TSTP Solution File: KRS192+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : KRS192+1 : TPTP v8.1.2. Bugfixed v5.4.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n011.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 05:51:36 EDT 2023
% Result : Theorem 10.86s 2.33s
% Output : Proof 13.13s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : KRS192+1 : TPTP v8.1.2. Bugfixed v5.4.0.
% 0.07/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.35 % Computer : n011.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Mon Aug 28 02:12:10 EDT 2023
% 0.20/0.35 % CPUTime :
% 0.20/0.65 ________ _____
% 0.20/0.65 ___ __ \_________(_)________________________________
% 0.20/0.65 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.20/0.65 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.20/0.65 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.20/0.65
% 0.20/0.65 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.65 (2023-06-19)
% 0.20/0.65
% 0.20/0.65 (c) Philipp Rümmer, 2009-2023
% 0.20/0.65 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.65 Amanda Stjerna.
% 0.20/0.65 Free software under BSD-3-Clause.
% 0.20/0.65
% 0.20/0.65 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.65
% 0.20/0.65 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.20/0.67 Running up to 7 provers in parallel.
% 0.20/0.68 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.68 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.68 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.68 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.68 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.68 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.20/0.68 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 3.49/1.25 Prover 1: Preprocessing ...
% 3.49/1.27 Prover 4: Preprocessing ...
% 3.49/1.31 Prover 0: Preprocessing ...
% 3.49/1.31 Prover 6: Preprocessing ...
% 3.49/1.31 Prover 5: Preprocessing ...
% 3.49/1.31 Prover 2: Preprocessing ...
% 3.49/1.31 Prover 3: Preprocessing ...
% 8.18/2.02 Prover 2: Proving ...
% 8.18/2.02 Prover 5: Proving ...
% 9.14/2.05 Prover 6: Proving ...
% 9.45/2.10 Prover 3: Constructing countermodel ...
% 9.45/2.10 Prover 1: Constructing countermodel ...
% 9.45/2.10 Prover 0: Proving ...
% 9.86/2.15 Prover 4: Constructing countermodel ...
% 10.86/2.33 Prover 3: proved (1650ms)
% 10.86/2.33
% 10.86/2.33 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 10.86/2.33
% 10.86/2.33 Prover 6: stopped
% 10.86/2.33 Prover 2: stopped
% 10.86/2.33 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 10.86/2.33 Prover 5: stopped
% 10.86/2.35 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 10.86/2.35 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 10.86/2.35 Prover 0: stopped
% 10.86/2.35 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 11.48/2.36 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 11.66/2.39 Prover 8: Preprocessing ...
% 11.66/2.40 Prover 10: Preprocessing ...
% 11.66/2.41 Prover 7: Preprocessing ...
% 11.66/2.42 Prover 11: Preprocessing ...
% 11.97/2.42 Prover 1: Found proof (size 25)
% 11.97/2.42 Prover 1: proved (1748ms)
% 11.97/2.42 Prover 4: stopped
% 11.97/2.43 Prover 13: Preprocessing ...
% 12.09/2.44 Prover 7: stopped
% 12.09/2.44 Prover 10: stopped
% 12.09/2.47 Prover 13: stopped
% 12.09/2.48 Prover 11: stopped
% 12.81/2.58 Prover 8: Warning: ignoring some quantifiers
% 12.81/2.59 Prover 8: Constructing countermodel ...
% 12.81/2.60 Prover 8: stopped
% 12.81/2.60
% 12.81/2.60 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 12.81/2.60
% 12.81/2.61 % SZS output start Proof for theBenchmark
% 12.81/2.61 Assumptions after simplification:
% 12.81/2.61 ---------------------------------
% 12.81/2.61
% 12.81/2.61 (isa)
% 13.13/2.64 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (isa(v0, v1) = v2) |
% 13.13/2.64 ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : ? [v5: int] : ( ~ (v5 =
% 13.13/2.64 0) & status(v3, v4, v1) = v5 & status(v3, v4, v0) = 0 & $i(v4) &
% 13.13/2.64 $i(v3))) & ! [v0: $i] : ! [v1: $i] : ( ~ (isa(v0, v1) = 0) | ~ $i(v1) |
% 13.13/2.64 ~ $i(v0) | ! [v2: $i] : ! [v3: $i] : ( ~ (status(v2, v3, v0) = 0) | ~
% 13.13/2.64 $i(v3) | ~ $i(v2) | status(v2, v3, v1) = 0))
% 13.13/2.64
% 13.13/2.64 (isa_wth_thm)
% 13.13/2.64 $i(wth) & $i(thm) & ? [v0: int] : ( ~ (v0 = 0) & isa(wth, thm) = v0)
% 13.13/2.64
% 13.13/2.64 (thm)
% 13.13/2.64 $i(thm) & ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (status(v0,
% 13.13/2.64 v1, thm) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : (
% 13.13/2.64 ~ (v4 = 0) & model(v3, v1) = v4 & model(v3, v0) = 0 & $i(v3))) & ! [v0:
% 13.13/2.64 $i] : ! [v1: $i] : ( ~ (status(v0, v1, thm) = 0) | ~ $i(v1) | ~ $i(v0) |
% 13.13/2.64 ! [v2: $i] : ( ~ (model(v2, v0) = 0) | ~ $i(v2) | model(v2, v1) = 0))
% 13.13/2.64
% 13.13/2.64 (wth)
% 13.13/2.64 $i(wth) & ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (status(v0,
% 13.13/2.64 v1, wth) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : (
% 13.13/2.64 ~ (v4 = 0) & model(v3, v1) = v4 & model(v3, v0) = 0 & $i(v3)) | ! [v3:
% 13.13/2.64 $i] : ! [v4: int] : (v4 = 0 | ~ (model(v3, v1) = v4) | ~ $i(v3)) | !
% 13.13/2.64 [v3: $i] : ! [v4: int] : (v4 = 0 | ~ (model(v3, v0) = v4) | ~ $i(v3) | ?
% 13.13/2.64 [v5: int] : ( ~ (v5 = 0) & model(v3, v1) = v5)) | ! [v3: $i] : ( ~
% 13.13/2.64 (model(v3, v0) = 0) | ~ $i(v3))) & ! [v0: $i] : ! [v1: $i] : ( ~
% 13.13/2.64 (status(v0, v1, wth) = 0) | ~ $i(v1) | ~ $i(v0) | ( ! [v2: $i] : ( ~
% 13.13/2.64 (model(v2, v0) = 0) | ~ $i(v2) | model(v2, v1) = 0) & ? [v2: $i] : ?
% 13.13/2.64 [v3: int] : ( ~ (v3 = 0) & model(v2, v1) = v3 & $i(v2)) & ? [v2: $i] : ?
% 13.13/2.64 [v3: int] : ( ~ (v3 = 0) & model(v2, v1) = 0 & model(v2, v0) = v3 &
% 13.13/2.64 $i(v2)) & ? [v2: $i] : (model(v2, v0) = 0 & $i(v2))))
% 13.13/2.64
% 13.13/2.64 (function-axioms)
% 13.13/2.65 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 13.13/2.65 [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (status(v4, v3, v2) = v1) | ~
% 13.13/2.65 (status(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 13.13/2.65 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (xora(v3, v2)
% 13.13/2.65 = v1) | ~ (xora(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 13.13/2.65 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (nevera(v3,
% 13.13/2.65 v2) = v1) | ~ (nevera(v3, v2) = v0)) & ! [v0: MultipleValueBool] : !
% 13.13/2.65 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (nota(v3,
% 13.13/2.65 v2) = v1) | ~ (nota(v3, v2) = v0)) & ! [v0: MultipleValueBool] : !
% 13.13/2.65 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (isa(v3,
% 13.13/2.65 v2) = v1) | ~ (isa(v3, v2) = v0)) & ! [v0: MultipleValueBool] : !
% 13.13/2.65 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 13.13/2.65 (mighta(v3, v2) = v1) | ~ (mighta(v3, v2) = v0)) & ! [v0:
% 13.13/2.65 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 13.13/2.65 : (v1 = v0 | ~ (model(v3, v2) = v1) | ~ (model(v3, v2) = v0)) & ! [v0: $i]
% 13.13/2.65 : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (not(v2) = v1) | ~ (not(v2) =
% 13.13/2.65 v0))
% 13.13/2.65
% 13.13/2.65 Further assumptions not needed in the proof:
% 13.13/2.65 --------------------------------------------
% 13.13/2.65 cax, completeness, contradiction, csa, eqv, esa, eth, mighta, mixed_pair,
% 13.13/2.65 nevera, noc, non_thm_spt, not, nota, sap, sat, sat_non_taut_pair, satisfiable,
% 13.13/2.65 sca, tac, tau, tautology, tca, unp, uns, wca, wec, wtc, xora
% 13.13/2.65
% 13.13/2.65 Those formulas are unsatisfiable:
% 13.13/2.65 ---------------------------------
% 13.13/2.65
% 13.13/2.65 Begin of proof
% 13.13/2.65 |
% 13.13/2.65 | ALPHA: (thm) implies:
% 13.13/2.65 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (status(v0, v1,
% 13.13/2.65 | thm) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] :
% 13.13/2.65 | ( ~ (v4 = 0) & model(v3, v1) = v4 & model(v3, v0) = 0 & $i(v3)))
% 13.13/2.65 |
% 13.13/2.65 | ALPHA: (wth) implies:
% 13.13/2.65 | (2) ! [v0: $i] : ! [v1: $i] : ( ~ (status(v0, v1, wth) = 0) | ~ $i(v1) |
% 13.13/2.65 | ~ $i(v0) | ( ! [v2: $i] : ( ~ (model(v2, v0) = 0) | ~ $i(v2) |
% 13.13/2.65 | model(v2, v1) = 0) & ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) &
% 13.13/2.65 | model(v2, v1) = v3 & $i(v2)) & ? [v2: $i] : ? [v3: int] : ( ~
% 13.13/2.65 | (v3 = 0) & model(v2, v1) = 0 & model(v2, v0) = v3 & $i(v2)) & ?
% 13.13/2.65 | [v2: $i] : (model(v2, v0) = 0 & $i(v2))))
% 13.13/2.65 |
% 13.13/2.65 | ALPHA: (isa) implies:
% 13.13/2.65 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (isa(v0, v1) =
% 13.13/2.65 | v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : ? [v5:
% 13.13/2.65 | int] : ( ~ (v5 = 0) & status(v3, v4, v1) = v5 & status(v3, v4, v0)
% 13.13/2.65 | = 0 & $i(v4) & $i(v3)))
% 13.13/2.65 |
% 13.13/2.65 | ALPHA: (isa_wth_thm) implies:
% 13.13/2.66 | (4) $i(thm)
% 13.13/2.66 | (5) $i(wth)
% 13.13/2.66 | (6) ? [v0: int] : ( ~ (v0 = 0) & isa(wth, thm) = v0)
% 13.13/2.66 |
% 13.13/2.66 | ALPHA: (function-axioms) implies:
% 13.13/2.66 | (7) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 13.13/2.66 | ! [v3: $i] : (v1 = v0 | ~ (model(v3, v2) = v1) | ~ (model(v3, v2) =
% 13.13/2.66 | v0))
% 13.13/2.66 |
% 13.13/2.66 | DELTA: instantiating (6) with fresh symbol all_30_0 gives:
% 13.13/2.66 | (8) ~ (all_30_0 = 0) & isa(wth, thm) = all_30_0
% 13.13/2.66 |
% 13.13/2.66 | ALPHA: (8) implies:
% 13.13/2.66 | (9) ~ (all_30_0 = 0)
% 13.13/2.66 | (10) isa(wth, thm) = all_30_0
% 13.13/2.66 |
% 13.13/2.66 | GROUND_INST: instantiating (3) with wth, thm, all_30_0, simplifying with (4),
% 13.13/2.66 | (5), (10) gives:
% 13.13/2.66 | (11) all_30_0 = 0 | ? [v0: $i] : ? [v1: $i] : ? [v2: int] : ( ~ (v2 = 0)
% 13.13/2.66 | & status(v0, v1, wth) = 0 & status(v0, v1, thm) = v2 & $i(v1) &
% 13.13/2.66 | $i(v0))
% 13.13/2.66 |
% 13.13/2.66 | BETA: splitting (11) gives:
% 13.13/2.66 |
% 13.13/2.66 | Case 1:
% 13.13/2.66 | |
% 13.13/2.66 | | (12) all_30_0 = 0
% 13.13/2.66 | |
% 13.13/2.66 | | REDUCE: (9), (12) imply:
% 13.13/2.66 | | (13) $false
% 13.13/2.66 | |
% 13.13/2.66 | | CLOSE: (13) is inconsistent.
% 13.13/2.66 | |
% 13.13/2.66 | Case 2:
% 13.13/2.66 | |
% 13.13/2.66 | | (14) ? [v0: $i] : ? [v1: $i] : ? [v2: int] : ( ~ (v2 = 0) & status(v0,
% 13.13/2.66 | | v1, wth) = 0 & status(v0, v1, thm) = v2 & $i(v1) & $i(v0))
% 13.13/2.66 | |
% 13.13/2.66 | | DELTA: instantiating (14) with fresh symbols all_73_0, all_73_1, all_73_2
% 13.13/2.66 | | gives:
% 13.13/2.66 | | (15) ~ (all_73_0 = 0) & status(all_73_2, all_73_1, wth) = 0 &
% 13.13/2.66 | | status(all_73_2, all_73_1, thm) = all_73_0 & $i(all_73_1) &
% 13.13/2.66 | | $i(all_73_2)
% 13.13/2.66 | |
% 13.13/2.66 | | ALPHA: (15) implies:
% 13.13/2.66 | | (16) ~ (all_73_0 = 0)
% 13.13/2.66 | | (17) $i(all_73_2)
% 13.13/2.66 | | (18) $i(all_73_1)
% 13.13/2.66 | | (19) status(all_73_2, all_73_1, thm) = all_73_0
% 13.13/2.66 | | (20) status(all_73_2, all_73_1, wth) = 0
% 13.13/2.66 | |
% 13.13/2.66 | | GROUND_INST: instantiating (1) with all_73_2, all_73_1, all_73_0,
% 13.13/2.66 | | simplifying with (17), (18), (19) gives:
% 13.13/2.66 | | (21) all_73_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & model(v0,
% 13.13/2.66 | | all_73_1) = v1 & model(v0, all_73_2) = 0 & $i(v0))
% 13.13/2.66 | |
% 13.13/2.67 | | GROUND_INST: instantiating (2) with all_73_2, all_73_1, simplifying with
% 13.13/2.67 | | (17), (18), (20) gives:
% 13.13/2.67 | | (22) ! [v0: $i] : ( ~ (model(v0, all_73_2) = 0) | ~ $i(v0) | model(v0,
% 13.13/2.67 | | all_73_1) = 0) & ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) &
% 13.13/2.67 | | model(v0, all_73_1) = v1 & $i(v0)) & ? [v0: $i] : ? [v1: int] :
% 13.13/2.67 | | ( ~ (v1 = 0) & model(v0, all_73_1) = 0 & model(v0, all_73_2) = v1 &
% 13.13/2.67 | | $i(v0)) & ? [v0: $i] : (model(v0, all_73_2) = 0 & $i(v0))
% 13.13/2.67 | |
% 13.13/2.67 | | ALPHA: (22) implies:
% 13.13/2.67 | | (23) ! [v0: $i] : ( ~ (model(v0, all_73_2) = 0) | ~ $i(v0) | model(v0,
% 13.13/2.67 | | all_73_1) = 0)
% 13.13/2.67 | |
% 13.13/2.67 | | BETA: splitting (21) gives:
% 13.13/2.67 | |
% 13.13/2.67 | | Case 1:
% 13.13/2.67 | | |
% 13.13/2.67 | | | (24) all_73_0 = 0
% 13.13/2.67 | | |
% 13.13/2.67 | | | REDUCE: (16), (24) imply:
% 13.13/2.67 | | | (25) $false
% 13.13/2.67 | | |
% 13.13/2.67 | | | CLOSE: (25) is inconsistent.
% 13.13/2.67 | | |
% 13.13/2.67 | | Case 2:
% 13.13/2.67 | | |
% 13.13/2.67 | | | (26) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & model(v0, all_73_1) =
% 13.13/2.67 | | | v1 & model(v0, all_73_2) = 0 & $i(v0))
% 13.13/2.67 | | |
% 13.13/2.67 | | | DELTA: instantiating (26) with fresh symbols all_91_0, all_91_1 gives:
% 13.13/2.67 | | | (27) ~ (all_91_0 = 0) & model(all_91_1, all_73_1) = all_91_0 &
% 13.13/2.67 | | | model(all_91_1, all_73_2) = 0 & $i(all_91_1)
% 13.13/2.67 | | |
% 13.13/2.67 | | | ALPHA: (27) implies:
% 13.13/2.67 | | | (28) ~ (all_91_0 = 0)
% 13.13/2.67 | | | (29) $i(all_91_1)
% 13.13/2.67 | | | (30) model(all_91_1, all_73_2) = 0
% 13.13/2.67 | | | (31) model(all_91_1, all_73_1) = all_91_0
% 13.13/2.67 | | |
% 13.13/2.67 | | | GROUND_INST: instantiating (23) with all_91_1, simplifying with (29), (30)
% 13.13/2.67 | | | gives:
% 13.13/2.67 | | | (32) model(all_91_1, all_73_1) = 0
% 13.13/2.67 | | |
% 13.13/2.67 | | | GROUND_INST: instantiating (7) with all_91_0, 0, all_73_1, all_91_1,
% 13.13/2.67 | | | simplifying with (31), (32) gives:
% 13.13/2.67 | | | (33) all_91_0 = 0
% 13.13/2.67 | | |
% 13.13/2.67 | | | REDUCE: (28), (33) imply:
% 13.13/2.67 | | | (34) $false
% 13.13/2.67 | | |
% 13.13/2.67 | | | CLOSE: (34) is inconsistent.
% 13.13/2.67 | | |
% 13.13/2.67 | | End of split
% 13.13/2.67 | |
% 13.13/2.67 | End of split
% 13.13/2.67 |
% 13.13/2.67 End of proof
% 13.13/2.67 % SZS output end Proof for theBenchmark
% 13.13/2.67
% 13.13/2.67 2021ms
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