TSTP Solution File: KLE037+1 by Bliksem---1.12
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : KLE037+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 01:36:48 EDT 2022
% Result : Theorem 0.69s 1.11s
% Output : Refutation 0.69s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : KLE037+1 : TPTP v8.1.0. Released v4.0.0.
% 0.11/0.12 % Command : bliksem %s
% 0.12/0.33 % Computer : n014.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 09:27:05 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.69/1.11 *** allocated 10000 integers for termspace/termends
% 0.69/1.11 *** allocated 10000 integers for clauses
% 0.69/1.11 *** allocated 10000 integers for justifications
% 0.69/1.11 Bliksem 1.12
% 0.69/1.11
% 0.69/1.11
% 0.69/1.11 Automatic Strategy Selection
% 0.69/1.11
% 0.69/1.11
% 0.69/1.11 Clauses:
% 0.69/1.11
% 0.69/1.11 { addition( X, Y ) = addition( Y, X ) }.
% 0.69/1.11 { addition( Z, addition( Y, X ) ) = addition( addition( Z, Y ), X ) }.
% 0.69/1.11 { addition( X, zero ) = X }.
% 0.69/1.11 { addition( X, X ) = X }.
% 0.69/1.11 { multiplication( X, multiplication( Y, Z ) ) = multiplication(
% 0.69/1.11 multiplication( X, Y ), Z ) }.
% 0.69/1.11 { multiplication( X, one ) = X }.
% 0.69/1.11 { multiplication( one, X ) = X }.
% 0.69/1.11 { multiplication( X, addition( Y, Z ) ) = addition( multiplication( X, Y )
% 0.69/1.11 , multiplication( X, Z ) ) }.
% 0.69/1.11 { multiplication( addition( X, Y ), Z ) = addition( multiplication( X, Z )
% 0.69/1.11 , multiplication( Y, Z ) ) }.
% 0.69/1.11 { multiplication( X, zero ) = zero }.
% 0.69/1.11 { multiplication( zero, X ) = zero }.
% 0.69/1.11 { ! leq( X, Y ), addition( X, Y ) = Y }.
% 0.69/1.11 { ! addition( X, Y ) = Y, leq( X, Y ) }.
% 0.69/1.11 { leq( addition( one, multiplication( X, star( X ) ) ), star( X ) ) }.
% 0.69/1.11 { leq( addition( one, multiplication( star( X ), X ) ), star( X ) ) }.
% 0.69/1.11 { ! leq( addition( multiplication( X, Y ), Z ), Y ), leq( multiplication(
% 0.69/1.11 star( X ), Z ), Y ) }.
% 0.69/1.11 { ! leq( addition( multiplication( X, Y ), Z ), X ), leq( multiplication( Z
% 0.69/1.11 , star( Y ) ), X ) }.
% 0.69/1.11 { ! leq( one, star( skol1 ) ) }.
% 0.69/1.11
% 0.69/1.11 percentage equality = 0.590909, percentage horn = 1.000000
% 0.69/1.11 This is a problem with some equality
% 0.69/1.11
% 0.69/1.11
% 0.69/1.11
% 0.69/1.11 Options Used:
% 0.69/1.11
% 0.69/1.11 useres = 1
% 0.69/1.11 useparamod = 1
% 0.69/1.11 useeqrefl = 1
% 0.69/1.11 useeqfact = 1
% 0.69/1.11 usefactor = 1
% 0.69/1.11 usesimpsplitting = 0
% 0.69/1.11 usesimpdemod = 5
% 0.69/1.11 usesimpres = 3
% 0.69/1.11
% 0.69/1.11 resimpinuse = 1000
% 0.69/1.11 resimpclauses = 20000
% 0.69/1.11 substype = eqrewr
% 0.69/1.11 backwardsubs = 1
% 0.69/1.11 selectoldest = 5
% 0.69/1.11
% 0.69/1.11 litorderings [0] = split
% 0.69/1.11 litorderings [1] = extend the termordering, first sorting on arguments
% 0.69/1.11
% 0.69/1.11 termordering = kbo
% 0.69/1.11
% 0.69/1.11 litapriori = 0
% 0.69/1.11 termapriori = 1
% 0.69/1.11 litaposteriori = 0
% 0.69/1.11 termaposteriori = 0
% 0.69/1.11 demodaposteriori = 0
% 0.69/1.11 ordereqreflfact = 0
% 0.69/1.11
% 0.69/1.11 litselect = negord
% 0.69/1.11
% 0.69/1.11 maxweight = 15
% 0.69/1.11 maxdepth = 30000
% 0.69/1.11 maxlength = 115
% 0.69/1.11 maxnrvars = 195
% 0.69/1.11 excuselevel = 1
% 0.69/1.11 increasemaxweight = 1
% 0.69/1.11
% 0.69/1.11 maxselected = 10000000
% 0.69/1.11 maxnrclauses = 10000000
% 0.69/1.11
% 0.69/1.11 showgenerated = 0
% 0.69/1.11 showkept = 0
% 0.69/1.11 showselected = 0
% 0.69/1.11 showdeleted = 0
% 0.69/1.11 showresimp = 1
% 0.69/1.11 showstatus = 2000
% 0.69/1.11
% 0.69/1.11 prologoutput = 0
% 0.69/1.11 nrgoals = 5000000
% 0.69/1.11 totalproof = 1
% 0.69/1.11
% 0.69/1.11 Symbols occurring in the translation:
% 0.69/1.11
% 0.69/1.11 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.69/1.11 . [1, 2] (w:1, o:19, a:1, s:1, b:0),
% 0.69/1.11 ! [4, 1] (w:0, o:13, a:1, s:1, b:0),
% 0.69/1.11 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.69/1.11 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.69/1.11 addition [37, 2] (w:1, o:43, a:1, s:1, b:0),
% 0.69/1.11 zero [39, 0] (w:1, o:9, a:1, s:1, b:0),
% 0.69/1.11 multiplication [40, 2] (w:1, o:45, a:1, s:1, b:0),
% 0.69/1.11 one [41, 0] (w:1, o:10, a:1, s:1, b:0),
% 0.69/1.11 leq [42, 2] (w:1, o:44, a:1, s:1, b:0),
% 0.69/1.11 star [43, 1] (w:1, o:18, a:1, s:1, b:0),
% 0.69/1.11 skol1 [45, 0] (w:1, o:12, a:1, s:1, b:1).
% 0.69/1.11
% 0.69/1.11
% 0.69/1.11 Starting Search:
% 0.69/1.11
% 0.69/1.11 *** allocated 15000 integers for clauses
% 0.69/1.11 *** allocated 22500 integers for clauses
% 0.69/1.11 *** allocated 33750 integers for clauses
% 0.69/1.11 *** allocated 50625 integers for clauses
% 0.69/1.11
% 0.69/1.11 Bliksems!, er is een bewijs:
% 0.69/1.11 % SZS status Theorem
% 0.69/1.11 % SZS output start Refutation
% 0.69/1.11
% 0.69/1.11 (1) {G0,W11,D4,L1,V3,M1} I { addition( Z, addition( Y, X ) ) ==> addition(
% 0.69/1.11 addition( Z, Y ), X ) }.
% 0.69/1.11 (3) {G0,W5,D3,L1,V1,M1} I { addition( X, X ) ==> X }.
% 0.69/1.11 (11) {G0,W8,D3,L2,V2,M2} I { ! leq( X, Y ), addition( X, Y ) ==> Y }.
% 0.69/1.11 (12) {G0,W8,D3,L2,V2,M2} I { ! addition( X, Y ) ==> Y, leq( X, Y ) }.
% 0.69/1.11 (14) {G0,W9,D5,L1,V1,M1} I { leq( addition( one, multiplication( star( X )
% 0.69/1.11 , X ) ), star( X ) ) }.
% 0.69/1.11 (17) {G0,W4,D3,L1,V0,M1} I { ! leq( one, star( skol1 ) ) }.
% 0.69/1.11 (24) {G1,W14,D4,L2,V3,M2} P(1,12) { ! addition( addition( X, Y ), Z ) ==>
% 0.69/1.11 addition( Y, Z ), leq( X, addition( Y, Z ) ) }.
% 0.69/1.11 (202) {G2,W5,D3,L1,V2,M1} P(3,24);q { leq( X, addition( X, Y ) ) }.
% 0.69/1.11 (216) {G3,W7,D4,L1,V3,M1} P(1,202) { leq( X, addition( addition( X, Y ), Z
% 0.69/1.11 ) ) }.
% 0.69/1.11 (308) {G4,W8,D3,L2,V3,M2} P(11,216) { leq( X, Z ), ! leq( addition( X, Y )
% 0.69/1.11 , Z ) }.
% 0.69/1.11 (607) {G5,W4,D3,L1,V1,M1} R(308,14) { leq( one, star( X ) ) }.
% 0.69/1.11 (625) {G6,W0,D0,L0,V0,M0} R(607,17) { }.
% 0.69/1.11
% 0.69/1.11
% 0.69/1.11 % SZS output end Refutation
% 0.69/1.11 found a proof!
% 0.69/1.11
% 0.69/1.11
% 0.69/1.11 Unprocessed initial clauses:
% 0.69/1.11
% 0.69/1.11 (627) {G0,W7,D3,L1,V2,M1} { addition( X, Y ) = addition( Y, X ) }.
% 0.69/1.11 (628) {G0,W11,D4,L1,V3,M1} { addition( Z, addition( Y, X ) ) = addition(
% 0.69/1.11 addition( Z, Y ), X ) }.
% 0.69/1.11 (629) {G0,W5,D3,L1,V1,M1} { addition( X, zero ) = X }.
% 0.69/1.11 (630) {G0,W5,D3,L1,V1,M1} { addition( X, X ) = X }.
% 0.69/1.11 (631) {G0,W11,D4,L1,V3,M1} { multiplication( X, multiplication( Y, Z ) ) =
% 0.69/1.11 multiplication( multiplication( X, Y ), Z ) }.
% 0.69/1.11 (632) {G0,W5,D3,L1,V1,M1} { multiplication( X, one ) = X }.
% 0.69/1.11 (633) {G0,W5,D3,L1,V1,M1} { multiplication( one, X ) = X }.
% 0.69/1.11 (634) {G0,W13,D4,L1,V3,M1} { multiplication( X, addition( Y, Z ) ) =
% 0.69/1.11 addition( multiplication( X, Y ), multiplication( X, Z ) ) }.
% 0.69/1.11 (635) {G0,W13,D4,L1,V3,M1} { multiplication( addition( X, Y ), Z ) =
% 0.69/1.11 addition( multiplication( X, Z ), multiplication( Y, Z ) ) }.
% 0.69/1.11 (636) {G0,W5,D3,L1,V1,M1} { multiplication( X, zero ) = zero }.
% 0.69/1.11 (637) {G0,W5,D3,L1,V1,M1} { multiplication( zero, X ) = zero }.
% 0.69/1.11 (638) {G0,W8,D3,L2,V2,M2} { ! leq( X, Y ), addition( X, Y ) = Y }.
% 0.69/1.11 (639) {G0,W8,D3,L2,V2,M2} { ! addition( X, Y ) = Y, leq( X, Y ) }.
% 0.69/1.11 (640) {G0,W9,D5,L1,V1,M1} { leq( addition( one, multiplication( X, star( X
% 0.69/1.11 ) ) ), star( X ) ) }.
% 0.69/1.11 (641) {G0,W9,D5,L1,V1,M1} { leq( addition( one, multiplication( star( X )
% 0.69/1.11 , X ) ), star( X ) ) }.
% 0.69/1.11 (642) {G0,W13,D4,L2,V3,M2} { ! leq( addition( multiplication( X, Y ), Z )
% 0.69/1.11 , Y ), leq( multiplication( star( X ), Z ), Y ) }.
% 0.69/1.11 (643) {G0,W13,D4,L2,V3,M2} { ! leq( addition( multiplication( X, Y ), Z )
% 0.69/1.11 , X ), leq( multiplication( Z, star( Y ) ), X ) }.
% 0.69/1.11 (644) {G0,W4,D3,L1,V0,M1} { ! leq( one, star( skol1 ) ) }.
% 0.69/1.11
% 0.69/1.11
% 0.69/1.11 Total Proof:
% 0.69/1.11
% 0.69/1.11 subsumption: (1) {G0,W11,D4,L1,V3,M1} I { addition( Z, addition( Y, X ) )
% 0.69/1.11 ==> addition( addition( Z, Y ), X ) }.
% 0.69/1.11 parent0: (628) {G0,W11,D4,L1,V3,M1} { addition( Z, addition( Y, X ) ) =
% 0.69/1.11 addition( addition( Z, Y ), X ) }.
% 0.69/1.11 substitution0:
% 0.69/1.11 X := X
% 0.69/1.11 Y := Y
% 0.69/1.11 Z := Z
% 0.69/1.11 end
% 0.69/1.11 permutation0:
% 0.69/1.11 0 ==> 0
% 0.69/1.11 end
% 0.69/1.11
% 0.69/1.11 subsumption: (3) {G0,W5,D3,L1,V1,M1} I { addition( X, X ) ==> X }.
% 0.69/1.11 parent0: (630) {G0,W5,D3,L1,V1,M1} { addition( X, X ) = X }.
% 0.69/1.11 substitution0:
% 0.69/1.11 X := X
% 0.69/1.11 end
% 0.69/1.11 permutation0:
% 0.69/1.11 0 ==> 0
% 0.69/1.11 end
% 0.69/1.11
% 0.69/1.11 subsumption: (11) {G0,W8,D3,L2,V2,M2} I { ! leq( X, Y ), addition( X, Y )
% 0.69/1.11 ==> Y }.
% 0.69/1.11 parent0: (638) {G0,W8,D3,L2,V2,M2} { ! leq( X, Y ), addition( X, Y ) = Y
% 0.69/1.11 }.
% 0.69/1.11 substitution0:
% 0.69/1.11 X := X
% 0.69/1.11 Y := Y
% 0.69/1.11 end
% 0.69/1.11 permutation0:
% 0.69/1.11 0 ==> 0
% 0.69/1.11 1 ==> 1
% 0.69/1.11 end
% 0.69/1.11
% 0.69/1.11 subsumption: (12) {G0,W8,D3,L2,V2,M2} I { ! addition( X, Y ) ==> Y, leq( X
% 0.69/1.11 , Y ) }.
% 0.69/1.11 parent0: (639) {G0,W8,D3,L2,V2,M2} { ! addition( X, Y ) = Y, leq( X, Y )
% 0.69/1.11 }.
% 0.69/1.11 substitution0:
% 0.69/1.11 X := X
% 0.69/1.11 Y := Y
% 0.69/1.11 end
% 0.69/1.11 permutation0:
% 0.69/1.11 0 ==> 0
% 0.69/1.11 1 ==> 1
% 0.69/1.11 end
% 0.69/1.11
% 0.69/1.11 subsumption: (14) {G0,W9,D5,L1,V1,M1} I { leq( addition( one,
% 0.69/1.11 multiplication( star( X ), X ) ), star( X ) ) }.
% 0.69/1.11 parent0: (641) {G0,W9,D5,L1,V1,M1} { leq( addition( one, multiplication(
% 0.69/1.11 star( X ), X ) ), star( X ) ) }.
% 0.69/1.11 substitution0:
% 0.69/1.11 X := X
% 0.69/1.11 end
% 0.69/1.11 permutation0:
% 0.69/1.11 0 ==> 0
% 0.69/1.11 end
% 0.69/1.11
% 0.69/1.11 subsumption: (17) {G0,W4,D3,L1,V0,M1} I { ! leq( one, star( skol1 ) ) }.
% 0.69/1.11 parent0: (644) {G0,W4,D3,L1,V0,M1} { ! leq( one, star( skol1 ) ) }.
% 0.69/1.11 substitution0:
% 0.69/1.11 end
% 0.69/1.11 permutation0:
% 0.69/1.11 0 ==> 0
% 0.69/1.11 end
% 0.69/1.11
% 0.69/1.11 eqswap: (697) {G0,W8,D3,L2,V2,M2} { ! Y ==> addition( X, Y ), leq( X, Y )
% 0.69/1.11 }.
% 0.69/1.11 parent0[0]: (12) {G0,W8,D3,L2,V2,M2} I { ! addition( X, Y ) ==> Y, leq( X,
% 0.69/1.11 Y ) }.
% 0.69/1.11 substitution0:
% 0.69/1.11 X := X
% 0.69/1.11 Y := Y
% 0.69/1.11 end
% 0.69/1.11
% 0.69/1.11 paramod: (698) {G1,W14,D4,L2,V3,M2} { ! addition( X, Y ) ==> addition(
% 0.69/1.11 addition( Z, X ), Y ), leq( Z, addition( X, Y ) ) }.
% 0.69/1.11 parent0[0]: (1) {G0,W11,D4,L1,V3,M1} I { addition( Z, addition( Y, X ) )
% 0.69/1.11 ==> addition( addition( Z, Y ), X ) }.
% 0.69/1.11 parent1[0; 5]: (697) {G0,W8,D3,L2,V2,M2} { ! Y ==> addition( X, Y ), leq(
% 0.69/1.11 X, Y ) }.
% 0.69/1.11 substitution0:
% 0.69/1.11 X := Y
% 0.69/1.11 Y := X
% 0.69/1.11 Z := Z
% 0.69/1.11 end
% 0.69/1.11 substitution1:
% 0.69/1.11 X := Z
% 0.69/1.11 Y := addition( X, Y )
% 0.69/1.11 end
% 0.69/1.11
% 0.69/1.11 eqswap: (699) {G1,W14,D4,L2,V3,M2} { ! addition( addition( Z, X ), Y ) ==>
% 0.69/1.11 addition( X, Y ), leq( Z, addition( X, Y ) ) }.
% 0.69/1.11 parent0[0]: (698) {G1,W14,D4,L2,V3,M2} { ! addition( X, Y ) ==> addition(
% 0.69/1.11 addition( Z, X ), Y ), leq( Z, addition( X, Y ) ) }.
% 0.69/1.11 substitution0:
% 0.69/1.11 X := X
% 0.69/1.11 Y := Y
% 0.69/1.11 Z := Z
% 0.69/1.11 end
% 0.69/1.11
% 0.69/1.11 subsumption: (24) {G1,W14,D4,L2,V3,M2} P(1,12) { ! addition( addition( X, Y
% 0.69/1.11 ), Z ) ==> addition( Y, Z ), leq( X, addition( Y, Z ) ) }.
% 0.69/1.11 parent0: (699) {G1,W14,D4,L2,V3,M2} { ! addition( addition( Z, X ), Y )
% 0.69/1.11 ==> addition( X, Y ), leq( Z, addition( X, Y ) ) }.
% 0.69/1.11 substitution0:
% 0.69/1.11 X := Y
% 0.69/1.11 Y := Z
% 0.69/1.11 Z := X
% 0.69/1.11 end
% 0.69/1.11 permutation0:
% 0.69/1.11 0 ==> 0
% 0.69/1.11 1 ==> 1
% 0.69/1.11 end
% 0.69/1.11
% 0.69/1.11 eqswap: (701) {G1,W14,D4,L2,V3,M2} { ! addition( Y, Z ) ==> addition(
% 0.69/1.11 addition( X, Y ), Z ), leq( X, addition( Y, Z ) ) }.
% 0.69/1.11 parent0[0]: (24) {G1,W14,D4,L2,V3,M2} P(1,12) { ! addition( addition( X, Y
% 0.69/1.11 ), Z ) ==> addition( Y, Z ), leq( X, addition( Y, Z ) ) }.
% 0.69/1.11 substitution0:
% 0.69/1.11 X := X
% 0.69/1.11 Y := Y
% 0.69/1.11 Z := Z
% 0.69/1.11 end
% 0.69/1.11
% 0.69/1.11 paramod: (704) {G1,W12,D3,L2,V2,M2} { ! addition( X, Y ) ==> addition( X,
% 0.69/1.11 Y ), leq( X, addition( X, Y ) ) }.
% 0.69/1.11 parent0[0]: (3) {G0,W5,D3,L1,V1,M1} I { addition( X, X ) ==> X }.
% 0.69/1.11 parent1[0; 6]: (701) {G1,W14,D4,L2,V3,M2} { ! addition( Y, Z ) ==>
% 0.69/1.11 addition( addition( X, Y ), Z ), leq( X, addition( Y, Z ) ) }.
% 0.69/1.11 substitution0:
% 0.69/1.11 X := X
% 0.69/1.11 end
% 0.69/1.11 substitution1:
% 0.69/1.11 X := X
% 0.69/1.11 Y := X
% 0.69/1.11 Z := Y
% 0.69/1.11 end
% 0.69/1.11
% 0.69/1.11 eqrefl: (707) {G0,W5,D3,L1,V2,M1} { leq( X, addition( X, Y ) ) }.
% 0.69/1.11 parent0[0]: (704) {G1,W12,D3,L2,V2,M2} { ! addition( X, Y ) ==> addition(
% 0.69/1.11 X, Y ), leq( X, addition( X, Y ) ) }.
% 0.69/1.11 substitution0:
% 0.69/1.11 X := X
% 0.69/1.11 Y := Y
% 0.69/1.11 end
% 0.69/1.11
% 0.69/1.11 subsumption: (202) {G2,W5,D3,L1,V2,M1} P(3,24);q { leq( X, addition( X, Y )
% 0.69/1.11 ) }.
% 0.69/1.11 parent0: (707) {G0,W5,D3,L1,V2,M1} { leq( X, addition( X, Y ) ) }.
% 0.69/1.11 substitution0:
% 0.69/1.11 X := X
% 0.69/1.11 Y := Y
% 0.69/1.11 end
% 0.69/1.11 permutation0:
% 0.69/1.11 0 ==> 0
% 0.69/1.11 end
% 0.69/1.11
% 0.69/1.11 paramod: (709) {G1,W7,D4,L1,V3,M1} { leq( X, addition( addition( X, Y ), Z
% 0.69/1.11 ) ) }.
% 0.69/1.11 parent0[0]: (1) {G0,W11,D4,L1,V3,M1} I { addition( Z, addition( Y, X ) )
% 0.69/1.11 ==> addition( addition( Z, Y ), X ) }.
% 0.69/1.11 parent1[0; 2]: (202) {G2,W5,D3,L1,V2,M1} P(3,24);q { leq( X, addition( X, Y
% 0.69/1.11 ) ) }.
% 0.69/1.11 substitution0:
% 0.69/1.11 X := Z
% 0.69/1.11 Y := Y
% 0.69/1.11 Z := X
% 0.69/1.11 end
% 0.69/1.11 substitution1:
% 0.69/1.11 X := X
% 0.69/1.11 Y := addition( Y, Z )
% 0.69/1.11 end
% 0.69/1.11
% 0.69/1.11 subsumption: (216) {G3,W7,D4,L1,V3,M1} P(1,202) { leq( X, addition(
% 0.69/1.11 addition( X, Y ), Z ) ) }.
% 0.69/1.11 parent0: (709) {G1,W7,D4,L1,V3,M1} { leq( X, addition( addition( X, Y ), Z
% 0.69/1.11 ) ) }.
% 0.69/1.11 substitution0:
% 0.69/1.11 X := X
% 0.69/1.11 Y := Y
% 0.69/1.11 Z := Z
% 0.69/1.11 end
% 0.69/1.11 permutation0:
% 0.69/1.11 0 ==> 0
% 0.69/1.11 end
% 0.69/1.11
% 0.69/1.11 paramod: (711) {G1,W8,D3,L2,V3,M2} { leq( X, Z ), ! leq( addition( X, Y )
% 0.69/1.11 , Z ) }.
% 0.69/1.11 parent0[1]: (11) {G0,W8,D3,L2,V2,M2} I { ! leq( X, Y ), addition( X, Y )
% 0.69/1.11 ==> Y }.
% 0.69/1.11 parent1[0; 2]: (216) {G3,W7,D4,L1,V3,M1} P(1,202) { leq( X, addition(
% 0.69/1.11 addition( X, Y ), Z ) ) }.
% 0.69/1.11 substitution0:
% 0.69/1.11 X := addition( X, Y )
% 0.69/1.11 Y := Z
% 0.69/1.11 end
% 0.69/1.11 substitution1:
% 0.69/1.11 X := X
% 0.69/1.11 Y := Y
% 0.69/1.11 Z := Z
% 0.69/1.11 end
% 0.69/1.11
% 0.69/1.11 subsumption: (308) {G4,W8,D3,L2,V3,M2} P(11,216) { leq( X, Z ), ! leq(
% 0.69/1.11 addition( X, Y ), Z ) }.
% 0.69/1.11 parent0: (711) {G1,W8,D3,L2,V3,M2} { leq( X, Z ), ! leq( addition( X, Y )
% 0.69/1.11 , Z ) }.
% 0.69/1.11 substitution0:
% 0.69/1.11 X := X
% 0.69/1.11 Y := Y
% 0.69/1.11 Z := Z
% 0.69/1.11 end
% 0.69/1.11 permutation0:
% 0.69/1.11 0 ==> 0
% 0.69/1.11 1 ==> 1
% 0.69/1.11 end
% 0.69/1.11
% 0.69/1.11 resolution: (715) {G1,W4,D3,L1,V1,M1} { leq( one, star( X ) ) }.
% 0.69/1.11 parent0[1]: (308) {G4,W8,D3,L2,V3,M2} P(11,216) { leq( X, Z ), ! leq(
% 0.69/1.11 addition( X, Y ), Z ) }.
% 0.69/1.11 parent1[0]: (14) {G0,W9,D5,L1,V1,M1} I { leq( addition( one, multiplication
% 0.69/1.11 ( star( X ), X ) ), star( X ) ) }.
% 0.69/1.11 substitution0:
% 0.69/1.11 X := one
% 0.69/1.11 Y := multiplication( star( X ), X )
% 0.69/1.11 Z := star( X )
% 0.69/1.11 end
% 0.69/1.11 substitution1:
% 0.69/1.11 X := X
% 0.69/1.11 end
% 0.69/1.11
% 0.69/1.11 subsumption: (607) {G5,W4,D3,L1,V1,M1} R(308,14) { leq( one, star( X ) )
% 0.69/1.11 }.
% 0.69/1.11 parent0: (715) {G1,W4,D3,L1,V1,M1} { leq( one, star( X ) ) }.
% 0.69/1.11 substitution0:
% 0.69/1.11 X := X
% 0.69/1.11 end
% 0.69/1.11 permutation0:
% 0.69/1.11 0 ==> 0
% 0.69/1.11 end
% 0.69/1.11
% 0.69/1.11 resolution: (716) {G1,W0,D0,L0,V0,M0} { }.
% 0.69/1.11 parent0[0]: (17) {G0,W4,D3,L1,V0,M1} I { ! leq( one, star( skol1 ) ) }.
% 0.69/1.11 parent1[0]: (607) {G5,W4,D3,L1,V1,M1} R(308,14) { leq( one, star( X ) ) }.
% 0.69/1.11 substitution0:
% 0.69/1.11 end
% 0.69/1.11 substitution1:
% 0.69/1.11 X := skol1
% 0.69/1.11 end
% 0.69/1.11
% 0.69/1.11 subsumption: (625) {G6,W0,D0,L0,V0,M0} R(607,17) { }.
% 0.69/1.11 parent0: (716) {G1,W0,D0,L0,V0,M0} { }.
% 0.69/1.11 substitution0:
% 0.69/1.11 end
% 0.69/1.11 permutation0:
% 0.69/1.11 end
% 0.69/1.11
% 0.69/1.11 Proof check complete!
% 0.69/1.11
% 0.69/1.11 Memory use:
% 0.69/1.11
% 0.69/1.11 space for terms: 7632
% 0.69/1.11 space for clauses: 36820
% 0.69/1.11
% 0.69/1.11
% 0.69/1.11 clauses generated: 3194
% 0.69/1.11 clauses kept: 626
% 0.69/1.11 clauses selected: 106
% 0.69/1.11 clauses deleted: 7
% 0.69/1.11 clauses inuse deleted: 0
% 0.69/1.11
% 0.69/1.11 subsentry: 4139
% 0.69/1.11 literals s-matched: 3196
% 0.69/1.11 literals matched: 3162
% 0.69/1.11 full subsumption: 240
% 0.69/1.11
% 0.69/1.11 checksum: -1726106036
% 0.69/1.11
% 0.69/1.11
% 0.69/1.11 Bliksem ended
%------------------------------------------------------------------------------