TSTP Solution File: SWC124+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SWC124+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 20:49:47 EDT 2023
% Result : Theorem 122.05s 16.77s
% Output : Proof 126.94s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWC124+1 : TPTP v8.1.2. Released v2.4.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.12/0.33 % Computer : n005.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Mon Aug 28 17:02:23 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.18/0.58 ________ _____
% 0.18/0.58 ___ __ \_________(_)________________________________
% 0.18/0.58 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.18/0.58 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.18/0.58 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.18/0.58
% 0.18/0.58 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.18/0.58 (2023-06-19)
% 0.18/0.58
% 0.18/0.58 (c) Philipp Rümmer, 2009-2023
% 0.18/0.58 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.18/0.58 Amanda Stjerna.
% 0.18/0.58 Free software under BSD-3-Clause.
% 0.18/0.58
% 0.18/0.58 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.18/0.58
% 0.18/0.58 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.18/0.60 Running up to 7 provers in parallel.
% 0.18/0.61 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.18/0.61 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.18/0.61 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.18/0.61 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.18/0.61 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.18/0.61 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.18/0.61 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 6.45/1.64 Prover 1: Preprocessing ...
% 6.45/1.64 Prover 4: Preprocessing ...
% 6.88/1.68 Prover 6: Preprocessing ...
% 6.88/1.68 Prover 2: Preprocessing ...
% 6.88/1.68 Prover 0: Preprocessing ...
% 6.88/1.68 Prover 5: Preprocessing ...
% 6.88/1.68 Prover 3: Preprocessing ...
% 15.71/2.96 Prover 2: Proving ...
% 16.87/3.03 Prover 1: Constructing countermodel ...
% 16.96/3.05 Prover 5: Constructing countermodel ...
% 16.96/3.10 Prover 6: Proving ...
% 17.51/3.11 Prover 3: Constructing countermodel ...
% 22.09/3.80 Prover 4: Constructing countermodel ...
% 24.83/4.10 Prover 0: Proving ...
% 72.16/10.30 Prover 2: stopped
% 72.54/10.31 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 74.00/10.52 Prover 3: gave up
% 74.00/10.52 Prover 7: Preprocessing ...
% 74.00/10.52 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 74.90/10.69 Prover 8: Preprocessing ...
% 75.59/10.76 Prover 7: Constructing countermodel ...
% 77.68/10.99 Prover 8: Warning: ignoring some quantifiers
% 77.88/11.01 Prover 8: Constructing countermodel ...
% 100.27/13.94 Prover 5: stopped
% 100.27/13.94 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889
% 100.78/14.14 Prover 9: Preprocessing ...
% 108.23/14.96 Prover 9: Constructing countermodel ...
% 115.58/15.95 Prover 1: stopped
% 115.58/15.95 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 116.96/16.13 Prover 10: Preprocessing ...
% 117.95/16.26 Prover 10: Constructing countermodel ...
% 122.05/16.77 Prover 9: proved (2827ms)
% 122.05/16.77
% 122.05/16.77 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 122.05/16.77
% 122.05/16.78 Prover 0: stopped
% 122.05/16.78 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 122.05/16.78 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 122.05/16.80 Prover 6: stopped
% 122.05/16.82 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 122.63/16.85 Prover 11: Preprocessing ...
% 123.23/16.94 Prover 13: Preprocessing ...
% 123.43/16.96 Prover 16: Preprocessing ...
% 124.31/17.09 Prover 16: Constructing countermodel ...
% 124.31/17.13 Prover 13: Constructing countermodel ...
% 125.12/17.20 Prover 10: Found proof (size 67)
% 125.12/17.20 Prover 10: proved (1244ms)
% 125.12/17.20 Prover 13: stopped
% 125.12/17.20 Prover 7: stopped
% 125.12/17.20 Prover 8: stopped
% 125.12/17.20 Prover 16: stopped
% 125.12/17.20 Prover 4: stopped
% 126.44/17.51 Prover 11: Constructing countermodel ...
% 126.55/17.52 Prover 11: stopped
% 126.60/17.52
% 126.60/17.52 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 126.60/17.52
% 126.60/17.54 % SZS output start Proof for theBenchmark
% 126.60/17.54 Assumptions after simplification:
% 126.60/17.54 ---------------------------------
% 126.60/17.54
% 126.60/17.54 (ax15)
% 126.60/17.55 ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ $i(v1) | ~ $i(v0) | ~ ssList(v1) |
% 126.60/17.55 ~ ssList(v0) | neq(v0, v1)) & ! [v0: $i] : ( ~ $i(v0) | ~ ssList(v0) | ~
% 126.60/17.55 neq(v0, v0))
% 126.60/17.55
% 126.60/17.55 (ax17)
% 126.60/17.55 $i(nil) & ssList(nil)
% 126.60/17.55
% 126.60/17.55 (ax28)
% 126.60/17.59 $i(nil) & ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (app(nil, v0) = v1) | ~
% 126.60/17.59 $i(v0) | ~ ssList(v0))
% 126.60/17.59
% 126.60/17.59 (ax45)
% 126.60/17.59 $i(nil) & ! [v0: $i] : ( ~ $i(v0) | ~ ssList(v0) | frontsegP(v0, nil))
% 126.60/17.59
% 126.60/17.59 (ax46)
% 126.60/17.59 $i(nil) & ! [v0: $i] : (v0 = nil | ~ $i(v0) | ~ frontsegP(nil, v0) | ~
% 126.60/17.59 ssList(v0)) & ( ~ ssList(nil) | frontsegP(nil, nil))
% 126.60/17.59
% 126.60/17.59 (ax5)
% 126.60/17.59 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (app(v1, v2) = v0) | ~ $i(v2) |
% 126.60/17.59 ~ $i(v1) | ~ $i(v0) | ~ ssList(v2) | ~ ssList(v1) | ~ ssList(v0) |
% 126.60/17.59 frontsegP(v0, v1)) & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~
% 126.60/17.59 frontsegP(v0, v1) | ~ ssList(v1) | ~ ssList(v0) | ? [v2: $i] : (app(v1,
% 126.60/17.59 v2) = v0 & $i(v2) & ssList(v2)))
% 126.60/17.59
% 126.60/17.59 (ax52)
% 126.60/17.60 $i(nil) & ! [v0: $i] : (v0 = nil | ~ $i(v0) | ~ rearsegP(nil, v0) | ~
% 126.60/17.60 ssList(v0)) & ( ~ ssList(nil) | rearsegP(nil, nil))
% 126.60/17.60
% 126.60/17.60 (ax58)
% 126.60/17.60 $i(nil) & ! [v0: $i] : (v0 = nil | ~ $i(v0) | ~ segmentP(nil, v0) | ~
% 126.60/17.60 ssList(v0)) & ( ~ ssList(nil) | segmentP(nil, nil))
% 126.60/17.60
% 126.60/17.60 (ax6)
% 126.60/17.60 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (app(v2, v1) = v0) | ~ $i(v2) |
% 126.60/17.60 ~ $i(v1) | ~ $i(v0) | ~ ssList(v2) | ~ ssList(v1) | ~ ssList(v0) |
% 126.60/17.60 rearsegP(v0, v1)) & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~
% 126.60/17.60 rearsegP(v0, v1) | ~ ssList(v1) | ~ ssList(v0) | ? [v2: $i] : (app(v2,
% 126.60/17.60 v1) = v0 & $i(v2) & ssList(v2)))
% 126.60/17.60
% 126.60/17.60 (ax7)
% 126.60/17.60 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 126.60/17.60 (app(v3, v4) = v0) | ~ (app(v2, v1) = v3) | ~ $i(v4) | ~ $i(v2) | ~
% 126.60/17.60 $i(v1) | ~ $i(v0) | ~ ssList(v4) | ~ ssList(v2) | ~ ssList(v1) | ~
% 126.60/17.60 ssList(v0) | segmentP(v0, v1)) & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~
% 126.60/17.60 $i(v0) | ~ segmentP(v0, v1) | ~ ssList(v1) | ~ ssList(v0) | ? [v2: $i] :
% 126.60/17.60 ? [v3: $i] : ? [v4: $i] : (app(v3, v4) = v0 & app(v2, v1) = v3 & $i(v4) &
% 126.60/17.60 $i(v3) & $i(v2) & ssList(v4) & ssList(v2)))
% 126.60/17.60
% 126.60/17.60 (ax82)
% 126.60/17.60 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 126.60/17.60 (app(v2, v3) = v4) | ~ (app(v0, v1) = v2) | ~ $i(v3) | ~ $i(v1) | ~
% 126.60/17.60 $i(v0) | ~ ssList(v3) | ~ ssList(v1) | ~ ssList(v0) | ? [v5: $i] :
% 126.60/17.60 (app(v1, v3) = v5 & app(v0, v5) = v4 & $i(v5) & $i(v4)))
% 126.60/17.60
% 126.60/17.60 (ax83)
% 126.60/17.61 $i(nil) & ! [v0: $i] : ! [v1: $i] : (v1 = nil | ~ (app(v0, v1) = nil) | ~
% 126.60/17.61 $i(v1) | ~ $i(v0) | ~ ssList(v1) | ~ ssList(v0)) & ! [v0: $i] : ! [v1:
% 126.60/17.61 $i] : (v0 = nil | ~ (app(v0, v1) = nil) | ~ $i(v1) | ~ $i(v0) | ~
% 126.60/17.61 ssList(v1) | ~ ssList(v0)) & ! [v0: $i] : (v0 = nil | ~ (app(nil, nil) =
% 126.60/17.61 v0) | ~ ssList(nil))
% 126.60/17.61
% 126.60/17.61 (ax84)
% 126.60/17.61 $i(nil) & ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (app(v0, nil) = v1) | ~
% 126.60/17.61 $i(v0) | ~ ssList(v0))
% 126.60/17.61
% 126.60/17.61 (co1)
% 126.60/17.61 $i(nil) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (app(v0, v2) = v1 & $i(v2)
% 126.60/17.61 & $i(v1) & $i(v0) & totalorderedP(v0) & ssList(v2) & ssList(v1) & ssList(v0)
% 126.60/17.61 & neq(v1, nil) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : !
% 126.60/17.61 [v7: $i] : ! [v8: $i] : ( ~ (cons(v6, nil) = v7) | ~ (cons(v3, nil) = v4)
% 126.60/17.61 | ~ (app(v8, v7) = v0) | ~ (app(v4, v5) = v2) | ~ $i(v8) | ~ $i(v6) |
% 126.60/17.61 ~ $i(v5) | ~ $i(v3) | ~ leq(v6, v3) | ~ ssList(v8) | ~ ssList(v5) | ~
% 126.60/17.61 ssItem(v6) | ~ ssItem(v3)) & ( ~ (v0 = nil) | v1 = nil) & ( ~
% 126.60/17.61 segmentP(v1, v0) | ~ neq(v0, nil)))
% 126.60/17.61
% 126.60/17.61 Further assumptions not needed in the proof:
% 126.60/17.61 --------------------------------------------
% 126.60/17.61 ax1, ax10, ax11, ax12, ax13, ax14, ax16, ax18, ax19, ax2, ax20, ax21, ax22,
% 126.60/17.61 ax23, ax24, ax25, ax26, ax27, ax29, ax3, ax30, ax31, ax32, ax33, ax34, ax35,
% 126.60/17.61 ax36, ax37, ax38, ax39, ax4, ax40, ax41, ax42, ax43, ax44, ax47, ax48, ax49,
% 126.60/17.61 ax50, ax51, ax53, ax54, ax55, ax56, ax57, ax59, ax60, ax61, ax62, ax63, ax64,
% 126.60/17.61 ax65, ax66, ax67, ax68, ax69, ax70, ax71, ax72, ax73, ax74, ax75, ax76, ax77,
% 126.60/17.61 ax78, ax79, ax8, ax80, ax81, ax85, ax86, ax87, ax88, ax89, ax9, ax90, ax91,
% 126.60/17.61 ax92, ax93, ax94, ax95
% 126.60/17.61
% 126.60/17.61 Those formulas are unsatisfiable:
% 126.60/17.61 ---------------------------------
% 126.60/17.61
% 126.60/17.61 Begin of proof
% 126.60/17.61 |
% 126.60/17.61 | ALPHA: (ax5) implies:
% 126.94/17.61 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ frontsegP(v0,
% 126.94/17.61 | v1) | ~ ssList(v1) | ~ ssList(v0) | ? [v2: $i] : (app(v1, v2) =
% 126.94/17.61 | v0 & $i(v2) & ssList(v2)))
% 126.94/17.61 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (app(v1, v2) = v0) | ~
% 126.94/17.61 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ ssList(v2) | ~ ssList(v1) | ~
% 126.94/17.61 | ssList(v0) | frontsegP(v0, v1))
% 126.94/17.61 |
% 126.94/17.61 | ALPHA: (ax6) implies:
% 126.94/17.61 | (3) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ rearsegP(v0,
% 126.94/17.61 | v1) | ~ ssList(v1) | ~ ssList(v0) | ? [v2: $i] : (app(v2, v1) =
% 126.94/17.61 | v0 & $i(v2) & ssList(v2)))
% 126.94/17.61 |
% 126.94/17.61 | ALPHA: (ax7) implies:
% 126.94/17.61 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (
% 126.94/17.61 | ~ (app(v3, v4) = v0) | ~ (app(v2, v1) = v3) | ~ $i(v4) | ~ $i(v2)
% 126.94/17.61 | | ~ $i(v1) | ~ $i(v0) | ~ ssList(v4) | ~ ssList(v2) | ~
% 126.94/17.61 | ssList(v1) | ~ ssList(v0) | segmentP(v0, v1))
% 126.94/17.61 |
% 126.94/17.61 | ALPHA: (ax15) implies:
% 126.94/17.61 | (5) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ $i(v1) | ~ $i(v0) | ~
% 126.94/17.61 | ssList(v1) | ~ ssList(v0) | neq(v0, v1))
% 126.94/17.61 |
% 126.94/17.61 | ALPHA: (ax17) implies:
% 126.94/17.61 | (6) ssList(nil)
% 126.94/17.62 |
% 126.94/17.62 | ALPHA: (ax28) implies:
% 126.94/17.62 | (7) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (app(nil, v0) = v1) | ~
% 126.94/17.62 | $i(v0) | ~ ssList(v0))
% 126.94/17.62 |
% 126.94/17.62 | ALPHA: (ax45) implies:
% 126.94/17.62 | (8) ! [v0: $i] : ( ~ $i(v0) | ~ ssList(v0) | frontsegP(v0, nil))
% 126.94/17.62 |
% 126.94/17.62 | ALPHA: (ax46) implies:
% 126.94/17.62 | (9) ~ ssList(nil) | frontsegP(nil, nil)
% 126.94/17.62 |
% 126.94/17.62 | ALPHA: (ax52) implies:
% 126.94/17.62 | (10) ~ ssList(nil) | rearsegP(nil, nil)
% 126.94/17.62 |
% 126.94/17.62 | ALPHA: (ax58) implies:
% 126.94/17.62 | (11) ~ ssList(nil) | segmentP(nil, nil)
% 126.94/17.62 |
% 126.94/17.62 | ALPHA: (ax83) implies:
% 126.94/17.62 | (12) ! [v0: $i] : (v0 = nil | ~ (app(nil, nil) = v0) | ~ ssList(nil))
% 126.94/17.62 |
% 126.94/17.62 | ALPHA: (ax84) implies:
% 126.94/17.62 | (13) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (app(v0, nil) = v1) | ~
% 126.94/17.62 | $i(v0) | ~ ssList(v0))
% 126.94/17.62 |
% 126.94/17.62 | ALPHA: (co1) implies:
% 126.94/17.62 | (14) $i(nil)
% 126.94/17.62 | (15) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (app(v0, v2) = v1 & $i(v2) &
% 126.94/17.62 | $i(v1) & $i(v0) & totalorderedP(v0) & ssList(v2) & ssList(v1) &
% 126.94/17.62 | ssList(v0) & neq(v1, nil) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i]
% 126.94/17.62 | : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ( ~ (cons(v6, nil) = v7)
% 126.94/17.62 | | ~ (cons(v3, nil) = v4) | ~ (app(v8, v7) = v0) | ~ (app(v4,
% 126.94/17.62 | v5) = v2) | ~ $i(v8) | ~ $i(v6) | ~ $i(v5) | ~ $i(v3) | ~
% 126.94/17.62 | leq(v6, v3) | ~ ssList(v8) | ~ ssList(v5) | ~ ssItem(v6) | ~
% 126.94/17.62 | ssItem(v3)) & ( ~ (v0 = nil) | v1 = nil) & ( ~ segmentP(v1, v0) |
% 126.94/17.62 | ~ neq(v0, nil)))
% 126.94/17.62 |
% 126.94/17.62 | DELTA: instantiating (15) with fresh symbols all_91_0, all_91_1, all_91_2
% 126.94/17.62 | gives:
% 126.94/17.62 | (16) app(all_91_2, all_91_0) = all_91_1 & $i(all_91_0) & $i(all_91_1) &
% 126.94/17.62 | $i(all_91_2) & totalorderedP(all_91_2) & ssList(all_91_0) &
% 126.94/17.62 | ssList(all_91_1) & ssList(all_91_2) & neq(all_91_1, nil) & ! [v0: $i]
% 126.94/17.62 | : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i]
% 126.94/17.62 | : ( ~ (cons(v3, nil) = v4) | ~ (cons(v0, nil) = v1) | ~ (app(v5, v4)
% 126.94/17.62 | = all_91_2) | ~ (app(v1, v2) = all_91_0) | ~ $i(v5) | ~ $i(v3)
% 126.94/17.62 | | ~ $i(v2) | ~ $i(v0) | ~ leq(v3, v0) | ~ ssList(v5) | ~
% 126.94/17.62 | ssList(v2) | ~ ssItem(v3) | ~ ssItem(v0)) & ( ~ (all_91_2 = nil) |
% 126.94/17.62 | all_91_1 = nil) & ( ~ segmentP(all_91_1, all_91_2) | ~
% 126.94/17.62 | neq(all_91_2, nil))
% 126.94/17.62 |
% 126.94/17.62 | ALPHA: (16) implies:
% 126.94/17.62 | (17) neq(all_91_1, nil)
% 126.94/17.62 | (18) ssList(all_91_2)
% 126.94/17.62 | (19) ssList(all_91_1)
% 126.94/17.62 | (20) ssList(all_91_0)
% 126.94/17.62 | (21) $i(all_91_2)
% 126.94/17.62 | (22) $i(all_91_1)
% 126.94/17.62 | (23) $i(all_91_0)
% 126.94/17.62 | (24) app(all_91_2, all_91_0) = all_91_1
% 126.94/17.62 | (25) ~ segmentP(all_91_1, all_91_2) | ~ neq(all_91_2, nil)
% 126.94/17.62 | (26) ~ (all_91_2 = nil) | all_91_1 = nil
% 126.94/17.62 |
% 126.94/17.62 | BETA: splitting (10) gives:
% 126.94/17.62 |
% 126.94/17.62 | Case 1:
% 126.94/17.62 | |
% 126.94/17.62 | | (27) ~ ssList(nil)
% 126.94/17.62 | |
% 126.94/17.62 | | PRED_UNIFY: (6), (27) imply:
% 126.94/17.62 | | (28) $false
% 126.94/17.63 | |
% 126.94/17.63 | | CLOSE: (28) is inconsistent.
% 126.94/17.63 | |
% 126.94/17.63 | Case 2:
% 126.94/17.63 | |
% 126.94/17.63 | | (29) rearsegP(nil, nil)
% 126.94/17.63 | |
% 126.94/17.63 | | BETA: splitting (9) gives:
% 126.94/17.63 | |
% 126.94/17.63 | | Case 1:
% 126.94/17.63 | | |
% 126.94/17.63 | | | (30) ~ ssList(nil)
% 126.94/17.63 | | |
% 126.94/17.63 | | | PRED_UNIFY: (6), (30) imply:
% 126.94/17.63 | | | (31) $false
% 126.94/17.63 | | |
% 126.94/17.63 | | | CLOSE: (31) is inconsistent.
% 126.94/17.63 | | |
% 126.94/17.63 | | Case 2:
% 126.94/17.63 | | |
% 126.94/17.63 | | | (32) frontsegP(nil, nil)
% 126.94/17.63 | | |
% 126.94/17.63 | | | BETA: splitting (11) gives:
% 126.94/17.63 | | |
% 126.94/17.63 | | | Case 1:
% 126.94/17.63 | | | |
% 126.94/17.63 | | | | (33) ~ ssList(nil)
% 126.94/17.63 | | | |
% 126.94/17.63 | | | | PRED_UNIFY: (6), (33) imply:
% 126.94/17.63 | | | | (34) $false
% 126.94/17.63 | | | |
% 126.94/17.63 | | | | CLOSE: (34) is inconsistent.
% 126.94/17.63 | | | |
% 126.94/17.63 | | | Case 2:
% 126.94/17.63 | | | |
% 126.94/17.63 | | | |
% 126.94/17.63 | | | | GROUND_INST: instantiating (5) with all_91_2, nil, simplifying with (6),
% 126.94/17.63 | | | | (14), (18), (21) gives:
% 126.94/17.63 | | | | (35) all_91_2 = nil | neq(all_91_2, nil)
% 126.94/17.63 | | | |
% 126.94/17.63 | | | | GROUND_INST: instantiating (8) with all_91_2, simplifying with (18),
% 126.94/17.63 | | | | (21) gives:
% 126.94/17.63 | | | | (36) frontsegP(all_91_2, nil)
% 126.94/17.63 | | | |
% 126.94/17.63 | | | | GROUND_INST: instantiating (1) with nil, nil, simplifying with (6),
% 126.94/17.63 | | | | (14), (32) gives:
% 126.94/17.63 | | | | (37) ? [v0: $i] : (app(nil, v0) = nil & $i(v0) & ssList(v0))
% 126.94/17.63 | | | |
% 126.94/17.63 | | | | GROUND_INST: instantiating (3) with nil, nil, simplifying with (6),
% 126.94/17.63 | | | | (14), (29) gives:
% 126.94/17.63 | | | | (38) ? [v0: $i] : (app(v0, nil) = nil & $i(v0) & ssList(v0))
% 126.94/17.63 | | | |
% 126.94/17.63 | | | | GROUND_INST: instantiating (2) with all_91_1, all_91_2, all_91_0,
% 126.94/17.63 | | | | simplifying with (18), (19), (20), (21), (22), (23), (24)
% 126.94/17.63 | | | | gives:
% 126.94/17.63 | | | | (39) frontsegP(all_91_1, all_91_2)
% 126.94/17.63 | | | |
% 126.94/17.63 | | | | DELTA: instantiating (38) with fresh symbol all_112_0 gives:
% 126.94/17.63 | | | | (40) app(all_112_0, nil) = nil & $i(all_112_0) & ssList(all_112_0)
% 126.94/17.63 | | | |
% 126.94/17.63 | | | | ALPHA: (40) implies:
% 126.94/17.63 | | | | (41) ssList(all_112_0)
% 126.94/17.63 | | | | (42) $i(all_112_0)
% 126.94/17.63 | | | | (43) app(all_112_0, nil) = nil
% 126.94/17.63 | | | |
% 126.94/17.63 | | | | DELTA: instantiating (37) with fresh symbol all_114_0 gives:
% 126.94/17.63 | | | | (44) app(nil, all_114_0) = nil & $i(all_114_0) & ssList(all_114_0)
% 126.94/17.63 | | | |
% 126.94/17.63 | | | | ALPHA: (44) implies:
% 126.94/17.63 | | | | (45) ssList(all_114_0)
% 126.94/17.63 | | | | (46) $i(all_114_0)
% 126.94/17.63 | | | | (47) app(nil, all_114_0) = nil
% 126.94/17.63 | | | |
% 126.94/17.63 | | | | GROUND_INST: instantiating (1) with all_91_2, nil, simplifying with (6),
% 126.94/17.63 | | | | (14), (18), (21), (36) gives:
% 126.94/17.63 | | | | (48) ? [v0: $i] : (app(nil, v0) = all_91_2 & $i(v0) & ssList(v0))
% 126.94/17.63 | | | |
% 126.94/17.63 | | | | GROUND_INST: instantiating (1) with all_91_1, all_91_2, simplifying with
% 126.94/17.63 | | | | (18), (19), (21), (22), (39) gives:
% 126.94/17.63 | | | | (49) ? [v0: $i] : (app(all_91_2, v0) = all_91_1 & $i(v0) &
% 126.94/17.63 | | | | ssList(v0))
% 126.94/17.63 | | | |
% 126.94/17.63 | | | | GROUND_INST: instantiating (ax82) with nil, all_114_0, nil, all_114_0,
% 126.94/17.63 | | | | nil, simplifying with (6), (14), (45), (46), (47) gives:
% 126.94/17.63 | | | | (50) ? [v0: $i] : (app(all_114_0, all_114_0) = v0 & app(nil, v0) =
% 126.94/17.63 | | | | nil & $i(v0))
% 126.94/17.63 | | | |
% 126.94/17.63 | | | | GROUND_INST: instantiating (7) with all_114_0, nil, simplifying with
% 126.94/17.63 | | | | (45), (46), (47) gives:
% 126.94/17.63 | | | | (51) all_114_0 = nil
% 126.94/17.63 | | | |
% 126.94/17.64 | | | | GROUND_INST: instantiating (13) with all_112_0, nil, simplifying with
% 126.94/17.64 | | | | (41), (42), (43) gives:
% 126.94/17.64 | | | | (52) all_112_0 = nil
% 126.94/17.64 | | | |
% 126.94/17.64 | | | | DELTA: instantiating (50) with fresh symbol all_132_0 gives:
% 126.94/17.64 | | | | (53) app(all_114_0, all_114_0) = all_132_0 & app(nil, all_132_0) =
% 126.94/17.64 | | | | nil & $i(all_132_0)
% 126.94/17.64 | | | |
% 126.94/17.64 | | | | ALPHA: (53) implies:
% 126.94/17.64 | | | | (54) $i(all_132_0)
% 126.94/17.64 | | | | (55) app(all_114_0, all_114_0) = all_132_0
% 126.94/17.64 | | | |
% 126.94/17.64 | | | | DELTA: instantiating (49) with fresh symbol all_134_0 gives:
% 126.94/17.64 | | | | (56) app(all_91_2, all_134_0) = all_91_1 & $i(all_134_0) &
% 126.94/17.64 | | | | ssList(all_134_0)
% 126.94/17.64 | | | |
% 126.94/17.64 | | | | ALPHA: (56) implies:
% 126.94/17.64 | | | | (57) ssList(all_134_0)
% 126.94/17.64 | | | | (58) $i(all_134_0)
% 126.94/17.64 | | | | (59) app(all_91_2, all_134_0) = all_91_1
% 126.94/17.64 | | | |
% 126.94/17.64 | | | | DELTA: instantiating (48) with fresh symbol all_152_0 gives:
% 126.94/17.64 | | | | (60) app(nil, all_152_0) = all_91_2 & $i(all_152_0) &
% 126.94/17.64 | | | | ssList(all_152_0)
% 126.94/17.64 | | | |
% 126.94/17.64 | | | | ALPHA: (60) implies:
% 126.94/17.64 | | | | (61) ssList(all_152_0)
% 126.94/17.64 | | | | (62) $i(all_152_0)
% 126.94/17.64 | | | | (63) app(nil, all_152_0) = all_91_2
% 126.94/17.64 | | | |
% 126.94/17.64 | | | | REDUCE: (51), (55) imply:
% 126.94/17.64 | | | | (64) app(nil, nil) = all_132_0
% 126.94/17.64 | | | |
% 126.94/17.64 | | | | GROUND_INST: instantiating (12) with all_132_0, simplifying with (6),
% 126.94/17.64 | | | | (64) gives:
% 126.94/17.64 | | | | (65) all_132_0 = nil
% 126.94/17.64 | | | |
% 126.94/17.64 | | | | GROUND_INST: instantiating (7) with all_152_0, all_91_2, simplifying
% 126.94/17.64 | | | | with (61), (62), (63) gives:
% 126.94/17.64 | | | | (66) all_152_0 = all_91_2
% 126.94/17.64 | | | |
% 126.94/17.64 | | | | GROUND_INST: instantiating (4) with all_91_1, all_152_0, nil, all_91_2,
% 126.94/17.64 | | | | all_134_0, simplifying with (6), (14), (19), (22), (57),
% 126.94/17.64 | | | | (58), (59), (61), (62), (63) gives:
% 126.94/17.64 | | | | (67) segmentP(all_91_1, all_152_0)
% 126.94/17.64 | | | |
% 126.94/17.64 | | | | REDUCE: (66), (67) imply:
% 126.94/17.64 | | | | (68) segmentP(all_91_1, all_91_2)
% 126.94/17.64 | | | |
% 126.94/17.64 | | | | BETA: splitting (25) gives:
% 126.94/17.64 | | | |
% 126.94/17.64 | | | | Case 1:
% 126.94/17.64 | | | | |
% 126.94/17.64 | | | | | (69) ~ neq(all_91_2, nil)
% 126.94/17.64 | | | | |
% 126.94/17.64 | | | | | BETA: splitting (35) gives:
% 126.94/17.64 | | | | |
% 126.94/17.64 | | | | | Case 1:
% 126.94/17.64 | | | | | |
% 126.94/17.64 | | | | | | (70) neq(all_91_2, nil)
% 126.94/17.64 | | | | | |
% 126.94/17.64 | | | | | | PRED_UNIFY: (69), (70) imply:
% 126.94/17.64 | | | | | | (71) $false
% 126.94/17.64 | | | | | |
% 126.94/17.64 | | | | | | CLOSE: (71) is inconsistent.
% 126.94/17.64 | | | | | |
% 126.94/17.64 | | | | | Case 2:
% 126.94/17.64 | | | | | |
% 126.94/17.64 | | | | | | (72) all_91_2 = nil
% 126.94/17.64 | | | | | |
% 126.94/17.64 | | | | | | REDUCE: (69), (72) imply:
% 126.94/17.64 | | | | | | (73) ~ neq(nil, nil)
% 126.94/17.64 | | | | | |
% 126.94/17.64 | | | | | | BETA: splitting (26) gives:
% 126.94/17.64 | | | | | |
% 126.94/17.64 | | | | | | Case 1:
% 126.94/17.64 | | | | | | |
% 126.94/17.64 | | | | | | | (74) ~ (all_91_2 = nil)
% 126.94/17.64 | | | | | | |
% 126.94/17.64 | | | | | | | REDUCE: (72), (74) imply:
% 126.94/17.64 | | | | | | | (75) $false
% 126.94/17.64 | | | | | | |
% 126.94/17.64 | | | | | | | CLOSE: (75) is inconsistent.
% 126.94/17.64 | | | | | | |
% 126.94/17.64 | | | | | | Case 2:
% 126.94/17.64 | | | | | | |
% 126.94/17.64 | | | | | | | (76) all_91_1 = nil
% 126.94/17.64 | | | | | | |
% 126.94/17.64 | | | | | | | REDUCE: (17), (76) imply:
% 126.94/17.64 | | | | | | | (77) neq(nil, nil)
% 126.94/17.64 | | | | | | |
% 126.94/17.64 | | | | | | | PRED_UNIFY: (73), (77) imply:
% 126.94/17.64 | | | | | | | (78) $false
% 126.94/17.64 | | | | | | |
% 126.94/17.64 | | | | | | | CLOSE: (78) is inconsistent.
% 126.94/17.64 | | | | | | |
% 126.94/17.64 | | | | | | End of split
% 126.94/17.64 | | | | | |
% 126.94/17.64 | | | | | End of split
% 126.94/17.64 | | | | |
% 126.94/17.64 | | | | Case 2:
% 126.94/17.64 | | | | |
% 126.94/17.64 | | | | | (79) ~ segmentP(all_91_1, all_91_2)
% 126.94/17.64 | | | | |
% 126.94/17.64 | | | | | PRED_UNIFY: (68), (79) imply:
% 126.94/17.64 | | | | | (80) $false
% 126.94/17.64 | | | | |
% 126.94/17.64 | | | | | CLOSE: (80) is inconsistent.
% 126.94/17.64 | | | | |
% 126.94/17.64 | | | | End of split
% 126.94/17.64 | | | |
% 126.94/17.64 | | | End of split
% 126.94/17.64 | | |
% 126.94/17.64 | | End of split
% 126.94/17.64 | |
% 126.94/17.64 | End of split
% 126.94/17.64 |
% 126.94/17.64 End of proof
% 126.94/17.64 % SZS output end Proof for theBenchmark
% 126.94/17.64
% 126.94/17.64 17060ms
%------------------------------------------------------------------------------