TSTP Solution File: SET676+3 by Bliksem---1.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SET676+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n014.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 22:51:20 EDT 2022
% Result : Theorem 0.46s 1.13s
% Output : Refutation 0.46s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : SET676+3 : TPTP v8.1.0. Released v2.2.0.
% 0.08/0.14 % Command : bliksem %s
% 0.13/0.35 % Computer : n014.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % DateTime : Sun Jul 10 12:24:35 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.46/1.12 *** allocated 10000 integers for termspace/termends
% 0.46/1.12 *** allocated 10000 integers for clauses
% 0.46/1.12 *** allocated 10000 integers for justifications
% 0.46/1.12 Bliksem 1.12
% 0.46/1.12
% 0.46/1.12
% 0.46/1.12 Automatic Strategy Selection
% 0.46/1.12
% 0.46/1.12
% 0.46/1.12 Clauses:
% 0.46/1.12
% 0.46/1.12 { ! ilf_type( X, set_type ), ! ilf_type( Y, set_type ), ilf_type(
% 0.46/1.12 cross_product( X, Y ), relation_type( X, Y ) ) }.
% 0.46/1.12 { ! ilf_type( X, set_type ), ! ilf_type( Y, set_type ), ! ilf_type( Z,
% 0.46/1.12 set_type ), ! member( Z, cross_product( X, Y ) ), ilf_type( skol1( T, U,
% 0.46/1.12 W ), set_type ) }.
% 0.46/1.12 { ! ilf_type( X, set_type ), ! ilf_type( Y, set_type ), ! ilf_type( Z,
% 0.46/1.12 set_type ), ! member( Z, cross_product( X, Y ) ), alpha1( X, Y, Z, skol1
% 0.46/1.12 ( X, Y, Z ) ) }.
% 0.46/1.12 { ! ilf_type( X, set_type ), ! ilf_type( Y, set_type ), ! ilf_type( Z,
% 0.46/1.12 set_type ), ! ilf_type( T, set_type ), ! alpha1( X, Y, Z, T ), member( Z
% 0.46/1.12 , cross_product( X, Y ) ) }.
% 0.46/1.12 { ! alpha1( X, Y, Z, T ), ilf_type( skol2( U, W, V0, V1 ), set_type ) }.
% 0.46/1.12 { ! alpha1( X, Y, Z, T ), alpha7( X, Y, Z, T, skol2( X, Y, Z, T ) ) }.
% 0.46/1.12 { ! ilf_type( U, set_type ), ! alpha7( X, Y, Z, T, U ), alpha1( X, Y, Z, T
% 0.46/1.12 ) }.
% 0.46/1.12 { ! alpha7( X, Y, Z, T, U ), member( T, X ) }.
% 0.46/1.12 { ! alpha7( X, Y, Z, T, U ), alpha4( Y, Z, T, U ) }.
% 0.46/1.12 { ! member( T, X ), ! alpha4( Y, Z, T, U ), alpha7( X, Y, Z, T, U ) }.
% 0.46/1.12 { ! alpha4( X, Y, Z, T ), member( T, X ) }.
% 0.46/1.12 { ! alpha4( X, Y, Z, T ), Y = ordered_pair( Z, T ) }.
% 0.46/1.12 { ! member( T, X ), ! Y = ordered_pair( Z, T ), alpha4( X, Y, Z, T ) }.
% 0.46/1.12 { ! ilf_type( X, set_type ), ! ilf_type( Y, set_type ), ilf_type(
% 0.46/1.12 cross_product( X, Y ), set_type ) }.
% 0.46/1.12 { ! ilf_type( X, set_type ), ! ilf_type( Y, set_type ), ! ilf_type( Y,
% 0.46/1.12 identity_relation_of_type( X ) ), ilf_type( Y, relation_type( X, X ) ) }
% 0.46/1.12 .
% 0.46/1.12 { ! ilf_type( X, set_type ), ! ilf_type( Y, set_type ), ! ilf_type( Y,
% 0.46/1.12 relation_type( X, X ) ), ilf_type( Y, identity_relation_of_type( X ) ) }
% 0.46/1.12 .
% 0.46/1.12 { ! ilf_type( X, set_type ), ilf_type( skol3( X ),
% 0.46/1.12 identity_relation_of_type( X ) ) }.
% 0.46/1.12 { ! ilf_type( X, set_type ), ! ilf_type( Y, set_type ), ilf_type(
% 0.46/1.12 ordered_pair( X, Y ), set_type ) }.
% 0.46/1.12 { ! ilf_type( X, set_type ), ! ilf_type( Y, set_type ), ! ilf_type( Z,
% 0.46/1.12 subset_type( cross_product( X, Y ) ) ), ilf_type( Z, relation_type( X, Y
% 0.46/1.12 ) ) }.
% 0.46/1.12 { ! ilf_type( X, set_type ), ! ilf_type( Y, set_type ), ! ilf_type( Z,
% 0.46/1.12 relation_type( X, Y ) ), ilf_type( Z, subset_type( cross_product( X, Y )
% 0.46/1.12 ) ) }.
% 0.46/1.12 { ! ilf_type( X, set_type ), ! ilf_type( Y, set_type ), ilf_type( skol4( X
% 0.46/1.12 , Y ), relation_type( Y, X ) ) }.
% 0.46/1.12 { ! ilf_type( X, set_type ), ! ilf_type( Y, set_type ), ! ilf_type( Y,
% 0.46/1.12 subset_type( X ) ), ilf_type( Y, member_type( power_set( X ) ) ) }.
% 0.46/1.12 { ! ilf_type( X, set_type ), ! ilf_type( Y, set_type ), ! ilf_type( Y,
% 0.46/1.12 member_type( power_set( X ) ) ), ilf_type( Y, subset_type( X ) ) }.
% 0.46/1.12 { ! ilf_type( X, set_type ), ilf_type( skol5( X ), subset_type( X ) ) }.
% 0.46/1.12 { ! ilf_type( X, set_type ), ! ilf_type( Y, set_type ), ! member( X,
% 0.46/1.12 power_set( Y ) ), ! ilf_type( Z, set_type ), alpha2( X, Y, Z ) }.
% 0.46/1.12 { ! ilf_type( X, set_type ), ! ilf_type( Y, set_type ), ilf_type( skol6( Z
% 0.46/1.12 , T ), set_type ), member( X, power_set( Y ) ) }.
% 0.46/1.12 { ! ilf_type( X, set_type ), ! ilf_type( Y, set_type ), ! alpha2( X, Y,
% 0.46/1.12 skol6( X, Y ) ), member( X, power_set( Y ) ) }.
% 0.46/1.12 { ! alpha2( X, Y, Z ), ! member( Z, X ), member( Z, Y ) }.
% 0.46/1.12 { member( Z, X ), alpha2( X, Y, Z ) }.
% 0.46/1.12 { ! member( Z, Y ), alpha2( X, Y, Z ) }.
% 0.46/1.12 { ! ilf_type( X, set_type ), ! empty( power_set( X ) ) }.
% 0.46/1.12 { ! ilf_type( X, set_type ), ilf_type( power_set( X ), set_type ) }.
% 0.46/1.12 { ! ilf_type( X, set_type ), empty( Y ), ! ilf_type( Y, set_type ), !
% 0.46/1.12 ilf_type( X, member_type( Y ) ), member( X, Y ) }.
% 0.46/1.12 { ! ilf_type( X, set_type ), empty( Y ), ! ilf_type( Y, set_type ), !
% 0.46/1.12 member( X, Y ), ilf_type( X, member_type( Y ) ) }.
% 0.46/1.12 { empty( X ), ! ilf_type( X, set_type ), ilf_type( skol7( X ), member_type
% 0.46/1.12 ( X ) ) }.
% 0.46/1.12 { ! ilf_type( X, set_type ), ! empty( X ), ! ilf_type( Y, set_type ), !
% 0.46/1.12 member( Y, X ) }.
% 0.46/1.12 { ! ilf_type( X, set_type ), ilf_type( skol8( Y ), set_type ), empty( X ) }
% 0.46/1.12 .
% 0.46/1.12 { ! ilf_type( X, set_type ), member( skol8( X ), X ), empty( X ) }.
% 0.46/1.12 { ! ilf_type( X, set_type ), ! relation_like( X ), ! ilf_type( Y, set_type
% 0.46/1.12 ), alpha5( X, Y ) }.
% 0.46/1.12 { ! ilf_type( X, set_type ), ilf_type( skol9( Y ), set_type ),
% 0.46/1.12 relation_like( X ) }.
% 0.46/1.12 { ! ilf_type( X, set_type ), ! alpha5( X, skol9( X ) ), relation_like( X )
% 0.46/1.12 }.
% 0.46/1.12 { ! alpha5( X, Y ), ! member( Y, X ), alpha3( Y ) }.
% 0.46/1.12 { member( Y, X ), alpha5( X, Y ) }.
% 0.46/1.12 { ! alpha3( Y ), alpha5( X, Y ) }.
% 0.46/1.12 { ! alpha3( X ), ilf_type( skol10( Y ), set_type ) }.
% 0.46/1.12 { ! alpha3( X ), alpha6( X, skol10( X ) ) }.
% 0.46/1.12 { ! ilf_type( Y, set_type ), ! alpha6( X, Y ), alpha3( X ) }.
% 0.46/1.12 { ! alpha6( X, Y ), ilf_type( skol11( Z, T ), set_type ) }.
% 0.46/1.12 { ! alpha6( X, Y ), X = ordered_pair( Y, skol11( X, Y ) ) }.
% 0.46/1.12 { ! ilf_type( Z, set_type ), ! X = ordered_pair( Y, Z ), alpha6( X, Y ) }.
% 0.46/1.12 { ! empty( X ), ! ilf_type( X, set_type ), relation_like( X ) }.
% 0.46/1.12 { ! ilf_type( X, set_type ), ! ilf_type( Y, set_type ), ! ilf_type( Z,
% 0.46/1.12 subset_type( cross_product( X, Y ) ) ), relation_like( Z ) }.
% 0.46/1.12 { ilf_type( X, set_type ) }.
% 0.46/1.12 { ilf_type( skol12, set_type ) }.
% 0.46/1.12 { ! ilf_type( cross_product( skol12, skol12 ), identity_relation_of_type(
% 0.46/1.12 skol12 ) ) }.
% 0.46/1.12
% 0.46/1.12 percentage equality = 0.024242, percentage horn = 0.836364
% 0.46/1.12 This is a problem with some equality
% 0.46/1.12
% 0.46/1.12
% 0.46/1.12
% 0.46/1.12 Options Used:
% 0.46/1.12
% 0.46/1.12 useres = 1
% 0.46/1.12 useparamod = 1
% 0.46/1.12 useeqrefl = 1
% 0.46/1.12 useeqfact = 1
% 0.46/1.12 usefactor = 1
% 0.46/1.12 usesimpsplitting = 0
% 0.46/1.12 usesimpdemod = 5
% 0.46/1.12 usesimpres = 3
% 0.46/1.12
% 0.46/1.12 resimpinuse = 1000
% 0.46/1.12 resimpclauses = 20000
% 0.46/1.12 substype = eqrewr
% 0.46/1.12 backwardsubs = 1
% 0.46/1.12 selectoldest = 5
% 0.46/1.12
% 0.46/1.12 litorderings [0] = split
% 0.46/1.12 litorderings [1] = extend the termordering, first sorting on arguments
% 0.46/1.12
% 0.46/1.12 termordering = kbo
% 0.46/1.12
% 0.46/1.12 litapriori = 0
% 0.46/1.12 termapriori = 1
% 0.46/1.12 litaposteriori = 0
% 0.46/1.12 termaposteriori = 0
% 0.46/1.12 demodaposteriori = 0
% 0.46/1.12 ordereqreflfact = 0
% 0.46/1.12
% 0.46/1.12 litselect = negord
% 0.46/1.12
% 0.46/1.12 maxweight = 15
% 0.46/1.12 maxdepth = 30000
% 0.46/1.12 maxlength = 115
% 0.46/1.12 maxnrvars = 195
% 0.46/1.12 excuselevel = 1
% 0.46/1.12 increasemaxweight = 1
% 0.46/1.12
% 0.46/1.12 maxselected = 10000000
% 0.46/1.12 maxnrclauses = 10000000
% 0.46/1.12
% 0.46/1.12 showgenerated = 0
% 0.46/1.12 showkept = 0
% 0.46/1.12 showselected = 0
% 0.46/1.12 showdeleted = 0
% 0.46/1.12 showresimp = 1
% 0.46/1.12 showstatus = 2000
% 0.46/1.12
% 0.46/1.12 prologoutput = 0
% 0.46/1.12 nrgoals = 5000000
% 0.46/1.12 totalproof = 1
% 0.46/1.12
% 0.46/1.12 Symbols occurring in the translation:
% 0.46/1.12
% 0.46/1.12 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.46/1.12 . [1, 2] (w:1, o:31, a:1, s:1, b:0),
% 0.46/1.12 ! [4, 1] (w:0, o:13, a:1, s:1, b:0),
% 0.46/1.12 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.46/1.12 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.46/1.12 set_type [36, 0] (w:1, o:7, a:1, s:1, b:0),
% 0.46/1.12 ilf_type [37, 2] (w:1, o:55, a:1, s:1, b:0),
% 0.46/1.12 cross_product [39, 2] (w:1, o:56, a:1, s:1, b:0),
% 0.46/1.12 relation_type [40, 2] (w:1, o:57, a:1, s:1, b:0),
% 0.46/1.12 member [42, 2] (w:1, o:58, a:1, s:1, b:0),
% 0.46/1.12 ordered_pair [45, 2] (w:1, o:59, a:1, s:1, b:0),
% 0.46/1.12 identity_relation_of_type [46, 1] (w:1, o:18, a:1, s:1, b:0),
% 0.46/1.12 subset_type [47, 1] (w:1, o:20, a:1, s:1, b:0),
% 0.46/1.12 power_set [48, 1] (w:1, o:21, a:1, s:1, b:0),
% 0.46/1.12 member_type [49, 1] (w:1, o:22, a:1, s:1, b:0),
% 0.46/1.12 empty [50, 1] (w:1, o:23, a:1, s:1, b:0),
% 0.46/1.12 relation_like [51, 1] (w:1, o:19, a:1, s:1, b:0),
% 0.46/1.12 alpha1 [52, 4] (w:1, o:67, a:1, s:1, b:1),
% 0.46/1.13 alpha2 [53, 3] (w:1, o:65, a:1, s:1, b:1),
% 0.46/1.13 alpha3 [54, 1] (w:1, o:24, a:1, s:1, b:1),
% 0.46/1.13 alpha4 [55, 4] (w:1, o:68, a:1, s:1, b:1),
% 0.46/1.13 alpha5 [56, 2] (w:1, o:60, a:1, s:1, b:1),
% 0.46/1.13 alpha6 [57, 2] (w:1, o:61, a:1, s:1, b:1),
% 0.46/1.13 alpha7 [58, 5] (w:1, o:70, a:1, s:1, b:1),
% 0.46/1.13 skol1 [59, 3] (w:1, o:66, a:1, s:1, b:1),
% 0.46/1.13 skol2 [60, 4] (w:1, o:69, a:1, s:1, b:1),
% 0.46/1.13 skol3 [61, 1] (w:1, o:25, a:1, s:1, b:1),
% 0.46/1.13 skol4 [62, 2] (w:1, o:62, a:1, s:1, b:1),
% 0.46/1.13 skol5 [63, 1] (w:1, o:26, a:1, s:1, b:1),
% 0.46/1.13 skol6 [64, 2] (w:1, o:63, a:1, s:1, b:1),
% 0.46/1.13 skol7 [65, 1] (w:1, o:27, a:1, s:1, b:1),
% 0.46/1.13 skol8 [66, 1] (w:1, o:28, a:1, s:1, b:1),
% 0.46/1.13 skol9 [67, 1] (w:1, o:29, a:1, s:1, b:1),
% 0.46/1.13 skol10 [68, 1] (w:1, o:30, a:1, s:1, b:1),
% 0.46/1.13 skol11 [69, 2] (w:1, o:64, a:1, s:1, b:1),
% 0.46/1.13 skol12 [70, 0] (w:1, o:12, a:1, s:1, b:1).
% 0.46/1.13
% 0.46/1.13
% 0.46/1.13 Starting Search:
% 0.46/1.13
% 0.46/1.13 *** allocated 15000 integers for clauses
% 0.46/1.13
% 0.46/1.13 Bliksems!, er is een bewijs:
% 0.46/1.13 % SZS status Theorem
% 0.46/1.13 % SZS output start Refutation
% 0.46/1.13
% 0.46/1.13 (0) {G0,W13,D3,L3,V2,M3} I { ! ilf_type( X, set_type ), ! ilf_type( Y,
% 0.46/1.13 set_type ), ilf_type( cross_product( X, Y ), relation_type( X, Y ) ) }.
% 0.46/1.13 (15) {G0,W15,D3,L4,V2,M4} I { ! ilf_type( X, set_type ), ! ilf_type( Y,
% 0.46/1.13 set_type ), ! ilf_type( Y, relation_type( X, X ) ), ilf_type( Y,
% 0.46/1.13 identity_relation_of_type( X ) ) }.
% 0.46/1.13 (52) {G0,W3,D2,L1,V1,M1} I { ilf_type( X, set_type ) }.
% 0.46/1.13 (53) {G0,W6,D3,L1,V0,M1} I { ! ilf_type( cross_product( skol12, skol12 ),
% 0.46/1.13 identity_relation_of_type( skol12 ) ) }.
% 0.46/1.13 (86) {G1,W7,D3,L1,V2,M1} S(0);r(52);r(52) { ilf_type( cross_product( X, Y )
% 0.46/1.13 , relation_type( X, Y ) ) }.
% 0.46/1.13 (204) {G1,W9,D3,L2,V2,M2} S(15);r(52);r(52) { ! ilf_type( Y, relation_type
% 0.46/1.13 ( X, X ) ), ilf_type( Y, identity_relation_of_type( X ) ) }.
% 0.46/1.13 (207) {G2,W0,D0,L0,V0,M0} R(204,53);r(86) { }.
% 0.46/1.13
% 0.46/1.13
% 0.46/1.13 % SZS output end Refutation
% 0.46/1.13 found a proof!
% 0.46/1.13
% 0.46/1.13
% 0.46/1.13 Unprocessed initial clauses:
% 0.46/1.13
% 0.46/1.13 (209) {G0,W13,D3,L3,V2,M3} { ! ilf_type( X, set_type ), ! ilf_type( Y,
% 0.46/1.13 set_type ), ilf_type( cross_product( X, Y ), relation_type( X, Y ) ) }.
% 0.46/1.13 (210) {G0,W20,D3,L5,V6,M5} { ! ilf_type( X, set_type ), ! ilf_type( Y,
% 0.46/1.13 set_type ), ! ilf_type( Z, set_type ), ! member( Z, cross_product( X, Y )
% 0.46/1.13 ), ilf_type( skol1( T, U, W ), set_type ) }.
% 0.46/1.13 (211) {G0,W22,D3,L5,V3,M5} { ! ilf_type( X, set_type ), ! ilf_type( Y,
% 0.46/1.13 set_type ), ! ilf_type( Z, set_type ), ! member( Z, cross_product( X, Y )
% 0.46/1.13 ), alpha1( X, Y, Z, skol1( X, Y, Z ) ) }.
% 0.46/1.13 (212) {G0,W22,D3,L6,V4,M6} { ! ilf_type( X, set_type ), ! ilf_type( Y,
% 0.46/1.13 set_type ), ! ilf_type( Z, set_type ), ! ilf_type( T, set_type ), !
% 0.46/1.13 alpha1( X, Y, Z, T ), member( Z, cross_product( X, Y ) ) }.
% 0.46/1.13 (213) {G0,W12,D3,L2,V8,M2} { ! alpha1( X, Y, Z, T ), ilf_type( skol2( U, W
% 0.46/1.13 , V0, V1 ), set_type ) }.
% 0.46/1.13 (214) {G0,W15,D3,L2,V4,M2} { ! alpha1( X, Y, Z, T ), alpha7( X, Y, Z, T,
% 0.46/1.13 skol2( X, Y, Z, T ) ) }.
% 0.46/1.13 (215) {G0,W14,D2,L3,V5,M3} { ! ilf_type( U, set_type ), ! alpha7( X, Y, Z
% 0.46/1.13 , T, U ), alpha1( X, Y, Z, T ) }.
% 0.46/1.13 (216) {G0,W9,D2,L2,V5,M2} { ! alpha7( X, Y, Z, T, U ), member( T, X ) }.
% 0.46/1.13 (217) {G0,W11,D2,L2,V5,M2} { ! alpha7( X, Y, Z, T, U ), alpha4( Y, Z, T, U
% 0.46/1.13 ) }.
% 0.46/1.13 (218) {G0,W14,D2,L3,V5,M3} { ! member( T, X ), ! alpha4( Y, Z, T, U ),
% 0.46/1.13 alpha7( X, Y, Z, T, U ) }.
% 0.46/1.13 (219) {G0,W8,D2,L2,V4,M2} { ! alpha4( X, Y, Z, T ), member( T, X ) }.
% 0.46/1.13 (220) {G0,W10,D3,L2,V4,M2} { ! alpha4( X, Y, Z, T ), Y = ordered_pair( Z,
% 0.46/1.13 T ) }.
% 0.46/1.13 (221) {G0,W13,D3,L3,V4,M3} { ! member( T, X ), ! Y = ordered_pair( Z, T )
% 0.46/1.13 , alpha4( X, Y, Z, T ) }.
% 0.46/1.13 (222) {G0,W11,D3,L3,V2,M3} { ! ilf_type( X, set_type ), ! ilf_type( Y,
% 0.46/1.13 set_type ), ilf_type( cross_product( X, Y ), set_type ) }.
% 0.46/1.13 (223) {G0,W15,D3,L4,V2,M4} { ! ilf_type( X, set_type ), ! ilf_type( Y,
% 0.46/1.13 set_type ), ! ilf_type( Y, identity_relation_of_type( X ) ), ilf_type( Y
% 0.46/1.13 , relation_type( X, X ) ) }.
% 0.46/1.13 (224) {G0,W15,D3,L4,V2,M4} { ! ilf_type( X, set_type ), ! ilf_type( Y,
% 0.46/1.13 set_type ), ! ilf_type( Y, relation_type( X, X ) ), ilf_type( Y,
% 0.46/1.13 identity_relation_of_type( X ) ) }.
% 0.46/1.13 (225) {G0,W8,D3,L2,V1,M2} { ! ilf_type( X, set_type ), ilf_type( skol3( X
% 0.46/1.13 ), identity_relation_of_type( X ) ) }.
% 0.46/1.13 (226) {G0,W11,D3,L3,V2,M3} { ! ilf_type( X, set_type ), ! ilf_type( Y,
% 0.46/1.13 set_type ), ilf_type( ordered_pair( X, Y ), set_type ) }.
% 0.46/1.13 (227) {G0,W17,D4,L4,V3,M4} { ! ilf_type( X, set_type ), ! ilf_type( Y,
% 0.46/1.13 set_type ), ! ilf_type( Z, subset_type( cross_product( X, Y ) ) ),
% 0.46/1.13 ilf_type( Z, relation_type( X, Y ) ) }.
% 0.46/1.13 (228) {G0,W17,D4,L4,V3,M4} { ! ilf_type( X, set_type ), ! ilf_type( Y,
% 0.46/1.13 set_type ), ! ilf_type( Z, relation_type( X, Y ) ), ilf_type( Z,
% 0.46/1.13 subset_type( cross_product( X, Y ) ) ) }.
% 0.46/1.13 (229) {G0,W13,D3,L3,V2,M3} { ! ilf_type( X, set_type ), ! ilf_type( Y,
% 0.46/1.13 set_type ), ilf_type( skol4( X, Y ), relation_type( Y, X ) ) }.
% 0.46/1.13 (230) {G0,W15,D4,L4,V2,M4} { ! ilf_type( X, set_type ), ! ilf_type( Y,
% 0.46/1.13 set_type ), ! ilf_type( Y, subset_type( X ) ), ilf_type( Y, member_type(
% 0.46/1.13 power_set( X ) ) ) }.
% 0.46/1.13 (231) {G0,W15,D4,L4,V2,M4} { ! ilf_type( X, set_type ), ! ilf_type( Y,
% 0.46/1.13 set_type ), ! ilf_type( Y, member_type( power_set( X ) ) ), ilf_type( Y,
% 0.46/1.13 subset_type( X ) ) }.
% 0.46/1.13 (232) {G0,W8,D3,L2,V1,M2} { ! ilf_type( X, set_type ), ilf_type( skol5( X
% 0.46/1.13 ), subset_type( X ) ) }.
% 0.46/1.13 (233) {G0,W17,D3,L5,V3,M5} { ! ilf_type( X, set_type ), ! ilf_type( Y,
% 0.46/1.13 set_type ), ! member( X, power_set( Y ) ), ! ilf_type( Z, set_type ),
% 0.46/1.13 alpha2( X, Y, Z ) }.
% 0.46/1.13 (234) {G0,W15,D3,L4,V4,M4} { ! ilf_type( X, set_type ), ! ilf_type( Y,
% 0.46/1.13 set_type ), ilf_type( skol6( Z, T ), set_type ), member( X, power_set( Y
% 0.46/1.13 ) ) }.
% 0.46/1.13 (235) {G0,W16,D3,L4,V2,M4} { ! ilf_type( X, set_type ), ! ilf_type( Y,
% 0.46/1.13 set_type ), ! alpha2( X, Y, skol6( X, Y ) ), member( X, power_set( Y ) )
% 0.46/1.13 }.
% 0.46/1.13 (236) {G0,W10,D2,L3,V3,M3} { ! alpha2( X, Y, Z ), ! member( Z, X ), member
% 0.46/1.13 ( Z, Y ) }.
% 0.46/1.13 (237) {G0,W7,D2,L2,V3,M2} { member( Z, X ), alpha2( X, Y, Z ) }.
% 0.46/1.13 (238) {G0,W7,D2,L2,V3,M2} { ! member( Z, Y ), alpha2( X, Y, Z ) }.
% 0.46/1.13 (239) {G0,W6,D3,L2,V1,M2} { ! ilf_type( X, set_type ), ! empty( power_set
% 0.46/1.13 ( X ) ) }.
% 0.46/1.13 (240) {G0,W7,D3,L2,V1,M2} { ! ilf_type( X, set_type ), ilf_type( power_set
% 0.46/1.13 ( X ), set_type ) }.
% 0.46/1.13 (241) {G0,W15,D3,L5,V2,M5} { ! ilf_type( X, set_type ), empty( Y ), !
% 0.46/1.13 ilf_type( Y, set_type ), ! ilf_type( X, member_type( Y ) ), member( X, Y
% 0.46/1.13 ) }.
% 0.46/1.13 (242) {G0,W15,D3,L5,V2,M5} { ! ilf_type( X, set_type ), empty( Y ), !
% 0.46/1.13 ilf_type( Y, set_type ), ! member( X, Y ), ilf_type( X, member_type( Y )
% 0.46/1.13 ) }.
% 0.46/1.13 (243) {G0,W10,D3,L3,V1,M3} { empty( X ), ! ilf_type( X, set_type ),
% 0.46/1.13 ilf_type( skol7( X ), member_type( X ) ) }.
% 0.46/1.13 (244) {G0,W11,D2,L4,V2,M4} { ! ilf_type( X, set_type ), ! empty( X ), !
% 0.46/1.13 ilf_type( Y, set_type ), ! member( Y, X ) }.
% 0.46/1.13 (245) {G0,W9,D3,L3,V2,M3} { ! ilf_type( X, set_type ), ilf_type( skol8( Y
% 0.46/1.13 ), set_type ), empty( X ) }.
% 0.46/1.13 (246) {G0,W9,D3,L3,V1,M3} { ! ilf_type( X, set_type ), member( skol8( X )
% 0.46/1.13 , X ), empty( X ) }.
% 0.46/1.13 (247) {G0,W11,D2,L4,V2,M4} { ! ilf_type( X, set_type ), ! relation_like( X
% 0.46/1.13 ), ! ilf_type( Y, set_type ), alpha5( X, Y ) }.
% 0.46/1.13 (248) {G0,W9,D3,L3,V2,M3} { ! ilf_type( X, set_type ), ilf_type( skol9( Y
% 0.46/1.13 ), set_type ), relation_like( X ) }.
% 0.46/1.13 (249) {G0,W9,D3,L3,V1,M3} { ! ilf_type( X, set_type ), ! alpha5( X, skol9
% 0.46/1.13 ( X ) ), relation_like( X ) }.
% 0.46/1.13 (250) {G0,W8,D2,L3,V2,M3} { ! alpha5( X, Y ), ! member( Y, X ), alpha3( Y
% 0.46/1.13 ) }.
% 0.46/1.13 (251) {G0,W6,D2,L2,V2,M2} { member( Y, X ), alpha5( X, Y ) }.
% 0.46/1.13 (252) {G0,W5,D2,L2,V2,M2} { ! alpha3( Y ), alpha5( X, Y ) }.
% 0.46/1.13 (253) {G0,W6,D3,L2,V2,M2} { ! alpha3( X ), ilf_type( skol10( Y ), set_type
% 0.46/1.13 ) }.
% 0.46/1.13 (254) {G0,W6,D3,L2,V1,M2} { ! alpha3( X ), alpha6( X, skol10( X ) ) }.
% 0.46/1.13 (255) {G0,W8,D2,L3,V2,M3} { ! ilf_type( Y, set_type ), ! alpha6( X, Y ),
% 0.46/1.13 alpha3( X ) }.
% 0.46/1.13 (256) {G0,W8,D3,L2,V4,M2} { ! alpha6( X, Y ), ilf_type( skol11( Z, T ),
% 0.46/1.13 set_type ) }.
% 0.46/1.13 (257) {G0,W10,D4,L2,V2,M2} { ! alpha6( X, Y ), X = ordered_pair( Y, skol11
% 0.46/1.13 ( X, Y ) ) }.
% 0.46/1.13 (258) {G0,W11,D3,L3,V3,M3} { ! ilf_type( Z, set_type ), ! X = ordered_pair
% 0.46/1.13 ( Y, Z ), alpha6( X, Y ) }.
% 0.46/1.13 (259) {G0,W7,D2,L3,V1,M3} { ! empty( X ), ! ilf_type( X, set_type ),
% 0.46/1.13 relation_like( X ) }.
% 0.46/1.13 (260) {G0,W14,D4,L4,V3,M4} { ! ilf_type( X, set_type ), ! ilf_type( Y,
% 0.46/1.13 set_type ), ! ilf_type( Z, subset_type( cross_product( X, Y ) ) ),
% 0.46/1.13 relation_like( Z ) }.
% 0.46/1.13 (261) {G0,W3,D2,L1,V1,M1} { ilf_type( X, set_type ) }.
% 0.46/1.13 (262) {G0,W3,D2,L1,V0,M1} { ilf_type( skol12, set_type ) }.
% 0.46/1.13 (263) {G0,W6,D3,L1,V0,M1} { ! ilf_type( cross_product( skol12, skol12 ),
% 0.46/1.13 identity_relation_of_type( skol12 ) ) }.
% 0.46/1.13
% 0.46/1.13
% 0.46/1.13 Total Proof:
% 0.46/1.13
% 0.46/1.13 subsumption: (0) {G0,W13,D3,L3,V2,M3} I { ! ilf_type( X, set_type ), !
% 0.46/1.13 ilf_type( Y, set_type ), ilf_type( cross_product( X, Y ), relation_type(
% 0.46/1.13 X, Y ) ) }.
% 0.46/1.13 parent0: (209) {G0,W13,D3,L3,V2,M3} { ! ilf_type( X, set_type ), !
% 0.46/1.13 ilf_type( Y, set_type ), ilf_type( cross_product( X, Y ), relation_type(
% 0.46/1.13 X, Y ) ) }.
% 0.46/1.13 substitution0:
% 0.46/1.13 X := X
% 0.46/1.13 Y := Y
% 0.46/1.13 end
% 0.46/1.13 permutation0:
% 0.46/1.13 0 ==> 0
% 0.46/1.13 1 ==> 1
% 0.46/1.13 2 ==> 2
% 0.46/1.13 end
% 0.46/1.13
% 0.46/1.13 subsumption: (15) {G0,W15,D3,L4,V2,M4} I { ! ilf_type( X, set_type ), !
% 0.46/1.13 ilf_type( Y, set_type ), ! ilf_type( Y, relation_type( X, X ) ), ilf_type
% 0.46/1.13 ( Y, identity_relation_of_type( X ) ) }.
% 0.46/1.13 parent0: (224) {G0,W15,D3,L4,V2,M4} { ! ilf_type( X, set_type ), !
% 0.46/1.13 ilf_type( Y, set_type ), ! ilf_type( Y, relation_type( X, X ) ), ilf_type
% 0.46/1.13 ( Y, identity_relation_of_type( X ) ) }.
% 0.46/1.13 substitution0:
% 0.46/1.13 X := X
% 0.46/1.13 Y := Y
% 0.46/1.13 end
% 0.46/1.13 permutation0:
% 0.46/1.13 0 ==> 0
% 0.46/1.13 1 ==> 1
% 0.46/1.13 2 ==> 2
% 0.46/1.13 3 ==> 3
% 0.46/1.13 end
% 0.46/1.13
% 0.46/1.13 subsumption: (52) {G0,W3,D2,L1,V1,M1} I { ilf_type( X, set_type ) }.
% 0.46/1.13 parent0: (261) {G0,W3,D2,L1,V1,M1} { ilf_type( X, set_type ) }.
% 0.46/1.13 substitution0:
% 0.46/1.13 X := X
% 0.46/1.13 end
% 0.46/1.13 permutation0:
% 0.46/1.13 0 ==> 0
% 0.46/1.13 end
% 0.46/1.13
% 0.46/1.13 *** allocated 22500 integers for clauses
% 0.46/1.13 subsumption: (53) {G0,W6,D3,L1,V0,M1} I { ! ilf_type( cross_product( skol12
% 0.46/1.13 , skol12 ), identity_relation_of_type( skol12 ) ) }.
% 0.46/1.13 parent0: (263) {G0,W6,D3,L1,V0,M1} { ! ilf_type( cross_product( skol12,
% 0.46/1.13 skol12 ), identity_relation_of_type( skol12 ) ) }.
% 0.46/1.13 substitution0:
% 0.46/1.13 end
% 0.46/1.13 permutation0:
% 0.46/1.13 0 ==> 0
% 0.46/1.13 end
% 0.46/1.13
% 0.46/1.13 resolution: (389) {G1,W10,D3,L2,V2,M2} { ! ilf_type( Y, set_type ),
% 0.46/1.13 ilf_type( cross_product( X, Y ), relation_type( X, Y ) ) }.
% 0.46/1.13 parent0[0]: (0) {G0,W13,D3,L3,V2,M3} I { ! ilf_type( X, set_type ), !
% 0.46/1.13 ilf_type( Y, set_type ), ilf_type( cross_product( X, Y ), relation_type(
% 0.46/1.13 X, Y ) ) }.
% 0.46/1.13 parent1[0]: (52) {G0,W3,D2,L1,V1,M1} I { ilf_type( X, set_type ) }.
% 0.46/1.13 substitution0:
% 0.46/1.13 X := X
% 0.46/1.13 Y := Y
% 0.46/1.13 end
% 0.46/1.13 substitution1:
% 0.46/1.13 X := X
% 0.46/1.13 end
% 0.46/1.13
% 0.46/1.13 resolution: (391) {G1,W7,D3,L1,V2,M1} { ilf_type( cross_product( Y, X ),
% 0.46/1.13 relation_type( Y, X ) ) }.
% 0.46/1.13 parent0[0]: (389) {G1,W10,D3,L2,V2,M2} { ! ilf_type( Y, set_type ),
% 0.46/1.13 ilf_type( cross_product( X, Y ), relation_type( X, Y ) ) }.
% 0.46/1.13 parent1[0]: (52) {G0,W3,D2,L1,V1,M1} I { ilf_type( X, set_type ) }.
% 0.46/1.13 substitution0:
% 0.46/1.13 X := Y
% 0.46/1.13 Y := X
% 0.46/1.13 end
% 0.46/1.13 substitution1:
% 0.46/1.13 X := X
% 0.46/1.13 end
% 0.46/1.13
% 0.46/1.13 subsumption: (86) {G1,W7,D3,L1,V2,M1} S(0);r(52);r(52) { ilf_type(
% 0.46/1.13 cross_product( X, Y ), relation_type( X, Y ) ) }.
% 0.46/1.13 parent0: (391) {G1,W7,D3,L1,V2,M1} { ilf_type( cross_product( Y, X ),
% 0.46/1.13 relation_type( Y, X ) ) }.
% 0.46/1.13 substitution0:
% 0.46/1.13 X := Y
% 0.46/1.13 Y := X
% 0.46/1.13 end
% 0.46/1.13 permutation0:
% 0.46/1.13 0 ==> 0
% 0.46/1.13 end
% 0.46/1.13
% 0.46/1.13 resolution: (394) {G1,W12,D3,L3,V2,M3} { ! ilf_type( Y, set_type ), !
% 0.46/1.13 ilf_type( Y, relation_type( X, X ) ), ilf_type( Y,
% 0.46/1.13 identity_relation_of_type( X ) ) }.
% 0.46/1.13 parent0[0]: (15) {G0,W15,D3,L4,V2,M4} I { ! ilf_type( X, set_type ), !
% 0.46/1.13 ilf_type( Y, set_type ), ! ilf_type( Y, relation_type( X, X ) ), ilf_type
% 0.46/1.13 ( Y, identity_relation_of_type( X ) ) }.
% 0.46/1.13 parent1[0]: (52) {G0,W3,D2,L1,V1,M1} I { ilf_type( X, set_type ) }.
% 0.46/1.13 substitution0:
% 0.46/1.13 X := X
% 0.46/1.13 Y := Y
% 0.46/1.13 end
% 0.46/1.13 substitution1:
% 0.46/1.13 X := X
% 0.46/1.13 end
% 0.46/1.13
% 0.46/1.13 resolution: (396) {G1,W9,D3,L2,V2,M2} { ! ilf_type( X, relation_type( Y, Y
% 0.46/1.13 ) ), ilf_type( X, identity_relation_of_type( Y ) ) }.
% 0.46/1.13 parent0[0]: (394) {G1,W12,D3,L3,V2,M3} { ! ilf_type( Y, set_type ), !
% 0.46/1.13 ilf_type( Y, relation_type( X, X ) ), ilf_type( Y,
% 0.46/1.13 identity_relation_of_type( X ) ) }.
% 0.46/1.13 parent1[0]: (52) {G0,W3,D2,L1,V1,M1} I { ilf_type( X, set_type ) }.
% 0.46/1.13 substitution0:
% 0.46/1.13 X := Y
% 0.46/1.13 Y := X
% 0.46/1.13 end
% 0.46/1.13 substitution1:
% 0.46/1.13 X := X
% 0.46/1.13 end
% 0.46/1.13
% 0.46/1.13 subsumption: (204) {G1,W9,D3,L2,V2,M2} S(15);r(52);r(52) { ! ilf_type( Y,
% 0.46/1.13 relation_type( X, X ) ), ilf_type( Y, identity_relation_of_type( X ) )
% 0.46/1.13 }.
% 0.46/1.13 parent0: (396) {G1,W9,D3,L2,V2,M2} { ! ilf_type( X, relation_type( Y, Y )
% 0.46/1.13 ), ilf_type( X, identity_relation_of_type( Y ) ) }.
% 0.46/1.13 substitution0:
% 0.46/1.13 X := Y
% 0.46/1.13 Y := X
% 0.46/1.13 end
% 0.46/1.13 permutation0:
% 0.46/1.13 0 ==> 0
% 0.46/1.13 1 ==> 1
% 0.46/1.13 end
% 0.46/1.13
% 0.46/1.13 resolution: (397) {G1,W7,D3,L1,V0,M1} { ! ilf_type( cross_product( skol12
% 0.46/1.13 , skol12 ), relation_type( skol12, skol12 ) ) }.
% 0.46/1.13 parent0[0]: (53) {G0,W6,D3,L1,V0,M1} I { ! ilf_type( cross_product( skol12
% 0.46/1.13 , skol12 ), identity_relation_of_type( skol12 ) ) }.
% 0.46/1.13 parent1[1]: (204) {G1,W9,D3,L2,V2,M2} S(15);r(52);r(52) { ! ilf_type( Y,
% 0.46/1.13 relation_type( X, X ) ), ilf_type( Y, identity_relation_of_type( X ) )
% 0.46/1.13 }.
% 0.46/1.13 substitution0:
% 0.46/1.13 end
% 0.46/1.13 substitution1:
% 0.46/1.13 X := skol12
% 0.46/1.13 Y := cross_product( skol12, skol12 )
% 0.46/1.13 end
% 0.46/1.13
% 0.46/1.13 resolution: (398) {G2,W0,D0,L0,V0,M0} { }.
% 0.46/1.13 parent0[0]: (397) {G1,W7,D3,L1,V0,M1} { ! ilf_type( cross_product( skol12
% 0.46/1.13 , skol12 ), relation_type( skol12, skol12 ) ) }.
% 0.46/1.13 parent1[0]: (86) {G1,W7,D3,L1,V2,M1} S(0);r(52);r(52) { ilf_type(
% 0.46/1.13 cross_product( X, Y ), relation_type( X, Y ) ) }.
% 0.46/1.13 substitution0:
% 0.46/1.13 end
% 0.46/1.13 substitution1:
% 0.46/1.13 X := skol12
% 0.46/1.13 Y := skol12
% 0.46/1.13 end
% 0.46/1.13
% 0.46/1.13 subsumption: (207) {G2,W0,D0,L0,V0,M0} R(204,53);r(86) { }.
% 0.46/1.13 parent0: (398) {G2,W0,D0,L0,V0,M0} { }.
% 0.46/1.13 substitution0:
% 0.46/1.13 end
% 0.46/1.13 permutation0:
% 0.46/1.13 end
% 0.46/1.13
% 0.46/1.13 Proof check complete!
% 0.46/1.13
% 0.46/1.13 Memory use:
% 0.46/1.13
% 0.46/1.13 space for terms: 4065
% 0.46/1.13 space for clauses: 11238
% 0.46/1.13
% 0.46/1.13
% 0.46/1.13 clauses generated: 312
% 0.46/1.13 clauses kept: 208
% 0.46/1.13 clauses selected: 57
% 0.46/1.13 clauses deleted: 20
% 0.46/1.13 clauses inuse deleted: 0
% 0.46/1.13
% 0.46/1.13 subsentry: 548
% 0.46/1.13 literals s-matched: 491
% 0.46/1.13 literals matched: 250
% 0.46/1.13 full subsumption: 44
% 0.46/1.13
% 0.46/1.13 checksum: -147247083
% 0.46/1.13
% 0.46/1.13
% 0.46/1.13 Bliksem ended
%------------------------------------------------------------------------------