TSTP Solution File: SET962+1 by Bliksem---1.12
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%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SET962+1 : TPTP v8.1.0. Bugfixed v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n028.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 22:53:38 EDT 2022
% Result : Theorem 0.71s 1.11s
% Output : Refutation 0.71s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SET962+1 : TPTP v8.1.0. Bugfixed v4.0.0.
% 0.07/0.13 % Command : bliksem %s
% 0.13/0.35 % Computer : n028.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % DateTime : Sat Jul 9 18:46:26 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.71/1.11 *** allocated 10000 integers for termspace/termends
% 0.71/1.11 *** allocated 10000 integers for clauses
% 0.71/1.11 *** allocated 10000 integers for justifications
% 0.71/1.11 Bliksem 1.12
% 0.71/1.11
% 0.71/1.11
% 0.71/1.11 Automatic Strategy Selection
% 0.71/1.11
% 0.71/1.11
% 0.71/1.11 Clauses:
% 0.71/1.11
% 0.71/1.11 { ! in( X, Y ), ! in( Y, X ) }.
% 0.71/1.11 { unordered_pair( X, Y ) = unordered_pair( Y, X ) }.
% 0.71/1.11 { ordered_pair( X, Y ) = unordered_pair( unordered_pair( X, Y ), singleton
% 0.71/1.11 ( X ) ) }.
% 0.71/1.11 { ! empty( ordered_pair( X, Y ) ) }.
% 0.71/1.11 { ! in( ordered_pair( X, Y ), cartesian_product2( Z, T ) ), in( X, Z ) }.
% 0.71/1.11 { ! in( ordered_pair( X, Y ), cartesian_product2( Z, T ) ), in( Y, T ) }.
% 0.71/1.11 { ! in( X, Z ), ! in( Y, T ), in( ordered_pair( X, Y ), cartesian_product2
% 0.71/1.11 ( Z, T ) ) }.
% 0.71/1.11 { empty( skol1 ) }.
% 0.71/1.11 { ! empty( skol2 ) }.
% 0.71/1.11 { cartesian_product2( skol3, skol3 ) = cartesian_product2( skol5, skol5 ) }
% 0.71/1.11 .
% 0.71/1.11 { ! skol3 = skol5 }.
% 0.71/1.11 { alpha1( X, Y, skol4( X, Y ) ), in( skol4( X, Y ), Y ), X = Y }.
% 0.71/1.11 { alpha1( X, Y, skol4( X, Y ) ), ! in( skol4( X, Y ), X ), X = Y }.
% 0.71/1.11 { ! alpha1( X, Y, Z ), in( Z, X ) }.
% 0.71/1.11 { ! alpha1( X, Y, Z ), ! in( Z, Y ) }.
% 0.71/1.11 { ! in( Z, X ), in( Z, Y ), alpha1( X, Y, Z ) }.
% 0.71/1.11
% 0.71/1.11 percentage equality = 0.206897, percentage horn = 0.812500
% 0.71/1.11 This is a problem with some equality
% 0.71/1.11
% 0.71/1.11
% 0.71/1.11
% 0.71/1.11 Options Used:
% 0.71/1.11
% 0.71/1.11 useres = 1
% 0.71/1.11 useparamod = 1
% 0.71/1.11 useeqrefl = 1
% 0.71/1.11 useeqfact = 1
% 0.71/1.11 usefactor = 1
% 0.71/1.11 usesimpsplitting = 0
% 0.71/1.11 usesimpdemod = 5
% 0.71/1.11 usesimpres = 3
% 0.71/1.11
% 0.71/1.11 resimpinuse = 1000
% 0.71/1.11 resimpclauses = 20000
% 0.71/1.11 substype = eqrewr
% 0.71/1.11 backwardsubs = 1
% 0.71/1.11 selectoldest = 5
% 0.71/1.11
% 0.71/1.11 litorderings [0] = split
% 0.71/1.11 litorderings [1] = extend the termordering, first sorting on arguments
% 0.71/1.11
% 0.71/1.11 termordering = kbo
% 0.71/1.11
% 0.71/1.11 litapriori = 0
% 0.71/1.11 termapriori = 1
% 0.71/1.11 litaposteriori = 0
% 0.71/1.11 termaposteriori = 0
% 0.71/1.11 demodaposteriori = 0
% 0.71/1.11 ordereqreflfact = 0
% 0.71/1.11
% 0.71/1.11 litselect = negord
% 0.71/1.11
% 0.71/1.11 maxweight = 15
% 0.71/1.11 maxdepth = 30000
% 0.71/1.11 maxlength = 115
% 0.71/1.11 maxnrvars = 195
% 0.71/1.11 excuselevel = 1
% 0.71/1.11 increasemaxweight = 1
% 0.71/1.11
% 0.71/1.11 maxselected = 10000000
% 0.71/1.11 maxnrclauses = 10000000
% 0.71/1.11
% 0.71/1.11 showgenerated = 0
% 0.71/1.11 showkept = 0
% 0.71/1.11 showselected = 0
% 0.71/1.11 showdeleted = 0
% 0.71/1.11 showresimp = 1
% 0.71/1.11 showstatus = 2000
% 0.71/1.11
% 0.71/1.11 prologoutput = 0
% 0.71/1.11 nrgoals = 5000000
% 0.71/1.11 totalproof = 1
% 0.71/1.11
% 0.71/1.11 Symbols occurring in the translation:
% 0.71/1.11
% 0.71/1.11 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.71/1.11 . [1, 2] (w:1, o:21, a:1, s:1, b:0),
% 0.71/1.11 ! [4, 1] (w:0, o:14, a:1, s:1, b:0),
% 0.71/1.11 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.71/1.11 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.71/1.11 in [37, 2] (w:1, o:45, a:1, s:1, b:0),
% 0.71/1.11 unordered_pair [38, 2] (w:1, o:46, a:1, s:1, b:0),
% 0.71/1.11 ordered_pair [39, 2] (w:1, o:47, a:1, s:1, b:0),
% 0.71/1.11 singleton [40, 1] (w:1, o:19, a:1, s:1, b:0),
% 0.71/1.11 empty [41, 1] (w:1, o:20, a:1, s:1, b:0),
% 0.71/1.11 cartesian_product2 [44, 2] (w:1, o:48, a:1, s:1, b:0),
% 0.71/1.11 alpha1 [45, 3] (w:1, o:50, a:1, s:1, b:1),
% 0.71/1.11 skol1 [46, 0] (w:1, o:10, a:1, s:1, b:1),
% 0.71/1.11 skol2 [47, 0] (w:1, o:11, a:1, s:1, b:1),
% 0.71/1.11 skol3 [48, 0] (w:1, o:12, a:1, s:1, b:1),
% 0.71/1.11 skol4 [49, 2] (w:1, o:49, a:1, s:1, b:1),
% 0.71/1.11 skol5 [50, 0] (w:1, o:13, a:1, s:1, b:1).
% 0.71/1.11
% 0.71/1.11
% 0.71/1.11 Starting Search:
% 0.71/1.11
% 0.71/1.11 *** allocated 15000 integers for clauses
% 0.71/1.11 *** allocated 22500 integers for clauses
% 0.71/1.11 *** allocated 33750 integers for clauses
% 0.71/1.11
% 0.71/1.11 Bliksems!, er is een bewijs:
% 0.71/1.11 % SZS status Theorem
% 0.71/1.11 % SZS output start Refutation
% 0.71/1.11
% 0.71/1.11 (5) {G0,W10,D3,L2,V4,M2} I { ! in( ordered_pair( X, Y ), cartesian_product2
% 0.71/1.11 ( Z, T ) ), in( Y, T ) }.
% 0.71/1.11 (6) {G0,W13,D3,L3,V4,M3} I { ! in( X, Z ), ! in( Y, T ), in( ordered_pair(
% 0.71/1.11 X, Y ), cartesian_product2( Z, T ) ) }.
% 0.71/1.11 (9) {G0,W7,D3,L1,V0,M1} I { cartesian_product2( skol5, skol5 ) ==>
% 0.71/1.11 cartesian_product2( skol3, skol3 ) }.
% 0.71/1.11 (10) {G0,W3,D2,L1,V0,M1} I { ! skol5 ==> skol3 }.
% 0.71/1.11 (11) {G0,W14,D3,L3,V2,M3} I { alpha1( X, Y, skol4( X, Y ) ), in( skol4( X,
% 0.71/1.11 Y ), Y ), X = Y }.
% 0.71/1.11 (12) {G0,W14,D3,L3,V2,M3} I { alpha1( X, Y, skol4( X, Y ) ), ! in( skol4( X
% 0.71/1.11 , Y ), X ), X = Y }.
% 0.71/1.11 (13) {G0,W7,D2,L2,V3,M2} I { ! alpha1( X, Y, Z ), in( Z, X ) }.
% 0.71/1.11 (14) {G0,W7,D2,L2,V3,M2} I { ! alpha1( X, Y, Z ), ! in( Z, Y ) }.
% 0.71/1.11 (17) {G1,W10,D3,L2,V2,M2} F(6) { ! in( X, Y ), in( ordered_pair( X, X ),
% 0.71/1.11 cartesian_product2( Y, Y ) ) }.
% 0.71/1.11 (71) {G1,W10,D3,L2,V2,M2} P(9,5) { ! in( ordered_pair( X, Y ),
% 0.71/1.11 cartesian_product2( skol3, skol3 ) ), in( Y, skol5 ) }.
% 0.71/1.11 (320) {G2,W6,D2,L2,V1,M2} R(71,17) { in( X, skol5 ), ! in( X, skol3 ) }.
% 0.71/1.11 (340) {G3,W7,D2,L2,V2,M2} R(320,13) { in( X, skol5 ), ! alpha1( skol3, Y, X
% 0.71/1.11 ) }.
% 0.71/1.11 (352) {G4,W13,D3,L3,V1,M3} R(340,11) { in( skol4( skol3, X ), skol5 ), in(
% 0.71/1.11 skol4( skol3, X ), X ), skol3 = X }.
% 0.71/1.11 (358) {G4,W8,D2,L2,V3,M2} R(340,14) { ! alpha1( skol3, X, Y ), ! alpha1( Z
% 0.71/1.11 , skol5, Y ) }.
% 0.71/1.11 (359) {G5,W4,D2,L1,V1,M1} F(358) { ! alpha1( skol3, skol5, X ) }.
% 0.71/1.11 (360) {G5,W8,D3,L2,V0,M2} F(352) { in( skol4( skol3, skol5 ), skol5 ),
% 0.71/1.11 skol5 ==> skol3 }.
% 0.71/1.11 (361) {G6,W8,D3,L2,V0,M2} R(359,12) { ! in( skol4( skol3, skol5 ), skol3 )
% 0.71/1.11 , skol5 ==> skol3 }.
% 0.71/1.11 (407) {G7,W5,D3,L1,V0,M1} S(361);r(10) { ! in( skol4( skol3, skol5 ), skol3
% 0.71/1.11 ) }.
% 0.71/1.11 (415) {G8,W9,D4,L1,V2,M1} R(407,5) { ! in( ordered_pair( X, skol4( skol3,
% 0.71/1.11 skol5 ) ), cartesian_product2( Y, skol3 ) ) }.
% 0.71/1.11 (421) {G6,W5,D3,L1,V0,M1} S(360);r(10) { in( skol4( skol3, skol5 ), skol5 )
% 0.71/1.11 }.
% 0.71/1.11 (433) {G9,W0,D0,L0,V0,M0} R(421,17);d(9);r(415) { }.
% 0.71/1.11
% 0.71/1.11
% 0.71/1.11 % SZS output end Refutation
% 0.71/1.11 found a proof!
% 0.71/1.11
% 0.71/1.11
% 0.71/1.11 Unprocessed initial clauses:
% 0.71/1.11
% 0.71/1.11 (435) {G0,W6,D2,L2,V2,M2} { ! in( X, Y ), ! in( Y, X ) }.
% 0.71/1.11 (436) {G0,W7,D3,L1,V2,M1} { unordered_pair( X, Y ) = unordered_pair( Y, X
% 0.71/1.11 ) }.
% 0.71/1.11 (437) {G0,W10,D4,L1,V2,M1} { ordered_pair( X, Y ) = unordered_pair(
% 0.71/1.11 unordered_pair( X, Y ), singleton( X ) ) }.
% 0.71/1.11 (438) {G0,W4,D3,L1,V2,M1} { ! empty( ordered_pair( X, Y ) ) }.
% 0.71/1.11 (439) {G0,W10,D3,L2,V4,M2} { ! in( ordered_pair( X, Y ),
% 0.71/1.11 cartesian_product2( Z, T ) ), in( X, Z ) }.
% 0.71/1.11 (440) {G0,W10,D3,L2,V4,M2} { ! in( ordered_pair( X, Y ),
% 0.71/1.11 cartesian_product2( Z, T ) ), in( Y, T ) }.
% 0.71/1.11 (441) {G0,W13,D3,L3,V4,M3} { ! in( X, Z ), ! in( Y, T ), in( ordered_pair
% 0.71/1.11 ( X, Y ), cartesian_product2( Z, T ) ) }.
% 0.71/1.11 (442) {G0,W2,D2,L1,V0,M1} { empty( skol1 ) }.
% 0.71/1.11 (443) {G0,W2,D2,L1,V0,M1} { ! empty( skol2 ) }.
% 0.71/1.11 (444) {G0,W7,D3,L1,V0,M1} { cartesian_product2( skol3, skol3 ) =
% 0.71/1.11 cartesian_product2( skol5, skol5 ) }.
% 0.71/1.11 (445) {G0,W3,D2,L1,V0,M1} { ! skol3 = skol5 }.
% 0.71/1.11 (446) {G0,W14,D3,L3,V2,M3} { alpha1( X, Y, skol4( X, Y ) ), in( skol4( X,
% 0.71/1.11 Y ), Y ), X = Y }.
% 0.71/1.11 (447) {G0,W14,D3,L3,V2,M3} { alpha1( X, Y, skol4( X, Y ) ), ! in( skol4( X
% 0.71/1.11 , Y ), X ), X = Y }.
% 0.71/1.11 (448) {G0,W7,D2,L2,V3,M2} { ! alpha1( X, Y, Z ), in( Z, X ) }.
% 0.71/1.11 (449) {G0,W7,D2,L2,V3,M2} { ! alpha1( X, Y, Z ), ! in( Z, Y ) }.
% 0.71/1.11 (450) {G0,W10,D2,L3,V3,M3} { ! in( Z, X ), in( Z, Y ), alpha1( X, Y, Z )
% 0.71/1.11 }.
% 0.71/1.11
% 0.71/1.11
% 0.71/1.11 Total Proof:
% 0.71/1.11
% 0.71/1.11 subsumption: (5) {G0,W10,D3,L2,V4,M2} I { ! in( ordered_pair( X, Y ),
% 0.71/1.11 cartesian_product2( Z, T ) ), in( Y, T ) }.
% 0.71/1.11 parent0: (440) {G0,W10,D3,L2,V4,M2} { ! in( ordered_pair( X, Y ),
% 0.71/1.11 cartesian_product2( Z, T ) ), in( Y, T ) }.
% 0.71/1.11 substitution0:
% 0.71/1.11 X := X
% 0.71/1.11 Y := Y
% 0.71/1.11 Z := Z
% 0.71/1.11 T := T
% 0.71/1.11 end
% 0.71/1.11 permutation0:
% 0.71/1.11 0 ==> 0
% 0.71/1.11 1 ==> 1
% 0.71/1.11 end
% 0.71/1.11
% 0.71/1.11 subsumption: (6) {G0,W13,D3,L3,V4,M3} I { ! in( X, Z ), ! in( Y, T ), in(
% 0.71/1.11 ordered_pair( X, Y ), cartesian_product2( Z, T ) ) }.
% 0.71/1.11 parent0: (441) {G0,W13,D3,L3,V4,M3} { ! in( X, Z ), ! in( Y, T ), in(
% 0.71/1.11 ordered_pair( X, Y ), cartesian_product2( Z, T ) ) }.
% 0.71/1.11 substitution0:
% 0.71/1.11 X := X
% 0.71/1.11 Y := Y
% 0.71/1.11 Z := Z
% 0.71/1.11 T := T
% 0.71/1.11 end
% 0.71/1.11 permutation0:
% 0.71/1.11 0 ==> 0
% 0.71/1.11 1 ==> 1
% 0.71/1.11 2 ==> 2
% 0.71/1.11 end
% 0.71/1.11
% 0.71/1.11 eqswap: (459) {G0,W7,D3,L1,V0,M1} { cartesian_product2( skol5, skol5 ) =
% 0.71/1.11 cartesian_product2( skol3, skol3 ) }.
% 0.71/1.11 parent0[0]: (444) {G0,W7,D3,L1,V0,M1} { cartesian_product2( skol3, skol3 )
% 0.71/1.11 = cartesian_product2( skol5, skol5 ) }.
% 0.71/1.11 substitution0:
% 0.71/1.11 end
% 0.71/1.11
% 0.71/1.11 subsumption: (9) {G0,W7,D3,L1,V0,M1} I { cartesian_product2( skol5, skol5 )
% 0.71/1.11 ==> cartesian_product2( skol3, skol3 ) }.
% 0.71/1.11 parent0: (459) {G0,W7,D3,L1,V0,M1} { cartesian_product2( skol5, skol5 ) =
% 0.71/1.11 cartesian_product2( skol3, skol3 ) }.
% 0.71/1.11 substitution0:
% 0.71/1.11 end
% 0.71/1.11 permutation0:
% 0.71/1.11 0 ==> 0
% 0.71/1.11 end
% 0.71/1.11
% 0.71/1.11 eqswap: (464) {G0,W3,D2,L1,V0,M1} { ! skol5 = skol3 }.
% 0.71/1.11 parent0[0]: (445) {G0,W3,D2,L1,V0,M1} { ! skol3 = skol5 }.
% 0.71/1.11 substitution0:
% 0.71/1.11 end
% 0.71/1.11
% 0.71/1.11 subsumption: (10) {G0,W3,D2,L1,V0,M1} I { ! skol5 ==> skol3 }.
% 0.71/1.11 parent0: (464) {G0,W3,D2,L1,V0,M1} { ! skol5 = skol3 }.
% 0.71/1.11 substitution0:
% 0.71/1.11 end
% 0.71/1.11 permutation0:
% 0.71/1.11 0 ==> 0
% 0.71/1.11 end
% 0.71/1.11
% 0.71/1.11 subsumption: (11) {G0,W14,D3,L3,V2,M3} I { alpha1( X, Y, skol4( X, Y ) ),
% 0.71/1.11 in( skol4( X, Y ), Y ), X = Y }.
% 0.71/1.11 parent0: (446) {G0,W14,D3,L3,V2,M3} { alpha1( X, Y, skol4( X, Y ) ), in(
% 0.71/1.11 skol4( X, Y ), Y ), X = Y }.
% 0.71/1.11 substitution0:
% 0.71/1.11 X := X
% 0.71/1.11 Y := Y
% 0.71/1.11 end
% 0.71/1.11 permutation0:
% 0.71/1.11 0 ==> 0
% 0.71/1.11 1 ==> 1
% 0.71/1.11 2 ==> 2
% 0.71/1.11 end
% 0.71/1.11
% 0.71/1.11 subsumption: (12) {G0,W14,D3,L3,V2,M3} I { alpha1( X, Y, skol4( X, Y ) ), !
% 0.71/1.11 in( skol4( X, Y ), X ), X = Y }.
% 0.71/1.11 parent0: (447) {G0,W14,D3,L3,V2,M3} { alpha1( X, Y, skol4( X, Y ) ), ! in
% 0.71/1.11 ( skol4( X, Y ), X ), X = Y }.
% 0.71/1.11 substitution0:
% 0.71/1.11 X := X
% 0.71/1.11 Y := Y
% 0.71/1.11 end
% 0.71/1.11 permutation0:
% 0.71/1.11 0 ==> 0
% 0.71/1.11 1 ==> 1
% 0.71/1.11 2 ==> 2
% 0.71/1.11 end
% 0.71/1.11
% 0.71/1.11 subsumption: (13) {G0,W7,D2,L2,V3,M2} I { ! alpha1( X, Y, Z ), in( Z, X )
% 0.71/1.11 }.
% 0.71/1.11 parent0: (448) {G0,W7,D2,L2,V3,M2} { ! alpha1( X, Y, Z ), in( Z, X ) }.
% 0.71/1.11 substitution0:
% 0.71/1.11 X := X
% 0.71/1.11 Y := Y
% 0.71/1.11 Z := Z
% 0.71/1.11 end
% 0.71/1.11 permutation0:
% 0.71/1.11 0 ==> 0
% 0.71/1.11 1 ==> 1
% 0.71/1.11 end
% 0.71/1.11
% 0.71/1.11 subsumption: (14) {G0,W7,D2,L2,V3,M2} I { ! alpha1( X, Y, Z ), ! in( Z, Y )
% 0.71/1.11 }.
% 0.71/1.11 parent0: (449) {G0,W7,D2,L2,V3,M2} { ! alpha1( X, Y, Z ), ! in( Z, Y ) }.
% 0.71/1.11 substitution0:
% 0.71/1.11 X := X
% 0.71/1.11 Y := Y
% 0.71/1.11 Z := Z
% 0.71/1.11 end
% 0.71/1.11 permutation0:
% 0.71/1.11 0 ==> 0
% 0.71/1.11 1 ==> 1
% 0.71/1.11 end
% 0.71/1.11
% 0.71/1.11 factor: (492) {G0,W10,D3,L2,V2,M2} { ! in( X, Y ), in( ordered_pair( X, X
% 0.71/1.11 ), cartesian_product2( Y, Y ) ) }.
% 0.71/1.11 parent0[0, 1]: (6) {G0,W13,D3,L3,V4,M3} I { ! in( X, Z ), ! in( Y, T ), in
% 0.71/1.11 ( ordered_pair( X, Y ), cartesian_product2( Z, T ) ) }.
% 0.71/1.11 substitution0:
% 0.71/1.11 X := X
% 0.71/1.11 Y := X
% 0.71/1.11 Z := Y
% 0.71/1.11 T := Y
% 0.71/1.11 end
% 0.71/1.11
% 0.71/1.11 subsumption: (17) {G1,W10,D3,L2,V2,M2} F(6) { ! in( X, Y ), in(
% 0.71/1.11 ordered_pair( X, X ), cartesian_product2( Y, Y ) ) }.
% 0.71/1.11 parent0: (492) {G0,W10,D3,L2,V2,M2} { ! in( X, Y ), in( ordered_pair( X, X
% 0.71/1.11 ), cartesian_product2( Y, Y ) ) }.
% 0.71/1.11 substitution0:
% 0.71/1.11 X := X
% 0.71/1.11 Y := Y
% 0.71/1.11 end
% 0.71/1.11 permutation0:
% 0.71/1.11 0 ==> 0
% 0.71/1.11 1 ==> 1
% 0.71/1.11 end
% 0.71/1.11
% 0.71/1.11 paramod: (494) {G1,W10,D3,L2,V2,M2} { ! in( ordered_pair( X, Y ),
% 0.71/1.11 cartesian_product2( skol3, skol3 ) ), in( Y, skol5 ) }.
% 0.71/1.11 parent0[0]: (9) {G0,W7,D3,L1,V0,M1} I { cartesian_product2( skol5, skol5 )
% 0.71/1.11 ==> cartesian_product2( skol3, skol3 ) }.
% 0.71/1.11 parent1[0; 5]: (5) {G0,W10,D3,L2,V4,M2} I { ! in( ordered_pair( X, Y ),
% 0.71/1.11 cartesian_product2( Z, T ) ), in( Y, T ) }.
% 0.71/1.11 substitution0:
% 0.71/1.11 end
% 0.71/1.11 substitution1:
% 0.71/1.11 X := X
% 0.71/1.11 Y := Y
% 0.71/1.11 Z := skol5
% 0.71/1.11 T := skol5
% 0.71/1.11 end
% 0.71/1.11
% 0.71/1.11 subsumption: (71) {G1,W10,D3,L2,V2,M2} P(9,5) { ! in( ordered_pair( X, Y )
% 0.71/1.11 , cartesian_product2( skol3, skol3 ) ), in( Y, skol5 ) }.
% 0.71/1.11 parent0: (494) {G1,W10,D3,L2,V2,M2} { ! in( ordered_pair( X, Y ),
% 0.71/1.11 cartesian_product2( skol3, skol3 ) ), in( Y, skol5 ) }.
% 0.71/1.11 substitution0:
% 0.71/1.11 X := X
% 0.71/1.11 Y := Y
% 0.71/1.11 end
% 0.71/1.11 permutation0:
% 0.71/1.11 0 ==> 0
% 0.71/1.11 1 ==> 1
% 0.71/1.11 end
% 0.71/1.11
% 0.71/1.11 resolution: (495) {G2,W6,D2,L2,V1,M2} { in( X, skol5 ), ! in( X, skol3 )
% 0.71/1.11 }.
% 0.71/1.11 parent0[0]: (71) {G1,W10,D3,L2,V2,M2} P(9,5) { ! in( ordered_pair( X, Y ),
% 0.71/1.11 cartesian_product2( skol3, skol3 ) ), in( Y, skol5 ) }.
% 0.71/1.11 parent1[1]: (17) {G1,W10,D3,L2,V2,M2} F(6) { ! in( X, Y ), in( ordered_pair
% 0.71/1.11 ( X, X ), cartesian_product2( Y, Y ) ) }.
% 0.71/1.11 substitution0:
% 0.71/1.11 X := X
% 0.71/1.11 Y := X
% 0.71/1.11 end
% 0.71/1.11 substitution1:
% 0.71/1.11 X := X
% 0.71/1.11 Y := skol3
% 0.71/1.11 end
% 0.71/1.11
% 0.71/1.11 subsumption: (320) {G2,W6,D2,L2,V1,M2} R(71,17) { in( X, skol5 ), ! in( X,
% 0.71/1.11 skol3 ) }.
% 0.71/1.11 parent0: (495) {G2,W6,D2,L2,V1,M2} { in( X, skol5 ), ! in( X, skol3 ) }.
% 0.71/1.11 substitution0:
% 0.71/1.11 X := X
% 0.71/1.11 end
% 0.71/1.11 permutation0:
% 0.71/1.11 0 ==> 0
% 0.71/1.11 1 ==> 1
% 0.71/1.11 end
% 0.71/1.11
% 0.71/1.11 resolution: (496) {G1,W7,D2,L2,V2,M2} { in( X, skol5 ), ! alpha1( skol3, Y
% 0.71/1.11 , X ) }.
% 0.71/1.11 parent0[1]: (320) {G2,W6,D2,L2,V1,M2} R(71,17) { in( X, skol5 ), ! in( X,
% 0.71/1.11 skol3 ) }.
% 0.71/1.11 parent1[1]: (13) {G0,W7,D2,L2,V3,M2} I { ! alpha1( X, Y, Z ), in( Z, X )
% 0.71/1.11 }.
% 0.71/1.11 substitution0:
% 0.71/1.11 X := X
% 0.71/1.11 end
% 0.71/1.11 substitution1:
% 0.71/1.11 X := skol3
% 0.71/1.11 Y := Y
% 0.71/1.11 Z := X
% 0.71/1.11 end
% 0.71/1.11
% 0.71/1.11 subsumption: (340) {G3,W7,D2,L2,V2,M2} R(320,13) { in( X, skol5 ), ! alpha1
% 0.71/1.11 ( skol3, Y, X ) }.
% 0.71/1.11 parent0: (496) {G1,W7,D2,L2,V2,M2} { in( X, skol5 ), ! alpha1( skol3, Y, X
% 0.71/1.11 ) }.
% 0.71/1.11 substitution0:
% 0.71/1.11 X := X
% 0.71/1.11 Y := Y
% 0.71/1.11 end
% 0.71/1.11 permutation0:
% 0.71/1.11 0 ==> 0
% 0.71/1.11 1 ==> 1
% 0.71/1.11 end
% 0.71/1.11
% 0.71/1.11 eqswap: (497) {G0,W14,D3,L3,V2,M3} { Y = X, alpha1( X, Y, skol4( X, Y ) )
% 0.71/1.11 , in( skol4( X, Y ), Y ) }.
% 0.71/1.11 parent0[2]: (11) {G0,W14,D3,L3,V2,M3} I { alpha1( X, Y, skol4( X, Y ) ), in
% 0.71/1.11 ( skol4( X, Y ), Y ), X = Y }.
% 0.71/1.11 substitution0:
% 0.71/1.11 X := X
% 0.71/1.11 Y := Y
% 0.71/1.11 end
% 0.71/1.11
% 0.71/1.11 resolution: (498) {G1,W13,D3,L3,V1,M3} { in( skol4( skol3, X ), skol5 ), X
% 0.71/1.11 = skol3, in( skol4( skol3, X ), X ) }.
% 0.71/1.11 parent0[1]: (340) {G3,W7,D2,L2,V2,M2} R(320,13) { in( X, skol5 ), ! alpha1
% 0.71/1.11 ( skol3, Y, X ) }.
% 0.71/1.11 parent1[1]: (497) {G0,W14,D3,L3,V2,M3} { Y = X, alpha1( X, Y, skol4( X, Y
% 0.71/1.11 ) ), in( skol4( X, Y ), Y ) }.
% 0.71/1.11 substitution0:
% 0.71/1.11 X := skol4( skol3, X )
% 0.71/1.11 Y := X
% 0.71/1.11 end
% 0.71/1.11 substitution1:
% 0.71/1.11 X := skol3
% 0.71/1.11 Y := X
% 0.71/1.11 end
% 0.71/1.11
% 0.71/1.11 eqswap: (499) {G1,W13,D3,L3,V1,M3} { skol3 = X, in( skol4( skol3, X ),
% 0.71/1.11 skol5 ), in( skol4( skol3, X ), X ) }.
% 0.71/1.11 parent0[1]: (498) {G1,W13,D3,L3,V1,M3} { in( skol4( skol3, X ), skol5 ), X
% 0.71/1.11 = skol3, in( skol4( skol3, X ), X ) }.
% 0.71/1.11 substitution0:
% 0.71/1.11 X := X
% 0.71/1.11 end
% 0.71/1.11
% 0.71/1.11 subsumption: (352) {G4,W13,D3,L3,V1,M3} R(340,11) { in( skol4( skol3, X ),
% 0.71/1.11 skol5 ), in( skol4( skol3, X ), X ), skol3 = X }.
% 0.71/1.11 parent0: (499) {G1,W13,D3,L3,V1,M3} { skol3 = X, in( skol4( skol3, X ),
% 0.71/1.11 skol5 ), in( skol4( skol3, X ), X ) }.
% 0.71/1.11 substitution0:
% 0.71/1.11 X := X
% 0.71/1.11 end
% 0.71/1.11 permutation0:
% 0.71/1.11 0 ==> 2
% 0.71/1.11 1 ==> 0
% 0.71/1.11 2 ==> 1
% 0.71/1.11 end
% 0.71/1.11
% 0.71/1.11 resolution: (502) {G1,W8,D2,L2,V3,M2} { ! alpha1( X, skol5, Y ), ! alpha1
% 0.71/1.11 ( skol3, Z, Y ) }.
% 0.71/1.11 parent0[1]: (14) {G0,W7,D2,L2,V3,M2} I { ! alpha1( X, Y, Z ), ! in( Z, Y )
% 0.71/1.11 }.
% 0.71/1.11 parent1[0]: (340) {G3,W7,D2,L2,V2,M2} R(320,13) { in( X, skol5 ), ! alpha1
% 0.71/1.11 ( skol3, Y, X ) }.
% 0.71/1.11 substitution0:
% 0.71/1.11 X := X
% 0.71/1.11 Y := skol5
% 0.71/1.11 Z := Y
% 0.71/1.11 end
% 0.71/1.11 substitution1:
% 0.71/1.11 X := Y
% 0.71/1.11 Y := Z
% 0.71/1.11 end
% 0.71/1.11
% 0.71/1.11 subsumption: (358) {G4,W8,D2,L2,V3,M2} R(340,14) { ! alpha1( skol3, X, Y )
% 0.71/1.11 , ! alpha1( Z, skol5, Y ) }.
% 0.71/1.11 parent0: (502) {G1,W8,D2,L2,V3,M2} { ! alpha1( X, skol5, Y ), ! alpha1(
% 0.71/1.11 skol3, Z, Y ) }.
% 0.71/1.11 substitution0:
% 0.71/1.11 X := Z
% 0.71/1.11 Y := Y
% 0.71/1.11 Z := X
% 0.71/1.11 end
% 0.71/1.11 permutation0:
% 0.71/1.11 0 ==> 1
% 0.71/1.11 1 ==> 0
% 0.71/1.11 end
% 0.71/1.11
% 0.71/1.11 factor: (504) {G4,W4,D2,L1,V1,M1} { ! alpha1( skol3, skol5, X ) }.
% 0.71/1.11 parent0[0, 1]: (358) {G4,W8,D2,L2,V3,M2} R(340,14) { ! alpha1( skol3, X, Y
% 0.71/1.11 ), ! alpha1( Z, skol5, Y ) }.
% 0.71/1.11 substitution0:
% 0.71/1.11 X := skol5
% 0.71/1.11 Y := X
% 0.71/1.11 Z := skol3
% 0.71/1.11 end
% 0.71/1.11
% 0.71/1.11 subsumption: (359) {G5,W4,D2,L1,V1,M1} F(358) { ! alpha1( skol3, skol5, X )
% 0.71/1.11 }.
% 0.71/1.11 parent0: (504) {G4,W4,D2,L1,V1,M1} { ! alpha1( skol3, skol5, X ) }.
% 0.71/1.11 substitution0:
% 0.71/1.11 X := X
% 0.71/1.11 end
% 0.71/1.11 permutation0:
% 0.71/1.11 0 ==> 0
% 0.71/1.11 end
% 0.71/1.11
% 0.71/1.11 eqswap: (505) {G4,W13,D3,L3,V1,M3} { X = skol3, in( skol4( skol3, X ),
% 0.71/1.11 skol5 ), in( skol4( skol3, X ), X ) }.
% 0.71/1.11 parent0[2]: (352) {G4,W13,D3,L3,V1,M3} R(340,11) { in( skol4( skol3, X ),
% 0.71/1.11 skol5 ), in( skol4( skol3, X ), X ), skol3 = X }.
% 0.71/1.11 substitution0:
% 0.71/1.11 X := X
% 0.71/1.11 end
% 0.71/1.11
% 0.71/1.11 factor: (507) {G4,W8,D3,L2,V0,M2} { skol5 = skol3, in( skol4( skol3, skol5
% 0.71/1.11 ), skol5 ) }.
% 0.71/1.11 parent0[1, 2]: (505) {G4,W13,D3,L3,V1,M3} { X = skol3, in( skol4( skol3, X
% 0.71/1.11 ), skol5 ), in( skol4( skol3, X ), X ) }.
% 0.71/1.11 substitution0:
% 0.71/1.11 X := skol5
% 0.71/1.11 end
% 0.71/1.11
% 0.71/1.11 subsumption: (360) {G5,W8,D3,L2,V0,M2} F(352) { in( skol4( skol3, skol5 ),
% 0.71/1.11 skol5 ), skol5 ==> skol3 }.
% 0.71/1.11 parent0: (507) {G4,W8,D3,L2,V0,M2} { skol5 = skol3, in( skol4( skol3,
% 0.71/1.11 skol5 ), skol5 ) }.
% 0.71/1.11 substitution0:
% 0.71/1.11 end
% 0.71/1.11 permutation0:
% 0.71/1.11 0 ==> 1
% 0.71/1.11 1 ==> 0
% 0.71/1.11 end
% 0.71/1.11
% 0.71/1.11 eqswap: (508) {G0,W14,D3,L3,V2,M3} { Y = X, alpha1( X, Y, skol4( X, Y ) )
% 0.71/1.11 , ! in( skol4( X, Y ), X ) }.
% 0.71/1.11 parent0[2]: (12) {G0,W14,D3,L3,V2,M3} I { alpha1( X, Y, skol4( X, Y ) ), !
% 0.71/1.11 in( skol4( X, Y ), X ), X = Y }.
% 0.71/1.11 substitution0:
% 0.71/1.11 X := X
% 0.71/1.11 Y := Y
% 0.71/1.11 end
% 0.71/1.11
% 0.71/1.11 resolution: (509) {G1,W8,D3,L2,V0,M2} { skol5 = skol3, ! in( skol4( skol3
% 0.71/1.11 , skol5 ), skol3 ) }.
% 0.71/1.11 parent0[0]: (359) {G5,W4,D2,L1,V1,M1} F(358) { ! alpha1( skol3, skol5, X )
% 0.71/1.11 }.
% 0.71/1.11 parent1[1]: (508) {G0,W14,D3,L3,V2,M3} { Y = X, alpha1( X, Y, skol4( X, Y
% 0.71/1.11 ) ), ! in( skol4( X, Y ), X ) }.
% 0.71/1.11 substitution0:
% 0.71/1.11 X := skol4( skol3, skol5 )
% 0.71/1.11 end
% 0.71/1.11 substitution1:
% 0.71/1.11 X := skol3
% 0.71/1.11 Y := skol5
% 0.71/1.11 end
% 0.71/1.11
% 0.71/1.11 subsumption: (361) {G6,W8,D3,L2,V0,M2} R(359,12) { ! in( skol4( skol3,
% 0.71/1.11 skol5 ), skol3 ), skol5 ==> skol3 }.
% 0.71/1.11 parent0: (509) {G1,W8,D3,L2,V0,M2} { skol5 = skol3, ! in( skol4( skol3,
% 0.71/1.11 skol5 ), skol3 ) }.
% 0.71/1.11 substitution0:
% 0.71/1.11 end
% 0.71/1.11 permutation0:
% 0.71/1.11 0 ==> 1
% 0.71/1.11 1 ==> 0
% 0.71/1.11 end
% 0.71/1.11
% 0.71/1.11 resolution: (513) {G1,W5,D3,L1,V0,M1} { ! in( skol4( skol3, skol5 ), skol3
% 0.71/1.11 ) }.
% 0.71/1.11 parent0[0]: (10) {G0,W3,D2,L1,V0,M1} I { ! skol5 ==> skol3 }.
% 0.71/1.11 parent1[1]: (361) {G6,W8,D3,L2,V0,M2} R(359,12) { ! in( skol4( skol3, skol5
% 0.71/1.11 ), skol3 ), skol5 ==> skol3 }.
% 0.71/1.11 substitution0:
% 0.71/1.11 end
% 0.71/1.11 substitution1:
% 0.71/1.11 end
% 0.71/1.11
% 0.71/1.11 subsumption: (407) {G7,W5,D3,L1,V0,M1} S(361);r(10) { ! in( skol4( skol3,
% 0.71/1.11 skol5 ), skol3 ) }.
% 0.71/1.11 parent0: (513) {G1,W5,D3,L1,V0,M1} { ! in( skol4( skol3, skol5 ), skol3 )
% 0.71/1.11 }.
% 0.71/1.11 substitution0:
% 0.71/1.11 end
% 0.71/1.11 permutation0:
% 0.71/1.11 0 ==> 0
% 0.71/1.11 end
% 0.71/1.11
% 0.71/1.11 resolution: (514) {G1,W9,D4,L1,V2,M1} { ! in( ordered_pair( X, skol4(
% 0.71/1.11 skol3, skol5 ) ), cartesian_product2( Y, skol3 ) ) }.
% 0.71/1.11 parent0[0]: (407) {G7,W5,D3,L1,V0,M1} S(361);r(10) { ! in( skol4( skol3,
% 0.71/1.11 skol5 ), skol3 ) }.
% 0.71/1.11 parent1[1]: (5) {G0,W10,D3,L2,V4,M2} I { ! in( ordered_pair( X, Y ),
% 0.71/1.11 cartesian_product2( Z, T ) ), in( Y, T ) }.
% 0.71/1.11 substitution0:
% 0.71/1.11 end
% 0.71/1.11 substitution1:
% 0.71/1.11 X := X
% 0.71/1.11 Y := skol4( skol3, skol5 )
% 0.71/1.11 Z := Y
% 0.71/1.11 T := skol3
% 0.71/1.11 end
% 0.71/1.11
% 0.71/1.11 subsumption: (415) {G8,W9,D4,L1,V2,M1} R(407,5) { ! in( ordered_pair( X,
% 0.71/1.11 skol4( skol3, skol5 ) ), cartesian_product2( Y, skol3 ) ) }.
% 0.71/1.11 parent0: (514) {G1,W9,D4,L1,V2,M1} { ! in( ordered_pair( X, skol4( skol3,
% 0.71/1.11 skol5 ) ), cartesian_product2( Y, skol3 ) ) }.
% 0.71/1.11 substitution0:
% 0.71/1.11 X := X
% 0.71/1.11 Y := Y
% 0.71/1.11 end
% 0.71/1.11 permutation0:
% 0.71/1.11 0 ==> 0
% 0.71/1.11 end
% 0.71/1.11
% 0.71/1.11 resolution: (517) {G1,W5,D3,L1,V0,M1} { in( skol4( skol3, skol5 ), skol5 )
% 0.71/1.11 }.
% 0.71/1.11 parent0[0]: (10) {G0,W3,D2,L1,V0,M1} I { ! skol5 ==> skol3 }.
% 0.71/1.11 parent1[1]: (360) {G5,W8,D3,L2,V0,M2} F(352) { in( skol4( skol3, skol5 ),
% 0.71/1.11 skol5 ), skol5 ==> skol3 }.
% 0.71/1.11 substitution0:
% 0.71/1.11 end
% 0.71/1.11 substitution1:
% 0.71/1.11 end
% 0.71/1.11
% 0.71/1.11 subsumption: (421) {G6,W5,D3,L1,V0,M1} S(360);r(10) { in( skol4( skol3,
% 0.71/1.11 skol5 ), skol5 ) }.
% 0.71/1.11 parent0: (517) {G1,W5,D3,L1,V0,M1} { in( skol4( skol3, skol5 ), skol5 )
% 0.71/1.11 }.
% 0.71/1.11 substitution0:
% 0.71/1.11 end
% 0.71/1.11 permutation0:
% 0.71/1.11 0 ==> 0
% 0.71/1.11 end
% 0.71/1.11
% 0.71/1.11 resolution: (519) {G2,W11,D4,L1,V0,M1} { in( ordered_pair( skol4( skol3,
% 0.71/1.11 skol5 ), skol4( skol3, skol5 ) ), cartesian_product2( skol5, skol5 ) )
% 0.71/1.11 }.
% 0.71/1.11 parent0[0]: (17) {G1,W10,D3,L2,V2,M2} F(6) { ! in( X, Y ), in( ordered_pair
% 0.71/1.11 ( X, X ), cartesian_product2( Y, Y ) ) }.
% 0.71/1.11 parent1[0]: (421) {G6,W5,D3,L1,V0,M1} S(360);r(10) { in( skol4( skol3,
% 0.71/1.11 skol5 ), skol5 ) }.
% 0.71/1.11 substitution0:
% 0.71/1.11 X := skol4( skol3, skol5 )
% 0.71/1.11 Y := skol5
% 0.71/1.11 end
% 0.71/1.11 substitution1:
% 0.71/1.11 end
% 0.71/1.11
% 0.71/1.11 paramod: (520) {G1,W11,D4,L1,V0,M1} { in( ordered_pair( skol4( skol3,
% 0.71/1.11 skol5 ), skol4( skol3, skol5 ) ), cartesian_product2( skol3, skol3 ) )
% 0.71/1.11 }.
% 0.71/1.11 parent0[0]: (9) {G0,W7,D3,L1,V0,M1} I { cartesian_product2( skol5, skol5 )
% 0.71/1.11 ==> cartesian_product2( skol3, skol3 ) }.
% 0.71/1.11 parent1[0; 8]: (519) {G2,W11,D4,L1,V0,M1} { in( ordered_pair( skol4( skol3
% 0.71/1.11 , skol5 ), skol4( skol3, skol5 ) ), cartesian_product2( skol5, skol5 ) )
% 0.71/1.11 }.
% 0.71/1.11 substitution0:
% 0.71/1.11 end
% 0.71/1.11 substitution1:
% 0.71/1.11 end
% 0.71/1.11
% 0.71/1.11 resolution: (521) {G2,W0,D0,L0,V0,M0} { }.
% 0.71/1.11 parent0[0]: (415) {G8,W9,D4,L1,V2,M1} R(407,5) { ! in( ordered_pair( X,
% 0.71/1.11 skol4( skol3, skol5 ) ), cartesian_product2( Y, skol3 ) ) }.
% 0.71/1.11 parent1[0]: (520) {G1,W11,D4,L1,V0,M1} { in( ordered_pair( skol4( skol3,
% 0.71/1.11 skol5 ), skol4( skol3, skol5 ) ), cartesian_product2( skol3, skol3 ) )
% 0.71/1.11 }.
% 0.71/1.11 substitution0:
% 0.71/1.11 X := skol4( skol3, skol5 )
% 0.71/1.11 Y := skol3
% 0.71/1.11 end
% 0.71/1.11 substitution1:
% 0.71/1.11 end
% 0.71/1.11
% 0.71/1.11 subsumption: (433) {G9,W0,D0,L0,V0,M0} R(421,17);d(9);r(415) { }.
% 0.71/1.11 parent0: (521) {G2,W0,D0,L0,V0,M0} { }.
% 0.71/1.11 substitution0:
% 0.71/1.11 end
% 0.71/1.11 permutation0:
% 0.71/1.11 end
% 0.71/1.11
% 0.71/1.11 Proof check complete!
% 0.71/1.11
% 0.71/1.11 Memory use:
% 0.71/1.11
% 0.71/1.11 space for terms: 6791
% 0.71/1.11 space for clauses: 23091
% 0.71/1.11
% 0.71/1.11
% 0.71/1.11 clauses generated: 1878
% 0.71/1.11 clauses kept: 434
% 0.71/1.11 clauses selected: 83
% 0.71/1.11 clauses deleted: 4
% 0.71/1.11 clauses inuse deleted: 0
% 0.71/1.11
% 0.71/1.11 subsentry: 8848
% 0.71/1.11 literals s-matched: 6541
% 0.71/1.11 literals matched: 5899
% 0.71/1.11 full subsumption: 2132
% 0.71/1.11
% 0.71/1.11 checksum: 390239500
% 0.71/1.11
% 0.71/1.11
% 0.71/1.11 Bliksem ended
%------------------------------------------------------------------------------