TSTP Solution File: SYN409+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SYN409+1 : TPTP v8.1.2. Released v2.0.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n006.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 : Fri Sep 1 03:27:34 EDT 2023
% Result : Theorem 3.33s 1.34s
% Output : Proof 4.34s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SYN409+1 : TPTP v8.1.2. Released v2.0.0.
% 0.10/0.12 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.10/0.32 % Computer : n006.cluster.edu
% 0.10/0.32 % Model : x86_64 x86_64
% 0.10/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.32 % Memory : 8042.1875MB
% 0.10/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.32 % CPULimit : 300
% 0.10/0.32 % WCLimit : 300
% 0.10/0.32 % DateTime : Sat Aug 26 21:15:07 EDT 2023
% 0.10/0.32 % CPUTime :
% 0.17/0.60 ________ _____
% 0.17/0.60 ___ __ \_________(_)________________________________
% 0.17/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.17/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.17/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.17/0.61
% 0.17/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.17/0.61 (2023-06-19)
% 0.17/0.61
% 0.17/0.61 (c) Philipp Rümmer, 2009-2023
% 0.17/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.17/0.61 Amanda Stjerna.
% 0.17/0.61 Free software under BSD-3-Clause.
% 0.17/0.61
% 0.17/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.17/0.61
% 0.17/0.61 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.17/0.62 Running up to 7 provers in parallel.
% 0.17/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.17/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.17/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.17/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.17/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.17/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 0.17/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 1.84/1.02 Prover 4: Preprocessing ...
% 1.84/1.02 Prover 1: Preprocessing ...
% 1.94/1.09 Prover 3: Preprocessing ...
% 1.94/1.09 Prover 0: Preprocessing ...
% 1.94/1.09 Prover 5: Preprocessing ...
% 1.94/1.09 Prover 2: Preprocessing ...
% 1.94/1.09 Prover 6: Preprocessing ...
% 2.36/1.14 Prover 1: Warning: ignoring some quantifiers
% 2.36/1.16 Prover 3: Warning: ignoring some quantifiers
% 2.69/1.17 Prover 5: Proving ...
% 2.69/1.17 Prover 4: Constructing countermodel ...
% 2.69/1.17 Prover 1: Constructing countermodel ...
% 2.69/1.17 Prover 3: Constructing countermodel ...
% 2.69/1.18 Prover 2: Proving ...
% 2.69/1.18 Prover 6: Proving ...
% 2.69/1.19 Prover 0: Proving ...
% 3.33/1.33 Prover 3: gave up
% 3.33/1.33 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 3.33/1.34 Prover 2: proved (703ms)
% 3.33/1.34 Prover 5: proved (696ms)
% 3.33/1.34
% 3.33/1.34 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.33/1.34
% 3.33/1.34 Prover 0: proved (706ms)
% 3.33/1.34
% 3.33/1.34 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.33/1.34
% 3.33/1.34
% 3.33/1.34 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.33/1.34
% 3.33/1.35 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 3.33/1.35 Prover 7: Preprocessing ...
% 3.33/1.35 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 3.33/1.35 Prover 6: stopped
% 3.33/1.35 Prover 8: Preprocessing ...
% 3.33/1.35 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 3.33/1.35 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 3.33/1.36 Prover 10: Preprocessing ...
% 3.33/1.36 Prover 13: Preprocessing ...
% 3.33/1.36 Prover 1: gave up
% 3.33/1.37 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 3.33/1.37 Prover 7: Warning: ignoring some quantifiers
% 3.33/1.37 Prover 10: Warning: ignoring some quantifiers
% 3.33/1.37 Prover 7: Constructing countermodel ...
% 3.33/1.37 Prover 10: Constructing countermodel ...
% 3.33/1.37 Prover 4: Found proof (size 15)
% 3.33/1.37 Prover 4: proved (736ms)
% 3.33/1.37 Prover 11: Preprocessing ...
% 3.33/1.37 Prover 10: stopped
% 3.33/1.38 Prover 7: stopped
% 3.33/1.38 Prover 13: Warning: ignoring some quantifiers
% 3.33/1.38 Prover 13: Constructing countermodel ...
% 3.33/1.39 Prover 13: stopped
% 3.33/1.39 Prover 8: Warning: ignoring some quantifiers
% 3.33/1.39 Prover 16: Preprocessing ...
% 3.33/1.39 Prover 8: Constructing countermodel ...
% 3.33/1.39 Prover 8: stopped
% 3.33/1.40 Prover 11: Constructing countermodel ...
% 3.33/1.40 Prover 11: stopped
% 3.33/1.41 Prover 16: Warning: ignoring some quantifiers
% 3.33/1.41 Prover 16: Constructing countermodel ...
% 3.33/1.41 Prover 16: stopped
% 3.33/1.41
% 3.33/1.41 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.33/1.41
% 3.33/1.42 % SZS output start Proof for theBenchmark
% 3.33/1.42 Assumptions after simplification:
% 3.33/1.42 ---------------------------------
% 3.33/1.43
% 3.33/1.43 (kalish246)
% 4.34/1.48 ? [v0: $i] : ? [v1: int] : ? [v2: $i] : ? [v3: $i] : ? [v4: any] : ?
% 4.34/1.48 [v5: any] : ($i(v3) & $i(v2) & $i(v0) & (( ~ (v1 = 0) & f(v0) = v1 & ! [v6:
% 4.34/1.48 $i] : ! [v7: int] : (v7 = 0 | ~ (f(v6) = v7) | ~ $i(v6))) | (f(v3)
% 4.34/1.48 = v5 & f(v2) = v4 & ! [v6: $i] : ! [v7: int] : (v7 = 0 | ~ (f(v6) =
% 4.34/1.48 v7) | ~ $i(v6)) & ( ~ (v5 = 0) | ~ (v4 = 0)))))
% 4.34/1.48
% 4.34/1.48 Those formulas are unsatisfiable:
% 4.34/1.48 ---------------------------------
% 4.34/1.48
% 4.34/1.48 Begin of proof
% 4.34/1.48 |
% 4.34/1.48 | DELTA: instantiating (kalish246) with fresh symbols all_3_0, all_3_1, all_3_2,
% 4.34/1.48 | all_3_3, all_3_4, all_3_5 gives:
% 4.34/1.49 | (1) $i(all_3_2) & $i(all_3_3) & $i(all_3_5) & (( ~ (all_3_4 = 0) &
% 4.34/1.49 | f(all_3_5) = all_3_4 & ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~
% 4.34/1.49 | (f(v0) = v1) | ~ $i(v0))) | (f(all_3_2) = all_3_0 & f(all_3_3) =
% 4.34/1.49 | all_3_1 & ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (f(v0) = v1) |
% 4.34/1.49 | ~ $i(v0)) & ( ~ (all_3_0 = 0) | ~ (all_3_1 = 0))))
% 4.34/1.49 |
% 4.34/1.49 | ALPHA: (1) implies:
% 4.34/1.49 | (2) $i(all_3_5)
% 4.34/1.49 | (3) $i(all_3_3)
% 4.34/1.49 | (4) $i(all_3_2)
% 4.34/1.50 | (5) ( ~ (all_3_4 = 0) & f(all_3_5) = all_3_4 & ! [v0: $i] : ! [v1: int] :
% 4.34/1.50 | (v1 = 0 | ~ (f(v0) = v1) | ~ $i(v0))) | (f(all_3_2) = all_3_0 &
% 4.34/1.50 | f(all_3_3) = all_3_1 & ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~
% 4.34/1.50 | (f(v0) = v1) | ~ $i(v0)) & ( ~ (all_3_0 = 0) | ~ (all_3_1 = 0)))
% 4.34/1.50 |
% 4.34/1.50 | BETA: splitting (5) gives:
% 4.34/1.50 |
% 4.34/1.50 | Case 1:
% 4.34/1.50 | |
% 4.34/1.50 | | (6) ~ (all_3_4 = 0) & f(all_3_5) = all_3_4 & ! [v0: $i] : ! [v1: int]
% 4.34/1.50 | | : (v1 = 0 | ~ (f(v0) = v1) | ~ $i(v0))
% 4.34/1.50 | |
% 4.34/1.50 | | ALPHA: (6) implies:
% 4.34/1.50 | | (7) ~ (all_3_4 = 0)
% 4.34/1.50 | | (8) f(all_3_5) = all_3_4
% 4.34/1.50 | | (9) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (f(v0) = v1) | ~ $i(v0))
% 4.34/1.50 | |
% 4.34/1.50 | | GROUND_INST: instantiating (9) with all_3_5, all_3_4, simplifying with (2),
% 4.34/1.50 | | (8) gives:
% 4.34/1.50 | | (10) all_3_4 = 0
% 4.34/1.51 | |
% 4.34/1.51 | | REDUCE: (7), (10) imply:
% 4.34/1.51 | | (11) $false
% 4.34/1.51 | |
% 4.34/1.51 | | CLOSE: (11) is inconsistent.
% 4.34/1.51 | |
% 4.34/1.51 | Case 2:
% 4.34/1.51 | |
% 4.34/1.51 | | (12) f(all_3_2) = all_3_0 & f(all_3_3) = all_3_1 & ! [v0: $i] : ! [v1:
% 4.34/1.51 | | int] : (v1 = 0 | ~ (f(v0) = v1) | ~ $i(v0)) & ( ~ (all_3_0 = 0)
% 4.34/1.51 | | | ~ (all_3_1 = 0))
% 4.34/1.51 | |
% 4.34/1.51 | | ALPHA: (12) implies:
% 4.34/1.51 | | (13) f(all_3_3) = all_3_1
% 4.34/1.51 | | (14) f(all_3_2) = all_3_0
% 4.34/1.51 | | (15) ~ (all_3_0 = 0) | ~ (all_3_1 = 0)
% 4.34/1.51 | | (16) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (f(v0) = v1) | ~ $i(v0))
% 4.34/1.51 | |
% 4.34/1.51 | | GROUND_INST: instantiating (16) with all_3_3, all_3_1, simplifying with (3),
% 4.34/1.51 | | (13) gives:
% 4.34/1.51 | | (17) all_3_1 = 0
% 4.34/1.51 | |
% 4.34/1.51 | | GROUND_INST: instantiating (16) with all_3_2, all_3_0, simplifying with (4),
% 4.34/1.51 | | (14) gives:
% 4.34/1.52 | | (18) all_3_0 = 0
% 4.34/1.52 | |
% 4.34/1.52 | | BETA: splitting (15) gives:
% 4.34/1.52 | |
% 4.34/1.52 | | Case 1:
% 4.34/1.52 | | |
% 4.34/1.52 | | | (19) ~ (all_3_0 = 0)
% 4.34/1.52 | | |
% 4.34/1.52 | | | REDUCE: (18), (19) imply:
% 4.34/1.52 | | | (20) $false
% 4.34/1.52 | | |
% 4.34/1.52 | | | CLOSE: (20) is inconsistent.
% 4.34/1.52 | | |
% 4.34/1.52 | | Case 2:
% 4.34/1.52 | | |
% 4.34/1.52 | | | (21) ~ (all_3_1 = 0)
% 4.34/1.52 | | |
% 4.34/1.52 | | | REDUCE: (17), (21) imply:
% 4.34/1.52 | | | (22) $false
% 4.34/1.52 | | |
% 4.34/1.52 | | | CLOSE: (22) is inconsistent.
% 4.34/1.52 | | |
% 4.34/1.52 | | End of split
% 4.34/1.52 | |
% 4.34/1.52 | End of split
% 4.34/1.52 |
% 4.34/1.52 End of proof
% 4.34/1.52 % SZS output end Proof for theBenchmark
% 4.34/1.52
% 4.34/1.52 912ms
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