TSTP Solution File: SWC006+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SWC006+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 : n017.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 20:49:08 EDT 2023
% Result : Theorem 21.82s 3.57s
% Output : Proof 29.49s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SWC006+1 : TPTP v8.1.2. Released v2.4.0.
% 0.12/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.34 % Computer : n017.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon Aug 28 17:44:57 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.60 ________ _____
% 0.20/0.60 ___ __ \_________(_)________________________________
% 0.20/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.20/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.20/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.20/0.60
% 0.20/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.60 (2023-06-19)
% 0.20/0.60
% 0.20/0.60 (c) Philipp Rümmer, 2009-2023
% 0.20/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.60 Amanda Stjerna.
% 0.20/0.60 Free software under BSD-3-Clause.
% 0.20/0.60
% 0.20/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.60
% 0.20/0.61 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.20/0.62 Running up to 7 provers in parallel.
% 0.20/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.20/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 4.97/1.41 Prover 4: Preprocessing ...
% 4.97/1.42 Prover 1: Preprocessing ...
% 5.66/1.44 Prover 3: Preprocessing ...
% 5.66/1.44 Prover 2: Preprocessing ...
% 5.66/1.44 Prover 5: Preprocessing ...
% 5.66/1.44 Prover 6: Preprocessing ...
% 5.66/1.44 Prover 0: Preprocessing ...
% 14.85/2.69 Prover 2: Proving ...
% 14.85/2.70 Prover 5: Constructing countermodel ...
% 14.85/2.74 Prover 1: Constructing countermodel ...
% 14.85/2.75 Prover 3: Constructing countermodel ...
% 14.85/2.76 Prover 6: Proving ...
% 20.60/3.39 Prover 4: Constructing countermodel ...
% 20.60/3.39 Prover 0: Proving ...
% 21.21/3.56 Prover 0: proved (2936ms)
% 21.82/3.57
% 21.82/3.57 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 21.82/3.57
% 21.82/3.57 Prover 5: stopped
% 21.82/3.57 Prover 3: stopped
% 21.82/3.59 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 21.82/3.59 Prover 2: stopped
% 21.82/3.60 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 21.82/3.60 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 21.82/3.60 Prover 6: stopped
% 22.19/3.60 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 22.19/3.61 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 23.65/3.82 Prover 7: Preprocessing ...
% 23.65/3.83 Prover 10: Preprocessing ...
% 23.65/3.83 Prover 8: Preprocessing ...
% 23.65/3.85 Prover 11: Preprocessing ...
% 23.65/3.86 Prover 13: Preprocessing ...
% 25.44/4.02 Prover 10: Constructing countermodel ...
% 25.44/4.06 Prover 7: Constructing countermodel ...
% 26.01/4.19 Prover 13: Constructing countermodel ...
% 26.01/4.20 Prover 8: Warning: ignoring some quantifiers
% 26.01/4.22 Prover 8: Constructing countermodel ...
% 27.53/4.32 Prover 10: Found proof (size 17)
% 27.53/4.32 Prover 10: proved (723ms)
% 27.53/4.32 Prover 4: stopped
% 27.53/4.32 Prover 13: stopped
% 27.53/4.32 Prover 7: stopped
% 27.53/4.32 Prover 1: stopped
% 27.74/4.33 Prover 8: stopped
% 29.02/4.70 Prover 11: Constructing countermodel ...
% 29.02/4.72 Prover 11: stopped
% 29.02/4.72
% 29.02/4.72 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 29.02/4.72
% 29.02/4.73 % SZS output start Proof for theBenchmark
% 29.02/4.73 Assumptions after simplification:
% 29.02/4.73 ---------------------------------
% 29.02/4.73
% 29.02/4.73 (ax17)
% 29.02/4.74 $i(nil) & ssList(nil)
% 29.02/4.74
% 29.02/4.74 (ax58)
% 29.02/4.74 $i(nil) & ! [v0: $i] : (v0 = nil | ~ $i(v0) | ~ segmentP(nil, v0) | ~
% 29.02/4.74 ssList(v0)) & ( ~ ssList(nil) | segmentP(nil, nil))
% 29.02/4.74
% 29.02/4.75 (co1)
% 29.49/4.79 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5:
% 29.49/4.79 $i] : (app(v4, v5) = v1 & app(v2, v5) = v0 & app(v2, v3) = v4 & $i(v5) &
% 29.49/4.79 $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & ssList(v5) & ssList(v3) &
% 29.49/4.79 ssList(v2) & ssList(v1) & ssList(v0) & ! [v6: $i] : ! [v7: $i] : ! [v8:
% 29.49/4.79 $i] : ! [v9: $i] : ( ~ (app(v8, v9) = v1) | ~ (app(v6, v7) = v8) | ~
% 29.49/4.79 $i(v9) | ~ $i(v7) | ~ $i(v6) | ~ ssList(v9) | ~ ssList(v7) | ~
% 29.49/4.79 ssList(v6) | ? [v10: $i] : ( ~ (v10 = v0) & app(v6, v9) = v10 &
% 29.49/4.79 $i(v10))))
% 29.49/4.79
% 29.49/4.79 (function-axioms)
% 29.49/4.79 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 29.49/4.79 (cons(v3, v2) = v1) | ~ (cons(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] :
% 29.49/4.79 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (app(v3, v2) = v1) | ~ (app(v3, v2)
% 29.49/4.79 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (tl(v2) =
% 29.49/4.79 v1) | ~ (tl(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 =
% 29.49/4.79 v0 | ~ (hd(v2) = v1) | ~ (hd(v2) = v0))
% 29.49/4.79
% 29.49/4.79 Further assumptions not needed in the proof:
% 29.49/4.79 --------------------------------------------
% 29.49/4.80 ax1, ax10, ax11, ax12, ax13, ax14, ax15, ax16, ax18, ax19, ax2, ax20, ax21,
% 29.49/4.80 ax22, ax23, ax24, ax25, ax26, ax27, ax28, ax29, ax3, ax30, ax31, ax32, ax33,
% 29.49/4.80 ax34, ax35, ax36, ax37, ax38, ax39, ax4, ax40, ax41, ax42, ax43, ax44, ax45,
% 29.49/4.80 ax46, ax47, ax48, ax49, ax5, ax50, ax51, ax52, ax53, ax54, ax55, ax56, ax57,
% 29.49/4.80 ax59, ax6, ax60, ax61, ax62, ax63, ax64, ax65, ax66, ax67, ax68, ax69, ax7,
% 29.49/4.80 ax70, ax71, ax72, ax73, ax74, ax75, ax76, ax77, ax78, ax79, ax8, ax80, ax81,
% 29.49/4.80 ax82, ax83, ax84, ax85, ax86, ax87, ax88, ax89, ax9, ax90, ax91, ax92, ax93,
% 29.49/4.80 ax94, ax95
% 29.49/4.80
% 29.49/4.80 Those formulas are unsatisfiable:
% 29.49/4.80 ---------------------------------
% 29.49/4.80
% 29.49/4.80 Begin of proof
% 29.49/4.80 |
% 29.49/4.80 | ALPHA: (ax17) implies:
% 29.49/4.80 | (1) ssList(nil)
% 29.49/4.80 |
% 29.49/4.80 | ALPHA: (ax58) implies:
% 29.49/4.80 | (2) ~ ssList(nil) | segmentP(nil, nil)
% 29.49/4.80 |
% 29.49/4.80 | ALPHA: (function-axioms) implies:
% 29.49/4.80 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 29.49/4.80 | (app(v3, v2) = v1) | ~ (app(v3, v2) = v0))
% 29.49/4.80 |
% 29.49/4.80 | DELTA: instantiating (co1) with fresh symbols all_91_0, all_91_1, all_91_2,
% 29.49/4.80 | all_91_3, all_91_4, all_91_5 gives:
% 29.49/4.81 | (4) app(all_91_1, all_91_0) = all_91_4 & app(all_91_3, all_91_0) = all_91_5
% 29.49/4.81 | & app(all_91_3, all_91_2) = all_91_1 & $i(all_91_0) & $i(all_91_1) &
% 29.49/4.81 | $i(all_91_2) & $i(all_91_3) & $i(all_91_4) & $i(all_91_5) &
% 29.49/4.81 | ssList(all_91_0) & ssList(all_91_2) & ssList(all_91_3) &
% 29.49/4.81 | ssList(all_91_4) & ssList(all_91_5) & ! [v0: $i] : ! [v1: $i] : !
% 29.49/4.81 | [v2: $i] : ! [v3: $i] : ( ~ (app(v2, v3) = all_91_4) | ~ (app(v0, v1)
% 29.49/4.81 | = v2) | ~ $i(v3) | ~ $i(v1) | ~ $i(v0) | ~ ssList(v3) | ~
% 29.49/4.81 | ssList(v1) | ~ ssList(v0) | ? [v4: any] : ( ~ (v4 = all_91_5) &
% 29.49/4.81 | app(v0, v3) = v4 & $i(v4)))
% 29.49/4.81 |
% 29.49/4.81 | ALPHA: (4) implies:
% 29.49/4.81 | (5) ssList(all_91_3)
% 29.49/4.81 | (6) ssList(all_91_2)
% 29.49/4.81 | (7) ssList(all_91_0)
% 29.49/4.81 | (8) $i(all_91_3)
% 29.49/4.81 | (9) $i(all_91_2)
% 29.49/4.82 | (10) $i(all_91_0)
% 29.49/4.82 | (11) app(all_91_3, all_91_2) = all_91_1
% 29.49/4.82 | (12) app(all_91_3, all_91_0) = all_91_5
% 29.49/4.82 | (13) app(all_91_1, all_91_0) = all_91_4
% 29.49/4.82 | (14) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (app(v2,
% 29.49/4.82 | v3) = all_91_4) | ~ (app(v0, v1) = v2) | ~ $i(v3) | ~ $i(v1)
% 29.49/4.82 | | ~ $i(v0) | ~ ssList(v3) | ~ ssList(v1) | ~ ssList(v0) | ?
% 29.49/4.82 | [v4: any] : ( ~ (v4 = all_91_5) & app(v0, v3) = v4 & $i(v4)))
% 29.49/4.82 |
% 29.49/4.82 | BETA: splitting (2) gives:
% 29.49/4.82 |
% 29.49/4.82 | Case 1:
% 29.49/4.82 | |
% 29.49/4.82 | | (15) ~ ssList(nil)
% 29.49/4.82 | |
% 29.49/4.82 | | PRED_UNIFY: (1), (15) imply:
% 29.49/4.82 | | (16) $false
% 29.49/4.82 | |
% 29.49/4.82 | | CLOSE: (16) is inconsistent.
% 29.49/4.82 | |
% 29.49/4.82 | Case 2:
% 29.49/4.82 | |
% 29.49/4.82 | |
% 29.49/4.82 | | GROUND_INST: instantiating (14) with all_91_3, all_91_2, all_91_1, all_91_0,
% 29.49/4.82 | | simplifying with (5), (6), (7), (8), (9), (10), (11), (13)
% 29.49/4.82 | | gives:
% 29.49/4.83 | | (17) ? [v0: any] : ( ~ (v0 = all_91_5) & app(all_91_3, all_91_0) = v0 &
% 29.49/4.83 | | $i(v0))
% 29.49/4.83 | |
% 29.49/4.83 | | DELTA: instantiating (17) with fresh symbol all_114_0 gives:
% 29.49/4.83 | | (18) ~ (all_114_0 = all_91_5) & app(all_91_3, all_91_0) = all_114_0 &
% 29.49/4.83 | | $i(all_114_0)
% 29.49/4.83 | |
% 29.49/4.83 | | ALPHA: (18) implies:
% 29.49/4.83 | | (19) ~ (all_114_0 = all_91_5)
% 29.49/4.83 | | (20) app(all_91_3, all_91_0) = all_114_0
% 29.49/4.83 | |
% 29.49/4.83 | | GROUND_INST: instantiating (3) with all_91_5, all_114_0, all_91_0, all_91_3,
% 29.49/4.83 | | simplifying with (12), (20) gives:
% 29.49/4.83 | | (21) all_114_0 = all_91_5
% 29.49/4.83 | |
% 29.49/4.83 | | REDUCE: (19), (21) imply:
% 29.49/4.83 | | (22) $false
% 29.49/4.83 | |
% 29.49/4.83 | | CLOSE: (22) is inconsistent.
% 29.49/4.83 | |
% 29.49/4.83 | End of split
% 29.49/4.83 |
% 29.49/4.83 End of proof
% 29.49/4.83 % SZS output end Proof for theBenchmark
% 29.49/4.83
% 29.49/4.83 4223ms
%------------------------------------------------------------------------------