TSTP Solution File: NUM837+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : NUM837+1 : TPTP v8.1.2. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n026.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 11:50:17 EDT 2023
% Result : Theorem 7.22s 1.71s
% Output : Proof 8.46s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : NUM837+1 : TPTP v8.1.2. Released v4.1.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.35 % Computer : n026.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Fri Aug 25 16:40:03 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.62 ________ _____
% 0.20/0.62 ___ __ \_________(_)________________________________
% 0.20/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.20/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.20/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.20/0.62
% 0.20/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.62 (2023-06-19)
% 0.20/0.62
% 0.20/0.62 (c) Philipp Rümmer, 2009-2023
% 0.20/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.62 Amanda Stjerna.
% 0.20/0.62 Free software under BSD-3-Clause.
% 0.20/0.62
% 0.20/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.62
% 0.20/0.62 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.20/0.63 Running up to 7 provers in parallel.
% 0.20/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.20/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.97/1.12 Prover 4: Preprocessing ...
% 2.97/1.12 Prover 1: Preprocessing ...
% 2.97/1.17 Prover 2: Preprocessing ...
% 2.97/1.17 Prover 5: Preprocessing ...
% 2.97/1.17 Prover 3: Preprocessing ...
% 2.97/1.17 Prover 6: Preprocessing ...
% 2.97/1.17 Prover 0: Preprocessing ...
% 5.82/1.58 Prover 5: Proving ...
% 6.41/1.59 Prover 1: Warning: ignoring some quantifiers
% 6.41/1.60 Prover 6: Proving ...
% 6.41/1.61 Prover 3: Warning: ignoring some quantifiers
% 6.41/1.61 Prover 4: Warning: ignoring some quantifiers
% 6.41/1.62 Prover 3: Constructing countermodel ...
% 6.41/1.63 Prover 2: Proving ...
% 6.41/1.63 Prover 1: Constructing countermodel ...
% 6.41/1.64 Prover 4: Constructing countermodel ...
% 6.41/1.65 Prover 0: Proving ...
% 7.22/1.71 Prover 3: proved (1069ms)
% 7.22/1.71
% 7.22/1.71 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 7.22/1.71
% 7.22/1.71 Prover 6: stopped
% 7.33/1.73 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 7.33/1.73 Prover 5: stopped
% 7.33/1.73 Prover 0: stopped
% 7.33/1.73 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 7.33/1.73 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 7.33/1.73 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 7.33/1.73 Prover 2: stopped
% 7.33/1.73 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 7.33/1.78 Prover 1: Found proof (size 8)
% 7.33/1.78 Prover 1: proved (1139ms)
% 7.33/1.79 Prover 7: Preprocessing ...
% 7.33/1.79 Prover 10: Preprocessing ...
% 7.33/1.79 Prover 4: stopped
% 7.33/1.80 Prover 11: Preprocessing ...
% 7.33/1.80 Prover 13: Preprocessing ...
% 7.33/1.80 Prover 8: Preprocessing ...
% 7.99/1.82 Prover 10: stopped
% 7.99/1.83 Prover 11: stopped
% 7.99/1.83 Prover 7: stopped
% 7.99/1.84 Prover 13: stopped
% 7.99/1.89 Prover 8: Warning: ignoring some quantifiers
% 8.46/1.90 Prover 8: Constructing countermodel ...
% 8.46/1.90 Prover 8: stopped
% 8.46/1.90
% 8.46/1.90 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 8.46/1.90
% 8.46/1.91 % SZS output start Proof for theBenchmark
% 8.46/1.91 Assumptions after simplification:
% 8.46/1.91 ---------------------------------
% 8.46/1.91
% 8.46/1.91 (def(cond(conseq(axiom(3)), 12), 1))
% 8.46/1.94 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (less(v1, v0) = v2) |
% 8.46/1.94 ~ $i(v1) | ~ $i(v0) | ! [v3: $i] : ( ~ (vplus(v1, v3) = v0) | ~ $i(v3)))
% 8.46/1.94 & ! [v0: $i] : ! [v1: $i] : ( ~ (less(v1, v0) = 0) | ~ $i(v1) | ~ $i(v0) |
% 8.46/1.94 ? [v2: $i] : (vplus(v1, v2) = v0 & $i(v2)))
% 8.46/1.94
% 8.46/1.94 (holds(conjunct1(170), 270, 0))
% 8.46/1.94 less(vd268, vd269) = 0 & $i(vd269) & $i(vd268)
% 8.46/1.94
% 8.46/1.94 (qe(171))
% 8.46/1.94 $i(vd269) & $i(vd268) & ! [v0: $i] : ( ~ (vplus(vd268, v0) = vd269) | ~
% 8.46/1.94 $i(v0))
% 8.46/1.94
% 8.46/1.94 Further assumptions not needed in the proof:
% 8.46/1.94 --------------------------------------------
% 8.46/1.94 ass(cond(12, 0), 0), ass(cond(140, 0), 0), ass(cond(147, 0), 0), ass(cond(158,
% 8.46/1.94 0), 0), ass(cond(163, 0), 0), ass(cond(20, 0), 0), ass(cond(33, 0), 0),
% 8.46/1.94 ass(cond(43, 0), 0), ass(cond(52, 0), 0), ass(cond(6, 0), 0), ass(cond(61, 0),
% 8.46/1.94 0), ass(cond(73, 0), 0), ass(cond(81, 0), 0), ass(cond(goal(130), 0), 0),
% 8.46/1.94 ass(cond(goal(130), 0), 1), ass(cond(goal(130), 0), 2), ass(cond(goal(130), 0),
% 8.46/1.94 3), ass(cond(goal(88), 0), 0), ass(cond(goal(88), 0), 1), ass(cond(goal(88),
% 8.46/1.94 0), 2), ass(cond(goal(88), 0), 3), def(cond(conseq(axiom(3)), 11), 1),
% 8.46/1.94 def(cond(conseq(axiom(3)), 16), 1), def(cond(conseq(axiom(3)), 17), 1),
% 8.46/1.94 holds(conjunct2(170), 272, 0), qu(antec(axiom(3)), imp(antec(axiom(3)))),
% 8.46/1.94 qu(cond(conseq(axiom(3)), 3), and(holds(definiens(29), 45, 0),
% 8.46/1.94 holds(definiens(29), 44, 0))), qu(restrictor(axiom(1)),
% 8.46/1.94 holds(scope(axiom(1)), 2, 0))
% 8.46/1.94
% 8.46/1.94 Those formulas are unsatisfiable:
% 8.46/1.94 ---------------------------------
% 8.46/1.94
% 8.46/1.94 Begin of proof
% 8.46/1.94 |
% 8.46/1.94 | ALPHA: (holds(conjunct1(170), 270, 0)) implies:
% 8.46/1.94 | (1) less(vd268, vd269) = 0
% 8.46/1.94 |
% 8.46/1.94 | ALPHA: (def(cond(conseq(axiom(3)), 12), 1)) implies:
% 8.46/1.94 | (2) ! [v0: $i] : ! [v1: $i] : ( ~ (less(v1, v0) = 0) | ~ $i(v1) | ~
% 8.46/1.95 | $i(v0) | ? [v2: $i] : (vplus(v1, v2) = v0 & $i(v2)))
% 8.46/1.95 |
% 8.46/1.95 | ALPHA: (qe(171)) implies:
% 8.46/1.95 | (3) $i(vd268)
% 8.46/1.95 | (4) $i(vd269)
% 8.46/1.95 | (5) ! [v0: $i] : ( ~ (vplus(vd268, v0) = vd269) | ~ $i(v0))
% 8.46/1.95 |
% 8.46/1.95 | GROUND_INST: instantiating (2) with vd269, vd268, simplifying with (1), (3),
% 8.46/1.95 | (4) gives:
% 8.46/1.95 | (6) ? [v0: $i] : (vplus(vd268, v0) = vd269 & $i(v0))
% 8.46/1.95 |
% 8.46/1.95 | DELTA: instantiating (6) with fresh symbol all_42_0 gives:
% 8.46/1.95 | (7) vplus(vd268, all_42_0) = vd269 & $i(all_42_0)
% 8.46/1.95 |
% 8.46/1.95 | ALPHA: (7) implies:
% 8.46/1.95 | (8) $i(all_42_0)
% 8.46/1.95 | (9) vplus(vd268, all_42_0) = vd269
% 8.46/1.95 |
% 8.46/1.95 | GROUND_INST: instantiating (5) with all_42_0, simplifying with (8), (9) gives:
% 8.46/1.95 | (10) $false
% 8.46/1.95 |
% 8.46/1.95 | CLOSE: (10) is inconsistent.
% 8.46/1.95 |
% 8.46/1.95 End of proof
% 8.46/1.95 % SZS output end Proof for theBenchmark
% 8.46/1.95
% 8.46/1.95 1334ms
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