TSTP Solution File: KLE167+1 by Bliksem---1.12
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%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : KLE167+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n004.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 01:37:37 EDT 2022
% Result : Theorem 0.82s 1.31s
% Output : Refutation 0.82s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : KLE167+1 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.13 % Command : bliksem %s
% 0.13/0.35 % Computer : n004.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 14:39:09 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.82/1.31 *** allocated 10000 integers for termspace/termends
% 0.82/1.31 *** allocated 10000 integers for clauses
% 0.82/1.31 *** allocated 10000 integers for justifications
% 0.82/1.31 Bliksem 1.12
% 0.82/1.31
% 0.82/1.31
% 0.82/1.31 Automatic Strategy Selection
% 0.82/1.31
% 0.82/1.31
% 0.82/1.31 Clauses:
% 0.82/1.31
% 0.82/1.31 { addition( X, Y ) = addition( Y, X ) }.
% 0.82/1.31 { addition( Z, addition( Y, X ) ) = addition( addition( Z, Y ), X ) }.
% 0.82/1.31 { addition( X, zero ) = X }.
% 0.82/1.31 { addition( X, X ) = X }.
% 0.82/1.31 { multiplication( X, multiplication( Y, Z ) ) = multiplication(
% 0.82/1.31 multiplication( X, Y ), Z ) }.
% 0.82/1.31 { multiplication( X, one ) = X }.
% 0.82/1.31 { multiplication( one, X ) = X }.
% 0.82/1.31 { multiplication( X, addition( Y, Z ) ) = addition( multiplication( X, Y )
% 0.82/1.31 , multiplication( X, Z ) ) }.
% 0.82/1.31 { multiplication( addition( X, Y ), Z ) = addition( multiplication( X, Z )
% 0.82/1.31 , multiplication( Y, Z ) ) }.
% 0.82/1.31 { multiplication( zero, X ) = zero }.
% 0.82/1.31 { addition( one, multiplication( X, star( X ) ) ) = star( X ) }.
% 0.82/1.31 { addition( one, multiplication( star( X ), X ) ) = star( X ) }.
% 0.82/1.31 { ! leq( addition( multiplication( X, Z ), Y ), Z ), leq( multiplication(
% 0.82/1.31 star( X ), Y ), Z ) }.
% 0.82/1.31 { ! leq( addition( multiplication( Z, X ), Y ), Z ), leq( multiplication( Y
% 0.82/1.31 , star( X ) ), Z ) }.
% 0.82/1.31 { strong_iteration( X ) = addition( multiplication( X, strong_iteration( X
% 0.82/1.31 ) ), one ) }.
% 0.82/1.31 { ! leq( Z, addition( multiplication( X, Z ), Y ) ), leq( Z, multiplication
% 0.82/1.31 ( strong_iteration( X ), Y ) ) }.
% 0.82/1.31 { strong_iteration( X ) = addition( star( X ), multiplication(
% 0.82/1.31 strong_iteration( X ), zero ) ) }.
% 0.82/1.31 { ! leq( X, Y ), addition( X, Y ) = Y }.
% 0.82/1.31 { ! addition( X, Y ) = Y, leq( X, Y ) }.
% 0.82/1.31 { multiplication( skol1, skol2 ) = zero, ! leq( skol1, multiplication(
% 0.82/1.31 skol1, star( skol2 ) ) ) }.
% 0.82/1.31 { ! leq( multiplication( skol1, star( skol2 ) ), skol1 ), ! leq( skol1,
% 0.82/1.31 multiplication( skol1, star( skol2 ) ) ) }.
% 0.82/1.31
% 0.82/1.31 percentage equality = 0.607143, percentage horn = 1.000000
% 0.82/1.31 This is a problem with some equality
% 0.82/1.31
% 0.82/1.31
% 0.82/1.31
% 0.82/1.31 Options Used:
% 0.82/1.31
% 0.82/1.31 useres = 1
% 0.82/1.31 useparamod = 1
% 0.82/1.31 useeqrefl = 1
% 0.82/1.31 useeqfact = 1
% 0.82/1.31 usefactor = 1
% 0.82/1.31 usesimpsplitting = 0
% 0.82/1.31 usesimpdemod = 5
% 0.82/1.31 usesimpres = 3
% 0.82/1.31
% 0.82/1.31 resimpinuse = 1000
% 0.82/1.31 resimpclauses = 20000
% 0.82/1.31 substype = eqrewr
% 0.82/1.31 backwardsubs = 1
% 0.82/1.31 selectoldest = 5
% 0.82/1.31
% 0.82/1.31 litorderings [0] = split
% 0.82/1.31 litorderings [1] = extend the termordering, first sorting on arguments
% 0.82/1.31
% 0.82/1.31 termordering = kbo
% 0.82/1.31
% 0.82/1.31 litapriori = 0
% 0.82/1.31 termapriori = 1
% 0.82/1.31 litaposteriori = 0
% 0.82/1.31 termaposteriori = 0
% 0.82/1.31 demodaposteriori = 0
% 0.82/1.31 ordereqreflfact = 0
% 0.82/1.31
% 0.82/1.31 litselect = negord
% 0.82/1.31
% 0.82/1.31 maxweight = 15
% 0.82/1.31 maxdepth = 30000
% 0.82/1.31 maxlength = 115
% 0.82/1.31 maxnrvars = 195
% 0.82/1.31 excuselevel = 1
% 0.82/1.31 increasemaxweight = 1
% 0.82/1.31
% 0.82/1.31 maxselected = 10000000
% 0.82/1.31 maxnrclauses = 10000000
% 0.82/1.31
% 0.82/1.31 showgenerated = 0
% 0.82/1.31 showkept = 0
% 0.82/1.31 showselected = 0
% 0.82/1.31 showdeleted = 0
% 0.82/1.31 showresimp = 1
% 0.82/1.31 showstatus = 2000
% 0.82/1.31
% 0.82/1.31 prologoutput = 0
% 0.82/1.31 nrgoals = 5000000
% 0.82/1.31 totalproof = 1
% 0.82/1.31
% 0.82/1.31 Symbols occurring in the translation:
% 0.82/1.31
% 0.82/1.31 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.82/1.31 . [1, 2] (w:1, o:22, a:1, s:1, b:0),
% 0.82/1.31 ! [4, 1] (w:0, o:15, a:1, s:1, b:0),
% 0.82/1.31 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.82/1.31 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.82/1.31 addition [37, 2] (w:1, o:46, a:1, s:1, b:0),
% 0.82/1.31 zero [39, 0] (w:1, o:9, a:1, s:1, b:0),
% 0.82/1.31 multiplication [40, 2] (w:1, o:48, a:1, s:1, b:0),
% 0.82/1.31 one [41, 0] (w:1, o:10, a:1, s:1, b:0),
% 0.82/1.31 star [42, 1] (w:1, o:20, a:1, s:1, b:0),
% 0.82/1.31 leq [43, 2] (w:1, o:47, a:1, s:1, b:0),
% 0.82/1.31 strong_iteration [44, 1] (w:1, o:21, a:1, s:1, b:0),
% 0.82/1.31 skol1 [47, 0] (w:1, o:13, a:1, s:1, b:1),
% 0.82/1.31 skol2 [48, 0] (w:1, o:14, a:1, s:1, b:1).
% 0.82/1.31
% 0.82/1.31
% 0.82/1.31 Starting Search:
% 0.82/1.31
% 0.82/1.31 *** allocated 15000 integers for clauses
% 0.82/1.31 *** allocated 22500 integers for clauses
% 0.82/1.31 *** allocated 33750 integers for clauses
% 0.82/1.31 *** allocated 50625 integers for clauses
% 0.82/1.31 *** allocated 15000 integers for termspace/termends
% 0.82/1.31 *** allocated 75937 integers for clauses
% 0.82/1.31 Resimplifying inuse:
% 0.82/1.31 Done
% 0.82/1.31
% 0.82/1.31
% 0.82/1.31 Bliksems!, er is een bewijs:
% 0.82/1.31 % SZS status Theorem
% 0.82/1.31 % SZS output start Refutation
% 0.82/1.31
% 0.82/1.31 (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X ) }.
% 0.82/1.31 (1) {G0,W11,D4,L1,V3,M1} I { addition( Z, addition( Y, X ) ) ==> addition(
% 0.82/1.31 addition( Z, Y ), X ) }.
% 0.82/1.31 (2) {G0,W5,D3,L1,V1,M1} I { addition( X, zero ) ==> X }.
% 0.82/1.31 (3) {G0,W5,D3,L1,V1,M1} I { addition( X, X ) ==> X }.
% 0.82/1.31 (5) {G0,W5,D3,L1,V1,M1} I { multiplication( X, one ) ==> X }.
% 0.82/1.31 (7) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Y ),
% 0.82/1.31 multiplication( X, Z ) ) ==> multiplication( X, addition( Y, Z ) ) }.
% 0.82/1.31 (11) {G0,W9,D5,L1,V1,M1} I { addition( one, multiplication( star( X ), X )
% 0.82/1.31 ) ==> star( X ) }.
% 0.82/1.31 (13) {G0,W13,D4,L2,V3,M2} I { ! leq( addition( multiplication( Z, X ), Y )
% 0.82/1.31 , Z ), leq( multiplication( Y, star( X ) ), Z ) }.
% 0.82/1.31 (17) {G0,W8,D3,L2,V2,M2} I { ! leq( X, Y ), addition( X, Y ) ==> Y }.
% 0.82/1.31 (18) {G0,W8,D3,L2,V2,M2} I { ! addition( X, Y ) ==> Y, leq( X, Y ) }.
% 0.82/1.31 (19) {G0,W11,D4,L2,V0,M2} I { multiplication( skol1, skol2 ) ==> zero, !
% 0.82/1.31 leq( skol1, multiplication( skol1, star( skol2 ) ) ) }.
% 0.82/1.31 (20) {G0,W12,D4,L2,V0,M2} I { ! leq( multiplication( skol1, star( skol2 ) )
% 0.82/1.31 , skol1 ), ! leq( skol1, multiplication( skol1, star( skol2 ) ) ) }.
% 0.82/1.31 (21) {G1,W5,D3,L1,V1,M1} P(0,2) { addition( zero, X ) ==> X }.
% 0.82/1.31 (23) {G1,W3,D2,L1,V1,M1} R(18,3) { leq( X, X ) }.
% 0.82/1.31 (26) {G1,W14,D4,L2,V3,M2} P(1,18) { ! addition( addition( X, Y ), Z ) ==>
% 0.82/1.31 addition( Y, Z ), leq( X, addition( Y, Z ) ) }.
% 0.82/1.31 (68) {G1,W16,D4,L2,V3,M2} P(7,18) { ! multiplication( X, addition( Y, Z ) )
% 0.82/1.31 ==> multiplication( X, Z ), leq( multiplication( X, Y ), multiplication
% 0.82/1.31 ( X, Z ) ) }.
% 0.82/1.31 (326) {G2,W6,D4,L1,V0,M1} R(20,13);d(19);d(21);r(23) { ! leq( skol1,
% 0.82/1.31 multiplication( skol1, star( skol2 ) ) ) }.
% 0.82/1.31 (357) {G2,W5,D3,L1,V2,M1} P(3,26);q { leq( X, addition( X, Y ) ) }.
% 0.82/1.31 (410) {G3,W4,D3,L1,V1,M1} P(11,357) { leq( one, star( X ) ) }.
% 0.82/1.31 (418) {G4,W7,D4,L1,V1,M1} R(410,17) { addition( one, star( X ) ) ==> star(
% 0.82/1.31 X ) }.
% 0.82/1.31 (1211) {G5,W6,D4,L1,V2,M1} P(418,68);q;d(5) { leq( Y, multiplication( Y,
% 0.82/1.31 star( X ) ) ) }.
% 0.82/1.31 (1230) {G6,W0,D0,L0,V0,M0} R(1211,326) { }.
% 0.82/1.31
% 0.82/1.31
% 0.82/1.31 % SZS output end Refutation
% 0.82/1.31 found a proof!
% 0.82/1.31
% 0.82/1.31 *** allocated 22500 integers for termspace/termends
% 0.82/1.31
% 0.82/1.31 Unprocessed initial clauses:
% 0.82/1.31
% 0.82/1.31 (1232) {G0,W7,D3,L1,V2,M1} { addition( X, Y ) = addition( Y, X ) }.
% 0.82/1.31 (1233) {G0,W11,D4,L1,V3,M1} { addition( Z, addition( Y, X ) ) = addition(
% 0.82/1.31 addition( Z, Y ), X ) }.
% 0.82/1.31 (1234) {G0,W5,D3,L1,V1,M1} { addition( X, zero ) = X }.
% 0.82/1.31 (1235) {G0,W5,D3,L1,V1,M1} { addition( X, X ) = X }.
% 0.82/1.31 (1236) {G0,W11,D4,L1,V3,M1} { multiplication( X, multiplication( Y, Z ) )
% 0.82/1.31 = multiplication( multiplication( X, Y ), Z ) }.
% 0.82/1.31 (1237) {G0,W5,D3,L1,V1,M1} { multiplication( X, one ) = X }.
% 0.82/1.31 (1238) {G0,W5,D3,L1,V1,M1} { multiplication( one, X ) = X }.
% 0.82/1.31 (1239) {G0,W13,D4,L1,V3,M1} { multiplication( X, addition( Y, Z ) ) =
% 0.82/1.31 addition( multiplication( X, Y ), multiplication( X, Z ) ) }.
% 0.82/1.31 (1240) {G0,W13,D4,L1,V3,M1} { multiplication( addition( X, Y ), Z ) =
% 0.82/1.31 addition( multiplication( X, Z ), multiplication( Y, Z ) ) }.
% 0.82/1.31 (1241) {G0,W5,D3,L1,V1,M1} { multiplication( zero, X ) = zero }.
% 0.82/1.31 (1242) {G0,W9,D5,L1,V1,M1} { addition( one, multiplication( X, star( X ) )
% 0.82/1.31 ) = star( X ) }.
% 0.82/1.31 (1243) {G0,W9,D5,L1,V1,M1} { addition( one, multiplication( star( X ), X )
% 0.82/1.31 ) = star( X ) }.
% 0.82/1.31 (1244) {G0,W13,D4,L2,V3,M2} { ! leq( addition( multiplication( X, Z ), Y )
% 0.82/1.31 , Z ), leq( multiplication( star( X ), Y ), Z ) }.
% 0.82/1.31 (1245) {G0,W13,D4,L2,V3,M2} { ! leq( addition( multiplication( Z, X ), Y )
% 0.82/1.31 , Z ), leq( multiplication( Y, star( X ) ), Z ) }.
% 0.82/1.31 (1246) {G0,W9,D5,L1,V1,M1} { strong_iteration( X ) = addition(
% 0.82/1.31 multiplication( X, strong_iteration( X ) ), one ) }.
% 0.82/1.31 (1247) {G0,W13,D4,L2,V3,M2} { ! leq( Z, addition( multiplication( X, Z ),
% 0.82/1.31 Y ) ), leq( Z, multiplication( strong_iteration( X ), Y ) ) }.
% 0.82/1.31 (1248) {G0,W10,D5,L1,V1,M1} { strong_iteration( X ) = addition( star( X )
% 0.82/1.31 , multiplication( strong_iteration( X ), zero ) ) }.
% 0.82/1.31 (1249) {G0,W8,D3,L2,V2,M2} { ! leq( X, Y ), addition( X, Y ) = Y }.
% 0.82/1.31 (1250) {G0,W8,D3,L2,V2,M2} { ! addition( X, Y ) = Y, leq( X, Y ) }.
% 0.82/1.31 (1251) {G0,W11,D4,L2,V0,M2} { multiplication( skol1, skol2 ) = zero, ! leq
% 0.82/1.31 ( skol1, multiplication( skol1, star( skol2 ) ) ) }.
% 0.82/1.31 (1252) {G0,W12,D4,L2,V0,M2} { ! leq( multiplication( skol1, star( skol2 )
% 0.82/1.31 ), skol1 ), ! leq( skol1, multiplication( skol1, star( skol2 ) ) ) }.
% 0.82/1.31
% 0.82/1.31
% 0.82/1.31 Total Proof:
% 0.82/1.31
% 0.82/1.31 subsumption: (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X
% 0.82/1.31 ) }.
% 0.82/1.31 parent0: (1232) {G0,W7,D3,L1,V2,M1} { addition( X, Y ) = addition( Y, X )
% 0.82/1.31 }.
% 0.82/1.31 substitution0:
% 0.82/1.31 X := X
% 0.82/1.31 Y := Y
% 0.82/1.31 end
% 0.82/1.31 permutation0:
% 0.82/1.31 0 ==> 0
% 0.82/1.31 end
% 0.82/1.31
% 0.82/1.31 subsumption: (1) {G0,W11,D4,L1,V3,M1} I { addition( Z, addition( Y, X ) )
% 0.82/1.31 ==> addition( addition( Z, Y ), X ) }.
% 0.82/1.31 parent0: (1233) {G0,W11,D4,L1,V3,M1} { addition( Z, addition( Y, X ) ) =
% 0.82/1.31 addition( addition( Z, Y ), X ) }.
% 0.82/1.31 substitution0:
% 0.82/1.31 X := X
% 0.82/1.31 Y := Y
% 0.82/1.31 Z := Z
% 0.82/1.31 end
% 0.82/1.31 permutation0:
% 0.82/1.31 0 ==> 0
% 0.82/1.31 end
% 0.82/1.31
% 0.82/1.31 subsumption: (2) {G0,W5,D3,L1,V1,M1} I { addition( X, zero ) ==> X }.
% 0.82/1.31 parent0: (1234) {G0,W5,D3,L1,V1,M1} { addition( X, zero ) = X }.
% 0.82/1.31 substitution0:
% 0.82/1.31 X := X
% 0.82/1.31 end
% 0.82/1.31 permutation0:
% 0.82/1.31 0 ==> 0
% 0.82/1.31 end
% 0.82/1.31
% 0.82/1.31 subsumption: (3) {G0,W5,D3,L1,V1,M1} I { addition( X, X ) ==> X }.
% 0.82/1.31 parent0: (1235) {G0,W5,D3,L1,V1,M1} { addition( X, X ) = X }.
% 0.82/1.31 substitution0:
% 0.82/1.31 X := X
% 0.82/1.31 end
% 0.82/1.31 permutation0:
% 0.82/1.31 0 ==> 0
% 0.82/1.31 end
% 0.82/1.31
% 0.82/1.31 subsumption: (5) {G0,W5,D3,L1,V1,M1} I { multiplication( X, one ) ==> X }.
% 0.82/1.31 parent0: (1237) {G0,W5,D3,L1,V1,M1} { multiplication( X, one ) = X }.
% 0.82/1.31 substitution0:
% 0.82/1.31 X := X
% 0.82/1.31 end
% 0.82/1.31 permutation0:
% 0.82/1.31 0 ==> 0
% 0.82/1.31 end
% 0.82/1.31
% 0.82/1.31 eqswap: (1270) {G0,W13,D4,L1,V3,M1} { addition( multiplication( X, Y ),
% 0.82/1.31 multiplication( X, Z ) ) = multiplication( X, addition( Y, Z ) ) }.
% 0.82/1.31 parent0[0]: (1239) {G0,W13,D4,L1,V3,M1} { multiplication( X, addition( Y,
% 0.82/1.31 Z ) ) = addition( multiplication( X, Y ), multiplication( X, Z ) ) }.
% 0.82/1.31 substitution0:
% 0.82/1.31 X := X
% 0.82/1.31 Y := Y
% 0.82/1.31 Z := Z
% 0.82/1.31 end
% 0.82/1.31
% 0.82/1.31 subsumption: (7) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Y )
% 0.82/1.31 , multiplication( X, Z ) ) ==> multiplication( X, addition( Y, Z ) ) }.
% 0.82/1.31 parent0: (1270) {G0,W13,D4,L1,V3,M1} { addition( multiplication( X, Y ),
% 0.82/1.31 multiplication( X, Z ) ) = multiplication( X, addition( Y, Z ) ) }.
% 0.82/1.31 substitution0:
% 0.82/1.31 X := X
% 0.82/1.31 Y := Y
% 0.82/1.31 Z := Z
% 0.82/1.31 end
% 0.82/1.31 permutation0:
% 0.82/1.31 0 ==> 0
% 0.82/1.31 end
% 0.82/1.31
% 0.82/1.31 subsumption: (11) {G0,W9,D5,L1,V1,M1} I { addition( one, multiplication(
% 0.82/1.31 star( X ), X ) ) ==> star( X ) }.
% 0.82/1.31 parent0: (1243) {G0,W9,D5,L1,V1,M1} { addition( one, multiplication( star
% 0.82/1.31 ( X ), X ) ) = star( X ) }.
% 0.82/1.31 substitution0:
% 0.82/1.31 X := X
% 0.82/1.31 end
% 0.82/1.31 permutation0:
% 0.82/1.31 0 ==> 0
% 0.82/1.31 end
% 0.82/1.31
% 0.82/1.31 subsumption: (13) {G0,W13,D4,L2,V3,M2} I { ! leq( addition( multiplication
% 0.82/1.31 ( Z, X ), Y ), Z ), leq( multiplication( Y, star( X ) ), Z ) }.
% 0.82/1.31 parent0: (1245) {G0,W13,D4,L2,V3,M2} { ! leq( addition( multiplication( Z
% 0.82/1.31 , X ), Y ), Z ), leq( multiplication( Y, star( X ) ), Z ) }.
% 0.82/1.31 substitution0:
% 0.82/1.31 X := X
% 0.82/1.31 Y := Y
% 0.82/1.31 Z := Z
% 0.82/1.31 end
% 0.82/1.31 permutation0:
% 0.82/1.31 0 ==> 0
% 0.82/1.31 1 ==> 1
% 0.82/1.31 end
% 0.82/1.31
% 0.82/1.31 subsumption: (17) {G0,W8,D3,L2,V2,M2} I { ! leq( X, Y ), addition( X, Y )
% 0.82/1.31 ==> Y }.
% 0.82/1.31 parent0: (1249) {G0,W8,D3,L2,V2,M2} { ! leq( X, Y ), addition( X, Y ) = Y
% 0.82/1.31 }.
% 0.82/1.31 substitution0:
% 0.82/1.31 X := X
% 0.82/1.31 Y := Y
% 0.82/1.31 end
% 0.82/1.31 permutation0:
% 0.82/1.31 0 ==> 0
% 0.82/1.31 1 ==> 1
% 0.82/1.31 end
% 0.82/1.31
% 0.82/1.31 subsumption: (18) {G0,W8,D3,L2,V2,M2} I { ! addition( X, Y ) ==> Y, leq( X
% 0.82/1.31 , Y ) }.
% 0.82/1.31 parent0: (1250) {G0,W8,D3,L2,V2,M2} { ! addition( X, Y ) = Y, leq( X, Y )
% 0.82/1.31 }.
% 0.82/1.31 substitution0:
% 0.82/1.31 X := X
% 0.82/1.31 Y := Y
% 0.82/1.31 end
% 0.82/1.31 permutation0:
% 0.82/1.31 0 ==> 0
% 0.82/1.31 1 ==> 1
% 0.82/1.31 end
% 0.82/1.31
% 0.82/1.31 subsumption: (19) {G0,W11,D4,L2,V0,M2} I { multiplication( skol1, skol2 )
% 0.82/1.31 ==> zero, ! leq( skol1, multiplication( skol1, star( skol2 ) ) ) }.
% 0.82/1.31 parent0: (1251) {G0,W11,D4,L2,V0,M2} { multiplication( skol1, skol2 ) =
% 0.82/1.31 zero, ! leq( skol1, multiplication( skol1, star( skol2 ) ) ) }.
% 0.82/1.31 substitution0:
% 0.82/1.31 end
% 0.82/1.31 permutation0:
% 0.82/1.31 0 ==> 0
% 0.82/1.31 1 ==> 1
% 0.82/1.31 end
% 0.82/1.31
% 0.82/1.31 *** allocated 113905 integers for clauses
% 0.82/1.31 subsumption: (20) {G0,W12,D4,L2,V0,M2} I { ! leq( multiplication( skol1,
% 0.82/1.31 star( skol2 ) ), skol1 ), ! leq( skol1, multiplication( skol1, star(
% 0.82/1.31 skol2 ) ) ) }.
% 0.82/1.31 parent0: (1252) {G0,W12,D4,L2,V0,M2} { ! leq( multiplication( skol1, star
% 0.82/1.31 ( skol2 ) ), skol1 ), ! leq( skol1, multiplication( skol1, star( skol2 )
% 0.82/1.31 ) ) }.
% 0.82/1.31 substitution0:
% 0.82/1.31 end
% 0.82/1.31 permutation0:
% 0.82/1.31 0 ==> 0
% 0.82/1.31 1 ==> 1
% 0.82/1.31 end
% 0.82/1.31
% 0.82/1.31 eqswap: (1354) {G0,W5,D3,L1,V1,M1} { X ==> addition( X, zero ) }.
% 0.82/1.31 parent0[0]: (2) {G0,W5,D3,L1,V1,M1} I { addition( X, zero ) ==> X }.
% 0.82/1.31 substitution0:
% 0.82/1.31 X := X
% 0.82/1.31 end
% 0.82/1.31
% 0.82/1.31 paramod: (1355) {G1,W5,D3,L1,V1,M1} { X ==> addition( zero, X ) }.
% 0.82/1.31 parent0[0]: (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X )
% 0.82/1.31 }.
% 0.82/1.31 parent1[0; 2]: (1354) {G0,W5,D3,L1,V1,M1} { X ==> addition( X, zero ) }.
% 0.82/1.31 substitution0:
% 0.82/1.31 X := X
% 0.82/1.31 Y := zero
% 0.82/1.31 end
% 0.82/1.31 substitution1:
% 0.82/1.31 X := X
% 0.82/1.31 end
% 0.82/1.31
% 0.82/1.31 eqswap: (1358) {G1,W5,D3,L1,V1,M1} { addition( zero, X ) ==> X }.
% 0.82/1.31 parent0[0]: (1355) {G1,W5,D3,L1,V1,M1} { X ==> addition( zero, X ) }.
% 0.82/1.31 substitution0:
% 0.82/1.31 X := X
% 0.82/1.31 end
% 0.82/1.31
% 0.82/1.31 subsumption: (21) {G1,W5,D3,L1,V1,M1} P(0,2) { addition( zero, X ) ==> X
% 0.82/1.31 }.
% 0.82/1.31 parent0: (1358) {G1,W5,D3,L1,V1,M1} { addition( zero, X ) ==> X }.
% 0.82/1.31 substitution0:
% 0.82/1.31 X := X
% 0.82/1.31 end
% 0.82/1.31 permutation0:
% 0.82/1.31 0 ==> 0
% 0.82/1.31 end
% 0.82/1.31
% 0.82/1.31 eqswap: (1359) {G0,W8,D3,L2,V2,M2} { ! Y ==> addition( X, Y ), leq( X, Y )
% 0.82/1.31 }.
% 0.82/1.31 parent0[0]: (18) {G0,W8,D3,L2,V2,M2} I { ! addition( X, Y ) ==> Y, leq( X,
% 0.82/1.31 Y ) }.
% 0.82/1.31 substitution0:
% 0.82/1.31 X := X
% 0.82/1.31 Y := Y
% 0.82/1.31 end
% 0.82/1.31
% 0.82/1.31 eqswap: (1360) {G0,W5,D3,L1,V1,M1} { X ==> addition( X, X ) }.
% 0.82/1.31 parent0[0]: (3) {G0,W5,D3,L1,V1,M1} I { addition( X, X ) ==> X }.
% 0.82/1.31 substitution0:
% 0.82/1.31 X := X
% 0.82/1.31 end
% 0.82/1.31
% 0.82/1.31 resolution: (1361) {G1,W3,D2,L1,V1,M1} { leq( X, X ) }.
% 0.82/1.31 parent0[0]: (1359) {G0,W8,D3,L2,V2,M2} { ! Y ==> addition( X, Y ), leq( X
% 0.82/1.31 , Y ) }.
% 0.82/1.31 parent1[0]: (1360) {G0,W5,D3,L1,V1,M1} { X ==> addition( X, X ) }.
% 0.82/1.31 substitution0:
% 0.82/1.31 X := X
% 0.82/1.31 Y := X
% 0.82/1.31 end
% 0.82/1.31 substitution1:
% 0.82/1.31 X := X
% 0.82/1.31 end
% 0.82/1.31
% 0.82/1.31 subsumption: (23) {G1,W3,D2,L1,V1,M1} R(18,3) { leq( X, X ) }.
% 0.82/1.31 parent0: (1361) {G1,W3,D2,L1,V1,M1} { leq( X, X ) }.
% 0.82/1.31 substitution0:
% 0.82/1.31 X := X
% 0.82/1.31 end
% 0.82/1.31 permutation0:
% 0.82/1.31 0 ==> 0
% 0.82/1.31 end
% 0.82/1.31
% 0.82/1.31 eqswap: (1363) {G0,W8,D3,L2,V2,M2} { ! Y ==> addition( X, Y ), leq( X, Y )
% 0.82/1.31 }.
% 0.82/1.31 parent0[0]: (18) {G0,W8,D3,L2,V2,M2} I { ! addition( X, Y ) ==> Y, leq( X,
% 0.82/1.31 Y ) }.
% 0.82/1.31 substitution0:
% 0.82/1.31 X := X
% 0.82/1.31 Y := Y
% 0.82/1.31 end
% 0.82/1.31
% 0.82/1.31 paramod: (1364) {G1,W14,D4,L2,V3,M2} { ! addition( X, Y ) ==> addition(
% 0.82/1.31 addition( Z, X ), Y ), leq( Z, addition( X, Y ) ) }.
% 0.82/1.31 parent0[0]: (1) {G0,W11,D4,L1,V3,M1} I { addition( Z, addition( Y, X ) )
% 0.82/1.31 ==> addition( addition( Z, Y ), X ) }.
% 0.82/1.31 parent1[0; 5]: (1363) {G0,W8,D3,L2,V2,M2} { ! Y ==> addition( X, Y ), leq
% 0.82/1.31 ( X, Y ) }.
% 0.82/1.31 substitution0:
% 0.82/1.31 X := Y
% 0.82/1.31 Y := X
% 0.82/1.31 Z := Z
% 0.82/1.31 end
% 0.82/1.31 substitution1:
% 0.82/1.31 X := Z
% 0.82/1.31 Y := addition( X, Y )
% 0.82/1.31 end
% 0.82/1.31
% 0.82/1.31 eqswap: (1365) {G1,W14,D4,L2,V3,M2} { ! addition( addition( Z, X ), Y )
% 0.82/1.31 ==> addition( X, Y ), leq( Z, addition( X, Y ) ) }.
% 0.82/1.31 parent0[0]: (1364) {G1,W14,D4,L2,V3,M2} { ! addition( X, Y ) ==> addition
% 0.82/1.31 ( addition( Z, X ), Y ), leq( Z, addition( X, Y ) ) }.
% 0.82/1.31 substitution0:
% 0.82/1.31 X := X
% 0.82/1.31 Y := Y
% 0.82/1.31 Z := Z
% 0.82/1.31 end
% 0.82/1.31
% 0.82/1.31 subsumption: (26) {G1,W14,D4,L2,V3,M2} P(1,18) { ! addition( addition( X, Y
% 0.82/1.31 ), Z ) ==> addition( Y, Z ), leq( X, addition( Y, Z ) ) }.
% 0.82/1.31 parent0: (1365) {G1,W14,D4,L2,V3,M2} { ! addition( addition( Z, X ), Y )
% 0.82/1.31 ==> addition( X, Y ), leq( Z, addition( X, Y ) ) }.
% 0.82/1.31 substitution0:
% 0.82/1.31 X := Y
% 0.82/1.31 Y := Z
% 0.82/1.31 Z := X
% 0.82/1.31 end
% 0.82/1.31 permutation0:
% 0.82/1.31 0 ==> 0
% 0.82/1.31 1 ==> 1
% 0.82/1.31 end
% 0.82/1.31
% 0.82/1.31 eqswap: (1367) {G0,W8,D3,L2,V2,M2} { ! Y ==> addition( X, Y ), leq( X, Y )
% 0.82/1.31 }.
% 0.82/1.31 parent0[0]: (18) {G0,W8,D3,L2,V2,M2} I { ! addition( X, Y ) ==> Y, leq( X,
% 0.82/1.31 Y ) }.
% 0.82/1.31 substitution0:
% 0.82/1.31 X := X
% 0.82/1.31 Y := Y
% 0.82/1.31 end
% 0.82/1.31
% 0.82/1.31 paramod: (1368) {G1,W16,D4,L2,V3,M2} { ! multiplication( X, Y ) ==>
% 0.82/1.31 multiplication( X, addition( Z, Y ) ), leq( multiplication( X, Z ),
% 0.82/1.31 multiplication( X, Y ) ) }.
% 0.82/1.31 parent0[0]: (7) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Y ),
% 0.82/1.31 multiplication( X, Z ) ) ==> multiplication( X, addition( Y, Z ) ) }.
% 0.82/1.31 parent1[0; 5]: (1367) {G0,W8,D3,L2,V2,M2} { ! Y ==> addition( X, Y ), leq
% 0.82/1.31 ( X, Y ) }.
% 0.82/1.31 substitution0:
% 0.82/1.31 X := X
% 0.82/1.31 Y := Z
% 0.82/1.31 Z := Y
% 0.82/1.31 end
% 0.82/1.31 substitution1:
% 0.82/1.31 X := multiplication( X, Z )
% 0.82/1.31 Y := multiplication( X, Y )
% 0.82/1.31 end
% 0.82/1.31
% 0.82/1.31 eqswap: (1369) {G1,W16,D4,L2,V3,M2} { ! multiplication( X, addition( Z, Y
% 0.82/1.31 ) ) ==> multiplication( X, Y ), leq( multiplication( X, Z ),
% 0.82/1.31 multiplication( X, Y ) ) }.
% 0.82/1.31 parent0[0]: (1368) {G1,W16,D4,L2,V3,M2} { ! multiplication( X, Y ) ==>
% 0.82/1.31 multiplication( X, addition( Z, Y ) ), leq( multiplication( X, Z ),
% 0.82/1.31 multiplication( X, Y ) ) }.
% 0.82/1.31 substitution0:
% 0.82/1.31 X := X
% 0.82/1.31 Y := Y
% 0.82/1.31 Z := Z
% 0.82/1.31 end
% 0.82/1.31
% 0.82/1.31 subsumption: (68) {G1,W16,D4,L2,V3,M2} P(7,18) { ! multiplication( X,
% 0.82/1.31 addition( Y, Z ) ) ==> multiplication( X, Z ), leq( multiplication( X, Y
% 0.82/1.31 ), multiplication( X, Z ) ) }.
% 0.82/1.31 parent0: (1369) {G1,W16,D4,L2,V3,M2} { ! multiplication( X, addition( Z, Y
% 0.82/1.31 ) ) ==> multiplication( X, Y ), leq( multiplication( X, Z ),
% 0.82/1.31 multiplication( X, Y ) ) }.
% 0.82/1.31 substitution0:
% 0.82/1.31 X := X
% 0.82/1.31 Y := Z
% 0.82/1.31 Z := Y
% 0.82/1.31 end
% 0.82/1.31 permutation0:
% 0.82/1.31 0 ==> 0
% 0.82/1.31 1 ==> 1
% 0.82/1.31 end
% 0.82/1.31
% 0.82/1.31 resolution: (1372) {G1,W13,D4,L2,V0,M2} { ! leq( skol1, multiplication(
% 0.82/1.31 skol1, star( skol2 ) ) ), ! leq( addition( multiplication( skol1, skol2 )
% 0.82/1.31 , skol1 ), skol1 ) }.
% 0.82/1.31 parent0[0]: (20) {G0,W12,D4,L2,V0,M2} I { ! leq( multiplication( skol1,
% 0.82/1.31 star( skol2 ) ), skol1 ), ! leq( skol1, multiplication( skol1, star(
% 0.82/1.31 skol2 ) ) ) }.
% 0.82/1.31 parent1[1]: (13) {G0,W13,D4,L2,V3,M2} I { ! leq( addition( multiplication(
% 0.82/1.31 Z, X ), Y ), Z ), leq( multiplication( Y, star( X ) ), Z ) }.
% 0.82/1.31 substitution0:
% 0.82/1.31 end
% 0.82/1.31 substitution1:
% 0.82/1.31 X := skol2
% 0.82/1.31 Y := skol1
% 0.82/1.31 Z := skol1
% 0.82/1.31 end
% 0.82/1.31
% 0.82/1.31 paramod: (1373) {G1,W17,D4,L3,V0,M3} { ! leq( addition( zero, skol1 ),
% 0.82/1.31 skol1 ), ! leq( skol1, multiplication( skol1, star( skol2 ) ) ), ! leq(
% 0.82/1.31 skol1, multiplication( skol1, star( skol2 ) ) ) }.
% 0.82/1.31 parent0[0]: (19) {G0,W11,D4,L2,V0,M2} I { multiplication( skol1, skol2 )
% 0.82/1.31 ==> zero, ! leq( skol1, multiplication( skol1, star( skol2 ) ) ) }.
% 0.82/1.31 parent1[1; 3]: (1372) {G1,W13,D4,L2,V0,M2} { ! leq( skol1, multiplication
% 0.82/1.31 ( skol1, star( skol2 ) ) ), ! leq( addition( multiplication( skol1, skol2
% 0.82/1.31 ), skol1 ), skol1 ) }.
% 0.82/1.31 substitution0:
% 0.82/1.31 end
% 0.82/1.31 substitution1:
% 0.82/1.31 end
% 0.82/1.31
% 0.82/1.31 factor: (1374) {G1,W11,D4,L2,V0,M2} { ! leq( addition( zero, skol1 ),
% 0.82/1.31 skol1 ), ! leq( skol1, multiplication( skol1, star( skol2 ) ) ) }.
% 0.82/1.31 parent0[1, 2]: (1373) {G1,W17,D4,L3,V0,M3} { ! leq( addition( zero, skol1
% 0.82/1.31 ), skol1 ), ! leq( skol1, multiplication( skol1, star( skol2 ) ) ), !
% 0.82/1.31 leq( skol1, multiplication( skol1, star( skol2 ) ) ) }.
% 0.82/1.31 substitution0:
% 0.82/1.31 end
% 0.82/1.31
% 0.82/1.31 paramod: (1375) {G2,W9,D4,L2,V0,M2} { ! leq( skol1, skol1 ), ! leq( skol1
% 0.82/1.31 , multiplication( skol1, star( skol2 ) ) ) }.
% 0.82/1.31 parent0[0]: (21) {G1,W5,D3,L1,V1,M1} P(0,2) { addition( zero, X ) ==> X }.
% 0.82/1.31 parent1[0; 2]: (1374) {G1,W11,D4,L2,V0,M2} { ! leq( addition( zero, skol1
% 0.82/1.31 ), skol1 ), ! leq( skol1, multiplication( skol1, star( skol2 ) ) ) }.
% 0.82/1.31 substitution0:
% 0.82/1.31 X := skol1
% 0.82/1.31 end
% 0.82/1.31 substitution1:
% 0.82/1.31 end
% 0.82/1.31
% 0.82/1.31 resolution: (1376) {G2,W6,D4,L1,V0,M1} { ! leq( skol1, multiplication(
% 0.82/1.31 skol1, star( skol2 ) ) ) }.
% 0.82/1.31 parent0[0]: (1375) {G2,W9,D4,L2,V0,M2} { ! leq( skol1, skol1 ), ! leq(
% 0.82/1.31 skol1, multiplication( skol1, star( skol2 ) ) ) }.
% 0.82/1.31 parent1[0]: (23) {G1,W3,D2,L1,V1,M1} R(18,3) { leq( X, X ) }.
% 0.82/1.31 substitution0:
% 0.82/1.31 end
% 0.82/1.31 substitution1:
% 0.82/1.31 X := skol1
% 0.82/1.31 end
% 0.82/1.31
% 0.82/1.31 subsumption: (326) {G2,W6,D4,L1,V0,M1} R(20,13);d(19);d(21);r(23) { ! leq(
% 0.82/1.31 skol1, multiplication( skol1, star( skol2 ) ) ) }.
% 0.82/1.31 parent0: (1376) {G2,W6,D4,L1,V0,M1} { ! leq( skol1, multiplication( skol1
% 0.82/1.31 , star( skol2 ) ) ) }.
% 0.82/1.31 substitution0:
% 0.82/1.31 end
% 0.82/1.31 permutation0:
% 0.82/1.31 0 ==> 0
% 0.82/1.31 end
% 0.82/1.31
% 0.82/1.31 eqswap: (1378) {G1,W14,D4,L2,V3,M2} { ! addition( Y, Z ) ==> addition(
% 0.82/1.31 addition( X, Y ), Z ), leq( X, addition( Y, Z ) ) }.
% 0.82/1.31 parent0[0]: (26) {G1,W14,D4,L2,V3,M2} P(1,18) { ! addition( addition( X, Y
% 0.82/1.31 ), Z ) ==> addition( Y, Z ), leq( X, addition( Y, Z ) ) }.
% 0.82/1.31 substitution0:
% 0.82/1.31 X := X
% 0.82/1.31 Y := Y
% 0.82/1.31 Z := Z
% 0.82/1.31 end
% 0.82/1.31
% 0.82/1.31 paramod: (1381) {G1,W12,D3,L2,V2,M2} { ! addition( X, Y ) ==> addition( X
% 0.82/1.31 , Y ), leq( X, addition( X, Y ) ) }.
% 0.82/1.31 parent0[0]: (3) {G0,W5,D3,L1,V1,M1} I { addition( X, X ) ==> X }.
% 0.82/1.31 parent1[0; 6]: (1378) {G1,W14,D4,L2,V3,M2} { ! addition( Y, Z ) ==>
% 0.82/1.31 addition( addition( X, Y ), Z ), leq( X, addition( Y, Z ) ) }.
% 0.82/1.31 substitution0:
% 0.82/1.31 X := X
% 0.82/1.31 end
% 0.82/1.31 substitution1:
% 0.82/1.31 X := X
% 0.82/1.31 Y := X
% 0.82/1.31 Z := Y
% 0.82/1.31 end
% 0.82/1.31
% 0.82/1.31 eqrefl: (1384) {G0,W5,D3,L1,V2,M1} { leq( X, addition( X, Y ) ) }.
% 0.82/1.31 parent0[0]: (1381) {G1,W12,D3,L2,V2,M2} { ! addition( X, Y ) ==> addition
% 0.82/1.31 ( X, Y ), leq( X, addition( X, Y ) ) }.
% 0.82/1.31 substitution0:
% 0.82/1.31 X := X
% 0.82/1.31 Y := Y
% 0.82/1.31 end
% 0.82/1.31
% 0.82/1.31 subsumption: (357) {G2,W5,D3,L1,V2,M1} P(3,26);q { leq( X, addition( X, Y )
% 0.82/1.31 ) }.
% 0.82/1.31 parent0: (1384) {G0,W5,D3,L1,V2,M1} { leq( X, addition( X, Y ) ) }.
% 0.82/1.31 substitution0:
% 0.82/1.31 X := X
% 0.82/1.31 Y := Y
% 0.82/1.31 end
% 0.82/1.31 permutation0:
% 0.82/1.31 0 ==> 0
% 0.82/1.31 end
% 0.82/1.31
% 0.82/1.31 paramod: (1386) {G1,W4,D3,L1,V1,M1} { leq( one, star( X ) ) }.
% 0.82/1.31 parent0[0]: (11) {G0,W9,D5,L1,V1,M1} I { addition( one, multiplication(
% 0.82/1.31 star( X ), X ) ) ==> star( X ) }.
% 0.82/1.31 parent1[0; 2]: (357) {G2,W5,D3,L1,V2,M1} P(3,26);q { leq( X, addition( X, Y
% 0.82/1.31 ) ) }.
% 0.82/1.31 substitution0:
% 0.82/1.31 X := X
% 0.82/1.31 end
% 0.82/1.31 substitution1:
% 0.82/1.31 X := one
% 0.82/1.31 Y := multiplication( star( X ), X )
% 0.82/1.31 end
% 0.82/1.31
% 0.82/1.31 subsumption: (410) {G3,W4,D3,L1,V1,M1} P(11,357) { leq( one, star( X ) )
% 0.82/1.31 }.
% 0.82/1.31 parent0: (1386) {G1,W4,D3,L1,V1,M1} { leq( one, star( X ) ) }.
% 0.82/1.31 substitution0:
% 0.82/1.31 X := X
% 0.82/1.31 end
% 0.82/1.31 permutation0:
% 0.82/1.31 0 ==> 0
% 0.82/1.31 end
% 0.82/1.31
% 0.82/1.31 eqswap: (1387) {G0,W8,D3,L2,V2,M2} { Y ==> addition( X, Y ), ! leq( X, Y )
% 0.82/1.31 }.
% 0.82/1.31 parent0[1]: (17) {G0,W8,D3,L2,V2,M2} I { ! leq( X, Y ), addition( X, Y )
% 0.82/1.31 ==> Y }.
% 0.82/1.31 substitution0:
% 0.82/1.31 X := X
% 0.82/1.31 Y := Y
% 0.82/1.31 end
% 0.82/1.31
% 0.82/1.31 resolution: (1388) {G1,W7,D4,L1,V1,M1} { star( X ) ==> addition( one, star
% 0.82/1.31 ( X ) ) }.
% 0.82/1.31 parent0[1]: (1387) {G0,W8,D3,L2,V2,M2} { Y ==> addition( X, Y ), ! leq( X
% 0.82/1.31 , Y ) }.
% 0.82/1.31 parent1[0]: (410) {G3,W4,D3,L1,V1,M1} P(11,357) { leq( one, star( X ) ) }.
% 0.82/1.31 substitution0:
% 0.82/1.31 X := one
% 0.82/1.31 Y := star( X )
% 0.82/1.31 end
% 0.82/1.31 substitution1:
% 0.82/1.31 X := X
% 0.82/1.31 end
% 0.82/1.31
% 0.82/1.31 eqswap: (1389) {G1,W7,D4,L1,V1,M1} { addition( one, star( X ) ) ==> star(
% 0.82/1.31 X ) }.
% 0.82/1.31 parent0[0]: (1388) {G1,W7,D4,L1,V1,M1} { star( X ) ==> addition( one, star
% 0.82/1.31 ( X ) ) }.
% 0.82/1.31 substitution0:
% 0.82/1.31 X := X
% 0.82/1.31 end
% 0.82/1.31
% 0.82/1.31 subsumption: (418) {G4,W7,D4,L1,V1,M1} R(410,17) { addition( one, star( X )
% 0.82/1.31 ) ==> star( X ) }.
% 0.82/1.31 parent0: (1389) {G1,W7,D4,L1,V1,M1} { addition( one, star( X ) ) ==> star
% 0.82/1.31 ( X ) }.
% 0.82/1.31 substitution0:
% 0.82/1.31 X := X
% 0.82/1.31 end
% 0.82/1.31 permutation0:
% 0.82/1.31 0 ==> 0
% 0.82/1.31 end
% 0.82/1.31
% 0.82/1.31 eqswap: (1391) {G1,W16,D4,L2,V3,M2} { ! multiplication( X, Z ) ==>
% 0.82/1.31 multiplication( X, addition( Y, Z ) ), leq( multiplication( X, Y ),
% 0.82/1.31 multiplication( X, Z ) ) }.
% 0.82/1.31 parent0[0]: (68) {G1,W16,D4,L2,V3,M2} P(7,18) { ! multiplication( X,
% 0.82/1.31 addition( Y, Z ) ) ==> multiplication( X, Z ), leq( multiplication( X, Y
% 0.82/1.31 ), multiplication( X, Z ) ) }.
% 0.82/1.31 substitution0:
% 0.82/1.31 X := X
% 0.82/1.31 Y := Y
% 0.82/1.31 Z := Z
% 0.82/1.31 end
% 0.82/1.31
% 0.82/1.31 paramod: (1393) {G2,W17,D4,L2,V2,M2} { ! multiplication( X, star( Y ) )
% 0.82/1.31 ==> multiplication( X, star( Y ) ), leq( multiplication( X, one ),
% 0.82/1.31 multiplication( X, star( Y ) ) ) }.
% 0.82/1.31 parent0[0]: (418) {G4,W7,D4,L1,V1,M1} R(410,17) { addition( one, star( X )
% 0.82/1.31 ) ==> star( X ) }.
% 0.82/1.31 parent1[0; 8]: (1391) {G1,W16,D4,L2,V3,M2} { ! multiplication( X, Z ) ==>
% 0.82/1.31 multiplication( X, addition( Y, Z ) ), leq( multiplication( X, Y ),
% 0.82/1.31 multiplication( X, Z ) ) }.
% 0.82/1.31 substitution0:
% 0.82/1.31 X := Y
% 0.82/1.31 end
% 0.82/1.31 substitution1:
% 0.82/1.31 X := X
% 0.82/1.31 Y := one
% 0.82/1.31 Z := star( Y )
% 0.82/1.31 end
% 0.82/1.31
% 0.82/1.31 eqrefl: (1394) {G0,W8,D4,L1,V2,M1} { leq( multiplication( X, one ),
% 0.82/1.31 multiplication( X, star( Y ) ) ) }.
% 0.82/1.31 parent0[0]: (1393) {G2,W17,D4,L2,V2,M2} { ! multiplication( X, star( Y ) )
% 0.82/1.31 ==> multiplication( X, star( Y ) ), leq( multiplication( X, one ),
% 0.82/1.31 multiplication( X, star( Y ) ) ) }.
% 0.82/1.31 substitution0:
% 0.82/1.31 X := X
% 0.82/1.31 Y := Y
% 0.82/1.31 end
% 0.82/1.31
% 0.82/1.31 paramod: (1395) {G1,W6,D4,L1,V2,M1} { leq( X, multiplication( X, star( Y )
% 0.82/1.31 ) ) }.
% 0.82/1.31 parent0[0]: (5) {G0,W5,D3,L1,V1,M1} I { multiplication( X, one ) ==> X }.
% 0.82/1.31 parent1[0; 1]: (1394) {G0,W8,D4,L1,V2,M1} { leq( multiplication( X, one )
% 0.82/1.31 , multiplication( X, star( Y ) ) ) }.
% 0.82/1.31 substitution0:
% 0.82/1.31 X := X
% 0.82/1.31 end
% 0.82/1.31 substitution1:
% 0.82/1.31 X := X
% 0.82/1.31 Y := Y
% 0.82/1.31 end
% 0.82/1.31
% 0.82/1.31 subsumption: (1211) {G5,W6,D4,L1,V2,M1} P(418,68);q;d(5) { leq( Y,
% 0.82/1.31 multiplication( Y, star( X ) ) ) }.
% 0.82/1.31 parent0: (1395) {G1,W6,D4,L1,V2,M1} { leq( X, multiplication( X, star( Y )
% 0.82/1.31 ) ) }.
% 0.82/1.31 substitution0:
% 0.82/1.31 X := Y
% 0.82/1.31 Y := X
% 0.82/1.31 end
% 0.82/1.31 permutation0:
% 0.82/1.31 0 ==> 0
% 0.82/1.31 end
% 0.82/1.31
% 0.82/1.31 resolution: (1396) {G3,W0,D0,L0,V0,M0} { }.
% 0.82/1.31 parent0[0]: (326) {G2,W6,D4,L1,V0,M1} R(20,13);d(19);d(21);r(23) { ! leq(
% 0.82/1.31 skol1, multiplication( skol1, star( skol2 ) ) ) }.
% 0.82/1.31 parent1[0]: (1211) {G5,W6,D4,L1,V2,M1} P(418,68);q;d(5) { leq( Y,
% 0.82/1.31 multiplication( Y, star( X ) ) ) }.
% 0.82/1.31 substitution0:
% 0.82/1.31 end
% 0.82/1.31 substitution1:
% 0.82/1.31 X := skol2
% 0.82/1.31 Y := skol1
% 0.82/1.31 end
% 0.82/1.31
% 0.82/1.31 subsumption: (1230) {G6,W0,D0,L0,V0,M0} R(1211,326) { }.
% 0.82/1.31 parent0: (1396) {G3,W0,D0,L0,V0,M0} { }.
% 0.82/1.31 substitution0:
% 0.82/1.31 end
% 0.82/1.31 permutation0:
% 0.82/1.31 end
% 0.82/1.31
% 0.82/1.31 Proof check complete!
% 0.82/1.31
% 0.82/1.31 Memory use:
% 0.82/1.31
% 0.82/1.31 space for terms: 14962
% 0.82/1.31 space for clauses: 73665
% 0.82/1.31
% 0.82/1.31
% 0.82/1.31 clauses generated: 15744
% 0.82/1.31 clauses kept: 1231
% 0.82/1.31 clauses selected: 206
% 0.82/1.31 clauses deleted: 65
% 0.82/1.31 clauses inuse deleted: 39
% 0.82/1.31
% 0.82/1.31 subsentry: 26546
% 0.82/1.31 literals s-matched: 20229
% 0.82/1.31 literals matched: 20003
% 0.82/1.31 full subsumption: 3362
% 0.82/1.31
% 0.82/1.31 checksum: -2114254000
% 0.82/1.31
% 0.82/1.31
% 0.82/1.31 Bliksem ended
%------------------------------------------------------------------------------