TSTP Solution File: KLE119+1 by Bliksem---1.12
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%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : KLE119+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n023.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 01:37:17 EDT 2022
% Result : Theorem 0.86s 1.22s
% Output : Refutation 0.86s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14 % Problem : KLE119+1 : TPTP v8.1.0. Released v4.0.0.
% 0.08/0.14 % Command : bliksem %s
% 0.14/0.36 % Computer : n023.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % DateTime : Thu Jun 16 13:12:35 EDT 2022
% 0.14/0.36 % CPUTime :
% 0.86/1.22 *** allocated 10000 integers for termspace/termends
% 0.86/1.22 *** allocated 10000 integers for clauses
% 0.86/1.22 *** allocated 10000 integers for justifications
% 0.86/1.22 Bliksem 1.12
% 0.86/1.22
% 0.86/1.22
% 0.86/1.22 Automatic Strategy Selection
% 0.86/1.22
% 0.86/1.22
% 0.86/1.22 Clauses:
% 0.86/1.22
% 0.86/1.22 { addition( X, Y ) = addition( Y, X ) }.
% 0.86/1.22 { addition( Z, addition( Y, X ) ) = addition( addition( Z, Y ), X ) }.
% 0.86/1.22 { addition( X, zero ) = X }.
% 0.86/1.22 { addition( X, X ) = X }.
% 0.86/1.22 { multiplication( X, multiplication( Y, Z ) ) = multiplication(
% 0.86/1.22 multiplication( X, Y ), Z ) }.
% 0.86/1.22 { multiplication( X, one ) = X }.
% 0.86/1.22 { multiplication( one, X ) = X }.
% 0.86/1.22 { multiplication( X, addition( Y, Z ) ) = addition( multiplication( X, Y )
% 0.86/1.22 , multiplication( X, Z ) ) }.
% 0.86/1.22 { multiplication( addition( X, Y ), Z ) = addition( multiplication( X, Z )
% 0.86/1.22 , multiplication( Y, Z ) ) }.
% 0.86/1.22 { multiplication( X, zero ) = zero }.
% 0.86/1.22 { multiplication( zero, X ) = zero }.
% 0.86/1.22 { ! leq( X, Y ), addition( X, Y ) = Y }.
% 0.86/1.22 { ! addition( X, Y ) = Y, leq( X, Y ) }.
% 0.86/1.22 { multiplication( antidomain( X ), X ) = zero }.
% 0.86/1.22 { addition( antidomain( multiplication( X, Y ) ), antidomain(
% 0.86/1.22 multiplication( X, antidomain( antidomain( Y ) ) ) ) ) = antidomain(
% 0.86/1.22 multiplication( X, antidomain( antidomain( Y ) ) ) ) }.
% 0.86/1.22 { addition( antidomain( antidomain( X ) ), antidomain( X ) ) = one }.
% 0.86/1.22 { domain( X ) = antidomain( antidomain( X ) ) }.
% 0.86/1.22 { multiplication( X, coantidomain( X ) ) = zero }.
% 0.86/1.22 { addition( coantidomain( multiplication( X, Y ) ), coantidomain(
% 0.86/1.22 multiplication( coantidomain( coantidomain( X ) ), Y ) ) ) = coantidomain
% 0.86/1.22 ( multiplication( coantidomain( coantidomain( X ) ), Y ) ) }.
% 0.86/1.22 { addition( coantidomain( coantidomain( X ) ), coantidomain( X ) ) = one }
% 0.86/1.22 .
% 0.86/1.22 { codomain( X ) = coantidomain( coantidomain( X ) ) }.
% 0.86/1.22 { c( X ) = antidomain( domain( X ) ) }.
% 0.86/1.22 { domain_difference( X, Y ) = multiplication( domain( X ), antidomain( Y )
% 0.86/1.22 ) }.
% 0.86/1.22 { forward_diamond( X, Y ) = domain( multiplication( X, domain( Y ) ) ) }.
% 0.86/1.22 { backward_diamond( X, Y ) = codomain( multiplication( codomain( Y ), X ) )
% 0.86/1.22 }.
% 0.86/1.22 { forward_box( X, Y ) = c( forward_diamond( X, c( Y ) ) ) }.
% 0.86/1.22 { backward_box( X, Y ) = c( backward_diamond( X, c( Y ) ) ) }.
% 0.86/1.22 { ! addition( backward_diamond( zero, domain( skol1 ) ), domain( skol2 ) )
% 0.86/1.22 = domain( skol2 ) }.
% 0.86/1.22
% 0.86/1.22 percentage equality = 0.933333, percentage horn = 1.000000
% 0.86/1.22 This is a pure equality problem
% 0.86/1.22
% 0.86/1.22
% 0.86/1.22
% 0.86/1.22 Options Used:
% 0.86/1.22
% 0.86/1.22 useres = 1
% 0.86/1.22 useparamod = 1
% 0.86/1.22 useeqrefl = 1
% 0.86/1.22 useeqfact = 1
% 0.86/1.22 usefactor = 1
% 0.86/1.22 usesimpsplitting = 0
% 0.86/1.22 usesimpdemod = 5
% 0.86/1.22 usesimpres = 3
% 0.86/1.22
% 0.86/1.22 resimpinuse = 1000
% 0.86/1.22 resimpclauses = 20000
% 0.86/1.22 substype = eqrewr
% 0.86/1.22 backwardsubs = 1
% 0.86/1.22 selectoldest = 5
% 0.86/1.22
% 0.86/1.22 litorderings [0] = split
% 0.86/1.22 litorderings [1] = extend the termordering, first sorting on arguments
% 0.86/1.22
% 0.86/1.22 termordering = kbo
% 0.86/1.22
% 0.86/1.22 litapriori = 0
% 0.86/1.22 termapriori = 1
% 0.86/1.22 litaposteriori = 0
% 0.86/1.22 termaposteriori = 0
% 0.86/1.22 demodaposteriori = 0
% 0.86/1.22 ordereqreflfact = 0
% 0.86/1.22
% 0.86/1.22 litselect = negord
% 0.86/1.22
% 0.86/1.22 maxweight = 15
% 0.86/1.22 maxdepth = 30000
% 0.86/1.22 maxlength = 115
% 0.86/1.22 maxnrvars = 195
% 0.86/1.22 excuselevel = 1
% 0.86/1.22 increasemaxweight = 1
% 0.86/1.22
% 0.86/1.22 maxselected = 10000000
% 0.86/1.22 maxnrclauses = 10000000
% 0.86/1.22
% 0.86/1.22 showgenerated = 0
% 0.86/1.22 showkept = 0
% 0.86/1.22 showselected = 0
% 0.86/1.22 showdeleted = 0
% 0.86/1.22 showresimp = 1
% 0.86/1.22 showstatus = 2000
% 0.86/1.22
% 0.86/1.22 prologoutput = 0
% 0.86/1.22 nrgoals = 5000000
% 0.86/1.22 totalproof = 1
% 0.86/1.22
% 0.86/1.22 Symbols occurring in the translation:
% 0.86/1.22
% 0.86/1.22 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.86/1.22 . [1, 2] (w:1, o:25, a:1, s:1, b:0),
% 0.86/1.22 ! [4, 1] (w:0, o:15, a:1, s:1, b:0),
% 0.86/1.22 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.86/1.22 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.86/1.22 addition [37, 2] (w:1, o:49, a:1, s:1, b:0),
% 0.86/1.22 zero [39, 0] (w:1, o:9, a:1, s:1, b:0),
% 0.86/1.22 multiplication [40, 2] (w:1, o:51, a:1, s:1, b:0),
% 0.86/1.22 one [41, 0] (w:1, o:10, a:1, s:1, b:0),
% 0.86/1.22 leq [42, 2] (w:1, o:50, a:1, s:1, b:0),
% 0.86/1.22 antidomain [44, 1] (w:1, o:20, a:1, s:1, b:0),
% 0.86/1.22 domain [46, 1] (w:1, o:24, a:1, s:1, b:0),
% 0.86/1.22 coantidomain [47, 1] (w:1, o:21, a:1, s:1, b:0),
% 0.86/1.22 codomain [48, 1] (w:1, o:22, a:1, s:1, b:0),
% 0.86/1.22 c [49, 1] (w:1, o:23, a:1, s:1, b:0),
% 0.86/1.22 domain_difference [50, 2] (w:1, o:52, a:1, s:1, b:0),
% 0.86/1.22 forward_diamond [51, 2] (w:1, o:53, a:1, s:1, b:0),
% 0.86/1.22 backward_diamond [52, 2] (w:1, o:54, a:1, s:1, b:0),
% 0.86/1.22 forward_box [53, 2] (w:1, o:55, a:1, s:1, b:0),
% 0.86/1.22 backward_box [54, 2] (w:1, o:56, a:1, s:1, b:0),
% 0.86/1.22 skol1 [55, 0] (w:1, o:13, a:1, s:1, b:1),
% 0.86/1.22 skol2 [56, 0] (w:1, o:14, a:1, s:1, b:1).
% 0.86/1.22
% 0.86/1.22
% 0.86/1.22 Starting Search:
% 0.86/1.22
% 0.86/1.22 *** allocated 15000 integers for clauses
% 0.86/1.22 *** allocated 22500 integers for clauses
% 0.86/1.22 *** allocated 33750 integers for clauses
% 0.86/1.22
% 0.86/1.22 Bliksems!, er is een bewijs:
% 0.86/1.22 % SZS status Theorem
% 0.86/1.22 % SZS output start Refutation
% 0.86/1.22
% 0.86/1.22 (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X ) }.
% 0.86/1.22 (2) {G0,W5,D3,L1,V1,M1} I { addition( X, zero ) ==> X }.
% 0.86/1.22 (6) {G0,W5,D3,L1,V1,M1} I { multiplication( one, X ) ==> X }.
% 0.86/1.22 (9) {G0,W5,D3,L1,V1,M1} I { multiplication( X, zero ) ==> zero }.
% 0.86/1.22 (17) {G0,W6,D4,L1,V1,M1} I { multiplication( X, coantidomain( X ) ) ==>
% 0.86/1.22 zero }.
% 0.86/1.22 (19) {G0,W8,D5,L1,V1,M1} I { addition( coantidomain( coantidomain( X ) ),
% 0.86/1.22 coantidomain( X ) ) ==> one }.
% 0.86/1.22 (20) {G0,W6,D4,L1,V1,M1} I { coantidomain( coantidomain( X ) ) ==> codomain
% 0.86/1.22 ( X ) }.
% 0.86/1.22 (24) {G0,W9,D5,L1,V2,M1} I { codomain( multiplication( codomain( Y ), X ) )
% 0.86/1.22 ==> backward_diamond( X, Y ) }.
% 0.86/1.22 (27) {G0,W10,D5,L1,V0,M1} I { ! addition( backward_diamond( zero, domain(
% 0.86/1.22 skol1 ) ), domain( skol2 ) ) ==> domain( skol2 ) }.
% 0.86/1.22 (28) {G1,W5,D3,L1,V1,M1} P(2,0) { addition( zero, X ) ==> X }.
% 0.86/1.22 (34) {G1,W7,D4,L1,V1,M1} P(20,17) { multiplication( coantidomain( X ),
% 0.86/1.22 codomain( X ) ) ==> zero }.
% 0.86/1.22 (35) {G1,W4,D3,L1,V0,M1} P(17,6) { coantidomain( one ) ==> zero }.
% 0.86/1.22 (36) {G2,W5,D3,L1,V0,M1} P(35,20) { codomain( one ) ==> coantidomain( zero
% 0.86/1.22 ) }.
% 0.86/1.22 (198) {G1,W7,D4,L1,V1,M1} S(19);d(20) { addition( codomain( X ),
% 0.86/1.22 coantidomain( X ) ) ==> one }.
% 0.86/1.22 (268) {G1,W6,D3,L1,V1,M1} P(9,24) { backward_diamond( zero, X ) ==>
% 0.86/1.22 codomain( zero ) }.
% 0.86/1.22 (337) {G3,W4,D3,L1,V0,M1} P(36,198);d(35);d(2) { coantidomain( zero ) ==>
% 0.86/1.22 one }.
% 0.86/1.22 (344) {G4,W4,D3,L1,V0,M1} P(337,34);d(6) { codomain( zero ) ==> zero }.
% 0.86/1.22 (345) {G5,W0,D0,L0,V0,M0} S(27);d(268);d(344);d(28);q { }.
% 0.86/1.22
% 0.86/1.22
% 0.86/1.22 % SZS output end Refutation
% 0.86/1.22 found a proof!
% 0.86/1.22
% 0.86/1.22
% 0.86/1.22 Unprocessed initial clauses:
% 0.86/1.22
% 0.86/1.22 (347) {G0,W7,D3,L1,V2,M1} { addition( X, Y ) = addition( Y, X ) }.
% 0.86/1.22 (348) {G0,W11,D4,L1,V3,M1} { addition( Z, addition( Y, X ) ) = addition(
% 0.86/1.22 addition( Z, Y ), X ) }.
% 0.86/1.22 (349) {G0,W5,D3,L1,V1,M1} { addition( X, zero ) = X }.
% 0.86/1.22 (350) {G0,W5,D3,L1,V1,M1} { addition( X, X ) = X }.
% 0.86/1.22 (351) {G0,W11,D4,L1,V3,M1} { multiplication( X, multiplication( Y, Z ) ) =
% 0.86/1.22 multiplication( multiplication( X, Y ), Z ) }.
% 0.86/1.22 (352) {G0,W5,D3,L1,V1,M1} { multiplication( X, one ) = X }.
% 0.86/1.22 (353) {G0,W5,D3,L1,V1,M1} { multiplication( one, X ) = X }.
% 0.86/1.22 (354) {G0,W13,D4,L1,V3,M1} { multiplication( X, addition( Y, Z ) ) =
% 0.86/1.22 addition( multiplication( X, Y ), multiplication( X, Z ) ) }.
% 0.86/1.22 (355) {G0,W13,D4,L1,V3,M1} { multiplication( addition( X, Y ), Z ) =
% 0.86/1.22 addition( multiplication( X, Z ), multiplication( Y, Z ) ) }.
% 0.86/1.22 (356) {G0,W5,D3,L1,V1,M1} { multiplication( X, zero ) = zero }.
% 0.86/1.22 (357) {G0,W5,D3,L1,V1,M1} { multiplication( zero, X ) = zero }.
% 0.86/1.22 (358) {G0,W8,D3,L2,V2,M2} { ! leq( X, Y ), addition( X, Y ) = Y }.
% 0.86/1.22 (359) {G0,W8,D3,L2,V2,M2} { ! addition( X, Y ) = Y, leq( X, Y ) }.
% 0.86/1.22 (360) {G0,W6,D4,L1,V1,M1} { multiplication( antidomain( X ), X ) = zero
% 0.86/1.22 }.
% 0.86/1.22 (361) {G0,W18,D7,L1,V2,M1} { addition( antidomain( multiplication( X, Y )
% 0.86/1.22 ), antidomain( multiplication( X, antidomain( antidomain( Y ) ) ) ) ) =
% 0.86/1.22 antidomain( multiplication( X, antidomain( antidomain( Y ) ) ) ) }.
% 0.86/1.22 (362) {G0,W8,D5,L1,V1,M1} { addition( antidomain( antidomain( X ) ),
% 0.86/1.22 antidomain( X ) ) = one }.
% 0.86/1.22 (363) {G0,W6,D4,L1,V1,M1} { domain( X ) = antidomain( antidomain( X ) )
% 0.86/1.22 }.
% 0.86/1.22 (364) {G0,W6,D4,L1,V1,M1} { multiplication( X, coantidomain( X ) ) = zero
% 0.86/1.22 }.
% 0.86/1.22 (365) {G0,W18,D7,L1,V2,M1} { addition( coantidomain( multiplication( X, Y
% 0.86/1.22 ) ), coantidomain( multiplication( coantidomain( coantidomain( X ) ), Y
% 0.86/1.22 ) ) ) = coantidomain( multiplication( coantidomain( coantidomain( X ) )
% 0.86/1.22 , Y ) ) }.
% 0.86/1.22 (366) {G0,W8,D5,L1,V1,M1} { addition( coantidomain( coantidomain( X ) ),
% 0.86/1.22 coantidomain( X ) ) = one }.
% 0.86/1.22 (367) {G0,W6,D4,L1,V1,M1} { codomain( X ) = coantidomain( coantidomain( X
% 0.86/1.22 ) ) }.
% 0.86/1.22 (368) {G0,W6,D4,L1,V1,M1} { c( X ) = antidomain( domain( X ) ) }.
% 0.86/1.22 (369) {G0,W9,D4,L1,V2,M1} { domain_difference( X, Y ) = multiplication(
% 0.86/1.22 domain( X ), antidomain( Y ) ) }.
% 0.86/1.22 (370) {G0,W9,D5,L1,V2,M1} { forward_diamond( X, Y ) = domain(
% 0.86/1.22 multiplication( X, domain( Y ) ) ) }.
% 0.86/1.22 (371) {G0,W9,D5,L1,V2,M1} { backward_diamond( X, Y ) = codomain(
% 0.86/1.22 multiplication( codomain( Y ), X ) ) }.
% 0.86/1.22 (372) {G0,W9,D5,L1,V2,M1} { forward_box( X, Y ) = c( forward_diamond( X, c
% 0.86/1.22 ( Y ) ) ) }.
% 0.86/1.22 (373) {G0,W9,D5,L1,V2,M1} { backward_box( X, Y ) = c( backward_diamond( X
% 0.86/1.22 , c( Y ) ) ) }.
% 0.86/1.22 (374) {G0,W10,D5,L1,V0,M1} { ! addition( backward_diamond( zero, domain(
% 0.86/1.22 skol1 ) ), domain( skol2 ) ) = domain( skol2 ) }.
% 0.86/1.22
% 0.86/1.22
% 0.86/1.22 Total Proof:
% 0.86/1.22
% 0.86/1.22 subsumption: (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X
% 0.86/1.22 ) }.
% 0.86/1.22 parent0: (347) {G0,W7,D3,L1,V2,M1} { addition( X, Y ) = addition( Y, X )
% 0.86/1.22 }.
% 0.86/1.22 substitution0:
% 0.86/1.22 X := X
% 0.86/1.22 Y := Y
% 0.86/1.22 end
% 0.86/1.22 permutation0:
% 0.86/1.22 0 ==> 0
% 0.86/1.22 end
% 0.86/1.22
% 0.86/1.22 subsumption: (2) {G0,W5,D3,L1,V1,M1} I { addition( X, zero ) ==> X }.
% 0.86/1.22 parent0: (349) {G0,W5,D3,L1,V1,M1} { addition( X, zero ) = X }.
% 0.86/1.22 substitution0:
% 0.86/1.22 X := X
% 0.86/1.22 end
% 0.86/1.22 permutation0:
% 0.86/1.22 0 ==> 0
% 0.86/1.22 end
% 0.86/1.22
% 0.86/1.22 subsumption: (6) {G0,W5,D3,L1,V1,M1} I { multiplication( one, X ) ==> X }.
% 0.86/1.22 parent0: (353) {G0,W5,D3,L1,V1,M1} { multiplication( one, X ) = X }.
% 0.86/1.22 substitution0:
% 0.86/1.22 X := X
% 0.86/1.22 end
% 0.86/1.22 permutation0:
% 0.86/1.22 0 ==> 0
% 0.86/1.22 end
% 0.86/1.22
% 0.86/1.22 subsumption: (9) {G0,W5,D3,L1,V1,M1} I { multiplication( X, zero ) ==> zero
% 0.86/1.22 }.
% 0.86/1.22 parent0: (356) {G0,W5,D3,L1,V1,M1} { multiplication( X, zero ) = zero }.
% 0.86/1.22 substitution0:
% 0.86/1.22 X := X
% 0.86/1.22 end
% 0.86/1.22 permutation0:
% 0.86/1.22 0 ==> 0
% 0.86/1.22 end
% 0.86/1.22
% 0.86/1.22 subsumption: (17) {G0,W6,D4,L1,V1,M1} I { multiplication( X, coantidomain(
% 0.86/1.22 X ) ) ==> zero }.
% 0.86/1.22 parent0: (364) {G0,W6,D4,L1,V1,M1} { multiplication( X, coantidomain( X )
% 0.86/1.22 ) = zero }.
% 0.86/1.22 substitution0:
% 0.86/1.22 X := X
% 0.86/1.22 end
% 0.86/1.22 permutation0:
% 0.86/1.22 0 ==> 0
% 0.86/1.22 end
% 0.86/1.22
% 0.86/1.22 subsumption: (19) {G0,W8,D5,L1,V1,M1} I { addition( coantidomain(
% 0.86/1.22 coantidomain( X ) ), coantidomain( X ) ) ==> one }.
% 0.86/1.22 parent0: (366) {G0,W8,D5,L1,V1,M1} { addition( coantidomain( coantidomain
% 0.86/1.22 ( X ) ), coantidomain( X ) ) = one }.
% 0.86/1.22 substitution0:
% 0.86/1.22 X := X
% 0.86/1.22 end
% 0.86/1.22 permutation0:
% 0.86/1.22 0 ==> 0
% 0.86/1.22 end
% 0.86/1.22
% 0.86/1.22 eqswap: (447) {G0,W6,D4,L1,V1,M1} { coantidomain( coantidomain( X ) ) =
% 0.86/1.22 codomain( X ) }.
% 0.86/1.22 parent0[0]: (367) {G0,W6,D4,L1,V1,M1} { codomain( X ) = coantidomain(
% 0.86/1.22 coantidomain( X ) ) }.
% 0.86/1.22 substitution0:
% 0.86/1.22 X := X
% 0.86/1.22 end
% 0.86/1.22
% 0.86/1.22 subsumption: (20) {G0,W6,D4,L1,V1,M1} I { coantidomain( coantidomain( X ) )
% 0.86/1.22 ==> codomain( X ) }.
% 0.86/1.22 parent0: (447) {G0,W6,D4,L1,V1,M1} { coantidomain( coantidomain( X ) ) =
% 0.86/1.22 codomain( X ) }.
% 0.86/1.22 substitution0:
% 0.86/1.22 X := X
% 0.86/1.22 end
% 0.86/1.22 permutation0:
% 0.86/1.22 0 ==> 0
% 0.86/1.22 end
% 0.86/1.22
% 0.86/1.22 eqswap: (471) {G0,W9,D5,L1,V2,M1} { codomain( multiplication( codomain( Y
% 0.86/1.22 ), X ) ) = backward_diamond( X, Y ) }.
% 0.86/1.22 parent0[0]: (371) {G0,W9,D5,L1,V2,M1} { backward_diamond( X, Y ) =
% 0.86/1.22 codomain( multiplication( codomain( Y ), X ) ) }.
% 0.86/1.22 substitution0:
% 0.86/1.22 X := X
% 0.86/1.22 Y := Y
% 0.86/1.22 end
% 0.86/1.22
% 0.86/1.22 subsumption: (24) {G0,W9,D5,L1,V2,M1} I { codomain( multiplication(
% 0.86/1.22 codomain( Y ), X ) ) ==> backward_diamond( X, Y ) }.
% 0.86/1.22 parent0: (471) {G0,W9,D5,L1,V2,M1} { codomain( multiplication( codomain( Y
% 0.86/1.22 ), X ) ) = backward_diamond( X, Y ) }.
% 0.86/1.22 substitution0:
% 0.86/1.22 X := X
% 0.86/1.22 Y := Y
% 0.86/1.22 end
% 0.86/1.22 permutation0:
% 0.86/1.22 0 ==> 0
% 0.86/1.22 end
% 0.86/1.22
% 0.86/1.22 subsumption: (27) {G0,W10,D5,L1,V0,M1} I { ! addition( backward_diamond(
% 0.86/1.22 zero, domain( skol1 ) ), domain( skol2 ) ) ==> domain( skol2 ) }.
% 0.86/1.22 parent0: (374) {G0,W10,D5,L1,V0,M1} { ! addition( backward_diamond( zero,
% 0.86/1.22 domain( skol1 ) ), domain( skol2 ) ) = domain( skol2 ) }.
% 0.86/1.22 substitution0:
% 0.86/1.22 end
% 0.86/1.22 permutation0:
% 0.86/1.22 0 ==> 0
% 0.86/1.22 end
% 0.86/1.22
% 0.86/1.22 eqswap: (499) {G0,W5,D3,L1,V1,M1} { X ==> addition( X, zero ) }.
% 0.86/1.22 parent0[0]: (2) {G0,W5,D3,L1,V1,M1} I { addition( X, zero ) ==> X }.
% 0.86/1.22 substitution0:
% 0.86/1.22 X := X
% 0.86/1.22 end
% 0.86/1.22
% 0.86/1.22 paramod: (500) {G1,W5,D3,L1,V1,M1} { X ==> addition( zero, X ) }.
% 0.86/1.22 parent0[0]: (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X )
% 0.86/1.22 }.
% 0.86/1.22 parent1[0; 2]: (499) {G0,W5,D3,L1,V1,M1} { X ==> addition( X, zero ) }.
% 0.86/1.22 substitution0:
% 0.86/1.22 X := X
% 0.86/1.22 Y := zero
% 0.86/1.22 end
% 0.86/1.22 substitution1:
% 0.86/1.22 X := X
% 0.86/1.22 end
% 0.86/1.22
% 0.86/1.22 eqswap: (503) {G1,W5,D3,L1,V1,M1} { addition( zero, X ) ==> X }.
% 0.86/1.22 parent0[0]: (500) {G1,W5,D3,L1,V1,M1} { X ==> addition( zero, X ) }.
% 0.86/1.23 substitution0:
% 0.86/1.23 X := X
% 0.86/1.23 end
% 0.86/1.23
% 0.86/1.23 subsumption: (28) {G1,W5,D3,L1,V1,M1} P(2,0) { addition( zero, X ) ==> X
% 0.86/1.23 }.
% 0.86/1.23 parent0: (503) {G1,W5,D3,L1,V1,M1} { addition( zero, X ) ==> X }.
% 0.86/1.23 substitution0:
% 0.86/1.23 X := X
% 0.86/1.23 end
% 0.86/1.23 permutation0:
% 0.86/1.23 0 ==> 0
% 0.86/1.23 end
% 0.86/1.23
% 0.86/1.23 eqswap: (505) {G0,W6,D4,L1,V1,M1} { zero ==> multiplication( X,
% 0.86/1.23 coantidomain( X ) ) }.
% 0.86/1.23 parent0[0]: (17) {G0,W6,D4,L1,V1,M1} I { multiplication( X, coantidomain( X
% 0.86/1.23 ) ) ==> zero }.
% 0.86/1.23 substitution0:
% 0.86/1.23 X := X
% 0.86/1.23 end
% 0.86/1.23
% 0.86/1.23 paramod: (506) {G1,W7,D4,L1,V1,M1} { zero ==> multiplication( coantidomain
% 0.86/1.23 ( X ), codomain( X ) ) }.
% 0.86/1.23 parent0[0]: (20) {G0,W6,D4,L1,V1,M1} I { coantidomain( coantidomain( X ) )
% 0.86/1.23 ==> codomain( X ) }.
% 0.86/1.23 parent1[0; 5]: (505) {G0,W6,D4,L1,V1,M1} { zero ==> multiplication( X,
% 0.86/1.23 coantidomain( X ) ) }.
% 0.86/1.23 substitution0:
% 0.86/1.23 X := X
% 0.86/1.23 end
% 0.86/1.23 substitution1:
% 0.86/1.23 X := coantidomain( X )
% 0.86/1.23 end
% 0.86/1.23
% 0.86/1.23 eqswap: (507) {G1,W7,D4,L1,V1,M1} { multiplication( coantidomain( X ),
% 0.86/1.23 codomain( X ) ) ==> zero }.
% 0.86/1.23 parent0[0]: (506) {G1,W7,D4,L1,V1,M1} { zero ==> multiplication(
% 0.86/1.23 coantidomain( X ), codomain( X ) ) }.
% 0.86/1.23 substitution0:
% 0.86/1.23 X := X
% 0.86/1.23 end
% 0.86/1.23
% 0.86/1.23 subsumption: (34) {G1,W7,D4,L1,V1,M1} P(20,17) { multiplication(
% 0.86/1.23 coantidomain( X ), codomain( X ) ) ==> zero }.
% 0.86/1.23 parent0: (507) {G1,W7,D4,L1,V1,M1} { multiplication( coantidomain( X ),
% 0.86/1.23 codomain( X ) ) ==> zero }.
% 0.86/1.23 substitution0:
% 0.86/1.23 X := X
% 0.86/1.23 end
% 0.86/1.23 permutation0:
% 0.86/1.23 0 ==> 0
% 0.86/1.23 end
% 0.86/1.23
% 0.86/1.23 eqswap: (508) {G0,W6,D4,L1,V1,M1} { zero ==> multiplication( X,
% 0.86/1.23 coantidomain( X ) ) }.
% 0.86/1.23 parent0[0]: (17) {G0,W6,D4,L1,V1,M1} I { multiplication( X, coantidomain( X
% 0.86/1.23 ) ) ==> zero }.
% 0.86/1.23 substitution0:
% 0.86/1.23 X := X
% 0.86/1.23 end
% 0.86/1.23
% 0.86/1.23 paramod: (510) {G1,W4,D3,L1,V0,M1} { zero ==> coantidomain( one ) }.
% 0.86/1.23 parent0[0]: (6) {G0,W5,D3,L1,V1,M1} I { multiplication( one, X ) ==> X }.
% 0.86/1.23 parent1[0; 2]: (508) {G0,W6,D4,L1,V1,M1} { zero ==> multiplication( X,
% 0.86/1.23 coantidomain( X ) ) }.
% 0.86/1.23 substitution0:
% 0.86/1.23 X := coantidomain( one )
% 0.86/1.23 end
% 0.86/1.23 substitution1:
% 0.86/1.23 X := one
% 0.86/1.23 end
% 0.86/1.23
% 0.86/1.23 eqswap: (511) {G1,W4,D3,L1,V0,M1} { coantidomain( one ) ==> zero }.
% 0.86/1.23 parent0[0]: (510) {G1,W4,D3,L1,V0,M1} { zero ==> coantidomain( one ) }.
% 0.86/1.23 substitution0:
% 0.86/1.23 end
% 0.86/1.23
% 0.86/1.23 subsumption: (35) {G1,W4,D3,L1,V0,M1} P(17,6) { coantidomain( one ) ==>
% 0.86/1.23 zero }.
% 0.86/1.23 parent0: (511) {G1,W4,D3,L1,V0,M1} { coantidomain( one ) ==> zero }.
% 0.86/1.23 substitution0:
% 0.86/1.23 end
% 0.86/1.23 permutation0:
% 0.86/1.23 0 ==> 0
% 0.86/1.23 end
% 0.86/1.23
% 0.86/1.23 eqswap: (513) {G0,W6,D4,L1,V1,M1} { codomain( X ) ==> coantidomain(
% 0.86/1.23 coantidomain( X ) ) }.
% 0.86/1.23 parent0[0]: (20) {G0,W6,D4,L1,V1,M1} I { coantidomain( coantidomain( X ) )
% 0.86/1.23 ==> codomain( X ) }.
% 0.86/1.23 substitution0:
% 0.86/1.23 X := X
% 0.86/1.23 end
% 0.86/1.23
% 0.86/1.23 paramod: (514) {G1,W5,D3,L1,V0,M1} { codomain( one ) ==> coantidomain(
% 0.86/1.23 zero ) }.
% 0.86/1.23 parent0[0]: (35) {G1,W4,D3,L1,V0,M1} P(17,6) { coantidomain( one ) ==> zero
% 0.86/1.23 }.
% 0.86/1.23 parent1[0; 4]: (513) {G0,W6,D4,L1,V1,M1} { codomain( X ) ==> coantidomain
% 0.86/1.23 ( coantidomain( X ) ) }.
% 0.86/1.23 substitution0:
% 0.86/1.23 end
% 0.86/1.23 substitution1:
% 0.86/1.23 X := one
% 0.86/1.23 end
% 0.86/1.23
% 0.86/1.23 subsumption: (36) {G2,W5,D3,L1,V0,M1} P(35,20) { codomain( one ) ==>
% 0.86/1.23 coantidomain( zero ) }.
% 0.86/1.23 parent0: (514) {G1,W5,D3,L1,V0,M1} { codomain( one ) ==> coantidomain(
% 0.86/1.23 zero ) }.
% 0.86/1.23 substitution0:
% 0.86/1.23 end
% 0.86/1.23 permutation0:
% 0.86/1.23 0 ==> 0
% 0.86/1.23 end
% 0.86/1.23
% 0.86/1.23 paramod: (518) {G1,W7,D4,L1,V1,M1} { addition( codomain( X ), coantidomain
% 0.86/1.23 ( X ) ) ==> one }.
% 0.86/1.23 parent0[0]: (20) {G0,W6,D4,L1,V1,M1} I { coantidomain( coantidomain( X ) )
% 0.86/1.23 ==> codomain( X ) }.
% 0.86/1.23 parent1[0; 2]: (19) {G0,W8,D5,L1,V1,M1} I { addition( coantidomain(
% 0.86/1.23 coantidomain( X ) ), coantidomain( X ) ) ==> one }.
% 0.86/1.23 substitution0:
% 0.86/1.23 X := X
% 0.86/1.23 end
% 0.86/1.23 substitution1:
% 0.86/1.23 X := X
% 0.86/1.23 end
% 0.86/1.23
% 0.86/1.23 subsumption: (198) {G1,W7,D4,L1,V1,M1} S(19);d(20) { addition( codomain( X
% 0.86/1.23 ), coantidomain( X ) ) ==> one }.
% 0.86/1.23 parent0: (518) {G1,W7,D4,L1,V1,M1} { addition( codomain( X ), coantidomain
% 0.86/1.23 ( X ) ) ==> one }.
% 0.86/1.23 substitution0:
% 0.86/1.23 X := X
% 0.86/1.23 end
% 0.86/1.23 permutation0:
% 0.86/1.23 0 ==> 0
% 0.86/1.23 end
% 0.86/1.23
% 0.86/1.23 eqswap: (521) {G0,W9,D5,L1,V2,M1} { backward_diamond( Y, X ) ==> codomain
% 0.86/1.23 ( multiplication( codomain( X ), Y ) ) }.
% 0.86/1.23 parent0[0]: (24) {G0,W9,D5,L1,V2,M1} I { codomain( multiplication( codomain
% 0.86/1.23 ( Y ), X ) ) ==> backward_diamond( X, Y ) }.
% 0.86/1.23 substitution0:
% 0.86/1.23 X := Y
% 0.86/1.23 Y := X
% 0.86/1.23 end
% 0.86/1.23
% 0.86/1.23 paramod: (522) {G1,W6,D3,L1,V1,M1} { backward_diamond( zero, X ) ==>
% 0.86/1.23 codomain( zero ) }.
% 0.86/1.23 parent0[0]: (9) {G0,W5,D3,L1,V1,M1} I { multiplication( X, zero ) ==> zero
% 0.86/1.23 }.
% 0.86/1.23 parent1[0; 5]: (521) {G0,W9,D5,L1,V2,M1} { backward_diamond( Y, X ) ==>
% 0.86/1.23 codomain( multiplication( codomain( X ), Y ) ) }.
% 0.86/1.23 substitution0:
% 0.86/1.23 X := codomain( X )
% 0.86/1.23 end
% 0.86/1.23 substitution1:
% 0.86/1.23 X := X
% 0.86/1.23 Y := zero
% 0.86/1.23 end
% 0.86/1.23
% 0.86/1.23 subsumption: (268) {G1,W6,D3,L1,V1,M1} P(9,24) { backward_diamond( zero, X
% 0.86/1.23 ) ==> codomain( zero ) }.
% 0.86/1.23 parent0: (522) {G1,W6,D3,L1,V1,M1} { backward_diamond( zero, X ) ==>
% 0.86/1.23 codomain( zero ) }.
% 0.86/1.23 substitution0:
% 0.86/1.23 X := X
% 0.86/1.23 end
% 0.86/1.23 permutation0:
% 0.86/1.23 0 ==> 0
% 0.86/1.23 end
% 0.86/1.23
% 0.86/1.23 eqswap: (525) {G1,W7,D4,L1,V1,M1} { one ==> addition( codomain( X ),
% 0.86/1.23 coantidomain( X ) ) }.
% 0.86/1.23 parent0[0]: (198) {G1,W7,D4,L1,V1,M1} S(19);d(20) { addition( codomain( X )
% 0.86/1.23 , coantidomain( X ) ) ==> one }.
% 0.86/1.23 substitution0:
% 0.86/1.23 X := X
% 0.86/1.23 end
% 0.86/1.23
% 0.86/1.23 paramod: (528) {G2,W7,D4,L1,V0,M1} { one ==> addition( coantidomain( zero
% 0.86/1.23 ), coantidomain( one ) ) }.
% 0.86/1.23 parent0[0]: (36) {G2,W5,D3,L1,V0,M1} P(35,20) { codomain( one ) ==>
% 0.86/1.23 coantidomain( zero ) }.
% 0.86/1.23 parent1[0; 3]: (525) {G1,W7,D4,L1,V1,M1} { one ==> addition( codomain( X )
% 0.86/1.23 , coantidomain( X ) ) }.
% 0.86/1.23 substitution0:
% 0.86/1.23 end
% 0.86/1.23 substitution1:
% 0.86/1.23 X := one
% 0.86/1.23 end
% 0.86/1.23
% 0.86/1.23 paramod: (529) {G2,W6,D4,L1,V0,M1} { one ==> addition( coantidomain( zero
% 0.86/1.23 ), zero ) }.
% 0.86/1.23 parent0[0]: (35) {G1,W4,D3,L1,V0,M1} P(17,6) { coantidomain( one ) ==> zero
% 0.86/1.23 }.
% 0.86/1.23 parent1[0; 5]: (528) {G2,W7,D4,L1,V0,M1} { one ==> addition( coantidomain
% 0.86/1.23 ( zero ), coantidomain( one ) ) }.
% 0.86/1.23 substitution0:
% 0.86/1.23 end
% 0.86/1.23 substitution1:
% 0.86/1.23 end
% 0.86/1.23
% 0.86/1.23 paramod: (530) {G1,W4,D3,L1,V0,M1} { one ==> coantidomain( zero ) }.
% 0.86/1.23 parent0[0]: (2) {G0,W5,D3,L1,V1,M1} I { addition( X, zero ) ==> X }.
% 0.86/1.23 parent1[0; 2]: (529) {G2,W6,D4,L1,V0,M1} { one ==> addition( coantidomain
% 0.86/1.23 ( zero ), zero ) }.
% 0.86/1.23 substitution0:
% 0.86/1.23 X := coantidomain( zero )
% 0.86/1.23 end
% 0.86/1.23 substitution1:
% 0.86/1.23 end
% 0.86/1.23
% 0.86/1.23 eqswap: (531) {G1,W4,D3,L1,V0,M1} { coantidomain( zero ) ==> one }.
% 0.86/1.23 parent0[0]: (530) {G1,W4,D3,L1,V0,M1} { one ==> coantidomain( zero ) }.
% 0.86/1.23 substitution0:
% 0.86/1.23 end
% 0.86/1.23
% 0.86/1.23 subsumption: (337) {G3,W4,D3,L1,V0,M1} P(36,198);d(35);d(2) { coantidomain
% 0.86/1.23 ( zero ) ==> one }.
% 0.86/1.23 parent0: (531) {G1,W4,D3,L1,V0,M1} { coantidomain( zero ) ==> one }.
% 0.86/1.23 substitution0:
% 0.86/1.23 end
% 0.86/1.23 permutation0:
% 0.86/1.23 0 ==> 0
% 0.86/1.23 end
% 0.86/1.23
% 0.86/1.23 eqswap: (533) {G1,W7,D4,L1,V1,M1} { zero ==> multiplication( coantidomain
% 0.86/1.23 ( X ), codomain( X ) ) }.
% 0.86/1.23 parent0[0]: (34) {G1,W7,D4,L1,V1,M1} P(20,17) { multiplication(
% 0.86/1.23 coantidomain( X ), codomain( X ) ) ==> zero }.
% 0.86/1.23 substitution0:
% 0.86/1.23 X := X
% 0.86/1.23 end
% 0.86/1.23
% 0.86/1.23 paramod: (535) {G2,W6,D4,L1,V0,M1} { zero ==> multiplication( one,
% 0.86/1.23 codomain( zero ) ) }.
% 0.86/1.23 parent0[0]: (337) {G3,W4,D3,L1,V0,M1} P(36,198);d(35);d(2) { coantidomain(
% 0.86/1.23 zero ) ==> one }.
% 0.86/1.23 parent1[0; 3]: (533) {G1,W7,D4,L1,V1,M1} { zero ==> multiplication(
% 0.86/1.23 coantidomain( X ), codomain( X ) ) }.
% 0.86/1.23 substitution0:
% 0.86/1.23 end
% 0.86/1.23 substitution1:
% 0.86/1.23 X := zero
% 0.86/1.23 end
% 0.86/1.23
% 0.86/1.23 paramod: (536) {G1,W4,D3,L1,V0,M1} { zero ==> codomain( zero ) }.
% 0.86/1.23 parent0[0]: (6) {G0,W5,D3,L1,V1,M1} I { multiplication( one, X ) ==> X }.
% 0.86/1.23 parent1[0; 2]: (535) {G2,W6,D4,L1,V0,M1} { zero ==> multiplication( one,
% 0.86/1.23 codomain( zero ) ) }.
% 0.86/1.23 substitution0:
% 0.86/1.23 X := codomain( zero )
% 0.86/1.23 end
% 0.86/1.23 substitution1:
% 0.86/1.23 end
% 0.86/1.23
% 0.86/1.23 eqswap: (537) {G1,W4,D3,L1,V0,M1} { codomain( zero ) ==> zero }.
% 0.86/1.23 parent0[0]: (536) {G1,W4,D3,L1,V0,M1} { zero ==> codomain( zero ) }.
% 0.86/1.23 substitution0:
% 0.86/1.23 end
% 0.86/1.23
% 0.86/1.23 subsumption: (344) {G4,W4,D3,L1,V0,M1} P(337,34);d(6) { codomain( zero )
% 0.86/1.23 ==> zero }.
% 0.86/1.23 parent0: (537) {G1,W4,D3,L1,V0,M1} { codomain( zero ) ==> zero }.
% 0.86/1.23 substitution0:
% 0.86/1.23 end
% 0.86/1.23 permutation0:
% 0.86/1.23 0 ==> 0
% 0.86/1.23 end
% 0.86/1.23
% 0.86/1.23 paramod: (542) {G1,W8,D4,L1,V0,M1} { ! addition( codomain( zero ), domain
% 0.86/1.23 ( skol2 ) ) ==> domain( skol2 ) }.
% 0.86/1.23 parent0[0]: (268) {G1,W6,D3,L1,V1,M1} P(9,24) { backward_diamond( zero, X )
% 0.86/1.23 ==> codomain( zero ) }.
% 0.86/1.23 parent1[0; 3]: (27) {G0,W10,D5,L1,V0,M1} I { ! addition( backward_diamond(
% 0.86/1.23 zero, domain( skol1 ) ), domain( skol2 ) ) ==> domain( skol2 ) }.
% 0.86/1.23 substitution0:
% 0.86/1.23 X := domain( skol1 )
% 0.86/1.23 end
% 0.86/1.23 substitution1:
% 0.86/1.23 end
% 0.86/1.23
% 0.86/1.23 paramod: (543) {G2,W7,D4,L1,V0,M1} { ! addition( zero, domain( skol2 ) )
% 0.86/1.23 ==> domain( skol2 ) }.
% 0.86/1.23 parent0[0]: (344) {G4,W4,D3,L1,V0,M1} P(337,34);d(6) { codomain( zero ) ==>
% 0.86/1.23 zero }.
% 0.86/1.23 parent1[0; 3]: (542) {G1,W8,D4,L1,V0,M1} { ! addition( codomain( zero ),
% 0.86/1.23 domain( skol2 ) ) ==> domain( skol2 ) }.
% 0.86/1.23 substitution0:
% 0.86/1.23 end
% 0.86/1.23 substitution1:
% 0.86/1.23 end
% 0.86/1.23
% 0.86/1.23 paramod: (544) {G2,W5,D3,L1,V0,M1} { ! domain( skol2 ) ==> domain( skol2 )
% 0.86/1.23 }.
% 0.86/1.23 parent0[0]: (28) {G1,W5,D3,L1,V1,M1} P(2,0) { addition( zero, X ) ==> X }.
% 0.86/1.23 parent1[0; 2]: (543) {G2,W7,D4,L1,V0,M1} { ! addition( zero, domain( skol2
% 0.86/1.23 ) ) ==> domain( skol2 ) }.
% 0.86/1.23 substitution0:
% 0.86/1.23 X := domain( skol2 )
% 0.86/1.23 end
% 0.86/1.23 substitution1:
% 0.86/1.23 end
% 0.86/1.23
% 0.86/1.23 eqrefl: (545) {G0,W0,D0,L0,V0,M0} { }.
% 0.86/1.23 parent0[0]: (544) {G2,W5,D3,L1,V0,M1} { ! domain( skol2 ) ==> domain(
% 0.86/1.23 skol2 ) }.
% 0.86/1.23 substitution0:
% 0.86/1.23 end
% 0.86/1.23
% 0.86/1.23 subsumption: (345) {G5,W0,D0,L0,V0,M0} S(27);d(268);d(344);d(28);q { }.
% 0.86/1.23 parent0: (545) {G0,W0,D0,L0,V0,M0} { }.
% 0.86/1.23 substitution0:
% 0.86/1.23 end
% 0.86/1.23 permutation0:
% 0.86/1.23 end
% 0.86/1.23
% 0.86/1.23 Proof check complete!
% 0.86/1.23
% 0.86/1.23 Memory use:
% 0.86/1.23
% 0.86/1.23 space for terms: 4047
% 0.86/1.23 space for clauses: 28130
% 0.86/1.23
% 0.86/1.23
% 0.86/1.23 clauses generated: 2011
% 0.86/1.23 clauses kept: 346
% 0.86/1.23 clauses selected: 76
% 0.86/1.23 clauses deleted: 10
% 0.86/1.23 clauses inuse deleted: 0
% 0.86/1.23
% 0.86/1.23 subsentry: 3582
% 0.86/1.23 literals s-matched: 1960
% 0.86/1.23 literals matched: 1960
% 0.86/1.23 full subsumption: 158
% 0.86/1.23
% 0.86/1.23 checksum: 339959707
% 0.86/1.23
% 0.86/1.23
% 0.86/1.23 Bliksem ended
%------------------------------------------------------------------------------