TSTP Solution File: SET931+1 by Bliksem---1.12
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%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SET931+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n009.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 0s
% DateTime : Mon Jul 18 22:53:28 EDT 2022
% Result : Theorem 0.72s 1.23s
% Output : Refutation 0.72s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SET931+1 : TPTP v8.1.0. Released v3.2.0.
% 0.11/0.13 % Command : bliksem %s
% 0.13/0.34 % Computer : n009.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 21:43:37 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.72/1.23 *** allocated 10000 integers for termspace/termends
% 0.72/1.23 *** allocated 10000 integers for clauses
% 0.72/1.23 *** allocated 10000 integers for justifications
% 0.72/1.23 Bliksem 1.12
% 0.72/1.23
% 0.72/1.23
% 0.72/1.23 Automatic Strategy Selection
% 0.72/1.23
% 0.72/1.23
% 0.72/1.23 Clauses:
% 0.72/1.23
% 0.72/1.23 { unordered_pair( X, Y ) = unordered_pair( Y, X ) }.
% 0.72/1.23 { empty( empty_set ) }.
% 0.72/1.23 { ! subset( X, unordered_pair( Y, Z ) ), X = empty_set, ! alpha1( X, Y, Z )
% 0.72/1.23 }.
% 0.72/1.23 { ! X = empty_set, subset( X, unordered_pair( Y, Z ) ) }.
% 0.72/1.23 { alpha1( X, Y, Z ), subset( X, unordered_pair( Y, Z ) ) }.
% 0.72/1.23 { ! alpha1( X, Y, Z ), ! X = singleton( Y ) }.
% 0.72/1.23 { ! alpha1( X, Y, Z ), alpha3( X, Y, Z ) }.
% 0.72/1.23 { X = singleton( Y ), ! alpha3( X, Y, Z ), alpha1( X, Y, Z ) }.
% 0.72/1.23 { ! alpha3( X, Y, Z ), ! X = singleton( Z ) }.
% 0.72/1.23 { ! alpha3( X, Y, Z ), ! X = unordered_pair( Y, Z ) }.
% 0.72/1.23 { X = singleton( Z ), X = unordered_pair( Y, Z ), alpha3( X, Y, Z ) }.
% 0.72/1.23 { empty( skol1 ) }.
% 0.72/1.23 { ! empty( skol2 ) }.
% 0.72/1.23 { subset( X, X ) }.
% 0.72/1.23 { ! set_difference( X, Y ) = empty_set, subset( X, Y ) }.
% 0.72/1.23 { ! subset( X, Y ), set_difference( X, Y ) = empty_set }.
% 0.72/1.23 { alpha5( skol3, skol4, skol5 ), skol3 = empty_set, ! alpha2( skol3, skol4
% 0.72/1.23 , skol5 ) }.
% 0.72/1.23 { alpha5( skol3, skol4, skol5 ), ! set_difference( skol3, unordered_pair(
% 0.72/1.23 skol4, skol5 ) ) = empty_set }.
% 0.72/1.23 { ! alpha5( X, Y, Z ), set_difference( X, unordered_pair( Y, Z ) ) =
% 0.72/1.23 empty_set }.
% 0.72/1.23 { ! alpha5( X, Y, Z ), ! X = empty_set }.
% 0.72/1.23 { ! alpha5( X, Y, Z ), alpha2( X, Y, Z ) }.
% 0.72/1.23 { ! set_difference( X, unordered_pair( Y, Z ) ) = empty_set, X = empty_set
% 0.72/1.23 , ! alpha2( X, Y, Z ), alpha5( X, Y, Z ) }.
% 0.72/1.23 { ! alpha2( X, Y, Z ), ! X = singleton( Y ) }.
% 0.72/1.23 { ! alpha2( X, Y, Z ), alpha4( X, Y, Z ) }.
% 0.72/1.23 { X = singleton( Y ), ! alpha4( X, Y, Z ), alpha2( X, Y, Z ) }.
% 0.72/1.23 { ! alpha4( X, Y, Z ), ! X = singleton( Z ) }.
% 0.72/1.23 { ! alpha4( X, Y, Z ), ! X = unordered_pair( Y, Z ) }.
% 0.72/1.23 { X = singleton( Z ), X = unordered_pair( Y, Z ), alpha4( X, Y, Z ) }.
% 0.72/1.23
% 0.72/1.23 percentage equality = 0.389831, percentage horn = 0.750000
% 0.72/1.23 This is a problem with some equality
% 0.72/1.23
% 0.72/1.23
% 0.72/1.23
% 0.72/1.23 Options Used:
% 0.72/1.23
% 0.72/1.23 useres = 1
% 0.72/1.23 useparamod = 1
% 0.72/1.23 useeqrefl = 1
% 0.72/1.23 useeqfact = 1
% 0.72/1.23 usefactor = 1
% 0.72/1.23 usesimpsplitting = 0
% 0.72/1.23 usesimpdemod = 5
% 0.72/1.23 usesimpres = 3
% 0.72/1.23
% 0.72/1.23 resimpinuse = 1000
% 0.72/1.23 resimpclauses = 20000
% 0.72/1.23 substype = eqrewr
% 0.72/1.23 backwardsubs = 1
% 0.72/1.23 selectoldest = 5
% 0.72/1.23
% 0.72/1.23 litorderings [0] = split
% 0.72/1.23 litorderings [1] = extend the termordering, first sorting on arguments
% 0.72/1.23
% 0.72/1.23 termordering = kbo
% 0.72/1.23
% 0.72/1.23 litapriori = 0
% 0.72/1.23 termapriori = 1
% 0.72/1.23 litaposteriori = 0
% 0.72/1.23 termaposteriori = 0
% 0.72/1.23 demodaposteriori = 0
% 0.72/1.23 ordereqreflfact = 0
% 0.72/1.23
% 0.72/1.23 litselect = negord
% 0.72/1.23
% 0.72/1.23 maxweight = 15
% 0.72/1.23 maxdepth = 30000
% 0.72/1.23 maxlength = 115
% 0.72/1.23 maxnrvars = 195
% 0.72/1.23 excuselevel = 1
% 0.72/1.23 increasemaxweight = 1
% 0.72/1.23
% 0.72/1.23 maxselected = 10000000
% 0.72/1.23 maxnrclauses = 10000000
% 0.72/1.23
% 0.72/1.23 showgenerated = 0
% 0.72/1.23 showkept = 0
% 0.72/1.23 showselected = 0
% 0.72/1.23 showdeleted = 0
% 0.72/1.23 showresimp = 1
% 0.72/1.23 showstatus = 2000
% 0.72/1.23
% 0.72/1.23 prologoutput = 0
% 0.72/1.23 nrgoals = 5000000
% 0.72/1.23 totalproof = 1
% 0.72/1.23
% 0.72/1.23 Symbols occurring in the translation:
% 0.72/1.23
% 0.72/1.23 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.72/1.23 . [1, 2] (w:1, o:22, a:1, s:1, b:0),
% 0.72/1.23 ! [4, 1] (w:0, o:15, a:1, s:1, b:0),
% 0.72/1.23 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.72/1.23 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.72/1.23 unordered_pair [37, 2] (w:1, o:46, a:1, s:1, b:0),
% 0.72/1.23 empty_set [38, 0] (w:1, o:8, a:1, s:1, b:0),
% 0.72/1.23 empty [39, 1] (w:1, o:20, a:1, s:1, b:0),
% 0.72/1.23 subset [41, 2] (w:1, o:47, a:1, s:1, b:0),
% 0.72/1.23 singleton [42, 1] (w:1, o:21, a:1, s:1, b:0),
% 0.72/1.23 set_difference [43, 2] (w:1, o:48, a:1, s:1, b:0),
% 0.72/1.23 alpha1 [44, 3] (w:1, o:49, a:1, s:1, b:1),
% 0.72/1.23 alpha2 [45, 3] (w:1, o:50, a:1, s:1, b:1),
% 0.72/1.23 alpha3 [46, 3] (w:1, o:51, a:1, s:1, b:1),
% 0.72/1.23 alpha4 [47, 3] (w:1, o:52, a:1, s:1, b:1),
% 0.72/1.23 alpha5 [48, 3] (w:1, o:53, a:1, s:1, b:1),
% 0.72/1.23 skol1 [49, 0] (w:1, o:10, a:1, s:1, b:1),
% 0.72/1.23 skol2 [50, 0] (w:1, o:11, a:1, s:1, b:1),
% 0.72/1.23 skol3 [51, 0] (w:1, o:12, a:1, s:1, b:1),
% 0.72/1.23 skol4 [52, 0] (w:1, o:13, a:1, s:1, b:1),
% 0.72/1.23 skol5 [53, 0] (w:1, o:14, a:1, s:1, b:1).
% 0.72/1.23
% 0.72/1.23
% 0.72/1.23 Starting Search:
% 0.72/1.23
% 0.72/1.23 *** allocated 15000 integers for clauses
% 0.72/1.23 *** allocated 22500 integers for clauses
% 0.72/1.23 *** allocated 33750 integers for clauses
% 0.72/1.23 *** allocated 15000 integers for termspace/termends
% 0.72/1.23 *** allocated 50625 integers for clauses
% 0.72/1.23 *** allocated 22500 integers for termspace/termends
% 0.72/1.23 Resimplifying inuse:
% 0.72/1.23 Done
% 0.72/1.23
% 0.72/1.23 *** allocated 75937 integers for clauses
% 0.72/1.23
% 0.72/1.23 Bliksems!, er is een bewijs:
% 0.72/1.23 % SZS status Theorem
% 0.72/1.23 % SZS output start Refutation
% 0.72/1.23
% 0.72/1.23 (2) {G0,W12,D3,L3,V3,M3} I { ! subset( X, unordered_pair( Y, Z ) ), X =
% 0.72/1.23 empty_set, ! alpha1( X, Y, Z ) }.
% 0.72/1.23 (3) {G0,W8,D3,L2,V3,M2} I { ! X = empty_set, subset( X, unordered_pair( Y,
% 0.72/1.23 Z ) ) }.
% 0.72/1.23 (4) {G0,W9,D3,L2,V3,M2} I { alpha1( X, Y, Z ), subset( X, unordered_pair( Y
% 0.72/1.23 , Z ) ) }.
% 0.72/1.23 (5) {G0,W8,D3,L2,V3,M2} I { ! alpha1( X, Y, Z ), ! X = singleton( Y ) }.
% 0.72/1.23 (6) {G0,W8,D2,L2,V3,M2} I { ! alpha1( X, Y, Z ), alpha3( X, Y, Z ) }.
% 0.72/1.23 (7) {G0,W12,D3,L3,V3,M3} I { X = singleton( Y ), ! alpha3( X, Y, Z ),
% 0.72/1.23 alpha1( X, Y, Z ) }.
% 0.72/1.23 (8) {G0,W8,D3,L2,V3,M2} I { ! alpha3( X, Y, Z ), ! X = singleton( Z ) }.
% 0.72/1.23 (10) {G0,W13,D3,L3,V3,M3} I { X = singleton( Z ), X = unordered_pair( Y, Z
% 0.72/1.23 ), alpha3( X, Y, Z ) }.
% 0.72/1.23 (13) {G0,W3,D2,L1,V1,M1} I { subset( X, X ) }.
% 0.72/1.23 (14) {G0,W8,D3,L2,V2,M2} I { ! set_difference( X, Y ) ==> empty_set, subset
% 0.72/1.23 ( X, Y ) }.
% 0.72/1.23 (15) {G0,W8,D3,L2,V2,M2} I { ! subset( X, Y ), set_difference( X, Y ) ==>
% 0.72/1.23 empty_set }.
% 0.72/1.23 (16) {G0,W11,D2,L3,V0,M3} I { alpha5( skol3, skol4, skol5 ), skol3 ==>
% 0.72/1.23 empty_set, ! alpha2( skol3, skol4, skol5 ) }.
% 0.72/1.23 (17) {G0,W11,D4,L2,V0,M2} I { alpha5( skol3, skol4, skol5 ), !
% 0.72/1.23 set_difference( skol3, unordered_pair( skol4, skol5 ) ) ==> empty_set }.
% 0.72/1.23 (18) {G0,W11,D4,L2,V3,M2} I { ! alpha5( X, Y, Z ), set_difference( X,
% 0.72/1.23 unordered_pair( Y, Z ) ) ==> empty_set }.
% 0.72/1.23 (19) {G0,W7,D2,L2,V3,M2} I { ! alpha5( X, Y, Z ), ! X = empty_set }.
% 0.72/1.23 (20) {G0,W8,D2,L2,V3,M2} I { ! alpha5( X, Y, Z ), alpha2( X, Y, Z ) }.
% 0.72/1.23 (22) {G0,W8,D3,L2,V3,M2} I { ! alpha2( X, Y, Z ), ! X = singleton( Y ) }.
% 0.72/1.23 (23) {G0,W8,D2,L2,V3,M2} I { ! alpha2( X, Y, Z ), alpha4( X, Y, Z ) }.
% 0.72/1.23 (24) {G0,W12,D3,L3,V3,M3} I { X = singleton( Y ), ! alpha4( X, Y, Z ),
% 0.72/1.23 alpha2( X, Y, Z ) }.
% 0.72/1.23 (25) {G0,W8,D3,L2,V3,M2} I { ! alpha4( X, Y, Z ), ! X = singleton( Z ) }.
% 0.72/1.23 (26) {G0,W9,D3,L2,V3,M2} I { ! alpha4( X, Y, Z ), ! X = unordered_pair( Y,
% 0.72/1.23 Z ) }.
% 0.72/1.23 (27) {G0,W13,D3,L3,V3,M3} I { X = singleton( Z ), X = unordered_pair( Y, Z
% 0.72/1.23 ), alpha4( X, Y, Z ) }.
% 0.72/1.23 (28) {G1,W5,D3,L1,V2,M1} Q(3) { subset( empty_set, unordered_pair( X, Y ) )
% 0.72/1.23 }.
% 0.72/1.23 (34) {G1,W4,D2,L1,V2,M1} Q(19) { ! alpha5( empty_set, X, Y ) }.
% 0.72/1.23 (48) {G1,W13,D3,L3,V5,M3} R(19,2) { ! alpha5( X, Y, Z ), ! subset( X,
% 0.72/1.23 unordered_pair( T, U ) ), ! alpha1( X, T, U ) }.
% 0.72/1.23 (56) {G1,W8,D2,L2,V3,M2} R(20,23) { ! alpha5( X, Y, Z ), alpha4( X, Y, Z )
% 0.72/1.23 }.
% 0.72/1.23 (63) {G1,W9,D3,L2,V3,M2} R(5,4) { ! X = singleton( Y ), subset( X,
% 0.72/1.23 unordered_pair( Y, Z ) ) }.
% 0.72/1.23 (92) {G2,W8,D3,L2,V3,M2} R(25,56) { ! X = singleton( Y ), ! alpha5( X, Z, Y
% 0.72/1.23 ) }.
% 0.72/1.23 (104) {G1,W8,D3,L2,V3,M2} R(8,6) { ! X = singleton( Y ), ! alpha1( X, Z, Y
% 0.72/1.23 ) }.
% 0.72/1.23 (113) {G2,W9,D3,L2,V3,M2} R(104,4) { ! X = singleton( Y ), subset( X,
% 0.72/1.23 unordered_pair( Z, Y ) ) }.
% 0.72/1.23 (116) {G1,W8,D3,L2,V3,M2} R(22,20) { ! X = singleton( Y ), ! alpha5( X, Y,
% 0.72/1.23 Z ) }.
% 0.72/1.23 (136) {G2,W7,D4,L1,V2,M1} R(15,28) { set_difference( empty_set,
% 0.72/1.23 unordered_pair( X, Y ) ) ==> empty_set }.
% 0.72/1.23 (137) {G1,W5,D3,L1,V1,M1} R(15,13) { set_difference( X, X ) ==> empty_set
% 0.72/1.23 }.
% 0.72/1.23 (309) {G1,W9,D3,L2,V0,M2} R(17,15) { alpha5( skol3, skol4, skol5 ), !
% 0.72/1.23 subset( skol3, unordered_pair( skol4, skol5 ) ) }.
% 0.72/1.23 (315) {G3,W8,D2,L2,V0,M2} P(16,17);d(136);q;r(34) { alpha5( skol3, skol4,
% 0.72/1.23 skol5 ), ! alpha2( skol3, skol4, skol5 ) }.
% 0.72/1.23 (333) {G3,W9,D3,L2,V2,M2} P(2,17);d(136);q;r(34) { ! subset( skol3,
% 0.72/1.23 unordered_pair( X, Y ) ), ! alpha1( skol3, X, Y ) }.
% 0.72/1.23 (351) {G1,W9,D3,L2,V3,M2} R(18,14) { ! alpha5( X, Y, Z ), subset( X,
% 0.72/1.23 unordered_pair( Y, Z ) ) }.
% 0.72/1.23 (536) {G2,W9,D3,L2,V3,M2} R(26,56) { ! X = unordered_pair( Y, Z ), ! alpha5
% 0.72/1.23 ( X, Y, Z ) }.
% 0.72/1.23 (754) {G4,W8,D2,L2,V2,M2} R(333,351) { ! alpha1( skol3, X, Y ), ! alpha5(
% 0.72/1.23 skol3, X, Y ) }.
% 0.72/1.23 (782) {G5,W8,D2,L2,V0,M2} R(754,315) { ! alpha1( skol3, skol4, skol5 ), !
% 0.72/1.23 alpha2( skol3, skol4, skol5 ) }.
% 0.72/1.23 (965) {G2,W4,D3,L1,V0,M1} R(309,63);r(116) { ! singleton( skol4 ) ==> skol3
% 0.72/1.23 }.
% 0.72/1.23 (968) {G3,W4,D3,L1,V0,M1} R(309,113);r(92) { ! singleton( skol5 ) ==> skol3
% 0.72/1.23 }.
% 0.72/1.23 (993) {G3,W11,D2,L3,V2,M3} P(24,965) { ! X = skol3, ! alpha4( X, skol4, Y )
% 0.72/1.23 , alpha2( X, skol4, Y ) }.
% 0.72/1.23 (1004) {G3,W11,D2,L3,V2,M3} P(7,965) { ! X = skol3, ! alpha3( X, skol4, Y )
% 0.72/1.23 , alpha1( X, skol4, Y ) }.
% 0.72/1.23 (1007) {G4,W8,D2,L2,V1,M2} Q(1004) { ! alpha3( skol3, skol4, X ), alpha1(
% 0.72/1.23 skol3, skol4, X ) }.
% 0.72/1.23 (1009) {G4,W8,D2,L2,V1,M2} Q(993) { ! alpha4( skol3, skol4, X ), alpha2(
% 0.72/1.23 skol3, skol4, X ) }.
% 0.72/1.23 (1045) {G2,W12,D2,L3,V5,M3} R(48,351) { ! alpha5( X, Y, Z ), ! alpha1( X, T
% 0.72/1.23 , U ), ! alpha5( X, T, U ) }.
% 0.72/1.23 (1048) {G3,W8,D2,L2,V3,M2} F(1045) { ! alpha5( X, Y, Z ), ! alpha1( X, Y, Z
% 0.72/1.23 ) }.
% 0.72/1.23 (1157) {G5,W13,D3,L3,V1,M3} R(1009,27) { alpha2( skol3, skol4, X ),
% 0.72/1.23 singleton( X ) ==> skol3, unordered_pair( skol4, X ) ==> skol3 }.
% 0.72/1.23 (1159) {G5,W8,D2,L2,V1,M2} R(1007,1048) { ! alpha3( skol3, skol4, X ), !
% 0.72/1.23 alpha5( skol3, skol4, X ) }.
% 0.72/1.23 (1166) {G6,W8,D2,L2,V0,M2} R(1007,782) { ! alpha3( skol3, skol4, skol5 ), !
% 0.72/1.23 alpha2( skol3, skol4, skol5 ) }.
% 0.72/1.23 (1176) {G6,W8,D3,L2,V1,M2} R(1159,10);r(536) { ! alpha5( skol3, skol4, X )
% 0.72/1.23 , singleton( X ) ==> skol3 }.
% 0.72/1.23 (1189) {G7,W9,D3,L2,V0,M2} R(1166,10);r(1157) { singleton( skol5 ) ==>
% 0.72/1.23 skol3, unordered_pair( skol4, skol5 ) ==> skol3 }.
% 0.72/1.23 (1383) {G8,W0,D0,L0,V0,M0} R(1176,17);d(1189);d(137);q;r(968) { }.
% 0.72/1.23
% 0.72/1.23
% 0.72/1.23 % SZS output end Refutation
% 0.72/1.23 found a proof!
% 0.72/1.23
% 0.72/1.23 *** allocated 33750 integers for termspace/termends
% 0.72/1.23
% 0.72/1.23 Unprocessed initial clauses:
% 0.72/1.23
% 0.72/1.23 (1385) {G0,W7,D3,L1,V2,M1} { unordered_pair( X, Y ) = unordered_pair( Y, X
% 0.72/1.23 ) }.
% 0.72/1.23 (1386) {G0,W2,D2,L1,V0,M1} { empty( empty_set ) }.
% 0.72/1.23 (1387) {G0,W12,D3,L3,V3,M3} { ! subset( X, unordered_pair( Y, Z ) ), X =
% 0.72/1.23 empty_set, ! alpha1( X, Y, Z ) }.
% 0.72/1.23 (1388) {G0,W8,D3,L2,V3,M2} { ! X = empty_set, subset( X, unordered_pair( Y
% 0.72/1.23 , Z ) ) }.
% 0.72/1.23 (1389) {G0,W9,D3,L2,V3,M2} { alpha1( X, Y, Z ), subset( X, unordered_pair
% 0.72/1.23 ( Y, Z ) ) }.
% 0.72/1.23 (1390) {G0,W8,D3,L2,V3,M2} { ! alpha1( X, Y, Z ), ! X = singleton( Y ) }.
% 0.72/1.23 (1391) {G0,W8,D2,L2,V3,M2} { ! alpha1( X, Y, Z ), alpha3( X, Y, Z ) }.
% 0.72/1.23 (1392) {G0,W12,D3,L3,V3,M3} { X = singleton( Y ), ! alpha3( X, Y, Z ),
% 0.72/1.23 alpha1( X, Y, Z ) }.
% 0.72/1.23 (1393) {G0,W8,D3,L2,V3,M2} { ! alpha3( X, Y, Z ), ! X = singleton( Z ) }.
% 0.72/1.23 (1394) {G0,W9,D3,L2,V3,M2} { ! alpha3( X, Y, Z ), ! X = unordered_pair( Y
% 0.72/1.23 , Z ) }.
% 0.72/1.23 (1395) {G0,W13,D3,L3,V3,M3} { X = singleton( Z ), X = unordered_pair( Y, Z
% 0.72/1.23 ), alpha3( X, Y, Z ) }.
% 0.72/1.23 (1396) {G0,W2,D2,L1,V0,M1} { empty( skol1 ) }.
% 0.72/1.23 (1397) {G0,W2,D2,L1,V0,M1} { ! empty( skol2 ) }.
% 0.72/1.23 (1398) {G0,W3,D2,L1,V1,M1} { subset( X, X ) }.
% 0.72/1.23 (1399) {G0,W8,D3,L2,V2,M2} { ! set_difference( X, Y ) = empty_set, subset
% 0.72/1.23 ( X, Y ) }.
% 0.72/1.23 (1400) {G0,W8,D3,L2,V2,M2} { ! subset( X, Y ), set_difference( X, Y ) =
% 0.72/1.23 empty_set }.
% 0.72/1.23 (1401) {G0,W11,D2,L3,V0,M3} { alpha5( skol3, skol4, skol5 ), skol3 =
% 0.72/1.23 empty_set, ! alpha2( skol3, skol4, skol5 ) }.
% 0.72/1.23 (1402) {G0,W11,D4,L2,V0,M2} { alpha5( skol3, skol4, skol5 ), !
% 0.72/1.23 set_difference( skol3, unordered_pair( skol4, skol5 ) ) = empty_set }.
% 0.72/1.23 (1403) {G0,W11,D4,L2,V3,M2} { ! alpha5( X, Y, Z ), set_difference( X,
% 0.72/1.23 unordered_pair( Y, Z ) ) = empty_set }.
% 0.72/1.23 (1404) {G0,W7,D2,L2,V3,M2} { ! alpha5( X, Y, Z ), ! X = empty_set }.
% 0.72/1.23 (1405) {G0,W8,D2,L2,V3,M2} { ! alpha5( X, Y, Z ), alpha2( X, Y, Z ) }.
% 0.72/1.23 (1406) {G0,W18,D4,L4,V3,M4} { ! set_difference( X, unordered_pair( Y, Z )
% 0.72/1.23 ) = empty_set, X = empty_set, ! alpha2( X, Y, Z ), alpha5( X, Y, Z ) }.
% 0.72/1.23 (1407) {G0,W8,D3,L2,V3,M2} { ! alpha2( X, Y, Z ), ! X = singleton( Y ) }.
% 0.72/1.23 (1408) {G0,W8,D2,L2,V3,M2} { ! alpha2( X, Y, Z ), alpha4( X, Y, Z ) }.
% 0.72/1.23 (1409) {G0,W12,D3,L3,V3,M3} { X = singleton( Y ), ! alpha4( X, Y, Z ),
% 0.72/1.23 alpha2( X, Y, Z ) }.
% 0.72/1.23 (1410) {G0,W8,D3,L2,V3,M2} { ! alpha4( X, Y, Z ), ! X = singleton( Z ) }.
% 0.72/1.23 (1411) {G0,W9,D3,L2,V3,M2} { ! alpha4( X, Y, Z ), ! X = unordered_pair( Y
% 0.72/1.23 , Z ) }.
% 0.72/1.23 (1412) {G0,W13,D3,L3,V3,M3} { X = singleton( Z ), X = unordered_pair( Y, Z
% 0.72/1.23 ), alpha4( X, Y, Z ) }.
% 0.72/1.23
% 0.72/1.23
% 0.72/1.23 Total Proof:
% 0.72/1.23
% 0.72/1.23 subsumption: (2) {G0,W12,D3,L3,V3,M3} I { ! subset( X, unordered_pair( Y, Z
% 0.72/1.23 ) ), X = empty_set, ! alpha1( X, Y, Z ) }.
% 0.72/1.23 parent0: (1387) {G0,W12,D3,L3,V3,M3} { ! subset( X, unordered_pair( Y, Z )
% 0.72/1.23 ), X = empty_set, ! alpha1( X, Y, Z ) }.
% 0.72/1.23 substitution0:
% 0.72/1.23 X := X
% 0.72/1.23 Y := Y
% 0.72/1.23 Z := Z
% 0.72/1.23 end
% 0.72/1.23 permutation0:
% 0.72/1.23 0 ==> 0
% 0.72/1.23 1 ==> 1
% 0.72/1.23 2 ==> 2
% 0.72/1.23 end
% 0.72/1.23
% 0.72/1.23 subsumption: (3) {G0,W8,D3,L2,V3,M2} I { ! X = empty_set, subset( X,
% 0.72/1.23 unordered_pair( Y, Z ) ) }.
% 0.72/1.23 parent0: (1388) {G0,W8,D3,L2,V3,M2} { ! X = empty_set, subset( X,
% 0.72/1.23 unordered_pair( Y, Z ) ) }.
% 0.72/1.23 substitution0:
% 0.72/1.23 X := X
% 0.72/1.23 Y := Y
% 0.72/1.23 Z := Z
% 0.72/1.23 end
% 0.72/1.23 permutation0:
% 0.72/1.23 0 ==> 0
% 0.72/1.23 1 ==> 1
% 0.72/1.23 end
% 0.72/1.23
% 0.72/1.23 subsumption: (4) {G0,W9,D3,L2,V3,M2} I { alpha1( X, Y, Z ), subset( X,
% 0.72/1.23 unordered_pair( Y, Z ) ) }.
% 0.72/1.23 parent0: (1389) {G0,W9,D3,L2,V3,M2} { alpha1( X, Y, Z ), subset( X,
% 0.72/1.23 unordered_pair( Y, Z ) ) }.
% 0.72/1.23 substitution0:
% 0.72/1.23 X := X
% 0.72/1.23 Y := Y
% 0.72/1.23 Z := Z
% 0.72/1.23 end
% 0.72/1.23 permutation0:
% 0.72/1.23 0 ==> 0
% 0.72/1.23 1 ==> 1
% 0.72/1.23 end
% 0.72/1.23
% 0.72/1.23 subsumption: (5) {G0,W8,D3,L2,V3,M2} I { ! alpha1( X, Y, Z ), ! X =
% 0.72/1.23 singleton( Y ) }.
% 0.72/1.23 parent0: (1390) {G0,W8,D3,L2,V3,M2} { ! alpha1( X, Y, Z ), ! X = singleton
% 0.72/1.23 ( Y ) }.
% 0.72/1.23 substitution0:
% 0.72/1.23 X := X
% 0.72/1.23 Y := Y
% 0.72/1.23 Z := Z
% 0.72/1.23 end
% 0.72/1.23 permutation0:
% 0.72/1.23 0 ==> 0
% 0.72/1.23 1 ==> 1
% 0.72/1.23 end
% 0.72/1.23
% 0.72/1.23 subsumption: (6) {G0,W8,D2,L2,V3,M2} I { ! alpha1( X, Y, Z ), alpha3( X, Y
% 0.72/1.23 , Z ) }.
% 0.72/1.23 parent0: (1391) {G0,W8,D2,L2,V3,M2} { ! alpha1( X, Y, Z ), alpha3( X, Y, Z
% 0.72/1.23 ) }.
% 0.72/1.23 substitution0:
% 0.72/1.23 X := X
% 0.72/1.23 Y := Y
% 0.72/1.23 Z := Z
% 0.72/1.23 end
% 0.72/1.23 permutation0:
% 0.72/1.23 0 ==> 0
% 0.72/1.23 1 ==> 1
% 0.72/1.23 end
% 0.72/1.23
% 0.72/1.23 subsumption: (7) {G0,W12,D3,L3,V3,M3} I { X = singleton( Y ), ! alpha3( X,
% 0.72/1.23 Y, Z ), alpha1( X, Y, Z ) }.
% 0.72/1.23 parent0: (1392) {G0,W12,D3,L3,V3,M3} { X = singleton( Y ), ! alpha3( X, Y
% 0.72/1.23 , Z ), alpha1( X, Y, Z ) }.
% 0.72/1.23 substitution0:
% 0.72/1.23 X := X
% 0.72/1.23 Y := Y
% 0.72/1.23 Z := Z
% 0.72/1.23 end
% 0.72/1.23 permutation0:
% 0.72/1.23 0 ==> 0
% 0.72/1.23 1 ==> 1
% 0.72/1.23 2 ==> 2
% 0.72/1.23 end
% 0.72/1.23
% 0.72/1.23 subsumption: (8) {G0,W8,D3,L2,V3,M2} I { ! alpha3( X, Y, Z ), ! X =
% 0.72/1.23 singleton( Z ) }.
% 0.72/1.23 parent0: (1393) {G0,W8,D3,L2,V3,M2} { ! alpha3( X, Y, Z ), ! X = singleton
% 0.72/1.23 ( Z ) }.
% 0.72/1.23 substitution0:
% 0.72/1.23 X := X
% 0.72/1.23 Y := Y
% 0.72/1.23 Z := Z
% 0.72/1.23 end
% 0.72/1.23 permutation0:
% 0.72/1.23 0 ==> 0
% 0.72/1.23 1 ==> 1
% 0.72/1.23 end
% 0.72/1.23
% 0.72/1.23 subsumption: (10) {G0,W13,D3,L3,V3,M3} I { X = singleton( Z ), X =
% 0.72/1.23 unordered_pair( Y, Z ), alpha3( X, Y, Z ) }.
% 0.72/1.23 parent0: (1395) {G0,W13,D3,L3,V3,M3} { X = singleton( Z ), X =
% 0.72/1.23 unordered_pair( Y, Z ), alpha3( X, Y, Z ) }.
% 0.72/1.23 substitution0:
% 0.72/1.23 X := X
% 0.72/1.23 Y := Y
% 0.72/1.23 Z := Z
% 0.72/1.23 end
% 0.72/1.23 permutation0:
% 0.72/1.23 0 ==> 0
% 0.72/1.23 1 ==> 1
% 0.72/1.23 2 ==> 2
% 0.72/1.23 end
% 0.72/1.23
% 0.72/1.23 subsumption: (13) {G0,W3,D2,L1,V1,M1} I { subset( X, X ) }.
% 0.72/1.23 parent0: (1398) {G0,W3,D2,L1,V1,M1} { subset( X, X ) }.
% 0.72/1.23 substitution0:
% 0.72/1.23 X := X
% 0.72/1.23 end
% 0.72/1.23 permutation0:
% 0.72/1.23 0 ==> 0
% 0.72/1.23 end
% 0.72/1.23
% 0.72/1.23 subsumption: (14) {G0,W8,D3,L2,V2,M2} I { ! set_difference( X, Y ) ==>
% 0.72/1.23 empty_set, subset( X, Y ) }.
% 0.72/1.23 parent0: (1399) {G0,W8,D3,L2,V2,M2} { ! set_difference( X, Y ) = empty_set
% 0.72/1.23 , subset( X, Y ) }.
% 0.72/1.23 substitution0:
% 0.72/1.23 X := X
% 0.72/1.23 Y := Y
% 0.72/1.23 end
% 0.72/1.23 permutation0:
% 0.72/1.23 0 ==> 0
% 0.72/1.23 1 ==> 1
% 0.72/1.23 end
% 0.72/1.23
% 0.72/1.23 subsumption: (15) {G0,W8,D3,L2,V2,M2} I { ! subset( X, Y ), set_difference
% 0.72/1.23 ( X, Y ) ==> empty_set }.
% 0.72/1.23 parent0: (1400) {G0,W8,D3,L2,V2,M2} { ! subset( X, Y ), set_difference( X
% 0.72/1.23 , Y ) = empty_set }.
% 0.72/1.23 substitution0:
% 0.72/1.23 X := X
% 0.72/1.23 Y := Y
% 0.72/1.23 end
% 0.72/1.23 permutation0:
% 0.72/1.23 0 ==> 0
% 0.72/1.23 1 ==> 1
% 0.72/1.23 end
% 0.72/1.23
% 0.72/1.23 subsumption: (16) {G0,W11,D2,L3,V0,M3} I { alpha5( skol3, skol4, skol5 ),
% 0.72/1.23 skol3 ==> empty_set, ! alpha2( skol3, skol4, skol5 ) }.
% 0.72/1.23 parent0: (1401) {G0,W11,D2,L3,V0,M3} { alpha5( skol3, skol4, skol5 ),
% 0.72/1.23 skol3 = empty_set, ! alpha2( skol3, skol4, skol5 ) }.
% 0.72/1.23 substitution0:
% 0.72/1.23 end
% 0.72/1.23 permutation0:
% 0.72/1.23 0 ==> 0
% 0.72/1.23 1 ==> 1
% 0.72/1.23 2 ==> 2
% 0.72/1.23 end
% 0.72/1.23
% 0.72/1.23 subsumption: (17) {G0,W11,D4,L2,V0,M2} I { alpha5( skol3, skol4, skol5 ), !
% 0.72/1.23 set_difference( skol3, unordered_pair( skol4, skol5 ) ) ==> empty_set
% 0.72/1.23 }.
% 0.72/1.23 parent0: (1402) {G0,W11,D4,L2,V0,M2} { alpha5( skol3, skol4, skol5 ), !
% 0.72/1.23 set_difference( skol3, unordered_pair( skol4, skol5 ) ) = empty_set }.
% 0.72/1.23 substitution0:
% 0.72/1.23 end
% 0.72/1.23 permutation0:
% 0.72/1.23 0 ==> 0
% 0.72/1.23 1 ==> 1
% 0.72/1.23 end
% 0.72/1.23
% 0.72/1.23 subsumption: (18) {G0,W11,D4,L2,V3,M2} I { ! alpha5( X, Y, Z ),
% 0.72/1.23 set_difference( X, unordered_pair( Y, Z ) ) ==> empty_set }.
% 0.72/1.23 parent0: (1403) {G0,W11,D4,L2,V3,M2} { ! alpha5( X, Y, Z ), set_difference
% 0.72/1.23 ( X, unordered_pair( Y, Z ) ) = empty_set }.
% 0.72/1.23 substitution0:
% 0.72/1.23 X := X
% 0.72/1.23 Y := Y
% 0.72/1.23 Z := Z
% 0.72/1.23 end
% 0.72/1.23 permutation0:
% 0.72/1.23 0 ==> 0
% 0.72/1.23 1 ==> 1
% 0.72/1.23 end
% 0.72/1.23
% 0.72/1.23 subsumption: (19) {G0,W7,D2,L2,V3,M2} I { ! alpha5( X, Y, Z ), ! X =
% 0.72/1.23 empty_set }.
% 0.72/1.23 parent0: (1404) {G0,W7,D2,L2,V3,M2} { ! alpha5( X, Y, Z ), ! X = empty_set
% 0.72/1.23 }.
% 0.72/1.23 substitution0:
% 0.72/1.23 X := X
% 0.72/1.23 Y := Y
% 0.72/1.23 Z := Z
% 0.72/1.23 end
% 0.72/1.23 permutation0:
% 0.72/1.23 0 ==> 0
% 0.72/1.23 1 ==> 1
% 0.72/1.23 end
% 0.72/1.23
% 0.72/1.23 subsumption: (20) {G0,W8,D2,L2,V3,M2} I { ! alpha5( X, Y, Z ), alpha2( X, Y
% 0.72/1.23 , Z ) }.
% 0.72/1.23 parent0: (1405) {G0,W8,D2,L2,V3,M2} { ! alpha5( X, Y, Z ), alpha2( X, Y, Z
% 0.72/1.23 ) }.
% 0.72/1.23 substitution0:
% 0.72/1.23 X := X
% 0.72/1.23 Y := Y
% 0.72/1.23 Z := Z
% 0.72/1.23 end
% 0.72/1.23 permutation0:
% 0.72/1.23 0 ==> 0
% 0.72/1.23 1 ==> 1
% 0.72/1.23 end
% 0.72/1.23
% 0.72/1.23 subsumption: (22) {G0,W8,D3,L2,V3,M2} I { ! alpha2( X, Y, Z ), ! X =
% 0.72/1.23 singleton( Y ) }.
% 0.72/1.23 parent0: (1407) {G0,W8,D3,L2,V3,M2} { ! alpha2( X, Y, Z ), ! X = singleton
% 0.72/1.23 ( Y ) }.
% 0.72/1.23 substitution0:
% 0.72/1.23 X := X
% 0.72/1.23 Y := Y
% 0.72/1.23 Z := Z
% 0.72/1.23 end
% 0.72/1.23 permutation0:
% 0.72/1.23 0 ==> 0
% 0.72/1.23 1 ==> 1
% 0.72/1.23 end
% 0.72/1.23
% 0.72/1.23 subsumption: (23) {G0,W8,D2,L2,V3,M2} I { ! alpha2( X, Y, Z ), alpha4( X, Y
% 0.72/1.23 , Z ) }.
% 0.72/1.23 parent0: (1408) {G0,W8,D2,L2,V3,M2} { ! alpha2( X, Y, Z ), alpha4( X, Y, Z
% 0.72/1.23 ) }.
% 0.72/1.23 substitution0:
% 0.72/1.23 X := X
% 0.72/1.23 Y := Y
% 0.72/1.23 Z := Z
% 0.72/1.23 end
% 0.72/1.23 permutation0:
% 0.72/1.23 0 ==> 0
% 0.72/1.23 1 ==> 1
% 0.72/1.23 end
% 0.72/1.23
% 0.72/1.23 subsumption: (24) {G0,W12,D3,L3,V3,M3} I { X = singleton( Y ), ! alpha4( X
% 0.72/1.23 , Y, Z ), alpha2( X, Y, Z ) }.
% 0.72/1.23 parent0: (1409) {G0,W12,D3,L3,V3,M3} { X = singleton( Y ), ! alpha4( X, Y
% 0.72/1.23 , Z ), alpha2( X, Y, Z ) }.
% 0.72/1.23 substitution0:
% 0.72/1.23 X := X
% 0.72/1.23 Y := Y
% 0.72/1.23 Z := Z
% 0.72/1.23 end
% 0.72/1.23 permutation0:
% 0.72/1.23 0 ==> 0
% 0.72/1.23 1 ==> 1
% 0.72/1.23 2 ==> 2
% 0.72/1.23 end
% 0.72/1.23
% 0.72/1.23 subsumption: (25) {G0,W8,D3,L2,V3,M2} I { ! alpha4( X, Y, Z ), ! X =
% 0.72/1.23 singleton( Z ) }.
% 0.72/1.23 parent0: (1410) {G0,W8,D3,L2,V3,M2} { ! alpha4( X, Y, Z ), ! X = singleton
% 0.72/1.23 ( Z ) }.
% 0.72/1.23 substitution0:
% 0.72/1.23 X := X
% 0.72/1.23 Y := Y
% 0.72/1.23 Z := Z
% 0.72/1.23 end
% 0.72/1.23 permutation0:
% 0.72/1.23 0 ==> 0
% 0.72/1.23 1 ==> 1
% 0.72/1.23 end
% 0.72/1.23
% 0.72/1.23 subsumption: (26) {G0,W9,D3,L2,V3,M2} I { ! alpha4( X, Y, Z ), ! X =
% 0.72/1.23 unordered_pair( Y, Z ) }.
% 0.72/1.23 parent0: (1411) {G0,W9,D3,L2,V3,M2} { ! alpha4( X, Y, Z ), ! X =
% 0.72/1.23 unordered_pair( Y, Z ) }.
% 0.72/1.23 substitution0:
% 0.72/1.23 X := X
% 0.72/1.23 Y := Y
% 0.72/1.23 Z := Z
% 0.72/1.23 end
% 0.72/1.23 permutation0:
% 0.72/1.23 0 ==> 0
% 0.72/1.23 1 ==> 1
% 0.72/1.23 end
% 0.72/1.23
% 0.72/1.23 subsumption: (27) {G0,W13,D3,L3,V3,M3} I { X = singleton( Z ), X =
% 0.72/1.23 unordered_pair( Y, Z ), alpha4( X, Y, Z ) }.
% 0.72/1.23 parent0: (1412) {G0,W13,D3,L3,V3,M3} { X = singleton( Z ), X =
% 0.72/1.23 unordered_pair( Y, Z ), alpha4( X, Y, Z ) }.
% 0.72/1.23 substitution0:
% 0.72/1.23 X := X
% 0.72/1.23 Y := Y
% 0.72/1.23 Z := Z
% 0.72/1.23 end
% 0.72/1.23 permutation0:
% 0.72/1.23 0 ==> 0
% 0.72/1.23 1 ==> 1
% 0.72/1.23 2 ==> 2
% 0.72/1.23 end
% 0.72/1.23
% 0.72/1.23 eqswap: (1667) {G0,W8,D3,L2,V3,M2} { ! empty_set = X, subset( X,
% 0.72/1.23 unordered_pair( Y, Z ) ) }.
% 0.72/1.23 parent0[0]: (3) {G0,W8,D3,L2,V3,M2} I { ! X = empty_set, subset( X,
% 0.72/1.23 unordered_pair( Y, Z ) ) }.
% 0.72/1.23 substitution0:
% 0.72/1.23 X := X
% 0.72/1.23 Y := Y
% 0.72/1.23 Z := Z
% 0.72/1.23 end
% 0.72/1.23
% 0.72/1.23 eqrefl: (1668) {G0,W5,D3,L1,V2,M1} { subset( empty_set, unordered_pair( X
% 0.72/1.23 , Y ) ) }.
% 0.72/1.23 parent0[0]: (1667) {G0,W8,D3,L2,V3,M2} { ! empty_set = X, subset( X,
% 0.72/1.23 unordered_pair( Y, Z ) ) }.
% 0.72/1.23 substitution0:
% 0.72/1.23 X := empty_set
% 0.72/1.23 Y := X
% 0.72/1.23 Z := Y
% 0.72/1.23 end
% 0.72/1.23
% 0.72/1.23 subsumption: (28) {G1,W5,D3,L1,V2,M1} Q(3) { subset( empty_set,
% 0.72/1.23 unordered_pair( X, Y ) ) }.
% 0.72/1.23 parent0: (1668) {G0,W5,D3,L1,V2,M1} { subset( empty_set, unordered_pair( X
% 0.72/1.23 , Y ) ) }.
% 0.72/1.23 substitution0:
% 0.72/1.23 X := X
% 0.72/1.23 Y := Y
% 0.72/1.23 end
% 0.72/1.23 permutation0:
% 0.72/1.23 0 ==> 0
% 0.72/1.23 end
% 0.72/1.23
% 0.72/1.23 eqswap: (1669) {G0,W7,D2,L2,V3,M2} { ! empty_set = X, ! alpha5( X, Y, Z )
% 0.72/1.23 }.
% 0.72/1.23 parent0[1]: (19) {G0,W7,D2,L2,V3,M2} I { ! alpha5( X, Y, Z ), ! X =
% 0.72/1.23 empty_set }.
% 0.72/1.23 substitution0:
% 0.72/1.23 X := X
% 0.72/1.23 Y := Y
% 0.72/1.23 Z := Z
% 0.72/1.23 end
% 0.72/1.23
% 0.72/1.23 eqrefl: (1670) {G0,W4,D2,L1,V2,M1} { ! alpha5( empty_set, X, Y ) }.
% 0.72/1.23 parent0[0]: (1669) {G0,W7,D2,L2,V3,M2} { ! empty_set = X, ! alpha5( X, Y,
% 0.72/1.23 Z ) }.
% 0.72/1.23 substitution0:
% 0.72/1.23 X := empty_set
% 0.72/1.23 Y := X
% 0.72/1.23 Z := Y
% 0.72/1.23 end
% 0.72/1.23
% 0.72/1.23 subsumption: (34) {G1,W4,D2,L1,V2,M1} Q(19) { ! alpha5( empty_set, X, Y )
% 0.72/1.23 }.
% 0.72/1.23 parent0: (1670) {G0,W4,D2,L1,V2,M1} { ! alpha5( empty_set, X, Y ) }.
% 0.72/1.23 substitution0:
% 0.72/1.23 X := X
% 0.72/1.23 Y := Y
% 0.72/1.23 end
% 0.72/1.23 permutation0:
% 0.72/1.23 0 ==> 0
% 0.72/1.23 end
% 0.72/1.23
% 0.72/1.23 eqswap: (1671) {G0,W7,D2,L2,V3,M2} { ! empty_set = X, ! alpha5( X, Y, Z )
% 0.72/1.23 }.
% 0.72/1.23 parent0[1]: (19) {G0,W7,D2,L2,V3,M2} I { ! alpha5( X, Y, Z ), ! X =
% 0.72/1.23 empty_set }.
% 0.72/1.23 substitution0:
% 0.72/1.23 X := X
% 0.72/1.23 Y := Y
% 0.72/1.23 Z := Z
% 0.72/1.23 end
% 0.72/1.23
% 0.72/1.23 eqswap: (1672) {G0,W12,D3,L3,V3,M3} { empty_set = X, ! subset( X,
% 0.72/1.23 unordered_pair( Y, Z ) ), ! alpha1( X, Y, Z ) }.
% 0.72/1.23 parent0[1]: (2) {G0,W12,D3,L3,V3,M3} I { ! subset( X, unordered_pair( Y, Z
% 0.72/1.23 ) ), X = empty_set, ! alpha1( X, Y, Z ) }.
% 0.72/1.23 substitution0:
% 0.72/1.23 X := X
% 0.72/1.23 Y := Y
% 0.72/1.23 Z := Z
% 0.72/1.23 end
% 0.72/1.23
% 0.72/1.23 resolution: (1673) {G1,W13,D3,L3,V5,M3} { ! alpha5( X, Y, Z ), ! subset( X
% 0.72/1.23 , unordered_pair( T, U ) ), ! alpha1( X, T, U ) }.
% 0.72/1.23 parent0[0]: (1671) {G0,W7,D2,L2,V3,M2} { ! empty_set = X, ! alpha5( X, Y,
% 0.72/1.23 Z ) }.
% 0.72/1.23 parent1[0]: (1672) {G0,W12,D3,L3,V3,M3} { empty_set = X, ! subset( X,
% 0.72/1.23 unordered_pair( Y, Z ) ), ! alpha1( X, Y, Z ) }.
% 0.72/1.23 substitution0:
% 0.72/1.23 X := X
% 0.72/1.23 Y := Y
% 0.72/1.23 Z := Z
% 0.72/1.23 end
% 0.72/1.23 substitution1:
% 0.72/1.23 X := X
% 0.72/1.23 Y := T
% 0.72/1.23 Z := U
% 0.72/1.23 end
% 0.72/1.23
% 0.72/1.23 subsumption: (48) {G1,W13,D3,L3,V5,M3} R(19,2) { ! alpha5( X, Y, Z ), !
% 0.72/1.23 subset( X, unordered_pair( T, U ) ), ! alpha1( X, T, U ) }.
% 0.72/1.23 parent0: (1673) {G1,W13,D3,L3,V5,M3} { ! alpha5( X, Y, Z ), ! subset( X,
% 0.72/1.23 unordered_pair( T, U ) ), ! alpha1( X, T, U ) }.
% 0.72/1.23 substitution0:
% 0.72/1.23 X := X
% 0.72/1.23 Y := Y
% 0.72/1.23 Z := Z
% 0.72/1.23 T := T
% 0.72/1.23 U := U
% 0.72/1.23 end
% 0.72/1.23 permutation0:
% 0.72/1.23 0 ==> 0
% 0.72/1.23 1 ==> 1
% 0.72/1.23 2 ==> 2
% 0.72/1.23 end
% 0.72/1.23
% 0.72/1.23 resolution: (1674) {G1,W8,D2,L2,V3,M2} { alpha4( X, Y, Z ), ! alpha5( X, Y
% 0.72/1.23 , Z ) }.
% 0.72/1.23 parent0[0]: (23) {G0,W8,D2,L2,V3,M2} I { ! alpha2( X, Y, Z ), alpha4( X, Y
% 0.72/1.23 , Z ) }.
% 0.72/1.23 parent1[1]: (20) {G0,W8,D2,L2,V3,M2} I { ! alpha5( X, Y, Z ), alpha2( X, Y
% 0.72/1.23 , Z ) }.
% 0.72/1.23 substitution0:
% 0.72/1.23 X := X
% 0.72/1.23 Y := Y
% 0.72/1.23 Z := Z
% 0.72/1.23 end
% 0.72/1.23 substitution1:
% 0.72/1.23 X := X
% 0.72/1.23 Y := Y
% 0.72/1.23 Z := Z
% 0.72/1.23 end
% 0.72/1.23
% 0.72/1.23 subsumption: (56) {G1,W8,D2,L2,V3,M2} R(20,23) { ! alpha5( X, Y, Z ),
% 0.72/1.23 alpha4( X, Y, Z ) }.
% 0.72/1.23 parent0: (1674) {G1,W8,D2,L2,V3,M2} { alpha4( X, Y, Z ), ! alpha5( X, Y, Z
% 0.72/1.23 ) }.
% 0.72/1.23 substitution0:
% 0.72/1.23 X := X
% 0.72/1.23 Y := Y
% 0.72/1.23 Z := Z
% 0.72/1.23 end
% 0.72/1.23 permutation0:
% 0.72/1.23 0 ==> 1
% 0.72/1.23 1 ==> 0
% 0.72/1.23 end
% 0.72/1.23
% 0.72/1.23 eqswap: (1675) {G0,W8,D3,L2,V3,M2} { ! singleton( Y ) = X, ! alpha1( X, Y
% 0.72/1.23 , Z ) }.
% 0.72/1.23 parent0[1]: (5) {G0,W8,D3,L2,V3,M2} I { ! alpha1( X, Y, Z ), ! X =
% 0.72/1.23 singleton( Y ) }.
% 0.72/1.23 substitution0:
% 0.72/1.23 X := X
% 0.72/1.23 Y := Y
% 0.72/1.23 Z := Z
% 0.72/1.23 end
% 0.72/1.23
% 0.72/1.23 resolution: (1676) {G1,W9,D3,L2,V3,M2} { ! singleton( X ) = Y, subset( Y,
% 0.72/1.23 unordered_pair( X, Z ) ) }.
% 0.72/1.23 parent0[1]: (1675) {G0,W8,D3,L2,V3,M2} { ! singleton( Y ) = X, ! alpha1( X
% 0.72/1.23 , Y, Z ) }.
% 0.72/1.23 parent1[0]: (4) {G0,W9,D3,L2,V3,M2} I { alpha1( X, Y, Z ), subset( X,
% 0.72/1.23 unordered_pair( Y, Z ) ) }.
% 0.72/1.23 substitution0:
% 0.72/1.23 X := Y
% 0.72/1.23 Y := X
% 0.72/1.23 Z := Z
% 0.72/1.23 end
% 0.72/1.23 substitution1:
% 0.72/1.23 X := Y
% 0.72/1.23 Y := X
% 0.72/1.23 Z := Z
% 0.72/1.23 end
% 0.72/1.23
% 0.72/1.23 eqswap: (1677) {G1,W9,D3,L2,V3,M2} { ! Y = singleton( X ), subset( Y,
% 0.72/1.23 unordered_pair( X, Z ) ) }.
% 0.72/1.23 parent0[0]: (1676) {G1,W9,D3,L2,V3,M2} { ! singleton( X ) = Y, subset( Y,
% 0.72/1.23 unordered_pair( X, Z ) ) }.
% 0.72/1.23 substitution0:
% 0.72/1.23 X := X
% 0.72/1.23 Y := Y
% 0.72/1.23 Z := Z
% 0.72/1.23 end
% 0.72/1.23
% 0.72/1.23 subsumption: (63) {G1,W9,D3,L2,V3,M2} R(5,4) { ! X = singleton( Y ), subset
% 0.72/1.23 ( X, unordered_pair( Y, Z ) ) }.
% 0.72/1.23 parent0: (1677) {G1,W9,D3,L2,V3,M2} { ! Y = singleton( X ), subset( Y,
% 0.72/1.23 unordered_pair( X, Z ) ) }.
% 0.72/1.23 substitution0:
% 0.72/1.23 X := Y
% 0.72/1.23 Y := X
% 0.72/1.23 Z := Z
% 0.72/1.23 end
% 0.72/1.23 permutation0:
% 0.72/1.23 0 ==> 0
% 0.72/1.23 1 ==> 1
% 0.72/1.23 end
% 0.72/1.23
% 0.72/1.23 eqswap: (1678) {G0,W8,D3,L2,V3,M2} { ! singleton( Y ) = X, ! alpha4( X, Z
% 0.72/1.23 , Y ) }.
% 0.72/1.23 parent0[1]: (25) {G0,W8,D3,L2,V3,M2} I { ! alpha4( X, Y, Z ), ! X =
% 0.72/1.23 singleton( Z ) }.
% 0.72/1.23 substitution0:
% 0.72/1.23 X := X
% 0.72/1.23 Y := Z
% 0.72/1.23 Z := Y
% 0.72/1.23 end
% 0.72/1.23
% 0.72/1.23 resolution: (1679) {G1,W8,D3,L2,V3,M2} { ! singleton( X ) = Y, ! alpha5( Y
% 0.72/1.23 , Z, X ) }.
% 0.72/1.23 parent0[1]: (1678) {G0,W8,D3,L2,V3,M2} { ! singleton( Y ) = X, ! alpha4( X
% 0.72/1.23 , Z, Y ) }.
% 0.72/1.23 parent1[1]: (56) {G1,W8,D2,L2,V3,M2} R(20,23) { ! alpha5( X, Y, Z ), alpha4
% 0.72/1.23 ( X, Y, Z ) }.
% 0.72/1.23 substitution0:
% 0.72/1.23 X := Y
% 0.72/1.23 Y := X
% 0.72/1.23 Z := Z
% 0.72/1.23 end
% 0.72/1.23 substitution1:
% 0.72/1.23 X := Y
% 0.72/1.23 Y := Z
% 0.72/1.23 Z := X
% 0.72/1.23 end
% 0.72/1.23
% 0.72/1.23 eqswap: (1680) {G1,W8,D3,L2,V3,M2} { ! Y = singleton( X ), ! alpha5( Y, Z
% 0.72/1.23 , X ) }.
% 0.72/1.23 parent0[0]: (1679) {G1,W8,D3,L2,V3,M2} { ! singleton( X ) = Y, ! alpha5( Y
% 0.72/1.23 , Z, X ) }.
% 0.72/1.23 substitution0:
% 0.72/1.23 X := X
% 0.72/1.23 Y := Y
% 0.72/1.23 Z := Z
% 0.72/1.23 end
% 0.72/1.23
% 0.72/1.23 subsumption: (92) {G2,W8,D3,L2,V3,M2} R(25,56) { ! X = singleton( Y ), !
% 0.72/1.23 alpha5( X, Z, Y ) }.
% 0.72/1.23 parent0: (1680) {G1,W8,D3,L2,V3,M2} { ! Y = singleton( X ), ! alpha5( Y, Z
% 0.72/1.23 , X ) }.
% 0.72/1.23 substitution0:
% 0.72/1.23 X := Y
% 0.72/1.23 Y := X
% 0.72/1.23 Z := Z
% 0.72/1.23 end
% 0.72/1.23 permutation0:
% 0.72/1.23 0 ==> 0
% 0.72/1.23 1 ==> 1
% 0.72/1.23 end
% 0.72/1.23
% 0.72/1.23 eqswap: (1681) {G0,W8,D3,L2,V3,M2} { ! singleton( Y ) = X, ! alpha3( X, Z
% 0.72/1.23 , Y ) }.
% 0.72/1.23 parent0[1]: (8) {G0,W8,D3,L2,V3,M2} I { ! alpha3( X, Y, Z ), ! X =
% 0.72/1.23 singleton( Z ) }.
% 0.72/1.23 substitution0:
% 0.72/1.23 X := X
% 0.72/1.23 Y := Z
% 0.72/1.23 Z := Y
% 0.72/1.23 end
% 0.72/1.23
% 0.72/1.23 resolution: (1682) {G1,W8,D3,L2,V3,M2} { ! singleton( X ) = Y, ! alpha1( Y
% 0.72/1.23 , Z, X ) }.
% 0.72/1.23 parent0[1]: (1681) {G0,W8,D3,L2,V3,M2} { ! singleton( Y ) = X, ! alpha3( X
% 0.72/1.23 , Z, Y ) }.
% 0.72/1.23 parent1[1]: (6) {G0,W8,D2,L2,V3,M2} I { ! alpha1( X, Y, Z ), alpha3( X, Y,
% 0.72/1.23 Z ) }.
% 0.72/1.23 substitution0:
% 0.72/1.23 X := Y
% 0.72/1.23 Y := X
% 0.72/1.23 Z := Z
% 0.72/1.23 end
% 0.72/1.23 substitution1:
% 0.72/1.23 X := Y
% 0.72/1.23 Y := Z
% 0.72/1.23 Z := X
% 0.72/1.23 end
% 0.72/1.23
% 0.72/1.23 eqswap: (1683) {G1,W8,D3,L2,V3,M2} { ! Y = singleton( X ), ! alpha1( Y, Z
% 0.72/1.23 , X ) }.
% 0.72/1.23 parent0[0]: (1682) {G1,W8,D3,L2,V3,M2} { ! singleton( X ) = Y, ! alpha1( Y
% 0.72/1.23 , Z, X ) }.
% 0.72/1.23 substitution0:
% 0.72/1.23 X := X
% 0.72/1.23 Y := Y
% 0.72/1.23 Z := Z
% 0.72/1.23 end
% 0.72/1.23
% 0.72/1.23 subsumption: (104) {G1,W8,D3,L2,V3,M2} R(8,6) { ! X = singleton( Y ), !
% 0.72/1.23 alpha1( X, Z, Y ) }.
% 0.72/1.23 parent0: (1683) {G1,W8,D3,L2,V3,M2} { ! Y = singleton( X ), ! alpha1( Y, Z
% 0.72/1.23 , X ) }.
% 0.72/1.23 substitution0:
% 0.72/1.23 X := Y
% 0.72/1.23 Y := X
% 0.72/1.23 Z := Z
% 0.72/1.23 end
% 0.72/1.23 permutation0:
% 0.72/1.23 0 ==> 0
% 0.72/1.23 1 ==> 1
% 0.72/1.23 end
% 0.72/1.23
% 0.72/1.23 eqswap: (1684) {G1,W8,D3,L2,V3,M2} { ! singleton( Y ) = X, ! alpha1( X, Z
% 0.72/1.23 , Y ) }.
% 0.72/1.23 parent0[0]: (104) {G1,W8,D3,L2,V3,M2} R(8,6) { ! X = singleton( Y ), !
% 0.72/1.23 alpha1( X, Z, Y ) }.
% 0.72/1.23 substitution0:
% 0.72/1.23 X := X
% 0.72/1.23 Y := Y
% 0.72/1.23 Z := Z
% 0.72/1.23 end
% 0.72/1.23
% 0.72/1.23 resolution: (1685) {G1,W9,D3,L2,V3,M2} { ! singleton( X ) = Y, subset( Y,
% 0.72/1.23 unordered_pair( Z, X ) ) }.
% 0.72/1.23 parent0[1]: (1684) {G1,W8,D3,L2,V3,M2} { ! singleton( Y ) = X, ! alpha1( X
% 0.72/1.23 , Z, Y ) }.
% 0.72/1.23 parent1[0]: (4) {G0,W9,D3,L2,V3,M2} I { alpha1( X, Y, Z ), subset( X,
% 0.72/1.23 unordered_pair( Y, Z ) ) }.
% 0.72/1.23 substitution0:
% 0.72/1.23 X := Y
% 0.72/1.23 Y := X
% 0.72/1.23 Z := Z
% 0.72/1.23 end
% 0.72/1.23 substitution1:
% 0.72/1.23 X := Y
% 0.72/1.23 Y := Z
% 0.72/1.23 Z := X
% 0.72/1.23 end
% 0.72/1.23
% 0.72/1.23 eqswap: (1686) {G1,W9,D3,L2,V3,M2} { ! Y = singleton( X ), subset( Y,
% 0.72/1.23 unordered_pair( Z, X ) ) }.
% 0.72/1.23 parent0[0]: (1685) {G1,W9,D3,L2,V3,M2} { ! singleton( X ) = Y, subset( Y,
% 0.72/1.23 unordered_pair( Z, X ) ) }.
% 0.72/1.23 substitution0:
% 0.72/1.23 X := X
% 0.72/1.23 Y := Y
% 0.72/1.23 Z := Z
% 0.72/1.23 end
% 0.72/1.23
% 0.72/1.23 subsumption: (113) {G2,W9,D3,L2,V3,M2} R(104,4) { ! X = singleton( Y ),
% 0.72/1.23 subset( X, unordered_pair( Z, Y ) ) }.
% 0.72/1.23 parent0: (1686) {G1,W9,D3,L2,V3,M2} { ! Y = singleton( X ), subset( Y,
% 0.72/1.23 unordered_pair( Z, X ) ) }.
% 0.72/1.23 substitution0:
% 0.72/1.23 X := Y
% 0.72/1.23 Y := X
% 0.72/1.23 Z := Z
% 0.72/1.23 end
% 0.72/1.23 permutation0:
% 0.72/1.23 0 ==> 0
% 0.72/1.23 1 ==> 1
% 0.72/1.23 end
% 0.72/1.23
% 0.72/1.23 eqswap: (1687) {G0,W8,D3,L2,V3,M2} { ! singleton( Y ) = X, ! alpha2( X, Y
% 0.72/1.23 , Z ) }.
% 0.72/1.23 parent0[1]: (22) {G0,W8,D3,L2,V3,M2} I { ! alpha2( X, Y, Z ), ! X =
% 0.72/1.23 singleton( Y ) }.
% 0.72/1.23 substitution0:
% 0.72/1.23 X := X
% 0.72/1.23 Y := Y
% 0.72/1.23 Z := Z
% 0.72/1.23 end
% 0.72/1.23
% 0.72/1.23 resolution: (1688) {G1,W8,D3,L2,V3,M2} { ! singleton( X ) = Y, ! alpha5( Y
% 0.72/1.23 , X, Z ) }.
% 0.72/1.23 parent0[1]: (1687) {G0,W8,D3,L2,V3,M2} { ! singleton( Y ) = X, ! alpha2( X
% 0.72/1.23 , Y, Z ) }.
% 0.72/1.23 parent1[1]: (20) {G0,W8,D2,L2,V3,M2} I { ! alpha5( X, Y, Z ), alpha2( X, Y
% 0.72/1.23 , Z ) }.
% 0.72/1.23 substitution0:
% 0.72/1.23 X := Y
% 0.72/1.23 Y := X
% 0.72/1.23 Z := Z
% 0.72/1.23 end
% 0.72/1.23 substitution1:
% 0.72/1.23 X := Y
% 0.72/1.23 Y := X
% 0.72/1.23 Z := Z
% 0.72/1.23 end
% 0.72/1.23
% 0.72/1.23 eqswap: (1689) {G1,W8,D3,L2,V3,M2} { ! Y = singleton( X ), ! alpha5( Y, X
% 0.72/1.23 , Z ) }.
% 0.72/1.23 parent0[0]: (1688) {G1,W8,D3,L2,V3,M2} { ! singleton( X ) = Y, ! alpha5( Y
% 0.72/1.23 , X, Z ) }.
% 0.72/1.23 substitution0:
% 0.72/1.23 X := X
% 0.72/1.23 Y := Y
% 0.72/1.23 Z := Z
% 0.72/1.23 end
% 0.72/1.23
% 0.72/1.23 subsumption: (116) {G1,W8,D3,L2,V3,M2} R(22,20) { ! X = singleton( Y ), !
% 0.72/1.23 alpha5( X, Y, Z ) }.
% 0.72/1.23 parent0: (1689) {G1,W8,D3,L2,V3,M2} { ! Y = singleton( X ), ! alpha5( Y, X
% 0.72/1.23 , Z ) }.
% 0.72/1.23 substitution0:
% 0.72/1.23 X := Y
% 0.72/1.23 Y := X
% 0.72/1.23 Z := Z
% 0.72/1.23 end
% 0.72/1.23 permutation0:
% 0.72/1.23 0 ==> 0
% 0.72/1.23 1 ==> 1
% 0.72/1.23 end
% 0.72/1.23
% 0.72/1.23 eqswap: (1690) {G0,W8,D3,L2,V2,M2} { empty_set ==> set_difference( X, Y )
% 0.72/1.23 , ! subset( X, Y ) }.
% 0.72/1.23 parent0[1]: (15) {G0,W8,D3,L2,V2,M2} I { ! subset( X, Y ), set_difference(
% 0.72/1.23 X, Y ) ==> empty_set }.
% 0.72/1.23 substitution0:
% 0.72/1.23 X := X
% 0.72/1.23 Y := Y
% 0.72/1.23 end
% 0.72/1.23
% 0.72/1.23 resolution: (1691) {G1,W7,D4,L1,V2,M1} { empty_set ==> set_difference(
% 0.72/1.23 empty_set, unordered_pair( X, Y ) ) }.
% 0.72/1.23 parent0[1]: (1690) {G0,W8,D3,L2,V2,M2} { empty_set ==> set_difference( X,
% 0.72/1.23 Y ), ! subset( X, Y ) }.
% 0.72/1.23 parent1[0]: (28) {G1,W5,D3,L1,V2,M1} Q(3) { subset( empty_set,
% 0.72/1.23 unordered_pair( X, Y ) ) }.
% 0.72/1.23 substitution0:
% 0.72/1.23 X := empty_set
% 0.72/1.23 Y := unordered_pair( X, Y )
% 0.72/1.23 end
% 0.72/1.23 substitution1:
% 0.72/1.23 X := X
% 0.72/1.23 Y := Y
% 0.72/1.23 end
% 0.72/1.23
% 0.72/1.23 eqswap: (1692) {G1,W7,D4,L1,V2,M1} { set_difference( empty_set,
% 0.72/1.23 unordered_pair( X, Y ) ) ==> empty_set }.
% 0.72/1.23 parent0[0]: (1691) {G1,W7,D4,L1,V2,M1} { empty_set ==> set_difference(
% 0.72/1.23 empty_set, unordered_pair( X, Y ) ) }.
% 0.72/1.23 substitution0:
% 0.72/1.23 X := X
% 0.72/1.23 Y := Y
% 0.72/1.23 end
% 0.72/1.23
% 0.72/1.23 subsumption: (136) {G2,W7,D4,L1,V2,M1} R(15,28) { set_difference( empty_set
% 0.72/1.23 , unordered_pair( X, Y ) ) ==> empty_set }.
% 0.72/1.23 parent0: (1692) {G1,W7,D4,L1,V2,M1} { set_difference( empty_set,
% 0.72/1.23 unordered_pair( X, Y ) ) ==> empty_set }.
% 0.72/1.23 substitution0:
% 0.72/1.23 X := X
% 0.72/1.23 Y := Y
% 0.72/1.23 end
% 0.72/1.23 permutation0:
% 0.72/1.23 0 ==> 0
% 0.72/1.23 end
% 0.72/1.23
% 0.72/1.23 eqswap: (1693) {G0,W8,D3,L2,V2,M2} { empty_set ==> set_difference( X, Y )
% 0.72/1.23 , ! subset( X, Y ) }.
% 0.72/1.23 parent0[1]: (15) {G0,W8,D3,L2,V2,M2} I { ! subset( X, Y ), set_difference(
% 0.72/1.23 X, Y ) ==> empty_set }.
% 0.72/1.23 substitution0:
% 0.72/1.23 X := X
% 0.72/1.23 Y := Y
% 0.72/1.23 end
% 0.72/1.23
% 0.72/1.23 resolution: (1694) {G1,W5,D3,L1,V1,M1} { empty_set ==> set_difference( X,
% 0.72/1.23 X ) }.
% 0.72/1.23 parent0[1]: (1693) {G0,W8,D3,L2,V2,M2} { empty_set ==> set_difference( X,
% 0.72/1.23 Y ), ! subset( X, Y ) }.
% 0.72/1.23 parent1[0]: (13) {G0,W3,D2,L1,V1,M1} I { subset( X, X ) }.
% 0.72/1.23 substitution0:
% 0.72/1.23 X := X
% 0.72/1.23 Y := X
% 0.72/1.23 end
% 0.72/1.23 substitution1:
% 0.72/1.23 X := X
% 0.72/1.23 end
% 0.72/1.23
% 0.72/1.23 eqswap: (1695) {G1,W5,D3,L1,V1,M1} { set_difference( X, X ) ==> empty_set
% 0.72/1.23 }.
% 0.72/1.23 parent0[0]: (1694) {G1,W5,D3,L1,V1,M1} { empty_set ==> set_difference( X,
% 0.72/1.23 X ) }.
% 0.72/1.23 substitution0:
% 0.72/1.23 X := X
% 0.72/1.23 end
% 0.72/1.23
% 0.72/1.23 subsumption: (137) {G1,W5,D3,L1,V1,M1} R(15,13) { set_difference( X, X )
% 0.72/1.23 ==> empty_set }.
% 0.72/1.23 parent0: (1695) {G1,W5,D3,L1,V1,M1} { set_difference( X, X ) ==> empty_set
% 0.72/1.23 }.
% 0.72/1.23 substitution0:
% 0.72/1.23 X := X
% 0.72/1.23 end
% 0.72/1.23 permutation0:
% 0.72/1.23 0 ==> 0
% 0.72/1.23 end
% 0.72/1.23
% 0.72/1.23 eqswap: (1696) {G0,W11,D4,L2,V0,M2} { ! empty_set ==> set_difference(
% 0.72/1.23 skol3, unordered_pair( skol4, skol5 ) ), alpha5( skol3, skol4, skol5 )
% 0.72/1.23 }.
% 0.72/1.23 parent0[1]: (17) {G0,W11,D4,L2,V0,M2} I { alpha5( skol3, skol4, skol5 ), !
% 0.72/1.23 set_difference( skol3, unordered_pair( skol4, skol5 ) ) ==> empty_set }.
% 0.72/1.23 substitution0:
% 0.72/1.23 end
% 0.72/1.23
% 0.72/1.23 eqswap: (1697) {G0,W8,D3,L2,V2,M2} { empty_set ==> set_difference( X, Y )
% 0.72/1.23 , ! subset( X, Y ) }.
% 0.72/1.23 parent0[1]: (15) {G0,W8,D3,L2,V2,M2} I { ! subset( X, Y ), set_difference(
% 0.72/1.23 X, Y ) ==> empty_set }.
% 0.72/1.23 substitution0:
% 0.72/1.23 X := X
% 0.72/1.23 Y := Y
% 0.72/1.23 end
% 0.72/1.23
% 0.72/1.23 resolution: (1698) {G1,W9,D3,L2,V0,M2} { alpha5( skol3, skol4, skol5 ), !
% 0.72/1.23 subset( skol3, unordered_pair( skol4, skol5 ) ) }.
% 0.72/1.23 parent0[0]: (1696) {G0,W11,D4,L2,V0,M2} { ! empty_set ==> set_difference(
% 0.72/1.23 skol3, unordered_pair( skol4, skol5 ) ), alpha5( skol3, skol4, skol5 )
% 0.72/1.23 }.
% 0.72/1.23 parent1[0]: (1697) {G0,W8,D3,L2,V2,M2} { empty_set ==> set_difference( X,
% 0.72/1.23 Y ), ! subset( X, Y ) }.
% 0.72/1.23 substitution0:
% 0.72/1.23 end
% 0.72/1.23 substitution1:
% 0.72/1.23 X := skol3
% 0.72/1.23 Y := unordered_pair( skol4, skol5 )
% 0.72/1.23 end
% 0.72/1.23
% 0.72/1.23 subsumption: (309) {G1,W9,D3,L2,V0,M2} R(17,15) { alpha5( skol3, skol4,
% 0.72/1.23 skol5 ), ! subset( skol3, unordered_pair( skol4, skol5 ) ) }.
% 0.72/1.23 parent0: (1698) {G1,W9,D3,L2,V0,M2} { alpha5( skol3, skol4, skol5 ), !
% 0.72/1.23 subset( skol3, unordered_pair( skol4, skol5 ) ) }.
% 0.72/1.23 substitution0:
% 0.72/1.23 end
% 0.72/1.23 permutation0:
% 0.72/1.23 0 ==> 0
% 0.72/1.23 1 ==> 1
% 0.72/1.23 end
% 0.72/1.23
% 0.72/1.23 eqswap: (1700) {G0,W11,D4,L2,V0,M2} { ! empty_set ==> set_difference(
% 0.72/1.23 skol3, unordered_pair( skol4, skol5 ) ), alpha5( skol3, skol4, skol5 )
% 0.72/1.23 }.
% 0.72/1.23 parent0[1]: (17) {G0,W11,D4,L2,V0,M2} I { alpha5( skol3, skol4, skol5 ), !
% 0.72/1.23 set_difference( skol3, unordered_pair( skol4, skol5 ) ) ==> empty_set }.
% 0.72/1.23 substitution0:
% 0.72/1.23 end
% 0.72/1.23
% 0.72/1.23 paramod: (1703) {G1,W19,D4,L4,V0,M4} { alpha5( empty_set, skol4, skol5 ),
% 0.72/1.23 alpha5( skol3, skol4, skol5 ), ! alpha2( skol3, skol4, skol5 ), !
% 0.72/1.23 empty_set ==> set_difference( skol3, unordered_pair( skol4, skol5 ) ) }.
% 0.72/1.23 parent0[1]: (16) {G0,W11,D2,L3,V0,M3} I { alpha5( skol3, skol4, skol5 ),
% 0.72/1.23 skol3 ==> empty_set, ! alpha2( skol3, skol4, skol5 ) }.
% 0.72/1.23 parent1[1; 1]: (1700) {G0,W11,D4,L2,V0,M2} { ! empty_set ==>
% 0.72/1.23 set_difference( skol3, unordered_pair( skol4, skol5 ) ), alpha5( skol3,
% 0.72/1.23 skol4, skol5 ) }.
% 0.72/1.23 substitution0:
% 0.72/1.23 end
% 0.72/1.23 substitution1:
% 0.72/1.23 end
% 0.72/1.23
% 0.72/1.23 paramod: (1705) {G1,W27,D4,L6,V0,M6} { ! empty_set ==> set_difference(
% 0.72/1.23 empty_set, unordered_pair( skol4, skol5 ) ), alpha5( skol3, skol4, skol5
% 0.72/1.23 ), ! alpha2( skol3, skol4, skol5 ), alpha5( empty_set, skol4, skol5 ),
% 0.72/1.23 alpha5( skol3, skol4, skol5 ), ! alpha2( skol3, skol4, skol5 ) }.
% 0.72/1.23 parent0[1]: (16) {G0,W11,D2,L3,V0,M3} I { alpha5( skol3, skol4, skol5 ),
% 0.72/1.23 skol3 ==> empty_set, ! alpha2( skol3, skol4, skol5 ) }.
% 0.72/1.23 parent1[3; 4]: (1703) {G1,W19,D4,L4,V0,M4} { alpha5( empty_set, skol4,
% 0.72/1.23 skol5 ), alpha5( skol3, skol4, skol5 ), ! alpha2( skol3, skol4, skol5 ),
% 0.72/1.23 ! empty_set ==> set_difference( skol3, unordered_pair( skol4, skol5 ) )
% 0.72/1.23 }.
% 0.72/1.23 substitution0:
% 0.72/1.23 end
% 0.72/1.23 substitution1:
% 0.72/1.23 end
% 0.72/1.23
% 0.72/1.23 factor: (1726) {G1,W23,D4,L5,V0,M5} { ! empty_set ==> set_difference(
% 0.72/1.23 empty_set, unordered_pair( skol4, skol5 ) ), alpha5( skol3, skol4, skol5
% 0.72/1.23 ), ! alpha2( skol3, skol4, skol5 ), alpha5( empty_set, skol4, skol5 ), !
% 0.72/1.38 alpha2( skol3, skol4, skol5 ) }.
% 0.72/1.38 parent0[1, 4]: (1705) {G1,W27,D4,L6,V0,M6} { ! empty_set ==>
% 0.72/1.38 set_difference( empty_set, unordered_pair( skol4, skol5 ) ), alpha5(
% 0.72/1.38 skol3, skol4, skol5 ), ! alpha2( skol3, skol4, skol5 ), alpha5( empty_set
% 0.72/1.38 , skol4, skol5 ), alpha5( skol3, skol4, skol5 ), ! alpha2( skol3, skol4,
% 0.72/1.38 skol5 ) }.
% 0.72/1.38 substitution0:
% 0.72/1.38 end
% 0.72/1.38
% 0.72/1.38 paramod: (1727) {G2,W19,D2,L5,V0,M5} { ! empty_set ==> empty_set, alpha5(
% 0.72/1.38 skol3, skol4, skol5 ), ! alpha2( skol3, skol4, skol5 ), alpha5( empty_set
% 0.72/1.38 , skol4, skol5 ), ! alpha2( skol3, skol4, skol5 ) }.
% 0.72/1.38 parent0[0]: (136) {G2,W7,D4,L1,V2,M1} R(15,28) { set_difference( empty_set
% 0.72/1.38 , unordered_pair( X, Y ) ) ==> empty_set }.
% 0.72/1.38 parent1[0; 3]: (1726) {G1,W23,D4,L5,V0,M5} { ! empty_set ==>
% 0.72/1.38 set_difference( empty_set, unordered_pair( skol4, skol5 ) ), alpha5(
% 0.72/1.38 skol3, skol4, skol5 ), ! alpha2( skol3, skol4, skol5 ), alpha5( empty_set
% 0.72/1.38 , skol4, skol5 ), ! alpha2( skol3, skol4, skol5 ) }.
% 0.72/1.38 substitution0:
% 0.72/1.38 X := skol4
% 0.72/1.38 Y := skol5
% 0.72/1.38 end
% 0.72/1.38 substitution1:
% 0.72/1.38 end
% 0.72/1.38
% 0.72/1.38 factor: (1728) {G2,W15,D2,L4,V0,M4} { ! empty_set ==> empty_set, alpha5(
% 0.72/1.38 skol3, skol4, skol5 ), ! alpha2( skol3, skol4, skol5 ), alpha5( empty_set
% 0.72/1.38 , skol4, skol5 ) }.
% 0.72/1.38 parent0[2, 4]: (1727) {G2,W19,D2,L5,V0,M5} { ! empty_set ==> empty_set,
% 0.72/1.38 alpha5( skol3, skol4, skol5 ), ! alpha2( skol3, skol4, skol5 ), alpha5(
% 0.72/1.38 empty_set, skol4, skol5 ), ! alpha2( skol3, skol4, skol5 ) }.
% 0.72/1.38 substitution0:
% 0.72/1.38 end
% 0.72/1.38
% 0.72/1.38 eqrefl: (1729) {G0,W12,D2,L3,V0,M3} { alpha5( skol3, skol4, skol5 ), !
% 0.72/1.38 alpha2( skol3, skol4, skol5 ), alpha5( empty_set, skol4, skol5 ) }.
% 0.72/1.38 parent0[0]: (1728) {G2,W15,D2,L4,V0,M4} { ! empty_set ==> empty_set,
% 0.72/1.38 alpha5( skol3, skol4, skol5 ), ! alpha2( skol3, skol4, skol5 ), alpha5(
% 0.72/1.38 empty_set, skol4, skol5 ) }.
% 0.72/1.38 substitution0:
% 0.72/1.38 end
% 0.72/1.38
% 0.72/1.38 resolution: (1730) {G1,W8,D2,L2,V0,M2} { alpha5( skol3, skol4, skol5 ), !
% 0.72/1.38 alpha2( skol3, skol4, skol5 ) }.
% 0.72/1.38 parent0[0]: (34) {G1,W4,D2,L1,V2,M1} Q(19) { ! alpha5( empty_set, X, Y )
% 0.72/1.38 }.
% 0.72/1.38 parent1[2]: (1729) {G0,W12,D2,L3,V0,M3} { alpha5( skol3, skol4, skol5 ), !
% 0.72/1.38 alpha2( skol3, skol4, skol5 ), alpha5( empty_set, skol4, skol5 ) }.
% 0.72/1.38 substitution0:
% 0.72/1.38 X := skol4
% 0.72/1.38 Y := skol5
% 0.72/1.38 end
% 0.72/1.38 substitution1:
% 0.72/1.38 end
% 0.72/1.38
% 0.72/1.38 subsumption: (315) {G3,W8,D2,L2,V0,M2} P(16,17);d(136);q;r(34) { alpha5(
% 0.72/1.38 skol3, skol4, skol5 ), ! alpha2( skol3, skol4, skol5 ) }.
% 0.72/1.38 parent0: (1730) {G1,W8,D2,L2,V0,M2} { alpha5( skol3, skol4, skol5 ), !
% 0.72/1.38 alpha2( skol3, skol4, skol5 ) }.
% 0.72/1.38 substitution0:
% 0.72/1.38 end
% 0.72/1.38 permutation0:
% 0.72/1.38 0 ==> 0
% 0.72/1.38 1 ==> 1
% 0.72/1.38 end
% 0.72/1.38
% 0.72/1.38 *** allocated 50625 integers for termspace/termends
% 0.72/1.38 *** allocated 15000 integers for justifications
% 0.72/1.38 *** allocated 113905 integers for clauses
% 0.72/1.38 *** allocated 22500 integers for justifications
% 0.72/1.38 *** allocated 75937 integers for termspace/termends
% 0.72/1.38 *** allocated 33750 integers for justifications
% 0.72/1.38 *** allocated 50625 integers for justifications
% 0.72/1.38 *** allocated 113905 integers for termspace/termends
% 0.72/1.38
% 0.72/1.38 ==> (333) {G3,W9,D3,L2,V2,M2} P(2,17);d(136);q;r(34) { ! subset( skol3,
% 0.72/1.38 unordered_pair( X, Y ) ), ! alpha1( skol3, X, Y ) }.
% 0.72/1.38
% 0.72/1.38
% 0.72/1.38
% 0.72/1.38 !!! Internal Problem: OH, OH, COULD NOT DERIVE GOAL !!!
% 0.72/1.38
% 0.72/1.38 Bliksem ended
%------------------------------------------------------------------------------