TSTP Solution File: KLE150+2 by Bliksem---1.12
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%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : KLE150+2 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n007.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 01:37:30 EDT 2022
% Result : Theorem 3.13s 3.52s
% Output : Refutation 3.13s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : KLE150+2 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.13 % Command : bliksem %s
% 0.13/0.35 % Computer : n007.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % DateTime : Thu Jun 16 08:15:11 EDT 2022
% 0.13/0.35 % CPUTime :
% 3.13/3.52 *** allocated 10000 integers for termspace/termends
% 3.13/3.52 *** allocated 10000 integers for clauses
% 3.13/3.52 *** allocated 10000 integers for justifications
% 3.13/3.52 Bliksem 1.12
% 3.13/3.52
% 3.13/3.52
% 3.13/3.52 Automatic Strategy Selection
% 3.13/3.52
% 3.13/3.52
% 3.13/3.52 Clauses:
% 3.13/3.52
% 3.13/3.52 { addition( X, Y ) = addition( Y, X ) }.
% 3.13/3.52 { addition( Z, addition( Y, X ) ) = addition( addition( Z, Y ), X ) }.
% 3.13/3.52 { addition( X, zero ) = X }.
% 3.13/3.52 { addition( X, X ) = X }.
% 3.13/3.52 { multiplication( X, multiplication( Y, Z ) ) = multiplication(
% 3.13/3.52 multiplication( X, Y ), Z ) }.
% 3.13/3.52 { multiplication( X, one ) = X }.
% 3.13/3.52 { multiplication( one, X ) = X }.
% 3.13/3.52 { multiplication( X, addition( Y, Z ) ) = addition( multiplication( X, Y )
% 3.13/3.52 , multiplication( X, Z ) ) }.
% 3.13/3.52 { multiplication( addition( X, Y ), Z ) = addition( multiplication( X, Z )
% 3.13/3.52 , multiplication( Y, Z ) ) }.
% 3.13/3.52 { multiplication( zero, X ) = zero }.
% 3.13/3.52 { addition( one, multiplication( X, star( X ) ) ) = star( X ) }.
% 3.13/3.52 { addition( one, multiplication( star( X ), X ) ) = star( X ) }.
% 3.13/3.52 { ! leq( addition( multiplication( X, Z ), Y ), Z ), leq( multiplication(
% 3.13/3.52 star( X ), Y ), Z ) }.
% 3.13/3.52 { ! leq( addition( multiplication( Z, X ), Y ), Z ), leq( multiplication( Y
% 3.13/3.52 , star( X ) ), Z ) }.
% 3.13/3.52 { strong_iteration( X ) = addition( multiplication( X, strong_iteration( X
% 3.13/3.52 ) ), one ) }.
% 3.13/3.52 { ! leq( Z, addition( multiplication( X, Z ), Y ) ), leq( Z, multiplication
% 3.13/3.52 ( strong_iteration( X ), Y ) ) }.
% 3.13/3.52 { strong_iteration( X ) = addition( star( X ), multiplication(
% 3.13/3.52 strong_iteration( X ), zero ) ) }.
% 3.13/3.52 { ! leq( X, Y ), addition( X, Y ) = Y }.
% 3.13/3.52 { ! addition( X, Y ) = Y, leq( X, Y ) }.
% 3.13/3.52 { ! leq( strong_iteration( multiplication( skol1, zero ) ), addition( one,
% 3.13/3.52 multiplication( skol1, zero ) ) ), ! leq( addition( one, multiplication(
% 3.13/3.52 skol1, zero ) ), strong_iteration( multiplication( skol1, zero ) ) ) }.
% 3.13/3.52
% 3.13/3.52 percentage equality = 0.615385, percentage horn = 1.000000
% 3.13/3.52 This is a problem with some equality
% 3.13/3.52
% 3.13/3.52
% 3.13/3.52
% 3.13/3.52 Options Used:
% 3.13/3.52
% 3.13/3.52 useres = 1
% 3.13/3.52 useparamod = 1
% 3.13/3.52 useeqrefl = 1
% 3.13/3.52 useeqfact = 1
% 3.13/3.52 usefactor = 1
% 3.13/3.52 usesimpsplitting = 0
% 3.13/3.52 usesimpdemod = 5
% 3.13/3.52 usesimpres = 3
% 3.13/3.52
% 3.13/3.52 resimpinuse = 1000
% 3.13/3.52 resimpclauses = 20000
% 3.13/3.52 substype = eqrewr
% 3.13/3.52 backwardsubs = 1
% 3.13/3.52 selectoldest = 5
% 3.13/3.52
% 3.13/3.52 litorderings [0] = split
% 3.13/3.52 litorderings [1] = extend the termordering, first sorting on arguments
% 3.13/3.52
% 3.13/3.52 termordering = kbo
% 3.13/3.52
% 3.13/3.52 litapriori = 0
% 3.13/3.52 termapriori = 1
% 3.13/3.52 litaposteriori = 0
% 3.13/3.52 termaposteriori = 0
% 3.13/3.52 demodaposteriori = 0
% 3.13/3.52 ordereqreflfact = 0
% 3.13/3.52
% 3.13/3.52 litselect = negord
% 3.13/3.52
% 3.13/3.52 maxweight = 15
% 3.13/3.52 maxdepth = 30000
% 3.13/3.52 maxlength = 115
% 3.13/3.52 maxnrvars = 195
% 3.13/3.52 excuselevel = 1
% 3.13/3.52 increasemaxweight = 1
% 3.13/3.52
% 3.13/3.52 maxselected = 10000000
% 3.13/3.52 maxnrclauses = 10000000
% 3.13/3.52
% 3.13/3.52 showgenerated = 0
% 3.13/3.52 showkept = 0
% 3.13/3.52 showselected = 0
% 3.13/3.52 showdeleted = 0
% 3.13/3.52 showresimp = 1
% 3.13/3.52 showstatus = 2000
% 3.13/3.52
% 3.13/3.52 prologoutput = 0
% 3.13/3.52 nrgoals = 5000000
% 3.13/3.52 totalproof = 1
% 3.13/3.52
% 3.13/3.52 Symbols occurring in the translation:
% 3.13/3.52
% 3.13/3.52 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 3.13/3.52 . [1, 2] (w:1, o:20, a:1, s:1, b:0),
% 3.13/3.52 ! [4, 1] (w:0, o:13, a:1, s:1, b:0),
% 3.13/3.52 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 3.13/3.52 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 3.13/3.52 addition [37, 2] (w:1, o:44, a:1, s:1, b:0),
% 3.13/3.52 zero [39, 0] (w:1, o:9, a:1, s:1, b:0),
% 3.13/3.52 multiplication [40, 2] (w:1, o:46, a:1, s:1, b:0),
% 3.13/3.52 one [41, 0] (w:1, o:10, a:1, s:1, b:0),
% 3.13/3.52 star [42, 1] (w:1, o:18, a:1, s:1, b:0),
% 3.13/3.52 leq [43, 2] (w:1, o:45, a:1, s:1, b:0),
% 3.13/3.52 strong_iteration [44, 1] (w:1, o:19, a:1, s:1, b:0),
% 3.13/3.52 skol1 [46, 0] (w:1, o:12, a:1, s:1, b:1).
% 3.13/3.52
% 3.13/3.52
% 3.13/3.52 Starting Search:
% 3.13/3.52
% 3.13/3.52 *** allocated 15000 integers for clauses
% 3.13/3.52 *** allocated 22500 integers for clauses
% 3.13/3.52 *** allocated 33750 integers for clauses
% 3.13/3.52 *** allocated 50625 integers for clauses
% 3.13/3.52 *** allocated 15000 integers for termspace/termends
% 3.13/3.52 *** allocated 75937 integers for clauses
% 3.13/3.52 Resimplifying inuse:
% 3.13/3.52 Done
% 3.13/3.52
% 3.13/3.52 *** allocated 22500 integers for termspace/termends
% 3.13/3.52 *** allocated 113905 integers for clauses
% 3.13/3.52 *** allocated 33750 integers for termspace/termends
% 3.13/3.52 *** allocated 170857 integers for clauses
% 3.13/3.52
% 3.13/3.52 Intermediate Status:
% 3.13/3.52 Generated: 22904
% 3.13/3.52 Kept: 2021
% 3.13/3.52 Inuse: 261
% 3.13/3.52 Deleted: 63
% 3.13/3.52 Deletedinuse: 34
% 3.13/3.52
% 3.13/3.52 Resimplifying inuse:
% 3.13/3.52 Done
% 3.13/3.52
% 3.13/3.52 *** allocated 50625 integers for termspace/termends
% 3.13/3.52 *** allocated 256285 integers for clauses
% 3.13/3.52 Resimplifying inuse:
% 3.13/3.52 Done
% 3.13/3.52
% 3.13/3.52 *** allocated 75937 integers for termspace/termends
% 3.13/3.52
% 3.13/3.52 Intermediate Status:
% 3.13/3.52 Generated: 48844
% 3.13/3.52 Kept: 4027
% 3.13/3.52 Inuse: 406
% 3.13/3.52 Deleted: 75
% 3.13/3.52 Deletedinuse: 36
% 3.13/3.52
% 3.13/3.52 Resimplifying inuse:
% 3.13/3.52 Done
% 3.13/3.52
% 3.13/3.52 *** allocated 384427 integers for clauses
% 3.13/3.52 Resimplifying inuse:
% 3.13/3.52 Done
% 3.13/3.52
% 3.13/3.52 *** allocated 113905 integers for termspace/termends
% 3.13/3.52
% 3.13/3.52 Intermediate Status:
% 3.13/3.52 Generated: 79522
% 3.13/3.52 Kept: 6086
% 3.13/3.52 Inuse: 600
% 3.13/3.52 Deleted: 123
% 3.13/3.52 Deletedinuse: 39
% 3.13/3.52
% 3.13/3.52 Resimplifying inuse:
% 3.13/3.52 Done
% 3.13/3.52
% 3.13/3.52 Resimplifying inuse:
% 3.13/3.52 Done
% 3.13/3.52
% 3.13/3.52 *** allocated 576640 integers for clauses
% 3.13/3.52
% 3.13/3.52 Intermediate Status:
% 3.13/3.52 Generated: 101533
% 3.13/3.52 Kept: 8202
% 3.13/3.52 Inuse: 717
% 3.13/3.52 Deleted: 137
% 3.13/3.52 Deletedinuse: 40
% 3.13/3.52
% 3.13/3.52 Resimplifying inuse:
% 3.13/3.52 Done
% 3.13/3.52
% 3.13/3.52 *** allocated 170857 integers for termspace/termends
% 3.13/3.52 Resimplifying inuse:
% 3.13/3.52 Done
% 3.13/3.52
% 3.13/3.52
% 3.13/3.52 Intermediate Status:
% 3.13/3.52 Generated: 131068
% 3.13/3.52 Kept: 10223
% 3.13/3.52 Inuse: 799
% 3.13/3.52 Deleted: 156
% 3.13/3.52 Deletedinuse: 42
% 3.13/3.52
% 3.13/3.52 Resimplifying inuse:
% 3.13/3.52 Done
% 3.13/3.52
% 3.13/3.52 *** allocated 864960 integers for clauses
% 3.13/3.52 Resimplifying inuse:
% 3.13/3.52 Done
% 3.13/3.52
% 3.13/3.52
% 3.13/3.52 Intermediate Status:
% 3.13/3.52 Generated: 170663
% 3.13/3.52 Kept: 12247
% 3.13/3.52 Inuse: 921
% 3.13/3.52 Deleted: 308
% 3.13/3.52 Deletedinuse: 142
% 3.13/3.52
% 3.13/3.52 Resimplifying inuse:
% 3.13/3.52 Done
% 3.13/3.52
% 3.13/3.52 Resimplifying inuse:
% 3.13/3.52 Done
% 3.13/3.52
% 3.13/3.52
% 3.13/3.52 Bliksems!, er is een bewijs:
% 3.13/3.52 % SZS status Theorem
% 3.13/3.52 % SZS output start Refutation
% 3.13/3.52
% 3.13/3.52 (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X ) }.
% 3.13/3.52 (1) {G0,W11,D4,L1,V3,M1} I { addition( Z, addition( Y, X ) ) ==> addition(
% 3.13/3.52 addition( Z, Y ), X ) }.
% 3.13/3.52 (3) {G0,W5,D3,L1,V1,M1} I { addition( X, X ) ==> X }.
% 3.13/3.52 (4) {G0,W11,D4,L1,V3,M1} I { multiplication( X, multiplication( Y, Z ) )
% 3.13/3.52 ==> multiplication( multiplication( X, Y ), Z ) }.
% 3.13/3.52 (9) {G0,W5,D3,L1,V1,M1} I { multiplication( zero, X ) ==> zero }.
% 3.13/3.52 (10) {G0,W9,D5,L1,V1,M1} I { addition( one, multiplication( X, star( X ) )
% 3.13/3.52 ) ==> star( X ) }.
% 3.13/3.52 (14) {G0,W9,D5,L1,V1,M1} I { addition( multiplication( X, strong_iteration
% 3.13/3.52 ( X ) ), one ) ==> strong_iteration( X ) }.
% 3.13/3.52 (16) {G0,W10,D5,L1,V1,M1} I { addition( star( X ), multiplication(
% 3.13/3.52 strong_iteration( X ), zero ) ) ==> strong_iteration( X ) }.
% 3.13/3.52 (17) {G0,W8,D3,L2,V2,M2} I { ! leq( X, Y ), addition( X, Y ) ==> Y }.
% 3.13/3.52 (18) {G0,W8,D3,L2,V2,M2} I { ! addition( X, Y ) ==> Y, leq( X, Y ) }.
% 3.13/3.52 (19) {G0,W20,D4,L2,V0,M2} I { ! leq( strong_iteration( multiplication(
% 3.13/3.52 skol1, zero ) ), addition( one, multiplication( skol1, zero ) ) ), ! leq
% 3.13/3.52 ( addition( one, multiplication( skol1, zero ) ), strong_iteration(
% 3.13/3.52 multiplication( skol1, zero ) ) ) }.
% 3.13/3.52 (22) {G1,W3,D2,L1,V1,M1} R(18,3) { leq( X, X ) }.
% 3.13/3.52 (25) {G1,W14,D4,L2,V3,M2} P(1,18) { ! addition( addition( X, Y ), Z ) ==>
% 3.13/3.52 addition( Y, Z ), leq( X, addition( Y, Z ) ) }.
% 3.13/3.52 (36) {G1,W8,D3,L2,V2,M2} P(17,0) { addition( Y, X ) ==> Y, ! leq( X, Y )
% 3.13/3.52 }.
% 3.13/3.52 (50) {G1,W9,D4,L1,V2,M1} P(9,4) { multiplication( multiplication( Y, zero )
% 3.13/3.52 , X ) ==> multiplication( Y, zero ) }.
% 3.13/3.52 (118) {G1,W13,D5,L1,V2,M1} P(10,1) { addition( addition( Y, one ),
% 3.13/3.52 multiplication( X, star( X ) ) ) ==> addition( Y, star( X ) ) }.
% 3.13/3.52 (120) {G1,W9,D5,L1,V1,M1} P(10,0) { addition( multiplication( X, star( X )
% 3.13/3.52 ), one ) ==> star( X ) }.
% 3.13/3.52 (298) {G1,W26,D6,L2,V0,M2} R(19,18);d(1) { ! leq( addition( one,
% 3.13/3.52 multiplication( skol1, zero ) ), strong_iteration( multiplication( skol1
% 3.13/3.52 , zero ) ) ), ! addition( addition( strong_iteration( multiplication(
% 3.13/3.52 skol1, zero ) ), one ), multiplication( skol1, zero ) ) ==> addition( one
% 3.13/3.52 , multiplication( skol1, zero ) ) }.
% 3.13/3.52 (319) {G2,W8,D3,L2,V3,M2} P(17,25);q { leq( X, addition( Y, Z ) ), ! leq( X
% 3.13/3.52 , Y ) }.
% 3.13/3.52 (800) {G2,W10,D4,L1,V1,M1} P(50,14) { addition( multiplication( X, zero ),
% 3.13/3.52 one ) ==> strong_iteration( multiplication( X, zero ) ) }.
% 3.13/3.52 (802) {G2,W10,D4,L1,V1,M1} P(50,10) { addition( one, multiplication( X,
% 3.13/3.52 zero ) ) ==> star( multiplication( X, zero ) ) }.
% 3.13/3.52 (1192) {G3,W8,D3,L2,V2,M2} P(16,319) { leq( Y, strong_iteration( X ) ), !
% 3.13/3.52 leq( Y, star( X ) ) }.
% 3.13/3.52 (1206) {G4,W11,D4,L2,V2,M2} R(1192,36) { ! leq( X, star( Y ) ), addition(
% 3.13/3.52 strong_iteration( Y ), X ) ==> strong_iteration( Y ) }.
% 3.13/3.52 (4078) {G2,W14,D5,L1,V2,M1} P(50,118) { addition( addition( Y, one ),
% 3.13/3.52 multiplication( X, zero ) ) ==> addition( Y, star( multiplication( X,
% 3.13/3.52 zero ) ) ) }.
% 3.13/3.52 (4165) {G3,W9,D4,L1,V1,M1} P(50,120);d(800) { strong_iteration(
% 3.13/3.52 multiplication( X, zero ) ) ==> star( multiplication( X, zero ) ) }.
% 3.13/3.52 (13455) {G5,W0,D0,L0,V0,M0} S(298);d(802);d(4078);d(4165);d(1206);d(4165);d
% 3.13/3.52 (802);q;r(22) { }.
% 3.13/3.52
% 3.13/3.52
% 3.13/3.52 % SZS output end Refutation
% 3.13/3.52 found a proof!
% 3.13/3.52
% 3.13/3.52
% 3.13/3.52 Unprocessed initial clauses:
% 3.13/3.52
% 3.13/3.52 (13457) {G0,W7,D3,L1,V2,M1} { addition( X, Y ) = addition( Y, X ) }.
% 3.13/3.52 (13458) {G0,W11,D4,L1,V3,M1} { addition( Z, addition( Y, X ) ) = addition
% 3.13/3.52 ( addition( Z, Y ), X ) }.
% 3.13/3.52 (13459) {G0,W5,D3,L1,V1,M1} { addition( X, zero ) = X }.
% 3.13/3.52 (13460) {G0,W5,D3,L1,V1,M1} { addition( X, X ) = X }.
% 3.13/3.52 (13461) {G0,W11,D4,L1,V3,M1} { multiplication( X, multiplication( Y, Z ) )
% 3.13/3.52 = multiplication( multiplication( X, Y ), Z ) }.
% 3.13/3.52 (13462) {G0,W5,D3,L1,V1,M1} { multiplication( X, one ) = X }.
% 3.13/3.52 (13463) {G0,W5,D3,L1,V1,M1} { multiplication( one, X ) = X }.
% 3.13/3.52 (13464) {G0,W13,D4,L1,V3,M1} { multiplication( X, addition( Y, Z ) ) =
% 3.13/3.52 addition( multiplication( X, Y ), multiplication( X, Z ) ) }.
% 3.13/3.52 (13465) {G0,W13,D4,L1,V3,M1} { multiplication( addition( X, Y ), Z ) =
% 3.13/3.52 addition( multiplication( X, Z ), multiplication( Y, Z ) ) }.
% 3.13/3.52 (13466) {G0,W5,D3,L1,V1,M1} { multiplication( zero, X ) = zero }.
% 3.13/3.52 (13467) {G0,W9,D5,L1,V1,M1} { addition( one, multiplication( X, star( X )
% 3.13/3.52 ) ) = star( X ) }.
% 3.13/3.52 (13468) {G0,W9,D5,L1,V1,M1} { addition( one, multiplication( star( X ), X
% 3.13/3.52 ) ) = star( X ) }.
% 3.13/3.52 (13469) {G0,W13,D4,L2,V3,M2} { ! leq( addition( multiplication( X, Z ), Y
% 3.13/3.52 ), Z ), leq( multiplication( star( X ), Y ), Z ) }.
% 3.13/3.52 (13470) {G0,W13,D4,L2,V3,M2} { ! leq( addition( multiplication( Z, X ), Y
% 3.13/3.52 ), Z ), leq( multiplication( Y, star( X ) ), Z ) }.
% 3.13/3.52 (13471) {G0,W9,D5,L1,V1,M1} { strong_iteration( X ) = addition(
% 3.13/3.52 multiplication( X, strong_iteration( X ) ), one ) }.
% 3.13/3.52 (13472) {G0,W13,D4,L2,V3,M2} { ! leq( Z, addition( multiplication( X, Z )
% 3.13/3.52 , Y ) ), leq( Z, multiplication( strong_iteration( X ), Y ) ) }.
% 3.13/3.52 (13473) {G0,W10,D5,L1,V1,M1} { strong_iteration( X ) = addition( star( X )
% 3.13/3.52 , multiplication( strong_iteration( X ), zero ) ) }.
% 3.13/3.52 (13474) {G0,W8,D3,L2,V2,M2} { ! leq( X, Y ), addition( X, Y ) = Y }.
% 3.13/3.52 (13475) {G0,W8,D3,L2,V2,M2} { ! addition( X, Y ) = Y, leq( X, Y ) }.
% 3.13/3.52 (13476) {G0,W20,D4,L2,V0,M2} { ! leq( strong_iteration( multiplication(
% 3.13/3.52 skol1, zero ) ), addition( one, multiplication( skol1, zero ) ) ), ! leq
% 3.13/3.52 ( addition( one, multiplication( skol1, zero ) ), strong_iteration(
% 3.13/3.52 multiplication( skol1, zero ) ) ) }.
% 3.13/3.52
% 3.13/3.52
% 3.13/3.52 Total Proof:
% 3.13/3.52
% 3.13/3.52 subsumption: (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X
% 3.13/3.52 ) }.
% 3.13/3.52 parent0: (13457) {G0,W7,D3,L1,V2,M1} { addition( X, Y ) = addition( Y, X )
% 3.13/3.52 }.
% 3.13/3.52 substitution0:
% 3.13/3.52 X := X
% 3.13/3.52 Y := Y
% 3.13/3.52 end
% 3.13/3.52 permutation0:
% 3.13/3.52 0 ==> 0
% 3.13/3.52 end
% 3.13/3.52
% 3.13/3.52 subsumption: (1) {G0,W11,D4,L1,V3,M1} I { addition( Z, addition( Y, X ) )
% 3.13/3.52 ==> addition( addition( Z, Y ), X ) }.
% 3.13/3.52 parent0: (13458) {G0,W11,D4,L1,V3,M1} { addition( Z, addition( Y, X ) ) =
% 3.13/3.52 addition( addition( Z, Y ), X ) }.
% 3.13/3.52 substitution0:
% 3.13/3.52 X := X
% 3.13/3.52 Y := Y
% 3.13/3.52 Z := Z
% 3.13/3.52 end
% 3.13/3.52 permutation0:
% 3.13/3.52 0 ==> 0
% 3.13/3.52 end
% 3.13/3.52
% 3.13/3.52 subsumption: (3) {G0,W5,D3,L1,V1,M1} I { addition( X, X ) ==> X }.
% 3.13/3.52 parent0: (13460) {G0,W5,D3,L1,V1,M1} { addition( X, X ) = X }.
% 3.13/3.52 substitution0:
% 3.13/3.52 X := X
% 3.13/3.52 end
% 3.13/3.52 permutation0:
% 3.13/3.52 0 ==> 0
% 3.13/3.52 end
% 3.13/3.52
% 3.13/3.52 subsumption: (4) {G0,W11,D4,L1,V3,M1} I { multiplication( X, multiplication
% 3.13/3.52 ( Y, Z ) ) ==> multiplication( multiplication( X, Y ), Z ) }.
% 3.13/3.52 parent0: (13461) {G0,W11,D4,L1,V3,M1} { multiplication( X, multiplication
% 3.13/3.52 ( Y, Z ) ) = multiplication( multiplication( X, Y ), Z ) }.
% 3.13/3.52 substitution0:
% 3.13/3.52 X := X
% 3.13/3.52 Y := Y
% 3.13/3.52 Z := Z
% 3.13/3.52 end
% 3.13/3.52 permutation0:
% 3.13/3.52 0 ==> 0
% 3.13/3.52 end
% 3.13/3.52
% 3.13/3.52 subsumption: (9) {G0,W5,D3,L1,V1,M1} I { multiplication( zero, X ) ==> zero
% 3.13/3.52 }.
% 3.13/3.52 parent0: (13466) {G0,W5,D3,L1,V1,M1} { multiplication( zero, X ) = zero
% 3.13/3.52 }.
% 3.13/3.52 substitution0:
% 3.13/3.52 X := X
% 3.13/3.52 end
% 3.13/3.52 permutation0:
% 3.13/3.52 0 ==> 0
% 3.13/3.52 end
% 3.13/3.52
% 3.13/3.52 subsumption: (10) {G0,W9,D5,L1,V1,M1} I { addition( one, multiplication( X
% 3.13/3.52 , star( X ) ) ) ==> star( X ) }.
% 3.13/3.52 parent0: (13467) {G0,W9,D5,L1,V1,M1} { addition( one, multiplication( X,
% 3.13/3.52 star( X ) ) ) = star( X ) }.
% 3.13/3.52 substitution0:
% 3.13/3.52 X := X
% 3.13/3.52 end
% 3.13/3.52 permutation0:
% 3.13/3.52 0 ==> 0
% 3.13/3.52 end
% 3.13/3.52
% 3.13/3.52 eqswap: (13515) {G0,W9,D5,L1,V1,M1} { addition( multiplication( X,
% 3.13/3.52 strong_iteration( X ) ), one ) = strong_iteration( X ) }.
% 3.13/3.52 parent0[0]: (13471) {G0,W9,D5,L1,V1,M1} { strong_iteration( X ) = addition
% 3.13/3.52 ( multiplication( X, strong_iteration( X ) ), one ) }.
% 3.13/3.52 substitution0:
% 3.13/3.52 X := X
% 3.13/3.52 end
% 3.13/3.52
% 3.13/3.52 subsumption: (14) {G0,W9,D5,L1,V1,M1} I { addition( multiplication( X,
% 3.13/3.52 strong_iteration( X ) ), one ) ==> strong_iteration( X ) }.
% 3.13/3.52 parent0: (13515) {G0,W9,D5,L1,V1,M1} { addition( multiplication( X,
% 3.13/3.52 strong_iteration( X ) ), one ) = strong_iteration( X ) }.
% 3.13/3.52 substitution0:
% 3.13/3.52 X := X
% 3.13/3.52 end
% 3.13/3.52 permutation0:
% 3.13/3.52 0 ==> 0
% 3.13/3.52 end
% 3.13/3.52
% 3.13/3.52 eqswap: (13528) {G0,W10,D5,L1,V1,M1} { addition( star( X ), multiplication
% 3.13/3.52 ( strong_iteration( X ), zero ) ) = strong_iteration( X ) }.
% 3.13/3.52 parent0[0]: (13473) {G0,W10,D5,L1,V1,M1} { strong_iteration( X ) =
% 3.13/3.52 addition( star( X ), multiplication( strong_iteration( X ), zero ) ) }.
% 3.13/3.52 substitution0:
% 3.13/3.52 X := X
% 3.13/3.52 end
% 3.13/3.52
% 3.13/3.52 subsumption: (16) {G0,W10,D5,L1,V1,M1} I { addition( star( X ),
% 3.13/3.52 multiplication( strong_iteration( X ), zero ) ) ==> strong_iteration( X )
% 3.13/3.52 }.
% 3.13/3.52 parent0: (13528) {G0,W10,D5,L1,V1,M1} { addition( star( X ),
% 3.13/3.52 multiplication( strong_iteration( X ), zero ) ) = strong_iteration( X )
% 3.13/3.52 }.
% 3.13/3.52 substitution0:
% 3.13/3.52 X := X
% 3.13/3.52 end
% 3.13/3.52 permutation0:
% 3.13/3.52 0 ==> 0
% 3.13/3.52 end
% 3.13/3.52
% 3.13/3.52 subsumption: (17) {G0,W8,D3,L2,V2,M2} I { ! leq( X, Y ), addition( X, Y )
% 3.13/3.52 ==> Y }.
% 3.13/3.52 parent0: (13474) {G0,W8,D3,L2,V2,M2} { ! leq( X, Y ), addition( X, Y ) = Y
% 3.13/3.52 }.
% 3.13/3.52 substitution0:
% 3.13/3.52 X := X
% 3.13/3.52 Y := Y
% 3.13/3.52 end
% 3.13/3.52 permutation0:
% 3.13/3.52 0 ==> 0
% 3.13/3.52 1 ==> 1
% 3.13/3.52 end
% 3.13/3.52
% 3.13/3.52 subsumption: (18) {G0,W8,D3,L2,V2,M2} I { ! addition( X, Y ) ==> Y, leq( X
% 3.13/3.52 , Y ) }.
% 3.13/3.52 parent0: (13475) {G0,W8,D3,L2,V2,M2} { ! addition( X, Y ) = Y, leq( X, Y )
% 3.13/3.52 }.
% 3.13/3.52 substitution0:
% 3.13/3.52 X := X
% 3.13/3.52 Y := Y
% 3.13/3.52 end
% 3.13/3.52 permutation0:
% 3.13/3.52 0 ==> 0
% 3.13/3.52 1 ==> 1
% 3.13/3.52 end
% 3.13/3.52
% 3.13/3.52 subsumption: (19) {G0,W20,D4,L2,V0,M2} I { ! leq( strong_iteration(
% 3.13/3.52 multiplication( skol1, zero ) ), addition( one, multiplication( skol1,
% 3.13/3.52 zero ) ) ), ! leq( addition( one, multiplication( skol1, zero ) ),
% 3.13/3.52 strong_iteration( multiplication( skol1, zero ) ) ) }.
% 3.13/3.52 parent0: (13476) {G0,W20,D4,L2,V0,M2} { ! leq( strong_iteration(
% 3.13/3.52 multiplication( skol1, zero ) ), addition( one, multiplication( skol1,
% 3.13/3.52 zero ) ) ), ! leq( addition( one, multiplication( skol1, zero ) ),
% 3.13/3.52 strong_iteration( multiplication( skol1, zero ) ) ) }.
% 3.13/3.52 substitution0:
% 3.13/3.52 end
% 3.13/3.52 permutation0:
% 3.13/3.52 0 ==> 0
% 3.13/3.52 1 ==> 1
% 3.13/3.52 end
% 3.13/3.52
% 3.13/3.52 eqswap: (13573) {G0,W8,D3,L2,V2,M2} { ! Y ==> addition( X, Y ), leq( X, Y
% 3.13/3.52 ) }.
% 3.13/3.52 parent0[0]: (18) {G0,W8,D3,L2,V2,M2} I { ! addition( X, Y ) ==> Y, leq( X,
% 3.13/3.52 Y ) }.
% 3.13/3.52 substitution0:
% 3.13/3.52 X := X
% 3.13/3.52 Y := Y
% 3.13/3.52 end
% 3.13/3.52
% 3.13/3.52 eqswap: (13574) {G0,W5,D3,L1,V1,M1} { X ==> addition( X, X ) }.
% 3.13/3.52 parent0[0]: (3) {G0,W5,D3,L1,V1,M1} I { addition( X, X ) ==> X }.
% 3.13/3.52 substitution0:
% 3.13/3.52 X := X
% 3.13/3.52 end
% 3.13/3.52
% 3.13/3.52 resolution: (13575) {G1,W3,D2,L1,V1,M1} { leq( X, X ) }.
% 3.13/3.52 parent0[0]: (13573) {G0,W8,D3,L2,V2,M2} { ! Y ==> addition( X, Y ), leq( X
% 3.13/3.52 , Y ) }.
% 3.13/3.52 parent1[0]: (13574) {G0,W5,D3,L1,V1,M1} { X ==> addition( X, X ) }.
% 3.13/3.52 substitution0:
% 3.13/3.52 X := X
% 3.13/3.52 Y := X
% 3.13/3.52 end
% 3.13/3.52 substitution1:
% 3.13/3.52 X := X
% 3.13/3.52 end
% 3.13/3.52
% 3.13/3.52 subsumption: (22) {G1,W3,D2,L1,V1,M1} R(18,3) { leq( X, X ) }.
% 3.13/3.52 parent0: (13575) {G1,W3,D2,L1,V1,M1} { leq( X, X ) }.
% 3.13/3.52 substitution0:
% 3.13/3.52 X := X
% 3.13/3.52 end
% 3.13/3.52 permutation0:
% 3.13/3.52 0 ==> 0
% 3.13/3.52 end
% 3.13/3.52
% 3.13/3.52 eqswap: (13577) {G0,W8,D3,L2,V2,M2} { ! Y ==> addition( X, Y ), leq( X, Y
% 3.13/3.52 ) }.
% 3.13/3.52 parent0[0]: (18) {G0,W8,D3,L2,V2,M2} I { ! addition( X, Y ) ==> Y, leq( X,
% 3.13/3.52 Y ) }.
% 3.13/3.52 substitution0:
% 3.13/3.52 X := X
% 3.13/3.52 Y := Y
% 3.13/3.52 end
% 3.13/3.52
% 3.13/3.52 paramod: (13578) {G1,W14,D4,L2,V3,M2} { ! addition( X, Y ) ==> addition(
% 3.13/3.52 addition( Z, X ), Y ), leq( Z, addition( X, Y ) ) }.
% 3.13/3.52 parent0[0]: (1) {G0,W11,D4,L1,V3,M1} I { addition( Z, addition( Y, X ) )
% 3.13/3.52 ==> addition( addition( Z, Y ), X ) }.
% 3.13/3.52 parent1[0; 5]: (13577) {G0,W8,D3,L2,V2,M2} { ! Y ==> addition( X, Y ), leq
% 3.13/3.52 ( X, Y ) }.
% 3.13/3.52 substitution0:
% 3.13/3.52 X := Y
% 3.13/3.52 Y := X
% 3.13/3.52 Z := Z
% 3.13/3.52 end
% 3.13/3.52 substitution1:
% 3.13/3.52 X := Z
% 3.13/3.52 Y := addition( X, Y )
% 3.13/3.52 end
% 3.13/3.52
% 3.13/3.52 eqswap: (13579) {G1,W14,D4,L2,V3,M2} { ! addition( addition( Z, X ), Y )
% 3.13/3.52 ==> addition( X, Y ), leq( Z, addition( X, Y ) ) }.
% 3.13/3.52 parent0[0]: (13578) {G1,W14,D4,L2,V3,M2} { ! addition( X, Y ) ==> addition
% 3.13/3.52 ( addition( Z, X ), Y ), leq( Z, addition( X, Y ) ) }.
% 3.13/3.52 substitution0:
% 3.13/3.52 X := X
% 3.13/3.52 Y := Y
% 3.13/3.52 Z := Z
% 3.13/3.52 end
% 3.13/3.52
% 3.13/3.52 subsumption: (25) {G1,W14,D4,L2,V3,M2} P(1,18) { ! addition( addition( X, Y
% 3.13/3.52 ), Z ) ==> addition( Y, Z ), leq( X, addition( Y, Z ) ) }.
% 3.13/3.52 parent0: (13579) {G1,W14,D4,L2,V3,M2} { ! addition( addition( Z, X ), Y )
% 3.13/3.52 ==> addition( X, Y ), leq( Z, addition( X, Y ) ) }.
% 3.13/3.52 substitution0:
% 3.13/3.52 X := Y
% 3.13/3.52 Y := Z
% 3.13/3.52 Z := X
% 3.13/3.52 end
% 3.13/3.52 permutation0:
% 3.13/3.52 0 ==> 0
% 3.13/3.52 1 ==> 1
% 3.13/3.52 end
% 3.13/3.52
% 3.13/3.52 eqswap: (13580) {G0,W8,D3,L2,V2,M2} { Y ==> addition( X, Y ), ! leq( X, Y
% 3.13/3.52 ) }.
% 3.13/3.52 parent0[1]: (17) {G0,W8,D3,L2,V2,M2} I { ! leq( X, Y ), addition( X, Y )
% 3.13/3.52 ==> Y }.
% 3.13/3.52 substitution0:
% 3.13/3.52 X := X
% 3.13/3.52 Y := Y
% 3.13/3.52 end
% 3.13/3.52
% 3.13/3.52 paramod: (13581) {G1,W8,D3,L2,V2,M2} { X ==> addition( X, Y ), ! leq( Y, X
% 3.13/3.52 ) }.
% 3.13/3.52 parent0[0]: (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X )
% 3.13/3.52 }.
% 3.13/3.52 parent1[0; 2]: (13580) {G0,W8,D3,L2,V2,M2} { Y ==> addition( X, Y ), ! leq
% 3.13/3.52 ( X, Y ) }.
% 3.13/3.52 substitution0:
% 3.13/3.52 X := Y
% 3.13/3.52 Y := X
% 3.13/3.52 end
% 3.13/3.52 substitution1:
% 3.13/3.52 X := Y
% 3.13/3.52 Y := X
% 3.13/3.52 end
% 3.13/3.52
% 3.13/3.52 eqswap: (13584) {G1,W8,D3,L2,V2,M2} { addition( X, Y ) ==> X, ! leq( Y, X
% 3.13/3.52 ) }.
% 3.13/3.52 parent0[0]: (13581) {G1,W8,D3,L2,V2,M2} { X ==> addition( X, Y ), ! leq( Y
% 3.13/3.52 , X ) }.
% 3.13/3.52 substitution0:
% 3.13/3.52 X := X
% 3.13/3.52 Y := Y
% 3.13/3.52 end
% 3.13/3.52
% 3.13/3.52 subsumption: (36) {G1,W8,D3,L2,V2,M2} P(17,0) { addition( Y, X ) ==> Y, !
% 3.13/3.52 leq( X, Y ) }.
% 3.13/3.52 parent0: (13584) {G1,W8,D3,L2,V2,M2} { addition( X, Y ) ==> X, ! leq( Y, X
% 3.13/3.52 ) }.
% 3.13/3.52 substitution0:
% 3.13/3.52 X := Y
% 3.13/3.52 Y := X
% 3.13/3.52 end
% 3.13/3.52 permutation0:
% 3.13/3.52 0 ==> 0
% 3.13/3.52 1 ==> 1
% 3.13/3.52 end
% 3.13/3.52
% 3.13/3.52 eqswap: (13586) {G0,W11,D4,L1,V3,M1} { multiplication( multiplication( X,
% 3.13/3.52 Y ), Z ) ==> multiplication( X, multiplication( Y, Z ) ) }.
% 3.13/3.52 parent0[0]: (4) {G0,W11,D4,L1,V3,M1} I { multiplication( X, multiplication
% 3.13/3.52 ( Y, Z ) ) ==> multiplication( multiplication( X, Y ), Z ) }.
% 3.13/3.52 substitution0:
% 3.13/3.52 X := X
% 3.13/3.52 Y := Y
% 3.13/3.52 Z := Z
% 3.13/3.52 end
% 3.13/3.52
% 3.13/3.52 paramod: (13591) {G1,W9,D4,L1,V2,M1} { multiplication( multiplication( X,
% 3.13/3.52 zero ), Y ) ==> multiplication( X, zero ) }.
% 3.13/3.52 parent0[0]: (9) {G0,W5,D3,L1,V1,M1} I { multiplication( zero, X ) ==> zero
% 3.13/3.52 }.
% 3.13/3.52 parent1[0; 8]: (13586) {G0,W11,D4,L1,V3,M1} { multiplication(
% 3.13/3.52 multiplication( X, Y ), Z ) ==> multiplication( X, multiplication( Y, Z )
% 3.13/3.52 ) }.
% 3.13/3.52 substitution0:
% 3.13/3.52 X := Y
% 3.13/3.52 end
% 3.13/3.52 substitution1:
% 3.13/3.52 X := X
% 3.13/3.52 Y := zero
% 3.13/3.52 Z := Y
% 3.13/3.52 end
% 3.13/3.52
% 3.13/3.52 subsumption: (50) {G1,W9,D4,L1,V2,M1} P(9,4) { multiplication(
% 3.13/3.52 multiplication( Y, zero ), X ) ==> multiplication( Y, zero ) }.
% 3.13/3.52 parent0: (13591) {G1,W9,D4,L1,V2,M1} { multiplication( multiplication( X,
% 3.13/3.52 zero ), Y ) ==> multiplication( X, zero ) }.
% 3.13/3.52 substitution0:
% 3.13/3.52 X := Y
% 3.13/3.52 Y := X
% 3.13/3.52 end
% 3.13/3.52 permutation0:
% 3.13/3.52 0 ==> 0
% 3.13/3.52 end
% 3.13/3.52
% 3.13/3.52 eqswap: (13600) {G0,W11,D4,L1,V3,M1} { addition( addition( X, Y ), Z ) ==>
% 3.13/3.52 addition( X, addition( Y, Z ) ) }.
% 3.13/3.52 parent0[0]: (1) {G0,W11,D4,L1,V3,M1} I { addition( Z, addition( Y, X ) )
% 3.13/3.52 ==> addition( addition( Z, Y ), X ) }.
% 3.13/3.52 substitution0:
% 3.13/3.52 X := Z
% 3.13/3.52 Y := Y
% 3.13/3.52 Z := X
% 3.13/3.52 end
% 3.13/3.52
% 3.13/3.52 paramod: (13602) {G1,W13,D5,L1,V2,M1} { addition( addition( X, one ),
% 3.13/3.52 multiplication( Y, star( Y ) ) ) ==> addition( X, star( Y ) ) }.
% 3.13/3.52 parent0[0]: (10) {G0,W9,D5,L1,V1,M1} I { addition( one, multiplication( X,
% 3.13/3.52 star( X ) ) ) ==> star( X ) }.
% 3.13/3.52 parent1[0; 11]: (13600) {G0,W11,D4,L1,V3,M1} { addition( addition( X, Y )
% 3.13/3.52 , Z ) ==> addition( X, addition( Y, Z ) ) }.
% 3.13/3.52 substitution0:
% 3.13/3.52 X := Y
% 3.13/3.52 end
% 3.13/3.52 substitution1:
% 3.13/3.52 X := X
% 3.13/3.52 Y := one
% 3.13/3.52 Z := multiplication( Y, star( Y ) )
% 3.13/3.52 end
% 3.13/3.52
% 3.13/3.52 subsumption: (118) {G1,W13,D5,L1,V2,M1} P(10,1) { addition( addition( Y,
% 3.13/3.52 one ), multiplication( X, star( X ) ) ) ==> addition( Y, star( X ) ) }.
% 3.13/3.52 parent0: (13602) {G1,W13,D5,L1,V2,M1} { addition( addition( X, one ),
% 3.13/3.52 multiplication( Y, star( Y ) ) ) ==> addition( X, star( Y ) ) }.
% 3.13/3.52 substitution0:
% 3.13/3.52 X := Y
% 3.13/3.52 Y := X
% 3.13/3.52 end
% 3.13/3.52 permutation0:
% 3.13/3.52 0 ==> 0
% 3.13/3.52 end
% 3.13/3.52
% 3.13/3.52 eqswap: (13605) {G0,W9,D5,L1,V1,M1} { star( X ) ==> addition( one,
% 3.13/3.52 multiplication( X, star( X ) ) ) }.
% 3.13/3.52 parent0[0]: (10) {G0,W9,D5,L1,V1,M1} I { addition( one, multiplication( X,
% 3.13/3.52 star( X ) ) ) ==> star( X ) }.
% 3.13/3.52 substitution0:
% 3.13/3.52 X := X
% 3.13/3.52 end
% 3.13/3.52
% 3.13/3.52 paramod: (13606) {G1,W9,D5,L1,V1,M1} { star( X ) ==> addition(
% 3.13/3.52 multiplication( X, star( X ) ), one ) }.
% 3.13/3.52 parent0[0]: (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X )
% 3.13/3.52 }.
% 3.13/3.52 parent1[0; 3]: (13605) {G0,W9,D5,L1,V1,M1} { star( X ) ==> addition( one,
% 3.13/3.52 multiplication( X, star( X ) ) ) }.
% 3.13/3.52 substitution0:
% 3.13/3.52 X := one
% 3.13/3.52 Y := multiplication( X, star( X ) )
% 3.13/3.52 end
% 3.13/3.52 substitution1:
% 3.13/3.52 X := X
% 3.13/3.52 end
% 3.13/3.52
% 3.13/3.52 eqswap: (13609) {G1,W9,D5,L1,V1,M1} { addition( multiplication( X, star( X
% 3.13/3.52 ) ), one ) ==> star( X ) }.
% 3.13/3.52 parent0[0]: (13606) {G1,W9,D5,L1,V1,M1} { star( X ) ==> addition(
% 3.13/3.52 multiplication( X, star( X ) ), one ) }.
% 3.13/3.52 substitution0:
% 3.13/3.52 X := X
% 3.13/3.52 end
% 3.13/3.52
% 3.13/3.52 subsumption: (120) {G1,W9,D5,L1,V1,M1} P(10,0) { addition( multiplication(
% 3.13/3.52 X, star( X ) ), one ) ==> star( X ) }.
% 3.13/3.52 parent0: (13609) {G1,W9,D5,L1,V1,M1} { addition( multiplication( X, star(
% 3.13/3.52 X ) ), one ) ==> star( X ) }.
% 3.13/3.52 substitution0:
% 3.13/3.52 X := X
% 3.13/3.52 end
% 3.13/3.52 permutation0:
% 3.13/3.52 0 ==> 0
% 3.13/3.52 end
% 3.13/3.52
% 3.13/3.52 eqswap: (13610) {G0,W8,D3,L2,V2,M2} { ! Y ==> addition( X, Y ), leq( X, Y
% 3.13/3.52 ) }.
% 3.13/3.52 parent0[0]: (18) {G0,W8,D3,L2,V2,M2} I { ! addition( X, Y ) ==> Y, leq( X,
% 3.13/3.52 Y ) }.
% 3.13/3.52 substitution0:
% 3.13/3.52 X := X
% 3.13/3.52 Y := Y
% 3.13/3.52 end
% 3.13/3.52
% 3.13/3.52 resolution: (13612) {G1,W26,D5,L2,V0,M2} { ! leq( addition( one,
% 3.13/3.52 multiplication( skol1, zero ) ), strong_iteration( multiplication( skol1
% 3.13/3.52 , zero ) ) ), ! addition( one, multiplication( skol1, zero ) ) ==>
% 3.13/3.52 addition( strong_iteration( multiplication( skol1, zero ) ), addition(
% 3.13/3.52 one, multiplication( skol1, zero ) ) ) }.
% 3.13/3.52 parent0[0]: (19) {G0,W20,D4,L2,V0,M2} I { ! leq( strong_iteration(
% 3.13/3.52 multiplication( skol1, zero ) ), addition( one, multiplication( skol1,
% 3.13/3.52 zero ) ) ), ! leq( addition( one, multiplication( skol1, zero ) ),
% 3.13/3.52 strong_iteration( multiplication( skol1, zero ) ) ) }.
% 3.13/3.52 parent1[1]: (13610) {G0,W8,D3,L2,V2,M2} { ! Y ==> addition( X, Y ), leq( X
% 3.13/3.52 , Y ) }.
% 3.13/3.52 substitution0:
% 3.13/3.52 end
% 3.13/3.52 substitution1:
% 3.13/3.52 X := strong_iteration( multiplication( skol1, zero ) )
% 3.13/3.52 Y := addition( one, multiplication( skol1, zero ) )
% 3.13/3.52 end
% 3.13/3.52
% 3.13/3.52 paramod: (13614) {G1,W26,D6,L2,V0,M2} { ! addition( one, multiplication(
% 3.13/3.52 skol1, zero ) ) ==> addition( addition( strong_iteration( multiplication
% 3.13/3.52 ( skol1, zero ) ), one ), multiplication( skol1, zero ) ), ! leq(
% 3.13/3.52 addition( one, multiplication( skol1, zero ) ), strong_iteration(
% 3.13/3.52 multiplication( skol1, zero ) ) ) }.
% 3.13/3.52 parent0[0]: (1) {G0,W11,D4,L1,V3,M1} I { addition( Z, addition( Y, X ) )
% 3.13/3.52 ==> addition( addition( Z, Y ), X ) }.
% 3.13/3.52 parent1[1; 7]: (13612) {G1,W26,D5,L2,V0,M2} { ! leq( addition( one,
% 3.13/3.52 multiplication( skol1, zero ) ), strong_iteration( multiplication( skol1
% 3.13/3.52 , zero ) ) ), ! addition( one, multiplication( skol1, zero ) ) ==>
% 3.13/3.52 addition( strong_iteration( multiplication( skol1, zero ) ), addition(
% 3.13/3.52 one, multiplication( skol1, zero ) ) ) }.
% 3.13/3.52 substitution0:
% 3.13/3.52 X := multiplication( skol1, zero )
% 3.13/3.52 Y := one
% 3.13/3.52 Z := strong_iteration( multiplication( skol1, zero ) )
% 3.13/3.52 end
% 3.13/3.52 substitution1:
% 3.13/3.52 end
% 3.13/3.52
% 3.13/3.52 eqswap: (13615) {G1,W26,D6,L2,V0,M2} { ! addition( addition(
% 3.13/3.52 strong_iteration( multiplication( skol1, zero ) ), one ), multiplication
% 3.13/3.52 ( skol1, zero ) ) ==> addition( one, multiplication( skol1, zero ) ), !
% 3.13/3.52 leq( addition( one, multiplication( skol1, zero ) ), strong_iteration(
% 3.13/3.52 multiplication( skol1, zero ) ) ) }.
% 3.13/3.52 parent0[0]: (13614) {G1,W26,D6,L2,V0,M2} { ! addition( one, multiplication
% 3.13/3.52 ( skol1, zero ) ) ==> addition( addition( strong_iteration(
% 3.13/3.52 multiplication( skol1, zero ) ), one ), multiplication( skol1, zero ) ),
% 3.13/3.52 ! leq( addition( one, multiplication( skol1, zero ) ), strong_iteration(
% 3.13/3.52 multiplication( skol1, zero ) ) ) }.
% 3.13/3.52 substitution0:
% 3.13/3.52 end
% 3.13/3.52
% 3.13/3.52 subsumption: (298) {G1,W26,D6,L2,V0,M2} R(19,18);d(1) { ! leq( addition(
% 3.13/3.52 one, multiplication( skol1, zero ) ), strong_iteration( multiplication(
% 3.13/3.52 skol1, zero ) ) ), ! addition( addition( strong_iteration( multiplication
% 3.13/3.52 ( skol1, zero ) ), one ), multiplication( skol1, zero ) ) ==> addition(
% 3.13/3.52 one, multiplication( skol1, zero ) ) }.
% 3.13/3.52 parent0: (13615) {G1,W26,D6,L2,V0,M2} { ! addition( addition(
% 3.13/3.52 strong_iteration( multiplication( skol1, zero ) ), one ), multiplication
% 3.13/3.52 ( skol1, zero ) ) ==> addition( one, multiplication( skol1, zero ) ), !
% 3.13/3.52 leq( addition( one, multiplication( skol1, zero ) ), strong_iteration(
% 3.13/3.52 multiplication( skol1, zero ) ) ) }.
% 3.13/3.52 substitution0:
% 3.13/3.52 end
% 3.13/3.52 permutation0:
% 3.13/3.52 0 ==> 1
% 3.13/3.52 1 ==> 0
% 3.13/3.52 end
% 3.13/3.52
% 3.13/3.52 eqswap: (13617) {G1,W14,D4,L2,V3,M2} { ! addition( Y, Z ) ==> addition(
% 3.13/3.52 addition( X, Y ), Z ), leq( X, addition( Y, Z ) ) }.
% 3.13/3.52 parent0[0]: (25) {G1,W14,D4,L2,V3,M2} P(1,18) { ! addition( addition( X, Y
% 3.13/3.52 ), Z ) ==> addition( Y, Z ), leq( X, addition( Y, Z ) ) }.
% 3.13/3.52 substitution0:
% 3.13/3.52 X := X
% 3.13/3.52 Y := Y
% 3.13/3.52 Z := Z
% 3.13/3.52 end
% 3.13/3.52
% 3.13/3.52 paramod: (13620) {G1,W15,D3,L3,V3,M3} { ! addition( X, Y ) ==> addition( X
% 3.13/3.52 , Y ), ! leq( Z, X ), leq( Z, addition( X, Y ) ) }.
% 3.13/3.52 parent0[1]: (17) {G0,W8,D3,L2,V2,M2} I { ! leq( X, Y ), addition( X, Y )
% 3.13/3.52 ==> Y }.
% 3.13/3.52 parent1[0; 6]: (13617) {G1,W14,D4,L2,V3,M2} { ! addition( Y, Z ) ==>
% 3.13/3.52 addition( addition( X, Y ), Z ), leq( X, addition( Y, Z ) ) }.
% 3.13/3.52 substitution0:
% 3.13/3.52 X := Z
% 3.13/3.52 Y := X
% 3.13/3.52 end
% 3.13/3.52 substitution1:
% 3.13/3.52 X := Z
% 3.13/3.52 Y := X
% 3.13/3.52 Z := Y
% 3.13/3.52 end
% 3.13/3.52
% 3.13/3.52 eqrefl: (13669) {G0,W8,D3,L2,V3,M2} { ! leq( Z, X ), leq( Z, addition( X,
% 3.13/3.52 Y ) ) }.
% 3.13/3.52 parent0[0]: (13620) {G1,W15,D3,L3,V3,M3} { ! addition( X, Y ) ==> addition
% 3.13/3.52 ( X, Y ), ! leq( Z, X ), leq( Z, addition( X, Y ) ) }.
% 3.13/3.52 substitution0:
% 3.13/3.52 X := X
% 3.13/3.52 Y := Y
% 3.13/3.52 Z := Z
% 3.13/3.52 end
% 3.13/3.52
% 3.13/3.52 subsumption: (319) {G2,W8,D3,L2,V3,M2} P(17,25);q { leq( X, addition( Y, Z
% 3.13/3.52 ) ), ! leq( X, Y ) }.
% 3.13/3.52 parent0: (13669) {G0,W8,D3,L2,V3,M2} { ! leq( Z, X ), leq( Z, addition( X
% 3.13/3.52 , Y ) ) }.
% 3.13/3.52 substitution0:
% 3.13/3.52 X := Y
% 3.13/3.52 Y := Z
% 3.13/3.52 Z := X
% 3.13/3.52 end
% 3.13/3.52 permutation0:
% 3.13/3.52 0 ==> 1
% 3.13/3.52 1 ==> 0
% 3.13/3.52 end
% 3.13/3.52
% 3.13/3.52 eqswap: (13671) {G0,W9,D5,L1,V1,M1} { strong_iteration( X ) ==> addition(
% 3.13/3.52 multiplication( X, strong_iteration( X ) ), one ) }.
% 3.13/3.52 parent0[0]: (14) {G0,W9,D5,L1,V1,M1} I { addition( multiplication( X,
% 3.13/3.52 strong_iteration( X ) ), one ) ==> strong_iteration( X ) }.
% 3.13/3.52 substitution0:
% 3.13/3.52 X := X
% 3.13/3.52 end
% 3.13/3.52
% 3.13/3.52 paramod: (13672) {G1,W10,D4,L1,V1,M1} { strong_iteration( multiplication(
% 3.13/3.52 X, zero ) ) ==> addition( multiplication( X, zero ), one ) }.
% 3.13/3.52 parent0[0]: (50) {G1,W9,D4,L1,V2,M1} P(9,4) { multiplication(
% 3.13/3.52 multiplication( Y, zero ), X ) ==> multiplication( Y, zero ) }.
% 3.13/3.52 parent1[0; 6]: (13671) {G0,W9,D5,L1,V1,M1} { strong_iteration( X ) ==>
% 3.13/3.52 addition( multiplication( X, strong_iteration( X ) ), one ) }.
% 3.13/3.52 substitution0:
% 3.13/3.52 X := strong_iteration( multiplication( X, zero ) )
% 3.13/3.52 Y := X
% 3.13/3.52 end
% 3.13/3.52 substitution1:
% 3.13/3.52 X := multiplication( X, zero )
% 3.13/3.52 end
% 3.13/3.52
% 3.13/3.52 eqswap: (13673) {G1,W10,D4,L1,V1,M1} { addition( multiplication( X, zero )
% 3.13/3.52 , one ) ==> strong_iteration( multiplication( X, zero ) ) }.
% 3.13/3.52 parent0[0]: (13672) {G1,W10,D4,L1,V1,M1} { strong_iteration(
% 3.13/3.52 multiplication( X, zero ) ) ==> addition( multiplication( X, zero ), one
% 3.13/3.52 ) }.
% 3.13/3.52 substitution0:
% 3.13/3.52 X := X
% 3.13/3.52 end
% 3.13/3.52
% 3.13/3.52 subsumption: (800) {G2,W10,D4,L1,V1,M1} P(50,14) { addition( multiplication
% 3.13/3.52 ( X, zero ), one ) ==> strong_iteration( multiplication( X, zero ) ) }.
% 3.13/3.52 parent0: (13673) {G1,W10,D4,L1,V1,M1} { addition( multiplication( X, zero
% 3.13/3.52 ), one ) ==> strong_iteration( multiplication( X, zero ) ) }.
% 3.13/3.52 substitution0:
% 3.13/3.52 X := X
% 3.13/3.52 end
% 3.13/3.52 permutation0:
% 3.13/3.52 0 ==> 0
% 3.13/3.52 end
% 3.13/3.52
% 3.13/3.52 eqswap: (13675) {G0,W9,D5,L1,V1,M1} { star( X ) ==> addition( one,
% 3.13/3.52 multiplication( X, star( X ) ) ) }.
% 3.13/3.52 parent0[0]: (10) {G0,W9,D5,L1,V1,M1} I { addition( one, multiplication( X,
% 3.13/3.52 star( X ) ) ) ==> star( X ) }.
% 3.13/3.52 substitution0:
% 3.13/3.52 X := X
% 3.13/3.52 end
% 3.13/3.52
% 3.13/3.52 paramod: (13676) {G1,W10,D4,L1,V1,M1} { star( multiplication( X, zero ) )
% 3.13/3.52 ==> addition( one, multiplication( X, zero ) ) }.
% 3.13/3.52 parent0[0]: (50) {G1,W9,D4,L1,V2,M1} P(9,4) { multiplication(
% 3.13/3.52 multiplication( Y, zero ), X ) ==> multiplication( Y, zero ) }.
% 3.13/3.52 parent1[0; 7]: (13675) {G0,W9,D5,L1,V1,M1} { star( X ) ==> addition( one,
% 3.13/3.52 multiplication( X, star( X ) ) ) }.
% 3.13/3.52 substitution0:
% 3.13/3.52 X := star( multiplication( X, zero ) )
% 3.13/3.52 Y := X
% 3.13/3.52 end
% 3.13/3.52 substitution1:
% 3.13/3.52 X := multiplication( X, zero )
% 3.13/3.52 end
% 3.13/3.52
% 3.13/3.52 eqswap: (13677) {G1,W10,D4,L1,V1,M1} { addition( one, multiplication( X,
% 3.13/3.52 zero ) ) ==> star( multiplication( X, zero ) ) }.
% 3.13/3.52 parent0[0]: (13676) {G1,W10,D4,L1,V1,M1} { star( multiplication( X, zero )
% 3.13/3.52 ) ==> addition( one, multiplication( X, zero ) ) }.
% 3.13/3.52 substitution0:
% 3.13/3.52 X := X
% 3.13/3.52 end
% 3.13/3.52
% 3.13/3.52 subsumption: (802) {G2,W10,D4,L1,V1,M1} P(50,10) { addition( one,
% 3.13/3.52 multiplication( X, zero ) ) ==> star( multiplication( X, zero ) ) }.
% 3.13/3.52 parent0: (13677) {G1,W10,D4,L1,V1,M1} { addition( one, multiplication( X,
% 3.13/3.52 zero ) ) ==> star( multiplication( X, zero ) ) }.
% 3.13/3.52 substitution0:
% 3.13/3.52 X := X
% 3.13/3.52 end
% 3.13/3.52 permutation0:
% 3.13/3.52 0 ==> 0
% 3.13/3.52 end
% 3.13/3.52
% 3.13/3.52 paramod: (13679) {G1,W8,D3,L2,V2,M2} { leq( X, strong_iteration( Y ) ), !
% 3.13/3.52 leq( X, star( Y ) ) }.
% 3.13/3.52 parent0[0]: (16) {G0,W10,D5,L1,V1,M1} I { addition( star( X ),
% 3.13/3.52 multiplication( strong_iteration( X ), zero ) ) ==> strong_iteration( X )
% 3.13/3.52 }.
% 3.13/3.52 parent1[0; 2]: (319) {G2,W8,D3,L2,V3,M2} P(17,25);q { leq( X, addition( Y,
% 3.13/3.52 Z ) ), ! leq( X, Y ) }.
% 3.13/3.52 substitution0:
% 3.13/3.52 X := Y
% 3.13/3.52 end
% 3.13/3.52 substitution1:
% 3.13/3.52 X := X
% 3.13/3.52 Y := star( Y )
% 3.13/3.52 Z := multiplication( strong_iteration( Y ), zero )
% 3.13/3.52 end
% 3.13/3.52
% 3.13/3.52 subsumption: (1192) {G3,W8,D3,L2,V2,M2} P(16,319) { leq( Y,
% 3.13/3.52 strong_iteration( X ) ), ! leq( Y, star( X ) ) }.
% 3.13/3.52 parent0: (13679) {G1,W8,D3,L2,V2,M2} { leq( X, strong_iteration( Y ) ), !
% 3.13/3.52 leq( X, star( Y ) ) }.
% 3.13/3.52 substitution0:
% 3.13/3.52 X := Y
% 3.13/3.52 Y := X
% 3.13/3.52 end
% 3.13/3.52 permutation0:
% 3.13/3.52 0 ==> 0
% 3.13/3.52 1 ==> 1
% 3.13/3.52 end
% 3.13/3.52
% 3.13/3.52 eqswap: (13680) {G1,W8,D3,L2,V2,M2} { X ==> addition( X, Y ), ! leq( Y, X
% 3.13/3.52 ) }.
% 3.13/3.52 parent0[0]: (36) {G1,W8,D3,L2,V2,M2} P(17,0) { addition( Y, X ) ==> Y, !
% 3.13/3.52 leq( X, Y ) }.
% 3.13/3.52 substitution0:
% 3.13/3.52 X := Y
% 3.13/3.52 Y := X
% 3.13/3.52 end
% 3.13/3.52
% 3.13/3.52 resolution: (13681) {G2,W11,D4,L2,V2,M2} { strong_iteration( X ) ==>
% 3.13/3.52 addition( strong_iteration( X ), Y ), ! leq( Y, star( X ) ) }.
% 3.13/3.52 parent0[1]: (13680) {G1,W8,D3,L2,V2,M2} { X ==> addition( X, Y ), ! leq( Y
% 3.13/3.52 , X ) }.
% 3.13/3.52 parent1[0]: (1192) {G3,W8,D3,L2,V2,M2} P(16,319) { leq( Y, strong_iteration
% 3.13/3.52 ( X ) ), ! leq( Y, star( X ) ) }.
% 3.13/3.52 substitution0:
% 3.13/3.52 X := strong_iteration( X )
% 3.13/3.52 Y := Y
% 3.13/3.52 end
% 3.13/3.52 substitution1:
% 3.13/3.52 X := X
% 3.13/3.52 Y := Y
% 3.13/3.52 end
% 3.13/3.52
% 3.13/3.52 eqswap: (13682) {G2,W11,D4,L2,V2,M2} { addition( strong_iteration( X ), Y
% 3.13/3.52 ) ==> strong_iteration( X ), ! leq( Y, star( X ) ) }.
% 3.13/3.52 parent0[0]: (13681) {G2,W11,D4,L2,V2,M2} { strong_iteration( X ) ==>
% 3.13/3.52 addition( strong_iteration( X ), Y ), ! leq( Y, star( X ) ) }.
% 3.13/3.52 substitution0:
% 3.13/3.52 X := X
% 3.13/3.52 Y := Y
% 3.13/3.52 end
% 3.13/3.52
% 3.13/3.52 subsumption: (1206) {G4,W11,D4,L2,V2,M2} R(1192,36) { ! leq( X, star( Y ) )
% 3.13/3.52 , addition( strong_iteration( Y ), X ) ==> strong_iteration( Y ) }.
% 3.13/3.52 parent0: (13682) {G2,W11,D4,L2,V2,M2} { addition( strong_iteration( X ), Y
% 3.13/3.52 ) ==> strong_iteration( X ), ! leq( Y, star( X ) ) }.
% 3.13/3.52 substitution0:
% 3.13/3.52 X := Y
% 3.13/3.52 Y := X
% 3.13/3.52 end
% 3.13/3.52 permutation0:
% 3.13/3.52 0 ==> 1
% 3.13/3.52 1 ==> 0
% 3.13/3.52 end
% 3.13/3.52
% 3.13/3.52 eqswap: (13684) {G1,W13,D5,L1,V2,M1} { addition( X, star( Y ) ) ==>
% 3.13/3.52 addition( addition( X, one ), multiplication( Y, star( Y ) ) ) }.
% 3.13/3.52 parent0[0]: (118) {G1,W13,D5,L1,V2,M1} P(10,1) { addition( addition( Y, one
% 3.13/3.52 ), multiplication( X, star( X ) ) ) ==> addition( Y, star( X ) ) }.
% 3.13/3.52 substitution0:
% 3.13/3.52 X := Y
% 3.13/3.52 Y := X
% 3.13/3.52 end
% 3.13/3.52
% 3.13/3.52 paramod: (13685) {G2,W14,D5,L1,V2,M1} { addition( X, star( multiplication
% 3.13/3.52 ( Y, zero ) ) ) ==> addition( addition( X, one ), multiplication( Y, zero
% 3.13/3.52 ) ) }.
% 3.13/3.52 parent0[0]: (50) {G1,W9,D4,L1,V2,M1} P(9,4) { multiplication(
% 3.13/3.52 multiplication( Y, zero ), X ) ==> multiplication( Y, zero ) }.
% 3.13/3.52 parent1[0; 11]: (13684) {G1,W13,D5,L1,V2,M1} { addition( X, star( Y ) )
% 3.13/3.52 ==> addition( addition( X, one ), multiplication( Y, star( Y ) ) ) }.
% 3.13/3.52 substitution0:
% 3.13/3.52 X := star( multiplication( Y, zero ) )
% 3.13/3.52 Y := Y
% 3.13/3.52 end
% 3.13/3.52 substitution1:
% 3.13/3.52 X := X
% 3.13/3.52 Y := multiplication( Y, zero )
% 3.13/3.52 end
% 3.13/3.52
% 3.13/3.52 eqswap: (13686) {G2,W14,D5,L1,V2,M1} { addition( addition( X, one ),
% 3.13/3.52 multiplication( Y, zero ) ) ==> addition( X, star( multiplication( Y,
% 3.13/3.52 zero ) ) ) }.
% 3.13/3.52 parent0[0]: (13685) {G2,W14,D5,L1,V2,M1} { addition( X, star(
% 3.13/3.52 multiplication( Y, zero ) ) ) ==> addition( addition( X, one ),
% 3.13/3.52 multiplication( Y, zero ) ) }.
% 3.13/3.52 substitution0:
% 3.13/3.52 X := X
% 3.13/3.52 Y := Y
% 3.13/3.52 end
% 3.13/3.52
% 3.13/3.52 subsumption: (4078) {G2,W14,D5,L1,V2,M1} P(50,118) { addition( addition( Y
% 3.13/3.52 , one ), multiplication( X, zero ) ) ==> addition( Y, star(
% 3.13/3.52 multiplication( X, zero ) ) ) }.
% 3.13/3.52 parent0: (13686) {G2,W14,D5,L1,V2,M1} { addition( addition( X, one ),
% 3.13/3.52 multiplication( Y, zero ) ) ==> addition( X, star( multiplication( Y,
% 3.13/3.52 zero ) ) ) }.
% 3.13/3.52 substitution0:
% 3.13/3.52 X := Y
% 3.13/3.52 Y := X
% 3.13/3.52 end
% 3.13/3.52 permutation0:
% 3.13/3.52 0 ==> 0
% 3.13/3.52 end
% 3.13/3.52
% 3.13/3.52 eqswap: (13688) {G1,W9,D5,L1,V1,M1} { star( X ) ==> addition(
% 3.13/3.52 multiplication( X, star( X ) ), one ) }.
% 3.13/3.52 parent0[0]: (120) {G1,W9,D5,L1,V1,M1} P(10,0) { addition( multiplication( X
% 3.13/3.52 , star( X ) ), one ) ==> star( X ) }.
% 3.13/3.52 substitution0:
% 3.13/3.52 X := X
% 3.13/3.52 end
% 3.13/3.52
% 3.13/3.52 paramod: (13690) {G2,W10,D4,L1,V1,M1} { star( multiplication( X, zero ) )
% 3.13/3.52 ==> addition( multiplication( X, zero ), one ) }.
% 3.13/3.52 parent0[0]: (50) {G1,W9,D4,L1,V2,M1} P(9,4) { multiplication(
% 3.13/3.52 multiplication( Y, zero ), X ) ==> multiplication( Y, zero ) }.
% 3.13/3.52 parent1[0; 6]: (13688) {G1,W9,D5,L1,V1,M1} { star( X ) ==> addition(
% 3.13/3.52 multiplication( X, star( X ) ), one ) }.
% 3.13/3.52 substitution0:
% 3.13/3.52 X := star( multiplication( X, zero ) )
% 3.13/3.52 Y := X
% 3.13/3.52 end
% 3.13/3.52 substitution1:
% 3.13/3.52 X := multiplication( X, zero )
% 3.13/3.52 end
% 3.13/3.52
% 3.13/3.52 paramod: (13691) {G3,W9,D4,L1,V1,M1} { star( multiplication( X, zero ) )
% 3.13/3.52 ==> strong_iteration( multiplication( X, zero ) ) }.
% 3.13/3.52 parent0[0]: (800) {G2,W10,D4,L1,V1,M1} P(50,14) { addition( multiplication
% 3.13/3.52 ( X, zero ), one ) ==> strong_iteration( multiplication( X, zero ) ) }.
% 3.13/3.52 parent1[0; 5]: (13690) {G2,W10,D4,L1,V1,M1} { star( multiplication( X,
% 3.13/3.52 zero ) ) ==> addition( multiplication( X, zero ), one ) }.
% 3.13/3.52 substitution0:
% 3.13/3.52 X := X
% 3.13/3.52 end
% 3.13/3.52 substitution1:
% 3.13/3.52 X := X
% 3.13/3.52 end
% 3.13/3.52
% 3.13/3.52 eqswap: (13692) {G3,W9,D4,L1,V1,M1} { strong_iteration( multiplication( X
% 3.13/3.52 , zero ) ) ==> star( multiplication( X, zero ) ) }.
% 3.13/3.52 parent0[0]: (13691) {G3,W9,D4,L1,V1,M1} { star( multiplication( X, zero )
% 3.13/3.52 ) ==> strong_iteration( multiplication( X, zero ) ) }.
% 3.13/3.52 substitution0:
% 3.13/3.52 X := X
% 3.13/3.52 end
% 3.13/3.52
% 3.13/3.52 subsumption: (4165) {G3,W9,D4,L1,V1,M1} P(50,120);d(800) { strong_iteration
% 3.13/3.52 ( multiplication( X, zero ) ) ==> star( multiplication( X, zero ) ) }.
% 3.13/3.52 parent0: (13692) {G3,W9,D4,L1,V1,M1} { strong_iteration( multiplication( X
% 3.13/3.52 , zero ) ) ==> star( multiplication( X, zero ) ) }.
% 3.13/3.52 substitution0:
% 3.13/3.52 X := X
% 3.13/3.52 end
% 3.13/3.52 permutation0:
% 3.13/3.52 0 ==> 0
% 3.13/3.52 end
% 3.13/3.52
% 3.13/3.52 paramod: (13701) {G2,W25,D6,L2,V0,M2} { ! addition( addition(
% 3.13/3.52 strong_iteration( multiplication( skol1, zero ) ), one ), multiplication
% 3.13/3.52 ( skol1, zero ) ) ==> star( multiplication( skol1, zero ) ), ! leq(
% 3.13/3.52 addition( one, multiplication( skol1, zero ) ), strong_iteration(
% 3.13/3.52 multiplication( skol1, zero ) ) ) }.
% 3.13/3.52 parent0[0]: (802) {G2,W10,D4,L1,V1,M1} P(50,10) { addition( one,
% 3.13/3.52 multiplication( X, zero ) ) ==> star( multiplication( X, zero ) ) }.
% 3.13/3.52 parent1[1; 12]: (298) {G1,W26,D6,L2,V0,M2} R(19,18);d(1) { ! leq( addition
% 3.13/3.52 ( one, multiplication( skol1, zero ) ), strong_iteration( multiplication
% 3.13/3.52 ( skol1, zero ) ) ), ! addition( addition( strong_iteration(
% 3.13/3.52 multiplication( skol1, zero ) ), one ), multiplication( skol1, zero ) )
% 3.13/3.52 ==> addition( one, multiplication( skol1, zero ) ) }.
% 3.13/3.52 substitution0:
% 3.13/3.52 X := skol1
% 3.13/3.52 end
% 3.13/3.52 substitution1:
% 3.13/3.52 end
% 3.13/3.52
% 3.13/3.52 paramod: (13703) {G3,W24,D5,L2,V0,M2} { ! addition( strong_iteration(
% 3.13/3.52 multiplication( skol1, zero ) ), star( multiplication( skol1, zero ) ) )
% 3.13/3.52 ==> star( multiplication( skol1, zero ) ), ! leq( addition( one,
% 3.13/3.52 multiplication( skol1, zero ) ), strong_iteration( multiplication( skol1
% 3.13/3.52 , zero ) ) ) }.
% 3.13/3.52 parent0[0]: (4078) {G2,W14,D5,L1,V2,M1} P(50,118) { addition( addition( Y,
% 3.13/3.52 one ), multiplication( X, zero ) ) ==> addition( Y, star( multiplication
% 3.13/3.52 ( X, zero ) ) ) }.
% 3.13/3.52 parent1[0; 2]: (13701) {G2,W25,D6,L2,V0,M2} { ! addition( addition(
% 3.13/3.52 strong_iteration( multiplication( skol1, zero ) ), one ), multiplication
% 3.13/3.52 ( skol1, zero ) ) ==> star( multiplication( skol1, zero ) ), ! leq(
% 3.13/3.52 addition( one, multiplication( skol1, zero ) ), strong_iteration(
% 3.13/3.52 multiplication( skol1, zero ) ) ) }.
% 3.13/3.52 substitution0:
% 3.13/3.52 X := skol1
% 3.13/3.52 Y := strong_iteration( multiplication( skol1, zero ) )
% 3.13/3.52 end
% 3.13/3.52 substitution1:
% 3.13/3.52 end
% 3.13/3.52
% 3.13/3.52 paramod: (13705) {G4,W24,D5,L2,V0,M2} { ! leq( addition( one,
% 3.13/3.52 multiplication( skol1, zero ) ), star( multiplication( skol1, zero ) ) )
% 3.13/3.52 , ! addition( strong_iteration( multiplication( skol1, zero ) ), star(
% 3.13/3.52 multiplication( skol1, zero ) ) ) ==> star( multiplication( skol1, zero )
% 3.13/3.52 ) }.
% 3.13/3.52 parent0[0]: (4165) {G3,W9,D4,L1,V1,M1} P(50,120);d(800) { strong_iteration
% 3.13/3.52 ( multiplication( X, zero ) ) ==> star( multiplication( X, zero ) ) }.
% 3.13/3.52 parent1[1; 7]: (13703) {G3,W24,D5,L2,V0,M2} { ! addition( strong_iteration
% 3.13/3.52 ( multiplication( skol1, zero ) ), star( multiplication( skol1, zero ) )
% 3.13/3.52 ) ==> star( multiplication( skol1, zero ) ), ! leq( addition( one,
% 3.13/3.52 multiplication( skol1, zero ) ), strong_iteration( multiplication( skol1
% 3.13/3.52 , zero ) ) ) }.
% 3.13/3.52 substitution0:
% 3.13/3.52 X := skol1
% 3.13/3.52 end
% 3.13/3.52 substitution1:
% 3.13/3.52 end
% 3.13/3.52
% 3.13/3.52 paramod: (13707) {G5,W28,D4,L3,V0,M3} { ! strong_iteration( multiplication
% 3.13/3.52 ( skol1, zero ) ) ==> star( multiplication( skol1, zero ) ), ! leq( star
% 3.13/3.52 ( multiplication( skol1, zero ) ), star( multiplication( skol1, zero ) )
% 3.13/3.52 ), ! leq( addition( one, multiplication( skol1, zero ) ), star(
% 3.13/3.52 multiplication( skol1, zero ) ) ) }.
% 3.13/3.52 parent0[1]: (1206) {G4,W11,D4,L2,V2,M2} R(1192,36) { ! leq( X, star( Y ) )
% 3.13/3.52 , addition( strong_iteration( Y ), X ) ==> strong_iteration( Y ) }.
% 3.13/3.52 parent1[1; 2]: (13705) {G4,W24,D5,L2,V0,M2} { ! leq( addition( one,
% 3.13/3.52 multiplication( skol1, zero ) ), star( multiplication( skol1, zero ) ) )
% 3.13/3.52 , ! addition( strong_iteration( multiplication( skol1, zero ) ), star(
% 3.13/3.52 multiplication( skol1, zero ) ) ) ==> star( multiplication( skol1, zero )
% 3.13/3.52 ) }.
% 3.13/3.52 substitution0:
% 3.13/3.52 X := star( multiplication( skol1, zero ) )
% 3.13/3.52 Y := multiplication( skol1, zero )
% 3.13/3.52 end
% 3.13/3.52 substitution1:
% 3.13/3.52 end
% 3.13/3.52
% 3.13/3.52 paramod: (13708) {G4,W28,D4,L3,V0,M3} { ! star( multiplication( skol1,
% 3.13/3.52 zero ) ) ==> star( multiplication( skol1, zero ) ), ! leq( star(
% 3.13/3.52 multiplication( skol1, zero ) ), star( multiplication( skol1, zero ) ) )
% 3.13/3.52 , ! leq( addition( one, multiplication( skol1, zero ) ), star(
% 3.13/3.52 multiplication( skol1, zero ) ) ) }.
% 3.13/3.52 parent0[0]: (4165) {G3,W9,D4,L1,V1,M1} P(50,120);d(800) { strong_iteration
% 3.13/3.52 ( multiplication( X, zero ) ) ==> star( multiplication( X, zero ) ) }.
% 3.13/3.52 parent1[0; 2]: (13707) {G5,W28,D4,L3,V0,M3} { ! strong_iteration(
% 3.13/3.52 multiplication( skol1, zero ) ) ==> star( multiplication( skol1, zero ) )
% 3.13/3.52 , ! leq( star( multiplication( skol1, zero ) ), star( multiplication(
% 3.13/3.52 skol1, zero ) ) ), ! leq( addition( one, multiplication( skol1, zero ) )
% 3.13/3.52 , star( multiplication( skol1, zero ) ) ) }.
% 3.13/3.52 substitution0:
% 3.13/3.52 X := skol1
% 3.13/3.52 end
% 3.13/3.52 substitution1:
% 3.13/3.52 end
% 3.13/3.52
% 3.13/3.52 paramod: (13709) {G3,W27,D4,L3,V0,M3} { ! leq( star( multiplication( skol1
% 3.13/3.52 , zero ) ), star( multiplication( skol1, zero ) ) ), ! star(
% 3.13/3.52 multiplication( skol1, zero ) ) ==> star( multiplication( skol1, zero ) )
% 3.13/3.52 , ! leq( star( multiplication( skol1, zero ) ), star( multiplication(
% 3.13/3.52 skol1, zero ) ) ) }.
% 3.13/3.52 parent0[0]: (802) {G2,W10,D4,L1,V1,M1} P(50,10) { addition( one,
% 3.13/3.52 multiplication( X, zero ) ) ==> star( multiplication( X, zero ) ) }.
% 3.13/3.52 parent1[2; 2]: (13708) {G4,W28,D4,L3,V0,M3} { ! star( multiplication(
% 3.13/3.52 skol1, zero ) ) ==> star( multiplication( skol1, zero ) ), ! leq( star(
% 3.13/3.52 multiplication( skol1, zero ) ), star( multiplication( skol1, zero ) ) )
% 3.13/3.52 , ! leq( addition( one, multiplication( skol1, zero ) ), star(
% 3.13/3.52 multiplication( skol1, zero ) ) ) }.
% 3.13/3.52 substitution0:
% 3.13/3.52 X := skol1
% 3.13/3.52 end
% 3.13/3.52 substitution1:
% 3.13/3.52 end
% 3.13/3.52
% 3.13/3.52 factor: (13710) {G3,W18,D4,L2,V0,M2} { ! leq( star( multiplication( skol1
% 3.13/3.52 , zero ) ), star( multiplication( skol1, zero ) ) ), ! star(
% 3.13/3.52 multiplication( skol1, zero ) ) ==> star( multiplication( skol1, zero ) )
% 3.13/3.52 }.
% 3.13/3.52 parent0[0, 2]: (13709) {G3,W27,D4,L3,V0,M3} { ! leq( star( multiplication
% 3.13/3.52 ( skol1, zero ) ), star( multiplication( skol1, zero ) ) ), ! star(
% 3.13/3.52 multiplication( skol1, zero ) ) ==> star( multiplication( skol1, zero ) )
% 3.13/3.52 , ! leq( star( multiplication( skol1, zero ) ), star( multiplication(
% 3.13/3.52 skol1, zero ) ) ) }.
% 3.13/3.52 substitution0:
% 3.13/3.52 end
% 3.13/3.52
% 3.13/3.52 eqrefl: (13711) {G0,W9,D4,L1,V0,M1} { ! leq( star( multiplication( skol1,
% 3.13/3.52 zero ) ), star( multiplication( skol1, zero ) ) ) }.
% 3.13/3.52 parent0[1]: (13710) {G3,W18,D4,L2,V0,M2} { ! leq( star( multiplication(
% 3.13/3.52 skol1, zero ) ), star( multiplication( skol1, zero ) ) ), ! star(
% 3.13/3.52 multiplication( skol1, zero ) ) ==> star( multiplication( skol1, zero ) )
% 3.13/3.52 }.
% 3.13/3.52 substitution0:
% 3.13/3.52 end
% 3.13/3.52
% 3.13/3.52 resolution: (13712) {G1,W0,D0,L0,V0,M0} { }.
% 3.13/3.52 parent0[0]: (13711) {G0,W9,D4,L1,V0,M1} { ! leq( star( multiplication(
% 3.13/3.52 skol1, zero ) ), star( multiplication( skol1, zero ) ) ) }.
% 3.13/3.52 parent1[0]: (22) {G1,W3,D2,L1,V1,M1} R(18,3) { leq( X, X ) }.
% 3.13/3.52 substitution0:
% 3.13/3.52 end
% 3.13/3.52 substitution1:
% 3.13/3.52 X := star( multiplication( skol1, zero ) )
% 3.13/3.52 end
% 3.13/3.52
% 3.13/3.52 subsumption: (13455) {G5,W0,D0,L0,V0,M0} S(298);d(802);d(4078);d(4165);d(
% 3.13/3.52 1206);d(4165);d(802);q;r(22) { }.
% 3.13/3.52 parent0: (13712) {G1,W0,D0,L0,V0,M0} { }.
% 3.13/3.52 substitution0:
% 3.13/3.52 end
% 3.13/3.52 permutation0:
% 3.13/3.52 end
% 3.13/3.52
% 3.13/3.52 Proof check complete!
% 3.13/3.52
% 3.13/3.52 Memory use:
% 3.13/3.52
% 3.13/3.52 space for terms: 167159
% 3.13/3.52 space for clauses: 723870
% 3.13/3.52
% 3.13/3.52
% 3.13/3.52 clauses generated: 189300
% 3.13/3.52 clauses kept: 13456
% 3.13/3.52 clauses selected: 965
% 3.13/3.52 clauses deleted: 407
% 3.13/3.52 clauses inuse deleted: 216
% 3.13/3.52
% 3.13/3.52 subsentry: 647074
% 3.13/3.52 literals s-matched: 402437
% 3.13/3.52 literals matched: 392175
% 3.13/3.52 full subsumption: 111569
% 3.13/3.52
% 3.13/3.52 checksum: -756943594
% 3.13/3.52
% 3.13/3.52
% 3.13/3.52 Bliksem ended
%------------------------------------------------------------------------------