TSTP Solution File: KLE007+2 by Bliksem---1.12
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%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : KLE007+2 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n010.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 01:36:32 EDT 2022
% Result : Theorem 0.95s 1.32s
% Output : Refutation 0.95s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : KLE007+2 : TPTP v8.1.0. Released v4.0.0.
% 0.11/0.13 % Command : bliksem %s
% 0.13/0.34 % Computer : n010.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % DateTime : Thu Jun 16 13:23:53 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.95/1.31 *** allocated 10000 integers for termspace/termends
% 0.95/1.31 *** allocated 10000 integers for clauses
% 0.95/1.31 *** allocated 10000 integers for justifications
% 0.95/1.31 Bliksem 1.12
% 0.95/1.31
% 0.95/1.31
% 0.95/1.31 Automatic Strategy Selection
% 0.95/1.31
% 0.95/1.31
% 0.95/1.31 Clauses:
% 0.95/1.31
% 0.95/1.31 { addition( X, Y ) = addition( Y, X ) }.
% 0.95/1.31 { addition( Z, addition( Y, X ) ) = addition( addition( Z, Y ), X ) }.
% 0.95/1.31 { addition( X, zero ) = X }.
% 0.95/1.31 { addition( X, X ) = X }.
% 0.95/1.31 { multiplication( X, multiplication( Y, Z ) ) = multiplication(
% 0.95/1.31 multiplication( X, Y ), Z ) }.
% 0.95/1.31 { multiplication( X, one ) = X }.
% 0.95/1.31 { multiplication( one, X ) = X }.
% 0.95/1.31 { multiplication( X, addition( Y, Z ) ) = addition( multiplication( X, Y )
% 0.95/1.31 , multiplication( X, Z ) ) }.
% 0.95/1.31 { multiplication( addition( X, Y ), Z ) = addition( multiplication( X, Z )
% 0.95/1.31 , multiplication( Y, Z ) ) }.
% 0.95/1.31 { multiplication( X, zero ) = zero }.
% 0.95/1.31 { multiplication( zero, X ) = zero }.
% 0.95/1.31 { ! leq( X, Y ), addition( X, Y ) = Y }.
% 0.95/1.31 { ! addition( X, Y ) = Y, leq( X, Y ) }.
% 0.95/1.31 { ! test( X ), complement( skol1( X ), X ) }.
% 0.95/1.31 { ! complement( Y, X ), test( X ) }.
% 0.95/1.31 { ! complement( Y, X ), multiplication( X, Y ) = zero }.
% 0.95/1.31 { ! complement( Y, X ), alpha1( X, Y ) }.
% 0.95/1.31 { ! multiplication( X, Y ) = zero, ! alpha1( X, Y ), complement( Y, X ) }.
% 0.95/1.31 { ! alpha1( X, Y ), multiplication( Y, X ) = zero }.
% 0.95/1.31 { ! alpha1( X, Y ), addition( X, Y ) = one }.
% 0.95/1.31 { ! multiplication( Y, X ) = zero, ! addition( X, Y ) = one, alpha1( X, Y )
% 0.95/1.31 }.
% 0.95/1.31 { ! test( X ), ! c( X ) = Y, complement( X, Y ) }.
% 0.95/1.31 { ! test( X ), ! complement( X, Y ), c( X ) = Y }.
% 0.95/1.31 { test( X ), c( X ) = zero }.
% 0.95/1.31 { test( skol3 ) }.
% 0.95/1.31 { test( skol2 ) }.
% 0.95/1.31 { ! leq( one, addition( multiplication( addition( skol2, c( skol2 ) ),
% 0.95/1.31 skol3 ), multiplication( addition( skol2, c( skol2 ) ), c( skol3 ) ) ) )
% 0.95/1.31 , ! leq( addition( multiplication( addition( skol2, c( skol2 ) ), skol3 )
% 0.95/1.31 , multiplication( addition( skol2, c( skol2 ) ), c( skol3 ) ) ), one ) }
% 0.95/1.31 .
% 0.95/1.31
% 0.95/1.31 percentage equality = 0.488889, percentage horn = 0.962963
% 0.95/1.31 This is a problem with some equality
% 0.95/1.31
% 0.95/1.31
% 0.95/1.31
% 0.95/1.31 Options Used:
% 0.95/1.31
% 0.95/1.31 useres = 1
% 0.95/1.31 useparamod = 1
% 0.95/1.31 useeqrefl = 1
% 0.95/1.31 useeqfact = 1
% 0.95/1.31 usefactor = 1
% 0.95/1.31 usesimpsplitting = 0
% 0.95/1.31 usesimpdemod = 5
% 0.95/1.31 usesimpres = 3
% 0.95/1.31
% 0.95/1.31 resimpinuse = 1000
% 0.95/1.31 resimpclauses = 20000
% 0.95/1.31 substype = eqrewr
% 0.95/1.31 backwardsubs = 1
% 0.95/1.31 selectoldest = 5
% 0.95/1.31
% 0.95/1.31 litorderings [0] = split
% 0.95/1.31 litorderings [1] = extend the termordering, first sorting on arguments
% 0.95/1.31
% 0.95/1.31 termordering = kbo
% 0.95/1.31
% 0.95/1.31 litapriori = 0
% 0.95/1.31 termapriori = 1
% 0.95/1.31 litaposteriori = 0
% 0.95/1.31 termaposteriori = 0
% 0.95/1.31 demodaposteriori = 0
% 0.95/1.31 ordereqreflfact = 0
% 0.95/1.31
% 0.95/1.31 litselect = negord
% 0.95/1.31
% 0.95/1.31 maxweight = 15
% 0.95/1.31 maxdepth = 30000
% 0.95/1.31 maxlength = 115
% 0.95/1.31 maxnrvars = 195
% 0.95/1.31 excuselevel = 1
% 0.95/1.31 increasemaxweight = 1
% 0.95/1.31
% 0.95/1.31 maxselected = 10000000
% 0.95/1.31 maxnrclauses = 10000000
% 0.95/1.31
% 0.95/1.31 showgenerated = 0
% 0.95/1.31 showkept = 0
% 0.95/1.31 showselected = 0
% 0.95/1.31 showdeleted = 0
% 0.95/1.31 showresimp = 1
% 0.95/1.31 showstatus = 2000
% 0.95/1.31
% 0.95/1.31 prologoutput = 0
% 0.95/1.31 nrgoals = 5000000
% 0.95/1.31 totalproof = 1
% 0.95/1.31
% 0.95/1.31 Symbols occurring in the translation:
% 0.95/1.31
% 0.95/1.31 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.95/1.31 . [1, 2] (w:1, o:23, a:1, s:1, b:0),
% 0.95/1.31 ! [4, 1] (w:0, o:15, a:1, s:1, b:0),
% 0.95/1.32 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.95/1.32 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.95/1.32 addition [37, 2] (w:1, o:47, a:1, s:1, b:0),
% 0.95/1.32 zero [39, 0] (w:1, o:9, a:1, s:1, b:0),
% 0.95/1.32 multiplication [40, 2] (w:1, o:49, a:1, s:1, b:0),
% 0.95/1.32 one [41, 0] (w:1, o:10, a:1, s:1, b:0),
% 0.95/1.32 leq [42, 2] (w:1, o:48, a:1, s:1, b:0),
% 0.95/1.32 test [44, 1] (w:1, o:21, a:1, s:1, b:0),
% 0.95/1.32 complement [46, 2] (w:1, o:50, a:1, s:1, b:0),
% 0.95/1.32 c [47, 1] (w:1, o:22, a:1, s:1, b:0),
% 0.95/1.32 alpha1 [48, 2] (w:1, o:51, a:1, s:1, b:1),
% 0.95/1.32 skol1 [49, 1] (w:1, o:20, a:1, s:1, b:1),
% 0.95/1.32 skol2 [50, 0] (w:1, o:13, a:1, s:1, b:1),
% 0.95/1.32 skol3 [51, 0] (w:1, o:14, a:1, s:1, b:1).
% 0.95/1.32
% 0.95/1.32
% 0.95/1.32 Starting Search:
% 0.95/1.32
% 0.95/1.32 *** allocated 15000 integers for clauses
% 0.95/1.32 *** allocated 22500 integers for clauses
% 0.95/1.32 *** allocated 33750 integers for clauses
% 0.95/1.32 *** allocated 50625 integers for clauses
% 0.95/1.32 *** allocated 15000 integers for termspace/termends
% 0.95/1.32 *** allocated 75937 integers for clauses
% 0.95/1.32 Resimplifying inuse:
% 0.95/1.32 Done
% 0.95/1.32
% 0.95/1.32 *** allocated 22500 integers for termspace/termends
% 0.95/1.32 *** allocated 113905 integers for clauses
% 0.95/1.32 *** allocated 33750 integers for termspace/termends
% 0.95/1.32
% 0.95/1.32 Intermediate Status:
% 0.95/1.32 Generated: 14793
% 0.95/1.32 Kept: 2086
% 0.95/1.32 Inuse: 230
% 0.95/1.32 Deleted: 53
% 0.95/1.32 Deletedinuse: 22
% 0.95/1.32
% 0.95/1.32 Resimplifying inuse:
% 0.95/1.32 Done
% 0.95/1.32
% 0.95/1.32 *** allocated 170857 integers for clauses
% 0.95/1.32
% 0.95/1.32 Bliksems!, er is een bewijs:
% 0.95/1.32 % SZS status Theorem
% 0.95/1.32 % SZS output start Refutation
% 0.95/1.32
% 0.95/1.32 (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X ) }.
% 0.95/1.32 (3) {G0,W5,D3,L1,V1,M1} I { addition( X, X ) ==> X }.
% 0.95/1.32 (6) {G0,W5,D3,L1,V1,M1} I { multiplication( one, X ) ==> X }.
% 0.95/1.32 (7) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Y ),
% 0.95/1.32 multiplication( X, Z ) ) ==> multiplication( X, addition( Y, Z ) ) }.
% 0.95/1.32 (12) {G0,W8,D3,L2,V2,M2} I { ! addition( X, Y ) ==> Y, leq( X, Y ) }.
% 0.95/1.32 (13) {G0,W6,D3,L2,V1,M2} I { ! test( X ), complement( skol1( X ), X ) }.
% 0.95/1.32 (15) {G0,W8,D3,L2,V2,M2} I { ! complement( Y, X ), multiplication( X, Y )
% 0.95/1.32 ==> zero }.
% 0.95/1.32 (16) {G0,W6,D2,L2,V2,M2} I { ! complement( Y, X ), alpha1( X, Y ) }.
% 0.95/1.32 (17) {G0,W11,D3,L3,V2,M3} I { ! multiplication( X, Y ) ==> zero, ! alpha1(
% 0.95/1.32 X, Y ), complement( Y, X ) }.
% 0.95/1.32 (18) {G0,W8,D3,L2,V2,M2} I { ! alpha1( X, Y ), multiplication( Y, X ) ==>
% 0.95/1.32 zero }.
% 0.95/1.32 (19) {G0,W8,D3,L2,V2,M2} I { ! alpha1( X, Y ), addition( X, Y ) ==> one }.
% 0.95/1.32 (20) {G0,W13,D3,L3,V2,M3} I { ! multiplication( Y, X ) ==> zero, ! addition
% 0.95/1.32 ( X, Y ) ==> one, alpha1( X, Y ) }.
% 0.95/1.32 (22) {G0,W9,D3,L3,V2,M3} I { ! test( X ), ! complement( X, Y ), c( X ) = Y
% 0.95/1.32 }.
% 0.95/1.32 (24) {G0,W2,D2,L1,V0,M1} I { test( skol3 ) }.
% 0.95/1.32 (25) {G0,W2,D2,L1,V0,M1} I { test( skol2 ) }.
% 0.95/1.32 (26) {G1,W22,D5,L2,V0,M2} I;d(7);d(7) { ! leq( one, multiplication(
% 0.95/1.32 addition( skol2, c( skol2 ) ), addition( skol3, c( skol3 ) ) ) ), ! leq(
% 0.95/1.32 multiplication( addition( skol2, c( skol2 ) ), addition( skol3, c( skol3
% 0.95/1.32 ) ) ), one ) }.
% 0.95/1.32 (145) {G1,W3,D2,L1,V1,M1} R(12,3) { leq( X, X ) }.
% 0.95/1.32 (179) {G1,W4,D3,L1,V0,M1} R(13,24) { complement( skol1( skol3 ), skol3 )
% 0.95/1.32 }.
% 0.95/1.32 (180) {G1,W4,D3,L1,V0,M1} R(13,25) { complement( skol1( skol2 ), skol2 )
% 0.95/1.32 }.
% 0.95/1.32 (183) {G2,W4,D3,L1,V0,M1} R(179,16) { alpha1( skol3, skol1( skol3 ) ) }.
% 0.95/1.32 (187) {G2,W4,D3,L1,V0,M1} R(180,16) { alpha1( skol2, skol1( skol2 ) ) }.
% 0.95/1.32 (190) {G2,W6,D4,L1,V0,M1} R(15,180) { multiplication( skol2, skol1( skol2 )
% 0.95/1.32 ) ==> zero }.
% 0.95/1.32 (191) {G2,W6,D4,L1,V0,M1} R(15,179) { multiplication( skol3, skol1( skol3 )
% 0.95/1.32 ) ==> zero }.
% 0.95/1.32 (232) {G3,W6,D4,L1,V0,M1} R(18,187) { multiplication( skol1( skol2 ), skol2
% 0.95/1.32 ) ==> zero }.
% 0.95/1.32 (233) {G3,W6,D4,L1,V0,M1} R(18,183) { multiplication( skol1( skol3 ), skol3
% 0.95/1.32 ) ==> zero }.
% 0.95/1.32 (258) {G3,W6,D4,L1,V0,M1} R(19,187) { addition( skol2, skol1( skol2 ) ) ==>
% 0.95/1.32 one }.
% 0.95/1.32 (259) {G3,W6,D4,L1,V0,M1} R(19,183) { addition( skol3, skol1( skol3 ) ) ==>
% 0.95/1.32 one }.
% 0.95/1.32 (2187) {G4,W6,D4,L1,V0,M1} P(258,0) { addition( skol1( skol2 ), skol2 ) ==>
% 0.95/1.32 one }.
% 0.95/1.32 (2224) {G5,W4,D3,L1,V0,M1} R(2187,20);d(190);q { alpha1( skol1( skol2 ),
% 0.95/1.32 skol2 ) }.
% 0.95/1.32 (2240) {G6,W4,D3,L1,V0,M1} R(2224,17);d(232);q { complement( skol2, skol1(
% 0.95/1.32 skol2 ) ) }.
% 0.95/1.32 (2245) {G7,W5,D3,L1,V0,M1} R(2240,22);r(25) { c( skol2 ) ==> skol1( skol2 )
% 0.95/1.32 }.
% 0.95/1.32 (2553) {G4,W6,D4,L1,V0,M1} P(259,0) { addition( skol1( skol3 ), skol3 ) ==>
% 0.95/1.32 one }.
% 0.95/1.32 (2605) {G5,W4,D3,L1,V0,M1} R(2553,20);d(191);q { alpha1( skol1( skol3 ),
% 0.95/1.32 skol3 ) }.
% 0.95/1.32 (2621) {G6,W4,D3,L1,V0,M1} R(2605,17);d(233);q { complement( skol3, skol1(
% 0.95/1.32 skol3 ) ) }.
% 0.95/1.32 (2626) {G7,W5,D3,L1,V0,M1} R(2621,22);r(24) { c( skol3 ) ==> skol1( skol3 )
% 0.95/1.32 }.
% 0.95/1.32 (2661) {G8,W0,D0,L0,V0,M0} P(2626,26);d(2245);d(2245);d(258);d(258);d(6);d(
% 0.95/1.32 6);d(259);d(259);f;r(145) { }.
% 0.95/1.32
% 0.95/1.32
% 0.95/1.32 % SZS output end Refutation
% 0.95/1.32 found a proof!
% 0.95/1.32
% 0.95/1.32
% 0.95/1.32 Unprocessed initial clauses:
% 0.95/1.32
% 0.95/1.32 (2663) {G0,W7,D3,L1,V2,M1} { addition( X, Y ) = addition( Y, X ) }.
% 0.95/1.32 (2664) {G0,W11,D4,L1,V3,M1} { addition( Z, addition( Y, X ) ) = addition(
% 0.95/1.32 addition( Z, Y ), X ) }.
% 0.95/1.32 (2665) {G0,W5,D3,L1,V1,M1} { addition( X, zero ) = X }.
% 0.95/1.32 (2666) {G0,W5,D3,L1,V1,M1} { addition( X, X ) = X }.
% 0.95/1.32 (2667) {G0,W11,D4,L1,V3,M1} { multiplication( X, multiplication( Y, Z ) )
% 0.95/1.32 = multiplication( multiplication( X, Y ), Z ) }.
% 0.95/1.32 (2668) {G0,W5,D3,L1,V1,M1} { multiplication( X, one ) = X }.
% 0.95/1.32 (2669) {G0,W5,D3,L1,V1,M1} { multiplication( one, X ) = X }.
% 0.95/1.32 (2670) {G0,W13,D4,L1,V3,M1} { multiplication( X, addition( Y, Z ) ) =
% 0.95/1.32 addition( multiplication( X, Y ), multiplication( X, Z ) ) }.
% 0.95/1.32 (2671) {G0,W13,D4,L1,V3,M1} { multiplication( addition( X, Y ), Z ) =
% 0.95/1.32 addition( multiplication( X, Z ), multiplication( Y, Z ) ) }.
% 0.95/1.32 (2672) {G0,W5,D3,L1,V1,M1} { multiplication( X, zero ) = zero }.
% 0.95/1.32 (2673) {G0,W5,D3,L1,V1,M1} { multiplication( zero, X ) = zero }.
% 0.95/1.32 (2674) {G0,W8,D3,L2,V2,M2} { ! leq( X, Y ), addition( X, Y ) = Y }.
% 0.95/1.32 (2675) {G0,W8,D3,L2,V2,M2} { ! addition( X, Y ) = Y, leq( X, Y ) }.
% 0.95/1.32 (2676) {G0,W6,D3,L2,V1,M2} { ! test( X ), complement( skol1( X ), X ) }.
% 0.95/1.32 (2677) {G0,W5,D2,L2,V2,M2} { ! complement( Y, X ), test( X ) }.
% 0.95/1.32 (2678) {G0,W8,D3,L2,V2,M2} { ! complement( Y, X ), multiplication( X, Y )
% 0.95/1.32 = zero }.
% 0.95/1.32 (2679) {G0,W6,D2,L2,V2,M2} { ! complement( Y, X ), alpha1( X, Y ) }.
% 0.95/1.32 (2680) {G0,W11,D3,L3,V2,M3} { ! multiplication( X, Y ) = zero, ! alpha1( X
% 0.95/1.32 , Y ), complement( Y, X ) }.
% 0.95/1.32 (2681) {G0,W8,D3,L2,V2,M2} { ! alpha1( X, Y ), multiplication( Y, X ) =
% 0.95/1.32 zero }.
% 0.95/1.32 (2682) {G0,W8,D3,L2,V2,M2} { ! alpha1( X, Y ), addition( X, Y ) = one }.
% 0.95/1.32 (2683) {G0,W13,D3,L3,V2,M3} { ! multiplication( Y, X ) = zero, ! addition
% 0.95/1.32 ( X, Y ) = one, alpha1( X, Y ) }.
% 0.95/1.32 (2684) {G0,W9,D3,L3,V2,M3} { ! test( X ), ! c( X ) = Y, complement( X, Y )
% 0.95/1.32 }.
% 0.95/1.32 (2685) {G0,W9,D3,L3,V2,M3} { ! test( X ), ! complement( X, Y ), c( X ) = Y
% 0.95/1.32 }.
% 0.95/1.32 (2686) {G0,W6,D3,L2,V1,M2} { test( X ), c( X ) = zero }.
% 0.95/1.32 (2687) {G0,W2,D2,L1,V0,M1} { test( skol3 ) }.
% 0.95/1.32 (2688) {G0,W2,D2,L1,V0,M1} { test( skol2 ) }.
% 0.95/1.32 (2689) {G0,W32,D6,L2,V0,M2} { ! leq( one, addition( multiplication(
% 0.95/1.32 addition( skol2, c( skol2 ) ), skol3 ), multiplication( addition( skol2,
% 0.95/1.32 c( skol2 ) ), c( skol3 ) ) ) ), ! leq( addition( multiplication( addition
% 0.95/1.32 ( skol2, c( skol2 ) ), skol3 ), multiplication( addition( skol2, c( skol2
% 0.95/1.32 ) ), c( skol3 ) ) ), one ) }.
% 0.95/1.32
% 0.95/1.32
% 0.95/1.32 Total Proof:
% 0.95/1.32
% 0.95/1.32 subsumption: (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X
% 0.95/1.32 ) }.
% 0.95/1.32 parent0: (2663) {G0,W7,D3,L1,V2,M1} { addition( X, Y ) = addition( Y, X )
% 0.95/1.32 }.
% 0.95/1.32 substitution0:
% 0.95/1.32 X := X
% 0.95/1.32 Y := Y
% 0.95/1.32 end
% 0.95/1.32 permutation0:
% 0.95/1.32 0 ==> 0
% 0.95/1.32 end
% 0.95/1.32
% 0.95/1.32 subsumption: (3) {G0,W5,D3,L1,V1,M1} I { addition( X, X ) ==> X }.
% 0.95/1.32 parent0: (2666) {G0,W5,D3,L1,V1,M1} { addition( X, X ) = X }.
% 0.95/1.32 substitution0:
% 0.95/1.32 X := X
% 0.95/1.32 end
% 0.95/1.32 permutation0:
% 0.95/1.32 0 ==> 0
% 0.95/1.32 end
% 0.95/1.32
% 0.95/1.32 subsumption: (6) {G0,W5,D3,L1,V1,M1} I { multiplication( one, X ) ==> X }.
% 0.95/1.32 parent0: (2669) {G0,W5,D3,L1,V1,M1} { multiplication( one, X ) = X }.
% 0.95/1.32 substitution0:
% 0.95/1.32 X := X
% 0.95/1.32 end
% 0.95/1.32 permutation0:
% 0.95/1.32 0 ==> 0
% 0.95/1.32 end
% 0.95/1.32
% 0.95/1.32 eqswap: (2705) {G0,W13,D4,L1,V3,M1} { addition( multiplication( X, Y ),
% 0.95/1.32 multiplication( X, Z ) ) = multiplication( X, addition( Y, Z ) ) }.
% 0.95/1.32 parent0[0]: (2670) {G0,W13,D4,L1,V3,M1} { multiplication( X, addition( Y,
% 0.95/1.32 Z ) ) = addition( multiplication( X, Y ), multiplication( X, Z ) ) }.
% 0.95/1.32 substitution0:
% 0.95/1.32 X := X
% 0.95/1.32 Y := Y
% 0.95/1.32 Z := Z
% 0.95/1.32 end
% 0.95/1.32
% 0.95/1.32 subsumption: (7) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Y )
% 0.95/1.32 , multiplication( X, Z ) ) ==> multiplication( X, addition( Y, Z ) ) }.
% 0.95/1.32 parent0: (2705) {G0,W13,D4,L1,V3,M1} { addition( multiplication( X, Y ),
% 0.95/1.32 multiplication( X, Z ) ) = multiplication( X, addition( Y, Z ) ) }.
% 0.95/1.32 substitution0:
% 0.95/1.32 X := X
% 0.95/1.32 Y := Y
% 0.95/1.32 Z := Z
% 0.95/1.32 end
% 0.95/1.32 permutation0:
% 0.95/1.32 0 ==> 0
% 0.95/1.32 end
% 0.95/1.32
% 0.95/1.32 subsumption: (12) {G0,W8,D3,L2,V2,M2} I { ! addition( X, Y ) ==> Y, leq( X
% 0.95/1.32 , Y ) }.
% 0.95/1.32 parent0: (2675) {G0,W8,D3,L2,V2,M2} { ! addition( X, Y ) = Y, leq( X, Y )
% 0.95/1.32 }.
% 0.95/1.32 substitution0:
% 0.95/1.32 X := X
% 0.95/1.32 Y := Y
% 0.95/1.32 end
% 0.95/1.32 permutation0:
% 0.95/1.32 0 ==> 0
% 0.95/1.32 1 ==> 1
% 0.95/1.32 end
% 0.95/1.32
% 0.95/1.32 subsumption: (13) {G0,W6,D3,L2,V1,M2} I { ! test( X ), complement( skol1( X
% 0.95/1.32 ), X ) }.
% 0.95/1.32 parent0: (2676) {G0,W6,D3,L2,V1,M2} { ! test( X ), complement( skol1( X )
% 0.95/1.32 , X ) }.
% 0.95/1.32 substitution0:
% 0.95/1.32 X := X
% 0.95/1.32 end
% 0.95/1.32 permutation0:
% 0.95/1.32 0 ==> 0
% 0.95/1.32 1 ==> 1
% 0.95/1.32 end
% 0.95/1.32
% 0.95/1.32 subsumption: (15) {G0,W8,D3,L2,V2,M2} I { ! complement( Y, X ),
% 0.95/1.32 multiplication( X, Y ) ==> zero }.
% 0.95/1.32 parent0: (2678) {G0,W8,D3,L2,V2,M2} { ! complement( Y, X ), multiplication
% 0.95/1.32 ( X, Y ) = zero }.
% 0.95/1.32 substitution0:
% 0.95/1.32 X := X
% 0.95/1.32 Y := Y
% 0.95/1.32 end
% 0.95/1.32 permutation0:
% 0.95/1.32 0 ==> 0
% 0.95/1.32 1 ==> 1
% 0.95/1.32 end
% 0.95/1.32
% 0.95/1.32 subsumption: (16) {G0,W6,D2,L2,V2,M2} I { ! complement( Y, X ), alpha1( X,
% 0.95/1.32 Y ) }.
% 0.95/1.32 parent0: (2679) {G0,W6,D2,L2,V2,M2} { ! complement( Y, X ), alpha1( X, Y )
% 0.95/1.32 }.
% 0.95/1.32 substitution0:
% 0.95/1.32 X := X
% 0.95/1.32 Y := Y
% 0.95/1.32 end
% 0.95/1.32 permutation0:
% 0.95/1.32 0 ==> 0
% 0.95/1.32 1 ==> 1
% 0.95/1.32 end
% 0.95/1.32
% 0.95/1.32 subsumption: (17) {G0,W11,D3,L3,V2,M3} I { ! multiplication( X, Y ) ==>
% 0.95/1.32 zero, ! alpha1( X, Y ), complement( Y, X ) }.
% 0.95/1.32 parent0: (2680) {G0,W11,D3,L3,V2,M3} { ! multiplication( X, Y ) = zero, !
% 0.95/1.32 alpha1( X, Y ), complement( Y, X ) }.
% 0.95/1.32 substitution0:
% 0.95/1.32 X := X
% 0.95/1.32 Y := Y
% 0.95/1.32 end
% 0.95/1.32 permutation0:
% 0.95/1.32 0 ==> 0
% 0.95/1.32 1 ==> 1
% 0.95/1.32 2 ==> 2
% 0.95/1.32 end
% 0.95/1.32
% 0.95/1.32 subsumption: (18) {G0,W8,D3,L2,V2,M2} I { ! alpha1( X, Y ), multiplication
% 0.95/1.32 ( Y, X ) ==> zero }.
% 0.95/1.32 parent0: (2681) {G0,W8,D3,L2,V2,M2} { ! alpha1( X, Y ), multiplication( Y
% 0.95/1.32 , X ) = zero }.
% 0.95/1.32 substitution0:
% 0.95/1.32 X := X
% 0.95/1.32 Y := Y
% 0.95/1.32 end
% 0.95/1.32 permutation0:
% 0.95/1.32 0 ==> 0
% 0.95/1.32 1 ==> 1
% 0.95/1.32 end
% 0.95/1.32
% 0.95/1.32 subsumption: (19) {G0,W8,D3,L2,V2,M2} I { ! alpha1( X, Y ), addition( X, Y
% 0.95/1.32 ) ==> one }.
% 0.95/1.32 parent0: (2682) {G0,W8,D3,L2,V2,M2} { ! alpha1( X, Y ), addition( X, Y ) =
% 0.95/1.32 one }.
% 0.95/1.32 substitution0:
% 0.95/1.32 X := X
% 0.95/1.32 Y := Y
% 0.95/1.32 end
% 0.95/1.32 permutation0:
% 0.95/1.32 0 ==> 0
% 0.95/1.32 1 ==> 1
% 0.95/1.32 end
% 0.95/1.32
% 0.95/1.32 subsumption: (20) {G0,W13,D3,L3,V2,M3} I { ! multiplication( Y, X ) ==>
% 0.95/1.32 zero, ! addition( X, Y ) ==> one, alpha1( X, Y ) }.
% 0.95/1.32 parent0: (2683) {G0,W13,D3,L3,V2,M3} { ! multiplication( Y, X ) = zero, !
% 0.95/1.32 addition( X, Y ) = one, alpha1( X, Y ) }.
% 0.95/1.32 substitution0:
% 0.95/1.32 X := X
% 0.95/1.32 Y := Y
% 0.95/1.32 end
% 0.95/1.32 permutation0:
% 0.95/1.32 0 ==> 0
% 0.95/1.32 1 ==> 1
% 0.95/1.32 2 ==> 2
% 0.95/1.32 end
% 0.95/1.32
% 0.95/1.32 subsumption: (22) {G0,W9,D3,L3,V2,M3} I { ! test( X ), ! complement( X, Y )
% 0.95/1.32 , c( X ) = Y }.
% 0.95/1.32 parent0: (2685) {G0,W9,D3,L3,V2,M3} { ! test( X ), ! complement( X, Y ), c
% 0.95/1.32 ( X ) = Y }.
% 0.95/1.32 substitution0:
% 0.95/1.32 X := X
% 0.95/1.32 Y := Y
% 0.95/1.32 end
% 0.95/1.32 permutation0:
% 0.95/1.32 0 ==> 0
% 0.95/1.32 1 ==> 1
% 0.95/1.32 2 ==> 2
% 0.95/1.32 end
% 0.95/1.32
% 0.95/1.32 subsumption: (24) {G0,W2,D2,L1,V0,M1} I { test( skol3 ) }.
% 0.95/1.32 parent0: (2687) {G0,W2,D2,L1,V0,M1} { test( skol3 ) }.
% 0.95/1.32 substitution0:
% 0.95/1.32 end
% 0.95/1.32 permutation0:
% 0.95/1.32 0 ==> 0
% 0.95/1.32 end
% 0.95/1.32
% 0.95/1.32 subsumption: (25) {G0,W2,D2,L1,V0,M1} I { test( skol2 ) }.
% 0.95/1.32 parent0: (2688) {G0,W2,D2,L1,V0,M1} { test( skol2 ) }.
% 0.95/1.32 substitution0:
% 0.95/1.32 end
% 0.95/1.32 permutation0:
% 0.95/1.32 0 ==> 0
% 0.95/1.32 end
% 0.95/1.32
% 0.95/1.32 *** allocated 50625 integers for termspace/termends
% 0.95/1.32 paramod: (2964) {G1,W27,D6,L2,V0,M2} { ! leq( multiplication( addition(
% 0.95/1.32 skol2, c( skol2 ) ), addition( skol3, c( skol3 ) ) ), one ), ! leq( one,
% 0.95/1.32 addition( multiplication( addition( skol2, c( skol2 ) ), skol3 ),
% 0.95/1.32 multiplication( addition( skol2, c( skol2 ) ), c( skol3 ) ) ) ) }.
% 0.95/1.32 parent0[0]: (7) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Y ),
% 0.95/1.32 multiplication( X, Z ) ) ==> multiplication( X, addition( Y, Z ) ) }.
% 0.95/1.32 parent1[1; 2]: (2689) {G0,W32,D6,L2,V0,M2} { ! leq( one, addition(
% 0.95/1.32 multiplication( addition( skol2, c( skol2 ) ), skol3 ), multiplication(
% 0.95/1.32 addition( skol2, c( skol2 ) ), c( skol3 ) ) ) ), ! leq( addition(
% 0.95/1.32 multiplication( addition( skol2, c( skol2 ) ), skol3 ), multiplication(
% 0.95/1.32 addition( skol2, c( skol2 ) ), c( skol3 ) ) ), one ) }.
% 0.95/1.32 substitution0:
% 0.95/1.32 X := addition( skol2, c( skol2 ) )
% 0.95/1.32 Y := skol3
% 0.95/1.32 Z := c( skol3 )
% 0.95/1.32 end
% 0.95/1.32 substitution1:
% 0.95/1.32 end
% 0.95/1.32
% 0.95/1.32 paramod: (2966) {G1,W22,D5,L2,V0,M2} { ! leq( one, multiplication(
% 0.95/1.32 addition( skol2, c( skol2 ) ), addition( skol3, c( skol3 ) ) ) ), ! leq(
% 0.95/1.32 multiplication( addition( skol2, c( skol2 ) ), addition( skol3, c( skol3
% 0.95/1.32 ) ) ), one ) }.
% 0.95/1.32 parent0[0]: (7) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Y ),
% 0.95/1.32 multiplication( X, Z ) ) ==> multiplication( X, addition( Y, Z ) ) }.
% 0.95/1.32 parent1[1; 3]: (2964) {G1,W27,D6,L2,V0,M2} { ! leq( multiplication(
% 0.95/1.32 addition( skol2, c( skol2 ) ), addition( skol3, c( skol3 ) ) ), one ), !
% 0.95/1.32 leq( one, addition( multiplication( addition( skol2, c( skol2 ) ), skol3
% 0.95/1.32 ), multiplication( addition( skol2, c( skol2 ) ), c( skol3 ) ) ) ) }.
% 0.95/1.32 substitution0:
% 0.95/1.32 X := addition( skol2, c( skol2 ) )
% 0.95/1.32 Y := skol3
% 0.95/1.32 Z := c( skol3 )
% 0.95/1.32 end
% 0.95/1.32 substitution1:
% 0.95/1.32 end
% 0.95/1.32
% 0.95/1.32 subsumption: (26) {G1,W22,D5,L2,V0,M2} I;d(7);d(7) { ! leq( one,
% 0.95/1.32 multiplication( addition( skol2, c( skol2 ) ), addition( skol3, c( skol3
% 0.95/1.32 ) ) ) ), ! leq( multiplication( addition( skol2, c( skol2 ) ), addition
% 0.95/1.32 ( skol3, c( skol3 ) ) ), one ) }.
% 0.95/1.32 parent0: (2966) {G1,W22,D5,L2,V0,M2} { ! leq( one, multiplication(
% 0.95/1.32 addition( skol2, c( skol2 ) ), addition( skol3, c( skol3 ) ) ) ), ! leq(
% 0.95/1.32 multiplication( addition( skol2, c( skol2 ) ), addition( skol3, c( skol3
% 0.95/1.32 ) ) ), one ) }.
% 0.95/1.32 substitution0:
% 0.95/1.32 end
% 0.95/1.32 permutation0:
% 0.95/1.32 0 ==> 0
% 0.95/1.32 1 ==> 1
% 0.95/1.32 end
% 0.95/1.32
% 0.95/1.32 eqswap: (2967) {G0,W8,D3,L2,V2,M2} { ! Y ==> addition( X, Y ), leq( X, Y )
% 0.95/1.32 }.
% 0.95/1.32 parent0[0]: (12) {G0,W8,D3,L2,V2,M2} I { ! addition( X, Y ) ==> Y, leq( X,
% 0.95/1.32 Y ) }.
% 0.95/1.32 substitution0:
% 0.95/1.32 X := X
% 0.95/1.32 Y := Y
% 0.95/1.32 end
% 0.95/1.32
% 0.95/1.32 eqswap: (2968) {G0,W5,D3,L1,V1,M1} { X ==> addition( X, X ) }.
% 0.95/1.32 parent0[0]: (3) {G0,W5,D3,L1,V1,M1} I { addition( X, X ) ==> X }.
% 0.95/1.32 substitution0:
% 0.95/1.32 X := X
% 0.95/1.32 end
% 0.95/1.32
% 0.95/1.32 resolution: (2969) {G1,W3,D2,L1,V1,M1} { leq( X, X ) }.
% 0.95/1.32 parent0[0]: (2967) {G0,W8,D3,L2,V2,M2} { ! Y ==> addition( X, Y ), leq( X
% 0.95/1.32 , Y ) }.
% 0.95/1.32 parent1[0]: (2968) {G0,W5,D3,L1,V1,M1} { X ==> addition( X, X ) }.
% 0.95/1.32 substitution0:
% 0.95/1.32 X := X
% 0.95/1.32 Y := X
% 0.95/1.32 end
% 0.95/1.32 substitution1:
% 0.95/1.32 X := X
% 0.95/1.32 end
% 0.95/1.32
% 0.95/1.32 subsumption: (145) {G1,W3,D2,L1,V1,M1} R(12,3) { leq( X, X ) }.
% 0.95/1.32 parent0: (2969) {G1,W3,D2,L1,V1,M1} { leq( X, X ) }.
% 0.95/1.32 substitution0:
% 0.95/1.32 X := X
% 0.95/1.32 end
% 0.95/1.32 permutation0:
% 0.95/1.32 0 ==> 0
% 0.95/1.32 end
% 0.95/1.32
% 0.95/1.32 resolution: (2970) {G1,W4,D3,L1,V0,M1} { complement( skol1( skol3 ), skol3
% 0.95/1.32 ) }.
% 0.95/1.32 parent0[0]: (13) {G0,W6,D3,L2,V1,M2} I { ! test( X ), complement( skol1( X
% 0.95/1.32 ), X ) }.
% 0.95/1.32 parent1[0]: (24) {G0,W2,D2,L1,V0,M1} I { test( skol3 ) }.
% 0.95/1.32 substitution0:
% 0.95/1.32 X := skol3
% 0.95/1.32 end
% 0.95/1.32 substitution1:
% 0.95/1.32 end
% 0.95/1.32
% 0.95/1.32 subsumption: (179) {G1,W4,D3,L1,V0,M1} R(13,24) { complement( skol1( skol3
% 0.95/1.32 ), skol3 ) }.
% 0.95/1.32 parent0: (2970) {G1,W4,D3,L1,V0,M1} { complement( skol1( skol3 ), skol3 )
% 0.95/1.32 }.
% 0.95/1.32 substitution0:
% 0.95/1.32 end
% 0.95/1.32 permutation0:
% 0.95/1.32 0 ==> 0
% 0.95/1.32 end
% 0.95/1.32
% 0.95/1.32 resolution: (2971) {G1,W4,D3,L1,V0,M1} { complement( skol1( skol2 ), skol2
% 0.95/1.32 ) }.
% 0.95/1.32 parent0[0]: (13) {G0,W6,D3,L2,V1,M2} I { ! test( X ), complement( skol1( X
% 0.95/1.32 ), X ) }.
% 0.95/1.32 parent1[0]: (25) {G0,W2,D2,L1,V0,M1} I { test( skol2 ) }.
% 0.95/1.32 substitution0:
% 0.95/1.32 X := skol2
% 0.95/1.32 end
% 0.95/1.32 substitution1:
% 0.95/1.32 end
% 0.95/1.32
% 0.95/1.32 subsumption: (180) {G1,W4,D3,L1,V0,M1} R(13,25) { complement( skol1( skol2
% 0.95/1.32 ), skol2 ) }.
% 0.95/1.32 parent0: (2971) {G1,W4,D3,L1,V0,M1} { complement( skol1( skol2 ), skol2 )
% 0.95/1.32 }.
% 0.95/1.32 substitution0:
% 0.95/1.32 end
% 0.95/1.32 permutation0:
% 0.95/1.32 0 ==> 0
% 0.95/1.32 end
% 0.95/1.32
% 0.95/1.32 resolution: (2972) {G1,W4,D3,L1,V0,M1} { alpha1( skol3, skol1( skol3 ) )
% 0.95/1.32 }.
% 0.95/1.32 parent0[0]: (16) {G0,W6,D2,L2,V2,M2} I { ! complement( Y, X ), alpha1( X, Y
% 0.95/1.32 ) }.
% 0.95/1.32 parent1[0]: (179) {G1,W4,D3,L1,V0,M1} R(13,24) { complement( skol1( skol3 )
% 0.95/1.32 , skol3 ) }.
% 0.95/1.32 substitution0:
% 0.95/1.32 X := skol3
% 0.95/1.32 Y := skol1( skol3 )
% 0.95/1.32 end
% 0.95/1.32 substitution1:
% 0.95/1.32 end
% 0.95/1.32
% 0.95/1.32 subsumption: (183) {G2,W4,D3,L1,V0,M1} R(179,16) { alpha1( skol3, skol1(
% 0.95/1.32 skol3 ) ) }.
% 0.95/1.32 parent0: (2972) {G1,W4,D3,L1,V0,M1} { alpha1( skol3, skol1( skol3 ) ) }.
% 0.95/1.32 substitution0:
% 0.95/1.32 end
% 0.95/1.32 permutation0:
% 0.95/1.32 0 ==> 0
% 0.95/1.32 end
% 0.95/1.32
% 0.95/1.32 resolution: (2973) {G1,W4,D3,L1,V0,M1} { alpha1( skol2, skol1( skol2 ) )
% 0.95/1.32 }.
% 0.95/1.32 parent0[0]: (16) {G0,W6,D2,L2,V2,M2} I { ! complement( Y, X ), alpha1( X, Y
% 0.95/1.32 ) }.
% 0.95/1.32 parent1[0]: (180) {G1,W4,D3,L1,V0,M1} R(13,25) { complement( skol1( skol2 )
% 0.95/1.32 , skol2 ) }.
% 0.95/1.32 substitution0:
% 0.95/1.32 X := skol2
% 0.95/1.32 Y := skol1( skol2 )
% 0.95/1.32 end
% 0.95/1.32 substitution1:
% 0.95/1.32 end
% 0.95/1.32
% 0.95/1.32 subsumption: (187) {G2,W4,D3,L1,V0,M1} R(180,16) { alpha1( skol2, skol1(
% 0.95/1.32 skol2 ) ) }.
% 0.95/1.32 parent0: (2973) {G1,W4,D3,L1,V0,M1} { alpha1( skol2, skol1( skol2 ) ) }.
% 0.95/1.32 substitution0:
% 0.95/1.32 end
% 0.95/1.32 permutation0:
% 0.95/1.32 0 ==> 0
% 0.95/1.32 end
% 0.95/1.32
% 0.95/1.32 eqswap: (2974) {G0,W8,D3,L2,V2,M2} { zero ==> multiplication( X, Y ), !
% 0.95/1.32 complement( Y, X ) }.
% 0.95/1.32 parent0[1]: (15) {G0,W8,D3,L2,V2,M2} I { ! complement( Y, X ),
% 0.95/1.32 multiplication( X, Y ) ==> zero }.
% 0.95/1.32 substitution0:
% 0.95/1.32 X := X
% 0.95/1.32 Y := Y
% 0.95/1.32 end
% 0.95/1.32
% 0.95/1.32 resolution: (2975) {G1,W6,D4,L1,V0,M1} { zero ==> multiplication( skol2,
% 0.95/1.32 skol1( skol2 ) ) }.
% 0.95/1.32 parent0[1]: (2974) {G0,W8,D3,L2,V2,M2} { zero ==> multiplication( X, Y ),
% 0.95/1.32 ! complement( Y, X ) }.
% 0.95/1.32 parent1[0]: (180) {G1,W4,D3,L1,V0,M1} R(13,25) { complement( skol1( skol2 )
% 0.95/1.32 , skol2 ) }.
% 0.95/1.32 substitution0:
% 0.95/1.32 X := skol2
% 0.95/1.32 Y := skol1( skol2 )
% 0.95/1.32 end
% 0.95/1.32 substitution1:
% 0.95/1.32 end
% 0.95/1.32
% 0.95/1.32 eqswap: (2976) {G1,W6,D4,L1,V0,M1} { multiplication( skol2, skol1( skol2 )
% 0.95/1.32 ) ==> zero }.
% 0.95/1.32 parent0[0]: (2975) {G1,W6,D4,L1,V0,M1} { zero ==> multiplication( skol2,
% 0.95/1.32 skol1( skol2 ) ) }.
% 0.95/1.32 substitution0:
% 0.95/1.32 end
% 0.95/1.32
% 0.95/1.32 subsumption: (190) {G2,W6,D4,L1,V0,M1} R(15,180) { multiplication( skol2,
% 0.95/1.32 skol1( skol2 ) ) ==> zero }.
% 0.95/1.32 parent0: (2976) {G1,W6,D4,L1,V0,M1} { multiplication( skol2, skol1( skol2
% 0.95/1.32 ) ) ==> zero }.
% 0.95/1.32 substitution0:
% 0.95/1.32 end
% 0.95/1.32 permutation0:
% 0.95/1.32 0 ==> 0
% 0.95/1.32 end
% 0.95/1.32
% 0.95/1.32 eqswap: (2977) {G0,W8,D3,L2,V2,M2} { zero ==> multiplication( X, Y ), !
% 0.95/1.32 complement( Y, X ) }.
% 0.95/1.32 parent0[1]: (15) {G0,W8,D3,L2,V2,M2} I { ! complement( Y, X ),
% 0.95/1.32 multiplication( X, Y ) ==> zero }.
% 0.95/1.32 substitution0:
% 0.95/1.32 X := X
% 0.95/1.32 Y := Y
% 0.95/1.32 end
% 0.95/1.32
% 0.95/1.32 resolution: (2978) {G1,W6,D4,L1,V0,M1} { zero ==> multiplication( skol3,
% 0.95/1.32 skol1( skol3 ) ) }.
% 0.95/1.32 parent0[1]: (2977) {G0,W8,D3,L2,V2,M2} { zero ==> multiplication( X, Y ),
% 0.95/1.32 ! complement( Y, X ) }.
% 0.95/1.32 parent1[0]: (179) {G1,W4,D3,L1,V0,M1} R(13,24) { complement( skol1( skol3 )
% 0.95/1.32 , skol3 ) }.
% 0.95/1.32 substitution0:
% 0.95/1.32 X := skol3
% 0.95/1.32 Y := skol1( skol3 )
% 0.95/1.32 end
% 0.95/1.32 substitution1:
% 0.95/1.32 end
% 0.95/1.32
% 0.95/1.32 eqswap: (2979) {G1,W6,D4,L1,V0,M1} { multiplication( skol3, skol1( skol3 )
% 0.95/1.32 ) ==> zero }.
% 0.95/1.32 parent0[0]: (2978) {G1,W6,D4,L1,V0,M1} { zero ==> multiplication( skol3,
% 0.95/1.32 skol1( skol3 ) ) }.
% 0.95/1.32 substitution0:
% 0.95/1.32 end
% 0.95/1.32
% 0.95/1.32 subsumption: (191) {G2,W6,D4,L1,V0,M1} R(15,179) { multiplication( skol3,
% 0.95/1.32 skol1( skol3 ) ) ==> zero }.
% 0.95/1.32 parent0: (2979) {G1,W6,D4,L1,V0,M1} { multiplication( skol3, skol1( skol3
% 0.95/1.32 ) ) ==> zero }.
% 0.95/1.32 substitution0:
% 0.95/1.32 end
% 0.95/1.32 permutation0:
% 0.95/1.32 0 ==> 0
% 0.95/1.32 end
% 0.95/1.32
% 0.95/1.32 eqswap: (2980) {G0,W8,D3,L2,V2,M2} { zero ==> multiplication( X, Y ), !
% 0.95/1.32 alpha1( Y, X ) }.
% 0.95/1.32 parent0[1]: (18) {G0,W8,D3,L2,V2,M2} I { ! alpha1( X, Y ), multiplication(
% 0.95/1.32 Y, X ) ==> zero }.
% 0.95/1.32 substitution0:
% 0.95/1.32 X := Y
% 0.95/1.32 Y := X
% 0.95/1.32 end
% 0.95/1.32
% 0.95/1.32 resolution: (2981) {G1,W6,D4,L1,V0,M1} { zero ==> multiplication( skol1(
% 0.95/1.32 skol2 ), skol2 ) }.
% 0.95/1.32 parent0[1]: (2980) {G0,W8,D3,L2,V2,M2} { zero ==> multiplication( X, Y ),
% 0.95/1.32 ! alpha1( Y, X ) }.
% 0.95/1.32 parent1[0]: (187) {G2,W4,D3,L1,V0,M1} R(180,16) { alpha1( skol2, skol1(
% 0.95/1.32 skol2 ) ) }.
% 0.95/1.32 substitution0:
% 0.95/1.32 X := skol1( skol2 )
% 0.95/1.32 Y := skol2
% 0.95/1.32 end
% 0.95/1.32 substitution1:
% 0.95/1.32 end
% 0.95/1.32
% 0.95/1.32 eqswap: (2982) {G1,W6,D4,L1,V0,M1} { multiplication( skol1( skol2 ), skol2
% 0.95/1.32 ) ==> zero }.
% 0.95/1.32 parent0[0]: (2981) {G1,W6,D4,L1,V0,M1} { zero ==> multiplication( skol1(
% 0.95/1.32 skol2 ), skol2 ) }.
% 0.95/1.32 substitution0:
% 0.95/1.32 end
% 0.95/1.32
% 0.95/1.32 subsumption: (232) {G3,W6,D4,L1,V0,M1} R(18,187) { multiplication( skol1(
% 0.95/1.32 skol2 ), skol2 ) ==> zero }.
% 0.95/1.32 parent0: (2982) {G1,W6,D4,L1,V0,M1} { multiplication( skol1( skol2 ),
% 0.95/1.32 skol2 ) ==> zero }.
% 0.95/1.32 substitution0:
% 0.95/1.32 end
% 0.95/1.32 permutation0:
% 0.95/1.32 0 ==> 0
% 0.95/1.32 end
% 0.95/1.32
% 0.95/1.32 eqswap: (2983) {G0,W8,D3,L2,V2,M2} { zero ==> multiplication( X, Y ), !
% 0.95/1.32 alpha1( Y, X ) }.
% 0.95/1.32 parent0[1]: (18) {G0,W8,D3,L2,V2,M2} I { ! alpha1( X, Y ), multiplication(
% 0.95/1.32 Y, X ) ==> zero }.
% 0.95/1.32 substitution0:
% 0.95/1.32 X := Y
% 0.95/1.32 Y := X
% 0.95/1.32 end
% 0.95/1.32
% 0.95/1.32 resolution: (2984) {G1,W6,D4,L1,V0,M1} { zero ==> multiplication( skol1(
% 0.95/1.32 skol3 ), skol3 ) }.
% 0.95/1.32 parent0[1]: (2983) {G0,W8,D3,L2,V2,M2} { zero ==> multiplication( X, Y ),
% 0.95/1.32 ! alpha1( Y, X ) }.
% 0.95/1.32 parent1[0]: (183) {G2,W4,D3,L1,V0,M1} R(179,16) { alpha1( skol3, skol1(
% 0.95/1.32 skol3 ) ) }.
% 0.95/1.32 substitution0:
% 0.95/1.32 X := skol1( skol3 )
% 0.95/1.32 Y := skol3
% 0.95/1.32 end
% 0.95/1.32 substitution1:
% 0.95/1.32 end
% 0.95/1.32
% 0.95/1.32 eqswap: (2985) {G1,W6,D4,L1,V0,M1} { multiplication( skol1( skol3 ), skol3
% 0.95/1.32 ) ==> zero }.
% 0.95/1.32 parent0[0]: (2984) {G1,W6,D4,L1,V0,M1} { zero ==> multiplication( skol1(
% 0.95/1.32 skol3 ), skol3 ) }.
% 0.95/1.32 substitution0:
% 0.95/1.32 end
% 0.95/1.32
% 0.95/1.32 subsumption: (233) {G3,W6,D4,L1,V0,M1} R(18,183) { multiplication( skol1(
% 0.95/1.32 skol3 ), skol3 ) ==> zero }.
% 0.95/1.32 parent0: (2985) {G1,W6,D4,L1,V0,M1} { multiplication( skol1( skol3 ),
% 0.95/1.32 skol3 ) ==> zero }.
% 0.95/1.32 substitution0:
% 0.95/1.32 end
% 0.95/1.32 permutation0:
% 0.95/1.32 0 ==> 0
% 0.95/1.32 end
% 0.95/1.32
% 0.95/1.32 eqswap: (2986) {G0,W8,D3,L2,V2,M2} { one ==> addition( X, Y ), ! alpha1( X
% 0.95/1.32 , Y ) }.
% 0.95/1.32 parent0[1]: (19) {G0,W8,D3,L2,V2,M2} I { ! alpha1( X, Y ), addition( X, Y )
% 0.95/1.32 ==> one }.
% 0.95/1.32 substitution0:
% 0.95/1.32 X := X
% 0.95/1.32 Y := Y
% 0.95/1.32 end
% 0.95/1.32
% 0.95/1.32 resolution: (2987) {G1,W6,D4,L1,V0,M1} { one ==> addition( skol2, skol1(
% 0.95/1.32 skol2 ) ) }.
% 0.95/1.32 parent0[1]: (2986) {G0,W8,D3,L2,V2,M2} { one ==> addition( X, Y ), !
% 0.95/1.32 alpha1( X, Y ) }.
% 0.95/1.32 parent1[0]: (187) {G2,W4,D3,L1,V0,M1} R(180,16) { alpha1( skol2, skol1(
% 0.95/1.32 skol2 ) ) }.
% 0.95/1.32 substitution0:
% 0.95/1.32 X := skol2
% 0.95/1.32 Y := skol1( skol2 )
% 0.95/1.32 end
% 0.95/1.32 substitution1:
% 0.95/1.32 end
% 0.95/1.32
% 0.95/1.32 eqswap: (2988) {G1,W6,D4,L1,V0,M1} { addition( skol2, skol1( skol2 ) ) ==>
% 0.95/1.32 one }.
% 0.95/1.32 parent0[0]: (2987) {G1,W6,D4,L1,V0,M1} { one ==> addition( skol2, skol1(
% 0.95/1.32 skol2 ) ) }.
% 0.95/1.32 substitution0:
% 0.95/1.32 end
% 0.95/1.32
% 0.95/1.32 subsumption: (258) {G3,W6,D4,L1,V0,M1} R(19,187) { addition( skol2, skol1(
% 0.95/1.32 skol2 ) ) ==> one }.
% 0.95/1.32 parent0: (2988) {G1,W6,D4,L1,V0,M1} { addition( skol2, skol1( skol2 ) )
% 0.95/1.32 ==> one }.
% 0.95/1.32 substitution0:
% 0.95/1.32 end
% 0.95/1.32 permutation0:
% 0.95/1.32 0 ==> 0
% 0.95/1.32 end
% 0.95/1.32
% 0.95/1.32 eqswap: (2989) {G0,W8,D3,L2,V2,M2} { one ==> addition( X, Y ), ! alpha1( X
% 0.95/1.32 , Y ) }.
% 0.95/1.32 parent0[1]: (19) {G0,W8,D3,L2,V2,M2} I { ! alpha1( X, Y ), addition( X, Y )
% 0.95/1.32 ==> one }.
% 0.95/1.32 substitution0:
% 0.95/1.32 X := X
% 0.95/1.32 Y := Y
% 0.95/1.32 end
% 0.95/1.32
% 0.95/1.32 resolution: (2990) {G1,W6,D4,L1,V0,M1} { one ==> addition( skol3, skol1(
% 0.95/1.32 skol3 ) ) }.
% 0.95/1.32 parent0[1]: (2989) {G0,W8,D3,L2,V2,M2} { one ==> addition( X, Y ), !
% 0.95/1.32 alpha1( X, Y ) }.
% 0.95/1.32 parent1[0]: (183) {G2,W4,D3,L1,V0,M1} R(179,16) { alpha1( skol3, skol1(
% 0.95/1.32 skol3 ) ) }.
% 0.95/1.32 substitution0:
% 0.95/1.32 X := skol3
% 0.95/1.32 Y := skol1( skol3 )
% 0.95/1.32 end
% 0.95/1.32 substitution1:
% 0.95/1.32 end
% 0.95/1.32
% 0.95/1.32 eqswap: (2991) {G1,W6,D4,L1,V0,M1} { addition( skol3, skol1( skol3 ) ) ==>
% 0.95/1.32 one }.
% 0.95/1.32 parent0[0]: (2990) {G1,W6,D4,L1,V0,M1} { one ==> addition( skol3, skol1(
% 0.95/1.32 skol3 ) ) }.
% 0.95/1.32 substitution0:
% 0.95/1.32 end
% 0.95/1.32
% 0.95/1.32 subsumption: (259) {G3,W6,D4,L1,V0,M1} R(19,183) { addition( skol3, skol1(
% 0.95/1.32 skol3 ) ) ==> one }.
% 0.95/1.32 parent0: (2991) {G1,W6,D4,L1,V0,M1} { addition( skol3, skol1( skol3 ) )
% 0.95/1.32 ==> one }.
% 0.95/1.32 substitution0:
% 0.95/1.32 end
% 0.95/1.32 permutation0:
% 0.95/1.32 0 ==> 0
% 0.95/1.32 end
% 0.95/1.32
% 0.95/1.32 eqswap: (2992) {G3,W6,D4,L1,V0,M1} { one ==> addition( skol2, skol1( skol2
% 0.95/1.32 ) ) }.
% 0.95/1.32 parent0[0]: (258) {G3,W6,D4,L1,V0,M1} R(19,187) { addition( skol2, skol1(
% 0.95/1.32 skol2 ) ) ==> one }.
% 0.95/1.32 substitution0:
% 0.95/1.32 end
% 0.95/1.32
% 0.95/1.32 paramod: (2993) {G1,W6,D4,L1,V0,M1} { one ==> addition( skol1( skol2 ),
% 0.95/1.32 skol2 ) }.
% 0.95/1.32 parent0[0]: (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X )
% 0.95/1.32 }.
% 0.95/1.32 parent1[0; 2]: (2992) {G3,W6,D4,L1,V0,M1} { one ==> addition( skol2, skol1
% 0.95/1.32 ( skol2 ) ) }.
% 0.95/1.32 substitution0:
% 0.95/1.32 X := skol2
% 0.95/1.32 Y := skol1( skol2 )
% 0.95/1.32 end
% 0.95/1.32 substitution1:
% 0.95/1.32 end
% 0.95/1.32
% 0.95/1.32 eqswap: (2996) {G1,W6,D4,L1,V0,M1} { addition( skol1( skol2 ), skol2 ) ==>
% 0.95/1.32 one }.
% 0.95/1.32 parent0[0]: (2993) {G1,W6,D4,L1,V0,M1} { one ==> addition( skol1( skol2 )
% 0.95/1.32 , skol2 ) }.
% 0.95/1.32 substitution0:
% 0.95/1.32 end
% 0.95/1.32
% 0.95/1.32 subsumption: (2187) {G4,W6,D4,L1,V0,M1} P(258,0) { addition( skol1( skol2 )
% 0.95/1.32 , skol2 ) ==> one }.
% 0.95/1.32 parent0: (2996) {G1,W6,D4,L1,V0,M1} { addition( skol1( skol2 ), skol2 )
% 0.95/1.32 ==> one }.
% 0.95/1.32 substitution0:
% 0.95/1.32 end
% 0.95/1.32 permutation0:
% 0.95/1.32 0 ==> 0
% 0.95/1.32 end
% 0.95/1.32
% 0.95/1.32 eqswap: (2997) {G4,W6,D4,L1,V0,M1} { one ==> addition( skol1( skol2 ),
% 0.95/1.32 skol2 ) }.
% 0.95/1.32 parent0[0]: (2187) {G4,W6,D4,L1,V0,M1} P(258,0) { addition( skol1( skol2 )
% 0.95/1.32 , skol2 ) ==> one }.
% 0.95/1.32 substitution0:
% 0.95/1.32 end
% 0.95/1.32
% 0.95/1.32 eqswap: (2999) {G0,W13,D3,L3,V2,M3} { ! one ==> addition( X, Y ), !
% 0.95/1.32 multiplication( Y, X ) ==> zero, alpha1( X, Y ) }.
% 0.95/1.32 parent0[1]: (20) {G0,W13,D3,L3,V2,M3} I { ! multiplication( Y, X ) ==> zero
% 0.95/1.32 , ! addition( X, Y ) ==> one, alpha1( X, Y ) }.
% 0.95/1.32 substitution0:
% 0.95/1.32 X := X
% 0.95/1.32 Y := Y
% 0.95/1.32 end
% 0.95/1.32
% 0.95/1.32 eqswap: (3000) {G0,W13,D3,L3,V2,M3} { ! zero ==> multiplication( X, Y ), !
% 0.95/1.32 one ==> addition( Y, X ), alpha1( Y, X ) }.
% 0.95/1.32 parent0[1]: (2999) {G0,W13,D3,L3,V2,M3} { ! one ==> addition( X, Y ), !
% 0.95/1.32 multiplication( Y, X ) ==> zero, alpha1( X, Y ) }.
% 0.95/1.32 substitution0:
% 0.95/1.32 X := Y
% 0.95/1.32 Y := X
% 0.95/1.32 end
% 0.95/1.32
% 0.95/1.32 resolution: (3002) {G1,W10,D4,L2,V0,M2} { ! zero ==> multiplication( skol2
% 0.95/1.32 , skol1( skol2 ) ), alpha1( skol1( skol2 ), skol2 ) }.
% 0.95/1.32 parent0[1]: (3000) {G0,W13,D3,L3,V2,M3} { ! zero ==> multiplication( X, Y
% 0.95/1.32 ), ! one ==> addition( Y, X ), alpha1( Y, X ) }.
% 0.95/1.32 parent1[0]: (2997) {G4,W6,D4,L1,V0,M1} { one ==> addition( skol1( skol2 )
% 0.95/1.32 , skol2 ) }.
% 0.95/1.32 substitution0:
% 0.95/1.32 X := skol2
% 0.95/1.32 Y := skol1( skol2 )
% 0.95/1.32 end
% 0.95/1.32 substitution1:
% 0.95/1.32 end
% 0.95/1.32
% 0.95/1.32 paramod: (3003) {G2,W7,D3,L2,V0,M2} { ! zero ==> zero, alpha1( skol1(
% 0.95/1.32 skol2 ), skol2 ) }.
% 0.95/1.32 parent0[0]: (190) {G2,W6,D4,L1,V0,M1} R(15,180) { multiplication( skol2,
% 0.95/1.32 skol1( skol2 ) ) ==> zero }.
% 0.95/1.32 parent1[0; 3]: (3002) {G1,W10,D4,L2,V0,M2} { ! zero ==> multiplication(
% 0.95/1.32 skol2, skol1( skol2 ) ), alpha1( skol1( skol2 ), skol2 ) }.
% 0.95/1.32 substitution0:
% 0.95/1.32 end
% 0.95/1.32 substitution1:
% 0.95/1.32 end
% 0.95/1.32
% 0.95/1.32 eqrefl: (3004) {G0,W4,D3,L1,V0,M1} { alpha1( skol1( skol2 ), skol2 ) }.
% 0.95/1.32 parent0[0]: (3003) {G2,W7,D3,L2,V0,M2} { ! zero ==> zero, alpha1( skol1(
% 0.95/1.32 skol2 ), skol2 ) }.
% 0.95/1.32 substitution0:
% 0.95/1.32 end
% 0.95/1.32
% 0.95/1.32 subsumption: (2224) {G5,W4,D3,L1,V0,M1} R(2187,20);d(190);q { alpha1( skol1
% 0.95/1.32 ( skol2 ), skol2 ) }.
% 0.95/1.32 parent0: (3004) {G0,W4,D3,L1,V0,M1} { alpha1( skol1( skol2 ), skol2 ) }.
% 0.95/1.32 substitution0:
% 0.95/1.32 end
% 0.95/1.32 permutation0:
% 0.95/1.32 0 ==> 0
% 0.95/1.32 end
% 0.95/1.32
% 0.95/1.32 eqswap: (3005) {G0,W11,D3,L3,V2,M3} { ! zero ==> multiplication( X, Y ), !
% 0.95/1.32 alpha1( X, Y ), complement( Y, X ) }.
% 0.95/1.32 parent0[0]: (17) {G0,W11,D3,L3,V2,M3} I { ! multiplication( X, Y ) ==> zero
% 0.95/1.32 , ! alpha1( X, Y ), complement( Y, X ) }.
% 0.95/1.32 substitution0:
% 0.95/1.32 X := X
% 0.95/1.32 Y := Y
% 0.95/1.32 end
% 0.95/1.32
% 0.95/1.32 resolution: (3007) {G1,W10,D4,L2,V0,M2} { ! zero ==> multiplication( skol1
% 0.95/1.32 ( skol2 ), skol2 ), complement( skol2, skol1( skol2 ) ) }.
% 0.95/1.32 parent0[1]: (3005) {G0,W11,D3,L3,V2,M3} { ! zero ==> multiplication( X, Y
% 0.95/1.32 ), ! alpha1( X, Y ), complement( Y, X ) }.
% 0.95/1.32 parent1[0]: (2224) {G5,W4,D3,L1,V0,M1} R(2187,20);d(190);q { alpha1( skol1
% 0.95/1.32 ( skol2 ), skol2 ) }.
% 0.95/1.32 substitution0:
% 0.95/1.32 X := skol1( skol2 )
% 0.95/1.32 Y := skol2
% 0.95/1.32 end
% 0.95/1.32 substitution1:
% 0.95/1.32 end
% 0.95/1.32
% 0.95/1.32 paramod: (3008) {G2,W7,D3,L2,V0,M2} { ! zero ==> zero, complement( skol2,
% 0.95/1.32 skol1( skol2 ) ) }.
% 0.95/1.32 parent0[0]: (232) {G3,W6,D4,L1,V0,M1} R(18,187) { multiplication( skol1(
% 0.95/1.32 skol2 ), skol2 ) ==> zero }.
% 0.95/1.32 parent1[0; 3]: (3007) {G1,W10,D4,L2,V0,M2} { ! zero ==> multiplication(
% 0.95/1.32 skol1( skol2 ), skol2 ), complement( skol2, skol1( skol2 ) ) }.
% 0.95/1.32 substitution0:
% 0.95/1.32 end
% 0.95/1.32 substitution1:
% 0.95/1.32 end
% 0.95/1.32
% 0.95/1.32 eqrefl: (3009) {G0,W4,D3,L1,V0,M1} { complement( skol2, skol1( skol2 ) )
% 0.95/1.32 }.
% 0.95/1.32 parent0[0]: (3008) {G2,W7,D3,L2,V0,M2} { ! zero ==> zero, complement(
% 0.95/1.32 skol2, skol1( skol2 ) ) }.
% 0.95/1.32 substitution0:
% 0.95/1.32 end
% 0.95/1.32
% 0.95/1.32 subsumption: (2240) {G6,W4,D3,L1,V0,M1} R(2224,17);d(232);q { complement(
% 0.95/1.32 skol2, skol1( skol2 ) ) }.
% 0.95/1.32 parent0: (3009) {G0,W4,D3,L1,V0,M1} { complement( skol2, skol1( skol2 ) )
% 0.95/1.32 }.
% 0.95/1.32 substitution0:
% 0.95/1.32 end
% 0.95/1.32 permutation0:
% 0.95/1.32 0 ==> 0
% 0.95/1.32 end
% 0.95/1.32
% 0.95/1.32 eqswap: (3010) {G0,W9,D3,L3,V2,M3} { Y = c( X ), ! test( X ), ! complement
% 0.95/1.32 ( X, Y ) }.
% 0.95/1.32 parent0[2]: (22) {G0,W9,D3,L3,V2,M3} I { ! test( X ), ! complement( X, Y )
% 0.95/1.32 , c( X ) = Y }.
% 0.95/1.32 substitution0:
% 0.95/1.32 X := X
% 0.95/1.32 Y := Y
% 0.95/1.32 end
% 0.95/1.32
% 0.95/1.32 resolution: (3011) {G1,W7,D3,L2,V0,M2} { skol1( skol2 ) = c( skol2 ), !
% 0.95/1.32 test( skol2 ) }.
% 0.95/1.32 parent0[2]: (3010) {G0,W9,D3,L3,V2,M3} { Y = c( X ), ! test( X ), !
% 0.95/1.32 complement( X, Y ) }.
% 0.95/1.32 parent1[0]: (2240) {G6,W4,D3,L1,V0,M1} R(2224,17);d(232);q { complement(
% 0.95/1.32 skol2, skol1( skol2 ) ) }.
% 0.95/1.32 substitution0:
% 0.95/1.32 X := skol2
% 0.95/1.32 Y := skol1( skol2 )
% 0.95/1.32 end
% 0.95/1.32 substitution1:
% 0.95/1.32 end
% 0.95/1.32
% 0.95/1.32 resolution: (3012) {G1,W5,D3,L1,V0,M1} { skol1( skol2 ) = c( skol2 ) }.
% 0.95/1.32 parent0[1]: (3011) {G1,W7,D3,L2,V0,M2} { skol1( skol2 ) = c( skol2 ), !
% 0.95/1.32 test( skol2 ) }.
% 0.95/1.32 parent1[0]: (25) {G0,W2,D2,L1,V0,M1} I { test( skol2 ) }.
% 0.95/1.32 substitution0:
% 0.95/1.32 end
% 0.95/1.32 substitution1:
% 0.95/1.32 end
% 0.95/1.32
% 0.95/1.32 eqswap: (3013) {G1,W5,D3,L1,V0,M1} { c( skol2 ) = skol1( skol2 ) }.
% 0.95/1.32 parent0[0]: (3012) {G1,W5,D3,L1,V0,M1} { skol1( skol2 ) = c( skol2 ) }.
% 0.95/1.32 substitution0:
% 0.95/1.32 end
% 0.95/1.32
% 0.95/1.32 subsumption: (2245) {G7,W5,D3,L1,V0,M1} R(2240,22);r(25) { c( skol2 ) ==>
% 0.95/1.32 skol1( skol2 ) }.
% 0.95/1.32 parent0: (3013) {G1,W5,D3,L1,V0,M1} { c( skol2 ) = skol1( skol2 ) }.
% 0.95/1.32 substitution0:
% 0.95/1.32 end
% 0.95/1.32 permutation0:
% 0.95/1.32 0 ==> 0
% 0.95/1.32 end
% 0.95/1.32
% 0.95/1.32 eqswap: (3014) {G3,W6,D4,L1,V0,M1} { one ==> addition( skol3, skol1( skol3
% 0.95/1.32 ) ) }.
% 0.95/1.32 parent0[0]: (259) {G3,W6,D4,L1,V0,M1} R(19,183) { addition( skol3, skol1(
% 0.95/1.32 skol3 ) ) ==> one }.
% 0.95/1.32 substitution0:
% 0.95/1.32 end
% 0.95/1.32
% 0.95/1.32 paramod: (3015) {G1,W6,D4,L1,V0,M1} { one ==> addition( skol1( skol3 ),
% 0.95/1.32 skol3 ) }.
% 0.95/1.32 parent0[0]: (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X )
% 0.95/1.32 }.
% 0.95/1.32 parent1[0; 2]: (3014) {G3,W6,D4,L1,V0,M1} { one ==> addition( skol3, skol1
% 0.95/1.32 ( skol3 ) ) }.
% 0.95/1.32 substitution0:
% 0.95/1.32 X := skol3
% 0.95/1.32 Y := skol1( skol3 )
% 0.95/1.32 end
% 0.95/1.32 substitution1:
% 0.95/1.32 end
% 0.95/1.32
% 0.95/1.32 eqswap: (3018) {G1,W6,D4,L1,V0,M1} { addition( skol1( skol3 ), skol3 ) ==>
% 0.95/1.32 one }.
% 0.95/1.32 parent0[0]: (3015) {G1,W6,D4,L1,V0,M1} { one ==> addition( skol1( skol3 )
% 0.95/1.32 , skol3 ) }.
% 0.95/1.32 substitution0:
% 0.95/1.32 end
% 0.95/1.32
% 0.95/1.32 subsumption: (2553) {G4,W6,D4,L1,V0,M1} P(259,0) { addition( skol1( skol3 )
% 0.95/1.32 , skol3 ) ==> one }.
% 0.95/1.32 parent0: (3018) {G1,W6,D4,L1,V0,M1} { addition( skol1( skol3 ), skol3 )
% 0.95/1.32 ==> one }.
% 0.95/1.32 substitution0:
% 0.95/1.32 end
% 0.95/1.32 permutation0:
% 0.95/1.32 0 ==> 0
% 0.95/1.32 end
% 0.95/1.32
% 0.95/1.32 eqswap: (3019) {G4,W6,D4,L1,V0,M1} { one ==> addition( skol1( skol3 ),
% 0.95/1.32 skol3 ) }.
% 0.95/1.32 parent0[0]: (2553) {G4,W6,D4,L1,V0,M1} P(259,0) { addition( skol1( skol3 )
% 0.95/1.32 , skol3 ) ==> one }.
% 0.95/1.32 substitution0:
% 0.95/1.32 end
% 0.95/1.32
% 0.95/1.32 eqswap: (3021) {G0,W13,D3,L3,V2,M3} { ! one ==> addition( X, Y ), !
% 0.95/1.32 multiplication( Y, X ) ==> zero, alpha1( X, Y ) }.
% 0.95/1.32 parent0[1]: (20) {G0,W13,D3,L3,V2,M3} I { ! multiplication( Y, X ) ==> zero
% 0.95/1.32 , ! addition( X, Y ) ==> one, alpha1( X, Y ) }.
% 0.95/1.32 substitution0:
% 0.95/1.32 X := X
% 0.95/1.32 Y := Y
% 0.95/1.32 end
% 0.95/1.32
% 0.95/1.32 eqswap: (3022) {G0,W13,D3,L3,V2,M3} { ! zero ==> multiplication( X, Y ), !
% 0.95/1.32 one ==> addition( Y, X ), alpha1( Y, X ) }.
% 0.95/1.32 parent0[1]: (3021) {G0,W13,D3,L3,V2,M3} { ! one ==> addition( X, Y ), !
% 0.95/1.32 multiplication( Y, X ) ==> zero, alpha1( X, Y ) }.
% 0.95/1.32 substitution0:
% 0.95/1.32 X := Y
% 0.95/1.32 Y := X
% 0.95/1.32 end
% 0.95/1.32
% 0.95/1.32 resolution: (3024) {G1,W10,D4,L2,V0,M2} { ! zero ==> multiplication( skol3
% 0.95/1.32 , skol1( skol3 ) ), alpha1( skol1( skol3 ), skol3 ) }.
% 0.95/1.32 parent0[1]: (3022) {G0,W13,D3,L3,V2,M3} { ! zero ==> multiplication( X, Y
% 0.95/1.32 ), ! one ==> addition( Y, X ), alpha1( Y, X ) }.
% 0.95/1.32 parent1[0]: (3019) {G4,W6,D4,L1,V0,M1} { one ==> addition( skol1( skol3 )
% 0.95/1.32 , skol3 ) }.
% 0.95/1.32 substitution0:
% 0.95/1.32 X := skol3
% 0.95/1.32 Y := skol1( skol3 )
% 0.95/1.32 end
% 0.95/1.32 substitution1:
% 0.95/1.32 end
% 0.95/1.32
% 0.95/1.32 paramod: (3025) {G2,W7,D3,L2,V0,M2} { ! zero ==> zero, alpha1( skol1(
% 0.95/1.32 skol3 ), skol3 ) }.
% 0.95/1.32 parent0[0]: (191) {G2,W6,D4,L1,V0,M1} R(15,179) { multiplication( skol3,
% 0.95/1.32 skol1( skol3 ) ) ==> zero }.
% 0.95/1.32 parent1[0; 3]: (3024) {G1,W10,D4,L2,V0,M2} { ! zero ==> multiplication(
% 0.95/1.32 skol3, skol1( skol3 ) ), alpha1( skol1( skol3 ), skol3 ) }.
% 0.95/1.32 substitution0:
% 0.95/1.32 end
% 0.95/1.32 substitution1:
% 0.95/1.32 end
% 0.95/1.32
% 0.95/1.32 eqrefl: (3026) {G0,W4,D3,L1,V0,M1} { alpha1( skol1( skol3 ), skol3 ) }.
% 0.95/1.32 parent0[0]: (3025) {G2,W7,D3,L2,V0,M2} { ! zero ==> zero, alpha1( skol1(
% 0.95/1.32 skol3 ), skol3 ) }.
% 0.95/1.32 substitution0:
% 0.95/1.32 end
% 0.95/1.32
% 0.95/1.32 subsumption: (2605) {G5,W4,D3,L1,V0,M1} R(2553,20);d(191);q { alpha1( skol1
% 0.95/1.32 ( skol3 ), skol3 ) }.
% 0.95/1.32 parent0: (3026) {G0,W4,D3,L1,V0,M1} { alpha1( skol1( skol3 ), skol3 ) }.
% 0.95/1.32 substitution0:
% 0.95/1.32 end
% 0.95/1.32 permutation0:
% 0.95/1.32 0 ==> 0
% 0.95/1.32 end
% 0.95/1.32
% 0.95/1.32 eqswap: (3027) {G0,W11,D3,L3,V2,M3} { ! zero ==> multiplication( X, Y ), !
% 0.95/1.32 alpha1( X, Y ), complement( Y, X ) }.
% 0.95/1.32 parent0[0]: (17) {G0,W11,D3,L3,V2,M3} I { ! multiplication( X, Y ) ==> zero
% 0.95/1.32 , ! alpha1( X, Y ), complement( Y, X ) }.
% 0.95/1.32 substitution0:
% 0.95/1.32 X := X
% 0.95/1.32 Y := Y
% 0.95/1.32 end
% 0.95/1.32
% 0.95/1.32 resolution: (3029) {G1,W10,D4,L2,V0,M2} { ! zero ==> multiplication( skol1
% 0.95/1.32 ( skol3 ), skol3 ), complement( skol3, skol1( skol3 ) ) }.
% 0.95/1.32 parent0[1]: (3027) {G0,W11,D3,L3,V2,M3} { ! zero ==> multiplication( X, Y
% 0.95/1.32 ), ! alpha1( X, Y ), complement( Y, X ) }.
% 0.95/1.32 parent1[0]: (2605) {G5,W4,D3,L1,V0,M1} R(2553,20);d(191);q { alpha1( skol1
% 0.95/1.32 ( skol3 ), skol3 ) }.
% 0.95/1.32 substitution0:
% 0.95/1.32 X := skol1( skol3 )
% 0.95/1.32 Y := skol3
% 0.95/1.32 end
% 0.95/1.32 substitution1:
% 0.95/1.32 end
% 0.95/1.32
% 0.95/1.32 paramod: (3030) {G2,W7,D3,L2,V0,M2} { ! zero ==> zero, complement( skol3,
% 0.95/1.32 skol1( skol3 ) ) }.
% 0.95/1.32 parent0[0]: (233) {G3,W6,D4,L1,V0,M1} R(18,183) { multiplication( skol1(
% 0.95/1.32 skol3 ), skol3 ) ==> zero }.
% 0.95/1.32 parent1[0; 3]: (3029) {G1,W10,D4,L2,V0,M2} { ! zero ==> multiplication(
% 0.95/1.32 skol1( skol3 ), skol3 ), complement( skol3, skol1( skol3 ) ) }.
% 0.95/1.32 substitution0:
% 0.95/1.32 end
% 0.95/1.32 substitution1:
% 0.95/1.32 end
% 0.95/1.32
% 0.95/1.32 eqrefl: (3031) {G0,W4,D3,L1,V0,M1} { complement( skol3, skol1( skol3 ) )
% 0.95/1.32 }.
% 0.95/1.32 parent0[0]: (3030) {G2,W7,D3,L2,V0,M2} { ! zero ==> zero, complement(
% 0.95/1.32 skol3, skol1( skol3 ) ) }.
% 0.95/1.32 substitution0:
% 0.95/1.32 end
% 0.95/1.32
% 0.95/1.32 subsumption: (2621) {G6,W4,D3,L1,V0,M1} R(2605,17);d(233);q { complement(
% 0.95/1.32 skol3, skol1( skol3 ) ) }.
% 0.95/1.32 parent0: (3031) {G0,W4,D3,L1,V0,M1} { complement( skol3, skol1( skol3 ) )
% 0.95/1.32 }.
% 0.95/1.32 substitution0:
% 0.95/1.32 end
% 0.95/1.32 permutation0:
% 0.95/1.32 0 ==> 0
% 0.95/1.32 end
% 0.95/1.32
% 0.95/1.32 eqswap: (3032) {G0,W9,D3,L3,V2,M3} { Y = c( X ), ! test( X ), ! complement
% 0.95/1.32 ( X, Y ) }.
% 0.95/1.32 parent0[2]: (22) {G0,W9,D3,L3,V2,M3} I { ! test( X ), ! complement( X, Y )
% 0.95/1.32 , c( X ) = Y }.
% 0.95/1.32 substitution0:
% 0.95/1.32 X := X
% 0.95/1.32 Y := Y
% 0.95/1.32 end
% 0.95/1.32
% 0.95/1.32 resolution: (3033) {G1,W7,D3,L2,V0,M2} { skol1( skol3 ) = c( skol3 ), !
% 0.95/1.32 test( skol3 ) }.
% 0.95/1.32 parent0[2]: (3032) {G0,W9,D3,L3,V2,M3} { Y = c( X ), ! test( X ), !
% 0.95/1.32 complement( X, Y ) }.
% 0.95/1.32 parent1[0]: (2621) {G6,W4,D3,L1,V0,M1} R(2605,17);d(233);q { complement(
% 0.95/1.32 skol3, skol1( skol3 ) ) }.
% 0.95/1.32 substitution0:
% 0.95/1.32 X := skol3
% 0.95/1.32 Y := skol1( skol3 )
% 0.95/1.32 end
% 0.95/1.32 substitution1:
% 0.95/1.32 end
% 0.95/1.32
% 0.95/1.32 resolution: (3034) {G1,W5,D3,L1,V0,M1} { skol1( skol3 ) = c( skol3 ) }.
% 0.95/1.32 parent0[1]: (3033) {G1,W7,D3,L2,V0,M2} { skol1( skol3 ) = c( skol3 ), !
% 0.95/1.32 test( skol3 ) }.
% 0.95/1.32 parent1[0]: (24) {G0,W2,D2,L1,V0,M1} I { test( skol3 ) }.
% 0.95/1.32 substitution0:
% 0.95/1.32 end
% 0.95/1.32 substitution1:
% 0.95/1.32 end
% 0.95/1.32
% 0.95/1.32 eqswap: (3035) {G1,W5,D3,L1,V0,M1} { c( skol3 ) = skol1( skol3 ) }.
% 0.95/1.32 parent0[0]: (3034) {G1,W5,D3,L1,V0,M1} { skol1( skol3 ) = c( skol3 ) }.
% 0.95/1.32 substitution0:
% 0.95/1.32 end
% 0.95/1.32
% 0.95/1.32 subsumption: (2626) {G7,W5,D3,L1,V0,M1} R(2621,22);r(24) { c( skol3 ) ==>
% 0.95/1.32 skol1( skol3 ) }.
% 0.95/1.32 parent0: (3035) {G1,W5,D3,L1,V0,M1} { c( skol3 ) = skol1( skol3 ) }.
% 0.95/1.32 substitution0:
% 0.95/1.32 end
% 0.95/1.32 permutation0:
% 0.95/1.32 0 ==> 0
% 0.95/1.32 end
% 0.95/1.32
% 0.95/1.32 paramod: (3046) {G2,W22,D5,L2,V0,M2} { ! leq( multiplication( addition(
% 0.95/1.32 skol2, c( skol2 ) ), addition( skol3, skol1( skol3 ) ) ), one ), ! leq(
% 0.95/1.32 one, multiplication( addition( skol2, c( skol2 ) ), addition( skol3, c(
% 0.95/1.32 skol3 ) ) ) ) }.
% 0.95/1.32 parent0[0]: (2626) {G7,W5,D3,L1,V0,M1} R(2621,22);r(24) { c( skol3 ) ==>
% 0.95/1.32 skol1( skol3 ) }.
% 0.95/1.32 parent1[1; 9]: (26) {G1,W22,D5,L2,V0,M2} I;d(7);d(7) { ! leq( one,
% 0.95/1.32 multiplication( addition( skol2, c( skol2 ) ), addition( skol3, c( skol3
% 0.95/1.32 ) ) ) ), ! leq( multiplication( addition( skol2, c( skol2 ) ), addition
% 0.95/1.32 ( skol3, c( skol3 ) ) ), one ) }.
% 0.95/1.32 substitution0:
% 0.95/1.32 end
% 0.95/1.32 substitution1:
% 0.95/1.32 end
% 0.95/1.32
% 0.95/1.32 paramod: (3047) {G3,W22,D5,L2,V0,M2} { ! leq( one, multiplication(
% 0.95/1.32 addition( skol2, c( skol2 ) ), addition( skol3, skol1( skol3 ) ) ) ), !
% 0.95/1.32 leq( multiplication( addition( skol2, c( skol2 ) ), addition( skol3,
% 0.95/1.32 skol1( skol3 ) ) ), one ) }.
% 0.95/1.32 parent0[0]: (2626) {G7,W5,D3,L1,V0,M1} R(2621,22);r(24) { c( skol3 ) ==>
% 0.95/1.32 skol1( skol3 ) }.
% 0.95/1.32 parent1[1; 10]: (3046) {G2,W22,D5,L2,V0,M2} { ! leq( multiplication(
% 0.95/1.32 addition( skol2, c( skol2 ) ), addition( skol3, skol1( skol3 ) ) ), one )
% 0.95/1.32 , ! leq( one, multiplication( addition( skol2, c( skol2 ) ), addition(
% 0.95/1.32 skol3, c( skol3 ) ) ) ) }.
% 0.95/1.32 substitution0:
% 0.95/1.32 end
% 0.95/1.32 substitution1:
% 0.95/1.32 end
% 0.95/1.32
% 0.95/1.32 paramod: (3092) {G4,W22,D5,L2,V0,M2} { ! leq( multiplication( addition(
% 0.95/1.32 skol2, skol1( skol2 ) ), addition( skol3, skol1( skol3 ) ) ), one ), !
% 0.95/1.32 leq( one, multiplication( addition( skol2, c( skol2 ) ), addition( skol3
% 0.95/1.32 , skol1( skol3 ) ) ) ) }.
% 0.95/1.32 parent0[0]: (2245) {G7,W5,D3,L1,V0,M1} R(2240,22);r(25) { c( skol2 ) ==>
% 0.95/1.32 skol1( skol2 ) }.
% 0.95/1.32 parent1[1; 5]: (3047) {G3,W22,D5,L2,V0,M2} { ! leq( one, multiplication(
% 0.95/1.32 addition( skol2, c( skol2 ) ), addition( skol3, skol1( skol3 ) ) ) ), !
% 0.95/1.32 leq( multiplication( addition( skol2, c( skol2 ) ), addition( skol3,
% 0.95/1.32 skol1( skol3 ) ) ), one ) }.
% 0.95/1.32 substitution0:
% 0.95/1.32 end
% 0.95/1.32 substitution1:
% 0.95/1.32 end
% 0.95/1.32
% 0.95/1.32 paramod: (3094) {G5,W22,D5,L2,V0,M2} { ! leq( one, multiplication(
% 0.95/1.32 addition( skol2, skol1( skol2 ) ), addition( skol3, skol1( skol3 ) ) ) )
% 0.95/1.32 , ! leq( multiplication( addition( skol2, skol1( skol2 ) ), addition(
% 0.95/1.32 skol3, skol1( skol3 ) ) ), one ) }.
% 0.95/1.32 parent0[0]: (2245) {G7,W5,D3,L1,V0,M1} R(2240,22);r(25) { c( skol2 ) ==>
% 0.95/1.32 skol1( skol2 ) }.
% 0.95/1.32 parent1[1; 6]: (3092) {G4,W22,D5,L2,V0,M2} { ! leq( multiplication(
% 0.95/1.32 addition( skol2, skol1( skol2 ) ), addition( skol3, skol1( skol3 ) ) ),
% 0.95/1.32 one ), ! leq( one, multiplication( addition( skol2, c( skol2 ) ),
% 0.95/1.32 addition( skol3, skol1( skol3 ) ) ) ) }.
% 0.95/1.32 substitution0:
% 0.95/1.32 end
% 0.95/1.32 substitution1:
% 0.95/1.32 end
% 0.95/1.32
% 0.95/1.32 paramod: (3096) {G4,W19,D5,L2,V0,M2} { ! leq( multiplication( one,
% 0.95/1.32 addition( skol3, skol1( skol3 ) ) ), one ), ! leq( one, multiplication(
% 0.95/1.32 addition( skol2, skol1( skol2 ) ), addition( skol3, skol1( skol3 ) ) ) )
% 0.95/1.32 }.
% 0.95/1.32 parent0[0]: (258) {G3,W6,D4,L1,V0,M1} R(19,187) { addition( skol2, skol1(
% 0.95/1.32 skol2 ) ) ==> one }.
% 0.95/1.32 parent1[1; 3]: (3094) {G5,W22,D5,L2,V0,M2} { ! leq( one, multiplication(
% 0.95/1.32 addition( skol2, skol1( skol2 ) ), addition( skol3, skol1( skol3 ) ) ) )
% 0.95/1.32 , ! leq( multiplication( addition( skol2, skol1( skol2 ) ), addition(
% 0.95/1.32 skol3, skol1( skol3 ) ) ), one ) }.
% 0.95/1.32 substitution0:
% 0.95/1.32 end
% 0.95/1.32 substitution1:
% 0.95/1.32 end
% 0.95/1.32
% 0.95/1.32 paramod: (3098) {G4,W16,D5,L2,V0,M2} { ! leq( one, multiplication( one,
% 0.95/1.32 addition( skol3, skol1( skol3 ) ) ) ), ! leq( multiplication( one,
% 0.95/1.32 addition( skol3, skol1( skol3 ) ) ), one ) }.
% 0.95/1.32 parent0[0]: (258) {G3,W6,D4,L1,V0,M1} R(19,187) { addition( skol2, skol1(
% 0.95/1.32 skol2 ) ) ==> one }.
% 0.95/1.32 parent1[1; 4]: (3096) {G4,W19,D5,L2,V0,M2} { ! leq( multiplication( one,
% 0.95/1.32 addition( skol3, skol1( skol3 ) ) ), one ), ! leq( one, multiplication(
% 0.95/1.32 addition( skol2, skol1( skol2 ) ), addition( skol3, skol1( skol3 ) ) ) )
% 0.95/1.32 }.
% 0.95/1.32 substitution0:
% 0.95/1.32 end
% 0.95/1.32 substitution1:
% 0.95/1.32 end
% 0.95/1.32
% 0.95/1.32 paramod: (3100) {G1,W14,D5,L2,V0,M2} { ! leq( addition( skol3, skol1(
% 0.95/1.32 skol3 ) ), one ), ! leq( one, multiplication( one, addition( skol3, skol1
% 0.95/1.32 ( skol3 ) ) ) ) }.
% 0.95/1.32 parent0[0]: (6) {G0,W5,D3,L1,V1,M1} I { multiplication( one, X ) ==> X }.
% 0.95/1.32 parent1[1; 2]: (3098) {G4,W16,D5,L2,V0,M2} { ! leq( one, multiplication(
% 0.95/1.32 one, addition( skol3, skol1( skol3 ) ) ) ), ! leq( multiplication( one,
% 0.95/1.32 addition( skol3, skol1( skol3 ) ) ), one ) }.
% 0.95/1.32 substitution0:
% 0.95/1.32 X := addition( skol3, skol1( skol3 ) )
% 0.95/1.32 end
% 0.95/1.32 substitution1:
% 0.95/1.32 end
% 0.95/1.32
% 0.95/1.32 paramod: (3102) {G1,W12,D4,L2,V0,M2} { ! leq( one, addition( skol3, skol1
% 0.95/1.32 ( skol3 ) ) ), ! leq( addition( skol3, skol1( skol3 ) ), one ) }.
% 0.95/1.32 parent0[0]: (6) {G0,W5,D3,L1,V1,M1} I { multiplication( one, X ) ==> X }.
% 0.95/1.32 parent1[1; 3]: (3100) {G1,W14,D5,L2,V0,M2} { ! leq( addition( skol3, skol1
% 0.95/1.32 ( skol3 ) ), one ), ! leq( one, multiplication( one, addition( skol3,
% 0.95/1.32 skol1( skol3 ) ) ) ) }.
% 0.95/1.32 substitution0:
% 0.95/1.32 X := addition( skol3, skol1( skol3 ) )
% 0.95/1.32 end
% 0.95/1.32 substitution1:
% 0.95/1.32 end
% 0.95/1.32
% 0.95/1.32 paramod: (3104) {G2,W9,D4,L2,V0,M2} { ! leq( one, one ), ! leq( one,
% 0.95/1.32 addition( skol3, skol1( skol3 ) ) ) }.
% 0.95/1.32 parent0[0]: (259) {G3,W6,D4,L1,V0,M1} R(19,183) { addition( skol3, skol1(
% 0.95/1.32 skol3 ) ) ==> one }.
% 0.95/1.32 parent1[1; 2]: (3102) {G1,W12,D4,L2,V0,M2} { ! leq( one, addition( skol3,
% 0.95/1.32 skol1( skol3 ) ) ), ! leq( addition( skol3, skol1( skol3 ) ), one ) }.
% 0.95/1.32 substitution0:
% 0.95/1.32 end
% 0.95/1.32 substitution1:
% 0.95/1.32 end
% 0.95/1.32
% 0.95/1.32 paramod: (3107) {G3,W6,D2,L2,V0,M2} { ! leq( one, one ), ! leq( one, one )
% 0.95/1.32 }.
% 0.95/1.32 parent0[0]: (259) {G3,W6,D4,L1,V0,M1} R(19,183) { addition( skol3, skol1(
% 0.95/1.32 skol3 ) ) ==> one }.
% 0.95/1.32 parent1[1; 3]: (3104) {G2,W9,D4,L2,V0,M2} { ! leq( one, one ), ! leq( one
% 0.95/1.32 , addition( skol3, skol1( skol3 ) ) ) }.
% 0.95/1.32 substitution0:
% 0.95/1.32 end
% 0.95/1.32 substitution1:
% 0.95/1.32 end
% 0.95/1.32
% 0.95/1.32 factor: (3108) {G3,W3,D2,L1,V0,M1} { ! leq( one, one ) }.
% 0.95/1.32 parent0[0, 1]: (3107) {G3,W6,D2,L2,V0,M2} { ! leq( one, one ), ! leq( one
% 0.95/1.32 , one ) }.
% 0.95/1.32 substitution0:
% 0.95/1.32 end
% 0.95/1.32
% 0.95/1.32 resolution: (3110) {G2,W0,D0,L0,V0,M0} { }.
% 0.95/1.32 parent0[0]: (3108) {G3,W3,D2,L1,V0,M1} { ! leq( one, one ) }.
% 0.95/1.32 parent1[0]: (145) {G1,W3,D2,L1,V1,M1} R(12,3) { leq( X, X ) }.
% 0.95/1.32 substitution0:
% 0.95/1.32 end
% 0.95/1.32 substitution1:
% 0.95/1.32 X := one
% 0.95/1.32 end
% 0.95/1.32
% 0.95/1.32 subsumption: (2661) {G8,W0,D0,L0,V0,M0} P(2626,26);d(2245);d(2245);d(258);d
% 0.95/1.32 (258);d(6);d(6);d(259);d(259);f;r(145) { }.
% 0.95/1.32 parent0: (3110) {G2,W0,D0,L0,V0,M0} { }.
% 0.95/1.32 substitution0:
% 0.95/1.32 end
% 0.95/1.32 permutation0:
% 0.95/1.32 end
% 0.95/1.32
% 0.95/1.32 Proof check complete!
% 0.95/1.32
% 0.95/1.32 Memory use:
% 0.95/1.32
% 0.95/1.32 space for terms: 31231
% 0.95/1.32 space for clauses: 141351
% 0.95/1.32
% 0.95/1.32
% 0.95/1.32 clauses generated: 17748
% 0.95/1.32 clauses kept: 2662
% 0.95/1.32 clauses selected: 284
% 0.95/1.32 clauses deleted: 91
% 0.95/1.32 clauses inuse deleted: 35
% 0.95/1.32
% 0.95/1.32 subsentry: 32509
% 0.95/1.32 literals s-matched: 22064
% 0.95/1.32 literals matched: 21621
% 0.95/1.32 full subsumption: 3187
% 0.95/1.32
% 0.95/1.32 checksum: 286725670
% 0.95/1.32
% 0.95/1.32
% 0.95/1.32 Bliksem ended
%------------------------------------------------------------------------------