TSTP Solution File: KLE021+2 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : KLE021+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 : n010.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 05:34:15 EDT 2023
% Result : Theorem 24.55s 3.96s
% Output : Proof 28.85s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : KLE021+2 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.12 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.33 % Computer : n010.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Tue Aug 29 11:46:03 EDT 2023
% 0.13/0.33 % CPUTime :
% 0.18/0.60 ________ _____
% 0.18/0.60 ___ __ \_________(_)________________________________
% 0.18/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.18/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.18/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.18/0.60
% 0.18/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.18/0.60 (2023-06-19)
% 0.18/0.60
% 0.18/0.60 (c) Philipp Rümmer, 2009-2023
% 0.18/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.18/0.60 Amanda Stjerna.
% 0.18/0.60 Free software under BSD-3-Clause.
% 0.18/0.60
% 0.18/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.18/0.60
% 0.18/0.60 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.18/0.61 Running up to 7 provers in parallel.
% 0.18/0.62 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.18/0.62 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.18/0.62 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.18/0.62 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.18/0.62 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.18/0.62 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.18/0.62 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.29/1.00 Prover 1: Preprocessing ...
% 2.29/1.00 Prover 4: Preprocessing ...
% 2.78/1.04 Prover 2: Preprocessing ...
% 2.78/1.04 Prover 6: Preprocessing ...
% 2.78/1.04 Prover 0: Preprocessing ...
% 2.78/1.04 Prover 3: Preprocessing ...
% 2.78/1.04 Prover 5: Preprocessing ...
% 4.49/1.32 Prover 3: Constructing countermodel ...
% 4.49/1.33 Prover 1: Constructing countermodel ...
% 4.49/1.35 Prover 6: Proving ...
% 4.49/1.35 Prover 5: Proving ...
% 4.49/1.37 Prover 4: Constructing countermodel ...
% 4.49/1.40 Prover 0: Proving ...
% 5.49/1.43 Prover 2: Proving ...
% 7.56/1.68 Prover 3: gave up
% 7.56/1.69 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 7.56/1.71 Prover 7: Preprocessing ...
% 8.64/1.83 Prover 7: Constructing countermodel ...
% 16.77/2.90 Prover 6: gave up
% 16.77/2.91 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 16.77/2.93 Prover 8: Preprocessing ...
% 17.47/3.00 Prover 8: Warning: ignoring some quantifiers
% 17.59/3.00 Prover 8: Constructing countermodel ...
% 19.15/3.25 Prover 8: gave up
% 19.83/3.29 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889
% 19.83/3.31 Prover 9: Preprocessing ...
% 20.66/3.42 Prover 9: Constructing countermodel ...
% 24.55/3.96 Prover 2: proved (3341ms)
% 24.55/3.96
% 24.55/3.96 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 24.55/3.96
% 24.55/3.96 Prover 9: stopped
% 24.55/3.97 Prover 0: stopped
% 24.55/3.97 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 24.55/3.97 Prover 5: stopped
% 24.55/3.98 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 24.55/3.98 Prover 10: Preprocessing ...
% 24.55/3.98 Prover 11: Preprocessing ...
% 24.55/3.99 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 24.55/3.99 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 25.31/4.01 Prover 16: Preprocessing ...
% 25.31/4.02 Prover 13: Preprocessing ...
% 25.31/4.06 Prover 10: Constructing countermodel ...
% 25.31/4.08 Prover 11: Constructing countermodel ...
% 25.31/4.09 Prover 16: Warning: ignoring some quantifiers
% 25.31/4.10 Prover 13: Warning: ignoring some quantifiers
% 25.31/4.10 Prover 13: Constructing countermodel ...
% 25.31/4.11 Prover 16: Constructing countermodel ...
% 25.31/4.13 Prover 10: gave up
% 25.31/4.14 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085
% 25.31/4.17 Prover 19: Preprocessing ...
% 26.81/4.20 Prover 19: Warning: ignoring some quantifiers
% 26.81/4.21 Prover 19: Constructing countermodel ...
% 26.81/4.22 Prover 13: gave up
% 28.29/4.41 Prover 11: Found proof (size 110)
% 28.29/4.41 Prover 11: proved (438ms)
% 28.29/4.41 Prover 19: stopped
% 28.29/4.41 Prover 16: stopped
% 28.29/4.41 Prover 1: stopped
% 28.29/4.41 Prover 4: stopped
% 28.29/4.41 Prover 7: stopped
% 28.29/4.41
% 28.29/4.41 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 28.29/4.41
% 28.29/4.42 % SZS output start Proof for theBenchmark
% 28.29/4.43 Assumptions after simplification:
% 28.29/4.43 ---------------------------------
% 28.29/4.43
% 28.29/4.43 (additive_commutativity)
% 28.29/4.45 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (addition(v1, v0) = v2) | ~
% 28.29/4.45 $i(v1) | ~ $i(v0) | (addition(v0, v1) = v2 & $i(v2))) & ! [v0: $i] : !
% 28.29/4.45 [v1: $i] : ! [v2: $i] : ( ~ (addition(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) |
% 28.29/4.45 (addition(v1, v0) = v2 & $i(v2)))
% 28.29/4.45
% 28.29/4.45 (additive_idempotence)
% 28.29/4.45 ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (addition(v0, v0) = v1) | ~ $i(v0))
% 28.29/4.45
% 28.29/4.45 (goals)
% 28.29/4.45 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5:
% 28.29/4.45 $i] : ? [v6: int] : ? [v7: int] : (c(v1) = v3 & test(v1) = 0 &
% 28.29/4.45 multiplication(v3, v0) = v4 & multiplication(v1, v0) = v2 & addition(v2, v4)
% 28.29/4.45 = v5 & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & (( ~ (v7 = 0) &
% 28.29/4.45 leq(v5, v0) = v7) | ( ~ (v6 = 0) & leq(v0, v5) = v6)))
% 28.29/4.45
% 28.29/4.45 (left_distributivity)
% 28.29/4.46 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 28.29/4.46 $i] : ( ~ (multiplication(v1, v2) = v4) | ~ (multiplication(v0, v2) = v3) |
% 28.29/4.46 ~ (addition(v3, v4) = v5) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: $i]
% 28.29/4.46 : (multiplication(v6, v2) = v5 & addition(v0, v1) = v6 & $i(v6) & $i(v5))) &
% 28.29/4.46 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 28.29/4.46 (multiplication(v3, v2) = v4) | ~ (addition(v0, v1) = v3) | ~ $i(v2) | ~
% 28.29/4.46 $i(v1) | ~ $i(v0) | ? [v5: $i] : ? [v6: $i] : (multiplication(v1, v2) =
% 28.29/4.46 v6 & multiplication(v0, v2) = v5 & addition(v5, v6) = v4 & $i(v6) & $i(v5)
% 28.29/4.46 & $i(v4)))
% 28.29/4.46
% 28.29/4.46 (multiplicative_left_identity)
% 28.29/4.46 $i(one) & ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (multiplication(one, v0) =
% 28.29/4.46 v1) | ~ $i(v0))
% 28.29/4.46
% 28.29/4.46 (order)
% 28.29/4.46 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v1 | ~ (addition(v0, v1) =
% 28.29/4.46 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ( ~ (v3 = 0) & leq(v0, v1) =
% 28.29/4.46 v3)) & ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (leq(v0,
% 28.29/4.46 v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ( ~ (v3 = v1) &
% 28.29/4.46 addition(v0, v1) = v3 & $i(v3))) & ! [v0: $i] : ! [v1: $i] : ( ~
% 28.29/4.46 (leq(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | addition(v0, v1) = v1) & ! [v0:
% 28.29/4.46 $i] : ! [v1: $i] : ( ~ (addition(v0, v1) = v1) | ~ $i(v1) | ~ $i(v0) |
% 28.29/4.46 leq(v0, v1) = 0)
% 28.29/4.46
% 28.29/4.46 (test_1)
% 28.29/4.46 ! [v0: $i] : ! [v1: int] : ! [v2: $i] : (v1 = 0 | ~ (test(v0) = v1) | ~
% 28.29/4.46 (complement(v2, v0) = 0) | ~ $i(v2) | ~ $i(v0)) & ! [v0: $i] : ( ~
% 28.29/4.46 (test(v0) = 0) | ~ $i(v0) | ? [v1: $i] : (complement(v1, v0) = 0 &
% 28.29/4.46 $i(v1)))
% 28.29/4.46
% 28.29/4.46 (test_2)
% 28.29/4.47 $i(one) & $i(zero) & ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~
% 28.29/4.47 (complement(v1, v0) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4:
% 28.29/4.47 $i] : ? [v5: $i] : (( ~ (v5 = one) & addition(v0, v1) = v5 & $i(v5)) | (
% 28.29/4.47 ~ (v4 = zero) & multiplication(v1, v0) = v4 & $i(v4)) | ( ~ (v3 = zero)
% 28.29/4.47 & multiplication(v0, v1) = v3 & $i(v3)))) & ! [v0: $i] : ! [v1: $i] :
% 28.29/4.47 ! [v2: $i] : ( ~ (multiplication(v1, v0) = v2) | ~ $i(v1) | ~ $i(v0) | ?
% 28.29/4.47 [v3: int] : ? [v4: $i] : ? [v5: $i] : ((v5 = one & v4 = zero & v2 = zero &
% 28.29/4.47 multiplication(v0, v1) = zero & addition(v0, v1) = one) | ( ~ (v3 = 0) &
% 28.29/4.47 complement(v1, v0) = v3))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (
% 28.29/4.47 ~ (multiplication(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ?
% 28.29/4.47 [v4: $i] : ? [v5: $i] : ((v5 = one & v4 = zero & v2 = zero &
% 28.29/4.47 multiplication(v1, v0) = zero & addition(v0, v1) = one) | ( ~ (v3 = 0) &
% 28.29/4.47 complement(v1, v0) = v3))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (
% 28.29/4.47 ~ (addition(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ? [v4:
% 28.29/4.47 $i] : ? [v5: $i] : ((v5 = zero & v4 = zero & v2 = one &
% 28.29/4.47 multiplication(v1, v0) = zero & multiplication(v0, v1) = zero) | ( ~ (v3
% 28.29/4.47 = 0) & complement(v1, v0) = v3))) & ! [v0: $i] : ! [v1: $i] : ( ~
% 28.29/4.47 (complement(v1, v0) = 0) | ~ $i(v1) | ~ $i(v0) | (multiplication(v1, v0) =
% 28.29/4.47 zero & multiplication(v0, v1) = zero & addition(v0, v1) = one)) & ! [v0:
% 28.29/4.47 $i] : ! [v1: $i] : ( ~ (multiplication(v1, v0) = zero) | ~ $i(v1) | ~
% 28.29/4.47 $i(v0) | ? [v2: $i] : ? [v3: $i] : ? [v4: int] : ((v4 = 0 &
% 28.29/4.47 complement(v1, v0) = 0) | ( ~ (v3 = one) & addition(v0, v1) = v3 &
% 28.29/4.47 $i(v3)) | ( ~ (v2 = zero) & multiplication(v0, v1) = v2 & $i(v2)))) & !
% 28.29/4.47 [v0: $i] : ! [v1: $i] : ( ~ (multiplication(v0, v1) = zero) | ~ $i(v1) | ~
% 28.29/4.47 $i(v0) | ? [v2: $i] : ? [v3: $i] : ? [v4: int] : ((v4 = 0 &
% 28.29/4.47 complement(v1, v0) = 0) | ( ~ (v3 = one) & addition(v0, v1) = v3 &
% 28.29/4.47 $i(v3)) | ( ~ (v2 = zero) & multiplication(v1, v0) = v2 & $i(v2)))) & !
% 28.29/4.47 [v0: $i] : ! [v1: $i] : ( ~ (addition(v0, v1) = one) | ~ $i(v1) | ~ $i(v0)
% 28.29/4.47 | ? [v2: $i] : ? [v3: $i] : ? [v4: int] : ((v4 = 0 & complement(v1, v0) =
% 28.29/4.47 0) | ( ~ (v3 = zero) & multiplication(v1, v0) = v3 & $i(v3)) | ( ~ (v2 =
% 28.29/4.47 zero) & multiplication(v0, v1) = v2 & $i(v2))))
% 28.29/4.47
% 28.29/4.47 (test_3)
% 28.29/4.47 ! [v0: $i] : ! [v1: $i] : ! [v2: any] : ( ~ (complement(v0, v1) = v2) | ~
% 28.29/4.47 $i(v1) | ~ $i(v0) | ? [v3: int] : ? [v4: $i] : (( ~ (v3 = 0) & test(v0) =
% 28.29/4.47 v3) | (( ~ (v2 = 0) | (v4 = v1 & c(v0) = v1)) & (v2 = 0 | ( ~ (v4 = v1)
% 28.29/4.47 & c(v0) = v4 & $i(v4))))))
% 28.29/4.47
% 28.29/4.47 (function-axioms)
% 28.29/4.47 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 28.29/4.47 [v3: $i] : (v1 = v0 | ~ (complement(v3, v2) = v1) | ~ (complement(v3, v2) =
% 28.29/4.47 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 28.29/4.47 $i] : ! [v3: $i] : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) =
% 28.29/4.47 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 |
% 28.29/4.47 ~ (multiplication(v3, v2) = v1) | ~ (multiplication(v3, v2) = v0)) & !
% 28.29/4.47 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 28.29/4.47 (addition(v3, v2) = v1) | ~ (addition(v3, v2) = v0)) & ! [v0: $i] : !
% 28.29/4.47 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (c(v2) = v1) | ~ (c(v2) = v0)) & !
% 28.29/4.47 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0
% 28.29/4.47 | ~ (test(v2) = v1) | ~ (test(v2) = v0))
% 28.29/4.47
% 28.29/4.47 Further assumptions not needed in the proof:
% 28.29/4.47 --------------------------------------------
% 28.29/4.47 additive_associativity, additive_identity, left_annihilation,
% 28.29/4.47 multiplicative_associativity, multiplicative_right_identity, right_annihilation,
% 28.29/4.47 right_distributivity, test_4
% 28.29/4.47
% 28.29/4.47 Those formulas are unsatisfiable:
% 28.29/4.47 ---------------------------------
% 28.29/4.47
% 28.29/4.47 Begin of proof
% 28.29/4.47 |
% 28.29/4.47 | ALPHA: (additive_commutativity) implies:
% 28.29/4.47 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (addition(v1, v0) = v2) |
% 28.29/4.47 | ~ $i(v1) | ~ $i(v0) | (addition(v0, v1) = v2 & $i(v2)))
% 28.29/4.47 |
% 28.29/4.47 | ALPHA: (multiplicative_left_identity) implies:
% 28.29/4.47 | (2) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (multiplication(one, v0) =
% 28.29/4.47 | v1) | ~ $i(v0))
% 28.29/4.47 |
% 28.29/4.47 | ALPHA: (left_distributivity) implies:
% 28.29/4.48 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 28.29/4.48 | ! [v5: $i] : ( ~ (multiplication(v1, v2) = v4) | ~ (multiplication(v0,
% 28.29/4.48 | v2) = v3) | ~ (addition(v3, v4) = v5) | ~ $i(v2) | ~ $i(v1) |
% 28.29/4.48 | ~ $i(v0) | ? [v6: $i] : (multiplication(v6, v2) = v5 & addition(v0,
% 28.29/4.48 | v1) = v6 & $i(v6) & $i(v5)))
% 28.29/4.48 |
% 28.29/4.48 | ALPHA: (order) implies:
% 28.29/4.48 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (leq(v0, v1) =
% 28.29/4.48 | v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ( ~ (v3 = v1) &
% 28.29/4.48 | addition(v0, v1) = v3 & $i(v3)))
% 28.29/4.48 |
% 28.29/4.48 | ALPHA: (test_1) implies:
% 28.29/4.48 | (5) ! [v0: $i] : ( ~ (test(v0) = 0) | ~ $i(v0) | ? [v1: $i] :
% 28.29/4.48 | (complement(v1, v0) = 0 & $i(v1)))
% 28.29/4.48 |
% 28.29/4.48 | ALPHA: (test_2) implies:
% 28.29/4.48 | (6) ! [v0: $i] : ! [v1: $i] : ( ~ (multiplication(v0, v1) = zero) | ~
% 28.29/4.48 | $i(v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: $i] : ? [v4: int] : ((v4
% 28.29/4.48 | = 0 & complement(v1, v0) = 0) | ( ~ (v3 = one) & addition(v0, v1)
% 28.29/4.48 | = v3 & $i(v3)) | ( ~ (v2 = zero) & multiplication(v1, v0) = v2 &
% 28.29/4.48 | $i(v2))))
% 28.29/4.48 | (7) ! [v0: $i] : ! [v1: $i] : ( ~ (complement(v1, v0) = 0) | ~ $i(v1) |
% 28.29/4.48 | ~ $i(v0) | (multiplication(v1, v0) = zero & multiplication(v0, v1) =
% 28.29/4.48 | zero & addition(v0, v1) = one))
% 28.29/4.48 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (addition(v0, v1) = v2) |
% 28.29/4.48 | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ? [v4: $i] : ? [v5: $i] :
% 28.29/4.48 | ((v5 = zero & v4 = zero & v2 = one & multiplication(v1, v0) = zero &
% 28.29/4.48 | multiplication(v0, v1) = zero) | ( ~ (v3 = 0) & complement(v1,
% 28.29/4.48 | v0) = v3)))
% 28.29/4.48 |
% 28.29/4.48 | ALPHA: (function-axioms) implies:
% 28.29/4.48 | (9) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 28.29/4.48 | (v1 = v0 | ~ (test(v2) = v1) | ~ (test(v2) = v0))
% 28.29/4.48 | (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (c(v2) = v1) |
% 28.29/4.48 | ~ (c(v2) = v0))
% 28.29/4.48 | (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 28.29/4.48 | (addition(v3, v2) = v1) | ~ (addition(v3, v2) = v0))
% 28.29/4.48 | (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 28.29/4.48 | (multiplication(v3, v2) = v1) | ~ (multiplication(v3, v2) = v0))
% 28.29/4.48 | (13) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 28.29/4.48 | : ! [v3: $i] : (v1 = v0 | ~ (complement(v3, v2) = v1) | ~
% 28.29/4.48 | (complement(v3, v2) = v0))
% 28.29/4.48 |
% 28.29/4.48 | DELTA: instantiating (goals) with fresh symbols all_20_0, all_20_1, all_20_2,
% 28.29/4.48 | all_20_3, all_20_4, all_20_5, all_20_6, all_20_7 gives:
% 28.29/4.48 | (14) c(all_20_6) = all_20_4 & test(all_20_6) = 0 & multiplication(all_20_4,
% 28.29/4.48 | all_20_7) = all_20_3 & multiplication(all_20_6, all_20_7) = all_20_5
% 28.29/4.48 | & addition(all_20_5, all_20_3) = all_20_2 & $i(all_20_2) &
% 28.29/4.48 | $i(all_20_3) & $i(all_20_4) & $i(all_20_5) & $i(all_20_6) &
% 28.29/4.48 | $i(all_20_7) & (( ~ (all_20_0 = 0) & leq(all_20_2, all_20_7) =
% 28.29/4.48 | all_20_0) | ( ~ (all_20_1 = 0) & leq(all_20_7, all_20_2) =
% 28.29/4.48 | all_20_1))
% 28.29/4.48 |
% 28.29/4.48 | ALPHA: (14) implies:
% 28.29/4.48 | (15) $i(all_20_7)
% 28.29/4.48 | (16) $i(all_20_6)
% 28.29/4.48 | (17) $i(all_20_5)
% 28.29/4.49 | (18) $i(all_20_4)
% 28.29/4.49 | (19) $i(all_20_3)
% 28.29/4.49 | (20) addition(all_20_5, all_20_3) = all_20_2
% 28.29/4.49 | (21) multiplication(all_20_6, all_20_7) = all_20_5
% 28.29/4.49 | (22) multiplication(all_20_4, all_20_7) = all_20_3
% 28.29/4.49 | (23) test(all_20_6) = 0
% 28.29/4.49 | (24) c(all_20_6) = all_20_4
% 28.29/4.49 | (25) ( ~ (all_20_0 = 0) & leq(all_20_2, all_20_7) = all_20_0) | ( ~
% 28.29/4.49 | (all_20_1 = 0) & leq(all_20_7, all_20_2) = all_20_1)
% 28.29/4.49 |
% 28.29/4.49 | GROUND_INST: instantiating (1) with all_20_3, all_20_5, all_20_2, simplifying
% 28.29/4.49 | with (17), (19), (20) gives:
% 28.29/4.49 | (26) addition(all_20_3, all_20_5) = all_20_2 & $i(all_20_2)
% 28.29/4.49 |
% 28.29/4.49 | ALPHA: (26) implies:
% 28.29/4.49 | (27) addition(all_20_3, all_20_5) = all_20_2
% 28.29/4.49 |
% 28.29/4.49 | GROUND_INST: instantiating (3) with all_20_6, all_20_4, all_20_7, all_20_5,
% 28.29/4.49 | all_20_3, all_20_2, simplifying with (15), (16), (18), (20),
% 28.29/4.49 | (21), (22) gives:
% 28.29/4.49 | (28) ? [v0: $i] : (multiplication(v0, all_20_7) = all_20_2 &
% 28.29/4.49 | addition(all_20_6, all_20_4) = v0 & $i(v0) & $i(all_20_2))
% 28.29/4.49 |
% 28.29/4.49 | GROUND_INST: instantiating (5) with all_20_6, simplifying with (16), (23)
% 28.29/4.49 | gives:
% 28.29/4.49 | (29) ? [v0: $i] : (complement(v0, all_20_6) = 0 & $i(v0))
% 28.29/4.49 |
% 28.29/4.49 | DELTA: instantiating (29) with fresh symbol all_28_0 gives:
% 28.29/4.49 | (30) complement(all_28_0, all_20_6) = 0 & $i(all_28_0)
% 28.29/4.49 |
% 28.29/4.49 | ALPHA: (30) implies:
% 28.29/4.49 | (31) $i(all_28_0)
% 28.29/4.49 | (32) complement(all_28_0, all_20_6) = 0
% 28.29/4.49 |
% 28.29/4.49 | DELTA: instantiating (28) with fresh symbol all_30_0 gives:
% 28.29/4.49 | (33) multiplication(all_30_0, all_20_7) = all_20_2 & addition(all_20_6,
% 28.29/4.49 | all_20_4) = all_30_0 & $i(all_30_0) & $i(all_20_2)
% 28.29/4.49 |
% 28.29/4.49 | ALPHA: (33) implies:
% 28.29/4.49 | (34) addition(all_20_6, all_20_4) = all_30_0
% 28.29/4.49 |
% 28.29/4.49 | GROUND_INST: instantiating (1) with all_20_4, all_20_6, all_30_0, simplifying
% 28.29/4.49 | with (16), (18), (34) gives:
% 28.29/4.49 | (35) addition(all_20_4, all_20_6) = all_30_0 & $i(all_30_0)
% 28.29/4.49 |
% 28.29/4.49 | ALPHA: (35) implies:
% 28.80/4.49 | (36) addition(all_20_4, all_20_6) = all_30_0
% 28.80/4.49 |
% 28.80/4.49 | GROUND_INST: instantiating (8) with all_20_6, all_20_4, all_30_0, simplifying
% 28.80/4.49 | with (16), (18), (34) gives:
% 28.80/4.49 | (37) ? [v0: int] : ? [v1: $i] : ? [v2: $i] : ((v2 = zero & v1 = zero &
% 28.80/4.49 | all_30_0 = one & multiplication(all_20_4, all_20_6) = zero &
% 28.80/4.49 | multiplication(all_20_6, all_20_4) = zero) | ( ~ (v0 = 0) &
% 28.80/4.49 | complement(all_20_4, all_20_6) = v0))
% 28.80/4.49 |
% 28.80/4.49 | GROUND_INST: instantiating (3) with all_20_4, all_20_6, all_20_7, all_20_3,
% 28.80/4.49 | all_20_5, all_20_2, simplifying with (15), (16), (18), (21),
% 28.80/4.49 | (22), (27) gives:
% 28.80/4.49 | (38) ? [v0: $i] : (multiplication(v0, all_20_7) = all_20_2 &
% 28.80/4.49 | addition(all_20_4, all_20_6) = v0 & $i(v0) & $i(all_20_2))
% 28.80/4.49 |
% 28.80/4.49 | GROUND_INST: instantiating (7) with all_20_6, all_28_0, simplifying with (16),
% 28.80/4.49 | (31), (32) gives:
% 28.80/4.49 | (39) multiplication(all_28_0, all_20_6) = zero & multiplication(all_20_6,
% 28.80/4.49 | all_28_0) = zero & addition(all_20_6, all_28_0) = one
% 28.80/4.49 |
% 28.80/4.49 | ALPHA: (39) implies:
% 28.80/4.49 | (40) addition(all_20_6, all_28_0) = one
% 28.80/4.49 | (41) multiplication(all_20_6, all_28_0) = zero
% 28.82/4.49 | (42) multiplication(all_28_0, all_20_6) = zero
% 28.82/4.49 |
% 28.82/4.49 | DELTA: instantiating (38) with fresh symbol all_43_0 gives:
% 28.82/4.49 | (43) multiplication(all_43_0, all_20_7) = all_20_2 & addition(all_20_4,
% 28.82/4.49 | all_20_6) = all_43_0 & $i(all_43_0) & $i(all_20_2)
% 28.82/4.50 |
% 28.82/4.50 | ALPHA: (43) implies:
% 28.82/4.50 | (44) $i(all_20_2)
% 28.82/4.50 | (45) addition(all_20_4, all_20_6) = all_43_0
% 28.82/4.50 | (46) multiplication(all_43_0, all_20_7) = all_20_2
% 28.82/4.50 |
% 28.82/4.50 | DELTA: instantiating (37) with fresh symbols all_49_0, all_49_1, all_49_2
% 28.82/4.50 | gives:
% 28.82/4.50 | (47) (all_49_0 = zero & all_49_1 = zero & all_30_0 = one &
% 28.82/4.50 | multiplication(all_20_4, all_20_6) = zero & multiplication(all_20_6,
% 28.82/4.50 | all_20_4) = zero) | ( ~ (all_49_2 = 0) & complement(all_20_4,
% 28.82/4.50 | all_20_6) = all_49_2)
% 28.82/4.50 |
% 28.82/4.50 | GROUND_INST: instantiating (11) with all_30_0, all_43_0, all_20_6, all_20_4,
% 28.82/4.50 | simplifying with (36), (45) gives:
% 28.82/4.50 | (48) all_43_0 = all_30_0
% 28.82/4.50 |
% 28.82/4.50 | REDUCE: (46), (48) imply:
% 28.82/4.50 | (49) multiplication(all_30_0, all_20_7) = all_20_2
% 28.82/4.50 |
% 28.82/4.50 | GROUND_INST: instantiating (1) with all_28_0, all_20_6, one, simplifying with
% 28.82/4.50 | (16), (31), (40) gives:
% 28.82/4.50 | (50) addition(all_28_0, all_20_6) = one & $i(one)
% 28.82/4.50 |
% 28.82/4.50 | ALPHA: (50) implies:
% 28.82/4.50 | (51) addition(all_28_0, all_20_6) = one
% 28.82/4.50 |
% 28.82/4.50 | GROUND_INST: instantiating (6) with all_28_0, all_20_6, simplifying with (16),
% 28.82/4.50 | (31), (42) gives:
% 28.82/4.50 | (52) ? [v0: $i] : ? [v1: $i] : ? [v2: int] : ((v2 = 0 &
% 28.82/4.50 | complement(all_20_6, all_28_0) = 0) | ( ~ (v1 = one) &
% 28.82/4.50 | addition(all_28_0, all_20_6) = v1 & $i(v1)) | ( ~ (v0 = zero) &
% 28.82/4.50 | multiplication(all_20_6, all_28_0) = v0 & $i(v0)))
% 28.82/4.50 |
% 28.82/4.50 | DELTA: instantiating (52) with fresh symbols all_63_0, all_63_1, all_63_2
% 28.82/4.50 | gives:
% 28.82/4.50 | (53) (all_63_0 = 0 & complement(all_20_6, all_28_0) = 0) | ( ~ (all_63_1 =
% 28.82/4.50 | one) & addition(all_28_0, all_20_6) = all_63_1 & $i(all_63_1)) | (
% 28.82/4.50 | ~ (all_63_2 = zero) & multiplication(all_20_6, all_28_0) = all_63_2
% 28.82/4.50 | & $i(all_63_2))
% 28.82/4.50 |
% 28.82/4.50 | BETA: splitting (53) gives:
% 28.82/4.50 |
% 28.82/4.50 | Case 1:
% 28.82/4.50 | |
% 28.82/4.50 | | (54) all_63_0 = 0 & complement(all_20_6, all_28_0) = 0
% 28.85/4.50 | |
% 28.85/4.50 | | ALPHA: (54) implies:
% 28.85/4.50 | | (55) complement(all_20_6, all_28_0) = 0
% 28.85/4.50 | |
% 28.85/4.50 | | GROUND_INST: instantiating (test_3) with all_20_6, all_28_0, 0, simplifying
% 28.85/4.50 | | with (16), (31), (55) gives:
% 28.85/4.50 | | (56) ? [v0: int] : ? [v1: int] : ((v1 = all_28_0 & c(all_20_6) =
% 28.85/4.50 | | all_28_0) | ( ~ (v0 = 0) & test(all_20_6) = v0))
% 28.85/4.50 | |
% 28.85/4.50 | | DELTA: instantiating (56) with fresh symbols all_86_0, all_86_1 gives:
% 28.85/4.50 | | (57) (all_86_0 = all_28_0 & c(all_20_6) = all_28_0) | ( ~ (all_86_1 = 0)
% 28.85/4.50 | | & test(all_20_6) = all_86_1)
% 28.85/4.50 | |
% 28.85/4.50 | | BETA: splitting (25) gives:
% 28.85/4.50 | |
% 28.85/4.50 | | Case 1:
% 28.85/4.50 | | |
% 28.85/4.50 | | | (58) ~ (all_20_0 = 0) & leq(all_20_2, all_20_7) = all_20_0
% 28.85/4.50 | | |
% 28.85/4.50 | | | ALPHA: (58) implies:
% 28.85/4.50 | | | (59) ~ (all_20_0 = 0)
% 28.85/4.50 | | | (60) leq(all_20_2, all_20_7) = all_20_0
% 28.85/4.50 | | |
% 28.85/4.50 | | | BETA: splitting (57) gives:
% 28.85/4.50 | | |
% 28.85/4.50 | | | Case 1:
% 28.85/4.50 | | | |
% 28.85/4.50 | | | | (61) all_86_0 = all_28_0 & c(all_20_6) = all_28_0
% 28.85/4.50 | | | |
% 28.85/4.50 | | | | ALPHA: (61) implies:
% 28.85/4.50 | | | | (62) c(all_20_6) = all_28_0
% 28.85/4.50 | | | |
% 28.85/4.50 | | | | GROUND_INST: instantiating (10) with all_20_4, all_28_0, all_20_6,
% 28.85/4.50 | | | | simplifying with (24), (62) gives:
% 28.85/4.50 | | | | (63) all_28_0 = all_20_4
% 28.85/4.50 | | | |
% 28.85/4.50 | | | | REDUCE: (32), (63) imply:
% 28.85/4.50 | | | | (64) complement(all_20_4, all_20_6) = 0
% 28.85/4.50 | | | |
% 28.85/4.50 | | | | BETA: splitting (47) gives:
% 28.85/4.50 | | | |
% 28.85/4.50 | | | | Case 1:
% 28.85/4.50 | | | | |
% 28.85/4.50 | | | | | (65) all_49_0 = zero & all_49_1 = zero & all_30_0 = one &
% 28.85/4.50 | | | | | multiplication(all_20_4, all_20_6) = zero &
% 28.85/4.50 | | | | | multiplication(all_20_6, all_20_4) = zero
% 28.85/4.50 | | | | |
% 28.85/4.50 | | | | | ALPHA: (65) implies:
% 28.85/4.50 | | | | | (66) all_30_0 = one
% 28.85/4.50 | | | | |
% 28.85/4.50 | | | | | REDUCE: (49), (66) imply:
% 28.85/4.50 | | | | | (67) multiplication(one, all_20_7) = all_20_2
% 28.85/4.50 | | | | |
% 28.85/4.50 | | | | | GROUND_INST: instantiating (2) with all_20_7, all_20_2, simplifying
% 28.85/4.50 | | | | | with (15), (67) gives:
% 28.85/4.50 | | | | | (68) all_20_2 = all_20_7
% 28.85/4.50 | | | | |
% 28.85/4.51 | | | | | GROUND_INST: instantiating (4) with all_20_2, all_20_7, all_20_0,
% 28.85/4.51 | | | | | simplifying with (15), (44), (60) gives:
% 28.85/4.51 | | | | | (69) all_20_0 = 0 | ? [v0: any] : ( ~ (v0 = all_20_7) &
% 28.85/4.51 | | | | | addition(all_20_2, all_20_7) = v0 & $i(v0))
% 28.85/4.51 | | | | |
% 28.85/4.51 | | | | | BETA: splitting (69) gives:
% 28.85/4.51 | | | | |
% 28.85/4.51 | | | | | Case 1:
% 28.85/4.51 | | | | | |
% 28.85/4.51 | | | | | | (70) all_20_0 = 0
% 28.85/4.51 | | | | | |
% 28.85/4.51 | | | | | | REDUCE: (59), (70) imply:
% 28.85/4.51 | | | | | | (71) $false
% 28.85/4.51 | | | | | |
% 28.85/4.51 | | | | | | CLOSE: (71) is inconsistent.
% 28.85/4.51 | | | | | |
% 28.85/4.51 | | | | | Case 2:
% 28.85/4.51 | | | | | |
% 28.85/4.51 | | | | | | (72) ? [v0: any] : ( ~ (v0 = all_20_7) & addition(all_20_2,
% 28.85/4.51 | | | | | | all_20_7) = v0 & $i(v0))
% 28.85/4.51 | | | | | |
% 28.85/4.51 | | | | | | DELTA: instantiating (72) with fresh symbol all_115_0 gives:
% 28.85/4.51 | | | | | | (73) ~ (all_115_0 = all_20_7) & addition(all_20_2, all_20_7) =
% 28.85/4.51 | | | | | | all_115_0 & $i(all_115_0)
% 28.85/4.51 | | | | | |
% 28.85/4.51 | | | | | | ALPHA: (73) implies:
% 28.85/4.51 | | | | | | (74) ~ (all_115_0 = all_20_7)
% 28.85/4.51 | | | | | | (75) addition(all_20_2, all_20_7) = all_115_0
% 28.85/4.51 | | | | | |
% 28.85/4.51 | | | | | | REDUCE: (68), (75) imply:
% 28.85/4.51 | | | | | | (76) addition(all_20_7, all_20_7) = all_115_0
% 28.85/4.51 | | | | | |
% 28.85/4.51 | | | | | | GROUND_INST: instantiating (additive_idempotence) with all_20_7,
% 28.85/4.51 | | | | | | all_115_0, simplifying with (15), (76) gives:
% 28.85/4.51 | | | | | | (77) all_115_0 = all_20_7
% 28.85/4.51 | | | | | |
% 28.85/4.51 | | | | | | REDUCE: (74), (77) imply:
% 28.85/4.51 | | | | | | (78) $false
% 28.85/4.51 | | | | | |
% 28.85/4.51 | | | | | | CLOSE: (78) is inconsistent.
% 28.85/4.51 | | | | | |
% 28.85/4.51 | | | | | End of split
% 28.85/4.51 | | | | |
% 28.85/4.51 | | | | Case 2:
% 28.85/4.51 | | | | |
% 28.85/4.51 | | | | | (79) ~ (all_49_2 = 0) & complement(all_20_4, all_20_6) = all_49_2
% 28.85/4.51 | | | | |
% 28.85/4.51 | | | | | REF_CLOSE: (13), (64), (79) are inconsistent by sub-proof #1.
% 28.85/4.51 | | | | |
% 28.85/4.51 | | | | End of split
% 28.85/4.51 | | | |
% 28.85/4.51 | | | Case 2:
% 28.85/4.51 | | | |
% 28.85/4.51 | | | | (80) ~ (all_86_1 = 0) & test(all_20_6) = all_86_1
% 28.85/4.51 | | | |
% 28.85/4.51 | | | | ALPHA: (80) implies:
% 28.85/4.51 | | | | (81) ~ (all_86_1 = 0)
% 28.85/4.51 | | | | (82) test(all_20_6) = all_86_1
% 28.85/4.51 | | | |
% 28.85/4.51 | | | | GROUND_INST: instantiating (9) with 0, all_86_1, all_20_6, simplifying
% 28.85/4.51 | | | | with (23), (82) gives:
% 28.85/4.51 | | | | (83) all_86_1 = 0
% 28.85/4.51 | | | |
% 28.85/4.51 | | | | REDUCE: (81), (83) imply:
% 28.85/4.51 | | | | (84) $false
% 28.85/4.51 | | | |
% 28.85/4.51 | | | | CLOSE: (84) is inconsistent.
% 28.85/4.51 | | | |
% 28.85/4.51 | | | End of split
% 28.85/4.51 | | |
% 28.85/4.51 | | Case 2:
% 28.85/4.51 | | |
% 28.85/4.51 | | | (85) ~ (all_20_1 = 0) & leq(all_20_7, all_20_2) = all_20_1
% 28.85/4.51 | | |
% 28.85/4.51 | | | ALPHA: (85) implies:
% 28.85/4.51 | | | (86) ~ (all_20_1 = 0)
% 28.85/4.51 | | | (87) leq(all_20_7, all_20_2) = all_20_1
% 28.85/4.51 | | |
% 28.85/4.51 | | | BETA: splitting (57) gives:
% 28.85/4.51 | | |
% 28.85/4.51 | | | Case 1:
% 28.85/4.51 | | | |
% 28.85/4.51 | | | | (88) all_86_0 = all_28_0 & c(all_20_6) = all_28_0
% 28.85/4.51 | | | |
% 28.85/4.51 | | | | ALPHA: (88) implies:
% 28.85/4.51 | | | | (89) c(all_20_6) = all_28_0
% 28.85/4.51 | | | |
% 28.85/4.51 | | | | GROUND_INST: instantiating (10) with all_20_4, all_28_0, all_20_6,
% 28.85/4.51 | | | | simplifying with (24), (89) gives:
% 28.85/4.51 | | | | (90) all_28_0 = all_20_4
% 28.85/4.51 | | | |
% 28.85/4.51 | | | | REDUCE: (32), (90) imply:
% 28.85/4.51 | | | | (91) complement(all_20_4, all_20_6) = 0
% 28.85/4.51 | | | |
% 28.85/4.51 | | | | BETA: splitting (47) gives:
% 28.85/4.51 | | | |
% 28.85/4.51 | | | | Case 1:
% 28.85/4.51 | | | | |
% 28.85/4.51 | | | | | (92) all_49_0 = zero & all_49_1 = zero & all_30_0 = one &
% 28.85/4.51 | | | | | multiplication(all_20_4, all_20_6) = zero &
% 28.85/4.51 | | | | | multiplication(all_20_6, all_20_4) = zero
% 28.85/4.51 | | | | |
% 28.85/4.51 | | | | | ALPHA: (92) implies:
% 28.85/4.51 | | | | | (93) all_30_0 = one
% 28.85/4.51 | | | | |
% 28.85/4.51 | | | | | REDUCE: (49), (93) imply:
% 28.85/4.51 | | | | | (94) multiplication(one, all_20_7) = all_20_2
% 28.85/4.51 | | | | |
% 28.85/4.51 | | | | | GROUND_INST: instantiating (2) with all_20_7, all_20_2, simplifying
% 28.85/4.51 | | | | | with (15), (94) gives:
% 28.85/4.51 | | | | | (95) all_20_2 = all_20_7
% 28.85/4.51 | | | | |
% 28.85/4.51 | | | | | GROUND_INST: instantiating (4) with all_20_7, all_20_2, all_20_1,
% 28.85/4.52 | | | | | simplifying with (15), (44), (87) gives:
% 28.85/4.52 | | | | | (96) all_20_1 = 0 | ? [v0: any] : ( ~ (v0 = all_20_2) &
% 28.85/4.52 | | | | | addition(all_20_7, all_20_2) = v0 & $i(v0))
% 28.85/4.52 | | | | |
% 28.85/4.52 | | | | | BETA: splitting (96) gives:
% 28.85/4.52 | | | | |
% 28.85/4.52 | | | | | Case 1:
% 28.85/4.52 | | | | | |
% 28.85/4.52 | | | | | | (97) all_20_1 = 0
% 28.85/4.52 | | | | | |
% 28.85/4.52 | | | | | | REDUCE: (86), (97) imply:
% 28.85/4.52 | | | | | | (98) $false
% 28.85/4.52 | | | | | |
% 28.85/4.52 | | | | | | CLOSE: (98) is inconsistent.
% 28.85/4.52 | | | | | |
% 28.85/4.52 | | | | | Case 2:
% 28.85/4.52 | | | | | |
% 28.85/4.52 | | | | | | (99) ? [v0: any] : ( ~ (v0 = all_20_2) & addition(all_20_7,
% 28.85/4.52 | | | | | | all_20_2) = v0 & $i(v0))
% 28.85/4.52 | | | | | |
% 28.85/4.52 | | | | | | DELTA: instantiating (99) with fresh symbol all_115_0 gives:
% 28.85/4.52 | | | | | | (100) ~ (all_115_0 = all_20_2) & addition(all_20_7, all_20_2) =
% 28.85/4.52 | | | | | | all_115_0 & $i(all_115_0)
% 28.85/4.52 | | | | | |
% 28.85/4.52 | | | | | | ALPHA: (100) implies:
% 28.85/4.52 | | | | | | (101) ~ (all_115_0 = all_20_2)
% 28.85/4.52 | | | | | | (102) addition(all_20_7, all_20_2) = all_115_0
% 28.85/4.52 | | | | | |
% 28.85/4.52 | | | | | | REDUCE: (95), (101) imply:
% 28.85/4.52 | | | | | | (103) ~ (all_115_0 = all_20_7)
% 28.85/4.52 | | | | | |
% 28.85/4.52 | | | | | | REDUCE: (95), (102) imply:
% 28.85/4.52 | | | | | | (104) addition(all_20_7, all_20_7) = all_115_0
% 28.85/4.52 | | | | | |
% 28.85/4.52 | | | | | | GROUND_INST: instantiating (additive_idempotence) with all_20_7,
% 28.85/4.52 | | | | | | all_115_0, simplifying with (15), (104) gives:
% 28.85/4.52 | | | | | | (105) all_115_0 = all_20_7
% 28.85/4.52 | | | | | |
% 28.85/4.52 | | | | | | REDUCE: (103), (105) imply:
% 28.85/4.52 | | | | | | (106) $false
% 28.85/4.52 | | | | | |
% 28.85/4.52 | | | | | | CLOSE: (106) is inconsistent.
% 28.85/4.52 | | | | | |
% 28.85/4.52 | | | | | End of split
% 28.85/4.52 | | | | |
% 28.85/4.52 | | | | Case 2:
% 28.85/4.52 | | | | |
% 28.85/4.52 | | | | | (107) ~ (all_49_2 = 0) & complement(all_20_4, all_20_6) = all_49_2
% 28.85/4.52 | | | | |
% 28.85/4.52 | | | | | REF_CLOSE: (13), (91), (107) are inconsistent by sub-proof #1.
% 28.85/4.52 | | | | |
% 28.85/4.52 | | | | End of split
% 28.85/4.52 | | | |
% 28.85/4.52 | | | Case 2:
% 28.85/4.52 | | | |
% 28.85/4.52 | | | | (108) ~ (all_86_1 = 0) & test(all_20_6) = all_86_1
% 28.85/4.52 | | | |
% 28.85/4.52 | | | | ALPHA: (108) implies:
% 28.85/4.52 | | | | (109) ~ (all_86_1 = 0)
% 28.85/4.52 | | | | (110) test(all_20_6) = all_86_1
% 28.85/4.52 | | | |
% 28.85/4.52 | | | | GROUND_INST: instantiating (9) with 0, all_86_1, all_20_6, simplifying
% 28.85/4.52 | | | | with (23), (110) gives:
% 28.85/4.52 | | | | (111) all_86_1 = 0
% 28.85/4.52 | | | |
% 28.85/4.52 | | | | REDUCE: (109), (111) imply:
% 28.85/4.52 | | | | (112) $false
% 28.85/4.52 | | | |
% 28.85/4.52 | | | | CLOSE: (112) is inconsistent.
% 28.85/4.52 | | | |
% 28.85/4.52 | | | End of split
% 28.85/4.52 | | |
% 28.85/4.52 | | End of split
% 28.85/4.52 | |
% 28.85/4.52 | Case 2:
% 28.85/4.52 | |
% 28.85/4.52 | | (113) ( ~ (all_63_1 = one) & addition(all_28_0, all_20_6) = all_63_1 &
% 28.85/4.52 | | $i(all_63_1)) | ( ~ (all_63_2 = zero) & multiplication(all_20_6,
% 28.85/4.52 | | all_28_0) = all_63_2 & $i(all_63_2))
% 28.85/4.52 | |
% 28.85/4.52 | | BETA: splitting (113) gives:
% 28.85/4.52 | |
% 28.85/4.52 | | Case 1:
% 28.85/4.52 | | |
% 28.85/4.52 | | | (114) ~ (all_63_1 = one) & addition(all_28_0, all_20_6) = all_63_1 &
% 28.85/4.52 | | | $i(all_63_1)
% 28.85/4.52 | | |
% 28.85/4.52 | | | ALPHA: (114) implies:
% 28.85/4.52 | | | (115) ~ (all_63_1 = one)
% 28.85/4.52 | | | (116) addition(all_28_0, all_20_6) = all_63_1
% 28.85/4.52 | | |
% 28.85/4.52 | | | GROUND_INST: instantiating (11) with one, all_63_1, all_20_6, all_28_0,
% 28.85/4.52 | | | simplifying with (51), (116) gives:
% 28.85/4.52 | | | (117) all_63_1 = one
% 28.85/4.52 | | |
% 28.85/4.52 | | | REDUCE: (115), (117) imply:
% 28.85/4.52 | | | (118) $false
% 28.85/4.52 | | |
% 28.85/4.52 | | | CLOSE: (118) is inconsistent.
% 28.85/4.52 | | |
% 28.85/4.52 | | Case 2:
% 28.85/4.52 | | |
% 28.85/4.52 | | | (119) ~ (all_63_2 = zero) & multiplication(all_20_6, all_28_0) =
% 28.85/4.52 | | | all_63_2 & $i(all_63_2)
% 28.85/4.52 | | |
% 28.85/4.52 | | | ALPHA: (119) implies:
% 28.85/4.52 | | | (120) ~ (all_63_2 = zero)
% 28.85/4.52 | | | (121) multiplication(all_20_6, all_28_0) = all_63_2
% 28.85/4.52 | | |
% 28.85/4.52 | | | GROUND_INST: instantiating (12) with zero, all_63_2, all_28_0, all_20_6,
% 28.85/4.52 | | | simplifying with (41), (121) gives:
% 28.85/4.52 | | | (122) all_63_2 = zero
% 28.85/4.52 | | |
% 28.85/4.52 | | | REDUCE: (120), (122) imply:
% 28.85/4.52 | | | (123) $false
% 28.85/4.52 | | |
% 28.85/4.52 | | | CLOSE: (123) is inconsistent.
% 28.85/4.52 | | |
% 28.85/4.52 | | End of split
% 28.85/4.52 | |
% 28.85/4.52 | End of split
% 28.85/4.52 |
% 28.85/4.52 End of proof
% 28.85/4.52
% 28.85/4.52 Sub-proof #1 shows that the following formulas are inconsistent:
% 28.85/4.52 ----------------------------------------------------------------
% 28.85/4.52 (1) ~ (all_49_2 = 0) & complement(all_20_4, all_20_6) = all_49_2
% 28.85/4.52 (2) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 28.85/4.52 ! [v3: $i] : (v1 = v0 | ~ (complement(v3, v2) = v1) | ~ (complement(v3,
% 28.85/4.52 v2) = v0))
% 28.85/4.52 (3) complement(all_20_4, all_20_6) = 0
% 28.85/4.52
% 28.85/4.52 Begin of proof
% 28.85/4.52 |
% 28.85/4.52 | ALPHA: (1) implies:
% 28.85/4.52 | (4) ~ (all_49_2 = 0)
% 28.85/4.52 | (5) complement(all_20_4, all_20_6) = all_49_2
% 28.85/4.52 |
% 28.85/4.52 | GROUND_INST: instantiating (2) with 0, all_49_2, all_20_6, all_20_4,
% 28.85/4.52 | simplifying with (3), (5) gives:
% 28.85/4.52 | (6) all_49_2 = 0
% 28.85/4.52 |
% 28.85/4.52 | REDUCE: (4), (6) imply:
% 28.85/4.52 | (7) $false
% 28.85/4.52 |
% 28.85/4.52 | CLOSE: (7) is inconsistent.
% 28.85/4.52 |
% 28.85/4.53 End of proof
% 28.85/4.53 % SZS output end Proof for theBenchmark
% 28.85/4.53
% 28.85/4.53 3924ms
%------------------------------------------------------------------------------