TSTP Solution File: SWC258+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SWC258+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 : n005.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 20:50:30 EDT 2023
% Result : Theorem 19.61s 3.39s
% Output : Proof 30.90s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SWC258+1 : TPTP v8.1.2. Released v2.4.0.
% 0.12/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.12/0.34 % Computer : n005.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Mon Aug 28 16:54:53 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.19/0.59 ________ _____
% 0.19/0.59 ___ __ \_________(_)________________________________
% 0.19/0.59 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.19/0.59 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.19/0.59 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.19/0.59
% 0.19/0.59 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.19/0.59 (2023-06-19)
% 0.19/0.59
% 0.19/0.59 (c) Philipp Rümmer, 2009-2023
% 0.19/0.59 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.19/0.59 Amanda Stjerna.
% 0.19/0.59 Free software under BSD-3-Clause.
% 0.19/0.59
% 0.19/0.59 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.19/0.59
% 0.19/0.59 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.19/0.61 Running up to 7 provers in parallel.
% 0.19/0.62 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.19/0.62 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.19/0.62 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.19/0.62 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.19/0.62 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.19/0.62 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.19/0.62 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 4.28/1.41 Prover 4: Preprocessing ...
% 4.28/1.41 Prover 1: Preprocessing ...
% 5.13/1.46 Prover 5: Preprocessing ...
% 5.13/1.46 Prover 3: Preprocessing ...
% 5.13/1.46 Prover 2: Preprocessing ...
% 5.13/1.46 Prover 6: Preprocessing ...
% 5.13/1.46 Prover 0: Preprocessing ...
% 14.18/2.67 Prover 2: Proving ...
% 14.18/2.69 Prover 5: Constructing countermodel ...
% 14.90/2.75 Prover 6: Proving ...
% 15.49/2.77 Prover 3: Constructing countermodel ...
% 15.49/2.79 Prover 1: Constructing countermodel ...
% 19.61/3.39 Prover 6: proved (2770ms)
% 19.61/3.39
% 19.61/3.39 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 19.61/3.39
% 19.61/3.40 Prover 3: stopped
% 19.61/3.40 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 19.61/3.40 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 19.61/3.40 Prover 5: stopped
% 19.61/3.40 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 19.61/3.40 Prover 2: stopped
% 19.61/3.42 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 20.69/3.47 Prover 4: Constructing countermodel ...
% 21.42/3.58 Prover 0: Proving ...
% 21.42/3.60 Prover 0: stopped
% 21.42/3.62 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 21.42/3.62 Prover 7: Preprocessing ...
% 21.42/3.62 Prover 11: Preprocessing ...
% 22.07/3.65 Prover 10: Preprocessing ...
% 22.40/3.68 Prover 8: Preprocessing ...
% 23.00/3.77 Prover 13: Preprocessing ...
% 23.46/3.84 Prover 10: Constructing countermodel ...
% 23.78/3.91 Prover 7: Constructing countermodel ...
% 23.78/4.01 Prover 13: Constructing countermodel ...
% 26.02/4.16 Prover 8: Warning: ignoring some quantifiers
% 26.02/4.18 Prover 8: Constructing countermodel ...
% 28.88/4.64 Prover 7: Found proof (size 14)
% 28.88/4.64 Prover 7: proved (1240ms)
% 28.88/4.64 Prover 8: stopped
% 28.88/4.64 Prover 13: stopped
% 28.88/4.64 Prover 1: stopped
% 28.88/4.64 Prover 4: stopped
% 28.88/4.64 Prover 10: stopped
% 30.61/4.85 Prover 11: Constructing countermodel ...
% 30.61/4.88 Prover 11: stopped
% 30.61/4.88
% 30.61/4.88 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 30.61/4.88
% 30.61/4.88 % SZS output start Proof for theBenchmark
% 30.61/4.89 Assumptions after simplification:
% 30.61/4.89 ---------------------------------
% 30.61/4.89
% 30.61/4.89 (ax65)
% 30.90/4.93 $i(nil) & ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) |
% 30.90/4.93 ~ ssItem(v0) | totalorderedP(v1))
% 30.90/4.93
% 30.90/4.93 (ax66)
% 30.90/4.93 $i(nil) & totalorderedP(nil)
% 30.90/4.93
% 30.90/4.93 (co1)
% 30.90/4.93 $i(nil) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ($i(v2) &
% 30.90/4.93 $i(v1) & $i(v0) & ssList(v1) & ssList(v0) & ~ totalorderedP(v0) & ((v3 = v0
% 30.90/4.93 & cons(v2, nil) = v0 & memberP(v1, v2) & ssItem(v2) & ! [v4: $i] : (v4
% 30.90/4.93 = v2 | ~ $i(v4) | ~ leq(v4, v2) | ~ memberP(v1, v4) | ~
% 30.90/4.93 ssItem(v4))) | (v1 = nil & v0 = nil)))
% 30.90/4.93
% 30.90/4.93 Further assumptions not needed in the proof:
% 30.90/4.93 --------------------------------------------
% 30.90/4.93 ax1, ax10, ax11, ax12, ax13, ax14, ax15, ax16, ax17, ax18, ax19, ax2, ax20,
% 30.90/4.93 ax21, ax22, ax23, ax24, ax25, ax26, ax27, ax28, ax29, ax3, ax30, ax31, ax32,
% 30.90/4.93 ax33, ax34, ax35, ax36, ax37, ax38, ax39, ax4, ax40, ax41, ax42, ax43, ax44,
% 30.90/4.93 ax45, ax46, ax47, ax48, ax49, ax5, ax50, ax51, ax52, ax53, ax54, ax55, ax56,
% 30.90/4.93 ax57, ax58, ax59, ax6, ax60, ax61, ax62, ax63, ax64, ax67, ax68, ax69, ax7,
% 30.90/4.93 ax70, ax71, ax72, ax73, ax74, ax75, ax76, ax77, ax78, ax79, ax8, ax80, ax81,
% 30.90/4.93 ax82, ax83, ax84, ax85, ax86, ax87, ax88, ax89, ax9, ax90, ax91, ax92, ax93,
% 30.90/4.93 ax94, ax95
% 30.90/4.93
% 30.90/4.93 Those formulas are unsatisfiable:
% 30.90/4.93 ---------------------------------
% 30.90/4.93
% 30.90/4.93 Begin of proof
% 30.90/4.93 |
% 30.90/4.93 | ALPHA: (ax65) implies:
% 30.90/4.94 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | ~
% 30.90/4.94 | ssItem(v0) | totalorderedP(v1))
% 30.90/4.94 |
% 30.90/4.94 | ALPHA: (ax66) implies:
% 30.90/4.94 | (2) totalorderedP(nil)
% 30.90/4.94 |
% 30.90/4.94 | ALPHA: (co1) implies:
% 30.90/4.94 | (3) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ($i(v2) &
% 30.90/4.94 | $i(v1) & $i(v0) & ssList(v1) & ssList(v0) & ~ totalorderedP(v0) &
% 30.90/4.94 | ((v3 = v0 & cons(v2, nil) = v0 & memberP(v1, v2) & ssItem(v2) & !
% 30.90/4.94 | [v4: $i] : (v4 = v2 | ~ $i(v4) | ~ leq(v4, v2) | ~ memberP(v1,
% 30.90/4.94 | v4) | ~ ssItem(v4))) | (v1 = nil & v0 = nil)))
% 30.90/4.94 |
% 30.90/4.94 | DELTA: instantiating (3) with fresh symbols all_91_0, all_91_1, all_91_2,
% 30.90/4.94 | all_91_3 gives:
% 30.90/4.94 | (4) $i(all_91_1) & $i(all_91_2) & $i(all_91_3) & ssList(all_91_2) &
% 30.90/4.94 | ssList(all_91_3) & ~ totalorderedP(all_91_3) & ((all_91_0 = all_91_3 &
% 30.90/4.94 | cons(all_91_1, nil) = all_91_3 & memberP(all_91_2, all_91_1) &
% 30.90/4.94 | ssItem(all_91_1) & ! [v0: any] : (v0 = all_91_1 | ~ $i(v0) | ~
% 30.90/4.94 | leq(v0, all_91_1) | ~ memberP(all_91_2, v0) | ~ ssItem(v0))) |
% 30.90/4.94 | (all_91_2 = nil & all_91_3 = nil))
% 30.90/4.94 |
% 30.90/4.94 | ALPHA: (4) implies:
% 30.90/4.94 | (5) ~ totalorderedP(all_91_3)
% 30.90/4.94 | (6) $i(all_91_1)
% 30.90/4.94 | (7) (all_91_0 = all_91_3 & cons(all_91_1, nil) = all_91_3 &
% 30.90/4.94 | memberP(all_91_2, all_91_1) & ssItem(all_91_1) & ! [v0: any] : (v0 =
% 30.90/4.94 | all_91_1 | ~ $i(v0) | ~ leq(v0, all_91_1) | ~ memberP(all_91_2,
% 30.90/4.94 | v0) | ~ ssItem(v0))) | (all_91_2 = nil & all_91_3 = nil)
% 30.90/4.94 |
% 30.90/4.94 | PRED_UNIFY: (2), (5) imply:
% 30.90/4.94 | (8) ~ (all_91_3 = nil)
% 30.90/4.94 |
% 30.90/4.94 | BETA: splitting (7) gives:
% 30.90/4.94 |
% 30.90/4.94 | Case 1:
% 30.90/4.94 | |
% 30.90/4.95 | | (9) all_91_0 = all_91_3 & cons(all_91_1, nil) = all_91_3 &
% 30.90/4.95 | | memberP(all_91_2, all_91_1) & ssItem(all_91_1) & ! [v0: any] : (v0 =
% 30.90/4.95 | | all_91_1 | ~ $i(v0) | ~ leq(v0, all_91_1) | ~ memberP(all_91_2,
% 30.90/4.95 | | v0) | ~ ssItem(v0))
% 30.90/4.95 | |
% 30.90/4.95 | | ALPHA: (9) implies:
% 30.90/4.95 | | (10) ssItem(all_91_1)
% 30.90/4.95 | | (11) cons(all_91_1, nil) = all_91_3
% 30.90/4.95 | |
% 30.90/4.95 | | GROUND_INST: instantiating (1) with all_91_1, all_91_3, simplifying with
% 30.90/4.95 | | (5), (6), (10), (11) gives:
% 30.90/4.95 | | (12) $false
% 30.90/4.95 | |
% 30.90/4.95 | | CLOSE: (12) is inconsistent.
% 30.90/4.95 | |
% 30.90/4.95 | Case 2:
% 30.90/4.95 | |
% 30.90/4.95 | | (13) all_91_2 = nil & all_91_3 = nil
% 30.90/4.95 | |
% 30.90/4.95 | | ALPHA: (13) implies:
% 30.90/4.95 | | (14) all_91_3 = nil
% 30.90/4.95 | |
% 30.90/4.95 | | REDUCE: (8), (14) imply:
% 30.90/4.95 | | (15) $false
% 30.90/4.95 | |
% 30.90/4.95 | | CLOSE: (15) is inconsistent.
% 30.90/4.95 | |
% 30.90/4.95 | End of split
% 30.90/4.95 |
% 30.90/4.95 End of proof
% 30.90/4.95 % SZS output end Proof for theBenchmark
% 30.90/4.95
% 30.90/4.95 4354ms
%------------------------------------------------------------------------------