TSTP Solution File: KLE007+1 by Bliksem---1.12
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%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : KLE007+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n009.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 01:36:32 EDT 2022
% Result : Theorem 0.87s 1.25s
% Output : Refutation 0.87s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : KLE007+1 : TPTP v8.1.0. Released v4.0.0.
% 0.11/0.12 % Command : bliksem %s
% 0.12/0.33 % Computer : n009.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 09:09:08 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.87/1.25 *** allocated 10000 integers for termspace/termends
% 0.87/1.25 *** allocated 10000 integers for clauses
% 0.87/1.25 *** allocated 10000 integers for justifications
% 0.87/1.25 Bliksem 1.12
% 0.87/1.25
% 0.87/1.25
% 0.87/1.25 Automatic Strategy Selection
% 0.87/1.25
% 0.87/1.25
% 0.87/1.25 Clauses:
% 0.87/1.25
% 0.87/1.25 { addition( X, Y ) = addition( Y, X ) }.
% 0.87/1.25 { addition( Z, addition( Y, X ) ) = addition( addition( Z, Y ), X ) }.
% 0.87/1.25 { addition( X, zero ) = X }.
% 0.87/1.25 { addition( X, X ) = X }.
% 0.87/1.25 { multiplication( X, multiplication( Y, Z ) ) = multiplication(
% 0.87/1.25 multiplication( X, Y ), Z ) }.
% 0.87/1.25 { multiplication( X, one ) = X }.
% 0.87/1.25 { multiplication( one, X ) = X }.
% 0.87/1.25 { multiplication( X, addition( Y, Z ) ) = addition( multiplication( X, Y )
% 0.87/1.25 , multiplication( X, Z ) ) }.
% 0.87/1.25 { multiplication( addition( X, Y ), Z ) = addition( multiplication( X, Z )
% 0.87/1.25 , multiplication( Y, Z ) ) }.
% 0.87/1.25 { multiplication( X, zero ) = zero }.
% 0.87/1.25 { multiplication( zero, X ) = zero }.
% 0.87/1.25 { ! leq( X, Y ), addition( X, Y ) = Y }.
% 0.87/1.25 { ! addition( X, Y ) = Y, leq( X, Y ) }.
% 0.87/1.25 { ! test( X ), complement( skol1( X ), X ) }.
% 0.87/1.25 { ! complement( Y, X ), test( X ) }.
% 0.87/1.25 { ! complement( Y, X ), multiplication( X, Y ) = zero }.
% 0.87/1.25 { ! complement( Y, X ), alpha1( X, Y ) }.
% 0.87/1.25 { ! multiplication( X, Y ) = zero, ! alpha1( X, Y ), complement( Y, X ) }.
% 0.87/1.25 { ! alpha1( X, Y ), multiplication( Y, X ) = zero }.
% 0.87/1.25 { ! alpha1( X, Y ), addition( X, Y ) = one }.
% 0.87/1.25 { ! multiplication( Y, X ) = zero, ! addition( X, Y ) = one, alpha1( X, Y )
% 0.87/1.25 }.
% 0.87/1.25 { ! test( X ), ! c( X ) = Y, complement( X, Y ) }.
% 0.87/1.25 { ! test( X ), ! complement( X, Y ), c( X ) = Y }.
% 0.87/1.25 { test( X ), c( X ) = zero }.
% 0.87/1.25 { test( skol3 ) }.
% 0.87/1.25 { test( skol2 ) }.
% 0.87/1.25 { ! one = addition( multiplication( addition( skol2, c( skol2 ) ), skol3 )
% 0.87/1.25 , multiplication( addition( skol2, c( skol2 ) ), c( skol3 ) ) ) }.
% 0.87/1.25
% 0.87/1.25 percentage equality = 0.522727, percentage horn = 0.962963
% 0.87/1.25 This is a problem with some equality
% 0.87/1.25
% 0.87/1.25
% 0.87/1.25
% 0.87/1.25 Options Used:
% 0.87/1.25
% 0.87/1.25 useres = 1
% 0.87/1.25 useparamod = 1
% 0.87/1.25 useeqrefl = 1
% 0.87/1.25 useeqfact = 1
% 0.87/1.25 usefactor = 1
% 0.87/1.25 usesimpsplitting = 0
% 0.87/1.25 usesimpdemod = 5
% 0.87/1.25 usesimpres = 3
% 0.87/1.25
% 0.87/1.25 resimpinuse = 1000
% 0.87/1.25 resimpclauses = 20000
% 0.87/1.25 substype = eqrewr
% 0.87/1.25 backwardsubs = 1
% 0.87/1.25 selectoldest = 5
% 0.87/1.25
% 0.87/1.25 litorderings [0] = split
% 0.87/1.25 litorderings [1] = extend the termordering, first sorting on arguments
% 0.87/1.25
% 0.87/1.25 termordering = kbo
% 0.87/1.25
% 0.87/1.25 litapriori = 0
% 0.87/1.25 termapriori = 1
% 0.87/1.25 litaposteriori = 0
% 0.87/1.25 termaposteriori = 0
% 0.87/1.25 demodaposteriori = 0
% 0.87/1.25 ordereqreflfact = 0
% 0.87/1.25
% 0.87/1.25 litselect = negord
% 0.87/1.25
% 0.87/1.25 maxweight = 15
% 0.87/1.25 maxdepth = 30000
% 0.87/1.25 maxlength = 115
% 0.87/1.25 maxnrvars = 195
% 0.87/1.25 excuselevel = 1
% 0.87/1.25 increasemaxweight = 1
% 0.87/1.25
% 0.87/1.25 maxselected = 10000000
% 0.87/1.25 maxnrclauses = 10000000
% 0.87/1.25
% 0.87/1.25 showgenerated = 0
% 0.87/1.25 showkept = 0
% 0.87/1.25 showselected = 0
% 0.87/1.25 showdeleted = 0
% 0.87/1.25 showresimp = 1
% 0.87/1.25 showstatus = 2000
% 0.87/1.25
% 0.87/1.25 prologoutput = 0
% 0.87/1.25 nrgoals = 5000000
% 0.87/1.25 totalproof = 1
% 0.87/1.25
% 0.87/1.25 Symbols occurring in the translation:
% 0.87/1.25
% 0.87/1.25 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.87/1.25 . [1, 2] (w:1, o:23, a:1, s:1, b:0),
% 0.87/1.25 ! [4, 1] (w:0, o:15, a:1, s:1, b:0),
% 0.87/1.25 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.87/1.25 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.87/1.25 addition [37, 2] (w:1, o:47, a:1, s:1, b:0),
% 0.87/1.25 zero [39, 0] (w:1, o:9, a:1, s:1, b:0),
% 0.87/1.25 multiplication [40, 2] (w:1, o:49, a:1, s:1, b:0),
% 0.87/1.25 one [41, 0] (w:1, o:10, a:1, s:1, b:0),
% 0.87/1.25 leq [42, 2] (w:1, o:48, a:1, s:1, b:0),
% 0.87/1.25 test [44, 1] (w:1, o:21, a:1, s:1, b:0),
% 0.87/1.25 complement [46, 2] (w:1, o:50, a:1, s:1, b:0),
% 0.87/1.25 c [47, 1] (w:1, o:22, a:1, s:1, b:0),
% 0.87/1.25 alpha1 [48, 2] (w:1, o:51, a:1, s:1, b:1),
% 0.87/1.25 skol1 [49, 1] (w:1, o:20, a:1, s:1, b:1),
% 0.87/1.25 skol2 [50, 0] (w:1, o:13, a:1, s:1, b:1),
% 0.87/1.25 skol3 [51, 0] (w:1, o:14, a:1, s:1, b:1).
% 0.87/1.25
% 0.87/1.25
% 0.87/1.25 Starting Search:
% 0.87/1.25
% 0.87/1.25 *** allocated 15000 integers for clauses
% 0.87/1.25 *** allocated 22500 integers for clauses
% 0.87/1.25 *** allocated 33750 integers for clauses
% 0.87/1.25 *** allocated 50625 integers for clauses
% 0.87/1.25 *** allocated 15000 integers for termspace/termends
% 0.87/1.25 *** allocated 75937 integers for clauses
% 0.87/1.25 Resimplifying inuse:
% 0.87/1.25 Done
% 0.87/1.25
% 0.87/1.25 *** allocated 22500 integers for termspace/termends
% 0.87/1.25 *** allocated 113905 integers for clauses
% 0.87/1.25 *** allocated 33750 integers for termspace/termends
% 0.87/1.25
% 0.87/1.25 Intermediate Status:
% 0.87/1.25 Generated: 13715
% 0.87/1.25 Kept: 2003
% 0.87/1.25 Inuse: 229
% 0.87/1.25 Deleted: 52
% 0.87/1.25 Deletedinuse: 22
% 0.87/1.25
% 0.87/1.25 Resimplifying inuse:
% 0.87/1.25 Done
% 0.87/1.25
% 0.87/1.25 *** allocated 170857 integers for clauses
% 0.87/1.25
% 0.87/1.25 Bliksems!, er is een bewijs:
% 0.87/1.25 % SZS status Theorem
% 0.87/1.25 % SZS output start Refutation
% 0.87/1.25
% 0.87/1.25 (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X ) }.
% 0.87/1.25 (6) {G0,W5,D3,L1,V1,M1} I { multiplication( one, X ) ==> X }.
% 0.87/1.25 (7) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Y ),
% 0.87/1.25 multiplication( X, Z ) ) ==> multiplication( X, addition( Y, Z ) ) }.
% 0.87/1.25 (16) {G0,W6,D2,L2,V2,M2} I { ! complement( Y, X ), alpha1( X, Y ) }.
% 0.87/1.25 (19) {G0,W8,D3,L2,V2,M2} I { ! alpha1( X, Y ), addition( X, Y ) ==> one }.
% 0.87/1.25 (21) {G0,W9,D3,L3,V2,M3} I { ! test( X ), ! c( X ) = Y, complement( X, Y )
% 0.87/1.25 }.
% 0.87/1.25 (24) {G0,W2,D2,L1,V0,M1} I { test( skol3 ) }.
% 0.87/1.25 (25) {G0,W2,D2,L1,V0,M1} I { test( skol2 ) }.
% 0.87/1.25 (26) {G1,W11,D5,L1,V0,M1} I;d(7) { ! multiplication( addition( skol2, c(
% 0.87/1.25 skol2 ) ), addition( skol3, c( skol3 ) ) ) ==> one }.
% 0.87/1.25 (27) {G1,W6,D3,L2,V1,M2} Q(21) { ! test( X ), complement( X, c( X ) ) }.
% 0.87/1.25 (37) {G2,W4,D3,L1,V0,M1} R(27,24) { complement( skol3, c( skol3 ) ) }.
% 0.87/1.25 (38) {G2,W4,D3,L1,V0,M1} R(27,25) { complement( skol2, c( skol2 ) ) }.
% 0.87/1.25 (39) {G3,W4,D3,L1,V0,M1} R(37,16) { alpha1( c( skol3 ), skol3 ) }.
% 0.87/1.25 (42) {G3,W4,D3,L1,V0,M1} R(38,16) { alpha1( c( skol2 ), skol2 ) }.
% 0.87/1.25 (261) {G4,W6,D4,L1,V0,M1} R(19,42) { addition( c( skol2 ), skol2 ) ==> one
% 0.87/1.25 }.
% 0.87/1.25 (262) {G4,W6,D4,L1,V0,M1} R(19,39) { addition( c( skol3 ), skol3 ) ==> one
% 0.87/1.25 }.
% 0.87/1.25 (446) {G5,W6,D4,L1,V0,M1} P(0,26);d(261);d(6) { ! addition( skol3, c( skol3
% 0.87/1.25 ) ) ==> one }.
% 0.87/1.25 (2218) {G6,W0,D0,L0,V0,M0} P(0,446);d(262);q { }.
% 0.87/1.25
% 0.87/1.25
% 0.87/1.25 % SZS output end Refutation
% 0.87/1.25 found a proof!
% 0.87/1.25
% 0.87/1.25
% 0.87/1.25 Unprocessed initial clauses:
% 0.87/1.25
% 0.87/1.25 (2220) {G0,W7,D3,L1,V2,M1} { addition( X, Y ) = addition( Y, X ) }.
% 0.87/1.25 (2221) {G0,W11,D4,L1,V3,M1} { addition( Z, addition( Y, X ) ) = addition(
% 0.87/1.25 addition( Z, Y ), X ) }.
% 0.87/1.25 (2222) {G0,W5,D3,L1,V1,M1} { addition( X, zero ) = X }.
% 0.87/1.25 (2223) {G0,W5,D3,L1,V1,M1} { addition( X, X ) = X }.
% 0.87/1.25 (2224) {G0,W11,D4,L1,V3,M1} { multiplication( X, multiplication( Y, Z ) )
% 0.87/1.25 = multiplication( multiplication( X, Y ), Z ) }.
% 0.87/1.25 (2225) {G0,W5,D3,L1,V1,M1} { multiplication( X, one ) = X }.
% 0.87/1.25 (2226) {G0,W5,D3,L1,V1,M1} { multiplication( one, X ) = X }.
% 0.87/1.25 (2227) {G0,W13,D4,L1,V3,M1} { multiplication( X, addition( Y, Z ) ) =
% 0.87/1.25 addition( multiplication( X, Y ), multiplication( X, Z ) ) }.
% 0.87/1.25 (2228) {G0,W13,D4,L1,V3,M1} { multiplication( addition( X, Y ), Z ) =
% 0.87/1.25 addition( multiplication( X, Z ), multiplication( Y, Z ) ) }.
% 0.87/1.25 (2229) {G0,W5,D3,L1,V1,M1} { multiplication( X, zero ) = zero }.
% 0.87/1.25 (2230) {G0,W5,D3,L1,V1,M1} { multiplication( zero, X ) = zero }.
% 0.87/1.25 (2231) {G0,W8,D3,L2,V2,M2} { ! leq( X, Y ), addition( X, Y ) = Y }.
% 0.87/1.25 (2232) {G0,W8,D3,L2,V2,M2} { ! addition( X, Y ) = Y, leq( X, Y ) }.
% 0.87/1.25 (2233) {G0,W6,D3,L2,V1,M2} { ! test( X ), complement( skol1( X ), X ) }.
% 0.87/1.25 (2234) {G0,W5,D2,L2,V2,M2} { ! complement( Y, X ), test( X ) }.
% 0.87/1.25 (2235) {G0,W8,D3,L2,V2,M2} { ! complement( Y, X ), multiplication( X, Y )
% 0.87/1.25 = zero }.
% 0.87/1.25 (2236) {G0,W6,D2,L2,V2,M2} { ! complement( Y, X ), alpha1( X, Y ) }.
% 0.87/1.25 (2237) {G0,W11,D3,L3,V2,M3} { ! multiplication( X, Y ) = zero, ! alpha1( X
% 0.87/1.25 , Y ), complement( Y, X ) }.
% 0.87/1.25 (2238) {G0,W8,D3,L2,V2,M2} { ! alpha1( X, Y ), multiplication( Y, X ) =
% 0.87/1.25 zero }.
% 0.87/1.25 (2239) {G0,W8,D3,L2,V2,M2} { ! alpha1( X, Y ), addition( X, Y ) = one }.
% 0.87/1.25 (2240) {G0,W13,D3,L3,V2,M3} { ! multiplication( Y, X ) = zero, ! addition
% 0.87/1.25 ( X, Y ) = one, alpha1( X, Y ) }.
% 0.87/1.25 (2241) {G0,W9,D3,L3,V2,M3} { ! test( X ), ! c( X ) = Y, complement( X, Y )
% 0.87/1.25 }.
% 0.87/1.25 (2242) {G0,W9,D3,L3,V2,M3} { ! test( X ), ! complement( X, Y ), c( X ) = Y
% 0.87/1.25 }.
% 0.87/1.25 (2243) {G0,W6,D3,L2,V1,M2} { test( X ), c( X ) = zero }.
% 0.87/1.25 (2244) {G0,W2,D2,L1,V0,M1} { test( skol3 ) }.
% 0.87/1.25 (2245) {G0,W2,D2,L1,V0,M1} { test( skol2 ) }.
% 0.87/1.25 (2246) {G0,W16,D6,L1,V0,M1} { ! one = addition( multiplication( addition(
% 0.87/1.25 skol2, c( skol2 ) ), skol3 ), multiplication( addition( skol2, c( skol2 )
% 0.87/1.25 ), c( skol3 ) ) ) }.
% 0.87/1.25
% 0.87/1.25
% 0.87/1.25 Total Proof:
% 0.87/1.25
% 0.87/1.25 subsumption: (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X
% 0.87/1.25 ) }.
% 0.87/1.25 parent0: (2220) {G0,W7,D3,L1,V2,M1} { addition( X, Y ) = addition( Y, X )
% 0.87/1.25 }.
% 0.87/1.25 substitution0:
% 0.87/1.25 X := X
% 0.87/1.25 Y := Y
% 0.87/1.25 end
% 0.87/1.25 permutation0:
% 0.87/1.25 0 ==> 0
% 0.87/1.25 end
% 0.87/1.25
% 0.87/1.25 subsumption: (6) {G0,W5,D3,L1,V1,M1} I { multiplication( one, X ) ==> X }.
% 0.87/1.25 parent0: (2226) {G0,W5,D3,L1,V1,M1} { multiplication( one, X ) = X }.
% 0.87/1.25 substitution0:
% 0.87/1.25 X := X
% 0.87/1.25 end
% 0.87/1.25 permutation0:
% 0.87/1.25 0 ==> 0
% 0.87/1.25 end
% 0.87/1.25
% 0.87/1.25 eqswap: (2259) {G0,W13,D4,L1,V3,M1} { addition( multiplication( X, Y ),
% 0.87/1.25 multiplication( X, Z ) ) = multiplication( X, addition( Y, Z ) ) }.
% 0.87/1.25 parent0[0]: (2227) {G0,W13,D4,L1,V3,M1} { multiplication( X, addition( Y,
% 0.87/1.25 Z ) ) = addition( multiplication( X, Y ), multiplication( X, Z ) ) }.
% 0.87/1.25 substitution0:
% 0.87/1.25 X := X
% 0.87/1.25 Y := Y
% 0.87/1.25 Z := Z
% 0.87/1.25 end
% 0.87/1.25
% 0.87/1.25 subsumption: (7) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Y )
% 0.87/1.25 , multiplication( X, Z ) ) ==> multiplication( X, addition( Y, Z ) ) }.
% 0.87/1.25 parent0: (2259) {G0,W13,D4,L1,V3,M1} { addition( multiplication( X, Y ),
% 0.87/1.25 multiplication( X, Z ) ) = multiplication( X, addition( Y, Z ) ) }.
% 0.87/1.25 substitution0:
% 0.87/1.25 X := X
% 0.87/1.25 Y := Y
% 0.87/1.25 Z := Z
% 0.87/1.25 end
% 0.87/1.25 permutation0:
% 0.87/1.25 0 ==> 0
% 0.87/1.25 end
% 0.87/1.25
% 0.87/1.25 subsumption: (16) {G0,W6,D2,L2,V2,M2} I { ! complement( Y, X ), alpha1( X,
% 0.87/1.25 Y ) }.
% 0.87/1.25 parent0: (2236) {G0,W6,D2,L2,V2,M2} { ! complement( Y, X ), alpha1( X, Y )
% 0.87/1.25 }.
% 0.87/1.25 substitution0:
% 0.87/1.25 X := X
% 0.87/1.25 Y := Y
% 0.87/1.25 end
% 0.87/1.25 permutation0:
% 0.87/1.25 0 ==> 0
% 0.87/1.25 1 ==> 1
% 0.87/1.25 end
% 0.87/1.25
% 0.87/1.25 subsumption: (19) {G0,W8,D3,L2,V2,M2} I { ! alpha1( X, Y ), addition( X, Y
% 0.87/1.25 ) ==> one }.
% 0.87/1.25 parent0: (2239) {G0,W8,D3,L2,V2,M2} { ! alpha1( X, Y ), addition( X, Y ) =
% 0.87/1.25 one }.
% 0.87/1.25 substitution0:
% 0.87/1.25 X := X
% 0.87/1.25 Y := Y
% 0.87/1.25 end
% 0.87/1.25 permutation0:
% 0.87/1.25 0 ==> 0
% 0.87/1.25 1 ==> 1
% 0.87/1.25 end
% 0.87/1.25
% 0.87/1.25 subsumption: (21) {G0,W9,D3,L3,V2,M3} I { ! test( X ), ! c( X ) = Y,
% 0.87/1.25 complement( X, Y ) }.
% 0.87/1.25 parent0: (2241) {G0,W9,D3,L3,V2,M3} { ! test( X ), ! c( X ) = Y,
% 0.87/1.25 complement( X, Y ) }.
% 0.87/1.25 substitution0:
% 0.87/1.25 X := X
% 0.87/1.25 Y := Y
% 0.87/1.25 end
% 0.87/1.25 permutation0:
% 0.87/1.25 0 ==> 0
% 0.87/1.25 1 ==> 1
% 0.87/1.25 2 ==> 2
% 0.87/1.25 end
% 0.87/1.25
% 0.87/1.25 subsumption: (24) {G0,W2,D2,L1,V0,M1} I { test( skol3 ) }.
% 0.87/1.25 parent0: (2244) {G0,W2,D2,L1,V0,M1} { test( skol3 ) }.
% 0.87/1.25 substitution0:
% 0.87/1.25 end
% 0.87/1.25 permutation0:
% 0.87/1.25 0 ==> 0
% 0.87/1.25 end
% 0.87/1.25
% 0.87/1.25 subsumption: (25) {G0,W2,D2,L1,V0,M1} I { test( skol2 ) }.
% 0.87/1.25 parent0: (2245) {G0,W2,D2,L1,V0,M1} { test( skol2 ) }.
% 0.87/1.25 substitution0:
% 0.87/1.26 end
% 0.87/1.26 permutation0:
% 0.87/1.26 0 ==> 0
% 0.87/1.26 end
% 0.87/1.26
% 0.87/1.26 paramod: (2405) {G1,W11,D5,L1,V0,M1} { ! one = multiplication( addition(
% 0.87/1.26 skol2, c( skol2 ) ), addition( skol3, c( skol3 ) ) ) }.
% 0.87/1.26 parent0[0]: (7) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Y ),
% 0.87/1.26 multiplication( X, Z ) ) ==> multiplication( X, addition( Y, Z ) ) }.
% 0.87/1.26 parent1[0; 3]: (2246) {G0,W16,D6,L1,V0,M1} { ! one = addition(
% 0.87/1.26 multiplication( addition( skol2, c( skol2 ) ), skol3 ), multiplication(
% 0.87/1.26 addition( skol2, c( skol2 ) ), c( skol3 ) ) ) }.
% 0.87/1.26 substitution0:
% 0.87/1.26 X := addition( skol2, c( skol2 ) )
% 0.87/1.26 Y := skol3
% 0.87/1.26 Z := c( skol3 )
% 0.87/1.26 end
% 0.87/1.26 substitution1:
% 0.87/1.26 end
% 0.87/1.26
% 0.87/1.26 eqswap: (2406) {G1,W11,D5,L1,V0,M1} { ! multiplication( addition( skol2, c
% 0.87/1.26 ( skol2 ) ), addition( skol3, c( skol3 ) ) ) = one }.
% 0.87/1.26 parent0[0]: (2405) {G1,W11,D5,L1,V0,M1} { ! one = multiplication( addition
% 0.87/1.26 ( skol2, c( skol2 ) ), addition( skol3, c( skol3 ) ) ) }.
% 0.87/1.26 substitution0:
% 0.87/1.26 end
% 0.87/1.26
% 0.87/1.26 subsumption: (26) {G1,W11,D5,L1,V0,M1} I;d(7) { ! multiplication( addition
% 0.87/1.26 ( skol2, c( skol2 ) ), addition( skol3, c( skol3 ) ) ) ==> one }.
% 0.87/1.26 parent0: (2406) {G1,W11,D5,L1,V0,M1} { ! multiplication( addition( skol2,
% 0.87/1.26 c( skol2 ) ), addition( skol3, c( skol3 ) ) ) = one }.
% 0.87/1.26 substitution0:
% 0.87/1.26 end
% 0.87/1.26 permutation0:
% 0.87/1.26 0 ==> 0
% 0.87/1.26 end
% 0.87/1.26
% 0.87/1.26 eqswap: (2407) {G0,W9,D3,L3,V2,M3} { ! Y = c( X ), ! test( X ), complement
% 0.87/1.26 ( X, Y ) }.
% 0.87/1.26 parent0[1]: (21) {G0,W9,D3,L3,V2,M3} I { ! test( X ), ! c( X ) = Y,
% 0.87/1.26 complement( X, Y ) }.
% 0.87/1.26 substitution0:
% 0.87/1.26 X := X
% 0.87/1.26 Y := Y
% 0.87/1.26 end
% 0.87/1.26
% 0.87/1.26 eqrefl: (2408) {G0,W6,D3,L2,V1,M2} { ! test( X ), complement( X, c( X ) )
% 0.87/1.26 }.
% 0.87/1.26 parent0[0]: (2407) {G0,W9,D3,L3,V2,M3} { ! Y = c( X ), ! test( X ),
% 0.87/1.26 complement( X, Y ) }.
% 0.87/1.26 substitution0:
% 0.87/1.26 X := X
% 0.87/1.26 Y := c( X )
% 0.87/1.26 end
% 0.87/1.26
% 0.87/1.26 subsumption: (27) {G1,W6,D3,L2,V1,M2} Q(21) { ! test( X ), complement( X, c
% 0.87/1.26 ( X ) ) }.
% 0.87/1.26 parent0: (2408) {G0,W6,D3,L2,V1,M2} { ! test( X ), complement( X, c( X ) )
% 0.87/1.26 }.
% 0.87/1.26 substitution0:
% 0.87/1.26 X := X
% 0.87/1.26 end
% 0.87/1.26 permutation0:
% 0.87/1.26 0 ==> 0
% 0.87/1.26 1 ==> 1
% 0.87/1.26 end
% 0.87/1.26
% 0.87/1.26 resolution: (2409) {G1,W4,D3,L1,V0,M1} { complement( skol3, c( skol3 ) )
% 0.87/1.26 }.
% 0.87/1.26 parent0[0]: (27) {G1,W6,D3,L2,V1,M2} Q(21) { ! test( X ), complement( X, c
% 0.87/1.26 ( X ) ) }.
% 0.87/1.26 parent1[0]: (24) {G0,W2,D2,L1,V0,M1} I { test( skol3 ) }.
% 0.87/1.26 substitution0:
% 0.87/1.26 X := skol3
% 0.87/1.26 end
% 0.87/1.26 substitution1:
% 0.87/1.26 end
% 0.87/1.26
% 0.87/1.26 subsumption: (37) {G2,W4,D3,L1,V0,M1} R(27,24) { complement( skol3, c(
% 0.87/1.26 skol3 ) ) }.
% 0.87/1.26 parent0: (2409) {G1,W4,D3,L1,V0,M1} { complement( skol3, c( skol3 ) ) }.
% 0.87/1.26 substitution0:
% 0.87/1.26 end
% 0.87/1.26 permutation0:
% 0.87/1.26 0 ==> 0
% 0.87/1.26 end
% 0.87/1.26
% 0.87/1.26 resolution: (2410) {G1,W4,D3,L1,V0,M1} { complement( skol2, c( skol2 ) )
% 0.87/1.26 }.
% 0.87/1.26 parent0[0]: (27) {G1,W6,D3,L2,V1,M2} Q(21) { ! test( X ), complement( X, c
% 0.87/1.26 ( X ) ) }.
% 0.87/1.26 parent1[0]: (25) {G0,W2,D2,L1,V0,M1} I { test( skol2 ) }.
% 0.87/1.26 substitution0:
% 0.87/1.26 X := skol2
% 0.87/1.26 end
% 0.87/1.26 substitution1:
% 0.87/1.26 end
% 0.87/1.26
% 0.87/1.26 subsumption: (38) {G2,W4,D3,L1,V0,M1} R(27,25) { complement( skol2, c(
% 0.87/1.26 skol2 ) ) }.
% 0.87/1.26 parent0: (2410) {G1,W4,D3,L1,V0,M1} { complement( skol2, c( skol2 ) ) }.
% 0.87/1.26 substitution0:
% 0.87/1.26 end
% 0.87/1.26 permutation0:
% 0.87/1.26 0 ==> 0
% 0.87/1.26 end
% 0.87/1.26
% 0.87/1.26 resolution: (2411) {G1,W4,D3,L1,V0,M1} { alpha1( c( skol3 ), skol3 ) }.
% 0.87/1.26 parent0[0]: (16) {G0,W6,D2,L2,V2,M2} I { ! complement( Y, X ), alpha1( X, Y
% 0.87/1.26 ) }.
% 0.87/1.26 parent1[0]: (37) {G2,W4,D3,L1,V0,M1} R(27,24) { complement( skol3, c( skol3
% 0.87/1.26 ) ) }.
% 0.87/1.26 substitution0:
% 0.87/1.26 X := c( skol3 )
% 0.87/1.26 Y := skol3
% 0.87/1.26 end
% 0.87/1.26 substitution1:
% 0.87/1.26 end
% 0.87/1.26
% 0.87/1.26 subsumption: (39) {G3,W4,D3,L1,V0,M1} R(37,16) { alpha1( c( skol3 ), skol3
% 0.87/1.26 ) }.
% 0.87/1.26 parent0: (2411) {G1,W4,D3,L1,V0,M1} { alpha1( c( skol3 ), skol3 ) }.
% 0.87/1.26 substitution0:
% 0.87/1.26 end
% 0.87/1.26 permutation0:
% 0.87/1.26 0 ==> 0
% 0.87/1.26 end
% 0.87/1.26
% 0.87/1.26 resolution: (2412) {G1,W4,D3,L1,V0,M1} { alpha1( c( skol2 ), skol2 ) }.
% 0.87/1.26 parent0[0]: (16) {G0,W6,D2,L2,V2,M2} I { ! complement( Y, X ), alpha1( X, Y
% 0.87/1.26 ) }.
% 0.87/1.26 parent1[0]: (38) {G2,W4,D3,L1,V0,M1} R(27,25) { complement( skol2, c( skol2
% 0.87/1.26 ) ) }.
% 0.87/1.26 substitution0:
% 0.87/1.26 X := c( skol2 )
% 0.87/1.26 Y := skol2
% 0.87/1.26 end
% 0.87/1.26 substitution1:
% 0.87/1.26 end
% 0.87/1.26
% 0.87/1.26 subsumption: (42) {G3,W4,D3,L1,V0,M1} R(38,16) { alpha1( c( skol2 ), skol2
% 0.87/1.26 ) }.
% 0.87/1.26 parent0: (2412) {G1,W4,D3,L1,V0,M1} { alpha1( c( skol2 ), skol2 ) }.
% 0.87/1.26 substitution0:
% 0.87/1.26 end
% 0.87/1.26 permutation0:
% 0.87/1.26 0 ==> 0
% 0.87/1.26 end
% 0.87/1.26
% 0.87/1.26 eqswap: (2413) {G0,W8,D3,L2,V2,M2} { one ==> addition( X, Y ), ! alpha1( X
% 0.87/1.26 , Y ) }.
% 0.87/1.26 parent0[1]: (19) {G0,W8,D3,L2,V2,M2} I { ! alpha1( X, Y ), addition( X, Y )
% 0.87/1.26 ==> one }.
% 0.87/1.26 substitution0:
% 0.87/1.26 X := X
% 0.87/1.26 Y := Y
% 0.87/1.26 end
% 0.87/1.26
% 0.87/1.26 resolution: (2414) {G1,W6,D4,L1,V0,M1} { one ==> addition( c( skol2 ),
% 0.87/1.26 skol2 ) }.
% 0.87/1.26 parent0[1]: (2413) {G0,W8,D3,L2,V2,M2} { one ==> addition( X, Y ), !
% 0.87/1.26 alpha1( X, Y ) }.
% 0.87/1.26 parent1[0]: (42) {G3,W4,D3,L1,V0,M1} R(38,16) { alpha1( c( skol2 ), skol2 )
% 0.87/1.26 }.
% 0.87/1.26 substitution0:
% 0.87/1.26 X := c( skol2 )
% 0.87/1.26 Y := skol2
% 0.87/1.26 end
% 0.87/1.26 substitution1:
% 0.87/1.26 end
% 0.87/1.26
% 0.87/1.26 eqswap: (2415) {G1,W6,D4,L1,V0,M1} { addition( c( skol2 ), skol2 ) ==> one
% 0.87/1.26 }.
% 0.87/1.26 parent0[0]: (2414) {G1,W6,D4,L1,V0,M1} { one ==> addition( c( skol2 ),
% 0.87/1.26 skol2 ) }.
% 0.87/1.26 substitution0:
% 0.87/1.26 end
% 0.87/1.26
% 0.87/1.26 subsumption: (261) {G4,W6,D4,L1,V0,M1} R(19,42) { addition( c( skol2 ),
% 0.87/1.26 skol2 ) ==> one }.
% 0.87/1.26 parent0: (2415) {G1,W6,D4,L1,V0,M1} { addition( c( skol2 ), skol2 ) ==>
% 0.87/1.26 one }.
% 0.87/1.26 substitution0:
% 0.87/1.26 end
% 0.87/1.26 permutation0:
% 0.87/1.26 0 ==> 0
% 0.87/1.26 end
% 0.87/1.26
% 0.87/1.26 eqswap: (2416) {G0,W8,D3,L2,V2,M2} { one ==> addition( X, Y ), ! alpha1( X
% 0.87/1.26 , Y ) }.
% 0.87/1.26 parent0[1]: (19) {G0,W8,D3,L2,V2,M2} I { ! alpha1( X, Y ), addition( X, Y )
% 0.87/1.26 ==> one }.
% 0.87/1.26 substitution0:
% 0.87/1.26 X := X
% 0.87/1.26 Y := Y
% 0.87/1.26 end
% 0.87/1.26
% 0.87/1.26 resolution: (2417) {G1,W6,D4,L1,V0,M1} { one ==> addition( c( skol3 ),
% 0.87/1.26 skol3 ) }.
% 0.87/1.26 parent0[1]: (2416) {G0,W8,D3,L2,V2,M2} { one ==> addition( X, Y ), !
% 0.87/1.26 alpha1( X, Y ) }.
% 0.87/1.26 parent1[0]: (39) {G3,W4,D3,L1,V0,M1} R(37,16) { alpha1( c( skol3 ), skol3 )
% 0.87/1.26 }.
% 0.87/1.26 substitution0:
% 0.87/1.26 X := c( skol3 )
% 0.87/1.26 Y := skol3
% 0.87/1.26 end
% 0.87/1.26 substitution1:
% 0.87/1.26 end
% 0.87/1.26
% 0.87/1.26 eqswap: (2418) {G1,W6,D4,L1,V0,M1} { addition( c( skol3 ), skol3 ) ==> one
% 0.87/1.26 }.
% 0.87/1.26 parent0[0]: (2417) {G1,W6,D4,L1,V0,M1} { one ==> addition( c( skol3 ),
% 0.87/1.26 skol3 ) }.
% 0.87/1.26 substitution0:
% 0.87/1.26 end
% 0.87/1.26
% 0.87/1.26 subsumption: (262) {G4,W6,D4,L1,V0,M1} R(19,39) { addition( c( skol3 ),
% 0.87/1.26 skol3 ) ==> one }.
% 0.87/1.26 parent0: (2418) {G1,W6,D4,L1,V0,M1} { addition( c( skol3 ), skol3 ) ==>
% 0.87/1.26 one }.
% 0.87/1.26 substitution0:
% 0.87/1.26 end
% 0.87/1.26 permutation0:
% 0.87/1.26 0 ==> 0
% 0.87/1.26 end
% 0.87/1.26
% 0.87/1.26 eqswap: (2419) {G1,W11,D5,L1,V0,M1} { ! one ==> multiplication( addition(
% 0.87/1.26 skol2, c( skol2 ) ), addition( skol3, c( skol3 ) ) ) }.
% 0.87/1.26 parent0[0]: (26) {G1,W11,D5,L1,V0,M1} I;d(7) { ! multiplication( addition(
% 0.87/1.26 skol2, c( skol2 ) ), addition( skol3, c( skol3 ) ) ) ==> one }.
% 0.87/1.26 substitution0:
% 0.87/1.26 end
% 0.87/1.26
% 0.87/1.26 paramod: (2422) {G1,W11,D5,L1,V0,M1} { ! one ==> multiplication( addition
% 0.87/1.26 ( c( skol2 ), skol2 ), addition( skol3, c( skol3 ) ) ) }.
% 0.87/1.26 parent0[0]: (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X )
% 0.87/1.26 }.
% 0.87/1.26 parent1[0; 4]: (2419) {G1,W11,D5,L1,V0,M1} { ! one ==> multiplication(
% 0.87/1.26 addition( skol2, c( skol2 ) ), addition( skol3, c( skol3 ) ) ) }.
% 0.87/1.26 substitution0:
% 0.87/1.26 X := skol2
% 0.87/1.26 Y := c( skol2 )
% 0.87/1.26 end
% 0.87/1.26 substitution1:
% 0.87/1.26 end
% 0.87/1.26
% 0.87/1.26 paramod: (2429) {G2,W8,D5,L1,V0,M1} { ! one ==> multiplication( one,
% 0.87/1.26 addition( skol3, c( skol3 ) ) ) }.
% 0.87/1.26 parent0[0]: (261) {G4,W6,D4,L1,V0,M1} R(19,42) { addition( c( skol2 ),
% 0.87/1.26 skol2 ) ==> one }.
% 0.87/1.26 parent1[0; 4]: (2422) {G1,W11,D5,L1,V0,M1} { ! one ==> multiplication(
% 0.87/1.26 addition( c( skol2 ), skol2 ), addition( skol3, c( skol3 ) ) ) }.
% 0.87/1.26 substitution0:
% 0.87/1.26 end
% 0.87/1.26 substitution1:
% 0.87/1.26 end
% 0.87/1.26
% 0.87/1.26 paramod: (2430) {G1,W6,D4,L1,V0,M1} { ! one ==> addition( skol3, c( skol3
% 0.87/1.26 ) ) }.
% 0.87/1.26 parent0[0]: (6) {G0,W5,D3,L1,V1,M1} I { multiplication( one, X ) ==> X }.
% 0.87/1.26 parent1[0; 3]: (2429) {G2,W8,D5,L1,V0,M1} { ! one ==> multiplication( one
% 0.87/1.26 , addition( skol3, c( skol3 ) ) ) }.
% 0.87/1.26 substitution0:
% 0.87/1.26 X := addition( skol3, c( skol3 ) )
% 0.87/1.26 end
% 0.87/1.26 substitution1:
% 0.87/1.26 end
% 0.87/1.26
% 0.87/1.26 eqswap: (2431) {G1,W6,D4,L1,V0,M1} { ! addition( skol3, c( skol3 ) ) ==>
% 0.87/1.26 one }.
% 0.87/1.26 parent0[0]: (2430) {G1,W6,D4,L1,V0,M1} { ! one ==> addition( skol3, c(
% 0.87/1.26 skol3 ) ) }.
% 0.87/1.26 substitution0:
% 0.87/1.26 end
% 0.87/1.26
% 0.87/1.26 subsumption: (446) {G5,W6,D4,L1,V0,M1} P(0,26);d(261);d(6) { ! addition(
% 0.87/1.26 skol3, c( skol3 ) ) ==> one }.
% 0.87/1.26 parent0: (2431) {G1,W6,D4,L1,V0,M1} { ! addition( skol3, c( skol3 ) ) ==>
% 0.87/1.26 one }.
% 0.87/1.26 substitution0:
% 0.87/1.26 end
% 0.87/1.26 permutation0:
% 0.87/1.26 0 ==> 0
% 0.87/1.26 end
% 0.87/1.26
% 0.87/1.26 eqswap: (2432) {G5,W6,D4,L1,V0,M1} { ! one ==> addition( skol3, c( skol3 )
% 0.87/1.26 ) }.
% 0.87/1.26 parent0[0]: (446) {G5,W6,D4,L1,V0,M1} P(0,26);d(261);d(6) { ! addition(
% 0.87/1.26 skol3, c( skol3 ) ) ==> one }.
% 0.87/1.26 substitution0:
% 0.87/1.26 end
% 0.87/1.26
% 0.87/1.26 paramod: (2434) {G1,W6,D4,L1,V0,M1} { ! one ==> addition( c( skol3 ),
% 0.87/1.26 skol3 ) }.
% 0.87/1.26 parent0[0]: (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X )
% 0.87/1.26 }.
% 0.87/1.26 parent1[0; 3]: (2432) {G5,W6,D4,L1,V0,M1} { ! one ==> addition( skol3, c(
% 0.87/1.26 skol3 ) ) }.
% 0.87/1.26 substitution0:
% 0.87/1.26 X := skol3
% 0.87/1.26 Y := c( skol3 )
% 0.87/1.26 end
% 0.87/1.26 substitution1:
% 0.87/1.26 end
% 0.87/1.26
% 0.87/1.26 paramod: (2436) {G2,W3,D2,L1,V0,M1} { ! one ==> one }.
% 0.87/1.26 parent0[0]: (262) {G4,W6,D4,L1,V0,M1} R(19,39) { addition( c( skol3 ),
% 0.87/1.26 skol3 ) ==> one }.
% 0.87/1.26 parent1[0; 3]: (2434) {G1,W6,D4,L1,V0,M1} { ! one ==> addition( c( skol3 )
% 0.87/1.26 , skol3 ) }.
% 0.87/1.26 substitution0:
% 0.87/1.26 end
% 0.87/1.26 substitution1:
% 0.87/1.26 end
% 0.87/1.26
% 0.87/1.26 eqrefl: (2437) {G0,W0,D0,L0,V0,M0} { }.
% 0.87/1.26 parent0[0]: (2436) {G2,W3,D2,L1,V0,M1} { ! one ==> one }.
% 0.87/1.26 substitution0:
% 0.87/1.26 end
% 0.87/1.26
% 0.87/1.26 subsumption: (2218) {G6,W0,D0,L0,V0,M0} P(0,446);d(262);q { }.
% 0.87/1.26 parent0: (2437) {G0,W0,D0,L0,V0,M0} { }.
% 0.87/1.26 substitution0:
% 0.87/1.26 end
% 0.87/1.26 permutation0:
% 0.87/1.26 end
% 0.87/1.26
% 0.87/1.26 Proof check complete!
% 0.87/1.26
% 0.87/1.26 Memory use:
% 0.87/1.26
% 0.87/1.26 space for terms: 26529
% 0.87/1.26 space for clauses: 116854
% 0.87/1.26
% 0.87/1.26
% 0.87/1.26 clauses generated: 14921
% 0.87/1.26 clauses kept: 2219
% 0.87/1.26 clauses selected: 240
% 0.87/1.26 clauses deleted: 80
% 0.87/1.26 clauses inuse deleted: 35
% 0.87/1.26
% 0.87/1.26 subsentry: 26336
% 0.87/1.26 literals s-matched: 18544
% 0.87/1.26 literals matched: 18091
% 0.87/1.26 full subsumption: 2437
% 0.87/1.26
% 0.87/1.26 checksum: -1284641959
% 0.87/1.26
% 0.87/1.26
% 0.87/1.26 Bliksem ended
%------------------------------------------------------------------------------