TSTP Solution File: KLE040+2 by Bliksem---1.12
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : KLE040+2 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n006.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 0s
% DateTime : Sun Jul 17 01:36:50 EDT 2022
% Result : Theorem 0.74s 1.56s
% Output : Refutation 0.74s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : KLE040+2 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.12 % Command : bliksem %s
% 0.12/0.33 % Computer : n006.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % DateTime : Thu Jun 16 09:22:41 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.74/1.56 *** allocated 10000 integers for termspace/termends
% 0.74/1.56 *** allocated 10000 integers for clauses
% 0.74/1.56 *** allocated 10000 integers for justifications
% 0.74/1.56 Bliksem 1.12
% 0.74/1.56
% 0.74/1.56
% 0.74/1.56 Automatic Strategy Selection
% 0.74/1.56
% 0.74/1.56
% 0.74/1.56 Clauses:
% 0.74/1.56
% 0.74/1.56 { addition( X, Y ) = addition( Y, X ) }.
% 0.74/1.56 { addition( Z, addition( Y, X ) ) = addition( addition( Z, Y ), X ) }.
% 0.74/1.56 { addition( X, zero ) = X }.
% 0.74/1.56 { addition( X, X ) = X }.
% 0.74/1.56 { multiplication( X, multiplication( Y, Z ) ) = multiplication(
% 0.74/1.56 multiplication( X, Y ), Z ) }.
% 0.74/1.56 { multiplication( X, one ) = X }.
% 0.74/1.56 { multiplication( one, X ) = X }.
% 0.74/1.56 { multiplication( X, addition( Y, Z ) ) = addition( multiplication( X, Y )
% 0.74/1.56 , multiplication( X, Z ) ) }.
% 0.74/1.56 { multiplication( addition( X, Y ), Z ) = addition( multiplication( X, Z )
% 0.74/1.56 , multiplication( Y, Z ) ) }.
% 0.74/1.56 { multiplication( X, zero ) = zero }.
% 0.74/1.56 { multiplication( zero, X ) = zero }.
% 0.74/1.56 { ! leq( X, Y ), addition( X, Y ) = Y }.
% 0.74/1.56 { ! addition( X, Y ) = Y, leq( X, Y ) }.
% 0.74/1.56 { leq( addition( one, multiplication( X, star( X ) ) ), star( X ) ) }.
% 0.74/1.56 { leq( addition( one, multiplication( star( X ), X ) ), star( X ) ) }.
% 0.74/1.56 { ! leq( addition( multiplication( X, Y ), Z ), Y ), leq( multiplication(
% 0.74/1.56 star( X ), Z ), Y ) }.
% 0.74/1.56 { ! leq( addition( multiplication( X, Y ), Z ), X ), leq( multiplication( Z
% 0.74/1.56 , star( Y ) ), X ) }.
% 0.74/1.56 { ! leq( multiplication( star( skol1 ), star( skol1 ) ), star( skol1 ) ), !
% 0.74/1.56 leq( star( skol1 ), multiplication( star( skol1 ), star( skol1 ) ) ) }.
% 0.74/1.56
% 0.74/1.56 percentage equality = 0.565217, percentage horn = 1.000000
% 0.74/1.56 This is a problem with some equality
% 0.74/1.56
% 0.74/1.56
% 0.74/1.56
% 0.74/1.56 Options Used:
% 0.74/1.56
% 0.74/1.56 useres = 1
% 0.74/1.56 useparamod = 1
% 0.74/1.56 useeqrefl = 1
% 0.74/1.56 useeqfact = 1
% 0.74/1.56 usefactor = 1
% 0.74/1.56 usesimpsplitting = 0
% 0.74/1.56 usesimpdemod = 5
% 0.74/1.56 usesimpres = 3
% 0.74/1.56
% 0.74/1.56 resimpinuse = 1000
% 0.74/1.56 resimpclauses = 20000
% 0.74/1.56 substype = eqrewr
% 0.74/1.56 backwardsubs = 1
% 0.74/1.56 selectoldest = 5
% 0.74/1.56
% 0.74/1.56 litorderings [0] = split
% 0.74/1.56 litorderings [1] = extend the termordering, first sorting on arguments
% 0.74/1.56
% 0.74/1.56 termordering = kbo
% 0.74/1.56
% 0.74/1.56 litapriori = 0
% 0.74/1.56 termapriori = 1
% 0.74/1.56 litaposteriori = 0
% 0.74/1.56 termaposteriori = 0
% 0.74/1.56 demodaposteriori = 0
% 0.74/1.56 ordereqreflfact = 0
% 0.74/1.56
% 0.74/1.56 litselect = negord
% 0.74/1.56
% 0.74/1.56 maxweight = 15
% 0.74/1.56 maxdepth = 30000
% 0.74/1.56 maxlength = 115
% 0.74/1.56 maxnrvars = 195
% 0.74/1.56 excuselevel = 1
% 0.74/1.56 increasemaxweight = 1
% 0.74/1.56
% 0.74/1.56 maxselected = 10000000
% 0.74/1.56 maxnrclauses = 10000000
% 0.74/1.56
% 0.74/1.56 showgenerated = 0
% 0.74/1.56 showkept = 0
% 0.74/1.56 showselected = 0
% 0.74/1.56 showdeleted = 0
% 0.74/1.56 showresimp = 1
% 0.74/1.56 showstatus = 2000
% 0.74/1.56
% 0.74/1.56 prologoutput = 0
% 0.74/1.56 nrgoals = 5000000
% 0.74/1.56 totalproof = 1
% 0.74/1.56
% 0.74/1.56 Symbols occurring in the translation:
% 0.74/1.56
% 0.74/1.56 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.74/1.56 . [1, 2] (w:1, o:19, a:1, s:1, b:0),
% 0.74/1.56 ! [4, 1] (w:0, o:13, a:1, s:1, b:0),
% 0.74/1.56 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.74/1.56 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.74/1.56 addition [37, 2] (w:1, o:43, a:1, s:1, b:0),
% 0.74/1.56 zero [39, 0] (w:1, o:9, a:1, s:1, b:0),
% 0.74/1.56 multiplication [40, 2] (w:1, o:45, a:1, s:1, b:0),
% 0.74/1.56 one [41, 0] (w:1, o:10, a:1, s:1, b:0),
% 0.74/1.56 leq [42, 2] (w:1, o:44, a:1, s:1, b:0),
% 0.74/1.56 star [43, 1] (w:1, o:18, a:1, s:1, b:0),
% 0.74/1.56 skol1 [45, 0] (w:1, o:12, a:1, s:1, b:1).
% 0.74/1.56
% 0.74/1.56
% 0.74/1.56 Starting Search:
% 0.74/1.56
% 0.74/1.56 *** allocated 15000 integers for clauses
% 0.74/1.56 *** allocated 22500 integers for clauses
% 0.74/1.56 *** allocated 33750 integers for clauses
% 0.74/1.56 *** allocated 50625 integers for clauses
% 0.74/1.56 *** allocated 15000 integers for termspace/termends
% 0.74/1.56 *** allocated 75937 integers for clauses
% 0.74/1.56 Resimplifying inuse:
% 0.74/1.56 Done
% 0.74/1.56
% 0.74/1.56 *** allocated 22500 integers for termspace/termends
% 0.74/1.56 *** allocated 113905 integers for clauses
% 0.74/1.56 *** allocated 33750 integers for termspace/termends
% 0.74/1.56
% 0.74/1.56 Intermediate Status:
% 0.74/1.56 Generated: 19472
% 0.74/1.56 Kept: 2050
% 0.74/1.56 Inuse: 214
% 0.74/1.56 Deleted: 61
% 0.74/1.56 Deletedinuse: 34
% 0.74/1.56
% 0.74/1.56 Resimplifying inuse:
% 0.74/1.56 Done
% 0.74/1.56
% 0.74/1.56 *** allocated 170857 integers for clauses
% 0.74/1.56 *** allocated 50625 integers for termspace/termends
% 0.74/1.56 Resimplifying inuse:
% 0.74/1.56 Done
% 0.74/1.56
% 0.74/1.56 *** allocated 256285 integers for clauses
% 0.74/1.56 *** allocated 75937 integers for termspace/termends
% 0.74/1.56
% 0.74/1.56 Intermediate Status:
% 0.74/1.56 Generated: 43302
% 0.74/1.56 Kept: 4063
% 0.74/1.56 Inuse: 378
% 0.74/1.56 Deleted: 117
% 0.74/1.56 Deletedinuse: 66
% 0.74/1.56
% 0.74/1.56 Resimplifying inuse:
% 0.74/1.56 Done
% 0.74/1.56
% 0.74/1.56
% 0.74/1.56 Bliksems!, er is een bewijs:
% 0.74/1.56 % SZS status Theorem
% 0.74/1.56 % SZS output start Refutation
% 0.74/1.56
% 0.74/1.56 (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X ) }.
% 0.74/1.56 (1) {G0,W11,D4,L1,V3,M1} I { addition( Z, addition( Y, X ) ) ==> addition(
% 0.74/1.56 addition( Z, Y ), X ) }.
% 0.74/1.56 (3) {G0,W5,D3,L1,V1,M1} I { addition( X, X ) ==> X }.
% 0.74/1.56 (5) {G0,W5,D3,L1,V1,M1} I { multiplication( X, one ) ==> X }.
% 0.74/1.56 (7) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Y ),
% 0.74/1.56 multiplication( X, Z ) ) ==> multiplication( X, addition( Y, Z ) ) }.
% 0.74/1.56 (11) {G0,W8,D3,L2,V2,M2} I { ! leq( X, Y ), addition( X, Y ) ==> Y }.
% 0.74/1.56 (12) {G0,W8,D3,L2,V2,M2} I { ! addition( X, Y ) ==> Y, leq( X, Y ) }.
% 0.74/1.56 (14) {G0,W9,D5,L1,V1,M1} I { leq( addition( one, multiplication( star( X )
% 0.74/1.56 , X ) ), star( X ) ) }.
% 0.74/1.56 (16) {G0,W13,D4,L2,V3,M2} I { ! leq( addition( multiplication( X, Y ), Z )
% 0.74/1.56 , X ), leq( multiplication( Z, star( Y ) ), X ) }.
% 0.74/1.56 (17) {G0,W16,D4,L2,V0,M2} I { ! leq( multiplication( star( skol1 ), star(
% 0.74/1.56 skol1 ) ), star( skol1 ) ), ! leq( star( skol1 ), multiplication( star(
% 0.74/1.56 skol1 ), star( skol1 ) ) ) }.
% 0.74/1.56 (20) {G1,W3,D2,L1,V1,M1} R(12,3) { leq( X, X ) }.
% 0.74/1.56 (23) {G1,W14,D4,L2,V3,M2} P(1,12) { ! addition( addition( X, Y ), Z ) ==>
% 0.74/1.56 addition( Y, Z ), leq( X, addition( Y, Z ) ) }.
% 0.74/1.56 (24) {G1,W11,D4,L1,V3,M1} P(1,0) { addition( addition( X, Y ), Z ) =
% 0.74/1.56 addition( addition( Y, Z ), X ) }.
% 0.74/1.56 (63) {G1,W16,D4,L2,V3,M2} P(7,12) { ! multiplication( X, addition( Y, Z ) )
% 0.74/1.56 ==> multiplication( X, Z ), leq( multiplication( X, Y ), multiplication
% 0.74/1.56 ( X, Z ) ) }.
% 0.74/1.56 (234) {G2,W5,D3,L1,V2,M1} P(3,23);q { leq( X, addition( X, Y ) ) }.
% 0.74/1.56 (239) {G3,W7,D4,L1,V3,M1} P(1,234) { leq( X, addition( addition( X, Y ), Z
% 0.74/1.56 ) ) }.
% 0.74/1.56 (240) {G3,W5,D3,L1,V2,M1} P(0,234) { leq( X, addition( Y, X ) ) }.
% 0.74/1.56 (251) {G4,W7,D4,L1,V3,M1} P(24,240) { leq( Z, addition( addition( Y, Z ), X
% 0.74/1.56 ) ) }.
% 0.74/1.56 (470) {G5,W8,D3,L2,V3,M2} P(11,251) { leq( Y, Z ), ! leq( addition( X, Y )
% 0.74/1.56 , Z ) }.
% 0.74/1.56 (483) {G4,W8,D3,L2,V3,M2} P(11,239) { leq( X, Z ), ! leq( addition( X, Y )
% 0.74/1.56 , Z ) }.
% 0.74/1.56 (577) {G5,W4,D3,L1,V1,M1} R(483,14) { leq( one, star( X ) ) }.
% 0.74/1.56 (593) {G6,W7,D4,L1,V1,M1} R(577,11) { addition( one, star( X ) ) ==> star(
% 0.74/1.56 X ) }.
% 0.74/1.56 (714) {G6,W7,D4,L1,V1,M1} R(470,14) { leq( multiplication( star( X ), X ),
% 0.74/1.56 star( X ) ) }.
% 0.74/1.56 (724) {G7,W10,D5,L1,V1,M1} R(714,11) { addition( multiplication( star( X )
% 0.74/1.56 , X ), star( X ) ) ==> star( X ) }.
% 0.74/1.56 (1700) {G7,W6,D4,L1,V2,M1} P(593,63);q;d(5) { leq( Y, multiplication( Y,
% 0.74/1.56 star( X ) ) ) }.
% 0.74/1.56 (1723) {G8,W8,D4,L1,V0,M1} R(1700,17) { ! leq( multiplication( star( skol1
% 0.74/1.56 ), star( skol1 ) ), star( skol1 ) ) }.
% 0.74/1.56 (4330) {G9,W0,D0,L0,V0,M0} R(1723,16);d(724);r(20) { }.
% 0.74/1.56
% 0.74/1.56
% 0.74/1.56 % SZS output end Refutation
% 0.74/1.56 found a proof!
% 0.74/1.56
% 0.74/1.56
% 0.74/1.56 Unprocessed initial clauses:
% 0.74/1.56
% 0.74/1.56 (4332) {G0,W7,D3,L1,V2,M1} { addition( X, Y ) = addition( Y, X ) }.
% 0.74/1.56 (4333) {G0,W11,D4,L1,V3,M1} { addition( Z, addition( Y, X ) ) = addition(
% 0.74/1.56 addition( Z, Y ), X ) }.
% 0.74/1.56 (4334) {G0,W5,D3,L1,V1,M1} { addition( X, zero ) = X }.
% 0.74/1.56 (4335) {G0,W5,D3,L1,V1,M1} { addition( X, X ) = X }.
% 0.74/1.56 (4336) {G0,W11,D4,L1,V3,M1} { multiplication( X, multiplication( Y, Z ) )
% 0.74/1.56 = multiplication( multiplication( X, Y ), Z ) }.
% 0.74/1.56 (4337) {G0,W5,D3,L1,V1,M1} { multiplication( X, one ) = X }.
% 0.74/1.57 (4338) {G0,W5,D3,L1,V1,M1} { multiplication( one, X ) = X }.
% 0.74/1.57 (4339) {G0,W13,D4,L1,V3,M1} { multiplication( X, addition( Y, Z ) ) =
% 0.74/1.57 addition( multiplication( X, Y ), multiplication( X, Z ) ) }.
% 0.74/1.57 (4340) {G0,W13,D4,L1,V3,M1} { multiplication( addition( X, Y ), Z ) =
% 0.74/1.57 addition( multiplication( X, Z ), multiplication( Y, Z ) ) }.
% 0.74/1.57 (4341) {G0,W5,D3,L1,V1,M1} { multiplication( X, zero ) = zero }.
% 0.74/1.57 (4342) {G0,W5,D3,L1,V1,M1} { multiplication( zero, X ) = zero }.
% 0.74/1.57 (4343) {G0,W8,D3,L2,V2,M2} { ! leq( X, Y ), addition( X, Y ) = Y }.
% 0.74/1.57 (4344) {G0,W8,D3,L2,V2,M2} { ! addition( X, Y ) = Y, leq( X, Y ) }.
% 0.74/1.57 (4345) {G0,W9,D5,L1,V1,M1} { leq( addition( one, multiplication( X, star(
% 0.74/1.57 X ) ) ), star( X ) ) }.
% 0.74/1.57 (4346) {G0,W9,D5,L1,V1,M1} { leq( addition( one, multiplication( star( X )
% 0.74/1.57 , X ) ), star( X ) ) }.
% 0.74/1.57 (4347) {G0,W13,D4,L2,V3,M2} { ! leq( addition( multiplication( X, Y ), Z )
% 0.74/1.57 , Y ), leq( multiplication( star( X ), Z ), Y ) }.
% 0.74/1.57 (4348) {G0,W13,D4,L2,V3,M2} { ! leq( addition( multiplication( X, Y ), Z )
% 0.74/1.57 , X ), leq( multiplication( Z, star( Y ) ), X ) }.
% 0.74/1.57 (4349) {G0,W16,D4,L2,V0,M2} { ! leq( multiplication( star( skol1 ), star(
% 0.74/1.57 skol1 ) ), star( skol1 ) ), ! leq( star( skol1 ), multiplication( star(
% 0.74/1.57 skol1 ), star( skol1 ) ) ) }.
% 0.74/1.57
% 0.74/1.57
% 0.74/1.57 Total Proof:
% 0.74/1.57
% 0.74/1.57 subsumption: (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X
% 0.74/1.57 ) }.
% 0.74/1.57 parent0: (4332) {G0,W7,D3,L1,V2,M1} { addition( X, Y ) = addition( Y, X )
% 0.74/1.57 }.
% 0.74/1.57 substitution0:
% 0.74/1.57 X := X
% 0.74/1.57 Y := Y
% 0.74/1.57 end
% 0.74/1.57 permutation0:
% 0.74/1.57 0 ==> 0
% 0.74/1.57 end
% 0.74/1.57
% 0.74/1.57 subsumption: (1) {G0,W11,D4,L1,V3,M1} I { addition( Z, addition( Y, X ) )
% 0.74/1.57 ==> addition( addition( Z, Y ), X ) }.
% 0.74/1.57 parent0: (4333) {G0,W11,D4,L1,V3,M1} { addition( Z, addition( Y, X ) ) =
% 0.74/1.57 addition( addition( Z, Y ), X ) }.
% 0.74/1.57 substitution0:
% 0.74/1.57 X := X
% 0.74/1.57 Y := Y
% 0.74/1.57 Z := Z
% 0.74/1.57 end
% 0.74/1.57 permutation0:
% 0.74/1.57 0 ==> 0
% 0.74/1.57 end
% 0.74/1.57
% 0.74/1.57 subsumption: (3) {G0,W5,D3,L1,V1,M1} I { addition( X, X ) ==> X }.
% 0.74/1.57 parent0: (4335) {G0,W5,D3,L1,V1,M1} { addition( X, X ) = X }.
% 0.74/1.57 substitution0:
% 0.74/1.57 X := X
% 0.74/1.57 end
% 0.74/1.57 permutation0:
% 0.74/1.57 0 ==> 0
% 0.74/1.57 end
% 0.74/1.57
% 0.74/1.57 subsumption: (5) {G0,W5,D3,L1,V1,M1} I { multiplication( X, one ) ==> X }.
% 0.74/1.57 parent0: (4337) {G0,W5,D3,L1,V1,M1} { multiplication( X, one ) = X }.
% 0.74/1.57 substitution0:
% 0.74/1.57 X := X
% 0.74/1.57 end
% 0.74/1.57 permutation0:
% 0.74/1.57 0 ==> 0
% 0.74/1.57 end
% 0.74/1.57
% 0.74/1.57 eqswap: (4365) {G0,W13,D4,L1,V3,M1} { addition( multiplication( X, Y ),
% 0.74/1.57 multiplication( X, Z ) ) = multiplication( X, addition( Y, Z ) ) }.
% 0.74/1.57 parent0[0]: (4339) {G0,W13,D4,L1,V3,M1} { multiplication( X, addition( Y,
% 0.74/1.57 Z ) ) = addition( multiplication( X, Y ), multiplication( X, Z ) ) }.
% 0.74/1.57 substitution0:
% 0.74/1.57 X := X
% 0.74/1.57 Y := Y
% 0.74/1.57 Z := Z
% 0.74/1.57 end
% 0.74/1.57
% 0.74/1.57 subsumption: (7) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Y )
% 0.74/1.57 , multiplication( X, Z ) ) ==> multiplication( X, addition( Y, Z ) ) }.
% 0.74/1.57 parent0: (4365) {G0,W13,D4,L1,V3,M1} { addition( multiplication( X, Y ),
% 0.74/1.57 multiplication( X, Z ) ) = multiplication( X, addition( Y, Z ) ) }.
% 0.74/1.57 substitution0:
% 0.74/1.57 X := X
% 0.74/1.57 Y := Y
% 0.74/1.57 Z := Z
% 0.74/1.57 end
% 0.74/1.57 permutation0:
% 0.74/1.57 0 ==> 0
% 0.74/1.57 end
% 0.74/1.57
% 0.74/1.57 subsumption: (11) {G0,W8,D3,L2,V2,M2} I { ! leq( X, Y ), addition( X, Y )
% 0.74/1.57 ==> Y }.
% 0.74/1.57 parent0: (4343) {G0,W8,D3,L2,V2,M2} { ! leq( X, Y ), addition( X, Y ) = Y
% 0.74/1.57 }.
% 0.74/1.57 substitution0:
% 0.74/1.57 X := X
% 0.74/1.57 Y := Y
% 0.74/1.57 end
% 0.74/1.57 permutation0:
% 0.74/1.57 0 ==> 0
% 0.74/1.57 1 ==> 1
% 0.74/1.57 end
% 0.74/1.57
% 0.74/1.57 subsumption: (12) {G0,W8,D3,L2,V2,M2} I { ! addition( X, Y ) ==> Y, leq( X
% 0.74/1.57 , Y ) }.
% 0.74/1.57 parent0: (4344) {G0,W8,D3,L2,V2,M2} { ! addition( X, Y ) = Y, leq( X, Y )
% 0.74/1.57 }.
% 0.74/1.57 substitution0:
% 0.74/1.57 X := X
% 0.74/1.57 Y := Y
% 0.74/1.57 end
% 0.74/1.57 permutation0:
% 0.74/1.57 0 ==> 0
% 0.74/1.57 1 ==> 1
% 0.74/1.57 end
% 0.74/1.57
% 0.74/1.57 subsumption: (14) {G0,W9,D5,L1,V1,M1} I { leq( addition( one,
% 0.74/1.57 multiplication( star( X ), X ) ), star( X ) ) }.
% 0.74/1.57 parent0: (4346) {G0,W9,D5,L1,V1,M1} { leq( addition( one, multiplication(
% 0.74/1.57 star( X ), X ) ), star( X ) ) }.
% 0.74/1.57 substitution0:
% 0.74/1.57 X := X
% 0.74/1.57 end
% 0.74/1.57 permutation0:
% 0.74/1.57 0 ==> 0
% 0.74/1.57 end
% 0.74/1.57
% 0.74/1.57 subsumption: (16) {G0,W13,D4,L2,V3,M2} I { ! leq( addition( multiplication
% 0.74/1.57 ( X, Y ), Z ), X ), leq( multiplication( Z, star( Y ) ), X ) }.
% 0.74/1.57 parent0: (4348) {G0,W13,D4,L2,V3,M2} { ! leq( addition( multiplication( X
% 0.74/1.57 , Y ), Z ), X ), leq( multiplication( Z, star( Y ) ), X ) }.
% 0.74/1.57 substitution0:
% 0.74/1.57 X := X
% 0.74/1.57 Y := Y
% 0.74/1.57 Z := Z
% 0.74/1.57 end
% 0.74/1.57 permutation0:
% 0.74/1.57 0 ==> 0
% 0.74/1.57 1 ==> 1
% 0.74/1.57 end
% 0.74/1.57
% 0.74/1.57 subsumption: (17) {G0,W16,D4,L2,V0,M2} I { ! leq( multiplication( star(
% 0.74/1.57 skol1 ), star( skol1 ) ), star( skol1 ) ), ! leq( star( skol1 ),
% 0.74/1.57 multiplication( star( skol1 ), star( skol1 ) ) ) }.
% 0.74/1.57 parent0: (4349) {G0,W16,D4,L2,V0,M2} { ! leq( multiplication( star( skol1
% 0.74/1.57 ), star( skol1 ) ), star( skol1 ) ), ! leq( star( skol1 ),
% 0.74/1.57 multiplication( star( skol1 ), star( skol1 ) ) ) }.
% 0.74/1.57 substitution0:
% 0.74/1.57 end
% 0.74/1.57 permutation0:
% 0.74/1.57 0 ==> 0
% 0.74/1.57 1 ==> 1
% 0.74/1.57 end
% 0.74/1.57
% 0.74/1.57 eqswap: (4425) {G0,W8,D3,L2,V2,M2} { ! Y ==> addition( X, Y ), leq( X, Y )
% 0.74/1.57 }.
% 0.74/1.57 parent0[0]: (12) {G0,W8,D3,L2,V2,M2} I { ! addition( X, Y ) ==> Y, leq( X,
% 0.74/1.57 Y ) }.
% 0.74/1.57 substitution0:
% 0.74/1.57 X := X
% 0.74/1.57 Y := Y
% 0.74/1.57 end
% 0.74/1.57
% 0.74/1.57 eqswap: (4426) {G0,W5,D3,L1,V1,M1} { X ==> addition( X, X ) }.
% 0.74/1.57 parent0[0]: (3) {G0,W5,D3,L1,V1,M1} I { addition( X, X ) ==> X }.
% 0.74/1.57 substitution0:
% 0.74/1.57 X := X
% 0.74/1.57 end
% 0.74/1.57
% 0.74/1.57 resolution: (4427) {G1,W3,D2,L1,V1,M1} { leq( X, X ) }.
% 0.74/1.57 parent0[0]: (4425) {G0,W8,D3,L2,V2,M2} { ! Y ==> addition( X, Y ), leq( X
% 0.74/1.57 , Y ) }.
% 0.74/1.57 parent1[0]: (4426) {G0,W5,D3,L1,V1,M1} { X ==> addition( X, X ) }.
% 0.74/1.57 substitution0:
% 0.74/1.57 X := X
% 0.74/1.57 Y := X
% 0.74/1.57 end
% 0.74/1.57 substitution1:
% 0.74/1.57 X := X
% 0.74/1.57 end
% 0.74/1.57
% 0.74/1.57 subsumption: (20) {G1,W3,D2,L1,V1,M1} R(12,3) { leq( X, X ) }.
% 0.74/1.57 parent0: (4427) {G1,W3,D2,L1,V1,M1} { leq( X, X ) }.
% 0.74/1.57 substitution0:
% 0.74/1.57 X := X
% 0.74/1.57 end
% 0.74/1.57 permutation0:
% 0.74/1.57 0 ==> 0
% 0.74/1.57 end
% 0.74/1.57
% 0.74/1.57 eqswap: (4429) {G0,W8,D3,L2,V2,M2} { ! Y ==> addition( X, Y ), leq( X, Y )
% 0.74/1.57 }.
% 0.74/1.57 parent0[0]: (12) {G0,W8,D3,L2,V2,M2} I { ! addition( X, Y ) ==> Y, leq( X,
% 0.74/1.57 Y ) }.
% 0.74/1.57 substitution0:
% 0.74/1.57 X := X
% 0.74/1.57 Y := Y
% 0.74/1.57 end
% 0.74/1.57
% 0.74/1.57 paramod: (4430) {G1,W14,D4,L2,V3,M2} { ! addition( X, Y ) ==> addition(
% 0.74/1.57 addition( Z, X ), Y ), leq( Z, addition( X, Y ) ) }.
% 0.74/1.57 parent0[0]: (1) {G0,W11,D4,L1,V3,M1} I { addition( Z, addition( Y, X ) )
% 0.74/1.57 ==> addition( addition( Z, Y ), X ) }.
% 0.74/1.57 parent1[0; 5]: (4429) {G0,W8,D3,L2,V2,M2} { ! Y ==> addition( X, Y ), leq
% 0.74/1.57 ( X, Y ) }.
% 0.74/1.57 substitution0:
% 0.74/1.57 X := Y
% 0.74/1.57 Y := X
% 0.74/1.57 Z := Z
% 0.74/1.57 end
% 0.74/1.57 substitution1:
% 0.74/1.57 X := Z
% 0.74/1.57 Y := addition( X, Y )
% 0.74/1.57 end
% 0.74/1.57
% 0.74/1.57 eqswap: (4431) {G1,W14,D4,L2,V3,M2} { ! addition( addition( Z, X ), Y )
% 0.74/1.57 ==> addition( X, Y ), leq( Z, addition( X, Y ) ) }.
% 0.74/1.57 parent0[0]: (4430) {G1,W14,D4,L2,V3,M2} { ! addition( X, Y ) ==> addition
% 0.74/1.57 ( addition( Z, X ), Y ), leq( Z, addition( X, Y ) ) }.
% 0.74/1.57 substitution0:
% 0.74/1.57 X := X
% 0.74/1.57 Y := Y
% 0.74/1.57 Z := Z
% 0.74/1.57 end
% 0.74/1.57
% 0.74/1.57 subsumption: (23) {G1,W14,D4,L2,V3,M2} P(1,12) { ! addition( addition( X, Y
% 0.74/1.57 ), Z ) ==> addition( Y, Z ), leq( X, addition( Y, Z ) ) }.
% 0.74/1.57 parent0: (4431) {G1,W14,D4,L2,V3,M2} { ! addition( addition( Z, X ), Y )
% 0.74/1.57 ==> addition( X, Y ), leq( Z, addition( X, Y ) ) }.
% 0.74/1.57 substitution0:
% 0.74/1.57 X := Y
% 0.74/1.57 Y := Z
% 0.74/1.57 Z := X
% 0.74/1.57 end
% 0.74/1.57 permutation0:
% 0.74/1.57 0 ==> 0
% 0.74/1.57 1 ==> 1
% 0.74/1.57 end
% 0.74/1.57
% 0.74/1.57 eqswap: (4432) {G0,W11,D4,L1,V3,M1} { addition( addition( X, Y ), Z ) ==>
% 0.74/1.57 addition( X, addition( Y, Z ) ) }.
% 0.74/1.57 parent0[0]: (1) {G0,W11,D4,L1,V3,M1} I { addition( Z, addition( Y, X ) )
% 0.74/1.57 ==> addition( addition( Z, Y ), X ) }.
% 0.74/1.57 substitution0:
% 0.74/1.57 X := Z
% 0.74/1.57 Y := Y
% 0.74/1.57 Z := X
% 0.74/1.57 end
% 0.74/1.57
% 0.74/1.57 paramod: (4435) {G1,W11,D4,L1,V3,M1} { addition( addition( X, Y ), Z ) ==>
% 0.74/1.57 addition( addition( Y, Z ), X ) }.
% 0.74/1.57 parent0[0]: (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X )
% 0.74/1.57 }.
% 0.74/1.57 parent1[0; 6]: (4432) {G0,W11,D4,L1,V3,M1} { addition( addition( X, Y ), Z
% 0.74/1.57 ) ==> addition( X, addition( Y, Z ) ) }.
% 0.74/1.57 substitution0:
% 0.74/1.57 X := X
% 0.74/1.57 Y := addition( Y, Z )
% 0.74/1.57 end
% 0.74/1.57 substitution1:
% 0.74/1.57 X := X
% 0.74/1.57 Y := Y
% 0.74/1.57 Z := Z
% 0.74/1.57 end
% 0.74/1.57
% 0.74/1.57 subsumption: (24) {G1,W11,D4,L1,V3,M1} P(1,0) { addition( addition( X, Y )
% 0.74/1.57 , Z ) = addition( addition( Y, Z ), X ) }.
% 0.74/1.57 parent0: (4435) {G1,W11,D4,L1,V3,M1} { addition( addition( X, Y ), Z ) ==>
% 0.74/1.57 addition( addition( Y, Z ), X ) }.
% 0.74/1.57 substitution0:
% 0.74/1.57 X := X
% 0.74/1.57 Y := Y
% 0.74/1.57 Z := Z
% 0.74/1.57 end
% 0.74/1.57 permutation0:
% 0.74/1.57 0 ==> 0
% 0.74/1.57 end
% 0.74/1.57
% 0.74/1.57 eqswap: (4450) {G0,W8,D3,L2,V2,M2} { ! Y ==> addition( X, Y ), leq( X, Y )
% 0.74/1.57 }.
% 0.74/1.57 parent0[0]: (12) {G0,W8,D3,L2,V2,M2} I { ! addition( X, Y ) ==> Y, leq( X,
% 0.74/1.57 Y ) }.
% 0.74/1.57 substitution0:
% 0.74/1.57 X := X
% 0.74/1.57 Y := Y
% 0.74/1.57 end
% 0.74/1.57
% 0.74/1.57 paramod: (4451) {G1,W16,D4,L2,V3,M2} { ! multiplication( X, Y ) ==>
% 0.74/1.57 multiplication( X, addition( Z, Y ) ), leq( multiplication( X, Z ),
% 0.74/1.57 multiplication( X, Y ) ) }.
% 0.74/1.57 parent0[0]: (7) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Y ),
% 0.74/1.57 multiplication( X, Z ) ) ==> multiplication( X, addition( Y, Z ) ) }.
% 0.74/1.57 parent1[0; 5]: (4450) {G0,W8,D3,L2,V2,M2} { ! Y ==> addition( X, Y ), leq
% 0.74/1.57 ( X, Y ) }.
% 0.74/1.57 substitution0:
% 0.74/1.57 X := X
% 0.74/1.57 Y := Z
% 0.74/1.57 Z := Y
% 0.74/1.57 end
% 0.74/1.57 substitution1:
% 0.74/1.57 X := multiplication( X, Z )
% 0.74/1.57 Y := multiplication( X, Y )
% 0.74/1.57 end
% 0.74/1.57
% 0.74/1.57 eqswap: (4452) {G1,W16,D4,L2,V3,M2} { ! multiplication( X, addition( Z, Y
% 0.74/1.57 ) ) ==> multiplication( X, Y ), leq( multiplication( X, Z ),
% 0.74/1.57 multiplication( X, Y ) ) }.
% 0.74/1.57 parent0[0]: (4451) {G1,W16,D4,L2,V3,M2} { ! multiplication( X, Y ) ==>
% 0.74/1.57 multiplication( X, addition( Z, Y ) ), leq( multiplication( X, Z ),
% 0.74/1.57 multiplication( X, Y ) ) }.
% 0.74/1.57 substitution0:
% 0.74/1.57 X := X
% 0.74/1.57 Y := Y
% 0.74/1.57 Z := Z
% 0.74/1.57 end
% 0.74/1.57
% 0.74/1.57 subsumption: (63) {G1,W16,D4,L2,V3,M2} P(7,12) { ! multiplication( X,
% 0.74/1.57 addition( Y, Z ) ) ==> multiplication( X, Z ), leq( multiplication( X, Y
% 0.74/1.57 ), multiplication( X, Z ) ) }.
% 0.74/1.57 parent0: (4452) {G1,W16,D4,L2,V3,M2} { ! multiplication( X, addition( Z, Y
% 0.74/1.57 ) ) ==> multiplication( X, Y ), leq( multiplication( X, Z ),
% 0.74/1.57 multiplication( X, Y ) ) }.
% 0.74/1.57 substitution0:
% 0.74/1.57 X := X
% 0.74/1.57 Y := Z
% 0.74/1.57 Z := Y
% 0.74/1.57 end
% 0.74/1.57 permutation0:
% 0.74/1.57 0 ==> 0
% 0.74/1.57 1 ==> 1
% 0.74/1.57 end
% 0.74/1.57
% 0.74/1.57 eqswap: (4454) {G1,W14,D4,L2,V3,M2} { ! addition( Y, Z ) ==> addition(
% 0.74/1.57 addition( X, Y ), Z ), leq( X, addition( Y, Z ) ) }.
% 0.74/1.57 parent0[0]: (23) {G1,W14,D4,L2,V3,M2} P(1,12) { ! addition( addition( X, Y
% 0.74/1.57 ), Z ) ==> addition( Y, Z ), leq( X, addition( Y, Z ) ) }.
% 0.74/1.57 substitution0:
% 0.74/1.57 X := X
% 0.74/1.57 Y := Y
% 0.74/1.57 Z := Z
% 0.74/1.57 end
% 0.74/1.57
% 0.74/1.57 paramod: (4457) {G1,W12,D3,L2,V2,M2} { ! addition( X, Y ) ==> addition( X
% 0.74/1.57 , Y ), leq( X, addition( X, Y ) ) }.
% 0.74/1.57 parent0[0]: (3) {G0,W5,D3,L1,V1,M1} I { addition( X, X ) ==> X }.
% 0.74/1.57 parent1[0; 6]: (4454) {G1,W14,D4,L2,V3,M2} { ! addition( Y, Z ) ==>
% 0.74/1.57 addition( addition( X, Y ), Z ), leq( X, addition( Y, Z ) ) }.
% 0.74/1.57 substitution0:
% 0.74/1.57 X := X
% 0.74/1.57 end
% 0.74/1.57 substitution1:
% 0.74/1.57 X := X
% 0.74/1.57 Y := X
% 0.74/1.57 Z := Y
% 0.74/1.57 end
% 0.74/1.57
% 0.74/1.57 eqrefl: (4460) {G0,W5,D3,L1,V2,M1} { leq( X, addition( X, Y ) ) }.
% 0.74/1.57 parent0[0]: (4457) {G1,W12,D3,L2,V2,M2} { ! addition( X, Y ) ==> addition
% 0.74/1.57 ( X, Y ), leq( X, addition( X, Y ) ) }.
% 0.74/1.57 substitution0:
% 0.74/1.57 X := X
% 0.74/1.57 Y := Y
% 0.74/1.57 end
% 0.74/1.57
% 0.74/1.57 subsumption: (234) {G2,W5,D3,L1,V2,M1} P(3,23);q { leq( X, addition( X, Y )
% 0.74/1.57 ) }.
% 0.74/1.57 parent0: (4460) {G0,W5,D3,L1,V2,M1} { leq( X, addition( X, Y ) ) }.
% 0.74/1.57 substitution0:
% 0.74/1.57 X := X
% 0.74/1.57 Y := Y
% 0.74/1.57 end
% 0.74/1.57 permutation0:
% 0.74/1.57 0 ==> 0
% 0.74/1.57 end
% 0.74/1.57
% 0.74/1.57 paramod: (4462) {G1,W7,D4,L1,V3,M1} { leq( X, addition( addition( X, Y ),
% 0.74/1.57 Z ) ) }.
% 0.74/1.57 parent0[0]: (1) {G0,W11,D4,L1,V3,M1} I { addition( Z, addition( Y, X ) )
% 0.74/1.57 ==> addition( addition( Z, Y ), X ) }.
% 0.74/1.57 parent1[0; 2]: (234) {G2,W5,D3,L1,V2,M1} P(3,23);q { leq( X, addition( X, Y
% 0.74/1.57 ) ) }.
% 0.74/1.57 substitution0:
% 0.74/1.57 X := Z
% 0.74/1.57 Y := Y
% 0.74/1.57 Z := X
% 0.74/1.57 end
% 0.74/1.57 substitution1:
% 0.74/1.57 X := X
% 0.74/1.57 Y := addition( Y, Z )
% 0.74/1.57 end
% 0.74/1.57
% 0.74/1.57 subsumption: (239) {G3,W7,D4,L1,V3,M1} P(1,234) { leq( X, addition(
% 0.74/1.57 addition( X, Y ), Z ) ) }.
% 0.74/1.57 parent0: (4462) {G1,W7,D4,L1,V3,M1} { leq( X, addition( addition( X, Y ),
% 0.74/1.57 Z ) ) }.
% 0.74/1.57 substitution0:
% 0.74/1.57 X := X
% 0.74/1.57 Y := Y
% 0.74/1.57 Z := Z
% 0.74/1.57 end
% 0.74/1.57 permutation0:
% 0.74/1.57 0 ==> 0
% 0.74/1.57 end
% 0.74/1.57
% 0.74/1.57 paramod: (4463) {G1,W5,D3,L1,V2,M1} { leq( X, addition( Y, X ) ) }.
% 0.74/1.57 parent0[0]: (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X )
% 0.74/1.57 }.
% 0.74/1.57 parent1[0; 2]: (234) {G2,W5,D3,L1,V2,M1} P(3,23);q { leq( X, addition( X, Y
% 0.74/1.57 ) ) }.
% 0.74/1.57 substitution0:
% 0.74/1.57 X := X
% 0.74/1.57 Y := Y
% 0.74/1.57 end
% 0.74/1.57 substitution1:
% 0.74/1.57 X := X
% 0.74/1.57 Y := Y
% 0.74/1.57 end
% 0.74/1.57
% 0.74/1.57 subsumption: (240) {G3,W5,D3,L1,V2,M1} P(0,234) { leq( X, addition( Y, X )
% 0.74/1.57 ) }.
% 0.74/1.57 parent0: (4463) {G1,W5,D3,L1,V2,M1} { leq( X, addition( Y, X ) ) }.
% 0.74/1.57 substitution0:
% 0.74/1.57 X := X
% 0.74/1.57 Y := Y
% 0.74/1.57 end
% 0.74/1.57 permutation0:
% 0.74/1.57 0 ==> 0
% 0.74/1.57 end
% 0.74/1.57
% 0.74/1.57 eqswap: (4465) {G1,W11,D4,L1,V3,M1} { addition( addition( Y, Z ), X ) =
% 0.74/1.57 addition( addition( X, Y ), Z ) }.
% 0.74/1.57 parent0[0]: (24) {G1,W11,D4,L1,V3,M1} P(1,0) { addition( addition( X, Y ),
% 0.74/1.57 Z ) = addition( addition( Y, Z ), X ) }.
% 0.74/1.57 substitution0:
% 0.74/1.57 X := X
% 0.74/1.57 Y := Y
% 0.74/1.57 Z := Z
% 0.74/1.57 end
% 0.74/1.57
% 0.74/1.57 paramod: (4466) {G2,W7,D4,L1,V3,M1} { leq( X, addition( addition( X, Y ),
% 0.74/1.57 Z ) ) }.
% 0.74/1.57 parent0[0]: (4465) {G1,W11,D4,L1,V3,M1} { addition( addition( Y, Z ), X )
% 0.74/1.57 = addition( addition( X, Y ), Z ) }.
% 0.74/1.57 parent1[0; 2]: (240) {G3,W5,D3,L1,V2,M1} P(0,234) { leq( X, addition( Y, X
% 0.74/1.57 ) ) }.
% 0.74/1.57 substitution0:
% 0.74/1.57 X := X
% 0.74/1.57 Y := Y
% 0.74/1.57 Z := Z
% 0.74/1.57 end
% 0.74/1.57 substitution1:
% 0.74/1.57 X := X
% 0.74/1.57 Y := addition( Y, Z )
% 0.74/1.57 end
% 0.74/1.57
% 0.74/1.57 paramod: (4467) {G2,W7,D4,L1,V3,M1} { leq( X, addition( addition( Z, X ),
% 0.74/1.57 Y ) ) }.
% 0.74/1.57 parent0[0]: (4465) {G1,W11,D4,L1,V3,M1} { addition( addition( Y, Z ), X )
% 0.74/1.57 = addition( addition( X, Y ), Z ) }.
% 0.74/1.57 parent1[0; 2]: (4466) {G2,W7,D4,L1,V3,M1} { leq( X, addition( addition( X
% 0.74/1.57 , Y ), Z ) ) }.
% 0.74/1.57 substitution0:
% 0.74/1.57 X := Z
% 0.74/1.57 Y := X
% 0.74/1.57 Z := Y
% 0.74/1.57 end
% 0.74/1.57 substitution1:
% 0.74/1.57 X := X
% 0.74/1.57 Y := Y
% 0.74/1.57 Z := Z
% 0.74/1.57 end
% 0.74/1.57
% 0.74/1.57 subsumption: (251) {G4,W7,D4,L1,V3,M1} P(24,240) { leq( Z, addition(
% 0.74/1.57 addition( Y, Z ), X ) ) }.
% 0.74/1.57 parent0: (4467) {G2,W7,D4,L1,V3,M1} { leq( X, addition( addition( Z, X ),
% 0.74/1.57 Y ) ) }.
% 0.74/1.57 substitution0:
% 0.74/1.57 X := Z
% 0.74/1.57 Y := X
% 0.74/1.57 Z := Y
% 0.74/1.57 end
% 0.74/1.57 permutation0:
% 0.74/1.57 0 ==> 0
% 0.74/1.57 end
% 0.74/1.57
% 0.74/1.57 paramod: (4470) {G1,W8,D3,L2,V3,M2} { leq( X, Z ), ! leq( addition( Y, X )
% 0.74/1.57 , Z ) }.
% 0.74/1.57 parent0[1]: (11) {G0,W8,D3,L2,V2,M2} I { ! leq( X, Y ), addition( X, Y )
% 0.74/1.57 ==> Y }.
% 0.74/1.57 parent1[0; 2]: (251) {G4,W7,D4,L1,V3,M1} P(24,240) { leq( Z, addition(
% 0.74/1.57 addition( Y, Z ), X ) ) }.
% 0.74/1.57 substitution0:
% 0.74/1.57 X := addition( Y, X )
% 0.74/1.57 Y := Z
% 0.74/1.57 end
% 0.74/1.57 substitution1:
% 0.74/1.57 X := Z
% 0.74/1.57 Y := Y
% 0.74/1.57 Z := X
% 0.74/1.57 end
% 0.74/1.57
% 0.74/1.57 subsumption: (470) {G5,W8,D3,L2,V3,M2} P(11,251) { leq( Y, Z ), ! leq(
% 0.74/1.57 addition( X, Y ), Z ) }.
% 0.74/1.57 parent0: (4470) {G1,W8,D3,L2,V3,M2} { leq( X, Z ), ! leq( addition( Y, X )
% 0.74/1.57 , Z ) }.
% 0.74/1.57 substitution0:
% 0.74/1.57 X := Y
% 0.74/1.57 Y := X
% 0.74/1.57 Z := Z
% 0.74/1.57 end
% 0.74/1.57 permutation0:
% 0.74/1.57 0 ==> 0
% 0.74/1.57 1 ==> 1
% 0.74/1.57 end
% 0.74/1.57
% 0.74/1.57 paramod: (4475) {G1,W8,D3,L2,V3,M2} { leq( X, Z ), ! leq( addition( X, Y )
% 0.74/1.57 , Z ) }.
% 0.74/1.57 parent0[1]: (11) {G0,W8,D3,L2,V2,M2} I { ! leq( X, Y ), addition( X, Y )
% 0.74/1.57 ==> Y }.
% 0.74/1.57 parent1[0; 2]: (239) {G3,W7,D4,L1,V3,M1} P(1,234) { leq( X, addition(
% 0.74/1.57 addition( X, Y ), Z ) ) }.
% 0.74/1.57 substitution0:
% 0.74/1.57 X := addition( X, Y )
% 0.74/1.57 Y := Z
% 0.74/1.57 end
% 0.74/1.57 substitution1:
% 0.74/1.57 X := X
% 0.74/1.57 Y := Y
% 0.74/1.57 Z := Z
% 0.74/1.57 end
% 0.74/1.57
% 0.74/1.57 subsumption: (483) {G4,W8,D3,L2,V3,M2} P(11,239) { leq( X, Z ), ! leq(
% 0.74/1.57 addition( X, Y ), Z ) }.
% 0.74/1.57 parent0: (4475) {G1,W8,D3,L2,V3,M2} { leq( X, Z ), ! leq( addition( X, Y )
% 0.74/1.57 , Z ) }.
% 0.74/1.57 substitution0:
% 0.74/1.57 X := X
% 0.74/1.57 Y := Y
% 0.74/1.57 Z := Z
% 0.74/1.57 end
% 0.74/1.57 permutation0:
% 0.74/1.57 0 ==> 0
% 0.74/1.57 1 ==> 1
% 0.74/1.57 end
% 0.74/1.57
% 0.74/1.57 resolution: (4479) {G1,W4,D3,L1,V1,M1} { leq( one, star( X ) ) }.
% 0.74/1.57 parent0[1]: (483) {G4,W8,D3,L2,V3,M2} P(11,239) { leq( X, Z ), ! leq(
% 0.74/1.57 addition( X, Y ), Z ) }.
% 0.74/1.57 parent1[0]: (14) {G0,W9,D5,L1,V1,M1} I { leq( addition( one, multiplication
% 0.74/1.57 ( star( X ), X ) ), star( X ) ) }.
% 0.74/1.57 substitution0:
% 0.74/1.57 X := one
% 0.74/1.57 Y := multiplication( star( X ), X )
% 0.74/1.57 Z := star( X )
% 0.74/1.57 end
% 0.74/1.57 substitution1:
% 0.74/1.57 X := X
% 0.74/1.57 end
% 0.74/1.57
% 0.74/1.57 subsumption: (577) {G5,W4,D3,L1,V1,M1} R(483,14) { leq( one, star( X ) )
% 0.74/1.57 }.
% 0.74/1.57 parent0: (4479) {G1,W4,D3,L1,V1,M1} { leq( one, star( X ) ) }.
% 0.74/1.57 substitution0:
% 0.74/1.57 X := X
% 0.74/1.57 end
% 0.74/1.57 permutation0:
% 0.74/1.57 0 ==> 0
% 0.74/1.57 end
% 0.74/1.57
% 0.74/1.57 eqswap: (4480) {G0,W8,D3,L2,V2,M2} { Y ==> addition( X, Y ), ! leq( X, Y )
% 0.74/1.57 }.
% 0.74/1.57 parent0[1]: (11) {G0,W8,D3,L2,V2,M2} I { ! leq( X, Y ), addition( X, Y )
% 0.74/1.57 ==> Y }.
% 0.74/1.57 substitution0:
% 0.74/1.57 X := X
% 0.74/1.57 Y := Y
% 0.74/1.57 end
% 0.74/1.57
% 0.74/1.57 resolution: (4481) {G1,W7,D4,L1,V1,M1} { star( X ) ==> addition( one, star
% 0.74/1.57 ( X ) ) }.
% 0.74/1.57 parent0[1]: (4480) {G0,W8,D3,L2,V2,M2} { Y ==> addition( X, Y ), ! leq( X
% 0.74/1.57 , Y ) }.
% 0.74/1.57 parent1[0]: (577) {G5,W4,D3,L1,V1,M1} R(483,14) { leq( one, star( X ) ) }.
% 0.74/1.57 substitution0:
% 0.74/1.57 X := one
% 0.74/1.57 Y := star( X )
% 0.74/1.57 end
% 0.74/1.57 substitution1:
% 0.74/1.57 X := X
% 0.74/1.57 end
% 0.74/1.57
% 0.74/1.57 eqswap: (4482) {G1,W7,D4,L1,V1,M1} { addition( one, star( X ) ) ==> star(
% 0.74/1.57 X ) }.
% 0.74/1.57 parent0[0]: (4481) {G1,W7,D4,L1,V1,M1} { star( X ) ==> addition( one, star
% 0.74/1.57 ( X ) ) }.
% 0.74/1.57 substitution0:
% 0.74/1.57 X := X
% 0.74/1.57 end
% 0.74/1.57
% 0.74/1.57 subsumption: (593) {G6,W7,D4,L1,V1,M1} R(577,11) { addition( one, star( X )
% 0.74/1.57 ) ==> star( X ) }.
% 0.74/1.57 parent0: (4482) {G1,W7,D4,L1,V1,M1} { addition( one, star( X ) ) ==> star
% 0.74/1.57 ( X ) }.
% 0.74/1.57 substitution0:
% 0.74/1.57 X := X
% 0.74/1.57 end
% 0.74/1.57 permutation0:
% 0.74/1.57 0 ==> 0
% 0.74/1.57 end
% 0.74/1.57
% 0.74/1.57 resolution: (4483) {G1,W7,D4,L1,V1,M1} { leq( multiplication( star( X ), X
% 0.74/1.57 ), star( X ) ) }.
% 0.74/1.57 parent0[1]: (470) {G5,W8,D3,L2,V3,M2} P(11,251) { leq( Y, Z ), ! leq(
% 0.74/1.57 addition( X, Y ), Z ) }.
% 0.74/1.57 parent1[0]: (14) {G0,W9,D5,L1,V1,M1} I { leq( addition( one, multiplication
% 0.74/1.57 ( star( X ), X ) ), star( X ) ) }.
% 0.74/1.57 substitution0:
% 0.74/1.57 X := one
% 0.74/1.57 Y := multiplication( star( X ), X )
% 0.74/1.57 Z := star( X )
% 0.74/1.57 end
% 0.74/1.57 substitution1:
% 0.74/1.57 X := X
% 0.74/1.57 end
% 0.74/1.57
% 0.74/1.57 subsumption: (714) {G6,W7,D4,L1,V1,M1} R(470,14) { leq( multiplication(
% 0.74/1.57 star( X ), X ), star( X ) ) }.
% 0.74/1.57 parent0: (4483) {G1,W7,D4,L1,V1,M1} { leq( multiplication( star( X ), X )
% 0.74/1.57 , star( X ) ) }.
% 0.74/1.57 substitution0:
% 0.74/1.57 X := X
% 0.74/1.57 end
% 0.74/1.57 permutation0:
% 0.74/1.57 0 ==> 0
% 0.74/1.57 end
% 0.74/1.57
% 0.74/1.57 eqswap: (4484) {G0,W8,D3,L2,V2,M2} { Y ==> addition( X, Y ), ! leq( X, Y )
% 0.74/1.57 }.
% 0.74/1.57 parent0[1]: (11) {G0,W8,D3,L2,V2,M2} I { ! leq( X, Y ), addition( X, Y )
% 0.74/1.57 ==> Y }.
% 0.74/1.57 substitution0:
% 0.74/1.57 X := X
% 0.74/1.57 Y := Y
% 0.74/1.57 end
% 0.74/1.57
% 0.74/1.57 resolution: (4485) {G1,W10,D5,L1,V1,M1} { star( X ) ==> addition(
% 0.74/1.57 multiplication( star( X ), X ), star( X ) ) }.
% 0.74/1.57 parent0[1]: (4484) {G0,W8,D3,L2,V2,M2} { Y ==> addition( X, Y ), ! leq( X
% 0.74/1.57 , Y ) }.
% 0.74/1.57 parent1[0]: (714) {G6,W7,D4,L1,V1,M1} R(470,14) { leq( multiplication( star
% 0.74/1.57 ( X ), X ), star( X ) ) }.
% 0.74/1.57 substitution0:
% 0.74/1.57 X := multiplication( star( X ), X )
% 0.74/1.57 Y := star( X )
% 0.74/1.57 end
% 0.74/1.57 substitution1:
% 0.74/1.57 X := X
% 0.74/1.57 end
% 0.74/1.57
% 0.74/1.57 eqswap: (4486) {G1,W10,D5,L1,V1,M1} { addition( multiplication( star( X )
% 0.74/1.57 , X ), star( X ) ) ==> star( X ) }.
% 0.74/1.57 parent0[0]: (4485) {G1,W10,D5,L1,V1,M1} { star( X ) ==> addition(
% 0.74/1.57 multiplication( star( X ), X ), star( X ) ) }.
% 0.74/1.57 substitution0:
% 0.74/1.57 X := X
% 0.74/1.57 end
% 0.74/1.57
% 0.74/1.57 subsumption: (724) {G7,W10,D5,L1,V1,M1} R(714,11) { addition(
% 0.74/1.57 multiplication( star( X ), X ), star( X ) ) ==> star( X ) }.
% 0.74/1.57 parent0: (4486) {G1,W10,D5,L1,V1,M1} { addition( multiplication( star( X )
% 0.74/1.57 , X ), star( X ) ) ==> star( X ) }.
% 0.74/1.57 substitution0:
% 0.74/1.57 X := X
% 0.74/1.57 end
% 0.74/1.57 permutation0:
% 0.74/1.57 0 ==> 0
% 0.74/1.57 end
% 0.74/1.57
% 0.74/1.57 eqswap: (4488) {G1,W16,D4,L2,V3,M2} { ! multiplication( X, Z ) ==>
% 0.74/1.57 multiplication( X, addition( Y, Z ) ), leq( multiplication( X, Y ),
% 0.74/1.57 multiplication( X, Z ) ) }.
% 0.74/1.57 parent0[0]: (63) {G1,W16,D4,L2,V3,M2} P(7,12) { ! multiplication( X,
% 0.74/1.57 addition( Y, Z ) ) ==> multiplication( X, Z ), leq( multiplication( X, Y
% 0.74/1.57 ), multiplication( X, Z ) ) }.
% 0.74/1.57 substitution0:
% 0.74/1.57 X := X
% 0.74/1.57 Y := Y
% 0.74/1.57 Z := Z
% 0.74/1.57 end
% 0.74/1.57
% 0.74/1.57 paramod: (4490) {G2,W17,D4,L2,V2,M2} { ! multiplication( X, star( Y ) )
% 0.74/1.57 ==> multiplication( X, star( Y ) ), leq( multiplication( X, one ),
% 0.74/1.57 multiplication( X, star( Y ) ) ) }.
% 0.74/1.57 parent0[0]: (593) {G6,W7,D4,L1,V1,M1} R(577,11) { addition( one, star( X )
% 0.74/1.57 ) ==> star( X ) }.
% 0.74/1.57 parent1[0; 8]: (4488) {G1,W16,D4,L2,V3,M2} { ! multiplication( X, Z ) ==>
% 0.74/1.57 multiplication( X, addition( Y, Z ) ), leq( multiplication( X, Y ),
% 0.74/1.57 multiplication( X, Z ) ) }.
% 0.74/1.57 substitution0:
% 0.74/1.57 X := Y
% 0.74/1.57 end
% 0.74/1.57 substitution1:
% 0.74/1.57 X := X
% 0.74/1.57 Y := one
% 0.74/1.57 Z := star( Y )
% 0.74/1.57 end
% 0.74/1.57
% 0.74/1.57 eqrefl: (4491) {G0,W8,D4,L1,V2,M1} { leq( multiplication( X, one ),
% 0.74/1.57 multiplication( X, star( Y ) ) ) }.
% 0.74/1.57 parent0[0]: (4490) {G2,W17,D4,L2,V2,M2} { ! multiplication( X, star( Y ) )
% 0.74/1.57 ==> multiplication( X, star( Y ) ), leq( multiplication( X, one ),
% 0.74/1.57 multiplication( X, star( Y ) ) ) }.
% 0.74/1.57 substitution0:
% 0.74/1.57 X := X
% 0.74/1.57 Y := Y
% 0.74/1.57 end
% 0.74/1.57
% 0.74/1.57 paramod: (4492) {G1,W6,D4,L1,V2,M1} { leq( X, multiplication( X, star( Y )
% 0.74/1.57 ) ) }.
% 0.74/1.57 parent0[0]: (5) {G0,W5,D3,L1,V1,M1} I { multiplication( X, one ) ==> X }.
% 0.74/1.57 parent1[0; 1]: (4491) {G0,W8,D4,L1,V2,M1} { leq( multiplication( X, one )
% 0.74/1.57 , multiplication( X, star( Y ) ) ) }.
% 0.74/1.57 substitution0:
% 0.74/1.57 X := X
% 0.74/1.57 end
% 0.74/1.57 substitution1:
% 0.74/1.57 X := X
% 0.74/1.57 Y := Y
% 0.74/1.57 end
% 0.74/1.57
% 0.74/1.57 subsumption: (1700) {G7,W6,D4,L1,V2,M1} P(593,63);q;d(5) { leq( Y,
% 0.74/1.57 multiplication( Y, star( X ) ) ) }.
% 0.74/1.57 parent0: (4492) {G1,W6,D4,L1,V2,M1} { leq( X, multiplication( X, star( Y )
% 0.74/1.57 ) ) }.
% 0.74/1.57 substitution0:
% 0.74/1.57 X := Y
% 0.74/1.57 Y := X
% 0.74/1.57 end
% 0.74/1.57 permutation0:
% 0.74/1.57 0 ==> 0
% 0.74/1.57 end
% 0.74/1.57
% 0.74/1.57 resolution: (4493) {G1,W8,D4,L1,V0,M1} { ! leq( multiplication( star(
% 0.74/1.57 skol1 ), star( skol1 ) ), star( skol1 ) ) }.
% 0.74/1.57 parent0[1]: (17) {G0,W16,D4,L2,V0,M2} I { ! leq( multiplication( star(
% 0.74/1.57 skol1 ), star( skol1 ) ), star( skol1 ) ), ! leq( star( skol1 ),
% 0.74/1.57 multiplication( star( skol1 ), star( skol1 ) ) ) }.
% 0.74/1.57 parent1[0]: (1700) {G7,W6,D4,L1,V2,M1} P(593,63);q;d(5) { leq( Y,
% 0.74/1.57 multiplication( Y, star( X ) ) ) }.
% 0.74/1.57 substitution0:
% 0.74/1.57 end
% 0.74/1.57 substitution1:
% 0.74/1.57 X := skol1
% 0.74/1.57 Y := star( skol1 )
% 0.74/1.57 end
% 0.74/1.57
% 0.74/1.57 subsumption: (1723) {G8,W8,D4,L1,V0,M1} R(1700,17) { ! leq( multiplication
% 0.74/1.57 ( star( skol1 ), star( skol1 ) ), star( skol1 ) ) }.
% 0.74/1.57 parent0: (4493) {G1,W8,D4,L1,V0,M1} { ! leq( multiplication( star( skol1 )
% 0.74/1.57 , star( skol1 ) ), star( skol1 ) ) }.
% 0.74/1.57 substitution0:
% 0.74/1.57 end
% 0.74/1.57 permutation0:
% 0.74/1.57 0 ==> 0
% 0.74/1.57 end
% 0.74/1.57
% 0.74/1.57 resolution: (4495) {G1,W10,D5,L1,V0,M1} { ! leq( addition( multiplication
% 0.74/1.57 ( star( skol1 ), skol1 ), star( skol1 ) ), star( skol1 ) ) }.
% 0.74/1.57 parent0[0]: (1723) {G8,W8,D4,L1,V0,M1} R(1700,17) { ! leq( multiplication(
% 0.74/1.57 star( skol1 ), star( skol1 ) ), star( skol1 ) ) }.
% 0.74/1.57 parent1[1]: (16) {G0,W13,D4,L2,V3,M2} I { ! leq( addition( multiplication(
% 0.74/1.57 X, Y ), Z ), X ), leq( multiplication( Z, star( Y ) ), X ) }.
% 0.74/1.57 substitution0:
% 0.74/1.57 end
% 0.74/1.57 substitution1:
% 0.74/1.57 X := star( skol1 )
% 0.74/1.57 Y := skol1
% 0.74/1.57 Z := star( skol1 )
% 0.74/1.57 end
% 0.74/1.57
% 0.74/1.57 paramod: (4496) {G2,W5,D3,L1,V0,M1} { ! leq( star( skol1 ), star( skol1 )
% 0.74/1.57 ) }.
% 0.74/1.57 parent0[0]: (724) {G7,W10,D5,L1,V1,M1} R(714,11) { addition( multiplication
% 0.74/1.57 ( star( X ), X ), star( X ) ) ==> star( X ) }.
% 0.74/1.57 parent1[0; 2]: (4495) {G1,W10,D5,L1,V0,M1} { ! leq( addition(
% 0.74/1.57 multiplication( star( skol1 ), skol1 ), star( skol1 ) ), star( skol1 ) )
% 0.74/1.57 }.
% 0.74/1.57 substitution0:
% 0.74/1.57 X := skol1
% 0.74/1.57 end
% 0.74/1.57 substitution1:
% 0.74/1.57 end
% 0.74/1.57
% 0.74/1.57 resolution: (4497) {G2,W0,D0,L0,V0,M0} { }.
% 0.74/1.57 parent0[0]: (4496) {G2,W5,D3,L1,V0,M1} { ! leq( star( skol1 ), star( skol1
% 0.74/1.57 ) ) }.
% 0.74/1.57 parent1[0]: (20) {G1,W3,D2,L1,V1,M1} R(12,3) { leq( X, X ) }.
% 0.74/1.57 substitution0:
% 0.74/1.57 end
% 0.74/1.57 substitution1:
% 0.74/1.57 X := star( skol1 )
% 0.74/1.57 end
% 0.74/1.57
% 0.74/1.57 subsumption: (4330) {G9,W0,D0,L0,V0,M0} R(1723,16);d(724);r(20) { }.
% 0.74/1.57 parent0: (4497) {G2,W0,D0,L0,V0,M0} { }.
% 0.74/1.57 substitution0:
% 0.74/1.57 end
% 0.74/1.57 permutation0:
% 0.74/1.57 end
% 0.74/1.57
% 0.74/1.57 Proof check complete!
% 0.74/1.57
% 0.74/1.57 Memory use:
% 0.74/1.57
% 0.74/1.57 space for terms: 55518
% 0.74/1.57 space for clauses: 212881
% 0.74/1.57
% 0.74/1.57
% 0.74/1.57 clauses generated: 47275
% 0.74/1.57 clauses kept: 4331
% 0.74/1.57 clauses selected: 410
% 0.74/1.57 clauses deleted: 134
% 0.74/1.57 clauses inuse deleted: 66
% 0.74/1.57
% 0.74/1.57 subsentry: 166154
% 0.74/1.57 literals s-matched: 109487
% 0.74/1.57 literals matched: 105121
% 0.74/1.57 full subsumption: 30831
% 0.74/1.57
% 0.74/1.57 checksum: -1816263914
% 0.74/1.57
% 0.74/1.57
% 0.74/1.57 Bliksem ended
%------------------------------------------------------------------------------