TSTP Solution File: NUM845+2 by Bliksem---1.12
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%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : NUM845+2 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n020.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 : Mon Jul 18 06:27:00 EDT 2022
% Result : Theorem 0.77s 1.15s
% Output : Refutation 0.77s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : NUM845+2 : TPTP v8.1.0. Released v4.1.0.
% 0.03/0.13 % Command : bliksem %s
% 0.13/0.34 % Computer : n020.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 Jul 7 03:26:29 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.77/1.15 *** allocated 10000 integers for termspace/termends
% 0.77/1.15 *** allocated 10000 integers for clauses
% 0.77/1.15 *** allocated 10000 integers for justifications
% 0.77/1.15 Bliksem 1.12
% 0.77/1.15
% 0.77/1.15
% 0.77/1.15 Automatic Strategy Selection
% 0.77/1.15
% 0.77/1.15
% 0.77/1.15 Clauses:
% 0.77/1.15
% 0.77/1.15 { vmul( vsucc( vd411 ), skol1 ) = vplus( vmul( vd411, skol1 ), skol1 ) }.
% 0.77/1.15 { ! vmul( vsucc( vd411 ), vsucc( skol1 ) ) = vplus( vmul( vd411, vsucc(
% 0.77/1.15 skol1 ) ), vsucc( skol1 ) ) }.
% 0.77/1.15 { ! vmul( vsucc( vd411 ), X ) = vplus( vmul( vd411, X ), X ), vplus( vplus
% 0.77/1.15 ( vmul( vd411, X ), vd411 ), vsucc( X ) ) = vplus( vmul( vd411, vsucc( X
% 0.77/1.15 ) ), vsucc( X ) ) }.
% 0.77/1.15 { ! vmul( vsucc( vd411 ), X ) = vplus( vmul( vd411, X ), X ), vplus( vmul(
% 0.77/1.15 vd411, X ), vplus( vd411, vsucc( X ) ) ) = vplus( vplus( vmul( vd411, X )
% 0.77/1.15 , vd411 ), vsucc( X ) ) }.
% 0.77/1.15 { ! vmul( vsucc( vd411 ), X ) = vplus( vmul( vd411, X ), X ), vplus( vmul(
% 0.77/1.15 vd411, X ), vsucc( vplus( vd411, X ) ) ) = vplus( vmul( vd411, X ), vplus
% 0.77/1.15 ( vd411, vsucc( X ) ) ) }.
% 0.77/1.15 { ! vmul( vsucc( vd411 ), X ) = vplus( vmul( vd411, X ), X ), vplus( vmul(
% 0.77/1.15 vd411, X ), vplus( vsucc( vd411 ), X ) ) = vplus( vmul( vd411, X ), vsucc
% 0.77/1.15 ( vplus( vd411, X ) ) ) }.
% 0.77/1.15 { ! vmul( vsucc( vd411 ), X ) = vplus( vmul( vd411, X ), X ), vplus( vmul(
% 0.77/1.15 vd411, X ), vplus( X, vsucc( vd411 ) ) ) = vplus( vmul( vd411, X ), vplus
% 0.77/1.15 ( vsucc( vd411 ), X ) ) }.
% 0.77/1.15 { ! vmul( vsucc( vd411 ), X ) = vplus( vmul( vd411, X ), X ), vplus( vplus
% 0.77/1.15 ( vmul( vd411, X ), X ), vsucc( vd411 ) ) = vplus( vmul( vd411, X ),
% 0.77/1.15 vplus( X, vsucc( vd411 ) ) ) }.
% 0.77/1.15 { ! vmul( vsucc( vd411 ), X ) = vplus( vmul( vd411, X ), X ), vplus( vmul(
% 0.77/1.15 vsucc( vd411 ), X ), vsucc( vd411 ) ) = vplus( vplus( vmul( vd411, X ), X
% 0.77/1.15 ), vsucc( vd411 ) ) }.
% 0.77/1.15 { ! vmul( vsucc( vd411 ), X ) = vplus( vmul( vd411, X ), X ), vmul( vsucc(
% 0.77/1.15 vd411 ), vsucc( X ) ) = vplus( vmul( vsucc( vd411 ), X ), vsucc( vd411 )
% 0.77/1.15 ) }.
% 0.77/1.15 { vsucc( vmul( vd411, v1 ) ) = vplus( vmul( vd411, v1 ), v1 ) }.
% 0.77/1.15 { vmul( X, vsucc( Y ) ) = vplus( vmul( X, Y ), X ) }.
% 0.77/1.15 { vmul( X, v1 ) = X }.
% 0.77/1.15 { vplus( Y, X ) = vplus( X, Y ) }.
% 0.77/1.15 { vplus( v1, X ) = vsucc( X ) }.
% 0.77/1.15 { vplus( vplus( X, Y ), Z ) = vplus( X, vplus( Y, Z ) ) }.
% 0.77/1.15 { vplus( X, vsucc( Y ) ) = vsucc( vplus( X, Y ) ) }.
% 0.77/1.15 { vplus( X, v1 ) = vsucc( X ) }.
% 0.77/1.15
% 0.77/1.15 percentage equality = 1.000000, percentage horn = 1.000000
% 0.77/1.15 This is a pure equality problem
% 0.77/1.15
% 0.77/1.15
% 0.77/1.15
% 0.77/1.15 Options Used:
% 0.77/1.15
% 0.77/1.15 useres = 1
% 0.77/1.15 useparamod = 1
% 0.77/1.15 useeqrefl = 1
% 0.77/1.15 useeqfact = 1
% 0.77/1.15 usefactor = 1
% 0.77/1.15 usesimpsplitting = 0
% 0.77/1.15 usesimpdemod = 5
% 0.77/1.15 usesimpres = 3
% 0.77/1.15
% 0.77/1.15 resimpinuse = 1000
% 0.77/1.15 resimpclauses = 20000
% 0.77/1.15 substype = eqrewr
% 0.77/1.15 backwardsubs = 1
% 0.77/1.15 selectoldest = 5
% 0.77/1.15
% 0.77/1.15 litorderings [0] = split
% 0.77/1.15 litorderings [1] = extend the termordering, first sorting on arguments
% 0.77/1.15
% 0.77/1.15 termordering = kbo
% 0.77/1.15
% 0.77/1.15 litapriori = 0
% 0.77/1.15 termapriori = 1
% 0.77/1.15 litaposteriori = 0
% 0.77/1.15 termaposteriori = 0
% 0.77/1.15 demodaposteriori = 0
% 0.77/1.15 ordereqreflfact = 0
% 0.77/1.15
% 0.77/1.15 litselect = negord
% 0.77/1.15
% 0.77/1.15 maxweight = 15
% 0.77/1.15 maxdepth = 30000
% 0.77/1.15 maxlength = 115
% 0.77/1.15 maxnrvars = 195
% 0.77/1.15 excuselevel = 1
% 0.77/1.15 increasemaxweight = 1
% 0.77/1.15
% 0.77/1.15 maxselected = 10000000
% 0.77/1.15 maxnrclauses = 10000000
% 0.77/1.15
% 0.77/1.15 showgenerated = 0
% 0.77/1.15 showkept = 0
% 0.77/1.15 showselected = 0
% 0.77/1.15 showdeleted = 0
% 0.77/1.15 showresimp = 1
% 0.77/1.15 showstatus = 2000
% 0.77/1.15
% 0.77/1.15 prologoutput = 0
% 0.77/1.15 nrgoals = 5000000
% 0.77/1.15 totalproof = 1
% 0.77/1.15
% 0.77/1.15 Symbols occurring in the translation:
% 0.77/1.15
% 0.77/1.15 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.77/1.15 . [1, 2] (w:1, o:27, a:1, s:1, b:0),
% 0.77/1.15 ! [4, 1] (w:0, o:21, a:1, s:1, b:0),
% 0.77/1.15 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.77/1.15 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.77/1.15 vd411 [36, 0] (w:1, o:9, a:1, s:1, b:0),
% 0.77/1.15 vsucc [37, 1] (w:1, o:26, a:1, s:1, b:0),
% 0.77/1.15 vmul [38, 2] (w:1, o:51, a:1, s:1, b:0),
% 0.77/1.15 vplus [39, 2] (w:1, o:52, a:1, s:1, b:0),
% 0.77/1.15 v1 [41, 0] (w:1, o:11, a:1, s:1, b:0),
% 0.77/1.15 skol1 [52, 0] (w:1, o:20, a:1, s:1, b:1).
% 0.77/1.15
% 0.77/1.15
% 0.77/1.15 Starting Search:
% 0.77/1.15
% 0.77/1.15 *** allocated 15000 integers for clauses
% 0.77/1.15
% 0.77/1.15 Bliksems!, er is een bewijs:
% 0.77/1.15 % SZS status Theorem
% 0.77/1.15 % SZS output start Refutation
% 0.77/1.15
% 0.77/1.15 (0) {G0,W10,D4,L1,V0,M1} I { vplus( vmul( vd411, skol1 ), skol1 ) ==> vmul
% 0.77/1.15 ( vsucc( vd411 ), skol1 ) }.
% 0.77/1.15 (1) {G0,W13,D5,L1,V0,M1} I { ! vplus( vmul( vd411, vsucc( skol1 ) ), vsucc
% 0.77/1.15 ( skol1 ) ) ==> vmul( vsucc( vd411 ), vsucc( skol1 ) ) }.
% 0.77/1.15 (9) {G0,W10,D4,L1,V2,M1} I { vplus( vmul( X, Y ), X ) ==> vmul( X, vsucc( Y
% 0.77/1.15 ) ) }.
% 0.77/1.15 (11) {G0,W7,D3,L1,V2,M1} I { vplus( Y, X ) = vplus( X, Y ) }.
% 0.77/1.15 (13) {G0,W11,D4,L1,V3,M1} I { vplus( X, vplus( Y, Z ) ) ==> vplus( vplus( X
% 0.77/1.15 , Y ), Z ) }.
% 0.77/1.15 (14) {G0,W9,D4,L1,V2,M1} I { vplus( X, vsucc( Y ) ) ==> vsucc( vplus( X, Y
% 0.77/1.15 ) ) }.
% 0.77/1.15 (19) {G1,W13,D6,L1,V2,M1} P(9,14) { vsucc( vplus( vmul( vsucc( X ), Y ), X
% 0.77/1.15 ) ) ==> vmul( vsucc( X ), vsucc( Y ) ) }.
% 0.77/1.15 (20) {G1,W10,D4,L1,V2,M1} P(9,11) { vplus( X, vmul( X, Y ) ) ==> vmul( X,
% 0.77/1.15 vsucc( Y ) ) }.
% 0.77/1.15 (25) {G1,W13,D6,L1,V0,M1} S(1);d(14) { ! vsucc( vplus( vmul( vd411, vsucc(
% 0.77/1.15 skol1 ) ), skol1 ) ) ==> vmul( vsucc( vd411 ), vsucc( skol1 ) ) }.
% 0.77/1.15 (34) {G1,W11,D4,L1,V3,M1} P(13,11) { vplus( vplus( X, Y ), Z ) = vplus(
% 0.77/1.15 vplus( Y, Z ), X ) }.
% 0.77/1.15 (47) {G2,W14,D5,L1,V3,M1} P(20,34) { vplus( vplus( vmul( X, Y ), Z ), X )
% 0.77/1.15 ==> vplus( vmul( X, vsucc( Y ) ), Z ) }.
% 0.77/1.15 (118) {G3,W13,D5,L1,V0,M1} P(0,47) { vplus( vmul( vd411, vsucc( skol1 ) ),
% 0.77/1.15 skol1 ) ==> vplus( vmul( vsucc( vd411 ), skol1 ), vd411 ) }.
% 0.77/1.15 (119) {G4,W0,D0,L0,V0,M0} P(118,25);d(19);q { }.
% 0.77/1.15
% 0.77/1.15
% 0.77/1.15 % SZS output end Refutation
% 0.77/1.15 found a proof!
% 0.77/1.15
% 0.77/1.15
% 0.77/1.15 Unprocessed initial clauses:
% 0.77/1.15
% 0.77/1.15 (121) {G0,W10,D4,L1,V0,M1} { vmul( vsucc( vd411 ), skol1 ) = vplus( vmul(
% 0.77/1.15 vd411, skol1 ), skol1 ) }.
% 0.77/1.15 (122) {G0,W13,D5,L1,V0,M1} { ! vmul( vsucc( vd411 ), vsucc( skol1 ) ) =
% 0.77/1.15 vplus( vmul( vd411, vsucc( skol1 ) ), vsucc( skol1 ) ) }.
% 0.77/1.15 (123) {G0,W26,D5,L2,V1,M2} { ! vmul( vsucc( vd411 ), X ) = vplus( vmul(
% 0.77/1.15 vd411, X ), X ), vplus( vplus( vmul( vd411, X ), vd411 ), vsucc( X ) ) =
% 0.77/1.15 vplus( vmul( vd411, vsucc( X ) ), vsucc( X ) ) }.
% 0.77/1.15 (124) {G0,W27,D5,L2,V1,M2} { ! vmul( vsucc( vd411 ), X ) = vplus( vmul(
% 0.77/1.15 vd411, X ), X ), vplus( vmul( vd411, X ), vplus( vd411, vsucc( X ) ) ) =
% 0.77/1.15 vplus( vplus( vmul( vd411, X ), vd411 ), vsucc( X ) ) }.
% 0.77/1.15 (125) {G0,W27,D5,L2,V1,M2} { ! vmul( vsucc( vd411 ), X ) = vplus( vmul(
% 0.77/1.15 vd411, X ), X ), vplus( vmul( vd411, X ), vsucc( vplus( vd411, X ) ) ) =
% 0.77/1.15 vplus( vmul( vd411, X ), vplus( vd411, vsucc( X ) ) ) }.
% 0.77/1.15 (126) {G0,W27,D5,L2,V1,M2} { ! vmul( vsucc( vd411 ), X ) = vplus( vmul(
% 0.77/1.15 vd411, X ), X ), vplus( vmul( vd411, X ), vplus( vsucc( vd411 ), X ) ) =
% 0.77/1.15 vplus( vmul( vd411, X ), vsucc( vplus( vd411, X ) ) ) }.
% 0.77/1.15 (127) {G0,W27,D5,L2,V1,M2} { ! vmul( vsucc( vd411 ), X ) = vplus( vmul(
% 0.77/1.15 vd411, X ), X ), vplus( vmul( vd411, X ), vplus( X, vsucc( vd411 ) ) ) =
% 0.77/1.15 vplus( vmul( vd411, X ), vplus( vsucc( vd411 ), X ) ) }.
% 0.77/1.15 (128) {G0,W27,D5,L2,V1,M2} { ! vmul( vsucc( vd411 ), X ) = vplus( vmul(
% 0.77/1.15 vd411, X ), X ), vplus( vplus( vmul( vd411, X ), X ), vsucc( vd411 ) ) =
% 0.77/1.15 vplus( vmul( vd411, X ), vplus( X, vsucc( vd411 ) ) ) }.
% 0.77/1.15 (129) {G0,W26,D5,L2,V1,M2} { ! vmul( vsucc( vd411 ), X ) = vplus( vmul(
% 0.77/1.15 vd411, X ), X ), vplus( vmul( vsucc( vd411 ), X ), vsucc( vd411 ) ) =
% 0.77/1.15 vplus( vplus( vmul( vd411, X ), X ), vsucc( vd411 ) ) }.
% 0.77/1.15 (130) {G0,W23,D5,L2,V1,M2} { ! vmul( vsucc( vd411 ), X ) = vplus( vmul(
% 0.77/1.15 vd411, X ), X ), vmul( vsucc( vd411 ), vsucc( X ) ) = vplus( vmul( vsucc
% 0.77/1.15 ( vd411 ), X ), vsucc( vd411 ) ) }.
% 0.77/1.15 (131) {G0,W10,D4,L1,V0,M1} { vsucc( vmul( vd411, v1 ) ) = vplus( vmul(
% 0.77/1.15 vd411, v1 ), v1 ) }.
% 0.77/1.15 (132) {G0,W10,D4,L1,V2,M1} { vmul( X, vsucc( Y ) ) = vplus( vmul( X, Y ),
% 0.77/1.15 X ) }.
% 0.77/1.15 (133) {G0,W5,D3,L1,V1,M1} { vmul( X, v1 ) = X }.
% 0.77/1.15 (134) {G0,W7,D3,L1,V2,M1} { vplus( Y, X ) = vplus( X, Y ) }.
% 0.77/1.15 (135) {G0,W6,D3,L1,V1,M1} { vplus( v1, X ) = vsucc( X ) }.
% 0.77/1.15 (136) {G0,W11,D4,L1,V3,M1} { vplus( vplus( X, Y ), Z ) = vplus( X, vplus(
% 0.77/1.15 Y, Z ) ) }.
% 0.77/1.15 (137) {G0,W9,D4,L1,V2,M1} { vplus( X, vsucc( Y ) ) = vsucc( vplus( X, Y )
% 0.77/1.15 ) }.
% 0.77/1.15 (138) {G0,W6,D3,L1,V1,M1} { vplus( X, v1 ) = vsucc( X ) }.
% 0.77/1.15
% 0.77/1.15
% 0.77/1.15 Total Proof:
% 0.77/1.15
% 0.77/1.15 eqswap: (139) {G0,W10,D4,L1,V0,M1} { vplus( vmul( vd411, skol1 ), skol1 )
% 0.77/1.15 = vmul( vsucc( vd411 ), skol1 ) }.
% 0.77/1.15 parent0[0]: (121) {G0,W10,D4,L1,V0,M1} { vmul( vsucc( vd411 ), skol1 ) =
% 0.77/1.15 vplus( vmul( vd411, skol1 ), skol1 ) }.
% 0.77/1.15 substitution0:
% 0.77/1.15 end
% 0.77/1.15
% 0.77/1.15 subsumption: (0) {G0,W10,D4,L1,V0,M1} I { vplus( vmul( vd411, skol1 ),
% 0.77/1.15 skol1 ) ==> vmul( vsucc( vd411 ), skol1 ) }.
% 0.77/1.15 parent0: (139) {G0,W10,D4,L1,V0,M1} { vplus( vmul( vd411, skol1 ), skol1 )
% 0.77/1.15 = vmul( vsucc( vd411 ), skol1 ) }.
% 0.77/1.15 substitution0:
% 0.77/1.15 end
% 0.77/1.15 permutation0:
% 0.77/1.15 0 ==> 0
% 0.77/1.15 end
% 0.77/1.15
% 0.77/1.15 eqswap: (141) {G0,W13,D5,L1,V0,M1} { ! vplus( vmul( vd411, vsucc( skol1 )
% 0.77/1.15 ), vsucc( skol1 ) ) = vmul( vsucc( vd411 ), vsucc( skol1 ) ) }.
% 0.77/1.15 parent0[0]: (122) {G0,W13,D5,L1,V0,M1} { ! vmul( vsucc( vd411 ), vsucc(
% 0.77/1.15 skol1 ) ) = vplus( vmul( vd411, vsucc( skol1 ) ), vsucc( skol1 ) ) }.
% 0.77/1.15 substitution0:
% 0.77/1.15 end
% 0.77/1.15
% 0.77/1.15 subsumption: (1) {G0,W13,D5,L1,V0,M1} I { ! vplus( vmul( vd411, vsucc(
% 0.77/1.15 skol1 ) ), vsucc( skol1 ) ) ==> vmul( vsucc( vd411 ), vsucc( skol1 ) )
% 0.77/1.15 }.
% 0.77/1.15 parent0: (141) {G0,W13,D5,L1,V0,M1} { ! vplus( vmul( vd411, vsucc( skol1 )
% 0.77/1.15 ), vsucc( skol1 ) ) = vmul( vsucc( vd411 ), vsucc( skol1 ) ) }.
% 0.77/1.15 substitution0:
% 0.77/1.15 end
% 0.77/1.15 permutation0:
% 0.77/1.15 0 ==> 0
% 0.77/1.15 end
% 0.77/1.15
% 0.77/1.15 eqswap: (169) {G0,W10,D4,L1,V2,M1} { vplus( vmul( X, Y ), X ) = vmul( X,
% 0.77/1.15 vsucc( Y ) ) }.
% 0.77/1.15 parent0[0]: (132) {G0,W10,D4,L1,V2,M1} { vmul( X, vsucc( Y ) ) = vplus(
% 0.77/1.15 vmul( X, Y ), X ) }.
% 0.77/1.15 substitution0:
% 0.77/1.15 X := X
% 0.77/1.15 Y := Y
% 0.77/1.15 end
% 0.77/1.15
% 0.77/1.15 subsumption: (9) {G0,W10,D4,L1,V2,M1} I { vplus( vmul( X, Y ), X ) ==> vmul
% 0.77/1.15 ( X, vsucc( Y ) ) }.
% 0.77/1.15 parent0: (169) {G0,W10,D4,L1,V2,M1} { vplus( vmul( X, Y ), X ) = vmul( X,
% 0.77/1.15 vsucc( Y ) ) }.
% 0.77/1.15 substitution0:
% 0.77/1.15 X := X
% 0.77/1.15 Y := Y
% 0.77/1.15 end
% 0.77/1.15 permutation0:
% 0.77/1.15 0 ==> 0
% 0.77/1.15 end
% 0.77/1.15
% 0.77/1.15 subsumption: (11) {G0,W7,D3,L1,V2,M1} I { vplus( Y, X ) = vplus( X, Y ) }.
% 0.77/1.15 parent0: (134) {G0,W7,D3,L1,V2,M1} { vplus( Y, X ) = vplus( X, Y ) }.
% 0.77/1.15 substitution0:
% 0.77/1.15 X := X
% 0.77/1.15 Y := Y
% 0.77/1.15 end
% 0.77/1.15 permutation0:
% 0.77/1.15 0 ==> 0
% 0.77/1.15 end
% 0.77/1.15
% 0.77/1.15 *** allocated 22500 integers for clauses
% 0.77/1.15 eqswap: (229) {G0,W11,D4,L1,V3,M1} { vplus( X, vplus( Y, Z ) ) = vplus(
% 0.77/1.15 vplus( X, Y ), Z ) }.
% 0.77/1.15 parent0[0]: (136) {G0,W11,D4,L1,V3,M1} { vplus( vplus( X, Y ), Z ) = vplus
% 0.77/1.15 ( X, vplus( Y, Z ) ) }.
% 0.77/1.15 substitution0:
% 0.77/1.15 X := X
% 0.77/1.15 Y := Y
% 0.77/1.15 Z := Z
% 0.77/1.15 end
% 0.77/1.15
% 0.77/1.15 subsumption: (13) {G0,W11,D4,L1,V3,M1} I { vplus( X, vplus( Y, Z ) ) ==>
% 0.77/1.15 vplus( vplus( X, Y ), Z ) }.
% 0.77/1.15 parent0: (229) {G0,W11,D4,L1,V3,M1} { vplus( X, vplus( Y, Z ) ) = vplus(
% 0.77/1.15 vplus( X, Y ), Z ) }.
% 0.77/1.15 substitution0:
% 0.77/1.15 X := X
% 0.77/1.15 Y := Y
% 0.77/1.15 Z := Z
% 0.77/1.15 end
% 0.77/1.15 permutation0:
% 0.77/1.15 0 ==> 0
% 0.77/1.15 end
% 0.77/1.15
% 0.77/1.15 subsumption: (14) {G0,W9,D4,L1,V2,M1} I { vplus( X, vsucc( Y ) ) ==> vsucc
% 0.77/1.15 ( vplus( X, Y ) ) }.
% 0.77/1.15 parent0: (137) {G0,W9,D4,L1,V2,M1} { vplus( X, vsucc( Y ) ) = vsucc( vplus
% 0.77/1.15 ( X, Y ) ) }.
% 0.77/1.15 substitution0:
% 0.77/1.15 X := X
% 0.77/1.15 Y := Y
% 0.77/1.15 end
% 0.77/1.15 permutation0:
% 0.77/1.15 0 ==> 0
% 0.77/1.15 end
% 0.77/1.15
% 0.77/1.15 eqswap: (262) {G0,W10,D4,L1,V2,M1} { vmul( X, vsucc( Y ) ) ==> vplus( vmul
% 0.77/1.15 ( X, Y ), X ) }.
% 0.77/1.15 parent0[0]: (9) {G0,W10,D4,L1,V2,M1} I { vplus( vmul( X, Y ), X ) ==> vmul
% 0.77/1.15 ( X, vsucc( Y ) ) }.
% 0.77/1.15 substitution0:
% 0.77/1.15 X := X
% 0.77/1.15 Y := Y
% 0.77/1.15 end
% 0.77/1.15
% 0.77/1.15 paramod: (264) {G1,W13,D6,L1,V2,M1} { vmul( vsucc( X ), vsucc( Y ) ) ==>
% 0.77/1.15 vsucc( vplus( vmul( vsucc( X ), Y ), X ) ) }.
% 0.77/1.15 parent0[0]: (14) {G0,W9,D4,L1,V2,M1} I { vplus( X, vsucc( Y ) ) ==> vsucc(
% 0.77/1.15 vplus( X, Y ) ) }.
% 0.77/1.15 parent1[0; 6]: (262) {G0,W10,D4,L1,V2,M1} { vmul( X, vsucc( Y ) ) ==>
% 0.77/1.15 vplus( vmul( X, Y ), X ) }.
% 0.77/1.15 substitution0:
% 0.77/1.15 X := vmul( vsucc( X ), Y )
% 0.77/1.15 Y := X
% 0.77/1.15 end
% 0.77/1.15 substitution1:
% 0.77/1.15 X := vsucc( X )
% 0.77/1.15 Y := Y
% 0.77/1.15 end
% 0.77/1.15
% 0.77/1.15 eqswap: (265) {G1,W13,D6,L1,V2,M1} { vsucc( vplus( vmul( vsucc( X ), Y ),
% 0.77/1.15 X ) ) ==> vmul( vsucc( X ), vsucc( Y ) ) }.
% 0.77/1.15 parent0[0]: (264) {G1,W13,D6,L1,V2,M1} { vmul( vsucc( X ), vsucc( Y ) )
% 0.77/1.15 ==> vsucc( vplus( vmul( vsucc( X ), Y ), X ) ) }.
% 0.77/1.15 substitution0:
% 0.77/1.15 X := X
% 0.77/1.15 Y := Y
% 0.77/1.15 end
% 0.77/1.15
% 0.77/1.15 subsumption: (19) {G1,W13,D6,L1,V2,M1} P(9,14) { vsucc( vplus( vmul( vsucc
% 0.77/1.15 ( X ), Y ), X ) ) ==> vmul( vsucc( X ), vsucc( Y ) ) }.
% 0.77/1.15 parent0: (265) {G1,W13,D6,L1,V2,M1} { vsucc( vplus( vmul( vsucc( X ), Y )
% 0.77/1.15 , X ) ) ==> vmul( vsucc( X ), vsucc( Y ) ) }.
% 0.77/1.15 substitution0:
% 0.77/1.15 X := X
% 0.77/1.15 Y := Y
% 0.77/1.15 end
% 0.77/1.15 permutation0:
% 0.77/1.15 0 ==> 0
% 0.77/1.15 end
% 0.77/1.15
% 0.77/1.15 eqswap: (266) {G0,W10,D4,L1,V2,M1} { vmul( X, vsucc( Y ) ) ==> vplus( vmul
% 0.77/1.15 ( X, Y ), X ) }.
% 0.77/1.15 parent0[0]: (9) {G0,W10,D4,L1,V2,M1} I { vplus( vmul( X, Y ), X ) ==> vmul
% 0.77/1.15 ( X, vsucc( Y ) ) }.
% 0.77/1.15 substitution0:
% 0.77/1.15 X := X
% 0.77/1.15 Y := Y
% 0.77/1.15 end
% 0.77/1.15
% 0.77/1.15 paramod: (267) {G1,W10,D4,L1,V2,M1} { vmul( X, vsucc( Y ) ) ==> vplus( X,
% 0.77/1.15 vmul( X, Y ) ) }.
% 0.77/1.15 parent0[0]: (11) {G0,W7,D3,L1,V2,M1} I { vplus( Y, X ) = vplus( X, Y ) }.
% 0.77/1.15 parent1[0; 5]: (266) {G0,W10,D4,L1,V2,M1} { vmul( X, vsucc( Y ) ) ==>
% 0.77/1.15 vplus( vmul( X, Y ), X ) }.
% 0.77/1.15 substitution0:
% 0.77/1.15 X := X
% 0.77/1.15 Y := vmul( X, Y )
% 0.77/1.15 end
% 0.77/1.15 substitution1:
% 0.77/1.15 X := X
% 0.77/1.15 Y := Y
% 0.77/1.15 end
% 0.77/1.15
% 0.77/1.15 eqswap: (270) {G1,W10,D4,L1,V2,M1} { vplus( X, vmul( X, Y ) ) ==> vmul( X
% 0.77/1.15 , vsucc( Y ) ) }.
% 0.77/1.15 parent0[0]: (267) {G1,W10,D4,L1,V2,M1} { vmul( X, vsucc( Y ) ) ==> vplus(
% 0.77/1.15 X, vmul( X, Y ) ) }.
% 0.77/1.15 substitution0:
% 0.77/1.15 X := X
% 0.77/1.15 Y := Y
% 0.77/1.15 end
% 0.77/1.15
% 0.77/1.15 subsumption: (20) {G1,W10,D4,L1,V2,M1} P(9,11) { vplus( X, vmul( X, Y ) )
% 0.77/1.15 ==> vmul( X, vsucc( Y ) ) }.
% 0.77/1.15 parent0: (270) {G1,W10,D4,L1,V2,M1} { vplus( X, vmul( X, Y ) ) ==> vmul( X
% 0.77/1.15 , vsucc( Y ) ) }.
% 0.77/1.15 substitution0:
% 0.77/1.15 X := X
% 0.77/1.15 Y := Y
% 0.77/1.15 end
% 0.77/1.15 permutation0:
% 0.77/1.15 0 ==> 0
% 0.77/1.15 end
% 0.77/1.15
% 0.77/1.15 paramod: (273) {G1,W13,D6,L1,V0,M1} { ! vsucc( vplus( vmul( vd411, vsucc(
% 0.77/1.15 skol1 ) ), skol1 ) ) ==> vmul( vsucc( vd411 ), vsucc( skol1 ) ) }.
% 0.77/1.15 parent0[0]: (14) {G0,W9,D4,L1,V2,M1} I { vplus( X, vsucc( Y ) ) ==> vsucc(
% 0.77/1.15 vplus( X, Y ) ) }.
% 0.77/1.15 parent1[0; 2]: (1) {G0,W13,D5,L1,V0,M1} I { ! vplus( vmul( vd411, vsucc(
% 0.77/1.15 skol1 ) ), vsucc( skol1 ) ) ==> vmul( vsucc( vd411 ), vsucc( skol1 ) )
% 0.77/1.15 }.
% 0.77/1.15 substitution0:
% 0.77/1.15 X := vmul( vd411, vsucc( skol1 ) )
% 0.77/1.15 Y := skol1
% 0.77/1.15 end
% 0.77/1.15 substitution1:
% 0.77/1.15 end
% 0.77/1.15
% 0.77/1.15 subsumption: (25) {G1,W13,D6,L1,V0,M1} S(1);d(14) { ! vsucc( vplus( vmul(
% 0.77/1.15 vd411, vsucc( skol1 ) ), skol1 ) ) ==> vmul( vsucc( vd411 ), vsucc( skol1
% 0.77/1.15 ) ) }.
% 0.77/1.15 parent0: (273) {G1,W13,D6,L1,V0,M1} { ! vsucc( vplus( vmul( vd411, vsucc(
% 0.77/1.15 skol1 ) ), skol1 ) ) ==> vmul( vsucc( vd411 ), vsucc( skol1 ) ) }.
% 0.77/1.15 substitution0:
% 0.77/1.15 end
% 0.77/1.15 permutation0:
% 0.77/1.15 0 ==> 0
% 0.77/1.15 end
% 0.77/1.15
% 0.77/1.15 eqswap: (275) {G0,W11,D4,L1,V3,M1} { vplus( vplus( X, Y ), Z ) ==> vplus(
% 0.77/1.15 X, vplus( Y, Z ) ) }.
% 0.77/1.15 parent0[0]: (13) {G0,W11,D4,L1,V3,M1} I { vplus( X, vplus( Y, Z ) ) ==>
% 0.77/1.15 vplus( vplus( X, Y ), Z ) }.
% 0.77/1.15 substitution0:
% 0.77/1.15 X := X
% 0.77/1.15 Y := Y
% 0.77/1.15 Z := Z
% 0.77/1.15 end
% 0.77/1.15
% 0.77/1.15 paramod: (278) {G1,W11,D4,L1,V3,M1} { vplus( vplus( X, Y ), Z ) ==> vplus
% 0.77/1.15 ( vplus( Y, Z ), X ) }.
% 0.77/1.15 parent0[0]: (11) {G0,W7,D3,L1,V2,M1} I { vplus( Y, X ) = vplus( X, Y ) }.
% 0.77/1.15 parent1[0; 6]: (275) {G0,W11,D4,L1,V3,M1} { vplus( vplus( X, Y ), Z ) ==>
% 0.77/1.15 vplus( X, vplus( Y, Z ) ) }.
% 0.77/1.15 substitution0:
% 0.77/1.15 X := vplus( Y, Z )
% 0.77/1.15 Y := X
% 0.77/1.15 end
% 0.77/1.15 substitution1:
% 0.77/1.15 X := X
% 0.77/1.15 Y := Y
% 0.77/1.15 Z := Z
% 0.77/1.15 end
% 0.77/1.15
% 0.77/1.15 subsumption: (34) {G1,W11,D4,L1,V3,M1} P(13,11) { vplus( vplus( X, Y ), Z )
% 0.77/1.15 = vplus( vplus( Y, Z ), X ) }.
% 0.77/1.15 parent0: (278) {G1,W11,D4,L1,V3,M1} { vplus( vplus( X, Y ), Z ) ==> vplus
% 0.77/1.15 ( vplus( Y, Z ), X ) }.
% 0.77/1.15 substitution0:
% 0.77/1.15 X := X
% 0.77/1.15 Y := Y
% 0.77/1.15 Z := Z
% 0.77/1.15 end
% 0.77/1.15 permutation0:
% 0.77/1.15 0 ==> 0
% 0.77/1.15 end
% 0.77/1.15
% 0.77/1.15 eqswap: (293) {G1,W11,D4,L1,V3,M1} { vplus( vplus( Y, Z ), X ) = vplus(
% 0.77/1.15 vplus( X, Y ), Z ) }.
% 0.77/1.15 parent0[0]: (34) {G1,W11,D4,L1,V3,M1} P(13,11) { vplus( vplus( X, Y ), Z )
% 0.77/1.15 = vplus( vplus( Y, Z ), X ) }.
% 0.77/1.15 substitution0:
% 0.77/1.15 X := X
% 0.77/1.15 Y := Y
% 0.77/1.15 Z := Z
% 0.77/1.15 end
% 0.77/1.15
% 0.77/1.15 paramod: (309) {G2,W14,D5,L1,V3,M1} { vplus( vplus( vmul( X, Y ), Z ), X )
% 0.77/1.15 = vplus( vmul( X, vsucc( Y ) ), Z ) }.
% 0.77/1.15 parent0[0]: (20) {G1,W10,D4,L1,V2,M1} P(9,11) { vplus( X, vmul( X, Y ) )
% 0.77/1.15 ==> vmul( X, vsucc( Y ) ) }.
% 0.77/1.15 parent1[0; 9]: (293) {G1,W11,D4,L1,V3,M1} { vplus( vplus( Y, Z ), X ) =
% 0.77/1.15 vplus( vplus( X, Y ), Z ) }.
% 0.77/1.15 substitution0:
% 0.77/1.15 X := X
% 0.77/1.15 Y := Y
% 0.77/1.15 end
% 0.77/1.15 substitution1:
% 0.77/1.15 X := X
% 0.77/1.15 Y := vmul( X, Y )
% 0.77/1.15 Z := Z
% 0.77/1.15 end
% 0.77/1.15
% 0.77/1.15 subsumption: (47) {G2,W14,D5,L1,V3,M1} P(20,34) { vplus( vplus( vmul( X, Y
% 0.77/1.15 ), Z ), X ) ==> vplus( vmul( X, vsucc( Y ) ), Z ) }.
% 0.77/1.15 parent0: (309) {G2,W14,D5,L1,V3,M1} { vplus( vplus( vmul( X, Y ), Z ), X )
% 0.77/1.15 = vplus( vmul( X, vsucc( Y ) ), Z ) }.
% 0.77/1.15 substitution0:
% 0.77/1.15 X := X
% 0.77/1.15 Y := Y
% 0.77/1.15 Z := Z
% 0.77/1.15 end
% 0.77/1.15 permutation0:
% 0.77/1.15 0 ==> 0
% 0.77/1.15 end
% 0.77/1.15
% 0.77/1.15 eqswap: (315) {G2,W14,D5,L1,V3,M1} { vplus( vmul( X, vsucc( Y ) ), Z ) ==>
% 0.77/1.15 vplus( vplus( vmul( X, Y ), Z ), X ) }.
% 0.77/1.15 parent0[0]: (47) {G2,W14,D5,L1,V3,M1} P(20,34) { vplus( vplus( vmul( X, Y )
% 0.77/1.15 , Z ), X ) ==> vplus( vmul( X, vsucc( Y ) ), Z ) }.
% 0.77/1.15 substitution0:
% 0.77/1.15 X := X
% 0.77/1.15 Y := Y
% 0.77/1.15 Z := Z
% 0.77/1.15 end
% 0.77/1.15
% 0.77/1.15 paramod: (316) {G1,W13,D5,L1,V0,M1} { vplus( vmul( vd411, vsucc( skol1 ) )
% 0.77/1.15 , skol1 ) ==> vplus( vmul( vsucc( vd411 ), skol1 ), vd411 ) }.
% 0.77/1.15 parent0[0]: (0) {G0,W10,D4,L1,V0,M1} I { vplus( vmul( vd411, skol1 ), skol1
% 0.77/1.15 ) ==> vmul( vsucc( vd411 ), skol1 ) }.
% 0.77/1.15 parent1[0; 8]: (315) {G2,W14,D5,L1,V3,M1} { vplus( vmul( X, vsucc( Y ) ),
% 0.77/1.15 Z ) ==> vplus( vplus( vmul( X, Y ), Z ), X ) }.
% 0.77/1.15 substitution0:
% 0.77/1.15 end
% 0.77/1.15 substitution1:
% 0.77/1.15 X := vd411
% 0.77/1.15 Y := skol1
% 0.77/1.15 Z := skol1
% 0.77/1.15 end
% 0.77/1.15
% 0.77/1.15 subsumption: (118) {G3,W13,D5,L1,V0,M1} P(0,47) { vplus( vmul( vd411, vsucc
% 0.77/1.15 ( skol1 ) ), skol1 ) ==> vplus( vmul( vsucc( vd411 ), skol1 ), vd411 )
% 0.77/1.15 }.
% 0.77/1.15 parent0: (316) {G1,W13,D5,L1,V0,M1} { vplus( vmul( vd411, vsucc( skol1 ) )
% 0.77/1.15 , skol1 ) ==> vplus( vmul( vsucc( vd411 ), skol1 ), vd411 ) }.
% 0.77/1.15 substitution0:
% 0.77/1.15 end
% 0.77/1.15 permutation0:
% 0.77/1.15 0 ==> 0
% 0.77/1.15 end
% 0.77/1.15
% 0.77/1.15 eqswap: (319) {G1,W13,D6,L1,V0,M1} { ! vmul( vsucc( vd411 ), vsucc( skol1
% 0.77/1.15 ) ) ==> vsucc( vplus( vmul( vd411, vsucc( skol1 ) ), skol1 ) ) }.
% 0.77/1.15 parent0[0]: (25) {G1,W13,D6,L1,V0,M1} S(1);d(14) { ! vsucc( vplus( vmul(
% 0.77/1.15 vd411, vsucc( skol1 ) ), skol1 ) ) ==> vmul( vsucc( vd411 ), vsucc( skol1
% 0.77/1.15 ) ) }.
% 0.77/1.15 substitution0:
% 0.77/1.15 end
% 0.77/1.15
% 0.77/1.15 paramod: (321) {G2,W13,D6,L1,V0,M1} { ! vmul( vsucc( vd411 ), vsucc( skol1
% 0.77/1.15 ) ) ==> vsucc( vplus( vmul( vsucc( vd411 ), skol1 ), vd411 ) ) }.
% 0.77/1.15 parent0[0]: (118) {G3,W13,D5,L1,V0,M1} P(0,47) { vplus( vmul( vd411, vsucc
% 0.77/1.15 ( skol1 ) ), skol1 ) ==> vplus( vmul( vsucc( vd411 ), skol1 ), vd411 )
% 0.77/1.16 }.
% 0.77/1.16 parent1[0; 8]: (319) {G1,W13,D6,L1,V0,M1} { ! vmul( vsucc( vd411 ), vsucc
% 0.77/1.16 ( skol1 ) ) ==> vsucc( vplus( vmul( vd411, vsucc( skol1 ) ), skol1 ) )
% 0.77/1.16 }.
% 0.77/1.16 substitution0:
% 0.77/1.16 end
% 0.77/1.16 substitution1:
% 0.77/1.16 end
% 0.77/1.16
% 0.77/1.16 paramod: (322) {G2,W11,D4,L1,V0,M1} { ! vmul( vsucc( vd411 ), vsucc( skol1
% 0.77/1.16 ) ) ==> vmul( vsucc( vd411 ), vsucc( skol1 ) ) }.
% 0.77/1.16 parent0[0]: (19) {G1,W13,D6,L1,V2,M1} P(9,14) { vsucc( vplus( vmul( vsucc(
% 0.77/1.16 X ), Y ), X ) ) ==> vmul( vsucc( X ), vsucc( Y ) ) }.
% 0.77/1.16 parent1[0; 7]: (321) {G2,W13,D6,L1,V0,M1} { ! vmul( vsucc( vd411 ), vsucc
% 0.77/1.16 ( skol1 ) ) ==> vsucc( vplus( vmul( vsucc( vd411 ), skol1 ), vd411 ) )
% 0.77/1.16 }.
% 0.77/1.16 substitution0:
% 0.77/1.16 X := vd411
% 0.77/1.16 Y := skol1
% 0.77/1.16 end
% 0.77/1.16 substitution1:
% 0.77/1.16 end
% 0.77/1.16
% 0.77/1.16 eqrefl: (323) {G0,W0,D0,L0,V0,M0} { }.
% 0.77/1.16 parent0[0]: (322) {G2,W11,D4,L1,V0,M1} { ! vmul( vsucc( vd411 ), vsucc(
% 0.77/1.16 skol1 ) ) ==> vmul( vsucc( vd411 ), vsucc( skol1 ) ) }.
% 0.77/1.16 substitution0:
% 0.77/1.16 end
% 0.77/1.16
% 0.77/1.16 subsumption: (119) {G4,W0,D0,L0,V0,M0} P(118,25);d(19);q { }.
% 0.77/1.16 parent0: (323) {G0,W0,D0,L0,V0,M0} { }.
% 0.77/1.16 substitution0:
% 0.77/1.16 end
% 0.77/1.16 permutation0:
% 0.77/1.16 end
% 0.77/1.16
% 0.77/1.16 Proof check complete!
% 0.77/1.16
% 0.77/1.16 Memory use:
% 0.77/1.16
% 0.77/1.16 space for terms: 2344
% 0.77/1.16 space for clauses: 13093
% 0.77/1.16
% 0.77/1.16
% 0.77/1.16 clauses generated: 3203
% 0.77/1.16 clauses kept: 120
% 0.77/1.16 clauses selected: 50
% 0.77/1.16 clauses deleted: 8
% 0.77/1.16 clauses inuse deleted: 0
% 0.77/1.16
% 0.77/1.16 subsentry: 3036
% 0.77/1.16 literals s-matched: 1684
% 0.77/1.16 literals matched: 1581
% 0.77/1.16 full subsumption: 0
% 0.77/1.16
% 0.77/1.16 checksum: 377053337
% 0.77/1.16
% 0.77/1.16
% 0.77/1.16 Bliksem ended
%------------------------------------------------------------------------------