TSTP Solution File: ARI618_1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : ARI618_1 : TPTP v8.1.2. Released v5.1.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n017.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 : Wed Aug 30 17:48:35 EDT 2023
% Result : Theorem 2.84s 1.25s
% Output : Proof 4.05s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : ARI618_1 : TPTP v8.1.2. Released v5.1.0.
% 0.13/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.34 % Computer : n017.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 : Tue Aug 29 17:19:28 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.65 ________ _____
% 0.20/0.65 ___ __ \_________(_)________________________________
% 0.20/0.65 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.20/0.65 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.20/0.65 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.20/0.65
% 0.20/0.65 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.65 (2023-06-19)
% 0.20/0.65
% 0.20/0.65 (c) Philipp Rümmer, 2009-2023
% 0.20/0.65 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.65 Amanda Stjerna.
% 0.20/0.65 Free software under BSD-3-Clause.
% 0.20/0.65
% 0.20/0.65 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.65
% 0.20/0.65 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.69/0.66 Running up to 7 provers in parallel.
% 0.69/0.68 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.69/0.68 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.69/0.68 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.69/0.68 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.69/0.68 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.69/0.68 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.69/0.68 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.28/1.07 Prover 1: Preprocessing ...
% 2.28/1.07 Prover 4: Preprocessing ...
% 2.44/1.11 Prover 3: Preprocessing ...
% 2.44/1.11 Prover 0: Preprocessing ...
% 2.44/1.11 Prover 5: Preprocessing ...
% 2.44/1.11 Prover 6: Preprocessing ...
% 2.44/1.12 Prover 2: Preprocessing ...
% 2.84/1.16 Prover 1: Constructing countermodel ...
% 2.84/1.16 Prover 3: Constructing countermodel ...
% 2.84/1.16 Prover 0: Proving ...
% 2.84/1.16 Prover 6: Proving ...
% 2.84/1.16 Prover 4: Constructing countermodel ...
% 2.84/1.17 Prover 5: Proving ...
% 2.84/1.18 Prover 2: Proving ...
% 2.84/1.25 Prover 3: proved (574ms)
% 2.84/1.25
% 2.84/1.25 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.84/1.25
% 2.84/1.25 Prover 0: proved (578ms)
% 2.84/1.25
% 2.84/1.25 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.84/1.25
% 2.84/1.25 Prover 5: stopped
% 2.84/1.26 Prover 2: stopped
% 2.84/1.26 Prover 6: stopped
% 2.84/1.26 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 2.84/1.26 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 2.84/1.26 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 2.84/1.26 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 2.84/1.26 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 2.84/1.27 Prover 7: Preprocessing ...
% 2.84/1.27 Prover 11: Preprocessing ...
% 2.84/1.27 Prover 13: Preprocessing ...
% 3.65/1.28 Prover 8: Preprocessing ...
% 3.65/1.28 Prover 10: Preprocessing ...
% 3.65/1.28 Prover 1: Found proof (size 17)
% 3.65/1.28 Prover 1: proved (610ms)
% 3.65/1.29 Prover 4: Found proof (size 16)
% 3.65/1.29 Prover 4: proved (612ms)
% 3.65/1.29 Prover 11: Constructing countermodel ...
% 3.65/1.29 Prover 11: stopped
% 3.65/1.29 Prover 7: Constructing countermodel ...
% 3.65/1.29 Prover 7: stopped
% 3.65/1.30 Prover 8: Warning: ignoring some quantifiers
% 3.65/1.30 Prover 8: Constructing countermodel ...
% 3.65/1.30 Prover 10: Constructing countermodel ...
% 3.65/1.30 Prover 10: stopped
% 3.65/1.30 Prover 8: stopped
% 3.65/1.30 Prover 13: Warning: ignoring some quantifiers
% 3.65/1.31 Prover 13: Constructing countermodel ...
% 3.65/1.31 Prover 13: stopped
% 3.65/1.31
% 3.65/1.31 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.65/1.31
% 3.65/1.31 % SZS output start Proof for theBenchmark
% 3.65/1.31 Assumptions after simplification:
% 3.65/1.31 ---------------------------------
% 3.65/1.31
% 3.65/1.31 (absolute_value_idempotent)
% 4.05/1.35 ! [v0: int] : ! [v1: int] : ( ~ ($lesseq(1, $difference($product(-1, v1),
% 4.05/1.35 v0))) | ~ (f(v0) = v1)) & ! [v0: int] : ! [v1: int] : ( ~
% 4.05/1.35 ($lesseq(1, $difference(v0, v1))) | ~ (f(v0) = v1)) & ! [v0: int] : !
% 4.05/1.35 [v1: int] : ( ~ ($lesseq(1, $difference(v1, v0))) | ~ ($lesseq(1, $sum(v1,
% 4.05/1.35 v0))) | ~ (f(v0) = v1)) & ? [v0: int] : ? [v1: int] : ? [v2: int]
% 4.05/1.35 : ( ~ (v2 = v1) & f(v1) = v2 & f(v0) = v1)
% 4.05/1.35
% 4.05/1.35 Those formulas are unsatisfiable:
% 4.05/1.35 ---------------------------------
% 4.05/1.35
% 4.05/1.35 Begin of proof
% 4.05/1.35 |
% 4.05/1.35 | ALPHA: (absolute_value_idempotent) implies:
% 4.05/1.35 | (1) ! [v0: int] : ! [v1: int] : ( ~ ($lesseq(1, $difference(v1, v0))) |
% 4.05/1.35 | ~ ($lesseq(1, $sum(v1, v0))) | ~ (f(v0) = v1))
% 4.05/1.35 | (2) ! [v0: int] : ! [v1: int] : ( ~ ($lesseq(1, $difference(v0, v1))) |
% 4.05/1.35 | ~ (f(v0) = v1))
% 4.05/1.36 | (3) ! [v0: int] : ! [v1: int] : ( ~ ($lesseq(1, $difference($product(-1,
% 4.05/1.36 | v1), v0))) | ~ (f(v0) = v1))
% 4.05/1.36 | (4) ? [v0: int] : ? [v1: int] : ? [v2: int] : ( ~ (v2 = v1) & f(v1) = v2
% 4.05/1.36 | & f(v0) = v1)
% 4.05/1.36 |
% 4.05/1.36 | DELTA: instantiating (4) with fresh symbols all_4_0, all_4_1, all_4_2 gives:
% 4.05/1.36 | (5) ~ (all_4_0 = all_4_1) & f(all_4_1) = all_4_0 & f(all_4_2) = all_4_1
% 4.05/1.36 |
% 4.05/1.36 | ALPHA: (5) implies:
% 4.05/1.36 | (6) ~ (all_4_0 = all_4_1)
% 4.05/1.36 | (7) f(all_4_2) = all_4_1
% 4.05/1.36 | (8) f(all_4_1) = all_4_0
% 4.05/1.36 |
% 4.05/1.36 | GROUND_INST: instantiating (3) with all_4_2, all_4_1, simplifying with (7)
% 4.05/1.36 | gives:
% 4.05/1.36 | (9) $lesseq(0, $sum(all_4_1, all_4_2))
% 4.05/1.36 |
% 4.05/1.36 | GROUND_INST: instantiating (2) with all_4_2, all_4_1, simplifying with (7)
% 4.05/1.36 | gives:
% 4.05/1.36 | (10) $lesseq(all_4_2, all_4_1)
% 4.05/1.36 |
% 4.05/1.36 | GROUND_INST: instantiating (2) with all_4_1, all_4_0, simplifying with (8)
% 4.05/1.36 | gives:
% 4.05/1.36 | (11) $lesseq(all_4_1, all_4_0)
% 4.05/1.36 |
% 4.05/1.36 | GROUND_INST: instantiating (1) with all_4_1, all_4_0, simplifying with (8)
% 4.05/1.36 | gives:
% 4.05/1.36 | (12) ~ ($lesseq(1, $difference(all_4_0, all_4_1))) | ~ ($lesseq(1,
% 4.05/1.36 | $sum(all_4_0, all_4_1)))
% 4.05/1.36 |
% 4.05/1.37 | STRENGTHEN: (6), (11) imply:
% 4.05/1.37 | (13) $lesseq(1, $difference(all_4_0, all_4_1))
% 4.05/1.37 |
% 4.05/1.37 | BETA: splitting (12) gives:
% 4.05/1.37 |
% 4.05/1.37 | Case 1:
% 4.05/1.37 | |
% 4.05/1.37 | | (14) $lesseq(all_4_0, all_4_1)
% 4.05/1.37 | |
% 4.05/1.37 | | COMBINE_INEQS: (13), (14) imply:
% 4.05/1.37 | | (15) $false
% 4.05/1.37 | |
% 4.05/1.37 | | CLOSE: (15) is inconsistent.
% 4.05/1.37 | |
% 4.05/1.37 | Case 2:
% 4.05/1.37 | |
% 4.05/1.37 | | (16) $lesseq(all_4_1, $product(-1, all_4_0))
% 4.05/1.37 | |
% 4.05/1.37 | | COMBINE_INEQS: (13), (16) imply:
% 4.05/1.37 | | (17) $lesseq(all_4_1, -1)
% 4.05/1.37 | |
% 4.05/1.37 | | SIMP: (17) implies:
% 4.05/1.37 | | (18) $lesseq(all_4_1, -1)
% 4.05/1.37 | |
% 4.05/1.37 | | COMBINE_INEQS: (10), (18) imply:
% 4.05/1.37 | | (19) $lesseq(all_4_2, -1)
% 4.05/1.37 | |
% 4.05/1.37 | | COMBINE_INEQS: (9), (18) imply:
% 4.05/1.37 | | (20) $lesseq(1, all_4_2)
% 4.05/1.37 | |
% 4.05/1.37 | | COMBINE_INEQS: (19), (20) imply:
% 4.05/1.37 | | (21) $false
% 4.05/1.37 | |
% 4.05/1.37 | | CLOSE: (21) is inconsistent.
% 4.05/1.37 | |
% 4.05/1.37 | End of split
% 4.05/1.37 |
% 4.05/1.37 End of proof
% 4.05/1.37 % SZS output end Proof for theBenchmark
% 4.05/1.37
% 4.05/1.37 718ms
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