TSTP Solution File: KLE022+2 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : KLE022+2 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n019.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 05:34:15 EDT 2023
% Result : Theorem 26.58s 4.34s
% Output : Proof 30.61s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : KLE022+2 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.17/0.34 % Computer : n019.cluster.edu
% 0.17/0.34 % Model : x86_64 x86_64
% 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34 % Memory : 8042.1875MB
% 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.34 % CPULimit : 300
% 0.17/0.34 % WCLimit : 300
% 0.17/0.34 % DateTime : Tue Aug 29 12:06:58 EDT 2023
% 0.17/0.34 % CPUTime :
% 0.19/0.61 ________ _____
% 0.19/0.61 ___ __ \_________(_)________________________________
% 0.19/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.19/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.19/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.19/0.61
% 0.19/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.19/0.61 (2023-06-19)
% 0.19/0.61
% 0.19/0.61 (c) Philipp Rümmer, 2009-2023
% 0.19/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.19/0.61 Amanda Stjerna.
% 0.19/0.61 Free software under BSD-3-Clause.
% 0.19/0.61
% 0.19/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.19/0.61
% 0.19/0.61 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.19/0.63 Running up to 7 provers in parallel.
% 0.19/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.19/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.19/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 0.19/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.19/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.19/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.19/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 2.22/1.03 Prover 4: Preprocessing ...
% 2.22/1.03 Prover 1: Preprocessing ...
% 2.86/1.08 Prover 3: Preprocessing ...
% 2.86/1.08 Prover 5: Preprocessing ...
% 2.86/1.08 Prover 0: Preprocessing ...
% 2.86/1.08 Prover 2: Preprocessing ...
% 2.86/1.08 Prover 6: Preprocessing ...
% 5.02/1.40 Prover 1: Constructing countermodel ...
% 5.02/1.43 Prover 6: Proving ...
% 5.02/1.43 Prover 3: Constructing countermodel ...
% 5.02/1.48 Prover 4: Constructing countermodel ...
% 5.02/1.48 Prover 0: Proving ...
% 5.82/1.50 Prover 5: Proving ...
% 6.11/1.53 Prover 2: Proving ...
% 7.11/1.75 Prover 3: gave up
% 7.82/1.76 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 8.04/1.81 Prover 7: Preprocessing ...
% 8.91/1.95 Prover 7: Constructing countermodel ...
% 17.83/3.14 Prover 6: gave up
% 17.83/3.14 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 17.83/3.17 Prover 8: Preprocessing ...
% 18.43/3.27 Prover 8: Warning: ignoring some quantifiers
% 18.43/3.27 Prover 8: Constructing countermodel ...
% 21.89/3.68 Prover 8: gave up
% 21.89/3.68 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889
% 22.13/3.72 Prover 9: Preprocessing ...
% 22.25/3.80 Prover 9: Constructing countermodel ...
% 26.58/4.33 Prover 2: proved (3698ms)
% 26.58/4.34
% 26.58/4.34 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 26.58/4.34
% 26.58/4.34 Prover 9: stopped
% 26.58/4.34 Prover 5: stopped
% 26.58/4.35 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 26.58/4.35 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 26.58/4.35 Prover 0: stopped
% 26.58/4.37 Prover 11: Preprocessing ...
% 26.58/4.37 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 26.58/4.37 Prover 10: Preprocessing ...
% 26.58/4.37 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 27.22/4.38 Prover 16: Preprocessing ...
% 27.22/4.39 Prover 13: Preprocessing ...
% 27.22/4.40 Prover 10: Constructing countermodel ...
% 27.46/4.42 Prover 16: Warning: ignoring some quantifiers
% 27.46/4.43 Prover 16: Constructing countermodel ...
% 27.65/4.43 Prover 11: Constructing countermodel ...
% 27.65/4.45 Prover 13: Warning: ignoring some quantifiers
% 27.65/4.46 Prover 13: Constructing countermodel ...
% 28.34/4.57 Prover 10: gave up
% 28.34/4.59 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085
% 28.87/4.61 Prover 19: Preprocessing ...
% 29.48/4.70 Prover 13: gave up
% 29.73/4.72 Prover 19: Warning: ignoring some quantifiers
% 29.73/4.73 Prover 19: Constructing countermodel ...
% 29.73/4.77 Prover 11: Found proof (size 110)
% 29.73/4.77 Prover 11: proved (434ms)
% 29.73/4.77 Prover 16: stopped
% 29.73/4.77 Prover 19: stopped
% 29.73/4.78 Prover 1: stopped
% 29.73/4.78 Prover 4: stopped
% 29.73/4.78 Prover 7: stopped
% 29.73/4.78
% 29.73/4.78 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 29.73/4.78
% 29.73/4.79 % SZS output start Proof for theBenchmark
% 29.73/4.80 Assumptions after simplification:
% 29.73/4.80 ---------------------------------
% 29.73/4.80
% 29.73/4.80 (additive_commutativity)
% 29.73/4.82 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (addition(v1, v0) = v2) | ~
% 29.73/4.82 $i(v1) | ~ $i(v0) | (addition(v0, v1) = v2 & $i(v2))) & ! [v0: $i] : !
% 29.73/4.82 [v1: $i] : ! [v2: $i] : ( ~ (addition(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) |
% 29.73/4.82 (addition(v1, v0) = v2 & $i(v2)))
% 29.73/4.82
% 29.73/4.82 (additive_idempotence)
% 29.73/4.82 ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (addition(v0, v0) = v1) | ~ $i(v0))
% 29.73/4.82
% 29.73/4.82 (goals)
% 29.73/4.83 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5:
% 29.73/4.83 $i] : ? [v6: int] : ? [v7: int] : (c(v1) = v3 & test(v1) = 0 &
% 29.73/4.83 multiplication(v0, v3) = v4 & multiplication(v0, v1) = v2 & addition(v2, v4)
% 29.73/4.83 = v5 & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & (( ~ (v7 = 0) &
% 29.73/4.83 leq(v5, v0) = v7) | ( ~ (v6 = 0) & leq(v0, v5) = v6)))
% 29.73/4.83
% 29.73/4.83 (multiplicative_right_identity)
% 29.73/4.83 $i(one) & ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (multiplication(v0, one) =
% 29.73/4.83 v1) | ~ $i(v0))
% 29.73/4.83
% 29.73/4.83 (order)
% 29.73/4.83 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v1 | ~ (addition(v0, v1) =
% 29.73/4.83 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ( ~ (v3 = 0) & leq(v0, v1) =
% 29.73/4.83 v3)) & ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (leq(v0,
% 29.73/4.83 v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ( ~ (v3 = v1) &
% 29.73/4.83 addition(v0, v1) = v3 & $i(v3))) & ! [v0: $i] : ! [v1: $i] : ( ~
% 29.73/4.83 (leq(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | addition(v0, v1) = v1) & ! [v0:
% 29.73/4.83 $i] : ! [v1: $i] : ( ~ (addition(v0, v1) = v1) | ~ $i(v1) | ~ $i(v0) |
% 29.73/4.83 leq(v0, v1) = 0)
% 29.73/4.83
% 29.73/4.83 (right_distributivity)
% 29.73/4.83 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 29.73/4.83 $i] : ( ~ (multiplication(v0, v2) = v4) | ~ (multiplication(v0, v1) = v3) |
% 29.73/4.83 ~ (addition(v3, v4) = v5) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: $i]
% 29.73/4.83 : (multiplication(v0, v6) = v5 & addition(v1, v2) = v6 & $i(v6) & $i(v5))) &
% 29.73/4.83 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 29.73/4.83 (multiplication(v0, v3) = v4) | ~ (addition(v1, v2) = v3) | ~ $i(v2) | ~
% 29.73/4.83 $i(v1) | ~ $i(v0) | ? [v5: $i] : ? [v6: $i] : (multiplication(v0, v2) =
% 29.73/4.83 v6 & multiplication(v0, v1) = v5 & addition(v5, v6) = v4 & $i(v6) & $i(v5)
% 29.73/4.83 & $i(v4)))
% 29.73/4.83
% 29.73/4.83 (test_1)
% 29.73/4.84 ! [v0: $i] : ! [v1: int] : ! [v2: $i] : (v1 = 0 | ~ (test(v0) = v1) | ~
% 29.73/4.84 (complement(v2, v0) = 0) | ~ $i(v2) | ~ $i(v0)) & ! [v0: $i] : ( ~
% 29.73/4.84 (test(v0) = 0) | ~ $i(v0) | ? [v1: $i] : (complement(v1, v0) = 0 &
% 29.73/4.84 $i(v1)))
% 29.73/4.84
% 29.73/4.84 (test_2)
% 29.73/4.84 $i(one) & $i(zero) & ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~
% 29.73/4.84 (complement(v1, v0) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4:
% 29.73/4.84 $i] : ? [v5: $i] : (( ~ (v5 = one) & addition(v0, v1) = v5 & $i(v5)) | (
% 29.73/4.84 ~ (v4 = zero) & multiplication(v1, v0) = v4 & $i(v4)) | ( ~ (v3 = zero)
% 29.73/4.84 & multiplication(v0, v1) = v3 & $i(v3)))) & ! [v0: $i] : ! [v1: $i] :
% 29.73/4.84 ! [v2: $i] : ( ~ (multiplication(v1, v0) = v2) | ~ $i(v1) | ~ $i(v0) | ?
% 29.73/4.84 [v3: int] : ? [v4: $i] : ? [v5: $i] : ((v5 = one & v4 = zero & v2 = zero &
% 29.73/4.84 multiplication(v0, v1) = zero & addition(v0, v1) = one) | ( ~ (v3 = 0) &
% 29.73/4.84 complement(v1, v0) = v3))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (
% 29.73/4.84 ~ (multiplication(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ?
% 29.73/4.84 [v4: $i] : ? [v5: $i] : ((v5 = one & v4 = zero & v2 = zero &
% 29.73/4.84 multiplication(v1, v0) = zero & addition(v0, v1) = one) | ( ~ (v3 = 0) &
% 29.73/4.84 complement(v1, v0) = v3))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (
% 29.73/4.84 ~ (addition(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ? [v4:
% 29.73/4.84 $i] : ? [v5: $i] : ((v5 = zero & v4 = zero & v2 = one &
% 29.73/4.84 multiplication(v1, v0) = zero & multiplication(v0, v1) = zero) | ( ~ (v3
% 29.73/4.84 = 0) & complement(v1, v0) = v3))) & ! [v0: $i] : ! [v1: $i] : ( ~
% 29.73/4.84 (complement(v1, v0) = 0) | ~ $i(v1) | ~ $i(v0) | (multiplication(v1, v0) =
% 29.73/4.84 zero & multiplication(v0, v1) = zero & addition(v0, v1) = one)) & ! [v0:
% 29.73/4.84 $i] : ! [v1: $i] : ( ~ (multiplication(v1, v0) = zero) | ~ $i(v1) | ~
% 29.73/4.84 $i(v0) | ? [v2: $i] : ? [v3: $i] : ? [v4: int] : ((v4 = 0 &
% 29.73/4.84 complement(v1, v0) = 0) | ( ~ (v3 = one) & addition(v0, v1) = v3 &
% 29.73/4.84 $i(v3)) | ( ~ (v2 = zero) & multiplication(v0, v1) = v2 & $i(v2)))) & !
% 29.73/4.84 [v0: $i] : ! [v1: $i] : ( ~ (multiplication(v0, v1) = zero) | ~ $i(v1) | ~
% 29.73/4.84 $i(v0) | ? [v2: $i] : ? [v3: $i] : ? [v4: int] : ((v4 = 0 &
% 29.73/4.84 complement(v1, v0) = 0) | ( ~ (v3 = one) & addition(v0, v1) = v3 &
% 29.73/4.84 $i(v3)) | ( ~ (v2 = zero) & multiplication(v1, v0) = v2 & $i(v2)))) & !
% 29.73/4.84 [v0: $i] : ! [v1: $i] : ( ~ (addition(v0, v1) = one) | ~ $i(v1) | ~ $i(v0)
% 29.73/4.84 | ? [v2: $i] : ? [v3: $i] : ? [v4: int] : ((v4 = 0 & complement(v1, v0) =
% 29.73/4.84 0) | ( ~ (v3 = zero) & multiplication(v1, v0) = v3 & $i(v3)) | ( ~ (v2 =
% 29.73/4.84 zero) & multiplication(v0, v1) = v2 & $i(v2))))
% 29.73/4.84
% 29.73/4.84 (test_3)
% 29.73/4.85 ! [v0: $i] : ! [v1: $i] : ! [v2: any] : ( ~ (complement(v0, v1) = v2) | ~
% 29.73/4.85 $i(v1) | ~ $i(v0) | ? [v3: int] : ? [v4: $i] : (( ~ (v3 = 0) & test(v0) =
% 29.73/4.85 v3) | (( ~ (v2 = 0) | (v4 = v1 & c(v0) = v1)) & (v2 = 0 | ( ~ (v4 = v1)
% 29.73/4.85 & c(v0) = v4 & $i(v4))))))
% 29.73/4.85
% 29.73/4.85 (function-axioms)
% 29.73/4.85 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 29.73/4.85 [v3: $i] : (v1 = v0 | ~ (complement(v3, v2) = v1) | ~ (complement(v3, v2) =
% 29.73/4.85 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 29.73/4.85 $i] : ! [v3: $i] : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) =
% 29.73/4.85 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 |
% 29.73/4.85 ~ (multiplication(v3, v2) = v1) | ~ (multiplication(v3, v2) = v0)) & !
% 29.73/4.85 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 29.73/4.85 (addition(v3, v2) = v1) | ~ (addition(v3, v2) = v0)) & ! [v0: $i] : !
% 29.73/4.85 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (c(v2) = v1) | ~ (c(v2) = v0)) & !
% 29.73/4.85 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0
% 29.73/4.85 | ~ (test(v2) = v1) | ~ (test(v2) = v0))
% 29.73/4.85
% 29.73/4.85 Further assumptions not needed in the proof:
% 29.73/4.85 --------------------------------------------
% 29.73/4.85 additive_associativity, additive_identity, left_annihilation,
% 29.73/4.85 left_distributivity, multiplicative_associativity, multiplicative_left_identity,
% 29.73/4.85 right_annihilation, test_4
% 29.73/4.85
% 29.73/4.85 Those formulas are unsatisfiable:
% 29.73/4.85 ---------------------------------
% 29.73/4.85
% 29.73/4.85 Begin of proof
% 29.73/4.85 |
% 29.73/4.85 | ALPHA: (additive_commutativity) implies:
% 29.73/4.85 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (addition(v1, v0) = v2) |
% 29.73/4.85 | ~ $i(v1) | ~ $i(v0) | (addition(v0, v1) = v2 & $i(v2)))
% 29.73/4.85 |
% 29.73/4.85 | ALPHA: (multiplicative_right_identity) implies:
% 29.73/4.85 | (2) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (multiplication(v0, one) =
% 29.73/4.85 | v1) | ~ $i(v0))
% 29.73/4.85 |
% 29.73/4.85 | ALPHA: (right_distributivity) implies:
% 29.73/4.85 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 29.73/4.85 | ! [v5: $i] : ( ~ (multiplication(v0, v2) = v4) | ~ (multiplication(v0,
% 29.73/4.85 | v1) = v3) | ~ (addition(v3, v4) = v5) | ~ $i(v2) | ~ $i(v1) |
% 29.73/4.85 | ~ $i(v0) | ? [v6: $i] : (multiplication(v0, v6) = v5 & addition(v1,
% 29.73/4.85 | v2) = v6 & $i(v6) & $i(v5)))
% 29.73/4.85 |
% 29.73/4.85 | ALPHA: (order) implies:
% 29.73/4.85 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (leq(v0, v1) =
% 29.73/4.85 | v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ( ~ (v3 = v1) &
% 29.73/4.85 | addition(v0, v1) = v3 & $i(v3)))
% 29.73/4.85 |
% 29.73/4.85 | ALPHA: (test_1) implies:
% 29.73/4.85 | (5) ! [v0: $i] : ( ~ (test(v0) = 0) | ~ $i(v0) | ? [v1: $i] :
% 29.73/4.85 | (complement(v1, v0) = 0 & $i(v1)))
% 29.73/4.85 |
% 29.73/4.85 | ALPHA: (test_2) implies:
% 29.73/4.86 | (6) ! [v0: $i] : ! [v1: $i] : ( ~ (multiplication(v0, v1) = zero) | ~
% 29.73/4.86 | $i(v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: $i] : ? [v4: int] : ((v4
% 29.73/4.86 | = 0 & complement(v1, v0) = 0) | ( ~ (v3 = one) & addition(v0, v1)
% 29.73/4.86 | = v3 & $i(v3)) | ( ~ (v2 = zero) & multiplication(v1, v0) = v2 &
% 29.73/4.86 | $i(v2))))
% 29.73/4.86 | (7) ! [v0: $i] : ! [v1: $i] : ( ~ (complement(v1, v0) = 0) | ~ $i(v1) |
% 29.73/4.86 | ~ $i(v0) | (multiplication(v1, v0) = zero & multiplication(v0, v1) =
% 29.73/4.86 | zero & addition(v0, v1) = one))
% 29.73/4.86 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (addition(v0, v1) = v2) |
% 29.73/4.86 | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ? [v4: $i] : ? [v5: $i] :
% 29.73/4.86 | ((v5 = zero & v4 = zero & v2 = one & multiplication(v1, v0) = zero &
% 29.73/4.86 | multiplication(v0, v1) = zero) | ( ~ (v3 = 0) & complement(v1,
% 29.73/4.86 | v0) = v3)))
% 29.73/4.86 |
% 29.73/4.86 | ALPHA: (function-axioms) implies:
% 29.73/4.86 | (9) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 29.73/4.86 | (v1 = v0 | ~ (test(v2) = v1) | ~ (test(v2) = v0))
% 29.73/4.86 | (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (c(v2) = v1) |
% 29.73/4.86 | ~ (c(v2) = v0))
% 29.73/4.86 | (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 29.73/4.86 | (addition(v3, v2) = v1) | ~ (addition(v3, v2) = v0))
% 29.73/4.86 | (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 29.73/4.86 | (multiplication(v3, v2) = v1) | ~ (multiplication(v3, v2) = v0))
% 29.73/4.86 | (13) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 29.73/4.86 | : ! [v3: $i] : (v1 = v0 | ~ (complement(v3, v2) = v1) | ~
% 29.73/4.86 | (complement(v3, v2) = v0))
% 29.73/4.86 |
% 29.73/4.86 | DELTA: instantiating (goals) with fresh symbols all_20_0, all_20_1, all_20_2,
% 29.73/4.86 | all_20_3, all_20_4, all_20_5, all_20_6, all_20_7 gives:
% 29.73/4.86 | (14) c(all_20_6) = all_20_4 & test(all_20_6) = 0 & multiplication(all_20_7,
% 29.73/4.86 | all_20_4) = all_20_3 & multiplication(all_20_7, all_20_6) = all_20_5
% 29.73/4.86 | & addition(all_20_5, all_20_3) = all_20_2 & $i(all_20_2) &
% 29.73/4.86 | $i(all_20_3) & $i(all_20_4) & $i(all_20_5) & $i(all_20_6) &
% 29.73/4.86 | $i(all_20_7) & (( ~ (all_20_0 = 0) & leq(all_20_2, all_20_7) =
% 29.73/4.86 | all_20_0) | ( ~ (all_20_1 = 0) & leq(all_20_7, all_20_2) =
% 29.73/4.86 | all_20_1))
% 29.73/4.86 |
% 29.73/4.86 | ALPHA: (14) implies:
% 29.73/4.86 | (15) $i(all_20_7)
% 29.73/4.86 | (16) $i(all_20_6)
% 29.73/4.86 | (17) $i(all_20_5)
% 29.73/4.86 | (18) $i(all_20_4)
% 29.73/4.86 | (19) $i(all_20_3)
% 29.73/4.86 | (20) addition(all_20_5, all_20_3) = all_20_2
% 29.73/4.86 | (21) multiplication(all_20_7, all_20_6) = all_20_5
% 29.73/4.86 | (22) multiplication(all_20_7, all_20_4) = all_20_3
% 29.73/4.86 | (23) test(all_20_6) = 0
% 29.73/4.86 | (24) c(all_20_6) = all_20_4
% 29.73/4.86 | (25) ( ~ (all_20_0 = 0) & leq(all_20_2, all_20_7) = all_20_0) | ( ~
% 29.73/4.86 | (all_20_1 = 0) & leq(all_20_7, all_20_2) = all_20_1)
% 29.73/4.86 |
% 29.73/4.86 | GROUND_INST: instantiating (1) with all_20_3, all_20_5, all_20_2, simplifying
% 29.73/4.86 | with (17), (19), (20) gives:
% 29.73/4.86 | (26) addition(all_20_3, all_20_5) = all_20_2 & $i(all_20_2)
% 29.73/4.86 |
% 29.73/4.86 | ALPHA: (26) implies:
% 29.73/4.86 | (27) addition(all_20_3, all_20_5) = all_20_2
% 29.73/4.86 |
% 29.73/4.86 | GROUND_INST: instantiating (3) with all_20_7, all_20_6, all_20_4, all_20_5,
% 29.73/4.87 | all_20_3, all_20_2, simplifying with (15), (16), (18), (20),
% 29.73/4.87 | (21), (22) gives:
% 29.73/4.87 | (28) ? [v0: $i] : (multiplication(all_20_7, v0) = all_20_2 &
% 29.73/4.87 | addition(all_20_6, all_20_4) = v0 & $i(v0) & $i(all_20_2))
% 29.73/4.87 |
% 29.73/4.87 | GROUND_INST: instantiating (5) with all_20_6, simplifying with (16), (23)
% 29.73/4.87 | gives:
% 29.73/4.87 | (29) ? [v0: $i] : (complement(v0, all_20_6) = 0 & $i(v0))
% 29.73/4.87 |
% 29.73/4.87 | DELTA: instantiating (29) with fresh symbol all_28_0 gives:
% 29.73/4.87 | (30) complement(all_28_0, all_20_6) = 0 & $i(all_28_0)
% 29.73/4.87 |
% 29.73/4.87 | ALPHA: (30) implies:
% 29.73/4.87 | (31) $i(all_28_0)
% 29.73/4.87 | (32) complement(all_28_0, all_20_6) = 0
% 29.73/4.87 |
% 29.73/4.87 | DELTA: instantiating (28) with fresh symbol all_30_0 gives:
% 30.61/4.87 | (33) multiplication(all_20_7, all_30_0) = all_20_2 & addition(all_20_6,
% 30.61/4.87 | all_20_4) = all_30_0 & $i(all_30_0) & $i(all_20_2)
% 30.61/4.87 |
% 30.61/4.87 | ALPHA: (33) implies:
% 30.61/4.87 | (34) addition(all_20_6, all_20_4) = all_30_0
% 30.61/4.87 |
% 30.61/4.87 | GROUND_INST: instantiating (1) with all_20_4, all_20_6, all_30_0, simplifying
% 30.61/4.87 | with (16), (18), (34) gives:
% 30.61/4.87 | (35) addition(all_20_4, all_20_6) = all_30_0 & $i(all_30_0)
% 30.61/4.87 |
% 30.61/4.87 | ALPHA: (35) implies:
% 30.61/4.87 | (36) addition(all_20_4, all_20_6) = all_30_0
% 30.61/4.87 |
% 30.61/4.87 | GROUND_INST: instantiating (8) with all_20_6, all_20_4, all_30_0, simplifying
% 30.61/4.87 | with (16), (18), (34) gives:
% 30.61/4.87 | (37) ? [v0: int] : ? [v1: $i] : ? [v2: $i] : ((v2 = zero & v1 = zero &
% 30.61/4.87 | all_30_0 = one & multiplication(all_20_4, all_20_6) = zero &
% 30.61/4.87 | multiplication(all_20_6, all_20_4) = zero) | ( ~ (v0 = 0) &
% 30.61/4.87 | complement(all_20_4, all_20_6) = v0))
% 30.61/4.87 |
% 30.61/4.87 | GROUND_INST: instantiating (3) with all_20_7, all_20_4, all_20_6, all_20_3,
% 30.61/4.87 | all_20_5, all_20_2, simplifying with (15), (16), (18), (21),
% 30.61/4.87 | (22), (27) gives:
% 30.61/4.87 | (38) ? [v0: $i] : (multiplication(all_20_7, v0) = all_20_2 &
% 30.61/4.87 | addition(all_20_4, all_20_6) = v0 & $i(v0) & $i(all_20_2))
% 30.61/4.87 |
% 30.61/4.87 | GROUND_INST: instantiating (7) with all_20_6, all_28_0, simplifying with (16),
% 30.61/4.87 | (31), (32) gives:
% 30.61/4.87 | (39) multiplication(all_28_0, all_20_6) = zero & multiplication(all_20_6,
% 30.61/4.87 | all_28_0) = zero & addition(all_20_6, all_28_0) = one
% 30.61/4.87 |
% 30.61/4.87 | ALPHA: (39) implies:
% 30.61/4.87 | (40) addition(all_20_6, all_28_0) = one
% 30.61/4.87 | (41) multiplication(all_20_6, all_28_0) = zero
% 30.61/4.87 | (42) multiplication(all_28_0, all_20_6) = zero
% 30.61/4.87 |
% 30.61/4.87 | DELTA: instantiating (38) with fresh symbol all_43_0 gives:
% 30.61/4.87 | (43) multiplication(all_20_7, all_43_0) = all_20_2 & addition(all_20_4,
% 30.61/4.87 | all_20_6) = all_43_0 & $i(all_43_0) & $i(all_20_2)
% 30.61/4.87 |
% 30.61/4.87 | ALPHA: (43) implies:
% 30.61/4.87 | (44) $i(all_20_2)
% 30.61/4.87 | (45) addition(all_20_4, all_20_6) = all_43_0
% 30.61/4.87 | (46) multiplication(all_20_7, all_43_0) = all_20_2
% 30.61/4.87 |
% 30.61/4.87 | DELTA: instantiating (37) with fresh symbols all_49_0, all_49_1, all_49_2
% 30.61/4.87 | gives:
% 30.61/4.87 | (47) (all_49_0 = zero & all_49_1 = zero & all_30_0 = one &
% 30.61/4.87 | multiplication(all_20_4, all_20_6) = zero & multiplication(all_20_6,
% 30.61/4.87 | all_20_4) = zero) | ( ~ (all_49_2 = 0) & complement(all_20_4,
% 30.61/4.87 | all_20_6) = all_49_2)
% 30.61/4.87 |
% 30.61/4.87 | GROUND_INST: instantiating (11) with all_30_0, all_43_0, all_20_6, all_20_4,
% 30.61/4.87 | simplifying with (36), (45) gives:
% 30.61/4.87 | (48) all_43_0 = all_30_0
% 30.61/4.87 |
% 30.61/4.87 | REDUCE: (46), (48) imply:
% 30.61/4.87 | (49) multiplication(all_20_7, all_30_0) = all_20_2
% 30.61/4.87 |
% 30.61/4.87 | GROUND_INST: instantiating (1) with all_28_0, all_20_6, one, simplifying with
% 30.61/4.87 | (16), (31), (40) gives:
% 30.61/4.87 | (50) addition(all_28_0, all_20_6) = one & $i(one)
% 30.61/4.87 |
% 30.61/4.87 | ALPHA: (50) implies:
% 30.61/4.87 | (51) addition(all_28_0, all_20_6) = one
% 30.61/4.87 |
% 30.61/4.88 | GROUND_INST: instantiating (6) with all_28_0, all_20_6, simplifying with (16),
% 30.61/4.88 | (31), (42) gives:
% 30.61/4.88 | (52) ? [v0: $i] : ? [v1: $i] : ? [v2: int] : ((v2 = 0 &
% 30.61/4.88 | complement(all_20_6, all_28_0) = 0) | ( ~ (v1 = one) &
% 30.61/4.88 | addition(all_28_0, all_20_6) = v1 & $i(v1)) | ( ~ (v0 = zero) &
% 30.61/4.88 | multiplication(all_20_6, all_28_0) = v0 & $i(v0)))
% 30.61/4.88 |
% 30.61/4.88 | DELTA: instantiating (52) with fresh symbols all_63_0, all_63_1, all_63_2
% 30.61/4.88 | gives:
% 30.61/4.88 | (53) (all_63_0 = 0 & complement(all_20_6, all_28_0) = 0) | ( ~ (all_63_1 =
% 30.61/4.88 | one) & addition(all_28_0, all_20_6) = all_63_1 & $i(all_63_1)) | (
% 30.61/4.88 | ~ (all_63_2 = zero) & multiplication(all_20_6, all_28_0) = all_63_2
% 30.61/4.88 | & $i(all_63_2))
% 30.61/4.88 |
% 30.61/4.88 | BETA: splitting (53) gives:
% 30.61/4.88 |
% 30.61/4.88 | Case 1:
% 30.61/4.88 | |
% 30.61/4.88 | | (54) all_63_0 = 0 & complement(all_20_6, all_28_0) = 0
% 30.61/4.88 | |
% 30.61/4.88 | | ALPHA: (54) implies:
% 30.61/4.88 | | (55) complement(all_20_6, all_28_0) = 0
% 30.61/4.88 | |
% 30.61/4.88 | | GROUND_INST: instantiating (test_3) with all_20_6, all_28_0, 0, simplifying
% 30.61/4.88 | | with (16), (31), (55) gives:
% 30.61/4.88 | | (56) ? [v0: int] : ? [v1: int] : ((v1 = all_28_0 & c(all_20_6) =
% 30.61/4.88 | | all_28_0) | ( ~ (v0 = 0) & test(all_20_6) = v0))
% 30.61/4.88 | |
% 30.61/4.88 | | DELTA: instantiating (56) with fresh symbols all_86_0, all_86_1 gives:
% 30.61/4.88 | | (57) (all_86_0 = all_28_0 & c(all_20_6) = all_28_0) | ( ~ (all_86_1 = 0)
% 30.61/4.88 | | & test(all_20_6) = all_86_1)
% 30.61/4.88 | |
% 30.61/4.88 | | BETA: splitting (25) gives:
% 30.61/4.88 | |
% 30.61/4.88 | | Case 1:
% 30.61/4.88 | | |
% 30.61/4.88 | | | (58) ~ (all_20_0 = 0) & leq(all_20_2, all_20_7) = all_20_0
% 30.61/4.88 | | |
% 30.61/4.88 | | | ALPHA: (58) implies:
% 30.61/4.88 | | | (59) ~ (all_20_0 = 0)
% 30.61/4.88 | | | (60) leq(all_20_2, all_20_7) = all_20_0
% 30.61/4.88 | | |
% 30.61/4.88 | | | BETA: splitting (57) gives:
% 30.61/4.88 | | |
% 30.61/4.88 | | | Case 1:
% 30.61/4.88 | | | |
% 30.61/4.88 | | | | (61) all_86_0 = all_28_0 & c(all_20_6) = all_28_0
% 30.61/4.88 | | | |
% 30.61/4.88 | | | | ALPHA: (61) implies:
% 30.61/4.88 | | | | (62) c(all_20_6) = all_28_0
% 30.61/4.88 | | | |
% 30.61/4.88 | | | | GROUND_INST: instantiating (10) with all_20_4, all_28_0, all_20_6,
% 30.61/4.88 | | | | simplifying with (24), (62) gives:
% 30.61/4.88 | | | | (63) all_28_0 = all_20_4
% 30.61/4.88 | | | |
% 30.61/4.88 | | | | REDUCE: (32), (63) imply:
% 30.61/4.88 | | | | (64) complement(all_20_4, all_20_6) = 0
% 30.61/4.88 | | | |
% 30.61/4.88 | | | | BETA: splitting (47) gives:
% 30.61/4.88 | | | |
% 30.61/4.88 | | | | Case 1:
% 30.61/4.88 | | | | |
% 30.61/4.88 | | | | | (65) all_49_0 = zero & all_49_1 = zero & all_30_0 = one &
% 30.61/4.88 | | | | | multiplication(all_20_4, all_20_6) = zero &
% 30.61/4.88 | | | | | multiplication(all_20_6, all_20_4) = zero
% 30.61/4.88 | | | | |
% 30.61/4.88 | | | | | ALPHA: (65) implies:
% 30.61/4.88 | | | | | (66) all_30_0 = one
% 30.61/4.88 | | | | |
% 30.61/4.88 | | | | | REDUCE: (49), (66) imply:
% 30.61/4.88 | | | | | (67) multiplication(all_20_7, one) = all_20_2
% 30.61/4.88 | | | | |
% 30.61/4.88 | | | | | GROUND_INST: instantiating (2) with all_20_7, all_20_2, simplifying
% 30.61/4.88 | | | | | with (15), (67) gives:
% 30.61/4.88 | | | | | (68) all_20_2 = all_20_7
% 30.61/4.88 | | | | |
% 30.61/4.88 | | | | | GROUND_INST: instantiating (4) with all_20_2, all_20_7, all_20_0,
% 30.61/4.88 | | | | | simplifying with (15), (44), (60) gives:
% 30.61/4.88 | | | | | (69) all_20_0 = 0 | ? [v0: any] : ( ~ (v0 = all_20_7) &
% 30.61/4.88 | | | | | addition(all_20_2, all_20_7) = v0 & $i(v0))
% 30.61/4.88 | | | | |
% 30.61/4.88 | | | | | BETA: splitting (69) gives:
% 30.61/4.88 | | | | |
% 30.61/4.88 | | | | | Case 1:
% 30.61/4.88 | | | | | |
% 30.61/4.88 | | | | | | (70) all_20_0 = 0
% 30.61/4.88 | | | | | |
% 30.61/4.88 | | | | | | REDUCE: (59), (70) imply:
% 30.61/4.88 | | | | | | (71) $false
% 30.61/4.89 | | | | | |
% 30.61/4.89 | | | | | | CLOSE: (71) is inconsistent.
% 30.61/4.89 | | | | | |
% 30.61/4.89 | | | | | Case 2:
% 30.61/4.89 | | | | | |
% 30.61/4.89 | | | | | | (72) ? [v0: any] : ( ~ (v0 = all_20_7) & addition(all_20_2,
% 30.61/4.89 | | | | | | all_20_7) = v0 & $i(v0))
% 30.61/4.89 | | | | | |
% 30.61/4.89 | | | | | | DELTA: instantiating (72) with fresh symbol all_115_0 gives:
% 30.61/4.89 | | | | | | (73) ~ (all_115_0 = all_20_7) & addition(all_20_2, all_20_7) =
% 30.61/4.89 | | | | | | all_115_0 & $i(all_115_0)
% 30.61/4.89 | | | | | |
% 30.61/4.89 | | | | | | ALPHA: (73) implies:
% 30.61/4.89 | | | | | | (74) ~ (all_115_0 = all_20_7)
% 30.61/4.89 | | | | | | (75) addition(all_20_2, all_20_7) = all_115_0
% 30.61/4.89 | | | | | |
% 30.61/4.89 | | | | | | REDUCE: (68), (75) imply:
% 30.61/4.89 | | | | | | (76) addition(all_20_7, all_20_7) = all_115_0
% 30.61/4.89 | | | | | |
% 30.61/4.89 | | | | | | GROUND_INST: instantiating (additive_idempotence) with all_20_7,
% 30.61/4.89 | | | | | | all_115_0, simplifying with (15), (76) gives:
% 30.61/4.89 | | | | | | (77) all_115_0 = all_20_7
% 30.61/4.89 | | | | | |
% 30.61/4.89 | | | | | | REDUCE: (74), (77) imply:
% 30.61/4.89 | | | | | | (78) $false
% 30.61/4.89 | | | | | |
% 30.61/4.89 | | | | | | CLOSE: (78) is inconsistent.
% 30.61/4.89 | | | | | |
% 30.61/4.89 | | | | | End of split
% 30.61/4.89 | | | | |
% 30.61/4.89 | | | | Case 2:
% 30.61/4.89 | | | | |
% 30.61/4.89 | | | | | (79) ~ (all_49_2 = 0) & complement(all_20_4, all_20_6) = all_49_2
% 30.61/4.89 | | | | |
% 30.61/4.89 | | | | | REF_CLOSE: (13), (64), (79) are inconsistent by sub-proof #1.
% 30.61/4.89 | | | | |
% 30.61/4.89 | | | | End of split
% 30.61/4.89 | | | |
% 30.61/4.89 | | | Case 2:
% 30.61/4.89 | | | |
% 30.61/4.89 | | | | (80) ~ (all_86_1 = 0) & test(all_20_6) = all_86_1
% 30.61/4.89 | | | |
% 30.61/4.89 | | | | ALPHA: (80) implies:
% 30.61/4.89 | | | | (81) ~ (all_86_1 = 0)
% 30.61/4.89 | | | | (82) test(all_20_6) = all_86_1
% 30.61/4.89 | | | |
% 30.61/4.89 | | | | GROUND_INST: instantiating (9) with 0, all_86_1, all_20_6, simplifying
% 30.61/4.89 | | | | with (23), (82) gives:
% 30.61/4.89 | | | | (83) all_86_1 = 0
% 30.61/4.89 | | | |
% 30.61/4.89 | | | | REDUCE: (81), (83) imply:
% 30.61/4.89 | | | | (84) $false
% 30.61/4.89 | | | |
% 30.61/4.89 | | | | CLOSE: (84) is inconsistent.
% 30.61/4.89 | | | |
% 30.61/4.89 | | | End of split
% 30.61/4.89 | | |
% 30.61/4.89 | | Case 2:
% 30.61/4.89 | | |
% 30.61/4.89 | | | (85) ~ (all_20_1 = 0) & leq(all_20_7, all_20_2) = all_20_1
% 30.61/4.89 | | |
% 30.61/4.89 | | | ALPHA: (85) implies:
% 30.61/4.89 | | | (86) ~ (all_20_1 = 0)
% 30.61/4.89 | | | (87) leq(all_20_7, all_20_2) = all_20_1
% 30.61/4.89 | | |
% 30.61/4.89 | | | BETA: splitting (57) gives:
% 30.61/4.89 | | |
% 30.61/4.89 | | | Case 1:
% 30.61/4.89 | | | |
% 30.61/4.89 | | | | (88) all_86_0 = all_28_0 & c(all_20_6) = all_28_0
% 30.61/4.89 | | | |
% 30.61/4.89 | | | | ALPHA: (88) implies:
% 30.61/4.89 | | | | (89) c(all_20_6) = all_28_0
% 30.61/4.89 | | | |
% 30.61/4.89 | | | | GROUND_INST: instantiating (10) with all_20_4, all_28_0, all_20_6,
% 30.61/4.89 | | | | simplifying with (24), (89) gives:
% 30.61/4.89 | | | | (90) all_28_0 = all_20_4
% 30.61/4.89 | | | |
% 30.61/4.89 | | | | REDUCE: (32), (90) imply:
% 30.61/4.89 | | | | (91) complement(all_20_4, all_20_6) = 0
% 30.61/4.89 | | | |
% 30.61/4.89 | | | | BETA: splitting (47) gives:
% 30.61/4.89 | | | |
% 30.61/4.89 | | | | Case 1:
% 30.61/4.89 | | | | |
% 30.61/4.89 | | | | | (92) all_49_0 = zero & all_49_1 = zero & all_30_0 = one &
% 30.61/4.89 | | | | | multiplication(all_20_4, all_20_6) = zero &
% 30.61/4.89 | | | | | multiplication(all_20_6, all_20_4) = zero
% 30.61/4.89 | | | | |
% 30.61/4.89 | | | | | ALPHA: (92) implies:
% 30.61/4.89 | | | | | (93) all_30_0 = one
% 30.61/4.89 | | | | |
% 30.61/4.89 | | | | | REDUCE: (49), (93) imply:
% 30.61/4.89 | | | | | (94) multiplication(all_20_7, one) = all_20_2
% 30.61/4.89 | | | | |
% 30.61/4.89 | | | | | GROUND_INST: instantiating (2) with all_20_7, all_20_2, simplifying
% 30.61/4.89 | | | | | with (15), (94) gives:
% 30.61/4.89 | | | | | (95) all_20_2 = all_20_7
% 30.61/4.89 | | | | |
% 30.61/4.89 | | | | | GROUND_INST: instantiating (4) with all_20_7, all_20_2, all_20_1,
% 30.61/4.89 | | | | | simplifying with (15), (44), (87) gives:
% 30.61/4.89 | | | | | (96) all_20_1 = 0 | ? [v0: any] : ( ~ (v0 = all_20_2) &
% 30.61/4.89 | | | | | addition(all_20_7, all_20_2) = v0 & $i(v0))
% 30.61/4.89 | | | | |
% 30.61/4.89 | | | | | BETA: splitting (96) gives:
% 30.61/4.89 | | | | |
% 30.61/4.89 | | | | | Case 1:
% 30.61/4.89 | | | | | |
% 30.61/4.89 | | | | | | (97) all_20_1 = 0
% 30.61/4.89 | | | | | |
% 30.61/4.89 | | | | | | REDUCE: (86), (97) imply:
% 30.61/4.89 | | | | | | (98) $false
% 30.61/4.89 | | | | | |
% 30.61/4.89 | | | | | | CLOSE: (98) is inconsistent.
% 30.61/4.89 | | | | | |
% 30.61/4.89 | | | | | Case 2:
% 30.61/4.89 | | | | | |
% 30.61/4.89 | | | | | | (99) ? [v0: any] : ( ~ (v0 = all_20_2) & addition(all_20_7,
% 30.61/4.89 | | | | | | all_20_2) = v0 & $i(v0))
% 30.61/4.89 | | | | | |
% 30.61/4.89 | | | | | | DELTA: instantiating (99) with fresh symbol all_115_0 gives:
% 30.61/4.89 | | | | | | (100) ~ (all_115_0 = all_20_2) & addition(all_20_7, all_20_2) =
% 30.61/4.89 | | | | | | all_115_0 & $i(all_115_0)
% 30.61/4.89 | | | | | |
% 30.61/4.89 | | | | | | ALPHA: (100) implies:
% 30.61/4.89 | | | | | | (101) ~ (all_115_0 = all_20_2)
% 30.61/4.89 | | | | | | (102) addition(all_20_7, all_20_2) = all_115_0
% 30.61/4.89 | | | | | |
% 30.61/4.89 | | | | | | REDUCE: (95), (101) imply:
% 30.61/4.89 | | | | | | (103) ~ (all_115_0 = all_20_7)
% 30.61/4.89 | | | | | |
% 30.61/4.89 | | | | | | REDUCE: (95), (102) imply:
% 30.61/4.89 | | | | | | (104) addition(all_20_7, all_20_7) = all_115_0
% 30.61/4.89 | | | | | |
% 30.61/4.89 | | | | | | GROUND_INST: instantiating (additive_idempotence) with all_20_7,
% 30.61/4.89 | | | | | | all_115_0, simplifying with (15), (104) gives:
% 30.61/4.89 | | | | | | (105) all_115_0 = all_20_7
% 30.61/4.89 | | | | | |
% 30.61/4.89 | | | | | | REDUCE: (103), (105) imply:
% 30.61/4.89 | | | | | | (106) $false
% 30.61/4.89 | | | | | |
% 30.61/4.90 | | | | | | CLOSE: (106) is inconsistent.
% 30.61/4.90 | | | | | |
% 30.61/4.90 | | | | | End of split
% 30.61/4.90 | | | | |
% 30.61/4.90 | | | | Case 2:
% 30.61/4.90 | | | | |
% 30.61/4.90 | | | | | (107) ~ (all_49_2 = 0) & complement(all_20_4, all_20_6) = all_49_2
% 30.61/4.90 | | | | |
% 30.61/4.90 | | | | | REF_CLOSE: (13), (91), (107) are inconsistent by sub-proof #1.
% 30.61/4.90 | | | | |
% 30.61/4.90 | | | | End of split
% 30.61/4.90 | | | |
% 30.61/4.90 | | | Case 2:
% 30.61/4.90 | | | |
% 30.61/4.90 | | | | (108) ~ (all_86_1 = 0) & test(all_20_6) = all_86_1
% 30.61/4.90 | | | |
% 30.61/4.90 | | | | ALPHA: (108) implies:
% 30.61/4.90 | | | | (109) ~ (all_86_1 = 0)
% 30.61/4.90 | | | | (110) test(all_20_6) = all_86_1
% 30.61/4.90 | | | |
% 30.61/4.90 | | | | GROUND_INST: instantiating (9) with 0, all_86_1, all_20_6, simplifying
% 30.61/4.90 | | | | with (23), (110) gives:
% 30.61/4.90 | | | | (111) all_86_1 = 0
% 30.61/4.90 | | | |
% 30.61/4.90 | | | | REDUCE: (109), (111) imply:
% 30.61/4.90 | | | | (112) $false
% 30.61/4.90 | | | |
% 30.61/4.90 | | | | CLOSE: (112) is inconsistent.
% 30.61/4.90 | | | |
% 30.61/4.90 | | | End of split
% 30.61/4.90 | | |
% 30.61/4.90 | | End of split
% 30.61/4.90 | |
% 30.61/4.90 | Case 2:
% 30.61/4.90 | |
% 30.61/4.90 | | (113) ( ~ (all_63_1 = one) & addition(all_28_0, all_20_6) = all_63_1 &
% 30.61/4.90 | | $i(all_63_1)) | ( ~ (all_63_2 = zero) & multiplication(all_20_6,
% 30.61/4.90 | | all_28_0) = all_63_2 & $i(all_63_2))
% 30.61/4.90 | |
% 30.61/4.90 | | BETA: splitting (113) gives:
% 30.61/4.90 | |
% 30.61/4.90 | | Case 1:
% 30.61/4.90 | | |
% 30.61/4.90 | | | (114) ~ (all_63_1 = one) & addition(all_28_0, all_20_6) = all_63_1 &
% 30.61/4.90 | | | $i(all_63_1)
% 30.61/4.90 | | |
% 30.61/4.90 | | | ALPHA: (114) implies:
% 30.61/4.90 | | | (115) ~ (all_63_1 = one)
% 30.61/4.90 | | | (116) addition(all_28_0, all_20_6) = all_63_1
% 30.61/4.90 | | |
% 30.61/4.90 | | | GROUND_INST: instantiating (11) with one, all_63_1, all_20_6, all_28_0,
% 30.61/4.90 | | | simplifying with (51), (116) gives:
% 30.61/4.90 | | | (117) all_63_1 = one
% 30.61/4.90 | | |
% 30.61/4.90 | | | REDUCE: (115), (117) imply:
% 30.61/4.90 | | | (118) $false
% 30.61/4.90 | | |
% 30.61/4.90 | | | CLOSE: (118) is inconsistent.
% 30.61/4.90 | | |
% 30.61/4.90 | | Case 2:
% 30.61/4.90 | | |
% 30.61/4.90 | | | (119) ~ (all_63_2 = zero) & multiplication(all_20_6, all_28_0) =
% 30.61/4.90 | | | all_63_2 & $i(all_63_2)
% 30.61/4.90 | | |
% 30.61/4.90 | | | ALPHA: (119) implies:
% 30.61/4.90 | | | (120) ~ (all_63_2 = zero)
% 30.61/4.90 | | | (121) multiplication(all_20_6, all_28_0) = all_63_2
% 30.61/4.90 | | |
% 30.61/4.90 | | | GROUND_INST: instantiating (12) with zero, all_63_2, all_28_0, all_20_6,
% 30.61/4.90 | | | simplifying with (41), (121) gives:
% 30.61/4.90 | | | (122) all_63_2 = zero
% 30.61/4.90 | | |
% 30.61/4.90 | | | REDUCE: (120), (122) imply:
% 30.61/4.90 | | | (123) $false
% 30.61/4.90 | | |
% 30.61/4.90 | | | CLOSE: (123) is inconsistent.
% 30.61/4.90 | | |
% 30.61/4.90 | | End of split
% 30.61/4.90 | |
% 30.61/4.90 | End of split
% 30.61/4.90 |
% 30.61/4.90 End of proof
% 30.61/4.90
% 30.61/4.90 Sub-proof #1 shows that the following formulas are inconsistent:
% 30.61/4.90 ----------------------------------------------------------------
% 30.61/4.90 (1) ~ (all_49_2 = 0) & complement(all_20_4, all_20_6) = all_49_2
% 30.61/4.90 (2) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 30.61/4.90 ! [v3: $i] : (v1 = v0 | ~ (complement(v3, v2) = v1) | ~ (complement(v3,
% 30.61/4.90 v2) = v0))
% 30.61/4.90 (3) complement(all_20_4, all_20_6) = 0
% 30.61/4.90
% 30.61/4.90 Begin of proof
% 30.61/4.90 |
% 30.61/4.90 | ALPHA: (1) implies:
% 30.61/4.90 | (4) ~ (all_49_2 = 0)
% 30.61/4.90 | (5) complement(all_20_4, all_20_6) = all_49_2
% 30.61/4.90 |
% 30.61/4.90 | GROUND_INST: instantiating (2) with 0, all_49_2, all_20_6, all_20_4,
% 30.61/4.90 | simplifying with (3), (5) gives:
% 30.61/4.90 | (6) all_49_2 = 0
% 30.61/4.90 |
% 30.61/4.90 | REDUCE: (4), (6) imply:
% 30.61/4.90 | (7) $false
% 30.61/4.90 |
% 30.61/4.90 | CLOSE: (7) is inconsistent.
% 30.61/4.90 |
% 30.61/4.90 End of proof
% 30.61/4.90 % SZS output end Proof for theBenchmark
% 30.61/4.90
% 30.61/4.90 4287ms
%------------------------------------------------------------------------------