TSTP Solution File: KLE133+1 by Bliksem---1.12
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%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : KLE133+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n018.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 01:37:21 EDT 2022
% Result : Theorem 2.74s 3.10s
% Output : Refutation 2.74s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : KLE133+1 : TPTP v8.1.0. Released v4.0.0.
% 0.10/0.12 % Command : bliksem %s
% 0.12/0.33 % Computer : n018.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % DateTime : Thu Jun 16 10:36:01 EDT 2022
% 0.12/0.33 % CPUTime :
% 2.74/3.10 *** allocated 10000 integers for termspace/termends
% 2.74/3.10 *** allocated 10000 integers for clauses
% 2.74/3.10 *** allocated 10000 integers for justifications
% 2.74/3.10 Bliksem 1.12
% 2.74/3.10
% 2.74/3.10
% 2.74/3.10 Automatic Strategy Selection
% 2.74/3.10
% 2.74/3.10
% 2.74/3.10 Clauses:
% 2.74/3.10
% 2.74/3.10 { addition( X, Y ) = addition( Y, X ) }.
% 2.74/3.10 { addition( Z, addition( Y, X ) ) = addition( addition( Z, Y ), X ) }.
% 2.74/3.10 { addition( X, zero ) = X }.
% 2.74/3.10 { addition( X, X ) = X }.
% 2.74/3.10 { multiplication( X, multiplication( Y, Z ) ) = multiplication(
% 2.74/3.10 multiplication( X, Y ), Z ) }.
% 2.74/3.10 { multiplication( X, one ) = X }.
% 2.74/3.10 { multiplication( one, X ) = X }.
% 2.74/3.10 { multiplication( X, addition( Y, Z ) ) = addition( multiplication( X, Y )
% 2.74/3.10 , multiplication( X, Z ) ) }.
% 2.74/3.10 { multiplication( addition( X, Y ), Z ) = addition( multiplication( X, Z )
% 2.74/3.10 , multiplication( Y, Z ) ) }.
% 2.74/3.10 { multiplication( X, zero ) = zero }.
% 2.74/3.10 { multiplication( zero, X ) = zero }.
% 2.74/3.10 { ! leq( X, Y ), addition( X, Y ) = Y }.
% 2.74/3.10 { ! addition( X, Y ) = Y, leq( X, Y ) }.
% 2.74/3.10 { multiplication( antidomain( X ), X ) = zero }.
% 2.74/3.10 { addition( antidomain( multiplication( X, Y ) ), antidomain(
% 2.74/3.10 multiplication( X, antidomain( antidomain( Y ) ) ) ) ) = antidomain(
% 2.74/3.10 multiplication( X, antidomain( antidomain( Y ) ) ) ) }.
% 2.74/3.10 { addition( antidomain( antidomain( X ) ), antidomain( X ) ) = one }.
% 2.74/3.10 { domain( X ) = antidomain( antidomain( X ) ) }.
% 2.74/3.10 { multiplication( X, coantidomain( X ) ) = zero }.
% 2.74/3.10 { addition( coantidomain( multiplication( X, Y ) ), coantidomain(
% 2.74/3.10 multiplication( coantidomain( coantidomain( X ) ), Y ) ) ) = coantidomain
% 2.74/3.10 ( multiplication( coantidomain( coantidomain( X ) ), Y ) ) }.
% 2.74/3.10 { addition( coantidomain( coantidomain( X ) ), coantidomain( X ) ) = one }
% 2.74/3.10 .
% 2.74/3.10 { codomain( X ) = coantidomain( coantidomain( X ) ) }.
% 2.74/3.10 { c( X ) = antidomain( domain( X ) ) }.
% 2.74/3.10 { domain_difference( X, Y ) = multiplication( domain( X ), antidomain( Y )
% 2.74/3.10 ) }.
% 2.74/3.10 { forward_diamond( X, Y ) = domain( multiplication( X, domain( Y ) ) ) }.
% 2.74/3.10 { backward_diamond( X, Y ) = codomain( multiplication( codomain( Y ), X ) )
% 2.74/3.10 }.
% 2.74/3.10 { forward_box( X, Y ) = c( forward_diamond( X, c( Y ) ) ) }.
% 2.74/3.10 { backward_box( X, Y ) = c( backward_diamond( X, c( Y ) ) ) }.
% 2.74/3.10 { forward_diamond( X, divergence( X ) ) = divergence( X ) }.
% 2.74/3.10 { ! addition( domain( X ), addition( forward_diamond( Y, domain( X ) ),
% 2.74/3.10 domain( Z ) ) ) = addition( forward_diamond( Y, domain( X ) ), domain( Z
% 2.74/3.10 ) ), addition( domain( X ), addition( divergence( Y ), forward_diamond(
% 2.74/3.10 star( Y ), domain( Z ) ) ) ) = addition( divergence( Y ), forward_diamond
% 2.74/3.10 ( star( Y ), domain( Z ) ) ) }.
% 2.74/3.10 { addition( domain( X ), forward_diamond( star( skol1 ), domain_difference
% 2.74/3.10 ( domain( X ), forward_diamond( skol1, domain( X ) ) ) ) ) =
% 2.74/3.10 forward_diamond( star( skol1 ), domain_difference( domain( X ),
% 2.74/3.10 forward_diamond( skol1, domain( X ) ) ) ) }.
% 2.74/3.10 { forward_diamond( skol1, forward_diamond( skol1, domain( X ) ) ) =
% 2.74/3.10 forward_diamond( skol1, domain( X ) ) }.
% 2.74/3.10 { ! addition( forward_diamond( skol1, domain( skol2 ) ), forward_diamond(
% 2.74/3.10 star( skol1 ), domain_difference( domain( skol2 ), forward_diamond( skol1
% 2.74/3.10 , domain( skol2 ) ) ) ) ) = forward_diamond( star( skol1 ),
% 2.74/3.10 domain_difference( domain( skol2 ), forward_diamond( skol1, domain( skol2
% 2.74/3.10 ) ) ) ) }.
% 2.74/3.10
% 2.74/3.10 percentage equality = 0.942857, percentage horn = 1.000000
% 2.74/3.10 This is a pure equality problem
% 2.74/3.10
% 2.74/3.10
% 2.74/3.10
% 2.74/3.10 Options Used:
% 2.74/3.10
% 2.74/3.10 useres = 1
% 2.74/3.10 useparamod = 1
% 2.74/3.10 useeqrefl = 1
% 2.74/3.10 useeqfact = 1
% 2.74/3.10 usefactor = 1
% 2.74/3.10 usesimpsplitting = 0
% 2.74/3.10 usesimpdemod = 5
% 2.74/3.10 usesimpres = 3
% 2.74/3.10
% 2.74/3.10 resimpinuse = 1000
% 2.74/3.10 resimpclauses = 20000
% 2.74/3.10 substype = eqrewr
% 2.74/3.10 backwardsubs = 1
% 2.74/3.10 selectoldest = 5
% 2.74/3.10
% 2.74/3.10 litorderings [0] = split
% 2.74/3.10 litorderings [1] = extend the termordering, first sorting on arguments
% 2.74/3.10
% 2.74/3.10 termordering = kbo
% 2.74/3.10
% 2.74/3.10 litapriori = 0
% 2.74/3.10 termapriori = 1
% 2.74/3.10 litaposteriori = 0
% 2.74/3.10 termaposteriori = 0
% 2.74/3.10 demodaposteriori = 0
% 2.74/3.10 ordereqreflfact = 0
% 2.74/3.10
% 2.74/3.10 litselect = negord
% 2.74/3.10
% 2.74/3.10 maxweight = 15
% 2.74/3.10 maxdepth = 30000
% 2.74/3.10 maxlength = 115
% 2.74/3.10 maxnrvars = 195
% 2.74/3.10 excuselevel = 1
% 2.74/3.10 increasemaxweight = 1
% 2.74/3.10
% 2.74/3.10 maxselected = 10000000
% 2.74/3.10 maxnrclauses = 10000000
% 2.74/3.10
% 2.74/3.10 showgenerated = 0
% 2.74/3.10 showkept = 0
% 2.74/3.10 showselected = 0
% 2.74/3.10 showdeleted = 0
% 2.74/3.10 showresimp = 1
% 2.74/3.10 showstatus = 2000
% 2.74/3.10
% 2.74/3.10 prologoutput = 0
% 2.74/3.10 nrgoals = 5000000
% 2.74/3.10 totalproof = 1
% 2.74/3.10
% 2.74/3.10 Symbols occurring in the translation:
% 2.74/3.10
% 2.74/3.10 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 2.74/3.10 . [1, 2] (w:1, o:29, a:1, s:1, b:0),
% 2.74/3.10 ! [4, 1] (w:0, o:17, a:1, s:1, b:0),
% 2.74/3.10 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 2.74/3.10 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 2.74/3.10 addition [37, 2] (w:1, o:53, a:1, s:1, b:0),
% 2.74/3.10 zero [39, 0] (w:1, o:9, a:1, s:1, b:0),
% 2.74/3.10 multiplication [40, 2] (w:1, o:55, a:1, s:1, b:0),
% 2.74/3.10 one [41, 0] (w:1, o:10, a:1, s:1, b:0),
% 2.74/3.10 leq [42, 2] (w:1, o:54, a:1, s:1, b:0),
% 2.74/3.10 antidomain [44, 1] (w:1, o:22, a:1, s:1, b:0),
% 2.74/3.10 domain [46, 1] (w:1, o:26, a:1, s:1, b:0),
% 2.74/3.10 coantidomain [47, 1] (w:1, o:23, a:1, s:1, b:0),
% 2.74/3.10 codomain [48, 1] (w:1, o:24, a:1, s:1, b:0),
% 2.74/3.10 c [49, 1] (w:1, o:25, a:1, s:1, b:0),
% 2.74/3.10 domain_difference [50, 2] (w:1, o:56, a:1, s:1, b:0),
% 2.74/3.10 forward_diamond [51, 2] (w:1, o:57, a:1, s:1, b:0),
% 2.74/3.10 backward_diamond [52, 2] (w:1, o:58, a:1, s:1, b:0),
% 2.74/3.10 forward_box [53, 2] (w:1, o:59, a:1, s:1, b:0),
% 2.74/3.10 backward_box [54, 2] (w:1, o:60, a:1, s:1, b:0),
% 2.74/3.10 divergence [55, 1] (w:1, o:27, a:1, s:1, b:0),
% 2.74/3.10 star [57, 1] (w:1, o:28, a:1, s:1, b:0),
% 2.74/3.10 skol1 [59, 0] (w:1, o:15, a:1, s:1, b:1),
% 2.74/3.10 skol2 [60, 0] (w:1, o:16, a:1, s:1, b:1).
% 2.74/3.10
% 2.74/3.10
% 2.74/3.10 Starting Search:
% 2.74/3.10
% 2.74/3.10 *** allocated 15000 integers for clauses
% 2.74/3.10 *** allocated 22500 integers for clauses
% 2.74/3.10 *** allocated 33750 integers for clauses
% 2.74/3.10 *** allocated 50625 integers for clauses
% 2.74/3.10 *** allocated 75937 integers for clauses
% 2.74/3.10 *** allocated 15000 integers for termspace/termends
% 2.74/3.10 *** allocated 113905 integers for clauses
% 2.74/3.10 Resimplifying inuse:
% 2.74/3.10 Done
% 2.74/3.10
% 2.74/3.10 *** allocated 22500 integers for termspace/termends
% 2.74/3.10 *** allocated 170857 integers for clauses
% 2.74/3.10 *** allocated 33750 integers for termspace/termends
% 2.74/3.10
% 2.74/3.10 Intermediate Status:
% 2.74/3.10 Generated: 16468
% 2.74/3.10 Kept: 2019
% 2.74/3.10 Inuse: 306
% 2.74/3.10 Deleted: 43
% 2.74/3.10 Deletedinuse: 17
% 2.74/3.10
% 2.74/3.10 Resimplifying inuse:
% 2.74/3.10 Done
% 2.74/3.10
% 2.74/3.10 *** allocated 256285 integers for clauses
% 2.74/3.10 *** allocated 50625 integers for termspace/termends
% 2.74/3.10 Resimplifying inuse:
% 2.74/3.10 Done
% 2.74/3.10
% 2.74/3.10
% 2.74/3.10 Intermediate Status:
% 2.74/3.10 Generated: 37588
% 2.74/3.10 Kept: 4037
% 2.74/3.10 Inuse: 502
% 2.74/3.10 Deleted: 162
% 2.74/3.10 Deletedinuse: 69
% 2.74/3.10
% 2.74/3.10 Resimplifying inuse:
% 2.74/3.10 Done
% 2.74/3.10
% 2.74/3.10 *** allocated 384427 integers for clauses
% 2.74/3.10 *** allocated 75937 integers for termspace/termends
% 2.74/3.10 Resimplifying inuse:
% 2.74/3.10 Done
% 2.74/3.10
% 2.74/3.10
% 2.74/3.10 Intermediate Status:
% 2.74/3.10 Generated: 69439
% 2.74/3.10 Kept: 6074
% 2.74/3.10 Inuse: 677
% 2.74/3.10 Deleted: 179
% 2.74/3.10 Deletedinuse: 69
% 2.74/3.10
% 2.74/3.10 Resimplifying inuse:
% 2.74/3.10 Done
% 2.74/3.10
% 2.74/3.10 *** allocated 113905 integers for termspace/termends
% 2.74/3.10 *** allocated 576640 integers for clauses
% 2.74/3.10 Resimplifying inuse:
% 2.74/3.10 Done
% 2.74/3.10
% 2.74/3.10
% 2.74/3.10 Intermediate Status:
% 2.74/3.10 Generated: 89201
% 2.74/3.10 Kept: 8088
% 2.74/3.10 Inuse: 831
% 2.74/3.10 Deleted: 191
% 2.74/3.10 Deletedinuse: 70
% 2.74/3.10
% 2.74/3.10 Resimplifying inuse:
% 2.74/3.10 Done
% 2.74/3.10
% 2.74/3.10 Resimplifying inuse:
% 2.74/3.10 Done
% 2.74/3.10
% 2.74/3.10 *** allocated 170857 integers for termspace/termends
% 2.74/3.10
% 2.74/3.10 Intermediate Status:
% 2.74/3.10 Generated: 109372
% 2.74/3.10 Kept: 10088
% 2.74/3.10 Inuse: 941
% 2.74/3.10 Deleted: 215
% 2.74/3.10 Deletedinuse: 71
% 2.74/3.10
% 2.74/3.10 Resimplifying inuse:
% 2.74/3.10 Done
% 2.74/3.10
% 2.74/3.10 *** allocated 864960 integers for clauses
% 2.74/3.10 Resimplifying inuse:
% 2.74/3.10 Done
% 2.74/3.10
% 2.74/3.10
% 2.74/3.10 Intermediate Status:
% 2.74/3.10 Generated: 142018
% 2.74/3.10 Kept: 12206
% 2.74/3.10 Inuse: 1133
% 2.74/3.10 Deleted: 267
% 2.74/3.10 Deletedinuse: 72
% 2.74/3.10
% 2.74/3.10 Resimplifying inuse:
% 2.74/3.10 Done
% 2.74/3.10
% 2.74/3.10
% 2.74/3.10 Bliksems!, er is een bewijs:
% 2.74/3.10 % SZS status Theorem
% 2.74/3.10 % SZS output start Refutation
% 2.74/3.10
% 2.74/3.10 (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X ) }.
% 2.74/3.10 (1) {G0,W11,D4,L1,V3,M1} I { addition( Z, addition( Y, X ) ) ==> addition(
% 2.74/3.10 addition( Z, Y ), X ) }.
% 2.74/3.10 (2) {G0,W5,D3,L1,V1,M1} I { addition( X, zero ) ==> X }.
% 2.74/3.10 (3) {G0,W5,D3,L1,V1,M1} I { addition( X, X ) ==> X }.
% 2.74/3.10 (5) {G0,W5,D3,L1,V1,M1} I { multiplication( X, one ) ==> X }.
% 2.74/3.10 (6) {G0,W5,D3,L1,V1,M1} I { multiplication( one, X ) ==> X }.
% 2.74/3.10 (7) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Y ),
% 2.74/3.10 multiplication( X, Z ) ) ==> multiplication( X, addition( Y, Z ) ) }.
% 2.74/3.10 (8) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Z ),
% 2.74/3.10 multiplication( Y, Z ) ) ==> multiplication( addition( X, Y ), Z ) }.
% 2.74/3.10 (9) {G0,W5,D3,L1,V1,M1} I { multiplication( X, zero ) ==> zero }.
% 2.74/3.10 (10) {G0,W5,D3,L1,V1,M1} I { multiplication( zero, X ) ==> zero }.
% 2.74/3.10 (11) {G0,W8,D3,L2,V2,M2} I { ! leq( X, Y ), addition( X, Y ) ==> Y }.
% 2.74/3.10 (12) {G0,W8,D3,L2,V2,M2} I { ! addition( X, Y ) ==> Y, leq( X, Y ) }.
% 2.74/3.10 (13) {G0,W6,D4,L1,V1,M1} I { multiplication( antidomain( X ), X ) ==> zero
% 2.74/3.10 }.
% 2.74/3.10 (15) {G0,W8,D5,L1,V1,M1} I { addition( antidomain( antidomain( X ) ),
% 2.74/3.10 antidomain( X ) ) ==> one }.
% 2.74/3.10 (16) {G0,W6,D4,L1,V1,M1} I { antidomain( antidomain( X ) ) ==> domain( X )
% 2.74/3.10 }.
% 2.74/3.10 (17) {G0,W6,D4,L1,V1,M1} I { multiplication( X, coantidomain( X ) ) ==>
% 2.74/3.10 zero }.
% 2.74/3.10 (19) {G0,W8,D5,L1,V1,M1} I { addition( coantidomain( coantidomain( X ) ),
% 2.74/3.10 coantidomain( X ) ) ==> one }.
% 2.74/3.10 (20) {G0,W6,D4,L1,V1,M1} I { coantidomain( coantidomain( X ) ) ==> codomain
% 2.74/3.10 ( X ) }.
% 2.74/3.10 (21) {G0,W6,D4,L1,V1,M1} I { antidomain( domain( X ) ) ==> c( X ) }.
% 2.74/3.10 (22) {G0,W9,D4,L1,V2,M1} I { multiplication( domain( X ), antidomain( Y ) )
% 2.74/3.10 ==> domain_difference( X, Y ) }.
% 2.74/3.10 (23) {G0,W9,D5,L1,V2,M1} I { domain( multiplication( X, domain( Y ) ) ) ==>
% 2.74/3.10 forward_diamond( X, Y ) }.
% 2.74/3.10 (29) {G0,W24,D7,L1,V1,M1} I { addition( domain( X ), forward_diamond( star
% 2.74/3.10 ( skol1 ), domain_difference( domain( X ), forward_diamond( skol1, domain
% 2.74/3.10 ( X ) ) ) ) ) ==> forward_diamond( star( skol1 ), domain_difference(
% 2.74/3.10 domain( X ), forward_diamond( skol1, domain( X ) ) ) ) }.
% 2.74/3.10 (30) {G0,W11,D5,L1,V1,M1} I { forward_diamond( skol1, forward_diamond(
% 2.74/3.10 skol1, domain( X ) ) ) ==> forward_diamond( skol1, domain( X ) ) }.
% 2.74/3.10 (31) {G0,W26,D7,L1,V0,M1} I { ! addition( forward_diamond( skol1, domain(
% 2.74/3.10 skol2 ) ), forward_diamond( star( skol1 ), domain_difference( domain(
% 2.74/3.10 skol2 ), forward_diamond( skol1, domain( skol2 ) ) ) ) ) ==>
% 2.74/3.10 forward_diamond( star( skol1 ), domain_difference( domain( skol2 ),
% 2.74/3.10 forward_diamond( skol1, domain( skol2 ) ) ) ) }.
% 2.74/3.10 (32) {G1,W5,D3,L1,V1,M1} P(2,0) { addition( zero, X ) ==> X }.
% 2.74/3.10 (37) {G1,W9,D4,L1,V2,M1} P(3,1) { addition( addition( Y, X ), X ) ==>
% 2.74/3.10 addition( Y, X ) }.
% 2.74/3.10 (38) {G1,W7,D4,L1,V1,M1} P(20,17) { multiplication( coantidomain( X ),
% 2.74/3.10 codomain( X ) ) ==> zero }.
% 2.74/3.10 (39) {G1,W4,D3,L1,V0,M1} P(17,6) { coantidomain( one ) ==> zero }.
% 2.74/3.10 (40) {G2,W5,D3,L1,V0,M1} P(39,20) { codomain( one ) ==> coantidomain( zero
% 2.74/3.10 ) }.
% 2.74/3.10 (41) {G1,W6,D4,L1,V1,M1} P(16,16);d(21) { domain( antidomain( X ) ) ==> c(
% 2.74/3.10 X ) }.
% 2.74/3.10 (42) {G1,W7,D4,L1,V1,M1} P(21,16) { domain( domain( X ) ) ==> antidomain( c
% 2.74/3.10 ( X ) ) }.
% 2.74/3.10 (48) {G1,W5,D3,L1,V1,M1} P(16,13);d(22) { domain_difference( X, X ) ==>
% 2.74/3.10 zero }.
% 2.74/3.10 (50) {G1,W4,D3,L1,V0,M1} P(13,5) { antidomain( one ) ==> zero }.
% 2.74/3.10 (51) {G2,W5,D3,L1,V0,M1} P(50,41) { domain( zero ) ==> c( one ) }.
% 2.74/3.10 (52) {G2,W5,D3,L1,V0,M1} P(50,16) { domain( one ) ==> antidomain( zero )
% 2.74/3.10 }.
% 2.74/3.10 (53) {G2,W11,D4,L1,V2,M1} P(13,7);d(32) { multiplication( antidomain( X ),
% 2.74/3.10 addition( X, Y ) ) ==> multiplication( antidomain( X ), Y ) }.
% 2.74/3.10 (57) {G2,W10,D5,L1,V2,M1} P(17,7);d(32) { multiplication( X, addition(
% 2.74/3.10 coantidomain( X ), Y ) ) ==> multiplication( X, Y ) }.
% 2.74/3.10 (71) {G2,W10,D5,L1,V2,M1} P(13,8);d(32) { multiplication( addition(
% 2.74/3.10 antidomain( X ), Y ), X ) ==> multiplication( Y, X ) }.
% 2.74/3.10 (92) {G1,W6,D2,L2,V1,M2} P(11,2) { zero = X, ! leq( X, zero ) }.
% 2.74/3.10 (94) {G2,W9,D2,L3,V2,M3} P(92,92) { X = Y, ! leq( Y, X ), ! leq( X, zero )
% 2.74/3.10 }.
% 2.74/3.10 (117) {G2,W10,D3,L2,V2,M2} P(92,0) { addition( Y, X ) ==> zero, ! leq(
% 2.74/3.10 addition( X, Y ), zero ) }.
% 2.74/3.10 (134) {G2,W6,D2,L2,V1,M2} R(12,92);d(2) { zero = X, ! X = zero }.
% 2.74/3.10 (135) {G2,W3,D2,L1,V1,M1} R(12,32) { leq( zero, X ) }.
% 2.74/3.10 (143) {G1,W8,D3,L2,V2,M2} P(0,12) { ! addition( Y, X ) ==> Y, leq( X, Y )
% 2.74/3.10 }.
% 2.74/3.10 (145) {G3,W6,D2,L2,V2,M2} P(92,135) { leq( X, Y ), ! leq( X, zero ) }.
% 2.74/3.10 (146) {G4,W6,D2,L2,V2,M2} R(145,12);d(2) { leq( X, Y ), ! X = zero }.
% 2.74/3.10 (180) {G1,W7,D4,L1,V1,M1} S(15);d(16) { addition( domain( X ), antidomain(
% 2.74/3.10 X ) ) ==> one }.
% 2.74/3.10 (189) {G3,W4,D3,L1,V0,M1} P(52,180);d(50);d(2) { antidomain( zero ) ==> one
% 2.74/3.10 }.
% 2.74/3.10 (193) {G2,W7,D4,L1,V1,M1} P(180,0) { addition( antidomain( X ), domain( X )
% 2.74/3.10 ) ==> one }.
% 2.74/3.10 (198) {G4,W4,D3,L1,V0,M1} P(189,16);d(50);d(51) { c( one ) ==> zero }.
% 2.74/3.10 (202) {G1,W7,D4,L1,V1,M1} S(19);d(20) { addition( codomain( X ),
% 2.74/3.10 coantidomain( X ) ) ==> one }.
% 2.74/3.10 (218) {G4,W6,D3,L1,V1,M1} P(189,22);d(5) { domain_difference( X, zero ) ==>
% 2.74/3.10 domain( X ) }.
% 2.74/3.10 (232) {G2,W10,D4,L1,V2,M1} P(41,22) { multiplication( c( X ), antidomain( Y
% 2.74/3.10 ) ) ==> domain_difference( antidomain( X ), Y ) }.
% 2.74/3.10 (254) {G5,W5,D3,L1,V1,M1} P(51,23);d(198);d(9);d(51);d(198) {
% 2.74/3.10 forward_diamond( X, zero ) ==> zero }.
% 2.74/3.10 (341) {G3,W4,D3,L1,V0,M1} P(40,202);d(39);d(2) { coantidomain( zero ) ==>
% 2.74/3.10 one }.
% 2.74/3.10 (344) {G2,W7,D4,L1,V1,M1} P(202,0) { addition( coantidomain( X ), codomain
% 2.74/3.10 ( X ) ) ==> one }.
% 2.74/3.10 (348) {G4,W4,D3,L1,V0,M1} P(341,38);d(6) { codomain( zero ) ==> zero }.
% 2.74/3.10 (368) {G1,W29,D7,L1,V2,M1} P(23,29) { addition( forward_diamond( X, Y ),
% 2.74/3.10 forward_diamond( star( skol1 ), domain_difference( forward_diamond( X, Y
% 2.74/3.10 ), forward_diamond( skol1, forward_diamond( X, Y ) ) ) ) ) ==>
% 2.74/3.10 forward_diamond( star( skol1 ), domain_difference( forward_diamond( X, Y
% 2.74/3.10 ), forward_diamond( skol1, forward_diamond( X, Y ) ) ) ) }.
% 2.74/3.10 (420) {G5,W6,D4,L1,V0,M1} P(134,31);d(32);d(218);d(42);q { !
% 2.74/3.10 forward_diamond( skol1, domain( skol2 ) ) ==> zero }.
% 2.74/3.10 (571) {G3,W7,D4,L1,V1,M1} P(180,53);d(5);d(21);d(232) { domain_difference(
% 2.74/3.10 antidomain( X ), X ) ==> c( X ) }.
% 2.74/3.10 (643) {G3,W6,D4,L1,V1,M1} P(344,57);d(5) { multiplication( X, codomain( X )
% 2.74/3.10 ) ==> X }.
% 2.74/3.10 (655) {G4,W7,D3,L2,V1,M2} P(134,643);d(9) { ! codomain( X ) ==> zero, zero
% 2.74/3.10 = X }.
% 2.74/3.10 (753) {G5,W7,D3,L2,V2,M2} P(655,135) { leq( X, Y ), ! codomain( X ) ==>
% 2.74/3.10 zero }.
% 2.74/3.10 (989) {G6,W7,D3,L2,V2,M2} P(92,753);q { leq( X, Y ), ! leq( codomain( X ),
% 2.74/3.10 zero ) }.
% 2.74/3.10 (1015) {G5,W4,D3,L1,V0,M1} S(51);d(198) { domain( zero ) ==> zero }.
% 2.74/3.10 (1076) {G3,W6,D4,L1,V1,M1} P(193,71);d(6) { multiplication( domain( X ), X
% 2.74/3.10 ) ==> X }.
% 2.74/3.10 (1090) {G4,W5,D3,L1,V1,M1} P(1076,22);d(571) { c( X ) ==> antidomain( X )
% 2.74/3.10 }.
% 2.74/3.10 (1091) {G4,W7,D3,L2,V1,M2} P(134,1076);d(10) { ! domain( X ) ==> zero, zero
% 2.74/3.10 = X }.
% 2.74/3.10 (1245) {G5,W7,D3,L2,V2,M2} P(1091,135) { leq( X, Y ), ! domain( X ) ==>
% 2.74/3.10 zero }.
% 2.74/3.10 (2023) {G5,W6,D4,L1,V1,M1} S(42);d(1090);d(16) { domain( domain( X ) ) ==>
% 2.74/3.10 domain( X ) }.
% 2.74/3.10 (2044) {G6,W8,D4,L1,V2,M1} P(2023,23);d(23) { forward_diamond( Y, domain( X
% 2.74/3.10 ) ) ==> forward_diamond( Y, X ) }.
% 2.74/3.10 (2099) {G7,W8,D3,L2,V1,M2} P(94,420);d(2044);r(146) { ! X = zero, ! leq(
% 2.74/3.10 forward_diamond( skol1, skol2 ), X ) }.
% 2.74/3.10 (2142) {G8,W5,D3,L1,V0,M1} Q(2099) { ! leq( forward_diamond( skol1, skol2 )
% 2.74/3.10 , zero ) }.
% 2.74/3.10 (2144) {G9,W6,D4,L1,V0,M1} R(2142,989) { ! leq( codomain( forward_diamond(
% 2.74/3.10 skol1, skol2 ) ), zero ) }.
% 2.74/3.10 (2151) {G10,W7,D5,L1,V0,M1} R(2144,1245) { ! domain( codomain(
% 2.74/3.10 forward_diamond( skol1, skol2 ) ) ) ==> zero }.
% 2.74/3.10 (2528) {G3,W8,D3,L2,V2,M2} P(117,37);d(32) { ! leq( addition( Y, X ), zero
% 2.74/3.10 ), Y = zero }.
% 2.74/3.10 (2676) {G11,W7,D4,L1,V1,M1} P(2528,2151);d(348);d(1015);q { ! leq( addition
% 2.74/3.10 ( forward_diamond( skol1, skol2 ), X ), zero ) }.
% 2.74/3.10 (3037) {G7,W9,D4,L1,V1,M1} S(30);d(2044) { forward_diamond( skol1,
% 2.74/3.10 forward_diamond( skol1, X ) ) ==> forward_diamond( skol1, X ) }.
% 2.74/3.10 (4693) {G12,W7,D4,L1,V1,M1} R(2676,143);d(1);d(32) { ! addition(
% 2.74/3.10 forward_diamond( skol1, skol2 ), X ) ==> zero }.
% 2.74/3.10 (13019) {G13,W0,D0,L0,V0,M0} P(368,4693);d(3037);d(48);d(254);q { }.
% 2.74/3.10
% 2.74/3.10
% 2.74/3.10 % SZS output end Refutation
% 2.74/3.10 found a proof!
% 2.74/3.10
% 2.74/3.10
% 2.74/3.10 Unprocessed initial clauses:
% 2.74/3.10
% 2.74/3.10 (13021) {G0,W7,D3,L1,V2,M1} { addition( X, Y ) = addition( Y, X ) }.
% 2.74/3.10 (13022) {G0,W11,D4,L1,V3,M1} { addition( Z, addition( Y, X ) ) = addition
% 2.74/3.10 ( addition( Z, Y ), X ) }.
% 2.74/3.10 (13023) {G0,W5,D3,L1,V1,M1} { addition( X, zero ) = X }.
% 2.74/3.10 (13024) {G0,W5,D3,L1,V1,M1} { addition( X, X ) = X }.
% 2.74/3.10 (13025) {G0,W11,D4,L1,V3,M1} { multiplication( X, multiplication( Y, Z ) )
% 2.74/3.10 = multiplication( multiplication( X, Y ), Z ) }.
% 2.74/3.10 (13026) {G0,W5,D3,L1,V1,M1} { multiplication( X, one ) = X }.
% 2.74/3.10 (13027) {G0,W5,D3,L1,V1,M1} { multiplication( one, X ) = X }.
% 2.74/3.10 (13028) {G0,W13,D4,L1,V3,M1} { multiplication( X, addition( Y, Z ) ) =
% 2.74/3.10 addition( multiplication( X, Y ), multiplication( X, Z ) ) }.
% 2.74/3.10 (13029) {G0,W13,D4,L1,V3,M1} { multiplication( addition( X, Y ), Z ) =
% 2.74/3.10 addition( multiplication( X, Z ), multiplication( Y, Z ) ) }.
% 2.74/3.10 (13030) {G0,W5,D3,L1,V1,M1} { multiplication( X, zero ) = zero }.
% 2.74/3.10 (13031) {G0,W5,D3,L1,V1,M1} { multiplication( zero, X ) = zero }.
% 2.74/3.10 (13032) {G0,W8,D3,L2,V2,M2} { ! leq( X, Y ), addition( X, Y ) = Y }.
% 2.74/3.10 (13033) {G0,W8,D3,L2,V2,M2} { ! addition( X, Y ) = Y, leq( X, Y ) }.
% 2.74/3.10 (13034) {G0,W6,D4,L1,V1,M1} { multiplication( antidomain( X ), X ) = zero
% 2.74/3.10 }.
% 2.74/3.10 (13035) {G0,W18,D7,L1,V2,M1} { addition( antidomain( multiplication( X, Y
% 2.74/3.10 ) ), antidomain( multiplication( X, antidomain( antidomain( Y ) ) ) ) )
% 2.74/3.10 = antidomain( multiplication( X, antidomain( antidomain( Y ) ) ) ) }.
% 2.74/3.10 (13036) {G0,W8,D5,L1,V1,M1} { addition( antidomain( antidomain( X ) ),
% 2.74/3.10 antidomain( X ) ) = one }.
% 2.74/3.10 (13037) {G0,W6,D4,L1,V1,M1} { domain( X ) = antidomain( antidomain( X ) )
% 2.74/3.10 }.
% 2.74/3.10 (13038) {G0,W6,D4,L1,V1,M1} { multiplication( X, coantidomain( X ) ) =
% 2.74/3.10 zero }.
% 2.74/3.10 (13039) {G0,W18,D7,L1,V2,M1} { addition( coantidomain( multiplication( X,
% 2.74/3.10 Y ) ), coantidomain( multiplication( coantidomain( coantidomain( X ) ), Y
% 2.74/3.10 ) ) ) = coantidomain( multiplication( coantidomain( coantidomain( X ) )
% 2.74/3.10 , Y ) ) }.
% 2.74/3.10 (13040) {G0,W8,D5,L1,V1,M1} { addition( coantidomain( coantidomain( X ) )
% 2.74/3.10 , coantidomain( X ) ) = one }.
% 2.74/3.10 (13041) {G0,W6,D4,L1,V1,M1} { codomain( X ) = coantidomain( coantidomain(
% 2.74/3.10 X ) ) }.
% 2.74/3.10 (13042) {G0,W6,D4,L1,V1,M1} { c( X ) = antidomain( domain( X ) ) }.
% 2.74/3.10 (13043) {G0,W9,D4,L1,V2,M1} { domain_difference( X, Y ) = multiplication(
% 2.74/3.10 domain( X ), antidomain( Y ) ) }.
% 2.74/3.10 (13044) {G0,W9,D5,L1,V2,M1} { forward_diamond( X, Y ) = domain(
% 2.74/3.10 multiplication( X, domain( Y ) ) ) }.
% 2.74/3.10 (13045) {G0,W9,D5,L1,V2,M1} { backward_diamond( X, Y ) = codomain(
% 2.74/3.10 multiplication( codomain( Y ), X ) ) }.
% 2.74/3.10 (13046) {G0,W9,D5,L1,V2,M1} { forward_box( X, Y ) = c( forward_diamond( X
% 2.74/3.10 , c( Y ) ) ) }.
% 2.74/3.10 (13047) {G0,W9,D5,L1,V2,M1} { backward_box( X, Y ) = c( backward_diamond(
% 2.74/3.10 X, c( Y ) ) ) }.
% 2.74/3.10 (13048) {G0,W7,D4,L1,V1,M1} { forward_diamond( X, divergence( X ) ) =
% 2.74/3.10 divergence( X ) }.
% 2.74/3.10 (13049) {G0,W38,D6,L2,V3,M2} { ! addition( domain( X ), addition(
% 2.74/3.10 forward_diamond( Y, domain( X ) ), domain( Z ) ) ) = addition(
% 2.74/3.10 forward_diamond( Y, domain( X ) ), domain( Z ) ), addition( domain( X ),
% 2.74/3.10 addition( divergence( Y ), forward_diamond( star( Y ), domain( Z ) ) ) )
% 2.74/3.10 = addition( divergence( Y ), forward_diamond( star( Y ), domain( Z ) ) )
% 2.74/3.10 }.
% 2.74/3.10 (13050) {G0,W24,D7,L1,V1,M1} { addition( domain( X ), forward_diamond(
% 2.74/3.10 star( skol1 ), domain_difference( domain( X ), forward_diamond( skol1,
% 2.74/3.10 domain( X ) ) ) ) ) = forward_diamond( star( skol1 ), domain_difference(
% 2.74/3.10 domain( X ), forward_diamond( skol1, domain( X ) ) ) ) }.
% 2.74/3.10 (13051) {G0,W11,D5,L1,V1,M1} { forward_diamond( skol1, forward_diamond(
% 2.74/3.10 skol1, domain( X ) ) ) = forward_diamond( skol1, domain( X ) ) }.
% 2.74/3.10 (13052) {G0,W26,D7,L1,V0,M1} { ! addition( forward_diamond( skol1, domain
% 2.74/3.10 ( skol2 ) ), forward_diamond( star( skol1 ), domain_difference( domain(
% 2.74/3.10 skol2 ), forward_diamond( skol1, domain( skol2 ) ) ) ) ) =
% 2.74/3.10 forward_diamond( star( skol1 ), domain_difference( domain( skol2 ),
% 2.74/3.10 forward_diamond( skol1, domain( skol2 ) ) ) ) }.
% 2.74/3.10
% 2.74/3.10
% 2.74/3.10 Total Proof:
% 2.74/3.10
% 2.74/3.10 subsumption: (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X
% 2.74/3.10 ) }.
% 2.74/3.10 parent0: (13021) {G0,W7,D3,L1,V2,M1} { addition( X, Y ) = addition( Y, X )
% 2.74/3.10 }.
% 2.74/3.10 substitution0:
% 2.74/3.10 X := X
% 2.74/3.10 Y := Y
% 2.74/3.10 end
% 2.74/3.10 permutation0:
% 2.74/3.10 0 ==> 0
% 2.74/3.10 end
% 2.74/3.10
% 2.74/3.10 subsumption: (1) {G0,W11,D4,L1,V3,M1} I { addition( Z, addition( Y, X ) )
% 2.74/3.10 ==> addition( addition( Z, Y ), X ) }.
% 2.74/3.10 parent0: (13022) {G0,W11,D4,L1,V3,M1} { addition( Z, addition( Y, X ) ) =
% 2.74/3.10 addition( addition( Z, Y ), X ) }.
% 2.74/3.10 substitution0:
% 2.74/3.10 X := X
% 2.74/3.10 Y := Y
% 2.74/3.10 Z := Z
% 2.74/3.10 end
% 2.74/3.10 permutation0:
% 2.74/3.10 0 ==> 0
% 2.74/3.10 end
% 2.74/3.10
% 2.74/3.10 subsumption: (2) {G0,W5,D3,L1,V1,M1} I { addition( X, zero ) ==> X }.
% 2.74/3.10 parent0: (13023) {G0,W5,D3,L1,V1,M1} { addition( X, zero ) = X }.
% 2.74/3.10 substitution0:
% 2.74/3.10 X := X
% 2.74/3.10 end
% 2.74/3.10 permutation0:
% 2.74/3.10 0 ==> 0
% 2.74/3.10 end
% 2.74/3.10
% 2.74/3.10 subsumption: (3) {G0,W5,D3,L1,V1,M1} I { addition( X, X ) ==> X }.
% 2.74/3.10 parent0: (13024) {G0,W5,D3,L1,V1,M1} { addition( X, X ) = X }.
% 2.74/3.10 substitution0:
% 2.74/3.10 X := X
% 2.74/3.10 end
% 2.74/3.10 permutation0:
% 2.74/3.10 0 ==> 0
% 2.74/3.10 end
% 2.74/3.10
% 2.74/3.10 subsumption: (5) {G0,W5,D3,L1,V1,M1} I { multiplication( X, one ) ==> X }.
% 2.74/3.10 parent0: (13026) {G0,W5,D3,L1,V1,M1} { multiplication( X, one ) = X }.
% 2.74/3.10 substitution0:
% 2.74/3.10 X := X
% 2.74/3.10 end
% 2.74/3.10 permutation0:
% 2.74/3.10 0 ==> 0
% 2.74/3.10 end
% 2.74/3.10
% 2.74/3.10 subsumption: (6) {G0,W5,D3,L1,V1,M1} I { multiplication( one, X ) ==> X }.
% 2.74/3.10 parent0: (13027) {G0,W5,D3,L1,V1,M1} { multiplication( one, X ) = X }.
% 2.74/3.10 substitution0:
% 2.74/3.10 X := X
% 2.74/3.10 end
% 2.74/3.10 permutation0:
% 2.74/3.10 0 ==> 0
% 2.74/3.10 end
% 2.74/3.10
% 2.74/3.10 eqswap: (13076) {G0,W13,D4,L1,V3,M1} { addition( multiplication( X, Y ),
% 2.74/3.10 multiplication( X, Z ) ) = multiplication( X, addition( Y, Z ) ) }.
% 2.74/3.10 parent0[0]: (13028) {G0,W13,D4,L1,V3,M1} { multiplication( X, addition( Y
% 2.74/3.10 , Z ) ) = addition( multiplication( X, Y ), multiplication( X, Z ) ) }.
% 2.74/3.10 substitution0:
% 2.74/3.10 X := X
% 2.74/3.10 Y := Y
% 2.74/3.10 Z := Z
% 2.74/3.10 end
% 2.74/3.10
% 2.74/3.10 subsumption: (7) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Y )
% 2.74/3.10 , multiplication( X, Z ) ) ==> multiplication( X, addition( Y, Z ) ) }.
% 2.74/3.10 parent0: (13076) {G0,W13,D4,L1,V3,M1} { addition( multiplication( X, Y ),
% 2.74/3.10 multiplication( X, Z ) ) = multiplication( X, addition( Y, Z ) ) }.
% 2.74/3.10 substitution0:
% 2.74/3.10 X := X
% 2.74/3.10 Y := Y
% 2.74/3.10 Z := Z
% 2.74/3.10 end
% 2.74/3.10 permutation0:
% 2.74/3.10 0 ==> 0
% 2.74/3.10 end
% 2.74/3.10
% 2.74/3.10 eqswap: (13084) {G0,W13,D4,L1,V3,M1} { addition( multiplication( X, Z ),
% 2.74/3.10 multiplication( Y, Z ) ) = multiplication( addition( X, Y ), Z ) }.
% 2.74/3.10 parent0[0]: (13029) {G0,W13,D4,L1,V3,M1} { multiplication( addition( X, Y
% 2.74/3.10 ), Z ) = addition( multiplication( X, Z ), multiplication( Y, Z ) ) }.
% 2.74/3.10 substitution0:
% 2.74/3.10 X := X
% 2.74/3.10 Y := Y
% 2.74/3.10 Z := Z
% 2.74/3.10 end
% 2.74/3.10
% 2.74/3.10 subsumption: (8) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Z )
% 2.74/3.10 , multiplication( Y, Z ) ) ==> multiplication( addition( X, Y ), Z ) }.
% 2.74/3.10 parent0: (13084) {G0,W13,D4,L1,V3,M1} { addition( multiplication( X, Z ),
% 2.74/3.10 multiplication( Y, Z ) ) = multiplication( addition( X, Y ), Z ) }.
% 2.74/3.10 substitution0:
% 2.74/3.10 X := X
% 2.74/3.10 Y := Y
% 2.74/3.10 Z := Z
% 2.74/3.10 end
% 2.74/3.10 permutation0:
% 2.74/3.10 0 ==> 0
% 2.74/3.10 end
% 2.74/3.10
% 2.74/3.10 subsumption: (9) {G0,W5,D3,L1,V1,M1} I { multiplication( X, zero ) ==> zero
% 2.74/3.10 }.
% 2.74/3.10 parent0: (13030) {G0,W5,D3,L1,V1,M1} { multiplication( X, zero ) = zero
% 2.74/3.10 }.
% 2.74/3.10 substitution0:
% 2.74/3.10 X := X
% 2.74/3.10 end
% 2.74/3.10 permutation0:
% 2.74/3.10 0 ==> 0
% 2.74/3.10 end
% 2.74/3.10
% 2.74/3.10 subsumption: (10) {G0,W5,D3,L1,V1,M1} I { multiplication( zero, X ) ==>
% 2.74/3.10 zero }.
% 2.74/3.10 parent0: (13031) {G0,W5,D3,L1,V1,M1} { multiplication( zero, X ) = zero
% 2.74/3.10 }.
% 2.74/3.10 substitution0:
% 2.74/3.10 X := X
% 2.74/3.10 end
% 2.74/3.10 permutation0:
% 2.74/3.10 0 ==> 0
% 2.74/3.10 end
% 2.74/3.10
% 2.74/3.10 subsumption: (11) {G0,W8,D3,L2,V2,M2} I { ! leq( X, Y ), addition( X, Y )
% 2.74/3.10 ==> Y }.
% 2.74/3.10 parent0: (13032) {G0,W8,D3,L2,V2,M2} { ! leq( X, Y ), addition( X, Y ) = Y
% 2.74/3.10 }.
% 2.74/3.10 substitution0:
% 2.74/3.10 X := X
% 2.74/3.10 Y := Y
% 2.74/3.10 end
% 2.74/3.10 permutation0:
% 2.74/3.10 0 ==> 0
% 2.74/3.10 1 ==> 1
% 2.74/3.10 end
% 2.74/3.10
% 2.74/3.10 subsumption: (12) {G0,W8,D3,L2,V2,M2} I { ! addition( X, Y ) ==> Y, leq( X
% 2.74/3.10 , Y ) }.
% 2.74/3.10 parent0: (13033) {G0,W8,D3,L2,V2,M2} { ! addition( X, Y ) = Y, leq( X, Y )
% 2.74/3.10 }.
% 2.74/3.10 substitution0:
% 2.74/3.10 X := X
% 2.74/3.10 Y := Y
% 2.74/3.10 end
% 2.74/3.10 permutation0:
% 2.74/3.10 0 ==> 0
% 2.74/3.10 1 ==> 1
% 2.74/3.10 end
% 2.74/3.10
% 2.74/3.10 subsumption: (13) {G0,W6,D4,L1,V1,M1} I { multiplication( antidomain( X ),
% 2.74/3.10 X ) ==> zero }.
% 2.74/3.10 parent0: (13034) {G0,W6,D4,L1,V1,M1} { multiplication( antidomain( X ), X
% 2.74/3.10 ) = zero }.
% 2.74/3.10 substitution0:
% 2.74/3.10 X := X
% 2.74/3.10 end
% 2.74/3.10 permutation0:
% 2.74/3.10 0 ==> 0
% 2.74/3.10 end
% 2.74/3.10
% 2.74/3.10 subsumption: (15) {G0,W8,D5,L1,V1,M1} I { addition( antidomain( antidomain
% 2.74/3.10 ( X ) ), antidomain( X ) ) ==> one }.
% 2.74/3.10 parent0: (13036) {G0,W8,D5,L1,V1,M1} { addition( antidomain( antidomain( X
% 2.74/3.10 ) ), antidomain( X ) ) = one }.
% 2.74/3.10 substitution0:
% 2.74/3.10 X := X
% 2.74/3.10 end
% 2.74/3.10 permutation0:
% 2.74/3.10 0 ==> 0
% 2.74/3.10 end
% 2.74/3.10
% 2.74/3.10 eqswap: (13170) {G0,W6,D4,L1,V1,M1} { antidomain( antidomain( X ) ) =
% 2.74/3.10 domain( X ) }.
% 2.74/3.10 parent0[0]: (13037) {G0,W6,D4,L1,V1,M1} { domain( X ) = antidomain(
% 2.74/3.10 antidomain( X ) ) }.
% 2.74/3.10 substitution0:
% 2.74/3.10 X := X
% 2.74/3.10 end
% 2.74/3.10
% 2.74/3.10 subsumption: (16) {G0,W6,D4,L1,V1,M1} I { antidomain( antidomain( X ) ) ==>
% 2.74/3.10 domain( X ) }.
% 2.74/3.10 parent0: (13170) {G0,W6,D4,L1,V1,M1} { antidomain( antidomain( X ) ) =
% 2.74/3.10 domain( X ) }.
% 2.74/3.10 substitution0:
% 2.74/3.10 X := X
% 2.74/3.10 end
% 2.74/3.10 permutation0:
% 2.74/3.10 0 ==> 0
% 2.74/3.10 end
% 2.74/3.10
% 2.74/3.10 subsumption: (17) {G0,W6,D4,L1,V1,M1} I { multiplication( X, coantidomain(
% 2.74/3.10 X ) ) ==> zero }.
% 2.74/3.10 parent0: (13038) {G0,W6,D4,L1,V1,M1} { multiplication( X, coantidomain( X
% 2.74/3.10 ) ) = zero }.
% 2.74/3.10 substitution0:
% 2.74/3.10 X := X
% 2.74/3.10 end
% 2.74/3.10 permutation0:
% 2.74/3.10 0 ==> 0
% 2.74/3.10 end
% 2.74/3.10
% 2.74/3.10 subsumption: (19) {G0,W8,D5,L1,V1,M1} I { addition( coantidomain(
% 2.74/3.10 coantidomain( X ) ), coantidomain( X ) ) ==> one }.
% 2.74/3.10 parent0: (13040) {G0,W8,D5,L1,V1,M1} { addition( coantidomain(
% 2.74/3.10 coantidomain( X ) ), coantidomain( X ) ) = one }.
% 2.74/3.10 substitution0:
% 2.74/3.10 X := X
% 2.74/3.10 end
% 2.74/3.10 permutation0:
% 2.74/3.10 0 ==> 0
% 2.74/3.11 end
% 2.74/3.11
% 2.74/3.11 eqswap: (13226) {G0,W6,D4,L1,V1,M1} { coantidomain( coantidomain( X ) ) =
% 2.74/3.11 codomain( X ) }.
% 2.74/3.11 parent0[0]: (13041) {G0,W6,D4,L1,V1,M1} { codomain( X ) = coantidomain(
% 2.74/3.11 coantidomain( X ) ) }.
% 2.74/3.11 substitution0:
% 2.74/3.11 X := X
% 2.74/3.11 end
% 2.74/3.11
% 2.74/3.11 subsumption: (20) {G0,W6,D4,L1,V1,M1} I { coantidomain( coantidomain( X ) )
% 2.74/3.11 ==> codomain( X ) }.
% 2.74/3.11 parent0: (13226) {G0,W6,D4,L1,V1,M1} { coantidomain( coantidomain( X ) ) =
% 2.74/3.11 codomain( X ) }.
% 2.74/3.11 substitution0:
% 2.74/3.11 X := X
% 2.74/3.11 end
% 2.74/3.11 permutation0:
% 2.74/3.11 0 ==> 0
% 2.74/3.11 end
% 2.74/3.11
% 2.74/3.11 eqswap: (13247) {G0,W6,D4,L1,V1,M1} { antidomain( domain( X ) ) = c( X )
% 2.74/3.11 }.
% 2.74/3.11 parent0[0]: (13042) {G0,W6,D4,L1,V1,M1} { c( X ) = antidomain( domain( X )
% 2.74/3.11 ) }.
% 2.74/3.11 substitution0:
% 2.74/3.11 X := X
% 2.74/3.11 end
% 2.74/3.11
% 2.74/3.11 subsumption: (21) {G0,W6,D4,L1,V1,M1} I { antidomain( domain( X ) ) ==> c(
% 2.74/3.11 X ) }.
% 2.74/3.11 parent0: (13247) {G0,W6,D4,L1,V1,M1} { antidomain( domain( X ) ) = c( X )
% 2.74/3.11 }.
% 2.74/3.11 substitution0:
% 2.74/3.11 X := X
% 2.74/3.11 end
% 2.74/3.11 permutation0:
% 2.74/3.11 0 ==> 0
% 2.74/3.11 end
% 2.74/3.11
% 2.74/3.11 eqswap: (13269) {G0,W9,D4,L1,V2,M1} { multiplication( domain( X ),
% 2.74/3.11 antidomain( Y ) ) = domain_difference( X, Y ) }.
% 2.74/3.11 parent0[0]: (13043) {G0,W9,D4,L1,V2,M1} { domain_difference( X, Y ) =
% 2.74/3.11 multiplication( domain( X ), antidomain( Y ) ) }.
% 2.74/3.11 substitution0:
% 2.74/3.11 X := X
% 2.74/3.11 Y := Y
% 2.74/3.11 end
% 2.74/3.11
% 2.74/3.11 subsumption: (22) {G0,W9,D4,L1,V2,M1} I { multiplication( domain( X ),
% 2.74/3.11 antidomain( Y ) ) ==> domain_difference( X, Y ) }.
% 2.74/3.11 parent0: (13269) {G0,W9,D4,L1,V2,M1} { multiplication( domain( X ),
% 2.74/3.11 antidomain( Y ) ) = domain_difference( X, Y ) }.
% 2.74/3.11 substitution0:
% 2.74/3.11 X := X
% 2.74/3.11 Y := Y
% 2.74/3.11 end
% 2.74/3.11 permutation0:
% 2.74/3.11 0 ==> 0
% 2.74/3.11 end
% 2.74/3.11
% 2.74/3.11 eqswap: (13292) {G0,W9,D5,L1,V2,M1} { domain( multiplication( X, domain( Y
% 2.74/3.11 ) ) ) = forward_diamond( X, Y ) }.
% 2.74/3.11 parent0[0]: (13044) {G0,W9,D5,L1,V2,M1} { forward_diamond( X, Y ) = domain
% 2.74/3.11 ( multiplication( X, domain( Y ) ) ) }.
% 2.74/3.11 substitution0:
% 2.74/3.11 X := X
% 2.74/3.11 Y := Y
% 2.74/3.11 end
% 2.74/3.11
% 2.74/3.11 subsumption: (23) {G0,W9,D5,L1,V2,M1} I { domain( multiplication( X, domain
% 2.74/3.11 ( Y ) ) ) ==> forward_diamond( X, Y ) }.
% 2.74/3.11 parent0: (13292) {G0,W9,D5,L1,V2,M1} { domain( multiplication( X, domain(
% 2.74/3.11 Y ) ) ) = forward_diamond( X, Y ) }.
% 2.74/3.11 substitution0:
% 2.74/3.11 X := X
% 2.74/3.11 Y := Y
% 2.74/3.11 end
% 2.74/3.11 permutation0:
% 2.74/3.11 0 ==> 0
% 2.74/3.11 end
% 2.74/3.11
% 2.74/3.11 subsumption: (29) {G0,W24,D7,L1,V1,M1} I { addition( domain( X ),
% 2.74/3.11 forward_diamond( star( skol1 ), domain_difference( domain( X ),
% 2.74/3.11 forward_diamond( skol1, domain( X ) ) ) ) ) ==> forward_diamond( star(
% 2.74/3.11 skol1 ), domain_difference( domain( X ), forward_diamond( skol1, domain(
% 2.74/3.11 X ) ) ) ) }.
% 2.74/3.11 parent0: (13050) {G0,W24,D7,L1,V1,M1} { addition( domain( X ),
% 2.74/3.11 forward_diamond( star( skol1 ), domain_difference( domain( X ),
% 2.74/3.11 forward_diamond( skol1, domain( X ) ) ) ) ) = forward_diamond( star(
% 2.74/3.11 skol1 ), domain_difference( domain( X ), forward_diamond( skol1, domain(
% 2.74/3.11 X ) ) ) ) }.
% 2.74/3.11 substitution0:
% 2.74/3.11 X := X
% 2.74/3.11 end
% 2.74/3.11 permutation0:
% 2.74/3.11 0 ==> 0
% 2.74/3.11 end
% 2.74/3.11
% 2.74/3.11 subsumption: (30) {G0,W11,D5,L1,V1,M1} I { forward_diamond( skol1,
% 2.74/3.11 forward_diamond( skol1, domain( X ) ) ) ==> forward_diamond( skol1,
% 2.74/3.11 domain( X ) ) }.
% 2.74/3.11 parent0: (13051) {G0,W11,D5,L1,V1,M1} { forward_diamond( skol1,
% 2.74/3.11 forward_diamond( skol1, domain( X ) ) ) = forward_diamond( skol1, domain
% 2.74/3.11 ( X ) ) }.
% 2.74/3.11 substitution0:
% 2.74/3.11 X := X
% 2.74/3.11 end
% 2.74/3.11 permutation0:
% 2.74/3.11 0 ==> 0
% 2.74/3.11 end
% 2.74/3.11
% 2.74/3.11 subsumption: (31) {G0,W26,D7,L1,V0,M1} I { ! addition( forward_diamond(
% 2.74/3.11 skol1, domain( skol2 ) ), forward_diamond( star( skol1 ),
% 2.74/3.11 domain_difference( domain( skol2 ), forward_diamond( skol1, domain( skol2
% 2.74/3.11 ) ) ) ) ) ==> forward_diamond( star( skol1 ), domain_difference( domain
% 2.74/3.11 ( skol2 ), forward_diamond( skol1, domain( skol2 ) ) ) ) }.
% 2.74/3.11 parent0: (13052) {G0,W26,D7,L1,V0,M1} { ! addition( forward_diamond( skol1
% 2.74/3.11 , domain( skol2 ) ), forward_diamond( star( skol1 ), domain_difference(
% 2.74/3.11 domain( skol2 ), forward_diamond( skol1, domain( skol2 ) ) ) ) ) =
% 2.74/3.11 forward_diamond( star( skol1 ), domain_difference( domain( skol2 ),
% 2.74/3.11 forward_diamond( skol1, domain( skol2 ) ) ) ) }.
% 2.74/3.11 substitution0:
% 2.74/3.11 end
% 2.74/3.11 permutation0:
% 2.74/3.11 0 ==> 0
% 2.74/3.11 end
% 2.74/3.11
% 2.74/3.11 eqswap: (13389) {G0,W5,D3,L1,V1,M1} { X ==> addition( X, zero ) }.
% 2.74/3.11 parent0[0]: (2) {G0,W5,D3,L1,V1,M1} I { addition( X, zero ) ==> X }.
% 2.74/3.11 substitution0:
% 2.74/3.11 X := X
% 2.74/3.11 end
% 2.74/3.11
% 2.74/3.11 paramod: (13390) {G1,W5,D3,L1,V1,M1} { X ==> addition( zero, X ) }.
% 2.74/3.11 parent0[0]: (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X )
% 2.74/3.11 }.
% 2.74/3.11 parent1[0; 2]: (13389) {G0,W5,D3,L1,V1,M1} { X ==> addition( X, zero ) }.
% 2.74/3.11 substitution0:
% 2.74/3.11 X := X
% 2.74/3.11 Y := zero
% 2.74/3.11 end
% 2.74/3.11 substitution1:
% 2.74/3.11 X := X
% 2.74/3.11 end
% 2.74/3.11
% 2.74/3.11 eqswap: (13393) {G1,W5,D3,L1,V1,M1} { addition( zero, X ) ==> X }.
% 2.74/3.11 parent0[0]: (13390) {G1,W5,D3,L1,V1,M1} { X ==> addition( zero, X ) }.
% 2.74/3.11 substitution0:
% 2.74/3.11 X := X
% 2.74/3.11 end
% 2.74/3.11
% 2.74/3.11 subsumption: (32) {G1,W5,D3,L1,V1,M1} P(2,0) { addition( zero, X ) ==> X
% 2.74/3.11 }.
% 2.74/3.11 parent0: (13393) {G1,W5,D3,L1,V1,M1} { addition( zero, X ) ==> X }.
% 2.74/3.11 substitution0:
% 2.74/3.11 X := X
% 2.74/3.11 end
% 2.74/3.11 permutation0:
% 2.74/3.11 0 ==> 0
% 2.74/3.11 end
% 2.74/3.11
% 2.74/3.11 eqswap: (13395) {G0,W11,D4,L1,V3,M1} { addition( addition( X, Y ), Z ) ==>
% 2.74/3.11 addition( X, addition( Y, Z ) ) }.
% 2.74/3.11 parent0[0]: (1) {G0,W11,D4,L1,V3,M1} I { addition( Z, addition( Y, X ) )
% 2.74/3.11 ==> addition( addition( Z, Y ), X ) }.
% 2.74/3.11 substitution0:
% 2.74/3.11 X := Z
% 2.74/3.11 Y := Y
% 2.74/3.11 Z := X
% 2.74/3.11 end
% 2.74/3.11
% 2.74/3.11 paramod: (13401) {G1,W9,D4,L1,V2,M1} { addition( addition( X, Y ), Y ) ==>
% 2.74/3.11 addition( X, Y ) }.
% 2.74/3.11 parent0[0]: (3) {G0,W5,D3,L1,V1,M1} I { addition( X, X ) ==> X }.
% 2.74/3.11 parent1[0; 8]: (13395) {G0,W11,D4,L1,V3,M1} { addition( addition( X, Y ),
% 2.74/3.11 Z ) ==> addition( X, addition( Y, Z ) ) }.
% 2.74/3.11 substitution0:
% 2.74/3.11 X := Y
% 2.74/3.11 end
% 2.74/3.11 substitution1:
% 2.74/3.11 X := X
% 2.74/3.11 Y := Y
% 2.74/3.11 Z := Y
% 2.74/3.11 end
% 2.74/3.11
% 2.74/3.11 subsumption: (37) {G1,W9,D4,L1,V2,M1} P(3,1) { addition( addition( Y, X ),
% 2.74/3.11 X ) ==> addition( Y, X ) }.
% 2.74/3.11 parent0: (13401) {G1,W9,D4,L1,V2,M1} { addition( addition( X, Y ), Y ) ==>
% 2.74/3.11 addition( X, Y ) }.
% 2.74/3.11 substitution0:
% 2.74/3.11 X := Y
% 2.74/3.11 Y := X
% 2.74/3.11 end
% 2.74/3.11 permutation0:
% 2.74/3.11 0 ==> 0
% 2.74/3.11 end
% 2.74/3.11
% 2.74/3.11 eqswap: (13407) {G0,W6,D4,L1,V1,M1} { zero ==> multiplication( X,
% 2.74/3.11 coantidomain( X ) ) }.
% 2.74/3.11 parent0[0]: (17) {G0,W6,D4,L1,V1,M1} I { multiplication( X, coantidomain( X
% 2.74/3.11 ) ) ==> zero }.
% 2.74/3.11 substitution0:
% 2.74/3.11 X := X
% 2.74/3.11 end
% 2.74/3.11
% 2.74/3.11 paramod: (13408) {G1,W7,D4,L1,V1,M1} { zero ==> multiplication(
% 2.74/3.11 coantidomain( X ), codomain( X ) ) }.
% 2.74/3.11 parent0[0]: (20) {G0,W6,D4,L1,V1,M1} I { coantidomain( coantidomain( X ) )
% 2.74/3.11 ==> codomain( X ) }.
% 2.74/3.11 parent1[0; 5]: (13407) {G0,W6,D4,L1,V1,M1} { zero ==> multiplication( X,
% 2.74/3.11 coantidomain( X ) ) }.
% 2.74/3.11 substitution0:
% 2.74/3.11 X := X
% 2.74/3.11 end
% 2.74/3.11 substitution1:
% 2.74/3.11 X := coantidomain( X )
% 2.74/3.11 end
% 2.74/3.11
% 2.74/3.11 eqswap: (13409) {G1,W7,D4,L1,V1,M1} { multiplication( coantidomain( X ),
% 2.74/3.11 codomain( X ) ) ==> zero }.
% 2.74/3.11 parent0[0]: (13408) {G1,W7,D4,L1,V1,M1} { zero ==> multiplication(
% 2.74/3.11 coantidomain( X ), codomain( X ) ) }.
% 2.74/3.11 substitution0:
% 2.74/3.11 X := X
% 2.74/3.11 end
% 2.74/3.11
% 2.74/3.11 subsumption: (38) {G1,W7,D4,L1,V1,M1} P(20,17) { multiplication(
% 2.74/3.11 coantidomain( X ), codomain( X ) ) ==> zero }.
% 2.74/3.11 parent0: (13409) {G1,W7,D4,L1,V1,M1} { multiplication( coantidomain( X ),
% 2.74/3.11 codomain( X ) ) ==> zero }.
% 2.74/3.11 substitution0:
% 2.74/3.11 X := X
% 2.74/3.11 end
% 2.74/3.11 permutation0:
% 2.74/3.11 0 ==> 0
% 2.74/3.11 end
% 2.74/3.11
% 2.74/3.11 eqswap: (13410) {G0,W6,D4,L1,V1,M1} { zero ==> multiplication( X,
% 2.74/3.11 coantidomain( X ) ) }.
% 2.74/3.11 parent0[0]: (17) {G0,W6,D4,L1,V1,M1} I { multiplication( X, coantidomain( X
% 2.74/3.11 ) ) ==> zero }.
% 2.74/3.11 substitution0:
% 2.74/3.11 X := X
% 2.74/3.11 end
% 2.74/3.11
% 2.74/3.11 paramod: (13412) {G1,W4,D3,L1,V0,M1} { zero ==> coantidomain( one ) }.
% 2.74/3.11 parent0[0]: (6) {G0,W5,D3,L1,V1,M1} I { multiplication( one, X ) ==> X }.
% 2.74/3.11 parent1[0; 2]: (13410) {G0,W6,D4,L1,V1,M1} { zero ==> multiplication( X,
% 2.74/3.11 coantidomain( X ) ) }.
% 2.74/3.11 substitution0:
% 2.74/3.11 X := coantidomain( one )
% 2.74/3.11 end
% 2.74/3.11 substitution1:
% 2.74/3.11 X := one
% 2.74/3.11 end
% 2.74/3.11
% 2.74/3.11 eqswap: (13413) {G1,W4,D3,L1,V0,M1} { coantidomain( one ) ==> zero }.
% 2.74/3.11 parent0[0]: (13412) {G1,W4,D3,L1,V0,M1} { zero ==> coantidomain( one ) }.
% 2.74/3.11 substitution0:
% 2.74/3.11 end
% 2.74/3.11
% 2.74/3.11 subsumption: (39) {G1,W4,D3,L1,V0,M1} P(17,6) { coantidomain( one ) ==>
% 2.74/3.11 zero }.
% 2.74/3.11 parent0: (13413) {G1,W4,D3,L1,V0,M1} { coantidomain( one ) ==> zero }.
% 2.74/3.11 substitution0:
% 2.74/3.11 end
% 2.74/3.11 permutation0:
% 2.74/3.11 0 ==> 0
% 2.74/3.11 end
% 2.74/3.11
% 2.74/3.11 eqswap: (13415) {G0,W6,D4,L1,V1,M1} { codomain( X ) ==> coantidomain(
% 2.74/3.11 coantidomain( X ) ) }.
% 2.74/3.11 parent0[0]: (20) {G0,W6,D4,L1,V1,M1} I { coantidomain( coantidomain( X ) )
% 2.74/3.11 ==> codomain( X ) }.
% 2.74/3.11 substitution0:
% 2.74/3.11 X := X
% 2.74/3.11 end
% 2.74/3.11
% 2.74/3.11 paramod: (13416) {G1,W5,D3,L1,V0,M1} { codomain( one ) ==> coantidomain(
% 2.74/3.11 zero ) }.
% 2.74/3.11 parent0[0]: (39) {G1,W4,D3,L1,V0,M1} P(17,6) { coantidomain( one ) ==> zero
% 2.74/3.11 }.
% 2.74/3.11 parent1[0; 4]: (13415) {G0,W6,D4,L1,V1,M1} { codomain( X ) ==>
% 2.74/3.11 coantidomain( coantidomain( X ) ) }.
% 2.74/3.11 substitution0:
% 2.74/3.11 end
% 2.74/3.11 substitution1:
% 2.74/3.11 X := one
% 2.74/3.11 end
% 2.74/3.11
% 2.74/3.11 subsumption: (40) {G2,W5,D3,L1,V0,M1} P(39,20) { codomain( one ) ==>
% 2.74/3.11 coantidomain( zero ) }.
% 2.74/3.11 parent0: (13416) {G1,W5,D3,L1,V0,M1} { codomain( one ) ==> coantidomain(
% 2.74/3.11 zero ) }.
% 2.74/3.11 substitution0:
% 2.74/3.11 end
% 2.74/3.11 permutation0:
% 2.74/3.11 0 ==> 0
% 2.74/3.11 end
% 2.74/3.11
% 2.74/3.11 eqswap: (13418) {G0,W6,D4,L1,V1,M1} { domain( X ) ==> antidomain(
% 2.74/3.11 antidomain( X ) ) }.
% 2.74/3.11 parent0[0]: (16) {G0,W6,D4,L1,V1,M1} I { antidomain( antidomain( X ) ) ==>
% 2.74/3.11 domain( X ) }.
% 2.74/3.11 substitution0:
% 2.74/3.11 X := X
% 2.74/3.11 end
% 2.74/3.11
% 2.74/3.11 paramod: (13422) {G1,W7,D4,L1,V1,M1} { domain( antidomain( X ) ) ==>
% 2.74/3.11 antidomain( domain( X ) ) }.
% 2.74/3.11 parent0[0]: (16) {G0,W6,D4,L1,V1,M1} I { antidomain( antidomain( X ) ) ==>
% 2.74/3.11 domain( X ) }.
% 2.74/3.11 parent1[0; 5]: (13418) {G0,W6,D4,L1,V1,M1} { domain( X ) ==> antidomain(
% 2.74/3.11 antidomain( X ) ) }.
% 2.74/3.11 substitution0:
% 2.74/3.11 X := X
% 2.74/3.11 end
% 2.74/3.11 substitution1:
% 2.74/3.11 X := antidomain( X )
% 2.74/3.11 end
% 2.74/3.11
% 2.74/3.11 paramod: (13423) {G1,W6,D4,L1,V1,M1} { domain( antidomain( X ) ) ==> c( X
% 2.74/3.11 ) }.
% 2.74/3.11 parent0[0]: (21) {G0,W6,D4,L1,V1,M1} I { antidomain( domain( X ) ) ==> c( X
% 2.74/3.11 ) }.
% 2.74/3.11 parent1[0; 4]: (13422) {G1,W7,D4,L1,V1,M1} { domain( antidomain( X ) ) ==>
% 2.74/3.11 antidomain( domain( X ) ) }.
% 2.74/3.11 substitution0:
% 2.74/3.11 X := X
% 2.74/3.11 end
% 2.74/3.11 substitution1:
% 2.74/3.11 X := X
% 2.74/3.11 end
% 2.74/3.11
% 2.74/3.11 subsumption: (41) {G1,W6,D4,L1,V1,M1} P(16,16);d(21) { domain( antidomain(
% 2.74/3.11 X ) ) ==> c( X ) }.
% 2.74/3.11 parent0: (13423) {G1,W6,D4,L1,V1,M1} { domain( antidomain( X ) ) ==> c( X
% 2.74/3.11 ) }.
% 2.74/3.11 substitution0:
% 2.74/3.11 X := X
% 2.74/3.11 end
% 2.74/3.11 permutation0:
% 2.74/3.11 0 ==> 0
% 2.74/3.11 end
% 2.74/3.11
% 2.74/3.11 eqswap: (13426) {G0,W6,D4,L1,V1,M1} { domain( X ) ==> antidomain(
% 2.74/3.11 antidomain( X ) ) }.
% 2.74/3.11 parent0[0]: (16) {G0,W6,D4,L1,V1,M1} I { antidomain( antidomain( X ) ) ==>
% 2.74/3.11 domain( X ) }.
% 2.74/3.11 substitution0:
% 2.74/3.11 X := X
% 2.74/3.11 end
% 2.74/3.11
% 2.74/3.11 paramod: (13427) {G1,W7,D4,L1,V1,M1} { domain( domain( X ) ) ==>
% 2.74/3.11 antidomain( c( X ) ) }.
% 2.74/3.11 parent0[0]: (21) {G0,W6,D4,L1,V1,M1} I { antidomain( domain( X ) ) ==> c( X
% 2.74/3.11 ) }.
% 2.74/3.11 parent1[0; 5]: (13426) {G0,W6,D4,L1,V1,M1} { domain( X ) ==> antidomain(
% 2.74/3.11 antidomain( X ) ) }.
% 2.74/3.11 substitution0:
% 2.74/3.11 X := X
% 2.74/3.11 end
% 2.74/3.11 substitution1:
% 2.74/3.11 X := domain( X )
% 2.74/3.11 end
% 2.74/3.11
% 2.74/3.11 subsumption: (42) {G1,W7,D4,L1,V1,M1} P(21,16) { domain( domain( X ) ) ==>
% 2.74/3.11 antidomain( c( X ) ) }.
% 2.74/3.11 parent0: (13427) {G1,W7,D4,L1,V1,M1} { domain( domain( X ) ) ==>
% 2.74/3.11 antidomain( c( X ) ) }.
% 2.74/3.11 substitution0:
% 2.74/3.11 X := X
% 2.74/3.11 end
% 2.74/3.11 permutation0:
% 2.74/3.11 0 ==> 0
% 2.74/3.11 end
% 2.74/3.11
% 2.74/3.11 eqswap: (13430) {G0,W6,D4,L1,V1,M1} { zero ==> multiplication( antidomain
% 2.74/3.11 ( X ), X ) }.
% 2.74/3.11 parent0[0]: (13) {G0,W6,D4,L1,V1,M1} I { multiplication( antidomain( X ), X
% 2.74/3.11 ) ==> zero }.
% 2.74/3.11 substitution0:
% 2.74/3.11 X := X
% 2.74/3.11 end
% 2.74/3.11
% 2.74/3.11 paramod: (13432) {G1,W7,D4,L1,V1,M1} { zero ==> multiplication( domain( X
% 2.74/3.11 ), antidomain( X ) ) }.
% 2.74/3.11 parent0[0]: (16) {G0,W6,D4,L1,V1,M1} I { antidomain( antidomain( X ) ) ==>
% 2.74/3.11 domain( X ) }.
% 2.74/3.11 parent1[0; 3]: (13430) {G0,W6,D4,L1,V1,M1} { zero ==> multiplication(
% 2.74/3.11 antidomain( X ), X ) }.
% 2.74/3.11 substitution0:
% 2.74/3.11 X := X
% 2.74/3.11 end
% 2.74/3.11 substitution1:
% 2.74/3.11 X := antidomain( X )
% 2.74/3.11 end
% 2.74/3.11
% 2.74/3.11 paramod: (13433) {G1,W5,D3,L1,V1,M1} { zero ==> domain_difference( X, X )
% 2.74/3.11 }.
% 2.74/3.11 parent0[0]: (22) {G0,W9,D4,L1,V2,M1} I { multiplication( domain( X ),
% 2.74/3.11 antidomain( Y ) ) ==> domain_difference( X, Y ) }.
% 2.74/3.11 parent1[0; 2]: (13432) {G1,W7,D4,L1,V1,M1} { zero ==> multiplication(
% 2.74/3.11 domain( X ), antidomain( X ) ) }.
% 2.74/3.11 substitution0:
% 2.74/3.11 X := X
% 2.74/3.11 Y := X
% 2.74/3.11 end
% 2.74/3.11 substitution1:
% 2.74/3.11 X := X
% 2.74/3.11 end
% 2.74/3.11
% 2.74/3.11 eqswap: (13434) {G1,W5,D3,L1,V1,M1} { domain_difference( X, X ) ==> zero
% 2.74/3.11 }.
% 2.74/3.11 parent0[0]: (13433) {G1,W5,D3,L1,V1,M1} { zero ==> domain_difference( X, X
% 2.74/3.11 ) }.
% 2.74/3.11 substitution0:
% 2.74/3.11 X := X
% 2.74/3.11 end
% 2.74/3.11
% 2.74/3.11 subsumption: (48) {G1,W5,D3,L1,V1,M1} P(16,13);d(22) { domain_difference( X
% 2.74/3.11 , X ) ==> zero }.
% 2.74/3.11 parent0: (13434) {G1,W5,D3,L1,V1,M1} { domain_difference( X, X ) ==> zero
% 2.74/3.11 }.
% 2.74/3.11 substitution0:
% 2.74/3.11 X := X
% 2.74/3.11 end
% 2.74/3.11 permutation0:
% 2.74/3.11 0 ==> 0
% 2.74/3.11 end
% 2.74/3.11
% 2.74/3.11 eqswap: (13435) {G0,W6,D4,L1,V1,M1} { zero ==> multiplication( antidomain
% 2.74/3.11 ( X ), X ) }.
% 2.74/3.11 parent0[0]: (13) {G0,W6,D4,L1,V1,M1} I { multiplication( antidomain( X ), X
% 2.74/3.11 ) ==> zero }.
% 2.74/3.11 substitution0:
% 2.74/3.11 X := X
% 2.74/3.11 end
% 2.74/3.11
% 2.74/3.11 paramod: (13437) {G1,W4,D3,L1,V0,M1} { zero ==> antidomain( one ) }.
% 2.74/3.11 parent0[0]: (5) {G0,W5,D3,L1,V1,M1} I { multiplication( X, one ) ==> X }.
% 2.74/3.11 parent1[0; 2]: (13435) {G0,W6,D4,L1,V1,M1} { zero ==> multiplication(
% 2.74/3.11 antidomain( X ), X ) }.
% 2.74/3.11 substitution0:
% 2.74/3.11 X := antidomain( one )
% 2.74/3.11 end
% 2.74/3.11 substitution1:
% 2.74/3.11 X := one
% 2.74/3.11 end
% 2.74/3.11
% 2.74/3.11 eqswap: (13438) {G1,W4,D3,L1,V0,M1} { antidomain( one ) ==> zero }.
% 2.74/3.11 parent0[0]: (13437) {G1,W4,D3,L1,V0,M1} { zero ==> antidomain( one ) }.
% 2.74/3.11 substitution0:
% 2.74/3.11 end
% 2.74/3.11
% 2.74/3.11 subsumption: (50) {G1,W4,D3,L1,V0,M1} P(13,5) { antidomain( one ) ==> zero
% 2.74/3.11 }.
% 2.74/3.11 parent0: (13438) {G1,W4,D3,L1,V0,M1} { antidomain( one ) ==> zero }.
% 2.74/3.11 substitution0:
% 2.74/3.11 end
% 2.74/3.11 permutation0:
% 2.74/3.11 0 ==> 0
% 2.74/3.11 end
% 2.74/3.11
% 2.74/3.11 eqswap: (13440) {G1,W6,D4,L1,V1,M1} { c( X ) ==> domain( antidomain( X ) )
% 2.74/3.11 }.
% 2.74/3.11 parent0[0]: (41) {G1,W6,D4,L1,V1,M1} P(16,16);d(21) { domain( antidomain( X
% 2.74/3.11 ) ) ==> c( X ) }.
% 2.74/3.11 substitution0:
% 2.74/3.11 X := X
% 2.74/3.11 end
% 2.74/3.11
% 2.74/3.11 paramod: (13441) {G2,W5,D3,L1,V0,M1} { c( one ) ==> domain( zero ) }.
% 2.74/3.11 parent0[0]: (50) {G1,W4,D3,L1,V0,M1} P(13,5) { antidomain( one ) ==> zero
% 2.74/3.11 }.
% 2.74/3.11 parent1[0; 4]: (13440) {G1,W6,D4,L1,V1,M1} { c( X ) ==> domain( antidomain
% 2.74/3.11 ( X ) ) }.
% 2.74/3.11 substitution0:
% 2.74/3.11 end
% 2.74/3.11 substitution1:
% 2.74/3.11 X := one
% 2.74/3.11 end
% 2.74/3.11
% 2.74/3.11 eqswap: (13442) {G2,W5,D3,L1,V0,M1} { domain( zero ) ==> c( one ) }.
% 2.74/3.11 parent0[0]: (13441) {G2,W5,D3,L1,V0,M1} { c( one ) ==> domain( zero ) }.
% 2.74/3.11 substitution0:
% 2.74/3.11 end
% 2.74/3.11
% 2.74/3.11 subsumption: (51) {G2,W5,D3,L1,V0,M1} P(50,41) { domain( zero ) ==> c( one
% 2.74/3.11 ) }.
% 2.74/3.11 parent0: (13442) {G2,W5,D3,L1,V0,M1} { domain( zero ) ==> c( one ) }.
% 2.74/3.11 substitution0:
% 2.74/3.11 end
% 2.74/3.11 permutation0:
% 2.74/3.11 0 ==> 0
% 2.74/3.11 end
% 2.74/3.11
% 2.74/3.11 eqswap: (13444) {G0,W6,D4,L1,V1,M1} { domain( X ) ==> antidomain(
% 2.74/3.11 antidomain( X ) ) }.
% 2.74/3.11 parent0[0]: (16) {G0,W6,D4,L1,V1,M1} I { antidomain( antidomain( X ) ) ==>
% 2.74/3.11 domain( X ) }.
% 2.74/3.11 substitution0:
% 2.74/3.11 X := X
% 2.74/3.11 end
% 2.74/3.11
% 2.74/3.11 paramod: (13445) {G1,W5,D3,L1,V0,M1} { domain( one ) ==> antidomain( zero
% 2.74/3.11 ) }.
% 2.74/3.11 parent0[0]: (50) {G1,W4,D3,L1,V0,M1} P(13,5) { antidomain( one ) ==> zero
% 2.74/3.11 }.
% 2.74/3.11 parent1[0; 4]: (13444) {G0,W6,D4,L1,V1,M1} { domain( X ) ==> antidomain(
% 2.74/3.11 antidomain( X ) ) }.
% 2.74/3.11 substitution0:
% 2.74/3.11 end
% 2.74/3.11 substitution1:
% 2.74/3.11 X := one
% 2.74/3.11 end
% 2.74/3.11
% 2.74/3.11 subsumption: (52) {G2,W5,D3,L1,V0,M1} P(50,16) { domain( one ) ==>
% 2.74/3.11 antidomain( zero ) }.
% 2.74/3.11 parent0: (13445) {G1,W5,D3,L1,V0,M1} { domain( one ) ==> antidomain( zero
% 2.74/3.11 ) }.
% 2.74/3.11 substitution0:
% 2.74/3.11 end
% 2.74/3.11 permutation0:
% 2.74/3.11 0 ==> 0
% 2.74/3.11 end
% 2.74/3.11
% 2.74/3.11 eqswap: (13448) {G0,W13,D4,L1,V3,M1} { multiplication( X, addition( Y, Z )
% 2.74/3.11 ) ==> addition( multiplication( X, Y ), multiplication( X, Z ) ) }.
% 2.74/3.11 parent0[0]: (7) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Y ),
% 2.74/3.11 multiplication( X, Z ) ) ==> multiplication( X, addition( Y, Z ) ) }.
% 2.74/3.11 substitution0:
% 2.74/3.11 X := X
% 2.74/3.11 Y := Y
% 2.74/3.11 Z := Z
% 2.74/3.11 end
% 2.74/3.11
% 2.74/3.11 paramod: (13451) {G1,W13,D5,L1,V2,M1} { multiplication( antidomain( X ),
% 2.74/3.11 addition( X, Y ) ) ==> addition( zero, multiplication( antidomain( X ), Y
% 2.74/3.11 ) ) }.
% 2.74/3.11 parent0[0]: (13) {G0,W6,D4,L1,V1,M1} I { multiplication( antidomain( X ), X
% 2.74/3.11 ) ==> zero }.
% 2.74/3.11 parent1[0; 8]: (13448) {G0,W13,D4,L1,V3,M1} { multiplication( X, addition
% 2.74/3.11 ( Y, Z ) ) ==> addition( multiplication( X, Y ), multiplication( X, Z ) )
% 2.74/3.11 }.
% 2.74/3.11 substitution0:
% 2.74/3.11 X := X
% 2.74/3.11 end
% 2.74/3.11 substitution1:
% 2.74/3.11 X := antidomain( X )
% 2.74/3.11 Y := X
% 2.74/3.11 Z := Y
% 2.74/3.11 end
% 2.74/3.11
% 2.74/3.11 paramod: (13453) {G2,W11,D4,L1,V2,M1} { multiplication( antidomain( X ),
% 2.74/3.11 addition( X, Y ) ) ==> multiplication( antidomain( X ), Y ) }.
% 2.74/3.11 parent0[0]: (32) {G1,W5,D3,L1,V1,M1} P(2,0) { addition( zero, X ) ==> X }.
% 2.74/3.11 parent1[0; 7]: (13451) {G1,W13,D5,L1,V2,M1} { multiplication( antidomain(
% 2.74/3.11 X ), addition( X, Y ) ) ==> addition( zero, multiplication( antidomain( X
% 2.74/3.11 ), Y ) ) }.
% 2.74/3.11 substitution0:
% 2.74/3.11 X := multiplication( antidomain( X ), Y )
% 2.74/3.11 end
% 2.74/3.11 substitution1:
% 2.74/3.11 X := X
% 2.74/3.11 Y := Y
% 2.74/3.11 end
% 2.74/3.11
% 2.74/3.11 subsumption: (53) {G2,W11,D4,L1,V2,M1} P(13,7);d(32) { multiplication(
% 2.74/3.11 antidomain( X ), addition( X, Y ) ) ==> multiplication( antidomain( X ),
% 2.74/3.11 Y ) }.
% 2.74/3.11 parent0: (13453) {G2,W11,D4,L1,V2,M1} { multiplication( antidomain( X ),
% 2.74/3.11 addition( X, Y ) ) ==> multiplication( antidomain( X ), Y ) }.
% 2.74/3.11 substitution0:
% 2.74/3.11 X := X
% 2.74/3.11 Y := Y
% 2.74/3.11 end
% 2.74/3.11 permutation0:
% 2.74/3.11 0 ==> 0
% 2.74/3.11 end
% 2.74/3.11
% 2.74/3.11 eqswap: (13456) {G0,W13,D4,L1,V3,M1} { multiplication( X, addition( Y, Z )
% 2.74/3.11 ) ==> addition( multiplication( X, Y ), multiplication( X, Z ) ) }.
% 2.74/3.11 parent0[0]: (7) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Y ),
% 2.74/3.11 multiplication( X, Z ) ) ==> multiplication( X, addition( Y, Z ) ) }.
% 2.74/3.11 substitution0:
% 2.74/3.11 X := X
% 2.74/3.11 Y := Y
% 2.74/3.11 Z := Z
% 2.74/3.11 end
% 2.74/3.11
% 2.74/3.11 paramod: (13458) {G1,W12,D5,L1,V2,M1} { multiplication( X, addition(
% 45.84/46.28 coantidomain( X ), Y ) ) ==> addition( zero, multiplication( X, Y ) ) }.
% 45.84/46.28 parent0[0]: (17) {G0,W6,D4,L1,V1,M1} I { multiplication( X, coantidomain( X
% 45.84/46.28 ) ) ==> zero }.
% 45.84/46.28 parent1[0; 8]: (13456) {G0,W13,D4,L1,V3,M1} { multiplication( X, addition
% 45.84/46.28 ( Y, Z ) ) ==> addition( multiplication( X, Y ), multiplication( X, Z ) )
% 45.84/46.28 }.
% 45.84/46.28 substitution0:
% 45.84/46.28 X := X
% 45.84/46.28 end
% 45.84/46.28 substitution1:
% 45.84/46.28 X := X
% 45.84/46.28 Y := coantidomain( X )
% 45.84/46.28 Z := Y
% 45.84/46.28 end
% 45.84/46.28
% 45.84/46.28 paramod: (13460) {G2,W10,D5,L1,V2,M1} { multiplication( X, addition(
% 45.84/46.28 coantidomain( X ), Y ) ) ==> multiplication( X, Y ) }.
% 45.84/46.28 parent0[0]: (32) {G1,W5,D3,L1,V1,M1} P(2,0) { addition( zero, X ) ==> X }.
% 45.84/46.28 parent1[0; 7]: (13458) {G1,W12,D5,L1,V2,M1} { multiplication( X, addition
% 45.84/46.28 ( coantidomain( X ), Y ) ) ==> addition( zero, multiplication( X, Y ) )
% 45.84/46.28 }.
% 45.84/46.28 substitution0:
% 45.84/46.28 X := multiplication( X, Y )
% 45.84/46.28 end
% 45.84/46.28 substitution1:
% 45.84/46.28 X := X
% 45.84/46.28 Y := Y
% 45.84/46.28 end
% 45.84/46.28
% 45.84/46.28 subsumption: (57) {G2,W10,D5,L1,V2,M1} P(17,7);d(32) { multiplication( X,
% 45.84/46.28 addition( coantidomain( X ), Y ) ) ==> multiplication( X, Y ) }.
% 45.84/46.28 parent0: (13460) {G2,W10,D5,L1,V2,M1} { multiplication( X, addition(
% 45.84/46.28 coantidomain( X ), Y ) ) ==> multiplication( X, Y ) }.
% 45.84/46.28 substitution0:
% 45.84/46.28 X := X
% 45.84/46.28 Y := Y
% 45.84/46.28 end
% 45.84/46.28 permutation0:
% 45.84/46.28 0 ==> 0
% 45.84/46.28 end
% 45.84/46.28
% 45.84/46.28 eqswap: (13463) {G0,W13,D4,L1,V3,M1} { multiplication( addition( X, Z ), Y
% 45.84/46.28 ) ==> addition( multiplication( X, Y ), multiplication( Z, Y ) ) }.
% 45.84/46.28 parent0[0]: (8) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Z ),
% 45.84/46.28 multiplication( Y, Z ) ) ==> multiplication( addition( X, Y ), Z ) }.
% 45.84/46.28 substitution0:
% 45.84/46.28 X := X
% 45.84/46.28 Y := Z
% 45.84/46.28 Z := Y
% 45.84/46.28 end
% 45.84/46.28
% 45.84/46.28 paramod: (13465) {G1,W12,D5,L1,V2,M1} { multiplication( addition(
% 45.84/46.28 antidomain( X ), Y ), X ) ==> addition( zero, multiplication( Y, X ) )
% 45.84/46.28 }.
% 45.84/46.28 parent0[0]: (13) {G0,W6,D4,L1,V1,M1} I { multiplication( antidomain( X ), X
% 45.84/46.28 ) ==> zero }.
% 45.84/46.28 parent1[0; 8]: (13463) {G0,W13,D4,L1,V3,M1} { multiplication( addition( X
% 45.84/46.28 , Z ), Y ) ==> addition( multiplication( X, Y ), multiplication( Z, Y ) )
% 45.84/46.28 }.
% 45.84/46.28 substitution0:
% 45.84/46.28 X := X
% 45.84/46.28 end
% 45.84/46.28 substitution1:
% 45.84/46.28 X := antidomain( X )
% 45.84/46.28 Y := X
% 45.84/46.28 Z := Y
% 45.84/46.28 end
% 45.84/46.28
% 45.84/46.28 paramod: (13467) {G2,W10,D5,L1,V2,M1} { multiplication( addition(
% 45.84/46.28 antidomain( X ), Y ), X ) ==> multiplication( Y, X ) }.
% 45.84/46.28 parent0[0]: (32) {G1,W5,D3,L1,V1,M1} P(2,0) { addition( zero, X ) ==> X }.
% 45.84/46.28 parent1[0; 7]: (13465) {G1,W12,D5,L1,V2,M1} { multiplication( addition(
% 45.84/46.28 antidomain( X ), Y ), X ) ==> addition( zero, multiplication( Y, X ) )
% 45.84/46.28 }.
% 45.84/46.28 substitution0:
% 45.84/46.28 X := multiplication( Y, X )
% 45.84/46.28 end
% 45.84/46.28 substitution1:
% 45.84/46.28 X := X
% 45.84/46.28 Y := Y
% 45.84/46.28 end
% 45.84/46.28
% 45.84/46.28 subsumption: (71) {G2,W10,D5,L1,V2,M1} P(13,8);d(32) { multiplication(
% 45.84/46.28 addition( antidomain( X ), Y ), X ) ==> multiplication( Y, X ) }.
% 45.84/46.28 parent0: (13467) {G2,W10,D5,L1,V2,M1} { multiplication( addition(
% 45.84/46.28 antidomain( X ), Y ), X ) ==> multiplication( Y, X ) }.
% 45.84/46.28 substitution0:
% 45.84/46.28 X := X
% 45.84/46.28 Y := Y
% 45.84/46.28 end
% 45.84/46.28 permutation0:
% 45.84/46.28 0 ==> 0
% 45.84/46.28 end
% 45.84/46.28
% 45.84/46.28 eqswap: (13469) {G0,W8,D3,L2,V2,M2} { Y ==> addition( X, Y ), ! leq( X, Y
% 45.84/46.28 ) }.
% 45.84/46.28 parent0[1]: (11) {G0,W8,D3,L2,V2,M2} I { ! leq( X, Y ), addition( X, Y )
% 45.84/46.28 ==> Y }.
% 45.84/46.28 substitution0:
% 45.84/46.28 X := X
% 45.84/46.28 Y := Y
% 45.84/46.28 end
% 45.84/46.28
% 45.84/46.28 paramod: (13471) {G1,W6,D2,L2,V1,M2} { zero ==> X, ! leq( X, zero ) }.
% 45.84/46.28 parent0[0]: (2) {G0,W5,D3,L1,V1,M1} I { addition( X, zero ) ==> X }.
% 45.84/46.28 parent1[0; 2]: (13469) {G0,W8,D3,L2,V2,M2} { Y ==> addition( X, Y ), ! leq
% 45.84/46.28 ( X, Y ) }.
% 45.84/46.28 substitution0:
% 45.84/46.28 X := X
% 45.84/46.28 end
% 45.84/46.28 substitution1:
% 45.84/46.28 X := X
% 45.84/46.28 Y := zero
% 45.84/46.28 end
% 45.84/46.28
% 45.84/46.28 subsumption: (92) {G1,W6,D2,L2,V1,M2} P(11,2) { zero = X, ! leq( X, zero )
% 45.84/46.28 }.
% 45.84/46.28 parent0: (13471) {G1,W6,D2,L2,V1,M2} { zero ==> X, ! leq( X, zero ) }.
% 45.84/46.28 substitution0:
% 45.84/46.28 X := X
% 45.84/46.28 end
% 45.84/46.28 permutation0:
% 45.84/46.28 0 ==> 0
% 45.84/46.28 1 ==> 1
% 45.84/46.28 end
% 45.84/46.28
% 45.84/46.28 *** allocated 256285 integers for termspace/termends
% 45.84/46.28 *** allocated 15000 integers for justifications
% 45.84/46.28 *** allocated 22500 integers for justifications
% 45.84/46.28 *** allocated 33750 integers for justifications
% 45.84/46.28 *** allocated 50625 integers for justifications
% 45.84/46.28 *** allocated 75937 integers for justifications
% 45.84/46.28 *** allocated 113905 integers for justifications
% 45.84/46.28 *** allocated 384427 integers for termspace/termends
% 45.84/46.28 *** allocated 170857 integers for justifications
% 45.84/46.28 eqswap: (13473) {G1,W6,D2,L2,V1,M2} { X = zero, ! leq( X, zero ) }.
% 45.84/46.28 parent0[0]: (92) {G1,W6,D2,L2,V1,M2} P(11,2) { zero = X, ! leq( X, zero )
% 45.84/46.29 }.
% 45.84/46.29 substitution0:
% 45.84/46.29 X := X
% 45.84/46.29 end
% 45.84/46.29
% 45.84/46.29 paramod: (13545) {G2,W9,D2,L3,V2,M3} { ! leq( X, Y ), ! leq( Y, zero ), X
% 45.84/46.29 = zero }.
% 45.84/46.29 parent0[0]: (92) {G1,W6,D2,L2,V1,M2} P(11,2) { zero = X, ! leq( X, zero )
% 45.84/46.29 }.
% 45.84/46.29 parent1[1; 3]: (13473) {G1,W6,D2,L2,V1,M2} { X = zero, ! leq( X, zero )
% 45.84/46.29 }.
% 45.84/46.29 substitution0:
% 45.84/46.29 X := Y
% 45.84/46.29 end
% 45.84/46.29 substitution1:
% 45.84/46.29 X := X
% 45.84/46.29 end
% 45.84/46.29
% 45.84/46.29 paramod: (13547) {G2,W12,D2,L4,V3,M4} { X = Y, ! leq( Y, zero ), ! leq( X
% 45.84/46.29 , Z ), ! leq( Z, zero ) }.
% 45.84/46.29 parent0[0]: (92) {G1,W6,D2,L2,V1,M2} P(11,2) { zero = X, ! leq( X, zero )
% 45.84/46.29 }.
% 45.84/46.29 parent1[2; 2]: (13545) {G2,W9,D2,L3,V2,M3} { ! leq( X, Y ), ! leq( Y, zero
% 45.84/46.29 ), X = zero }.
% 45.84/46.29 substitution0:
% 45.84/46.29 X := Y
% 45.84/46.29 end
% 45.84/46.29 substitution1:
% 45.84/46.29 X := X
% 45.84/46.29 Y := Z
% 45.84/46.29 end
% 45.84/46.29
% 45.84/46.29 eqswap: (13580) {G2,W12,D2,L4,V3,M4} { Y = X, ! leq( Y, zero ), ! leq( X,
% 45.84/46.29 Z ), ! leq( Z, zero ) }.
% 45.84/46.29 parent0[0]: (13547) {G2,W12,D2,L4,V3,M4} { X = Y, ! leq( Y, zero ), ! leq
% 45.84/46.29 ( X, Z ), ! leq( Z, zero ) }.
% 45.84/46.29 substitution0:
% 45.84/46.29 X := X
% 45.84/46.29 Y := Y
% 45.84/46.29 Z := Z
% 45.84/46.29 end
% 45.84/46.29
% 45.84/46.29 factor: (13583) {G2,W9,D2,L3,V2,M3} { X = Y, ! leq( X, zero ), ! leq( Y, X
% 45.84/46.29 ) }.
% 45.84/46.29 parent0[1, 3]: (13580) {G2,W12,D2,L4,V3,M4} { Y = X, ! leq( Y, zero ), !
% 45.84/46.29 leq( X, Z ), ! leq( Z, zero ) }.
% 45.84/46.29 substitution0:
% 45.84/46.29 X := Y
% 45.84/46.29 Y := X
% 45.84/46.29 Z := X
% 45.84/46.29 end
% 45.84/46.29
% 45.84/46.29 subsumption: (94) {G2,W9,D2,L3,V2,M3} P(92,92) { X = Y, ! leq( Y, X ), !
% 45.84/46.29 leq( X, zero ) }.
% 45.84/46.29 parent0: (13583) {G2,W9,D2,L3,V2,M3} { X = Y, ! leq( X, zero ), ! leq( Y,
% 45.84/46.29 X ) }.
% 45.84/46.29 substitution0:
% 45.84/46.29 X := X
% 45.84/46.29 Y := Y
% 45.84/46.29 end
% 45.84/46.29 permutation0:
% 45.84/46.29 0 ==> 0
% 45.84/46.29 1 ==> 2
% 45.84/46.29 2 ==> 1
% 45.84/46.29 end
% 45.84/46.29
% 45.84/46.29 eqswap: (17150) {G1,W6,D2,L2,V1,M2} { X = zero, ! leq( X, zero ) }.
% 45.84/46.29 parent0[0]: (92) {G1,W6,D2,L2,V1,M2} P(11,2) { zero = X, ! leq( X, zero )
% 45.84/46.29 }.
% 45.84/46.29 substitution0:
% 45.84/46.29 X := X
% 45.84/46.29 end
% 45.84/46.29
% 45.84/46.29 paramod: (17152) {G1,W10,D3,L2,V2,M2} { addition( X, Y ) = zero, ! leq(
% 45.84/46.29 addition( Y, X ), zero ) }.
% 45.84/46.29 parent0[0]: (17150) {G1,W6,D2,L2,V1,M2} { X = zero, ! leq( X, zero ) }.
% 45.84/46.29 parent1[0; 4]: (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y,
% 45.84/46.29 X ) }.
% 45.84/46.29 substitution0:
% 45.84/46.29 X := addition( Y, X )
% 45.84/46.29 end
% 45.84/46.29 substitution1:
% 45.84/46.29 X := X
% 45.84/46.29 Y := Y
% 45.84/46.29 end
% 45.84/46.29
% 45.84/46.29 subsumption: (117) {G2,W10,D3,L2,V2,M2} P(92,0) { addition( Y, X ) ==> zero
% 45.84/46.29 , ! leq( addition( X, Y ), zero ) }.
% 45.84/46.29 parent0: (17152) {G1,W10,D3,L2,V2,M2} { addition( X, Y ) = zero, ! leq(
% 45.84/46.29 addition( Y, X ), zero ) }.
% 45.84/46.29 substitution0:
% 45.84/46.29 X := Y
% 45.84/46.29 Y := X
% 45.84/46.29 end
% 45.84/46.29 permutation0:
% 45.84/46.29 0 ==> 0
% 45.84/46.29 1 ==> 1
% 45.84/46.29 end
% 45.84/46.29
% 45.84/46.29 eqswap: (17193) {G0,W8,D3,L2,V2,M2} { ! Y ==> addition( X, Y ), leq( X, Y
% 45.84/46.29 ) }.
% 45.84/46.29 parent0[0]: (12) {G0,W8,D3,L2,V2,M2} I { ! addition( X, Y ) ==> Y, leq( X,
% 45.84/46.29 Y ) }.
% 45.84/46.29 substitution0:
% 45.84/46.29 X := X
% 45.84/46.29 Y := Y
% 45.84/46.29 end
% 45.84/46.29
% 45.84/46.29 eqswap: (17194) {G1,W6,D2,L2,V1,M2} { X = zero, ! leq( X, zero ) }.
% 45.84/46.29 parent0[0]: (92) {G1,W6,D2,L2,V1,M2} P(11,2) { zero = X, ! leq( X, zero )
% 45.84/46.29 }.
% 45.84/46.29 substitution0:
% 45.84/46.29 X := X
% 45.84/46.29 end
% 45.84/46.29
% 45.84/46.29 resolution: (17196) {G1,W8,D3,L2,V1,M2} { X = zero, ! zero ==> addition( X
% 45.84/46.29 , zero ) }.
% 45.84/46.29 parent0[1]: (17194) {G1,W6,D2,L2,V1,M2} { X = zero, ! leq( X, zero ) }.
% 45.84/46.29 parent1[1]: (17193) {G0,W8,D3,L2,V2,M2} { ! Y ==> addition( X, Y ), leq( X
% 45.84/46.29 , Y ) }.
% 45.84/46.29 substitution0:
% 45.84/46.29 X := X
% 45.84/46.29 end
% 45.84/46.29 substitution1:
% 45.84/46.29 X := X
% 45.84/46.29 Y := zero
% 45.84/46.29 end
% 45.84/46.29
% 45.84/46.29 paramod: (17197) {G1,W6,D2,L2,V1,M2} { ! zero ==> X, X = zero }.
% 45.84/46.29 parent0[0]: (2) {G0,W5,D3,L1,V1,M1} I { addition( X, zero ) ==> X }.
% 45.84/46.29 parent1[1; 3]: (17196) {G1,W8,D3,L2,V1,M2} { X = zero, ! zero ==> addition
% 45.84/46.29 ( X, zero ) }.
% 45.84/46.29 substitution0:
% 45.84/46.29 X := X
% 45.84/46.29 end
% 45.84/46.29 substitution1:
% 45.84/46.29 X := X
% 45.84/46.29 end
% 45.84/46.29
% 45.84/46.29 eqswap: (17199) {G1,W6,D2,L2,V1,M2} { zero = X, ! zero ==> X }.
% 45.84/46.29 parent0[1]: (17197) {G1,W6,D2,L2,V1,M2} { ! zero ==> X, X = zero }.
% 45.84/46.29 substitution0:
% 45.84/46.29 X := X
% 45.84/46.29 end
% 45.84/46.29
% 45.84/46.29 eqswap: (17200) {G1,W6,D2,L2,V1,M2} { ! X ==> zero, zero = X }.
% 45.84/46.29 parent0[1]: (17199) {G1,W6,D2,L2,V1,M2} { zero = X, ! zero ==> X }.
% 45.84/46.29 substitution0:
% 45.84/46.29 X := X
% 45.84/46.29 end
% 45.84/46.29
% 45.84/46.29 subsumption: (134) {G2,W6,D2,L2,V1,M2} R(12,92);d(2) { zero = X, ! X = zero
% 45.84/46.29 }.
% 45.84/46.29 parent0: (17200) {G1,W6,D2,L2,V1,M2} { ! X ==> zero, zero = X }.
% 45.84/46.29 substitution0:
% 45.84/46.29 X := X
% 45.84/46.29 end
% 45.84/46.29 permutation0:
% 45.84/46.29 0 ==> 1
% 45.84/46.29 1 ==> 0
% 45.84/46.29 end
% 45.84/46.29
% 45.84/46.29 eqswap: (17201) {G0,W8,D3,L2,V2,M2} { ! Y ==> addition( X, Y ), leq( X, Y
% 45.84/46.29 ) }.
% 45.84/46.29 parent0[0]: (12) {G0,W8,D3,L2,V2,M2} I { ! addition( X, Y ) ==> Y, leq( X,
% 45.84/46.29 Y ) }.
% 45.84/46.29 substitution0:
% 45.84/46.29 X := X
% 45.84/46.29 Y := Y
% 47.32/47.69 end
% 47.32/47.69
% 47.32/47.69 eqswap: (17202) {G1,W5,D3,L1,V1,M1} { X ==> addition( zero, X ) }.
% 47.32/47.69 parent0[0]: (32) {G1,W5,D3,L1,V1,M1} P(2,0) { addition( zero, X ) ==> X }.
% 47.32/47.69 substitution0:
% 47.32/47.69 X := X
% 47.32/47.69 end
% 47.32/47.69
% 47.32/47.69 resolution: (17203) {G1,W3,D2,L1,V1,M1} { leq( zero, X ) }.
% 47.32/47.69 parent0[0]: (17201) {G0,W8,D3,L2,V2,M2} { ! Y ==> addition( X, Y ), leq( X
% 47.32/47.69 , Y ) }.
% 47.32/47.69 parent1[0]: (17202) {G1,W5,D3,L1,V1,M1} { X ==> addition( zero, X ) }.
% 47.32/47.69 substitution0:
% 47.32/47.69 X := zero
% 47.32/47.69 Y := X
% 47.32/47.69 end
% 47.32/47.69 substitution1:
% 47.32/47.69 X := X
% 47.32/47.69 end
% 47.32/47.69
% 47.32/47.69 subsumption: (135) {G2,W3,D2,L1,V1,M1} R(12,32) { leq( zero, X ) }.
% 47.32/47.69 parent0: (17203) {G1,W3,D2,L1,V1,M1} { leq( zero, X ) }.
% 47.32/47.69 substitution0:
% 47.32/47.69 X := X
% 47.32/47.69 end
% 47.32/47.69 permutation0:
% 47.32/47.69 0 ==> 0
% 47.32/47.69 end
% 47.32/47.69
% 47.32/47.69 eqswap: (17204) {G0,W8,D3,L2,V2,M2} { ! Y ==> addition( X, Y ), leq( X, Y
% 47.32/47.69 ) }.
% 47.32/47.69 parent0[0]: (12) {G0,W8,D3,L2,V2,M2} I { ! addition( X, Y ) ==> Y, leq( X,
% 47.32/47.69 Y ) }.
% 47.32/47.69 substitution0:
% 47.32/47.69 X := X
% 47.32/47.69 Y := Y
% 47.32/47.69 end
% 47.32/47.69
% 47.32/47.69 paramod: (17205) {G1,W8,D3,L2,V2,M2} { ! X ==> addition( X, Y ), leq( Y, X
% 47.32/47.69 ) }.
% 47.32/47.69 parent0[0]: (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X )
% 47.32/47.69 }.
% 47.32/47.69 parent1[0; 3]: (17204) {G0,W8,D3,L2,V2,M2} { ! Y ==> addition( X, Y ), leq
% 47.32/47.69 ( X, Y ) }.
% 47.32/47.69 substitution0:
% 47.32/47.69 X := Y
% 47.32/47.69 Y := X
% 47.32/47.69 end
% 47.32/47.69 substitution1:
% 47.32/47.69 X := Y
% 47.32/47.69 Y := X
% 47.32/47.69 end
% 47.32/47.69
% 47.32/47.69 eqswap: (17208) {G1,W8,D3,L2,V2,M2} { ! addition( X, Y ) ==> X, leq( Y, X
% 47.32/47.69 ) }.
% 47.32/47.69 parent0[0]: (17205) {G1,W8,D3,L2,V2,M2} { ! X ==> addition( X, Y ), leq( Y
% 47.32/47.69 , X ) }.
% 47.32/47.69 substitution0:
% 47.32/47.69 X := X
% 47.32/47.69 Y := Y
% 47.32/47.69 end
% 47.32/47.69
% 47.32/47.69 subsumption: (143) {G1,W8,D3,L2,V2,M2} P(0,12) { ! addition( Y, X ) ==> Y,
% 47.32/47.69 leq( X, Y ) }.
% 47.32/47.69 parent0: (17208) {G1,W8,D3,L2,V2,M2} { ! addition( X, Y ) ==> X, leq( Y, X
% 47.32/47.69 ) }.
% 47.32/47.69 substitution0:
% 47.32/47.69 X := Y
% 47.32/47.69 Y := X
% 47.32/47.69 end
% 47.32/47.69 permutation0:
% 47.32/47.69 0 ==> 0
% 47.32/47.69 1 ==> 1
% 47.32/47.69 end
% 47.32/47.69
% 47.32/47.69 paramod: (17221) {G2,W6,D2,L2,V2,M2} { leq( Y, X ), ! leq( Y, zero ) }.
% 47.32/47.69 parent0[0]: (92) {G1,W6,D2,L2,V1,M2} P(11,2) { zero = X, ! leq( X, zero )
% 47.32/47.69 }.
% 47.32/47.69 parent1[0; 1]: (135) {G2,W3,D2,L1,V1,M1} R(12,32) { leq( zero, X ) }.
% 47.32/47.69 substitution0:
% 47.32/47.69 X := Y
% 47.32/47.69 end
% 47.32/47.69 substitution1:
% 47.32/47.69 X := X
% 47.32/47.69 end
% 47.32/47.69
% 47.32/47.69 subsumption: (145) {G3,W6,D2,L2,V2,M2} P(92,135) { leq( X, Y ), ! leq( X,
% 47.32/47.69 zero ) }.
% 47.32/47.69 parent0: (17221) {G2,W6,D2,L2,V2,M2} { leq( Y, X ), ! leq( Y, zero ) }.
% 47.32/47.69 substitution0:
% 47.32/47.69 X := Y
% 47.32/47.69 Y := X
% 47.32/47.69 end
% 47.32/47.69 permutation0:
% 47.32/47.69 0 ==> 0
% 47.32/47.69 1 ==> 1
% 47.32/47.69 end
% 47.32/47.69
% 47.32/47.69 eqswap: (17675) {G0,W8,D3,L2,V2,M2} { ! Y ==> addition( X, Y ), leq( X, Y
% 47.32/47.69 ) }.
% 47.32/47.69 parent0[0]: (12) {G0,W8,D3,L2,V2,M2} I { ! addition( X, Y ) ==> Y, leq( X,
% 47.32/47.69 Y ) }.
% 47.32/47.69 substitution0:
% 47.32/47.69 X := X
% 47.32/47.69 Y := Y
% 47.32/47.69 end
% 47.32/47.69
% 47.32/47.69 resolution: (17677) {G1,W8,D3,L2,V2,M2} { leq( X, Y ), ! zero ==> addition
% 47.32/47.69 ( X, zero ) }.
% 47.32/47.69 parent0[1]: (145) {G3,W6,D2,L2,V2,M2} P(92,135) { leq( X, Y ), ! leq( X,
% 47.32/47.69 zero ) }.
% 47.32/47.69 parent1[1]: (17675) {G0,W8,D3,L2,V2,M2} { ! Y ==> addition( X, Y ), leq( X
% 47.32/47.69 , Y ) }.
% 47.32/47.69 substitution0:
% 47.32/47.69 X := X
% 47.32/47.69 Y := Y
% 47.32/47.69 end
% 47.32/47.69 substitution1:
% 47.32/47.69 X := X
% 47.32/47.69 Y := zero
% 47.32/47.69 end
% 47.32/47.69
% 47.32/47.69 paramod: (17678) {G1,W6,D2,L2,V2,M2} { ! zero ==> X, leq( X, Y ) }.
% 47.32/47.69 parent0[0]: (2) {G0,W5,D3,L1,V1,M1} I { addition( X, zero ) ==> X }.
% 47.32/47.69 parent1[1; 3]: (17677) {G1,W8,D3,L2,V2,M2} { leq( X, Y ), ! zero ==>
% 47.32/47.69 addition( X, zero ) }.
% 47.32/47.69 substitution0:
% 47.32/47.69 X := X
% 47.32/47.69 end
% 47.32/47.69 substitution1:
% 47.32/47.69 X := X
% 47.32/47.69 Y := Y
% 47.32/47.69 end
% 47.32/47.69
% 47.32/47.69 eqswap: (17679) {G1,W6,D2,L2,V2,M2} { ! X ==> zero, leq( X, Y ) }.
% 47.32/47.69 parent0[0]: (17678) {G1,W6,D2,L2,V2,M2} { ! zero ==> X, leq( X, Y ) }.
% 47.32/47.69 substitution0:
% 47.32/47.69 X := X
% 47.32/47.69 Y := Y
% 47.32/47.69 end
% 47.32/47.69
% 47.32/47.69 subsumption: (146) {G4,W6,D2,L2,V2,M2} R(145,12);d(2) { leq( X, Y ), ! X =
% 47.32/47.69 zero }.
% 47.32/47.69 parent0: (17679) {G1,W6,D2,L2,V2,M2} { ! X ==> zero, leq( X, Y ) }.
% 47.32/47.69 substitution0:
% 47.32/47.69 X := X
% 47.32/47.69 Y := Y
% 47.32/47.69 end
% 47.32/47.69 permutation0:
% 47.32/47.69 0 ==> 1
% 47.32/47.69 1 ==> 0
% 47.32/47.69 end
% 47.32/47.69
% 47.32/47.69 paramod: (17682) {G1,W7,D4,L1,V1,M1} { addition( domain( X ), antidomain(
% 47.32/47.69 X ) ) ==> one }.
% 47.32/47.69 parent0[0]: (16) {G0,W6,D4,L1,V1,M1} I { antidomain( antidomain( X ) ) ==>
% 47.32/47.69 domain( X ) }.
% 47.32/47.69 parent1[0; 2]: (15) {G0,W8,D5,L1,V1,M1} I { addition( antidomain(
% 47.32/47.69 antidomain( X ) ), antidomain( X ) ) ==> one }.
% 47.32/47.69 substitution0:
% 47.32/47.69 X := X
% 47.32/47.69 end
% 47.32/47.69 substitution1:
% 47.32/47.69 X := X
% 47.32/47.69 end
% 47.32/47.69
% 47.32/47.69 subsumption: (180) {G1,W7,D4,L1,V1,M1} S(15);d(16) { addition( domain( X )
% 47.32/47.69 , antidomain( X ) ) ==> one }.
% 47.32/47.69 parent0: (17682) {G1,W7,D4,L1,V1,M1} { addition( domain( X ), antidomain(
% 47.32/47.69 X ) ) ==> one }.
% 47.32/47.69 substitution0:
% 47.32/47.69 X := X
% 47.32/47.69 end
% 47.32/47.69 permutation0:
% 47.32/47.69 0 ==> 0
% 47.32/47.69 end
% 47.32/47.69
% 47.32/47.69 eqswap: (17685) {G1,W7,D4,L1,V1,M1} { one ==> addition( domain( X ),
% 47.32/47.69 antidomain( X ) ) }.
% 47.32/47.69 parent0[0]: (180) {G1,W7,D4,L1,V1,M1} S(15);d(16) { addition( domain( X ),
% 47.32/47.69 antidomain( X ) ) ==> one }.
% 47.32/47.69 substitution0:
% 47.32/47.69 X := X
% 47.32/47.69 end
% 47.32/47.69
% 47.32/47.69 paramod: (17688) {G2,W7,D4,L1,V0,M1} { one ==> addition( antidomain( zero
% 47.32/47.69 ), antidomain( one ) ) }.
% 47.32/47.69 parent0[0]: (52) {G2,W5,D3,L1,V0,M1} P(50,16) { domain( one ) ==>
% 47.32/47.69 antidomain( zero ) }.
% 47.32/47.69 parent1[0; 3]: (17685) {G1,W7,D4,L1,V1,M1} { one ==> addition( domain( X )
% 47.32/47.69 , antidomain( X ) ) }.
% 47.32/47.69 substitution0:
% 47.32/47.69 end
% 47.32/47.69 substitution1:
% 47.32/47.69 X := one
% 47.32/47.69 end
% 47.32/47.69
% 47.32/47.69 paramod: (17689) {G2,W6,D4,L1,V0,M1} { one ==> addition( antidomain( zero
% 47.32/47.69 ), zero ) }.
% 47.32/47.69 parent0[0]: (50) {G1,W4,D3,L1,V0,M1} P(13,5) { antidomain( one ) ==> zero
% 47.32/47.69 }.
% 47.32/47.69 parent1[0; 5]: (17688) {G2,W7,D4,L1,V0,M1} { one ==> addition( antidomain
% 47.32/47.69 ( zero ), antidomain( one ) ) }.
% 47.32/47.69 substitution0:
% 47.32/47.69 end
% 47.32/47.69 substitution1:
% 47.32/47.69 end
% 47.32/47.69
% 47.32/47.69 paramod: (17690) {G1,W4,D3,L1,V0,M1} { one ==> antidomain( zero ) }.
% 47.32/47.69 parent0[0]: (2) {G0,W5,D3,L1,V1,M1} I { addition( X, zero ) ==> X }.
% 47.32/47.69 parent1[0; 2]: (17689) {G2,W6,D4,L1,V0,M1} { one ==> addition( antidomain
% 47.32/47.69 ( zero ), zero ) }.
% 47.32/47.69 substitution0:
% 47.32/47.69 X := antidomain( zero )
% 47.32/47.69 end
% 47.32/47.69 substitution1:
% 47.32/47.69 end
% 47.32/47.69
% 47.32/47.69 eqswap: (17691) {G1,W4,D3,L1,V0,M1} { antidomain( zero ) ==> one }.
% 47.32/47.69 parent0[0]: (17690) {G1,W4,D3,L1,V0,M1} { one ==> antidomain( zero ) }.
% 47.32/47.69 substitution0:
% 47.32/47.69 end
% 47.32/47.69
% 47.32/47.69 subsumption: (189) {G3,W4,D3,L1,V0,M1} P(52,180);d(50);d(2) { antidomain(
% 47.32/47.69 zero ) ==> one }.
% 47.32/47.69 parent0: (17691) {G1,W4,D3,L1,V0,M1} { antidomain( zero ) ==> one }.
% 47.32/47.69 substitution0:
% 47.32/47.69 end
% 47.32/47.69 permutation0:
% 47.32/47.69 0 ==> 0
% 47.32/47.69 end
% 47.32/47.69
% 47.32/47.69 eqswap: (17692) {G1,W7,D4,L1,V1,M1} { one ==> addition( domain( X ),
% 47.32/47.69 antidomain( X ) ) }.
% 47.32/47.69 parent0[0]: (180) {G1,W7,D4,L1,V1,M1} S(15);d(16) { addition( domain( X ),
% 47.32/47.69 antidomain( X ) ) ==> one }.
% 47.32/47.69 substitution0:
% 47.32/47.69 X := X
% 47.32/47.69 end
% 47.32/47.69
% 47.32/47.69 paramod: (17693) {G1,W7,D4,L1,V1,M1} { one ==> addition( antidomain( X ),
% 47.32/47.69 domain( X ) ) }.
% 47.32/47.69 parent0[0]: (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X )
% 47.32/47.69 }.
% 47.32/47.69 parent1[0; 2]: (17692) {G1,W7,D4,L1,V1,M1} { one ==> addition( domain( X )
% 47.32/47.69 , antidomain( X ) ) }.
% 47.32/47.69 substitution0:
% 47.32/47.69 X := domain( X )
% 47.32/47.69 Y := antidomain( X )
% 47.32/47.69 end
% 47.32/47.69 substitution1:
% 47.32/47.69 X := X
% 47.32/47.69 end
% 47.32/47.69
% 47.32/47.69 eqswap: (17696) {G1,W7,D4,L1,V1,M1} { addition( antidomain( X ), domain( X
% 47.32/47.69 ) ) ==> one }.
% 47.32/47.69 parent0[0]: (17693) {G1,W7,D4,L1,V1,M1} { one ==> addition( antidomain( X
% 47.32/47.69 ), domain( X ) ) }.
% 47.32/47.69 substitution0:
% 47.32/47.69 X := X
% 47.32/47.69 end
% 47.32/47.69
% 47.32/47.69 subsumption: (193) {G2,W7,D4,L1,V1,M1} P(180,0) { addition( antidomain( X )
% 47.32/47.69 , domain( X ) ) ==> one }.
% 47.32/47.69 parent0: (17696) {G1,W7,D4,L1,V1,M1} { addition( antidomain( X ), domain(
% 47.32/47.69 X ) ) ==> one }.
% 47.32/47.69 substitution0:
% 47.32/47.69 X := X
% 47.32/47.69 end
% 47.32/47.69 permutation0:
% 47.32/47.69 0 ==> 0
% 47.32/47.69 end
% 47.32/47.69
% 47.32/47.69 eqswap: (17698) {G0,W6,D4,L1,V1,M1} { domain( X ) ==> antidomain(
% 47.32/47.69 antidomain( X ) ) }.
% 47.32/47.69 parent0[0]: (16) {G0,W6,D4,L1,V1,M1} I { antidomain( antidomain( X ) ) ==>
% 47.32/47.69 domain( X ) }.
% 47.32/47.69 substitution0:
% 47.32/47.69 X := X
% 47.32/47.69 end
% 47.32/47.69
% 47.32/47.69 paramod: (17701) {G1,W5,D3,L1,V0,M1} { domain( zero ) ==> antidomain( one
% 47.32/47.69 ) }.
% 47.32/47.69 parent0[0]: (189) {G3,W4,D3,L1,V0,M1} P(52,180);d(50);d(2) { antidomain(
% 47.32/47.69 zero ) ==> one }.
% 47.32/47.69 parent1[0; 4]: (17698) {G0,W6,D4,L1,V1,M1} { domain( X ) ==> antidomain(
% 47.32/47.69 antidomain( X ) ) }.
% 47.32/47.69 substitution0:
% 47.32/47.69 end
% 47.32/47.69 substitution1:
% 47.32/47.69 X := zero
% 47.32/47.69 end
% 47.32/47.69
% 47.32/47.69 paramod: (17702) {G2,W4,D3,L1,V0,M1} { domain( zero ) ==> zero }.
% 47.32/47.69 parent0[0]: (50) {G1,W4,D3,L1,V0,M1} P(13,5) { antidomain( one ) ==> zero
% 47.32/47.69 }.
% 47.32/47.69 parent1[0; 3]: (17701) {G1,W5,D3,L1,V0,M1} { domain( zero ) ==> antidomain
% 47.32/47.69 ( one ) }.
% 47.32/47.69 substitution0:
% 47.32/47.69 end
% 47.32/47.69 substitution1:
% 47.32/47.69 end
% 47.32/47.69
% 47.32/47.69 paramod: (17703) {G3,W4,D3,L1,V0,M1} { c( one ) ==> zero }.
% 47.32/47.69 parent0[0]: (51) {G2,W5,D3,L1,V0,M1} P(50,41) { domain( zero ) ==> c( one )
% 47.32/47.69 }.
% 47.32/47.69 parent1[0; 1]: (17702) {G2,W4,D3,L1,V0,M1} { domain( zero ) ==> zero }.
% 47.32/47.69 substitution0:
% 47.32/47.69 end
% 47.32/47.69 substitution1:
% 47.32/47.69 end
% 47.32/47.69
% 47.32/47.69 subsumption: (198) {G4,W4,D3,L1,V0,M1} P(189,16);d(50);d(51) { c( one ) ==>
% 47.32/47.69 zero }.
% 47.32/47.69 parent0: (17703) {G3,W4,D3,L1,V0,M1} { c( one ) ==> zero }.
% 47.32/47.69 substitution0:
% 47.32/47.69 end
% 47.32/47.69 permutation0:
% 47.32/47.69 0 ==> 0
% 47.32/47.69 end
% 47.32/47.69
% 47.32/47.69 paramod: (17707) {G1,W7,D4,L1,V1,M1} { addition( codomain( X ),
% 47.32/47.69 coantidomain( X ) ) ==> one }.
% 47.32/47.69 parent0[0]: (20) {G0,W6,D4,L1,V1,M1} I { coantidomain( coantidomain( X ) )
% 47.32/47.69 ==> codomain( X ) }.
% 47.32/47.69 parent1[0; 2]: (19) {G0,W8,D5,L1,V1,M1} I { addition( coantidomain(
% 47.32/47.69 coantidomain( X ) ), coantidomain( X ) ) ==> one }.
% 47.32/47.69 substitution0:
% 47.32/47.69 X := X
% 47.32/47.69 end
% 47.32/47.69 substitution1:
% 47.32/47.69 X := X
% 47.32/47.69 end
% 47.32/47.69
% 47.32/47.69 subsumption: (202) {G1,W7,D4,L1,V1,M1} S(19);d(20) { addition( codomain( X
% 47.32/47.69 ), coantidomain( X ) ) ==> one }.
% 47.32/47.69 parent0: (17707) {G1,W7,D4,L1,V1,M1} { addition( codomain( X ),
% 47.32/47.69 coantidomain( X ) ) ==> one }.
% 47.32/47.69 substitution0:
% 47.32/47.69 X := X
% 47.32/47.69 end
% 47.32/47.69 permutation0:
% 47.32/47.69 0 ==> 0
% 47.32/47.69 end
% 47.32/47.69
% 47.32/47.69 eqswap: (17710) {G0,W9,D4,L1,V2,M1} { domain_difference( X, Y ) ==>
% 47.32/47.69 multiplication( domain( X ), antidomain( Y ) ) }.
% 47.32/47.69 parent0[0]: (22) {G0,W9,D4,L1,V2,M1} I { multiplication( domain( X ),
% 47.32/47.69 antidomain( Y ) ) ==> domain_difference( X, Y ) }.
% 47.32/47.69 substitution0:
% 47.32/47.69 X := X
% 47.32/47.69 Y := Y
% 47.32/47.69 end
% 47.32/47.69
% 47.32/47.69 paramod: (17712) {G1,W8,D4,L1,V1,M1} { domain_difference( X, zero ) ==>
% 47.32/47.69 multiplication( domain( X ), one ) }.
% 47.32/47.69 parent0[0]: (189) {G3,W4,D3,L1,V0,M1} P(52,180);d(50);d(2) { antidomain(
% 47.32/47.69 zero ) ==> one }.
% 47.32/47.69 parent1[0; 7]: (17710) {G0,W9,D4,L1,V2,M1} { domain_difference( X, Y ) ==>
% 47.32/47.69 multiplication( domain( X ), antidomain( Y ) ) }.
% 47.32/47.69 substitution0:
% 47.32/47.69 end
% 47.32/47.69 substitution1:
% 47.32/47.69 X := X
% 47.32/47.69 Y := zero
% 47.32/47.69 end
% 47.32/47.69
% 47.32/47.69 paramod: (17713) {G1,W6,D3,L1,V1,M1} { domain_difference( X, zero ) ==>
% 47.32/47.69 domain( X ) }.
% 47.32/47.69 parent0[0]: (5) {G0,W5,D3,L1,V1,M1} I { multiplication( X, one ) ==> X }.
% 47.32/47.69 parent1[0; 4]: (17712) {G1,W8,D4,L1,V1,M1} { domain_difference( X, zero )
% 47.32/47.69 ==> multiplication( domain( X ), one ) }.
% 47.32/47.69 substitution0:
% 47.32/47.69 X := domain( X )
% 47.32/47.69 end
% 47.32/47.69 substitution1:
% 47.32/47.69 X := X
% 47.32/47.69 end
% 47.32/47.69
% 47.32/47.69 subsumption: (218) {G4,W6,D3,L1,V1,M1} P(189,22);d(5) { domain_difference(
% 47.32/47.69 X, zero ) ==> domain( X ) }.
% 47.32/47.69 parent0: (17713) {G1,W6,D3,L1,V1,M1} { domain_difference( X, zero ) ==>
% 47.32/47.69 domain( X ) }.
% 47.32/47.69 substitution0:
% 47.32/47.69 X := X
% 47.32/47.69 end
% 47.32/47.69 permutation0:
% 47.32/47.69 0 ==> 0
% 47.32/47.69 end
% 47.32/47.69
% 47.32/47.69 eqswap: (17716) {G0,W9,D4,L1,V2,M1} { domain_difference( X, Y ) ==>
% 47.32/47.69 multiplication( domain( X ), antidomain( Y ) ) }.
% 47.32/47.69 parent0[0]: (22) {G0,W9,D4,L1,V2,M1} I { multiplication( domain( X ),
% 47.32/47.69 antidomain( Y ) ) ==> domain_difference( X, Y ) }.
% 47.32/47.69 substitution0:
% 47.32/47.69 X := X
% 47.32/47.69 Y := Y
% 47.32/47.69 end
% 47.32/47.69
% 47.32/47.69 paramod: (17717) {G1,W10,D4,L1,V2,M1} { domain_difference( antidomain( X )
% 47.32/47.69 , Y ) ==> multiplication( c( X ), antidomain( Y ) ) }.
% 47.32/47.69 parent0[0]: (41) {G1,W6,D4,L1,V1,M1} P(16,16);d(21) { domain( antidomain( X
% 47.32/47.69 ) ) ==> c( X ) }.
% 47.32/47.69 parent1[0; 6]: (17716) {G0,W9,D4,L1,V2,M1} { domain_difference( X, Y ) ==>
% 47.32/47.69 multiplication( domain( X ), antidomain( Y ) ) }.
% 47.32/47.69 substitution0:
% 47.32/47.69 X := X
% 47.32/47.69 end
% 47.32/47.69 substitution1:
% 47.32/47.69 X := antidomain( X )
% 47.32/47.69 Y := Y
% 47.32/47.69 end
% 47.32/47.69
% 47.32/47.69 eqswap: (17718) {G1,W10,D4,L1,V2,M1} { multiplication( c( X ), antidomain
% 47.32/47.69 ( Y ) ) ==> domain_difference( antidomain( X ), Y ) }.
% 47.32/47.69 parent0[0]: (17717) {G1,W10,D4,L1,V2,M1} { domain_difference( antidomain(
% 47.32/47.69 X ), Y ) ==> multiplication( c( X ), antidomain( Y ) ) }.
% 47.32/47.69 substitution0:
% 47.32/47.69 X := X
% 47.32/47.69 Y := Y
% 47.32/47.69 end
% 47.32/47.69
% 47.32/47.69 subsumption: (232) {G2,W10,D4,L1,V2,M1} P(41,22) { multiplication( c( X ),
% 47.32/47.69 antidomain( Y ) ) ==> domain_difference( antidomain( X ), Y ) }.
% 47.32/47.69 parent0: (17718) {G1,W10,D4,L1,V2,M1} { multiplication( c( X ), antidomain
% 47.32/47.69 ( Y ) ) ==> domain_difference( antidomain( X ), Y ) }.
% 47.32/47.69 substitution0:
% 47.32/47.69 X := X
% 47.32/47.69 Y := Y
% 47.32/47.69 end
% 47.32/47.69 permutation0:
% 47.32/47.69 0 ==> 0
% 47.32/47.69 end
% 47.32/47.69
% 47.32/47.69 eqswap: (17720) {G0,W9,D5,L1,V2,M1} { forward_diamond( X, Y ) ==> domain(
% 47.32/47.69 multiplication( X, domain( Y ) ) ) }.
% 47.32/47.69 parent0[0]: (23) {G0,W9,D5,L1,V2,M1} I { domain( multiplication( X, domain
% 47.32/47.69 ( Y ) ) ) ==> forward_diamond( X, Y ) }.
% 47.32/47.69 substitution0:
% 47.32/47.69 X := X
% 47.32/47.69 Y := Y
% 47.32/47.69 end
% 47.32/47.69
% 47.32/47.69 paramod: (17725) {G1,W9,D5,L1,V1,M1} { forward_diamond( X, zero ) ==>
% 47.32/47.69 domain( multiplication( X, c( one ) ) ) }.
% 47.32/47.69 parent0[0]: (51) {G2,W5,D3,L1,V0,M1} P(50,41) { domain( zero ) ==> c( one )
% 47.32/47.69 }.
% 47.32/47.69 parent1[0; 7]: (17720) {G0,W9,D5,L1,V2,M1} { forward_diamond( X, Y ) ==>
% 47.32/47.69 domain( multiplication( X, domain( Y ) ) ) }.
% 47.32/47.69 substitution0:
% 47.32/47.69 end
% 47.32/47.69 substitution1:
% 47.32/47.69 X := X
% 47.32/47.69 Y := zero
% 47.32/47.69 end
% 47.32/47.69
% 47.32/47.69 paramod: (17726) {G2,W8,D4,L1,V1,M1} { forward_diamond( X, zero ) ==>
% 47.32/47.69 domain( multiplication( X, zero ) ) }.
% 47.32/47.69 parent0[0]: (198) {G4,W4,D3,L1,V0,M1} P(189,16);d(50);d(51) { c( one ) ==>
% 47.32/47.69 zero }.
% 47.32/47.69 parent1[0; 7]: (17725) {G1,W9,D5,L1,V1,M1} { forward_diamond( X, zero )
% 47.32/47.69 ==> domain( multiplication( X, c( one ) ) ) }.
% 47.32/47.69 substitution0:
% 47.32/47.69 end
% 47.32/47.69 substitution1:
% 47.32/47.69 X := X
% 47.32/47.69 end
% 47.32/47.69
% 47.32/47.69 paramod: (17727) {G1,W6,D3,L1,V1,M1} { forward_diamond( X, zero ) ==>
% 47.32/47.69 domain( zero ) }.
% 47.32/47.69 parent0[0]: (9) {G0,W5,D3,L1,V1,M1} I { multiplication( X, zero ) ==> zero
% 47.32/47.69 }.
% 47.32/47.69 parent1[0; 5]: (17726) {G2,W8,D4,L1,V1,M1} { forward_diamond( X, zero )
% 47.32/47.69 ==> domain( multiplication( X, zero ) ) }.
% 47.32/47.69 substitution0:
% 47.32/47.69 X := X
% 47.32/47.69 end
% 47.32/47.69 substitution1:
% 47.32/47.69 X := X
% 47.32/47.69 end
% 47.32/47.69
% 47.32/47.69 paramod: (17728) {G2,W6,D3,L1,V1,M1} { forward_diamond( X, zero ) ==> c(
% 47.32/47.69 one ) }.
% 47.32/47.69 parent0[0]: (51) {G2,W5,D3,L1,V0,M1} P(50,41) { domain( zero ) ==> c( one )
% 47.32/47.69 }.
% 47.32/47.69 parent1[0; 4]: (17727) {G1,W6,D3,L1,V1,M1} { forward_diamond( X, zero )
% 47.32/47.69 ==> domain( zero ) }.
% 47.32/47.69 substitution0:
% 47.32/47.69 end
% 47.32/47.69 substitution1:
% 47.32/47.69 X := X
% 47.32/47.69 end
% 47.32/47.69
% 47.32/47.69 paramod: (17729) {G3,W5,D3,L1,V1,M1} { forward_diamond( X, zero ) ==> zero
% 47.32/47.69 }.
% 47.32/47.69 parent0[0]: (198) {G4,W4,D3,L1,V0,M1} P(189,16);d(50);d(51) { c( one ) ==>
% 47.32/47.69 zero }.
% 47.32/47.69 parent1[0; 4]: (17728) {G2,W6,D3,L1,V1,M1} { forward_diamond( X, zero )
% 47.32/47.69 ==> c( one ) }.
% 47.32/47.69 substitution0:
% 47.32/47.69 end
% 47.32/47.69 substitution1:
% 47.32/47.69 X := X
% 47.32/47.69 end
% 47.32/47.69
% 47.32/47.69 subsumption: (254) {G5,W5,D3,L1,V1,M1} P(51,23);d(198);d(9);d(51);d(198) {
% 47.32/47.69 forward_diamond( X, zero ) ==> zero }.
% 47.32/47.69 parent0: (17729) {G3,W5,D3,L1,V1,M1} { forward_diamond( X, zero ) ==> zero
% 47.32/47.69 }.
% 47.32/47.69 substitution0:
% 47.32/47.69 X := X
% 47.32/47.69 end
% 47.32/47.69 permutation0:
% 47.32/47.69 0 ==> 0
% 47.32/47.69 end
% 47.32/47.69
% 47.32/47.69 eqswap: (17732) {G1,W7,D4,L1,V1,M1} { one ==> addition( codomain( X ),
% 47.32/47.69 coantidomain( X ) ) }.
% 47.32/47.69 parent0[0]: (202) {G1,W7,D4,L1,V1,M1} S(19);d(20) { addition( codomain( X )
% 47.32/47.69 , coantidomain( X ) ) ==> one }.
% 47.32/47.69 substitution0:
% 47.32/47.69 X := X
% 47.32/47.69 end
% 47.32/47.69
% 47.32/47.69 paramod: (17735) {G2,W7,D4,L1,V0,M1} { one ==> addition( coantidomain(
% 47.32/47.69 zero ), coantidomain( one ) ) }.
% 47.32/47.69 parent0[0]: (40) {G2,W5,D3,L1,V0,M1} P(39,20) { codomain( one ) ==>
% 47.32/47.69 coantidomain( zero ) }.
% 47.32/47.69 parent1[0; 3]: (17732) {G1,W7,D4,L1,V1,M1} { one ==> addition( codomain( X
% 47.32/47.69 ), coantidomain( X ) ) }.
% 47.32/47.69 substitution0:
% 47.32/47.69 end
% 47.32/47.69 substitution1:
% 47.32/47.69 X := one
% 47.32/47.69 end
% 47.32/47.69
% 47.32/47.69 paramod: (17736) {G2,W6,D4,L1,V0,M1} { one ==> addition( coantidomain(
% 47.32/47.69 zero ), zero ) }.
% 47.32/47.69 parent0[0]: (39) {G1,W4,D3,L1,V0,M1} P(17,6) { coantidomain( one ) ==> zero
% 47.32/47.69 }.
% 47.32/47.69 parent1[0; 5]: (17735) {G2,W7,D4,L1,V0,M1} { one ==> addition(
% 47.32/47.69 coantidomain( zero ), coantidomain( one ) ) }.
% 47.32/47.69 substitution0:
% 47.32/47.69 end
% 47.32/47.69 substitution1:
% 47.32/47.69 end
% 47.32/47.69
% 47.32/47.69 paramod: (17737) {G1,W4,D3,L1,V0,M1} { one ==> coantidomain( zero ) }.
% 47.32/47.69 parent0[0]: (2) {G0,W5,D3,L1,V1,M1} I { addition( X, zero ) ==> X }.
% 47.32/47.69 parent1[0; 2]: (17736) {G2,W6,D4,L1,V0,M1} { one ==> addition(
% 47.32/47.69 coantidomain( zero ), zero ) }.
% 47.32/47.69 substitution0:
% 47.32/47.69 X := coantidomain( zero )
% 47.32/47.69 end
% 47.32/47.69 substitution1:
% 47.32/47.69 end
% 47.32/47.69
% 47.32/47.69 eqswap: (17738) {G1,W4,D3,L1,V0,M1} { coantidomain( zero ) ==> one }.
% 47.32/47.69 parent0[0]: (17737) {G1,W4,D3,L1,V0,M1} { one ==> coantidomain( zero ) }.
% 47.32/47.69 substitution0:
% 47.32/47.69 end
% 47.32/47.69
% 47.32/47.69 subsumption: (341) {G3,W4,D3,L1,V0,M1} P(40,202);d(39);d(2) { coantidomain
% 47.32/47.69 ( zero ) ==> one }.
% 47.32/47.69 parent0: (17738) {G1,W4,D3,L1,V0,M1} { coantidomain( zero ) ==> one }.
% 47.32/47.69 substitution0:
% 47.32/47.69 end
% 47.32/47.69 permutation0:
% 47.32/47.69 0 ==> 0
% 47.32/47.69 end
% 47.32/47.69
% 47.32/47.69 eqswap: (17739) {G1,W7,D4,L1,V1,M1} { one ==> addition( codomain( X ),
% 47.32/47.69 coantidomain( X ) ) }.
% 47.32/47.69 parent0[0]: (202) {G1,W7,D4,L1,V1,M1} S(19);d(20) { addition( codomain( X )
% 47.32/47.69 , coantidomain( X ) ) ==> one }.
% 47.32/47.69 substitution0:
% 47.32/47.69 X := X
% 47.32/47.69 end
% 47.32/47.69
% 47.32/47.69 paramod: (17740) {G1,W7,D4,L1,V1,M1} { one ==> addition( coantidomain( X )
% 47.32/47.69 , codomain( X ) ) }.
% 47.32/47.69 parent0[0]: (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X )
% 47.32/47.69 }.
% 47.32/47.69 parent1[0; 2]: (17739) {G1,W7,D4,L1,V1,M1} { one ==> addition( codomain( X
% 47.32/47.69 ), coantidomain( X ) ) }.
% 47.32/47.69 substitution0:
% 47.32/47.69 X := codomain( X )
% 47.32/47.69 Y := coantidomain( X )
% 47.32/47.69 end
% 47.32/47.69 substitution1:
% 47.32/47.69 X := X
% 47.32/47.69 end
% 47.32/47.69
% 47.32/47.69 eqswap: (17743) {G1,W7,D4,L1,V1,M1} { addition( coantidomain( X ),
% 47.32/47.69 codomain( X ) ) ==> one }.
% 47.32/47.69 parent0[0]: (17740) {G1,W7,D4,L1,V1,M1} { one ==> addition( coantidomain(
% 47.32/47.69 X ), codomain( X ) ) }.
% 47.32/47.69 substitution0:
% 47.32/47.69 X := X
% 47.32/47.69 end
% 47.32/47.69
% 47.32/47.69 subsumption: (344) {G2,W7,D4,L1,V1,M1} P(202,0) { addition( coantidomain( X
% 47.32/47.69 ), codomain( X ) ) ==> one }.
% 47.32/47.69 parent0: (17743) {G1,W7,D4,L1,V1,M1} { addition( coantidomain( X ),
% 47.32/47.69 codomain( X ) ) ==> one }.
% 47.32/47.69 substitution0:
% 47.32/47.69 X := X
% 47.32/47.69 end
% 47.32/47.69 permutation0:
% 47.32/47.69 0 ==> 0
% 47.32/47.69 end
% 47.32/47.69
% 47.32/47.69 eqswap: (17745) {G1,W7,D4,L1,V1,M1} { zero ==> multiplication(
% 47.32/47.69 coantidomain( X ), codomain( X ) ) }.
% 47.32/47.69 parent0[0]: (38) {G1,W7,D4,L1,V1,M1} P(20,17) { multiplication(
% 47.32/47.69 coantidomain( X ), codomain( X ) ) ==> zero }.
% 47.32/47.69 substitution0:
% 47.32/47.69 X := X
% 47.32/47.69 end
% 47.32/47.69
% 47.32/47.69 paramod: (17747) {G2,W6,D4,L1,V0,M1} { zero ==> multiplication( one,
% 47.32/47.69 codomain( zero ) ) }.
% 47.32/47.69 parent0[0]: (341) {G3,W4,D3,L1,V0,M1} P(40,202);d(39);d(2) { coantidomain(
% 47.32/47.69 zero ) ==> one }.
% 47.32/47.69 parent1[0; 3]: (17745) {G1,W7,D4,L1,V1,M1} { zero ==> multiplication(
% 47.32/47.69 coantidomain( X ), codomain( X ) ) }.
% 47.32/47.69 substitution0:
% 47.32/47.69 end
% 47.32/47.69 substitution1:
% 47.32/47.69 X := zero
% 47.32/47.69 end
% 47.32/47.69
% 47.32/47.69 paramod: (17748) {G1,W4,D3,L1,V0,M1} { zero ==> codomain( zero ) }.
% 47.32/47.69 parent0[0]: (6) {G0,W5,D3,L1,V1,M1} I { multiplication( one, X ) ==> X }.
% 47.32/47.69 parent1[0; 2]: (17747) {G2,W6,D4,L1,V0,M1} { zero ==> multiplication( one
% 47.32/47.69 , codomain( zero ) ) }.
% 47.32/47.69 substitution0:
% 47.32/47.69 X := codomain( zero )
% 47.32/47.69 end
% 47.32/47.69 substitution1:
% 47.32/47.69 end
% 47.32/47.69
% 47.32/47.69 eqswap: (17749) {G1,W4,D3,L1,V0,M1} { codomain( zero ) ==> zero }.
% 47.32/47.69 parent0[0]: (17748) {G1,W4,D3,L1,V0,M1} { zero ==> codomain( zero ) }.
% 47.32/47.69 substitution0:
% 47.32/47.69 end
% 47.32/47.69
% 47.32/47.69 subsumption: (348) {G4,W4,D3,L1,V0,M1} P(341,38);d(6) { codomain( zero )
% 47.32/47.69 ==> zero }.
% 47.32/47.69 parent0: (17749) {G1,W4,D3,L1,V0,M1} { codomain( zero ) ==> zero }.
% 47.32/47.69 substitution0:
% 47.32/47.69 end
% 47.32/47.69 permutation0:
% 47.32/47.69 0 ==> 0
% 47.32/47.69 end
% 47.32/47.69
% 47.32/47.69 eqswap: (17751) {G0,W24,D7,L1,V1,M1} { forward_diamond( star( skol1 ),
% 47.32/47.69 domain_difference( domain( X ), forward_diamond( skol1, domain( X ) ) ) )
% 47.32/47.69 ==> addition( domain( X ), forward_diamond( star( skol1 ),
% 47.32/47.69 domain_difference( domain( X ), forward_diamond( skol1, domain( X ) ) ) )
% 47.32/47.69 ) }.
% 47.32/47.69 parent0[0]: (29) {G0,W24,D7,L1,V1,M1} I { addition( domain( X ),
% 47.32/47.69 forward_diamond( star( skol1 ), domain_difference( domain( X ),
% 47.32/47.69 forward_diamond( skol1, domain( X ) ) ) ) ) ==> forward_diamond( star(
% 47.32/47.69 skol1 ), domain_difference( domain( X ), forward_diamond( skol1, domain(
% 47.32/47.69 X ) ) ) ) }.
% 47.32/47.69 substitution0:
% 47.32/47.69 X := X
% 47.32/47.69 end
% 47.32/47.69
% 47.32/47.69 paramod: (17756) {G1,W37,D8,L1,V2,M1} { forward_diamond( star( skol1 ),
% 47.32/47.69 domain_difference( domain( multiplication( X, domain( Y ) ) ),
% 47.32/47.69 forward_diamond( skol1, domain( multiplication( X, domain( Y ) ) ) ) ) )
% 47.32/47.69 ==> addition( domain( multiplication( X, domain( Y ) ) ), forward_diamond
% 47.32/47.69 ( star( skol1 ), domain_difference( domain( multiplication( X, domain( Y
% 47.32/47.69 ) ) ), forward_diamond( skol1, forward_diamond( X, Y ) ) ) ) ) }.
% 47.32/47.69 parent0[0]: (23) {G0,W9,D5,L1,V2,M1} I { domain( multiplication( X, domain
% 47.32/47.69 ( Y ) ) ) ==> forward_diamond( X, Y ) }.
% 47.32/47.69 parent1[0; 34]: (17751) {G0,W24,D7,L1,V1,M1} { forward_diamond( star(
% 47.32/47.69 skol1 ), domain_difference( domain( X ), forward_diamond( skol1, domain(
% 47.32/47.69 X ) ) ) ) ==> addition( domain( X ), forward_diamond( star( skol1 ),
% 47.32/47.69 domain_difference( domain( X ), forward_diamond( skol1, domain( X ) ) ) )
% 47.32/47.69 ) }.
% 47.32/47.69 substitution0:
% 47.32/47.69 X := X
% 47.32/47.69 Y := Y
% 47.32/47.69 end
% 47.32/47.69 substitution1:
% 47.32/47.69 X := multiplication( X, domain( Y ) )
% 47.32/47.69 end
% 47.32/47.69
% 47.32/47.69 paramod: (17760) {G1,W35,D8,L1,V2,M1} { forward_diamond( star( skol1 ),
% 47.32/47.69 domain_difference( domain( multiplication( X, domain( Y ) ) ),
% 47.32/47.69 forward_diamond( skol1, domain( multiplication( X, domain( Y ) ) ) ) ) )
% 47.32/47.69 ==> addition( domain( multiplication( X, domain( Y ) ) ), forward_diamond
% 47.32/47.69 ( star( skol1 ), domain_difference( forward_diamond( X, Y ),
% 47.32/47.69 forward_diamond( skol1, forward_diamond( X, Y ) ) ) ) ) }.
% 47.32/47.69 parent0[0]: (23) {G0,W9,D5,L1,V2,M1} I { domain( multiplication( X, domain
% 47.32/47.69 ( Y ) ) ) ==> forward_diamond( X, Y ) }.
% 47.32/47.69 parent1[0; 27]: (17756) {G1,W37,D8,L1,V2,M1} { forward_diamond( star(
% 47.32/47.69 skol1 ), domain_difference( domain( multiplication( X, domain( Y ) ) ),
% 47.32/47.69 forward_diamond( skol1, domain( multiplication( X, domain( Y ) ) ) ) ) )
% 47.32/47.69 ==> addition( domain( multiplication( X, domain( Y ) ) ), forward_diamond
% 47.32/47.69 ( star( skol1 ), domain_difference( domain( multiplication( X, domain( Y
% 47.32/47.69 ) ) ), forward_diamond( skol1, forward_diamond( X, Y ) ) ) ) ) }.
% 47.32/47.69 substitution0:
% 47.32/47.69 X := X
% 47.32/47.69 Y := Y
% 47.32/47.69 end
% 47.32/47.69 substitution1:
% 47.32/47.69 X := X
% 47.32/47.69 Y := Y
% 47.32/47.69 end
% 47.32/47.69
% 47.32/47.69 paramod: (17763) {G1,W33,D8,L1,V2,M1} { forward_diamond( star( skol1 ),
% 47.32/47.69 domain_difference( domain( multiplication( X, domain( Y ) ) ),
% 47.32/47.69 forward_diamond( skol1, domain( multiplication( X, domain( Y ) ) ) ) ) )
% 47.32/47.69 ==> addition( forward_diamond( X, Y ), forward_diamond( star( skol1 ),
% 47.32/47.69 domain_difference( forward_diamond( X, Y ), forward_diamond( skol1,
% 47.32/47.69 forward_diamond( X, Y ) ) ) ) ) }.
% 47.32/47.69 parent0[0]: (23) {G0,W9,D5,L1,V2,M1} I { domain( multiplication( X, domain
% 47.32/47.69 ( Y ) ) ) ==> forward_diamond( X, Y ) }.
% 47.32/47.69 parent1[0; 18]: (17760) {G1,W35,D8,L1,V2,M1} { forward_diamond( star(
% 47.32/47.69 skol1 ), domain_difference( domain( multiplication( X, domain( Y ) ) ),
% 47.32/47.69 forward_diamond( skol1, domain( multiplication( X, domain( Y ) ) ) ) ) )
% 47.32/47.69 ==> addition( domain( multiplication( X, domain( Y ) ) ), forward_diamond
% 47.32/47.69 ( star( skol1 ), domain_difference( forward_diamond( X, Y ),
% 47.32/47.69 forward_diamond( skol1, forward_diamond( X, Y ) ) ) ) ) }.
% 47.32/47.69 substitution0:
% 47.32/47.69 X := X
% 47.32/47.69 Y := Y
% 47.32/47.69 end
% 47.32/47.69 substitution1:
% 47.32/47.69 X := X
% 47.32/47.69 Y := Y
% 47.32/47.69 end
% 47.32/47.69
% 47.32/47.69 paramod: (17765) {G1,W31,D7,L1,V2,M1} { forward_diamond( star( skol1 ),
% 47.32/47.69 domain_difference( domain( multiplication( X, domain( Y ) ) ),
% 47.32/47.69 forward_diamond( skol1, forward_diamond( X, Y ) ) ) ) ==> addition(
% 47.32/47.69 forward_diamond( X, Y ), forward_diamond( star( skol1 ),
% 47.32/47.69 domain_difference( forward_diamond( X, Y ), forward_diamond( skol1,
% 47.32/47.69 forward_diamond( X, Y ) ) ) ) ) }.
% 47.32/47.69 parent0[0]: (23) {G0,W9,D5,L1,V2,M1} I { domain( multiplication( X, domain
% 47.32/47.69 ( Y ) ) ) ==> forward_diamond( X, Y ) }.
% 47.32/47.69 parent1[0; 12]: (17763) {G1,W33,D8,L1,V2,M1} { forward_diamond( star(
% 47.32/47.69 skol1 ), domain_difference( domain( multiplication( X, domain( Y ) ) ),
% 47.32/47.69 forward_diamond( skol1, domain( multiplication( X, domain( Y ) ) ) ) ) )
% 47.32/47.69 ==> addition( forward_diamond( X, Y ), forward_diamond( star( skol1 ),
% 47.32/47.69 domain_difference( forward_diamond( X, Y ), forward_diamond( skol1,
% 47.32/47.69 forward_diamond( X, Y ) ) ) ) ) }.
% 47.32/47.69 substitution0:
% 47.32/47.69 X := X
% 47.32/47.69 Y := Y
% 47.32/47.69 end
% 47.32/47.69 substitution1:
% 47.32/47.69 X := X
% 47.32/47.69 Y := Y
% 47.32/47.69 end
% 47.32/47.69
% 47.32/47.69 paramod: (17766) {G1,W29,D7,L1,V2,M1} { forward_diamond( star( skol1 ),
% 47.32/47.69 domain_difference( forward_diamond( X, Y ), forward_diamond( skol1,
% 47.32/47.69 forward_diamond( X, Y ) ) ) ) ==> addition( forward_diamond( X, Y ),
% 47.32/47.69 forward_diamond( star( skol1 ), domain_difference( forward_diamond( X, Y
% 47.32/47.69 ), forward_diamond( skol1, forward_diamond( X, Y ) ) ) ) ) }.
% 47.32/47.69 parent0[0]: (23) {G0,W9,D5,L1,V2,M1} I { domain( multiplication( X, domain
% 47.32/47.69 ( Y ) ) ) ==> forward_diamond( X, Y ) }.
% 47.32/47.69 parent1[0; 5]: (17765) {G1,W31,D7,L1,V2,M1} { forward_diamond( star( skol1
% 47.32/47.69 ), domain_difference( domain( multiplication( X, domain( Y ) ) ),
% 47.32/47.69 forward_diamond( skol1, forward_diamond( X, Y ) ) ) ) ==> addition(
% 47.32/47.69 forward_diamond( X, Y ), forward_diamond( star( skol1 ),
% 47.32/47.69 domain_difference( forward_diamond( X, Y ), forward_diamond( skol1,
% 47.32/47.69 forward_diamond( X, Y ) ) ) ) ) }.
% 47.32/47.69 substitution0:
% 47.32/47.69 X := X
% 47.32/47.69 Y := Y
% 47.32/47.69 end
% 47.32/47.69 substitution1:
% 47.32/47.69 X := X
% 47.32/47.69 Y := Y
% 47.32/47.69 end
% 47.32/47.69
% 47.32/47.69 eqswap: (17783) {G1,W29,D7,L1,V2,M1} { addition( forward_diamond( X, Y ),
% 47.32/47.69 forward_diamond( star( skol1 ), domain_difference( forward_diamond( X, Y
% 47.32/47.69 ), forward_diamond( skol1, forward_diamond( X, Y ) ) ) ) ) ==>
% 47.32/47.69 forward_diamond( star( skol1 ), domain_difference( forward_diamond( X, Y
% 47.32/47.69 ), forward_diamond( skol1, forward_diamond( X, Y ) ) ) ) }.
% 47.32/47.69 parent0[0]: (17766) {G1,W29,D7,L1,V2,M1} { forward_diamond( star( skol1 )
% 47.32/47.69 , domain_difference( forward_diamond( X, Y ), forward_diamond( skol1,
% 47.32/47.69 forward_diamond( X, Y ) ) ) ) ==> addition( forward_diamond( X, Y ),
% 47.32/47.69 forward_diamond( star( skol1 ), domain_difference( forward_diamond( X, Y
% 47.32/47.69 ), forward_diamond( skol1, forward_diamond( X, Y ) ) ) ) ) }.
% 47.32/47.69 substitution0:
% 47.32/47.69 X := X
% 47.32/47.69 Y := Y
% 47.32/47.69 end
% 47.32/47.69
% 47.32/47.69 subsumption: (368) {G1,W29,D7,L1,V2,M1} P(23,29) { addition(
% 47.32/47.69 forward_diamond( X, Y ), forward_diamond( star( skol1 ),
% 47.32/47.69 domain_difference( forward_diamond( X, Y ), forward_diamond( skol1,
% 47.32/47.69 forward_diamond( X, Y ) ) ) ) ) ==> forward_diamond( star( skol1 ),
% 47.32/47.69 domain_difference( forward_diamond( X, Y ), forward_diamond( skol1,
% 47.32/47.69 forward_diamond( X, Y ) ) ) ) }.
% 47.32/47.69 parent0: (17783) {G1,W29,D7,L1,V2,M1} { addition( forward_diamond( X, Y )
% 47.32/47.69 , forward_diamond( star( skol1 ), domain_difference( forward_diamond( X,
% 47.32/47.69 Y ), forward_diamond( skol1, forward_diamond( X, Y ) ) ) ) ) ==>
% 47.32/47.69 forward_diamond( star( skol1 ), domain_difference( forward_diamond( X, Y
% 68.52/68.96 ), forward_diamond( skol1, forward_diamond( X, Y ) ) ) ) }.
% 68.52/68.96 substitution0:
% 68.52/68.96 X := X
% 68.52/68.96 Y := Y
% 68.52/68.96 end
% 68.52/68.96 permutation0:
% 68.52/68.96 0 ==> 0
% 68.52/68.96 end
% 68.52/68.96
% 68.52/68.96
% 68.52/68.96 ==> (420) {G5,W6,D4,L1,V0,M1} P(134,31);d(32);d(218);d(42);q { !
% 68.52/68.96 forward_diamond( skol1, domain( skol2 ) ) ==> zero }.
% 68.52/68.96
% 68.52/68.96
% 68.52/68.96
% 68.52/68.96 !!! Internal Problem: OH, OH, COULD NOT DERIVE GOAL !!!
% 68.52/68.96
% 68.52/68.96 Bliksem ended
%------------------------------------------------------------------------------