TSTP Solution File: SYN922+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SYN922+1 : TPTP v8.1.2. Released v3.1.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n023.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 03:29:13 EDT 2023
% Result : Theorem 3.36s 1.14s
% Output : Proof 3.85s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SYN922+1 : TPTP v8.1.2. Released v3.1.0.
% 0.06/0.12 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.12/0.33 % Computer : n023.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Sat Aug 26 20:33:26 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.52/0.60 ________ _____
% 0.52/0.60 ___ __ \_________(_)________________________________
% 0.52/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.52/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.52/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.52/0.60
% 0.52/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.52/0.60 (2023-06-19)
% 0.52/0.60
% 0.52/0.60 (c) Philipp Rümmer, 2009-2023
% 0.52/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.52/0.60 Amanda Stjerna.
% 0.52/0.60 Free software under BSD-3-Clause.
% 0.52/0.60
% 0.52/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.52/0.60
% 0.52/0.60 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.52/0.62 Running up to 7 provers in parallel.
% 0.52/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.52/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.52/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.52/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.52/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.52/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 0.52/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 1.53/0.92 Prover 1: Preprocessing ...
% 1.53/0.92 Prover 4: Preprocessing ...
% 2.04/0.96 Prover 0: Preprocessing ...
% 2.04/0.96 Prover 5: Preprocessing ...
% 2.04/0.96 Prover 6: Preprocessing ...
% 2.04/0.96 Prover 3: Preprocessing ...
% 2.04/0.96 Prover 2: Preprocessing ...
% 2.28/1.02 Prover 5: Proving ...
% 2.28/1.02 Prover 2: Proving ...
% 2.28/1.02 Prover 0: Proving ...
% 2.28/1.02 Prover 1: Constructing countermodel ...
% 2.28/1.02 Prover 3: Constructing countermodel ...
% 2.28/1.02 Prover 4: Constructing countermodel ...
% 2.28/1.02 Prover 6: Proving ...
% 3.36/1.13 Prover 3: proved (504ms)
% 3.36/1.13
% 3.36/1.14 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.36/1.14
% 3.36/1.14 Prover 5: stopped
% 3.36/1.14 Prover 0: proved (514ms)
% 3.36/1.14
% 3.36/1.14 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.36/1.14
% 3.36/1.14 Prover 2: proved (513ms)
% 3.36/1.14
% 3.36/1.14 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.36/1.14
% 3.36/1.14 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 3.36/1.14 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 3.36/1.14 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 3.36/1.15 Prover 6: stopped
% 3.36/1.15 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 3.36/1.15 Prover 7: Preprocessing ...
% 3.36/1.15 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 3.36/1.15 Prover 8: Preprocessing ...
% 3.36/1.15 Prover 10: Preprocessing ...
% 3.36/1.15 Prover 11: Preprocessing ...
% 3.36/1.15 Prover 7: Warning: ignoring some quantifiers
% 3.36/1.15 Prover 7: Constructing countermodel ...
% 3.36/1.16 Prover 4: Found proof (size 20)
% 3.36/1.16 Prover 4: proved (532ms)
% 3.36/1.16 Prover 13: Preprocessing ...
% 3.36/1.16 Prover 10: Warning: ignoring some quantifiers
% 3.36/1.16 Prover 10: Constructing countermodel ...
% 3.36/1.16 Prover 1: Found proof (size 22)
% 3.36/1.16 Prover 1: proved (539ms)
% 3.36/1.16 Prover 10: stopped
% 3.36/1.16 Prover 7: stopped
% 3.61/1.17 Prover 13: Warning: ignoring some quantifiers
% 3.61/1.17 Prover 13: Constructing countermodel ...
% 3.61/1.17 Prover 13: stopped
% 3.61/1.18 Prover 11: Constructing countermodel ...
% 3.61/1.18 Prover 8: Warning: ignoring some quantifiers
% 3.61/1.18 Prover 11: stopped
% 3.61/1.18 Prover 8: Constructing countermodel ...
% 3.61/1.18 Prover 8: stopped
% 3.61/1.18
% 3.61/1.18 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.61/1.18
% 3.61/1.19 % SZS output start Proof for theBenchmark
% 3.61/1.19 Assumptions after simplification:
% 3.61/1.19 ---------------------------------
% 3.61/1.19
% 3.61/1.19 (prove_this)
% 3.85/1.23 ? [v0: $i] : ? [v1: any] : ? [v2: any] : ? [v3: $i] : ? [v4: int] : ?
% 3.85/1.23 [v5: $i] : ? [v6: int] : ($i(v5) & $i(v3) & $i(v0) & ! [v7: $i] : ! [v8:
% 3.85/1.23 int] : (v8 = 0 | ~ (q(v7) = v8) | ~ $i(v7)) & ! [v7: $i] : ! [v8: int]
% 3.85/1.23 : (v8 = 0 | ~ (p(v7) = v8) | ~ $i(v7)) & (( ~ (v6 = 0) & p(v5) = v6) | ( ~
% 3.85/1.23 (v4 = 0) & q(v3) = v4) | (q(v0) = v2 & p(v0) = v1 & ( ~ (v2 = 0) | ~
% 3.85/1.23 (v1 = 0)))))
% 3.85/1.23
% 3.85/1.23 Those formulas are unsatisfiable:
% 3.85/1.23 ---------------------------------
% 3.85/1.23
% 3.85/1.23 Begin of proof
% 3.85/1.24 |
% 3.85/1.24 | DELTA: instantiating (prove_this) with fresh symbols all_3_0, all_3_1,
% 3.85/1.24 | all_3_2, all_3_3, all_3_4, all_3_5, all_3_6 gives:
% 3.85/1.24 | (1) $i(all_3_1) & $i(all_3_3) & $i(all_3_6) & ! [v0: $i] : ! [v1: int] :
% 3.85/1.24 | (v1 = 0 | ~ (q(v0) = v1) | ~ $i(v0)) & ! [v0: $i] : ! [v1: int] :
% 3.85/1.24 | (v1 = 0 | ~ (p(v0) = v1) | ~ $i(v0)) & (( ~ (all_3_0 = 0) &
% 3.85/1.24 | p(all_3_1) = all_3_0) | ( ~ (all_3_2 = 0) & q(all_3_3) = all_3_2) |
% 3.85/1.24 | (q(all_3_6) = all_3_4 & p(all_3_6) = all_3_5 & ( ~ (all_3_4 = 0) | ~
% 3.85/1.24 | (all_3_5 = 0))))
% 3.85/1.24 |
% 3.85/1.24 | ALPHA: (1) implies:
% 3.85/1.24 | (2) $i(all_3_6)
% 3.85/1.24 | (3) $i(all_3_3)
% 3.85/1.24 | (4) $i(all_3_1)
% 3.85/1.24 | (5) ( ~ (all_3_0 = 0) & p(all_3_1) = all_3_0) | ( ~ (all_3_2 = 0) &
% 3.85/1.24 | q(all_3_3) = all_3_2) | (q(all_3_6) = all_3_4 & p(all_3_6) = all_3_5
% 3.85/1.24 | & ( ~ (all_3_4 = 0) | ~ (all_3_5 = 0)))
% 3.85/1.25 | (6) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (p(v0) = v1) | ~ $i(v0))
% 3.85/1.25 | (7) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (q(v0) = v1) | ~ $i(v0))
% 3.85/1.25 |
% 3.85/1.25 | BETA: splitting (5) gives:
% 3.85/1.25 |
% 3.85/1.25 | Case 1:
% 3.85/1.25 | |
% 3.85/1.25 | | (8) ~ (all_3_0 = 0) & p(all_3_1) = all_3_0
% 3.85/1.25 | |
% 3.85/1.25 | | ALPHA: (8) implies:
% 3.85/1.25 | | (9) ~ (all_3_0 = 0)
% 3.85/1.25 | | (10) p(all_3_1) = all_3_0
% 3.85/1.25 | |
% 3.85/1.25 | | GROUND_INST: instantiating (6) with all_3_1, all_3_0, simplifying with (4),
% 3.85/1.25 | | (10) gives:
% 3.85/1.25 | | (11) all_3_0 = 0
% 3.85/1.25 | |
% 3.85/1.25 | | REDUCE: (9), (11) imply:
% 3.85/1.25 | | (12) $false
% 3.85/1.25 | |
% 3.85/1.25 | | CLOSE: (12) is inconsistent.
% 3.85/1.25 | |
% 3.85/1.25 | Case 2:
% 3.85/1.25 | |
% 3.85/1.25 | | (13) ( ~ (all_3_2 = 0) & q(all_3_3) = all_3_2) | (q(all_3_6) = all_3_4 &
% 3.85/1.25 | | p(all_3_6) = all_3_5 & ( ~ (all_3_4 = 0) | ~ (all_3_5 = 0)))
% 3.85/1.25 | |
% 3.85/1.25 | | BETA: splitting (13) gives:
% 3.85/1.25 | |
% 3.85/1.25 | | Case 1:
% 3.85/1.25 | | |
% 3.85/1.25 | | | (14) ~ (all_3_2 = 0) & q(all_3_3) = all_3_2
% 3.85/1.25 | | |
% 3.85/1.25 | | | ALPHA: (14) implies:
% 3.85/1.25 | | | (15) ~ (all_3_2 = 0)
% 3.85/1.25 | | | (16) q(all_3_3) = all_3_2
% 3.85/1.25 | | |
% 3.85/1.25 | | | GROUND_INST: instantiating (7) with all_3_3, all_3_2, simplifying with
% 3.85/1.25 | | | (3), (16) gives:
% 3.85/1.25 | | | (17) all_3_2 = 0
% 3.85/1.25 | | |
% 3.85/1.25 | | | REDUCE: (15), (17) imply:
% 3.85/1.25 | | | (18) $false
% 3.85/1.25 | | |
% 3.85/1.25 | | | CLOSE: (18) is inconsistent.
% 3.85/1.25 | | |
% 3.85/1.25 | | Case 2:
% 3.85/1.25 | | |
% 3.85/1.26 | | | (19) q(all_3_6) = all_3_4 & p(all_3_6) = all_3_5 & ( ~ (all_3_4 = 0) |
% 3.85/1.26 | | | ~ (all_3_5 = 0))
% 3.85/1.26 | | |
% 3.85/1.26 | | | ALPHA: (19) implies:
% 3.85/1.26 | | | (20) p(all_3_6) = all_3_5
% 3.85/1.26 | | | (21) q(all_3_6) = all_3_4
% 3.85/1.26 | | | (22) ~ (all_3_4 = 0) | ~ (all_3_5 = 0)
% 3.85/1.26 | | |
% 3.85/1.26 | | | GROUND_INST: instantiating (6) with all_3_6, all_3_5, simplifying with
% 3.85/1.26 | | | (2), (20) gives:
% 3.85/1.26 | | | (23) all_3_5 = 0
% 3.85/1.26 | | |
% 3.85/1.26 | | | GROUND_INST: instantiating (7) with all_3_6, all_3_4, simplifying with
% 3.85/1.26 | | | (2), (21) gives:
% 3.85/1.26 | | | (24) all_3_4 = 0
% 3.85/1.26 | | |
% 3.85/1.26 | | | BETA: splitting (22) gives:
% 3.85/1.26 | | |
% 3.85/1.26 | | | Case 1:
% 3.85/1.26 | | | |
% 3.85/1.26 | | | | (25) ~ (all_3_4 = 0)
% 3.85/1.26 | | | |
% 3.85/1.26 | | | | REDUCE: (24), (25) imply:
% 3.85/1.26 | | | | (26) $false
% 3.85/1.26 | | | |
% 3.85/1.26 | | | | CLOSE: (26) is inconsistent.
% 3.85/1.26 | | | |
% 3.85/1.26 | | | Case 2:
% 3.85/1.26 | | | |
% 3.85/1.26 | | | | (27) ~ (all_3_5 = 0)
% 3.85/1.26 | | | |
% 3.85/1.26 | | | | REDUCE: (23), (27) imply:
% 3.85/1.26 | | | | (28) $false
% 3.85/1.26 | | | |
% 3.85/1.26 | | | | CLOSE: (28) is inconsistent.
% 3.85/1.26 | | | |
% 3.85/1.26 | | | End of split
% 3.85/1.26 | | |
% 3.85/1.26 | | End of split
% 3.85/1.26 | |
% 3.85/1.26 | End of split
% 3.85/1.26 |
% 3.85/1.26 End of proof
% 3.85/1.26 % SZS output end Proof for theBenchmark
% 3.85/1.26
% 3.85/1.26 655ms
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