TSTP Solution File: SWC213+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SWC213+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 20:50:16 EDT 2023
% Result : Theorem 21.38s 3.51s
% Output : Proof 29.68s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : SWC213+1 : TPTP v8.1.2. Released v2.4.0.
% 0.11/0.12 % 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
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Mon Aug 28 17:05:40 EDT 2023
% 0.12/0.33 % CPUTime :
% 0.60/0.59 ________ _____
% 0.60/0.59 ___ __ \_________(_)________________________________
% 0.60/0.59 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.60/0.59 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.60/0.59 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.60/0.59
% 0.60/0.59 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.60/0.59 (2023-06-19)
% 0.60/0.59
% 0.60/0.59 (c) Philipp Rümmer, 2009-2023
% 0.60/0.59 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.60/0.59 Amanda Stjerna.
% 0.60/0.59 Free software under BSD-3-Clause.
% 0.60/0.59
% 0.60/0.59 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.60/0.59
% 0.60/0.59 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.65/0.61 Running up to 7 provers in parallel.
% 0.65/0.62 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.65/0.62 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.65/0.62 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.65/0.62 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.65/0.62 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.65/0.62 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.65/0.62 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 4.81/1.37 Prover 1: Preprocessing ...
% 4.81/1.38 Prover 4: Preprocessing ...
% 5.28/1.41 Prover 0: Preprocessing ...
% 5.28/1.41 Prover 3: Preprocessing ...
% 5.28/1.41 Prover 6: Preprocessing ...
% 5.28/1.41 Prover 2: Preprocessing ...
% 5.28/1.41 Prover 5: Preprocessing ...
% 13.07/2.49 Prover 2: Proving ...
% 14.33/2.61 Prover 5: Constructing countermodel ...
% 14.33/2.64 Prover 1: Constructing countermodel ...
% 14.33/2.66 Prover 6: Proving ...
% 15.40/2.76 Prover 3: Constructing countermodel ...
% 20.83/3.49 Prover 4: Constructing countermodel ...
% 21.38/3.51 Prover 3: proved (2894ms)
% 21.38/3.51
% 21.38/3.51 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 21.38/3.51
% 21.38/3.51 Prover 5: stopped
% 21.38/3.52 Prover 2: stopped
% 21.38/3.53 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 21.38/3.53 Prover 6: stopped
% 21.38/3.54 Prover 0: Proving ...
% 21.38/3.54 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 21.38/3.54 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 21.38/3.54 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 21.38/3.54 Prover 0: stopped
% 21.38/3.55 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 23.16/3.76 Prover 7: Preprocessing ...
% 23.74/3.80 Prover 10: Preprocessing ...
% 23.74/3.82 Prover 11: Preprocessing ...
% 23.74/3.83 Prover 8: Preprocessing ...
% 23.74/3.87 Prover 13: Preprocessing ...
% 25.39/4.03 Prover 10: Constructing countermodel ...
% 25.39/4.03 Prover 7: Constructing countermodel ...
% 25.88/4.14 Prover 13: Constructing countermodel ...
% 26.46/4.16 Prover 8: Warning: ignoring some quantifiers
% 26.54/4.18 Prover 8: Constructing countermodel ...
% 27.03/4.30 Prover 10: Found proof (size 14)
% 27.03/4.30 Prover 10: proved (767ms)
% 27.03/4.30 Prover 13: stopped
% 27.03/4.30 Prover 7: stopped
% 27.03/4.30 Prover 4: stopped
% 27.03/4.30 Prover 1: stopped
% 27.03/4.30 Prover 8: stopped
% 29.36/4.77 Prover 11: Constructing countermodel ...
% 29.45/4.80 Prover 11: stopped
% 29.45/4.80
% 29.45/4.80 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 29.45/4.80
% 29.45/4.80 % SZS output start Proof for theBenchmark
% 29.45/4.81 Assumptions after simplification:
% 29.45/4.81 ---------------------------------
% 29.45/4.81
% 29.45/4.82 (ax15)
% 29.61/4.83 ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ $i(v1) | ~ $i(v0) | ~ ssList(v1) |
% 29.61/4.83 ~ ssList(v0) | neq(v0, v1)) & ! [v0: $i] : ( ~ $i(v0) | ~ ssList(v0) | ~
% 29.61/4.83 neq(v0, v0))
% 29.61/4.83
% 29.61/4.83 (ax17)
% 29.61/4.83 $i(nil) & ssList(nil)
% 29.61/4.83
% 29.61/4.83 (co1)
% 29.68/4.87 $i(nil) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i]
% 29.68/4.87 : (app(v3, v4) = v1 & app(v2, v0) = v3 & $i(v4) & $i(v3) & $i(v2) & $i(v1) &
% 29.68/4.87 $i(v0) & equalelemsP(v0) & ssList(v4) & ssList(v2) & ssList(v1) & ssList(v0)
% 29.68/4.87 & neq(v1, nil) & ~ neq(v0, nil) & ! [v5: $i] : ! [v6: $i] : ! [v7: $i] :
% 29.68/4.87 ! [v8: $i] : ( ~ (cons(v5, nil) = v6) | ~ (app(v8, v6) = v0) | ~ (app(v6,
% 29.68/4.87 v7) = v4) | ~ $i(v8) | ~ $i(v7) | ~ $i(v5) | ~ ssList(v8) | ~
% 29.68/4.87 ssList(v7) | ~ ssItem(v5)) & ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : !
% 29.68/4.87 [v8: $i] : ( ~ (cons(v5, nil) = v6) | ~ (app(v7, v6) = v2) | ~ (app(v6,
% 29.68/4.87 v8) = v0) | ~ $i(v8) | ~ $i(v7) | ~ $i(v5) | ~ ssList(v8) | ~
% 29.68/4.87 ssList(v7) | ~ ssItem(v5)) & ( ~ (v0 = nil) | v1 = nil))
% 29.68/4.87
% 29.68/4.87 Further assumptions not needed in the proof:
% 29.68/4.87 --------------------------------------------
% 29.68/4.87 ax1, ax10, ax11, ax12, ax13, ax14, ax16, ax18, ax19, ax2, ax20, ax21, ax22,
% 29.68/4.87 ax23, ax24, ax25, ax26, ax27, ax28, ax29, ax3, ax30, ax31, ax32, ax33, ax34,
% 29.68/4.87 ax35, ax36, ax37, ax38, ax39, ax4, ax40, ax41, ax42, ax43, ax44, ax45, ax46,
% 29.68/4.87 ax47, ax48, ax49, ax5, ax50, ax51, ax52, ax53, ax54, ax55, ax56, ax57, ax58,
% 29.68/4.87 ax59, ax6, ax60, ax61, ax62, ax63, ax64, ax65, ax66, ax67, ax68, ax69, ax7,
% 29.68/4.87 ax70, ax71, ax72, ax73, ax74, ax75, ax76, ax77, ax78, ax79, ax8, ax80, ax81,
% 29.68/4.87 ax82, ax83, ax84, ax85, ax86, ax87, ax88, ax89, ax9, ax90, ax91, ax92, ax93,
% 29.68/4.87 ax94, ax95
% 29.68/4.87
% 29.68/4.88 Those formulas are unsatisfiable:
% 29.68/4.88 ---------------------------------
% 29.68/4.88
% 29.68/4.88 Begin of proof
% 29.68/4.88 |
% 29.68/4.88 | ALPHA: (ax15) implies:
% 29.68/4.88 | (1) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ $i(v1) | ~ $i(v0) | ~
% 29.68/4.88 | ssList(v1) | ~ ssList(v0) | neq(v0, v1))
% 29.68/4.88 |
% 29.68/4.88 | ALPHA: (ax17) implies:
% 29.68/4.88 | (2) ssList(nil)
% 29.68/4.88 |
% 29.68/4.88 | ALPHA: (co1) implies:
% 29.68/4.88 | (3) $i(nil)
% 29.68/4.89 | (4) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 29.68/4.89 | (app(v3, v4) = v1 & app(v2, v0) = v3 & $i(v4) & $i(v3) & $i(v2) &
% 29.68/4.89 | $i(v1) & $i(v0) & equalelemsP(v0) & ssList(v4) & ssList(v2) &
% 29.68/4.89 | ssList(v1) & ssList(v0) & neq(v1, nil) & ~ neq(v0, nil) & ! [v5:
% 29.68/4.89 | $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ( ~ (cons(v5, nil)
% 29.68/4.89 | = v6) | ~ (app(v8, v6) = v0) | ~ (app(v6, v7) = v4) | ~ $i(v8)
% 29.68/4.89 | | ~ $i(v7) | ~ $i(v5) | ~ ssList(v8) | ~ ssList(v7) | ~
% 29.68/4.89 | ssItem(v5)) & ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i]
% 29.68/4.89 | : ( ~ (cons(v5, nil) = v6) | ~ (app(v7, v6) = v2) | ~ (app(v6, v8)
% 29.68/4.89 | = v0) | ~ $i(v8) | ~ $i(v7) | ~ $i(v5) | ~ ssList(v8) | ~
% 29.68/4.89 | ssList(v7) | ~ ssItem(v5)) & ( ~ (v0 = nil) | v1 = nil))
% 29.68/4.89 |
% 29.68/4.89 | DELTA: instantiating (4) with fresh symbols all_91_0, all_91_1, all_91_2,
% 29.68/4.89 | all_91_3, all_91_4 gives:
% 29.68/4.89 | (5) app(all_91_1, all_91_0) = all_91_3 & app(all_91_2, all_91_4) = all_91_1
% 29.68/4.89 | & $i(all_91_0) & $i(all_91_1) & $i(all_91_2) & $i(all_91_3) &
% 29.68/4.89 | $i(all_91_4) & equalelemsP(all_91_4) & ssList(all_91_0) &
% 29.68/4.89 | ssList(all_91_2) & ssList(all_91_3) & ssList(all_91_4) & neq(all_91_3,
% 29.68/4.89 | nil) & ~ neq(all_91_4, nil) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 29.68/4.89 | $i] : ! [v3: $i] : ( ~ (cons(v0, nil) = v1) | ~ (app(v3, v1) =
% 29.68/4.89 | all_91_4) | ~ (app(v1, v2) = all_91_0) | ~ $i(v3) | ~ $i(v2) |
% 29.68/4.89 | ~ $i(v0) | ~ ssList(v3) | ~ ssList(v2) | ~ ssItem(v0)) & ! [v0:
% 29.68/4.89 | $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (cons(v0, nil) =
% 29.68/4.89 | v1) | ~ (app(v2, v1) = all_91_2) | ~ (app(v1, v3) = all_91_4) |
% 29.68/4.89 | ~ $i(v3) | ~ $i(v2) | ~ $i(v0) | ~ ssList(v3) | ~ ssList(v2) | ~
% 29.68/4.89 | ssItem(v0)) & ( ~ (all_91_4 = nil) | all_91_3 = nil)
% 29.68/4.89 |
% 29.68/4.89 | ALPHA: (5) implies:
% 29.68/4.89 | (6) ~ neq(all_91_4, nil)
% 29.68/4.89 | (7) neq(all_91_3, nil)
% 29.68/4.89 | (8) ssList(all_91_4)
% 29.68/4.89 | (9) $i(all_91_4)
% 29.68/4.89 | (10) ~ (all_91_4 = nil) | all_91_3 = nil
% 29.68/4.89 |
% 29.68/4.89 | GROUND_INST: instantiating (1) with all_91_4, nil, simplifying with (2), (3),
% 29.68/4.89 | (6), (8), (9) gives:
% 29.68/4.89 | (11) all_91_4 = nil
% 29.68/4.89 |
% 29.68/4.89 | REDUCE: (6), (11) imply:
% 29.68/4.90 | (12) ~ neq(nil, nil)
% 29.68/4.90 |
% 29.68/4.90 | BETA: splitting (10) gives:
% 29.68/4.90 |
% 29.68/4.90 | Case 1:
% 29.68/4.90 | |
% 29.68/4.90 | | (13) ~ (all_91_4 = nil)
% 29.68/4.90 | |
% 29.68/4.90 | | REDUCE: (11), (13) imply:
% 29.68/4.90 | | (14) $false
% 29.68/4.90 | |
% 29.68/4.90 | | CLOSE: (14) is inconsistent.
% 29.68/4.90 | |
% 29.68/4.90 | Case 2:
% 29.68/4.90 | |
% 29.68/4.90 | | (15) all_91_3 = nil
% 29.68/4.90 | |
% 29.68/4.90 | | REDUCE: (7), (15) imply:
% 29.68/4.90 | | (16) neq(nil, nil)
% 29.68/4.90 | |
% 29.68/4.90 | | PRED_UNIFY: (12), (16) imply:
% 29.68/4.90 | | (17) $false
% 29.68/4.90 | |
% 29.68/4.90 | | CLOSE: (17) is inconsistent.
% 29.68/4.90 | |
% 29.68/4.90 | End of split
% 29.68/4.90 |
% 29.68/4.90 End of proof
% 29.68/4.90 % SZS output end Proof for theBenchmark
% 29.68/4.90
% 29.68/4.90 4305ms
%------------------------------------------------------------------------------