TSTP Solution File: KLE022+3 by Bliksem---1.12
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%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : KLE022+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n016.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 0.70s 1.12s
% Output : Refutation 0.70s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : KLE022+3 : TPTP v8.1.0. Released v4.0.0.
% 0.12/0.13 % Command : bliksem %s
% 0.13/0.35 % Computer : n016.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % DateTime : Thu Jun 16 09:17:34 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.70/1.12 *** allocated 10000 integers for termspace/termends
% 0.70/1.12 *** allocated 10000 integers for clauses
% 0.70/1.12 *** allocated 10000 integers for justifications
% 0.70/1.12 Bliksem 1.12
% 0.70/1.12
% 0.70/1.12
% 0.70/1.12 Automatic Strategy Selection
% 0.70/1.12
% 0.70/1.12
% 0.70/1.12 Clauses:
% 0.70/1.12
% 0.70/1.12 { addition( X, Y ) = addition( Y, X ) }.
% 0.70/1.12 { addition( Z, addition( Y, X ) ) = addition( addition( Z, Y ), X ) }.
% 0.70/1.12 { addition( X, zero ) = X }.
% 0.70/1.12 { addition( X, X ) = X }.
% 0.70/1.12 { multiplication( X, multiplication( Y, Z ) ) = multiplication(
% 0.70/1.12 multiplication( X, Y ), Z ) }.
% 0.70/1.12 { multiplication( X, one ) = X }.
% 0.70/1.12 { multiplication( one, X ) = X }.
% 0.70/1.12 { multiplication( X, addition( Y, Z ) ) = addition( multiplication( X, Y )
% 0.70/1.12 , multiplication( X, Z ) ) }.
% 0.70/1.12 { multiplication( addition( X, Y ), Z ) = addition( multiplication( X, Z )
% 0.70/1.12 , multiplication( Y, Z ) ) }.
% 0.70/1.12 { multiplication( X, zero ) = zero }.
% 0.70/1.12 { multiplication( zero, X ) = zero }.
% 0.70/1.12 { ! leq( X, Y ), addition( X, Y ) = Y }.
% 0.70/1.12 { ! addition( X, Y ) = Y, leq( X, Y ) }.
% 0.70/1.12 { ! test( X ), complement( skol1( X ), X ) }.
% 0.70/1.12 { ! complement( Y, X ), test( X ) }.
% 0.70/1.12 { ! complement( Y, X ), multiplication( X, Y ) = zero }.
% 0.70/1.12 { ! complement( Y, X ), alpha1( X, Y ) }.
% 0.70/1.12 { ! multiplication( X, Y ) = zero, ! alpha1( X, Y ), complement( Y, X ) }.
% 0.70/1.12 { ! alpha1( X, Y ), multiplication( Y, X ) = zero }.
% 0.70/1.12 { ! alpha1( X, Y ), addition( X, Y ) = one }.
% 0.70/1.12 { ! multiplication( Y, X ) = zero, ! addition( X, Y ) = one, alpha1( X, Y )
% 0.70/1.12 }.
% 0.70/1.12 { ! test( X ), ! c( X ) = Y, complement( X, Y ) }.
% 0.70/1.12 { ! test( X ), ! complement( X, Y ), c( X ) = Y }.
% 0.70/1.12 { test( X ), c( X ) = zero }.
% 0.70/1.12 { ! test( X ), ! test( Y ), c( addition( X, Y ) ) = multiplication( c( X )
% 0.70/1.12 , c( Y ) ) }.
% 0.70/1.12 { ! test( X ), ! test( Y ), c( multiplication( X, Y ) ) = addition( c( X )
% 0.70/1.12 , c( Y ) ) }.
% 0.70/1.12 { test( skol2 ) }.
% 0.70/1.12 { ! skol3 = addition( multiplication( skol3, skol2 ), multiplication( skol3
% 0.70/1.12 , c( skol2 ) ) ) }.
% 0.70/1.12
% 0.70/1.12 percentage equality = 0.510204, percentage horn = 0.964286
% 0.70/1.12 This is a problem with some equality
% 0.70/1.12
% 0.70/1.12
% 0.70/1.12
% 0.70/1.12 Options Used:
% 0.70/1.12
% 0.70/1.12 useres = 1
% 0.70/1.12 useparamod = 1
% 0.70/1.12 useeqrefl = 1
% 0.70/1.12 useeqfact = 1
% 0.70/1.12 usefactor = 1
% 0.70/1.12 usesimpsplitting = 0
% 0.70/1.12 usesimpdemod = 5
% 0.70/1.12 usesimpres = 3
% 0.70/1.12
% 0.70/1.12 resimpinuse = 1000
% 0.70/1.12 resimpclauses = 20000
% 0.70/1.12 substype = eqrewr
% 0.70/1.12 backwardsubs = 1
% 0.70/1.12 selectoldest = 5
% 0.70/1.12
% 0.70/1.12 litorderings [0] = split
% 0.70/1.12 litorderings [1] = extend the termordering, first sorting on arguments
% 0.70/1.12
% 0.70/1.12 termordering = kbo
% 0.70/1.12
% 0.70/1.12 litapriori = 0
% 0.70/1.12 termapriori = 1
% 0.70/1.12 litaposteriori = 0
% 0.70/1.12 termaposteriori = 0
% 0.70/1.12 demodaposteriori = 0
% 0.70/1.12 ordereqreflfact = 0
% 0.70/1.12
% 0.70/1.12 litselect = negord
% 0.70/1.12
% 0.70/1.12 maxweight = 15
% 0.70/1.12 maxdepth = 30000
% 0.70/1.12 maxlength = 115
% 0.70/1.12 maxnrvars = 195
% 0.70/1.12 excuselevel = 1
% 0.70/1.12 increasemaxweight = 1
% 0.70/1.12
% 0.70/1.12 maxselected = 10000000
% 0.70/1.12 maxnrclauses = 10000000
% 0.70/1.12
% 0.70/1.12 showgenerated = 0
% 0.70/1.12 showkept = 0
% 0.70/1.12 showselected = 0
% 0.70/1.12 showdeleted = 0
% 0.70/1.12 showresimp = 1
% 0.70/1.12 showstatus = 2000
% 0.70/1.12
% 0.70/1.12 prologoutput = 0
% 0.70/1.12 nrgoals = 5000000
% 0.70/1.12 totalproof = 1
% 0.70/1.12
% 0.70/1.12 Symbols occurring in the translation:
% 0.70/1.12
% 0.70/1.12 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.70/1.12 . [1, 2] (w:1, o:23, a:1, s:1, b:0),
% 0.70/1.12 ! [4, 1] (w:0, o:15, a:1, s:1, b:0),
% 0.70/1.12 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.70/1.12 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.70/1.12 addition [37, 2] (w:1, o:47, a:1, s:1, b:0),
% 0.70/1.12 zero [39, 0] (w:1, o:9, a:1, s:1, b:0),
% 0.70/1.12 multiplication [40, 2] (w:1, o:49, a:1, s:1, b:0),
% 0.70/1.12 one [41, 0] (w:1, o:10, a:1, s:1, b:0),
% 0.70/1.12 leq [42, 2] (w:1, o:48, a:1, s:1, b:0),
% 0.70/1.12 test [44, 1] (w:1, o:21, a:1, s:1, b:0),
% 0.70/1.12 complement [46, 2] (w:1, o:50, a:1, s:1, b:0),
% 0.70/1.12 c [47, 1] (w:1, o:22, a:1, s:1, b:0),
% 0.70/1.12 alpha1 [48, 2] (w:1, o:51, a:1, s:1, b:1),
% 0.70/1.12 skol1 [49, 1] (w:1, o:20, a:1, s:1, b:1),
% 0.70/1.12 skol2 [50, 0] (w:1, o:13, a:1, s:1, b:1),
% 0.70/1.12 skol3 [51, 0] (w:1, o:14, a:1, s:1, b:1).
% 0.70/1.12
% 0.70/1.12
% 0.70/1.12 Starting Search:
% 0.70/1.12
% 0.70/1.12 *** allocated 15000 integers for clauses
% 0.70/1.12 *** allocated 22500 integers for clauses
% 0.70/1.12 *** allocated 33750 integers for clauses
% 0.70/1.12
% 0.70/1.12 Bliksems!, er is een bewijs:
% 0.70/1.12 % SZS status Theorem
% 0.70/1.12 % SZS output start Refutation
% 0.70/1.12
% 0.70/1.12 (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X ) }.
% 0.70/1.12 (5) {G0,W5,D3,L1,V1,M1} I { multiplication( X, one ) ==> X }.
% 0.70/1.12 (7) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Y ),
% 0.70/1.12 multiplication( X, Z ) ) ==> multiplication( X, addition( Y, Z ) ) }.
% 0.70/1.12 (16) {G0,W6,D2,L2,V2,M2} I { ! complement( Y, X ), alpha1( X, Y ) }.
% 0.70/1.12 (19) {G0,W8,D3,L2,V2,M2} I { ! alpha1( X, Y ), addition( X, Y ) ==> one }.
% 0.70/1.12 (21) {G0,W9,D3,L3,V2,M3} I { ! test( X ), ! c( X ) = Y, complement( X, Y )
% 0.70/1.12 }.
% 0.70/1.12 (26) {G0,W2,D2,L1,V0,M1} I { test( skol2 ) }.
% 0.70/1.12 (27) {G1,W8,D5,L1,V0,M1} I;d(7) { ! multiplication( skol3, addition( skol2
% 0.70/1.12 , c( skol2 ) ) ) ==> skol3 }.
% 0.70/1.12 (28) {G1,W6,D3,L2,V1,M2} Q(21) { ! test( X ), complement( X, c( X ) ) }.
% 0.70/1.12 (40) {G2,W4,D3,L1,V0,M1} R(28,26) { complement( skol2, c( skol2 ) ) }.
% 0.70/1.12 (41) {G3,W4,D3,L1,V0,M1} R(40,16) { alpha1( c( skol2 ), skol2 ) }.
% 0.70/1.12 (271) {G4,W6,D4,L1,V0,M1} R(19,41) { addition( c( skol2 ), skol2 ) ==> one
% 0.70/1.12 }.
% 0.70/1.12 (515) {G5,W0,D0,L0,V0,M0} P(0,27);d(271);d(5);q { }.
% 0.70/1.12
% 0.70/1.12
% 0.70/1.12 % SZS output end Refutation
% 0.70/1.12 found a proof!
% 0.70/1.12
% 0.70/1.12
% 0.70/1.12 Unprocessed initial clauses:
% 0.70/1.12
% 0.70/1.12 (517) {G0,W7,D3,L1,V2,M1} { addition( X, Y ) = addition( Y, X ) }.
% 0.70/1.12 (518) {G0,W11,D4,L1,V3,M1} { addition( Z, addition( Y, X ) ) = addition(
% 0.70/1.12 addition( Z, Y ), X ) }.
% 0.70/1.12 (519) {G0,W5,D3,L1,V1,M1} { addition( X, zero ) = X }.
% 0.70/1.12 (520) {G0,W5,D3,L1,V1,M1} { addition( X, X ) = X }.
% 0.70/1.12 (521) {G0,W11,D4,L1,V3,M1} { multiplication( X, multiplication( Y, Z ) ) =
% 0.70/1.12 multiplication( multiplication( X, Y ), Z ) }.
% 0.70/1.12 (522) {G0,W5,D3,L1,V1,M1} { multiplication( X, one ) = X }.
% 0.70/1.12 (523) {G0,W5,D3,L1,V1,M1} { multiplication( one, X ) = X }.
% 0.70/1.12 (524) {G0,W13,D4,L1,V3,M1} { multiplication( X, addition( Y, Z ) ) =
% 0.70/1.12 addition( multiplication( X, Y ), multiplication( X, Z ) ) }.
% 0.70/1.12 (525) {G0,W13,D4,L1,V3,M1} { multiplication( addition( X, Y ), Z ) =
% 0.70/1.12 addition( multiplication( X, Z ), multiplication( Y, Z ) ) }.
% 0.70/1.12 (526) {G0,W5,D3,L1,V1,M1} { multiplication( X, zero ) = zero }.
% 0.70/1.12 (527) {G0,W5,D3,L1,V1,M1} { multiplication( zero, X ) = zero }.
% 0.70/1.12 (528) {G0,W8,D3,L2,V2,M2} { ! leq( X, Y ), addition( X, Y ) = Y }.
% 0.70/1.12 (529) {G0,W8,D3,L2,V2,M2} { ! addition( X, Y ) = Y, leq( X, Y ) }.
% 0.70/1.12 (530) {G0,W6,D3,L2,V1,M2} { ! test( X ), complement( skol1( X ), X ) }.
% 0.70/1.12 (531) {G0,W5,D2,L2,V2,M2} { ! complement( Y, X ), test( X ) }.
% 0.70/1.12 (532) {G0,W8,D3,L2,V2,M2} { ! complement( Y, X ), multiplication( X, Y ) =
% 0.70/1.12 zero }.
% 0.70/1.12 (533) {G0,W6,D2,L2,V2,M2} { ! complement( Y, X ), alpha1( X, Y ) }.
% 0.70/1.12 (534) {G0,W11,D3,L3,V2,M3} { ! multiplication( X, Y ) = zero, ! alpha1( X
% 0.70/1.12 , Y ), complement( Y, X ) }.
% 0.70/1.12 (535) {G0,W8,D3,L2,V2,M2} { ! alpha1( X, Y ), multiplication( Y, X ) =
% 0.70/1.12 zero }.
% 0.70/1.12 (536) {G0,W8,D3,L2,V2,M2} { ! alpha1( X, Y ), addition( X, Y ) = one }.
% 0.70/1.12 (537) {G0,W13,D3,L3,V2,M3} { ! multiplication( Y, X ) = zero, ! addition(
% 0.70/1.12 X, Y ) = one, alpha1( X, Y ) }.
% 0.70/1.12 (538) {G0,W9,D3,L3,V2,M3} { ! test( X ), ! c( X ) = Y, complement( X, Y )
% 0.70/1.12 }.
% 0.70/1.12 (539) {G0,W9,D3,L3,V2,M3} { ! test( X ), ! complement( X, Y ), c( X ) = Y
% 0.70/1.12 }.
% 0.70/1.12 (540) {G0,W6,D3,L2,V1,M2} { test( X ), c( X ) = zero }.
% 0.70/1.12 (541) {G0,W14,D4,L3,V2,M3} { ! test( X ), ! test( Y ), c( addition( X, Y )
% 0.70/1.12 ) = multiplication( c( X ), c( Y ) ) }.
% 0.70/1.12 (542) {G0,W14,D4,L3,V2,M3} { ! test( X ), ! test( Y ), c( multiplication(
% 0.70/1.12 X, Y ) ) = addition( c( X ), c( Y ) ) }.
% 0.70/1.12 (543) {G0,W2,D2,L1,V0,M1} { test( skol2 ) }.
% 0.70/1.12 (544) {G0,W10,D5,L1,V0,M1} { ! skol3 = addition( multiplication( skol3,
% 0.70/1.12 skol2 ), multiplication( skol3, c( skol2 ) ) ) }.
% 0.70/1.12
% 0.70/1.12
% 0.70/1.12 Total Proof:
% 0.70/1.12
% 0.70/1.12 subsumption: (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X
% 0.70/1.12 ) }.
% 0.70/1.12 parent0: (517) {G0,W7,D3,L1,V2,M1} { addition( X, Y ) = addition( Y, X )
% 0.70/1.12 }.
% 0.70/1.12 substitution0:
% 0.70/1.12 X := X
% 0.70/1.12 Y := Y
% 0.70/1.12 end
% 0.70/1.12 permutation0:
% 0.70/1.12 0 ==> 0
% 0.70/1.12 end
% 0.70/1.12
% 0.70/1.12 subsumption: (5) {G0,W5,D3,L1,V1,M1} I { multiplication( X, one ) ==> X }.
% 0.70/1.12 parent0: (522) {G0,W5,D3,L1,V1,M1} { multiplication( X, one ) = X }.
% 0.70/1.12 substitution0:
% 0.70/1.12 X := X
% 0.70/1.12 end
% 0.70/1.12 permutation0:
% 0.70/1.12 0 ==> 0
% 0.70/1.12 end
% 0.70/1.12
% 0.70/1.12 eqswap: (556) {G0,W13,D4,L1,V3,M1} { addition( multiplication( X, Y ),
% 0.70/1.12 multiplication( X, Z ) ) = multiplication( X, addition( Y, Z ) ) }.
% 0.70/1.12 parent0[0]: (524) {G0,W13,D4,L1,V3,M1} { multiplication( X, addition( Y, Z
% 0.70/1.12 ) ) = addition( multiplication( X, Y ), multiplication( X, Z ) ) }.
% 0.70/1.12 substitution0:
% 0.70/1.12 X := X
% 0.70/1.12 Y := Y
% 0.70/1.12 Z := Z
% 0.70/1.12 end
% 0.70/1.12
% 0.70/1.12 subsumption: (7) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Y )
% 0.70/1.12 , multiplication( X, Z ) ) ==> multiplication( X, addition( Y, Z ) ) }.
% 0.70/1.12 parent0: (556) {G0,W13,D4,L1,V3,M1} { addition( multiplication( X, Y ),
% 0.70/1.12 multiplication( X, Z ) ) = multiplication( X, addition( Y, Z ) ) }.
% 0.70/1.12 substitution0:
% 0.70/1.12 X := X
% 0.70/1.12 Y := Y
% 0.70/1.12 Z := Z
% 0.70/1.12 end
% 0.70/1.12 permutation0:
% 0.70/1.12 0 ==> 0
% 0.70/1.12 end
% 0.70/1.12
% 0.70/1.12 subsumption: (16) {G0,W6,D2,L2,V2,M2} I { ! complement( Y, X ), alpha1( X,
% 0.70/1.12 Y ) }.
% 0.70/1.12 parent0: (533) {G0,W6,D2,L2,V2,M2} { ! complement( Y, X ), alpha1( X, Y )
% 0.70/1.12 }.
% 0.70/1.12 substitution0:
% 0.70/1.12 X := X
% 0.70/1.12 Y := Y
% 0.70/1.12 end
% 0.70/1.12 permutation0:
% 0.70/1.12 0 ==> 0
% 0.70/1.12 1 ==> 1
% 0.70/1.12 end
% 0.70/1.12
% 0.70/1.12 subsumption: (19) {G0,W8,D3,L2,V2,M2} I { ! alpha1( X, Y ), addition( X, Y
% 0.70/1.12 ) ==> one }.
% 0.70/1.12 parent0: (536) {G0,W8,D3,L2,V2,M2} { ! alpha1( X, Y ), addition( X, Y ) =
% 0.70/1.12 one }.
% 0.70/1.12 substitution0:
% 0.70/1.12 X := X
% 0.70/1.12 Y := Y
% 0.70/1.12 end
% 0.70/1.12 permutation0:
% 0.70/1.12 0 ==> 0
% 0.70/1.12 1 ==> 1
% 0.70/1.12 end
% 0.70/1.12
% 0.70/1.12 subsumption: (21) {G0,W9,D3,L3,V2,M3} I { ! test( X ), ! c( X ) = Y,
% 0.70/1.12 complement( X, Y ) }.
% 0.70/1.12 parent0: (538) {G0,W9,D3,L3,V2,M3} { ! test( X ), ! c( X ) = Y, complement
% 0.70/1.12 ( X, Y ) }.
% 0.70/1.12 substitution0:
% 0.70/1.12 X := X
% 0.70/1.12 Y := Y
% 0.70/1.12 end
% 0.70/1.12 permutation0:
% 0.70/1.12 0 ==> 0
% 0.70/1.12 1 ==> 1
% 0.70/1.12 2 ==> 2
% 0.70/1.12 end
% 0.70/1.12
% 0.70/1.12 subsumption: (26) {G0,W2,D2,L1,V0,M1} I { test( skol2 ) }.
% 0.70/1.12 parent0: (543) {G0,W2,D2,L1,V0,M1} { test( skol2 ) }.
% 0.70/1.12 substitution0:
% 0.70/1.12 end
% 0.70/1.12 permutation0:
% 0.70/1.12 0 ==> 0
% 0.70/1.12 end
% 0.70/1.12
% 0.70/1.12 *** allocated 50625 integers for clauses
% 0.70/1.12 paramod: (693) {G1,W8,D5,L1,V0,M1} { ! skol3 = multiplication( skol3,
% 0.70/1.12 addition( skol2, c( skol2 ) ) ) }.
% 0.70/1.12 parent0[0]: (7) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Y ),
% 0.70/1.12 multiplication( X, Z ) ) ==> multiplication( X, addition( Y, Z ) ) }.
% 0.70/1.12 parent1[0; 3]: (544) {G0,W10,D5,L1,V0,M1} { ! skol3 = addition(
% 0.70/1.12 multiplication( skol3, skol2 ), multiplication( skol3, c( skol2 ) ) ) }.
% 0.70/1.12 substitution0:
% 0.70/1.12 X := skol3
% 0.70/1.12 Y := skol2
% 0.70/1.12 Z := c( skol2 )
% 0.70/1.12 end
% 0.70/1.12 substitution1:
% 0.70/1.12 end
% 0.70/1.12
% 0.70/1.12 eqswap: (694) {G1,W8,D5,L1,V0,M1} { ! multiplication( skol3, addition(
% 0.70/1.12 skol2, c( skol2 ) ) ) = skol3 }.
% 0.70/1.12 parent0[0]: (693) {G1,W8,D5,L1,V0,M1} { ! skol3 = multiplication( skol3,
% 0.70/1.12 addition( skol2, c( skol2 ) ) ) }.
% 0.70/1.12 substitution0:
% 0.70/1.12 end
% 0.70/1.12
% 0.70/1.12 subsumption: (27) {G1,W8,D5,L1,V0,M1} I;d(7) { ! multiplication( skol3,
% 0.70/1.12 addition( skol2, c( skol2 ) ) ) ==> skol3 }.
% 0.70/1.12 parent0: (694) {G1,W8,D5,L1,V0,M1} { ! multiplication( skol3, addition(
% 0.70/1.12 skol2, c( skol2 ) ) ) = skol3 }.
% 0.70/1.12 substitution0:
% 0.70/1.12 end
% 0.70/1.12 permutation0:
% 0.70/1.12 0 ==> 0
% 0.70/1.12 end
% 0.70/1.12
% 0.70/1.12 eqswap: (695) {G0,W9,D3,L3,V2,M3} { ! Y = c( X ), ! test( X ), complement
% 0.70/1.12 ( X, Y ) }.
% 0.70/1.12 parent0[1]: (21) {G0,W9,D3,L3,V2,M3} I { ! test( X ), ! c( X ) = Y,
% 0.70/1.12 complement( X, Y ) }.
% 0.70/1.12 substitution0:
% 0.70/1.12 X := X
% 0.70/1.12 Y := Y
% 0.70/1.12 end
% 0.70/1.12
% 0.70/1.12 eqrefl: (696) {G0,W6,D3,L2,V1,M2} { ! test( X ), complement( X, c( X ) )
% 0.70/1.12 }.
% 0.70/1.12 parent0[0]: (695) {G0,W9,D3,L3,V2,M3} { ! Y = c( X ), ! test( X ),
% 0.70/1.12 complement( X, Y ) }.
% 0.70/1.12 substitution0:
% 0.70/1.12 X := X
% 0.70/1.12 Y := c( X )
% 0.70/1.12 end
% 0.70/1.12
% 0.70/1.12 subsumption: (28) {G1,W6,D3,L2,V1,M2} Q(21) { ! test( X ), complement( X, c
% 0.70/1.12 ( X ) ) }.
% 0.70/1.12 parent0: (696) {G0,W6,D3,L2,V1,M2} { ! test( X ), complement( X, c( X ) )
% 0.70/1.12 }.
% 0.70/1.12 substitution0:
% 0.70/1.12 X := X
% 0.70/1.12 end
% 0.70/1.12 permutation0:
% 0.70/1.12 0 ==> 0
% 0.70/1.12 1 ==> 1
% 0.70/1.12 end
% 0.70/1.12
% 0.70/1.12 resolution: (697) {G1,W4,D3,L1,V0,M1} { complement( skol2, c( skol2 ) )
% 0.70/1.12 }.
% 0.70/1.12 parent0[0]: (28) {G1,W6,D3,L2,V1,M2} Q(21) { ! test( X ), complement( X, c
% 0.70/1.12 ( X ) ) }.
% 0.70/1.12 parent1[0]: (26) {G0,W2,D2,L1,V0,M1} I { test( skol2 ) }.
% 0.70/1.12 substitution0:
% 0.70/1.12 X := skol2
% 0.70/1.12 end
% 0.70/1.12 substitution1:
% 0.70/1.12 end
% 0.70/1.12
% 0.70/1.12 subsumption: (40) {G2,W4,D3,L1,V0,M1} R(28,26) { complement( skol2, c(
% 0.70/1.12 skol2 ) ) }.
% 0.70/1.12 parent0: (697) {G1,W4,D3,L1,V0,M1} { complement( skol2, c( skol2 ) ) }.
% 0.70/1.12 substitution0:
% 0.70/1.12 end
% 0.70/1.12 permutation0:
% 0.70/1.12 0 ==> 0
% 0.70/1.12 end
% 0.70/1.12
% 0.70/1.12 resolution: (698) {G1,W4,D3,L1,V0,M1} { alpha1( c( skol2 ), skol2 ) }.
% 0.70/1.12 parent0[0]: (16) {G0,W6,D2,L2,V2,M2} I { ! complement( Y, X ), alpha1( X, Y
% 0.70/1.12 ) }.
% 0.70/1.12 parent1[0]: (40) {G2,W4,D3,L1,V0,M1} R(28,26) { complement( skol2, c( skol2
% 0.70/1.12 ) ) }.
% 0.70/1.12 substitution0:
% 0.70/1.12 X := c( skol2 )
% 0.70/1.12 Y := skol2
% 0.70/1.12 end
% 0.70/1.12 substitution1:
% 0.70/1.12 end
% 0.70/1.12
% 0.70/1.12 subsumption: (41) {G3,W4,D3,L1,V0,M1} R(40,16) { alpha1( c( skol2 ), skol2
% 0.70/1.12 ) }.
% 0.70/1.12 parent0: (698) {G1,W4,D3,L1,V0,M1} { alpha1( c( skol2 ), skol2 ) }.
% 0.70/1.12 substitution0:
% 0.70/1.12 end
% 0.70/1.12 permutation0:
% 0.70/1.12 0 ==> 0
% 0.70/1.12 end
% 0.70/1.12
% 0.70/1.12 eqswap: (699) {G0,W8,D3,L2,V2,M2} { one ==> addition( X, Y ), ! alpha1( X
% 0.70/1.12 , Y ) }.
% 0.70/1.12 parent0[1]: (19) {G0,W8,D3,L2,V2,M2} I { ! alpha1( X, Y ), addition( X, Y )
% 0.70/1.12 ==> one }.
% 0.70/1.12 substitution0:
% 0.70/1.12 X := X
% 0.70/1.12 Y := Y
% 0.70/1.12 end
% 0.70/1.12
% 0.70/1.12 resolution: (700) {G1,W6,D4,L1,V0,M1} { one ==> addition( c( skol2 ),
% 0.70/1.12 skol2 ) }.
% 0.70/1.12 parent0[1]: (699) {G0,W8,D3,L2,V2,M2} { one ==> addition( X, Y ), ! alpha1
% 0.70/1.12 ( X, Y ) }.
% 0.70/1.12 parent1[0]: (41) {G3,W4,D3,L1,V0,M1} R(40,16) { alpha1( c( skol2 ), skol2 )
% 0.70/1.12 }.
% 0.70/1.12 substitution0:
% 0.70/1.12 X := c( skol2 )
% 0.70/1.12 Y := skol2
% 0.70/1.12 end
% 0.70/1.12 substitution1:
% 0.70/1.12 end
% 0.70/1.12
% 0.70/1.12 eqswap: (701) {G1,W6,D4,L1,V0,M1} { addition( c( skol2 ), skol2 ) ==> one
% 0.70/1.12 }.
% 0.70/1.12 parent0[0]: (700) {G1,W6,D4,L1,V0,M1} { one ==> addition( c( skol2 ),
% 0.70/1.12 skol2 ) }.
% 0.70/1.12 substitution0:
% 0.70/1.12 end
% 0.70/1.12
% 0.70/1.12 subsumption: (271) {G4,W6,D4,L1,V0,M1} R(19,41) { addition( c( skol2 ),
% 0.70/1.12 skol2 ) ==> one }.
% 0.70/1.12 parent0: (701) {G1,W6,D4,L1,V0,M1} { addition( c( skol2 ), skol2 ) ==> one
% 0.70/1.12 }.
% 0.70/1.12 substitution0:
% 0.70/1.12 end
% 0.70/1.12 permutation0:
% 0.70/1.12 0 ==> 0
% 0.70/1.12 end
% 0.70/1.12
% 0.70/1.12 eqswap: (702) {G1,W8,D5,L1,V0,M1} { ! skol3 ==> multiplication( skol3,
% 0.70/1.12 addition( skol2, c( skol2 ) ) ) }.
% 0.70/1.12 parent0[0]: (27) {G1,W8,D5,L1,V0,M1} I;d(7) { ! multiplication( skol3,
% 0.70/1.12 addition( skol2, c( skol2 ) ) ) ==> skol3 }.
% 0.70/1.12 substitution0:
% 0.70/1.12 end
% 0.70/1.12
% 0.70/1.12 paramod: (705) {G1,W8,D5,L1,V0,M1} { ! skol3 ==> multiplication( skol3,
% 0.70/1.12 addition( c( skol2 ), skol2 ) ) }.
% 0.70/1.12 parent0[0]: (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X )
% 0.70/1.12 }.
% 0.70/1.12 parent1[0; 5]: (702) {G1,W8,D5,L1,V0,M1} { ! skol3 ==> multiplication(
% 0.70/1.12 skol3, addition( skol2, c( skol2 ) ) ) }.
% 0.70/1.12 substitution0:
% 0.70/1.12 X := skol2
% 0.70/1.12 Y := c( skol2 )
% 0.70/1.12 end
% 0.70/1.12 substitution1:
% 0.70/1.12 end
% 0.70/1.12
% 0.70/1.12 paramod: (707) {G2,W5,D3,L1,V0,M1} { ! skol3 ==> multiplication( skol3,
% 0.70/1.12 one ) }.
% 0.70/1.12 parent0[0]: (271) {G4,W6,D4,L1,V0,M1} R(19,41) { addition( c( skol2 ),
% 0.70/1.12 skol2 ) ==> one }.
% 0.70/1.12 parent1[0; 5]: (705) {G1,W8,D5,L1,V0,M1} { ! skol3 ==> multiplication(
% 0.70/1.12 skol3, addition( c( skol2 ), skol2 ) ) }.
% 0.70/1.12 substitution0:
% 0.70/1.12 end
% 0.70/1.12 substitution1:
% 0.70/1.12 end
% 0.70/1.12
% 0.70/1.12 paramod: (708) {G1,W3,D2,L1,V0,M1} { ! skol3 ==> skol3 }.
% 0.70/1.12 parent0[0]: (5) {G0,W5,D3,L1,V1,M1} I { multiplication( X, one ) ==> X }.
% 0.70/1.12 parent1[0; 3]: (707) {G2,W5,D3,L1,V0,M1} { ! skol3 ==> multiplication(
% 0.70/1.12 skol3, one ) }.
% 0.70/1.12 substitution0:
% 0.70/1.12 X := skol3
% 0.70/1.12 end
% 0.70/1.12 substitution1:
% 0.70/1.12 end
% 0.70/1.12
% 0.70/1.12 eqrefl: (709) {G0,W0,D0,L0,V0,M0} { }.
% 0.70/1.12 parent0[0]: (708) {G1,W3,D2,L1,V0,M1} { ! skol3 ==> skol3 }.
% 0.70/1.12 substitution0:
% 0.70/1.12 end
% 0.70/1.12
% 0.70/1.12 subsumption: (515) {G5,W0,D0,L0,V0,M0} P(0,27);d(271);d(5);q { }.
% 0.70/1.12 parent0: (709) {G0,W0,D0,L0,V0,M0} { }.
% 0.70/1.12 substitution0:
% 0.70/1.12 end
% 0.70/1.12 permutation0:
% 0.70/1.12 end
% 0.70/1.12
% 0.70/1.12 Proof check complete!
% 0.70/1.12
% 0.70/1.12 Memory use:
% 0.70/1.12
% 0.70/1.12 space for terms: 6149
% 0.70/1.12 space for clauses: 30712
% 0.70/1.12
% 0.70/1.12
% 0.70/1.12 clauses generated: 1845
% 0.70/1.12 clauses kept: 516
% 0.70/1.12 clauses selected: 80
% 0.70/1.12 clauses deleted: 6
% 0.70/1.12 clauses inuse deleted: 0
% 0.70/1.12
% 0.70/1.12 subsentry: 2905
% 0.70/1.12 literals s-matched: 1848
% 0.70/1.12 literals matched: 1847
% 0.70/1.12 full subsumption: 205
% 0.70/1.12
% 0.70/1.12 checksum: 122229770
% 0.70/1.12
% 0.70/1.12
% 0.70/1.12 Bliksem ended
%------------------------------------------------------------------------------