TSTP Solution File: SWC220+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SWC220+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 : n025.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 20:50:18 EDT 2023
% Result : Theorem 24.29s 4.02s
% Output : Proof 33.77s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWC220+1 : TPTP v8.1.2. Released v2.4.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.14/0.35 % Computer : n025.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Mon Aug 28 15:58:24 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.21/0.60 ________ _____
% 0.21/0.60 ___ __ \_________(_)________________________________
% 0.21/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.21/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.21/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.21/0.60
% 0.21/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.21/0.60 (2023-06-19)
% 0.21/0.60
% 0.21/0.60 (c) Philipp Rümmer, 2009-2023
% 0.21/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.21/0.60 Amanda Stjerna.
% 0.21/0.60 Free software under BSD-3-Clause.
% 0.21/0.60
% 0.21/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.21/0.60
% 0.21/0.60 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.21/0.61 Running up to 7 provers in parallel.
% 0.21/0.62 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.21/0.62 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.21/0.62 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.21/0.62 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.21/0.62 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.21/0.62 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 0.21/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 6.51/1.60 Prover 1: Preprocessing ...
% 6.51/1.61 Prover 4: Preprocessing ...
% 6.51/1.64 Prover 5: Preprocessing ...
% 6.51/1.64 Prover 3: Preprocessing ...
% 6.51/1.64 Prover 0: Preprocessing ...
% 6.51/1.64 Prover 6: Preprocessing ...
% 6.51/1.64 Prover 2: Preprocessing ...
% 15.29/2.82 Prover 2: Proving ...
% 15.29/2.83 Prover 5: Constructing countermodel ...
% 15.85/2.89 Prover 1: Constructing countermodel ...
% 16.29/2.96 Prover 6: Proving ...
% 16.61/2.99 Prover 3: Constructing countermodel ...
% 20.96/3.56 Prover 4: Constructing countermodel ...
% 20.96/3.58 Prover 0: Proving ...
% 24.29/4.02 Prover 0: proved (3403ms)
% 24.29/4.02
% 24.29/4.02 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 24.29/4.02
% 24.29/4.02 Prover 3: stopped
% 24.29/4.02 Prover 2: stopped
% 24.29/4.03 Prover 5: stopped
% 24.29/4.04 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 24.29/4.04 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 24.29/4.04 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 24.29/4.04 Prover 6: stopped
% 24.29/4.05 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 24.29/4.06 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 26.17/4.29 Prover 8: Preprocessing ...
% 26.72/4.32 Prover 13: Preprocessing ...
% 26.72/4.32 Prover 7: Preprocessing ...
% 26.72/4.33 Prover 10: Preprocessing ...
% 26.72/4.34 Prover 11: Preprocessing ...
% 28.44/4.57 Prover 10: Constructing countermodel ...
% 28.44/4.59 Prover 7: Constructing countermodel ...
% 28.44/4.65 Prover 13: Constructing countermodel ...
% 29.44/4.73 Prover 8: Warning: ignoring some quantifiers
% 29.44/4.74 Prover 8: Constructing countermodel ...
% 32.45/5.07 Prover 10: Found proof (size 16)
% 32.45/5.07 Prover 10: proved (1032ms)
% 32.45/5.07 Prover 4: stopped
% 32.45/5.07 Prover 7: stopped
% 32.45/5.07 Prover 13: stopped
% 32.45/5.07 Prover 1: stopped
% 32.45/5.08 Prover 8: stopped
% 33.25/5.28 Prover 11: Constructing countermodel ...
% 33.25/5.30 Prover 11: stopped
% 33.25/5.30
% 33.25/5.30 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 33.25/5.30
% 33.25/5.31 % SZS output start Proof for theBenchmark
% 33.25/5.32 Assumptions after simplification:
% 33.25/5.32 ---------------------------------
% 33.25/5.32
% 33.25/5.32 (ax17)
% 33.25/5.32 $i(nil) & ssList(nil)
% 33.25/5.32
% 33.25/5.32 (ax58)
% 33.25/5.33 $i(nil) & ! [v0: $i] : (v0 = nil | ~ $i(v0) | ~ segmentP(nil, v0) | ~
% 33.25/5.33 ssList(v0)) & ( ~ ssList(nil) | segmentP(nil, nil))
% 33.25/5.33
% 33.25/5.33 (co1)
% 33.25/5.36 $i(nil) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i]
% 33.25/5.36 : ? [v5: $i] : ? [v6: $i] : ( ~ (v0 = nil) & cons(v2, nil) = v3 & app(v5,
% 33.25/5.37 v6) = v0 & app(v4, v3) = v5 & $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) &
% 33.25/5.37 $i(v1) & $i(v0) & ssList(v6) & ssList(v4) & ssList(v1) & ssList(v0) &
% 33.25/5.37 ssItem(v2) & ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : ! [v10: $i] : !
% 33.25/5.37 [v11: $i] : ( ~ (cons(v7, nil) = v8) | ~ (app(v10, v11) = v0) | ~ (app(v9,
% 33.25/5.37 v8) = v10) | ~ $i(v11) | ~ $i(v9) | ~ $i(v7) | ~ ssList(v11) | ~
% 33.25/5.37 ssList(v9) | ~ ssItem(v7) | ? [v12: $i] : ($i(v12) & leq(v7, v12) &
% 33.25/5.37 memberP(v11, v12) & memberP(v9, v12) & ssItem(v12) & ~ leq(v12, v7))) &
% 33.25/5.37 ! [v7: $i] : ( ~ $i(v7) | ~ leq(v2, v7) | ~ memberP(v6, v7) | ~
% 33.25/5.37 memberP(v4, v7) | ~ ssItem(v7) | leq(v7, v2)))
% 33.25/5.37
% 33.25/5.37 Further assumptions not needed in the proof:
% 33.25/5.37 --------------------------------------------
% 33.25/5.37 ax1, ax10, ax11, ax12, ax13, ax14, ax15, ax16, ax18, ax19, ax2, ax20, ax21,
% 33.25/5.37 ax22, ax23, ax24, ax25, ax26, ax27, ax28, ax29, ax3, ax30, ax31, ax32, ax33,
% 33.25/5.37 ax34, ax35, ax36, ax37, ax38, ax39, ax4, ax40, ax41, ax42, ax43, ax44, ax45,
% 33.25/5.37 ax46, ax47, ax48, ax49, ax5, ax50, ax51, ax52, ax53, ax54, ax55, ax56, ax57,
% 33.25/5.37 ax59, ax6, ax60, ax61, ax62, ax63, ax64, ax65, ax66, ax67, ax68, ax69, ax7,
% 33.25/5.37 ax70, ax71, ax72, ax73, ax74, ax75, ax76, ax77, ax78, ax79, ax8, ax80, ax81,
% 33.25/5.37 ax82, ax83, ax84, ax85, ax86, ax87, ax88, ax89, ax9, ax90, ax91, ax92, ax93,
% 33.25/5.37 ax94, ax95
% 33.25/5.37
% 33.25/5.37 Those formulas are unsatisfiable:
% 33.25/5.37 ---------------------------------
% 33.25/5.37
% 33.25/5.37 Begin of proof
% 33.25/5.37 |
% 33.25/5.37 | ALPHA: (ax17) implies:
% 33.25/5.37 | (1) ssList(nil)
% 33.25/5.37 |
% 33.25/5.37 | ALPHA: (ax58) implies:
% 33.25/5.37 | (2) ~ ssList(nil) | segmentP(nil, nil)
% 33.25/5.37 |
% 33.25/5.37 | ALPHA: (co1) implies:
% 33.25/5.37 | (3) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 33.25/5.37 | ? [v5: $i] : ? [v6: $i] : ( ~ (v0 = nil) & cons(v2, nil) = v3 &
% 33.25/5.37 | app(v5, v6) = v0 & app(v4, v3) = v5 & $i(v6) & $i(v5) & $i(v4) &
% 33.25/5.37 | $i(v3) & $i(v2) & $i(v1) & $i(v0) & ssList(v6) & ssList(v4) &
% 33.25/5.37 | ssList(v1) & ssList(v0) & ssItem(v2) & ! [v7: $i] : ! [v8: $i] : !
% 33.25/5.37 | [v9: $i] : ! [v10: $i] : ! [v11: $i] : ( ~ (cons(v7, nil) = v8) |
% 33.25/5.37 | ~ (app(v10, v11) = v0) | ~ (app(v9, v8) = v10) | ~ $i(v11) | ~
% 33.25/5.37 | $i(v9) | ~ $i(v7) | ~ ssList(v11) | ~ ssList(v9) | ~ ssItem(v7)
% 33.25/5.37 | | ? [v12: $i] : ($i(v12) & leq(v7, v12) & memberP(v11, v12) &
% 33.25/5.37 | memberP(v9, v12) & ssItem(v12) & ~ leq(v12, v7))) & ! [v7: $i]
% 33.25/5.37 | : ( ~ $i(v7) | ~ leq(v2, v7) | ~ memberP(v6, v7) | ~ memberP(v4,
% 33.25/5.37 | v7) | ~ ssItem(v7) | leq(v7, v2)))
% 33.25/5.37 |
% 33.25/5.37 | DELTA: instantiating (3) with fresh symbols all_91_0, all_91_1, all_91_2,
% 33.25/5.37 | all_91_3, all_91_4, all_91_5, all_91_6 gives:
% 33.25/5.38 | (4) ~ (all_91_6 = nil) & cons(all_91_4, nil) = all_91_3 & app(all_91_1,
% 33.25/5.38 | all_91_0) = all_91_6 & app(all_91_2, all_91_3) = all_91_1 &
% 33.25/5.38 | $i(all_91_0) & $i(all_91_1) & $i(all_91_2) & $i(all_91_3) &
% 33.25/5.38 | $i(all_91_4) & $i(all_91_5) & $i(all_91_6) & ssList(all_91_0) &
% 33.25/5.38 | ssList(all_91_2) & ssList(all_91_5) & ssList(all_91_6) &
% 33.25/5.38 | ssItem(all_91_4) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 33.25/5.38 | $i] : ! [v4: $i] : ( ~ (cons(v0, nil) = v1) | ~ (app(v3, v4) =
% 33.25/5.38 | all_91_6) | ~ (app(v2, v1) = v3) | ~ $i(v4) | ~ $i(v2) | ~
% 33.25/5.38 | $i(v0) | ~ ssList(v4) | ~ ssList(v2) | ~ ssItem(v0) | ? [v5: $i]
% 33.25/5.38 | : ($i(v5) & leq(v0, v5) & memberP(v4, v5) & memberP(v2, v5) &
% 33.25/5.38 | ssItem(v5) & ~ leq(v5, v0))) & ! [v0: $i] : ( ~ $i(v0) | ~
% 33.25/5.38 | leq(all_91_4, v0) | ~ memberP(all_91_0, v0) | ~ memberP(all_91_2,
% 33.25/5.38 | v0) | ~ ssItem(v0) | leq(v0, all_91_4))
% 33.25/5.38 |
% 33.25/5.38 | ALPHA: (4) implies:
% 33.77/5.38 | (5) ssItem(all_91_4)
% 33.77/5.38 | (6) ssList(all_91_2)
% 33.77/5.38 | (7) ssList(all_91_0)
% 33.77/5.38 | (8) $i(all_91_4)
% 33.77/5.38 | (9) $i(all_91_2)
% 33.77/5.38 | (10) $i(all_91_0)
% 33.77/5.38 | (11) app(all_91_2, all_91_3) = all_91_1
% 33.77/5.38 | (12) app(all_91_1, all_91_0) = all_91_6
% 33.77/5.38 | (13) cons(all_91_4, nil) = all_91_3
% 33.77/5.38 | (14) ! [v0: $i] : ( ~ $i(v0) | ~ leq(all_91_4, v0) | ~ memberP(all_91_0,
% 33.77/5.38 | v0) | ~ memberP(all_91_2, v0) | ~ ssItem(v0) | leq(v0,
% 33.77/5.38 | all_91_4))
% 33.77/5.38 | (15) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 33.77/5.38 | ( ~ (cons(v0, nil) = v1) | ~ (app(v3, v4) = all_91_6) | ~ (app(v2,
% 33.77/5.38 | v1) = v3) | ~ $i(v4) | ~ $i(v2) | ~ $i(v0) | ~ ssList(v4) |
% 33.77/5.38 | ~ ssList(v2) | ~ ssItem(v0) | ? [v5: $i] : ($i(v5) & leq(v0, v5) &
% 33.77/5.38 | memberP(v4, v5) & memberP(v2, v5) & ssItem(v5) & ~ leq(v5, v0)))
% 33.77/5.38 |
% 33.77/5.38 | BETA: splitting (2) gives:
% 33.77/5.38 |
% 33.77/5.38 | Case 1:
% 33.77/5.38 | |
% 33.77/5.38 | | (16) ~ ssList(nil)
% 33.77/5.38 | |
% 33.77/5.38 | | PRED_UNIFY: (1), (16) imply:
% 33.77/5.38 | | (17) $false
% 33.77/5.38 | |
% 33.77/5.38 | | CLOSE: (17) is inconsistent.
% 33.77/5.38 | |
% 33.77/5.38 | Case 2:
% 33.77/5.38 | |
% 33.77/5.38 | |
% 33.77/5.39 | | GROUND_INST: instantiating (15) with all_91_4, all_91_3, all_91_2, all_91_1,
% 33.77/5.39 | | all_91_0, simplifying with (5), (6), (7), (8), (9), (10), (11),
% 33.77/5.39 | | (12), (13) gives:
% 33.77/5.39 | | (18) ? [v0: $i] : ($i(v0) & leq(all_91_4, v0) & memberP(all_91_0, v0) &
% 33.77/5.39 | | memberP(all_91_2, v0) & ssItem(v0) & ~ leq(v0, all_91_4))
% 33.77/5.39 | |
% 33.77/5.39 | | DELTA: instantiating (18) with fresh symbol all_116_0 gives:
% 33.77/5.39 | | (19) $i(all_116_0) & leq(all_91_4, all_116_0) & memberP(all_91_0,
% 33.77/5.39 | | all_116_0) & memberP(all_91_2, all_116_0) & ssItem(all_116_0) & ~
% 33.77/5.39 | | leq(all_116_0, all_91_4)
% 33.77/5.39 | |
% 33.77/5.39 | | ALPHA: (19) implies:
% 33.77/5.39 | | (20) ~ leq(all_116_0, all_91_4)
% 33.77/5.39 | | (21) ssItem(all_116_0)
% 33.77/5.39 | | (22) memberP(all_91_2, all_116_0)
% 33.77/5.39 | | (23) memberP(all_91_0, all_116_0)
% 33.77/5.39 | | (24) leq(all_91_4, all_116_0)
% 33.77/5.39 | | (25) $i(all_116_0)
% 33.77/5.39 | |
% 33.77/5.39 | | GROUND_INST: instantiating (14) with all_116_0, simplifying with (20), (21),
% 33.77/5.39 | | (22), (23), (24), (25) gives:
% 33.77/5.39 | | (26) $false
% 33.77/5.39 | |
% 33.77/5.39 | | CLOSE: (26) is inconsistent.
% 33.77/5.39 | |
% 33.77/5.39 | End of split
% 33.77/5.39 |
% 33.77/5.39 End of proof
% 33.77/5.39 % SZS output end Proof for theBenchmark
% 33.77/5.39
% 33.77/5.39 4790ms
%------------------------------------------------------------------------------