TSTP Solution File: KLE065+1 by Bliksem---1.12
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%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : KLE065+1 : 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 01:36:59 EDT 2022
% Result : Theorem 0.73s 1.09s
% Output : Refutation 0.73s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : KLE065+1 : TPTP v8.1.0. Released v4.0.0.
% 0.11/0.12 % Command : bliksem %s
% 0.13/0.33 % Computer : n009.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % DateTime : Thu Jun 16 07:35:37 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.73/1.09 *** allocated 10000 integers for termspace/termends
% 0.73/1.09 *** allocated 10000 integers for clauses
% 0.73/1.09 *** allocated 10000 integers for justifications
% 0.73/1.09 Bliksem 1.12
% 0.73/1.09
% 0.73/1.09
% 0.73/1.09 Automatic Strategy Selection
% 0.73/1.09
% 0.73/1.09
% 0.73/1.09 Clauses:
% 0.73/1.09
% 0.73/1.09 { addition( X, Y ) = addition( Y, X ) }.
% 0.73/1.09 { addition( Z, addition( Y, X ) ) = addition( addition( Z, Y ), X ) }.
% 0.73/1.09 { addition( X, zero ) = X }.
% 0.73/1.09 { addition( X, X ) = X }.
% 0.73/1.09 { multiplication( X, multiplication( Y, Z ) ) = multiplication(
% 0.73/1.09 multiplication( X, Y ), Z ) }.
% 0.73/1.09 { multiplication( X, one ) = X }.
% 0.73/1.09 { multiplication( one, X ) = X }.
% 0.73/1.09 { multiplication( X, addition( Y, Z ) ) = addition( multiplication( X, Y )
% 0.73/1.09 , multiplication( X, Z ) ) }.
% 0.73/1.09 { multiplication( addition( X, Y ), Z ) = addition( multiplication( X, Z )
% 0.73/1.09 , multiplication( Y, Z ) ) }.
% 0.73/1.09 { multiplication( X, zero ) = zero }.
% 0.73/1.09 { multiplication( zero, X ) = zero }.
% 0.73/1.09 { ! leq( X, Y ), addition( X, Y ) = Y }.
% 0.73/1.09 { ! addition( X, Y ) = Y, leq( X, Y ) }.
% 0.73/1.09 { addition( X, multiplication( domain( X ), X ) ) = multiplication( domain
% 0.73/1.09 ( X ), X ) }.
% 0.73/1.09 { domain( multiplication( X, Y ) ) = domain( multiplication( X, domain( Y )
% 0.73/1.09 ) ) }.
% 0.73/1.09 { addition( domain( X ), one ) = one }.
% 0.73/1.09 { domain( zero ) = zero }.
% 0.73/1.09 { domain( addition( X, Y ) ) = addition( domain( X ), domain( Y ) ) }.
% 0.73/1.09 { multiplication( skol1, skol2 ) = zero }.
% 0.73/1.09 { ! multiplication( skol1, domain( skol2 ) ) = zero }.
% 0.73/1.09
% 0.73/1.09 percentage equality = 0.909091, percentage horn = 1.000000
% 0.73/1.09 This is a pure equality problem
% 0.73/1.09
% 0.73/1.09
% 0.73/1.09
% 0.73/1.09 Options Used:
% 0.73/1.09
% 0.73/1.09 useres = 1
% 0.73/1.09 useparamod = 1
% 0.73/1.09 useeqrefl = 1
% 0.73/1.09 useeqfact = 1
% 0.73/1.09 usefactor = 1
% 0.73/1.09 usesimpsplitting = 0
% 0.73/1.09 usesimpdemod = 5
% 0.73/1.09 usesimpres = 3
% 0.73/1.09
% 0.73/1.09 resimpinuse = 1000
% 0.73/1.09 resimpclauses = 20000
% 0.73/1.09 substype = eqrewr
% 0.73/1.09 backwardsubs = 1
% 0.73/1.09 selectoldest = 5
% 0.73/1.09
% 0.73/1.09 litorderings [0] = split
% 0.73/1.09 litorderings [1] = extend the termordering, first sorting on arguments
% 0.73/1.09
% 0.73/1.09 termordering = kbo
% 0.73/1.09
% 0.73/1.09 litapriori = 0
% 0.73/1.09 termapriori = 1
% 0.73/1.09 litaposteriori = 0
% 0.73/1.09 termaposteriori = 0
% 0.73/1.09 demodaposteriori = 0
% 0.73/1.09 ordereqreflfact = 0
% 0.73/1.09
% 0.73/1.09 litselect = negord
% 0.73/1.09
% 0.73/1.09 maxweight = 15
% 0.73/1.09 maxdepth = 30000
% 0.73/1.09 maxlength = 115
% 0.73/1.09 maxnrvars = 195
% 0.73/1.09 excuselevel = 1
% 0.73/1.09 increasemaxweight = 1
% 0.73/1.09
% 0.73/1.09 maxselected = 10000000
% 0.73/1.09 maxnrclauses = 10000000
% 0.73/1.09
% 0.73/1.09 showgenerated = 0
% 0.73/1.09 showkept = 0
% 0.73/1.09 showselected = 0
% 0.73/1.09 showdeleted = 0
% 0.73/1.09 showresimp = 1
% 0.73/1.09 showstatus = 2000
% 0.73/1.09
% 0.73/1.09 prologoutput = 0
% 0.73/1.09 nrgoals = 5000000
% 0.73/1.09 totalproof = 1
% 0.73/1.09
% 0.73/1.09 Symbols occurring in the translation:
% 0.73/1.09
% 0.73/1.09 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.73/1.09 . [1, 2] (w:1, o:21, a:1, s:1, b:0),
% 0.73/1.09 ! [4, 1] (w:0, o:15, a:1, s:1, b:0),
% 0.73/1.09 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.73/1.09 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.73/1.09 addition [37, 2] (w:1, o:45, a:1, s:1, b:0),
% 0.73/1.09 zero [39, 0] (w:1, o:9, a:1, s:1, b:0),
% 0.73/1.09 multiplication [40, 2] (w:1, o:47, a:1, s:1, b:0),
% 0.73/1.09 one [41, 0] (w:1, o:10, a:1, s:1, b:0),
% 0.73/1.09 leq [42, 2] (w:1, o:46, a:1, s:1, b:0),
% 0.73/1.09 domain [44, 1] (w:1, o:20, a:1, s:1, b:0),
% 0.73/1.09 skol1 [46, 0] (w:1, o:13, a:1, s:1, b:1),
% 0.73/1.09 skol2 [47, 0] (w:1, o:14, a:1, s:1, b:1).
% 0.73/1.09
% 0.73/1.09
% 0.73/1.09 Starting Search:
% 0.73/1.09
% 0.73/1.09 *** allocated 15000 integers for clauses
% 0.73/1.09 *** allocated 22500 integers for clauses
% 0.73/1.09 *** allocated 33750 integers for clauses
% 0.73/1.09
% 0.73/1.09 Bliksems!, er is een bewijs:
% 0.73/1.09 % SZS status Theorem
% 0.73/1.09 % SZS output start Refutation
% 0.73/1.09
% 0.73/1.09 (2) {G0,W5,D3,L1,V1,M1} I { addition( X, zero ) ==> X }.
% 0.73/1.09 (3) {G0,W5,D3,L1,V1,M1} I { addition( X, X ) ==> X }.
% 0.73/1.09 (10) {G0,W5,D3,L1,V1,M1} I { multiplication( zero, X ) ==> zero }.
% 0.73/1.09 (11) {G0,W8,D3,L2,V2,M2} I { ! leq( X, Y ), addition( X, Y ) ==> Y }.
% 0.73/1.09 (12) {G0,W8,D3,L2,V2,M2} I { ! addition( X, Y ) ==> Y, leq( X, Y ) }.
% 0.73/1.09 (13) {G0,W11,D5,L1,V1,M1} I { addition( X, multiplication( domain( X ), X )
% 0.73/1.09 ) ==> multiplication( domain( X ), X ) }.
% 0.73/1.09 (14) {G0,W10,D5,L1,V2,M1} I { domain( multiplication( X, domain( Y ) ) )
% 0.73/1.09 ==> domain( multiplication( X, Y ) ) }.
% 0.73/1.09 (16) {G0,W4,D3,L1,V0,M1} I { domain( zero ) ==> zero }.
% 0.73/1.09 (18) {G0,W5,D3,L1,V0,M1} I { multiplication( skol1, skol2 ) ==> zero }.
% 0.73/1.09 (19) {G0,W6,D4,L1,V0,M1} I { ! multiplication( skol1, domain( skol2 ) ) ==>
% 0.73/1.09 zero }.
% 0.73/1.09 (30) {G1,W3,D2,L1,V1,M1} R(12,3) { leq( X, X ) }.
% 0.73/1.09 (55) {G1,W6,D2,L2,V1,M2} P(11,2) { zero = X, ! leq( X, zero ) }.
% 0.73/1.09 (90) {G1,W6,D4,L1,V1,M1} R(13,12) { leq( X, multiplication( domain( X ), X
% 0.73/1.09 ) ) }.
% 0.73/1.09 (119) {G2,W6,D4,L1,V0,M1} P(55,19);q { ! leq( multiplication( skol1, domain
% 0.73/1.09 ( skol2 ) ), zero ) }.
% 0.73/1.09 (326) {G2,W7,D3,L2,V1,M2} P(55,90);d(10) { ! leq( domain( X ), zero ), leq
% 0.73/1.09 ( X, zero ) }.
% 0.73/1.09 (424) {G3,W0,D0,L0,V0,M0} R(326,119);d(14);d(18);d(16);r(30) { }.
% 0.73/1.09
% 0.73/1.09
% 0.73/1.09 % SZS output end Refutation
% 0.73/1.09 found a proof!
% 0.73/1.09
% 0.73/1.09
% 0.73/1.09 Unprocessed initial clauses:
% 0.73/1.09
% 0.73/1.09 (426) {G0,W7,D3,L1,V2,M1} { addition( X, Y ) = addition( Y, X ) }.
% 0.73/1.09 (427) {G0,W11,D4,L1,V3,M1} { addition( Z, addition( Y, X ) ) = addition(
% 0.73/1.09 addition( Z, Y ), X ) }.
% 0.73/1.09 (428) {G0,W5,D3,L1,V1,M1} { addition( X, zero ) = X }.
% 0.73/1.09 (429) {G0,W5,D3,L1,V1,M1} { addition( X, X ) = X }.
% 0.73/1.09 (430) {G0,W11,D4,L1,V3,M1} { multiplication( X, multiplication( Y, Z ) ) =
% 0.73/1.09 multiplication( multiplication( X, Y ), Z ) }.
% 0.73/1.09 (431) {G0,W5,D3,L1,V1,M1} { multiplication( X, one ) = X }.
% 0.73/1.09 (432) {G0,W5,D3,L1,V1,M1} { multiplication( one, X ) = X }.
% 0.73/1.09 (433) {G0,W13,D4,L1,V3,M1} { multiplication( X, addition( Y, Z ) ) =
% 0.73/1.09 addition( multiplication( X, Y ), multiplication( X, Z ) ) }.
% 0.73/1.09 (434) {G0,W13,D4,L1,V3,M1} { multiplication( addition( X, Y ), Z ) =
% 0.73/1.09 addition( multiplication( X, Z ), multiplication( Y, Z ) ) }.
% 0.73/1.09 (435) {G0,W5,D3,L1,V1,M1} { multiplication( X, zero ) = zero }.
% 0.73/1.09 (436) {G0,W5,D3,L1,V1,M1} { multiplication( zero, X ) = zero }.
% 0.73/1.09 (437) {G0,W8,D3,L2,V2,M2} { ! leq( X, Y ), addition( X, Y ) = Y }.
% 0.73/1.09 (438) {G0,W8,D3,L2,V2,M2} { ! addition( X, Y ) = Y, leq( X, Y ) }.
% 0.73/1.09 (439) {G0,W11,D5,L1,V1,M1} { addition( X, multiplication( domain( X ), X )
% 0.73/1.09 ) = multiplication( domain( X ), X ) }.
% 0.73/1.09 (440) {G0,W10,D5,L1,V2,M1} { domain( multiplication( X, Y ) ) = domain(
% 0.73/1.09 multiplication( X, domain( Y ) ) ) }.
% 0.73/1.09 (441) {G0,W6,D4,L1,V1,M1} { addition( domain( X ), one ) = one }.
% 0.73/1.09 (442) {G0,W4,D3,L1,V0,M1} { domain( zero ) = zero }.
% 0.73/1.09 (443) {G0,W10,D4,L1,V2,M1} { domain( addition( X, Y ) ) = addition( domain
% 0.73/1.09 ( X ), domain( Y ) ) }.
% 0.73/1.09 (444) {G0,W5,D3,L1,V0,M1} { multiplication( skol1, skol2 ) = zero }.
% 0.73/1.09 (445) {G0,W6,D4,L1,V0,M1} { ! multiplication( skol1, domain( skol2 ) ) =
% 0.73/1.09 zero }.
% 0.73/1.09
% 0.73/1.09
% 0.73/1.09 Total Proof:
% 0.73/1.09
% 0.73/1.09 subsumption: (2) {G0,W5,D3,L1,V1,M1} I { addition( X, zero ) ==> X }.
% 0.73/1.09 parent0: (428) {G0,W5,D3,L1,V1,M1} { addition( X, zero ) = X }.
% 0.73/1.09 substitution0:
% 0.73/1.09 X := X
% 0.73/1.09 end
% 0.73/1.09 permutation0:
% 0.73/1.09 0 ==> 0
% 0.73/1.09 end
% 0.73/1.09
% 0.73/1.09 subsumption: (3) {G0,W5,D3,L1,V1,M1} I { addition( X, X ) ==> X }.
% 0.73/1.09 parent0: (429) {G0,W5,D3,L1,V1,M1} { addition( X, X ) = X }.
% 0.73/1.09 substitution0:
% 0.73/1.09 X := X
% 0.73/1.09 end
% 0.73/1.09 permutation0:
% 0.73/1.09 0 ==> 0
% 0.73/1.09 end
% 0.73/1.09
% 0.73/1.09 subsumption: (10) {G0,W5,D3,L1,V1,M1} I { multiplication( zero, X ) ==>
% 0.73/1.09 zero }.
% 0.73/1.09 parent0: (436) {G0,W5,D3,L1,V1,M1} { multiplication( zero, X ) = zero }.
% 0.73/1.09 substitution0:
% 0.73/1.09 X := X
% 0.73/1.09 end
% 0.73/1.09 permutation0:
% 0.73/1.09 0 ==> 0
% 0.73/1.09 end
% 0.73/1.09
% 0.73/1.09 subsumption: (11) {G0,W8,D3,L2,V2,M2} I { ! leq( X, Y ), addition( X, Y )
% 0.73/1.09 ==> Y }.
% 0.73/1.09 parent0: (437) {G0,W8,D3,L2,V2,M2} { ! leq( X, Y ), addition( X, Y ) = Y
% 0.73/1.09 }.
% 0.73/1.09 substitution0:
% 0.73/1.09 X := X
% 0.73/1.09 Y := Y
% 0.73/1.09 end
% 0.73/1.09 permutation0:
% 0.73/1.09 0 ==> 0
% 0.73/1.09 1 ==> 1
% 0.73/1.09 end
% 0.73/1.09
% 0.73/1.09 subsumption: (12) {G0,W8,D3,L2,V2,M2} I { ! addition( X, Y ) ==> Y, leq( X
% 0.73/1.09 , Y ) }.
% 0.73/1.09 parent0: (438) {G0,W8,D3,L2,V2,M2} { ! addition( X, Y ) = Y, leq( X, Y )
% 0.73/1.09 }.
% 0.73/1.09 substitution0:
% 0.73/1.09 X := X
% 0.73/1.09 Y := Y
% 0.73/1.09 end
% 0.73/1.09 permutation0:
% 0.73/1.09 0 ==> 0
% 0.73/1.09 1 ==> 1
% 0.73/1.09 end
% 0.73/1.09
% 0.73/1.09 subsumption: (13) {G0,W11,D5,L1,V1,M1} I { addition( X, multiplication(
% 0.73/1.09 domain( X ), X ) ) ==> multiplication( domain( X ), X ) }.
% 0.73/1.09 parent0: (439) {G0,W11,D5,L1,V1,M1} { addition( X, multiplication( domain
% 0.73/1.09 ( X ), X ) ) = multiplication( domain( X ), X ) }.
% 0.73/1.09 substitution0:
% 0.73/1.09 X := X
% 0.73/1.09 end
% 0.73/1.09 permutation0:
% 0.73/1.09 0 ==> 0
% 0.73/1.09 end
% 0.73/1.09
% 0.73/1.09 eqswap: (510) {G0,W10,D5,L1,V2,M1} { domain( multiplication( X, domain( Y
% 0.73/1.09 ) ) ) = domain( multiplication( X, Y ) ) }.
% 0.73/1.09 parent0[0]: (440) {G0,W10,D5,L1,V2,M1} { domain( multiplication( X, Y ) )
% 0.73/1.09 = domain( multiplication( X, domain( Y ) ) ) }.
% 0.73/1.09 substitution0:
% 0.73/1.09 X := X
% 0.73/1.09 Y := Y
% 0.73/1.09 end
% 0.73/1.09
% 0.73/1.09 subsumption: (14) {G0,W10,D5,L1,V2,M1} I { domain( multiplication( X,
% 0.73/1.09 domain( Y ) ) ) ==> domain( multiplication( X, Y ) ) }.
% 0.73/1.09 parent0: (510) {G0,W10,D5,L1,V2,M1} { domain( multiplication( X, domain( Y
% 0.73/1.09 ) ) ) = domain( multiplication( X, Y ) ) }.
% 0.73/1.09 substitution0:
% 0.73/1.09 X := X
% 0.73/1.09 Y := Y
% 0.73/1.09 end
% 0.73/1.09 permutation0:
% 0.73/1.09 0 ==> 0
% 0.73/1.09 end
% 0.73/1.09
% 0.73/1.09 subsumption: (16) {G0,W4,D3,L1,V0,M1} I { domain( zero ) ==> zero }.
% 0.73/1.09 parent0: (442) {G0,W4,D3,L1,V0,M1} { domain( zero ) = zero }.
% 0.73/1.09 substitution0:
% 0.73/1.09 end
% 0.73/1.09 permutation0:
% 0.73/1.09 0 ==> 0
% 0.73/1.09 end
% 0.73/1.09
% 0.73/1.09 subsumption: (18) {G0,W5,D3,L1,V0,M1} I { multiplication( skol1, skol2 )
% 0.73/1.09 ==> zero }.
% 0.73/1.09 parent0: (444) {G0,W5,D3,L1,V0,M1} { multiplication( skol1, skol2 ) = zero
% 0.73/1.09 }.
% 0.73/1.09 substitution0:
% 0.73/1.09 end
% 0.73/1.09 permutation0:
% 0.73/1.09 0 ==> 0
% 0.73/1.09 end
% 0.73/1.09
% 0.73/1.09 subsumption: (19) {G0,W6,D4,L1,V0,M1} I { ! multiplication( skol1, domain(
% 0.73/1.09 skol2 ) ) ==> zero }.
% 0.73/1.09 parent0: (445) {G0,W6,D4,L1,V0,M1} { ! multiplication( skol1, domain(
% 0.73/1.09 skol2 ) ) = zero }.
% 0.73/1.09 substitution0:
% 0.73/1.09 end
% 0.73/1.09 permutation0:
% 0.73/1.09 0 ==> 0
% 0.73/1.09 end
% 0.73/1.09
% 0.73/1.09 eqswap: (564) {G0,W8,D3,L2,V2,M2} { ! Y ==> addition( X, Y ), leq( X, Y )
% 0.73/1.09 }.
% 0.73/1.09 parent0[0]: (12) {G0,W8,D3,L2,V2,M2} I { ! addition( X, Y ) ==> Y, leq( X,
% 0.73/1.09 Y ) }.
% 0.73/1.09 substitution0:
% 0.73/1.09 X := X
% 0.73/1.09 Y := Y
% 0.73/1.09 end
% 0.73/1.09
% 0.73/1.09 eqswap: (565) {G0,W5,D3,L1,V1,M1} { X ==> addition( X, X ) }.
% 0.73/1.09 parent0[0]: (3) {G0,W5,D3,L1,V1,M1} I { addition( X, X ) ==> X }.
% 0.73/1.09 substitution0:
% 0.73/1.09 X := X
% 0.73/1.09 end
% 0.73/1.09
% 0.73/1.09 resolution: (566) {G1,W3,D2,L1,V1,M1} { leq( X, X ) }.
% 0.73/1.09 parent0[0]: (564) {G0,W8,D3,L2,V2,M2} { ! Y ==> addition( X, Y ), leq( X,
% 0.73/1.09 Y ) }.
% 0.73/1.09 parent1[0]: (565) {G0,W5,D3,L1,V1,M1} { X ==> addition( X, X ) }.
% 0.73/1.09 substitution0:
% 0.73/1.09 X := X
% 0.73/1.09 Y := X
% 0.73/1.09 end
% 0.73/1.09 substitution1:
% 0.73/1.09 X := X
% 0.73/1.09 end
% 0.73/1.09
% 0.73/1.09 subsumption: (30) {G1,W3,D2,L1,V1,M1} R(12,3) { leq( X, X ) }.
% 0.73/1.09 parent0: (566) {G1,W3,D2,L1,V1,M1} { leq( X, X ) }.
% 0.73/1.09 substitution0:
% 0.73/1.09 X := X
% 0.73/1.09 end
% 0.73/1.09 permutation0:
% 0.73/1.09 0 ==> 0
% 0.73/1.09 end
% 0.73/1.09
% 0.73/1.09 eqswap: (567) {G0,W8,D3,L2,V2,M2} { Y ==> addition( X, Y ), ! leq( X, Y )
% 0.73/1.09 }.
% 0.73/1.09 parent0[1]: (11) {G0,W8,D3,L2,V2,M2} I { ! leq( X, Y ), addition( X, Y )
% 0.73/1.09 ==> Y }.
% 0.73/1.09 substitution0:
% 0.73/1.09 X := X
% 0.73/1.09 Y := Y
% 0.73/1.09 end
% 0.73/1.09
% 0.73/1.09 paramod: (569) {G1,W6,D2,L2,V1,M2} { zero ==> X, ! leq( X, zero ) }.
% 0.73/1.09 parent0[0]: (2) {G0,W5,D3,L1,V1,M1} I { addition( X, zero ) ==> X }.
% 0.73/1.09 parent1[0; 2]: (567) {G0,W8,D3,L2,V2,M2} { Y ==> addition( X, Y ), ! leq(
% 0.73/1.09 X, Y ) }.
% 0.73/1.09 substitution0:
% 0.73/1.09 X := X
% 0.73/1.09 end
% 0.73/1.09 substitution1:
% 0.73/1.09 X := X
% 0.73/1.09 Y := zero
% 0.73/1.09 end
% 0.73/1.09
% 0.73/1.09 subsumption: (55) {G1,W6,D2,L2,V1,M2} P(11,2) { zero = X, ! leq( X, zero )
% 0.73/1.09 }.
% 0.73/1.09 parent0: (569) {G1,W6,D2,L2,V1,M2} { zero ==> X, ! leq( X, zero ) }.
% 0.73/1.09 substitution0:
% 0.73/1.09 X := X
% 0.73/1.09 end
% 0.73/1.09 permutation0:
% 0.73/1.09 0 ==> 0
% 0.73/1.09 1 ==> 1
% 0.73/1.09 end
% 0.73/1.09
% 0.73/1.09 eqswap: (571) {G0,W11,D5,L1,V1,M1} { multiplication( domain( X ), X ) ==>
% 0.73/1.09 addition( X, multiplication( domain( X ), X ) ) }.
% 0.73/1.09 parent0[0]: (13) {G0,W11,D5,L1,V1,M1} I { addition( X, multiplication(
% 0.73/1.09 domain( X ), X ) ) ==> multiplication( domain( X ), X ) }.
% 0.73/1.09 substitution0:
% 0.73/1.09 X := X
% 0.73/1.09 end
% 0.73/1.09
% 0.73/1.09 eqswap: (572) {G0,W8,D3,L2,V2,M2} { ! Y ==> addition( X, Y ), leq( X, Y )
% 0.73/1.09 }.
% 0.73/1.09 parent0[0]: (12) {G0,W8,D3,L2,V2,M2} I { ! addition( X, Y ) ==> Y, leq( X,
% 0.73/1.09 Y ) }.
% 0.73/1.09 substitution0:
% 0.73/1.09 X := X
% 0.73/1.09 Y := Y
% 0.73/1.09 end
% 0.73/1.09
% 0.73/1.09 resolution: (573) {G1,W6,D4,L1,V1,M1} { leq( X, multiplication( domain( X
% 0.73/1.09 ), X ) ) }.
% 0.73/1.09 parent0[0]: (572) {G0,W8,D3,L2,V2,M2} { ! Y ==> addition( X, Y ), leq( X,
% 0.73/1.09 Y ) }.
% 0.73/1.09 parent1[0]: (571) {G0,W11,D5,L1,V1,M1} { multiplication( domain( X ), X )
% 0.73/1.09 ==> addition( X, multiplication( domain( X ), X ) ) }.
% 0.73/1.09 substitution0:
% 0.73/1.09 X := X
% 0.73/1.09 Y := multiplication( domain( X ), X )
% 0.73/1.09 end
% 0.73/1.09 substitution1:
% 0.73/1.09 X := X
% 0.73/1.09 end
% 0.73/1.09
% 0.73/1.09 subsumption: (90) {G1,W6,D4,L1,V1,M1} R(13,12) { leq( X, multiplication(
% 0.73/1.09 domain( X ), X ) ) }.
% 0.73/1.09 parent0: (573) {G1,W6,D4,L1,V1,M1} { leq( X, multiplication( domain( X ),
% 0.73/1.09 X ) ) }.
% 0.73/1.09 substitution0:
% 0.73/1.09 X := X
% 0.73/1.09 end
% 0.73/1.09 permutation0:
% 0.73/1.09 0 ==> 0
% 0.73/1.09 end
% 0.73/1.09
% 0.73/1.09 eqswap: (574) {G1,W6,D2,L2,V1,M2} { X = zero, ! leq( X, zero ) }.
% 0.73/1.09 parent0[0]: (55) {G1,W6,D2,L2,V1,M2} P(11,2) { zero = X, ! leq( X, zero )
% 0.73/1.09 }.
% 0.73/1.09 substitution0:
% 0.73/1.09 X := X
% 0.73/1.09 end
% 0.73/1.09
% 0.73/1.09 eqswap: (575) {G0,W6,D4,L1,V0,M1} { ! zero ==> multiplication( skol1,
% 0.73/1.09 domain( skol2 ) ) }.
% 0.73/1.09 parent0[0]: (19) {G0,W6,D4,L1,V0,M1} I { ! multiplication( skol1, domain(
% 0.73/1.09 skol2 ) ) ==> zero }.
% 0.73/1.09 substitution0:
% 0.73/1.09 end
% 0.73/1.09
% 0.73/1.09 paramod: (577) {G1,W9,D4,L2,V0,M2} { ! zero ==> zero, ! leq(
% 0.73/1.09 multiplication( skol1, domain( skol2 ) ), zero ) }.
% 0.73/1.09 parent0[0]: (574) {G1,W6,D2,L2,V1,M2} { X = zero, ! leq( X, zero ) }.
% 0.73/1.09 parent1[0; 3]: (575) {G0,W6,D4,L1,V0,M1} { ! zero ==> multiplication(
% 0.73/1.09 skol1, domain( skol2 ) ) }.
% 0.73/1.09 substitution0:
% 0.73/1.09 X := multiplication( skol1, domain( skol2 ) )
% 0.73/1.09 end
% 0.73/1.09 substitution1:
% 0.73/1.09 end
% 0.73/1.09
% 0.73/1.09 eqrefl: (628) {G0,W6,D4,L1,V0,M1} { ! leq( multiplication( skol1, domain(
% 0.73/1.09 skol2 ) ), zero ) }.
% 0.73/1.09 parent0[0]: (577) {G1,W9,D4,L2,V0,M2} { ! zero ==> zero, ! leq(
% 0.73/1.09 multiplication( skol1, domain( skol2 ) ), zero ) }.
% 0.73/1.09 substitution0:
% 0.73/1.09 end
% 0.73/1.09
% 0.73/1.09 subsumption: (119) {G2,W6,D4,L1,V0,M1} P(55,19);q { ! leq( multiplication(
% 0.73/1.09 skol1, domain( skol2 ) ), zero ) }.
% 0.73/1.09 parent0: (628) {G0,W6,D4,L1,V0,M1} { ! leq( multiplication( skol1, domain
% 0.73/1.09 ( skol2 ) ), zero ) }.
% 0.73/1.09 substitution0:
% 0.73/1.09 end
% 0.73/1.09 permutation0:
% 0.73/1.09 0 ==> 0
% 0.73/1.09 end
% 0.73/1.09
% 0.73/1.09 eqswap: (629) {G1,W6,D2,L2,V1,M2} { X = zero, ! leq( X, zero ) }.
% 0.73/1.09 parent0[0]: (55) {G1,W6,D2,L2,V1,M2} P(11,2) { zero = X, ! leq( X, zero )
% 0.73/1.09 }.
% 0.73/1.09 substitution0:
% 0.73/1.09 X := X
% 0.73/1.09 end
% 0.73/1.09
% 0.73/1.09 paramod: (632) {G2,W9,D3,L2,V1,M2} { leq( X, multiplication( zero, X ) ),
% 0.73/1.09 ! leq( domain( X ), zero ) }.
% 0.73/1.09 parent0[0]: (629) {G1,W6,D2,L2,V1,M2} { X = zero, ! leq( X, zero ) }.
% 0.73/1.09 parent1[0; 3]: (90) {G1,W6,D4,L1,V1,M1} R(13,12) { leq( X, multiplication(
% 0.73/1.09 domain( X ), X ) ) }.
% 0.73/1.09 substitution0:
% 0.73/1.09 X := domain( X )
% 0.73/1.09 end
% 0.73/1.09 substitution1:
% 0.73/1.09 X := X
% 0.73/1.09 end
% 0.73/1.09
% 0.73/1.09 paramod: (653) {G1,W7,D3,L2,V1,M2} { leq( X, zero ), ! leq( domain( X ),
% 0.73/1.09 zero ) }.
% 0.73/1.09 parent0[0]: (10) {G0,W5,D3,L1,V1,M1} I { multiplication( zero, X ) ==> zero
% 0.73/1.09 }.
% 0.73/1.09 parent1[0; 2]: (632) {G2,W9,D3,L2,V1,M2} { leq( X, multiplication( zero, X
% 0.73/1.09 ) ), ! leq( domain( X ), zero ) }.
% 0.73/1.09 substitution0:
% 0.73/1.09 X := X
% 0.73/1.09 end
% 0.73/1.09 substitution1:
% 0.73/1.09 X := X
% 0.73/1.09 end
% 0.73/1.09
% 0.73/1.09 subsumption: (326) {G2,W7,D3,L2,V1,M2} P(55,90);d(10) { ! leq( domain( X )
% 0.73/1.09 , zero ), leq( X, zero ) }.
% 0.73/1.09 parent0: (653) {G1,W7,D3,L2,V1,M2} { leq( X, zero ), ! leq( domain( X ),
% 0.73/1.09 zero ) }.
% 0.73/1.09 substitution0:
% 0.73/1.09 X := X
% 0.73/1.09 end
% 0.73/1.09 permutation0:
% 0.73/1.09 0 ==> 1
% 0.73/1.09 1 ==> 0
% 0.73/1.09 end
% 0.73/1.09
% 0.73/1.09 resolution: (657) {G3,W7,D5,L1,V0,M1} { ! leq( domain( multiplication(
% 0.73/1.09 skol1, domain( skol2 ) ) ), zero ) }.
% 0.73/1.09 parent0[0]: (119) {G2,W6,D4,L1,V0,M1} P(55,19);q { ! leq( multiplication(
% 0.73/1.09 skol1, domain( skol2 ) ), zero ) }.
% 0.73/1.09 parent1[1]: (326) {G2,W7,D3,L2,V1,M2} P(55,90);d(10) { ! leq( domain( X ),
% 0.73/1.09 zero ), leq( X, zero ) }.
% 0.73/1.09 substitution0:
% 0.73/1.09 end
% 0.73/1.09 substitution1:
% 0.73/1.09 X := multiplication( skol1, domain( skol2 ) )
% 0.73/1.09 end
% 0.73/1.09
% 0.73/1.09 paramod: (658) {G1,W6,D4,L1,V0,M1} { ! leq( domain( multiplication( skol1
% 0.73/1.09 , skol2 ) ), zero ) }.
% 0.73/1.09 parent0[0]: (14) {G0,W10,D5,L1,V2,M1} I { domain( multiplication( X, domain
% 0.73/1.09 ( Y ) ) ) ==> domain( multiplication( X, Y ) ) }.
% 0.73/1.09 parent1[0; 2]: (657) {G3,W7,D5,L1,V0,M1} { ! leq( domain( multiplication(
% 0.73/1.09 skol1, domain( skol2 ) ) ), zero ) }.
% 0.73/1.09 substitution0:
% 0.73/1.09 X := skol1
% 0.73/1.09 Y := skol2
% 0.73/1.09 end
% 0.73/1.09 substitution1:
% 0.73/1.09 end
% 0.73/1.09
% 0.73/1.09 paramod: (659) {G1,W4,D3,L1,V0,M1} { ! leq( domain( zero ), zero ) }.
% 0.73/1.09 parent0[0]: (18) {G0,W5,D3,L1,V0,M1} I { multiplication( skol1, skol2 ) ==>
% 0.73/1.09 zero }.
% 0.73/1.09 parent1[0; 3]: (658) {G1,W6,D4,L1,V0,M1} { ! leq( domain( multiplication(
% 0.73/1.09 skol1, skol2 ) ), zero ) }.
% 0.73/1.09 substitution0:
% 0.73/1.09 end
% 0.73/1.09 substitution1:
% 0.73/1.09 end
% 0.73/1.09
% 0.73/1.09 paramod: (660) {G1,W3,D2,L1,V0,M1} { ! leq( zero, zero ) }.
% 0.73/1.09 parent0[0]: (16) {G0,W4,D3,L1,V0,M1} I { domain( zero ) ==> zero }.
% 0.73/1.09 parent1[0; 2]: (659) {G1,W4,D3,L1,V0,M1} { ! leq( domain( zero ), zero )
% 0.73/1.09 }.
% 0.73/1.09 substitution0:
% 0.73/1.09 end
% 0.73/1.09 substitution1:
% 0.73/1.09 end
% 0.73/1.09
% 0.73/1.09 resolution: (661) {G2,W0,D0,L0,V0,M0} { }.
% 0.73/1.09 parent0[0]: (660) {G1,W3,D2,L1,V0,M1} { ! leq( zero, zero ) }.
% 0.73/1.09 parent1[0]: (30) {G1,W3,D2,L1,V1,M1} R(12,3) { leq( X, X ) }.
% 0.73/1.09 substitution0:
% 0.73/1.09 end
% 0.73/1.09 substitution1:
% 0.73/1.09 X := zero
% 0.73/1.09 end
% 0.73/1.09
% 0.73/1.09 subsumption: (424) {G3,W0,D0,L0,V0,M0} R(326,119);d(14);d(18);d(16);r(30)
% 0.73/1.09 { }.
% 0.73/1.09 parent0: (661) {G2,W0,D0,L0,V0,M0} { }.
% 0.73/1.09 substitution0:
% 0.73/1.09 end
% 0.73/1.09 permutation0:
% 0.73/1.09 end
% 0.73/1.09
% 0.73/1.09 Proof check complete!
% 0.73/1.09
% 0.73/1.09 Memory use:
% 0.73/1.09
% 0.73/1.09 space for terms: 4879
% 0.73/1.09 space for clauses: 29291
% 0.73/1.09
% 0.73/1.09
% 0.73/1.09 clauses generated: 2905
% 0.73/1.09 clauses kept: 425
% 0.73/1.09 clauses selected: 112
% 0.73/1.09 clauses deleted: 0
% 0.73/1.09 clauses inuse deleted: 0
% 0.73/1.09
% 0.73/1.09 subsentry: 4157
% 0.73/1.09 literals s-matched: 3326
% 0.73/1.09 literals matched: 3325
% 0.73/1.09 full subsumption: 89
% 0.73/1.09
% 0.73/1.09 checksum: 2047006401
% 0.73/1.09
% 0.73/1.09
% 0.73/1.09 Bliksem ended
%------------------------------------------------------------------------------