TSTP Solution File: NUM847+2 by Bliksem---1.12
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%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : NUM847+2 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n029.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 06:27:01 EDT 2022
% Result : Theorem 0.72s 1.08s
% Output : Refutation 0.72s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : NUM847+2 : TPTP v8.1.0. Released v4.1.0.
% 0.03/0.13 % Command : bliksem %s
% 0.14/0.34 % Computer : n029.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % DateTime : Fri Jul 8 01:32:59 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.72/1.08 *** allocated 10000 integers for termspace/termends
% 0.72/1.08 *** allocated 10000 integers for clauses
% 0.72/1.08 *** allocated 10000 integers for justifications
% 0.72/1.08 Bliksem 1.12
% 0.72/1.08
% 0.72/1.08
% 0.72/1.08 Automatic Strategy Selection
% 0.72/1.08
% 0.72/1.08
% 0.72/1.08 Clauses:
% 0.72/1.08
% 0.72/1.08 { ! vplus( vplus( vmul( vd436, vd437 ), vmul( vd436, vd439 ) ), vd436 ) =
% 0.72/1.08 vplus( vmul( vd436, vd437 ), vplus( vmul( vd436, vd439 ), vd436 ) ) }.
% 0.72/1.08 { vplus( vmul( vd436, vplus( vd437, vd439 ) ), vd436 ) = vplus( vplus( vmul
% 0.72/1.08 ( vd436, vd437 ), vmul( vd436, vd439 ) ), vd436 ) }.
% 0.72/1.08 { vmul( vd436, vsucc( vplus( vd437, vd439 ) ) ) = vplus( vmul( vd436, vplus
% 0.72/1.08 ( vd437, vd439 ) ), vd436 ) }.
% 0.72/1.08 { vmul( vd436, vplus( vd437, vsucc( vd439 ) ) ) = vmul( vd436, vsucc( vplus
% 0.72/1.08 ( vd437, vd439 ) ) ) }.
% 0.72/1.08 { vmul( vd436, vplus( vd437, vd439 ) ) = vplus( vmul( vd436, vd437 ), vmul
% 0.72/1.08 ( vd436, vd439 ) ) }.
% 0.72/1.08 { vplus( vmul( vd436, vd437 ), vd436 ) = vplus( vmul( vd436, vd437 ), vmul
% 0.72/1.08 ( vd436, v1 ) ) }.
% 0.72/1.08 { vmul( vd436, vsucc( vd437 ) ) = vplus( vmul( vd436, vd437 ), vd436 ) }.
% 0.72/1.08 { vmul( vd436, vplus( vd437, v1 ) ) = vmul( vd436, vsucc( vd437 ) ) }.
% 0.72/1.08 { vmul( v1, X ) = X }.
% 0.72/1.08 { vmul( X, vsucc( Y ) ) = vplus( vmul( X, Y ), X ) }.
% 0.72/1.08 { vmul( X, v1 ) = X }.
% 0.72/1.08 { ! less( X, vplus( Y, v1 ) ), leq( X, Y ) }.
% 0.72/1.08 { ! greater( X, Y ), geq( X, vplus( Y, v1 ) ) }.
% 0.72/1.08 { vplus( Y, X ) = vplus( X, Y ) }.
% 0.72/1.08 { vplus( vsucc( X ), Y ) = vsucc( vplus( X, Y ) ) }.
% 0.72/1.08 { vplus( v1, X ) = vsucc( X ) }.
% 0.72/1.08 { vplus( vplus( X, Y ), Z ) = vplus( X, vplus( Y, Z ) ) }.
% 0.72/1.08 { vplus( X, vsucc( Y ) ) = vsucc( vplus( X, Y ) ) }.
% 0.72/1.08 { vplus( X, v1 ) = vsucc( X ) }.
% 0.72/1.08 { X = v1, X = vsucc( vskolem2( X ) ) }.
% 0.72/1.08 { ! vsucc( X ) = X }.
% 0.72/1.08
% 0.72/1.08 percentage equality = 0.833333, percentage horn = 0.952381
% 0.72/1.08 This is a pure equality problem
% 0.72/1.08
% 0.72/1.08
% 0.72/1.08
% 0.72/1.08 Options Used:
% 0.72/1.08
% 0.72/1.08 useres = 1
% 0.72/1.08 useparamod = 1
% 0.72/1.08 useeqrefl = 1
% 0.72/1.08 useeqfact = 1
% 0.72/1.08 usefactor = 1
% 0.72/1.08 usesimpsplitting = 0
% 0.72/1.08 usesimpdemod = 5
% 0.72/1.08 usesimpres = 3
% 0.72/1.08
% 0.72/1.08 resimpinuse = 1000
% 0.72/1.08 resimpclauses = 20000
% 0.72/1.08 substype = eqrewr
% 0.72/1.08 backwardsubs = 1
% 0.72/1.08 selectoldest = 5
% 0.72/1.08
% 0.72/1.08 litorderings [0] = split
% 0.72/1.08 litorderings [1] = extend the termordering, first sorting on arguments
% 0.72/1.08
% 0.72/1.08 termordering = kbo
% 0.72/1.08
% 0.72/1.08 litapriori = 0
% 0.72/1.08 termapriori = 1
% 0.72/1.08 litaposteriori = 0
% 0.72/1.08 termaposteriori = 0
% 0.72/1.08 demodaposteriori = 0
% 0.72/1.08 ordereqreflfact = 0
% 0.72/1.08
% 0.72/1.08 litselect = negord
% 0.72/1.08
% 0.72/1.08 maxweight = 15
% 0.72/1.08 maxdepth = 30000
% 0.72/1.08 maxlength = 115
% 0.72/1.08 maxnrvars = 195
% 0.72/1.08 excuselevel = 1
% 0.72/1.08 increasemaxweight = 1
% 0.72/1.08
% 0.72/1.08 maxselected = 10000000
% 0.72/1.08 maxnrclauses = 10000000
% 0.72/1.08
% 0.72/1.08 showgenerated = 0
% 0.72/1.08 showkept = 0
% 0.72/1.08 showselected = 0
% 0.72/1.08 showdeleted = 0
% 0.72/1.08 showresimp = 1
% 0.72/1.08 showstatus = 2000
% 0.72/1.08
% 0.72/1.08 prologoutput = 0
% 0.72/1.08 nrgoals = 5000000
% 0.72/1.08 totalproof = 1
% 0.72/1.08
% 0.72/1.08 Symbols occurring in the translation:
% 0.72/1.08
% 0.72/1.08 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.72/1.08 . [1, 2] (w:1, o:36, a:1, s:1, b:0),
% 0.72/1.08 ! [4, 1] (w:0, o:29, a:1, s:1, b:0),
% 0.72/1.08 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.72/1.08 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.72/1.08 vd436 [35, 0] (w:1, o:6, a:1, s:1, b:0),
% 0.72/1.08 vd437 [36, 0] (w:1, o:7, a:1, s:1, b:0),
% 0.72/1.08 vmul [37, 2] (w:1, o:60, a:1, s:1, b:0),
% 0.72/1.08 vd439 [38, 0] (w:1, o:8, a:1, s:1, b:0),
% 0.72/1.08 vplus [39, 2] (w:1, o:61, a:1, s:1, b:0),
% 0.72/1.08 vsucc [40, 1] (w:1, o:34, a:1, s:1, b:0),
% 0.72/1.08 v1 [41, 0] (w:1, o:9, a:1, s:1, b:0),
% 0.72/1.08 less [47, 2] (w:1, o:62, a:1, s:1, b:0),
% 0.72/1.08 leq [48, 2] (w:1, o:63, a:1, s:1, b:0),
% 0.72/1.08 greater [51, 2] (w:1, o:64, a:1, s:1, b:0),
% 0.72/1.08 geq [52, 2] (w:1, o:65, a:1, s:1, b:0),
% 0.72/1.08 vskolem2 [64, 1] (w:1, o:35, a:1, s:1, b:0).
% 0.72/1.08
% 0.72/1.08
% 0.72/1.08 Starting Search:
% 0.72/1.08
% 0.72/1.08
% 0.72/1.08 Bliksems!, er is een bewijs:
% 0.72/1.08 % SZS status Theorem
% 0.72/1.08 % SZS output start Refutation
% 0.72/1.08
% 0.72/1.08 (0) {G0,W19,D5,L1,V0,M1} I { ! vplus( vmul( vd436, vd437 ), vplus( vmul(
% 0.72/1.08 vd436, vd439 ), vd436 ) ) ==> vplus( vplus( vmul( vd436, vd437 ), vmul(
% 0.72/1.08 vd436, vd439 ) ), vd436 ) }.
% 0.72/1.08 (16) {G0,W11,D4,L1,V3,M1} I { vplus( X, vplus( Y, Z ) ) ==> vplus( vplus( X
% 0.72/1.08 , Y ), Z ) }.
% 0.72/1.08 (21) {G1,W0,D0,L0,V0,M0} S(0);d(16);q { }.
% 0.72/1.08
% 0.72/1.08
% 0.72/1.08 % SZS output end Refutation
% 0.72/1.08 found a proof!
% 0.72/1.08
% 0.72/1.08
% 0.72/1.08 Unprocessed initial clauses:
% 0.72/1.08
% 0.72/1.08 (23) {G0,W19,D5,L1,V0,M1} { ! vplus( vplus( vmul( vd436, vd437 ), vmul(
% 0.72/1.08 vd436, vd439 ) ), vd436 ) = vplus( vmul( vd436, vd437 ), vplus( vmul(
% 0.72/1.08 vd436, vd439 ), vd436 ) ) }.
% 0.72/1.08 (24) {G0,W17,D5,L1,V0,M1} { vplus( vmul( vd436, vplus( vd437, vd439 ) ),
% 0.72/1.08 vd436 ) = vplus( vplus( vmul( vd436, vd437 ), vmul( vd436, vd439 ) ),
% 0.72/1.08 vd436 ) }.
% 0.72/1.08 (25) {G0,W14,D5,L1,V0,M1} { vmul( vd436, vsucc( vplus( vd437, vd439 ) ) )
% 0.72/1.08 = vplus( vmul( vd436, vplus( vd437, vd439 ) ), vd436 ) }.
% 0.72/1.08 (26) {G0,W13,D5,L1,V0,M1} { vmul( vd436, vplus( vd437, vsucc( vd439 ) ) )
% 0.72/1.08 = vmul( vd436, vsucc( vplus( vd437, vd439 ) ) ) }.
% 0.72/1.08 (27) {G0,W13,D4,L1,V0,M1} { vmul( vd436, vplus( vd437, vd439 ) ) = vplus(
% 0.72/1.08 vmul( vd436, vd437 ), vmul( vd436, vd439 ) ) }.
% 0.72/1.08 (28) {G0,W13,D4,L1,V0,M1} { vplus( vmul( vd436, vd437 ), vd436 ) = vplus(
% 0.72/1.08 vmul( vd436, vd437 ), vmul( vd436, v1 ) ) }.
% 0.72/1.08 (29) {G0,W10,D4,L1,V0,M1} { vmul( vd436, vsucc( vd437 ) ) = vplus( vmul(
% 0.72/1.08 vd436, vd437 ), vd436 ) }.
% 0.72/1.08 (30) {G0,W10,D4,L1,V0,M1} { vmul( vd436, vplus( vd437, v1 ) ) = vmul(
% 0.72/1.08 vd436, vsucc( vd437 ) ) }.
% 0.72/1.08 (31) {G0,W5,D3,L1,V1,M1} { vmul( v1, X ) = X }.
% 0.72/1.08 (32) {G0,W10,D4,L1,V2,M1} { vmul( X, vsucc( Y ) ) = vplus( vmul( X, Y ), X
% 0.72/1.08 ) }.
% 0.72/1.08 (33) {G0,W5,D3,L1,V1,M1} { vmul( X, v1 ) = X }.
% 0.72/1.08 (34) {G0,W8,D3,L2,V2,M2} { ! less( X, vplus( Y, v1 ) ), leq( X, Y ) }.
% 0.72/1.08 (35) {G0,W8,D3,L2,V2,M2} { ! greater( X, Y ), geq( X, vplus( Y, v1 ) ) }.
% 0.72/1.08 (36) {G0,W7,D3,L1,V2,M1} { vplus( Y, X ) = vplus( X, Y ) }.
% 0.72/1.08 (37) {G0,W9,D4,L1,V2,M1} { vplus( vsucc( X ), Y ) = vsucc( vplus( X, Y ) )
% 0.72/1.08 }.
% 0.72/1.08 (38) {G0,W6,D3,L1,V1,M1} { vplus( v1, X ) = vsucc( X ) }.
% 0.72/1.08 (39) {G0,W11,D4,L1,V3,M1} { vplus( vplus( X, Y ), Z ) = vplus( X, vplus( Y
% 0.72/1.08 , Z ) ) }.
% 0.72/1.08 (40) {G0,W9,D4,L1,V2,M1} { vplus( X, vsucc( Y ) ) = vsucc( vplus( X, Y ) )
% 0.72/1.08 }.
% 0.72/1.08 (41) {G0,W6,D3,L1,V1,M1} { vplus( X, v1 ) = vsucc( X ) }.
% 0.72/1.08 (42) {G0,W8,D4,L2,V1,M2} { X = v1, X = vsucc( vskolem2( X ) ) }.
% 0.72/1.08 (43) {G0,W4,D3,L1,V1,M1} { ! vsucc( X ) = X }.
% 0.72/1.08
% 0.72/1.08
% 0.72/1.08 Total Proof:
% 0.72/1.08
% 0.72/1.08 eqswap: (44) {G0,W19,D5,L1,V0,M1} { ! vplus( vmul( vd436, vd437 ), vplus(
% 0.72/1.08 vmul( vd436, vd439 ), vd436 ) ) = vplus( vplus( vmul( vd436, vd437 ),
% 0.72/1.08 vmul( vd436, vd439 ) ), vd436 ) }.
% 0.72/1.08 parent0[0]: (23) {G0,W19,D5,L1,V0,M1} { ! vplus( vplus( vmul( vd436, vd437
% 0.72/1.08 ), vmul( vd436, vd439 ) ), vd436 ) = vplus( vmul( vd436, vd437 ), vplus
% 0.72/1.08 ( vmul( vd436, vd439 ), vd436 ) ) }.
% 0.72/1.08 substitution0:
% 0.72/1.08 end
% 0.72/1.08
% 0.72/1.08 subsumption: (0) {G0,W19,D5,L1,V0,M1} I { ! vplus( vmul( vd436, vd437 ),
% 0.72/1.08 vplus( vmul( vd436, vd439 ), vd436 ) ) ==> vplus( vplus( vmul( vd436,
% 0.72/1.08 vd437 ), vmul( vd436, vd439 ) ), vd436 ) }.
% 0.72/1.08 parent0: (44) {G0,W19,D5,L1,V0,M1} { ! vplus( vmul( vd436, vd437 ), vplus
% 0.72/1.08 ( vmul( vd436, vd439 ), vd436 ) ) = vplus( vplus( vmul( vd436, vd437 ),
% 0.72/1.08 vmul( vd436, vd439 ) ), vd436 ) }.
% 0.72/1.08 substitution0:
% 0.72/1.08 end
% 0.72/1.08 permutation0:
% 0.72/1.08 0 ==> 0
% 0.72/1.08 end
% 0.72/1.08
% 0.72/1.08 eqswap: (58) {G0,W11,D4,L1,V3,M1} { vplus( X, vplus( Y, Z ) ) = vplus(
% 0.72/1.08 vplus( X, Y ), Z ) }.
% 0.72/1.08 parent0[0]: (39) {G0,W11,D4,L1,V3,M1} { vplus( vplus( X, Y ), Z ) = vplus
% 0.72/1.08 ( X, vplus( Y, Z ) ) }.
% 0.72/1.08 substitution0:
% 0.72/1.08 X := X
% 0.72/1.08 Y := Y
% 0.72/1.08 Z := Z
% 0.72/1.08 end
% 0.72/1.08
% 0.72/1.08 subsumption: (16) {G0,W11,D4,L1,V3,M1} I { vplus( X, vplus( Y, Z ) ) ==>
% 0.72/1.08 vplus( vplus( X, Y ), Z ) }.
% 0.72/1.08 parent0: (58) {G0,W11,D4,L1,V3,M1} { vplus( X, vplus( Y, Z ) ) = vplus(
% 0.72/1.08 vplus( X, Y ), Z ) }.
% 0.72/1.08 substitution0:
% 0.72/1.08 X := X
% 0.72/1.08 Y := Y
% 0.72/1.08 Z := Z
% 0.72/1.08 end
% 0.72/1.08 permutation0:
% 0.72/1.08 0 ==> 0
% 0.72/1.08 end
% 0.72/1.08
% 0.72/1.08 paramod: (61) {G1,W19,D5,L1,V0,M1} { ! vplus( vplus( vmul( vd436, vd437 )
% 0.72/1.08 , vmul( vd436, vd439 ) ), vd436 ) ==> vplus( vplus( vmul( vd436, vd437 )
% 0.72/1.08 , vmul( vd436, vd439 ) ), vd436 ) }.
% 0.72/1.08 parent0[0]: (16) {G0,W11,D4,L1,V3,M1} I { vplus( X, vplus( Y, Z ) ) ==>
% 0.72/1.08 vplus( vplus( X, Y ), Z ) }.
% 0.72/1.08 parent1[0; 2]: (0) {G0,W19,D5,L1,V0,M1} I { ! vplus( vmul( vd436, vd437 ),
% 0.72/1.08 vplus( vmul( vd436, vd439 ), vd436 ) ) ==> vplus( vplus( vmul( vd436,
% 0.72/1.08 vd437 ), vmul( vd436, vd439 ) ), vd436 ) }.
% 0.72/1.08 substitution0:
% 0.72/1.08 X := vmul( vd436, vd437 )
% 0.72/1.08 Y := vmul( vd436, vd439 )
% 0.72/1.08 Z := vd436
% 0.72/1.08 end
% 0.72/1.08 substitution1:
% 0.72/1.08 end
% 0.72/1.08
% 0.72/1.08 eqrefl: (62) {G0,W0,D0,L0,V0,M0} { }.
% 0.72/1.08 parent0[0]: (61) {G1,W19,D5,L1,V0,M1} { ! vplus( vplus( vmul( vd436, vd437
% 0.72/1.08 ), vmul( vd436, vd439 ) ), vd436 ) ==> vplus( vplus( vmul( vd436, vd437
% 0.72/1.08 ), vmul( vd436, vd439 ) ), vd436 ) }.
% 0.72/1.08 substitution0:
% 0.72/1.08 end
% 0.72/1.08
% 0.72/1.08 subsumption: (21) {G1,W0,D0,L0,V0,M0} S(0);d(16);q { }.
% 0.72/1.08 parent0: (62) {G0,W0,D0,L0,V0,M0} { }.
% 0.72/1.08 substitution0:
% 0.72/1.08 end
% 0.72/1.08 permutation0:
% 0.72/1.08 end
% 0.72/1.08
% 0.72/1.08 Proof check complete!
% 0.72/1.08
% 0.72/1.08 Memory use:
% 0.72/1.08
% 0.72/1.08 space for terms: 715
% 0.72/1.08 space for clauses: 2278
% 0.72/1.08
% 0.72/1.08
% 0.72/1.08 clauses generated: 34
% 0.72/1.08 clauses kept: 22
% 0.72/1.08 clauses selected: 5
% 0.72/1.08 clauses deleted: 1
% 0.72/1.08 clauses inuse deleted: 0
% 0.72/1.08
% 0.72/1.08 subsentry: 98
% 0.72/1.08 literals s-matched: 49
% 0.72/1.08 literals matched: 49
% 0.72/1.08 full subsumption: 0
% 0.72/1.08
% 0.72/1.08 checksum: -1541994140
% 0.72/1.08
% 0.72/1.08
% 0.72/1.08 Bliksem ended
%------------------------------------------------------------------------------