TSTP Solution File: KLE022+4 by Bliksem---1.12
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%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : KLE022+4 : 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 01:36:42 EDT 2022
% Result : Theorem 0.79s 1.14s
% Output : Refutation 0.79s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : KLE022+4 : TPTP v8.1.0. Released v4.0.0.
% 0.04/0.14 % Command : bliksem %s
% 0.14/0.35 % Computer : n006.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % DateTime : Thu Jun 16 13:01:56 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.79/1.14 *** allocated 10000 integers for termspace/termends
% 0.79/1.14 *** allocated 10000 integers for clauses
% 0.79/1.14 *** allocated 10000 integers for justifications
% 0.79/1.14 Bliksem 1.12
% 0.79/1.14
% 0.79/1.14
% 0.79/1.14 Automatic Strategy Selection
% 0.79/1.14
% 0.79/1.14
% 0.79/1.14 Clauses:
% 0.79/1.14
% 0.79/1.14 { addition( X, Y ) = addition( Y, X ) }.
% 0.79/1.14 { addition( Z, addition( Y, X ) ) = addition( addition( Z, Y ), X ) }.
% 0.79/1.14 { addition( X, zero ) = X }.
% 0.79/1.14 { addition( X, X ) = X }.
% 0.79/1.14 { multiplication( X, multiplication( Y, Z ) ) = multiplication(
% 0.79/1.14 multiplication( X, Y ), Z ) }.
% 0.79/1.14 { multiplication( X, one ) = X }.
% 0.79/1.14 { multiplication( one, X ) = X }.
% 0.79/1.14 { multiplication( X, addition( Y, Z ) ) = addition( multiplication( X, Y )
% 0.79/1.14 , multiplication( X, Z ) ) }.
% 0.79/1.14 { multiplication( addition( X, Y ), Z ) = addition( multiplication( X, Z )
% 0.79/1.14 , multiplication( Y, Z ) ) }.
% 0.79/1.14 { multiplication( X, zero ) = zero }.
% 0.79/1.14 { multiplication( zero, X ) = zero }.
% 0.79/1.14 { ! leq( X, Y ), addition( X, Y ) = Y }.
% 0.79/1.14 { ! addition( X, Y ) = Y, leq( X, Y ) }.
% 0.79/1.14 { ! test( X ), complement( skol1( X ), X ) }.
% 0.79/1.14 { ! complement( Y, X ), test( X ) }.
% 0.79/1.14 { ! complement( Y, X ), multiplication( X, Y ) = zero }.
% 0.79/1.14 { ! complement( Y, X ), alpha1( X, Y ) }.
% 0.79/1.14 { ! multiplication( X, Y ) = zero, ! alpha1( X, Y ), complement( Y, X ) }.
% 0.79/1.14 { ! alpha1( X, Y ), multiplication( Y, X ) = zero }.
% 0.79/1.14 { ! alpha1( X, Y ), addition( X, Y ) = one }.
% 0.79/1.14 { ! multiplication( Y, X ) = zero, ! addition( X, Y ) = one, alpha1( X, Y )
% 0.79/1.14 }.
% 0.79/1.14 { ! test( X ), ! c( X ) = Y, complement( X, Y ) }.
% 0.79/1.14 { ! test( X ), ! complement( X, Y ), c( X ) = Y }.
% 0.79/1.14 { test( X ), c( X ) = zero }.
% 0.79/1.14 { ! test( X ), ! test( Y ), c( addition( X, Y ) ) = multiplication( c( X )
% 0.79/1.14 , c( Y ) ) }.
% 0.79/1.14 { ! test( X ), ! test( Y ), c( multiplication( X, Y ) ) = addition( c( X )
% 0.79/1.14 , c( Y ) ) }.
% 0.79/1.14 { test( skol2 ) }.
% 0.79/1.14 { ! leq( skol3, addition( multiplication( skol3, skol2 ), multiplication(
% 0.79/1.14 skol3, c( skol2 ) ) ) ), ! leq( addition( multiplication( skol3, skol2 )
% 0.79/1.14 , multiplication( skol3, c( skol2 ) ) ), skol3 ) }.
% 0.79/1.14
% 0.79/1.14 percentage equality = 0.480000, percentage horn = 0.964286
% 0.79/1.14 This is a problem with some equality
% 0.79/1.14
% 0.79/1.14
% 0.79/1.14
% 0.79/1.14 Options Used:
% 0.79/1.14
% 0.79/1.14 useres = 1
% 0.79/1.14 useparamod = 1
% 0.79/1.14 useeqrefl = 1
% 0.79/1.14 useeqfact = 1
% 0.79/1.14 usefactor = 1
% 0.79/1.14 usesimpsplitting = 0
% 0.79/1.14 usesimpdemod = 5
% 0.79/1.14 usesimpres = 3
% 0.79/1.14
% 0.79/1.14 resimpinuse = 1000
% 0.79/1.14 resimpclauses = 20000
% 0.79/1.14 substype = eqrewr
% 0.79/1.14 backwardsubs = 1
% 0.79/1.14 selectoldest = 5
% 0.79/1.14
% 0.79/1.14 litorderings [0] = split
% 0.79/1.14 litorderings [1] = extend the termordering, first sorting on arguments
% 0.79/1.14
% 0.79/1.14 termordering = kbo
% 0.79/1.14
% 0.79/1.14 litapriori = 0
% 0.79/1.14 termapriori = 1
% 0.79/1.14 litaposteriori = 0
% 0.79/1.14 termaposteriori = 0
% 0.79/1.14 demodaposteriori = 0
% 0.79/1.14 ordereqreflfact = 0
% 0.79/1.14
% 0.79/1.14 litselect = negord
% 0.79/1.14
% 0.79/1.14 maxweight = 15
% 0.79/1.14 maxdepth = 30000
% 0.79/1.14 maxlength = 115
% 0.79/1.14 maxnrvars = 195
% 0.79/1.14 excuselevel = 1
% 0.79/1.14 increasemaxweight = 1
% 0.79/1.14
% 0.79/1.14 maxselected = 10000000
% 0.79/1.14 maxnrclauses = 10000000
% 0.79/1.14
% 0.79/1.14 showgenerated = 0
% 0.79/1.14 showkept = 0
% 0.79/1.14 showselected = 0
% 0.79/1.14 showdeleted = 0
% 0.79/1.14 showresimp = 1
% 0.79/1.14 showstatus = 2000
% 0.79/1.14
% 0.79/1.14 prologoutput = 0
% 0.79/1.14 nrgoals = 5000000
% 0.79/1.14 totalproof = 1
% 0.79/1.14
% 0.79/1.14 Symbols occurring in the translation:
% 0.79/1.14
% 0.79/1.14 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.79/1.14 . [1, 2] (w:1, o:23, a:1, s:1, b:0),
% 0.79/1.14 ! [4, 1] (w:0, o:15, a:1, s:1, b:0),
% 0.79/1.14 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.79/1.14 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.79/1.14 addition [37, 2] (w:1, o:47, a:1, s:1, b:0),
% 0.79/1.14 zero [39, 0] (w:1, o:9, a:1, s:1, b:0),
% 0.79/1.14 multiplication [40, 2] (w:1, o:49, a:1, s:1, b:0),
% 0.79/1.14 one [41, 0] (w:1, o:10, a:1, s:1, b:0),
% 0.79/1.14 leq [42, 2] (w:1, o:48, a:1, s:1, b:0),
% 0.79/1.14 test [44, 1] (w:1, o:21, a:1, s:1, b:0),
% 0.79/1.14 complement [46, 2] (w:1, o:50, a:1, s:1, b:0),
% 0.79/1.14 c [47, 1] (w:1, o:22, a:1, s:1, b:0),
% 0.79/1.14 alpha1 [48, 2] (w:1, o:51, a:1, s:1, b:1),
% 0.79/1.14 skol1 [49, 1] (w:1, o:20, a:1, s:1, b:1),
% 0.79/1.14 skol2 [50, 0] (w:1, o:13, a:1, s:1, b:1),
% 0.79/1.14 skol3 [51, 0] (w:1, o:14, a:1, s:1, b:1).
% 0.79/1.14
% 0.79/1.14
% 0.79/1.14 Starting Search:
% 0.79/1.14
% 0.79/1.14 *** allocated 15000 integers for clauses
% 0.79/1.14 *** allocated 22500 integers for clauses
% 0.79/1.14 *** allocated 33750 integers for clauses
% 0.79/1.14
% 0.79/1.14 Bliksems!, er is een bewijs:
% 0.79/1.14 % SZS status Theorem
% 0.79/1.14 % SZS output start Refutation
% 0.79/1.14
% 0.79/1.14 (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X ) }.
% 0.79/1.14 (3) {G0,W5,D3,L1,V1,M1} I { addition( X, X ) ==> X }.
% 0.79/1.14 (5) {G0,W5,D3,L1,V1,M1} I { multiplication( X, one ) ==> X }.
% 0.79/1.14 (7) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Y ),
% 0.79/1.14 multiplication( X, Z ) ) ==> multiplication( X, addition( Y, Z ) ) }.
% 0.79/1.14 (12) {G0,W8,D3,L2,V2,M2} I { ! addition( X, Y ) ==> Y, leq( X, Y ) }.
% 0.79/1.14 (16) {G0,W6,D2,L2,V2,M2} I { ! complement( Y, X ), alpha1( X, Y ) }.
% 0.79/1.14 (19) {G0,W8,D3,L2,V2,M2} I { ! alpha1( X, Y ), addition( X, Y ) ==> one }.
% 0.79/1.14 (21) {G0,W9,D3,L3,V2,M3} I { ! test( X ), ! c( X ) = Y, complement( X, Y )
% 0.79/1.14 }.
% 0.79/1.14 (26) {G0,W2,D2,L1,V0,M1} I { test( skol2 ) }.
% 0.79/1.14 (27) {G1,W16,D5,L2,V0,M2} I;d(7);d(7) { ! leq( skol3, multiplication( skol3
% 0.79/1.14 , addition( skol2, c( skol2 ) ) ) ), ! leq( multiplication( skol3,
% 0.79/1.14 addition( skol2, c( skol2 ) ) ), skol3 ) }.
% 0.79/1.14 (28) {G1,W6,D3,L2,V1,M2} Q(21) { ! test( X ), complement( X, c( X ) ) }.
% 0.79/1.14 (40) {G2,W4,D3,L1,V0,M1} R(28,26) { complement( skol2, c( skol2 ) ) }.
% 0.79/1.14 (41) {G3,W4,D3,L1,V0,M1} R(40,16) { alpha1( c( skol2 ), skol2 ) }.
% 0.79/1.14 (161) {G1,W3,D2,L1,V1,M1} R(12,3) { leq( X, X ) }.
% 0.79/1.14 (271) {G4,W6,D4,L1,V0,M1} R(19,41) { addition( c( skol2 ), skol2 ) ==> one
% 0.79/1.14 }.
% 0.79/1.14 (502) {G5,W0,D0,L0,V0,M0} P(0,27);d(271);d(271);d(5);d(5);f;r(161) { }.
% 0.79/1.14
% 0.79/1.14
% 0.79/1.14 % SZS output end Refutation
% 0.79/1.14 found a proof!
% 0.79/1.14
% 0.79/1.14
% 0.79/1.14 Unprocessed initial clauses:
% 0.79/1.14
% 0.79/1.14 (504) {G0,W7,D3,L1,V2,M1} { addition( X, Y ) = addition( Y, X ) }.
% 0.79/1.14 (505) {G0,W11,D4,L1,V3,M1} { addition( Z, addition( Y, X ) ) = addition(
% 0.79/1.14 addition( Z, Y ), X ) }.
% 0.79/1.14 (506) {G0,W5,D3,L1,V1,M1} { addition( X, zero ) = X }.
% 0.79/1.14 (507) {G0,W5,D3,L1,V1,M1} { addition( X, X ) = X }.
% 0.79/1.14 (508) {G0,W11,D4,L1,V3,M1} { multiplication( X, multiplication( Y, Z ) ) =
% 0.79/1.14 multiplication( multiplication( X, Y ), Z ) }.
% 0.79/1.14 (509) {G0,W5,D3,L1,V1,M1} { multiplication( X, one ) = X }.
% 0.79/1.14 (510) {G0,W5,D3,L1,V1,M1} { multiplication( one, X ) = X }.
% 0.79/1.14 (511) {G0,W13,D4,L1,V3,M1} { multiplication( X, addition( Y, Z ) ) =
% 0.79/1.14 addition( multiplication( X, Y ), multiplication( X, Z ) ) }.
% 0.79/1.14 (512) {G0,W13,D4,L1,V3,M1} { multiplication( addition( X, Y ), Z ) =
% 0.79/1.14 addition( multiplication( X, Z ), multiplication( Y, Z ) ) }.
% 0.79/1.14 (513) {G0,W5,D3,L1,V1,M1} { multiplication( X, zero ) = zero }.
% 0.79/1.14 (514) {G0,W5,D3,L1,V1,M1} { multiplication( zero, X ) = zero }.
% 0.79/1.14 (515) {G0,W8,D3,L2,V2,M2} { ! leq( X, Y ), addition( X, Y ) = Y }.
% 0.79/1.14 (516) {G0,W8,D3,L2,V2,M2} { ! addition( X, Y ) = Y, leq( X, Y ) }.
% 0.79/1.14 (517) {G0,W6,D3,L2,V1,M2} { ! test( X ), complement( skol1( X ), X ) }.
% 0.79/1.14 (518) {G0,W5,D2,L2,V2,M2} { ! complement( Y, X ), test( X ) }.
% 0.79/1.14 (519) {G0,W8,D3,L2,V2,M2} { ! complement( Y, X ), multiplication( X, Y ) =
% 0.79/1.14 zero }.
% 0.79/1.14 (520) {G0,W6,D2,L2,V2,M2} { ! complement( Y, X ), alpha1( X, Y ) }.
% 0.79/1.14 (521) {G0,W11,D3,L3,V2,M3} { ! multiplication( X, Y ) = zero, ! alpha1( X
% 0.79/1.14 , Y ), complement( Y, X ) }.
% 0.79/1.14 (522) {G0,W8,D3,L2,V2,M2} { ! alpha1( X, Y ), multiplication( Y, X ) =
% 0.79/1.14 zero }.
% 0.79/1.14 (523) {G0,W8,D3,L2,V2,M2} { ! alpha1( X, Y ), addition( X, Y ) = one }.
% 0.79/1.14 (524) {G0,W13,D3,L3,V2,M3} { ! multiplication( Y, X ) = zero, ! addition(
% 0.79/1.14 X, Y ) = one, alpha1( X, Y ) }.
% 0.79/1.14 (525) {G0,W9,D3,L3,V2,M3} { ! test( X ), ! c( X ) = Y, complement( X, Y )
% 0.79/1.14 }.
% 0.79/1.14 (526) {G0,W9,D3,L3,V2,M3} { ! test( X ), ! complement( X, Y ), c( X ) = Y
% 0.79/1.14 }.
% 0.79/1.14 (527) {G0,W6,D3,L2,V1,M2} { test( X ), c( X ) = zero }.
% 0.79/1.14 (528) {G0,W14,D4,L3,V2,M3} { ! test( X ), ! test( Y ), c( addition( X, Y )
% 0.79/1.14 ) = multiplication( c( X ), c( Y ) ) }.
% 0.79/1.14 (529) {G0,W14,D4,L3,V2,M3} { ! test( X ), ! test( Y ), c( multiplication(
% 0.79/1.14 X, Y ) ) = addition( c( X ), c( Y ) ) }.
% 0.79/1.14 (530) {G0,W2,D2,L1,V0,M1} { test( skol2 ) }.
% 0.79/1.14 (531) {G0,W20,D5,L2,V0,M2} { ! leq( skol3, addition( multiplication( skol3
% 0.79/1.14 , skol2 ), multiplication( skol3, c( skol2 ) ) ) ), ! leq( addition(
% 0.79/1.14 multiplication( skol3, skol2 ), multiplication( skol3, c( skol2 ) ) ),
% 0.79/1.14 skol3 ) }.
% 0.79/1.14
% 0.79/1.14
% 0.79/1.14 Total Proof:
% 0.79/1.14
% 0.79/1.14 subsumption: (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X
% 0.79/1.14 ) }.
% 0.79/1.14 parent0: (504) {G0,W7,D3,L1,V2,M1} { addition( X, Y ) = addition( Y, X )
% 0.79/1.14 }.
% 0.79/1.14 substitution0:
% 0.79/1.14 X := X
% 0.79/1.14 Y := Y
% 0.79/1.14 end
% 0.79/1.14 permutation0:
% 0.79/1.14 0 ==> 0
% 0.79/1.14 end
% 0.79/1.14
% 0.79/1.14 subsumption: (3) {G0,W5,D3,L1,V1,M1} I { addition( X, X ) ==> X }.
% 0.79/1.14 parent0: (507) {G0,W5,D3,L1,V1,M1} { addition( X, X ) = X }.
% 0.79/1.14 substitution0:
% 0.79/1.14 X := X
% 0.79/1.14 end
% 0.79/1.14 permutation0:
% 0.79/1.14 0 ==> 0
% 0.79/1.14 end
% 0.79/1.14
% 0.79/1.14 subsumption: (5) {G0,W5,D3,L1,V1,M1} I { multiplication( X, one ) ==> X }.
% 0.79/1.14 parent0: (509) {G0,W5,D3,L1,V1,M1} { multiplication( X, one ) = X }.
% 0.79/1.14 substitution0:
% 0.79/1.14 X := X
% 0.79/1.14 end
% 0.79/1.14 permutation0:
% 0.79/1.14 0 ==> 0
% 0.79/1.14 end
% 0.79/1.14
% 0.79/1.14 eqswap: (546) {G0,W13,D4,L1,V3,M1} { addition( multiplication( X, Y ),
% 0.79/1.14 multiplication( X, Z ) ) = multiplication( X, addition( Y, Z ) ) }.
% 0.79/1.14 parent0[0]: (511) {G0,W13,D4,L1,V3,M1} { multiplication( X, addition( Y, Z
% 0.79/1.14 ) ) = addition( multiplication( X, Y ), multiplication( X, Z ) ) }.
% 0.79/1.14 substitution0:
% 0.79/1.14 X := X
% 0.79/1.14 Y := Y
% 0.79/1.14 Z := Z
% 0.79/1.14 end
% 0.79/1.14
% 0.79/1.14 subsumption: (7) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Y )
% 0.79/1.14 , multiplication( X, Z ) ) ==> multiplication( X, addition( Y, Z ) ) }.
% 0.79/1.14 parent0: (546) {G0,W13,D4,L1,V3,M1} { addition( multiplication( X, Y ),
% 0.79/1.14 multiplication( X, Z ) ) = multiplication( X, addition( Y, Z ) ) }.
% 0.79/1.14 substitution0:
% 0.79/1.14 X := X
% 0.79/1.14 Y := Y
% 0.79/1.14 Z := Z
% 0.79/1.14 end
% 0.79/1.14 permutation0:
% 0.79/1.14 0 ==> 0
% 0.79/1.14 end
% 0.79/1.14
% 0.79/1.14 subsumption: (12) {G0,W8,D3,L2,V2,M2} I { ! addition( X, Y ) ==> Y, leq( X
% 0.79/1.14 , Y ) }.
% 0.79/1.14 parent0: (516) {G0,W8,D3,L2,V2,M2} { ! addition( X, Y ) = Y, leq( X, Y )
% 0.79/1.14 }.
% 0.79/1.14 substitution0:
% 0.79/1.14 X := X
% 0.79/1.14 Y := Y
% 0.79/1.14 end
% 0.79/1.14 permutation0:
% 0.79/1.14 0 ==> 0
% 0.79/1.14 1 ==> 1
% 0.79/1.14 end
% 0.79/1.14
% 0.79/1.14 subsumption: (16) {G0,W6,D2,L2,V2,M2} I { ! complement( Y, X ), alpha1( X,
% 0.79/1.14 Y ) }.
% 0.79/1.14 parent0: (520) {G0,W6,D2,L2,V2,M2} { ! complement( Y, X ), alpha1( X, Y )
% 0.79/1.14 }.
% 0.79/1.14 substitution0:
% 0.79/1.14 X := X
% 0.79/1.14 Y := Y
% 0.79/1.14 end
% 0.79/1.14 permutation0:
% 0.79/1.14 0 ==> 0
% 0.79/1.14 1 ==> 1
% 0.79/1.14 end
% 0.79/1.14
% 0.79/1.14 subsumption: (19) {G0,W8,D3,L2,V2,M2} I { ! alpha1( X, Y ), addition( X, Y
% 0.79/1.14 ) ==> one }.
% 0.79/1.14 parent0: (523) {G0,W8,D3,L2,V2,M2} { ! alpha1( X, Y ), addition( X, Y ) =
% 0.79/1.14 one }.
% 0.79/1.14 substitution0:
% 0.79/1.14 X := X
% 0.79/1.14 Y := Y
% 0.79/1.14 end
% 0.79/1.14 permutation0:
% 0.79/1.14 0 ==> 0
% 0.79/1.14 1 ==> 1
% 0.79/1.14 end
% 0.79/1.14
% 0.79/1.14 subsumption: (21) {G0,W9,D3,L3,V2,M3} I { ! test( X ), ! c( X ) = Y,
% 0.79/1.14 complement( X, Y ) }.
% 0.79/1.14 parent0: (525) {G0,W9,D3,L3,V2,M3} { ! test( X ), ! c( X ) = Y, complement
% 0.79/1.14 ( X, Y ) }.
% 0.79/1.14 substitution0:
% 0.79/1.14 X := X
% 0.79/1.14 Y := Y
% 0.79/1.14 end
% 0.79/1.14 permutation0:
% 0.79/1.14 0 ==> 0
% 0.79/1.14 1 ==> 1
% 0.79/1.14 2 ==> 2
% 0.79/1.14 end
% 0.79/1.14
% 0.79/1.14 subsumption: (26) {G0,W2,D2,L1,V0,M1} I { test( skol2 ) }.
% 0.79/1.14 parent0: (530) {G0,W2,D2,L1,V0,M1} { test( skol2 ) }.
% 0.79/1.14 substitution0:
% 0.79/1.14 end
% 0.79/1.14 permutation0:
% 0.79/1.14 0 ==> 0
% 0.79/1.14 end
% 0.79/1.14
% 0.79/1.14 *** allocated 50625 integers for clauses
% 0.79/1.14 paramod: (723) {G1,W18,D5,L2,V0,M2} { ! leq( multiplication( skol3,
% 0.79/1.14 addition( skol2, c( skol2 ) ) ), skol3 ), ! leq( skol3, addition(
% 0.79/1.14 multiplication( skol3, skol2 ), multiplication( skol3, c( skol2 ) ) ) )
% 0.79/1.14 }.
% 0.79/1.14 parent0[0]: (7) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Y ),
% 0.79/1.14 multiplication( X, Z ) ) ==> multiplication( X, addition( Y, Z ) ) }.
% 0.79/1.14 parent1[1; 2]: (531) {G0,W20,D5,L2,V0,M2} { ! leq( skol3, addition(
% 0.79/1.14 multiplication( skol3, skol2 ), multiplication( skol3, c( skol2 ) ) ) ),
% 0.79/1.14 ! leq( addition( multiplication( skol3, skol2 ), multiplication( skol3, c
% 0.79/1.14 ( skol2 ) ) ), skol3 ) }.
% 0.79/1.14 substitution0:
% 0.79/1.14 X := skol3
% 0.79/1.14 Y := skol2
% 0.79/1.14 Z := c( skol2 )
% 0.79/1.14 end
% 0.79/1.14 substitution1:
% 0.79/1.14 end
% 0.79/1.14
% 0.79/1.14 paramod: (725) {G1,W16,D5,L2,V0,M2} { ! leq( skol3, multiplication( skol3
% 0.79/1.14 , addition( skol2, c( skol2 ) ) ) ), ! leq( multiplication( skol3,
% 0.79/1.14 addition( skol2, c( skol2 ) ) ), skol3 ) }.
% 0.79/1.14 parent0[0]: (7) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Y ),
% 0.79/1.14 multiplication( X, Z ) ) ==> multiplication( X, addition( Y, Z ) ) }.
% 0.79/1.14 parent1[1; 3]: (723) {G1,W18,D5,L2,V0,M2} { ! leq( multiplication( skol3,
% 0.79/1.14 addition( skol2, c( skol2 ) ) ), skol3 ), ! leq( skol3, addition(
% 0.79/1.14 multiplication( skol3, skol2 ), multiplication( skol3, c( skol2 ) ) ) )
% 0.79/1.14 }.
% 0.79/1.14 substitution0:
% 0.79/1.14 X := skol3
% 0.79/1.14 Y := skol2
% 0.79/1.14 Z := c( skol2 )
% 0.79/1.14 end
% 0.79/1.14 substitution1:
% 0.79/1.14 end
% 0.79/1.14
% 0.79/1.14 subsumption: (27) {G1,W16,D5,L2,V0,M2} I;d(7);d(7) { ! leq( skol3,
% 0.79/1.14 multiplication( skol3, addition( skol2, c( skol2 ) ) ) ), ! leq(
% 0.79/1.14 multiplication( skol3, addition( skol2, c( skol2 ) ) ), skol3 ) }.
% 0.79/1.14 parent0: (725) {G1,W16,D5,L2,V0,M2} { ! leq( skol3, multiplication( skol3
% 0.79/1.14 , addition( skol2, c( skol2 ) ) ) ), ! leq( multiplication( skol3,
% 0.79/1.14 addition( skol2, c( skol2 ) ) ), skol3 ) }.
% 0.79/1.14 substitution0:
% 0.79/1.14 end
% 0.79/1.14 permutation0:
% 0.79/1.14 0 ==> 0
% 0.79/1.14 1 ==> 1
% 0.79/1.14 end
% 0.79/1.14
% 0.79/1.14 eqswap: (726) {G0,W9,D3,L3,V2,M3} { ! Y = c( X ), ! test( X ), complement
% 0.79/1.14 ( X, Y ) }.
% 0.79/1.14 parent0[1]: (21) {G0,W9,D3,L3,V2,M3} I { ! test( X ), ! c( X ) = Y,
% 0.79/1.14 complement( X, Y ) }.
% 0.79/1.14 substitution0:
% 0.79/1.14 X := X
% 0.79/1.14 Y := Y
% 0.79/1.14 end
% 0.79/1.14
% 0.79/1.14 eqrefl: (727) {G0,W6,D3,L2,V1,M2} { ! test( X ), complement( X, c( X ) )
% 0.79/1.14 }.
% 0.79/1.14 parent0[0]: (726) {G0,W9,D3,L3,V2,M3} { ! Y = c( X ), ! test( X ),
% 0.79/1.14 complement( X, Y ) }.
% 0.79/1.14 substitution0:
% 0.79/1.14 X := X
% 0.79/1.14 Y := c( X )
% 0.79/1.14 end
% 0.79/1.14
% 0.79/1.14 subsumption: (28) {G1,W6,D3,L2,V1,M2} Q(21) { ! test( X ), complement( X, c
% 0.79/1.14 ( X ) ) }.
% 0.79/1.14 parent0: (727) {G0,W6,D3,L2,V1,M2} { ! test( X ), complement( X, c( X ) )
% 0.79/1.14 }.
% 0.79/1.14 substitution0:
% 0.79/1.14 X := X
% 0.79/1.14 end
% 0.79/1.14 permutation0:
% 0.79/1.14 0 ==> 0
% 0.79/1.14 1 ==> 1
% 0.79/1.14 end
% 0.79/1.14
% 0.79/1.14 resolution: (728) {G1,W4,D3,L1,V0,M1} { complement( skol2, c( skol2 ) )
% 0.79/1.14 }.
% 0.79/1.14 parent0[0]: (28) {G1,W6,D3,L2,V1,M2} Q(21) { ! test( X ), complement( X, c
% 0.79/1.14 ( X ) ) }.
% 0.79/1.14 parent1[0]: (26) {G0,W2,D2,L1,V0,M1} I { test( skol2 ) }.
% 0.79/1.14 substitution0:
% 0.79/1.14 X := skol2
% 0.79/1.14 end
% 0.79/1.14 substitution1:
% 0.79/1.14 end
% 0.79/1.14
% 0.79/1.14 subsumption: (40) {G2,W4,D3,L1,V0,M1} R(28,26) { complement( skol2, c(
% 0.79/1.14 skol2 ) ) }.
% 0.79/1.14 parent0: (728) {G1,W4,D3,L1,V0,M1} { complement( skol2, c( skol2 ) ) }.
% 0.79/1.14 substitution0:
% 0.79/1.14 end
% 0.79/1.14 permutation0:
% 0.79/1.14 0 ==> 0
% 0.79/1.14 end
% 0.79/1.14
% 0.79/1.14 resolution: (729) {G1,W4,D3,L1,V0,M1} { alpha1( c( skol2 ), skol2 ) }.
% 0.79/1.14 parent0[0]: (16) {G0,W6,D2,L2,V2,M2} I { ! complement( Y, X ), alpha1( X, Y
% 0.79/1.14 ) }.
% 0.79/1.14 parent1[0]: (40) {G2,W4,D3,L1,V0,M1} R(28,26) { complement( skol2, c( skol2
% 0.79/1.14 ) ) }.
% 0.79/1.14 substitution0:
% 0.79/1.14 X := c( skol2 )
% 0.79/1.14 Y := skol2
% 0.79/1.14 end
% 0.79/1.14 substitution1:
% 0.79/1.14 end
% 0.79/1.14
% 0.79/1.14 subsumption: (41) {G3,W4,D3,L1,V0,M1} R(40,16) { alpha1( c( skol2 ), skol2
% 0.79/1.14 ) }.
% 0.79/1.14 parent0: (729) {G1,W4,D3,L1,V0,M1} { alpha1( c( skol2 ), skol2 ) }.
% 0.79/1.14 substitution0:
% 0.79/1.14 end
% 0.79/1.14 permutation0:
% 0.79/1.14 0 ==> 0
% 0.79/1.14 end
% 0.79/1.14
% 0.79/1.14 eqswap: (730) {G0,W8,D3,L2,V2,M2} { ! Y ==> addition( X, Y ), leq( X, Y )
% 0.79/1.14 }.
% 0.79/1.14 parent0[0]: (12) {G0,W8,D3,L2,V2,M2} I { ! addition( X, Y ) ==> Y, leq( X,
% 0.79/1.14 Y ) }.
% 0.79/1.14 substitution0:
% 0.79/1.14 X := X
% 0.79/1.14 Y := Y
% 0.79/1.14 end
% 0.79/1.14
% 0.79/1.14 eqswap: (731) {G0,W5,D3,L1,V1,M1} { X ==> addition( X, X ) }.
% 0.79/1.14 parent0[0]: (3) {G0,W5,D3,L1,V1,M1} I { addition( X, X ) ==> X }.
% 0.79/1.14 substitution0:
% 0.79/1.14 X := X
% 0.79/1.14 end
% 0.79/1.14
% 0.79/1.14 resolution: (732) {G1,W3,D2,L1,V1,M1} { leq( X, X ) }.
% 0.79/1.14 parent0[0]: (730) {G0,W8,D3,L2,V2,M2} { ! Y ==> addition( X, Y ), leq( X,
% 0.79/1.14 Y ) }.
% 0.79/1.14 parent1[0]: (731) {G0,W5,D3,L1,V1,M1} { X ==> addition( X, X ) }.
% 0.79/1.14 substitution0:
% 0.79/1.14 X := X
% 0.79/1.14 Y := X
% 0.79/1.14 end
% 0.79/1.14 substitution1:
% 0.79/1.14 X := X
% 0.79/1.14 end
% 0.79/1.14
% 0.79/1.14 subsumption: (161) {G1,W3,D2,L1,V1,M1} R(12,3) { leq( X, X ) }.
% 0.79/1.14 parent0: (732) {G1,W3,D2,L1,V1,M1} { leq( X, X ) }.
% 0.79/1.14 substitution0:
% 0.79/1.14 X := X
% 0.79/1.14 end
% 0.79/1.14 permutation0:
% 0.79/1.14 0 ==> 0
% 0.79/1.14 end
% 0.79/1.14
% 0.79/1.14 eqswap: (733) {G0,W8,D3,L2,V2,M2} { one ==> addition( X, Y ), ! alpha1( X
% 0.79/1.14 , Y ) }.
% 0.79/1.14 parent0[1]: (19) {G0,W8,D3,L2,V2,M2} I { ! alpha1( X, Y ), addition( X, Y )
% 0.79/1.14 ==> one }.
% 0.79/1.14 substitution0:
% 0.79/1.14 X := X
% 0.79/1.14 Y := Y
% 0.79/1.14 end
% 0.79/1.14
% 0.79/1.14 resolution: (734) {G1,W6,D4,L1,V0,M1} { one ==> addition( c( skol2 ),
% 0.79/1.14 skol2 ) }.
% 0.79/1.14 parent0[1]: (733) {G0,W8,D3,L2,V2,M2} { one ==> addition( X, Y ), ! alpha1
% 0.79/1.14 ( X, Y ) }.
% 0.79/1.14 parent1[0]: (41) {G3,W4,D3,L1,V0,M1} R(40,16) { alpha1( c( skol2 ), skol2 )
% 0.79/1.14 }.
% 0.79/1.14 substitution0:
% 0.79/1.14 X := c( skol2 )
% 0.79/1.14 Y := skol2
% 0.79/1.14 end
% 0.79/1.14 substitution1:
% 0.79/1.14 end
% 0.79/1.14
% 0.79/1.14 eqswap: (735) {G1,W6,D4,L1,V0,M1} { addition( c( skol2 ), skol2 ) ==> one
% 0.79/1.14 }.
% 0.79/1.14 parent0[0]: (734) {G1,W6,D4,L1,V0,M1} { one ==> addition( c( skol2 ),
% 0.79/1.14 skol2 ) }.
% 0.79/1.14 substitution0:
% 0.79/1.14 end
% 0.79/1.14
% 0.79/1.14 subsumption: (271) {G4,W6,D4,L1,V0,M1} R(19,41) { addition( c( skol2 ),
% 0.79/1.14 skol2 ) ==> one }.
% 0.79/1.14 parent0: (735) {G1,W6,D4,L1,V0,M1} { addition( c( skol2 ), skol2 ) ==> one
% 0.79/1.14 }.
% 0.79/1.14 substitution0:
% 0.79/1.14 end
% 0.79/1.14 permutation0:
% 0.79/1.14 0 ==> 0
% 0.79/1.14 end
% 0.79/1.14
% 0.79/1.14 paramod: (741) {G1,W16,D5,L2,V0,M2} { ! leq( multiplication( skol3,
% 0.79/1.14 addition( c( skol2 ), skol2 ) ), skol3 ), ! leq( skol3, multiplication(
% 0.79/1.14 skol3, addition( skol2, c( skol2 ) ) ) ) }.
% 0.79/1.14 parent0[0]: (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X )
% 0.79/1.14 }.
% 0.79/1.14 parent1[1; 4]: (27) {G1,W16,D5,L2,V0,M2} I;d(7);d(7) { ! leq( skol3,
% 0.79/1.14 multiplication( skol3, addition( skol2, c( skol2 ) ) ) ), ! leq(
% 0.79/1.14 multiplication( skol3, addition( skol2, c( skol2 ) ) ), skol3 ) }.
% 0.79/1.14 substitution0:
% 0.79/1.14 X := skol2
% 0.79/1.14 Y := c( skol2 )
% 0.79/1.14 end
% 0.79/1.14 substitution1:
% 0.79/1.14 end
% 0.79/1.14
% 0.79/1.14 paramod: (743) {G1,W16,D5,L2,V0,M2} { ! leq( skol3, multiplication( skol3
% 0.79/1.14 , addition( c( skol2 ), skol2 ) ) ), ! leq( multiplication( skol3,
% 0.79/1.14 addition( c( skol2 ), skol2 ) ), skol3 ) }.
% 0.79/1.14 parent0[0]: (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X )
% 0.79/1.14 }.
% 0.79/1.14 parent1[1; 5]: (741) {G1,W16,D5,L2,V0,M2} { ! leq( multiplication( skol3,
% 0.79/1.14 addition( c( skol2 ), skol2 ) ), skol3 ), ! leq( skol3, multiplication(
% 0.79/1.14 skol3, addition( skol2, c( skol2 ) ) ) ) }.
% 0.79/1.14 substitution0:
% 0.79/1.14 X := skol2
% 0.79/1.14 Y := c( skol2 )
% 0.79/1.14 end
% 0.79/1.14 substitution1:
% 0.79/1.14 end
% 0.79/1.14
% 0.79/1.14 paramod: (746) {G2,W13,D5,L2,V0,M2} { ! leq( multiplication( skol3, one )
% 0.79/1.14 , skol3 ), ! leq( skol3, multiplication( skol3, addition( c( skol2 ),
% 0.79/1.14 skol2 ) ) ) }.
% 0.79/1.14 parent0[0]: (271) {G4,W6,D4,L1,V0,M1} R(19,41) { addition( c( skol2 ),
% 0.79/1.14 skol2 ) ==> one }.
% 0.79/1.14 parent1[1; 4]: (743) {G1,W16,D5,L2,V0,M2} { ! leq( skol3, multiplication(
% 0.79/1.14 skol3, addition( c( skol2 ), skol2 ) ) ), ! leq( multiplication( skol3,
% 0.79/1.14 addition( c( skol2 ), skol2 ) ), skol3 ) }.
% 0.79/1.14 substitution0:
% 0.79/1.14 end
% 0.79/1.14 substitution1:
% 0.79/1.14 end
% 0.79/1.14
% 0.79/1.14 paramod: (748) {G3,W10,D3,L2,V0,M2} { ! leq( skol3, multiplication( skol3
% 0.79/1.14 , one ) ), ! leq( multiplication( skol3, one ), skol3 ) }.
% 0.79/1.14 parent0[0]: (271) {G4,W6,D4,L1,V0,M1} R(19,41) { addition( c( skol2 ),
% 0.79/1.14 skol2 ) ==> one }.
% 0.79/1.14 parent1[1; 5]: (746) {G2,W13,D5,L2,V0,M2} { ! leq( multiplication( skol3,
% 0.79/1.14 one ), skol3 ), ! leq( skol3, multiplication( skol3, addition( c( skol2 )
% 0.79/1.14 , skol2 ) ) ) }.
% 0.79/1.14 substitution0:
% 0.79/1.14 end
% 0.79/1.14 substitution1:
% 0.79/1.14 end
% 0.79/1.14
% 0.79/1.14 paramod: (750) {G1,W8,D3,L2,V0,M2} { ! leq( skol3, skol3 ), ! leq( skol3,
% 0.79/1.14 multiplication( skol3, one ) ) }.
% 0.79/1.14 parent0[0]: (5) {G0,W5,D3,L1,V1,M1} I { multiplication( X, one ) ==> X }.
% 0.79/1.14 parent1[1; 2]: (748) {G3,W10,D3,L2,V0,M2} { ! leq( skol3, multiplication(
% 0.79/1.14 skol3, one ) ), ! leq( multiplication( skol3, one ), skol3 ) }.
% 0.79/1.14 substitution0:
% 0.79/1.14 X := skol3
% 0.79/1.14 end
% 0.79/1.14 substitution1:
% 0.79/1.14 end
% 0.79/1.14
% 0.79/1.14 paramod: (753) {G1,W6,D2,L2,V0,M2} { ! leq( skol3, skol3 ), ! leq( skol3,
% 0.79/1.14 skol3 ) }.
% 0.79/1.14 parent0[0]: (5) {G0,W5,D3,L1,V1,M1} I { multiplication( X, one ) ==> X }.
% 0.79/1.14 parent1[1; 3]: (750) {G1,W8,D3,L2,V0,M2} { ! leq( skol3, skol3 ), ! leq(
% 0.79/1.14 skol3, multiplication( skol3, one ) ) }.
% 0.79/1.14 substitution0:
% 0.79/1.14 X := skol3
% 0.79/1.14 end
% 0.79/1.14 substitution1:
% 0.79/1.14 end
% 0.79/1.14
% 0.79/1.14 factor: (754) {G1,W3,D2,L1,V0,M1} { ! leq( skol3, skol3 ) }.
% 0.79/1.14 parent0[0, 1]: (753) {G1,W6,D2,L2,V0,M2} { ! leq( skol3, skol3 ), ! leq(
% 0.79/1.14 skol3, skol3 ) }.
% 0.79/1.14 substitution0:
% 0.79/1.14 end
% 0.79/1.14
% 0.79/1.14 resolution: (756) {G2,W0,D0,L0,V0,M0} { }.
% 0.79/1.14 parent0[0]: (754) {G1,W3,D2,L1,V0,M1} { ! leq( skol3, skol3 ) }.
% 0.79/1.14 parent1[0]: (161) {G1,W3,D2,L1,V1,M1} R(12,3) { leq( X, X ) }.
% 0.79/1.14 substitution0:
% 0.79/1.14 end
% 0.79/1.14 substitution1:
% 0.79/1.14 X := skol3
% 0.79/1.14 end
% 0.79/1.14
% 0.79/1.14 subsumption: (502) {G5,W0,D0,L0,V0,M0} P(0,27);d(271);d(271);d(5);d(5);f;r(
% 0.79/1.14 161) { }.
% 0.79/1.14 parent0: (756) {G2,W0,D0,L0,V0,M0} { }.
% 0.79/1.14 substitution0:
% 0.79/1.14 end
% 0.79/1.14 permutation0:
% 0.79/1.14 end
% 0.79/1.14
% 0.79/1.14 Proof check complete!
% 0.79/1.14
% 0.79/1.14 Memory use:
% 0.79/1.14
% 0.79/1.14 space for terms: 6009
% 0.79/1.14 space for clauses: 29786
% 0.79/1.14
% 0.79/1.14
% 0.79/1.14 clauses generated: 1917
% 0.79/1.14 clauses kept: 503
% 0.79/1.14 clauses selected: 80
% 0.79/1.14 clauses deleted: 6
% 0.79/1.14 clauses inuse deleted: 0
% 0.79/1.14
% 0.79/1.14 subsentry: 3184
% 0.79/1.14 literals s-matched: 1997
% 0.79/1.14 literals matched: 1996
% 0.79/1.14 full subsumption: 205
% 0.79/1.14
% 0.79/1.14 checksum: -721305279
% 0.79/1.14
% 0.79/1.14
% 0.79/1.14 Bliksem ended
%------------------------------------------------------------------------------