TSTP Solution File: KLE066+1 by Bliksem---1.12
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%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : KLE066+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n023.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 01:36:59 EDT 2022
% Result : Theorem 0.82s 1.18s
% Output : Refutation 0.82s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.14 % Problem : KLE066+1 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.15 % Command : bliksem %s
% 0.15/0.36 % Computer : n023.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % DateTime : Thu Jun 16 15:33:35 EDT 2022
% 0.15/0.37 % CPUTime :
% 0.82/1.18 *** allocated 10000 integers for termspace/termends
% 0.82/1.18 *** allocated 10000 integers for clauses
% 0.82/1.18 *** allocated 10000 integers for justifications
% 0.82/1.18 Bliksem 1.12
% 0.82/1.18
% 0.82/1.18
% 0.82/1.18 Automatic Strategy Selection
% 0.82/1.18
% 0.82/1.18
% 0.82/1.18 Clauses:
% 0.82/1.18
% 0.82/1.18 { addition( X, Y ) = addition( Y, X ) }.
% 0.82/1.18 { addition( Z, addition( Y, X ) ) = addition( addition( Z, Y ), X ) }.
% 0.82/1.18 { addition( X, zero ) = X }.
% 0.82/1.18 { addition( X, X ) = X }.
% 0.82/1.18 { multiplication( X, multiplication( Y, Z ) ) = multiplication(
% 0.82/1.18 multiplication( X, Y ), Z ) }.
% 0.82/1.18 { multiplication( X, one ) = X }.
% 0.82/1.18 { multiplication( one, X ) = X }.
% 0.82/1.18 { multiplication( X, addition( Y, Z ) ) = addition( multiplication( X, Y )
% 0.82/1.18 , multiplication( X, Z ) ) }.
% 0.82/1.18 { multiplication( addition( X, Y ), Z ) = addition( multiplication( X, Z )
% 0.82/1.18 , multiplication( Y, Z ) ) }.
% 0.82/1.18 { multiplication( X, zero ) = zero }.
% 0.82/1.18 { multiplication( zero, X ) = zero }.
% 0.82/1.18 { ! leq( X, Y ), addition( X, Y ) = Y }.
% 0.82/1.18 { ! addition( X, Y ) = Y, leq( X, Y ) }.
% 0.82/1.18 { addition( X, multiplication( domain( X ), X ) ) = multiplication( domain
% 0.82/1.18 ( X ), X ) }.
% 0.82/1.18 { domain( multiplication( X, Y ) ) = domain( multiplication( X, domain( Y )
% 0.82/1.18 ) ) }.
% 0.82/1.18 { addition( domain( X ), one ) = one }.
% 0.82/1.18 { domain( zero ) = zero }.
% 0.82/1.18 { domain( addition( X, Y ) ) = addition( domain( X ), domain( Y ) ) }.
% 0.82/1.18 { multiplication( skol1, domain( skol2 ) ) = zero }.
% 0.82/1.18 { ! multiplication( skol1, skol2 ) = zero }.
% 0.82/1.18
% 0.82/1.18 percentage equality = 0.909091, percentage horn = 1.000000
% 0.82/1.18 This is a pure equality problem
% 0.82/1.18
% 0.82/1.18
% 0.82/1.18
% 0.82/1.18 Options Used:
% 0.82/1.18
% 0.82/1.18 useres = 1
% 0.82/1.18 useparamod = 1
% 0.82/1.18 useeqrefl = 1
% 0.82/1.18 useeqfact = 1
% 0.82/1.18 usefactor = 1
% 0.82/1.18 usesimpsplitting = 0
% 0.82/1.18 usesimpdemod = 5
% 0.82/1.18 usesimpres = 3
% 0.82/1.18
% 0.82/1.18 resimpinuse = 1000
% 0.82/1.18 resimpclauses = 20000
% 0.82/1.18 substype = eqrewr
% 0.82/1.18 backwardsubs = 1
% 0.82/1.18 selectoldest = 5
% 0.82/1.18
% 0.82/1.18 litorderings [0] = split
% 0.82/1.18 litorderings [1] = extend the termordering, first sorting on arguments
% 0.82/1.18
% 0.82/1.18 termordering = kbo
% 0.82/1.18
% 0.82/1.18 litapriori = 0
% 0.82/1.18 termapriori = 1
% 0.82/1.18 litaposteriori = 0
% 0.82/1.18 termaposteriori = 0
% 0.82/1.18 demodaposteriori = 0
% 0.82/1.18 ordereqreflfact = 0
% 0.82/1.18
% 0.82/1.18 litselect = negord
% 0.82/1.18
% 0.82/1.18 maxweight = 15
% 0.82/1.18 maxdepth = 30000
% 0.82/1.18 maxlength = 115
% 0.82/1.18 maxnrvars = 195
% 0.82/1.18 excuselevel = 1
% 0.82/1.18 increasemaxweight = 1
% 0.82/1.18
% 0.82/1.18 maxselected = 10000000
% 0.82/1.18 maxnrclauses = 10000000
% 0.82/1.18
% 0.82/1.18 showgenerated = 0
% 0.82/1.18 showkept = 0
% 0.82/1.18 showselected = 0
% 0.82/1.18 showdeleted = 0
% 0.82/1.18 showresimp = 1
% 0.82/1.18 showstatus = 2000
% 0.82/1.18
% 0.82/1.18 prologoutput = 0
% 0.82/1.18 nrgoals = 5000000
% 0.82/1.18 totalproof = 1
% 0.82/1.18
% 0.82/1.18 Symbols occurring in the translation:
% 0.82/1.18
% 0.82/1.18 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.82/1.18 . [1, 2] (w:1, o:21, a:1, s:1, b:0),
% 0.82/1.18 ! [4, 1] (w:0, o:15, a:1, s:1, b:0),
% 0.82/1.18 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.82/1.18 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.82/1.18 addition [37, 2] (w:1, o:45, a:1, s:1, b:0),
% 0.82/1.18 zero [39, 0] (w:1, o:9, a:1, s:1, b:0),
% 0.82/1.18 multiplication [40, 2] (w:1, o:47, a:1, s:1, b:0),
% 0.82/1.18 one [41, 0] (w:1, o:10, a:1, s:1, b:0),
% 0.82/1.18 leq [42, 2] (w:1, o:46, a:1, s:1, b:0),
% 0.82/1.18 domain [44, 1] (w:1, o:20, a:1, s:1, b:0),
% 0.82/1.18 skol1 [46, 0] (w:1, o:13, a:1, s:1, b:1),
% 0.82/1.18 skol2 [47, 0] (w:1, o:14, a:1, s:1, b:1).
% 0.82/1.18
% 0.82/1.18
% 0.82/1.18 Starting Search:
% 0.82/1.18
% 0.82/1.18 *** allocated 15000 integers for clauses
% 0.82/1.18 *** allocated 22500 integers for clauses
% 0.82/1.18 *** allocated 33750 integers for clauses
% 0.82/1.18
% 0.82/1.18 Bliksems!, er is een bewijs:
% 0.82/1.18 % SZS status Theorem
% 0.82/1.18 % SZS output start Refutation
% 0.82/1.18
% 0.82/1.18 (2) {G0,W5,D3,L1,V1,M1} I { addition( X, zero ) ==> X }.
% 0.82/1.18 (4) {G0,W11,D4,L1,V3,M1} I { multiplication( X, multiplication( Y, Z ) )
% 0.82/1.18 ==> multiplication( multiplication( X, Y ), Z ) }.
% 0.82/1.18 (10) {G0,W5,D3,L1,V1,M1} I { multiplication( zero, X ) ==> zero }.
% 0.82/1.18 (11) {G0,W8,D3,L2,V2,M2} I { ! leq( X, Y ), addition( X, Y ) ==> Y }.
% 0.82/1.18 (12) {G0,W8,D3,L2,V2,M2} I { ! addition( X, Y ) ==> Y, leq( X, Y ) }.
% 0.82/1.18 (13) {G0,W11,D5,L1,V1,M1} I { addition( X, multiplication( domain( X ), X )
% 0.82/1.18 ) ==> multiplication( domain( X ), X ) }.
% 0.82/1.18 (14) {G0,W10,D5,L1,V2,M1} I { domain( multiplication( X, domain( Y ) ) )
% 0.82/1.18 ==> domain( multiplication( X, Y ) ) }.
% 0.82/1.18 (16) {G0,W4,D3,L1,V0,M1} I { domain( zero ) ==> zero }.
% 0.82/1.18 (18) {G0,W6,D4,L1,V0,M1} I { multiplication( skol1, domain( skol2 ) ) ==>
% 0.82/1.18 zero }.
% 0.82/1.18 (19) {G0,W5,D3,L1,V0,M1} I { ! multiplication( skol1, skol2 ) ==> zero }.
% 0.82/1.18 (53) {G1,W6,D2,L2,V1,M2} P(11,2) { zero = X, ! leq( X, zero ) }.
% 0.82/1.18 (89) {G1,W6,D4,L1,V1,M1} R(13,12) { leq( X, multiplication( domain( X ), X
% 0.82/1.18 ) ) }.
% 0.82/1.18 (114) {G2,W5,D3,L1,V0,M1} P(53,19);q { ! leq( multiplication( skol1, skol2
% 0.82/1.18 ), zero ) }.
% 0.82/1.18 (130) {G1,W6,D4,L1,V0,M1} P(18,14);d(16) { domain( multiplication( skol1,
% 0.82/1.18 skol2 ) ) ==> zero }.
% 0.82/1.18 (342) {G3,W0,D0,L0,V0,M0} P(130,89);d(4);d(10);d(10);r(114) { }.
% 0.82/1.18
% 0.82/1.18
% 0.82/1.18 % SZS output end Refutation
% 0.82/1.18 found a proof!
% 0.82/1.18
% 0.82/1.18
% 0.82/1.18 Unprocessed initial clauses:
% 0.82/1.18
% 0.82/1.18 (344) {G0,W7,D3,L1,V2,M1} { addition( X, Y ) = addition( Y, X ) }.
% 0.82/1.18 (345) {G0,W11,D4,L1,V3,M1} { addition( Z, addition( Y, X ) ) = addition(
% 0.82/1.18 addition( Z, Y ), X ) }.
% 0.82/1.18 (346) {G0,W5,D3,L1,V1,M1} { addition( X, zero ) = X }.
% 0.82/1.18 (347) {G0,W5,D3,L1,V1,M1} { addition( X, X ) = X }.
% 0.82/1.18 (348) {G0,W11,D4,L1,V3,M1} { multiplication( X, multiplication( Y, Z ) ) =
% 0.82/1.18 multiplication( multiplication( X, Y ), Z ) }.
% 0.82/1.18 (349) {G0,W5,D3,L1,V1,M1} { multiplication( X, one ) = X }.
% 0.82/1.18 (350) {G0,W5,D3,L1,V1,M1} { multiplication( one, X ) = X }.
% 0.82/1.18 (351) {G0,W13,D4,L1,V3,M1} { multiplication( X, addition( Y, Z ) ) =
% 0.82/1.18 addition( multiplication( X, Y ), multiplication( X, Z ) ) }.
% 0.82/1.18 (352) {G0,W13,D4,L1,V3,M1} { multiplication( addition( X, Y ), Z ) =
% 0.82/1.18 addition( multiplication( X, Z ), multiplication( Y, Z ) ) }.
% 0.82/1.18 (353) {G0,W5,D3,L1,V1,M1} { multiplication( X, zero ) = zero }.
% 0.82/1.18 (354) {G0,W5,D3,L1,V1,M1} { multiplication( zero, X ) = zero }.
% 0.82/1.18 (355) {G0,W8,D3,L2,V2,M2} { ! leq( X, Y ), addition( X, Y ) = Y }.
% 0.82/1.18 (356) {G0,W8,D3,L2,V2,M2} { ! addition( X, Y ) = Y, leq( X, Y ) }.
% 0.82/1.18 (357) {G0,W11,D5,L1,V1,M1} { addition( X, multiplication( domain( X ), X )
% 0.82/1.18 ) = multiplication( domain( X ), X ) }.
% 0.82/1.18 (358) {G0,W10,D5,L1,V2,M1} { domain( multiplication( X, Y ) ) = domain(
% 0.82/1.18 multiplication( X, domain( Y ) ) ) }.
% 0.82/1.18 (359) {G0,W6,D4,L1,V1,M1} { addition( domain( X ), one ) = one }.
% 0.82/1.18 (360) {G0,W4,D3,L1,V0,M1} { domain( zero ) = zero }.
% 0.82/1.18 (361) {G0,W10,D4,L1,V2,M1} { domain( addition( X, Y ) ) = addition( domain
% 0.82/1.18 ( X ), domain( Y ) ) }.
% 0.82/1.18 (362) {G0,W6,D4,L1,V0,M1} { multiplication( skol1, domain( skol2 ) ) =
% 0.82/1.18 zero }.
% 0.82/1.18 (363) {G0,W5,D3,L1,V0,M1} { ! multiplication( skol1, skol2 ) = zero }.
% 0.82/1.18
% 0.82/1.18
% 0.82/1.18 Total Proof:
% 0.82/1.18
% 0.82/1.18 subsumption: (2) {G0,W5,D3,L1,V1,M1} I { addition( X, zero ) ==> X }.
% 0.82/1.18 parent0: (346) {G0,W5,D3,L1,V1,M1} { addition( X, zero ) = X }.
% 0.82/1.18 substitution0:
% 0.82/1.18 X := X
% 0.82/1.18 end
% 0.82/1.18 permutation0:
% 0.82/1.18 0 ==> 0
% 0.82/1.18 end
% 0.82/1.18
% 0.82/1.18 subsumption: (4) {G0,W11,D4,L1,V3,M1} I { multiplication( X, multiplication
% 0.82/1.18 ( Y, Z ) ) ==> multiplication( multiplication( X, Y ), Z ) }.
% 0.82/1.18 parent0: (348) {G0,W11,D4,L1,V3,M1} { multiplication( X, multiplication( Y
% 0.82/1.18 , Z ) ) = multiplication( multiplication( X, Y ), Z ) }.
% 0.82/1.18 substitution0:
% 0.82/1.18 X := X
% 0.82/1.18 Y := Y
% 0.82/1.18 Z := Z
% 0.82/1.18 end
% 0.82/1.18 permutation0:
% 0.82/1.18 0 ==> 0
% 0.82/1.18 end
% 0.82/1.18
% 0.82/1.18 subsumption: (10) {G0,W5,D3,L1,V1,M1} I { multiplication( zero, X ) ==>
% 0.82/1.18 zero }.
% 0.82/1.18 parent0: (354) {G0,W5,D3,L1,V1,M1} { multiplication( zero, X ) = zero }.
% 0.82/1.18 substitution0:
% 0.82/1.18 X := X
% 0.82/1.18 end
% 0.82/1.18 permutation0:
% 0.82/1.18 0 ==> 0
% 0.82/1.18 end
% 0.82/1.18
% 0.82/1.18 subsumption: (11) {G0,W8,D3,L2,V2,M2} I { ! leq( X, Y ), addition( X, Y )
% 0.82/1.18 ==> Y }.
% 0.82/1.18 parent0: (355) {G0,W8,D3,L2,V2,M2} { ! leq( X, Y ), addition( X, Y ) = Y
% 0.82/1.18 }.
% 0.82/1.18 substitution0:
% 0.82/1.18 X := X
% 0.82/1.18 Y := Y
% 0.82/1.18 end
% 0.82/1.18 permutation0:
% 0.82/1.18 0 ==> 0
% 0.82/1.18 1 ==> 1
% 0.82/1.18 end
% 0.82/1.18
% 0.82/1.18 subsumption: (12) {G0,W8,D3,L2,V2,M2} I { ! addition( X, Y ) ==> Y, leq( X
% 0.82/1.18 , Y ) }.
% 0.82/1.18 parent0: (356) {G0,W8,D3,L2,V2,M2} { ! addition( X, Y ) = Y, leq( X, Y )
% 0.82/1.18 }.
% 0.82/1.18 substitution0:
% 0.82/1.18 X := X
% 0.82/1.18 Y := Y
% 0.82/1.18 end
% 0.82/1.18 permutation0:
% 0.82/1.18 0 ==> 0
% 0.82/1.18 1 ==> 1
% 0.82/1.18 end
% 0.82/1.18
% 0.82/1.18 subsumption: (13) {G0,W11,D5,L1,V1,M1} I { addition( X, multiplication(
% 0.82/1.18 domain( X ), X ) ) ==> multiplication( domain( X ), X ) }.
% 0.82/1.18 parent0: (357) {G0,W11,D5,L1,V1,M1} { addition( X, multiplication( domain
% 0.82/1.18 ( X ), X ) ) = multiplication( domain( X ), X ) }.
% 0.82/1.18 substitution0:
% 0.82/1.18 X := X
% 0.82/1.18 end
% 0.82/1.18 permutation0:
% 0.82/1.18 0 ==> 0
% 0.82/1.18 end
% 0.82/1.18
% 0.82/1.18 eqswap: (429) {G0,W10,D5,L1,V2,M1} { domain( multiplication( X, domain( Y
% 0.82/1.18 ) ) ) = domain( multiplication( X, Y ) ) }.
% 0.82/1.18 parent0[0]: (358) {G0,W10,D5,L1,V2,M1} { domain( multiplication( X, Y ) )
% 0.82/1.18 = domain( multiplication( X, domain( Y ) ) ) }.
% 0.82/1.18 substitution0:
% 0.82/1.18 X := X
% 0.82/1.18 Y := Y
% 0.82/1.18 end
% 0.82/1.18
% 0.82/1.18 subsumption: (14) {G0,W10,D5,L1,V2,M1} I { domain( multiplication( X,
% 0.82/1.19 domain( Y ) ) ) ==> domain( multiplication( X, Y ) ) }.
% 0.82/1.19 parent0: (429) {G0,W10,D5,L1,V2,M1} { domain( multiplication( X, domain( Y
% 0.82/1.19 ) ) ) = domain( multiplication( X, Y ) ) }.
% 0.82/1.19 substitution0:
% 0.82/1.19 X := X
% 0.82/1.19 Y := Y
% 0.82/1.19 end
% 0.82/1.19 permutation0:
% 0.82/1.19 0 ==> 0
% 0.82/1.19 end
% 0.82/1.19
% 0.82/1.19 subsumption: (16) {G0,W4,D3,L1,V0,M1} I { domain( zero ) ==> zero }.
% 0.82/1.19 parent0: (360) {G0,W4,D3,L1,V0,M1} { domain( zero ) = zero }.
% 0.82/1.19 substitution0:
% 0.82/1.19 end
% 0.82/1.19 permutation0:
% 0.82/1.19 0 ==> 0
% 0.82/1.19 end
% 0.82/1.19
% 0.82/1.19 subsumption: (18) {G0,W6,D4,L1,V0,M1} I { multiplication( skol1, domain(
% 0.82/1.19 skol2 ) ) ==> zero }.
% 0.82/1.19 parent0: (362) {G0,W6,D4,L1,V0,M1} { multiplication( skol1, domain( skol2
% 0.82/1.19 ) ) = zero }.
% 0.82/1.19 substitution0:
% 0.82/1.19 end
% 0.82/1.19 permutation0:
% 0.82/1.19 0 ==> 0
% 0.82/1.19 end
% 0.82/1.19
% 0.82/1.19 subsumption: (19) {G0,W5,D3,L1,V0,M1} I { ! multiplication( skol1, skol2 )
% 0.82/1.19 ==> zero }.
% 0.82/1.19 parent0: (363) {G0,W5,D3,L1,V0,M1} { ! multiplication( skol1, skol2 ) =
% 0.82/1.19 zero }.
% 0.82/1.19 substitution0:
% 0.82/1.19 end
% 0.82/1.19 permutation0:
% 0.82/1.19 0 ==> 0
% 0.82/1.19 end
% 0.82/1.19
% 0.82/1.19 eqswap: (483) {G0,W8,D3,L2,V2,M2} { Y ==> addition( X, Y ), ! leq( X, Y )
% 0.82/1.19 }.
% 0.82/1.19 parent0[1]: (11) {G0,W8,D3,L2,V2,M2} I { ! leq( X, Y ), addition( X, Y )
% 0.82/1.19 ==> Y }.
% 0.82/1.19 substitution0:
% 0.82/1.19 X := X
% 0.82/1.19 Y := Y
% 0.82/1.19 end
% 0.82/1.19
% 0.82/1.19 paramod: (485) {G1,W6,D2,L2,V1,M2} { zero ==> X, ! leq( X, zero ) }.
% 0.82/1.19 parent0[0]: (2) {G0,W5,D3,L1,V1,M1} I { addition( X, zero ) ==> X }.
% 0.82/1.19 parent1[0; 2]: (483) {G0,W8,D3,L2,V2,M2} { Y ==> addition( X, Y ), ! leq(
% 0.82/1.19 X, Y ) }.
% 0.82/1.19 substitution0:
% 0.82/1.19 X := X
% 0.82/1.19 end
% 0.82/1.19 substitution1:
% 0.82/1.19 X := X
% 0.82/1.19 Y := zero
% 0.82/1.19 end
% 0.82/1.19
% 0.82/1.19 subsumption: (53) {G1,W6,D2,L2,V1,M2} P(11,2) { zero = X, ! leq( X, zero )
% 0.82/1.19 }.
% 0.82/1.19 parent0: (485) {G1,W6,D2,L2,V1,M2} { zero ==> X, ! leq( X, zero ) }.
% 0.82/1.19 substitution0:
% 0.82/1.19 X := X
% 0.82/1.19 end
% 0.82/1.19 permutation0:
% 0.82/1.19 0 ==> 0
% 0.82/1.19 1 ==> 1
% 0.82/1.19 end
% 0.82/1.19
% 0.82/1.19 eqswap: (487) {G0,W11,D5,L1,V1,M1} { multiplication( domain( X ), X ) ==>
% 0.82/1.19 addition( X, multiplication( domain( X ), X ) ) }.
% 0.82/1.19 parent0[0]: (13) {G0,W11,D5,L1,V1,M1} I { addition( X, multiplication(
% 0.82/1.19 domain( X ), X ) ) ==> multiplication( domain( X ), X ) }.
% 0.82/1.19 substitution0:
% 0.82/1.19 X := X
% 0.82/1.19 end
% 0.82/1.19
% 0.82/1.19 eqswap: (488) {G0,W8,D3,L2,V2,M2} { ! Y ==> addition( X, Y ), leq( X, Y )
% 0.82/1.19 }.
% 0.82/1.19 parent0[0]: (12) {G0,W8,D3,L2,V2,M2} I { ! addition( X, Y ) ==> Y, leq( X,
% 0.82/1.19 Y ) }.
% 0.82/1.19 substitution0:
% 0.82/1.19 X := X
% 0.82/1.19 Y := Y
% 0.82/1.19 end
% 0.82/1.19
% 0.82/1.19 resolution: (489) {G1,W6,D4,L1,V1,M1} { leq( X, multiplication( domain( X
% 0.82/1.19 ), X ) ) }.
% 0.82/1.19 parent0[0]: (488) {G0,W8,D3,L2,V2,M2} { ! Y ==> addition( X, Y ), leq( X,
% 0.82/1.19 Y ) }.
% 0.82/1.19 parent1[0]: (487) {G0,W11,D5,L1,V1,M1} { multiplication( domain( X ), X )
% 0.82/1.19 ==> addition( X, multiplication( domain( X ), X ) ) }.
% 0.82/1.19 substitution0:
% 0.82/1.19 X := X
% 0.82/1.19 Y := multiplication( domain( X ), X )
% 0.82/1.19 end
% 0.82/1.19 substitution1:
% 0.82/1.19 X := X
% 0.82/1.19 end
% 0.82/1.19
% 0.82/1.19 subsumption: (89) {G1,W6,D4,L1,V1,M1} R(13,12) { leq( X, multiplication(
% 0.82/1.19 domain( X ), X ) ) }.
% 0.82/1.19 parent0: (489) {G1,W6,D4,L1,V1,M1} { leq( X, multiplication( domain( X ),
% 0.82/1.19 X ) ) }.
% 0.82/1.19 substitution0:
% 0.82/1.19 X := X
% 0.82/1.19 end
% 0.82/1.19 permutation0:
% 0.82/1.19 0 ==> 0
% 0.82/1.19 end
% 0.82/1.19
% 0.82/1.19 eqswap: (490) {G1,W6,D2,L2,V1,M2} { X = zero, ! leq( X, zero ) }.
% 0.82/1.19 parent0[0]: (53) {G1,W6,D2,L2,V1,M2} P(11,2) { zero = X, ! leq( X, zero )
% 0.82/1.19 }.
% 0.82/1.19 substitution0:
% 0.82/1.19 X := X
% 0.82/1.19 end
% 0.82/1.19
% 0.82/1.19 eqswap: (491) {G0,W5,D3,L1,V0,M1} { ! zero ==> multiplication( skol1,
% 0.82/1.19 skol2 ) }.
% 0.82/1.19 parent0[0]: (19) {G0,W5,D3,L1,V0,M1} I { ! multiplication( skol1, skol2 )
% 0.82/1.19 ==> zero }.
% 0.82/1.19 substitution0:
% 0.82/1.19 end
% 0.82/1.19
% 0.82/1.19 paramod: (493) {G1,W8,D3,L2,V0,M2} { ! zero ==> zero, ! leq(
% 0.82/1.19 multiplication( skol1, skol2 ), zero ) }.
% 0.82/1.19 parent0[0]: (490) {G1,W6,D2,L2,V1,M2} { X = zero, ! leq( X, zero ) }.
% 0.82/1.19 parent1[0; 3]: (491) {G0,W5,D3,L1,V0,M1} { ! zero ==> multiplication(
% 0.82/1.19 skol1, skol2 ) }.
% 0.82/1.19 substitution0:
% 0.82/1.19 X := multiplication( skol1, skol2 )
% 0.82/1.19 end
% 0.82/1.19 substitution1:
% 0.82/1.19 end
% 0.82/1.19
% 0.82/1.19 eqrefl: (547) {G0,W5,D3,L1,V0,M1} { ! leq( multiplication( skol1, skol2 )
% 0.82/1.19 , zero ) }.
% 0.82/1.19 parent0[0]: (493) {G1,W8,D3,L2,V0,M2} { ! zero ==> zero, ! leq(
% 0.82/1.19 multiplication( skol1, skol2 ), zero ) }.
% 0.82/1.19 substitution0:
% 0.82/1.19 end
% 0.82/1.19
% 0.82/1.19 subsumption: (114) {G2,W5,D3,L1,V0,M1} P(53,19);q { ! leq( multiplication(
% 0.82/1.19 skol1, skol2 ), zero ) }.
% 0.82/1.19 parent0: (547) {G0,W5,D3,L1,V0,M1} { ! leq( multiplication( skol1, skol2 )
% 0.82/1.19 , zero ) }.
% 0.82/1.19 substitution0:
% 0.82/1.19 end
% 0.82/1.19 permutation0:
% 0.82/1.19 0 ==> 0
% 0.82/1.19 end
% 0.82/1.19
% 0.82/1.19 eqswap: (549) {G0,W10,D5,L1,V2,M1} { domain( multiplication( X, Y ) ) ==>
% 0.82/1.19 domain( multiplication( X, domain( Y ) ) ) }.
% 0.82/1.19 parent0[0]: (14) {G0,W10,D5,L1,V2,M1} I { domain( multiplication( X, domain
% 0.82/1.19 ( Y ) ) ) ==> domain( multiplication( X, Y ) ) }.
% 0.82/1.19 substitution0:
% 0.82/1.19 X := X
% 0.82/1.19 Y := Y
% 0.82/1.19 end
% 0.82/1.19
% 0.82/1.19 paramod: (552) {G1,W7,D4,L1,V0,M1} { domain( multiplication( skol1, skol2
% 0.82/1.19 ) ) ==> domain( zero ) }.
% 0.82/1.19 parent0[0]: (18) {G0,W6,D4,L1,V0,M1} I { multiplication( skol1, domain(
% 0.82/1.19 skol2 ) ) ==> zero }.
% 0.82/1.19 parent1[0; 6]: (549) {G0,W10,D5,L1,V2,M1} { domain( multiplication( X, Y )
% 0.82/1.19 ) ==> domain( multiplication( X, domain( Y ) ) ) }.
% 0.82/1.19 substitution0:
% 0.82/1.19 end
% 0.82/1.19 substitution1:
% 0.82/1.19 X := skol1
% 0.82/1.19 Y := skol2
% 0.82/1.19 end
% 0.82/1.19
% 0.82/1.19 paramod: (553) {G1,W6,D4,L1,V0,M1} { domain( multiplication( skol1, skol2
% 0.82/1.19 ) ) ==> zero }.
% 0.82/1.19 parent0[0]: (16) {G0,W4,D3,L1,V0,M1} I { domain( zero ) ==> zero }.
% 0.82/1.19 parent1[0; 5]: (552) {G1,W7,D4,L1,V0,M1} { domain( multiplication( skol1,
% 0.82/1.19 skol2 ) ) ==> domain( zero ) }.
% 0.82/1.19 substitution0:
% 0.82/1.19 end
% 0.82/1.19 substitution1:
% 0.82/1.19 end
% 0.82/1.19
% 0.82/1.19 subsumption: (130) {G1,W6,D4,L1,V0,M1} P(18,14);d(16) { domain(
% 0.82/1.19 multiplication( skol1, skol2 ) ) ==> zero }.
% 0.82/1.19 parent0: (553) {G1,W6,D4,L1,V0,M1} { domain( multiplication( skol1, skol2
% 0.82/1.19 ) ) ==> zero }.
% 0.82/1.19 substitution0:
% 0.82/1.19 end
% 0.82/1.19 permutation0:
% 0.82/1.19 0 ==> 0
% 0.82/1.19 end
% 0.82/1.19
% 0.82/1.19 paramod: (559) {G2,W9,D4,L1,V0,M1} { leq( multiplication( skol1, skol2 ),
% 0.82/1.19 multiplication( zero, multiplication( skol1, skol2 ) ) ) }.
% 0.82/1.19 parent0[0]: (130) {G1,W6,D4,L1,V0,M1} P(18,14);d(16) { domain(
% 0.82/1.19 multiplication( skol1, skol2 ) ) ==> zero }.
% 0.82/1.19 parent1[0; 5]: (89) {G1,W6,D4,L1,V1,M1} R(13,12) { leq( X, multiplication(
% 0.82/1.19 domain( X ), X ) ) }.
% 0.82/1.19 substitution0:
% 0.82/1.19 end
% 0.82/1.19 substitution1:
% 0.82/1.19 X := multiplication( skol1, skol2 )
% 0.82/1.19 end
% 0.82/1.19
% 0.82/1.19 paramod: (560) {G1,W9,D4,L1,V0,M1} { leq( multiplication( skol1, skol2 ),
% 0.82/1.19 multiplication( multiplication( zero, skol1 ), skol2 ) ) }.
% 0.82/1.19 parent0[0]: (4) {G0,W11,D4,L1,V3,M1} I { multiplication( X, multiplication
% 0.82/1.19 ( Y, Z ) ) ==> multiplication( multiplication( X, Y ), Z ) }.
% 0.82/1.19 parent1[0; 4]: (559) {G2,W9,D4,L1,V0,M1} { leq( multiplication( skol1,
% 0.82/1.19 skol2 ), multiplication( zero, multiplication( skol1, skol2 ) ) ) }.
% 0.82/1.19 substitution0:
% 0.82/1.19 X := zero
% 0.82/1.19 Y := skol1
% 0.82/1.19 Z := skol2
% 0.82/1.19 end
% 0.82/1.19 substitution1:
% 0.82/1.19 end
% 0.82/1.19
% 0.82/1.19 paramod: (561) {G1,W7,D3,L1,V0,M1} { leq( multiplication( skol1, skol2 ),
% 0.82/1.19 multiplication( zero, skol2 ) ) }.
% 0.82/1.19 parent0[0]: (10) {G0,W5,D3,L1,V1,M1} I { multiplication( zero, X ) ==> zero
% 0.82/1.19 }.
% 0.82/1.19 parent1[0; 5]: (560) {G1,W9,D4,L1,V0,M1} { leq( multiplication( skol1,
% 0.82/1.19 skol2 ), multiplication( multiplication( zero, skol1 ), skol2 ) ) }.
% 0.82/1.19 substitution0:
% 0.82/1.19 X := skol1
% 0.82/1.19 end
% 0.82/1.19 substitution1:
% 0.82/1.19 end
% 0.82/1.19
% 0.82/1.19 paramod: (563) {G1,W5,D3,L1,V0,M1} { leq( multiplication( skol1, skol2 ),
% 0.82/1.19 zero ) }.
% 0.82/1.19 parent0[0]: (10) {G0,W5,D3,L1,V1,M1} I { multiplication( zero, X ) ==> zero
% 0.82/1.19 }.
% 0.82/1.19 parent1[0; 4]: (561) {G1,W7,D3,L1,V0,M1} { leq( multiplication( skol1,
% 0.82/1.19 skol2 ), multiplication( zero, skol2 ) ) }.
% 0.82/1.19 substitution0:
% 0.82/1.19 X := skol2
% 0.82/1.19 end
% 0.82/1.19 substitution1:
% 0.82/1.19 end
% 0.82/1.19
% 0.82/1.19 resolution: (564) {G2,W0,D0,L0,V0,M0} { }.
% 0.82/1.19 parent0[0]: (114) {G2,W5,D3,L1,V0,M1} P(53,19);q { ! leq( multiplication(
% 0.82/1.19 skol1, skol2 ), zero ) }.
% 0.82/1.19 parent1[0]: (563) {G1,W5,D3,L1,V0,M1} { leq( multiplication( skol1, skol2
% 0.82/1.19 ), zero ) }.
% 0.82/1.19 substitution0:
% 0.82/1.19 end
% 0.82/1.19 substitution1:
% 0.82/1.19 end
% 0.82/1.19
% 0.82/1.19 subsumption: (342) {G3,W0,D0,L0,V0,M0} P(130,89);d(4);d(10);d(10);r(114) {
% 0.82/1.19 }.
% 0.82/1.19 parent0: (564) {G2,W0,D0,L0,V0,M0} { }.
% 0.82/1.19 substitution0:
% 0.82/1.19 end
% 0.82/1.19 permutation0:
% 0.82/1.19 end
% 0.82/1.19
% 0.82/1.19 Proof check complete!
% 0.82/1.19
% 0.82/1.19 Memory use:
% 0.82/1.19
% 0.82/1.19 space for terms: 3955
% 0.82/1.19 space for clauses: 23760
% 0.82/1.19
% 0.82/1.19
% 0.82/1.19 clauses generated: 2124
% 0.82/1.19 clauses kept: 343
% 0.82/1.19 clauses selected: 90
% 0.82/1.19 clauses deleted: 0
% 0.82/1.19 clauses inuse deleted: 0
% 0.82/1.19
% 0.82/1.19 subsentry: 3005
% 0.82/1.19 literals s-matched: 2391
% 0.82/1.19 literals matched: 2390
% 0.82/1.19 full subsumption: 73
% 0.82/1.19
% 0.82/1.19 checksum: 505196751
% 0.82/1.19
% 0.82/1.19
% 0.82/1.19 Bliksem ended
%------------------------------------------------------------------------------