TSTP Solution File: ARI669_1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : ARI669_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 17:48:45 EDT 2023
% Result : Theorem 3.56s 1.30s
% Output : Proof 4.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ARI669_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 18:28:30 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
% 0.20/0.63 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.20/0.64 Running up to 7 provers in parallel.
% 0.20/0.66 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.66 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.66 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.66 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.66 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.20/0.66 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.66 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 1.92/1.01 Prover 1: Preprocessing ...
% 1.92/1.01 Prover 6: Preprocessing ...
% 1.92/1.01 Prover 0: Preprocessing ...
% 1.92/1.01 Prover 5: Preprocessing ...
% 1.92/1.01 Prover 4: Preprocessing ...
% 1.92/1.01 Prover 2: Preprocessing ...
% 1.92/1.01 Prover 3: Preprocessing ...
% 2.41/1.07 Prover 5: Constructing countermodel ...
% 2.41/1.07 Prover 6: Constructing countermodel ...
% 2.41/1.07 Prover 4: Constructing countermodel ...
% 2.41/1.07 Prover 2: Constructing countermodel ...
% 2.41/1.07 Prover 0: Constructing countermodel ...
% 2.41/1.07 Prover 3: Constructing countermodel ...
% 2.41/1.07 Prover 1: Constructing countermodel ...
% 3.56/1.30 Prover 3: proved (645ms)
% 3.56/1.30 Prover 2: proved (656ms)
% 3.56/1.30
% 3.56/1.30 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.56/1.30
% 3.56/1.31
% 3.56/1.31 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.56/1.31
% 3.56/1.31 Prover 0: stopped
% 3.56/1.31 Prover 5: stopped
% 3.56/1.31 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 3.56/1.31 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 3.56/1.31 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 3.56/1.31 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 3.56/1.31 Prover 6: stopped
% 3.56/1.32 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 3.56/1.32 Prover 8: Preprocessing ...
% 3.56/1.32 Prover 10: Preprocessing ...
% 3.56/1.32 Prover 8: Constructing countermodel ...
% 3.56/1.32 Prover 7: Preprocessing ...
% 3.56/1.32 Prover 13: Preprocessing ...
% 3.56/1.33 Prover 10: Constructing countermodel ...
% 4.22/1.33 Prover 7: Constructing countermodel ...
% 4.22/1.33 Prover 13: Constructing countermodel ...
% 4.22/1.34 Prover 11: Preprocessing ...
% 4.22/1.36 Prover 11: Constructing countermodel ...
% 4.22/1.39 Prover 4: Found proof (size 34)
% 4.22/1.39 Prover 4: proved (726ms)
% 4.22/1.39 Prover 13: stopped
% 4.22/1.39 Prover 11: stopped
% 4.22/1.39 Prover 10: stopped
% 4.22/1.39 Prover 8: stopped
% 4.22/1.39 Prover 1: Found proof (size 34)
% 4.22/1.39 Prover 1: proved (743ms)
% 4.22/1.39 Prover 7: stopped
% 4.22/1.39
% 4.22/1.39 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.22/1.39
% 4.22/1.39 % SZS output start Proof for theBenchmark
% 4.22/1.40 Assumptions after simplification:
% 4.22/1.40 ---------------------------------
% 4.22/1.40
% 4.22/1.40 (conj)
% 4.22/1.41 ? [v0: int] : ? [v1: int] : ? [v2: int] : ($product(v1, c) = v2 &
% 4.22/1.41 $product(v0, b) = v1 & $product(a, b) = v0 & ((v2 = 0 & ~ (c = 0) & ~ (b =
% 4.22/1.41 0) & ~ (a = 0)) | ( ~ (v2 = 0) & (c = 0 | b = 0 | a = 0))))
% 4.22/1.41
% 4.22/1.41 Those formulas are unsatisfiable:
% 4.22/1.41 ---------------------------------
% 4.22/1.41
% 4.22/1.41 Begin of proof
% 4.22/1.41 |
% 4.22/1.41 | DELTA: instantiating (conj) with fresh symbols all_2_0, all_2_1, all_2_2
% 4.22/1.41 | gives:
% 4.22/1.41 | (1) $product(all_2_1, c) = all_2_0 & $product(all_2_2, b) = all_2_1 &
% 4.22/1.41 | $product(a, b) = all_2_2 & ((all_2_0 = 0 & ~ (c = 0) & ~ (b = 0) & ~
% 4.22/1.41 | (a = 0)) | ( ~ (all_2_0 = 0) & (c = 0 | b = 0 | a = 0)))
% 4.22/1.41 |
% 4.22/1.41 | ALPHA: (1) implies:
% 4.22/1.41 | (2) $product(a, b) = all_2_2
% 4.22/1.41 | (3) $product(all_2_2, b) = all_2_1
% 4.22/1.41 | (4) $product(all_2_1, c) = all_2_0
% 4.22/1.41 | (5) (all_2_0 = 0 & ~ (c = 0) & ~ (b = 0) & ~ (a = 0)) | ( ~ (all_2_0 =
% 4.22/1.41 | 0) & (c = 0 | b = 0 | a = 0))
% 4.22/1.41 |
% 4.22/1.42 | BETA: splitting (5) gives:
% 4.22/1.42 |
% 4.22/1.42 | Case 1:
% 4.22/1.42 | |
% 4.22/1.42 | | (6) all_2_0 = 0 & ~ (c = 0) & ~ (b = 0) & ~ (a = 0)
% 4.22/1.42 | |
% 4.22/1.42 | | ALPHA: (6) implies:
% 4.22/1.42 | | (7) all_2_0 = 0
% 4.22/1.42 | | (8) ~ (a = 0)
% 4.22/1.42 | | (9) ~ (b = 0)
% 4.22/1.42 | | (10) ~ (c = 0)
% 4.22/1.42 | |
% 4.22/1.42 | | REDUCE: (4), (7) imply:
% 4.22/1.42 | | (11) $product(all_2_1, c) = 0
% 4.22/1.42 | |
% 4.22/1.42 | | THEORY_AXIOM GroebnerMultiplication:
% 4.22/1.42 | | (12) ! [v0: int] : ! [v1: int] : ! [v2: int] : ! [v3: int] : ! [v4:
% 4.22/1.42 | | int] : (v2 = 0 | v1 = 0 | v0 = 0 | ~ ($product(v4, v2) = 0) | ~
% 4.22/1.42 | | ($product(v3, v1) = v4) | ~ ($product(v0, v1) = v3))
% 4.22/1.42 | |
% 4.22/1.42 | | GROUND_INST: instantiating (12) with a, b, c, all_2_2, all_2_1, simplifying
% 4.22/1.42 | | with (2), (3), (11) gives:
% 4.22/1.42 | | (13) c = 0 | b = 0 | a = 0
% 4.22/1.42 | |
% 4.22/1.42 | | BETA: splitting (13) gives:
% 4.22/1.42 | |
% 4.22/1.42 | | Case 1:
% 4.22/1.42 | | |
% 4.22/1.42 | | | (14) b = 0
% 4.22/1.42 | | |
% 4.22/1.42 | | | REDUCE: (9), (14) imply:
% 4.22/1.42 | | | (15) $false
% 4.22/1.42 | | |
% 4.22/1.42 | | | CLOSE: (15) is inconsistent.
% 4.22/1.42 | | |
% 4.22/1.42 | | Case 2:
% 4.22/1.42 | | |
% 4.22/1.42 | | | (16) c = 0 | a = 0
% 4.22/1.42 | | |
% 4.22/1.42 | | | BETA: splitting (16) gives:
% 4.22/1.42 | | |
% 4.22/1.42 | | | Case 1:
% 4.22/1.42 | | | |
% 4.22/1.42 | | | | (17) c = 0
% 4.22/1.42 | | | |
% 4.22/1.42 | | | | REDUCE: (10), (17) imply:
% 4.22/1.42 | | | | (18) $false
% 4.22/1.42 | | | |
% 4.22/1.42 | | | | CLOSE: (18) is inconsistent.
% 4.22/1.42 | | | |
% 4.22/1.42 | | | Case 2:
% 4.22/1.42 | | | |
% 4.22/1.42 | | | | (19) a = 0
% 4.22/1.42 | | | |
% 4.22/1.42 | | | | REDUCE: (8), (19) imply:
% 4.22/1.42 | | | | (20) $false
% 4.22/1.42 | | | |
% 4.22/1.42 | | | | CLOSE: (20) is inconsistent.
% 4.22/1.42 | | | |
% 4.22/1.42 | | | End of split
% 4.22/1.42 | | |
% 4.22/1.42 | | End of split
% 4.22/1.42 | |
% 4.22/1.42 | Case 2:
% 4.22/1.42 | |
% 4.22/1.42 | | (21) ~ (all_2_0 = 0) & (c = 0 | b = 0 | a = 0)
% 4.22/1.42 | |
% 4.22/1.42 | | ALPHA: (21) implies:
% 4.22/1.43 | | (22) ~ (all_2_0 = 0)
% 4.22/1.43 | | (23) c = 0 | b = 0 | a = 0
% 4.22/1.43 | |
% 4.22/1.43 | | BETA: splitting (23) gives:
% 4.22/1.43 | |
% 4.22/1.43 | | Case 1:
% 4.22/1.43 | | |
% 4.22/1.43 | | | (24) b = 0
% 4.22/1.43 | | |
% 4.22/1.43 | | | REDUCE: (3), (24) imply:
% 4.22/1.43 | | | (25) $product(all_2_2, 0) = all_2_1
% 4.22/1.43 | | |
% 4.22/1.43 | | | THEORY_AXIOM GroebnerMultiplication:
% 4.22/1.43 | | | (26) ! [v0: int] : ! [v1: int] : ! [v2: int] : ! [v3: int] : (v3 =
% 4.22/1.43 | | | 0 | ~ ($product(v2, v0) = v3) | ~ ($product(v1, 0) = v2))
% 4.22/1.43 | | |
% 4.22/1.43 | | | GROUND_INST: instantiating (26) with c, all_2_2, all_2_1, all_2_0,
% 4.22/1.43 | | | simplifying with (4), (25) gives:
% 4.22/1.43 | | | (27) all_2_0 = 0
% 4.22/1.43 | | |
% 4.22/1.43 | | | REDUCE: (22), (27) imply:
% 4.22/1.43 | | | (28) $false
% 4.22/1.43 | | |
% 4.22/1.43 | | | CLOSE: (28) is inconsistent.
% 4.22/1.43 | | |
% 4.22/1.43 | | Case 2:
% 4.22/1.43 | | |
% 4.22/1.43 | | | (29) c = 0 | a = 0
% 4.22/1.43 | | |
% 4.22/1.43 | | | BETA: splitting (29) gives:
% 4.22/1.43 | | |
% 4.22/1.43 | | | Case 1:
% 4.22/1.43 | | | |
% 4.22/1.43 | | | | (30) c = 0
% 4.22/1.43 | | | |
% 4.22/1.43 | | | | REDUCE: (4), (30) imply:
% 4.22/1.43 | | | | (31) $product(all_2_1, 0) = all_2_0
% 4.22/1.43 | | | |
% 4.22/1.43 | | | | THEORY_AXIOM GroebnerMultiplication:
% 4.22/1.43 | | | | (32) ! [v0: int] : ! [v1: int] : (v1 = 0 | ~ ($product(v0, 0) =
% 4.22/1.43 | | | | v1))
% 4.22/1.43 | | | |
% 4.22/1.43 | | | | GROUND_INST: instantiating (32) with all_2_1, all_2_0, simplifying with
% 4.22/1.43 | | | | (31) gives:
% 4.22/1.43 | | | | (33) all_2_0 = 0
% 4.22/1.43 | | | |
% 4.22/1.43 | | | | REDUCE: (22), (33) imply:
% 4.22/1.43 | | | | (34) $false
% 4.22/1.43 | | | |
% 4.22/1.43 | | | | CLOSE: (34) is inconsistent.
% 4.22/1.43 | | | |
% 4.22/1.43 | | | Case 2:
% 4.22/1.43 | | | |
% 4.22/1.43 | | | | (35) a = 0
% 4.22/1.43 | | | |
% 4.22/1.43 | | | | REDUCE: (2), (35) imply:
% 4.22/1.43 | | | | (36) $product(0, b) = all_2_2
% 4.22/1.43 | | | |
% 4.22/1.43 | | | | THEORY_AXIOM GroebnerMultiplication:
% 4.22/1.43 | | | | (37) ! [v0: int] : ! [v1: int] : ! [v2: int] : ! [v3: int] : !
% 4.22/1.43 | | | | [v4: int] : (v4 = 0 | ~ ($product(v3, v1) = v4) | ~
% 4.22/1.43 | | | | ($product(v2, v0) = v3) | ~ ($product(0, v0) = v2))
% 4.22/1.43 | | | |
% 4.22/1.43 | | | | GROUND_INST: instantiating (37) with b, c, all_2_2, all_2_1, all_2_0,
% 4.22/1.43 | | | | simplifying with (3), (4), (36) gives:
% 4.22/1.43 | | | | (38) all_2_0 = 0
% 4.22/1.43 | | | |
% 4.22/1.43 | | | | REDUCE: (22), (38) imply:
% 4.22/1.43 | | | | (39) $false
% 4.22/1.43 | | | |
% 4.22/1.43 | | | | CLOSE: (39) is inconsistent.
% 4.22/1.43 | | | |
% 4.22/1.43 | | | End of split
% 4.22/1.43 | | |
% 4.22/1.43 | | End of split
% 4.22/1.43 | |
% 4.22/1.43 | End of split
% 4.22/1.43 |
% 4.22/1.43 End of proof
% 4.22/1.43 % SZS output end Proof for theBenchmark
% 4.22/1.43
% 4.22/1.43 807ms
%------------------------------------------------------------------------------