TSTP Solution File: SET979+1 by Bliksem---1.12
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%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SET979+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n013.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 22:53:44 EDT 2022
% Result : Theorem 0.69s 1.08s
% Output : Refutation 0.69s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : SET979+1 : TPTP v8.1.0. Released v3.2.0.
% 0.10/0.12 % Command : bliksem %s
% 0.12/0.33 % Computer : n013.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % DateTime : Sat Jul 9 21:03:59 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.69/1.08 *** allocated 10000 integers for termspace/termends
% 0.69/1.08 *** allocated 10000 integers for clauses
% 0.69/1.08 *** allocated 10000 integers for justifications
% 0.69/1.08 Bliksem 1.12
% 0.69/1.08
% 0.69/1.08
% 0.69/1.08 Automatic Strategy Selection
% 0.69/1.08
% 0.69/1.08
% 0.69/1.08 Clauses:
% 0.69/1.08
% 0.69/1.08 { unordered_pair( X, Y ) = unordered_pair( Y, X ) }.
% 0.69/1.08 { set_union2( X, Y ) = set_union2( Y, X ) }.
% 0.69/1.08 { empty( X ), ! empty( set_union2( X, Y ) ) }.
% 0.69/1.08 { empty( X ), ! empty( set_union2( Y, X ) ) }.
% 0.69/1.08 { set_union2( X, X ) = X }.
% 0.69/1.08 { empty( skol1 ) }.
% 0.69/1.08 { ! empty( skol2 ) }.
% 0.69/1.08 { cartesian_product2( set_union2( X, Y ), Z ) = set_union2(
% 0.69/1.08 cartesian_product2( X, Z ), cartesian_product2( Y, Z ) ) }.
% 0.69/1.08 { cartesian_product2( Z, set_union2( X, Y ) ) = set_union2(
% 0.69/1.08 cartesian_product2( Z, X ), cartesian_product2( Z, Y ) ) }.
% 0.69/1.08 { ! cartesian_product2( unordered_pair( skol3, skol4 ), skol5 ) =
% 0.69/1.08 set_union2( cartesian_product2( singleton( skol3 ), skol5 ),
% 0.69/1.08 cartesian_product2( singleton( skol4 ), skol5 ) ), ! cartesian_product2(
% 0.69/1.08 skol5, unordered_pair( skol3, skol4 ) ) = set_union2( cartesian_product2
% 0.69/1.08 ( skol5, singleton( skol3 ) ), cartesian_product2( skol5, singleton(
% 0.69/1.08 skol4 ) ) ) }.
% 0.69/1.08 { unordered_pair( X, Y ) = set_union2( singleton( X ), singleton( Y ) ) }.
% 0.69/1.08
% 0.69/1.08 percentage equality = 0.571429, percentage horn = 1.000000
% 0.69/1.08 This is a problem with some equality
% 0.69/1.08
% 0.69/1.08
% 0.69/1.08
% 0.69/1.08 Options Used:
% 0.69/1.08
% 0.69/1.08 useres = 1
% 0.69/1.08 useparamod = 1
% 0.69/1.08 useeqrefl = 1
% 0.69/1.08 useeqfact = 1
% 0.69/1.08 usefactor = 1
% 0.69/1.08 usesimpsplitting = 0
% 0.69/1.08 usesimpdemod = 5
% 0.69/1.08 usesimpres = 3
% 0.69/1.08
% 0.69/1.08 resimpinuse = 1000
% 0.69/1.08 resimpclauses = 20000
% 0.69/1.08 substype = eqrewr
% 0.69/1.08 backwardsubs = 1
% 0.69/1.08 selectoldest = 5
% 0.69/1.08
% 0.69/1.08 litorderings [0] = split
% 0.69/1.08 litorderings [1] = extend the termordering, first sorting on arguments
% 0.69/1.08
% 0.69/1.08 termordering = kbo
% 0.69/1.08
% 0.69/1.08 litapriori = 0
% 0.69/1.08 termapriori = 1
% 0.69/1.08 litaposteriori = 0
% 0.69/1.08 termaposteriori = 0
% 0.69/1.08 demodaposteriori = 0
% 0.69/1.08 ordereqreflfact = 0
% 0.69/1.08
% 0.69/1.08 litselect = negord
% 0.69/1.08
% 0.69/1.08 maxweight = 15
% 0.69/1.08 maxdepth = 30000
% 0.69/1.08 maxlength = 115
% 0.69/1.08 maxnrvars = 195
% 0.69/1.08 excuselevel = 1
% 0.69/1.08 increasemaxweight = 1
% 0.69/1.08
% 0.69/1.08 maxselected = 10000000
% 0.69/1.08 maxnrclauses = 10000000
% 0.69/1.08
% 0.69/1.08 showgenerated = 0
% 0.69/1.08 showkept = 0
% 0.69/1.08 showselected = 0
% 0.69/1.08 showdeleted = 0
% 0.69/1.08 showresimp = 1
% 0.69/1.08 showstatus = 2000
% 0.69/1.08
% 0.69/1.08 prologoutput = 0
% 0.69/1.08 nrgoals = 5000000
% 0.69/1.08 totalproof = 1
% 0.69/1.08
% 0.69/1.08 Symbols occurring in the translation:
% 0.69/1.08
% 0.69/1.08 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.69/1.08 . [1, 2] (w:1, o:21, a:1, s:1, b:0),
% 0.69/1.08 ! [4, 1] (w:0, o:14, a:1, s:1, b:0),
% 0.69/1.08 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.69/1.08 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.69/1.08 unordered_pair [37, 2] (w:1, o:45, a:1, s:1, b:0),
% 0.69/1.08 set_union2 [38, 2] (w:1, o:46, a:1, s:1, b:0),
% 0.69/1.08 empty [39, 1] (w:1, o:19, a:1, s:1, b:0),
% 0.69/1.08 cartesian_product2 [41, 2] (w:1, o:47, a:1, s:1, b:0),
% 0.69/1.08 singleton [42, 1] (w:1, o:20, a:1, s:1, b:0),
% 0.69/1.08 skol1 [43, 0] (w:1, o:9, a:1, s:1, b:1),
% 0.69/1.08 skol2 [44, 0] (w:1, o:10, a:1, s:1, b:1),
% 0.69/1.08 skol3 [45, 0] (w:1, o:11, a:1, s:1, b:1),
% 0.69/1.08 skol4 [46, 0] (w:1, o:12, a:1, s:1, b:1),
% 0.69/1.08 skol5 [47, 0] (w:1, o:13, a:1, s:1, b:1).
% 0.69/1.08
% 0.69/1.08
% 0.69/1.08 Starting Search:
% 0.69/1.08
% 0.69/1.08
% 0.69/1.08 Bliksems!, er is een bewijs:
% 0.69/1.08 % SZS status Theorem
% 0.69/1.08 % SZS output start Refutation
% 0.69/1.08
% 0.69/1.08 (7) {G0,W13,D4,L1,V3,M1} I { set_union2( cartesian_product2( X, Z ),
% 0.69/1.08 cartesian_product2( Y, Z ) ) ==> cartesian_product2( set_union2( X, Y ),
% 0.69/1.08 Z ) }.
% 0.69/1.08 (8) {G0,W13,D4,L1,V3,M1} I { set_union2( cartesian_product2( Z, X ),
% 0.69/1.08 cartesian_product2( Z, Y ) ) ==> cartesian_product2( Z, set_union2( X, Y
% 0.69/1.08 ) ) }.
% 0.69/1.08 (9) {G1,W26,D5,L2,V0,M2} I;d(7);d(8) { ! cartesian_product2( set_union2(
% 0.69/1.08 singleton( skol3 ), singleton( skol4 ) ), skol5 ) ==> cartesian_product2
% 0.69/1.08 ( unordered_pair( skol3, skol4 ), skol5 ), ! cartesian_product2( skol5,
% 0.69/1.08 set_union2( singleton( skol3 ), singleton( skol4 ) ) ) ==>
% 0.69/1.08 cartesian_product2( skol5, unordered_pair( skol3, skol4 ) ) }.
% 0.69/1.08 (10) {G0,W9,D4,L1,V2,M1} I { set_union2( singleton( X ), singleton( Y ) )
% 0.69/1.08 ==> unordered_pair( X, Y ) }.
% 0.69/1.08 (107) {G2,W0,D0,L0,V0,M0} S(9);d(10);q;d(10);q { }.
% 0.69/1.08
% 0.69/1.08
% 0.69/1.08 % SZS output end Refutation
% 0.69/1.08 found a proof!
% 0.69/1.08
% 0.69/1.08
% 0.69/1.08 Unprocessed initial clauses:
% 0.69/1.08
% 0.69/1.08 (109) {G0,W7,D3,L1,V2,M1} { unordered_pair( X, Y ) = unordered_pair( Y, X
% 0.69/1.08 ) }.
% 0.69/1.08 (110) {G0,W7,D3,L1,V2,M1} { set_union2( X, Y ) = set_union2( Y, X ) }.
% 0.69/1.08 (111) {G0,W6,D3,L2,V2,M2} { empty( X ), ! empty( set_union2( X, Y ) ) }.
% 0.69/1.08 (112) {G0,W6,D3,L2,V2,M2} { empty( X ), ! empty( set_union2( Y, X ) ) }.
% 0.69/1.08 (113) {G0,W5,D3,L1,V1,M1} { set_union2( X, X ) = X }.
% 0.69/1.08 (114) {G0,W2,D2,L1,V0,M1} { empty( skol1 ) }.
% 0.69/1.08 (115) {G0,W2,D2,L1,V0,M1} { ! empty( skol2 ) }.
% 0.69/1.08 (116) {G0,W13,D4,L1,V3,M1} { cartesian_product2( set_union2( X, Y ), Z ) =
% 0.69/1.08 set_union2( cartesian_product2( X, Z ), cartesian_product2( Y, Z ) ) }.
% 0.69/1.08 (117) {G0,W13,D4,L1,V3,M1} { cartesian_product2( Z, set_union2( X, Y ) ) =
% 0.69/1.08 set_union2( cartesian_product2( Z, X ), cartesian_product2( Z, Y ) ) }.
% 0.69/1.08 (118) {G0,W30,D5,L2,V0,M2} { ! cartesian_product2( unordered_pair( skol3,
% 0.69/1.08 skol4 ), skol5 ) = set_union2( cartesian_product2( singleton( skol3 ),
% 0.69/1.08 skol5 ), cartesian_product2( singleton( skol4 ), skol5 ) ), !
% 0.69/1.08 cartesian_product2( skol5, unordered_pair( skol3, skol4 ) ) = set_union2
% 0.69/1.08 ( cartesian_product2( skol5, singleton( skol3 ) ), cartesian_product2(
% 0.69/1.08 skol5, singleton( skol4 ) ) ) }.
% 0.69/1.08 (119) {G0,W9,D4,L1,V2,M1} { unordered_pair( X, Y ) = set_union2( singleton
% 0.69/1.08 ( X ), singleton( Y ) ) }.
% 0.69/1.08
% 0.69/1.08
% 0.69/1.08 Total Proof:
% 0.69/1.08
% 0.69/1.08 eqswap: (121) {G0,W13,D4,L1,V3,M1} { set_union2( cartesian_product2( X, Z
% 0.69/1.08 ), cartesian_product2( Y, Z ) ) = cartesian_product2( set_union2( X, Y )
% 0.69/1.08 , Z ) }.
% 0.69/1.08 parent0[0]: (116) {G0,W13,D4,L1,V3,M1} { cartesian_product2( set_union2( X
% 0.69/1.08 , Y ), Z ) = set_union2( cartesian_product2( X, Z ), cartesian_product2(
% 0.69/1.08 Y, Z ) ) }.
% 0.69/1.08 substitution0:
% 0.69/1.08 X := X
% 0.69/1.08 Y := Y
% 0.69/1.08 Z := Z
% 0.69/1.08 end
% 0.69/1.08
% 0.69/1.08 subsumption: (7) {G0,W13,D4,L1,V3,M1} I { set_union2( cartesian_product2( X
% 0.69/1.08 , Z ), cartesian_product2( Y, Z ) ) ==> cartesian_product2( set_union2( X
% 0.69/1.08 , Y ), Z ) }.
% 0.69/1.08 parent0: (121) {G0,W13,D4,L1,V3,M1} { set_union2( cartesian_product2( X, Z
% 0.69/1.08 ), cartesian_product2( Y, Z ) ) = cartesian_product2( set_union2( X, Y )
% 0.69/1.08 , Z ) }.
% 0.69/1.08 substitution0:
% 0.69/1.08 X := X
% 0.69/1.08 Y := Y
% 0.69/1.08 Z := Z
% 0.69/1.08 end
% 0.69/1.08 permutation0:
% 0.69/1.08 0 ==> 0
% 0.69/1.08 end
% 0.69/1.08
% 0.69/1.08 eqswap: (124) {G0,W13,D4,L1,V3,M1} { set_union2( cartesian_product2( X, Y
% 0.69/1.08 ), cartesian_product2( X, Z ) ) = cartesian_product2( X, set_union2( Y,
% 0.69/1.08 Z ) ) }.
% 0.69/1.08 parent0[0]: (117) {G0,W13,D4,L1,V3,M1} { cartesian_product2( Z, set_union2
% 0.69/1.08 ( X, Y ) ) = set_union2( cartesian_product2( Z, X ), cartesian_product2(
% 0.69/1.08 Z, Y ) ) }.
% 0.69/1.08 substitution0:
% 0.69/1.08 X := Y
% 0.69/1.08 Y := Z
% 0.69/1.08 Z := X
% 0.69/1.08 end
% 0.69/1.08
% 0.69/1.08 subsumption: (8) {G0,W13,D4,L1,V3,M1} I { set_union2( cartesian_product2( Z
% 0.69/1.08 , X ), cartesian_product2( Z, Y ) ) ==> cartesian_product2( Z, set_union2
% 0.69/1.08 ( X, Y ) ) }.
% 0.69/1.08 parent0: (124) {G0,W13,D4,L1,V3,M1} { set_union2( cartesian_product2( X, Y
% 0.69/1.08 ), cartesian_product2( X, Z ) ) = cartesian_product2( X, set_union2( Y,
% 0.69/1.08 Z ) ) }.
% 0.69/1.08 substitution0:
% 0.69/1.08 X := Z
% 0.69/1.08 Y := X
% 0.69/1.08 Z := Y
% 0.69/1.08 end
% 0.69/1.08 permutation0:
% 0.69/1.08 0 ==> 0
% 0.69/1.08 end
% 0.69/1.08
% 0.69/1.08 paramod: (153) {G1,W28,D5,L2,V0,M2} { ! cartesian_product2( unordered_pair
% 0.69/1.08 ( skol3, skol4 ), skol5 ) = cartesian_product2( set_union2( singleton(
% 0.69/1.08 skol3 ), singleton( skol4 ) ), skol5 ), ! cartesian_product2( skol5,
% 0.69/1.08 unordered_pair( skol3, skol4 ) ) = set_union2( cartesian_product2( skol5
% 0.69/1.08 , singleton( skol3 ) ), cartesian_product2( skol5, singleton( skol4 ) ) )
% 0.69/1.08 }.
% 0.69/1.08 parent0[0]: (7) {G0,W13,D4,L1,V3,M1} I { set_union2( cartesian_product2( X
% 0.69/1.08 , Z ), cartesian_product2( Y, Z ) ) ==> cartesian_product2( set_union2( X
% 0.69/1.08 , Y ), Z ) }.
% 0.69/1.08 parent1[0; 7]: (118) {G0,W30,D5,L2,V0,M2} { ! cartesian_product2(
% 0.69/1.08 unordered_pair( skol3, skol4 ), skol5 ) = set_union2( cartesian_product2
% 0.69/1.08 ( singleton( skol3 ), skol5 ), cartesian_product2( singleton( skol4 ),
% 0.69/1.08 skol5 ) ), ! cartesian_product2( skol5, unordered_pair( skol3, skol4 ) )
% 0.69/1.08 = set_union2( cartesian_product2( skol5, singleton( skol3 ) ),
% 0.69/1.08 cartesian_product2( skol5, singleton( skol4 ) ) ) }.
% 0.69/1.08 substitution0:
% 0.69/1.08 X := singleton( skol3 )
% 0.69/1.08 Y := singleton( skol4 )
% 0.69/1.08 Z := skol5
% 0.69/1.08 end
% 0.69/1.08 substitution1:
% 0.69/1.08 end
% 0.69/1.08
% 0.69/1.08 paramod: (154) {G1,W26,D5,L2,V0,M2} { ! cartesian_product2( skol5,
% 0.69/1.08 unordered_pair( skol3, skol4 ) ) = cartesian_product2( skol5, set_union2
% 0.69/1.08 ( singleton( skol3 ), singleton( skol4 ) ) ), ! cartesian_product2(
% 0.69/1.08 unordered_pair( skol3, skol4 ), skol5 ) = cartesian_product2( set_union2
% 0.69/1.08 ( singleton( skol3 ), singleton( skol4 ) ), skol5 ) }.
% 0.69/1.08 parent0[0]: (8) {G0,W13,D4,L1,V3,M1} I { set_union2( cartesian_product2( Z
% 0.69/1.08 , X ), cartesian_product2( Z, Y ) ) ==> cartesian_product2( Z, set_union2
% 0.69/1.08 ( X, Y ) ) }.
% 0.69/1.08 parent1[1; 7]: (153) {G1,W28,D5,L2,V0,M2} { ! cartesian_product2(
% 0.69/1.08 unordered_pair( skol3, skol4 ), skol5 ) = cartesian_product2( set_union2
% 0.69/1.08 ( singleton( skol3 ), singleton( skol4 ) ), skol5 ), ! cartesian_product2
% 0.69/1.08 ( skol5, unordered_pair( skol3, skol4 ) ) = set_union2(
% 0.69/1.08 cartesian_product2( skol5, singleton( skol3 ) ), cartesian_product2(
% 0.69/1.08 skol5, singleton( skol4 ) ) ) }.
% 0.69/1.08 substitution0:
% 0.69/1.08 X := singleton( skol3 )
% 0.69/1.08 Y := singleton( skol4 )
% 0.69/1.08 Z := skol5
% 0.69/1.08 end
% 0.69/1.08 substitution1:
% 0.69/1.08 end
% 0.69/1.08
% 0.69/1.08 eqswap: (156) {G1,W26,D5,L2,V0,M2} { ! cartesian_product2( set_union2(
% 0.69/1.08 singleton( skol3 ), singleton( skol4 ) ), skol5 ) = cartesian_product2(
% 0.69/1.08 unordered_pair( skol3, skol4 ), skol5 ), ! cartesian_product2( skol5,
% 0.69/1.08 unordered_pair( skol3, skol4 ) ) = cartesian_product2( skol5, set_union2
% 0.69/1.08 ( singleton( skol3 ), singleton( skol4 ) ) ) }.
% 0.69/1.08 parent0[1]: (154) {G1,W26,D5,L2,V0,M2} { ! cartesian_product2( skol5,
% 0.69/1.08 unordered_pair( skol3, skol4 ) ) = cartesian_product2( skol5, set_union2
% 0.69/1.08 ( singleton( skol3 ), singleton( skol4 ) ) ), ! cartesian_product2(
% 0.69/1.08 unordered_pair( skol3, skol4 ), skol5 ) = cartesian_product2( set_union2
% 0.69/1.08 ( singleton( skol3 ), singleton( skol4 ) ), skol5 ) }.
% 0.69/1.08 substitution0:
% 0.69/1.08 end
% 0.69/1.08
% 0.69/1.08 eqswap: (157) {G1,W26,D5,L2,V0,M2} { ! cartesian_product2( skol5,
% 0.69/1.08 set_union2( singleton( skol3 ), singleton( skol4 ) ) ) =
% 0.69/1.08 cartesian_product2( skol5, unordered_pair( skol3, skol4 ) ), !
% 0.69/1.08 cartesian_product2( set_union2( singleton( skol3 ), singleton( skol4 ) )
% 0.69/1.08 , skol5 ) = cartesian_product2( unordered_pair( skol3, skol4 ), skol5 )
% 0.69/1.08 }.
% 0.69/1.08 parent0[1]: (156) {G1,W26,D5,L2,V0,M2} { ! cartesian_product2( set_union2
% 0.69/1.08 ( singleton( skol3 ), singleton( skol4 ) ), skol5 ) = cartesian_product2
% 0.69/1.08 ( unordered_pair( skol3, skol4 ), skol5 ), ! cartesian_product2( skol5,
% 0.69/1.08 unordered_pair( skol3, skol4 ) ) = cartesian_product2( skol5, set_union2
% 0.69/1.08 ( singleton( skol3 ), singleton( skol4 ) ) ) }.
% 0.69/1.08 substitution0:
% 0.69/1.08 end
% 0.69/1.08
% 0.69/1.08 subsumption: (9) {G1,W26,D5,L2,V0,M2} I;d(7);d(8) { ! cartesian_product2(
% 0.69/1.08 set_union2( singleton( skol3 ), singleton( skol4 ) ), skol5 ) ==>
% 0.69/1.08 cartesian_product2( unordered_pair( skol3, skol4 ), skol5 ), !
% 0.69/1.08 cartesian_product2( skol5, set_union2( singleton( skol3 ), singleton(
% 0.69/1.08 skol4 ) ) ) ==> cartesian_product2( skol5, unordered_pair( skol3, skol4 )
% 0.69/1.08 ) }.
% 0.69/1.08 parent0: (157) {G1,W26,D5,L2,V0,M2} { ! cartesian_product2( skol5,
% 0.69/1.08 set_union2( singleton( skol3 ), singleton( skol4 ) ) ) =
% 0.69/1.08 cartesian_product2( skol5, unordered_pair( skol3, skol4 ) ), !
% 0.69/1.08 cartesian_product2( set_union2( singleton( skol3 ), singleton( skol4 ) )
% 0.69/1.08 , skol5 ) = cartesian_product2( unordered_pair( skol3, skol4 ), skol5 )
% 0.69/1.08 }.
% 0.69/1.08 substitution0:
% 0.69/1.08 end
% 0.69/1.08 permutation0:
% 0.69/1.08 0 ==> 1
% 0.69/1.08 1 ==> 0
% 0.69/1.08 end
% 0.69/1.08
% 0.69/1.08 eqswap: (164) {G0,W9,D4,L1,V2,M1} { set_union2( singleton( X ), singleton
% 0.69/1.08 ( Y ) ) = unordered_pair( X, Y ) }.
% 0.69/1.08 parent0[0]: (119) {G0,W9,D4,L1,V2,M1} { unordered_pair( X, Y ) =
% 0.69/1.08 set_union2( singleton( X ), singleton( Y ) ) }.
% 0.69/1.08 substitution0:
% 0.69/1.08 X := X
% 0.69/1.08 Y := Y
% 0.69/1.08 end
% 0.69/1.08
% 0.69/1.08 subsumption: (10) {G0,W9,D4,L1,V2,M1} I { set_union2( singleton( X ),
% 0.69/1.08 singleton( Y ) ) ==> unordered_pair( X, Y ) }.
% 0.69/1.08 parent0: (164) {G0,W9,D4,L1,V2,M1} { set_union2( singleton( X ), singleton
% 0.69/1.08 ( Y ) ) = unordered_pair( X, Y ) }.
% 0.69/1.08 substitution0:
% 0.69/1.08 X := X
% 0.69/1.08 Y := Y
% 0.69/1.08 end
% 0.69/1.08 permutation0:
% 0.69/1.08 0 ==> 0
% 0.69/1.08 end
% 0.69/1.08
% 0.69/1.08 paramod: (171) {G1,W24,D5,L2,V0,M2} { ! cartesian_product2( skol5,
% 0.69/1.08 unordered_pair( skol3, skol4 ) ) ==> cartesian_product2( skol5,
% 0.69/1.08 unordered_pair( skol3, skol4 ) ), ! cartesian_product2( set_union2(
% 0.69/1.08 singleton( skol3 ), singleton( skol4 ) ), skol5 ) ==> cartesian_product2
% 0.69/1.08 ( unordered_pair( skol3, skol4 ), skol5 ) }.
% 0.69/1.08 parent0[0]: (10) {G0,W9,D4,L1,V2,M1} I { set_union2( singleton( X ),
% 0.69/1.08 singleton( Y ) ) ==> unordered_pair( X, Y ) }.
% 0.69/1.08 parent1[1; 4]: (9) {G1,W26,D5,L2,V0,M2} I;d(7);d(8) { ! cartesian_product2
% 0.69/1.08 ( set_union2( singleton( skol3 ), singleton( skol4 ) ), skol5 ) ==>
% 0.69/1.08 cartesian_product2( unordered_pair( skol3, skol4 ), skol5 ), !
% 0.69/1.08 cartesian_product2( skol5, set_union2( singleton( skol3 ), singleton(
% 0.69/1.08 skol4 ) ) ) ==> cartesian_product2( skol5, unordered_pair( skol3, skol4 )
% 0.69/1.08 ) }.
% 0.69/1.08 substitution0:
% 0.69/1.08 X := skol3
% 0.69/1.08 Y := skol4
% 0.69/1.08 end
% 0.69/1.08 substitution1:
% 0.69/1.08 end
% 0.69/1.08
% 0.69/1.08 eqrefl: (173) {G0,W13,D5,L1,V0,M1} { ! cartesian_product2( set_union2(
% 0.69/1.08 singleton( skol3 ), singleton( skol4 ) ), skol5 ) ==> cartesian_product2
% 0.69/1.08 ( unordered_pair( skol3, skol4 ), skol5 ) }.
% 0.69/1.08 parent0[0]: (171) {G1,W24,D5,L2,V0,M2} { ! cartesian_product2( skol5,
% 0.69/1.08 unordered_pair( skol3, skol4 ) ) ==> cartesian_product2( skol5,
% 0.69/1.08 unordered_pair( skol3, skol4 ) ), ! cartesian_product2( set_union2(
% 0.69/1.08 singleton( skol3 ), singleton( skol4 ) ), skol5 ) ==> cartesian_product2
% 0.69/1.08 ( unordered_pair( skol3, skol4 ), skol5 ) }.
% 0.69/1.08 substitution0:
% 0.69/1.08 end
% 0.69/1.08
% 0.69/1.08 paramod: (174) {G1,W11,D4,L1,V0,M1} { ! cartesian_product2( unordered_pair
% 0.69/1.08 ( skol3, skol4 ), skol5 ) ==> cartesian_product2( unordered_pair( skol3,
% 0.69/1.08 skol4 ), skol5 ) }.
% 0.69/1.08 parent0[0]: (10) {G0,W9,D4,L1,V2,M1} I { set_union2( singleton( X ),
% 0.69/1.08 singleton( Y ) ) ==> unordered_pair( X, Y ) }.
% 0.69/1.08 parent1[0; 3]: (173) {G0,W13,D5,L1,V0,M1} { ! cartesian_product2(
% 0.69/1.08 set_union2( singleton( skol3 ), singleton( skol4 ) ), skol5 ) ==>
% 0.69/1.08 cartesian_product2( unordered_pair( skol3, skol4 ), skol5 ) }.
% 0.69/1.08 substitution0:
% 0.69/1.08 X := skol3
% 0.69/1.08 Y := skol4
% 0.69/1.08 end
% 0.69/1.08 substitution1:
% 0.69/1.08 end
% 0.69/1.08
% 0.69/1.08 eqrefl: (175) {G0,W0,D0,L0,V0,M0} { }.
% 0.69/1.08 parent0[0]: (174) {G1,W11,D4,L1,V0,M1} { ! cartesian_product2(
% 0.69/1.08 unordered_pair( skol3, skol4 ), skol5 ) ==> cartesian_product2(
% 0.69/1.08 unordered_pair( skol3, skol4 ), skol5 ) }.
% 0.69/1.08 substitution0:
% 0.69/1.08 end
% 0.69/1.08
% 0.69/1.08 subsumption: (107) {G2,W0,D0,L0,V0,M0} S(9);d(10);q;d(10);q { }.
% 0.69/1.08 parent0: (175) {G0,W0,D0,L0,V0,M0} { }.
% 0.69/1.08 substitution0:
% 0.69/1.08 end
% 0.69/1.08 permutation0:
% 0.69/1.08 end
% 0.69/1.08
% 0.69/1.08 Proof check complete!
% 0.69/1.08
% 0.69/1.08 Memory use:
% 0.69/1.08
% 0.69/1.08 space for terms: 1482
% 0.69/1.08 space for clauses: 7403
% 0.69/1.08
% 0.69/1.08
% 0.69/1.08 clauses generated: 298
% 0.69/1.08 clauses kept: 108
% 0.69/1.08 clauses selected: 25
% 0.69/1.08 clauses deleted: 1
% 0.69/1.08 clauses inuse deleted: 0
% 0.69/1.08
% 0.69/1.08 subsentry: 681
% 0.69/1.08 literals s-matched: 533
% 0.69/1.08 literals matched: 533
% 0.69/1.08 full subsumption: 0
% 0.69/1.08
% 0.69/1.08 checksum: 107013418
% 0.69/1.08
% 0.69/1.08
% 0.69/1.08 Bliksem ended
%------------------------------------------------------------------------------