TSTP Solution File: SWC398+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SWC398+1 : TPTP v8.1.2. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n028.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 : Thu Aug 31 20:51:14 EDT 2023
% Result : Theorem 27.24s 4.32s
% Output : Proof 34.39s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWC398+1 : TPTP v8.1.2. Released v2.4.0.
% 0.07/0.12 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.12/0.33 % Computer : n028.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 : Mon Aug 28 15:14:09 EDT 2023
% 0.12/0.33 % CPUTime :
% 0.19/0.59 ________ _____
% 0.19/0.59 ___ __ \_________(_)________________________________
% 0.19/0.59 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.19/0.59 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.19/0.59 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.19/0.59
% 0.19/0.59 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.19/0.59 (2023-06-19)
% 0.19/0.59
% 0.19/0.59 (c) Philipp Rümmer, 2009-2023
% 0.19/0.59 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.19/0.59 Amanda Stjerna.
% 0.19/0.59 Free software under BSD-3-Clause.
% 0.19/0.59
% 0.19/0.59 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.19/0.59
% 0.19/0.59 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.19/0.60 Running up to 7 provers in parallel.
% 0.19/0.62 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.19/0.62 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.19/0.62 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.19/0.62 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.19/0.62 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.19/0.62 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.19/0.62 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 6.76/1.59 Prover 4: Preprocessing ...
% 6.81/1.60 Prover 1: Preprocessing ...
% 6.84/1.61 Prover 6: Preprocessing ...
% 6.84/1.61 Prover 0: Preprocessing ...
% 6.84/1.61 Prover 2: Preprocessing ...
% 6.84/1.61 Prover 3: Preprocessing ...
% 6.84/1.61 Prover 5: Preprocessing ...
% 17.09/3.02 Prover 2: Proving ...
% 17.66/3.06 Prover 5: Constructing countermodel ...
% 17.66/3.06 Prover 6: Proving ...
% 17.66/3.10 Prover 1: Constructing countermodel ...
% 18.23/3.17 Prover 3: Constructing countermodel ...
% 24.70/3.99 Prover 4: Constructing countermodel ...
% 24.70/4.02 Prover 0: Proving ...
% 27.24/4.32 Prover 3: proved (3700ms)
% 27.24/4.32
% 27.24/4.32 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 27.24/4.32
% 27.24/4.32 Prover 5: stopped
% 27.24/4.34 Prover 2: stopped
% 27.24/4.35 Prover 6: stopped
% 27.24/4.37 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 27.24/4.37 Prover 0: stopped
% 27.79/4.37 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 27.79/4.37 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 27.79/4.37 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 27.79/4.37 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 28.65/4.51 Prover 8: Preprocessing ...
% 28.65/4.51 Prover 7: Preprocessing ...
% 28.65/4.51 Prover 13: Preprocessing ...
% 28.86/4.52 Prover 10: Preprocessing ...
% 28.92/4.54 Prover 11: Preprocessing ...
% 30.07/4.72 Prover 10: Constructing countermodel ...
% 31.13/4.82 Prover 7: Constructing countermodel ...
% 31.22/4.88 Prover 8: Warning: ignoring some quantifiers
% 31.22/4.89 Prover 10: Found proof (size 7)
% 31.22/4.89 Prover 10: proved (537ms)
% 31.22/4.89 Prover 1: stopped
% 31.22/4.89 Prover 4: stopped
% 31.22/4.89 Prover 7: stopped
% 31.22/4.89 Prover 8: Constructing countermodel ...
% 31.22/4.91 Prover 8: stopped
% 31.84/4.92 Prover 13: Constructing countermodel ...
% 31.84/4.94 Prover 13: stopped
% 33.80/5.41 Prover 11: Constructing countermodel ...
% 33.97/5.43 Prover 11: stopped
% 33.97/5.43
% 33.97/5.43 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 33.97/5.43
% 33.97/5.44 % SZS output start Proof for theBenchmark
% 34.04/5.45 Assumptions after simplification:
% 34.04/5.45 ---------------------------------
% 34.04/5.45
% 34.04/5.45 (ax36)
% 34.04/5.50 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (app(v1, v2) = v3)
% 34.04/5.50 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ memberP(v3, v0) | ~ ssList(v2) |
% 34.04/5.50 ~ ssList(v1) | ~ ssItem(v0) | memberP(v2, v0) | memberP(v1, v0)) & ! [v0:
% 34.04/5.50 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (app(v1, v2) = v3) | ~
% 34.04/5.50 $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ memberP(v2, v0) | ~ ssList(v2) | ~
% 34.04/5.50 ssList(v1) | ~ ssItem(v0) | memberP(v3, v0)) & ! [v0: $i] : ! [v1: $i] :
% 34.04/5.50 ! [v2: $i] : ! [v3: $i] : ( ~ (app(v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~
% 34.04/5.50 $i(v0) | ~ memberP(v1, v0) | ~ ssList(v2) | ~ ssList(v1) | ~ ssItem(v0)
% 34.04/5.50 | memberP(v3, v0))
% 34.04/5.50
% 34.04/5.50 (co1)
% 34.04/5.51 $i(nil) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : (app(v0, v3)
% 34.04/5.51 = v1 & $i(v3) & $i(v2) & $i(v1) & $i(v0) & equalelemsP(v0) & memberP(v0, v2)
% 34.04/5.51 & ssList(v3) & ssList(v1) & ssList(v0) & ssItem(v2) & ~ memberP(v1, v2) &
% 34.04/5.51 ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ( ~ (cons(v4, nil) =
% 34.04/5.51 v5) | ~ (app(v7, v5) = v0) | ~ (app(v5, v6) = v3) | ~ $i(v7) | ~
% 34.04/5.51 $i(v6) | ~ $i(v4) | ~ ssList(v7) | ~ ssList(v6) | ~ ssItem(v4)) & ( ~
% 34.04/5.51 (v0 = nil) | v1 = nil))
% 34.04/5.51
% 34.04/5.51 Further assumptions not needed in the proof:
% 34.04/5.51 --------------------------------------------
% 34.04/5.51 ax1, ax10, ax11, ax12, ax13, ax14, ax15, ax16, ax17, ax18, ax19, ax2, ax20,
% 34.04/5.51 ax21, ax22, ax23, ax24, ax25, ax26, ax27, ax28, ax29, ax3, ax30, ax31, ax32,
% 34.04/5.51 ax33, ax34, ax35, ax37, ax38, ax39, ax4, ax40, ax41, ax42, ax43, ax44, ax45,
% 34.04/5.51 ax46, ax47, ax48, ax49, ax5, ax50, ax51, ax52, ax53, ax54, ax55, ax56, ax57,
% 34.04/5.51 ax58, ax59, ax6, ax60, ax61, ax62, ax63, ax64, ax65, ax66, ax67, ax68, ax69,
% 34.04/5.51 ax7, ax70, ax71, ax72, ax73, ax74, ax75, ax76, ax77, ax78, ax79, ax8, ax80,
% 34.04/5.51 ax81, ax82, ax83, ax84, ax85, ax86, ax87, ax88, ax89, ax9, ax90, ax91, ax92,
% 34.04/5.51 ax93, ax94, ax95
% 34.04/5.51
% 34.04/5.51 Those formulas are unsatisfiable:
% 34.04/5.51 ---------------------------------
% 34.04/5.51
% 34.04/5.51 Begin of proof
% 34.04/5.51 |
% 34.04/5.51 | ALPHA: (ax36) implies:
% 34.39/5.52 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (app(v1,
% 34.39/5.52 | v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ memberP(v1,
% 34.39/5.52 | v0) | ~ ssList(v2) | ~ ssList(v1) | ~ ssItem(v0) | memberP(v3,
% 34.39/5.52 | v0))
% 34.39/5.52 |
% 34.39/5.52 | ALPHA: (co1) implies:
% 34.39/5.52 | (2) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : (app(v0, v3) =
% 34.39/5.52 | v1 & $i(v3) & $i(v2) & $i(v1) & $i(v0) & equalelemsP(v0) &
% 34.39/5.52 | memberP(v0, v2) & ssList(v3) & ssList(v1) & ssList(v0) & ssItem(v2) &
% 34.39/5.52 | ~ memberP(v1, v2) & ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : !
% 34.39/5.52 | [v7: $i] : ( ~ (cons(v4, nil) = v5) | ~ (app(v7, v5) = v0) | ~
% 34.39/5.52 | (app(v5, v6) = v3) | ~ $i(v7) | ~ $i(v6) | ~ $i(v4) | ~
% 34.39/5.52 | ssList(v7) | ~ ssList(v6) | ~ ssItem(v4)) & ( ~ (v0 = nil) | v1 =
% 34.39/5.52 | nil))
% 34.39/5.52 |
% 34.39/5.52 | DELTA: instantiating (2) with fresh symbols all_91_0, all_91_1, all_91_2,
% 34.39/5.52 | all_91_3 gives:
% 34.39/5.53 | (3) app(all_91_3, all_91_0) = all_91_2 & $i(all_91_0) & $i(all_91_1) &
% 34.39/5.53 | $i(all_91_2) & $i(all_91_3) & equalelemsP(all_91_3) & memberP(all_91_3,
% 34.39/5.53 | all_91_1) & ssList(all_91_0) & ssList(all_91_2) & ssList(all_91_3) &
% 34.39/5.53 | ssItem(all_91_1) & ~ memberP(all_91_2, all_91_1) & ! [v0: $i] : !
% 34.39/5.53 | [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (cons(v0, nil) = v1) | ~
% 34.39/5.53 | (app(v3, v1) = all_91_3) | ~ (app(v1, v2) = all_91_0) | ~ $i(v3) |
% 34.39/5.53 | ~ $i(v2) | ~ $i(v0) | ~ ssList(v3) | ~ ssList(v2) | ~ ssItem(v0))
% 34.39/5.53 | & ( ~ (all_91_3 = nil) | all_91_2 = nil)
% 34.39/5.53 |
% 34.39/5.53 | ALPHA: (3) implies:
% 34.39/5.53 | (4) ~ memberP(all_91_2, all_91_1)
% 34.39/5.53 | (5) ssItem(all_91_1)
% 34.39/5.53 | (6) ssList(all_91_3)
% 34.39/5.53 | (7) ssList(all_91_0)
% 34.39/5.53 | (8) memberP(all_91_3, all_91_1)
% 34.39/5.53 | (9) $i(all_91_3)
% 34.39/5.53 | (10) $i(all_91_1)
% 34.39/5.53 | (11) $i(all_91_0)
% 34.39/5.53 | (12) app(all_91_3, all_91_0) = all_91_2
% 34.39/5.53 |
% 34.39/5.53 | GROUND_INST: instantiating (1) with all_91_1, all_91_3, all_91_0, all_91_2,
% 34.39/5.53 | simplifying with (4), (5), (6), (7), (8), (9), (10), (11), (12)
% 34.39/5.53 | gives:
% 34.39/5.53 | (13) $false
% 34.39/5.54 |
% 34.39/5.54 | CLOSE: (13) is inconsistent.
% 34.39/5.54 |
% 34.39/5.54 End of proof
% 34.39/5.54 % SZS output end Proof for theBenchmark
% 34.39/5.54
% 34.39/5.54 4944ms
%------------------------------------------------------------------------------