TSTP Solution File: SET662+3 by Bliksem---1.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SET662+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n004.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 22:51:13 EDT 2022
% Result : Theorem 0.73s 1.24s
% Output : Refutation 0.73s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET662+3 : TPTP v8.1.0. Released v2.2.0.
% 0.12/0.13 % Command : bliksem %s
% 0.13/0.34 % Computer : n004.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % DateTime : Sun Jul 10 03:35:22 EDT 2022
% 0.19/0.34 % CPUTime :
% 0.73/1.24 *** allocated 10000 integers for termspace/termends
% 0.73/1.24 *** allocated 10000 integers for clauses
% 0.73/1.24 *** allocated 10000 integers for justifications
% 0.73/1.24 Bliksem 1.12
% 0.73/1.24
% 0.73/1.24
% 0.73/1.24 Automatic Strategy Selection
% 0.73/1.24
% 0.73/1.24
% 0.73/1.24 Clauses:
% 0.73/1.24
% 0.73/1.24 { ! ilf_type( X, set_type ), ! ilf_type( Y, set_type ), subset( empty_set,
% 0.73/1.24 cross_product( X, Y ) ) }.
% 0.73/1.24 { ! ilf_type( X, set_type ), ! ilf_type( Y, set_type ), ! ilf_type( Z,
% 0.73/1.24 subset_type( cross_product( X, Y ) ) ), ilf_type( Z, relation_type( X, Y
% 0.73/1.24 ) ) }.
% 0.73/1.24 { ! ilf_type( X, set_type ), ! ilf_type( Y, set_type ), ! ilf_type( Z,
% 0.73/1.24 relation_type( X, Y ) ), ilf_type( Z, subset_type( cross_product( X, Y )
% 0.73/1.24 ) ) }.
% 0.73/1.24 { ! ilf_type( X, set_type ), ! ilf_type( Y, set_type ), ilf_type( skol1( X
% 0.73/1.24 , Y ), relation_type( Y, X ) ) }.
% 0.73/1.24 { ! ilf_type( X, set_type ), ! member( X, empty_set ) }.
% 0.73/1.24 { empty( empty_set ) }.
% 0.73/1.24 { type( empty_set, set_type ) }.
% 0.73/1.24 { ! ilf_type( X, set_type ), ! ilf_type( Y, set_type ), ilf_type(
% 0.73/1.24 cross_product( X, Y ), set_type ) }.
% 0.73/1.24 { ! ilf_type( X, set_type ), ! ilf_type( Y, set_type ), ! ilf_type( Y,
% 0.73/1.24 subset_type( X ) ), ilf_type( Y, member_type( power_set( X ) ) ) }.
% 0.73/1.24 { ! ilf_type( X, set_type ), ! ilf_type( Y, set_type ), ! ilf_type( Y,
% 0.73/1.24 member_type( power_set( X ) ) ), ilf_type( Y, subset_type( X ) ) }.
% 0.73/1.24 { ! ilf_type( X, set_type ), ilf_type( skol2( X ), subset_type( X ) ) }.
% 0.73/1.24 { ! ilf_type( X, set_type ), ! ilf_type( Y, set_type ), ! subset( X, Y ), !
% 0.73/1.24 ilf_type( Z, set_type ), alpha1( X, Y, Z ) }.
% 0.73/1.24 { ! ilf_type( X, set_type ), ! ilf_type( Y, set_type ), ilf_type( skol3( Z
% 0.73/1.24 , T ), set_type ), subset( X, Y ) }.
% 0.73/1.24 { ! ilf_type( X, set_type ), ! ilf_type( Y, set_type ), ! alpha1( X, Y,
% 0.73/1.24 skol3( X, Y ) ), subset( X, Y ) }.
% 0.73/1.24 { ! alpha1( X, Y, Z ), ! member( Z, X ), member( Z, Y ) }.
% 0.73/1.24 { member( Z, X ), alpha1( X, Y, Z ) }.
% 0.73/1.24 { ! member( Z, Y ), alpha1( X, Y, Z ) }.
% 0.73/1.24 { ! ilf_type( X, set_type ), subset( X, X ) }.
% 0.73/1.24 { ! ilf_type( X, set_type ), ! empty( X ), ! ilf_type( Y, set_type ), !
% 0.73/1.24 member( Y, X ) }.
% 0.73/1.24 { ! ilf_type( X, set_type ), ilf_type( skol4( Y ), set_type ), empty( X ) }
% 0.73/1.24 .
% 0.73/1.24 { ! ilf_type( X, set_type ), member( skol4( X ), X ), empty( X ) }.
% 0.73/1.24 { ! ilf_type( X, set_type ), ! ilf_type( Y, set_type ), ! member( X,
% 0.73/1.24 power_set( Y ) ), ! ilf_type( Z, set_type ), alpha2( X, Y, Z ) }.
% 0.73/1.24 { ! ilf_type( X, set_type ), ! ilf_type( Y, set_type ), ilf_type( skol5( Z
% 0.73/1.24 , T ), set_type ), member( X, power_set( Y ) ) }.
% 0.73/1.24 { ! ilf_type( X, set_type ), ! ilf_type( Y, set_type ), ! alpha2( X, Y,
% 0.73/1.24 skol5( X, Y ) ), member( X, power_set( Y ) ) }.
% 0.73/1.24 { ! alpha2( X, Y, Z ), ! member( Z, X ), member( Z, Y ) }.
% 0.73/1.24 { member( Z, X ), alpha2( X, Y, Z ) }.
% 0.73/1.24 { ! member( Z, Y ), alpha2( X, Y, Z ) }.
% 0.73/1.24 { ! ilf_type( X, set_type ), ! empty( power_set( X ) ) }.
% 0.73/1.24 { ! ilf_type( X, set_type ), ilf_type( power_set( X ), set_type ) }.
% 0.73/1.24 { ! ilf_type( X, set_type ), empty( Y ), ! ilf_type( Y, set_type ), !
% 0.73/1.24 ilf_type( X, member_type( Y ) ), member( X, Y ) }.
% 0.73/1.24 { ! ilf_type( X, set_type ), empty( Y ), ! ilf_type( Y, set_type ), !
% 0.73/1.24 member( X, Y ), ilf_type( X, member_type( Y ) ) }.
% 0.73/1.24 { empty( X ), ! ilf_type( X, set_type ), ilf_type( skol6( X ), member_type
% 0.73/1.24 ( X ) ) }.
% 0.73/1.24 { ! ilf_type( X, set_type ), ! relation_like( X ), ! ilf_type( Y, set_type
% 0.73/1.24 ), alpha4( X, Y ) }.
% 0.73/1.24 { ! ilf_type( X, set_type ), ilf_type( skol7( Y ), set_type ),
% 0.73/1.24 relation_like( X ) }.
% 0.73/1.24 { ! ilf_type( X, set_type ), ! alpha4( X, skol7( X ) ), relation_like( X )
% 0.73/1.24 }.
% 0.73/1.24 { ! alpha4( X, Y ), ! member( Y, X ), alpha3( Y ) }.
% 0.73/1.24 { member( Y, X ), alpha4( X, Y ) }.
% 0.73/1.24 { ! alpha3( Y ), alpha4( X, Y ) }.
% 0.73/1.24 { ! alpha3( X ), ilf_type( skol8( Y ), set_type ) }.
% 0.73/1.24 { ! alpha3( X ), alpha5( X, skol8( X ) ) }.
% 0.73/1.24 { ! ilf_type( Y, set_type ), ! alpha5( X, Y ), alpha3( X ) }.
% 0.73/1.24 { ! alpha5( X, Y ), ilf_type( skol9( Z, T ), set_type ) }.
% 0.73/1.24 { ! alpha5( X, Y ), X = ordered_pair( Y, skol9( X, Y ) ) }.
% 0.73/1.24 { ! ilf_type( Z, set_type ), ! X = ordered_pair( Y, Z ), alpha5( X, Y ) }.
% 0.73/1.24 { ! empty( X ), ! ilf_type( X, set_type ), relation_like( X ) }.
% 0.73/1.24 { ! ilf_type( X, set_type ), ! ilf_type( Y, set_type ), ! ilf_type( Z,
% 0.73/1.24 subset_type( cross_product( X, Y ) ) ), relation_like( Z ) }.
% 0.73/1.24 { ! ilf_type( X, set_type ), ! ilf_type( Y, set_type ), ilf_type(
% 0.73/1.24 ordered_pair( X, Y ), set_type ) }.
% 0.73/1.24 { ilf_type( X, set_type ) }.
% 0.73/1.24 { ilf_type( skol10, set_type ) }.
% 0.73/1.24 { ilf_type( skol11, set_type ) }.
% 0.73/1.24 { ! ilf_type( empty_set, relation_type( skol10, skol11 ) ) }.
% 0.73/1.24
% 0.73/1.24 percentage equality = 0.013793, percentage horn = 0.784314
% 0.73/1.24 This is a problem with some equality
% 0.73/1.24
% 0.73/1.24
% 0.73/1.24
% 0.73/1.24 Options Used:
% 0.73/1.24
% 0.73/1.24 useres = 1
% 0.73/1.24 useparamod = 1
% 0.73/1.24 useeqrefl = 1
% 0.73/1.24 useeqfact = 1
% 0.73/1.24 usefactor = 1
% 0.73/1.24 usesimpsplitting = 0
% 0.73/1.24 usesimpdemod = 5
% 0.73/1.24 usesimpres = 3
% 0.73/1.24
% 0.73/1.24 resimpinuse = 1000
% 0.73/1.24 resimpclauses = 20000
% 0.73/1.24 substype = eqrewr
% 0.73/1.24 backwardsubs = 1
% 0.73/1.24 selectoldest = 5
% 0.73/1.24
% 0.73/1.24 litorderings [0] = split
% 0.73/1.24 litorderings [1] = extend the termordering, first sorting on arguments
% 0.73/1.24
% 0.73/1.24 termordering = kbo
% 0.73/1.24
% 0.73/1.24 litapriori = 0
% 0.73/1.24 termapriori = 1
% 0.73/1.24 litaposteriori = 0
% 0.73/1.24 termaposteriori = 0
% 0.73/1.24 demodaposteriori = 0
% 0.73/1.24 ordereqreflfact = 0
% 0.73/1.24
% 0.73/1.24 litselect = negord
% 0.73/1.24
% 0.73/1.24 maxweight = 15
% 0.73/1.24 maxdepth = 30000
% 0.73/1.24 maxlength = 115
% 0.73/1.24 maxnrvars = 195
% 0.73/1.24 excuselevel = 1
% 0.73/1.24 increasemaxweight = 1
% 0.73/1.24
% 0.73/1.24 maxselected = 10000000
% 0.73/1.24 maxnrclauses = 10000000
% 0.73/1.24
% 0.73/1.24 showgenerated = 0
% 0.73/1.24 showkept = 0
% 0.73/1.24 showselected = 0
% 0.73/1.24 showdeleted = 0
% 0.73/1.24 showresimp = 1
% 0.73/1.24 showstatus = 2000
% 0.73/1.24
% 0.73/1.24 prologoutput = 0
% 0.73/1.24 nrgoals = 5000000
% 0.73/1.24 totalproof = 1
% 0.73/1.24
% 0.73/1.24 Symbols occurring in the translation:
% 0.73/1.24
% 0.73/1.24 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.73/1.24 . [1, 2] (w:1, o:30, a:1, s:1, b:0),
% 0.73/1.24 ! [4, 1] (w:0, o:14, a:1, s:1, b:0),
% 0.73/1.24 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.73/1.24 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.73/1.24 set_type [36, 0] (w:1, o:7, a:1, s:1, b:0),
% 0.73/1.24 ilf_type [37, 2] (w:1, o:54, a:1, s:1, b:0),
% 0.73/1.24 empty_set [39, 0] (w:1, o:9, a:1, s:1, b:0),
% 0.73/1.24 cross_product [40, 2] (w:1, o:55, a:1, s:1, b:0),
% 0.73/1.24 subset [41, 2] (w:1, o:57, a:1, s:1, b:0),
% 0.73/1.24 subset_type [43, 1] (w:1, o:20, a:1, s:1, b:0),
% 0.73/1.24 relation_type [44, 2] (w:1, o:56, a:1, s:1, b:0),
% 0.73/1.24 member [46, 2] (w:1, o:58, a:1, s:1, b:0),
% 0.73/1.24 empty [47, 1] (w:1, o:21, a:1, s:1, b:0),
% 0.73/1.24 type [48, 2] (w:1, o:63, a:1, s:1, b:0),
% 0.73/1.24 power_set [49, 1] (w:1, o:22, a:1, s:1, b:0),
% 0.73/1.24 member_type [50, 1] (w:1, o:23, a:1, s:1, b:0),
% 0.73/1.24 relation_like [51, 1] (w:1, o:19, a:1, s:1, b:0),
% 0.73/1.24 ordered_pair [52, 2] (w:1, o:64, a:1, s:1, b:0),
% 0.73/1.24 alpha1 [53, 3] (w:1, o:67, a:1, s:1, b:1),
% 0.73/1.24 alpha2 [54, 3] (w:1, o:68, a:1, s:1, b:1),
% 0.73/1.24 alpha3 [55, 1] (w:1, o:24, a:1, s:1, b:1),
% 0.73/1.24 alpha4 [56, 2] (w:1, o:65, a:1, s:1, b:1),
% 0.73/1.24 alpha5 [57, 2] (w:1, o:66, a:1, s:1, b:1),
% 0.73/1.24 skol1 [58, 2] (w:1, o:59, a:1, s:1, b:1),
% 0.73/1.24 skol2 [59, 1] (w:1, o:25, a:1, s:1, b:1),
% 0.73/1.24 skol3 [60, 2] (w:1, o:60, a:1, s:1, b:1),
% 0.73/1.24 skol4 [61, 1] (w:1, o:26, a:1, s:1, b:1),
% 0.73/1.24 skol5 [62, 2] (w:1, o:61, a:1, s:1, b:1),
% 0.73/1.24 skol6 [63, 1] (w:1, o:27, a:1, s:1, b:1),
% 0.73/1.24 skol7 [64, 1] (w:1, o:28, a:1, s:1, b:1),
% 0.73/1.24 skol8 [65, 1] (w:1, o:29, a:1, s:1, b:1),
% 0.73/1.24 skol9 [66, 2] (w:1, o:62, a:1, s:1, b:1),
% 0.73/1.24 skol10 [67, 0] (w:1, o:12, a:1, s:1, b:1),
% 0.73/1.24 skol11 [68, 0] (w:1, o:13, a:1, s:1, b:1).
% 0.73/1.24
% 0.73/1.24
% 0.73/1.24 Starting Search:
% 0.73/1.24
% 0.73/1.24 *** allocated 15000 integers for clauses
% 0.73/1.24 *** allocated 22500 integers for clauses
% 0.73/1.24 *** allocated 33750 integers for clauses
% 0.73/1.24 *** allocated 50625 integers for clauses
% 0.73/1.24 *** allocated 15000 integers for termspace/termends
% 0.73/1.24 Resimplifying inuse:
% 0.73/1.24 Done
% 0.73/1.24
% 0.73/1.24 *** allocated 22500 integers for termspace/termends
% 0.73/1.24 *** allocated 75937 integers for clauses
% 0.73/1.24 *** allocated 33750 integers for termspace/termends
% 0.73/1.24 *** allocated 113905 integers for clauses
% 0.73/1.24
% 0.73/1.24 Intermediate Status:
% 0.73/1.24 Generated: 7893
% 0.73/1.24 Kept: 2030
% 0.73/1.24 Inuse: 318
% 0.73/1.24 Deleted: 66
% 0.73/1.24 Deletedinuse: 8
% 0.73/1.24
% 0.73/1.24 Resimplifying inuse:
% 0.73/1.24 Done
% 0.73/1.24
% 0.73/1.24 *** allocated 50625 integers for termspace/termends
% 0.73/1.24 *** allocated 170857 integers for clauses
% 0.73/1.24 Resimplifying inuse:
% 0.73/1.24 Done
% 0.73/1.24
% 0.73/1.24 *** allocated 75937 integers for termspace/termends
% 0.73/1.24
% 0.73/1.24 Intermediate Status:
% 0.73/1.24 Generated: 14438
% 0.73/1.24 Kept: 4117
% 0.73/1.24 Inuse: 421
% 0.73/1.24 Deleted: 68
% 0.73/1.24 Deletedinuse: 8
% 0.73/1.24
% 0.73/1.24 Resimplifying inuse:
% 0.73/1.24 Done
% 0.73/1.24
% 0.73/1.24 *** allocated 256285 integers for clauses
% 0.73/1.24
% 0.73/1.24 Bliksems!, er is een bewijs:
% 0.73/1.24 % SZS status Theorem
% 0.73/1.24 % SZS output start Refutation
% 0.73/1.24
% 0.73/1.24 (1) {G0,W17,D4,L4,V3,M4} I { ! ilf_type( X, set_type ), ! ilf_type( Y,
% 0.73/1.24 set_type ), ! ilf_type( Z, subset_type( cross_product( X, Y ) ) ),
% 0.73/1.24 ilf_type( Z, relation_type( X, Y ) ) }.
% 0.73/1.24 (4) {G0,W6,D2,L2,V1,M2} I { ! ilf_type( X, set_type ), ! member( X,
% 0.73/1.24 empty_set ) }.
% 0.73/1.24 (9) {G0,W15,D4,L4,V2,M4} I { ! ilf_type( X, set_type ), ! ilf_type( Y,
% 0.73/1.24 set_type ), ! ilf_type( Y, member_type( power_set( X ) ) ), ilf_type( Y,
% 0.73/1.24 subset_type( X ) ) }.
% 0.73/1.24 (23) {G0,W16,D3,L4,V2,M4} I { ! ilf_type( X, set_type ), ! ilf_type( Y,
% 0.73/1.24 set_type ), ! alpha2( X, Y, skol5( X, Y ) ), member( X, power_set( Y ) )
% 0.73/1.24 }.
% 0.73/1.24 (25) {G0,W7,D2,L2,V3,M2} I { member( Z, X ), alpha2( X, Y, Z ) }.
% 0.73/1.24 (27) {G0,W6,D3,L2,V1,M2} I { ! ilf_type( X, set_type ), ! empty( power_set
% 0.73/1.24 ( X ) ) }.
% 0.73/1.24 (30) {G0,W15,D3,L5,V2,M5} I { ! ilf_type( X, set_type ), empty( Y ), !
% 0.73/1.24 ilf_type( Y, set_type ), ! member( X, Y ), ilf_type( X, member_type( Y )
% 0.73/1.24 ) }.
% 0.73/1.24 (47) {G0,W3,D2,L1,V1,M1} I { ilf_type( X, set_type ) }.
% 0.73/1.24 (48) {G0,W5,D3,L1,V0,M1} I { ! ilf_type( empty_set, relation_type( skol10,
% 0.73/1.24 skol11 ) ) }.
% 0.73/1.24 (71) {G1,W11,D4,L2,V3,M2} S(1);r(47);r(47) { ! ilf_type( Z, subset_type(
% 0.73/1.24 cross_product( X, Y ) ) ), ilf_type( Z, relation_type( X, Y ) ) }.
% 0.73/1.24 (76) {G1,W3,D2,L1,V1,M1} S(4);r(47) { ! member( X, empty_set ) }.
% 0.73/1.24 (79) {G1,W3,D3,L1,V1,M1} S(27);r(47) { ! empty( power_set( X ) ) }.
% 0.73/1.24 (83) {G2,W4,D2,L1,V2,M1} R(25,76) { alpha2( empty_set, X, Y ) }.
% 0.73/1.24 (86) {G1,W9,D4,L2,V2,M2} S(9);r(47);r(47) { ! ilf_type( Y, member_type(
% 0.73/1.24 power_set( X ) ) ), ilf_type( Y, subset_type( X ) ) }.
% 0.73/1.24 (164) {G1,W10,D3,L2,V2,M2} S(23);r(47);r(47) { ! alpha2( X, Y, skol5( X, Y
% 0.73/1.24 ) ), member( X, power_set( Y ) ) }.
% 0.73/1.24 (200) {G1,W9,D3,L3,V2,M3} S(30);r(47);r(47) { empty( Y ), ! member( X, Y )
% 0.73/1.24 , ilf_type( X, member_type( Y ) ) }.
% 0.73/1.24 (527) {G2,W6,D4,L1,V0,M1} R(71,48) { ! ilf_type( empty_set, subset_type(
% 0.73/1.24 cross_product( skol10, skol11 ) ) ) }.
% 0.73/1.24 (622) {G3,W7,D5,L1,V0,M1} R(86,527) { ! ilf_type( empty_set, member_type(
% 0.73/1.24 power_set( cross_product( skol10, skol11 ) ) ) ) }.
% 0.73/1.24 (1776) {G3,W4,D3,L1,V1,M1} R(164,83) { member( empty_set, power_set( X ) )
% 0.73/1.24 }.
% 0.73/1.24 (4219) {G4,W5,D4,L1,V1,M1} R(200,1776);r(79) { ilf_type( empty_set,
% 0.73/1.24 member_type( power_set( X ) ) ) }.
% 0.73/1.24 (4590) {G5,W0,D0,L0,V0,M0} R(4219,622) { }.
% 0.73/1.24
% 0.73/1.24
% 0.73/1.24 % SZS output end Refutation
% 0.73/1.24 found a proof!
% 0.73/1.24
% 0.73/1.24
% 0.73/1.24 Unprocessed initial clauses:
% 0.73/1.24
% 0.73/1.24 (4592) {G0,W11,D3,L3,V2,M3} { ! ilf_type( X, set_type ), ! ilf_type( Y,
% 0.73/1.24 set_type ), subset( empty_set, cross_product( X, Y ) ) }.
% 0.73/1.24 (4593) {G0,W17,D4,L4,V3,M4} { ! ilf_type( X, set_type ), ! ilf_type( Y,
% 0.73/1.24 set_type ), ! ilf_type( Z, subset_type( cross_product( X, Y ) ) ),
% 0.73/1.24 ilf_type( Z, relation_type( X, Y ) ) }.
% 0.73/1.24 (4594) {G0,W17,D4,L4,V3,M4} { ! ilf_type( X, set_type ), ! ilf_type( Y,
% 0.73/1.24 set_type ), ! ilf_type( Z, relation_type( X, Y ) ), ilf_type( Z,
% 0.73/1.24 subset_type( cross_product( X, Y ) ) ) }.
% 0.73/1.24 (4595) {G0,W13,D3,L3,V2,M3} { ! ilf_type( X, set_type ), ! ilf_type( Y,
% 0.73/1.24 set_type ), ilf_type( skol1( X, Y ), relation_type( Y, X ) ) }.
% 0.73/1.24 (4596) {G0,W6,D2,L2,V1,M2} { ! ilf_type( X, set_type ), ! member( X,
% 0.73/1.24 empty_set ) }.
% 0.73/1.24 (4597) {G0,W2,D2,L1,V0,M1} { empty( empty_set ) }.
% 0.73/1.24 (4598) {G0,W3,D2,L1,V0,M1} { type( empty_set, set_type ) }.
% 0.73/1.24 (4599) {G0,W11,D3,L3,V2,M3} { ! ilf_type( X, set_type ), ! ilf_type( Y,
% 0.73/1.24 set_type ), ilf_type( cross_product( X, Y ), set_type ) }.
% 0.73/1.24 (4600) {G0,W15,D4,L4,V2,M4} { ! ilf_type( X, set_type ), ! ilf_type( Y,
% 0.73/1.24 set_type ), ! ilf_type( Y, subset_type( X ) ), ilf_type( Y, member_type(
% 0.73/1.24 power_set( X ) ) ) }.
% 0.73/1.24 (4601) {G0,W15,D4,L4,V2,M4} { ! ilf_type( X, set_type ), ! ilf_type( Y,
% 0.73/1.24 set_type ), ! ilf_type( Y, member_type( power_set( X ) ) ), ilf_type( Y,
% 0.73/1.24 subset_type( X ) ) }.
% 0.73/1.24 (4602) {G0,W8,D3,L2,V1,M2} { ! ilf_type( X, set_type ), ilf_type( skol2( X
% 0.73/1.24 ), subset_type( X ) ) }.
% 0.73/1.24 (4603) {G0,W16,D2,L5,V3,M5} { ! ilf_type( X, set_type ), ! ilf_type( Y,
% 0.73/1.24 set_type ), ! subset( X, Y ), ! ilf_type( Z, set_type ), alpha1( X, Y, Z
% 0.73/1.24 ) }.
% 0.73/1.24 (4604) {G0,W14,D3,L4,V4,M4} { ! ilf_type( X, set_type ), ! ilf_type( Y,
% 0.73/1.24 set_type ), ilf_type( skol3( Z, T ), set_type ), subset( X, Y ) }.
% 0.73/1.24 (4605) {G0,W15,D3,L4,V2,M4} { ! ilf_type( X, set_type ), ! ilf_type( Y,
% 0.73/1.24 set_type ), ! alpha1( X, Y, skol3( X, Y ) ), subset( X, Y ) }.
% 0.73/1.24 (4606) {G0,W10,D2,L3,V3,M3} { ! alpha1( X, Y, Z ), ! member( Z, X ),
% 0.73/1.24 member( Z, Y ) }.
% 0.73/1.24 (4607) {G0,W7,D2,L2,V3,M2} { member( Z, X ), alpha1( X, Y, Z ) }.
% 0.73/1.24 (4608) {G0,W7,D2,L2,V3,M2} { ! member( Z, Y ), alpha1( X, Y, Z ) }.
% 0.73/1.24 (4609) {G0,W6,D2,L2,V1,M2} { ! ilf_type( X, set_type ), subset( X, X ) }.
% 0.73/1.24 (4610) {G0,W11,D2,L4,V2,M4} { ! ilf_type( X, set_type ), ! empty( X ), !
% 0.73/1.24 ilf_type( Y, set_type ), ! member( Y, X ) }.
% 0.73/1.24 (4611) {G0,W9,D3,L3,V2,M3} { ! ilf_type( X, set_type ), ilf_type( skol4( Y
% 0.73/1.24 ), set_type ), empty( X ) }.
% 0.73/1.24 (4612) {G0,W9,D3,L3,V1,M3} { ! ilf_type( X, set_type ), member( skol4( X )
% 0.73/1.24 , X ), empty( X ) }.
% 0.73/1.24 (4613) {G0,W17,D3,L5,V3,M5} { ! ilf_type( X, set_type ), ! ilf_type( Y,
% 0.73/1.24 set_type ), ! member( X, power_set( Y ) ), ! ilf_type( Z, set_type ),
% 0.73/1.24 alpha2( X, Y, Z ) }.
% 0.73/1.24 (4614) {G0,W15,D3,L4,V4,M4} { ! ilf_type( X, set_type ), ! ilf_type( Y,
% 0.73/1.24 set_type ), ilf_type( skol5( Z, T ), set_type ), member( X, power_set( Y
% 0.73/1.24 ) ) }.
% 0.73/1.24 (4615) {G0,W16,D3,L4,V2,M4} { ! ilf_type( X, set_type ), ! ilf_type( Y,
% 0.73/1.24 set_type ), ! alpha2( X, Y, skol5( X, Y ) ), member( X, power_set( Y ) )
% 0.73/1.24 }.
% 0.73/1.24 (4616) {G0,W10,D2,L3,V3,M3} { ! alpha2( X, Y, Z ), ! member( Z, X ),
% 0.73/1.24 member( Z, Y ) }.
% 0.73/1.24 (4617) {G0,W7,D2,L2,V3,M2} { member( Z, X ), alpha2( X, Y, Z ) }.
% 0.73/1.24 (4618) {G0,W7,D2,L2,V3,M2} { ! member( Z, Y ), alpha2( X, Y, Z ) }.
% 0.73/1.24 (4619) {G0,W6,D3,L2,V1,M2} { ! ilf_type( X, set_type ), ! empty( power_set
% 0.73/1.24 ( X ) ) }.
% 0.73/1.24 (4620) {G0,W7,D3,L2,V1,M2} { ! ilf_type( X, set_type ), ilf_type(
% 0.73/1.24 power_set( X ), set_type ) }.
% 0.73/1.24 (4621) {G0,W15,D3,L5,V2,M5} { ! ilf_type( X, set_type ), empty( Y ), !
% 0.73/1.24 ilf_type( Y, set_type ), ! ilf_type( X, member_type( Y ) ), member( X, Y
% 0.73/1.24 ) }.
% 0.73/1.24 (4622) {G0,W15,D3,L5,V2,M5} { ! ilf_type( X, set_type ), empty( Y ), !
% 0.73/1.24 ilf_type( Y, set_type ), ! member( X, Y ), ilf_type( X, member_type( Y )
% 0.73/1.24 ) }.
% 0.73/1.24 (4623) {G0,W10,D3,L3,V1,M3} { empty( X ), ! ilf_type( X, set_type ),
% 0.73/1.24 ilf_type( skol6( X ), member_type( X ) ) }.
% 0.73/1.24 (4624) {G0,W11,D2,L4,V2,M4} { ! ilf_type( X, set_type ), ! relation_like(
% 0.73/1.24 X ), ! ilf_type( Y, set_type ), alpha4( X, Y ) }.
% 0.73/1.24 (4625) {G0,W9,D3,L3,V2,M3} { ! ilf_type( X, set_type ), ilf_type( skol7( Y
% 0.73/1.24 ), set_type ), relation_like( X ) }.
% 0.73/1.24 (4626) {G0,W9,D3,L3,V1,M3} { ! ilf_type( X, set_type ), ! alpha4( X, skol7
% 0.73/1.24 ( X ) ), relation_like( X ) }.
% 0.73/1.24 (4627) {G0,W8,D2,L3,V2,M3} { ! alpha4( X, Y ), ! member( Y, X ), alpha3( Y
% 0.73/1.24 ) }.
% 0.73/1.24 (4628) {G0,W6,D2,L2,V2,M2} { member( Y, X ), alpha4( X, Y ) }.
% 0.73/1.24 (4629) {G0,W5,D2,L2,V2,M2} { ! alpha3( Y ), alpha4( X, Y ) }.
% 0.73/1.24 (4630) {G0,W6,D3,L2,V2,M2} { ! alpha3( X ), ilf_type( skol8( Y ), set_type
% 0.73/1.24 ) }.
% 0.73/1.24 (4631) {G0,W6,D3,L2,V1,M2} { ! alpha3( X ), alpha5( X, skol8( X ) ) }.
% 0.73/1.24 (4632) {G0,W8,D2,L3,V2,M3} { ! ilf_type( Y, set_type ), ! alpha5( X, Y ),
% 0.73/1.24 alpha3( X ) }.
% 0.73/1.24 (4633) {G0,W8,D3,L2,V4,M2} { ! alpha5( X, Y ), ilf_type( skol9( Z, T ),
% 0.73/1.24 set_type ) }.
% 0.73/1.24 (4634) {G0,W10,D4,L2,V2,M2} { ! alpha5( X, Y ), X = ordered_pair( Y, skol9
% 0.73/1.24 ( X, Y ) ) }.
% 0.73/1.24 (4635) {G0,W11,D3,L3,V3,M3} { ! ilf_type( Z, set_type ), ! X =
% 0.73/1.24 ordered_pair( Y, Z ), alpha5( X, Y ) }.
% 0.73/1.24 (4636) {G0,W7,D2,L3,V1,M3} { ! empty( X ), ! ilf_type( X, set_type ),
% 0.73/1.24 relation_like( X ) }.
% 0.73/1.24 (4637) {G0,W14,D4,L4,V3,M4} { ! ilf_type( X, set_type ), ! ilf_type( Y,
% 0.73/1.24 set_type ), ! ilf_type( Z, subset_type( cross_product( X, Y ) ) ),
% 0.73/1.24 relation_like( Z ) }.
% 0.73/1.24 (4638) {G0,W11,D3,L3,V2,M3} { ! ilf_type( X, set_type ), ! ilf_type( Y,
% 0.73/1.24 set_type ), ilf_type( ordered_pair( X, Y ), set_type ) }.
% 0.73/1.24 (4639) {G0,W3,D2,L1,V1,M1} { ilf_type( X, set_type ) }.
% 0.73/1.24 (4640) {G0,W3,D2,L1,V0,M1} { ilf_type( skol10, set_type ) }.
% 0.73/1.24 (4641) {G0,W3,D2,L1,V0,M1} { ilf_type( skol11, set_type ) }.
% 0.73/1.24 (4642) {G0,W5,D3,L1,V0,M1} { ! ilf_type( empty_set, relation_type( skol10
% 0.73/1.24 , skol11 ) ) }.
% 0.73/1.24
% 0.73/1.24
% 0.73/1.24 Total Proof:
% 0.73/1.24
% 0.73/1.24 subsumption: (1) {G0,W17,D4,L4,V3,M4} I { ! ilf_type( X, set_type ), !
% 0.73/1.24 ilf_type( Y, set_type ), ! ilf_type( Z, subset_type( cross_product( X, Y
% 0.73/1.24 ) ) ), ilf_type( Z, relation_type( X, Y ) ) }.
% 0.73/1.24 parent0: (4593) {G0,W17,D4,L4,V3,M4} { ! ilf_type( X, set_type ), !
% 0.73/1.24 ilf_type( Y, set_type ), ! ilf_type( Z, subset_type( cross_product( X, Y
% 0.73/1.24 ) ) ), ilf_type( Z, relation_type( X, Y ) ) }.
% 0.73/1.24 substitution0:
% 0.73/1.24 X := X
% 0.73/1.24 Y := Y
% 0.73/1.24 Z := Z
% 0.73/1.24 end
% 0.73/1.24 permutation0:
% 0.73/1.24 0 ==> 0
% 0.73/1.24 1 ==> 1
% 0.73/1.24 2 ==> 2
% 0.73/1.24 3 ==> 3
% 0.73/1.24 end
% 0.73/1.24
% 0.73/1.24 subsumption: (4) {G0,W6,D2,L2,V1,M2} I { ! ilf_type( X, set_type ), !
% 0.73/1.24 member( X, empty_set ) }.
% 0.73/1.24 parent0: (4596) {G0,W6,D2,L2,V1,M2} { ! ilf_type( X, set_type ), ! member
% 0.73/1.24 ( X, empty_set ) }.
% 0.73/1.24 substitution0:
% 0.73/1.24 X := X
% 0.73/1.24 end
% 0.73/1.24 permutation0:
% 0.73/1.24 0 ==> 0
% 0.73/1.24 1 ==> 1
% 0.73/1.24 end
% 0.73/1.24
% 0.73/1.24 subsumption: (9) {G0,W15,D4,L4,V2,M4} I { ! ilf_type( X, set_type ), !
% 0.73/1.24 ilf_type( Y, set_type ), ! ilf_type( Y, member_type( power_set( X ) ) ),
% 0.73/1.24 ilf_type( Y, subset_type( X ) ) }.
% 0.73/1.24 parent0: (4601) {G0,W15,D4,L4,V2,M4} { ! ilf_type( X, set_type ), !
% 0.73/1.24 ilf_type( Y, set_type ), ! ilf_type( Y, member_type( power_set( X ) ) ),
% 0.73/1.24 ilf_type( Y, subset_type( X ) ) }.
% 0.73/1.24 substitution0:
% 0.73/1.24 X := X
% 0.73/1.24 Y := Y
% 0.73/1.24 end
% 0.73/1.24 permutation0:
% 0.73/1.24 0 ==> 0
% 0.73/1.24 1 ==> 1
% 0.73/1.24 2 ==> 2
% 0.73/1.24 3 ==> 3
% 0.73/1.24 end
% 0.73/1.24
% 0.73/1.24 subsumption: (23) {G0,W16,D3,L4,V2,M4} I { ! ilf_type( X, set_type ), !
% 0.73/1.24 ilf_type( Y, set_type ), ! alpha2( X, Y, skol5( X, Y ) ), member( X,
% 0.73/1.24 power_set( Y ) ) }.
% 0.73/1.24 parent0: (4615) {G0,W16,D3,L4,V2,M4} { ! ilf_type( X, set_type ), !
% 0.73/1.24 ilf_type( Y, set_type ), ! alpha2( X, Y, skol5( X, Y ) ), member( X,
% 0.73/1.24 power_set( Y ) ) }.
% 0.73/1.24 substitution0:
% 0.73/1.24 X := X
% 0.73/1.24 Y := Y
% 0.73/1.24 end
% 0.73/1.24 permutation0:
% 0.73/1.24 0 ==> 0
% 0.73/1.24 1 ==> 1
% 0.73/1.24 2 ==> 2
% 0.73/1.24 3 ==> 3
% 0.73/1.24 end
% 0.73/1.24
% 0.73/1.24 subsumption: (25) {G0,W7,D2,L2,V3,M2} I { member( Z, X ), alpha2( X, Y, Z )
% 0.73/1.24 }.
% 0.73/1.24 parent0: (4617) {G0,W7,D2,L2,V3,M2} { member( Z, X ), alpha2( X, Y, Z )
% 0.73/1.24 }.
% 0.73/1.24 substitution0:
% 0.73/1.24 X := X
% 0.73/1.24 Y := Y
% 0.73/1.24 Z := Z
% 0.73/1.24 end
% 0.73/1.24 permutation0:
% 0.73/1.24 0 ==> 0
% 0.73/1.24 1 ==> 1
% 0.73/1.24 end
% 0.73/1.24
% 0.73/1.24 subsumption: (27) {G0,W6,D3,L2,V1,M2} I { ! ilf_type( X, set_type ), !
% 0.73/1.24 empty( power_set( X ) ) }.
% 0.73/1.24 parent0: (4619) {G0,W6,D3,L2,V1,M2} { ! ilf_type( X, set_type ), ! empty(
% 0.73/1.24 power_set( X ) ) }.
% 0.73/1.24 substitution0:
% 0.73/1.24 X := X
% 0.73/1.24 end
% 0.73/1.24 permutation0:
% 0.73/1.24 0 ==> 0
% 0.73/1.24 1 ==> 1
% 0.73/1.24 end
% 0.73/1.24
% 0.73/1.24 subsumption: (30) {G0,W15,D3,L5,V2,M5} I { ! ilf_type( X, set_type ), empty
% 0.73/1.24 ( Y ), ! ilf_type( Y, set_type ), ! member( X, Y ), ilf_type( X,
% 0.73/1.24 member_type( Y ) ) }.
% 0.73/1.24 parent0: (4622) {G0,W15,D3,L5,V2,M5} { ! ilf_type( X, set_type ), empty( Y
% 0.73/1.24 ), ! ilf_type( Y, set_type ), ! member( X, Y ), ilf_type( X, member_type
% 0.73/1.24 ( Y ) ) }.
% 0.73/1.24 substitution0:
% 0.73/1.24 X := X
% 0.73/1.24 Y := Y
% 0.73/1.24 end
% 0.73/1.24 permutation0:
% 0.73/1.24 0 ==> 0
% 0.73/1.24 1 ==> 1
% 0.73/1.24 2 ==> 2
% 0.73/1.24 3 ==> 3
% 0.73/1.24 4 ==> 4
% 0.73/1.24 end
% 0.73/1.24
% 0.73/1.24 subsumption: (47) {G0,W3,D2,L1,V1,M1} I { ilf_type( X, set_type ) }.
% 0.73/1.24 parent0: (4639) {G0,W3,D2,L1,V1,M1} { ilf_type( X, set_type ) }.
% 0.73/1.24 substitution0:
% 0.73/1.24 X := X
% 0.73/1.24 end
% 0.73/1.24 permutation0:
% 0.73/1.24 0 ==> 0
% 0.73/1.24 end
% 0.73/1.24
% 0.73/1.24 subsumption: (48) {G0,W5,D3,L1,V0,M1} I { ! ilf_type( empty_set,
% 0.73/1.24 relation_type( skol10, skol11 ) ) }.
% 0.73/1.24 parent0: (4642) {G0,W5,D3,L1,V0,M1} { ! ilf_type( empty_set, relation_type
% 0.73/1.24 ( skol10, skol11 ) ) }.
% 0.73/1.24 substitution0:
% 0.73/1.24 end
% 0.73/1.24 permutation0:
% 0.73/1.24 0 ==> 0
% 0.73/1.24 end
% 0.73/1.24
% 0.73/1.24 resolution: (4794) {G1,W14,D4,L3,V3,M3} { ! ilf_type( Y, set_type ), !
% 0.73/1.24 ilf_type( Z, subset_type( cross_product( X, Y ) ) ), ilf_type( Z,
% 0.73/1.24 relation_type( X, Y ) ) }.
% 0.73/1.24 parent0[0]: (1) {G0,W17,D4,L4,V3,M4} I { ! ilf_type( X, set_type ), !
% 0.73/1.24 ilf_type( Y, set_type ), ! ilf_type( Z, subset_type( cross_product( X, Y
% 0.73/1.24 ) ) ), ilf_type( Z, relation_type( X, Y ) ) }.
% 0.73/1.24 parent1[0]: (47) {G0,W3,D2,L1,V1,M1} I { ilf_type( X, set_type ) }.
% 0.73/1.24 substitution0:
% 0.73/1.24 X := X
% 0.73/1.24 Y := Y
% 0.73/1.24 Z := Z
% 0.73/1.24 end
% 0.73/1.24 substitution1:
% 0.73/1.24 X := X
% 0.73/1.24 end
% 0.73/1.24
% 0.73/1.24 resolution: (4796) {G1,W11,D4,L2,V3,M2} { ! ilf_type( Y, subset_type(
% 0.73/1.24 cross_product( Z, X ) ) ), ilf_type( Y, relation_type( Z, X ) ) }.
% 0.73/1.24 parent0[0]: (4794) {G1,W14,D4,L3,V3,M3} { ! ilf_type( Y, set_type ), !
% 0.73/1.24 ilf_type( Z, subset_type( cross_product( X, Y ) ) ), ilf_type( Z,
% 0.73/1.24 relation_type( X, Y ) ) }.
% 0.73/1.24 parent1[0]: (47) {G0,W3,D2,L1,V1,M1} I { ilf_type( X, set_type ) }.
% 0.73/1.24 substitution0:
% 0.73/1.24 X := Z
% 0.73/1.24 Y := X
% 0.73/1.24 Z := Y
% 0.73/1.24 end
% 0.73/1.24 substitution1:
% 0.73/1.24 X := X
% 0.73/1.24 end
% 0.73/1.24
% 0.73/1.24 subsumption: (71) {G1,W11,D4,L2,V3,M2} S(1);r(47);r(47) { ! ilf_type( Z,
% 0.73/1.24 subset_type( cross_product( X, Y ) ) ), ilf_type( Z, relation_type( X, Y
% 0.73/1.24 ) ) }.
% 0.73/1.24 parent0: (4796) {G1,W11,D4,L2,V3,M2} { ! ilf_type( Y, subset_type(
% 0.73/1.24 cross_product( Z, X ) ) ), ilf_type( Y, relation_type( Z, X ) ) }.
% 0.73/1.24 substitution0:
% 0.73/1.24 X := Y
% 0.73/1.24 Y := Z
% 0.73/1.24 Z := X
% 0.73/1.24 end
% 0.73/1.24 permutation0:
% 0.73/1.24 0 ==> 0
% 0.73/1.24 1 ==> 1
% 0.73/1.24 end
% 0.73/1.24
% 0.73/1.24 resolution: (4797) {G1,W3,D2,L1,V1,M1} { ! member( X, empty_set ) }.
% 0.73/1.24 parent0[0]: (4) {G0,W6,D2,L2,V1,M2} I { ! ilf_type( X, set_type ), ! member
% 0.73/1.24 ( X, empty_set ) }.
% 0.73/1.24 parent1[0]: (47) {G0,W3,D2,L1,V1,M1} I { ilf_type( X, set_type ) }.
% 0.73/1.24 substitution0:
% 0.73/1.24 X := X
% 0.73/1.24 end
% 0.73/1.24 substitution1:
% 0.73/1.24 X := X
% 0.73/1.24 end
% 0.73/1.24
% 0.73/1.24 subsumption: (76) {G1,W3,D2,L1,V1,M1} S(4);r(47) { ! member( X, empty_set )
% 0.73/1.24 }.
% 0.73/1.24 parent0: (4797) {G1,W3,D2,L1,V1,M1} { ! member( X, empty_set ) }.
% 0.73/1.24 substitution0:
% 0.73/1.24 X := X
% 0.73/1.24 end
% 0.73/1.24 permutation0:
% 0.73/1.24 0 ==> 0
% 0.73/1.24 end
% 0.73/1.24
% 0.73/1.24 resolution: (4798) {G1,W3,D3,L1,V1,M1} { ! empty( power_set( X ) ) }.
% 0.73/1.24 parent0[0]: (27) {G0,W6,D3,L2,V1,M2} I { ! ilf_type( X, set_type ), ! empty
% 0.73/1.24 ( power_set( X ) ) }.
% 0.73/1.24 parent1[0]: (47) {G0,W3,D2,L1,V1,M1} I { ilf_type( X, set_type ) }.
% 0.73/1.24 substitution0:
% 0.73/1.24 X := X
% 0.73/1.24 end
% 0.73/1.24 substitution1:
% 0.73/1.24 X := X
% 0.73/1.24 end
% 0.73/1.24
% 0.73/1.24 subsumption: (79) {G1,W3,D3,L1,V1,M1} S(27);r(47) { ! empty( power_set( X )
% 0.73/1.24 ) }.
% 0.73/1.24 parent0: (4798) {G1,W3,D3,L1,V1,M1} { ! empty( power_set( X ) ) }.
% 0.73/1.24 substitution0:
% 0.73/1.24 X := X
% 0.73/1.24 end
% 0.73/1.24 permutation0:
% 0.73/1.24 0 ==> 0
% 0.73/1.24 end
% 0.73/1.24
% 0.73/1.24 resolution: (4799) {G1,W4,D2,L1,V2,M1} { alpha2( empty_set, Y, X ) }.
% 0.73/1.24 parent0[0]: (76) {G1,W3,D2,L1,V1,M1} S(4);r(47) { ! member( X, empty_set )
% 0.73/1.24 }.
% 0.73/1.24 parent1[0]: (25) {G0,W7,D2,L2,V3,M2} I { member( Z, X ), alpha2( X, Y, Z )
% 0.73/1.24 }.
% 0.73/1.24 substitution0:
% 0.73/1.24 X := X
% 0.73/1.24 end
% 0.73/1.24 substitution1:
% 0.73/1.24 X := empty_set
% 0.73/1.24 Y := Y
% 0.73/1.24 Z := X
% 0.73/1.24 end
% 0.73/1.24
% 0.73/1.24 subsumption: (83) {G2,W4,D2,L1,V2,M1} R(25,76) { alpha2( empty_set, X, Y )
% 0.73/1.24 }.
% 0.73/1.24 parent0: (4799) {G1,W4,D2,L1,V2,M1} { alpha2( empty_set, Y, X ) }.
% 0.73/1.24 substitution0:
% 0.73/1.24 X := Y
% 0.73/1.24 Y := X
% 0.73/1.24 end
% 0.73/1.24 permutation0:
% 0.73/1.24 0 ==> 0
% 0.73/1.24 end
% 0.73/1.24
% 0.73/1.24 resolution: (4802) {G1,W12,D4,L3,V2,M3} { ! ilf_type( Y, set_type ), !
% 0.73/1.24 ilf_type( Y, member_type( power_set( X ) ) ), ilf_type( Y, subset_type( X
% 0.73/1.24 ) ) }.
% 0.73/1.24 parent0[0]: (9) {G0,W15,D4,L4,V2,M4} I { ! ilf_type( X, set_type ), !
% 0.73/1.24 ilf_type( Y, set_type ), ! ilf_type( Y, member_type( power_set( X ) ) ),
% 0.73/1.24 ilf_type( Y, subset_type( X ) ) }.
% 0.73/1.24 parent1[0]: (47) {G0,W3,D2,L1,V1,M1} I { ilf_type( X, set_type ) }.
% 0.73/1.25 substitution0:
% 0.73/1.25 X := X
% 0.73/1.25 Y := Y
% 0.73/1.25 end
% 0.73/1.25 substitution1:
% 0.73/1.25 X := X
% 0.73/1.25 end
% 0.73/1.25
% 0.73/1.25 resolution: (4804) {G1,W9,D4,L2,V2,M2} { ! ilf_type( X, member_type(
% 0.73/1.25 power_set( Y ) ) ), ilf_type( X, subset_type( Y ) ) }.
% 0.73/1.25 parent0[0]: (4802) {G1,W12,D4,L3,V2,M3} { ! ilf_type( Y, set_type ), !
% 0.73/1.25 ilf_type( Y, member_type( power_set( X ) ) ), ilf_type( Y, subset_type( X
% 0.73/1.25 ) ) }.
% 0.73/1.25 parent1[0]: (47) {G0,W3,D2,L1,V1,M1} I { ilf_type( X, set_type ) }.
% 0.73/1.25 substitution0:
% 0.73/1.25 X := Y
% 0.73/1.25 Y := X
% 0.73/1.25 end
% 0.73/1.25 substitution1:
% 0.73/1.25 X := X
% 0.73/1.25 end
% 0.73/1.25
% 0.73/1.25 subsumption: (86) {G1,W9,D4,L2,V2,M2} S(9);r(47);r(47) { ! ilf_type( Y,
% 0.73/1.25 member_type( power_set( X ) ) ), ilf_type( Y, subset_type( X ) ) }.
% 0.73/1.25 parent0: (4804) {G1,W9,D4,L2,V2,M2} { ! ilf_type( X, member_type(
% 0.73/1.25 power_set( Y ) ) ), ilf_type( X, subset_type( Y ) ) }.
% 0.73/1.25 substitution0:
% 0.73/1.25 X := Y
% 0.73/1.25 Y := X
% 0.73/1.25 end
% 0.73/1.25 permutation0:
% 0.73/1.25 0 ==> 0
% 0.73/1.25 1 ==> 1
% 0.73/1.25 end
% 0.73/1.25
% 0.73/1.25 resolution: (4807) {G1,W13,D3,L3,V2,M3} { ! ilf_type( Y, set_type ), !
% 0.73/1.25 alpha2( X, Y, skol5( X, Y ) ), member( X, power_set( Y ) ) }.
% 0.73/1.25 parent0[0]: (23) {G0,W16,D3,L4,V2,M4} I { ! ilf_type( X, set_type ), !
% 0.73/1.25 ilf_type( Y, set_type ), ! alpha2( X, Y, skol5( X, Y ) ), member( X,
% 0.73/1.25 power_set( Y ) ) }.
% 0.73/1.25 parent1[0]: (47) {G0,W3,D2,L1,V1,M1} I { ilf_type( X, set_type ) }.
% 0.73/1.25 substitution0:
% 0.73/1.25 X := X
% 0.73/1.25 Y := Y
% 0.73/1.25 end
% 0.73/1.25 substitution1:
% 0.73/1.25 X := X
% 0.73/1.25 end
% 0.73/1.25
% 0.73/1.25 resolution: (4809) {G1,W10,D3,L2,V2,M2} { ! alpha2( Y, X, skol5( Y, X ) )
% 0.73/1.25 , member( Y, power_set( X ) ) }.
% 0.73/1.25 parent0[0]: (4807) {G1,W13,D3,L3,V2,M3} { ! ilf_type( Y, set_type ), !
% 0.73/1.25 alpha2( X, Y, skol5( X, Y ) ), member( X, power_set( Y ) ) }.
% 0.73/1.25 parent1[0]: (47) {G0,W3,D2,L1,V1,M1} I { ilf_type( X, set_type ) }.
% 0.73/1.25 substitution0:
% 0.73/1.25 X := Y
% 0.73/1.25 Y := X
% 0.73/1.25 end
% 0.73/1.25 substitution1:
% 0.73/1.25 X := X
% 0.73/1.25 end
% 0.73/1.25
% 0.73/1.25 subsumption: (164) {G1,W10,D3,L2,V2,M2} S(23);r(47);r(47) { ! alpha2( X, Y
% 0.73/1.25 , skol5( X, Y ) ), member( X, power_set( Y ) ) }.
% 0.73/1.25 parent0: (4809) {G1,W10,D3,L2,V2,M2} { ! alpha2( Y, X, skol5( Y, X ) ),
% 0.73/1.25 member( Y, power_set( X ) ) }.
% 0.73/1.25 substitution0:
% 0.73/1.25 X := Y
% 0.73/1.25 Y := X
% 0.73/1.25 end
% 0.73/1.25 permutation0:
% 0.73/1.25 0 ==> 0
% 0.73/1.25 1 ==> 1
% 0.73/1.25 end
% 0.73/1.25
% 0.73/1.25 resolution: (4812) {G1,W12,D3,L4,V2,M4} { empty( Y ), ! ilf_type( Y,
% 0.73/1.25 set_type ), ! member( X, Y ), ilf_type( X, member_type( Y ) ) }.
% 0.73/1.25 parent0[0]: (30) {G0,W15,D3,L5,V2,M5} I { ! ilf_type( X, set_type ), empty
% 0.73/1.25 ( Y ), ! ilf_type( Y, set_type ), ! member( X, Y ), ilf_type( X,
% 0.73/1.25 member_type( Y ) ) }.
% 0.73/1.25 parent1[0]: (47) {G0,W3,D2,L1,V1,M1} I { ilf_type( X, set_type ) }.
% 0.73/1.25 substitution0:
% 0.73/1.25 X := X
% 0.73/1.25 Y := Y
% 0.73/1.25 end
% 0.73/1.25 substitution1:
% 0.73/1.25 X := X
% 0.73/1.25 end
% 0.73/1.25
% 0.73/1.25 resolution: (4814) {G1,W9,D3,L3,V2,M3} { empty( X ), ! member( Y, X ),
% 0.73/1.25 ilf_type( Y, member_type( X ) ) }.
% 0.73/1.25 parent0[1]: (4812) {G1,W12,D3,L4,V2,M4} { empty( Y ), ! ilf_type( Y,
% 0.73/1.25 set_type ), ! member( X, Y ), ilf_type( X, member_type( Y ) ) }.
% 0.73/1.25 parent1[0]: (47) {G0,W3,D2,L1,V1,M1} I { ilf_type( X, set_type ) }.
% 0.73/1.25 substitution0:
% 0.73/1.25 X := Y
% 0.73/1.25 Y := X
% 0.73/1.25 end
% 0.73/1.25 substitution1:
% 0.73/1.25 X := X
% 0.73/1.25 end
% 0.73/1.25
% 0.73/1.25 subsumption: (200) {G1,W9,D3,L3,V2,M3} S(30);r(47);r(47) { empty( Y ), !
% 0.73/1.25 member( X, Y ), ilf_type( X, member_type( Y ) ) }.
% 0.73/1.25 parent0: (4814) {G1,W9,D3,L3,V2,M3} { empty( X ), ! member( Y, X ),
% 0.73/1.25 ilf_type( Y, member_type( X ) ) }.
% 0.73/1.25 substitution0:
% 0.73/1.25 X := Y
% 0.73/1.25 Y := X
% 0.73/1.25 end
% 0.73/1.25 permutation0:
% 0.73/1.25 0 ==> 0
% 0.73/1.25 1 ==> 1
% 0.73/1.25 2 ==> 2
% 0.73/1.25 end
% 0.73/1.25
% 0.73/1.25 resolution: (4815) {G1,W6,D4,L1,V0,M1} { ! ilf_type( empty_set,
% 0.73/1.25 subset_type( cross_product( skol10, skol11 ) ) ) }.
% 0.73/1.25 parent0[0]: (48) {G0,W5,D3,L1,V0,M1} I { ! ilf_type( empty_set,
% 0.73/1.25 relation_type( skol10, skol11 ) ) }.
% 0.73/1.25 parent1[1]: (71) {G1,W11,D4,L2,V3,M2} S(1);r(47);r(47) { ! ilf_type( Z,
% 0.73/1.25 subset_type( cross_product( X, Y ) ) ), ilf_type( Z, relation_type( X, Y
% 0.73/1.25 ) ) }.
% 0.73/1.25 substitution0:
% 0.73/1.25 end
% 0.73/1.25 substitution1:
% 0.73/1.25 X := skol10
% 0.73/1.25 Y := skol11
% 0.73/1.25 Z := empty_set
% 0.73/1.25 end
% 0.73/1.25
% 0.73/1.25 subsumption: (527) {G2,W6,D4,L1,V0,M1} R(71,48) { ! ilf_type( empty_set,
% 0.73/1.25 subset_type( cross_product( skol10, skol11 ) ) ) }.
% 0.73/1.25 parent0: (4815) {G1,W6,D4,L1,V0,M1} { ! ilf_type( empty_set, subset_type(
% 0.73/1.25 cross_product( skol10, skol11 ) ) ) }.
% 0.73/1.25 substitution0:
% 0.73/1.25 end
% 0.73/1.25 permutation0:
% 0.73/1.25 0 ==> 0
% 0.73/1.25 end
% 0.73/1.25
% 0.73/1.25 resolution: (4816) {G2,W7,D5,L1,V0,M1} { ! ilf_type( empty_set,
% 0.73/1.25 member_type( power_set( cross_product( skol10, skol11 ) ) ) ) }.
% 0.73/1.25 parent0[0]: (527) {G2,W6,D4,L1,V0,M1} R(71,48) { ! ilf_type( empty_set,
% 0.73/1.25 subset_type( cross_product( skol10, skol11 ) ) ) }.
% 0.73/1.25 parent1[1]: (86) {G1,W9,D4,L2,V2,M2} S(9);r(47);r(47) { ! ilf_type( Y,
% 0.73/1.25 member_type( power_set( X ) ) ), ilf_type( Y, subset_type( X ) ) }.
% 0.73/1.25 substitution0:
% 0.73/1.25 end
% 0.73/1.25 substitution1:
% 0.73/1.25 X := cross_product( skol10, skol11 )
% 0.73/1.25 Y := empty_set
% 0.73/1.25 end
% 0.73/1.25
% 0.73/1.25 subsumption: (622) {G3,W7,D5,L1,V0,M1} R(86,527) { ! ilf_type( empty_set,
% 0.73/1.25 member_type( power_set( cross_product( skol10, skol11 ) ) ) ) }.
% 0.73/1.25 parent0: (4816) {G2,W7,D5,L1,V0,M1} { ! ilf_type( empty_set, member_type(
% 0.73/1.25 power_set( cross_product( skol10, skol11 ) ) ) ) }.
% 0.73/1.25 substitution0:
% 0.73/1.25 end
% 0.73/1.25 permutation0:
% 0.73/1.25 0 ==> 0
% 0.73/1.25 end
% 0.73/1.25
% 0.73/1.25 resolution: (4817) {G2,W4,D3,L1,V1,M1} { member( empty_set, power_set( X )
% 0.73/1.25 ) }.
% 0.73/1.25 parent0[0]: (164) {G1,W10,D3,L2,V2,M2} S(23);r(47);r(47) { ! alpha2( X, Y,
% 0.73/1.25 skol5( X, Y ) ), member( X, power_set( Y ) ) }.
% 0.73/1.25 parent1[0]: (83) {G2,W4,D2,L1,V2,M1} R(25,76) { alpha2( empty_set, X, Y )
% 0.73/1.25 }.
% 0.73/1.25 substitution0:
% 0.73/1.25 X := empty_set
% 0.73/1.25 Y := X
% 0.73/1.25 end
% 0.73/1.25 substitution1:
% 0.73/1.25 X := X
% 0.73/1.25 Y := skol5( empty_set, X )
% 0.73/1.25 end
% 0.73/1.25
% 0.73/1.25 subsumption: (1776) {G3,W4,D3,L1,V1,M1} R(164,83) { member( empty_set,
% 0.73/1.25 power_set( X ) ) }.
% 0.73/1.25 parent0: (4817) {G2,W4,D3,L1,V1,M1} { member( empty_set, power_set( X ) )
% 0.73/1.25 }.
% 0.73/1.25 substitution0:
% 0.73/1.25 X := X
% 0.73/1.25 end
% 0.73/1.25 permutation0:
% 0.73/1.25 0 ==> 0
% 0.73/1.25 end
% 0.73/1.25
% 0.73/1.25 resolution: (4818) {G2,W8,D4,L2,V1,M2} { empty( power_set( X ) ), ilf_type
% 0.73/1.25 ( empty_set, member_type( power_set( X ) ) ) }.
% 0.73/1.25 parent0[1]: (200) {G1,W9,D3,L3,V2,M3} S(30);r(47);r(47) { empty( Y ), !
% 0.73/1.25 member( X, Y ), ilf_type( X, member_type( Y ) ) }.
% 0.73/1.25 parent1[0]: (1776) {G3,W4,D3,L1,V1,M1} R(164,83) { member( empty_set,
% 0.73/1.25 power_set( X ) ) }.
% 0.73/1.25 substitution0:
% 0.73/1.25 X := empty_set
% 0.73/1.25 Y := power_set( X )
% 0.73/1.25 end
% 0.73/1.25 substitution1:
% 0.73/1.25 X := X
% 0.73/1.25 end
% 0.73/1.25
% 0.73/1.25 resolution: (4819) {G2,W5,D4,L1,V1,M1} { ilf_type( empty_set, member_type
% 0.73/1.25 ( power_set( X ) ) ) }.
% 0.73/1.25 parent0[0]: (79) {G1,W3,D3,L1,V1,M1} S(27);r(47) { ! empty( power_set( X )
% 0.73/1.25 ) }.
% 0.73/1.25 parent1[0]: (4818) {G2,W8,D4,L2,V1,M2} { empty( power_set( X ) ), ilf_type
% 0.73/1.25 ( empty_set, member_type( power_set( X ) ) ) }.
% 0.73/1.25 substitution0:
% 0.73/1.25 X := X
% 0.73/1.25 end
% 0.73/1.25 substitution1:
% 0.73/1.25 X := X
% 0.73/1.25 end
% 0.73/1.25
% 0.73/1.25 subsumption: (4219) {G4,W5,D4,L1,V1,M1} R(200,1776);r(79) { ilf_type(
% 0.73/1.25 empty_set, member_type( power_set( X ) ) ) }.
% 0.73/1.25 parent0: (4819) {G2,W5,D4,L1,V1,M1} { ilf_type( empty_set, member_type(
% 0.73/1.25 power_set( X ) ) ) }.
% 0.73/1.25 substitution0:
% 0.73/1.25 X := X
% 0.73/1.25 end
% 0.73/1.25 permutation0:
% 0.73/1.25 0 ==> 0
% 0.73/1.25 end
% 0.73/1.25
% 0.73/1.25 resolution: (4820) {G4,W0,D0,L0,V0,M0} { }.
% 0.73/1.25 parent0[0]: (622) {G3,W7,D5,L1,V0,M1} R(86,527) { ! ilf_type( empty_set,
% 0.73/1.25 member_type( power_set( cross_product( skol10, skol11 ) ) ) ) }.
% 0.73/1.25 parent1[0]: (4219) {G4,W5,D4,L1,V1,M1} R(200,1776);r(79) { ilf_type(
% 0.73/1.25 empty_set, member_type( power_set( X ) ) ) }.
% 0.73/1.25 substitution0:
% 0.73/1.25 end
% 0.73/1.25 substitution1:
% 0.73/1.25 X := cross_product( skol10, skol11 )
% 0.73/1.25 end
% 0.73/1.25
% 0.73/1.25 subsumption: (4590) {G5,W0,D0,L0,V0,M0} R(4219,622) { }.
% 0.73/1.25 parent0: (4820) {G4,W0,D0,L0,V0,M0} { }.
% 0.73/1.25 substitution0:
% 0.73/1.25 end
% 0.73/1.25 permutation0:
% 0.73/1.25 end
% 0.73/1.25
% 0.73/1.25 Proof check complete!
% 0.73/1.25
% 0.73/1.25 Memory use:
% 0.73/1.25
% 0.73/1.25 space for terms: 56812
% 0.73/1.25 space for clauses: 190228
% 0.73/1.25
% 0.73/1.25
% 0.73/1.25 clauses generated: 15834
% 0.73/1.25 clauses kept: 4591
% 0.73/1.25 clauses selected: 452
% 0.73/1.25 clauses deleted: 68
% 0.73/1.25 clauses inuse deleted: 8
% 0.73/1.25
% 0.73/1.25 subsentry: 36841
% 0.73/1.25 literals s-matched: 29560
% 0.73/1.25 literals matched: 28685
% 0.73/1.25 full subsumption: 1652
% 0.73/1.25
% 0.73/1.25 checksum: 1194876903
% 0.73/1.25
% 0.73/1.25
% 0.73/1.25 Bliksem ended
%------------------------------------------------------------------------------