TSTP Solution File: NUN088+3 by Princess---230619
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% File : Princess---230619
% Problem : NUN088+3 : TPTP v8.1.2. Released v7.3.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n008.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 12:51:06 EDT 2023
% Result : Theorem 4.61s 1.39s
% Output : Proof 5.89s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : NUN088+3 : TPTP v8.1.2. Released v7.3.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.18/0.35 % Computer : n008.cluster.edu
% 0.18/0.35 % Model : x86_64 x86_64
% 0.18/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.35 % Memory : 8042.1875MB
% 0.18/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.18/0.35 % CPULimit : 300
% 0.18/0.35 % WCLimit : 300
% 0.18/0.35 % DateTime : Sun Aug 27 09:52:17 EDT 2023
% 0.18/0.35 % CPUTime :
% 0.20/0.60 ________ _____
% 0.20/0.60 ___ __ \_________(_)________________________________
% 0.20/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.20/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.20/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.20/0.60
% 0.20/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.60 (2023-06-19)
% 0.20/0.60
% 0.20/0.60 (c) Philipp Rümmer, 2009-2023
% 0.20/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.60 Amanda Stjerna.
% 0.20/0.60 Free software under BSD-3-Clause.
% 0.20/0.60
% 0.20/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.60
% 0.20/0.60 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.20/0.61 Running up to 7 provers in parallel.
% 0.20/0.62 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.62 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.62 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.62 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.62 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.62 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.20/0.62 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.50/1.02 Prover 1: Preprocessing ...
% 2.50/1.02 Prover 4: Preprocessing ...
% 2.50/1.05 Prover 3: Preprocessing ...
% 2.50/1.05 Prover 0: Preprocessing ...
% 2.50/1.05 Prover 2: Preprocessing ...
% 2.50/1.05 Prover 6: Preprocessing ...
% 2.50/1.06 Prover 5: Preprocessing ...
% 3.91/1.26 Prover 4: Warning: ignoring some quantifiers
% 3.91/1.27 Prover 1: Warning: ignoring some quantifiers
% 3.91/1.29 Prover 1: Constructing countermodel ...
% 3.91/1.29 Prover 4: Constructing countermodel ...
% 3.91/1.30 Prover 3: Warning: ignoring some quantifiers
% 3.91/1.30 Prover 5: Proving ...
% 3.91/1.30 Prover 2: Proving ...
% 3.91/1.30 Prover 0: Proving ...
% 4.61/1.30 Prover 6: Proving ...
% 4.61/1.31 Prover 3: Constructing countermodel ...
% 4.61/1.38 Prover 5: proved (761ms)
% 4.61/1.39
% 4.61/1.39 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.61/1.39
% 4.61/1.39 Prover 2: proved (765ms)
% 4.61/1.39
% 4.61/1.39 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.61/1.39
% 4.61/1.39 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 4.61/1.39 Prover 3: stopped
% 4.61/1.39 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 4.61/1.39 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 4.61/1.40 Prover 0: stopped
% 4.61/1.40 Prover 6: stopped
% 4.61/1.40 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 4.61/1.41 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 4.61/1.42 Prover 4: Found proof (size 4)
% 4.61/1.42 Prover 4: proved (799ms)
% 4.61/1.43 Prover 1: Found proof (size 4)
% 4.61/1.43 Prover 1: proved (808ms)
% 4.61/1.43 Prover 8: Preprocessing ...
% 4.61/1.45 Prover 13: Preprocessing ...
% 4.61/1.46 Prover 10: Preprocessing ...
% 4.61/1.47 Prover 7: Preprocessing ...
% 4.61/1.47 Prover 13: stopped
% 4.61/1.47 Prover 10: stopped
% 4.61/1.47 Prover 11: Preprocessing ...
% 4.61/1.49 Prover 7: stopped
% 4.61/1.50 Prover 11: stopped
% 5.89/1.52 Prover 8: Warning: ignoring some quantifiers
% 5.89/1.53 Prover 8: Constructing countermodel ...
% 5.89/1.54 Prover 8: stopped
% 5.89/1.54
% 5.89/1.54 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.89/1.54
% 5.89/1.54 % SZS output start Proof for theBenchmark
% 5.89/1.54 Assumptions after simplification:
% 5.89/1.54 ---------------------------------
% 5.89/1.54
% 5.89/1.54 (axiom_7a)
% 5.89/1.57 ! [v0: $i] : ! [v1: $i] : ( ~ (r2(v0, v1) = 0) | ~ (r1(v1) = 0) | ~ $i(v1)
% 5.89/1.57 | ~ $i(v0))
% 5.89/1.57
% 5.89/1.57 (zerouneqone2)
% 5.89/1.57 ? [v0: $i] : (r2(v0, v0) = 0 & r1(v0) = 0 & $i(v0))
% 5.89/1.57
% 5.89/1.57 Further assumptions not needed in the proof:
% 5.89/1.57 --------------------------------------------
% 5.89/1.57 axiom_1, axiom_1a, axiom_2, axiom_2a, axiom_3, axiom_3a, axiom_4, axiom_4a,
% 5.89/1.57 axiom_5a, axiom_6a
% 5.89/1.57
% 5.89/1.57 Those formulas are unsatisfiable:
% 5.89/1.57 ---------------------------------
% 5.89/1.57
% 5.89/1.57 Begin of proof
% 5.89/1.57 |
% 5.89/1.57 | DELTA: instantiating (zerouneqone2) with fresh symbol all_5_0 gives:
% 5.89/1.57 | (1) r2(all_5_0, all_5_0) = 0 & r1(all_5_0) = 0 & $i(all_5_0)
% 5.89/1.57 |
% 5.89/1.58 | ALPHA: (1) implies:
% 5.89/1.58 | (2) $i(all_5_0)
% 5.89/1.58 | (3) r1(all_5_0) = 0
% 5.89/1.58 | (4) r2(all_5_0, all_5_0) = 0
% 5.89/1.58 |
% 5.89/1.58 | GROUND_INST: instantiating (axiom_7a) with all_5_0, all_5_0, simplifying with
% 5.89/1.58 | (2), (3), (4) gives:
% 5.89/1.58 | (5) $false
% 5.89/1.58 |
% 5.89/1.58 | CLOSE: (5) is inconsistent.
% 5.89/1.58 |
% 5.89/1.58 End of proof
% 5.89/1.58 % SZS output end Proof for theBenchmark
% 5.89/1.58
% 5.89/1.58 980ms
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