TSTP Solution File: SET968+1 by Bliksem---1.12
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%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SET968+1 : TPTP v8.1.0. Released v3.2.0.
% 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 22:53:40 EDT 2022
% Result : Theorem 0.82s 1.18s
% Output : Refutation 0.82s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : SET968+1 : TPTP v8.1.0. Released v3.2.0.
% 0.06/0.12 % Command : bliksem %s
% 0.12/0.33 % Computer : n028.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 : Mon Jul 11 02:54:58 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.82/1.18 *** allocated 10000 integers for termspace/termends
% 0.82/1.18 *** allocated 10000 integers for clauses
% 0.82/1.18 *** allocated 10000 integers for justifications
% 0.82/1.18 Bliksem 1.12
% 0.82/1.18
% 0.82/1.18
% 0.82/1.18 Automatic Strategy Selection
% 0.82/1.18
% 0.82/1.18
% 0.82/1.18 Clauses:
% 0.82/1.18
% 0.82/1.18 { set_union2( X, Y ) = set_union2( Y, X ) }.
% 0.82/1.18 { empty( X ), ! empty( set_union2( X, Y ) ) }.
% 0.82/1.18 { empty( X ), ! empty( set_union2( Y, X ) ) }.
% 0.82/1.18 { set_union2( X, X ) = X }.
% 0.82/1.18 { empty( skol1 ) }.
% 0.82/1.18 { ! empty( skol2 ) }.
% 0.82/1.18 { cartesian_product2( set_union2( X, Y ), Z ) = set_union2(
% 0.82/1.18 cartesian_product2( X, Z ), cartesian_product2( Y, Z ) ) }.
% 0.82/1.18 { cartesian_product2( Z, set_union2( X, Y ) ) = set_union2(
% 0.82/1.18 cartesian_product2( Z, X ), cartesian_product2( Z, Y ) ) }.
% 0.82/1.18 { ! cartesian_product2( set_union2( skol3, skol4 ), set_union2( skol5,
% 0.82/1.18 skol6 ) ) = set_union2( set_union2( set_union2( cartesian_product2( skol3
% 0.82/1.18 , skol5 ), cartesian_product2( skol3, skol6 ) ), cartesian_product2(
% 0.82/1.18 skol4, skol5 ) ), cartesian_product2( skol4, skol6 ) ) }.
% 0.82/1.18 { set_union2( set_union2( X, Y ), Z ) = set_union2( X, set_union2( Y, Z ) )
% 0.82/1.18 }.
% 0.82/1.18
% 0.82/1.18 percentage equality = 0.500000, percentage horn = 1.000000
% 0.82/1.18 This is a problem with some equality
% 0.82/1.18
% 0.82/1.18
% 0.82/1.18
% 0.82/1.18 Options Used:
% 0.82/1.18
% 0.82/1.18 useres = 1
% 0.82/1.18 useparamod = 1
% 0.82/1.18 useeqrefl = 1
% 0.82/1.18 useeqfact = 1
% 0.82/1.18 usefactor = 1
% 0.82/1.18 usesimpsplitting = 0
% 0.82/1.18 usesimpdemod = 5
% 0.82/1.18 usesimpres = 3
% 0.82/1.18
% 0.82/1.18 resimpinuse = 1000
% 0.82/1.18 resimpclauses = 20000
% 0.82/1.18 substype = eqrewr
% 0.82/1.18 backwardsubs = 1
% 0.82/1.18 selectoldest = 5
% 0.82/1.18
% 0.82/1.18 litorderings [0] = split
% 0.82/1.18 litorderings [1] = extend the termordering, first sorting on arguments
% 0.82/1.18
% 0.82/1.18 termordering = kbo
% 0.82/1.18
% 0.82/1.18 litapriori = 0
% 0.82/1.18 termapriori = 1
% 0.82/1.18 litaposteriori = 0
% 0.82/1.18 termaposteriori = 0
% 0.82/1.18 demodaposteriori = 0
% 0.82/1.18 ordereqreflfact = 0
% 0.82/1.18
% 0.82/1.18 litselect = negord
% 0.82/1.18
% 0.82/1.18 maxweight = 15
% 0.82/1.18 maxdepth = 30000
% 0.82/1.18 maxlength = 115
% 0.82/1.18 maxnrvars = 195
% 0.82/1.18 excuselevel = 1
% 0.82/1.18 increasemaxweight = 1
% 0.82/1.18
% 0.82/1.18 maxselected = 10000000
% 0.82/1.18 maxnrclauses = 10000000
% 0.82/1.18
% 0.82/1.18 showgenerated = 0
% 0.82/1.18 showkept = 0
% 0.82/1.18 showselected = 0
% 0.82/1.18 showdeleted = 0
% 0.82/1.18 showresimp = 1
% 0.82/1.18 showstatus = 2000
% 0.82/1.18
% 0.82/1.18 prologoutput = 0
% 0.82/1.18 nrgoals = 5000000
% 0.82/1.18 totalproof = 1
% 0.82/1.18
% 0.82/1.18 Symbols occurring in the translation:
% 0.82/1.18
% 0.82/1.18 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.82/1.18 . [1, 2] (w:1, o:22, a:1, s:1, b:0),
% 0.82/1.18 ! [4, 1] (w:0, o:16, a:1, s:1, b:0),
% 0.82/1.18 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.82/1.18 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.82/1.18 set_union2 [37, 2] (w:1, o:46, a:1, s:1, b:0),
% 0.82/1.18 empty [38, 1] (w:1, o:21, a:1, s:1, b:0),
% 0.82/1.18 cartesian_product2 [40, 2] (w:1, o:47, a:1, s:1, b:0),
% 0.82/1.18 skol1 [42, 0] (w:1, o:10, a:1, s:1, b:1),
% 0.82/1.18 skol2 [43, 0] (w:1, o:11, a:1, s:1, b:1),
% 0.82/1.18 skol3 [44, 0] (w:1, o:12, a:1, s:1, b:1),
% 0.82/1.18 skol4 [45, 0] (w:1, o:13, a:1, s:1, b:1),
% 0.82/1.18 skol5 [46, 0] (w:1, o:14, a:1, s:1, b:1),
% 0.82/1.18 skol6 [47, 0] (w:1, o:15, a:1, s:1, b:1).
% 0.82/1.18
% 0.82/1.18
% 0.82/1.18 Starting Search:
% 0.82/1.18
% 0.82/1.18 *** allocated 15000 integers for clauses
% 0.82/1.18 *** allocated 22500 integers for clauses
% 0.82/1.18
% 0.82/1.18 Bliksems!, er is een bewijs:
% 0.82/1.18 % SZS status Theorem
% 0.82/1.18 % SZS output start Refutation
% 0.82/1.18
% 0.82/1.18 (6) {G0,W13,D4,L1,V3,M1} I { set_union2( cartesian_product2( X, Z ),
% 0.82/1.18 cartesian_product2( Y, Z ) ) ==> cartesian_product2( set_union2( X, Y ),
% 0.82/1.18 Z ) }.
% 0.82/1.18 (7) {G0,W13,D4,L1,V3,M1} I { set_union2( cartesian_product2( Z, X ),
% 0.82/1.18 cartesian_product2( Z, Y ) ) ==> cartesian_product2( Z, set_union2( X, Y
% 0.82/1.18 ) ) }.
% 0.82/1.18 (8) {G1,W21,D6,L1,V0,M1} I;d(7) { ! set_union2( set_union2(
% 0.82/1.18 cartesian_product2( skol3, set_union2( skol5, skol6 ) ),
% 0.82/1.18 cartesian_product2( skol4, skol5 ) ), cartesian_product2( skol4, skol6 )
% 0.82/1.18 ) ==> cartesian_product2( set_union2( skol3, skol4 ), set_union2( skol5
% 0.82/1.18 , skol6 ) ) }.
% 0.82/1.18 (9) {G0,W11,D4,L1,V3,M1} I { set_union2( X, set_union2( Y, Z ) ) ==>
% 0.82/1.18 set_union2( set_union2( X, Y ), Z ) }.
% 0.82/1.18 (71) {G1,W17,D5,L1,V4,M1} P(7,9) { set_union2( set_union2( T,
% 0.82/1.18 cartesian_product2( X, Y ) ), cartesian_product2( X, Z ) ) ==> set_union2
% 0.82/1.18 ( T, cartesian_product2( X, set_union2( Y, Z ) ) ) }.
% 0.82/1.18 (234) {G2,W0,D0,L0,V0,M0} P(71,8);d(6);q { }.
% 0.82/1.18
% 0.82/1.18
% 0.82/1.18 % SZS output end Refutation
% 0.82/1.18 found a proof!
% 0.82/1.18
% 0.82/1.18
% 0.82/1.18 Unprocessed initial clauses:
% 0.82/1.18
% 0.82/1.18 (236) {G0,W7,D3,L1,V2,M1} { set_union2( X, Y ) = set_union2( Y, X ) }.
% 0.82/1.18 (237) {G0,W6,D3,L2,V2,M2} { empty( X ), ! empty( set_union2( X, Y ) ) }.
% 0.82/1.18 (238) {G0,W6,D3,L2,V2,M2} { empty( X ), ! empty( set_union2( Y, X ) ) }.
% 0.82/1.18 (239) {G0,W5,D3,L1,V1,M1} { set_union2( X, X ) = X }.
% 0.82/1.18 (240) {G0,W2,D2,L1,V0,M1} { empty( skol1 ) }.
% 0.82/1.18 (241) {G0,W2,D2,L1,V0,M1} { ! empty( skol2 ) }.
% 0.82/1.18 (242) {G0,W13,D4,L1,V3,M1} { cartesian_product2( set_union2( X, Y ), Z ) =
% 0.82/1.18 set_union2( cartesian_product2( X, Z ), cartesian_product2( Y, Z ) ) }.
% 0.82/1.18 (243) {G0,W13,D4,L1,V3,M1} { cartesian_product2( Z, set_union2( X, Y ) ) =
% 0.82/1.18 set_union2( cartesian_product2( Z, X ), cartesian_product2( Z, Y ) ) }.
% 0.82/1.18 (244) {G0,W23,D6,L1,V0,M1} { ! cartesian_product2( set_union2( skol3,
% 0.82/1.18 skol4 ), set_union2( skol5, skol6 ) ) = set_union2( set_union2(
% 0.82/1.18 set_union2( cartesian_product2( skol3, skol5 ), cartesian_product2( skol3
% 0.82/1.18 , skol6 ) ), cartesian_product2( skol4, skol5 ) ), cartesian_product2(
% 0.82/1.18 skol4, skol6 ) ) }.
% 0.82/1.18 (245) {G0,W11,D4,L1,V3,M1} { set_union2( set_union2( X, Y ), Z ) =
% 0.82/1.18 set_union2( X, set_union2( Y, Z ) ) }.
% 0.82/1.18
% 0.82/1.18
% 0.82/1.18 Total Proof:
% 0.82/1.18
% 0.82/1.18 eqswap: (247) {G0,W13,D4,L1,V3,M1} { set_union2( cartesian_product2( X, Z
% 0.82/1.18 ), cartesian_product2( Y, Z ) ) = cartesian_product2( set_union2( X, Y )
% 0.82/1.18 , Z ) }.
% 0.82/1.18 parent0[0]: (242) {G0,W13,D4,L1,V3,M1} { cartesian_product2( set_union2( X
% 0.82/1.18 , Y ), Z ) = set_union2( cartesian_product2( X, Z ), cartesian_product2(
% 0.82/1.18 Y, Z ) ) }.
% 0.82/1.18 substitution0:
% 0.82/1.18 X := X
% 0.82/1.18 Y := Y
% 0.82/1.18 Z := Z
% 0.82/1.18 end
% 0.82/1.18
% 0.82/1.18 subsumption: (6) {G0,W13,D4,L1,V3,M1} I { set_union2( cartesian_product2( X
% 0.82/1.18 , Z ), cartesian_product2( Y, Z ) ) ==> cartesian_product2( set_union2( X
% 0.82/1.18 , Y ), Z ) }.
% 0.82/1.18 parent0: (247) {G0,W13,D4,L1,V3,M1} { set_union2( cartesian_product2( X, Z
% 0.82/1.18 ), cartesian_product2( Y, Z ) ) = cartesian_product2( set_union2( X, Y )
% 0.82/1.18 , Z ) }.
% 0.82/1.18 substitution0:
% 0.82/1.18 X := X
% 0.82/1.18 Y := Y
% 0.82/1.18 Z := Z
% 0.82/1.18 end
% 0.82/1.18 permutation0:
% 0.82/1.18 0 ==> 0
% 0.82/1.18 end
% 0.82/1.18
% 0.82/1.18 eqswap: (250) {G0,W13,D4,L1,V3,M1} { set_union2( cartesian_product2( X, Y
% 0.82/1.18 ), cartesian_product2( X, Z ) ) = cartesian_product2( X, set_union2( Y,
% 0.82/1.18 Z ) ) }.
% 0.82/1.18 parent0[0]: (243) {G0,W13,D4,L1,V3,M1} { cartesian_product2( Z, set_union2
% 0.82/1.18 ( X, Y ) ) = set_union2( cartesian_product2( Z, X ), cartesian_product2(
% 0.82/1.18 Z, Y ) ) }.
% 0.82/1.18 substitution0:
% 0.82/1.18 X := Y
% 0.82/1.18 Y := Z
% 0.82/1.18 Z := X
% 0.82/1.18 end
% 0.82/1.18
% 0.82/1.18 subsumption: (7) {G0,W13,D4,L1,V3,M1} I { set_union2( cartesian_product2( Z
% 0.82/1.18 , X ), cartesian_product2( Z, Y ) ) ==> cartesian_product2( Z, set_union2
% 0.82/1.18 ( X, Y ) ) }.
% 0.82/1.18 parent0: (250) {G0,W13,D4,L1,V3,M1} { set_union2( cartesian_product2( X, Y
% 0.82/1.18 ), cartesian_product2( X, Z ) ) = cartesian_product2( X, set_union2( Y,
% 0.82/1.18 Z ) ) }.
% 0.82/1.18 substitution0:
% 0.82/1.18 X := Z
% 0.82/1.18 Y := X
% 0.82/1.18 Z := Y
% 0.82/1.18 end
% 0.82/1.18 permutation0:
% 0.82/1.18 0 ==> 0
% 0.82/1.18 end
% 0.82/1.18
% 0.82/1.18 paramod: (266) {G1,W21,D6,L1,V0,M1} { ! cartesian_product2( set_union2(
% 0.82/1.18 skol3, skol4 ), set_union2( skol5, skol6 ) ) = set_union2( set_union2(
% 0.82/1.18 cartesian_product2( skol3, set_union2( skol5, skol6 ) ),
% 0.82/1.18 cartesian_product2( skol4, skol5 ) ), cartesian_product2( skol4, skol6 )
% 0.82/1.18 ) }.
% 0.82/1.18 parent0[0]: (7) {G0,W13,D4,L1,V3,M1} I { set_union2( cartesian_product2( Z
% 0.82/1.18 , X ), cartesian_product2( Z, Y ) ) ==> cartesian_product2( Z, set_union2
% 0.82/1.18 ( X, Y ) ) }.
% 0.82/1.18 parent1[0; 11]: (244) {G0,W23,D6,L1,V0,M1} { ! cartesian_product2(
% 0.82/1.18 set_union2( skol3, skol4 ), set_union2( skol5, skol6 ) ) = set_union2(
% 0.82/1.18 set_union2( set_union2( cartesian_product2( skol3, skol5 ),
% 0.82/1.18 cartesian_product2( skol3, skol6 ) ), cartesian_product2( skol4, skol5 )
% 0.82/1.18 ), cartesian_product2( skol4, skol6 ) ) }.
% 0.82/1.18 substitution0:
% 0.82/1.18 X := skol5
% 0.82/1.18 Y := skol6
% 0.82/1.18 Z := skol3
% 0.82/1.18 end
% 0.82/1.18 substitution1:
% 0.82/1.18 end
% 0.82/1.18
% 0.82/1.18 eqswap: (267) {G1,W21,D6,L1,V0,M1} { ! set_union2( set_union2(
% 0.82/1.18 cartesian_product2( skol3, set_union2( skol5, skol6 ) ),
% 0.82/1.18 cartesian_product2( skol4, skol5 ) ), cartesian_product2( skol4, skol6 )
% 0.82/1.18 ) = cartesian_product2( set_union2( skol3, skol4 ), set_union2( skol5,
% 0.82/1.18 skol6 ) ) }.
% 0.82/1.18 parent0[0]: (266) {G1,W21,D6,L1,V0,M1} { ! cartesian_product2( set_union2
% 0.82/1.18 ( skol3, skol4 ), set_union2( skol5, skol6 ) ) = set_union2( set_union2(
% 0.82/1.18 cartesian_product2( skol3, set_union2( skol5, skol6 ) ),
% 0.82/1.18 cartesian_product2( skol4, skol5 ) ), cartesian_product2( skol4, skol6 )
% 0.82/1.18 ) }.
% 0.82/1.18 substitution0:
% 0.82/1.18 end
% 0.82/1.18
% 0.82/1.18 subsumption: (8) {G1,W21,D6,L1,V0,M1} I;d(7) { ! set_union2( set_union2(
% 0.82/1.18 cartesian_product2( skol3, set_union2( skol5, skol6 ) ),
% 0.82/1.18 cartesian_product2( skol4, skol5 ) ), cartesian_product2( skol4, skol6 )
% 0.82/1.18 ) ==> cartesian_product2( set_union2( skol3, skol4 ), set_union2( skol5
% 0.82/1.18 , skol6 ) ) }.
% 0.82/1.18 parent0: (267) {G1,W21,D6,L1,V0,M1} { ! set_union2( set_union2(
% 0.82/1.18 cartesian_product2( skol3, set_union2( skol5, skol6 ) ),
% 0.82/1.18 cartesian_product2( skol4, skol5 ) ), cartesian_product2( skol4, skol6 )
% 0.82/1.18 ) = cartesian_product2( set_union2( skol3, skol4 ), set_union2( skol5,
% 0.82/1.18 skol6 ) ) }.
% 0.82/1.18 substitution0:
% 0.82/1.18 end
% 0.82/1.18 permutation0:
% 0.82/1.18 0 ==> 0
% 0.82/1.18 end
% 0.82/1.18
% 0.82/1.18 eqswap: (272) {G0,W11,D4,L1,V3,M1} { set_union2( X, set_union2( Y, Z ) ) =
% 0.82/1.18 set_union2( set_union2( X, Y ), Z ) }.
% 0.82/1.18 parent0[0]: (245) {G0,W11,D4,L1,V3,M1} { set_union2( set_union2( X, Y ), Z
% 0.82/1.18 ) = set_union2( X, set_union2( Y, Z ) ) }.
% 0.82/1.18 substitution0:
% 0.82/1.18 X := X
% 0.82/1.18 Y := Y
% 0.82/1.18 Z := Z
% 0.82/1.18 end
% 0.82/1.18
% 0.82/1.18 subsumption: (9) {G0,W11,D4,L1,V3,M1} I { set_union2( X, set_union2( Y, Z )
% 0.82/1.18 ) ==> set_union2( set_union2( X, Y ), Z ) }.
% 0.82/1.18 parent0: (272) {G0,W11,D4,L1,V3,M1} { set_union2( X, set_union2( Y, Z ) )
% 0.82/1.18 = set_union2( set_union2( X, Y ), Z ) }.
% 0.82/1.18 substitution0:
% 0.82/1.18 X := X
% 0.82/1.18 Y := Y
% 0.82/1.18 Z := Z
% 0.82/1.18 end
% 0.82/1.18 permutation0:
% 0.82/1.18 0 ==> 0
% 0.82/1.18 end
% 0.82/1.18
% 0.82/1.18 eqswap: (274) {G0,W11,D4,L1,V3,M1} { set_union2( set_union2( X, Y ), Z )
% 0.82/1.18 ==> set_union2( X, set_union2( Y, Z ) ) }.
% 0.82/1.18 parent0[0]: (9) {G0,W11,D4,L1,V3,M1} I { set_union2( X, set_union2( Y, Z )
% 0.82/1.18 ) ==> set_union2( set_union2( X, Y ), Z ) }.
% 0.82/1.18 substitution0:
% 0.82/1.18 X := X
% 0.82/1.18 Y := Y
% 0.82/1.18 Z := Z
% 0.82/1.18 end
% 0.82/1.18
% 0.82/1.18 paramod: (278) {G1,W17,D5,L1,V4,M1} { set_union2( set_union2( X,
% 0.82/1.18 cartesian_product2( Y, Z ) ), cartesian_product2( Y, T ) ) ==> set_union2
% 0.82/1.18 ( X, cartesian_product2( Y, set_union2( Z, T ) ) ) }.
% 0.82/1.18 parent0[0]: (7) {G0,W13,D4,L1,V3,M1} I { set_union2( cartesian_product2( Z
% 0.82/1.18 , X ), cartesian_product2( Z, Y ) ) ==> cartesian_product2( Z, set_union2
% 0.82/1.18 ( X, Y ) ) }.
% 0.82/1.18 parent1[0; 12]: (274) {G0,W11,D4,L1,V3,M1} { set_union2( set_union2( X, Y
% 0.82/1.18 ), Z ) ==> set_union2( X, set_union2( Y, Z ) ) }.
% 0.82/1.18 substitution0:
% 0.82/1.18 X := Z
% 0.82/1.18 Y := T
% 0.82/1.18 Z := Y
% 0.82/1.18 end
% 0.82/1.18 substitution1:
% 0.82/1.18 X := X
% 0.82/1.18 Y := cartesian_product2( Y, Z )
% 0.82/1.18 Z := cartesian_product2( Y, T )
% 0.82/1.18 end
% 0.82/1.18
% 0.82/1.18 subsumption: (71) {G1,W17,D5,L1,V4,M1} P(7,9) { set_union2( set_union2( T,
% 0.82/1.18 cartesian_product2( X, Y ) ), cartesian_product2( X, Z ) ) ==> set_union2
% 0.82/1.18 ( T, cartesian_product2( X, set_union2( Y, Z ) ) ) }.
% 0.82/1.18 parent0: (278) {G1,W17,D5,L1,V4,M1} { set_union2( set_union2( X,
% 0.82/1.18 cartesian_product2( Y, Z ) ), cartesian_product2( Y, T ) ) ==> set_union2
% 0.82/1.18 ( X, cartesian_product2( Y, set_union2( Z, T ) ) ) }.
% 0.82/1.18 substitution0:
% 0.82/1.18 X := T
% 0.82/1.18 Y := X
% 0.82/1.18 Z := Y
% 0.82/1.18 T := Z
% 0.82/1.18 end
% 0.82/1.18 permutation0:
% 0.82/1.18 0 ==> 0
% 0.82/1.18 end
% 0.82/1.18
% 0.82/1.18 eqswap: (282) {G1,W21,D6,L1,V0,M1} { ! cartesian_product2( set_union2(
% 0.82/1.18 skol3, skol4 ), set_union2( skol5, skol6 ) ) ==> set_union2( set_union2(
% 0.82/1.18 cartesian_product2( skol3, set_union2( skol5, skol6 ) ),
% 0.82/1.18 cartesian_product2( skol4, skol5 ) ), cartesian_product2( skol4, skol6 )
% 0.82/1.18 ) }.
% 0.82/1.18 parent0[0]: (8) {G1,W21,D6,L1,V0,M1} I;d(7) { ! set_union2( set_union2(
% 0.82/1.18 cartesian_product2( skol3, set_union2( skol5, skol6 ) ),
% 0.82/1.18 cartesian_product2( skol4, skol5 ) ), cartesian_product2( skol4, skol6 )
% 0.82/1.18 ) ==> cartesian_product2( set_union2( skol3, skol4 ), set_union2( skol5
% 0.82/1.18 , skol6 ) ) }.
% 0.82/1.18 substitution0:
% 0.82/1.18 end
% 0.82/1.18
% 0.82/1.18 paramod: (284) {G2,W19,D5,L1,V0,M1} { ! cartesian_product2( set_union2(
% 0.82/1.18 skol3, skol4 ), set_union2( skol5, skol6 ) ) ==> set_union2(
% 0.82/1.18 cartesian_product2( skol3, set_union2( skol5, skol6 ) ),
% 0.82/1.18 cartesian_product2( skol4, set_union2( skol5, skol6 ) ) ) }.
% 0.82/1.18 parent0[0]: (71) {G1,W17,D5,L1,V4,M1} P(7,9) { set_union2( set_union2( T,
% 0.82/1.18 cartesian_product2( X, Y ) ), cartesian_product2( X, Z ) ) ==> set_union2
% 0.82/1.18 ( T, cartesian_product2( X, set_union2( Y, Z ) ) ) }.
% 0.82/1.18 parent1[0; 9]: (282) {G1,W21,D6,L1,V0,M1} { ! cartesian_product2(
% 0.82/1.18 set_union2( skol3, skol4 ), set_union2( skol5, skol6 ) ) ==> set_union2(
% 0.82/1.18 set_union2( cartesian_product2( skol3, set_union2( skol5, skol6 ) ),
% 0.82/1.18 cartesian_product2( skol4, skol5 ) ), cartesian_product2( skol4, skol6 )
% 0.82/1.18 ) }.
% 0.82/1.18 substitution0:
% 0.82/1.18 X := skol4
% 0.82/1.18 Y := skol5
% 0.82/1.18 Z := skol6
% 0.82/1.18 T := cartesian_product2( skol3, set_union2( skol5, skol6 ) )
% 0.82/1.18 end
% 0.82/1.18 substitution1:
% 0.82/1.18 end
% 0.82/1.18
% 0.82/1.18 paramod: (285) {G1,W15,D4,L1,V0,M1} { ! cartesian_product2( set_union2(
% 0.82/1.18 skol3, skol4 ), set_union2( skol5, skol6 ) ) ==> cartesian_product2(
% 0.82/1.18 set_union2( skol3, skol4 ), set_union2( skol5, skol6 ) ) }.
% 0.82/1.18 parent0[0]: (6) {G0,W13,D4,L1,V3,M1} I { set_union2( cartesian_product2( X
% 0.82/1.18 , Z ), cartesian_product2( Y, Z ) ) ==> cartesian_product2( set_union2( X
% 0.82/1.18 , Y ), Z ) }.
% 0.82/1.18 parent1[0; 9]: (284) {G2,W19,D5,L1,V0,M1} { ! cartesian_product2(
% 0.82/1.18 set_union2( skol3, skol4 ), set_union2( skol5, skol6 ) ) ==> set_union2(
% 0.82/1.18 cartesian_product2( skol3, set_union2( skol5, skol6 ) ),
% 0.82/1.18 cartesian_product2( skol4, set_union2( skol5, skol6 ) ) ) }.
% 0.82/1.18 substitution0:
% 0.82/1.18 X := skol3
% 0.82/1.18 Y := skol4
% 0.82/1.18 Z := set_union2( skol5, skol6 )
% 0.82/1.18 end
% 0.82/1.18 substitution1:
% 0.82/1.18 end
% 0.82/1.18
% 0.82/1.18 eqrefl: (286) {G0,W0,D0,L0,V0,M0} { }.
% 0.82/1.18 parent0[0]: (285) {G1,W15,D4,L1,V0,M1} { ! cartesian_product2( set_union2
% 0.82/1.18 ( skol3, skol4 ), set_union2( skol5, skol6 ) ) ==> cartesian_product2(
% 0.82/1.18 set_union2( skol3, skol4 ), set_union2( skol5, skol6 ) ) }.
% 0.82/1.18 substitution0:
% 0.82/1.18 end
% 0.82/1.18
% 0.82/1.18 subsumption: (234) {G2,W0,D0,L0,V0,M0} P(71,8);d(6);q { }.
% 0.82/1.18 parent0: (286) {G0,W0,D0,L0,V0,M0} { }.
% 0.82/1.18 substitution0:
% 0.82/1.18 end
% 0.82/1.18 permutation0:
% 0.82/1.18 end
% 0.82/1.18
% 0.82/1.18 Proof check complete!
% 0.82/1.18
% 0.82/1.18 Memory use:
% 0.82/1.18
% 0.82/1.18 space for terms: 3473
% 0.82/1.18 space for clauses: 15052
% 0.82/1.18
% 0.82/1.18
% 0.82/1.18 clauses generated: 22189
% 0.82/1.18 clauses kept: 235
% 0.82/1.18 clauses selected: 185
% 0.82/1.18 clauses deleted: 1
% 0.82/1.18 clauses inuse deleted: 0
% 0.82/1.18
% 0.82/1.18 subsentry: 96447
% 0.82/1.18 literals s-matched: 95971
% 0.82/1.18 literals matched: 95971
% 0.82/1.18 full subsumption: 0
% 0.82/1.18
% 0.82/1.18 checksum: 55497177
% 0.82/1.18
% 0.82/1.18
% 0.82/1.18 Bliksem ended
%------------------------------------------------------------------------------