TSTP Solution File: KLE022+2 by Bliksem---1.12
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%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : KLE022+2 : 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 01:36:41 EDT 2022
% Result : Theorem 0.46s 1.07s
% Output : Refutation 0.46s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : KLE022+2 : TPTP v8.1.0. Released v4.0.0.
% 0.10/0.12 % 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 13:42:22 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.46/1.07 *** allocated 10000 integers for termspace/termends
% 0.46/1.07 *** allocated 10000 integers for clauses
% 0.46/1.07 *** allocated 10000 integers for justifications
% 0.46/1.07 Bliksem 1.12
% 0.46/1.07
% 0.46/1.07
% 0.46/1.07 Automatic Strategy Selection
% 0.46/1.07
% 0.46/1.07
% 0.46/1.07 Clauses:
% 0.46/1.07
% 0.46/1.07 { addition( X, Y ) = addition( Y, X ) }.
% 0.46/1.07 { addition( Z, addition( Y, X ) ) = addition( addition( Z, Y ), X ) }.
% 0.46/1.07 { addition( X, zero ) = X }.
% 0.46/1.07 { addition( X, X ) = X }.
% 0.46/1.07 { multiplication( X, multiplication( Y, Z ) ) = multiplication(
% 0.46/1.07 multiplication( X, Y ), Z ) }.
% 0.46/1.07 { multiplication( X, one ) = X }.
% 0.46/1.07 { multiplication( one, X ) = X }.
% 0.46/1.07 { multiplication( X, addition( Y, Z ) ) = addition( multiplication( X, Y )
% 0.46/1.07 , multiplication( X, Z ) ) }.
% 0.46/1.07 { multiplication( addition( X, Y ), Z ) = addition( multiplication( X, Z )
% 0.46/1.07 , multiplication( Y, Z ) ) }.
% 0.46/1.07 { multiplication( X, zero ) = zero }.
% 0.46/1.07 { multiplication( zero, X ) = zero }.
% 0.46/1.07 { ! leq( X, Y ), addition( X, Y ) = Y }.
% 0.46/1.07 { ! addition( X, Y ) = Y, leq( X, Y ) }.
% 0.46/1.07 { ! test( X ), complement( skol1( X ), X ) }.
% 0.46/1.07 { ! complement( Y, X ), test( X ) }.
% 0.46/1.07 { ! complement( Y, X ), multiplication( X, Y ) = zero }.
% 0.46/1.07 { ! complement( Y, X ), alpha1( X, Y ) }.
% 0.46/1.07 { ! multiplication( X, Y ) = zero, ! alpha1( X, Y ), complement( Y, X ) }.
% 0.46/1.07 { ! alpha1( X, Y ), multiplication( Y, X ) = zero }.
% 0.46/1.07 { ! alpha1( X, Y ), addition( X, Y ) = one }.
% 0.46/1.07 { ! multiplication( Y, X ) = zero, ! addition( X, Y ) = one, alpha1( X, Y )
% 0.46/1.07 }.
% 0.46/1.07 { ! test( X ), ! c( X ) = Y, complement( X, Y ) }.
% 0.46/1.07 { ! test( X ), ! complement( X, Y ), c( X ) = Y }.
% 0.46/1.07 { test( X ), c( X ) = zero }.
% 0.46/1.07 { test( skol2 ) }.
% 0.46/1.07 { ! leq( skol3, addition( multiplication( skol3, skol2 ), multiplication(
% 0.46/1.07 skol3, c( skol2 ) ) ) ), ! leq( addition( multiplication( skol3, skol2 )
% 0.46/1.07 , multiplication( skol3, c( skol2 ) ) ), skol3 ) }.
% 0.46/1.07
% 0.46/1.07 percentage equality = 0.500000, percentage horn = 0.961538
% 0.46/1.07 This is a problem with some equality
% 0.46/1.07
% 0.46/1.07
% 0.46/1.07
% 0.46/1.07 Options Used:
% 0.46/1.07
% 0.46/1.07 useres = 1
% 0.46/1.07 useparamod = 1
% 0.46/1.07 useeqrefl = 1
% 0.46/1.07 useeqfact = 1
% 0.46/1.07 usefactor = 1
% 0.46/1.07 usesimpsplitting = 0
% 0.46/1.07 usesimpdemod = 5
% 0.46/1.07 usesimpres = 3
% 0.46/1.07
% 0.46/1.07 resimpinuse = 1000
% 0.46/1.07 resimpclauses = 20000
% 0.46/1.07 substype = eqrewr
% 0.46/1.07 backwardsubs = 1
% 0.46/1.07 selectoldest = 5
% 0.46/1.07
% 0.46/1.07 litorderings [0] = split
% 0.46/1.07 litorderings [1] = extend the termordering, first sorting on arguments
% 0.46/1.07
% 0.46/1.07 termordering = kbo
% 0.46/1.07
% 0.46/1.07 litapriori = 0
% 0.46/1.07 termapriori = 1
% 0.46/1.07 litaposteriori = 0
% 0.46/1.07 termaposteriori = 0
% 0.46/1.07 demodaposteriori = 0
% 0.46/1.07 ordereqreflfact = 0
% 0.46/1.07
% 0.46/1.07 litselect = negord
% 0.46/1.07
% 0.46/1.07 maxweight = 15
% 0.46/1.07 maxdepth = 30000
% 0.46/1.07 maxlength = 115
% 0.46/1.07 maxnrvars = 195
% 0.46/1.07 excuselevel = 1
% 0.46/1.07 increasemaxweight = 1
% 0.46/1.07
% 0.46/1.07 maxselected = 10000000
% 0.46/1.07 maxnrclauses = 10000000
% 0.46/1.07
% 0.46/1.07 showgenerated = 0
% 0.46/1.07 showkept = 0
% 0.46/1.07 showselected = 0
% 0.46/1.07 showdeleted = 0
% 0.46/1.07 showresimp = 1
% 0.46/1.07 showstatus = 2000
% 0.46/1.07
% 0.46/1.07 prologoutput = 0
% 0.46/1.07 nrgoals = 5000000
% 0.46/1.07 totalproof = 1
% 0.46/1.07
% 0.46/1.07 Symbols occurring in the translation:
% 0.46/1.07
% 0.46/1.07 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.46/1.07 . [1, 2] (w:1, o:23, a:1, s:1, b:0),
% 0.46/1.07 ! [4, 1] (w:0, o:15, a:1, s:1, b:0),
% 0.46/1.07 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.46/1.07 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.46/1.07 addition [37, 2] (w:1, o:47, a:1, s:1, b:0),
% 0.46/1.07 zero [39, 0] (w:1, o:9, a:1, s:1, b:0),
% 0.46/1.07 multiplication [40, 2] (w:1, o:49, a:1, s:1, b:0),
% 0.46/1.07 one [41, 0] (w:1, o:10, a:1, s:1, b:0),
% 0.46/1.07 leq [42, 2] (w:1, o:48, a:1, s:1, b:0),
% 0.46/1.07 test [44, 1] (w:1, o:21, a:1, s:1, b:0),
% 0.46/1.07 complement [46, 2] (w:1, o:50, a:1, s:1, b:0),
% 0.46/1.07 c [47, 1] (w:1, o:22, a:1, s:1, b:0),
% 0.46/1.07 alpha1 [48, 2] (w:1, o:51, a:1, s:1, b:1),
% 0.46/1.07 skol1 [49, 1] (w:1, o:20, a:1, s:1, b:1),
% 0.46/1.07 skol2 [50, 0] (w:1, o:13, a:1, s:1, b:1),
% 0.46/1.07 skol3 [51, 0] (w:1, o:14, a:1, s:1, b:1).
% 0.46/1.07
% 0.46/1.07
% 0.46/1.07 Starting Search:
% 0.46/1.07
% 0.46/1.07 *** allocated 15000 integers for clauses
% 0.46/1.07 *** allocated 22500 integers for clauses
% 0.46/1.07 *** allocated 33750 integers for clauses
% 0.46/1.07
% 0.46/1.07 Bliksems!, er is een bewijs:
% 0.46/1.07 % SZS status Theorem
% 0.46/1.07 % SZS output start Refutation
% 0.46/1.07
% 0.46/1.07 (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X ) }.
% 0.46/1.07 (3) {G0,W5,D3,L1,V1,M1} I { addition( X, X ) ==> X }.
% 0.46/1.07 (5) {G0,W5,D3,L1,V1,M1} I { multiplication( X, one ) ==> X }.
% 0.46/1.07 (7) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Y ),
% 0.46/1.07 multiplication( X, Z ) ) ==> multiplication( X, addition( Y, Z ) ) }.
% 0.46/1.07 (12) {G0,W8,D3,L2,V2,M2} I { ! addition( X, Y ) ==> Y, leq( X, Y ) }.
% 0.46/1.07 (16) {G0,W6,D2,L2,V2,M2} I { ! complement( Y, X ), alpha1( X, Y ) }.
% 0.46/1.07 (19) {G0,W8,D3,L2,V2,M2} I { ! alpha1( X, Y ), addition( X, Y ) ==> one }.
% 0.46/1.07 (21) {G0,W9,D3,L3,V2,M3} I { ! test( X ), ! c( X ) = Y, complement( X, Y )
% 0.46/1.07 }.
% 0.46/1.07 (24) {G0,W2,D2,L1,V0,M1} I { test( skol2 ) }.
% 0.46/1.07 (25) {G1,W16,D5,L2,V0,M2} I;d(7);d(7) { ! leq( skol3, multiplication( skol3
% 0.46/1.07 , addition( skol2, c( skol2 ) ) ) ), ! leq( multiplication( skol3,
% 0.46/1.07 addition( skol2, c( skol2 ) ) ), skol3 ) }.
% 0.46/1.07 (26) {G1,W6,D3,L2,V1,M2} Q(21) { ! test( X ), complement( X, c( X ) ) }.
% 0.46/1.07 (36) {G2,W4,D3,L1,V0,M1} R(26,24) { complement( skol2, c( skol2 ) ) }.
% 0.46/1.07 (37) {G3,W4,D3,L1,V0,M1} R(36,16) { alpha1( c( skol2 ), skol2 ) }.
% 0.46/1.07 (157) {G1,W3,D2,L1,V1,M1} R(12,3) { leq( X, X ) }.
% 0.46/1.07 (267) {G4,W6,D4,L1,V0,M1} R(19,37) { addition( c( skol2 ), skol2 ) ==> one
% 0.46/1.07 }.
% 0.46/1.07 (438) {G5,W0,D0,L0,V0,M0} P(0,25);d(267);d(267);d(5);d(5);f;r(157) { }.
% 0.46/1.07
% 0.46/1.07
% 0.46/1.07 % SZS output end Refutation
% 0.46/1.07 found a proof!
% 0.46/1.07
% 0.46/1.07
% 0.46/1.07 Unprocessed initial clauses:
% 0.46/1.07
% 0.46/1.07 (440) {G0,W7,D3,L1,V2,M1} { addition( X, Y ) = addition( Y, X ) }.
% 0.46/1.07 (441) {G0,W11,D4,L1,V3,M1} { addition( Z, addition( Y, X ) ) = addition(
% 0.46/1.07 addition( Z, Y ), X ) }.
% 0.46/1.07 (442) {G0,W5,D3,L1,V1,M1} { addition( X, zero ) = X }.
% 0.46/1.07 (443) {G0,W5,D3,L1,V1,M1} { addition( X, X ) = X }.
% 0.46/1.07 (444) {G0,W11,D4,L1,V3,M1} { multiplication( X, multiplication( Y, Z ) ) =
% 0.46/1.07 multiplication( multiplication( X, Y ), Z ) }.
% 0.46/1.07 (445) {G0,W5,D3,L1,V1,M1} { multiplication( X, one ) = X }.
% 0.46/1.07 (446) {G0,W5,D3,L1,V1,M1} { multiplication( one, X ) = X }.
% 0.46/1.07 (447) {G0,W13,D4,L1,V3,M1} { multiplication( X, addition( Y, Z ) ) =
% 0.46/1.07 addition( multiplication( X, Y ), multiplication( X, Z ) ) }.
% 0.46/1.07 (448) {G0,W13,D4,L1,V3,M1} { multiplication( addition( X, Y ), Z ) =
% 0.46/1.07 addition( multiplication( X, Z ), multiplication( Y, Z ) ) }.
% 0.46/1.07 (449) {G0,W5,D3,L1,V1,M1} { multiplication( X, zero ) = zero }.
% 0.46/1.07 (450) {G0,W5,D3,L1,V1,M1} { multiplication( zero, X ) = zero }.
% 0.46/1.07 (451) {G0,W8,D3,L2,V2,M2} { ! leq( X, Y ), addition( X, Y ) = Y }.
% 0.46/1.07 (452) {G0,W8,D3,L2,V2,M2} { ! addition( X, Y ) = Y, leq( X, Y ) }.
% 0.46/1.07 (453) {G0,W6,D3,L2,V1,M2} { ! test( X ), complement( skol1( X ), X ) }.
% 0.46/1.07 (454) {G0,W5,D2,L2,V2,M2} { ! complement( Y, X ), test( X ) }.
% 0.46/1.07 (455) {G0,W8,D3,L2,V2,M2} { ! complement( Y, X ), multiplication( X, Y ) =
% 0.46/1.07 zero }.
% 0.46/1.07 (456) {G0,W6,D2,L2,V2,M2} { ! complement( Y, X ), alpha1( X, Y ) }.
% 0.46/1.07 (457) {G0,W11,D3,L3,V2,M3} { ! multiplication( X, Y ) = zero, ! alpha1( X
% 0.46/1.07 , Y ), complement( Y, X ) }.
% 0.46/1.07 (458) {G0,W8,D3,L2,V2,M2} { ! alpha1( X, Y ), multiplication( Y, X ) =
% 0.46/1.07 zero }.
% 0.46/1.07 (459) {G0,W8,D3,L2,V2,M2} { ! alpha1( X, Y ), addition( X, Y ) = one }.
% 0.46/1.07 (460) {G0,W13,D3,L3,V2,M3} { ! multiplication( Y, X ) = zero, ! addition(
% 0.46/1.07 X, Y ) = one, alpha1( X, Y ) }.
% 0.46/1.07 (461) {G0,W9,D3,L3,V2,M3} { ! test( X ), ! c( X ) = Y, complement( X, Y )
% 0.46/1.07 }.
% 0.46/1.07 (462) {G0,W9,D3,L3,V2,M3} { ! test( X ), ! complement( X, Y ), c( X ) = Y
% 0.46/1.07 }.
% 0.46/1.07 (463) {G0,W6,D3,L2,V1,M2} { test( X ), c( X ) = zero }.
% 0.46/1.07 (464) {G0,W2,D2,L1,V0,M1} { test( skol2 ) }.
% 0.46/1.07 (465) {G0,W20,D5,L2,V0,M2} { ! leq( skol3, addition( multiplication( skol3
% 0.46/1.07 , skol2 ), multiplication( skol3, c( skol2 ) ) ) ), ! leq( addition(
% 0.46/1.07 multiplication( skol3, skol2 ), multiplication( skol3, c( skol2 ) ) ),
% 0.46/1.07 skol3 ) }.
% 0.46/1.07
% 0.46/1.07
% 0.46/1.07 Total Proof:
% 0.46/1.07
% 0.46/1.07 subsumption: (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X
% 0.46/1.07 ) }.
% 0.46/1.07 parent0: (440) {G0,W7,D3,L1,V2,M1} { addition( X, Y ) = addition( Y, X )
% 0.46/1.07 }.
% 0.46/1.07 substitution0:
% 0.46/1.07 X := X
% 0.46/1.07 Y := Y
% 0.46/1.07 end
% 0.46/1.07 permutation0:
% 0.46/1.07 0 ==> 0
% 0.46/1.07 end
% 0.46/1.07
% 0.46/1.07 subsumption: (3) {G0,W5,D3,L1,V1,M1} I { addition( X, X ) ==> X }.
% 0.46/1.07 parent0: (443) {G0,W5,D3,L1,V1,M1} { addition( X, X ) = X }.
% 0.46/1.07 substitution0:
% 0.46/1.07 X := X
% 0.46/1.07 end
% 0.46/1.07 permutation0:
% 0.46/1.07 0 ==> 0
% 0.46/1.07 end
% 0.46/1.07
% 0.46/1.07 subsumption: (5) {G0,W5,D3,L1,V1,M1} I { multiplication( X, one ) ==> X }.
% 0.46/1.07 parent0: (445) {G0,W5,D3,L1,V1,M1} { multiplication( X, one ) = X }.
% 0.46/1.07 substitution0:
% 0.46/1.07 X := X
% 0.46/1.07 end
% 0.46/1.07 permutation0:
% 0.46/1.07 0 ==> 0
% 0.46/1.07 end
% 0.46/1.07
% 0.46/1.07 eqswap: (480) {G0,W13,D4,L1,V3,M1} { addition( multiplication( X, Y ),
% 0.46/1.07 multiplication( X, Z ) ) = multiplication( X, addition( Y, Z ) ) }.
% 0.46/1.07 parent0[0]: (447) {G0,W13,D4,L1,V3,M1} { multiplication( X, addition( Y, Z
% 0.46/1.07 ) ) = addition( multiplication( X, Y ), multiplication( X, Z ) ) }.
% 0.46/1.07 substitution0:
% 0.46/1.07 X := X
% 0.46/1.07 Y := Y
% 0.46/1.07 Z := Z
% 0.46/1.07 end
% 0.46/1.07
% 0.46/1.07 subsumption: (7) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Y )
% 0.46/1.07 , multiplication( X, Z ) ) ==> multiplication( X, addition( Y, Z ) ) }.
% 0.46/1.07 parent0: (480) {G0,W13,D4,L1,V3,M1} { addition( multiplication( X, Y ),
% 0.46/1.07 multiplication( X, Z ) ) = multiplication( X, addition( Y, Z ) ) }.
% 0.46/1.07 substitution0:
% 0.46/1.07 X := X
% 0.46/1.07 Y := Y
% 0.46/1.07 Z := Z
% 0.46/1.07 end
% 0.46/1.07 permutation0:
% 0.46/1.07 0 ==> 0
% 0.46/1.07 end
% 0.46/1.07
% 0.46/1.07 subsumption: (12) {G0,W8,D3,L2,V2,M2} I { ! addition( X, Y ) ==> Y, leq( X
% 0.46/1.07 , Y ) }.
% 0.46/1.07 parent0: (452) {G0,W8,D3,L2,V2,M2} { ! addition( X, Y ) = Y, leq( X, Y )
% 0.46/1.07 }.
% 0.46/1.07 substitution0:
% 0.46/1.07 X := X
% 0.46/1.07 Y := Y
% 0.46/1.07 end
% 0.46/1.07 permutation0:
% 0.46/1.07 0 ==> 0
% 0.46/1.07 1 ==> 1
% 0.46/1.07 end
% 0.46/1.07
% 0.46/1.07 subsumption: (16) {G0,W6,D2,L2,V2,M2} I { ! complement( Y, X ), alpha1( X,
% 0.46/1.07 Y ) }.
% 0.46/1.07 parent0: (456) {G0,W6,D2,L2,V2,M2} { ! complement( Y, X ), alpha1( X, Y )
% 0.46/1.07 }.
% 0.46/1.07 substitution0:
% 0.46/1.07 X := X
% 0.46/1.07 Y := Y
% 0.46/1.07 end
% 0.46/1.07 permutation0:
% 0.46/1.07 0 ==> 0
% 0.46/1.07 1 ==> 1
% 0.46/1.07 end
% 0.46/1.07
% 0.46/1.07 subsumption: (19) {G0,W8,D3,L2,V2,M2} I { ! alpha1( X, Y ), addition( X, Y
% 0.46/1.07 ) ==> one }.
% 0.46/1.07 parent0: (459) {G0,W8,D3,L2,V2,M2} { ! alpha1( X, Y ), addition( X, Y ) =
% 0.46/1.07 one }.
% 0.46/1.07 substitution0:
% 0.46/1.07 X := X
% 0.46/1.07 Y := Y
% 0.46/1.07 end
% 0.46/1.07 permutation0:
% 0.46/1.07 0 ==> 0
% 0.46/1.07 1 ==> 1
% 0.46/1.07 end
% 0.46/1.07
% 0.46/1.07 subsumption: (21) {G0,W9,D3,L3,V2,M3} I { ! test( X ), ! c( X ) = Y,
% 0.46/1.07 complement( X, Y ) }.
% 0.46/1.07 parent0: (461) {G0,W9,D3,L3,V2,M3} { ! test( X ), ! c( X ) = Y, complement
% 0.46/1.07 ( X, Y ) }.
% 0.46/1.07 substitution0:
% 0.46/1.07 X := X
% 0.46/1.07 Y := Y
% 0.46/1.07 end
% 0.46/1.07 permutation0:
% 0.46/1.07 0 ==> 0
% 0.46/1.07 1 ==> 1
% 0.46/1.07 2 ==> 2
% 0.46/1.07 end
% 0.46/1.07
% 0.46/1.07 subsumption: (24) {G0,W2,D2,L1,V0,M1} I { test( skol2 ) }.
% 0.46/1.07 parent0: (464) {G0,W2,D2,L1,V0,M1} { test( skol2 ) }.
% 0.46/1.07 substitution0:
% 0.46/1.07 end
% 0.46/1.07 permutation0:
% 0.46/1.07 0 ==> 0
% 0.46/1.07 end
% 0.46/1.07
% 0.46/1.07 paramod: (641) {G1,W18,D5,L2,V0,M2} { ! leq( multiplication( skol3,
% 0.46/1.07 addition( skol2, c( skol2 ) ) ), skol3 ), ! leq( skol3, addition(
% 0.46/1.07 multiplication( skol3, skol2 ), multiplication( skol3, c( skol2 ) ) ) )
% 0.46/1.07 }.
% 0.46/1.07 parent0[0]: (7) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Y ),
% 0.46/1.07 multiplication( X, Z ) ) ==> multiplication( X, addition( Y, Z ) ) }.
% 0.46/1.07 parent1[1; 2]: (465) {G0,W20,D5,L2,V0,M2} { ! leq( skol3, addition(
% 0.46/1.07 multiplication( skol3, skol2 ), multiplication( skol3, c( skol2 ) ) ) ),
% 0.46/1.07 ! leq( addition( multiplication( skol3, skol2 ), multiplication( skol3, c
% 0.46/1.07 ( skol2 ) ) ), skol3 ) }.
% 0.46/1.07 substitution0:
% 0.46/1.07 X := skol3
% 0.46/1.07 Y := skol2
% 0.46/1.07 Z := c( skol2 )
% 0.46/1.07 end
% 0.46/1.07 substitution1:
% 0.46/1.07 end
% 0.46/1.07
% 0.46/1.07 paramod: (643) {G1,W16,D5,L2,V0,M2} { ! leq( skol3, multiplication( skol3
% 0.46/1.07 , addition( skol2, c( skol2 ) ) ) ), ! leq( multiplication( skol3,
% 0.46/1.07 addition( skol2, c( skol2 ) ) ), skol3 ) }.
% 0.46/1.07 parent0[0]: (7) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Y ),
% 0.46/1.07 multiplication( X, Z ) ) ==> multiplication( X, addition( Y, Z ) ) }.
% 0.46/1.07 parent1[1; 3]: (641) {G1,W18,D5,L2,V0,M2} { ! leq( multiplication( skol3,
% 0.46/1.07 addition( skol2, c( skol2 ) ) ), skol3 ), ! leq( skol3, addition(
% 0.46/1.07 multiplication( skol3, skol2 ), multiplication( skol3, c( skol2 ) ) ) )
% 0.46/1.07 }.
% 0.46/1.07 substitution0:
% 0.46/1.07 X := skol3
% 0.46/1.07 Y := skol2
% 0.46/1.07 Z := c( skol2 )
% 0.46/1.07 end
% 0.46/1.07 substitution1:
% 0.46/1.07 end
% 0.46/1.07
% 0.46/1.07 subsumption: (25) {G1,W16,D5,L2,V0,M2} I;d(7);d(7) { ! leq( skol3,
% 0.46/1.07 multiplication( skol3, addition( skol2, c( skol2 ) ) ) ), ! leq(
% 0.46/1.07 multiplication( skol3, addition( skol2, c( skol2 ) ) ), skol3 ) }.
% 0.46/1.07 parent0: (643) {G1,W16,D5,L2,V0,M2} { ! leq( skol3, multiplication( skol3
% 0.46/1.07 , addition( skol2, c( skol2 ) ) ) ), ! leq( multiplication( skol3,
% 0.46/1.07 addition( skol2, c( skol2 ) ) ), skol3 ) }.
% 0.46/1.07 substitution0:
% 0.46/1.07 end
% 0.46/1.07 permutation0:
% 0.46/1.07 0 ==> 0
% 0.46/1.07 1 ==> 1
% 0.46/1.07 end
% 0.46/1.07
% 0.46/1.07 eqswap: (644) {G0,W9,D3,L3,V2,M3} { ! Y = c( X ), ! test( X ), complement
% 0.46/1.07 ( X, Y ) }.
% 0.46/1.07 parent0[1]: (21) {G0,W9,D3,L3,V2,M3} I { ! test( X ), ! c( X ) = Y,
% 0.46/1.07 complement( X, Y ) }.
% 0.46/1.07 substitution0:
% 0.46/1.07 X := X
% 0.46/1.07 Y := Y
% 0.46/1.07 end
% 0.46/1.07
% 0.46/1.07 eqrefl: (645) {G0,W6,D3,L2,V1,M2} { ! test( X ), complement( X, c( X ) )
% 0.46/1.07 }.
% 0.46/1.07 parent0[0]: (644) {G0,W9,D3,L3,V2,M3} { ! Y = c( X ), ! test( X ),
% 0.46/1.07 complement( X, Y ) }.
% 0.46/1.07 substitution0:
% 0.46/1.07 X := X
% 0.46/1.07 Y := c( X )
% 0.46/1.07 end
% 0.46/1.07
% 0.46/1.07 subsumption: (26) {G1,W6,D3,L2,V1,M2} Q(21) { ! test( X ), complement( X, c
% 0.46/1.07 ( X ) ) }.
% 0.46/1.07 parent0: (645) {G0,W6,D3,L2,V1,M2} { ! test( X ), complement( X, c( X ) )
% 0.46/1.07 }.
% 0.46/1.07 substitution0:
% 0.46/1.07 X := X
% 0.46/1.07 end
% 0.46/1.07 permutation0:
% 0.46/1.07 0 ==> 0
% 0.46/1.07 1 ==> 1
% 0.46/1.07 end
% 0.46/1.07
% 0.46/1.07 resolution: (646) {G1,W4,D3,L1,V0,M1} { complement( skol2, c( skol2 ) )
% 0.46/1.07 }.
% 0.46/1.07 parent0[0]: (26) {G1,W6,D3,L2,V1,M2} Q(21) { ! test( X ), complement( X, c
% 0.46/1.07 ( X ) ) }.
% 0.46/1.07 parent1[0]: (24) {G0,W2,D2,L1,V0,M1} I { test( skol2 ) }.
% 0.46/1.07 substitution0:
% 0.46/1.07 X := skol2
% 0.46/1.07 end
% 0.46/1.07 substitution1:
% 0.46/1.07 end
% 0.46/1.07
% 0.46/1.07 subsumption: (36) {G2,W4,D3,L1,V0,M1} R(26,24) { complement( skol2, c(
% 0.46/1.07 skol2 ) ) }.
% 0.46/1.07 parent0: (646) {G1,W4,D3,L1,V0,M1} { complement( skol2, c( skol2 ) ) }.
% 0.46/1.07 substitution0:
% 0.46/1.07 end
% 0.46/1.07 permutation0:
% 0.46/1.07 0 ==> 0
% 0.46/1.07 end
% 0.46/1.07
% 0.46/1.07 resolution: (647) {G1,W4,D3,L1,V0,M1} { alpha1( c( skol2 ), skol2 ) }.
% 0.46/1.07 parent0[0]: (16) {G0,W6,D2,L2,V2,M2} I { ! complement( Y, X ), alpha1( X, Y
% 0.46/1.07 ) }.
% 0.46/1.07 parent1[0]: (36) {G2,W4,D3,L1,V0,M1} R(26,24) { complement( skol2, c( skol2
% 0.46/1.07 ) ) }.
% 0.46/1.07 substitution0:
% 0.46/1.07 X := c( skol2 )
% 0.46/1.07 Y := skol2
% 0.46/1.07 end
% 0.46/1.07 substitution1:
% 0.46/1.07 end
% 0.46/1.07
% 0.46/1.07 subsumption: (37) {G3,W4,D3,L1,V0,M1} R(36,16) { alpha1( c( skol2 ), skol2
% 0.46/1.07 ) }.
% 0.46/1.07 parent0: (647) {G1,W4,D3,L1,V0,M1} { alpha1( c( skol2 ), skol2 ) }.
% 0.46/1.07 substitution0:
% 0.46/1.07 end
% 0.46/1.07 permutation0:
% 0.46/1.07 0 ==> 0
% 0.46/1.07 end
% 0.46/1.07
% 0.46/1.07 eqswap: (648) {G0,W8,D3,L2,V2,M2} { ! Y ==> addition( X, Y ), leq( X, Y )
% 0.46/1.07 }.
% 0.46/1.07 parent0[0]: (12) {G0,W8,D3,L2,V2,M2} I { ! addition( X, Y ) ==> Y, leq( X,
% 0.46/1.07 Y ) }.
% 0.46/1.07 substitution0:
% 0.46/1.07 X := X
% 0.46/1.07 Y := Y
% 0.46/1.07 end
% 0.46/1.07
% 0.46/1.07 eqswap: (649) {G0,W5,D3,L1,V1,M1} { X ==> addition( X, X ) }.
% 0.46/1.07 parent0[0]: (3) {G0,W5,D3,L1,V1,M1} I { addition( X, X ) ==> X }.
% 0.46/1.07 substitution0:
% 0.46/1.07 X := X
% 0.46/1.07 end
% 0.46/1.07
% 0.46/1.07 resolution: (650) {G1,W3,D2,L1,V1,M1} { leq( X, X ) }.
% 0.46/1.07 parent0[0]: (648) {G0,W8,D3,L2,V2,M2} { ! Y ==> addition( X, Y ), leq( X,
% 0.46/1.07 Y ) }.
% 0.46/1.07 parent1[0]: (649) {G0,W5,D3,L1,V1,M1} { X ==> addition( X, X ) }.
% 0.46/1.07 substitution0:
% 0.46/1.07 X := X
% 0.46/1.07 Y := X
% 0.46/1.07 end
% 0.46/1.07 substitution1:
% 0.46/1.07 X := X
% 0.46/1.07 end
% 0.46/1.07
% 0.46/1.07 subsumption: (157) {G1,W3,D2,L1,V1,M1} R(12,3) { leq( X, X ) }.
% 0.46/1.07 parent0: (650) {G1,W3,D2,L1,V1,M1} { leq( X, X ) }.
% 0.46/1.07 substitution0:
% 0.46/1.07 X := X
% 0.46/1.07 end
% 0.46/1.07 permutation0:
% 0.46/1.07 0 ==> 0
% 0.46/1.07 end
% 0.46/1.07
% 0.46/1.07 eqswap: (651) {G0,W8,D3,L2,V2,M2} { one ==> addition( X, Y ), ! alpha1( X
% 0.46/1.07 , Y ) }.
% 0.46/1.07 parent0[1]: (19) {G0,W8,D3,L2,V2,M2} I { ! alpha1( X, Y ), addition( X, Y )
% 0.46/1.07 ==> one }.
% 0.46/1.07 substitution0:
% 0.46/1.07 X := X
% 0.46/1.07 Y := Y
% 0.46/1.07 end
% 0.46/1.07
% 0.46/1.07 resolution: (652) {G1,W6,D4,L1,V0,M1} { one ==> addition( c( skol2 ),
% 0.46/1.07 skol2 ) }.
% 0.46/1.07 parent0[1]: (651) {G0,W8,D3,L2,V2,M2} { one ==> addition( X, Y ), ! alpha1
% 0.46/1.07 ( X, Y ) }.
% 0.46/1.07 parent1[0]: (37) {G3,W4,D3,L1,V0,M1} R(36,16) { alpha1( c( skol2 ), skol2 )
% 0.46/1.07 }.
% 0.46/1.07 substitution0:
% 0.46/1.07 X := c( skol2 )
% 0.46/1.07 Y := skol2
% 0.46/1.07 end
% 0.46/1.07 substitution1:
% 0.46/1.07 end
% 0.46/1.07
% 0.46/1.07 eqswap: (653) {G1,W6,D4,L1,V0,M1} { addition( c( skol2 ), skol2 ) ==> one
% 0.46/1.07 }.
% 0.46/1.07 parent0[0]: (652) {G1,W6,D4,L1,V0,M1} { one ==> addition( c( skol2 ),
% 0.46/1.07 skol2 ) }.
% 0.46/1.07 substitution0:
% 0.46/1.07 end
% 0.46/1.07
% 0.46/1.07 subsumption: (267) {G4,W6,D4,L1,V0,M1} R(19,37) { addition( c( skol2 ),
% 0.46/1.07 skol2 ) ==> one }.
% 0.46/1.07 parent0: (653) {G1,W6,D4,L1,V0,M1} { addition( c( skol2 ), skol2 ) ==> one
% 0.46/1.07 }.
% 0.46/1.07 substitution0:
% 0.46/1.07 end
% 0.46/1.07 permutation0:
% 0.46/1.07 0 ==> 0
% 0.46/1.07 end
% 0.46/1.07
% 0.46/1.07 paramod: (659) {G1,W16,D5,L2,V0,M2} { ! leq( multiplication( skol3,
% 0.46/1.07 addition( c( skol2 ), skol2 ) ), skol3 ), ! leq( skol3, multiplication(
% 0.46/1.07 skol3, addition( skol2, c( skol2 ) ) ) ) }.
% 0.46/1.07 parent0[0]: (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X )
% 0.46/1.07 }.
% 0.46/1.07 parent1[1; 4]: (25) {G1,W16,D5,L2,V0,M2} I;d(7);d(7) { ! leq( skol3,
% 0.46/1.07 multiplication( skol3, addition( skol2, c( skol2 ) ) ) ), ! leq(
% 0.46/1.07 multiplication( skol3, addition( skol2, c( skol2 ) ) ), skol3 ) }.
% 0.46/1.07 substitution0:
% 0.46/1.07 X := skol2
% 0.46/1.07 Y := c( skol2 )
% 0.46/1.07 end
% 0.46/1.07 substitution1:
% 0.46/1.07 end
% 0.46/1.07
% 0.46/1.07 paramod: (661) {G1,W16,D5,L2,V0,M2} { ! leq( skol3, multiplication( skol3
% 0.46/1.07 , addition( c( skol2 ), skol2 ) ) ), ! leq( multiplication( skol3,
% 0.46/1.07 addition( c( skol2 ), skol2 ) ), skol3 ) }.
% 0.46/1.07 parent0[0]: (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X )
% 0.46/1.07 }.
% 0.46/1.07 parent1[1; 5]: (659) {G1,W16,D5,L2,V0,M2} { ! leq( multiplication( skol3,
% 0.46/1.07 addition( c( skol2 ), skol2 ) ), skol3 ), ! leq( skol3, multiplication(
% 0.46/1.07 skol3, addition( skol2, c( skol2 ) ) ) ) }.
% 0.46/1.07 substitution0:
% 0.46/1.07 X := skol2
% 0.46/1.07 Y := c( skol2 )
% 0.46/1.07 end
% 0.46/1.07 substitution1:
% 0.46/1.07 end
% 0.46/1.07
% 0.46/1.07 paramod: (664) {G2,W13,D5,L2,V0,M2} { ! leq( multiplication( skol3, one )
% 0.46/1.07 , skol3 ), ! leq( skol3, multiplication( skol3, addition( c( skol2 ),
% 0.46/1.07 skol2 ) ) ) }.
% 0.46/1.07 parent0[0]: (267) {G4,W6,D4,L1,V0,M1} R(19,37) { addition( c( skol2 ),
% 0.46/1.07 skol2 ) ==> one }.
% 0.46/1.07 parent1[1; 4]: (661) {G1,W16,D5,L2,V0,M2} { ! leq( skol3, multiplication(
% 0.46/1.07 skol3, addition( c( skol2 ), skol2 ) ) ), ! leq( multiplication( skol3,
% 0.46/1.07 addition( c( skol2 ), skol2 ) ), skol3 ) }.
% 0.46/1.07 substitution0:
% 0.46/1.07 end
% 0.46/1.07 substitution1:
% 0.46/1.07 end
% 0.46/1.07
% 0.46/1.07 paramod: (666) {G3,W10,D3,L2,V0,M2} { ! leq( skol3, multiplication( skol3
% 0.46/1.07 , one ) ), ! leq( multiplication( skol3, one ), skol3 ) }.
% 0.46/1.07 parent0[0]: (267) {G4,W6,D4,L1,V0,M1} R(19,37) { addition( c( skol2 ),
% 0.46/1.07 skol2 ) ==> one }.
% 0.46/1.07 parent1[1; 5]: (664) {G2,W13,D5,L2,V0,M2} { ! leq( multiplication( skol3,
% 0.46/1.07 one ), skol3 ), ! leq( skol3, multiplication( skol3, addition( c( skol2 )
% 0.46/1.07 , skol2 ) ) ) }.
% 0.46/1.07 substitution0:
% 0.46/1.07 end
% 0.46/1.07 substitution1:
% 0.46/1.07 end
% 0.46/1.07
% 0.46/1.07 paramod: (668) {G1,W8,D3,L2,V0,M2} { ! leq( skol3, skol3 ), ! leq( skol3,
% 0.46/1.07 multiplication( skol3, one ) ) }.
% 0.46/1.07 parent0[0]: (5) {G0,W5,D3,L1,V1,M1} I { multiplication( X, one ) ==> X }.
% 0.46/1.07 parent1[1; 2]: (666) {G3,W10,D3,L2,V0,M2} { ! leq( skol3, multiplication(
% 0.46/1.07 skol3, one ) ), ! leq( multiplication( skol3, one ), skol3 ) }.
% 0.46/1.07 substitution0:
% 0.46/1.07 X := skol3
% 0.46/1.07 end
% 0.46/1.07 substitution1:
% 0.46/1.07 end
% 0.46/1.07
% 0.46/1.07 paramod: (671) {G1,W6,D2,L2,V0,M2} { ! leq( skol3, skol3 ), ! leq( skol3,
% 0.46/1.07 skol3 ) }.
% 0.46/1.07 parent0[0]: (5) {G0,W5,D3,L1,V1,M1} I { multiplication( X, one ) ==> X }.
% 0.46/1.07 parent1[1; 3]: (668) {G1,W8,D3,L2,V0,M2} { ! leq( skol3, skol3 ), ! leq(
% 0.46/1.07 skol3, multiplication( skol3, one ) ) }.
% 0.46/1.07 substitution0:
% 0.46/1.07 X := skol3
% 0.46/1.07 end
% 0.46/1.07 substitution1:
% 0.46/1.07 end
% 0.46/1.07
% 0.46/1.07 factor: (672) {G1,W3,D2,L1,V0,M1} { ! leq( skol3, skol3 ) }.
% 0.46/1.07 parent0[0, 1]: (671) {G1,W6,D2,L2,V0,M2} { ! leq( skol3, skol3 ), ! leq(
% 0.46/1.07 skol3, skol3 ) }.
% 0.46/1.07 substitution0:
% 0.46/1.07 end
% 0.46/1.07
% 0.46/1.07 resolution: (674) {G2,W0,D0,L0,V0,M0} { }.
% 0.46/1.07 parent0[0]: (672) {G1,W3,D2,L1,V0,M1} { ! leq( skol3, skol3 ) }.
% 0.46/1.07 parent1[0]: (157) {G1,W3,D2,L1,V1,M1} R(12,3) { leq( X, X ) }.
% 0.46/1.07 substitution0:
% 0.46/1.07 end
% 0.46/1.07 substitution1:
% 0.46/1.07 X := skol3
% 0.46/1.07 end
% 0.46/1.07
% 0.46/1.07 subsumption: (438) {G5,W0,D0,L0,V0,M0} P(0,25);d(267);d(267);d(5);d(5);f;r(
% 0.46/1.07 157) { }.
% 0.46/1.07 parent0: (674) {G2,W0,D0,L0,V0,M0} { }.
% 0.46/1.07 substitution0:
% 0.46/1.07 end
% 0.46/1.07 permutation0:
% 0.46/1.07 end
% 0.46/1.07
% 0.46/1.07 Proof check complete!
% 0.46/1.07
% 0.46/1.07 Memory use:
% 0.46/1.07
% 0.46/1.07 space for terms: 4869
% 0.46/1.07 space for clauses: 25009
% 0.46/1.07
% 0.46/1.07
% 0.46/1.07 clauses generated: 1690
% 0.46/1.07 clauses kept: 439
% 0.46/1.07 clauses selected: 76
% 0.46/1.07 clauses deleted: 0
% 0.46/1.07 clauses inuse deleted: 0
% 0.46/1.07
% 0.46/1.07 subsentry: 2853
% 0.46/1.07 literals s-matched: 1769
% 0.46/1.07 literals matched: 1769
% 0.46/1.07 full subsumption: 90
% 0.46/1.07
% 0.46/1.07 checksum: -403749433
% 0.46/1.07
% 0.46/1.07
% 0.46/1.07 Bliksem ended
%------------------------------------------------------------------------------