TSTP Solution File: NUN089+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : NUN089+1 : TPTP v8.1.2. Released v7.3.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n023.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 12:51:07 EDT 2023
% Result : Theorem 6.20s 1.57s
% Output : Proof 8.83s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : NUN089+1 : TPTP v8.1.2. Released v7.3.0.
% 0.07/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.35 % Computer : n023.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 : Sun Aug 27 09:18:56 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.60/0.63 ________ _____
% 0.60/0.63 ___ __ \_________(_)________________________________
% 0.60/0.63 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.60/0.63 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.60/0.63 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.60/0.63
% 0.60/0.63 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.60/0.63 (2023-06-19)
% 0.60/0.63
% 0.60/0.63 (c) Philipp Rümmer, 2009-2023
% 0.60/0.63 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.60/0.63 Amanda Stjerna.
% 0.60/0.63 Free software under BSD-3-Clause.
% 0.60/0.63
% 0.60/0.63 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.60/0.63
% 0.60/0.63 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.68/0.64 Running up to 7 provers in parallel.
% 0.68/0.66 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.68/0.66 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.68/0.66 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.68/0.66 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.68/0.66 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.68/0.66 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.68/0.66 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.97/1.13 Prover 1: Preprocessing ...
% 2.97/1.13 Prover 4: Preprocessing ...
% 3.48/1.17 Prover 5: Preprocessing ...
% 3.48/1.17 Prover 0: Preprocessing ...
% 3.48/1.17 Prover 3: Preprocessing ...
% 3.48/1.17 Prover 6: Preprocessing ...
% 3.48/1.17 Prover 2: Preprocessing ...
% 5.02/1.43 Prover 2: Proving ...
% 5.02/1.43 Prover 5: Proving ...
% 5.71/1.49 Prover 3: Warning: ignoring some quantifiers
% 5.71/1.49 Prover 6: Proving ...
% 5.71/1.51 Prover 3: Constructing countermodel ...
% 6.02/1.52 Prover 1: Warning: ignoring some quantifiers
% 6.20/1.54 Prover 1: Constructing countermodel ...
% 6.20/1.55 Prover 4: Warning: ignoring some quantifiers
% 6.20/1.57 Prover 2: proved (926ms)
% 6.20/1.57
% 6.20/1.57 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.20/1.57
% 6.20/1.57 Prover 5: proved (914ms)
% 6.20/1.57
% 6.20/1.57 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.20/1.57
% 6.20/1.57 Prover 3: stopped
% 6.20/1.58 Prover 6: stopped
% 6.20/1.58 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 6.20/1.58 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 6.20/1.58 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 6.20/1.58 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 6.20/1.59 Prover 4: Constructing countermodel ...
% 6.20/1.60 Prover 0: Proving ...
% 6.20/1.62 Prover 0: stopped
% 6.79/1.63 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 6.79/1.65 Prover 11: Preprocessing ...
% 6.79/1.66 Prover 10: Preprocessing ...
% 6.79/1.66 Prover 8: Preprocessing ...
% 6.79/1.67 Prover 7: Preprocessing ...
% 6.79/1.69 Prover 13: Preprocessing ...
% 7.91/1.77 Prover 7: Warning: ignoring some quantifiers
% 7.91/1.78 Prover 10: Warning: ignoring some quantifiers
% 8.05/1.79 Prover 7: Constructing countermodel ...
% 8.05/1.80 Prover 10: Constructing countermodel ...
% 8.05/1.80 Prover 13: Warning: ignoring some quantifiers
% 8.28/1.82 Prover 1: Found proof (size 14)
% 8.28/1.82 Prover 1: proved (1177ms)
% 8.28/1.82 Prover 4: stopped
% 8.28/1.82 Prover 10: stopped
% 8.36/1.83 Prover 13: Constructing countermodel ...
% 8.36/1.83 Prover 7: stopped
% 8.36/1.84 Prover 13: stopped
% 8.36/1.85 Prover 8: Warning: ignoring some quantifiers
% 8.36/1.86 Prover 8: Constructing countermodel ...
% 8.36/1.87 Prover 8: stopped
% 8.36/1.88 Prover 11: Warning: ignoring some quantifiers
% 8.36/1.89 Prover 11: Constructing countermodel ...
% 8.36/1.90 Prover 11: stopped
% 8.36/1.90
% 8.36/1.90 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 8.36/1.90
% 8.36/1.90 % SZS output start Proof for theBenchmark
% 8.36/1.91 Assumptions after simplification:
% 8.36/1.91 ---------------------------------
% 8.36/1.91
% 8.36/1.91 (axiom_7a)
% 8.83/1.93 ! [v0: $i] : ! [v1: $i] : ( ~ (r2(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | !
% 8.83/1.93 [v2: $i] : ( ~ (r1(v2) = 0) | ~ $i(v2) | ? [v3: int] : ( ~ (v3 = 0) &
% 8.83/1.93 id(v2, v1) = v3)))
% 8.83/1.93
% 8.83/1.93 (zerounidtwo)
% 8.83/1.93 ? [v0: $i] : ($i(v0) & ? [v1: $i] : (r2(v1, v0) = 0 & $i(v1) & ? [v2: $i] :
% 8.83/1.93 (r2(v2, v1) = 0 & r1(v2) = 0 & $i(v2))) & ? [v1: $i] : (r1(v1) = 0 &
% 8.83/1.93 id(v1, v0) = 0 & $i(v1)))
% 8.83/1.93
% 8.83/1.93 (function-axioms)
% 8.83/1.94 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 8.83/1.94 [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (r4(v4, v3, v2) = v1) | ~ (r4(v4, v3,
% 8.83/1.94 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] :
% 8.83/1.94 ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (r3(v4, v3, v2) = v1) |
% 8.83/1.94 ~ (r3(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 8.83/1.94 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (r2(v3, v2) =
% 8.83/1.94 v1) | ~ (r2(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 8.83/1.94 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (id(v3, v2) =
% 8.83/1.94 v1) | ~ (id(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 8.83/1.94 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (r1(v2) = v1) | ~ (r1(v2)
% 8.83/1.94 = v0))
% 8.83/1.94
% 8.83/1.94 Further assumptions not needed in the proof:
% 8.83/1.94 --------------------------------------------
% 8.83/1.94 axiom_1, axiom_10, axiom_11, axiom_1a, axiom_2, axiom_2a, axiom_3, axiom_3a,
% 8.83/1.94 axiom_4, axiom_4a, axiom_5, axiom_5a, axiom_6, axiom_6a, axiom_7, axiom_8,
% 8.83/1.94 axiom_9
% 8.83/1.94
% 8.83/1.94 Those formulas are unsatisfiable:
% 8.83/1.94 ---------------------------------
% 8.83/1.94
% 8.83/1.94 Begin of proof
% 8.83/1.94 |
% 8.83/1.94 | ALPHA: (function-axioms) implies:
% 8.83/1.94 | (1) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 8.83/1.94 | ! [v3: $i] : (v1 = v0 | ~ (id(v3, v2) = v1) | ~ (id(v3, v2) = v0))
% 8.83/1.94 |
% 8.83/1.95 | DELTA: instantiating (zerounidtwo) with fresh symbol all_19_0 gives:
% 8.83/1.95 | (2) $i(all_19_0) & ? [v0: $i] : (r2(v0, all_19_0) = 0 & $i(v0) & ? [v1:
% 8.83/1.95 | $i] : (r2(v1, v0) = 0 & r1(v1) = 0 & $i(v1))) & ? [v0: $i] :
% 8.83/1.95 | (r1(v0) = 0 & id(v0, all_19_0) = 0 & $i(v0))
% 8.83/1.95 |
% 8.83/1.95 | ALPHA: (2) implies:
% 8.83/1.95 | (3) $i(all_19_0)
% 8.83/1.95 | (4) ? [v0: $i] : (r1(v0) = 0 & id(v0, all_19_0) = 0 & $i(v0))
% 8.83/1.95 | (5) ? [v0: $i] : (r2(v0, all_19_0) = 0 & $i(v0) & ? [v1: $i] : (r2(v1,
% 8.83/1.95 | v0) = 0 & r1(v1) = 0 & $i(v1)))
% 8.83/1.95 |
% 8.83/1.95 | DELTA: instantiating (4) with fresh symbol all_25_0 gives:
% 8.83/1.95 | (6) r1(all_25_0) = 0 & id(all_25_0, all_19_0) = 0 & $i(all_25_0)
% 8.83/1.95 |
% 8.83/1.95 | ALPHA: (6) implies:
% 8.83/1.95 | (7) $i(all_25_0)
% 8.83/1.95 | (8) id(all_25_0, all_19_0) = 0
% 8.83/1.95 | (9) r1(all_25_0) = 0
% 8.83/1.95 |
% 8.83/1.95 | DELTA: instantiating (5) with fresh symbol all_27_0 gives:
% 8.83/1.95 | (10) r2(all_27_0, all_19_0) = 0 & $i(all_27_0) & ? [v0: $i] : (r2(v0,
% 8.83/1.95 | all_27_0) = 0 & r1(v0) = 0 & $i(v0))
% 8.83/1.95 |
% 8.83/1.95 | ALPHA: (10) implies:
% 8.83/1.95 | (11) $i(all_27_0)
% 8.83/1.95 | (12) r2(all_27_0, all_19_0) = 0
% 8.83/1.95 |
% 8.83/1.95 | GROUND_INST: instantiating (axiom_7a) with all_27_0, all_19_0, simplifying
% 8.83/1.95 | with (3), (11), (12) gives:
% 8.83/1.95 | (13) ! [v0: $i] : ( ~ (r1(v0) = 0) | ~ $i(v0) | ? [v1: int] : ( ~ (v1 =
% 8.83/1.95 | 0) & id(v0, all_19_0) = v1))
% 8.83/1.95 |
% 8.83/1.95 | GROUND_INST: instantiating (13) with all_25_0, simplifying with (7), (9)
% 8.83/1.96 | gives:
% 8.83/1.96 | (14) ? [v0: int] : ( ~ (v0 = 0) & id(all_25_0, all_19_0) = v0)
% 8.83/1.96 |
% 8.83/1.96 | DELTA: instantiating (14) with fresh symbol all_45_0 gives:
% 8.83/1.96 | (15) ~ (all_45_0 = 0) & id(all_25_0, all_19_0) = all_45_0
% 8.83/1.96 |
% 8.83/1.96 | ALPHA: (15) implies:
% 8.83/1.96 | (16) ~ (all_45_0 = 0)
% 8.83/1.96 | (17) id(all_25_0, all_19_0) = all_45_0
% 8.83/1.96 |
% 8.83/1.96 | GROUND_INST: instantiating (1) with 0, all_45_0, all_19_0, all_25_0,
% 8.83/1.96 | simplifying with (8), (17) gives:
% 8.83/1.96 | (18) all_45_0 = 0
% 8.83/1.96 |
% 8.83/1.96 | REDUCE: (16), (18) imply:
% 8.83/1.96 | (19) $false
% 8.83/1.96 |
% 8.83/1.96 | CLOSE: (19) is inconsistent.
% 8.83/1.96 |
% 8.83/1.96 End of proof
% 8.83/1.96 % SZS output end Proof for theBenchmark
% 8.83/1.96
% 8.83/1.96 1332ms
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