TSTP Solution File: SYN398+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SYN398+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 : n021.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 03:27:32 EDT 2023
% Result : Theorem 2.77s 1.14s
% Output : Proof 3.71s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.12 % Problem : SYN398+1 : TPTP v8.1.2. Released v2.0.0.
% 0.09/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.34 % Computer : n021.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sat Aug 26 18:52:57 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.57 ________ _____
% 0.20/0.58 ___ __ \_________(_)________________________________
% 0.20/0.58 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.20/0.58 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.20/0.58 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.20/0.58
% 0.20/0.58 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.58 (2023-06-19)
% 0.20/0.58
% 0.20/0.58 (c) Philipp Rümmer, 2009-2023
% 0.20/0.58 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.58 Amanda Stjerna.
% 0.20/0.58 Free software under BSD-3-Clause.
% 0.20/0.58
% 0.20/0.58 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.58
% 0.20/0.58 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.20/0.59 Running up to 7 provers in parallel.
% 0.20/0.60 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.60 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.60 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.60 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.60 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.60 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.20/0.60 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 1.97/0.95 Prover 1: Preprocessing ...
% 1.97/0.95 Prover 4: Preprocessing ...
% 1.97/0.99 Prover 6: Preprocessing ...
% 1.97/0.99 Prover 2: Preprocessing ...
% 1.97/0.99 Prover 0: Preprocessing ...
% 1.97/0.99 Prover 5: Preprocessing ...
% 1.97/0.99 Prover 3: Preprocessing ...
% 2.40/1.03 Prover 1: Warning: ignoring some quantifiers
% 2.40/1.04 Prover 3: Warning: ignoring some quantifiers
% 2.40/1.04 Prover 4: Constructing countermodel ...
% 2.40/1.04 Prover 3: Constructing countermodel ...
% 2.40/1.04 Prover 1: Constructing countermodel ...
% 2.40/1.04 Prover 0: Proving ...
% 2.40/1.04 Prover 6: Proving ...
% 2.40/1.04 Prover 2: Proving ...
% 2.40/1.04 Prover 5: Proving ...
% 2.77/1.14 Prover 2: proved (540ms)
% 2.77/1.14
% 2.77/1.14 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.77/1.14
% 2.77/1.15 Prover 0: proved (541ms)
% 2.77/1.15
% 2.77/1.15 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.77/1.15
% 2.77/1.15 Prover 5: stopped
% 2.77/1.15 Prover 3: gave up
% 2.77/1.15 Prover 6: stopped
% 2.77/1.15 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 2.77/1.15 Prover 1: gave up
% 3.36/1.17 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 3.36/1.17 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 3.36/1.17 Prover 7: Preprocessing ...
% 3.36/1.17 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 3.36/1.17 Prover 10: Preprocessing ...
% 3.36/1.17 Prover 4: Found proof (size 11)
% 3.36/1.17 Prover 11: Preprocessing ...
% 3.36/1.17 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 3.36/1.17 Prover 4: proved (571ms)
% 3.36/1.17 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 3.36/1.18 Prover 10: Warning: ignoring some quantifiers
% 3.36/1.18 Prover 10: Constructing countermodel ...
% 3.36/1.18 Prover 16: Preprocessing ...
% 3.36/1.18 Prover 10: stopped
% 3.36/1.18 Prover 7: Warning: ignoring some quantifiers
% 3.36/1.18 Prover 7: Constructing countermodel ...
% 3.36/1.18 Prover 8: Preprocessing ...
% 3.36/1.18 Prover 7: stopped
% 3.51/1.19 Prover 11: Constructing countermodel ...
% 3.51/1.19 Prover 13: Preprocessing ...
% 3.51/1.19 Prover 11: stopped
% 3.51/1.19 Prover 16: Warning: ignoring some quantifiers
% 3.51/1.19 Prover 16: Constructing countermodel ...
% 3.51/1.19 Prover 16: stopped
% 3.51/1.19 Prover 13: Warning: ignoring some quantifiers
% 3.51/1.19 Prover 13: Constructing countermodel ...
% 3.51/1.19 Prover 8: Warning: ignoring some quantifiers
% 3.51/1.20 Prover 13: stopped
% 3.51/1.20 Prover 8: Constructing countermodel ...
% 3.51/1.20 Prover 8: stopped
% 3.51/1.20
% 3.51/1.20 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.51/1.20
% 3.51/1.20 % SZS output start Proof for theBenchmark
% 3.51/1.21 Assumptions after simplification:
% 3.51/1.21 ---------------------------------
% 3.51/1.21
% 3.51/1.21 (kalish215)
% 3.71/1.25 ? [v0: $i] : ? [v1: int] : ? [v2: $i] : ? [v3: int] : ($i(v2) & $i(v0) &
% 3.71/1.25 ! [v4: $i] : ! [v5: int] : (v5 = 0 | ~ (f(v4) = v5) | ~ $i(v4)) & (( ~
% 3.71/1.25 (v3 = 0) & f(v2) = v3 & p) | ( ~ (v1 = 0) & f(v0) = v1 & p)))
% 3.71/1.25
% 3.71/1.25 Those formulas are unsatisfiable:
% 3.71/1.25 ---------------------------------
% 3.71/1.25
% 3.71/1.25 Begin of proof
% 3.71/1.25 |
% 3.71/1.25 | DELTA: instantiating (kalish215) with fresh symbols all_3_0, all_3_1, all_3_2,
% 3.71/1.25 | all_3_3 gives:
% 3.71/1.25 | (1) $i(all_3_1) & $i(all_3_3) & ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~
% 3.71/1.25 | (f(v0) = v1) | ~ $i(v0)) & (( ~ (all_3_0 = 0) & f(all_3_1) = all_3_0
% 3.71/1.25 | & p) | ( ~ (all_3_2 = 0) & f(all_3_3) = all_3_2 & p))
% 3.71/1.25 |
% 3.71/1.25 | ALPHA: (1) implies:
% 3.71/1.25 | (2) $i(all_3_3)
% 3.71/1.25 | (3) $i(all_3_1)
% 3.71/1.26 | (4) ( ~ (all_3_0 = 0) & f(all_3_1) = all_3_0 & p) | ( ~ (all_3_2 = 0) &
% 3.71/1.26 | f(all_3_3) = all_3_2 & p)
% 3.71/1.26 | (5) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (f(v0) = v1) | ~ $i(v0))
% 3.71/1.26 |
% 3.71/1.26 | BETA: splitting (4) gives:
% 3.71/1.26 |
% 3.71/1.26 | Case 1:
% 3.71/1.26 | |
% 3.71/1.26 | | (6) ~ (all_3_0 = 0) & f(all_3_1) = all_3_0 & p
% 3.71/1.26 | |
% 3.71/1.26 | | ALPHA: (6) implies:
% 3.71/1.26 | | (7) ~ (all_3_0 = 0)
% 3.71/1.26 | | (8) f(all_3_1) = all_3_0
% 3.71/1.26 | |
% 3.71/1.26 | | GROUND_INST: instantiating (5) with all_3_1, all_3_0, simplifying with (3),
% 3.71/1.26 | | (8) gives:
% 3.71/1.26 | | (9) all_3_0 = 0
% 3.71/1.26 | |
% 3.71/1.26 | | REDUCE: (7), (9) imply:
% 3.71/1.26 | | (10) $false
% 3.71/1.26 | |
% 3.71/1.26 | | CLOSE: (10) is inconsistent.
% 3.71/1.26 | |
% 3.71/1.26 | Case 2:
% 3.71/1.26 | |
% 3.71/1.26 | | (11) ~ (all_3_2 = 0) & f(all_3_3) = all_3_2 & p
% 3.71/1.26 | |
% 3.71/1.26 | | ALPHA: (11) implies:
% 3.71/1.26 | | (12) ~ (all_3_2 = 0)
% 3.71/1.26 | | (13) f(all_3_3) = all_3_2
% 3.71/1.26 | |
% 3.71/1.26 | | GROUND_INST: instantiating (5) with all_3_3, all_3_2, simplifying with (2),
% 3.71/1.26 | | (13) gives:
% 3.71/1.26 | | (14) all_3_2 = 0
% 3.71/1.26 | |
% 3.71/1.26 | | REDUCE: (12), (14) imply:
% 3.71/1.26 | | (15) $false
% 3.71/1.26 | |
% 3.71/1.26 | | CLOSE: (15) is inconsistent.
% 3.71/1.26 | |
% 3.71/1.26 | End of split
% 3.71/1.26 |
% 3.71/1.26 End of proof
% 3.71/1.26 % SZS output end Proof for theBenchmark
% 3.71/1.26
% 3.71/1.26 687ms
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