TSTP Solution File: KLE038+1 by Bliksem---1.12
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%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : KLE038+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n014.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 01:36:49 EDT 2022
% Result : Theorem 0.83s 1.21s
% Output : Refutation 0.83s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : KLE038+1 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.13 % Command : bliksem %s
% 0.13/0.34 % Computer : n014.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 09:15:05 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.83/1.21 *** allocated 10000 integers for termspace/termends
% 0.83/1.21 *** allocated 10000 integers for clauses
% 0.83/1.21 *** allocated 10000 integers for justifications
% 0.83/1.21 Bliksem 1.12
% 0.83/1.21
% 0.83/1.21
% 0.83/1.21 Automatic Strategy Selection
% 0.83/1.21
% 0.83/1.21
% 0.83/1.21 Clauses:
% 0.83/1.21
% 0.83/1.21 { addition( X, Y ) = addition( Y, X ) }.
% 0.83/1.21 { addition( Z, addition( Y, X ) ) = addition( addition( Z, Y ), X ) }.
% 0.83/1.21 { addition( X, zero ) = X }.
% 0.83/1.21 { addition( X, X ) = X }.
% 0.83/1.21 { multiplication( X, multiplication( Y, Z ) ) = multiplication(
% 0.83/1.21 multiplication( X, Y ), Z ) }.
% 0.83/1.21 { multiplication( X, one ) = X }.
% 0.83/1.21 { multiplication( one, X ) = X }.
% 0.83/1.21 { multiplication( X, addition( Y, Z ) ) = addition( multiplication( X, Y )
% 0.83/1.21 , multiplication( X, Z ) ) }.
% 0.83/1.21 { multiplication( addition( X, Y ), Z ) = addition( multiplication( X, Z )
% 0.83/1.21 , multiplication( Y, Z ) ) }.
% 0.83/1.21 { multiplication( X, zero ) = zero }.
% 0.83/1.21 { multiplication( zero, X ) = zero }.
% 0.83/1.21 { ! leq( X, Y ), addition( X, Y ) = Y }.
% 0.83/1.21 { ! addition( X, Y ) = Y, leq( X, Y ) }.
% 0.83/1.21 { leq( addition( one, multiplication( X, star( X ) ) ), star( X ) ) }.
% 0.83/1.21 { leq( addition( one, multiplication( star( X ), X ) ), star( X ) ) }.
% 0.83/1.21 { ! leq( addition( multiplication( X, Y ), Z ), Y ), leq( multiplication(
% 0.83/1.21 star( X ), Z ), Y ) }.
% 0.83/1.21 { ! leq( addition( multiplication( X, Y ), Z ), X ), leq( multiplication( Z
% 0.83/1.21 , star( Y ) ), X ) }.
% 0.83/1.21 { ! leq( skol1, star( skol1 ) ) }.
% 0.83/1.21
% 0.83/1.21 percentage equality = 0.590909, percentage horn = 1.000000
% 0.83/1.21 This is a problem with some equality
% 0.83/1.21
% 0.83/1.21
% 0.83/1.21
% 0.83/1.21 Options Used:
% 0.83/1.21
% 0.83/1.21 useres = 1
% 0.83/1.21 useparamod = 1
% 0.83/1.21 useeqrefl = 1
% 0.83/1.21 useeqfact = 1
% 0.83/1.21 usefactor = 1
% 0.83/1.21 usesimpsplitting = 0
% 0.83/1.21 usesimpdemod = 5
% 0.83/1.21 usesimpres = 3
% 0.83/1.21
% 0.83/1.21 resimpinuse = 1000
% 0.83/1.21 resimpclauses = 20000
% 0.83/1.21 substype = eqrewr
% 0.83/1.21 backwardsubs = 1
% 0.83/1.21 selectoldest = 5
% 0.83/1.21
% 0.83/1.21 litorderings [0] = split
% 0.83/1.21 litorderings [1] = extend the termordering, first sorting on arguments
% 0.83/1.21
% 0.83/1.21 termordering = kbo
% 0.83/1.21
% 0.83/1.21 litapriori = 0
% 0.83/1.21 termapriori = 1
% 0.83/1.21 litaposteriori = 0
% 0.83/1.21 termaposteriori = 0
% 0.83/1.21 demodaposteriori = 0
% 0.83/1.21 ordereqreflfact = 0
% 0.83/1.21
% 0.83/1.21 litselect = negord
% 0.83/1.21
% 0.83/1.21 maxweight = 15
% 0.83/1.21 maxdepth = 30000
% 0.83/1.21 maxlength = 115
% 0.83/1.21 maxnrvars = 195
% 0.83/1.21 excuselevel = 1
% 0.83/1.21 increasemaxweight = 1
% 0.83/1.21
% 0.83/1.21 maxselected = 10000000
% 0.83/1.21 maxnrclauses = 10000000
% 0.83/1.21
% 0.83/1.21 showgenerated = 0
% 0.83/1.21 showkept = 0
% 0.83/1.21 showselected = 0
% 0.83/1.21 showdeleted = 0
% 0.83/1.21 showresimp = 1
% 0.83/1.21 showstatus = 2000
% 0.83/1.21
% 0.83/1.21 prologoutput = 0
% 0.83/1.21 nrgoals = 5000000
% 0.83/1.21 totalproof = 1
% 0.83/1.21
% 0.83/1.21 Symbols occurring in the translation:
% 0.83/1.21
% 0.83/1.21 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.83/1.21 . [1, 2] (w:1, o:19, a:1, s:1, b:0),
% 0.83/1.21 ! [4, 1] (w:0, o:13, a:1, s:1, b:0),
% 0.83/1.21 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.83/1.21 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.83/1.21 addition [37, 2] (w:1, o:43, a:1, s:1, b:0),
% 0.83/1.21 zero [39, 0] (w:1, o:9, a:1, s:1, b:0),
% 0.83/1.21 multiplication [40, 2] (w:1, o:45, a:1, s:1, b:0),
% 0.83/1.21 one [41, 0] (w:1, o:10, a:1, s:1, b:0),
% 0.83/1.21 leq [42, 2] (w:1, o:44, a:1, s:1, b:0),
% 0.83/1.21 star [43, 1] (w:1, o:18, a:1, s:1, b:0),
% 0.83/1.21 skol1 [45, 0] (w:1, o:12, a:1, s:1, b:1).
% 0.83/1.21
% 0.83/1.21
% 0.83/1.21 Starting Search:
% 0.83/1.21
% 0.83/1.21 *** allocated 15000 integers for clauses
% 0.83/1.21 *** allocated 22500 integers for clauses
% 0.83/1.21 *** allocated 33750 integers for clauses
% 0.83/1.21 *** allocated 50625 integers for clauses
% 0.83/1.21 *** allocated 15000 integers for termspace/termends
% 0.83/1.21 *** allocated 75937 integers for clauses
% 0.83/1.21 Resimplifying inuse:
% 0.83/1.21 Done
% 0.83/1.21
% 0.83/1.21 *** allocated 22500 integers for termspace/termends
% 0.83/1.21
% 0.83/1.21 Bliksems!, er is een bewijs:
% 0.83/1.21 % SZS status Theorem
% 0.83/1.21 % SZS output start Refutation
% 0.83/1.21
% 0.83/1.21 (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X ) }.
% 0.83/1.21 (1) {G0,W11,D4,L1,V3,M1} I { addition( Z, addition( Y, X ) ) ==> addition(
% 0.83/1.21 addition( Z, Y ), X ) }.
% 0.83/1.21 (3) {G0,W5,D3,L1,V1,M1} I { addition( X, X ) ==> X }.
% 0.83/1.21 (5) {G0,W5,D3,L1,V1,M1} I { multiplication( X, one ) ==> X }.
% 0.83/1.21 (7) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Y ),
% 0.83/1.21 multiplication( X, Z ) ) ==> multiplication( X, addition( Y, Z ) ) }.
% 0.83/1.21 (11) {G0,W8,D3,L2,V2,M2} I { ! leq( X, Y ), addition( X, Y ) ==> Y }.
% 0.83/1.21 (12) {G0,W8,D3,L2,V2,M2} I { ! addition( X, Y ) ==> Y, leq( X, Y ) }.
% 0.83/1.21 (13) {G0,W9,D5,L1,V1,M1} I { leq( addition( one, multiplication( X, star( X
% 0.83/1.21 ) ) ), star( X ) ) }.
% 0.83/1.21 (14) {G0,W9,D5,L1,V1,M1} I { leq( addition( one, multiplication( star( X )
% 0.83/1.21 , X ) ), star( X ) ) }.
% 0.83/1.21 (17) {G0,W4,D3,L1,V0,M1} I { ! leq( skol1, star( skol1 ) ) }.
% 0.83/1.21 (24) {G1,W14,D4,L2,V3,M2} P(1,12) { ! addition( addition( X, Y ), Z ) ==>
% 0.83/1.21 addition( Y, Z ), leq( X, addition( Y, Z ) ) }.
% 0.83/1.21 (27) {G1,W11,D4,L1,V3,M1} P(1,0) { addition( addition( X, Y ), Z ) =
% 0.83/1.21 addition( addition( Y, Z ), X ) }.
% 0.83/1.21 (62) {G1,W16,D4,L2,V3,M2} P(7,12) { ! multiplication( X, addition( Y, Z ) )
% 0.83/1.21 ==> multiplication( X, Z ), leq( multiplication( X, Y ), multiplication
% 0.83/1.21 ( X, Z ) ) }.
% 0.83/1.21 (198) {G2,W5,D3,L1,V2,M1} P(3,24);q { leq( X, addition( X, Y ) ) }.
% 0.83/1.21 (212) {G3,W7,D4,L1,V3,M1} P(1,198) { leq( X, addition( addition( X, Y ), Z
% 0.83/1.21 ) ) }.
% 0.83/1.21 (213) {G3,W5,D3,L1,V2,M1} P(0,198) { leq( X, addition( Y, X ) ) }.
% 0.83/1.21 (259) {G4,W7,D4,L1,V3,M1} P(27,213) { leq( Z, addition( addition( Y, Z ), X
% 0.83/1.21 ) ) }.
% 0.83/1.21 (297) {G5,W8,D3,L2,V3,M2} P(11,259) { leq( Y, Z ), ! leq( addition( X, Y )
% 0.83/1.21 , Z ) }.
% 0.83/1.21 (307) {G4,W8,D3,L2,V3,M2} P(11,212) { leq( X, Z ), ! leq( addition( X, Y )
% 0.83/1.21 , Z ) }.
% 0.83/1.21 (594) {G5,W4,D3,L1,V1,M1} R(307,14) { leq( one, star( X ) ) }.
% 0.83/1.21 (597) {G5,W6,D3,L1,V1,M1} R(307,17) { ! leq( addition( skol1, X ), star(
% 0.83/1.21 skol1 ) ) }.
% 0.83/1.21 (611) {G6,W7,D4,L1,V1,M1} R(594,11) { addition( one, star( X ) ) ==> star(
% 0.83/1.21 X ) }.
% 0.83/1.21 (617) {G6,W7,D3,L2,V1,M2} P(11,597) { ! leq( X, star( skol1 ) ), ! leq(
% 0.83/1.21 skol1, X ) }.
% 0.83/1.21 (826) {G6,W7,D4,L1,V1,M1} R(297,13) { leq( multiplication( X, star( X ) ),
% 0.83/1.21 star( X ) ) }.
% 0.83/1.21 (853) {G7,W6,D4,L1,V0,M1} R(826,617) { ! leq( skol1, multiplication( skol1
% 0.83/1.21 , star( skol1 ) ) ) }.
% 0.83/1.21 (1382) {G7,W6,D4,L1,V2,M1} P(611,62);q;d(5) { leq( Y, multiplication( Y,
% 0.83/1.21 star( X ) ) ) }.
% 0.83/1.21 (1399) {G8,W0,D0,L0,V0,M0} R(1382,853) { }.
% 0.83/1.21
% 0.83/1.21
% 0.83/1.21 % SZS output end Refutation
% 0.83/1.21 found a proof!
% 0.83/1.21
% 0.83/1.21
% 0.83/1.21 Unprocessed initial clauses:
% 0.83/1.21
% 0.83/1.21 (1401) {G0,W7,D3,L1,V2,M1} { addition( X, Y ) = addition( Y, X ) }.
% 0.83/1.21 (1402) {G0,W11,D4,L1,V3,M1} { addition( Z, addition( Y, X ) ) = addition(
% 0.83/1.21 addition( Z, Y ), X ) }.
% 0.83/1.21 (1403) {G0,W5,D3,L1,V1,M1} { addition( X, zero ) = X }.
% 0.83/1.21 (1404) {G0,W5,D3,L1,V1,M1} { addition( X, X ) = X }.
% 0.83/1.21 (1405) {G0,W11,D4,L1,V3,M1} { multiplication( X, multiplication( Y, Z ) )
% 0.83/1.21 = multiplication( multiplication( X, Y ), Z ) }.
% 0.83/1.21 (1406) {G0,W5,D3,L1,V1,M1} { multiplication( X, one ) = X }.
% 0.83/1.21 (1407) {G0,W5,D3,L1,V1,M1} { multiplication( one, X ) = X }.
% 0.83/1.21 (1408) {G0,W13,D4,L1,V3,M1} { multiplication( X, addition( Y, Z ) ) =
% 0.83/1.21 addition( multiplication( X, Y ), multiplication( X, Z ) ) }.
% 0.83/1.21 (1409) {G0,W13,D4,L1,V3,M1} { multiplication( addition( X, Y ), Z ) =
% 0.83/1.21 addition( multiplication( X, Z ), multiplication( Y, Z ) ) }.
% 0.83/1.21 (1410) {G0,W5,D3,L1,V1,M1} { multiplication( X, zero ) = zero }.
% 0.83/1.21 (1411) {G0,W5,D3,L1,V1,M1} { multiplication( zero, X ) = zero }.
% 0.83/1.21 (1412) {G0,W8,D3,L2,V2,M2} { ! leq( X, Y ), addition( X, Y ) = Y }.
% 0.83/1.21 (1413) {G0,W8,D3,L2,V2,M2} { ! addition( X, Y ) = Y, leq( X, Y ) }.
% 0.83/1.21 (1414) {G0,W9,D5,L1,V1,M1} { leq( addition( one, multiplication( X, star(
% 0.83/1.21 X ) ) ), star( X ) ) }.
% 0.83/1.21 (1415) {G0,W9,D5,L1,V1,M1} { leq( addition( one, multiplication( star( X )
% 0.83/1.21 , X ) ), star( X ) ) }.
% 0.83/1.21 (1416) {G0,W13,D4,L2,V3,M2} { ! leq( addition( multiplication( X, Y ), Z )
% 0.83/1.21 , Y ), leq( multiplication( star( X ), Z ), Y ) }.
% 0.83/1.21 (1417) {G0,W13,D4,L2,V3,M2} { ! leq( addition( multiplication( X, Y ), Z )
% 0.83/1.21 , X ), leq( multiplication( Z, star( Y ) ), X ) }.
% 0.83/1.21 (1418) {G0,W4,D3,L1,V0,M1} { ! leq( skol1, star( skol1 ) ) }.
% 0.83/1.21
% 0.83/1.21
% 0.83/1.21 Total Proof:
% 0.83/1.21
% 0.83/1.21 subsumption: (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X
% 0.83/1.21 ) }.
% 0.83/1.21 parent0: (1401) {G0,W7,D3,L1,V2,M1} { addition( X, Y ) = addition( Y, X )
% 0.83/1.21 }.
% 0.83/1.21 substitution0:
% 0.83/1.21 X := X
% 0.83/1.21 Y := Y
% 0.83/1.21 end
% 0.83/1.21 permutation0:
% 0.83/1.21 0 ==> 0
% 0.83/1.21 end
% 0.83/1.21
% 0.83/1.21 subsumption: (1) {G0,W11,D4,L1,V3,M1} I { addition( Z, addition( Y, X ) )
% 0.83/1.21 ==> addition( addition( Z, Y ), X ) }.
% 0.83/1.21 parent0: (1402) {G0,W11,D4,L1,V3,M1} { addition( Z, addition( Y, X ) ) =
% 0.83/1.21 addition( addition( Z, Y ), X ) }.
% 0.83/1.21 substitution0:
% 0.83/1.21 X := X
% 0.83/1.21 Y := Y
% 0.83/1.21 Z := Z
% 0.83/1.21 end
% 0.83/1.21 permutation0:
% 0.83/1.21 0 ==> 0
% 0.83/1.21 end
% 0.83/1.21
% 0.83/1.21 subsumption: (3) {G0,W5,D3,L1,V1,M1} I { addition( X, X ) ==> X }.
% 0.83/1.21 parent0: (1404) {G0,W5,D3,L1,V1,M1} { addition( X, X ) = X }.
% 0.83/1.21 substitution0:
% 0.83/1.21 X := X
% 0.83/1.21 end
% 0.83/1.21 permutation0:
% 0.83/1.21 0 ==> 0
% 0.83/1.21 end
% 0.83/1.21
% 0.83/1.21 subsumption: (5) {G0,W5,D3,L1,V1,M1} I { multiplication( X, one ) ==> X }.
% 0.83/1.21 parent0: (1406) {G0,W5,D3,L1,V1,M1} { multiplication( X, one ) = X }.
% 0.83/1.21 substitution0:
% 0.83/1.21 X := X
% 0.83/1.21 end
% 0.83/1.21 permutation0:
% 0.83/1.21 0 ==> 0
% 0.83/1.21 end
% 0.83/1.21
% 0.83/1.21 eqswap: (1434) {G0,W13,D4,L1,V3,M1} { addition( multiplication( X, Y ),
% 0.83/1.21 multiplication( X, Z ) ) = multiplication( X, addition( Y, Z ) ) }.
% 0.83/1.21 parent0[0]: (1408) {G0,W13,D4,L1,V3,M1} { multiplication( X, addition( Y,
% 0.83/1.21 Z ) ) = addition( multiplication( X, Y ), multiplication( X, Z ) ) }.
% 0.83/1.21 substitution0:
% 0.83/1.21 X := X
% 0.83/1.21 Y := Y
% 0.83/1.21 Z := Z
% 0.83/1.21 end
% 0.83/1.21
% 0.83/1.21 subsumption: (7) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Y )
% 0.83/1.21 , multiplication( X, Z ) ) ==> multiplication( X, addition( Y, Z ) ) }.
% 0.83/1.21 parent0: (1434) {G0,W13,D4,L1,V3,M1} { addition( multiplication( X, Y ),
% 0.83/1.21 multiplication( X, Z ) ) = multiplication( X, addition( Y, Z ) ) }.
% 0.83/1.21 substitution0:
% 0.83/1.21 X := X
% 0.83/1.21 Y := Y
% 0.83/1.21 Z := Z
% 0.83/1.21 end
% 0.83/1.21 permutation0:
% 0.83/1.21 0 ==> 0
% 0.83/1.21 end
% 0.83/1.21
% 0.83/1.21 subsumption: (11) {G0,W8,D3,L2,V2,M2} I { ! leq( X, Y ), addition( X, Y )
% 0.83/1.21 ==> Y }.
% 0.83/1.21 parent0: (1412) {G0,W8,D3,L2,V2,M2} { ! leq( X, Y ), addition( X, Y ) = Y
% 0.83/1.21 }.
% 0.83/1.21 substitution0:
% 0.83/1.21 X := X
% 0.83/1.21 Y := Y
% 0.83/1.21 end
% 0.83/1.21 permutation0:
% 0.83/1.21 0 ==> 0
% 0.83/1.21 1 ==> 1
% 0.83/1.21 end
% 0.83/1.21
% 0.83/1.21 subsumption: (12) {G0,W8,D3,L2,V2,M2} I { ! addition( X, Y ) ==> Y, leq( X
% 0.83/1.21 , Y ) }.
% 0.83/1.21 parent0: (1413) {G0,W8,D3,L2,V2,M2} { ! addition( X, Y ) = Y, leq( X, Y )
% 0.83/1.21 }.
% 0.83/1.21 substitution0:
% 0.83/1.21 X := X
% 0.83/1.21 Y := Y
% 0.83/1.21 end
% 0.83/1.21 permutation0:
% 0.83/1.21 0 ==> 0
% 0.83/1.21 1 ==> 1
% 0.83/1.21 end
% 0.83/1.21
% 0.83/1.21 subsumption: (13) {G0,W9,D5,L1,V1,M1} I { leq( addition( one,
% 0.83/1.21 multiplication( X, star( X ) ) ), star( X ) ) }.
% 0.83/1.21 parent0: (1414) {G0,W9,D5,L1,V1,M1} { leq( addition( one, multiplication(
% 0.83/1.21 X, star( X ) ) ), star( X ) ) }.
% 0.83/1.21 substitution0:
% 0.83/1.21 X := X
% 0.83/1.21 end
% 0.83/1.21 permutation0:
% 0.83/1.21 0 ==> 0
% 0.83/1.21 end
% 0.83/1.21
% 0.83/1.21 subsumption: (14) {G0,W9,D5,L1,V1,M1} I { leq( addition( one,
% 0.83/1.21 multiplication( star( X ), X ) ), star( X ) ) }.
% 0.83/1.21 parent0: (1415) {G0,W9,D5,L1,V1,M1} { leq( addition( one, multiplication(
% 0.83/1.21 star( X ), X ) ), star( X ) ) }.
% 0.83/1.21 substitution0:
% 0.83/1.21 X := X
% 0.83/1.21 end
% 0.83/1.21 permutation0:
% 0.83/1.21 0 ==> 0
% 0.83/1.21 end
% 0.83/1.21
% 0.83/1.21 subsumption: (17) {G0,W4,D3,L1,V0,M1} I { ! leq( skol1, star( skol1 ) ) }.
% 0.83/1.21 parent0: (1418) {G0,W4,D3,L1,V0,M1} { ! leq( skol1, star( skol1 ) ) }.
% 0.83/1.21 substitution0:
% 0.83/1.21 end
% 0.83/1.21 permutation0:
% 0.83/1.21 0 ==> 0
% 0.83/1.21 end
% 0.83/1.21
% 0.83/1.21 eqswap: (1495) {G0,W8,D3,L2,V2,M2} { ! Y ==> addition( X, Y ), leq( X, Y )
% 0.83/1.21 }.
% 0.83/1.21 parent0[0]: (12) {G0,W8,D3,L2,V2,M2} I { ! addition( X, Y ) ==> Y, leq( X,
% 0.83/1.21 Y ) }.
% 0.83/1.21 substitution0:
% 0.83/1.21 X := X
% 0.83/1.21 Y := Y
% 0.83/1.21 end
% 0.83/1.21
% 0.83/1.21 paramod: (1496) {G1,W14,D4,L2,V3,M2} { ! addition( X, Y ) ==> addition(
% 0.83/1.21 addition( Z, X ), Y ), leq( Z, addition( X, Y ) ) }.
% 0.83/1.21 parent0[0]: (1) {G0,W11,D4,L1,V3,M1} I { addition( Z, addition( Y, X ) )
% 0.83/1.21 ==> addition( addition( Z, Y ), X ) }.
% 0.83/1.21 parent1[0; 5]: (1495) {G0,W8,D3,L2,V2,M2} { ! Y ==> addition( X, Y ), leq
% 0.83/1.21 ( X, Y ) }.
% 0.83/1.21 substitution0:
% 0.83/1.21 X := Y
% 0.83/1.21 Y := X
% 0.83/1.21 Z := Z
% 0.83/1.21 end
% 0.83/1.21 substitution1:
% 0.83/1.21 X := Z
% 0.83/1.21 Y := addition( X, Y )
% 0.83/1.21 end
% 0.83/1.21
% 0.83/1.21 eqswap: (1497) {G1,W14,D4,L2,V3,M2} { ! addition( addition( Z, X ), Y )
% 0.83/1.21 ==> addition( X, Y ), leq( Z, addition( X, Y ) ) }.
% 0.83/1.21 parent0[0]: (1496) {G1,W14,D4,L2,V3,M2} { ! addition( X, Y ) ==> addition
% 0.83/1.21 ( addition( Z, X ), Y ), leq( Z, addition( X, Y ) ) }.
% 0.83/1.21 substitution0:
% 0.83/1.21 X := X
% 0.83/1.21 Y := Y
% 0.83/1.21 Z := Z
% 0.83/1.21 end
% 0.83/1.21
% 0.83/1.21 subsumption: (24) {G1,W14,D4,L2,V3,M2} P(1,12) { ! addition( addition( X, Y
% 0.83/1.21 ), Z ) ==> addition( Y, Z ), leq( X, addition( Y, Z ) ) }.
% 0.83/1.21 parent0: (1497) {G1,W14,D4,L2,V3,M2} { ! addition( addition( Z, X ), Y )
% 0.83/1.21 ==> addition( X, Y ), leq( Z, addition( X, Y ) ) }.
% 0.83/1.21 substitution0:
% 0.83/1.21 X := Y
% 0.83/1.21 Y := Z
% 0.83/1.21 Z := X
% 0.83/1.21 end
% 0.83/1.21 permutation0:
% 0.83/1.21 0 ==> 0
% 0.83/1.21 1 ==> 1
% 0.83/1.21 end
% 0.83/1.21
% 0.83/1.21 eqswap: (1498) {G0,W11,D4,L1,V3,M1} { addition( addition( X, Y ), Z ) ==>
% 0.83/1.21 addition( X, addition( Y, Z ) ) }.
% 0.83/1.21 parent0[0]: (1) {G0,W11,D4,L1,V3,M1} I { addition( Z, addition( Y, X ) )
% 0.83/1.21 ==> addition( addition( Z, Y ), X ) }.
% 0.83/1.21 substitution0:
% 0.83/1.21 X := Z
% 0.83/1.21 Y := Y
% 0.83/1.21 Z := X
% 0.83/1.21 end
% 0.83/1.21
% 0.83/1.21 paramod: (1501) {G1,W11,D4,L1,V3,M1} { addition( addition( X, Y ), Z ) ==>
% 0.83/1.21 addition( addition( Y, Z ), X ) }.
% 0.83/1.21 parent0[0]: (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X )
% 0.83/1.21 }.
% 0.83/1.21 parent1[0; 6]: (1498) {G0,W11,D4,L1,V3,M1} { addition( addition( X, Y ), Z
% 0.83/1.21 ) ==> addition( X, addition( Y, Z ) ) }.
% 0.83/1.21 substitution0:
% 0.83/1.21 X := X
% 0.83/1.21 Y := addition( Y, Z )
% 0.83/1.21 end
% 0.83/1.21 substitution1:
% 0.83/1.21 X := X
% 0.83/1.21 Y := Y
% 0.83/1.21 Z := Z
% 0.83/1.21 end
% 0.83/1.21
% 0.83/1.21 subsumption: (27) {G1,W11,D4,L1,V3,M1} P(1,0) { addition( addition( X, Y )
% 0.83/1.21 , Z ) = addition( addition( Y, Z ), X ) }.
% 0.83/1.21 parent0: (1501) {G1,W11,D4,L1,V3,M1} { addition( addition( X, Y ), Z ) ==>
% 0.83/1.21 addition( addition( Y, Z ), X ) }.
% 0.83/1.21 substitution0:
% 0.83/1.21 X := X
% 0.83/1.21 Y := Y
% 0.83/1.21 Z := Z
% 0.83/1.21 end
% 0.83/1.21 permutation0:
% 0.83/1.21 0 ==> 0
% 0.83/1.21 end
% 0.83/1.21
% 0.83/1.21 eqswap: (1516) {G0,W8,D3,L2,V2,M2} { ! Y ==> addition( X, Y ), leq( X, Y )
% 0.83/1.21 }.
% 0.83/1.21 parent0[0]: (12) {G0,W8,D3,L2,V2,M2} I { ! addition( X, Y ) ==> Y, leq( X,
% 0.83/1.21 Y ) }.
% 0.83/1.21 substitution0:
% 0.83/1.21 X := X
% 0.83/1.21 Y := Y
% 0.83/1.21 end
% 0.83/1.21
% 0.83/1.21 paramod: (1517) {G1,W16,D4,L2,V3,M2} { ! multiplication( X, Y ) ==>
% 0.83/1.21 multiplication( X, addition( Z, Y ) ), leq( multiplication( X, Z ),
% 0.83/1.21 multiplication( X, Y ) ) }.
% 0.83/1.21 parent0[0]: (7) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Y ),
% 0.83/1.21 multiplication( X, Z ) ) ==> multiplication( X, addition( Y, Z ) ) }.
% 0.83/1.21 parent1[0; 5]: (1516) {G0,W8,D3,L2,V2,M2} { ! Y ==> addition( X, Y ), leq
% 0.83/1.21 ( X, Y ) }.
% 0.83/1.21 substitution0:
% 0.83/1.21 X := X
% 0.83/1.21 Y := Z
% 0.83/1.21 Z := Y
% 0.83/1.21 end
% 0.83/1.21 substitution1:
% 0.83/1.21 X := multiplication( X, Z )
% 0.83/1.21 Y := multiplication( X, Y )
% 0.83/1.21 end
% 0.83/1.21
% 0.83/1.21 eqswap: (1518) {G1,W16,D4,L2,V3,M2} { ! multiplication( X, addition( Z, Y
% 0.83/1.21 ) ) ==> multiplication( X, Y ), leq( multiplication( X, Z ),
% 0.83/1.21 multiplication( X, Y ) ) }.
% 0.83/1.21 parent0[0]: (1517) {G1,W16,D4,L2,V3,M2} { ! multiplication( X, Y ) ==>
% 0.83/1.21 multiplication( X, addition( Z, Y ) ), leq( multiplication( X, Z ),
% 0.83/1.21 multiplication( X, Y ) ) }.
% 0.83/1.21 substitution0:
% 0.83/1.21 X := X
% 0.83/1.21 Y := Y
% 0.83/1.21 Z := Z
% 0.83/1.21 end
% 0.83/1.21
% 0.83/1.21 subsumption: (62) {G1,W16,D4,L2,V3,M2} P(7,12) { ! multiplication( X,
% 0.83/1.21 addition( Y, Z ) ) ==> multiplication( X, Z ), leq( multiplication( X, Y
% 0.83/1.21 ), multiplication( X, Z ) ) }.
% 0.83/1.21 parent0: (1518) {G1,W16,D4,L2,V3,M2} { ! multiplication( X, addition( Z, Y
% 0.83/1.21 ) ) ==> multiplication( X, Y ), leq( multiplication( X, Z ),
% 0.83/1.21 multiplication( X, Y ) ) }.
% 0.83/1.21 substitution0:
% 0.83/1.21 X := X
% 0.83/1.21 Y := Z
% 0.83/1.21 Z := Y
% 0.83/1.21 end
% 0.83/1.21 permutation0:
% 0.83/1.21 0 ==> 0
% 0.83/1.21 1 ==> 1
% 0.83/1.21 end
% 0.83/1.21
% 0.83/1.21 eqswap: (1520) {G1,W14,D4,L2,V3,M2} { ! addition( Y, Z ) ==> addition(
% 0.83/1.21 addition( X, Y ), Z ), leq( X, addition( Y, Z ) ) }.
% 0.83/1.21 parent0[0]: (24) {G1,W14,D4,L2,V3,M2} P(1,12) { ! addition( addition( X, Y
% 0.83/1.21 ), Z ) ==> addition( Y, Z ), leq( X, addition( Y, Z ) ) }.
% 0.83/1.21 substitution0:
% 0.83/1.21 X := X
% 0.83/1.21 Y := Y
% 0.83/1.21 Z := Z
% 0.83/1.21 end
% 0.83/1.21
% 0.83/1.21 paramod: (1523) {G1,W12,D3,L2,V2,M2} { ! addition( X, Y ) ==> addition( X
% 0.83/1.21 , Y ), leq( X, addition( X, Y ) ) }.
% 0.83/1.21 parent0[0]: (3) {G0,W5,D3,L1,V1,M1} I { addition( X, X ) ==> X }.
% 0.83/1.21 parent1[0; 6]: (1520) {G1,W14,D4,L2,V3,M2} { ! addition( Y, Z ) ==>
% 0.83/1.21 addition( addition( X, Y ), Z ), leq( X, addition( Y, Z ) ) }.
% 0.83/1.21 substitution0:
% 0.83/1.21 X := X
% 0.83/1.21 end
% 0.83/1.21 substitution1:
% 0.83/1.21 X := X
% 0.83/1.21 Y := X
% 0.83/1.21 Z := Y
% 0.83/1.21 end
% 0.83/1.21
% 0.83/1.21 eqrefl: (1526) {G0,W5,D3,L1,V2,M1} { leq( X, addition( X, Y ) ) }.
% 0.83/1.21 parent0[0]: (1523) {G1,W12,D3,L2,V2,M2} { ! addition( X, Y ) ==> addition
% 0.83/1.21 ( X, Y ), leq( X, addition( X, Y ) ) }.
% 0.83/1.21 substitution0:
% 0.83/1.21 X := X
% 0.83/1.21 Y := Y
% 0.83/1.21 end
% 0.83/1.21
% 0.83/1.21 subsumption: (198) {G2,W5,D3,L1,V2,M1} P(3,24);q { leq( X, addition( X, Y )
% 0.83/1.21 ) }.
% 0.83/1.21 parent0: (1526) {G0,W5,D3,L1,V2,M1} { leq( X, addition( X, Y ) ) }.
% 0.83/1.21 substitution0:
% 0.83/1.21 X := X
% 0.83/1.21 Y := Y
% 0.83/1.21 end
% 0.83/1.21 permutation0:
% 0.83/1.21 0 ==> 0
% 0.83/1.21 end
% 0.83/1.21
% 0.83/1.21 paramod: (1528) {G1,W7,D4,L1,V3,M1} { leq( X, addition( addition( X, Y ),
% 0.83/1.21 Z ) ) }.
% 0.83/1.21 parent0[0]: (1) {G0,W11,D4,L1,V3,M1} I { addition( Z, addition( Y, X ) )
% 0.83/1.21 ==> addition( addition( Z, Y ), X ) }.
% 0.83/1.21 parent1[0; 2]: (198) {G2,W5,D3,L1,V2,M1} P(3,24);q { leq( X, addition( X, Y
% 0.83/1.21 ) ) }.
% 0.83/1.21 substitution0:
% 0.83/1.21 X := Z
% 0.83/1.21 Y := Y
% 0.83/1.21 Z := X
% 0.83/1.21 end
% 0.83/1.21 substitution1:
% 0.83/1.21 X := X
% 0.83/1.21 Y := addition( Y, Z )
% 0.83/1.21 end
% 0.83/1.21
% 0.83/1.21 subsumption: (212) {G3,W7,D4,L1,V3,M1} P(1,198) { leq( X, addition(
% 0.83/1.21 addition( X, Y ), Z ) ) }.
% 0.83/1.21 parent0: (1528) {G1,W7,D4,L1,V3,M1} { leq( X, addition( addition( X, Y ),
% 0.83/1.21 Z ) ) }.
% 0.83/1.21 substitution0:
% 0.83/1.21 X := X
% 0.83/1.21 Y := Y
% 0.83/1.21 Z := Z
% 0.83/1.21 end
% 0.83/1.21 permutation0:
% 0.83/1.21 0 ==> 0
% 0.83/1.21 end
% 0.83/1.21
% 0.83/1.21 paramod: (1529) {G1,W5,D3,L1,V2,M1} { leq( X, addition( Y, X ) ) }.
% 0.83/1.21 parent0[0]: (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X )
% 0.83/1.21 }.
% 0.83/1.21 parent1[0; 2]: (198) {G2,W5,D3,L1,V2,M1} P(3,24);q { leq( X, addition( X, Y
% 0.83/1.21 ) ) }.
% 0.83/1.21 substitution0:
% 0.83/1.21 X := X
% 0.83/1.21 Y := Y
% 0.83/1.21 end
% 0.83/1.21 substitution1:
% 0.83/1.21 X := X
% 0.83/1.21 Y := Y
% 0.83/1.21 end
% 0.83/1.21
% 0.83/1.21 subsumption: (213) {G3,W5,D3,L1,V2,M1} P(0,198) { leq( X, addition( Y, X )
% 0.83/1.21 ) }.
% 0.83/1.21 parent0: (1529) {G1,W5,D3,L1,V2,M1} { leq( X, addition( Y, X ) ) }.
% 0.83/1.21 substitution0:
% 0.83/1.21 X := X
% 0.83/1.21 Y := Y
% 0.83/1.21 end
% 0.83/1.21 permutation0:
% 0.83/1.21 0 ==> 0
% 0.83/1.21 end
% 0.83/1.21
% 0.83/1.21 eqswap: (1531) {G1,W11,D4,L1,V3,M1} { addition( addition( Y, Z ), X ) =
% 0.83/1.21 addition( addition( X, Y ), Z ) }.
% 0.83/1.21 parent0[0]: (27) {G1,W11,D4,L1,V3,M1} P(1,0) { addition( addition( X, Y ),
% 0.83/1.21 Z ) = addition( addition( Y, Z ), X ) }.
% 0.83/1.21 substitution0:
% 0.83/1.21 X := X
% 0.83/1.21 Y := Y
% 0.83/1.21 Z := Z
% 0.83/1.21 end
% 0.83/1.21
% 0.83/1.21 paramod: (1532) {G2,W7,D4,L1,V3,M1} { leq( X, addition( addition( X, Y ),
% 0.83/1.21 Z ) ) }.
% 0.83/1.21 parent0[0]: (1531) {G1,W11,D4,L1,V3,M1} { addition( addition( Y, Z ), X )
% 0.83/1.21 = addition( addition( X, Y ), Z ) }.
% 0.83/1.21 parent1[0; 2]: (213) {G3,W5,D3,L1,V2,M1} P(0,198) { leq( X, addition( Y, X
% 0.83/1.21 ) ) }.
% 0.83/1.21 substitution0:
% 0.83/1.21 X := X
% 0.83/1.21 Y := Y
% 0.83/1.21 Z := Z
% 0.83/1.21 end
% 0.83/1.21 substitution1:
% 0.83/1.21 X := X
% 0.83/1.21 Y := addition( Y, Z )
% 0.83/1.21 end
% 0.83/1.21
% 0.83/1.21 paramod: (1533) {G2,W7,D4,L1,V3,M1} { leq( X, addition( addition( Z, X ),
% 0.83/1.21 Y ) ) }.
% 0.83/1.21 parent0[0]: (1531) {G1,W11,D4,L1,V3,M1} { addition( addition( Y, Z ), X )
% 0.83/1.21 = addition( addition( X, Y ), Z ) }.
% 0.83/1.21 parent1[0; 2]: (1532) {G2,W7,D4,L1,V3,M1} { leq( X, addition( addition( X
% 0.83/1.21 , Y ), Z ) ) }.
% 0.83/1.21 substitution0:
% 0.83/1.21 X := Z
% 0.83/1.21 Y := X
% 0.83/1.21 Z := Y
% 0.83/1.21 end
% 0.83/1.21 substitution1:
% 0.83/1.21 X := X
% 0.83/1.21 Y := Y
% 0.83/1.21 Z := Z
% 0.83/1.21 end
% 0.83/1.21
% 0.83/1.21 subsumption: (259) {G4,W7,D4,L1,V3,M1} P(27,213) { leq( Z, addition(
% 0.83/1.21 addition( Y, Z ), X ) ) }.
% 0.83/1.21 parent0: (1533) {G2,W7,D4,L1,V3,M1} { leq( X, addition( addition( Z, X ),
% 0.83/1.21 Y ) ) }.
% 0.83/1.21 substitution0:
% 0.83/1.21 X := Z
% 0.83/1.21 Y := X
% 0.83/1.21 Z := Y
% 0.83/1.21 end
% 0.83/1.21 permutation0:
% 0.83/1.21 0 ==> 0
% 0.83/1.21 end
% 0.83/1.21
% 0.83/1.21 paramod: (1536) {G1,W8,D3,L2,V3,M2} { leq( X, Z ), ! leq( addition( Y, X )
% 0.83/1.21 , Z ) }.
% 0.83/1.21 parent0[1]: (11) {G0,W8,D3,L2,V2,M2} I { ! leq( X, Y ), addition( X, Y )
% 0.83/1.21 ==> Y }.
% 0.83/1.21 parent1[0; 2]: (259) {G4,W7,D4,L1,V3,M1} P(27,213) { leq( Z, addition(
% 0.83/1.21 addition( Y, Z ), X ) ) }.
% 0.83/1.21 substitution0:
% 0.83/1.21 X := addition( Y, X )
% 0.83/1.21 Y := Z
% 0.83/1.21 end
% 0.83/1.21 substitution1:
% 0.83/1.21 X := Z
% 0.83/1.21 Y := Y
% 0.83/1.21 Z := X
% 0.83/1.21 end
% 0.83/1.21
% 0.83/1.21 subsumption: (297) {G5,W8,D3,L2,V3,M2} P(11,259) { leq( Y, Z ), ! leq(
% 0.83/1.21 addition( X, Y ), Z ) }.
% 0.83/1.21 parent0: (1536) {G1,W8,D3,L2,V3,M2} { leq( X, Z ), ! leq( addition( Y, X )
% 0.83/1.21 , Z ) }.
% 0.83/1.21 substitution0:
% 0.83/1.21 X := Y
% 0.83/1.21 Y := X
% 0.83/1.21 Z := Z
% 0.83/1.21 end
% 0.83/1.21 permutation0:
% 0.83/1.21 0 ==> 0
% 0.83/1.21 1 ==> 1
% 0.83/1.21 end
% 0.83/1.21
% 0.83/1.21 paramod: (1541) {G1,W8,D3,L2,V3,M2} { leq( X, Z ), ! leq( addition( X, Y )
% 0.83/1.21 , Z ) }.
% 0.83/1.21 parent0[1]: (11) {G0,W8,D3,L2,V2,M2} I { ! leq( X, Y ), addition( X, Y )
% 0.83/1.21 ==> Y }.
% 0.83/1.21 parent1[0; 2]: (212) {G3,W7,D4,L1,V3,M1} P(1,198) { leq( X, addition(
% 0.83/1.21 addition( X, Y ), Z ) ) }.
% 0.83/1.21 substitution0:
% 0.83/1.21 X := addition( X, Y )
% 0.83/1.21 Y := Z
% 0.83/1.21 end
% 0.83/1.21 substitution1:
% 0.83/1.21 X := X
% 0.83/1.21 Y := Y
% 0.83/1.21 Z := Z
% 0.83/1.21 end
% 0.83/1.21
% 0.83/1.21 subsumption: (307) {G4,W8,D3,L2,V3,M2} P(11,212) { leq( X, Z ), ! leq(
% 0.83/1.21 addition( X, Y ), Z ) }.
% 0.83/1.21 parent0: (1541) {G1,W8,D3,L2,V3,M2} { leq( X, Z ), ! leq( addition( X, Y )
% 0.83/1.21 , Z ) }.
% 0.83/1.21 substitution0:
% 0.83/1.21 X := X
% 0.83/1.21 Y := Y
% 0.83/1.21 Z := Z
% 0.83/1.21 end
% 0.83/1.21 permutation0:
% 0.83/1.21 0 ==> 0
% 0.83/1.21 1 ==> 1
% 0.83/1.21 end
% 0.83/1.21
% 0.83/1.21 resolution: (1545) {G1,W4,D3,L1,V1,M1} { leq( one, star( X ) ) }.
% 0.83/1.21 parent0[1]: (307) {G4,W8,D3,L2,V3,M2} P(11,212) { leq( X, Z ), ! leq(
% 0.83/1.21 addition( X, Y ), Z ) }.
% 0.83/1.21 parent1[0]: (14) {G0,W9,D5,L1,V1,M1} I { leq( addition( one, multiplication
% 0.83/1.21 ( star( X ), X ) ), star( X ) ) }.
% 0.83/1.21 substitution0:
% 0.83/1.21 X := one
% 0.83/1.21 Y := multiplication( star( X ), X )
% 0.83/1.21 Z := star( X )
% 0.83/1.21 end
% 0.83/1.21 substitution1:
% 0.83/1.21 X := X
% 0.83/1.21 end
% 0.83/1.21
% 0.83/1.21 subsumption: (594) {G5,W4,D3,L1,V1,M1} R(307,14) { leq( one, star( X ) )
% 0.83/1.21 }.
% 0.83/1.21 parent0: (1545) {G1,W4,D3,L1,V1,M1} { leq( one, star( X ) ) }.
% 0.83/1.21 substitution0:
% 0.83/1.21 X := X
% 0.83/1.21 end
% 0.83/1.21 permutation0:
% 0.83/1.21 0 ==> 0
% 0.83/1.21 end
% 0.83/1.21
% 0.83/1.21 resolution: (1546) {G1,W6,D3,L1,V1,M1} { ! leq( addition( skol1, X ), star
% 0.83/1.21 ( skol1 ) ) }.
% 0.83/1.21 parent0[0]: (17) {G0,W4,D3,L1,V0,M1} I { ! leq( skol1, star( skol1 ) ) }.
% 0.83/1.21 parent1[0]: (307) {G4,W8,D3,L2,V3,M2} P(11,212) { leq( X, Z ), ! leq(
% 0.83/1.21 addition( X, Y ), Z ) }.
% 0.83/1.21 substitution0:
% 0.83/1.21 end
% 0.83/1.21 substitution1:
% 0.83/1.21 X := skol1
% 0.83/1.21 Y := X
% 0.83/1.21 Z := star( skol1 )
% 0.83/1.21 end
% 0.83/1.21
% 0.83/1.21 subsumption: (597) {G5,W6,D3,L1,V1,M1} R(307,17) { ! leq( addition( skol1,
% 0.83/1.21 X ), star( skol1 ) ) }.
% 0.83/1.21 parent0: (1546) {G1,W6,D3,L1,V1,M1} { ! leq( addition( skol1, X ), star(
% 0.83/1.21 skol1 ) ) }.
% 0.83/1.21 substitution0:
% 0.83/1.21 X := X
% 0.83/1.21 end
% 0.83/1.21 permutation0:
% 0.83/1.21 0 ==> 0
% 0.83/1.21 end
% 0.83/1.21
% 0.83/1.21 eqswap: (1547) {G0,W8,D3,L2,V2,M2} { Y ==> addition( X, Y ), ! leq( X, Y )
% 0.83/1.21 }.
% 0.83/1.21 parent0[1]: (11) {G0,W8,D3,L2,V2,M2} I { ! leq( X, Y ), addition( X, Y )
% 0.83/1.21 ==> Y }.
% 0.83/1.21 substitution0:
% 0.83/1.21 X := X
% 0.83/1.21 Y := Y
% 0.83/1.21 end
% 0.83/1.21
% 0.83/1.21 resolution: (1548) {G1,W7,D4,L1,V1,M1} { star( X ) ==> addition( one, star
% 0.83/1.21 ( X ) ) }.
% 0.83/1.21 parent0[1]: (1547) {G0,W8,D3,L2,V2,M2} { Y ==> addition( X, Y ), ! leq( X
% 0.83/1.21 , Y ) }.
% 0.83/1.21 parent1[0]: (594) {G5,W4,D3,L1,V1,M1} R(307,14) { leq( one, star( X ) ) }.
% 0.83/1.21 substitution0:
% 0.83/1.21 X := one
% 0.83/1.21 Y := star( X )
% 0.83/1.21 end
% 0.83/1.21 substitution1:
% 0.83/1.21 X := X
% 0.83/1.21 end
% 0.83/1.21
% 0.83/1.21 eqswap: (1549) {G1,W7,D4,L1,V1,M1} { addition( one, star( X ) ) ==> star(
% 0.83/1.21 X ) }.
% 0.83/1.21 parent0[0]: (1548) {G1,W7,D4,L1,V1,M1} { star( X ) ==> addition( one, star
% 0.83/1.21 ( X ) ) }.
% 0.83/1.21 substitution0:
% 0.83/1.21 X := X
% 0.83/1.21 end
% 0.83/1.21
% 0.83/1.21 subsumption: (611) {G6,W7,D4,L1,V1,M1} R(594,11) { addition( one, star( X )
% 0.83/1.21 ) ==> star( X ) }.
% 0.83/1.21 parent0: (1549) {G1,W7,D4,L1,V1,M1} { addition( one, star( X ) ) ==> star
% 0.83/1.21 ( X ) }.
% 0.83/1.21 substitution0:
% 0.83/1.21 X := X
% 0.83/1.21 end
% 0.83/1.21 permutation0:
% 0.83/1.21 0 ==> 0
% 0.83/1.21 end
% 0.83/1.21
% 0.83/1.21 paramod: (1551) {G1,W7,D3,L2,V1,M2} { ! leq( X, star( skol1 ) ), ! leq(
% 0.83/1.21 skol1, X ) }.
% 0.83/1.21 parent0[1]: (11) {G0,W8,D3,L2,V2,M2} I { ! leq( X, Y ), addition( X, Y )
% 0.83/1.21 ==> Y }.
% 0.83/1.21 parent1[0; 2]: (597) {G5,W6,D3,L1,V1,M1} R(307,17) { ! leq( addition( skol1
% 0.83/1.21 , X ), star( skol1 ) ) }.
% 0.83/1.21 substitution0:
% 0.83/1.21 X := skol1
% 0.83/1.21 Y := X
% 0.83/1.21 end
% 0.83/1.21 substitution1:
% 0.83/1.21 X := X
% 0.83/1.21 end
% 0.83/1.21
% 0.83/1.21 subsumption: (617) {G6,W7,D3,L2,V1,M2} P(11,597) { ! leq( X, star( skol1 )
% 0.83/1.21 ), ! leq( skol1, X ) }.
% 0.83/1.21 parent0: (1551) {G1,W7,D3,L2,V1,M2} { ! leq( X, star( skol1 ) ), ! leq(
% 0.83/1.21 skol1, X ) }.
% 0.83/1.21 substitution0:
% 0.83/1.21 X := X
% 0.83/1.21 end
% 0.83/1.21 permutation0:
% 0.83/1.21 0 ==> 0
% 0.83/1.21 1 ==> 1
% 0.83/1.21 end
% 0.83/1.21
% 0.83/1.21 resolution: (1552) {G1,W7,D4,L1,V1,M1} { leq( multiplication( X, star( X )
% 0.83/1.21 ), star( X ) ) }.
% 0.83/1.21 parent0[1]: (297) {G5,W8,D3,L2,V3,M2} P(11,259) { leq( Y, Z ), ! leq(
% 0.83/1.21 addition( X, Y ), Z ) }.
% 0.83/1.21 parent1[0]: (13) {G0,W9,D5,L1,V1,M1} I { leq( addition( one, multiplication
% 0.83/1.21 ( X, star( X ) ) ), star( X ) ) }.
% 0.83/1.21 substitution0:
% 0.83/1.21 X := one
% 0.83/1.21 Y := multiplication( X, star( X ) )
% 0.83/1.21 Z := star( X )
% 0.83/1.21 end
% 0.83/1.21 substitution1:
% 0.83/1.21 X := X
% 0.83/1.21 end
% 0.83/1.21
% 0.83/1.21 subsumption: (826) {G6,W7,D4,L1,V1,M1} R(297,13) { leq( multiplication( X,
% 0.83/1.21 star( X ) ), star( X ) ) }.
% 0.83/1.21 parent0: (1552) {G1,W7,D4,L1,V1,M1} { leq( multiplication( X, star( X ) )
% 0.83/1.21 , star( X ) ) }.
% 0.83/1.21 substitution0:
% 0.83/1.21 X := X
% 0.83/1.21 end
% 0.83/1.21 permutation0:
% 0.83/1.21 0 ==> 0
% 0.83/1.21 end
% 0.83/1.21
% 0.83/1.21 resolution: (1553) {G7,W6,D4,L1,V0,M1} { ! leq( skol1, multiplication(
% 0.83/1.21 skol1, star( skol1 ) ) ) }.
% 0.83/1.21 parent0[0]: (617) {G6,W7,D3,L2,V1,M2} P(11,597) { ! leq( X, star( skol1 ) )
% 0.83/1.21 , ! leq( skol1, X ) }.
% 0.83/1.21 parent1[0]: (826) {G6,W7,D4,L1,V1,M1} R(297,13) { leq( multiplication( X,
% 0.83/1.21 star( X ) ), star( X ) ) }.
% 0.83/1.21 substitution0:
% 0.83/1.21 X := multiplication( skol1, star( skol1 ) )
% 0.83/1.21 end
% 0.83/1.21 substitution1:
% 0.83/1.21 X := skol1
% 0.83/1.21 end
% 0.83/1.21
% 0.83/1.21 subsumption: (853) {G7,W6,D4,L1,V0,M1} R(826,617) { ! leq( skol1,
% 0.83/1.21 multiplication( skol1, star( skol1 ) ) ) }.
% 0.83/1.21 parent0: (1553) {G7,W6,D4,L1,V0,M1} { ! leq( skol1, multiplication( skol1
% 0.83/1.21 , star( skol1 ) ) ) }.
% 0.83/1.21 substitution0:
% 0.83/1.21 end
% 0.83/1.21 permutation0:
% 0.83/1.21 0 ==> 0
% 0.83/1.21 end
% 0.83/1.21
% 0.83/1.21 eqswap: (1555) {G1,W16,D4,L2,V3,M2} { ! multiplication( X, Z ) ==>
% 0.83/1.21 multiplication( X, addition( Y, Z ) ), leq( multiplication( X, Y ),
% 0.83/1.21 multiplication( X, Z ) ) }.
% 0.83/1.21 parent0[0]: (62) {G1,W16,D4,L2,V3,M2} P(7,12) { ! multiplication( X,
% 0.83/1.21 addition( Y, Z ) ) ==> multiplication( X, Z ), leq( multiplication( X, Y
% 0.83/1.21 ), multiplication( X, Z ) ) }.
% 0.83/1.21 substitution0:
% 0.83/1.21 X := X
% 0.83/1.21 Y := Y
% 0.83/1.21 Z := Z
% 0.83/1.21 end
% 0.83/1.21
% 0.83/1.21 paramod: (1557) {G2,W17,D4,L2,V2,M2} { ! multiplication( X, star( Y ) )
% 0.83/1.21 ==> multiplication( X, star( Y ) ), leq( multiplication( X, one ),
% 0.83/1.21 multiplication( X, star( Y ) ) ) }.
% 0.83/1.21 parent0[0]: (611) {G6,W7,D4,L1,V1,M1} R(594,11) { addition( one, star( X )
% 0.83/1.21 ) ==> star( X ) }.
% 0.83/1.21 parent1[0; 8]: (1555) {G1,W16,D4,L2,V3,M2} { ! multiplication( X, Z ) ==>
% 0.83/1.21 multiplication( X, addition( Y, Z ) ), leq( multiplication( X, Y ),
% 0.83/1.21 multiplication( X, Z ) ) }.
% 0.83/1.21 substitution0:
% 0.83/1.21 X := Y
% 0.83/1.21 end
% 0.83/1.21 substitution1:
% 0.83/1.21 X := X
% 0.83/1.21 Y := one
% 0.83/1.21 Z := star( Y )
% 0.83/1.21 end
% 0.83/1.21
% 0.83/1.21 eqrefl: (1558) {G0,W8,D4,L1,V2,M1} { leq( multiplication( X, one ),
% 0.83/1.21 multiplication( X, star( Y ) ) ) }.
% 0.83/1.21 parent0[0]: (1557) {G2,W17,D4,L2,V2,M2} { ! multiplication( X, star( Y ) )
% 0.83/1.21 ==> multiplication( X, star( Y ) ), leq( multiplication( X, one ),
% 0.83/1.21 multiplication( X, star( Y ) ) ) }.
% 0.83/1.21 substitution0:
% 0.83/1.21 X := X
% 0.83/1.21 Y := Y
% 0.83/1.21 end
% 0.83/1.21
% 0.83/1.21 paramod: (1559) {G1,W6,D4,L1,V2,M1} { leq( X, multiplication( X, star( Y )
% 0.83/1.21 ) ) }.
% 0.83/1.21 parent0[0]: (5) {G0,W5,D3,L1,V1,M1} I { multiplication( X, one ) ==> X }.
% 0.83/1.21 parent1[0; 1]: (1558) {G0,W8,D4,L1,V2,M1} { leq( multiplication( X, one )
% 0.83/1.21 , multiplication( X, star( Y ) ) ) }.
% 0.83/1.21 substitution0:
% 0.83/1.21 X := X
% 0.83/1.21 end
% 0.83/1.21 substitution1:
% 0.83/1.21 X := X
% 0.83/1.21 Y := Y
% 0.83/1.21 end
% 0.83/1.21
% 0.83/1.21 subsumption: (1382) {G7,W6,D4,L1,V2,M1} P(611,62);q;d(5) { leq( Y,
% 0.83/1.21 multiplication( Y, star( X ) ) ) }.
% 0.83/1.21 parent0: (1559) {G1,W6,D4,L1,V2,M1} { leq( X, multiplication( X, star( Y )
% 0.83/1.21 ) ) }.
% 0.83/1.21 substitution0:
% 0.83/1.21 X := Y
% 0.83/1.21 Y := X
% 0.83/1.21 end
% 0.83/1.21 permutation0:
% 0.83/1.21 0 ==> 0
% 0.83/1.21 end
% 0.83/1.21
% 0.83/1.21 resolution: (1560) {G8,W0,D0,L0,V0,M0} { }.
% 0.83/1.21 parent0[0]: (853) {G7,W6,D4,L1,V0,M1} R(826,617) { ! leq( skol1,
% 0.83/1.21 multiplication( skol1, star( skol1 ) ) ) }.
% 0.83/1.21 parent1[0]: (1382) {G7,W6,D4,L1,V2,M1} P(611,62);q;d(5) { leq( Y,
% 0.83/1.21 multiplication( Y, star( X ) ) ) }.
% 0.83/1.21 substitution0:
% 0.83/1.21 end
% 0.83/1.21 substitution1:
% 0.83/1.21 X := skol1
% 0.83/1.21 Y := skol1
% 0.83/1.21 end
% 0.83/1.21
% 0.83/1.21 subsumption: (1399) {G8,W0,D0,L0,V0,M0} R(1382,853) { }.
% 0.83/1.21 parent0: (1560) {G8,W0,D0,L0,V0,M0} { }.
% 0.83/1.21 substitution0:
% 0.83/1.21 end
% 0.83/1.21 permutation0:
% 0.83/1.21 end
% 0.83/1.21
% 0.83/1.21 Proof check complete!
% 0.83/1.21
% 0.83/1.21 Memory use:
% 0.83/1.21
% 0.83/1.21 space for terms: 17847
% 0.83/1.21 space for clauses: 71131
% 0.83/1.21
% 0.83/1.21
% 0.83/1.21 clauses generated: 10504
% 0.83/1.21 clauses kept: 1400
% 0.83/1.21 clauses selected: 193
% 0.83/1.21 clauses deleted: 32
% 0.83/1.21 clauses inuse deleted: 23
% 0.83/1.21
% 0.83/1.21 subsentry: 22684
% 0.83/1.21 literals s-matched: 16208
% 0.83/1.21 literals matched: 15447
% 0.83/1.21 full subsumption: 2026
% 0.83/1.21
% 0.83/1.21 checksum: 612699136
% 0.83/1.21
% 0.83/1.21
% 0.83/1.21 Bliksem ended
%------------------------------------------------------------------------------