%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : KLE141+2 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n004.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 01:37:24 EDT 2022
% Result : Theorem 1.26s 1.65s
% Output : Refutation 1.26s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : KLE141+2 : TPTP v8.1.0. Released v4.0.0.
% 0.13/0.14 % Command : bliksem %s
% 0.14/0.35 % Computer : n004.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % DateTime : Thu Jun 16 15:05:08 EDT 2022
% 0.14/0.36 % CPUTime :
% 1.26/1.65 *** allocated 10000 integers for termspace/termends
% 1.26/1.65 *** allocated 10000 integers for clauses
% 1.26/1.65 *** allocated 10000 integers for justifications
% 1.26/1.65 Bliksem 1.12
% 1.26/1.65
% 1.26/1.65
% 1.26/1.65 Automatic Strategy Selection
% 1.26/1.65
% 1.26/1.65
% 1.26/1.65 Clauses:
% 1.26/1.65
% 1.26/1.65 { addition( X, Y ) = addition( Y, X ) }.
% 1.26/1.65 { addition( Z, addition( Y, X ) ) = addition( addition( Z, Y ), X ) }.
% 1.26/1.65 { addition( X, zero ) = X }.
% 1.26/1.65 { addition( X, X ) = X }.
% 1.26/1.65 { multiplication( X, multiplication( Y, Z ) ) = multiplication(
% 1.26/1.65 multiplication( X, Y ), Z ) }.
% 1.26/1.65 { multiplication( X, one ) = X }.
% 1.26/1.65 { multiplication( one, X ) = X }.
% 1.26/1.65 { multiplication( X, addition( Y, Z ) ) = addition( multiplication( X, Y )
% 1.26/1.65 , multiplication( X, Z ) ) }.
% 1.26/1.65 { multiplication( addition( X, Y ), Z ) = addition( multiplication( X, Z )
% 1.26/1.65 , multiplication( Y, Z ) ) }.
% 1.26/1.65 { multiplication( zero, X ) = zero }.
% 1.26/1.65 { addition( one, multiplication( X, star( X ) ) ) = star( X ) }.
% 1.26/1.65 { addition( one, multiplication( star( X ), X ) ) = star( X ) }.
% 1.26/1.65 { ! leq( addition( multiplication( X, Z ), Y ), Z ), leq( multiplication(
% 1.26/1.65 star( X ), Y ), Z ) }.
% 1.26/1.65 { ! leq( addition( multiplication( Z, X ), Y ), Z ), leq( multiplication( Y
% 1.26/1.65 , star( X ) ), Z ) }.
% 1.26/1.65 { strong_iteration( X ) = addition( multiplication( X, strong_iteration( X
% 1.26/1.65 ) ), one ) }.
% 1.26/1.65 { ! leq( Z, addition( multiplication( X, Z ), Y ) ), leq( Z, multiplication
% 1.26/1.65 ( strong_iteration( X ), Y ) ) }.
% 1.26/1.65 { strong_iteration( X ) = addition( star( X ), multiplication(
% 1.26/1.65 strong_iteration( X ), zero ) ) }.
% 1.26/1.65 { ! leq( X, Y ), addition( X, Y ) = Y }.
% 1.26/1.65 { ! addition( X, Y ) = Y, leq( X, Y ) }.
% 1.26/1.65 { ! leq( multiplication( strong_iteration( one ), skol1 ), strong_iteration
% 1.26/1.65 ( one ) ), ! leq( strong_iteration( one ), multiplication(
% 1.26/1.65 strong_iteration( one ), skol1 ) ) }.
% 1.26/1.65
% 1.26/1.65 percentage equality = 0.615385, percentage horn = 1.000000
% 1.26/1.65 This is a problem with some equality
% 1.26/1.65
% 1.26/1.65
% 1.26/1.65
% 1.26/1.65 Options Used:
% 1.26/1.65
% 1.26/1.65 useres = 1
% 1.26/1.65 useparamod = 1
% 1.26/1.65 useeqrefl = 1
% 1.26/1.65 useeqfact = 1
% 1.26/1.65 usefactor = 1
% 1.26/1.65 usesimpsplitting = 0
% 1.26/1.65 usesimpdemod = 5
% 1.26/1.65 usesimpres = 3
% 1.26/1.65
% 1.26/1.65 resimpinuse = 1000
% 1.26/1.65 resimpclauses = 20000
% 1.26/1.65 substype = eqrewr
% 1.26/1.65 backwardsubs = 1
% 1.26/1.65 selectoldest = 5
% 1.26/1.65
% 1.26/1.65 litorderings [0] = split
% 1.26/1.65 litorderings [1] = extend the termordering, first sorting on arguments
% 1.26/1.65
% 1.26/1.65 termordering = kbo
% 1.26/1.65
% 1.26/1.65 litapriori = 0
% 1.26/1.65 termapriori = 1
% 1.26/1.65 litaposteriori = 0
% 1.26/1.65 termaposteriori = 0
% 1.26/1.65 demodaposteriori = 0
% 1.26/1.65 ordereqreflfact = 0
% 1.26/1.65
% 1.26/1.65 litselect = negord
% 1.26/1.65
% 1.26/1.65 maxweight = 15
% 1.26/1.65 maxdepth = 30000
% 1.26/1.65 maxlength = 115
% 1.26/1.65 maxnrvars = 195
% 1.26/1.65 excuselevel = 1
% 1.26/1.65 increasemaxweight = 1
% 1.26/1.65
% 1.26/1.65 maxselected = 10000000
% 1.26/1.65 maxnrclauses = 10000000
% 1.26/1.65
% 1.26/1.65 showgenerated = 0
% 1.26/1.65 showkept = 0
% 1.26/1.65 showselected = 0
% 1.26/1.65 showdeleted = 0
% 1.26/1.65 showresimp = 1
% 1.26/1.65 showstatus = 2000
% 1.26/1.65
% 1.26/1.65 prologoutput = 0
% 1.26/1.65 nrgoals = 5000000
% 1.26/1.65 totalproof = 1
% 1.26/1.65
% 1.26/1.65 Symbols occurring in the translation:
% 1.26/1.65
% 1.26/1.65 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 1.26/1.65 . [1, 2] (w:1, o:20, a:1, s:1, b:0),
% 1.26/1.65 ! [4, 1] (w:0, o:13, a:1, s:1, b:0),
% 1.26/1.65 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 1.26/1.65 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 1.26/1.65 addition [37, 2] (w:1, o:44, a:1, s:1, b:0),
% 1.26/1.65 zero [39, 0] (w:1, o:9, a:1, s:1, b:0),
% 1.26/1.65 multiplication [40, 2] (w:1, o:46, a:1, s:1, b:0),
% 1.26/1.65 one [41, 0] (w:1, o:10, a:1, s:1, b:0),
% 1.26/1.65 star [42, 1] (w:1, o:18, a:1, s:1, b:0),
% 1.26/1.65 leq [43, 2] (w:1, o:45, a:1, s:1, b:0),
% 1.26/1.65 strong_iteration [44, 1] (w:1, o:19, a:1, s:1, b:0),
% 1.26/1.65 skol1 [46, 0] (w:1, o:12, a:1, s:1, b:1).
% 1.26/1.65
% 1.26/1.65
% 1.26/1.65 Starting Search:
% 1.26/1.65
% 1.26/1.65 *** allocated 15000 integers for clauses
% 1.26/1.65 *** allocated 22500 integers for clauses
% 1.26/1.65 *** allocated 33750 integers for clauses
% 1.26/1.65 *** allocated 50625 integers for clauses
% 1.26/1.65 *** allocated 15000 integers for termspace/termends
% 1.26/1.65 *** allocated 75937 integers for clauses
% 1.26/1.65 Resimplifying inuse:
% 1.26/1.65 Done
% 1.26/1.65
% 1.26/1.65 *** allocated 22500 integers for termspace/termends
% 1.26/1.65 *** allocated 113905 integers for clauses
% 1.26/1.65 *** allocated 33750 integers for termspace/termends
% 1.26/1.65
% 1.26/1.65 Intermediate Status:
% 1.26/1.65 Generated: 20415
% 1.26/1.65 Kept: 2026
% 1.26/1.65 Inuse: 218
% 1.26/1.65 Deleted: 58
% 1.26/1.65 Deletedinuse: 30
% 1.26/1.65
% 1.26/1.65 Resimplifying inuse:
% 1.26/1.65 Done
% 1.26/1.65
% 1.26/1.65 *** allocated 170857 integers for clauses
% 1.26/1.65 *** allocated 50625 integers for termspace/termends
% 1.26/1.65 Resimplifying inuse:
% 1.26/1.65 Done
% 1.26/1.65
% 1.26/1.65 *** allocated 256285 integers for clauses
% 1.26/1.65 *** allocated 75937 integers for termspace/termends
% 1.26/1.65
% 1.26/1.65 Intermediate Status:
% 1.26/1.65 Generated: 37586
% 1.26/1.65 Kept: 4078
% 1.26/1.65 Inuse: 327
% 1.26/1.65 Deleted: 80
% 1.26/1.65 Deletedinuse: 31
% 1.26/1.65
% 1.26/1.65 Resimplifying inuse:
% 1.26/1.65 Done
% 1.26/1.65
% 1.26/1.65 *** allocated 384427 integers for clauses
% 1.26/1.65 Resimplifying inuse:
% 1.26/1.65 Done
% 1.26/1.65
% 1.26/1.65
% 1.26/1.65 Bliksems!, er is een bewijs:
% 1.26/1.65 % SZS status Theorem
% 1.26/1.65 % SZS output start Refutation
% 1.26/1.65
% 1.26/1.65 (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X ) }.
% 1.26/1.65 (1) {G0,W11,D4,L1,V3,M1} I { addition( Z, addition( Y, X ) ) ==> addition(
% 1.26/1.65 addition( Z, Y ), X ) }.
% 1.26/1.65 (2) {G0,W5,D3,L1,V1,M1} I { addition( X, zero ) ==> X }.
% 1.26/1.65 (3) {G0,W5,D3,L1,V1,M1} I { addition( X, X ) ==> X }.
% 1.26/1.65 (5) {G0,W5,D3,L1,V1,M1} I { multiplication( X, one ) ==> X }.
% 1.26/1.65 (6) {G0,W5,D3,L1,V1,M1} I { multiplication( one, X ) ==> X }.
% 1.26/1.65 (7) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Y ),
% 1.26/1.65 multiplication( X, Z ) ) ==> multiplication( X, addition( Y, Z ) ) }.
% 1.26/1.65 (8) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Z ),
% 1.26/1.65 multiplication( Y, Z ) ) ==> multiplication( addition( X, Y ), Z ) }.
% 1.26/1.65 (15) {G0,W13,D4,L2,V3,M2} I { ! leq( Z, addition( multiplication( X, Z ), Y
% 1.26/1.65 ) ), leq( Z, multiplication( strong_iteration( X ), Y ) ) }.
% 1.26/1.65 (17) {G0,W8,D3,L2,V2,M2} I { ! leq( X, Y ), addition( X, Y ) ==> Y }.
% 1.26/1.65 (18) {G0,W8,D3,L2,V2,M2} I { ! addition( X, Y ) ==> Y, leq( X, Y ) }.
% 1.26/1.65 (19) {G0,W14,D4,L2,V0,M2} I { ! leq( multiplication( strong_iteration( one
% 1.26/1.65 ), skol1 ), strong_iteration( one ) ), ! leq( strong_iteration( one ),
% 1.26/1.65 multiplication( strong_iteration( one ), skol1 ) ) }.
% 1.26/1.65 (20) {G1,W5,D3,L1,V1,M1} P(0,2) { addition( zero, X ) ==> X }.
% 1.26/1.65 (25) {G1,W14,D4,L2,V3,M2} P(1,18) { ! addition( addition( X, Y ), Z ) ==>
% 1.26/1.65 addition( Y, Z ), leq( X, addition( Y, Z ) ) }.
% 1.26/1.65 (26) {G1,W11,D4,L1,V3,M1} P(1,0) { addition( addition( X, Y ), Z ) =
% 1.26/1.65 addition( addition( Y, Z ), X ) }.
% 1.26/1.65 (35) {G1,W12,D4,L2,V3,M2} P(17,1) { addition( addition( Z, X ), Y ) ==>
% 1.26/1.65 addition( Z, Y ), ! leq( X, Y ) }.
% 1.26/1.65 (36) {G1,W8,D3,L2,V2,M2} P(17,0) { addition( Y, X ) ==> Y, ! leq( X, Y )
% 1.26/1.65 }.
% 1.26/1.65 (67) {G1,W16,D4,L2,V3,M2} P(7,18) { ! multiplication( X, addition( Y, Z ) )
% 1.26/1.65 ==> multiplication( X, Z ), leq( multiplication( X, Y ), multiplication
% 1.26/1.65 ( X, Z ) ) }.
% 1.26/1.65 (102) {G1,W11,D4,L1,V2,M1} P(6,8) { addition( multiplication( Y, X ), X ) =
% 1.26/1.65 multiplication( addition( Y, one ), X ) }.
% 1.26/1.65 (323) {G2,W5,D3,L1,V2,M1} P(3,25);q { leq( X, addition( X, Y ) ) }.
% 1.26/1.65 (333) {G3,W5,D3,L1,V2,M1} P(0,323) { leq( X, addition( Y, X ) ) }.
% 1.26/1.65 (363) {G4,W7,D4,L1,V3,M1} P(26,333) { leq( Z, addition( addition( Y, Z ), X
% 1.26/1.65 ) ) }.
% 1.26/1.65 (615) {G5,W8,D3,L2,V3,M2} P(35,363) { leq( Y, addition( X, Z ) ), ! leq( Y
% 1.26/1.65 , Z ) }.
% 1.26/1.65 (1802) {G2,W7,D3,L1,V2,M1} P(20,67);q { leq( multiplication( Y, zero ),
% 1.26/1.65 multiplication( Y, X ) ) }.
% 1.26/1.65 (1877) {G3,W5,D3,L1,V1,M1} P(5,1802) { leq( multiplication( X, zero ), X )
% 1.26/1.65 }.
% 1.26/1.65 (1881) {G4,W7,D4,L1,V1,M1} R(1877,36) { addition( X, multiplication( X,
% 1.26/1.65 zero ) ) ==> X }.
% 1.26/1.65 (1885) {G4,W7,D4,L1,V1,M1} R(1877,17) { addition( multiplication( X, zero )
% 1.26/1.65 , X ) ==> X }.
% 1.26/1.65 (2154) {G6,W8,D3,L2,V2,M2} P(1881,615) { leq( Y, X ), ! leq( Y,
% 1.26/1.65 multiplication( X, zero ) ) }.
% 1.26/1.65 (4213) {G5,W8,D5,L1,V3,M1} P(102,15);r(363) { leq( Y, multiplication(
% 1.26/1.65 strong_iteration( addition( X, one ) ), Z ) ) }.
% 1.26/1.65 (5485) {G7,W6,D4,L1,V2,M1} R(4213,2154) { leq( X, strong_iteration(
% 1.26/1.65 addition( Y, one ) ) ) }.
% 1.26/1.65 (5505) {G6,W6,D4,L1,V2,M1} P(1885,4213) { leq( X, multiplication(
% 1.26/1.65 strong_iteration( one ), Y ) ) }.
% 1.26/1.65 (5534) {G8,W4,D3,L1,V1,M1} P(1885,5485) { leq( X, strong_iteration( one ) )
% 1.26/1.65 }.
% 1.26/1.65 (5547) {G9,W0,D0,L0,V0,M0} R(5534,19);r(5505) { }.
% 1.26/1.65
% 1.26/1.65
% 1.26/1.65 % SZS output end Refutation
% 1.26/1.65 found a proof!
% 1.26/1.65
% 1.26/1.65
% 1.26/1.65 Unprocessed initial clauses:
% 1.26/1.65
% 1.26/1.65 (5549) {G0,W7,D3,L1,V2,M1} { addition( X, Y ) = addition( Y, X ) }.
% 1.26/1.65 (5550) {G0,W11,D4,L1,V3,M1} { addition( Z, addition( Y, X ) ) = addition(
% 1.26/1.65 addition( Z, Y ), X ) }.
% 1.26/1.65 (5551) {G0,W5,D3,L1,V1,M1} { addition( X, zero ) = X }.
% 1.26/1.65 (5552) {G0,W5,D3,L1,V1,M1} { addition( X, X ) = X }.
% 1.26/1.65 (5553) {G0,W11,D4,L1,V3,M1} { multiplication( X, multiplication( Y, Z ) )
% 1.26/1.65 = multiplication( multiplication( X, Y ), Z ) }.
% 1.26/1.65 (5554) {G0,W5,D3,L1,V1,M1} { multiplication( X, one ) = X }.
% 1.26/1.65 (5555) {G0,W5,D3,L1,V1,M1} { multiplication( one, X ) = X }.
% 1.26/1.65 (5556) {G0,W13,D4,L1,V3,M1} { multiplication( X, addition( Y, Z ) ) =
% 1.26/1.65 addition( multiplication( X, Y ), multiplication( X, Z ) ) }.
% 1.26/1.65 (5557) {G0,W13,D4,L1,V3,M1} { multiplication( addition( X, Y ), Z ) =
% 1.26/1.65 addition( multiplication( X, Z ), multiplication( Y, Z ) ) }.
% 1.26/1.65 (5558) {G0,W5,D3,L1,V1,M1} { multiplication( zero, X ) = zero }.
% 1.26/1.65 (5559) {G0,W9,D5,L1,V1,M1} { addition( one, multiplication( X, star( X ) )
% 1.26/1.65 ) = star( X ) }.
% 1.26/1.65 (5560) {G0,W9,D5,L1,V1,M1} { addition( one, multiplication( star( X ), X )
% 1.26/1.65 ) = star( X ) }.
% 1.26/1.65 (5561) {G0,W13,D4,L2,V3,M2} { ! leq( addition( multiplication( X, Z ), Y )
% 1.26/1.65 , Z ), leq( multiplication( star( X ), Y ), Z ) }.
% 1.26/1.65 (5562) {G0,W13,D4,L2,V3,M2} { ! leq( addition( multiplication( Z, X ), Y )
% 1.26/1.65 , Z ), leq( multiplication( Y, star( X ) ), Z ) }.
% 1.26/1.65 (5563) {G0,W9,D5,L1,V1,M1} { strong_iteration( X ) = addition(
% 1.26/1.65 multiplication( X, strong_iteration( X ) ), one ) }.
% 1.26/1.65 (5564) {G0,W13,D4,L2,V3,M2} { ! leq( Z, addition( multiplication( X, Z ),
% 1.26/1.65 Y ) ), leq( Z, multiplication( strong_iteration( X ), Y ) ) }.
% 1.26/1.65 (5565) {G0,W10,D5,L1,V1,M1} { strong_iteration( X ) = addition( star( X )
% 1.26/1.65 , multiplication( strong_iteration( X ), zero ) ) }.
% 1.26/1.65 (5566) {G0,W8,D3,L2,V2,M2} { ! leq( X, Y ), addition( X, Y ) = Y }.
% 1.26/1.65 (5567) {G0,W8,D3,L2,V2,M2} { ! addition( X, Y ) = Y, leq( X, Y ) }.
% 1.26/1.65 (5568) {G0,W14,D4,L2,V0,M2} { ! leq( multiplication( strong_iteration( one
% 1.26/1.65 ), skol1 ), strong_iteration( one ) ), ! leq( strong_iteration( one ),
% 1.26/1.65 multiplication( strong_iteration( one ), skol1 ) ) }.
% 1.26/1.65
% 1.26/1.65
% 1.26/1.65 Total Proof:
% 1.26/1.65
% 1.26/1.65 subsumption: (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X
% 1.26/1.65 ) }.
% 1.26/1.65 parent0: (5549) {G0,W7,D3,L1,V2,M1} { addition( X, Y ) = addition( Y, X )
% 1.26/1.65 }.
% 1.26/1.65 substitution0:
% 1.26/1.65 X := X
% 1.26/1.65 Y := Y
% 1.26/1.65 end
% 1.26/1.65 permutation0:
% 1.26/1.65 0 ==> 0
% 1.26/1.65 end
% 1.26/1.65
% 1.26/1.65 subsumption: (1) {G0,W11,D4,L1,V3,M1} I { addition( Z, addition( Y, X ) )
% 1.26/1.65 ==> addition( addition( Z, Y ), X ) }.
% 1.26/1.65 parent0: (5550) {G0,W11,D4,L1,V3,M1} { addition( Z, addition( Y, X ) ) =
% 1.26/1.65 addition( addition( Z, Y ), X ) }.
% 1.26/1.65 substitution0:
% 1.26/1.65 X := X
% 1.26/1.65 Y := Y
% 1.26/1.65 Z := Z
% 1.26/1.65 end
% 1.26/1.65 permutation0:
% 1.26/1.65 0 ==> 0
% 1.26/1.65 end
% 1.26/1.65
% 1.26/1.65 subsumption: (2) {G0,W5,D3,L1,V1,M1} I { addition( X, zero ) ==> X }.
% 1.26/1.65 parent0: (5551) {G0,W5,D3,L1,V1,M1} { addition( X, zero ) = X }.
% 1.26/1.65 substitution0:
% 1.26/1.65 X := X
% 1.26/1.65 end
% 1.26/1.65 permutation0:
% 1.26/1.65 0 ==> 0
% 1.26/1.65 end
% 1.26/1.65
% 1.26/1.65 subsumption: (3) {G0,W5,D3,L1,V1,M1} I { addition( X, X ) ==> X }.
% 1.26/1.65 parent0: (5552) {G0,W5,D3,L1,V1,M1} { addition( X, X ) = X }.
% 1.26/1.65 substitution0:
% 1.26/1.65 X := X
% 1.26/1.65 end
% 1.26/1.65 permutation0:
% 1.26/1.65 0 ==> 0
% 1.26/1.65 end
% 1.26/1.65
% 1.26/1.65 subsumption: (5) {G0,W5,D3,L1,V1,M1} I { multiplication( X, one ) ==> X }.
% 1.26/1.65 parent0: (5554) {G0,W5,D3,L1,V1,M1} { multiplication( X, one ) = X }.
% 1.26/1.65 substitution0:
% 1.26/1.65 X := X
% 1.26/1.65 end
% 1.26/1.65 permutation0:
% 1.26/1.65 0 ==> 0
% 1.26/1.65 end
% 1.26/1.65
% 1.26/1.65 subsumption: (6) {G0,W5,D3,L1,V1,M1} I { multiplication( one, X ) ==> X }.
% 1.26/1.65 parent0: (5555) {G0,W5,D3,L1,V1,M1} { multiplication( one, X ) = X }.
% 1.26/1.65 substitution0:
% 1.26/1.65 X := X
% 1.26/1.65 end
% 1.26/1.65 permutation0:
% 1.26/1.65 0 ==> 0
% 1.26/1.65 end
% 1.26/1.65
% 1.26/1.65 eqswap: (5592) {G0,W13,D4,L1,V3,M1} { addition( multiplication( X, Y ),
% 1.26/1.65 multiplication( X, Z ) ) = multiplication( X, addition( Y, Z ) ) }.
% 1.26/1.65 parent0[0]: (5556) {G0,W13,D4,L1,V3,M1} { multiplication( X, addition( Y,
% 1.26/1.65 Z ) ) = addition( multiplication( X, Y ), multiplication( X, Z ) ) }.
% 1.26/1.65 substitution0:
% 1.26/1.65 X := X
% 1.26/1.65 Y := Y
% 1.26/1.65 Z := Z
% 1.26/1.65 end
% 1.26/1.65
% 1.26/1.65 subsumption: (7) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Y )
% 1.26/1.65 , multiplication( X, Z ) ) ==> multiplication( X, addition( Y, Z ) ) }.
% 1.26/1.65 parent0: (5592) {G0,W13,D4,L1,V3,M1} { addition( multiplication( X, Y ),
% 1.26/1.65 multiplication( X, Z ) ) = multiplication( X, addition( Y, Z ) ) }.
% 1.26/1.65 substitution0:
% 1.26/1.65 X := X
% 1.26/1.65 Y := Y
% 1.26/1.65 Z := Z
% 1.26/1.65 end
% 1.26/1.65 permutation0:
% 1.26/1.65 0 ==> 0
% 1.26/1.65 end
% 1.26/1.65
% 1.26/1.65 eqswap: (5600) {G0,W13,D4,L1,V3,M1} { addition( multiplication( X, Z ),
% 1.26/1.65 multiplication( Y, Z ) ) = multiplication( addition( X, Y ), Z ) }.
% 1.26/1.65 parent0[0]: (5557) {G0,W13,D4,L1,V3,M1} { multiplication( addition( X, Y )
% 1.26/1.65 , Z ) = addition( multiplication( X, Z ), multiplication( Y, Z ) ) }.
% 1.26/1.65 substitution0:
% 1.26/1.65 X := X
% 1.26/1.65 Y := Y
% 1.26/1.65 Z := Z
% 1.26/1.65 end
% 1.26/1.65
% 1.26/1.65 subsumption: (8) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Z )
% 1.26/1.65 , multiplication( Y, Z ) ) ==> multiplication( addition( X, Y ), Z ) }.
% 1.26/1.65 parent0: (5600) {G0,W13,D4,L1,V3,M1} { addition( multiplication( X, Z ),
% 1.26/1.65 multiplication( Y, Z ) ) = multiplication( addition( X, Y ), Z ) }.
% 1.26/1.65 substitution0:
% 1.26/1.65 X := X
% 1.26/1.65 Y := Y
% 1.26/1.65 Z := Z
% 1.26/1.65 end
% 1.26/1.65 permutation0:
% 1.26/1.65 0 ==> 0
% 1.26/1.65 end
% 1.26/1.65
% 1.26/1.65 subsumption: (15) {G0,W13,D4,L2,V3,M2} I { ! leq( Z, addition(
% 1.26/1.65 multiplication( X, Z ), Y ) ), leq( Z, multiplication( strong_iteration(
% 1.26/1.65 X ), Y ) ) }.
% 1.26/1.65 parent0: (5564) {G0,W13,D4,L2,V3,M2} { ! leq( Z, addition( multiplication
% 1.26/1.65 ( X, Z ), Y ) ), leq( Z, multiplication( strong_iteration( X ), Y ) ) }.
% 1.26/1.65 substitution0:
% 1.26/1.65 X := X
% 1.26/1.65 Y := Y
% 1.26/1.65 Z := Z
% 1.26/1.65 end
% 1.26/1.65 permutation0:
% 1.26/1.65 0 ==> 0
% 1.26/1.65 1 ==> 1
% 1.26/1.65 end
% 1.26/1.65
% 1.26/1.65 subsumption: (17) {G0,W8,D3,L2,V2,M2} I { ! leq( X, Y ), addition( X, Y )
% 1.26/1.65 ==> Y }.
% 1.26/1.65 parent0: (5566) {G0,W8,D3,L2,V2,M2} { ! leq( X, Y ), addition( X, Y ) = Y
% 1.26/1.65 }.
% 1.26/1.65 substitution0:
% 1.26/1.65 X := X
% 1.26/1.65 Y := Y
% 1.26/1.65 end
% 1.26/1.65 permutation0:
% 1.26/1.65 0 ==> 0
% 1.26/1.65 1 ==> 1
% 1.26/1.65 end
% 1.26/1.65
% 1.26/1.65 subsumption: (18) {G0,W8,D3,L2,V2,M2} I { ! addition( X, Y ) ==> Y, leq( X
% 1.26/1.65 , Y ) }.
% 1.26/1.65 parent0: (5567) {G0,W8,D3,L2,V2,M2} { ! addition( X, Y ) = Y, leq( X, Y )
% 1.26/1.65 }.
% 1.26/1.65 substitution0:
% 1.26/1.65 X := X
% 1.26/1.65 Y := Y
% 1.26/1.65 end
% 1.26/1.65 permutation0:
% 1.26/1.65 0 ==> 0
% 1.26/1.65 1 ==> 1
% 1.26/1.65 end
% 1.26/1.65
% 1.26/1.65 subsumption: (19) {G0,W14,D4,L2,V0,M2} I { ! leq( multiplication(
% 1.26/1.65 strong_iteration( one ), skol1 ), strong_iteration( one ) ), ! leq(
% 1.26/1.65 strong_iteration( one ), multiplication( strong_iteration( one ), skol1 )
% 1.26/1.65 ) }.
% 1.26/1.65 parent0: (5568) {G0,W14,D4,L2,V0,M2} { ! leq( multiplication(
% 1.26/1.65 strong_iteration( one ), skol1 ), strong_iteration( one ) ), ! leq(
% 1.26/1.65 strong_iteration( one ), multiplication( strong_iteration( one ), skol1 )
% 1.26/1.65 ) }.
% 1.26/1.65 substitution0:
% 1.26/1.65 end
% 1.26/1.65 permutation0:
% 1.26/1.65 0 ==> 0
% 1.26/1.65 1 ==> 1
% 1.26/1.65 end
% 1.26/1.65
% 1.26/1.65 eqswap: (5657) {G0,W5,D3,L1,V1,M1} { X ==> addition( X, zero ) }.
% 1.26/1.65 parent0[0]: (2) {G0,W5,D3,L1,V1,M1} I { addition( X, zero ) ==> X }.
% 1.26/1.65 substitution0:
% 1.26/1.65 X := X
% 1.26/1.65 end
% 1.26/1.65
% 1.26/1.65 paramod: (5658) {G1,W5,D3,L1,V1,M1} { X ==> addition( zero, X ) }.
% 1.26/1.65 parent0[0]: (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X )
% 1.26/1.65 }.
% 1.26/1.65 parent1[0; 2]: (5657) {G0,W5,D3,L1,V1,M1} { X ==> addition( X, zero ) }.
% 1.26/1.65 substitution0:
% 1.26/1.65 X := X
% 1.26/1.65 Y := zero
% 1.26/1.65 end
% 1.26/1.65 substitution1:
% 1.26/1.65 X := X
% 1.26/1.65 end
% 1.26/1.65
% 1.26/1.65 eqswap: (5661) {G1,W5,D3,L1,V1,M1} { addition( zero, X ) ==> X }.
% 1.26/1.65 parent0[0]: (5658) {G1,W5,D3,L1,V1,M1} { X ==> addition( zero, X ) }.
% 1.26/1.65 substitution0:
% 1.26/1.65 X := X
% 1.26/1.65 end
% 1.26/1.65
% 1.26/1.65 subsumption: (20) {G1,W5,D3,L1,V1,M1} P(0,2) { addition( zero, X ) ==> X
% 1.26/1.65 }.
% 1.26/1.65 parent0: (5661) {G1,W5,D3,L1,V1,M1} { addition( zero, X ) ==> X }.
% 1.26/1.65 substitution0:
% 1.26/1.65 X := X
% 1.26/1.65 end
% 1.26/1.65 permutation0:
% 1.26/1.65 0 ==> 0
% 1.26/1.65 end
% 1.26/1.65
% 1.26/1.65 eqswap: (5663) {G0,W8,D3,L2,V2,M2} { ! Y ==> addition( X, Y ), leq( X, Y )
% 1.26/1.65 }.
% 1.26/1.65 parent0[0]: (18) {G0,W8,D3,L2,V2,M2} I { ! addition( X, Y ) ==> Y, leq( X,
% 1.26/1.65 Y ) }.
% 1.26/1.65 substitution0:
% 1.26/1.65 X := X
% 1.26/1.65 Y := Y
% 1.26/1.65 end
% 1.26/1.65
% 1.26/1.65 paramod: (5664) {G1,W14,D4,L2,V3,M2} { ! addition( X, Y ) ==> addition(
% 1.26/1.65 addition( Z, X ), Y ), leq( Z, addition( X, Y ) ) }.
% 1.26/1.65 parent0[0]: (1) {G0,W11,D4,L1,V3,M1} I { addition( Z, addition( Y, X ) )
% 1.26/1.65 ==> addition( addition( Z, Y ), X ) }.
% 1.26/1.65 parent1[0; 5]: (5663) {G0,W8,D3,L2,V2,M2} { ! Y ==> addition( X, Y ), leq
% 1.26/1.65 ( X, Y ) }.
% 1.26/1.65 substitution0:
% 1.26/1.65 X := Y
% 1.26/1.65 Y := X
% 1.26/1.65 Z := Z
% 1.26/1.65 end
% 1.26/1.65 substitution1:
% 1.26/1.65 X := Z
% 1.26/1.65 Y := addition( X, Y )
% 1.26/1.65 end
% 1.26/1.65
% 1.26/1.65 eqswap: (5665) {G1,W14,D4,L2,V3,M2} { ! addition( addition( Z, X ), Y )
% 1.26/1.65 ==> addition( X, Y ), leq( Z, addition( X, Y ) ) }.
% 1.26/1.65 parent0[0]: (5664) {G1,W14,D4,L2,V3,M2} { ! addition( X, Y ) ==> addition
% 1.26/1.65 ( addition( Z, X ), Y ), leq( Z, addition( X, Y ) ) }.
% 1.26/1.65 substitution0:
% 1.26/1.65 X := X
% 1.26/1.65 Y := Y
% 1.26/1.65 Z := Z
% 1.26/1.65 end
% 1.26/1.65
% 1.26/1.65 subsumption: (25) {G1,W14,D4,L2,V3,M2} P(1,18) { ! addition( addition( X, Y
% 1.26/1.65 ), Z ) ==> addition( Y, Z ), leq( X, addition( Y, Z ) ) }.
% 1.26/1.65 parent0: (5665) {G1,W14,D4,L2,V3,M2} { ! addition( addition( Z, X ), Y )
% 1.26/1.65 ==> addition( X, Y ), leq( Z, addition( X, Y ) ) }.
% 1.26/1.65 substitution0:
% 1.26/1.65 X := Y
% 1.26/1.65 Y := Z
% 1.26/1.65 Z := X
% 1.26/1.65 end
% 1.26/1.65 permutation0:
% 1.26/1.65 0 ==> 0
% 1.26/1.65 1 ==> 1
% 1.26/1.65 end
% 1.26/1.65
% 1.26/1.65 eqswap: (5666) {G0,W11,D4,L1,V3,M1} { addition( addition( X, Y ), Z ) ==>
% 1.26/1.65 addition( X, addition( Y, Z ) ) }.
% 1.26/1.65 parent0[0]: (1) {G0,W11,D4,L1,V3,M1} I { addition( Z, addition( Y, X ) )
% 1.26/1.65 ==> addition( addition( Z, Y ), X ) }.
% 1.26/1.65 substitution0:
% 1.26/1.65 X := Z
% 1.26/1.65 Y := Y
% 1.26/1.65 Z := X
% 1.26/1.65 end
% 1.26/1.65
% 1.26/1.65 paramod: (5669) {G1,W11,D4,L1,V3,M1} { addition( addition( X, Y ), Z ) ==>
% 1.26/1.65 addition( addition( Y, Z ), X ) }.
% 1.26/1.65 parent0[0]: (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X )
% 1.26/1.65 }.
% 1.26/1.65 parent1[0; 6]: (5666) {G0,W11,D4,L1,V3,M1} { addition( addition( X, Y ), Z
% 1.26/1.65 ) ==> addition( X, addition( Y, Z ) ) }.
% 1.26/1.65 substitution0:
% 1.26/1.65 X := X
% 1.26/1.65 Y := addition( Y, Z )
% 1.26/1.65 end
% 1.26/1.65 substitution1:
% 1.26/1.65 X := X
% 1.26/1.65 Y := Y
% 1.26/1.65 Z := Z
% 1.26/1.65 end
% 1.26/1.65
% 1.26/1.65 subsumption: (26) {G1,W11,D4,L1,V3,M1} P(1,0) { addition( addition( X, Y )
% 1.26/1.65 , Z ) = addition( addition( Y, Z ), X ) }.
% 1.26/1.65 parent0: (5669) {G1,W11,D4,L1,V3,M1} { addition( addition( X, Y ), Z ) ==>
% 1.26/1.65 addition( addition( Y, Z ), X ) }.
% 1.26/1.65 substitution0:
% 1.26/1.65 X := X
% 1.26/1.65 Y := Y
% 1.26/1.65 Z := Z
% 1.26/1.65 end
% 1.26/1.65 permutation0:
% 1.26/1.65 0 ==> 0
% 1.26/1.65 end
% 1.26/1.65
% 1.26/1.65 eqswap: (5684) {G0,W11,D4,L1,V3,M1} { addition( addition( X, Y ), Z ) ==>
% 1.26/1.65 addition( X, addition( Y, Z ) ) }.
% 1.26/1.65 parent0[0]: (1) {G0,W11,D4,L1,V3,M1} I { addition( Z, addition( Y, X ) )
% 1.26/1.65 ==> addition( addition( Z, Y ), X ) }.
% 1.26/1.65 substitution0:
% 1.26/1.65 X := Z
% 1.26/1.65 Y := Y
% 1.26/1.65 Z := X
% 1.26/1.65 end
% 1.26/1.65
% 1.26/1.65 paramod: (5690) {G1,W12,D4,L2,V3,M2} { addition( addition( X, Y ), Z ) ==>
% 1.26/1.65 addition( X, Z ), ! leq( Y, Z ) }.
% 1.26/1.65 parent0[1]: (17) {G0,W8,D3,L2,V2,M2} I { ! leq( X, Y ), addition( X, Y )
% 1.26/1.65 ==> Y }.
% 1.26/1.65 parent1[0; 8]: (5684) {G0,W11,D4,L1,V3,M1} { addition( addition( X, Y ), Z
% 1.26/1.65 ) ==> addition( X, addition( Y, Z ) ) }.
% 1.26/1.65 substitution0:
% 1.26/1.65 X := Y
% 1.26/1.65 Y := Z
% 1.26/1.65 end
% 1.26/1.65 substitution1:
% 1.26/1.65 X := X
% 1.26/1.65 Y := Y
% 1.26/1.65 Z := Z
% 1.26/1.65 end
% 1.26/1.65
% 1.26/1.65 subsumption: (35) {G1,W12,D4,L2,V3,M2} P(17,1) { addition( addition( Z, X )
% 1.26/1.65 , Y ) ==> addition( Z, Y ), ! leq( X, Y ) }.
% 1.26/1.65 parent0: (5690) {G1,W12,D4,L2,V3,M2} { addition( addition( X, Y ), Z ) ==>
% 1.26/1.65 addition( X, Z ), ! leq( Y, Z ) }.
% 1.26/1.65 substitution0:
% 1.26/1.65 X := Z
% 1.26/1.65 Y := X
% 1.26/1.65 Z := Y
% 1.26/1.65 end
% 1.26/1.65 permutation0:
% 1.26/1.65 0 ==> 0
% 1.26/1.65 1 ==> 1
% 1.26/1.65 end
% 1.26/1.65
% 1.26/1.65 eqswap: (5737) {G0,W8,D3,L2,V2,M2} { Y ==> addition( X, Y ), ! leq( X, Y )
% 1.26/1.65 }.
% 1.26/1.65 parent0[1]: (17) {G0,W8,D3,L2,V2,M2} I { ! leq( X, Y ), addition( X, Y )
% 1.26/1.65 ==> Y }.
% 1.26/1.65 substitution0:
% 1.26/1.65 X := X
% 1.26/1.65 Y := Y
% 1.26/1.65 end
% 1.26/1.65
% 1.26/1.65 paramod: (5738) {G1,W8,D3,L2,V2,M2} { X ==> addition( X, Y ), ! leq( Y, X
% 1.26/1.65 ) }.
% 1.26/1.65 parent0[0]: (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X )
% 1.26/1.65 }.
% 1.26/1.65 parent1[0; 2]: (5737) {G0,W8,D3,L2,V2,M2} { Y ==> addition( X, Y ), ! leq
% 1.26/1.65 ( X, Y ) }.
% 1.26/1.65 substitution0:
% 1.26/1.65 X := Y
% 1.26/1.65 Y := X
% 1.26/1.65 end
% 1.26/1.65 substitution1:
% 1.26/1.65 X := Y
% 1.26/1.65 Y := X
% 1.26/1.65 end
% 1.26/1.65
% 1.26/1.65 eqswap: (5741) {G1,W8,D3,L2,V2,M2} { addition( X, Y ) ==> X, ! leq( Y, X )
% 1.26/1.65 }.
% 1.26/1.65 parent0[0]: (5738) {G1,W8,D3,L2,V2,M2} { X ==> addition( X, Y ), ! leq( Y
% 1.26/1.65 , X ) }.
% 1.26/1.65 substitution0:
% 1.26/1.65 X := X
% 1.26/1.65 Y := Y
% 1.26/1.65 end
% 1.26/1.65
% 1.26/1.65 subsumption: (36) {G1,W8,D3,L2,V2,M2} P(17,0) { addition( Y, X ) ==> Y, !
% 1.26/1.65 leq( X, Y ) }.
% 1.26/1.65 parent0: (5741) {G1,W8,D3,L2,V2,M2} { addition( X, Y ) ==> X, ! leq( Y, X
% 1.26/1.65 ) }.
% 1.26/1.65 substitution0:
% 1.26/1.65 X := Y
% 1.26/1.65 Y := X
% 1.26/1.65 end
% 1.26/1.65 permutation0:
% 1.26/1.65 0 ==> 0
% 1.26/1.65 1 ==> 1
% 1.26/1.65 end
% 1.26/1.65
% 1.26/1.65 eqswap: (5743) {G0,W8,D3,L2,V2,M2} { ! Y ==> addition( X, Y ), leq( X, Y )
% 1.26/1.65 }.
% 1.26/1.65 parent0[0]: (18) {G0,W8,D3,L2,V2,M2} I { ! addition( X, Y ) ==> Y, leq( X,
% 1.26/1.65 Y ) }.
% 1.26/1.65 substitution0:
% 1.26/1.65 X := X
% 1.26/1.65 Y := Y
% 1.26/1.65 end
% 1.26/1.65
% 1.26/1.65 paramod: (5744) {G1,W16,D4,L2,V3,M2} { ! multiplication( X, Y ) ==>
% 1.26/1.65 multiplication( X, addition( Z, Y ) ), leq( multiplication( X, Z ),
% 1.26/1.65 multiplication( X, Y ) ) }.
% 1.26/1.65 parent0[0]: (7) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Y ),
% 1.26/1.65 multiplication( X, Z ) ) ==> multiplication( X, addition( Y, Z ) ) }.
% 1.26/1.65 parent1[0; 5]: (5743) {G0,W8,D3,L2,V2,M2} { ! Y ==> addition( X, Y ), leq
% 1.26/1.65 ( X, Y ) }.
% 1.26/1.65 substitution0:
% 1.26/1.65 X := X
% 1.26/1.65 Y := Z
% 1.26/1.65 Z := Y
% 1.26/1.65 end
% 1.26/1.65 substitution1:
% 1.26/1.65 X := multiplication( X, Z )
% 1.26/1.65 Y := multiplication( X, Y )
% 1.26/1.65 end
% 1.26/1.65
% 1.26/1.65 eqswap: (5745) {G1,W16,D4,L2,V3,M2} { ! multiplication( X, addition( Z, Y
% 1.26/1.65 ) ) ==> multiplication( X, Y ), leq( multiplication( X, Z ),
% 1.26/1.65 multiplication( X, Y ) ) }.
% 1.26/1.65 parent0[0]: (5744) {G1,W16,D4,L2,V3,M2} { ! multiplication( X, Y ) ==>
% 1.26/1.65 multiplication( X, addition( Z, Y ) ), leq( multiplication( X, Z ),
% 1.26/1.65 multiplication( X, Y ) ) }.
% 1.26/1.65 substitution0:
% 1.26/1.65 X := X
% 1.26/1.65 Y := Y
% 1.26/1.65 Z := Z
% 1.26/1.65 end
% 1.26/1.65
% 1.26/1.65 subsumption: (67) {G1,W16,D4,L2,V3,M2} P(7,18) { ! multiplication( X,
% 1.26/1.65 addition( Y, Z ) ) ==> multiplication( X, Z ), leq( multiplication( X, Y
% 1.26/1.65 ), multiplication( X, Z ) ) }.
% 1.26/1.65 parent0: (5745) {G1,W16,D4,L2,V3,M2} { ! multiplication( X, addition( Z, Y
% 1.26/1.65 ) ) ==> multiplication( X, Y ), leq( multiplication( X, Z ),
% 1.26/1.65 multiplication( X, Y ) ) }.
% 1.26/1.65 substitution0:
% 1.26/1.65 X := X
% 1.26/1.65 Y := Z
% 1.26/1.65 Z := Y
% 1.26/1.65 end
% 1.26/1.65 permutation0:
% 1.26/1.65 0 ==> 0
% 1.26/1.65 1 ==> 1
% 1.26/1.65 end
% 1.26/1.65
% 1.26/1.65 eqswap: (5747) {G0,W13,D4,L1,V3,M1} { multiplication( addition( X, Z ), Y
% 1.26/1.65 ) ==> addition( multiplication( X, Y ), multiplication( Z, Y ) ) }.
% 1.26/1.65 parent0[0]: (8) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Z ),
% 1.26/1.65 multiplication( Y, Z ) ) ==> multiplication( addition( X, Y ), Z ) }.
% 1.26/1.65 substitution0:
% 1.26/1.65 X := X
% 1.26/1.65 Y := Z
% 1.26/1.65 Z := Y
% 1.26/1.65 end
% 1.26/1.65
% 1.26/1.65 paramod: (5749) {G1,W11,D4,L1,V2,M1} { multiplication( addition( X, one )
% 1.26/1.65 , Y ) ==> addition( multiplication( X, Y ), Y ) }.
% 1.26/1.65 parent0[0]: (6) {G0,W5,D3,L1,V1,M1} I { multiplication( one, X ) ==> X }.
% 1.26/1.65 parent1[0; 10]: (5747) {G0,W13,D4,L1,V3,M1} { multiplication( addition( X
% 1.26/1.65 , Z ), Y ) ==> addition( multiplication( X, Y ), multiplication( Z, Y ) )
% 1.26/1.65 }.
% 1.26/1.65 substitution0:
% 1.26/1.65 X := Y
% 1.26/1.65 end
% 1.26/1.65 substitution1:
% 1.26/1.65 X := X
% 1.26/1.65 Y := Y
% 1.26/1.65 Z := one
% 1.26/1.65 end
% 1.26/1.65
% 1.26/1.65 eqswap: (5751) {G1,W11,D4,L1,V2,M1} { addition( multiplication( X, Y ), Y
% 1.26/1.65 ) ==> multiplication( addition( X, one ), Y ) }.
% 1.26/1.65 parent0[0]: (5749) {G1,W11,D4,L1,V2,M1} { multiplication( addition( X, one
% 1.26/1.65 ), Y ) ==> addition( multiplication( X, Y ), Y ) }.
% 1.26/1.65 substitution0:
% 1.26/1.65 X := X
% 1.26/1.65 Y := Y
% 1.26/1.65 end
% 1.26/1.65
% 1.26/1.65 subsumption: (102) {G1,W11,D4,L1,V2,M1} P(6,8) { addition( multiplication(
% 1.26/1.65 Y, X ), X ) = multiplication( addition( Y, one ), X ) }.
% 1.26/1.65 parent0: (5751) {G1,W11,D4,L1,V2,M1} { addition( multiplication( X, Y ), Y
% 1.26/1.65 ) ==> multiplication( addition( X, one ), Y ) }.
% 1.26/1.65 substitution0:
% 1.26/1.65 X := Y
% 1.26/1.65 Y := X
% 1.26/1.65 end
% 1.26/1.65 permutation0:
% 1.26/1.65 0 ==> 0
% 1.26/1.65 end
% 1.26/1.65
% 1.26/1.65 eqswap: (5753) {G1,W14,D4,L2,V3,M2} { ! addition( Y, Z ) ==> addition(
% 1.26/1.65 addition( X, Y ), Z ), leq( X, addition( Y, Z ) ) }.
% 1.26/1.65 parent0[0]: (25) {G1,W14,D4,L2,V3,M2} P(1,18) { ! addition( addition( X, Y
% 1.26/1.65 ), Z ) ==> addition( Y, Z ), leq( X, addition( Y, Z ) ) }.
% 1.26/1.65 substitution0:
% 1.26/1.65 X := X
% 1.26/1.65 Y := Y
% 1.26/1.65 Z := Z
% 1.26/1.65 end
% 1.26/1.65
% 1.26/1.65 paramod: (5756) {G1,W12,D3,L2,V2,M2} { ! addition( X, Y ) ==> addition( X
% 1.26/1.65 , Y ), leq( X, addition( X, Y ) ) }.
% 1.26/1.65 parent0[0]: (3) {G0,W5,D3,L1,V1,M1} I { addition( X, X ) ==> X }.
% 1.26/1.65 parent1[0; 6]: (5753) {G1,W14,D4,L2,V3,M2} { ! addition( Y, Z ) ==>
% 1.26/1.65 addition( addition( X, Y ), Z ), leq( X, addition( Y, Z ) ) }.
% 1.26/1.65 substitution0:
% 1.26/1.65 X := X
% 1.26/1.65 end
% 1.26/1.65 substitution1:
% 1.26/1.65 X := X
% 1.26/1.65 Y := X
% 1.26/1.65 Z := Y
% 1.26/1.65 end
% 1.26/1.65
% 1.26/1.65 eqrefl: (5759) {G0,W5,D3,L1,V2,M1} { leq( X, addition( X, Y ) ) }.
% 1.26/1.65 parent0[0]: (5756) {G1,W12,D3,L2,V2,M2} { ! addition( X, Y ) ==> addition
% 1.26/1.65 ( X, Y ), leq( X, addition( X, Y ) ) }.
% 1.26/1.65 substitution0:
% 1.26/1.65 X := X
% 1.26/1.65 Y := Y
% 1.26/1.65 end
% 1.26/1.65
% 1.26/1.65 subsumption: (323) {G2,W5,D3,L1,V2,M1} P(3,25);q { leq( X, addition( X, Y )
% 1.26/1.65 ) }.
% 1.26/1.65 parent0: (5759) {G0,W5,D3,L1,V2,M1} { leq( X, addition( X, Y ) ) }.
% 1.26/1.65 substitution0:
% 1.26/1.65 X := X
% 1.26/1.65 Y := Y
% 1.26/1.65 end
% 1.26/1.65 permutation0:
% 1.26/1.65 0 ==> 0
% 1.26/1.65 end
% 1.26/1.65
% 1.26/1.65 paramod: (5760) {G1,W5,D3,L1,V2,M1} { leq( X, addition( Y, X ) ) }.
% 1.26/1.65 parent0[0]: (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X )
% 1.26/1.65 }.
% 1.26/1.65 parent1[0; 2]: (323) {G2,W5,D3,L1,V2,M1} P(3,25);q { leq( X, addition( X, Y
% 1.26/1.65 ) ) }.
% 1.26/1.65 substitution0:
% 1.26/1.65 X := X
% 1.26/1.65 Y := Y
% 1.26/1.65 end
% 1.26/1.65 substitution1:
% 1.26/1.65 X := X
% 1.26/1.65 Y := Y
% 1.26/1.65 end
% 1.26/1.65
% 1.26/1.65 subsumption: (333) {G3,W5,D3,L1,V2,M1} P(0,323) { leq( X, addition( Y, X )
% 1.26/1.65 ) }.
% 1.26/1.65 parent0: (5760) {G1,W5,D3,L1,V2,M1} { leq( X, addition( Y, X ) ) }.
% 1.26/1.65 substitution0:
% 1.26/1.65 X := X
% 1.26/1.65 Y := Y
% 1.26/1.65 end
% 1.26/1.65 permutation0:
% 1.26/1.65 0 ==> 0
% 1.26/1.65 end
% 1.26/1.65
% 1.26/1.65 eqswap: (5762) {G1,W11,D4,L1,V3,M1} { addition( addition( Y, Z ), X ) =
% 1.26/1.65 addition( addition( X, Y ), Z ) }.
% 1.26/1.65 parent0[0]: (26) {G1,W11,D4,L1,V3,M1} P(1,0) { addition( addition( X, Y ),
% 1.26/1.65 Z ) = addition( addition( Y, Z ), X ) }.
% 1.26/1.65 substitution0:
% 1.26/1.65 X := X
% 1.26/1.65 Y := Y
% 1.26/1.65 Z := Z
% 1.26/1.65 end
% 1.26/1.65
% 1.26/1.65 paramod: (5763) {G2,W7,D4,L1,V3,M1} { leq( X, addition( addition( X, Y ),
% 1.26/1.65 Z ) ) }.
% 1.26/1.65 parent0[0]: (5762) {G1,W11,D4,L1,V3,M1} { addition( addition( Y, Z ), X )
% 1.26/1.65 = addition( addition( X, Y ), Z ) }.
% 1.26/1.65 parent1[0; 2]: (333) {G3,W5,D3,L1,V2,M1} P(0,323) { leq( X, addition( Y, X
% 1.26/1.65 ) ) }.
% 1.26/1.65 substitution0:
% 1.26/1.65 X := X
% 1.26/1.65 Y := Y
% 1.26/1.65 Z := Z
% 1.26/1.65 end
% 1.26/1.65 substitution1:
% 1.26/1.65 X := X
% 1.26/1.65 Y := addition( Y, Z )
% 1.26/1.65 end
% 1.26/1.65
% 1.26/1.65 paramod: (5764) {G2,W7,D4,L1,V3,M1} { leq( X, addition( addition( Z, X ),
% 1.26/1.65 Y ) ) }.
% 1.26/1.65 parent0[0]: (5762) {G1,W11,D4,L1,V3,M1} { addition( addition( Y, Z ), X )
% 1.26/1.65 = addition( addition( X, Y ), Z ) }.
% 1.26/1.65 parent1[0; 2]: (5763) {G2,W7,D4,L1,V3,M1} { leq( X, addition( addition( X
% 1.26/1.65 , Y ), Z ) ) }.
% 1.26/1.65 substitution0:
% 1.26/1.65 X := Z
% 1.26/1.65 Y := X
% 1.26/1.65 Z := Y
% 1.26/1.65 end
% 1.26/1.65 substitution1:
% 1.26/1.65 X := X
% 1.26/1.65 Y := Y
% 1.26/1.65 Z := Z
% 1.26/1.65 end
% 1.26/1.65
% 1.26/1.65 subsumption: (363) {G4,W7,D4,L1,V3,M1} P(26,333) { leq( Z, addition(
% 1.26/1.65 addition( Y, Z ), X ) ) }.
% 1.26/1.65 parent0: (5764) {G2,W7,D4,L1,V3,M1} { leq( X, addition( addition( Z, X ),
% 1.26/1.65 Y ) ) }.
% 1.26/1.65 substitution0:
% 1.26/1.65 X := Z
% 1.26/1.65 Y := X
% 1.26/1.65 Z := Y
% 1.26/1.65 end
% 1.26/1.65 permutation0:
% 1.26/1.65 0 ==> 0
% 1.26/1.65 end
% 1.26/1.65
% 1.26/1.65 paramod: (5767) {G2,W8,D3,L2,V3,M2} { leq( X, addition( Y, Z ) ), ! leq( X
% 1.26/1.65 , Z ) }.
% 1.26/1.65 parent0[0]: (35) {G1,W12,D4,L2,V3,M2} P(17,1) { addition( addition( Z, X )
% 1.26/1.65 , Y ) ==> addition( Z, Y ), ! leq( X, Y ) }.
% 1.26/1.65 parent1[0; 2]: (363) {G4,W7,D4,L1,V3,M1} P(26,333) { leq( Z, addition(
% 1.26/1.65 addition( Y, Z ), X ) ) }.
% 1.26/1.65 substitution0:
% 1.26/1.65 X := X
% 1.26/1.65 Y := Z
% 1.26/1.65 Z := Y
% 1.26/1.65 end
% 1.26/1.65 substitution1:
% 1.26/1.65 X := Z
% 1.26/1.65 Y := Y
% 1.26/1.65 Z := X
% 1.26/1.65 end
% 1.26/1.65
% 1.26/1.65 subsumption: (615) {G5,W8,D3,L2,V3,M2} P(35,363) { leq( Y, addition( X, Z )
% 1.26/1.65 ), ! leq( Y, Z ) }.
% 1.26/1.65 parent0: (5767) {G2,W8,D3,L2,V3,M2} { leq( X, addition( Y, Z ) ), ! leq( X
% 1.26/1.65 , Z ) }.
% 1.26/1.65 substitution0:
% 1.26/1.65 X := Y
% 1.26/1.65 Y := X
% 1.26/1.65 Z := Z
% 1.26/1.65 end
% 1.26/1.65 permutation0:
% 1.26/1.65 0 ==> 0
% 1.26/1.65 1 ==> 1
% 1.26/1.65 end
% 1.26/1.65
% 1.26/1.65 eqswap: (5771) {G1,W16,D4,L2,V3,M2} { ! multiplication( X, Z ) ==>
% 1.26/1.65 multiplication( X, addition( Y, Z ) ), leq( multiplication( X, Y ),
% 1.26/1.65 multiplication( X, Z ) ) }.
% 1.26/1.65 parent0[0]: (67) {G1,W16,D4,L2,V3,M2} P(7,18) { ! multiplication( X,
% 1.26/1.65 addition( Y, Z ) ) ==> multiplication( X, Z ), leq( multiplication( X, Y
% 1.26/1.65 ), multiplication( X, Z ) ) }.
% 1.26/1.65 substitution0:
% 1.26/1.65 X := X
% 1.26/1.65 Y := Y
% 1.26/1.65 Z := Z
% 1.26/1.65 end
% 1.26/1.65
% 1.26/1.65 paramod: (5772) {G2,W14,D3,L2,V2,M2} { ! multiplication( X, Y ) ==>
% 1.26/1.65 multiplication( X, Y ), leq( multiplication( X, zero ), multiplication( X
% 1.26/1.65 , Y ) ) }.
% 1.26/1.65 parent0[0]: (20) {G1,W5,D3,L1,V1,M1} P(0,2) { addition( zero, X ) ==> X }.
% 1.26/1.65 parent1[0; 7]: (5771) {G1,W16,D4,L2,V3,M2} { ! multiplication( X, Z ) ==>
% 1.26/1.65 multiplication( X, addition( Y, Z ) ), leq( multiplication( X, Y ),
% 1.26/1.65 multiplication( X, Z ) ) }.
% 1.26/1.65 substitution0:
% 1.26/1.65 X := Y
% 1.26/1.65 end
% 1.26/1.65 substitution1:
% 1.26/1.65 X := X
% 1.26/1.65 Y := zero
% 1.26/1.65 Z := Y
% 1.26/1.65 end
% 1.26/1.65
% 1.26/1.65 eqrefl: (5773) {G0,W7,D3,L1,V2,M1} { leq( multiplication( X, zero ),
% 1.26/1.65 multiplication( X, Y ) ) }.
% 1.26/1.65 parent0[0]: (5772) {G2,W14,D3,L2,V2,M2} { ! multiplication( X, Y ) ==>
% 1.26/1.65 multiplication( X, Y ), leq( multiplication( X, zero ), multiplication( X
% 1.26/1.65 , Y ) ) }.
% 1.26/1.65 substitution0:
% 1.26/1.65 X := X
% 1.26/1.65 Y := Y
% 1.26/1.65 end
% 1.26/1.65
% 1.26/1.65 subsumption: (1802) {G2,W7,D3,L1,V2,M1} P(20,67);q { leq( multiplication( Y
% 1.26/1.65 , zero ), multiplication( Y, X ) ) }.
% 1.26/1.65 parent0: (5773) {G0,W7,D3,L1,V2,M1} { leq( multiplication( X, zero ),
% 1.26/1.65 multiplication( X, Y ) ) }.
% 1.26/1.65 substitution0:
% 1.26/1.65 X := Y
% 1.26/1.65 Y := X
% 1.26/1.65 end
% 1.26/1.65 permutation0:
% 1.26/1.65 0 ==> 0
% 1.26/1.65 end
% 1.26/1.65
% 1.26/1.65 paramod: (5775) {G1,W5,D3,L1,V1,M1} { leq( multiplication( X, zero ), X )
% 1.26/1.65 }.
% 1.26/1.65 parent0[0]: (5) {G0,W5,D3,L1,V1,M1} I { multiplication( X, one ) ==> X }.
% 1.26/1.65 parent1[0; 4]: (1802) {G2,W7,D3,L1,V2,M1} P(20,67);q { leq( multiplication
% 1.26/1.65 ( Y, zero ), multiplication( Y, X ) ) }.
% 1.26/1.65 substitution0:
% 1.26/1.65 X := X
% 1.26/1.65 end
% 1.26/1.65 substitution1:
% 1.26/1.65 X := one
% 1.26/1.65 Y := X
% 1.26/1.65 end
% 1.26/1.65
% 1.26/1.65 subsumption: (1877) {G3,W5,D3,L1,V1,M1} P(5,1802) { leq( multiplication( X
% 1.26/1.65 , zero ), X ) }.
% 1.26/1.65 parent0: (5775) {G1,W5,D3,L1,V1,M1} { leq( multiplication( X, zero ), X )
% 1.26/1.65 }.
% 1.26/1.65 substitution0:
% 1.26/1.65 X := X
% 1.26/1.65 end
% 1.26/1.65 permutation0:
% 1.26/1.65 0 ==> 0
% 1.26/1.65 end
% 1.26/1.65
% 1.26/1.65 eqswap: (5776) {G1,W8,D3,L2,V2,M2} { X ==> addition( X, Y ), ! leq( Y, X )
% 1.26/1.65 }.
% 1.26/1.65 parent0[0]: (36) {G1,W8,D3,L2,V2,M2} P(17,0) { addition( Y, X ) ==> Y, !
% 1.26/1.65 leq( X, Y ) }.
% 1.26/1.65 substitution0:
% 1.26/1.65 X := Y
% 1.26/1.65 Y := X
% 1.26/1.65 end
% 1.26/1.65
% 1.26/1.65 resolution: (5777) {G2,W7,D4,L1,V1,M1} { X ==> addition( X, multiplication
% 1.26/1.65 ( X, zero ) ) }.
% 1.26/1.65 parent0[1]: (5776) {G1,W8,D3,L2,V2,M2} { X ==> addition( X, Y ), ! leq( Y
% 1.26/1.65 , X ) }.
% 1.26/1.65 parent1[0]: (1877) {G3,W5,D3,L1,V1,M1} P(5,1802) { leq( multiplication( X,
% 1.26/1.65 zero ), X ) }.
% 1.26/1.65 substitution0:
% 1.26/1.65 X := X
% 1.26/1.65 Y := multiplication( X, zero )
% 1.26/1.65 end
% 1.26/1.65 substitution1:
% 1.26/1.65 X := X
% 1.26/1.65 end
% 1.26/1.65
% 1.26/1.65 eqswap: (5778) {G2,W7,D4,L1,V1,M1} { addition( X, multiplication( X, zero
% 1.26/1.65 ) ) ==> X }.
% 1.26/1.65 parent0[0]: (5777) {G2,W7,D4,L1,V1,M1} { X ==> addition( X, multiplication
% 1.26/1.65 ( X, zero ) ) }.
% 1.26/1.65 substitution0:
% 1.26/1.65 X := X
% 1.26/1.65 end
% 1.26/1.65
% 1.26/1.65 subsumption: (1881) {G4,W7,D4,L1,V1,M1} R(1877,36) { addition( X,
% 1.26/1.65 multiplication( X, zero ) ) ==> X }.
% 1.26/1.65 parent0: (5778) {G2,W7,D4,L1,V1,M1} { addition( X, multiplication( X, zero
% 1.26/1.65 ) ) ==> X }.
% 1.26/1.65 substitution0:
% 1.26/1.65 X := X
% 1.26/1.65 end
% 1.26/1.65 permutation0:
% 1.26/1.65 0 ==> 0
% 1.26/1.65 end
% 1.26/1.65
% 1.26/1.65 eqswap: (5779) {G0,W8,D3,L2,V2,M2} { Y ==> addition( X, Y ), ! leq( X, Y )
% 1.26/1.65 }.
% 1.26/1.65 parent0[1]: (17) {G0,W8,D3,L2,V2,M2} I { ! leq( X, Y ), addition( X, Y )
% 1.26/1.65 ==> Y }.
% 1.26/1.65 substitution0:
% 1.26/1.65 X := X
% 1.26/1.65 Y := Y
% 1.26/1.65 end
% 1.26/1.65
% 1.26/1.65 resolution: (5780) {G1,W7,D4,L1,V1,M1} { X ==> addition( multiplication( X
% 1.26/1.65 , zero ), X ) }.
% 1.26/1.65 parent0[1]: (5779) {G0,W8,D3,L2,V2,M2} { Y ==> addition( X, Y ), ! leq( X
% 1.26/1.65 , Y ) }.
% 1.26/1.65 parent1[0]: (1877) {G3,W5,D3,L1,V1,M1} P(5,1802) { leq( multiplication( X,
% 1.26/1.65 zero ), X ) }.
% 1.26/1.65 substitution0:
% 1.26/1.65 X := multiplication( X, zero )
% 1.26/1.65 Y := X
% 1.26/1.65 end
% 1.26/1.65 substitution1:
% 1.26/1.65 X := X
% 1.26/1.65 end
% 1.26/1.65
% 1.26/1.65 eqswap: (5781) {G1,W7,D4,L1,V1,M1} { addition( multiplication( X, zero ),
% 1.26/1.65 X ) ==> X }.
% 1.26/1.65 parent0[0]: (5780) {G1,W7,D4,L1,V1,M1} { X ==> addition( multiplication( X
% 1.26/1.65 , zero ), X ) }.
% 1.26/1.65 substitution0:
% 1.26/1.65 X := X
% 1.26/1.65 end
% 1.26/1.65
% 1.26/1.65 subsumption: (1885) {G4,W7,D4,L1,V1,M1} R(1877,17) { addition(
% 1.26/1.65 multiplication( X, zero ), X ) ==> X }.
% 1.26/1.65 parent0: (5781) {G1,W7,D4,L1,V1,M1} { addition( multiplication( X, zero )
% 1.26/1.65 , X ) ==> X }.
% 1.26/1.65 substitution0:
% 1.26/1.65 X := X
% 1.26/1.65 end
% 1.26/1.65 permutation0:
% 1.26/1.65 0 ==> 0
% 1.26/1.65 end
% 1.26/1.65
% 1.26/1.65 paramod: (5783) {G5,W8,D3,L2,V2,M2} { leq( X, Y ), ! leq( X,
% 1.26/1.65 multiplication( Y, zero ) ) }.
% 1.26/1.65 parent0[0]: (1881) {G4,W7,D4,L1,V1,M1} R(1877,36) { addition( X,
% 1.26/1.65 multiplication( X, zero ) ) ==> X }.
% 1.26/1.65 parent1[0; 2]: (615) {G5,W8,D3,L2,V3,M2} P(35,363) { leq( Y, addition( X, Z
% 1.26/1.65 ) ), ! leq( Y, Z ) }.
% 1.26/1.65 substitution0:
% 1.26/1.65 X := Y
% 1.26/1.65 end
% 1.26/1.65 substitution1:
% 1.26/1.65 X := Y
% 1.26/1.65 Y := X
% 1.26/1.65 Z := multiplication( Y, zero )
% 1.26/1.65 end
% 1.26/1.65
% 1.26/1.65 subsumption: (2154) {G6,W8,D3,L2,V2,M2} P(1881,615) { leq( Y, X ), ! leq( Y
% 1.26/1.65 , multiplication( X, zero ) ) }.
% 1.26/1.65 parent0: (5783) {G5,W8,D3,L2,V2,M2} { leq( X, Y ), ! leq( X,
% 1.26/1.65 multiplication( Y, zero ) ) }.
% 1.26/1.65 substitution0:
% 1.26/1.65 X := Y
% 1.26/1.65 Y := X
% 1.26/1.65 end
% 1.26/1.65 permutation0:
% 1.26/1.65 0 ==> 0
% 1.26/1.65 1 ==> 1
% 1.26/1.65 end
% 1.26/1.65
% 1.26/1.65 eqswap: (5784) {G1,W11,D4,L1,V2,M1} { multiplication( addition( X, one ),
% 1.26/1.65 Y ) = addition( multiplication( X, Y ), Y ) }.
% 1.26/1.65 parent0[0]: (102) {G1,W11,D4,L1,V2,M1} P(6,8) { addition( multiplication( Y
% 1.26/1.65 , X ), X ) = multiplication( addition( Y, one ), X ) }.
% 1.26/1.65 substitution0:
% 1.26/1.65 X := Y
% 1.26/1.65 Y := X
% 1.26/1.65 end
% 1.26/1.65
% 1.26/1.65 paramod: (5785) {G1,W17,D5,L2,V3,M2} { ! leq( X, addition( addition(
% 1.26/1.65 multiplication( Y, X ), X ), Z ) ), leq( X, multiplication(
% 1.26/1.65 strong_iteration( addition( Y, one ) ), Z ) ) }.
% 1.26/1.65 parent0[0]: (5784) {G1,W11,D4,L1,V2,M1} { multiplication( addition( X, one
% 1.26/1.65 ), Y ) = addition( multiplication( X, Y ), Y ) }.
% 1.26/1.65 parent1[0; 4]: (15) {G0,W13,D4,L2,V3,M2} I { ! leq( Z, addition(
% 1.26/1.65 multiplication( X, Z ), Y ) ), leq( Z, multiplication( strong_iteration(
% 1.26/1.65 X ), Y ) ) }.
% 1.26/1.65 substitution0:
% 1.26/1.65 X := Y
% 1.26/1.65 Y := X
% 1.26/1.65 end
% 1.26/1.65 substitution1:
% 1.26/1.65 X := addition( Y, one )
% 1.26/1.65 Y := Z
% 1.26/1.65 Z := X
% 1.26/1.65 end
% 1.26/1.65
% 1.26/1.65 resolution: (5786) {G2,W8,D5,L1,V3,M1} { leq( X, multiplication(
% 1.26/1.65 strong_iteration( addition( Y, one ) ), Z ) ) }.
% 1.26/1.65 parent0[0]: (5785) {G1,W17,D5,L2,V3,M2} { ! leq( X, addition( addition(
% 1.26/1.65 multiplication( Y, X ), X ), Z ) ), leq( X, multiplication(
% 1.26/1.65 strong_iteration( addition( Y, one ) ), Z ) ) }.
% 1.26/1.65 parent1[0]: (363) {G4,W7,D4,L1,V3,M1} P(26,333) { leq( Z, addition(
% 1.26/1.65 addition( Y, Z ), X ) ) }.
% 1.26/1.65 substitution0:
% 1.26/1.65 X := X
% 1.26/1.65 Y := Y
% 1.26/1.65 Z := Z
% 1.26/1.65 end
% 1.26/1.65 substitution1:
% 1.26/1.65 X := Z
% 1.26/1.65 Y := multiplication( Y, X )
% 1.26/1.65 Z := X
% 1.26/1.65 end
% 1.26/1.65
% 1.26/1.65 subsumption: (4213) {G5,W8,D5,L1,V3,M1} P(102,15);r(363) { leq( Y,
% 1.26/1.65 multiplication( strong_iteration( addition( X, one ) ), Z ) ) }.
% 1.26/1.65 parent0: (5786) {G2,W8,D5,L1,V3,M1} { leq( X, multiplication(
% 1.26/1.65 strong_iteration( addition( Y, one ) ), Z ) ) }.
% 1.26/1.65 substitution0:
% 1.26/1.65 X := Y
% 1.26/1.65 Y := X
% 1.26/1.65 Z := Z
% 1.26/1.65 end
% 1.26/1.65 permutation0:
% 1.26/1.65 0 ==> 0
% 1.26/1.65 end
% 1.26/1.65
% 1.26/1.65 resolution: (5787) {G6,W6,D4,L1,V2,M1} { leq( X, strong_iteration(
% 1.26/1.65 addition( Y, one ) ) ) }.
% 1.26/1.65 parent0[1]: (2154) {G6,W8,D3,L2,V2,M2} P(1881,615) { leq( Y, X ), ! leq( Y
% 1.26/1.65 , multiplication( X, zero ) ) }.
% 1.26/1.65 parent1[0]: (4213) {G5,W8,D5,L1,V3,M1} P(102,15);r(363) { leq( Y,
% 1.26/1.65 multiplication( strong_iteration( addition( X, one ) ), Z ) ) }.
% 1.26/1.65 substitution0:
% 1.26/1.65 X := strong_iteration( addition( Y, one ) )
% 1.26/1.65 Y := X
% 1.26/1.65 end
% 1.26/1.65 substitution1:
% 1.26/1.65 X := Y
% 1.26/1.65 Y := X
% 1.26/1.65 Z := zero
% 1.26/1.65 end
% 1.26/1.65
% 1.26/1.65 subsumption: (5485) {G7,W6,D4,L1,V2,M1} R(4213,2154) { leq( X,
% 1.26/1.65 strong_iteration( addition( Y, one ) ) ) }.
% 1.26/1.65 parent0: (5787) {G6,W6,D4,L1,V2,M1} { leq( X, strong_iteration( addition(
% 1.26/1.65 Y, one ) ) ) }.
% 1.26/1.65 substitution0:
% 1.26/1.65 X := X
% 1.26/1.65 Y := Y
% 1.26/1.65 end
% 1.26/1.65 permutation0:
% 1.26/1.65 0 ==> 0
% 1.26/1.65 end
% 1.26/1.65
% 1.26/1.65 paramod: (5789) {G5,W6,D4,L1,V2,M1} { leq( X, multiplication(
% 1.26/1.65 strong_iteration( one ), Y ) ) }.
% 1.26/1.65 parent0[0]: (1885) {G4,W7,D4,L1,V1,M1} R(1877,17) { addition(
% 1.26/1.65 multiplication( X, zero ), X ) ==> X }.
% 1.26/1.65 parent1[0; 4]: (4213) {G5,W8,D5,L1,V3,M1} P(102,15);r(363) { leq( Y,
% 1.26/1.65 multiplication( strong_iteration( addition( X, one ) ), Z ) ) }.
% 1.26/1.65 substitution0:
% 1.26/1.65 X := one
% 1.26/1.65 end
% 1.26/1.65 substitution1:
% 1.26/1.65 X := multiplication( one, zero )
% 1.26/1.65 Y := X
% 1.26/1.65 Z := Y
% 1.26/1.65 end
% 1.26/1.65
% 1.26/1.65 subsumption: (5505) {G6,W6,D4,L1,V2,M1} P(1885,4213) { leq( X,
% 1.26/1.65 multiplication( strong_iteration( one ), Y ) ) }.
% 1.26/1.65 parent0: (5789) {G5,W6,D4,L1,V2,M1} { leq( X, multiplication(
% 1.26/1.65 strong_iteration( one ), Y ) ) }.
% 1.26/1.65 substitution0:
% 1.26/1.65 X := X
% 1.26/1.65 Y := Y
% 1.26/1.65 end
% 1.26/1.65 permutation0:
% 1.26/1.65 0 ==> 0
% 1.26/1.65 end
% 1.26/1.65
% 1.26/1.65 paramod: (5791) {G5,W4,D3,L1,V1,M1} { leq( X, strong_iteration( one ) )
% 1.26/1.65 }.
% 1.26/1.65 parent0[0]: (1885) {G4,W7,D4,L1,V1,M1} R(1877,17) { addition(
% 1.26/1.65 multiplication( X, zero ), X ) ==> X }.
% 1.26/1.65 parent1[0; 3]: (5485) {G7,W6,D4,L1,V2,M1} R(4213,2154) { leq( X,
% 1.26/1.65 strong_iteration( addition( Y, one ) ) ) }.
% 1.26/1.65 substitution0:
% 1.26/1.65 X := one
% 1.26/1.65 end
% 1.26/1.65 substitution1:
% 1.26/1.65 X := X
% 1.26/1.65 Y := multiplication( one, zero )
% 1.26/1.65 end
% 1.26/1.65
% 1.26/1.65 subsumption: (5534) {G8,W4,D3,L1,V1,M1} P(1885,5485) { leq( X,
% 1.26/1.65 strong_iteration( one ) ) }.
% 1.26/1.65 parent0: (5791) {G5,W4,D3,L1,V1,M1} { leq( X, strong_iteration( one ) )
% 1.26/1.65 }.
% 1.26/1.65 substitution0:
% 1.26/1.65 X := X
% 1.26/1.65 end
% 1.26/1.65 permutation0:
% 1.26/1.65 0 ==> 0
% 1.26/1.65 end
% 1.26/1.65
% 1.26/1.65 resolution: (5792) {G1,W7,D4,L1,V0,M1} { ! leq( strong_iteration( one ),
% 1.26/1.65 multiplication( strong_iteration( one ), skol1 ) ) }.
% 1.26/1.65 parent0[0]: (19) {G0,W14,D4,L2,V0,M2} I { ! leq( multiplication(
% 1.26/1.65 strong_iteration( one ), skol1 ), strong_iteration( one ) ), ! leq(
% 1.26/1.65 strong_iteration( one ), multiplication( strong_iteration( one ), skol1 )
% 1.26/1.65 ) }.
% 1.26/1.65 parent1[0]: (5534) {G8,W4,D3,L1,V1,M1} P(1885,5485) { leq( X,
% 1.26/1.65 strong_iteration( one ) ) }.
% 1.26/1.65 substitution0:
% 1.26/1.65 end
% 1.26/1.65 substitution1:
% 1.26/1.65 X := multiplication( strong_iteration( one ), skol1 )
% 1.26/1.65 end
% 1.26/1.65
% 1.26/1.65 resolution: (5793) {G2,W0,D0,L0,V0,M0} { }.
% 1.26/1.65 parent0[0]: (5792) {G1,W7,D4,L1,V0,M1} { ! leq( strong_iteration( one ),
% 1.26/1.65 multiplication( strong_iteration( one ), skol1 ) ) }.
% 1.26/1.65 parent1[0]: (5505) {G6,W6,D4,L1,V2,M1} P(1885,4213) { leq( X,
% 1.26/1.65 multiplication( strong_iteration( one ), Y ) ) }.
% 1.26/1.65 substitution0:
% 1.26/1.65 end
% 1.26/1.65 substitution1:
% 1.26/1.65 X := strong_iteration( one )
% 1.26/1.65 Y := skol1
% 1.26/1.65 end
% 1.26/1.65
% 1.26/1.65 subsumption: (5547) {G9,W0,D0,L0,V0,M0} R(5534,19);r(5505) { }.
% 1.26/1.65 parent0: (5793) {G2,W0,D0,L0,V0,M0} { }.
% 1.26/1.65 substitution0:
% 1.26/1.65 end
% 1.26/1.65 permutation0:
% 1.26/1.65 end
% 1.26/1.65
% 1.26/1.65 Proof check complete!
% 1.26/1.65
% 1.26/1.65 Memory use:
% 1.26/1.65
% 1.26/1.65 space for terms: 69740
% 1.26/1.65 space for clauses: 301061
% 1.26/1.65
% 1.26/1.65
% 1.26/1.65 clauses generated: 49117
% 1.26/1.65 clauses kept: 5548
% 1.26/1.65 clauses selected: 378
% 1.26/1.65 clauses deleted: 86
% 1.26/1.65 clauses inuse deleted: 36
% 1.26/1.65
% 1.26/1.65 subsentry: 180331
% 1.26/1.65 literals s-matched: 113404
% 1.26/1.65 literals matched: 107751
% 1.26/1.65 full subsumption: 32550
% 1.26/1.65
% 1.26/1.65 checksum: -1936458303
% 1.26/1.65
% 1.26/1.65
% 1.26/1.65 Bliksem ended
%------------------------------------------------------------------------------