,D2,L2,V1,M2} { ! ordinal( X ), epsilon_connected( X ) }.
% 0.71/1.13 (1837) {G0,W4,D2,L2,V1,M2} { ! empty( X ), relation( X ) }.
% 0.71/1.13 (1838) {G0,W8,D2,L4,V1,M4} { ! relation( X ), ! empty( X ), ! function( X
% 0.71/1.13 ), relation( X ) }.
% 0.71/1.13 (1839) {G0,W8,D2,L4,V1,M4} { ! relation( X ), ! empty( X ), ! function( X
% 0.71/1.13 ), function( X ) }.
% 0.71/1.13 (1840) {G0,W8,D2,L4,V1,M4} { ! relation( X ), ! empty( X ), ! function( X
% 0.71/1.13 ), one_to_one( X ) }.
% 0.71/1.13 (1841) {G0,W6,D2,L3,V1,M3} { ! epsilon_transitive( X ), !
% 0.71/1.13 epsilon_connected( X ), ordinal( X ) }.
% 0.71/1.13 (1842) {G0,W4,D2,L2,V1,M2} { ! empty( X ), epsilon_transitive( X ) }.
% 0.71/1.13 (1843) {G0,W4,D2,L2,V1,M2} { ! empty( X ), epsilon_connected( X ) }.
% 0.71/1.13 (1844) {G0,W4,D2,L2,V1,M2} { ! empty( X ), ordinal( X ) }.
% 0.71/1.13 (1845) {G0,W9,D3,L4,V1,M4} { ! relation( X ), ! function( X ), !
% 0.71/1.13 transfinite_sequence( X ), ordinal( relation_dom( X ) ) }.
% 0.71/1.13 (1846) {G0,W9,D3,L4,V1,M4} { ! relation( X ), ! function( X ), ! ordinal(
% 0.71/1.13 relation_dom( X ) ), transfinite_sequence( X ) }.
% 0.71/1.13 (1847) {G0,W13,D3,L5,V2,M5} { ! relation( X ), ! function( X ), !
% 0.71/1.13 transfinite_sequence( X ), ! transfinite_sequence_of( X, Y ), subset(
% 0.71/1.13 relation_rng( X ), Y ) }.
% 0.71/1.13 (1848) {G0,W13,D3,L5,V2,M5} { ! relation( X ), ! function( X ), !
% 0.71/1.13 transfinite_sequence( X ), ! subset( relation_rng( X ), Y ),
% 0.71/1.13 transfinite_sequence_of( X, Y ) }.
% 0.71/1.13 (1849) {G0,W5,D2,L2,V2,M2} { ! transfinite_sequence_of( X, Y ), relation(
% 0.71/1.13 X ) }.
% 0.71/1.13 (1850) {G0,W5,D2,L2,V2,M2} { ! transfinite_sequence_of( X, Y ), function(
% 0.71/1.13 X ) }.
% 0.71/1.13 (1851) {G0,W5,D2,L2,V2,M2} { ! transfinite_sequence_of( X, Y ),
% 0.71/1.13 transfinite_sequence( X ) }.
% 0.71/1.13 (1852) {G0,W4,D3,L1,V1,M1} { transfinite_sequence_of( skol1( X ), X ) }.
% 0.71/1.13 (1853) {G0,W4,D3,L1,V1,M1} { element( skol2( X ), X ) }.
% 0.71/1.13 (1854) {G0,W2,D2,L1,V0,M1} { empty( empty_set ) }.
% 0.71/1.13 (1855) {G0,W2,D2,L1,V0,M1} { relation( empty_set ) }.
% 0.71/1.13 (1856) {G0,W2,D2,L1,V0,M1} { relation_empty_yielding( empty_set ) }.
% 0.71/1.13 (1857) {G0,W2,D2,L1,V0,M1} { empty( empty_set ) }.
% 0.71/1.13 (1858) {G0,W2,D2,L1,V0,M1} { relation( empty_set ) }.
% 0.71/1.13 (1859) {G0,W2,D2,L1,V0,M1} { relation_empty_yielding( empty_set ) }.
% 0.71/1.13 (1860) {G0,W2,D2,L1,V0,M1} { function( empty_set ) }.
% 0.71/1.13 (1861) {G0,W2,D2,L1,V0,M1} { one_to_one( empty_set ) }.
% 0.71/1.13 (1862) {G0,W2,D2,L1,V0,M1} { empty( empty_set ) }.
% 0.71/1.13 (1863) {G0,W2,D2,L1,V0,M1} { epsilon_transitive( empty_set ) }.
% 0.71/1.13 (1864) {G0,W2,D2,L1,V0,M1} { epsilon_connected( empty_set ) }.
% 0.71/1.13 (1865) {G0,W2,D2,L1,V0,M1} { ordinal( empty_set ) }.
% 0.71/1.13 (1866) {G0,W2,D2,L1,V0,M1} { empty( empty_set ) }.
% 0.71/1.13 (1867) {G0,W2,D2,L1,V0,M1} { relation( empty_set ) }.
% 0.71/1.13 (1868) {G0,W7,D3,L3,V1,M3} { empty( X ), ! relation( X ), ! empty(
% 0.71/1.13 relation_dom( X ) ) }.
% 0.71/1.13 (1869) {G0,W9,D3,L4,V1,M4} { ! relation( X ), ! relation_non_empty( X ), !
% 0.71/1.13 function( X ), with_non_empty_elements( relation_rng( X ) ) }.
% 0.71/1.13 (1870) {G0,W7,D3,L3,V1,M3} { empty( X ), ! relation( X ), ! empty(
% 0.71/1.13 relation_rng( X ) ) }.
% 0.71/1.13 (1871) {G0,W5,D3,L2,V1,M2} { ! empty( X ), empty( relation_dom( X ) ) }.
% 0.71/1.13 (1872) {G0,W5,D3,L2,V1,M2} { ! empty( X ), relation( relation_dom( X ) )
% 0.71/1.13 }.
% 0.71/1.13 (1873) {G0,W5,D3,L2,V1,M2} { ! empty( X ), empty( relation_rng( X ) ) }.
% 0.71/1.13 (1874) {G0,W5,D3,L2,V1,M2} { ! empty( X ), relation( relation_rng( X ) )
% 0.71/1.13 }.
% 0.71/1.13 (1875) {G0,W2,D2,L1,V0,M1} { relation( skol3 ) }.
% 0.71/1.13 (1876) {G0,W2,D2,L1,V0,M1} { function( skol3 ) }.
% 0.71/1.13 (1877) {G0,W2,D2,L1,V0,M1} { epsilon_transitive( skol4 ) }.
% 0.71/1.13 (1878) {G0,W2,D2,L1,V0,M1} { epsilon_connected( skol4 ) }.
% 0.71/1.13 (1879) {G0,W2,D2,L1,V0,M1} { ordinal( skol4 ) }.
% 0.71/1.13 (1880) {G0,W2,D2,L1,V0,M1} { empty( skol5 ) }.
% 0.71/1.13 (1881) {G0,W2,D2,L1,V0,M1} { relation( skol5 ) }.
% 0.71/1.13 (1882) {G0,W2,D2,L1,V0,M1} { empty( skol6 ) }.
% 0.71/1.13 (1883) {G0,W2,D2,L1,V0,M1} { relation( skol7 ) }.
% 0.71/1.13 (1884) {G0,W2,D2,L1,V0,M1} { empty( skol7 ) }.
% 0.71/1.13 (1885) {G0,W2,D2,L1,V0,M1} { function( skol7 ) }.
% 0.71/1.13 (1886) {G0,W2,D2,L1,V0,M1} { relation( skol8 ) }.
% 0.71/1.13 (1887) {G0,W2,D2,L1,V0,M1} { function( skol8 ) }.
% 0.71/1.13 (1888) {G0,W2,D2,L1,V0,M1} { one_to_one( skol8 ) }.
% 0.71/1.13 (1889) {G0,W2,D2,L1,V0,M1} { empty( skol8 ) }.
% 0.71/1.13 (1890) {G0,W2,D2,L1,V0,M1} { epsilon_transitive( skol8 ) }.
% 0.71/1.13 (1891) {G0,W2,D2,L1,V0,M1} { epsilon_connected( skol8 ) }.
% 0.71/1.13 (1892) {G0,W2,D2,L1,V0,M1} { ordinal( skol8 ) }.
% 0.71/1.13 (1893) {G0,W2,D2,L1,V0,M1} { ! empty( skol9 ) }.
% 0.71/1.13 (1894) {G0,W2,D2,L1,V0,M1} { relation( skol9 ) }.
% 0.71/1.13 (1895) {G0,W2,D2,L1,V0,M1} { ! empty( skol10 ) }.
% 0.71/1.13 (1896) {G0,W2,D2,L1,V0,M1} { relation( skol11 ) }.
% 0.71/1.13 (1897) {G0,W2,D2,L1,V0,M1} { function( skol11 ) }.
% 0.71/1.13 (1898) {G0,W2,D2,L1,V0,M1} { one_to_one( skol11 ) }.
% 0.71/1.13 (1899) {G0,W2,D2,L1,V0,M1} { ! empty( skol12 ) }.
% 0.71/1.13 (1900) {G0,W2,D2,L1,V0,M1} { epsilon_transitive( skol12 ) }.
% 0.71/1.13 (1901) {G0,W2,D2,L1,V0,M1} { epsilon_connected( skol12 ) }.
% 0.71/1.13 (1902) {G0,W2,D2,L1,V0,M1} { ordinal( skol12 ) }.
% 0.71/1.13 (1903) {G0,W2,D2,L1,V0,M1} { relation( skol13 ) }.
% 0.71/1.13 (1904) {G0,W2,D2,L1,V0,M1} { relation_empty_yielding( skol13 ) }.
% 0.71/1.13 (1905) {G0,W2,D2,L1,V0,M1} { relation( skol14 ) }.
% 0.71/1.13 (1906) {G0,W2,D2,L1,V0,M1} { relation_empty_yielding( skol14 ) }.
% 0.71/1.13 (1907) {G0,W2,D2,L1,V0,M1} { function( skol14 ) }.
% 0.71/1.13 (1908) {G0,W2,D2,L1,V0,M1} { relation( skol15 ) }.
% 0.71/1.13 (1909) {G0,W2,D2,L1,V0,M1} { function( skol15 ) }.
% 0.71/1.13 (1910) {G0,W2,D2,L1,V0,M1} { transfinite_sequence( skol15 ) }.
% 0.71/1.13 (1911) {G0,W2,D2,L1,V0,M1} { relation( skol16 ) }.
% 0.71/1.13 (1912) {G0,W2,D2,L1,V0,M1} { relation_non_empty( skol16 ) }.
% 0.71/1.13 (1913) {G0,W2,D2,L1,V0,M1} { function( skol16 ) }.
% 0.71/1.13 (1914) {G0,W3,D2,L1,V1,M1} { subset( X, X ) }.
% 0.71/1.13 (1915) {G0,W6,D2,L2,V2,M2} { ! in( X, Y ), element( X, Y ) }.
% 0.71/1.13 (1916) {G0,W8,D2,L3,V2,M3} { ! element( X, Y ), empty( Y ), in( X, Y ) }.
% 0.71/1.13 (1917) {G0,W7,D3,L2,V2,M2} { ! element( X, powerset( Y ) ), subset( X, Y )
% 0.71/1.13 }.
% 0.71/1.13 (1918) {G0,W7,D3,L2,V2,M2} { ! subset( X, Y ), element( X, powerset( Y ) )
% 0.71/1.13 }.
% 0.71/1.13 (1919) {G0,W2,D2,L1,V0,M1} { relation( skol17 ) }.
% 0.71/1.13 (1920) {G0,W2,D2,L1,V0,M1} { function( skol17 ) }.
% 0.71/1.13 (1921) {G0,W3,D3,L1,V0,M1} { ordinal( relation_dom( skol17 ) ) }.
% 0.71/1.13 (1922) {G0,W4,D3,L1,V0,M1} { ! transfinite_sequence_of( skol17,
% 0.71/1.13 relation_rng( skol17 ) ) }.
% 0.71/1.13 (1923) {G0,W10,D3,L3,V3,M3} { ! in( X, Z ), ! element( Z, powerset( Y ) )
% 0.71/1.13 , element( X, Y ) }.
% 0.71/1.13 (1924) {G0,W9,D3,L3,V3,M3} { ! in( X, Y ), ! element( Y, powerset( Z ) ),
% 0.71/1.13 ! empty( Z ) }.
% 0.71/1.13 (1925) {G0,W5,D2,L2,V1,M2} { ! empty( X ), X = empty_set }.
% 0.71/1.13 (1926) {G0,W5,D2,L2,V2,M2} { ! in( X, Y ), ! empty( Y ) }.
% 0.71/1.13 (1927) {G0,W7,D2,L3,V2,M3} { ! empty( X ), X = Y, ! empty( Y ) }.
% 0.71/1.13
% 0.71/1.13
% 0.71/1.13 Total Proof:
% 0.71/1.13
% 0.71/1.13 subsumption: (11) {G0,W9,D3,L4,V1,M4} I { ! relation( X ), ! function( X )
% 0.71/1.13 , ! ordinal( relation_dom( X ) ), transfinite_sequence( X ) }.
% 0.71/1.13 parent0: (1846) {G0,W9,D3,L4,V1,M4} { ! relation( X ), ! function( X ), !
% 0.71/1.13 ordinal( relation_dom( X ) ), transfinite_sequence( X ) }.
% 0.71/1.13 substitution0:
% 0.71/1.13 X := X
% 0.71/1.13 end
% 0.71/1.13 permutation0:
% 0.71/1.13 0 ==> 0
% 0.71/1.13 1 ==> 1
% 0.71/1.13 2 ==> 2
% 0.71/1.13 3 ==> 3
% 0.71/1.13 end
% 0.71/1.13
% 0.71/1.13 subsumption: (13) {G0,W13,D3,L5,V2,M5} I { ! relation( X ), ! function( X )
% 0.71/1.13 , ! transfinite_sequence( X ), ! subset( relation_rng( X ), Y ),
% 0.71/1.13 transfinite_sequence_of( X, Y ) }.
% 0.71/1.13 parent0: (1848) {G0,W13,D3,L5,V2,M5} { ! relation( X ), ! function( X ), !
% 0.71/1.13 transfinite_sequence( X ), ! subset( relation_rng( X ), Y ),
% 0.71/1.13 transfinite_sequence_of( X, Y ) }.
% 0.71/1.13 substitution0:
% 0.71/1.13 X := X
% 0.71/1.13 Y := Y
% 0.71/1.13 end
% 0.71/1.13 permutation0:
% 0.71/1.13 0 ==> 0
% 0.71/1.13 1 ==> 1
% 0.71/1.13 2 ==> 2
% 0.71/1.13 3 ==> 3
% 0.71/1.13 4 ==> 4
% 0.71/1.13 end
% 0.71/1.13
% 0.71/1.13 subsumption: (73) {G0,W3,D2,L1,V1,M1} I { subset( X, X ) }.
% 0.71/1.13 parent0: (1914) {G0,W3,D2,L1,V1,M1} { subset( X, X ) }.
% 0.71/1.13 substitution0:
% 0.71/1.13 X := X
% 0.71/1.13 end
% 0.71/1.13 permutation0:
% 0.71/1.13 0 ==> 0
% 0.71/1.13 end
% 0.71/1.13
% 0.71/1.13 subsumption: (78) {G0,W2,D2,L1,V0,M1} I { relation( skol17 ) }.
% 0.71/1.13 parent0: (1919) {G0,W2,D2,L1,V0,M1} { relation( skol17 ) }.
% 0.71/1.13 substitution0:
% 0.71/1.13 end
% 0.71/1.13 permutation0:
% 0.71/1.13 0 ==> 0
% 0.71/1.13 end
% 0.71/1.13
% 0.71/1.13 subsumption: (79) {G0,W2,D2,L1,V0,M1} I { function( skol17 ) }.
% 0.71/1.13 parent0: (1920) {G0,W2,D2,L1,V0,M1} { function( skol17 ) }.
% 0.71/1.13 substitution0:
% 0.71/1.13 end
% 0.71/1.13 permutation0:
% 0.71/1.13 0 ==> 0
% 0.71/1.13 end
% 0.71/1.13
% 0.71/1.13 subsumption: (80) {G0,W3,D3,L1,V0,M1} I { ordinal( relation_dom( skol17 ) )
% 0.71/1.13 }.
% 0.71/1.13 parent0: (1921) {G0,W3,D3,L1,V0,M1} { ordinal( relation_dom( skol17 ) )
% 0.71/1.13 }.
% 0.71/1.13 substitution0:
% 0.71/1.13 end
% 0.71/1.13 permutation0:
% 0.71/1.13 0 ==> 0
% 0.71/1.13 end
% 0.71/1.13
% 0.71/1.13 subsumption: (81) {G0,W4,D3,L1,V0,M1} I { ! transfinite_sequence_of( skol17
% 0.71/1.13 , relation_rng( skol17 ) ) }.
% 0.71/1.13 parent0: (1922) {G0,W4,D3,L1,V0,M1} { ! transfinite_sequence_of( skol17,
% 0.71/1.13 relation_rng( skol17 ) ) }.
% 0.71/1.13 substitution0:
% 0.71/1.13 end
% 0.71/1.13 permutation0:
% 0.71/1.13 0 ==> 0
% 0.71/1.13 end
% 0.71/1.13
% 0.71/1.13 resolution: (1935) {G1,W10,D3,L4,V1,M4} { ! relation( X ), ! function( X )
% 0.71/1.13 , ! transfinite_sequence( X ), transfinite_sequence_of( X, relation_rng(
% 0.71/1.13 X ) ) }.
% 0.71/1.13 parent0[3]: (13) {G0,W13,D3,L5,V2,M5} I { ! relation( X ), ! function( X )
% 0.71/1.13 , ! transfinite_sequence( X ), ! subset( relation_rng( X ), Y ),
% 0.71/1.13 transfinite_sequence_of( X, Y ) }.
% 0.71/1.13 parent1[0]: (73) {G0,W3,D2,L1,V1,M1} I { subset( X, X ) }.
% 0.71/1.13 substitution0:
% 0.71/1.13 X := X
% 0.71/1.13 Y := relation_rng( X )
% 0.71/1.13 end
% 0.71/1.13 substitution1:
% 0.71/1.13 X := relation_rng( X )
% 0.71/1.13 end
% 0.71/1.13
% 0.71/1.13 subsumption: (170) {G1,W10,D3,L4,V1,M4} R(73,13) { ! relation( X ), !
% 0.71/1.13 function( X ), ! transfinite_sequence( X ), transfinite_sequence_of( X,
% 0.71/1.13 relation_rng( X ) ) }.
% 0.71/1.13 parent0: (1935) {G1,W10,D3,L4,V1,M4} { ! relation( X ), ! function( X ), !
% 0.71/1.13 transfinite_sequence( X ), transfinite_sequence_of( X, relation_rng( X )
% 0.71/1.13 ) }.
% 0.71/1.13 substitution0:
% 0.71/1.13 X := X
% 0.71/1.13 end
% 0.71/1.13 permutation0:
% 0.71/1.13 0 ==> 0
% 0.71/1.13 1 ==> 1
% 0.71/1.13 2 ==> 2
% 0.71/1.13 3 ==> 3
% 0.71/1.13 end
% 0.71/1.13
% 0.71/1.13 resolution: (1936) {G1,W6,D2,L3,V0,M3} { ! relation( skol17 ), ! function
% 0.71/1.13 ( skol17 ), transfinite_sequence( skol17 ) }.
% 0.71/1.13 parent0[2]: (11) {G0,W9,D3,L4,V1,M4} I { ! relation( X ), ! function( X ),
% 0.71/1.13 ! ordinal( relation_dom( X ) ), transfinite_sequence( X ) }.
% 0.71/1.13 parent1[0]: (80) {G0,W3,D3,L1,V0,M1} I { ordinal( relation_dom( skol17 ) )
% 0.71/1.13 }.
% 0.71/1.13 substitution0:
% 0.71/1.13 X := skol17
% 0.71/1.13 end
% 0.71/1.13 substitution1:
% 0.71/1.13 end
% 0.71/1.13
% 0.71/1.13 resolution: (1937) {G1,W4,D2,L2,V0,M2} { ! function( skol17 ),
% 0.71/1.13 transfinite_sequence( skol17 ) }.
% 0.71/1.13 parent0[0]: (1936) {G1,W6,D2,L3,V0,M3} { ! relation( skol17 ), ! function
% 0.71/1.13 ( skol17 ), transfinite_sequence( skol17 ) }.
% 0.71/1.13 parent1[0]: (78) {G0,W2,D2,L1,V0,M1} I { relation( skol17 ) }.
% 0.71/1.13 substitution0:
% 0.71/1.13 end
% 0.71/1.13 substitution1:
% 0.71/1.13 end
% 0.71/1.13
% 0.71/1.13 subsumption: (171) {G1,W4,D2,L2,V0,M2} R(80,11);r(78) { ! function( skol17
% 0.71/1.13 ), transfinite_sequence( skol17 ) }.
% 0.71/1.13 parent0: (1937) {G1,W4,D2,L2,V0,M2} { ! function( skol17 ),
% 0.71/1.13 transfinite_sequence( skol17 ) }.
% 0.71/1.13 substitution0:
% 0.71/1.13 end
% 0.71/1.13 permutation0:
% 0.71/1.13 0 ==> 0
% 0.71/1.13 1 ==> 1
% 0.71/1.13 end
% 0.71/1.13
% 0.71/1.13 resolution: (1938) {G1,W2,D2,L1,V0,M1} { transfinite_sequence( skol17 )
% 0.71/1.13 }.
% 0.71/1.13 parent0[0]: (171) {G1,W4,D2,L2,V0,M2} R(80,11);r(78) { ! function( skol17 )
% 0.71/1.13 , transfinite_sequence( skol17 ) }.
% 0.71/1.13 parent1[0]: (79) {G0,W2,D2,L1,V0,M1} I { function( skol17 ) }.
% 0.71/1.13 substitution0:
% 0.71/1.13 end
% 0.71/1.13 substitution1:
% 0.71/1.13 end
% 0.71/1.13
% 0.71/1.13 subsumption: (185) {G2,W2,D2,L1,V0,M1} S(171);r(79) { transfinite_sequence
% 0.71/1.13 ( skol17 ) }.
% 0.71/1.13 parent0: (1938) {G1,W2,D2,L1,V0,M1} { transfinite_sequence( skol17 ) }.
% 0.71/1.13 substitution0:
% 0.71/1.13 end
% 0.71/1.13 permutation0:
% 0.71/1.13 0 ==> 0
% 0.71/1.13 end
% 0.71/1.13
% 0.71/1.13 resolution: (1939) {G1,W6,D2,L3,V0,M3} { ! relation( skol17 ), ! function
% 0.71/1.13 ( skol17 ), ! transfinite_sequence( skol17 ) }.
% 0.71/1.13 parent0[0]: (81) {G0,W4,D3,L1,V0,M1} I { ! transfinite_sequence_of( skol17
% 0.71/1.13 , relation_rng( skol17 ) ) }.
% 0.71/1.13 parent1[3]: (170) {G1,W10,D3,L4,V1,M4} R(73,13) { ! relation( X ), !
% 0.71/1.13 function( X ), ! transfinite_sequence( X ), transfinite_sequence_of( X,
% 0.71/1.13 relation_rng( X ) ) }.
% 0.71/1.13 substitution0:
% 0.71/1.13 end
% 0.71/1.13 substitution1:
% 0.71/1.13 X := skol17
% 0.71/1.13 end
% 0.71/1.13
% 0.71/1.13 resolution: (1940) {G1,W4,D2,L2,V0,M2} { ! function( skol17 ), !
% 0.71/1.13 transfinite_sequence( skol17 ) }.
% 0.71/1.13 parent0[0]: (1939) {G1,W6,D2,L3,V0,M3} { ! relation( skol17 ), ! function
% 0.71/1.13 ( skol17 ), ! transfinite_sequence( skol17 ) }.
% 0.71/1.13 parent1[0]: (78) {G0,W2,D2,L1,V0,M1} I { relation( skol17 ) }.
% 0.71/1.13 substitution0:
% 0.71/1.13 end
% 0.71/1.13 substitution1:
% 0.71/1.13 end
% 0.71/1.13
% 0.71/1.13 subsumption: (1818) {G2,W4,D2,L2,V0,M2} R(170,81);r(78) { ! function(
% 0.71/1.13 skol17 ), ! transfinite_sequence( skol17 ) }.
% 0.71/1.13 parent0: (1940) {G1,W4,D2,L2,V0,M2} { ! function( skol17 ), !
% 0.71/1.13 transfinite_sequence( skol17 ) }.
% 0.71/1.13 substitution0:
% 0.71/1.13 end
% 0.71/1.13 permutation0:
% 0.71/1.13 0 ==> 0
% 0.71/1.13 1 ==> 1
% 0.71/1.13 end
% 0.71/1.13
% 0.71/1.13 resolution: (1941) {G1,W2,D2,L1,V0,M1} { ! transfinite_sequence( skol17 )
% 0.71/1.13 }.
% 0.71/1.13 parent0[0]: (1818) {G2,W4,D2,L2,V0,M2} R(170,81);r(78) { ! function( skol17
% 0.71/1.13 ), ! transfinite_sequence( skol17 ) }.
% 0.71/1.13 parent1[0]: (79) {G0,W2,D2,L1,V0,M1} I { function( skol17 ) }.
% 0.71/1.13 substitution0:
% 0.71/1.13 end
% 0.71/1.13 substitution1:
% 0.71/1.13 end
% 0.71/1.13
% 0.71/1.13 resolution: (1942) {G2,W0,D0,L0,V0,M0} { }.
% 0.71/1.13 parent0[0]: (1941) {G1,W2,D2,L1,V0,M1} { ! transfinite_sequence( skol17 )
% 0.71/1.13 }.
% 0.71/1.13 parent1[0]: (185) {G2,W2,D2,L1,V0,M1} S(171);r(79) { transfinite_sequence(
% 0.71/1.13 skol17 ) }.
% 0.71/1.13 substitution0:
% 0.71/1.13 end
% 0.71/1.13 substitution1:
% 0.71/1.13 end
% 0.71/1.13
% 0.71/1.13 subsumption: (1831) {G3,W0,D0,L0,V0,M0} S(1818);r(79);r(185) { }.
% 0.71/1.13 parent0: (1942) {G2,W0,D0,L0,V0,M0} { }.
% 0.71/1.13 substitution0:
% 0.71/1.13 end
% 0.71/1.13 permutation0:
% 0.71/1.13 end
% 0.71/1.13
% 0.71/1.13 Proof check complete!
% 0.71/1.13
% 0.71/1.13 Memory use:
% 0.71/1.13
% 0.71/1.13 space for terms: 18854
% 0.71/1.13 space for clauses: 83526
% 0.71/1.13
% 0.71/1.13
% 0.71/1.13 clauses generated: 7125
% 0.71/1.13 clauses kept: 1832
% 0.71/1.13 clauses selected: 383
% 0.71/1.13 clauses deleted: 146
% 0.71/1.13 clauses inuse deleted: 62
% 0.71/1.13
% 0.71/1.13 subsentry: 11107
% 0.71/1.13 literals s-matched: 8046
% 0.71/1.13 literals matched: 7721
% 0.71/1.13 full subsumption: 938
% 0.71/1.13
% 0.71/1.13 checksum: -2121295454
% 0.71/1.13
% 0.71/1.13
% 0.71/1.13 Bliksem ended
%------------------------------------------------------------------------------