TSTP Solution File: SWC317+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SWC317+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 20:50:48 EDT 2023
% Result : Theorem 23.37s 3.76s
% Output : Proof 31.67s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWC317+1 : TPTP v8.1.2. Released v2.4.0.
% 0.07/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.34 % Computer : n024.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 15:05:23 EDT 2023
% 0.13/0.34 % 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/sandbox/benchmark/theBenchmark.p ...
% 0.20/0.63 Running up to 7 provers in parallel.
% 0.20/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.20/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 5.83/1.48 Prover 4: Preprocessing ...
% 5.83/1.48 Prover 2: Preprocessing ...
% 5.83/1.48 Prover 0: Preprocessing ...
% 5.83/1.48 Prover 3: Preprocessing ...
% 5.83/1.49 Prover 5: Preprocessing ...
% 6.17/1.50 Prover 6: Preprocessing ...
% 6.17/1.52 Prover 1: Preprocessing ...
% 15.38/2.74 Prover 1: Constructing countermodel ...
% 15.38/2.75 Prover 2: Proving ...
% 15.38/2.75 Prover 3: Constructing countermodel ...
% 15.38/2.76 Prover 5: Constructing countermodel ...
% 15.38/2.79 Prover 6: Proving ...
% 21.67/3.55 Prover 4: Constructing countermodel ...
% 22.52/3.65 Prover 0: Proving ...
% 23.37/3.76 Prover 0: proved (3126ms)
% 23.37/3.76
% 23.37/3.76 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 23.37/3.76
% 23.37/3.77 Prover 5: stopped
% 23.37/3.78 Prover 3: proved (3128ms)
% 23.37/3.78
% 23.37/3.78 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 23.37/3.78
% 23.37/3.78 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 23.37/3.78 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 23.37/3.78 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 23.37/3.78 Prover 6: stopped
% 23.37/3.78 Prover 2: stopped
% 23.37/3.78 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 23.37/3.78 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 24.86/3.97 Prover 8: Preprocessing ...
% 24.86/3.99 Prover 13: Preprocessing ...
% 24.86/4.01 Prover 11: Preprocessing ...
% 25.40/4.03 Prover 7: Preprocessing ...
% 25.40/4.03 Prover 10: Preprocessing ...
% 27.06/4.25 Prover 10: Constructing countermodel ...
% 27.22/4.27 Prover 7: Constructing countermodel ...
% 27.75/4.34 Prover 13: Constructing countermodel ...
% 28.11/4.39 Prover 8: Warning: ignoring some quantifiers
% 28.11/4.41 Prover 8: Constructing countermodel ...
% 28.73/4.55 Prover 10: Found proof (size 18)
% 28.73/4.55 Prover 10: proved (768ms)
% 28.73/4.55 Prover 4: stopped
% 28.73/4.55 Prover 7: stopped
% 28.73/4.55 Prover 1: stopped
% 28.73/4.55 Prover 8: stopped
% 28.73/4.55 Prover 13: stopped
% 31.41/5.03 Prover 11: Constructing countermodel ...
% 31.41/5.05 Prover 11: stopped
% 31.41/5.05
% 31.41/5.05 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 31.41/5.05
% 31.41/5.06 % SZS output start Proof for theBenchmark
% 31.41/5.07 Assumptions after simplification:
% 31.41/5.07 ---------------------------------
% 31.41/5.07
% 31.41/5.07 (ax17)
% 31.41/5.07 $i(nil) & ssList(nil)
% 31.41/5.07
% 31.41/5.07 (ax58)
% 31.41/5.08 $i(nil) & ! [v0: $i] : (v0 = nil | ~ $i(v0) | ~ segmentP(nil, v0) | ~
% 31.41/5.08 ssList(v0)) & ( ~ ssList(nil) | segmentP(nil, nil))
% 31.41/5.08
% 31.41/5.08 (co1)
% 31.67/5.12 $i(nil) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i]
% 31.67/5.12 : (cons(v2, nil) = v3 & app(v4, v3) = v1 & app(v3, v4) = v0 & $i(v4) & $i(v3)
% 31.67/5.12 & $i(v2) & $i(v1) & $i(v0) & ssList(v4) & ssList(v1) & ssList(v0) & neq(v1,
% 31.67/5.12 nil) & ssItem(v2) & ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ( ~
% 31.67/5.12 (cons(v5, nil) = v6) | ~ (app(v6, v7) = v0) | ~ $i(v7) | ~ $i(v5) | ~
% 31.67/5.12 ssList(v7) | ~ ssItem(v5) | ? [v8: $i] : ( ~ (v8 = v1) & app(v7, v6) =
% 31.67/5.12 v8 & $i(v8))))
% 31.67/5.12
% 31.67/5.12 (function-axioms)
% 31.67/5.12 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 31.67/5.12 (cons(v3, v2) = v1) | ~ (cons(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] :
% 31.67/5.12 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (app(v3, v2) = v1) | ~ (app(v3, v2)
% 31.67/5.12 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (tl(v2) =
% 31.67/5.13 v1) | ~ (tl(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 =
% 31.67/5.13 v0 | ~ (hd(v2) = v1) | ~ (hd(v2) = v0))
% 31.67/5.13
% 31.67/5.13 Further assumptions not needed in the proof:
% 31.67/5.13 --------------------------------------------
% 31.67/5.13 ax1, ax10, ax11, ax12, ax13, ax14, ax15, ax16, ax18, ax19, ax2, ax20, ax21,
% 31.67/5.13 ax22, ax23, ax24, ax25, ax26, ax27, ax28, ax29, ax3, ax30, ax31, ax32, ax33,
% 31.67/5.13 ax34, ax35, ax36, ax37, ax38, ax39, ax4, ax40, ax41, ax42, ax43, ax44, ax45,
% 31.67/5.13 ax46, ax47, ax48, ax49, ax5, ax50, ax51, ax52, ax53, ax54, ax55, ax56, ax57,
% 31.67/5.13 ax59, ax6, ax60, ax61, ax62, ax63, ax64, ax65, ax66, ax67, ax68, ax69, ax7,
% 31.67/5.13 ax70, ax71, ax72, ax73, ax74, ax75, ax76, ax77, ax78, ax79, ax8, ax80, ax81,
% 31.67/5.13 ax82, ax83, ax84, ax85, ax86, ax87, ax88, ax89, ax9, ax90, ax91, ax92, ax93,
% 31.67/5.13 ax94, ax95
% 31.67/5.13
% 31.67/5.13 Those formulas are unsatisfiable:
% 31.67/5.13 ---------------------------------
% 31.67/5.13
% 31.67/5.13 Begin of proof
% 31.67/5.13 |
% 31.67/5.13 | ALPHA: (ax17) implies:
% 31.67/5.13 | (1) ssList(nil)
% 31.67/5.13 |
% 31.67/5.13 | ALPHA: (ax58) implies:
% 31.67/5.13 | (2) ~ ssList(nil) | segmentP(nil, nil)
% 31.67/5.13 |
% 31.67/5.13 | ALPHA: (co1) implies:
% 31.67/5.13 | (3) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 31.67/5.13 | (cons(v2, nil) = v3 & app(v4, v3) = v1 & app(v3, v4) = v0 & $i(v4) &
% 31.67/5.13 | $i(v3) & $i(v2) & $i(v1) & $i(v0) & ssList(v4) & ssList(v1) &
% 31.67/5.13 | ssList(v0) & neq(v1, nil) & ssItem(v2) & ! [v5: $i] : ! [v6: $i] :
% 31.67/5.13 | ! [v7: $i] : ( ~ (cons(v5, nil) = v6) | ~ (app(v6, v7) = v0) | ~
% 31.67/5.13 | $i(v7) | ~ $i(v5) | ~ ssList(v7) | ~ ssItem(v5) | ? [v8: $i] :
% 31.67/5.13 | ( ~ (v8 = v1) & app(v7, v6) = v8 & $i(v8))))
% 31.67/5.13 |
% 31.67/5.13 | ALPHA: (function-axioms) implies:
% 31.67/5.14 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 31.67/5.14 | (app(v3, v2) = v1) | ~ (app(v3, v2) = v0))
% 31.67/5.14 |
% 31.67/5.14 | DELTA: instantiating (3) with fresh symbols all_91_0, all_91_1, all_91_2,
% 31.67/5.14 | all_91_3, all_91_4 gives:
% 31.67/5.14 | (5) cons(all_91_2, nil) = all_91_1 & app(all_91_0, all_91_1) = all_91_3 &
% 31.67/5.14 | app(all_91_1, all_91_0) = all_91_4 & $i(all_91_0) & $i(all_91_1) &
% 31.67/5.14 | $i(all_91_2) & $i(all_91_3) & $i(all_91_4) & ssList(all_91_0) &
% 31.67/5.14 | ssList(all_91_3) & ssList(all_91_4) & neq(all_91_3, nil) &
% 31.67/5.14 | ssItem(all_91_2) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 31.67/5.14 | (cons(v0, nil) = v1) | ~ (app(v1, v2) = all_91_4) | ~ $i(v2) | ~
% 31.67/5.14 | $i(v0) | ~ ssList(v2) | ~ ssItem(v0) | ? [v3: any] : ( ~ (v3 =
% 31.67/5.14 | all_91_3) & app(v2, v1) = v3 & $i(v3)))
% 31.67/5.14 |
% 31.67/5.14 | ALPHA: (5) implies:
% 31.67/5.14 | (6) ssItem(all_91_2)
% 31.67/5.14 | (7) ssList(all_91_0)
% 31.67/5.14 | (8) $i(all_91_2)
% 31.67/5.14 | (9) $i(all_91_0)
% 31.67/5.14 | (10) app(all_91_1, all_91_0) = all_91_4
% 31.67/5.14 | (11) app(all_91_0, all_91_1) = all_91_3
% 31.67/5.14 | (12) cons(all_91_2, nil) = all_91_1
% 31.67/5.14 | (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (cons(v0, nil) = v1) |
% 31.67/5.14 | ~ (app(v1, v2) = all_91_4) | ~ $i(v2) | ~ $i(v0) | ~ ssList(v2) |
% 31.67/5.14 | ~ ssItem(v0) | ? [v3: any] : ( ~ (v3 = all_91_3) & app(v2, v1) =
% 31.67/5.14 | v3 & $i(v3)))
% 31.67/5.14 |
% 31.67/5.14 | BETA: splitting (2) gives:
% 31.67/5.14 |
% 31.67/5.15 | Case 1:
% 31.67/5.15 | |
% 31.67/5.15 | | (14) ~ ssList(nil)
% 31.67/5.15 | |
% 31.67/5.15 | | PRED_UNIFY: (1), (14) imply:
% 31.67/5.15 | | (15) $false
% 31.67/5.15 | |
% 31.67/5.15 | | CLOSE: (15) is inconsistent.
% 31.67/5.15 | |
% 31.67/5.15 | Case 2:
% 31.67/5.15 | |
% 31.67/5.15 | |
% 31.67/5.15 | | GROUND_INST: instantiating (13) with all_91_2, all_91_1, all_91_0,
% 31.67/5.15 | | simplifying with (6), (7), (8), (9), (10), (12) gives:
% 31.67/5.15 | | (16) ? [v0: any] : ( ~ (v0 = all_91_3) & app(all_91_0, all_91_1) = v0 &
% 31.67/5.15 | | $i(v0))
% 31.67/5.15 | |
% 31.67/5.15 | | DELTA: instantiating (16) with fresh symbol all_116_0 gives:
% 31.67/5.15 | | (17) ~ (all_116_0 = all_91_3) & app(all_91_0, all_91_1) = all_116_0 &
% 31.67/5.15 | | $i(all_116_0)
% 31.67/5.15 | |
% 31.67/5.15 | | ALPHA: (17) implies:
% 31.67/5.15 | | (18) ~ (all_116_0 = all_91_3)
% 31.67/5.15 | | (19) app(all_91_0, all_91_1) = all_116_0
% 31.67/5.15 | |
% 31.67/5.15 | | GROUND_INST: instantiating (4) with all_91_3, all_116_0, all_91_1, all_91_0,
% 31.67/5.15 | | simplifying with (11), (19) gives:
% 31.67/5.15 | | (20) all_116_0 = all_91_3
% 31.67/5.15 | |
% 31.67/5.15 | | REDUCE: (18), (20) imply:
% 31.67/5.15 | | (21) $false
% 31.67/5.15 | |
% 31.67/5.15 | | CLOSE: (21) is inconsistent.
% 31.67/5.15 | |
% 31.67/5.15 | End of split
% 31.67/5.15 |
% 31.67/5.15 End of proof
% 31.67/5.15 % SZS output end Proof for theBenchmark
% 31.67/5.15
% 31.67/5.15 4534ms
%------------------------------------------------------------------------------