TSTP Solution File: ALG040+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : ALG040+1 : TPTP v8.1.2. Released v2.7.0.
% 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 : Wed Aug 30 16:35:49 EDT 2023
% Result : Theorem 9.28s 2.03s
% Output : Proof 25.72s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : ALG040+1 : TPTP v8.1.2. Released v2.7.0.
% 0.11/0.12 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.12/0.33 % Computer : n011.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.34 % DateTime : Mon Aug 28 02:59:55 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.19/0.60 ________ _____
% 0.19/0.60 ___ __ \_________(_)________________________________
% 0.19/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.19/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.19/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.19/0.60
% 0.19/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.19/0.60 (2023-06-19)
% 0.19/0.60
% 0.19/0.60 (c) Philipp Rümmer, 2009-2023
% 0.19/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.19/0.60 Amanda Stjerna.
% 0.19/0.60 Free software under BSD-3-Clause.
% 0.19/0.60
% 0.19/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.19/0.60
% 0.19/0.60 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.19/0.61 Running up to 7 provers in parallel.
% 0.19/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.19/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.19/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.19/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.19/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.19/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.19/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 1.96/1.01 Prover 1: Preprocessing ...
% 1.96/1.01 Prover 4: Preprocessing ...
% 2.49/1.06 Prover 3: Preprocessing ...
% 2.49/1.06 Prover 0: Preprocessing ...
% 2.49/1.06 Prover 6: Preprocessing ...
% 2.49/1.06 Prover 5: Preprocessing ...
% 2.49/1.07 Prover 2: Preprocessing ...
% 4.22/1.35 Prover 3: Constructing countermodel ...
% 4.22/1.35 Prover 6: Proving ...
% 4.22/1.35 Prover 5: Constructing countermodel ...
% 4.22/1.36 Prover 1: Constructing countermodel ...
% 4.22/1.38 Prover 2: Proving ...
% 4.22/1.40 Prover 4: Constructing countermodel ...
% 5.05/1.41 Prover 0: Proving ...
% 5.05/1.44 Prover 3: gave up
% 5.05/1.45 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 5.31/1.46 Prover 1: gave up
% 5.31/1.46 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 5.31/1.48 Prover 7: Preprocessing ...
% 5.31/1.48 Prover 8: Preprocessing ...
% 5.96/1.56 Prover 8: Warning: ignoring some quantifiers
% 5.96/1.57 Prover 7: Constructing countermodel ...
% 5.96/1.57 Prover 8: Constructing countermodel ...
% 5.96/1.58 Prover 7: gave up
% 6.35/1.59 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889
% 6.35/1.61 Prover 9: Preprocessing ...
% 6.83/1.66 Prover 8: gave up
% 6.92/1.66 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 6.92/1.70 Prover 10: Preprocessing ...
% 7.50/1.76 Prover 9: Constructing countermodel ...
% 7.50/1.76 Prover 10: Constructing countermodel ...
% 7.50/1.77 Prover 10: gave up
% 7.50/1.78 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 7.50/1.80 Prover 11: Preprocessing ...
% 8.55/1.91 Prover 11: Constructing countermodel ...
% 9.28/2.03 Prover 9: proved (440ms)
% 9.28/2.03
% 9.28/2.03 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 9.28/2.03
% 9.28/2.03 Prover 5: stopped
% 9.28/2.03 Prover 6: stopped
% 9.69/2.04 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 9.69/2.04 Prover 0: stopped
% 9.69/2.04 Prover 2: stopped
% 9.69/2.04 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 9.69/2.04 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085
% 9.69/2.04 Prover 13: Preprocessing ...
% 9.69/2.05 Prover 16: Preprocessing ...
% 9.69/2.05 Prover 19: Preprocessing ...
% 9.69/2.08 Prover 16: Constructing countermodel ...
% 10.07/2.10 Prover 19: Warning: ignoring some quantifiers
% 10.07/2.11 Prover 19: Constructing countermodel ...
% 10.07/2.11 Prover 13: Constructing countermodel ...
% 24.93/4.04 Prover 11: Found proof (size 191)
% 24.93/4.04 Prover 11: proved (2258ms)
% 24.93/4.04 Prover 16: stopped
% 24.93/4.04 Prover 19: stopped
% 24.93/4.04 Prover 4: stopped
% 24.93/4.05 Prover 13: stopped
% 24.93/4.05
% 24.93/4.05 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 24.93/4.05
% 25.13/4.07 % SZS output start Proof for theBenchmark
% 25.13/4.07 Assumptions after simplification:
% 25.13/4.07 ---------------------------------
% 25.13/4.07
% 25.13/4.07 (ax1)
% 25.13/4.10 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (op1(v0, v1) = v2) | ~
% 25.13/4.10 (sorti1(v0) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ? [v4: int] :
% 25.13/4.10 ((v4 = 0 & sorti1(v2) = 0) | ( ~ (v3 = 0) & sorti1(v1) = v3))) & ! [v0: $i]
% 25.13/4.10 : ! [v1: $i] : ( ~ (sorti1(v1) = 0) | ~ (sorti1(v0) = 0) | ~ $i(v1) | ~
% 25.13/4.10 $i(v0) | ? [v2: $i] : (op1(v0, v1) = v2 & sorti1(v2) = 0 & $i(v2)))
% 25.13/4.10
% 25.13/4.10 (ax2)
% 25.13/4.10 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (op2(v0, v1) = v2) | ~
% 25.13/4.10 (sorti2(v0) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ? [v4: int] :
% 25.13/4.10 ((v4 = 0 & sorti2(v2) = 0) | ( ~ (v3 = 0) & sorti2(v1) = v3))) & ! [v0: $i]
% 25.13/4.10 : ! [v1: $i] : ( ~ (sorti2(v1) = 0) | ~ (sorti2(v0) = 0) | ~ $i(v1) | ~
% 25.13/4.10 $i(v0) | ? [v2: $i] : (op2(v0, v1) = v2 & sorti2(v2) = 0 & $i(v2)))
% 25.13/4.10
% 25.13/4.10 (ax3)
% 25.13/4.10 ? [v0: $i] : (sorti1(v0) = 0 & $i(v0) & ! [v1: $i] : ! [v2: $i] : (v2 = v0
% 25.13/4.10 | ~ (op1(v1, v1) = v2) | ~ $i(v1) | ? [v3: int] : ( ~ (v3 = 0) &
% 25.13/4.10 sorti1(v1) = v3)) & ! [v1: $i] : ( ~ (sorti1(v1) = 0) | ~ $i(v1) |
% 25.13/4.10 op1(v1, v1) = v0))
% 25.13/4.10
% 25.13/4.10 (ax4)
% 25.13/4.11 ! [v0: $i] : ( ~ (sorti2(v0) = 0) | ~ $i(v0) | ? [v1: $i] : ? [v2: $i] : (
% 25.13/4.11 ~ (v2 = v0) & op2(v1, v1) = v2 & sorti2(v1) = 0 & $i(v2) & $i(v1)))
% 25.13/4.11
% 25.13/4.11 (co1)
% 25.48/4.13 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (j(v2) = v3) | ~
% 25.48/4.13 (j(v0) = v1) | ~ $i(v2) | ~ $i(v0) | ? [v4: int] : ? [v5: $i] : ? [v6:
% 25.48/4.13 $i] : ? [v7: $i] : ((v7 = v6 & j(v5) = v6 & op2(v0, v2) = v5 & op1(v1,
% 25.48/4.13 v3) = v6 & $i(v6) & $i(v5)) | ( ~ (v4 = 0) & sorti2(v2) = v4) | ( ~
% 25.48/4.13 (v4 = 0) & sorti2(v0) = v4))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 25.48/4.13 : ! [v3: $i] : ( ~ (j(v0) = v1) | ~ (op2(v0, v2) = v3) | ~ $i(v2) | ~
% 25.48/4.13 $i(v0) | ? [v4: int] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ((v7 = v5
% 25.48/4.13 & j(v3) = v5 & j(v2) = v6 & op1(v1, v6) = v5 & $i(v6) & $i(v5)) | ( ~
% 25.48/4.13 (v4 = 0) & sorti2(v2) = v4) | ( ~ (v4 = 0) & sorti2(v0) = v4))) & !
% 25.48/4.13 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (h(v2) = v3) | ~
% 25.48/4.13 (h(v0) = v1) | ~ $i(v2) | ~ $i(v0) | ? [v4: int] : ? [v5: $i] : ? [v6:
% 25.48/4.13 $i] : ? [v7: $i] : ((v7 = v6 & h(v5) = v6 & op2(v1, v3) = v6 & op1(v0,
% 25.48/4.13 v2) = v5 & $i(v6) & $i(v5)) | ( ~ (v4 = 0) & sorti1(v2) = v4) | ( ~
% 25.48/4.13 (v4 = 0) & sorti1(v0) = v4))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 25.48/4.13 : ! [v3: $i] : ( ~ (h(v0) = v1) | ~ (op1(v0, v2) = v3) | ~ $i(v2) | ~
% 25.48/4.13 $i(v0) | ? [v4: int] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ((v7 = v5
% 25.48/4.13 & h(v3) = v5 & h(v2) = v6 & op2(v1, v6) = v5 & $i(v6) & $i(v5)) | ( ~
% 25.48/4.13 (v4 = 0) & sorti1(v2) = v4) | ( ~ (v4 = 0) & sorti1(v0) = v4))) & !
% 25.48/4.13 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (j(v0) = v1) | ~ (sorti2(v2) = 0)
% 25.48/4.13 | ~ $i(v2) | ~ $i(v0) | ? [v3: any] : ? [v4: $i] : ? [v5: $i] : ? [v6:
% 25.48/4.13 $i] : ((v6 = v4 & j(v3) = v4 & j(v2) = v5 & op2(v0, v2) = v3 & op1(v1, v5)
% 25.48/4.13 = v4 & $i(v5) & $i(v4) & $i(v3)) | ( ~ (v3 = 0) & sorti2(v0) = v3))) &
% 25.48/4.13 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (h(v0) = v1) | ~ (sorti1(v2) =
% 25.48/4.13 0) | ~ $i(v2) | ~ $i(v0) | ? [v3: any] : ? [v4: $i] : ? [v5: $i] : ?
% 25.48/4.13 [v6: $i] : ((v6 = v4 & h(v3) = v4 & h(v2) = v5 & op2(v1, v5) = v4 & op1(v0,
% 25.48/4.13 v2) = v3 & $i(v5) & $i(v4) & $i(v3)) | ( ~ (v3 = 0) & sorti1(v0) =
% 25.48/4.13 v3))) & ! [v0: $i] : ! [v1: $i] : ( ~ (j(v0) = v1) | ~ $i(v0) | ?
% 25.48/4.13 [v2: int] : ? [v3: $i] : ((v3 = v0 & h(v1) = v0) | ( ~ (v2 = 0) &
% 25.48/4.13 sorti2(v0) = v2))) & ! [v0: $i] : ! [v1: $i] : ( ~ (j(v0) = v1) | ~
% 25.48/4.13 $i(v0) | ? [v2: int] : ? [v3: int] : ((v3 = 0 & sorti1(v1) = 0) | ( ~ (v2
% 25.48/4.13 = 0) & sorti2(v0) = v2))) & ! [v0: $i] : ! [v1: $i] : ( ~ (h(v0) =
% 25.48/4.13 v1) | ~ $i(v0) | ? [v2: int] : ? [v3: $i] : ((v3 = v0 & j(v1) = v0) | (
% 25.48/4.13 ~ (v2 = 0) & sorti1(v0) = v2))) & ! [v0: $i] : ! [v1: $i] : ( ~ (h(v0)
% 25.48/4.13 = v1) | ~ $i(v0) | ? [v2: int] : ? [v3: int] : ((v3 = 0 & sorti2(v1) =
% 25.48/4.13 0) | ( ~ (v2 = 0) & sorti1(v0) = v2))) & ! [v0: $i] : ( ~ (sorti2(v0) =
% 25.48/4.13 0) | ~ $i(v0) | ? [v1: $i] : (j(v0) = v1 & h(v1) = v0 & $i(v1))) & !
% 25.48/4.13 [v0: $i] : ( ~ (sorti2(v0) = 0) | ~ $i(v0) | ? [v1: $i] : (j(v0) = v1 &
% 25.48/4.13 sorti1(v1) = 0 & $i(v1))) & ! [v0: $i] : ( ~ (sorti2(v0) = 0) | ~ $i(v0)
% 25.48/4.13 | ? [v1: $i] : (j(v0) = v1 & $i(v1) & ! [v2: $i] : ! [v3: $i] : ( ~
% 25.48/4.13 (j(v2) = v3) | ~ $i(v2) | ? [v4: int] : ? [v5: $i] : ? [v6: $i] : ?
% 25.48/4.13 [v7: $i] : ((v7 = v6 & j(v5) = v6 & op2(v0, v2) = v5 & op1(v1, v3) = v6
% 25.48/4.13 & $i(v6) & $i(v5)) | ( ~ (v4 = 0) & sorti2(v2) = v4))) & ! [v2: $i]
% 25.48/4.13 : ! [v3: $i] : ( ~ (op2(v0, v2) = v3) | ~ $i(v2) | ? [v4: int] : ?
% 25.48/4.13 [v5: $i] : ? [v6: $i] : ? [v7: $i] : ((v7 = v5 & j(v3) = v5 & j(v2) =
% 25.48/4.13 v6 & op1(v1, v6) = v5 & $i(v6) & $i(v5)) | ( ~ (v4 = 0) & sorti2(v2)
% 25.48/4.13 = v4))) & ! [v2: $i] : ( ~ (sorti2(v2) = 0) | ~ $i(v2) | ? [v3:
% 25.48/4.13 $i] : ? [v4: $i] : ? [v5: $i] : (j(v3) = v4 & j(v2) = v5 & op2(v0,
% 25.48/4.13 v2) = v3 & op1(v1, v5) = v4 & $i(v5) & $i(v4) & $i(v3))))) & ! [v0:
% 25.48/4.13 $i] : ( ~ (sorti1(v0) = 0) | ~ $i(v0) | ? [v1: $i] : (j(v1) = v0 & h(v0) =
% 25.48/4.13 v1 & $i(v1))) & ! [v0: $i] : ( ~ (sorti1(v0) = 0) | ~ $i(v0) | ? [v1:
% 25.48/4.13 $i] : (h(v0) = v1 & sorti2(v1) = 0 & $i(v1))) & ! [v0: $i] : ( ~
% 25.48/4.13 (sorti1(v0) = 0) | ~ $i(v0) | ? [v1: $i] : (h(v0) = v1 & $i(v1) & ! [v2:
% 25.48/4.13 $i] : ! [v3: $i] : ( ~ (h(v2) = v3) | ~ $i(v2) | ? [v4: int] : ?
% 25.48/4.13 [v5: $i] : ? [v6: $i] : ? [v7: $i] : ((v7 = v6 & h(v5) = v6 & op2(v1,
% 25.48/4.13 v3) = v6 & op1(v0, v2) = v5 & $i(v6) & $i(v5)) | ( ~ (v4 = 0) &
% 25.48/4.13 sorti1(v2) = v4))) & ! [v2: $i] : ! [v3: $i] : ( ~ (op1(v0, v2) =
% 25.48/4.13 v3) | ~ $i(v2) | ? [v4: int] : ? [v5: $i] : ? [v6: $i] : ? [v7:
% 25.48/4.13 $i] : ((v7 = v5 & h(v3) = v5 & h(v2) = v6 & op2(v1, v6) = v5 & $i(v6)
% 25.48/4.13 & $i(v5)) | ( ~ (v4 = 0) & sorti1(v2) = v4))) & ! [v2: $i] : ( ~
% 25.48/4.13 (sorti1(v2) = 0) | ~ $i(v2) | ? [v3: $i] : ? [v4: $i] : ? [v5: $i] :
% 25.48/4.13 (h(v3) = v4 & h(v2) = v5 & op2(v1, v5) = v4 & op1(v0, v2) = v3 & $i(v5)
% 25.48/4.13 & $i(v4) & $i(v3)))))
% 25.48/4.13
% 25.48/4.13 (function-axioms)
% 25.48/4.13 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (op2(v3,
% 25.48/4.13 v2) = v1) | ~ (op2(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 25.48/4.13 $i] : ! [v3: $i] : (v1 = v0 | ~ (op1(v3, v2) = v1) | ~ (op1(v3, v2) =
% 25.48/4.13 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (j(v2) =
% 25.48/4.14 v1) | ~ (j(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 =
% 25.48/4.14 v0 | ~ (h(v2) = v1) | ~ (h(v2) = v0)) & ! [v0: MultipleValueBool] : !
% 25.48/4.14 [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (sorti2(v2) = v1) | ~
% 25.48/4.14 (sorti2(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool]
% 25.48/4.14 : ! [v2: $i] : (v1 = v0 | ~ (sorti1(v2) = v1) | ~ (sorti1(v2) = v0))
% 25.48/4.14
% 25.48/4.14 Those formulas are unsatisfiable:
% 25.48/4.14 ---------------------------------
% 25.48/4.14
% 25.48/4.14 Begin of proof
% 25.48/4.14 |
% 25.48/4.14 | ALPHA: (ax1) implies:
% 25.48/4.14 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ (sorti1(v1) = 0) | ~ (sorti1(v0) = 0)
% 25.48/4.14 | | ~ $i(v1) | ~ $i(v0) | ? [v2: $i] : (op1(v0, v1) = v2 &
% 25.48/4.14 | sorti1(v2) = 0 & $i(v2)))
% 25.48/4.14 |
% 25.48/4.14 | ALPHA: (ax2) implies:
% 25.48/4.14 | (2) ! [v0: $i] : ! [v1: $i] : ( ~ (sorti2(v1) = 0) | ~ (sorti2(v0) = 0)
% 25.48/4.14 | | ~ $i(v1) | ~ $i(v0) | ? [v2: $i] : (op2(v0, v1) = v2 &
% 25.48/4.14 | sorti2(v2) = 0 & $i(v2)))
% 25.48/4.14 |
% 25.48/4.14 | ALPHA: (co1) implies:
% 25.48/4.14 | (3) ! [v0: $i] : ( ~ (sorti1(v0) = 0) | ~ $i(v0) | ? [v1: $i] : (h(v0) =
% 25.48/4.14 | v1 & $i(v1) & ! [v2: $i] : ! [v3: $i] : ( ~ (h(v2) = v3) | ~
% 25.48/4.14 | $i(v2) | ? [v4: int] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] :
% 25.48/4.14 | ((v7 = v6 & h(v5) = v6 & op2(v1, v3) = v6 & op1(v0, v2) = v5 &
% 25.48/4.14 | $i(v6) & $i(v5)) | ( ~ (v4 = 0) & sorti1(v2) = v4))) & !
% 25.48/4.14 | [v2: $i] : ! [v3: $i] : ( ~ (op1(v0, v2) = v3) | ~ $i(v2) | ?
% 25.48/4.14 | [v4: int] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ((v7 = v5 &
% 25.48/4.14 | h(v3) = v5 & h(v2) = v6 & op2(v1, v6) = v5 & $i(v6) & $i(v5))
% 25.48/4.14 | | ( ~ (v4 = 0) & sorti1(v2) = v4))) & ! [v2: $i] : ( ~
% 25.48/4.14 | (sorti1(v2) = 0) | ~ $i(v2) | ? [v3: $i] : ? [v4: $i] : ?
% 25.48/4.14 | [v5: $i] : (h(v3) = v4 & h(v2) = v5 & op2(v1, v5) = v4 & op1(v0,
% 25.48/4.14 | v2) = v3 & $i(v5) & $i(v4) & $i(v3)))))
% 25.48/4.14 | (4) ! [v0: $i] : ( ~ (sorti1(v0) = 0) | ~ $i(v0) | ? [v1: $i] : (h(v0) =
% 25.48/4.14 | v1 & sorti2(v1) = 0 & $i(v1)))
% 25.48/4.15 | (5) ! [v0: $i] : ( ~ (sorti1(v0) = 0) | ~ $i(v0) | ? [v1: $i] : (j(v1) =
% 25.48/4.15 | v0 & h(v0) = v1 & $i(v1)))
% 25.48/4.15 | (6) ! [v0: $i] : ( ~ (sorti2(v0) = 0) | ~ $i(v0) | ? [v1: $i] : (j(v0) =
% 25.48/4.15 | v1 & $i(v1) & ! [v2: $i] : ! [v3: $i] : ( ~ (j(v2) = v3) | ~
% 25.48/4.15 | $i(v2) | ? [v4: int] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] :
% 25.48/4.15 | ((v7 = v6 & j(v5) = v6 & op2(v0, v2) = v5 & op1(v1, v3) = v6 &
% 25.48/4.15 | $i(v6) & $i(v5)) | ( ~ (v4 = 0) & sorti2(v2) = v4))) & !
% 25.48/4.15 | [v2: $i] : ! [v3: $i] : ( ~ (op2(v0, v2) = v3) | ~ $i(v2) | ?
% 25.48/4.15 | [v4: int] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ((v7 = v5 &
% 25.48/4.15 | j(v3) = v5 & j(v2) = v6 & op1(v1, v6) = v5 & $i(v6) & $i(v5))
% 25.48/4.15 | | ( ~ (v4 = 0) & sorti2(v2) = v4))) & ! [v2: $i] : ( ~
% 25.48/4.15 | (sorti2(v2) = 0) | ~ $i(v2) | ? [v3: $i] : ? [v4: $i] : ?
% 25.48/4.15 | [v5: $i] : (j(v3) = v4 & j(v2) = v5 & op2(v0, v2) = v3 & op1(v1,
% 25.48/4.15 | v5) = v4 & $i(v5) & $i(v4) & $i(v3)))))
% 25.48/4.15 | (7) ! [v0: $i] : ( ~ (sorti2(v0) = 0) | ~ $i(v0) | ? [v1: $i] : (j(v0) =
% 25.48/4.15 | v1 & sorti1(v1) = 0 & $i(v1)))
% 25.48/4.15 | (8) ! [v0: $i] : ( ~ (sorti2(v0) = 0) | ~ $i(v0) | ? [v1: $i] : (j(v0) =
% 25.48/4.15 | v1 & h(v1) = v0 & $i(v1)))
% 25.48/4.15 | (9) ! [v0: $i] : ! [v1: $i] : ( ~ (j(v0) = v1) | ~ $i(v0) | ? [v2: int]
% 25.48/4.15 | : ? [v3: $i] : ((v3 = v0 & h(v1) = v0) | ( ~ (v2 = 0) & sorti2(v0) =
% 25.48/4.15 | v2)))
% 25.48/4.15 | (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (j(v0) = v1) | ~
% 25.48/4.15 | (sorti2(v2) = 0) | ~ $i(v2) | ~ $i(v0) | ? [v3: any] : ? [v4:
% 25.48/4.15 | $i] : ? [v5: $i] : ? [v6: $i] : ((v6 = v4 & j(v3) = v4 & j(v2) =
% 25.48/4.15 | v5 & op2(v0, v2) = v3 & op1(v1, v5) = v4 & $i(v5) & $i(v4) &
% 25.48/4.15 | $i(v3)) | ( ~ (v3 = 0) & sorti2(v0) = v3)))
% 25.48/4.15 |
% 25.48/4.15 | ALPHA: (function-axioms) implies:
% 25.48/4.15 | (11) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 25.48/4.15 | : (v1 = v0 | ~ (sorti2(v2) = v1) | ~ (sorti2(v2) = v0))
% 25.48/4.15 | (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (h(v2) = v1) |
% 25.48/4.15 | ~ (h(v2) = v0))
% 25.48/4.16 | (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (j(v2) = v1) |
% 25.48/4.16 | ~ (j(v2) = v0))
% 25.48/4.16 | (14) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 25.48/4.16 | (op1(v3, v2) = v1) | ~ (op1(v3, v2) = v0))
% 25.48/4.16 | (15) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 25.48/4.16 | (op2(v3, v2) = v1) | ~ (op2(v3, v2) = v0))
% 25.48/4.16 |
% 25.48/4.16 | DELTA: instantiating (ax3) with fresh symbol all_7_0 gives:
% 25.48/4.16 | (16) sorti1(all_7_0) = 0 & $i(all_7_0) & ! [v0: $i] : ! [v1: int] : (v1 =
% 25.48/4.16 | all_7_0 | ~ (op1(v0, v0) = v1) | ~ $i(v0) | ? [v2: int] : ( ~ (v2
% 25.48/4.16 | = 0) & sorti1(v0) = v2)) & ! [v0: $i] : ( ~ (sorti1(v0) = 0) |
% 25.48/4.16 | ~ $i(v0) | op1(v0, v0) = all_7_0)
% 25.48/4.16 |
% 25.48/4.16 | ALPHA: (16) implies:
% 25.48/4.16 | (17) $i(all_7_0)
% 25.48/4.16 | (18) sorti1(all_7_0) = 0
% 25.48/4.16 | (19) ! [v0: $i] : ( ~ (sorti1(v0) = 0) | ~ $i(v0) | op1(v0, v0) =
% 25.48/4.16 | all_7_0)
% 25.48/4.16 |
% 25.48/4.16 | GROUND_INST: instantiating (1) with all_7_0, all_7_0, simplifying with (17),
% 25.48/4.16 | (18) gives:
% 25.48/4.16 | (20) ? [v0: $i] : (op1(all_7_0, all_7_0) = v0 & sorti1(v0) = 0 & $i(v0))
% 25.48/4.16 |
% 25.48/4.16 | GROUND_INST: instantiating (19) with all_7_0, simplifying with (17), (18)
% 25.48/4.16 | gives:
% 25.48/4.16 | (21) op1(all_7_0, all_7_0) = all_7_0
% 25.48/4.16 |
% 25.48/4.16 | GROUND_INST: instantiating (5) with all_7_0, simplifying with (17), (18)
% 25.48/4.16 | gives:
% 25.48/4.16 | (22) ? [v0: $i] : (j(v0) = all_7_0 & h(all_7_0) = v0 & $i(v0))
% 25.48/4.16 |
% 25.48/4.16 | GROUND_INST: instantiating (4) with all_7_0, simplifying with (17), (18)
% 25.48/4.16 | gives:
% 25.48/4.16 | (23) ? [v0: $i] : (h(all_7_0) = v0 & sorti2(v0) = 0 & $i(v0))
% 25.48/4.16 |
% 25.48/4.16 | GROUND_INST: instantiating (3) with all_7_0, simplifying with (17), (18)
% 25.48/4.16 | gives:
% 25.48/4.17 | (24) ? [v0: $i] : (h(all_7_0) = v0 & $i(v0) & ! [v1: $i] : ! [v2: $i] :
% 25.48/4.17 | ( ~ (h(v1) = v2) | ~ $i(v1) | ? [v3: int] : ? [v4: $i] : ? [v5:
% 25.48/4.17 | $i] : ? [v6: $i] : ((v6 = v5 & h(v4) = v5 & op2(v0, v2) = v5 &
% 25.48/4.17 | op1(all_7_0, v1) = v4 & $i(v5) & $i(v4)) | ( ~ (v3 = 0) &
% 25.48/4.17 | sorti1(v1) = v3))) & ! [v1: $i] : ! [v2: $i] : ( ~
% 25.48/4.17 | (op1(all_7_0, v1) = v2) | ~ $i(v1) | ? [v3: int] : ? [v4: $i] :
% 25.48/4.17 | ? [v5: $i] : ? [v6: $i] : ((v6 = v4 & h(v2) = v4 & h(v1) = v5 &
% 25.48/4.17 | op2(v0, v5) = v4 & $i(v5) & $i(v4)) | ( ~ (v3 = 0) &
% 25.48/4.17 | sorti1(v1) = v3))) & ! [v1: $i] : ( ~ (sorti1(v1) = 0) | ~
% 25.48/4.17 | $i(v1) | ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : (h(v2) = v3 &
% 25.48/4.17 | h(v1) = v4 & op2(v0, v4) = v3 & op1(all_7_0, v1) = v2 & $i(v4) &
% 25.48/4.17 | $i(v3) & $i(v2))))
% 25.48/4.17 |
% 25.48/4.17 | DELTA: instantiating (20) with fresh symbol all_16_0 gives:
% 25.48/4.17 | (25) op1(all_7_0, all_7_0) = all_16_0 & sorti1(all_16_0) = 0 & $i(all_16_0)
% 25.48/4.17 |
% 25.48/4.17 | ALPHA: (25) implies:
% 25.48/4.17 | (26) sorti1(all_16_0) = 0
% 25.48/4.17 | (27) op1(all_7_0, all_7_0) = all_16_0
% 25.48/4.17 |
% 25.48/4.17 | DELTA: instantiating (23) with fresh symbol all_18_0 gives:
% 25.48/4.17 | (28) h(all_7_0) = all_18_0 & sorti2(all_18_0) = 0 & $i(all_18_0)
% 25.48/4.17 |
% 25.48/4.17 | ALPHA: (28) implies:
% 25.48/4.17 | (29) sorti2(all_18_0) = 0
% 25.48/4.17 | (30) h(all_7_0) = all_18_0
% 25.48/4.17 |
% 25.48/4.17 | DELTA: instantiating (22) with fresh symbol all_20_0 gives:
% 25.48/4.17 | (31) j(all_20_0) = all_7_0 & h(all_7_0) = all_20_0 & $i(all_20_0)
% 25.48/4.17 |
% 25.48/4.17 | ALPHA: (31) implies:
% 25.48/4.17 | (32) h(all_7_0) = all_20_0
% 25.48/4.17 | (33) j(all_20_0) = all_7_0
% 25.48/4.17 |
% 25.48/4.17 | DELTA: instantiating (24) with fresh symbol all_22_0 gives:
% 25.48/4.17 | (34) h(all_7_0) = all_22_0 & $i(all_22_0) & ! [v0: $i] : ! [v1: $i] : ( ~
% 25.48/4.17 | (h(v0) = v1) | ~ $i(v0) | ? [v2: int] : ? [v3: $i] : ? [v4: $i]
% 25.48/4.17 | : ? [v5: $i] : ((v5 = v4 & h(v3) = v4 & op2(all_22_0, v1) = v4 &
% 25.48/4.17 | op1(all_7_0, v0) = v3 & $i(v4) & $i(v3)) | ( ~ (v2 = 0) &
% 25.48/4.17 | sorti1(v0) = v2))) & ! [v0: $i] : ! [v1: $i] : ( ~
% 25.48/4.17 | (op1(all_7_0, v0) = v1) | ~ $i(v0) | ? [v2: int] : ? [v3: $i] :
% 25.48/4.17 | ? [v4: $i] : ? [v5: $i] : ((v5 = v3 & h(v1) = v3 & h(v0) = v4 &
% 25.48/4.17 | op2(all_22_0, v4) = v3 & $i(v4) & $i(v3)) | ( ~ (v2 = 0) &
% 25.48/4.17 | sorti1(v0) = v2))) & ! [v0: $i] : ( ~ (sorti1(v0) = 0) | ~
% 25.48/4.17 | $i(v0) | ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : (h(v1) = v2 &
% 25.48/4.17 | h(v0) = v3 & op2(all_22_0, v3) = v2 & op1(all_7_0, v0) = v1 &
% 25.48/4.17 | $i(v3) & $i(v2) & $i(v1)))
% 25.48/4.17 |
% 25.48/4.17 | ALPHA: (34) implies:
% 25.48/4.17 | (35) h(all_7_0) = all_22_0
% 25.48/4.17 | (36) ! [v0: $i] : ( ~ (sorti1(v0) = 0) | ~ $i(v0) | ? [v1: $i] : ? [v2:
% 25.48/4.17 | $i] : ? [v3: $i] : (h(v1) = v2 & h(v0) = v3 & op2(all_22_0, v3) =
% 25.48/4.17 | v2 & op1(all_7_0, v0) = v1 & $i(v3) & $i(v2) & $i(v1)))
% 25.48/4.17 |
% 25.48/4.17 | GROUND_INST: instantiating (36) with all_7_0, simplifying with (17), (18)
% 25.48/4.17 | gives:
% 25.48/4.17 | (37) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (h(v0) = v1 & h(all_7_0) =
% 25.48/4.17 | v2 & op2(all_22_0, v2) = v1 & op1(all_7_0, all_7_0) = v0 & $i(v2) &
% 25.48/4.17 | $i(v1) & $i(v0))
% 25.48/4.17 |
% 25.48/4.17 | DELTA: instantiating (37) with fresh symbols all_25_0, all_25_1, all_25_2
% 25.48/4.17 | gives:
% 25.48/4.17 | (38) h(all_25_2) = all_25_1 & h(all_7_0) = all_25_0 & op2(all_22_0,
% 25.48/4.17 | all_25_0) = all_25_1 & op1(all_7_0, all_7_0) = all_25_2 &
% 25.48/4.17 | $i(all_25_0) & $i(all_25_1) & $i(all_25_2)
% 25.48/4.17 |
% 25.48/4.17 | ALPHA: (38) implies:
% 25.48/4.17 | (39) $i(all_25_1)
% 25.72/4.17 | (40) op1(all_7_0, all_7_0) = all_25_2
% 25.72/4.17 | (41) op2(all_22_0, all_25_0) = all_25_1
% 25.72/4.18 | (42) h(all_7_0) = all_25_0
% 25.72/4.18 | (43) h(all_25_2) = all_25_1
% 25.72/4.18 |
% 25.72/4.18 | GROUND_INST: instantiating (14) with all_16_0, all_25_2, all_7_0, all_7_0,
% 25.72/4.18 | simplifying with (27), (40) gives:
% 25.72/4.18 | (44) all_25_2 = all_16_0
% 25.72/4.18 |
% 25.72/4.18 | GROUND_INST: instantiating (14) with all_7_0, all_25_2, all_7_0, all_7_0,
% 25.72/4.18 | simplifying with (21), (40) gives:
% 25.72/4.18 | (45) all_25_2 = all_7_0
% 25.72/4.18 |
% 25.72/4.18 | GROUND_INST: instantiating (12) with all_20_0, all_22_0, all_7_0, simplifying
% 25.72/4.18 | with (32), (35) gives:
% 25.72/4.18 | (46) all_22_0 = all_20_0
% 25.72/4.18 |
% 25.72/4.18 | GROUND_INST: instantiating (12) with all_22_0, all_25_0, all_7_0, simplifying
% 25.72/4.18 | with (35), (42) gives:
% 25.72/4.18 | (47) all_25_0 = all_22_0
% 25.72/4.18 |
% 25.72/4.18 | GROUND_INST: instantiating (12) with all_18_0, all_25_0, all_7_0, simplifying
% 25.72/4.18 | with (30), (42) gives:
% 25.72/4.18 | (48) all_25_0 = all_18_0
% 25.72/4.18 |
% 25.72/4.18 | COMBINE_EQS: (47), (48) imply:
% 25.72/4.18 | (49) all_22_0 = all_18_0
% 25.72/4.18 |
% 25.72/4.18 | SIMP: (49) implies:
% 25.72/4.18 | (50) all_22_0 = all_18_0
% 25.72/4.18 |
% 25.72/4.18 | COMBINE_EQS: (44), (45) imply:
% 25.72/4.18 | (51) all_16_0 = all_7_0
% 25.72/4.18 |
% 25.72/4.18 | COMBINE_EQS: (46), (50) imply:
% 25.72/4.18 | (52) all_20_0 = all_18_0
% 25.72/4.18 |
% 25.72/4.18 | SIMP: (52) implies:
% 25.72/4.18 | (53) all_20_0 = all_18_0
% 25.72/4.18 |
% 25.72/4.18 | REDUCE: (33), (53) imply:
% 25.72/4.18 | (54) j(all_18_0) = all_7_0
% 25.72/4.18 |
% 25.72/4.18 | REDUCE: (43), (45) imply:
% 25.72/4.18 | (55) h(all_7_0) = all_25_1
% 25.72/4.18 |
% 25.72/4.18 | REDUCE: (41), (48), (50) imply:
% 25.72/4.18 | (56) op2(all_18_0, all_18_0) = all_25_1
% 25.72/4.18 |
% 25.72/4.18 | GROUND_INST: instantiating (12) with all_18_0, all_25_1, all_7_0, simplifying
% 25.72/4.18 | with (30), (55) gives:
% 25.72/4.18 | (57) all_25_1 = all_18_0
% 25.72/4.18 |
% 25.72/4.18 | REDUCE: (56), (57) imply:
% 25.72/4.18 | (58) op2(all_18_0, all_18_0) = all_18_0
% 25.72/4.18 |
% 25.72/4.18 | REDUCE: (39), (57) imply:
% 25.72/4.18 | (59) $i(all_18_0)
% 25.72/4.18 |
% 25.72/4.18 | GROUND_INST: instantiating (ax4) with all_18_0, simplifying with (29), (59)
% 25.72/4.18 | gives:
% 25.72/4.18 | (60) ? [v0: $i] : ? [v1: any] : ( ~ (v1 = all_18_0) & op2(v0, v0) = v1 &
% 25.72/4.18 | sorti2(v0) = 0 & $i(v1) & $i(v0))
% 25.72/4.18 |
% 25.72/4.18 | GROUND_INST: instantiating (6) with all_18_0, simplifying with (29), (59)
% 25.72/4.18 | gives:
% 25.72/4.18 | (61) ? [v0: $i] : (j(all_18_0) = v0 & $i(v0) & ! [v1: $i] : ! [v2: $i] :
% 25.72/4.18 | ( ~ (j(v1) = v2) | ~ $i(v1) | ? [v3: int] : ? [v4: $i] : ? [v5:
% 25.72/4.18 | $i] : ? [v6: $i] : ((v6 = v5 & j(v4) = v5 & op2(all_18_0, v1) =
% 25.72/4.18 | v4 & op1(v0, v2) = v5 & $i(v5) & $i(v4)) | ( ~ (v3 = 0) &
% 25.72/4.18 | sorti2(v1) = v3))) & ! [v1: $i] : ! [v2: $i] : ( ~
% 25.72/4.18 | (op2(all_18_0, v1) = v2) | ~ $i(v1) | ? [v3: int] : ? [v4: $i]
% 25.72/4.18 | : ? [v5: $i] : ? [v6: $i] : ((v6 = v4 & j(v2) = v4 & j(v1) = v5
% 25.72/4.18 | & op1(v0, v5) = v4 & $i(v5) & $i(v4)) | ( ~ (v3 = 0) &
% 25.72/4.18 | sorti2(v1) = v3))) & ! [v1: $i] : ( ~ (sorti2(v1) = 0) | ~
% 25.72/4.18 | $i(v1) | ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : (j(v2) = v3 &
% 25.72/4.18 | j(v1) = v4 & op2(all_18_0, v1) = v2 & op1(v0, v4) = v3 & $i(v4)
% 25.72/4.18 | & $i(v3) & $i(v2))))
% 25.72/4.18 |
% 25.72/4.18 | DELTA: instantiating (60) with fresh symbols all_40_0, all_40_1 gives:
% 25.72/4.18 | (62) ~ (all_40_0 = all_18_0) & op2(all_40_1, all_40_1) = all_40_0 &
% 25.72/4.18 | sorti2(all_40_1) = 0 & $i(all_40_0) & $i(all_40_1)
% 25.72/4.18 |
% 25.72/4.18 | ALPHA: (62) implies:
% 25.72/4.18 | (63) ~ (all_40_0 = all_18_0)
% 25.72/4.18 | (64) $i(all_40_1)
% 25.72/4.18 | (65) sorti2(all_40_1) = 0
% 25.72/4.18 | (66) op2(all_40_1, all_40_1) = all_40_0
% 25.72/4.18 |
% 25.72/4.18 | DELTA: instantiating (61) with fresh symbol all_42_0 gives:
% 25.72/4.19 | (67) j(all_18_0) = all_42_0 & $i(all_42_0) & ! [v0: $i] : ! [v1: $i] : (
% 25.72/4.19 | ~ (j(v0) = v1) | ~ $i(v0) | ? [v2: int] : ? [v3: $i] : ? [v4:
% 25.72/4.19 | $i] : ? [v5: $i] : ((v5 = v4 & j(v3) = v4 & op2(all_18_0, v0) =
% 25.72/4.19 | v3 & op1(all_42_0, v1) = v4 & $i(v4) & $i(v3)) | ( ~ (v2 = 0) &
% 25.72/4.19 | sorti2(v0) = v2))) & ! [v0: $i] : ! [v1: $i] : ( ~
% 25.72/4.19 | (op2(all_18_0, v0) = v1) | ~ $i(v0) | ? [v2: int] : ? [v3: $i] :
% 25.72/4.19 | ? [v4: $i] : ? [v5: $i] : ((v5 = v3 & j(v1) = v3 & j(v0) = v4 &
% 25.72/4.19 | op1(all_42_0, v4) = v3 & $i(v4) & $i(v3)) | ( ~ (v2 = 0) &
% 25.72/4.19 | sorti2(v0) = v2))) & ! [v0: $i] : ( ~ (sorti2(v0) = 0) | ~
% 25.72/4.19 | $i(v0) | ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : (j(v1) = v2 &
% 25.72/4.19 | j(v0) = v3 & op2(all_18_0, v0) = v1 & op1(all_42_0, v3) = v2 &
% 25.72/4.19 | $i(v3) & $i(v2) & $i(v1)))
% 25.72/4.19 |
% 25.72/4.19 | ALPHA: (67) implies:
% 25.72/4.19 | (68) j(all_18_0) = all_42_0
% 25.72/4.19 | (69) ! [v0: $i] : ( ~ (sorti2(v0) = 0) | ~ $i(v0) | ? [v1: $i] : ? [v2:
% 25.72/4.19 | $i] : ? [v3: $i] : (j(v1) = v2 & j(v0) = v3 & op2(all_18_0, v0) =
% 25.72/4.19 | v1 & op1(all_42_0, v3) = v2 & $i(v3) & $i(v2) & $i(v1)))
% 25.72/4.19 | (70) ! [v0: $i] : ! [v1: $i] : ( ~ (op2(all_18_0, v0) = v1) | ~ $i(v0) |
% 25.72/4.19 | ? [v2: int] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ((v5 = v3 &
% 25.72/4.19 | j(v1) = v3 & j(v0) = v4 & op1(all_42_0, v4) = v3 & $i(v4) &
% 25.72/4.19 | $i(v3)) | ( ~ (v2 = 0) & sorti2(v0) = v2)))
% 25.72/4.19 | (71) ! [v0: $i] : ! [v1: $i] : ( ~ (j(v0) = v1) | ~ $i(v0) | ? [v2:
% 25.72/4.19 | int] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ((v5 = v4 & j(v3)
% 25.72/4.19 | = v4 & op2(all_18_0, v0) = v3 & op1(all_42_0, v1) = v4 & $i(v4)
% 25.72/4.19 | & $i(v3)) | ( ~ (v2 = 0) & sorti2(v0) = v2)))
% 25.72/4.19 |
% 25.72/4.19 | GROUND_INST: instantiating (69) with all_18_0, simplifying with (29), (59)
% 25.72/4.19 | gives:
% 25.72/4.19 | (72) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (j(v0) = v1 & j(all_18_0) =
% 25.72/4.19 | v2 & op2(all_18_0, all_18_0) = v0 & op1(all_42_0, v2) = v1 & $i(v2)
% 25.72/4.19 | & $i(v1) & $i(v0))
% 25.72/4.19 |
% 25.72/4.19 | GROUND_INST: instantiating (70) with all_18_0, all_18_0, simplifying with
% 25.72/4.19 | (58), (59) gives:
% 25.72/4.19 | (73) ? [v0: int] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ((v3 = v1 &
% 25.72/4.19 | j(all_18_0) = v2 & j(all_18_0) = v1 & op1(all_42_0, v2) = v1 &
% 25.72/4.19 | $i(v2) & $i(v1)) | ( ~ (v0 = 0) & sorti2(all_18_0) = v0))
% 25.72/4.19 |
% 25.72/4.19 | GROUND_INST: instantiating (71) with all_18_0, all_7_0, simplifying with (54),
% 25.72/4.19 | (59) gives:
% 25.72/4.19 | (74) ? [v0: int] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ((v3 = v2 &
% 25.72/4.19 | j(v1) = v2 & op2(all_18_0, all_18_0) = v1 & op1(all_42_0, all_7_0)
% 25.72/4.19 | = v2 & $i(v2) & $i(v1)) | ( ~ (v0 = 0) & sorti2(all_18_0) = v0))
% 25.72/4.19 |
% 25.72/4.19 | DELTA: instantiating (72) with fresh symbols all_45_0, all_45_1, all_45_2
% 25.72/4.19 | gives:
% 25.72/4.19 | (75) j(all_45_2) = all_45_1 & j(all_18_0) = all_45_0 & op2(all_18_0,
% 25.72/4.19 | all_18_0) = all_45_2 & op1(all_42_0, all_45_0) = all_45_1 &
% 25.72/4.19 | $i(all_45_0) & $i(all_45_1) & $i(all_45_2)
% 25.72/4.19 |
% 25.72/4.19 | ALPHA: (75) implies:
% 25.72/4.19 | (76) $i(all_45_2)
% 25.72/4.19 | (77) op2(all_18_0, all_18_0) = all_45_2
% 25.72/4.19 | (78) j(all_18_0) = all_45_0
% 25.72/4.19 | (79) j(all_45_2) = all_45_1
% 25.72/4.19 |
% 25.72/4.19 | DELTA: instantiating (74) with fresh symbols all_47_0, all_47_1, all_47_2,
% 25.72/4.19 | all_47_3 gives:
% 25.72/4.19 | (80) (all_47_0 = all_47_1 & j(all_47_2) = all_47_1 & op2(all_18_0,
% 25.72/4.19 | all_18_0) = all_47_2 & op1(all_42_0, all_7_0) = all_47_1 &
% 25.72/4.19 | $i(all_47_1) & $i(all_47_2)) | ( ~ (all_47_3 = 0) & sorti2(all_18_0)
% 25.72/4.19 | = all_47_3)
% 25.72/4.19 |
% 25.72/4.19 | DELTA: instantiating (73) with fresh symbols all_48_0, all_48_1, all_48_2,
% 25.72/4.19 | all_48_3 gives:
% 25.72/4.19 | (81) (all_48_0 = all_48_2 & j(all_18_0) = all_48_1 & j(all_18_0) = all_48_2
% 25.72/4.19 | & op1(all_42_0, all_48_1) = all_48_2 & $i(all_48_1) & $i(all_48_2))
% 25.72/4.19 | | ( ~ (all_48_3 = 0) & sorti2(all_18_0) = all_48_3)
% 25.72/4.19 |
% 25.72/4.19 | BETA: splitting (81) gives:
% 25.72/4.19 |
% 25.72/4.19 | Case 1:
% 25.72/4.19 | |
% 25.72/4.19 | | (82) all_48_0 = all_48_2 & j(all_18_0) = all_48_1 & j(all_18_0) =
% 25.72/4.19 | | all_48_2 & op1(all_42_0, all_48_1) = all_48_2 & $i(all_48_1) &
% 25.72/4.19 | | $i(all_48_2)
% 25.72/4.19 | |
% 25.72/4.19 | | ALPHA: (82) implies:
% 25.72/4.19 | | (83) j(all_18_0) = all_48_2
% 25.72/4.19 | | (84) j(all_18_0) = all_48_1
% 25.72/4.19 | |
% 25.72/4.19 | | BETA: splitting (80) gives:
% 25.72/4.19 | |
% 25.72/4.19 | | Case 1:
% 25.72/4.19 | | |
% 25.72/4.19 | | | (85) all_47_0 = all_47_1 & j(all_47_2) = all_47_1 & op2(all_18_0,
% 25.72/4.19 | | | all_18_0) = all_47_2 & op1(all_42_0, all_7_0) = all_47_1 &
% 25.72/4.19 | | | $i(all_47_1) & $i(all_47_2)
% 25.72/4.19 | | |
% 25.72/4.19 | | | ALPHA: (85) implies:
% 25.72/4.19 | | | (86) op2(all_18_0, all_18_0) = all_47_2
% 25.72/4.20 | | | (87) j(all_47_2) = all_47_1
% 25.72/4.20 | | |
% 25.72/4.20 | | | GROUND_INST: instantiating (15) with all_18_0, all_47_2, all_18_0,
% 25.72/4.20 | | | all_18_0, simplifying with (58), (86) gives:
% 25.72/4.20 | | | (88) all_47_2 = all_18_0
% 25.72/4.20 | | |
% 25.72/4.20 | | | GROUND_INST: instantiating (15) with all_45_2, all_47_2, all_18_0,
% 25.72/4.20 | | | all_18_0, simplifying with (77), (86) gives:
% 25.72/4.20 | | | (89) all_47_2 = all_45_2
% 25.72/4.20 | | |
% 25.72/4.20 | | | GROUND_INST: instantiating (13) with all_7_0, all_48_2, all_18_0,
% 25.72/4.20 | | | simplifying with (54), (83) gives:
% 25.72/4.20 | | | (90) all_48_2 = all_7_0
% 25.72/4.20 | | |
% 25.72/4.20 | | | GROUND_INST: instantiating (13) with all_45_0, all_48_2, all_18_0,
% 25.72/4.20 | | | simplifying with (78), (83) gives:
% 25.72/4.20 | | | (91) all_48_2 = all_45_0
% 25.72/4.20 | | |
% 25.72/4.20 | | | GROUND_INST: instantiating (13) with all_45_0, all_48_1, all_18_0,
% 25.72/4.20 | | | simplifying with (78), (84) gives:
% 25.72/4.20 | | | (92) all_48_1 = all_45_0
% 25.72/4.20 | | |
% 25.72/4.20 | | | GROUND_INST: instantiating (13) with all_42_0, all_48_1, all_18_0,
% 25.72/4.20 | | | simplifying with (68), (84) gives:
% 25.72/4.20 | | | (93) all_48_1 = all_42_0
% 25.72/4.20 | | |
% 25.72/4.20 | | | COMBINE_EQS: (92), (93) imply:
% 25.72/4.20 | | | (94) all_45_0 = all_42_0
% 25.72/4.20 | | |
% 25.72/4.20 | | | SIMP: (94) implies:
% 25.72/4.20 | | | (95) all_45_0 = all_42_0
% 25.72/4.20 | | |
% 25.72/4.20 | | | COMBINE_EQS: (90), (91) imply:
% 25.72/4.20 | | | (96) all_45_0 = all_7_0
% 25.72/4.20 | | |
% 25.72/4.20 | | | SIMP: (96) implies:
% 25.72/4.20 | | | (97) all_45_0 = all_7_0
% 25.72/4.20 | | |
% 25.72/4.20 | | | COMBINE_EQS: (88), (89) imply:
% 25.72/4.20 | | | (98) all_45_2 = all_18_0
% 25.72/4.20 | | |
% 25.72/4.20 | | | COMBINE_EQS: (95), (97) imply:
% 25.72/4.20 | | | (99) all_42_0 = all_7_0
% 25.72/4.20 | | |
% 25.72/4.20 | | | SIMP: (99) implies:
% 25.72/4.20 | | | (100) all_42_0 = all_7_0
% 25.72/4.20 | | |
% 25.72/4.20 | | | REDUCE: (87), (88) imply:
% 25.72/4.20 | | | (101) j(all_18_0) = all_47_1
% 25.72/4.20 | | |
% 25.72/4.20 | | | REDUCE: (79), (98) imply:
% 25.72/4.20 | | | (102) j(all_18_0) = all_45_1
% 25.72/4.20 | | |
% 25.72/4.20 | | | GROUND_INST: instantiating (13) with all_7_0, all_47_1, all_18_0,
% 25.72/4.20 | | | simplifying with (54), (101) gives:
% 25.72/4.20 | | | (103) all_47_1 = all_7_0
% 25.72/4.20 | | |
% 25.72/4.20 | | | GROUND_INST: instantiating (13) with all_45_1, all_47_1, all_18_0,
% 25.72/4.20 | | | simplifying with (101), (102) gives:
% 25.72/4.20 | | | (104) all_47_1 = all_45_1
% 25.72/4.20 | | |
% 25.72/4.20 | | | COMBINE_EQS: (103), (104) imply:
% 25.72/4.20 | | | (105) all_45_1 = all_7_0
% 25.72/4.20 | | |
% 25.72/4.20 | | | GROUND_INST: instantiating (10) with all_18_0, all_7_0, all_40_1,
% 25.72/4.20 | | | simplifying with (54), (59), (64), (65) gives:
% 25.72/4.20 | | | (106) ? [v0: any] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ((v3 =
% 25.72/4.20 | | | v1 & j(v0) = v1 & j(all_40_1) = v2 & op2(all_18_0, all_40_1)
% 25.72/4.20 | | | = v0 & op1(all_7_0, v2) = v1 & $i(v2) & $i(v1) & $i(v0)) | (
% 25.72/4.20 | | | ~ (v0 = 0) & sorti2(all_18_0) = v0))
% 25.72/4.20 | | |
% 25.72/4.20 | | | GROUND_INST: instantiating (2) with all_40_1, all_40_1, simplifying with
% 25.72/4.20 | | | (64), (65) gives:
% 25.72/4.20 | | | (107) ? [v0: $i] : (op2(all_40_1, all_40_1) = v0 & sorti2(v0) = 0 &
% 25.72/4.20 | | | $i(v0))
% 25.72/4.20 | | |
% 25.72/4.20 | | | GROUND_INST: instantiating (69) with all_40_1, simplifying with (64), (65)
% 25.72/4.20 | | | gives:
% 25.72/4.20 | | | (108) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (j(v0) = v1 &
% 25.72/4.20 | | | j(all_40_1) = v2 & op2(all_18_0, all_40_1) = v0 & op1(all_42_0,
% 25.72/4.20 | | | v2) = v1 & $i(v2) & $i(v1) & $i(v0))
% 25.72/4.20 | | |
% 25.72/4.20 | | | GROUND_INST: instantiating (8) with all_40_1, simplifying with (64), (65)
% 25.72/4.20 | | | gives:
% 25.72/4.20 | | | (109) ? [v0: $i] : (j(all_40_1) = v0 & h(v0) = all_40_1 & $i(v0))
% 25.72/4.20 | | |
% 25.72/4.20 | | | GROUND_INST: instantiating (7) with all_40_1, simplifying with (64), (65)
% 25.72/4.20 | | | gives:
% 25.72/4.20 | | | (110) ? [v0: $i] : (j(all_40_1) = v0 & sorti1(v0) = 0 & $i(v0))
% 25.72/4.20 | | |
% 25.72/4.20 | | | GROUND_INST: instantiating (6) with all_40_1, simplifying with (64), (65)
% 25.72/4.20 | | | gives:
% 25.72/4.20 | | | (111) ? [v0: $i] : (j(all_40_1) = v0 & $i(v0) & ! [v1: $i] : ! [v2:
% 25.72/4.20 | | | $i] : ( ~ (j(v1) = v2) | ~ $i(v1) | ? [v3: int] : ? [v4:
% 25.72/4.20 | | | $i] : ? [v5: $i] : ? [v6: $i] : ((v6 = v5 & j(v4) = v5 &
% 25.72/4.20 | | | op2(all_40_1, v1) = v4 & op1(v0, v2) = v5 & $i(v5) &
% 25.72/4.20 | | | $i(v4)) | ( ~ (v3 = 0) & sorti2(v1) = v3))) & ! [v1: $i]
% 25.72/4.20 | | | : ! [v2: $i] : ( ~ (op2(all_40_1, v1) = v2) | ~ $i(v1) | ?
% 25.72/4.20 | | | [v3: int] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ((v6 =
% 25.72/4.20 | | | v4 & j(v2) = v4 & j(v1) = v5 & op1(v0, v5) = v4 & $i(v5)
% 25.72/4.20 | | | & $i(v4)) | ( ~ (v3 = 0) & sorti2(v1) = v3))) & ! [v1:
% 25.72/4.20 | | | $i] : ( ~ (sorti2(v1) = 0) | ~ $i(v1) | ? [v2: $i] : ?
% 25.72/4.20 | | | [v3: $i] : ? [v4: $i] : (j(v2) = v3 & j(v1) = v4 &
% 25.72/4.20 | | | op2(all_40_1, v1) = v2 & op1(v0, v4) = v3 & $i(v4) & $i(v3)
% 25.72/4.20 | | | & $i(v2))))
% 25.72/4.20 | | |
% 25.72/4.20 | | | DELTA: instantiating (110) with fresh symbol all_70_0 gives:
% 25.72/4.20 | | | (112) j(all_40_1) = all_70_0 & sorti1(all_70_0) = 0 & $i(all_70_0)
% 25.72/4.20 | | |
% 25.72/4.20 | | | ALPHA: (112) implies:
% 25.72/4.20 | | | (113) sorti1(all_70_0) = 0
% 25.72/4.20 | | | (114) j(all_40_1) = all_70_0
% 25.72/4.20 | | |
% 25.72/4.20 | | | DELTA: instantiating (109) with fresh symbol all_72_0 gives:
% 25.72/4.20 | | | (115) j(all_40_1) = all_72_0 & h(all_72_0) = all_40_1 & $i(all_72_0)
% 25.72/4.20 | | |
% 25.72/4.20 | | | ALPHA: (115) implies:
% 25.72/4.21 | | | (116) $i(all_72_0)
% 25.72/4.21 | | | (117) j(all_40_1) = all_72_0
% 25.72/4.21 | | |
% 25.72/4.21 | | | DELTA: instantiating (107) with fresh symbol all_74_0 gives:
% 25.72/4.21 | | | (118) op2(all_40_1, all_40_1) = all_74_0 & sorti2(all_74_0) = 0 &
% 25.72/4.21 | | | $i(all_74_0)
% 25.72/4.21 | | |
% 25.72/4.21 | | | ALPHA: (118) implies:
% 25.72/4.21 | | | (119) $i(all_74_0)
% 25.72/4.21 | | | (120) sorti2(all_74_0) = 0
% 25.72/4.21 | | | (121) op2(all_40_1, all_40_1) = all_74_0
% 25.72/4.21 | | |
% 25.72/4.21 | | | DELTA: instantiating (108) with fresh symbols all_83_0, all_83_1, all_83_2
% 25.72/4.21 | | | gives:
% 25.72/4.21 | | | (122) j(all_83_2) = all_83_1 & j(all_40_1) = all_83_0 & op2(all_18_0,
% 25.72/4.21 | | | all_40_1) = all_83_2 & op1(all_42_0, all_83_0) = all_83_1 &
% 25.72/4.21 | | | $i(all_83_0) & $i(all_83_1) & $i(all_83_2)
% 25.72/4.21 | | |
% 25.72/4.21 | | | ALPHA: (122) implies:
% 25.72/4.21 | | | (123) j(all_40_1) = all_83_0
% 25.72/4.21 | | |
% 25.72/4.21 | | | DELTA: instantiating (106) with fresh symbols all_85_0, all_85_1,
% 25.72/4.21 | | | all_85_2, all_85_3 gives:
% 25.72/4.21 | | | (124) (all_85_0 = all_85_2 & j(all_85_3) = all_85_2 & j(all_40_1) =
% 25.72/4.21 | | | all_85_1 & op2(all_18_0, all_40_1) = all_85_3 & op1(all_7_0,
% 25.72/4.21 | | | all_85_1) = all_85_2 & $i(all_85_1) & $i(all_85_2) &
% 25.72/4.21 | | | $i(all_85_3)) | ( ~ (all_85_3 = 0) & sorti2(all_18_0) =
% 25.72/4.21 | | | all_85_3)
% 25.72/4.21 | | |
% 25.72/4.21 | | | DELTA: instantiating (111) with fresh symbol all_86_0 gives:
% 25.72/4.21 | | | (125) j(all_40_1) = all_86_0 & $i(all_86_0) & ! [v0: $i] : ! [v1: $i]
% 25.72/4.21 | | | : ( ~ (j(v0) = v1) | ~ $i(v0) | ? [v2: int] : ? [v3: $i] : ?
% 25.72/4.21 | | | [v4: $i] : ? [v5: $i] : ((v5 = v4 & j(v3) = v4 & op2(all_40_1,
% 25.72/4.21 | | | v0) = v3 & op1(all_86_0, v1) = v4 & $i(v4) & $i(v3)) | (
% 25.72/4.21 | | | ~ (v2 = 0) & sorti2(v0) = v2))) & ! [v0: $i] : ! [v1: $i]
% 25.72/4.21 | | | : ( ~ (op2(all_40_1, v0) = v1) | ~ $i(v0) | ? [v2: int] : ?
% 25.72/4.21 | | | [v3: $i] : ? [v4: $i] : ? [v5: $i] : ((v5 = v3 & j(v1) = v3 &
% 25.72/4.21 | | | j(v0) = v4 & op1(all_86_0, v4) = v3 & $i(v4) & $i(v3)) | (
% 25.72/4.21 | | | ~ (v2 = 0) & sorti2(v0) = v2))) & ! [v0: $i] : ( ~
% 25.72/4.21 | | | (sorti2(v0) = 0) | ~ $i(v0) | ? [v1: $i] : ? [v2: $i] : ?
% 25.72/4.21 | | | [v3: $i] : (j(v1) = v2 & j(v0) = v3 & op2(all_40_1, v0) = v1 &
% 25.72/4.21 | | | op1(all_86_0, v3) = v2 & $i(v3) & $i(v2) & $i(v1)))
% 25.72/4.21 | | |
% 25.72/4.21 | | | ALPHA: (125) implies:
% 25.72/4.21 | | | (126) j(all_40_1) = all_86_0
% 25.72/4.21 | | | (127) ! [v0: $i] : ( ~ (sorti2(v0) = 0) | ~ $i(v0) | ? [v1: $i] : ?
% 25.72/4.21 | | | [v2: $i] : ? [v3: $i] : (j(v1) = v2 & j(v0) = v3 &
% 25.72/4.21 | | | op2(all_40_1, v0) = v1 & op1(all_86_0, v3) = v2 & $i(v3) &
% 25.72/4.21 | | | $i(v2) & $i(v1)))
% 25.72/4.21 | | | (128) ! [v0: $i] : ! [v1: $i] : ( ~ (op2(all_40_1, v0) = v1) | ~
% 25.72/4.21 | | | $i(v0) | ? [v2: int] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i]
% 25.72/4.21 | | | : ((v5 = v3 & j(v1) = v3 & j(v0) = v4 & op1(all_86_0, v4) = v3
% 25.72/4.21 | | | & $i(v4) & $i(v3)) | ( ~ (v2 = 0) & sorti2(v0) = v2)))
% 25.72/4.21 | | |
% 25.72/4.21 | | | GROUND_INST: instantiating (127) with all_18_0, simplifying with (29),
% 25.72/4.21 | | | (59) gives:
% 25.72/4.21 | | | (129) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (j(v0) = v1 &
% 25.72/4.21 | | | j(all_18_0) = v2 & op2(all_40_1, all_18_0) = v0 & op1(all_86_0,
% 25.72/4.21 | | | v2) = v1 & $i(v2) & $i(v1) & $i(v0))
% 25.72/4.21 | | |
% 25.72/4.21 | | | GROUND_INST: instantiating (127) with all_40_1, simplifying with (64),
% 25.72/4.21 | | | (65) gives:
% 25.72/4.21 | | | (130) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (j(v0) = v1 &
% 25.72/4.21 | | | j(all_40_1) = v2 & op2(all_40_1, all_40_1) = v0 & op1(all_86_0,
% 25.72/4.21 | | | v2) = v1 & $i(v2) & $i(v1) & $i(v0))
% 25.72/4.21 | | |
% 25.72/4.21 | | | GROUND_INST: instantiating (128) with all_40_1, all_40_0, simplifying with
% 25.72/4.21 | | | (64), (66) gives:
% 25.72/4.21 | | | (131) ? [v0: int] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ((v3 =
% 25.72/4.21 | | | v1 & j(all_40_0) = v1 & j(all_40_1) = v2 & op1(all_86_0, v2)
% 25.72/4.21 | | | = v1 & $i(v2) & $i(v1)) | ( ~ (v0 = 0) & sorti2(all_40_1) =
% 25.72/4.21 | | | v0))
% 25.72/4.21 | | |
% 25.72/4.21 | | | DELTA: instantiating (130) with fresh symbols all_89_0, all_89_1, all_89_2
% 25.72/4.21 | | | gives:
% 25.72/4.21 | | | (132) j(all_89_2) = all_89_1 & j(all_40_1) = all_89_0 & op2(all_40_1,
% 25.72/4.21 | | | all_40_1) = all_89_2 & op1(all_86_0, all_89_0) = all_89_1 &
% 25.72/4.21 | | | $i(all_89_0) & $i(all_89_1) & $i(all_89_2)
% 25.72/4.21 | | |
% 25.72/4.21 | | | ALPHA: (132) implies:
% 25.72/4.21 | | | (133) op2(all_40_1, all_40_1) = all_89_2
% 25.72/4.21 | | | (134) j(all_40_1) = all_89_0
% 25.72/4.21 | | | (135) j(all_89_2) = all_89_1
% 25.72/4.21 | | |
% 25.72/4.21 | | | DELTA: instantiating (129) with fresh symbols all_91_0, all_91_1, all_91_2
% 25.72/4.21 | | | gives:
% 25.72/4.21 | | | (136) j(all_91_2) = all_91_1 & j(all_18_0) = all_91_0 & op2(all_40_1,
% 25.72/4.21 | | | all_18_0) = all_91_2 & op1(all_86_0, all_91_0) = all_91_1 &
% 25.72/4.21 | | | $i(all_91_0) & $i(all_91_1) & $i(all_91_2)
% 25.72/4.21 | | |
% 25.72/4.21 | | | ALPHA: (136) implies:
% 25.72/4.21 | | | (137) $i(all_91_0)
% 25.72/4.21 | | | (138) j(all_18_0) = all_91_0
% 25.72/4.21 | | |
% 25.72/4.21 | | | DELTA: instantiating (131) with fresh symbols all_94_0, all_94_1,
% 25.72/4.21 | | | all_94_2, all_94_3 gives:
% 25.72/4.21 | | | (139) (all_94_0 = all_94_2 & j(all_40_0) = all_94_2 & j(all_40_1) =
% 25.72/4.21 | | | all_94_1 & op1(all_86_0, all_94_1) = all_94_2 & $i(all_94_1) &
% 25.72/4.21 | | | $i(all_94_2)) | ( ~ (all_94_3 = 0) & sorti2(all_40_1) =
% 25.72/4.21 | | | all_94_3)
% 25.72/4.21 | | |
% 25.72/4.21 | | | BETA: splitting (124) gives:
% 25.72/4.21 | | |
% 25.72/4.21 | | | Case 1:
% 25.72/4.21 | | | |
% 25.72/4.22 | | | | (140) all_85_0 = all_85_2 & j(all_85_3) = all_85_2 & j(all_40_1) =
% 25.72/4.22 | | | | all_85_1 & op2(all_18_0, all_40_1) = all_85_3 & op1(all_7_0,
% 25.72/4.22 | | | | all_85_1) = all_85_2 & $i(all_85_1) & $i(all_85_2) &
% 25.72/4.22 | | | | $i(all_85_3)
% 25.72/4.22 | | | |
% 25.72/4.22 | | | | ALPHA: (140) implies:
% 25.72/4.22 | | | | (141) j(all_40_1) = all_85_1
% 25.72/4.22 | | | |
% 25.72/4.22 | | | | BETA: splitting (139) gives:
% 25.72/4.22 | | | |
% 25.72/4.22 | | | | Case 1:
% 25.72/4.22 | | | | |
% 25.72/4.22 | | | | | (142) all_94_0 = all_94_2 & j(all_40_0) = all_94_2 & j(all_40_1) =
% 25.72/4.22 | | | | | all_94_1 & op1(all_86_0, all_94_1) = all_94_2 & $i(all_94_1)
% 25.72/4.22 | | | | | & $i(all_94_2)
% 25.72/4.22 | | | | |
% 25.72/4.22 | | | | | ALPHA: (142) implies:
% 25.72/4.22 | | | | | (143) op1(all_86_0, all_94_1) = all_94_2
% 25.72/4.22 | | | | | (144) j(all_40_1) = all_94_1
% 25.72/4.22 | | | | | (145) j(all_40_0) = all_94_2
% 25.72/4.22 | | | | |
% 25.72/4.22 | | | | | GROUND_INST: instantiating (15) with all_40_0, all_89_2, all_40_1,
% 25.72/4.22 | | | | | all_40_1, simplifying with (66), (133) gives:
% 25.72/4.22 | | | | | (146) all_89_2 = all_40_0
% 25.72/4.22 | | | | |
% 25.72/4.22 | | | | | GROUND_INST: instantiating (15) with all_74_0, all_89_2, all_40_1,
% 25.72/4.22 | | | | | all_40_1, simplifying with (121), (133) gives:
% 25.72/4.22 | | | | | (147) all_89_2 = all_74_0
% 25.72/4.22 | | | | |
% 25.72/4.22 | | | | | GROUND_INST: instantiating (13) with all_7_0, all_91_0, all_18_0,
% 25.72/4.22 | | | | | simplifying with (54), (138) gives:
% 25.72/4.22 | | | | | (148) all_91_0 = all_7_0
% 25.72/4.22 | | | | |
% 25.72/4.22 | | | | | GROUND_INST: instantiating (13) with all_83_0, all_85_1, all_40_1,
% 25.72/4.22 | | | | | simplifying with (123), (141) gives:
% 25.72/4.22 | | | | | (149) all_85_1 = all_83_0
% 25.72/4.22 | | | | |
% 25.72/4.22 | | | | | GROUND_INST: instantiating (13) with all_83_0, all_86_0, all_40_1,
% 25.72/4.22 | | | | | simplifying with (123), (126) gives:
% 25.72/4.22 | | | | | (150) all_86_0 = all_83_0
% 25.72/4.22 | | | | |
% 25.72/4.22 | | | | | GROUND_INST: instantiating (13) with all_70_0, all_86_0, all_40_1,
% 25.72/4.22 | | | | | simplifying with (114), (126) gives:
% 25.72/4.22 | | | | | (151) all_86_0 = all_70_0
% 25.72/4.22 | | | | |
% 25.72/4.22 | | | | | GROUND_INST: instantiating (13) with all_85_1, all_89_0, all_40_1,
% 25.72/4.22 | | | | | simplifying with (134), (141) gives:
% 25.72/4.22 | | | | | (152) all_89_0 = all_85_1
% 25.72/4.22 | | | | |
% 25.72/4.22 | | | | | GROUND_INST: instantiating (13) with all_89_0, all_94_1, all_40_1,
% 25.72/4.22 | | | | | simplifying with (134), (144) gives:
% 25.72/4.22 | | | | | (153) all_94_1 = all_89_0
% 25.72/4.22 | | | | |
% 25.72/4.22 | | | | | GROUND_INST: instantiating (13) with all_72_0, all_94_1, all_40_1,
% 25.72/4.22 | | | | | simplifying with (117), (144) gives:
% 25.72/4.22 | | | | | (154) all_94_1 = all_72_0
% 25.72/4.22 | | | | |
% 25.72/4.22 | | | | | COMBINE_EQS: (153), (154) imply:
% 25.72/4.22 | | | | | (155) all_89_0 = all_72_0
% 25.72/4.22 | | | | |
% 25.72/4.22 | | | | | SIMP: (155) implies:
% 25.72/4.22 | | | | | (156) all_89_0 = all_72_0
% 25.72/4.22 | | | | |
% 25.72/4.22 | | | | | COMBINE_EQS: (152), (156) imply:
% 25.72/4.22 | | | | | (157) all_85_1 = all_72_0
% 25.72/4.22 | | | | |
% 25.72/4.22 | | | | | SIMP: (157) implies:
% 25.72/4.22 | | | | | (158) all_85_1 = all_72_0
% 25.72/4.22 | | | | |
% 25.72/4.22 | | | | | COMBINE_EQS: (146), (147) imply:
% 25.72/4.22 | | | | | (159) all_74_0 = all_40_0
% 25.72/4.22 | | | | |
% 25.72/4.22 | | | | | COMBINE_EQS: (150), (151) imply:
% 25.72/4.22 | | | | | (160) all_83_0 = all_70_0
% 25.72/4.22 | | | | |
% 25.72/4.22 | | | | | SIMP: (160) implies:
% 25.72/4.22 | | | | | (161) all_83_0 = all_70_0
% 25.72/4.22 | | | | |
% 25.72/4.22 | | | | | COMBINE_EQS: (149), (158) imply:
% 25.72/4.22 | | | | | (162) all_83_0 = all_72_0
% 25.72/4.22 | | | | |
% 25.72/4.22 | | | | | SIMP: (162) implies:
% 25.72/4.22 | | | | | (163) all_83_0 = all_72_0
% 25.72/4.22 | | | | |
% 25.72/4.22 | | | | | COMBINE_EQS: (161), (163) imply:
% 25.72/4.22 | | | | | (164) all_72_0 = all_70_0
% 25.72/4.22 | | | | |
% 25.72/4.22 | | | | | COMBINE_EQS: (154), (164) imply:
% 25.72/4.22 | | | | | (165) all_94_1 = all_70_0
% 25.72/4.22 | | | | |
% 25.72/4.22 | | | | | REDUCE: (135), (146) imply:
% 25.72/4.22 | | | | | (166) j(all_40_0) = all_89_1
% 25.72/4.22 | | | | |
% 25.72/4.22 | | | | | REDUCE: (120), (159) imply:
% 25.72/4.22 | | | | | (167) sorti2(all_40_0) = 0
% 25.72/4.22 | | | | |
% 25.72/4.22 | | | | | REDUCE: (143), (151), (165) imply:
% 25.72/4.22 | | | | | (168) op1(all_70_0, all_70_0) = all_94_2
% 25.72/4.22 | | | | |
% 25.72/4.22 | | | | | REDUCE: (119), (159) imply:
% 25.72/4.22 | | | | | (169) $i(all_40_0)
% 25.72/4.22 | | | | |
% 25.72/4.22 | | | | | REDUCE: (116), (164) imply:
% 25.72/4.22 | | | | | (170) $i(all_70_0)
% 25.72/4.22 | | | | |
% 25.72/4.22 | | | | | GROUND_INST: instantiating (13) with all_94_2, all_89_1, all_40_0,
% 25.72/4.22 | | | | | simplifying with (145), (166) gives:
% 25.72/4.22 | | | | | (171) all_94_2 = all_89_1
% 25.72/4.22 | | | | |
% 25.72/4.22 | | | | | REDUCE: (168), (171) imply:
% 25.72/4.22 | | | | | (172) op1(all_70_0, all_70_0) = all_89_1
% 25.72/4.22 | | | | |
% 25.72/4.22 | | | | | GROUND_INST: instantiating (19) with all_70_0, simplifying with (113),
% 25.72/4.22 | | | | | (170) gives:
% 25.72/4.22 | | | | | (173) op1(all_70_0, all_70_0) = all_7_0
% 25.72/4.22 | | | | |
% 25.72/4.22 | | | | | GROUND_INST: instantiating (3) with all_70_0, simplifying with (113),
% 25.72/4.22 | | | | | (170) gives:
% 25.72/4.22 | | | | | (174) ? [v0: $i] : (h(all_70_0) = v0 & $i(v0) & ! [v1: $i] : !
% 25.72/4.22 | | | | | [v2: $i] : ( ~ (h(v1) = v2) | ~ $i(v1) | ? [v3: int] : ?
% 25.72/4.22 | | | | | [v4: $i] : ? [v5: $i] : ? [v6: $i] : ((v6 = v5 & h(v4)
% 25.72/4.22 | | | | | = v5 & op2(v0, v2) = v5 & op1(all_70_0, v1) = v4 &
% 25.72/4.22 | | | | | $i(v5) & $i(v4)) | ( ~ (v3 = 0) & sorti1(v1) = v3)))
% 25.72/4.22 | | | | | & ! [v1: $i] : ! [v2: $i] : ( ~ (op1(all_70_0, v1) = v2)
% 25.72/4.22 | | | | | | ~ $i(v1) | ? [v3: int] : ? [v4: $i] : ? [v5: $i] :
% 25.72/4.22 | | | | | ? [v6: $i] : ((v6 = v4 & h(v2) = v4 & h(v1) = v5 &
% 25.72/4.22 | | | | | op2(v0, v5) = v4 & $i(v5) & $i(v4)) | ( ~ (v3 = 0) &
% 25.72/4.22 | | | | | sorti1(v1) = v3))) & ! [v1: $i] : ( ~ (sorti1(v1) =
% 25.72/4.22 | | | | | 0) | ~ $i(v1) | ? [v2: $i] : ? [v3: $i] : ? [v4:
% 25.72/4.22 | | | | | $i] : (h(v2) = v3 & h(v1) = v4 & op2(v0, v4) = v3 &
% 25.72/4.22 | | | | | op1(all_70_0, v1) = v2 & $i(v4) & $i(v3) & $i(v2))))
% 25.72/4.22 | | | | |
% 25.72/4.22 | | | | | GROUND_INST: instantiating (9) with all_40_0, all_89_1, simplifying
% 25.72/4.22 | | | | | with (166), (169) gives:
% 25.72/4.22 | | | | | (175) ? [v0: int] : ? [v1: int] : ((v1 = all_40_0 & h(all_89_1) =
% 25.72/4.22 | | | | | all_40_0) | ( ~ (v0 = 0) & sorti2(all_40_0) = v0))
% 25.72/4.22 | | | | |
% 25.72/4.22 | | | | | DELTA: instantiating (175) with fresh symbols all_217_0, all_217_1
% 25.72/4.22 | | | | | gives:
% 25.72/4.22 | | | | | (176) (all_217_0 = all_40_0 & h(all_89_1) = all_40_0) | ( ~
% 25.72/4.22 | | | | | (all_217_1 = 0) & sorti2(all_40_0) = all_217_1)
% 25.72/4.22 | | | | |
% 25.72/4.22 | | | | | DELTA: instantiating (174) with fresh symbol all_323_0 gives:
% 25.72/4.23 | | | | | (177) h(all_70_0) = all_323_0 & $i(all_323_0) & ! [v0: $i] : !
% 25.72/4.23 | | | | | [v1: $i] : ( ~ (h(v0) = v1) | ~ $i(v0) | ? [v2: int] : ?
% 25.72/4.23 | | | | | [v3: $i] : ? [v4: $i] : ? [v5: $i] : ((v5 = v4 & h(v3) =
% 25.72/4.23 | | | | | v4 & op2(all_323_0, v1) = v4 & op1(all_70_0, v0) = v3 &
% 25.72/4.23 | | | | | $i(v4) & $i(v3)) | ( ~ (v2 = 0) & sorti1(v0) = v2))) &
% 25.72/4.23 | | | | | ! [v0: $i] : ! [v1: $i] : ( ~ (op1(all_70_0, v0) = v1) | ~
% 25.72/4.23 | | | | | $i(v0) | ? [v2: int] : ? [v3: $i] : ? [v4: $i] : ? [v5:
% 25.72/4.23 | | | | | $i] : ((v5 = v3 & h(v1) = v3 & h(v0) = v4 &
% 25.72/4.23 | | | | | op2(all_323_0, v4) = v3 & $i(v4) & $i(v3)) | ( ~ (v2 =
% 25.72/4.23 | | | | | 0) & sorti1(v0) = v2))) & ! [v0: $i] : ( ~
% 25.72/4.23 | | | | | (sorti1(v0) = 0) | ~ $i(v0) | ? [v1: $i] : ? [v2: $i] :
% 25.72/4.23 | | | | | ? [v3: $i] : (h(v1) = v2 & h(v0) = v3 & op2(all_323_0, v3)
% 25.72/4.23 | | | | | = v2 & op1(all_70_0, v0) = v1 & $i(v3) & $i(v2) &
% 25.72/4.23 | | | | | $i(v1)))
% 25.72/4.23 | | | | |
% 25.72/4.23 | | | | | ALPHA: (177) implies:
% 25.72/4.23 | | | | | (178) ! [v0: $i] : ( ~ (sorti1(v0) = 0) | ~ $i(v0) | ? [v1: $i]
% 25.72/4.23 | | | | | : ? [v2: $i] : ? [v3: $i] : (h(v1) = v2 & h(v0) = v3 &
% 25.72/4.23 | | | | | op2(all_323_0, v3) = v2 & op1(all_70_0, v0) = v1 & $i(v3)
% 25.72/4.23 | | | | | & $i(v2) & $i(v1)))
% 25.72/4.23 | | | | |
% 25.72/4.23 | | | | | GROUND_INST: instantiating (178) with all_7_0, simplifying with (17),
% 25.72/4.23 | | | | | (18) gives:
% 25.72/4.23 | | | | | (179) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (h(v0) = v1 &
% 25.72/4.23 | | | | | h(all_7_0) = v2 & op2(all_323_0, v2) = v1 & op1(all_70_0,
% 25.72/4.23 | | | | | all_7_0) = v0 & $i(v2) & $i(v1) & $i(v0))
% 25.72/4.23 | | | | |
% 25.72/4.23 | | | | | DELTA: instantiating (179) with fresh symbols all_397_0, all_397_1,
% 25.72/4.23 | | | | | all_397_2 gives:
% 25.72/4.23 | | | | | (180) h(all_397_2) = all_397_1 & h(all_7_0) = all_397_0 &
% 25.72/4.23 | | | | | op2(all_323_0, all_397_0) = all_397_1 & op1(all_70_0,
% 25.72/4.23 | | | | | all_7_0) = all_397_2 & $i(all_397_0) & $i(all_397_1) &
% 25.72/4.23 | | | | | $i(all_397_2)
% 25.72/4.23 | | | | |
% 25.72/4.23 | | | | | ALPHA: (180) implies:
% 25.72/4.23 | | | | | (181) h(all_7_0) = all_397_0
% 25.72/4.23 | | | | |
% 25.72/4.23 | | | | | BETA: splitting (176) gives:
% 25.72/4.23 | | | | |
% 25.72/4.23 | | | | | Case 1:
% 25.72/4.23 | | | | | |
% 25.72/4.23 | | | | | |
% 25.72/4.23 | | | | | | GROUND_INST: instantiating (14) with all_89_1, all_7_0, all_70_0,
% 25.72/4.23 | | | | | | all_70_0, simplifying with (172), (173) gives:
% 25.72/4.23 | | | | | | (182) all_89_1 = all_7_0
% 25.72/4.23 | | | | | |
% 25.72/4.23 | | | | | | BETA: splitting (176) gives:
% 25.72/4.23 | | | | | |
% 25.72/4.23 | | | | | | Case 1:
% 25.72/4.23 | | | | | | |
% 25.72/4.23 | | | | | | | (183) all_217_0 = all_40_0 & h(all_89_1) = all_40_0
% 25.72/4.23 | | | | | | |
% 25.72/4.23 | | | | | | | ALPHA: (183) implies:
% 25.72/4.23 | | | | | | | (184) h(all_89_1) = all_40_0
% 25.72/4.23 | | | | | | |
% 25.72/4.23 | | | | | | | REDUCE: (182), (184) imply:
% 25.72/4.23 | | | | | | | (185) h(all_7_0) = all_40_0
% 25.72/4.23 | | | | | | |
% 25.72/4.23 | | | | | | | GROUND_INST: instantiating (12) with all_18_0, all_397_0, all_7_0,
% 25.72/4.23 | | | | | | | simplifying with (30), (181) gives:
% 25.72/4.23 | | | | | | | (186) all_397_0 = all_18_0
% 25.72/4.23 | | | | | | |
% 25.72/4.23 | | | | | | | GROUND_INST: instantiating (12) with all_40_0, all_397_0, all_7_0,
% 25.72/4.23 | | | | | | | simplifying with (181), (185) gives:
% 25.72/4.23 | | | | | | | (187) all_397_0 = all_40_0
% 25.72/4.23 | | | | | | |
% 25.72/4.23 | | | | | | | COMBINE_EQS: (186), (187) imply:
% 25.72/4.23 | | | | | | | (188) all_40_0 = all_18_0
% 25.72/4.23 | | | | | | |
% 25.72/4.23 | | | | | | | REDUCE: (63), (188) imply:
% 25.72/4.23 | | | | | | | (189) $false
% 25.72/4.23 | | | | | | |
% 25.72/4.23 | | | | | | | CLOSE: (189) is inconsistent.
% 25.72/4.23 | | | | | | |
% 25.72/4.23 | | | | | | Case 2:
% 25.72/4.23 | | | | | | |
% 25.72/4.23 | | | | | | | (190) ~ (all_217_1 = 0) & sorti2(all_40_0) = all_217_1
% 25.72/4.23 | | | | | | |
% 25.72/4.23 | | | | | | | ALPHA: (190) implies:
% 25.72/4.23 | | | | | | | (191) ~ (all_217_1 = 0)
% 25.72/4.23 | | | | | | | (192) sorti2(all_40_0) = all_217_1
% 25.72/4.23 | | | | | | |
% 25.72/4.23 | | | | | | | REF_CLOSE: (11), (167), (191), (192) are inconsistent by sub-proof
% 25.72/4.23 | | | | | | | #1.
% 25.72/4.23 | | | | | | |
% 25.72/4.23 | | | | | | End of split
% 25.72/4.23 | | | | | |
% 25.72/4.23 | | | | | Case 2:
% 25.72/4.23 | | | | | |
% 25.72/4.23 | | | | | | (193) ~ (all_217_1 = 0) & sorti2(all_40_0) = all_217_1
% 25.72/4.23 | | | | | |
% 25.72/4.23 | | | | | | ALPHA: (193) implies:
% 25.72/4.23 | | | | | | (194) ~ (all_217_1 = 0)
% 25.72/4.23 | | | | | | (195) sorti2(all_40_0) = all_217_1
% 25.72/4.23 | | | | | |
% 25.72/4.23 | | | | | | REF_CLOSE: (11), (167), (194), (195) are inconsistent by sub-proof
% 25.72/4.23 | | | | | | #1.
% 25.72/4.23 | | | | | |
% 25.72/4.23 | | | | | End of split
% 25.72/4.23 | | | | |
% 25.72/4.23 | | | | Case 2:
% 25.72/4.23 | | | | |
% 25.72/4.23 | | | | | (196) ~ (all_94_3 = 0) & sorti2(all_40_1) = all_94_3
% 25.72/4.23 | | | | |
% 25.72/4.23 | | | | | ALPHA: (196) implies:
% 25.72/4.23 | | | | | (197) ~ (all_94_3 = 0)
% 25.72/4.23 | | | | | (198) sorti2(all_40_1) = all_94_3
% 25.72/4.23 | | | | |
% 25.72/4.23 | | | | | GROUND_INST: instantiating (11) with 0, all_94_3, all_40_1,
% 25.72/4.23 | | | | | simplifying with (65), (198) gives:
% 25.72/4.23 | | | | | (199) all_94_3 = 0
% 25.72/4.23 | | | | |
% 25.72/4.23 | | | | | REDUCE: (197), (199) imply:
% 25.72/4.23 | | | | | (200) $false
% 25.72/4.23 | | | | |
% 25.72/4.23 | | | | | CLOSE: (200) is inconsistent.
% 25.72/4.23 | | | | |
% 25.72/4.23 | | | | End of split
% 25.72/4.23 | | | |
% 25.72/4.23 | | | Case 2:
% 25.72/4.23 | | | |
% 25.72/4.23 | | | | (201) ~ (all_85_3 = 0) & sorti2(all_18_0) = all_85_3
% 25.72/4.23 | | | |
% 25.72/4.23 | | | | ALPHA: (201) implies:
% 25.72/4.23 | | | | (202) ~ (all_85_3 = 0)
% 25.72/4.23 | | | | (203) sorti2(all_18_0) = all_85_3
% 25.72/4.23 | | | |
% 25.72/4.23 | | | | GROUND_INST: instantiating (11) with 0, all_85_3, all_18_0, simplifying
% 25.72/4.23 | | | | with (29), (203) gives:
% 25.72/4.23 | | | | (204) all_85_3 = 0
% 25.72/4.23 | | | |
% 25.72/4.23 | | | | REDUCE: (202), (204) imply:
% 25.72/4.23 | | | | (205) $false
% 25.72/4.23 | | | |
% 25.72/4.23 | | | | CLOSE: (205) is inconsistent.
% 25.72/4.23 | | | |
% 25.72/4.23 | | | End of split
% 25.72/4.23 | | |
% 25.72/4.24 | | Case 2:
% 25.72/4.24 | | |
% 25.72/4.24 | | | (206) ~ (all_47_3 = 0) & sorti2(all_18_0) = all_47_3
% 25.72/4.24 | | |
% 25.72/4.24 | | | ALPHA: (206) implies:
% 25.72/4.24 | | | (207) ~ (all_47_3 = 0)
% 25.72/4.24 | | | (208) sorti2(all_18_0) = all_47_3
% 25.72/4.24 | | |
% 25.72/4.24 | | | GROUND_INST: instantiating (11) with 0, all_47_3, all_18_0, simplifying
% 25.72/4.24 | | | with (29), (208) gives:
% 25.72/4.24 | | | (209) all_47_3 = 0
% 25.72/4.24 | | |
% 25.72/4.24 | | | REDUCE: (207), (209) imply:
% 25.72/4.24 | | | (210) $false
% 25.72/4.24 | | |
% 25.72/4.24 | | | CLOSE: (210) is inconsistent.
% 25.72/4.24 | | |
% 25.72/4.24 | | End of split
% 25.72/4.24 | |
% 25.72/4.24 | Case 2:
% 25.72/4.24 | |
% 25.72/4.24 | | (211) ~ (all_48_3 = 0) & sorti2(all_18_0) = all_48_3
% 25.72/4.24 | |
% 25.72/4.24 | | ALPHA: (211) implies:
% 25.72/4.24 | | (212) ~ (all_48_3 = 0)
% 25.72/4.24 | | (213) sorti2(all_18_0) = all_48_3
% 25.72/4.24 | |
% 25.72/4.24 | | GROUND_INST: instantiating (11) with 0, all_48_3, all_18_0, simplifying with
% 25.72/4.24 | | (29), (213) gives:
% 25.72/4.24 | | (214) all_48_3 = 0
% 25.72/4.24 | |
% 25.72/4.24 | | REDUCE: (212), (214) imply:
% 25.72/4.24 | | (215) $false
% 25.72/4.24 | |
% 25.72/4.24 | | CLOSE: (215) is inconsistent.
% 25.72/4.24 | |
% 25.72/4.24 | End of split
% 25.72/4.24 |
% 25.72/4.24 End of proof
% 25.72/4.24
% 25.72/4.24 Sub-proof #1 shows that the following formulas are inconsistent:
% 25.72/4.24 ----------------------------------------------------------------
% 25.72/4.24 (1) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 25.72/4.24 (v1 = v0 | ~ (sorti2(v2) = v1) | ~ (sorti2(v2) = v0))
% 25.72/4.24 (2) sorti2(all_40_0) = all_217_1
% 25.72/4.24 (3) sorti2(all_40_0) = 0
% 25.72/4.24 (4) ~ (all_217_1 = 0)
% 25.72/4.24
% 25.72/4.24 Begin of proof
% 25.72/4.24 |
% 25.72/4.24 | GROUND_INST: instantiating (1) with 0, all_217_1, all_40_0, simplifying with
% 25.72/4.24 | (2), (3) gives:
% 25.72/4.24 | (5) all_217_1 = 0
% 25.72/4.24 |
% 25.72/4.24 | REDUCE: (4), (5) imply:
% 25.72/4.24 | (6) $false
% 25.72/4.24 |
% 25.72/4.24 | CLOSE: (6) is inconsistent.
% 25.72/4.24 |
% 25.72/4.24 End of proof
% 25.72/4.24 % SZS output end Proof for theBenchmark
% 25.72/4.24
% 25.72/4.24 3638ms
%------------------------------------------------------------------------------