TSTP Solution File: SWC179+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SWC179+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 : 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 : Thu Aug 31 20:50:06 EDT 2023
% Result : Theorem 21.23s 3.58s
% Output : Proof 41.87s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SWC179+1 : TPTP v8.1.2. Released v2.4.0.
% 0.12/0.12 % 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
% 0.18/0.33 % CPULimit : 300
% 0.18/0.33 % WCLimit : 300
% 0.18/0.33 % DateTime : Mon Aug 28 16:56:40 EDT 2023
% 0.18/0.33 % CPUTime :
% 0.62/0.62 ________ _____
% 0.62/0.62 ___ __ \_________(_)________________________________
% 0.62/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.62/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.62/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.62/0.62
% 0.62/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.62/0.62 (2023-06-19)
% 0.62/0.62
% 0.62/0.62 (c) Philipp Rümmer, 2009-2023
% 0.62/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.62/0.62 Amanda Stjerna.
% 0.62/0.62 Free software under BSD-3-Clause.
% 0.62/0.62
% 0.62/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.62/0.62
% 0.62/0.62 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.68/0.63 Running up to 7 provers in parallel.
% 0.72/0.65 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.72/0.65 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.72/0.65 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.72/0.65 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.72/0.65 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.72/0.65 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.72/0.65 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 5.06/1.45 Prover 1: Preprocessing ...
% 5.06/1.45 Prover 4: Preprocessing ...
% 5.68/1.48 Prover 5: Preprocessing ...
% 5.68/1.48 Prover 3: Preprocessing ...
% 5.68/1.48 Prover 2: Preprocessing ...
% 5.68/1.48 Prover 0: Preprocessing ...
% 5.68/1.49 Prover 6: Preprocessing ...
% 15.01/2.71 Prover 2: Proving ...
% 15.83/2.86 Prover 5: Constructing countermodel ...
% 15.83/2.87 Prover 1: Constructing countermodel ...
% 15.83/2.88 Prover 3: Constructing countermodel ...
% 16.57/2.91 Prover 6: Proving ...
% 21.23/3.57 Prover 6: proved (2925ms)
% 21.23/3.57
% 21.23/3.58 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 21.23/3.58
% 21.23/3.58 Prover 5: stopped
% 21.23/3.58 Prover 2: stopped
% 21.79/3.59 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 21.79/3.59 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 21.79/3.59 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 21.79/3.61 Prover 3: stopped
% 21.79/3.61 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 22.89/3.74 Prover 4: Constructing countermodel ...
% 23.53/3.82 Prover 10: Preprocessing ...
% 24.10/3.89 Prover 11: Preprocessing ...
% 24.10/3.89 Prover 0: Proving ...
% 24.10/3.93 Prover 0: stopped
% 24.10/3.93 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 24.10/3.93 Prover 8: Preprocessing ...
% 24.10/3.95 Prover 7: Preprocessing ...
% 25.20/4.04 Prover 13: Preprocessing ...
% 25.79/4.10 Prover 10: Constructing countermodel ...
% 26.31/4.18 Prover 7: Constructing countermodel ...
% 26.31/4.25 Prover 8: Warning: ignoring some quantifiers
% 26.31/4.26 Prover 8: Constructing countermodel ...
% 27.21/4.30 Prover 13: Constructing countermodel ...
% 32.09/4.96 Prover 11: Constructing countermodel ...
% 41.22/6.14 Prover 7: Found proof (size 14)
% 41.22/6.15 Prover 7: proved (2569ms)
% 41.22/6.15 Prover 11: stopped
% 41.22/6.15 Prover 8: stopped
% 41.22/6.15 Prover 1: stopped
% 41.22/6.15 Prover 10: stopped
% 41.22/6.15 Prover 4: stopped
% 41.22/6.15 Prover 13: stopped
% 41.22/6.15
% 41.22/6.15 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 41.22/6.15
% 41.22/6.15 % SZS output start Proof for theBenchmark
% 41.22/6.16 Assumptions after simplification:
% 41.22/6.16 ---------------------------------
% 41.22/6.16
% 41.22/6.16 (ax71)
% 41.22/6.18 $i(nil) & ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) |
% 41.22/6.18 ~ ssItem(v0) | duplicatefreeP(v1))
% 41.22/6.18
% 41.22/6.18 (ax72)
% 41.22/6.18 $i(nil) & duplicatefreeP(nil)
% 41.22/6.18
% 41.22/6.18 (co1)
% 41.22/6.18 $i(nil) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i]
% 41.22/6.18 : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ($i(v6) & $i(v4) & $i(v2) & $i(v1)
% 41.22/6.18 & $i(v0) & ssList(v1) & ssList(v0) & ~ duplicatefreeP(v0) & ((v7 = v1 & v3
% 41.22/6.18 = v0 & cons(v2, nil) = v0 & app(v5, v6) = v1 & app(v4, v0) = v5 & $i(v5)
% 41.22/6.18 & ssList(v6) & ssList(v4) & ssItem(v2) & ! [v8: $i] : ( ~ $i(v8) | ~
% 41.22/6.18 lt(v8, v2) | ~ memberP(v6, v8) | ~ ssItem(v8)) & ! [v8: $i] : ( ~
% 41.22/6.18 $i(v8) | ~ lt(v2, v8) | ~ memberP(v4, v8) | ~ ssItem(v8))) | (v1 =
% 41.22/6.18 nil & v0 = nil)))
% 41.22/6.18
% 41.22/6.18 Further assumptions not needed in the proof:
% 41.22/6.18 --------------------------------------------
% 41.22/6.19 ax1, ax10, ax11, ax12, ax13, ax14, ax15, ax16, ax17, ax18, ax19, ax2, ax20,
% 41.22/6.19 ax21, ax22, ax23, ax24, ax25, ax26, ax27, ax28, ax29, ax3, ax30, ax31, ax32,
% 41.22/6.19 ax33, ax34, ax35, ax36, ax37, ax38, ax39, ax4, ax40, ax41, ax42, ax43, ax44,
% 41.22/6.19 ax45, ax46, ax47, ax48, ax49, ax5, ax50, ax51, ax52, ax53, ax54, ax55, ax56,
% 41.22/6.19 ax57, ax58, ax59, ax6, ax60, ax61, ax62, ax63, ax64, ax65, ax66, ax67, ax68,
% 41.22/6.19 ax69, ax7, ax70, ax73, ax74, ax75, ax76, ax77, ax78, ax79, ax8, ax80, ax81,
% 41.22/6.19 ax82, ax83, ax84, ax85, ax86, ax87, ax88, ax89, ax9, ax90, ax91, ax92, ax93,
% 41.22/6.19 ax94, ax95
% 41.22/6.19
% 41.22/6.19 Those formulas are unsatisfiable:
% 41.22/6.19 ---------------------------------
% 41.22/6.19
% 41.22/6.19 Begin of proof
% 41.22/6.19 |
% 41.22/6.19 | ALPHA: (ax71) implies:
% 41.22/6.19 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | ~
% 41.85/6.19 | ssItem(v0) | duplicatefreeP(v1))
% 41.85/6.19 |
% 41.85/6.19 | ALPHA: (ax72) implies:
% 41.85/6.19 | (2) duplicatefreeP(nil)
% 41.85/6.19 |
% 41.85/6.19 | ALPHA: (co1) implies:
% 41.85/6.19 | (3) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 41.85/6.19 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ($i(v6) & $i(v4) & $i(v2) &
% 41.85/6.19 | $i(v1) & $i(v0) & ssList(v1) & ssList(v0) & ~ duplicatefreeP(v0) &
% 41.85/6.19 | ((v7 = v1 & v3 = v0 & cons(v2, nil) = v0 & app(v5, v6) = v1 & app(v4,
% 41.85/6.19 | v0) = v5 & $i(v5) & ssList(v6) & ssList(v4) & ssItem(v2) & !
% 41.85/6.19 | [v8: $i] : ( ~ $i(v8) | ~ lt(v8, v2) | ~ memberP(v6, v8) | ~
% 41.85/6.19 | ssItem(v8)) & ! [v8: $i] : ( ~ $i(v8) | ~ lt(v2, v8) | ~
% 41.85/6.19 | memberP(v4, v8) | ~ ssItem(v8))) | (v1 = nil & v0 = nil)))
% 41.85/6.19 |
% 41.85/6.19 | DELTA: instantiating (3) with fresh symbols all_91_0, all_91_1, all_91_2,
% 41.85/6.19 | all_91_3, all_91_4, all_91_5, all_91_6, all_91_7 gives:
% 41.87/6.19 | (4) $i(all_91_1) & $i(all_91_3) & $i(all_91_5) & $i(all_91_6) &
% 41.87/6.19 | $i(all_91_7) & ssList(all_91_6) & ssList(all_91_7) & ~
% 41.87/6.19 | duplicatefreeP(all_91_7) & ((all_91_0 = all_91_6 & all_91_4 = all_91_7
% 41.87/6.19 | & cons(all_91_5, nil) = all_91_7 & app(all_91_2, all_91_1) =
% 41.87/6.19 | all_91_6 & app(all_91_3, all_91_7) = all_91_2 & $i(all_91_2) &
% 41.87/6.19 | ssList(all_91_1) & ssList(all_91_3) & ssItem(all_91_5) & ! [v0:
% 41.87/6.19 | $i] : ( ~ $i(v0) | ~ lt(v0, all_91_5) | ~ memberP(all_91_1, v0)
% 41.87/6.19 | | ~ ssItem(v0)) & ! [v0: $i] : ( ~ $i(v0) | ~ lt(all_91_5, v0)
% 41.87/6.19 | | ~ memberP(all_91_3, v0) | ~ ssItem(v0))) | (all_91_6 = nil &
% 41.87/6.19 | all_91_7 = nil))
% 41.87/6.19 |
% 41.87/6.19 | ALPHA: (4) implies:
% 41.87/6.20 | (5) ~ duplicatefreeP(all_91_7)
% 41.87/6.20 | (6) $i(all_91_5)
% 41.87/6.20 | (7) (all_91_0 = all_91_6 & all_91_4 = all_91_7 & cons(all_91_5, nil) =
% 41.87/6.20 | all_91_7 & app(all_91_2, all_91_1) = all_91_6 & app(all_91_3,
% 41.87/6.20 | all_91_7) = all_91_2 & $i(all_91_2) & ssList(all_91_1) &
% 41.87/6.20 | ssList(all_91_3) & ssItem(all_91_5) & ! [v0: $i] : ( ~ $i(v0) | ~
% 41.87/6.20 | lt(v0, all_91_5) | ~ memberP(all_91_1, v0) | ~ ssItem(v0)) & !
% 41.87/6.20 | [v0: $i] : ( ~ $i(v0) | ~ lt(all_91_5, v0) | ~ memberP(all_91_3,
% 41.87/6.20 | v0) | ~ ssItem(v0))) | (all_91_6 = nil & all_91_7 = nil)
% 41.87/6.20 |
% 41.87/6.20 | PRED_UNIFY: (2), (5) imply:
% 41.87/6.20 | (8) ~ (all_91_7 = nil)
% 41.87/6.20 |
% 41.87/6.20 | BETA: splitting (7) gives:
% 41.87/6.20 |
% 41.87/6.20 | Case 1:
% 41.87/6.20 | |
% 41.87/6.20 | | (9) all_91_0 = all_91_6 & all_91_4 = all_91_7 & cons(all_91_5, nil) =
% 41.87/6.20 | | all_91_7 & app(all_91_2, all_91_1) = all_91_6 & app(all_91_3,
% 41.87/6.20 | | all_91_7) = all_91_2 & $i(all_91_2) & ssList(all_91_1) &
% 41.87/6.20 | | ssList(all_91_3) & ssItem(all_91_5) & ! [v0: $i] : ( ~ $i(v0) | ~
% 41.87/6.20 | | lt(v0, all_91_5) | ~ memberP(all_91_1, v0) | ~ ssItem(v0)) & !
% 41.87/6.20 | | [v0: $i] : ( ~ $i(v0) | ~ lt(all_91_5, v0) | ~ memberP(all_91_3,
% 41.87/6.20 | | v0) | ~ ssItem(v0))
% 41.87/6.20 | |
% 41.87/6.20 | | ALPHA: (9) implies:
% 41.87/6.20 | | (10) ssItem(all_91_5)
% 41.87/6.20 | | (11) cons(all_91_5, nil) = all_91_7
% 41.87/6.20 | |
% 41.87/6.20 | | GROUND_INST: instantiating (1) with all_91_5, all_91_7, simplifying with
% 41.87/6.20 | | (5), (6), (10), (11) gives:
% 41.87/6.20 | | (12) $false
% 41.87/6.20 | |
% 41.87/6.20 | | CLOSE: (12) is inconsistent.
% 41.87/6.20 | |
% 41.87/6.20 | Case 2:
% 41.87/6.20 | |
% 41.87/6.20 | | (13) all_91_6 = nil & all_91_7 = nil
% 41.87/6.20 | |
% 41.87/6.20 | | ALPHA: (13) implies:
% 41.87/6.20 | | (14) all_91_7 = nil
% 41.87/6.20 | |
% 41.87/6.20 | | REDUCE: (8), (14) imply:
% 41.87/6.20 | | (15) $false
% 41.87/6.20 | |
% 41.87/6.20 | | CLOSE: (15) is inconsistent.
% 41.87/6.20 | |
% 41.87/6.20 | End of split
% 41.87/6.20 |
% 41.87/6.20 End of proof
% 41.87/6.20 % SZS output end Proof for theBenchmark
% 41.87/6.20
% 41.87/6.20 5584ms
%------------------------------------------------------------------------------