TSTP Solution File: KLE007+3 by Bliksem---1.12
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%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : KLE007+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n019.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 01:36:33 EDT 2022
% Result : Theorem 0.73s 1.27s
% Output : Refutation 0.73s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : KLE007+3 : TPTP v8.1.0. Released v4.0.0.
% 0.11/0.12 % Command : bliksem %s
% 0.12/0.33 % Computer : n019.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 12:00:24 EDT 2022
% 0.18/0.33 % CPUTime :
% 0.73/1.27 *** allocated 10000 integers for termspace/termends
% 0.73/1.27 *** allocated 10000 integers for clauses
% 0.73/1.27 *** allocated 10000 integers for justifications
% 0.73/1.27 Bliksem 1.12
% 0.73/1.27
% 0.73/1.27
% 0.73/1.27 Automatic Strategy Selection
% 0.73/1.27
% 0.73/1.27
% 0.73/1.27 Clauses:
% 0.73/1.27
% 0.73/1.27 { addition( X, Y ) = addition( Y, X ) }.
% 0.73/1.27 { addition( Z, addition( Y, X ) ) = addition( addition( Z, Y ), X ) }.
% 0.73/1.27 { addition( X, zero ) = X }.
% 0.73/1.27 { addition( X, X ) = X }.
% 0.73/1.27 { multiplication( X, multiplication( Y, Z ) ) = multiplication(
% 0.73/1.27 multiplication( X, Y ), Z ) }.
% 0.73/1.27 { multiplication( X, one ) = X }.
% 0.73/1.27 { multiplication( one, X ) = X }.
% 0.73/1.27 { multiplication( X, addition( Y, Z ) ) = addition( multiplication( X, Y )
% 0.73/1.27 , multiplication( X, Z ) ) }.
% 0.73/1.27 { multiplication( addition( X, Y ), Z ) = addition( multiplication( X, Z )
% 0.73/1.27 , multiplication( Y, Z ) ) }.
% 0.73/1.27 { multiplication( X, zero ) = zero }.
% 0.73/1.27 { multiplication( zero, X ) = zero }.
% 0.73/1.27 { ! leq( X, Y ), addition( X, Y ) = Y }.
% 0.73/1.27 { ! addition( X, Y ) = Y, leq( X, Y ) }.
% 0.73/1.27 { ! test( X ), complement( skol1( X ), X ) }.
% 0.73/1.27 { ! complement( Y, X ), test( X ) }.
% 0.73/1.27 { ! complement( Y, X ), multiplication( X, Y ) = zero }.
% 0.73/1.27 { ! complement( Y, X ), alpha1( X, Y ) }.
% 0.73/1.27 { ! multiplication( X, Y ) = zero, ! alpha1( X, Y ), complement( Y, X ) }.
% 0.73/1.27 { ! alpha1( X, Y ), multiplication( Y, X ) = zero }.
% 0.73/1.27 { ! alpha1( X, Y ), addition( X, Y ) = one }.
% 0.73/1.27 { ! multiplication( Y, X ) = zero, ! addition( X, Y ) = one, alpha1( X, Y )
% 0.73/1.27 }.
% 0.73/1.27 { ! test( X ), ! c( X ) = Y, complement( X, Y ) }.
% 0.73/1.27 { ! test( X ), ! complement( X, Y ), c( X ) = Y }.
% 0.73/1.27 { test( X ), c( X ) = zero }.
% 0.73/1.27 { ! test( X ), ! test( Y ), c( addition( X, Y ) ) = multiplication( c( X )
% 0.73/1.27 , c( Y ) ) }.
% 0.73/1.27 { ! test( X ), ! test( Y ), c( multiplication( X, Y ) ) = addition( c( X )
% 0.73/1.27 , c( Y ) ) }.
% 0.73/1.27 { test( skol3 ) }.
% 0.73/1.27 { test( skol2 ) }.
% 0.73/1.27 { ! one = addition( multiplication( addition( skol2, c( skol2 ) ), skol3 )
% 0.73/1.27 , multiplication( addition( skol2, c( skol2 ) ), c( skol3 ) ) ) }.
% 0.73/1.27
% 0.73/1.27 percentage equality = 0.500000, percentage horn = 0.965517
% 0.73/1.27 This is a problem with some equality
% 0.73/1.27
% 0.73/1.27
% 0.73/1.27
% 0.73/1.27 Options Used:
% 0.73/1.27
% 0.73/1.27 useres = 1
% 0.73/1.27 useparamod = 1
% 0.73/1.27 useeqrefl = 1
% 0.73/1.27 useeqfact = 1
% 0.73/1.27 usefactor = 1
% 0.73/1.27 usesimpsplitting = 0
% 0.73/1.27 usesimpdemod = 5
% 0.73/1.27 usesimpres = 3
% 0.73/1.27
% 0.73/1.27 resimpinuse = 1000
% 0.73/1.27 resimpclauses = 20000
% 0.73/1.27 substype = eqrewr
% 0.73/1.27 backwardsubs = 1
% 0.73/1.27 selectoldest = 5
% 0.73/1.27
% 0.73/1.27 litorderings [0] = split
% 0.73/1.27 litorderings [1] = extend the termordering, first sorting on arguments
% 0.73/1.27
% 0.73/1.27 termordering = kbo
% 0.73/1.27
% 0.73/1.27 litapriori = 0
% 0.73/1.27 termapriori = 1
% 0.73/1.27 litaposteriori = 0
% 0.73/1.27 termaposteriori = 0
% 0.73/1.27 demodaposteriori = 0
% 0.73/1.27 ordereqreflfact = 0
% 0.73/1.27
% 0.73/1.27 litselect = negord
% 0.73/1.27
% 0.73/1.27 maxweight = 15
% 0.73/1.27 maxdepth = 30000
% 0.73/1.27 maxlength = 115
% 0.73/1.27 maxnrvars = 195
% 0.73/1.27 excuselevel = 1
% 0.73/1.27 increasemaxweight = 1
% 0.73/1.27
% 0.73/1.27 maxselected = 10000000
% 0.73/1.27 maxnrclauses = 10000000
% 0.73/1.27
% 0.73/1.27 showgenerated = 0
% 0.73/1.27 showkept = 0
% 0.73/1.27 showselected = 0
% 0.73/1.27 showdeleted = 0
% 0.73/1.27 showresimp = 1
% 0.73/1.27 showstatus = 2000
% 0.73/1.27
% 0.73/1.27 prologoutput = 0
% 0.73/1.27 nrgoals = 5000000
% 0.73/1.27 totalproof = 1
% 0.73/1.27
% 0.73/1.27 Symbols occurring in the translation:
% 0.73/1.27
% 0.73/1.27 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.73/1.27 . [1, 2] (w:1, o:23, a:1, s:1, b:0),
% 0.73/1.27 ! [4, 1] (w:0, o:15, a:1, s:1, b:0),
% 0.73/1.27 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.73/1.27 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.73/1.27 addition [37, 2] (w:1, o:47, a:1, s:1, b:0),
% 0.73/1.27 zero [39, 0] (w:1, o:9, a:1, s:1, b:0),
% 0.73/1.27 multiplication [40, 2] (w:1, o:49, a:1, s:1, b:0),
% 0.73/1.27 one [41, 0] (w:1, o:10, a:1, s:1, b:0),
% 0.73/1.27 leq [42, 2] (w:1, o:48, a:1, s:1, b:0),
% 0.73/1.27 test [44, 1] (w:1, o:21, a:1, s:1, b:0),
% 0.73/1.27 complement [46, 2] (w:1, o:50, a:1, s:1, b:0),
% 0.73/1.27 c [47, 1] (w:1, o:22, a:1, s:1, b:0),
% 0.73/1.27 alpha1 [48, 2] (w:1, o:51, a:1, s:1, b:1),
% 0.73/1.27 skol1 [49, 1] (w:1, o:20, a:1, s:1, b:1),
% 0.73/1.27 skol2 [50, 0] (w:1, o:13, a:1, s:1, b:1),
% 0.73/1.27 skol3 [51, 0] (w:1, o:14, a:1, s:1, b:1).
% 0.73/1.27
% 0.73/1.27
% 0.73/1.27 Starting Search:
% 0.73/1.27
% 0.73/1.27 *** allocated 15000 integers for clauses
% 0.73/1.27 *** allocated 22500 integers for clauses
% 0.73/1.27 *** allocated 33750 integers for clauses
% 0.73/1.27 *** allocated 50625 integers for clauses
% 0.73/1.27 *** allocated 15000 integers for termspace/termends
% 0.73/1.27 *** allocated 75937 integers for clauses
% 0.73/1.27 Resimplifying inuse:
% 0.73/1.27 Done
% 0.73/1.27
% 0.73/1.27 *** allocated 22500 integers for termspace/termends
% 0.73/1.27 *** allocated 113905 integers for clauses
% 0.73/1.27 *** allocated 33750 integers for termspace/termends
% 0.73/1.27
% 0.73/1.27 Intermediate Status:
% 0.73/1.27 Generated: 12633
% 0.73/1.27 Kept: 2055
% 0.73/1.27 Inuse: 216
% 0.73/1.27 Deleted: 41
% 0.73/1.27 Deletedinuse: 22
% 0.73/1.27
% 0.73/1.27 Resimplifying inuse:
% 0.73/1.27 Done
% 0.73/1.27
% 0.73/1.27 *** allocated 170857 integers for clauses
% 0.73/1.27
% 0.73/1.27 Bliksems!, er is een bewijs:
% 0.73/1.27 % SZS status Theorem
% 0.73/1.27 % SZS output start Refutation
% 0.73/1.27
% 0.73/1.27 (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X ) }.
% 0.73/1.27 (6) {G0,W5,D3,L1,V1,M1} I { multiplication( one, X ) ==> X }.
% 0.73/1.27 (7) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Y ),
% 0.73/1.27 multiplication( X, Z ) ) ==> multiplication( X, addition( Y, Z ) ) }.
% 0.73/1.27 (16) {G0,W6,D2,L2,V2,M2} I { ! complement( Y, X ), alpha1( X, Y ) }.
% 0.73/1.27 (19) {G0,W8,D3,L2,V2,M2} I { ! alpha1( X, Y ), addition( X, Y ) ==> one }.
% 0.73/1.27 (21) {G0,W9,D3,L3,V2,M3} I { ! test( X ), ! c( X ) = Y, complement( X, Y )
% 0.73/1.27 }.
% 0.73/1.27 (26) {G0,W2,D2,L1,V0,M1} I { test( skol3 ) }.
% 0.73/1.27 (27) {G0,W2,D2,L1,V0,M1} I { test( skol2 ) }.
% 0.73/1.27 (28) {G1,W11,D5,L1,V0,M1} I;d(7) { ! multiplication( addition( skol2, c(
% 0.73/1.27 skol2 ) ), addition( skol3, c( skol3 ) ) ) ==> one }.
% 0.73/1.27 (29) {G1,W6,D3,L2,V1,M2} Q(21) { ! test( X ), complement( X, c( X ) ) }.
% 0.73/1.27 (41) {G2,W4,D3,L1,V0,M1} R(29,26) { complement( skol3, c( skol3 ) ) }.
% 0.73/1.27 (42) {G2,W4,D3,L1,V0,M1} R(29,27) { complement( skol2, c( skol2 ) ) }.
% 0.73/1.27 (43) {G3,W4,D3,L1,V0,M1} R(41,16) { alpha1( c( skol3 ), skol3 ) }.
% 0.73/1.27 (46) {G3,W4,D3,L1,V0,M1} R(42,16) { alpha1( c( skol2 ), skol2 ) }.
% 0.73/1.27 (265) {G4,W6,D4,L1,V0,M1} R(19,46) { addition( c( skol2 ), skol2 ) ==> one
% 0.73/1.27 }.
% 0.73/1.27 (266) {G4,W6,D4,L1,V0,M1} R(19,43) { addition( c( skol3 ), skol3 ) ==> one
% 0.73/1.27 }.
% 0.73/1.27 (527) {G5,W6,D4,L1,V0,M1} P(0,28);d(265);d(6) { ! addition( skol3, c( skol3
% 0.73/1.27 ) ) ==> one }.
% 0.73/1.27 (2247) {G6,W0,D0,L0,V0,M0} P(0,527);d(266);q { }.
% 0.73/1.27
% 0.73/1.27
% 0.73/1.27 % SZS output end Refutation
% 0.73/1.27 found a proof!
% 0.73/1.27
% 0.73/1.27
% 0.73/1.27 Unprocessed initial clauses:
% 0.73/1.27
% 0.73/1.27 (2249) {G0,W7,D3,L1,V2,M1} { addition( X, Y ) = addition( Y, X ) }.
% 0.73/1.27 (2250) {G0,W11,D4,L1,V3,M1} { addition( Z, addition( Y, X ) ) = addition(
% 0.73/1.27 addition( Z, Y ), X ) }.
% 0.73/1.27 (2251) {G0,W5,D3,L1,V1,M1} { addition( X, zero ) = X }.
% 0.73/1.27 (2252) {G0,W5,D3,L1,V1,M1} { addition( X, X ) = X }.
% 0.73/1.27 (2253) {G0,W11,D4,L1,V3,M1} { multiplication( X, multiplication( Y, Z ) )
% 0.73/1.27 = multiplication( multiplication( X, Y ), Z ) }.
% 0.73/1.27 (2254) {G0,W5,D3,L1,V1,M1} { multiplication( X, one ) = X }.
% 0.73/1.27 (2255) {G0,W5,D3,L1,V1,M1} { multiplication( one, X ) = X }.
% 0.73/1.27 (2256) {G0,W13,D4,L1,V3,M1} { multiplication( X, addition( Y, Z ) ) =
% 0.73/1.27 addition( multiplication( X, Y ), multiplication( X, Z ) ) }.
% 0.73/1.27 (2257) {G0,W13,D4,L1,V3,M1} { multiplication( addition( X, Y ), Z ) =
% 0.73/1.27 addition( multiplication( X, Z ), multiplication( Y, Z ) ) }.
% 0.73/1.27 (2258) {G0,W5,D3,L1,V1,M1} { multiplication( X, zero ) = zero }.
% 0.73/1.27 (2259) {G0,W5,D3,L1,V1,M1} { multiplication( zero, X ) = zero }.
% 0.73/1.27 (2260) {G0,W8,D3,L2,V2,M2} { ! leq( X, Y ), addition( X, Y ) = Y }.
% 0.73/1.27 (2261) {G0,W8,D3,L2,V2,M2} { ! addition( X, Y ) = Y, leq( X, Y ) }.
% 0.73/1.27 (2262) {G0,W6,D3,L2,V1,M2} { ! test( X ), complement( skol1( X ), X ) }.
% 0.73/1.27 (2263) {G0,W5,D2,L2,V2,M2} { ! complement( Y, X ), test( X ) }.
% 0.73/1.27 (2264) {G0,W8,D3,L2,V2,M2} { ! complement( Y, X ), multiplication( X, Y )
% 0.73/1.27 = zero }.
% 0.73/1.27 (2265) {G0,W6,D2,L2,V2,M2} { ! complement( Y, X ), alpha1( X, Y ) }.
% 0.73/1.27 (2266) {G0,W11,D3,L3,V2,M3} { ! multiplication( X, Y ) = zero, ! alpha1( X
% 0.73/1.27 , Y ), complement( Y, X ) }.
% 0.73/1.27 (2267) {G0,W8,D3,L2,V2,M2} { ! alpha1( X, Y ), multiplication( Y, X ) =
% 0.73/1.27 zero }.
% 0.73/1.27 (2268) {G0,W8,D3,L2,V2,M2} { ! alpha1( X, Y ), addition( X, Y ) = one }.
% 0.73/1.27 (2269) {G0,W13,D3,L3,V2,M3} { ! multiplication( Y, X ) = zero, ! addition
% 0.73/1.27 ( X, Y ) = one, alpha1( X, Y ) }.
% 0.73/1.27 (2270) {G0,W9,D3,L3,V2,M3} { ! test( X ), ! c( X ) = Y, complement( X, Y )
% 0.73/1.27 }.
% 0.73/1.27 (2271) {G0,W9,D3,L3,V2,M3} { ! test( X ), ! complement( X, Y ), c( X ) = Y
% 0.73/1.27 }.
% 0.73/1.27 (2272) {G0,W6,D3,L2,V1,M2} { test( X ), c( X ) = zero }.
% 0.73/1.27 (2273) {G0,W14,D4,L3,V2,M3} { ! test( X ), ! test( Y ), c( addition( X, Y
% 0.73/1.27 ) ) = multiplication( c( X ), c( Y ) ) }.
% 0.73/1.27 (2274) {G0,W14,D4,L3,V2,M3} { ! test( X ), ! test( Y ), c( multiplication
% 0.73/1.27 ( X, Y ) ) = addition( c( X ), c( Y ) ) }.
% 0.73/1.27 (2275) {G0,W2,D2,L1,V0,M1} { test( skol3 ) }.
% 0.73/1.27 (2276) {G0,W2,D2,L1,V0,M1} { test( skol2 ) }.
% 0.73/1.27 (2277) {G0,W16,D6,L1,V0,M1} { ! one = addition( multiplication( addition(
% 0.73/1.27 skol2, c( skol2 ) ), skol3 ), multiplication( addition( skol2, c( skol2 )
% 0.73/1.27 ), c( skol3 ) ) ) }.
% 0.73/1.27
% 0.73/1.27
% 0.73/1.27 Total Proof:
% 0.73/1.27
% 0.73/1.27 subsumption: (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X
% 0.73/1.27 ) }.
% 0.73/1.27 parent0: (2249) {G0,W7,D3,L1,V2,M1} { addition( X, Y ) = addition( Y, X )
% 0.73/1.27 }.
% 0.73/1.27 substitution0:
% 0.73/1.27 X := X
% 0.73/1.27 Y := Y
% 0.73/1.27 end
% 0.73/1.27 permutation0:
% 0.73/1.27 0 ==> 0
% 0.73/1.27 end
% 0.73/1.27
% 0.73/1.27 subsumption: (6) {G0,W5,D3,L1,V1,M1} I { multiplication( one, X ) ==> X }.
% 0.73/1.27 parent0: (2255) {G0,W5,D3,L1,V1,M1} { multiplication( one, X ) = X }.
% 0.73/1.27 substitution0:
% 0.73/1.27 X := X
% 0.73/1.27 end
% 0.73/1.27 permutation0:
% 0.73/1.27 0 ==> 0
% 0.73/1.27 end
% 0.73/1.27
% 0.73/1.27 eqswap: (2290) {G0,W13,D4,L1,V3,M1} { addition( multiplication( X, Y ),
% 0.73/1.27 multiplication( X, Z ) ) = multiplication( X, addition( Y, Z ) ) }.
% 0.73/1.27 parent0[0]: (2256) {G0,W13,D4,L1,V3,M1} { multiplication( X, addition( Y,
% 0.73/1.27 Z ) ) = addition( multiplication( X, Y ), multiplication( X, Z ) ) }.
% 0.73/1.27 substitution0:
% 0.73/1.27 X := X
% 0.73/1.27 Y := Y
% 0.73/1.27 Z := Z
% 0.73/1.27 end
% 0.73/1.27
% 0.73/1.27 subsumption: (7) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Y )
% 0.73/1.27 , multiplication( X, Z ) ) ==> multiplication( X, addition( Y, Z ) ) }.
% 0.73/1.27 parent0: (2290) {G0,W13,D4,L1,V3,M1} { addition( multiplication( X, Y ),
% 0.73/1.27 multiplication( X, Z ) ) = multiplication( X, addition( Y, Z ) ) }.
% 0.73/1.27 substitution0:
% 0.73/1.27 X := X
% 0.73/1.27 Y := Y
% 0.73/1.27 Z := Z
% 0.73/1.27 end
% 0.73/1.27 permutation0:
% 0.73/1.27 0 ==> 0
% 0.73/1.27 end
% 0.73/1.27
% 0.73/1.27 subsumption: (16) {G0,W6,D2,L2,V2,M2} I { ! complement( Y, X ), alpha1( X,
% 0.73/1.27 Y ) }.
% 0.73/1.27 parent0: (2265) {G0,W6,D2,L2,V2,M2} { ! complement( Y, X ), alpha1( X, Y )
% 0.73/1.27 }.
% 0.73/1.27 substitution0:
% 0.73/1.27 X := X
% 0.73/1.27 Y := Y
% 0.73/1.27 end
% 0.73/1.27 permutation0:
% 0.73/1.27 0 ==> 0
% 0.73/1.27 1 ==> 1
% 0.73/1.27 end
% 0.73/1.27
% 0.73/1.27 subsumption: (19) {G0,W8,D3,L2,V2,M2} I { ! alpha1( X, Y ), addition( X, Y
% 0.73/1.27 ) ==> one }.
% 0.73/1.27 parent0: (2268) {G0,W8,D3,L2,V2,M2} { ! alpha1( X, Y ), addition( X, Y ) =
% 0.73/1.27 one }.
% 0.73/1.27 substitution0:
% 0.73/1.27 X := X
% 0.73/1.27 Y := Y
% 0.73/1.27 end
% 0.73/1.27 permutation0:
% 0.73/1.27 0 ==> 0
% 0.73/1.27 1 ==> 1
% 0.73/1.27 end
% 0.73/1.27
% 0.73/1.27 subsumption: (21) {G0,W9,D3,L3,V2,M3} I { ! test( X ), ! c( X ) = Y,
% 0.73/1.27 complement( X, Y ) }.
% 0.73/1.27 parent0: (2270) {G0,W9,D3,L3,V2,M3} { ! test( X ), ! c( X ) = Y,
% 0.73/1.27 complement( X, Y ) }.
% 0.73/1.27 substitution0:
% 0.73/1.27 X := X
% 0.73/1.27 Y := Y
% 0.73/1.27 end
% 0.73/1.27 permutation0:
% 0.73/1.27 0 ==> 0
% 0.73/1.27 1 ==> 1
% 0.73/1.27 2 ==> 2
% 0.73/1.27 end
% 0.73/1.27
% 0.73/1.27 subsumption: (26) {G0,W2,D2,L1,V0,M1} I { test( skol3 ) }.
% 0.73/1.27 parent0: (2275) {G0,W2,D2,L1,V0,M1} { test( skol3 ) }.
% 0.73/1.27 substitution0:
% 0.73/1.27 end
% 0.73/1.27 permutation0:
% 0.73/1.27 0 ==> 0
% 0.73/1.27 end
% 0.73/1.27
% 0.73/1.27 subsumption: (27) {G0,W2,D2,L1,V0,M1} I { test( skol2 ) }.
% 0.73/1.27 parent0: (2276) {G0,W2,D2,L1,V0,M1} { test( skol2 ) }.
% 0.73/1.27 substitution0:
% 0.73/1.27 end
% 0.73/1.27 permutation0:
% 0.73/1.27 0 ==> 0
% 0.73/1.27 end
% 0.73/1.27
% 0.73/1.27 paramod: (2456) {G1,W11,D5,L1,V0,M1} { ! one = multiplication( addition(
% 0.73/1.27 skol2, c( skol2 ) ), addition( skol3, c( skol3 ) ) ) }.
% 0.73/1.27 parent0[0]: (7) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Y ),
% 0.73/1.27 multiplication( X, Z ) ) ==> multiplication( X, addition( Y, Z ) ) }.
% 0.73/1.27 parent1[0; 3]: (2277) {G0,W16,D6,L1,V0,M1} { ! one = addition(
% 0.73/1.27 multiplication( addition( skol2, c( skol2 ) ), skol3 ), multiplication(
% 0.73/1.27 addition( skol2, c( skol2 ) ), c( skol3 ) ) ) }.
% 0.73/1.27 substitution0:
% 0.73/1.27 X := addition( skol2, c( skol2 ) )
% 0.73/1.27 Y := skol3
% 0.73/1.27 Z := c( skol3 )
% 0.73/1.27 end
% 0.73/1.27 substitution1:
% 0.73/1.27 end
% 0.73/1.27
% 0.73/1.27 eqswap: (2457) {G1,W11,D5,L1,V0,M1} { ! multiplication( addition( skol2, c
% 0.73/1.27 ( skol2 ) ), addition( skol3, c( skol3 ) ) ) = one }.
% 0.73/1.27 parent0[0]: (2456) {G1,W11,D5,L1,V0,M1} { ! one = multiplication( addition
% 0.73/1.27 ( skol2, c( skol2 ) ), addition( skol3, c( skol3 ) ) ) }.
% 0.73/1.27 substitution0:
% 0.73/1.27 end
% 0.73/1.27
% 0.73/1.27 subsumption: (28) {G1,W11,D5,L1,V0,M1} I;d(7) { ! multiplication( addition
% 0.73/1.27 ( skol2, c( skol2 ) ), addition( skol3, c( skol3 ) ) ) ==> one }.
% 0.73/1.27 parent0: (2457) {G1,W11,D5,L1,V0,M1} { ! multiplication( addition( skol2,
% 0.73/1.27 c( skol2 ) ), addition( skol3, c( skol3 ) ) ) = one }.
% 0.73/1.27 substitution0:
% 0.73/1.27 end
% 0.73/1.27 permutation0:
% 0.73/1.27 0 ==> 0
% 0.73/1.27 end
% 0.73/1.27
% 0.73/1.27 eqswap: (2458) {G0,W9,D3,L3,V2,M3} { ! Y = c( X ), ! test( X ), complement
% 0.73/1.27 ( X, Y ) }.
% 0.73/1.27 parent0[1]: (21) {G0,W9,D3,L3,V2,M3} I { ! test( X ), ! c( X ) = Y,
% 0.73/1.27 complement( X, Y ) }.
% 0.73/1.27 substitution0:
% 0.73/1.27 X := X
% 0.73/1.27 Y := Y
% 0.73/1.27 end
% 0.73/1.27
% 0.73/1.27 eqrefl: (2459) {G0,W6,D3,L2,V1,M2} { ! test( X ), complement( X, c( X ) )
% 0.73/1.27 }.
% 0.73/1.27 parent0[0]: (2458) {G0,W9,D3,L3,V2,M3} { ! Y = c( X ), ! test( X ),
% 0.73/1.27 complement( X, Y ) }.
% 0.73/1.27 substitution0:
% 0.73/1.27 X := X
% 0.73/1.27 Y := c( X )
% 0.73/1.27 end
% 0.73/1.27
% 0.73/1.27 subsumption: (29) {G1,W6,D3,L2,V1,M2} Q(21) { ! test( X ), complement( X, c
% 0.73/1.27 ( X ) ) }.
% 0.73/1.27 parent0: (2459) {G0,W6,D3,L2,V1,M2} { ! test( X ), complement( X, c( X ) )
% 0.73/1.27 }.
% 0.73/1.27 substitution0:
% 0.73/1.27 X := X
% 0.73/1.27 end
% 0.73/1.27 permutation0:
% 0.73/1.27 0 ==> 0
% 0.73/1.27 1 ==> 1
% 0.73/1.27 end
% 0.73/1.27
% 0.73/1.27 resolution: (2460) {G1,W4,D3,L1,V0,M1} { complement( skol3, c( skol3 ) )
% 0.73/1.27 }.
% 0.73/1.27 parent0[0]: (29) {G1,W6,D3,L2,V1,M2} Q(21) { ! test( X ), complement( X, c
% 0.73/1.27 ( X ) ) }.
% 0.73/1.27 parent1[0]: (26) {G0,W2,D2,L1,V0,M1} I { test( skol3 ) }.
% 0.73/1.27 substitution0:
% 0.73/1.27 X := skol3
% 0.73/1.27 end
% 0.73/1.27 substitution1:
% 0.73/1.27 end
% 0.73/1.27
% 0.73/1.27 subsumption: (41) {G2,W4,D3,L1,V0,M1} R(29,26) { complement( skol3, c(
% 0.73/1.27 skol3 ) ) }.
% 0.73/1.27 parent0: (2460) {G1,W4,D3,L1,V0,M1} { complement( skol3, c( skol3 ) ) }.
% 0.73/1.27 substitution0:
% 0.73/1.27 end
% 0.73/1.27 permutation0:
% 0.73/1.27 0 ==> 0
% 0.73/1.27 end
% 0.73/1.27
% 0.73/1.27 resolution: (2461) {G1,W4,D3,L1,V0,M1} { complement( skol2, c( skol2 ) )
% 0.73/1.27 }.
% 0.73/1.27 parent0[0]: (29) {G1,W6,D3,L2,V1,M2} Q(21) { ! test( X ), complement( X, c
% 0.73/1.27 ( X ) ) }.
% 0.73/1.27 parent1[0]: (27) {G0,W2,D2,L1,V0,M1} I { test( skol2 ) }.
% 0.73/1.27 substitution0:
% 0.73/1.27 X := skol2
% 0.73/1.27 end
% 0.73/1.27 substitution1:
% 0.73/1.27 end
% 0.73/1.27
% 0.73/1.27 subsumption: (42) {G2,W4,D3,L1,V0,M1} R(29,27) { complement( skol2, c(
% 0.73/1.27 skol2 ) ) }.
% 0.73/1.27 parent0: (2461) {G1,W4,D3,L1,V0,M1} { complement( skol2, c( skol2 ) ) }.
% 0.73/1.27 substitution0:
% 0.73/1.27 end
% 0.73/1.27 permutation0:
% 0.73/1.27 0 ==> 0
% 0.73/1.27 end
% 0.73/1.27
% 0.73/1.27 resolution: (2462) {G1,W4,D3,L1,V0,M1} { alpha1( c( skol3 ), skol3 ) }.
% 0.73/1.27 parent0[0]: (16) {G0,W6,D2,L2,V2,M2} I { ! complement( Y, X ), alpha1( X, Y
% 0.73/1.27 ) }.
% 0.73/1.27 parent1[0]: (41) {G2,W4,D3,L1,V0,M1} R(29,26) { complement( skol3, c( skol3
% 0.73/1.27 ) ) }.
% 0.73/1.27 substitution0:
% 0.73/1.27 X := c( skol3 )
% 0.73/1.27 Y := skol3
% 0.73/1.27 end
% 0.73/1.27 substitution1:
% 0.73/1.27 end
% 0.73/1.27
% 0.73/1.27 subsumption: (43) {G3,W4,D3,L1,V0,M1} R(41,16) { alpha1( c( skol3 ), skol3
% 0.73/1.27 ) }.
% 0.73/1.27 parent0: (2462) {G1,W4,D3,L1,V0,M1} { alpha1( c( skol3 ), skol3 ) }.
% 0.73/1.27 substitution0:
% 0.73/1.27 end
% 0.73/1.27 permutation0:
% 0.73/1.27 0 ==> 0
% 0.73/1.27 end
% 0.73/1.27
% 0.73/1.27 resolution: (2463) {G1,W4,D3,L1,V0,M1} { alpha1( c( skol2 ), skol2 ) }.
% 0.73/1.27 parent0[0]: (16) {G0,W6,D2,L2,V2,M2} I { ! complement( Y, X ), alpha1( X, Y
% 0.73/1.27 ) }.
% 0.73/1.27 parent1[0]: (42) {G2,W4,D3,L1,V0,M1} R(29,27) { complement( skol2, c( skol2
% 0.73/1.27 ) ) }.
% 0.73/1.27 substitution0:
% 0.73/1.27 X := c( skol2 )
% 0.73/1.27 Y := skol2
% 0.73/1.27 end
% 0.73/1.27 substitution1:
% 0.73/1.27 end
% 0.73/1.27
% 0.73/1.27 subsumption: (46) {G3,W4,D3,L1,V0,M1} R(42,16) { alpha1( c( skol2 ), skol2
% 0.73/1.27 ) }.
% 0.73/1.27 parent0: (2463) {G1,W4,D3,L1,V0,M1} { alpha1( c( skol2 ), skol2 ) }.
% 0.73/1.27 substitution0:
% 0.73/1.27 end
% 0.73/1.27 permutation0:
% 0.73/1.27 0 ==> 0
% 0.73/1.27 end
% 0.73/1.27
% 0.73/1.27 eqswap: (2464) {G0,W8,D3,L2,V2,M2} { one ==> addition( X, Y ), ! alpha1( X
% 0.73/1.27 , Y ) }.
% 0.73/1.27 parent0[1]: (19) {G0,W8,D3,L2,V2,M2} I { ! alpha1( X, Y ), addition( X, Y )
% 0.73/1.27 ==> one }.
% 0.73/1.27 substitution0:
% 0.73/1.27 X := X
% 0.73/1.27 Y := Y
% 0.73/1.27 end
% 0.73/1.27
% 0.73/1.27 resolution: (2465) {G1,W6,D4,L1,V0,M1} { one ==> addition( c( skol2 ),
% 0.73/1.27 skol2 ) }.
% 0.73/1.27 parent0[1]: (2464) {G0,W8,D3,L2,V2,M2} { one ==> addition( X, Y ), !
% 0.73/1.27 alpha1( X, Y ) }.
% 0.73/1.27 parent1[0]: (46) {G3,W4,D3,L1,V0,M1} R(42,16) { alpha1( c( skol2 ), skol2 )
% 0.73/1.27 }.
% 0.73/1.27 substitution0:
% 0.73/1.27 X := c( skol2 )
% 0.73/1.27 Y := skol2
% 0.73/1.27 end
% 0.73/1.27 substitution1:
% 0.73/1.27 end
% 0.73/1.27
% 0.73/1.27 eqswap: (2466) {G1,W6,D4,L1,V0,M1} { addition( c( skol2 ), skol2 ) ==> one
% 0.73/1.27 }.
% 0.73/1.27 parent0[0]: (2465) {G1,W6,D4,L1,V0,M1} { one ==> addition( c( skol2 ),
% 0.73/1.27 skol2 ) }.
% 0.73/1.27 substitution0:
% 0.73/1.27 end
% 0.73/1.27
% 0.73/1.27 subsumption: (265) {G4,W6,D4,L1,V0,M1} R(19,46) { addition( c( skol2 ),
% 0.73/1.27 skol2 ) ==> one }.
% 0.73/1.27 parent0: (2466) {G1,W6,D4,L1,V0,M1} { addition( c( skol2 ), skol2 ) ==>
% 0.73/1.27 one }.
% 0.73/1.27 substitution0:
% 0.73/1.27 end
% 0.73/1.27 permutation0:
% 0.73/1.27 0 ==> 0
% 0.73/1.27 end
% 0.73/1.27
% 0.73/1.27 eqswap: (2467) {G0,W8,D3,L2,V2,M2} { one ==> addition( X, Y ), ! alpha1( X
% 0.73/1.27 , Y ) }.
% 0.73/1.27 parent0[1]: (19) {G0,W8,D3,L2,V2,M2} I { ! alpha1( X, Y ), addition( X, Y )
% 0.73/1.27 ==> one }.
% 0.73/1.27 substitution0:
% 0.73/1.27 X := X
% 0.73/1.27 Y := Y
% 0.73/1.27 end
% 0.73/1.27
% 0.73/1.27 resolution: (2468) {G1,W6,D4,L1,V0,M1} { one ==> addition( c( skol3 ),
% 0.73/1.27 skol3 ) }.
% 0.73/1.27 parent0[1]: (2467) {G0,W8,D3,L2,V2,M2} { one ==> addition( X, Y ), !
% 0.73/1.27 alpha1( X, Y ) }.
% 0.73/1.27 parent1[0]: (43) {G3,W4,D3,L1,V0,M1} R(41,16) { alpha1( c( skol3 ), skol3 )
% 0.73/1.27 }.
% 0.73/1.27 substitution0:
% 0.73/1.27 X := c( skol3 )
% 0.73/1.27 Y := skol3
% 0.73/1.27 end
% 0.73/1.27 substitution1:
% 0.73/1.27 end
% 0.73/1.27
% 0.73/1.27 eqswap: (2469) {G1,W6,D4,L1,V0,M1} { addition( c( skol3 ), skol3 ) ==> one
% 0.73/1.27 }.
% 0.73/1.27 parent0[0]: (2468) {G1,W6,D4,L1,V0,M1} { one ==> addition( c( skol3 ),
% 0.73/1.27 skol3 ) }.
% 0.73/1.27 substitution0:
% 0.73/1.27 end
% 0.73/1.27
% 0.73/1.27 subsumption: (266) {G4,W6,D4,L1,V0,M1} R(19,43) { addition( c( skol3 ),
% 0.73/1.27 skol3 ) ==> one }.
% 0.73/1.27 parent0: (2469) {G1,W6,D4,L1,V0,M1} { addition( c( skol3 ), skol3 ) ==>
% 0.73/1.27 one }.
% 0.73/1.27 substitution0:
% 0.73/1.27 end
% 0.73/1.27 permutation0:
% 0.73/1.27 0 ==> 0
% 0.73/1.27 end
% 0.73/1.27
% 0.73/1.27 eqswap: (2470) {G1,W11,D5,L1,V0,M1} { ! one ==> multiplication( addition(
% 0.73/1.27 skol2, c( skol2 ) ), addition( skol3, c( skol3 ) ) ) }.
% 0.73/1.27 parent0[0]: (28) {G1,W11,D5,L1,V0,M1} I;d(7) { ! multiplication( addition(
% 0.73/1.27 skol2, c( skol2 ) ), addition( skol3, c( skol3 ) ) ) ==> one }.
% 0.73/1.27 substitution0:
% 0.73/1.27 end
% 0.73/1.27
% 0.73/1.27 paramod: (2473) {G1,W11,D5,L1,V0,M1} { ! one ==> multiplication( addition
% 0.73/1.27 ( c( skol2 ), skol2 ), addition( skol3, c( skol3 ) ) ) }.
% 0.73/1.27 parent0[0]: (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X )
% 0.73/1.27 }.
% 0.73/1.27 parent1[0; 4]: (2470) {G1,W11,D5,L1,V0,M1} { ! one ==> multiplication(
% 0.73/1.27 addition( skol2, c( skol2 ) ), addition( skol3, c( skol3 ) ) ) }.
% 0.73/1.27 substitution0:
% 0.73/1.27 X := skol2
% 0.73/1.27 Y := c( skol2 )
% 0.73/1.27 end
% 0.73/1.27 substitution1:
% 0.73/1.27 end
% 0.73/1.27
% 0.73/1.27 paramod: (2480) {G2,W8,D5,L1,V0,M1} { ! one ==> multiplication( one,
% 0.73/1.27 addition( skol3, c( skol3 ) ) ) }.
% 0.73/1.27 parent0[0]: (265) {G4,W6,D4,L1,V0,M1} R(19,46) { addition( c( skol2 ),
% 0.73/1.27 skol2 ) ==> one }.
% 0.73/1.27 parent1[0; 4]: (2473) {G1,W11,D5,L1,V0,M1} { ! one ==> multiplication(
% 0.73/1.27 addition( c( skol2 ), skol2 ), addition( skol3, c( skol3 ) ) ) }.
% 0.73/1.27 substitution0:
% 0.73/1.27 end
% 0.73/1.27 substitution1:
% 0.73/1.27 end
% 0.73/1.27
% 0.73/1.27 paramod: (2481) {G1,W6,D4,L1,V0,M1} { ! one ==> addition( skol3, c( skol3
% 0.73/1.27 ) ) }.
% 0.73/1.27 parent0[0]: (6) {G0,W5,D3,L1,V1,M1} I { multiplication( one, X ) ==> X }.
% 0.73/1.27 parent1[0; 3]: (2480) {G2,W8,D5,L1,V0,M1} { ! one ==> multiplication( one
% 0.73/1.27 , addition( skol3, c( skol3 ) ) ) }.
% 0.73/1.27 substitution0:
% 0.73/1.27 X := addition( skol3, c( skol3 ) )
% 0.73/1.27 end
% 0.73/1.27 substitution1:
% 0.73/1.27 end
% 0.73/1.27
% 0.73/1.27 eqswap: (2482) {G1,W6,D4,L1,V0,M1} { ! addition( skol3, c( skol3 ) ) ==>
% 0.73/1.27 one }.
% 0.73/1.27 parent0[0]: (2481) {G1,W6,D4,L1,V0,M1} { ! one ==> addition( skol3, c(
% 0.73/1.27 skol3 ) ) }.
% 0.73/1.27 substitution0:
% 0.73/1.27 end
% 0.73/1.27
% 0.73/1.27 subsumption: (527) {G5,W6,D4,L1,V0,M1} P(0,28);d(265);d(6) { ! addition(
% 0.73/1.27 skol3, c( skol3 ) ) ==> one }.
% 0.73/1.27 parent0: (2482) {G1,W6,D4,L1,V0,M1} { ! addition( skol3, c( skol3 ) ) ==>
% 0.73/1.27 one }.
% 0.73/1.27 substitution0:
% 0.73/1.27 end
% 0.73/1.27 permutation0:
% 0.73/1.27 0 ==> 0
% 0.73/1.27 end
% 0.73/1.27
% 0.73/1.27 eqswap: (2483) {G5,W6,D4,L1,V0,M1} { ! one ==> addition( skol3, c( skol3 )
% 0.73/1.27 ) }.
% 0.73/1.27 parent0[0]: (527) {G5,W6,D4,L1,V0,M1} P(0,28);d(265);d(6) { ! addition(
% 0.73/1.27 skol3, c( skol3 ) ) ==> one }.
% 0.73/1.27 substitution0:
% 0.73/1.27 end
% 0.73/1.27
% 0.73/1.27 paramod: (2485) {G1,W6,D4,L1,V0,M1} { ! one ==> addition( c( skol3 ),
% 0.73/1.27 skol3 ) }.
% 0.73/1.27 parent0[0]: (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X )
% 0.73/1.27 }.
% 0.73/1.27 parent1[0; 3]: (2483) {G5,W6,D4,L1,V0,M1} { ! one ==> addition( skol3, c(
% 0.73/1.27 skol3 ) ) }.
% 0.73/1.27 substitution0:
% 0.73/1.27 X := skol3
% 0.73/1.27 Y := c( skol3 )
% 0.73/1.27 end
% 0.73/1.27 substitution1:
% 0.73/1.27 end
% 0.73/1.27
% 0.73/1.27 paramod: (2487) {G2,W3,D2,L1,V0,M1} { ! one ==> one }.
% 0.73/1.27 parent0[0]: (266) {G4,W6,D4,L1,V0,M1} R(19,43) { addition( c( skol3 ),
% 0.73/1.27 skol3 ) ==> one }.
% 0.73/1.27 parent1[0; 3]: (2485) {G1,W6,D4,L1,V0,M1} { ! one ==> addition( c( skol3 )
% 0.73/1.27 , skol3 ) }.
% 0.73/1.27 substitution0:
% 0.73/1.27 end
% 0.73/1.27 substitution1:
% 0.73/1.27 end
% 0.73/1.27
% 0.73/1.27 eqrefl: (2488) {G0,W0,D0,L0,V0,M0} { }.
% 0.73/1.27 parent0[0]: (2487) {G2,W3,D2,L1,V0,M1} { ! one ==> one }.
% 0.73/1.27 substitution0:
% 0.73/1.27 end
% 0.73/1.27
% 0.73/1.27 subsumption: (2247) {G6,W0,D0,L0,V0,M0} P(0,527);d(266);q { }.
% 0.73/1.27 parent0: (2488) {G0,W0,D0,L0,V0,M0} { }.
% 0.73/1.27 substitution0:
% 0.73/1.27 end
% 0.73/1.27 permutation0:
% 0.73/1.27 end
% 0.73/1.27
% 0.73/1.27 Proof check complete!
% 0.73/1.27
% 0.73/1.27 Memory use:
% 0.73/1.27
% 0.73/1.27 space for terms: 27192
% 0.73/1.27 space for clauses: 121613
% 0.73/1.27
% 0.73/1.27
% 0.73/1.27 clauses generated: 14331
% 0.73/1.27 clauses kept: 2248
% 0.73/1.27 clauses selected: 240
% 0.73/1.27 clauses deleted: 71
% 0.73/1.27 clauses inuse deleted: 32
% 0.73/1.27
% 0.73/1.27 subsentry: 24656
% 0.73/1.27 literals s-matched: 16535
% 0.73/1.27 literals matched: 16236
% 0.73/1.27 full subsumption: 1821
% 0.73/1.27
% 0.73/1.27 checksum: 2040218435
% 0.73/1.27
% 0.73/1.27
% 0.73/1.27 Bliksem ended
%------------------------------------------------------------------------------