TSTP Solution File: NUM846+2 by Bliksem---1.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : NUM846+2 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n010.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 0.68s 1.06s
% Output : Refutation 0.68s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : NUM846+2 : TPTP v8.1.0. Released v4.1.0.
% 0.10/0.12 % Command : bliksem %s
% 0.13/0.33 % Computer : n010.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % DateTime : Tue Jul 5 14:25:32 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.68/1.06 *** allocated 10000 integers for termspace/termends
% 0.68/1.06 *** allocated 10000 integers for clauses
% 0.68/1.06 *** allocated 10000 integers for justifications
% 0.68/1.06 Bliksem 1.12
% 0.68/1.06
% 0.68/1.06
% 0.68/1.06 Automatic Strategy Selection
% 0.68/1.06
% 0.68/1.06
% 0.68/1.06 Clauses:
% 0.68/1.06
% 0.68/1.06 { ! vplus( vmul( vd436, vplus( vd437, vd439 ) ), vd436 ) = vplus( vplus(
% 0.68/1.06 vmul( vd436, vd437 ), vmul( vd436, vd439 ) ), vd436 ) }.
% 0.68/1.06 { vmul( vd436, vsucc( vplus( vd437, vd439 ) ) ) = vplus( vmul( vd436, vplus
% 0.68/1.06 ( vd437, vd439 ) ), vd436 ) }.
% 0.68/1.06 { vmul( vd436, vplus( vd437, vsucc( vd439 ) ) ) = vmul( vd436, vsucc( vplus
% 0.68/1.06 ( vd437, vd439 ) ) ) }.
% 0.68/1.06 { vmul( vd436, vplus( vd437, vd439 ) ) = vplus( vmul( vd436, vd437 ), vmul
% 0.68/1.06 ( vd436, vd439 ) ) }.
% 0.68/1.06 { vplus( vmul( vd436, vd437 ), vd436 ) = vplus( vmul( vd436, vd437 ), vmul
% 0.68/1.06 ( vd436, v1 ) ) }.
% 0.68/1.06 { vmul( vd436, vsucc( vd437 ) ) = vplus( vmul( vd436, vd437 ), vd436 ) }.
% 0.68/1.06 { vmul( vd436, vplus( vd437, v1 ) ) = vmul( vd436, vsucc( vd437 ) ) }.
% 0.68/1.06 { vmul( X, Y ) = vmul( Y, X ) }.
% 0.68/1.06 { vmul( v1, X ) = X }.
% 0.68/1.06 { vmul( X, vsucc( Y ) ) = vplus( vmul( X, Y ), X ) }.
% 0.68/1.06 { vmul( X, v1 ) = X }.
% 0.68/1.06 { ! less( X, vplus( Y, v1 ) ), leq( X, Y ) }.
% 0.68/1.06 { ! greater( X, Y ), geq( X, vplus( Y, v1 ) ) }.
% 0.68/1.06 { geq( X, v1 ) }.
% 0.68/1.06 { vplus( Y, X ) = vplus( X, Y ) }.
% 0.68/1.06 { vplus( vsucc( X ), Y ) = vsucc( vplus( X, Y ) ) }.
% 0.68/1.06 { vplus( v1, X ) = vsucc( X ) }.
% 0.68/1.06 { vplus( vplus( X, Y ), Z ) = vplus( X, vplus( Y, Z ) ) }.
% 0.68/1.06 { vplus( X, vsucc( Y ) ) = vsucc( vplus( X, Y ) ) }.
% 0.68/1.06 { vplus( X, v1 ) = vsucc( X ) }.
% 0.68/1.06 { X = v1, X = vsucc( vskolem2( X ) ) }.
% 0.68/1.06 { ! vsucc( X ) = X }.
% 0.68/1.06 { X = Y, ! vsucc( X ) = vsucc( Y ) }.
% 0.68/1.06
% 0.68/1.06 percentage equality = 0.814815, percentage horn = 0.956522
% 0.68/1.06 This is a pure equality problem
% 0.68/1.06
% 0.68/1.06
% 0.68/1.06
% 0.68/1.06 Options Used:
% 0.68/1.06
% 0.68/1.06 useres = 1
% 0.68/1.06 useparamod = 1
% 0.68/1.06 useeqrefl = 1
% 0.68/1.06 useeqfact = 1
% 0.68/1.06 usefactor = 1
% 0.68/1.06 usesimpsplitting = 0
% 0.68/1.06 usesimpdemod = 5
% 0.68/1.06 usesimpres = 3
% 0.68/1.06
% 0.68/1.06 resimpinuse = 1000
% 0.68/1.06 resimpclauses = 20000
% 0.68/1.06 substype = eqrewr
% 0.68/1.06 backwardsubs = 1
% 0.68/1.06 selectoldest = 5
% 0.68/1.06
% 0.68/1.06 litorderings [0] = split
% 0.68/1.06 litorderings [1] = extend the termordering, first sorting on arguments
% 0.68/1.06
% 0.68/1.06 termordering = kbo
% 0.68/1.06
% 0.68/1.06 litapriori = 0
% 0.68/1.06 termapriori = 1
% 0.68/1.06 litaposteriori = 0
% 0.68/1.06 termaposteriori = 0
% 0.68/1.06 demodaposteriori = 0
% 0.68/1.06 ordereqreflfact = 0
% 0.68/1.06
% 0.68/1.06 litselect = negord
% 0.68/1.06
% 0.68/1.06 maxweight = 15
% 0.68/1.06 maxdepth = 30000
% 0.68/1.06 maxlength = 115
% 0.68/1.06 maxnrvars = 195
% 0.68/1.06 excuselevel = 1
% 0.68/1.06 increasemaxweight = 1
% 0.68/1.06
% 0.68/1.06 maxselected = 10000000
% 0.68/1.06 maxnrclauses = 10000000
% 0.68/1.06
% 0.68/1.06 showgenerated = 0
% 0.68/1.06 showkept = 0
% 0.68/1.06 showselected = 0
% 0.68/1.06 showdeleted = 0
% 0.68/1.06 showresimp = 1
% 0.68/1.06 showstatus = 2000
% 0.68/1.06
% 0.68/1.06 prologoutput = 0
% 0.68/1.06 nrgoals = 5000000
% 0.68/1.06 totalproof = 1
% 0.68/1.06
% 0.68/1.06 Symbols occurring in the translation:
% 0.68/1.06
% 0.68/1.06 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.68/1.06 . [1, 2] (w:1, o:41, a:1, s:1, b:0),
% 0.68/1.06 ! [4, 1] (w:0, o:34, a:1, s:1, b:0),
% 0.68/1.06 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.68/1.06 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.68/1.06 vd436 [35, 0] (w:1, o:6, a:1, s:1, b:0),
% 0.68/1.06 vd437 [36, 0] (w:1, o:7, a:1, s:1, b:0),
% 0.68/1.06 vd439 [37, 0] (w:1, o:8, a:1, s:1, b:0),
% 0.68/1.06 vplus [38, 2] (w:1, o:65, a:1, s:1, b:0),
% 0.68/1.06 vmul [39, 2] (w:1, o:66, a:1, s:1, b:0),
% 0.68/1.06 vsucc [40, 1] (w:1, o:39, a:1, s:1, b:0),
% 0.68/1.06 v1 [41, 0] (w:1, o:9, a:1, s:1, b:0),
% 0.68/1.06 less [49, 2] (w:1, o:67, a:1, s:1, b:0),
% 0.68/1.06 leq [50, 2] (w:1, o:68, a:1, s:1, b:0),
% 0.68/1.06 greater [53, 2] (w:1, o:69, a:1, s:1, b:0),
% 0.68/1.06 geq [54, 2] (w:1, o:70, a:1, s:1, b:0),
% 0.68/1.06 vskolem2 [67, 1] (w:1, o:40, a:1, s:1, b:0).
% 0.68/1.06
% 0.68/1.06
% 0.68/1.06 Starting Search:
% 0.68/1.06
% 0.68/1.06
% 0.68/1.06 Bliksems!, er is een bewijs:
% 0.68/1.06 % SZS status Theorem
% 0.68/1.06 % SZS output start Refutation
% 0.68/1.06
% 0.68/1.06 (0) {G0,W17,D5,L1,V0,M1} I { ! vplus( vplus( vmul( vd436, vd437 ), vmul(
% 0.68/1.06 vd436, vd439 ) ), vd436 ) ==> vplus( vmul( vd436, vplus( vd437, vd439 ) )
% 0.68/1.06 , vd436 ) }.
% 0.68/1.06 (3) {G0,W13,D4,L1,V0,M1} I { vplus( vmul( vd436, vd437 ), vmul( vd436,
% 0.68/1.06 vd439 ) ) ==> vmul( vd436, vplus( vd437, vd439 ) ) }.
% 0.68/1.06 (23) {G1,W0,D0,L0,V0,M0} S(0);d(3);q { }.
% 0.68/1.06
% 0.68/1.06
% 0.68/1.06 % SZS output end Refutation
% 0.68/1.06 found a proof!
% 0.68/1.06
% 0.68/1.06
% 0.68/1.06 Unprocessed initial clauses:
% 0.68/1.06
% 0.68/1.06 (25) {G0,W17,D5,L1,V0,M1} { ! vplus( vmul( vd436, vplus( vd437, vd439 ) )
% 0.68/1.06 , vd436 ) = vplus( vplus( vmul( vd436, vd437 ), vmul( vd436, vd439 ) ),
% 0.68/1.06 vd436 ) }.
% 0.68/1.06 (26) {G0,W14,D5,L1,V0,M1} { vmul( vd436, vsucc( vplus( vd437, vd439 ) ) )
% 0.68/1.06 = vplus( vmul( vd436, vplus( vd437, vd439 ) ), vd436 ) }.
% 0.68/1.06 (27) {G0,W13,D5,L1,V0,M1} { vmul( vd436, vplus( vd437, vsucc( vd439 ) ) )
% 0.68/1.06 = vmul( vd436, vsucc( vplus( vd437, vd439 ) ) ) }.
% 0.68/1.06 (28) {G0,W13,D4,L1,V0,M1} { vmul( vd436, vplus( vd437, vd439 ) ) = vplus(
% 0.68/1.06 vmul( vd436, vd437 ), vmul( vd436, vd439 ) ) }.
% 0.68/1.06 (29) {G0,W13,D4,L1,V0,M1} { vplus( vmul( vd436, vd437 ), vd436 ) = vplus(
% 0.68/1.06 vmul( vd436, vd437 ), vmul( vd436, v1 ) ) }.
% 0.68/1.06 (30) {G0,W10,D4,L1,V0,M1} { vmul( vd436, vsucc( vd437 ) ) = vplus( vmul(
% 0.68/1.06 vd436, vd437 ), vd436 ) }.
% 0.68/1.06 (31) {G0,W10,D4,L1,V0,M1} { vmul( vd436, vplus( vd437, v1 ) ) = vmul(
% 0.68/1.06 vd436, vsucc( vd437 ) ) }.
% 0.68/1.06 (32) {G0,W7,D3,L1,V2,M1} { vmul( X, Y ) = vmul( Y, X ) }.
% 0.68/1.06 (33) {G0,W5,D3,L1,V1,M1} { vmul( v1, X ) = X }.
% 0.68/1.06 (34) {G0,W10,D4,L1,V2,M1} { vmul( X, vsucc( Y ) ) = vplus( vmul( X, Y ), X
% 0.68/1.06 ) }.
% 0.68/1.06 (35) {G0,W5,D3,L1,V1,M1} { vmul( X, v1 ) = X }.
% 0.68/1.06 (36) {G0,W8,D3,L2,V2,M2} { ! less( X, vplus( Y, v1 ) ), leq( X, Y ) }.
% 0.68/1.06 (37) {G0,W8,D3,L2,V2,M2} { ! greater( X, Y ), geq( X, vplus( Y, v1 ) ) }.
% 0.68/1.06 (38) {G0,W3,D2,L1,V1,M1} { geq( X, v1 ) }.
% 0.68/1.06 (39) {G0,W7,D3,L1,V2,M1} { vplus( Y, X ) = vplus( X, Y ) }.
% 0.68/1.06 (40) {G0,W9,D4,L1,V2,M1} { vplus( vsucc( X ), Y ) = vsucc( vplus( X, Y ) )
% 0.68/1.06 }.
% 0.68/1.06 (41) {G0,W6,D3,L1,V1,M1} { vplus( v1, X ) = vsucc( X ) }.
% 0.68/1.06 (42) {G0,W11,D4,L1,V3,M1} { vplus( vplus( X, Y ), Z ) = vplus( X, vplus( Y
% 0.68/1.06 , Z ) ) }.
% 0.68/1.06 (43) {G0,W9,D4,L1,V2,M1} { vplus( X, vsucc( Y ) ) = vsucc( vplus( X, Y ) )
% 0.68/1.06 }.
% 0.68/1.06 (44) {G0,W6,D3,L1,V1,M1} { vplus( X, v1 ) = vsucc( X ) }.
% 0.68/1.06 (45) {G0,W8,D4,L2,V1,M2} { X = v1, X = vsucc( vskolem2( X ) ) }.
% 0.68/1.06 (46) {G0,W4,D3,L1,V1,M1} { ! vsucc( X ) = X }.
% 0.68/1.06 (47) {G0,W8,D3,L2,V2,M2} { X = Y, ! vsucc( X ) = vsucc( Y ) }.
% 0.68/1.06
% 0.68/1.06
% 0.68/1.06 Total Proof:
% 0.68/1.06
% 0.68/1.06 eqswap: (48) {G0,W17,D5,L1,V0,M1} { ! vplus( vplus( vmul( vd436, vd437 ),
% 0.68/1.06 vmul( vd436, vd439 ) ), vd436 ) = vplus( vmul( vd436, vplus( vd437, vd439
% 0.68/1.06 ) ), vd436 ) }.
% 0.68/1.06 parent0[0]: (25) {G0,W17,D5,L1,V0,M1} { ! vplus( vmul( vd436, vplus( vd437
% 0.68/1.06 , vd439 ) ), vd436 ) = vplus( vplus( vmul( vd436, vd437 ), vmul( vd436,
% 0.68/1.06 vd439 ) ), vd436 ) }.
% 0.68/1.06 substitution0:
% 0.68/1.06 end
% 0.68/1.06
% 0.68/1.06 subsumption: (0) {G0,W17,D5,L1,V0,M1} I { ! vplus( vplus( vmul( vd436,
% 0.68/1.06 vd437 ), vmul( vd436, vd439 ) ), vd436 ) ==> vplus( vmul( vd436, vplus(
% 0.68/1.06 vd437, vd439 ) ), vd436 ) }.
% 0.68/1.06 parent0: (48) {G0,W17,D5,L1,V0,M1} { ! vplus( vplus( vmul( vd436, vd437 )
% 0.68/1.06 , vmul( vd436, vd439 ) ), vd436 ) = vplus( vmul( vd436, vplus( vd437,
% 0.68/1.06 vd439 ) ), vd436 ) }.
% 0.68/1.06 substitution0:
% 0.68/1.06 end
% 0.68/1.06 permutation0:
% 0.68/1.06 0 ==> 0
% 0.68/1.06 end
% 0.68/1.06
% 0.68/1.06 eqswap: (52) {G0,W13,D4,L1,V0,M1} { vplus( vmul( vd436, vd437 ), vmul(
% 0.68/1.06 vd436, vd439 ) ) = vmul( vd436, vplus( vd437, vd439 ) ) }.
% 0.68/1.06 parent0[0]: (28) {G0,W13,D4,L1,V0,M1} { vmul( vd436, vplus( vd437, vd439 )
% 0.68/1.06 ) = vplus( vmul( vd436, vd437 ), vmul( vd436, vd439 ) ) }.
% 0.68/1.06 substitution0:
% 0.68/1.06 end
% 0.68/1.06
% 0.68/1.06 subsumption: (3) {G0,W13,D4,L1,V0,M1} I { vplus( vmul( vd436, vd437 ), vmul
% 0.68/1.06 ( vd436, vd439 ) ) ==> vmul( vd436, vplus( vd437, vd439 ) ) }.
% 0.68/1.06 parent0: (52) {G0,W13,D4,L1,V0,M1} { vplus( vmul( vd436, vd437 ), vmul(
% 0.68/1.06 vd436, vd439 ) ) = vmul( vd436, vplus( vd437, vd439 ) ) }.
% 0.68/1.06 substitution0:
% 0.68/1.06 end
% 0.68/1.06 permutation0:
% 0.68/1.06 0 ==> 0
% 0.68/1.06 end
% 0.68/1.06
% 0.68/1.06 paramod: (55) {G1,W15,D5,L1,V0,M1} { ! vplus( vmul( vd436, vplus( vd437,
% 0.68/1.06 vd439 ) ), vd436 ) ==> vplus( vmul( vd436, vplus( vd437, vd439 ) ), vd436
% 0.68/1.06 ) }.
% 0.68/1.06 parent0[0]: (3) {G0,W13,D4,L1,V0,M1} I { vplus( vmul( vd436, vd437 ), vmul
% 0.68/1.06 ( vd436, vd439 ) ) ==> vmul( vd436, vplus( vd437, vd439 ) ) }.
% 0.68/1.06 parent1[0; 3]: (0) {G0,W17,D5,L1,V0,M1} I { ! vplus( vplus( vmul( vd436,
% 0.68/1.06 vd437 ), vmul( vd436, vd439 ) ), vd436 ) ==> vplus( vmul( vd436, vplus(
% 0.68/1.06 vd437, vd439 ) ), vd436 ) }.
% 0.68/1.06 substitution0:
% 0.68/1.06 end
% 0.68/1.06 substitution1:
% 0.68/1.06 end
% 0.68/1.06
% 0.68/1.06 eqrefl: (56) {G0,W0,D0,L0,V0,M0} { }.
% 0.68/1.06 parent0[0]: (55) {G1,W15,D5,L1,V0,M1} { ! vplus( vmul( vd436, vplus( vd437
% 0.68/1.06 , vd439 ) ), vd436 ) ==> vplus( vmul( vd436, vplus( vd437, vd439 ) ),
% 0.68/1.06 vd436 ) }.
% 0.68/1.06 substitution0:
% 0.68/1.06 end
% 0.68/1.06
% 0.68/1.06 subsumption: (23) {G1,W0,D0,L0,V0,M0} S(0);d(3);q { }.
% 0.68/1.06 parent0: (56) {G0,W0,D0,L0,V0,M0} { }.
% 0.68/1.06 substitution0:
% 0.68/1.06 end
% 0.68/1.06 permutation0:
% 0.68/1.06 end
% 0.68/1.06
% 0.68/1.06 Proof check complete!
% 0.68/1.06
% 0.68/1.06 Memory use:
% 0.68/1.06
% 0.68/1.06 space for terms: 732
% 0.68/1.06 space for clauses: 2285
% 0.68/1.06
% 0.68/1.06
% 0.68/1.06 clauses generated: 33
% 0.68/1.06 clauses kept: 24
% 0.68/1.06 clauses selected: 5
% 0.68/1.06 clauses deleted: 1
% 0.68/1.06 clauses inuse deleted: 0
% 0.68/1.06
% 0.68/1.06 subsentry: 36
% 0.68/1.06 literals s-matched: 17
% 0.68/1.06 literals matched: 17
% 0.68/1.06 full subsumption: 0
% 0.68/1.06
% 0.68/1.06 checksum: -1630649171
% 0.68/1.06
% 0.68/1.06
% 0.68/1.06 Bliksem ended
%------------------------------------------------------------------------------