TSTP Solution File: SWC210+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SWC210+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 : n008.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 20:50:15 EDT 2023
% Result : Theorem 22.28s 3.75s
% Output : Proof 29.23s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SWC210+1 : TPTP v8.1.2. Released v2.4.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.14/0.34 % Computer : n008.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.35 % DateTime : Mon Aug 28 16:59:17 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.21/0.61 ________ _____
% 0.21/0.61 ___ __ \_________(_)________________________________
% 0.21/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.21/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.21/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.21/0.61
% 0.21/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.21/0.61 (2023-06-19)
% 0.21/0.61
% 0.21/0.61 (c) Philipp Rümmer, 2009-2023
% 0.21/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.21/0.61 Amanda Stjerna.
% 0.21/0.61 Free software under BSD-3-Clause.
% 0.21/0.61
% 0.21/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.21/0.61
% 0.21/0.61 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.21/0.63 Running up to 7 provers in parallel.
% 0.21/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.21/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.21/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.21/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.21/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.21/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.21/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 6.46/1.63 Prover 1: Preprocessing ...
% 6.81/1.67 Prover 4: Preprocessing ...
% 6.81/1.68 Prover 5: Preprocessing ...
% 6.81/1.68 Prover 2: Preprocessing ...
% 6.81/1.68 Prover 6: Preprocessing ...
% 6.81/1.68 Prover 3: Preprocessing ...
% 6.81/1.68 Prover 0: Preprocessing ...
% 15.41/3.00 Prover 2: Proving ...
% 15.41/3.01 Prover 5: Constructing countermodel ...
% 17.09/3.04 Prover 6: Proving ...
% 17.09/3.07 Prover 1: Constructing countermodel ...
% 17.09/3.08 Prover 3: Constructing countermodel ...
% 22.28/3.75 Prover 3: proved (3110ms)
% 22.28/3.75
% 22.28/3.75 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 22.28/3.75
% 22.28/3.75 Prover 2: stopped
% 22.28/3.76 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 22.28/3.76 Prover 6: stopped
% 22.28/3.77 Prover 5: stopped
% 22.28/3.78 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 22.28/3.78 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 22.28/3.78 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 22.28/3.79 Prover 4: Constructing countermodel ...
% 23.45/3.91 Prover 10: Preprocessing ...
% 23.45/3.94 Prover 7: Preprocessing ...
% 23.45/3.97 Prover 8: Preprocessing ...
% 24.21/3.98 Prover 11: Preprocessing ...
% 24.55/4.08 Prover 0: Proving ...
% 24.55/4.09 Prover 0: stopped
% 25.07/4.11 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 25.68/4.22 Prover 13: Preprocessing ...
% 25.68/4.23 Prover 10: Constructing countermodel ...
% 26.42/4.30 Prover 7: Constructing countermodel ...
% 26.42/4.45 Prover 1: Found proof (size 33)
% 26.42/4.45 Prover 1: proved (3815ms)
% 26.42/4.45 Prover 4: stopped
% 26.42/4.45 Prover 7: stopped
% 27.48/4.46 Prover 10: Found proof (size 11)
% 27.48/4.46 Prover 10: proved (689ms)
% 27.91/4.50 Prover 13: Constructing countermodel ...
% 27.91/4.50 Prover 8: Warning: ignoring some quantifiers
% 27.91/4.51 Prover 8: Constructing countermodel ...
% 27.91/4.51 Prover 13: stopped
% 28.01/4.52 Prover 8: stopped
% 29.23/4.88 Prover 11: Constructing countermodel ...
% 29.23/4.90 Prover 11: stopped
% 29.23/4.90
% 29.23/4.90 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 29.23/4.90
% 29.23/4.91 % SZS output start Proof for theBenchmark
% 29.23/4.91 Assumptions after simplification:
% 29.23/4.91 ---------------------------------
% 29.23/4.91
% 29.23/4.91 (ax15)
% 29.23/4.95 ! [v0: $i] : ( ~ (ssList(v0) = 0) | ~ $i(v0) | ! [v1: $i] : ! [v2: any] :
% 29.23/4.95 ( ~ (neq(v0, v1) = v2) | ~ $i(v1) | ? [v3: int] : ( ~ (v3 = 0) &
% 29.23/4.95 ssList(v1) = v3) | (( ~ (v2 = 0) | ~ (v1 = v0)) & (v2 = 0 | v1 = v0))))
% 29.23/4.95
% 29.23/4.95 (ax17)
% 29.23/4.95 ssList(nil) = 0 & $i(nil)
% 29.23/4.95
% 29.23/4.95 (ax39)
% 29.23/4.95 $i(nil) & ? [v0: int] : ( ~ (v0 = 0) & singletonP(nil) = v0)
% 29.23/4.95
% 29.23/4.95 (co1)
% 29.23/4.95 $i(nil) & ? [v0: $i] : ? [v1: any] : (ssList(v0) = 0 & neq(v0, nil) = v1 &
% 29.23/4.95 $i(v0) & ? [v2: $i] : ( ~ (v1 = 0) & singletonP(v0) = 0 & ssList(v2) = 0 &
% 29.23/4.95 neq(v2, nil) = 0 & $i(v2)))
% 29.23/4.95
% 29.23/4.95 (function-axioms)
% 29.23/4.97 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 29.23/4.97 [v3: $i] : (v1 = v0 | ~ (gt(v3, v2) = v1) | ~ (gt(v3, v2) = v0)) & ! [v0:
% 29.23/4.97 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 29.23/4.97 : (v1 = v0 | ~ (geq(v3, v2) = v1) | ~ (geq(v3, v2) = v0)) & ! [v0:
% 29.23/4.97 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 29.23/4.97 : (v1 = v0 | ~ (lt(v3, v2) = v1) | ~ (lt(v3, v2) = v0)) & ! [v0:
% 29.23/4.97 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 29.23/4.97 : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0)) & ! [v0:
% 29.23/4.97 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 29.23/4.97 : (v1 = v0 | ~ (segmentP(v3, v2) = v1) | ~ (segmentP(v3, v2) = v0)) & !
% 29.23/4.97 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 29.23/4.97 $i] : (v1 = v0 | ~ (rearsegP(v3, v2) = v1) | ~ (rearsegP(v3, v2) = v0)) &
% 29.23/4.97 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 29.23/4.97 $i] : (v1 = v0 | ~ (frontsegP(v3, v2) = v1) | ~ (frontsegP(v3, v2) = v0))
% 29.23/4.97 & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 29.23/4.97 [v3: $i] : (v1 = v0 | ~ (memberP(v3, v2) = v1) | ~ (memberP(v3, v2) = v0)) &
% 29.23/4.97 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 29.23/4.97 (cons(v3, v2) = v1) | ~ (cons(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] :
% 29.23/4.97 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (app(v3, v2) = v1) | ~ (app(v3, v2)
% 29.23/4.97 = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 29.23/4.97 $i] : ! [v3: $i] : (v1 = v0 | ~ (neq(v3, v2) = v1) | ~ (neq(v3, v2) =
% 29.23/4.97 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (tl(v2) =
% 29.23/4.97 v1) | ~ (tl(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 =
% 29.23/4.97 v0 | ~ (hd(v2) = v1) | ~ (hd(v2) = v0)) & ! [v0: MultipleValueBool] : !
% 29.23/4.97 [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (equalelemsP(v2) = v1) |
% 29.23/4.97 ~ (equalelemsP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 29.23/4.98 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (duplicatefreeP(v2) = v1) |
% 29.23/4.98 ~ (duplicatefreeP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 29.23/4.98 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (strictorderedP(v2) = v1) |
% 29.23/4.98 ~ (strictorderedP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 29.23/4.98 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (totalorderedP(v2) = v1) |
% 29.23/4.98 ~ (totalorderedP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 29.23/4.98 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (strictorderP(v2) = v1) |
% 29.23/4.98 ~ (strictorderP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 29.23/4.98 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (totalorderP(v2) = v1) | ~
% 29.23/4.98 (totalorderP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 29.23/4.98 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (cyclefreeP(v2) = v1) | ~
% 29.23/4.98 (cyclefreeP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 29.23/4.98 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (singletonP(v2) = v1) | ~
% 29.23/4.98 (singletonP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 29.23/4.98 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (ssList(v2) = v1) | ~
% 29.23/4.98 (ssList(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool]
% 29.23/4.98 : ! [v2: $i] : (v1 = v0 | ~ (ssItem(v2) = v1) | ~ (ssItem(v2) = v0))
% 29.23/4.98
% 29.23/4.98 Further assumptions not needed in the proof:
% 29.23/4.98 --------------------------------------------
% 29.23/4.98 ax1, ax10, ax11, ax12, ax13, ax14, ax16, ax18, ax19, ax2, ax20, ax21, ax22,
% 29.23/4.98 ax23, ax24, ax25, ax26, ax27, ax28, ax29, ax3, ax30, ax31, ax32, ax33, ax34,
% 29.23/4.98 ax35, ax36, ax37, ax38, ax4, ax40, ax41, ax42, ax43, ax44, ax45, ax46, ax47,
% 29.23/4.98 ax48, ax49, ax5, ax50, ax51, ax52, ax53, ax54, ax55, ax56, ax57, ax58, ax59,
% 29.23/4.98 ax6, ax60, ax61, ax62, ax63, ax64, ax65, ax66, ax67, ax68, ax69, ax7, ax70,
% 29.23/4.98 ax71, ax72, ax73, ax74, ax75, ax76, ax77, ax78, ax79, ax8, ax80, ax81, ax82,
% 29.23/4.98 ax83, ax84, ax85, ax86, ax87, ax88, ax89, ax9, ax90, ax91, ax92, ax93, ax94,
% 29.23/4.98 ax95
% 29.23/4.98
% 29.23/4.98 Those formulas are unsatisfiable:
% 29.23/4.98 ---------------------------------
% 29.23/4.98
% 29.23/4.98 Begin of proof
% 29.23/4.98 |
% 29.23/4.98 | ALPHA: (ax17) implies:
% 29.23/4.98 | (1) ssList(nil) = 0
% 29.23/4.98 |
% 29.23/4.98 | ALPHA: (ax39) implies:
% 29.23/4.98 | (2) ? [v0: int] : ( ~ (v0 = 0) & singletonP(nil) = v0)
% 29.23/4.98 |
% 29.23/4.98 | ALPHA: (co1) implies:
% 29.23/4.98 | (3) $i(nil)
% 29.23/4.98 | (4) ? [v0: $i] : ? [v1: any] : (ssList(v0) = 0 & neq(v0, nil) = v1 &
% 29.23/4.98 | $i(v0) & ? [v2: $i] : ( ~ (v1 = 0) & singletonP(v0) = 0 & ssList(v2)
% 29.23/4.98 | = 0 & neq(v2, nil) = 0 & $i(v2)))
% 29.23/4.98 |
% 29.23/4.98 | ALPHA: (function-axioms) implies:
% 29.23/4.98 | (5) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 29.23/4.98 | (v1 = v0 | ~ (ssList(v2) = v1) | ~ (ssList(v2) = v0))
% 29.23/4.99 | (6) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 29.23/4.99 | (v1 = v0 | ~ (singletonP(v2) = v1) | ~ (singletonP(v2) = v0))
% 29.23/4.99 |
% 29.23/4.99 | DELTA: instantiating (2) with fresh symbol all_89_0 gives:
% 29.23/4.99 | (7) ~ (all_89_0 = 0) & singletonP(nil) = all_89_0
% 29.23/4.99 |
% 29.23/4.99 | ALPHA: (7) implies:
% 29.23/4.99 | (8) ~ (all_89_0 = 0)
% 29.23/4.99 | (9) singletonP(nil) = all_89_0
% 29.23/4.99 |
% 29.23/4.99 | DELTA: instantiating (4) with fresh symbols all_93_0, all_93_1 gives:
% 29.23/4.99 | (10) ssList(all_93_1) = 0 & neq(all_93_1, nil) = all_93_0 & $i(all_93_1) &
% 29.23/4.99 | ? [v0: $i] : ( ~ (all_93_0 = 0) & singletonP(all_93_1) = 0 &
% 29.23/4.99 | ssList(v0) = 0 & neq(v0, nil) = 0 & $i(v0))
% 29.23/4.99 |
% 29.23/4.99 | ALPHA: (10) implies:
% 29.23/4.99 | (11) $i(all_93_1)
% 29.23/4.99 | (12) neq(all_93_1, nil) = all_93_0
% 29.23/4.99 | (13) ssList(all_93_1) = 0
% 29.23/4.99 | (14) ? [v0: $i] : ( ~ (all_93_0 = 0) & singletonP(all_93_1) = 0 &
% 29.23/4.99 | ssList(v0) = 0 & neq(v0, nil) = 0 & $i(v0))
% 29.23/4.99 |
% 29.23/4.99 | DELTA: instantiating (14) with fresh symbol all_97_0 gives:
% 29.23/4.99 | (15) ~ (all_93_0 = 0) & singletonP(all_93_1) = 0 & ssList(all_97_0) = 0 &
% 29.23/4.99 | neq(all_97_0, nil) = 0 & $i(all_97_0)
% 29.23/4.99 |
% 29.23/4.99 | ALPHA: (15) implies:
% 29.23/4.99 | (16) ~ (all_93_0 = 0)
% 29.23/4.99 | (17) singletonP(all_93_1) = 0
% 29.23/4.99 |
% 29.23/4.99 | GROUND_INST: instantiating (ax15) with all_93_1, simplifying with (11), (13)
% 29.23/4.99 | gives:
% 29.23/4.99 | (18) ! [v0: $i] : ! [v1: any] : ( ~ (neq(all_93_1, v0) = v1) | ~ $i(v0)
% 29.23/4.99 | | ? [v2: int] : ( ~ (v2 = 0) & ssList(v0) = v2) | (( ~ (v1 = 0) |
% 29.23/4.99 | ~ (v0 = all_93_1)) & (v1 = 0 | v0 = all_93_1)))
% 29.23/4.99 |
% 29.23/4.99 | GROUND_INST: instantiating (18) with nil, all_93_0, simplifying with (3), (12)
% 29.23/4.99 | gives:
% 29.23/5.00 | (19) ? [v0: int] : ( ~ (v0 = 0) & ssList(nil) = v0) | (( ~ (all_93_0 = 0)
% 29.23/5.00 | | ~ (all_93_1 = nil)) & (all_93_0 = 0 | all_93_1 = nil))
% 29.23/5.00 |
% 29.23/5.00 | BETA: splitting (19) gives:
% 29.23/5.00 |
% 29.23/5.00 | Case 1:
% 29.23/5.00 | |
% 29.23/5.00 | | (20) ? [v0: int] : ( ~ (v0 = 0) & ssList(nil) = v0)
% 29.23/5.00 | |
% 29.23/5.00 | | DELTA: instantiating (20) with fresh symbol all_270_0 gives:
% 29.23/5.00 | | (21) ~ (all_270_0 = 0) & ssList(nil) = all_270_0
% 29.23/5.00 | |
% 29.23/5.00 | | ALPHA: (21) implies:
% 29.23/5.00 | | (22) ~ (all_270_0 = 0)
% 29.23/5.00 | | (23) ssList(nil) = all_270_0
% 29.23/5.00 | |
% 29.23/5.00 | | DELTA: instantiating (20) with fresh symbol all_272_0 gives:
% 29.23/5.00 | | (24) ~ (all_272_0 = 0) & ssList(nil) = all_272_0
% 29.23/5.00 | |
% 29.23/5.00 | | ALPHA: (24) implies:
% 29.23/5.00 | | (25) ssList(nil) = all_272_0
% 29.23/5.00 | |
% 29.23/5.00 | | GROUND_INST: instantiating (5) with 0, all_272_0, nil, simplifying with (1),
% 29.23/5.00 | | (25) gives:
% 29.23/5.00 | | (26) all_272_0 = 0
% 29.23/5.00 | |
% 29.23/5.00 | | GROUND_INST: instantiating (5) with all_270_0, all_272_0, nil, simplifying
% 29.23/5.00 | | with (23), (25) gives:
% 29.23/5.00 | | (27) all_272_0 = all_270_0
% 29.23/5.00 | |
% 29.23/5.00 | | COMBINE_EQS: (26), (27) imply:
% 29.23/5.00 | | (28) all_270_0 = 0
% 29.23/5.00 | |
% 29.23/5.00 | | REDUCE: (22), (28) imply:
% 29.23/5.00 | | (29) $false
% 29.23/5.00 | |
% 29.23/5.00 | | CLOSE: (29) is inconsistent.
% 29.23/5.00 | |
% 29.23/5.00 | Case 2:
% 29.23/5.00 | |
% 29.23/5.00 | | (30) ( ~ (all_93_0 = 0) | ~ (all_93_1 = nil)) & (all_93_0 = 0 | all_93_1
% 29.23/5.00 | | = nil)
% 29.23/5.00 | |
% 29.23/5.00 | | ALPHA: (30) implies:
% 29.23/5.00 | | (31) all_93_0 = 0 | all_93_1 = nil
% 29.23/5.00 | |
% 29.23/5.00 | | BETA: splitting (31) gives:
% 29.23/5.00 | |
% 29.23/5.00 | | Case 1:
% 29.23/5.00 | | |
% 29.23/5.00 | | | (32) all_93_1 = nil
% 29.23/5.00 | | |
% 29.23/5.00 | | | REDUCE: (17), (32) imply:
% 29.23/5.00 | | | (33) singletonP(nil) = 0
% 29.23/5.00 | | |
% 29.23/5.00 | | | GROUND_INST: instantiating (6) with all_89_0, 0, nil, simplifying with
% 29.23/5.00 | | | (9), (33) gives:
% 29.23/5.00 | | | (34) all_89_0 = 0
% 29.23/5.00 | | |
% 29.23/5.00 | | | REDUCE: (8), (34) imply:
% 29.23/5.00 | | | (35) $false
% 29.23/5.00 | | |
% 29.23/5.00 | | | CLOSE: (35) is inconsistent.
% 29.23/5.00 | | |
% 29.23/5.00 | | Case 2:
% 29.23/5.00 | | |
% 29.23/5.00 | | | (36) all_93_0 = 0
% 29.23/5.00 | | |
% 29.23/5.00 | | | REDUCE: (16), (36) imply:
% 29.23/5.00 | | | (37) $false
% 29.23/5.00 | | |
% 29.23/5.00 | | | CLOSE: (37) is inconsistent.
% 29.23/5.00 | | |
% 29.23/5.00 | | End of split
% 29.23/5.00 | |
% 29.23/5.00 | End of split
% 29.23/5.00 |
% 29.23/5.00 End of proof
% 29.23/5.01 % SZS output end Proof for theBenchmark
% 29.23/5.01
% 29.23/5.01 4391ms
%------------------------------------------------------------------------------