TSTP Solution File: SET643+3 by Bliksem---1.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SET643+3 : TPTP v8.1.0. Released v2.2.0.
% 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 : Mon Jul 18 22:51:05 EDT 2022
% Result : Theorem 0.83s 1.20s
% Output : Refutation 0.83s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : SET643+3 : TPTP v8.1.0. Released v2.2.0.
% 0.10/0.12 % Command : bliksem %s
% 0.13/0.33 % Computer : n003.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % DateTime : Sun Jul 10 04:10:14 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.76/1.15 *** allocated 10000 integers for termspace/termends
% 0.76/1.15 *** allocated 10000 integers for clauses
% 0.76/1.15 *** allocated 10000 integers for justifications
% 0.76/1.15 Bliksem 1.12
% 0.76/1.15
% 0.76/1.15
% 0.76/1.15 Automatic Strategy Selection
% 0.76/1.15
% 0.76/1.15
% 0.76/1.15 Clauses:
% 0.76/1.15
% 0.76/1.15 { ! ilf_type( X, set_type ), ! ilf_type( Y, set_type ), ! ilf_type( Z,
% 0.76/1.15 set_type ), ! subset( X, cross_product( Y, Z ) ), ilf_type( X,
% 0.76/1.15 relation_type( Y, Z ) ) }.
% 0.76/1.15 { ! ilf_type( X, set_type ), ! ilf_type( Y, set_type ), ! ilf_type( Z,
% 0.76/1.15 set_type ), ! member( Z, cross_product( X, Y ) ), ilf_type( skol1( T, U,
% 0.76/1.15 W ), set_type ) }.
% 0.76/1.15 { ! ilf_type( X, set_type ), ! ilf_type( Y, set_type ), ! ilf_type( Z,
% 0.76/1.15 set_type ), ! member( Z, cross_product( X, Y ) ), alpha1( X, Y, Z, skol1
% 0.76/1.15 ( X, Y, Z ) ) }.
% 0.76/1.15 { ! ilf_type( X, set_type ), ! ilf_type( Y, set_type ), ! ilf_type( Z,
% 0.76/1.15 set_type ), ! ilf_type( T, set_type ), ! alpha1( X, Y, Z, T ), member( Z
% 0.76/1.15 , cross_product( X, Y ) ) }.
% 0.76/1.15 { ! alpha1( X, Y, Z, T ), ilf_type( skol2( U, W, V0, V1 ), set_type ) }.
% 0.76/1.15 { ! alpha1( X, Y, Z, T ), alpha8( X, Y, Z, T, skol2( X, Y, Z, T ) ) }.
% 0.76/1.15 { ! ilf_type( U, set_type ), ! alpha8( X, Y, Z, T, U ), alpha1( X, Y, Z, T
% 0.76/1.15 ) }.
% 0.76/1.15 { ! alpha8( X, Y, Z, T, U ), member( T, X ) }.
% 0.76/1.15 { ! alpha8( X, Y, Z, T, U ), alpha5( Y, Z, T, U ) }.
% 0.76/1.15 { ! member( T, X ), ! alpha5( Y, Z, T, U ), alpha8( X, Y, Z, T, U ) }.
% 0.76/1.15 { ! alpha5( X, Y, Z, T ), member( T, X ) }.
% 0.76/1.15 { ! alpha5( X, Y, Z, T ), Y = ordered_pair( Z, T ) }.
% 0.76/1.15 { ! member( T, X ), ! Y = ordered_pair( Z, T ), alpha5( X, Y, Z, T ) }.
% 0.76/1.15 { ! ilf_type( X, set_type ), ! ilf_type( Y, set_type ), ilf_type(
% 0.76/1.15 cross_product( X, Y ), set_type ) }.
% 0.76/1.15 { ! ilf_type( X, set_type ), ! ilf_type( Y, set_type ), ! ilf_type( Z,
% 0.76/1.15 subset_type( cross_product( X, Y ) ) ), ilf_type( Z, relation_type( X, Y
% 0.76/1.15 ) ) }.
% 0.76/1.15 { ! ilf_type( X, set_type ), ! ilf_type( Y, set_type ), ! ilf_type( Z,
% 0.76/1.15 relation_type( X, Y ) ), ilf_type( Z, subset_type( cross_product( X, Y )
% 0.76/1.15 ) ) }.
% 0.76/1.15 { ! ilf_type( X, set_type ), ! ilf_type( Y, set_type ), ilf_type( skol3( X
% 0.76/1.15 , Y ), relation_type( Y, X ) ) }.
% 0.76/1.15 { ! ilf_type( X, set_type ), ! ilf_type( Y, set_type ), ilf_type(
% 0.76/1.15 ordered_pair( X, Y ), set_type ) }.
% 0.76/1.15 { ! ilf_type( X, set_type ), ! ilf_type( Y, set_type ), ! ilf_type( Y,
% 0.76/1.15 subset_type( X ) ), ilf_type( Y, member_type( power_set( X ) ) ) }.
% 0.76/1.15 { ! ilf_type( X, set_type ), ! ilf_type( Y, set_type ), ! ilf_type( Y,
% 0.76/1.15 member_type( power_set( X ) ) ), ilf_type( Y, subset_type( X ) ) }.
% 0.76/1.15 { ! ilf_type( X, set_type ), ilf_type( skol4( X ), subset_type( X ) ) }.
% 0.76/1.15 { ! ilf_type( X, set_type ), ! ilf_type( Y, set_type ), ! subset( X, Y ), !
% 0.76/1.15 ilf_type( Z, set_type ), alpha2( X, Y, Z ) }.
% 0.76/1.15 { ! ilf_type( X, set_type ), ! ilf_type( Y, set_type ), ilf_type( skol5( Z
% 0.76/1.15 , T ), set_type ), subset( X, Y ) }.
% 0.76/1.15 { ! ilf_type( X, set_type ), ! ilf_type( Y, set_type ), ! alpha2( X, Y,
% 0.76/1.15 skol5( X, Y ) ), subset( X, Y ) }.
% 0.76/1.15 { ! alpha2( X, Y, Z ), ! member( Z, X ), member( Z, Y ) }.
% 0.76/1.15 { member( Z, X ), alpha2( X, Y, Z ) }.
% 0.76/1.15 { ! member( Z, Y ), alpha2( X, Y, Z ) }.
% 0.76/1.15 { ! ilf_type( X, set_type ), subset( X, X ) }.
% 0.76/1.15 { ! ilf_type( X, set_type ), ! ilf_type( Y, set_type ), ! member( X,
% 0.76/1.15 power_set( Y ) ), ! ilf_type( Z, set_type ), alpha3( X, Y, Z ) }.
% 0.76/1.15 { ! ilf_type( X, set_type ), ! ilf_type( Y, set_type ), ilf_type( skol6( Z
% 0.76/1.15 , T ), set_type ), member( X, power_set( Y ) ) }.
% 0.76/1.15 { ! ilf_type( X, set_type ), ! ilf_type( Y, set_type ), ! alpha3( X, Y,
% 0.76/1.15 skol6( X, Y ) ), member( X, power_set( Y ) ) }.
% 0.76/1.15 { ! alpha3( X, Y, Z ), ! member( Z, X ), member( Z, Y ) }.
% 0.76/1.15 { member( Z, X ), alpha3( X, Y, Z ) }.
% 0.76/1.15 { ! member( Z, Y ), alpha3( X, Y, Z ) }.
% 0.76/1.15 { ! ilf_type( X, set_type ), ! empty( power_set( X ) ) }.
% 0.76/1.15 { ! ilf_type( X, set_type ), ilf_type( power_set( X ), set_type ) }.
% 0.76/1.15 { ! ilf_type( X, set_type ), empty( Y ), ! ilf_type( Y, set_type ), !
% 0.76/1.15 ilf_type( X, member_type( Y ) ), member( X, Y ) }.
% 0.76/1.15 { ! ilf_type( X, set_type ), empty( Y ), ! ilf_type( Y, set_type ), !
% 0.76/1.15 member( X, Y ), ilf_type( X, member_type( Y ) ) }.
% 0.76/1.15 { empty( X ), ! ilf_type( X, set_type ), ilf_type( skol7( X ), member_type
% 0.76/1.15 ( X ) ) }.
% 0.76/1.15 { ! ilf_type( X, set_type ), ! empty( X ), ! ilf_type( Y, set_type ), !
% 0.76/1.15 member( Y, X ) }.
% 0.76/1.15 { ! ilf_type( X, set_type ), ilf_type( skol8( Y ), set_type ), empty( X ) }
% 0.83/1.20 .
% 0.83/1.20 { ! ilf_type( X, set_type ), member( skol8( X ), X ), empty( X ) }.
% 0.83/1.20 { ! ilf_type( X, set_type ), ! relation_like( X ), ! ilf_type( Y, set_type
% 0.83/1.20 ), alpha6( X, Y ) }.
% 0.83/1.20 { ! ilf_type( X, set_type ), ilf_type( skol9( Y ), set_type ),
% 0.83/1.20 relation_like( X ) }.
% 0.83/1.20 { ! ilf_type( X, set_type ), ! alpha6( X, skol9( X ) ), relation_like( X )
% 0.83/1.20 }.
% 0.83/1.20 { ! alpha6( X, Y ), ! member( Y, X ), alpha4( Y ) }.
% 0.83/1.20 { member( Y, X ), alpha6( X, Y ) }.
% 0.83/1.20 { ! alpha4( Y ), alpha6( X, Y ) }.
% 0.83/1.20 { ! alpha4( X ), ilf_type( skol10( Y ), set_type ) }.
% 0.83/1.20 { ! alpha4( X ), alpha7( X, skol10( X ) ) }.
% 0.83/1.20 { ! ilf_type( Y, set_type ), ! alpha7( X, Y ), alpha4( X ) }.
% 0.83/1.20 { ! alpha7( X, Y ), ilf_type( skol11( Z, T ), set_type ) }.
% 0.83/1.20 { ! alpha7( X, Y ), X = ordered_pair( Y, skol11( X, Y ) ) }.
% 0.83/1.20 { ! ilf_type( Z, set_type ), ! X = ordered_pair( Y, Z ), alpha7( X, Y ) }.
% 0.83/1.20 { ! empty( X ), ! ilf_type( X, set_type ), relation_like( X ) }.
% 0.83/1.20 { ! ilf_type( X, set_type ), ! ilf_type( Y, set_type ), ! ilf_type( Z,
% 0.83/1.20 subset_type( cross_product( X, Y ) ) ), relation_like( Z ) }.
% 0.83/1.20 { ilf_type( X, set_type ) }.
% 0.83/1.20 { ilf_type( skol12, set_type ) }.
% 0.83/1.20 { ilf_type( skol13, set_type ) }.
% 0.83/1.20 { ! ilf_type( cross_product( skol12, skol13 ), relation_type( skol12,
% 0.83/1.20 skol13 ) ) }.
% 0.83/1.20
% 0.83/1.20 percentage equality = 0.022222, percentage horn = 0.816667
% 0.83/1.20 This is a problem with some equality
% 0.83/1.20
% 0.83/1.20
% 0.83/1.20
% 0.83/1.20 Options Used:
% 0.83/1.20
% 0.83/1.20 useres = 1
% 0.83/1.20 useparamod = 1
% 0.83/1.20 useeqrefl = 1
% 0.83/1.20 useeqfact = 1
% 0.83/1.20 usefactor = 1
% 0.83/1.20 usesimpsplitting = 0
% 0.83/1.20 usesimpdemod = 5
% 0.83/1.20 usesimpres = 3
% 0.83/1.20
% 0.83/1.20 resimpinuse = 1000
% 0.83/1.20 resimpclauses = 20000
% 0.83/1.20 substype = eqrewr
% 0.83/1.20 backwardsubs = 1
% 0.83/1.20 selectoldest = 5
% 0.83/1.20
% 0.83/1.20 litorderings [0] = split
% 0.83/1.20 litorderings [1] = extend the termordering, first sorting on arguments
% 0.83/1.20
% 0.83/1.20 termordering = kbo
% 0.83/1.20
% 0.83/1.20 litapriori = 0
% 0.83/1.20 termapriori = 1
% 0.83/1.20 litaposteriori = 0
% 0.83/1.20 termaposteriori = 0
% 0.83/1.20 demodaposteriori = 0
% 0.83/1.20 ordereqreflfact = 0
% 0.83/1.20
% 0.83/1.20 litselect = negord
% 0.83/1.20
% 0.83/1.20 maxweight = 15
% 0.83/1.20 maxdepth = 30000
% 0.83/1.20 maxlength = 115
% 0.83/1.20 maxnrvars = 195
% 0.83/1.20 excuselevel = 1
% 0.83/1.20 increasemaxweight = 1
% 0.83/1.20
% 0.83/1.20 maxselected = 10000000
% 0.83/1.20 maxnrclauses = 10000000
% 0.83/1.20
% 0.83/1.20 showgenerated = 0
% 0.83/1.20 showkept = 0
% 0.83/1.20 showselected = 0
% 0.83/1.20 showdeleted = 0
% 0.83/1.20 showresimp = 1
% 0.83/1.20 showstatus = 2000
% 0.83/1.20
% 0.83/1.20 prologoutput = 0
% 0.83/1.20 nrgoals = 5000000
% 0.83/1.20 totalproof = 1
% 0.83/1.20
% 0.83/1.20 Symbols occurring in the translation:
% 0.83/1.20
% 0.83/1.20 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.83/1.20 . [1, 2] (w:1, o:30, a:1, s:1, b:0),
% 0.83/1.20 ! [4, 1] (w:0, o:14, a:1, s:1, b:0),
% 0.83/1.20 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.83/1.20 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.83/1.20 set_type [36, 0] (w:1, o:7, a:1, s:1, b:0),
% 0.83/1.20 ilf_type [37, 2] (w:1, o:54, a:1, s:1, b:0),
% 0.83/1.20 cross_product [40, 2] (w:1, o:55, a:1, s:1, b:0),
% 0.83/1.20 subset [41, 2] (w:1, o:57, a:1, s:1, b:0),
% 0.83/1.20 relation_type [42, 2] (w:1, o:56, a:1, s:1, b:0),
% 0.83/1.20 member [43, 2] (w:1, o:58, a:1, s:1, b:0),
% 0.83/1.20 ordered_pair [46, 2] (w:1, o:59, a:1, s:1, b:0),
% 0.83/1.20 subset_type [47, 1] (w:1, o:20, a:1, s:1, b:0),
% 0.83/1.20 power_set [48, 1] (w:1, o:21, a:1, s:1, b:0),
% 0.83/1.20 member_type [49, 1] (w:1, o:22, a:1, s:1, b:0),
% 0.83/1.20 empty [50, 1] (w:1, o:23, a:1, s:1, b:0),
% 0.83/1.20 relation_like [51, 1] (w:1, o:19, a:1, s:1, b:0),
% 0.83/1.20 alpha1 [52, 4] (w:1, o:69, a:1, s:1, b:1),
% 0.83/1.20 alpha2 [53, 3] (w:1, o:66, a:1, s:1, b:1),
% 0.83/1.20 alpha3 [54, 3] (w:1, o:67, a:1, s:1, b:1),
% 0.83/1.20 alpha4 [55, 1] (w:1, o:24, a:1, s:1, b:1),
% 0.83/1.20 alpha5 [56, 4] (w:1, o:70, a:1, s:1, b:1),
% 0.83/1.20 alpha6 [57, 2] (w:1, o:60, a:1, s:1, b:1),
% 0.83/1.20 alpha7 [58, 2] (w:1, o:61, a:1, s:1, b:1),
% 0.83/1.20 alpha8 [59, 5] (w:1, o:72, a:1, s:1, b:1),
% 0.83/1.20 skol1 [60, 3] (w:1, o:68, a:1, s:1, b:1),
% 0.83/1.20 skol2 [61, 4] (w:1, o:71, a:1, s:1, b:1),
% 0.83/1.20 skol3 [62, 2] (w:1, o:62, a:1, s:1, b:1),
% 0.83/1.20 skol4 [63, 1] (w:1, o:25, a:1, s:1, b:1),
% 0.83/1.20 skol5 [64, 2] (w:1, o:63, a:1, s:1, b:1),
% 0.83/1.20 skol6 [65, 2] (w:1, o:64, a:1, s:1, b:1),
% 0.83/1.20 skol7 [66, 1] (w:1, o:26, a:1, s:1, b:1),
% 0.83/1.20 skol8 [67, 1] (w:1, o:27, a:1, s:1, b:1),
% 0.83/1.20 skol9 [68, 1] (w:1, o:28, a:1, s:1, b:1),
% 0.83/1.20 skol10 [69, 1] (w:1, o:29, a:1, s:1, b:1),
% 0.83/1.20 skol11 [70, 2] (w:1, o:65, a:1, s:1, b:1),
% 0.83/1.20 skol12 [71, 0] (w:1, o:12, a:1, s:1, b:1),
% 0.83/1.20 skol13 [72, 0] (w:1, o:13, a:1, s:1, b:1).
% 0.83/1.20
% 0.83/1.20
% 0.83/1.20 Starting Search:
% 0.83/1.20
% 0.83/1.20 *** allocated 15000 integers for clauses
% 0.83/1.20 *** allocated 22500 integers for clauses
% 0.83/1.20 *** allocated 33750 integers for clauses
% 0.83/1.20 *** allocated 15000 integers for termspace/termends
% 0.83/1.20 *** allocated 50625 integers for clauses
% 0.83/1.20 Resimplifying inuse:
% 0.83/1.20 Done
% 0.83/1.20
% 0.83/1.20 *** allocated 22500 integers for termspace/termends
% 0.83/1.20 *** allocated 75937 integers for clauses
% 0.83/1.20 *** allocated 33750 integers for termspace/termends
% 0.83/1.20 *** allocated 113905 integers for clauses
% 0.83/1.20
% 0.83/1.20 Intermediate Status:
% 0.83/1.20 Generated: 3812
% 0.83/1.20 Kept: 2005
% 0.83/1.20 Inuse: 241
% 0.83/1.20 Deleted: 106
% 0.83/1.20 Deletedinuse: 34
% 0.83/1.20
% 0.83/1.20 Resimplifying inuse:
% 0.83/1.20 Done
% 0.83/1.20
% 0.83/1.20
% 0.83/1.20 Bliksems!, er is een bewijs:
% 0.83/1.20 % SZS status Theorem
% 0.83/1.20 % SZS output start Refutation
% 0.83/1.20
% 0.83/1.20 (0) {G0,W19,D3,L5,V3,M5} I { ! ilf_type( X, set_type ), ! ilf_type( Y,
% 0.83/1.20 set_type ), ! ilf_type( Z, set_type ), ! subset( X, cross_product( Y, Z )
% 0.83/1.20 ), ilf_type( X, relation_type( Y, Z ) ) }.
% 0.83/1.20 (27) {G0,W6,D2,L2,V1,M2} I { ! ilf_type( X, set_type ), subset( X, X ) }.
% 0.83/1.20 (56) {G0,W3,D2,L1,V1,M1} I { ilf_type( X, set_type ) }.
% 0.83/1.20 (57) {G0,W7,D3,L1,V0,M1} I { ! ilf_type( cross_product( skol12, skol13 ),
% 0.83/1.20 relation_type( skol12, skol13 ) ) }.
% 0.83/1.20 (94) {G1,W10,D3,L2,V3,M2} S(0);r(56);r(56);r(56) { ! subset( X,
% 0.83/1.20 cross_product( Y, Z ) ), ilf_type( X, relation_type( Y, Z ) ) }.
% 0.83/1.20 (96) {G1,W3,D2,L1,V1,M1} S(27);r(56) { subset( X, X ) }.
% 0.83/1.20 (2326) {G2,W0,D0,L0,V0,M0} R(94,57);r(96) { }.
% 0.83/1.20
% 0.83/1.20
% 0.83/1.20 % SZS output end Refutation
% 0.83/1.20 found a proof!
% 0.83/1.20
% 0.83/1.20
% 0.83/1.20 Unprocessed initial clauses:
% 0.83/1.20
% 0.83/1.20 (2328) {G0,W19,D3,L5,V3,M5} { ! ilf_type( X, set_type ), ! ilf_type( Y,
% 0.83/1.20 set_type ), ! ilf_type( Z, set_type ), ! subset( X, cross_product( Y, Z )
% 0.83/1.20 ), ilf_type( X, relation_type( Y, Z ) ) }.
% 0.83/1.20 (2329) {G0,W20,D3,L5,V6,M5} { ! ilf_type( X, set_type ), ! ilf_type( Y,
% 0.83/1.20 set_type ), ! ilf_type( Z, set_type ), ! member( Z, cross_product( X, Y )
% 0.83/1.20 ), ilf_type( skol1( T, U, W ), set_type ) }.
% 0.83/1.20 (2330) {G0,W22,D3,L5,V3,M5} { ! ilf_type( X, set_type ), ! ilf_type( Y,
% 0.83/1.20 set_type ), ! ilf_type( Z, set_type ), ! member( Z, cross_product( X, Y )
% 0.83/1.20 ), alpha1( X, Y, Z, skol1( X, Y, Z ) ) }.
% 0.83/1.20 (2331) {G0,W22,D3,L6,V4,M6} { ! ilf_type( X, set_type ), ! ilf_type( Y,
% 0.83/1.20 set_type ), ! ilf_type( Z, set_type ), ! ilf_type( T, set_type ), !
% 0.83/1.20 alpha1( X, Y, Z, T ), member( Z, cross_product( X, Y ) ) }.
% 0.83/1.20 (2332) {G0,W12,D3,L2,V8,M2} { ! alpha1( X, Y, Z, T ), ilf_type( skol2( U,
% 0.83/1.20 W, V0, V1 ), set_type ) }.
% 0.83/1.20 (2333) {G0,W15,D3,L2,V4,M2} { ! alpha1( X, Y, Z, T ), alpha8( X, Y, Z, T,
% 0.83/1.20 skol2( X, Y, Z, T ) ) }.
% 0.83/1.20 (2334) {G0,W14,D2,L3,V5,M3} { ! ilf_type( U, set_type ), ! alpha8( X, Y, Z
% 0.83/1.20 , T, U ), alpha1( X, Y, Z, T ) }.
% 0.83/1.20 (2335) {G0,W9,D2,L2,V5,M2} { ! alpha8( X, Y, Z, T, U ), member( T, X ) }.
% 0.83/1.20 (2336) {G0,W11,D2,L2,V5,M2} { ! alpha8( X, Y, Z, T, U ), alpha5( Y, Z, T,
% 0.83/1.20 U ) }.
% 0.83/1.20 (2337) {G0,W14,D2,L3,V5,M3} { ! member( T, X ), ! alpha5( Y, Z, T, U ),
% 0.83/1.20 alpha8( X, Y, Z, T, U ) }.
% 0.83/1.20 (2338) {G0,W8,D2,L2,V4,M2} { ! alpha5( X, Y, Z, T ), member( T, X ) }.
% 0.83/1.20 (2339) {G0,W10,D3,L2,V4,M2} { ! alpha5( X, Y, Z, T ), Y = ordered_pair( Z
% 0.83/1.20 , T ) }.
% 0.83/1.20 (2340) {G0,W13,D3,L3,V4,M3} { ! member( T, X ), ! Y = ordered_pair( Z, T )
% 0.83/1.20 , alpha5( X, Y, Z, T ) }.
% 0.83/1.20 (2341) {G0,W11,D3,L3,V2,M3} { ! ilf_type( X, set_type ), ! ilf_type( Y,
% 0.83/1.20 set_type ), ilf_type( cross_product( X, Y ), set_type ) }.
% 0.83/1.20 (2342) {G0,W17,D4,L4,V3,M4} { ! ilf_type( X, set_type ), ! ilf_type( Y,
% 0.83/1.20 set_type ), ! ilf_type( Z, subset_type( cross_product( X, Y ) ) ),
% 0.83/1.20 ilf_type( Z, relation_type( X, Y ) ) }.
% 0.83/1.20 (2343) {G0,W17,D4,L4,V3,M4} { ! ilf_type( X, set_type ), ! ilf_type( Y,
% 0.83/1.20 set_type ), ! ilf_type( Z, relation_type( X, Y ) ), ilf_type( Z,
% 0.83/1.20 subset_type( cross_product( X, Y ) ) ) }.
% 0.83/1.20 (2344) {G0,W13,D3,L3,V2,M3} { ! ilf_type( X, set_type ), ! ilf_type( Y,
% 0.83/1.20 set_type ), ilf_type( skol3( X, Y ), relation_type( Y, X ) ) }.
% 0.83/1.20 (2345) {G0,W11,D3,L3,V2,M3} { ! ilf_type( X, set_type ), ! ilf_type( Y,
% 0.83/1.20 set_type ), ilf_type( ordered_pair( X, Y ), set_type ) }.
% 0.83/1.20 (2346) {G0,W15,D4,L4,V2,M4} { ! ilf_type( X, set_type ), ! ilf_type( Y,
% 0.83/1.20 set_type ), ! ilf_type( Y, subset_type( X ) ), ilf_type( Y, member_type(
% 0.83/1.20 power_set( X ) ) ) }.
% 0.83/1.20 (2347) {G0,W15,D4,L4,V2,M4} { ! ilf_type( X, set_type ), ! ilf_type( Y,
% 0.83/1.20 set_type ), ! ilf_type( Y, member_type( power_set( X ) ) ), ilf_type( Y,
% 0.83/1.20 subset_type( X ) ) }.
% 0.83/1.20 (2348) {G0,W8,D3,L2,V1,M2} { ! ilf_type( X, set_type ), ilf_type( skol4( X
% 0.83/1.20 ), subset_type( X ) ) }.
% 0.83/1.20 (2349) {G0,W16,D2,L5,V3,M5} { ! ilf_type( X, set_type ), ! ilf_type( Y,
% 0.83/1.20 set_type ), ! subset( X, Y ), ! ilf_type( Z, set_type ), alpha2( X, Y, Z
% 0.83/1.20 ) }.
% 0.83/1.20 (2350) {G0,W14,D3,L4,V4,M4} { ! ilf_type( X, set_type ), ! ilf_type( Y,
% 0.83/1.20 set_type ), ilf_type( skol5( Z, T ), set_type ), subset( X, Y ) }.
% 0.83/1.20 (2351) {G0,W15,D3,L4,V2,M4} { ! ilf_type( X, set_type ), ! ilf_type( Y,
% 0.83/1.20 set_type ), ! alpha2( X, Y, skol5( X, Y ) ), subset( X, Y ) }.
% 0.83/1.20 (2352) {G0,W10,D2,L3,V3,M3} { ! alpha2( X, Y, Z ), ! member( Z, X ),
% 0.83/1.20 member( Z, Y ) }.
% 0.83/1.20 (2353) {G0,W7,D2,L2,V3,M2} { member( Z, X ), alpha2( X, Y, Z ) }.
% 0.83/1.20 (2354) {G0,W7,D2,L2,V3,M2} { ! member( Z, Y ), alpha2( X, Y, Z ) }.
% 0.83/1.20 (2355) {G0,W6,D2,L2,V1,M2} { ! ilf_type( X, set_type ), subset( X, X ) }.
% 0.83/1.20 (2356) {G0,W17,D3,L5,V3,M5} { ! ilf_type( X, set_type ), ! ilf_type( Y,
% 0.83/1.20 set_type ), ! member( X, power_set( Y ) ), ! ilf_type( Z, set_type ),
% 0.83/1.20 alpha3( X, Y, Z ) }.
% 0.83/1.20 (2357) {G0,W15,D3,L4,V4,M4} { ! ilf_type( X, set_type ), ! ilf_type( Y,
% 0.83/1.20 set_type ), ilf_type( skol6( Z, T ), set_type ), member( X, power_set( Y
% 0.83/1.20 ) ) }.
% 0.83/1.20 (2358) {G0,W16,D3,L4,V2,M4} { ! ilf_type( X, set_type ), ! ilf_type( Y,
% 0.83/1.20 set_type ), ! alpha3( X, Y, skol6( X, Y ) ), member( X, power_set( Y ) )
% 0.83/1.20 }.
% 0.83/1.20 (2359) {G0,W10,D2,L3,V3,M3} { ! alpha3( X, Y, Z ), ! member( Z, X ),
% 0.83/1.20 member( Z, Y ) }.
% 0.83/1.20 (2360) {G0,W7,D2,L2,V3,M2} { member( Z, X ), alpha3( X, Y, Z ) }.
% 0.83/1.20 (2361) {G0,W7,D2,L2,V3,M2} { ! member( Z, Y ), alpha3( X, Y, Z ) }.
% 0.83/1.20 (2362) {G0,W6,D3,L2,V1,M2} { ! ilf_type( X, set_type ), ! empty( power_set
% 0.83/1.20 ( X ) ) }.
% 0.83/1.20 (2363) {G0,W7,D3,L2,V1,M2} { ! ilf_type( X, set_type ), ilf_type(
% 0.83/1.20 power_set( X ), set_type ) }.
% 0.83/1.20 (2364) {G0,W15,D3,L5,V2,M5} { ! ilf_type( X, set_type ), empty( Y ), !
% 0.83/1.20 ilf_type( Y, set_type ), ! ilf_type( X, member_type( Y ) ), member( X, Y
% 0.83/1.20 ) }.
% 0.83/1.20 (2365) {G0,W15,D3,L5,V2,M5} { ! ilf_type( X, set_type ), empty( Y ), !
% 0.83/1.20 ilf_type( Y, set_type ), ! member( X, Y ), ilf_type( X, member_type( Y )
% 0.83/1.20 ) }.
% 0.83/1.20 (2366) {G0,W10,D3,L3,V1,M3} { empty( X ), ! ilf_type( X, set_type ),
% 0.83/1.20 ilf_type( skol7( X ), member_type( X ) ) }.
% 0.83/1.20 (2367) {G0,W11,D2,L4,V2,M4} { ! ilf_type( X, set_type ), ! empty( X ), !
% 0.83/1.20 ilf_type( Y, set_type ), ! member( Y, X ) }.
% 0.83/1.20 (2368) {G0,W9,D3,L3,V2,M3} { ! ilf_type( X, set_type ), ilf_type( skol8( Y
% 0.83/1.20 ), set_type ), empty( X ) }.
% 0.83/1.20 (2369) {G0,W9,D3,L3,V1,M3} { ! ilf_type( X, set_type ), member( skol8( X )
% 0.83/1.20 , X ), empty( X ) }.
% 0.83/1.20 (2370) {G0,W11,D2,L4,V2,M4} { ! ilf_type( X, set_type ), ! relation_like(
% 0.83/1.20 X ), ! ilf_type( Y, set_type ), alpha6( X, Y ) }.
% 0.83/1.20 (2371) {G0,W9,D3,L3,V2,M3} { ! ilf_type( X, set_type ), ilf_type( skol9( Y
% 0.83/1.20 ), set_type ), relation_like( X ) }.
% 0.83/1.20 (2372) {G0,W9,D3,L3,V1,M3} { ! ilf_type( X, set_type ), ! alpha6( X, skol9
% 0.83/1.20 ( X ) ), relation_like( X ) }.
% 0.83/1.20 (2373) {G0,W8,D2,L3,V2,M3} { ! alpha6( X, Y ), ! member( Y, X ), alpha4( Y
% 0.83/1.20 ) }.
% 0.83/1.20 (2374) {G0,W6,D2,L2,V2,M2} { member( Y, X ), alpha6( X, Y ) }.
% 0.83/1.20 (2375) {G0,W5,D2,L2,V2,M2} { ! alpha4( Y ), alpha6( X, Y ) }.
% 0.83/1.20 (2376) {G0,W6,D3,L2,V2,M2} { ! alpha4( X ), ilf_type( skol10( Y ),
% 0.83/1.20 set_type ) }.
% 0.83/1.20 (2377) {G0,W6,D3,L2,V1,M2} { ! alpha4( X ), alpha7( X, skol10( X ) ) }.
% 0.83/1.20 (2378) {G0,W8,D2,L3,V2,M3} { ! ilf_type( Y, set_type ), ! alpha7( X, Y ),
% 0.83/1.20 alpha4( X ) }.
% 0.83/1.20 (2379) {G0,W8,D3,L2,V4,M2} { ! alpha7( X, Y ), ilf_type( skol11( Z, T ),
% 0.83/1.20 set_type ) }.
% 0.83/1.20 (2380) {G0,W10,D4,L2,V2,M2} { ! alpha7( X, Y ), X = ordered_pair( Y,
% 0.83/1.20 skol11( X, Y ) ) }.
% 0.83/1.20 (2381) {G0,W11,D3,L3,V3,M3} { ! ilf_type( Z, set_type ), ! X =
% 0.83/1.20 ordered_pair( Y, Z ), alpha7( X, Y ) }.
% 0.83/1.20 (2382) {G0,W7,D2,L3,V1,M3} { ! empty( X ), ! ilf_type( X, set_type ),
% 0.83/1.20 relation_like( X ) }.
% 0.83/1.20 (2383) {G0,W14,D4,L4,V3,M4} { ! ilf_type( X, set_type ), ! ilf_type( Y,
% 0.83/1.20 set_type ), ! ilf_type( Z, subset_type( cross_product( X, Y ) ) ),
% 0.83/1.20 relation_like( Z ) }.
% 0.83/1.20 (2384) {G0,W3,D2,L1,V1,M1} { ilf_type( X, set_type ) }.
% 0.83/1.20 (2385) {G0,W3,D2,L1,V0,M1} { ilf_type( skol12, set_type ) }.
% 0.83/1.20 (2386) {G0,W3,D2,L1,V0,M1} { ilf_type( skol13, set_type ) }.
% 0.83/1.20 (2387) {G0,W7,D3,L1,V0,M1} { ! ilf_type( cross_product( skol12, skol13 ),
% 0.83/1.20 relation_type( skol12, skol13 ) ) }.
% 0.83/1.20
% 0.83/1.20
% 0.83/1.20 Total Proof:
% 0.83/1.20
% 0.83/1.20 subsumption: (0) {G0,W19,D3,L5,V3,M5} I { ! ilf_type( X, set_type ), !
% 0.83/1.20 ilf_type( Y, set_type ), ! ilf_type( Z, set_type ), ! subset( X,
% 0.83/1.20 cross_product( Y, Z ) ), ilf_type( X, relation_type( Y, Z ) ) }.
% 0.83/1.20 parent0: (2328) {G0,W19,D3,L5,V3,M5} { ! ilf_type( X, set_type ), !
% 0.83/1.20 ilf_type( Y, set_type ), ! ilf_type( Z, set_type ), ! subset( X,
% 0.83/1.20 cross_product( Y, Z ) ), ilf_type( X, relation_type( Y, Z ) ) }.
% 0.83/1.20 substitution0:
% 0.83/1.20 X := X
% 0.83/1.20 Y := Y
% 0.83/1.20 Z := Z
% 0.83/1.20 end
% 0.83/1.20 permutation0:
% 0.83/1.20 0 ==> 0
% 0.83/1.20 1 ==> 1
% 0.83/1.20 2 ==> 2
% 0.83/1.20 3 ==> 3
% 0.83/1.20 4 ==> 4
% 0.83/1.20 end
% 0.83/1.20
% 0.83/1.20 subsumption: (27) {G0,W6,D2,L2,V1,M2} I { ! ilf_type( X, set_type ), subset
% 0.83/1.20 ( X, X ) }.
% 0.83/1.20 parent0: (2355) {G0,W6,D2,L2,V1,M2} { ! ilf_type( X, set_type ), subset( X
% 0.83/1.20 , X ) }.
% 0.83/1.20 substitution0:
% 0.83/1.20 X := X
% 0.83/1.20 end
% 0.83/1.20 permutation0:
% 0.83/1.20 0 ==> 0
% 0.83/1.20 1 ==> 1
% 0.83/1.20 end
% 0.83/1.20
% 0.83/1.20 subsumption: (56) {G0,W3,D2,L1,V1,M1} I { ilf_type( X, set_type ) }.
% 0.83/1.20 parent0: (2384) {G0,W3,D2,L1,V1,M1} { ilf_type( X, set_type ) }.
% 0.83/1.20 substitution0:
% 0.83/1.20 X := X
% 0.83/1.20 end
% 0.83/1.20 permutation0:
% 0.83/1.20 0 ==> 0
% 0.83/1.20 end
% 0.83/1.20
% 0.83/1.20 *** allocated 50625 integers for termspace/termends
% 0.83/1.20 subsumption: (57) {G0,W7,D3,L1,V0,M1} I { ! ilf_type( cross_product( skol12
% 0.83/1.20 , skol13 ), relation_type( skol12, skol13 ) ) }.
% 0.83/1.20 parent0: (2387) {G0,W7,D3,L1,V0,M1} { ! ilf_type( cross_product( skol12,
% 0.83/1.20 skol13 ), relation_type( skol12, skol13 ) ) }.
% 0.83/1.20 substitution0:
% 0.83/1.20 end
% 0.83/1.20 permutation0:
% 0.83/1.20 0 ==> 0
% 0.83/1.20 end
% 0.83/1.20
% 0.83/1.20 resolution: (2558) {G1,W16,D3,L4,V3,M4} { ! ilf_type( Y, set_type ), !
% 0.83/1.20 ilf_type( Z, set_type ), ! subset( X, cross_product( Y, Z ) ), ilf_type(
% 0.83/1.20 X, relation_type( Y, Z ) ) }.
% 0.83/1.20 parent0[0]: (0) {G0,W19,D3,L5,V3,M5} I { ! ilf_type( X, set_type ), !
% 0.83/1.20 ilf_type( Y, set_type ), ! ilf_type( Z, set_type ), ! subset( X,
% 0.83/1.20 cross_product( Y, Z ) ), ilf_type( X, relation_type( Y, Z ) ) }.
% 0.83/1.20 parent1[0]: (56) {G0,W3,D2,L1,V1,M1} I { ilf_type( X, set_type ) }.
% 0.83/1.20 substitution0:
% 0.83/1.20 X := X
% 0.83/1.20 Y := Y
% 0.83/1.20 Z := Z
% 0.83/1.20 end
% 0.83/1.20 substitution1:
% 0.83/1.20 X := X
% 0.83/1.20 end
% 0.83/1.20
% 0.83/1.20 resolution: (2565) {G1,W13,D3,L3,V3,M3} { ! ilf_type( Y, set_type ), !
% 0.83/1.20 subset( Z, cross_product( X, Y ) ), ilf_type( Z, relation_type( X, Y ) )
% 0.83/1.20 }.
% 0.83/1.20 parent0[0]: (2558) {G1,W16,D3,L4,V3,M4} { ! ilf_type( Y, set_type ), !
% 0.83/1.20 ilf_type( Z, set_type ), ! subset( X, cross_product( Y, Z ) ), ilf_type(
% 0.83/1.20 X, relation_type( Y, Z ) ) }.
% 0.83/1.20 parent1[0]: (56) {G0,W3,D2,L1,V1,M1} I { ilf_type( X, set_type ) }.
% 0.83/1.20 substitution0:
% 0.83/1.20 X := Z
% 0.83/1.20 Y := X
% 0.83/1.20 Z := Y
% 0.83/1.20 end
% 0.83/1.20 substitution1:
% 0.83/1.20 X := X
% 0.83/1.20 end
% 0.83/1.20
% 0.83/1.20 resolution: (2567) {G1,W10,D3,L2,V3,M2} { ! subset( Y, cross_product( Z, X
% 0.83/1.20 ) ), ilf_type( Y, relation_type( Z, X ) ) }.
% 0.83/1.20 parent0[0]: (2565) {G1,W13,D3,L3,V3,M3} { ! ilf_type( Y, set_type ), !
% 0.83/1.20 subset( Z, cross_product( X, Y ) ), ilf_type( Z, relation_type( X, Y ) )
% 0.83/1.20 }.
% 0.83/1.20 parent1[0]: (56) {G0,W3,D2,L1,V1,M1} I { ilf_type( X, set_type ) }.
% 0.83/1.20 substitution0:
% 0.83/1.20 X := Z
% 0.83/1.20 Y := X
% 0.83/1.20 Z := Y
% 0.83/1.20 end
% 0.83/1.20 substitution1:
% 0.83/1.20 X := X
% 0.83/1.20 end
% 0.83/1.20
% 0.83/1.20 subsumption: (94) {G1,W10,D3,L2,V3,M2} S(0);r(56);r(56);r(56) { ! subset( X
% 0.83/1.20 , cross_product( Y, Z ) ), ilf_type( X, relation_type( Y, Z ) ) }.
% 0.83/1.20 parent0: (2567) {G1,W10,D3,L2,V3,M2} { ! subset( Y, cross_product( Z, X )
% 0.83/1.20 ), ilf_type( Y, relation_type( Z, X ) ) }.
% 0.83/1.20 substitution0:
% 0.83/1.20 X := Z
% 0.83/1.20 Y := X
% 0.83/1.20 Z := Y
% 0.83/1.20 end
% 0.83/1.20 permutation0:
% 0.83/1.20 0 ==> 0
% 0.83/1.20 1 ==> 1
% 0.83/1.20 end
% 0.83/1.20
% 0.83/1.20 resolution: (2568) {G1,W3,D2,L1,V1,M1} { subset( X, X ) }.
% 0.83/1.20 parent0[0]: (27) {G0,W6,D2,L2,V1,M2} I { ! ilf_type( X, set_type ), subset
% 0.83/1.20 ( X, X ) }.
% 0.83/1.20 parent1[0]: (56) {G0,W3,D2,L1,V1,M1} I { ilf_type( X, set_type ) }.
% 0.83/1.20 substitution0:
% 0.83/1.20 X := X
% 0.83/1.20 end
% 0.83/1.20 substitution1:
% 0.83/1.20 X := X
% 0.83/1.20 end
% 0.83/1.20
% 0.83/1.20 subsumption: (96) {G1,W3,D2,L1,V1,M1} S(27);r(56) { subset( X, X ) }.
% 0.83/1.20 parent0: (2568) {G1,W3,D2,L1,V1,M1} { subset( X, X ) }.
% 0.83/1.20 substitution0:
% 0.83/1.20 X := X
% 0.83/1.20 end
% 0.83/1.20 permutation0:
% 0.83/1.20 0 ==> 0
% 0.83/1.20 end
% 0.83/1.20
% 0.83/1.20 resolution: (2569) {G1,W7,D3,L1,V0,M1} { ! subset( cross_product( skol12,
% 0.83/1.20 skol13 ), cross_product( skol12, skol13 ) ) }.
% 0.83/1.20 parent0[0]: (57) {G0,W7,D3,L1,V0,M1} I { ! ilf_type( cross_product( skol12
% 0.83/1.20 , skol13 ), relation_type( skol12, skol13 ) ) }.
% 0.83/1.20 parent1[1]: (94) {G1,W10,D3,L2,V3,M2} S(0);r(56);r(56);r(56) { ! subset( X
% 0.83/1.20 , cross_product( Y, Z ) ), ilf_type( X, relation_type( Y, Z ) ) }.
% 0.83/1.20 substitution0:
% 0.83/1.20 end
% 0.83/1.20 substitution1:
% 0.83/1.20 X := cross_product( skol12, skol13 )
% 0.83/1.20 Y := skol12
% 0.83/1.20 Z := skol13
% 0.83/1.20 end
% 0.83/1.20
% 0.83/1.20 resolution: (2570) {G2,W0,D0,L0,V0,M0} { }.
% 0.83/1.20 parent0[0]: (2569) {G1,W7,D3,L1,V0,M1} { ! subset( cross_product( skol12,
% 0.83/1.20 skol13 ), cross_product( skol12, skol13 ) ) }.
% 0.83/1.20 parent1[0]: (96) {G1,W3,D2,L1,V1,M1} S(27);r(56) { subset( X, X ) }.
% 0.83/1.20 substitution0:
% 0.83/1.20 end
% 0.83/1.20 substitution1:
% 0.83/1.20 X := cross_product( skol12, skol13 )
% 0.83/1.20 end
% 0.83/1.20
% 0.83/1.20 subsumption: (2326) {G2,W0,D0,L0,V0,M0} R(94,57);r(96) { }.
% 0.83/1.20 parent0: (2570) {G2,W0,D0,L0,V0,M0} { }.
% 0.83/1.20 substitution0:
% 0.83/1.20 end
% 0.83/1.20 permutation0:
% 0.83/1.20 end
% 0.83/1.20
% 0.83/1.20 Proof check complete!
% 0.83/1.20
% 0.83/1.20 Memory use:
% 0.83/1.20
% 0.83/1.20 space for terms: 30513
% 0.83/1.20 space for clauses: 100926
% 0.83/1.20
% 0.83/1.20
% 0.83/1.20 clauses generated: 4458
% 0.83/1.20 clauses kept: 2327
% 0.83/1.20 clauses selected: 259
% 0.83/1.20 clauses deleted: 121
% 0.83/1.20 clauses inuse deleted: 44
% 0.83/1.20
% 0.83/1.20 subsentry: 10388
% 0.83/1.20 literals s-matched: 9422
% 0.83/1.20 literals matched: 8673
% 0.83/1.20 full subsumption: 504
% 0.83/1.20
% 0.83/1.20 checksum: 645301035
% 0.83/1.20
% 0.83/1.20
% 0.83/1.20 Bliksem ended
%------------------------------------------------------------------------------