TSTP Solution File: KLE021+1 by Bliksem---1.12
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%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : KLE021+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n027.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 : Sun Jul 17 01:36:40 EDT 2022
% Result : Theorem 0.44s 1.08s
% Output : Refutation 0.44s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : KLE021+1 : TPTP v8.1.0. Released v4.0.0.
% 0.06/0.12 % Command : bliksem %s
% 0.12/0.33 % Computer : n027.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 : Thu Jun 16 15:26:50 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.44/1.08 *** allocated 10000 integers for termspace/termends
% 0.44/1.08 *** allocated 10000 integers for clauses
% 0.44/1.08 *** allocated 10000 integers for justifications
% 0.44/1.08 Bliksem 1.12
% 0.44/1.08
% 0.44/1.08
% 0.44/1.08 Automatic Strategy Selection
% 0.44/1.08
% 0.44/1.08
% 0.44/1.08 Clauses:
% 0.44/1.08
% 0.44/1.08 { addition( X, Y ) = addition( Y, X ) }.
% 0.44/1.08 { addition( Z, addition( Y, X ) ) = addition( addition( Z, Y ), X ) }.
% 0.44/1.08 { addition( X, zero ) = X }.
% 0.44/1.08 { addition( X, X ) = X }.
% 0.44/1.08 { multiplication( X, multiplication( Y, Z ) ) = multiplication(
% 0.44/1.08 multiplication( X, Y ), Z ) }.
% 0.44/1.08 { multiplication( X, one ) = X }.
% 0.44/1.08 { multiplication( one, X ) = X }.
% 0.44/1.08 { multiplication( X, addition( Y, Z ) ) = addition( multiplication( X, Y )
% 0.44/1.08 , multiplication( X, Z ) ) }.
% 0.44/1.08 { multiplication( addition( X, Y ), Z ) = addition( multiplication( X, Z )
% 0.44/1.08 , multiplication( Y, Z ) ) }.
% 0.44/1.08 { multiplication( X, zero ) = zero }.
% 0.44/1.08 { multiplication( zero, X ) = zero }.
% 0.44/1.08 { ! leq( X, Y ), addition( X, Y ) = Y }.
% 0.44/1.08 { ! addition( X, Y ) = Y, leq( X, Y ) }.
% 0.44/1.08 { ! test( X ), complement( skol1( X ), X ) }.
% 0.44/1.08 { ! complement( Y, X ), test( X ) }.
% 0.44/1.08 { ! complement( Y, X ), multiplication( X, Y ) = zero }.
% 0.44/1.08 { ! complement( Y, X ), alpha1( X, Y ) }.
% 0.44/1.08 { ! multiplication( X, Y ) = zero, ! alpha1( X, Y ), complement( Y, X ) }.
% 0.44/1.08 { ! alpha1( X, Y ), multiplication( Y, X ) = zero }.
% 0.44/1.08 { ! alpha1( X, Y ), addition( X, Y ) = one }.
% 0.44/1.08 { ! multiplication( Y, X ) = zero, ! addition( X, Y ) = one, alpha1( X, Y )
% 0.44/1.08 }.
% 0.44/1.08 { ! test( X ), ! c( X ) = Y, complement( X, Y ) }.
% 0.44/1.08 { ! test( X ), ! complement( X, Y ), c( X ) = Y }.
% 0.44/1.08 { test( X ), c( X ) = zero }.
% 0.44/1.08 { test( skol2 ) }.
% 0.44/1.08 { ! skol3 = addition( multiplication( skol2, skol3 ), multiplication( c(
% 0.44/1.08 skol2 ), skol3 ) ) }.
% 0.44/1.08
% 0.44/1.08 percentage equality = 0.534884, percentage horn = 0.961538
% 0.44/1.08 This is a problem with some equality
% 0.44/1.08
% 0.44/1.08
% 0.44/1.08
% 0.44/1.08 Options Used:
% 0.44/1.08
% 0.44/1.08 useres = 1
% 0.44/1.08 useparamod = 1
% 0.44/1.08 useeqrefl = 1
% 0.44/1.08 useeqfact = 1
% 0.44/1.08 usefactor = 1
% 0.44/1.08 usesimpsplitting = 0
% 0.44/1.08 usesimpdemod = 5
% 0.44/1.08 usesimpres = 3
% 0.44/1.08
% 0.44/1.08 resimpinuse = 1000
% 0.44/1.08 resimpclauses = 20000
% 0.44/1.08 substype = eqrewr
% 0.44/1.08 backwardsubs = 1
% 0.44/1.08 selectoldest = 5
% 0.44/1.08
% 0.44/1.08 litorderings [0] = split
% 0.44/1.08 litorderings [1] = extend the termordering, first sorting on arguments
% 0.44/1.08
% 0.44/1.08 termordering = kbo
% 0.44/1.08
% 0.44/1.08 litapriori = 0
% 0.44/1.08 termapriori = 1
% 0.44/1.08 litaposteriori = 0
% 0.44/1.08 termaposteriori = 0
% 0.44/1.08 demodaposteriori = 0
% 0.44/1.08 ordereqreflfact = 0
% 0.44/1.08
% 0.44/1.08 litselect = negord
% 0.44/1.08
% 0.44/1.08 maxweight = 15
% 0.44/1.08 maxdepth = 30000
% 0.44/1.08 maxlength = 115
% 0.44/1.08 maxnrvars = 195
% 0.44/1.08 excuselevel = 1
% 0.44/1.08 increasemaxweight = 1
% 0.44/1.08
% 0.44/1.08 maxselected = 10000000
% 0.44/1.08 maxnrclauses = 10000000
% 0.44/1.08
% 0.44/1.08 showgenerated = 0
% 0.44/1.08 showkept = 0
% 0.44/1.08 showselected = 0
% 0.44/1.08 showdeleted = 0
% 0.44/1.08 showresimp = 1
% 0.44/1.08 showstatus = 2000
% 0.44/1.08
% 0.44/1.08 prologoutput = 0
% 0.44/1.08 nrgoals = 5000000
% 0.44/1.08 totalproof = 1
% 0.44/1.08
% 0.44/1.08 Symbols occurring in the translation:
% 0.44/1.08
% 0.44/1.08 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.44/1.08 . [1, 2] (w:1, o:23, a:1, s:1, b:0),
% 0.44/1.08 ! [4, 1] (w:0, o:15, a:1, s:1, b:0),
% 0.44/1.08 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.44/1.08 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.44/1.08 addition [37, 2] (w:1, o:47, a:1, s:1, b:0),
% 0.44/1.08 zero [39, 0] (w:1, o:9, a:1, s:1, b:0),
% 0.44/1.08 multiplication [40, 2] (w:1, o:49, a:1, s:1, b:0),
% 0.44/1.08 one [41, 0] (w:1, o:10, a:1, s:1, b:0),
% 0.44/1.08 leq [42, 2] (w:1, o:48, a:1, s:1, b:0),
% 0.44/1.08 test [44, 1] (w:1, o:21, a:1, s:1, b:0),
% 0.44/1.08 complement [46, 2] (w:1, o:50, a:1, s:1, b:0),
% 0.44/1.08 c [47, 1] (w:1, o:22, a:1, s:1, b:0),
% 0.44/1.08 alpha1 [48, 2] (w:1, o:51, a:1, s:1, b:1),
% 0.44/1.08 skol1 [49, 1] (w:1, o:20, a:1, s:1, b:1),
% 0.44/1.08 skol2 [50, 0] (w:1, o:13, a:1, s:1, b:1),
% 0.44/1.08 skol3 [51, 0] (w:1, o:14, a:1, s:1, b:1).
% 0.44/1.08
% 0.44/1.08
% 0.44/1.08 Starting Search:
% 0.44/1.08
% 0.44/1.08 *** allocated 15000 integers for clauses
% 0.44/1.08 *** allocated 22500 integers for clauses
% 0.44/1.08 *** allocated 33750 integers for clauses
% 0.44/1.08
% 0.44/1.08 Bliksems!, er is een bewijs:
% 0.44/1.08 % SZS status Theorem
% 0.44/1.08 % SZS output start Refutation
% 0.44/1.08
% 0.44/1.08 (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X ) }.
% 0.44/1.08 (6) {G0,W5,D3,L1,V1,M1} I { multiplication( one, X ) ==> X }.
% 0.44/1.08 (8) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Z ),
% 0.44/1.08 multiplication( Y, Z ) ) ==> multiplication( addition( X, Y ), Z ) }.
% 0.44/1.08 (16) {G0,W6,D2,L2,V2,M2} I { ! complement( Y, X ), alpha1( X, Y ) }.
% 0.44/1.08 (19) {G0,W8,D3,L2,V2,M2} I { ! alpha1( X, Y ), addition( X, Y ) ==> one }.
% 0.44/1.08 (21) {G0,W9,D3,L3,V2,M3} I { ! test( X ), ! c( X ) = Y, complement( X, Y )
% 0.44/1.08 }.
% 0.44/1.08 (24) {G0,W2,D2,L1,V0,M1} I { test( skol2 ) }.
% 0.44/1.08 (25) {G1,W8,D5,L1,V0,M1} I;d(8) { ! multiplication( addition( skol2, c(
% 0.44/1.08 skol2 ) ), skol3 ) ==> skol3 }.
% 0.44/1.08 (26) {G1,W6,D3,L2,V1,M2} Q(21) { ! test( X ), complement( X, c( X ) ) }.
% 0.44/1.08 (36) {G2,W4,D3,L1,V0,M1} R(26,24) { complement( skol2, c( skol2 ) ) }.
% 0.44/1.08 (37) {G3,W4,D3,L1,V0,M1} R(36,16) { alpha1( c( skol2 ), skol2 ) }.
% 0.44/1.08 (267) {G4,W6,D4,L1,V0,M1} R(19,37) { addition( c( skol2 ), skol2 ) ==> one
% 0.44/1.08 }.
% 0.44/1.08 (451) {G5,W0,D0,L0,V0,M0} P(0,25);d(267);d(6);q { }.
% 0.44/1.08
% 0.44/1.08
% 0.44/1.08 % SZS output end Refutation
% 0.44/1.08 found a proof!
% 0.44/1.08
% 0.44/1.08
% 0.44/1.08 Unprocessed initial clauses:
% 0.44/1.08
% 0.44/1.08 (453) {G0,W7,D3,L1,V2,M1} { addition( X, Y ) = addition( Y, X ) }.
% 0.44/1.08 (454) {G0,W11,D4,L1,V3,M1} { addition( Z, addition( Y, X ) ) = addition(
% 0.44/1.08 addition( Z, Y ), X ) }.
% 0.44/1.08 (455) {G0,W5,D3,L1,V1,M1} { addition( X, zero ) = X }.
% 0.44/1.08 (456) {G0,W5,D3,L1,V1,M1} { addition( X, X ) = X }.
% 0.44/1.08 (457) {G0,W11,D4,L1,V3,M1} { multiplication( X, multiplication( Y, Z ) ) =
% 0.44/1.08 multiplication( multiplication( X, Y ), Z ) }.
% 0.44/1.08 (458) {G0,W5,D3,L1,V1,M1} { multiplication( X, one ) = X }.
% 0.44/1.08 (459) {G0,W5,D3,L1,V1,M1} { multiplication( one, X ) = X }.
% 0.44/1.08 (460) {G0,W13,D4,L1,V3,M1} { multiplication( X, addition( Y, Z ) ) =
% 0.44/1.08 addition( multiplication( X, Y ), multiplication( X, Z ) ) }.
% 0.44/1.08 (461) {G0,W13,D4,L1,V3,M1} { multiplication( addition( X, Y ), Z ) =
% 0.44/1.08 addition( multiplication( X, Z ), multiplication( Y, Z ) ) }.
% 0.44/1.08 (462) {G0,W5,D3,L1,V1,M1} { multiplication( X, zero ) = zero }.
% 0.44/1.08 (463) {G0,W5,D3,L1,V1,M1} { multiplication( zero, X ) = zero }.
% 0.44/1.08 (464) {G0,W8,D3,L2,V2,M2} { ! leq( X, Y ), addition( X, Y ) = Y }.
% 0.44/1.08 (465) {G0,W8,D3,L2,V2,M2} { ! addition( X, Y ) = Y, leq( X, Y ) }.
% 0.44/1.08 (466) {G0,W6,D3,L2,V1,M2} { ! test( X ), complement( skol1( X ), X ) }.
% 0.44/1.08 (467) {G0,W5,D2,L2,V2,M2} { ! complement( Y, X ), test( X ) }.
% 0.44/1.08 (468) {G0,W8,D3,L2,V2,M2} { ! complement( Y, X ), multiplication( X, Y ) =
% 0.44/1.08 zero }.
% 0.44/1.08 (469) {G0,W6,D2,L2,V2,M2} { ! complement( Y, X ), alpha1( X, Y ) }.
% 0.44/1.08 (470) {G0,W11,D3,L3,V2,M3} { ! multiplication( X, Y ) = zero, ! alpha1( X
% 0.44/1.08 , Y ), complement( Y, X ) }.
% 0.44/1.08 (471) {G0,W8,D3,L2,V2,M2} { ! alpha1( X, Y ), multiplication( Y, X ) =
% 0.44/1.08 zero }.
% 0.44/1.08 (472) {G0,W8,D3,L2,V2,M2} { ! alpha1( X, Y ), addition( X, Y ) = one }.
% 0.44/1.08 (473) {G0,W13,D3,L3,V2,M3} { ! multiplication( Y, X ) = zero, ! addition(
% 0.44/1.08 X, Y ) = one, alpha1( X, Y ) }.
% 0.44/1.08 (474) {G0,W9,D3,L3,V2,M3} { ! test( X ), ! c( X ) = Y, complement( X, Y )
% 0.44/1.08 }.
% 0.44/1.08 (475) {G0,W9,D3,L3,V2,M3} { ! test( X ), ! complement( X, Y ), c( X ) = Y
% 0.44/1.08 }.
% 0.44/1.08 (476) {G0,W6,D3,L2,V1,M2} { test( X ), c( X ) = zero }.
% 0.44/1.08 (477) {G0,W2,D2,L1,V0,M1} { test( skol2 ) }.
% 0.44/1.08 (478) {G0,W10,D5,L1,V0,M1} { ! skol3 = addition( multiplication( skol2,
% 0.44/1.08 skol3 ), multiplication( c( skol2 ), skol3 ) ) }.
% 0.44/1.08
% 0.44/1.08
% 0.44/1.08 Total Proof:
% 0.44/1.08
% 0.44/1.08 subsumption: (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X
% 0.44/1.08 ) }.
% 0.44/1.08 parent0: (453) {G0,W7,D3,L1,V2,M1} { addition( X, Y ) = addition( Y, X )
% 0.44/1.08 }.
% 0.44/1.08 substitution0:
% 0.44/1.08 X := X
% 0.44/1.08 Y := Y
% 0.44/1.08 end
% 0.44/1.08 permutation0:
% 0.44/1.08 0 ==> 0
% 0.44/1.08 end
% 0.44/1.08
% 0.44/1.08 subsumption: (6) {G0,W5,D3,L1,V1,M1} I { multiplication( one, X ) ==> X }.
% 0.44/1.08 parent0: (459) {G0,W5,D3,L1,V1,M1} { multiplication( one, X ) = X }.
% 0.44/1.08 substitution0:
% 0.44/1.08 X := X
% 0.44/1.08 end
% 0.44/1.08 permutation0:
% 0.44/1.08 0 ==> 0
% 0.44/1.08 end
% 0.44/1.08
% 0.44/1.08 eqswap: (492) {G0,W13,D4,L1,V3,M1} { addition( multiplication( X, Z ),
% 0.44/1.08 multiplication( Y, Z ) ) = multiplication( addition( X, Y ), Z ) }.
% 0.44/1.08 parent0[0]: (461) {G0,W13,D4,L1,V3,M1} { multiplication( addition( X, Y )
% 0.44/1.08 , Z ) = addition( multiplication( X, Z ), multiplication( Y, Z ) ) }.
% 0.44/1.08 substitution0:
% 0.44/1.08 X := X
% 0.44/1.08 Y := Y
% 0.44/1.08 Z := Z
% 0.44/1.08 end
% 0.44/1.08
% 0.44/1.08 subsumption: (8) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Z )
% 0.44/1.08 , multiplication( Y, Z ) ) ==> multiplication( addition( X, Y ), Z ) }.
% 0.44/1.08 parent0: (492) {G0,W13,D4,L1,V3,M1} { addition( multiplication( X, Z ),
% 0.44/1.08 multiplication( Y, Z ) ) = multiplication( addition( X, Y ), Z ) }.
% 0.44/1.08 substitution0:
% 0.44/1.08 X := X
% 0.44/1.08 Y := Y
% 0.44/1.08 Z := Z
% 0.44/1.08 end
% 0.44/1.08 permutation0:
% 0.44/1.08 0 ==> 0
% 0.44/1.08 end
% 0.44/1.08
% 0.44/1.08 subsumption: (16) {G0,W6,D2,L2,V2,M2} I { ! complement( Y, X ), alpha1( X,
% 0.72/1.08 Y ) }.
% 0.72/1.08 parent0: (469) {G0,W6,D2,L2,V2,M2} { ! complement( Y, X ), alpha1( X, Y )
% 0.72/1.08 }.
% 0.72/1.08 substitution0:
% 0.72/1.08 X := X
% 0.72/1.08 Y := Y
% 0.72/1.08 end
% 0.72/1.08 permutation0:
% 0.72/1.08 0 ==> 0
% 0.72/1.08 1 ==> 1
% 0.72/1.08 end
% 0.72/1.08
% 0.72/1.08 subsumption: (19) {G0,W8,D3,L2,V2,M2} I { ! alpha1( X, Y ), addition( X, Y
% 0.72/1.08 ) ==> one }.
% 0.72/1.08 parent0: (472) {G0,W8,D3,L2,V2,M2} { ! alpha1( X, Y ), addition( X, Y ) =
% 0.72/1.08 one }.
% 0.72/1.08 substitution0:
% 0.72/1.08 X := X
% 0.72/1.08 Y := Y
% 0.72/1.08 end
% 0.72/1.08 permutation0:
% 0.72/1.08 0 ==> 0
% 0.72/1.08 1 ==> 1
% 0.72/1.08 end
% 0.72/1.08
% 0.72/1.08 subsumption: (21) {G0,W9,D3,L3,V2,M3} I { ! test( X ), ! c( X ) = Y,
% 0.72/1.08 complement( X, Y ) }.
% 0.72/1.08 parent0: (474) {G0,W9,D3,L3,V2,M3} { ! test( X ), ! c( X ) = Y, complement
% 0.72/1.08 ( X, Y ) }.
% 0.72/1.08 substitution0:
% 0.72/1.08 X := X
% 0.72/1.08 Y := Y
% 0.72/1.08 end
% 0.72/1.08 permutation0:
% 0.72/1.08 0 ==> 0
% 0.72/1.08 1 ==> 1
% 0.72/1.08 2 ==> 2
% 0.72/1.08 end
% 0.72/1.08
% 0.72/1.08 subsumption: (24) {G0,W2,D2,L1,V0,M1} I { test( skol2 ) }.
% 0.72/1.08 parent0: (477) {G0,W2,D2,L1,V0,M1} { test( skol2 ) }.
% 0.72/1.08 substitution0:
% 0.72/1.08 end
% 0.72/1.08 permutation0:
% 0.72/1.08 0 ==> 0
% 0.72/1.08 end
% 0.72/1.08
% 0.72/1.08 paramod: (615) {G1,W8,D5,L1,V0,M1} { ! skol3 = multiplication( addition(
% 0.72/1.08 skol2, c( skol2 ) ), skol3 ) }.
% 0.72/1.08 parent0[0]: (8) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Z ),
% 0.72/1.08 multiplication( Y, Z ) ) ==> multiplication( addition( X, Y ), Z ) }.
% 0.72/1.08 parent1[0; 3]: (478) {G0,W10,D5,L1,V0,M1} { ! skol3 = addition(
% 0.72/1.08 multiplication( skol2, skol3 ), multiplication( c( skol2 ), skol3 ) ) }.
% 0.72/1.08 substitution0:
% 0.72/1.08 X := skol2
% 0.72/1.08 Y := c( skol2 )
% 0.72/1.08 Z := skol3
% 0.72/1.08 end
% 0.72/1.08 substitution1:
% 0.72/1.08 end
% 0.72/1.08
% 0.72/1.08 eqswap: (616) {G1,W8,D5,L1,V0,M1} { ! multiplication( addition( skol2, c(
% 0.72/1.08 skol2 ) ), skol3 ) = skol3 }.
% 0.72/1.08 parent0[0]: (615) {G1,W8,D5,L1,V0,M1} { ! skol3 = multiplication( addition
% 0.72/1.08 ( skol2, c( skol2 ) ), skol3 ) }.
% 0.72/1.08 substitution0:
% 0.72/1.08 end
% 0.72/1.08
% 0.72/1.08 subsumption: (25) {G1,W8,D5,L1,V0,M1} I;d(8) { ! multiplication( addition(
% 0.72/1.08 skol2, c( skol2 ) ), skol3 ) ==> skol3 }.
% 0.72/1.08 parent0: (616) {G1,W8,D5,L1,V0,M1} { ! multiplication( addition( skol2, c
% 0.72/1.08 ( skol2 ) ), skol3 ) = skol3 }.
% 0.72/1.08 substitution0:
% 0.72/1.08 end
% 0.72/1.08 permutation0:
% 0.72/1.08 0 ==> 0
% 0.72/1.08 end
% 0.72/1.08
% 0.72/1.08 eqswap: (617) {G0,W9,D3,L3,V2,M3} { ! Y = c( X ), ! test( X ), complement
% 0.72/1.08 ( X, Y ) }.
% 0.72/1.08 parent0[1]: (21) {G0,W9,D3,L3,V2,M3} I { ! test( X ), ! c( X ) = Y,
% 0.72/1.08 complement( X, Y ) }.
% 0.72/1.08 substitution0:
% 0.72/1.08 X := X
% 0.72/1.08 Y := Y
% 0.72/1.08 end
% 0.72/1.08
% 0.72/1.08 eqrefl: (618) {G0,W6,D3,L2,V1,M2} { ! test( X ), complement( X, c( X ) )
% 0.72/1.08 }.
% 0.72/1.08 parent0[0]: (617) {G0,W9,D3,L3,V2,M3} { ! Y = c( X ), ! test( X ),
% 0.72/1.08 complement( X, Y ) }.
% 0.72/1.08 substitution0:
% 0.72/1.08 X := X
% 0.72/1.08 Y := c( X )
% 0.72/1.08 end
% 0.72/1.08
% 0.72/1.08 subsumption: (26) {G1,W6,D3,L2,V1,M2} Q(21) { ! test( X ), complement( X, c
% 0.72/1.08 ( X ) ) }.
% 0.72/1.08 parent0: (618) {G0,W6,D3,L2,V1,M2} { ! test( X ), complement( X, c( X ) )
% 0.72/1.08 }.
% 0.72/1.08 substitution0:
% 0.72/1.08 X := X
% 0.72/1.08 end
% 0.72/1.08 permutation0:
% 0.72/1.08 0 ==> 0
% 0.72/1.08 1 ==> 1
% 0.72/1.08 end
% 0.72/1.08
% 0.72/1.08 resolution: (619) {G1,W4,D3,L1,V0,M1} { complement( skol2, c( skol2 ) )
% 0.72/1.08 }.
% 0.72/1.08 parent0[0]: (26) {G1,W6,D3,L2,V1,M2} Q(21) { ! test( X ), complement( X, c
% 0.72/1.08 ( X ) ) }.
% 0.72/1.08 parent1[0]: (24) {G0,W2,D2,L1,V0,M1} I { test( skol2 ) }.
% 0.72/1.08 substitution0:
% 0.72/1.08 X := skol2
% 0.72/1.08 end
% 0.72/1.08 substitution1:
% 0.72/1.08 end
% 0.72/1.08
% 0.72/1.08 subsumption: (36) {G2,W4,D3,L1,V0,M1} R(26,24) { complement( skol2, c(
% 0.72/1.08 skol2 ) ) }.
% 0.72/1.08 parent0: (619) {G1,W4,D3,L1,V0,M1} { complement( skol2, c( skol2 ) ) }.
% 0.72/1.08 substitution0:
% 0.72/1.08 end
% 0.72/1.08 permutation0:
% 0.72/1.08 0 ==> 0
% 0.72/1.08 end
% 0.72/1.08
% 0.72/1.08 resolution: (620) {G1,W4,D3,L1,V0,M1} { alpha1( c( skol2 ), skol2 ) }.
% 0.72/1.08 parent0[0]: (16) {G0,W6,D2,L2,V2,M2} I { ! complement( Y, X ), alpha1( X, Y
% 0.72/1.08 ) }.
% 0.72/1.08 parent1[0]: (36) {G2,W4,D3,L1,V0,M1} R(26,24) { complement( skol2, c( skol2
% 0.72/1.08 ) ) }.
% 0.72/1.08 substitution0:
% 0.72/1.08 X := c( skol2 )
% 0.72/1.08 Y := skol2
% 0.72/1.08 end
% 0.72/1.08 substitution1:
% 0.72/1.08 end
% 0.72/1.08
% 0.72/1.08 subsumption: (37) {G3,W4,D3,L1,V0,M1} R(36,16) { alpha1( c( skol2 ), skol2
% 0.72/1.08 ) }.
% 0.72/1.08 parent0: (620) {G1,W4,D3,L1,V0,M1} { alpha1( c( skol2 ), skol2 ) }.
% 0.72/1.08 substitution0:
% 0.72/1.08 end
% 0.72/1.08 permutation0:
% 0.72/1.08 0 ==> 0
% 0.72/1.08 end
% 0.72/1.08
% 0.72/1.08 eqswap: (621) {G0,W8,D3,L2,V2,M2} { one ==> addition( X, Y ), ! alpha1( X
% 0.72/1.08 , Y ) }.
% 0.72/1.08 parent0[1]: (19) {G0,W8,D3,L2,V2,M2} I { ! alpha1( X, Y ), addition( X, Y )
% 0.72/1.08 ==> one }.
% 0.72/1.08 substitution0:
% 0.72/1.08 X := X
% 0.72/1.08 Y := Y
% 0.72/1.08 end
% 0.72/1.08
% 0.72/1.08 resolution: (622) {G1,W6,D4,L1,V0,M1} { one ==> addition( c( skol2 ),
% 0.72/1.08 skol2 ) }.
% 0.72/1.08 parent0[1]: (621) {G0,W8,D3,L2,V2,M2} { one ==> addition( X, Y ), ! alpha1
% 0.72/1.08 ( X, Y ) }.
% 0.72/1.08 parent1[0]: (37) {G3,W4,D3,L1,V0,M1} R(36,16) { alpha1( c( skol2 ), skol2 )
% 0.72/1.08 }.
% 0.72/1.08 substitution0:
% 0.72/1.08 X := c( skol2 )
% 0.72/1.08 Y := skol2
% 0.72/1.08 end
% 0.72/1.08 substitution1:
% 0.72/1.08 end
% 0.72/1.08
% 0.72/1.08 eqswap: (623) {G1,W6,D4,L1,V0,M1} { addition( c( skol2 ), skol2 ) ==> one
% 0.72/1.08 }.
% 0.72/1.08 parent0[0]: (622) {G1,W6,D4,L1,V0,M1} { one ==> addition( c( skol2 ),
% 0.72/1.08 skol2 ) }.
% 0.72/1.08 substitution0:
% 0.72/1.08 end
% 0.72/1.08
% 0.72/1.08 subsumption: (267) {G4,W6,D4,L1,V0,M1} R(19,37) { addition( c( skol2 ),
% 0.72/1.08 skol2 ) ==> one }.
% 0.72/1.08 parent0: (623) {G1,W6,D4,L1,V0,M1} { addition( c( skol2 ), skol2 ) ==> one
% 0.72/1.08 }.
% 0.72/1.08 substitution0:
% 0.72/1.08 end
% 0.72/1.08 permutation0:
% 0.72/1.08 0 ==> 0
% 0.72/1.08 end
% 0.72/1.08
% 0.72/1.08 eqswap: (624) {G1,W8,D5,L1,V0,M1} { ! skol3 ==> multiplication( addition(
% 0.72/1.08 skol2, c( skol2 ) ), skol3 ) }.
% 0.72/1.08 parent0[0]: (25) {G1,W8,D5,L1,V0,M1} I;d(8) { ! multiplication( addition(
% 0.72/1.08 skol2, c( skol2 ) ), skol3 ) ==> skol3 }.
% 0.72/1.08 substitution0:
% 0.72/1.08 end
% 0.72/1.08
% 0.72/1.08 paramod: (627) {G1,W8,D5,L1,V0,M1} { ! skol3 ==> multiplication( addition
% 0.72/1.08 ( c( skol2 ), skol2 ), skol3 ) }.
% 0.72/1.08 parent0[0]: (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X )
% 0.72/1.08 }.
% 0.72/1.08 parent1[0; 4]: (624) {G1,W8,D5,L1,V0,M1} { ! skol3 ==> multiplication(
% 0.72/1.08 addition( skol2, c( skol2 ) ), skol3 ) }.
% 0.72/1.08 substitution0:
% 0.72/1.08 X := skol2
% 0.72/1.08 Y := c( skol2 )
% 0.72/1.08 end
% 0.72/1.08 substitution1:
% 0.72/1.08 end
% 0.72/1.08
% 0.72/1.08 paramod: (629) {G2,W5,D3,L1,V0,M1} { ! skol3 ==> multiplication( one,
% 0.72/1.08 skol3 ) }.
% 0.72/1.08 parent0[0]: (267) {G4,W6,D4,L1,V0,M1} R(19,37) { addition( c( skol2 ),
% 0.72/1.08 skol2 ) ==> one }.
% 0.72/1.08 parent1[0; 4]: (627) {G1,W8,D5,L1,V0,M1} { ! skol3 ==> multiplication(
% 0.72/1.08 addition( c( skol2 ), skol2 ), skol3 ) }.
% 0.72/1.08 substitution0:
% 0.72/1.08 end
% 0.72/1.08 substitution1:
% 0.72/1.08 end
% 0.72/1.08
% 0.72/1.08 paramod: (630) {G1,W3,D2,L1,V0,M1} { ! skol3 ==> skol3 }.
% 0.72/1.08 parent0[0]: (6) {G0,W5,D3,L1,V1,M1} I { multiplication( one, X ) ==> X }.
% 0.72/1.08 parent1[0; 3]: (629) {G2,W5,D3,L1,V0,M1} { ! skol3 ==> multiplication( one
% 0.72/1.08 , skol3 ) }.
% 0.72/1.08 substitution0:
% 0.72/1.08 X := skol3
% 0.72/1.08 end
% 0.72/1.08 substitution1:
% 0.72/1.08 end
% 0.72/1.08
% 0.72/1.08 eqrefl: (631) {G0,W0,D0,L0,V0,M0} { }.
% 0.72/1.08 parent0[0]: (630) {G1,W3,D2,L1,V0,M1} { ! skol3 ==> skol3 }.
% 0.72/1.08 substitution0:
% 0.72/1.08 end
% 0.72/1.08
% 0.72/1.08 subsumption: (451) {G5,W0,D0,L0,V0,M0} P(0,25);d(267);d(6);q { }.
% 0.72/1.08 parent0: (631) {G0,W0,D0,L0,V0,M0} { }.
% 0.72/1.08 substitution0:
% 0.72/1.08 end
% 0.72/1.08 permutation0:
% 0.72/1.08 end
% 0.72/1.08
% 0.72/1.08 Proof check complete!
% 0.72/1.08
% 0.72/1.08 Memory use:
% 0.72/1.08
% 0.72/1.08 space for terms: 5009
% 0.72/1.08 space for clauses: 25933
% 0.72/1.08
% 0.72/1.08
% 0.72/1.08 clauses generated: 1618
% 0.72/1.08 clauses kept: 452
% 0.72/1.08 clauses selected: 76
% 0.72/1.08 clauses deleted: 0
% 0.72/1.08 clauses inuse deleted: 0
% 0.72/1.08
% 0.72/1.08 subsentry: 2592
% 0.72/1.08 literals s-matched: 1628
% 0.72/1.08 literals matched: 1628
% 0.72/1.08 full subsumption: 90
% 0.72/1.08
% 0.72/1.08 checksum: 1942018401
% 0.72/1.08
% 0.72/1.08
% 0.72/1.08 Bliksem ended
%------------------------------------------------------------------------------