TSTP Solution File: KLE142+2 by Bliksem---1.12
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%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : KLE142+2 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n020.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 01:37:25 EDT 2022
% Result : Theorem 1.33s 1.77s
% Output : Refutation 1.33s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : KLE142+2 : TPTP v8.1.0. Released v4.0.0.
% 0.11/0.13 % Command : bliksem %s
% 0.13/0.34 % Computer : n020.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 09:24:04 EDT 2022
% 0.13/0.35 % CPUTime :
% 1.33/1.77 *** allocated 10000 integers for termspace/termends
% 1.33/1.77 *** allocated 10000 integers for clauses
% 1.33/1.77 *** allocated 10000 integers for justifications
% 1.33/1.77 Bliksem 1.12
% 1.33/1.77
% 1.33/1.77
% 1.33/1.77 Automatic Strategy Selection
% 1.33/1.77
% 1.33/1.77
% 1.33/1.77 Clauses:
% 1.33/1.77
% 1.33/1.77 { addition( X, Y ) = addition( Y, X ) }.
% 1.33/1.77 { addition( Z, addition( Y, X ) ) = addition( addition( Z, Y ), X ) }.
% 1.33/1.77 { addition( X, zero ) = X }.
% 1.33/1.77 { addition( X, X ) = X }.
% 1.33/1.77 { multiplication( X, multiplication( Y, Z ) ) = multiplication(
% 1.33/1.77 multiplication( X, Y ), Z ) }.
% 1.33/1.77 { multiplication( X, one ) = X }.
% 1.33/1.77 { multiplication( one, X ) = X }.
% 1.33/1.77 { multiplication( X, addition( Y, Z ) ) = addition( multiplication( X, Y )
% 1.33/1.77 , multiplication( X, Z ) ) }.
% 1.33/1.77 { multiplication( addition( X, Y ), Z ) = addition( multiplication( X, Z )
% 1.33/1.77 , multiplication( Y, Z ) ) }.
% 1.33/1.77 { multiplication( zero, X ) = zero }.
% 1.33/1.77 { addition( one, multiplication( X, star( X ) ) ) = star( X ) }.
% 1.33/1.77 { addition( one, multiplication( star( X ), X ) ) = star( X ) }.
% 1.33/1.77 { ! leq( addition( multiplication( X, Z ), Y ), Z ), leq( multiplication(
% 1.33/1.77 star( X ), Y ), Z ) }.
% 1.33/1.77 { ! leq( addition( multiplication( Z, X ), Y ), Z ), leq( multiplication( Y
% 1.33/1.77 , star( X ) ), Z ) }.
% 1.33/1.77 { strong_iteration( X ) = addition( multiplication( X, strong_iteration( X
% 1.33/1.77 ) ), one ) }.
% 1.33/1.77 { ! leq( Z, addition( multiplication( X, Z ), Y ) ), leq( Z, multiplication
% 1.33/1.77 ( strong_iteration( X ), Y ) ) }.
% 1.33/1.77 { strong_iteration( X ) = addition( star( X ), multiplication(
% 1.33/1.77 strong_iteration( X ), zero ) ) }.
% 1.33/1.77 { ! leq( X, Y ), addition( X, Y ) = Y }.
% 1.33/1.77 { ! addition( X, Y ) = Y, leq( X, Y ) }.
% 1.33/1.77 { ! leq( strong_iteration( strong_iteration( skol1 ) ), strong_iteration(
% 1.33/1.77 one ) ), ! leq( strong_iteration( one ), strong_iteration(
% 1.33/1.77 strong_iteration( skol1 ) ) ) }.
% 1.33/1.77
% 1.33/1.77 percentage equality = 0.615385, percentage horn = 1.000000
% 1.33/1.77 This is a problem with some equality
% 1.33/1.77
% 1.33/1.77
% 1.33/1.77
% 1.33/1.77 Options Used:
% 1.33/1.77
% 1.33/1.77 useres = 1
% 1.33/1.77 useparamod = 1
% 1.33/1.77 useeqrefl = 1
% 1.33/1.77 useeqfact = 1
% 1.33/1.77 usefactor = 1
% 1.33/1.77 usesimpsplitting = 0
% 1.33/1.77 usesimpdemod = 5
% 1.33/1.77 usesimpres = 3
% 1.33/1.77
% 1.33/1.77 resimpinuse = 1000
% 1.33/1.77 resimpclauses = 20000
% 1.33/1.77 substype = eqrewr
% 1.33/1.77 backwardsubs = 1
% 1.33/1.77 selectoldest = 5
% 1.33/1.77
% 1.33/1.77 litorderings [0] = split
% 1.33/1.77 litorderings [1] = extend the termordering, first sorting on arguments
% 1.33/1.77
% 1.33/1.77 termordering = kbo
% 1.33/1.77
% 1.33/1.77 litapriori = 0
% 1.33/1.77 termapriori = 1
% 1.33/1.77 litaposteriori = 0
% 1.33/1.77 termaposteriori = 0
% 1.33/1.77 demodaposteriori = 0
% 1.33/1.77 ordereqreflfact = 0
% 1.33/1.77
% 1.33/1.77 litselect = negord
% 1.33/1.77
% 1.33/1.77 maxweight = 15
% 1.33/1.77 maxdepth = 30000
% 1.33/1.77 maxlength = 115
% 1.33/1.77 maxnrvars = 195
% 1.33/1.77 excuselevel = 1
% 1.33/1.77 increasemaxweight = 1
% 1.33/1.77
% 1.33/1.77 maxselected = 10000000
% 1.33/1.77 maxnrclauses = 10000000
% 1.33/1.77
% 1.33/1.77 showgenerated = 0
% 1.33/1.77 showkept = 0
% 1.33/1.77 showselected = 0
% 1.33/1.77 showdeleted = 0
% 1.33/1.77 showresimp = 1
% 1.33/1.77 showstatus = 2000
% 1.33/1.77
% 1.33/1.77 prologoutput = 0
% 1.33/1.77 nrgoals = 5000000
% 1.33/1.77 totalproof = 1
% 1.33/1.77
% 1.33/1.77 Symbols occurring in the translation:
% 1.33/1.77
% 1.33/1.77 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 1.33/1.77 . [1, 2] (w:1, o:20, a:1, s:1, b:0),
% 1.33/1.77 ! [4, 1] (w:0, o:13, a:1, s:1, b:0),
% 1.33/1.77 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 1.33/1.77 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 1.33/1.77 addition [37, 2] (w:1, o:44, a:1, s:1, b:0),
% 1.33/1.77 zero [39, 0] (w:1, o:9, a:1, s:1, b:0),
% 1.33/1.77 multiplication [40, 2] (w:1, o:46, a:1, s:1, b:0),
% 1.33/1.77 one [41, 0] (w:1, o:10, a:1, s:1, b:0),
% 1.33/1.77 star [42, 1] (w:1, o:18, a:1, s:1, b:0),
% 1.33/1.77 leq [43, 2] (w:1, o:45, a:1, s:1, b:0),
% 1.33/1.77 strong_iteration [44, 1] (w:1, o:19, a:1, s:1, b:0),
% 1.33/1.77 skol1 [46, 0] (w:1, o:12, a:1, s:1, b:1).
% 1.33/1.77
% 1.33/1.77
% 1.33/1.77 Starting Search:
% 1.33/1.77
% 1.33/1.77 *** allocated 15000 integers for clauses
% 1.33/1.77 *** allocated 22500 integers for clauses
% 1.33/1.77 *** allocated 33750 integers for clauses
% 1.33/1.77 *** allocated 50625 integers for clauses
% 1.33/1.77 *** allocated 15000 integers for termspace/termends
% 1.33/1.77 *** allocated 75937 integers for clauses
% 1.33/1.77 Resimplifying inuse:
% 1.33/1.77 Done
% 1.33/1.77
% 1.33/1.77 *** allocated 22500 integers for termspace/termends
% 1.33/1.77 *** allocated 113905 integers for clauses
% 1.33/1.77 *** allocated 33750 integers for termspace/termends
% 1.33/1.77
% 1.33/1.77 Intermediate Status:
% 1.33/1.77 Generated: 21706
% 1.33/1.77 Kept: 2058
% 1.33/1.77 Inuse: 233
% 1.33/1.77 Deleted: 53
% 1.33/1.77 Deletedinuse: 30
% 1.33/1.77
% 1.33/1.77 Resimplifying inuse:
% 1.33/1.77 Done
% 1.33/1.77
% 1.33/1.77 *** allocated 170857 integers for clauses
% 1.33/1.77 *** allocated 50625 integers for termspace/termends
% 1.33/1.77 Resimplifying inuse:
% 1.33/1.77 Done
% 1.33/1.77
% 1.33/1.77 *** allocated 256285 integers for clauses
% 1.33/1.77 *** allocated 75937 integers for termspace/termends
% 1.33/1.77
% 1.33/1.77 Intermediate Status:
% 1.33/1.77 Generated: 48165
% 1.33/1.77 Kept: 4123
% 1.33/1.77 Inuse: 389
% 1.33/1.77 Deleted: 84
% 1.33/1.77 Deletedinuse: 31
% 1.33/1.77
% 1.33/1.77 Resimplifying inuse:
% 1.33/1.77 Done
% 1.33/1.77
% 1.33/1.77 *** allocated 384427 integers for clauses
% 1.33/1.77 Resimplifying inuse:
% 1.33/1.77 Done
% 1.33/1.77
% 1.33/1.77 *** allocated 113905 integers for termspace/termends
% 1.33/1.77
% 1.33/1.77 Bliksems!, er is een bewijs:
% 1.33/1.77 % SZS status Theorem
% 1.33/1.77 % SZS output start Refutation
% 1.33/1.77
% 1.33/1.77 (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X ) }.
% 1.33/1.77 (1) {G0,W11,D4,L1,V3,M1} I { addition( Z, addition( Y, X ) ) ==> addition(
% 1.33/1.77 addition( Z, Y ), X ) }.
% 1.33/1.77 (2) {G0,W5,D3,L1,V1,M1} I { addition( X, zero ) ==> X }.
% 1.33/1.77 (3) {G0,W5,D3,L1,V1,M1} I { addition( X, X ) ==> X }.
% 1.33/1.77 (5) {G0,W5,D3,L1,V1,M1} I { multiplication( X, one ) ==> X }.
% 1.33/1.77 (6) {G0,W5,D3,L1,V1,M1} I { multiplication( one, X ) ==> X }.
% 1.33/1.77 (7) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Y ),
% 1.33/1.77 multiplication( X, Z ) ) ==> multiplication( X, addition( Y, Z ) ) }.
% 1.33/1.77 (8) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Z ),
% 1.33/1.77 multiplication( Y, Z ) ) ==> multiplication( addition( X, Y ), Z ) }.
% 1.33/1.77 (14) {G0,W9,D5,L1,V1,M1} I { addition( multiplication( X, strong_iteration
% 1.33/1.77 ( X ) ), one ) ==> strong_iteration( X ) }.
% 1.33/1.77 (15) {G0,W13,D4,L2,V3,M2} I { ! leq( Z, addition( multiplication( X, Z ), Y
% 1.33/1.77 ) ), leq( Z, multiplication( strong_iteration( X ), Y ) ) }.
% 1.33/1.77 (17) {G0,W8,D3,L2,V2,M2} I { ! leq( X, Y ), addition( X, Y ) ==> Y }.
% 1.33/1.77 (18) {G0,W8,D3,L2,V2,M2} I { ! addition( X, Y ) ==> Y, leq( X, Y ) }.
% 1.33/1.77 (19) {G0,W12,D4,L2,V0,M2} I { ! leq( strong_iteration( strong_iteration(
% 1.33/1.77 skol1 ) ), strong_iteration( one ) ), ! leq( strong_iteration( one ),
% 1.33/1.77 strong_iteration( strong_iteration( skol1 ) ) ) }.
% 1.33/1.77 (20) {G1,W5,D3,L1,V1,M1} P(0,2) { addition( zero, X ) ==> X }.
% 1.33/1.77 (25) {G1,W14,D4,L2,V3,M2} P(1,18) { ! addition( addition( X, Y ), Z ) ==>
% 1.33/1.77 addition( Y, Z ), leq( X, addition( Y, Z ) ) }.
% 1.33/1.77 (26) {G1,W11,D4,L1,V3,M1} P(1,0) { addition( addition( X, Y ), Z ) =
% 1.33/1.77 addition( addition( Y, Z ), X ) }.
% 1.33/1.77 (29) {G1,W9,D4,L1,V2,M1} P(3,1) { addition( addition( Y, X ), X ) ==>
% 1.33/1.77 addition( Y, X ) }.
% 1.33/1.77 (35) {G1,W12,D4,L2,V3,M2} P(17,1) { addition( addition( Z, X ), Y ) ==>
% 1.33/1.77 addition( Z, Y ), ! leq( X, Y ) }.
% 1.33/1.77 (36) {G1,W8,D3,L2,V2,M2} P(17,0) { addition( Y, X ) ==> Y, ! leq( X, Y )
% 1.33/1.77 }.
% 1.33/1.77 (67) {G1,W16,D4,L2,V3,M2} P(7,18) { ! multiplication( X, addition( Y, Z ) )
% 1.33/1.77 ==> multiplication( X, Z ), leq( multiplication( X, Y ), multiplication
% 1.33/1.77 ( X, Z ) ) }.
% 1.33/1.77 (102) {G1,W11,D4,L1,V2,M1} P(6,8) { addition( multiplication( Y, X ), X ) =
% 1.33/1.77 multiplication( addition( Y, one ), X ) }.
% 1.33/1.77 (324) {G2,W5,D3,L1,V2,M1} P(3,25);q { leq( X, addition( X, Y ) ) }.
% 1.33/1.77 (363) {G3,W5,D3,L1,V2,M1} P(0,324) { leq( X, addition( Y, X ) ) }.
% 1.33/1.77 (366) {G4,W7,D4,L1,V3,M1} P(26,363) { leq( Z, addition( addition( Y, Z ), X
% 1.33/1.77 ) ) }.
% 1.33/1.77 (418) {G2,W7,D4,L1,V1,M1} P(14,29) { addition( strong_iteration( X ), one )
% 1.33/1.77 ==> strong_iteration( X ) }.
% 1.33/1.77 (674) {G5,W8,D3,L2,V3,M2} P(35,366) { leq( Y, addition( X, Z ) ), ! leq( Y
% 1.33/1.77 , Z ) }.
% 1.33/1.77 (1634) {G2,W7,D3,L1,V2,M1} P(20,67);q { leq( multiplication( Y, zero ),
% 1.33/1.77 multiplication( Y, X ) ) }.
% 1.33/1.77 (1729) {G3,W5,D3,L1,V1,M1} P(5,1634) { leq( multiplication( X, zero ), X )
% 1.33/1.77 }.
% 1.33/1.77 (1733) {G4,W7,D4,L1,V1,M1} R(1729,36) { addition( X, multiplication( X,
% 1.33/1.77 zero ) ) ==> X }.
% 1.33/1.77 (1737) {G4,W7,D4,L1,V1,M1} R(1729,17) { addition( multiplication( X, zero )
% 1.33/1.77 , X ) ==> X }.
% 1.33/1.77 (2097) {G6,W8,D3,L2,V2,M2} P(1733,674) { leq( Y, X ), ! leq( Y,
% 1.33/1.77 multiplication( X, zero ) ) }.
% 1.33/1.77 (3562) {G5,W8,D5,L1,V3,M1} P(102,15);r(366) { leq( Y, multiplication(
% 1.33/1.77 strong_iteration( addition( X, one ) ), Z ) ) }.
% 1.33/1.77 (6060) {G7,W6,D4,L1,V2,M1} R(3562,2097) { leq( X, strong_iteration(
% 1.33/1.77 addition( Y, one ) ) ) }.
% 1.33/1.77 (6098) {G8,W4,D3,L1,V1,M1} P(1737,6060) { leq( X, strong_iteration( one ) )
% 1.33/1.77 }.
% 1.33/1.77 (6099) {G8,W5,D4,L1,V2,M1} P(418,6060) { leq( Y, strong_iteration(
% 1.33/1.77 strong_iteration( X ) ) ) }.
% 1.33/1.77 (6115) {G9,W0,D0,L0,V0,M0} R(6098,19);r(6099) { }.
% 1.33/1.77
% 1.33/1.77
% 1.33/1.77 % SZS output end Refutation
% 1.33/1.77 found a proof!
% 1.33/1.77
% 1.33/1.77
% 1.33/1.77 Unprocessed initial clauses:
% 1.33/1.77
% 1.33/1.77 (6117) {G0,W7,D3,L1,V2,M1} { addition( X, Y ) = addition( Y, X ) }.
% 1.33/1.77 (6118) {G0,W11,D4,L1,V3,M1} { addition( Z, addition( Y, X ) ) = addition(
% 1.33/1.77 addition( Z, Y ), X ) }.
% 1.33/1.77 (6119) {G0,W5,D3,L1,V1,M1} { addition( X, zero ) = X }.
% 1.33/1.77 (6120) {G0,W5,D3,L1,V1,M1} { addition( X, X ) = X }.
% 1.33/1.77 (6121) {G0,W11,D4,L1,V3,M1} { multiplication( X, multiplication( Y, Z ) )
% 1.33/1.77 = multiplication( multiplication( X, Y ), Z ) }.
% 1.33/1.77 (6122) {G0,W5,D3,L1,V1,M1} { multiplication( X, one ) = X }.
% 1.33/1.77 (6123) {G0,W5,D3,L1,V1,M1} { multiplication( one, X ) = X }.
% 1.33/1.77 (6124) {G0,W13,D4,L1,V3,M1} { multiplication( X, addition( Y, Z ) ) =
% 1.33/1.77 addition( multiplication( X, Y ), multiplication( X, Z ) ) }.
% 1.33/1.77 (6125) {G0,W13,D4,L1,V3,M1} { multiplication( addition( X, Y ), Z ) =
% 1.33/1.77 addition( multiplication( X, Z ), multiplication( Y, Z ) ) }.
% 1.33/1.77 (6126) {G0,W5,D3,L1,V1,M1} { multiplication( zero, X ) = zero }.
% 1.33/1.77 (6127) {G0,W9,D5,L1,V1,M1} { addition( one, multiplication( X, star( X ) )
% 1.33/1.77 ) = star( X ) }.
% 1.33/1.77 (6128) {G0,W9,D5,L1,V1,M1} { addition( one, multiplication( star( X ), X )
% 1.33/1.77 ) = star( X ) }.
% 1.33/1.77 (6129) {G0,W13,D4,L2,V3,M2} { ! leq( addition( multiplication( X, Z ), Y )
% 1.33/1.77 , Z ), leq( multiplication( star( X ), Y ), Z ) }.
% 1.33/1.77 (6130) {G0,W13,D4,L2,V3,M2} { ! leq( addition( multiplication( Z, X ), Y )
% 1.33/1.77 , Z ), leq( multiplication( Y, star( X ) ), Z ) }.
% 1.33/1.77 (6131) {G0,W9,D5,L1,V1,M1} { strong_iteration( X ) = addition(
% 1.33/1.77 multiplication( X, strong_iteration( X ) ), one ) }.
% 1.33/1.77 (6132) {G0,W13,D4,L2,V3,M2} { ! leq( Z, addition( multiplication( X, Z ),
% 1.33/1.77 Y ) ), leq( Z, multiplication( strong_iteration( X ), Y ) ) }.
% 1.33/1.77 (6133) {G0,W10,D5,L1,V1,M1} { strong_iteration( X ) = addition( star( X )
% 1.33/1.77 , multiplication( strong_iteration( X ), zero ) ) }.
% 1.33/1.77 (6134) {G0,W8,D3,L2,V2,M2} { ! leq( X, Y ), addition( X, Y ) = Y }.
% 1.33/1.77 (6135) {G0,W8,D3,L2,V2,M2} { ! addition( X, Y ) = Y, leq( X, Y ) }.
% 1.33/1.77 (6136) {G0,W12,D4,L2,V0,M2} { ! leq( strong_iteration( strong_iteration(
% 1.33/1.77 skol1 ) ), strong_iteration( one ) ), ! leq( strong_iteration( one ),
% 1.33/1.77 strong_iteration( strong_iteration( skol1 ) ) ) }.
% 1.33/1.77
% 1.33/1.77
% 1.33/1.77 Total Proof:
% 1.33/1.77
% 1.33/1.77 subsumption: (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X
% 1.33/1.77 ) }.
% 1.33/1.77 parent0: (6117) {G0,W7,D3,L1,V2,M1} { addition( X, Y ) = addition( Y, X )
% 1.33/1.77 }.
% 1.33/1.77 substitution0:
% 1.33/1.77 X := X
% 1.33/1.77 Y := Y
% 1.33/1.77 end
% 1.33/1.77 permutation0:
% 1.33/1.77 0 ==> 0
% 1.33/1.77 end
% 1.33/1.77
% 1.33/1.77 subsumption: (1) {G0,W11,D4,L1,V3,M1} I { addition( Z, addition( Y, X ) )
% 1.33/1.77 ==> addition( addition( Z, Y ), X ) }.
% 1.33/1.77 parent0: (6118) {G0,W11,D4,L1,V3,M1} { addition( Z, addition( Y, X ) ) =
% 1.33/1.77 addition( addition( Z, Y ), X ) }.
% 1.33/1.77 substitution0:
% 1.33/1.77 X := X
% 1.33/1.77 Y := Y
% 1.33/1.77 Z := Z
% 1.33/1.77 end
% 1.33/1.77 permutation0:
% 1.33/1.77 0 ==> 0
% 1.33/1.77 end
% 1.33/1.77
% 1.33/1.77 subsumption: (2) {G0,W5,D3,L1,V1,M1} I { addition( X, zero ) ==> X }.
% 1.33/1.77 parent0: (6119) {G0,W5,D3,L1,V1,M1} { addition( X, zero ) = X }.
% 1.33/1.77 substitution0:
% 1.33/1.77 X := X
% 1.33/1.77 end
% 1.33/1.77 permutation0:
% 1.33/1.77 0 ==> 0
% 1.33/1.77 end
% 1.33/1.77
% 1.33/1.77 subsumption: (3) {G0,W5,D3,L1,V1,M1} I { addition( X, X ) ==> X }.
% 1.33/1.77 parent0: (6120) {G0,W5,D3,L1,V1,M1} { addition( X, X ) = X }.
% 1.33/1.77 substitution0:
% 1.33/1.77 X := X
% 1.33/1.77 end
% 1.33/1.77 permutation0:
% 1.33/1.77 0 ==> 0
% 1.33/1.77 end
% 1.33/1.77
% 1.33/1.77 subsumption: (5) {G0,W5,D3,L1,V1,M1} I { multiplication( X, one ) ==> X }.
% 1.33/1.77 parent0: (6122) {G0,W5,D3,L1,V1,M1} { multiplication( X, one ) = X }.
% 1.33/1.77 substitution0:
% 1.33/1.77 X := X
% 1.33/1.77 end
% 1.33/1.77 permutation0:
% 1.33/1.77 0 ==> 0
% 1.33/1.77 end
% 1.33/1.77
% 1.33/1.77 subsumption: (6) {G0,W5,D3,L1,V1,M1} I { multiplication( one, X ) ==> X }.
% 1.33/1.77 parent0: (6123) {G0,W5,D3,L1,V1,M1} { multiplication( one, X ) = X }.
% 1.33/1.77 substitution0:
% 1.33/1.77 X := X
% 1.33/1.77 end
% 1.33/1.77 permutation0:
% 1.33/1.77 0 ==> 0
% 1.33/1.77 end
% 1.33/1.77
% 1.33/1.77 eqswap: (6160) {G0,W13,D4,L1,V3,M1} { addition( multiplication( X, Y ),
% 1.33/1.77 multiplication( X, Z ) ) = multiplication( X, addition( Y, Z ) ) }.
% 1.33/1.77 parent0[0]: (6124) {G0,W13,D4,L1,V3,M1} { multiplication( X, addition( Y,
% 1.33/1.77 Z ) ) = addition( multiplication( X, Y ), multiplication( X, Z ) ) }.
% 1.33/1.77 substitution0:
% 1.33/1.77 X := X
% 1.33/1.77 Y := Y
% 1.33/1.77 Z := Z
% 1.33/1.77 end
% 1.33/1.77
% 1.33/1.77 subsumption: (7) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Y )
% 1.33/1.77 , multiplication( X, Z ) ) ==> multiplication( X, addition( Y, Z ) ) }.
% 1.33/1.77 parent0: (6160) {G0,W13,D4,L1,V3,M1} { addition( multiplication( X, Y ),
% 1.33/1.77 multiplication( X, Z ) ) = multiplication( X, addition( Y, Z ) ) }.
% 1.33/1.77 substitution0:
% 1.33/1.77 X := X
% 1.33/1.77 Y := Y
% 1.33/1.77 Z := Z
% 1.33/1.77 end
% 1.33/1.77 permutation0:
% 1.33/1.77 0 ==> 0
% 1.33/1.77 end
% 1.33/1.77
% 1.33/1.77 eqswap: (6168) {G0,W13,D4,L1,V3,M1} { addition( multiplication( X, Z ),
% 1.33/1.77 multiplication( Y, Z ) ) = multiplication( addition( X, Y ), Z ) }.
% 1.33/1.77 parent0[0]: (6125) {G0,W13,D4,L1,V3,M1} { multiplication( addition( X, Y )
% 1.33/1.77 , Z ) = addition( multiplication( X, Z ), multiplication( Y, Z ) ) }.
% 1.33/1.77 substitution0:
% 1.33/1.77 X := X
% 1.33/1.77 Y := Y
% 1.33/1.77 Z := Z
% 1.33/1.77 end
% 1.33/1.77
% 1.33/1.77 subsumption: (8) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Z )
% 1.33/1.77 , multiplication( Y, Z ) ) ==> multiplication( addition( X, Y ), Z ) }.
% 1.33/1.77 parent0: (6168) {G0,W13,D4,L1,V3,M1} { addition( multiplication( X, Z ),
% 1.33/1.77 multiplication( Y, Z ) ) = multiplication( addition( X, Y ), Z ) }.
% 1.33/1.77 substitution0:
% 1.33/1.77 X := X
% 1.33/1.77 Y := Y
% 1.33/1.77 Z := Z
% 1.33/1.77 end
% 1.33/1.77 permutation0:
% 1.33/1.77 0 ==> 0
% 1.33/1.77 end
% 1.33/1.77
% 1.33/1.77 eqswap: (6180) {G0,W9,D5,L1,V1,M1} { addition( multiplication( X,
% 1.33/1.77 strong_iteration( X ) ), one ) = strong_iteration( X ) }.
% 1.33/1.77 parent0[0]: (6131) {G0,W9,D5,L1,V1,M1} { strong_iteration( X ) = addition
% 1.33/1.77 ( multiplication( X, strong_iteration( X ) ), one ) }.
% 1.33/1.77 substitution0:
% 1.33/1.77 X := X
% 1.33/1.77 end
% 1.33/1.77
% 1.33/1.77 subsumption: (14) {G0,W9,D5,L1,V1,M1} I { addition( multiplication( X,
% 1.33/1.77 strong_iteration( X ) ), one ) ==> strong_iteration( X ) }.
% 1.33/1.77 parent0: (6180) {G0,W9,D5,L1,V1,M1} { addition( multiplication( X,
% 1.33/1.77 strong_iteration( X ) ), one ) = strong_iteration( X ) }.
% 1.33/1.77 substitution0:
% 1.33/1.77 X := X
% 1.33/1.77 end
% 1.33/1.77 permutation0:
% 1.33/1.77 0 ==> 0
% 1.33/1.77 end
% 1.33/1.77
% 1.33/1.77 subsumption: (15) {G0,W13,D4,L2,V3,M2} I { ! leq( Z, addition(
% 1.33/1.77 multiplication( X, Z ), Y ) ), leq( Z, multiplication( strong_iteration(
% 1.33/1.77 X ), Y ) ) }.
% 1.33/1.77 parent0: (6132) {G0,W13,D4,L2,V3,M2} { ! leq( Z, addition( multiplication
% 1.33/1.77 ( X, Z ), Y ) ), leq( Z, multiplication( strong_iteration( X ), Y ) ) }.
% 1.33/1.77 substitution0:
% 1.33/1.77 X := X
% 1.33/1.77 Y := Y
% 1.33/1.77 Z := Z
% 1.33/1.77 end
% 1.33/1.77 permutation0:
% 1.33/1.77 0 ==> 0
% 1.33/1.77 1 ==> 1
% 1.33/1.77 end
% 1.33/1.77
% 1.33/1.77 subsumption: (17) {G0,W8,D3,L2,V2,M2} I { ! leq( X, Y ), addition( X, Y )
% 1.33/1.77 ==> Y }.
% 1.33/1.77 parent0: (6134) {G0,W8,D3,L2,V2,M2} { ! leq( X, Y ), addition( X, Y ) = Y
% 1.33/1.77 }.
% 1.33/1.77 substitution0:
% 1.33/1.77 X := X
% 1.33/1.77 Y := Y
% 1.33/1.77 end
% 1.33/1.77 permutation0:
% 1.33/1.77 0 ==> 0
% 1.33/1.77 1 ==> 1
% 1.33/1.77 end
% 1.33/1.77
% 1.33/1.77 subsumption: (18) {G0,W8,D3,L2,V2,M2} I { ! addition( X, Y ) ==> Y, leq( X
% 1.33/1.77 , Y ) }.
% 1.33/1.77 parent0: (6135) {G0,W8,D3,L2,V2,M2} { ! addition( X, Y ) = Y, leq( X, Y )
% 1.33/1.77 }.
% 1.33/1.77 substitution0:
% 1.33/1.77 X := X
% 1.33/1.77 Y := Y
% 1.33/1.77 end
% 1.33/1.77 permutation0:
% 1.33/1.77 0 ==> 0
% 1.33/1.77 1 ==> 1
% 1.33/1.77 end
% 1.33/1.77
% 1.33/1.77 subsumption: (19) {G0,W12,D4,L2,V0,M2} I { ! leq( strong_iteration(
% 1.33/1.77 strong_iteration( skol1 ) ), strong_iteration( one ) ), ! leq(
% 1.33/1.77 strong_iteration( one ), strong_iteration( strong_iteration( skol1 ) ) )
% 1.33/1.77 }.
% 1.33/1.77 parent0: (6136) {G0,W12,D4,L2,V0,M2} { ! leq( strong_iteration(
% 1.33/1.77 strong_iteration( skol1 ) ), strong_iteration( one ) ), ! leq(
% 1.33/1.77 strong_iteration( one ), strong_iteration( strong_iteration( skol1 ) ) )
% 1.33/1.77 }.
% 1.33/1.77 substitution0:
% 1.33/1.77 end
% 1.33/1.77 permutation0:
% 1.33/1.77 0 ==> 0
% 1.33/1.77 1 ==> 1
% 1.33/1.77 end
% 1.33/1.77
% 1.33/1.77 eqswap: (6237) {G0,W5,D3,L1,V1,M1} { X ==> addition( X, zero ) }.
% 1.33/1.77 parent0[0]: (2) {G0,W5,D3,L1,V1,M1} I { addition( X, zero ) ==> X }.
% 1.33/1.77 substitution0:
% 1.33/1.77 X := X
% 1.33/1.77 end
% 1.33/1.77
% 1.33/1.77 paramod: (6238) {G1,W5,D3,L1,V1,M1} { X ==> addition( zero, X ) }.
% 1.33/1.77 parent0[0]: (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X )
% 1.33/1.77 }.
% 1.33/1.77 parent1[0; 2]: (6237) {G0,W5,D3,L1,V1,M1} { X ==> addition( X, zero ) }.
% 1.33/1.77 substitution0:
% 1.33/1.77 X := X
% 1.33/1.77 Y := zero
% 1.33/1.77 end
% 1.33/1.77 substitution1:
% 1.33/1.77 X := X
% 1.33/1.77 end
% 1.33/1.77
% 1.33/1.77 eqswap: (6241) {G1,W5,D3,L1,V1,M1} { addition( zero, X ) ==> X }.
% 1.33/1.77 parent0[0]: (6238) {G1,W5,D3,L1,V1,M1} { X ==> addition( zero, X ) }.
% 1.33/1.77 substitution0:
% 1.33/1.77 X := X
% 1.33/1.77 end
% 1.33/1.77
% 1.33/1.77 subsumption: (20) {G1,W5,D3,L1,V1,M1} P(0,2) { addition( zero, X ) ==> X
% 1.33/1.77 }.
% 1.33/1.77 parent0: (6241) {G1,W5,D3,L1,V1,M1} { addition( zero, X ) ==> X }.
% 1.33/1.77 substitution0:
% 1.33/1.77 X := X
% 1.33/1.77 end
% 1.33/1.77 permutation0:
% 1.33/1.77 0 ==> 0
% 1.33/1.77 end
% 1.33/1.77
% 1.33/1.77 eqswap: (6243) {G0,W8,D3,L2,V2,M2} { ! Y ==> addition( X, Y ), leq( X, Y )
% 1.33/1.77 }.
% 1.33/1.77 parent0[0]: (18) {G0,W8,D3,L2,V2,M2} I { ! addition( X, Y ) ==> Y, leq( X,
% 1.33/1.77 Y ) }.
% 1.33/1.77 substitution0:
% 1.33/1.77 X := X
% 1.33/1.77 Y := Y
% 1.33/1.77 end
% 1.33/1.77
% 1.33/1.77 paramod: (6244) {G1,W14,D4,L2,V3,M2} { ! addition( X, Y ) ==> addition(
% 1.33/1.77 addition( Z, X ), Y ), leq( Z, addition( X, Y ) ) }.
% 1.33/1.77 parent0[0]: (1) {G0,W11,D4,L1,V3,M1} I { addition( Z, addition( Y, X ) )
% 1.33/1.77 ==> addition( addition( Z, Y ), X ) }.
% 1.33/1.77 parent1[0; 5]: (6243) {G0,W8,D3,L2,V2,M2} { ! Y ==> addition( X, Y ), leq
% 1.33/1.77 ( X, Y ) }.
% 1.33/1.77 substitution0:
% 1.33/1.77 X := Y
% 1.33/1.77 Y := X
% 1.33/1.77 Z := Z
% 1.33/1.77 end
% 1.33/1.77 substitution1:
% 1.33/1.77 X := Z
% 1.33/1.77 Y := addition( X, Y )
% 1.33/1.77 end
% 1.33/1.77
% 1.33/1.77 eqswap: (6245) {G1,W14,D4,L2,V3,M2} { ! addition( addition( Z, X ), Y )
% 1.33/1.77 ==> addition( X, Y ), leq( Z, addition( X, Y ) ) }.
% 1.33/1.77 parent0[0]: (6244) {G1,W14,D4,L2,V3,M2} { ! addition( X, Y ) ==> addition
% 1.33/1.77 ( addition( Z, X ), Y ), leq( Z, addition( X, Y ) ) }.
% 1.33/1.77 substitution0:
% 1.33/1.77 X := X
% 1.33/1.77 Y := Y
% 1.33/1.77 Z := Z
% 1.33/1.77 end
% 1.33/1.77
% 1.33/1.77 subsumption: (25) {G1,W14,D4,L2,V3,M2} P(1,18) { ! addition( addition( X, Y
% 1.33/1.77 ), Z ) ==> addition( Y, Z ), leq( X, addition( Y, Z ) ) }.
% 1.33/1.77 parent0: (6245) {G1,W14,D4,L2,V3,M2} { ! addition( addition( Z, X ), Y )
% 1.33/1.77 ==> addition( X, Y ), leq( Z, addition( X, Y ) ) }.
% 1.33/1.77 substitution0:
% 1.33/1.77 X := Y
% 1.33/1.77 Y := Z
% 1.33/1.77 Z := X
% 1.33/1.77 end
% 1.33/1.77 permutation0:
% 1.33/1.77 0 ==> 0
% 1.33/1.77 1 ==> 1
% 1.33/1.77 end
% 1.33/1.77
% 1.33/1.77 eqswap: (6246) {G0,W11,D4,L1,V3,M1} { addition( addition( X, Y ), Z ) ==>
% 1.33/1.77 addition( X, addition( Y, Z ) ) }.
% 1.33/1.77 parent0[0]: (1) {G0,W11,D4,L1,V3,M1} I { addition( Z, addition( Y, X ) )
% 1.33/1.77 ==> addition( addition( Z, Y ), X ) }.
% 1.33/1.77 substitution0:
% 1.33/1.77 X := Z
% 1.33/1.77 Y := Y
% 1.33/1.77 Z := X
% 1.33/1.77 end
% 1.33/1.77
% 1.33/1.77 paramod: (6249) {G1,W11,D4,L1,V3,M1} { addition( addition( X, Y ), Z ) ==>
% 1.33/1.77 addition( addition( Y, Z ), X ) }.
% 1.33/1.77 parent0[0]: (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X )
% 1.33/1.77 }.
% 1.33/1.77 parent1[0; 6]: (6246) {G0,W11,D4,L1,V3,M1} { addition( addition( X, Y ), Z
% 1.33/1.77 ) ==> addition( X, addition( Y, Z ) ) }.
% 1.33/1.77 substitution0:
% 1.33/1.77 X := X
% 1.33/1.77 Y := addition( Y, Z )
% 1.33/1.77 end
% 1.33/1.77 substitution1:
% 1.33/1.77 X := X
% 1.33/1.77 Y := Y
% 1.33/1.77 Z := Z
% 1.33/1.77 end
% 1.33/1.77
% 1.33/1.77 subsumption: (26) {G1,W11,D4,L1,V3,M1} P(1,0) { addition( addition( X, Y )
% 1.33/1.77 , Z ) = addition( addition( Y, Z ), X ) }.
% 1.33/1.77 parent0: (6249) {G1,W11,D4,L1,V3,M1} { addition( addition( X, Y ), Z ) ==>
% 1.33/1.77 addition( addition( Y, Z ), X ) }.
% 1.33/1.77 substitution0:
% 1.33/1.77 X := X
% 1.33/1.77 Y := Y
% 1.33/1.77 Z := Z
% 1.33/1.77 end
% 1.33/1.77 permutation0:
% 1.33/1.77 0 ==> 0
% 1.33/1.77 end
% 1.33/1.77
% 1.33/1.77 eqswap: (6264) {G0,W11,D4,L1,V3,M1} { addition( addition( X, Y ), Z ) ==>
% 1.33/1.77 addition( X, addition( Y, Z ) ) }.
% 1.33/1.77 parent0[0]: (1) {G0,W11,D4,L1,V3,M1} I { addition( Z, addition( Y, X ) )
% 1.33/1.77 ==> addition( addition( Z, Y ), X ) }.
% 1.33/1.77 substitution0:
% 1.33/1.77 X := Z
% 1.33/1.77 Y := Y
% 1.33/1.77 Z := X
% 1.33/1.77 end
% 1.33/1.77
% 1.33/1.77 paramod: (6270) {G1,W9,D4,L1,V2,M1} { addition( addition( X, Y ), Y ) ==>
% 1.33/1.77 addition( X, Y ) }.
% 1.33/1.77 parent0[0]: (3) {G0,W5,D3,L1,V1,M1} I { addition( X, X ) ==> X }.
% 1.33/1.77 parent1[0; 8]: (6264) {G0,W11,D4,L1,V3,M1} { addition( addition( X, Y ), Z
% 1.33/1.77 ) ==> addition( X, addition( Y, Z ) ) }.
% 1.33/1.77 substitution0:
% 1.33/1.77 X := Y
% 1.33/1.77 end
% 1.33/1.77 substitution1:
% 1.33/1.77 X := X
% 1.33/1.77 Y := Y
% 1.33/1.77 Z := Y
% 1.33/1.77 end
% 1.33/1.77
% 1.33/1.77 subsumption: (29) {G1,W9,D4,L1,V2,M1} P(3,1) { addition( addition( Y, X ),
% 1.33/1.77 X ) ==> addition( Y, X ) }.
% 1.33/1.77 parent0: (6270) {G1,W9,D4,L1,V2,M1} { addition( addition( X, Y ), Y ) ==>
% 1.33/1.77 addition( X, Y ) }.
% 1.33/1.77 substitution0:
% 1.33/1.77 X := Y
% 1.33/1.77 Y := X
% 1.33/1.77 end
% 1.33/1.77 permutation0:
% 1.33/1.77 0 ==> 0
% 1.33/1.77 end
% 1.33/1.77
% 1.33/1.77 eqswap: (6276) {G0,W11,D4,L1,V3,M1} { addition( addition( X, Y ), Z ) ==>
% 1.33/1.77 addition( X, addition( Y, Z ) ) }.
% 1.33/1.77 parent0[0]: (1) {G0,W11,D4,L1,V3,M1} I { addition( Z, addition( Y, X ) )
% 1.33/1.77 ==> addition( addition( Z, Y ), X ) }.
% 1.33/1.77 substitution0:
% 1.33/1.77 X := Z
% 1.33/1.77 Y := Y
% 1.33/1.77 Z := X
% 1.33/1.77 end
% 1.33/1.77
% 1.33/1.77 paramod: (6282) {G1,W12,D4,L2,V3,M2} { addition( addition( X, Y ), Z ) ==>
% 1.33/1.77 addition( X, Z ), ! leq( Y, Z ) }.
% 1.33/1.77 parent0[1]: (17) {G0,W8,D3,L2,V2,M2} I { ! leq( X, Y ), addition( X, Y )
% 1.33/1.77 ==> Y }.
% 1.33/1.77 parent1[0; 8]: (6276) {G0,W11,D4,L1,V3,M1} { addition( addition( X, Y ), Z
% 1.33/1.77 ) ==> addition( X, addition( Y, Z ) ) }.
% 1.33/1.77 substitution0:
% 1.33/1.77 X := Y
% 1.33/1.77 Y := Z
% 1.33/1.77 end
% 1.33/1.77 substitution1:
% 1.33/1.77 X := X
% 1.33/1.77 Y := Y
% 1.33/1.77 Z := Z
% 1.33/1.77 end
% 1.33/1.77
% 1.33/1.77 subsumption: (35) {G1,W12,D4,L2,V3,M2} P(17,1) { addition( addition( Z, X )
% 1.33/1.77 , Y ) ==> addition( Z, Y ), ! leq( X, Y ) }.
% 1.33/1.77 parent0: (6282) {G1,W12,D4,L2,V3,M2} { addition( addition( X, Y ), Z ) ==>
% 1.33/1.77 addition( X, Z ), ! leq( Y, Z ) }.
% 1.33/1.77 substitution0:
% 1.33/1.77 X := Z
% 1.33/1.77 Y := X
% 1.33/1.77 Z := Y
% 1.33/1.77 end
% 1.33/1.77 permutation0:
% 1.33/1.77 0 ==> 0
% 1.33/1.77 1 ==> 1
% 1.33/1.77 end
% 1.33/1.77
% 1.33/1.77 eqswap: (6329) {G0,W8,D3,L2,V2,M2} { Y ==> addition( X, Y ), ! leq( X, Y )
% 1.33/1.77 }.
% 1.33/1.77 parent0[1]: (17) {G0,W8,D3,L2,V2,M2} I { ! leq( X, Y ), addition( X, Y )
% 1.33/1.77 ==> Y }.
% 1.33/1.77 substitution0:
% 1.33/1.77 X := X
% 1.33/1.77 Y := Y
% 1.33/1.77 end
% 1.33/1.77
% 1.33/1.77 paramod: (6330) {G1,W8,D3,L2,V2,M2} { X ==> addition( X, Y ), ! leq( Y, X
% 1.33/1.77 ) }.
% 1.33/1.77 parent0[0]: (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X )
% 1.33/1.77 }.
% 1.33/1.77 parent1[0; 2]: (6329) {G0,W8,D3,L2,V2,M2} { Y ==> addition( X, Y ), ! leq
% 1.33/1.77 ( X, Y ) }.
% 1.33/1.77 substitution0:
% 1.33/1.77 X := Y
% 1.33/1.77 Y := X
% 1.33/1.77 end
% 1.33/1.77 substitution1:
% 1.33/1.77 X := Y
% 1.33/1.77 Y := X
% 1.33/1.77 end
% 1.33/1.77
% 1.33/1.77 eqswap: (6333) {G1,W8,D3,L2,V2,M2} { addition( X, Y ) ==> X, ! leq( Y, X )
% 1.33/1.77 }.
% 1.33/1.77 parent0[0]: (6330) {G1,W8,D3,L2,V2,M2} { X ==> addition( X, Y ), ! leq( Y
% 1.33/1.77 , X ) }.
% 1.33/1.77 substitution0:
% 1.33/1.77 X := X
% 1.33/1.77 Y := Y
% 1.33/1.77 end
% 1.33/1.77
% 1.33/1.77 subsumption: (36) {G1,W8,D3,L2,V2,M2} P(17,0) { addition( Y, X ) ==> Y, !
% 1.33/1.77 leq( X, Y ) }.
% 1.33/1.77 parent0: (6333) {G1,W8,D3,L2,V2,M2} { addition( X, Y ) ==> X, ! leq( Y, X
% 1.33/1.77 ) }.
% 1.33/1.77 substitution0:
% 1.33/1.77 X := Y
% 1.33/1.77 Y := X
% 1.33/1.77 end
% 1.33/1.77 permutation0:
% 1.33/1.77 0 ==> 0
% 1.33/1.77 1 ==> 1
% 1.33/1.77 end
% 1.33/1.77
% 1.33/1.77 eqswap: (6335) {G0,W8,D3,L2,V2,M2} { ! Y ==> addition( X, Y ), leq( X, Y )
% 1.33/1.77 }.
% 1.33/1.77 parent0[0]: (18) {G0,W8,D3,L2,V2,M2} I { ! addition( X, Y ) ==> Y, leq( X,
% 1.33/1.77 Y ) }.
% 1.33/1.77 substitution0:
% 1.33/1.77 X := X
% 1.33/1.77 Y := Y
% 1.33/1.77 end
% 1.33/1.77
% 1.33/1.77 paramod: (6336) {G1,W16,D4,L2,V3,M2} { ! multiplication( X, Y ) ==>
% 1.33/1.77 multiplication( X, addition( Z, Y ) ), leq( multiplication( X, Z ),
% 1.33/1.77 multiplication( X, Y ) ) }.
% 1.33/1.77 parent0[0]: (7) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Y ),
% 1.33/1.77 multiplication( X, Z ) ) ==> multiplication( X, addition( Y, Z ) ) }.
% 1.33/1.77 parent1[0; 5]: (6335) {G0,W8,D3,L2,V2,M2} { ! Y ==> addition( X, Y ), leq
% 1.33/1.77 ( X, Y ) }.
% 1.33/1.77 substitution0:
% 1.33/1.77 X := X
% 1.33/1.77 Y := Z
% 1.33/1.77 Z := Y
% 1.33/1.77 end
% 1.33/1.77 substitution1:
% 1.33/1.77 X := multiplication( X, Z )
% 1.33/1.77 Y := multiplication( X, Y )
% 1.33/1.77 end
% 1.33/1.77
% 1.33/1.77 eqswap: (6337) {G1,W16,D4,L2,V3,M2} { ! multiplication( X, addition( Z, Y
% 1.33/1.77 ) ) ==> multiplication( X, Y ), leq( multiplication( X, Z ),
% 1.33/1.77 multiplication( X, Y ) ) }.
% 1.33/1.77 parent0[0]: (6336) {G1,W16,D4,L2,V3,M2} { ! multiplication( X, Y ) ==>
% 1.33/1.77 multiplication( X, addition( Z, Y ) ), leq( multiplication( X, Z ),
% 1.33/1.77 multiplication( X, Y ) ) }.
% 1.33/1.77 substitution0:
% 1.33/1.77 X := X
% 1.33/1.77 Y := Y
% 1.33/1.77 Z := Z
% 1.33/1.77 end
% 1.33/1.77
% 1.33/1.77 subsumption: (67) {G1,W16,D4,L2,V3,M2} P(7,18) { ! multiplication( X,
% 1.33/1.77 addition( Y, Z ) ) ==> multiplication( X, Z ), leq( multiplication( X, Y
% 1.33/1.77 ), multiplication( X, Z ) ) }.
% 1.33/1.77 parent0: (6337) {G1,W16,D4,L2,V3,M2} { ! multiplication( X, addition( Z, Y
% 1.33/1.77 ) ) ==> multiplication( X, Y ), leq( multiplication( X, Z ),
% 1.33/1.77 multiplication( X, Y ) ) }.
% 1.33/1.77 substitution0:
% 1.33/1.77 X := X
% 1.33/1.77 Y := Z
% 1.33/1.77 Z := Y
% 1.33/1.77 end
% 1.33/1.77 permutation0:
% 1.33/1.77 0 ==> 0
% 1.33/1.77 1 ==> 1
% 1.33/1.77 end
% 1.33/1.77
% 1.33/1.77 eqswap: (6339) {G0,W13,D4,L1,V3,M1} { multiplication( addition( X, Z ), Y
% 1.33/1.77 ) ==> addition( multiplication( X, Y ), multiplication( Z, Y ) ) }.
% 1.33/1.77 parent0[0]: (8) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Z ),
% 1.33/1.77 multiplication( Y, Z ) ) ==> multiplication( addition( X, Y ), Z ) }.
% 1.33/1.77 substitution0:
% 1.33/1.77 X := X
% 1.33/1.77 Y := Z
% 1.33/1.77 Z := Y
% 1.33/1.77 end
% 1.33/1.77
% 1.33/1.77 paramod: (6341) {G1,W11,D4,L1,V2,M1} { multiplication( addition( X, one )
% 1.33/1.77 , Y ) ==> addition( multiplication( X, Y ), Y ) }.
% 1.33/1.77 parent0[0]: (6) {G0,W5,D3,L1,V1,M1} I { multiplication( one, X ) ==> X }.
% 1.33/1.77 parent1[0; 10]: (6339) {G0,W13,D4,L1,V3,M1} { multiplication( addition( X
% 1.33/1.77 , Z ), Y ) ==> addition( multiplication( X, Y ), multiplication( Z, Y ) )
% 1.33/1.77 }.
% 1.33/1.77 substitution0:
% 1.33/1.77 X := Y
% 1.33/1.77 end
% 1.33/1.77 substitution1:
% 1.33/1.77 X := X
% 1.33/1.77 Y := Y
% 1.33/1.77 Z := one
% 1.33/1.77 end
% 1.33/1.77
% 1.33/1.77 eqswap: (6343) {G1,W11,D4,L1,V2,M1} { addition( multiplication( X, Y ), Y
% 1.33/1.77 ) ==> multiplication( addition( X, one ), Y ) }.
% 1.33/1.77 parent0[0]: (6341) {G1,W11,D4,L1,V2,M1} { multiplication( addition( X, one
% 1.33/1.77 ), Y ) ==> addition( multiplication( X, Y ), Y ) }.
% 1.33/1.77 substitution0:
% 1.33/1.77 X := X
% 1.33/1.77 Y := Y
% 1.33/1.77 end
% 1.33/1.77
% 1.33/1.77 subsumption: (102) {G1,W11,D4,L1,V2,M1} P(6,8) { addition( multiplication(
% 1.33/1.77 Y, X ), X ) = multiplication( addition( Y, one ), X ) }.
% 1.33/1.77 parent0: (6343) {G1,W11,D4,L1,V2,M1} { addition( multiplication( X, Y ), Y
% 1.33/1.77 ) ==> multiplication( addition( X, one ), Y ) }.
% 1.33/1.77 substitution0:
% 1.33/1.77 X := Y
% 1.33/1.77 Y := X
% 1.33/1.77 end
% 1.33/1.77 permutation0:
% 1.33/1.77 0 ==> 0
% 1.33/1.77 end
% 1.33/1.77
% 1.33/1.77 eqswap: (6345) {G1,W14,D4,L2,V3,M2} { ! addition( Y, Z ) ==> addition(
% 1.33/1.77 addition( X, Y ), Z ), leq( X, addition( Y, Z ) ) }.
% 1.33/1.77 parent0[0]: (25) {G1,W14,D4,L2,V3,M2} P(1,18) { ! addition( addition( X, Y
% 1.33/1.77 ), Z ) ==> addition( Y, Z ), leq( X, addition( Y, Z ) ) }.
% 1.33/1.77 substitution0:
% 1.33/1.77 X := X
% 1.33/1.77 Y := Y
% 1.33/1.77 Z := Z
% 1.33/1.77 end
% 1.33/1.77
% 1.33/1.77 paramod: (6348) {G1,W12,D3,L2,V2,M2} { ! addition( X, Y ) ==> addition( X
% 1.33/1.77 , Y ), leq( X, addition( X, Y ) ) }.
% 1.33/1.77 parent0[0]: (3) {G0,W5,D3,L1,V1,M1} I { addition( X, X ) ==> X }.
% 1.33/1.77 parent1[0; 6]: (6345) {G1,W14,D4,L2,V3,M2} { ! addition( Y, Z ) ==>
% 1.33/1.77 addition( addition( X, Y ), Z ), leq( X, addition( Y, Z ) ) }.
% 1.33/1.77 substitution0:
% 1.33/1.77 X := X
% 1.33/1.77 end
% 1.33/1.77 substitution1:
% 1.33/1.77 X := X
% 1.33/1.77 Y := X
% 1.33/1.77 Z := Y
% 1.33/1.77 end
% 1.33/1.77
% 1.33/1.77 eqrefl: (6351) {G0,W5,D3,L1,V2,M1} { leq( X, addition( X, Y ) ) }.
% 1.33/1.77 parent0[0]: (6348) {G1,W12,D3,L2,V2,M2} { ! addition( X, Y ) ==> addition
% 1.33/1.77 ( X, Y ), leq( X, addition( X, Y ) ) }.
% 1.33/1.77 substitution0:
% 1.33/1.77 X := X
% 1.33/1.77 Y := Y
% 1.33/1.77 end
% 1.33/1.77
% 1.33/1.77 subsumption: (324) {G2,W5,D3,L1,V2,M1} P(3,25);q { leq( X, addition( X, Y )
% 1.33/1.77 ) }.
% 1.33/1.77 parent0: (6351) {G0,W5,D3,L1,V2,M1} { leq( X, addition( X, Y ) ) }.
% 1.33/1.77 substitution0:
% 1.33/1.77 X := X
% 1.33/1.77 Y := Y
% 1.33/1.77 end
% 1.33/1.77 permutation0:
% 1.33/1.77 0 ==> 0
% 1.33/1.77 end
% 1.33/1.77
% 1.33/1.77 paramod: (6352) {G1,W5,D3,L1,V2,M1} { leq( X, addition( Y, X ) ) }.
% 1.33/1.77 parent0[0]: (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X )
% 1.33/1.77 }.
% 1.33/1.77 parent1[0; 2]: (324) {G2,W5,D3,L1,V2,M1} P(3,25);q { leq( X, addition( X, Y
% 1.33/1.77 ) ) }.
% 1.33/1.77 substitution0:
% 1.33/1.77 X := X
% 1.33/1.77 Y := Y
% 1.33/1.77 end
% 1.33/1.77 substitution1:
% 1.33/1.77 X := X
% 1.33/1.77 Y := Y
% 1.33/1.77 end
% 1.33/1.77
% 1.33/1.77 subsumption: (363) {G3,W5,D3,L1,V2,M1} P(0,324) { leq( X, addition( Y, X )
% 1.33/1.77 ) }.
% 1.33/1.77 parent0: (6352) {G1,W5,D3,L1,V2,M1} { leq( X, addition( Y, X ) ) }.
% 1.33/1.77 substitution0:
% 1.33/1.77 X := X
% 1.33/1.77 Y := Y
% 1.33/1.77 end
% 1.33/1.77 permutation0:
% 1.33/1.77 0 ==> 0
% 1.33/1.77 end
% 1.33/1.77
% 1.33/1.77 eqswap: (6354) {G1,W11,D4,L1,V3,M1} { addition( addition( Y, Z ), X ) =
% 1.33/1.77 addition( addition( X, Y ), Z ) }.
% 1.33/1.77 parent0[0]: (26) {G1,W11,D4,L1,V3,M1} P(1,0) { addition( addition( X, Y ),
% 1.33/1.77 Z ) = addition( addition( Y, Z ), X ) }.
% 1.33/1.77 substitution0:
% 1.33/1.77 X := X
% 1.33/1.77 Y := Y
% 1.33/1.77 Z := Z
% 1.33/1.77 end
% 1.33/1.77
% 1.33/1.77 paramod: (6355) {G2,W7,D4,L1,V3,M1} { leq( X, addition( addition( X, Y ),
% 1.33/1.77 Z ) ) }.
% 1.33/1.77 parent0[0]: (6354) {G1,W11,D4,L1,V3,M1} { addition( addition( Y, Z ), X )
% 1.33/1.77 = addition( addition( X, Y ), Z ) }.
% 1.33/1.77 parent1[0; 2]: (363) {G3,W5,D3,L1,V2,M1} P(0,324) { leq( X, addition( Y, X
% 1.33/1.77 ) ) }.
% 1.33/1.77 substitution0:
% 1.33/1.77 X := X
% 1.33/1.77 Y := Y
% 1.33/1.77 Z := Z
% 1.33/1.77 end
% 1.33/1.77 substitution1:
% 1.33/1.77 X := X
% 1.33/1.77 Y := addition( Y, Z )
% 1.33/1.77 end
% 1.33/1.77
% 1.33/1.77 paramod: (6356) {G2,W7,D4,L1,V3,M1} { leq( X, addition( addition( Z, X ),
% 1.33/1.77 Y ) ) }.
% 1.33/1.77 parent0[0]: (6354) {G1,W11,D4,L1,V3,M1} { addition( addition( Y, Z ), X )
% 1.33/1.77 = addition( addition( X, Y ), Z ) }.
% 1.33/1.77 parent1[0; 2]: (6355) {G2,W7,D4,L1,V3,M1} { leq( X, addition( addition( X
% 1.33/1.77 , Y ), Z ) ) }.
% 1.33/1.77 substitution0:
% 1.33/1.77 X := Z
% 1.33/1.77 Y := X
% 1.33/1.77 Z := Y
% 1.33/1.77 end
% 1.33/1.77 substitution1:
% 1.33/1.77 X := X
% 1.33/1.77 Y := Y
% 1.33/1.77 Z := Z
% 1.33/1.77 end
% 1.33/1.77
% 1.33/1.77 subsumption: (366) {G4,W7,D4,L1,V3,M1} P(26,363) { leq( Z, addition(
% 1.33/1.77 addition( Y, Z ), X ) ) }.
% 1.33/1.77 parent0: (6356) {G2,W7,D4,L1,V3,M1} { leq( X, addition( addition( Z, X ),
% 1.33/1.77 Y ) ) }.
% 1.33/1.77 substitution0:
% 1.33/1.77 X := Z
% 1.33/1.77 Y := X
% 1.33/1.77 Z := Y
% 1.33/1.77 end
% 1.33/1.77 permutation0:
% 1.33/1.77 0 ==> 0
% 1.33/1.77 end
% 1.33/1.77
% 1.33/1.77 eqswap: (6359) {G1,W9,D4,L1,V2,M1} { addition( X, Y ) ==> addition(
% 1.33/1.77 addition( X, Y ), Y ) }.
% 1.33/1.77 parent0[0]: (29) {G1,W9,D4,L1,V2,M1} P(3,1) { addition( addition( Y, X ), X
% 1.33/1.77 ) ==> addition( Y, X ) }.
% 1.33/1.77 substitution0:
% 1.33/1.77 X := Y
% 1.33/1.77 Y := X
% 1.33/1.77 end
% 1.33/1.77
% 1.33/1.77 paramod: (6361) {G1,W11,D5,L1,V1,M1} { addition( multiplication( X,
% 1.33/1.77 strong_iteration( X ) ), one ) ==> addition( strong_iteration( X ), one )
% 1.33/1.77 }.
% 1.33/1.77 parent0[0]: (14) {G0,W9,D5,L1,V1,M1} I { addition( multiplication( X,
% 1.33/1.77 strong_iteration( X ) ), one ) ==> strong_iteration( X ) }.
% 1.33/1.77 parent1[0; 8]: (6359) {G1,W9,D4,L1,V2,M1} { addition( X, Y ) ==> addition
% 1.33/1.77 ( addition( X, Y ), Y ) }.
% 1.33/1.77 substitution0:
% 1.33/1.77 X := X
% 1.33/1.77 end
% 1.33/1.77 substitution1:
% 1.33/1.77 X := multiplication( X, strong_iteration( X ) )
% 1.33/1.77 Y := one
% 1.33/1.77 end
% 1.33/1.77
% 1.33/1.77 paramod: (6362) {G1,W7,D4,L1,V1,M1} { strong_iteration( X ) ==> addition(
% 1.33/1.77 strong_iteration( X ), one ) }.
% 1.33/1.77 parent0[0]: (14) {G0,W9,D5,L1,V1,M1} I { addition( multiplication( X,
% 1.33/1.77 strong_iteration( X ) ), one ) ==> strong_iteration( X ) }.
% 1.33/1.77 parent1[0; 1]: (6361) {G1,W11,D5,L1,V1,M1} { addition( multiplication( X,
% 1.33/1.77 strong_iteration( X ) ), one ) ==> addition( strong_iteration( X ), one )
% 1.33/1.77 }.
% 1.33/1.77 substitution0:
% 1.33/1.77 X := X
% 1.33/1.77 end
% 1.33/1.77 substitution1:
% 1.33/1.77 X := X
% 1.33/1.77 end
% 1.33/1.77
% 1.33/1.77 eqswap: (6364) {G1,W7,D4,L1,V1,M1} { addition( strong_iteration( X ), one
% 1.33/1.77 ) ==> strong_iteration( X ) }.
% 1.33/1.77 parent0[0]: (6362) {G1,W7,D4,L1,V1,M1} { strong_iteration( X ) ==>
% 1.33/1.77 addition( strong_iteration( X ), one ) }.
% 1.33/1.77 substitution0:
% 1.33/1.77 X := X
% 1.33/1.77 end
% 1.33/1.77
% 1.33/1.77 subsumption: (418) {G2,W7,D4,L1,V1,M1} P(14,29) { addition(
% 1.33/1.77 strong_iteration( X ), one ) ==> strong_iteration( X ) }.
% 1.33/1.77 parent0: (6364) {G1,W7,D4,L1,V1,M1} { addition( strong_iteration( X ), one
% 1.33/1.77 ) ==> strong_iteration( X ) }.
% 1.33/1.77 substitution0:
% 1.33/1.77 X := X
% 1.33/1.77 end
% 1.33/1.77 permutation0:
% 1.33/1.77 0 ==> 0
% 1.33/1.77 end
% 1.33/1.77
% 1.33/1.77 paramod: (6367) {G2,W8,D3,L2,V3,M2} { leq( X, addition( Y, Z ) ), ! leq( X
% 1.33/1.77 , Z ) }.
% 1.33/1.77 parent0[0]: (35) {G1,W12,D4,L2,V3,M2} P(17,1) { addition( addition( Z, X )
% 1.33/1.77 , Y ) ==> addition( Z, Y ), ! leq( X, Y ) }.
% 1.33/1.77 parent1[0; 2]: (366) {G4,W7,D4,L1,V3,M1} P(26,363) { leq( Z, addition(
% 1.33/1.77 addition( Y, Z ), X ) ) }.
% 1.33/1.77 substitution0:
% 1.33/1.77 X := X
% 1.33/1.77 Y := Z
% 1.33/1.77 Z := Y
% 1.33/1.77 end
% 1.33/1.77 substitution1:
% 1.33/1.77 X := Z
% 1.33/1.77 Y := Y
% 1.33/1.77 Z := X
% 1.33/1.77 end
% 1.33/1.77
% 1.33/1.77 subsumption: (674) {G5,W8,D3,L2,V3,M2} P(35,366) { leq( Y, addition( X, Z )
% 1.33/1.77 ), ! leq( Y, Z ) }.
% 1.33/1.77 parent0: (6367) {G2,W8,D3,L2,V3,M2} { leq( X, addition( Y, Z ) ), ! leq( X
% 1.33/1.77 , Z ) }.
% 1.33/1.77 substitution0:
% 1.33/1.77 X := Y
% 1.33/1.77 Y := X
% 1.33/1.77 Z := Z
% 1.33/1.77 end
% 1.33/1.77 permutation0:
% 1.33/1.77 0 ==> 0
% 1.33/1.77 1 ==> 1
% 1.33/1.77 end
% 1.33/1.77
% 1.33/1.77 eqswap: (6371) {G1,W16,D4,L2,V3,M2} { ! multiplication( X, Z ) ==>
% 1.33/1.77 multiplication( X, addition( Y, Z ) ), leq( multiplication( X, Y ),
% 1.33/1.77 multiplication( X, Z ) ) }.
% 1.33/1.77 parent0[0]: (67) {G1,W16,D4,L2,V3,M2} P(7,18) { ! multiplication( X,
% 1.33/1.77 addition( Y, Z ) ) ==> multiplication( X, Z ), leq( multiplication( X, Y
% 1.33/1.77 ), multiplication( X, Z ) ) }.
% 1.33/1.77 substitution0:
% 1.33/1.77 X := X
% 1.33/1.77 Y := Y
% 1.33/1.77 Z := Z
% 1.33/1.77 end
% 1.33/1.77
% 1.33/1.77 paramod: (6372) {G2,W14,D3,L2,V2,M2} { ! multiplication( X, Y ) ==>
% 1.33/1.77 multiplication( X, Y ), leq( multiplication( X, zero ), multiplication( X
% 1.33/1.77 , Y ) ) }.
% 1.33/1.77 parent0[0]: (20) {G1,W5,D3,L1,V1,M1} P(0,2) { addition( zero, X ) ==> X }.
% 1.33/1.77 parent1[0; 7]: (6371) {G1,W16,D4,L2,V3,M2} { ! multiplication( X, Z ) ==>
% 1.33/1.77 multiplication( X, addition( Y, Z ) ), leq( multiplication( X, Y ),
% 1.33/1.77 multiplication( X, Z ) ) }.
% 1.33/1.77 substitution0:
% 1.33/1.77 X := Y
% 1.33/1.77 end
% 1.33/1.77 substitution1:
% 1.33/1.77 X := X
% 1.33/1.77 Y := zero
% 1.33/1.77 Z := Y
% 1.33/1.77 end
% 1.33/1.77
% 1.33/1.77 eqrefl: (6373) {G0,W7,D3,L1,V2,M1} { leq( multiplication( X, zero ),
% 1.33/1.77 multiplication( X, Y ) ) }.
% 1.33/1.77 parent0[0]: (6372) {G2,W14,D3,L2,V2,M2} { ! multiplication( X, Y ) ==>
% 1.33/1.77 multiplication( X, Y ), leq( multiplication( X, zero ), multiplication( X
% 1.33/1.77 , Y ) ) }.
% 1.33/1.77 substitution0:
% 1.33/1.77 X := X
% 1.33/1.77 Y := Y
% 1.33/1.77 end
% 1.33/1.77
% 1.33/1.77 subsumption: (1634) {G2,W7,D3,L1,V2,M1} P(20,67);q { leq( multiplication( Y
% 1.33/1.77 , zero ), multiplication( Y, X ) ) }.
% 1.33/1.77 parent0: (6373) {G0,W7,D3,L1,V2,M1} { leq( multiplication( X, zero ),
% 1.33/1.77 multiplication( X, Y ) ) }.
% 1.33/1.77 substitution0:
% 1.33/1.77 X := Y
% 1.33/1.77 Y := X
% 1.33/1.77 end
% 1.33/1.77 permutation0:
% 1.33/1.77 0 ==> 0
% 1.33/1.77 end
% 1.33/1.77
% 1.33/1.77 paramod: (6375) {G1,W5,D3,L1,V1,M1} { leq( multiplication( X, zero ), X )
% 1.33/1.77 }.
% 1.33/1.77 parent0[0]: (5) {G0,W5,D3,L1,V1,M1} I { multiplication( X, one ) ==> X }.
% 1.33/1.77 parent1[0; 4]: (1634) {G2,W7,D3,L1,V2,M1} P(20,67);q { leq( multiplication
% 1.33/1.77 ( Y, zero ), multiplication( Y, X ) ) }.
% 1.33/1.77 substitution0:
% 1.33/1.77 X := X
% 1.33/1.77 end
% 1.33/1.77 substitution1:
% 1.33/1.77 X := one
% 1.33/1.77 Y := X
% 1.33/1.77 end
% 1.33/1.77
% 1.33/1.77 subsumption: (1729) {G3,W5,D3,L1,V1,M1} P(5,1634) { leq( multiplication( X
% 1.33/1.77 , zero ), X ) }.
% 1.33/1.77 parent0: (6375) {G1,W5,D3,L1,V1,M1} { leq( multiplication( X, zero ), X )
% 1.33/1.77 }.
% 1.33/1.77 substitution0:
% 1.33/1.77 X := X
% 1.33/1.77 end
% 1.33/1.77 permutation0:
% 1.33/1.77 0 ==> 0
% 1.33/1.77 end
% 1.33/1.77
% 1.33/1.77 eqswap: (6376) {G1,W8,D3,L2,V2,M2} { X ==> addition( X, Y ), ! leq( Y, X )
% 1.33/1.77 }.
% 1.33/1.77 parent0[0]: (36) {G1,W8,D3,L2,V2,M2} P(17,0) { addition( Y, X ) ==> Y, !
% 1.33/1.77 leq( X, Y ) }.
% 1.33/1.77 substitution0:
% 1.33/1.77 X := Y
% 1.33/1.77 Y := X
% 1.33/1.77 end
% 1.33/1.77
% 1.33/1.77 resolution: (6377) {G2,W7,D4,L1,V1,M1} { X ==> addition( X, multiplication
% 1.33/1.77 ( X, zero ) ) }.
% 1.33/1.77 parent0[1]: (6376) {G1,W8,D3,L2,V2,M2} { X ==> addition( X, Y ), ! leq( Y
% 1.33/1.77 , X ) }.
% 1.33/1.77 parent1[0]: (1729) {G3,W5,D3,L1,V1,M1} P(5,1634) { leq( multiplication( X,
% 1.33/1.77 zero ), X ) }.
% 1.33/1.77 substitution0:
% 1.33/1.77 X := X
% 1.33/1.77 Y := multiplication( X, zero )
% 1.33/1.77 end
% 1.33/1.77 substitution1:
% 1.33/1.77 X := X
% 1.33/1.77 end
% 1.33/1.77
% 1.33/1.77 eqswap: (6378) {G2,W7,D4,L1,V1,M1} { addition( X, multiplication( X, zero
% 1.33/1.77 ) ) ==> X }.
% 1.33/1.77 parent0[0]: (6377) {G2,W7,D4,L1,V1,M1} { X ==> addition( X, multiplication
% 1.33/1.77 ( X, zero ) ) }.
% 1.33/1.77 substitution0:
% 1.33/1.77 X := X
% 1.33/1.77 end
% 1.33/1.77
% 1.33/1.77 subsumption: (1733) {G4,W7,D4,L1,V1,M1} R(1729,36) { addition( X,
% 1.33/1.77 multiplication( X, zero ) ) ==> X }.
% 1.33/1.77 parent0: (6378) {G2,W7,D4,L1,V1,M1} { addition( X, multiplication( X, zero
% 1.33/1.77 ) ) ==> X }.
% 1.33/1.77 substitution0:
% 1.33/1.77 X := X
% 1.33/1.77 end
% 1.33/1.77 permutation0:
% 1.33/1.77 0 ==> 0
% 1.33/1.77 end
% 1.33/1.77
% 1.33/1.77 eqswap: (6379) {G0,W8,D3,L2,V2,M2} { Y ==> addition( X, Y ), ! leq( X, Y )
% 1.33/1.77 }.
% 1.33/1.77 parent0[1]: (17) {G0,W8,D3,L2,V2,M2} I { ! leq( X, Y ), addition( X, Y )
% 1.33/1.77 ==> Y }.
% 1.33/1.77 substitution0:
% 1.33/1.77 X := X
% 1.33/1.77 Y := Y
% 1.33/1.77 end
% 1.33/1.77
% 1.33/1.77 resolution: (6380) {G1,W7,D4,L1,V1,M1} { X ==> addition( multiplication( X
% 1.33/1.77 , zero ), X ) }.
% 1.33/1.77 parent0[1]: (6379) {G0,W8,D3,L2,V2,M2} { Y ==> addition( X, Y ), ! leq( X
% 1.33/1.77 , Y ) }.
% 1.33/1.77 parent1[0]: (1729) {G3,W5,D3,L1,V1,M1} P(5,1634) { leq( multiplication( X,
% 1.33/1.77 zero ), X ) }.
% 1.33/1.77 substitution0:
% 1.33/1.77 X := multiplication( X, zero )
% 1.33/1.77 Y := X
% 1.33/1.77 end
% 1.33/1.77 substitution1:
% 1.33/1.77 X := X
% 1.33/1.77 end
% 1.33/1.77
% 1.33/1.77 eqswap: (6381) {G1,W7,D4,L1,V1,M1} { addition( multiplication( X, zero ),
% 1.33/1.77 X ) ==> X }.
% 1.33/1.77 parent0[0]: (6380) {G1,W7,D4,L1,V1,M1} { X ==> addition( multiplication( X
% 1.33/1.77 , zero ), X ) }.
% 1.33/1.77 substitution0:
% 1.33/1.77 X := X
% 1.33/1.77 end
% 1.33/1.77
% 1.33/1.77 subsumption: (1737) {G4,W7,D4,L1,V1,M1} R(1729,17) { addition(
% 1.33/1.77 multiplication( X, zero ), X ) ==> X }.
% 1.33/1.77 parent0: (6381) {G1,W7,D4,L1,V1,M1} { addition( multiplication( X, zero )
% 1.33/1.77 , X ) ==> X }.
% 1.33/1.77 substitution0:
% 1.33/1.77 X := X
% 1.33/1.77 end
% 1.33/1.77 permutation0:
% 1.33/1.77 0 ==> 0
% 1.33/1.77 end
% 1.33/1.77
% 1.33/1.77 paramod: (6383) {G5,W8,D3,L2,V2,M2} { leq( X, Y ), ! leq( X,
% 1.33/1.77 multiplication( Y, zero ) ) }.
% 1.33/1.77 parent0[0]: (1733) {G4,W7,D4,L1,V1,M1} R(1729,36) { addition( X,
% 1.33/1.77 multiplication( X, zero ) ) ==> X }.
% 1.33/1.77 parent1[0; 2]: (674) {G5,W8,D3,L2,V3,M2} P(35,366) { leq( Y, addition( X, Z
% 1.33/1.77 ) ), ! leq( Y, Z ) }.
% 1.33/1.77 substitution0:
% 1.33/1.77 X := Y
% 1.33/1.77 end
% 1.33/1.77 substitution1:
% 1.33/1.77 X := Y
% 1.33/1.77 Y := X
% 1.33/1.77 Z := multiplication( Y, zero )
% 1.33/1.77 end
% 1.33/1.77
% 1.33/1.77 subsumption: (2097) {G6,W8,D3,L2,V2,M2} P(1733,674) { leq( Y, X ), ! leq( Y
% 1.33/1.77 , multiplication( X, zero ) ) }.
% 1.33/1.77 parent0: (6383) {G5,W8,D3,L2,V2,M2} { leq( X, Y ), ! leq( X,
% 1.33/1.77 multiplication( Y, zero ) ) }.
% 1.33/1.77 substitution0:
% 1.33/1.77 X := Y
% 1.33/1.77 Y := X
% 1.33/1.77 end
% 1.33/1.77 permutation0:
% 1.33/1.77 0 ==> 0
% 1.33/1.77 1 ==> 1
% 1.33/1.77 end
% 1.33/1.77
% 1.33/1.77 eqswap: (6384) {G1,W11,D4,L1,V2,M1} { multiplication( addition( X, one ),
% 1.33/1.77 Y ) = addition( multiplication( X, Y ), Y ) }.
% 1.33/1.77 parent0[0]: (102) {G1,W11,D4,L1,V2,M1} P(6,8) { addition( multiplication( Y
% 1.33/1.77 , X ), X ) = multiplication( addition( Y, one ), X ) }.
% 1.33/1.77 substitution0:
% 1.33/1.77 X := Y
% 1.33/1.77 Y := X
% 1.33/1.77 end
% 1.33/1.77
% 1.33/1.77 paramod: (6385) {G1,W17,D5,L2,V3,M2} { ! leq( X, addition( addition(
% 1.33/1.77 multiplication( Y, X ), X ), Z ) ), leq( X, multiplication(
% 1.33/1.77 strong_iteration( addition( Y, one ) ), Z ) ) }.
% 1.33/1.77 parent0[0]: (6384) {G1,W11,D4,L1,V2,M1} { multiplication( addition( X, one
% 1.33/1.77 ), Y ) = addition( multiplication( X, Y ), Y ) }.
% 1.33/1.77 parent1[0; 4]: (15) {G0,W13,D4,L2,V3,M2} I { ! leq( Z, addition(
% 1.33/1.77 multiplication( X, Z ), Y ) ), leq( Z, multiplication( strong_iteration(
% 1.33/1.77 X ), Y ) ) }.
% 1.33/1.77 substitution0:
% 1.33/1.77 X := Y
% 1.33/1.77 Y := X
% 1.33/1.77 end
% 1.33/1.77 substitution1:
% 1.33/1.77 X := addition( Y, one )
% 1.33/1.77 Y := Z
% 1.33/1.77 Z := X
% 1.33/1.77 end
% 1.33/1.77
% 1.33/1.77 resolution: (6386) {G2,W8,D5,L1,V3,M1} { leq( X, multiplication(
% 1.33/1.77 strong_iteration( addition( Y, one ) ), Z ) ) }.
% 1.33/1.77 parent0[0]: (6385) {G1,W17,D5,L2,V3,M2} { ! leq( X, addition( addition(
% 1.33/1.77 multiplication( Y, X ), X ), Z ) ), leq( X, multiplication(
% 1.33/1.77 strong_iteration( addition( Y, one ) ), Z ) ) }.
% 1.33/1.77 parent1[0]: (366) {G4,W7,D4,L1,V3,M1} P(26,363) { leq( Z, addition(
% 1.33/1.77 addition( Y, Z ), X ) ) }.
% 1.33/1.77 substitution0:
% 1.33/1.77 X := X
% 1.33/1.77 Y := Y
% 1.33/1.77 Z := Z
% 1.33/1.77 end
% 1.33/1.77 substitution1:
% 1.33/1.77 X := Z
% 1.33/1.77 Y := multiplication( Y, X )
% 1.33/1.77 Z := X
% 1.33/1.77 end
% 1.33/1.77
% 1.33/1.77 subsumption: (3562) {G5,W8,D5,L1,V3,M1} P(102,15);r(366) { leq( Y,
% 1.33/1.77 multiplication( strong_iteration( addition( X, one ) ), Z ) ) }.
% 1.33/1.77 parent0: (6386) {G2,W8,D5,L1,V3,M1} { leq( X, multiplication(
% 1.33/1.77 strong_iteration( addition( Y, one ) ), Z ) ) }.
% 1.33/1.77 substitution0:
% 1.33/1.77 X := Y
% 1.33/1.77 Y := X
% 1.33/1.77 Z := Z
% 1.33/1.77 end
% 1.33/1.77 permutation0:
% 1.33/1.77 0 ==> 0
% 1.33/1.77 end
% 1.33/1.77
% 1.33/1.77 resolution: (6387) {G6,W6,D4,L1,V2,M1} { leq( X, strong_iteration(
% 1.33/1.77 addition( Y, one ) ) ) }.
% 1.33/1.77 parent0[1]: (2097) {G6,W8,D3,L2,V2,M2} P(1733,674) { leq( Y, X ), ! leq( Y
% 1.33/1.77 , multiplication( X, zero ) ) }.
% 1.33/1.77 parent1[0]: (3562) {G5,W8,D5,L1,V3,M1} P(102,15);r(366) { leq( Y,
% 1.33/1.77 multiplication( strong_iteration( addition( X, one ) ), Z ) ) }.
% 1.33/1.77 substitution0:
% 1.33/1.77 X := strong_iteration( addition( Y, one ) )
% 1.33/1.77 Y := X
% 1.33/1.77 end
% 1.33/1.77 substitution1:
% 1.33/1.77 X := Y
% 1.33/1.77 Y := X
% 1.33/1.77 Z := zero
% 1.33/1.77 end
% 1.33/1.77
% 1.33/1.77 subsumption: (6060) {G7,W6,D4,L1,V2,M1} R(3562,2097) { leq( X,
% 1.33/1.77 strong_iteration( addition( Y, one ) ) ) }.
% 1.33/1.77 parent0: (6387) {G6,W6,D4,L1,V2,M1} { leq( X, strong_iteration( addition(
% 1.33/1.77 Y, one ) ) ) }.
% 1.33/1.77 substitution0:
% 1.33/1.77 X := X
% 1.33/1.77 Y := Y
% 1.33/1.77 end
% 1.33/1.77 permutation0:
% 1.33/1.77 0 ==> 0
% 1.33/1.77 end
% 1.33/1.77
% 1.33/1.77 paramod: (6389) {G5,W4,D3,L1,V1,M1} { leq( X, strong_iteration( one ) )
% 1.33/1.77 }.
% 1.33/1.77 parent0[0]: (1737) {G4,W7,D4,L1,V1,M1} R(1729,17) { addition(
% 1.33/1.77 multiplication( X, zero ), X ) ==> X }.
% 1.33/1.77 parent1[0; 3]: (6060) {G7,W6,D4,L1,V2,M1} R(3562,2097) { leq( X,
% 1.33/1.77 strong_iteration( addition( Y, one ) ) ) }.
% 1.33/1.77 substitution0:
% 1.33/1.77 X := one
% 1.33/1.77 end
% 1.33/1.77 substitution1:
% 1.33/1.77 X := X
% 1.33/1.77 Y := multiplication( one, zero )
% 1.33/1.77 end
% 1.33/1.77
% 1.33/1.77 subsumption: (6098) {G8,W4,D3,L1,V1,M1} P(1737,6060) { leq( X,
% 1.33/1.77 strong_iteration( one ) ) }.
% 1.33/1.77 parent0: (6389) {G5,W4,D3,L1,V1,M1} { leq( X, strong_iteration( one ) )
% 1.33/1.77 }.
% 1.33/1.77 substitution0:
% 1.33/1.77 X := X
% 1.33/1.77 end
% 1.33/1.77 permutation0:
% 1.33/1.77 0 ==> 0
% 1.33/1.77 end
% 1.33/1.77
% 1.33/1.77 paramod: (6391) {G3,W5,D4,L1,V2,M1} { leq( X, strong_iteration(
% 1.33/1.77 strong_iteration( Y ) ) ) }.
% 1.33/1.77 parent0[0]: (418) {G2,W7,D4,L1,V1,M1} P(14,29) { addition( strong_iteration
% 1.33/1.77 ( X ), one ) ==> strong_iteration( X ) }.
% 1.33/1.77 parent1[0; 3]: (6060) {G7,W6,D4,L1,V2,M1} R(3562,2097) { leq( X,
% 1.33/1.77 strong_iteration( addition( Y, one ) ) ) }.
% 1.33/1.77 substitution0:
% 1.33/1.77 X := Y
% 1.33/1.77 end
% 1.33/1.77 substitution1:
% 1.33/1.77 X := X
% 1.33/1.77 Y := strong_iteration( Y )
% 1.33/1.77 end
% 1.33/1.77
% 1.33/1.77 subsumption: (6099) {G8,W5,D4,L1,V2,M1} P(418,6060) { leq( Y,
% 1.33/1.77 strong_iteration( strong_iteration( X ) ) ) }.
% 1.33/1.77 parent0: (6391) {G3,W5,D4,L1,V2,M1} { leq( X, strong_iteration(
% 1.33/1.77 strong_iteration( Y ) ) ) }.
% 1.33/1.77 substitution0:
% 1.33/1.77 X := Y
% 1.33/1.77 Y := X
% 1.33/1.77 end
% 1.33/1.77 permutation0:
% 1.33/1.77 0 ==> 0
% 1.33/1.77 end
% 1.33/1.77
% 1.33/1.77 resolution: (6392) {G1,W6,D4,L1,V0,M1} { ! leq( strong_iteration( one ),
% 1.33/1.77 strong_iteration( strong_iteration( skol1 ) ) ) }.
% 1.33/1.77 parent0[0]: (19) {G0,W12,D4,L2,V0,M2} I { ! leq( strong_iteration(
% 1.33/1.77 strong_iteration( skol1 ) ), strong_iteration( one ) ), ! leq(
% 1.33/1.77 strong_iteration( one ), strong_iteration( strong_iteration( skol1 ) ) )
% 1.33/1.77 }.
% 1.33/1.77 parent1[0]: (6098) {G8,W4,D3,L1,V1,M1} P(1737,6060) { leq( X,
% 1.33/1.77 strong_iteration( one ) ) }.
% 1.33/1.77 substitution0:
% 1.33/1.77 end
% 1.33/1.77 substitution1:
% 1.33/1.77 X := strong_iteration( strong_iteration( skol1 ) )
% 1.33/1.77 end
% 1.33/1.77
% 1.33/1.77 resolution: (6393) {G2,W0,D0,L0,V0,M0} { }.
% 1.33/1.77 parent0[0]: (6392) {G1,W6,D4,L1,V0,M1} { ! leq( strong_iteration( one ),
% 1.33/1.77 strong_iteration( strong_iteration( skol1 ) ) ) }.
% 1.33/1.77 parent1[0]: (6099) {G8,W5,D4,L1,V2,M1} P(418,6060) { leq( Y,
% 1.33/1.77 strong_iteration( strong_iteration( X ) ) ) }.
% 1.33/1.77 substitution0:
% 1.33/1.77 end
% 1.33/1.77 substitution1:
% 1.33/1.77 X := skol1
% 1.33/1.77 Y := strong_iteration( one )
% 1.33/1.77 end
% 1.33/1.77
% 1.33/1.77 subsumption: (6115) {G9,W0,D0,L0,V0,M0} R(6098,19);r(6099) { }.
% 1.33/1.77 parent0: (6393) {G2,W0,D0,L0,V0,M0} { }.
% 1.33/1.77 substitution0:
% 1.33/1.77 end
% 1.33/1.77 permutation0:
% 1.33/1.77 end
% 1.33/1.77
% 1.33/1.77 Proof check complete!
% 1.33/1.77
% 1.33/1.77 Memory use:
% 1.33/1.77
% 1.33/1.77 space for terms: 76080
% 1.33/1.77 space for clauses: 329929
% 1.33/1.77
% 1.33/1.77
% 1.33/1.77 clauses generated: 64346
% 1.33/1.77 clauses kept: 6116
% 1.33/1.77 clauses selected: 487
% 1.33/1.77 clauses deleted: 100
% 1.33/1.77 clauses inuse deleted: 33
% 1.33/1.77
% 1.33/1.77 subsentry: 215504
% 1.33/1.77 literals s-matched: 140673
% 1.33/1.77 literals matched: 135047
% 1.33/1.77 full subsumption: 40192
% 1.33/1.77
% 1.33/1.77 checksum: 1020462026
% 1.33/1.77
% 1.33/1.77
% 1.33/1.77 Bliksem ended
%------------------------------------------------------------------------------