TSTP Solution File: SWV997_1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SWV997_1 : TPTP v8.1.2. Released v5.0.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n012.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 : 300s
% DateTime : Thu Aug 31 22:58:21 EDT 2023
% Result : Theorem 5.70s 1.54s
% Output : Proof 7.10s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SWV997_1 : TPTP v8.1.2. Released v5.0.0.
% 0.00/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.14/0.35 % Computer : n012.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 % WCLimit : 300
% 0.14/0.35 % DateTime : Tue Aug 29 05:12:09 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.22/0.61 ________ _____
% 0.22/0.61 ___ __ \_________(_)________________________________
% 0.22/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.22/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.22/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.22/0.61
% 0.22/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.22/0.61 (2023-06-19)
% 0.22/0.61
% 0.22/0.61 (c) Philipp Rümmer, 2009-2023
% 0.22/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.22/0.61 Amanda Stjerna.
% 0.22/0.61 Free software under BSD-3-Clause.
% 0.22/0.61
% 0.22/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.22/0.61
% 0.22/0.61 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.22/0.63 Running up to 7 provers in parallel.
% 0.22/0.65 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.22/0.65 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.22/0.65 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.22/0.65 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.22/0.65 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.22/0.65 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.22/0.65 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.76/1.10 Prover 4: Preprocessing ...
% 2.76/1.11 Prover 1: Preprocessing ...
% 2.76/1.14 Prover 5: Preprocessing ...
% 2.76/1.14 Prover 6: Preprocessing ...
% 2.76/1.14 Prover 3: Preprocessing ...
% 2.76/1.14 Prover 2: Preprocessing ...
% 2.76/1.14 Prover 0: Preprocessing ...
% 4.24/1.41 Prover 1: Constructing countermodel ...
% 4.24/1.42 Prover 3: Constructing countermodel ...
% 4.24/1.42 Prover 6: Proving ...
% 4.24/1.42 Prover 5: Proving ...
% 4.24/1.43 Prover 0: Proving ...
% 4.24/1.43 Prover 4: Constructing countermodel ...
% 5.14/1.47 Prover 2: Proving ...
% 5.70/1.53 Prover 0: proved (892ms)
% 5.70/1.54
% 5.70/1.54 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.70/1.54
% 5.70/1.54 Prover 3: stopped
% 5.70/1.55 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 5.70/1.55 Prover 2: stopped
% 5.70/1.55 Prover 6: stopped
% 6.11/1.59 Prover 5: stopped
% 6.11/1.60 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 6.11/1.60 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 6.11/1.60 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 6.11/1.60 Prover 1: Found proof (size 21)
% 6.11/1.60 Prover 1: proved (961ms)
% 6.11/1.60 Prover 8: Preprocessing ...
% 6.11/1.60 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 6.11/1.61 Prover 4: Found proof (size 20)
% 6.11/1.61 Prover 4: proved (962ms)
% 6.11/1.61 Prover 7: Preprocessing ...
% 6.11/1.62 Prover 10: Preprocessing ...
% 6.11/1.64 Prover 11: Preprocessing ...
% 6.11/1.64 Prover 10: stopped
% 6.11/1.64 Prover 7: stopped
% 6.11/1.64 Prover 13: Preprocessing ...
% 6.11/1.66 Prover 11: stopped
% 6.11/1.66 Prover 8: Warning: ignoring some quantifiers
% 6.71/1.66 Prover 8: Constructing countermodel ...
% 6.71/1.67 Prover 8: stopped
% 6.71/1.67 Prover 13: stopped
% 6.71/1.67
% 6.71/1.67 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.71/1.67
% 6.71/1.67 % SZS output start Proof for theBenchmark
% 6.71/1.67 Assumptions after simplification:
% 6.71/1.67 ---------------------------------
% 6.71/1.67
% 6.71/1.67 (0)
% 6.84/1.71 ? [v0: int] : ( ~ (z4 = z3) & ~ (z4 = z2) & ~ (z4 = z1) & ~ (z3 = z2) & ~
% 6.84/1.71 (z3 = z1) & $lesseq(v0, 2) & $lesseq(1, $difference(z1, z2)) & b(z3) = 5 &
% 6.84/1.71 b(z2) = v0 & a(z3) = 1 & a(z2) = 10 & a(z1) = 6 & ! [v1: int] : ! [v2:
% 6.84/1.71 int] : ! [v3: int] : ! [v4: int] : (v3 = v2 | v3 = v1 | ~ ($lesseq(v4,
% 6.84/1.71 2)) | ~ ($lesseq(1, $difference(v1, v2))) | ~ (b(v3) = 5) | ~
% 6.84/1.71 (b(v2) = v4) | ~ (a(v1) = 7) | ? [v5: int] : ( ~ (v5 = 10) & a(v2) =
% 6.84/1.71 v5)) & ! [v1: int] : ! [v2: int] : ! [v3: int] : ! [v4: int] : (v3 =
% 6.84/1.71 v2 | v3 = v1 | ~ ($lesseq(v4, 2)) | ~ ($lesseq(1, $difference(v1, v2)))
% 6.84/1.71 | ~ (b(v3) = 5) | ~ (b(v2) = v4) | ~ (a(v1) = 6) | ? [v5: int] : ( ~
% 6.84/1.71 (v5 = 10) & a(v2) = v5)) & ! [v1: int] : ! [v2: int] : ! [v3: int] :
% 6.84/1.71 ! [v4: int] : (v3 = v2 | v3 = v1 | ~ ($lesseq(v4, 2)) | ~ ($lesseq(1,
% 6.84/1.71 $difference(v1, v2))) | ~ (b(v2) = v4) | ~ (a(v3) = 8) | ~ (a(v1) =
% 6.84/1.71 7) | ? [v5: int] : ( ~ (v5 = 10) & a(v2) = v5)) & ! [v1: int] : !
% 6.84/1.71 [v2: int] : ! [v3: int] : ( ~ ($lesseq(v3, 2)) | ~ ($lesseq(1,
% 6.84/1.71 $difference(v1, v2))) | ~ (b(v2) = v3) | ~ (a(v1) = 9) | ? [v4:
% 6.84/1.71 int] : ( ~ (v4 = 10) & a(v2) = v4)) & ! [v1: int] : ! [v2: int] : !
% 6.84/1.71 [v3: int] : ( ~ ($lesseq(v3, 2)) | ~ ($lesseq(1, $difference(v1, v2))) | ~
% 6.84/1.71 (b(v2) = v3) | ~ (a(v1) = 8) | ? [v4: int] : ( ~ (v4 = 10) & a(v2) =
% 6.84/1.71 v4)) & ! [v1: int] : ! [v2: int] : (v2 = v1 | ~ (a(v2) = 10) | ~
% 6.84/1.71 (a(v1) = 10)) & ! [v1: int] : ! [v2: int] : ( ~ ($lesseq(v2, 0) | ~
% 6.84/1.71 (b(v1) = v2)) & ! [v1: int] : ! [v2: int] : ( ~ ($lesseq(v2, 0) | ~
% 6.84/1.71 (a(v1) = v2)) & ! [v1: int] : ! [v2: int] : ( ~ ($lesseq(13, v2)) |
% 6.84/1.71 ~ (a(v1) = v2)) & ! [v1: int] : ! [v2: int] : ( ~ ($lesseq(6, v2)) |
% 6.84/1.71 ~ (b(v1) = v2)))
% 6.84/1.71
% 6.84/1.71 (function-axioms)
% 6.84/1.71 ! [v0: int] : ! [v1: int] : ! [v2: int] : (v1 = v0 | ~ (b(v2) = v1) | ~
% 6.84/1.71 (b(v2) = v0)) & ! [v0: int] : ! [v1: int] : ! [v2: int] : (v1 = v0 | ~
% 6.84/1.71 (a(v2) = v1) | ~ (a(v2) = v0))
% 6.84/1.71
% 6.84/1.71 Those formulas are unsatisfiable:
% 6.84/1.71 ---------------------------------
% 6.84/1.71
% 6.84/1.71 Begin of proof
% 6.84/1.71 |
% 6.84/1.71 | ALPHA: (function-axioms) implies:
% 6.84/1.71 | (1) ! [v0: int] : ! [v1: int] : ! [v2: int] : (v1 = v0 | ~ (a(v2) = v1)
% 6.84/1.71 | | ~ (a(v2) = v0))
% 6.84/1.71 |
% 6.84/1.71 | DELTA: instantiating (0) with fresh symbol all_3_0 gives:
% 7.03/1.73 | (2) ~ (z4 = z3) & ~ (z4 = z2) & ~ (z4 = z1) & ~ (z3 = z2) & ~ (z3 =
% 7.03/1.73 | z1) & $lesseq(all_3_0, 2) & $lesseq(1, $difference(z1, z2)) & b(z3) =
% 7.03/1.73 | 5 & b(z2) = all_3_0 & a(z3) = 1 & a(z2) = 10 & a(z1) = 6 & ! [v0: int]
% 7.03/1.73 | : ! [v1: int] : ! [v2: int] : ! [v3: int] : (v2 = v1 | v2 = v0 | ~
% 7.03/1.73 | ($lesseq(v3, 2)) | ~ ($lesseq(1, $difference(v0, v1))) | ~ (b(v2) =
% 7.03/1.73 | 5) | ~ (b(v1) = v3) | ~ (a(v0) = 7) | ? [v4: int] : ( ~ (v4 =
% 7.03/1.73 | 10) & a(v1) = v4)) & ! [v0: int] : ! [v1: int] : ! [v2: int] :
% 7.03/1.73 | ! [v3: int] : (v2 = v1 | v2 = v0 | ~ ($lesseq(v3, 2)) | ~
% 7.03/1.73 | ($lesseq(1, $difference(v0, v1))) | ~ (b(v2) = 5) | ~ (b(v1) = v3)
% 7.03/1.73 | | ~ (a(v0) = 6) | ? [v4: int] : ( ~ (v4 = 10) & a(v1) = v4)) & !
% 7.03/1.73 | [v0: int] : ! [v1: int] : ! [v2: int] : ! [v3: int] : (v2 = v1 | v2
% 7.03/1.73 | = v0 | ~ ($lesseq(v3, 2)) | ~ ($lesseq(1, $difference(v0, v1))) |
% 7.03/1.73 | ~ (b(v1) = v3) | ~ (a(v2) = 8) | ~ (a(v0) = 7) | ? [v4: int] : ( ~
% 7.03/1.73 | (v4 = 10) & a(v1) = v4)) & ! [v0: int] : ! [v1: int] : ! [v2:
% 7.03/1.73 | int] : ( ~ ($lesseq(v2, 2)) | ~ ($lesseq(1, $difference(v0, v1))) |
% 7.03/1.73 | ~ (b(v1) = v2) | ~ (a(v0) = 9) | ? [v3: int] : ( ~ (v3 = 10) &
% 7.03/1.73 | a(v1) = v3)) & ! [v0: int] : ! [v1: int] : ! [v2: int] : ( ~
% 7.03/1.73 | ($lesseq(v2, 2)) | ~ ($lesseq(1, $difference(v0, v1))) | ~ (b(v1) =
% 7.03/1.73 | v2) | ~ (a(v0) = 8) | ? [v3: int] : ( ~ (v3 = 10) & a(v1) = v3))
% 7.03/1.73 | & ! [v0: int] : ! [v1: int] : (v1 = v0 | ~ (a(v1) = 10) | ~ (a(v0)
% 7.03/1.73 | = 10)) & ! [v0: int] : ! [v1: int] : ( ~ ($lesseq(v1, 0) | ~
% 7.03/1.73 | (b(v0) = v1)) & ! [v0: int] : ! [v1: int] : ( ~ ($lesseq(v1, 0) |
% 7.03/1.73 | ~ (a(v0) = v1)) & ! [v0: int] : ! [v1: int] : ( ~ ($lesseq(13,
% 7.03/1.73 | v1)) | ~ (a(v0) = v1)) & ! [v0: int] : ! [v1: int] : ( ~
% 7.03/1.73 | ($lesseq(6, v1)) | ~ (b(v0) = v1))
% 7.03/1.73 |
% 7.03/1.73 | ALPHA: (2) implies:
% 7.03/1.73 | (3) ~ (z3 = z1)
% 7.03/1.73 | (4) ~ (z3 = z2)
% 7.03/1.73 | (5) $lesseq(1, $difference(z1, z2))
% 7.03/1.73 | (6) $lesseq(all_3_0, 2)
% 7.03/1.73 | (7) a(z1) = 6
% 7.03/1.73 | (8) a(z2) = 10
% 7.03/1.73 | (9) b(z2) = all_3_0
% 7.03/1.73 | (10) b(z3) = 5
% 7.03/1.73 | (11) ! [v0: int] : ! [v1: int] : ! [v2: int] : ! [v3: int] : (v2 = v1 |
% 7.03/1.73 | v2 = v0 | ~ ($lesseq(v3, 2)) | ~ ($lesseq(1, $difference(v0, v1)))
% 7.03/1.73 | | ~ (b(v2) = 5) | ~ (b(v1) = v3) | ~ (a(v0) = 6) | ? [v4: int] :
% 7.03/1.73 | ( ~ (v4 = 10) & a(v1) = v4))
% 7.03/1.73 |
% 7.03/1.73 | GROUND_INST: instantiating (11) with z1, z2, z3, all_3_0, simplifying with
% 7.03/1.73 | (7), (9), (10) gives:
% 7.03/1.73 | (12) z3 = z2 | z3 = z1 | ~ ($lesseq(all_3_0, 2)) | ~ ($lesseq(1,
% 7.03/1.73 | $difference(z1, z2))) | ? [v0: int] : ( ~ (v0 = 10) & a(z2) = v0)
% 7.03/1.73 |
% 7.03/1.73 | BETA: splitting (12) gives:
% 7.03/1.73 |
% 7.03/1.73 | Case 1:
% 7.03/1.73 | |
% 7.03/1.73 | | (13) $lesseq(z1, z2)
% 7.03/1.73 | |
% 7.03/1.73 | | COMBINE_INEQS: (5), (13) imply:
% 7.03/1.74 | | (14) $false
% 7.10/1.74 | |
% 7.10/1.74 | | CLOSE: (14) is inconsistent.
% 7.10/1.74 | |
% 7.10/1.74 | Case 2:
% 7.10/1.74 | |
% 7.10/1.74 | | (15) z3 = z2 | z3 = z1 | ~ ($lesseq(all_3_0, 2)) | ? [v0: int] : ( ~
% 7.10/1.74 | | (v0 = 10) & a(z2) = v0)
% 7.10/1.74 | |
% 7.10/1.74 | | BETA: splitting (15) gives:
% 7.10/1.74 | |
% 7.10/1.74 | | Case 1:
% 7.10/1.74 | | |
% 7.10/1.74 | | | (16) $lesseq(3, all_3_0)
% 7.10/1.74 | | |
% 7.10/1.74 | | | COMBINE_INEQS: (6), (16) imply:
% 7.10/1.74 | | | (17) $false
% 7.10/1.74 | | |
% 7.10/1.74 | | | CLOSE: (17) is inconsistent.
% 7.10/1.74 | | |
% 7.10/1.74 | | Case 2:
% 7.10/1.74 | | |
% 7.10/1.74 | | | (18) z3 = z2 | z3 = z1 | ? [v0: int] : ( ~ (v0 = 10) & a(z2) = v0)
% 7.10/1.74 | | |
% 7.10/1.74 | | | BETA: splitting (18) gives:
% 7.10/1.74 | | |
% 7.10/1.74 | | | Case 1:
% 7.10/1.74 | | | |
% 7.10/1.74 | | | | (19) z3 = z2
% 7.10/1.74 | | | |
% 7.10/1.74 | | | | REDUCE: (4), (19) imply:
% 7.10/1.74 | | | | (20) $false
% 7.10/1.74 | | | |
% 7.10/1.74 | | | | CLOSE: (20) is inconsistent.
% 7.10/1.74 | | | |
% 7.10/1.74 | | | Case 2:
% 7.10/1.74 | | | |
% 7.10/1.74 | | | | (21) z3 = z1 | ? [v0: int] : ( ~ (v0 = 10) & a(z2) = v0)
% 7.10/1.74 | | | |
% 7.10/1.74 | | | | BETA: splitting (21) gives:
% 7.10/1.74 | | | |
% 7.10/1.74 | | | | Case 1:
% 7.10/1.74 | | | | |
% 7.10/1.74 | | | | | (22) z3 = z1
% 7.10/1.74 | | | | |
% 7.10/1.74 | | | | | REDUCE: (3), (22) imply:
% 7.10/1.74 | | | | | (23) $false
% 7.10/1.74 | | | | |
% 7.10/1.74 | | | | | CLOSE: (23) is inconsistent.
% 7.10/1.74 | | | | |
% 7.10/1.74 | | | | Case 2:
% 7.10/1.74 | | | | |
% 7.10/1.74 | | | | | (24) ? [v0: int] : ( ~ (v0 = 10) & a(z2) = v0)
% 7.10/1.74 | | | | |
% 7.10/1.74 | | | | | DELTA: instantiating (24) with fresh symbol all_30_0 gives:
% 7.10/1.74 | | | | | (25) ~ (all_30_0 = 10) & a(z2) = all_30_0
% 7.10/1.74 | | | | |
% 7.10/1.74 | | | | | ALPHA: (25) implies:
% 7.10/1.74 | | | | | (26) ~ (all_30_0 = 10)
% 7.10/1.74 | | | | | (27) a(z2) = all_30_0
% 7.10/1.74 | | | | |
% 7.10/1.74 | | | | | GROUND_INST: instantiating (1) with 10, all_30_0, z2, simplifying with
% 7.10/1.74 | | | | | (8), (27) gives:
% 7.10/1.74 | | | | | (28) all_30_0 = 10
% 7.10/1.74 | | | | |
% 7.10/1.74 | | | | | REDUCE: (26), (28) imply:
% 7.10/1.74 | | | | | (29) $false
% 7.10/1.74 | | | | |
% 7.10/1.74 | | | | | CLOSE: (29) is inconsistent.
% 7.10/1.74 | | | | |
% 7.10/1.74 | | | | End of split
% 7.10/1.74 | | | |
% 7.10/1.74 | | | End of split
% 7.10/1.74 | | |
% 7.10/1.74 | | End of split
% 7.10/1.74 | |
% 7.10/1.74 | End of split
% 7.10/1.74 |
% 7.10/1.74 End of proof
% 7.10/1.74 % SZS output end Proof for theBenchmark
% 7.10/1.74
% 7.10/1.74 1130ms
%------------------------------------------------------------------------------