TSTP Solution File: SWC373+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SWC373+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 : n022.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 20:51:06 EDT 2023
% Result : Theorem 122.84s 16.80s
% Output : Proof 123.45s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SWC373+1 : TPTP v8.1.2. Released v2.4.0.
% 0.07/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.35 % Computer : n022.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Mon Aug 28 18:17:39 EDT 2023
% 0.13/0.35 % 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.
% 0.20/0.65 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.65 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.65 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.65 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.65 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.65 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 0.20/0.65 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 5.78/1.57 Prover 4: Preprocessing ...
% 6.24/1.58 Prover 6: Preprocessing ...
% 6.24/1.58 Prover 5: Preprocessing ...
% 6.24/1.58 Prover 2: Preprocessing ...
% 6.24/1.58 Prover 3: Preprocessing ...
% 6.24/1.58 Prover 1: Preprocessing ...
% 6.24/1.59 Prover 0: Preprocessing ...
% 16.29/2.98 Prover 2: Proving ...
% 16.29/2.99 Prover 5: Constructing countermodel ...
% 17.54/3.09 Prover 1: Constructing countermodel ...
% 17.54/3.11 Prover 3: Constructing countermodel ...
% 17.54/3.17 Prover 6: Proving ...
% 22.35/3.84 Prover 0: Proving ...
% 23.45/3.95 Prover 4: Constructing countermodel ...
% 72.78/10.33 Prover 2: stopped
% 72.78/10.34 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 73.67/10.51 Prover 7: Preprocessing ...
% 76.45/10.82 Prover 7: Constructing countermodel ...
% 98.06/13.55 Prover 3: gave up
% 98.06/13.55 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 99.34/13.72 Prover 8: Preprocessing ...
% 101.12/13.99 Prover 5: stopped
% 101.12/14.01 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889
% 101.83/14.06 Prover 8: Warning: ignoring some quantifiers
% 101.83/14.06 Prover 8: Constructing countermodel ...
% 102.24/14.13 Prover 9: Preprocessing ...
% 109.89/15.09 Prover 9: Constructing countermodel ...
% 116.98/16.01 Prover 1: stopped
% 116.98/16.03 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 117.42/16.11 Prover 10: Preprocessing ...
% 118.55/16.23 Prover 10: Constructing countermodel ...
% 122.84/16.80 Prover 10: Found proof (size 22)
% 122.84/16.80 Prover 10: proved (772ms)
% 122.84/16.80 Prover 0: stopped
% 122.84/16.80 Prover 6: stopped
% 122.84/16.80 Prover 8: stopped
% 122.84/16.80 Prover 9: stopped
% 122.84/16.80 Prover 7: stopped
% 122.84/16.80 Prover 4: stopped
% 122.84/16.80
% 122.84/16.80 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 122.84/16.80
% 122.84/16.81 % SZS output start Proof for theBenchmark
% 122.84/16.81 Assumptions after simplification:
% 122.84/16.81 ---------------------------------
% 122.84/16.81
% 122.84/16.81 (ax17)
% 122.84/16.82 $i(nil) & ssList(nil)
% 122.84/16.82
% 122.84/16.82 (ax42)
% 122.84/16.82 ! [v0: $i] : ( ~ $i(v0) | ~ ssList(v0) | frontsegP(v0, v0))
% 122.84/16.82
% 122.84/16.82 (ax5)
% 123.45/16.84 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (app(v1, v2) = v0) | ~ $i(v2) |
% 123.45/16.84 ~ $i(v1) | ~ $i(v0) | ~ ssList(v2) | ~ ssList(v1) | ~ ssList(v0) |
% 123.45/16.84 frontsegP(v0, v1)) & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~
% 123.45/16.84 frontsegP(v0, v1) | ~ ssList(v1) | ~ ssList(v0) | ? [v2: $i] : (app(v1,
% 123.45/16.84 v2) = v0 & $i(v2) & ssList(v2)))
% 123.45/16.84
% 123.45/16.84 (ax58)
% 123.45/16.84 $i(nil) & ! [v0: $i] : (v0 = nil | ~ $i(v0) | ~ segmentP(nil, v0) | ~
% 123.45/16.84 ssList(v0)) & ( ~ ssList(nil) | segmentP(nil, nil))
% 123.45/16.84
% 123.45/16.84 (ax6)
% 123.45/16.85 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (app(v2, v1) = v0) | ~ $i(v2) |
% 123.45/16.85 ~ $i(v1) | ~ $i(v0) | ~ ssList(v2) | ~ ssList(v1) | ~ ssList(v0) |
% 123.45/16.85 rearsegP(v0, v1)) & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~
% 123.45/16.85 rearsegP(v0, v1) | ~ ssList(v1) | ~ ssList(v0) | ? [v2: $i] : (app(v2,
% 123.45/16.85 v1) = v0 & $i(v2) & ssList(v2)))
% 123.45/16.85
% 123.45/16.85 (ax7)
% 123.45/16.85 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 123.45/16.85 (app(v3, v4) = v0) | ~ (app(v2, v1) = v3) | ~ $i(v4) | ~ $i(v2) | ~
% 123.45/16.85 $i(v1) | ~ $i(v0) | ~ ssList(v4) | ~ ssList(v2) | ~ ssList(v1) | ~
% 123.45/16.85 ssList(v0) | segmentP(v0, v1)) & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~
% 123.45/16.85 $i(v0) | ~ segmentP(v0, v1) | ~ ssList(v1) | ~ ssList(v0) | ? [v2: $i] :
% 123.45/16.85 ? [v3: $i] : ? [v4: $i] : (app(v3, v4) = v0 & app(v2, v1) = v3 & $i(v4) &
% 123.45/16.85 $i(v3) & $i(v2) & ssList(v4) & ssList(v2)))
% 123.45/16.85
% 123.45/16.85 (co1)
% 123.45/16.85 ? [v0: $i] : ? [v1: $i] : ($i(v1) & $i(v0) & rearsegP(v1, v0) & ssList(v1) &
% 123.45/16.85 ssList(v0) & ~ segmentP(v1, v0))
% 123.45/16.85
% 123.45/16.85 Further assumptions not needed in the proof:
% 123.45/16.85 --------------------------------------------
% 123.45/16.85 ax1, ax10, ax11, ax12, ax13, ax14, ax15, ax16, ax18, ax19, ax2, ax20, ax21,
% 123.45/16.85 ax22, ax23, ax24, ax25, ax26, ax27, ax28, ax29, ax3, ax30, ax31, ax32, ax33,
% 123.45/16.85 ax34, ax35, ax36, ax37, ax38, ax39, ax4, ax40, ax41, ax43, ax44, ax45, ax46,
% 123.45/16.85 ax47, ax48, ax49, ax50, ax51, ax52, ax53, ax54, ax55, ax56, ax57, ax59, ax60,
% 123.45/16.85 ax61, ax62, ax63, ax64, ax65, ax66, ax67, ax68, ax69, ax70, ax71, ax72, ax73,
% 123.45/16.85 ax74, ax75, ax76, ax77, ax78, ax79, ax8, ax80, ax81, ax82, ax83, ax84, ax85,
% 123.45/16.85 ax86, ax87, ax88, ax89, ax9, ax90, ax91, ax92, ax93, ax94, ax95
% 123.45/16.85
% 123.45/16.85 Those formulas are unsatisfiable:
% 123.45/16.85 ---------------------------------
% 123.45/16.85
% 123.45/16.85 Begin of proof
% 123.45/16.85 |
% 123.45/16.85 | ALPHA: (ax5) implies:
% 123.45/16.86 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ frontsegP(v0,
% 123.45/16.86 | v1) | ~ ssList(v1) | ~ ssList(v0) | ? [v2: $i] : (app(v1, v2) =
% 123.45/16.86 | v0 & $i(v2) & ssList(v2)))
% 123.45/16.86 |
% 123.45/16.86 | ALPHA: (ax6) implies:
% 123.45/16.86 | (2) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ rearsegP(v0,
% 123.45/16.86 | v1) | ~ ssList(v1) | ~ ssList(v0) | ? [v2: $i] : (app(v2, v1) =
% 123.45/16.86 | v0 & $i(v2) & ssList(v2)))
% 123.45/16.86 |
% 123.45/16.86 | ALPHA: (ax7) implies:
% 123.45/16.86 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (
% 123.45/16.86 | ~ (app(v3, v4) = v0) | ~ (app(v2, v1) = v3) | ~ $i(v4) | ~ $i(v2)
% 123.45/16.86 | | ~ $i(v1) | ~ $i(v0) | ~ ssList(v4) | ~ ssList(v2) | ~
% 123.45/16.86 | ssList(v1) | ~ ssList(v0) | segmentP(v0, v1))
% 123.45/16.86 |
% 123.45/16.86 | ALPHA: (ax17) implies:
% 123.45/16.86 | (4) ssList(nil)
% 123.45/16.86 |
% 123.45/16.86 | ALPHA: (ax58) implies:
% 123.45/16.86 | (5) ~ ssList(nil) | segmentP(nil, nil)
% 123.45/16.86 |
% 123.45/16.86 | DELTA: instantiating (co1) with fresh symbols all_91_0, all_91_1 gives:
% 123.45/16.86 | (6) $i(all_91_0) & $i(all_91_1) & rearsegP(all_91_0, all_91_1) &
% 123.45/16.86 | ssList(all_91_0) & ssList(all_91_1) & ~ segmentP(all_91_0, all_91_1)
% 123.45/16.86 |
% 123.45/16.86 | ALPHA: (6) implies:
% 123.45/16.86 | (7) ~ segmentP(all_91_0, all_91_1)
% 123.45/16.86 | (8) ssList(all_91_1)
% 123.45/16.86 | (9) ssList(all_91_0)
% 123.45/16.86 | (10) rearsegP(all_91_0, all_91_1)
% 123.45/16.86 | (11) $i(all_91_1)
% 123.45/16.86 | (12) $i(all_91_0)
% 123.45/16.86 |
% 123.45/16.86 | BETA: splitting (5) gives:
% 123.45/16.86 |
% 123.45/16.86 | Case 1:
% 123.45/16.86 | |
% 123.45/16.86 | | (13) ~ ssList(nil)
% 123.45/16.86 | |
% 123.45/16.86 | | PRED_UNIFY: (4), (13) imply:
% 123.45/16.86 | | (14) $false
% 123.45/16.86 | |
% 123.45/16.86 | | CLOSE: (14) is inconsistent.
% 123.45/16.86 | |
% 123.45/16.86 | Case 2:
% 123.45/16.86 | |
% 123.45/16.86 | |
% 123.45/16.86 | | GROUND_INST: instantiating (ax42) with all_91_0, simplifying with (9), (12)
% 123.45/16.86 | | gives:
% 123.45/16.86 | | (15) frontsegP(all_91_0, all_91_0)
% 123.45/16.86 | |
% 123.45/16.87 | | GROUND_INST: instantiating (2) with all_91_0, all_91_1, simplifying with
% 123.45/16.87 | | (8), (9), (10), (11), (12) gives:
% 123.45/16.87 | | (16) ? [v0: $i] : (app(v0, all_91_1) = all_91_0 & $i(v0) & ssList(v0))
% 123.45/16.87 | |
% 123.45/16.87 | | DELTA: instantiating (16) with fresh symbol all_111_0 gives:
% 123.45/16.87 | | (17) app(all_111_0, all_91_1) = all_91_0 & $i(all_111_0) &
% 123.45/16.87 | | ssList(all_111_0)
% 123.45/16.87 | |
% 123.45/16.87 | | ALPHA: (17) implies:
% 123.45/16.87 | | (18) ssList(all_111_0)
% 123.45/16.87 | | (19) $i(all_111_0)
% 123.45/16.87 | | (20) app(all_111_0, all_91_1) = all_91_0
% 123.45/16.87 | |
% 123.45/16.87 | | GROUND_INST: instantiating (1) with all_91_0, all_91_0, simplifying with
% 123.45/16.87 | | (9), (12), (15) gives:
% 123.45/16.87 | | (21) ? [v0: $i] : (app(all_91_0, v0) = all_91_0 & $i(v0) & ssList(v0))
% 123.45/16.87 | |
% 123.45/16.87 | | DELTA: instantiating (21) with fresh symbol all_143_0 gives:
% 123.45/16.87 | | (22) app(all_91_0, all_143_0) = all_91_0 & $i(all_143_0) &
% 123.45/16.87 | | ssList(all_143_0)
% 123.45/16.87 | |
% 123.45/16.87 | | ALPHA: (22) implies:
% 123.45/16.87 | | (23) ssList(all_143_0)
% 123.45/16.87 | | (24) $i(all_143_0)
% 123.45/16.87 | | (25) app(all_91_0, all_143_0) = all_91_0
% 123.45/16.87 | |
% 123.45/16.87 | | GROUND_INST: instantiating (3) with all_91_0, all_91_1, all_111_0, all_91_0,
% 123.45/16.87 | | all_143_0, simplifying with (7), (8), (9), (11), (12), (18),
% 123.45/16.87 | | (19), (20), (23), (24), (25) gives:
% 123.45/16.87 | | (26) $false
% 123.45/16.87 | |
% 123.45/16.87 | | CLOSE: (26) is inconsistent.
% 123.45/16.87 | |
% 123.45/16.87 | End of split
% 123.45/16.87 |
% 123.45/16.87 End of proof
% 123.45/16.87 % SZS output end Proof for theBenchmark
% 123.45/16.87
% 123.45/16.87 16248ms
%------------------------------------------------------------------------------