TSTP Solution File: ARI673_1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : ARI673_1 : TPTP v8.1.2. Released v6.3.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n014.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 17:48:46 EDT 2023
% Result : Theorem 3.51s 1.25s
% Output : Proof 3.94s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : ARI673_1 : TPTP v8.1.2. Released v6.3.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.35 % Computer : n014.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 : Tue Aug 29 18:26:29 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.62 ________ _____
% 0.20/0.62 ___ __ \_________(_)________________________________
% 0.20/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.20/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.20/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.20/0.62
% 0.20/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.62 (2023-06-19)
% 0.20/0.62
% 0.20/0.62 (c) Philipp Rümmer, 2009-2023
% 0.20/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.62 Amanda Stjerna.
% 0.20/0.62 Free software under BSD-3-Clause.
% 0.20/0.62
% 0.20/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.62
% 0.20/0.62 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.20/0.63 Running up to 7 provers in parallel.
% 0.20/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.20/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 1.97/1.03 Prover 0: Preprocessing ...
% 1.97/1.03 Prover 2: Preprocessing ...
% 1.97/1.03 Prover 1: Preprocessing ...
% 1.97/1.03 Prover 3: Preprocessing ...
% 1.97/1.03 Prover 4: Preprocessing ...
% 1.97/1.03 Prover 6: Preprocessing ...
% 1.97/1.04 Prover 5: Preprocessing ...
% 2.45/1.09 Prover 5: Constructing countermodel ...
% 2.45/1.09 Prover 4: Constructing countermodel ...
% 2.45/1.09 Prover 3: Constructing countermodel ...
% 2.45/1.09 Prover 2: Constructing countermodel ...
% 2.45/1.09 Prover 1: Constructing countermodel ...
% 2.45/1.09 Prover 0: Constructing countermodel ...
% 2.45/1.09 Prover 6: Constructing countermodel ...
% 3.51/1.25 Prover 3: proved (612ms)
% 3.51/1.25 Prover 2: proved (612ms)
% 3.51/1.25 Prover 5: proved (609ms)
% 3.51/1.25
% 3.51/1.25 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.51/1.25
% 3.51/1.25
% 3.51/1.25 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.51/1.25
% 3.51/1.25
% 3.51/1.25 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.51/1.25
% 3.51/1.26 Prover 6: stopped
% 3.51/1.26 Prover 0: stopped
% 3.51/1.26 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 3.51/1.26 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 3.51/1.26 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 3.51/1.26 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 3.51/1.26 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 3.51/1.27 Prover 11: Preprocessing ...
% 3.51/1.27 Prover 7: Preprocessing ...
% 3.51/1.27 Prover 13: Preprocessing ...
% 3.51/1.27 Prover 8: Preprocessing ...
% 3.51/1.27 Prover 10: Preprocessing ...
% 3.51/1.28 Prover 7: Constructing countermodel ...
% 3.51/1.28 Prover 8: Constructing countermodel ...
% 3.51/1.28 Prover 10: Constructing countermodel ...
% 3.51/1.29 Prover 11: Constructing countermodel ...
% 3.51/1.29 Prover 13: Constructing countermodel ...
% 3.51/1.29 Prover 4: Found proof (size 28)
% 3.51/1.29 Prover 4: proved (654ms)
% 3.51/1.29 Prover 1: stopped
% 3.94/1.29 Prover 11: stopped
% 3.94/1.29 Prover 8: stopped
% 3.94/1.29 Prover 13: stopped
% 3.94/1.29 Prover 7: stopped
% 3.94/1.30 Prover 10: stopped
% 3.94/1.30
% 3.94/1.30 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.94/1.30
% 3.94/1.30 % SZS output start Proof for theBenchmark
% 3.94/1.31 Assumptions after simplification:
% 3.94/1.31 ---------------------------------
% 3.94/1.31
% 3.94/1.31 (conj)
% 3.94/1.31 ? [v0: int] : ($product(a, a) = v0 & ((v0 = 1 & ~ (a = 1) & ~ (a = -1)) | (
% 3.94/1.31 ~ (v0 = 1) & (a = 1 | a = -1))))
% 3.94/1.31
% 3.94/1.31 Those formulas are unsatisfiable:
% 3.94/1.31 ---------------------------------
% 3.94/1.32
% 3.94/1.32 Begin of proof
% 3.94/1.32 |
% 3.94/1.32 | DELTA: instantiating (conj) with fresh symbol all_2_0 gives:
% 3.94/1.32 | (1) $product(a, a) = all_2_0 & ((all_2_0 = 1 & ~ (a = 1) & ~ (a = -1)) |
% 3.94/1.32 | ( ~ (all_2_0 = 1) & (a = 1 | a = -1)))
% 3.94/1.32 |
% 3.94/1.32 | ALPHA: (1) implies:
% 3.94/1.32 | (2) $product(a, a) = all_2_0
% 3.94/1.32 | (3) (all_2_0 = 1 & ~ (a = 1) & ~ (a = -1)) | ( ~ (all_2_0 = 1) & (a = 1 |
% 3.94/1.32 | a = -1))
% 3.94/1.32 |
% 3.94/1.32 | BETA: splitting (3) gives:
% 3.94/1.32 |
% 3.94/1.32 | Case 1:
% 3.94/1.32 | |
% 3.94/1.32 | | (4) all_2_0 = 1 & ~ (a = 1) & ~ (a = -1)
% 3.94/1.32 | |
% 3.94/1.32 | | ALPHA: (4) implies:
% 3.94/1.32 | | (5) all_2_0 = 1
% 3.94/1.32 | | (6) ~ (a = -1)
% 3.94/1.32 | | (7) ~ (a = 1)
% 3.94/1.32 | |
% 3.94/1.32 | | REDUCE: (2), (5) imply:
% 3.94/1.32 | | (8) $product(a, a) = 1
% 3.94/1.32 | |
% 3.94/1.33 | | THEORY_AXIOM GroebnerMultiplication:
% 3.94/1.33 | | (9) ! [v0: int] : ( ~ ($lesseq(v0, -2)) | ~ ($product(v0, v0) = 1))
% 3.94/1.33 | |
% 3.94/1.33 | | GROUND_INST: instantiating (9) with a, simplifying with (8) gives:
% 3.94/1.33 | | (10) $lesseq(-1, a)
% 3.94/1.33 | |
% 3.94/1.33 | | THEORY_AXIOM GroebnerMultiplication:
% 3.94/1.33 | | (11) ! [v0: int] : ( ~ ($lesseq(2, v0)) | ~ ($product(v0, v0) = 1))
% 3.94/1.33 | |
% 3.94/1.33 | | GROUND_INST: instantiating (11) with a, simplifying with (8) gives:
% 3.94/1.33 | | (12) $lesseq(a, 1)
% 3.94/1.33 | |
% 3.94/1.33 | | STRENGTHEN: (7), (12) imply:
% 3.94/1.33 | | (13) $lesseq(a, 0)
% 3.94/1.33 | |
% 3.94/1.33 | | STRENGTHEN: (6), (10) imply:
% 3.94/1.33 | | (14) $lesseq(0, a)
% 3.94/1.33 | |
% 3.94/1.33 | | ANTI_SYMM: (13), (14) imply:
% 3.94/1.33 | | (15) a = 0
% 3.94/1.33 | |
% 3.94/1.33 | | REDUCE: (8), (15) imply:
% 3.94/1.33 | | (16) $product(0, 0) = 1
% 3.94/1.33 | |
% 3.94/1.33 | | THEORY_AXIOM GroebnerMultiplication:
% 3.94/1.33 | | (17) ~ ($product(0, 0) = 1)
% 3.94/1.33 | |
% 3.94/1.33 | | PRED_UNIFY: (16), (17) imply:
% 3.94/1.33 | | (18) $false
% 3.94/1.34 | |
% 3.94/1.34 | | CLOSE: (18) is inconsistent.
% 3.94/1.34 | |
% 3.94/1.34 | Case 2:
% 3.94/1.34 | |
% 3.94/1.34 | | (19) ~ (all_2_0 = 1) & (a = 1 | a = -1)
% 3.94/1.34 | |
% 3.94/1.34 | | ALPHA: (19) implies:
% 3.94/1.34 | | (20) ~ (all_2_0 = 1)
% 3.94/1.34 | | (21) a = 1 | a = -1
% 3.94/1.34 | |
% 3.94/1.34 | | BETA: splitting (21) gives:
% 3.94/1.34 | |
% 3.94/1.34 | | Case 1:
% 3.94/1.34 | | |
% 3.94/1.34 | | | (22) a = 1
% 3.94/1.34 | | |
% 3.94/1.34 | | | REDUCE: (2), (22) imply:
% 3.94/1.34 | | | (23) $product(1, 1) = all_2_0
% 3.94/1.34 | | |
% 3.94/1.34 | | | THEORY_AXIOM GroebnerMultiplication:
% 3.94/1.34 | | | (24) ! [v0: int] : (v0 = 1 | ~ ($product(1, 1) = v0))
% 3.94/1.34 | | |
% 3.94/1.34 | | | GROUND_INST: instantiating (24) with all_2_0, simplifying with (23) gives:
% 3.94/1.34 | | | (25) all_2_0 = 1
% 3.94/1.34 | | |
% 3.94/1.34 | | | REDUCE: (20), (25) imply:
% 3.94/1.34 | | | (26) $false
% 3.94/1.34 | | |
% 3.94/1.34 | | | CLOSE: (26) is inconsistent.
% 3.94/1.34 | | |
% 3.94/1.34 | | Case 2:
% 3.94/1.34 | | |
% 3.94/1.34 | | | (27) a = -1
% 3.94/1.34 | | |
% 3.94/1.34 | | | REDUCE: (2), (27) imply:
% 3.94/1.34 | | | (28) $product(-1, -1) = all_2_0
% 3.94/1.34 | | |
% 3.94/1.34 | | | THEORY_AXIOM GroebnerMultiplication:
% 3.94/1.34 | | | (29) ! [v0: int] : (v0 = 1 | ~ ($product(-1, -1) = v0))
% 3.94/1.34 | | |
% 3.94/1.34 | | | GROUND_INST: instantiating (29) with all_2_0, simplifying with (28) gives:
% 3.94/1.34 | | | (30) all_2_0 = 1
% 3.94/1.34 | | |
% 3.94/1.35 | | | REDUCE: (20), (30) imply:
% 3.94/1.35 | | | (31) $false
% 3.94/1.35 | | |
% 3.94/1.35 | | | CLOSE: (31) is inconsistent.
% 3.94/1.35 | | |
% 3.94/1.35 | | End of split
% 3.94/1.35 | |
% 3.94/1.35 | End of split
% 3.94/1.35 |
% 3.94/1.35 End of proof
% 3.94/1.35 % SZS output end Proof for theBenchmark
% 3.94/1.35
% 3.94/1.35 727ms
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