TSTP Solution File: SEU267+1 by Bliksem---1.12
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%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SEU267+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n032.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 : Tue Jul 19 07:12:00 EDT 2022
% Result : Theorem 0.44s 0.86s
% Output : Refutation 0.44s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.08 % Problem : SEU267+1 : TPTP v8.1.0. Released v3.3.0.
% 0.00/0.09 % Command : bliksem %s
% 0.08/0.28 % Computer : n032.cluster.edu
% 0.08/0.28 % Model : x86_64 x86_64
% 0.08/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.28 % Memory : 8042.1875MB
% 0.08/0.28 % OS : Linux 3.10.0-693.el7.x86_64
% 0.08/0.28 % CPULimit : 300
% 0.08/0.28 % DateTime : Sun Jun 19 10:01:48 EDT 2022
% 0.08/0.28 % CPUTime :
% 0.44/0.86 *** allocated 10000 integers for termspace/termends
% 0.44/0.86 *** allocated 10000 integers for clauses
% 0.44/0.86 *** allocated 10000 integers for justifications
% 0.44/0.86 Bliksem 1.12
% 0.44/0.86
% 0.44/0.86
% 0.44/0.86 Automatic Strategy Selection
% 0.44/0.86
% 0.44/0.86
% 0.44/0.86 Clauses:
% 0.44/0.86
% 0.44/0.86 { element( skol1( X ), X ) }.
% 0.44/0.86 { && }.
% 0.44/0.86 { ! element( X, Y ), empty( Y ), in( X, Y ) }.
% 0.44/0.86 { ! in( X, Y ), ! in( Y, X ) }.
% 0.44/0.86 { && }.
% 0.44/0.86 { empty( empty_set ) }.
% 0.44/0.86 { ! in( X, Y ), element( X, Y ) }.
% 0.44/0.86 { empty( skol2 ) }.
% 0.44/0.86 { ! empty( skol3 ) }.
% 0.44/0.86 { ! empty( X ), X = empty_set }.
% 0.44/0.86 { ! in( X, Y ), ! empty( Y ) }.
% 0.44/0.86 { ! empty( X ), X = Y, ! empty( Y ) }.
% 0.44/0.86 { && }.
% 0.44/0.86 { && }.
% 0.44/0.86 { && }.
% 0.44/0.86 { ! empty( ordered_pair( X, Y ) ) }.
% 0.44/0.86 { ! pair_first( ordered_pair( skol4, skol7 ) ) = skol4, ! pair_second(
% 0.44/0.86 ordered_pair( skol4, skol7 ) ) = skol7 }.
% 0.44/0.86 { ! X = ordered_pair( Y, Z ), ! T = pair_first( X ), ! X = ordered_pair( U
% 0.44/0.86 , W ), T = U }.
% 0.44/0.86 { ! X = ordered_pair( Y, Z ), ! T = skol5( U, T ), T = pair_first( X ) }.
% 0.44/0.86 { ! X = ordered_pair( Y, Z ), X = ordered_pair( skol5( X, T ), skol8( X, T
% 0.44/0.86 ) ), T = pair_first( X ) }.
% 0.44/0.86 { ! X = ordered_pair( Y, Z ), ! T = pair_second( X ), ! X = ordered_pair( W
% 0.44/0.86 , U ), T = U }.
% 0.44/0.86 { ! X = ordered_pair( Y, Z ), ! T = skol6( U, T ), T = pair_second( X ) }.
% 0.44/0.86 { ! X = ordered_pair( Y, Z ), X = ordered_pair( skol9( X, T ), skol6( X, T
% 0.44/0.86 ) ), T = pair_second( X ) }.
% 0.44/0.86
% 0.44/0.86 percentage equality = 0.571429, percentage horn = 0.842105
% 0.44/0.86 This is a problem with some equality
% 0.44/0.86
% 0.44/0.86
% 0.44/0.86
% 0.44/0.86 Options Used:
% 0.44/0.86
% 0.44/0.86 useres = 1
% 0.44/0.86 useparamod = 1
% 0.44/0.86 useeqrefl = 1
% 0.44/0.86 useeqfact = 1
% 0.44/0.86 usefactor = 1
% 0.44/0.86 usesimpsplitting = 0
% 0.44/0.86 usesimpdemod = 5
% 0.44/0.86 usesimpres = 3
% 0.44/0.86
% 0.44/0.86 resimpinuse = 1000
% 0.44/0.86 resimpclauses = 20000
% 0.44/0.86 substype = eqrewr
% 0.44/0.86 backwardsubs = 1
% 0.44/0.86 selectoldest = 5
% 0.44/0.86
% 0.44/0.86 litorderings [0] = split
% 0.44/0.86 litorderings [1] = extend the termordering, first sorting on arguments
% 0.44/0.86
% 0.44/0.86 termordering = kbo
% 0.44/0.86
% 0.44/0.86 litapriori = 0
% 0.44/0.86 termapriori = 1
% 0.44/0.86 litaposteriori = 0
% 0.44/0.86 termaposteriori = 0
% 0.44/0.86 demodaposteriori = 0
% 0.44/0.86 ordereqreflfact = 0
% 0.44/0.86
% 0.44/0.86 litselect = negord
% 0.44/0.86
% 0.44/0.86 maxweight = 15
% 0.44/0.86 maxdepth = 30000
% 0.44/0.86 maxlength = 115
% 0.44/0.86 maxnrvars = 195
% 0.44/0.86 excuselevel = 1
% 0.44/0.86 increasemaxweight = 1
% 0.44/0.86
% 0.44/0.86 maxselected = 10000000
% 0.44/0.86 maxnrclauses = 10000000
% 0.44/0.86
% 0.44/0.86 showgenerated = 0
% 0.44/0.86 showkept = 0
% 0.44/0.86 showselected = 0
% 0.44/0.86 showdeleted = 0
% 0.44/0.86 showresimp = 1
% 0.44/0.86 showstatus = 2000
% 0.44/0.86
% 0.44/0.86 prologoutput = 0
% 0.44/0.86 nrgoals = 5000000
% 0.44/0.86 totalproof = 1
% 0.44/0.86
% 0.44/0.86 Symbols occurring in the translation:
% 0.44/0.86
% 0.44/0.86 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.44/0.86 . [1, 2] (w:1, o:24, a:1, s:1, b:0),
% 0.44/0.86 && [3, 0] (w:1, o:4, a:1, s:1, b:0),
% 0.44/0.86 ! [4, 1] (w:0, o:15, a:1, s:1, b:0),
% 0.44/0.86 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.44/0.86 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.44/0.86 element [37, 2] (w:1, o:48, a:1, s:1, b:0),
% 0.44/0.86 empty [38, 1] (w:1, o:20, a:1, s:1, b:0),
% 0.44/0.86 in [39, 2] (w:1, o:49, a:1, s:1, b:0),
% 0.44/0.86 empty_set [40, 0] (w:1, o:8, a:1, s:1, b:0),
% 0.44/0.86 ordered_pair [41, 2] (w:1, o:50, a:1, s:1, b:0),
% 0.44/0.86 pair_first [42, 1] (w:1, o:21, a:1, s:1, b:0),
% 0.44/0.86 pair_second [43, 1] (w:1, o:22, a:1, s:1, b:0),
% 0.44/0.86 skol1 [46, 1] (w:1, o:23, a:1, s:1, b:1),
% 0.44/0.86 skol2 [47, 0] (w:1, o:11, a:1, s:1, b:1),
% 0.44/0.86 skol3 [48, 0] (w:1, o:12, a:1, s:1, b:1),
% 0.44/0.86 skol4 [49, 0] (w:1, o:13, a:1, s:1, b:1),
% 0.44/0.86 skol5 [50, 2] (w:1, o:51, a:1, s:1, b:1),
% 0.44/0.86 skol6 [51, 2] (w:1, o:52, a:1, s:1, b:1),
% 0.44/0.86 skol7 [52, 0] (w:1, o:14, a:1, s:1, b:1),
% 0.44/0.86 skol8 [53, 2] (w:1, o:53, a:1, s:1, b:1),
% 0.44/0.86 skol9 [54, 2] (w:1, o:54, a:1, s:1, b:1).
% 0.44/0.86
% 0.44/0.86
% 0.44/0.86 Starting Search:
% 0.44/0.86
% 0.44/0.86
% 0.44/0.86 Bliksems!, er is een bewijs:
% 0.44/0.86 % SZS status Theorem
% 0.44/0.86 % SZS output start Refutation
% 0.44/0.86
% 0.44/0.86 (12) {G0,W12,D4,L2,V0,M2} I { ! pair_first( ordered_pair( skol4, skol7 ) )
% 0.44/0.86 ==> skol4, ! pair_second( ordered_pair( skol4, skol7 ) ) ==> skol7 }.
% 0.44/0.86 (13) {G0,W17,D3,L4,V6,M4} I { ! X = ordered_pair( Y, Z ), ! T = pair_first
% 0.44/0.86 ( X ), ! X = ordered_pair( U, W ), T = U }.
% 0.44/0.86 (16) {G0,W17,D3,L4,V6,M4} I { ! X = ordered_pair( Y, Z ), ! T = pair_second
% 0.44/0.86 ( X ), ! X = ordered_pair( W, U ), T = U }.
% 0.44/0.86 (22) {G1,W16,D4,L3,V5,M3} Q(13) { ! ordered_pair( X, Y ) = ordered_pair( Z
% 0.44/0.86 , T ), ! U = pair_first( ordered_pair( X, Y ) ), U = X }.
% 0.44/0.86 (24) {G2,W13,D4,L2,V4,M2} Q(22) { ! ordered_pair( X, Y ) = ordered_pair( Z
% 0.44/0.86 , T ), pair_first( ordered_pair( X, Y ) ) ==> X }.
% 0.44/0.86 (25) {G3,W6,D4,L1,V2,M1} Q(24) { pair_first( ordered_pair( X, Y ) ) ==> X
% 0.44/0.86 }.
% 0.44/0.86 (31) {G1,W16,D4,L3,V5,M3} Q(16) { ! ordered_pair( X, Y ) = ordered_pair( Z
% 0.44/0.86 , T ), ! U = pair_second( ordered_pair( X, Y ) ), U = Y }.
% 0.44/0.86 (33) {G2,W13,D4,L2,V4,M2} Q(31) { ! ordered_pair( X, Y ) = ordered_pair( Z
% 0.44/0.86 , T ), pair_second( ordered_pair( X, Y ) ) ==> Y }.
% 0.44/0.86 (34) {G3,W6,D4,L1,V2,M1} Q(33) { pair_second( ordered_pair( X, Y ) ) ==> Y
% 0.44/0.86 }.
% 0.44/0.86 (69) {G4,W0,D0,L0,V0,M0} S(12);d(25);q;d(34);q { }.
% 0.44/0.86
% 0.44/0.86
% 0.44/0.86 % SZS output end Refutation
% 0.44/0.86 found a proof!
% 0.44/0.86
% 0.44/0.86
% 0.44/0.86 Unprocessed initial clauses:
% 0.44/0.86
% 0.44/0.86 (71) {G0,W4,D3,L1,V1,M1} { element( skol1( X ), X ) }.
% 0.44/0.86 (72) {G0,W1,D1,L1,V0,M1} { && }.
% 0.44/0.86 (73) {G0,W8,D2,L3,V2,M3} { ! element( X, Y ), empty( Y ), in( X, Y ) }.
% 0.44/0.86 (74) {G0,W6,D2,L2,V2,M2} { ! in( X, Y ), ! in( Y, X ) }.
% 0.44/0.86 (75) {G0,W1,D1,L1,V0,M1} { && }.
% 0.44/0.86 (76) {G0,W2,D2,L1,V0,M1} { empty( empty_set ) }.
% 0.44/0.86 (77) {G0,W6,D2,L2,V2,M2} { ! in( X, Y ), element( X, Y ) }.
% 0.44/0.86 (78) {G0,W2,D2,L1,V0,M1} { empty( skol2 ) }.
% 0.44/0.86 (79) {G0,W2,D2,L1,V0,M1} { ! empty( skol3 ) }.
% 0.44/0.86 (80) {G0,W5,D2,L2,V1,M2} { ! empty( X ), X = empty_set }.
% 0.44/0.86 (81) {G0,W5,D2,L2,V2,M2} { ! in( X, Y ), ! empty( Y ) }.
% 0.44/0.86 (82) {G0,W7,D2,L3,V2,M3} { ! empty( X ), X = Y, ! empty( Y ) }.
% 0.44/0.86 (83) {G0,W1,D1,L1,V0,M1} { && }.
% 0.44/0.86 (84) {G0,W1,D1,L1,V0,M1} { && }.
% 0.44/0.86 (85) {G0,W1,D1,L1,V0,M1} { && }.
% 0.44/0.86 (86) {G0,W4,D3,L1,V2,M1} { ! empty( ordered_pair( X, Y ) ) }.
% 0.44/0.86 (87) {G0,W12,D4,L2,V0,M2} { ! pair_first( ordered_pair( skol4, skol7 ) ) =
% 0.44/0.86 skol4, ! pair_second( ordered_pair( skol4, skol7 ) ) = skol7 }.
% 0.44/0.86 (88) {G0,W17,D3,L4,V6,M4} { ! X = ordered_pair( Y, Z ), ! T = pair_first(
% 0.44/0.86 X ), ! X = ordered_pair( U, W ), T = U }.
% 0.44/0.86 (89) {G0,W14,D3,L3,V5,M3} { ! X = ordered_pair( Y, Z ), ! T = skol5( U, T
% 0.44/0.86 ), T = pair_first( X ) }.
% 0.44/0.86 (90) {G0,W18,D4,L3,V4,M3} { ! X = ordered_pair( Y, Z ), X = ordered_pair(
% 0.44/0.86 skol5( X, T ), skol8( X, T ) ), T = pair_first( X ) }.
% 0.44/0.86 (91) {G0,W17,D3,L4,V6,M4} { ! X = ordered_pair( Y, Z ), ! T = pair_second
% 0.44/0.86 ( X ), ! X = ordered_pair( W, U ), T = U }.
% 0.44/0.86 (92) {G0,W14,D3,L3,V5,M3} { ! X = ordered_pair( Y, Z ), ! T = skol6( U, T
% 0.44/0.86 ), T = pair_second( X ) }.
% 0.44/0.86 (93) {G0,W18,D4,L3,V4,M3} { ! X = ordered_pair( Y, Z ), X = ordered_pair(
% 0.44/0.86 skol9( X, T ), skol6( X, T ) ), T = pair_second( X ) }.
% 0.44/0.86
% 0.44/0.86
% 0.44/0.86 Total Proof:
% 0.44/0.86
% 0.44/0.86 subsumption: (12) {G0,W12,D4,L2,V0,M2} I { ! pair_first( ordered_pair(
% 0.44/0.86 skol4, skol7 ) ) ==> skol4, ! pair_second( ordered_pair( skol4, skol7 ) )
% 0.44/0.86 ==> skol7 }.
% 0.44/0.86 parent0: (87) {G0,W12,D4,L2,V0,M2} { ! pair_first( ordered_pair( skol4,
% 0.44/0.86 skol7 ) ) = skol4, ! pair_second( ordered_pair( skol4, skol7 ) ) = skol7
% 0.44/0.86 }.
% 0.44/0.86 substitution0:
% 0.44/0.86 end
% 0.44/0.86 permutation0:
% 0.44/0.86 0 ==> 0
% 0.44/0.86 1 ==> 1
% 0.44/0.86 end
% 0.44/0.86
% 0.44/0.86 subsumption: (13) {G0,W17,D3,L4,V6,M4} I { ! X = ordered_pair( Y, Z ), ! T
% 0.44/0.86 = pair_first( X ), ! X = ordered_pair( U, W ), T = U }.
% 0.44/0.86 parent0: (88) {G0,W17,D3,L4,V6,M4} { ! X = ordered_pair( Y, Z ), ! T =
% 0.44/0.86 pair_first( X ), ! X = ordered_pair( U, W ), T = U }.
% 0.44/0.86 substitution0:
% 0.44/0.86 X := X
% 0.44/0.86 Y := Y
% 0.44/0.86 Z := Z
% 0.44/0.86 T := T
% 0.44/0.86 U := U
% 0.44/0.86 W := W
% 0.44/0.86 end
% 0.44/0.86 permutation0:
% 0.44/0.86 0 ==> 0
% 0.44/0.86 1 ==> 1
% 0.44/0.86 2 ==> 2
% 0.44/0.86 3 ==> 3
% 0.44/0.86 end
% 0.44/0.86
% 0.44/0.86 subsumption: (16) {G0,W17,D3,L4,V6,M4} I { ! X = ordered_pair( Y, Z ), ! T
% 0.44/0.86 = pair_second( X ), ! X = ordered_pair( W, U ), T = U }.
% 0.44/0.86 parent0: (91) {G0,W17,D3,L4,V6,M4} { ! X = ordered_pair( Y, Z ), ! T =
% 0.44/0.86 pair_second( X ), ! X = ordered_pair( W, U ), T = U }.
% 0.44/0.86 substitution0:
% 0.44/0.86 X := X
% 0.44/0.86 Y := Y
% 0.44/0.86 Z := Z
% 0.44/0.86 T := T
% 0.44/0.86 U := U
% 0.44/0.86 W := W
% 0.44/0.86 end
% 0.44/0.86 permutation0:
% 0.44/0.86 0 ==> 0
% 0.44/0.86 1 ==> 1
% 0.44/0.86 2 ==> 2
% 0.44/0.86 3 ==> 3
% 0.44/0.86 end
% 0.44/0.86
% 0.44/0.86 eqswap: (190) {G0,W17,D3,L4,V6,M4} { ! pair_first( Y ) = X, ! Y =
% 0.44/0.86 ordered_pair( Z, T ), ! Y = ordered_pair( U, W ), X = U }.
% 0.44/0.86 parent0[1]: (13) {G0,W17,D3,L4,V6,M4} I { ! X = ordered_pair( Y, Z ), ! T =
% 0.44/0.86 pair_first( X ), ! X = ordered_pair( U, W ), T = U }.
% 0.44/0.86 substitution0:
% 0.44/0.86 X := Y
% 0.44/0.86 Y := Z
% 0.44/0.86 Z := T
% 0.44/0.86 T := X
% 0.44/0.86 U := U
% 0.44/0.86 W := W
% 0.44/0.86 end
% 0.44/0.86
% 0.44/0.86 eqrefl: (203) {G0,W16,D4,L3,V5,M3} { ! pair_first( ordered_pair( X, Y ) )
% 0.44/0.86 = Z, ! ordered_pair( X, Y ) = ordered_pair( T, U ), Z = X }.
% 0.44/0.86 parent0[2]: (190) {G0,W17,D3,L4,V6,M4} { ! pair_first( Y ) = X, ! Y =
% 0.44/0.86 ordered_pair( Z, T ), ! Y = ordered_pair( U, W ), X = U }.
% 0.44/0.86 substitution0:
% 0.44/0.86 X := Z
% 0.44/0.86 Y := ordered_pair( X, Y )
% 0.44/0.86 Z := T
% 0.44/0.86 T := U
% 0.44/0.86 U := X
% 0.44/0.86 W := Y
% 0.44/0.86 end
% 0.44/0.86
% 0.44/0.86 eqswap: (204) {G0,W16,D4,L3,V5,M3} { ! Z = pair_first( ordered_pair( X, Y
% 0.44/0.86 ) ), ! ordered_pair( X, Y ) = ordered_pair( T, U ), Z = X }.
% 0.44/0.86 parent0[0]: (203) {G0,W16,D4,L3,V5,M3} { ! pair_first( ordered_pair( X, Y
% 0.44/0.86 ) ) = Z, ! ordered_pair( X, Y ) = ordered_pair( T, U ), Z = X }.
% 0.44/0.86 substitution0:
% 0.44/0.86 X := X
% 0.44/0.86 Y := Y
% 0.44/0.86 Z := Z
% 0.44/0.86 T := T
% 0.44/0.86 U := U
% 0.44/0.86 end
% 0.44/0.86
% 0.44/0.86 subsumption: (22) {G1,W16,D4,L3,V5,M3} Q(13) { ! ordered_pair( X, Y ) =
% 0.44/0.86 ordered_pair( Z, T ), ! U = pair_first( ordered_pair( X, Y ) ), U = X }.
% 0.44/0.86 parent0: (204) {G0,W16,D4,L3,V5,M3} { ! Z = pair_first( ordered_pair( X, Y
% 0.44/0.86 ) ), ! ordered_pair( X, Y ) = ordered_pair( T, U ), Z = X }.
% 0.44/0.86 substitution0:
% 0.44/0.86 X := X
% 0.44/0.86 Y := Y
% 0.44/0.86 Z := U
% 0.44/0.86 T := Z
% 0.44/0.86 U := T
% 0.44/0.86 end
% 0.44/0.86 permutation0:
% 0.44/0.86 0 ==> 1
% 0.44/0.86 1 ==> 0
% 0.44/0.86 2 ==> 2
% 0.44/0.86 end
% 0.44/0.86
% 0.44/0.86 eqswap: (228) {G1,W16,D4,L3,V5,M3} { ! ordered_pair( Z, T ) = ordered_pair
% 0.44/0.86 ( X, Y ), ! U = pair_first( ordered_pair( X, Y ) ), U = X }.
% 0.44/0.86 parent0[0]: (22) {G1,W16,D4,L3,V5,M3} Q(13) { ! ordered_pair( X, Y ) =
% 0.44/0.86 ordered_pair( Z, T ), ! U = pair_first( ordered_pair( X, Y ) ), U = X }.
% 0.44/0.86 substitution0:
% 0.44/0.86 X := X
% 0.44/0.86 Y := Y
% 0.44/0.86 Z := Z
% 0.44/0.86 T := T
% 0.44/0.86 U := U
% 0.44/0.86 end
% 0.44/0.86
% 0.44/0.86 eqrefl: (236) {G0,W13,D4,L2,V4,M2} { ! ordered_pair( X, Y ) = ordered_pair
% 0.44/0.86 ( Z, T ), pair_first( ordered_pair( Z, T ) ) = Z }.
% 0.44/0.86 parent0[1]: (228) {G1,W16,D4,L3,V5,M3} { ! ordered_pair( Z, T ) =
% 0.44/0.86 ordered_pair( X, Y ), ! U = pair_first( ordered_pair( X, Y ) ), U = X }.
% 0.44/0.86 substitution0:
% 0.44/0.86 X := Z
% 0.44/0.86 Y := T
% 0.44/0.86 Z := X
% 0.44/0.86 T := Y
% 0.44/0.86 U := pair_first( ordered_pair( Z, T ) )
% 0.44/0.86 end
% 0.44/0.86
% 0.44/0.86 eqswap: (237) {G0,W13,D4,L2,V4,M2} { ! ordered_pair( Z, T ) = ordered_pair
% 0.44/0.86 ( X, Y ), pair_first( ordered_pair( Z, T ) ) = Z }.
% 0.44/0.86 parent0[0]: (236) {G0,W13,D4,L2,V4,M2} { ! ordered_pair( X, Y ) =
% 0.44/0.86 ordered_pair( Z, T ), pair_first( ordered_pair( Z, T ) ) = Z }.
% 0.44/0.86 substitution0:
% 0.44/0.86 X := X
% 0.44/0.86 Y := Y
% 0.44/0.86 Z := Z
% 0.44/0.86 T := T
% 0.44/0.86 end
% 0.44/0.86
% 0.44/0.86 subsumption: (24) {G2,W13,D4,L2,V4,M2} Q(22) { ! ordered_pair( X, Y ) =
% 0.44/0.86 ordered_pair( Z, T ), pair_first( ordered_pair( X, Y ) ) ==> X }.
% 0.44/0.86 parent0: (237) {G0,W13,D4,L2,V4,M2} { ! ordered_pair( Z, T ) =
% 0.44/0.86 ordered_pair( X, Y ), pair_first( ordered_pair( Z, T ) ) = Z }.
% 0.44/0.86 substitution0:
% 0.44/0.86 X := Z
% 0.44/0.86 Y := T
% 0.44/0.86 Z := X
% 0.44/0.86 T := Y
% 0.44/0.86 end
% 0.44/0.86 permutation0:
% 0.44/0.86 0 ==> 0
% 0.44/0.86 1 ==> 1
% 0.44/0.86 end
% 0.44/0.86
% 0.44/0.86 eqswap: (243) {G2,W13,D4,L2,V4,M2} { ! ordered_pair( Z, T ) = ordered_pair
% 0.44/0.86 ( X, Y ), pair_first( ordered_pair( X, Y ) ) ==> X }.
% 0.44/0.86 parent0[0]: (24) {G2,W13,D4,L2,V4,M2} Q(22) { ! ordered_pair( X, Y ) =
% 0.44/0.86 ordered_pair( Z, T ), pair_first( ordered_pair( X, Y ) ) ==> X }.
% 0.44/0.86 substitution0:
% 0.44/0.86 X := X
% 0.44/0.86 Y := Y
% 0.44/0.86 Z := Z
% 0.44/0.86 T := T
% 0.44/0.86 end
% 0.44/0.86
% 0.44/0.86 eqrefl: (246) {G0,W6,D4,L1,V2,M1} { pair_first( ordered_pair( X, Y ) ) ==>
% 0.44/0.86 X }.
% 0.44/0.86 parent0[0]: (243) {G2,W13,D4,L2,V4,M2} { ! ordered_pair( Z, T ) =
% 0.44/0.86 ordered_pair( X, Y ), pair_first( ordered_pair( X, Y ) ) ==> X }.
% 0.44/0.86 substitution0:
% 0.44/0.86 X := X
% 0.44/0.86 Y := Y
% 0.44/0.86 Z := X
% 0.44/0.86 T := Y
% 0.44/0.86 end
% 0.44/0.86
% 0.44/0.86 subsumption: (25) {G3,W6,D4,L1,V2,M1} Q(24) { pair_first( ordered_pair( X,
% 0.44/0.86 Y ) ) ==> X }.
% 0.44/0.86 parent0: (246) {G0,W6,D4,L1,V2,M1} { pair_first( ordered_pair( X, Y ) )
% 0.44/0.86 ==> X }.
% 0.44/0.86 substitution0:
% 0.44/0.86 X := X
% 0.44/0.86 Y := Y
% 0.44/0.86 end
% 0.44/0.86 permutation0:
% 0.44/0.86 0 ==> 0
% 0.44/0.86 end
% 0.44/0.86
% 0.44/0.86 eqswap: (248) {G0,W17,D3,L4,V6,M4} { ! pair_second( Y ) = X, ! Y =
% 0.44/0.86 ordered_pair( Z, T ), ! Y = ordered_pair( U, W ), X = W }.
% 0.44/0.86 parent0[1]: (16) {G0,W17,D3,L4,V6,M4} I { ! X = ordered_pair( Y, Z ), ! T =
% 0.44/0.86 pair_second( X ), ! X = ordered_pair( W, U ), T = U }.
% 0.44/0.86 substitution0:
% 0.44/0.86 X := Y
% 0.44/0.86 Y := Z
% 0.44/0.86 Z := T
% 0.44/0.86 T := X
% 0.44/0.86 U := W
% 0.44/0.86 W := U
% 0.44/0.86 end
% 0.44/0.86
% 0.44/0.86 eqrefl: (261) {G0,W16,D4,L3,V5,M3} { ! pair_second( ordered_pair( X, Y ) )
% 0.44/0.86 = Z, ! ordered_pair( X, Y ) = ordered_pair( T, U ), Z = Y }.
% 0.44/0.86 parent0[2]: (248) {G0,W17,D3,L4,V6,M4} { ! pair_second( Y ) = X, ! Y =
% 0.44/0.86 ordered_pair( Z, T ), ! Y = ordered_pair( U, W ), X = W }.
% 0.44/0.86 substitution0:
% 0.44/0.86 X := Z
% 0.44/0.86 Y := ordered_pair( X, Y )
% 0.44/0.86 Z := T
% 0.44/0.86 T := U
% 0.44/0.86 U := X
% 0.44/0.86 W := Y
% 0.44/0.86 end
% 0.44/0.86
% 0.44/0.86 eqswap: (262) {G0,W16,D4,L3,V5,M3} { ! Z = pair_second( ordered_pair( X, Y
% 0.44/0.86 ) ), ! ordered_pair( X, Y ) = ordered_pair( T, U ), Z = Y }.
% 0.44/0.86 parent0[0]: (261) {G0,W16,D4,L3,V5,M3} { ! pair_second( ordered_pair( X, Y
% 0.44/0.86 ) ) = Z, ! ordered_pair( X, Y ) = ordered_pair( T, U ), Z = Y }.
% 0.44/0.86 substitution0:
% 0.44/0.86 X := X
% 0.44/0.86 Y := Y
% 0.44/0.86 Z := Z
% 0.44/0.86 T := T
% 0.44/0.86 U := U
% 0.44/0.86 end
% 0.44/0.86
% 0.44/0.86 subsumption: (31) {G1,W16,D4,L3,V5,M3} Q(16) { ! ordered_pair( X, Y ) =
% 0.44/0.86 ordered_pair( Z, T ), ! U = pair_second( ordered_pair( X, Y ) ), U = Y
% 0.44/0.86 }.
% 0.44/0.86 parent0: (262) {G0,W16,D4,L3,V5,M3} { ! Z = pair_second( ordered_pair( X,
% 0.44/0.86 Y ) ), ! ordered_pair( X, Y ) = ordered_pair( T, U ), Z = Y }.
% 0.44/0.86 substitution0:
% 0.44/0.86 X := X
% 0.44/0.86 Y := Y
% 0.44/0.86 Z := U
% 0.44/0.86 T := Z
% 0.44/0.86 U := T
% 0.44/0.86 end
% 0.44/0.86 permutation0:
% 0.44/0.86 0 ==> 1
% 0.44/0.86 1 ==> 0
% 0.44/0.86 2 ==> 2
% 0.44/0.86 end
% 0.44/0.86
% 0.44/0.86 eqswap: (286) {G1,W16,D4,L3,V5,M3} { ! ordered_pair( Z, T ) = ordered_pair
% 0.44/0.86 ( X, Y ), ! U = pair_second( ordered_pair( X, Y ) ), U = Y }.
% 0.44/0.86 parent0[0]: (31) {G1,W16,D4,L3,V5,M3} Q(16) { ! ordered_pair( X, Y ) =
% 0.44/0.86 ordered_pair( Z, T ), ! U = pair_second( ordered_pair( X, Y ) ), U = Y
% 0.44/0.86 }.
% 0.44/0.86 substitution0:
% 0.44/0.86 X := X
% 0.44/0.86 Y := Y
% 0.44/0.86 Z := Z
% 0.44/0.86 T := T
% 0.44/0.86 U := U
% 0.44/0.86 end
% 0.44/0.86
% 0.44/0.86 eqrefl: (294) {G0,W13,D4,L2,V4,M2} { ! ordered_pair( X, Y ) = ordered_pair
% 0.44/0.86 ( Z, T ), pair_second( ordered_pair( Z, T ) ) = T }.
% 0.44/0.86 parent0[1]: (286) {G1,W16,D4,L3,V5,M3} { ! ordered_pair( Z, T ) =
% 0.44/0.86 ordered_pair( X, Y ), ! U = pair_second( ordered_pair( X, Y ) ), U = Y
% 0.44/0.86 }.
% 0.44/0.86 substitution0:
% 0.44/0.86 X := Z
% 0.44/0.86 Y := T
% 0.44/0.86 Z := X
% 0.44/0.86 T := Y
% 0.44/0.86 U := pair_second( ordered_pair( Z, T ) )
% 0.44/0.86 end
% 0.44/0.86
% 0.44/0.86 eqswap: (295) {G0,W13,D4,L2,V4,M2} { ! ordered_pair( Z, T ) = ordered_pair
% 0.44/0.86 ( X, Y ), pair_second( ordered_pair( Z, T ) ) = T }.
% 0.44/0.86 parent0[0]: (294) {G0,W13,D4,L2,V4,M2} { ! ordered_pair( X, Y ) =
% 0.44/0.86 ordered_pair( Z, T ), pair_second( ordered_pair( Z, T ) ) = T }.
% 0.44/0.86 substitution0:
% 0.44/0.86 X := X
% 0.44/0.86 Y := Y
% 0.44/0.86 Z := Z
% 0.44/0.86 T := T
% 0.44/0.86 end
% 0.44/0.86
% 0.44/0.86 subsumption: (33) {G2,W13,D4,L2,V4,M2} Q(31) { ! ordered_pair( X, Y ) =
% 0.44/0.86 ordered_pair( Z, T ), pair_second( ordered_pair( X, Y ) ) ==> Y }.
% 0.44/0.86 parent0: (295) {G0,W13,D4,L2,V4,M2} { ! ordered_pair( Z, T ) =
% 0.44/0.86 ordered_pair( X, Y ), pair_second( ordered_pair( Z, T ) ) = T }.
% 0.44/0.86 substitution0:
% 0.44/0.86 X := Z
% 0.44/0.86 Y := T
% 0.44/0.86 Z := X
% 0.44/0.86 T := Y
% 0.44/0.86 end
% 0.44/0.86 permutation0:
% 0.44/0.86 0 ==> 0
% 0.44/0.86 1 ==> 1
% 0.44/0.86 end
% 0.44/0.86
% 0.44/0.86 eqswap: (301) {G2,W13,D4,L2,V4,M2} { ! ordered_pair( Z, T ) = ordered_pair
% 0.44/0.86 ( X, Y ), pair_second( ordered_pair( X, Y ) ) ==> Y }.
% 0.44/0.86 parent0[0]: (33) {G2,W13,D4,L2,V4,M2} Q(31) { ! ordered_pair( X, Y ) =
% 0.44/0.86 ordered_pair( Z, T ), pair_second( ordered_pair( X, Y ) ) ==> Y }.
% 0.44/0.86 substitution0:
% 0.44/0.86 X := X
% 0.44/0.86 Y := Y
% 0.44/0.86 Z := Z
% 0.44/0.86 T := T
% 0.44/0.86 end
% 0.44/0.86
% 0.44/0.86 eqrefl: (304) {G0,W6,D4,L1,V2,M1} { pair_second( ordered_pair( X, Y ) )
% 0.44/0.86 ==> Y }.
% 0.44/0.86 parent0[0]: (301) {G2,W13,D4,L2,V4,M2} { ! ordered_pair( Z, T ) =
% 0.44/0.86 ordered_pair( X, Y ), pair_second( ordered_pair( X, Y ) ) ==> Y }.
% 0.44/0.86 substitution0:
% 0.44/0.86 X := X
% 0.44/0.86 Y := Y
% 0.44/0.86 Z := X
% 0.44/0.86 T := Y
% 0.44/0.86 end
% 0.44/0.86
% 0.44/0.86 subsumption: (34) {G3,W6,D4,L1,V2,M1} Q(33) { pair_second( ordered_pair( X
% 0.44/0.86 , Y ) ) ==> Y }.
% 0.44/0.86 parent0: (304) {G0,W6,D4,L1,V2,M1} { pair_second( ordered_pair( X, Y ) )
% 0.44/0.86 ==> Y }.
% 0.44/0.86 substitution0:
% 0.44/0.86 X := X
% 0.44/0.86 Y := Y
% 0.44/0.86 end
% 0.44/0.86 permutation0:
% 0.44/0.86 0 ==> 0
% 0.44/0.86 end
% 0.44/0.86
% 0.44/0.86 paramod: (311) {G1,W9,D4,L2,V0,M2} { ! skol4 ==> skol4, ! pair_second(
% 0.44/0.86 ordered_pair( skol4, skol7 ) ) ==> skol7 }.
% 0.44/0.86 parent0[0]: (25) {G3,W6,D4,L1,V2,M1} Q(24) { pair_first( ordered_pair( X, Y
% 0.44/0.86 ) ) ==> X }.
% 0.44/0.86 parent1[0; 2]: (12) {G0,W12,D4,L2,V0,M2} I { ! pair_first( ordered_pair(
% 0.44/0.86 skol4, skol7 ) ) ==> skol4, ! pair_second( ordered_pair( skol4, skol7 ) )
% 0.44/0.86 ==> skol7 }.
% 0.44/0.86 substitution0:
% 0.44/0.86 X := skol4
% 0.44/0.86 Y := skol7
% 0.44/0.86 end
% 0.44/0.86 substitution1:
% 0.44/0.86 end
% 0.44/0.86
% 0.44/0.86 eqrefl: (312) {G0,W6,D4,L1,V0,M1} { ! pair_second( ordered_pair( skol4,
% 0.44/0.86 skol7 ) ) ==> skol7 }.
% 0.44/0.86 parent0[0]: (311) {G1,W9,D4,L2,V0,M2} { ! skol4 ==> skol4, ! pair_second(
% 0.44/0.86 ordered_pair( skol4, skol7 ) ) ==> skol7 }.
% 0.44/0.86 substitution0:
% 0.44/0.86 end
% 0.44/0.86
% 0.44/0.86 paramod: (313) {G1,W3,D2,L1,V0,M1} { ! skol7 ==> skol7 }.
% 0.44/0.86 parent0[0]: (34) {G3,W6,D4,L1,V2,M1} Q(33) { pair_second( ordered_pair( X,
% 0.44/0.86 Y ) ) ==> Y }.
% 0.44/0.86 parent1[0; 2]: (312) {G0,W6,D4,L1,V0,M1} { ! pair_second( ordered_pair(
% 0.44/0.86 skol4, skol7 ) ) ==> skol7 }.
% 0.44/0.86 substitution0:
% 0.44/0.86 X := skol4
% 0.44/0.86 Y := skol7
% 0.44/0.86 end
% 0.44/0.86 substitution1:
% 0.44/0.86 end
% 0.44/0.86
% 0.44/0.86 eqrefl: (314) {G0,W0,D0,L0,V0,M0} { }.
% 0.44/0.86 parent0[0]: (313) {G1,W3,D2,L1,V0,M1} { ! skol7 ==> skol7 }.
% 0.44/0.86 substitution0:
% 0.44/0.86 end
% 0.44/0.86
% 0.44/0.86 subsumption: (69) {G4,W0,D0,L0,V0,M0} S(12);d(25);q;d(34);q { }.
% 0.44/0.86 parent0: (314) {G0,W0,D0,L0,V0,M0} { }.
% 0.44/0.86 substitution0:
% 0.44/0.86 end
% 0.44/0.86 permutation0:
% 0.44/0.86 end
% 0.44/0.86
% 0.44/0.86 Proof check complete!
% 0.44/0.86
% 0.44/0.86 Memory use:
% 0.44/0.86
% 0.44/0.86 space for terms: 1105
% 0.44/0.86 space for clauses: 3643
% 0.44/0.86
% 0.44/0.86
% 0.44/0.86 clauses generated: 230
% 0.44/0.86 clauses kept: 70
% 0.44/0.86 clauses selected: 25
% 0.44/0.86 clauses deleted: 1
% 0.44/0.86 clauses inuse deleted: 0
% 0.44/0.86
% 0.44/0.86 subsentry: 4349
% 0.44/0.86 literals s-matched: 1636
% 0.44/0.86 literals matched: 1636
% 0.44/0.86 full subsumption: 274
% 0.44/0.86
% 0.44/0.86 checksum: 816653440
% 0.44/0.86
% 0.44/0.86
% 0.44/0.86 Bliksem ended
%------------------------------------------------------------------------------