TSTP Solution File: SWC039+1 by Princess---230619
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SWC039+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 : n003.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 20:49:20 EDT 2023
% Result : Theorem 28.88s 4.53s
% Output : Proof 39.38s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SWC039+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 : n003.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 17:57:40 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.61/0.65 ________ _____
% 0.61/0.65 ___ __ \_________(_)________________________________
% 0.61/0.65 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.61/0.65 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.61/0.65 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.61/0.65
% 0.61/0.65 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.61/0.65 (2023-06-19)
% 0.61/0.65
% 0.61/0.65 (c) Philipp Rümmer, 2009-2023
% 0.61/0.65 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.61/0.65 Amanda Stjerna.
% 0.61/0.65 Free software under BSD-3-Clause.
% 0.61/0.65
% 0.61/0.65 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.61/0.65
% 0.61/0.65 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.61/0.66 Running up to 7 provers in parallel.
% 0.61/0.67 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.61/0.67 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.61/0.67 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.61/0.67 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.61/0.67 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.61/0.67 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.61/0.67 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 5.23/1.46 Prover 1: Preprocessing ...
% 5.23/1.47 Prover 4: Preprocessing ...
% 5.59/1.49 Prover 3: Preprocessing ...
% 5.59/1.49 Prover 0: Preprocessing ...
% 5.59/1.49 Prover 6: Preprocessing ...
% 5.59/1.49 Prover 5: Preprocessing ...
% 5.59/1.49 Prover 2: Preprocessing ...
% 14.75/2.70 Prover 2: Proving ...
% 14.75/2.72 Prover 5: Constructing countermodel ...
% 14.75/2.73 Prover 6: Proving ...
% 14.75/2.74 Prover 1: Constructing countermodel ...
% 14.75/2.75 Prover 3: Constructing countermodel ...
% 22.68/3.71 Prover 4: Constructing countermodel ...
% 24.13/3.89 Prover 0: Proving ...
% 28.88/4.53 Prover 3: proved (3860ms)
% 28.88/4.53
% 28.88/4.53 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 28.88/4.53
% 28.88/4.53 Prover 5: stopped
% 28.88/4.53 Prover 2: stopped
% 28.88/4.53 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 28.88/4.53 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 28.88/4.53 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 28.88/4.57 Prover 0: stopped
% 28.88/4.57 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 29.50/4.60 Prover 6: stopped
% 29.50/4.61 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 31.39/4.86 Prover 8: Preprocessing ...
% 32.09/4.94 Prover 10: Preprocessing ...
% 32.09/4.96 Prover 11: Preprocessing ...
% 32.09/4.96 Prover 13: Preprocessing ...
% 32.09/4.98 Prover 7: Preprocessing ...
% 33.73/5.21 Prover 10: Constructing countermodel ...
% 33.73/5.26 Prover 13: Constructing countermodel ...
% 34.61/5.27 Prover 7: Constructing countermodel ...
% 34.61/5.30 Prover 8: Warning: ignoring some quantifiers
% 34.61/5.32 Prover 8: Constructing countermodel ...
% 37.57/5.67 Prover 10: Found proof (size 20)
% 37.57/5.67 Prover 10: proved (1134ms)
% 37.57/5.67 Prover 7: stopped
% 37.57/5.67 Prover 13: stopped
% 37.57/5.67 Prover 1: stopped
% 37.57/5.67 Prover 8: stopped
% 37.57/5.67 Prover 4: stopped
% 39.13/5.97 Prover 11: Constructing countermodel ...
% 39.13/6.00 Prover 11: stopped
% 39.13/6.00
% 39.13/6.00 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 39.13/6.00
% 39.13/6.00 % SZS output start Proof for theBenchmark
% 39.27/6.01 Assumptions after simplification:
% 39.27/6.01 ---------------------------------
% 39.27/6.01
% 39.27/6.01 (ax54)
% 39.27/6.02 ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ $i(v1) | ~ $i(v0) | ~ segmentP(v1,
% 39.27/6.02 v0) | ~ segmentP(v0, v1) | ~ ssList(v1) | ~ ssList(v0))
% 39.27/6.02
% 39.27/6.02 (ax57)
% 39.27/6.02 $i(nil) & ! [v0: $i] : ( ~ $i(v0) | ~ ssList(v0) | segmentP(v0, nil))
% 39.27/6.02
% 39.27/6.02 (ax58)
% 39.27/6.03 $i(nil) & ! [v0: $i] : (v0 = nil | ~ $i(v0) | ~ segmentP(nil, v0) | ~
% 39.27/6.03 ssList(v0)) & ( ~ ssList(nil) | segmentP(nil, nil))
% 39.27/6.03
% 39.27/6.03 (ax7)
% 39.38/6.07 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 39.38/6.07 (app(v3, v4) = v0) | ~ (app(v2, v1) = v3) | ~ $i(v4) | ~ $i(v2) | ~
% 39.38/6.07 $i(v1) | ~ $i(v0) | ~ ssList(v4) | ~ ssList(v2) | ~ ssList(v1) | ~
% 39.38/6.07 ssList(v0) | segmentP(v0, v1)) & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~
% 39.38/6.07 $i(v0) | ~ segmentP(v0, v1) | ~ ssList(v1) | ~ ssList(v0) | ? [v2: $i] :
% 39.38/6.07 ? [v3: $i] : ? [v4: $i] : (app(v3, v4) = v0 & app(v2, v1) = v3 & $i(v4) &
% 39.38/6.07 $i(v3) & $i(v2) & ssList(v4) & ssList(v2)))
% 39.38/6.07
% 39.38/6.07 (ax82)
% 39.38/6.07 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 39.38/6.07 (app(v2, v3) = v4) | ~ (app(v0, v1) = v2) | ~ $i(v3) | ~ $i(v1) | ~
% 39.38/6.07 $i(v0) | ~ ssList(v3) | ~ ssList(v1) | ~ ssList(v0) | ? [v5: $i] :
% 39.38/6.07 (app(v1, v3) = v5 & app(v0, v5) = v4 & $i(v5) & $i(v4)))
% 39.38/6.07
% 39.38/6.07 (co1)
% 39.38/6.07 $i(nil) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i]
% 39.38/6.07 : ( ~ (v0 = nil) & cons(v1, nil) = v0 & app(v3, v4) = nil & app(v2, v0) = v3 &
% 39.38/6.07 $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & ssList(v4) & ssList(v2) &
% 39.38/6.07 ssList(v0) & ssList(nil) & ssItem(v1) & ! [v5: $i] : ( ~ $i(v5) | ~ lt(v5,
% 39.38/6.07 v1) | ~ memberP(v4, v5) | ~ ssItem(v5)) & ! [v5: $i] : ( ~ $i(v5) |
% 39.38/6.07 ~ lt(v1, v5) | ~ memberP(v2, v5) | ~ ssItem(v5)))
% 39.38/6.07
% 39.38/6.07 Further assumptions not needed in the proof:
% 39.38/6.07 --------------------------------------------
% 39.38/6.08 ax1, ax10, ax11, ax12, ax13, ax14, ax15, ax16, ax17, ax18, ax19, ax2, ax20,
% 39.38/6.08 ax21, ax22, ax23, ax24, ax25, ax26, ax27, ax28, ax29, ax3, ax30, ax31, ax32,
% 39.38/6.08 ax33, ax34, ax35, ax36, ax37, ax38, ax39, ax4, ax40, ax41, ax42, ax43, ax44,
% 39.38/6.08 ax45, ax46, ax47, ax48, ax49, ax5, ax50, ax51, ax52, ax53, ax55, ax56, ax59,
% 39.38/6.08 ax6, ax60, ax61, ax62, ax63, ax64, ax65, ax66, ax67, ax68, ax69, ax70, ax71,
% 39.38/6.08 ax72, ax73, ax74, ax75, ax76, ax77, ax78, ax79, ax8, ax80, ax81, ax83, ax84,
% 39.38/6.08 ax85, ax86, ax87, ax88, ax89, ax9, ax90, ax91, ax92, ax93, ax94, ax95
% 39.38/6.08
% 39.38/6.08 Those formulas are unsatisfiable:
% 39.38/6.08 ---------------------------------
% 39.38/6.08
% 39.38/6.08 Begin of proof
% 39.38/6.08 |
% 39.38/6.08 | ALPHA: (ax7) implies:
% 39.38/6.08 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (
% 39.38/6.08 | ~ (app(v3, v4) = v0) | ~ (app(v2, v1) = v3) | ~ $i(v4) | ~ $i(v2)
% 39.38/6.08 | | ~ $i(v1) | ~ $i(v0) | ~ ssList(v4) | ~ ssList(v2) | ~
% 39.38/6.08 | ssList(v1) | ~ ssList(v0) | segmentP(v0, v1))
% 39.38/6.08 |
% 39.38/6.08 | ALPHA: (ax57) implies:
% 39.38/6.08 | (2) ! [v0: $i] : ( ~ $i(v0) | ~ ssList(v0) | segmentP(v0, nil))
% 39.38/6.08 |
% 39.38/6.08 | ALPHA: (ax58) implies:
% 39.38/6.08 | (3) ~ ssList(nil) | segmentP(nil, nil)
% 39.38/6.08 |
% 39.38/6.08 | ALPHA: (co1) implies:
% 39.38/6.08 | (4) $i(nil)
% 39.38/6.09 | (5) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : (
% 39.38/6.09 | ~ (v0 = nil) & cons(v1, nil) = v0 & app(v3, v4) = nil & app(v2, v0) =
% 39.38/6.09 | v3 & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & ssList(v4) &
% 39.38/6.09 | ssList(v2) & ssList(v0) & ssList(nil) & ssItem(v1) & ! [v5: $i] : (
% 39.38/6.09 | ~ $i(v5) | ~ lt(v5, v1) | ~ memberP(v4, v5) | ~ ssItem(v5)) & !
% 39.38/6.09 | [v5: $i] : ( ~ $i(v5) | ~ lt(v1, v5) | ~ memberP(v2, v5) | ~
% 39.38/6.09 | ssItem(v5)))
% 39.38/6.09 |
% 39.38/6.09 | DELTA: instantiating (5) with fresh symbols all_91_0, all_91_1, all_91_2,
% 39.38/6.09 | all_91_3, all_91_4 gives:
% 39.38/6.09 | (6) ~ (all_91_4 = nil) & cons(all_91_3, nil) = all_91_4 & app(all_91_1,
% 39.38/6.09 | all_91_0) = nil & app(all_91_2, all_91_4) = all_91_1 & $i(all_91_0) &
% 39.38/6.09 | $i(all_91_1) & $i(all_91_2) & $i(all_91_3) & $i(all_91_4) &
% 39.38/6.09 | ssList(all_91_0) & ssList(all_91_2) & ssList(all_91_4) & ssList(nil) &
% 39.38/6.09 | ssItem(all_91_3) & ! [v0: $i] : ( ~ $i(v0) | ~ lt(v0, all_91_3) | ~
% 39.38/6.09 | memberP(all_91_0, v0) | ~ ssItem(v0)) & ! [v0: $i] : ( ~ $i(v0) |
% 39.38/6.09 | ~ lt(all_91_3, v0) | ~ memberP(all_91_2, v0) | ~ ssItem(v0))
% 39.38/6.09 |
% 39.38/6.09 | ALPHA: (6) implies:
% 39.38/6.09 | (7) ~ (all_91_4 = nil)
% 39.38/6.09 | (8) ssList(nil)
% 39.38/6.09 | (9) ssList(all_91_4)
% 39.38/6.09 | (10) ssList(all_91_2)
% 39.38/6.09 | (11) ssList(all_91_0)
% 39.38/6.09 | (12) $i(all_91_4)
% 39.38/6.09 | (13) $i(all_91_2)
% 39.38/6.09 | (14) $i(all_91_0)
% 39.38/6.09 | (15) app(all_91_2, all_91_4) = all_91_1
% 39.38/6.09 | (16) app(all_91_1, all_91_0) = nil
% 39.38/6.09 |
% 39.38/6.09 | BETA: splitting (3) gives:
% 39.38/6.09 |
% 39.38/6.09 | Case 1:
% 39.38/6.09 | |
% 39.38/6.09 | | (17) ~ ssList(nil)
% 39.38/6.09 | |
% 39.38/6.09 | | PRED_UNIFY: (8), (17) imply:
% 39.38/6.09 | | (18) $false
% 39.38/6.09 | |
% 39.38/6.09 | | CLOSE: (18) is inconsistent.
% 39.38/6.09 | |
% 39.38/6.09 | Case 2:
% 39.38/6.09 | |
% 39.38/6.09 | |
% 39.38/6.09 | | GROUND_INST: instantiating (2) with all_91_4, simplifying with (9), (12)
% 39.38/6.09 | | gives:
% 39.38/6.09 | | (19) segmentP(all_91_4, nil)
% 39.38/6.09 | |
% 39.38/6.10 | | GROUND_INST: instantiating (1) with nil, all_91_4, all_91_2, all_91_1,
% 39.38/6.10 | | all_91_0, simplifying with (4), (8), (9), (10), (11), (12),
% 39.38/6.10 | | (13), (14), (15), (16) gives:
% 39.38/6.10 | | (20) segmentP(nil, all_91_4)
% 39.38/6.10 | |
% 39.38/6.10 | | GROUND_INST: instantiating (ax82) with all_91_2, all_91_4, all_91_1,
% 39.38/6.10 | | all_91_0, nil, simplifying with (9), (10), (11), (12), (13),
% 39.38/6.10 | | (14), (15), (16) gives:
% 39.38/6.10 | | (21) ? [v0: $i] : (app(all_91_2, v0) = nil & app(all_91_4, all_91_0) =
% 39.38/6.10 | | v0 & $i(v0) & $i(nil))
% 39.38/6.10 | |
% 39.38/6.10 | | DELTA: instantiating (21) with fresh symbol all_116_0 gives:
% 39.38/6.10 | | (22) app(all_91_2, all_116_0) = nil & app(all_91_4, all_91_0) = all_116_0
% 39.38/6.10 | | & $i(all_116_0) & $i(nil)
% 39.38/6.10 | |
% 39.38/6.10 | | GROUND_INST: instantiating (ax54) with nil, all_91_4, simplifying with (4),
% 39.38/6.10 | | (8), (9), (12), (19), (20) gives:
% 39.38/6.10 | | (23) all_91_4 = nil
% 39.38/6.10 | |
% 39.38/6.10 | | REDUCE: (7), (23) imply:
% 39.38/6.10 | | (24) $false
% 39.38/6.10 | |
% 39.38/6.10 | | CLOSE: (24) is inconsistent.
% 39.38/6.10 | |
% 39.38/6.10 | End of split
% 39.38/6.10 |
% 39.38/6.10 End of proof
% 39.38/6.10 % SZS output end Proof for theBenchmark
% 39.38/6.10
% 39.38/6.10 5450ms
%------------------------------------------------------------------------------