TSTP Solution File: SWC252+1 by Princess---230619
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- Process Solution
%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SWC252+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 20:50:28 EDT 2023
% Result : Theorem 245.70s 33.39s
% Output : Proof 246.30s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : SWC252+1 : TPTP v8.1.2. Released v2.4.0.
% 0.12/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.14/0.35 % Computer : n024.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Mon Aug 28 15:17:23 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.19/0.61 ________ _____
% 0.19/0.61 ___ __ \_________(_)________________________________
% 0.19/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.19/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.19/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.19/0.61
% 0.19/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.19/0.61 (2023-06-19)
% 0.19/0.61
% 0.19/0.61 (c) Philipp Rümmer, 2009-2023
% 0.19/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.19/0.61 Amanda Stjerna.
% 0.19/0.61 Free software under BSD-3-Clause.
% 0.19/0.61
% 0.19/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.19/0.61
% 0.19/0.61 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.19/0.62 Running up to 7 provers in parallel.
% 0.19/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.19/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.19/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.19/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.19/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.19/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.19/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 6.36/1.64 Prover 4: Preprocessing ...
% 6.36/1.64 Prover 1: Preprocessing ...
% 6.91/1.68 Prover 2: Preprocessing ...
% 6.91/1.68 Prover 3: Preprocessing ...
% 6.91/1.68 Prover 6: Preprocessing ...
% 6.91/1.68 Prover 5: Preprocessing ...
% 6.91/1.68 Prover 0: Preprocessing ...
% 16.25/2.97 Prover 2: Proving ...
% 16.75/3.02 Prover 5: Constructing countermodel ...
% 16.75/3.03 Prover 1: Constructing countermodel ...
% 17.47/3.12 Prover 3: Constructing countermodel ...
% 17.47/3.17 Prover 6: Proving ...
% 22.68/3.80 Prover 4: Constructing countermodel ...
% 23.92/3.96 Prover 0: Proving ...
% 72.83/10.33 Prover 2: stopped
% 72.83/10.34 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 73.95/10.54 Prover 7: Preprocessing ...
% 75.81/10.74 Prover 7: Constructing countermodel ...
% 115.41/15.97 Prover 1: stopped
% 116.21/16.00 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 117.72/16.21 Prover 8: Preprocessing ...
% 119.64/16.47 Prover 8: Warning: ignoring some quantifiers
% 119.64/16.48 Prover 8: Constructing countermodel ...
% 130.46/17.88 Prover 6: stopped
% 130.46/17.88 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889
% 130.95/17.97 Prover 9: Preprocessing ...
% 136.81/18.70 Prover 9: Constructing countermodel ...
% 201.72/27.56 Prover 5: stopped
% 201.72/27.58 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 202.81/27.70 Prover 10: Preprocessing ...
% 203.92/27.83 Prover 10: Constructing countermodel ...
% 205.19/27.97 Prover 4: stopped
% 205.19/27.99 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 206.28/28.11 Prover 11: Preprocessing ...
% 212.07/28.88 Prover 11: Constructing countermodel ...
% 227.98/31.01 Prover 7: stopped
% 227.98/31.02 Prover 12: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=2024365391
% 228.35/31.09 Prover 12: Preprocessing ...
% 230.75/31.43 Prover 12: Proving ...
% 236.35/32.18 Prover 12: stopped
% 236.35/32.18 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 237.20/32.24 Prover 13: Preprocessing ...
% 238.60/32.45 Prover 13: Constructing countermodel ...
% 244.85/33.37 Prover 10: Found proof (size 79)
% 244.85/33.38 Prover 10: proved (5797ms)
% 244.85/33.38 Prover 13: stopped
% 244.85/33.38 Prover 8: stopped
% 244.85/33.38 Prover 0: stopped
% 244.85/33.38 Prover 3: stopped
% 244.85/33.38 Prover 9: stopped
% 245.70/33.39 Prover 11: stopped
% 245.70/33.39
% 245.70/33.39 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 245.70/33.39
% 245.70/33.39 % SZS output start Proof for theBenchmark
% 245.70/33.40 Assumptions after simplification:
% 245.70/33.40 ---------------------------------
% 245.70/33.40
% 245.70/33.40 (ax17)
% 245.70/33.40 $i(nil) & ssList(nil)
% 245.70/33.40
% 245.70/33.40 (ax19)
% 245.70/33.43 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v4 = v2
% 245.70/33.43 | ~ (cons(v4, v1) = v3) | ~ (cons(v2, v0) = v3) | ~ $i(v4) | ~ $i(v2) |
% 245.70/33.43 ~ $i(v1) | ~ $i(v0) | ~ ssList(v1) | ~ ssList(v0) | ~ ssItem(v4) | ~
% 245.70/33.43 ssItem(v2)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : !
% 245.70/33.43 [v4: $i] : (v1 = v0 | ~ (cons(v4, v1) = v3) | ~ (cons(v2, v0) = v3) | ~
% 245.70/33.43 $i(v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ ssList(v1) | ~ ssList(v0) |
% 245.70/33.43 ~ ssItem(v4) | ~ ssItem(v2))
% 245.70/33.43
% 245.70/33.43 (ax20)
% 245.70/33.43 $i(nil) & ! [v0: $i] : (v0 = nil | ~ $i(v0) | ~ ssList(v0) | ? [v1: $i] :
% 245.70/33.43 ? [v2: $i] : (cons(v2, v1) = v0 & $i(v2) & $i(v1) & ssList(v1) &
% 245.70/33.43 ssItem(v2)))
% 245.70/33.43
% 245.70/33.43 (ax23)
% 245.70/33.43 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (cons(v1, v0) = v2) | ~ $i(v1)
% 245.70/33.43 | ~ $i(v0) | ~ ssList(v0) | ~ ssItem(v1) | hd(v2) = v1)
% 245.70/33.43
% 245.70/33.43 (ax25)
% 245.70/33.43 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (cons(v1, v0) = v2) | ~ $i(v1)
% 245.70/33.43 | ~ $i(v0) | ~ ssList(v0) | ~ ssItem(v1) | tl(v2) = v0)
% 245.70/33.43
% 245.70/33.43 (ax28)
% 245.70/33.43 $i(nil) & ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (app(nil, v0) = v1) | ~
% 245.70/33.43 $i(v0) | ~ ssList(v0))
% 245.70/33.43
% 245.70/33.43 (ax4)
% 245.70/33.44 $i(nil) & ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v1, nil) = v0) | ~ $i(v1) |
% 245.70/33.44 ~ $i(v0) | ~ ssList(v0) | ~ ssItem(v1) | singletonP(v0)) & ! [v0: $i] : (
% 245.70/33.44 ~ $i(v0) | ~ singletonP(v0) | ~ ssList(v0) | ? [v1: $i] : (cons(v1, nil)
% 245.70/33.44 = v0 & $i(v1) & ssItem(v1)))
% 245.70/33.44
% 245.70/33.44 (ax46)
% 245.70/33.44 $i(nil) & ! [v0: $i] : (v0 = nil | ~ $i(v0) | ~ frontsegP(nil, v0) | ~
% 245.70/33.44 ssList(v0)) & ( ~ ssList(nil) | frontsegP(nil, nil))
% 245.70/33.44
% 245.70/33.44 (ax5)
% 245.70/33.44 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (app(v1, v2) = v0) | ~ $i(v2) |
% 245.70/33.44 ~ $i(v1) | ~ $i(v0) | ~ ssList(v2) | ~ ssList(v1) | ~ ssList(v0) |
% 245.70/33.44 frontsegP(v0, v1)) & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~
% 245.70/33.44 frontsegP(v0, v1) | ~ ssList(v1) | ~ ssList(v0) | ? [v2: $i] : (app(v1,
% 245.70/33.44 v2) = v0 & $i(v2) & ssList(v2)))
% 245.70/33.44
% 245.70/33.44 (ax55)
% 245.70/33.44 ! [v0: $i] : ( ~ $i(v0) | ~ ssList(v0) | segmentP(v0, v0))
% 245.70/33.44
% 245.70/33.44 (ax58)
% 245.70/33.44 $i(nil) & ! [v0: $i] : (v0 = nil | ~ $i(v0) | ~ segmentP(nil, v0) | ~
% 245.70/33.44 ssList(v0)) & ( ~ ssList(nil) | segmentP(nil, nil))
% 245.70/33.44
% 245.70/33.44 (ax7)
% 245.70/33.45 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 245.70/33.45 (app(v3, v4) = v0) | ~ (app(v2, v1) = v3) | ~ $i(v4) | ~ $i(v2) | ~
% 245.70/33.45 $i(v1) | ~ $i(v0) | ~ ssList(v4) | ~ ssList(v2) | ~ ssList(v1) | ~
% 245.70/33.45 ssList(v0) | segmentP(v0, v1)) & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~
% 245.70/33.45 $i(v0) | ~ segmentP(v0, v1) | ~ ssList(v1) | ~ ssList(v0) | ? [v2: $i] :
% 245.70/33.45 ? [v3: $i] : ? [v4: $i] : (app(v3, v4) = v0 & app(v2, v1) = v3 & $i(v4) &
% 245.70/33.45 $i(v3) & $i(v2) & ssList(v4) & ssList(v2)))
% 245.70/33.45
% 245.70/33.45 (ax77)
% 245.70/33.45 $i(nil) & ! [v0: $i] : ! [v1: $i] : ( ~ (tl(v0) = v1) | ~ $i(v0) | ~
% 245.70/33.45 ssList(v0) | ? [v2: $i] : (hd(v0) = v2 & $i(v2) & ! [v3: $i] : (v3 = v0 |
% 245.70/33.45 v3 = nil | v0 = nil | ~ (tl(v3) = v1) | ~ $i(v3) | ~ ssList(v3) | ?
% 245.70/33.45 [v4: $i] : ( ~ (v4 = v2) & hd(v3) = v4 & $i(v4)))))
% 245.70/33.45
% 245.70/33.45 (ax82)
% 245.70/33.45 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 245.70/33.45 (app(v2, v3) = v4) | ~ (app(v0, v1) = v2) | ~ $i(v3) | ~ $i(v1) | ~
% 245.70/33.45 $i(v0) | ~ ssList(v3) | ~ ssList(v1) | ~ ssList(v0) | ? [v5: $i] :
% 245.70/33.45 (app(v1, v3) = v5 & app(v0, v5) = v4 & $i(v5) & $i(v4)))
% 245.70/33.45
% 246.30/33.45 (ax83)
% 246.30/33.45 $i(nil) & ! [v0: $i] : ! [v1: $i] : (v1 = nil | ~ (app(v0, v1) = nil) | ~
% 246.30/33.45 $i(v1) | ~ $i(v0) | ~ ssList(v1) | ~ ssList(v0)) & ! [v0: $i] : ! [v1:
% 246.30/33.45 $i] : (v0 = nil | ~ (app(v0, v1) = nil) | ~ $i(v1) | ~ $i(v0) | ~
% 246.30/33.46 ssList(v1) | ~ ssList(v0)) & ! [v0: $i] : (v0 = nil | ~ (app(nil, nil) =
% 246.30/33.46 v0) | ~ ssList(nil))
% 246.30/33.46
% 246.30/33.46 (ax86)
% 246.30/33.46 $i(nil) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v0 = nil |
% 246.30/33.46 ~ (tl(v0) = v1) | ~ (app(v1, v2) = v3) | ~ $i(v2) | ~ $i(v0) | ~
% 246.30/33.46 ssList(v2) | ~ ssList(v0) | ? [v4: $i] : (tl(v4) = v3 & app(v0, v2) = v4 &
% 246.30/33.46 $i(v4) & $i(v3)))
% 246.30/33.46
% 246.30/33.46 (ax93)
% 246.30/33.46 ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ $i(v1) | ~ $i(v0) | ~ leq(v0, v1)
% 246.30/33.46 | ~ ssItem(v1) | ~ ssItem(v0) | lt(v0, v1)) & ! [v0: $i] : ! [v1: $i] :
% 246.30/33.46 ( ~ $i(v1) | ~ $i(v0) | ~ lt(v0, v1) | ~ ssItem(v1) | ~ ssItem(v0) |
% 246.30/33.46 leq(v0, v1)) & ! [v0: $i] : ( ~ $i(v0) | ~ lt(v0, v0) | ~ ssItem(v0))
% 246.30/33.46
% 246.30/33.46 (co1)
% 246.30/33.46 $i(nil) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ( ~ (v0 = nil) & cons(v2,
% 246.30/33.46 nil) = v0 & $i(v2) & $i(v1) & $i(v0) & memberP(v1, v2) & ssList(v1) &
% 246.30/33.46 ssList(v0) & ssItem(v2) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6:
% 246.30/33.46 $i] : ! [v7: $i] : ( ~ (cons(v3, nil) = v4) | ~ (app(v6, v7) = v0) | ~
% 246.30/33.46 (app(v5, v4) = v6) | ~ $i(v7) | ~ $i(v5) | ~ $i(v3) | ~ ssList(v7) |
% 246.30/33.46 ~ ssList(v5) | ~ ssItem(v3) | ? [v8: $i] : ($i(v8) & lt(v3, v8) &
% 246.30/33.46 memberP(v7, v8) & memberP(v5, v8) & ssItem(v8) & ~ leq(v3, v8))))
% 246.30/33.46
% 246.30/33.46 (function-axioms)
% 246.30/33.47 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 246.30/33.47 (cons(v3, v2) = v1) | ~ (cons(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] :
% 246.30/33.47 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (app(v3, v2) = v1) | ~ (app(v3, v2)
% 246.30/33.47 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (tl(v2) =
% 246.30/33.47 v1) | ~ (tl(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 =
% 246.30/33.47 v0 | ~ (hd(v2) = v1) | ~ (hd(v2) = v0))
% 246.30/33.47
% 246.30/33.47 Further assumptions not needed in the proof:
% 246.30/33.47 --------------------------------------------
% 246.30/33.47 ax1, ax10, ax11, ax12, ax13, ax14, ax15, ax16, ax18, ax2, ax21, ax22, ax24,
% 246.30/33.47 ax26, ax27, ax29, ax3, ax30, ax31, ax32, ax33, ax34, ax35, ax36, ax37, ax38,
% 246.30/33.47 ax39, ax40, ax41, ax42, ax43, ax44, ax45, ax47, ax48, ax49, ax50, ax51, ax52,
% 246.30/33.47 ax53, ax54, ax56, ax57, ax59, ax6, ax60, ax61, ax62, ax63, ax64, ax65, ax66,
% 246.30/33.47 ax67, ax68, ax69, ax70, ax71, ax72, ax73, ax74, ax75, ax76, ax78, ax79, ax8,
% 246.30/33.47 ax80, ax81, ax84, ax85, ax87, ax88, ax89, ax9, ax90, ax91, ax92, ax94, ax95
% 246.30/33.47
% 246.30/33.47 Those formulas are unsatisfiable:
% 246.30/33.47 ---------------------------------
% 246.30/33.47
% 246.30/33.47 Begin of proof
% 246.30/33.47 |
% 246.30/33.47 | ALPHA: (ax4) implies:
% 246.30/33.47 | (1) ! [v0: $i] : ( ~ $i(v0) | ~ singletonP(v0) | ~ ssList(v0) | ? [v1:
% 246.30/33.47 | $i] : (cons(v1, nil) = v0 & $i(v1) & ssItem(v1)))
% 246.30/33.47 | (2) ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v1, nil) = v0) | ~ $i(v1) | ~
% 246.30/33.47 | $i(v0) | ~ ssList(v0) | ~ ssItem(v1) | singletonP(v0))
% 246.30/33.47 |
% 246.30/33.47 | ALPHA: (ax5) implies:
% 246.30/33.47 | (3) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ frontsegP(v0,
% 246.30/33.47 | v1) | ~ ssList(v1) | ~ ssList(v0) | ? [v2: $i] : (app(v1, v2) =
% 246.30/33.47 | v0 & $i(v2) & ssList(v2)))
% 246.30/33.47 |
% 246.30/33.47 | ALPHA: (ax7) implies:
% 246.30/33.47 | (4) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ segmentP(v0,
% 246.30/33.47 | v1) | ~ ssList(v1) | ~ ssList(v0) | ? [v2: $i] : ? [v3: $i] :
% 246.30/33.47 | ? [v4: $i] : (app(v3, v4) = v0 & app(v2, v1) = v3 & $i(v4) & $i(v3) &
% 246.30/33.47 | $i(v2) & ssList(v4) & ssList(v2)))
% 246.30/33.47 |
% 246.30/33.47 | ALPHA: (ax17) implies:
% 246.30/33.47 | (5) ssList(nil)
% 246.30/33.47 |
% 246.30/33.47 | ALPHA: (ax19) implies:
% 246.30/33.47 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 246.30/33.47 | (v1 = v0 | ~ (cons(v4, v1) = v3) | ~ (cons(v2, v0) = v3) | ~ $i(v4)
% 246.30/33.47 | | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ ssList(v1) | ~ ssList(v0) |
% 246.30/33.47 | ~ ssItem(v4) | ~ ssItem(v2))
% 246.30/33.47 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 246.30/33.47 | (v4 = v2 | ~ (cons(v4, v1) = v3) | ~ (cons(v2, v0) = v3) | ~ $i(v4)
% 246.30/33.47 | | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ ssList(v1) | ~ ssList(v0) |
% 246.30/33.47 | ~ ssItem(v4) | ~ ssItem(v2))
% 246.30/33.47 |
% 246.30/33.48 | ALPHA: (ax20) implies:
% 246.30/33.48 | (8) ! [v0: $i] : (v0 = nil | ~ $i(v0) | ~ ssList(v0) | ? [v1: $i] : ?
% 246.30/33.48 | [v2: $i] : (cons(v2, v1) = v0 & $i(v2) & $i(v1) & ssList(v1) &
% 246.30/33.48 | ssItem(v2)))
% 246.30/33.48 |
% 246.30/33.48 | ALPHA: (ax28) implies:
% 246.30/33.48 | (9) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (app(nil, v0) = v1) | ~
% 246.30/33.48 | $i(v0) | ~ ssList(v0))
% 246.30/33.48 |
% 246.30/33.48 | ALPHA: (ax46) implies:
% 246.30/33.48 | (10) ~ ssList(nil) | frontsegP(nil, nil)
% 246.30/33.48 |
% 246.30/33.48 | ALPHA: (ax58) implies:
% 246.30/33.48 | (11) ~ ssList(nil) | segmentP(nil, nil)
% 246.30/33.48 |
% 246.30/33.48 | ALPHA: (ax77) implies:
% 246.30/33.48 | (12) ! [v0: $i] : ! [v1: $i] : ( ~ (tl(v0) = v1) | ~ $i(v0) | ~
% 246.30/33.48 | ssList(v0) | ? [v2: $i] : (hd(v0) = v2 & $i(v2) & ! [v3: $i] : (v3
% 246.30/33.48 | = v0 | v3 = nil | v0 = nil | ~ (tl(v3) = v1) | ~ $i(v3) | ~
% 246.30/33.48 | ssList(v3) | ? [v4: $i] : ( ~ (v4 = v2) & hd(v3) = v4 &
% 246.30/33.48 | $i(v4)))))
% 246.30/33.48 |
% 246.30/33.48 | ALPHA: (ax83) implies:
% 246.30/33.48 | (13) ! [v0: $i] : (v0 = nil | ~ (app(nil, nil) = v0) | ~ ssList(nil))
% 246.30/33.48 |
% 246.30/33.48 | ALPHA: (ax86) implies:
% 246.30/33.48 | (14) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v0 = nil | ~
% 246.30/33.48 | (tl(v0) = v1) | ~ (app(v1, v2) = v3) | ~ $i(v2) | ~ $i(v0) | ~
% 246.30/33.48 | ssList(v2) | ~ ssList(v0) | ? [v4: $i] : (tl(v4) = v3 & app(v0,
% 246.30/33.48 | v2) = v4 & $i(v4) & $i(v3)))
% 246.30/33.48 |
% 246.30/33.48 | ALPHA: (ax93) implies:
% 246.30/33.48 | (15) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ lt(v0, v1) |
% 246.30/33.48 | ~ ssItem(v1) | ~ ssItem(v0) | leq(v0, v1))
% 246.30/33.48 |
% 246.30/33.48 | ALPHA: (co1) implies:
% 246.30/33.48 | (16) $i(nil)
% 246.30/33.48 | (17) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ( ~ (v0 = nil) & cons(v2,
% 246.30/33.48 | nil) = v0 & $i(v2) & $i(v1) & $i(v0) & memberP(v1, v2) &
% 246.30/33.48 | ssList(v1) & ssList(v0) & ssItem(v2) & ! [v3: $i] : ! [v4: $i] :
% 246.30/33.48 | ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ( ~ (cons(v3, nil) = v4) |
% 246.30/33.48 | ~ (app(v6, v7) = v0) | ~ (app(v5, v4) = v6) | ~ $i(v7) | ~
% 246.30/33.48 | $i(v5) | ~ $i(v3) | ~ ssList(v7) | ~ ssList(v5) | ~ ssItem(v3)
% 246.30/33.48 | | ? [v8: $i] : ($i(v8) & lt(v3, v8) & memberP(v7, v8) &
% 246.30/33.48 | memberP(v5, v8) & ssItem(v8) & ~ leq(v3, v8))))
% 246.30/33.48 |
% 246.30/33.48 | ALPHA: (function-axioms) implies:
% 246.30/33.48 | (18) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (hd(v2) = v1)
% 246.30/33.48 | | ~ (hd(v2) = v0))
% 246.30/33.48 |
% 246.30/33.48 | DELTA: instantiating (17) with fresh symbols all_91_0, all_91_1, all_91_2
% 246.30/33.48 | gives:
% 246.30/33.49 | (19) ~ (all_91_2 = nil) & cons(all_91_0, nil) = all_91_2 & $i(all_91_0) &
% 246.30/33.49 | $i(all_91_1) & $i(all_91_2) & memberP(all_91_1, all_91_0) &
% 246.30/33.49 | ssList(all_91_1) & ssList(all_91_2) & ssItem(all_91_0) & ! [v0: $i] :
% 246.30/33.49 | ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (cons(v0,
% 246.30/33.49 | nil) = v1) | ~ (app(v3, v4) = all_91_2) | ~ (app(v2, v1) = v3)
% 246.30/33.49 | | ~ $i(v4) | ~ $i(v2) | ~ $i(v0) | ~ ssList(v4) | ~ ssList(v2)
% 246.30/33.49 | | ~ ssItem(v0) | ? [v5: $i] : ($i(v5) & lt(v0, v5) & memberP(v4,
% 246.30/33.49 | v5) & memberP(v2, v5) & ssItem(v5) & ~ leq(v0, v5)))
% 246.30/33.49 |
% 246.30/33.49 | ALPHA: (19) implies:
% 246.30/33.49 | (20) ~ (all_91_2 = nil)
% 246.30/33.49 | (21) ssItem(all_91_0)
% 246.30/33.49 | (22) ssList(all_91_2)
% 246.30/33.49 | (23) $i(all_91_2)
% 246.30/33.49 | (24) $i(all_91_0)
% 246.30/33.49 | (25) cons(all_91_0, nil) = all_91_2
% 246.30/33.49 | (26) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 246.30/33.49 | ( ~ (cons(v0, nil) = v1) | ~ (app(v3, v4) = all_91_2) | ~ (app(v2,
% 246.30/33.49 | v1) = v3) | ~ $i(v4) | ~ $i(v2) | ~ $i(v0) | ~ ssList(v4) |
% 246.30/33.49 | ~ ssList(v2) | ~ ssItem(v0) | ? [v5: $i] : ($i(v5) & lt(v0, v5) &
% 246.30/33.49 | memberP(v4, v5) & memberP(v2, v5) & ssItem(v5) & ~ leq(v0, v5)))
% 246.30/33.49 |
% 246.30/33.49 | BETA: splitting (10) gives:
% 246.30/33.49 |
% 246.30/33.49 | Case 1:
% 246.30/33.49 | |
% 246.30/33.49 | | (27) ~ ssList(nil)
% 246.30/33.49 | |
% 246.30/33.49 | | PRED_UNIFY: (5), (27) imply:
% 246.30/33.49 | | (28) $false
% 246.30/33.49 | |
% 246.30/33.49 | | CLOSE: (28) is inconsistent.
% 246.30/33.49 | |
% 246.30/33.49 | Case 2:
% 246.30/33.49 | |
% 246.30/33.49 | | (29) frontsegP(nil, nil)
% 246.30/33.49 | |
% 246.30/33.49 | | BETA: splitting (11) gives:
% 246.30/33.49 | |
% 246.30/33.49 | | Case 1:
% 246.30/33.49 | | |
% 246.30/33.49 | | | (30) ~ ssList(nil)
% 246.30/33.49 | | |
% 246.30/33.49 | | | PRED_UNIFY: (5), (30) imply:
% 246.30/33.49 | | | (31) $false
% 246.30/33.49 | | |
% 246.30/33.49 | | | CLOSE: (31) is inconsistent.
% 246.30/33.49 | | |
% 246.30/33.49 | | Case 2:
% 246.30/33.49 | | |
% 246.30/33.49 | | |
% 246.30/33.49 | | | GROUND_INST: instantiating (8) with all_91_2, simplifying with (22), (23)
% 246.30/33.49 | | | gives:
% 246.30/33.49 | | | (32) all_91_2 = nil | ? [v0: $i] : ? [v1: $i] : (cons(v1, v0) =
% 246.30/33.49 | | | all_91_2 & $i(v1) & $i(v0) & ssList(v0) & ssItem(v1))
% 246.30/33.49 | | |
% 246.30/33.49 | | | GROUND_INST: instantiating (ax55) with all_91_2, simplifying with (22),
% 246.30/33.49 | | | (23) gives:
% 246.30/33.49 | | | (33) segmentP(all_91_2, all_91_2)
% 246.30/33.49 | | |
% 246.30/33.49 | | | GROUND_INST: instantiating (3) with nil, nil, simplifying with (5), (16),
% 246.30/33.49 | | | (29) gives:
% 246.30/33.49 | | | (34) ? [v0: $i] : (app(nil, v0) = nil & $i(v0) & ssList(v0))
% 246.30/33.49 | | |
% 246.30/33.49 | | | GROUND_INST: instantiating (ax25) with nil, all_91_0, all_91_2,
% 246.30/33.49 | | | simplifying with (5), (16), (21), (24), (25) gives:
% 246.30/33.49 | | | (35) tl(all_91_2) = nil
% 246.30/33.49 | | |
% 246.30/33.50 | | | GROUND_INST: instantiating (2) with all_91_2, all_91_0, simplifying with
% 246.30/33.50 | | | (21), (22), (23), (24), (25) gives:
% 246.30/33.50 | | | (36) singletonP(all_91_2)
% 246.30/33.50 | | |
% 246.30/33.50 | | | DELTA: instantiating (34) with fresh symbol all_112_0 gives:
% 246.30/33.50 | | | (37) app(nil, all_112_0) = nil & $i(all_112_0) & ssList(all_112_0)
% 246.30/33.50 | | |
% 246.30/33.50 | | | ALPHA: (37) implies:
% 246.30/33.50 | | | (38) ssList(all_112_0)
% 246.30/33.50 | | | (39) $i(all_112_0)
% 246.30/33.50 | | | (40) app(nil, all_112_0) = nil
% 246.30/33.50 | | |
% 246.30/33.50 | | | BETA: splitting (32) gives:
% 246.30/33.50 | | |
% 246.30/33.50 | | | Case 1:
% 246.30/33.50 | | | |
% 246.30/33.50 | | | | (41) all_91_2 = nil
% 246.30/33.50 | | | |
% 246.30/33.50 | | | | REDUCE: (20), (41) imply:
% 246.30/33.50 | | | | (42) $false
% 246.30/33.50 | | | |
% 246.30/33.50 | | | | CLOSE: (42) is inconsistent.
% 246.30/33.50 | | | |
% 246.30/33.50 | | | Case 2:
% 246.30/33.50 | | | |
% 246.30/33.50 | | | | (43) ? [v0: $i] : ? [v1: $i] : (cons(v1, v0) = all_91_2 & $i(v1) &
% 246.30/33.50 | | | | $i(v0) & ssList(v0) & ssItem(v1))
% 246.30/33.50 | | | |
% 246.30/33.50 | | | | DELTA: instantiating (43) with fresh symbols all_140_0, all_140_1 gives:
% 246.30/33.50 | | | | (44) cons(all_140_0, all_140_1) = all_91_2 & $i(all_140_0) &
% 246.30/33.50 | | | | $i(all_140_1) & ssList(all_140_1) & ssItem(all_140_0)
% 246.30/33.50 | | | |
% 246.30/33.50 | | | | ALPHA: (44) implies:
% 246.30/33.50 | | | | (45) ssItem(all_140_0)
% 246.30/33.50 | | | | (46) ssList(all_140_1)
% 246.30/33.50 | | | | (47) $i(all_140_1)
% 246.30/33.50 | | | | (48) $i(all_140_0)
% 246.30/33.50 | | | | (49) cons(all_140_0, all_140_1) = all_91_2
% 246.30/33.50 | | | |
% 246.30/33.50 | | | | GROUND_INST: instantiating (1) with all_91_2, simplifying with (22),
% 246.30/33.50 | | | | (23), (36) gives:
% 246.30/33.50 | | | | (50) ? [v0: $i] : (cons(v0, nil) = all_91_2 & $i(v0) & ssItem(v0))
% 246.30/33.50 | | | |
% 246.30/33.50 | | | | GROUND_INST: instantiating (4) with all_91_2, all_91_2, simplifying with
% 246.30/33.50 | | | | (22), (23), (33) gives:
% 246.30/33.50 | | | | (51) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (app(v1, v2) =
% 246.30/33.50 | | | | all_91_2 & app(v0, all_91_2) = v1 & $i(v2) & $i(v1) & $i(v0) &
% 246.30/33.50 | | | | ssList(v2) & ssList(v0))
% 246.30/33.50 | | | |
% 246.30/33.50 | | | | GROUND_INST: instantiating (ax82) with nil, all_112_0, nil, all_112_0,
% 246.30/33.50 | | | | nil, simplifying with (5), (16), (38), (39), (40) gives:
% 246.30/33.50 | | | | (52) ? [v0: $i] : (app(all_112_0, all_112_0) = v0 & app(nil, v0) =
% 246.30/33.50 | | | | nil & $i(v0))
% 246.30/33.50 | | | |
% 246.30/33.50 | | | | GROUND_INST: instantiating (9) with all_112_0, nil, simplifying with
% 246.30/33.50 | | | | (38), (39), (40) gives:
% 246.30/33.50 | | | | (53) all_112_0 = nil
% 246.30/33.50 | | | |
% 246.30/33.50 | | | | GROUND_INST: instantiating (7) with all_140_1, nil, all_140_0, all_91_2,
% 246.30/33.50 | | | | all_91_0, simplifying with (5), (16), (21), (24), (25),
% 246.30/33.50 | | | | (45), (46), (47), (48), (49) gives:
% 246.30/33.50 | | | | (54) all_140_0 = all_91_0
% 246.30/33.50 | | | |
% 246.30/33.50 | | | | GROUND_INST: instantiating (6) with all_140_1, nil, all_140_0, all_91_2,
% 246.30/33.50 | | | | all_91_0, simplifying with (5), (16), (21), (24), (25),
% 246.30/33.50 | | | | (45), (46), (47), (48), (49) gives:
% 246.30/33.50 | | | | (55) all_140_1 = nil
% 246.30/33.50 | | | |
% 246.30/33.50 | | | | GROUND_INST: instantiating (ax23) with all_140_1, all_140_0, all_91_2,
% 246.30/33.50 | | | | simplifying with (45), (46), (47), (48), (49) gives:
% 246.30/33.50 | | | | (56) hd(all_91_2) = all_140_0
% 246.30/33.51 | | | |
% 246.30/33.51 | | | | GROUND_INST: instantiating (14) with all_91_2, nil, all_112_0, nil,
% 246.30/33.51 | | | | simplifying with (22), (23), (35), (38), (39), (40) gives:
% 246.30/33.51 | | | | (57) all_91_2 = nil | ? [v0: $i] : (tl(v0) = nil & app(all_91_2,
% 246.30/33.51 | | | | all_112_0) = v0 & $i(v0) & $i(nil))
% 246.30/33.51 | | | |
% 246.30/33.51 | | | | GROUND_INST: instantiating (12) with all_91_2, nil, simplifying with
% 246.30/33.51 | | | | (22), (23), (35) gives:
% 246.30/33.51 | | | | (58) ? [v0: $i] : (hd(all_91_2) = v0 & $i(v0) & ! [v1: any] : (v1 =
% 246.30/33.51 | | | | all_91_2 | v1 = nil | all_91_2 = nil | ~ (tl(v1) = nil) |
% 246.30/33.51 | | | | ~ $i(v1) | ~ ssList(v1) | ? [v2: $i] : ( ~ (v2 = v0) &
% 246.30/33.51 | | | | hd(v1) = v2 & $i(v2))))
% 246.30/33.51 | | | |
% 246.30/33.51 | | | | DELTA: instantiating (52) with fresh symbol all_148_0 gives:
% 246.30/33.51 | | | | (59) app(all_112_0, all_112_0) = all_148_0 & app(nil, all_148_0) =
% 246.30/33.51 | | | | nil & $i(all_148_0)
% 246.30/33.51 | | | |
% 246.30/33.51 | | | | ALPHA: (59) implies:
% 246.30/33.51 | | | | (60) $i(all_148_0)
% 246.30/33.51 | | | | (61) app(all_112_0, all_112_0) = all_148_0
% 246.30/33.51 | | | |
% 246.30/33.51 | | | | DELTA: instantiating (50) with fresh symbol all_160_0 gives:
% 246.30/33.51 | | | | (62) cons(all_160_0, nil) = all_91_2 & $i(all_160_0) &
% 246.30/33.51 | | | | ssItem(all_160_0)
% 246.30/33.51 | | | |
% 246.30/33.51 | | | | ALPHA: (62) implies:
% 246.30/33.51 | | | | (63) ssItem(all_160_0)
% 246.30/33.51 | | | | (64) $i(all_160_0)
% 246.30/33.51 | | | | (65) cons(all_160_0, nil) = all_91_2
% 246.30/33.51 | | | |
% 246.30/33.51 | | | | DELTA: instantiating (51) with fresh symbols all_174_0, all_174_1,
% 246.30/33.51 | | | | all_174_2 gives:
% 246.30/33.51 | | | | (66) app(all_174_1, all_174_0) = all_91_2 & app(all_174_2, all_91_2)
% 246.30/33.51 | | | | = all_174_1 & $i(all_174_0) & $i(all_174_1) & $i(all_174_2) &
% 246.30/33.51 | | | | ssList(all_174_0) & ssList(all_174_2)
% 246.30/33.51 | | | |
% 246.30/33.51 | | | | ALPHA: (66) implies:
% 246.30/33.51 | | | | (67) ssList(all_174_2)
% 246.30/33.51 | | | | (68) ssList(all_174_0)
% 246.30/33.51 | | | | (69) $i(all_174_2)
% 246.30/33.51 | | | | (70) $i(all_174_0)
% 246.30/33.51 | | | | (71) app(all_174_2, all_91_2) = all_174_1
% 246.30/33.51 | | | | (72) app(all_174_1, all_174_0) = all_91_2
% 246.30/33.51 | | | |
% 246.30/33.51 | | | | DELTA: instantiating (58) with fresh symbol all_180_0 gives:
% 246.30/33.51 | | | | (73) hd(all_91_2) = all_180_0 & $i(all_180_0) & ! [v0: any] : (v0 =
% 246.30/33.51 | | | | all_91_2 | v0 = nil | all_91_2 = nil | ~ (tl(v0) = nil) | ~
% 246.30/33.51 | | | | $i(v0) | ~ ssList(v0) | ? [v1: any] : ( ~ (v1 = all_180_0) &
% 246.30/33.51 | | | | hd(v0) = v1 & $i(v1)))
% 246.30/33.51 | | | |
% 246.30/33.51 | | | | ALPHA: (73) implies:
% 246.30/33.51 | | | | (74) $i(all_180_0)
% 246.30/33.51 | | | | (75) hd(all_91_2) = all_180_0
% 246.30/33.51 | | | |
% 246.30/33.51 | | | | REDUCE: (54), (56) imply:
% 246.30/33.51 | | | | (76) hd(all_91_2) = all_91_0
% 246.30/33.51 | | | |
% 246.30/33.51 | | | | REDUCE: (53), (61) imply:
% 246.30/33.51 | | | | (77) app(nil, nil) = all_148_0
% 246.30/33.51 | | | |
% 246.30/33.51 | | | | BETA: splitting (57) gives:
% 246.30/33.51 | | | |
% 246.30/33.51 | | | | Case 1:
% 246.30/33.51 | | | | |
% 246.30/33.51 | | | | | (78) all_91_2 = nil
% 246.30/33.51 | | | | |
% 246.30/33.51 | | | | | REDUCE: (20), (78) imply:
% 246.30/33.51 | | | | | (79) $false
% 246.30/33.51 | | | | |
% 246.30/33.51 | | | | | CLOSE: (79) is inconsistent.
% 246.30/33.51 | | | | |
% 246.30/33.51 | | | | Case 2:
% 246.30/33.51 | | | | |
% 246.30/33.51 | | | | |
% 246.30/33.51 | | | | | GROUND_INST: instantiating (13) with all_148_0, simplifying with (5),
% 246.30/33.51 | | | | | (77) gives:
% 246.30/33.51 | | | | | (80) all_148_0 = nil
% 246.30/33.51 | | | | |
% 246.30/33.51 | | | | | GROUND_INST: instantiating (18) with all_91_0, all_180_0, all_91_2,
% 246.30/33.51 | | | | | simplifying with (75), (76) gives:
% 246.30/33.51 | | | | | (81) all_180_0 = all_91_0
% 246.30/33.51 | | | | |
% 246.30/33.52 | | | | | GROUND_INST: instantiating (7) with nil, nil, all_91_0, all_91_2,
% 246.30/33.52 | | | | | all_160_0, simplifying with (5), (16), (21), (24), (25),
% 246.30/33.52 | | | | | (63), (64), (65) gives:
% 246.30/33.52 | | | | | (82) all_160_0 = all_91_0
% 246.30/33.52 | | | | |
% 246.30/33.52 | | | | | GROUND_INST: instantiating (26) with all_160_0, all_91_2, all_174_2,
% 246.30/33.52 | | | | | all_174_1, all_174_0, simplifying with (63), (64), (65),
% 246.30/33.52 | | | | | (67), (68), (69), (70), (71), (72) gives:
% 246.30/33.52 | | | | | (83) ? [v0: $i] : ($i(v0) & lt(all_160_0, v0) & memberP(all_174_0,
% 246.30/33.52 | | | | | v0) & memberP(all_174_2, v0) & ssItem(v0) & ~
% 246.30/33.52 | | | | | leq(all_160_0, v0))
% 246.30/33.52 | | | | |
% 246.30/33.52 | | | | | DELTA: instantiating (83) with fresh symbol all_296_0 gives:
% 246.30/33.52 | | | | | (84) $i(all_296_0) & lt(all_160_0, all_296_0) & memberP(all_174_0,
% 246.30/33.52 | | | | | all_296_0) & memberP(all_174_2, all_296_0) &
% 246.30/33.52 | | | | | ssItem(all_296_0) & ~ leq(all_160_0, all_296_0)
% 246.30/33.52 | | | | |
% 246.30/33.52 | | | | | ALPHA: (84) implies:
% 246.30/33.52 | | | | | (85) ~ leq(all_160_0, all_296_0)
% 246.30/33.52 | | | | | (86) ssItem(all_296_0)
% 246.30/33.52 | | | | | (87) lt(all_160_0, all_296_0)
% 246.30/33.52 | | | | | (88) $i(all_296_0)
% 246.30/33.52 | | | | |
% 246.30/33.52 | | | | | REDUCE: (82), (87) imply:
% 246.30/33.52 | | | | | (89) lt(all_91_0, all_296_0)
% 246.30/33.52 | | | | |
% 246.30/33.52 | | | | | REDUCE: (82), (85) imply:
% 246.30/33.52 | | | | | (90) ~ leq(all_91_0, all_296_0)
% 246.30/33.52 | | | | |
% 246.30/33.52 | | | | | GROUND_INST: instantiating (15) with all_91_0, all_296_0, simplifying
% 246.30/33.52 | | | | | with (21), (24), (86), (88), (89), (90) gives:
% 246.30/33.52 | | | | | (91) $false
% 246.30/33.52 | | | | |
% 246.30/33.52 | | | | | CLOSE: (91) is inconsistent.
% 246.30/33.52 | | | | |
% 246.30/33.52 | | | | End of split
% 246.30/33.52 | | | |
% 246.30/33.52 | | | End of split
% 246.30/33.52 | | |
% 246.30/33.52 | | End of split
% 246.30/33.52 | |
% 246.30/33.52 | End of split
% 246.30/33.52 |
% 246.30/33.52 End of proof
% 246.30/33.52 % SZS output end Proof for theBenchmark
% 246.30/33.52
% 246.30/33.52 32909ms
%------------------------------------------------------------------------------