%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : KLE114+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n021.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 01:37:16 EDT 2022
% Result : Theorem 0.44s 1.09s
% Output : Refutation 0.44s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : KLE114+1 : TPTP v8.1.0. Released v4.0.0.
% 0.11/0.12 % Command : bliksem %s
% 0.12/0.34 % Computer : n021.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % DateTime : Thu Jun 16 12:05:14 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.44/1.09 *** allocated 10000 integers for termspace/termends
% 0.44/1.09 *** allocated 10000 integers for clauses
% 0.44/1.09 *** allocated 10000 integers for justifications
% 0.44/1.09 Bliksem 1.12
% 0.44/1.09
% 0.44/1.09
% 0.44/1.09 Automatic Strategy Selection
% 0.44/1.09
% 0.44/1.09
% 0.44/1.09 Clauses:
% 0.44/1.09
% 0.44/1.09 { addition( X, Y ) = addition( Y, X ) }.
% 0.44/1.09 { addition( Z, addition( Y, X ) ) = addition( addition( Z, Y ), X ) }.
% 0.44/1.09 { addition( X, zero ) = X }.
% 0.44/1.09 { addition( X, X ) = X }.
% 0.44/1.09 { multiplication( X, multiplication( Y, Z ) ) = multiplication(
% 0.44/1.09 multiplication( X, Y ), Z ) }.
% 0.44/1.09 { multiplication( X, one ) = X }.
% 0.44/1.09 { multiplication( one, X ) = X }.
% 0.44/1.09 { multiplication( X, addition( Y, Z ) ) = addition( multiplication( X, Y )
% 0.44/1.09 , multiplication( X, Z ) ) }.
% 0.44/1.09 { multiplication( addition( X, Y ), Z ) = addition( multiplication( X, Z )
% 0.44/1.09 , multiplication( Y, Z ) ) }.
% 0.44/1.09 { multiplication( X, zero ) = zero }.
% 0.44/1.09 { multiplication( zero, X ) = zero }.
% 0.44/1.09 { ! leq( X, Y ), addition( X, Y ) = Y }.
% 0.44/1.09 { ! addition( X, Y ) = Y, leq( X, Y ) }.
% 0.44/1.09 { multiplication( antidomain( X ), X ) = zero }.
% 0.44/1.09 { addition( antidomain( multiplication( X, Y ) ), antidomain(
% 0.44/1.09 multiplication( X, antidomain( antidomain( Y ) ) ) ) ) = antidomain(
% 0.44/1.09 multiplication( X, antidomain( antidomain( Y ) ) ) ) }.
% 0.44/1.09 { addition( antidomain( antidomain( X ) ), antidomain( X ) ) = one }.
% 0.44/1.09 { domain( X ) = antidomain( antidomain( X ) ) }.
% 0.44/1.09 { multiplication( X, coantidomain( X ) ) = zero }.
% 0.44/1.09 { addition( coantidomain( multiplication( X, Y ) ), coantidomain(
% 0.44/1.09 multiplication( coantidomain( coantidomain( X ) ), Y ) ) ) = coantidomain
% 0.44/1.09 ( multiplication( coantidomain( coantidomain( X ) ), Y ) ) }.
% 0.44/1.09 { addition( coantidomain( coantidomain( X ) ), coantidomain( X ) ) = one }
% 0.44/1.09 .
% 0.44/1.09 { codomain( X ) = coantidomain( coantidomain( X ) ) }.
% 0.44/1.09 { c( X ) = antidomain( domain( X ) ) }.
% 0.44/1.09 { domain_difference( X, Y ) = multiplication( domain( X ), antidomain( Y )
% 0.44/1.09 ) }.
% 0.44/1.09 { forward_diamond( X, Y ) = domain( multiplication( X, domain( Y ) ) ) }.
% 0.44/1.09 { backward_diamond( X, Y ) = codomain( multiplication( codomain( Y ), X ) )
% 0.44/1.09 }.
% 0.44/1.09 { forward_box( X, Y ) = c( forward_diamond( X, c( Y ) ) ) }.
% 0.44/1.09 { backward_box( X, Y ) = c( backward_diamond( X, c( Y ) ) ) }.
% 0.44/1.09 { ! forward_box( skol1, one ) = one }.
% 0.44/1.09
% 0.44/1.09 percentage equality = 0.933333, percentage horn = 1.000000
% 0.44/1.09 This is a pure equality problem
% 0.44/1.09
% 0.44/1.09
% 0.44/1.09
% 0.44/1.09 Options Used:
% 0.44/1.09
% 0.44/1.09 useres = 1
% 0.44/1.09 useparamod = 1
% 0.44/1.09 useeqrefl = 1
% 0.44/1.09 useeqfact = 1
% 0.44/1.09 usefactor = 1
% 0.44/1.09 usesimpsplitting = 0
% 0.44/1.09 usesimpdemod = 5
% 0.44/1.09 usesimpres = 3
% 0.44/1.09
% 0.44/1.09 resimpinuse = 1000
% 0.44/1.09 resimpclauses = 20000
% 0.44/1.09 substype = eqrewr
% 0.44/1.09 backwardsubs = 1
% 0.44/1.09 selectoldest = 5
% 0.44/1.09
% 0.44/1.09 litorderings [0] = split
% 0.44/1.09 litorderings [1] = extend the termordering, first sorting on arguments
% 0.44/1.09
% 0.44/1.09 termordering = kbo
% 0.44/1.09
% 0.44/1.09 litapriori = 0
% 0.44/1.09 termapriori = 1
% 0.44/1.09 litaposteriori = 0
% 0.44/1.09 termaposteriori = 0
% 0.44/1.09 demodaposteriori = 0
% 0.44/1.09 ordereqreflfact = 0
% 0.44/1.09
% 0.44/1.09 litselect = negord
% 0.44/1.09
% 0.44/1.09 maxweight = 15
% 0.44/1.09 maxdepth = 30000
% 0.44/1.09 maxlength = 115
% 0.44/1.09 maxnrvars = 195
% 0.44/1.09 excuselevel = 1
% 0.44/1.09 increasemaxweight = 1
% 0.44/1.09
% 0.44/1.09 maxselected = 10000000
% 0.44/1.09 maxnrclauses = 10000000
% 0.44/1.09
% 0.44/1.09 showgenerated = 0
% 0.44/1.09 showkept = 0
% 0.44/1.09 showselected = 0
% 0.44/1.09 showdeleted = 0
% 0.44/1.09 showresimp = 1
% 0.44/1.09 showstatus = 2000
% 0.44/1.09
% 0.44/1.09 prologoutput = 0
% 0.44/1.09 nrgoals = 5000000
% 0.44/1.09 totalproof = 1
% 0.44/1.09
% 0.44/1.09 Symbols occurring in the translation:
% 0.44/1.09
% 0.44/1.09 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.44/1.09 . [1, 2] (w:1, o:24, a:1, s:1, b:0),
% 0.44/1.09 ! [4, 1] (w:0, o:14, a:1, s:1, b:0),
% 0.44/1.09 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.44/1.09 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.44/1.09 addition [37, 2] (w:1, o:48, a:1, s:1, b:0),
% 0.44/1.09 zero [39, 0] (w:1, o:9, a:1, s:1, b:0),
% 0.44/1.09 multiplication [40, 2] (w:1, o:50, a:1, s:1, b:0),
% 0.44/1.09 one [41, 0] (w:1, o:10, a:1, s:1, b:0),
% 0.44/1.09 leq [42, 2] (w:1, o:49, a:1, s:1, b:0),
% 0.44/1.09 antidomain [44, 1] (w:1, o:19, a:1, s:1, b:0),
% 0.44/1.09 domain [46, 1] (w:1, o:23, a:1, s:1, b:0),
% 0.44/1.09 coantidomain [47, 1] (w:1, o:20, a:1, s:1, b:0),
% 0.44/1.09 codomain [48, 1] (w:1, o:21, a:1, s:1, b:0),
% 0.44/1.09 c [49, 1] (w:1, o:22, a:1, s:1, b:0),
% 0.44/1.09 domain_difference [50, 2] (w:1, o:51, a:1, s:1, b:0),
% 0.44/1.09 forward_diamond [51, 2] (w:1, o:52, a:1, s:1, b:0),
% 0.44/1.09 backward_diamond [52, 2] (w:1, o:53, a:1, s:1, b:0),
% 0.44/1.09 forward_box [53, 2] (w:1, o:54, a:1, s:1, b:0),
% 0.44/1.09 backward_box [54, 2] (w:1, o:55, a:1, s:1, b:0),
% 0.44/1.09 skol1 [55, 0] (w:1, o:13, a:1, s:1, b:1).
% 0.44/1.09
% 0.44/1.09
% 0.44/1.09 Starting Search:
% 0.44/1.09
% 0.44/1.09 *** allocated 15000 integers for clauses
% 0.44/1.09 *** allocated 22500 integers for clauses
% 0.44/1.09 *** allocated 33750 integers for clauses
% 0.44/1.09
% 0.44/1.09 Bliksems!, er is een bewijs:
% 0.44/1.09 % SZS status Theorem
% 0.44/1.09 % SZS output start Refutation
% 0.44/1.09
% 0.44/1.09 (2) {G0,W5,D3,L1,V1,M1} I { addition( X, zero ) ==> X }.
% 0.44/1.09 (5) {G0,W5,D3,L1,V1,M1} I { multiplication( X, one ) ==> X }.
% 0.44/1.09 (9) {G0,W5,D3,L1,V1,M1} I { multiplication( X, zero ) ==> zero }.
% 0.44/1.09 (13) {G0,W6,D4,L1,V1,M1} I { multiplication( antidomain( X ), X ) ==> zero
% 0.44/1.09 }.
% 0.44/1.09 (15) {G0,W8,D5,L1,V1,M1} I { addition( antidomain( antidomain( X ) ),
% 0.44/1.09 antidomain( X ) ) ==> one }.
% 0.44/1.09 (16) {G0,W6,D4,L1,V1,M1} I { antidomain( antidomain( X ) ) ==> domain( X )
% 0.44/1.09 }.
% 0.44/1.09 (21) {G0,W6,D4,L1,V1,M1} I { antidomain( domain( X ) ) ==> c( X ) }.
% 0.44/1.09 (23) {G0,W9,D5,L1,V2,M1} I { domain( multiplication( X, domain( Y ) ) ) ==>
% 0.44/1.09 forward_diamond( X, Y ) }.
% 0.44/1.09 (25) {G0,W9,D5,L1,V2,M1} I { c( forward_diamond( X, c( Y ) ) ) ==>
% 0.44/1.09 forward_box( X, Y ) }.
% 0.44/1.09 (27) {G0,W5,D3,L1,V0,M1} I { ! forward_box( skol1, one ) ==> one }.
% 0.44/1.09 (38) {G1,W6,D4,L1,V1,M1} P(16,16);d(21) { domain( antidomain( X ) ) ==> c(
% 0.44/1.09 X ) }.
% 0.44/1.09 (46) {G1,W4,D3,L1,V0,M1} P(13,5) { antidomain( one ) ==> zero }.
% 0.44/1.09 (47) {G2,W5,D3,L1,V0,M1} P(46,38) { domain( zero ) ==> c( one ) }.
% 0.44/1.09 (48) {G2,W5,D3,L1,V0,M1} P(46,16) { domain( one ) ==> antidomain( zero )
% 0.44/1.09 }.
% 0.44/1.09 (182) {G1,W7,D4,L1,V1,M1} S(15);d(16) { addition( domain( X ), antidomain(
% 0.44/1.09 X ) ) ==> one }.
% 0.44/1.09 (196) {G3,W4,D3,L1,V0,M1} P(48,182);d(46);d(2) { antidomain( zero ) ==> one
% 0.44/1.09 }.
% 0.44/1.09 (205) {G4,W4,D3,L1,V0,M1} P(196,38);d(48);d(196) { c( zero ) ==> one }.
% 0.44/1.09 (206) {G4,W4,D3,L1,V0,M1} P(196,16);d(46);d(47) { c( one ) ==> zero }.
% 0.44/1.09 (244) {G5,W5,D3,L1,V1,M1} P(47,23);d(206);d(9);d(47);d(206) {
% 0.44/1.09 forward_diamond( X, zero ) ==> zero }.
% 0.44/1.09 (280) {G6,W5,D3,L1,V1,M1} P(206,25);d(244);d(205) { forward_box( X, one )
% 0.44/1.09 ==> one }.
% 0.44/1.09 (290) {G7,W0,D0,L0,V0,M0} R(280,27) { }.
% 0.44/1.09
% 0.44/1.09
% 0.44/1.09 % SZS output end Refutation
% 0.44/1.09 found a proof!
% 0.44/1.09
% 0.44/1.09
% 0.44/1.09 Unprocessed initial clauses:
% 0.44/1.09
% 0.44/1.09 (292) {G0,W7,D3,L1,V2,M1} { addition( X, Y ) = addition( Y, X ) }.
% 0.44/1.09 (293) {G0,W11,D4,L1,V3,M1} { addition( Z, addition( Y, X ) ) = addition(
% 0.44/1.09 addition( Z, Y ), X ) }.
% 0.44/1.09 (294) {G0,W5,D3,L1,V1,M1} { addition( X, zero ) = X }.
% 0.44/1.09 (295) {G0,W5,D3,L1,V1,M1} { addition( X, X ) = X }.
% 0.44/1.09 (296) {G0,W11,D4,L1,V3,M1} { multiplication( X, multiplication( Y, Z ) ) =
% 0.44/1.09 multiplication( multiplication( X, Y ), Z ) }.
% 0.44/1.09 (297) {G0,W5,D3,L1,V1,M1} { multiplication( X, one ) = X }.
% 0.44/1.09 (298) {G0,W5,D3,L1,V1,M1} { multiplication( one, X ) = X }.
% 0.44/1.09 (299) {G0,W13,D4,L1,V3,M1} { multiplication( X, addition( Y, Z ) ) =
% 0.44/1.09 addition( multiplication( X, Y ), multiplication( X, Z ) ) }.
% 0.44/1.09 (300) {G0,W13,D4,L1,V3,M1} { multiplication( addition( X, Y ), Z ) =
% 0.44/1.09 addition( multiplication( X, Z ), multiplication( Y, Z ) ) }.
% 0.44/1.09 (301) {G0,W5,D3,L1,V1,M1} { multiplication( X, zero ) = zero }.
% 0.44/1.09 (302) {G0,W5,D3,L1,V1,M1} { multiplication( zero, X ) = zero }.
% 0.44/1.09 (303) {G0,W8,D3,L2,V2,M2} { ! leq( X, Y ), addition( X, Y ) = Y }.
% 0.44/1.09 (304) {G0,W8,D3,L2,V2,M2} { ! addition( X, Y ) = Y, leq( X, Y ) }.
% 0.44/1.09 (305) {G0,W6,D4,L1,V1,M1} { multiplication( antidomain( X ), X ) = zero
% 0.44/1.09 }.
% 0.44/1.09 (306) {G0,W18,D7,L1,V2,M1} { addition( antidomain( multiplication( X, Y )
% 0.44/1.09 ), antidomain( multiplication( X, antidomain( antidomain( Y ) ) ) ) ) =
% 0.44/1.09 antidomain( multiplication( X, antidomain( antidomain( Y ) ) ) ) }.
% 0.44/1.09 (307) {G0,W8,D5,L1,V1,M1} { addition( antidomain( antidomain( X ) ),
% 0.44/1.09 antidomain( X ) ) = one }.
% 0.44/1.09 (308) {G0,W6,D4,L1,V1,M1} { domain( X ) = antidomain( antidomain( X ) )
% 0.44/1.09 }.
% 0.44/1.09 (309) {G0,W6,D4,L1,V1,M1} { multiplication( X, coantidomain( X ) ) = zero
% 0.44/1.09 }.
% 0.44/1.09 (310) {G0,W18,D7,L1,V2,M1} { addition( coantidomain( multiplication( X, Y
% 0.44/1.09 ) ), coantidomain( multiplication( coantidomain( coantidomain( X ) ), Y
% 0.44/1.09 ) ) ) = coantidomain( multiplication( coantidomain( coantidomain( X ) )
% 0.44/1.09 , Y ) ) }.
% 0.44/1.09 (311) {G0,W8,D5,L1,V1,M1} { addition( coantidomain( coantidomain( X ) ),
% 0.44/1.09 coantidomain( X ) ) = one }.
% 0.44/1.09 (312) {G0,W6,D4,L1,V1,M1} { codomain( X ) = coantidomain( coantidomain( X
% 0.44/1.09 ) ) }.
% 0.44/1.09 (313) {G0,W6,D4,L1,V1,M1} { c( X ) = antidomain( domain( X ) ) }.
% 0.44/1.09 (314) {G0,W9,D4,L1,V2,M1} { domain_difference( X, Y ) = multiplication(
% 0.44/1.09 domain( X ), antidomain( Y ) ) }.
% 0.44/1.09 (315) {G0,W9,D5,L1,V2,M1} { forward_diamond( X, Y ) = domain(
% 0.44/1.09 multiplication( X, domain( Y ) ) ) }.
% 0.44/1.09 (316) {G0,W9,D5,L1,V2,M1} { backward_diamond( X, Y ) = codomain(
% 0.44/1.09 multiplication( codomain( Y ), X ) ) }.
% 0.44/1.09 (317) {G0,W9,D5,L1,V2,M1} { forward_box( X, Y ) = c( forward_diamond( X, c
% 0.44/1.09 ( Y ) ) ) }.
% 0.44/1.09 (318) {G0,W9,D5,L1,V2,M1} { backward_box( X, Y ) = c( backward_diamond( X
% 0.44/1.09 , c( Y ) ) ) }.
% 0.44/1.09 (319) {G0,W5,D3,L1,V0,M1} { ! forward_box( skol1, one ) = one }.
% 0.44/1.09
% 0.44/1.09
% 0.44/1.09 Total Proof:
% 0.44/1.09
% 0.44/1.09 subsumption: (2) {G0,W5,D3,L1,V1,M1} I { addition( X, zero ) ==> X }.
% 0.44/1.09 parent0: (294) {G0,W5,D3,L1,V1,M1} { addition( X, zero ) = X }.
% 0.44/1.09 substitution0:
% 0.44/1.09 X := X
% 0.44/1.09 end
% 0.44/1.09 permutation0:
% 0.44/1.09 0 ==> 0
% 0.44/1.09 end
% 0.44/1.09
% 0.44/1.09 subsumption: (5) {G0,W5,D3,L1,V1,M1} I { multiplication( X, one ) ==> X }.
% 0.44/1.09 parent0: (297) {G0,W5,D3,L1,V1,M1} { multiplication( X, one ) = X }.
% 0.44/1.09 substitution0:
% 0.44/1.09 X := X
% 0.44/1.09 end
% 0.44/1.09 permutation0:
% 0.44/1.09 0 ==> 0
% 0.44/1.09 end
% 0.44/1.09
% 0.44/1.09 subsumption: (9) {G0,W5,D3,L1,V1,M1} I { multiplication( X, zero ) ==> zero
% 0.44/1.09 }.
% 0.44/1.09 parent0: (301) {G0,W5,D3,L1,V1,M1} { multiplication( X, zero ) = zero }.
% 0.44/1.09 substitution0:
% 0.44/1.09 X := X
% 0.44/1.09 end
% 0.44/1.09 permutation0:
% 0.44/1.09 0 ==> 0
% 0.44/1.09 end
% 0.44/1.09
% 0.44/1.09 subsumption: (13) {G0,W6,D4,L1,V1,M1} I { multiplication( antidomain( X ),
% 0.44/1.09 X ) ==> zero }.
% 0.44/1.09 parent0: (305) {G0,W6,D4,L1,V1,M1} { multiplication( antidomain( X ), X )
% 0.44/1.09 = zero }.
% 0.44/1.09 substitution0:
% 0.44/1.09 X := X
% 0.44/1.09 end
% 0.44/1.09 permutation0:
% 0.44/1.09 0 ==> 0
% 0.44/1.09 end
% 0.44/1.09
% 0.44/1.09 subsumption: (15) {G0,W8,D5,L1,V1,M1} I { addition( antidomain( antidomain
% 0.44/1.09 ( X ) ), antidomain( X ) ) ==> one }.
% 0.44/1.09 parent0: (307) {G0,W8,D5,L1,V1,M1} { addition( antidomain( antidomain( X )
% 0.44/1.09 ), antidomain( X ) ) = one }.
% 0.44/1.09 substitution0:
% 0.44/1.09 X := X
% 0.44/1.09 end
% 0.44/1.09 permutation0:
% 0.44/1.09 0 ==> 0
% 0.44/1.09 end
% 0.44/1.09
% 0.44/1.09 eqswap: (379) {G0,W6,D4,L1,V1,M1} { antidomain( antidomain( X ) ) = domain
% 0.44/1.09 ( X ) }.
% 0.44/1.09 parent0[0]: (308) {G0,W6,D4,L1,V1,M1} { domain( X ) = antidomain(
% 0.44/1.09 antidomain( X ) ) }.
% 0.44/1.09 substitution0:
% 0.44/1.09 X := X
% 0.44/1.09 end
% 0.44/1.09
% 0.44/1.09 subsumption: (16) {G0,W6,D4,L1,V1,M1} I { antidomain( antidomain( X ) ) ==>
% 0.44/1.09 domain( X ) }.
% 0.44/1.09 parent0: (379) {G0,W6,D4,L1,V1,M1} { antidomain( antidomain( X ) ) =
% 0.44/1.09 domain( X ) }.
% 0.44/1.09 substitution0:
% 0.44/1.09 X := X
% 0.44/1.09 end
% 0.44/1.09 permutation0:
% 0.44/1.09 0 ==> 0
% 0.44/1.09 end
% 0.44/1.09
% 0.44/1.09 eqswap: (400) {G0,W6,D4,L1,V1,M1} { antidomain( domain( X ) ) = c( X ) }.
% 0.44/1.09 parent0[0]: (313) {G0,W6,D4,L1,V1,M1} { c( X ) = antidomain( domain( X ) )
% 0.44/1.09 }.
% 0.44/1.09 substitution0:
% 0.44/1.09 X := X
% 0.44/1.09 end
% 0.44/1.09
% 0.44/1.09 subsumption: (21) {G0,W6,D4,L1,V1,M1} I { antidomain( domain( X ) ) ==> c(
% 0.44/1.09 X ) }.
% 0.44/1.09 parent0: (400) {G0,W6,D4,L1,V1,M1} { antidomain( domain( X ) ) = c( X )
% 0.44/1.09 }.
% 0.44/1.09 substitution0:
% 0.44/1.09 X := X
% 0.44/1.09 end
% 0.44/1.09 permutation0:
% 0.44/1.09 0 ==> 0
% 0.44/1.09 end
% 0.44/1.09
% 0.44/1.09 eqswap: (423) {G0,W9,D5,L1,V2,M1} { domain( multiplication( X, domain( Y )
% 0.44/1.09 ) ) = forward_diamond( X, Y ) }.
% 0.44/1.09 parent0[0]: (315) {G0,W9,D5,L1,V2,M1} { forward_diamond( X, Y ) = domain(
% 0.44/1.09 multiplication( X, domain( Y ) ) ) }.
% 0.44/1.09 substitution0:
% 0.44/1.09 X := X
% 0.44/1.09 Y := Y
% 0.44/1.09 end
% 0.44/1.09
% 0.44/1.09 subsumption: (23) {G0,W9,D5,L1,V2,M1} I { domain( multiplication( X, domain
% 0.44/1.09 ( Y ) ) ) ==> forward_diamond( X, Y ) }.
% 0.44/1.09 parent0: (423) {G0,W9,D5,L1,V2,M1} { domain( multiplication( X, domain( Y
% 0.44/1.09 ) ) ) = forward_diamond( X, Y ) }.
% 0.44/1.09 substitution0:
% 0.44/1.09 X := X
% 0.44/1.09 Y := Y
% 0.44/1.09 end
% 0.44/1.09 permutation0:
% 0.44/1.09 0 ==> 0
% 0.44/1.09 end
% 0.44/1.09
% 0.44/1.09 eqswap: (448) {G0,W9,D5,L1,V2,M1} { c( forward_diamond( X, c( Y ) ) ) =
% 0.44/1.09 forward_box( X, Y ) }.
% 0.44/1.09 parent0[0]: (317) {G0,W9,D5,L1,V2,M1} { forward_box( X, Y ) = c(
% 0.44/1.09 forward_diamond( X, c( Y ) ) ) }.
% 0.44/1.09 substitution0:
% 0.44/1.09 X := X
% 0.44/1.09 Y := Y
% 0.44/1.09 end
% 0.44/1.09
% 0.44/1.09 subsumption: (25) {G0,W9,D5,L1,V2,M1} I { c( forward_diamond( X, c( Y ) ) )
% 0.44/1.09 ==> forward_box( X, Y ) }.
% 0.44/1.09 parent0: (448) {G0,W9,D5,L1,V2,M1} { c( forward_diamond( X, c( Y ) ) ) =
% 0.44/1.09 forward_box( X, Y ) }.
% 0.44/1.09 substitution0:
% 0.44/1.09 X := X
% 0.44/1.09 Y := Y
% 0.44/1.09 end
% 0.44/1.09 permutation0:
% 0.44/1.09 0 ==> 0
% 0.44/1.09 end
% 0.44/1.09
% 0.44/1.09 subsumption: (27) {G0,W5,D3,L1,V0,M1} I { ! forward_box( skol1, one ) ==>
% 0.44/1.09 one }.
% 0.44/1.09 parent0: (319) {G0,W5,D3,L1,V0,M1} { ! forward_box( skol1, one ) = one }.
% 0.44/1.09 substitution0:
% 0.44/1.09 end
% 0.44/1.09 permutation0:
% 0.44/1.09 0 ==> 0
% 0.44/1.09 end
% 0.44/1.09
% 0.44/1.09 eqswap: (476) {G0,W6,D4,L1,V1,M1} { domain( X ) ==> antidomain( antidomain
% 0.44/1.09 ( X ) ) }.
% 0.44/1.09 parent0[0]: (16) {G0,W6,D4,L1,V1,M1} I { antidomain( antidomain( X ) ) ==>
% 0.44/1.09 domain( X ) }.
% 0.44/1.09 substitution0:
% 0.44/1.09 X := X
% 0.44/1.09 end
% 0.44/1.09
% 0.44/1.09 paramod: (480) {G1,W7,D4,L1,V1,M1} { domain( antidomain( X ) ) ==>
% 0.44/1.09 antidomain( domain( X ) ) }.
% 0.44/1.09 parent0[0]: (16) {G0,W6,D4,L1,V1,M1} I { antidomain( antidomain( X ) ) ==>
% 0.44/1.09 domain( X ) }.
% 0.44/1.09 parent1[0; 5]: (476) {G0,W6,D4,L1,V1,M1} { domain( X ) ==> antidomain(
% 0.44/1.09 antidomain( X ) ) }.
% 0.44/1.09 substitution0:
% 0.44/1.09 X := X
% 0.44/1.09 end
% 0.44/1.09 substitution1:
% 0.44/1.09 X := antidomain( X )
% 0.44/1.09 end
% 0.44/1.09
% 0.44/1.09 paramod: (481) {G1,W6,D4,L1,V1,M1} { domain( antidomain( X ) ) ==> c( X )
% 0.44/1.09 }.
% 0.44/1.09 parent0[0]: (21) {G0,W6,D4,L1,V1,M1} I { antidomain( domain( X ) ) ==> c( X
% 0.44/1.09 ) }.
% 0.44/1.09 parent1[0; 4]: (480) {G1,W7,D4,L1,V1,M1} { domain( antidomain( X ) ) ==>
% 0.44/1.09 antidomain( domain( X ) ) }.
% 0.44/1.09 substitution0:
% 0.44/1.09 X := X
% 0.44/1.09 end
% 0.44/1.09 substitution1:
% 0.44/1.09 X := X
% 0.44/1.09 end
% 0.44/1.09
% 0.44/1.09 subsumption: (38) {G1,W6,D4,L1,V1,M1} P(16,16);d(21) { domain( antidomain(
% 0.44/1.09 X ) ) ==> c( X ) }.
% 0.44/1.09 parent0: (481) {G1,W6,D4,L1,V1,M1} { domain( antidomain( X ) ) ==> c( X )
% 0.44/1.09 }.
% 0.44/1.09 substitution0:
% 0.44/1.09 X := X
% 0.44/1.09 end
% 0.44/1.09 permutation0:
% 0.44/1.09 0 ==> 0
% 0.44/1.09 end
% 0.44/1.09
% 0.44/1.09 eqswap: (483) {G0,W6,D4,L1,V1,M1} { zero ==> multiplication( antidomain( X
% 0.44/1.09 ), X ) }.
% 0.44/1.09 parent0[0]: (13) {G0,W6,D4,L1,V1,M1} I { multiplication( antidomain( X ), X
% 0.44/1.09 ) ==> zero }.
% 0.44/1.09 substitution0:
% 0.44/1.09 X := X
% 0.44/1.09 end
% 0.44/1.09
% 0.44/1.09 paramod: (485) {G1,W4,D3,L1,V0,M1} { zero ==> antidomain( one ) }.
% 0.44/1.09 parent0[0]: (5) {G0,W5,D3,L1,V1,M1} I { multiplication( X, one ) ==> X }.
% 0.44/1.09 parent1[0; 2]: (483) {G0,W6,D4,L1,V1,M1} { zero ==> multiplication(
% 0.44/1.09 antidomain( X ), X ) }.
% 0.44/1.09 substitution0:
% 0.44/1.09 X := antidomain( one )
% 0.44/1.09 end
% 0.44/1.09 substitution1:
% 0.44/1.09 X := one
% 0.44/1.09 end
% 0.44/1.09
% 0.44/1.09 eqswap: (486) {G1,W4,D3,L1,V0,M1} { antidomain( one ) ==> zero }.
% 0.44/1.09 parent0[0]: (485) {G1,W4,D3,L1,V0,M1} { zero ==> antidomain( one ) }.
% 0.44/1.09 substitution0:
% 0.44/1.09 end
% 0.44/1.09
% 0.44/1.09 subsumption: (46) {G1,W4,D3,L1,V0,M1} P(13,5) { antidomain( one ) ==> zero
% 0.44/1.09 }.
% 0.44/1.09 parent0: (486) {G1,W4,D3,L1,V0,M1} { antidomain( one ) ==> zero }.
% 0.44/1.09 substitution0:
% 0.44/1.09 end
% 0.44/1.09 permutation0:
% 0.44/1.09 0 ==> 0
% 0.44/1.09 end
% 0.44/1.09
% 0.44/1.09 eqswap: (488) {G1,W6,D4,L1,V1,M1} { c( X ) ==> domain( antidomain( X ) )
% 0.44/1.09 }.
% 0.44/1.09 parent0[0]: (38) {G1,W6,D4,L1,V1,M1} P(16,16);d(21) { domain( antidomain( X
% 0.44/1.09 ) ) ==> c( X ) }.
% 0.44/1.09 substitution0:
% 0.44/1.09 X := X
% 0.44/1.09 end
% 0.44/1.09
% 0.44/1.09 paramod: (489) {G2,W5,D3,L1,V0,M1} { c( one ) ==> domain( zero ) }.
% 0.44/1.09 parent0[0]: (46) {G1,W4,D3,L1,V0,M1} P(13,5) { antidomain( one ) ==> zero
% 0.44/1.09 }.
% 0.44/1.09 parent1[0; 4]: (488) {G1,W6,D4,L1,V1,M1} { c( X ) ==> domain( antidomain(
% 0.44/1.09 X ) ) }.
% 0.44/1.09 substitution0:
% 0.44/1.09 end
% 0.44/1.09 substitution1:
% 0.44/1.09 X := one
% 0.44/1.09 end
% 0.44/1.09
% 0.44/1.09 eqswap: (490) {G2,W5,D3,L1,V0,M1} { domain( zero ) ==> c( one ) }.
% 0.44/1.09 parent0[0]: (489) {G2,W5,D3,L1,V0,M1} { c( one ) ==> domain( zero ) }.
% 0.44/1.09 substitution0:
% 0.44/1.09 end
% 0.44/1.09
% 0.44/1.09 subsumption: (47) {G2,W5,D3,L1,V0,M1} P(46,38) { domain( zero ) ==> c( one
% 0.44/1.09 ) }.
% 0.44/1.09 parent0: (490) {G2,W5,D3,L1,V0,M1} { domain( zero ) ==> c( one ) }.
% 0.44/1.09 substitution0:
% 0.44/1.09 end
% 0.44/1.09 permutation0:
% 0.44/1.09 0 ==> 0
% 0.44/1.09 end
% 0.44/1.09
% 0.44/1.09 eqswap: (492) {G0,W6,D4,L1,V1,M1} { domain( X ) ==> antidomain( antidomain
% 0.44/1.09 ( X ) ) }.
% 0.44/1.09 parent0[0]: (16) {G0,W6,D4,L1,V1,M1} I { antidomain( antidomain( X ) ) ==>
% 0.44/1.09 domain( X ) }.
% 0.44/1.09 substitution0:
% 0.44/1.09 X := X
% 0.44/1.09 end
% 0.44/1.09
% 0.44/1.09 paramod: (493) {G1,W5,D3,L1,V0,M1} { domain( one ) ==> antidomain( zero )
% 0.44/1.09 }.
% 0.44/1.09 parent0[0]: (46) {G1,W4,D3,L1,V0,M1} P(13,5) { antidomain( one ) ==> zero
% 0.44/1.09 }.
% 0.44/1.09 parent1[0; 4]: (492) {G0,W6,D4,L1,V1,M1} { domain( X ) ==> antidomain(
% 0.44/1.09 antidomain( X ) ) }.
% 0.44/1.09 substitution0:
% 0.44/1.09 end
% 0.44/1.09 substitution1:
% 0.44/1.09 X := one
% 0.44/1.09 end
% 0.44/1.09
% 0.44/1.09 subsumption: (48) {G2,W5,D3,L1,V0,M1} P(46,16) { domain( one ) ==>
% 0.44/1.09 antidomain( zero ) }.
% 0.44/1.09 parent0: (493) {G1,W5,D3,L1,V0,M1} { domain( one ) ==> antidomain( zero )
% 0.44/1.09 }.
% 0.44/1.09 substitution0:
% 0.44/1.09 end
% 0.44/1.09 permutation0:
% 0.44/1.09 0 ==> 0
% 0.44/1.09 end
% 0.44/1.09
% 0.44/1.09 paramod: (497) {G1,W7,D4,L1,V1,M1} { addition( domain( X ), antidomain( X
% 0.44/1.09 ) ) ==> one }.
% 0.44/1.09 parent0[0]: (16) {G0,W6,D4,L1,V1,M1} I { antidomain( antidomain( X ) ) ==>
% 0.44/1.09 domain( X ) }.
% 0.44/1.09 parent1[0; 2]: (15) {G0,W8,D5,L1,V1,M1} I { addition( antidomain(
% 0.44/1.09 antidomain( X ) ), antidomain( X ) ) ==> one }.
% 0.44/1.09 substitution0:
% 0.44/1.09 X := X
% 0.44/1.09 end
% 0.44/1.09 substitution1:
% 0.44/1.09 X := X
% 0.44/1.09 end
% 0.44/1.09
% 0.44/1.09 subsumption: (182) {G1,W7,D4,L1,V1,M1} S(15);d(16) { addition( domain( X )
% 0.44/1.09 , antidomain( X ) ) ==> one }.
% 0.44/1.09 parent0: (497) {G1,W7,D4,L1,V1,M1} { addition( domain( X ), antidomain( X
% 0.44/1.09 ) ) ==> one }.
% 0.44/1.09 substitution0:
% 0.44/1.09 X := X
% 0.44/1.09 end
% 0.44/1.09 permutation0:
% 0.44/1.09 0 ==> 0
% 0.44/1.09 end
% 0.44/1.09
% 0.44/1.09 eqswap: (500) {G1,W7,D4,L1,V1,M1} { one ==> addition( domain( X ),
% 0.44/1.09 antidomain( X ) ) }.
% 0.44/1.09 parent0[0]: (182) {G1,W7,D4,L1,V1,M1} S(15);d(16) { addition( domain( X ),
% 0.44/1.09 antidomain( X ) ) ==> one }.
% 0.44/1.09 substitution0:
% 0.44/1.09 X := X
% 0.44/1.09 end
% 0.44/1.09
% 0.44/1.09 paramod: (503) {G2,W7,D4,L1,V0,M1} { one ==> addition( antidomain( zero )
% 0.44/1.09 , antidomain( one ) ) }.
% 0.44/1.09 parent0[0]: (48) {G2,W5,D3,L1,V0,M1} P(46,16) { domain( one ) ==>
% 0.44/1.09 antidomain( zero ) }.
% 0.44/1.09 parent1[0; 3]: (500) {G1,W7,D4,L1,V1,M1} { one ==> addition( domain( X ),
% 0.44/1.09 antidomain( X ) ) }.
% 0.44/1.09 substitution0:
% 0.44/1.09 end
% 0.44/1.09 substitution1:
% 0.44/1.09 X := one
% 0.44/1.09 end
% 0.44/1.09
% 0.44/1.09 paramod: (504) {G2,W6,D4,L1,V0,M1} { one ==> addition( antidomain( zero )
% 0.44/1.09 , zero ) }.
% 0.44/1.09 parent0[0]: (46) {G1,W4,D3,L1,V0,M1} P(13,5) { antidomain( one ) ==> zero
% 0.44/1.09 }.
% 0.44/1.09 parent1[0; 5]: (503) {G2,W7,D4,L1,V0,M1} { one ==> addition( antidomain(
% 0.44/1.09 zero ), antidomain( one ) ) }.
% 0.44/1.09 substitution0:
% 0.44/1.09 end
% 0.44/1.09 substitution1:
% 0.44/1.09 end
% 0.44/1.09
% 0.44/1.09 paramod: (505) {G1,W4,D3,L1,V0,M1} { one ==> antidomain( zero ) }.
% 0.44/1.09 parent0[0]: (2) {G0,W5,D3,L1,V1,M1} I { addition( X, zero ) ==> X }.
% 0.44/1.09 parent1[0; 2]: (504) {G2,W6,D4,L1,V0,M1} { one ==> addition( antidomain(
% 0.44/1.09 zero ), zero ) }.
% 0.44/1.09 substitution0:
% 0.44/1.09 X := antidomain( zero )
% 0.44/1.09 end
% 0.44/1.09 substitution1:
% 0.44/1.09 end
% 0.44/1.09
% 0.44/1.09 eqswap: (506) {G1,W4,D3,L1,V0,M1} { antidomain( zero ) ==> one }.
% 0.44/1.09 parent0[0]: (505) {G1,W4,D3,L1,V0,M1} { one ==> antidomain( zero ) }.
% 0.44/1.09 substitution0:
% 0.44/1.09 end
% 0.44/1.09
% 0.44/1.09 subsumption: (196) {G3,W4,D3,L1,V0,M1} P(48,182);d(46);d(2) { antidomain(
% 0.44/1.09 zero ) ==> one }.
% 0.44/1.09 parent0: (506) {G1,W4,D3,L1,V0,M1} { antidomain( zero ) ==> one }.
% 0.44/1.09 substitution0:
% 0.44/1.09 end
% 0.44/1.09 permutation0:
% 0.44/1.09 0 ==> 0
% 0.44/1.09 end
% 0.44/1.09
% 0.44/1.09 eqswap: (508) {G1,W6,D4,L1,V1,M1} { c( X ) ==> domain( antidomain( X ) )
% 0.44/1.09 }.
% 0.44/1.09 parent0[0]: (38) {G1,W6,D4,L1,V1,M1} P(16,16);d(21) { domain( antidomain( X
% 0.44/1.09 ) ) ==> c( X ) }.
% 0.44/1.09 substitution0:
% 0.44/1.09 X := X
% 0.44/1.09 end
% 0.44/1.09
% 0.44/1.09 paramod: (511) {G2,W5,D3,L1,V0,M1} { c( zero ) ==> domain( one ) }.
% 0.44/1.09 parent0[0]: (196) {G3,W4,D3,L1,V0,M1} P(48,182);d(46);d(2) { antidomain(
% 0.44/1.09 zero ) ==> one }.
% 0.44/1.09 parent1[0; 4]: (508) {G1,W6,D4,L1,V1,M1} { c( X ) ==> domain( antidomain(
% 0.44/1.09 X ) ) }.
% 0.44/1.09 substitution0:
% 0.44/1.09 end
% 0.44/1.09 substitution1:
% 0.44/1.09 X := zero
% 0.44/1.09 end
% 0.44/1.09
% 0.44/1.09 paramod: (512) {G3,W5,D3,L1,V0,M1} { c( zero ) ==> antidomain( zero ) }.
% 0.44/1.09 parent0[0]: (48) {G2,W5,D3,L1,V0,M1} P(46,16) { domain( one ) ==>
% 0.44/1.09 antidomain( zero ) }.
% 0.44/1.09 parent1[0; 3]: (511) {G2,W5,D3,L1,V0,M1} { c( zero ) ==> domain( one ) }.
% 0.44/1.09 substitution0:
% 0.44/1.09 end
% 0.44/1.09 substitution1:
% 0.44/1.09 end
% 0.44/1.09
% 0.44/1.09 paramod: (513) {G4,W4,D3,L1,V0,M1} { c( zero ) ==> one }.
% 0.44/1.09 parent0[0]: (196) {G3,W4,D3,L1,V0,M1} P(48,182);d(46);d(2) { antidomain(
% 0.44/1.09 zero ) ==> one }.
% 0.44/1.09 parent1[0; 3]: (512) {G3,W5,D3,L1,V0,M1} { c( zero ) ==> antidomain( zero
% 0.44/1.09 ) }.
% 0.44/1.09 substitution0:
% 0.44/1.09 end
% 0.44/1.09 substitution1:
% 0.44/1.09 end
% 0.44/1.09
% 0.44/1.09 subsumption: (205) {G4,W4,D3,L1,V0,M1} P(196,38);d(48);d(196) { c( zero )
% 0.44/1.09 ==> one }.
% 0.44/1.09 parent0: (513) {G4,W4,D3,L1,V0,M1} { c( zero ) ==> one }.
% 0.44/1.09 substitution0:
% 0.44/1.09 end
% 0.44/1.09 permutation0:
% 0.44/1.09 0 ==> 0
% 0.44/1.09 end
% 0.44/1.09
% 0.44/1.09 eqswap: (516) {G0,W6,D4,L1,V1,M1} { domain( X ) ==> antidomain( antidomain
% 0.44/1.09 ( X ) ) }.
% 0.44/1.09 parent0[0]: (16) {G0,W6,D4,L1,V1,M1} I { antidomain( antidomain( X ) ) ==>
% 0.44/1.09 domain( X ) }.
% 0.44/1.09 substitution0:
% 0.44/1.09 X := X
% 0.44/1.09 end
% 0.44/1.09
% 0.44/1.09 paramod: (519) {G1,W5,D3,L1,V0,M1} { domain( zero ) ==> antidomain( one )
% 0.44/1.09 }.
% 0.44/1.09 parent0[0]: (196) {G3,W4,D3,L1,V0,M1} P(48,182);d(46);d(2) { antidomain(
% 0.44/1.09 zero ) ==> one }.
% 0.44/1.09 parent1[0; 4]: (516) {G0,W6,D4,L1,V1,M1} { domain( X ) ==> antidomain(
% 0.44/1.09 antidomain( X ) ) }.
% 0.44/1.09 substitution0:
% 0.44/1.09 end
% 0.44/1.09 substitution1:
% 0.44/1.09 X := zero
% 0.44/1.09 end
% 0.44/1.09
% 0.44/1.09 paramod: (520) {G2,W4,D3,L1,V0,M1} { domain( zero ) ==> zero }.
% 0.44/1.09 parent0[0]: (46) {G1,W4,D3,L1,V0,M1} P(13,5) { antidomain( one ) ==> zero
% 0.44/1.09 }.
% 0.44/1.09 parent1[0; 3]: (519) {G1,W5,D3,L1,V0,M1} { domain( zero ) ==> antidomain(
% 0.44/1.09 one ) }.
% 0.44/1.09 substitution0:
% 0.44/1.09 end
% 0.44/1.09 substitution1:
% 0.44/1.09 end
% 0.44/1.09
% 0.44/1.09 paramod: (521) {G3,W4,D3,L1,V0,M1} { c( one ) ==> zero }.
% 0.44/1.09 parent0[0]: (47) {G2,W5,D3,L1,V0,M1} P(46,38) { domain( zero ) ==> c( one )
% 0.44/1.09 }.
% 0.44/1.09 parent1[0; 1]: (520) {G2,W4,D3,L1,V0,M1} { domain( zero ) ==> zero }.
% 0.44/1.09 substitution0:
% 0.44/1.09 end
% 0.44/1.09 substitution1:
% 0.44/1.09 end
% 0.44/1.09
% 0.44/1.09 subsumption: (206) {G4,W4,D3,L1,V0,M1} P(196,16);d(46);d(47) { c( one ) ==>
% 0.44/1.09 zero }.
% 0.44/1.09 parent0: (521) {G3,W4,D3,L1,V0,M1} { c( one ) ==> zero }.
% 0.44/1.09 substitution0:
% 0.44/1.09 end
% 0.44/1.09 permutation0:
% 0.44/1.09 0 ==> 0
% 0.44/1.09 end
% 0.44/1.09
% 0.44/1.09 eqswap: (524) {G0,W9,D5,L1,V2,M1} { forward_diamond( X, Y ) ==> domain(
% 0.44/1.09 multiplication( X, domain( Y ) ) ) }.
% 0.44/1.09 parent0[0]: (23) {G0,W9,D5,L1,V2,M1} I { domain( multiplication( X, domain
% 0.44/1.09 ( Y ) ) ) ==> forward_diamond( X, Y ) }.
% 0.44/1.09 substitution0:
% 0.44/1.09 X := X
% 0.44/1.09 Y := Y
% 0.44/1.09 end
% 0.44/1.09
% 0.44/1.09 paramod: (529) {G1,W9,D5,L1,V1,M1} { forward_diamond( X, zero ) ==> domain
% 0.44/1.09 ( multiplication( X, c( one ) ) ) }.
% 0.44/1.09 parent0[0]: (47) {G2,W5,D3,L1,V0,M1} P(46,38) { domain( zero ) ==> c( one )
% 0.44/1.09 }.
% 0.44/1.09 parent1[0; 7]: (524) {G0,W9,D5,L1,V2,M1} { forward_diamond( X, Y ) ==>
% 0.44/1.09 domain( multiplication( X, domain( Y ) ) ) }.
% 0.44/1.09 substitution0:
% 0.44/1.09 end
% 0.44/1.09 substitution1:
% 0.44/1.09 X := X
% 0.44/1.09 Y := zero
% 0.44/1.09 end
% 0.44/1.09
% 0.44/1.09 paramod: (530) {G2,W8,D4,L1,V1,M1} { forward_diamond( X, zero ) ==> domain
% 0.44/1.09 ( multiplication( X, zero ) ) }.
% 0.44/1.09 parent0[0]: (206) {G4,W4,D3,L1,V0,M1} P(196,16);d(46);d(47) { c( one ) ==>
% 0.44/1.09 zero }.
% 0.44/1.09 parent1[0; 7]: (529) {G1,W9,D5,L1,V1,M1} { forward_diamond( X, zero ) ==>
% 0.44/1.09 domain( multiplication( X, c( one ) ) ) }.
% 0.44/1.09 substitution0:
% 0.44/1.09 end
% 0.44/1.09 substitution1:
% 0.44/1.09 X := X
% 0.44/1.09 end
% 0.44/1.09
% 0.44/1.09 paramod: (531) {G1,W6,D3,L1,V1,M1} { forward_diamond( X, zero ) ==> domain
% 0.44/1.09 ( zero ) }.
% 0.44/1.09 parent0[0]: (9) {G0,W5,D3,L1,V1,M1} I { multiplication( X, zero ) ==> zero
% 0.44/1.09 }.
% 0.44/1.09 parent1[0; 5]: (530) {G2,W8,D4,L1,V1,M1} { forward_diamond( X, zero ) ==>
% 0.44/1.09 domain( multiplication( X, zero ) ) }.
% 0.44/1.09 substitution0:
% 0.44/1.09 X := X
% 0.44/1.09 end
% 0.44/1.09 substitution1:
% 0.44/1.09 X := X
% 0.44/1.09 end
% 0.44/1.09
% 0.44/1.09 paramod: (532) {G2,W6,D3,L1,V1,M1} { forward_diamond( X, zero ) ==> c( one
% 0.44/1.09 ) }.
% 0.44/1.09 parent0[0]: (47) {G2,W5,D3,L1,V0,M1} P(46,38) { domain( zero ) ==> c( one )
% 0.44/1.09 }.
% 0.44/1.09 parent1[0; 4]: (531) {G1,W6,D3,L1,V1,M1} { forward_diamond( X, zero ) ==>
% 0.44/1.09 domain( zero ) }.
% 0.44/1.09 substitution0:
% 0.44/1.09 end
% 0.44/1.09 substitution1:
% 0.44/1.09 X := X
% 0.44/1.09 end
% 0.44/1.09
% 0.44/1.09 paramod: (533) {G3,W5,D3,L1,V1,M1} { forward_diamond( X, zero ) ==> zero
% 0.44/1.09 }.
% 0.44/1.09 parent0[0]: (206) {G4,W4,D3,L1,V0,M1} P(196,16);d(46);d(47) { c( one ) ==>
% 0.44/1.09 zero }.
% 0.44/1.09 parent1[0; 4]: (532) {G2,W6,D3,L1,V1,M1} { forward_diamond( X, zero ) ==>
% 0.44/1.09 c( one ) }.
% 0.44/1.09 substitution0:
% 0.44/1.09 end
% 0.44/1.09 substitution1:
% 0.44/1.09 X := X
% 0.44/1.09 end
% 0.44/1.09
% 0.44/1.09 subsumption: (244) {G5,W5,D3,L1,V1,M1} P(47,23);d(206);d(9);d(47);d(206) {
% 0.44/1.09 forward_diamond( X, zero ) ==> zero }.
% 0.44/1.09 parent0: (533) {G3,W5,D3,L1,V1,M1} { forward_diamond( X, zero ) ==> zero
% 0.44/1.09 }.
% 0.44/1.09 substitution0:
% 0.44/1.09 X := X
% 0.44/1.09 end
% 0.44/1.09 permutation0:
% 0.44/1.09 0 ==> 0
% 0.44/1.09 end
% 0.44/1.09
% 0.44/1.09 eqswap: (536) {G0,W9,D5,L1,V2,M1} { forward_box( X, Y ) ==> c(
% 0.44/1.09 forward_diamond( X, c( Y ) ) ) }.
% 0.44/1.09 parent0[0]: (25) {G0,W9,D5,L1,V2,M1} I { c( forward_diamond( X, c( Y ) ) )
% 0.44/1.09 ==> forward_box( X, Y ) }.
% 0.44/1.09 substitution0:
% 0.44/1.09 X := X
% 0.44/1.09 Y := Y
% 0.44/1.09 end
% 0.44/1.09
% 0.44/1.09 paramod: (539) {G1,W8,D4,L1,V1,M1} { forward_box( X, one ) ==> c(
% 0.44/1.09 forward_diamond( X, zero ) ) }.
% 0.44/1.09 parent0[0]: (206) {G4,W4,D3,L1,V0,M1} P(196,16);d(46);d(47) { c( one ) ==>
% 0.44/1.09 zero }.
% 0.44/1.09 parent1[0; 7]: (536) {G0,W9,D5,L1,V2,M1} { forward_box( X, Y ) ==> c(
% 0.44/1.09 forward_diamond( X, c( Y ) ) ) }.
% 0.44/1.09 substitution0:
% 0.44/1.09 end
% 0.44/1.09 substitution1:
% 0.44/1.09 X := X
% 0.44/1.09 Y := one
% 0.44/1.09 end
% 0.44/1.09
% 0.44/1.09 paramod: (540) {G2,W6,D3,L1,V1,M1} { forward_box( X, one ) ==> c( zero )
% 0.44/1.09 }.
% 0.44/1.09 parent0[0]: (244) {G5,W5,D3,L1,V1,M1} P(47,23);d(206);d(9);d(47);d(206) {
% 0.44/1.09 forward_diamond( X, zero ) ==> zero }.
% 0.44/1.09 parent1[0; 5]: (539) {G1,W8,D4,L1,V1,M1} { forward_box( X, one ) ==> c(
% 0.44/1.09 forward_diamond( X, zero ) ) }.
% 0.44/1.09 substitution0:
% 0.44/1.09 X := X
% 0.44/1.09 end
% 0.44/1.09 substitution1:
% 0.44/1.09 X := X
% 0.44/1.09 end
% 0.44/1.09
% 0.44/1.09 paramod: (541) {G3,W5,D3,L1,V1,M1} { forward_box( X, one ) ==> one }.
% 0.44/1.09 parent0[0]: (205) {G4,W4,D3,L1,V0,M1} P(196,38);d(48);d(196) { c( zero )
% 0.44/1.09 ==> one }.
% 0.44/1.09 parent1[0; 4]: (540) {G2,W6,D3,L1,V1,M1} { forward_box( X, one ) ==> c(
% 0.44/1.09 zero ) }.
% 0.44/1.09 substitution0:
% 0.44/1.09 end
% 0.44/1.09 substitution1:
% 0.44/1.09 X := X
% 0.44/1.09 end
% 0.44/1.09
% 0.44/1.09 subsumption: (280) {G6,W5,D3,L1,V1,M1} P(206,25);d(244);d(205) {
% 0.44/1.09 forward_box( X, one ) ==> one }.
% 0.44/1.09 parent0: (541) {G3,W5,D3,L1,V1,M1} { forward_box( X, one ) ==> one }.
% 0.44/1.09 substitution0:
% 0.44/1.09 X := X
% 0.44/1.09 end
% 0.44/1.09 permutation0:
% 0.44/1.09 0 ==> 0
% 0.44/1.09 end
% 0.44/1.09
% 0.44/1.09 eqswap: (543) {G6,W5,D3,L1,V1,M1} { one ==> forward_box( X, one ) }.
% 0.44/1.09 parent0[0]: (280) {G6,W5,D3,L1,V1,M1} P(206,25);d(244);d(205) { forward_box
% 0.44/1.09 ( X, one ) ==> one }.
% 0.44/1.09 substitution0:
% 0.44/1.09 X := X
% 0.44/1.09 end
% 0.44/1.09
% 0.44/1.09 eqswap: (544) {G0,W5,D3,L1,V0,M1} { ! one ==> forward_box( skol1, one )
% 0.44/1.09 }.
% 0.44/1.09 parent0[0]: (27) {G0,W5,D3,L1,V0,M1} I { ! forward_box( skol1, one ) ==>
% 0.44/1.09 one }.
% 0.44/1.09 substitution0:
% 0.44/1.09 end
% 0.44/1.09
% 0.44/1.09 resolution: (545) {G1,W0,D0,L0,V0,M0} { }.
% 0.44/1.09 parent0[0]: (544) {G0,W5,D3,L1,V0,M1} { ! one ==> forward_box( skol1, one
% 0.44/1.09 ) }.
% 0.44/1.09 parent1[0]: (543) {G6,W5,D3,L1,V1,M1} { one ==> forward_box( X, one ) }.
% 0.44/1.09 substitution0:
% 0.44/1.09 end
% 0.44/1.09 substitution1:
% 0.44/1.09 X := skol1
% 0.44/1.09 end
% 0.44/1.09
% 0.44/1.09 subsumption: (290) {G7,W0,D0,L0,V0,M0} R(280,27) { }.
% 0.44/1.09 parent0: (545) {G1,W0,D0,L0,V0,M0} { }.
% 0.44/1.09 substitution0:
% 0.44/1.09 end
% 0.44/1.09 permutation0:
% 0.44/1.09 end
% 0.44/1.09
% 0.44/1.09 Proof check complete!
% 0.44/1.09
% 0.44/1.09 Memory use:
% 0.44/1.09
% 0.44/1.09 space for terms: 3456
% 0.44/1.09 space for clauses: 23225
% 0.44/1.09
% 0.44/1.09
% 0.44/1.09 clauses generated: 1370
% 0.44/1.09 clauses kept: 291
% 0.44/1.09 clauses selected: 67
% 0.44/1.09 clauses deleted: 11
% 0.44/1.09 clauses inuse deleted: 0
% 0.44/1.09
% 0.44/1.09 subsentry: 2834
% 0.44/1.09 literals s-matched: 1483
% 0.44/1.09 literals matched: 1483
% 0.44/1.09 full subsumption: 127
% 0.44/1.09
% 0.44/1.09 checksum: 1892697275
% 0.44/1.09
% 0.44/1.09
% 0.44/1.09 Bliksem ended
%------------------------------------------------------------------------------