TSTP Solution File: ITP004_1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : ITP004_1 : TPTP v8.1.2. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n025.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 04:08:22 EDT 2023
% Result : Theorem 28.74s 4.63s
% Output : Proof 46.49s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : ITP004_1 : TPTP v8.1.2. Bugfixed v7.5.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.35 % Computer : n025.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Sun Aug 27 13:42:39 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.62 ________ _____
% 0.20/0.62 ___ __ \_________(_)________________________________
% 0.20/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.20/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.20/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.20/0.62
% 0.20/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.62 (2023-06-19)
% 0.20/0.62
% 0.20/0.62 (c) Philipp Rümmer, 2009-2023
% 0.20/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.62 Amanda Stjerna.
% 0.20/0.62 Free software under BSD-3-Clause.
% 0.20/0.62
% 0.20/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.62
% 0.20/0.62 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.20/0.63 Running up to 7 provers in parallel.
% 0.20/0.65 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.65 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.65 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.65 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.65 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.65 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.20/0.65 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 3.62/1.21 Prover 4: Preprocessing ...
% 3.62/1.21 Prover 1: Preprocessing ...
% 3.74/1.25 Prover 6: Preprocessing ...
% 3.74/1.25 Prover 0: Preprocessing ...
% 3.74/1.25 Prover 3: Preprocessing ...
% 3.74/1.25 Prover 2: Preprocessing ...
% 3.74/1.25 Prover 5: Preprocessing ...
% 9.34/2.01 Prover 1: Warning: ignoring some quantifiers
% 9.88/2.08 Prover 4: Warning: ignoring some quantifiers
% 9.88/2.09 Prover 3: Warning: ignoring some quantifiers
% 9.88/2.12 Prover 1: Constructing countermodel ...
% 9.88/2.13 Prover 6: Proving ...
% 9.88/2.15 Prover 0: Proving ...
% 9.88/2.15 Prover 4: Constructing countermodel ...
% 9.88/2.16 Prover 3: Constructing countermodel ...
% 11.77/2.34 Prover 5: Proving ...
% 11.77/2.37 Prover 2: Proving ...
% 17.82/3.14 Prover 3: gave up
% 17.82/3.14 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 18.31/3.22 Prover 7: Preprocessing ...
% 20.57/3.51 Prover 7: Warning: ignoring some quantifiers
% 20.57/3.52 Prover 7: Constructing countermodel ...
% 21.19/3.74 Prover 1: gave up
% 21.19/3.76 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 23.03/3.84 Prover 8: Preprocessing ...
% 24.66/4.07 Prover 8: Warning: ignoring some quantifiers
% 24.85/4.10 Prover 8: Constructing countermodel ...
% 28.74/4.62 Prover 0: proved (3986ms)
% 28.74/4.62
% 28.74/4.63 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 28.74/4.63
% 28.74/4.65 Prover 2: stopped
% 28.74/4.65 Prover 5: stopped
% 28.74/4.66 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 28.74/4.66 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 28.74/4.66 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 29.29/4.71 Prover 6: stopped
% 29.29/4.72 Prover 10: Preprocessing ...
% 29.29/4.72 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 29.29/4.74 Prover 13: Preprocessing ...
% 29.29/4.75 Prover 11: Preprocessing ...
% 30.22/4.81 Prover 16: Preprocessing ...
% 30.45/4.87 Prover 10: Warning: ignoring some quantifiers
% 30.45/4.89 Prover 10: Constructing countermodel ...
% 30.45/4.97 Prover 11: Warning: ignoring some quantifiers
% 30.45/4.99 Prover 11: Constructing countermodel ...
% 31.20/5.06 Prover 16: Warning: ignoring some quantifiers
% 31.20/5.07 Prover 16: Constructing countermodel ...
% 32.26/5.10 Prover 13: Warning: ignoring some quantifiers
% 32.26/5.14 Prover 13: Constructing countermodel ...
% 33.36/5.28 Prover 8: gave up
% 33.36/5.29 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085
% 34.57/5.41 Prover 19: Preprocessing ...
% 35.67/5.59 Prover 19: Warning: ignoring some quantifiers
% 35.86/5.64 Prover 19: Constructing countermodel ...
% 35.86/5.66 Prover 10: gave up
% 45.43/6.80 Prover 4: Found proof (size 313)
% 45.43/6.80 Prover 4: proved (6157ms)
% 45.43/6.80 Prover 7: stopped
% 45.43/6.80 Prover 11: stopped
% 45.43/6.80 Prover 13: stopped
% 45.43/6.80 Prover 16: stopped
% 45.43/6.80 Prover 19: stopped
% 45.43/6.80
% 45.43/6.80 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 45.43/6.80
% 45.43/6.84 % SZS output start Proof for theBenchmark
% 45.43/6.84 Assumptions after simplification:
% 45.43/6.84 ---------------------------------
% 45.43/6.84
% 45.43/6.84 (arityeq1_2Ec_2Ebool_2E_7E_2E1)
% 45.75/6.87 mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29(mono_2Ec_2Ebool_2E_7E_2E0)
% 45.75/6.87 & ! [v0: mono_2Etyop_2Emin_2Ebool] : ! [v1: int] : (v1 = 0 | ~ (p(v0) = v1)
% 45.75/6.87 | ~ mono_2Etyop_2Emin_2Ebool(v0) | ? [v2: mono_2Etyop_2Emin_2Ebool] :
% 45.75/6.87 (mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool(mono_2Ec_2Ebool_2E_7E_2E0,
% 45.75/6.87 v0) = v2 & p(v2) = 0 & mono_2Etyop_2Emin_2Ebool(v2))) & ! [v0:
% 45.75/6.87 mono_2Etyop_2Emin_2Ebool] : ! [v1: mono_2Etyop_2Emin_2Ebool] : ( ~
% 45.75/6.87 (mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool(mono_2Ec_2Ebool_2E_7E_2E0,
% 45.75/6.87 v0) = v1) | ~ mono_2Etyop_2Emin_2Ebool(v0) | ? [v2: any] : ? [v3:
% 45.75/6.87 any] : (p(v1) = v3 & p(v0) = v2 & (v3 = 0 | v2 = 0))) & ! [v0:
% 45.75/6.87 mono_2Etyop_2Emin_2Ebool] : ! [v1: mono_2Etyop_2Emin_2Ebool] : ( ~
% 45.75/6.87 (mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool(mono_2Ec_2Ebool_2E_7E_2E0,
% 45.75/6.87 v0) = v1) | ~ mono_2Etyop_2Emin_2Ebool(v0) | ? [v2: any] : ? [v3:
% 45.75/6.87 any] : (p(v1) = v2 & p(v0) = v3 & ( ~ (v3 = 0) | ~ (v2 = 0)))) & ! [v0:
% 45.75/6.87 mono_2Etyop_2Emin_2Ebool] : ( ~ (p(v0) = 0) | ~
% 45.75/6.87 mono_2Etyop_2Emin_2Ebool(v0) | ? [v1: mono_2Etyop_2Emin_2Ebool] : ? [v2:
% 45.75/6.87 int] : ( ~ (v2 = 0) &
% 45.75/6.87 mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool(mono_2Ec_2Ebool_2E_7E_2E0,
% 45.75/6.87 v0) = v1 & p(v1) = v2 & mono_2Etyop_2Emin_2Ebool(v1)))
% 45.75/6.87
% 45.75/6.87 (arityeq1_2Ec_2Epred__set_2ECHOICE_2E1_2Emono_2EA_27a)
% 45.75/6.87 d(tyop_2Emin_2Ebool) & u(c_2Epred__set_2ECHOICE_2E0) & ! [v0: d] : ! [v1: u]
% 45.75/6.87 : ! [v2: d] : ! [v3: du] : ( ~ (tyop_2Emin_2Efun(v0, tyop_2Emin_2Ebool) =
% 45.75/6.87 v2) | ~ (s(v2, v1) = v3) | ~ d(v0) | ~ u(v1) | ? [v4: u] : ? [v5: du]
% 45.75/6.87 : ? [v6: d] : ? [v7: du] : ? [v8: u] : (c_2Epred__set_2ECHOICE_2E1(v3) =
% 45.75/6.87 v4 & tyop_2Emin_2Efun(v2, v0) = v6 & app_2E2(v7, v3) = v8 & s(v6,
% 45.75/6.87 c_2Epred__set_2ECHOICE_2E0) = v7 & s(v0, v8) = v5 & s(v0, v4) = v5 &
% 45.75/6.87 du(v7) & du(v5) & d(v6) & u(v8) & u(v4)))
% 45.75/6.87
% 45.75/6.87 (arityeq1_2Ec_2Epred__set_2EREST_2E1_2Emono_2EA_27a)
% 45.75/6.88 d(tyop_2Emin_2Ebool) & u(c_2Epred__set_2EREST_2E0) & ! [v0: d] : ! [v1: u] :
% 45.75/6.88 ! [v2: d] : ! [v3: du] : ( ~ (tyop_2Emin_2Efun(v0, tyop_2Emin_2Ebool) = v2)
% 45.75/6.88 | ~ (s(v2, v1) = v3) | ~ d(v0) | ~ u(v1) | ? [v4: u] : ? [v5: du] : ?
% 45.75/6.88 [v6: d] : ? [v7: du] : ? [v8: u] : (c_2Epred__set_2EREST_2E1(v3) = v4 &
% 45.75/6.88 tyop_2Emin_2Efun(v2, v2) = v6 & app_2E2(v7, v3) = v8 & s(v6,
% 45.75/6.88 c_2Epred__set_2EREST_2E0) = v7 & s(v2, v8) = v5 & s(v2, v4) = v5 &
% 45.75/6.88 du(v7) & du(v5) & d(v6) & u(v8) & u(v4)))
% 45.75/6.88
% 45.75/6.88 (arityeq2_2Ec_2Ebool_2EIN_2E2_2Emono_2EA_27a)
% 45.75/6.88 d(tyop_2Emin_2Ebool) & u(c_2Ebool_2EIN_2E0) & ! [v0: d] : ! [v1: u] : !
% 45.75/6.88 [v2: u] : ! [v3: du] : ! [v4: d] : ! [v5: du] : ! [v6: d] : ! [v7: d] :
% 45.75/6.88 ! [v8: du] : ! [v9: u] : ! [v10: du] : ! [v11: u] : ( ~
% 45.75/6.88 (tyop_2Emin_2Efun(v4, tyop_2Emin_2Ebool) = v6) | ~ (tyop_2Emin_2Efun(v0,
% 45.75/6.88 v6) = v7) | ~ (tyop_2Emin_2Efun(v0, tyop_2Emin_2Ebool) = v4) | ~
% 45.75/6.88 (app_2E2(v10, v5) = v11) | ~ (app_2E2(v8, v3) = v9) | ~ (s(v7,
% 45.75/6.88 c_2Ebool_2EIN_2E0) = v8) | ~ (s(v6, v9) = v10) | ~ (s(v4, v2) = v5) |
% 45.75/6.88 ~ (s(v0, v1) = v3) | ~ d(v0) | ~ u(v2) | ~ u(v1) | ? [v12: u] : ? [v13:
% 45.75/6.88 du] : ? [v14: mono_2Etyop_2Emin_2Ebool] : ? [v15: du] :
% 45.75/6.88 (c_2Ebool_2EIN_2E2(v3, v5) = v12 & j_mono_2Etyop_2Emin_2Ebool(v15) = v14 &
% 45.75/6.88 j_mono_2Etyop_2Emin_2Ebool(v13) = v14 & s(tyop_2Emin_2Ebool, v12) = v13 &
% 45.75/6.88 s(tyop_2Emin_2Ebool, v11) = v15 & mono_2Etyop_2Emin_2Ebool(v14) & du(v15)
% 45.75/6.88 & du(v13) & u(v12))) & ! [v0: d] : ! [v1: u] : ! [v2: u] : ! [v3: du]
% 45.75/6.88 : ! [v4: d] : ! [v5: du] : ! [v6: u] : ( ~ (c_2Ebool_2EIN_2E2(v3, v5) = v6)
% 45.75/6.88 | ~ (tyop_2Emin_2Efun(v0, tyop_2Emin_2Ebool) = v4) | ~ (s(v4, v2) = v5) |
% 45.75/6.88 ~ (s(v0, v1) = v3) | ~ d(v0) | ~ u(v2) | ~ u(v1) | ? [v7: du] : ? [v8:
% 45.75/6.88 mono_2Etyop_2Emin_2Ebool] : ? [v9: d] : ? [v10: d] : ? [v11: du] : ?
% 45.75/6.88 [v12: u] : ? [v13: du] : ? [v14: u] : ? [v15: du] :
% 45.75/6.88 (j_mono_2Etyop_2Emin_2Ebool(v15) = v8 & j_mono_2Etyop_2Emin_2Ebool(v7) = v8
% 45.75/6.88 & tyop_2Emin_2Efun(v4, tyop_2Emin_2Ebool) = v9 & tyop_2Emin_2Efun(v0, v9)
% 45.75/6.88 = v10 & app_2E2(v13, v5) = v14 & app_2E2(v11, v3) = v12 & s(v10,
% 45.75/6.88 c_2Ebool_2EIN_2E0) = v11 & s(v9, v12) = v13 & s(tyop_2Emin_2Ebool, v14)
% 45.75/6.88 = v15 & s(tyop_2Emin_2Ebool, v6) = v7 & mono_2Etyop_2Emin_2Ebool(v8) &
% 45.75/6.88 du(v15) & du(v13) & du(v11) & du(v7) & d(v10) & d(v9) & u(v14) & u(v12)))
% 45.75/6.88
% 45.75/6.88 (arityeq2_2Ec_2Epred__set_2ESUBSET_2E2_2Emono_2EA_27a)
% 45.75/6.88 d(tyop_2Emin_2Ebool) & u(c_2Epred__set_2ESUBSET_2E0) & ! [v0: d] : ! [v1: u]
% 45.75/6.88 : ! [v2: u] : ! [v3: d] : ! [v4: du] : ! [v5: du] : ! [v6: d] : ! [v7:
% 45.75/6.88 d] : ! [v8: du] : ! [v9: u] : ! [v10: du] : ! [v11: u] : ( ~
% 45.75/6.88 (tyop_2Emin_2Efun(v3, v6) = v7) | ~ (tyop_2Emin_2Efun(v3,
% 45.75/6.88 tyop_2Emin_2Ebool) = v6) | ~ (tyop_2Emin_2Efun(v0, tyop_2Emin_2Ebool) =
% 45.75/6.88 v3) | ~ (app_2E2(v10, v5) = v11) | ~ (app_2E2(v8, v4) = v9) | ~ (s(v7,
% 45.75/6.88 c_2Epred__set_2ESUBSET_2E0) = v8) | ~ (s(v6, v9) = v10) | ~ (s(v3, v2)
% 45.75/6.89 = v5) | ~ (s(v3, v1) = v4) | ~ d(v0) | ~ u(v2) | ~ u(v1) | ? [v12: u]
% 45.75/6.89 : ? [v13: du] : ? [v14: mono_2Etyop_2Emin_2Ebool] : ? [v15: du] :
% 45.75/6.89 (c_2Epred__set_2ESUBSET_2E2(v4, v5) = v12 & j_mono_2Etyop_2Emin_2Ebool(v15)
% 45.75/6.89 = v14 & j_mono_2Etyop_2Emin_2Ebool(v13) = v14 & s(tyop_2Emin_2Ebool, v12)
% 45.75/6.89 = v13 & s(tyop_2Emin_2Ebool, v11) = v15 & mono_2Etyop_2Emin_2Ebool(v14) &
% 45.75/6.89 du(v15) & du(v13) & u(v12))) & ! [v0: d] : ! [v1: u] : ! [v2: u] : !
% 45.75/6.89 [v3: d] : ! [v4: du] : ! [v5: du] : ! [v6: u] : ( ~
% 45.75/6.89 (c_2Epred__set_2ESUBSET_2E2(v4, v5) = v6) | ~ (tyop_2Emin_2Efun(v0,
% 45.75/6.89 tyop_2Emin_2Ebool) = v3) | ~ (s(v3, v2) = v5) | ~ (s(v3, v1) = v4) |
% 45.75/6.89 ~ d(v0) | ~ u(v2) | ~ u(v1) | ? [v7: du] : ? [v8:
% 45.75/6.89 mono_2Etyop_2Emin_2Ebool] : ? [v9: d] : ? [v10: d] : ? [v11: du] : ?
% 45.75/6.89 [v12: u] : ? [v13: du] : ? [v14: u] : ? [v15: du] :
% 45.75/6.89 (j_mono_2Etyop_2Emin_2Ebool(v15) = v8 & j_mono_2Etyop_2Emin_2Ebool(v7) = v8
% 45.75/6.89 & tyop_2Emin_2Efun(v3, v9) = v10 & tyop_2Emin_2Efun(v3, tyop_2Emin_2Ebool)
% 45.75/6.89 = v9 & app_2E2(v13, v5) = v14 & app_2E2(v11, v4) = v12 & s(v10,
% 45.75/6.89 c_2Epred__set_2ESUBSET_2E0) = v11 & s(v9, v12) = v13 &
% 45.75/6.89 s(tyop_2Emin_2Ebool, v14) = v15 & s(tyop_2Emin_2Ebool, v6) = v7 &
% 45.75/6.89 mono_2Etyop_2Emin_2Ebool(v8) & du(v15) & du(v13) & du(v11) & du(v7) &
% 45.75/6.89 d(v10) & d(v9) & u(v14) & u(v12)))
% 45.75/6.89
% 45.75/6.89 (ij_2Emono_2Etyop_2Emin_2Ebool)
% 45.75/6.89 d(tyop_2Emin_2Ebool) & ! [v0: u] : ! [v1: du] : ( ~ (s(tyop_2Emin_2Ebool,
% 45.75/6.89 v0) = v1) | ~ u(v0) | ? [v2: mono_2Etyop_2Emin_2Ebool] : ? [v3: u] :
% 45.75/6.89 (i_mono_2Etyop_2Emin_2Ebool(v2) = v3 & j_mono_2Etyop_2Emin_2Ebool(v1) = v2 &
% 45.75/6.89 s(tyop_2Emin_2Ebool, v3) = v1 & mono_2Etyop_2Emin_2Ebool(v2) & du(v1) &
% 45.75/6.89 u(v3)))
% 45.75/6.89
% 45.75/6.89 (reserved_2Eho_2Ebool__cases__ax)
% 45.75/6.89 mono_2Etyop_2Emin_2Ebool(mono_2Ec_2Ebool_2ET_2E0) &
% 45.75/6.89 mono_2Etyop_2Emin_2Ebool(mono_2Ec_2Ebool_2EF_2E0) & ? [v0:
% 45.75/6.89 mono_2Etyop_2Emin_2Ebool] : (v0 = mono_2Ec_2Ebool_2ET_2E0 | v0 =
% 45.75/6.89 mono_2Ec_2Ebool_2EF_2E0 | ~ mono_2Etyop_2Emin_2Ebool(v0))
% 45.75/6.89
% 45.75/6.89 (reserved_2Eho_2Eboolext)
% 45.75/6.89 ! [v0: mono_2Etyop_2Emin_2Ebool] : ! [v1: mono_2Etyop_2Emin_2Ebool] : !
% 45.75/6.89 [v2: int] : ! [v3: int] : (v3 = 0 | v2 = 0 | v1 = v0 | ~ (p(v1) = v3) | ~
% 45.75/6.89 (p(v0) = v2) | ~ mono_2Etyop_2Emin_2Ebool(v1) | ~
% 45.75/6.89 mono_2Etyop_2Emin_2Ebool(v0)) & ! [v0: mono_2Etyop_2Emin_2Ebool] : ! [v1:
% 45.75/6.89 mono_2Etyop_2Emin_2Ebool] : (v1 = v0 | ~ (p(v1) = 0) | ~ (p(v0) = 0) | ~
% 45.75/6.89 mono_2Etyop_2Emin_2Ebool(v1) | ~ mono_2Etyop_2Emin_2Ebool(v0))
% 45.75/6.89
% 45.75/6.89 (reserved_2Eho_2Ei__thm)
% 45.75/6.89 u(combin_i_2E0) & ! [v0: d] : ! [v1: u] : ! [v2: du] : ( ~ (s(v0, v1) = v2)
% 45.75/6.89 | ~ d(v0) | ~ u(v1) | ? [v3: d] : ? [v4: du] : ? [v5: u] :
% 45.75/6.89 (tyop_2Emin_2Efun(v0, v0) = v3 & app_2E2(v4, v2) = v5 & s(v3, combin_i_2E0)
% 45.75/6.89 = v4 & s(v0, v5) = v2 & du(v4) & du(v2) & d(v3) & u(v5)))
% 45.75/6.89
% 45.75/6.89 (reserved_2Eho_2Enotfalse)
% 45.75/6.89 mono_2Etyop_2Emin_2Ebool(mono_2Ec_2Ebool_2EF_2E0) & ? [v0: int] : ( ~ (v0 =
% 45.75/6.89 0) & p(mono_2Ec_2Ebool_2EF_2E0) = v0)
% 45.75/6.89
% 45.75/6.89 (reserved_2Eho_2Etruth)
% 45.75/6.89 p(mono_2Ec_2Ebool_2ET_2E0) = 0 &
% 45.75/6.89 mono_2Etyop_2Emin_2Ebool(mono_2Ec_2Ebool_2ET_2E0)
% 45.75/6.89
% 45.75/6.89 (reserved_2Elogic_2E_7E)
% 45.75/6.89 ! [v0: mono_2Etyop_2Emin_2Ebool] : ! [v1: int] : (v1 = 0 | ~ (p(v0) = v1) |
% 45.75/6.89 ~ mono_2Etyop_2Emin_2Ebool(v0) | ? [v2: mono_2Etyop_2Emin_2Ebool] :
% 45.75/6.89 (mono_2Ec_2Ebool_2E_7E_2E1(v0) = v2 & p(v2) = 0 &
% 45.75/6.89 mono_2Etyop_2Emin_2Ebool(v2))) & ! [v0: mono_2Etyop_2Emin_2Ebool] : !
% 45.75/6.89 [v1: mono_2Etyop_2Emin_2Ebool] : ( ~ (mono_2Ec_2Ebool_2E_7E_2E1(v0) = v1) | ~
% 45.75/6.89 mono_2Etyop_2Emin_2Ebool(v0) | ? [v2: any] : ? [v3: any] : (p(v1) = v3 &
% 45.75/6.89 p(v0) = v2 & (v3 = 0 | v2 = 0))) & ! [v0: mono_2Etyop_2Emin_2Ebool] : !
% 45.75/6.89 [v1: mono_2Etyop_2Emin_2Ebool] : ( ~ (mono_2Ec_2Ebool_2E_7E_2E1(v0) = v1) | ~
% 45.75/6.89 mono_2Etyop_2Emin_2Ebool(v0) | ? [v2: any] : ? [v3: any] : (p(v1) = v2 &
% 45.75/6.89 p(v0) = v3 & ( ~ (v3 = 0) | ~ (v2 = 0)))) & ! [v0:
% 45.75/6.89 mono_2Etyop_2Emin_2Ebool] : ( ~ (p(v0) = 0) | ~
% 45.75/6.89 mono_2Etyop_2Emin_2Ebool(v0) | ? [v1: mono_2Etyop_2Emin_2Ebool] : ? [v2:
% 45.75/6.89 int] : ( ~ (v2 = 0) & mono_2Ec_2Ebool_2E_7E_2E1(v0) = v1 & p(v1) = v2 &
% 45.75/6.89 mono_2Etyop_2Emin_2Ebool(v1)))
% 45.75/6.89
% 45.75/6.89 (thm_2Epred__set_2EIN__DELETE)
% 45.75/6.90 d(tyop_2Emin_2Ebool) & ! [v0: d] : ! [v1: u] : ! [v2: u] : ! [v3: u] : !
% 45.75/6.90 [v4: du] : ! [v5: d] : ! [v6: du] : ! [v7: du] : ! [v8: u] : ! [v9: du] :
% 45.75/6.90 ! [v10: u] : (v7 = v4 | ~ (c_2Ebool_2EIN_2E2(v4, v9) = v10) | ~
% 45.75/6.90 (c_2Epred__set_2EDELETE_2E2(v6, v7) = v8) | ~ (tyop_2Emin_2Efun(v0,
% 45.75/6.90 tyop_2Emin_2Ebool) = v5) | ~ (s(v5, v8) = v9) | ~ (s(v5, v1) = v6) |
% 45.75/6.90 ~ (s(v0, v3) = v7) | ~ (s(v0, v2) = v4) | ~ d(v0) | ~ u(v3) | ~ u(v2) |
% 45.75/6.90 ~ u(v1) | ? [v11: u] : ? [v12: du] : ? [v13: mono_2Etyop_2Emin_2Ebool] :
% 45.75/6.90 ? [v14: any] : ? [v15: du] : ? [v16: mono_2Etyop_2Emin_2Ebool] : ? [v17:
% 45.75/6.90 any] : (c_2Ebool_2EIN_2E2(v4, v6) = v11 & j_mono_2Etyop_2Emin_2Ebool(v15)
% 45.75/6.90 = v16 & j_mono_2Etyop_2Emin_2Ebool(v12) = v13 & p(v16) = v17 & p(v13) =
% 45.75/6.90 v14 & s(tyop_2Emin_2Ebool, v11) = v12 & s(tyop_2Emin_2Ebool, v10) = v15 &
% 45.75/6.90 mono_2Etyop_2Emin_2Ebool(v16) & mono_2Etyop_2Emin_2Ebool(v13) & du(v15) &
% 45.75/6.90 du(v12) & u(v11) & ( ~ (v14 = 0) | v17 = 0))) & ! [v0: d] : ! [v1: u] :
% 45.75/6.90 ! [v2: u] : ! [v3: u] : ! [v4: du] : ! [v5: d] : ! [v6: du] : ! [v7: du]
% 45.75/6.90 : ! [v8: u] : ! [v9: du] : ! [v10: u] : ( ~ (c_2Ebool_2EIN_2E2(v4, v9) =
% 45.75/6.90 v10) | ~ (c_2Epred__set_2EDELETE_2E2(v6, v7) = v8) | ~
% 45.75/6.90 (tyop_2Emin_2Efun(v0, tyop_2Emin_2Ebool) = v5) | ~ (s(v5, v8) = v9) | ~
% 45.75/6.90 (s(v5, v1) = v6) | ~ (s(v0, v3) = v7) | ~ (s(v0, v2) = v4) | ~ d(v0) | ~
% 45.75/6.90 u(v3) | ~ u(v2) | ~ u(v1) | ? [v11: du] : ? [v12:
% 45.75/6.90 mono_2Etyop_2Emin_2Ebool] : ? [v13: any] : ? [v14: u] : ? [v15: du] :
% 45.75/6.90 ? [v16: mono_2Etyop_2Emin_2Ebool] : ? [v17: any] : (c_2Ebool_2EIN_2E2(v4,
% 45.75/6.90 v6) = v14 & j_mono_2Etyop_2Emin_2Ebool(v15) = v16 &
% 45.75/6.90 j_mono_2Etyop_2Emin_2Ebool(v11) = v12 & p(v16) = v17 & p(v12) = v13 &
% 45.75/6.90 s(tyop_2Emin_2Ebool, v14) = v15 & s(tyop_2Emin_2Ebool, v10) = v11 &
% 45.75/6.90 mono_2Etyop_2Emin_2Ebool(v16) & mono_2Etyop_2Emin_2Ebool(v12) & du(v15) &
% 45.75/6.90 du(v11) & u(v14) & ( ~ (v13 = 0) | (v17 = 0 & ~ (v7 = v4)))))
% 45.75/6.90
% 45.75/6.90 (thm_2Epred__set_2EREST__DEF)
% 45.75/6.90 d(tyop_2Emin_2Ebool) & ! [v0: d] : ! [v1: u] : ! [v2: d] : ! [v3: du] : (
% 45.75/6.90 ~ (tyop_2Emin_2Efun(v0, tyop_2Emin_2Ebool) = v2) | ~ (s(v2, v1) = v3) | ~
% 45.75/6.90 d(v0) | ~ u(v1) | ? [v4: u] : ? [v5: du] : ? [v6: u] : ? [v7: du] : ?
% 45.75/6.90 [v8: u] : (c_2Epred__set_2EREST_2E1(v3) = v4 &
% 45.75/6.90 c_2Epred__set_2EDELETE_2E2(v3, v7) = v8 & c_2Epred__set_2ECHOICE_2E1(v3) =
% 45.75/6.90 v6 & s(v2, v8) = v5 & s(v2, v4) = v5 & s(v0, v6) = v7 & du(v7) & du(v5) &
% 45.75/6.90 u(v8) & u(v6) & u(v4)))
% 45.75/6.90
% 45.75/6.90 (thm_2Epred__set_2EREST__SUBSET)
% 45.75/6.90 d(tyop_2Emin_2Ebool) & ? [v0: d] : ? [v1: u] : ? [v2: d] : ? [v3: du] : ?
% 45.75/6.90 [v4: u] : ? [v5: du] : ? [v6: u] : ? [v7: du] : ? [v8:
% 45.75/6.90 mono_2Etyop_2Emin_2Ebool] : ? [v9: int] : ( ~ (v9 = 0) &
% 45.75/6.90 c_2Epred__set_2ESUBSET_2E2(v5, v3) = v6 & c_2Epred__set_2EREST_2E1(v3) = v4
% 45.75/6.90 & j_mono_2Etyop_2Emin_2Ebool(v7) = v8 & p(v8) = v9 & tyop_2Emin_2Efun(v0,
% 45.75/6.90 tyop_2Emin_2Ebool) = v2 & s(v2, v4) = v5 & s(v2, v1) = v3 &
% 45.75/6.90 s(tyop_2Emin_2Ebool, v6) = v7 & mono_2Etyop_2Emin_2Ebool(v8) & du(v7) &
% 45.75/6.90 du(v5) & du(v3) & d(v2) & d(v0) & u(v6) & u(v4) & u(v1))
% 45.75/6.90
% 45.75/6.90 (thm_2Epred__set_2ESUBSET__DEF)
% 45.75/6.90 d(tyop_2Emin_2Ebool) & ! [v0: d] : ! [v1: u] : ! [v2: u] : ! [v3: d] : !
% 45.75/6.90 [v4: du] : ! [v5: du] : ! [v6: u] : ! [v7: u] : ! [v8: du] : ( ~
% 45.75/6.90 (c_2Epred__set_2ESUBSET_2E2(v4, v5) = v6) | ~ (tyop_2Emin_2Efun(v0,
% 45.75/6.90 tyop_2Emin_2Ebool) = v3) | ~ (s(v3, v2) = v5) | ~ (s(v3, v1) = v4) |
% 45.75/6.90 ~ (s(v0, v7) = v8) | ~ d(v0) | ~ u(v7) | ~ u(v2) | ~ u(v1) | ? [v9:
% 45.75/6.90 any] : ? [v10: any] : ? [v11: any] : ? [v12: any] : ? [v13: u] : ?
% 45.75/6.90 [v14: du] : ? [v15: mono_2Etyop_2Emin_2Ebool] : ? [v16: any] : (( ~ (v11 =
% 45.75/6.90 0) & j_mono_2Etyop_2Emin_2Ebool(v9) = v10 & p(v10) = v11 &
% 45.75/6.90 s(tyop_2Emin_2Ebool, v6) = v9 & mono_2Etyop_2Emin_2Ebool(v10) & du(v9))
% 45.75/6.90 | (c_2Ebool_2EIN_2E2(v8, v5) = v13 & c_2Ebool_2EIN_2E2(v8, v4) = v9 &
% 45.75/6.90 j_mono_2Etyop_2Emin_2Ebool(v14) = v15 & j_mono_2Etyop_2Emin_2Ebool(v10)
% 45.75/6.90 = v11 & p(v15) = v16 & p(v11) = v12 & s(tyop_2Emin_2Ebool, v13) = v14 &
% 45.75/6.91 s(tyop_2Emin_2Ebool, v9) = v10 & mono_2Etyop_2Emin_2Ebool(v15) &
% 45.75/6.91 mono_2Etyop_2Emin_2Ebool(v11) & du(v14) & du(v10) & u(v13) & u(v9) & ( ~
% 45.75/6.91 (v12 = 0) | v16 = 0)))) & ! [v0: d] : ! [v1: u] : ! [v2: u] : !
% 45.75/6.91 [v3: d] : ! [v4: du] : ! [v5: du] : ! [v6: u] : ( ~
% 45.75/6.91 (c_2Epred__set_2ESUBSET_2E2(v4, v5) = v6) | ~ (tyop_2Emin_2Efun(v0,
% 45.75/6.91 tyop_2Emin_2Ebool) = v3) | ~ (s(v3, v2) = v5) | ~ (s(v3, v1) = v4) |
% 45.75/6.91 ~ d(v0) | ~ u(v2) | ~ u(v1) | ? [v7: du] : ? [v8:
% 45.75/6.91 mono_2Etyop_2Emin_2Ebool] : ? [v9: int] : ? [v10: u] : ? [v11: du] : ?
% 45.75/6.91 [v12: u] : ? [v13: du] : ? [v14: mono_2Etyop_2Emin_2Ebool] : ? [v15: int]
% 45.75/6.91 : ? [v16: u] : ? [v17: du] : ? [v18: mono_2Etyop_2Emin_2Ebool] : ? [v19:
% 45.75/6.91 int] : (u(v10) & ((v15 = 0 & ~ (v19 = 0) & c_2Ebool_2EIN_2E2(v11, v5) =
% 45.75/6.91 v16 & c_2Ebool_2EIN_2E2(v11, v4) = v12 &
% 45.75/6.91 j_mono_2Etyop_2Emin_2Ebool(v17) = v18 &
% 45.75/6.91 j_mono_2Etyop_2Emin_2Ebool(v13) = v14 & p(v18) = v19 & p(v14) = 0 &
% 45.75/6.91 s(v0, v10) = v11 & s(tyop_2Emin_2Ebool, v16) = v17 &
% 45.75/6.91 s(tyop_2Emin_2Ebool, v12) = v13 & mono_2Etyop_2Emin_2Ebool(v18) &
% 45.75/6.91 mono_2Etyop_2Emin_2Ebool(v14) & du(v17) & du(v13) & du(v11) & u(v16) &
% 45.75/6.91 u(v12)) | (v9 = 0 & j_mono_2Etyop_2Emin_2Ebool(v7) = v8 & p(v8) = 0 &
% 45.75/6.91 s(tyop_2Emin_2Ebool, v6) = v7 & mono_2Etyop_2Emin_2Ebool(v8) &
% 45.75/6.91 du(v7)))))
% 45.75/6.91
% 45.75/6.91 (function-axioms)
% 45.75/6.91 ! [v0: u] : ! [v1: u] : ! [v2: du] : ! [v3: du] : (v1 = v0 | ~
% 45.75/6.91 (c_2Epred__set_2ESUBSET_2E2(v3, v2) = v1) | ~
% 45.75/6.91 (c_2Epred__set_2ESUBSET_2E2(v3, v2) = v0)) & ! [v0: u] : ! [v1: u] : !
% 45.75/6.91 [v2: du] : ! [v3: du] : (v1 = v0 | ~ (c_2Ebool_2EIN_2E2(v3, v2) = v1) | ~
% 45.75/6.91 (c_2Ebool_2EIN_2E2(v3, v2) = v0)) & ! [v0: u] : ! [v1: u] : ! [v2: du] :
% 45.75/6.91 ! [v3: du] : (v1 = v0 | ~ (c_2Epred__set_2EDELETE_2E2(v3, v2) = v1) | ~
% 45.75/6.91 (c_2Epred__set_2EDELETE_2E2(v3, v2) = v0)) & ! [v0:
% 45.75/6.91 mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29] : !
% 45.75/6.91 [v1: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29] : !
% 45.75/6.91 [v2: mono_2Etyop_2Emin_2Ebool] : ! [v3:
% 45.75/6.91 mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29]
% 45.75/6.91 : (v1 = v0 | ~
% 45.75/6.91 (mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29(v3,
% 45.75/6.91 v2) = v1) | ~
% 45.75/6.91 (mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29(v3,
% 45.75/6.91 v2) = v0)) & ! [v0: mono_2Etyop_2Emin_2Ebool] : ! [v1:
% 45.75/6.91 mono_2Etyop_2Emin_2Ebool] : ! [v2: mono_2Etyop_2Emin_2Ebool] : ! [v3:
% 45.75/6.91 mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29] : (v1 =
% 45.75/6.91 v0 | ~
% 45.75/6.91 (mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool(v3,
% 45.75/6.91 v2) = v1) | ~
% 45.75/6.91 (mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool(v3,
% 45.75/6.91 v2) = v0)) & ! [v0: u] : ! [v1: u] : ! [v2: du] : ! [v3: du] : (v1 =
% 45.75/6.91 v0 | ~ (c_2Emin_2E_3D_2E2(v3, v2) = v1) | ~ (c_2Emin_2E_3D_2E2(v3, v2) =
% 45.75/6.91 v0)) & ! [v0: mono_2Etyop_2Emin_2Ebool] : ! [v1:
% 45.75/6.91 mono_2Etyop_2Emin_2Ebool] : ! [v2: mono_2Etyop_2Emin_2Ebool] : ! [v3:
% 45.75/6.91 mono_2Etyop_2Emin_2Ebool] : (v1 = v0 | ~
% 45.75/6.91 (mono_2Ec_2Emin_2E_3D_3D_3E_2E2(v3, v2) = v1) | ~
% 45.75/6.91 (mono_2Ec_2Emin_2E_3D_3D_3E_2E2(v3, v2) = v0)) & ! [v0:
% 45.75/6.91 mono_2Etyop_2Emin_2Ebool] : ! [v1: mono_2Etyop_2Emin_2Ebool] : ! [v2:
% 45.75/6.91 mono_2Etyop_2Emin_2Ebool] : ! [v3: mono_2Etyop_2Emin_2Ebool] : (v1 = v0 |
% 45.75/6.91 ~ (mono_2Ec_2Ebool_2E_5C_2F_2E2(v3, v2) = v1) | ~
% 45.75/6.91 (mono_2Ec_2Ebool_2E_5C_2F_2E2(v3, v2) = v0)) & ! [v0:
% 45.75/6.91 mono_2Etyop_2Emin_2Ebool] : ! [v1: mono_2Etyop_2Emin_2Ebool] : ! [v2:
% 45.75/6.91 mono_2Etyop_2Emin_2Ebool] : ! [v3: mono_2Etyop_2Emin_2Ebool] : (v1 = v0 |
% 45.75/6.91 ~ (mono_2Ec_2Ebool_2E_2F_5C_2E2(v3, v2) = v1) | ~
% 45.75/6.91 (mono_2Ec_2Ebool_2E_2F_5C_2E2(v3, v2) = v0)) & ! [v0: d] : ! [v1: d] : !
% 45.75/6.91 [v2: d] : ! [v3: d] : (v1 = v0 | ~ (tyop_2Emin_2Efun(v3, v2) = v1) | ~
% 45.75/6.91 (tyop_2Emin_2Efun(v3, v2) = v0)) & ! [v0: u] : ! [v1: u] : ! [v2: du] :
% 45.75/6.91 ! [v3: du] : (v1 = v0 | ~ (app_2E2(v3, v2) = v1) | ~ (app_2E2(v3, v2) = v0))
% 45.75/6.91 & ! [v0: du] : ! [v1: du] : ! [v2: u] : ! [v3: d] : (v1 = v0 | ~ (s(v3,
% 45.75/6.91 v2) = v1) | ~ (s(v3, v2) = v0)) & ! [v0: u] : ! [v1: u] : ! [v2: du]
% 45.75/6.91 : (v1 = v0 | ~ (c_2Epred__set_2EREST_2E1(v2) = v1) | ~
% 45.75/6.91 (c_2Epred__set_2EREST_2E1(v2) = v0)) & ! [v0: u] : ! [v1: u] : ! [v2: du]
% 45.75/6.91 : (v1 = v0 | ~ (c_2Epred__set_2ECHOICE_2E1(v2) = v1) | ~
% 45.75/6.91 (c_2Epred__set_2ECHOICE_2E1(v2) = v0)) & ! [v0:
% 45.75/6.91 mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29]
% 45.75/6.91 : ! [v1:
% 45.75/6.91 mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29]
% 45.75/6.91 : ! [v2: du] : (v1 = v0 | ~
% 45.75/6.91 (j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29(v2)
% 45.75/6.91 = v1) | ~
% 45.75/6.91 (j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29(v2)
% 45.75/6.91 = v0)) & ! [v0: u] : ! [v1: u] : ! [v2:
% 45.75/6.91 mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29]
% 45.75/6.91 : (v1 = v0 | ~
% 45.75/6.91 (i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29(v2)
% 45.75/6.91 = v1) | ~
% 45.75/6.91 (i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29(v2)
% 45.75/6.91 = v0)) & ! [v0:
% 45.75/6.91 mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29] : !
% 45.75/6.91 [v1: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29] : !
% 45.75/6.91 [v2: du] : (v1 = v0 | ~
% 45.75/6.91 (j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29(v2) =
% 45.75/6.91 v1) | ~
% 45.75/6.91 (j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29(v2) =
% 45.75/6.91 v0)) & ! [v0: u] : ! [v1: u] : ! [v2:
% 45.75/6.91 mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29] : (v1 =
% 45.75/6.91 v0 | ~
% 45.75/6.91 (i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29(v2) =
% 45.75/6.91 v1) | ~
% 45.75/6.91 (i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29(v2) =
% 45.75/6.91 v0)) & ! [v0: u] : ! [v1: u] : ! [v2: mono_2Etyop_2Emin_2Ebool] : (v1 =
% 45.75/6.91 v0 | ~ (i_mono_2Etyop_2Emin_2Ebool(v2) = v1) | ~
% 45.75/6.91 (i_mono_2Etyop_2Emin_2Ebool(v2) = v0)) & ! [v0: u] : ! [v1: u] : ! [v2:
% 45.75/6.91 du] : (v1 = v0 | ~ (c_2Ebool_2E_3F_2E1(v2) = v1) | ~
% 45.75/6.91 (c_2Ebool_2E_3F_2E1(v2) = v0)) & ! [v0: u] : ! [v1: u] : ! [v2: du] : (v1
% 45.75/6.91 = v0 | ~ (c_2Ebool_2E_21_2E1(v2) = v1) | ~ (c_2Ebool_2E_21_2E1(v2) = v0))
% 45.75/6.91 & ! [v0: mono_2Etyop_2Emin_2Ebool] : ! [v1: mono_2Etyop_2Emin_2Ebool] : !
% 45.75/6.91 [v2: du] : (v1 = v0 | ~ (j_mono_2Etyop_2Emin_2Ebool(v2) = v1) | ~
% 45.75/6.91 (j_mono_2Etyop_2Emin_2Ebool(v2) = v0)) & ! [v0: mono_2Etyop_2Emin_2Ebool] :
% 45.75/6.91 ! [v1: mono_2Etyop_2Emin_2Ebool] : ! [v2: mono_2Etyop_2Emin_2Ebool] : (v1 =
% 45.75/6.91 v0 | ~ (mono_2Ec_2Ebool_2E_7E_2E1(v2) = v1) | ~
% 45.75/6.91 (mono_2Ec_2Ebool_2E_7E_2E1(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 45.75/6.91 MultipleValueBool] : ! [v2: mono_2Etyop_2Emin_2Ebool] : (v1 = v0 | ~
% 45.75/6.91 (p(v2) = v1) | ~ (p(v2) = v0))
% 45.75/6.91
% 45.75/6.91 Further assumptions not needed in the proof:
% 45.75/6.91 --------------------------------------------
% 45.75/6.91 arityeq1_2Ec_2Ebool_2E_21_2E1_2Emono_2EA_27a,
% 45.75/6.91 arityeq1_2Ec_2Ebool_2E_3F_2E1_2Emono_2EA_27a, arityeq2_2Ec_2Ebool_2E_2F_5C_2E2,
% 45.75/6.91 arityeq2_2Ec_2Ebool_2E_5C_2F_2E2, arityeq2_2Ec_2Emin_2E_3D_2E2_2Emono_2EA_27a,
% 45.75/6.91 arityeq2_2Ec_2Emin_2E_3D_3D_3E_2E2,
% 45.75/6.91 arityeq2_2Ec_2Epred__set_2EDELETE_2E2_2Emono_2EA_27a,
% 45.75/6.91 ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,
% 45.75/6.91 ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29,
% 45.75/6.91 ji_2Emono_2Etyop_2Emin_2Ebool,
% 45.75/6.91 ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,
% 45.75/6.91 ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29,
% 45.75/6.91 monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool,
% 45.75/6.91 monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,
% 45.75/6.91 reserved_2Eho_2Eeq__ext, reserved_2Eho_2Ek__thm, reserved_2Eho_2Es__thm,
% 45.75/6.91 reserved_2Elogic_2E_2F_5C, reserved_2Elogic_2E_3D, reserved_2Elogic_2E_3D_3D_3E,
% 45.75/6.91 reserved_2Elogic_2E_5C_2F, reserved_2Equant_2E_21, reserved_2Equant_2E_3F
% 45.75/6.91
% 45.75/6.91 Those formulas are unsatisfiable:
% 45.75/6.91 ---------------------------------
% 45.75/6.91
% 45.75/6.91 Begin of proof
% 45.75/6.92 |
% 45.75/6.92 | ALPHA: (reserved_2Eho_2Eboolext) implies:
% 45.75/6.92 | (1) ! [v0: mono_2Etyop_2Emin_2Ebool] : ! [v1: mono_2Etyop_2Emin_2Ebool] :
% 45.75/6.92 | (v1 = v0 | ~ (p(v1) = 0) | ~ (p(v0) = 0) | ~
% 45.75/6.92 | mono_2Etyop_2Emin_2Ebool(v1) | ~ mono_2Etyop_2Emin_2Ebool(v0))
% 45.75/6.92 | (2) ! [v0: mono_2Etyop_2Emin_2Ebool] : ! [v1: mono_2Etyop_2Emin_2Ebool] :
% 45.75/6.92 | ! [v2: int] : ! [v3: int] : (v3 = 0 | v2 = 0 | v1 = v0 | ~ (p(v1) =
% 45.75/6.92 | v3) | ~ (p(v0) = v2) | ~ mono_2Etyop_2Emin_2Ebool(v1) | ~
% 45.75/6.92 | mono_2Etyop_2Emin_2Ebool(v0))
% 45.75/6.92 |
% 45.75/6.92 | ALPHA: (reserved_2Eho_2Etruth) implies:
% 45.75/6.92 | (3) p(mono_2Ec_2Ebool_2ET_2E0) = 0
% 45.75/6.92 |
% 45.75/6.92 | ALPHA: (reserved_2Eho_2Enotfalse) implies:
% 45.75/6.92 | (4) ? [v0: int] : ( ~ (v0 = 0) & p(mono_2Ec_2Ebool_2EF_2E0) = v0)
% 45.75/6.92 |
% 45.75/6.92 | ALPHA: (reserved_2Eho_2Ebool__cases__ax) implies:
% 45.75/6.92 | (5) mono_2Etyop_2Emin_2Ebool(mono_2Ec_2Ebool_2EF_2E0)
% 45.75/6.92 | (6) mono_2Etyop_2Emin_2Ebool(mono_2Ec_2Ebool_2ET_2E0)
% 45.75/6.92 |
% 45.75/6.92 | ALPHA: (reserved_2Eho_2Ei__thm) implies:
% 45.75/6.92 | (7) ! [v0: d] : ! [v1: u] : ! [v2: du] : ( ~ (s(v0, v1) = v2) | ~ d(v0)
% 45.75/6.92 | | ~ u(v1) | ? [v3: d] : ? [v4: du] : ? [v5: u] :
% 45.75/6.92 | (tyop_2Emin_2Efun(v0, v0) = v3 & app_2E2(v4, v2) = v5 & s(v3,
% 45.75/6.92 | combin_i_2E0) = v4 & s(v0, v5) = v2 & du(v4) & du(v2) & d(v3) &
% 45.75/6.92 | u(v5)))
% 45.75/6.92 |
% 45.75/6.92 | ALPHA: (reserved_2Elogic_2E_7E) implies:
% 45.75/6.92 | (8) ! [v0: mono_2Etyop_2Emin_2Ebool] : ( ~ (p(v0) = 0) | ~
% 45.75/6.92 | mono_2Etyop_2Emin_2Ebool(v0) | ? [v1: mono_2Etyop_2Emin_2Ebool] : ?
% 45.75/6.92 | [v2: int] : ( ~ (v2 = 0) & mono_2Ec_2Ebool_2E_7E_2E1(v0) = v1 & p(v1)
% 45.75/6.92 | = v2 & mono_2Etyop_2Emin_2Ebool(v1)))
% 45.75/6.92 | (9) ! [v0: mono_2Etyop_2Emin_2Ebool] : ! [v1: int] : (v1 = 0 | ~ (p(v0)
% 45.75/6.92 | = v1) | ~ mono_2Etyop_2Emin_2Ebool(v0) | ? [v2:
% 45.75/6.92 | mono_2Etyop_2Emin_2Ebool] : (mono_2Ec_2Ebool_2E_7E_2E1(v0) = v2 &
% 45.75/6.92 | p(v2) = 0 & mono_2Etyop_2Emin_2Ebool(v2)))
% 45.75/6.92 |
% 45.75/6.92 | ALPHA: (ij_2Emono_2Etyop_2Emin_2Ebool) implies:
% 45.75/6.92 | (10) ! [v0: u] : ! [v1: du] : ( ~ (s(tyop_2Emin_2Ebool, v0) = v1) | ~
% 45.75/6.92 | u(v0) | ? [v2: mono_2Etyop_2Emin_2Ebool] : ? [v3: u] :
% 45.75/6.92 | (i_mono_2Etyop_2Emin_2Ebool(v2) = v3 &
% 45.75/6.92 | j_mono_2Etyop_2Emin_2Ebool(v1) = v2 & s(tyop_2Emin_2Ebool, v3) =
% 45.75/6.92 | v1 & mono_2Etyop_2Emin_2Ebool(v2) & du(v1) & u(v3)))
% 45.75/6.92 |
% 45.75/6.92 | ALPHA: (arityeq1_2Ec_2Epred__set_2ECHOICE_2E1_2Emono_2EA_27a) implies:
% 45.75/6.93 | (11) ! [v0: d] : ! [v1: u] : ! [v2: d] : ! [v3: du] : ( ~
% 45.75/6.93 | (tyop_2Emin_2Efun(v0, tyop_2Emin_2Ebool) = v2) | ~ (s(v2, v1) = v3)
% 45.75/6.93 | | ~ d(v0) | ~ u(v1) | ? [v4: u] : ? [v5: du] : ? [v6: d] : ?
% 45.75/6.93 | [v7: du] : ? [v8: u] : (c_2Epred__set_2ECHOICE_2E1(v3) = v4 &
% 45.75/6.93 | tyop_2Emin_2Efun(v2, v0) = v6 & app_2E2(v7, v3) = v8 & s(v6,
% 45.75/6.93 | c_2Epred__set_2ECHOICE_2E0) = v7 & s(v0, v8) = v5 & s(v0, v4) =
% 45.75/6.93 | v5 & du(v7) & du(v5) & d(v6) & u(v8) & u(v4)))
% 45.75/6.93 |
% 45.75/6.93 | ALPHA: (arityeq2_2Ec_2Ebool_2EIN_2E2_2Emono_2EA_27a) implies:
% 45.75/6.93 | (12) ! [v0: d] : ! [v1: u] : ! [v2: u] : ! [v3: du] : ! [v4: d] : !
% 45.75/6.93 | [v5: du] : ! [v6: u] : ( ~ (c_2Ebool_2EIN_2E2(v3, v5) = v6) | ~
% 45.75/6.93 | (tyop_2Emin_2Efun(v0, tyop_2Emin_2Ebool) = v4) | ~ (s(v4, v2) = v5)
% 45.75/6.93 | | ~ (s(v0, v1) = v3) | ~ d(v0) | ~ u(v2) | ~ u(v1) | ? [v7: du]
% 45.75/6.93 | : ? [v8: mono_2Etyop_2Emin_2Ebool] : ? [v9: d] : ? [v10: d] : ?
% 45.75/6.93 | [v11: du] : ? [v12: u] : ? [v13: du] : ? [v14: u] : ? [v15: du]
% 45.75/6.93 | : (j_mono_2Etyop_2Emin_2Ebool(v15) = v8 &
% 45.75/6.93 | j_mono_2Etyop_2Emin_2Ebool(v7) = v8 & tyop_2Emin_2Efun(v4,
% 45.75/6.93 | tyop_2Emin_2Ebool) = v9 & tyop_2Emin_2Efun(v0, v9) = v10 &
% 45.75/6.93 | app_2E2(v13, v5) = v14 & app_2E2(v11, v3) = v12 & s(v10,
% 45.75/6.93 | c_2Ebool_2EIN_2E0) = v11 & s(v9, v12) = v13 &
% 45.75/6.93 | s(tyop_2Emin_2Ebool, v14) = v15 & s(tyop_2Emin_2Ebool, v6) = v7 &
% 45.75/6.93 | mono_2Etyop_2Emin_2Ebool(v8) & du(v15) & du(v13) & du(v11) &
% 45.75/6.93 | du(v7) & d(v10) & d(v9) & u(v14) & u(v12)))
% 45.75/6.93 |
% 45.75/6.93 | ALPHA: (arityeq1_2Ec_2Epred__set_2EREST_2E1_2Emono_2EA_27a) implies:
% 45.75/6.93 | (13) ! [v0: d] : ! [v1: u] : ! [v2: d] : ! [v3: du] : ( ~
% 45.75/6.93 | (tyop_2Emin_2Efun(v0, tyop_2Emin_2Ebool) = v2) | ~ (s(v2, v1) = v3)
% 45.75/6.93 | | ~ d(v0) | ~ u(v1) | ? [v4: u] : ? [v5: du] : ? [v6: d] : ?
% 45.75/6.93 | [v7: du] : ? [v8: u] : (c_2Epred__set_2EREST_2E1(v3) = v4 &
% 45.75/6.93 | tyop_2Emin_2Efun(v2, v2) = v6 & app_2E2(v7, v3) = v8 & s(v6,
% 45.75/6.93 | c_2Epred__set_2EREST_2E0) = v7 & s(v2, v8) = v5 & s(v2, v4) = v5
% 45.75/6.93 | & du(v7) & du(v5) & d(v6) & u(v8) & u(v4)))
% 45.75/6.93 |
% 45.75/6.93 | ALPHA: (arityeq2_2Ec_2Epred__set_2ESUBSET_2E2_2Emono_2EA_27a) implies:
% 45.75/6.93 | (14) ! [v0: d] : ! [v1: u] : ! [v2: u] : ! [v3: d] : ! [v4: du] : !
% 45.75/6.93 | [v5: du] : ! [v6: u] : ( ~ (c_2Epred__set_2ESUBSET_2E2(v4, v5) = v6)
% 45.75/6.93 | | ~ (tyop_2Emin_2Efun(v0, tyop_2Emin_2Ebool) = v3) | ~ (s(v3, v2)
% 45.75/6.93 | = v5) | ~ (s(v3, v1) = v4) | ~ d(v0) | ~ u(v2) | ~ u(v1) | ?
% 45.75/6.93 | [v7: du] : ? [v8: mono_2Etyop_2Emin_2Ebool] : ? [v9: d] : ? [v10:
% 45.75/6.93 | d] : ? [v11: du] : ? [v12: u] : ? [v13: du] : ? [v14: u] : ?
% 45.75/6.93 | [v15: du] : (j_mono_2Etyop_2Emin_2Ebool(v15) = v8 &
% 45.75/6.93 | j_mono_2Etyop_2Emin_2Ebool(v7) = v8 & tyop_2Emin_2Efun(v3, v9) =
% 45.75/6.93 | v10 & tyop_2Emin_2Efun(v3, tyop_2Emin_2Ebool) = v9 & app_2E2(v13,
% 45.75/6.93 | v5) = v14 & app_2E2(v11, v4) = v12 & s(v10,
% 45.75/6.93 | c_2Epred__set_2ESUBSET_2E0) = v11 & s(v9, v12) = v13 &
% 45.75/6.93 | s(tyop_2Emin_2Ebool, v14) = v15 & s(tyop_2Emin_2Ebool, v6) = v7 &
% 45.75/6.93 | mono_2Etyop_2Emin_2Ebool(v8) & du(v15) & du(v13) & du(v11) &
% 45.75/6.93 | du(v7) & d(v10) & d(v9) & u(v14) & u(v12)))
% 45.75/6.93 |
% 45.75/6.93 | ALPHA: (arityeq1_2Ec_2Ebool_2E_7E_2E1) implies:
% 45.75/6.93 | (15) ! [v0: mono_2Etyop_2Emin_2Ebool] : ( ~ (p(v0) = 0) | ~
% 45.75/6.93 | mono_2Etyop_2Emin_2Ebool(v0) | ? [v1: mono_2Etyop_2Emin_2Ebool] :
% 45.75/6.93 | ? [v2: int] : ( ~ (v2 = 0) &
% 45.75/6.93 | mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool(mono_2Ec_2Ebool_2E_7E_2E0,
% 45.75/6.93 | v0) = v1 & p(v1) = v2 & mono_2Etyop_2Emin_2Ebool(v1)))
% 45.75/6.93 | (16) ! [v0: mono_2Etyop_2Emin_2Ebool] : ! [v1: int] : (v1 = 0 | ~ (p(v0)
% 45.75/6.93 | = v1) | ~ mono_2Etyop_2Emin_2Ebool(v0) | ? [v2:
% 45.75/6.93 | mono_2Etyop_2Emin_2Ebool] :
% 45.75/6.93 | (mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool(mono_2Ec_2Ebool_2E_7E_2E0,
% 45.75/6.93 | v0) = v2 & p(v2) = 0 & mono_2Etyop_2Emin_2Ebool(v2)))
% 45.75/6.93 |
% 45.75/6.93 | ALPHA: (thm_2Epred__set_2ESUBSET__DEF) implies:
% 45.75/6.93 | (17) ! [v0: d] : ! [v1: u] : ! [v2: u] : ! [v3: d] : ! [v4: du] : !
% 45.75/6.93 | [v5: du] : ! [v6: u] : ( ~ (c_2Epred__set_2ESUBSET_2E2(v4, v5) = v6)
% 45.75/6.93 | | ~ (tyop_2Emin_2Efun(v0, tyop_2Emin_2Ebool) = v3) | ~ (s(v3, v2)
% 45.75/6.93 | = v5) | ~ (s(v3, v1) = v4) | ~ d(v0) | ~ u(v2) | ~ u(v1) | ?
% 45.75/6.93 | [v7: du] : ? [v8: mono_2Etyop_2Emin_2Ebool] : ? [v9: int] : ?
% 45.75/6.93 | [v10: u] : ? [v11: du] : ? [v12: u] : ? [v13: du] : ? [v14:
% 45.75/6.93 | mono_2Etyop_2Emin_2Ebool] : ? [v15: int] : ? [v16: u] : ? [v17:
% 45.75/6.93 | du] : ? [v18: mono_2Etyop_2Emin_2Ebool] : ? [v19: int] : (u(v10)
% 45.75/6.93 | & ((v15 = 0 & ~ (v19 = 0) & c_2Ebool_2EIN_2E2(v11, v5) = v16 &
% 45.75/6.93 | c_2Ebool_2EIN_2E2(v11, v4) = v12 &
% 45.75/6.93 | j_mono_2Etyop_2Emin_2Ebool(v17) = v18 &
% 45.75/6.93 | j_mono_2Etyop_2Emin_2Ebool(v13) = v14 & p(v18) = v19 & p(v14)
% 45.75/6.93 | = 0 & s(v0, v10) = v11 & s(tyop_2Emin_2Ebool, v16) = v17 &
% 45.75/6.93 | s(tyop_2Emin_2Ebool, v12) = v13 &
% 45.75/6.93 | mono_2Etyop_2Emin_2Ebool(v18) & mono_2Etyop_2Emin_2Ebool(v14)
% 45.75/6.93 | & du(v17) & du(v13) & du(v11) & u(v16) & u(v12)) | (v9 = 0 &
% 45.75/6.93 | j_mono_2Etyop_2Emin_2Ebool(v7) = v8 & p(v8) = 0 &
% 45.75/6.93 | s(tyop_2Emin_2Ebool, v6) = v7 & mono_2Etyop_2Emin_2Ebool(v8) &
% 45.75/6.93 | du(v7)))))
% 45.75/6.93 |
% 45.75/6.93 | ALPHA: (thm_2Epred__set_2EIN__DELETE) implies:
% 45.75/6.94 | (18) ! [v0: d] : ! [v1: u] : ! [v2: u] : ! [v3: u] : ! [v4: du] : !
% 45.75/6.94 | [v5: d] : ! [v6: du] : ! [v7: du] : ! [v8: u] : ! [v9: du] : !
% 45.75/6.94 | [v10: u] : ( ~ (c_2Ebool_2EIN_2E2(v4, v9) = v10) | ~
% 45.75/6.94 | (c_2Epred__set_2EDELETE_2E2(v6, v7) = v8) | ~ (tyop_2Emin_2Efun(v0,
% 45.75/6.94 | tyop_2Emin_2Ebool) = v5) | ~ (s(v5, v8) = v9) | ~ (s(v5, v1) =
% 45.75/6.94 | v6) | ~ (s(v0, v3) = v7) | ~ (s(v0, v2) = v4) | ~ d(v0) | ~
% 45.75/6.94 | u(v3) | ~ u(v2) | ~ u(v1) | ? [v11: du] : ? [v12:
% 45.75/6.94 | mono_2Etyop_2Emin_2Ebool] : ? [v13: any] : ? [v14: u] : ? [v15:
% 45.75/6.94 | du] : ? [v16: mono_2Etyop_2Emin_2Ebool] : ? [v17: any] :
% 45.75/6.94 | (c_2Ebool_2EIN_2E2(v4, v6) = v14 & j_mono_2Etyop_2Emin_2Ebool(v15) =
% 45.75/6.94 | v16 & j_mono_2Etyop_2Emin_2Ebool(v11) = v12 & p(v16) = v17 &
% 45.75/6.94 | p(v12) = v13 & s(tyop_2Emin_2Ebool, v14) = v15 &
% 45.75/6.94 | s(tyop_2Emin_2Ebool, v10) = v11 & mono_2Etyop_2Emin_2Ebool(v16) &
% 45.75/6.94 | mono_2Etyop_2Emin_2Ebool(v12) & du(v15) & du(v11) & u(v14) & ( ~
% 45.75/6.94 | (v13 = 0) | (v17 = 0 & ~ (v7 = v4)))))
% 45.75/6.94 |
% 45.75/6.94 | ALPHA: (thm_2Epred__set_2EREST__DEF) implies:
% 45.75/6.94 | (19) ! [v0: d] : ! [v1: u] : ! [v2: d] : ! [v3: du] : ( ~
% 45.75/6.94 | (tyop_2Emin_2Efun(v0, tyop_2Emin_2Ebool) = v2) | ~ (s(v2, v1) = v3)
% 45.75/6.94 | | ~ d(v0) | ~ u(v1) | ? [v4: u] : ? [v5: du] : ? [v6: u] : ?
% 45.75/6.94 | [v7: du] : ? [v8: u] : (c_2Epred__set_2EREST_2E1(v3) = v4 &
% 45.75/6.94 | c_2Epred__set_2EDELETE_2E2(v3, v7) = v8 &
% 45.75/6.94 | c_2Epred__set_2ECHOICE_2E1(v3) = v6 & s(v2, v8) = v5 & s(v2, v4) =
% 45.75/6.94 | v5 & s(v0, v6) = v7 & du(v7) & du(v5) & u(v8) & u(v6) & u(v4)))
% 45.75/6.94 |
% 45.75/6.94 | ALPHA: (thm_2Epred__set_2EREST__SUBSET) implies:
% 45.75/6.94 | (20) ? [v0: d] : ? [v1: u] : ? [v2: d] : ? [v3: du] : ? [v4: u] : ?
% 45.75/6.94 | [v5: du] : ? [v6: u] : ? [v7: du] : ? [v8:
% 45.75/6.94 | mono_2Etyop_2Emin_2Ebool] : ? [v9: int] : ( ~ (v9 = 0) &
% 45.75/6.94 | c_2Epred__set_2ESUBSET_2E2(v5, v3) = v6 &
% 45.75/6.94 | c_2Epred__set_2EREST_2E1(v3) = v4 & j_mono_2Etyop_2Emin_2Ebool(v7) =
% 45.75/6.94 | v8 & p(v8) = v9 & tyop_2Emin_2Efun(v0, tyop_2Emin_2Ebool) = v2 &
% 45.75/6.94 | s(v2, v4) = v5 & s(v2, v1) = v3 & s(tyop_2Emin_2Ebool, v6) = v7 &
% 45.75/6.94 | mono_2Etyop_2Emin_2Ebool(v8) & du(v7) & du(v5) & du(v3) & d(v2) &
% 45.75/6.94 | d(v0) & u(v6) & u(v4) & u(v1))
% 45.75/6.94 |
% 45.75/6.94 | ALPHA: (function-axioms) implies:
% 45.75/6.94 | (21) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 45.75/6.94 | mono_2Etyop_2Emin_2Ebool] : (v1 = v0 | ~ (p(v2) = v1) | ~ (p(v2) =
% 45.75/6.94 | v0))
% 45.75/6.94 | (22) ! [v0: mono_2Etyop_2Emin_2Ebool] : ! [v1: mono_2Etyop_2Emin_2Ebool]
% 45.75/6.94 | : ! [v2: mono_2Etyop_2Emin_2Ebool] : (v1 = v0 | ~
% 45.75/6.94 | (mono_2Ec_2Ebool_2E_7E_2E1(v2) = v1) | ~
% 45.75/6.94 | (mono_2Ec_2Ebool_2E_7E_2E1(v2) = v0))
% 45.75/6.94 | (23) ! [v0: mono_2Etyop_2Emin_2Ebool] : ! [v1: mono_2Etyop_2Emin_2Ebool]
% 45.75/6.94 | : ! [v2: du] : (v1 = v0 | ~ (j_mono_2Etyop_2Emin_2Ebool(v2) = v1) |
% 45.75/6.94 | ~ (j_mono_2Etyop_2Emin_2Ebool(v2) = v0))
% 45.75/6.94 | (24) ! [v0: u] : ! [v1: u] : ! [v2: du] : (v1 = v0 | ~
% 45.75/6.94 | (c_2Epred__set_2ECHOICE_2E1(v2) = v1) | ~
% 45.75/6.94 | (c_2Epred__set_2ECHOICE_2E1(v2) = v0))
% 45.75/6.94 | (25) ! [v0: u] : ! [v1: u] : ! [v2: du] : (v1 = v0 | ~
% 45.75/6.94 | (c_2Epred__set_2EREST_2E1(v2) = v1) | ~
% 45.75/6.94 | (c_2Epred__set_2EREST_2E1(v2) = v0))
% 45.75/6.94 | (26) ! [v0: du] : ! [v1: du] : ! [v2: u] : ! [v3: d] : (v1 = v0 | ~
% 45.75/6.94 | (s(v3, v2) = v1) | ~ (s(v3, v2) = v0))
% 45.75/6.94 | (27) ! [v0: mono_2Etyop_2Emin_2Ebool] : ! [v1: mono_2Etyop_2Emin_2Ebool]
% 45.75/6.94 | : ! [v2: mono_2Etyop_2Emin_2Ebool] : ! [v3:
% 45.75/6.94 | mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29]
% 45.75/6.94 | : (v1 = v0 | ~
% 45.75/6.94 | (mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool(v3,
% 45.75/6.94 | v2) = v1) | ~
% 45.75/6.94 | (mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool(v3,
% 45.75/6.94 | v2) = v0))
% 45.75/6.94 | (28) ! [v0: u] : ! [v1: u] : ! [v2: du] : ! [v3: du] : (v1 = v0 | ~
% 45.75/6.94 | (c_2Ebool_2EIN_2E2(v3, v2) = v1) | ~ (c_2Ebool_2EIN_2E2(v3, v2) =
% 45.75/6.94 | v0))
% 45.75/6.94 |
% 45.75/6.94 | DELTA: instantiating (4) with fresh symbol all_45_0 gives:
% 45.75/6.94 | (29) ~ (all_45_0 = 0) & p(mono_2Ec_2Ebool_2EF_2E0) = all_45_0
% 45.75/6.94 |
% 45.75/6.94 | ALPHA: (29) implies:
% 45.75/6.94 | (30) ~ (all_45_0 = 0)
% 45.75/6.94 | (31) p(mono_2Ec_2Ebool_2EF_2E0) = all_45_0
% 45.75/6.94 |
% 45.75/6.94 | DELTA: instantiating (20) with fresh symbols all_60_0, all_60_1, all_60_2,
% 45.75/6.94 | all_60_3, all_60_4, all_60_5, all_60_6, all_60_7, all_60_8, all_60_9
% 45.75/6.94 | gives:
% 45.75/6.94 | (32) ~ (all_60_0 = 0) & c_2Epred__set_2ESUBSET_2E2(all_60_4, all_60_6) =
% 45.75/6.94 | all_60_3 & c_2Epred__set_2EREST_2E1(all_60_6) = all_60_5 &
% 45.75/6.94 | j_mono_2Etyop_2Emin_2Ebool(all_60_2) = all_60_1 & p(all_60_1) =
% 45.75/6.94 | all_60_0 & tyop_2Emin_2Efun(all_60_9, tyop_2Emin_2Ebool) = all_60_7 &
% 45.75/6.94 | s(all_60_7, all_60_5) = all_60_4 & s(all_60_7, all_60_8) = all_60_6 &
% 45.75/6.94 | s(tyop_2Emin_2Ebool, all_60_3) = all_60_2 &
% 45.75/6.94 | mono_2Etyop_2Emin_2Ebool(all_60_1) & du(all_60_2) & du(all_60_4) &
% 45.75/6.94 | du(all_60_6) & d(all_60_7) & d(all_60_9) & u(all_60_3) & u(all_60_5) &
% 45.75/6.94 | u(all_60_8)
% 45.75/6.94 |
% 45.75/6.94 | ALPHA: (32) implies:
% 45.75/6.95 | (33) ~ (all_60_0 = 0)
% 45.75/6.95 | (34) u(all_60_8)
% 45.75/6.95 | (35) u(all_60_5)
% 45.75/6.95 | (36) u(all_60_3)
% 45.75/6.95 | (37) d(all_60_9)
% 45.75/6.95 | (38) d(all_60_7)
% 45.75/6.95 | (39) mono_2Etyop_2Emin_2Ebool(all_60_1)
% 45.75/6.95 | (40) s(tyop_2Emin_2Ebool, all_60_3) = all_60_2
% 45.75/6.95 | (41) s(all_60_7, all_60_8) = all_60_6
% 45.75/6.95 | (42) s(all_60_7, all_60_5) = all_60_4
% 45.75/6.95 | (43) tyop_2Emin_2Efun(all_60_9, tyop_2Emin_2Ebool) = all_60_7
% 45.75/6.95 | (44) p(all_60_1) = all_60_0
% 45.75/6.95 | (45) j_mono_2Etyop_2Emin_2Ebool(all_60_2) = all_60_1
% 45.75/6.95 | (46) c_2Epred__set_2EREST_2E1(all_60_6) = all_60_5
% 45.75/6.95 | (47) c_2Epred__set_2ESUBSET_2E2(all_60_4, all_60_6) = all_60_3
% 45.75/6.95 |
% 45.75/6.95 | GROUND_INST: instantiating (10) with all_60_3, all_60_2, simplifying with
% 45.75/6.95 | (36), (40) gives:
% 45.75/6.95 | (48) ? [v0: mono_2Etyop_2Emin_2Ebool] : ? [v1: u] :
% 45.75/6.95 | (i_mono_2Etyop_2Emin_2Ebool(v0) = v1 &
% 45.75/6.95 | j_mono_2Etyop_2Emin_2Ebool(all_60_2) = v0 & s(tyop_2Emin_2Ebool, v1)
% 45.75/6.95 | = all_60_2 & mono_2Etyop_2Emin_2Ebool(v0) & du(all_60_2) & u(v1))
% 45.75/6.95 |
% 45.75/6.95 | GROUND_INST: instantiating (7) with all_60_7, all_60_8, all_60_6, simplifying
% 45.75/6.95 | with (34), (38), (41) gives:
% 45.75/6.95 | (49) ? [v0: d] : ? [v1: du] : ? [v2: u] : (tyop_2Emin_2Efun(all_60_7,
% 45.75/6.95 | all_60_7) = v0 & app_2E2(v1, all_60_6) = v2 & s(v0, combin_i_2E0)
% 45.75/6.95 | = v1 & s(all_60_7, v2) = all_60_6 & du(v1) & du(all_60_6) & d(v0) &
% 45.75/6.95 | u(v2))
% 45.75/6.95 |
% 45.75/6.95 | GROUND_INST: instantiating (7) with all_60_7, all_60_5, all_60_4, simplifying
% 45.75/6.95 | with (35), (38), (42) gives:
% 45.75/6.95 | (50) ? [v0: d] : ? [v1: du] : ? [v2: u] : (tyop_2Emin_2Efun(all_60_7,
% 45.75/6.95 | all_60_7) = v0 & app_2E2(v1, all_60_4) = v2 & s(v0, combin_i_2E0)
% 45.75/6.95 | = v1 & s(all_60_7, v2) = all_60_4 & du(v1) & du(all_60_4) & d(v0) &
% 45.75/6.95 | u(v2))
% 45.75/6.95 |
% 45.75/6.95 | GROUND_INST: instantiating (19) with all_60_9, all_60_8, all_60_7, all_60_6,
% 45.75/6.95 | simplifying with (34), (37), (41), (43) gives:
% 45.75/6.95 | (51) ? [v0: u] : ? [v1: du] : ? [v2: u] : ? [v3: du] : ? [v4: u] :
% 45.75/6.95 | (c_2Epred__set_2EREST_2E1(all_60_6) = v0 &
% 45.75/6.95 | c_2Epred__set_2EDELETE_2E2(all_60_6, v3) = v4 &
% 45.75/6.95 | c_2Epred__set_2ECHOICE_2E1(all_60_6) = v2 & s(all_60_7, v4) = v1 &
% 45.75/6.95 | s(all_60_7, v0) = v1 & s(all_60_9, v2) = v3 & du(v3) & du(v1) &
% 45.75/6.95 | u(v4) & u(v2) & u(v0))
% 45.75/6.95 |
% 45.75/6.95 | GROUND_INST: instantiating (13) with all_60_9, all_60_8, all_60_7, all_60_6,
% 45.75/6.95 | simplifying with (34), (37), (41), (43) gives:
% 45.75/6.95 | (52) ? [v0: u] : ? [v1: du] : ? [v2: d] : ? [v3: du] : ? [v4: u] :
% 45.75/6.95 | (c_2Epred__set_2EREST_2E1(all_60_6) = v0 & tyop_2Emin_2Efun(all_60_7,
% 45.75/6.95 | all_60_7) = v2 & app_2E2(v3, all_60_6) = v4 & s(v2,
% 45.75/6.95 | c_2Epred__set_2EREST_2E0) = v3 & s(all_60_7, v4) = v1 &
% 45.75/6.95 | s(all_60_7, v0) = v1 & du(v3) & du(v1) & d(v2) & u(v4) & u(v0))
% 45.75/6.95 |
% 45.75/6.95 | GROUND_INST: instantiating (11) with all_60_9, all_60_8, all_60_7, all_60_6,
% 45.75/6.95 | simplifying with (34), (37), (41), (43) gives:
% 45.75/6.95 | (53) ? [v0: u] : ? [v1: du] : ? [v2: d] : ? [v3: du] : ? [v4: u] :
% 45.75/6.95 | (c_2Epred__set_2ECHOICE_2E1(all_60_6) = v0 &
% 45.75/6.95 | tyop_2Emin_2Efun(all_60_7, all_60_9) = v2 & app_2E2(v3, all_60_6) =
% 45.75/6.95 | v4 & s(v2, c_2Epred__set_2ECHOICE_2E0) = v3 & s(all_60_9, v4) = v1 &
% 45.75/6.95 | s(all_60_9, v0) = v1 & du(v3) & du(v1) & d(v2) & u(v4) & u(v0))
% 45.75/6.95 |
% 45.75/6.95 | GROUND_INST: instantiating (16) with mono_2Ec_2Ebool_2EF_2E0, all_45_0,
% 45.75/6.95 | simplifying with (5), (31) gives:
% 45.75/6.95 | (54) all_45_0 = 0 | ? [v0: mono_2Etyop_2Emin_2Ebool] :
% 45.75/6.95 | (mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool(mono_2Ec_2Ebool_2E_7E_2E0,
% 45.75/6.95 | mono_2Ec_2Ebool_2EF_2E0) = v0 & p(v0) = 0 &
% 45.75/6.95 | mono_2Etyop_2Emin_2Ebool(v0))
% 45.75/6.95 |
% 45.75/6.95 | GROUND_INST: instantiating (15) with mono_2Ec_2Ebool_2ET_2E0, simplifying with
% 45.75/6.95 | (3), (6) gives:
% 45.75/6.95 | (55) ? [v0: mono_2Etyop_2Emin_2Ebool] : ? [v1: int] : ( ~ (v1 = 0) &
% 45.75/6.95 | mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool(mono_2Ec_2Ebool_2E_7E_2E0,
% 45.75/6.95 | mono_2Ec_2Ebool_2ET_2E0) = v0 & p(v0) = v1 &
% 45.75/6.95 | mono_2Etyop_2Emin_2Ebool(v0))
% 45.75/6.95 |
% 45.75/6.95 | GROUND_INST: instantiating (8) with mono_2Ec_2Ebool_2ET_2E0, simplifying with
% 45.75/6.95 | (3), (6) gives:
% 45.75/6.95 | (56) ? [v0: mono_2Etyop_2Emin_2Ebool] : ? [v1: int] : ( ~ (v1 = 0) &
% 45.75/6.95 | mono_2Ec_2Ebool_2E_7E_2E1(mono_2Ec_2Ebool_2ET_2E0) = v0 & p(v0) = v1
% 45.75/6.95 | & mono_2Etyop_2Emin_2Ebool(v0))
% 45.75/6.95 |
% 45.75/6.95 | GROUND_INST: instantiating (2) with mono_2Ec_2Ebool_2EF_2E0, all_60_1,
% 45.75/6.95 | all_45_0, all_60_0, simplifying with (5), (31), (39), (44) gives:
% 45.75/6.95 | (57) all_60_0 = 0 | all_60_1 = mono_2Ec_2Ebool_2EF_2E0 | all_45_0 = 0
% 45.75/6.95 |
% 45.75/6.96 | GROUND_INST: instantiating (16) with all_60_1, all_60_0, simplifying with
% 45.75/6.96 | (39), (44) gives:
% 45.75/6.96 | (58) all_60_0 = 0 | ? [v0: mono_2Etyop_2Emin_2Ebool] :
% 45.75/6.96 | (mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool(mono_2Ec_2Ebool_2E_7E_2E0,
% 45.75/6.96 | all_60_1) = v0 & p(v0) = 0 & mono_2Etyop_2Emin_2Ebool(v0))
% 45.75/6.96 |
% 45.75/6.96 | GROUND_INST: instantiating (9) with all_60_1, all_60_0, simplifying with (39),
% 45.75/6.96 | (44) gives:
% 45.75/6.96 | (59) all_60_0 = 0 | ? [v0: mono_2Etyop_2Emin_2Ebool] :
% 45.75/6.96 | (mono_2Ec_2Ebool_2E_7E_2E1(all_60_1) = v0 & p(v0) = 0 &
% 45.75/6.96 | mono_2Etyop_2Emin_2Ebool(v0))
% 45.75/6.96 |
% 45.75/6.96 | GROUND_INST: instantiating (17) with all_60_9, all_60_5, all_60_8, all_60_7,
% 45.75/6.96 | all_60_4, all_60_6, all_60_3, simplifying with (34), (35), (37),
% 45.75/6.96 | (41), (42), (43), (47) gives:
% 45.75/6.96 | (60) ? [v0: du] : ? [v1: mono_2Etyop_2Emin_2Ebool] : ? [v2: int] : ?
% 45.75/6.96 | [v3: u] : ? [v4: du] : ? [v5: u] : ? [v6: du] : ? [v7:
% 45.75/6.96 | mono_2Etyop_2Emin_2Ebool] : ? [v8: int] : ? [v9: u] : ? [v10: du]
% 45.75/6.96 | : ? [v11: mono_2Etyop_2Emin_2Ebool] : ? [v12: int] : (u(v3) & ((v8 =
% 45.75/6.96 | 0 & ~ (v12 = 0) & c_2Ebool_2EIN_2E2(v4, all_60_4) = v5 &
% 45.75/6.96 | c_2Ebool_2EIN_2E2(v4, all_60_6) = v9 &
% 45.75/6.96 | j_mono_2Etyop_2Emin_2Ebool(v10) = v11 &
% 45.75/6.96 | j_mono_2Etyop_2Emin_2Ebool(v6) = v7 & p(v11) = v12 & p(v7) = 0 &
% 45.75/6.96 | s(all_60_9, v3) = v4 & s(tyop_2Emin_2Ebool, v9) = v10 &
% 45.75/6.96 | s(tyop_2Emin_2Ebool, v5) = v6 & mono_2Etyop_2Emin_2Ebool(v11) &
% 45.75/6.96 | mono_2Etyop_2Emin_2Ebool(v7) & du(v10) & du(v6) & du(v4) & u(v9)
% 45.75/6.96 | & u(v5)) | (v2 = 0 & j_mono_2Etyop_2Emin_2Ebool(v0) = v1 & p(v1)
% 45.75/6.96 | = 0 & s(tyop_2Emin_2Ebool, all_60_3) = v0 &
% 45.75/6.96 | mono_2Etyop_2Emin_2Ebool(v1) & du(v0))))
% 45.75/6.96 |
% 45.75/6.96 | GROUND_INST: instantiating (14) with all_60_9, all_60_5, all_60_8, all_60_7,
% 45.75/6.96 | all_60_4, all_60_6, all_60_3, simplifying with (34), (35), (37),
% 45.75/6.96 | (41), (42), (43), (47) gives:
% 45.75/6.96 | (61) ? [v0: du] : ? [v1: mono_2Etyop_2Emin_2Ebool] : ? [v2: d] : ? [v3:
% 45.75/6.96 | d] : ? [v4: du] : ? [v5: u] : ? [v6: du] : ? [v7: u] : ? [v8:
% 45.75/6.96 | du] : (j_mono_2Etyop_2Emin_2Ebool(v8) = v1 &
% 45.75/6.96 | j_mono_2Etyop_2Emin_2Ebool(v0) = v1 & tyop_2Emin_2Efun(all_60_7, v2)
% 45.75/6.96 | = v3 & tyop_2Emin_2Efun(all_60_7, tyop_2Emin_2Ebool) = v2 &
% 45.75/6.96 | app_2E2(v6, all_60_6) = v7 & app_2E2(v4, all_60_4) = v5 & s(v3,
% 45.75/6.96 | c_2Epred__set_2ESUBSET_2E0) = v4 & s(v2, v5) = v6 &
% 45.75/6.96 | s(tyop_2Emin_2Ebool, v7) = v8 & s(tyop_2Emin_2Ebool, all_60_3) = v0
% 45.75/6.96 | & mono_2Etyop_2Emin_2Ebool(v1) & du(v8) & du(v6) & du(v4) & du(v0) &
% 45.75/6.96 | d(v3) & d(v2) & u(v7) & u(v5))
% 45.75/6.96 |
% 45.75/6.96 | DELTA: instantiating (56) with fresh symbols all_81_0, all_81_1 gives:
% 45.75/6.96 | (62) ~ (all_81_0 = 0) & mono_2Ec_2Ebool_2E_7E_2E1(mono_2Ec_2Ebool_2ET_2E0)
% 45.75/6.96 | = all_81_1 & p(all_81_1) = all_81_0 &
% 45.75/6.96 | mono_2Etyop_2Emin_2Ebool(all_81_1)
% 45.75/6.96 |
% 45.75/6.96 | ALPHA: (62) implies:
% 45.75/6.96 | (63) ~ (all_81_0 = 0)
% 45.75/6.96 | (64) mono_2Etyop_2Emin_2Ebool(all_81_1)
% 45.75/6.96 | (65) p(all_81_1) = all_81_0
% 45.75/6.96 | (66) mono_2Ec_2Ebool_2E_7E_2E1(mono_2Ec_2Ebool_2ET_2E0) = all_81_1
% 45.75/6.96 |
% 45.75/6.96 | DELTA: instantiating (55) with fresh symbols all_83_0, all_83_1 gives:
% 45.75/6.96 | (67) ~ (all_83_0 = 0) &
% 45.75/6.96 | mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool(mono_2Ec_2Ebool_2E_7E_2E0,
% 45.75/6.96 | mono_2Ec_2Ebool_2ET_2E0) = all_83_1 & p(all_83_1) = all_83_0 &
% 45.75/6.96 | mono_2Etyop_2Emin_2Ebool(all_83_1)
% 45.75/6.96 |
% 45.75/6.96 | ALPHA: (67) implies:
% 45.75/6.96 | (68) ~ (all_83_0 = 0)
% 45.75/6.96 | (69) mono_2Etyop_2Emin_2Ebool(all_83_1)
% 45.75/6.96 | (70) p(all_83_1) = all_83_0
% 45.75/6.96 | (71) mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool(mono_2Ec_2Ebool_2E_7E_2E0,
% 45.75/6.96 | mono_2Ec_2Ebool_2ET_2E0) = all_83_1
% 45.75/6.96 |
% 45.75/6.96 | DELTA: instantiating (48) with fresh symbols all_85_0, all_85_1 gives:
% 45.75/6.96 | (72) i_mono_2Etyop_2Emin_2Ebool(all_85_1) = all_85_0 &
% 45.75/6.96 | j_mono_2Etyop_2Emin_2Ebool(all_60_2) = all_85_1 & s(tyop_2Emin_2Ebool,
% 45.75/6.96 | all_85_0) = all_60_2 & mono_2Etyop_2Emin_2Ebool(all_85_1) &
% 45.75/6.96 | du(all_60_2) & u(all_85_0)
% 45.75/6.96 |
% 45.75/6.96 | ALPHA: (72) implies:
% 45.75/6.96 | (73) j_mono_2Etyop_2Emin_2Ebool(all_60_2) = all_85_1
% 45.75/6.96 |
% 45.75/6.96 | DELTA: instantiating (50) with fresh symbols all_87_0, all_87_1, all_87_2
% 45.75/6.96 | gives:
% 45.75/6.96 | (74) tyop_2Emin_2Efun(all_60_7, all_60_7) = all_87_2 & app_2E2(all_87_1,
% 45.75/6.96 | all_60_4) = all_87_0 & s(all_87_2, combin_i_2E0) = all_87_1 &
% 45.75/6.96 | s(all_60_7, all_87_0) = all_60_4 & du(all_87_1) & du(all_60_4) &
% 45.75/6.96 | d(all_87_2) & u(all_87_0)
% 45.75/6.96 |
% 45.75/6.96 | ALPHA: (74) implies:
% 45.75/6.96 | (75) u(all_87_0)
% 45.75/6.96 | (76) s(all_60_7, all_87_0) = all_60_4
% 45.75/6.96 |
% 45.75/6.96 | DELTA: instantiating (49) with fresh symbols all_89_0, all_89_1, all_89_2
% 45.75/6.96 | gives:
% 45.75/6.96 | (77) tyop_2Emin_2Efun(all_60_7, all_60_7) = all_89_2 & app_2E2(all_89_1,
% 45.75/6.96 | all_60_6) = all_89_0 & s(all_89_2, combin_i_2E0) = all_89_1 &
% 45.75/6.96 | s(all_60_7, all_89_0) = all_60_6 & du(all_89_1) & du(all_60_6) &
% 45.75/6.96 | d(all_89_2) & u(all_89_0)
% 45.75/6.96 |
% 45.75/6.96 | ALPHA: (77) implies:
% 45.75/6.96 | (78) u(all_89_0)
% 45.75/6.96 | (79) s(all_60_7, all_89_0) = all_60_6
% 45.75/6.96 |
% 45.75/6.96 | DELTA: instantiating (52) with fresh symbols all_93_0, all_93_1, all_93_2,
% 45.75/6.96 | all_93_3, all_93_4 gives:
% 45.75/6.96 | (80) c_2Epred__set_2EREST_2E1(all_60_6) = all_93_4 &
% 45.75/6.96 | tyop_2Emin_2Efun(all_60_7, all_60_7) = all_93_2 & app_2E2(all_93_1,
% 45.75/6.96 | all_60_6) = all_93_0 & s(all_93_2, c_2Epred__set_2EREST_2E0) =
% 45.75/6.96 | all_93_1 & s(all_60_7, all_93_0) = all_93_3 & s(all_60_7, all_93_4) =
% 45.75/6.96 | all_93_3 & du(all_93_1) & du(all_93_3) & d(all_93_2) & u(all_93_0) &
% 45.75/6.96 | u(all_93_4)
% 45.75/6.96 |
% 45.75/6.96 | ALPHA: (80) implies:
% 45.75/6.96 | (81) c_2Epred__set_2EREST_2E1(all_60_6) = all_93_4
% 45.75/6.96 |
% 45.75/6.96 | DELTA: instantiating (51) with fresh symbols all_99_0, all_99_1, all_99_2,
% 45.75/6.96 | all_99_3, all_99_4 gives:
% 45.75/6.97 | (82) c_2Epred__set_2EREST_2E1(all_60_6) = all_99_4 &
% 45.75/6.97 | c_2Epred__set_2EDELETE_2E2(all_60_6, all_99_1) = all_99_0 &
% 45.75/6.97 | c_2Epred__set_2ECHOICE_2E1(all_60_6) = all_99_2 & s(all_60_7,
% 45.75/6.97 | all_99_0) = all_99_3 & s(all_60_7, all_99_4) = all_99_3 &
% 45.75/6.97 | s(all_60_9, all_99_2) = all_99_1 & du(all_99_1) & du(all_99_3) &
% 45.75/6.97 | u(all_99_0) & u(all_99_2) & u(all_99_4)
% 45.75/6.97 |
% 45.75/6.97 | ALPHA: (82) implies:
% 45.75/6.97 | (83) s(all_60_9, all_99_2) = all_99_1
% 45.75/6.97 | (84) s(all_60_7, all_99_4) = all_99_3
% 45.75/6.97 | (85) s(all_60_7, all_99_0) = all_99_3
% 45.75/6.97 | (86) c_2Epred__set_2ECHOICE_2E1(all_60_6) = all_99_2
% 45.75/6.97 | (87) c_2Epred__set_2EDELETE_2E2(all_60_6, all_99_1) = all_99_0
% 45.75/6.97 | (88) c_2Epred__set_2EREST_2E1(all_60_6) = all_99_4
% 45.75/6.97 |
% 45.75/6.97 | DELTA: instantiating (53) with fresh symbols all_103_0, all_103_1, all_103_2,
% 45.75/6.97 | all_103_3, all_103_4 gives:
% 45.75/6.97 | (89) c_2Epred__set_2ECHOICE_2E1(all_60_6) = all_103_4 &
% 45.75/6.97 | tyop_2Emin_2Efun(all_60_7, all_60_9) = all_103_2 & app_2E2(all_103_1,
% 45.75/6.97 | all_60_6) = all_103_0 & s(all_103_2, c_2Epred__set_2ECHOICE_2E0) =
% 45.75/6.97 | all_103_1 & s(all_60_9, all_103_0) = all_103_3 & s(all_60_9,
% 45.75/6.97 | all_103_4) = all_103_3 & du(all_103_1) & du(all_103_3) &
% 45.75/6.97 | d(all_103_2) & u(all_103_0) & u(all_103_4)
% 45.75/6.97 |
% 45.75/6.97 | ALPHA: (89) implies:
% 45.75/6.97 | (90) u(all_103_4)
% 45.75/6.97 | (91) s(all_60_9, all_103_4) = all_103_3
% 45.75/6.97 | (92) c_2Epred__set_2ECHOICE_2E1(all_60_6) = all_103_4
% 45.75/6.97 |
% 45.75/6.97 | DELTA: instantiating (61) with fresh symbols all_113_0, all_113_1, all_113_2,
% 45.75/6.97 | all_113_3, all_113_4, all_113_5, all_113_6, all_113_7, all_113_8 gives:
% 45.75/6.97 | (93) j_mono_2Etyop_2Emin_2Ebool(all_113_0) = all_113_7 &
% 45.75/6.97 | j_mono_2Etyop_2Emin_2Ebool(all_113_8) = all_113_7 &
% 45.75/6.97 | tyop_2Emin_2Efun(all_60_7, all_113_6) = all_113_5 &
% 45.75/6.97 | tyop_2Emin_2Efun(all_60_7, tyop_2Emin_2Ebool) = all_113_6 &
% 45.75/6.97 | app_2E2(all_113_2, all_60_6) = all_113_1 & app_2E2(all_113_4,
% 45.75/6.97 | all_60_4) = all_113_3 & s(all_113_5, c_2Epred__set_2ESUBSET_2E0) =
% 45.75/6.97 | all_113_4 & s(all_113_6, all_113_3) = all_113_2 & s(tyop_2Emin_2Ebool,
% 45.75/6.97 | all_113_1) = all_113_0 & s(tyop_2Emin_2Ebool, all_60_3) = all_113_8
% 45.75/6.97 | & mono_2Etyop_2Emin_2Ebool(all_113_7) & du(all_113_0) & du(all_113_2)
% 45.75/6.97 | & du(all_113_4) & du(all_113_8) & d(all_113_5) & d(all_113_6) &
% 45.75/6.97 | u(all_113_1) & u(all_113_3)
% 45.75/6.97 |
% 45.75/6.97 | ALPHA: (93) implies:
% 45.75/6.97 | (94) mono_2Etyop_2Emin_2Ebool(all_113_7)
% 45.75/6.97 | (95) s(tyop_2Emin_2Ebool, all_60_3) = all_113_8
% 45.75/6.97 | (96) j_mono_2Etyop_2Emin_2Ebool(all_113_8) = all_113_7
% 45.75/6.97 |
% 45.75/6.97 | DELTA: instantiating (60) with fresh symbols all_123_0, all_123_1, all_123_2,
% 45.75/6.97 | all_123_3, all_123_4, all_123_5, all_123_6, all_123_7, all_123_8,
% 45.75/6.97 | all_123_9, all_123_10, all_123_11, all_123_12 gives:
% 45.75/6.97 | (97) u(all_123_9) & ((all_123_4 = 0 & ~ (all_123_0 = 0) &
% 45.75/6.97 | c_2Ebool_2EIN_2E2(all_123_8, all_60_4) = all_123_7 &
% 45.75/6.97 | c_2Ebool_2EIN_2E2(all_123_8, all_60_6) = all_123_3 &
% 45.75/6.97 | j_mono_2Etyop_2Emin_2Ebool(all_123_2) = all_123_1 &
% 45.75/6.97 | j_mono_2Etyop_2Emin_2Ebool(all_123_6) = all_123_5 & p(all_123_1) =
% 45.75/6.97 | all_123_0 & p(all_123_5) = 0 & s(all_60_9, all_123_9) = all_123_8
% 45.75/6.97 | & s(tyop_2Emin_2Ebool, all_123_3) = all_123_2 &
% 45.75/6.97 | s(tyop_2Emin_2Ebool, all_123_7) = all_123_6 &
% 45.75/6.97 | mono_2Etyop_2Emin_2Ebool(all_123_1) &
% 45.75/6.97 | mono_2Etyop_2Emin_2Ebool(all_123_5) & du(all_123_2) &
% 45.75/6.97 | du(all_123_6) & du(all_123_8) & u(all_123_3) & u(all_123_7)) |
% 45.75/6.97 | (all_123_10 = 0 & j_mono_2Etyop_2Emin_2Ebool(all_123_12) =
% 45.75/6.97 | all_123_11 & p(all_123_11) = 0 & s(tyop_2Emin_2Ebool, all_60_3) =
% 45.75/6.97 | all_123_12 & mono_2Etyop_2Emin_2Ebool(all_123_11) &
% 45.75/6.97 | du(all_123_12)))
% 45.75/6.97 |
% 45.75/6.97 | ALPHA: (97) implies:
% 45.75/6.97 | (98) u(all_123_9)
% 45.75/6.98 | (99) (all_123_4 = 0 & ~ (all_123_0 = 0) & c_2Ebool_2EIN_2E2(all_123_8,
% 45.75/6.98 | all_60_4) = all_123_7 & c_2Ebool_2EIN_2E2(all_123_8, all_60_6) =
% 45.75/6.98 | all_123_3 & j_mono_2Etyop_2Emin_2Ebool(all_123_2) = all_123_1 &
% 45.75/6.98 | j_mono_2Etyop_2Emin_2Ebool(all_123_6) = all_123_5 & p(all_123_1) =
% 45.75/6.98 | all_123_0 & p(all_123_5) = 0 & s(all_60_9, all_123_9) = all_123_8 &
% 45.75/6.98 | s(tyop_2Emin_2Ebool, all_123_3) = all_123_2 & s(tyop_2Emin_2Ebool,
% 45.75/6.98 | all_123_7) = all_123_6 & mono_2Etyop_2Emin_2Ebool(all_123_1) &
% 45.75/6.98 | mono_2Etyop_2Emin_2Ebool(all_123_5) & du(all_123_2) & du(all_123_6)
% 45.75/6.98 | & du(all_123_8) & u(all_123_3) & u(all_123_7)) | (all_123_10 = 0 &
% 45.75/6.98 | j_mono_2Etyop_2Emin_2Ebool(all_123_12) = all_123_11 & p(all_123_11)
% 45.75/6.98 | = 0 & s(tyop_2Emin_2Ebool, all_60_3) = all_123_12 &
% 45.75/6.98 | mono_2Etyop_2Emin_2Ebool(all_123_11) & du(all_123_12))
% 45.75/6.98 |
% 45.75/6.98 | BETA: splitting (57) gives:
% 45.75/6.98 |
% 45.89/6.98 | Case 1:
% 45.89/6.98 | |
% 45.89/6.98 | | (100) all_60_0 = 0
% 45.89/6.98 | |
% 45.89/6.98 | | REDUCE: (33), (100) imply:
% 45.89/6.98 | | (101) $false
% 45.89/6.98 | |
% 45.89/6.98 | | CLOSE: (101) is inconsistent.
% 45.89/6.98 | |
% 45.89/6.98 | Case 2:
% 45.89/6.98 | |
% 45.89/6.98 | | (102) all_60_1 = mono_2Ec_2Ebool_2EF_2E0 | all_45_0 = 0
% 45.89/6.98 | |
% 45.89/6.98 | | BETA: splitting (102) gives:
% 45.89/6.98 | |
% 45.89/6.98 | | Case 1:
% 45.89/6.98 | | |
% 45.89/6.98 | | | (103) all_45_0 = 0
% 45.89/6.98 | | |
% 45.89/6.98 | | | REDUCE: (30), (103) imply:
% 45.89/6.98 | | | (104) $false
% 45.89/6.98 | | |
% 45.89/6.98 | | | CLOSE: (104) is inconsistent.
% 45.89/6.98 | | |
% 45.89/6.98 | | Case 2:
% 45.89/6.98 | | |
% 45.89/6.98 | | | (105) all_60_1 = mono_2Ec_2Ebool_2EF_2E0
% 45.89/6.98 | | |
% 45.89/6.98 | | | REDUCE: (45), (105) imply:
% 45.89/6.98 | | | (106) j_mono_2Etyop_2Emin_2Ebool(all_60_2) = mono_2Ec_2Ebool_2EF_2E0
% 45.89/6.98 | | |
% 45.89/6.98 | | | REDUCE: (44), (105) imply:
% 45.89/6.98 | | | (107) p(mono_2Ec_2Ebool_2EF_2E0) = all_60_0
% 45.89/6.98 | | |
% 45.89/6.98 | | | BETA: splitting (59) gives:
% 45.89/6.98 | | |
% 45.89/6.98 | | | Case 1:
% 45.89/6.98 | | | |
% 45.89/6.98 | | | | (108) all_60_0 = 0
% 45.89/6.98 | | | |
% 45.89/6.98 | | | | REDUCE: (33), (108) imply:
% 45.89/6.98 | | | | (109) $false
% 45.89/6.98 | | | |
% 45.89/6.98 | | | | CLOSE: (109) is inconsistent.
% 45.89/6.98 | | | |
% 45.89/6.98 | | | Case 2:
% 45.89/6.98 | | | |
% 45.89/6.98 | | | | (110) ? [v0: mono_2Etyop_2Emin_2Ebool] :
% 45.89/6.98 | | | | (mono_2Ec_2Ebool_2E_7E_2E1(all_60_1) = v0 & p(v0) = 0 &
% 45.89/6.98 | | | | mono_2Etyop_2Emin_2Ebool(v0))
% 45.89/6.98 | | | |
% 45.89/6.98 | | | | DELTA: instantiating (110) with fresh symbol all_136_0 gives:
% 45.89/6.98 | | | | (111) mono_2Ec_2Ebool_2E_7E_2E1(all_60_1) = all_136_0 & p(all_136_0)
% 45.89/6.98 | | | | = 0 & mono_2Etyop_2Emin_2Ebool(all_136_0)
% 45.89/6.98 | | | |
% 45.89/6.98 | | | | ALPHA: (111) implies:
% 45.89/6.98 | | | | (112) mono_2Etyop_2Emin_2Ebool(all_136_0)
% 45.89/6.98 | | | | (113) p(all_136_0) = 0
% 45.89/6.98 | | | | (114) mono_2Ec_2Ebool_2E_7E_2E1(all_60_1) = all_136_0
% 45.89/6.98 | | | |
% 45.89/6.98 | | | | REDUCE: (105), (114) imply:
% 45.89/6.98 | | | | (115) mono_2Ec_2Ebool_2E_7E_2E1(mono_2Ec_2Ebool_2EF_2E0) = all_136_0
% 45.89/6.98 | | | |
% 45.89/6.98 | | | | BETA: splitting (58) gives:
% 45.89/6.98 | | | |
% 45.89/6.98 | | | | Case 1:
% 45.89/6.98 | | | | |
% 45.89/6.98 | | | | | (116) all_60_0 = 0
% 45.89/6.98 | | | | |
% 45.89/6.98 | | | | | REDUCE: (33), (116) imply:
% 45.89/6.98 | | | | | (117) $false
% 45.89/6.98 | | | | |
% 45.89/6.98 | | | | | CLOSE: (117) is inconsistent.
% 45.89/6.98 | | | | |
% 45.89/6.98 | | | | Case 2:
% 45.89/6.98 | | | | |
% 45.89/6.98 | | | | | (118) ? [v0: mono_2Etyop_2Emin_2Ebool] :
% 45.89/6.98 | | | | | (mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool(mono_2Ec_2Ebool_2E_7E_2E0,
% 45.89/6.98 | | | | | all_60_1) = v0 & p(v0) = 0 &
% 45.89/6.98 | | | | | mono_2Etyop_2Emin_2Ebool(v0))
% 45.89/6.98 | | | | |
% 45.89/6.98 | | | | | DELTA: instantiating (118) with fresh symbol all_142_0 gives:
% 45.89/6.98 | | | | | (119) mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool(mono_2Ec_2Ebool_2E_7E_2E0,
% 45.89/6.98 | | | | | all_60_1) = all_142_0 & p(all_142_0) = 0 &
% 45.89/6.98 | | | | | mono_2Etyop_2Emin_2Ebool(all_142_0)
% 45.89/6.98 | | | | |
% 45.89/6.98 | | | | | ALPHA: (119) implies:
% 45.89/6.98 | | | | | (120) mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool(mono_2Ec_2Ebool_2E_7E_2E0,
% 45.89/6.98 | | | | | all_60_1) = all_142_0
% 45.89/6.98 | | | | |
% 45.89/6.98 | | | | | REDUCE: (105), (120) imply:
% 45.89/6.98 | | | | | (121) mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool(mono_2Ec_2Ebool_2E_7E_2E0,
% 45.89/6.98 | | | | | mono_2Ec_2Ebool_2EF_2E0) = all_142_0
% 45.89/6.98 | | | | |
% 45.89/6.98 | | | | | BETA: splitting (54) gives:
% 45.89/6.98 | | | | |
% 45.89/6.98 | | | | | Case 1:
% 45.89/6.98 | | | | | |
% 45.89/6.98 | | | | | | (122) all_45_0 = 0
% 45.89/6.98 | | | | | |
% 45.89/6.98 | | | | | | REDUCE: (30), (122) imply:
% 45.89/6.98 | | | | | | (123) $false
% 45.89/6.98 | | | | | |
% 45.89/6.98 | | | | | | CLOSE: (123) is inconsistent.
% 45.89/6.98 | | | | | |
% 45.89/6.98 | | | | | Case 2:
% 45.89/6.98 | | | | | |
% 45.89/6.98 | | | | | | (124) ? [v0: mono_2Etyop_2Emin_2Ebool] :
% 45.89/6.98 | | | | | | (mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool(mono_2Ec_2Ebool_2E_7E_2E0,
% 45.89/6.98 | | | | | | mono_2Ec_2Ebool_2EF_2E0) = v0 & p(v0) = 0 &
% 45.89/6.98 | | | | | | mono_2Etyop_2Emin_2Ebool(v0))
% 45.89/6.98 | | | | | |
% 45.89/6.98 | | | | | | DELTA: instantiating (124) with fresh symbol all_147_0 gives:
% 45.89/6.98 | | | | | | (125) mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool(mono_2Ec_2Ebool_2E_7E_2E0,
% 45.89/6.98 | | | | | | mono_2Ec_2Ebool_2EF_2E0) = all_147_0 & p(all_147_0) = 0 &
% 45.89/6.98 | | | | | | mono_2Etyop_2Emin_2Ebool(all_147_0)
% 45.89/6.98 | | | | | |
% 45.89/6.98 | | | | | | ALPHA: (125) implies:
% 45.89/6.98 | | | | | | (126) mono_2Etyop_2Emin_2Ebool(all_147_0)
% 45.89/6.98 | | | | | | (127) p(all_147_0) = 0
% 45.89/6.98 | | | | | | (128) mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool(mono_2Ec_2Ebool_2E_7E_2E0,
% 45.89/6.98 | | | | | | mono_2Ec_2Ebool_2EF_2E0) = all_147_0
% 45.89/6.98 | | | | | |
% 45.89/6.98 | | | | | | GROUND_INST: instantiating (26) with all_60_2, all_113_8, all_60_3,
% 45.89/6.98 | | | | | | tyop_2Emin_2Ebool, simplifying with (40), (95) gives:
% 45.89/6.98 | | | | | | (129) all_113_8 = all_60_2
% 45.89/6.98 | | | | | |
% 45.89/6.98 | | | | | | GROUND_INST: instantiating (21) with all_45_0, all_60_0,
% 45.89/6.98 | | | | | | mono_2Ec_2Ebool_2EF_2E0, simplifying with (31), (107)
% 45.89/6.98 | | | | | | gives:
% 45.89/6.98 | | | | | | (130) all_60_0 = all_45_0
% 45.89/6.98 | | | | | |
% 45.89/6.98 | | | | | | GROUND_INST: instantiating (23) with mono_2Ec_2Ebool_2EF_2E0,
% 45.89/6.98 | | | | | | all_85_1, all_60_2, simplifying with (73), (106) gives:
% 45.89/6.98 | | | | | | (131) all_85_1 = mono_2Ec_2Ebool_2EF_2E0
% 45.89/6.98 | | | | | |
% 45.89/6.98 | | | | | | GROUND_INST: instantiating (27) with all_142_0, all_147_0,
% 45.89/6.98 | | | | | | mono_2Ec_2Ebool_2EF_2E0, mono_2Ec_2Ebool_2E_7E_2E0,
% 45.89/6.98 | | | | | | simplifying with (121), (128) gives:
% 45.89/6.98 | | | | | | (132) all_147_0 = all_142_0
% 45.89/6.98 | | | | | |
% 45.89/6.98 | | | | | | GROUND_INST: instantiating (24) with all_99_2, all_103_4, all_60_6,
% 45.89/6.98 | | | | | | simplifying with (86), (92) gives:
% 45.89/6.98 | | | | | | (133) all_103_4 = all_99_2
% 45.89/6.98 | | | | | |
% 45.89/6.98 | | | | | | GROUND_INST: instantiating (25) with all_60_5, all_99_4, all_60_6,
% 45.89/6.98 | | | | | | simplifying with (46), (88) gives:
% 45.89/6.98 | | | | | | (134) all_99_4 = all_60_5
% 45.89/6.98 | | | | | |
% 45.89/6.98 | | | | | | GROUND_INST: instantiating (25) with all_93_4, all_99_4, all_60_6,
% 45.89/6.98 | | | | | | simplifying with (81), (88) gives:
% 45.89/6.98 | | | | | | (135) all_99_4 = all_93_4
% 45.89/6.98 | | | | | |
% 45.89/6.98 | | | | | | COMBINE_EQS: (134), (135) imply:
% 45.89/6.98 | | | | | | (136) all_93_4 = all_60_5
% 45.89/6.98 | | | | | |
% 45.89/6.98 | | | | | | REDUCE: (96), (129) imply:
% 45.89/6.98 | | | | | | (137) j_mono_2Etyop_2Emin_2Ebool(all_60_2) = all_113_7
% 45.89/6.98 | | | | | |
% 45.89/6.98 | | | | | | REDUCE: (127), (132) imply:
% 45.89/6.98 | | | | | | (138) p(all_142_0) = 0
% 45.89/6.98 | | | | | |
% 45.89/6.98 | | | | | | REDUCE: (84), (134) imply:
% 45.89/6.98 | | | | | | (139) s(all_60_7, all_60_5) = all_99_3
% 45.89/6.98 | | | | | |
% 45.89/6.98 | | | | | | REDUCE: (91), (133) imply:
% 45.89/6.99 | | | | | | (140) s(all_60_9, all_99_2) = all_103_3
% 45.89/6.99 | | | | | |
% 45.89/6.99 | | | | | | REDUCE: (126), (132) imply:
% 45.89/6.99 | | | | | | (141) mono_2Etyop_2Emin_2Ebool(all_142_0)
% 45.89/6.99 | | | | | |
% 45.89/6.99 | | | | | | REDUCE: (90), (133) imply:
% 45.89/6.99 | | | | | | (142) u(all_99_2)
% 45.89/6.99 | | | | | |
% 45.89/6.99 | | | | | | GROUND_INST: instantiating (26) with all_99_1, all_103_3, all_99_2,
% 45.89/6.99 | | | | | | all_60_9, simplifying with (83), (140) gives:
% 45.89/6.99 | | | | | | (143) all_103_3 = all_99_1
% 45.89/6.99 | | | | | |
% 45.89/6.99 | | | | | | GROUND_INST: instantiating (26) with all_60_4, all_99_3, all_60_5,
% 45.89/6.99 | | | | | | all_60_7, simplifying with (42), (139) gives:
% 45.89/6.99 | | | | | | (144) all_99_3 = all_60_4
% 45.89/6.99 | | | | | |
% 45.89/6.99 | | | | | | GROUND_INST: instantiating (23) with mono_2Ec_2Ebool_2EF_2E0,
% 45.89/6.99 | | | | | | all_113_7, all_60_2, simplifying with (106), (137)
% 45.89/6.99 | | | | | | gives:
% 45.89/6.99 | | | | | | (145) all_113_7 = mono_2Ec_2Ebool_2EF_2E0
% 45.89/6.99 | | | | | |
% 45.89/6.99 | | | | | | REDUCE: (85), (144) imply:
% 45.89/6.99 | | | | | | (146) s(all_60_7, all_99_0) = all_60_4
% 45.89/6.99 | | | | | |
% 45.89/6.99 | | | | | | BETA: splitting (99) gives:
% 45.89/6.99 | | | | | |
% 45.89/6.99 | | | | | | Case 1:
% 45.89/6.99 | | | | | | |
% 45.89/6.99 | | | | | | | (147) all_123_4 = 0 & ~ (all_123_0 = 0) &
% 45.89/6.99 | | | | | | | c_2Ebool_2EIN_2E2(all_123_8, all_60_4) = all_123_7 &
% 45.89/6.99 | | | | | | | c_2Ebool_2EIN_2E2(all_123_8, all_60_6) = all_123_3 &
% 45.89/6.99 | | | | | | | j_mono_2Etyop_2Emin_2Ebool(all_123_2) = all_123_1 &
% 45.89/6.99 | | | | | | | j_mono_2Etyop_2Emin_2Ebool(all_123_6) = all_123_5 &
% 45.89/6.99 | | | | | | | p(all_123_1) = all_123_0 & p(all_123_5) = 0 & s(all_60_9,
% 45.89/6.99 | | | | | | | all_123_9) = all_123_8 & s(tyop_2Emin_2Ebool,
% 45.89/6.99 | | | | | | | all_123_3) = all_123_2 & s(tyop_2Emin_2Ebool,
% 45.89/6.99 | | | | | | | all_123_7) = all_123_6 &
% 45.89/6.99 | | | | | | | mono_2Etyop_2Emin_2Ebool(all_123_1) &
% 45.89/6.99 | | | | | | | mono_2Etyop_2Emin_2Ebool(all_123_5) & du(all_123_2) &
% 45.89/6.99 | | | | | | | du(all_123_6) & du(all_123_8) & u(all_123_3) &
% 45.89/6.99 | | | | | | | u(all_123_7)
% 45.89/6.99 | | | | | | |
% 45.89/6.99 | | | | | | | ALPHA: (147) implies:
% 45.89/6.99 | | | | | | | (148) ~ (all_123_0 = 0)
% 45.89/6.99 | | | | | | | (149) u(all_123_7)
% 45.89/6.99 | | | | | | | (150) u(all_123_3)
% 45.89/6.99 | | | | | | | (151) mono_2Etyop_2Emin_2Ebool(all_123_5)
% 45.89/6.99 | | | | | | | (152) mono_2Etyop_2Emin_2Ebool(all_123_1)
% 45.89/6.99 | | | | | | | (153) s(tyop_2Emin_2Ebool, all_123_7) = all_123_6
% 45.89/6.99 | | | | | | | (154) s(tyop_2Emin_2Ebool, all_123_3) = all_123_2
% 45.89/6.99 | | | | | | | (155) s(all_60_9, all_123_9) = all_123_8
% 45.89/6.99 | | | | | | | (156) p(all_123_5) = 0
% 45.89/6.99 | | | | | | | (157) p(all_123_1) = all_123_0
% 45.89/6.99 | | | | | | | (158) j_mono_2Etyop_2Emin_2Ebool(all_123_6) = all_123_5
% 45.89/6.99 | | | | | | | (159) j_mono_2Etyop_2Emin_2Ebool(all_123_2) = all_123_1
% 45.89/6.99 | | | | | | | (160) c_2Ebool_2EIN_2E2(all_123_8, all_60_6) = all_123_3
% 45.89/6.99 | | | | | | | (161) c_2Ebool_2EIN_2E2(all_123_8, all_60_4) = all_123_7
% 45.89/6.99 | | | | | | |
% 45.89/6.99 | | | | | | | GROUND_INST: instantiating (10) with all_123_7, all_123_6,
% 45.89/6.99 | | | | | | | simplifying with (149), (153) gives:
% 45.89/6.99 | | | | | | | (162) ? [v0: mono_2Etyop_2Emin_2Ebool] : ? [v1: u] :
% 45.89/6.99 | | | | | | | (i_mono_2Etyop_2Emin_2Ebool(v0) = v1 &
% 45.89/6.99 | | | | | | | j_mono_2Etyop_2Emin_2Ebool(all_123_6) = v0 &
% 45.89/6.99 | | | | | | | s(tyop_2Emin_2Ebool, v1) = all_123_6 &
% 45.89/6.99 | | | | | | | mono_2Etyop_2Emin_2Ebool(v0) & du(all_123_6) & u(v1))
% 45.89/6.99 | | | | | | |
% 45.89/6.99 | | | | | | | GROUND_INST: instantiating (10) with all_123_3, all_123_2,
% 45.89/6.99 | | | | | | | simplifying with (150), (154) gives:
% 45.89/6.99 | | | | | | | (163) ? [v0: mono_2Etyop_2Emin_2Ebool] : ? [v1: u] :
% 45.89/6.99 | | | | | | | (i_mono_2Etyop_2Emin_2Ebool(v0) = v1 &
% 45.89/6.99 | | | | | | | j_mono_2Etyop_2Emin_2Ebool(all_123_2) = v0 &
% 45.89/6.99 | | | | | | | s(tyop_2Emin_2Ebool, v1) = all_123_2 &
% 45.89/6.99 | | | | | | | mono_2Etyop_2Emin_2Ebool(v0) & du(all_123_2) & u(v1))
% 45.89/6.99 | | | | | | |
% 45.89/6.99 | | | | | | | GROUND_INST: instantiating (2) with mono_2Ec_2Ebool_2EF_2E0,
% 45.89/6.99 | | | | | | | all_81_1, all_45_0, all_81_0, simplifying with (5),
% 45.89/6.99 | | | | | | | (31), (64), (65) gives:
% 45.89/6.99 | | | | | | | (164) all_81_0 = 0 | all_81_1 = mono_2Ec_2Ebool_2EF_2E0 |
% 45.89/6.99 | | | | | | | all_45_0 = 0
% 45.89/6.99 | | | | | | |
% 45.89/6.99 | | | | | | | GROUND_INST: instantiating (9) with all_81_1, all_81_0,
% 45.89/6.99 | | | | | | | simplifying with (64), (65) gives:
% 45.89/6.99 | | | | | | | (165) all_81_0 = 0 | ? [v0: mono_2Etyop_2Emin_2Ebool] :
% 45.89/6.99 | | | | | | | (mono_2Ec_2Ebool_2E_7E_2E1(all_81_1) = v0 & p(v0) = 0 &
% 45.89/6.99 | | | | | | | mono_2Etyop_2Emin_2Ebool(v0))
% 45.89/6.99 | | | | | | |
% 45.89/6.99 | | | | | | | GROUND_INST: instantiating (2) with all_81_1, all_83_1, all_81_0,
% 45.89/6.99 | | | | | | | all_83_0, simplifying with (64), (65), (69), (70)
% 45.89/6.99 | | | | | | | gives:
% 45.89/6.99 | | | | | | | (166) all_83_0 = 0 | all_83_1 = all_81_1 | all_81_0 = 0
% 45.89/6.99 | | | | | | |
% 45.89/6.99 | | | | | | | GROUND_INST: instantiating (9) with all_83_1, all_83_0,
% 45.89/6.99 | | | | | | | simplifying with (69), (70) gives:
% 45.89/6.99 | | | | | | | (167) all_83_0 = 0 | ? [v0: mono_2Etyop_2Emin_2Ebool] :
% 45.89/6.99 | | | | | | | (mono_2Ec_2Ebool_2E_7E_2E1(all_83_1) = v0 & p(v0) = 0 &
% 45.89/6.99 | | | | | | | mono_2Etyop_2Emin_2Ebool(v0))
% 45.89/6.99 | | | | | | |
% 45.89/6.99 | | | | | | | GROUND_INST: instantiating (15) with all_123_5, simplifying with
% 45.89/6.99 | | | | | | | (151), (156) gives:
% 45.89/6.99 | | | | | | | (168) ? [v0: mono_2Etyop_2Emin_2Ebool] : ? [v1: int] : ( ~
% 45.89/6.99 | | | | | | | (v1 = 0) &
% 45.89/6.99 | | | | | | | mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool(mono_2Ec_2Ebool_2E_7E_2E0,
% 45.89/6.99 | | | | | | | all_123_5) = v0 & p(v0) = v1 &
% 45.89/6.99 | | | | | | | mono_2Etyop_2Emin_2Ebool(v0))
% 45.89/6.99 | | | | | | |
% 45.89/6.99 | | | | | | | GROUND_INST: instantiating (8) with all_123_5, simplifying with
% 45.89/6.99 | | | | | | | (151), (156) gives:
% 45.89/6.99 | | | | | | | (169) ? [v0: mono_2Etyop_2Emin_2Ebool] : ? [v1: int] : ( ~
% 45.89/6.99 | | | | | | | (v1 = 0) & mono_2Ec_2Ebool_2E_7E_2E1(all_123_5) = v0 &
% 45.89/6.99 | | | | | | | p(v0) = v1 & mono_2Etyop_2Emin_2Ebool(v0))
% 45.89/6.99 | | | | | | |
% 45.89/6.99 | | | | | | | GROUND_INST: instantiating (2) with all_81_1, all_123_1, all_81_0,
% 45.89/6.99 | | | | | | | all_123_0, simplifying with (64), (65), (152), (157)
% 45.89/6.99 | | | | | | | gives:
% 45.89/6.99 | | | | | | | (170) all_123_0 = 0 | all_123_1 = all_81_1 | all_81_0 = 0
% 45.89/6.99 | | | | | | |
% 45.89/6.99 | | | | | | | GROUND_INST: instantiating (9) with all_123_1, all_123_0,
% 45.89/6.99 | | | | | | | simplifying with (152), (157) gives:
% 45.89/6.99 | | | | | | | (171) all_123_0 = 0 | ? [v0: mono_2Etyop_2Emin_2Ebool] :
% 45.89/6.99 | | | | | | | (mono_2Ec_2Ebool_2E_7E_2E1(all_123_1) = v0 & p(v0) = 0 &
% 45.89/6.99 | | | | | | | mono_2Etyop_2Emin_2Ebool(v0))
% 45.89/6.99 | | | | | | |
% 45.89/6.99 | | | | | | | GROUND_INST: instantiating (1) with mono_2Ec_2Ebool_2ET_2E0,
% 45.89/6.99 | | | | | | | all_136_0, simplifying with (3), (6), (112), (113)
% 45.89/6.99 | | | | | | | gives:
% 45.89/6.99 | | | | | | | (172) all_136_0 = mono_2Ec_2Ebool_2ET_2E0
% 45.89/6.99 | | | | | | |
% 45.89/6.99 | | | | | | | GROUND_INST: instantiating (15) with all_136_0, simplifying with
% 45.89/6.99 | | | | | | | (112), (113) gives:
% 45.89/6.99 | | | | | | | (173) ? [v0: mono_2Etyop_2Emin_2Ebool] : ? [v1: int] : ( ~
% 45.89/6.99 | | | | | | | (v1 = 0) &
% 45.89/6.99 | | | | | | | mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool(mono_2Ec_2Ebool_2E_7E_2E0,
% 45.89/6.99 | | | | | | | all_136_0) = v0 & p(v0) = v1 &
% 45.89/6.99 | | | | | | | mono_2Etyop_2Emin_2Ebool(v0))
% 45.89/6.99 | | | | | | |
% 45.89/6.99 | | | | | | | GROUND_INST: instantiating (8) with all_136_0, simplifying with
% 45.89/6.99 | | | | | | | (112), (113) gives:
% 45.89/6.99 | | | | | | | (174) ? [v0: mono_2Etyop_2Emin_2Ebool] : ? [v1: int] : ( ~
% 45.89/6.99 | | | | | | | (v1 = 0) & mono_2Ec_2Ebool_2E_7E_2E1(all_136_0) = v0 &
% 45.89/6.99 | | | | | | | p(v0) = v1 & mono_2Etyop_2Emin_2Ebool(v0))
% 45.89/6.99 | | | | | | |
% 45.89/6.99 | | | | | | | GROUND_INST: instantiating (1) with all_136_0, all_142_0,
% 45.89/6.99 | | | | | | | simplifying with (112), (113), (138), (141) gives:
% 45.89/6.99 | | | | | | | (175) all_142_0 = all_136_0
% 45.89/6.99 | | | | | | |
% 45.89/6.99 | | | | | | | GROUND_INST: instantiating (1) with all_123_5, all_142_0,
% 45.89/6.99 | | | | | | | simplifying with (138), (141), (151), (156) gives:
% 45.89/6.99 | | | | | | | (176) all_142_0 = all_123_5
% 45.89/6.99 | | | | | | |
% 45.89/6.99 | | | | | | | GROUND_INST: instantiating (15) with all_142_0, simplifying with
% 45.89/6.99 | | | | | | | (138), (141) gives:
% 45.89/7.00 | | | | | | | (177) ? [v0: mono_2Etyop_2Emin_2Ebool] : ? [v1: int] : ( ~
% 45.89/7.00 | | | | | | | (v1 = 0) &
% 45.89/7.00 | | | | | | | mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool(mono_2Ec_2Ebool_2E_7E_2E0,
% 45.89/7.00 | | | | | | | all_142_0) = v0 & p(v0) = v1 &
% 45.89/7.00 | | | | | | | mono_2Etyop_2Emin_2Ebool(v0))
% 45.89/7.00 | | | | | | |
% 45.89/7.00 | | | | | | | GROUND_INST: instantiating (8) with all_142_0, simplifying with
% 45.89/7.00 | | | | | | | (138), (141) gives:
% 45.89/7.00 | | | | | | | (178) ? [v0: mono_2Etyop_2Emin_2Ebool] : ? [v1: int] : ( ~
% 45.89/7.00 | | | | | | | (v1 = 0) & mono_2Ec_2Ebool_2E_7E_2E1(all_142_0) = v0 &
% 45.89/7.00 | | | | | | | p(v0) = v1 & mono_2Etyop_2Emin_2Ebool(v0))
% 45.89/7.00 | | | | | | |
% 45.89/7.00 | | | | | | | GROUND_INST: instantiating (12) with all_60_9, all_123_9,
% 45.89/7.00 | | | | | | | all_89_0, all_123_8, all_60_7, all_60_6, all_123_3,
% 45.89/7.00 | | | | | | | simplifying with (37), (43), (78), (79), (98), (155),
% 45.89/7.00 | | | | | | | (160) gives:
% 45.89/7.00 | | | | | | | (179) ? [v0: du] : ? [v1: mono_2Etyop_2Emin_2Ebool] : ? [v2:
% 45.89/7.00 | | | | | | | d] : ? [v3: d] : ? [v4: du] : ? [v5: u] : ? [v6:
% 45.89/7.00 | | | | | | | du] : ? [v7: u] : ? [v8: du] :
% 45.89/7.00 | | | | | | | (j_mono_2Etyop_2Emin_2Ebool(v8) = v1 &
% 45.89/7.00 | | | | | | | j_mono_2Etyop_2Emin_2Ebool(v0) = v1 &
% 45.89/7.00 | | | | | | | tyop_2Emin_2Efun(all_60_7, tyop_2Emin_2Ebool) = v2 &
% 45.89/7.00 | | | | | | | tyop_2Emin_2Efun(all_60_9, v2) = v3 & app_2E2(v6,
% 45.89/7.00 | | | | | | | all_60_6) = v7 & app_2E2(v4, all_123_8) = v5 & s(v3,
% 45.89/7.00 | | | | | | | c_2Ebool_2EIN_2E0) = v4 & s(v2, v5) = v6 &
% 45.89/7.00 | | | | | | | s(tyop_2Emin_2Ebool, v7) = v8 & s(tyop_2Emin_2Ebool,
% 45.89/7.00 | | | | | | | all_123_3) = v0 & mono_2Etyop_2Emin_2Ebool(v1) &
% 45.89/7.00 | | | | | | | du(v8) & du(v6) & du(v4) & du(v0) & d(v3) & d(v2) &
% 45.89/7.00 | | | | | | | u(v7) & u(v5))
% 45.89/7.00 | | | | | | |
% 45.89/7.00 | | | | | | | GROUND_INST: instantiating (18) with all_60_9, all_89_0,
% 45.89/7.00 | | | | | | | all_123_9, all_99_2, all_123_8, all_60_7, all_60_6,
% 45.89/7.00 | | | | | | | all_99_1, all_99_0, all_60_4, all_123_7, simplifying
% 45.89/7.00 | | | | | | | with (37), (43), (78), (79), (83), (87), (98), (142),
% 45.89/7.00 | | | | | | | (146), (155), (161) gives:
% 45.89/7.00 | | | | | | | (180) ? [v0: du] : ? [v1: mono_2Etyop_2Emin_2Ebool] : ? [v2:
% 45.89/7.00 | | | | | | | any] : ? [v3: u] : ? [v4: du] : ? [v5:
% 45.89/7.00 | | | | | | | mono_2Etyop_2Emin_2Ebool] : ? [v6: any] :
% 45.89/7.00 | | | | | | | (c_2Ebool_2EIN_2E2(all_123_8, all_60_6) = v3 &
% 45.89/7.00 | | | | | | | j_mono_2Etyop_2Emin_2Ebool(v4) = v5 &
% 45.89/7.00 | | | | | | | j_mono_2Etyop_2Emin_2Ebool(v0) = v1 & p(v5) = v6 &
% 45.89/7.00 | | | | | | | p(v1) = v2 & s(tyop_2Emin_2Ebool, v3) = v4 &
% 45.89/7.00 | | | | | | | s(tyop_2Emin_2Ebool, all_123_7) = v0 &
% 45.89/7.00 | | | | | | | mono_2Etyop_2Emin_2Ebool(v5) &
% 45.89/7.00 | | | | | | | mono_2Etyop_2Emin_2Ebool(v1) & du(v4) & du(v0) & u(v3)
% 45.89/7.00 | | | | | | | & ( ~ (v2 = 0) | (v6 = 0 & ~ (all_123_8 = all_99_1))))
% 45.89/7.00 | | | | | | |
% 45.89/7.00 | | | | | | | GROUND_INST: instantiating (12) with all_60_9, all_123_9,
% 45.89/7.00 | | | | | | | all_87_0, all_123_8, all_60_7, all_60_4, all_123_7,
% 45.89/7.00 | | | | | | | simplifying with (37), (43), (75), (76), (98), (155),
% 45.89/7.00 | | | | | | | (161) gives:
% 45.89/7.00 | | | | | | | (181) ? [v0: du] : ? [v1: mono_2Etyop_2Emin_2Ebool] : ? [v2:
% 45.89/7.00 | | | | | | | d] : ? [v3: d] : ? [v4: du] : ? [v5: u] : ? [v6:
% 45.89/7.00 | | | | | | | du] : ? [v7: u] : ? [v8: du] :
% 45.89/7.00 | | | | | | | (j_mono_2Etyop_2Emin_2Ebool(v8) = v1 &
% 45.89/7.00 | | | | | | | j_mono_2Etyop_2Emin_2Ebool(v0) = v1 &
% 45.89/7.00 | | | | | | | tyop_2Emin_2Efun(all_60_7, tyop_2Emin_2Ebool) = v2 &
% 45.89/7.00 | | | | | | | tyop_2Emin_2Efun(all_60_9, v2) = v3 & app_2E2(v6,
% 45.89/7.00 | | | | | | | all_60_4) = v7 & app_2E2(v4, all_123_8) = v5 & s(v3,
% 45.89/7.00 | | | | | | | c_2Ebool_2EIN_2E0) = v4 & s(v2, v5) = v6 &
% 45.89/7.00 | | | | | | | s(tyop_2Emin_2Ebool, v7) = v8 & s(tyop_2Emin_2Ebool,
% 45.89/7.00 | | | | | | | all_123_7) = v0 & mono_2Etyop_2Emin_2Ebool(v1) &
% 45.89/7.00 | | | | | | | du(v8) & du(v6) & du(v4) & du(v0) & d(v3) & d(v2) &
% 45.89/7.00 | | | | | | | u(v7) & u(v5))
% 45.89/7.00 | | | | | | |
% 45.89/7.00 | | | | | | | COMBINE_EQS: (175), (176) imply:
% 45.89/7.00 | | | | | | | (182) all_136_0 = all_123_5
% 45.89/7.00 | | | | | | |
% 45.89/7.00 | | | | | | | SIMP: (182) implies:
% 45.89/7.00 | | | | | | | (183) all_136_0 = all_123_5
% 45.89/7.00 | | | | | | |
% 45.89/7.00 | | | | | | | COMBINE_EQS: (172), (183) imply:
% 45.89/7.00 | | | | | | | (184) all_123_5 = mono_2Ec_2Ebool_2ET_2E0
% 45.89/7.00 | | | | | | |
% 45.89/7.00 | | | | | | | COMBINE_EQS: (176), (184) imply:
% 45.89/7.00 | | | | | | | (185) all_142_0 = mono_2Ec_2Ebool_2ET_2E0
% 45.89/7.00 | | | | | | |
% 45.89/7.00 | | | | | | | DELTA: instantiating (174) with fresh symbols all_167_0, all_167_1
% 45.89/7.00 | | | | | | | gives:
% 45.89/7.00 | | | | | | | (186) ~ (all_167_0 = 0) & mono_2Ec_2Ebool_2E_7E_2E1(all_136_0)
% 45.89/7.00 | | | | | | | = all_167_1 & p(all_167_1) = all_167_0 &
% 45.89/7.00 | | | | | | | mono_2Etyop_2Emin_2Ebool(all_167_1)
% 45.89/7.00 | | | | | | |
% 45.89/7.00 | | | | | | | ALPHA: (186) implies:
% 45.89/7.00 | | | | | | | (187) ~ (all_167_0 = 0)
% 45.89/7.00 | | | | | | | (188) p(all_167_1) = all_167_0
% 45.89/7.00 | | | | | | | (189) mono_2Ec_2Ebool_2E_7E_2E1(all_136_0) = all_167_1
% 45.89/7.00 | | | | | | |
% 45.89/7.00 | | | | | | | DELTA: instantiating (173) with fresh symbols all_169_0, all_169_1
% 45.89/7.00 | | | | | | | gives:
% 45.89/7.00 | | | | | | | (190) ~ (all_169_0 = 0) &
% 45.89/7.00 | | | | | | | mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool(mono_2Ec_2Ebool_2E_7E_2E0,
% 45.89/7.00 | | | | | | | all_136_0) = all_169_1 & p(all_169_1) = all_169_0 &
% 45.89/7.00 | | | | | | | mono_2Etyop_2Emin_2Ebool(all_169_1)
% 45.89/7.00 | | | | | | |
% 45.89/7.00 | | | | | | | ALPHA: (190) implies:
% 45.89/7.00 | | | | | | | (191) p(all_169_1) = all_169_0
% 45.89/7.00 | | | | | | | (192) mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool(mono_2Ec_2Ebool_2E_7E_2E0,
% 45.89/7.00 | | | | | | | all_136_0) = all_169_1
% 45.89/7.00 | | | | | | |
% 45.89/7.00 | | | | | | | DELTA: instantiating (169) with fresh symbols all_171_0, all_171_1
% 45.89/7.00 | | | | | | | gives:
% 45.89/7.00 | | | | | | | (193) ~ (all_171_0 = 0) & mono_2Ec_2Ebool_2E_7E_2E1(all_123_5)
% 45.89/7.00 | | | | | | | = all_171_1 & p(all_171_1) = all_171_0 &
% 45.89/7.00 | | | | | | | mono_2Etyop_2Emin_2Ebool(all_171_1)
% 45.89/7.00 | | | | | | |
% 45.89/7.00 | | | | | | | ALPHA: (193) implies:
% 45.89/7.00 | | | | | | | (194) p(all_171_1) = all_171_0
% 45.89/7.00 | | | | | | | (195) mono_2Ec_2Ebool_2E_7E_2E1(all_123_5) = all_171_1
% 45.89/7.00 | | | | | | |
% 45.89/7.00 | | | | | | | DELTA: instantiating (168) with fresh symbols all_173_0, all_173_1
% 45.89/7.00 | | | | | | | gives:
% 45.89/7.00 | | | | | | | (196) ~ (all_173_0 = 0) &
% 45.89/7.00 | | | | | | | mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool(mono_2Ec_2Ebool_2E_7E_2E0,
% 45.89/7.00 | | | | | | | all_123_5) = all_173_1 & p(all_173_1) = all_173_0 &
% 45.89/7.00 | | | | | | | mono_2Etyop_2Emin_2Ebool(all_173_1)
% 45.89/7.00 | | | | | | |
% 45.89/7.00 | | | | | | | ALPHA: (196) implies:
% 45.89/7.00 | | | | | | | (197) p(all_173_1) = all_173_0
% 45.89/7.00 | | | | | | | (198) mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool(mono_2Ec_2Ebool_2E_7E_2E0,
% 45.89/7.00 | | | | | | | all_123_5) = all_173_1
% 45.89/7.00 | | | | | | |
% 45.89/7.00 | | | | | | | DELTA: instantiating (178) with fresh symbols all_175_0, all_175_1
% 45.89/7.00 | | | | | | | gives:
% 45.89/7.00 | | | | | | | (199) ~ (all_175_0 = 0) & mono_2Ec_2Ebool_2E_7E_2E1(all_142_0)
% 45.89/7.00 | | | | | | | = all_175_1 & p(all_175_1) = all_175_0 &
% 45.89/7.00 | | | | | | | mono_2Etyop_2Emin_2Ebool(all_175_1)
% 45.89/7.00 | | | | | | |
% 45.89/7.00 | | | | | | | ALPHA: (199) implies:
% 45.89/7.00 | | | | | | | (200) p(all_175_1) = all_175_0
% 45.89/7.00 | | | | | | | (201) mono_2Ec_2Ebool_2E_7E_2E1(all_142_0) = all_175_1
% 45.89/7.00 | | | | | | |
% 45.89/7.00 | | | | | | | DELTA: instantiating (177) with fresh symbols all_177_0, all_177_1
% 45.89/7.00 | | | | | | | gives:
% 45.89/7.00 | | | | | | | (202) ~ (all_177_0 = 0) &
% 45.89/7.00 | | | | | | | mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool(mono_2Ec_2Ebool_2E_7E_2E0,
% 45.89/7.00 | | | | | | | all_142_0) = all_177_1 & p(all_177_1) = all_177_0 &
% 45.89/7.00 | | | | | | | mono_2Etyop_2Emin_2Ebool(all_177_1)
% 45.89/7.00 | | | | | | |
% 45.89/7.00 | | | | | | | ALPHA: (202) implies:
% 45.89/7.00 | | | | | | | (203) p(all_177_1) = all_177_0
% 45.89/7.00 | | | | | | | (204) mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool(mono_2Ec_2Ebool_2E_7E_2E0,
% 45.89/7.00 | | | | | | | all_142_0) = all_177_1
% 45.89/7.00 | | | | | | |
% 45.89/7.00 | | | | | | | DELTA: instantiating (163) with fresh symbols all_179_0, all_179_1
% 45.89/7.00 | | | | | | | gives:
% 45.89/7.00 | | | | | | | (205) i_mono_2Etyop_2Emin_2Ebool(all_179_1) = all_179_0 &
% 45.89/7.00 | | | | | | | j_mono_2Etyop_2Emin_2Ebool(all_123_2) = all_179_1 &
% 45.89/7.00 | | | | | | | s(tyop_2Emin_2Ebool, all_179_0) = all_123_2 &
% 45.89/7.00 | | | | | | | mono_2Etyop_2Emin_2Ebool(all_179_1) & du(all_123_2) &
% 45.89/7.00 | | | | | | | u(all_179_0)
% 45.89/7.00 | | | | | | |
% 45.89/7.00 | | | | | | | ALPHA: (205) implies:
% 45.89/7.00 | | | | | | | (206) j_mono_2Etyop_2Emin_2Ebool(all_123_2) = all_179_1
% 45.89/7.00 | | | | | | |
% 45.89/7.00 | | | | | | | DELTA: instantiating (162) with fresh symbols all_189_0, all_189_1
% 45.89/7.00 | | | | | | | gives:
% 45.89/7.00 | | | | | | | (207) i_mono_2Etyop_2Emin_2Ebool(all_189_1) = all_189_0 &
% 45.89/7.00 | | | | | | | j_mono_2Etyop_2Emin_2Ebool(all_123_6) = all_189_1 &
% 45.89/7.00 | | | | | | | s(tyop_2Emin_2Ebool, all_189_0) = all_123_6 &
% 45.89/7.00 | | | | | | | mono_2Etyop_2Emin_2Ebool(all_189_1) & du(all_123_6) &
% 45.89/7.00 | | | | | | | u(all_189_0)
% 45.89/7.00 | | | | | | |
% 45.89/7.00 | | | | | | | ALPHA: (207) implies:
% 45.89/7.00 | | | | | | | (208) j_mono_2Etyop_2Emin_2Ebool(all_123_6) = all_189_1
% 45.89/7.00 | | | | | | |
% 45.89/7.00 | | | | | | | DELTA: instantiating (180) with fresh symbols all_293_0,
% 45.89/7.00 | | | | | | | all_293_1, all_293_2, all_293_3, all_293_4, all_293_5,
% 45.89/7.00 | | | | | | | all_293_6 gives:
% 45.89/7.01 | | | | | | | (209) c_2Ebool_2EIN_2E2(all_123_8, all_60_6) = all_293_3 &
% 45.89/7.01 | | | | | | | j_mono_2Etyop_2Emin_2Ebool(all_293_2) = all_293_1 &
% 45.89/7.01 | | | | | | | j_mono_2Etyop_2Emin_2Ebool(all_293_6) = all_293_5 &
% 45.89/7.01 | | | | | | | p(all_293_1) = all_293_0 & p(all_293_5) = all_293_4 &
% 45.89/7.01 | | | | | | | s(tyop_2Emin_2Ebool, all_293_3) = all_293_2 &
% 45.89/7.01 | | | | | | | s(tyop_2Emin_2Ebool, all_123_7) = all_293_6 &
% 45.89/7.01 | | | | | | | mono_2Etyop_2Emin_2Ebool(all_293_1) &
% 45.89/7.01 | | | | | | | mono_2Etyop_2Emin_2Ebool(all_293_5) & du(all_293_2) &
% 45.89/7.01 | | | | | | | du(all_293_6) & u(all_293_3) & ( ~ (all_293_4 = 0) |
% 45.89/7.01 | | | | | | | (all_293_0 = 0 & ~ (all_123_8 = all_99_1)))
% 45.89/7.01 | | | | | | |
% 45.89/7.01 | | | | | | | ALPHA: (209) implies:
% 45.89/7.01 | | | | | | | (210) s(tyop_2Emin_2Ebool, all_123_7) = all_293_6
% 45.89/7.01 | | | | | | | (211) s(tyop_2Emin_2Ebool, all_293_3) = all_293_2
% 45.89/7.01 | | | | | | | (212) p(all_293_5) = all_293_4
% 45.89/7.01 | | | | | | | (213) p(all_293_1) = all_293_0
% 45.89/7.01 | | | | | | | (214) j_mono_2Etyop_2Emin_2Ebool(all_293_6) = all_293_5
% 45.89/7.01 | | | | | | | (215) j_mono_2Etyop_2Emin_2Ebool(all_293_2) = all_293_1
% 45.89/7.01 | | | | | | | (216) c_2Ebool_2EIN_2E2(all_123_8, all_60_6) = all_293_3
% 45.89/7.01 | | | | | | | (217) ~ (all_293_4 = 0) | (all_293_0 = 0 & ~ (all_123_8 =
% 45.89/7.01 | | | | | | | all_99_1))
% 45.89/7.01 | | | | | | |
% 45.89/7.01 | | | | | | | DELTA: instantiating (181) with fresh symbols all_379_0,
% 45.89/7.01 | | | | | | | all_379_1, all_379_2, all_379_3, all_379_4, all_379_5,
% 45.89/7.01 | | | | | | | all_379_6, all_379_7, all_379_8 gives:
% 45.89/7.01 | | | | | | | (218) j_mono_2Etyop_2Emin_2Ebool(all_379_0) = all_379_7 &
% 45.89/7.01 | | | | | | | j_mono_2Etyop_2Emin_2Ebool(all_379_8) = all_379_7 &
% 45.89/7.01 | | | | | | | tyop_2Emin_2Efun(all_60_7, tyop_2Emin_2Ebool) = all_379_6
% 45.89/7.01 | | | | | | | & tyop_2Emin_2Efun(all_60_9, all_379_6) = all_379_5 &
% 45.89/7.01 | | | | | | | app_2E2(all_379_2, all_60_4) = all_379_1 &
% 45.89/7.01 | | | | | | | app_2E2(all_379_4, all_123_8) = all_379_3 & s(all_379_5,
% 45.89/7.01 | | | | | | | c_2Ebool_2EIN_2E0) = all_379_4 & s(all_379_6,
% 45.89/7.01 | | | | | | | all_379_3) = all_379_2 & s(tyop_2Emin_2Ebool,
% 45.89/7.01 | | | | | | | all_379_1) = all_379_0 & s(tyop_2Emin_2Ebool,
% 45.89/7.01 | | | | | | | all_123_7) = all_379_8 &
% 45.89/7.01 | | | | | | | mono_2Etyop_2Emin_2Ebool(all_379_7) & du(all_379_0) &
% 45.89/7.01 | | | | | | | du(all_379_2) & du(all_379_4) & du(all_379_8) &
% 45.89/7.01 | | | | | | | d(all_379_5) & d(all_379_6) & u(all_379_1) & u(all_379_3)
% 45.89/7.01 | | | | | | |
% 45.89/7.01 | | | | | | | ALPHA: (218) implies:
% 45.89/7.01 | | | | | | | (219) s(tyop_2Emin_2Ebool, all_123_7) = all_379_8
% 45.89/7.01 | | | | | | | (220) j_mono_2Etyop_2Emin_2Ebool(all_379_8) = all_379_7
% 45.89/7.01 | | | | | | |
% 45.89/7.01 | | | | | | | DELTA: instantiating (179) with fresh symbols all_381_0,
% 45.89/7.01 | | | | | | | all_381_1, all_381_2, all_381_3, all_381_4, all_381_5,
% 45.89/7.01 | | | | | | | all_381_6, all_381_7, all_381_8 gives:
% 45.89/7.01 | | | | | | | (221) j_mono_2Etyop_2Emin_2Ebool(all_381_0) = all_381_7 &
% 45.89/7.01 | | | | | | | j_mono_2Etyop_2Emin_2Ebool(all_381_8) = all_381_7 &
% 45.89/7.01 | | | | | | | tyop_2Emin_2Efun(all_60_7, tyop_2Emin_2Ebool) = all_381_6
% 45.89/7.01 | | | | | | | & tyop_2Emin_2Efun(all_60_9, all_381_6) = all_381_5 &
% 45.89/7.01 | | | | | | | app_2E2(all_381_2, all_60_6) = all_381_1 &
% 45.89/7.01 | | | | | | | app_2E2(all_381_4, all_123_8) = all_381_3 & s(all_381_5,
% 45.89/7.01 | | | | | | | c_2Ebool_2EIN_2E0) = all_381_4 & s(all_381_6,
% 45.89/7.01 | | | | | | | all_381_3) = all_381_2 & s(tyop_2Emin_2Ebool,
% 45.89/7.01 | | | | | | | all_381_1) = all_381_0 & s(tyop_2Emin_2Ebool,
% 45.89/7.01 | | | | | | | all_123_3) = all_381_8 &
% 45.89/7.01 | | | | | | | mono_2Etyop_2Emin_2Ebool(all_381_7) & du(all_381_0) &
% 45.89/7.01 | | | | | | | du(all_381_2) & du(all_381_4) & du(all_381_8) &
% 45.89/7.01 | | | | | | | d(all_381_5) & d(all_381_6) & u(all_381_1) & u(all_381_3)
% 45.89/7.01 | | | | | | |
% 45.89/7.01 | | | | | | | ALPHA: (221) implies:
% 45.89/7.01 | | | | | | | (222) s(tyop_2Emin_2Ebool, all_123_3) = all_381_8
% 45.89/7.01 | | | | | | | (223) j_mono_2Etyop_2Emin_2Ebool(all_381_8) = all_381_7
% 45.89/7.01 | | | | | | |
% 45.89/7.01 | | | | | | | REDUCE: (185), (204) imply:
% 45.89/7.01 | | | | | | | (224) mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool(mono_2Ec_2Ebool_2E_7E_2E0,
% 45.89/7.01 | | | | | | | mono_2Ec_2Ebool_2ET_2E0) = all_177_1
% 45.89/7.01 | | | | | | |
% 45.89/7.01 | | | | | | | REDUCE: (172), (192) imply:
% 45.89/7.01 | | | | | | | (225) mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool(mono_2Ec_2Ebool_2E_7E_2E0,
% 45.89/7.01 | | | | | | | mono_2Ec_2Ebool_2ET_2E0) = all_169_1
% 45.89/7.01 | | | | | | |
% 45.89/7.01 | | | | | | | REDUCE: (184), (198) imply:
% 45.89/7.01 | | | | | | | (226) mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool(mono_2Ec_2Ebool_2E_7E_2E0,
% 45.89/7.01 | | | | | | | mono_2Ec_2Ebool_2ET_2E0) = all_173_1
% 45.89/7.01 | | | | | | |
% 45.89/7.01 | | | | | | | REDUCE: (158), (184) imply:
% 45.89/7.01 | | | | | | | (227) j_mono_2Etyop_2Emin_2Ebool(all_123_6) =
% 45.89/7.01 | | | | | | | mono_2Ec_2Ebool_2ET_2E0
% 45.89/7.01 | | | | | | |
% 45.89/7.01 | | | | | | | REDUCE: (185), (201) imply:
% 45.89/7.01 | | | | | | | (228) mono_2Ec_2Ebool_2E_7E_2E1(mono_2Ec_2Ebool_2ET_2E0) =
% 45.89/7.01 | | | | | | | all_175_1
% 45.89/7.01 | | | | | | |
% 45.89/7.01 | | | | | | | REDUCE: (172), (189) imply:
% 45.89/7.01 | | | | | | | (229) mono_2Ec_2Ebool_2E_7E_2E1(mono_2Ec_2Ebool_2ET_2E0) =
% 45.89/7.01 | | | | | | | all_167_1
% 45.89/7.01 | | | | | | |
% 45.89/7.01 | | | | | | | REDUCE: (184), (195) imply:
% 45.89/7.01 | | | | | | | (230) mono_2Ec_2Ebool_2E_7E_2E1(mono_2Ec_2Ebool_2ET_2E0) =
% 45.89/7.01 | | | | | | | all_171_1
% 45.89/7.01 | | | | | | |
% 45.89/7.01 | | | | | | | REDUCE: (115), (172) imply:
% 45.89/7.01 | | | | | | | (231) mono_2Ec_2Ebool_2E_7E_2E1(mono_2Ec_2Ebool_2EF_2E0) =
% 45.89/7.01 | | | | | | | mono_2Ec_2Ebool_2ET_2E0
% 45.89/7.01 | | | | | | |
% 45.89/7.01 | | | | | | | BETA: splitting (166) gives:
% 45.89/7.01 | | | | | | |
% 45.89/7.01 | | | | | | | Case 1:
% 45.89/7.01 | | | | | | | |
% 45.89/7.01 | | | | | | | | (232) all_83_0 = 0
% 45.89/7.01 | | | | | | | |
% 45.89/7.01 | | | | | | | | REDUCE: (68), (232) imply:
% 45.89/7.01 | | | | | | | | (233) $false
% 45.89/7.01 | | | | | | | |
% 45.89/7.01 | | | | | | | | CLOSE: (233) is inconsistent.
% 45.89/7.01 | | | | | | | |
% 45.89/7.01 | | | | | | | Case 2:
% 45.89/7.01 | | | | | | | |
% 45.89/7.01 | | | | | | | | (234) all_83_1 = all_81_1 | all_81_0 = 0
% 45.89/7.01 | | | | | | | |
% 45.89/7.01 | | | | | | | | BETA: splitting (167) gives:
% 45.89/7.01 | | | | | | | |
% 45.89/7.01 | | | | | | | | Case 1:
% 45.89/7.01 | | | | | | | | |
% 45.89/7.01 | | | | | | | | | (235) all_83_0 = 0
% 45.89/7.01 | | | | | | | | |
% 45.89/7.01 | | | | | | | | | REDUCE: (68), (235) imply:
% 45.89/7.01 | | | | | | | | | (236) $false
% 45.89/7.01 | | | | | | | | |
% 45.89/7.01 | | | | | | | | | CLOSE: (236) is inconsistent.
% 45.89/7.01 | | | | | | | | |
% 45.89/7.01 | | | | | | | | Case 2:
% 45.89/7.01 | | | | | | | | |
% 45.89/7.01 | | | | | | | | | (237) ? [v0: mono_2Etyop_2Emin_2Ebool] :
% 45.89/7.01 | | | | | | | | | (mono_2Ec_2Ebool_2E_7E_2E1(all_83_1) = v0 & p(v0) = 0
% 45.89/7.01 | | | | | | | | | & mono_2Etyop_2Emin_2Ebool(v0))
% 45.89/7.01 | | | | | | | | |
% 45.89/7.01 | | | | | | | | | DELTA: instantiating (237) with fresh symbol all_414_0 gives:
% 45.89/7.01 | | | | | | | | | (238) mono_2Ec_2Ebool_2E_7E_2E1(all_83_1) = all_414_0 &
% 45.89/7.01 | | | | | | | | | p(all_414_0) = 0 &
% 45.89/7.01 | | | | | | | | | mono_2Etyop_2Emin_2Ebool(all_414_0)
% 45.89/7.01 | | | | | | | | |
% 45.89/7.01 | | | | | | | | | ALPHA: (238) implies:
% 45.89/7.01 | | | | | | | | | (239) p(all_414_0) = 0
% 45.89/7.01 | | | | | | | | | (240) mono_2Ec_2Ebool_2E_7E_2E1(all_83_1) = all_414_0
% 45.89/7.01 | | | | | | | | |
% 45.89/7.01 | | | | | | | | | BETA: splitting (164) gives:
% 45.89/7.01 | | | | | | | | |
% 45.89/7.01 | | | | | | | | | Case 1:
% 45.89/7.01 | | | | | | | | | |
% 45.89/7.01 | | | | | | | | | | (241) all_81_0 = 0
% 45.89/7.01 | | | | | | | | | |
% 45.89/7.01 | | | | | | | | | | REDUCE: (63), (241) imply:
% 45.89/7.01 | | | | | | | | | | (242) $false
% 45.89/7.01 | | | | | | | | | |
% 45.89/7.01 | | | | | | | | | | CLOSE: (242) is inconsistent.
% 45.89/7.01 | | | | | | | | | |
% 45.89/7.01 | | | | | | | | | Case 2:
% 45.89/7.01 | | | | | | | | | |
% 45.89/7.01 | | | | | | | | | | (243) all_81_1 = mono_2Ec_2Ebool_2EF_2E0 | all_45_0 = 0
% 45.89/7.01 | | | | | | | | | |
% 45.89/7.01 | | | | | | | | | | BETA: splitting (171) gives:
% 45.89/7.01 | | | | | | | | | |
% 45.89/7.01 | | | | | | | | | | Case 1:
% 45.89/7.01 | | | | | | | | | | |
% 45.89/7.01 | | | | | | | | | | | (244) all_123_0 = 0
% 45.89/7.01 | | | | | | | | | | |
% 45.89/7.01 | | | | | | | | | | | REDUCE: (148), (244) imply:
% 45.89/7.01 | | | | | | | | | | | (245) $false
% 45.89/7.01 | | | | | | | | | | |
% 45.89/7.01 | | | | | | | | | | | CLOSE: (245) is inconsistent.
% 45.89/7.01 | | | | | | | | | | |
% 45.89/7.01 | | | | | | | | | | Case 2:
% 45.89/7.01 | | | | | | | | | | |
% 46.49/7.01 | | | | | | | | | | | (246) ? [v0: mono_2Etyop_2Emin_2Ebool] :
% 46.49/7.01 | | | | | | | | | | | (mono_2Ec_2Ebool_2E_7E_2E1(all_123_1) = v0 & p(v0)
% 46.49/7.01 | | | | | | | | | | | = 0 & mono_2Etyop_2Emin_2Ebool(v0))
% 46.49/7.01 | | | | | | | | | | |
% 46.49/7.01 | | | | | | | | | | | DELTA: instantiating (246) with fresh symbol all_437_0
% 46.49/7.01 | | | | | | | | | | | gives:
% 46.49/7.01 | | | | | | | | | | | (247) mono_2Ec_2Ebool_2E_7E_2E1(all_123_1) = all_437_0 &
% 46.49/7.01 | | | | | | | | | | | p(all_437_0) = 0 &
% 46.49/7.01 | | | | | | | | | | | mono_2Etyop_2Emin_2Ebool(all_437_0)
% 46.49/7.01 | | | | | | | | | | |
% 46.49/7.01 | | | | | | | | | | | ALPHA: (247) implies:
% 46.49/7.01 | | | | | | | | | | | (248) mono_2Ec_2Ebool_2E_7E_2E1(all_123_1) = all_437_0
% 46.49/7.01 | | | | | | | | | | |
% 46.49/7.01 | | | | | | | | | | | BETA: splitting (165) gives:
% 46.49/7.01 | | | | | | | | | | |
% 46.49/7.01 | | | | | | | | | | | Case 1:
% 46.49/7.01 | | | | | | | | | | | |
% 46.49/7.01 | | | | | | | | | | | | (249) all_81_0 = 0
% 46.49/7.01 | | | | | | | | | | | |
% 46.49/7.01 | | | | | | | | | | | | REDUCE: (63), (249) imply:
% 46.49/7.01 | | | | | | | | | | | | (250) $false
% 46.49/7.01 | | | | | | | | | | | |
% 46.49/7.01 | | | | | | | | | | | | CLOSE: (250) is inconsistent.
% 46.49/7.01 | | | | | | | | | | | |
% 46.49/7.01 | | | | | | | | | | | Case 2:
% 46.49/7.01 | | | | | | | | | | | |
% 46.49/7.01 | | | | | | | | | | | | (251) ? [v0: mono_2Etyop_2Emin_2Ebool] :
% 46.49/7.01 | | | | | | | | | | | | (mono_2Ec_2Ebool_2E_7E_2E1(all_81_1) = v0 & p(v0)
% 46.49/7.01 | | | | | | | | | | | | = 0 & mono_2Etyop_2Emin_2Ebool(v0))
% 46.49/7.01 | | | | | | | | | | | |
% 46.49/7.01 | | | | | | | | | | | | DELTA: instantiating (251) with fresh symbol all_446_0
% 46.49/7.01 | | | | | | | | | | | | gives:
% 46.49/7.01 | | | | | | | | | | | | (252) mono_2Ec_2Ebool_2E_7E_2E1(all_81_1) = all_446_0 &
% 46.49/7.01 | | | | | | | | | | | | p(all_446_0) = 0 &
% 46.49/7.01 | | | | | | | | | | | | mono_2Etyop_2Emin_2Ebool(all_446_0)
% 46.49/7.01 | | | | | | | | | | | |
% 46.49/7.01 | | | | | | | | | | | | ALPHA: (252) implies:
% 46.49/7.01 | | | | | | | | | | | | (253) mono_2Ec_2Ebool_2E_7E_2E1(all_81_1) = all_446_0
% 46.49/7.01 | | | | | | | | | | | |
% 46.49/7.01 | | | | | | | | | | | | BETA: splitting (243) gives:
% 46.49/7.01 | | | | | | | | | | | |
% 46.49/7.01 | | | | | | | | | | | | Case 1:
% 46.49/7.01 | | | | | | | | | | | | |
% 46.49/7.01 | | | | | | | | | | | | | (254) all_45_0 = 0
% 46.49/7.01 | | | | | | | | | | | | |
% 46.49/7.01 | | | | | | | | | | | | | REDUCE: (30), (254) imply:
% 46.49/7.01 | | | | | | | | | | | | | (255) $false
% 46.49/7.01 | | | | | | | | | | | | |
% 46.49/7.01 | | | | | | | | | | | | | CLOSE: (255) is inconsistent.
% 46.49/7.01 | | | | | | | | | | | | |
% 46.49/7.01 | | | | | | | | | | | | Case 2:
% 46.49/7.01 | | | | | | | | | | | | |
% 46.49/7.01 | | | | | | | | | | | | | (256) all_81_1 = mono_2Ec_2Ebool_2EF_2E0
% 46.49/7.01 | | | | | | | | | | | | |
% 46.49/7.01 | | | | | | | | | | | | | REDUCE: (253), (256) imply:
% 46.49/7.01 | | | | | | | | | | | | | (257) mono_2Ec_2Ebool_2E_7E_2E1(mono_2Ec_2Ebool_2EF_2E0)
% 46.49/7.01 | | | | | | | | | | | | | = all_446_0
% 46.49/7.01 | | | | | | | | | | | | |
% 46.49/7.01 | | | | | | | | | | | | | REDUCE: (66), (256) imply:
% 46.49/7.01 | | | | | | | | | | | | | (258) mono_2Ec_2Ebool_2E_7E_2E1(mono_2Ec_2Ebool_2ET_2E0)
% 46.49/7.01 | | | | | | | | | | | | | = mono_2Ec_2Ebool_2EF_2E0
% 46.49/7.01 | | | | | | | | | | | | |
% 46.49/7.01 | | | | | | | | | | | | | REDUCE: (65), (256) imply:
% 46.49/7.01 | | | | | | | | | | | | | (259) p(mono_2Ec_2Ebool_2EF_2E0) = all_81_0
% 46.49/7.01 | | | | | | | | | | | | |
% 46.49/7.01 | | | | | | | | | | | | | BETA: splitting (234) gives:
% 46.49/7.01 | | | | | | | | | | | | |
% 46.49/7.01 | | | | | | | | | | | | | Case 1:
% 46.49/7.01 | | | | | | | | | | | | | |
% 46.49/7.01 | | | | | | | | | | | | | | (260) all_81_0 = 0
% 46.49/7.01 | | | | | | | | | | | | | |
% 46.49/7.01 | | | | | | | | | | | | | | REDUCE: (63), (260) imply:
% 46.49/7.01 | | | | | | | | | | | | | | (261) $false
% 46.49/7.01 | | | | | | | | | | | | | |
% 46.49/7.01 | | | | | | | | | | | | | | CLOSE: (261) is inconsistent.
% 46.49/7.01 | | | | | | | | | | | | | |
% 46.49/7.01 | | | | | | | | | | | | | Case 2:
% 46.49/7.01 | | | | | | | | | | | | | |
% 46.49/7.01 | | | | | | | | | | | | | | (262) all_83_1 = all_81_1
% 46.49/7.01 | | | | | | | | | | | | | |
% 46.49/7.01 | | | | | | | | | | | | | | COMBINE_EQS: (256), (262) imply:
% 46.49/7.01 | | | | | | | | | | | | | | (263) all_83_1 = mono_2Ec_2Ebool_2EF_2E0
% 46.49/7.01 | | | | | | | | | | | | | |
% 46.49/7.02 | | | | | | | | | | | | | | REDUCE: (71), (263) imply:
% 46.49/7.02 | | | | | | | | | | | | | | (264) mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool(mono_2Ec_2Ebool_2E_7E_2E0,
% 46.49/7.02 | | | | | | | | | | | | | | mono_2Ec_2Ebool_2ET_2E0) =
% 46.49/7.02 | | | | | | | | | | | | | | mono_2Ec_2Ebool_2EF_2E0
% 46.49/7.02 | | | | | | | | | | | | | |
% 46.49/7.02 | | | | | | | | | | | | | | REDUCE: (240), (263) imply:
% 46.49/7.02 | | | | | | | | | | | | | | (265) mono_2Ec_2Ebool_2E_7E_2E1(mono_2Ec_2Ebool_2EF_2E0)
% 46.49/7.02 | | | | | | | | | | | | | | = all_414_0
% 46.49/7.02 | | | | | | | | | | | | | |
% 46.49/7.02 | | | | | | | | | | | | | | REDUCE: (70), (263) imply:
% 46.49/7.02 | | | | | | | | | | | | | | (266) p(mono_2Ec_2Ebool_2EF_2E0) = all_83_0
% 46.49/7.02 | | | | | | | | | | | | | |
% 46.49/7.02 | | | | | | | | | | | | | | BETA: splitting (170) gives:
% 46.49/7.02 | | | | | | | | | | | | | |
% 46.49/7.02 | | | | | | | | | | | | | | Case 1:
% 46.49/7.02 | | | | | | | | | | | | | | |
% 46.49/7.02 | | | | | | | | | | | | | | | (267) all_123_0 = 0
% 46.49/7.02 | | | | | | | | | | | | | | |
% 46.49/7.02 | | | | | | | | | | | | | | | REDUCE: (148), (267) imply:
% 46.49/7.02 | | | | | | | | | | | | | | | (268) $false
% 46.49/7.02 | | | | | | | | | | | | | | |
% 46.49/7.02 | | | | | | | | | | | | | | | CLOSE: (268) is inconsistent.
% 46.49/7.02 | | | | | | | | | | | | | | |
% 46.49/7.02 | | | | | | | | | | | | | | Case 2:
% 46.49/7.02 | | | | | | | | | | | | | | |
% 46.49/7.02 | | | | | | | | | | | | | | | (269) all_123_1 = all_81_1 | all_81_0 = 0
% 46.49/7.02 | | | | | | | | | | | | | | |
% 46.49/7.02 | | | | | | | | | | | | | | | BETA: splitting (269) gives:
% 46.49/7.02 | | | | | | | | | | | | | | |
% 46.49/7.02 | | | | | | | | | | | | | | | Case 1:
% 46.49/7.02 | | | | | | | | | | | | | | | |
% 46.49/7.02 | | | | | | | | | | | | | | | | (270) all_81_0 = 0
% 46.49/7.02 | | | | | | | | | | | | | | | |
% 46.49/7.02 | | | | | | | | | | | | | | | | REDUCE: (63), (270) imply:
% 46.49/7.02 | | | | | | | | | | | | | | | | (271) $false
% 46.49/7.02 | | | | | | | | | | | | | | | |
% 46.49/7.02 | | | | | | | | | | | | | | | | CLOSE: (271) is inconsistent.
% 46.49/7.02 | | | | | | | | | | | | | | | |
% 46.49/7.02 | | | | | | | | | | | | | | | Case 2:
% 46.49/7.02 | | | | | | | | | | | | | | | |
% 46.49/7.02 | | | | | | | | | | | | | | | | (272) all_123_1 = all_81_1
% 46.49/7.02 | | | | | | | | | | | | | | | |
% 46.49/7.02 | | | | | | | | | | | | | | | | COMBINE_EQS: (256), (272) imply:
% 46.49/7.02 | | | | | | | | | | | | | | | | (273) all_123_1 = mono_2Ec_2Ebool_2EF_2E0
% 46.49/7.02 | | | | | | | | | | | | | | | |
% 46.49/7.02 | | | | | | | | | | | | | | | | REDUCE: (159), (273) imply:
% 46.49/7.02 | | | | | | | | | | | | | | | | (274) j_mono_2Etyop_2Emin_2Ebool(all_123_2) =
% 46.49/7.02 | | | | | | | | | | | | | | | | mono_2Ec_2Ebool_2EF_2E0
% 46.49/7.02 | | | | | | | | | | | | | | | |
% 46.49/7.02 | | | | | | | | | | | | | | | | REDUCE: (248), (273) imply:
% 46.49/7.02 | | | | | | | | | | | | | | | | (275) mono_2Ec_2Ebool_2E_7E_2E1(mono_2Ec_2Ebool_2EF_2E0)
% 46.49/7.02 | | | | | | | | | | | | | | | | = all_437_0
% 46.49/7.02 | | | | | | | | | | | | | | | |
% 46.49/7.02 | | | | | | | | | | | | | | | | REDUCE: (157), (273) imply:
% 46.49/7.02 | | | | | | | | | | | | | | | | (276) p(mono_2Ec_2Ebool_2EF_2E0) = all_123_0
% 46.49/7.02 | | | | | | | | | | | | | | | |
% 46.49/7.02 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (26) with all_123_6, all_379_8,
% 46.49/7.02 | | | | | | | | | | | | | | | | all_123_7, tyop_2Emin_2Ebool, simplifying with
% 46.49/7.02 | | | | | | | | | | | | | | | | (153), (219) gives:
% 46.49/7.02 | | | | | | | | | | | | | | | | (277) all_379_8 = all_123_6
% 46.49/7.02 | | | | | | | | | | | | | | | |
% 46.49/7.02 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (26) with all_293_6, all_379_8,
% 46.49/7.02 | | | | | | | | | | | | | | | | all_123_7, tyop_2Emin_2Ebool, simplifying with
% 46.49/7.02 | | | | | | | | | | | | | | | | (210), (219) gives:
% 46.49/7.02 | | | | | | | | | | | | | | | | (278) all_379_8 = all_293_6
% 46.49/7.02 | | | | | | | | | | | | | | | |
% 46.49/7.02 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (26) with all_123_2, all_381_8,
% 46.49/7.02 | | | | | | | | | | | | | | | | all_123_3, tyop_2Emin_2Ebool, simplifying with
% 46.49/7.02 | | | | | | | | | | | | | | | | (154), (222) gives:
% 46.49/7.02 | | | | | | | | | | | | | | | | (279) all_381_8 = all_123_2
% 46.49/7.02 | | | | | | | | | | | | | | | |
% 46.49/7.02 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (21) with all_45_0, all_123_0,
% 46.49/7.02 | | | | | | | | | | | | | | | | mono_2Ec_2Ebool_2EF_2E0, simplifying with (31),
% 46.49/7.02 | | | | | | | | | | | | | | | | (276) gives:
% 46.49/7.02 | | | | | | | | | | | | | | | | (280) all_123_0 = all_45_0
% 46.49/7.02 | | | | | | | | | | | | | | | |
% 46.49/7.02 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (21) with all_83_0, all_123_0,
% 46.49/7.02 | | | | | | | | | | | | | | | | mono_2Ec_2Ebool_2EF_2E0, simplifying with (266),
% 46.49/7.02 | | | | | | | | | | | | | | | | (276) gives:
% 46.49/7.02 | | | | | | | | | | | | | | | | (281) all_123_0 = all_83_0
% 46.49/7.02 | | | | | | | | | | | | | | | |
% 46.49/7.02 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (21) with all_81_0, all_123_0,
% 46.49/7.02 | | | | | | | | | | | | | | | | mono_2Ec_2Ebool_2EF_2E0, simplifying with (259),
% 46.49/7.02 | | | | | | | | | | | | | | | | (276) gives:
% 46.49/7.02 | | | | | | | | | | | | | | | | (282) all_123_0 = all_81_0
% 46.49/7.02 | | | | | | | | | | | | | | | |
% 46.49/7.02 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (22) with all_437_0, all_446_0,
% 46.49/7.02 | | | | | | | | | | | | | | | | mono_2Ec_2Ebool_2EF_2E0, simplifying with (257),
% 46.49/7.02 | | | | | | | | | | | | | | | | (275) gives:
% 46.49/7.02 | | | | | | | | | | | | | | | | (283) all_446_0 = all_437_0
% 46.49/7.02 | | | | | | | | | | | | | | | |
% 46.49/7.02 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (22) with all_414_0, all_446_0,
% 46.49/7.02 | | | | | | | | | | | | | | | | mono_2Ec_2Ebool_2EF_2E0, simplifying with (257),
% 46.49/7.02 | | | | | | | | | | | | | | | | (265) gives:
% 46.49/7.02 | | | | | | | | | | | | | | | | (284) all_446_0 = all_414_0
% 46.49/7.02 | | | | | | | | | | | | | | | |
% 46.49/7.02 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (22) with mono_2Ec_2Ebool_2ET_2E0,
% 46.49/7.02 | | | | | | | | | | | | | | | | all_446_0, mono_2Ec_2Ebool_2EF_2E0, simplifying
% 46.49/7.02 | | | | | | | | | | | | | | | | with (231), (257) gives:
% 46.49/7.02 | | | | | | | | | | | | | | | | (285) all_446_0 = mono_2Ec_2Ebool_2ET_2E0
% 46.49/7.02 | | | | | | | | | | | | | | | |
% 46.49/7.02 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (22) with mono_2Ec_2Ebool_2EF_2E0,
% 46.49/7.02 | | | | | | | | | | | | | | | | all_171_1, mono_2Ec_2Ebool_2ET_2E0, simplifying
% 46.49/7.02 | | | | | | | | | | | | | | | | with (230), (258) gives:
% 46.49/7.02 | | | | | | | | | | | | | | | | (286) all_171_1 = mono_2Ec_2Ebool_2EF_2E0
% 46.49/7.02 | | | | | | | | | | | | | | | |
% 46.49/7.02 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (22) with all_171_1, all_175_1,
% 46.49/7.02 | | | | | | | | | | | | | | | | mono_2Ec_2Ebool_2ET_2E0, simplifying with (228),
% 46.49/7.02 | | | | | | | | | | | | | | | | (230) gives:
% 46.49/7.02 | | | | | | | | | | | | | | | | (287) all_175_1 = all_171_1
% 46.49/7.02 | | | | | | | | | | | | | | | |
% 46.49/7.02 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (22) with all_167_1, all_175_1,
% 46.49/7.02 | | | | | | | | | | | | | | | | mono_2Ec_2Ebool_2ET_2E0, simplifying with (228),
% 46.49/7.02 | | | | | | | | | | | | | | | | (229) gives:
% 46.49/7.02 | | | | | | | | | | | | | | | | (288) all_175_1 = all_167_1
% 46.49/7.02 | | | | | | | | | | | | | | | |
% 46.49/7.02 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (23) with mono_2Ec_2Ebool_2ET_2E0,
% 46.49/7.02 | | | | | | | | | | | | | | | | all_189_1, all_123_6, simplifying with (208),
% 46.49/7.02 | | | | | | | | | | | | | | | | (227) gives:
% 46.49/7.02 | | | | | | | | | | | | | | | | (289) all_189_1 = mono_2Ec_2Ebool_2ET_2E0
% 46.49/7.02 | | | | | | | | | | | | | | | |
% 46.49/7.02 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (23) with mono_2Ec_2Ebool_2EF_2E0,
% 46.49/7.02 | | | | | | | | | | | | | | | | all_179_1, all_123_2, simplifying with (206),
% 46.49/7.02 | | | | | | | | | | | | | | | | (274) gives:
% 46.49/7.02 | | | | | | | | | | | | | | | | (290) all_179_1 = mono_2Ec_2Ebool_2EF_2E0
% 46.49/7.02 | | | | | | | | | | | | | | | |
% 46.49/7.02 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (27) with all_169_1, all_173_1,
% 46.49/7.02 | | | | | | | | | | | | | | | | mono_2Ec_2Ebool_2ET_2E0,
% 46.49/7.02 | | | | | | | | | | | | | | | | mono_2Ec_2Ebool_2E_7E_2E0, simplifying with (225),
% 46.49/7.02 | | | | | | | | | | | | | | | | (226) gives:
% 46.49/7.02 | | | | | | | | | | | | | | | | (291) all_173_1 = all_169_1
% 46.49/7.02 | | | | | | | | | | | | | | | |
% 46.49/7.02 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (27) with all_173_1, all_177_1,
% 46.49/7.02 | | | | | | | | | | | | | | | | mono_2Ec_2Ebool_2ET_2E0,
% 46.49/7.02 | | | | | | | | | | | | | | | | mono_2Ec_2Ebool_2E_7E_2E0, simplifying with (224),
% 46.49/7.02 | | | | | | | | | | | | | | | | (226) gives:
% 46.49/7.02 | | | | | | | | | | | | | | | | (292) all_177_1 = all_173_1
% 46.49/7.02 | | | | | | | | | | | | | | | |
% 46.49/7.02 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (27) with mono_2Ec_2Ebool_2EF_2E0,
% 46.49/7.02 | | | | | | | | | | | | | | | | all_177_1, mono_2Ec_2Ebool_2ET_2E0,
% 46.49/7.02 | | | | | | | | | | | | | | | | mono_2Ec_2Ebool_2E_7E_2E0, simplifying with (224),
% 46.49/7.02 | | | | | | | | | | | | | | | | (264) gives:
% 46.49/7.02 | | | | | | | | | | | | | | | | (293) all_177_1 = mono_2Ec_2Ebool_2EF_2E0
% 46.49/7.02 | | | | | | | | | | | | | | | |
% 46.49/7.02 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (28) with all_123_3, all_293_3,
% 46.49/7.02 | | | | | | | | | | | | | | | | all_60_6, all_123_8, simplifying with (160), (216)
% 46.49/7.02 | | | | | | | | | | | | | | | | gives:
% 46.49/7.02 | | | | | | | | | | | | | | | | (294) all_293_3 = all_123_3
% 46.49/7.02 | | | | | | | | | | | | | | | |
% 46.49/7.02 | | | | | | | | | | | | | | | | COMBINE_EQS: (283), (285) imply:
% 46.49/7.02 | | | | | | | | | | | | | | | | (295) all_437_0 = mono_2Ec_2Ebool_2ET_2E0
% 46.49/7.02 | | | | | | | | | | | | | | | |
% 46.49/7.02 | | | | | | | | | | | | | | | | COMBINE_EQS: (283), (284) imply:
% 46.49/7.02 | | | | | | | | | | | | | | | | (296) all_437_0 = all_414_0
% 46.49/7.02 | | | | | | | | | | | | | | | |
% 46.49/7.02 | | | | | | | | | | | | | | | | COMBINE_EQS: (295), (296) imply:
% 46.49/7.02 | | | | | | | | | | | | | | | | (297) all_414_0 = mono_2Ec_2Ebool_2ET_2E0
% 46.49/7.02 | | | | | | | | | | | | | | | |
% 46.49/7.02 | | | | | | | | | | | | | | | | SIMP: (297) implies:
% 46.49/7.02 | | | | | | | | | | | | | | | | (298) all_414_0 = mono_2Ec_2Ebool_2ET_2E0
% 46.49/7.02 | | | | | | | | | | | | | | | |
% 46.49/7.02 | | | | | | | | | | | | | | | | COMBINE_EQS: (277), (278) imply:
% 46.49/7.02 | | | | | | | | | | | | | | | | (299) all_293_6 = all_123_6
% 46.49/7.02 | | | | | | | | | | | | | | | |
% 46.49/7.02 | | | | | | | | | | | | | | | | SIMP: (299) implies:
% 46.49/7.02 | | | | | | | | | | | | | | | | (300) all_293_6 = all_123_6
% 46.49/7.02 | | | | | | | | | | | | | | | |
% 46.49/7.02 | | | | | | | | | | | | | | | | COMBINE_EQS: (292), (293) imply:
% 46.49/7.02 | | | | | | | | | | | | | | | | (301) all_173_1 = mono_2Ec_2Ebool_2EF_2E0
% 46.49/7.02 | | | | | | | | | | | | | | | |
% 46.49/7.02 | | | | | | | | | | | | | | | | SIMP: (301) implies:
% 46.49/7.02 | | | | | | | | | | | | | | | | (302) all_173_1 = mono_2Ec_2Ebool_2EF_2E0
% 46.49/7.02 | | | | | | | | | | | | | | | |
% 46.49/7.02 | | | | | | | | | | | | | | | | COMBINE_EQS: (287), (288) imply:
% 46.49/7.02 | | | | | | | | | | | | | | | | (303) all_171_1 = all_167_1
% 46.49/7.02 | | | | | | | | | | | | | | | |
% 46.49/7.02 | | | | | | | | | | | | | | | | SIMP: (303) implies:
% 46.49/7.02 | | | | | | | | | | | | | | | | (304) all_171_1 = all_167_1
% 46.49/7.02 | | | | | | | | | | | | | | | |
% 46.49/7.02 | | | | | | | | | | | | | | | | COMBINE_EQS: (291), (302) imply:
% 46.49/7.02 | | | | | | | | | | | | | | | | (305) all_169_1 = mono_2Ec_2Ebool_2EF_2E0
% 46.49/7.02 | | | | | | | | | | | | | | | |
% 46.49/7.02 | | | | | | | | | | | | | | | | SIMP: (305) implies:
% 46.49/7.02 | | | | | | | | | | | | | | | | (306) all_169_1 = mono_2Ec_2Ebool_2EF_2E0
% 46.49/7.02 | | | | | | | | | | | | | | | |
% 46.49/7.02 | | | | | | | | | | | | | | | | COMBINE_EQS: (286), (304) imply:
% 46.49/7.02 | | | | | | | | | | | | | | | | (307) all_167_1 = mono_2Ec_2Ebool_2EF_2E0
% 46.49/7.02 | | | | | | | | | | | | | | | |
% 46.49/7.02 | | | | | | | | | | | | | | | | COMBINE_EQS: (280), (281) imply:
% 46.49/7.02 | | | | | | | | | | | | | | | | (308) all_83_0 = all_45_0
% 46.49/7.02 | | | | | | | | | | | | | | | |
% 46.49/7.02 | | | | | | | | | | | | | | | | COMBINE_EQS: (281), (282) imply:
% 46.49/7.02 | | | | | | | | | | | | | | | | (309) all_83_0 = all_81_0
% 46.49/7.02 | | | | | | | | | | | | | | | |
% 46.49/7.02 | | | | | | | | | | | | | | | | COMBINE_EQS: (308), (309) imply:
% 46.49/7.02 | | | | | | | | | | | | | | | | (310) all_81_0 = all_45_0
% 46.49/7.02 | | | | | | | | | | | | | | | |
% 46.49/7.02 | | | | | | | | | | | | | | | | COMBINE_EQS: (288), (307) imply:
% 46.49/7.02 | | | | | | | | | | | | | | | | (311) all_175_1 = mono_2Ec_2Ebool_2EF_2E0
% 46.49/7.02 | | | | | | | | | | | | | | | |
% 46.49/7.02 | | | | | | | | | | | | | | | | REDUCE: (223), (279) imply:
% 46.49/7.02 | | | | | | | | | | | | | | | | (312) j_mono_2Etyop_2Emin_2Ebool(all_123_2) = all_381_7
% 46.49/7.02 | | | | | | | | | | | | | | | |
% 46.49/7.02 | | | | | | | | | | | | | | | | REDUCE: (220), (277) imply:
% 46.49/7.02 | | | | | | | | | | | | | | | | (313) j_mono_2Etyop_2Emin_2Ebool(all_123_6) = all_379_7
% 46.49/7.02 | | | | | | | | | | | | | | | |
% 46.49/7.02 | | | | | | | | | | | | | | | | REDUCE: (214), (300) imply:
% 46.49/7.02 | | | | | | | | | | | | | | | | (314) j_mono_2Etyop_2Emin_2Ebool(all_123_6) = all_293_5
% 46.49/7.02 | | | | | | | | | | | | | | | |
% 46.49/7.02 | | | | | | | | | | | | | | | | REDUCE: (203), (293) imply:
% 46.49/7.02 | | | | | | | | | | | | | | | | (315) p(mono_2Ec_2Ebool_2EF_2E0) = all_177_0
% 46.49/7.02 | | | | | | | | | | | | | | | |
% 46.49/7.02 | | | | | | | | | | | | | | | | REDUCE: (200), (311) imply:
% 46.49/7.02 | | | | | | | | | | | | | | | | (316) p(mono_2Ec_2Ebool_2EF_2E0) = all_175_0
% 46.49/7.02 | | | | | | | | | | | | | | | |
% 46.49/7.02 | | | | | | | | | | | | | | | | REDUCE: (197), (302) imply:
% 46.49/7.02 | | | | | | | | | | | | | | | | (317) p(mono_2Ec_2Ebool_2EF_2E0) = all_173_0
% 46.49/7.02 | | | | | | | | | | | | | | | |
% 46.49/7.02 | | | | | | | | | | | | | | | | REDUCE: (194), (286) imply:
% 46.49/7.02 | | | | | | | | | | | | | | | | (318) p(mono_2Ec_2Ebool_2EF_2E0) = all_171_0
% 46.49/7.02 | | | | | | | | | | | | | | | |
% 46.49/7.02 | | | | | | | | | | | | | | | | REDUCE: (191), (306) imply:
% 46.49/7.02 | | | | | | | | | | | | | | | | (319) p(mono_2Ec_2Ebool_2EF_2E0) = all_169_0
% 46.49/7.02 | | | | | | | | | | | | | | | |
% 46.49/7.02 | | | | | | | | | | | | | | | | REDUCE: (188), (307) imply:
% 46.49/7.02 | | | | | | | | | | | | | | | | (320) p(mono_2Ec_2Ebool_2EF_2E0) = all_167_0
% 46.49/7.02 | | | | | | | | | | | | | | | |
% 46.49/7.02 | | | | | | | | | | | | | | | | REDUCE: (211), (294) imply:
% 46.49/7.02 | | | | | | | | | | | | | | | | (321) s(tyop_2Emin_2Ebool, all_123_3) = all_293_2
% 46.49/7.02 | | | | | | | | | | | | | | | |
% 46.49/7.02 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (26) with all_123_2, all_293_2,
% 46.49/7.02 | | | | | | | | | | | | | | | | all_123_3, tyop_2Emin_2Ebool, simplifying with
% 46.49/7.02 | | | | | | | | | | | | | | | | (154), (321) gives:
% 46.49/7.02 | | | | | | | | | | | | | | | | (322) all_293_2 = all_123_2
% 46.49/7.02 | | | | | | | | | | | | | | | |
% 46.49/7.02 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (21) with all_173_0, all_175_0,
% 46.49/7.02 | | | | | | | | | | | | | | | | mono_2Ec_2Ebool_2EF_2E0, simplifying with (316),
% 46.49/7.02 | | | | | | | | | | | | | | | | (317) gives:
% 46.49/7.02 | | | | | | | | | | | | | | | | (323) all_175_0 = all_173_0
% 46.49/7.02 | | | | | | | | | | | | | | | |
% 46.49/7.02 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (21) with all_171_0, all_175_0,
% 46.49/7.02 | | | | | | | | | | | | | | | | mono_2Ec_2Ebool_2EF_2E0, simplifying with (316),
% 46.49/7.02 | | | | | | | | | | | | | | | | (318) gives:
% 46.49/7.02 | | | | | | | | | | | | | | | | (324) all_175_0 = all_171_0
% 46.49/7.02 | | | | | | | | | | | | | | | |
% 46.49/7.02 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (21) with all_169_0, all_175_0,
% 46.49/7.02 | | | | | | | | | | | | | | | | mono_2Ec_2Ebool_2EF_2E0, simplifying with (316),
% 46.49/7.02 | | | | | | | | | | | | | | | | (319) gives:
% 46.49/7.02 | | | | | | | | | | | | | | | | (325) all_175_0 = all_169_0
% 46.49/7.02 | | | | | | | | | | | | | | | |
% 46.49/7.02 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (21) with all_167_0, all_175_0,
% 46.49/7.02 | | | | | | | | | | | | | | | | mono_2Ec_2Ebool_2EF_2E0, simplifying with (316),
% 46.49/7.02 | | | | | | | | | | | | | | | | (320) gives:
% 46.49/7.02 | | | | | | | | | | | | | | | | (326) all_175_0 = all_167_0
% 46.49/7.02 | | | | | | | | | | | | | | | |
% 46.49/7.02 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (21) with all_45_0, all_177_0,
% 46.49/7.02 | | | | | | | | | | | | | | | | mono_2Ec_2Ebool_2EF_2E0, simplifying with (31),
% 46.49/7.02 | | | | | | | | | | | | | | | | (315) gives:
% 46.49/7.02 | | | | | | | | | | | | | | | | (327) all_177_0 = all_45_0
% 46.49/7.02 | | | | | | | | | | | | | | | |
% 46.49/7.02 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (21) with all_171_0, all_177_0,
% 46.49/7.02 | | | | | | | | | | | | | | | | mono_2Ec_2Ebool_2EF_2E0, simplifying with (315),
% 46.49/7.02 | | | | | | | | | | | | | | | | (318) gives:
% 46.49/7.02 | | | | | | | | | | | | | | | | (328) all_177_0 = all_171_0
% 46.49/7.02 | | | | | | | | | | | | | | | |
% 46.49/7.03 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (23) with mono_2Ec_2Ebool_2ET_2E0,
% 46.49/7.03 | | | | | | | | | | | | | | | | all_379_7, all_123_6, simplifying with (227),
% 46.49/7.03 | | | | | | | | | | | | | | | | (313) gives:
% 46.49/7.03 | | | | | | | | | | | | | | | | (329) all_379_7 = mono_2Ec_2Ebool_2ET_2E0
% 46.49/7.03 | | | | | | | | | | | | | | | |
% 46.49/7.03 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (23) with all_293_5, all_379_7,
% 46.49/7.03 | | | | | | | | | | | | | | | | all_123_6, simplifying with (313), (314) gives:
% 46.49/7.03 | | | | | | | | | | | | | | | | (330) all_379_7 = all_293_5
% 46.49/7.03 | | | | | | | | | | | | | | | |
% 46.49/7.03 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (23) with mono_2Ec_2Ebool_2EF_2E0,
% 46.49/7.03 | | | | | | | | | | | | | | | | all_381_7, all_123_2, simplifying with (274),
% 46.49/7.03 | | | | | | | | | | | | | | | | (312) gives:
% 46.49/7.03 | | | | | | | | | | | | | | | | (331) all_381_7 = mono_2Ec_2Ebool_2EF_2E0
% 46.49/7.03 | | | | | | | | | | | | | | | |
% 46.49/7.03 | | | | | | | | | | | | | | | | COMBINE_EQS: (329), (330) imply:
% 46.49/7.03 | | | | | | | | | | | | | | | | (332) all_293_5 = mono_2Ec_2Ebool_2ET_2E0
% 46.49/7.03 | | | | | | | | | | | | | | | |
% 46.49/7.03 | | | | | | | | | | | | | | | | COMBINE_EQS: (327), (328) imply:
% 46.49/7.03 | | | | | | | | | | | | | | | | (333) all_171_0 = all_45_0
% 46.49/7.03 | | | | | | | | | | | | | | | |
% 46.49/7.03 | | | | | | | | | | | | | | | | SIMP: (333) implies:
% 46.49/7.03 | | | | | | | | | | | | | | | | (334) all_171_0 = all_45_0
% 46.49/7.03 | | | | | | | | | | | | | | | |
% 46.49/7.03 | | | | | | | | | | | | | | | | COMBINE_EQS: (323), (324) imply:
% 46.49/7.03 | | | | | | | | | | | | | | | | (335) all_173_0 = all_171_0
% 46.49/7.03 | | | | | | | | | | | | | | | |
% 46.49/7.03 | | | | | | | | | | | | | | | | COMBINE_EQS: (323), (325) imply:
% 46.49/7.03 | | | | | | | | | | | | | | | | (336) all_173_0 = all_169_0
% 46.49/7.03 | | | | | | | | | | | | | | | |
% 46.49/7.03 | | | | | | | | | | | | | | | | COMBINE_EQS: (323), (326) imply:
% 46.49/7.03 | | | | | | | | | | | | | | | | (337) all_173_0 = all_167_0
% 46.49/7.03 | | | | | | | | | | | | | | | |
% 46.49/7.03 | | | | | | | | | | | | | | | | COMBINE_EQS: (336), (337) imply:
% 46.49/7.03 | | | | | | | | | | | | | | | | (338) all_169_0 = all_167_0
% 46.49/7.03 | | | | | | | | | | | | | | | |
% 46.49/7.03 | | | | | | | | | | | | | | | | COMBINE_EQS: (335), (336) imply:
% 46.49/7.03 | | | | | | | | | | | | | | | | (339) all_171_0 = all_169_0
% 46.49/7.03 | | | | | | | | | | | | | | | |
% 46.49/7.03 | | | | | | | | | | | | | | | | SIMP: (339) implies:
% 46.49/7.03 | | | | | | | | | | | | | | | | (340) all_171_0 = all_169_0
% 46.49/7.03 | | | | | | | | | | | | | | | |
% 46.49/7.03 | | | | | | | | | | | | | | | | COMBINE_EQS: (334), (340) imply:
% 46.49/7.03 | | | | | | | | | | | | | | | | (341) all_169_0 = all_45_0
% 46.49/7.03 | | | | | | | | | | | | | | | |
% 46.49/7.03 | | | | | | | | | | | | | | | | SIMP: (341) implies:
% 46.49/7.03 | | | | | | | | | | | | | | | | (342) all_169_0 = all_45_0
% 46.49/7.03 | | | | | | | | | | | | | | | |
% 46.49/7.03 | | | | | | | | | | | | | | | | COMBINE_EQS: (338), (342) imply:
% 46.49/7.03 | | | | | | | | | | | | | | | | (343) all_167_0 = all_45_0
% 46.49/7.03 | | | | | | | | | | | | | | | |
% 46.49/7.03 | | | | | | | | | | | | | | | | REDUCE: (215), (322) imply:
% 46.49/7.03 | | | | | | | | | | | | | | | | (344) j_mono_2Etyop_2Emin_2Ebool(all_123_2) = all_293_1
% 46.49/7.03 | | | | | | | | | | | | | | | |
% 46.49/7.03 | | | | | | | | | | | | | | | | REDUCE: (212), (332) imply:
% 46.49/7.03 | | | | | | | | | | | | | | | | (345) p(mono_2Ec_2Ebool_2ET_2E0) = all_293_4
% 46.49/7.03 | | | | | | | | | | | | | | | |
% 46.49/7.03 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (21) with 0, all_293_4,
% 46.49/7.03 | | | | | | | | | | | | | | | | mono_2Ec_2Ebool_2ET_2E0, simplifying with (3),
% 46.49/7.03 | | | | | | | | | | | | | | | | (345) gives:
% 46.49/7.03 | | | | | | | | | | | | | | | | (346) all_293_4 = 0
% 46.49/7.03 | | | | | | | | | | | | | | | |
% 46.49/7.03 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (23) with mono_2Ec_2Ebool_2EF_2E0,
% 46.49/7.03 | | | | | | | | | | | | | | | | all_293_1, all_123_2, simplifying with (274),
% 46.49/7.03 | | | | | | | | | | | | | | | | (344) gives:
% 46.49/7.03 | | | | | | | | | | | | | | | | (347) all_293_1 = mono_2Ec_2Ebool_2EF_2E0
% 46.49/7.03 | | | | | | | | | | | | | | | |
% 46.49/7.03 | | | | | | | | | | | | | | | | REDUCE: (213), (347) imply:
% 46.49/7.03 | | | | | | | | | | | | | | | | (348) p(mono_2Ec_2Ebool_2EF_2E0) = all_293_0
% 46.49/7.03 | | | | | | | | | | | | | | | |
% 46.49/7.03 | | | | | | | | | | | | | | | | BETA: splitting (217) gives:
% 46.49/7.03 | | | | | | | | | | | | | | | |
% 46.49/7.03 | | | | | | | | | | | | | | | | Case 1:
% 46.49/7.03 | | | | | | | | | | | | | | | | |
% 46.49/7.03 | | | | | | | | | | | | | | | | | (349) ~ (all_293_4 = 0)
% 46.49/7.03 | | | | | | | | | | | | | | | | |
% 46.49/7.03 | | | | | | | | | | | | | | | | | REDUCE: (346), (349) imply:
% 46.49/7.03 | | | | | | | | | | | | | | | | | (350) $false
% 46.49/7.03 | | | | | | | | | | | | | | | | |
% 46.49/7.03 | | | | | | | | | | | | | | | | | CLOSE: (350) is inconsistent.
% 46.49/7.03 | | | | | | | | | | | | | | | | |
% 46.49/7.03 | | | | | | | | | | | | | | | | Case 2:
% 46.49/7.03 | | | | | | | | | | | | | | | | |
% 46.49/7.03 | | | | | | | | | | | | | | | | | (351) all_293_0 = 0 & ~ (all_123_8 = all_99_1)
% 46.49/7.03 | | | | | | | | | | | | | | | | |
% 46.49/7.03 | | | | | | | | | | | | | | | | | ALPHA: (351) implies:
% 46.49/7.03 | | | | | | | | | | | | | | | | | (352) all_293_0 = 0
% 46.49/7.03 | | | | | | | | | | | | | | | | |
% 46.49/7.03 | | | | | | | | | | | | | | | | | REDUCE: (348), (352) imply:
% 46.49/7.03 | | | | | | | | | | | | | | | | | (353) p(mono_2Ec_2Ebool_2EF_2E0) = 0
% 46.49/7.03 | | | | | | | | | | | | | | | | |
% 46.49/7.03 | | | | | | | | | | | | | | | | | REF_CLOSE: (21), (30), (31), (353) are inconsistent by
% 46.49/7.03 | | | | | | | | | | | | | | | | | sub-proof #1.
% 46.49/7.03 | | | | | | | | | | | | | | | | |
% 46.49/7.03 | | | | | | | | | | | | | | | | End of split
% 46.49/7.03 | | | | | | | | | | | | | | | |
% 46.49/7.03 | | | | | | | | | | | | | | | End of split
% 46.49/7.03 | | | | | | | | | | | | | | |
% 46.49/7.03 | | | | | | | | | | | | | | End of split
% 46.49/7.03 | | | | | | | | | | | | | |
% 46.49/7.03 | | | | | | | | | | | | | End of split
% 46.49/7.03 | | | | | | | | | | | | |
% 46.49/7.03 | | | | | | | | | | | | End of split
% 46.49/7.03 | | | | | | | | | | | |
% 46.49/7.03 | | | | | | | | | | | End of split
% 46.49/7.03 | | | | | | | | | | |
% 46.49/7.03 | | | | | | | | | | End of split
% 46.49/7.03 | | | | | | | | | |
% 46.49/7.03 | | | | | | | | | End of split
% 46.49/7.03 | | | | | | | | |
% 46.49/7.03 | | | | | | | | End of split
% 46.49/7.03 | | | | | | | |
% 46.49/7.03 | | | | | | | End of split
% 46.49/7.03 | | | | | | |
% 46.49/7.03 | | | | | | Case 2:
% 46.49/7.03 | | | | | | |
% 46.49/7.03 | | | | | | | (354) all_123_10 = 0 & j_mono_2Etyop_2Emin_2Ebool(all_123_12) =
% 46.49/7.03 | | | | | | | all_123_11 & p(all_123_11) = 0 & s(tyop_2Emin_2Ebool,
% 46.49/7.03 | | | | | | | all_60_3) = all_123_12 &
% 46.49/7.03 | | | | | | | mono_2Etyop_2Emin_2Ebool(all_123_11) & du(all_123_12)
% 46.49/7.03 | | | | | | |
% 46.49/7.03 | | | | | | | ALPHA: (354) implies:
% 46.49/7.03 | | | | | | | (355) s(tyop_2Emin_2Ebool, all_60_3) = all_123_12
% 46.49/7.03 | | | | | | | (356) p(all_123_11) = 0
% 46.49/7.03 | | | | | | | (357) j_mono_2Etyop_2Emin_2Ebool(all_123_12) = all_123_11
% 46.49/7.03 | | | | | | |
% 46.49/7.03 | | | | | | | GROUND_INST: instantiating (26) with all_60_2, all_123_12,
% 46.49/7.03 | | | | | | | all_60_3, tyop_2Emin_2Ebool, simplifying with (40),
% 46.49/7.03 | | | | | | | (355) gives:
% 46.49/7.03 | | | | | | | (358) all_123_12 = all_60_2
% 46.49/7.03 | | | | | | |
% 46.49/7.03 | | | | | | | REDUCE: (357), (358) imply:
% 46.49/7.03 | | | | | | | (359) j_mono_2Etyop_2Emin_2Ebool(all_60_2) = all_123_11
% 46.49/7.03 | | | | | | |
% 46.49/7.03 | | | | | | | GROUND_INST: instantiating (23) with mono_2Ec_2Ebool_2EF_2E0,
% 46.49/7.03 | | | | | | | all_123_11, all_60_2, simplifying with (106), (359)
% 46.49/7.03 | | | | | | | gives:
% 46.49/7.03 | | | | | | | (360) all_123_11 = mono_2Ec_2Ebool_2EF_2E0
% 46.49/7.03 | | | | | | |
% 46.49/7.03 | | | | | | | REDUCE: (356), (360) imply:
% 46.49/7.03 | | | | | | | (361) p(mono_2Ec_2Ebool_2EF_2E0) = 0
% 46.49/7.03 | | | | | | |
% 46.49/7.03 | | | | | | | REF_CLOSE: (21), (30), (31), (361) are inconsistent by sub-proof
% 46.49/7.03 | | | | | | | #1.
% 46.49/7.03 | | | | | | |
% 46.49/7.03 | | | | | | End of split
% 46.49/7.03 | | | | | |
% 46.49/7.03 | | | | | End of split
% 46.49/7.03 | | | | |
% 46.49/7.03 | | | | End of split
% 46.49/7.03 | | | |
% 46.49/7.03 | | | End of split
% 46.49/7.03 | | |
% 46.49/7.03 | | End of split
% 46.49/7.03 | |
% 46.49/7.03 | End of split
% 46.49/7.03 |
% 46.49/7.03 End of proof
% 46.49/7.03
% 46.49/7.03 Sub-proof #1 shows that the following formulas are inconsistent:
% 46.49/7.03 ----------------------------------------------------------------
% 46.49/7.03 (1) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 46.49/7.03 mono_2Etyop_2Emin_2Ebool] : (v1 = v0 | ~ (p(v2) = v1) | ~ (p(v2) =
% 46.49/7.03 v0))
% 46.49/7.03 (2) p(mono_2Ec_2Ebool_2EF_2E0) = all_45_0
% 46.49/7.03 (3) p(mono_2Ec_2Ebool_2EF_2E0) = 0
% 46.49/7.03 (4) ~ (all_45_0 = 0)
% 46.49/7.03
% 46.49/7.03 Begin of proof
% 46.49/7.03 |
% 46.49/7.03 | GROUND_INST: instantiating (1) with all_45_0, 0, mono_2Ec_2Ebool_2EF_2E0,
% 46.49/7.03 | simplifying with (2), (3) gives:
% 46.49/7.03 | (5) all_45_0 = 0
% 46.49/7.03 |
% 46.49/7.03 | REDUCE: (4), (5) imply:
% 46.49/7.03 | (6) $false
% 46.49/7.03 |
% 46.49/7.03 | CLOSE: (6) is inconsistent.
% 46.49/7.03 |
% 46.49/7.03 End of proof
% 46.49/7.03 % SZS output end Proof for theBenchmark
% 46.49/7.03
% 46.49/7.03 6414ms
%------------------------------------------------------------------------------