TSTP Solution File: KLE083+1 by Bliksem---1.12
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%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : KLE083+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n022.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 01:37:04 EDT 2022
% Result : Theorem 0.71s 1.14s
% Output : Refutation 0.71s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : KLE083+1 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.13 % Command : bliksem %s
% 0.13/0.33 % Computer : n022.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 15:35:02 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.71/1.14 *** allocated 10000 integers for termspace/termends
% 0.71/1.14 *** allocated 10000 integers for clauses
% 0.71/1.14 *** allocated 10000 integers for justifications
% 0.71/1.14 Bliksem 1.12
% 0.71/1.14
% 0.71/1.14
% 0.71/1.14 Automatic Strategy Selection
% 0.71/1.14
% 0.71/1.14
% 0.71/1.14 Clauses:
% 0.71/1.14
% 0.71/1.14 { addition( X, Y ) = addition( Y, X ) }.
% 0.71/1.14 { addition( Z, addition( Y, X ) ) = addition( addition( Z, Y ), X ) }.
% 0.71/1.14 { addition( X, zero ) = X }.
% 0.71/1.14 { addition( X, X ) = X }.
% 0.71/1.14 { multiplication( X, multiplication( Y, Z ) ) = multiplication(
% 0.71/1.14 multiplication( X, Y ), Z ) }.
% 0.71/1.14 { multiplication( X, one ) = X }.
% 0.71/1.14 { multiplication( one, X ) = X }.
% 0.71/1.14 { multiplication( X, addition( Y, Z ) ) = addition( multiplication( X, Y )
% 0.71/1.14 , multiplication( X, Z ) ) }.
% 0.71/1.14 { multiplication( addition( X, Y ), Z ) = addition( multiplication( X, Z )
% 0.71/1.14 , multiplication( Y, Z ) ) }.
% 0.71/1.14 { multiplication( X, zero ) = zero }.
% 0.71/1.14 { multiplication( zero, X ) = zero }.
% 0.71/1.14 { ! leq( X, Y ), addition( X, Y ) = Y }.
% 0.71/1.14 { ! addition( X, Y ) = Y, leq( X, Y ) }.
% 0.71/1.14 { multiplication( antidomain( X ), X ) = zero }.
% 0.71/1.14 { addition( antidomain( multiplication( X, Y ) ), antidomain(
% 0.71/1.14 multiplication( X, antidomain( antidomain( Y ) ) ) ) ) = antidomain(
% 0.71/1.14 multiplication( X, antidomain( antidomain( Y ) ) ) ) }.
% 0.71/1.14 { addition( antidomain( antidomain( X ) ), antidomain( X ) ) = one }.
% 0.71/1.14 { domain( X ) = antidomain( antidomain( X ) ) }.
% 0.71/1.14 { multiplication( X, coantidomain( X ) ) = zero }.
% 0.71/1.14 { addition( coantidomain( multiplication( X, Y ) ), coantidomain(
% 0.71/1.14 multiplication( coantidomain( coantidomain( X ) ), Y ) ) ) = coantidomain
% 0.71/1.14 ( multiplication( coantidomain( coantidomain( X ) ), Y ) ) }.
% 0.71/1.14 { addition( coantidomain( coantidomain( X ) ), coantidomain( X ) ) = one }
% 0.71/1.14 .
% 0.71/1.14 { codomain( X ) = coantidomain( coantidomain( X ) ) }.
% 0.71/1.14 { ! skol1 = multiplication( domain( skol1 ), skol1 ) }.
% 0.71/1.14
% 0.71/1.14 percentage equality = 0.916667, percentage horn = 1.000000
% 0.71/1.14 This is a pure equality problem
% 0.71/1.14
% 0.71/1.14
% 0.71/1.14
% 0.71/1.14 Options Used:
% 0.71/1.14
% 0.71/1.14 useres = 1
% 0.71/1.14 useparamod = 1
% 0.71/1.14 useeqrefl = 1
% 0.71/1.14 useeqfact = 1
% 0.71/1.14 usefactor = 1
% 0.71/1.14 usesimpsplitting = 0
% 0.71/1.14 usesimpdemod = 5
% 0.71/1.14 usesimpres = 3
% 0.71/1.14
% 0.71/1.14 resimpinuse = 1000
% 0.71/1.14 resimpclauses = 20000
% 0.71/1.14 substype = eqrewr
% 0.71/1.14 backwardsubs = 1
% 0.71/1.14 selectoldest = 5
% 0.71/1.14
% 0.71/1.14 litorderings [0] = split
% 0.71/1.14 litorderings [1] = extend the termordering, first sorting on arguments
% 0.71/1.14
% 0.71/1.14 termordering = kbo
% 0.71/1.14
% 0.71/1.14 litapriori = 0
% 0.71/1.14 termapriori = 1
% 0.71/1.14 litaposteriori = 0
% 0.71/1.14 termaposteriori = 0
% 0.71/1.14 demodaposteriori = 0
% 0.71/1.14 ordereqreflfact = 0
% 0.71/1.14
% 0.71/1.14 litselect = negord
% 0.71/1.14
% 0.71/1.14 maxweight = 15
% 0.71/1.14 maxdepth = 30000
% 0.71/1.14 maxlength = 115
% 0.71/1.14 maxnrvars = 195
% 0.71/1.14 excuselevel = 1
% 0.71/1.14 increasemaxweight = 1
% 0.71/1.14
% 0.71/1.14 maxselected = 10000000
% 0.71/1.14 maxnrclauses = 10000000
% 0.71/1.14
% 0.71/1.14 showgenerated = 0
% 0.71/1.14 showkept = 0
% 0.71/1.14 showselected = 0
% 0.71/1.14 showdeleted = 0
% 0.71/1.14 showresimp = 1
% 0.71/1.14 showstatus = 2000
% 0.71/1.14
% 0.71/1.14 prologoutput = 0
% 0.71/1.14 nrgoals = 5000000
% 0.71/1.14 totalproof = 1
% 0.71/1.14
% 0.71/1.14 Symbols occurring in the translation:
% 0.71/1.14
% 0.71/1.14 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.71/1.14 . [1, 2] (w:1, o:23, a:1, s:1, b:0),
% 0.71/1.14 ! [4, 1] (w:0, o:14, a:1, s:1, b:0),
% 0.71/1.14 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.71/1.14 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.71/1.14 addition [37, 2] (w:1, o:47, a:1, s:1, b:0),
% 0.71/1.14 zero [39, 0] (w:1, o:9, a:1, s:1, b:0),
% 0.71/1.14 multiplication [40, 2] (w:1, o:49, a:1, s:1, b:0),
% 0.71/1.14 one [41, 0] (w:1, o:10, a:1, s:1, b:0),
% 0.71/1.14 leq [42, 2] (w:1, o:48, a:1, s:1, b:0),
% 0.71/1.14 antidomain [44, 1] (w:1, o:19, a:1, s:1, b:0),
% 0.71/1.14 domain [46, 1] (w:1, o:22, a:1, s:1, b:0),
% 0.71/1.14 coantidomain [47, 1] (w:1, o:20, a:1, s:1, b:0),
% 0.71/1.14 codomain [48, 1] (w:1, o:21, a:1, s:1, b:0),
% 0.71/1.14 skol1 [49, 0] (w:1, o:13, a:1, s:1, b:1).
% 0.71/1.14
% 0.71/1.14
% 0.71/1.14 Starting Search:
% 0.71/1.14
% 0.71/1.14 *** allocated 15000 integers for clauses
% 0.71/1.14 *** allocated 22500 integers for clauses
% 0.71/1.14 *** allocated 33750 integers for clauses
% 0.71/1.14 *** allocated 50625 integers for clauses
% 0.71/1.14 *** allocated 75937 integers for clauses
% 0.71/1.14 *** allocated 15000 integers for termspace/termends
% 0.71/1.14 Resimplifying inuse:
% 0.71/1.14 Done
% 0.71/1.14
% 0.71/1.14 *** allocated 113905 integers for clauses
% 0.71/1.14
% 0.71/1.14 Bliksems!, er is een bewijs:
% 0.71/1.14 % SZS status Theorem
% 0.71/1.14 % SZS output start Refutation
% 0.71/1.14
% 0.71/1.14 (2) {G0,W5,D3,L1,V1,M1} I { addition( X, zero ) ==> X }.
% 0.71/1.14 (6) {G0,W5,D3,L1,V1,M1} I { multiplication( one, X ) ==> X }.
% 0.71/1.14 (8) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Z ),
% 0.71/1.14 multiplication( Y, Z ) ) ==> multiplication( addition( X, Y ), Z ) }.
% 0.71/1.14 (13) {G0,W6,D4,L1,V1,M1} I { multiplication( antidomain( X ), X ) ==> zero
% 0.71/1.14 }.
% 0.71/1.14 (15) {G0,W8,D5,L1,V1,M1} I { addition( antidomain( antidomain( X ) ),
% 0.71/1.14 antidomain( X ) ) ==> one }.
% 0.71/1.14 (16) {G0,W6,D4,L1,V1,M1} I { antidomain( antidomain( X ) ) ==> domain( X )
% 0.71/1.14 }.
% 0.71/1.14 (21) {G0,W6,D4,L1,V0,M1} I { ! multiplication( domain( skol1 ), skol1 ) ==>
% 0.71/1.14 skol1 }.
% 0.71/1.14 (66) {G1,W10,D5,L1,V2,M1} P(13,8);d(2) { multiplication( addition( Y,
% 0.71/1.14 antidomain( X ) ), X ) ==> multiplication( Y, X ) }.
% 0.71/1.14 (143) {G1,W7,D4,L1,V1,M1} S(15);d(16) { addition( domain( X ), antidomain(
% 0.71/1.14 X ) ) ==> one }.
% 0.71/1.14 (1091) {G2,W6,D4,L1,V1,M1} P(143,66);d(6) { multiplication( domain( X ), X
% 0.71/1.14 ) ==> X }.
% 0.71/1.14 (1096) {G3,W0,D0,L0,V0,M0} R(1091,21) { }.
% 0.71/1.14
% 0.71/1.14
% 0.71/1.14 % SZS output end Refutation
% 0.71/1.14 found a proof!
% 0.71/1.14
% 0.71/1.14
% 0.71/1.14 Unprocessed initial clauses:
% 0.71/1.14
% 0.71/1.14 (1098) {G0,W7,D3,L1,V2,M1} { addition( X, Y ) = addition( Y, X ) }.
% 0.71/1.14 (1099) {G0,W11,D4,L1,V3,M1} { addition( Z, addition( Y, X ) ) = addition(
% 0.71/1.14 addition( Z, Y ), X ) }.
% 0.71/1.14 (1100) {G0,W5,D3,L1,V1,M1} { addition( X, zero ) = X }.
% 0.71/1.14 (1101) {G0,W5,D3,L1,V1,M1} { addition( X, X ) = X }.
% 0.71/1.14 (1102) {G0,W11,D4,L1,V3,M1} { multiplication( X, multiplication( Y, Z ) )
% 0.71/1.14 = multiplication( multiplication( X, Y ), Z ) }.
% 0.71/1.14 (1103) {G0,W5,D3,L1,V1,M1} { multiplication( X, one ) = X }.
% 0.71/1.14 (1104) {G0,W5,D3,L1,V1,M1} { multiplication( one, X ) = X }.
% 0.71/1.14 (1105) {G0,W13,D4,L1,V3,M1} { multiplication( X, addition( Y, Z ) ) =
% 0.71/1.14 addition( multiplication( X, Y ), multiplication( X, Z ) ) }.
% 0.71/1.14 (1106) {G0,W13,D4,L1,V3,M1} { multiplication( addition( X, Y ), Z ) =
% 0.71/1.14 addition( multiplication( X, Z ), multiplication( Y, Z ) ) }.
% 0.71/1.14 (1107) {G0,W5,D3,L1,V1,M1} { multiplication( X, zero ) = zero }.
% 0.71/1.14 (1108) {G0,W5,D3,L1,V1,M1} { multiplication( zero, X ) = zero }.
% 0.71/1.14 (1109) {G0,W8,D3,L2,V2,M2} { ! leq( X, Y ), addition( X, Y ) = Y }.
% 0.71/1.14 (1110) {G0,W8,D3,L2,V2,M2} { ! addition( X, Y ) = Y, leq( X, Y ) }.
% 0.71/1.14 (1111) {G0,W6,D4,L1,V1,M1} { multiplication( antidomain( X ), X ) = zero
% 0.71/1.14 }.
% 0.71/1.14 (1112) {G0,W18,D7,L1,V2,M1} { addition( antidomain( multiplication( X, Y )
% 0.71/1.14 ), antidomain( multiplication( X, antidomain( antidomain( Y ) ) ) ) ) =
% 0.71/1.14 antidomain( multiplication( X, antidomain( antidomain( Y ) ) ) ) }.
% 0.71/1.14 (1113) {G0,W8,D5,L1,V1,M1} { addition( antidomain( antidomain( X ) ),
% 0.71/1.14 antidomain( X ) ) = one }.
% 0.71/1.14 (1114) {G0,W6,D4,L1,V1,M1} { domain( X ) = antidomain( antidomain( X ) )
% 0.71/1.14 }.
% 0.71/1.14 (1115) {G0,W6,D4,L1,V1,M1} { multiplication( X, coantidomain( X ) ) = zero
% 0.71/1.14 }.
% 0.71/1.14 (1116) {G0,W18,D7,L1,V2,M1} { addition( coantidomain( multiplication( X, Y
% 0.71/1.14 ) ), coantidomain( multiplication( coantidomain( coantidomain( X ) ), Y
% 0.71/1.14 ) ) ) = coantidomain( multiplication( coantidomain( coantidomain( X ) )
% 0.71/1.14 , Y ) ) }.
% 0.71/1.14 (1117) {G0,W8,D5,L1,V1,M1} { addition( coantidomain( coantidomain( X ) ),
% 0.71/1.14 coantidomain( X ) ) = one }.
% 0.71/1.14 (1118) {G0,W6,D4,L1,V1,M1} { codomain( X ) = coantidomain( coantidomain( X
% 0.71/1.14 ) ) }.
% 0.71/1.14 (1119) {G0,W6,D4,L1,V0,M1} { ! skol1 = multiplication( domain( skol1 ),
% 0.71/1.14 skol1 ) }.
% 0.71/1.14
% 0.71/1.14
% 0.71/1.14 Total Proof:
% 0.71/1.14
% 0.71/1.14 subsumption: (2) {G0,W5,D3,L1,V1,M1} I { addition( X, zero ) ==> X }.
% 0.71/1.14 parent0: (1100) {G0,W5,D3,L1,V1,M1} { addition( X, zero ) = X }.
% 0.71/1.14 substitution0:
% 0.71/1.14 X := X
% 0.71/1.14 end
% 0.71/1.14 permutation0:
% 0.71/1.14 0 ==> 0
% 0.71/1.14 end
% 0.71/1.14
% 0.71/1.14 subsumption: (6) {G0,W5,D3,L1,V1,M1} I { multiplication( one, X ) ==> X }.
% 0.71/1.14 parent0: (1104) {G0,W5,D3,L1,V1,M1} { multiplication( one, X ) = X }.
% 0.71/1.14 substitution0:
% 0.71/1.14 X := X
% 0.71/1.14 end
% 0.71/1.14 permutation0:
% 0.71/1.14 0 ==> 0
% 0.71/1.14 end
% 0.71/1.14
% 0.71/1.14 eqswap: (1135) {G0,W13,D4,L1,V3,M1} { addition( multiplication( X, Z ),
% 0.71/1.14 multiplication( Y, Z ) ) = multiplication( addition( X, Y ), Z ) }.
% 0.71/1.14 parent0[0]: (1106) {G0,W13,D4,L1,V3,M1} { multiplication( addition( X, Y )
% 0.71/1.14 , Z ) = addition( multiplication( X, Z ), multiplication( Y, Z ) ) }.
% 0.71/1.14 substitution0:
% 0.71/1.14 X := X
% 0.71/1.14 Y := Y
% 0.71/1.14 Z := Z
% 0.71/1.14 end
% 0.71/1.14
% 0.71/1.14 subsumption: (8) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Z )
% 0.71/1.14 , multiplication( Y, Z ) ) ==> multiplication( addition( X, Y ), Z ) }.
% 0.71/1.14 parent0: (1135) {G0,W13,D4,L1,V3,M1} { addition( multiplication( X, Z ),
% 0.71/1.14 multiplication( Y, Z ) ) = multiplication( addition( X, Y ), Z ) }.
% 0.71/1.14 substitution0:
% 0.71/1.14 X := X
% 0.71/1.14 Y := Y
% 0.71/1.14 Z := Z
% 0.71/1.14 end
% 0.71/1.14 permutation0:
% 0.71/1.14 0 ==> 0
% 0.71/1.14 end
% 0.71/1.14
% 0.71/1.14 subsumption: (13) {G0,W6,D4,L1,V1,M1} I { multiplication( antidomain( X ),
% 0.71/1.14 X ) ==> zero }.
% 0.71/1.14 parent0: (1111) {G0,W6,D4,L1,V1,M1} { multiplication( antidomain( X ), X )
% 0.71/1.14 = zero }.
% 0.71/1.14 substitution0:
% 0.71/1.14 X := X
% 0.71/1.14 end
% 0.71/1.14 permutation0:
% 0.71/1.14 0 ==> 0
% 0.71/1.14 end
% 0.71/1.14
% 0.71/1.14 subsumption: (15) {G0,W8,D5,L1,V1,M1} I { addition( antidomain( antidomain
% 0.71/1.14 ( X ) ), antidomain( X ) ) ==> one }.
% 0.71/1.14 parent0: (1113) {G0,W8,D5,L1,V1,M1} { addition( antidomain( antidomain( X
% 0.71/1.14 ) ), antidomain( X ) ) = one }.
% 0.71/1.14 substitution0:
% 0.71/1.14 X := X
% 0.71/1.14 end
% 0.71/1.14 permutation0:
% 0.71/1.14 0 ==> 0
% 0.71/1.14 end
% 0.71/1.14
% 0.71/1.14 eqswap: (1179) {G0,W6,D4,L1,V1,M1} { antidomain( antidomain( X ) ) =
% 0.71/1.14 domain( X ) }.
% 0.71/1.14 parent0[0]: (1114) {G0,W6,D4,L1,V1,M1} { domain( X ) = antidomain(
% 0.71/1.14 antidomain( X ) ) }.
% 0.71/1.14 substitution0:
% 0.71/1.14 X := X
% 0.71/1.14 end
% 0.71/1.14
% 0.71/1.14 subsumption: (16) {G0,W6,D4,L1,V1,M1} I { antidomain( antidomain( X ) ) ==>
% 0.71/1.14 domain( X ) }.
% 0.71/1.14 parent0: (1179) {G0,W6,D4,L1,V1,M1} { antidomain( antidomain( X ) ) =
% 0.71/1.14 domain( X ) }.
% 0.71/1.14 substitution0:
% 0.71/1.14 X := X
% 0.71/1.14 end
% 0.71/1.14 permutation0:
% 0.71/1.14 0 ==> 0
% 0.71/1.14 end
% 0.71/1.14
% 0.71/1.14 eqswap: (1200) {G0,W6,D4,L1,V0,M1} { ! multiplication( domain( skol1 ),
% 0.71/1.14 skol1 ) = skol1 }.
% 0.71/1.14 parent0[0]: (1119) {G0,W6,D4,L1,V0,M1} { ! skol1 = multiplication( domain
% 0.71/1.14 ( skol1 ), skol1 ) }.
% 0.71/1.14 substitution0:
% 0.71/1.14 end
% 0.71/1.14
% 0.71/1.14 subsumption: (21) {G0,W6,D4,L1,V0,M1} I { ! multiplication( domain( skol1 )
% 0.71/1.14 , skol1 ) ==> skol1 }.
% 0.71/1.14 parent0: (1200) {G0,W6,D4,L1,V0,M1} { ! multiplication( domain( skol1 ),
% 0.71/1.14 skol1 ) = skol1 }.
% 0.71/1.14 substitution0:
% 0.71/1.14 end
% 0.71/1.14 permutation0:
% 0.71/1.14 0 ==> 0
% 0.71/1.14 end
% 0.71/1.14
% 0.71/1.14 eqswap: (1202) {G0,W13,D4,L1,V3,M1} { multiplication( addition( X, Z ), Y
% 0.71/1.14 ) ==> addition( multiplication( X, Y ), multiplication( Z, Y ) ) }.
% 0.71/1.14 parent0[0]: (8) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Z ),
% 0.71/1.14 multiplication( Y, Z ) ) ==> multiplication( addition( X, Y ), Z ) }.
% 0.71/1.14 substitution0:
% 0.71/1.14 X := X
% 0.71/1.14 Y := Z
% 0.71/1.14 Z := Y
% 0.71/1.14 end
% 0.71/1.14
% 0.71/1.14 paramod: (1205) {G1,W12,D5,L1,V2,M1} { multiplication( addition( X,
% 0.71/1.14 antidomain( Y ) ), Y ) ==> addition( multiplication( X, Y ), zero ) }.
% 0.71/1.14 parent0[0]: (13) {G0,W6,D4,L1,V1,M1} I { multiplication( antidomain( X ), X
% 0.71/1.14 ) ==> zero }.
% 0.71/1.14 parent1[0; 11]: (1202) {G0,W13,D4,L1,V3,M1} { multiplication( addition( X
% 0.71/1.14 , Z ), Y ) ==> addition( multiplication( X, Y ), multiplication( Z, Y ) )
% 0.71/1.14 }.
% 0.71/1.14 substitution0:
% 0.71/1.14 X := Y
% 0.71/1.14 end
% 0.71/1.14 substitution1:
% 0.71/1.14 X := X
% 0.71/1.14 Y := Y
% 0.71/1.14 Z := antidomain( Y )
% 0.71/1.14 end
% 0.71/1.14
% 0.71/1.14 paramod: (1206) {G1,W10,D5,L1,V2,M1} { multiplication( addition( X,
% 0.71/1.14 antidomain( Y ) ), Y ) ==> multiplication( X, Y ) }.
% 0.71/1.14 parent0[0]: (2) {G0,W5,D3,L1,V1,M1} I { addition( X, zero ) ==> X }.
% 0.71/1.14 parent1[0; 7]: (1205) {G1,W12,D5,L1,V2,M1} { multiplication( addition( X,
% 0.71/1.14 antidomain( Y ) ), Y ) ==> addition( multiplication( X, Y ), zero ) }.
% 0.71/1.14 substitution0:
% 0.71/1.14 X := multiplication( X, Y )
% 0.71/1.14 end
% 0.71/1.14 substitution1:
% 0.71/1.14 X := X
% 0.71/1.14 Y := Y
% 0.71/1.14 end
% 0.71/1.14
% 0.71/1.14 subsumption: (66) {G1,W10,D5,L1,V2,M1} P(13,8);d(2) { multiplication(
% 0.71/1.14 addition( Y, antidomain( X ) ), X ) ==> multiplication( Y, X ) }.
% 0.71/1.14 parent0: (1206) {G1,W10,D5,L1,V2,M1} { multiplication( addition( X,
% 0.71/1.14 antidomain( Y ) ), Y ) ==> multiplication( X, Y ) }.
% 0.71/1.14 substitution0:
% 0.71/1.14 X := Y
% 0.71/1.14 Y := X
% 0.71/1.14 end
% 0.71/1.14 permutation0:
% 0.71/1.14 0 ==> 0
% 0.71/1.14 end
% 0.71/1.14
% 0.71/1.14 paramod: (1210) {G1,W7,D4,L1,V1,M1} { addition( domain( X ), antidomain( X
% 0.71/1.14 ) ) ==> one }.
% 0.71/1.14 parent0[0]: (16) {G0,W6,D4,L1,V1,M1} I { antidomain( antidomain( X ) ) ==>
% 0.71/1.14 domain( X ) }.
% 0.71/1.14 parent1[0; 2]: (15) {G0,W8,D5,L1,V1,M1} I { addition( antidomain(
% 0.71/1.14 antidomain( X ) ), antidomain( X ) ) ==> one }.
% 0.71/1.14 substitution0:
% 0.71/1.14 X := X
% 0.71/1.14 end
% 0.71/1.14 substitution1:
% 0.71/1.14 X := X
% 0.71/1.14 end
% 0.71/1.14
% 0.71/1.14 subsumption: (143) {G1,W7,D4,L1,V1,M1} S(15);d(16) { addition( domain( X )
% 0.71/1.14 , antidomain( X ) ) ==> one }.
% 0.71/1.14 parent0: (1210) {G1,W7,D4,L1,V1,M1} { addition( domain( X ), antidomain( X
% 0.71/1.14 ) ) ==> one }.
% 0.71/1.14 substitution0:
% 0.71/1.14 X := X
% 0.71/1.14 end
% 0.71/1.14 permutation0:
% 0.71/1.14 0 ==> 0
% 0.71/1.14 end
% 0.71/1.14
% 0.71/1.14 eqswap: (1213) {G1,W10,D5,L1,V2,M1} { multiplication( X, Y ) ==>
% 0.71/1.14 multiplication( addition( X, antidomain( Y ) ), Y ) }.
% 0.71/1.14 parent0[0]: (66) {G1,W10,D5,L1,V2,M1} P(13,8);d(2) { multiplication(
% 0.71/1.14 addition( Y, antidomain( X ) ), X ) ==> multiplication( Y, X ) }.
% 0.71/1.14 substitution0:
% 0.71/1.14 X := Y
% 0.71/1.14 Y := X
% 0.71/1.14 end
% 0.71/1.14
% 0.71/1.14 paramod: (1215) {G2,W8,D4,L1,V1,M1} { multiplication( domain( X ), X ) ==>
% 0.71/1.14 multiplication( one, X ) }.
% 0.71/1.14 parent0[0]: (143) {G1,W7,D4,L1,V1,M1} S(15);d(16) { addition( domain( X ),
% 0.71/1.14 antidomain( X ) ) ==> one }.
% 0.71/1.14 parent1[0; 6]: (1213) {G1,W10,D5,L1,V2,M1} { multiplication( X, Y ) ==>
% 0.71/1.14 multiplication( addition( X, antidomain( Y ) ), Y ) }.
% 0.71/1.14 substitution0:
% 0.71/1.14 X := X
% 0.71/1.14 end
% 0.71/1.14 substitution1:
% 0.71/1.14 X := domain( X )
% 0.71/1.14 Y := X
% 0.71/1.14 end
% 0.71/1.14
% 0.71/1.14 paramod: (1216) {G1,W6,D4,L1,V1,M1} { multiplication( domain( X ), X ) ==>
% 0.71/1.14 X }.
% 0.71/1.14 parent0[0]: (6) {G0,W5,D3,L1,V1,M1} I { multiplication( one, X ) ==> X }.
% 0.71/1.14 parent1[0; 5]: (1215) {G2,W8,D4,L1,V1,M1} { multiplication( domain( X ), X
% 0.71/1.14 ) ==> multiplication( one, X ) }.
% 0.71/1.14 substitution0:
% 0.71/1.14 X := X
% 0.71/1.14 end
% 0.71/1.14 substitution1:
% 0.71/1.14 X := X
% 0.71/1.14 end
% 0.71/1.14
% 0.71/1.14 subsumption: (1091) {G2,W6,D4,L1,V1,M1} P(143,66);d(6) { multiplication(
% 0.71/1.14 domain( X ), X ) ==> X }.
% 0.71/1.14 parent0: (1216) {G1,W6,D4,L1,V1,M1} { multiplication( domain( X ), X ) ==>
% 0.71/1.14 X }.
% 0.71/1.14 substitution0:
% 0.71/1.14 X := X
% 0.71/1.14 end
% 0.71/1.14 permutation0:
% 0.71/1.14 0 ==> 0
% 0.71/1.14 end
% 0.71/1.14
% 0.71/1.14 eqswap: (1218) {G2,W6,D4,L1,V1,M1} { X ==> multiplication( domain( X ), X
% 0.71/1.14 ) }.
% 0.71/1.14 parent0[0]: (1091) {G2,W6,D4,L1,V1,M1} P(143,66);d(6) { multiplication(
% 0.71/1.14 domain( X ), X ) ==> X }.
% 0.71/1.14 substitution0:
% 0.71/1.14 X := X
% 0.71/1.14 end
% 0.71/1.14
% 0.71/1.14 eqswap: (1219) {G0,W6,D4,L1,V0,M1} { ! skol1 ==> multiplication( domain(
% 0.71/1.14 skol1 ), skol1 ) }.
% 0.71/1.14 parent0[0]: (21) {G0,W6,D4,L1,V0,M1} I { ! multiplication( domain( skol1 )
% 0.71/1.14 , skol1 ) ==> skol1 }.
% 0.71/1.14 substitution0:
% 0.71/1.14 end
% 0.71/1.14
% 0.71/1.14 resolution: (1220) {G1,W0,D0,L0,V0,M0} { }.
% 0.71/1.14 parent0[0]: (1219) {G0,W6,D4,L1,V0,M1} { ! skol1 ==> multiplication(
% 0.71/1.14 domain( skol1 ), skol1 ) }.
% 0.71/1.14 parent1[0]: (1218) {G2,W6,D4,L1,V1,M1} { X ==> multiplication( domain( X )
% 0.71/1.14 , X ) }.
% 0.71/1.14 substitution0:
% 0.71/1.14 end
% 0.71/1.14 substitution1:
% 0.71/1.14 X := skol1
% 0.71/1.14 end
% 0.71/1.14
% 0.71/1.14 subsumption: (1096) {G3,W0,D0,L0,V0,M0} R(1091,21) { }.
% 0.71/1.14 parent0: (1220) {G1,W0,D0,L0,V0,M0} { }.
% 0.71/1.14 substitution0:
% 0.71/1.14 end
% 0.71/1.14 permutation0:
% 0.71/1.14 end
% 0.71/1.14
% 0.71/1.14 Proof check complete!
% 0.71/1.14
% 0.71/1.14 Memory use:
% 0.71/1.14
% 0.71/1.14 space for terms: 12510
% 0.71/1.14 space for clauses: 76078
% 0.71/1.14
% 0.71/1.14
% 0.71/1.14 clauses generated: 7897
% 0.71/1.14 clauses kept: 1097
% 0.71/1.14 clauses selected: 199
% 0.71/1.14 clauses deleted: 17
% 0.71/1.14 clauses inuse deleted: 4
% 0.71/1.14
% 0.71/1.14 subsentry: 9193
% 0.71/1.14 literals s-matched: 6397
% 0.71/1.14 literals matched: 6325
% 0.71/1.14 full subsumption: 374
% 0.71/1.14
% 0.71/1.14 checksum: -1191323418
% 0.71/1.14
% 0.71/1.14
% 0.71/1.14 Bliksem ended
%------------------------------------------------------------------------------