TSTP Solution File: KLE022+1 by Bliksem---1.12
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%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : KLE022+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n006.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 01:36:41 EDT 2022
% Result : Theorem 0.68s 1.11s
% Output : Refutation 0.68s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : KLE022+1 : TPTP v8.1.0. Released v4.0.0.
% 0.12/0.13 % Command : bliksem %s
% 0.13/0.34 % Computer : n006.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % DateTime : Thu Jun 16 16:17:26 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.68/1.11 *** allocated 10000 integers for termspace/termends
% 0.68/1.11 *** allocated 10000 integers for clauses
% 0.68/1.11 *** allocated 10000 integers for justifications
% 0.68/1.11 Bliksem 1.12
% 0.68/1.11
% 0.68/1.11
% 0.68/1.11 Automatic Strategy Selection
% 0.68/1.11
% 0.68/1.11
% 0.68/1.11 Clauses:
% 0.68/1.11
% 0.68/1.11 { addition( X, Y ) = addition( Y, X ) }.
% 0.68/1.11 { addition( Z, addition( Y, X ) ) = addition( addition( Z, Y ), X ) }.
% 0.68/1.11 { addition( X, zero ) = X }.
% 0.68/1.11 { addition( X, X ) = X }.
% 0.68/1.11 { multiplication( X, multiplication( Y, Z ) ) = multiplication(
% 0.68/1.11 multiplication( X, Y ), Z ) }.
% 0.68/1.11 { multiplication( X, one ) = X }.
% 0.68/1.11 { multiplication( one, X ) = X }.
% 0.68/1.11 { multiplication( X, addition( Y, Z ) ) = addition( multiplication( X, Y )
% 0.68/1.11 , multiplication( X, Z ) ) }.
% 0.68/1.11 { multiplication( addition( X, Y ), Z ) = addition( multiplication( X, Z )
% 0.68/1.11 , multiplication( Y, Z ) ) }.
% 0.68/1.11 { multiplication( X, zero ) = zero }.
% 0.68/1.11 { multiplication( zero, X ) = zero }.
% 0.68/1.11 { ! leq( X, Y ), addition( X, Y ) = Y }.
% 0.68/1.11 { ! addition( X, Y ) = Y, leq( X, Y ) }.
% 0.68/1.11 { ! test( X ), complement( skol1( X ), X ) }.
% 0.68/1.11 { ! complement( Y, X ), test( X ) }.
% 0.68/1.11 { ! complement( Y, X ), multiplication( X, Y ) = zero }.
% 0.68/1.11 { ! complement( Y, X ), alpha1( X, Y ) }.
% 0.68/1.11 { ! multiplication( X, Y ) = zero, ! alpha1( X, Y ), complement( Y, X ) }.
% 0.68/1.11 { ! alpha1( X, Y ), multiplication( Y, X ) = zero }.
% 0.68/1.11 { ! alpha1( X, Y ), addition( X, Y ) = one }.
% 0.68/1.11 { ! multiplication( Y, X ) = zero, ! addition( X, Y ) = one, alpha1( X, Y )
% 0.68/1.11 }.
% 0.68/1.11 { ! test( X ), ! c( X ) = Y, complement( X, Y ) }.
% 0.68/1.11 { ! test( X ), ! complement( X, Y ), c( X ) = Y }.
% 0.68/1.11 { test( X ), c( X ) = zero }.
% 0.68/1.11 { test( skol2 ) }.
% 0.68/1.11 { ! skol3 = addition( multiplication( skol3, skol2 ), multiplication( skol3
% 0.68/1.11 , c( skol2 ) ) ) }.
% 0.68/1.11
% 0.68/1.11 percentage equality = 0.534884, percentage horn = 0.961538
% 0.68/1.11 This is a problem with some equality
% 0.68/1.11
% 0.68/1.11
% 0.68/1.11
% 0.68/1.11 Options Used:
% 0.68/1.11
% 0.68/1.11 useres = 1
% 0.68/1.11 useparamod = 1
% 0.68/1.11 useeqrefl = 1
% 0.68/1.11 useeqfact = 1
% 0.68/1.11 usefactor = 1
% 0.68/1.11 usesimpsplitting = 0
% 0.68/1.11 usesimpdemod = 5
% 0.68/1.11 usesimpres = 3
% 0.68/1.11
% 0.68/1.11 resimpinuse = 1000
% 0.68/1.11 resimpclauses = 20000
% 0.68/1.11 substype = eqrewr
% 0.68/1.11 backwardsubs = 1
% 0.68/1.11 selectoldest = 5
% 0.68/1.11
% 0.68/1.11 litorderings [0] = split
% 0.68/1.11 litorderings [1] = extend the termordering, first sorting on arguments
% 0.68/1.11
% 0.68/1.11 termordering = kbo
% 0.68/1.11
% 0.68/1.11 litapriori = 0
% 0.68/1.11 termapriori = 1
% 0.68/1.11 litaposteriori = 0
% 0.68/1.11 termaposteriori = 0
% 0.68/1.11 demodaposteriori = 0
% 0.68/1.11 ordereqreflfact = 0
% 0.68/1.11
% 0.68/1.11 litselect = negord
% 0.68/1.11
% 0.68/1.11 maxweight = 15
% 0.68/1.11 maxdepth = 30000
% 0.68/1.11 maxlength = 115
% 0.68/1.11 maxnrvars = 195
% 0.68/1.11 excuselevel = 1
% 0.68/1.11 increasemaxweight = 1
% 0.68/1.11
% 0.68/1.11 maxselected = 10000000
% 0.68/1.11 maxnrclauses = 10000000
% 0.68/1.11
% 0.68/1.11 showgenerated = 0
% 0.68/1.11 showkept = 0
% 0.68/1.11 showselected = 0
% 0.68/1.11 showdeleted = 0
% 0.68/1.11 showresimp = 1
% 0.68/1.11 showstatus = 2000
% 0.68/1.11
% 0.68/1.11 prologoutput = 0
% 0.68/1.11 nrgoals = 5000000
% 0.68/1.11 totalproof = 1
% 0.68/1.11
% 0.68/1.11 Symbols occurring in the translation:
% 0.68/1.11
% 0.68/1.11 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.68/1.11 . [1, 2] (w:1, o:23, a:1, s:1, b:0),
% 0.68/1.11 ! [4, 1] (w:0, o:15, a:1, s:1, b:0),
% 0.68/1.11 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.68/1.11 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.68/1.11 addition [37, 2] (w:1, o:47, a:1, s:1, b:0),
% 0.68/1.11 zero [39, 0] (w:1, o:9, a:1, s:1, b:0),
% 0.68/1.11 multiplication [40, 2] (w:1, o:49, a:1, s:1, b:0),
% 0.68/1.11 one [41, 0] (w:1, o:10, a:1, s:1, b:0),
% 0.68/1.11 leq [42, 2] (w:1, o:48, a:1, s:1, b:0),
% 0.68/1.11 test [44, 1] (w:1, o:21, a:1, s:1, b:0),
% 0.68/1.11 complement [46, 2] (w:1, o:50, a:1, s:1, b:0),
% 0.68/1.11 c [47, 1] (w:1, o:22, a:1, s:1, b:0),
% 0.68/1.11 alpha1 [48, 2] (w:1, o:51, a:1, s:1, b:1),
% 0.68/1.11 skol1 [49, 1] (w:1, o:20, a:1, s:1, b:1),
% 0.68/1.11 skol2 [50, 0] (w:1, o:13, a:1, s:1, b:1),
% 0.68/1.11 skol3 [51, 0] (w:1, o:14, a:1, s:1, b:1).
% 0.68/1.11
% 0.68/1.11
% 0.68/1.11 Starting Search:
% 0.68/1.11
% 0.68/1.11 *** allocated 15000 integers for clauses
% 0.68/1.11 *** allocated 22500 integers for clauses
% 0.68/1.11 *** allocated 33750 integers for clauses
% 0.68/1.11
% 0.68/1.11 Bliksems!, er is een bewijs:
% 0.68/1.11 % SZS status Theorem
% 0.68/1.11 % SZS output start Refutation
% 0.68/1.11
% 0.68/1.11 (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X ) }.
% 0.68/1.11 (5) {G0,W5,D3,L1,V1,M1} I { multiplication( X, one ) ==> X }.
% 0.68/1.11 (7) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Y ),
% 0.68/1.11 multiplication( X, Z ) ) ==> multiplication( X, addition( Y, Z ) ) }.
% 0.68/1.11 (16) {G0,W6,D2,L2,V2,M2} I { ! complement( Y, X ), alpha1( X, Y ) }.
% 0.68/1.11 (19) {G0,W8,D3,L2,V2,M2} I { ! alpha1( X, Y ), addition( X, Y ) ==> one }.
% 0.68/1.11 (21) {G0,W9,D3,L3,V2,M3} I { ! test( X ), ! c( X ) = Y, complement( X, Y )
% 0.68/1.11 }.
% 0.68/1.11 (24) {G0,W2,D2,L1,V0,M1} I { test( skol2 ) }.
% 0.68/1.11 (25) {G1,W8,D5,L1,V0,M1} I;d(7) { ! multiplication( skol3, addition( skol2
% 0.68/1.11 , c( skol2 ) ) ) ==> skol3 }.
% 0.68/1.11 (26) {G1,W6,D3,L2,V1,M2} Q(21) { ! test( X ), complement( X, c( X ) ) }.
% 0.68/1.11 (36) {G2,W4,D3,L1,V0,M1} R(26,24) { complement( skol2, c( skol2 ) ) }.
% 0.68/1.11 (37) {G3,W4,D3,L1,V0,M1} R(36,16) { alpha1( c( skol2 ), skol2 ) }.
% 0.68/1.11 (267) {G4,W6,D4,L1,V0,M1} R(19,37) { addition( c( skol2 ), skol2 ) ==> one
% 0.68/1.11 }.
% 0.68/1.11 (451) {G5,W0,D0,L0,V0,M0} P(0,25);d(267);d(5);q { }.
% 0.68/1.11
% 0.68/1.11
% 0.68/1.11 % SZS output end Refutation
% 0.68/1.11 found a proof!
% 0.68/1.11
% 0.68/1.11
% 0.68/1.11 Unprocessed initial clauses:
% 0.68/1.11
% 0.68/1.11 (453) {G0,W7,D3,L1,V2,M1} { addition( X, Y ) = addition( Y, X ) }.
% 0.68/1.11 (454) {G0,W11,D4,L1,V3,M1} { addition( Z, addition( Y, X ) ) = addition(
% 0.68/1.11 addition( Z, Y ), X ) }.
% 0.68/1.11 (455) {G0,W5,D3,L1,V1,M1} { addition( X, zero ) = X }.
% 0.68/1.11 (456) {G0,W5,D3,L1,V1,M1} { addition( X, X ) = X }.
% 0.68/1.11 (457) {G0,W11,D4,L1,V3,M1} { multiplication( X, multiplication( Y, Z ) ) =
% 0.68/1.11 multiplication( multiplication( X, Y ), Z ) }.
% 0.68/1.11 (458) {G0,W5,D3,L1,V1,M1} { multiplication( X, one ) = X }.
% 0.68/1.11 (459) {G0,W5,D3,L1,V1,M1} { multiplication( one, X ) = X }.
% 0.68/1.11 (460) {G0,W13,D4,L1,V3,M1} { multiplication( X, addition( Y, Z ) ) =
% 0.68/1.11 addition( multiplication( X, Y ), multiplication( X, Z ) ) }.
% 0.68/1.11 (461) {G0,W13,D4,L1,V3,M1} { multiplication( addition( X, Y ), Z ) =
% 0.68/1.11 addition( multiplication( X, Z ), multiplication( Y, Z ) ) }.
% 0.68/1.11 (462) {G0,W5,D3,L1,V1,M1} { multiplication( X, zero ) = zero }.
% 0.68/1.11 (463) {G0,W5,D3,L1,V1,M1} { multiplication( zero, X ) = zero }.
% 0.68/1.11 (464) {G0,W8,D3,L2,V2,M2} { ! leq( X, Y ), addition( X, Y ) = Y }.
% 0.68/1.11 (465) {G0,W8,D3,L2,V2,M2} { ! addition( X, Y ) = Y, leq( X, Y ) }.
% 0.68/1.11 (466) {G0,W6,D3,L2,V1,M2} { ! test( X ), complement( skol1( X ), X ) }.
% 0.68/1.11 (467) {G0,W5,D2,L2,V2,M2} { ! complement( Y, X ), test( X ) }.
% 0.68/1.11 (468) {G0,W8,D3,L2,V2,M2} { ! complement( Y, X ), multiplication( X, Y ) =
% 0.68/1.11 zero }.
% 0.68/1.11 (469) {G0,W6,D2,L2,V2,M2} { ! complement( Y, X ), alpha1( X, Y ) }.
% 0.68/1.11 (470) {G0,W11,D3,L3,V2,M3} { ! multiplication( X, Y ) = zero, ! alpha1( X
% 0.68/1.11 , Y ), complement( Y, X ) }.
% 0.68/1.11 (471) {G0,W8,D3,L2,V2,M2} { ! alpha1( X, Y ), multiplication( Y, X ) =
% 0.68/1.11 zero }.
% 0.68/1.11 (472) {G0,W8,D3,L2,V2,M2} { ! alpha1( X, Y ), addition( X, Y ) = one }.
% 0.68/1.11 (473) {G0,W13,D3,L3,V2,M3} { ! multiplication( Y, X ) = zero, ! addition(
% 0.68/1.11 X, Y ) = one, alpha1( X, Y ) }.
% 0.68/1.11 (474) {G0,W9,D3,L3,V2,M3} { ! test( X ), ! c( X ) = Y, complement( X, Y )
% 0.68/1.11 }.
% 0.68/1.11 (475) {G0,W9,D3,L3,V2,M3} { ! test( X ), ! complement( X, Y ), c( X ) = Y
% 0.68/1.11 }.
% 0.68/1.11 (476) {G0,W6,D3,L2,V1,M2} { test( X ), c( X ) = zero }.
% 0.68/1.11 (477) {G0,W2,D2,L1,V0,M1} { test( skol2 ) }.
% 0.68/1.11 (478) {G0,W10,D5,L1,V0,M1} { ! skol3 = addition( multiplication( skol3,
% 0.68/1.11 skol2 ), multiplication( skol3, c( skol2 ) ) ) }.
% 0.68/1.11
% 0.68/1.11
% 0.68/1.11 Total Proof:
% 0.68/1.11
% 0.68/1.11 subsumption: (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X
% 0.68/1.11 ) }.
% 0.68/1.11 parent0: (453) {G0,W7,D3,L1,V2,M1} { addition( X, Y ) = addition( Y, X )
% 0.68/1.11 }.
% 0.68/1.11 substitution0:
% 0.68/1.11 X := X
% 0.68/1.11 Y := Y
% 0.68/1.11 end
% 0.68/1.11 permutation0:
% 0.68/1.11 0 ==> 0
% 0.68/1.11 end
% 0.68/1.11
% 0.68/1.11 subsumption: (5) {G0,W5,D3,L1,V1,M1} I { multiplication( X, one ) ==> X }.
% 0.68/1.11 parent0: (458) {G0,W5,D3,L1,V1,M1} { multiplication( X, one ) = X }.
% 0.68/1.11 substitution0:
% 0.68/1.11 X := X
% 0.68/1.11 end
% 0.68/1.11 permutation0:
% 0.68/1.11 0 ==> 0
% 0.68/1.11 end
% 0.68/1.11
% 0.68/1.11 eqswap: (490) {G0,W13,D4,L1,V3,M1} { addition( multiplication( X, Y ),
% 0.68/1.11 multiplication( X, Z ) ) = multiplication( X, addition( Y, Z ) ) }.
% 0.68/1.11 parent0[0]: (460) {G0,W13,D4,L1,V3,M1} { multiplication( X, addition( Y, Z
% 0.68/1.11 ) ) = addition( multiplication( X, Y ), multiplication( X, Z ) ) }.
% 0.68/1.11 substitution0:
% 0.68/1.11 X := X
% 0.68/1.11 Y := Y
% 0.68/1.11 Z := Z
% 0.68/1.11 end
% 0.68/1.11
% 0.68/1.11 subsumption: (7) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Y )
% 0.68/1.11 , multiplication( X, Z ) ) ==> multiplication( X, addition( Y, Z ) ) }.
% 0.68/1.11 parent0: (490) {G0,W13,D4,L1,V3,M1} { addition( multiplication( X, Y ),
% 0.68/1.11 multiplication( X, Z ) ) = multiplication( X, addition( Y, Z ) ) }.
% 0.68/1.11 substitution0:
% 0.68/1.11 X := X
% 0.68/1.11 Y := Y
% 0.68/1.11 Z := Z
% 0.68/1.11 end
% 0.68/1.11 permutation0:
% 0.68/1.11 0 ==> 0
% 0.68/1.11 end
% 0.68/1.11
% 0.68/1.11 subsumption: (16) {G0,W6,D2,L2,V2,M2} I { ! complement( Y, X ), alpha1( X,
% 0.68/1.11 Y ) }.
% 0.68/1.11 parent0: (469) {G0,W6,D2,L2,V2,M2} { ! complement( Y, X ), alpha1( X, Y )
% 0.68/1.11 }.
% 0.68/1.11 substitution0:
% 0.68/1.11 X := X
% 0.68/1.11 Y := Y
% 0.68/1.11 end
% 0.68/1.11 permutation0:
% 0.68/1.11 0 ==> 0
% 0.68/1.11 1 ==> 1
% 0.68/1.11 end
% 0.68/1.11
% 0.68/1.11 subsumption: (19) {G0,W8,D3,L2,V2,M2} I { ! alpha1( X, Y ), addition( X, Y
% 0.68/1.11 ) ==> one }.
% 0.68/1.11 parent0: (472) {G0,W8,D3,L2,V2,M2} { ! alpha1( X, Y ), addition( X, Y ) =
% 0.68/1.11 one }.
% 0.68/1.11 substitution0:
% 0.68/1.11 X := X
% 0.68/1.11 Y := Y
% 0.68/1.11 end
% 0.68/1.11 permutation0:
% 0.68/1.11 0 ==> 0
% 0.68/1.11 1 ==> 1
% 0.68/1.11 end
% 0.68/1.11
% 0.68/1.11 subsumption: (21) {G0,W9,D3,L3,V2,M3} I { ! test( X ), ! c( X ) = Y,
% 0.68/1.11 complement( X, Y ) }.
% 0.68/1.11 parent0: (474) {G0,W9,D3,L3,V2,M3} { ! test( X ), ! c( X ) = Y, complement
% 0.68/1.11 ( X, Y ) }.
% 0.68/1.11 substitution0:
% 0.68/1.11 X := X
% 0.68/1.11 Y := Y
% 0.68/1.11 end
% 0.68/1.11 permutation0:
% 0.68/1.11 0 ==> 0
% 0.68/1.11 1 ==> 1
% 0.68/1.11 2 ==> 2
% 0.68/1.11 end
% 0.68/1.11
% 0.68/1.11 subsumption: (24) {G0,W2,D2,L1,V0,M1} I { test( skol2 ) }.
% 0.68/1.11 parent0: (477) {G0,W2,D2,L1,V0,M1} { test( skol2 ) }.
% 0.68/1.11 substitution0:
% 0.68/1.11 end
% 0.68/1.11 permutation0:
% 0.68/1.11 0 ==> 0
% 0.68/1.11 end
% 0.68/1.11
% 0.68/1.11 paramod: (613) {G1,W8,D5,L1,V0,M1} { ! skol3 = multiplication( skol3,
% 0.68/1.11 addition( skol2, c( skol2 ) ) ) }.
% 0.68/1.11 parent0[0]: (7) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Y ),
% 0.68/1.11 multiplication( X, Z ) ) ==> multiplication( X, addition( Y, Z ) ) }.
% 0.68/1.11 parent1[0; 3]: (478) {G0,W10,D5,L1,V0,M1} { ! skol3 = addition(
% 0.68/1.11 multiplication( skol3, skol2 ), multiplication( skol3, c( skol2 ) ) ) }.
% 0.68/1.11 substitution0:
% 0.68/1.11 X := skol3
% 0.68/1.11 Y := skol2
% 0.68/1.11 Z := c( skol2 )
% 0.68/1.11 end
% 0.68/1.11 substitution1:
% 0.68/1.11 end
% 0.68/1.11
% 0.68/1.11 eqswap: (614) {G1,W8,D5,L1,V0,M1} { ! multiplication( skol3, addition(
% 0.68/1.11 skol2, c( skol2 ) ) ) = skol3 }.
% 0.68/1.11 parent0[0]: (613) {G1,W8,D5,L1,V0,M1} { ! skol3 = multiplication( skol3,
% 0.68/1.11 addition( skol2, c( skol2 ) ) ) }.
% 0.68/1.11 substitution0:
% 0.68/1.11 end
% 0.68/1.11
% 0.68/1.11 subsumption: (25) {G1,W8,D5,L1,V0,M1} I;d(7) { ! multiplication( skol3,
% 0.68/1.11 addition( skol2, c( skol2 ) ) ) ==> skol3 }.
% 0.68/1.11 parent0: (614) {G1,W8,D5,L1,V0,M1} { ! multiplication( skol3, addition(
% 0.68/1.11 skol2, c( skol2 ) ) ) = skol3 }.
% 0.68/1.11 substitution0:
% 0.68/1.11 end
% 0.68/1.11 permutation0:
% 0.68/1.11 0 ==> 0
% 0.68/1.11 end
% 0.68/1.11
% 0.68/1.11 eqswap: (615) {G0,W9,D3,L3,V2,M3} { ! Y = c( X ), ! test( X ), complement
% 0.68/1.11 ( X, Y ) }.
% 0.68/1.11 parent0[1]: (21) {G0,W9,D3,L3,V2,M3} I { ! test( X ), ! c( X ) = Y,
% 0.68/1.11 complement( X, Y ) }.
% 0.68/1.11 substitution0:
% 0.68/1.11 X := X
% 0.68/1.11 Y := Y
% 0.68/1.11 end
% 0.68/1.11
% 0.68/1.11 eqrefl: (616) {G0,W6,D3,L2,V1,M2} { ! test( X ), complement( X, c( X ) )
% 0.68/1.11 }.
% 0.68/1.11 parent0[0]: (615) {G0,W9,D3,L3,V2,M3} { ! Y = c( X ), ! test( X ),
% 0.68/1.11 complement( X, Y ) }.
% 0.68/1.11 substitution0:
% 0.68/1.11 X := X
% 0.68/1.11 Y := c( X )
% 0.68/1.11 end
% 0.68/1.11
% 0.68/1.11 subsumption: (26) {G1,W6,D3,L2,V1,M2} Q(21) { ! test( X ), complement( X, c
% 0.68/1.11 ( X ) ) }.
% 0.68/1.11 parent0: (616) {G0,W6,D3,L2,V1,M2} { ! test( X ), complement( X, c( X ) )
% 0.68/1.11 }.
% 0.68/1.11 substitution0:
% 0.68/1.11 X := X
% 0.68/1.11 end
% 0.68/1.11 permutation0:
% 0.68/1.11 0 ==> 0
% 0.68/1.11 1 ==> 1
% 0.68/1.11 end
% 0.68/1.11
% 0.68/1.11 resolution: (617) {G1,W4,D3,L1,V0,M1} { complement( skol2, c( skol2 ) )
% 0.68/1.11 }.
% 0.68/1.11 parent0[0]: (26) {G1,W6,D3,L2,V1,M2} Q(21) { ! test( X ), complement( X, c
% 0.68/1.11 ( X ) ) }.
% 0.68/1.11 parent1[0]: (24) {G0,W2,D2,L1,V0,M1} I { test( skol2 ) }.
% 0.68/1.11 substitution0:
% 0.68/1.11 X := skol2
% 0.68/1.11 end
% 0.68/1.11 substitution1:
% 0.68/1.11 end
% 0.68/1.11
% 0.68/1.11 subsumption: (36) {G2,W4,D3,L1,V0,M1} R(26,24) { complement( skol2, c(
% 0.68/1.11 skol2 ) ) }.
% 0.68/1.11 parent0: (617) {G1,W4,D3,L1,V0,M1} { complement( skol2, c( skol2 ) ) }.
% 0.68/1.11 substitution0:
% 0.68/1.11 end
% 0.68/1.11 permutation0:
% 0.68/1.11 0 ==> 0
% 0.68/1.11 end
% 0.68/1.11
% 0.68/1.11 resolution: (618) {G1,W4,D3,L1,V0,M1} { alpha1( c( skol2 ), skol2 ) }.
% 0.68/1.11 parent0[0]: (16) {G0,W6,D2,L2,V2,M2} I { ! complement( Y, X ), alpha1( X, Y
% 0.68/1.11 ) }.
% 0.68/1.11 parent1[0]: (36) {G2,W4,D3,L1,V0,M1} R(26,24) { complement( skol2, c( skol2
% 0.68/1.11 ) ) }.
% 0.68/1.11 substitution0:
% 0.68/1.11 X := c( skol2 )
% 0.68/1.11 Y := skol2
% 0.68/1.11 end
% 0.68/1.11 substitution1:
% 0.68/1.11 end
% 0.68/1.11
% 0.68/1.11 subsumption: (37) {G3,W4,D3,L1,V0,M1} R(36,16) { alpha1( c( skol2 ), skol2
% 0.68/1.11 ) }.
% 0.68/1.11 parent0: (618) {G1,W4,D3,L1,V0,M1} { alpha1( c( skol2 ), skol2 ) }.
% 0.68/1.11 substitution0:
% 0.68/1.11 end
% 0.68/1.11 permutation0:
% 0.68/1.11 0 ==> 0
% 0.68/1.11 end
% 0.68/1.11
% 0.68/1.11 eqswap: (619) {G0,W8,D3,L2,V2,M2} { one ==> addition( X, Y ), ! alpha1( X
% 0.68/1.11 , Y ) }.
% 0.68/1.11 parent0[1]: (19) {G0,W8,D3,L2,V2,M2} I { ! alpha1( X, Y ), addition( X, Y )
% 0.68/1.11 ==> one }.
% 0.68/1.11 substitution0:
% 0.68/1.11 X := X
% 0.68/1.11 Y := Y
% 0.68/1.11 end
% 0.68/1.11
% 0.68/1.11 resolution: (620) {G1,W6,D4,L1,V0,M1} { one ==> addition( c( skol2 ),
% 0.68/1.11 skol2 ) }.
% 0.68/1.11 parent0[1]: (619) {G0,W8,D3,L2,V2,M2} { one ==> addition( X, Y ), ! alpha1
% 0.68/1.11 ( X, Y ) }.
% 0.68/1.11 parent1[0]: (37) {G3,W4,D3,L1,V0,M1} R(36,16) { alpha1( c( skol2 ), skol2 )
% 0.68/1.11 }.
% 0.68/1.11 substitution0:
% 0.68/1.11 X := c( skol2 )
% 0.68/1.11 Y := skol2
% 0.68/1.11 end
% 0.68/1.11 substitution1:
% 0.68/1.11 end
% 0.68/1.11
% 0.68/1.11 eqswap: (621) {G1,W6,D4,L1,V0,M1} { addition( c( skol2 ), skol2 ) ==> one
% 0.68/1.11 }.
% 0.68/1.11 parent0[0]: (620) {G1,W6,D4,L1,V0,M1} { one ==> addition( c( skol2 ),
% 0.68/1.11 skol2 ) }.
% 0.68/1.11 substitution0:
% 0.68/1.11 end
% 0.68/1.11
% 0.68/1.11 subsumption: (267) {G4,W6,D4,L1,V0,M1} R(19,37) { addition( c( skol2 ),
% 0.68/1.11 skol2 ) ==> one }.
% 0.68/1.11 parent0: (621) {G1,W6,D4,L1,V0,M1} { addition( c( skol2 ), skol2 ) ==> one
% 0.68/1.11 }.
% 0.68/1.11 substitution0:
% 0.68/1.11 end
% 0.68/1.11 permutation0:
% 0.68/1.11 0 ==> 0
% 0.68/1.11 end
% 0.68/1.11
% 0.68/1.11 eqswap: (622) {G1,W8,D5,L1,V0,M1} { ! skol3 ==> multiplication( skol3,
% 0.68/1.11 addition( skol2, c( skol2 ) ) ) }.
% 0.68/1.11 parent0[0]: (25) {G1,W8,D5,L1,V0,M1} I;d(7) { ! multiplication( skol3,
% 0.68/1.11 addition( skol2, c( skol2 ) ) ) ==> skol3 }.
% 0.68/1.11 substitution0:
% 0.68/1.11 end
% 0.68/1.11
% 0.68/1.11 paramod: (625) {G1,W8,D5,L1,V0,M1} { ! skol3 ==> multiplication( skol3,
% 0.68/1.11 addition( c( skol2 ), skol2 ) ) }.
% 0.68/1.11 parent0[0]: (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X )
% 0.68/1.11 }.
% 0.68/1.11 parent1[0; 5]: (622) {G1,W8,D5,L1,V0,M1} { ! skol3 ==> multiplication(
% 0.68/1.11 skol3, addition( skol2, c( skol2 ) ) ) }.
% 0.68/1.11 substitution0:
% 0.68/1.11 X := skol2
% 0.68/1.11 Y := c( skol2 )
% 0.68/1.11 end
% 0.68/1.11 substitution1:
% 0.68/1.11 end
% 0.68/1.11
% 0.68/1.11 paramod: (627) {G2,W5,D3,L1,V0,M1} { ! skol3 ==> multiplication( skol3,
% 0.68/1.11 one ) }.
% 0.68/1.11 parent0[0]: (267) {G4,W6,D4,L1,V0,M1} R(19,37) { addition( c( skol2 ),
% 0.68/1.11 skol2 ) ==> one }.
% 0.68/1.11 parent1[0; 5]: (625) {G1,W8,D5,L1,V0,M1} { ! skol3 ==> multiplication(
% 0.68/1.11 skol3, addition( c( skol2 ), skol2 ) ) }.
% 0.68/1.11 substitution0:
% 0.68/1.11 end
% 0.68/1.11 substitution1:
% 0.68/1.11 end
% 0.68/1.11
% 0.68/1.11 paramod: (628) {G1,W3,D2,L1,V0,M1} { ! skol3 ==> skol3 }.
% 0.68/1.11 parent0[0]: (5) {G0,W5,D3,L1,V1,M1} I { multiplication( X, one ) ==> X }.
% 0.68/1.11 parent1[0; 3]: (627) {G2,W5,D3,L1,V0,M1} { ! skol3 ==> multiplication(
% 0.68/1.11 skol3, one ) }.
% 0.68/1.11 substitution0:
% 0.68/1.11 X := skol3
% 0.68/1.11 end
% 0.68/1.11 substitution1:
% 0.68/1.11 end
% 0.68/1.11
% 0.68/1.11 eqrefl: (629) {G0,W0,D0,L0,V0,M0} { }.
% 0.68/1.11 parent0[0]: (628) {G1,W3,D2,L1,V0,M1} { ! skol3 ==> skol3 }.
% 0.68/1.11 substitution0:
% 0.68/1.11 end
% 0.68/1.11
% 0.68/1.11 subsumption: (451) {G5,W0,D0,L0,V0,M0} P(0,25);d(267);d(5);q { }.
% 0.68/1.11 parent0: (629) {G0,W0,D0,L0,V0,M0} { }.
% 0.68/1.11 substitution0:
% 0.68/1.11 end
% 0.68/1.11 permutation0:
% 0.68/1.11 end
% 0.68/1.11
% 0.68/1.11 Proof check complete!
% 0.68/1.11
% 0.68/1.11 Memory use:
% 0.68/1.11
% 0.68/1.11 space for terms: 5009
% 0.68/1.11 space for clauses: 25935
% 0.68/1.11
% 0.68/1.11
% 0.68/1.11 clauses generated: 1618
% 0.68/1.11 clauses kept: 452
% 0.68/1.11 clauses selected: 76
% 0.68/1.11 clauses deleted: 0
% 0.68/1.11 clauses inuse deleted: 0
% 0.68/1.11
% 0.68/1.11 subsentry: 2580
% 0.68/1.11 literals s-matched: 1622
% 0.68/1.11 literals matched: 1622
% 0.68/1.11 full subsumption: 90
% 0.68/1.11
% 0.68/1.11 checksum: 900180450
% 0.68/1.11
% 0.68/1.11
% 0.68/1.11 Bliksem ended
%------------------------------------------------------------------------------