TSTP Solution File: KLE137+1 by Bliksem---1.12
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%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : KLE137+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n011.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 0s
% DateTime : Sun Jul 17 01:37:22 EDT 2022
% Result : Theorem 0.69s 1.13s
% Output : Refutation 0.69s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : KLE137+1 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.12 % Command : bliksem %s
% 0.12/0.33 % Computer : n011.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 08:34:51 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.69/1.13 *** allocated 10000 integers for termspace/termends
% 0.69/1.13 *** allocated 10000 integers for clauses
% 0.69/1.13 *** allocated 10000 integers for justifications
% 0.69/1.13 Bliksem 1.12
% 0.69/1.13
% 0.69/1.13
% 0.69/1.13 Automatic Strategy Selection
% 0.69/1.13
% 0.69/1.13
% 0.69/1.13 Clauses:
% 0.69/1.13
% 0.69/1.13 { addition( X, Y ) = addition( Y, X ) }.
% 0.69/1.13 { addition( Z, addition( Y, X ) ) = addition( addition( Z, Y ), X ) }.
% 0.69/1.13 { addition( X, zero ) = X }.
% 0.69/1.13 { addition( X, X ) = X }.
% 0.69/1.13 { multiplication( X, multiplication( Y, Z ) ) = multiplication(
% 0.69/1.13 multiplication( X, Y ), Z ) }.
% 0.69/1.13 { multiplication( X, one ) = X }.
% 0.69/1.13 { multiplication( one, X ) = X }.
% 0.69/1.13 { multiplication( X, addition( Y, Z ) ) = addition( multiplication( X, Y )
% 0.69/1.13 , multiplication( X, Z ) ) }.
% 0.69/1.13 { multiplication( addition( X, Y ), Z ) = addition( multiplication( X, Z )
% 0.69/1.13 , multiplication( Y, Z ) ) }.
% 0.69/1.13 { multiplication( zero, X ) = zero }.
% 0.69/1.13 { addition( one, multiplication( X, star( X ) ) ) = star( X ) }.
% 0.69/1.13 { addition( one, multiplication( star( X ), X ) ) = star( X ) }.
% 0.69/1.13 { ! leq( addition( multiplication( X, Z ), Y ), Z ), leq( multiplication(
% 0.69/1.13 star( X ), Y ), Z ) }.
% 0.69/1.13 { ! leq( addition( multiplication( Z, X ), Y ), Z ), leq( multiplication( Y
% 0.69/1.13 , star( X ) ), Z ) }.
% 0.69/1.13 { strong_iteration( X ) = addition( multiplication( X, strong_iteration( X
% 0.69/1.13 ) ), one ) }.
% 0.69/1.13 { ! leq( Z, addition( multiplication( X, Z ), Y ) ), leq( Z, multiplication
% 0.69/1.13 ( strong_iteration( X ), Y ) ) }.
% 0.69/1.13 { strong_iteration( X ) = addition( star( X ), multiplication(
% 0.69/1.13 strong_iteration( X ), zero ) ) }.
% 0.69/1.13 { ! leq( X, Y ), addition( X, Y ) = Y }.
% 0.69/1.13 { ! addition( X, Y ) = Y, leq( X, Y ) }.
% 0.69/1.13 { ! leq( skol1, strong_iteration( one ) ) }.
% 0.69/1.13
% 0.69/1.13 percentage equality = 0.640000, percentage horn = 1.000000
% 0.69/1.13 This is a problem with some equality
% 0.69/1.13
% 0.69/1.13
% 0.69/1.13
% 0.69/1.13 Options Used:
% 0.69/1.13
% 0.69/1.13 useres = 1
% 0.69/1.13 useparamod = 1
% 0.69/1.13 useeqrefl = 1
% 0.69/1.13 useeqfact = 1
% 0.69/1.13 usefactor = 1
% 0.69/1.13 usesimpsplitting = 0
% 0.69/1.13 usesimpdemod = 5
% 0.69/1.13 usesimpres = 3
% 0.69/1.13
% 0.69/1.13 resimpinuse = 1000
% 0.69/1.13 resimpclauses = 20000
% 0.69/1.13 substype = eqrewr
% 0.69/1.13 backwardsubs = 1
% 0.69/1.13 selectoldest = 5
% 0.69/1.13
% 0.69/1.13 litorderings [0] = split
% 0.69/1.13 litorderings [1] = extend the termordering, first sorting on arguments
% 0.69/1.13
% 0.69/1.13 termordering = kbo
% 0.69/1.13
% 0.69/1.13 litapriori = 0
% 0.69/1.13 termapriori = 1
% 0.69/1.13 litaposteriori = 0
% 0.69/1.13 termaposteriori = 0
% 0.69/1.13 demodaposteriori = 0
% 0.69/1.13 ordereqreflfact = 0
% 0.69/1.13
% 0.69/1.13 litselect = negord
% 0.69/1.13
% 0.69/1.13 maxweight = 15
% 0.69/1.13 maxdepth = 30000
% 0.69/1.13 maxlength = 115
% 0.69/1.13 maxnrvars = 195
% 0.69/1.13 excuselevel = 1
% 0.69/1.13 increasemaxweight = 1
% 0.69/1.13
% 0.69/1.13 maxselected = 10000000
% 0.69/1.13 maxnrclauses = 10000000
% 0.69/1.13
% 0.69/1.13 showgenerated = 0
% 0.69/1.13 showkept = 0
% 0.69/1.13 showselected = 0
% 0.69/1.13 showdeleted = 0
% 0.69/1.13 showresimp = 1
% 0.69/1.13 showstatus = 2000
% 0.69/1.13
% 0.69/1.13 prologoutput = 0
% 0.69/1.13 nrgoals = 5000000
% 0.69/1.13 totalproof = 1
% 0.69/1.13
% 0.69/1.13 Symbols occurring in the translation:
% 0.69/1.13
% 0.69/1.13 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.69/1.13 . [1, 2] (w:1, o:20, a:1, s:1, b:0),
% 0.69/1.13 ! [4, 1] (w:0, o:13, a:1, s:1, b:0),
% 0.69/1.13 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.69/1.13 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.69/1.13 addition [37, 2] (w:1, o:44, a:1, s:1, b:0),
% 0.69/1.13 zero [39, 0] (w:1, o:9, a:1, s:1, b:0),
% 0.69/1.13 multiplication [40, 2] (w:1, o:46, a:1, s:1, b:0),
% 0.69/1.13 one [41, 0] (w:1, o:10, a:1, s:1, b:0),
% 0.69/1.13 star [42, 1] (w:1, o:18, a:1, s:1, b:0),
% 0.69/1.13 leq [43, 2] (w:1, o:45, a:1, s:1, b:0),
% 0.69/1.13 strong_iteration [44, 1] (w:1, o:19, a:1, s:1, b:0),
% 0.69/1.13 skol1 [46, 0] (w:1, o:12, a:1, s:1, b:1).
% 0.69/1.13
% 0.69/1.13
% 0.69/1.13 Starting Search:
% 0.69/1.13
% 0.69/1.13 *** allocated 15000 integers for clauses
% 0.69/1.13 *** allocated 22500 integers for clauses
% 0.69/1.13 *** allocated 33750 integers for clauses
% 0.69/1.13 *** allocated 50625 integers for clauses
% 0.69/1.13 *** allocated 75937 integers for clauses
% 0.69/1.13 *** allocated 15000 integers for termspace/termends
% 0.69/1.13
% 0.69/1.13 Bliksems!, er is een bewijs:
% 0.69/1.13 % SZS status Theorem
% 0.69/1.13 % SZS output start Refutation
% 0.69/1.13
% 0.69/1.13 (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X ) }.
% 0.69/1.13 (1) {G0,W11,D4,L1,V3,M1} I { addition( Z, addition( Y, X ) ) ==> addition(
% 0.69/1.13 addition( Z, Y ), X ) }.
% 0.69/1.13 (2) {G0,W5,D3,L1,V1,M1} I { addition( X, zero ) ==> X }.
% 0.69/1.13 (3) {G0,W5,D3,L1,V1,M1} I { addition( X, X ) ==> X }.
% 0.69/1.13 (6) {G0,W5,D3,L1,V1,M1} I { multiplication( one, X ) ==> X }.
% 0.69/1.13 (15) {G0,W13,D4,L2,V3,M2} I { ! leq( Z, addition( multiplication( X, Z ), Y
% 0.69/1.13 ) ), leq( Z, multiplication( strong_iteration( X ), Y ) ) }.
% 0.69/1.13 (16) {G0,W10,D5,L1,V1,M1} I { addition( star( X ), multiplication(
% 0.69/1.13 strong_iteration( X ), zero ) ) ==> strong_iteration( X ) }.
% 0.69/1.13 (17) {G0,W8,D3,L2,V2,M2} I { ! leq( X, Y ), addition( X, Y ) ==> Y }.
% 0.69/1.13 (18) {G0,W8,D3,L2,V2,M2} I { ! addition( X, Y ) ==> Y, leq( X, Y ) }.
% 0.69/1.13 (19) {G0,W4,D3,L1,V0,M1} I { ! leq( skol1, strong_iteration( one ) ) }.
% 0.69/1.13 (22) {G1,W3,D2,L1,V1,M1} R(18,3) { leq( X, X ) }.
% 0.69/1.13 (26) {G1,W14,D4,L2,V3,M2} P(1,18) { ! addition( addition( X, Y ), Z ) ==>
% 0.69/1.13 addition( Y, Z ), leq( X, addition( Y, Z ) ) }.
% 0.69/1.13 (293) {G2,W5,D3,L1,V2,M1} P(3,26);q { leq( X, addition( X, Y ) ) }.
% 0.69/1.13 (308) {G3,W7,D4,L1,V3,M1} P(1,293) { leq( X, addition( addition( X, Y ), Z
% 0.69/1.13 ) ) }.
% 0.69/1.13 (309) {G3,W5,D3,L1,V2,M1} P(0,293) { leq( X, addition( Y, X ) ) }.
% 0.69/1.13 (321) {G4,W7,D4,L1,V1,M1} P(16,309) { leq( multiplication( strong_iteration
% 0.69/1.13 ( X ), zero ), strong_iteration( X ) ) }.
% 0.69/1.13 (501) {G4,W8,D3,L2,V3,M2} P(17,308) { leq( X, Z ), ! leq( addition( X, Y )
% 0.69/1.13 , Z ) }.
% 0.69/1.13 (829) {G5,W6,D3,L1,V1,M1} R(501,19) { ! leq( addition( skol1, X ),
% 0.69/1.13 strong_iteration( one ) ) }.
% 0.69/1.13 (870) {G6,W7,D3,L2,V1,M2} P(17,829) { ! leq( X, strong_iteration( one ) ),
% 0.69/1.13 ! leq( skol1, X ) }.
% 0.69/1.13 (889) {G7,W6,D4,L1,V0,M1} R(870,321) { ! leq( skol1, multiplication(
% 0.69/1.13 strong_iteration( one ), zero ) ) }.
% 0.69/1.13 (941) {G8,W0,D0,L0,V0,M0} R(889,15);d(2);d(6);r(22) { }.
% 0.69/1.13
% 0.69/1.13
% 0.69/1.13 % SZS output end Refutation
% 0.69/1.13 found a proof!
% 0.69/1.13
% 0.69/1.13
% 0.69/1.13 Unprocessed initial clauses:
% 0.69/1.13
% 0.69/1.13 (943) {G0,W7,D3,L1,V2,M1} { addition( X, Y ) = addition( Y, X ) }.
% 0.69/1.13 (944) {G0,W11,D4,L1,V3,M1} { addition( Z, addition( Y, X ) ) = addition(
% 0.69/1.13 addition( Z, Y ), X ) }.
% 0.69/1.13 (945) {G0,W5,D3,L1,V1,M1} { addition( X, zero ) = X }.
% 0.69/1.13 (946) {G0,W5,D3,L1,V1,M1} { addition( X, X ) = X }.
% 0.69/1.13 (947) {G0,W11,D4,L1,V3,M1} { multiplication( X, multiplication( Y, Z ) ) =
% 0.69/1.13 multiplication( multiplication( X, Y ), Z ) }.
% 0.69/1.13 (948) {G0,W5,D3,L1,V1,M1} { multiplication( X, one ) = X }.
% 0.69/1.13 (949) {G0,W5,D3,L1,V1,M1} { multiplication( one, X ) = X }.
% 0.69/1.13 (950) {G0,W13,D4,L1,V3,M1} { multiplication( X, addition( Y, Z ) ) =
% 0.69/1.13 addition( multiplication( X, Y ), multiplication( X, Z ) ) }.
% 0.69/1.13 (951) {G0,W13,D4,L1,V3,M1} { multiplication( addition( X, Y ), Z ) =
% 0.69/1.13 addition( multiplication( X, Z ), multiplication( Y, Z ) ) }.
% 0.69/1.13 (952) {G0,W5,D3,L1,V1,M1} { multiplication( zero, X ) = zero }.
% 0.69/1.13 (953) {G0,W9,D5,L1,V1,M1} { addition( one, multiplication( X, star( X ) )
% 0.69/1.13 ) = star( X ) }.
% 0.69/1.13 (954) {G0,W9,D5,L1,V1,M1} { addition( one, multiplication( star( X ), X )
% 0.69/1.13 ) = star( X ) }.
% 0.69/1.13 (955) {G0,W13,D4,L2,V3,M2} { ! leq( addition( multiplication( X, Z ), Y )
% 0.69/1.13 , Z ), leq( multiplication( star( X ), Y ), Z ) }.
% 0.69/1.13 (956) {G0,W13,D4,L2,V3,M2} { ! leq( addition( multiplication( Z, X ), Y )
% 0.69/1.13 , Z ), leq( multiplication( Y, star( X ) ), Z ) }.
% 0.69/1.13 (957) {G0,W9,D5,L1,V1,M1} { strong_iteration( X ) = addition(
% 0.69/1.13 multiplication( X, strong_iteration( X ) ), one ) }.
% 0.69/1.13 (958) {G0,W13,D4,L2,V3,M2} { ! leq( Z, addition( multiplication( X, Z ), Y
% 0.69/1.13 ) ), leq( Z, multiplication( strong_iteration( X ), Y ) ) }.
% 0.69/1.13 (959) {G0,W10,D5,L1,V1,M1} { strong_iteration( X ) = addition( star( X ),
% 0.69/1.13 multiplication( strong_iteration( X ), zero ) ) }.
% 0.69/1.13 (960) {G0,W8,D3,L2,V2,M2} { ! leq( X, Y ), addition( X, Y ) = Y }.
% 0.69/1.13 (961) {G0,W8,D3,L2,V2,M2} { ! addition( X, Y ) = Y, leq( X, Y ) }.
% 0.69/1.13 (962) {G0,W4,D3,L1,V0,M1} { ! leq( skol1, strong_iteration( one ) ) }.
% 0.69/1.13
% 0.69/1.13
% 0.69/1.13 Total Proof:
% 0.69/1.13
% 0.69/1.13 subsumption: (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X
% 0.69/1.13 ) }.
% 0.69/1.13 parent0: (943) {G0,W7,D3,L1,V2,M1} { addition( X, Y ) = addition( Y, X )
% 0.69/1.13 }.
% 0.69/1.13 substitution0:
% 0.69/1.13 X := X
% 0.69/1.13 Y := Y
% 0.69/1.13 end
% 0.69/1.13 permutation0:
% 0.69/1.13 0 ==> 0
% 0.69/1.13 end
% 0.69/1.13
% 0.69/1.13 subsumption: (1) {G0,W11,D4,L1,V3,M1} I { addition( Z, addition( Y, X ) )
% 0.69/1.13 ==> addition( addition( Z, Y ), X ) }.
% 0.69/1.13 parent0: (944) {G0,W11,D4,L1,V3,M1} { addition( Z, addition( Y, X ) ) =
% 0.69/1.13 addition( addition( Z, Y ), X ) }.
% 0.69/1.13 substitution0:
% 0.69/1.13 X := X
% 0.69/1.13 Y := Y
% 0.69/1.13 Z := Z
% 0.69/1.13 end
% 0.69/1.13 permutation0:
% 0.69/1.13 0 ==> 0
% 0.69/1.13 end
% 0.69/1.13
% 0.69/1.13 subsumption: (2) {G0,W5,D3,L1,V1,M1} I { addition( X, zero ) ==> X }.
% 0.69/1.13 parent0: (945) {G0,W5,D3,L1,V1,M1} { addition( X, zero ) = X }.
% 0.69/1.13 substitution0:
% 0.69/1.13 X := X
% 0.69/1.13 end
% 0.69/1.13 permutation0:
% 0.69/1.13 0 ==> 0
% 0.69/1.13 end
% 0.69/1.13
% 0.69/1.13 subsumption: (3) {G0,W5,D3,L1,V1,M1} I { addition( X, X ) ==> X }.
% 0.69/1.13 parent0: (946) {G0,W5,D3,L1,V1,M1} { addition( X, X ) = X }.
% 0.69/1.13 substitution0:
% 0.69/1.13 X := X
% 0.69/1.13 end
% 0.69/1.13 permutation0:
% 0.69/1.13 0 ==> 0
% 0.69/1.13 end
% 0.69/1.13
% 0.69/1.13 subsumption: (6) {G0,W5,D3,L1,V1,M1} I { multiplication( one, X ) ==> X }.
% 0.69/1.13 parent0: (949) {G0,W5,D3,L1,V1,M1} { multiplication( one, X ) = X }.
% 0.69/1.13 substitution0:
% 0.69/1.13 X := X
% 0.69/1.13 end
% 0.69/1.13 permutation0:
% 0.69/1.13 0 ==> 0
% 0.69/1.13 end
% 0.69/1.13
% 0.69/1.13 subsumption: (15) {G0,W13,D4,L2,V3,M2} I { ! leq( Z, addition(
% 0.69/1.13 multiplication( X, Z ), Y ) ), leq( Z, multiplication( strong_iteration(
% 0.69/1.13 X ), Y ) ) }.
% 0.69/1.13 parent0: (958) {G0,W13,D4,L2,V3,M2} { ! leq( Z, addition( multiplication(
% 0.69/1.13 X, Z ), Y ) ), leq( Z, multiplication( strong_iteration( X ), Y ) ) }.
% 0.69/1.13 substitution0:
% 0.69/1.13 X := X
% 0.69/1.13 Y := Y
% 0.69/1.13 Z := Z
% 0.69/1.13 end
% 0.69/1.13 permutation0:
% 0.69/1.13 0 ==> 0
% 0.69/1.13 1 ==> 1
% 0.69/1.13 end
% 0.69/1.13
% 0.69/1.13 eqswap: (999) {G0,W10,D5,L1,V1,M1} { addition( star( X ), multiplication(
% 0.69/1.13 strong_iteration( X ), zero ) ) = strong_iteration( X ) }.
% 0.69/1.13 parent0[0]: (959) {G0,W10,D5,L1,V1,M1} { strong_iteration( X ) = addition
% 0.69/1.13 ( star( X ), multiplication( strong_iteration( X ), zero ) ) }.
% 0.69/1.13 substitution0:
% 0.69/1.13 X := X
% 0.69/1.13 end
% 0.69/1.13
% 0.69/1.13 subsumption: (16) {G0,W10,D5,L1,V1,M1} I { addition( star( X ),
% 0.69/1.13 multiplication( strong_iteration( X ), zero ) ) ==> strong_iteration( X )
% 0.69/1.13 }.
% 0.69/1.13 parent0: (999) {G0,W10,D5,L1,V1,M1} { addition( star( X ), multiplication
% 0.69/1.13 ( strong_iteration( X ), zero ) ) = strong_iteration( X ) }.
% 0.69/1.13 substitution0:
% 0.69/1.13 X := X
% 0.69/1.13 end
% 0.69/1.13 permutation0:
% 0.69/1.13 0 ==> 0
% 0.69/1.13 end
% 0.69/1.13
% 0.69/1.13 subsumption: (17) {G0,W8,D3,L2,V2,M2} I { ! leq( X, Y ), addition( X, Y )
% 0.69/1.13 ==> Y }.
% 0.69/1.13 parent0: (960) {G0,W8,D3,L2,V2,M2} { ! leq( X, Y ), addition( X, Y ) = Y
% 0.69/1.13 }.
% 0.69/1.13 substitution0:
% 0.69/1.13 X := X
% 0.69/1.13 Y := Y
% 0.69/1.13 end
% 0.69/1.13 permutation0:
% 0.69/1.13 0 ==> 0
% 0.69/1.13 1 ==> 1
% 0.69/1.13 end
% 0.69/1.13
% 0.69/1.13 subsumption: (18) {G0,W8,D3,L2,V2,M2} I { ! addition( X, Y ) ==> Y, leq( X
% 0.69/1.13 , Y ) }.
% 0.69/1.13 parent0: (961) {G0,W8,D3,L2,V2,M2} { ! addition( X, Y ) = Y, leq( X, Y )
% 0.69/1.13 }.
% 0.69/1.13 substitution0:
% 0.69/1.13 X := X
% 0.69/1.13 Y := Y
% 0.69/1.13 end
% 0.69/1.13 permutation0:
% 0.69/1.13 0 ==> 0
% 0.69/1.13 1 ==> 1
% 0.69/1.13 end
% 0.69/1.13
% 0.69/1.13 subsumption: (19) {G0,W4,D3,L1,V0,M1} I { ! leq( skol1, strong_iteration(
% 0.69/1.13 one ) ) }.
% 0.69/1.13 parent0: (962) {G0,W4,D3,L1,V0,M1} { ! leq( skol1, strong_iteration( one )
% 0.69/1.13 ) }.
% 0.69/1.13 substitution0:
% 0.69/1.13 end
% 0.69/1.13 permutation0:
% 0.69/1.13 0 ==> 0
% 0.69/1.13 end
% 0.69/1.13
% 0.69/1.13 eqswap: (1044) {G0,W8,D3,L2,V2,M2} { ! Y ==> addition( X, Y ), leq( X, Y )
% 0.69/1.13 }.
% 0.69/1.13 parent0[0]: (18) {G0,W8,D3,L2,V2,M2} I { ! addition( X, Y ) ==> Y, leq( X,
% 0.69/1.13 Y ) }.
% 0.69/1.13 substitution0:
% 0.69/1.13 X := X
% 0.69/1.13 Y := Y
% 0.69/1.13 end
% 0.69/1.13
% 0.69/1.13 eqswap: (1045) {G0,W5,D3,L1,V1,M1} { X ==> addition( X, X ) }.
% 0.69/1.13 parent0[0]: (3) {G0,W5,D3,L1,V1,M1} I { addition( X, X ) ==> X }.
% 0.69/1.13 substitution0:
% 0.69/1.13 X := X
% 0.69/1.13 end
% 0.69/1.13
% 0.69/1.13 resolution: (1046) {G1,W3,D2,L1,V1,M1} { leq( X, X ) }.
% 0.69/1.13 parent0[0]: (1044) {G0,W8,D3,L2,V2,M2} { ! Y ==> addition( X, Y ), leq( X
% 0.69/1.13 , Y ) }.
% 0.69/1.13 parent1[0]: (1045) {G0,W5,D3,L1,V1,M1} { X ==> addition( X, X ) }.
% 0.69/1.13 substitution0:
% 0.69/1.13 X := X
% 0.69/1.13 Y := X
% 0.69/1.13 end
% 0.69/1.13 substitution1:
% 0.69/1.13 X := X
% 0.69/1.13 end
% 0.69/1.13
% 0.69/1.13 subsumption: (22) {G1,W3,D2,L1,V1,M1} R(18,3) { leq( X, X ) }.
% 0.69/1.13 parent0: (1046) {G1,W3,D2,L1,V1,M1} { leq( X, X ) }.
% 0.69/1.13 substitution0:
% 0.69/1.13 X := X
% 0.69/1.13 end
% 0.69/1.13 permutation0:
% 0.69/1.13 0 ==> 0
% 0.69/1.13 end
% 0.69/1.13
% 0.69/1.13 eqswap: (1048) {G0,W8,D3,L2,V2,M2} { ! Y ==> addition( X, Y ), leq( X, Y )
% 0.69/1.13 }.
% 0.69/1.13 parent0[0]: (18) {G0,W8,D3,L2,V2,M2} I { ! addition( X, Y ) ==> Y, leq( X,
% 0.69/1.13 Y ) }.
% 0.69/1.13 substitution0:
% 0.69/1.13 X := X
% 0.69/1.13 Y := Y
% 0.69/1.13 end
% 0.69/1.13
% 0.69/1.13 paramod: (1049) {G1,W14,D4,L2,V3,M2} { ! addition( X, Y ) ==> addition(
% 0.69/1.13 addition( Z, X ), Y ), leq( Z, addition( X, Y ) ) }.
% 0.69/1.13 parent0[0]: (1) {G0,W11,D4,L1,V3,M1} I { addition( Z, addition( Y, X ) )
% 0.69/1.13 ==> addition( addition( Z, Y ), X ) }.
% 0.69/1.13 parent1[0; 5]: (1048) {G0,W8,D3,L2,V2,M2} { ! Y ==> addition( X, Y ), leq
% 0.69/1.13 ( X, Y ) }.
% 0.69/1.13 substitution0:
% 0.69/1.13 X := Y
% 0.69/1.13 Y := X
% 0.69/1.13 Z := Z
% 0.69/1.13 end
% 0.69/1.13 substitution1:
% 0.69/1.13 X := Z
% 0.69/1.13 Y := addition( X, Y )
% 0.69/1.13 end
% 0.69/1.13
% 0.69/1.13 eqswap: (1050) {G1,W14,D4,L2,V3,M2} { ! addition( addition( Z, X ), Y )
% 0.69/1.13 ==> addition( X, Y ), leq( Z, addition( X, Y ) ) }.
% 0.69/1.13 parent0[0]: (1049) {G1,W14,D4,L2,V3,M2} { ! addition( X, Y ) ==> addition
% 0.69/1.13 ( addition( Z, X ), Y ), leq( Z, addition( X, Y ) ) }.
% 0.69/1.13 substitution0:
% 0.69/1.13 X := X
% 0.69/1.13 Y := Y
% 0.69/1.13 Z := Z
% 0.69/1.13 end
% 0.69/1.13
% 0.69/1.13 subsumption: (26) {G1,W14,D4,L2,V3,M2} P(1,18) { ! addition( addition( X, Y
% 0.69/1.13 ), Z ) ==> addition( Y, Z ), leq( X, addition( Y, Z ) ) }.
% 0.69/1.13 parent0: (1050) {G1,W14,D4,L2,V3,M2} { ! addition( addition( Z, X ), Y )
% 0.69/1.13 ==> addition( X, Y ), leq( Z, addition( X, Y ) ) }.
% 0.69/1.13 substitution0:
% 0.69/1.13 X := Y
% 0.69/1.13 Y := Z
% 0.69/1.13 Z := X
% 0.69/1.13 end
% 0.69/1.13 permutation0:
% 0.69/1.13 0 ==> 0
% 0.69/1.13 1 ==> 1
% 0.69/1.13 end
% 0.69/1.13
% 0.69/1.13 eqswap: (1052) {G1,W14,D4,L2,V3,M2} { ! addition( Y, Z ) ==> addition(
% 0.69/1.13 addition( X, Y ), Z ), leq( X, addition( Y, Z ) ) }.
% 0.69/1.13 parent0[0]: (26) {G1,W14,D4,L2,V3,M2} P(1,18) { ! addition( addition( X, Y
% 0.69/1.13 ), Z ) ==> addition( Y, Z ), leq( X, addition( Y, Z ) ) }.
% 0.69/1.13 substitution0:
% 0.69/1.13 X := X
% 0.69/1.13 Y := Y
% 0.69/1.13 Z := Z
% 0.69/1.13 end
% 0.69/1.13
% 0.69/1.13 paramod: (1055) {G1,W12,D3,L2,V2,M2} { ! addition( X, Y ) ==> addition( X
% 0.69/1.13 , Y ), leq( X, addition( X, Y ) ) }.
% 0.69/1.13 parent0[0]: (3) {G0,W5,D3,L1,V1,M1} I { addition( X, X ) ==> X }.
% 0.69/1.13 parent1[0; 6]: (1052) {G1,W14,D4,L2,V3,M2} { ! addition( Y, Z ) ==>
% 0.69/1.13 addition( addition( X, Y ), Z ), leq( X, addition( Y, Z ) ) }.
% 0.69/1.13 substitution0:
% 0.69/1.13 X := X
% 0.69/1.13 end
% 0.69/1.13 substitution1:
% 0.69/1.13 X := X
% 0.69/1.13 Y := X
% 0.69/1.13 Z := Y
% 0.69/1.13 end
% 0.69/1.13
% 0.69/1.13 eqrefl: (1058) {G0,W5,D3,L1,V2,M1} { leq( X, addition( X, Y ) ) }.
% 0.69/1.13 parent0[0]: (1055) {G1,W12,D3,L2,V2,M2} { ! addition( X, Y ) ==> addition
% 0.69/1.13 ( X, Y ), leq( X, addition( X, Y ) ) }.
% 0.69/1.13 substitution0:
% 0.69/1.13 X := X
% 0.69/1.13 Y := Y
% 0.69/1.13 end
% 0.69/1.13
% 0.69/1.13 subsumption: (293) {G2,W5,D3,L1,V2,M1} P(3,26);q { leq( X, addition( X, Y )
% 0.69/1.13 ) }.
% 0.69/1.13 parent0: (1058) {G0,W5,D3,L1,V2,M1} { leq( X, addition( X, Y ) ) }.
% 0.69/1.13 substitution0:
% 0.69/1.13 X := X
% 0.69/1.13 Y := Y
% 0.69/1.13 end
% 0.69/1.13 permutation0:
% 0.69/1.13 0 ==> 0
% 0.69/1.13 end
% 0.69/1.13
% 0.69/1.13 paramod: (1060) {G1,W7,D4,L1,V3,M1} { leq( X, addition( addition( X, Y ),
% 0.69/1.13 Z ) ) }.
% 0.69/1.13 parent0[0]: (1) {G0,W11,D4,L1,V3,M1} I { addition( Z, addition( Y, X ) )
% 0.69/1.13 ==> addition( addition( Z, Y ), X ) }.
% 0.69/1.13 parent1[0; 2]: (293) {G2,W5,D3,L1,V2,M1} P(3,26);q { leq( X, addition( X, Y
% 0.69/1.13 ) ) }.
% 0.69/1.13 substitution0:
% 0.69/1.13 X := Z
% 0.69/1.13 Y := Y
% 0.69/1.13 Z := X
% 0.69/1.13 end
% 0.69/1.13 substitution1:
% 0.69/1.13 X := X
% 0.69/1.13 Y := addition( Y, Z )
% 0.69/1.13 end
% 0.69/1.13
% 0.69/1.13 subsumption: (308) {G3,W7,D4,L1,V3,M1} P(1,293) { leq( X, addition(
% 0.69/1.13 addition( X, Y ), Z ) ) }.
% 0.69/1.13 parent0: (1060) {G1,W7,D4,L1,V3,M1} { leq( X, addition( addition( X, Y ),
% 0.69/1.13 Z ) ) }.
% 0.69/1.13 substitution0:
% 0.69/1.13 X := X
% 0.69/1.13 Y := Y
% 0.69/1.13 Z := Z
% 0.69/1.13 end
% 0.69/1.13 permutation0:
% 0.69/1.13 0 ==> 0
% 0.69/1.13 end
% 0.69/1.13
% 0.69/1.13 paramod: (1061) {G1,W5,D3,L1,V2,M1} { leq( X, addition( Y, X ) ) }.
% 0.69/1.13 parent0[0]: (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X )
% 0.69/1.13 }.
% 0.69/1.13 parent1[0; 2]: (293) {G2,W5,D3,L1,V2,M1} P(3,26);q { leq( X, addition( X, Y
% 0.69/1.13 ) ) }.
% 0.69/1.13 substitution0:
% 0.69/1.13 X := X
% 0.69/1.13 Y := Y
% 0.69/1.13 end
% 0.69/1.13 substitution1:
% 0.69/1.13 X := X
% 0.69/1.13 Y := Y
% 0.69/1.13 end
% 0.69/1.13
% 0.69/1.13 subsumption: (309) {G3,W5,D3,L1,V2,M1} P(0,293) { leq( X, addition( Y, X )
% 0.69/1.13 ) }.
% 0.69/1.13 parent0: (1061) {G1,W5,D3,L1,V2,M1} { leq( X, addition( Y, X ) ) }.
% 0.69/1.13 substitution0:
% 0.69/1.13 X := X
% 0.69/1.13 Y := Y
% 0.69/1.13 end
% 0.69/1.13 permutation0:
% 0.69/1.13 0 ==> 0
% 0.69/1.13 end
% 0.69/1.13
% 0.69/1.13 paramod: (1064) {G1,W7,D4,L1,V1,M1} { leq( multiplication(
% 0.69/1.13 strong_iteration( X ), zero ), strong_iteration( X ) ) }.
% 0.69/1.13 parent0[0]: (16) {G0,W10,D5,L1,V1,M1} I { addition( star( X ),
% 0.69/1.13 multiplication( strong_iteration( X ), zero ) ) ==> strong_iteration( X )
% 0.69/1.13 }.
% 0.69/1.13 parent1[0; 5]: (309) {G3,W5,D3,L1,V2,M1} P(0,293) { leq( X, addition( Y, X
% 0.69/1.13 ) ) }.
% 0.69/1.13 substitution0:
% 0.69/1.13 X := X
% 0.69/1.13 end
% 0.69/1.13 substitution1:
% 0.69/1.13 X := multiplication( strong_iteration( X ), zero )
% 0.69/1.13 Y := star( X )
% 0.69/1.13 end
% 0.69/1.13
% 0.69/1.13 subsumption: (321) {G4,W7,D4,L1,V1,M1} P(16,309) { leq( multiplication(
% 0.69/1.13 strong_iteration( X ), zero ), strong_iteration( X ) ) }.
% 0.69/1.13 parent0: (1064) {G1,W7,D4,L1,V1,M1} { leq( multiplication(
% 0.69/1.13 strong_iteration( X ), zero ), strong_iteration( X ) ) }.
% 0.69/1.13 substitution0:
% 0.69/1.13 X := X
% 0.69/1.13 end
% 0.69/1.13 permutation0:
% 0.69/1.13 0 ==> 0
% 0.69/1.13 end
% 0.69/1.13
% 0.69/1.13 paramod: (1066) {G1,W8,D3,L2,V3,M2} { leq( X, Z ), ! leq( addition( X, Y )
% 0.69/1.13 , Z ) }.
% 0.69/1.13 parent0[1]: (17) {G0,W8,D3,L2,V2,M2} I { ! leq( X, Y ), addition( X, Y )
% 0.69/1.13 ==> Y }.
% 0.69/1.13 parent1[0; 2]: (308) {G3,W7,D4,L1,V3,M1} P(1,293) { leq( X, addition(
% 0.69/1.13 addition( X, Y ), Z ) ) }.
% 0.69/1.13 substitution0:
% 0.69/1.13 X := addition( X, Y )
% 0.69/1.13 Y := Z
% 0.69/1.13 end
% 0.69/1.13 substitution1:
% 0.69/1.13 X := X
% 0.69/1.13 Y := Y
% 0.69/1.13 Z := Z
% 0.69/1.13 end
% 0.69/1.13
% 0.69/1.13 subsumption: (501) {G4,W8,D3,L2,V3,M2} P(17,308) { leq( X, Z ), ! leq(
% 0.69/1.13 addition( X, Y ), Z ) }.
% 0.69/1.13 parent0: (1066) {G1,W8,D3,L2,V3,M2} { leq( X, Z ), ! leq( addition( X, Y )
% 0.69/1.13 , Z ) }.
% 0.69/1.13 substitution0:
% 0.69/1.13 X := X
% 0.69/1.13 Y := Y
% 0.69/1.13 Z := Z
% 0.69/1.13 end
% 0.69/1.13 permutation0:
% 0.69/1.13 0 ==> 0
% 0.69/1.13 1 ==> 1
% 0.69/1.13 end
% 0.69/1.13
% 0.69/1.13 resolution: (1070) {G1,W6,D3,L1,V1,M1} { ! leq( addition( skol1, X ),
% 0.69/1.13 strong_iteration( one ) ) }.
% 0.69/1.13 parent0[0]: (19) {G0,W4,D3,L1,V0,M1} I { ! leq( skol1, strong_iteration(
% 0.69/1.13 one ) ) }.
% 0.69/1.13 parent1[0]: (501) {G4,W8,D3,L2,V3,M2} P(17,308) { leq( X, Z ), ! leq(
% 0.69/1.13 addition( X, Y ), Z ) }.
% 0.69/1.13 substitution0:
% 0.69/1.13 end
% 0.69/1.13 substitution1:
% 0.69/1.13 X := skol1
% 0.69/1.13 Y := X
% 0.69/1.13 Z := strong_iteration( one )
% 0.69/1.13 end
% 0.69/1.13
% 0.69/1.13 subsumption: (829) {G5,W6,D3,L1,V1,M1} R(501,19) { ! leq( addition( skol1,
% 0.69/1.13 X ), strong_iteration( one ) ) }.
% 0.69/1.13 parent0: (1070) {G1,W6,D3,L1,V1,M1} { ! leq( addition( skol1, X ),
% 0.69/1.13 strong_iteration( one ) ) }.
% 0.69/1.13 substitution0:
% 0.69/1.13 X := X
% 0.69/1.13 end
% 0.69/1.13 permutation0:
% 0.69/1.13 0 ==> 0
% 0.69/1.13 end
% 0.69/1.13
% 0.69/1.13 paramod: (1072) {G1,W7,D3,L2,V1,M2} { ! leq( X, strong_iteration( one ) )
% 0.69/1.13 , ! leq( skol1, X ) }.
% 0.69/1.13 parent0[1]: (17) {G0,W8,D3,L2,V2,M2} I { ! leq( X, Y ), addition( X, Y )
% 0.69/1.13 ==> Y }.
% 0.69/1.13 parent1[0; 2]: (829) {G5,W6,D3,L1,V1,M1} R(501,19) { ! leq( addition( skol1
% 0.69/1.13 , X ), strong_iteration( one ) ) }.
% 0.69/1.13 substitution0:
% 0.69/1.13 X := skol1
% 0.69/1.13 Y := X
% 0.69/1.13 end
% 0.69/1.13 substitution1:
% 0.69/1.13 X := X
% 0.69/1.13 end
% 0.69/1.13
% 0.69/1.13 subsumption: (870) {G6,W7,D3,L2,V1,M2} P(17,829) { ! leq( X,
% 0.69/1.13 strong_iteration( one ) ), ! leq( skol1, X ) }.
% 0.69/1.13 parent0: (1072) {G1,W7,D3,L2,V1,M2} { ! leq( X, strong_iteration( one ) )
% 0.69/1.13 , ! leq( skol1, X ) }.
% 0.69/1.13 substitution0:
% 0.69/1.13 X := X
% 0.69/1.13 end
% 0.69/1.13 permutation0:
% 0.69/1.13 0 ==> 0
% 0.69/1.13 1 ==> 1
% 0.69/1.13 end
% 0.69/1.13
% 0.69/1.13 resolution: (1073) {G5,W6,D4,L1,V0,M1} { ! leq( skol1, multiplication(
% 0.69/1.13 strong_iteration( one ), zero ) ) }.
% 0.69/1.13 parent0[0]: (870) {G6,W7,D3,L2,V1,M2} P(17,829) { ! leq( X,
% 0.69/1.13 strong_iteration( one ) ), ! leq( skol1, X ) }.
% 0.69/1.13 parent1[0]: (321) {G4,W7,D4,L1,V1,M1} P(16,309) { leq( multiplication(
% 0.69/1.13 strong_iteration( X ), zero ), strong_iteration( X ) ) }.
% 0.69/1.13 substitution0:
% 0.69/1.13 X := multiplication( strong_iteration( one ), zero )
% 0.69/1.13 end
% 0.69/1.13 substitution1:
% 0.69/1.13 X := one
% 0.69/1.13 end
% 0.69/1.13
% 0.69/1.13 subsumption: (889) {G7,W6,D4,L1,V0,M1} R(870,321) { ! leq( skol1,
% 0.69/1.13 multiplication( strong_iteration( one ), zero ) ) }.
% 0.69/1.13 parent0: (1073) {G5,W6,D4,L1,V0,M1} { ! leq( skol1, multiplication(
% 0.69/1.13 strong_iteration( one ), zero ) ) }.
% 0.69/1.13 substitution0:
% 0.69/1.13 end
% 0.69/1.13 permutation0:
% 0.69/1.13 0 ==> 0
% 0.69/1.13 end
% 0.69/1.13
% 0.69/1.13 resolution: (1076) {G1,W7,D4,L1,V0,M1} { ! leq( skol1, addition(
% 0.69/1.13 multiplication( one, skol1 ), zero ) ) }.
% 0.69/1.13 parent0[0]: (889) {G7,W6,D4,L1,V0,M1} R(870,321) { ! leq( skol1,
% 0.69/1.13 multiplication( strong_iteration( one ), zero ) ) }.
% 0.69/1.13 parent1[1]: (15) {G0,W13,D4,L2,V3,M2} I { ! leq( Z, addition(
% 0.69/1.13 multiplication( X, Z ), Y ) ), leq( Z, multiplication( strong_iteration(
% 0.69/1.13 X ), Y ) ) }.
% 0.69/1.13 substitution0:
% 0.69/1.13 end
% 0.69/1.13 substitution1:
% 0.69/1.13 X := one
% 0.69/1.13 Y := zero
% 0.69/1.13 Z := skol1
% 0.69/1.13 end
% 0.69/1.13
% 0.69/1.13 paramod: (1077) {G1,W5,D3,L1,V0,M1} { ! leq( skol1, multiplication( one,
% 0.69/1.13 skol1 ) ) }.
% 0.69/1.13 parent0[0]: (2) {G0,W5,D3,L1,V1,M1} I { addition( X, zero ) ==> X }.
% 0.69/1.13 parent1[0; 3]: (1076) {G1,W7,D4,L1,V0,M1} { ! leq( skol1, addition(
% 0.69/1.13 multiplication( one, skol1 ), zero ) ) }.
% 0.69/1.13 substitution0:
% 0.69/1.13 X := multiplication( one, skol1 )
% 0.69/1.13 end
% 0.69/1.13 substitution1:
% 0.69/1.13 end
% 0.69/1.13
% 0.69/1.13 paramod: (1078) {G1,W3,D2,L1,V0,M1} { ! leq( skol1, skol1 ) }.
% 0.69/1.13 parent0[0]: (6) {G0,W5,D3,L1,V1,M1} I { multiplication( one, X ) ==> X }.
% 0.69/1.13 parent1[0; 3]: (1077) {G1,W5,D3,L1,V0,M1} { ! leq( skol1, multiplication(
% 0.69/1.13 one, skol1 ) ) }.
% 0.69/1.13 substitution0:
% 0.69/1.13 X := skol1
% 0.69/1.13 end
% 0.69/1.13 substitution1:
% 0.69/1.13 end
% 0.69/1.13
% 0.69/1.13 resolution: (1079) {G2,W0,D0,L0,V0,M0} { }.
% 0.69/1.13 parent0[0]: (1078) {G1,W3,D2,L1,V0,M1} { ! leq( skol1, skol1 ) }.
% 0.69/1.13 parent1[0]: (22) {G1,W3,D2,L1,V1,M1} R(18,3) { leq( X, X ) }.
% 0.69/1.13 substitution0:
% 0.69/1.13 end
% 0.69/1.13 substitution1:
% 0.69/1.13 X := skol1
% 0.69/1.13 end
% 0.69/1.13
% 0.69/1.13 subsumption: (941) {G8,W0,D0,L0,V0,M0} R(889,15);d(2);d(6);r(22) { }.
% 0.69/1.13 parent0: (1079) {G2,W0,D0,L0,V0,M0} { }.
% 0.69/1.13 substitution0:
% 0.69/1.13 end
% 0.69/1.13 permutation0:
% 0.69/1.13 end
% 0.69/1.13
% 0.69/1.13 Proof check complete!
% 0.69/1.13
% 0.69/1.13 Memory use:
% 0.69/1.13
% 0.69/1.13 space for terms: 11504
% 0.69/1.13 space for clauses: 57898
% 0.69/1.13
% 0.69/1.13
% 0.69/1.13 clauses generated: 5233
% 0.69/1.13 clauses kept: 942
% 0.69/1.13 clauses selected: 156
% 0.69/1.13 clauses deleted: 12
% 0.69/1.13 clauses inuse deleted: 0
% 0.69/1.13
% 0.69/1.13 subsentry: 6420
% 0.69/1.13 literals s-matched: 5287
% 0.69/1.13 literals matched: 5182
% 0.69/1.13 full subsumption: 426
% 0.69/1.13
% 0.69/1.13 checksum: -576367806
% 0.69/1.13
% 0.69/1.13
% 0.69/1.13 Bliksem ended
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