TSTP Solution File: SYN053+1 by Princess---230619
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SYN053+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 : n032.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 03:26:21 EDT 2023
% Result : Theorem 2.58s 1.01s
% Output : Proof 3.10s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : SYN053+1 : TPTP v8.1.2. Released v2.0.0.
% 0.00/0.10 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.12/0.29 % Computer : n032.cluster.edu
% 0.12/0.29 % Model : x86_64 x86_64
% 0.12/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.29 % Memory : 8042.1875MB
% 0.12/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.29 % CPULimit : 300
% 0.12/0.29 % WCLimit : 300
% 0.12/0.29 % DateTime : Sat Aug 26 17:12:14 EDT 2023
% 0.12/0.29 % CPUTime :
% 0.14/0.51 ________ _____
% 0.14/0.51 ___ __ \_________(_)________________________________
% 0.14/0.51 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.14/0.51 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.14/0.51 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.14/0.51
% 0.14/0.51 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.14/0.51 (2023-06-19)
% 0.14/0.51
% 0.14/0.51 (c) Philipp Rümmer, 2009-2023
% 0.14/0.51 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.14/0.51 Amanda Stjerna.
% 0.14/0.51 Free software under BSD-3-Clause.
% 0.14/0.51
% 0.14/0.51 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.14/0.51
% 0.14/0.51 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.14/0.52 Running up to 7 provers in parallel.
% 0.14/0.54 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.14/0.54 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.14/0.54 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.14/0.54 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.14/0.54 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.14/0.54 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.14/0.54 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 0.14/0.82 Prover 4: Preprocessing ...
% 0.14/0.82 Prover 1: Preprocessing ...
% 0.14/0.87 Prover 3: Preprocessing ...
% 0.14/0.87 Prover 2: Preprocessing ...
% 0.14/0.87 Prover 6: Preprocessing ...
% 0.14/0.87 Prover 0: Preprocessing ...
% 0.14/0.87 Prover 5: Preprocessing ...
% 1.78/0.93 Prover 1: Constructing countermodel ...
% 1.78/0.93 Prover 4: Constructing countermodel ...
% 1.78/0.93 Prover 2: Proving ...
% 1.78/0.93 Prover 5: Proving ...
% 1.78/0.93 Prover 3: Constructing countermodel ...
% 1.78/0.93 Prover 0: Proving ...
% 1.78/0.94 Prover 6: Proving ...
% 2.58/1.01 Prover 2: proved (477ms)
% 2.58/1.01
% 2.58/1.01 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.58/1.01
% 2.58/1.01 Prover 3: stopped
% 2.58/1.02 Prover 0: stopped
% 2.58/1.02 Prover 5: stopped
% 2.58/1.02 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 2.58/1.02 Prover 6: stopped
% 2.58/1.02 Prover 7: Preprocessing ...
% 2.58/1.02 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 2.58/1.02 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 2.58/1.03 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 2.58/1.03 Prover 10: Preprocessing ...
% 2.58/1.03 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 2.58/1.03 Prover 11: Preprocessing ...
% 2.58/1.04 Prover 7: Warning: ignoring some quantifiers
% 2.58/1.04 Prover 7: Constructing countermodel ...
% 2.58/1.04 Prover 8: Preprocessing ...
% 2.58/1.04 Prover 4: Found proof (size 11)
% 2.58/1.04 Prover 4: proved (508ms)
% 2.58/1.04 Prover 1: stopped
% 2.58/1.05 Prover 7: stopped
% 2.58/1.05 Prover 13: Preprocessing ...
% 2.58/1.05 Prover 10: Warning: ignoring some quantifiers
% 2.58/1.05 Prover 10: Constructing countermodel ...
% 2.58/1.05 Prover 10: stopped
% 2.58/1.06 Prover 11: Constructing countermodel ...
% 2.58/1.06 Prover 11: stopped
% 2.58/1.06 Prover 13: Warning: ignoring some quantifiers
% 2.58/1.06 Prover 13: Constructing countermodel ...
% 2.58/1.06 Prover 13: stopped
% 2.58/1.06 Prover 8: Warning: ignoring some quantifiers
% 2.58/1.06 Prover 8: Constructing countermodel ...
% 2.58/1.07 Prover 8: stopped
% 2.58/1.07
% 2.58/1.07 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.58/1.07
% 2.58/1.07 % SZS output start Proof for theBenchmark
% 2.58/1.07 Assumptions after simplification:
% 2.58/1.07 ---------------------------------
% 2.58/1.07
% 2.58/1.07 (pel23)
% 3.10/1.12 ? [v0: $i] : ? [v1: int] : ? [v2: $i] : ? [v3: int] : ($i(v2) & $i(v0) &
% 3.10/1.12 (( ~ (v3 = 0) & big_f(v2) = v3 & ~ p & ! [v4: $i] : ! [v5: int] : (v5 = 0
% 3.10/1.12 | ~ (big_f(v4) = v5) | ~ $i(v4))) | ( ~ (v1 = 0) & big_f(v0) = v1 &
% 3.10/1.12 ~ p & ! [v4: $i] : ! [v5: int] : (v5 = 0 | ~ (big_f(v4) = v5) | ~
% 3.10/1.12 $i(v4)))))
% 3.10/1.12
% 3.10/1.12 Those formulas are unsatisfiable:
% 3.10/1.12 ---------------------------------
% 3.10/1.12
% 3.10/1.12 Begin of proof
% 3.10/1.12 |
% 3.10/1.12 | DELTA: instantiating (pel23) with fresh symbols all_3_0, all_3_1, all_3_2,
% 3.10/1.12 | all_3_3 gives:
% 3.10/1.12 | (1) $i(all_3_1) & $i(all_3_3) & (( ~ (all_3_0 = 0) & big_f(all_3_1) =
% 3.10/1.12 | all_3_0 & ~ p & ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~
% 3.10/1.12 | (big_f(v0) = v1) | ~ $i(v0))) | ( ~ (all_3_2 = 0) &
% 3.10/1.12 | big_f(all_3_3) = all_3_2 & ~ p & ! [v0: $i] : ! [v1: int] : (v1
% 3.10/1.12 | = 0 | ~ (big_f(v0) = v1) | ~ $i(v0))))
% 3.10/1.12 |
% 3.10/1.12 | ALPHA: (1) implies:
% 3.10/1.12 | (2) $i(all_3_3)
% 3.10/1.12 | (3) $i(all_3_1)
% 3.10/1.12 | (4) ( ~ (all_3_0 = 0) & big_f(all_3_1) = all_3_0 & ~ p & ! [v0: $i] : !
% 3.10/1.12 | [v1: int] : (v1 = 0 | ~ (big_f(v0) = v1) | ~ $i(v0))) | ( ~
% 3.10/1.13 | (all_3_2 = 0) & big_f(all_3_3) = all_3_2 & ~ p & ! [v0: $i] : !
% 3.10/1.13 | [v1: int] : (v1 = 0 | ~ (big_f(v0) = v1) | ~ $i(v0)))
% 3.10/1.13 |
% 3.10/1.13 | BETA: splitting (4) gives:
% 3.10/1.13 |
% 3.10/1.13 | Case 1:
% 3.10/1.13 | |
% 3.10/1.13 | | (5) ~ (all_3_0 = 0) & big_f(all_3_1) = all_3_0 & ~ p & ! [v0: $i] : !
% 3.10/1.13 | | [v1: int] : (v1 = 0 | ~ (big_f(v0) = v1) | ~ $i(v0))
% 3.10/1.13 | |
% 3.10/1.13 | | ALPHA: (5) implies:
% 3.10/1.13 | | (6) ~ (all_3_0 = 0)
% 3.10/1.13 | | (7) big_f(all_3_1) = all_3_0
% 3.10/1.13 | | (8) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (big_f(v0) = v1) | ~
% 3.10/1.13 | | $i(v0))
% 3.10/1.13 | |
% 3.10/1.13 | | GROUND_INST: instantiating (8) with all_3_1, all_3_0, simplifying with (3),
% 3.10/1.13 | | (7) gives:
% 3.10/1.13 | | (9) all_3_0 = 0
% 3.10/1.13 | |
% 3.10/1.13 | | REDUCE: (6), (9) imply:
% 3.10/1.13 | | (10) $false
% 3.10/1.13 | |
% 3.10/1.13 | | CLOSE: (10) is inconsistent.
% 3.10/1.13 | |
% 3.10/1.13 | Case 2:
% 3.10/1.13 | |
% 3.10/1.13 | | (11) ~ (all_3_2 = 0) & big_f(all_3_3) = all_3_2 & ~ p & ! [v0: $i] :
% 3.10/1.13 | | ! [v1: int] : (v1 = 0 | ~ (big_f(v0) = v1) | ~ $i(v0))
% 3.10/1.13 | |
% 3.10/1.13 | | ALPHA: (11) implies:
% 3.10/1.13 | | (12) ~ (all_3_2 = 0)
% 3.10/1.13 | | (13) big_f(all_3_3) = all_3_2
% 3.10/1.13 | | (14) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (big_f(v0) = v1) | ~
% 3.10/1.13 | | $i(v0))
% 3.10/1.13 | |
% 3.10/1.13 | | GROUND_INST: instantiating (14) with all_3_3, all_3_2, simplifying with (2),
% 3.10/1.13 | | (13) gives:
% 3.10/1.14 | | (15) all_3_2 = 0
% 3.10/1.14 | |
% 3.10/1.14 | | REDUCE: (12), (15) imply:
% 3.10/1.14 | | (16) $false
% 3.10/1.14 | |
% 3.10/1.14 | | CLOSE: (16) is inconsistent.
% 3.10/1.14 | |
% 3.10/1.14 | End of split
% 3.10/1.14 |
% 3.10/1.14 End of proof
% 3.10/1.14 % SZS output end Proof for theBenchmark
% 3.10/1.14
% 3.10/1.14 623ms
%------------------------------------------------------------------------------