TSTP Solution File: SWC402+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SWC402+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 : n024.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 20:51:15 EDT 2023
% Result : Theorem 134.75s 18.60s
% Output : Proof 135.02s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SWC402+1 : TPTP v8.1.2. Released v2.4.0.
% 0.07/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.35 % Computer : n024.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Mon Aug 28 14:37:23 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.62 ________ _____
% 0.20/0.62 ___ __ \_________(_)________________________________
% 0.20/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.20/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.20/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.20/0.62
% 0.20/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.62 (2023-06-19)
% 0.20/0.62
% 0.20/0.62 (c) Philipp Rümmer, 2009-2023
% 0.20/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.62 Amanda Stjerna.
% 0.20/0.62 Free software under BSD-3-Clause.
% 0.20/0.62
% 0.20/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.62
% 0.20/0.62 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.20/0.64 Running up to 7 provers in parallel.
% 0.20/0.65 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.65 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.65 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.65 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.65 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.65 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.20/0.65 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 5.64/1.53 Prover 4: Preprocessing ...
% 5.64/1.57 Prover 1: Preprocessing ...
% 5.64/1.57 Prover 0: Preprocessing ...
% 5.64/1.57 Prover 5: Preprocessing ...
% 5.64/1.57 Prover 3: Preprocessing ...
% 5.64/1.57 Prover 6: Preprocessing ...
% 5.64/1.57 Prover 2: Preprocessing ...
% 16.62/3.02 Prover 2: Proving ...
% 16.62/3.02 Prover 5: Constructing countermodel ...
% 17.18/3.11 Prover 6: Proving ...
% 17.59/3.11 Prover 3: Constructing countermodel ...
% 17.59/3.12 Prover 1: Constructing countermodel ...
% 28.00/4.60 Prover 4: Constructing countermodel ...
% 30.64/4.85 Prover 0: Proving ...
% 73.62/10.53 Prover 2: stopped
% 73.62/10.55 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 75.26/10.85 Prover 7: Preprocessing ...
% 77.69/11.10 Prover 7: Constructing countermodel ...
% 100.19/13.99 Prover 5: stopped
% 100.19/14.01 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 101.17/14.15 Prover 8: Preprocessing ...
% 104.18/14.51 Prover 8: Warning: ignoring some quantifiers
% 104.18/14.52 Prover 8: Constructing countermodel ...
% 114.62/15.99 Prover 1: stopped
% 114.62/15.99 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889
% 116.29/16.13 Prover 9: Preprocessing ...
% 123.90/17.16 Prover 9: Constructing countermodel ...
% 128.91/17.98 Prover 6: stopped
% 128.91/18.00 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 131.03/18.16 Prover 10: Preprocessing ...
% 132.54/18.31 Prover 10: Constructing countermodel ...
% 134.01/18.59 Prover 10: Found proof (size 16)
% 134.01/18.59 Prover 10: proved (585ms)
% 134.01/18.59 Prover 9: stopped
% 134.01/18.59 Prover 3: stopped
% 134.01/18.59 Prover 7: stopped
% 134.72/18.59 Prover 8: stopped
% 134.75/18.60 Prover 0: stopped
% 134.75/18.60 Prover 4: stopped
% 134.75/18.60
% 134.75/18.60 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 134.75/18.60
% 134.75/18.61 % SZS output start Proof for theBenchmark
% 134.75/18.61 Assumptions after simplification:
% 134.75/18.61 ---------------------------------
% 134.75/18.61
% 134.75/18.61 (ax17)
% 134.75/18.61 $i(nil) & ssList(nil)
% 134.75/18.61
% 134.75/18.61 (ax26)
% 134.75/18.64 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (app(v0, v1) = v2) | ~ $i(v1) |
% 134.75/18.64 ~ $i(v0) | ~ ssList(v1) | ~ ssList(v0) | ssList(v2))
% 134.75/18.64
% 134.75/18.64 (ax36)
% 134.75/18.65 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (app(v1, v2) = v3)
% 134.75/18.65 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ memberP(v3, v0) | ~ ssList(v2) |
% 134.75/18.65 ~ ssList(v1) | ~ ssItem(v0) | memberP(v2, v0) | memberP(v1, v0)) & ! [v0:
% 134.75/18.65 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (app(v1, v2) = v3) | ~
% 134.75/18.65 $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ memberP(v2, v0) | ~ ssList(v2) | ~
% 134.75/18.65 ssList(v1) | ~ ssItem(v0) | memberP(v3, v0)) & ! [v0: $i] : ! [v1: $i] :
% 134.75/18.65 ! [v2: $i] : ! [v3: $i] : ( ~ (app(v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~
% 134.75/18.65 $i(v0) | ~ memberP(v1, v0) | ~ ssList(v2) | ~ ssList(v1) | ~ ssItem(v0)
% 134.75/18.65 | memberP(v3, v0))
% 134.75/18.65
% 134.75/18.65 (ax58)
% 134.75/18.65 $i(nil) & ! [v0: $i] : (v0 = nil | ~ $i(v0) | ~ segmentP(nil, v0) | ~
% 134.75/18.65 ssList(v0)) & ( ~ ssList(nil) | segmentP(nil, nil))
% 134.75/18.65
% 134.75/18.65 (co1)
% 134.75/18.66 $i(nil) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i]
% 134.75/18.66 : ? [v5: $i] : (app(v4, v5) = v1 & app(v3, v0) = v4 & $i(v5) & $i(v4) &
% 134.75/18.66 $i(v3) & $i(v2) & $i(v1) & $i(v0) & totalorderedP(v0) & memberP(v0, v2) &
% 134.75/18.66 ssList(v5) & ssList(v3) & ssList(v1) & ssList(v0) & ssItem(v2) & ~
% 134.75/18.66 memberP(v1, v2) & ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : !
% 134.75/18.66 [v10: $i] : ! [v11: $i] : ( ~ (cons(v9, nil) = v10) | ~ (cons(v6, nil) =
% 134.75/18.66 v7) | ~ (app(v11, v10) = v0) | ~ (app(v7, v8) = v5) | ~ $i(v11) | ~
% 134.75/18.66 $i(v9) | ~ $i(v8) | ~ $i(v6) | ~ leq(v9, v6) | ~ ssList(v11) | ~
% 134.75/18.66 ssList(v8) | ~ ssItem(v9) | ~ ssItem(v6)) & ! [v6: $i] : ! [v7: $i] :
% 134.75/18.66 ! [v8: $i] : ! [v9: $i] : ! [v10: $i] : ! [v11: $i] : ( ~ (cons(v9, nil)
% 134.75/18.66 = v10) | ~ (cons(v6, nil) = v7) | ~ (app(v10, v11) = v0) | ~ (app(v8,
% 134.75/18.66 v7) = v3) | ~ $i(v11) | ~ $i(v9) | ~ $i(v8) | ~ $i(v6) | ~
% 134.75/18.66 leq(v6, v9) | ~ ssList(v11) | ~ ssList(v8) | ~ ssItem(v9) | ~
% 134.75/18.66 ssItem(v6)) & ( ~ (v0 = nil) | v1 = nil))
% 134.75/18.66
% 134.75/18.66 Further assumptions not needed in the proof:
% 134.75/18.66 --------------------------------------------
% 134.75/18.66 ax1, ax10, ax11, ax12, ax13, ax14, ax15, ax16, ax18, ax19, ax2, ax20, ax21,
% 134.75/18.66 ax22, ax23, ax24, ax25, ax27, ax28, ax29, ax3, ax30, ax31, ax32, ax33, ax34,
% 134.75/18.66 ax35, ax37, ax38, ax39, ax4, ax40, ax41, ax42, ax43, ax44, ax45, ax46, ax47,
% 134.75/18.66 ax48, ax49, ax5, ax50, ax51, ax52, ax53, ax54, ax55, ax56, ax57, ax59, ax6,
% 134.75/18.66 ax60, ax61, ax62, ax63, ax64, ax65, ax66, ax67, ax68, ax69, ax7, ax70, ax71,
% 134.75/18.66 ax72, ax73, ax74, ax75, ax76, ax77, ax78, ax79, ax8, ax80, ax81, ax82, ax83,
% 134.75/18.66 ax84, ax85, ax86, ax87, ax88, ax89, ax9, ax90, ax91, ax92, ax93, ax94, ax95
% 134.75/18.66
% 134.75/18.66 Those formulas are unsatisfiable:
% 134.75/18.66 ---------------------------------
% 134.75/18.66
% 134.75/18.66 Begin of proof
% 134.75/18.66 |
% 135.02/18.66 | ALPHA: (ax17) implies:
% 135.02/18.66 | (1) ssList(nil)
% 135.02/18.66 |
% 135.02/18.66 | ALPHA: (ax36) implies:
% 135.02/18.66 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (app(v1,
% 135.02/18.66 | v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ memberP(v1,
% 135.02/18.66 | v0) | ~ ssList(v2) | ~ ssList(v1) | ~ ssItem(v0) | memberP(v3,
% 135.02/18.66 | v0))
% 135.02/18.66 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (app(v1,
% 135.02/18.66 | v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ memberP(v2,
% 135.02/18.66 | v0) | ~ ssList(v2) | ~ ssList(v1) | ~ ssItem(v0) | memberP(v3,
% 135.02/18.66 | v0))
% 135.02/18.66 |
% 135.02/18.66 | ALPHA: (ax58) implies:
% 135.02/18.67 | (4) ~ ssList(nil) | segmentP(nil, nil)
% 135.02/18.67 |
% 135.02/18.67 | ALPHA: (co1) implies:
% 135.02/18.67 | (5) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 135.02/18.67 | ? [v5: $i] : (app(v4, v5) = v1 & app(v3, v0) = v4 & $i(v5) & $i(v4) &
% 135.02/18.67 | $i(v3) & $i(v2) & $i(v1) & $i(v0) & totalorderedP(v0) & memberP(v0,
% 135.02/18.67 | v2) & ssList(v5) & ssList(v3) & ssList(v1) & ssList(v0) &
% 135.02/18.67 | ssItem(v2) & ~ memberP(v1, v2) & ! [v6: $i] : ! [v7: $i] : ! [v8:
% 135.02/18.67 | $i] : ! [v9: $i] : ! [v10: $i] : ! [v11: $i] : ( ~ (cons(v9,
% 135.02/18.67 | nil) = v10) | ~ (cons(v6, nil) = v7) | ~ (app(v11, v10) = v0)
% 135.02/18.67 | | ~ (app(v7, v8) = v5) | ~ $i(v11) | ~ $i(v9) | ~ $i(v8) | ~
% 135.02/18.67 | $i(v6) | ~ leq(v9, v6) | ~ ssList(v11) | ~ ssList(v8) | ~
% 135.02/18.67 | ssItem(v9) | ~ ssItem(v6)) & ! [v6: $i] : ! [v7: $i] : ! [v8:
% 135.02/18.67 | $i] : ! [v9: $i] : ! [v10: $i] : ! [v11: $i] : ( ~ (cons(v9,
% 135.02/18.67 | nil) = v10) | ~ (cons(v6, nil) = v7) | ~ (app(v10, v11) = v0)
% 135.02/18.67 | | ~ (app(v8, v7) = v3) | ~ $i(v11) | ~ $i(v9) | ~ $i(v8) | ~
% 135.02/18.67 | $i(v6) | ~ leq(v6, v9) | ~ ssList(v11) | ~ ssList(v8) | ~
% 135.02/18.67 | ssItem(v9) | ~ ssItem(v6)) & ( ~ (v0 = nil) | v1 = nil))
% 135.02/18.67 |
% 135.02/18.67 | DELTA: instantiating (5) with fresh symbols all_91_0, all_91_1, all_91_2,
% 135.02/18.67 | all_91_3, all_91_4, all_91_5 gives:
% 135.02/18.68 | (6) app(all_91_1, all_91_0) = all_91_4 & app(all_91_2, all_91_5) = all_91_1
% 135.02/18.68 | & $i(all_91_0) & $i(all_91_1) & $i(all_91_2) & $i(all_91_3) &
% 135.02/18.68 | $i(all_91_4) & $i(all_91_5) & totalorderedP(all_91_5) &
% 135.02/18.68 | memberP(all_91_5, all_91_3) & ssList(all_91_0) & ssList(all_91_2) &
% 135.02/18.68 | ssList(all_91_4) & ssList(all_91_5) & ssItem(all_91_3) & ~
% 135.02/18.68 | memberP(all_91_4, all_91_3) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 135.02/18.68 | ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (cons(v3, nil) = v4) | ~
% 135.02/18.68 | (cons(v0, nil) = v1) | ~ (app(v5, v4) = all_91_5) | ~ (app(v1, v2)
% 135.02/18.68 | = all_91_0) | ~ $i(v5) | ~ $i(v3) | ~ $i(v2) | ~ $i(v0) | ~
% 135.02/18.68 | leq(v3, v0) | ~ ssList(v5) | ~ ssList(v2) | ~ ssItem(v3) | ~
% 135.02/18.68 | ssItem(v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] :
% 135.02/18.68 | ! [v4: $i] : ! [v5: $i] : ( ~ (cons(v3, nil) = v4) | ~ (cons(v0,
% 135.02/18.68 | nil) = v1) | ~ (app(v4, v5) = all_91_5) | ~ (app(v2, v1) =
% 135.02/18.68 | all_91_2) | ~ $i(v5) | ~ $i(v3) | ~ $i(v2) | ~ $i(v0) | ~
% 135.02/18.68 | leq(v0, v3) | ~ ssList(v5) | ~ ssList(v2) | ~ ssItem(v3) | ~
% 135.02/18.68 | ssItem(v0)) & ( ~ (all_91_5 = nil) | all_91_4 = nil)
% 135.02/18.68 |
% 135.02/18.68 | ALPHA: (6) implies:
% 135.02/18.68 | (7) ~ memberP(all_91_4, all_91_3)
% 135.02/18.68 | (8) ssItem(all_91_3)
% 135.02/18.68 | (9) ssList(all_91_5)
% 135.02/18.68 | (10) ssList(all_91_2)
% 135.02/18.68 | (11) ssList(all_91_0)
% 135.02/18.68 | (12) memberP(all_91_5, all_91_3)
% 135.02/18.68 | (13) $i(all_91_5)
% 135.02/18.68 | (14) $i(all_91_3)
% 135.02/18.68 | (15) $i(all_91_2)
% 135.02/18.68 | (16) $i(all_91_1)
% 135.02/18.68 | (17) $i(all_91_0)
% 135.02/18.68 | (18) app(all_91_2, all_91_5) = all_91_1
% 135.02/18.68 | (19) app(all_91_1, all_91_0) = all_91_4
% 135.02/18.68 |
% 135.02/18.68 | BETA: splitting (4) gives:
% 135.02/18.68 |
% 135.02/18.68 | Case 1:
% 135.02/18.68 | |
% 135.02/18.68 | | (20) ~ ssList(nil)
% 135.02/18.68 | |
% 135.02/18.68 | | PRED_UNIFY: (1), (20) imply:
% 135.02/18.68 | | (21) $false
% 135.02/18.68 | |
% 135.02/18.68 | | CLOSE: (21) is inconsistent.
% 135.02/18.68 | |
% 135.02/18.68 | Case 2:
% 135.02/18.68 | |
% 135.02/18.68 | |
% 135.02/18.68 | | GROUND_INST: instantiating (3) with all_91_3, all_91_2, all_91_5, all_91_1,
% 135.02/18.68 | | simplifying with (8), (9), (10), (12), (13), (14), (15), (18)
% 135.02/18.68 | | gives:
% 135.02/18.68 | | (22) memberP(all_91_1, all_91_3)
% 135.02/18.68 | |
% 135.02/18.69 | | GROUND_INST: instantiating (ax26) with all_91_2, all_91_5, all_91_1,
% 135.02/18.69 | | simplifying with (9), (10), (13), (15), (18) gives:
% 135.02/18.69 | | (23) ssList(all_91_1)
% 135.02/18.69 | |
% 135.02/18.69 | | GROUND_INST: instantiating (2) with all_91_3, all_91_1, all_91_0, all_91_4,
% 135.02/18.69 | | simplifying with (7), (8), (11), (14), (16), (17), (19), (22),
% 135.02/18.69 | | (23) gives:
% 135.02/18.69 | | (24) $false
% 135.02/18.69 | |
% 135.02/18.69 | | CLOSE: (24) is inconsistent.
% 135.02/18.69 | |
% 135.02/18.69 | End of split
% 135.02/18.69 |
% 135.02/18.69 End of proof
% 135.02/18.69 % SZS output end Proof for theBenchmark
% 135.02/18.69
% 135.02/18.69 18062ms
%------------------------------------------------------------------------------