TSTP Solution File: SWC037+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SWC037+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 : n010.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 20:49:19 EDT 2023
% Result : Theorem 26.59s 4.36s
% Output : Proof 31.15s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SWC037+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 : n010.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 14:35:19 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.61 ________ _____
% 0.20/0.61 ___ __ \_________(_)________________________________
% 0.20/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.20/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.20/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.20/0.61
% 0.20/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.61 (2023-06-19)
% 0.20/0.61
% 0.20/0.61 (c) Philipp Rümmer, 2009-2023
% 0.20/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.61 Amanda Stjerna.
% 0.20/0.61 Free software under BSD-3-Clause.
% 0.20/0.61
% 0.20/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.61
% 0.20/0.61 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.20/0.62 Running up to 7 provers in parallel.
% 0.20/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.20/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 6.21/1.62 Prover 1: Preprocessing ...
% 6.88/1.64 Prover 6: Preprocessing ...
% 6.88/1.64 Prover 5: Preprocessing ...
% 6.88/1.64 Prover 3: Preprocessing ...
% 6.88/1.64 Prover 2: Preprocessing ...
% 6.88/1.64 Prover 0: Preprocessing ...
% 6.88/1.64 Prover 4: Preprocessing ...
% 16.98/3.06 Prover 2: Proving ...
% 17.56/3.08 Prover 5: Constructing countermodel ...
% 17.56/3.10 Prover 6: Proving ...
% 17.56/3.12 Prover 1: Constructing countermodel ...
% 18.32/3.19 Prover 3: Constructing countermodel ...
% 23.63/3.96 Prover 4: Constructing countermodel ...
% 23.63/3.99 Prover 0: Proving ...
% 26.59/4.35 Prover 3: proved (3724ms)
% 26.59/4.35
% 26.59/4.36 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 26.59/4.36
% 26.59/4.36 Prover 5: stopped
% 26.59/4.36 Prover 2: stopped
% 26.59/4.37 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 26.59/4.37 Prover 0: stopped
% 26.59/4.37 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 26.59/4.37 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 26.59/4.37 Prover 6: stopped
% 27.30/4.38 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 27.30/4.38 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 27.63/4.49 Prover 10: Preprocessing ...
% 28.26/4.53 Prover 7: Preprocessing ...
% 28.26/4.55 Prover 8: Preprocessing ...
% 28.26/4.57 Prover 13: Preprocessing ...
% 28.26/4.57 Prover 11: Preprocessing ...
% 29.43/4.70 Prover 1: Found proof (size 77)
% 29.43/4.70 Prover 1: proved (4071ms)
% 29.43/4.70 Prover 4: stopped
% 29.43/4.74 Prover 13: stopped
% 29.43/4.74 Prover 10: Constructing countermodel ...
% 29.43/4.76 Prover 10: stopped
% 29.43/4.77 Prover 7: Constructing countermodel ...
% 30.26/4.79 Prover 7: stopped
% 30.26/4.79 Prover 11: stopped
% 30.82/4.91 Prover 8: Warning: ignoring some quantifiers
% 30.82/4.92 Prover 8: Constructing countermodel ...
% 30.82/4.93 Prover 8: stopped
% 30.82/4.93
% 30.82/4.93 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 30.82/4.93
% 30.82/4.93 % SZS output start Proof for theBenchmark
% 30.82/4.94 Assumptions after simplification:
% 30.82/4.94 ---------------------------------
% 30.82/4.94
% 30.82/4.94 (ax15)
% 30.82/4.96 ! [v0: $i] : ( ~ (ssList(v0) = 0) | ~ $i(v0) | ! [v1: $i] : ! [v2: any] :
% 30.82/4.96 ( ~ (neq(v0, v1) = v2) | ~ $i(v1) | ? [v3: int] : ( ~ (v3 = 0) &
% 30.82/4.96 ssList(v1) = v3) | (( ~ (v2 = 0) | ~ (v1 = v0)) & (v2 = 0 | v1 = v0))))
% 30.82/4.96
% 30.82/4.96 (ax54)
% 30.82/4.96 ! [v0: $i] : ( ~ (ssList(v0) = 0) | ~ $i(v0) | ! [v1: $i] : (v1 = v0 | ~
% 30.82/4.96 (segmentP(v0, v1) = 0) | ~ $i(v1) | ? [v2: any] : ? [v3: any] :
% 30.82/4.96 (segmentP(v1, v0) = v3 & ssList(v1) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0)))))
% 30.82/4.96
% 30.82/4.96 (ax58)
% 30.82/4.96 $i(nil) & ! [v0: $i] : ! [v1: any] : ( ~ (segmentP(nil, v0) = v1) | ~
% 30.82/4.96 $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & ssList(v0) = v2) | (( ~ (v1 = 0) | v0
% 30.82/4.96 = nil) & ( ~ (v0 = nil) | v1 = 0)))
% 30.82/4.96
% 30.82/4.96 (co1)
% 30.82/4.97 $i(nil) & ? [v0: $i] : ( ~ (v0 = nil) & ssList(v0) = 0 & ssList(nil) = 0 &
% 30.82/4.97 $i(v0) & ? [v1: $i] : (segmentP(v0, v1) = 0 & segmentP(nil, v1) = 0 &
% 30.82/4.97 ssList(v1) = 0 & neq(v1, nil) = 0 & $i(v1)))
% 30.82/4.97
% 30.82/4.97 (function-axioms)
% 30.82/4.97 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 30.82/4.97 [v3: $i] : (v1 = v0 | ~ (gt(v3, v2) = v1) | ~ (gt(v3, v2) = v0)) & ! [v0:
% 30.82/4.97 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 30.82/4.97 : (v1 = v0 | ~ (geq(v3, v2) = v1) | ~ (geq(v3, v2) = v0)) & ! [v0:
% 30.82/4.97 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 30.82/4.97 : (v1 = v0 | ~ (lt(v3, v2) = v1) | ~ (lt(v3, v2) = v0)) & ! [v0:
% 30.82/4.97 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 30.82/4.97 : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0)) & ! [v0:
% 30.82/4.97 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 30.82/4.97 : (v1 = v0 | ~ (segmentP(v3, v2) = v1) | ~ (segmentP(v3, v2) = v0)) & !
% 30.82/4.97 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 30.82/4.97 $i] : (v1 = v0 | ~ (rearsegP(v3, v2) = v1) | ~ (rearsegP(v3, v2) = v0)) &
% 30.82/4.97 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 30.82/4.97 $i] : (v1 = v0 | ~ (frontsegP(v3, v2) = v1) | ~ (frontsegP(v3, v2) = v0))
% 30.82/4.97 & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 30.82/4.97 [v3: $i] : (v1 = v0 | ~ (memberP(v3, v2) = v1) | ~ (memberP(v3, v2) = v0)) &
% 30.82/4.97 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 30.82/4.97 (cons(v3, v2) = v1) | ~ (cons(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] :
% 30.82/4.97 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (app(v3, v2) = v1) | ~ (app(v3, v2)
% 30.82/4.97 = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 30.82/4.97 $i] : ! [v3: $i] : (v1 = v0 | ~ (neq(v3, v2) = v1) | ~ (neq(v3, v2) =
% 30.82/4.97 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (tl(v2) =
% 30.82/4.97 v1) | ~ (tl(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 =
% 30.82/4.97 v0 | ~ (hd(v2) = v1) | ~ (hd(v2) = v0)) & ! [v0: MultipleValueBool] : !
% 30.82/4.97 [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (equalelemsP(v2) = v1) |
% 30.82/4.97 ~ (equalelemsP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 30.82/4.97 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (duplicatefreeP(v2) = v1) |
% 30.82/4.97 ~ (duplicatefreeP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 30.82/4.97 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (strictorderedP(v2) = v1) |
% 30.82/4.97 ~ (strictorderedP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 30.82/4.97 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (totalorderedP(v2) = v1) |
% 30.82/4.97 ~ (totalorderedP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 30.82/4.97 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (strictorderP(v2) = v1) |
% 30.82/4.97 ~ (strictorderP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 30.82/4.97 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (totalorderP(v2) = v1) | ~
% 30.82/4.97 (totalorderP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 31.15/4.97 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (cyclefreeP(v2) = v1) | ~
% 31.15/4.97 (cyclefreeP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 31.15/4.98 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (singletonP(v2) = v1) | ~
% 31.15/4.98 (singletonP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 31.15/4.98 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (ssList(v2) = v1) | ~
% 31.15/4.98 (ssList(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool]
% 31.15/4.98 : ! [v2: $i] : (v1 = v0 | ~ (ssItem(v2) = v1) | ~ (ssItem(v2) = v0))
% 31.15/4.98
% 31.15/4.98 Further assumptions not needed in the proof:
% 31.15/4.98 --------------------------------------------
% 31.15/4.98 ax1, ax10, ax11, ax12, ax13, ax14, ax16, ax17, ax18, ax19, ax2, ax20, ax21,
% 31.15/4.98 ax22, ax23, ax24, ax25, ax26, ax27, ax28, ax29, ax3, ax30, ax31, ax32, ax33,
% 31.15/4.98 ax34, ax35, ax36, ax37, ax38, ax39, ax4, ax40, ax41, ax42, ax43, ax44, ax45,
% 31.15/4.98 ax46, ax47, ax48, ax49, ax5, ax50, ax51, ax52, ax53, ax55, ax56, ax57, ax59,
% 31.15/4.98 ax6, ax60, ax61, ax62, ax63, ax64, ax65, ax66, ax67, ax68, ax69, ax7, ax70,
% 31.15/4.98 ax71, ax72, ax73, ax74, ax75, ax76, ax77, ax78, ax79, ax8, ax80, ax81, ax82,
% 31.15/4.98 ax83, ax84, ax85, ax86, ax87, ax88, ax89, ax9, ax90, ax91, ax92, ax93, ax94,
% 31.15/4.98 ax95
% 31.15/4.98
% 31.15/4.98 Those formulas are unsatisfiable:
% 31.15/4.98 ---------------------------------
% 31.15/4.98
% 31.15/4.98 Begin of proof
% 31.15/4.98 |
% 31.15/4.98 | ALPHA: (ax58) implies:
% 31.15/4.98 | (1) ! [v0: $i] : ! [v1: any] : ( ~ (segmentP(nil, v0) = v1) | ~ $i(v0) |
% 31.15/4.98 | ? [v2: int] : ( ~ (v2 = 0) & ssList(v0) = v2) | (( ~ (v1 = 0) | v0 =
% 31.15/4.98 | nil) & ( ~ (v0 = nil) | v1 = 0)))
% 31.15/4.98 |
% 31.15/4.98 | ALPHA: (co1) implies:
% 31.15/4.98 | (2) $i(nil)
% 31.15/4.98 | (3) ? [v0: $i] : ( ~ (v0 = nil) & ssList(v0) = 0 & ssList(nil) = 0 &
% 31.15/4.98 | $i(v0) & ? [v1: $i] : (segmentP(v0, v1) = 0 & segmentP(nil, v1) = 0
% 31.15/4.98 | & ssList(v1) = 0 & neq(v1, nil) = 0 & $i(v1)))
% 31.15/4.98 |
% 31.15/4.98 | ALPHA: (function-axioms) implies:
% 31.15/4.98 | (4) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 31.15/4.98 | (v1 = v0 | ~ (ssList(v2) = v1) | ~ (ssList(v2) = v0))
% 31.15/4.98 |
% 31.15/4.98 | DELTA: instantiating (3) with fresh symbol all_93_0 gives:
% 31.15/4.98 | (5) ~ (all_93_0 = nil) & ssList(all_93_0) = 0 & ssList(nil) = 0 &
% 31.15/4.98 | $i(all_93_0) & ? [v0: $i] : (segmentP(all_93_0, v0) = 0 &
% 31.15/4.98 | segmentP(nil, v0) = 0 & ssList(v0) = 0 & neq(v0, nil) = 0 & $i(v0))
% 31.15/4.98 |
% 31.15/4.98 | ALPHA: (5) implies:
% 31.15/4.98 | (6) ~ (all_93_0 = nil)
% 31.15/4.98 | (7) $i(all_93_0)
% 31.15/4.98 | (8) ssList(nil) = 0
% 31.15/4.98 | (9) ssList(all_93_0) = 0
% 31.15/4.98 | (10) ? [v0: $i] : (segmentP(all_93_0, v0) = 0 & segmentP(nil, v0) = 0 &
% 31.15/4.98 | ssList(v0) = 0 & neq(v0, nil) = 0 & $i(v0))
% 31.15/4.98 |
% 31.15/4.98 | DELTA: instantiating (10) with fresh symbol all_97_0 gives:
% 31.15/4.98 | (11) segmentP(all_93_0, all_97_0) = 0 & segmentP(nil, all_97_0) = 0 &
% 31.15/4.98 | ssList(all_97_0) = 0 & neq(all_97_0, nil) = 0 & $i(all_97_0)
% 31.15/4.98 |
% 31.15/4.98 | ALPHA: (11) implies:
% 31.15/4.98 | (12) $i(all_97_0)
% 31.15/4.98 | (13) neq(all_97_0, nil) = 0
% 31.15/4.98 | (14) ssList(all_97_0) = 0
% 31.15/4.98 | (15) segmentP(nil, all_97_0) = 0
% 31.15/4.98 | (16) segmentP(all_93_0, all_97_0) = 0
% 31.15/4.98 |
% 31.15/4.99 | GROUND_INST: instantiating (ax54) with nil, simplifying with (2), (8) gives:
% 31.15/4.99 | (17) ! [v0: $i] : (v0 = nil | ~ (segmentP(nil, v0) = 0) | ~ $i(v0) | ?
% 31.15/4.99 | [v1: any] : ? [v2: any] : (segmentP(v0, nil) = v2 & ssList(v0) = v1
% 31.15/4.99 | & ( ~ (v2 = 0) | ~ (v1 = 0))))
% 31.15/4.99 |
% 31.15/4.99 | GROUND_INST: instantiating (ax54) with all_93_0, simplifying with (7), (9)
% 31.15/4.99 | gives:
% 31.15/4.99 | (18) ! [v0: any] : (v0 = all_93_0 | ~ (segmentP(all_93_0, v0) = 0) | ~
% 31.15/4.99 | $i(v0) | ? [v1: any] : ? [v2: any] : (segmentP(v0, all_93_0) = v2
% 31.15/4.99 | & ssList(v0) = v1 & ( ~ (v2 = 0) | ~ (v1 = 0))))
% 31.15/4.99 |
% 31.15/4.99 | GROUND_INST: instantiating (ax15) with all_97_0, simplifying with (12), (14)
% 31.15/4.99 | gives:
% 31.15/4.99 | (19) ! [v0: $i] : ! [v1: any] : ( ~ (neq(all_97_0, v0) = v1) | ~ $i(v0)
% 31.15/4.99 | | ? [v2: int] : ( ~ (v2 = 0) & ssList(v0) = v2) | (( ~ (v1 = 0) |
% 31.15/4.99 | ~ (v0 = all_97_0)) & (v1 = 0 | v0 = all_97_0)))
% 31.15/4.99 |
% 31.15/4.99 | GROUND_INST: instantiating (1) with all_97_0, 0, simplifying with (12), (15)
% 31.15/4.99 | gives:
% 31.15/4.99 | (20) all_97_0 = nil | ? [v0: int] : ( ~ (v0 = 0) & ssList(all_97_0) = v0)
% 31.15/4.99 |
% 31.15/4.99 | GROUND_INST: instantiating (17) with all_97_0, simplifying with (12), (15)
% 31.15/4.99 | gives:
% 31.15/4.99 | (21) all_97_0 = nil | ? [v0: any] : ? [v1: any] : (segmentP(all_97_0,
% 31.15/4.99 | nil) = v1 & ssList(all_97_0) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 31.15/4.99 |
% 31.15/4.99 | GROUND_INST: instantiating (18) with all_97_0, simplifying with (12), (16)
% 31.15/4.99 | gives:
% 31.15/4.99 | (22) all_97_0 = all_93_0 | ? [v0: any] : ? [v1: any] :
% 31.15/4.99 | (segmentP(all_97_0, all_93_0) = v1 & ssList(all_97_0) = v0 & ( ~ (v1 =
% 31.15/4.99 | 0) | ~ (v0 = 0)))
% 31.15/4.99 |
% 31.15/4.99 | GROUND_INST: instantiating (19) with nil, 0, simplifying with (2) gives:
% 31.15/4.99 | (23) ~ (all_97_0 = nil) | ~ (neq(nil, nil) = 0) | ? [v0: int] : ( ~ (v0
% 31.15/4.99 | = 0) & ssList(nil) = v0)
% 31.15/4.99 |
% 31.15/4.99 | BETA: splitting (20) gives:
% 31.15/4.99 |
% 31.15/4.99 | Case 1:
% 31.15/4.99 | |
% 31.15/4.99 | | (24) all_97_0 = nil
% 31.15/4.99 | |
% 31.15/4.99 | | REDUCE: (13), (24) imply:
% 31.15/4.99 | | (25) neq(nil, nil) = 0
% 31.15/4.99 | |
% 31.15/4.99 | | BETA: splitting (23) gives:
% 31.15/4.99 | |
% 31.15/4.99 | | Case 1:
% 31.15/4.99 | | |
% 31.15/4.99 | | | (26) ~ (neq(nil, nil) = 0)
% 31.15/4.99 | | |
% 31.15/4.99 | | | PRED_UNIFY: (25), (26) imply:
% 31.15/4.99 | | | (27) $false
% 31.15/4.99 | | |
% 31.15/4.99 | | | CLOSE: (27) is inconsistent.
% 31.15/4.99 | | |
% 31.15/4.99 | | Case 2:
% 31.15/4.99 | | |
% 31.15/4.99 | | | (28) ~ (all_97_0 = nil) | ? [v0: int] : ( ~ (v0 = 0) & ssList(nil) =
% 31.15/4.99 | | | v0)
% 31.15/4.99 | | |
% 31.15/4.99 | | | BETA: splitting (28) gives:
% 31.15/4.99 | | |
% 31.15/4.99 | | | Case 1:
% 31.15/4.99 | | | |
% 31.15/4.99 | | | | (29) ~ (all_97_0 = nil)
% 31.15/4.99 | | | |
% 31.15/4.99 | | | | REDUCE: (24), (29) imply:
% 31.15/4.99 | | | | (30) $false
% 31.15/4.99 | | | |
% 31.15/4.99 | | | | CLOSE: (30) is inconsistent.
% 31.15/4.99 | | | |
% 31.15/4.99 | | | Case 2:
% 31.15/4.99 | | | |
% 31.15/4.99 | | | | (31) ? [v0: int] : ( ~ (v0 = 0) & ssList(nil) = v0)
% 31.15/5.00 | | | |
% 31.15/5.00 | | | | DELTA: instantiating (31) with fresh symbol all_295_0 gives:
% 31.15/5.00 | | | | (32) ~ (all_295_0 = 0) & ssList(nil) = all_295_0
% 31.15/5.00 | | | |
% 31.15/5.00 | | | | ALPHA: (32) implies:
% 31.15/5.00 | | | | (33) ~ (all_295_0 = 0)
% 31.15/5.00 | | | | (34) ssList(nil) = all_295_0
% 31.15/5.00 | | | |
% 31.15/5.00 | | | | DELTA: instantiating (31) with fresh symbol all_297_0 gives:
% 31.15/5.00 | | | | (35) ~ (all_297_0 = 0) & ssList(nil) = all_297_0
% 31.15/5.00 | | | |
% 31.15/5.00 | | | | ALPHA: (35) implies:
% 31.15/5.00 | | | | (36) ssList(nil) = all_297_0
% 31.15/5.00 | | | |
% 31.15/5.00 | | | | DELTA: instantiating (31) with fresh symbol all_299_0 gives:
% 31.15/5.00 | | | | (37) ~ (all_299_0 = 0) & ssList(nil) = all_299_0
% 31.15/5.00 | | | |
% 31.15/5.00 | | | | ALPHA: (37) implies:
% 31.15/5.00 | | | | (38) ssList(nil) = all_299_0
% 31.15/5.00 | | | |
% 31.15/5.00 | | | | BETA: splitting (22) gives:
% 31.15/5.00 | | | |
% 31.15/5.00 | | | | Case 1:
% 31.15/5.00 | | | | |
% 31.15/5.00 | | | | | (39) all_97_0 = all_93_0
% 31.15/5.00 | | | | |
% 31.15/5.00 | | | | | COMBINE_EQS: (24), (39) imply:
% 31.15/5.00 | | | | | (40) all_93_0 = nil
% 31.15/5.00 | | | | |
% 31.15/5.00 | | | | | SIMP: (40) implies:
% 31.15/5.00 | | | | | (41) all_93_0 = nil
% 31.15/5.00 | | | | |
% 31.15/5.00 | | | | | REDUCE: (6), (41) imply:
% 31.15/5.00 | | | | | (42) $false
% 31.15/5.00 | | | | |
% 31.15/5.00 | | | | | CLOSE: (42) is inconsistent.
% 31.15/5.00 | | | | |
% 31.15/5.00 | | | | Case 2:
% 31.15/5.00 | | | | |
% 31.15/5.00 | | | | | (43) ? [v0: any] : ? [v1: any] : (segmentP(all_97_0, all_93_0) =
% 31.15/5.00 | | | | | v1 & ssList(all_97_0) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 31.15/5.00 | | | | |
% 31.15/5.00 | | | | | DELTA: instantiating (43) with fresh symbols all_304_0, all_304_1
% 31.15/5.00 | | | | | gives:
% 31.15/5.00 | | | | | (44) segmentP(all_97_0, all_93_0) = all_304_0 & ssList(all_97_0) =
% 31.15/5.00 | | | | | all_304_1 & ( ~ (all_304_0 = 0) | ~ (all_304_1 = 0))
% 31.15/5.00 | | | | |
% 31.15/5.00 | | | | | ALPHA: (44) implies:
% 31.15/5.00 | | | | | (45) ssList(all_97_0) = all_304_1
% 31.15/5.00 | | | | |
% 31.15/5.00 | | | | | REDUCE: (24), (45) imply:
% 31.15/5.00 | | | | | (46) ssList(nil) = all_304_1
% 31.15/5.00 | | | | |
% 31.15/5.00 | | | | | DELTA: instantiating (31) with fresh symbol all_316_0 gives:
% 31.15/5.00 | | | | | (47) ~ (all_316_0 = 0) & ssList(nil) = all_316_0
% 31.15/5.00 | | | | |
% 31.15/5.00 | | | | | ALPHA: (47) implies:
% 31.15/5.00 | | | | | (48) ssList(nil) = all_316_0
% 31.15/5.00 | | | | |
% 31.15/5.00 | | | | | GROUND_INST: instantiating (4) with 0, all_299_0, nil, simplifying
% 31.15/5.00 | | | | | with (8), (38) gives:
% 31.15/5.00 | | | | | (49) all_299_0 = 0
% 31.15/5.00 | | | | |
% 31.15/5.00 | | | | | GROUND_INST: instantiating (4) with all_299_0, all_304_1, nil,
% 31.15/5.00 | | | | | simplifying with (38), (46) gives:
% 31.15/5.00 | | | | | (50) all_304_1 = all_299_0
% 31.15/5.00 | | | | |
% 31.15/5.00 | | | | | GROUND_INST: instantiating (4) with all_297_0, all_304_1, nil,
% 31.15/5.00 | | | | | simplifying with (36), (46) gives:
% 31.15/5.00 | | | | | (51) all_304_1 = all_297_0
% 31.15/5.00 | | | | |
% 31.15/5.00 | | | | | GROUND_INST: instantiating (4) with all_304_1, all_316_0, nil,
% 31.15/5.00 | | | | | simplifying with (46), (48) gives:
% 31.15/5.00 | | | | | (52) all_316_0 = all_304_1
% 31.15/5.00 | | | | |
% 31.15/5.00 | | | | | GROUND_INST: instantiating (4) with all_295_0, all_316_0, nil,
% 31.15/5.00 | | | | | simplifying with (34), (48) gives:
% 31.15/5.00 | | | | | (53) all_316_0 = all_295_0
% 31.15/5.00 | | | | |
% 31.15/5.00 | | | | | COMBINE_EQS: (52), (53) imply:
% 31.15/5.00 | | | | | (54) all_304_1 = all_295_0
% 31.15/5.00 | | | | |
% 31.15/5.00 | | | | | SIMP: (54) implies:
% 31.15/5.00 | | | | | (55) all_304_1 = all_295_0
% 31.15/5.00 | | | | |
% 31.15/5.00 | | | | | COMBINE_EQS: (50), (51) imply:
% 31.15/5.00 | | | | | (56) all_299_0 = all_297_0
% 31.15/5.00 | | | | |
% 31.15/5.00 | | | | | SIMP: (56) implies:
% 31.15/5.00 | | | | | (57) all_299_0 = all_297_0
% 31.15/5.00 | | | | |
% 31.15/5.00 | | | | | COMBINE_EQS: (51), (55) imply:
% 31.15/5.00 | | | | | (58) all_297_0 = all_295_0
% 31.15/5.00 | | | | |
% 31.15/5.00 | | | | | COMBINE_EQS: (49), (57) imply:
% 31.15/5.00 | | | | | (59) all_297_0 = 0
% 31.15/5.00 | | | | |
% 31.15/5.00 | | | | | SIMP: (59) implies:
% 31.15/5.00 | | | | | (60) all_297_0 = 0
% 31.15/5.00 | | | | |
% 31.15/5.00 | | | | | COMBINE_EQS: (58), (60) imply:
% 31.15/5.00 | | | | | (61) all_295_0 = 0
% 31.15/5.00 | | | | |
% 31.15/5.00 | | | | | REDUCE: (33), (61) imply:
% 31.15/5.00 | | | | | (62) $false
% 31.15/5.00 | | | | |
% 31.15/5.00 | | | | | CLOSE: (62) is inconsistent.
% 31.15/5.00 | | | | |
% 31.15/5.00 | | | | End of split
% 31.15/5.00 | | | |
% 31.15/5.00 | | | End of split
% 31.15/5.00 | | |
% 31.15/5.00 | | End of split
% 31.15/5.00 | |
% 31.15/5.00 | Case 2:
% 31.15/5.00 | |
% 31.15/5.00 | | (63) ~ (all_97_0 = nil)
% 31.15/5.00 | | (64) ? [v0: int] : ( ~ (v0 = 0) & ssList(all_97_0) = v0)
% 31.15/5.00 | |
% 31.15/5.00 | | DELTA: instantiating (64) with fresh symbol all_267_0 gives:
% 31.15/5.00 | | (65) ~ (all_267_0 = 0) & ssList(all_97_0) = all_267_0
% 31.15/5.00 | |
% 31.15/5.00 | | ALPHA: (65) implies:
% 31.15/5.00 | | (66) ~ (all_267_0 = 0)
% 31.15/5.00 | | (67) ssList(all_97_0) = all_267_0
% 31.15/5.00 | |
% 31.15/5.00 | | DELTA: instantiating (64) with fresh symbol all_271_0 gives:
% 31.15/5.00 | | (68) ~ (all_271_0 = 0) & ssList(all_97_0) = all_271_0
% 31.15/5.00 | |
% 31.15/5.00 | | ALPHA: (68) implies:
% 31.15/5.00 | | (69) ssList(all_97_0) = all_271_0
% 31.15/5.00 | |
% 31.15/5.00 | | BETA: splitting (21) gives:
% 31.15/5.00 | |
% 31.15/5.00 | | Case 1:
% 31.15/5.00 | | |
% 31.15/5.00 | | | (70) all_97_0 = nil
% 31.15/5.00 | | |
% 31.15/5.00 | | | REDUCE: (63), (70) imply:
% 31.15/5.01 | | | (71) $false
% 31.15/5.01 | | |
% 31.15/5.01 | | | CLOSE: (71) is inconsistent.
% 31.15/5.01 | | |
% 31.15/5.01 | | Case 2:
% 31.15/5.01 | | |
% 31.15/5.01 | | | (72) ? [v0: any] : ? [v1: any] : (segmentP(all_97_0, nil) = v1 &
% 31.15/5.01 | | | ssList(all_97_0) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 31.15/5.01 | | |
% 31.15/5.01 | | | DELTA: instantiating (72) with fresh symbols all_291_0, all_291_1 gives:
% 31.15/5.01 | | | (73) segmentP(all_97_0, nil) = all_291_0 & ssList(all_97_0) = all_291_1
% 31.15/5.01 | | | & ( ~ (all_291_0 = 0) | ~ (all_291_1 = 0))
% 31.15/5.01 | | |
% 31.15/5.01 | | | ALPHA: (73) implies:
% 31.15/5.01 | | | (74) ssList(all_97_0) = all_291_1
% 31.15/5.01 | | |
% 31.15/5.01 | | | GROUND_INST: instantiating (4) with 0, all_271_0, all_97_0, simplifying
% 31.15/5.01 | | | with (14), (69) gives:
% 31.15/5.01 | | | (75) all_271_0 = 0
% 31.15/5.01 | | |
% 31.15/5.01 | | | GROUND_INST: instantiating (4) with all_271_0, all_291_1, all_97_0,
% 31.15/5.01 | | | simplifying with (69), (74) gives:
% 31.15/5.01 | | | (76) all_291_1 = all_271_0
% 31.15/5.01 | | |
% 31.15/5.01 | | | GROUND_INST: instantiating (4) with all_267_0, all_291_1, all_97_0,
% 31.15/5.01 | | | simplifying with (67), (74) gives:
% 31.15/5.01 | | | (77) all_291_1 = all_267_0
% 31.15/5.01 | | |
% 31.15/5.01 | | | COMBINE_EQS: (76), (77) imply:
% 31.15/5.01 | | | (78) all_271_0 = all_267_0
% 31.15/5.01 | | |
% 31.15/5.01 | | | SIMP: (78) implies:
% 31.15/5.01 | | | (79) all_271_0 = all_267_0
% 31.15/5.01 | | |
% 31.15/5.01 | | | COMBINE_EQS: (75), (79) imply:
% 31.15/5.01 | | | (80) all_267_0 = 0
% 31.15/5.01 | | |
% 31.15/5.01 | | | REDUCE: (66), (80) imply:
% 31.15/5.01 | | | (81) $false
% 31.15/5.01 | | |
% 31.15/5.01 | | | CLOSE: (81) is inconsistent.
% 31.15/5.01 | | |
% 31.15/5.01 | | End of split
% 31.15/5.01 | |
% 31.15/5.01 | End of split
% 31.15/5.01 |
% 31.15/5.01 End of proof
% 31.15/5.01 % SZS output end Proof for theBenchmark
% 31.15/5.01
% 31.15/5.01 4402ms
%------------------------------------------------------------------------------