TSTP Solution File: KLE054+1 by Bliksem---1.12
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%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : KLE054+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n017.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 01:36:56 EDT 2022
% Result : Theorem 0.44s 1.15s
% Output : Refutation 0.44s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : KLE054+1 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.13 % Command : bliksem %s
% 0.13/0.34 % Computer : n017.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % DateTime : Thu Jun 16 11:01:55 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.44/1.15 *** allocated 10000 integers for termspace/termends
% 0.44/1.15 *** allocated 10000 integers for clauses
% 0.44/1.15 *** allocated 10000 integers for justifications
% 0.44/1.15 Bliksem 1.12
% 0.44/1.15
% 0.44/1.15
% 0.44/1.15 Automatic Strategy Selection
% 0.44/1.15
% 0.44/1.15
% 0.44/1.15 Clauses:
% 0.44/1.15
% 0.44/1.15 { addition( X, Y ) = addition( Y, X ) }.
% 0.44/1.15 { addition( Z, addition( Y, X ) ) = addition( addition( Z, Y ), X ) }.
% 0.44/1.15 { addition( X, zero ) = X }.
% 0.44/1.15 { addition( X, X ) = X }.
% 0.44/1.15 { multiplication( X, multiplication( Y, Z ) ) = multiplication(
% 0.44/1.15 multiplication( X, Y ), Z ) }.
% 0.44/1.15 { multiplication( X, one ) = X }.
% 0.44/1.15 { multiplication( one, X ) = X }.
% 0.44/1.15 { multiplication( X, addition( Y, Z ) ) = addition( multiplication( X, Y )
% 0.44/1.15 , multiplication( X, Z ) ) }.
% 0.44/1.15 { multiplication( addition( X, Y ), Z ) = addition( multiplication( X, Z )
% 0.44/1.15 , multiplication( Y, Z ) ) }.
% 0.44/1.15 { multiplication( X, zero ) = zero }.
% 0.44/1.15 { multiplication( zero, X ) = zero }.
% 0.44/1.15 { ! leq( X, Y ), addition( X, Y ) = Y }.
% 0.44/1.15 { ! addition( X, Y ) = Y, leq( X, Y ) }.
% 0.44/1.15 { addition( X, multiplication( domain( X ), X ) ) = multiplication( domain
% 0.44/1.15 ( X ), X ) }.
% 0.44/1.15 { domain( multiplication( X, Y ) ) = domain( multiplication( X, domain( Y )
% 0.44/1.15 ) ) }.
% 0.44/1.15 { addition( domain( X ), one ) = one }.
% 0.44/1.15 { domain( zero ) = zero }.
% 0.44/1.15 { domain( addition( X, Y ) ) = addition( domain( X ), domain( Y ) ) }.
% 0.44/1.15 { ! addition( domain( multiplication( skol1, skol2 ) ), domain( skol1 ) ) =
% 0.44/1.15 domain( skol1 ) }.
% 0.44/1.15
% 0.44/1.15 percentage equality = 0.904762, percentage horn = 1.000000
% 0.44/1.15 This is a pure equality problem
% 0.44/1.15
% 0.44/1.15
% 0.44/1.15
% 0.44/1.15 Options Used:
% 0.44/1.15
% 0.44/1.15 useres = 1
% 0.44/1.15 useparamod = 1
% 0.44/1.15 useeqrefl = 1
% 0.44/1.15 useeqfact = 1
% 0.44/1.15 usefactor = 1
% 0.44/1.15 usesimpsplitting = 0
% 0.44/1.15 usesimpdemod = 5
% 0.44/1.15 usesimpres = 3
% 0.44/1.15
% 0.44/1.15 resimpinuse = 1000
% 0.44/1.15 resimpclauses = 20000
% 0.44/1.15 substype = eqrewr
% 0.44/1.15 backwardsubs = 1
% 0.44/1.15 selectoldest = 5
% 0.44/1.15
% 0.44/1.15 litorderings [0] = split
% 0.44/1.15 litorderings [1] = extend the termordering, first sorting on arguments
% 0.44/1.15
% 0.44/1.15 termordering = kbo
% 0.44/1.15
% 0.44/1.15 litapriori = 0
% 0.44/1.15 termapriori = 1
% 0.44/1.15 litaposteriori = 0
% 0.44/1.15 termaposteriori = 0
% 0.44/1.15 demodaposteriori = 0
% 0.44/1.15 ordereqreflfact = 0
% 0.44/1.15
% 0.44/1.15 litselect = negord
% 0.44/1.15
% 0.44/1.15 maxweight = 15
% 0.44/1.15 maxdepth = 30000
% 0.44/1.15 maxlength = 115
% 0.44/1.15 maxnrvars = 195
% 0.44/1.15 excuselevel = 1
% 0.44/1.15 increasemaxweight = 1
% 0.44/1.15
% 0.44/1.15 maxselected = 10000000
% 0.44/1.15 maxnrclauses = 10000000
% 0.44/1.15
% 0.44/1.15 showgenerated = 0
% 0.44/1.15 showkept = 0
% 0.44/1.15 showselected = 0
% 0.44/1.15 showdeleted = 0
% 0.44/1.15 showresimp = 1
% 0.44/1.15 showstatus = 2000
% 0.44/1.15
% 0.44/1.15 prologoutput = 0
% 0.44/1.15 nrgoals = 5000000
% 0.44/1.15 totalproof = 1
% 0.44/1.15
% 0.44/1.15 Symbols occurring in the translation:
% 0.44/1.15
% 0.44/1.15 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.44/1.15 . [1, 2] (w:1, o:21, a:1, s:1, b:0),
% 0.44/1.15 ! [4, 1] (w:0, o:15, a:1, s:1, b:0),
% 0.44/1.15 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.44/1.15 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.44/1.15 addition [37, 2] (w:1, o:45, a:1, s:1, b:0),
% 0.44/1.15 zero [39, 0] (w:1, o:9, a:1, s:1, b:0),
% 0.44/1.15 multiplication [40, 2] (w:1, o:47, a:1, s:1, b:0),
% 0.44/1.15 one [41, 0] (w:1, o:10, a:1, s:1, b:0),
% 0.44/1.15 leq [42, 2] (w:1, o:46, a:1, s:1, b:0),
% 0.44/1.15 domain [44, 1] (w:1, o:20, a:1, s:1, b:0),
% 0.44/1.15 skol1 [46, 0] (w:1, o:13, a:1, s:1, b:1),
% 0.44/1.15 skol2 [47, 0] (w:1, o:14, a:1, s:1, b:1).
% 0.44/1.15
% 0.44/1.15
% 0.44/1.15 Starting Search:
% 0.44/1.15
% 0.44/1.15 *** allocated 15000 integers for clauses
% 0.44/1.15 *** allocated 22500 integers for clauses
% 0.44/1.15 *** allocated 33750 integers for clauses
% 0.44/1.15 *** allocated 50625 integers for clauses
% 0.44/1.15 *** allocated 15000 integers for termspace/termends
% 0.44/1.15 *** allocated 75937 integers for clauses
% 0.44/1.15
% 0.44/1.15 Bliksems!, er is een bewijs:
% 0.44/1.15 % SZS status Theorem
% 0.44/1.15 % SZS output start Refutation
% 0.44/1.15
% 0.44/1.15 (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X ) }.
% 0.44/1.15 (5) {G0,W5,D3,L1,V1,M1} I { multiplication( X, one ) ==> X }.
% 0.44/1.15 (7) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Y ),
% 0.44/1.15 multiplication( X, Z ) ) ==> multiplication( X, addition( Y, Z ) ) }.
% 0.44/1.15 (13) {G0,W11,D5,L1,V1,M1} I { addition( X, multiplication( domain( X ), X )
% 0.44/1.15 ) ==> multiplication( domain( X ), X ) }.
% 0.44/1.15 (14) {G0,W10,D5,L1,V2,M1} I { domain( multiplication( X, domain( Y ) ) )
% 0.44/1.15 ==> domain( multiplication( X, Y ) ) }.
% 0.44/1.15 (15) {G0,W6,D4,L1,V1,M1} I { addition( domain( X ), one ) ==> one }.
% 0.44/1.15 (17) {G0,W10,D4,L1,V2,M1} I { addition( domain( X ), domain( Y ) ) ==>
% 0.44/1.15 domain( addition( X, Y ) ) }.
% 0.44/1.15 (18) {G1,W9,D5,L1,V0,M1} I;d(17) { ! domain( addition( multiplication(
% 0.44/1.15 skol1, skol2 ), skol1 ) ) ==> domain( skol1 ) }.
% 0.44/1.15 (20) {G1,W6,D4,L1,V1,M1} P(15,0) { addition( one, domain( X ) ) ==> one }.
% 0.44/1.15 (50) {G1,W11,D4,L1,V2,M1} P(5,7) { addition( multiplication( X, Y ), X ) =
% 0.44/1.15 multiplication( X, addition( Y, one ) ) }.
% 0.44/1.15 (120) {G2,W4,D3,L1,V0,M1} P(5,13);d(20) { domain( one ) ==> one }.
% 0.44/1.15 (154) {G3,W6,D4,L1,V1,M1} P(120,17);d(15) { domain( addition( X, one ) )
% 0.44/1.15 ==> one }.
% 0.44/1.15 (168) {G4,W9,D5,L1,V2,M1} P(154,14);d(5) { domain( multiplication( Y,
% 0.44/1.15 addition( X, one ) ) ) ==> domain( Y ) }.
% 0.44/1.15 (895) {G5,W0,D0,L0,V0,M0} P(50,18);d(168);q { }.
% 0.44/1.15
% 0.44/1.15
% 0.44/1.15 % SZS output end Refutation
% 0.44/1.15 found a proof!
% 0.44/1.15
% 0.44/1.15
% 0.44/1.15 Unprocessed initial clauses:
% 0.44/1.15
% 0.44/1.15 (897) {G0,W7,D3,L1,V2,M1} { addition( X, Y ) = addition( Y, X ) }.
% 0.44/1.15 (898) {G0,W11,D4,L1,V3,M1} { addition( Z, addition( Y, X ) ) = addition(
% 0.44/1.15 addition( Z, Y ), X ) }.
% 0.44/1.15 (899) {G0,W5,D3,L1,V1,M1} { addition( X, zero ) = X }.
% 0.44/1.15 (900) {G0,W5,D3,L1,V1,M1} { addition( X, X ) = X }.
% 0.44/1.15 (901) {G0,W11,D4,L1,V3,M1} { multiplication( X, multiplication( Y, Z ) ) =
% 0.44/1.15 multiplication( multiplication( X, Y ), Z ) }.
% 0.44/1.15 (902) {G0,W5,D3,L1,V1,M1} { multiplication( X, one ) = X }.
% 0.44/1.15 (903) {G0,W5,D3,L1,V1,M1} { multiplication( one, X ) = X }.
% 0.44/1.15 (904) {G0,W13,D4,L1,V3,M1} { multiplication( X, addition( Y, Z ) ) =
% 0.44/1.15 addition( multiplication( X, Y ), multiplication( X, Z ) ) }.
% 0.44/1.15 (905) {G0,W13,D4,L1,V3,M1} { multiplication( addition( X, Y ), Z ) =
% 0.44/1.15 addition( multiplication( X, Z ), multiplication( Y, Z ) ) }.
% 0.44/1.15 (906) {G0,W5,D3,L1,V1,M1} { multiplication( X, zero ) = zero }.
% 0.44/1.15 (907) {G0,W5,D3,L1,V1,M1} { multiplication( zero, X ) = zero }.
% 0.44/1.15 (908) {G0,W8,D3,L2,V2,M2} { ! leq( X, Y ), addition( X, Y ) = Y }.
% 0.44/1.15 (909) {G0,W8,D3,L2,V2,M2} { ! addition( X, Y ) = Y, leq( X, Y ) }.
% 0.44/1.15 (910) {G0,W11,D5,L1,V1,M1} { addition( X, multiplication( domain( X ), X )
% 0.44/1.15 ) = multiplication( domain( X ), X ) }.
% 0.44/1.15 (911) {G0,W10,D5,L1,V2,M1} { domain( multiplication( X, Y ) ) = domain(
% 0.44/1.15 multiplication( X, domain( Y ) ) ) }.
% 0.44/1.15 (912) {G0,W6,D4,L1,V1,M1} { addition( domain( X ), one ) = one }.
% 0.44/1.15 (913) {G0,W4,D3,L1,V0,M1} { domain( zero ) = zero }.
% 0.44/1.15 (914) {G0,W10,D4,L1,V2,M1} { domain( addition( X, Y ) ) = addition( domain
% 0.44/1.15 ( X ), domain( Y ) ) }.
% 0.44/1.15 (915) {G0,W10,D5,L1,V0,M1} { ! addition( domain( multiplication( skol1,
% 0.44/1.15 skol2 ) ), domain( skol1 ) ) = domain( skol1 ) }.
% 0.44/1.15
% 0.44/1.15
% 0.44/1.15 Total Proof:
% 0.44/1.15
% 0.44/1.15 subsumption: (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X
% 0.44/1.15 ) }.
% 0.44/1.15 parent0: (897) {G0,W7,D3,L1,V2,M1} { addition( X, Y ) = addition( Y, X )
% 0.44/1.15 }.
% 0.44/1.15 substitution0:
% 0.44/1.15 X := X
% 0.44/1.15 Y := Y
% 0.44/1.15 end
% 0.44/1.15 permutation0:
% 0.44/1.15 0 ==> 0
% 0.44/1.15 end
% 0.44/1.15
% 0.44/1.15 subsumption: (5) {G0,W5,D3,L1,V1,M1} I { multiplication( X, one ) ==> X }.
% 0.44/1.15 parent0: (902) {G0,W5,D3,L1,V1,M1} { multiplication( X, one ) = X }.
% 0.44/1.15 substitution0:
% 0.44/1.15 X := X
% 0.44/1.15 end
% 0.44/1.15 permutation0:
% 0.44/1.15 0 ==> 0
% 0.44/1.15 end
% 0.44/1.15
% 0.44/1.15 eqswap: (927) {G0,W13,D4,L1,V3,M1} { addition( multiplication( X, Y ),
% 0.44/1.15 multiplication( X, Z ) ) = multiplication( X, addition( Y, Z ) ) }.
% 0.44/1.15 parent0[0]: (904) {G0,W13,D4,L1,V3,M1} { multiplication( X, addition( Y, Z
% 0.44/1.15 ) ) = addition( multiplication( X, Y ), multiplication( X, Z ) ) }.
% 0.44/1.15 substitution0:
% 0.44/1.15 X := X
% 0.44/1.15 Y := Y
% 0.44/1.15 Z := Z
% 0.44/1.15 end
% 0.44/1.15
% 0.44/1.15 subsumption: (7) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Y )
% 0.44/1.15 , multiplication( X, Z ) ) ==> multiplication( X, addition( Y, Z ) ) }.
% 0.44/1.15 parent0: (927) {G0,W13,D4,L1,V3,M1} { addition( multiplication( X, Y ),
% 0.44/1.15 multiplication( X, Z ) ) = multiplication( X, addition( Y, Z ) ) }.
% 0.44/1.15 substitution0:
% 0.44/1.15 X := X
% 0.44/1.15 Y := Y
% 0.44/1.15 Z := Z
% 0.44/1.15 end
% 0.44/1.15 permutation0:
% 0.44/1.15 0 ==> 0
% 0.44/1.15 end
% 0.44/1.15
% 0.44/1.15 subsumption: (13) {G0,W11,D5,L1,V1,M1} I { addition( X, multiplication(
% 0.44/1.15 domain( X ), X ) ) ==> multiplication( domain( X ), X ) }.
% 0.44/1.15 parent0: (910) {G0,W11,D5,L1,V1,M1} { addition( X, multiplication( domain
% 0.44/1.15 ( X ), X ) ) = multiplication( domain( X ), X ) }.
% 0.44/1.15 substitution0:
% 0.44/1.15 X := X
% 0.44/1.15 end
% 0.44/1.15 permutation0:
% 0.44/1.15 0 ==> 0
% 0.44/1.15 end
% 0.44/1.15
% 0.44/1.15 eqswap: (954) {G0,W10,D5,L1,V2,M1} { domain( multiplication( X, domain( Y
% 0.44/1.15 ) ) ) = domain( multiplication( X, Y ) ) }.
% 0.44/1.15 parent0[0]: (911) {G0,W10,D5,L1,V2,M1} { domain( multiplication( X, Y ) )
% 0.44/1.15 = domain( multiplication( X, domain( Y ) ) ) }.
% 0.44/1.15 substitution0:
% 0.44/1.15 X := X
% 0.44/1.15 Y := Y
% 0.44/1.15 end
% 0.44/1.15
% 0.44/1.15 subsumption: (14) {G0,W10,D5,L1,V2,M1} I { domain( multiplication( X,
% 0.44/1.15 domain( Y ) ) ) ==> domain( multiplication( X, Y ) ) }.
% 0.44/1.15 parent0: (954) {G0,W10,D5,L1,V2,M1} { domain( multiplication( X, domain( Y
% 0.44/1.15 ) ) ) = domain( multiplication( X, Y ) ) }.
% 0.44/1.15 substitution0:
% 0.44/1.15 X := X
% 0.44/1.15 Y := Y
% 0.44/1.15 end
% 0.44/1.15 permutation0:
% 0.44/1.15 0 ==> 0
% 0.44/1.15 end
% 0.44/1.15
% 0.44/1.15 subsumption: (15) {G0,W6,D4,L1,V1,M1} I { addition( domain( X ), one ) ==>
% 0.44/1.15 one }.
% 0.44/1.15 parent0: (912) {G0,W6,D4,L1,V1,M1} { addition( domain( X ), one ) = one
% 0.44/1.15 }.
% 0.44/1.15 substitution0:
% 0.44/1.15 X := X
% 0.44/1.15 end
% 0.44/1.15 permutation0:
% 0.44/1.15 0 ==> 0
% 0.44/1.15 end
% 0.44/1.15
% 0.44/1.15 eqswap: (986) {G0,W10,D4,L1,V2,M1} { addition( domain( X ), domain( Y ) )
% 0.44/1.15 = domain( addition( X, Y ) ) }.
% 0.44/1.15 parent0[0]: (914) {G0,W10,D4,L1,V2,M1} { domain( addition( X, Y ) ) =
% 0.44/1.15 addition( domain( X ), domain( Y ) ) }.
% 0.44/1.15 substitution0:
% 0.44/1.15 X := X
% 0.44/1.15 Y := Y
% 0.44/1.15 end
% 0.44/1.15
% 0.44/1.15 subsumption: (17) {G0,W10,D4,L1,V2,M1} I { addition( domain( X ), domain( Y
% 0.44/1.15 ) ) ==> domain( addition( X, Y ) ) }.
% 0.44/1.15 parent0: (986) {G0,W10,D4,L1,V2,M1} { addition( domain( X ), domain( Y ) )
% 0.44/1.15 = domain( addition( X, Y ) ) }.
% 0.44/1.15 substitution0:
% 0.44/1.15 X := X
% 0.44/1.15 Y := Y
% 0.44/1.15 end
% 0.44/1.15 permutation0:
% 0.44/1.15 0 ==> 0
% 0.44/1.15 end
% 0.44/1.15
% 0.44/1.15 paramod: (1026) {G1,W9,D5,L1,V0,M1} { ! domain( addition( multiplication(
% 0.44/1.15 skol1, skol2 ), skol1 ) ) = domain( skol1 ) }.
% 0.44/1.15 parent0[0]: (17) {G0,W10,D4,L1,V2,M1} I { addition( domain( X ), domain( Y
% 0.44/1.15 ) ) ==> domain( addition( X, Y ) ) }.
% 0.44/1.15 parent1[0; 2]: (915) {G0,W10,D5,L1,V0,M1} { ! addition( domain(
% 0.44/1.15 multiplication( skol1, skol2 ) ), domain( skol1 ) ) = domain( skol1 ) }.
% 0.44/1.15 substitution0:
% 0.44/1.15 X := multiplication( skol1, skol2 )
% 0.44/1.15 Y := skol1
% 0.44/1.15 end
% 0.44/1.15 substitution1:
% 0.44/1.15 end
% 0.44/1.15
% 0.44/1.15 subsumption: (18) {G1,W9,D5,L1,V0,M1} I;d(17) { ! domain( addition(
% 0.44/1.15 multiplication( skol1, skol2 ), skol1 ) ) ==> domain( skol1 ) }.
% 0.44/1.15 parent0: (1026) {G1,W9,D5,L1,V0,M1} { ! domain( addition( multiplication(
% 0.44/1.15 skol1, skol2 ), skol1 ) ) = domain( skol1 ) }.
% 0.44/1.15 substitution0:
% 0.44/1.15 end
% 0.44/1.15 permutation0:
% 0.44/1.15 0 ==> 0
% 0.44/1.15 end
% 0.44/1.15
% 0.44/1.15 eqswap: (1028) {G0,W6,D4,L1,V1,M1} { one ==> addition( domain( X ), one )
% 0.44/1.15 }.
% 0.44/1.15 parent0[0]: (15) {G0,W6,D4,L1,V1,M1} I { addition( domain( X ), one ) ==>
% 0.44/1.15 one }.
% 0.44/1.15 substitution0:
% 0.44/1.15 X := X
% 0.44/1.15 end
% 0.44/1.15
% 0.44/1.15 paramod: (1029) {G1,W6,D4,L1,V1,M1} { one ==> addition( one, domain( X ) )
% 0.44/1.15 }.
% 0.44/1.15 parent0[0]: (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X )
% 0.44/1.15 }.
% 0.44/1.15 parent1[0; 2]: (1028) {G0,W6,D4,L1,V1,M1} { one ==> addition( domain( X )
% 0.44/1.15 , one ) }.
% 0.44/1.15 substitution0:
% 0.44/1.15 X := domain( X )
% 0.44/1.15 Y := one
% 0.44/1.15 end
% 0.44/1.15 substitution1:
% 0.44/1.15 X := X
% 0.44/1.15 end
% 0.44/1.15
% 0.44/1.15 eqswap: (1032) {G1,W6,D4,L1,V1,M1} { addition( one, domain( X ) ) ==> one
% 0.44/1.15 }.
% 0.44/1.15 parent0[0]: (1029) {G1,W6,D4,L1,V1,M1} { one ==> addition( one, domain( X
% 0.44/1.15 ) ) }.
% 0.44/1.15 substitution0:
% 0.44/1.15 X := X
% 0.44/1.15 end
% 0.44/1.15
% 0.44/1.15 subsumption: (20) {G1,W6,D4,L1,V1,M1} P(15,0) { addition( one, domain( X )
% 0.44/1.15 ) ==> one }.
% 0.44/1.15 parent0: (1032) {G1,W6,D4,L1,V1,M1} { addition( one, domain( X ) ) ==> one
% 0.44/1.15 }.
% 0.44/1.15 substitution0:
% 0.44/1.15 X := X
% 0.44/1.15 end
% 0.44/1.15 permutation0:
% 0.44/1.15 0 ==> 0
% 0.44/1.15 end
% 0.44/1.15
% 0.44/1.15 eqswap: (1034) {G0,W13,D4,L1,V3,M1} { multiplication( X, addition( Y, Z )
% 0.44/1.15 ) ==> addition( multiplication( X, Y ), multiplication( X, Z ) ) }.
% 0.44/1.15 parent0[0]: (7) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Y ),
% 0.44/1.15 multiplication( X, Z ) ) ==> multiplication( X, addition( Y, Z ) ) }.
% 0.44/1.15 substitution0:
% 0.44/1.15 X := X
% 0.44/1.15 Y := Y
% 0.44/1.15 Z := Z
% 0.44/1.15 end
% 0.44/1.15
% 0.44/1.15 paramod: (1036) {G1,W11,D4,L1,V2,M1} { multiplication( X, addition( Y, one
% 0.44/1.15 ) ) ==> addition( multiplication( X, Y ), X ) }.
% 0.44/1.15 parent0[0]: (5) {G0,W5,D3,L1,V1,M1} I { multiplication( X, one ) ==> X }.
% 0.44/1.15 parent1[0; 10]: (1034) {G0,W13,D4,L1,V3,M1} { multiplication( X, addition
% 0.44/1.15 ( Y, Z ) ) ==> addition( multiplication( X, Y ), multiplication( X, Z ) )
% 0.44/1.15 }.
% 0.44/1.15 substitution0:
% 0.44/1.15 X := X
% 0.44/1.15 end
% 0.44/1.15 substitution1:
% 0.44/1.15 X := X
% 0.44/1.15 Y := Y
% 0.44/1.15 Z := one
% 0.44/1.15 end
% 0.44/1.15
% 0.44/1.15 eqswap: (1038) {G1,W11,D4,L1,V2,M1} { addition( multiplication( X, Y ), X
% 0.44/1.15 ) ==> multiplication( X, addition( Y, one ) ) }.
% 0.44/1.15 parent0[0]: (1036) {G1,W11,D4,L1,V2,M1} { multiplication( X, addition( Y,
% 0.44/1.15 one ) ) ==> addition( multiplication( X, Y ), X ) }.
% 0.44/1.15 substitution0:
% 0.44/1.15 X := X
% 0.44/1.15 Y := Y
% 0.44/1.15 end
% 0.44/1.15
% 0.44/1.15 subsumption: (50) {G1,W11,D4,L1,V2,M1} P(5,7) { addition( multiplication( X
% 0.44/1.15 , Y ), X ) = multiplication( X, addition( Y, one ) ) }.
% 0.44/1.15 parent0: (1038) {G1,W11,D4,L1,V2,M1} { addition( multiplication( X, Y ), X
% 0.44/1.15 ) ==> multiplication( X, addition( Y, one ) ) }.
% 0.44/1.15 substitution0:
% 0.44/1.15 X := X
% 0.44/1.15 Y := Y
% 0.44/1.15 end
% 0.44/1.15 permutation0:
% 0.44/1.15 0 ==> 0
% 0.44/1.15 end
% 0.44/1.15
% 0.44/1.15 eqswap: (1040) {G0,W11,D5,L1,V1,M1} { multiplication( domain( X ), X ) ==>
% 0.44/1.15 addition( X, multiplication( domain( X ), X ) ) }.
% 0.44/1.15 parent0[0]: (13) {G0,W11,D5,L1,V1,M1} I { addition( X, multiplication(
% 0.44/1.15 domain( X ), X ) ) ==> multiplication( domain( X ), X ) }.
% 0.44/1.15 substitution0:
% 0.44/1.15 X := X
% 0.44/1.15 end
% 0.44/1.15
% 0.44/1.15 paramod: (1043) {G1,W9,D4,L1,V0,M1} { multiplication( domain( one ), one )
% 0.44/1.15 ==> addition( one, domain( one ) ) }.
% 0.44/1.15 parent0[0]: (5) {G0,W5,D3,L1,V1,M1} I { multiplication( X, one ) ==> X }.
% 0.44/1.15 parent1[0; 7]: (1040) {G0,W11,D5,L1,V1,M1} { multiplication( domain( X ),
% 0.44/1.15 X ) ==> addition( X, multiplication( domain( X ), X ) ) }.
% 0.44/1.15 substitution0:
% 0.44/1.15 X := domain( one )
% 0.44/1.15 end
% 0.44/1.15 substitution1:
% 0.44/1.15 X := one
% 0.44/1.15 end
% 0.44/1.15
% 0.44/1.15 paramod: (1044) {G1,W7,D4,L1,V0,M1} { domain( one ) ==> addition( one,
% 0.44/1.15 domain( one ) ) }.
% 0.44/1.15 parent0[0]: (5) {G0,W5,D3,L1,V1,M1} I { multiplication( X, one ) ==> X }.
% 0.44/1.15 parent1[0; 1]: (1043) {G1,W9,D4,L1,V0,M1} { multiplication( domain( one )
% 0.44/1.15 , one ) ==> addition( one, domain( one ) ) }.
% 0.44/1.15 substitution0:
% 0.44/1.15 X := domain( one )
% 0.44/1.15 end
% 0.44/1.15 substitution1:
% 0.44/1.15 end
% 0.44/1.15
% 0.44/1.15 paramod: (1047) {G2,W4,D3,L1,V0,M1} { domain( one ) ==> one }.
% 0.44/1.15 parent0[0]: (20) {G1,W6,D4,L1,V1,M1} P(15,0) { addition( one, domain( X ) )
% 0.44/1.15 ==> one }.
% 0.44/1.15 parent1[0; 3]: (1044) {G1,W7,D4,L1,V0,M1} { domain( one ) ==> addition(
% 0.44/1.15 one, domain( one ) ) }.
% 0.44/1.15 substitution0:
% 0.44/1.15 X := one
% 0.44/1.15 end
% 0.44/1.15 substitution1:
% 0.44/1.15 end
% 0.44/1.15
% 0.44/1.15 subsumption: (120) {G2,W4,D3,L1,V0,M1} P(5,13);d(20) { domain( one ) ==>
% 0.44/1.15 one }.
% 0.44/1.15 parent0: (1047) {G2,W4,D3,L1,V0,M1} { domain( one ) ==> one }.
% 0.44/1.15 substitution0:
% 0.44/1.15 end
% 0.44/1.15 permutation0:
% 0.44/1.15 0 ==> 0
% 0.44/1.15 end
% 0.44/1.15
% 0.44/1.15 eqswap: (1050) {G0,W10,D4,L1,V2,M1} { domain( addition( X, Y ) ) ==>
% 0.44/1.15 addition( domain( X ), domain( Y ) ) }.
% 0.44/1.15 parent0[0]: (17) {G0,W10,D4,L1,V2,M1} I { addition( domain( X ), domain( Y
% 0.44/1.15 ) ) ==> domain( addition( X, Y ) ) }.
% 0.44/1.15 substitution0:
% 0.44/1.15 X := X
% 0.44/1.15 Y := Y
% 0.44/1.15 end
% 0.44/1.15
% 0.44/1.15 paramod: (1053) {G1,W9,D4,L1,V1,M1} { domain( addition( X, one ) ) ==>
% 0.44/1.15 addition( domain( X ), one ) }.
% 0.44/1.15 parent0[0]: (120) {G2,W4,D3,L1,V0,M1} P(5,13);d(20) { domain( one ) ==> one
% 0.44/1.15 }.
% 0.44/1.15 parent1[0; 8]: (1050) {G0,W10,D4,L1,V2,M1} { domain( addition( X, Y ) )
% 0.44/1.15 ==> addition( domain( X ), domain( Y ) ) }.
% 0.44/1.15 substitution0:
% 0.44/1.15 end
% 0.44/1.15 substitution1:
% 0.44/1.15 X := X
% 0.44/1.15 Y := one
% 0.44/1.15 end
% 0.44/1.15
% 0.44/1.15 paramod: (1054) {G1,W6,D4,L1,V1,M1} { domain( addition( X, one ) ) ==> one
% 0.44/1.15 }.
% 0.44/1.15 parent0[0]: (15) {G0,W6,D4,L1,V1,M1} I { addition( domain( X ), one ) ==>
% 0.44/1.15 one }.
% 0.44/1.15 parent1[0; 5]: (1053) {G1,W9,D4,L1,V1,M1} { domain( addition( X, one ) )
% 0.44/1.15 ==> addition( domain( X ), one ) }.
% 0.44/1.15 substitution0:
% 0.44/1.15 X := X
% 0.44/1.15 end
% 0.44/1.15 substitution1:
% 0.44/1.15 X := X
% 0.44/1.15 end
% 0.44/1.15
% 0.44/1.15 subsumption: (154) {G3,W6,D4,L1,V1,M1} P(120,17);d(15) { domain( addition(
% 0.44/1.15 X, one ) ) ==> one }.
% 0.44/1.15 parent0: (1054) {G1,W6,D4,L1,V1,M1} { domain( addition( X, one ) ) ==> one
% 0.44/1.15 }.
% 0.44/1.15 substitution0:
% 0.44/1.15 X := X
% 0.44/1.15 end
% 0.44/1.15 permutation0:
% 0.44/1.15 0 ==> 0
% 0.44/1.15 end
% 0.44/1.15
% 0.44/1.15 eqswap: (1057) {G0,W10,D5,L1,V2,M1} { domain( multiplication( X, Y ) ) ==>
% 0.44/1.15 domain( multiplication( X, domain( Y ) ) ) }.
% 0.44/1.15 parent0[0]: (14) {G0,W10,D5,L1,V2,M1} I { domain( multiplication( X, domain
% 0.44/1.15 ( Y ) ) ) ==> domain( multiplication( X, Y ) ) }.
% 0.44/1.15 substitution0:
% 0.44/1.15 X := X
% 0.44/1.15 Y := Y
% 0.44/1.15 end
% 0.44/1.15
% 0.44/1.15 paramod: (1059) {G1,W11,D5,L1,V2,M1} { domain( multiplication( X, addition
% 0.44/1.15 ( Y, one ) ) ) ==> domain( multiplication( X, one ) ) }.
% 0.44/1.15 parent0[0]: (154) {G3,W6,D4,L1,V1,M1} P(120,17);d(15) { domain( addition( X
% 0.44/1.15 , one ) ) ==> one }.
% 0.44/1.15 parent1[0; 10]: (1057) {G0,W10,D5,L1,V2,M1} { domain( multiplication( X, Y
% 0.44/1.15 ) ) ==> domain( multiplication( X, domain( Y ) ) ) }.
% 0.44/1.15 substitution0:
% 0.44/1.15 X := Y
% 0.44/1.15 end
% 0.44/1.15 substitution1:
% 0.44/1.15 X := X
% 0.44/1.15 Y := addition( Y, one )
% 0.44/1.15 end
% 0.44/1.15
% 0.44/1.15 paramod: (1060) {G1,W9,D5,L1,V2,M1} { domain( multiplication( X, addition
% 0.44/1.15 ( Y, one ) ) ) ==> domain( X ) }.
% 0.44/1.15 parent0[0]: (5) {G0,W5,D3,L1,V1,M1} I { multiplication( X, one ) ==> X }.
% 0.44/1.15 parent1[0; 8]: (1059) {G1,W11,D5,L1,V2,M1} { domain( multiplication( X,
% 0.44/1.15 addition( Y, one ) ) ) ==> domain( multiplication( X, one ) ) }.
% 0.44/1.15 substitution0:
% 0.44/1.15 X := X
% 0.44/1.15 end
% 0.44/1.15 substitution1:
% 0.44/1.15 X := X
% 0.44/1.15 Y := Y
% 0.44/1.15 end
% 0.44/1.15
% 0.44/1.15 subsumption: (168) {G4,W9,D5,L1,V2,M1} P(154,14);d(5) { domain(
% 0.44/1.15 multiplication( Y, addition( X, one ) ) ) ==> domain( Y ) }.
% 0.44/1.15 parent0: (1060) {G1,W9,D5,L1,V2,M1} { domain( multiplication( X, addition
% 0.44/1.15 ( Y, one ) ) ) ==> domain( X ) }.
% 0.44/1.15 substitution0:
% 0.44/1.15 X := Y
% 0.44/1.15 Y := X
% 0.44/1.15 end
% 0.44/1.15 permutation0:
% 0.44/1.15 0 ==> 0
% 0.44/1.15 end
% 0.44/1.15
% 0.44/1.15 eqswap: (1063) {G1,W9,D5,L1,V0,M1} { ! domain( skol1 ) ==> domain(
% 0.44/1.15 addition( multiplication( skol1, skol2 ), skol1 ) ) }.
% 0.44/1.15 parent0[0]: (18) {G1,W9,D5,L1,V0,M1} I;d(17) { ! domain( addition(
% 0.44/1.15 multiplication( skol1, skol2 ), skol1 ) ) ==> domain( skol1 ) }.
% 0.44/1.15 substitution0:
% 0.44/1.15 end
% 0.44/1.15
% 0.44/1.15 paramod: (1065) {G2,W9,D5,L1,V0,M1} { ! domain( skol1 ) ==> domain(
% 0.44/1.15 multiplication( skol1, addition( skol2, one ) ) ) }.
% 0.44/1.15 parent0[0]: (50) {G1,W11,D4,L1,V2,M1} P(5,7) { addition( multiplication( X
% 0.44/1.15 , Y ), X ) = multiplication( X, addition( Y, one ) ) }.
% 0.44/1.15 parent1[0; 5]: (1063) {G1,W9,D5,L1,V0,M1} { ! domain( skol1 ) ==> domain(
% 0.44/1.15 addition( multiplication( skol1, skol2 ), skol1 ) ) }.
% 0.44/1.15 substitution0:
% 0.44/1.15 X := skol1
% 0.44/1.15 Y := skol2
% 0.44/1.15 end
% 0.44/1.15 substitution1:
% 0.44/1.15 end
% 0.44/1.15
% 0.44/1.15 paramod: (1066) {G3,W5,D3,L1,V0,M1} { ! domain( skol1 ) ==> domain( skol1
% 0.44/1.15 ) }.
% 0.44/1.15 parent0[0]: (168) {G4,W9,D5,L1,V2,M1} P(154,14);d(5) { domain(
% 0.44/1.15 multiplication( Y, addition( X, one ) ) ) ==> domain( Y ) }.
% 0.44/1.15 parent1[0; 4]: (1065) {G2,W9,D5,L1,V0,M1} { ! domain( skol1 ) ==> domain(
% 0.44/1.15 multiplication( skol1, addition( skol2, one ) ) ) }.
% 0.44/1.15 substitution0:
% 0.44/1.15 X := skol2
% 0.44/1.15 Y := skol1
% 0.44/1.15 end
% 0.44/1.15 substitution1:
% 0.44/1.15 end
% 0.44/1.15
% 0.44/1.15 eqrefl: (1067) {G0,W0,D0,L0,V0,M0} { }.
% 0.44/1.15 parent0[0]: (1066) {G3,W5,D3,L1,V0,M1} { ! domain( skol1 ) ==> domain(
% 0.44/1.15 skol1 ) }.
% 0.44/1.15 substitution0:
% 0.44/1.15 end
% 0.44/1.15
% 0.44/1.15 subsumption: (895) {G5,W0,D0,L0,V0,M0} P(50,18);d(168);q { }.
% 0.44/1.15 parent0: (1067) {G0,W0,D0,L0,V0,M0} { }.
% 0.44/1.15 substitution0:
% 0.44/1.15 end
% 0.44/1.15 permutation0:
% 0.44/1.15 end
% 0.44/1.15
% 0.44/1.15 Proof check complete!
% 0.44/1.15
% 0.44/1.15 Memory use:
% 0.44/1.15
% 0.44/1.15 space for terms: 10658
% 0.44/1.15 space for clauses: 53891
% 0.44/1.15
% 0.44/1.15
% 0.44/1.15 clauses generated: 8495
% 0.44/1.15 clauses kept: 896
% 0.44/1.15 clauses selected: 156
% 0.44/1.15 clauses deleted: 5
% 0.44/1.15 clauses inuse deleted: 0
% 0.44/1.15
% 0.44/1.15 subsentry: 10597
% 0.44/1.15 literals s-matched: 8137
% 0.44/1.15 literals matched: 8057
% 0.44/1.15 full subsumption: 604
% 0.44/1.15
% 0.44/1.15 checksum: 168822818
% 0.44/1.15
% 0.44/1.15
% 0.44/1.15 Bliksem ended
%------------------------------------------------------------------------------