TSTP Solution File: KLE061+1 by Bliksem---1.12
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%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : KLE061+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n013.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 01:36:58 EDT 2022
% Result : Theorem 0.94s 1.37s
% Output : Refutation 0.94s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : KLE061+1 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.13 % Command : bliksem %s
% 0.13/0.34 % Computer : n013.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 11:57:14 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.94/1.37 *** allocated 10000 integers for termspace/termends
% 0.94/1.37 *** allocated 10000 integers for clauses
% 0.94/1.37 *** allocated 10000 integers for justifications
% 0.94/1.37 Bliksem 1.12
% 0.94/1.37
% 0.94/1.37
% 0.94/1.37 Automatic Strategy Selection
% 0.94/1.37
% 0.94/1.37
% 0.94/1.37 Clauses:
% 0.94/1.37
% 0.94/1.37 { addition( X, Y ) = addition( Y, X ) }.
% 0.94/1.37 { addition( Z, addition( Y, X ) ) = addition( addition( Z, Y ), X ) }.
% 0.94/1.37 { addition( X, zero ) = X }.
% 0.94/1.37 { addition( X, X ) = X }.
% 0.94/1.37 { multiplication( X, multiplication( Y, Z ) ) = multiplication(
% 0.94/1.37 multiplication( X, Y ), Z ) }.
% 0.94/1.37 { multiplication( X, one ) = X }.
% 0.94/1.37 { multiplication( one, X ) = X }.
% 0.94/1.37 { multiplication( X, addition( Y, Z ) ) = addition( multiplication( X, Y )
% 0.94/1.37 , multiplication( X, Z ) ) }.
% 0.94/1.37 { multiplication( addition( X, Y ), Z ) = addition( multiplication( X, Z )
% 0.94/1.37 , multiplication( Y, Z ) ) }.
% 0.94/1.37 { multiplication( X, zero ) = zero }.
% 0.94/1.37 { multiplication( zero, X ) = zero }.
% 0.94/1.37 { ! leq( X, Y ), addition( X, Y ) = Y }.
% 0.94/1.37 { ! addition( X, Y ) = Y, leq( X, Y ) }.
% 0.94/1.37 { addition( X, multiplication( domain( X ), X ) ) = multiplication( domain
% 0.94/1.37 ( X ), X ) }.
% 0.94/1.37 { domain( multiplication( X, Y ) ) = domain( multiplication( X, domain( Y )
% 0.94/1.37 ) ) }.
% 0.94/1.37 { addition( domain( X ), one ) = one }.
% 0.94/1.37 { domain( zero ) = zero }.
% 0.94/1.37 { domain( addition( X, Y ) ) = addition( domain( X ), domain( Y ) ) }.
% 0.94/1.37 { ! multiplication( domain( skol1 ), domain( skol1 ) ) = domain( skol1 ) }
% 0.94/1.37 .
% 0.94/1.37
% 0.94/1.37 percentage equality = 0.904762, percentage horn = 1.000000
% 0.94/1.37 This is a pure equality problem
% 0.94/1.37
% 0.94/1.37
% 0.94/1.37
% 0.94/1.37 Options Used:
% 0.94/1.37
% 0.94/1.37 useres = 1
% 0.94/1.37 useparamod = 1
% 0.94/1.37 useeqrefl = 1
% 0.94/1.37 useeqfact = 1
% 0.94/1.37 usefactor = 1
% 0.94/1.37 usesimpsplitting = 0
% 0.94/1.37 usesimpdemod = 5
% 0.94/1.37 usesimpres = 3
% 0.94/1.37
% 0.94/1.37 resimpinuse = 1000
% 0.94/1.37 resimpclauses = 20000
% 0.94/1.37 substype = eqrewr
% 0.94/1.37 backwardsubs = 1
% 0.94/1.37 selectoldest = 5
% 0.94/1.37
% 0.94/1.37 litorderings [0] = split
% 0.94/1.37 litorderings [1] = extend the termordering, first sorting on arguments
% 0.94/1.37
% 0.94/1.37 termordering = kbo
% 0.94/1.37
% 0.94/1.37 litapriori = 0
% 0.94/1.37 termapriori = 1
% 0.94/1.37 litaposteriori = 0
% 0.94/1.37 termaposteriori = 0
% 0.94/1.37 demodaposteriori = 0
% 0.94/1.37 ordereqreflfact = 0
% 0.94/1.37
% 0.94/1.37 litselect = negord
% 0.94/1.37
% 0.94/1.37 maxweight = 15
% 0.94/1.37 maxdepth = 30000
% 0.94/1.37 maxlength = 115
% 0.94/1.37 maxnrvars = 195
% 0.94/1.37 excuselevel = 1
% 0.94/1.37 increasemaxweight = 1
% 0.94/1.37
% 0.94/1.37 maxselected = 10000000
% 0.94/1.37 maxnrclauses = 10000000
% 0.94/1.37
% 0.94/1.37 showgenerated = 0
% 0.94/1.37 showkept = 0
% 0.94/1.37 showselected = 0
% 0.94/1.37 showdeleted = 0
% 0.94/1.37 showresimp = 1
% 0.94/1.37 showstatus = 2000
% 0.94/1.37
% 0.94/1.37 prologoutput = 0
% 0.94/1.37 nrgoals = 5000000
% 0.94/1.37 totalproof = 1
% 0.94/1.37
% 0.94/1.37 Symbols occurring in the translation:
% 0.94/1.37
% 0.94/1.37 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.94/1.37 . [1, 2] (w:1, o:20, a:1, s:1, b:0),
% 0.94/1.37 ! [4, 1] (w:0, o:14, a:1, s:1, b:0),
% 0.94/1.37 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.94/1.37 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.94/1.37 addition [37, 2] (w:1, o:44, a:1, s:1, b:0),
% 0.94/1.37 zero [39, 0] (w:1, o:9, a:1, s:1, b:0),
% 0.94/1.37 multiplication [40, 2] (w:1, o:46, a:1, s:1, b:0),
% 0.94/1.37 one [41, 0] (w:1, o:10, a:1, s:1, b:0),
% 0.94/1.37 leq [42, 2] (w:1, o:45, a:1, s:1, b:0),
% 0.94/1.37 domain [44, 1] (w:1, o:19, a:1, s:1, b:0),
% 0.94/1.37 skol1 [46, 0] (w:1, o:13, a:1, s:1, b:1).
% 0.94/1.37
% 0.94/1.37
% 0.94/1.37 Starting Search:
% 0.94/1.37
% 0.94/1.37 *** allocated 15000 integers for clauses
% 0.94/1.37 *** allocated 22500 integers for clauses
% 0.94/1.37 *** allocated 33750 integers for clauses
% 0.94/1.37 *** allocated 50625 integers for clauses
% 0.94/1.37 *** allocated 15000 integers for termspace/termends
% 0.94/1.37 *** allocated 75937 integers for clauses
% 0.94/1.37 Resimplifying inuse:
% 0.94/1.37 Done
% 0.94/1.37
% 0.94/1.37 *** allocated 22500 integers for termspace/termends
% 0.94/1.37 *** allocated 113905 integers for clauses
% 0.94/1.37 *** allocated 33750 integers for termspace/termends
% 0.94/1.37
% 0.94/1.37 Intermediate Status:
% 0.94/1.37 Generated: 16058
% 0.94/1.37 Kept: 2003
% 0.94/1.37 Inuse: 226
% 0.94/1.37 Deleted: 19
% 0.94/1.37 Deletedinuse: 10
% 0.94/1.37
% 0.94/1.37 Resimplifying inuse:
% 0.94/1.37 Done
% 0.94/1.37
% 0.94/1.37 *** allocated 170857 integers for clauses
% 0.94/1.37 *** allocated 50625 integers for termspace/termends
% 0.94/1.37 Resimplifying inuse:
% 0.94/1.37
% 0.94/1.37 Bliksems!, er is een bewijs:
% 0.94/1.37 % SZS status Theorem
% 0.94/1.37 % SZS output start Refutation
% 0.94/1.37
% 0.94/1.37 (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X ) }.
% 0.94/1.37 (6) {G0,W5,D3,L1,V1,M1} I { multiplication( one, X ) ==> X }.
% 0.94/1.37 (8) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Z ),
% 0.94/1.37 multiplication( Y, Z ) ) ==> multiplication( addition( X, Y ), Z ) }.
% 0.94/1.37 (13) {G0,W11,D5,L1,V1,M1} I { addition( X, multiplication( domain( X ), X )
% 0.94/1.37 ) ==> multiplication( domain( X ), X ) }.
% 0.94/1.37 (14) {G0,W10,D5,L1,V2,M1} I { domain( multiplication( X, domain( Y ) ) )
% 0.94/1.37 ==> domain( multiplication( X, Y ) ) }.
% 0.94/1.37 (15) {G0,W6,D4,L1,V1,M1} I { addition( domain( X ), one ) ==> one }.
% 0.94/1.37 (18) {G0,W8,D4,L1,V0,M1} I { ! multiplication( domain( skol1 ), domain(
% 0.94/1.37 skol1 ) ) ==> domain( skol1 ) }.
% 0.94/1.37 (20) {G1,W6,D4,L1,V1,M1} P(15,0) { addition( one, domain( X ) ) ==> one }.
% 0.94/1.37 (85) {G1,W11,D4,L1,V2,M1} P(6,8) { addition( X, multiplication( Y, X ) ) =
% 0.94/1.37 multiplication( addition( one, Y ), X ) }.
% 0.94/1.37 (139) {G1,W6,D4,L1,V1,M1} P(6,14);d(6) { domain( domain( X ) ) ==> domain(
% 0.94/1.37 X ) }.
% 0.94/1.37 (2688) {G2,W6,D4,L1,V1,M1} P(85,13);d(20);d(6) { multiplication( domain( X
% 0.94/1.37 ), X ) ==> X }.
% 0.94/1.37 (2708) {G3,W8,D4,L1,V1,M1} P(139,2688) { multiplication( domain( X ),
% 0.94/1.37 domain( X ) ) ==> domain( X ) }.
% 0.94/1.37 (3028) {G4,W0,D0,L0,V0,M0} S(18);d(2708);q { }.
% 0.94/1.37
% 0.94/1.37
% 0.94/1.37 % SZS output end Refutation
% 0.94/1.37 found a proof!
% 0.94/1.37
% 0.94/1.37
% 0.94/1.37 Unprocessed initial clauses:
% 0.94/1.37
% 0.94/1.37 (3030) {G0,W7,D3,L1,V2,M1} { addition( X, Y ) = addition( Y, X ) }.
% 0.94/1.37 (3031) {G0,W11,D4,L1,V3,M1} { addition( Z, addition( Y, X ) ) = addition(
% 0.94/1.37 addition( Z, Y ), X ) }.
% 0.94/1.37 (3032) {G0,W5,D3,L1,V1,M1} { addition( X, zero ) = X }.
% 0.94/1.37 (3033) {G0,W5,D3,L1,V1,M1} { addition( X, X ) = X }.
% 0.94/1.37 (3034) {G0,W11,D4,L1,V3,M1} { multiplication( X, multiplication( Y, Z ) )
% 0.94/1.37 = multiplication( multiplication( X, Y ), Z ) }.
% 0.94/1.37 (3035) {G0,W5,D3,L1,V1,M1} { multiplication( X, one ) = X }.
% 0.94/1.37 (3036) {G0,W5,D3,L1,V1,M1} { multiplication( one, X ) = X }.
% 0.94/1.37 (3037) {G0,W13,D4,L1,V3,M1} { multiplication( X, addition( Y, Z ) ) =
% 0.94/1.37 addition( multiplication( X, Y ), multiplication( X, Z ) ) }.
% 0.94/1.37 (3038) {G0,W13,D4,L1,V3,M1} { multiplication( addition( X, Y ), Z ) =
% 0.94/1.37 addition( multiplication( X, Z ), multiplication( Y, Z ) ) }.
% 0.94/1.37 (3039) {G0,W5,D3,L1,V1,M1} { multiplication( X, zero ) = zero }.
% 0.94/1.37 (3040) {G0,W5,D3,L1,V1,M1} { multiplication( zero, X ) = zero }.
% 0.94/1.37 (3041) {G0,W8,D3,L2,V2,M2} { ! leq( X, Y ), addition( X, Y ) = Y }.
% 0.94/1.37 (3042) {G0,W8,D3,L2,V2,M2} { ! addition( X, Y ) = Y, leq( X, Y ) }.
% 0.94/1.37 (3043) {G0,W11,D5,L1,V1,M1} { addition( X, multiplication( domain( X ), X
% 0.94/1.37 ) ) = multiplication( domain( X ), X ) }.
% 0.94/1.37 (3044) {G0,W10,D5,L1,V2,M1} { domain( multiplication( X, Y ) ) = domain(
% 0.94/1.37 multiplication( X, domain( Y ) ) ) }.
% 0.94/1.37 (3045) {G0,W6,D4,L1,V1,M1} { addition( domain( X ), one ) = one }.
% 0.94/1.37 (3046) {G0,W4,D3,L1,V0,M1} { domain( zero ) = zero }.
% 0.94/1.37 (3047) {G0,W10,D4,L1,V2,M1} { domain( addition( X, Y ) ) = addition(
% 0.94/1.37 domain( X ), domain( Y ) ) }.
% 0.94/1.37 (3048) {G0,W8,D4,L1,V0,M1} { ! multiplication( domain( skol1 ), domain(
% 0.94/1.37 skol1 ) ) = domain( skol1 ) }.
% 0.94/1.37
% 0.94/1.37
% 0.94/1.37 Total Proof:
% 0.94/1.37
% 0.94/1.37 subsumption: (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X
% 0.94/1.37 ) }.
% 0.94/1.37 parent0: (3030) {G0,W7,D3,L1,V2,M1} { addition( X, Y ) = addition( Y, X )
% 0.94/1.37 }.
% 0.94/1.37 substitution0:
% 0.94/1.37 X := X
% 0.94/1.37 Y := Y
% 0.94/1.37 end
% 0.94/1.37 permutation0:
% 0.94/1.37 0 ==> 0
% 0.94/1.37 end
% 0.94/1.37
% 0.94/1.37 subsumption: (6) {G0,W5,D3,L1,V1,M1} I { multiplication( one, X ) ==> X }.
% 0.94/1.37 parent0: (3036) {G0,W5,D3,L1,V1,M1} { multiplication( one, X ) = X }.
% 0.94/1.37 substitution0:
% 0.94/1.37 X := X
% 0.94/1.37 end
% 0.94/1.37 permutation0:
% 0.94/1.37 0 ==> 0
% 0.94/1.37 end
% 0.94/1.37
% 0.94/1.37 eqswap: (3062) {G0,W13,D4,L1,V3,M1} { addition( multiplication( X, Z ),
% 0.94/1.37 multiplication( Y, Z ) ) = multiplication( addition( X, Y ), Z ) }.
% 0.94/1.37 parent0[0]: (3038) {G0,W13,D4,L1,V3,M1} { multiplication( addition( X, Y )
% 0.94/1.37 , Z ) = addition( multiplication( X, Z ), multiplication( Y, Z ) ) }.
% 0.94/1.37 substitution0:
% 0.94/1.37 X := X
% 0.94/1.37 Y := Y
% 0.94/1.37 Z := Z
% 0.94/1.37 end
% 0.94/1.37
% 0.94/1.37 subsumption: (8) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Z )
% 0.94/1.37 , multiplication( Y, Z ) ) ==> multiplication( addition( X, Y ), Z ) }.
% 0.94/1.37 parent0: (3062) {G0,W13,D4,L1,V3,M1} { addition( multiplication( X, Z ),
% 0.94/1.37 multiplication( Y, Z ) ) = multiplication( addition( X, Y ), Z ) }.
% 0.94/1.37 substitution0:
% 0.94/1.37 X := X
% 0.94/1.37 Y := Y
% 0.94/1.37 Z := Z
% 0.94/1.37 end
% 0.94/1.37 permutation0:
% 0.94/1.37 0 ==> 0
% 0.94/1.37 end
% 0.94/1.37
% 0.94/1.37 subsumption: (13) {G0,W11,D5,L1,V1,M1} I { addition( X, multiplication(
% 0.94/1.37 domain( X ), X ) ) ==> multiplication( domain( X ), X ) }.
% 0.94/1.37 parent0: (3043) {G0,W11,D5,L1,V1,M1} { addition( X, multiplication( domain
% 0.94/1.37 ( X ), X ) ) = multiplication( domain( X ), X ) }.
% 0.94/1.37 substitution0:
% 0.94/1.37 X := X
% 0.94/1.37 end
% 0.94/1.37 permutation0:
% 0.94/1.37 0 ==> 0
% 0.94/1.37 end
% 0.94/1.37
% 0.94/1.37 eqswap: (3089) {G0,W10,D5,L1,V2,M1} { domain( multiplication( X, domain( Y
% 0.94/1.37 ) ) ) = domain( multiplication( X, Y ) ) }.
% 0.94/1.37 parent0[0]: (3044) {G0,W10,D5,L1,V2,M1} { domain( multiplication( X, Y ) )
% 0.94/1.37 = domain( multiplication( X, domain( Y ) ) ) }.
% 0.94/1.37 substitution0:
% 0.94/1.37 X := X
% 0.94/1.37 Y := Y
% 0.94/1.37 end
% 0.94/1.37
% 0.94/1.37 subsumption: (14) {G0,W10,D5,L1,V2,M1} I { domain( multiplication( X,
% 0.94/1.37 domain( Y ) ) ) ==> domain( multiplication( X, Y ) ) }.
% 0.94/1.37 parent0: (3089) {G0,W10,D5,L1,V2,M1} { domain( multiplication( X, domain(
% 0.94/1.37 Y ) ) ) = domain( multiplication( X, Y ) ) }.
% 0.94/1.37 substitution0:
% 0.94/1.37 X := X
% 0.94/1.37 Y := Y
% 0.94/1.37 end
% 0.94/1.37 permutation0:
% 0.94/1.37 0 ==> 0
% 0.94/1.37 end
% 0.94/1.37
% 0.94/1.37 subsumption: (15) {G0,W6,D4,L1,V1,M1} I { addition( domain( X ), one ) ==>
% 0.94/1.37 one }.
% 0.94/1.37 parent0: (3045) {G0,W6,D4,L1,V1,M1} { addition( domain( X ), one ) = one
% 0.94/1.37 }.
% 0.94/1.37 substitution0:
% 0.94/1.37 X := X
% 0.94/1.37 end
% 0.94/1.37 permutation0:
% 0.94/1.37 0 ==> 0
% 0.94/1.37 end
% 0.94/1.37
% 0.94/1.37 subsumption: (18) {G0,W8,D4,L1,V0,M1} I { ! multiplication( domain( skol1 )
% 0.94/1.37 , domain( skol1 ) ) ==> domain( skol1 ) }.
% 0.94/1.37 parent0: (3048) {G0,W8,D4,L1,V0,M1} { ! multiplication( domain( skol1 ),
% 0.94/1.37 domain( skol1 ) ) = domain( skol1 ) }.
% 0.94/1.37 substitution0:
% 0.94/1.37 end
% 0.94/1.37 permutation0:
% 0.94/1.37 0 ==> 0
% 0.94/1.37 end
% 0.94/1.37
% 0.94/1.37 eqswap: (3123) {G0,W6,D4,L1,V1,M1} { one ==> addition( domain( X ), one )
% 0.94/1.37 }.
% 0.94/1.37 parent0[0]: (15) {G0,W6,D4,L1,V1,M1} I { addition( domain( X ), one ) ==>
% 0.94/1.37 one }.
% 0.94/1.37 substitution0:
% 0.94/1.37 X := X
% 0.94/1.37 end
% 0.94/1.37
% 0.94/1.37 paramod: (3124) {G1,W6,D4,L1,V1,M1} { one ==> addition( one, domain( X ) )
% 0.94/1.37 }.
% 0.94/1.37 parent0[0]: (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X )
% 0.94/1.37 }.
% 0.94/1.37 parent1[0; 2]: (3123) {G0,W6,D4,L1,V1,M1} { one ==> addition( domain( X )
% 0.94/1.37 , one ) }.
% 0.94/1.37 substitution0:
% 0.94/1.37 X := domain( X )
% 0.94/1.37 Y := one
% 0.94/1.37 end
% 0.94/1.37 substitution1:
% 0.94/1.37 X := X
% 0.94/1.37 end
% 0.94/1.37
% 0.94/1.37 eqswap: (3127) {G1,W6,D4,L1,V1,M1} { addition( one, domain( X ) ) ==> one
% 0.94/1.37 }.
% 0.94/1.37 parent0[0]: (3124) {G1,W6,D4,L1,V1,M1} { one ==> addition( one, domain( X
% 0.94/1.37 ) ) }.
% 0.94/1.37 substitution0:
% 0.94/1.37 X := X
% 0.94/1.37 end
% 0.94/1.37
% 0.94/1.37 subsumption: (20) {G1,W6,D4,L1,V1,M1} P(15,0) { addition( one, domain( X )
% 0.94/1.37 ) ==> one }.
% 0.94/1.37 parent0: (3127) {G1,W6,D4,L1,V1,M1} { addition( one, domain( X ) ) ==> one
% 0.94/1.37 }.
% 0.94/1.37 substitution0:
% 0.94/1.37 X := X
% 0.94/1.37 end
% 0.94/1.37 permutation0:
% 0.94/1.37 0 ==> 0
% 0.94/1.37 end
% 0.94/1.37
% 0.94/1.37 eqswap: (3129) {G0,W13,D4,L1,V3,M1} { multiplication( addition( X, Z ), Y
% 0.94/1.37 ) ==> addition( multiplication( X, Y ), multiplication( Z, Y ) ) }.
% 0.94/1.37 parent0[0]: (8) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Z ),
% 0.94/1.37 multiplication( Y, Z ) ) ==> multiplication( addition( X, Y ), Z ) }.
% 0.94/1.37 substitution0:
% 0.94/1.37 X := X
% 0.94/1.37 Y := Z
% 0.94/1.37 Z := Y
% 0.94/1.37 end
% 0.94/1.37
% 0.94/1.37 paramod: (3130) {G1,W11,D4,L1,V2,M1} { multiplication( addition( one, X )
% 0.94/1.37 , Y ) ==> addition( Y, multiplication( X, Y ) ) }.
% 0.94/1.37 parent0[0]: (6) {G0,W5,D3,L1,V1,M1} I { multiplication( one, X ) ==> X }.
% 0.94/1.37 parent1[0; 7]: (3129) {G0,W13,D4,L1,V3,M1} { multiplication( addition( X,
% 0.94/1.37 Z ), Y ) ==> addition( multiplication( X, Y ), multiplication( Z, Y ) )
% 0.94/1.37 }.
% 0.94/1.37 substitution0:
% 0.94/1.37 X := Y
% 0.94/1.37 end
% 0.94/1.37 substitution1:
% 0.94/1.37 X := one
% 0.94/1.37 Y := Y
% 0.94/1.37 Z := X
% 0.94/1.37 end
% 0.94/1.37
% 0.94/1.37 eqswap: (3132) {G1,W11,D4,L1,V2,M1} { addition( Y, multiplication( X, Y )
% 0.94/1.37 ) ==> multiplication( addition( one, X ), Y ) }.
% 0.94/1.37 parent0[0]: (3130) {G1,W11,D4,L1,V2,M1} { multiplication( addition( one, X
% 0.94/1.37 ), Y ) ==> addition( Y, multiplication( X, Y ) ) }.
% 0.94/1.37 substitution0:
% 0.94/1.37 X := X
% 0.94/1.37 Y := Y
% 0.94/1.37 end
% 0.94/1.37
% 0.94/1.37 subsumption: (85) {G1,W11,D4,L1,V2,M1} P(6,8) { addition( X, multiplication
% 0.94/1.37 ( Y, X ) ) = multiplication( addition( one, Y ), X ) }.
% 0.94/1.37 parent0: (3132) {G1,W11,D4,L1,V2,M1} { addition( Y, multiplication( X, Y )
% 0.94/1.37 ) ==> multiplication( addition( one, X ), Y ) }.
% 0.94/1.37 substitution0:
% 0.94/1.37 X := Y
% 0.94/1.37 Y := X
% 0.94/1.37 end
% 0.94/1.37 permutation0:
% 0.94/1.37 0 ==> 0
% 0.94/1.37 end
% 0.94/1.37
% 0.94/1.37 eqswap: (3135) {G0,W10,D5,L1,V2,M1} { domain( multiplication( X, Y ) ) ==>
% 0.94/1.37 domain( multiplication( X, domain( Y ) ) ) }.
% 0.94/1.37 parent0[0]: (14) {G0,W10,D5,L1,V2,M1} I { domain( multiplication( X, domain
% 0.94/1.37 ( Y ) ) ) ==> domain( multiplication( X, Y ) ) }.
% 0.94/1.37 substitution0:
% 0.94/1.37 X := X
% 0.94/1.37 Y := Y
% 0.94/1.37 end
% 0.94/1.37
% 0.94/1.37 paramod: (3138) {G1,W8,D4,L1,V1,M1} { domain( multiplication( one, X ) )
% 0.94/1.37 ==> domain( domain( X ) ) }.
% 0.94/1.37 parent0[0]: (6) {G0,W5,D3,L1,V1,M1} I { multiplication( one, X ) ==> X }.
% 0.94/1.37 parent1[0; 6]: (3135) {G0,W10,D5,L1,V2,M1} { domain( multiplication( X, Y
% 0.94/1.37 ) ) ==> domain( multiplication( X, domain( Y ) ) ) }.
% 0.94/1.37 substitution0:
% 0.94/1.37 X := domain( X )
% 0.94/1.37 end
% 0.94/1.37 substitution1:
% 0.94/1.37 X := one
% 0.94/1.37 Y := X
% 0.94/1.37 end
% 0.94/1.37
% 0.94/1.37 paramod: (3140) {G1,W6,D4,L1,V1,M1} { domain( X ) ==> domain( domain( X )
% 0.94/1.37 ) }.
% 0.94/1.37 parent0[0]: (6) {G0,W5,D3,L1,V1,M1} I { multiplication( one, X ) ==> X }.
% 0.94/1.37 parent1[0; 2]: (3138) {G1,W8,D4,L1,V1,M1} { domain( multiplication( one, X
% 0.94/1.37 ) ) ==> domain( domain( X ) ) }.
% 0.94/1.37 substitution0:
% 0.94/1.37 X := X
% 0.94/1.37 end
% 0.94/1.37 substitution1:
% 0.94/1.37 X := X
% 0.94/1.37 end
% 0.94/1.37
% 0.94/1.37 eqswap: (3141) {G1,W6,D4,L1,V1,M1} { domain( domain( X ) ) ==> domain( X )
% 0.94/1.37 }.
% 0.94/1.37 parent0[0]: (3140) {G1,W6,D4,L1,V1,M1} { domain( X ) ==> domain( domain( X
% 0.94/1.37 ) ) }.
% 0.94/1.37 substitution0:
% 0.94/1.37 X := X
% 0.94/1.37 end
% 0.94/1.37
% 0.94/1.37 subsumption: (139) {G1,W6,D4,L1,V1,M1} P(6,14);d(6) { domain( domain( X ) )
% 0.94/1.37 ==> domain( X ) }.
% 0.94/1.37 parent0: (3141) {G1,W6,D4,L1,V1,M1} { domain( domain( X ) ) ==> domain( X
% 0.94/1.37 ) }.
% 0.94/1.37 substitution0:
% 0.94/1.37 X := X
% 0.94/1.37 end
% 0.94/1.37 permutation0:
% 0.94/1.37 0 ==> 0
% 0.94/1.37 end
% 0.94/1.37
% 0.94/1.37 eqswap: (3142) {G1,W11,D4,L1,V2,M1} { multiplication( addition( one, Y ),
% 0.94/1.37 X ) = addition( X, multiplication( Y, X ) ) }.
% 0.94/1.37 parent0[0]: (85) {G1,W11,D4,L1,V2,M1} P(6,8) { addition( X, multiplication
% 0.94/1.37 ( Y, X ) ) = multiplication( addition( one, Y ), X ) }.
% 0.94/1.37 substitution0:
% 0.94/1.37 X := X
% 0.94/1.37 Y := Y
% 0.94/1.37 end
% 0.94/1.37
% 0.94/1.37 paramod: (3147) {G1,W11,D5,L1,V1,M1} { multiplication( addition( one,
% 0.94/1.37 domain( X ) ), X ) = multiplication( domain( X ), X ) }.
% 0.94/1.37 parent0[0]: (13) {G0,W11,D5,L1,V1,M1} I { addition( X, multiplication(
% 0.94/1.37 domain( X ), X ) ) ==> multiplication( domain( X ), X ) }.
% 0.94/1.37 parent1[0; 7]: (3142) {G1,W11,D4,L1,V2,M1} { multiplication( addition( one
% 0.94/1.37 , Y ), X ) = addition( X, multiplication( Y, X ) ) }.
% 0.94/1.37 substitution0:
% 0.94/1.37 X := X
% 0.94/1.37 end
% 0.94/1.37 substitution1:
% 0.94/1.37 X := X
% 0.94/1.37 Y := domain( X )
% 0.94/1.37 end
% 0.94/1.37
% 0.94/1.37 paramod: (3148) {G2,W8,D4,L1,V1,M1} { multiplication( one, X ) =
% 0.94/1.37 multiplication( domain( X ), X ) }.
% 0.94/1.37 parent0[0]: (20) {G1,W6,D4,L1,V1,M1} P(15,0) { addition( one, domain( X ) )
% 0.94/1.37 ==> one }.
% 0.94/1.37 parent1[0; 2]: (3147) {G1,W11,D5,L1,V1,M1} { multiplication( addition( one
% 0.94/1.37 , domain( X ) ), X ) = multiplication( domain( X ), X ) }.
% 0.94/1.37 substitution0:
% 0.94/1.37 X := X
% 0.94/1.37 end
% 0.94/1.37 substitution1:
% 0.94/1.37 X := X
% 0.94/1.37 end
% 0.94/1.37
% 0.94/1.37 paramod: (3149) {G1,W6,D4,L1,V1,M1} { X = multiplication( domain( X ), X )
% 0.94/1.37 }.
% 0.94/1.37 parent0[0]: (6) {G0,W5,D3,L1,V1,M1} I { multiplication( one, X ) ==> X }.
% 0.94/1.37 parent1[0; 1]: (3148) {G2,W8,D4,L1,V1,M1} { multiplication( one, X ) =
% 0.94/1.37 multiplication( domain( X ), X ) }.
% 0.94/1.37 substitution0:
% 0.94/1.37 X := X
% 0.94/1.37 end
% 0.94/1.37 substitution1:
% 0.94/1.37 X := X
% 0.94/1.37 end
% 0.94/1.37
% 0.94/1.37 eqswap: (3150) {G1,W6,D4,L1,V1,M1} { multiplication( domain( X ), X ) = X
% 0.94/1.37 }.
% 0.94/1.37 parent0[0]: (3149) {G1,W6,D4,L1,V1,M1} { X = multiplication( domain( X ),
% 0.94/1.37 X ) }.
% 0.94/1.37 substitution0:
% 0.94/1.37 X := X
% 0.94/1.37 end
% 0.94/1.37
% 0.94/1.37 subsumption: (2688) {G2,W6,D4,L1,V1,M1} P(85,13);d(20);d(6) {
% 0.94/1.37 multiplication( domain( X ), X ) ==> X }.
% 0.94/1.37 parent0: (3150) {G1,W6,D4,L1,V1,M1} { multiplication( domain( X ), X ) = X
% 0.94/1.37 }.
% 0.94/1.37 substitution0:
% 0.94/1.37 X := X
% 0.94/1.37 end
% 0.94/1.37 permutation0:
% 0.94/1.37 0 ==> 0
% 0.94/1.37 end
% 0.94/1.37
% 0.94/1.37 eqswap: (3152) {G2,W6,D4,L1,V1,M1} { X ==> multiplication( domain( X ), X
% 0.94/1.37 ) }.
% 0.94/1.37 parent0[0]: (2688) {G2,W6,D4,L1,V1,M1} P(85,13);d(20);d(6) { multiplication
% 0.94/1.37 ( domain( X ), X ) ==> X }.
% 0.94/1.37 substitution0:
% 0.94/1.37 X := X
% 0.94/1.37 end
% 0.94/1.37
% 0.94/1.37 paramod: (3153) {G2,W8,D4,L1,V1,M1} { domain( X ) ==> multiplication(
% 0.94/1.37 domain( X ), domain( X ) ) }.
% 0.94/1.37 parent0[0]: (139) {G1,W6,D4,L1,V1,M1} P(6,14);d(6) { domain( domain( X ) )
% 0.94/1.37 ==> domain( X ) }.
% 0.94/1.37 parent1[0; 4]: (3152) {G2,W6,D4,L1,V1,M1} { X ==> multiplication( domain(
% 0.94/1.37 X ), X ) }.
% 0.94/1.37 substitution0:
% 0.94/1.37 X := X
% 0.94/1.37 end
% 0.94/1.37 substitution1:
% 0.94/1.37 X := domain( X )
% 0.94/1.37 end
% 0.94/1.37
% 0.94/1.37 eqswap: (3154) {G2,W8,D4,L1,V1,M1} { multiplication( domain( X ), domain(
% 0.94/1.37 X ) ) ==> domain( X ) }.
% 0.94/1.37 parent0[0]: (3153) {G2,W8,D4,L1,V1,M1} { domain( X ) ==> multiplication(
% 0.94/1.37 domain( X ), domain( X ) ) }.
% 0.94/1.37 substitution0:
% 0.94/1.37 X := X
% 0.94/1.37 end
% 0.94/1.37
% 0.94/1.37 subsumption: (2708) {G3,W8,D4,L1,V1,M1} P(139,2688) { multiplication(
% 0.94/1.37 domain( X ), domain( X ) ) ==> domain( X ) }.
% 0.94/1.37 parent0: (3154) {G2,W8,D4,L1,V1,M1} { multiplication( domain( X ), domain
% 0.94/1.37 ( X ) ) ==> domain( X ) }.
% 0.94/1.37 substitution0:
% 0.94/1.37 X := X
% 0.94/1.37 end
% 0.94/1.37 permutation0:
% 0.94/1.37 0 ==> 0
% 0.94/1.37 end
% 0.94/1.37
% 0.94/1.37 paramod: (3157) {G1,W5,D3,L1,V0,M1} { ! domain( skol1 ) ==> domain( skol1
% 0.94/1.37 ) }.
% 0.94/1.37 parent0[0]: (2708) {G3,W8,D4,L1,V1,M1} P(139,2688) { multiplication( domain
% 0.94/1.37 ( X ), domain( X ) ) ==> domain( X ) }.
% 0.94/1.37 parent1[0; 2]: (18) {G0,W8,D4,L1,V0,M1} I { ! multiplication( domain( skol1
% 0.94/1.37 ), domain( skol1 ) ) ==> domain( skol1 ) }.
% 0.94/1.37 substitution0:
% 0.94/1.37 X := skol1
% 0.94/1.37 end
% 0.94/1.37 substitution1:
% 0.94/1.37 end
% 0.94/1.37
% 0.94/1.37 eqrefl: (3158) {G0,W0,D0,L0,V0,M0} { }.
% 0.94/1.37 parent0[0]: (3157) {G1,W5,D3,L1,V0,M1} { ! domain( skol1 ) ==> domain(
% 0.94/1.37 skol1 ) }.
% 0.94/1.37 substitution0:
% 0.94/1.37 end
% 0.94/1.37
% 0.94/1.37 subsumption: (3028) {G4,W0,D0,L0,V0,M0} S(18);d(2708);q { }.
% 0.94/1.37 parent0: (3158) {G0,W0,D0,L0,V0,M0} { }.
% 0.94/1.37 substitution0:
% 0.94/1.37 end
% 0.94/1.37 permutation0:
% 0.94/1.37 end
% 0.94/1.37
% 0.94/1.37 Proof check complete!
% 0.94/1.37
% 0.94/1.37 Memory use:
% 0.94/1.37
% 0.94/1.37 space for terms: 38800
% 0.94/1.37 space for clauses: 154571
% 0.94/1.37
% 0.94/1.37
% 0.94/1.37 clauses generated: 26522
% 0.94/1.37 clauses kept: 3029
% 0.94/1.37 clauses selected: 289
% 0.94/1.37 clauses deleted: 37
% 0.94/1.37 clauses inuse deleted: 17
% 0.94/1.37
% 0.94/1.37 subsentry: 66165
% 0.94/1.37 literals s-matched: 44339
% 0.94/1.37 literals matched: 42196
% 0.94/1.37 full subsumption: 7995
% 0.94/1.37
% 0.94/1.37 checksum: -827825170
% 0.94/1.37
% 0.94/1.37
% 0.94/1.37 Bliksem ended
%------------------------------------------------------------------------------