TSTP Solution File: COM007+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : COM007+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n003.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 : Wed Aug 30 18:44:13 EDT 2023
% Result : Theorem 15.69s 2.84s
% Output : Proof 16.52s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : COM007+1 : TPTP v8.1.2. Released v3.2.0.
% 0.06/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.34 % Computer : n003.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 : Tue Aug 29 13:35:11 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.47/0.61 ________ _____
% 0.47/0.61 ___ __ \_________(_)________________________________
% 0.47/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.47/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.47/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.47/0.61
% 0.47/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.47/0.61 (2023-06-19)
% 0.47/0.61
% 0.47/0.61 (c) Philipp Rümmer, 2009-2023
% 0.47/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.47/0.61 Amanda Stjerna.
% 0.47/0.61 Free software under BSD-3-Clause.
% 0.47/0.61
% 0.47/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.47/0.61
% 0.47/0.61 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.47/0.62 Running up to 7 provers in parallel.
% 0.47/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.47/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.47/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.47/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.47/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.47/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 0.47/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 2.10/1.03 Prover 1: Preprocessing ...
% 2.10/1.03 Prover 4: Preprocessing ...
% 2.67/1.08 Prover 2: Preprocessing ...
% 2.67/1.08 Prover 5: Preprocessing ...
% 2.67/1.08 Prover 6: Preprocessing ...
% 2.67/1.08 Prover 0: Preprocessing ...
% 2.67/1.08 Prover 3: Preprocessing ...
% 3.16/1.25 Prover 5: Proving ...
% 3.16/1.25 Prover 2: Proving ...
% 3.86/1.27 Prover 6: Constructing countermodel ...
% 3.86/1.28 Prover 1: Constructing countermodel ...
% 3.86/1.29 Prover 3: Constructing countermodel ...
% 3.86/1.31 Prover 0: Proving ...
% 4.36/1.33 Prover 4: Constructing countermodel ...
% 4.36/1.34 Prover 3: gave up
% 4.36/1.34 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 4.36/1.35 Prover 1: gave up
% 4.36/1.35 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 4.36/1.35 Prover 6: gave up
% 4.36/1.36 Prover 7: Preprocessing ...
% 4.60/1.36 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889
% 4.60/1.36 Prover 8: Preprocessing ...
% 4.60/1.38 Prover 7: Warning: ignoring some quantifiers
% 4.60/1.39 Prover 9: Preprocessing ...
% 4.60/1.40 Prover 7: Constructing countermodel ...
% 5.05/1.45 Prover 8: Warning: ignoring some quantifiers
% 5.05/1.46 Prover 8: Constructing countermodel ...
% 5.30/1.50 Prover 8: gave up
% 5.30/1.50 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 5.30/1.50 Prover 9: Constructing countermodel ...
% 5.30/1.52 Prover 10: Preprocessing ...
% 5.83/1.56 Prover 10: Warning: ignoring some quantifiers
% 5.83/1.56 Prover 10: Constructing countermodel ...
% 15.69/2.84 Prover 9: proved (1474ms)
% 15.69/2.84
% 15.69/2.84 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 15.69/2.84
% 15.69/2.85 Prover 0: stopped
% 15.69/2.85 Prover 2: stopped
% 15.69/2.86 Prover 5: stopped
% 15.69/2.86 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 15.69/2.86 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 15.69/2.86 Prover 4: Found proof (size 104)
% 15.69/2.86 Prover 4: proved (2219ms)
% 15.69/2.86 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085
% 15.69/2.86 Prover 10: stopped
% 15.69/2.86 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 15.69/2.86 Prover 7: stopped
% 15.69/2.86 Prover 11: Preprocessing ...
% 15.69/2.86 Prover 13: Preprocessing ...
% 15.69/2.87 Prover 19: Preprocessing ...
% 15.69/2.87 Prover 16: Preprocessing ...
% 15.69/2.88 Prover 13: Warning: ignoring some quantifiers
% 15.69/2.88 Prover 13: Constructing countermodel ...
% 15.69/2.88 Prover 13: stopped
% 15.69/2.89 Prover 11: stopped
% 15.69/2.89 Prover 16: Warning: ignoring some quantifiers
% 15.69/2.89 Prover 16: Constructing countermodel ...
% 15.69/2.89 Prover 16: stopped
% 15.69/2.90 Prover 19: Warning: ignoring some quantifiers
% 15.69/2.90 Prover 19: Constructing countermodel ...
% 15.69/2.90 Prover 19: stopped
% 15.69/2.90
% 15.69/2.90 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 15.69/2.90
% 15.69/2.91 % SZS output start Proof for theBenchmark
% 15.69/2.91 Assumptions after simplification:
% 15.69/2.91 ---------------------------------
% 15.69/2.91
% 15.69/2.91 (assumption)
% 16.21/2.93 reflexive_rewrite(a, c) = 0 & reflexive_rewrite(a, b) = 0 & $i(c) & $i(b) &
% 16.21/2.93 $i(a)
% 16.21/2.93
% 16.21/2.93 (equalish_in_reflexive_rewrite)
% 16.21/2.93 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (reflexive_rewrite(v0,
% 16.21/2.93 v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ( ~ (v3 = 0) &
% 16.21/2.93 equalish(v0, v1) = v3)) & ! [v0: $i] : ! [v1: $i] : ( ~ (equalish(v0,
% 16.21/2.93 v1) = 0) | ~ $i(v1) | ~ $i(v0) | reflexive_rewrite(v0, v1) = 0)
% 16.21/2.93
% 16.21/2.93 (equalish_or_rewrite)
% 16.21/2.94 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (rewrite(v0, v1) = v2)
% 16.21/2.94 | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : (equalish(v0, v1) =
% 16.21/2.94 v4 & reflexive_rewrite(v0, v1) = v3 & ( ~ (v3 = 0) | v4 = 0))) & ! [v0:
% 16.21/2.94 $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (equalish(v0, v1) = v2) | ~
% 16.21/2.94 $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : (rewrite(v0, v1) = v4 &
% 16.21/2.94 reflexive_rewrite(v0, v1) = v3 & ( ~ (v3 = 0) | v4 = 0))) & ! [v0: $i] :
% 16.21/2.94 ! [v1: $i] : ( ~ (reflexive_rewrite(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ?
% 16.21/2.94 [v2: any] : ? [v3: any] : (rewrite(v0, v1) = v3 & equalish(v0, v1) = v2 &
% 16.21/2.94 (v3 = 0 | v2 = 0)))
% 16.21/2.94
% 16.21/2.94 (goal_ax)
% 16.21/2.94 $i(c) & $i(b) & ! [v0: $i] : ( ~ (reflexive_rewrite(c, v0) = 0) | ~ $i(v0) |
% 16.21/2.94 goal | ? [v1: int] : ( ~ (v1 = 0) & reflexive_rewrite(b, v0) = v1)) & !
% 16.21/2.94 [v0: $i] : ( ~ (reflexive_rewrite(b, v0) = 0) | ~ $i(v0) | goal | ? [v1:
% 16.21/2.94 int] : ( ~ (v1 = 0) & reflexive_rewrite(c, v0) = v1))
% 16.21/2.94
% 16.21/2.94 (goal_to_be_proved)
% 16.21/2.94 ~ goal
% 16.21/2.94
% 16.21/2.94 (reflexivity)
% 16.21/2.94 ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (equalish(v0, v0) = v1) | ~ $i(v0))
% 16.21/2.94
% 16.21/2.94 (rewrite_diamond)
% 16.21/2.94 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (rewrite(v0, v2) = 0) | ~
% 16.21/2.94 (rewrite(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] :
% 16.21/2.94 (rewrite(v2, v3) = 0 & rewrite(v1, v3) = 0 & $i(v3)))
% 16.21/2.94
% 16.21/2.94 (rewrite_in_reflexive_rewrite)
% 16.21/2.94 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (reflexive_rewrite(v0,
% 16.21/2.94 v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ( ~ (v3 = 0) &
% 16.21/2.94 rewrite(v0, v1) = v3)) & ! [v0: $i] : ! [v1: $i] : ( ~ (rewrite(v0, v1)
% 16.21/2.94 = 0) | ~ $i(v1) | ~ $i(v0) | reflexive_rewrite(v0, v1) = 0)
% 16.21/2.94
% 16.21/2.94 (substitution)
% 16.21/2.95 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 16.21/2.95 (equalish(v0, v1) = 0) | ~ (reflexive_rewrite(v0, v2) = v3) | ~ $i(v2) |
% 16.21/2.95 ~ $i(v1) | ~ $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & reflexive_rewrite(v1,
% 16.21/2.95 v2) = v4)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] :
% 16.21/2.95 (v3 = 0 | ~ (reflexive_rewrite(v1, v2) = 0) | ~ (reflexive_rewrite(v0, v2) =
% 16.21/2.95 v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: int] : ( ~ (v4 = 0) &
% 16.21/2.95 equalish(v0, v1) = v4)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 16.21/2.95 (equalish(v0, v1) = 0) | ~ (reflexive_rewrite(v1, v2) = 0) | ~ $i(v2) | ~
% 16.21/2.95 $i(v1) | ~ $i(v0) | reflexive_rewrite(v0, v2) = 0)
% 16.21/2.95
% 16.21/2.95 (symmtery)
% 16.21/2.95 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (equalish(v1, v0) =
% 16.21/2.95 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ( ~ (v3 = 0) & equalish(v0,
% 16.21/2.95 v1) = v3)) & ! [v0: $i] : ! [v1: $i] : ( ~ (equalish(v0, v1) = 0) | ~
% 16.21/2.95 $i(v1) | ~ $i(v0) | equalish(v1, v0) = 0)
% 16.21/2.95
% 16.21/2.95 (function-axioms)
% 16.21/2.95 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 16.21/2.95 [v3: $i] : (v1 = v0 | ~ (rewrite(v3, v2) = v1) | ~ (rewrite(v3, v2) = v0)) &
% 16.21/2.95 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 16.21/2.95 [v3: $i] : (v1 = v0 | ~ (equalish(v3, v2) = v1) | ~ (equalish(v3, v2) = v0))
% 16.21/2.95 & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 16.21/2.95 [v3: $i] : (v1 = v0 | ~ (reflexive_rewrite(v3, v2) = v1) | ~
% 16.21/2.95 (reflexive_rewrite(v3, v2) = v0))
% 16.21/2.95
% 16.21/2.95 Those formulas are unsatisfiable:
% 16.21/2.95 ---------------------------------
% 16.21/2.95
% 16.21/2.95 Begin of proof
% 16.21/2.95 |
% 16.21/2.95 | ALPHA: (assumption) implies:
% 16.21/2.95 | (1) $i(a)
% 16.21/2.95 | (2) reflexive_rewrite(a, b) = 0
% 16.21/2.95 | (3) reflexive_rewrite(a, c) = 0
% 16.21/2.95 |
% 16.21/2.95 | ALPHA: (goal_ax) implies:
% 16.21/2.95 | (4) $i(b)
% 16.21/2.95 | (5) $i(c)
% 16.21/2.95 | (6) ! [v0: $i] : ( ~ (reflexive_rewrite(b, v0) = 0) | ~ $i(v0) | goal |
% 16.21/2.95 | ? [v1: int] : ( ~ (v1 = 0) & reflexive_rewrite(c, v0) = v1))
% 16.21/2.95 | (7) ! [v0: $i] : ( ~ (reflexive_rewrite(c, v0) = 0) | ~ $i(v0) | goal |
% 16.21/2.95 | ? [v1: int] : ( ~ (v1 = 0) & reflexive_rewrite(b, v0) = v1))
% 16.21/2.95 |
% 16.21/2.95 | ALPHA: (symmtery) implies:
% 16.21/2.95 | (8) ! [v0: $i] : ! [v1: $i] : ( ~ (equalish(v0, v1) = 0) | ~ $i(v1) | ~
% 16.21/2.95 | $i(v0) | equalish(v1, v0) = 0)
% 16.21/2.95 |
% 16.21/2.95 | ALPHA: (substitution) implies:
% 16.21/2.96 | (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (equalish(v0, v1) = 0) |
% 16.21/2.96 | ~ (reflexive_rewrite(v1, v2) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0)
% 16.21/2.96 | | reflexive_rewrite(v0, v2) = 0)
% 16.21/2.96 | (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 16.21/2.96 | (reflexive_rewrite(v1, v2) = 0) | ~ (reflexive_rewrite(v0, v2) =
% 16.21/2.96 | v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: int] : ( ~ (v4 =
% 16.21/2.96 | 0) & equalish(v0, v1) = v4))
% 16.21/2.96 | (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 16.21/2.96 | (equalish(v0, v1) = 0) | ~ (reflexive_rewrite(v0, v2) = v3) | ~
% 16.21/2.96 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: int] : ( ~ (v4 = 0) &
% 16.21/2.96 | reflexive_rewrite(v1, v2) = v4))
% 16.21/2.96 |
% 16.21/2.96 | ALPHA: (equalish_in_reflexive_rewrite) implies:
% 16.21/2.96 | (12) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~
% 16.21/2.96 | (reflexive_rewrite(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3:
% 16.21/2.96 | int] : ( ~ (v3 = 0) & equalish(v0, v1) = v3))
% 16.21/2.96 |
% 16.21/2.96 | ALPHA: (rewrite_in_reflexive_rewrite) implies:
% 16.21/2.96 | (13) ! [v0: $i] : ! [v1: $i] : ( ~ (rewrite(v0, v1) = 0) | ~ $i(v1) | ~
% 16.21/2.96 | $i(v0) | reflexive_rewrite(v0, v1) = 0)
% 16.21/2.96 |
% 16.21/2.96 | ALPHA: (equalish_or_rewrite) implies:
% 16.21/2.96 | (14) ! [v0: $i] : ! [v1: $i] : ( ~ (reflexive_rewrite(v0, v1) = 0) | ~
% 16.21/2.96 | $i(v1) | ~ $i(v0) | ? [v2: any] : ? [v3: any] : (rewrite(v0, v1)
% 16.21/2.96 | = v3 & equalish(v0, v1) = v2 & (v3 = 0 | v2 = 0)))
% 16.21/2.96 | (15) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (equalish(v0,
% 16.21/2.96 | v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any]
% 16.21/2.96 | : (rewrite(v0, v1) = v4 & reflexive_rewrite(v0, v1) = v3 & ( ~ (v3 =
% 16.21/2.96 | 0) | v4 = 0)))
% 16.21/2.96 |
% 16.21/2.96 | ALPHA: (function-axioms) implies:
% 16.21/2.96 | (16) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 16.21/2.96 | : ! [v3: $i] : (v1 = v0 | ~ (reflexive_rewrite(v3, v2) = v1) | ~
% 16.21/2.96 | (reflexive_rewrite(v3, v2) = v0))
% 16.21/2.96 | (17) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 16.21/2.96 | : ! [v3: $i] : (v1 = v0 | ~ (equalish(v3, v2) = v1) | ~
% 16.21/2.96 | (equalish(v3, v2) = v0))
% 16.21/2.96 |
% 16.21/2.96 | GROUND_INST: instantiating (14) with a, b, simplifying with (1), (2), (4)
% 16.21/2.96 | gives:
% 16.21/2.96 | (18) ? [v0: any] : ? [v1: any] : (rewrite(a, b) = v1 & equalish(a, b) =
% 16.21/2.96 | v0 & (v1 = 0 | v0 = 0))
% 16.21/2.96 |
% 16.21/2.96 | GROUND_INST: instantiating (14) with a, c, simplifying with (1), (3), (5)
% 16.21/2.96 | gives:
% 16.21/2.96 | (19) ? [v0: any] : ? [v1: any] : (rewrite(a, c) = v1 & equalish(a, c) =
% 16.21/2.96 | v0 & (v1 = 0 | v0 = 0))
% 16.21/2.96 |
% 16.21/2.96 | DELTA: instantiating (19) with fresh symbols all_17_0, all_17_1 gives:
% 16.21/2.96 | (20) rewrite(a, c) = all_17_0 & equalish(a, c) = all_17_1 & (all_17_0 = 0 |
% 16.21/2.96 | all_17_1 = 0)
% 16.21/2.96 |
% 16.21/2.96 | ALPHA: (20) implies:
% 16.21/2.97 | (21) equalish(a, c) = all_17_1
% 16.21/2.97 | (22) rewrite(a, c) = all_17_0
% 16.21/2.97 | (23) all_17_0 = 0 | all_17_1 = 0
% 16.21/2.97 |
% 16.21/2.97 | DELTA: instantiating (18) with fresh symbols all_19_0, all_19_1 gives:
% 16.21/2.97 | (24) rewrite(a, b) = all_19_0 & equalish(a, b) = all_19_1 & (all_19_0 = 0 |
% 16.21/2.97 | all_19_1 = 0)
% 16.21/2.97 |
% 16.21/2.97 | ALPHA: (24) implies:
% 16.21/2.97 | (25) equalish(a, b) = all_19_1
% 16.21/2.97 | (26) rewrite(a, b) = all_19_0
% 16.21/2.97 | (27) all_19_0 = 0 | all_19_1 = 0
% 16.21/2.97 |
% 16.21/2.97 | BETA: splitting (23) gives:
% 16.21/2.97 |
% 16.21/2.97 | Case 1:
% 16.21/2.97 | |
% 16.21/2.97 | | (28) all_17_0 = 0
% 16.21/2.97 | |
% 16.21/2.97 | | REDUCE: (22), (28) imply:
% 16.21/2.97 | | (29) rewrite(a, c) = 0
% 16.21/2.97 | |
% 16.21/2.97 | | GROUND_INST: instantiating (rewrite_diamond) with a, c, c, simplifying with
% 16.21/2.97 | | (1), (5), (29) gives:
% 16.21/2.97 | | (30) ? [v0: $i] : (rewrite(c, v0) = 0 & $i(v0))
% 16.21/2.97 | |
% 16.21/2.97 | | DELTA: instantiating (30) with fresh symbol all_33_0 gives:
% 16.21/2.97 | | (31) rewrite(c, all_33_0) = 0 & $i(all_33_0)
% 16.21/2.97 | |
% 16.21/2.97 | | ALPHA: (31) implies:
% 16.21/2.97 | | (32) $i(all_33_0)
% 16.21/2.97 | | (33) rewrite(c, all_33_0) = 0
% 16.21/2.97 | |
% 16.21/2.97 | | GROUND_INST: instantiating (13) with c, all_33_0, simplifying with (5),
% 16.21/2.97 | | (32), (33) gives:
% 16.21/2.97 | | (34) reflexive_rewrite(c, all_33_0) = 0
% 16.21/2.97 | |
% 16.21/2.97 | | GROUND_INST: instantiating (7) with all_33_0, simplifying with (32), (34),
% 16.21/2.97 | | (goal_to_be_proved) gives:
% 16.21/2.97 | | (35) ? [v0: int] : ( ~ (v0 = 0) & reflexive_rewrite(b, all_33_0) = v0)
% 16.21/2.97 | |
% 16.21/2.97 | | DELTA: instantiating (35) with fresh symbol all_51_0 gives:
% 16.21/2.97 | | (36) ~ (all_51_0 = 0) & reflexive_rewrite(b, all_33_0) = all_51_0
% 16.21/2.97 | |
% 16.21/2.97 | | ALPHA: (36) implies:
% 16.21/2.97 | | (37) ~ (all_51_0 = 0)
% 16.21/2.97 | | (38) reflexive_rewrite(b, all_33_0) = all_51_0
% 16.21/2.97 | |
% 16.21/2.97 | | GROUND_INST: instantiating (10) with b, c, all_33_0, all_51_0, simplifying
% 16.21/2.97 | | with (4), (5), (32), (34), (38) gives:
% 16.21/2.97 | | (39) all_51_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & equalish(b, c) = v0)
% 16.21/2.97 | |
% 16.21/2.97 | | GROUND_INST: instantiating (12) with b, all_33_0, all_51_0, simplifying with
% 16.21/2.97 | | (4), (32), (38) gives:
% 16.21/2.97 | | (40) all_51_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & equalish(b, all_33_0) =
% 16.21/2.97 | | v0)
% 16.21/2.97 | |
% 16.21/2.97 | | BETA: splitting (39) gives:
% 16.21/2.97 | |
% 16.21/2.97 | | Case 1:
% 16.21/2.97 | | |
% 16.21/2.97 | | | (41) all_51_0 = 0
% 16.21/2.97 | | |
% 16.21/2.97 | | | REDUCE: (37), (41) imply:
% 16.21/2.97 | | | (42) $false
% 16.21/2.97 | | |
% 16.21/2.97 | | | CLOSE: (42) is inconsistent.
% 16.21/2.97 | | |
% 16.21/2.97 | | Case 2:
% 16.21/2.97 | | |
% 16.21/2.97 | | | (43) ? [v0: int] : ( ~ (v0 = 0) & equalish(b, c) = v0)
% 16.21/2.97 | | |
% 16.21/2.97 | | | DELTA: instantiating (43) with fresh symbol all_78_0 gives:
% 16.21/2.97 | | | (44) ~ (all_78_0 = 0) & equalish(b, c) = all_78_0
% 16.21/2.97 | | |
% 16.21/2.97 | | | ALPHA: (44) implies:
% 16.21/2.97 | | | (45) ~ (all_78_0 = 0)
% 16.21/2.97 | | | (46) equalish(b, c) = all_78_0
% 16.21/2.97 | | |
% 16.21/2.97 | | | BETA: splitting (40) gives:
% 16.21/2.97 | | |
% 16.21/2.97 | | | Case 1:
% 16.21/2.97 | | | |
% 16.21/2.97 | | | | (47) all_51_0 = 0
% 16.21/2.97 | | | |
% 16.21/2.97 | | | | REDUCE: (37), (47) imply:
% 16.21/2.97 | | | | (48) $false
% 16.21/2.97 | | | |
% 16.21/2.97 | | | | CLOSE: (48) is inconsistent.
% 16.21/2.97 | | | |
% 16.21/2.97 | | | Case 2:
% 16.21/2.97 | | | |
% 16.21/2.97 | | | |
% 16.21/2.97 | | | | GROUND_INST: instantiating (15) with b, c, all_78_0, simplifying with
% 16.21/2.98 | | | | (4), (5), (46) gives:
% 16.21/2.98 | | | | (49) all_78_0 = 0 | ? [v0: any] : ? [v1: any] : (rewrite(b, c) = v1
% 16.21/2.98 | | | | & reflexive_rewrite(b, c) = v0 & ( ~ (v0 = 0) | v1 = 0))
% 16.21/2.98 | | | |
% 16.21/2.98 | | | | BETA: splitting (49) gives:
% 16.21/2.98 | | | |
% 16.21/2.98 | | | | Case 1:
% 16.21/2.98 | | | | |
% 16.21/2.98 | | | | | (50) all_78_0 = 0
% 16.21/2.98 | | | | |
% 16.21/2.98 | | | | | REDUCE: (45), (50) imply:
% 16.21/2.98 | | | | | (51) $false
% 16.21/2.98 | | | | |
% 16.21/2.98 | | | | | CLOSE: (51) is inconsistent.
% 16.21/2.98 | | | | |
% 16.21/2.98 | | | | Case 2:
% 16.21/2.98 | | | | |
% 16.21/2.98 | | | | | (52) ? [v0: any] : ? [v1: any] : (rewrite(b, c) = v1 &
% 16.21/2.98 | | | | | reflexive_rewrite(b, c) = v0 & ( ~ (v0 = 0) | v1 = 0))
% 16.21/2.98 | | | | |
% 16.21/2.98 | | | | | DELTA: instantiating (52) with fresh symbols all_113_0, all_113_1
% 16.21/2.98 | | | | | gives:
% 16.21/2.98 | | | | | (53) rewrite(b, c) = all_113_0 & reflexive_rewrite(b, c) =
% 16.21/2.98 | | | | | all_113_1 & ( ~ (all_113_1 = 0) | all_113_0 = 0)
% 16.21/2.98 | | | | |
% 16.21/2.98 | | | | | ALPHA: (53) implies:
% 16.21/2.98 | | | | | (54) reflexive_rewrite(b, c) = all_113_1
% 16.21/2.98 | | | | |
% 16.52/2.98 | | | | | GROUND_INST: instantiating (10) with b, a, c, all_113_1, simplifying
% 16.52/2.98 | | | | | with (1), (3), (4), (5), (54) gives:
% 16.52/2.98 | | | | | (55) all_113_1 = 0 | ? [v0: int] : ( ~ (v0 = 0) & equalish(b, a) =
% 16.52/2.98 | | | | | v0)
% 16.52/2.98 | | | | |
% 16.52/2.98 | | | | | BETA: splitting (27) gives:
% 16.52/2.98 | | | | |
% 16.52/2.98 | | | | | Case 1:
% 16.52/2.98 | | | | | |
% 16.52/2.98 | | | | | | (56) all_19_0 = 0
% 16.52/2.98 | | | | | |
% 16.52/2.98 | | | | | | REDUCE: (26), (56) imply:
% 16.52/2.98 | | | | | | (57) rewrite(a, b) = 0
% 16.52/2.98 | | | | | |
% 16.52/2.98 | | | | | | GROUND_INST: instantiating (rewrite_diamond) with a, c, b,
% 16.52/2.98 | | | | | | simplifying with (1), (4), (5), (29), (57) gives:
% 16.52/2.98 | | | | | | (58) ? [v0: $i] : (rewrite(c, v0) = 0 & rewrite(b, v0) = 0 &
% 16.52/2.98 | | | | | | $i(v0))
% 16.52/2.98 | | | | | |
% 16.52/2.98 | | | | | | DELTA: instantiating (58) with fresh symbol all_190_0 gives:
% 16.52/2.98 | | | | | | (59) rewrite(c, all_190_0) = 0 & rewrite(b, all_190_0) = 0 &
% 16.52/2.98 | | | | | | $i(all_190_0)
% 16.52/2.98 | | | | | |
% 16.52/2.98 | | | | | | ALPHA: (59) implies:
% 16.52/2.98 | | | | | | (60) $i(all_190_0)
% 16.52/2.98 | | | | | | (61) rewrite(b, all_190_0) = 0
% 16.52/2.98 | | | | | | (62) rewrite(c, all_190_0) = 0
% 16.52/2.98 | | | | | |
% 16.52/2.98 | | | | | | GROUND_INST: instantiating (13) with b, all_190_0, simplifying with
% 16.52/2.98 | | | | | | (4), (60), (61) gives:
% 16.52/2.98 | | | | | | (63) reflexive_rewrite(b, all_190_0) = 0
% 16.52/2.98 | | | | | |
% 16.52/2.98 | | | | | | GROUND_INST: instantiating (13) with c, all_190_0, simplifying with
% 16.52/2.98 | | | | | | (5), (60), (62) gives:
% 16.52/2.98 | | | | | | (64) reflexive_rewrite(c, all_190_0) = 0
% 16.52/2.98 | | | | | |
% 16.52/2.98 | | | | | | GROUND_INST: instantiating (7) with all_190_0, simplifying with
% 16.52/2.98 | | | | | | (60), (64), (goal_to_be_proved) gives:
% 16.52/2.98 | | | | | | (65) ? [v0: int] : ( ~ (v0 = 0) & reflexive_rewrite(b,
% 16.52/2.98 | | | | | | all_190_0) = v0)
% 16.52/2.98 | | | | | |
% 16.52/2.98 | | | | | | DELTA: instantiating (65) with fresh symbol all_239_0 gives:
% 16.52/2.98 | | | | | | (66) ~ (all_239_0 = 0) & reflexive_rewrite(b, all_190_0) =
% 16.52/2.98 | | | | | | all_239_0
% 16.52/2.98 | | | | | |
% 16.52/2.98 | | | | | | ALPHA: (66) implies:
% 16.52/2.98 | | | | | | (67) ~ (all_239_0 = 0)
% 16.52/2.98 | | | | | | (68) reflexive_rewrite(b, all_190_0) = all_239_0
% 16.52/2.98 | | | | | |
% 16.52/2.98 | | | | | | GROUND_INST: instantiating (16) with 0, all_239_0, all_190_0, b,
% 16.52/2.98 | | | | | | simplifying with (63), (68) gives:
% 16.52/2.98 | | | | | | (69) all_239_0 = 0
% 16.52/2.98 | | | | | |
% 16.52/2.98 | | | | | | REDUCE: (67), (69) imply:
% 16.52/2.98 | | | | | | (70) $false
% 16.52/2.98 | | | | | |
% 16.52/2.98 | | | | | | CLOSE: (70) is inconsistent.
% 16.52/2.98 | | | | | |
% 16.52/2.98 | | | | | Case 2:
% 16.52/2.98 | | | | | |
% 16.52/2.98 | | | | | | (71) all_19_1 = 0
% 16.52/2.98 | | | | | |
% 16.52/2.98 | | | | | | REDUCE: (25), (71) imply:
% 16.52/2.98 | | | | | | (72) equalish(a, b) = 0
% 16.52/2.98 | | | | | |
% 16.52/2.98 | | | | | | GROUND_INST: instantiating (8) with a, b, simplifying with (1), (4),
% 16.52/2.98 | | | | | | (72) gives:
% 16.52/2.98 | | | | | | (73) equalish(b, a) = 0
% 16.52/2.98 | | | | | |
% 16.52/2.98 | | | | | | BETA: splitting (55) gives:
% 16.52/2.98 | | | | | |
% 16.52/2.98 | | | | | | Case 1:
% 16.52/2.98 | | | | | | |
% 16.52/2.98 | | | | | | | (74) all_113_1 = 0
% 16.52/2.99 | | | | | | |
% 16.52/2.99 | | | | | | | REDUCE: (54), (74) imply:
% 16.52/2.99 | | | | | | | (75) reflexive_rewrite(b, c) = 0
% 16.52/2.99 | | | | | | |
% 16.52/2.99 | | | | | | | GROUND_INST: instantiating (6) with c, simplifying with (5), (75),
% 16.52/2.99 | | | | | | | (goal_to_be_proved) gives:
% 16.52/2.99 | | | | | | | (76) ? [v0: int] : ( ~ (v0 = 0) & reflexive_rewrite(c, c) =
% 16.52/2.99 | | | | | | | v0)
% 16.52/2.99 | | | | | | |
% 16.52/2.99 | | | | | | | GROUND_INST: instantiating (11) with b, a, all_33_0, all_51_0,
% 16.52/2.99 | | | | | | | simplifying with (1), (4), (32), (38), (73) gives:
% 16.52/2.99 | | | | | | | (77) all_51_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) &
% 16.52/2.99 | | | | | | | reflexive_rewrite(a, all_33_0) = v0)
% 16.52/2.99 | | | | | | |
% 16.52/2.99 | | | | | | | DELTA: instantiating (76) with fresh symbol all_206_0 gives:
% 16.52/2.99 | | | | | | | (78) ~ (all_206_0 = 0) & reflexive_rewrite(c, c) = all_206_0
% 16.52/2.99 | | | | | | |
% 16.52/2.99 | | | | | | | ALPHA: (78) implies:
% 16.52/2.99 | | | | | | | (79) ~ (all_206_0 = 0)
% 16.52/2.99 | | | | | | | (80) reflexive_rewrite(c, c) = all_206_0
% 16.52/2.99 | | | | | | |
% 16.52/2.99 | | | | | | | BETA: splitting (77) gives:
% 16.52/2.99 | | | | | | |
% 16.52/2.99 | | | | | | | Case 1:
% 16.52/2.99 | | | | | | | |
% 16.52/2.99 | | | | | | | | (81) all_51_0 = 0
% 16.52/2.99 | | | | | | | |
% 16.52/2.99 | | | | | | | | REDUCE: (37), (81) imply:
% 16.52/2.99 | | | | | | | | (82) $false
% 16.52/2.99 | | | | | | | |
% 16.52/2.99 | | | | | | | | CLOSE: (82) is inconsistent.
% 16.52/2.99 | | | | | | | |
% 16.52/2.99 | | | | | | | Case 2:
% 16.52/2.99 | | | | | | | |
% 16.52/2.99 | | | | | | | |
% 16.52/2.99 | | | | | | | | GROUND_INST: instantiating (12) with c, c, all_206_0,
% 16.52/2.99 | | | | | | | | simplifying with (5), (80) gives:
% 16.52/2.99 | | | | | | | | (83) all_206_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) &
% 16.52/2.99 | | | | | | | | equalish(c, c) = v0)
% 16.52/2.99 | | | | | | | |
% 16.52/2.99 | | | | | | | | BETA: splitting (83) gives:
% 16.52/2.99 | | | | | | | |
% 16.52/2.99 | | | | | | | | Case 1:
% 16.52/2.99 | | | | | | | | |
% 16.52/2.99 | | | | | | | | | (84) all_206_0 = 0
% 16.52/2.99 | | | | | | | | |
% 16.52/2.99 | | | | | | | | | REDUCE: (79), (84) imply:
% 16.52/2.99 | | | | | | | | | (85) $false
% 16.52/2.99 | | | | | | | | |
% 16.52/2.99 | | | | | | | | | CLOSE: (85) is inconsistent.
% 16.52/2.99 | | | | | | | | |
% 16.52/2.99 | | | | | | | | Case 2:
% 16.52/2.99 | | | | | | | | |
% 16.52/2.99 | | | | | | | | | (86) ? [v0: int] : ( ~ (v0 = 0) & equalish(c, c) = v0)
% 16.52/2.99 | | | | | | | | |
% 16.52/2.99 | | | | | | | | | DELTA: instantiating (86) with fresh symbol all_255_0 gives:
% 16.52/2.99 | | | | | | | | | (87) ~ (all_255_0 = 0) & equalish(c, c) = all_255_0
% 16.52/2.99 | | | | | | | | |
% 16.52/2.99 | | | | | | | | | ALPHA: (87) implies:
% 16.52/2.99 | | | | | | | | | (88) ~ (all_255_0 = 0)
% 16.52/2.99 | | | | | | | | | (89) equalish(c, c) = all_255_0
% 16.52/2.99 | | | | | | | | |
% 16.52/2.99 | | | | | | | | | GROUND_INST: instantiating (reflexivity) with c, all_255_0,
% 16.52/2.99 | | | | | | | | | simplifying with (5), (89) gives:
% 16.52/2.99 | | | | | | | | | (90) all_255_0 = 0
% 16.52/2.99 | | | | | | | | |
% 16.52/2.99 | | | | | | | | | REDUCE: (88), (90) imply:
% 16.52/2.99 | | | | | | | | | (91) $false
% 16.52/2.99 | | | | | | | | |
% 16.52/2.99 | | | | | | | | | CLOSE: (91) is inconsistent.
% 16.52/2.99 | | | | | | | | |
% 16.52/2.99 | | | | | | | | End of split
% 16.52/2.99 | | | | | | | |
% 16.52/2.99 | | | | | | | End of split
% 16.52/2.99 | | | | | | |
% 16.52/2.99 | | | | | | Case 2:
% 16.52/2.99 | | | | | | |
% 16.52/2.99 | | | | | | | (92) ? [v0: int] : ( ~ (v0 = 0) & equalish(b, a) = v0)
% 16.52/2.99 | | | | | | |
% 16.52/2.99 | | | | | | | DELTA: instantiating (92) with fresh symbol all_186_0 gives:
% 16.52/2.99 | | | | | | | (93) ~ (all_186_0 = 0) & equalish(b, a) = all_186_0
% 16.52/2.99 | | | | | | |
% 16.52/2.99 | | | | | | | ALPHA: (93) implies:
% 16.52/2.99 | | | | | | | (94) ~ (all_186_0 = 0)
% 16.52/2.99 | | | | | | | (95) equalish(b, a) = all_186_0
% 16.52/2.99 | | | | | | |
% 16.52/2.99 | | | | | | | GROUND_INST: instantiating (17) with 0, all_186_0, a, b,
% 16.52/2.99 | | | | | | | simplifying with (73), (95) gives:
% 16.52/2.99 | | | | | | | (96) all_186_0 = 0
% 16.52/2.99 | | | | | | |
% 16.52/2.99 | | | | | | | REDUCE: (94), (96) imply:
% 16.52/2.99 | | | | | | | (97) $false
% 16.52/2.99 | | | | | | |
% 16.52/2.99 | | | | | | | CLOSE: (97) is inconsistent.
% 16.52/2.99 | | | | | | |
% 16.52/2.99 | | | | | | End of split
% 16.52/2.99 | | | | | |
% 16.52/2.99 | | | | | End of split
% 16.52/2.99 | | | | |
% 16.52/2.99 | | | | End of split
% 16.52/2.99 | | | |
% 16.52/2.99 | | | End of split
% 16.52/2.99 | | |
% 16.52/2.99 | | End of split
% 16.52/2.99 | |
% 16.52/2.99 | Case 2:
% 16.52/2.99 | |
% 16.52/2.99 | | (98) all_17_1 = 0
% 16.52/2.99 | |
% 16.52/2.99 | | REDUCE: (21), (98) imply:
% 16.52/2.99 | | (99) equalish(a, c) = 0
% 16.52/2.99 | |
% 16.52/2.99 | | GROUND_INST: instantiating (8) with a, c, simplifying with (1), (5), (99)
% 16.52/2.99 | | gives:
% 16.52/2.99 | | (100) equalish(c, a) = 0
% 16.52/2.99 | |
% 16.52/2.99 | | GROUND_INST: instantiating (9) with c, a, b, simplifying with (1), (2), (4),
% 16.52/2.99 | | (5), (100) gives:
% 16.52/2.99 | | (101) reflexive_rewrite(c, b) = 0
% 16.52/2.99 | |
% 16.52/2.99 | | GROUND_INST: instantiating (7) with b, simplifying with (4), (101),
% 16.52/3.00 | | (goal_to_be_proved) gives:
% 16.52/3.00 | | (102) ? [v0: int] : ( ~ (v0 = 0) & reflexive_rewrite(b, b) = v0)
% 16.52/3.00 | |
% 16.52/3.00 | | DELTA: instantiating (102) with fresh symbol all_48_0 gives:
% 16.52/3.00 | | (103) ~ (all_48_0 = 0) & reflexive_rewrite(b, b) = all_48_0
% 16.52/3.00 | |
% 16.52/3.00 | | ALPHA: (103) implies:
% 16.52/3.00 | | (104) ~ (all_48_0 = 0)
% 16.52/3.00 | | (105) reflexive_rewrite(b, b) = all_48_0
% 16.52/3.00 | |
% 16.52/3.00 | | GROUND_INST: instantiating (12) with b, b, all_48_0, simplifying with (4),
% 16.52/3.00 | | (105) gives:
% 16.52/3.00 | | (106) all_48_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & equalish(b, b) = v0)
% 16.52/3.00 | |
% 16.52/3.00 | | BETA: splitting (106) gives:
% 16.52/3.00 | |
% 16.52/3.00 | | Case 1:
% 16.52/3.00 | | |
% 16.52/3.00 | | | (107) all_48_0 = 0
% 16.52/3.00 | | |
% 16.52/3.00 | | | REDUCE: (104), (107) imply:
% 16.52/3.00 | | | (108) $false
% 16.52/3.00 | | |
% 16.52/3.00 | | | CLOSE: (108) is inconsistent.
% 16.52/3.00 | | |
% 16.52/3.00 | | Case 2:
% 16.52/3.00 | | |
% 16.52/3.00 | | | (109) ? [v0: int] : ( ~ (v0 = 0) & equalish(b, b) = v0)
% 16.52/3.00 | | |
% 16.52/3.00 | | | DELTA: instantiating (109) with fresh symbol all_84_0 gives:
% 16.52/3.00 | | | (110) ~ (all_84_0 = 0) & equalish(b, b) = all_84_0
% 16.52/3.00 | | |
% 16.52/3.00 | | | ALPHA: (110) implies:
% 16.52/3.00 | | | (111) ~ (all_84_0 = 0)
% 16.52/3.00 | | | (112) equalish(b, b) = all_84_0
% 16.52/3.00 | | |
% 16.52/3.00 | | | GROUND_INST: instantiating (reflexivity) with b, all_84_0, simplifying
% 16.52/3.00 | | | with (4), (112) gives:
% 16.52/3.00 | | | (113) all_84_0 = 0
% 16.52/3.00 | | |
% 16.52/3.00 | | | REDUCE: (111), (113) imply:
% 16.52/3.00 | | | (114) $false
% 16.52/3.00 | | |
% 16.52/3.00 | | | CLOSE: (114) is inconsistent.
% 16.52/3.00 | | |
% 16.52/3.00 | | End of split
% 16.52/3.00 | |
% 16.52/3.00 | End of split
% 16.52/3.00 |
% 16.52/3.00 End of proof
% 16.52/3.00 % SZS output end Proof for theBenchmark
% 16.52/3.00
% 16.52/3.00 2387ms
%------------------------------------------------------------------------------