TSTP Solution File: KLE055+1 by Bliksem---1.12
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%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : KLE055+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n032.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 0.54s 0.95s
% Output : Refutation 0.54s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : KLE055+1 : TPTP v8.1.0. Released v4.0.0.
% 0.00/0.10 % Command : bliksem %s
% 0.11/0.30 % Computer : n032.cluster.edu
% 0.11/0.30 % Model : x86_64 x86_64
% 0.11/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.30 % Memory : 8042.1875MB
% 0.11/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.30 % CPULimit : 300
% 0.11/0.30 % DateTime : Thu Jun 16 11:42:00 EDT 2022
% 0.11/0.30 % CPUTime :
% 0.54/0.95 *** allocated 10000 integers for termspace/termends
% 0.54/0.95 *** allocated 10000 integers for clauses
% 0.54/0.95 *** allocated 10000 integers for justifications
% 0.54/0.95 Bliksem 1.12
% 0.54/0.95
% 0.54/0.95
% 0.54/0.95 Automatic Strategy Selection
% 0.54/0.95
% 0.54/0.95
% 0.54/0.95 Clauses:
% 0.54/0.95
% 0.54/0.95 { addition( X, Y ) = addition( Y, X ) }.
% 0.54/0.95 { addition( Z, addition( Y, X ) ) = addition( addition( Z, Y ), X ) }.
% 0.54/0.95 { addition( X, zero ) = X }.
% 0.54/0.95 { addition( X, X ) = X }.
% 0.54/0.95 { multiplication( X, multiplication( Y, Z ) ) = multiplication(
% 0.54/0.95 multiplication( X, Y ), Z ) }.
% 0.54/0.95 { multiplication( X, one ) = X }.
% 0.54/0.95 { multiplication( one, X ) = X }.
% 0.54/0.95 { multiplication( X, addition( Y, Z ) ) = addition( multiplication( X, Y )
% 0.54/0.95 , multiplication( X, Z ) ) }.
% 0.54/0.95 { multiplication( addition( X, Y ), Z ) = addition( multiplication( X, Z )
% 0.54/0.95 , multiplication( Y, Z ) ) }.
% 0.54/0.95 { multiplication( X, zero ) = zero }.
% 0.54/0.95 { multiplication( zero, X ) = zero }.
% 0.54/0.95 { ! leq( X, Y ), addition( X, Y ) = Y }.
% 0.54/0.95 { ! addition( X, Y ) = Y, leq( X, Y ) }.
% 0.54/0.95 { addition( X, multiplication( domain( X ), X ) ) = multiplication( domain
% 0.54/0.95 ( X ), X ) }.
% 0.54/0.95 { domain( multiplication( X, Y ) ) = domain( multiplication( X, domain( Y )
% 0.54/0.95 ) ) }.
% 0.54/0.95 { addition( domain( X ), one ) = one }.
% 0.54/0.95 { domain( zero ) = zero }.
% 0.54/0.95 { domain( addition( X, Y ) ) = addition( domain( X ), domain( Y ) ) }.
% 0.54/0.95 { addition( skol1, one ) = one }.
% 0.54/0.95 { ! addition( skol1, domain( skol1 ) ) = domain( skol1 ) }.
% 0.54/0.95
% 0.54/0.95 percentage equality = 0.909091, percentage horn = 1.000000
% 0.54/0.95 This is a pure equality problem
% 0.54/0.95
% 0.54/0.95
% 0.54/0.95
% 0.54/0.95 Options Used:
% 0.54/0.95
% 0.54/0.95 useres = 1
% 0.54/0.95 useparamod = 1
% 0.54/0.95 useeqrefl = 1
% 0.54/0.95 useeqfact = 1
% 0.54/0.95 usefactor = 1
% 0.54/0.95 usesimpsplitting = 0
% 0.54/0.95 usesimpdemod = 5
% 0.54/0.95 usesimpres = 3
% 0.54/0.95
% 0.54/0.95 resimpinuse = 1000
% 0.54/0.95 resimpclauses = 20000
% 0.54/0.95 substype = eqrewr
% 0.54/0.95 backwardsubs = 1
% 0.54/0.95 selectoldest = 5
% 0.54/0.95
% 0.54/0.95 litorderings [0] = split
% 0.54/0.95 litorderings [1] = extend the termordering, first sorting on arguments
% 0.54/0.95
% 0.54/0.95 termordering = kbo
% 0.54/0.95
% 0.54/0.95 litapriori = 0
% 0.54/0.95 termapriori = 1
% 0.54/0.95 litaposteriori = 0
% 0.54/0.95 termaposteriori = 0
% 0.54/0.95 demodaposteriori = 0
% 0.54/0.95 ordereqreflfact = 0
% 0.54/0.95
% 0.54/0.95 litselect = negord
% 0.54/0.95
% 0.54/0.95 maxweight = 15
% 0.54/0.95 maxdepth = 30000
% 0.54/0.95 maxlength = 115
% 0.54/0.95 maxnrvars = 195
% 0.54/0.95 excuselevel = 1
% 0.54/0.95 increasemaxweight = 1
% 0.54/0.95
% 0.54/0.95 maxselected = 10000000
% 0.54/0.95 maxnrclauses = 10000000
% 0.54/0.95
% 0.54/0.95 showgenerated = 0
% 0.54/0.95 showkept = 0
% 0.54/0.95 showselected = 0
% 0.54/0.95 showdeleted = 0
% 0.54/0.95 showresimp = 1
% 0.54/0.95 showstatus = 2000
% 0.54/0.95
% 0.54/0.95 prologoutput = 0
% 0.54/0.95 nrgoals = 5000000
% 0.54/0.95 totalproof = 1
% 0.54/0.95
% 0.54/0.95 Symbols occurring in the translation:
% 0.54/0.95
% 0.54/0.95 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.54/0.95 . [1, 2] (w:1, o:20, a:1, s:1, b:0),
% 0.54/0.95 ! [4, 1] (w:0, o:14, a:1, s:1, b:0),
% 0.54/0.95 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.54/0.95 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.54/0.95 addition [37, 2] (w:1, o:44, a:1, s:1, b:0),
% 0.54/0.95 zero [39, 0] (w:1, o:9, a:1, s:1, b:0),
% 0.54/0.95 multiplication [40, 2] (w:1, o:46, a:1, s:1, b:0),
% 0.54/0.95 one [41, 0] (w:1, o:10, a:1, s:1, b:0),
% 0.54/0.95 leq [42, 2] (w:1, o:45, a:1, s:1, b:0),
% 0.54/0.95 domain [44, 1] (w:1, o:19, a:1, s:1, b:0),
% 0.54/0.95 skol1 [46, 0] (w:1, o:13, a:1, s:1, b:1).
% 0.54/0.95
% 0.54/0.95
% 0.54/0.95 Starting Search:
% 0.54/0.95
% 0.54/0.95 *** allocated 15000 integers for clauses
% 0.54/0.95 *** allocated 22500 integers for clauses
% 0.54/0.95 *** allocated 33750 integers for clauses
% 0.54/0.95 *** allocated 50625 integers for clauses
% 0.54/0.95 *** allocated 75937 integers for clauses
% 0.54/0.95
% 0.54/0.95 Bliksems!, er is een bewijs:
% 0.54/0.95 % SZS status Theorem
% 0.54/0.95 % SZS output start Refutation
% 0.54/0.95
% 0.54/0.95 (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X ) }.
% 0.54/0.95 (5) {G0,W5,D3,L1,V1,M1} I { multiplication( X, one ) ==> X }.
% 0.54/0.95 (6) {G0,W5,D3,L1,V1,M1} I { multiplication( one, X ) ==> X }.
% 0.54/0.95 (7) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Y ),
% 0.54/0.95 multiplication( X, Z ) ) ==> multiplication( X, addition( Y, Z ) ) }.
% 0.54/0.95 (8) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Z ),
% 0.54/0.95 multiplication( Y, Z ) ) ==> multiplication( addition( X, Y ), Z ) }.
% 0.54/0.95 (11) {G0,W8,D3,L2,V2,M2} I { ! leq( X, Y ), addition( X, Y ) ==> Y }.
% 0.54/0.95 (12) {G0,W8,D3,L2,V2,M2} I { ! addition( X, Y ) ==> Y, leq( X, Y ) }.
% 0.54/0.95 (13) {G0,W11,D5,L1,V1,M1} I { addition( X, multiplication( domain( X ), X )
% 0.54/0.95 ) ==> multiplication( domain( X ), X ) }.
% 0.54/0.95 (15) {G0,W6,D4,L1,V1,M1} I { addition( domain( X ), one ) ==> one }.
% 0.54/0.95 (18) {G0,W5,D3,L1,V0,M1} I { addition( skol1, one ) ==> one }.
% 0.54/0.95 (19) {G0,W7,D4,L1,V0,M1} I { ! addition( skol1, domain( skol1 ) ) ==>
% 0.54/0.95 domain( skol1 ) }.
% 0.54/0.95 (29) {G1,W6,D4,L1,V1,M1} P(15,0) { addition( one, domain( X ) ) ==> one }.
% 0.54/0.95 (41) {G1,W16,D4,L2,V3,M2} P(7,12) { ! multiplication( X, addition( Y, Z ) )
% 0.54/0.95 ==> multiplication( X, Z ), leq( multiplication( X, Y ), multiplication
% 0.54/0.95 ( X, Z ) ) }.
% 0.54/0.95 (51) {G1,W11,D4,L1,V2,M1} P(6,8) { addition( X, multiplication( Y, X ) ) =
% 0.54/0.95 multiplication( addition( one, Y ), X ) }.
% 0.54/0.95 (57) {G1,W4,D3,L1,V0,M1} R(11,19) { ! leq( skol1, domain( skol1 ) ) }.
% 0.54/0.95 (363) {G2,W5,D3,L1,V1,M1} P(18,41);q;d(5) { leq( multiplication( X, skol1 )
% 0.54/0.95 , X ) }.
% 0.54/0.95 (803) {G2,W6,D4,L1,V1,M1} P(51,13);d(29);d(6) { multiplication( domain( X )
% 0.54/0.95 , X ) ==> X }.
% 0.54/0.95 (820) {G3,W0,D0,L0,V0,M0} P(803,363);r(57) { }.
% 0.54/0.95
% 0.54/0.95
% 0.54/0.95 % SZS output end Refutation
% 0.54/0.95 found a proof!
% 0.54/0.95
% 0.54/0.95
% 0.54/0.95 Unprocessed initial clauses:
% 0.54/0.95
% 0.54/0.95 (822) {G0,W7,D3,L1,V2,M1} { addition( X, Y ) = addition( Y, X ) }.
% 0.54/0.95 (823) {G0,W11,D4,L1,V3,M1} { addition( Z, addition( Y, X ) ) = addition(
% 0.54/0.95 addition( Z, Y ), X ) }.
% 0.54/0.95 (824) {G0,W5,D3,L1,V1,M1} { addition( X, zero ) = X }.
% 0.54/0.95 (825) {G0,W5,D3,L1,V1,M1} { addition( X, X ) = X }.
% 0.54/0.95 (826) {G0,W11,D4,L1,V3,M1} { multiplication( X, multiplication( Y, Z ) ) =
% 0.54/0.95 multiplication( multiplication( X, Y ), Z ) }.
% 0.54/0.95 (827) {G0,W5,D3,L1,V1,M1} { multiplication( X, one ) = X }.
% 0.54/0.95 (828) {G0,W5,D3,L1,V1,M1} { multiplication( one, X ) = X }.
% 0.54/0.95 (829) {G0,W13,D4,L1,V3,M1} { multiplication( X, addition( Y, Z ) ) =
% 0.54/0.95 addition( multiplication( X, Y ), multiplication( X, Z ) ) }.
% 0.54/0.95 (830) {G0,W13,D4,L1,V3,M1} { multiplication( addition( X, Y ), Z ) =
% 0.54/0.95 addition( multiplication( X, Z ), multiplication( Y, Z ) ) }.
% 0.54/0.95 (831) {G0,W5,D3,L1,V1,M1} { multiplication( X, zero ) = zero }.
% 0.54/0.95 (832) {G0,W5,D3,L1,V1,M1} { multiplication( zero, X ) = zero }.
% 0.54/0.95 (833) {G0,W8,D3,L2,V2,M2} { ! leq( X, Y ), addition( X, Y ) = Y }.
% 0.54/0.95 (834) {G0,W8,D3,L2,V2,M2} { ! addition( X, Y ) = Y, leq( X, Y ) }.
% 0.54/0.95 (835) {G0,W11,D5,L1,V1,M1} { addition( X, multiplication( domain( X ), X )
% 0.54/0.95 ) = multiplication( domain( X ), X ) }.
% 0.54/0.95 (836) {G0,W10,D5,L1,V2,M1} { domain( multiplication( X, Y ) ) = domain(
% 0.54/0.95 multiplication( X, domain( Y ) ) ) }.
% 0.54/0.95 (837) {G0,W6,D4,L1,V1,M1} { addition( domain( X ), one ) = one }.
% 0.54/0.95 (838) {G0,W4,D3,L1,V0,M1} { domain( zero ) = zero }.
% 0.54/0.95 (839) {G0,W10,D4,L1,V2,M1} { domain( addition( X, Y ) ) = addition( domain
% 0.54/0.95 ( X ), domain( Y ) ) }.
% 0.54/0.95 (840) {G0,W5,D3,L1,V0,M1} { addition( skol1, one ) = one }.
% 0.54/0.95 (841) {G0,W7,D4,L1,V0,M1} { ! addition( skol1, domain( skol1 ) ) = domain
% 0.54/0.95 ( skol1 ) }.
% 0.54/0.95
% 0.54/0.95
% 0.54/0.95 Total Proof:
% 0.54/0.95
% 0.54/0.95 subsumption: (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X
% 0.54/0.95 ) }.
% 0.54/0.95 parent0: (822) {G0,W7,D3,L1,V2,M1} { addition( X, Y ) = addition( Y, X )
% 0.54/0.95 }.
% 0.54/0.95 substitution0:
% 0.54/0.95 X := X
% 0.54/0.95 Y := Y
% 0.54/0.95 end
% 0.54/0.95 permutation0:
% 0.54/0.95 0 ==> 0
% 0.54/0.95 end
% 0.54/0.95
% 0.54/0.95 subsumption: (5) {G0,W5,D3,L1,V1,M1} I { multiplication( X, one ) ==> X }.
% 0.54/0.95 parent0: (827) {G0,W5,D3,L1,V1,M1} { multiplication( X, one ) = X }.
% 0.54/0.95 substitution0:
% 0.54/0.95 X := X
% 0.54/0.95 end
% 0.54/0.95 permutation0:
% 0.54/0.95 0 ==> 0
% 0.54/0.95 end
% 0.54/0.95
% 0.54/0.95 subsumption: (6) {G0,W5,D3,L1,V1,M1} I { multiplication( one, X ) ==> X }.
% 0.54/0.95 parent0: (828) {G0,W5,D3,L1,V1,M1} { multiplication( one, X ) = X }.
% 0.54/0.95 substitution0:
% 0.54/0.95 X := X
% 0.54/0.95 end
% 0.54/0.95 permutation0:
% 0.54/0.95 0 ==> 0
% 0.54/0.95 end
% 0.54/0.95
% 0.54/0.95 *** allocated 15000 integers for termspace/termends
% 0.54/0.95 eqswap: (859) {G0,W13,D4,L1,V3,M1} { addition( multiplication( X, Y ),
% 0.54/0.95 multiplication( X, Z ) ) = multiplication( X, addition( Y, Z ) ) }.
% 0.54/0.95 parent0[0]: (829) {G0,W13,D4,L1,V3,M1} { multiplication( X, addition( Y, Z
% 0.54/0.95 ) ) = addition( multiplication( X, Y ), multiplication( X, Z ) ) }.
% 0.54/0.95 substitution0:
% 0.54/0.95 X := X
% 0.54/0.95 Y := Y
% 0.54/0.95 Z := Z
% 0.54/0.95 end
% 0.54/0.95
% 0.54/0.95 subsumption: (7) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Y )
% 0.54/0.95 , multiplication( X, Z ) ) ==> multiplication( X, addition( Y, Z ) ) }.
% 0.54/0.95 parent0: (859) {G0,W13,D4,L1,V3,M1} { addition( multiplication( X, Y ),
% 0.54/0.95 multiplication( X, Z ) ) = multiplication( X, addition( Y, Z ) ) }.
% 0.54/0.95 substitution0:
% 0.54/0.95 X := X
% 0.54/0.95 Y := Y
% 0.54/0.95 Z := Z
% 0.54/0.95 end
% 0.54/0.95 permutation0:
% 0.54/0.95 0 ==> 0
% 0.54/0.95 end
% 0.54/0.95
% 0.54/0.95 eqswap: (867) {G0,W13,D4,L1,V3,M1} { addition( multiplication( X, Z ),
% 0.54/0.95 multiplication( Y, Z ) ) = multiplication( addition( X, Y ), Z ) }.
% 0.54/0.95 parent0[0]: (830) {G0,W13,D4,L1,V3,M1} { multiplication( addition( X, Y )
% 0.54/0.95 , Z ) = addition( multiplication( X, Z ), multiplication( Y, Z ) ) }.
% 0.54/0.95 substitution0:
% 0.54/0.95 X := X
% 0.54/0.95 Y := Y
% 0.54/0.95 Z := Z
% 0.54/0.95 end
% 0.54/0.95
% 0.54/0.95 subsumption: (8) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Z )
% 0.54/0.95 , multiplication( Y, Z ) ) ==> multiplication( addition( X, Y ), Z ) }.
% 0.54/0.95 parent0: (867) {G0,W13,D4,L1,V3,M1} { addition( multiplication( X, Z ),
% 0.54/0.95 multiplication( Y, Z ) ) = multiplication( addition( X, Y ), Z ) }.
% 0.54/0.95 substitution0:
% 0.54/0.95 X := X
% 0.54/0.95 Y := Y
% 0.54/0.95 Z := Z
% 0.54/0.95 end
% 0.54/0.95 permutation0:
% 0.54/0.95 0 ==> 0
% 0.54/0.95 end
% 0.54/0.95
% 0.54/0.95 subsumption: (11) {G0,W8,D3,L2,V2,M2} I { ! leq( X, Y ), addition( X, Y )
% 0.54/0.95 ==> Y }.
% 0.54/0.95 parent0: (833) {G0,W8,D3,L2,V2,M2} { ! leq( X, Y ), addition( X, Y ) = Y
% 0.54/0.95 }.
% 0.54/0.95 substitution0:
% 0.54/0.95 X := X
% 0.54/0.95 Y := Y
% 0.54/0.95 end
% 0.54/0.95 permutation0:
% 0.54/0.95 0 ==> 0
% 0.54/0.95 1 ==> 1
% 0.54/0.95 end
% 0.54/0.95
% 0.54/0.95 subsumption: (12) {G0,W8,D3,L2,V2,M2} I { ! addition( X, Y ) ==> Y, leq( X
% 0.54/0.95 , Y ) }.
% 0.54/0.95 parent0: (834) {G0,W8,D3,L2,V2,M2} { ! addition( X, Y ) = Y, leq( X, Y )
% 0.54/0.95 }.
% 0.54/0.95 substitution0:
% 0.54/0.95 X := X
% 0.54/0.95 Y := Y
% 0.54/0.95 end
% 0.54/0.95 permutation0:
% 0.54/0.95 0 ==> 0
% 0.54/0.95 1 ==> 1
% 0.54/0.95 end
% 0.54/0.95
% 0.54/0.95 subsumption: (13) {G0,W11,D5,L1,V1,M1} I { addition( X, multiplication(
% 0.54/0.95 domain( X ), X ) ) ==> multiplication( domain( X ), X ) }.
% 0.54/0.95 parent0: (835) {G0,W11,D5,L1,V1,M1} { addition( X, multiplication( domain
% 0.54/0.95 ( X ), X ) ) = multiplication( domain( X ), X ) }.
% 0.54/0.95 substitution0:
% 0.54/0.95 X := X
% 0.54/0.95 end
% 0.54/0.95 permutation0:
% 0.54/0.95 0 ==> 0
% 0.54/0.95 end
% 0.54/0.95
% 0.54/0.95 subsumption: (15) {G0,W6,D4,L1,V1,M1} I { addition( domain( X ), one ) ==>
% 0.54/0.95 one }.
% 0.54/0.95 parent0: (837) {G0,W6,D4,L1,V1,M1} { addition( domain( X ), one ) = one
% 0.54/0.95 }.
% 0.54/0.95 substitution0:
% 0.54/0.95 X := X
% 0.54/0.95 end
% 0.54/0.95 permutation0:
% 0.54/0.95 0 ==> 0
% 0.54/0.95 end
% 0.54/0.95
% 0.54/0.95 subsumption: (18) {G0,W5,D3,L1,V0,M1} I { addition( skol1, one ) ==> one
% 0.54/0.95 }.
% 0.54/0.95 parent0: (840) {G0,W5,D3,L1,V0,M1} { addition( skol1, one ) = one }.
% 0.54/0.95 substitution0:
% 0.54/0.95 end
% 0.54/0.95 permutation0:
% 0.54/0.95 0 ==> 0
% 0.54/0.95 end
% 0.54/0.95
% 0.54/0.95 subsumption: (19) {G0,W7,D4,L1,V0,M1} I { ! addition( skol1, domain( skol1
% 0.54/0.95 ) ) ==> domain( skol1 ) }.
% 0.54/0.95 parent0: (841) {G0,W7,D4,L1,V0,M1} { ! addition( skol1, domain( skol1 ) )
% 0.54/0.95 = domain( skol1 ) }.
% 0.54/0.95 substitution0:
% 0.54/0.95 end
% 0.54/0.95 permutation0:
% 0.54/0.95 0 ==> 0
% 0.54/0.95 end
% 0.54/0.95
% 0.54/0.95 eqswap: (956) {G0,W6,D4,L1,V1,M1} { one ==> addition( domain( X ), one )
% 0.54/0.95 }.
% 0.54/0.95 parent0[0]: (15) {G0,W6,D4,L1,V1,M1} I { addition( domain( X ), one ) ==>
% 0.54/0.95 one }.
% 0.54/0.95 substitution0:
% 0.54/0.95 X := X
% 0.54/0.95 end
% 0.54/0.95
% 0.54/0.95 paramod: (957) {G1,W6,D4,L1,V1,M1} { one ==> addition( one, domain( X ) )
% 0.54/0.95 }.
% 0.54/0.95 parent0[0]: (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X )
% 0.54/0.95 }.
% 0.54/0.95 parent1[0; 2]: (956) {G0,W6,D4,L1,V1,M1} { one ==> addition( domain( X ),
% 0.54/0.95 one ) }.
% 0.54/0.95 substitution0:
% 0.54/0.95 X := domain( X )
% 0.54/0.95 Y := one
% 0.54/0.95 end
% 0.54/0.95 substitution1:
% 0.54/0.95 X := X
% 0.54/0.95 end
% 0.54/0.95
% 0.54/0.95 eqswap: (960) {G1,W6,D4,L1,V1,M1} { addition( one, domain( X ) ) ==> one
% 0.54/0.95 }.
% 0.54/0.95 parent0[0]: (957) {G1,W6,D4,L1,V1,M1} { one ==> addition( one, domain( X )
% 0.54/0.95 ) }.
% 0.54/0.95 substitution0:
% 0.54/0.95 X := X
% 0.54/0.95 end
% 0.54/0.95
% 0.54/0.95 subsumption: (29) {G1,W6,D4,L1,V1,M1} P(15,0) { addition( one, domain( X )
% 0.54/0.95 ) ==> one }.
% 0.54/0.95 parent0: (960) {G1,W6,D4,L1,V1,M1} { addition( one, domain( X ) ) ==> one
% 0.54/0.95 }.
% 0.54/0.95 substitution0:
% 0.54/0.95 X := X
% 0.54/0.95 end
% 0.54/0.95 permutation0:
% 0.54/0.95 0 ==> 0
% 0.54/0.95 end
% 0.54/0.95
% 0.54/0.95 eqswap: (962) {G0,W8,D3,L2,V2,M2} { ! Y ==> addition( X, Y ), leq( X, Y )
% 0.54/0.95 }.
% 0.54/0.95 parent0[0]: (12) {G0,W8,D3,L2,V2,M2} I { ! addition( X, Y ) ==> Y, leq( X,
% 0.54/0.95 Y ) }.
% 0.54/0.95 substitution0:
% 0.54/0.95 X := X
% 0.54/0.95 Y := Y
% 0.54/0.95 end
% 0.54/0.95
% 0.54/0.95 paramod: (963) {G1,W16,D4,L2,V3,M2} { ! multiplication( X, Y ) ==>
% 0.54/0.95 multiplication( X, addition( Z, Y ) ), leq( multiplication( X, Z ),
% 0.54/0.95 multiplication( X, Y ) ) }.
% 0.54/0.95 parent0[0]: (7) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Y ),
% 0.54/0.95 multiplication( X, Z ) ) ==> multiplication( X, addition( Y, Z ) ) }.
% 0.54/0.95 parent1[0; 5]: (962) {G0,W8,D3,L2,V2,M2} { ! Y ==> addition( X, Y ), leq(
% 0.54/0.95 X, Y ) }.
% 0.54/0.95 substitution0:
% 0.54/0.95 X := X
% 0.54/0.95 Y := Z
% 0.54/0.95 Z := Y
% 0.54/0.95 end
% 0.54/0.95 substitution1:
% 0.54/0.95 X := multiplication( X, Z )
% 0.54/0.95 Y := multiplication( X, Y )
% 0.54/0.95 end
% 0.54/0.95
% 0.54/0.95 eqswap: (964) {G1,W16,D4,L2,V3,M2} { ! multiplication( X, addition( Z, Y )
% 0.54/0.95 ) ==> multiplication( X, Y ), leq( multiplication( X, Z ),
% 0.54/0.95 multiplication( X, Y ) ) }.
% 0.54/0.95 parent0[0]: (963) {G1,W16,D4,L2,V3,M2} { ! multiplication( X, Y ) ==>
% 0.54/0.95 multiplication( X, addition( Z, Y ) ), leq( multiplication( X, Z ),
% 0.54/0.95 multiplication( X, Y ) ) }.
% 0.54/0.95 substitution0:
% 0.54/0.95 X := X
% 0.54/0.95 Y := Y
% 0.54/0.95 Z := Z
% 0.54/0.95 end
% 0.54/0.95
% 0.54/0.95 subsumption: (41) {G1,W16,D4,L2,V3,M2} P(7,12) { ! multiplication( X,
% 0.54/0.95 addition( Y, Z ) ) ==> multiplication( X, Z ), leq( multiplication( X, Y
% 0.54/0.95 ), multiplication( X, Z ) ) }.
% 0.54/0.95 parent0: (964) {G1,W16,D4,L2,V3,M2} { ! multiplication( X, addition( Z, Y
% 0.54/0.95 ) ) ==> multiplication( X, Y ), leq( multiplication( X, Z ),
% 0.54/0.95 multiplication( X, Y ) ) }.
% 0.54/0.95 substitution0:
% 0.54/0.95 X := X
% 0.54/0.95 Y := Z
% 0.54/0.95 Z := Y
% 0.54/0.95 end
% 0.54/0.95 permutation0:
% 0.54/0.95 0 ==> 0
% 0.54/0.95 1 ==> 1
% 0.54/0.95 end
% 0.54/0.95
% 0.54/0.95 eqswap: (966) {G0,W13,D4,L1,V3,M1} { multiplication( addition( X, Z ), Y )
% 0.54/0.95 ==> addition( multiplication( X, Y ), multiplication( Z, Y ) ) }.
% 0.54/0.95 parent0[0]: (8) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Z ),
% 0.54/0.95 multiplication( Y, Z ) ) ==> multiplication( addition( X, Y ), Z ) }.
% 0.54/0.95 substitution0:
% 0.54/0.95 X := X
% 0.54/0.95 Y := Z
% 0.54/0.95 Z := Y
% 0.54/0.95 end
% 0.54/0.95
% 0.54/0.95 paramod: (967) {G1,W11,D4,L1,V2,M1} { multiplication( addition( one, X ),
% 0.54/0.95 Y ) ==> addition( Y, multiplication( X, Y ) ) }.
% 0.54/0.95 parent0[0]: (6) {G0,W5,D3,L1,V1,M1} I { multiplication( one, X ) ==> X }.
% 0.54/0.95 parent1[0; 7]: (966) {G0,W13,D4,L1,V3,M1} { multiplication( addition( X, Z
% 0.54/0.95 ), Y ) ==> addition( multiplication( X, Y ), multiplication( Z, Y ) )
% 0.54/0.95 }.
% 0.54/0.95 substitution0:
% 0.54/0.95 X := Y
% 0.54/0.95 end
% 0.54/0.95 substitution1:
% 0.54/0.95 X := one
% 0.54/0.95 Y := Y
% 0.54/0.95 Z := X
% 0.54/0.95 end
% 0.54/0.95
% 0.54/0.95 eqswap: (969) {G1,W11,D4,L1,V2,M1} { addition( Y, multiplication( X, Y ) )
% 0.54/0.95 ==> multiplication( addition( one, X ), Y ) }.
% 0.54/0.95 parent0[0]: (967) {G1,W11,D4,L1,V2,M1} { multiplication( addition( one, X
% 0.54/0.95 ), Y ) ==> addition( Y, multiplication( X, Y ) ) }.
% 0.54/0.95 substitution0:
% 0.54/0.95 X := X
% 0.54/0.95 Y := Y
% 0.54/0.95 end
% 0.54/0.95
% 0.54/0.95 subsumption: (51) {G1,W11,D4,L1,V2,M1} P(6,8) { addition( X, multiplication
% 0.54/0.95 ( Y, X ) ) = multiplication( addition( one, Y ), X ) }.
% 0.54/0.95 parent0: (969) {G1,W11,D4,L1,V2,M1} { addition( Y, multiplication( X, Y )
% 0.54/0.95 ) ==> multiplication( addition( one, X ), Y ) }.
% 0.54/0.95 substitution0:
% 0.54/0.95 X := Y
% 0.54/0.95 Y := X
% 0.54/0.95 end
% 0.54/0.95 permutation0:
% 0.54/0.95 0 ==> 0
% 0.54/0.95 end
% 0.54/0.95
% 0.54/0.95 eqswap: (971) {G0,W8,D3,L2,V2,M2} { Y ==> addition( X, Y ), ! leq( X, Y )
% 0.54/0.95 }.
% 0.54/0.95 parent0[1]: (11) {G0,W8,D3,L2,V2,M2} I { ! leq( X, Y ), addition( X, Y )
% 0.54/0.95 ==> Y }.
% 0.54/0.95 substitution0:
% 0.54/0.95 X := X
% 0.54/0.95 Y := Y
% 0.54/0.95 end
% 0.54/0.95
% 0.54/0.95 eqswap: (972) {G0,W7,D4,L1,V0,M1} { ! domain( skol1 ) ==> addition( skol1
% 0.54/0.95 , domain( skol1 ) ) }.
% 0.54/0.95 parent0[0]: (19) {G0,W7,D4,L1,V0,M1} I { ! addition( skol1, domain( skol1 )
% 0.54/0.95 ) ==> domain( skol1 ) }.
% 0.54/0.95 substitution0:
% 0.54/0.95 end
% 0.54/0.95
% 0.54/0.95 resolution: (973) {G1,W4,D3,L1,V0,M1} { ! leq( skol1, domain( skol1 ) )
% 0.54/0.95 }.
% 0.54/0.95 parent0[0]: (972) {G0,W7,D4,L1,V0,M1} { ! domain( skol1 ) ==> addition(
% 0.54/0.95 skol1, domain( skol1 ) ) }.
% 0.54/0.95 parent1[0]: (971) {G0,W8,D3,L2,V2,M2} { Y ==> addition( X, Y ), ! leq( X,
% 0.54/0.95 Y ) }.
% 0.54/0.95 substitution0:
% 0.54/0.95 end
% 0.54/0.95 substitution1:
% 0.54/0.95 X := skol1
% 0.54/0.95 Y := domain( skol1 )
% 0.54/0.95 end
% 0.54/0.95
% 0.54/0.95 subsumption: (57) {G1,W4,D3,L1,V0,M1} R(11,19) { ! leq( skol1, domain(
% 0.54/0.95 skol1 ) ) }.
% 0.54/0.95 parent0: (973) {G1,W4,D3,L1,V0,M1} { ! leq( skol1, domain( skol1 ) ) }.
% 0.54/0.95 substitution0:
% 0.54/0.95 end
% 0.54/0.95 permutation0:
% 0.54/0.95 0 ==> 0
% 0.54/0.95 end
% 0.54/0.95
% 0.54/0.95 eqswap: (975) {G1,W16,D4,L2,V3,M2} { ! multiplication( X, Z ) ==>
% 0.54/0.95 multiplication( X, addition( Y, Z ) ), leq( multiplication( X, Y ),
% 0.54/0.95 multiplication( X, Z ) ) }.
% 0.54/0.95 parent0[0]: (41) {G1,W16,D4,L2,V3,M2} P(7,12) { ! multiplication( X,
% 0.54/0.95 addition( Y, Z ) ) ==> multiplication( X, Z ), leq( multiplication( X, Y
% 0.54/0.95 ), multiplication( X, Z ) ) }.
% 0.54/0.95 substitution0:
% 0.54/0.95 X := X
% 0.54/0.95 Y := Y
% 0.54/0.95 Z := Z
% 0.54/0.95 end
% 0.54/0.95
% 0.54/0.95 paramod: (977) {G1,W14,D3,L2,V1,M2} { ! multiplication( X, one ) ==>
% 0.54/0.95 multiplication( X, one ), leq( multiplication( X, skol1 ), multiplication
% 0.54/0.95 ( X, one ) ) }.
% 0.54/0.95 parent0[0]: (18) {G0,W5,D3,L1,V0,M1} I { addition( skol1, one ) ==> one }.
% 0.54/0.95 parent1[0; 7]: (975) {G1,W16,D4,L2,V3,M2} { ! multiplication( X, Z ) ==>
% 0.54/0.95 multiplication( X, addition( Y, Z ) ), leq( multiplication( X, Y ),
% 0.54/0.95 multiplication( X, Z ) ) }.
% 0.54/0.95 substitution0:
% 0.54/0.95 end
% 0.54/0.95 substitution1:
% 0.54/0.95 X := X
% 0.54/0.95 Y := skol1
% 0.54/0.95 Z := one
% 0.54/0.95 end
% 0.54/0.95
% 0.54/0.95 eqrefl: (978) {G0,W7,D3,L1,V1,M1} { leq( multiplication( X, skol1 ),
% 0.54/0.95 multiplication( X, one ) ) }.
% 0.54/0.95 parent0[0]: (977) {G1,W14,D3,L2,V1,M2} { ! multiplication( X, one ) ==>
% 0.54/0.95 multiplication( X, one ), leq( multiplication( X, skol1 ), multiplication
% 0.54/0.95 ( X, one ) ) }.
% 0.54/0.95 substitution0:
% 0.54/0.95 X := X
% 0.54/0.95 end
% 0.54/0.95
% 0.54/0.95 paramod: (979) {G1,W5,D3,L1,V1,M1} { leq( multiplication( X, skol1 ), X )
% 0.54/0.95 }.
% 0.54/0.95 parent0[0]: (5) {G0,W5,D3,L1,V1,M1} I { multiplication( X, one ) ==> X }.
% 0.54/0.95 parent1[0; 4]: (978) {G0,W7,D3,L1,V1,M1} { leq( multiplication( X, skol1 )
% 0.54/0.95 , multiplication( X, one ) ) }.
% 0.54/0.95 substitution0:
% 0.54/0.95 X := X
% 0.54/0.95 end
% 0.54/0.95 substitution1:
% 0.54/0.95 X := X
% 0.54/0.95 end
% 0.54/0.95
% 0.54/0.95 subsumption: (363) {G2,W5,D3,L1,V1,M1} P(18,41);q;d(5) { leq(
% 0.54/0.95 multiplication( X, skol1 ), X ) }.
% 0.54/0.95 parent0: (979) {G1,W5,D3,L1,V1,M1} { leq( multiplication( X, skol1 ), X )
% 0.54/0.95 }.
% 0.54/0.95 substitution0:
% 0.54/0.95 X := X
% 0.54/0.95 end
% 0.54/0.95 permutation0:
% 0.54/0.95 0 ==> 0
% 0.54/0.95 end
% 0.54/0.95
% 0.54/0.95 eqswap: (980) {G1,W11,D4,L1,V2,M1} { multiplication( addition( one, Y ), X
% 0.54/0.95 ) = addition( X, multiplication( Y, X ) ) }.
% 0.54/0.95 parent0[0]: (51) {G1,W11,D4,L1,V2,M1} P(6,8) { addition( X, multiplication
% 0.54/0.95 ( Y, X ) ) = multiplication( addition( one, Y ), X ) }.
% 0.54/0.95 substitution0:
% 0.54/0.95 X := X
% 0.54/0.95 Y := Y
% 0.54/0.95 end
% 0.54/0.95
% 0.54/0.95 paramod: (985) {G1,W11,D5,L1,V1,M1} { multiplication( addition( one,
% 0.54/0.95 domain( X ) ), X ) = multiplication( domain( X ), X ) }.
% 0.54/0.95 parent0[0]: (13) {G0,W11,D5,L1,V1,M1} I { addition( X, multiplication(
% 0.54/0.95 domain( X ), X ) ) ==> multiplication( domain( X ), X ) }.
% 0.54/0.95 parent1[0; 7]: (980) {G1,W11,D4,L1,V2,M1} { multiplication( addition( one
% 0.54/0.95 , Y ), X ) = addition( X, multiplication( Y, X ) ) }.
% 0.54/0.95 substitution0:
% 0.54/0.95 X := X
% 0.54/0.95 end
% 0.54/0.95 substitution1:
% 0.54/0.95 X := X
% 0.54/0.95 Y := domain( X )
% 0.54/0.95 end
% 0.54/0.95
% 0.54/0.95 paramod: (986) {G2,W8,D4,L1,V1,M1} { multiplication( one, X ) =
% 0.54/0.95 multiplication( domain( X ), X ) }.
% 0.54/0.95 parent0[0]: (29) {G1,W6,D4,L1,V1,M1} P(15,0) { addition( one, domain( X ) )
% 0.54/0.95 ==> one }.
% 0.54/0.95 parent1[0; 2]: (985) {G1,W11,D5,L1,V1,M1} { multiplication( addition( one
% 0.54/0.95 , domain( X ) ), X ) = multiplication( domain( X ), X ) }.
% 0.54/0.95 substitution0:
% 0.54/0.95 X := X
% 0.54/0.95 end
% 0.54/0.95 substitution1:
% 0.54/0.95 X := X
% 0.54/0.95 end
% 0.54/0.95
% 0.54/0.95 paramod: (987) {G1,W6,D4,L1,V1,M1} { X = multiplication( domain( X ), X )
% 0.54/0.95 }.
% 0.54/0.95 parent0[0]: (6) {G0,W5,D3,L1,V1,M1} I { multiplication( one, X ) ==> X }.
% 0.54/0.95 parent1[0; 1]: (986) {G2,W8,D4,L1,V1,M1} { multiplication( one, X ) =
% 0.54/0.95 multiplication( domain( X ), X ) }.
% 0.54/0.95 substitution0:
% 0.54/0.95 X := X
% 0.54/0.95 end
% 0.54/0.95 substitution1:
% 0.54/0.95 X := X
% 0.54/0.95 end
% 0.54/0.95
% 0.54/0.95 eqswap: (988) {G1,W6,D4,L1,V1,M1} { multiplication( domain( X ), X ) = X
% 0.54/0.95 }.
% 0.54/0.95 parent0[0]: (987) {G1,W6,D4,L1,V1,M1} { X = multiplication( domain( X ), X
% 0.54/0.95 ) }.
% 0.54/0.95 substitution0:
% 0.54/0.95 X := X
% 0.54/0.95 end
% 0.54/0.95
% 0.54/0.95 subsumption: (803) {G2,W6,D4,L1,V1,M1} P(51,13);d(29);d(6) { multiplication
% 0.54/0.95 ( domain( X ), X ) ==> X }.
% 0.54/0.95 parent0: (988) {G1,W6,D4,L1,V1,M1} { multiplication( domain( X ), X ) = X
% 0.54/0.95 }.
% 0.54/0.95 substitution0:
% 0.54/0.95 X := X
% 0.54/0.95 end
% 0.54/0.95 permutation0:
% 0.54/0.95 0 ==> 0
% 0.54/0.95 end
% 0.54/0.95
% 0.54/0.95 paramod: (990) {G3,W4,D3,L1,V0,M1} { leq( skol1, domain( skol1 ) ) }.
% 0.54/0.95 parent0[0]: (803) {G2,W6,D4,L1,V1,M1} P(51,13);d(29);d(6) { multiplication
% 0.54/0.95 ( domain( X ), X ) ==> X }.
% 0.54/0.95 parent1[0; 1]: (363) {G2,W5,D3,L1,V1,M1} P(18,41);q;d(5) { leq(
% 0.54/0.95 multiplication( X, skol1 ), X ) }.
% 0.54/0.95 substitution0:
% 0.54/0.95 X := skol1
% 0.54/0.95 end
% 0.54/0.95 substitution1:
% 0.54/0.95 X := domain( skol1 )
% 0.54/0.95 end
% 0.54/0.95
% 0.54/0.95 resolution: (991) {G2,W0,D0,L0,V0,M0} { }.
% 0.54/0.95 parent0[0]: (57) {G1,W4,D3,L1,V0,M1} R(11,19) { ! leq( skol1, domain( skol1
% 0.54/0.95 ) ) }.
% 0.54/0.95 parent1[0]: (990) {G3,W4,D3,L1,V0,M1} { leq( skol1, domain( skol1 ) ) }.
% 0.54/0.95 substitution0:
% 0.54/0.95 end
% 0.54/0.95 substitution1:
% 0.54/0.95 end
% 0.54/0.95
% 0.54/0.95 subsumption: (820) {G3,W0,D0,L0,V0,M0} P(803,363);r(57) { }.
% 0.54/0.95 parent0: (991) {G2,W0,D0,L0,V0,M0} { }.
% 0.54/0.95 substitution0:
% 0.54/0.95 end
% 0.54/0.95 permutation0:
% 0.54/0.95 end
% 0.54/0.95
% 0.54/0.95 Proof check complete!
% 0.54/0.95
% 0.54/0.95 Memory use:
% 0.54/0.95
% 0.54/0.95 space for terms: 9681
% 0.54/0.95 space for clauses: 55170
% 0.54/0.95
% 0.54/0.95
% 0.54/0.95 clauses generated: 5420
% 0.54/0.95 clauses kept: 821
% 0.54/0.95 clauses selected: 141
% 0.54/0.95 clauses deleted: 6
% 0.54/0.95 clauses inuse deleted: 0
% 0.54/0.95
% 0.54/0.95 subsentry: 6269
% 0.54/0.95 literals s-matched: 4724
% 0.54/0.95 literals matched: 4683
% 0.54/0.95 full subsumption: 231
% 0.54/0.95
% 0.54/0.95 checksum: 841756458
% 0.54/0.95
% 0.54/0.95
% 0.54/0.95 Bliksem ended
%------------------------------------------------------------------------------