TSTP Solution File: KLE129+1 by Bliksem---1.12
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%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : KLE129+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n006.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 01:37:20 EDT 2022
% Result : Theorem 6.95s 7.37s
% Output : Refutation 6.95s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12 % Problem : KLE129+1 : TPTP v8.1.0. Released v4.0.0.
% 0.08/0.13 % Command : bliksem %s
% 0.12/0.34 % Computer : n006.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 09:39:41 EDT 2022
% 0.12/0.34 % CPUTime :
% 6.95/7.37 *** allocated 10000 integers for termspace/termends
% 6.95/7.37 *** allocated 10000 integers for clauses
% 6.95/7.37 *** allocated 10000 integers for justifications
% 6.95/7.37 Bliksem 1.12
% 6.95/7.37
% 6.95/7.37
% 6.95/7.37 Automatic Strategy Selection
% 6.95/7.37
% 6.95/7.37
% 6.95/7.37 Clauses:
% 6.95/7.37
% 6.95/7.37 { addition( X, Y ) = addition( Y, X ) }.
% 6.95/7.37 { addition( Z, addition( Y, X ) ) = addition( addition( Z, Y ), X ) }.
% 6.95/7.37 { addition( X, zero ) = X }.
% 6.95/7.37 { addition( X, X ) = X }.
% 6.95/7.37 { multiplication( X, multiplication( Y, Z ) ) = multiplication(
% 6.95/7.37 multiplication( X, Y ), Z ) }.
% 6.95/7.37 { multiplication( X, one ) = X }.
% 6.95/7.37 { multiplication( one, X ) = X }.
% 6.95/7.37 { multiplication( X, addition( Y, Z ) ) = addition( multiplication( X, Y )
% 6.95/7.37 , multiplication( X, Z ) ) }.
% 6.95/7.37 { multiplication( addition( X, Y ), Z ) = addition( multiplication( X, Z )
% 6.95/7.37 , multiplication( Y, Z ) ) }.
% 6.95/7.37 { multiplication( X, zero ) = zero }.
% 6.95/7.37 { multiplication( zero, X ) = zero }.
% 6.95/7.37 { ! leq( X, Y ), addition( X, Y ) = Y }.
% 6.95/7.37 { ! addition( X, Y ) = Y, leq( X, Y ) }.
% 6.95/7.37 { multiplication( antidomain( X ), X ) = zero }.
% 6.95/7.37 { addition( antidomain( multiplication( X, Y ) ), antidomain(
% 6.95/7.37 multiplication( X, antidomain( antidomain( Y ) ) ) ) ) = antidomain(
% 6.95/7.37 multiplication( X, antidomain( antidomain( Y ) ) ) ) }.
% 6.95/7.37 { addition( antidomain( antidomain( X ) ), antidomain( X ) ) = one }.
% 6.95/7.37 { domain( X ) = antidomain( antidomain( X ) ) }.
% 6.95/7.37 { multiplication( X, coantidomain( X ) ) = zero }.
% 6.95/7.37 { addition( coantidomain( multiplication( X, Y ) ), coantidomain(
% 6.95/7.37 multiplication( coantidomain( coantidomain( X ) ), Y ) ) ) = coantidomain
% 6.95/7.37 ( multiplication( coantidomain( coantidomain( X ) ), Y ) ) }.
% 6.95/7.37 { addition( coantidomain( coantidomain( X ) ), coantidomain( X ) ) = one }
% 6.95/7.37 .
% 6.95/7.37 { codomain( X ) = coantidomain( coantidomain( X ) ) }.
% 6.95/7.37 { c( X ) = antidomain( domain( X ) ) }.
% 6.95/7.37 { domain_difference( X, Y ) = multiplication( domain( X ), antidomain( Y )
% 6.95/7.37 ) }.
% 6.95/7.37 { forward_diamond( X, Y ) = domain( multiplication( X, domain( Y ) ) ) }.
% 6.95/7.37 { backward_diamond( X, Y ) = codomain( multiplication( codomain( Y ), X ) )
% 6.95/7.37 }.
% 6.95/7.37 { forward_box( X, Y ) = c( forward_diamond( X, c( Y ) ) ) }.
% 6.95/7.37 { backward_box( X, Y ) = c( backward_diamond( X, c( Y ) ) ) }.
% 6.95/7.37 { forward_diamond( X, divergence( X ) ) = divergence( X ) }.
% 6.95/7.37 { ! addition( domain( X ), addition( forward_diamond( Y, domain( X ) ),
% 6.95/7.37 domain( Z ) ) ) = addition( forward_diamond( Y, domain( X ) ), domain( Z
% 6.95/7.37 ) ), addition( domain( X ), addition( divergence( Y ), forward_diamond(
% 6.95/7.37 star( Y ), domain( Z ) ) ) ) = addition( divergence( Y ), forward_diamond
% 6.95/7.37 ( star( Y ), domain( Z ) ) ) }.
% 6.95/7.37 { ! addition( domain( X ), forward_diamond( skol1, domain( X ) ) ) =
% 6.95/7.37 forward_diamond( skol1, domain( X ) ), domain( X ) = zero }.
% 6.95/7.37 { ! divergence( skol1 ) = zero }.
% 6.95/7.37
% 6.95/7.37 percentage equality = 0.942857, percentage horn = 1.000000
% 6.95/7.37 This is a pure equality problem
% 6.95/7.37
% 6.95/7.37
% 6.95/7.37
% 6.95/7.37 Options Used:
% 6.95/7.37
% 6.95/7.37 useres = 1
% 6.95/7.37 useparamod = 1
% 6.95/7.37 useeqrefl = 1
% 6.95/7.37 useeqfact = 1
% 6.95/7.37 usefactor = 1
% 6.95/7.37 usesimpsplitting = 0
% 6.95/7.37 usesimpdemod = 5
% 6.95/7.37 usesimpres = 3
% 6.95/7.37
% 6.95/7.37 resimpinuse = 1000
% 6.95/7.37 resimpclauses = 20000
% 6.95/7.37 substype = eqrewr
% 6.95/7.37 backwardsubs = 1
% 6.95/7.37 selectoldest = 5
% 6.95/7.37
% 6.95/7.37 litorderings [0] = split
% 6.95/7.37 litorderings [1] = extend the termordering, first sorting on arguments
% 6.95/7.37
% 6.95/7.37 termordering = kbo
% 6.95/7.37
% 6.95/7.37 litapriori = 0
% 6.95/7.37 termapriori = 1
% 6.95/7.37 litaposteriori = 0
% 6.95/7.37 termaposteriori = 0
% 6.95/7.37 demodaposteriori = 0
% 6.95/7.37 ordereqreflfact = 0
% 6.95/7.37
% 6.95/7.37 litselect = negord
% 6.95/7.37
% 6.95/7.37 maxweight = 15
% 6.95/7.37 maxdepth = 30000
% 6.95/7.37 maxlength = 115
% 6.95/7.37 maxnrvars = 195
% 6.95/7.37 excuselevel = 1
% 6.95/7.37 increasemaxweight = 1
% 6.95/7.37
% 6.95/7.37 maxselected = 10000000
% 6.95/7.37 maxnrclauses = 10000000
% 6.95/7.37
% 6.95/7.37 showgenerated = 0
% 6.95/7.37 showkept = 0
% 6.95/7.37 showselected = 0
% 6.95/7.37 showdeleted = 0
% 6.95/7.37 showresimp = 1
% 6.95/7.37 showstatus = 2000
% 6.95/7.37
% 6.95/7.37 prologoutput = 0
% 6.95/7.37 nrgoals = 5000000
% 6.95/7.37 totalproof = 1
% 6.95/7.37
% 6.95/7.37 Symbols occurring in the translation:
% 6.95/7.37
% 6.95/7.37 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 6.95/7.37 . [1, 2] (w:1, o:27, a:1, s:1, b:0),
% 6.95/7.37 ! [4, 1] (w:0, o:15, a:1, s:1, b:0),
% 6.95/7.37 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 6.95/7.37 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 6.95/7.37 addition [37, 2] (w:1, o:51, a:1, s:1, b:0),
% 6.95/7.37 zero [39, 0] (w:1, o:9, a:1, s:1, b:0),
% 6.95/7.37 multiplication [40, 2] (w:1, o:53, a:1, s:1, b:0),
% 6.95/7.37 one [41, 0] (w:1, o:10, a:1, s:1, b:0),
% 6.95/7.37 leq [42, 2] (w:1, o:52, a:1, s:1, b:0),
% 6.95/7.37 antidomain [44, 1] (w:1, o:20, a:1, s:1, b:0),
% 6.95/7.37 domain [46, 1] (w:1, o:24, a:1, s:1, b:0),
% 6.95/7.37 coantidomain [47, 1] (w:1, o:21, a:1, s:1, b:0),
% 6.95/7.37 codomain [48, 1] (w:1, o:22, a:1, s:1, b:0),
% 6.95/7.37 c [49, 1] (w:1, o:23, a:1, s:1, b:0),
% 6.95/7.37 domain_difference [50, 2] (w:1, o:54, a:1, s:1, b:0),
% 6.95/7.37 forward_diamond [51, 2] (w:1, o:55, a:1, s:1, b:0),
% 6.95/7.37 backward_diamond [52, 2] (w:1, o:56, a:1, s:1, b:0),
% 6.95/7.37 forward_box [53, 2] (w:1, o:57, a:1, s:1, b:0),
% 6.95/7.37 backward_box [54, 2] (w:1, o:58, a:1, s:1, b:0),
% 6.95/7.37 divergence [55, 1] (w:1, o:25, a:1, s:1, b:0),
% 6.95/7.37 star [57, 1] (w:1, o:26, a:1, s:1, b:0),
% 6.95/7.37 skol1 [58, 0] (w:1, o:14, a:1, s:1, b:1).
% 6.95/7.37
% 6.95/7.37
% 6.95/7.37 Starting Search:
% 6.95/7.37
% 6.95/7.37 *** allocated 15000 integers for clauses
% 6.95/7.37 *** allocated 22500 integers for clauses
% 6.95/7.37 *** allocated 33750 integers for clauses
% 6.95/7.37 *** allocated 50625 integers for clauses
% 6.95/7.37 *** allocated 75937 integers for clauses
% 6.95/7.37 *** allocated 15000 integers for termspace/termends
% 6.95/7.37 *** allocated 113905 integers for clauses
% 6.95/7.37 Resimplifying inuse:
% 6.95/7.37 Done
% 6.95/7.37
% 6.95/7.37 *** allocated 22500 integers for termspace/termends
% 6.95/7.37 *** allocated 170857 integers for clauses
% 6.95/7.37 *** allocated 33750 integers for termspace/termends
% 6.95/7.37
% 6.95/7.37 Intermediate Status:
% 6.95/7.37 Generated: 15719
% 6.95/7.37 Kept: 2006
% 6.95/7.37 Inuse: 311
% 6.95/7.37 Deleted: 90
% 6.95/7.37 Deletedinuse: 52
% 6.95/7.37
% 6.95/7.37 Resimplifying inuse:
% 6.95/7.37 Done
% 6.95/7.37
% 6.95/7.37 *** allocated 256285 integers for clauses
% 6.95/7.37 *** allocated 50625 integers for termspace/termends
% 6.95/7.37 Resimplifying inuse:
% 6.95/7.37 Done
% 6.95/7.37
% 6.95/7.37
% 6.95/7.37 Intermediate Status:
% 6.95/7.37 Generated: 39533
% 6.95/7.37 Kept: 4054
% 6.95/7.37 Inuse: 483
% 6.95/7.37 Deleted: 140
% 6.95/7.37 Deletedinuse: 67
% 6.95/7.37
% 6.95/7.37 Resimplifying inuse:
% 6.95/7.37 Done
% 6.95/7.37
% 6.95/7.37 *** allocated 75937 integers for termspace/termends
% 6.95/7.37 *** allocated 384427 integers for clauses
% 6.95/7.37 Resimplifying inuse:
% 6.95/7.37 Done
% 6.95/7.37
% 6.95/7.37
% 6.95/7.37 Intermediate Status:
% 6.95/7.37 Generated: 59209
% 6.95/7.37 Kept: 6057
% 6.95/7.37 Inuse: 632
% 6.95/7.37 Deleted: 153
% 6.95/7.37 Deletedinuse: 67
% 6.95/7.37
% 6.95/7.37 Resimplifying inuse:
% 6.95/7.37 Done
% 6.95/7.37
% 6.95/7.37 *** allocated 113905 integers for termspace/termends
% 6.95/7.37 *** allocated 576640 integers for clauses
% 6.95/7.37 Resimplifying inuse:
% 6.95/7.37 Done
% 6.95/7.37
% 6.95/7.37
% 6.95/7.37 Intermediate Status:
% 6.95/7.37 Generated: 85794
% 6.95/7.37 Kept: 8233
% 6.95/7.37 Inuse: 771
% 6.95/7.37 Deleted: 174
% 6.95/7.37 Deletedinuse: 68
% 6.95/7.37
% 6.95/7.37 Resimplifying inuse:
% 6.95/7.37 Done
% 6.95/7.37
% 6.95/7.37 *** allocated 170857 integers for termspace/termends
% 6.95/7.37 Resimplifying inuse:
% 6.95/7.37 Done
% 6.95/7.37
% 6.95/7.37
% 6.95/7.37 Intermediate Status:
% 6.95/7.37 Generated: 111911
% 6.95/7.37 Kept: 10242
% 6.95/7.37 Inuse: 848
% 6.95/7.37 Deleted: 199
% 6.95/7.37 Deletedinuse: 70
% 6.95/7.37
% 6.95/7.37 Resimplifying inuse:
% 6.95/7.37 Done
% 6.95/7.37
% 6.95/7.37 Resimplifying inuse:
% 6.95/7.37 Done
% 6.95/7.37
% 6.95/7.37 *** allocated 864960 integers for clauses
% 6.95/7.37
% 6.95/7.37 Intermediate Status:
% 6.95/7.37 Generated: 143157
% 6.95/7.37 Kept: 12242
% 6.95/7.37 Inuse: 958
% 6.95/7.37 Deleted: 227
% 6.95/7.37 Deletedinuse: 70
% 6.95/7.37
% 6.95/7.37 Resimplifying inuse:
% 6.95/7.37 Done
% 6.95/7.37
% 6.95/7.37 Resimplifying inuse:
% 6.95/7.37 Done
% 6.95/7.37
% 6.95/7.37 *** allocated 256285 integers for termspace/termends
% 6.95/7.37
% 6.95/7.37 Intermediate Status:
% 6.95/7.37 Generated: 181516
% 6.95/7.37 Kept: 14267
% 6.95/7.37 Inuse: 1143
% 6.95/7.37 Deleted: 307
% 6.95/7.37 Deletedinuse: 76
% 6.95/7.37
% 6.95/7.37 Resimplifying inuse:
% 6.95/7.37 Done
% 6.95/7.37
% 6.95/7.37 Resimplifying inuse:
% 6.95/7.37 Done
% 6.95/7.37
% 6.95/7.37
% 6.95/7.37 Intermediate Status:
% 6.95/7.37 Generated: 201746
% 6.95/7.37 Kept: 16270
% 6.95/7.37 Inuse: 1215
% 6.95/7.37 Deleted: 318
% 6.95/7.37 Deletedinuse: 78
% 6.95/7.37
% 6.95/7.37 Resimplifying inuse:
% 6.95/7.37 Done
% 6.95/7.37
% 6.95/7.37 Resimplifying inuse:
% 6.95/7.37 Done
% 6.95/7.37
% 6.95/7.37 *** allocated 1297440 integers for clauses
% 6.95/7.37
% 6.95/7.37 Intermediate Status:
% 6.95/7.37 Generated: 217705
% 6.95/7.37 Kept: 18270
% 6.95/7.37 Inuse: 1286
% 6.95/7.37 Deleted: 330
% 6.95/7.37 Deletedinuse: 78
% 6.95/7.37
% 6.95/7.37 Resimplifying inuse:
% 6.95/7.37 Done
% 6.95/7.37
% 6.95/7.37 Resimplifying inuse:
% 6.95/7.37 Done
% 6.95/7.37
% 6.95/7.37 *** allocated 384427 integers for termspace/termends
% 6.95/7.37 Resimplifying clauses:
% 6.95/7.37 Done
% 6.95/7.37
% 6.95/7.37
% 6.95/7.37 Intermediate Status:
% 6.95/7.37 Generated: 245681
% 6.95/7.37 Kept: 20367
% 6.95/7.37 Inuse: 1387
% 6.95/7.37 Deleted: 2969
% 6.95/7.37 Deletedinuse: 78
% 6.95/7.37
% 6.95/7.37 Resimplifying inuse:
% 6.95/7.37 Done
% 6.95/7.37
% 6.95/7.37 Resimplifying inuse:
% 6.95/7.37 Done
% 6.95/7.37
% 6.95/7.37
% 6.95/7.37 Intermediate Status:
% 6.95/7.37 Generated: 291430
% 6.95/7.37 Kept: 22370
% 6.95/7.37 Inuse: 1525
% 6.95/7.37 Deleted: 2973
% 6.95/7.37 Deletedinuse: 82
% 6.95/7.37
% 6.95/7.37 Resimplifying inuse:
% 6.95/7.37 Done
% 6.95/7.37
% 6.95/7.37 Resimplifying inuse:
% 6.95/7.37 Done
% 6.95/7.37
% 6.95/7.37
% 6.95/7.37 Intermediate Status:
% 6.95/7.37 Generated: 324981
% 6.95/7.37 Kept: 24377
% 6.95/7.37 Inuse: 1631
% 6.95/7.37 Deleted: 2976
% 6.95/7.37 Deletedinuse: 82
% 6.95/7.37
% 6.95/7.37 Resimplifying inuse:
% 6.95/7.37 Done
% 6.95/7.37
% 6.95/7.37
% 6.95/7.37 Bliksems!, er is een bewijs:
% 6.95/7.37 % SZS status Theorem
% 6.95/7.37 % SZS output start Refutation
% 6.95/7.37
% 6.95/7.37 (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X ) }.
% 6.95/7.37 (1) {G0,W11,D4,L1,V3,M1} I { addition( Z, addition( Y, X ) ) ==> addition(
% 6.95/7.37 addition( Z, Y ), X ) }.
% 6.95/7.37 (2) {G0,W5,D3,L1,V1,M1} I { addition( X, zero ) ==> X }.
% 6.95/7.37 (3) {G0,W5,D3,L1,V1,M1} I { addition( X, X ) ==> X }.
% 6.95/7.37 (5) {G0,W5,D3,L1,V1,M1} I { multiplication( X, one ) ==> X }.
% 6.95/7.37 (6) {G0,W5,D3,L1,V1,M1} I { multiplication( one, X ) ==> X }.
% 6.95/7.37 (7) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Y ),
% 6.95/7.37 multiplication( X, Z ) ) ==> multiplication( X, addition( Y, Z ) ) }.
% 6.95/7.37 (8) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Z ),
% 6.95/7.37 multiplication( Y, Z ) ) ==> multiplication( addition( X, Y ), Z ) }.
% 6.95/7.37 (9) {G0,W5,D3,L1,V1,M1} I { multiplication( X, zero ) ==> zero }.
% 6.95/7.37 (10) {G0,W5,D3,L1,V1,M1} I { multiplication( zero, X ) ==> zero }.
% 6.95/7.37 (11) {G0,W8,D3,L2,V2,M2} I { ! leq( X, Y ), addition( X, Y ) ==> Y }.
% 6.95/7.37 (12) {G0,W8,D3,L2,V2,M2} I { ! addition( X, Y ) ==> Y, leq( X, Y ) }.
% 6.95/7.37 (13) {G0,W6,D4,L1,V1,M1} I { multiplication( antidomain( X ), X ) ==> zero
% 6.95/7.37 }.
% 6.95/7.37 (15) {G0,W8,D5,L1,V1,M1} I { addition( antidomain( antidomain( X ) ),
% 6.95/7.37 antidomain( X ) ) ==> one }.
% 6.95/7.37 (16) {G0,W6,D4,L1,V1,M1} I { antidomain( antidomain( X ) ) ==> domain( X )
% 6.95/7.37 }.
% 6.95/7.37 (17) {G0,W6,D4,L1,V1,M1} I { multiplication( X, coantidomain( X ) ) ==>
% 6.95/7.37 zero }.
% 6.95/7.37 (19) {G0,W8,D5,L1,V1,M1} I { addition( coantidomain( coantidomain( X ) ),
% 6.95/7.37 coantidomain( X ) ) ==> one }.
% 6.95/7.37 (20) {G0,W6,D4,L1,V1,M1} I { coantidomain( coantidomain( X ) ) ==> codomain
% 6.95/7.37 ( X ) }.
% 6.95/7.37 (21) {G0,W6,D4,L1,V1,M1} I { antidomain( domain( X ) ) ==> c( X ) }.
% 6.95/7.37 (22) {G0,W9,D4,L1,V2,M1} I { multiplication( domain( X ), antidomain( Y ) )
% 6.95/7.37 ==> domain_difference( X, Y ) }.
% 6.95/7.37 (23) {G0,W9,D5,L1,V2,M1} I { domain( multiplication( X, domain( Y ) ) ) ==>
% 6.95/7.37 forward_diamond( X, Y ) }.
% 6.95/7.37 (27) {G0,W7,D4,L1,V1,M1} I { forward_diamond( X, divergence( X ) ) ==>
% 6.95/7.37 divergence( X ) }.
% 6.95/7.37 (29) {G0,W16,D5,L2,V1,M2} I { ! addition( domain( X ), forward_diamond(
% 6.95/7.37 skol1, domain( X ) ) ) ==> forward_diamond( skol1, domain( X ) ), domain
% 6.95/7.37 ( X ) ==> zero }.
% 6.95/7.37 (30) {G0,W4,D3,L1,V0,M1} I { ! divergence( skol1 ) ==> zero }.
% 6.95/7.37 (31) {G1,W5,D3,L1,V1,M1} P(2,0) { addition( zero, X ) ==> X }.
% 6.95/7.37 (33) {G1,W9,D4,L1,V2,M1} P(3,1) { addition( addition( Y, X ), X ) ==>
% 6.95/7.37 addition( Y, X ) }.
% 6.95/7.37 (36) {G1,W7,D4,L1,V1,M1} P(20,20) { codomain( coantidomain( X ) ) ==>
% 6.95/7.37 coantidomain( codomain( X ) ) }.
% 6.95/7.37 (38) {G1,W4,D3,L1,V0,M1} P(17,6) { coantidomain( one ) ==> zero }.
% 6.95/7.37 (39) {G2,W5,D3,L1,V0,M1} P(38,20) { codomain( one ) ==> coantidomain( zero
% 6.95/7.37 ) }.
% 6.95/7.37 (41) {G1,W6,D4,L1,V1,M1} P(16,16);d(21) { domain( antidomain( X ) ) ==> c(
% 6.95/7.37 X ) }.
% 6.95/7.37 (42) {G1,W7,D4,L1,V1,M1} P(21,16) { domain( domain( X ) ) ==> antidomain( c
% 6.95/7.37 ( X ) ) }.
% 6.95/7.37 (52) {G2,W11,D4,L1,V2,M1} P(13,7);d(31) { multiplication( antidomain( X ),
% 6.95/7.37 addition( X, Y ) ) ==> multiplication( antidomain( X ), Y ) }.
% 6.95/7.37 (56) {G2,W10,D5,L1,V2,M1} P(17,7);d(31) { multiplication( X, addition(
% 6.95/7.37 coantidomain( X ), Y ) ) ==> multiplication( X, Y ) }.
% 6.95/7.37 (65) {G1,W10,D5,L1,V2,M1} P(13,8);d(2) { multiplication( addition( Y,
% 6.95/7.37 antidomain( X ) ), X ) ==> multiplication( Y, X ) }.
% 6.95/7.37 (66) {G2,W11,D4,L1,V2,M1} P(17,8);d(31) { multiplication( addition( X, Y )
% 6.95/7.37 , coantidomain( X ) ) ==> multiplication( Y, coantidomain( X ) ) }.
% 6.95/7.37 (86) {G1,W6,D2,L2,V1,M2} P(11,2) { zero = X, ! leq( X, zero ) }.
% 6.95/7.37 (87) {G1,W8,D3,L2,V2,M2} P(11,0) { addition( Y, X ) ==> Y, ! leq( X, Y )
% 6.95/7.37 }.
% 6.95/7.37 (115) {G2,W4,D3,L1,V0,M1} P(86,30);q { ! leq( divergence( skol1 ), zero )
% 6.95/7.37 }.
% 6.95/7.37 (136) {G2,W6,D2,L2,V1,M2} R(12,86);d(2) { zero = X, ! X = zero }.
% 6.95/7.37 (138) {G1,W3,D2,L1,V1,M1} R(12,3) { leq( X, X ) }.
% 6.95/7.37 (141) {G1,W16,D4,L2,V3,M2} P(7,12) { ! multiplication( X, addition( Y, Z )
% 6.95/7.37 ) ==> multiplication( X, Z ), leq( multiplication( X, Y ),
% 6.95/7.37 multiplication( X, Z ) ) }.
% 6.95/7.37 (183) {G1,W7,D4,L1,V1,M1} S(15);d(16) { addition( domain( X ), antidomain(
% 6.95/7.37 X ) ) ==> one }.
% 6.95/7.37 (207) {G1,W7,D4,L1,V1,M1} S(19);d(20) { addition( codomain( X ),
% 6.95/7.37 coantidomain( X ) ) ==> one }.
% 6.95/7.37 (233) {G2,W10,D4,L1,V2,M1} P(41,22) { multiplication( c( X ), antidomain( Y
% 6.95/7.37 ) ) ==> domain_difference( antidomain( X ), Y ) }.
% 6.95/7.37 (349) {G3,W4,D3,L1,V0,M1} P(39,207);d(38);d(2) { coantidomain( zero ) ==>
% 6.95/7.37 one }.
% 6.95/7.37 (352) {G2,W7,D4,L1,V1,M1} P(207,0) { addition( coantidomain( X ), codomain
% 6.95/7.37 ( X ) ) ==> one }.
% 6.95/7.37 (360) {G4,W4,D3,L1,V0,M1} P(349,20);d(38) { codomain( zero ) ==> zero }.
% 6.95/7.37 (483) {G2,W6,D4,L1,V1,M1} P(183,33) { addition( one, antidomain( X ) ) ==>
% 6.95/7.37 one }.
% 6.95/7.37 (551) {G3,W6,D4,L1,V1,M1} P(16,483) { addition( one, domain( X ) ) ==> one
% 6.95/7.37 }.
% 6.95/7.37 (560) {G4,W6,D4,L1,V1,M1} P(551,0) { addition( domain( X ), one ) ==> one
% 6.95/7.37 }.
% 6.95/7.37 (561) {G5,W4,D3,L1,V1,M1} R(560,12) { leq( domain( X ), one ) }.
% 6.95/7.37 (572) {G6,W5,D3,L1,V2,M1} P(23,561) { leq( forward_diamond( X, Y ), one )
% 6.95/7.37 }.
% 6.95/7.37 (581) {G3,W7,D4,L1,V1,M1} P(183,52);d(5);d(21);d(233) { domain_difference(
% 6.95/7.37 antidomain( X ), X ) ==> c( X ) }.
% 6.95/7.37 (590) {G7,W4,D3,L1,V1,M1} P(27,572) { leq( divergence( X ), one ) }.
% 6.95/7.37 (591) {G8,W6,D4,L1,V1,M1} R(590,11) { addition( divergence( X ), one ) ==>
% 6.95/7.37 one }.
% 6.95/7.37 (646) {G3,W6,D4,L1,V1,M1} P(352,56);d(5) { multiplication( X, codomain( X )
% 6.95/7.37 ) ==> X }.
% 6.95/7.37 (657) {G4,W9,D5,L1,V1,M1} P(36,646) { multiplication( coantidomain( X ),
% 6.95/7.37 coantidomain( codomain( X ) ) ) ==> coantidomain( X ) }.
% 6.95/7.37 (660) {G4,W7,D3,L2,V1,M2} P(136,646);d(9) { ! codomain( X ) ==> zero, zero
% 6.95/7.37 = X }.
% 6.95/7.37 (737) {G5,W5,D4,L1,V0,M1} P(660,115);r(138) { ! codomain( divergence( skol1
% 6.95/7.37 ) ) ==> zero }.
% 6.95/7.37 (780) {G6,W6,D5,L1,V0,M1} P(660,737);q { ! codomain( codomain( divergence(
% 6.95/7.37 skol1 ) ) ) ==> zero }.
% 6.95/7.37 (786) {G7,W6,D5,L1,V0,M1} P(86,780);q { ! leq( codomain( codomain(
% 6.95/7.37 divergence( skol1 ) ) ), zero ) }.
% 6.95/7.37 (970) {G2,W6,D4,L1,V1,M1} P(183,65);d(6) { multiplication( domain( X ), X )
% 6.95/7.37 ==> X }.
% 6.95/7.37 (985) {G4,W5,D3,L1,V1,M1} P(970,22);d(581) { c( X ) ==> antidomain( X ) }.
% 6.95/7.37 (986) {G3,W7,D3,L2,V1,M2} P(136,970);d(10) { ! domain( X ) ==> zero, zero =
% 6.95/7.37 X }.
% 6.95/7.37 (1007) {G5,W6,D4,L1,V1,M1} S(42);d(985);d(16) { domain( domain( X ) ) ==>
% 6.95/7.37 domain( X ) }.
% 6.95/7.37 (1023) {G5,W6,D4,L1,V1,M1} P(207,66);d(6);d(657) { coantidomain( codomain(
% 6.95/7.37 X ) ) ==> coantidomain( X ) }.
% 6.95/7.37 (1053) {G6,W6,D4,L1,V1,M1} P(36,1023);d(20);d(20) { codomain( codomain( X )
% 6.95/7.37 ) ==> codomain( X ) }.
% 6.95/7.37 (1071) {G6,W8,D4,L1,V2,M1} P(1007,23);d(23) { forward_diamond( Y, domain( X
% 6.95/7.37 ) ) ==> forward_diamond( Y, X ) }.
% 6.95/7.37 (1072) {G6,W8,D4,L1,V2,M1} P(23,1007) { domain( forward_diamond( X, Y ) )
% 6.95/7.37 ==> forward_diamond( X, Y ) }.
% 6.95/7.37 (1223) {G8,W5,D4,L1,V0,M1} P(986,786);d(1053);d(360);r(138) { ! domain(
% 6.95/7.37 divergence( skol1 ) ) ==> zero }.
% 6.95/7.37 (1312) {G9,W9,D5,L1,V0,M1} R(1223,29);d(1071);d(27) { ! addition( domain(
% 6.95/7.37 divergence( skol1 ) ), divergence( skol1 ) ) ==> divergence( skol1 ) }.
% 6.95/7.37 (3141) {G9,W6,D4,L1,V2,M1} P(591,141);q;d(5) { leq( multiplication( Y,
% 6.95/7.37 divergence( X ) ), Y ) }.
% 6.95/7.37 (3179) {G10,W6,D4,L1,V1,M1} P(970,3141) { leq( divergence( X ), domain(
% 6.95/7.37 divergence( X ) ) ) }.
% 6.95/7.37 (3405) {G11,W10,D5,L1,V1,M1} R(3179,87) { addition( domain( divergence( X )
% 6.95/7.37 ), divergence( X ) ) ==> domain( divergence( X ) ) }.
% 6.95/7.37 (20082) {G12,W6,D4,L1,V0,M1} S(1312);d(3405) { ! domain( divergence( skol1
% 6.95/7.37 ) ) ==> divergence( skol1 ) }.
% 6.95/7.37 (24874) {G7,W6,D4,L1,V1,M1} P(27,1072) { domain( divergence( X ) ) ==>
% 6.95/7.37 divergence( X ) }.
% 6.95/7.37 (24876) {G13,W0,D0,L0,V0,M0} R(24874,20082) { }.
% 6.95/7.37
% 6.95/7.37
% 6.95/7.37 % SZS output end Refutation
% 6.95/7.37 found a proof!
% 6.95/7.37
% 6.95/7.37
% 6.95/7.37 Unprocessed initial clauses:
% 6.95/7.37
% 6.95/7.37 (24878) {G0,W7,D3,L1,V2,M1} { addition( X, Y ) = addition( Y, X ) }.
% 6.95/7.37 (24879) {G0,W11,D4,L1,V3,M1} { addition( Z, addition( Y, X ) ) = addition
% 6.95/7.37 ( addition( Z, Y ), X ) }.
% 6.95/7.37 (24880) {G0,W5,D3,L1,V1,M1} { addition( X, zero ) = X }.
% 6.95/7.37 (24881) {G0,W5,D3,L1,V1,M1} { addition( X, X ) = X }.
% 6.95/7.37 (24882) {G0,W11,D4,L1,V3,M1} { multiplication( X, multiplication( Y, Z ) )
% 6.95/7.37 = multiplication( multiplication( X, Y ), Z ) }.
% 6.95/7.37 (24883) {G0,W5,D3,L1,V1,M1} { multiplication( X, one ) = X }.
% 6.95/7.37 (24884) {G0,W5,D3,L1,V1,M1} { multiplication( one, X ) = X }.
% 6.95/7.37 (24885) {G0,W13,D4,L1,V3,M1} { multiplication( X, addition( Y, Z ) ) =
% 6.95/7.37 addition( multiplication( X, Y ), multiplication( X, Z ) ) }.
% 6.95/7.37 (24886) {G0,W13,D4,L1,V3,M1} { multiplication( addition( X, Y ), Z ) =
% 6.95/7.37 addition( multiplication( X, Z ), multiplication( Y, Z ) ) }.
% 6.95/7.37 (24887) {G0,W5,D3,L1,V1,M1} { multiplication( X, zero ) = zero }.
% 6.95/7.37 (24888) {G0,W5,D3,L1,V1,M1} { multiplication( zero, X ) = zero }.
% 6.95/7.37 (24889) {G0,W8,D3,L2,V2,M2} { ! leq( X, Y ), addition( X, Y ) = Y }.
% 6.95/7.37 (24890) {G0,W8,D3,L2,V2,M2} { ! addition( X, Y ) = Y, leq( X, Y ) }.
% 6.95/7.37 (24891) {G0,W6,D4,L1,V1,M1} { multiplication( antidomain( X ), X ) = zero
% 6.95/7.37 }.
% 6.95/7.37 (24892) {G0,W18,D7,L1,V2,M1} { addition( antidomain( multiplication( X, Y
% 6.95/7.37 ) ), antidomain( multiplication( X, antidomain( antidomain( Y ) ) ) ) )
% 6.95/7.37 = antidomain( multiplication( X, antidomain( antidomain( Y ) ) ) ) }.
% 6.95/7.37 (24893) {G0,W8,D5,L1,V1,M1} { addition( antidomain( antidomain( X ) ),
% 6.95/7.37 antidomain( X ) ) = one }.
% 6.95/7.37 (24894) {G0,W6,D4,L1,V1,M1} { domain( X ) = antidomain( antidomain( X ) )
% 6.95/7.37 }.
% 6.95/7.37 (24895) {G0,W6,D4,L1,V1,M1} { multiplication( X, coantidomain( X ) ) =
% 6.95/7.37 zero }.
% 6.95/7.37 (24896) {G0,W18,D7,L1,V2,M1} { addition( coantidomain( multiplication( X,
% 6.95/7.37 Y ) ), coantidomain( multiplication( coantidomain( coantidomain( X ) ), Y
% 6.95/7.37 ) ) ) = coantidomain( multiplication( coantidomain( coantidomain( X ) )
% 6.95/7.37 , Y ) ) }.
% 6.95/7.37 (24897) {G0,W8,D5,L1,V1,M1} { addition( coantidomain( coantidomain( X ) )
% 6.95/7.37 , coantidomain( X ) ) = one }.
% 6.95/7.37 (24898) {G0,W6,D4,L1,V1,M1} { codomain( X ) = coantidomain( coantidomain(
% 6.95/7.37 X ) ) }.
% 6.95/7.37 (24899) {G0,W6,D4,L1,V1,M1} { c( X ) = antidomain( domain( X ) ) }.
% 6.95/7.37 (24900) {G0,W9,D4,L1,V2,M1} { domain_difference( X, Y ) = multiplication(
% 6.95/7.37 domain( X ), antidomain( Y ) ) }.
% 6.95/7.37 (24901) {G0,W9,D5,L1,V2,M1} { forward_diamond( X, Y ) = domain(
% 6.95/7.37 multiplication( X, domain( Y ) ) ) }.
% 6.95/7.37 (24902) {G0,W9,D5,L1,V2,M1} { backward_diamond( X, Y ) = codomain(
% 6.95/7.37 multiplication( codomain( Y ), X ) ) }.
% 6.95/7.37 (24903) {G0,W9,D5,L1,V2,M1} { forward_box( X, Y ) = c( forward_diamond( X
% 6.95/7.37 , c( Y ) ) ) }.
% 6.95/7.37 (24904) {G0,W9,D5,L1,V2,M1} { backward_box( X, Y ) = c( backward_diamond(
% 6.95/7.37 X, c( Y ) ) ) }.
% 6.95/7.37 (24905) {G0,W7,D4,L1,V1,M1} { forward_diamond( X, divergence( X ) ) =
% 6.95/7.37 divergence( X ) }.
% 6.95/7.37 (24906) {G0,W38,D6,L2,V3,M2} { ! addition( domain( X ), addition(
% 6.95/7.37 forward_diamond( Y, domain( X ) ), domain( Z ) ) ) = addition(
% 6.95/7.37 forward_diamond( Y, domain( X ) ), domain( Z ) ), addition( domain( X ),
% 6.95/7.37 addition( divergence( Y ), forward_diamond( star( Y ), domain( Z ) ) ) )
% 6.95/7.37 = addition( divergence( Y ), forward_diamond( star( Y ), domain( Z ) ) )
% 6.95/7.37 }.
% 6.95/7.37 (24907) {G0,W16,D5,L2,V1,M2} { ! addition( domain( X ), forward_diamond(
% 6.95/7.37 skol1, domain( X ) ) ) = forward_diamond( skol1, domain( X ) ), domain( X
% 6.95/7.37 ) = zero }.
% 6.95/7.37 (24908) {G0,W4,D3,L1,V0,M1} { ! divergence( skol1 ) = zero }.
% 6.95/7.37
% 6.95/7.37
% 6.95/7.37 Total Proof:
% 6.95/7.37
% 6.95/7.37 subsumption: (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X
% 6.95/7.37 ) }.
% 6.95/7.37 parent0: (24878) {G0,W7,D3,L1,V2,M1} { addition( X, Y ) = addition( Y, X )
% 6.95/7.37 }.
% 6.95/7.37 substitution0:
% 6.95/7.37 X := X
% 6.95/7.37 Y := Y
% 6.95/7.37 end
% 6.95/7.37 permutation0:
% 6.95/7.37 0 ==> 0
% 6.95/7.37 end
% 6.95/7.37
% 6.95/7.37 subsumption: (1) {G0,W11,D4,L1,V3,M1} I { addition( Z, addition( Y, X ) )
% 6.95/7.37 ==> addition( addition( Z, Y ), X ) }.
% 6.95/7.37 parent0: (24879) {G0,W11,D4,L1,V3,M1} { addition( Z, addition( Y, X ) ) =
% 6.95/7.37 addition( addition( Z, Y ), X ) }.
% 6.95/7.37 substitution0:
% 6.95/7.37 X := X
% 6.95/7.37 Y := Y
% 6.95/7.37 Z := Z
% 6.95/7.37 end
% 6.95/7.37 permutation0:
% 6.95/7.37 0 ==> 0
% 6.95/7.37 end
% 6.95/7.37
% 6.95/7.37 subsumption: (2) {G0,W5,D3,L1,V1,M1} I { addition( X, zero ) ==> X }.
% 6.95/7.37 parent0: (24880) {G0,W5,D3,L1,V1,M1} { addition( X, zero ) = X }.
% 6.95/7.37 substitution0:
% 6.95/7.37 X := X
% 6.95/7.37 end
% 6.95/7.37 permutation0:
% 6.95/7.37 0 ==> 0
% 6.95/7.37 end
% 6.95/7.37
% 6.95/7.37 subsumption: (3) {G0,W5,D3,L1,V1,M1} I { addition( X, X ) ==> X }.
% 6.95/7.37 parent0: (24881) {G0,W5,D3,L1,V1,M1} { addition( X, X ) = X }.
% 6.95/7.37 substitution0:
% 6.95/7.37 X := X
% 6.95/7.37 end
% 6.95/7.37 permutation0:
% 6.95/7.37 0 ==> 0
% 6.95/7.37 end
% 6.95/7.37
% 6.95/7.37 subsumption: (5) {G0,W5,D3,L1,V1,M1} I { multiplication( X, one ) ==> X }.
% 6.95/7.37 parent0: (24883) {G0,W5,D3,L1,V1,M1} { multiplication( X, one ) = X }.
% 6.95/7.37 substitution0:
% 6.95/7.37 X := X
% 6.95/7.37 end
% 6.95/7.37 permutation0:
% 6.95/7.37 0 ==> 0
% 6.95/7.37 end
% 6.95/7.37
% 6.95/7.37 subsumption: (6) {G0,W5,D3,L1,V1,M1} I { multiplication( one, X ) ==> X }.
% 6.95/7.37 parent0: (24884) {G0,W5,D3,L1,V1,M1} { multiplication( one, X ) = X }.
% 6.95/7.37 substitution0:
% 6.95/7.37 X := X
% 6.95/7.37 end
% 6.95/7.37 permutation0:
% 6.95/7.37 0 ==> 0
% 6.95/7.37 end
% 6.95/7.37
% 6.95/7.37 eqswap: (24932) {G0,W13,D4,L1,V3,M1} { addition( multiplication( X, Y ),
% 6.95/7.37 multiplication( X, Z ) ) = multiplication( X, addition( Y, Z ) ) }.
% 6.95/7.37 parent0[0]: (24885) {G0,W13,D4,L1,V3,M1} { multiplication( X, addition( Y
% 6.95/7.37 , Z ) ) = addition( multiplication( X, Y ), multiplication( X, Z ) ) }.
% 6.95/7.37 substitution0:
% 6.95/7.37 X := X
% 6.95/7.37 Y := Y
% 6.95/7.37 Z := Z
% 6.95/7.37 end
% 6.95/7.37
% 6.95/7.37 subsumption: (7) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Y )
% 6.95/7.37 , multiplication( X, Z ) ) ==> multiplication( X, addition( Y, Z ) ) }.
% 6.95/7.37 parent0: (24932) {G0,W13,D4,L1,V3,M1} { addition( multiplication( X, Y ),
% 6.95/7.37 multiplication( X, Z ) ) = multiplication( X, addition( Y, Z ) ) }.
% 6.95/7.37 substitution0:
% 6.95/7.37 X := X
% 6.95/7.37 Y := Y
% 6.95/7.37 Z := Z
% 6.95/7.37 end
% 6.95/7.37 permutation0:
% 6.95/7.37 0 ==> 0
% 6.95/7.37 end
% 6.95/7.37
% 6.95/7.37 eqswap: (24940) {G0,W13,D4,L1,V3,M1} { addition( multiplication( X, Z ),
% 6.95/7.37 multiplication( Y, Z ) ) = multiplication( addition( X, Y ), Z ) }.
% 6.95/7.37 parent0[0]: (24886) {G0,W13,D4,L1,V3,M1} { multiplication( addition( X, Y
% 6.95/7.37 ), Z ) = addition( multiplication( X, Z ), multiplication( Y, Z ) ) }.
% 6.95/7.37 substitution0:
% 6.95/7.37 X := X
% 6.95/7.37 Y := Y
% 6.95/7.37 Z := Z
% 6.95/7.37 end
% 6.95/7.37
% 6.95/7.37 subsumption: (8) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Z )
% 6.95/7.37 , multiplication( Y, Z ) ) ==> multiplication( addition( X, Y ), Z ) }.
% 6.95/7.37 parent0: (24940) {G0,W13,D4,L1,V3,M1} { addition( multiplication( X, Z ),
% 6.95/7.37 multiplication( Y, Z ) ) = multiplication( addition( X, Y ), Z ) }.
% 6.95/7.37 substitution0:
% 6.95/7.37 X := X
% 6.95/7.37 Y := Y
% 6.95/7.37 Z := Z
% 6.95/7.37 end
% 6.95/7.37 permutation0:
% 6.95/7.37 0 ==> 0
% 6.95/7.37 end
% 6.95/7.37
% 6.95/7.37 subsumption: (9) {G0,W5,D3,L1,V1,M1} I { multiplication( X, zero ) ==> zero
% 6.95/7.37 }.
% 6.95/7.37 parent0: (24887) {G0,W5,D3,L1,V1,M1} { multiplication( X, zero ) = zero
% 6.95/7.37 }.
% 6.95/7.37 substitution0:
% 6.95/7.37 X := X
% 6.95/7.37 end
% 6.95/7.37 permutation0:
% 6.95/7.37 0 ==> 0
% 6.95/7.37 end
% 6.95/7.37
% 6.95/7.37 subsumption: (10) {G0,W5,D3,L1,V1,M1} I { multiplication( zero, X ) ==>
% 6.95/7.37 zero }.
% 6.95/7.37 parent0: (24888) {G0,W5,D3,L1,V1,M1} { multiplication( zero, X ) = zero
% 6.95/7.37 }.
% 6.95/7.37 substitution0:
% 6.95/7.37 X := X
% 6.95/7.37 end
% 6.95/7.37 permutation0:
% 6.95/7.37 0 ==> 0
% 6.95/7.37 end
% 6.95/7.37
% 6.95/7.37 subsumption: (11) {G0,W8,D3,L2,V2,M2} I { ! leq( X, Y ), addition( X, Y )
% 6.95/7.37 ==> Y }.
% 6.95/7.37 parent0: (24889) {G0,W8,D3,L2,V2,M2} { ! leq( X, Y ), addition( X, Y ) = Y
% 6.95/7.37 }.
% 6.95/7.37 substitution0:
% 6.95/7.37 X := X
% 6.95/7.37 Y := Y
% 6.95/7.37 end
% 6.95/7.37 permutation0:
% 6.95/7.37 0 ==> 0
% 6.95/7.37 1 ==> 1
% 6.95/7.37 end
% 6.95/7.37
% 6.95/7.37 subsumption: (12) {G0,W8,D3,L2,V2,M2} I { ! addition( X, Y ) ==> Y, leq( X
% 6.95/7.37 , Y ) }.
% 6.95/7.37 parent0: (24890) {G0,W8,D3,L2,V2,M2} { ! addition( X, Y ) = Y, leq( X, Y )
% 6.95/7.37 }.
% 6.95/7.37 substitution0:
% 6.95/7.37 X := X
% 6.95/7.37 Y := Y
% 6.95/7.37 end
% 6.95/7.37 permutation0:
% 6.95/7.37 0 ==> 0
% 6.95/7.37 1 ==> 1
% 6.95/7.37 end
% 6.95/7.37
% 6.95/7.37 subsumption: (13) {G0,W6,D4,L1,V1,M1} I { multiplication( antidomain( X ),
% 6.95/7.37 X ) ==> zero }.
% 6.95/7.37 parent0: (24891) {G0,W6,D4,L1,V1,M1} { multiplication( antidomain( X ), X
% 6.95/7.37 ) = zero }.
% 6.95/7.37 substitution0:
% 6.95/7.37 X := X
% 6.95/7.37 end
% 6.95/7.37 permutation0:
% 6.95/7.37 0 ==> 0
% 6.95/7.37 end
% 6.95/7.37
% 6.95/7.37 subsumption: (15) {G0,W8,D5,L1,V1,M1} I { addition( antidomain( antidomain
% 6.95/7.37 ( X ) ), antidomain( X ) ) ==> one }.
% 6.95/7.37 parent0: (24893) {G0,W8,D5,L1,V1,M1} { addition( antidomain( antidomain( X
% 6.95/7.37 ) ), antidomain( X ) ) = one }.
% 6.95/7.37 substitution0:
% 6.95/7.37 X := X
% 6.95/7.37 end
% 6.95/7.37 permutation0:
% 6.95/7.37 0 ==> 0
% 6.95/7.37 end
% 6.95/7.37
% 6.95/7.37 eqswap: (25026) {G0,W6,D4,L1,V1,M1} { antidomain( antidomain( X ) ) =
% 6.95/7.37 domain( X ) }.
% 6.95/7.37 parent0[0]: (24894) {G0,W6,D4,L1,V1,M1} { domain( X ) = antidomain(
% 6.95/7.37 antidomain( X ) ) }.
% 6.95/7.37 substitution0:
% 6.95/7.37 X := X
% 6.95/7.37 end
% 6.95/7.37
% 6.95/7.37 subsumption: (16) {G0,W6,D4,L1,V1,M1} I { antidomain( antidomain( X ) ) ==>
% 6.95/7.37 domain( X ) }.
% 6.95/7.37 parent0: (25026) {G0,W6,D4,L1,V1,M1} { antidomain( antidomain( X ) ) =
% 6.95/7.37 domain( X ) }.
% 6.95/7.37 substitution0:
% 6.95/7.37 X := X
% 6.95/7.37 end
% 6.95/7.37 permutation0:
% 6.95/7.37 0 ==> 0
% 6.95/7.37 end
% 6.95/7.37
% 6.95/7.37 subsumption: (17) {G0,W6,D4,L1,V1,M1} I { multiplication( X, coantidomain(
% 6.95/7.37 X ) ) ==> zero }.
% 6.95/7.37 parent0: (24895) {G0,W6,D4,L1,V1,M1} { multiplication( X, coantidomain( X
% 6.95/7.37 ) ) = zero }.
% 6.95/7.37 substitution0:
% 6.95/7.37 X := X
% 6.95/7.37 end
% 6.95/7.37 permutation0:
% 6.95/7.37 0 ==> 0
% 6.95/7.37 end
% 6.95/7.37
% 6.95/7.37 subsumption: (19) {G0,W8,D5,L1,V1,M1} I { addition( coantidomain(
% 6.95/7.37 coantidomain( X ) ), coantidomain( X ) ) ==> one }.
% 6.95/7.37 parent0: (24897) {G0,W8,D5,L1,V1,M1} { addition( coantidomain(
% 6.95/7.37 coantidomain( X ) ), coantidomain( X ) ) = one }.
% 6.95/7.37 substitution0:
% 6.95/7.37 X := X
% 6.95/7.37 end
% 6.95/7.37 permutation0:
% 6.95/7.37 0 ==> 0
% 6.95/7.37 end
% 6.95/7.37
% 6.95/7.37 eqswap: (25082) {G0,W6,D4,L1,V1,M1} { coantidomain( coantidomain( X ) ) =
% 6.95/7.37 codomain( X ) }.
% 6.95/7.37 parent0[0]: (24898) {G0,W6,D4,L1,V1,M1} { codomain( X ) = coantidomain(
% 6.95/7.37 coantidomain( X ) ) }.
% 6.95/7.37 substitution0:
% 6.95/7.37 X := X
% 6.95/7.37 end
% 6.95/7.37
% 6.95/7.37 subsumption: (20) {G0,W6,D4,L1,V1,M1} I { coantidomain( coantidomain( X ) )
% 6.95/7.37 ==> codomain( X ) }.
% 6.95/7.37 parent0: (25082) {G0,W6,D4,L1,V1,M1} { coantidomain( coantidomain( X ) ) =
% 6.95/7.37 codomain( X ) }.
% 6.95/7.37 substitution0:
% 6.95/7.37 X := X
% 6.95/7.37 end
% 6.95/7.37 permutation0:
% 6.95/7.37 0 ==> 0
% 6.95/7.37 end
% 6.95/7.37
% 6.95/7.37 eqswap: (25103) {G0,W6,D4,L1,V1,M1} { antidomain( domain( X ) ) = c( X )
% 6.95/7.37 }.
% 6.95/7.37 parent0[0]: (24899) {G0,W6,D4,L1,V1,M1} { c( X ) = antidomain( domain( X )
% 6.95/7.37 ) }.
% 6.95/7.37 substitution0:
% 6.95/7.37 X := X
% 6.95/7.37 end
% 6.95/7.37
% 6.95/7.37 subsumption: (21) {G0,W6,D4,L1,V1,M1} I { antidomain( domain( X ) ) ==> c(
% 6.95/7.37 X ) }.
% 6.95/7.37 parent0: (25103) {G0,W6,D4,L1,V1,M1} { antidomain( domain( X ) ) = c( X )
% 6.95/7.37 }.
% 6.95/7.37 substitution0:
% 6.95/7.37 X := X
% 6.95/7.37 end
% 6.95/7.37 permutation0:
% 6.95/7.37 0 ==> 0
% 6.95/7.37 end
% 6.95/7.37
% 6.95/7.37 eqswap: (25125) {G0,W9,D4,L1,V2,M1} { multiplication( domain( X ),
% 6.95/7.37 antidomain( Y ) ) = domain_difference( X, Y ) }.
% 6.95/7.37 parent0[0]: (24900) {G0,W9,D4,L1,V2,M1} { domain_difference( X, Y ) =
% 6.95/7.37 multiplication( domain( X ), antidomain( Y ) ) }.
% 6.95/7.37 substitution0:
% 6.95/7.37 X := X
% 6.95/7.37 Y := Y
% 6.95/7.37 end
% 6.95/7.37
% 6.95/7.37 subsumption: (22) {G0,W9,D4,L1,V2,M1} I { multiplication( domain( X ),
% 6.95/7.37 antidomain( Y ) ) ==> domain_difference( X, Y ) }.
% 6.95/7.37 parent0: (25125) {G0,W9,D4,L1,V2,M1} { multiplication( domain( X ),
% 6.95/7.37 antidomain( Y ) ) = domain_difference( X, Y ) }.
% 6.95/7.37 substitution0:
% 6.95/7.37 X := X
% 6.95/7.37 Y := Y
% 6.95/7.37 end
% 6.95/7.37 permutation0:
% 6.95/7.37 0 ==> 0
% 6.95/7.37 end
% 6.95/7.37
% 6.95/7.37 eqswap: (25148) {G0,W9,D5,L1,V2,M1} { domain( multiplication( X, domain( Y
% 6.95/7.37 ) ) ) = forward_diamond( X, Y ) }.
% 6.95/7.37 parent0[0]: (24901) {G0,W9,D5,L1,V2,M1} { forward_diamond( X, Y ) = domain
% 6.95/7.37 ( multiplication( X, domain( Y ) ) ) }.
% 6.95/7.37 substitution0:
% 6.95/7.37 X := X
% 6.95/7.37 Y := Y
% 6.95/7.37 end
% 6.95/7.37
% 6.95/7.37 subsumption: (23) {G0,W9,D5,L1,V2,M1} I { domain( multiplication( X, domain
% 6.95/7.37 ( Y ) ) ) ==> forward_diamond( X, Y ) }.
% 6.95/7.37 parent0: (25148) {G0,W9,D5,L1,V2,M1} { domain( multiplication( X, domain(
% 6.95/7.37 Y ) ) ) = forward_diamond( X, Y ) }.
% 6.95/7.37 substitution0:
% 6.95/7.37 X := X
% 6.95/7.37 Y := Y
% 6.95/7.37 end
% 6.95/7.37 permutation0:
% 6.95/7.37 0 ==> 0
% 6.95/7.37 end
% 6.95/7.37
% 6.95/7.37 subsumption: (27) {G0,W7,D4,L1,V1,M1} I { forward_diamond( X, divergence( X
% 6.95/7.37 ) ) ==> divergence( X ) }.
% 6.95/7.37 parent0: (24905) {G0,W7,D4,L1,V1,M1} { forward_diamond( X, divergence( X )
% 6.95/7.37 ) = divergence( X ) }.
% 6.95/7.37 substitution0:
% 6.95/7.37 X := X
% 6.95/7.37 end
% 6.95/7.37 permutation0:
% 6.95/7.37 0 ==> 0
% 6.95/7.37 end
% 6.95/7.37
% 6.95/7.37 subsumption: (29) {G0,W16,D5,L2,V1,M2} I { ! addition( domain( X ),
% 6.95/7.37 forward_diamond( skol1, domain( X ) ) ) ==> forward_diamond( skol1,
% 6.95/7.37 domain( X ) ), domain( X ) ==> zero }.
% 6.95/7.37 parent0: (24907) {G0,W16,D5,L2,V1,M2} { ! addition( domain( X ),
% 6.95/7.37 forward_diamond( skol1, domain( X ) ) ) = forward_diamond( skol1, domain
% 6.95/7.37 ( X ) ), domain( X ) = zero }.
% 6.95/7.37 substitution0:
% 6.95/7.37 X := X
% 6.95/7.37 end
% 6.95/7.37 permutation0:
% 6.95/7.37 0 ==> 0
% 6.95/7.37 1 ==> 1
% 6.95/7.37 end
% 6.95/7.37
% 6.95/7.37 subsumption: (30) {G0,W4,D3,L1,V0,M1} I { ! divergence( skol1 ) ==> zero
% 6.95/7.37 }.
% 6.95/7.37 parent0: (24908) {G0,W4,D3,L1,V0,M1} { ! divergence( skol1 ) = zero }.
% 6.95/7.37 substitution0:
% 6.95/7.37 end
% 6.95/7.37 permutation0:
% 6.95/7.37 0 ==> 0
% 6.95/7.37 end
% 6.95/7.37
% 6.95/7.37 eqswap: (25243) {G0,W5,D3,L1,V1,M1} { X ==> addition( X, zero ) }.
% 6.95/7.37 parent0[0]: (2) {G0,W5,D3,L1,V1,M1} I { addition( X, zero ) ==> X }.
% 6.95/7.37 substitution0:
% 6.95/7.37 X := X
% 6.95/7.37 end
% 6.95/7.37
% 6.95/7.37 paramod: (25244) {G1,W5,D3,L1,V1,M1} { X ==> addition( zero, X ) }.
% 6.95/7.37 parent0[0]: (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X )
% 6.95/7.37 }.
% 6.95/7.37 parent1[0; 2]: (25243) {G0,W5,D3,L1,V1,M1} { X ==> addition( X, zero ) }.
% 6.95/7.37 substitution0:
% 6.95/7.37 X := X
% 6.95/7.37 Y := zero
% 6.95/7.37 end
% 6.95/7.37 substitution1:
% 6.95/7.37 X := X
% 6.95/7.37 end
% 6.95/7.37
% 6.95/7.37 eqswap: (25247) {G1,W5,D3,L1,V1,M1} { addition( zero, X ) ==> X }.
% 6.95/7.37 parent0[0]: (25244) {G1,W5,D3,L1,V1,M1} { X ==> addition( zero, X ) }.
% 6.95/7.37 substitution0:
% 6.95/7.37 X := X
% 6.95/7.37 end
% 6.95/7.37
% 6.95/7.37 subsumption: (31) {G1,W5,D3,L1,V1,M1} P(2,0) { addition( zero, X ) ==> X
% 6.95/7.37 }.
% 6.95/7.37 parent0: (25247) {G1,W5,D3,L1,V1,M1} { addition( zero, X ) ==> X }.
% 6.95/7.37 substitution0:
% 6.95/7.37 X := X
% 6.95/7.37 end
% 6.95/7.37 permutation0:
% 6.95/7.37 0 ==> 0
% 6.95/7.37 end
% 6.95/7.37
% 6.95/7.37 eqswap: (25249) {G0,W11,D4,L1,V3,M1} { addition( addition( X, Y ), Z ) ==>
% 6.95/7.37 addition( X, addition( Y, Z ) ) }.
% 6.95/7.37 parent0[0]: (1) {G0,W11,D4,L1,V3,M1} I { addition( Z, addition( Y, X ) )
% 6.95/7.37 ==> addition( addition( Z, Y ), X ) }.
% 6.95/7.37 substitution0:
% 6.95/7.37 X := Z
% 6.95/7.37 Y := Y
% 6.95/7.37 Z := X
% 6.95/7.37 end
% 6.95/7.37
% 6.95/7.37 paramod: (25255) {G1,W9,D4,L1,V2,M1} { addition( addition( X, Y ), Y ) ==>
% 6.95/7.37 addition( X, Y ) }.
% 6.95/7.37 parent0[0]: (3) {G0,W5,D3,L1,V1,M1} I { addition( X, X ) ==> X }.
% 6.95/7.37 parent1[0; 8]: (25249) {G0,W11,D4,L1,V3,M1} { addition( addition( X, Y ),
% 6.95/7.37 Z ) ==> addition( X, addition( Y, Z ) ) }.
% 6.95/7.37 substitution0:
% 6.95/7.37 X := Y
% 6.95/7.37 end
% 6.95/7.37 substitution1:
% 6.95/7.37 X := X
% 6.95/7.37 Y := Y
% 6.95/7.37 Z := Y
% 6.95/7.37 end
% 6.95/7.37
% 6.95/7.37 subsumption: (33) {G1,W9,D4,L1,V2,M1} P(3,1) { addition( addition( Y, X ),
% 6.95/7.37 X ) ==> addition( Y, X ) }.
% 6.95/7.37 parent0: (25255) {G1,W9,D4,L1,V2,M1} { addition( addition( X, Y ), Y ) ==>
% 6.95/7.37 addition( X, Y ) }.
% 6.95/7.37 substitution0:
% 6.95/7.37 X := Y
% 6.95/7.37 Y := X
% 6.95/7.37 end
% 6.95/7.37 permutation0:
% 6.95/7.37 0 ==> 0
% 6.95/7.37 end
% 6.95/7.37
% 6.95/7.37 eqswap: (25260) {G0,W6,D4,L1,V1,M1} { codomain( X ) ==> coantidomain(
% 6.95/7.37 coantidomain( X ) ) }.
% 6.95/7.37 parent0[0]: (20) {G0,W6,D4,L1,V1,M1} I { coantidomain( coantidomain( X ) )
% 6.95/7.37 ==> codomain( X ) }.
% 6.95/7.37 substitution0:
% 6.95/7.37 X := X
% 6.95/7.37 end
% 6.95/7.37
% 6.95/7.37 paramod: (25263) {G1,W7,D4,L1,V1,M1} { codomain( coantidomain( X ) ) ==>
% 6.95/7.37 coantidomain( codomain( X ) ) }.
% 6.95/7.37 parent0[0]: (20) {G0,W6,D4,L1,V1,M1} I { coantidomain( coantidomain( X ) )
% 6.95/7.37 ==> codomain( X ) }.
% 6.95/7.37 parent1[0; 5]: (25260) {G0,W6,D4,L1,V1,M1} { codomain( X ) ==>
% 6.95/7.37 coantidomain( coantidomain( X ) ) }.
% 6.95/7.37 substitution0:
% 6.95/7.37 X := X
% 6.95/7.37 end
% 6.95/7.37 substitution1:
% 6.95/7.37 X := coantidomain( X )
% 6.95/7.37 end
% 6.95/7.37
% 6.95/7.37 subsumption: (36) {G1,W7,D4,L1,V1,M1} P(20,20) { codomain( coantidomain( X
% 6.95/7.37 ) ) ==> coantidomain( codomain( X ) ) }.
% 6.95/7.37 parent0: (25263) {G1,W7,D4,L1,V1,M1} { codomain( coantidomain( X ) ) ==>
% 6.95/7.37 coantidomain( codomain( X ) ) }.
% 6.95/7.37 substitution0:
% 6.95/7.37 X := X
% 6.95/7.37 end
% 6.95/7.37 permutation0:
% 6.95/7.37 0 ==> 0
% 6.95/7.37 end
% 6.95/7.37
% 6.95/7.37 eqswap: (25265) {G0,W6,D4,L1,V1,M1} { zero ==> multiplication( X,
% 6.95/7.37 coantidomain( X ) ) }.
% 6.95/7.37 parent0[0]: (17) {G0,W6,D4,L1,V1,M1} I { multiplication( X, coantidomain( X
% 6.95/7.37 ) ) ==> zero }.
% 6.95/7.37 substitution0:
% 6.95/7.37 X := X
% 6.95/7.37 end
% 6.95/7.37
% 6.95/7.37 paramod: (25267) {G1,W4,D3,L1,V0,M1} { zero ==> coantidomain( one ) }.
% 6.95/7.37 parent0[0]: (6) {G0,W5,D3,L1,V1,M1} I { multiplication( one, X ) ==> X }.
% 6.95/7.37 parent1[0; 2]: (25265) {G0,W6,D4,L1,V1,M1} { zero ==> multiplication( X,
% 6.95/7.37 coantidomain( X ) ) }.
% 6.95/7.37 substitution0:
% 6.95/7.37 X := coantidomain( one )
% 6.95/7.37 end
% 6.95/7.37 substitution1:
% 6.95/7.37 X := one
% 6.95/7.37 end
% 6.95/7.37
% 6.95/7.37 eqswap: (25268) {G1,W4,D3,L1,V0,M1} { coantidomain( one ) ==> zero }.
% 6.95/7.37 parent0[0]: (25267) {G1,W4,D3,L1,V0,M1} { zero ==> coantidomain( one ) }.
% 6.95/7.37 substitution0:
% 6.95/7.37 end
% 6.95/7.37
% 6.95/7.37 subsumption: (38) {G1,W4,D3,L1,V0,M1} P(17,6) { coantidomain( one ) ==>
% 6.95/7.37 zero }.
% 6.95/7.37 parent0: (25268) {G1,W4,D3,L1,V0,M1} { coantidomain( one ) ==> zero }.
% 6.95/7.37 substitution0:
% 6.95/7.37 end
% 6.95/7.37 permutation0:
% 6.95/7.37 0 ==> 0
% 6.95/7.37 end
% 6.95/7.37
% 6.95/7.37 eqswap: (25270) {G0,W6,D4,L1,V1,M1} { codomain( X ) ==> coantidomain(
% 6.95/7.37 coantidomain( X ) ) }.
% 6.95/7.37 parent0[0]: (20) {G0,W6,D4,L1,V1,M1} I { coantidomain( coantidomain( X ) )
% 6.95/7.37 ==> codomain( X ) }.
% 6.95/7.37 substitution0:
% 6.95/7.37 X := X
% 6.95/7.37 end
% 6.95/7.37
% 6.95/7.37 paramod: (25271) {G1,W5,D3,L1,V0,M1} { codomain( one ) ==> coantidomain(
% 6.95/7.37 zero ) }.
% 6.95/7.37 parent0[0]: (38) {G1,W4,D3,L1,V0,M1} P(17,6) { coantidomain( one ) ==> zero
% 6.95/7.37 }.
% 6.95/7.37 parent1[0; 4]: (25270) {G0,W6,D4,L1,V1,M1} { codomain( X ) ==>
% 6.95/7.37 coantidomain( coantidomain( X ) ) }.
% 6.95/7.37 substitution0:
% 6.95/7.37 end
% 6.95/7.37 substitution1:
% 6.95/7.37 X := one
% 6.95/7.37 end
% 6.95/7.37
% 6.95/7.37 subsumption: (39) {G2,W5,D3,L1,V0,M1} P(38,20) { codomain( one ) ==>
% 6.95/7.37 coantidomain( zero ) }.
% 6.95/7.37 parent0: (25271) {G1,W5,D3,L1,V0,M1} { codomain( one ) ==> coantidomain(
% 6.95/7.37 zero ) }.
% 6.95/7.37 substitution0:
% 6.95/7.37 end
% 6.95/7.37 permutation0:
% 6.95/7.37 0 ==> 0
% 6.95/7.37 end
% 6.95/7.37
% 6.95/7.37 eqswap: (25273) {G0,W6,D4,L1,V1,M1} { domain( X ) ==> antidomain(
% 6.95/7.37 antidomain( X ) ) }.
% 6.95/7.37 parent0[0]: (16) {G0,W6,D4,L1,V1,M1} I { antidomain( antidomain( X ) ) ==>
% 6.95/7.37 domain( X ) }.
% 6.95/7.37 substitution0:
% 6.95/7.37 X := X
% 6.95/7.37 end
% 6.95/7.37
% 6.95/7.37 paramod: (25277) {G1,W7,D4,L1,V1,M1} { domain( antidomain( X ) ) ==>
% 6.95/7.37 antidomain( domain( X ) ) }.
% 6.95/7.37 parent0[0]: (16) {G0,W6,D4,L1,V1,M1} I { antidomain( antidomain( X ) ) ==>
% 6.95/7.37 domain( X ) }.
% 6.95/7.37 parent1[0; 5]: (25273) {G0,W6,D4,L1,V1,M1} { domain( X ) ==> antidomain(
% 6.95/7.37 antidomain( X ) ) }.
% 6.95/7.37 substitution0:
% 6.95/7.37 X := X
% 6.95/7.37 end
% 6.95/7.37 substitution1:
% 6.95/7.37 X := antidomain( X )
% 6.95/7.37 end
% 6.95/7.37
% 6.95/7.37 paramod: (25278) {G1,W6,D4,L1,V1,M1} { domain( antidomain( X ) ) ==> c( X
% 6.95/7.37 ) }.
% 6.95/7.37 parent0[0]: (21) {G0,W6,D4,L1,V1,M1} I { antidomain( domain( X ) ) ==> c( X
% 6.95/7.37 ) }.
% 6.95/7.37 parent1[0; 4]: (25277) {G1,W7,D4,L1,V1,M1} { domain( antidomain( X ) ) ==>
% 6.95/7.37 antidomain( domain( X ) ) }.
% 6.95/7.37 substitution0:
% 6.95/7.37 X := X
% 6.95/7.37 end
% 6.95/7.37 substitution1:
% 6.95/7.37 X := X
% 6.95/7.37 end
% 6.95/7.37
% 6.95/7.37 subsumption: (41) {G1,W6,D4,L1,V1,M1} P(16,16);d(21) { domain( antidomain(
% 6.95/7.37 X ) ) ==> c( X ) }.
% 6.95/7.37 parent0: (25278) {G1,W6,D4,L1,V1,M1} { domain( antidomain( X ) ) ==> c( X
% 6.95/7.37 ) }.
% 6.95/7.37 substitution0:
% 6.95/7.37 X := X
% 6.95/7.37 end
% 6.95/7.37 permutation0:
% 6.95/7.37 0 ==> 0
% 6.95/7.37 end
% 6.95/7.37
% 6.95/7.37 eqswap: (25281) {G0,W6,D4,L1,V1,M1} { domain( X ) ==> antidomain(
% 6.95/7.37 antidomain( X ) ) }.
% 6.95/7.37 parent0[0]: (16) {G0,W6,D4,L1,V1,M1} I { antidomain( antidomain( X ) ) ==>
% 6.95/7.37 domain( X ) }.
% 6.95/7.37 substitution0:
% 6.95/7.37 X := X
% 6.95/7.37 end
% 6.95/7.37
% 6.95/7.37 paramod: (25282) {G1,W7,D4,L1,V1,M1} { domain( domain( X ) ) ==>
% 6.95/7.37 antidomain( c( X ) ) }.
% 6.95/7.37 parent0[0]: (21) {G0,W6,D4,L1,V1,M1} I { antidomain( domain( X ) ) ==> c( X
% 6.95/7.37 ) }.
% 6.95/7.37 parent1[0; 5]: (25281) {G0,W6,D4,L1,V1,M1} { domain( X ) ==> antidomain(
% 6.95/7.37 antidomain( X ) ) }.
% 6.95/7.37 substitution0:
% 6.95/7.37 X := X
% 6.95/7.37 end
% 6.95/7.37 substitution1:
% 6.95/7.37 X := domain( X )
% 6.95/7.37 end
% 6.95/7.37
% 6.95/7.37 subsumption: (42) {G1,W7,D4,L1,V1,M1} P(21,16) { domain( domain( X ) ) ==>
% 6.95/7.37 antidomain( c( X ) ) }.
% 6.95/7.37 parent0: (25282) {G1,W7,D4,L1,V1,M1} { domain( domain( X ) ) ==>
% 6.95/7.37 antidomain( c( X ) ) }.
% 6.95/7.37 substitution0:
% 6.95/7.37 X := X
% 6.95/7.37 end
% 6.95/7.37 permutation0:
% 6.95/7.37 0 ==> 0
% 6.95/7.37 end
% 6.95/7.37
% 6.95/7.37 eqswap: (25285) {G0,W13,D4,L1,V3,M1} { multiplication( X, addition( Y, Z )
% 6.95/7.37 ) ==> addition( multiplication( X, Y ), multiplication( X, Z ) ) }.
% 6.95/7.37 parent0[0]: (7) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Y ),
% 6.95/7.37 multiplication( X, Z ) ) ==> multiplication( X, addition( Y, Z ) ) }.
% 6.95/7.37 substitution0:
% 6.95/7.37 X := X
% 6.95/7.37 Y := Y
% 6.95/7.37 Z := Z
% 6.95/7.37 end
% 6.95/7.37
% 6.95/7.37 paramod: (25288) {G1,W13,D5,L1,V2,M1} { multiplication( antidomain( X ),
% 6.95/7.37 addition( X, Y ) ) ==> addition( zero, multiplication( antidomain( X ), Y
% 6.95/7.37 ) ) }.
% 6.95/7.37 parent0[0]: (13) {G0,W6,D4,L1,V1,M1} I { multiplication( antidomain( X ), X
% 6.95/7.37 ) ==> zero }.
% 6.95/7.37 parent1[0; 8]: (25285) {G0,W13,D4,L1,V3,M1} { multiplication( X, addition
% 6.95/7.37 ( Y, Z ) ) ==> addition( multiplication( X, Y ), multiplication( X, Z ) )
% 6.95/7.37 }.
% 6.95/7.37 substitution0:
% 6.95/7.37 X := X
% 6.95/7.37 end
% 6.95/7.37 substitution1:
% 6.95/7.37 X := antidomain( X )
% 6.95/7.37 Y := X
% 6.95/7.37 Z := Y
% 6.95/7.37 end
% 6.95/7.37
% 6.95/7.37 paramod: (25290) {G2,W11,D4,L1,V2,M1} { multiplication( antidomain( X ),
% 6.95/7.37 addition( X, Y ) ) ==> multiplication( antidomain( X ), Y ) }.
% 6.95/7.37 parent0[0]: (31) {G1,W5,D3,L1,V1,M1} P(2,0) { addition( zero, X ) ==> X }.
% 6.95/7.37 parent1[0; 7]: (25288) {G1,W13,D5,L1,V2,M1} { multiplication( antidomain(
% 6.95/7.37 X ), addition( X, Y ) ) ==> addition( zero, multiplication( antidomain( X
% 6.95/7.37 ), Y ) ) }.
% 6.95/7.37 substitution0:
% 6.95/7.37 X := multiplication( antidomain( X ), Y )
% 6.95/7.37 end
% 6.95/7.37 substitution1:
% 6.95/7.37 X := X
% 6.95/7.37 Y := Y
% 6.95/7.37 end
% 6.95/7.37
% 6.95/7.37 subsumption: (52) {G2,W11,D4,L1,V2,M1} P(13,7);d(31) { multiplication(
% 6.95/7.37 antidomain( X ), addition( X, Y ) ) ==> multiplication( antidomain( X ),
% 6.95/7.37 Y ) }.
% 6.95/7.37 parent0: (25290) {G2,W11,D4,L1,V2,M1} { multiplication( antidomain( X ),
% 6.95/7.37 addition( X, Y ) ) ==> multiplication( antidomain( X ), Y ) }.
% 6.95/7.37 substitution0:
% 6.95/7.37 X := X
% 6.95/7.37 Y := Y
% 6.95/7.37 end
% 6.95/7.37 permutation0:
% 6.95/7.37 0 ==> 0
% 6.95/7.37 end
% 6.95/7.37
% 6.95/7.37 eqswap: (25293) {G0,W13,D4,L1,V3,M1} { multiplication( X, addition( Y, Z )
% 6.95/7.37 ) ==> addition( multiplication( X, Y ), multiplication( X, Z ) ) }.
% 6.95/7.37 parent0[0]: (7) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Y ),
% 6.95/7.37 multiplication( X, Z ) ) ==> multiplication( X, addition( Y, Z ) ) }.
% 6.95/7.37 substitution0:
% 6.95/7.37 X := X
% 6.95/7.37 Y := Y
% 6.95/7.37 Z := Z
% 6.95/7.37 end
% 6.95/7.37
% 6.95/7.37 paramod: (25295) {G1,W12,D5,L1,V2,M1} { multiplication( X, addition(
% 6.95/7.37 coantidomain( X ), Y ) ) ==> addition( zero, multiplication( X, Y ) ) }.
% 6.95/7.37 parent0[0]: (17) {G0,W6,D4,L1,V1,M1} I { multiplication( X, coantidomain( X
% 6.95/7.37 ) ) ==> zero }.
% 6.95/7.37 parent1[0; 8]: (25293) {G0,W13,D4,L1,V3,M1} { multiplication( X, addition
% 6.95/7.37 ( Y, Z ) ) ==> addition( multiplication( X, Y ), multiplication( X, Z ) )
% 6.95/7.37 }.
% 6.95/7.37 substitution0:
% 6.95/7.37 X := X
% 6.95/7.37 end
% 6.95/7.37 substitution1:
% 6.95/7.37 X := X
% 6.95/7.37 Y := coantidomain( X )
% 6.95/7.37 Z := Y
% 6.95/7.37 end
% 6.95/7.37
% 6.95/7.37 paramod: (25297) {G2,W10,D5,L1,V2,M1} { multiplication( X, addition(
% 6.95/7.37 coantidomain( X ), Y ) ) ==> multiplication( X, Y ) }.
% 6.95/7.37 parent0[0]: (31) {G1,W5,D3,L1,V1,M1} P(2,0) { addition( zero, X ) ==> X }.
% 6.95/7.37 parent1[0; 7]: (25295) {G1,W12,D5,L1,V2,M1} { multiplication( X, addition
% 6.95/7.37 ( coantidomain( X ), Y ) ) ==> addition( zero, multiplication( X, Y ) )
% 6.95/7.37 }.
% 6.95/7.37 substitution0:
% 6.95/7.37 X := multiplication( X, Y )
% 6.95/7.37 end
% 6.95/7.37 substitution1:
% 6.95/7.37 X := X
% 6.95/7.37 Y := Y
% 6.95/7.37 end
% 6.95/7.37
% 6.95/7.37 subsumption: (56) {G2,W10,D5,L1,V2,M1} P(17,7);d(31) { multiplication( X,
% 6.95/7.37 addition( coantidomain( X ), Y ) ) ==> multiplication( X, Y ) }.
% 6.95/7.37 parent0: (25297) {G2,W10,D5,L1,V2,M1} { multiplication( X, addition(
% 6.95/7.37 coantidomain( X ), Y ) ) ==> multiplication( X, Y ) }.
% 6.95/7.37 substitution0:
% 6.95/7.37 X := X
% 6.95/7.37 Y := Y
% 6.95/7.37 end
% 6.95/7.37 permutation0:
% 6.95/7.37 0 ==> 0
% 6.95/7.37 end
% 6.95/7.37
% 6.95/7.37 eqswap: (25300) {G0,W13,D4,L1,V3,M1} { multiplication( addition( X, Z ), Y
% 6.95/7.37 ) ==> addition( multiplication( X, Y ), multiplication( Z, Y ) ) }.
% 6.95/7.37 parent0[0]: (8) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Z ),
% 6.95/7.37 multiplication( Y, Z ) ) ==> multiplication( addition( X, Y ), Z ) }.
% 6.95/7.37 substitution0:
% 6.95/7.37 X := X
% 6.95/7.37 Y := Z
% 6.95/7.37 Z := Y
% 6.95/7.37 end
% 6.95/7.37
% 6.95/7.37 paramod: (25303) {G1,W12,D5,L1,V2,M1} { multiplication( addition( X,
% 6.95/7.37 antidomain( Y ) ), Y ) ==> addition( multiplication( X, Y ), zero ) }.
% 6.95/7.37 parent0[0]: (13) {G0,W6,D4,L1,V1,M1} I { multiplication( antidomain( X ), X
% 6.95/7.37 ) ==> zero }.
% 6.95/7.37 parent1[0; 11]: (25300) {G0,W13,D4,L1,V3,M1} { multiplication( addition( X
% 6.95/7.37 , Z ), Y ) ==> addition( multiplication( X, Y ), multiplication( Z, Y ) )
% 6.95/7.37 }.
% 6.95/7.37 substitution0:
% 6.95/7.37 X := Y
% 6.95/7.37 end
% 6.95/7.37 substitution1:
% 6.95/7.37 X := X
% 6.95/7.37 Y := Y
% 6.95/7.37 Z := antidomain( Y )
% 6.95/7.37 end
% 6.95/7.37
% 6.95/7.37 paramod: (25304) {G1,W10,D5,L1,V2,M1} { multiplication( addition( X,
% 6.95/7.37 antidomain( Y ) ), Y ) ==> multiplication( X, Y ) }.
% 6.95/7.37 parent0[0]: (2) {G0,W5,D3,L1,V1,M1} I { addition( X, zero ) ==> X }.
% 6.95/7.37 parent1[0; 7]: (25303) {G1,W12,D5,L1,V2,M1} { multiplication( addition( X
% 6.95/7.37 , antidomain( Y ) ), Y ) ==> addition( multiplication( X, Y ), zero ) }.
% 6.95/7.37 substitution0:
% 6.95/7.37 X := multiplication( X, Y )
% 6.95/7.37 end
% 6.95/7.37 substitution1:
% 6.95/7.37 X := X
% 6.95/7.37 Y := Y
% 6.95/7.37 end
% 6.95/7.37
% 6.95/7.37 subsumption: (65) {G1,W10,D5,L1,V2,M1} P(13,8);d(2) { multiplication(
% 6.95/7.37 addition( Y, antidomain( X ) ), X ) ==> multiplication( Y, X ) }.
% 6.95/7.37 parent0: (25304) {G1,W10,D5,L1,V2,M1} { multiplication( addition( X,
% 6.95/7.37 antidomain( Y ) ), Y ) ==> multiplication( X, Y ) }.
% 6.95/7.37 substitution0:
% 6.95/7.37 X := Y
% 6.95/7.37 Y := X
% 6.95/7.37 end
% 6.95/7.37 permutation0:
% 6.95/7.37 0 ==> 0
% 6.95/7.37 end
% 6.95/7.37
% 6.95/7.37 eqswap: (25307) {G0,W13,D4,L1,V3,M1} { multiplication( addition( X, Z ), Y
% 6.95/7.37 ) ==> addition( multiplication( X, Y ), multiplication( Z, Y ) ) }.
% 6.95/7.37 parent0[0]: (8) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Z ),
% 6.95/7.37 multiplication( Y, Z ) ) ==> multiplication( addition( X, Y ), Z ) }.
% 6.95/7.37 substitution0:
% 6.95/7.37 X := X
% 6.95/7.37 Y := Z
% 6.95/7.37 Z := Y
% 6.95/7.37 end
% 6.95/7.37
% 6.95/7.37 paramod: (25310) {G1,W13,D5,L1,V2,M1} { multiplication( addition( X, Y ),
% 6.95/7.37 coantidomain( X ) ) ==> addition( zero, multiplication( Y, coantidomain(
% 6.95/7.37 X ) ) ) }.
% 6.95/7.37 parent0[0]: (17) {G0,W6,D4,L1,V1,M1} I { multiplication( X, coantidomain( X
% 6.95/7.37 ) ) ==> zero }.
% 6.95/7.37 parent1[0; 8]: (25307) {G0,W13,D4,L1,V3,M1} { multiplication( addition( X
% 6.95/7.37 , Z ), Y ) ==> addition( multiplication( X, Y ), multiplication( Z, Y ) )
% 6.95/7.37 }.
% 6.95/7.37 substitution0:
% 6.95/7.37 X := X
% 6.95/7.37 end
% 6.95/7.37 substitution1:
% 6.95/7.37 X := X
% 6.95/7.37 Y := coantidomain( X )
% 6.95/7.37 Z := Y
% 6.95/7.37 end
% 6.95/7.37
% 6.95/7.37 paramod: (25312) {G2,W11,D4,L1,V2,M1} { multiplication( addition( X, Y ),
% 6.95/7.37 coantidomain( X ) ) ==> multiplication( Y, coantidomain( X ) ) }.
% 6.95/7.37 parent0[0]: (31) {G1,W5,D3,L1,V1,M1} P(2,0) { addition( zero, X ) ==> X }.
% 6.95/7.37 parent1[0; 7]: (25310) {G1,W13,D5,L1,V2,M1} { multiplication( addition( X
% 6.95/7.37 , Y ), coantidomain( X ) ) ==> addition( zero, multiplication( Y,
% 6.95/7.37 coantidomain( X ) ) ) }.
% 6.95/7.37 substitution0:
% 6.95/7.37 X := multiplication( Y, coantidomain( X ) )
% 6.95/7.37 end
% 6.95/7.37 substitution1:
% 6.95/7.37 X := X
% 6.95/7.37 Y := Y
% 6.95/7.37 end
% 6.95/7.37
% 6.95/7.37 subsumption: (66) {G2,W11,D4,L1,V2,M1} P(17,8);d(31) { multiplication(
% 6.95/7.37 addition( X, Y ), coantidomain( X ) ) ==> multiplication( Y, coantidomain
% 6.95/7.37 ( X ) ) }.
% 6.95/7.37 parent0: (25312) {G2,W11,D4,L1,V2,M1} { multiplication( addition( X, Y ),
% 6.95/7.37 coantidomain( X ) ) ==> multiplication( Y, coantidomain( X ) ) }.
% 6.95/7.37 substitution0:
% 6.95/7.37 X := X
% 6.95/7.37 Y := Y
% 6.95/7.37 end
% 6.95/7.37 permutation0:
% 6.95/7.37 0 ==> 0
% 6.95/7.37 end
% 6.95/7.37
% 6.95/7.37 eqswap: (25314) {G0,W8,D3,L2,V2,M2} { Y ==> addition( X, Y ), ! leq( X, Y
% 6.95/7.37 ) }.
% 6.95/7.37 parent0[1]: (11) {G0,W8,D3,L2,V2,M2} I { ! leq( X, Y ), addition( X, Y )
% 6.95/7.37 ==> Y }.
% 6.95/7.37 substitution0:
% 6.95/7.37 X := X
% 6.95/7.37 Y := Y
% 6.95/7.37 end
% 6.95/7.37
% 6.95/7.37 paramod: (25316) {G1,W6,D2,L2,V1,M2} { zero ==> X, ! leq( X, zero ) }.
% 6.95/7.37 parent0[0]: (2) {G0,W5,D3,L1,V1,M1} I { addition( X, zero ) ==> X }.
% 6.95/7.37 parent1[0; 2]: (25314) {G0,W8,D3,L2,V2,M2} { Y ==> addition( X, Y ), ! leq
% 6.95/7.37 ( X, Y ) }.
% 6.95/7.37 substitution0:
% 6.95/7.37 X := X
% 6.95/7.37 end
% 6.95/7.37 substitution1:
% 6.95/7.37 X := X
% 6.95/7.37 Y := zero
% 6.95/7.37 end
% 6.95/7.37
% 6.95/7.37 subsumption: (86) {G1,W6,D2,L2,V1,M2} P(11,2) { zero = X, ! leq( X, zero )
% 6.95/7.37 }.
% 6.95/7.37 parent0: (25316) {G1,W6,D2,L2,V1,M2} { zero ==> X, ! leq( X, zero ) }.
% 6.95/7.37 substitution0:
% 6.95/7.37 X := X
% 6.95/7.37 end
% 6.95/7.37 permutation0:
% 6.95/7.37 0 ==> 0
% 6.95/7.37 1 ==> 1
% 6.95/7.37 end
% 6.95/7.37
% 6.95/7.37 eqswap: (25318) {G0,W8,D3,L2,V2,M2} { Y ==> addition( X, Y ), ! leq( X, Y
% 6.95/7.37 ) }.
% 6.95/7.37 parent0[1]: (11) {G0,W8,D3,L2,V2,M2} I { ! leq( X, Y ), addition( X, Y )
% 6.95/7.37 ==> Y }.
% 6.95/7.37 substitution0:
% 6.95/7.37 X := X
% 6.95/7.37 Y := Y
% 6.95/7.37 end
% 6.95/7.37
% 6.95/7.37 paramod: (25319) {G1,W8,D3,L2,V2,M2} { X ==> addition( X, Y ), ! leq( Y, X
% 6.95/7.37 ) }.
% 6.95/7.37 parent0[0]: (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X )
% 6.95/7.37 }.
% 6.95/7.37 parent1[0; 2]: (25318) {G0,W8,D3,L2,V2,M2} { Y ==> addition( X, Y ), ! leq
% 6.95/7.37 ( X, Y ) }.
% 6.95/7.37 substitution0:
% 6.95/7.37 X := Y
% 6.95/7.37 Y := X
% 6.95/7.37 end
% 6.95/7.37 substitution1:
% 6.95/7.37 X := Y
% 6.95/7.37 Y := X
% 6.95/7.37 end
% 6.95/7.37
% 6.95/7.37 eqswap: (25322) {G1,W8,D3,L2,V2,M2} { addition( X, Y ) ==> X, ! leq( Y, X
% 6.95/7.37 ) }.
% 6.95/7.37 parent0[0]: (25319) {G1,W8,D3,L2,V2,M2} { X ==> addition( X, Y ), ! leq( Y
% 6.95/7.37 , X ) }.
% 6.95/7.37 substitution0:
% 6.95/7.37 X := X
% 6.95/7.37 Y := Y
% 6.95/7.37 end
% 6.95/7.37
% 6.95/7.37 subsumption: (87) {G1,W8,D3,L2,V2,M2} P(11,0) { addition( Y, X ) ==> Y, !
% 6.95/7.37 leq( X, Y ) }.
% 6.95/7.37 parent0: (25322) {G1,W8,D3,L2,V2,M2} { addition( X, Y ) ==> X, ! leq( Y, X
% 6.95/7.37 ) }.
% 6.95/7.37 substitution0:
% 6.95/7.37 X := Y
% 6.95/7.37 Y := X
% 6.95/7.37 end
% 6.95/7.37 permutation0:
% 6.95/7.37 0 ==> 0
% 6.95/7.37 1 ==> 1
% 6.95/7.37 end
% 6.95/7.37
% 6.95/7.37 eqswap: (25323) {G1,W6,D2,L2,V1,M2} { X = zero, ! leq( X, zero ) }.
% 6.95/7.37 parent0[0]: (86) {G1,W6,D2,L2,V1,M2} P(11,2) { zero = X, ! leq( X, zero )
% 6.95/7.37 }.
% 6.95/7.37 substitution0:
% 6.95/7.37 X := X
% 6.95/7.37 end
% 6.95/7.37
% 6.95/7.37 eqswap: (25324) {G0,W4,D3,L1,V0,M1} { ! zero ==> divergence( skol1 ) }.
% 6.95/7.37 parent0[0]: (30) {G0,W4,D3,L1,V0,M1} I { ! divergence( skol1 ) ==> zero }.
% 6.95/7.37 substitution0:
% 6.95/7.37 end
% 6.95/7.37
% 6.95/7.37 paramod: (25326) {G1,W7,D3,L2,V0,M2} { ! zero ==> zero, ! leq( divergence
% 6.95/7.37 ( skol1 ), zero ) }.
% 6.95/7.37 parent0[0]: (25323) {G1,W6,D2,L2,V1,M2} { X = zero, ! leq( X, zero ) }.
% 6.95/7.37 parent1[0; 3]: (25324) {G0,W4,D3,L1,V0,M1} { ! zero ==> divergence( skol1
% 6.95/7.37 ) }.
% 6.95/7.37 substitution0:
% 6.95/7.37 X := divergence( skol1 )
% 6.95/7.37 end
% 6.95/7.37 substitution1:
% 6.95/7.37 end
% 6.95/7.37
% 6.95/7.37 eqrefl: (25385) {G0,W4,D3,L1,V0,M1} { ! leq( divergence( skol1 ), zero )
% 6.95/7.37 }.
% 6.95/7.37 parent0[0]: (25326) {G1,W7,D3,L2,V0,M2} { ! zero ==> zero, ! leq(
% 6.95/7.37 divergence( skol1 ), zero ) }.
% 6.95/7.37 substitution0:
% 6.95/7.37 end
% 6.95/7.37
% 6.95/7.37 subsumption: (115) {G2,W4,D3,L1,V0,M1} P(86,30);q { ! leq( divergence(
% 6.95/7.37 skol1 ), zero ) }.
% 6.95/7.37 parent0: (25385) {G0,W4,D3,L1,V0,M1} { ! leq( divergence( skol1 ), zero )
% 6.95/7.37 }.
% 6.95/7.37 substitution0:
% 6.95/7.37 end
% 6.95/7.37 permutation0:
% 6.95/7.37 0 ==> 0
% 6.95/7.37 end
% 6.95/7.37
% 6.95/7.37 eqswap: (25386) {G0,W8,D3,L2,V2,M2} { ! Y ==> addition( X, Y ), leq( X, Y
% 6.95/7.37 ) }.
% 6.95/7.37 parent0[0]: (12) {G0,W8,D3,L2,V2,M2} I { ! addition( X, Y ) ==> Y, leq( X,
% 6.95/7.37 Y ) }.
% 6.95/7.37 substitution0:
% 6.95/7.37 X := X
% 6.95/7.37 Y := Y
% 6.95/7.37 end
% 6.95/7.37
% 6.95/7.37 eqswap: (25387) {G1,W6,D2,L2,V1,M2} { X = zero, ! leq( X, zero ) }.
% 6.95/7.37 parent0[0]: (86) {G1,W6,D2,L2,V1,M2} P(11,2) { zero = X, ! leq( X, zero )
% 6.95/7.37 }.
% 6.95/7.37 substitution0:
% 6.95/7.37 X := X
% 6.95/7.37 end
% 6.95/7.37
% 6.95/7.37 resolution: (25389) {G1,W8,D3,L2,V1,M2} { X = zero, ! zero ==> addition( X
% 6.95/7.37 , zero ) }.
% 6.95/7.37 parent0[1]: (25387) {G1,W6,D2,L2,V1,M2} { X = zero, ! leq( X, zero ) }.
% 6.95/7.37 parent1[1]: (25386) {G0,W8,D3,L2,V2,M2} { ! Y ==> addition( X, Y ), leq( X
% 6.95/7.37 , Y ) }.
% 6.95/7.37 substitution0:
% 6.95/7.37 X := X
% 6.95/7.37 end
% 6.95/7.37 substitution1:
% 6.95/7.37 X := X
% 6.95/7.37 Y := zero
% 6.95/7.37 end
% 6.95/7.37
% 6.95/7.37 paramod: (25390) {G1,W6,D2,L2,V1,M2} { ! zero ==> X, X = zero }.
% 6.95/7.37 parent0[0]: (2) {G0,W5,D3,L1,V1,M1} I { addition( X, zero ) ==> X }.
% 6.95/7.37 parent1[1; 3]: (25389) {G1,W8,D3,L2,V1,M2} { X = zero, ! zero ==> addition
% 6.95/7.37 ( X, zero ) }.
% 6.95/7.37 substitution0:
% 6.95/7.37 X := X
% 6.95/7.37 end
% 6.95/7.37 substitution1:
% 6.95/7.37 X := X
% 6.95/7.37 end
% 6.95/7.37
% 6.95/7.37 eqswap: (25392) {G1,W6,D2,L2,V1,M2} { zero = X, ! zero ==> X }.
% 6.95/7.37 parent0[1]: (25390) {G1,W6,D2,L2,V1,M2} { ! zero ==> X, X = zero }.
% 6.95/7.37 substitution0:
% 6.95/7.37 X := X
% 6.95/7.37 end
% 6.95/7.37
% 6.95/7.37 eqswap: (25393) {G1,W6,D2,L2,V1,M2} { ! X ==> zero, zero = X }.
% 6.95/7.37 parent0[1]: (25392) {G1,W6,D2,L2,V1,M2} { zero = X, ! zero ==> X }.
% 6.95/7.37 substitution0:
% 6.95/7.37 X := X
% 6.95/7.37 end
% 6.95/7.37
% 6.95/7.37 subsumption: (136) {G2,W6,D2,L2,V1,M2} R(12,86);d(2) { zero = X, ! X = zero
% 6.95/7.37 }.
% 6.95/7.37 parent0: (25393) {G1,W6,D2,L2,V1,M2} { ! X ==> zero, zero = X }.
% 6.95/7.37 substitution0:
% 6.95/7.37 X := X
% 6.95/7.37 end
% 6.95/7.37 permutation0:
% 6.95/7.37 0 ==> 1
% 6.95/7.37 1 ==> 0
% 6.95/7.37 end
% 6.95/7.37
% 6.95/7.37 eqswap: (25394) {G0,W8,D3,L2,V2,M2} { ! Y ==> addition( X, Y ), leq( X, Y
% 6.95/7.37 ) }.
% 6.95/7.37 parent0[0]: (12) {G0,W8,D3,L2,V2,M2} I { ! addition( X, Y ) ==> Y, leq( X,
% 6.95/7.37 Y ) }.
% 6.95/7.37 substitution0:
% 6.95/7.37 X := X
% 6.95/7.37 Y := Y
% 6.95/7.37 end
% 6.95/7.37
% 6.95/7.37 eqswap: (25395) {G0,W5,D3,L1,V1,M1} { X ==> addition( X, X ) }.
% 6.95/7.37 parent0[0]: (3) {G0,W5,D3,L1,V1,M1} I { addition( X, X ) ==> X }.
% 6.95/7.37 substitution0:
% 6.95/7.37 X := X
% 6.95/7.37 end
% 6.95/7.37
% 6.95/7.37 resolution: (25396) {G1,W3,D2,L1,V1,M1} { leq( X, X ) }.
% 6.95/7.37 parent0[0]: (25394) {G0,W8,D3,L2,V2,M2} { ! Y ==> addition( X, Y ), leq( X
% 6.95/7.37 , Y ) }.
% 6.95/7.37 parent1[0]: (25395) {G0,W5,D3,L1,V1,M1} { X ==> addition( X, X ) }.
% 6.95/7.37 substitution0:
% 6.95/7.37 X := X
% 6.95/7.37 Y := X
% 6.95/7.37 end
% 6.95/7.37 substitution1:
% 6.95/7.37 X := X
% 6.95/7.37 end
% 6.95/7.37
% 6.95/7.37 subsumption: (138) {G1,W3,D2,L1,V1,M1} R(12,3) { leq( X, X ) }.
% 6.95/7.37 parent0: (25396) {G1,W3,D2,L1,V1,M1} { leq( X, X ) }.
% 6.95/7.37 substitution0:
% 6.95/7.37 X := X
% 6.95/7.37 end
% 6.95/7.37 permutation0:
% 6.95/7.37 0 ==> 0
% 6.95/7.37 end
% 6.95/7.37
% 6.95/7.37 eqswap: (25398) {G0,W8,D3,L2,V2,M2} { ! Y ==> addition( X, Y ), leq( X, Y
% 6.95/7.37 ) }.
% 6.95/7.37 parent0[0]: (12) {G0,W8,D3,L2,V2,M2} I { ! addition( X, Y ) ==> Y, leq( X,
% 6.95/7.37 Y ) }.
% 6.95/7.37 substitution0:
% 6.95/7.37 X := X
% 6.95/7.37 Y := Y
% 6.95/7.37 end
% 6.95/7.37
% 6.95/7.37 paramod: (25399) {G1,W16,D4,L2,V3,M2} { ! multiplication( X, Y ) ==>
% 6.95/7.37 multiplication( X, addition( Z, Y ) ), leq( multiplication( X, Z ),
% 6.95/7.37 multiplication( X, Y ) ) }.
% 6.95/7.37 parent0[0]: (7) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Y ),
% 6.95/7.37 multiplication( X, Z ) ) ==> multiplication( X, addition( Y, Z ) ) }.
% 6.95/7.37 parent1[0; 5]: (25398) {G0,W8,D3,L2,V2,M2} { ! Y ==> addition( X, Y ), leq
% 6.95/7.37 ( X, Y ) }.
% 6.95/7.37 substitution0:
% 6.95/7.37 X := X
% 6.95/7.37 Y := Z
% 6.95/7.37 Z := Y
% 6.95/7.37 end
% 6.95/7.37 substitution1:
% 6.95/7.37 X := multiplication( X, Z )
% 6.95/7.37 Y := multiplication( X, Y )
% 6.95/7.37 end
% 6.95/7.37
% 6.95/7.37 eqswap: (25400) {G1,W16,D4,L2,V3,M2} { ! multiplication( X, addition( Z, Y
% 6.95/7.37 ) ) ==> multiplication( X, Y ), leq( multiplication( X, Z ),
% 6.95/7.37 multiplication( X, Y ) ) }.
% 6.95/7.37 parent0[0]: (25399) {G1,W16,D4,L2,V3,M2} { ! multiplication( X, Y ) ==>
% 6.95/7.37 multiplication( X, addition( Z, Y ) ), leq( multiplication( X, Z ),
% 6.95/7.37 multiplication( X, Y ) ) }.
% 6.95/7.37 substitution0:
% 6.95/7.37 X := X
% 6.95/7.37 Y := Y
% 6.95/7.37 Z := Z
% 6.95/7.37 end
% 6.95/7.37
% 6.95/7.37 subsumption: (141) {G1,W16,D4,L2,V3,M2} P(7,12) { ! multiplication( X,
% 6.95/7.37 addition( Y, Z ) ) ==> multiplication( X, Z ), leq( multiplication( X, Y
% 6.95/7.37 ), multiplication( X, Z ) ) }.
% 6.95/7.37 parent0: (25400) {G1,W16,D4,L2,V3,M2} { ! multiplication( X, addition( Z,
% 6.95/7.37 Y ) ) ==> multiplication( X, Y ), leq( multiplication( X, Z ),
% 6.95/7.37 multiplication( X, Y ) ) }.
% 6.95/7.37 substitution0:
% 6.95/7.37 X := X
% 6.95/7.37 Y := Z
% 6.95/7.37 Z := Y
% 6.95/7.37 end
% 6.95/7.37 permutation0:
% 6.95/7.37 0 ==> 0
% 6.95/7.37 1 ==> 1
% 6.95/7.37 end
% 6.95/7.37
% 6.95/7.37 paramod: (25403) {G1,W7,D4,L1,V1,M1} { addition( domain( X ), antidomain(
% 6.95/7.37 X ) ) ==> one }.
% 6.95/7.37 parent0[0]: (16) {G0,W6,D4,L1,V1,M1} I { antidomain( antidomain( X ) ) ==>
% 6.95/7.37 domain( X ) }.
% 6.95/7.37 parent1[0; 2]: (15) {G0,W8,D5,L1,V1,M1} I { addition( antidomain(
% 6.95/7.37 antidomain( X ) ), antidomain( X ) ) ==> one }.
% 6.95/7.37 substitution0:
% 6.95/7.37 X := X
% 6.95/7.37 end
% 6.95/7.37 substitution1:
% 6.95/7.37 X := X
% 6.95/7.37 end
% 6.95/7.37
% 6.95/7.37 subsumption: (183) {G1,W7,D4,L1,V1,M1} S(15);d(16) { addition( domain( X )
% 6.95/7.37 , antidomain( X ) ) ==> one }.
% 6.95/7.37 parent0: (25403) {G1,W7,D4,L1,V1,M1} { addition( domain( X ), antidomain(
% 6.95/7.37 X ) ) ==> one }.
% 6.95/7.37 substitution0:
% 6.95/7.37 X := X
% 6.95/7.37 end
% 6.95/7.37 permutation0:
% 6.95/7.37 0 ==> 0
% 6.95/7.37 end
% 6.95/7.37
% 6.95/7.37 paramod: (25407) {G1,W7,D4,L1,V1,M1} { addition( codomain( X ),
% 6.95/7.37 coantidomain( X ) ) ==> one }.
% 6.95/7.37 parent0[0]: (20) {G0,W6,D4,L1,V1,M1} I { coantidomain( coantidomain( X ) )
% 6.95/7.37 ==> codomain( X ) }.
% 6.95/7.37 parent1[0; 2]: (19) {G0,W8,D5,L1,V1,M1} I { addition( coantidomain(
% 6.95/7.37 coantidomain( X ) ), coantidomain( X ) ) ==> one }.
% 6.95/7.37 substitution0:
% 6.95/7.37 X := X
% 6.95/7.37 end
% 6.95/7.37 substitution1:
% 6.95/7.37 X := X
% 6.95/7.37 end
% 6.95/7.37
% 6.95/7.37 subsumption: (207) {G1,W7,D4,L1,V1,M1} S(19);d(20) { addition( codomain( X
% 6.95/7.37 ), coantidomain( X ) ) ==> one }.
% 6.95/7.37 parent0: (25407) {G1,W7,D4,L1,V1,M1} { addition( codomain( X ),
% 6.95/7.37 coantidomain( X ) ) ==> one }.
% 6.95/7.37 substitution0:
% 6.95/7.37 X := X
% 6.95/7.37 end
% 6.95/7.37 permutation0:
% 6.95/7.37 0 ==> 0
% 6.95/7.37 end
% 6.95/7.37
% 6.95/7.37 eqswap: (25410) {G0,W9,D4,L1,V2,M1} { domain_difference( X, Y ) ==>
% 6.95/7.37 multiplication( domain( X ), antidomain( Y ) ) }.
% 6.95/7.37 parent0[0]: (22) {G0,W9,D4,L1,V2,M1} I { multiplication( domain( X ),
% 6.95/7.37 antidomain( Y ) ) ==> domain_difference( X, Y ) }.
% 6.95/7.37 substitution0:
% 6.95/7.37 X := X
% 6.95/7.37 Y := Y
% 6.95/7.37 end
% 6.95/7.37
% 6.95/7.37 paramod: (25411) {G1,W10,D4,L1,V2,M1} { domain_difference( antidomain( X )
% 6.95/7.37 , Y ) ==> multiplication( c( X ), antidomain( Y ) ) }.
% 6.95/7.37 parent0[0]: (41) {G1,W6,D4,L1,V1,M1} P(16,16);d(21) { domain( antidomain( X
% 6.95/7.37 ) ) ==> c( X ) }.
% 6.95/7.37 parent1[0; 6]: (25410) {G0,W9,D4,L1,V2,M1} { domain_difference( X, Y ) ==>
% 6.95/7.37 multiplication( domain( X ), antidomain( Y ) ) }.
% 6.95/7.37 substitution0:
% 6.95/7.37 X := X
% 6.95/7.37 end
% 6.95/7.37 substitution1:
% 6.95/7.37 X := antidomain( X )
% 6.95/7.37 Y := Y
% 6.95/7.37 end
% 6.95/7.37
% 6.95/7.37 eqswap: (25412) {G1,W10,D4,L1,V2,M1} { multiplication( c( X ), antidomain
% 6.95/7.37 ( Y ) ) ==> domain_difference( antidomain( X ), Y ) }.
% 6.95/7.37 parent0[0]: (25411) {G1,W10,D4,L1,V2,M1} { domain_difference( antidomain(
% 6.95/7.37 X ), Y ) ==> multiplication( c( X ), antidomain( Y ) ) }.
% 6.95/7.37 substitution0:
% 6.95/7.37 X := X
% 6.95/7.37 Y := Y
% 6.95/7.37 end
% 6.95/7.37
% 6.95/7.37 subsumption: (233) {G2,W10,D4,L1,V2,M1} P(41,22) { multiplication( c( X ),
% 6.95/7.37 antidomain( Y ) ) ==> domain_difference( antidomain( X ), Y ) }.
% 6.95/7.37 parent0: (25412) {G1,W10,D4,L1,V2,M1} { multiplication( c( X ), antidomain
% 6.95/7.37 ( Y ) ) ==> domain_difference( antidomain( X ), Y ) }.
% 6.95/7.37 substitution0:
% 6.95/7.37 X := X
% 6.95/7.37 Y := Y
% 6.95/7.37 end
% 6.95/7.37 permutation0:
% 6.95/7.37 0 ==> 0
% 6.95/7.37 end
% 6.95/7.37
% 6.95/7.37 eqswap: (25414) {G1,W7,D4,L1,V1,M1} { one ==> addition( codomain( X ),
% 6.95/7.37 coantidomain( X ) ) }.
% 6.95/7.37 parent0[0]: (207) {G1,W7,D4,L1,V1,M1} S(19);d(20) { addition( codomain( X )
% 6.95/7.37 , coantidomain( X ) ) ==> one }.
% 6.95/7.37 substitution0:
% 6.95/7.37 X := X
% 6.95/7.37 end
% 6.95/7.37
% 6.95/7.37 paramod: (25417) {G2,W7,D4,L1,V0,M1} { one ==> addition( coantidomain(
% 6.95/7.37 zero ), coantidomain( one ) ) }.
% 6.95/7.37 parent0[0]: (39) {G2,W5,D3,L1,V0,M1} P(38,20) { codomain( one ) ==>
% 6.95/7.37 coantidomain( zero ) }.
% 6.95/7.37 parent1[0; 3]: (25414) {G1,W7,D4,L1,V1,M1} { one ==> addition( codomain( X
% 6.95/7.37 ), coantidomain( X ) ) }.
% 6.95/7.37 substitution0:
% 6.95/7.37 end
% 6.95/7.37 substitution1:
% 6.95/7.37 X := one
% 6.95/7.37 end
% 6.95/7.37
% 6.95/7.37 paramod: (25418) {G2,W6,D4,L1,V0,M1} { one ==> addition( coantidomain(
% 6.95/7.37 zero ), zero ) }.
% 6.95/7.37 parent0[0]: (38) {G1,W4,D3,L1,V0,M1} P(17,6) { coantidomain( one ) ==> zero
% 6.95/7.37 }.
% 6.95/7.37 parent1[0; 5]: (25417) {G2,W7,D4,L1,V0,M1} { one ==> addition(
% 6.95/7.37 coantidomain( zero ), coantidomain( one ) ) }.
% 6.95/7.37 substitution0:
% 6.95/7.37 end
% 6.95/7.37 substitution1:
% 6.95/7.37 end
% 6.95/7.37
% 6.95/7.37 paramod: (25419) {G1,W4,D3,L1,V0,M1} { one ==> coantidomain( zero ) }.
% 6.95/7.37 parent0[0]: (2) {G0,W5,D3,L1,V1,M1} I { addition( X, zero ) ==> X }.
% 6.95/7.37 parent1[0; 2]: (25418) {G2,W6,D4,L1,V0,M1} { one ==> addition(
% 6.95/7.37 coantidomain( zero ), zero ) }.
% 6.95/7.37 substitution0:
% 6.95/7.37 X := coantidomain( zero )
% 6.95/7.37 end
% 6.95/7.37 substitution1:
% 6.95/7.37 end
% 6.95/7.37
% 6.95/7.37 eqswap: (25420) {G1,W4,D3,L1,V0,M1} { coantidomain( zero ) ==> one }.
% 6.95/7.37 parent0[0]: (25419) {G1,W4,D3,L1,V0,M1} { one ==> coantidomain( zero ) }.
% 6.95/7.37 substitution0:
% 6.95/7.37 end
% 6.95/7.37
% 6.95/7.37 subsumption: (349) {G3,W4,D3,L1,V0,M1} P(39,207);d(38);d(2) { coantidomain
% 6.95/7.37 ( zero ) ==> one }.
% 6.95/7.37 parent0: (25420) {G1,W4,D3,L1,V0,M1} { coantidomain( zero ) ==> one }.
% 6.95/7.37 substitution0:
% 6.95/7.37 end
% 6.95/7.37 permutation0:
% 6.95/7.37 0 ==> 0
% 6.95/7.37 end
% 6.95/7.37
% 6.95/7.37 eqswap: (25421) {G1,W7,D4,L1,V1,M1} { one ==> addition( codomain( X ),
% 6.95/7.37 coantidomain( X ) ) }.
% 6.95/7.37 parent0[0]: (207) {G1,W7,D4,L1,V1,M1} S(19);d(20) { addition( codomain( X )
% 6.95/7.37 , coantidomain( X ) ) ==> one }.
% 6.95/7.37 substitution0:
% 6.95/7.37 X := X
% 6.95/7.37 end
% 6.95/7.37
% 6.95/7.37 paramod: (25422) {G1,W7,D4,L1,V1,M1} { one ==> addition( coantidomain( X )
% 6.95/7.37 , codomain( X ) ) }.
% 6.95/7.37 parent0[0]: (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X )
% 6.95/7.37 }.
% 6.95/7.37 parent1[0; 2]: (25421) {G1,W7,D4,L1,V1,M1} { one ==> addition( codomain( X
% 6.95/7.37 ), coantidomain( X ) ) }.
% 6.95/7.37 substitution0:
% 6.95/7.37 X := codomain( X )
% 6.95/7.37 Y := coantidomain( X )
% 6.95/7.37 end
% 6.95/7.37 substitution1:
% 6.95/7.37 X := X
% 6.95/7.37 end
% 6.95/7.37
% 6.95/7.37 eqswap: (25425) {G1,W7,D4,L1,V1,M1} { addition( coantidomain( X ),
% 6.95/7.37 codomain( X ) ) ==> one }.
% 6.95/7.37 parent0[0]: (25422) {G1,W7,D4,L1,V1,M1} { one ==> addition( coantidomain(
% 6.95/7.37 X ), codomain( X ) ) }.
% 6.95/7.37 substitution0:
% 6.95/7.37 X := X
% 6.95/7.37 end
% 6.95/7.37
% 6.95/7.37 subsumption: (352) {G2,W7,D4,L1,V1,M1} P(207,0) { addition( coantidomain( X
% 6.95/7.37 ), codomain( X ) ) ==> one }.
% 6.95/7.37 parent0: (25425) {G1,W7,D4,L1,V1,M1} { addition( coantidomain( X ),
% 6.95/7.37 codomain( X ) ) ==> one }.
% 6.95/7.37 substitution0:
% 6.95/7.37 X := X
% 6.95/7.37 end
% 6.95/7.37 permutation0:
% 6.95/7.37 0 ==> 0
% 6.95/7.37 end
% 6.95/7.37
% 6.95/7.37 eqswap: (25427) {G0,W6,D4,L1,V1,M1} { codomain( X ) ==> coantidomain(
% 6.95/7.37 coantidomain( X ) ) }.
% 6.95/7.37 parent0[0]: (20) {G0,W6,D4,L1,V1,M1} I { coantidomain( coantidomain( X ) )
% 6.95/7.37 ==> codomain( X ) }.
% 6.95/7.37 substitution0:
% 6.95/7.37 X := X
% 6.95/7.37 end
% 6.95/7.37
% 6.95/7.37 paramod: (25429) {G1,W5,D3,L1,V0,M1} { codomain( zero ) ==> coantidomain(
% 6.95/7.37 one ) }.
% 6.95/7.37 parent0[0]: (349) {G3,W4,D3,L1,V0,M1} P(39,207);d(38);d(2) { coantidomain(
% 6.95/7.37 zero ) ==> one }.
% 6.95/7.37 parent1[0; 4]: (25427) {G0,W6,D4,L1,V1,M1} { codomain( X ) ==>
% 6.95/7.37 coantidomain( coantidomain( X ) ) }.
% 6.95/7.37 substitution0:
% 6.95/7.37 end
% 6.95/7.37 substitution1:
% 6.95/7.37 X := zero
% 6.95/7.37 end
% 6.95/7.37
% 6.95/7.37 paramod: (25430) {G2,W4,D3,L1,V0,M1} { codomain( zero ) ==> zero }.
% 6.95/7.37 parent0[0]: (38) {G1,W4,D3,L1,V0,M1} P(17,6) { coantidomain( one ) ==> zero
% 6.95/7.37 }.
% 6.95/7.37 parent1[0; 3]: (25429) {G1,W5,D3,L1,V0,M1} { codomain( zero ) ==>
% 6.95/7.37 coantidomain( one ) }.
% 6.95/7.37 substitution0:
% 6.95/7.37 end
% 6.95/7.37 substitution1:
% 6.95/7.37 end
% 6.95/7.37
% 6.95/7.37 subsumption: (360) {G4,W4,D3,L1,V0,M1} P(349,20);d(38) { codomain( zero )
% 6.95/7.37 ==> zero }.
% 6.95/7.37 parent0: (25430) {G2,W4,D3,L1,V0,M1} { codomain( zero ) ==> zero }.
% 6.95/7.37 substitution0:
% 6.95/7.37 end
% 6.95/7.37 permutation0:
% 6.95/7.37 0 ==> 0
% 6.95/7.37 end
% 6.95/7.37
% 6.95/7.37 eqswap: (25433) {G1,W9,D4,L1,V2,M1} { addition( X, Y ) ==> addition(
% 6.95/7.37 addition( X, Y ), Y ) }.
% 6.95/7.37 parent0[0]: (33) {G1,W9,D4,L1,V2,M1} P(3,1) { addition( addition( Y, X ), X
% 6.95/7.37 ) ==> addition( Y, X ) }.
% 6.95/7.37 substitution0:
% 6.95/7.37 X := Y
% 6.95/7.37 Y := X
% 6.95/7.37 end
% 6.95/7.37
% 6.95/7.37 paramod: (25435) {G2,W10,D4,L1,V1,M1} { addition( domain( X ), antidomain
% 6.95/7.37 ( X ) ) ==> addition( one, antidomain( X ) ) }.
% 6.95/7.37 parent0[0]: (183) {G1,W7,D4,L1,V1,M1} S(15);d(16) { addition( domain( X ),
% 6.95/7.37 antidomain( X ) ) ==> one }.
% 6.95/7.37 parent1[0; 7]: (25433) {G1,W9,D4,L1,V2,M1} { addition( X, Y ) ==> addition
% 6.95/7.37 ( addition( X, Y ), Y ) }.
% 6.95/7.37 substitution0:
% 6.95/7.37 X := X
% 6.95/7.37 end
% 6.95/7.37 substitution1:
% 6.95/7.37 X := domain( X )
% 6.95/7.37 Y := antidomain( X )
% 6.95/7.37 end
% 6.95/7.37
% 6.95/7.37 paramod: (25436) {G2,W6,D4,L1,V1,M1} { one ==> addition( one, antidomain(
% 6.95/7.37 X ) ) }.
% 6.95/7.37 parent0[0]: (183) {G1,W7,D4,L1,V1,M1} S(15);d(16) { addition( domain( X ),
% 6.95/7.37 antidomain( X ) ) ==> one }.
% 6.95/7.37 parent1[0; 1]: (25435) {G2,W10,D4,L1,V1,M1} { addition( domain( X ),
% 6.95/7.37 antidomain( X ) ) ==> addition( one, antidomain( X ) ) }.
% 6.95/7.37 substitution0:
% 6.95/7.37 X := X
% 6.95/7.37 end
% 6.95/7.37 substitution1:
% 6.95/7.37 X := X
% 6.95/7.37 end
% 6.95/7.37
% 6.95/7.37 eqswap: (25438) {G2,W6,D4,L1,V1,M1} { addition( one, antidomain( X ) ) ==>
% 6.95/7.37 one }.
% 6.95/7.37 parent0[0]: (25436) {G2,W6,D4,L1,V1,M1} { one ==> addition( one,
% 6.95/7.37 antidomain( X ) ) }.
% 6.95/7.37 substitution0:
% 6.95/7.37 X := X
% 6.95/7.37 end
% 6.95/7.37
% 6.95/7.37 subsumption: (483) {G2,W6,D4,L1,V1,M1} P(183,33) { addition( one,
% 6.95/7.37 antidomain( X ) ) ==> one }.
% 6.95/7.37 parent0: (25438) {G2,W6,D4,L1,V1,M1} { addition( one, antidomain( X ) )
% 6.95/7.37 ==> one }.
% 6.95/7.37 substitution0:
% 6.95/7.37 X := X
% 6.95/7.37 end
% 6.95/7.37 permutation0:
% 6.95/7.37 0 ==> 0
% 6.95/7.37 end
% 6.95/7.37
% 6.95/7.37 eqswap: (25441) {G2,W6,D4,L1,V1,M1} { one ==> addition( one, antidomain( X
% 6.95/7.37 ) ) }.
% 6.95/7.37 parent0[0]: (483) {G2,W6,D4,L1,V1,M1} P(183,33) { addition( one, antidomain
% 6.95/7.37 ( X ) ) ==> one }.
% 6.95/7.37 substitution0:
% 6.95/7.37 X := X
% 6.95/7.37 end
% 6.95/7.37
% 6.95/7.37 paramod: (25442) {G1,W6,D4,L1,V1,M1} { one ==> addition( one, domain( X )
% 6.95/7.37 ) }.
% 6.95/7.37 parent0[0]: (16) {G0,W6,D4,L1,V1,M1} I { antidomain( antidomain( X ) ) ==>
% 6.95/7.37 domain( X ) }.
% 6.95/7.37 parent1[0; 4]: (25441) {G2,W6,D4,L1,V1,M1} { one ==> addition( one,
% 6.95/7.37 antidomain( X ) ) }.
% 6.95/7.37 substitution0:
% 6.95/7.37 X := X
% 6.95/7.37 end
% 6.95/7.37 substitution1:
% 6.95/7.37 X := antidomain( X )
% 6.95/7.37 end
% 6.95/7.37
% 6.95/7.37 eqswap: (25443) {G1,W6,D4,L1,V1,M1} { addition( one, domain( X ) ) ==> one
% 6.95/7.37 }.
% 6.95/7.37 parent0[0]: (25442) {G1,W6,D4,L1,V1,M1} { one ==> addition( one, domain( X
% 6.95/7.37 ) ) }.
% 6.95/7.37 substitution0:
% 6.95/7.37 X := X
% 6.95/7.37 end
% 6.95/7.37
% 6.95/7.37 subsumption: (551) {G3,W6,D4,L1,V1,M1} P(16,483) { addition( one, domain( X
% 6.95/7.37 ) ) ==> one }.
% 6.95/7.37 parent0: (25443) {G1,W6,D4,L1,V1,M1} { addition( one, domain( X ) ) ==>
% 6.95/7.37 one }.
% 6.95/7.37 substitution0:
% 6.95/7.37 X := X
% 6.95/7.37 end
% 6.95/7.37 permutation0:
% 6.95/7.37 0 ==> 0
% 6.95/7.37 end
% 6.95/7.37
% 6.95/7.37 eqswap: (25444) {G3,W6,D4,L1,V1,M1} { one ==> addition( one, domain( X ) )
% 6.95/7.37 }.
% 6.95/7.37 parent0[0]: (551) {G3,W6,D4,L1,V1,M1} P(16,483) { addition( one, domain( X
% 6.95/7.37 ) ) ==> one }.
% 6.95/7.37 substitution0:
% 6.95/7.37 X := X
% 6.95/7.37 end
% 6.95/7.37
% 6.95/7.37 paramod: (25445) {G1,W6,D4,L1,V1,M1} { one ==> addition( domain( X ), one
% 6.95/7.37 ) }.
% 6.95/7.37 parent0[0]: (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X )
% 6.95/7.37 }.
% 6.95/7.37 parent1[0; 2]: (25444) {G3,W6,D4,L1,V1,M1} { one ==> addition( one, domain
% 6.95/7.37 ( X ) ) }.
% 6.95/7.37 substitution0:
% 6.95/7.37 X := one
% 6.95/7.37 Y := domain( X )
% 6.95/7.37 end
% 6.95/7.37 substitution1:
% 6.95/7.37 X := X
% 6.95/7.37 end
% 6.95/7.37
% 6.95/7.37 eqswap: (25448) {G1,W6,D4,L1,V1,M1} { addition( domain( X ), one ) ==> one
% 6.95/7.37 }.
% 6.95/7.37 parent0[0]: (25445) {G1,W6,D4,L1,V1,M1} { one ==> addition( domain( X ),
% 6.95/7.37 one ) }.
% 6.95/7.37 substitution0:
% 6.95/7.37 X := X
% 6.95/7.37 end
% 6.95/7.37
% 6.95/7.37 subsumption: (560) {G4,W6,D4,L1,V1,M1} P(551,0) { addition( domain( X ),
% 6.95/7.37 one ) ==> one }.
% 6.95/7.37 parent0: (25448) {G1,W6,D4,L1,V1,M1} { addition( domain( X ), one ) ==>
% 6.95/7.37 one }.
% 6.95/7.37 substitution0:
% 6.95/7.37 X := X
% 6.95/7.37 end
% 6.95/7.37 permutation0:
% 6.95/7.37 0 ==> 0
% 6.95/7.37 end
% 6.95/7.37
% 6.95/7.37 eqswap: (25449) {G4,W6,D4,L1,V1,M1} { one ==> addition( domain( X ), one )
% 6.95/7.37 }.
% 6.95/7.37 parent0[0]: (560) {G4,W6,D4,L1,V1,M1} P(551,0) { addition( domain( X ), one
% 6.95/7.37 ) ==> one }.
% 6.95/7.37 substitution0:
% 6.95/7.37 X := X
% 6.95/7.37 end
% 6.95/7.37
% 6.95/7.37 eqswap: (25450) {G0,W8,D3,L2,V2,M2} { ! Y ==> addition( X, Y ), leq( X, Y
% 6.95/7.37 ) }.
% 6.95/7.37 parent0[0]: (12) {G0,W8,D3,L2,V2,M2} I { ! addition( X, Y ) ==> Y, leq( X,
% 6.95/7.37 Y ) }.
% 6.95/7.37 substitution0:
% 6.95/7.37 X := X
% 6.95/7.37 Y := Y
% 6.95/7.37 end
% 6.95/7.37
% 6.95/7.37 resolution: (25451) {G1,W4,D3,L1,V1,M1} { leq( domain( X ), one ) }.
% 6.95/7.37 parent0[0]: (25450) {G0,W8,D3,L2,V2,M2} { ! Y ==> addition( X, Y ), leq( X
% 6.95/7.37 , Y ) }.
% 6.95/7.37 parent1[0]: (25449) {G4,W6,D4,L1,V1,M1} { one ==> addition( domain( X ),
% 6.95/7.37 one ) }.
% 6.95/7.37 substitution0:
% 6.95/7.37 X := domain( X )
% 6.95/7.37 Y := one
% 6.95/7.37 end
% 6.95/7.37 substitution1:
% 6.95/7.37 X := X
% 6.95/7.37 end
% 6.95/7.37
% 6.95/7.37 subsumption: (561) {G5,W4,D3,L1,V1,M1} R(560,12) { leq( domain( X ), one )
% 6.95/7.37 }.
% 6.95/7.37 parent0: (25451) {G1,W4,D3,L1,V1,M1} { leq( domain( X ), one ) }.
% 6.95/7.37 substitution0:
% 6.95/7.37 X := X
% 6.95/7.37 end
% 6.95/7.37 permutation0:
% 6.95/7.37 0 ==> 0
% 6.95/7.37 end
% 6.95/7.37
% 6.95/7.37 paramod: (25453) {G1,W5,D3,L1,V2,M1} { leq( forward_diamond( X, Y ), one )
% 6.95/7.37 }.
% 6.95/7.37 parent0[0]: (23) {G0,W9,D5,L1,V2,M1} I { domain( multiplication( X, domain
% 6.95/7.37 ( Y ) ) ) ==> forward_diamond( X, Y ) }.
% 6.95/7.37 parent1[0; 1]: (561) {G5,W4,D3,L1,V1,M1} R(560,12) { leq( domain( X ), one
% 6.95/7.37 ) }.
% 6.95/7.37 substitution0:
% 6.95/7.37 X := X
% 6.95/7.37 Y := Y
% 6.95/7.37 end
% 6.95/7.37 substitution1:
% 6.95/7.37 X := multiplication( X, domain( Y ) )
% 6.95/7.37 end
% 6.95/7.37
% 6.95/7.37 subsumption: (572) {G6,W5,D3,L1,V2,M1} P(23,561) { leq( forward_diamond( X
% 6.95/7.37 , Y ), one ) }.
% 6.95/7.37 parent0: (25453) {G1,W5,D3,L1,V2,M1} { leq( forward_diamond( X, Y ), one )
% 6.95/7.37 }.
% 6.95/7.37 substitution0:
% 6.95/7.37 X := X
% 6.95/7.37 Y := Y
% 6.95/7.37 end
% 6.95/7.37 permutation0:
% 6.95/7.37 0 ==> 0
% 6.95/7.37 end
% 6.95/7.37
% 6.95/7.37 eqswap: (25455) {G2,W11,D4,L1,V2,M1} { multiplication( antidomain( X ), Y
% 6.95/7.37 ) ==> multiplication( antidomain( X ), addition( X, Y ) ) }.
% 6.95/7.37 parent0[0]: (52) {G2,W11,D4,L1,V2,M1} P(13,7);d(31) { multiplication(
% 6.95/7.37 antidomain( X ), addition( X, Y ) ) ==> multiplication( antidomain( X ),
% 6.95/7.37 Y ) }.
% 6.95/7.37 substitution0:
% 6.95/7.37 X := X
% 6.95/7.37 Y := Y
% 6.95/7.37 end
% 6.95/7.37
% 6.95/7.37 paramod: (25459) {G2,W12,D5,L1,V1,M1} { multiplication( antidomain( domain
% 6.95/7.37 ( X ) ), antidomain( X ) ) ==> multiplication( antidomain( domain( X ) )
% 6.95/7.37 , one ) }.
% 6.95/7.37 parent0[0]: (183) {G1,W7,D4,L1,V1,M1} S(15);d(16) { addition( domain( X ),
% 6.95/7.37 antidomain( X ) ) ==> one }.
% 6.95/7.37 parent1[0; 11]: (25455) {G2,W11,D4,L1,V2,M1} { multiplication( antidomain
% 6.95/7.37 ( X ), Y ) ==> multiplication( antidomain( X ), addition( X, Y ) ) }.
% 6.95/7.37 substitution0:
% 6.95/7.37 X := X
% 6.95/7.37 end
% 6.95/7.37 substitution1:
% 6.95/7.37 X := domain( X )
% 6.95/7.37 Y := antidomain( X )
% 6.95/7.37 end
% 6.95/7.37
% 6.95/7.37 paramod: (25460) {G1,W10,D5,L1,V1,M1} { multiplication( antidomain( domain
% 6.95/7.37 ( X ) ), antidomain( X ) ) ==> antidomain( domain( X ) ) }.
% 6.95/7.37 parent0[0]: (5) {G0,W5,D3,L1,V1,M1} I { multiplication( X, one ) ==> X }.
% 6.95/7.37 parent1[0; 7]: (25459) {G2,W12,D5,L1,V1,M1} { multiplication( antidomain(
% 6.95/7.37 domain( X ) ), antidomain( X ) ) ==> multiplication( antidomain( domain(
% 6.95/7.37 X ) ), one ) }.
% 6.95/7.37 substitution0:
% 6.95/7.37 X := antidomain( domain( X ) )
% 6.95/7.37 end
% 6.95/7.37 substitution1:
% 6.95/7.37 X := X
% 6.95/7.37 end
% 6.95/7.37
% 6.95/7.37 paramod: (25462) {G1,W9,D5,L1,V1,M1} { multiplication( antidomain( domain
% 6.95/7.37 ( X ) ), antidomain( X ) ) ==> c( X ) }.
% 6.95/7.37 parent0[0]: (21) {G0,W6,D4,L1,V1,M1} I { antidomain( domain( X ) ) ==> c( X
% 6.95/7.37 ) }.
% 6.95/7.37 parent1[0; 7]: (25460) {G1,W10,D5,L1,V1,M1} { multiplication( antidomain(
% 6.95/7.37 domain( X ) ), antidomain( X ) ) ==> antidomain( domain( X ) ) }.
% 6.95/7.37 substitution0:
% 6.95/7.37 X := X
% 6.95/7.37 end
% 6.95/7.37 substitution1:
% 6.95/7.37 X := X
% 6.95/7.37 end
% 6.95/7.37
% 6.95/7.37 paramod: (25463) {G1,W8,D4,L1,V1,M1} { multiplication( c( X ), antidomain
% 6.95/7.37 ( X ) ) ==> c( X ) }.
% 6.95/7.37 parent0[0]: (21) {G0,W6,D4,L1,V1,M1} I { antidomain( domain( X ) ) ==> c( X
% 6.95/7.37 ) }.
% 6.95/7.37 parent1[0; 2]: (25462) {G1,W9,D5,L1,V1,M1} { multiplication( antidomain(
% 6.95/7.37 domain( X ) ), antidomain( X ) ) ==> c( X ) }.
% 6.95/7.37 substitution0:
% 6.95/7.37 X := X
% 6.95/7.37 end
% 6.95/7.37 substitution1:
% 6.95/7.37 X := X
% 6.95/7.37 end
% 6.95/7.37
% 6.95/7.37 paramod: (25464) {G2,W7,D4,L1,V1,M1} { domain_difference( antidomain( X )
% 6.95/7.37 , X ) ==> c( X ) }.
% 6.95/7.37 parent0[0]: (233) {G2,W10,D4,L1,V2,M1} P(41,22) { multiplication( c( X ),
% 6.95/7.37 antidomain( Y ) ) ==> domain_difference( antidomain( X ), Y ) }.
% 6.95/7.37 parent1[0; 1]: (25463) {G1,W8,D4,L1,V1,M1} { multiplication( c( X ),
% 6.95/7.37 antidomain( X ) ) ==> c( X ) }.
% 6.95/7.37 substitution0:
% 6.95/7.37 X := X
% 6.95/7.37 Y := X
% 6.95/7.37 end
% 6.95/7.37 substitution1:
% 6.95/7.37 X := X
% 6.95/7.37 end
% 6.95/7.37
% 6.95/7.37 subsumption: (581) {G3,W7,D4,L1,V1,M1} P(183,52);d(5);d(21);d(233) {
% 6.95/7.37 domain_difference( antidomain( X ), X ) ==> c( X ) }.
% 6.95/7.37 parent0: (25464) {G2,W7,D4,L1,V1,M1} { domain_difference( antidomain( X )
% 6.95/7.37 , X ) ==> c( X ) }.
% 6.95/7.37 substitution0:
% 6.95/7.37 X := X
% 6.95/7.37 end
% 6.95/7.37 permutation0:
% 6.95/7.37 0 ==> 0
% 6.95/7.37 end
% 6.95/7.37
% 6.95/7.37 paramod: (25467) {G1,W4,D3,L1,V1,M1} { leq( divergence( X ), one ) }.
% 6.95/7.37 parent0[0]: (27) {G0,W7,D4,L1,V1,M1} I { forward_diamond( X, divergence( X
% 6.95/7.37 ) ) ==> divergence( X ) }.
% 6.95/7.37 parent1[0; 1]: (572) {G6,W5,D3,L1,V2,M1} P(23,561) { leq( forward_diamond(
% 6.95/7.37 X, Y ), one ) }.
% 6.95/7.37 substitution0:
% 6.95/7.37 X := X
% 6.95/7.37 end
% 6.95/7.37 substitution1:
% 6.95/7.37 X := X
% 6.95/7.37 Y := divergence( X )
% 6.95/7.37 end
% 6.95/7.37
% 6.95/7.37 subsumption: (590) {G7,W4,D3,L1,V1,M1} P(27,572) { leq( divergence( X ),
% 6.95/7.37 one ) }.
% 6.95/7.37 parent0: (25467) {G1,W4,D3,L1,V1,M1} { leq( divergence( X ), one ) }.
% 6.95/7.37 substitution0:
% 6.95/7.37 X := X
% 6.95/7.37 end
% 6.95/7.37 permutation0:
% 6.95/7.37 0 ==> 0
% 6.95/7.37 end
% 6.95/7.37
% 6.95/7.37 eqswap: (25468) {G0,W8,D3,L2,V2,M2} { Y ==> addition( X, Y ), ! leq( X, Y
% 6.95/7.37 ) }.
% 6.95/7.37 parent0[1]: (11) {G0,W8,D3,L2,V2,M2} I { ! leq( X, Y ), addition( X, Y )
% 6.95/7.37 ==> Y }.
% 6.95/7.37 substitution0:
% 6.95/7.37 X := X
% 6.95/7.37 Y := Y
% 6.95/7.37 end
% 6.95/7.37
% 6.95/7.37 resolution: (25469) {G1,W6,D4,L1,V1,M1} { one ==> addition( divergence( X
% 6.95/7.37 ), one ) }.
% 6.95/7.37 parent0[1]: (25468) {G0,W8,D3,L2,V2,M2} { Y ==> addition( X, Y ), ! leq( X
% 6.95/7.37 , Y ) }.
% 6.95/7.37 parent1[0]: (590) {G7,W4,D3,L1,V1,M1} P(27,572) { leq( divergence( X ), one
% 6.95/7.37 ) }.
% 6.95/7.37 substitution0:
% 6.95/7.37 X := divergence( X )
% 6.95/7.37 Y := one
% 6.95/7.37 end
% 6.95/7.37 substitution1:
% 6.95/7.37 X := X
% 6.95/7.37 end
% 6.95/7.37
% 6.95/7.37 eqswap: (25470) {G1,W6,D4,L1,V1,M1} { addition( divergence( X ), one ) ==>
% 6.95/7.37 one }.
% 6.95/7.37 parent0[0]: (25469) {G1,W6,D4,L1,V1,M1} { one ==> addition( divergence( X
% 6.95/7.37 ), one ) }.
% 6.95/7.37 substitution0:
% 6.95/7.37 X := X
% 6.95/7.37 end
% 6.95/7.37
% 6.95/7.37 subsumption: (591) {G8,W6,D4,L1,V1,M1} R(590,11) { addition( divergence( X
% 6.95/7.37 ), one ) ==> one }.
% 6.95/7.37 parent0: (25470) {G1,W6,D4,L1,V1,M1} { addition( divergence( X ), one )
% 6.95/7.37 ==> one }.
% 6.95/7.37 substitution0:
% 6.95/7.37 X := X
% 6.95/7.37 end
% 6.95/7.37 permutation0:
% 6.95/7.37 0 ==> 0
% 6.95/7.37 end
% 6.95/7.37
% 6.95/7.37 eqswap: (25472) {G2,W10,D5,L1,V2,M1} { multiplication( X, Y ) ==>
% 6.95/7.37 multiplication( X, addition( coantidomain( X ), Y ) ) }.
% 6.95/7.37 parent0[0]: (56) {G2,W10,D5,L1,V2,M1} P(17,7);d(31) { multiplication( X,
% 6.95/7.37 addition( coantidomain( X ), Y ) ) ==> multiplication( X, Y ) }.
% 6.95/7.37 substitution0:
% 6.95/7.37 X := X
% 6.95/7.37 Y := Y
% 6.95/7.37 end
% 6.95/7.37
% 6.95/7.37 paramod: (25474) {G3,W8,D4,L1,V1,M1} { multiplication( X, codomain( X ) )
% 6.95/7.37 ==> multiplication( X, one ) }.
% 6.95/7.37 parent0[0]: (352) {G2,W7,D4,L1,V1,M1} P(207,0) { addition( coantidomain( X
% 6.95/7.37 ), codomain( X ) ) ==> one }.
% 6.95/7.37 parent1[0; 7]: (25472) {G2,W10,D5,L1,V2,M1} { multiplication( X, Y ) ==>
% 6.95/7.37 multiplication( X, addition( coantidomain( X ), Y ) ) }.
% 6.95/7.37 substitution0:
% 6.95/7.37 X := X
% 6.95/7.37 end
% 6.95/7.37 substitution1:
% 6.95/7.37 X := X
% 6.95/7.37 Y := codomain( X )
% 6.95/7.37 end
% 6.95/7.37
% 6.95/7.37 paramod: (25475) {G1,W6,D4,L1,V1,M1} { multiplication( X, codomain( X ) )
% 6.95/7.37 ==> X }.
% 6.95/7.37 parent0[0]: (5) {G0,W5,D3,L1,V1,M1} I { multiplication( X, one ) ==> X }.
% 6.95/7.37 parent1[0; 5]: (25474) {G3,W8,D4,L1,V1,M1} { multiplication( X, codomain(
% 6.95/7.37 X ) ) ==> multiplication( X, one ) }.
% 6.95/7.37 substitution0:
% 6.95/7.37 X := X
% 6.95/7.37 end
% 6.95/7.37 substitution1:
% 6.95/7.37 X := X
% 6.95/7.37 end
% 6.95/7.37
% 6.95/7.37 subsumption: (646) {G3,W6,D4,L1,V1,M1} P(352,56);d(5) { multiplication( X,
% 6.95/7.37 codomain( X ) ) ==> X }.
% 6.95/7.37 parent0: (25475) {G1,W6,D4,L1,V1,M1} { multiplication( X, codomain( X ) )
% 6.95/7.37 ==> X }.
% 6.95/7.37 substitution0:
% 6.95/7.37 X := X
% 6.95/7.37 end
% 6.95/7.37 permutation0:
% 6.95/7.37 0 ==> 0
% 6.95/7.37 end
% 6.95/7.37
% 6.95/7.37 eqswap: (25478) {G3,W6,D4,L1,V1,M1} { X ==> multiplication( X, codomain( X
% 6.95/7.37 ) ) }.
% 6.95/7.37 parent0[0]: (646) {G3,W6,D4,L1,V1,M1} P(352,56);d(5) { multiplication( X,
% 6.95/7.37 codomain( X ) ) ==> X }.
% 6.95/7.37 substitution0:
% 6.95/7.37 X := X
% 6.95/7.37 end
% 6.95/7.37
% 6.95/7.37 paramod: (25479) {G2,W9,D5,L1,V1,M1} { coantidomain( X ) ==>
% 6.95/7.37 multiplication( coantidomain( X ), coantidomain( codomain( X ) ) ) }.
% 6.95/7.37 parent0[0]: (36) {G1,W7,D4,L1,V1,M1} P(20,20) { codomain( coantidomain( X )
% 6.95/7.37 ) ==> coantidomain( codomain( X ) ) }.
% 6.95/7.37 parent1[0; 6]: (25478) {G3,W6,D4,L1,V1,M1} { X ==> multiplication( X,
% 6.95/7.37 codomain( X ) ) }.
% 6.95/7.37 substitution0:
% 6.95/7.37 X := X
% 6.95/7.37 end
% 6.95/7.37 substitution1:
% 6.95/7.37 X := coantidomain( X )
% 6.95/7.37 end
% 6.95/7.37
% 6.95/7.37 eqswap: (25480) {G2,W9,D5,L1,V1,M1} { multiplication( coantidomain( X ),
% 6.95/7.37 coantidomain( codomain( X ) ) ) ==> coantidomain( X ) }.
% 6.95/7.37 parent0[0]: (25479) {G2,W9,D5,L1,V1,M1} { coantidomain( X ) ==>
% 6.95/7.37 multiplication( coantidomain( X ), coantidomain( codomain( X ) ) ) }.
% 6.95/7.37 substitution0:
% 6.95/7.37 X := X
% 6.95/7.37 end
% 6.95/7.37
% 6.95/7.37 subsumption: (657) {G4,W9,D5,L1,V1,M1} P(36,646) { multiplication(
% 6.95/7.37 coantidomain( X ), coantidomain( codomain( X ) ) ) ==> coantidomain( X )
% 6.95/7.37 }.
% 6.95/7.37 parent0: (25480) {G2,W9,D5,L1,V1,M1} { multiplication( coantidomain( X ),
% 6.95/7.37 coantidomain( codomain( X ) ) ) ==> coantidomain( X ) }.
% 6.95/7.37 substitution0:
% 6.95/7.37 X := X
% 6.95/7.37 end
% 6.95/7.37 permutation0:
% 6.95/7.37 0 ==> 0
% 6.95/7.37 end
% 6.95/7.37
% 6.95/7.37 eqswap: (25481) {G2,W6,D2,L2,V1,M2} { X = zero, ! X = zero }.
% 6.95/7.37 parent0[0]: (136) {G2,W6,D2,L2,V1,M2} R(12,86);d(2) { zero = X, ! X = zero
% 6.95/7.37 }.
% 6.95/7.37 substitution0:
% 6.95/7.37 X := X
% 6.95/7.37 end
% 6.95/7.37
% 6.95/7.37 eqswap: (25484) {G3,W6,D4,L1,V1,M1} { X ==> multiplication( X, codomain( X
% 6.95/7.37 ) ) }.
% 6.95/7.37 parent0[0]: (646) {G3,W6,D4,L1,V1,M1} P(352,56);d(5) { multiplication( X,
% 6.95/7.37 codomain( X ) ) ==> X }.
% 6.95/7.37 substituCputime limit exceeded (core dumped)
%------------------------------------------------------------------------------