TSTP Solution File: SWW101+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SWW101+1 : TPTP v8.1.2. Released v5.2.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n031.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 : Fri Sep 1 00:49:18 EDT 2023
% Result : Theorem 37.44s 5.92s
% Output : Proof 41.50s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SWW101+1 : TPTP v8.1.2. Released v5.2.0.
% 0.00/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.15/0.36 % Computer : n031.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Sun Aug 27 20:07:54 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.22/0.62 ________ _____
% 0.22/0.62 ___ __ \_________(_)________________________________
% 0.22/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.22/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.22/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.22/0.62
% 0.22/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.22/0.62 (2023-06-19)
% 0.22/0.62
% 0.22/0.62 (c) Philipp Rümmer, 2009-2023
% 0.22/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.22/0.62 Amanda Stjerna.
% 0.22/0.62 Free software under BSD-3-Clause.
% 0.22/0.62
% 0.22/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.22/0.62
% 0.22/0.62 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.22/0.63 Running up to 7 provers in parallel.
% 0.22/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.22/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.22/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.22/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.22/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.22/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.22/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 3.17/1.18 Prover 4: Preprocessing ...
% 3.44/1.20 Prover 1: Preprocessing ...
% 3.44/1.23 Prover 0: Preprocessing ...
% 3.44/1.23 Prover 2: Preprocessing ...
% 3.44/1.23 Prover 3: Preprocessing ...
% 3.44/1.23 Prover 6: Preprocessing ...
% 3.44/1.23 Prover 5: Preprocessing ...
% 8.46/1.93 Prover 6: Proving ...
% 8.91/1.96 Prover 3: Constructing countermodel ...
% 8.91/1.97 Prover 1: Constructing countermodel ...
% 8.91/2.01 Prover 4: Constructing countermodel ...
% 9.11/2.07 Prover 0: Proving ...
% 9.86/2.10 Prover 5: Proving ...
% 10.68/2.20 Prover 3: gave up
% 10.68/2.22 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 11.12/2.28 Prover 7: Preprocessing ...
% 11.12/2.28 Prover 2: Proving ...
% 11.12/2.30 Prover 6: gave up
% 11.12/2.30 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 11.12/2.35 Prover 1: gave up
% 11.12/2.35 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889
% 11.87/2.36 Prover 8: Preprocessing ...
% 12.16/2.40 Prover 9: Preprocessing ...
% 12.97/2.52 Prover 7: Warning: ignoring some quantifiers
% 12.97/2.56 Prover 7: Constructing countermodel ...
% 12.97/2.62 Prover 8: Warning: ignoring some quantifiers
% 12.97/2.63 Prover 8: Constructing countermodel ...
% 14.90/2.77 Prover 9: Constructing countermodel ...
% 18.35/3.30 Prover 7: gave up
% 18.35/3.31 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 19.24/3.37 Prover 8: gave up
% 19.24/3.37 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 19.24/3.38 Prover 10: Preprocessing ...
% 19.24/3.42 Prover 11: Preprocessing ...
% 21.16/3.61 Prover 10: Warning: ignoring some quantifiers
% 21.16/3.61 Prover 10: Constructing countermodel ...
% 21.51/3.66 Prover 11: Constructing countermodel ...
% 22.30/3.78 Prover 10: gave up
% 22.30/3.78 Prover 12: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=2024365391
% 22.68/3.83 Prover 12: Preprocessing ...
% 24.50/4.09 Prover 12: Proving ...
% 37.44/5.91 Prover 4: Found proof (size 1034)
% 37.44/5.91 Prover 4: proved (5267ms)
% 37.44/5.91 Prover 5: stopped
% 37.44/5.91 Prover 0: stopped
% 37.44/5.91 Prover 11: stopped
% 37.44/5.91 Prover 2: stopped
% 37.44/5.91 Prover 9: stopped
% 37.44/5.91 Prover 12: stopped
% 37.44/5.91
% 37.44/5.92 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 37.44/5.92
% 40.35/6.34 % SZS output start Proof for theBenchmark
% 40.35/6.34 Assumptions after simplification:
% 40.35/6.34 ---------------------------------
% 40.35/6.34
% 40.35/6.34 (def_bool)
% 40.35/6.37 $i(true) & $i(false) & ! [v0: $i] : (v0 = true | v0 = false | ~ (bool(v0) =
% 40.35/6.37 0) | ~ $i(v0)) & ! [v0: int] : (v0 = 0 | ~ (bool(true) = v0)) & ! [v0:
% 40.35/6.37 int] : (v0 = 0 | ~ (bool(false) = v0))
% 40.35/6.37
% 40.35/6.37 (def_f1)
% 40.35/6.37 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 40.35/6.37 (impl(v1, v2) = v3) | ~ (impl(v0, v3) = v4) | ~ $i(v2) | ~ $i(v1) | ~
% 40.35/6.37 $i(v0) | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : (f1(v0, v1, v2) = v5 &
% 40.35/6.37 lazy_impl(v6, v7) = v5 & impl(v4, v2) = v7 & prop(v2) = v6 & $i(v7) &
% 40.35/6.37 $i(v6) & $i(v5))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i]
% 40.65/6.37 : ( ~ (f1(v0, v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: $i]
% 40.65/6.37 : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : (lazy_impl(v4, v7) = v3 &
% 40.65/6.37 impl(v6, v2) = v7 & impl(v1, v2) = v5 & impl(v0, v5) = v6 & prop(v2) = v4
% 40.65/6.37 & $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3)))
% 40.65/6.37
% 40.65/6.37 (def_f2)
% 40.65/6.38 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 40.65/6.38 (lazy_impl(v0, v3) = v4) | ~ (impl(v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) |
% 40.65/6.38 ~ $i(v0) | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : (f2(v0, v1, v2) = v5 &
% 40.65/6.38 lazy_impl(v6, v7) = v5 & impl(v4, v2) = v7 & prop(v2) = v6 & $i(v7) &
% 40.65/6.38 $i(v6) & $i(v5))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i]
% 40.65/6.38 : ( ~ (f2(v0, v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: $i]
% 40.65/6.38 : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : (lazy_impl(v4, v7) = v3 &
% 40.65/6.38 lazy_impl(v0, v5) = v6 & impl(v6, v2) = v7 & impl(v1, v2) = v5 & prop(v2)
% 40.65/6.38 = v4 & $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3)))
% 40.65/6.38
% 40.65/6.38 (def_f3)
% 40.65/6.38 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 40.65/6.38 $i] : ! [v6: $i] : ( ~ (impl(v4, v2) = v5) | ~ (impl(v3, v5) = v6) | ~
% 40.65/6.38 (impl(v1, v2) = v4) | ~ (impl(v0, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~
% 40.65/6.38 $i(v0) | ? [v7: $i] : ? [v8: $i] : (f3(v0, v1, v2) = v7 & lazy_impl(v8,
% 40.65/6.38 v6) = v7 & prop(v2) = v8 & $i(v8) & $i(v7))) & ! [v0: $i] : ! [v1: $i]
% 40.65/6.38 : ! [v2: $i] : ! [v3: $i] : ( ~ (f3(v0, v1, v2) = v3) | ~ $i(v2) | ~
% 40.65/6.38 $i(v1) | ~ $i(v0) | ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] :
% 40.65/6.38 ? [v8: $i] : (lazy_impl(v4, v8) = v3 & impl(v6, v2) = v7 & impl(v5, v7) =
% 40.65/6.38 v8 & impl(v1, v2) = v6 & impl(v0, v2) = v5 & prop(v2) = v4 & $i(v8) &
% 40.65/6.38 $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3)))
% 40.65/6.38
% 40.65/6.38 (def_f7)
% 40.65/6.38 ! [v0: $i] : ! [v1: $i] : ( ~ (f7(v0) = v1) | ~ $i(v0) | ? [v2: $i] :
% 40.65/6.38 (lazy_impl(v2, v0) = v1 & prop(v0) = v2 & $i(v2) & $i(v1))) & ! [v0: $i] :
% 40.65/6.38 ! [v1: $i] : ( ~ (prop(v0) = v1) | ~ $i(v0) | ? [v2: $i] : (f7(v0) = v2 &
% 40.65/6.38 lazy_impl(v1, v0) = v2 & $i(v2)))
% 40.65/6.38
% 40.65/6.38 (def_false1)
% 40.65/6.39 false1 = false & $i(false)
% 40.65/6.39
% 40.65/6.39 (def_false2)
% 40.65/6.39 $i(false2) & ? [v0: $i] : ? [v1: $i] : (f7(v0) = v1 & phi(v1) = false2 &
% 40.65/6.39 $i(v1) & $i(v0) & ! [v2: $i] : ! [v3: $i] : ( ~ (f7(v2) = v3) | ~ $i(v2)
% 40.65/6.39 | ? [v4: int] : ( ~ (v4 = 0) & forallprefers(v3, v1) = v4)))
% 40.65/6.39
% 40.65/6.39 (def_forallprefers)
% 40.65/6.39 $i(true) & $i(false) & ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~
% 40.65/6.39 (forallprefers(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ?
% 40.65/6.39 [v4: any] : ? [v5: any] : ? [v6: any] : (d(v1) = v4 & d(v0) = v3 &
% 40.65/6.39 bool(v1) = v6 & bool(v0) = v5 & ( ~ (v4 = 0) | (v3 = 0 & ( ~ (v6 = 0) | v5
% 40.65/6.39 = 0))))) & ! [v0: $i] : ! [v1: $i] : (v1 = true | ~
% 40.65/6.39 (forallprefers(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: any] : ? [v3:
% 40.65/6.39 any] : ? [v4: any] : (d(v1) = 0 & d(v0) = v2 & bool(v1) = v4 & bool(v0) =
% 40.65/6.39 v3 & ( ~ (v2 = 0) | (v4 = 0 & ~ (v3 = 0))))) & ! [v0: $i] : ! [v1: $i]
% 40.65/6.39 : (v0 = false | ~ (forallprefers(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ?
% 40.65/6.39 [v2: any] : ? [v3: any] : ? [v4: any] : (d(v1) = 0 & d(v0) = v2 & bool(v1)
% 40.65/6.39 = v4 & bool(v0) = v3 & ( ~ (v2 = 0) | (v4 = 0 & ~ (v3 = 0))))) & ! [v0:
% 40.65/6.39 int] : (v0 = 0 | ~ (forallprefers(false, true) = v0))
% 40.65/6.39
% 40.65/6.39 (def_phi)
% 40.65/6.39 $i(err) & ! [v0: $i] : ! [v1: $i] : ( ~ (phi(v0) = v1) | ~ $i(v0) | ? [v2:
% 40.65/6.39 any] : (d(v0) = v2 & ((v2 = 0 & v1 = v0) | (v1 = err & ~ (v2 = 0))))) &
% 40.65/6.39 ! [v0: $i] : ! [v1: any] : ( ~ (d(v0) = v1) | ~ $i(v0) | ? [v2: $i] :
% 40.65/6.39 (phi(v0) = v2 & $i(v2) & ((v2 = v0 & v1 = 0) | (v2 = err & ~ (v1 = 0)))))
% 40.65/6.39
% 40.65/6.39 (distinct_false_true_err)
% 40.65/6.39 ~ (err = true) & ~ (err = false) & ~ (true = false) & $i(err) & $i(true) &
% 40.65/6.39 $i(false)
% 40.65/6.39
% 40.65/6.39 (false1_false2)
% 40.65/6.39 ~ (false2 = false1) & $i(false2) & $i(false1)
% 40.65/6.39
% 40.65/6.39 (false_true_err_in_d)
% 40.65/6.40 d(err) = 0 & d(true) = 0 & d(false) = 0 & $i(err) & $i(true) & $i(false)
% 40.65/6.40
% 40.65/6.40 (impl_axiom1)
% 40.65/6.40 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (impl(v0, v1) = v2) | ~ $i(v1)
% 40.65/6.40 | ~ $i(v0) | ? [v3: any] : ? [v4: $i] : (phi(v0) = v4 & bool(v0) = v3 &
% 40.65/6.40 $i(v4) & (v4 = v2 | v3 = 0)))
% 40.65/6.40
% 40.65/6.40 (impl_axiom3)
% 40.65/6.40 $i(true) & $i(false) & ! [v0: $i] : ! [v1: $i] : (v1 = true | ~
% 40.65/6.40 (impl(false, v0) = v1) | ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & bool(v0)
% 40.65/6.40 = v2)) & ! [v0: $i] : ( ~ (bool(v0) = 0) | ~ $i(v0) | impl(false, v0) =
% 40.65/6.40 true)
% 40.65/6.40
% 40.65/6.40 (impl_axiom4)
% 40.65/6.40 $i(true) & ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (impl(true, v0) = v1) |
% 40.65/6.40 ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & bool(v0) = v2)) & ! [v0: $i] : ( ~
% 40.65/6.40 (bool(v0) = 0) | ~ $i(v0) | impl(true, v0) = v0)
% 40.65/6.40
% 40.65/6.40 (lazy_and1_axiom3)
% 40.65/6.40 $i(true) & ! [v0: $i] : ! [v1: $i] : ( ~ (lazy_and1(true, v0) = v1) | ~
% 40.65/6.40 $i(v0) | (phi(v0) = v1 & $i(v1))) & ! [v0: $i] : ! [v1: $i] : ( ~ (phi(v0)
% 40.65/6.40 = v1) | ~ $i(v0) | (lazy_and1(true, v0) = v1 & $i(v1)))
% 40.65/6.40
% 40.65/6.40 (lazy_impl_axiom1)
% 40.65/6.40 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (lazy_impl(v0, v1) = v2) | ~
% 40.65/6.40 $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: $i] : (phi(v0) = v4 & bool(v0) =
% 40.65/6.40 v3 & $i(v4) & (v4 = v2 | v3 = 0)))
% 40.65/6.40
% 40.65/6.40 (lazy_impl_axiom2)
% 40.65/6.40 $i(true) & $i(false) & ! [v0: $i] : ! [v1: $i] : (v1 = true | ~
% 40.65/6.40 (lazy_impl(false, v0) = v1) | ~ $i(v0))
% 40.65/6.40
% 40.65/6.40 (lazy_impl_axiom3)
% 40.65/6.40 $i(true) & ! [v0: $i] : ! [v1: $i] : ( ~ (lazy_impl(true, v0) = v1) | ~
% 40.65/6.40 $i(v0) | (phi(v0) = v1 & $i(v1))) & ! [v0: $i] : ! [v1: $i] : ( ~ (phi(v0)
% 40.65/6.40 = v1) | ~ $i(v0) | (lazy_impl(true, v0) = v1 & $i(v1)))
% 40.65/6.40
% 40.65/6.40 (not1_axiom1)
% 40.65/6.41 ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (bool(v0) = v1) | ~ $i(v0) | ?
% 40.65/6.41 [v2: $i] : (not1(v0) = v2 & phi(v0) = v2 & $i(v2))) & ! [v0: $i] : ! [v1:
% 40.65/6.41 $i] : ( ~ (not1(v0) = v1) | ~ $i(v0) | ? [v2: any] : ? [v3: $i] :
% 40.65/6.41 (phi(v0) = v3 & bool(v0) = v2 & $i(v3) & (v3 = v1 | v2 = 0))) & ! [v0: $i]
% 40.65/6.41 : ! [v1: $i] : ( ~ (phi(v0) = v1) | ~ $i(v0) | ? [v2: any] : ? [v3: $i] :
% 40.65/6.41 (not1(v0) = v3 & bool(v0) = v2 & $i(v3) & (v3 = v1 | v2 = 0)))
% 40.65/6.41
% 40.65/6.41 (not1_axiom2)
% 40.65/6.41 not1(false) = true & $i(true) & $i(false)
% 40.65/6.41
% 40.65/6.41 (not1_axiom3)
% 40.65/6.41 not1(true) = false & $i(true) & $i(false)
% 40.65/6.41
% 40.65/6.41 (prop_false)
% 40.65/6.41 $i(false) & ! [v0: $i] : ! [v1: $i] : (v1 = false | ~ (prop(v0) = v1) | ~
% 40.65/6.41 $i(v0) | bool(v0) = 0) & ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (bool(v0)
% 40.65/6.41 = v1) | ~ $i(v0) | prop(v0) = false) & ! [v0: $i] : ( ~ (prop(v0) =
% 40.65/6.41 false) | ~ $i(v0) | ? [v1: int] : ( ~ (v1 = 0) & bool(v0) = v1)) & !
% 40.65/6.41 [v0: $i] : ( ~ (bool(v0) = 0) | ~ $i(v0) | ? [v1: $i] : ( ~ (v1 = false) &
% 40.65/6.41 prop(v0) = v1 & $i(v1)))
% 40.65/6.41
% 40.65/6.41 (prop_true)
% 40.65/6.41 $i(true) & ! [v0: $i] : ! [v1: $i] : (v1 = true | ~ (prop(v0) = v1) | ~
% 40.65/6.41 $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & bool(v0) = v2)) & ! [v0: $i] : !
% 40.65/6.41 [v1: int] : (v1 = 0 | ~ (bool(v0) = v1) | ~ $i(v0) | ? [v2: $i] : ( ~ (v2 =
% 40.65/6.41 true) & prop(v0) = v2 & $i(v2))) & ! [v0: $i] : ( ~ (prop(v0) = true) |
% 40.65/6.41 ~ $i(v0) | bool(v0) = 0) & ! [v0: $i] : ( ~ (bool(v0) = 0) | ~ $i(v0) |
% 40.65/6.41 prop(v0) = true)
% 40.65/6.41
% 40.65/6.41 (function-axioms)
% 40.65/6.42 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0
% 40.65/6.42 | ~ (f4(v4, v3, v2) = v1) | ~ (f4(v4, v3, v2) = v0)) & ! [v0: $i] : !
% 40.65/6.42 [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (f3(v4, v3,
% 40.65/6.42 v2) = v1) | ~ (f3(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 40.65/6.42 [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (f2(v4, v3, v2) = v1) |
% 40.65/6.42 ~ (f2(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 40.65/6.42 $i] : ! [v4: $i] : (v1 = v0 | ~ (f1(v4, v3, v2) = v1) | ~ (f1(v4, v3, v2)
% 40.65/6.42 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0
% 40.65/6.42 | ~ (f6(v3, v2) = v1) | ~ (f6(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] :
% 40.65/6.42 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (f5(v3, v2) = v1) | ~ (f5(v3, v2) =
% 40.65/6.42 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 |
% 40.65/6.42 ~ (apply(v3, v2) = v1) | ~ (apply(v3, v2) = v0)) & ! [v0: $i] : ! [v1:
% 40.65/6.42 $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (or2(v3, v2) = v1) | ~
% 40.65/6.42 (or2(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i]
% 40.65/6.42 : (v1 = v0 | ~ (or1(v3, v2) = v1) | ~ (or1(v3, v2) = v0)) & ! [v0: $i] : !
% 40.65/6.42 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (lazy_and2(v3, v2) = v1)
% 40.65/6.42 | ~ (lazy_and2(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 40.65/6.42 ! [v3: $i] : (v1 = v0 | ~ (lazy_and1(v3, v2) = v1) | ~ (lazy_and1(v3, v2) =
% 40.65/6.42 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 |
% 40.65/6.42 ~ (and2(v3, v2) = v1) | ~ (and2(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i]
% 40.65/6.42 : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (and1(v3, v2) = v1) | ~ (and1(v3,
% 40.65/6.42 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1
% 40.65/6.42 = v0 | ~ (lazy_impl(v3, v2) = v1) | ~ (lazy_impl(v3, v2) = v0)) & ! [v0:
% 40.65/6.42 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (impl(v3, v2)
% 40.65/6.42 = v1) | ~ (impl(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 40.65/6.42 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 40.65/6.42 (existsprefers(v3, v2) = v1) | ~ (existsprefers(v3, v2) = v0)) & ! [v0:
% 40.65/6.42 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 40.65/6.42 : (v1 = v0 | ~ (forallprefers(v3, v2) = v1) | ~ (forallprefers(v3, v2) =
% 40.65/6.42 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (not2(v2) =
% 40.65/6.42 v1) | ~ (not2(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1
% 40.65/6.42 = v0 | ~ (not1(v2) = v1) | ~ (not1(v2) = v0)) & ! [v0: $i] : ! [v1: $i]
% 40.65/6.42 : ! [v2: $i] : (v1 = v0 | ~ (f7(v2) = v1) | ~ (f7(v2) = v0)) & ! [v0: $i]
% 40.65/6.42 : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (exists2(v2) = v1) | ~
% 40.65/6.42 (exists2(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 |
% 40.65/6.42 ~ (exists1(v2) = v1) | ~ (exists1(v2) = v0)) & ! [v0: $i] : ! [v1: $i] :
% 40.65/6.42 ! [v2: $i] : (v1 = v0 | ~ (prop(v2) = v1) | ~ (prop(v2) = v0)) & ! [v0: $i]
% 40.65/6.42 : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (phi(v2) = v1) | ~ (phi(v2) =
% 40.65/6.42 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 40.65/6.42 $i] : (v1 = v0 | ~ (d(v2) = v1) | ~ (d(v2) = v0)) & ! [v0:
% 40.65/6.42 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 |
% 40.65/6.42 ~ (bool(v2) = v1) | ~ (bool(v2) = v0))
% 40.65/6.42
% 40.65/6.42 Further assumptions not needed in the proof:
% 40.65/6.42 --------------------------------------------
% 40.65/6.42 and1_axiom1, and1_axiom2, and1_axiom3, and1_axiom4, def_and2, def_exists2,
% 40.65/6.42 def_existsprefers, def_f4, def_f5, def_f6, def_lazy_and2, def_not2, def_or2,
% 40.65/6.42 exists1_axiom1, impl_axiom2, lazy_and1_axiom1, lazy_and1_axiom2, or1_axiom1,
% 40.65/6.42 or1_axiom2, or1_axiom3, or1_axiom4
% 40.65/6.42
% 40.65/6.42 Those formulas are unsatisfiable:
% 40.65/6.42 ---------------------------------
% 40.65/6.42
% 40.65/6.42 Begin of proof
% 40.65/6.42 |
% 40.65/6.42 | ALPHA: (def_bool) implies:
% 40.65/6.42 | (1) ! [v0: int] : (v0 = 0 | ~ (bool(false) = v0))
% 40.65/6.42 | (2) ! [v0: int] : (v0 = 0 | ~ (bool(true) = v0))
% 40.65/6.42 | (3) ! [v0: $i] : (v0 = true | v0 = false | ~ (bool(v0) = 0) | ~ $i(v0))
% 40.65/6.42 |
% 40.65/6.42 | ALPHA: (distinct_false_true_err) implies:
% 40.65/6.42 | (4) ~ (err = true)
% 40.65/6.42 |
% 40.65/6.42 | ALPHA: (false_true_err_in_d) implies:
% 40.65/6.42 | (5) d(false) = 0
% 40.65/6.42 | (6) d(true) = 0
% 40.65/6.42 | (7) d(err) = 0
% 40.65/6.42 |
% 40.65/6.42 | ALPHA: (def_forallprefers) implies:
% 40.65/6.42 | (8) ! [v0: int] : (v0 = 0 | ~ (forallprefers(false, true) = v0))
% 40.65/6.42 |
% 40.65/6.42 | ALPHA: (def_phi) implies:
% 40.65/6.42 | (9) $i(err)
% 40.65/6.43 | (10) ! [v0: $i] : ! [v1: any] : ( ~ (d(v0) = v1) | ~ $i(v0) | ? [v2:
% 40.65/6.43 | $i] : (phi(v0) = v2 & $i(v2) & ((v2 = v0 & v1 = 0) | (v2 = err &
% 40.65/6.43 | ~ (v1 = 0)))))
% 40.65/6.43 | (11) ! [v0: $i] : ! [v1: $i] : ( ~ (phi(v0) = v1) | ~ $i(v0) | ? [v2:
% 40.65/6.43 | any] : (d(v0) = v2 & ((v2 = 0 & v1 = v0) | (v1 = err & ~ (v2 =
% 40.65/6.43 | 0)))))
% 40.65/6.43 |
% 40.65/6.43 | ALPHA: (prop_true) implies:
% 40.65/6.43 | (12) ! [v0: $i] : ( ~ (bool(v0) = 0) | ~ $i(v0) | prop(v0) = true)
% 40.65/6.43 | (13) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (bool(v0) = v1) | ~ $i(v0)
% 40.65/6.43 | | ? [v2: $i] : ( ~ (v2 = true) & prop(v0) = v2 & $i(v2)))
% 40.65/6.43 | (14) ! [v0: $i] : ! [v1: $i] : (v1 = true | ~ (prop(v0) = v1) | ~
% 40.65/6.43 | $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & bool(v0) = v2))
% 40.65/6.43 |
% 40.65/6.43 | ALPHA: (prop_false) implies:
% 40.65/6.43 | (15) ! [v0: $i] : ( ~ (bool(v0) = 0) | ~ $i(v0) | ? [v1: $i] : ( ~ (v1 =
% 40.65/6.43 | false) & prop(v0) = v1 & $i(v1)))
% 40.65/6.43 | (16) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (bool(v0) = v1) | ~ $i(v0)
% 40.65/6.43 | | prop(v0) = false)
% 40.65/6.43 | (17) ! [v0: $i] : ! [v1: $i] : (v1 = false | ~ (prop(v0) = v1) | ~
% 40.65/6.43 | $i(v0) | bool(v0) = 0)
% 40.65/6.43 |
% 40.65/6.43 | ALPHA: (impl_axiom3) implies:
% 40.65/6.43 | (18) ! [v0: $i] : ( ~ (bool(v0) = 0) | ~ $i(v0) | impl(false, v0) = true)
% 40.65/6.43 |
% 40.65/6.43 | ALPHA: (impl_axiom4) implies:
% 40.65/6.43 | (19) ! [v0: $i] : ( ~ (bool(v0) = 0) | ~ $i(v0) | impl(true, v0) = v0)
% 40.65/6.43 |
% 40.65/6.43 | ALPHA: (lazy_impl_axiom2) implies:
% 40.65/6.43 | (20) ! [v0: $i] : ! [v1: $i] : (v1 = true | ~ (lazy_impl(false, v0) =
% 40.65/6.43 | v1) | ~ $i(v0))
% 40.65/6.43 |
% 40.65/6.43 | ALPHA: (lazy_impl_axiom3) implies:
% 40.65/6.43 | (21) ! [v0: $i] : ! [v1: $i] : ( ~ (phi(v0) = v1) | ~ $i(v0) |
% 40.65/6.43 | (lazy_impl(true, v0) = v1 & $i(v1)))
% 40.65/6.43 | (22) ! [v0: $i] : ! [v1: $i] : ( ~ (lazy_impl(true, v0) = v1) | ~ $i(v0)
% 40.65/6.43 | | (phi(v0) = v1 & $i(v1)))
% 40.65/6.43 |
% 40.65/6.43 | ALPHA: (def_f1) implies:
% 40.65/6.43 | (23) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 40.65/6.43 | ( ~ (impl(v1, v2) = v3) | ~ (impl(v0, v3) = v4) | ~ $i(v2) | ~
% 40.65/6.43 | $i(v1) | ~ $i(v0) | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] :
% 40.65/6.43 | (f1(v0, v1, v2) = v5 & lazy_impl(v6, v7) = v5 & impl(v4, v2) = v7 &
% 40.65/6.43 | prop(v2) = v6 & $i(v7) & $i(v6) & $i(v5)))
% 40.65/6.43 |
% 40.65/6.43 | ALPHA: (lazy_and1_axiom3) implies:
% 40.65/6.43 | (24) ! [v0: $i] : ! [v1: $i] : ( ~ (phi(v0) = v1) | ~ $i(v0) |
% 40.65/6.43 | (lazy_and1(true, v0) = v1 & $i(v1)))
% 40.65/6.43 |
% 40.65/6.43 | ALPHA: (def_f2) implies:
% 40.65/6.43 | (25) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 40.65/6.43 | ( ~ (lazy_impl(v0, v3) = v4) | ~ (impl(v1, v2) = v3) | ~ $i(v2) | ~
% 40.65/6.43 | $i(v1) | ~ $i(v0) | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] :
% 40.65/6.43 | (f2(v0, v1, v2) = v5 & lazy_impl(v6, v7) = v5 & impl(v4, v2) = v7 &
% 40.65/6.43 | prop(v2) = v6 & $i(v7) & $i(v6) & $i(v5)))
% 40.65/6.43 |
% 40.65/6.43 | ALPHA: (def_f3) implies:
% 40.65/6.44 | (26) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 40.65/6.44 | ! [v5: $i] : ! [v6: $i] : ( ~ (impl(v4, v2) = v5) | ~ (impl(v3, v5)
% 40.65/6.44 | = v6) | ~ (impl(v1, v2) = v4) | ~ (impl(v0, v2) = v3) | ~
% 40.65/6.44 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v7: $i] : ? [v8: $i] : (f3(v0,
% 40.65/6.44 | v1, v2) = v7 & lazy_impl(v8, v6) = v7 & prop(v2) = v8 & $i(v8) &
% 40.65/6.44 | $i(v7)))
% 40.65/6.44 |
% 40.65/6.44 | ALPHA: (def_false1) implies:
% 40.65/6.44 | (27) false1 = false
% 40.65/6.44 |
% 40.65/6.44 | ALPHA: (def_f7) implies:
% 40.65/6.44 | (28) ! [v0: $i] : ! [v1: $i] : ( ~ (prop(v0) = v1) | ~ $i(v0) | ? [v2:
% 40.65/6.44 | $i] : (f7(v0) = v2 & lazy_impl(v1, v0) = v2 & $i(v2)))
% 40.65/6.44 | (29) ! [v0: $i] : ! [v1: $i] : ( ~ (f7(v0) = v1) | ~ $i(v0) | ? [v2:
% 40.65/6.44 | $i] : (lazy_impl(v2, v0) = v1 & prop(v0) = v2 & $i(v2) & $i(v1)))
% 40.65/6.44 |
% 40.65/6.44 | ALPHA: (def_false2) implies:
% 40.65/6.44 | (30) ? [v0: $i] : ? [v1: $i] : (f7(v0) = v1 & phi(v1) = false2 & $i(v1) &
% 40.65/6.44 | $i(v0) & ! [v2: $i] : ! [v3: $i] : ( ~ (f7(v2) = v3) | ~ $i(v2) |
% 40.65/6.44 | ? [v4: int] : ( ~ (v4 = 0) & forallprefers(v3, v1) = v4)))
% 40.65/6.44 |
% 40.65/6.44 | ALPHA: (not1_axiom1) implies:
% 40.65/6.44 | (31) ! [v0: $i] : ! [v1: $i] : ( ~ (phi(v0) = v1) | ~ $i(v0) | ? [v2:
% 40.65/6.44 | any] : ? [v3: $i] : (not1(v0) = v3 & bool(v0) = v2 & $i(v3) & (v3
% 40.65/6.44 | = v1 | v2 = 0)))
% 40.65/6.44 | (32) ! [v0: $i] : ! [v1: $i] : ( ~ (not1(v0) = v1) | ~ $i(v0) | ? [v2:
% 40.65/6.44 | any] : ? [v3: $i] : (phi(v0) = v3 & bool(v0) = v2 & $i(v3) & (v3
% 40.65/6.44 | = v1 | v2 = 0)))
% 40.65/6.44 | (33) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (bool(v0) = v1) | ~ $i(v0)
% 40.65/6.44 | | ? [v2: $i] : (not1(v0) = v2 & phi(v0) = v2 & $i(v2)))
% 40.65/6.44 |
% 40.65/6.44 | ALPHA: (not1_axiom2) implies:
% 40.65/6.44 | (34) not1(false) = true
% 40.65/6.44 |
% 40.65/6.44 | ALPHA: (not1_axiom3) implies:
% 40.65/6.44 | (35) $i(true)
% 40.65/6.44 | (36) not1(true) = false
% 40.65/6.44 |
% 40.65/6.44 | ALPHA: (false1_false2) implies:
% 40.65/6.44 | (37) ~ (false2 = false1)
% 40.65/6.44 | (38) $i(false1)
% 40.65/6.44 |
% 40.65/6.44 | ALPHA: (function-axioms) implies:
% 40.65/6.44 | (39) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 40.65/6.44 | : (v1 = v0 | ~ (bool(v2) = v1) | ~ (bool(v2) = v0))
% 40.65/6.44 | (40) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (phi(v2) = v1)
% 40.65/6.44 | | ~ (phi(v2) = v0))
% 40.65/6.44 | (41) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (prop(v2) =
% 40.65/6.44 | v1) | ~ (prop(v2) = v0))
% 40.65/6.44 | (42) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (not1(v2) =
% 40.65/6.44 | v1) | ~ (not1(v2) = v0))
% 40.65/6.44 | (43) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 40.65/6.44 | (impl(v3, v2) = v1) | ~ (impl(v3, v2) = v0))
% 40.65/6.44 | (44) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 40.65/6.44 | (lazy_impl(v3, v2) = v1) | ~ (lazy_impl(v3, v2) = v0))
% 40.65/6.44 | (45) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 40.65/6.44 | (lazy_and1(v3, v2) = v1) | ~ (lazy_and1(v3, v2) = v0))
% 40.65/6.44 | (46) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 40.65/6.44 | (v1 = v0 | ~ (f2(v4, v3, v2) = v1) | ~ (f2(v4, v3, v2) = v0))
% 40.65/6.44 |
% 40.65/6.44 | DELTA: instantiating (30) with fresh symbols all_42_0, all_42_1 gives:
% 40.65/6.45 | (47) f7(all_42_1) = all_42_0 & phi(all_42_0) = false2 & $i(all_42_0) &
% 40.65/6.45 | $i(all_42_1) & ! [v0: $i] : ! [v1: $i] : ( ~ (f7(v0) = v1) | ~
% 40.65/6.45 | $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & forallprefers(v1, all_42_0) =
% 40.65/6.45 | v2))
% 40.65/6.45 |
% 40.65/6.45 | ALPHA: (47) implies:
% 40.65/6.45 | (48) $i(all_42_1)
% 40.65/6.45 | (49) $i(all_42_0)
% 40.65/6.45 | (50) phi(all_42_0) = false2
% 40.65/6.45 | (51) f7(all_42_1) = all_42_0
% 40.65/6.45 | (52) ! [v0: $i] : ! [v1: $i] : ( ~ (f7(v0) = v1) | ~ $i(v0) | ? [v2:
% 40.65/6.45 | int] : ( ~ (v2 = 0) & forallprefers(v1, all_42_0) = v2))
% 40.65/6.45 |
% 40.65/6.45 | REDUCE: (27), (37) imply:
% 40.65/6.45 | (53) ~ (false2 = false)
% 40.65/6.45 |
% 40.65/6.45 | REDUCE: (27), (38) imply:
% 40.65/6.45 | (54) $i(false)
% 40.65/6.45 |
% 40.65/6.45 | GROUND_INST: instantiating (10) with false, 0, simplifying with (5), (54)
% 40.65/6.45 | gives:
% 40.65/6.45 | (55) phi(false) = false
% 40.65/6.45 |
% 40.65/6.45 | GROUND_INST: instantiating (10) with true, 0, simplifying with (6), (35)
% 40.65/6.45 | gives:
% 40.65/6.45 | (56) phi(true) = true
% 40.65/6.45 |
% 40.65/6.45 | GROUND_INST: instantiating (10) with err, 0, simplifying with (7), (9) gives:
% 40.65/6.45 | (57) phi(err) = err
% 40.65/6.45 |
% 40.65/6.45 | GROUND_INST: instantiating (31) with all_42_0, false2, simplifying with (49),
% 40.65/6.45 | (50) gives:
% 40.65/6.45 | (58) ? [v0: any] : ? [v1: $i] : (not1(all_42_0) = v1 & bool(all_42_0) =
% 40.65/6.45 | v0 & $i(v1) & (v1 = false2 | v0 = 0))
% 40.65/6.45 |
% 40.65/6.45 | GROUND_INST: instantiating (11) with all_42_0, false2, simplifying with (49),
% 40.65/6.45 | (50) gives:
% 40.65/6.45 | (59) ? [v0: any] : (d(all_42_0) = v0 & ((v0 = 0 & all_42_0 = false2) |
% 40.65/6.45 | (false2 = err & ~ (v0 = 0))))
% 40.65/6.45 |
% 40.65/6.45 | GROUND_INST: instantiating (24) with all_42_0, false2, simplifying with (49),
% 40.65/6.45 | (50) gives:
% 40.65/6.45 | (60) lazy_and1(true, all_42_0) = false2 & $i(false2)
% 40.65/6.45 |
% 40.65/6.45 | ALPHA: (60) implies:
% 40.65/6.45 | (61) lazy_and1(true, all_42_0) = false2
% 40.65/6.45 |
% 40.65/6.45 | GROUND_INST: instantiating (21) with all_42_0, false2, simplifying with (49),
% 40.65/6.45 | (50) gives:
% 40.65/6.45 | (62) lazy_impl(true, all_42_0) = false2 & $i(false2)
% 40.65/6.45 |
% 40.65/6.45 | ALPHA: (62) implies:
% 40.65/6.45 | (63) lazy_impl(true, all_42_0) = false2
% 40.65/6.45 |
% 40.65/6.45 | GROUND_INST: instantiating (29) with all_42_1, all_42_0, simplifying with
% 40.65/6.45 | (48), (51) gives:
% 40.65/6.45 | (64) ? [v0: $i] : (lazy_impl(v0, all_42_1) = all_42_0 & prop(all_42_1) =
% 40.65/6.45 | v0 & $i(v0) & $i(all_42_0))
% 40.65/6.45 |
% 40.65/6.45 | GROUND_INST: instantiating (32) with false, true, simplifying with (34), (54)
% 40.65/6.45 | gives:
% 40.65/6.45 | (65) ? [v0: any] : ? [v1: $i] : (phi(false) = v1 & bool(false) = v0 &
% 40.65/6.45 | $i(v1) & (v1 = true | v0 = 0))
% 40.65/6.45 |
% 40.65/6.45 | GROUND_INST: instantiating (32) with true, false, simplifying with (35), (36)
% 40.65/6.45 | gives:
% 40.65/6.45 | (66) ? [v0: any] : ? [v1: $i] : (phi(true) = v1 & bool(true) = v0 &
% 40.65/6.45 | $i(v1) & (v1 = false | v0 = 0))
% 40.65/6.45 |
% 40.65/6.45 | DELTA: instantiating (64) with fresh symbol all_53_0 gives:
% 40.65/6.45 | (67) lazy_impl(all_53_0, all_42_1) = all_42_0 & prop(all_42_1) = all_53_0 &
% 40.65/6.45 | $i(all_53_0) & $i(all_42_0)
% 40.65/6.45 |
% 40.65/6.45 | ALPHA: (67) implies:
% 40.65/6.45 | (68) $i(all_53_0)
% 40.65/6.45 | (69) prop(all_42_1) = all_53_0
% 40.65/6.45 | (70) lazy_impl(all_53_0, all_42_1) = all_42_0
% 40.65/6.45 |
% 40.65/6.45 | DELTA: instantiating (58) with fresh symbols all_55_0, all_55_1 gives:
% 40.65/6.45 | (71) not1(all_42_0) = all_55_0 & bool(all_42_0) = all_55_1 & $i(all_55_0) &
% 40.65/6.46 | (all_55_0 = false2 | all_55_1 = 0)
% 40.65/6.46 |
% 40.65/6.46 | ALPHA: (71) implies:
% 40.65/6.46 | (72) bool(all_42_0) = all_55_1
% 40.65/6.46 | (73) not1(all_42_0) = all_55_0
% 40.65/6.46 | (74) all_55_0 = false2 | all_55_1 = 0
% 40.65/6.46 |
% 40.65/6.46 | DELTA: instantiating (66) with fresh symbols all_57_0, all_57_1 gives:
% 40.65/6.46 | (75) phi(true) = all_57_0 & bool(true) = all_57_1 & $i(all_57_0) &
% 40.65/6.46 | (all_57_0 = false | all_57_1 = 0)
% 40.65/6.46 |
% 40.65/6.46 | ALPHA: (75) implies:
% 40.65/6.46 | (76) $i(all_57_0)
% 40.65/6.46 | (77) bool(true) = all_57_1
% 40.65/6.46 | (78) phi(true) = all_57_0
% 40.65/6.46 |
% 40.65/6.46 | DELTA: instantiating (59) with fresh symbol all_59_0 gives:
% 40.65/6.46 | (79) d(all_42_0) = all_59_0 & ((all_59_0 = 0 & all_42_0 = false2) | (false2
% 40.65/6.46 | = err & ~ (all_59_0 = 0)))
% 40.65/6.46 |
% 40.65/6.46 | ALPHA: (79) implies:
% 40.65/6.46 | (80) d(all_42_0) = all_59_0
% 40.65/6.46 | (81) (all_59_0 = 0 & all_42_0 = false2) | (false2 = err & ~ (all_59_0 =
% 40.65/6.46 | 0))
% 40.65/6.46 |
% 40.65/6.46 | DELTA: instantiating (65) with fresh symbols all_61_0, all_61_1 gives:
% 40.65/6.46 | (82) phi(false) = all_61_0 & bool(false) = all_61_1 & $i(all_61_0) &
% 40.65/6.46 | (all_61_0 = true | all_61_1 = 0)
% 40.65/6.46 |
% 40.65/6.46 | ALPHA: (82) implies:
% 40.65/6.46 | (83) $i(all_61_0)
% 40.65/6.46 | (84) bool(false) = all_61_1
% 40.65/6.46 | (85) phi(false) = all_61_0
% 40.65/6.46 |
% 40.65/6.46 | GROUND_INST: instantiating (1) with all_61_1, simplifying with (84) gives:
% 40.65/6.46 | (86) all_61_1 = 0
% 40.65/6.46 |
% 40.65/6.46 | GROUND_INST: instantiating (2) with all_57_1, simplifying with (77) gives:
% 40.65/6.46 | (87) all_57_1 = 0
% 40.65/6.46 |
% 40.65/6.46 | GROUND_INST: instantiating (40) with false, all_61_0, false, simplifying with
% 40.65/6.46 | (55), (85) gives:
% 40.65/6.46 | (88) all_61_0 = false
% 40.65/6.46 |
% 40.65/6.46 | GROUND_INST: instantiating (40) with true, all_57_0, true, simplifying with
% 40.65/6.46 | (56), (78) gives:
% 40.65/6.46 | (89) all_57_0 = true
% 40.65/6.46 |
% 40.65/6.46 | REDUCE: (77), (87) imply:
% 40.65/6.46 | (90) bool(true) = 0
% 40.65/6.46 |
% 40.65/6.46 | REDUCE: (84), (86) imply:
% 40.65/6.46 | (91) bool(false) = 0
% 40.65/6.46 |
% 40.65/6.46 | GROUND_INST: instantiating (19) with false, simplifying with (54), (91) gives:
% 40.65/6.46 | (92) impl(true, false) = false
% 40.65/6.46 |
% 40.65/6.46 | GROUND_INST: instantiating (18) with false, simplifying with (54), (91) gives:
% 40.65/6.46 | (93) impl(false, false) = true
% 40.65/6.46 |
% 40.65/6.46 | GROUND_INST: instantiating (12) with false, simplifying with (54), (91) gives:
% 40.65/6.46 | (94) prop(false) = true
% 40.65/6.46 |
% 40.65/6.46 | GROUND_INST: instantiating (15) with false, simplifying with (54), (91) gives:
% 40.65/6.46 | (95) ? [v0: $i] : ( ~ (v0 = false) & prop(false) = v0 & $i(v0))
% 40.65/6.46 |
% 40.65/6.46 | GROUND_INST: instantiating (19) with true, simplifying with (35), (90) gives:
% 40.65/6.46 | (96) impl(true, true) = true
% 40.65/6.46 |
% 40.65/6.46 | GROUND_INST: instantiating (18) with true, simplifying with (35), (90) gives:
% 40.65/6.46 | (97) impl(false, true) = true
% 40.65/6.46 |
% 40.65/6.46 | GROUND_INST: instantiating (12) with true, simplifying with (35), (90) gives:
% 40.65/6.46 | (98) prop(true) = true
% 40.65/6.46 |
% 40.65/6.46 | GROUND_INST: instantiating (15) with true, simplifying with (35), (90) gives:
% 40.65/6.46 | (99) ? [v0: $i] : ( ~ (v0 = false) & prop(true) = v0 & $i(v0))
% 40.65/6.46 |
% 40.65/6.46 | GROUND_INST: instantiating (10) with all_42_0, all_59_0, simplifying with
% 40.65/6.46 | (49), (80) gives:
% 40.65/6.46 | (100) ? [v0: $i] : (phi(all_42_0) = v0 & $i(v0) & ((v0 = all_42_0 &
% 40.65/6.46 | all_59_0 = 0) | (v0 = err & ~ (all_59_0 = 0))))
% 40.65/6.46 |
% 40.65/6.46 | GROUND_INST: instantiating (24) with false, false, simplifying with (54), (55)
% 40.65/6.46 | gives:
% 40.65/6.46 | (101) lazy_and1(true, false) = false
% 40.65/6.46 |
% 40.65/6.46 | GROUND_INST: instantiating (21) with false, false, simplifying with (54), (55)
% 40.65/6.46 | gives:
% 40.65/6.46 | (102) lazy_impl(true, false) = false
% 40.65/6.46 |
% 40.65/6.46 | GROUND_INST: instantiating (24) with true, true, simplifying with (35), (56)
% 40.65/6.46 | gives:
% 40.65/6.46 | (103) lazy_and1(true, true) = true
% 40.65/6.46 |
% 40.65/6.46 | GROUND_INST: instantiating (21) with true, true, simplifying with (35), (56)
% 40.65/6.46 | gives:
% 40.65/6.47 | (104) lazy_impl(true, true) = true
% 40.65/6.47 |
% 40.65/6.47 | GROUND_INST: instantiating (31) with err, err, simplifying with (9), (57)
% 40.65/6.47 | gives:
% 40.65/6.47 | (105) ? [v0: any] : ? [v1: $i] : (not1(err) = v1 & bool(err) = v0 &
% 40.65/6.47 | $i(v1) & (v1 = err | v0 = 0))
% 40.65/6.47 |
% 40.65/6.47 | GROUND_INST: instantiating (21) with err, err, simplifying with (9), (57)
% 40.65/6.47 | gives:
% 40.65/6.47 | (106) lazy_impl(true, err) = err
% 40.65/6.47 |
% 40.65/6.47 | GROUND_INST: instantiating (14) with all_42_1, all_53_0, simplifying with
% 40.65/6.47 | (48), (69) gives:
% 40.65/6.47 | (107) all_53_0 = true | ? [v0: int] : ( ~ (v0 = 0) & bool(all_42_1) = v0)
% 40.65/6.47 |
% 40.65/6.47 | GROUND_INST: instantiating (17) with all_42_1, all_53_0, simplifying with
% 40.65/6.47 | (48), (69) gives:
% 40.65/6.47 | (108) all_53_0 = false | bool(all_42_1) = 0
% 40.65/6.47 |
% 40.65/6.47 | GROUND_INST: instantiating (lazy_impl_axiom1) with all_53_0, all_42_1,
% 40.65/6.47 | all_42_0, simplifying with (48), (68), (70) gives:
% 40.65/6.47 | (109) ? [v0: any] : ? [v1: $i] : (phi(all_53_0) = v1 & bool(all_53_0) =
% 40.65/6.47 | v0 & $i(v1) & (v1 = all_42_0 | v0 = 0))
% 40.65/6.47 |
% 40.65/6.47 | GROUND_INST: instantiating (32) with all_42_0, all_55_0, simplifying with
% 40.65/6.47 | (49), (73) gives:
% 40.65/6.47 | (110) ? [v0: any] : ? [v1: $i] : (phi(all_42_0) = v1 & bool(all_42_0) =
% 40.65/6.47 | v0 & $i(v1) & (v1 = all_55_0 | v0 = 0))
% 40.65/6.47 |
% 40.65/6.47 | DELTA: instantiating (95) with fresh symbol all_73_0 gives:
% 41.13/6.47 | (111) ~ (all_73_0 = false) & prop(false) = all_73_0 & $i(all_73_0)
% 41.13/6.47 |
% 41.13/6.47 | ALPHA: (111) implies:
% 41.13/6.47 | (112) ~ (all_73_0 = false)
% 41.13/6.47 | (113) $i(all_73_0)
% 41.13/6.47 | (114) prop(false) = all_73_0
% 41.13/6.47 |
% 41.13/6.47 | DELTA: instantiating (99) with fresh symbol all_75_0 gives:
% 41.13/6.47 | (115) ~ (all_75_0 = false) & prop(true) = all_75_0 & $i(all_75_0)
% 41.13/6.47 |
% 41.13/6.47 | ALPHA: (115) implies:
% 41.13/6.47 | (116) prop(true) = all_75_0
% 41.13/6.47 |
% 41.13/6.47 | DELTA: instantiating (110) with fresh symbols all_77_0, all_77_1 gives:
% 41.13/6.47 | (117) phi(all_42_0) = all_77_0 & bool(all_42_0) = all_77_1 & $i(all_77_0) &
% 41.13/6.47 | (all_77_0 = all_55_0 | all_77_1 = 0)
% 41.13/6.47 |
% 41.13/6.47 | ALPHA: (117) implies:
% 41.13/6.47 | (118) $i(all_77_0)
% 41.13/6.47 | (119) bool(all_42_0) = all_77_1
% 41.13/6.47 | (120) phi(all_42_0) = all_77_0
% 41.13/6.47 |
% 41.13/6.47 | DELTA: instantiating (109) with fresh symbols all_79_0, all_79_1 gives:
% 41.13/6.47 | (121) phi(all_53_0) = all_79_0 & bool(all_53_0) = all_79_1 & $i(all_79_0) &
% 41.13/6.47 | (all_79_0 = all_42_0 | all_79_1 = 0)
% 41.13/6.47 |
% 41.13/6.47 | ALPHA: (121) implies:
% 41.13/6.47 | (122) bool(all_53_0) = all_79_1
% 41.13/6.47 | (123) phi(all_53_0) = all_79_0
% 41.13/6.47 | (124) all_79_0 = all_42_0 | all_79_1 = 0
% 41.13/6.47 |
% 41.13/6.47 | DELTA: instantiating (105) with fresh symbols all_81_0, all_81_1 gives:
% 41.13/6.47 | (125) not1(err) = all_81_0 & bool(err) = all_81_1 & $i(all_81_0) &
% 41.13/6.47 | (all_81_0 = err | all_81_1 = 0)
% 41.13/6.47 |
% 41.13/6.47 | ALPHA: (125) implies:
% 41.13/6.47 | (126) bool(err) = all_81_1
% 41.13/6.47 | (127) not1(err) = all_81_0
% 41.13/6.47 | (128) all_81_0 = err | all_81_1 = 0
% 41.13/6.47 |
% 41.13/6.47 | DELTA: instantiating (100) with fresh symbol all_83_0 gives:
% 41.13/6.47 | (129) phi(all_42_0) = all_83_0 & $i(all_83_0) & ((all_83_0 = all_42_0 &
% 41.13/6.47 | all_59_0 = 0) | (all_83_0 = err & ~ (all_59_0 = 0)))
% 41.13/6.47 |
% 41.13/6.47 | ALPHA: (129) implies:
% 41.13/6.47 | (130) phi(all_42_0) = all_83_0
% 41.13/6.47 |
% 41.13/6.47 | GROUND_INST: instantiating (39) with all_55_1, all_77_1, all_42_0, simplifying
% 41.13/6.47 | with (72), (119) gives:
% 41.13/6.47 | (131) all_77_1 = all_55_1
% 41.13/6.47 |
% 41.13/6.47 | GROUND_INST: instantiating (40) with false2, all_83_0, all_42_0, simplifying
% 41.13/6.47 | with (50), (130) gives:
% 41.13/6.47 | (132) all_83_0 = false2
% 41.13/6.47 |
% 41.13/6.47 | GROUND_INST: instantiating (40) with all_77_0, all_83_0, all_42_0, simplifying
% 41.13/6.47 | with (120), (130) gives:
% 41.13/6.47 | (133) all_83_0 = all_77_0
% 41.13/6.47 |
% 41.13/6.47 | GROUND_INST: instantiating (41) with true, all_73_0, false, simplifying with
% 41.13/6.47 | (94), (114) gives:
% 41.13/6.47 | (134) all_73_0 = true
% 41.13/6.47 |
% 41.13/6.48 | GROUND_INST: instantiating (41) with true, all_75_0, true, simplifying with
% 41.13/6.48 | (98), (116) gives:
% 41.13/6.48 | (135) all_75_0 = true
% 41.13/6.48 |
% 41.13/6.48 | COMBINE_EQS: (132), (133) imply:
% 41.13/6.48 | (136) all_77_0 = false2
% 41.13/6.48 |
% 41.13/6.48 | REDUCE: (112), (134) imply:
% 41.13/6.48 | (137) ~ (true = false)
% 41.13/6.48 |
% 41.13/6.48 | REDUCE: (118), (136) imply:
% 41.13/6.48 | (138) $i(false2)
% 41.13/6.48 |
% 41.13/6.48 | GROUND_INST: instantiating (16) with all_53_0, all_79_1, simplifying with
% 41.13/6.48 | (68), (122) gives:
% 41.13/6.48 | (139) all_79_1 = 0 | prop(all_53_0) = false
% 41.13/6.48 |
% 41.13/6.48 | GROUND_INST: instantiating (13) with all_53_0, all_79_1, simplifying with
% 41.13/6.48 | (68), (122) gives:
% 41.13/6.48 | (140) all_79_1 = 0 | ? [v0: $i] : ( ~ (v0 = true) & prop(all_53_0) = v0 &
% 41.13/6.48 | $i(v0))
% 41.13/6.48 |
% 41.13/6.48 | GROUND_INST: instantiating (33) with all_53_0, all_79_1, simplifying with
% 41.13/6.48 | (68), (122) gives:
% 41.13/6.48 | (141) all_79_1 = 0 | ? [v0: $i] : (not1(all_53_0) = v0 & phi(all_53_0) =
% 41.13/6.48 | v0 & $i(v0))
% 41.13/6.48 |
% 41.13/6.48 | GROUND_INST: instantiating (31) with all_53_0, all_79_0, simplifying with
% 41.13/6.48 | (68), (123) gives:
% 41.13/6.48 | (142) ? [v0: any] : ? [v1: $i] : (not1(all_53_0) = v1 & bool(all_53_0) =
% 41.13/6.48 | v0 & $i(v1) & (v1 = all_79_0 | v0 = 0))
% 41.13/6.48 |
% 41.13/6.48 | GROUND_INST: instantiating (11) with all_53_0, all_79_0, simplifying with
% 41.13/6.48 | (68), (123) gives:
% 41.13/6.48 | (143) ? [v0: any] : (d(all_53_0) = v0 & ((v0 = 0 & all_79_0 = all_53_0) |
% 41.13/6.48 | (all_79_0 = err & ~ (v0 = 0))))
% 41.13/6.48 |
% 41.13/6.48 | GROUND_INST: instantiating (24) with all_53_0, all_79_0, simplifying with
% 41.13/6.48 | (68), (123) gives:
% 41.13/6.48 | (144) lazy_and1(true, all_53_0) = all_79_0 & $i(all_79_0)
% 41.13/6.48 |
% 41.13/6.48 | ALPHA: (144) implies:
% 41.13/6.48 | (145) lazy_and1(true, all_53_0) = all_79_0
% 41.13/6.48 |
% 41.13/6.48 | GROUND_INST: instantiating (21) with all_53_0, all_79_0, simplifying with
% 41.13/6.48 | (68), (123) gives:
% 41.13/6.48 | (146) lazy_impl(true, all_53_0) = all_79_0 & $i(all_79_0)
% 41.13/6.48 |
% 41.13/6.48 | ALPHA: (146) implies:
% 41.13/6.48 | (147) lazy_impl(true, all_53_0) = all_79_0
% 41.13/6.48 |
% 41.13/6.48 | GROUND_INST: instantiating (28) with false, true, simplifying with (54), (94)
% 41.13/6.48 | gives:
% 41.13/6.48 | (148) ? [v0: $i] : (f7(false) = v0 & lazy_impl(true, false) = v0 & $i(v0))
% 41.13/6.48 |
% 41.13/6.48 | GROUND_INST: instantiating (28) with true, true, simplifying with (35), (98)
% 41.13/6.48 | gives:
% 41.13/6.48 | (149) ? [v0: $i] : (f7(true) = v0 & lazy_impl(true, true) = v0 & $i(v0))
% 41.13/6.48 |
% 41.13/6.48 | GROUND_INST: instantiating (23) with false, false, true, true, true,
% 41.13/6.48 | simplifying with (35), (54), (97) gives:
% 41.13/6.48 | (150) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (f1(false, false, true) =
% 41.13/6.48 | v0 & lazy_impl(v1, v2) = v0 & impl(true, true) = v2 & prop(true) =
% 41.13/6.48 | v1 & $i(v2) & $i(v1) & $i(v0))
% 41.13/6.48 |
% 41.13/6.48 | GROUND_INST: instantiating (23) with false, false, false, true, true,
% 41.13/6.48 | simplifying with (54), (93), (97) gives:
% 41.13/6.48 | (151) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (f1(false, false, false) =
% 41.13/6.48 | v0 & lazy_impl(v1, v2) = v0 & impl(true, false) = v2 & prop(false)
% 41.13/6.48 | = v1 & $i(v2) & $i(v1) & $i(v0))
% 41.13/6.48 |
% 41.13/6.48 | GROUND_INST: instantiating (26) with false, false, false, true, true, false,
% 41.13/6.48 | false, simplifying with (54), (92), (93) gives:
% 41.13/6.48 | (152) ? [v0: $i] : ? [v1: $i] : (f3(false, false, false) = v0 &
% 41.13/6.48 | lazy_impl(v1, false) = v0 & prop(false) = v1 & $i(v1) & $i(v0))
% 41.13/6.48 |
% 41.13/6.49 | GROUND_INST: instantiating (23) with true, true, false, false, false,
% 41.13/6.49 | simplifying with (35), (54), (92) gives:
% 41.13/6.49 | (153) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (f1(true, true, false) = v0
% 41.13/6.49 | & lazy_impl(v1, v2) = v0 & impl(false, false) = v2 & prop(false) =
% 41.13/6.49 | v1 & $i(v2) & $i(v1) & $i(v0))
% 41.13/6.49 |
% 41.13/6.49 | GROUND_INST: instantiating (26) with true, false, false, false, true, false,
% 41.13/6.49 | true, simplifying with (35), (54), (92), (93) gives:
% 41.13/6.49 | (154) ? [v0: $i] : ? [v1: $i] : (f3(true, false, false) = v0 &
% 41.13/6.49 | lazy_impl(v1, true) = v0 & prop(false) = v1 & $i(v1) & $i(v0))
% 41.13/6.49 |
% 41.13/6.49 | GROUND_INST: instantiating (23) with false, true, false, false, true,
% 41.13/6.49 | simplifying with (35), (54), (92), (93) gives:
% 41.13/6.49 | (155) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (f1(false, true, false) =
% 41.13/6.49 | v0 & lazy_impl(v1, v2) = v0 & impl(true, false) = v2 & prop(false)
% 41.13/6.49 | = v1 & $i(v2) & $i(v1) & $i(v0))
% 41.13/6.49 |
% 41.13/6.49 | GROUND_INST: instantiating (26) with true, true, false, false, false, true,
% 41.13/6.49 | true, simplifying with (35), (54), (92), (93), (97) gives:
% 41.13/6.49 | (156) ? [v0: $i] : ? [v1: $i] : (f3(true, true, false) = v0 &
% 41.13/6.49 | lazy_impl(v1, true) = v0 & prop(false) = v1 & $i(v1) & $i(v0))
% 41.13/6.49 |
% 41.13/6.49 | GROUND_INST: instantiating (26) with true, true, true, true, true, true, true,
% 41.13/6.49 | simplifying with (35), (96) gives:
% 41.13/6.49 | (157) ? [v0: $i] : ? [v1: $i] : (f3(true, true, true) = v0 &
% 41.13/6.49 | lazy_impl(v1, true) = v0 & prop(true) = v1 & $i(v1) & $i(v0))
% 41.13/6.49 |
% 41.13/6.49 | GROUND_INST: instantiating (26) with false, true, true, true, true, true,
% 41.13/6.49 | true, simplifying with (35), (54), (96), (97) gives:
% 41.13/6.49 | (158) ? [v0: $i] : ? [v1: $i] : (f3(false, true, true) = v0 &
% 41.13/6.49 | lazy_impl(v1, true) = v0 & prop(true) = v1 & $i(v1) & $i(v0))
% 41.13/6.49 |
% 41.13/6.49 | GROUND_INST: instantiating (23) with true, true, true, true, true, simplifying
% 41.13/6.49 | with (35), (96) gives:
% 41.13/6.49 | (159) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (f1(true, true, true) = v0
% 41.13/6.49 | & lazy_impl(v1, v2) = v0 & impl(true, true) = v2 & prop(true) = v1
% 41.13/6.49 | & $i(v2) & $i(v1) & $i(v0))
% 41.13/6.49 |
% 41.13/6.49 | GROUND_INST: instantiating (23) with false, true, true, true, true,
% 41.13/6.49 | simplifying with (35), (54), (96), (97) gives:
% 41.13/6.49 | (160) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (f1(false, true, true) = v0
% 41.13/6.49 | & lazy_impl(v1, v2) = v0 & impl(true, true) = v2 & prop(true) = v1
% 41.13/6.49 | & $i(v2) & $i(v1) & $i(v0))
% 41.13/6.49 |
% 41.13/6.49 | GROUND_INST: instantiating (23) with true, false, true, true, true,
% 41.13/6.49 | simplifying with (35), (54), (96), (97) gives:
% 41.13/6.49 | (161) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (f1(true, false, true) = v0
% 41.13/6.49 | & lazy_impl(v1, v2) = v0 & impl(true, true) = v2 & prop(true) = v1
% 41.13/6.49 | & $i(v2) & $i(v1) & $i(v0))
% 41.13/6.49 |
% 41.25/6.49 | GROUND_INST: instantiating (26) with false, true, false, true, false, true,
% 41.25/6.49 | true, simplifying with (35), (54), (92), (93), (96) gives:
% 41.25/6.49 | (162) ? [v0: $i] : ? [v1: $i] : (f3(false, true, false) = v0 &
% 41.25/6.49 | lazy_impl(v1, true) = v0 & prop(false) = v1 & $i(v1) & $i(v0))
% 41.25/6.49 |
% 41.25/6.49 | GROUND_INST: instantiating (23) with true, false, false, true, true,
% 41.25/6.49 | simplifying with (35), (54), (93), (96) gives:
% 41.25/6.49 | (163) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (f1(true, false, false) =
% 41.25/6.49 | v0 & lazy_impl(v1, v2) = v0 & impl(true, false) = v2 & prop(false)
% 41.25/6.49 | = v1 & $i(v2) & $i(v1) & $i(v0))
% 41.25/6.49 |
% 41.25/6.49 | GROUND_INST: instantiating (25) with true, true, false, false, false,
% 41.25/6.49 | simplifying with (35), (54), (92), (102) gives:
% 41.25/6.50 | (164) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (f2(true, true, false) = v0
% 41.25/6.50 | & lazy_impl(v1, v2) = v0 & impl(false, false) = v2 & prop(false) =
% 41.25/6.50 | v1 & $i(v2) & $i(v1) & $i(v0))
% 41.25/6.50 |
% 41.25/6.50 | GROUND_INST: instantiating (25) with true, true, true, true, true, simplifying
% 41.25/6.50 | with (35), (96), (104) gives:
% 41.25/6.50 | (165) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (f2(true, true, true) = v0
% 41.25/6.50 | & lazy_impl(v1, v2) = v0 & impl(true, true) = v2 & prop(true) = v1
% 41.25/6.50 | & $i(v2) & $i(v1) & $i(v0))
% 41.25/6.50 |
% 41.25/6.50 | GROUND_INST: instantiating (25) with true, false, true, true, true,
% 41.25/6.50 | simplifying with (35), (54), (97), (104) gives:
% 41.25/6.50 | (166) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (f2(true, false, true) = v0
% 41.25/6.50 | & lazy_impl(v1, v2) = v0 & impl(true, true) = v2 & prop(true) = v1
% 41.25/6.50 | & $i(v2) & $i(v1) & $i(v0))
% 41.25/6.50 |
% 41.25/6.50 | GROUND_INST: instantiating (25) with true, false, false, true, true,
% 41.25/6.50 | simplifying with (35), (54), (93), (104) gives:
% 41.25/6.50 | (167) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (f2(true, false, false) =
% 41.25/6.50 | v0 & lazy_impl(v1, v2) = v0 & impl(true, false) = v2 & prop(false)
% 41.25/6.50 | = v1 & $i(v2) & $i(v1) & $i(v0))
% 41.25/6.50 |
% 41.25/6.50 | GROUND_INST: instantiating (32) with err, all_81_0, simplifying with (9),
% 41.25/6.50 | (127) gives:
% 41.25/6.50 | (168) ? [v0: any] : ? [v1: $i] : (phi(err) = v1 & bool(err) = v0 & $i(v1)
% 41.25/6.50 | & (v1 = all_81_0 | v0 = 0))
% 41.25/6.50 |
% 41.25/6.50 | DELTA: instantiating (149) with fresh symbol all_95_0 gives:
% 41.25/6.50 | (169) f7(true) = all_95_0 & lazy_impl(true, true) = all_95_0 & $i(all_95_0)
% 41.25/6.50 |
% 41.25/6.50 | ALPHA: (169) implies:
% 41.25/6.50 | (170) lazy_impl(true, true) = all_95_0
% 41.25/6.50 |
% 41.25/6.50 | DELTA: instantiating (148) with fresh symbol all_97_0 gives:
% 41.25/6.50 | (171) f7(false) = all_97_0 & lazy_impl(true, false) = all_97_0 &
% 41.25/6.50 | $i(all_97_0)
% 41.25/6.50 |
% 41.25/6.50 | ALPHA: (171) implies:
% 41.25/6.50 | (172) lazy_impl(true, false) = all_97_0
% 41.25/6.50 | (173) f7(false) = all_97_0
% 41.25/6.50 |
% 41.25/6.50 | DELTA: instantiating (143) with fresh symbol all_99_0 gives:
% 41.25/6.50 | (174) d(all_53_0) = all_99_0 & ((all_99_0 = 0 & all_79_0 = all_53_0) |
% 41.25/6.50 | (all_79_0 = err & ~ (all_99_0 = 0)))
% 41.25/6.50 |
% 41.25/6.50 | ALPHA: (174) implies:
% 41.25/6.50 | (175) d(all_53_0) = all_99_0
% 41.25/6.50 | (176) (all_99_0 = 0 & all_79_0 = all_53_0) | (all_79_0 = err & ~ (all_99_0
% 41.25/6.50 | = 0))
% 41.25/6.50 |
% 41.25/6.50 | DELTA: instantiating (152) with fresh symbols all_101_0, all_101_1 gives:
% 41.25/6.50 | (177) f3(false, false, false) = all_101_1 & lazy_impl(all_101_0, false) =
% 41.25/6.50 | all_101_1 & prop(false) = all_101_0 & $i(all_101_0) & $i(all_101_1)
% 41.25/6.50 |
% 41.25/6.50 | ALPHA: (177) implies:
% 41.25/6.50 | (178) $i(all_101_1)
% 41.25/6.50 | (179) prop(false) = all_101_0
% 41.25/6.50 | (180) lazy_impl(all_101_0, false) = all_101_1
% 41.25/6.50 |
% 41.25/6.50 | DELTA: instantiating (168) with fresh symbols all_103_0, all_103_1 gives:
% 41.25/6.50 | (181) phi(err) = all_103_0 & bool(err) = all_103_1 & $i(all_103_0) &
% 41.25/6.50 | (all_103_0 = all_81_0 | all_103_1 = 0)
% 41.25/6.50 |
% 41.25/6.50 | ALPHA: (181) implies:
% 41.25/6.50 | (182) bool(err) = all_103_1
% 41.25/6.50 | (183) phi(err) = all_103_0
% 41.25/6.50 |
% 41.25/6.50 | DELTA: instantiating (142) with fresh symbols all_105_0, all_105_1 gives:
% 41.25/6.50 | (184) not1(all_53_0) = all_105_0 & bool(all_53_0) = all_105_1 &
% 41.25/6.50 | $i(all_105_0) & (all_105_0 = all_79_0 | all_105_1 = 0)
% 41.25/6.50 |
% 41.25/6.50 | ALPHA: (184) implies:
% 41.25/6.50 | (185) $i(all_105_0)
% 41.25/6.50 | (186) bool(all_53_0) = all_105_1
% 41.25/6.50 | (187) not1(all_53_0) = all_105_0
% 41.25/6.50 |
% 41.25/6.50 | DELTA: instantiating (162) with fresh symbols all_107_0, all_107_1 gives:
% 41.25/6.50 | (188) f3(false, true, false) = all_107_1 & lazy_impl(all_107_0, true) =
% 41.25/6.50 | all_107_1 & prop(false) = all_107_0 & $i(all_107_0) & $i(all_107_1)
% 41.25/6.50 |
% 41.25/6.50 | ALPHA: (188) implies:
% 41.25/6.50 | (189) prop(false) = all_107_0
% 41.25/6.50 |
% 41.25/6.50 | DELTA: instantiating (157) with fresh symbols all_113_0, all_113_1 gives:
% 41.25/6.50 | (190) f3(true, true, true) = all_113_1 & lazy_impl(all_113_0, true) =
% 41.25/6.50 | all_113_1 & prop(true) = all_113_0 & $i(all_113_0) & $i(all_113_1)
% 41.25/6.50 |
% 41.25/6.50 | ALPHA: (190) implies:
% 41.25/6.50 | (191) prop(true) = all_113_0
% 41.25/6.50 | (192) lazy_impl(all_113_0, true) = all_113_1
% 41.25/6.50 |
% 41.25/6.50 | DELTA: instantiating (154) with fresh symbols all_115_0, all_115_1 gives:
% 41.25/6.50 | (193) f3(true, false, false) = all_115_1 & lazy_impl(all_115_0, true) =
% 41.25/6.50 | all_115_1 & prop(false) = all_115_0 & $i(all_115_0) & $i(all_115_1)
% 41.25/6.50 |
% 41.25/6.50 | ALPHA: (193) implies:
% 41.25/6.50 | (194) prop(false) = all_115_0
% 41.25/6.50 |
% 41.25/6.50 | DELTA: instantiating (156) with fresh symbols all_117_0, all_117_1 gives:
% 41.25/6.50 | (195) f3(true, true, false) = all_117_1 & lazy_impl(all_117_0, true) =
% 41.25/6.50 | all_117_1 & prop(false) = all_117_0 & $i(all_117_0) & $i(all_117_1)
% 41.25/6.50 |
% 41.25/6.50 | ALPHA: (195) implies:
% 41.25/6.50 | (196) prop(false) = all_117_0
% 41.25/6.50 | (197) lazy_impl(all_117_0, true) = all_117_1
% 41.25/6.50 |
% 41.25/6.50 | DELTA: instantiating (158) with fresh symbols all_119_0, all_119_1 gives:
% 41.25/6.50 | (198) f3(false, true, true) = all_119_1 & lazy_impl(all_119_0, true) =
% 41.25/6.50 | all_119_1 & prop(true) = all_119_0 & $i(all_119_0) & $i(all_119_1)
% 41.25/6.50 |
% 41.25/6.50 | ALPHA: (198) implies:
% 41.25/6.50 | (199) prop(true) = all_119_0
% 41.25/6.50 | (200) lazy_impl(all_119_0, true) = all_119_1
% 41.25/6.50 |
% 41.25/6.50 | DELTA: instantiating (153) with fresh symbols all_121_0, all_121_1, all_121_2
% 41.25/6.50 | gives:
% 41.25/6.50 | (201) f1(true, true, false) = all_121_2 & lazy_impl(all_121_1, all_121_0) =
% 41.25/6.50 | all_121_2 & impl(false, false) = all_121_0 & prop(false) = all_121_1
% 41.25/6.50 | & $i(all_121_0) & $i(all_121_1) & $i(all_121_2)
% 41.25/6.50 |
% 41.25/6.50 | ALPHA: (201) implies:
% 41.25/6.50 | (202) prop(false) = all_121_1
% 41.25/6.50 | (203) impl(false, false) = all_121_0
% 41.25/6.50 | (204) lazy_impl(all_121_1, all_121_0) = all_121_2
% 41.25/6.50 |
% 41.25/6.50 | DELTA: instantiating (167) with fresh symbols all_123_0, all_123_1, all_123_2
% 41.25/6.50 | gives:
% 41.25/6.50 | (205) f2(true, false, false) = all_123_2 & lazy_impl(all_123_1, all_123_0)
% 41.25/6.50 | = all_123_2 & impl(true, false) = all_123_0 & prop(false) = all_123_1
% 41.25/6.50 | & $i(all_123_0) & $i(all_123_1) & $i(all_123_2)
% 41.25/6.50 |
% 41.25/6.50 | ALPHA: (205) implies:
% 41.25/6.50 | (206) prop(false) = all_123_1
% 41.25/6.50 | (207) impl(true, false) = all_123_0
% 41.25/6.50 | (208) lazy_impl(all_123_1, all_123_0) = all_123_2
% 41.25/6.50 |
% 41.25/6.50 | DELTA: instantiating (165) with fresh symbols all_125_0, all_125_1, all_125_2
% 41.25/6.50 | gives:
% 41.25/6.50 | (209) f2(true, true, true) = all_125_2 & lazy_impl(all_125_1, all_125_0) =
% 41.25/6.50 | all_125_2 & impl(true, true) = all_125_0 & prop(true) = all_125_1 &
% 41.25/6.50 | $i(all_125_0) & $i(all_125_1) & $i(all_125_2)
% 41.25/6.50 |
% 41.25/6.50 | ALPHA: (209) implies:
% 41.25/6.51 | (210) prop(true) = all_125_1
% 41.25/6.51 | (211) impl(true, true) = all_125_0
% 41.25/6.51 | (212) lazy_impl(all_125_1, all_125_0) = all_125_2
% 41.25/6.51 | (213) f2(true, true, true) = all_125_2
% 41.25/6.51 |
% 41.25/6.51 | DELTA: instantiating (166) with fresh symbols all_127_0, all_127_1, all_127_2
% 41.25/6.51 | gives:
% 41.25/6.51 | (214) f2(true, false, true) = all_127_2 & lazy_impl(all_127_1, all_127_0) =
% 41.25/6.51 | all_127_2 & impl(true, true) = all_127_0 & prop(true) = all_127_1 &
% 41.25/6.51 | $i(all_127_0) & $i(all_127_1) & $i(all_127_2)
% 41.25/6.51 |
% 41.25/6.51 | ALPHA: (214) implies:
% 41.25/6.51 | (215) prop(true) = all_127_1
% 41.25/6.51 | (216) impl(true, true) = all_127_0
% 41.25/6.51 | (217) lazy_impl(all_127_1, all_127_0) = all_127_2
% 41.25/6.51 |
% 41.25/6.51 | DELTA: instantiating (163) with fresh symbols all_129_0, all_129_1, all_129_2
% 41.25/6.51 | gives:
% 41.25/6.51 | (218) f1(true, false, false) = all_129_2 & lazy_impl(all_129_1, all_129_0)
% 41.25/6.51 | = all_129_2 & impl(true, false) = all_129_0 & prop(false) = all_129_1
% 41.25/6.51 | & $i(all_129_0) & $i(all_129_1) & $i(all_129_2)
% 41.25/6.51 |
% 41.25/6.51 | ALPHA: (218) implies:
% 41.25/6.51 | (219) prop(false) = all_129_1
% 41.25/6.51 | (220) impl(true, false) = all_129_0
% 41.25/6.51 | (221) lazy_impl(all_129_1, all_129_0) = all_129_2
% 41.25/6.51 |
% 41.25/6.51 | DELTA: instantiating (161) with fresh symbols all_131_0, all_131_1, all_131_2
% 41.25/6.51 | gives:
% 41.25/6.51 | (222) f1(true, false, true) = all_131_2 & lazy_impl(all_131_1, all_131_0) =
% 41.25/6.51 | all_131_2 & impl(true, true) = all_131_0 & prop(true) = all_131_1 &
% 41.25/6.51 | $i(all_131_0) & $i(all_131_1) & $i(all_131_2)
% 41.25/6.51 |
% 41.25/6.51 | ALPHA: (222) implies:
% 41.25/6.51 | (223) prop(true) = all_131_1
% 41.25/6.51 | (224) impl(true, true) = all_131_0
% 41.25/6.51 | (225) lazy_impl(all_131_1, all_131_0) = all_131_2
% 41.25/6.51 |
% 41.25/6.51 | DELTA: instantiating (160) with fresh symbols all_133_0, all_133_1, all_133_2
% 41.25/6.51 | gives:
% 41.25/6.51 | (226) f1(false, true, true) = all_133_2 & lazy_impl(all_133_1, all_133_0) =
% 41.25/6.51 | all_133_2 & impl(true, true) = all_133_0 & prop(true) = all_133_1 &
% 41.25/6.51 | $i(all_133_0) & $i(all_133_1) & $i(all_133_2)
% 41.25/6.51 |
% 41.25/6.51 | ALPHA: (226) implies:
% 41.25/6.51 | (227) prop(true) = all_133_1
% 41.25/6.51 | (228) impl(true, true) = all_133_0
% 41.25/6.51 |
% 41.25/6.51 | DELTA: instantiating (159) with fresh symbols all_135_0, all_135_1, all_135_2
% 41.25/6.51 | gives:
% 41.25/6.51 | (229) f1(true, true, true) = all_135_2 & lazy_impl(all_135_1, all_135_0) =
% 41.25/6.51 | all_135_2 & impl(true, true) = all_135_0 & prop(true) = all_135_1 &
% 41.25/6.51 | $i(all_135_0) & $i(all_135_1) & $i(all_135_2)
% 41.25/6.51 |
% 41.25/6.51 | ALPHA: (229) implies:
% 41.25/6.51 | (230) prop(true) = all_135_1
% 41.25/6.51 | (231) impl(true, true) = all_135_0
% 41.25/6.51 | (232) lazy_impl(all_135_1, all_135_0) = all_135_2
% 41.25/6.51 |
% 41.25/6.51 | DELTA: instantiating (164) with fresh symbols all_137_0, all_137_1, all_137_2
% 41.25/6.51 | gives:
% 41.25/6.51 | (233) f2(true, true, false) = all_137_2 & lazy_impl(all_137_1, all_137_0) =
% 41.25/6.51 | all_137_2 & impl(false, false) = all_137_0 & prop(false) = all_137_1
% 41.25/6.51 | & $i(all_137_0) & $i(all_137_1) & $i(all_137_2)
% 41.25/6.51 |
% 41.25/6.51 | ALPHA: (233) implies:
% 41.25/6.51 | (234) prop(false) = all_137_1
% 41.25/6.51 | (235) impl(false, false) = all_137_0
% 41.25/6.51 | (236) lazy_impl(all_137_1, all_137_0) = all_137_2
% 41.25/6.51 | (237) f2(true, true, false) = all_137_2
% 41.25/6.51 |
% 41.25/6.51 | DELTA: instantiating (151) with fresh symbols all_139_0, all_139_1, all_139_2
% 41.25/6.51 | gives:
% 41.25/6.51 | (238) f1(false, false, false) = all_139_2 & lazy_impl(all_139_1, all_139_0)
% 41.25/6.51 | = all_139_2 & impl(true, false) = all_139_0 & prop(false) = all_139_1
% 41.25/6.51 | & $i(all_139_0) & $i(all_139_1) & $i(all_139_2)
% 41.25/6.51 |
% 41.25/6.51 | ALPHA: (238) implies:
% 41.25/6.51 | (239) prop(false) = all_139_1
% 41.25/6.51 | (240) impl(true, false) = all_139_0
% 41.25/6.51 | (241) lazy_impl(all_139_1, all_139_0) = all_139_2
% 41.25/6.51 |
% 41.25/6.51 | DELTA: instantiating (150) with fresh symbols all_141_0, all_141_1, all_141_2
% 41.25/6.51 | gives:
% 41.25/6.51 | (242) f1(false, false, true) = all_141_2 & lazy_impl(all_141_1, all_141_0)
% 41.25/6.51 | = all_141_2 & impl(true, true) = all_141_0 & prop(true) = all_141_1 &
% 41.25/6.51 | $i(all_141_0) & $i(all_141_1) & $i(all_141_2)
% 41.25/6.51 |
% 41.25/6.51 | ALPHA: (242) implies:
% 41.25/6.51 | (243) prop(true) = all_141_1
% 41.25/6.51 | (244) impl(true, true) = all_141_0
% 41.25/6.51 | (245) lazy_impl(all_141_1, all_141_0) = all_141_2
% 41.25/6.51 |
% 41.25/6.51 | DELTA: instantiating (155) with fresh symbols all_143_0, all_143_1, all_143_2
% 41.25/6.51 | gives:
% 41.25/6.51 | (246) f1(false, true, false) = all_143_2 & lazy_impl(all_143_1, all_143_0)
% 41.25/6.51 | = all_143_2 & impl(true, false) = all_143_0 & prop(false) = all_143_1
% 41.25/6.51 | & $i(all_143_0) & $i(all_143_1) & $i(all_143_2)
% 41.25/6.51 |
% 41.25/6.51 | ALPHA: (246) implies:
% 41.25/6.51 | (247) prop(false) = all_143_1
% 41.25/6.51 | (248) impl(true, false) = all_143_0
% 41.25/6.51 | (249) lazy_impl(all_143_1, all_143_0) = all_143_2
% 41.25/6.51 |
% 41.25/6.51 | GROUND_INST: instantiating (39) with all_81_1, all_103_1, err, simplifying
% 41.25/6.51 | with (126), (182) gives:
% 41.25/6.51 | (250) all_103_1 = all_81_1
% 41.25/6.51 |
% 41.25/6.51 | GROUND_INST: instantiating (39) with all_79_1, all_105_1, all_53_0,
% 41.25/6.51 | simplifying with (122), (186) gives:
% 41.25/6.51 | (251) all_105_1 = all_79_1
% 41.25/6.51 |
% 41.25/6.51 | GROUND_INST: instantiating (40) with err, all_103_0, err, simplifying with
% 41.25/6.51 | (57), (183) gives:
% 41.25/6.51 | (252) all_103_0 = err
% 41.25/6.51 |
% 41.25/6.51 | GROUND_INST: instantiating (41) with all_101_0, all_107_0, false, simplifying
% 41.25/6.51 | with (179), (189) gives:
% 41.25/6.51 | (253) all_107_0 = all_101_0
% 41.25/6.51 |
% 41.25/6.51 | GROUND_INST: instantiating (41) with true, all_121_1, false, simplifying with
% 41.25/6.51 | (94), (202) gives:
% 41.25/6.51 | (254) all_121_1 = true
% 41.25/6.51 |
% 41.25/6.51 | GROUND_INST: instantiating (41) with all_115_0, all_121_1, false, simplifying
% 41.25/6.51 | with (194), (202) gives:
% 41.25/6.51 | (255) all_121_1 = all_115_0
% 41.25/6.51 |
% 41.25/6.51 | GROUND_INST: instantiating (41) with all_107_0, all_121_1, false, simplifying
% 41.25/6.51 | with (189), (202) gives:
% 41.25/6.51 | (256) all_121_1 = all_107_0
% 41.25/6.51 |
% 41.25/6.51 | GROUND_INST: instantiating (41) with all_121_1, all_123_1, false, simplifying
% 41.25/6.51 | with (202), (206) gives:
% 41.25/6.51 | (257) all_123_1 = all_121_1
% 41.25/6.51 |
% 41.25/6.51 | GROUND_INST: instantiating (41) with all_123_1, all_129_1, false, simplifying
% 41.25/6.51 | with (206), (219) gives:
% 41.25/6.51 | (258) all_129_1 = all_123_1
% 41.25/6.51 |
% 41.25/6.51 | GROUND_INST: instantiating (41) with all_129_1, all_137_1, false, simplifying
% 41.25/6.51 | with (219), (234) gives:
% 41.25/6.51 | (259) all_137_1 = all_129_1
% 41.25/6.51 |
% 41.25/6.51 | GROUND_INST: instantiating (41) with all_137_1, all_139_1, false, simplifying
% 41.25/6.51 | with (234), (239) gives:
% 41.25/6.51 | (260) all_139_1 = all_137_1
% 41.25/6.51 |
% 41.25/6.51 | GROUND_INST: instantiating (41) with all_139_1, all_143_1, false, simplifying
% 41.25/6.51 | with (239), (247) gives:
% 41.25/6.51 | (261) all_143_1 = all_139_1
% 41.25/6.51 |
% 41.25/6.51 | GROUND_INST: instantiating (41) with all_117_0, all_143_1, false, simplifying
% 41.25/6.51 | with (196), (247) gives:
% 41.25/6.51 | (262) all_143_1 = all_117_0
% 41.25/6.51 |
% 41.25/6.51 | GROUND_INST: instantiating (41) with all_113_0, all_119_0, true, simplifying
% 41.25/6.51 | with (191), (199) gives:
% 41.25/6.51 | (263) all_119_0 = all_113_0
% 41.25/6.51 |
% 41.25/6.51 | GROUND_INST: instantiating (41) with all_119_0, all_125_1, true, simplifying
% 41.25/6.51 | with (199), (210) gives:
% 41.25/6.51 | (264) all_125_1 = all_119_0
% 41.25/6.51 |
% 41.25/6.51 | GROUND_INST: instantiating (41) with all_125_1, all_127_1, true, simplifying
% 41.25/6.51 | with (210), (215) gives:
% 41.25/6.51 | (265) all_127_1 = all_125_1
% 41.25/6.51 |
% 41.25/6.51 | GROUND_INST: instantiating (41) with true, all_133_1, true, simplifying with
% 41.25/6.51 | (98), (227) gives:
% 41.25/6.51 | (266) all_133_1 = true
% 41.25/6.51 |
% 41.25/6.51 | GROUND_INST: instantiating (41) with all_133_1, all_135_1, true, simplifying
% 41.25/6.51 | with (227), (230) gives:
% 41.25/6.51 | (267) all_135_1 = all_133_1
% 41.25/6.51 |
% 41.25/6.51 | GROUND_INST: instantiating (41) with all_127_1, all_135_1, true, simplifying
% 41.25/6.51 | with (215), (230) gives:
% 41.25/6.51 | (268) all_135_1 = all_127_1
% 41.25/6.51 |
% 41.25/6.51 | GROUND_INST: instantiating (41) with all_135_1, all_141_1, true, simplifying
% 41.25/6.51 | with (230), (243) gives:
% 41.25/6.51 | (269) all_141_1 = all_135_1
% 41.25/6.51 |
% 41.25/6.51 | GROUND_INST: instantiating (41) with all_131_1, all_141_1, true, simplifying
% 41.25/6.51 | with (223), (243) gives:
% 41.25/6.51 | (270) all_141_1 = all_131_1
% 41.25/6.51 |
% 41.25/6.51 | GROUND_INST: instantiating (43) with true, all_137_0, false, false,
% 41.25/6.51 | simplifying with (93), (235) gives:
% 41.25/6.51 | (271) all_137_0 = true
% 41.25/6.51 |
% 41.25/6.52 | GROUND_INST: instantiating (43) with all_121_0, all_137_0, false, false,
% 41.25/6.52 | simplifying with (203), (235) gives:
% 41.25/6.52 | (272) all_137_0 = all_121_0
% 41.25/6.52 |
% 41.25/6.52 | GROUND_INST: instantiating (43) with false, all_129_0, false, true,
% 41.25/6.52 | simplifying with (92), (220) gives:
% 41.25/6.52 | (273) all_129_0 = false
% 41.25/6.52 |
% 41.25/6.52 | GROUND_INST: instantiating (43) with all_139_0, all_143_0, false, true,
% 41.25/6.52 | simplifying with (240), (248) gives:
% 41.25/6.52 | (274) all_143_0 = all_139_0
% 41.25/6.52 |
% 41.25/6.52 | GROUND_INST: instantiating (43) with all_129_0, all_143_0, false, true,
% 41.25/6.52 | simplifying with (220), (248) gives:
% 41.25/6.52 | (275) all_143_0 = all_129_0
% 41.25/6.52 |
% 41.25/6.52 | GROUND_INST: instantiating (43) with all_123_0, all_143_0, false, true,
% 41.25/6.52 | simplifying with (207), (248) gives:
% 41.25/6.52 | (276) all_143_0 = all_123_0
% 41.25/6.52 |
% 41.25/6.52 | GROUND_INST: instantiating (43) with all_131_0, all_133_0, true, true,
% 41.25/6.52 | simplifying with (224), (228) gives:
% 41.25/6.52 | (277) all_133_0 = all_131_0
% 41.25/6.52 |
% 41.25/6.52 | GROUND_INST: instantiating (43) with all_125_0, all_133_0, true, true,
% 41.25/6.52 | simplifying with (211), (228) gives:
% 41.25/6.52 | (278) all_133_0 = all_125_0
% 41.25/6.52 |
% 41.25/6.52 | GROUND_INST: instantiating (43) with true, all_135_0, true, true, simplifying
% 41.25/6.52 | with (96), (231) gives:
% 41.25/6.52 | (279) all_135_0 = true
% 41.25/6.52 |
% 41.25/6.52 | GROUND_INST: instantiating (43) with all_131_0, all_135_0, true, true,
% 41.25/6.52 | simplifying with (224), (231) gives:
% 41.25/6.52 | (280) all_135_0 = all_131_0
% 41.25/6.52 |
% 41.25/6.52 | GROUND_INST: instantiating (43) with all_135_0, all_141_0, true, true,
% 41.25/6.52 | simplifying with (231), (244) gives:
% 41.25/6.52 | (281) all_141_0 = all_135_0
% 41.25/6.52 |
% 41.25/6.52 | GROUND_INST: instantiating (43) with all_127_0, all_141_0, true, true,
% 41.25/6.52 | simplifying with (216), (244) gives:
% 41.25/6.52 | (282) all_141_0 = all_127_0
% 41.25/6.52 |
% 41.25/6.52 | GROUND_INST: instantiating (44) with false, all_97_0, false, true, simplifying
% 41.25/6.52 | with (102), (172) gives:
% 41.25/6.52 | (283) all_97_0 = false
% 41.25/6.52 |
% 41.25/6.52 | GROUND_INST: instantiating (44) with true, all_95_0, true, true, simplifying
% 41.25/6.52 | with (104), (170) gives:
% 41.25/6.52 | (284) all_95_0 = true
% 41.25/6.52 |
% 41.25/6.52 | COMBINE_EQS: (274), (276) imply:
% 41.25/6.52 | (285) all_139_0 = all_123_0
% 41.25/6.52 |
% 41.25/6.52 | COMBINE_EQS: (274), (275) imply:
% 41.25/6.52 | (286) all_139_0 = all_129_0
% 41.25/6.52 |
% 41.25/6.52 | COMBINE_EQS: (261), (262) imply:
% 41.25/6.52 | (287) all_139_1 = all_117_0
% 41.25/6.52 |
% 41.25/6.52 | SIMP: (287) implies:
% 41.25/6.52 | (288) all_139_1 = all_117_0
% 41.25/6.52 |
% 41.25/6.52 | COMBINE_EQS: (281), (282) imply:
% 41.25/6.52 | (289) all_135_0 = all_127_0
% 41.25/6.52 |
% 41.25/6.52 | SIMP: (289) implies:
% 41.25/6.52 | (290) all_135_0 = all_127_0
% 41.25/6.52 |
% 41.25/6.52 | COMBINE_EQS: (269), (270) imply:
% 41.25/6.52 | (291) all_135_1 = all_131_1
% 41.25/6.52 |
% 41.25/6.52 | SIMP: (291) implies:
% 41.25/6.52 | (292) all_135_1 = all_131_1
% 41.25/6.52 |
% 41.25/6.52 | COMBINE_EQS: (285), (286) imply:
% 41.25/6.52 | (293) all_129_0 = all_123_0
% 41.25/6.52 |
% 41.25/6.52 | SIMP: (293) implies:
% 41.25/6.52 | (294) all_129_0 = all_123_0
% 41.25/6.52 |
% 41.25/6.52 | COMBINE_EQS: (260), (288) imply:
% 41.25/6.52 | (295) all_137_1 = all_117_0
% 41.25/6.52 |
% 41.25/6.52 | SIMP: (295) implies:
% 41.25/6.52 | (296) all_137_1 = all_117_0
% 41.25/6.52 |
% 41.25/6.52 | COMBINE_EQS: (271), (272) imply:
% 41.25/6.52 | (297) all_121_0 = true
% 41.25/6.52 |
% 41.25/6.52 | COMBINE_EQS: (259), (296) imply:
% 41.25/6.52 | (298) all_129_1 = all_117_0
% 41.25/6.52 |
% 41.25/6.52 | SIMP: (298) implies:
% 41.25/6.52 | (299) all_129_1 = all_117_0
% 41.25/6.52 |
% 41.25/6.52 | COMBINE_EQS: (279), (290) imply:
% 41.25/6.52 | (300) all_127_0 = true
% 41.25/6.52 |
% 41.25/6.52 | COMBINE_EQS: (280), (290) imply:
% 41.25/6.52 | (301) all_131_0 = all_127_0
% 41.25/6.52 |
% 41.25/6.52 | SIMP: (301) implies:
% 41.25/6.52 | (302) all_131_0 = all_127_0
% 41.25/6.52 |
% 41.25/6.52 | COMBINE_EQS: (267), (292) imply:
% 41.25/6.52 | (303) all_133_1 = all_131_1
% 41.25/6.52 |
% 41.25/6.52 | SIMP: (303) implies:
% 41.25/6.52 | (304) all_133_1 = all_131_1
% 41.25/6.52 |
% 41.25/6.52 | COMBINE_EQS: (268), (292) imply:
% 41.25/6.52 | (305) all_131_1 = all_127_1
% 41.25/6.52 |
% 41.25/6.52 | COMBINE_EQS: (277), (278) imply:
% 41.25/6.52 | (306) all_131_0 = all_125_0
% 41.25/6.52 |
% 41.25/6.52 | SIMP: (306) implies:
% 41.25/6.52 | (307) all_131_0 = all_125_0
% 41.25/6.52 |
% 41.25/6.52 | COMBINE_EQS: (266), (304) imply:
% 41.25/6.52 | (308) all_131_1 = true
% 41.25/6.52 |
% 41.25/6.52 | SIMP: (308) implies:
% 41.25/6.52 | (309) all_131_1 = true
% 41.25/6.52 |
% 41.25/6.52 | COMBINE_EQS: (302), (307) imply:
% 41.25/6.52 | (310) all_127_0 = all_125_0
% 41.25/6.52 |
% 41.25/6.52 | SIMP: (310) implies:
% 41.25/6.52 | (311) all_127_0 = all_125_0
% 41.25/6.52 |
% 41.25/6.52 | COMBINE_EQS: (305), (309) imply:
% 41.25/6.52 | (312) all_127_1 = true
% 41.25/6.52 |
% 41.25/6.52 | SIMP: (312) implies:
% 41.25/6.52 | (313) all_127_1 = true
% 41.25/6.52 |
% 41.25/6.52 | COMBINE_EQS: (273), (294) imply:
% 41.25/6.52 | (314) all_123_0 = false
% 41.25/6.52 |
% 41.25/6.52 | COMBINE_EQS: (258), (299) imply:
% 41.25/6.52 | (315) all_123_1 = all_117_0
% 41.25/6.52 |
% 41.25/6.52 | SIMP: (315) implies:
% 41.25/6.52 | (316) all_123_1 = all_117_0
% 41.25/6.52 |
% 41.25/6.52 | COMBINE_EQS: (300), (311) imply:
% 41.25/6.52 | (317) all_125_0 = true
% 41.25/6.52 |
% 41.25/6.52 | SIMP: (317) implies:
% 41.25/6.52 | (318) all_125_0 = true
% 41.25/6.52 |
% 41.25/6.52 | COMBINE_EQS: (265), (313) imply:
% 41.25/6.52 | (319) all_125_1 = true
% 41.25/6.52 |
% 41.25/6.52 | SIMP: (319) implies:
% 41.25/6.52 | (320) all_125_1 = true
% 41.25/6.52 |
% 41.25/6.52 | COMBINE_EQS: (264), (320) imply:
% 41.25/6.52 | (321) all_119_0 = true
% 41.25/6.52 |
% 41.25/6.52 | SIMP: (321) implies:
% 41.25/6.52 | (322) all_119_0 = true
% 41.25/6.52 |
% 41.25/6.52 | COMBINE_EQS: (257), (316) imply:
% 41.25/6.52 | (323) all_121_1 = all_117_0
% 41.25/6.52 |
% 41.25/6.52 | SIMP: (323) implies:
% 41.25/6.52 | (324) all_121_1 = all_117_0
% 41.25/6.52 |
% 41.25/6.52 | COMBINE_EQS: (255), (324) imply:
% 41.25/6.52 | (325) all_117_0 = all_115_0
% 41.25/6.52 |
% 41.25/6.52 | COMBINE_EQS: (256), (324) imply:
% 41.25/6.52 | (326) all_117_0 = all_107_0
% 41.25/6.52 |
% 41.25/6.52 | COMBINE_EQS: (254), (324) imply:
% 41.25/6.52 | (327) all_117_0 = true
% 41.25/6.52 |
% 41.25/6.52 | COMBINE_EQS: (263), (322) imply:
% 41.25/6.52 | (328) all_113_0 = true
% 41.25/6.52 |
% 41.25/6.52 | SIMP: (328) implies:
% 41.25/6.52 | (329) all_113_0 = true
% 41.25/6.52 |
% 41.25/6.52 | COMBINE_EQS: (325), (327) imply:
% 41.25/6.52 | (330) all_115_0 = true
% 41.25/6.52 |
% 41.25/6.52 | COMBINE_EQS: (325), (326) imply:
% 41.25/6.52 | (331) all_115_0 = all_107_0
% 41.25/6.52 |
% 41.25/6.52 | COMBINE_EQS: (330), (331) imply:
% 41.25/6.52 | (332) all_107_0 = true
% 41.25/6.52 |
% 41.25/6.52 | SIMP: (332) implies:
% 41.25/6.52 | (333) all_107_0 = true
% 41.25/6.52 |
% 41.25/6.52 | COMBINE_EQS: (253), (333) imply:
% 41.25/6.52 | (334) all_101_0 = true
% 41.25/6.52 |
% 41.25/6.52 | COMBINE_EQS: (316), (327) imply:
% 41.25/6.52 | (335) all_123_1 = true
% 41.25/6.52 |
% 41.25/6.52 | COMBINE_EQS: (299), (327) imply:
% 41.25/6.52 | (336) all_129_1 = true
% 41.25/6.52 |
% 41.25/6.52 | COMBINE_EQS: (307), (318) imply:
% 41.25/6.52 | (337) all_131_0 = true
% 41.25/6.52 |
% 41.25/6.52 | COMBINE_EQS: (292), (309) imply:
% 41.25/6.52 | (338) all_135_1 = true
% 41.25/6.52 |
% 41.25/6.52 | COMBINE_EQS: (296), (327) imply:
% 41.25/6.52 | (339) all_137_1 = true
% 41.25/6.52 |
% 41.25/6.52 | COMBINE_EQS: (288), (327) imply:
% 41.25/6.52 | (340) all_139_1 = true
% 41.25/6.52 |
% 41.25/6.52 | COMBINE_EQS: (285), (314) imply:
% 41.25/6.52 | (341) all_139_0 = false
% 41.25/6.52 |
% 41.25/6.52 | COMBINE_EQS: (270), (309) imply:
% 41.25/6.52 | (342) all_141_1 = true
% 41.25/6.52 |
% 41.25/6.52 | COMBINE_EQS: (282), (300) imply:
% 41.25/6.52 | (343) all_141_0 = true
% 41.25/6.52 |
% 41.25/6.52 | COMBINE_EQS: (262), (327) imply:
% 41.25/6.52 | (344) all_143_1 = true
% 41.25/6.52 |
% 41.25/6.52 | COMBINE_EQS: (274), (341) imply:
% 41.25/6.52 | (345) all_143_0 = false
% 41.25/6.52 |
% 41.25/6.52 | REDUCE: (173), (283) imply:
% 41.25/6.52 | (346) f7(false) = false
% 41.25/6.52 |
% 41.25/6.52 | REDUCE: (249), (344), (345) imply:
% 41.25/6.52 | (347) lazy_impl(true, false) = all_143_2
% 41.25/6.52 |
% 41.25/6.52 | REDUCE: (245), (342), (343) imply:
% 41.25/6.52 | (348) lazy_impl(true, true) = all_141_2
% 41.25/6.52 |
% 41.25/6.52 | REDUCE: (241), (340), (341) imply:
% 41.25/6.52 | (349) lazy_impl(true, false) = all_139_2
% 41.25/6.52 |
% 41.25/6.52 | REDUCE: (236), (271), (339) imply:
% 41.25/6.52 | (350) lazy_impl(true, true) = all_137_2
% 41.25/6.52 |
% 41.25/6.52 | REDUCE: (232), (279), (338) imply:
% 41.25/6.52 | (351) lazy_impl(true, true) = all_135_2
% 41.25/6.52 |
% 41.25/6.52 | REDUCE: (225), (309), (337) imply:
% 41.25/6.52 | (352) lazy_impl(true, true) = all_131_2
% 41.25/6.52 |
% 41.25/6.52 | REDUCE: (221), (273), (336) imply:
% 41.25/6.52 | (353) lazy_impl(true, false) = all_129_2
% 41.25/6.52 |
% 41.25/6.52 | REDUCE: (217), (300), (313) imply:
% 41.25/6.52 | (354) lazy_impl(true, true) = all_127_2
% 41.25/6.52 |
% 41.25/6.52 | REDUCE: (212), (318), (320) imply:
% 41.25/6.53 | (355) lazy_impl(true, true) = all_125_2
% 41.25/6.53 |
% 41.25/6.53 | REDUCE: (208), (314), (335) imply:
% 41.25/6.53 | (356) lazy_impl(true, false) = all_123_2
% 41.25/6.53 |
% 41.25/6.53 | REDUCE: (204), (254), (297) imply:
% 41.25/6.53 | (357) lazy_impl(true, true) = all_121_2
% 41.25/6.53 |
% 41.25/6.53 | REDUCE: (200), (322) imply:
% 41.25/6.53 | (358) lazy_impl(true, true) = all_119_1
% 41.25/6.53 |
% 41.25/6.53 | REDUCE: (197), (327) imply:
% 41.25/6.53 | (359) lazy_impl(true, true) = all_117_1
% 41.25/6.53 |
% 41.25/6.53 | REDUCE: (192), (329) imply:
% 41.25/6.53 | (360) lazy_impl(true, true) = all_113_1
% 41.25/6.53 |
% 41.25/6.53 | REDUCE: (180), (334) imply:
% 41.25/6.53 | (361) lazy_impl(true, false) = all_101_1
% 41.25/6.53 |
% 41.25/6.53 | GROUND_INST: instantiating (44) with false, all_123_2, false, true,
% 41.25/6.53 | simplifying with (102), (356) gives:
% 41.25/6.53 | (362) all_123_2 = false
% 41.25/6.53 |
% 41.25/6.53 | GROUND_INST: instantiating (44) with all_129_2, all_139_2, false, true,
% 41.25/6.53 | simplifying with (349), (353) gives:
% 41.25/6.53 | (363) all_139_2 = all_129_2
% 41.25/6.53 |
% 41.25/6.53 | GROUND_INST: instantiating (44) with all_123_2, all_139_2, false, true,
% 41.25/6.53 | simplifying with (349), (356) gives:
% 41.25/6.53 | (364) all_139_2 = all_123_2
% 41.25/6.53 |
% 41.25/6.53 | GROUND_INST: instantiating (44) with all_139_2, all_143_2, false, true,
% 41.25/6.53 | simplifying with (347), (349) gives:
% 41.25/6.53 | (365) all_143_2 = all_139_2
% 41.25/6.53 |
% 41.25/6.53 | GROUND_INST: instantiating (44) with all_101_1, all_143_2, false, true,
% 41.25/6.53 | simplifying with (347), (361) gives:
% 41.25/6.53 | (366) all_143_2 = all_101_1
% 41.25/6.53 |
% 41.25/6.53 | GROUND_INST: instantiating (44) with all_117_1, all_121_2, true, true,
% 41.25/6.53 | simplifying with (357), (359) gives:
% 41.25/6.53 | (367) all_121_2 = all_117_1
% 41.25/6.53 |
% 41.25/6.53 | GROUND_INST: instantiating (44) with all_121_2, all_125_2, true, true,
% 41.25/6.53 | simplifying with (355), (357) gives:
% 41.25/6.53 | (368) all_125_2 = all_121_2
% 41.25/6.53 |
% 41.25/6.53 | GROUND_INST: instantiating (44) with all_125_2, all_127_2, true, true,
% 41.25/6.53 | simplifying with (354), (355) gives:
% 41.25/6.53 | (369) all_127_2 = all_125_2
% 41.25/6.53 |
% 41.25/6.53 | GROUND_INST: instantiating (44) with all_121_2, all_131_2, true, true,
% 41.25/6.53 | simplifying with (352), (357) gives:
% 41.25/6.53 | (370) all_131_2 = all_121_2
% 41.25/6.53 |
% 41.25/6.53 | GROUND_INST: instantiating (44) with all_131_2, all_135_2, true, true,
% 41.25/6.53 | simplifying with (351), (352) gives:
% 41.25/6.53 | (371) all_135_2 = all_131_2
% 41.25/6.53 |
% 41.25/6.53 | GROUND_INST: instantiating (44) with all_119_1, all_135_2, true, true,
% 41.25/6.53 | simplifying with (351), (358) gives:
% 41.25/6.53 | (372) all_135_2 = all_119_1
% 41.25/6.53 |
% 41.25/6.53 | GROUND_INST: instantiating (44) with true, all_137_2, true, true, simplifying
% 41.25/6.53 | with (104), (350) gives:
% 41.25/6.53 | (373) all_137_2 = true
% 41.25/6.53 |
% 41.25/6.53 | GROUND_INST: instantiating (44) with all_121_2, all_137_2, true, true,
% 41.25/6.53 | simplifying with (350), (357) gives:
% 41.25/6.53 | (374) all_137_2 = all_121_2
% 41.25/6.53 |
% 41.25/6.53 | GROUND_INST: instantiating (44) with all_127_2, all_141_2, true, true,
% 41.25/6.53 | simplifying with (348), (354) gives:
% 41.25/6.53 | (375) all_141_2 = all_127_2
% 41.25/6.53 |
% 41.25/6.53 | GROUND_INST: instantiating (44) with all_113_1, all_141_2, true, true,
% 41.25/6.53 | simplifying with (348), (360) gives:
% 41.25/6.53 | (376) all_141_2 = all_113_1
% 41.25/6.53 |
% 41.25/6.53 | COMBINE_EQS: (365), (366) imply:
% 41.25/6.53 | (377) all_139_2 = all_101_1
% 41.25/6.53 |
% 41.25/6.53 | SIMP: (377) implies:
% 41.25/6.53 | (378) all_139_2 = all_101_1
% 41.25/6.53 |
% 41.25/6.53 | COMBINE_EQS: (375), (376) imply:
% 41.25/6.53 | (379) all_127_2 = all_113_1
% 41.25/6.53 |
% 41.25/6.53 | SIMP: (379) implies:
% 41.25/6.53 | (380) all_127_2 = all_113_1
% 41.25/6.53 |
% 41.25/6.53 | COMBINE_EQS: (363), (378) imply:
% 41.25/6.53 | (381) all_129_2 = all_101_1
% 41.25/6.53 |
% 41.25/6.53 | COMBINE_EQS: (363), (364) imply:
% 41.25/6.53 | (382) all_129_2 = all_123_2
% 41.25/6.53 |
% 41.25/6.53 | COMBINE_EQS: (373), (374) imply:
% 41.25/6.53 | (383) all_121_2 = true
% 41.25/6.53 |
% 41.25/6.53 | SIMP: (383) implies:
% 41.25/6.53 | (384) all_121_2 = true
% 41.25/6.53 |
% 41.25/6.53 | COMBINE_EQS: (371), (372) imply:
% 41.25/6.53 | (385) all_131_2 = all_119_1
% 41.25/6.53 |
% 41.25/6.53 | SIMP: (385) implies:
% 41.25/6.53 | (386) all_131_2 = all_119_1
% 41.25/6.53 |
% 41.25/6.53 | COMBINE_EQS: (370), (386) imply:
% 41.25/6.53 | (387) all_121_2 = all_119_1
% 41.25/6.53 |
% 41.25/6.53 | SIMP: (387) implies:
% 41.25/6.53 | (388) all_121_2 = all_119_1
% 41.25/6.53 |
% 41.25/6.53 | COMBINE_EQS: (381), (382) imply:
% 41.25/6.53 | (389) all_123_2 = all_101_1
% 41.25/6.53 |
% 41.25/6.53 | SIMP: (389) implies:
% 41.25/6.53 | (390) all_123_2 = all_101_1
% 41.25/6.53 |
% 41.25/6.53 | COMBINE_EQS: (369), (380) imply:
% 41.25/6.53 | (391) all_125_2 = all_113_1
% 41.25/6.53 |
% 41.25/6.53 | SIMP: (391) implies:
% 41.25/6.53 | (392) all_125_2 = all_113_1
% 41.25/6.53 |
% 41.25/6.53 | COMBINE_EQS: (368), (392) imply:
% 41.25/6.53 | (393) all_121_2 = all_113_1
% 41.25/6.53 |
% 41.25/6.53 | SIMP: (393) implies:
% 41.25/6.53 | (394) all_121_2 = all_113_1
% 41.25/6.53 |
% 41.25/6.53 | COMBINE_EQS: (362), (390) imply:
% 41.25/6.53 | (395) all_101_1 = false
% 41.25/6.53 |
% 41.25/6.53 | COMBINE_EQS: (384), (388) imply:
% 41.25/6.53 | (396) all_119_1 = true
% 41.25/6.53 |
% 41.25/6.53 | COMBINE_EQS: (388), (394) imply:
% 41.25/6.53 | (397) all_119_1 = all_113_1
% 41.25/6.53 |
% 41.25/6.53 | COMBINE_EQS: (367), (388) imply:
% 41.25/6.53 | (398) all_119_1 = all_117_1
% 41.25/6.53 |
% 41.25/6.53 | COMBINE_EQS: (396), (398) imply:
% 41.25/6.53 | (399) all_117_1 = true
% 41.25/6.53 |
% 41.25/6.53 | COMBINE_EQS: (397), (398) imply:
% 41.25/6.53 | (400) all_117_1 = all_113_1
% 41.25/6.53 |
% 41.25/6.53 | COMBINE_EQS: (399), (400) imply:
% 41.25/6.53 | (401) all_113_1 = true
% 41.25/6.53 |
% 41.25/6.53 | COMBINE_EQS: (392), (401) imply:
% 41.25/6.53 | (402) all_125_2 = true
% 41.25/6.53 |
% 41.25/6.53 | REDUCE: (213), (402) imply:
% 41.25/6.53 | (403) f2(true, true, true) = true
% 41.25/6.53 |
% 41.25/6.53 | REDUCE: (237), (373) imply:
% 41.25/6.53 | (404) f2(true, true, false) = true
% 41.25/6.53 |
% 41.25/6.53 | GROUND_INST: instantiating (10) with all_53_0, all_99_0, simplifying with
% 41.25/6.53 | (68), (175) gives:
% 41.25/6.53 | (405) ? [v0: $i] : (phi(all_53_0) = v0 & $i(v0) & ((v0 = all_53_0 &
% 41.25/6.53 | all_99_0 = 0) | (v0 = err & ~ (all_99_0 = 0))))
% 41.25/6.53 |
% 41.25/6.53 | GROUND_INST: instantiating (52) with false, false, simplifying with (54),
% 41.25/6.53 | (346) gives:
% 41.25/6.53 | (406) ? [v0: int] : ( ~ (v0 = 0) & forallprefers(false, all_42_0) = v0)
% 41.25/6.53 |
% 41.25/6.53 | GROUND_INST: instantiating (32) with all_53_0, all_105_0, simplifying with
% 41.25/6.53 | (68), (187) gives:
% 41.25/6.53 | (407) ? [v0: any] : ? [v1: $i] : (phi(all_53_0) = v1 & bool(all_53_0) =
% 41.25/6.53 | v0 & $i(v1) & (v1 = all_105_0 | v0 = 0))
% 41.25/6.53 |
% 41.25/6.53 | DELTA: instantiating (406) with fresh symbol all_160_0 gives:
% 41.25/6.53 | (408) ~ (all_160_0 = 0) & forallprefers(false, all_42_0) = all_160_0
% 41.25/6.53 |
% 41.25/6.53 | ALPHA: (408) implies:
% 41.25/6.53 | (409) ~ (all_160_0 = 0)
% 41.25/6.53 | (410) forallprefers(false, all_42_0) = all_160_0
% 41.25/6.53 |
% 41.25/6.53 | DELTA: instantiating (407) with fresh symbols all_162_0, all_162_1 gives:
% 41.25/6.53 | (411) phi(all_53_0) = all_162_0 & bool(all_53_0) = all_162_1 &
% 41.25/6.53 | $i(all_162_0) & (all_162_0 = all_105_0 | all_162_1 = 0)
% 41.25/6.53 |
% 41.25/6.53 | ALPHA: (411) implies:
% 41.25/6.53 | (412) $i(all_162_0)
% 41.25/6.53 | (413) bool(all_53_0) = all_162_1
% 41.25/6.53 | (414) phi(all_53_0) = all_162_0
% 41.25/6.53 | (415) all_162_0 = all_105_0 | all_162_1 = 0
% 41.25/6.53 |
% 41.25/6.53 | DELTA: instantiating (405) with fresh symbol all_164_0 gives:
% 41.25/6.53 | (416) phi(all_53_0) = all_164_0 & $i(all_164_0) & ((all_164_0 = all_53_0 &
% 41.25/6.53 | all_99_0 = 0) | (all_164_0 = err & ~ (all_99_0 = 0)))
% 41.25/6.53 |
% 41.25/6.53 | ALPHA: (416) implies:
% 41.25/6.53 | (417) phi(all_53_0) = all_164_0
% 41.25/6.53 |
% 41.25/6.53 | GROUND_INST: instantiating (39) with all_79_1, all_162_1, all_53_0,
% 41.25/6.53 | simplifying with (122), (413) gives:
% 41.25/6.53 | (418) all_162_1 = all_79_1
% 41.25/6.53 |
% 41.25/6.53 | GROUND_INST: instantiating (40) with all_79_0, all_164_0, all_53_0,
% 41.25/6.53 | simplifying with (123), (417) gives:
% 41.25/6.53 | (419) all_164_0 = all_79_0
% 41.25/6.53 |
% 41.25/6.53 | GROUND_INST: instantiating (40) with all_162_0, all_164_0, all_53_0,
% 41.25/6.53 | simplifying with (414), (417) gives:
% 41.25/6.53 | (420) all_164_0 = all_162_0
% 41.25/6.53 |
% 41.25/6.53 | COMBINE_EQS: (419), (420) imply:
% 41.25/6.53 | (421) all_162_0 = all_79_0
% 41.25/6.53 |
% 41.25/6.53 | REDUCE: (412), (421) imply:
% 41.25/6.53 | (422) $i(all_79_0)
% 41.25/6.53 |
% 41.25/6.53 | BETA: splitting (74) gives:
% 41.25/6.53 |
% 41.25/6.53 | Case 1:
% 41.25/6.53 | |
% 41.25/6.53 | | (423) all_55_1 = 0
% 41.25/6.53 | |
% 41.25/6.53 | | REDUCE: (72), (423) imply:
% 41.25/6.53 | | (424) bool(all_42_0) = 0
% 41.25/6.53 | |
% 41.25/6.53 | | BETA: splitting (81) gives:
% 41.25/6.53 | |
% 41.25/6.53 | | Case 1:
% 41.25/6.53 | | |
% 41.25/6.53 | | | (425) all_59_0 = 0 & all_42_0 = false2
% 41.25/6.53 | | |
% 41.25/6.53 | | | ALPHA: (425) implies:
% 41.25/6.53 | | | (426) all_42_0 = false2
% 41.25/6.53 | | |
% 41.25/6.53 | | | REDUCE: (410), (426) imply:
% 41.25/6.53 | | | (427) forallprefers(false, false2) = all_160_0
% 41.25/6.53 | | |
% 41.25/6.53 | | | REDUCE: (424), (426) imply:
% 41.25/6.53 | | | (428) bool(false2) = 0
% 41.25/6.53 | | |
% 41.25/6.53 | | | GROUND_INST: instantiating (3) with false2, simplifying with (138), (428)
% 41.25/6.53 | | | gives:
% 41.25/6.53 | | | (429) false2 = true | false2 = false
% 41.25/6.53 | | |
% 41.25/6.53 | | | BETA: splitting (429) gives:
% 41.25/6.53 | | |
% 41.25/6.53 | | | Case 1:
% 41.25/6.53 | | | |
% 41.25/6.53 | | | | (430) false2 = true
% 41.25/6.53 | | | |
% 41.25/6.53 | | | | REDUCE: (427), (430) imply:
% 41.25/6.53 | | | | (431) forallprefers(false, true) = all_160_0
% 41.25/6.53 | | | |
% 41.25/6.53 | | | | GROUND_INST: instantiating (8) with all_160_0, simplifying with (431)
% 41.25/6.53 | | | | gives:
% 41.25/6.53 | | | | (432) all_160_0 = 0
% 41.25/6.53 | | | |
% 41.25/6.53 | | | | REDUCE: (409), (432) imply:
% 41.25/6.53 | | | | (433) $false
% 41.25/6.54 | | | |
% 41.25/6.54 | | | | CLOSE: (433) is inconsistent.
% 41.25/6.54 | | | |
% 41.25/6.54 | | | Case 2:
% 41.25/6.54 | | | |
% 41.25/6.54 | | | | (434) false2 = false
% 41.25/6.54 | | | |
% 41.25/6.54 | | | | REDUCE: (53), (434) imply:
% 41.25/6.54 | | | | (435) $false
% 41.25/6.54 | | | |
% 41.25/6.54 | | | | CLOSE: (435) is inconsistent.
% 41.25/6.54 | | | |
% 41.25/6.54 | | | End of split
% 41.25/6.54 | | |
% 41.25/6.54 | | Case 2:
% 41.25/6.54 | | |
% 41.25/6.54 | | | (436) false2 = err & ~ (all_59_0 = 0)
% 41.25/6.54 | | |
% 41.25/6.54 | | | ALPHA: (436) implies:
% 41.25/6.54 | | | (437) false2 = err
% 41.25/6.54 | | |
% 41.25/6.54 | | | REDUCE: (53), (437) imply:
% 41.25/6.54 | | | (438) ~ (err = false)
% 41.25/6.54 | | |
% 41.25/6.54 | | | REDUCE: (61), (437) imply:
% 41.25/6.54 | | | (439) lazy_and1(true, all_42_0) = err
% 41.25/6.54 | | |
% 41.25/6.54 | | | REDUCE: (63), (437) imply:
% 41.25/6.54 | | | (440) lazy_impl(true, all_42_0) = err
% 41.25/6.54 | | |
% 41.25/6.54 | | | BETA: splitting (108) gives:
% 41.25/6.54 | | |
% 41.25/6.54 | | | Case 1:
% 41.25/6.54 | | | |
% 41.25/6.54 | | | | (441) bool(all_42_1) = 0
% 41.25/6.54 | | | |
% 41.25/6.54 | | | | BETA: splitting (107) gives:
% 41.25/6.54 | | | |
% 41.25/6.54 | | | | Case 1:
% 41.25/6.54 | | | | |
% 41.25/6.54 | | | | | (442) all_53_0 = true
% 41.25/6.54 | | | | |
% 41.25/6.54 | | | | | REDUCE: (187), (442) imply:
% 41.25/6.54 | | | | | (443) not1(true) = all_105_0
% 41.25/6.54 | | | | |
% 41.25/6.54 | | | | | REDUCE: (145), (442) imply:
% 41.25/6.54 | | | | | (444) lazy_and1(true, true) = all_79_0
% 41.25/6.54 | | | | |
% 41.25/6.54 | | | | | REDUCE: (70), (442) imply:
% 41.25/6.54 | | | | | (445) lazy_impl(true, all_42_1) = all_42_0
% 41.25/6.54 | | | | |
% 41.25/6.54 | | | | | REDUCE: (147), (442) imply:
% 41.25/6.54 | | | | | (446) lazy_impl(true, true) = all_79_0
% 41.25/6.54 | | | | |
% 41.25/6.54 | | | | | REDUCE: (69), (442) imply:
% 41.25/6.54 | | | | | (447) prop(all_42_1) = true
% 41.25/6.54 | | | | |
% 41.25/6.54 | | | | | GROUND_INST: instantiating (45) with true, all_79_0, true, true,
% 41.25/6.54 | | | | | simplifying with (103), (444) gives:
% 41.25/6.54 | | | | | (448) all_79_0 = true
% 41.25/6.54 | | | | |
% 41.25/6.54 | | | | | GROUND_INST: instantiating (42) with false, all_105_0, true,
% 41.25/6.54 | | | | | simplifying with (36), (443) gives:
% 41.25/6.54 | | | | | (449) all_105_0 = false
% 41.25/6.54 | | | | |
% 41.25/6.54 | | | | | GROUND_INST: instantiating (19) with all_42_1, simplifying with (48),
% 41.25/6.54 | | | | | (441) gives:
% 41.25/6.54 | | | | | (450) impl(true, all_42_1) = all_42_1
% 41.25/6.54 | | | | |
% 41.25/6.54 | | | | | GROUND_INST: instantiating (18) with all_42_1, simplifying with (48),
% 41.25/6.54 | | | | | (441) gives:
% 41.25/6.54 | | | | | (451) impl(false, all_42_1) = true
% 41.25/6.54 | | | | |
% 41.25/6.54 | | | | | GROUND_INST: instantiating (3) with all_42_0, simplifying with (49),
% 41.25/6.54 | | | | | (424) gives:
% 41.25/6.54 | | | | | (452) all_42_0 = true | all_42_0 = false
% 41.25/6.54 | | | | |
% 41.25/6.54 | | | | | GROUND_INST: instantiating (19) with all_42_0, simplifying with (49),
% 41.25/6.54 | | | | | (424) gives:
% 41.25/6.54 | | | | | (453) impl(true, all_42_0) = all_42_0
% 41.25/6.54 | | | | |
% 41.25/6.54 | | | | | GROUND_INST: instantiating (18) with all_42_0, simplifying with (49),
% 41.25/6.54 | | | | | (424) gives:
% 41.25/6.54 | | | | | (454) impl(false, all_42_0) = true
% 41.25/6.54 | | | | |
% 41.25/6.54 | | | | | GROUND_INST: instantiating (12) with all_42_0, simplifying with (49),
% 41.25/6.54 | | | | | (424) gives:
% 41.25/6.54 | | | | | (455) prop(all_42_0) = true
% 41.25/6.54 | | | | |
% 41.25/6.54 | | | | | GROUND_INST: instantiating (15) with all_42_0, simplifying with (49),
% 41.25/6.54 | | | | | (424) gives:
% 41.25/6.54 | | | | | (456) ? [v0: $i] : ( ~ (v0 = false) & prop(all_42_0) = v0 &
% 41.25/6.54 | | | | | $i(v0))
% 41.25/6.54 | | | | |
% 41.25/6.54 | | | | | GROUND_INST: instantiating (22) with all_42_1, all_42_0, simplifying
% 41.25/6.54 | | | | | with (48), (445) gives:
% 41.25/6.54 | | | | | (457) phi(all_42_1) = all_42_0 & $i(all_42_0)
% 41.25/6.54 | | | | |
% 41.25/6.54 | | | | | ALPHA: (457) implies:
% 41.25/6.54 | | | | | (458) phi(all_42_1) = all_42_0
% 41.25/6.54 | | | | |
% 41.25/6.54 | | | | | DELTA: instantiating (456) with fresh symbol all_207_0 gives:
% 41.25/6.54 | | | | | (459) ~ (all_207_0 = false) & prop(all_42_0) = all_207_0 &
% 41.25/6.54 | | | | | $i(all_207_0)
% 41.25/6.54 | | | | |
% 41.25/6.54 | | | | | ALPHA: (459) implies:
% 41.25/6.54 | | | | | (460) $i(all_207_0)
% 41.25/6.54 | | | | | (461) prop(all_42_0) = all_207_0
% 41.25/6.54 | | | | |
% 41.25/6.54 | | | | | GROUND_INST: instantiating (41) with true, all_207_0, all_42_0,
% 41.25/6.54 | | | | | simplifying with (455), (461) gives:
% 41.25/6.54 | | | | | (462) all_207_0 = true
% 41.25/6.54 | | | | |
% 41.25/6.54 | | | | | BETA: splitting (128) gives:
% 41.25/6.54 | | | | |
% 41.25/6.54 | | | | | Case 1:
% 41.25/6.54 | | | | | |
% 41.25/6.54 | | | | | | (463) all_81_1 = 0
% 41.25/6.54 | | | | | |
% 41.25/6.54 | | | | | | REDUCE: (126), (463) imply:
% 41.25/6.54 | | | | | | (464) bool(err) = 0
% 41.25/6.54 | | | | | |
% 41.25/6.54 | | | | | | GROUND_INST: instantiating (3) with err, simplifying with (9), (464)
% 41.25/6.54 | | | | | | gives:
% 41.25/6.54 | | | | | | (465) err = true | err = false
% 41.25/6.54 | | | | | |
% 41.25/6.54 | | | | | | BETA: splitting (465) gives:
% 41.25/6.54 | | | | | |
% 41.25/6.54 | | | | | | Case 1:
% 41.25/6.54 | | | | | | |
% 41.25/6.54 | | | | | | | (466) err = true
% 41.25/6.54 | | | | | | |
% 41.25/6.54 | | | | | | | REDUCE: (4), (466) imply:
% 41.25/6.54 | | | | | | | (467) $false
% 41.25/6.54 | | | | | | |
% 41.25/6.54 | | | | | | | CLOSE: (467) is inconsistent.
% 41.25/6.54 | | | | | | |
% 41.25/6.54 | | | | | | Case 2:
% 41.25/6.54 | | | | | | |
% 41.25/6.54 | | | | | | | (468) err = false
% 41.25/6.54 | | | | | | |
% 41.25/6.54 | | | | | | | REDUCE: (438), (468) imply:
% 41.25/6.54 | | | | | | | (469) $false
% 41.25/6.54 | | | | | | |
% 41.25/6.54 | | | | | | | CLOSE: (469) is inconsistent.
% 41.25/6.54 | | | | | | |
% 41.25/6.54 | | | | | | End of split
% 41.25/6.54 | | | | | |
% 41.25/6.54 | | | | | Case 2:
% 41.25/6.54 | | | | | |
% 41.25/6.54 | | | | | | (470) ~ (all_81_1 = 0)
% 41.25/6.54 | | | | | |
% 41.25/6.54 | | | | | | GROUND_INST: instantiating (11) with all_42_1, all_42_0, simplifying
% 41.25/6.54 | | | | | | with (48), (458) gives:
% 41.25/6.54 | | | | | | (471) ? [v0: any] : (d(all_42_1) = v0 & ((v0 = 0 & all_42_0 =
% 41.25/6.54 | | | | | | all_42_1) | (all_42_0 = err & ~ (v0 = 0))))
% 41.25/6.54 | | | | | |
% 41.25/6.54 | | | | | | GROUND_INST: instantiating (24) with all_42_1, all_42_0, simplifying
% 41.25/6.54 | | | | | | with (48), (458) gives:
% 41.25/6.54 | | | | | | (472) lazy_and1(true, all_42_1) = all_42_0 & $i(all_42_0)
% 41.25/6.54 | | | | | |
% 41.25/6.54 | | | | | | GROUND_INST: instantiating (28) with all_42_0, true, simplifying
% 41.25/6.54 | | | | | | with (49), (455) gives:
% 41.25/6.54 | | | | | | (473) ? [v0: $i] : (f7(all_42_0) = v0 & lazy_impl(true,
% 41.25/6.54 | | | | | | all_42_0) = v0 & $i(v0))
% 41.25/6.54 | | | | | |
% 41.25/6.54 | | | | | | GROUND_INST: instantiating (23) with true, false, all_42_1, true,
% 41.25/6.54 | | | | | | true, simplifying with (35), (48), (54), (96), (451)
% 41.25/6.54 | | | | | | gives:
% 41.25/6.54 | | | | | | (474) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (f1(true, false,
% 41.25/6.54 | | | | | | all_42_1) = v0 & lazy_impl(v1, v2) = v0 & impl(true,
% 41.25/6.54 | | | | | | all_42_1) = v2 & prop(all_42_1) = v1 & $i(v2) & $i(v1)
% 41.25/6.54 | | | | | | & $i(v0))
% 41.25/6.54 | | | | | |
% 41.25/6.54 | | | | | | GROUND_INST: instantiating (23) with false, false, all_42_1, true,
% 41.25/6.54 | | | | | | true, simplifying with (48), (54), (97), (451) gives:
% 41.25/6.54 | | | | | | (475) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (f1(false, false,
% 41.25/6.54 | | | | | | all_42_1) = v0 & lazy_impl(v1, v2) = v0 & impl(true,
% 41.25/6.54 | | | | | | all_42_1) = v2 & prop(all_42_1) = v1 & $i(v2) & $i(v1)
% 41.25/6.54 | | | | | | & $i(v0))
% 41.25/6.54 | | | | | |
% 41.25/6.54 | | | | | | GROUND_INST: instantiating (25) with true, false, all_42_1, true,
% 41.25/6.54 | | | | | | true, simplifying with (35), (48), (54), (104), (451)
% 41.25/6.54 | | | | | | gives:
% 41.25/6.54 | | | | | | (476) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (f2(true, false,
% 41.25/6.54 | | | | | | all_42_1) = v0 & lazy_impl(v1, v2) = v0 & impl(true,
% 41.25/6.54 | | | | | | all_42_1) = v2 & prop(all_42_1) = v1 & $i(v2) & $i(v1)
% 41.25/6.54 | | | | | | & $i(v0))
% 41.25/6.54 | | | | | |
% 41.25/6.54 | | | | | | GROUND_INST: instantiating (23) with true, false, all_42_0, true,
% 41.25/6.54 | | | | | | true, simplifying with (35), (49), (54), (96), (454)
% 41.25/6.54 | | | | | | gives:
% 41.25/6.54 | | | | | | (477) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (f1(true, false,
% 41.25/6.54 | | | | | | all_42_0) = v0 & lazy_impl(v1, v2) = v0 & impl(true,
% 41.25/6.54 | | | | | | all_42_0) = v2 & prop(all_42_0) = v1 & $i(v2) & $i(v1)
% 41.25/6.54 | | | | | | & $i(v0))
% 41.25/6.54 | | | | | |
% 41.25/6.54 | | | | | | GROUND_INST: instantiating (23) with false, false, all_42_0, true,
% 41.25/6.55 | | | | | | true, simplifying with (49), (54), (97), (454) gives:
% 41.25/6.55 | | | | | | (478) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (f1(false, false,
% 41.25/6.55 | | | | | | all_42_0) = v0 & lazy_impl(v1, v2) = v0 & impl(true,
% 41.25/6.55 | | | | | | all_42_0) = v2 & prop(all_42_0) = v1 & $i(v2) & $i(v1)
% 41.25/6.55 | | | | | | & $i(v0))
% 41.25/6.55 | | | | | |
% 41.25/6.55 | | | | | | GROUND_INST: instantiating (25) with true, false, all_42_0, true,
% 41.25/6.55 | | | | | | true, simplifying with (35), (49), (54), (104), (454)
% 41.25/6.55 | | | | | | gives:
% 41.25/6.55 | | | | | | (479) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (f2(true, false,
% 41.25/6.55 | | | | | | all_42_0) = v0 & lazy_impl(v1, v2) = v0 & impl(true,
% 41.25/6.55 | | | | | | all_42_0) = v2 & prop(all_42_0) = v1 & $i(v2) & $i(v1)
% 41.25/6.55 | | | | | | & $i(v0))
% 41.25/6.55 | | | | | |
% 41.25/6.55 | | | | | | GROUND_INST: instantiating (26) with false, false, all_42_1, true,
% 41.25/6.55 | | | | | | true, all_42_1, all_42_1, simplifying with (48), (54),
% 41.25/6.55 | | | | | | (450), (451) gives:
% 41.25/6.55 | | | | | | (480) ? [v0: $i] : ? [v1: $i] : (f3(false, false, all_42_1) =
% 41.25/6.55 | | | | | | v0 & lazy_impl(v1, all_42_1) = v0 & prop(all_42_1) = v1 &
% 41.25/6.55 | | | | | | $i(v1) & $i(v0))
% 41.25/6.55 | | | | | |
% 41.25/6.55 | | | | | | GROUND_INST: instantiating (23) with true, true, all_42_1, all_42_1,
% 41.25/6.55 | | | | | | all_42_1, simplifying with (35), (48), (450) gives:
% 41.25/6.55 | | | | | | (481) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (f1(true, true,
% 41.25/6.55 | | | | | | all_42_1) = v0 & lazy_impl(v1, v2) = v0 &
% 41.25/6.55 | | | | | | impl(all_42_1, all_42_1) = v2 & prop(all_42_1) = v1 &
% 41.25/6.55 | | | | | | $i(v2) & $i(v1) & $i(v0))
% 41.25/6.55 | | | | | |
% 41.25/6.55 | | | | | | GROUND_INST: instantiating (23) with false, true, all_42_1,
% 41.25/6.55 | | | | | | all_42_1, true, simplifying with (35), (48), (54),
% 41.25/6.55 | | | | | | (450), (451) gives:
% 41.25/6.55 | | | | | | (482) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (f1(false, true,
% 41.25/6.55 | | | | | | all_42_1) = v0 & lazy_impl(v1, v2) = v0 & impl(true,
% 41.25/6.55 | | | | | | all_42_1) = v2 & prop(all_42_1) = v1 & $i(v2) & $i(v1)
% 41.25/6.55 | | | | | | & $i(v0))
% 41.25/6.55 | | | | | |
% 41.25/6.55 | | | | | | GROUND_INST: instantiating (25) with true, true, all_42_1, all_42_1,
% 41.25/6.55 | | | | | | all_42_0, simplifying with (35), (48), (445), (450)
% 41.25/6.55 | | | | | | gives:
% 41.25/6.55 | | | | | | (483) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (f2(true, true,
% 41.25/6.55 | | | | | | all_42_1) = v0 & lazy_impl(v1, v2) = v0 &
% 41.25/6.55 | | | | | | impl(all_42_0, all_42_1) = v2 & prop(all_42_1) = v1 &
% 41.25/6.55 | | | | | | $i(v2) & $i(v1) & $i(v0))
% 41.25/6.55 | | | | | |
% 41.25/6.55 | | | | | | GROUND_INST: instantiating (26) with false, false, all_42_0, true,
% 41.25/6.55 | | | | | | true, all_42_0, all_42_0, simplifying with (49), (54),
% 41.25/6.55 | | | | | | (453), (454) gives:
% 41.25/6.55 | | | | | | (484) ? [v0: $i] : ? [v1: $i] : (f3(false, false, all_42_0) =
% 41.25/6.55 | | | | | | v0 & lazy_impl(v1, all_42_0) = v0 & prop(all_42_0) = v1 &
% 41.25/6.55 | | | | | | $i(v1) & $i(v0))
% 41.25/6.55 | | | | | |
% 41.25/6.55 | | | | | | GROUND_INST: instantiating (23) with true, true, all_42_0, all_42_0,
% 41.25/6.55 | | | | | | all_42_0, simplifying with (35), (49), (453) gives:
% 41.25/6.55 | | | | | | (485) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (f1(true, true,
% 41.25/6.55 | | | | | | all_42_0) = v0 & lazy_impl(v1, v2) = v0 &
% 41.25/6.55 | | | | | | impl(all_42_0, all_42_0) = v2 & prop(all_42_0) = v1 &
% 41.25/6.55 | | | | | | $i(v2) & $i(v1) & $i(v0))
% 41.25/6.55 | | | | | |
% 41.25/6.55 | | | | | | GROUND_INST: instantiating (23) with false, true, all_42_0,
% 41.25/6.55 | | | | | | all_42_0, true, simplifying with (35), (49), (54),
% 41.25/6.55 | | | | | | (453), (454) gives:
% 41.25/6.55 | | | | | | (486) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (f1(false, true,
% 41.25/6.55 | | | | | | all_42_0) = v0 & lazy_impl(v1, v2) = v0 & impl(true,
% 41.25/6.55 | | | | | | all_42_0) = v2 & prop(all_42_0) = v1 & $i(v2) & $i(v1)
% 41.25/6.55 | | | | | | & $i(v0))
% 41.25/6.55 | | | | | |
% 41.25/6.55 | | | | | | GROUND_INST: instantiating (25) with true, true, all_42_0, all_42_0,
% 41.25/6.55 | | | | | | err, simplifying with (35), (49), (440), (453) gives:
% 41.25/6.55 | | | | | | (487) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (f2(true, true,
% 41.25/6.55 | | | | | | all_42_0) = v0 & lazy_impl(v1, v2) = v0 & impl(err,
% 41.25/6.55 | | | | | | all_42_0) = v2 & prop(all_42_0) = v1 & $i(v2) & $i(v1)
% 41.25/6.55 | | | | | | & $i(v0))
% 41.25/6.55 | | | | | |
% 41.25/6.55 | | | | | | DELTA: instantiating (473) with fresh symbol all_231_0 gives:
% 41.25/6.55 | | | | | | (488) f7(all_42_0) = all_231_0 & lazy_impl(true, all_42_0) =
% 41.25/6.55 | | | | | | all_231_0 & $i(all_231_0)
% 41.25/6.55 | | | | | |
% 41.25/6.55 | | | | | | ALPHA: (488) implies:
% 41.25/6.55 | | | | | | (489) lazy_impl(true, all_42_0) = all_231_0
% 41.25/6.55 | | | | | |
% 41.25/6.55 | | | | | | DELTA: instantiating (480) with fresh symbols all_233_0, all_233_1
% 41.25/6.55 | | | | | | gives:
% 41.25/6.55 | | | | | | (490) f3(false, false, all_42_1) = all_233_1 &
% 41.25/6.55 | | | | | | lazy_impl(all_233_0, all_42_1) = all_233_1 & prop(all_42_1)
% 41.25/6.55 | | | | | | = all_233_0 & $i(all_233_0) & $i(all_233_1)
% 41.25/6.55 | | | | | |
% 41.25/6.55 | | | | | | ALPHA: (490) implies:
% 41.25/6.55 | | | | | | (491) $i(all_233_1)
% 41.25/6.55 | | | | | | (492) $i(all_233_0)
% 41.25/6.55 | | | | | | (493) prop(all_42_1) = all_233_0
% 41.25/6.55 | | | | | | (494) lazy_impl(all_233_0, all_42_1) = all_233_1
% 41.25/6.55 | | | | | |
% 41.25/6.55 | | | | | | DELTA: instantiating (484) with fresh symbols all_235_0, all_235_1
% 41.25/6.55 | | | | | | gives:
% 41.25/6.55 | | | | | | (495) f3(false, false, all_42_0) = all_235_1 &
% 41.25/6.55 | | | | | | lazy_impl(all_235_0, all_42_0) = all_235_1 & prop(all_42_0)
% 41.25/6.55 | | | | | | = all_235_0 & $i(all_235_0) & $i(all_235_1)
% 41.25/6.55 | | | | | |
% 41.25/6.55 | | | | | | ALPHA: (495) implies:
% 41.25/6.55 | | | | | | (496) $i(all_235_1)
% 41.25/6.55 | | | | | | (497) prop(all_42_0) = all_235_0
% 41.25/6.55 | | | | | | (498) lazy_impl(all_235_0, all_42_0) = all_235_1
% 41.25/6.55 | | | | | |
% 41.25/6.55 | | | | | | DELTA: instantiating (471) with fresh symbol all_237_0 gives:
% 41.25/6.55 | | | | | | (499) d(all_42_1) = all_237_0 & ((all_237_0 = 0 & all_42_0 =
% 41.25/6.55 | | | | | | all_42_1) | (all_42_0 = err & ~ (all_237_0 = 0)))
% 41.25/6.55 | | | | | |
% 41.25/6.55 | | | | | | ALPHA: (499) implies:
% 41.25/6.55 | | | | | | (500) d(all_42_1) = all_237_0
% 41.25/6.55 | | | | | |
% 41.25/6.55 | | | | | | DELTA: instantiating (479) with fresh symbols all_241_0, all_241_1,
% 41.25/6.55 | | | | | | all_241_2 gives:
% 41.25/6.55 | | | | | | (501) f2(true, false, all_42_0) = all_241_2 &
% 41.25/6.55 | | | | | | lazy_impl(all_241_1, all_241_0) = all_241_2 & impl(true,
% 41.25/6.55 | | | | | | all_42_0) = all_241_0 & prop(all_42_0) = all_241_1 &
% 41.25/6.55 | | | | | | $i(all_241_0) & $i(all_241_1) & $i(all_241_2)
% 41.25/6.55 | | | | | |
% 41.25/6.55 | | | | | | ALPHA: (501) implies:
% 41.25/6.55 | | | | | | (502) prop(all_42_0) = all_241_1
% 41.25/6.55 | | | | | | (503) impl(true, all_42_0) = all_241_0
% 41.25/6.55 | | | | | | (504) lazy_impl(all_241_1, all_241_0) = all_241_2
% 41.25/6.55 | | | | | |
% 41.25/6.55 | | | | | | DELTA: instantiating (478) with fresh symbols all_243_0, all_243_1,
% 41.25/6.55 | | | | | | all_243_2 gives:
% 41.25/6.55 | | | | | | (505) f1(false, false, all_42_0) = all_243_2 &
% 41.25/6.55 | | | | | | lazy_impl(all_243_1, all_243_0) = all_243_2 & impl(true,
% 41.25/6.55 | | | | | | all_42_0) = all_243_0 & prop(all_42_0) = all_243_1 &
% 41.25/6.55 | | | | | | $i(all_243_0) & $i(all_243_1) & $i(all_243_2)
% 41.25/6.55 | | | | | |
% 41.25/6.55 | | | | | | ALPHA: (505) implies:
% 41.25/6.55 | | | | | | (506) prop(all_42_0) = all_243_1
% 41.25/6.55 | | | | | | (507) impl(true, all_42_0) = all_243_0
% 41.25/6.55 | | | | | | (508) lazy_impl(all_243_1, all_243_0) = all_243_2
% 41.25/6.55 | | | | | |
% 41.25/6.55 | | | | | | DELTA: instantiating (477) with fresh symbols all_245_0, all_245_1,
% 41.25/6.55 | | | | | | all_245_2 gives:
% 41.25/6.55 | | | | | | (509) f1(true, false, all_42_0) = all_245_2 &
% 41.25/6.55 | | | | | | lazy_impl(all_245_1, all_245_0) = all_245_2 & impl(true,
% 41.25/6.55 | | | | | | all_42_0) = all_245_0 & prop(all_42_0) = all_245_1 &
% 41.25/6.55 | | | | | | $i(all_245_0) & $i(all_245_1) & $i(all_245_2)
% 41.25/6.55 | | | | | |
% 41.25/6.55 | | | | | | ALPHA: (509) implies:
% 41.25/6.55 | | | | | | (510) prop(all_42_0) = all_245_1
% 41.25/6.55 | | | | | | (511) impl(true, all_42_0) = all_245_0
% 41.25/6.55 | | | | | | (512) lazy_impl(all_245_1, all_245_0) = all_245_2
% 41.25/6.55 | | | | | |
% 41.25/6.55 | | | | | | DELTA: instantiating (482) with fresh symbols all_247_0, all_247_1,
% 41.25/6.55 | | | | | | all_247_2 gives:
% 41.25/6.55 | | | | | | (513) f1(false, true, all_42_1) = all_247_2 &
% 41.25/6.55 | | | | | | lazy_impl(all_247_1, all_247_0) = all_247_2 & impl(true,
% 41.25/6.55 | | | | | | all_42_1) = all_247_0 & prop(all_42_1) = all_247_1 &
% 41.25/6.55 | | | | | | $i(all_247_0) & $i(all_247_1) & $i(all_247_2)
% 41.25/6.55 | | | | | |
% 41.25/6.55 | | | | | | ALPHA: (513) implies:
% 41.25/6.55 | | | | | | (514) $i(all_247_0)
% 41.25/6.55 | | | | | | (515) prop(all_42_1) = all_247_1
% 41.25/6.55 | | | | | | (516) impl(true, all_42_1) = all_247_0
% 41.25/6.55 | | | | | | (517) lazy_impl(all_247_1, all_247_0) = all_247_2
% 41.25/6.55 | | | | | |
% 41.25/6.55 | | | | | | DELTA: instantiating (481) with fresh symbols all_249_0, all_249_1,
% 41.25/6.55 | | | | | | all_249_2 gives:
% 41.25/6.55 | | | | | | (518) f1(true, true, all_42_1) = all_249_2 & lazy_impl(all_249_1,
% 41.25/6.55 | | | | | | all_249_0) = all_249_2 & impl(all_42_1, all_42_1) =
% 41.25/6.55 | | | | | | all_249_0 & prop(all_42_1) = all_249_1 & $i(all_249_0) &
% 41.25/6.55 | | | | | | $i(all_249_1) & $i(all_249_2)
% 41.25/6.55 | | | | | |
% 41.25/6.55 | | | | | | ALPHA: (518) implies:
% 41.25/6.55 | | | | | | (519) prop(all_42_1) = all_249_1
% 41.25/6.55 | | | | | | (520) impl(all_42_1, all_42_1) = all_249_0
% 41.25/6.55 | | | | | | (521) lazy_impl(all_249_1, all_249_0) = all_249_2
% 41.25/6.55 | | | | | |
% 41.25/6.55 | | | | | | DELTA: instantiating (487) with fresh symbols all_251_0, all_251_1,
% 41.25/6.55 | | | | | | all_251_2 gives:
% 41.25/6.55 | | | | | | (522) f2(true, true, all_42_0) = all_251_2 & lazy_impl(all_251_1,
% 41.25/6.55 | | | | | | all_251_0) = all_251_2 & impl(err, all_42_0) = all_251_0
% 41.25/6.55 | | | | | | & prop(all_42_0) = all_251_1 & $i(all_251_0) &
% 41.25/6.55 | | | | | | $i(all_251_1) & $i(all_251_2)
% 41.25/6.55 | | | | | |
% 41.25/6.55 | | | | | | ALPHA: (522) implies:
% 41.25/6.55 | | | | | | (523) prop(all_42_0) = all_251_1
% 41.25/6.55 | | | | | | (524) impl(err, all_42_0) = all_251_0
% 41.25/6.55 | | | | | | (525) lazy_impl(all_251_1, all_251_0) = all_251_2
% 41.25/6.55 | | | | | | (526) f2(true, true, all_42_0) = all_251_2
% 41.25/6.55 | | | | | |
% 41.25/6.55 | | | | | | DELTA: instantiating (483) with fresh symbols all_253_0, all_253_1,
% 41.25/6.55 | | | | | | all_253_2 gives:
% 41.25/6.55 | | | | | | (527) f2(true, true, all_42_1) = all_253_2 & lazy_impl(all_253_1,
% 41.25/6.55 | | | | | | all_253_0) = all_253_2 & impl(all_42_0, all_42_1) =
% 41.25/6.55 | | | | | | all_253_0 & prop(all_42_1) = all_253_1 & $i(all_253_0) &
% 41.25/6.55 | | | | | | $i(all_253_1) & $i(all_253_2)
% 41.25/6.55 | | | | | |
% 41.25/6.55 | | | | | | ALPHA: (527) implies:
% 41.25/6.55 | | | | | | (528) prop(all_42_1) = all_253_1
% 41.25/6.55 | | | | | | (529) impl(all_42_0, all_42_1) = all_253_0
% 41.25/6.55 | | | | | | (530) lazy_impl(all_253_1, all_253_0) = all_253_2
% 41.25/6.55 | | | | | | (531) f2(true, true, all_42_1) = all_253_2
% 41.25/6.55 | | | | | |
% 41.25/6.55 | | | | | | DELTA: instantiating (486) with fresh symbols all_255_0, all_255_1,
% 41.25/6.55 | | | | | | all_255_2 gives:
% 41.25/6.55 | | | | | | (532) f1(false, true, all_42_0) = all_255_2 &
% 41.25/6.55 | | | | | | lazy_impl(all_255_1, all_255_0) = all_255_2 & impl(true,
% 41.25/6.55 | | | | | | all_42_0) = all_255_0 & prop(all_42_0) = all_255_1 &
% 41.25/6.55 | | | | | | $i(all_255_0) & $i(all_255_1) & $i(all_255_2)
% 41.25/6.55 | | | | | |
% 41.25/6.55 | | | | | | ALPHA: (532) implies:
% 41.25/6.55 | | | | | | (533) prop(all_42_0) = all_255_1
% 41.25/6.55 | | | | | | (534) impl(true, all_42_0) = all_255_0
% 41.25/6.55 | | | | | | (535) lazy_impl(all_255_1, all_255_0) = all_255_2
% 41.25/6.55 | | | | | |
% 41.25/6.55 | | | | | | DELTA: instantiating (485) with fresh symbols all_257_0, all_257_1,
% 41.25/6.55 | | | | | | all_257_2 gives:
% 41.25/6.55 | | | | | | (536) f1(true, true, all_42_0) = all_257_2 & lazy_impl(all_257_1,
% 41.25/6.55 | | | | | | all_257_0) = all_257_2 & impl(all_42_0, all_42_0) =
% 41.25/6.55 | | | | | | all_257_0 & prop(all_42_0) = all_257_1 & $i(all_257_0) &
% 41.25/6.55 | | | | | | $i(all_257_1) & $i(all_257_2)
% 41.25/6.55 | | | | | |
% 41.25/6.55 | | | | | | ALPHA: (536) implies:
% 41.25/6.55 | | | | | | (537) prop(all_42_0) = all_257_1
% 41.25/6.55 | | | | | | (538) impl(all_42_0, all_42_0) = all_257_0
% 41.25/6.55 | | | | | | (539) lazy_impl(all_257_1, all_257_0) = all_257_2
% 41.25/6.55 | | | | | |
% 41.25/6.55 | | | | | | DELTA: instantiating (474) with fresh symbols all_259_0, all_259_1,
% 41.25/6.55 | | | | | | all_259_2 gives:
% 41.25/6.55 | | | | | | (540) f1(true, false, all_42_1) = all_259_2 &
% 41.25/6.55 | | | | | | lazy_impl(all_259_1, all_259_0) = all_259_2 & impl(true,
% 41.25/6.55 | | | | | | all_42_1) = all_259_0 & prop(all_42_1) = all_259_1 &
% 41.25/6.55 | | | | | | $i(all_259_0) & $i(all_259_1) & $i(all_259_2)
% 41.25/6.55 | | | | | |
% 41.25/6.55 | | | | | | ALPHA: (540) implies:
% 41.25/6.55 | | | | | | (541) prop(all_42_1) = all_259_1
% 41.25/6.55 | | | | | | (542) impl(true, all_42_1) = all_259_0
% 41.25/6.55 | | | | | | (543) lazy_impl(all_259_1, all_259_0) = all_259_2
% 41.25/6.55 | | | | | |
% 41.25/6.55 | | | | | | DELTA: instantiating (476) with fresh symbols all_261_0, all_261_1,
% 41.25/6.55 | | | | | | all_261_2 gives:
% 41.25/6.56 | | | | | | (544) f2(true, false, all_42_1) = all_261_2 &
% 41.25/6.56 | | | | | | lazy_impl(all_261_1, all_261_0) = all_261_2 & impl(true,
% 41.25/6.56 | | | | | | all_42_1) = all_261_0 & prop(all_42_1) = all_261_1 &
% 41.25/6.56 | | | | | | $i(all_261_0) & $i(all_261_1) & $i(all_261_2)
% 41.25/6.56 | | | | | |
% 41.25/6.56 | | | | | | ALPHA: (544) implies:
% 41.25/6.56 | | | | | | (545) prop(all_42_1) = all_261_1
% 41.25/6.56 | | | | | | (546) impl(true, all_42_1) = all_261_0
% 41.25/6.56 | | | | | | (547) lazy_impl(all_261_1, all_261_0) = all_261_2
% 41.25/6.56 | | | | | |
% 41.25/6.56 | | | | | | DELTA: instantiating (475) with fresh symbols all_263_0, all_263_1,
% 41.25/6.56 | | | | | | all_263_2 gives:
% 41.25/6.56 | | | | | | (548) f1(false, false, all_42_1) = all_263_2 &
% 41.25/6.56 | | | | | | lazy_impl(all_263_1, all_263_0) = all_263_2 & impl(true,
% 41.25/6.56 | | | | | | all_42_1) = all_263_0 & prop(all_42_1) = all_263_1 &
% 41.25/6.56 | | | | | | $i(all_263_0) & $i(all_263_1) & $i(all_263_2)
% 41.25/6.56 | | | | | |
% 41.25/6.56 | | | | | | ALPHA: (548) implies:
% 41.25/6.56 | | | | | | (549) prop(all_42_1) = all_263_1
% 41.25/6.56 | | | | | | (550) impl(true, all_42_1) = all_263_0
% 41.25/6.56 | | | | | | (551) lazy_impl(all_263_1, all_263_0) = all_263_2
% 41.25/6.56 | | | | | |
% 41.25/6.56 | | | | | | GROUND_INST: instantiating (41) with all_249_1, all_253_1, all_42_1,
% 41.25/6.56 | | | | | | simplifying with (519), (528) gives:
% 41.25/6.56 | | | | | | (552) all_253_1 = all_249_1
% 41.25/6.56 | | | | | |
% 41.25/6.56 | | | | | | GROUND_INST: instantiating (41) with all_233_0, all_253_1, all_42_1,
% 41.25/6.56 | | | | | | simplifying with (493), (528) gives:
% 41.25/6.56 | | | | | | (553) all_253_1 = all_233_0
% 41.25/6.56 | | | | | |
% 41.25/6.56 | | | | | | GROUND_INST: instantiating (41) with all_253_1, all_259_1, all_42_1,
% 41.25/6.56 | | | | | | simplifying with (528), (541) gives:
% 41.25/6.56 | | | | | | (554) all_259_1 = all_253_1
% 41.25/6.56 | | | | | |
% 41.25/6.56 | | | | | | GROUND_INST: instantiating (41) with true, all_261_1, all_42_1,
% 41.25/6.56 | | | | | | simplifying with (447), (545) gives:
% 41.25/6.56 | | | | | | (555) all_261_1 = true
% 41.25/6.56 | | | | | |
% 41.25/6.56 | | | | | | GROUND_INST: instantiating (41) with all_249_1, all_261_1, all_42_1,
% 41.25/6.56 | | | | | | simplifying with (519), (545) gives:
% 41.25/6.56 | | | | | | (556) all_261_1 = all_249_1
% 41.25/6.56 | | | | | |
% 41.25/6.56 | | | | | | GROUND_INST: instantiating (41) with all_259_1, all_263_1, all_42_1,
% 41.25/6.56 | | | | | | simplifying with (541), (549) gives:
% 41.25/6.56 | | | | | | (557) all_263_1 = all_259_1
% 41.25/6.56 | | | | | |
% 41.25/6.56 | | | | | | GROUND_INST: instantiating (41) with all_247_1, all_263_1, all_42_1,
% 41.25/6.56 | | | | | | simplifying with (515), (549) gives:
% 41.25/6.56 | | | | | | (558) all_263_1 = all_247_1
% 41.25/6.56 | | | | | |
% 41.25/6.56 | | | | | | GROUND_INST: instantiating (41) with all_243_1, all_245_1, all_42_0,
% 41.25/6.56 | | | | | | simplifying with (506), (510) gives:
% 41.25/6.56 | | | | | | (559) all_245_1 = all_243_1
% 41.25/6.56 | | | | | |
% 41.25/6.56 | | | | | | GROUND_INST: instantiating (41) with all_235_0, all_245_1, all_42_0,
% 41.25/6.56 | | | | | | simplifying with (497), (510) gives:
% 41.25/6.56 | | | | | | (560) all_245_1 = all_235_0
% 41.25/6.56 | | | | | |
% 41.25/6.56 | | | | | | GROUND_INST: instantiating (41) with all_245_1, all_251_1, all_42_0,
% 41.25/6.56 | | | | | | simplifying with (510), (523) gives:
% 41.25/6.56 | | | | | | (561) all_251_1 = all_245_1
% 41.25/6.56 | | | | | |
% 41.25/6.56 | | | | | | GROUND_INST: instantiating (41) with all_245_1, all_255_1, all_42_0,
% 41.25/6.56 | | | | | | simplifying with (510), (533) gives:
% 41.25/6.56 | | | | | | (562) all_255_1 = all_245_1
% 41.25/6.56 | | | | | |
% 41.25/6.56 | | | | | | GROUND_INST: instantiating (41) with all_241_1, all_255_1, all_42_0,
% 41.25/6.56 | | | | | | simplifying with (502), (533) gives:
% 41.25/6.56 | | | | | | (563) all_255_1 = all_241_1
% 41.25/6.56 | | | | | |
% 41.25/6.56 | | | | | | GROUND_INST: instantiating (41) with true, all_257_1, all_42_0,
% 41.25/6.56 | | | | | | simplifying with (455), (537) gives:
% 41.25/6.56 | | | | | | (564) all_257_1 = true
% 41.25/6.56 | | | | | |
% 41.25/6.56 | | | | | | GROUND_INST: instantiating (41) with all_251_1, all_257_1, all_42_0,
% 41.25/6.56 | | | | | | simplifying with (523), (537) gives:
% 41.25/6.56 | | | | | | (565) all_257_1 = all_251_1
% 41.25/6.56 | | | | | |
% 41.25/6.56 | | | | | | GROUND_INST: instantiating (43) with all_42_1, all_261_0, all_42_1,
% 41.25/6.56 | | | | | | true, simplifying with (450), (546) gives:
% 41.25/6.56 | | | | | | (566) all_261_0 = all_42_1
% 41.25/6.56 | | | | | |
% 41.25/6.56 | | | | | | GROUND_INST: instantiating (43) with all_247_0, all_261_0, all_42_1,
% 41.25/6.56 | | | | | | true, simplifying with (516), (546) gives:
% 41.25/6.56 | | | | | | (567) all_261_0 = all_247_0
% 41.25/6.56 | | | | | |
% 41.25/6.56 | | | | | | GROUND_INST: instantiating (43) with all_261_0, all_263_0, all_42_1,
% 41.25/6.56 | | | | | | true, simplifying with (546), (550) gives:
% 41.25/6.56 | | | | | | (568) all_263_0 = all_261_0
% 41.25/6.56 | | | | | |
% 41.25/6.56 | | | | | | GROUND_INST: instantiating (43) with all_259_0, all_263_0, all_42_1,
% 41.25/6.56 | | | | | | true, simplifying with (542), (550) gives:
% 41.25/6.56 | | | | | | (569) all_263_0 = all_259_0
% 41.25/6.56 | | | | | |
% 41.25/6.56 | | | | | | GROUND_INST: instantiating (43) with all_42_0, all_255_0, all_42_0,
% 41.25/6.56 | | | | | | true, simplifying with (453), (534) gives:
% 41.25/6.56 | | | | | | (570) all_255_0 = all_42_0
% 41.25/6.56 | | | | | |
% 41.25/6.56 | | | | | | GROUND_INST: instantiating (43) with all_245_0, all_255_0, all_42_0,
% 41.25/6.56 | | | | | | true, simplifying with (511), (534) gives:
% 41.25/6.56 | | | | | | (571) all_255_0 = all_245_0
% 41.25/6.56 | | | | | |
% 41.25/6.56 | | | | | | GROUND_INST: instantiating (43) with all_243_0, all_255_0, all_42_0,
% 41.25/6.56 | | | | | | true, simplifying with (507), (534) gives:
% 41.25/6.56 | | | | | | (572) all_255_0 = all_243_0
% 41.25/6.56 | | | | | |
% 41.25/6.56 | | | | | | GROUND_INST: instantiating (43) with all_241_0, all_255_0, all_42_0,
% 41.25/6.56 | | | | | | true, simplifying with (503), (534) gives:
% 41.25/6.56 | | | | | | (573) all_255_0 = all_241_0
% 41.25/6.56 | | | | | |
% 41.25/6.56 | | | | | | GROUND_INST: instantiating (44) with err, all_231_0, all_42_0, true,
% 41.25/6.56 | | | | | | simplifying with (440), (489) gives:
% 41.25/6.56 | | | | | | (574) all_231_0 = err
% 41.25/6.56 | | | | | |
% 41.25/6.56 | | | | | | COMBINE_EQS: (568), (569) imply:
% 41.25/6.56 | | | | | | (575) all_261_0 = all_259_0
% 41.25/6.56 | | | | | |
% 41.25/6.56 | | | | | | SIMP: (575) implies:
% 41.25/6.56 | | | | | | (576) all_261_0 = all_259_0
% 41.25/6.56 | | | | | |
% 41.25/6.56 | | | | | | COMBINE_EQS: (557), (558) imply:
% 41.25/6.56 | | | | | | (577) all_259_1 = all_247_1
% 41.25/6.56 | | | | | |
% 41.25/6.56 | | | | | | SIMP: (577) implies:
% 41.25/6.56 | | | | | | (578) all_259_1 = all_247_1
% 41.25/6.56 | | | | | |
% 41.25/6.56 | | | | | | COMBINE_EQS: (566), (576) imply:
% 41.25/6.56 | | | | | | (579) all_259_0 = all_42_1
% 41.25/6.56 | | | | | |
% 41.25/6.56 | | | | | | COMBINE_EQS: (567), (576) imply:
% 41.25/6.56 | | | | | | (580) all_259_0 = all_247_0
% 41.25/6.56 | | | | | |
% 41.25/6.56 | | | | | | COMBINE_EQS: (555), (556) imply:
% 41.25/6.56 | | | | | | (581) all_249_1 = true
% 41.25/6.56 | | | | | |
% 41.25/6.56 | | | | | | SIMP: (581) implies:
% 41.25/6.56 | | | | | | (582) all_249_1 = true
% 41.25/6.56 | | | | | |
% 41.25/6.56 | | | | | | COMBINE_EQS: (579), (580) imply:
% 41.25/6.56 | | | | | | (583) all_247_0 = all_42_1
% 41.25/6.56 | | | | | |
% 41.25/6.56 | | | | | | COMBINE_EQS: (554), (578) imply:
% 41.25/6.56 | | | | | | (584) all_253_1 = all_247_1
% 41.25/6.56 | | | | | |
% 41.25/6.56 | | | | | | SIMP: (584) implies:
% 41.25/6.56 | | | | | | (585) all_253_1 = all_247_1
% 41.25/6.56 | | | | | |
% 41.25/6.56 | | | | | | COMBINE_EQS: (564), (565) imply:
% 41.25/6.56 | | | | | | (586) all_251_1 = true
% 41.25/6.56 | | | | | |
% 41.25/6.56 | | | | | | SIMP: (586) implies:
% 41.25/6.56 | | | | | | (587) all_251_1 = true
% 41.25/6.56 | | | | | |
% 41.25/6.56 | | | | | | COMBINE_EQS: (571), (572) imply:
% 41.25/6.56 | | | | | | (588) all_245_0 = all_243_0
% 41.25/6.56 | | | | | |
% 41.25/6.56 | | | | | | COMBINE_EQS: (570), (571) imply:
% 41.25/6.56 | | | | | | (589) all_245_0 = all_42_0
% 41.25/6.56 | | | | | |
% 41.25/6.56 | | | | | | COMBINE_EQS: (571), (573) imply:
% 41.25/6.56 | | | | | | (590) all_245_0 = all_241_0
% 41.25/6.56 | | | | | |
% 41.25/6.56 | | | | | | COMBINE_EQS: (562), (563) imply:
% 41.25/6.56 | | | | | | (591) all_245_1 = all_241_1
% 41.25/6.56 | | | | | |
% 41.25/6.56 | | | | | | SIMP: (591) implies:
% 41.25/6.56 | | | | | | (592) all_245_1 = all_241_1
% 41.25/6.56 | | | | | |
% 41.25/6.56 | | | | | | COMBINE_EQS: (552), (585) imply:
% 41.25/6.56 | | | | | | (593) all_249_1 = all_247_1
% 41.25/6.56 | | | | | |
% 41.25/6.56 | | | | | | SIMP: (593) implies:
% 41.25/6.56 | | | | | | (594) all_249_1 = all_247_1
% 41.25/6.56 | | | | | |
% 41.25/6.56 | | | | | | COMBINE_EQS: (553), (585) imply:
% 41.25/6.56 | | | | | | (595) all_247_1 = all_233_0
% 41.25/6.56 | | | | | |
% 41.25/6.56 | | | | | | COMBINE_EQS: (561), (587) imply:
% 41.25/6.56 | | | | | | (596) all_245_1 = true
% 41.25/6.56 | | | | | |
% 41.25/6.56 | | | | | | SIMP: (596) implies:
% 41.25/6.56 | | | | | | (597) all_245_1 = true
% 41.25/6.56 | | | | | |
% 41.25/6.56 | | | | | | COMBINE_EQS: (582), (594) imply:
% 41.25/6.56 | | | | | | (598) all_247_1 = true
% 41.25/6.56 | | | | | |
% 41.25/6.56 | | | | | | SIMP: (598) implies:
% 41.25/6.56 | | | | | | (599) all_247_1 = true
% 41.25/6.56 | | | | | |
% 41.25/6.56 | | | | | | COMBINE_EQS: (595), (599) imply:
% 41.25/6.56 | | | | | | (600) all_233_0 = true
% 41.25/6.56 | | | | | |
% 41.25/6.56 | | | | | | SIMP: (600) implies:
% 41.25/6.56 | | | | | | (601) all_233_0 = true
% 41.25/6.56 | | | | | |
% 41.25/6.56 | | | | | | COMBINE_EQS: (588), (589) imply:
% 41.25/6.56 | | | | | | (602) all_243_0 = all_42_0
% 41.25/6.56 | | | | | |
% 41.25/6.56 | | | | | | COMBINE_EQS: (588), (590) imply:
% 41.25/6.56 | | | | | | (603) all_243_0 = all_241_0
% 41.25/6.56 | | | | | |
% 41.25/6.56 | | | | | | COMBINE_EQS: (559), (560) imply:
% 41.25/6.56 | | | | | | (604) all_243_1 = all_235_0
% 41.25/6.56 | | | | | |
% 41.25/6.56 | | | | | | COMBINE_EQS: (559), (592) imply:
% 41.25/6.56 | | | | | | (605) all_243_1 = all_241_1
% 41.25/6.56 | | | | | |
% 41.25/6.56 | | | | | | COMBINE_EQS: (559), (597) imply:
% 41.25/6.56 | | | | | | (606) all_243_1 = true
% 41.25/6.56 | | | | | |
% 41.25/6.56 | | | | | | COMBINE_EQS: (602), (603) imply:
% 41.25/6.56 | | | | | | (607) all_241_0 = all_42_0
% 41.25/6.56 | | | | | |
% 41.25/6.56 | | | | | | COMBINE_EQS: (604), (605) imply:
% 41.25/6.56 | | | | | | (608) all_241_1 = all_235_0
% 41.25/6.56 | | | | | |
% 41.25/6.56 | | | | | | COMBINE_EQS: (605), (606) imply:
% 41.25/6.56 | | | | | | (609) all_241_1 = true
% 41.25/6.56 | | | | | |
% 41.25/6.56 | | | | | | COMBINE_EQS: (608), (609) imply:
% 41.25/6.56 | | | | | | (610) all_235_0 = true
% 41.25/6.56 | | | | | |
% 41.25/6.56 | | | | | | COMBINE_EQS: (585), (599) imply:
% 41.25/6.56 | | | | | | (611) all_253_1 = true
% 41.25/6.56 | | | | | |
% 41.25/6.56 | | | | | | COMBINE_EQS: (563), (609) imply:
% 41.25/6.56 | | | | | | (612) all_255_1 = true
% 41.25/6.56 | | | | | |
% 41.25/6.56 | | | | | | COMBINE_EQS: (578), (599) imply:
% 41.25/6.56 | | | | | | (613) all_259_1 = true
% 41.25/6.56 | | | | | |
% 41.25/6.56 | | | | | | COMBINE_EQS: (558), (599) imply:
% 41.25/6.56 | | | | | | (614) all_263_1 = true
% 41.25/6.56 | | | | | |
% 41.25/6.56 | | | | | | COMBINE_EQS: (569), (579) imply:
% 41.25/6.56 | | | | | | (615) all_263_0 = all_42_1
% 41.25/6.56 | | | | | |
% 41.25/6.56 | | | | | | REDUCE: (551), (614), (615) imply:
% 41.25/6.56 | | | | | | (616) lazy_impl(true, all_42_1) = all_263_2
% 41.25/6.56 | | | | | |
% 41.25/6.56 | | | | | | REDUCE: (547), (555), (566) imply:
% 41.25/6.56 | | | | | | (617) lazy_impl(true, all_42_1) = all_261_2
% 41.25/6.56 | | | | | |
% 41.25/6.56 | | | | | | REDUCE: (543), (579), (613) imply:
% 41.25/6.56 | | | | | | (618) lazy_impl(true, all_42_1) = all_259_2
% 41.25/6.56 | | | | | |
% 41.25/6.56 | | | | | | REDUCE: (539), (564) imply:
% 41.25/6.56 | | | | | | (619) lazy_impl(true, all_257_0) = all_257_2
% 41.25/6.56 | | | | | |
% 41.25/6.56 | | | | | | REDUCE: (535), (570), (612) imply:
% 41.25/6.56 | | | | | | (620) lazy_impl(true, all_42_0) = all_255_2
% 41.25/6.56 | | | | | |
% 41.25/6.56 | | | | | | REDUCE: (530), (611) imply:
% 41.25/6.56 | | | | | | (621) lazy_impl(true, all_253_0) = all_253_2
% 41.25/6.56 | | | | | |
% 41.25/6.56 | | | | | | REDUCE: (525), (587) imply:
% 41.25/6.56 | | | | | | (622) lazy_impl(true, all_251_0) = all_251_2
% 41.25/6.56 | | | | | |
% 41.25/6.56 | | | | | | REDUCE: (521), (582) imply:
% 41.25/6.56 | | | | | | (623) lazy_impl(true, all_249_0) = all_249_2
% 41.25/6.56 | | | | | |
% 41.25/6.56 | | | | | | REDUCE: (517), (583), (599) imply:
% 41.25/6.56 | | | | | | (624) lazy_impl(true, all_42_1) = all_247_2
% 41.25/6.56 | | | | | |
% 41.25/6.56 | | | | | | REDUCE: (512), (589), (597) imply:
% 41.25/6.56 | | | | | | (625) lazy_impl(true, all_42_0) = all_245_2
% 41.25/6.56 | | | | | |
% 41.25/6.56 | | | | | | REDUCE: (508), (602), (606) imply:
% 41.25/6.56 | | | | | | (626) lazy_impl(true, all_42_0) = all_243_2
% 41.25/6.56 | | | | | |
% 41.25/6.56 | | | | | | REDUCE: (504), (607), (609) imply:
% 41.25/6.56 | | | | | | (627) lazy_impl(true, all_42_0) = all_241_2
% 41.25/6.56 | | | | | |
% 41.25/6.56 | | | | | | REDUCE: (498), (610) imply:
% 41.25/6.56 | | | | | | (628) lazy_impl(true, all_42_0) = all_235_1
% 41.25/6.56 | | | | | |
% 41.25/6.56 | | | | | | REDUCE: (494), (601) imply:
% 41.25/6.56 | | | | | | (629) lazy_impl(true, all_42_1) = all_233_1
% 41.25/6.56 | | | | | |
% 41.25/6.56 | | | | | | GROUND_INST: instantiating (44) with all_247_2, all_259_2, all_42_1,
% 41.25/6.56 | | | | | | true, simplifying with (618), (624) gives:
% 41.25/6.56 | | | | | | (630) all_259_2 = all_247_2
% 41.25/6.56 | | | | | |
% 41.25/6.56 | | | | | | GROUND_INST: instantiating (44) with all_247_2, all_261_2, all_42_1,
% 41.25/6.56 | | | | | | true, simplifying with (617), (624) gives:
% 41.25/6.56 | | | | | | (631) all_261_2 = all_247_2
% 41.25/6.56 | | | | | |
% 41.25/6.56 | | | | | | GROUND_INST: instantiating (44) with all_233_1, all_261_2, all_42_1,
% 41.25/6.56 | | | | | | true, simplifying with (617), (629) gives:
% 41.25/6.56 | | | | | | (632) all_261_2 = all_233_1
% 41.25/6.56 | | | | | |
% 41.25/6.56 | | | | | | GROUND_INST: instantiating (44) with all_42_0, all_263_2, all_42_1,
% 41.25/6.56 | | | | | | true, simplifying with (445), (616) gives:
% 41.25/6.56 | | | | | | (633) all_263_2 = all_42_0
% 41.25/6.56 | | | | | |
% 41.25/6.56 | | | | | | GROUND_INST: instantiating (44) with all_259_2, all_263_2, all_42_1,
% 41.25/6.56 | | | | | | true, simplifying with (616), (618) gives:
% 41.25/6.56 | | | | | | (634) all_263_2 = all_259_2
% 41.25/6.56 | | | | | |
% 41.25/6.56 | | | | | | GROUND_INST: instantiating (44) with err, all_241_2, all_42_0, true,
% 41.25/6.56 | | | | | | simplifying with (440), (627) gives:
% 41.25/6.56 | | | | | | (635) all_241_2 = err
% 41.25/6.56 | | | | | |
% 41.25/6.56 | | | | | | GROUND_INST: instantiating (44) with all_243_2, all_245_2, all_42_0,
% 41.25/6.56 | | | | | | true, simplifying with (625), (626) gives:
% 41.25/6.56 | | | | | | (636) all_245_2 = all_243_2
% 41.25/6.56 | | | | | |
% 41.25/6.56 | | | | | | GROUND_INST: instantiating (44) with all_241_2, all_245_2, all_42_0,
% 41.25/6.56 | | | | | | true, simplifying with (625), (627) gives:
% 41.25/6.56 | | | | | | (637) all_245_2 = all_241_2
% 41.25/6.56 | | | | | |
% 41.25/6.56 | | | | | | GROUND_INST: instantiating (44) with all_245_2, all_255_2, all_42_0,
% 41.25/6.56 | | | | | | true, simplifying with (620), (625) gives:
% 41.25/6.56 | | | | | | (638) all_255_2 = all_245_2
% 41.25/6.56 | | | | | |
% 41.25/6.56 | | | | | | GROUND_INST: instantiating (44) with all_235_1, all_255_2, all_42_0,
% 41.25/6.56 | | | | | | true, simplifying with (620), (628) gives:
% 41.25/6.56 | | | | | | (639) all_255_2 = all_235_1
% 41.25/6.56 | | | | | |
% 41.25/6.56 | | | | | | COMBINE_EQS: (633), (634) imply:
% 41.25/6.56 | | | | | | (640) all_259_2 = all_42_0
% 41.25/6.56 | | | | | |
% 41.25/6.56 | | | | | | SIMP: (640) implies:
% 41.25/6.56 | | | | | | (641) all_259_2 = all_42_0
% 41.25/6.56 | | | | | |
% 41.25/6.56 | | | | | | COMBINE_EQS: (631), (632) imply:
% 41.25/6.56 | | | | | | (642) all_247_2 = all_233_1
% 41.25/6.56 | | | | | |
% 41.25/6.56 | | | | | | SIMP: (642) implies:
% 41.25/6.56 | | | | | | (643) all_247_2 = all_233_1
% 41.25/6.56 | | | | | |
% 41.25/6.56 | | | | | | COMBINE_EQS: (630), (641) imply:
% 41.25/6.56 | | | | | | (644) all_247_2 = all_42_0
% 41.25/6.56 | | | | | |
% 41.25/6.56 | | | | | | SIMP: (644) implies:
% 41.25/6.56 | | | | | | (645) all_247_2 = all_42_0
% 41.25/6.56 | | | | | |
% 41.25/6.56 | | | | | | COMBINE_EQS: (638), (639) imply:
% 41.25/6.56 | | | | | | (646) all_245_2 = all_235_1
% 41.25/6.56 | | | | | |
% 41.25/6.56 | | | | | | SIMP: (646) implies:
% 41.25/6.56 | | | | | | (647) all_245_2 = all_235_1
% 41.25/6.56 | | | | | |
% 41.25/6.56 | | | | | | COMBINE_EQS: (643), (645) imply:
% 41.25/6.56 | | | | | | (648) all_233_1 = all_42_0
% 41.25/6.56 | | | | | |
% 41.25/6.56 | | | | | | SIMP: (648) implies:
% 41.25/6.56 | | | | | | (649) all_233_1 = all_42_0
% 41.25/6.56 | | | | | |
% 41.25/6.56 | | | | | | COMBINE_EQS: (636), (647) imply:
% 41.25/6.56 | | | | | | (650) all_243_2 = all_235_1
% 41.25/6.56 | | | | | |
% 41.25/6.56 | | | | | | COMBINE_EQS: (636), (637) imply:
% 41.25/6.56 | | | | | | (651) all_243_2 = all_241_2
% 41.25/6.56 | | | | | |
% 41.25/6.56 | | | | | | COMBINE_EQS: (650), (651) imply:
% 41.25/6.56 | | | | | | (652) all_241_2 = all_235_1
% 41.25/6.56 | | | | | |
% 41.25/6.56 | | | | | | SIMP: (652) implies:
% 41.25/6.56 | | | | | | (653) all_241_2 = all_235_1
% 41.25/6.56 | | | | | |
% 41.25/6.56 | | | | | | COMBINE_EQS: (635), (653) imply:
% 41.25/6.56 | | | | | | (654) all_235_1 = err
% 41.25/6.56 | | | | | |
% 41.25/6.56 | | | | | | SIMP: (654) implies:
% 41.25/6.56 | | | | | | (655) all_235_1 = err
% 41.25/6.56 | | | | | |
% 41.25/6.56 | | | | | | GROUND_INST: instantiating (10) with all_42_1, all_237_0,
% 41.25/6.56 | | | | | | simplifying with (48), (500) gives:
% 41.25/6.57 | | | | | | (656) ? [v0: $i] : (phi(all_42_1) = v0 & $i(v0) & ((v0 =
% 41.25/6.57 | | | | | | all_42_1 & all_237_0 = 0) | (v0 = err & ~ (all_237_0
% 41.25/6.57 | | | | | | = 0))))
% 41.25/6.57 | | | | | |
% 41.25/6.57 | | | | | | GROUND_INST: instantiating (impl_axiom1) with err, all_42_0,
% 41.25/6.57 | | | | | | all_251_0, simplifying with (9), (49), (524) gives:
% 41.25/6.57 | | | | | | (657) ? [v0: any] : ? [v1: $i] : (phi(err) = v1 & bool(err) =
% 41.25/6.57 | | | | | | v0 & $i(v1) & (v1 = all_251_0 | v0 = 0))
% 41.25/6.57 | | | | | |
% 41.25/6.57 | | | | | | GROUND_INST: instantiating (25) with true, all_42_1, all_42_1,
% 41.25/6.57 | | | | | | all_249_0, all_249_2, simplifying with (35), (48),
% 41.25/6.57 | | | | | | (520), (623) gives:
% 41.25/6.57 | | | | | | (658) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (f2(true,
% 41.25/6.57 | | | | | | all_42_1, all_42_1) = v0 & lazy_impl(v1, v2) = v0 &
% 41.25/6.57 | | | | | | impl(all_249_2, all_42_1) = v2 & prop(all_42_1) = v1 &
% 41.25/6.57 | | | | | | $i(v2) & $i(v1) & $i(v0))
% 41.25/6.57 | | | | | |
% 41.25/6.57 | | | | | | GROUND_INST: instantiating (25) with true, all_42_0, all_42_1,
% 41.25/6.57 | | | | | | all_253_0, all_253_2, simplifying with (35), (48),
% 41.25/6.57 | | | | | | (49), (529), (621) gives:
% 41.25/6.57 | | | | | | (659) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (f2(true,
% 41.25/6.57 | | | | | | all_42_0, all_42_1) = v0 & lazy_impl(v1, v2) = v0 &
% 41.25/6.57 | | | | | | impl(all_253_2, all_42_1) = v2 & prop(all_42_1) = v1 &
% 41.25/6.57 | | | | | | $i(v2) & $i(v1) & $i(v0))
% 41.25/6.57 | | | | | |
% 41.25/6.57 | | | | | | GROUND_INST: instantiating (25) with true, all_42_0, all_42_0,
% 41.25/6.57 | | | | | | all_257_0, all_257_2, simplifying with (35), (49),
% 41.25/6.57 | | | | | | (538), (619) gives:
% 41.25/6.57 | | | | | | (660) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (f2(true,
% 41.25/6.57 | | | | | | all_42_0, all_42_0) = v0 & lazy_impl(v1, v2) = v0 &
% 41.25/6.57 | | | | | | impl(all_257_2, all_42_0) = v2 & prop(all_42_0) = v1 &
% 41.25/6.57 | | | | | | $i(v2) & $i(v1) & $i(v0))
% 41.25/6.57 | | | | | |
% 41.25/6.57 | | | | | | DELTA: instantiating (657) with fresh symbols all_287_0, all_287_1
% 41.25/6.57 | | | | | | gives:
% 41.25/6.57 | | | | | | (661) phi(err) = all_287_0 & bool(err) = all_287_1 &
% 41.25/6.57 | | | | | | $i(all_287_0) & (all_287_0 = all_251_0 | all_287_1 = 0)
% 41.25/6.57 | | | | | |
% 41.25/6.57 | | | | | | ALPHA: (661) implies:
% 41.25/6.57 | | | | | | (662) bool(err) = all_287_1
% 41.25/6.57 | | | | | | (663) phi(err) = all_287_0
% 41.25/6.57 | | | | | | (664) all_287_0 = all_251_0 | all_287_1 = 0
% 41.25/6.57 | | | | | |
% 41.25/6.57 | | | | | | DELTA: instantiating (656) with fresh symbol all_289_0 gives:
% 41.25/6.57 | | | | | | (665) phi(all_42_1) = all_289_0 & $i(all_289_0) & ((all_289_0 =
% 41.25/6.57 | | | | | | all_42_1 & all_237_0 = 0) | (all_289_0 = err & ~
% 41.25/6.57 | | | | | | (all_237_0 = 0)))
% 41.25/6.57 | | | | | |
% 41.25/6.57 | | | | | | ALPHA: (665) implies:
% 41.25/6.57 | | | | | | (666) phi(all_42_1) = all_289_0
% 41.25/6.57 | | | | | | (667) (all_289_0 = all_42_1 & all_237_0 = 0) | (all_289_0 = err &
% 41.25/6.57 | | | | | | ~ (all_237_0 = 0))
% 41.25/6.57 | | | | | |
% 41.25/6.57 | | | | | | DELTA: instantiating (658) with fresh symbols all_293_0, all_293_1,
% 41.25/6.57 | | | | | | all_293_2 gives:
% 41.25/6.57 | | | | | | (668) f2(true, all_42_1, all_42_1) = all_293_2 &
% 41.25/6.57 | | | | | | lazy_impl(all_293_1, all_293_0) = all_293_2 &
% 41.25/6.57 | | | | | | impl(all_249_2, all_42_1) = all_293_0 & prop(all_42_1) =
% 41.25/6.57 | | | | | | all_293_1 & $i(all_293_0) & $i(all_293_1) & $i(all_293_2)
% 41.25/6.57 | | | | | |
% 41.25/6.57 | | | | | | ALPHA: (668) implies:
% 41.25/6.57 | | | | | | (669) f2(true, all_42_1, all_42_1) = all_293_2
% 41.25/6.57 | | | | | |
% 41.25/6.57 | | | | | | DELTA: instantiating (660) with fresh symbols all_295_0, all_295_1,
% 41.25/6.57 | | | | | | all_295_2 gives:
% 41.25/6.57 | | | | | | (670) f2(true, all_42_0, all_42_0) = all_295_2 &
% 41.25/6.57 | | | | | | lazy_impl(all_295_1, all_295_0) = all_295_2 &
% 41.25/6.57 | | | | | | impl(all_257_2, all_42_0) = all_295_0 & prop(all_42_0) =
% 41.25/6.57 | | | | | | all_295_1 & $i(all_295_0) & $i(all_295_1) & $i(all_295_2)
% 41.25/6.57 | | | | | |
% 41.25/6.57 | | | | | | ALPHA: (670) implies:
% 41.25/6.57 | | | | | | (671) f2(true, all_42_0, all_42_0) = all_295_2
% 41.25/6.57 | | | | | |
% 41.25/6.57 | | | | | | DELTA: instantiating (659) with fresh symbols all_301_0, all_301_1,
% 41.25/6.57 | | | | | | all_301_2 gives:
% 41.25/6.57 | | | | | | (672) f2(true, all_42_0, all_42_1) = all_301_2 &
% 41.25/6.57 | | | | | | lazy_impl(all_301_1, all_301_0) = all_301_2 &
% 41.25/6.57 | | | | | | impl(all_253_2, all_42_1) = all_301_0 & prop(all_42_1) =
% 41.25/6.57 | | | | | | all_301_1 & $i(all_301_0) & $i(all_301_1) & $i(all_301_2)
% 41.25/6.57 | | | | | |
% 41.25/6.57 | | | | | | ALPHA: (672) implies:
% 41.25/6.57 | | | | | | (673) f2(true, all_42_0, all_42_1) = all_301_2
% 41.25/6.57 | | | | | |
% 41.25/6.57 | | | | | | GROUND_INST: instantiating (39) with all_81_1, all_287_1, err,
% 41.25/6.57 | | | | | | simplifying with (126), (662) gives:
% 41.25/6.57 | | | | | | (674) all_287_1 = all_81_1
% 41.25/6.57 | | | | | |
% 41.25/6.57 | | | | | | GROUND_INST: instantiating (40) with err, all_287_0, err,
% 41.25/6.57 | | | | | | simplifying with (57), (663) gives:
% 41.25/6.57 | | | | | | (675) all_287_0 = err
% 41.25/6.57 | | | | | |
% 41.25/6.57 | | | | | | GROUND_INST: instantiating (40) with all_42_0, all_289_0, all_42_1,
% 41.25/6.57 | | | | | | simplifying with (458), (666) gives:
% 41.25/6.57 | | | | | | (676) all_289_0 = all_42_0
% 41.25/6.57 | | | | | |
% 41.25/6.57 | | | | | | BETA: splitting (664) gives:
% 41.25/6.57 | | | | | |
% 41.25/6.57 | | | | | | Case 1:
% 41.25/6.57 | | | | | | |
% 41.25/6.57 | | | | | | | (677) all_287_1 = 0
% 41.25/6.57 | | | | | | |
% 41.25/6.57 | | | | | | | COMBINE_EQS: (674), (677) imply:
% 41.25/6.57 | | | | | | | (678) all_81_1 = 0
% 41.25/6.57 | | | | | | |
% 41.25/6.57 | | | | | | | REDUCE: (470), (678) imply:
% 41.25/6.57 | | | | | | | (679) $false
% 41.25/6.57 | | | | | | |
% 41.25/6.57 | | | | | | | CLOSE: (679) is inconsistent.
% 41.25/6.57 | | | | | | |
% 41.25/6.57 | | | | | | Case 2:
% 41.25/6.57 | | | | | | |
% 41.25/6.57 | | | | | | | (680) all_287_0 = all_251_0
% 41.25/6.57 | | | | | | |
% 41.25/6.57 | | | | | | | COMBINE_EQS: (675), (680) imply:
% 41.25/6.57 | | | | | | | (681) all_251_0 = err
% 41.25/6.57 | | | | | | |
% 41.25/6.57 | | | | | | | REDUCE: (622), (681) imply:
% 41.25/6.57 | | | | | | | (682) lazy_impl(true, err) = all_251_2
% 41.25/6.57 | | | | | | |
% 41.25/6.57 | | | | | | | GROUND_INST: instantiating (44) with err, all_251_2, err, true,
% 41.25/6.57 | | | | | | | simplifying with (106), (682) gives:
% 41.25/6.57 | | | | | | | (683) all_251_2 = err
% 41.25/6.57 | | | | | | |
% 41.25/6.57 | | | | | | | REDUCE: (526), (683) imply:
% 41.25/6.57 | | | | | | | (684) f2(true, true, all_42_0) = err
% 41.25/6.57 | | | | | | |
% 41.25/6.57 | | | | | | | BETA: splitting (452) gives:
% 41.25/6.57 | | | | | | |
% 41.25/6.57 | | | | | | | Case 1:
% 41.25/6.57 | | | | | | | |
% 41.25/6.57 | | | | | | | | (685) all_42_0 = true
% 41.25/6.57 | | | | | | | |
% 41.25/6.57 | | | | | | | | COMBINE_EQS: (676), (685) imply:
% 41.25/6.57 | | | | | | | | (686) all_289_0 = true
% 41.25/6.57 | | | | | | | |
% 41.25/6.57 | | | | | | | | REDUCE: (671), (685) imply:
% 41.25/6.57 | | | | | | | | (687) f2(true, true, true) = all_295_2
% 41.25/6.57 | | | | | | | |
% 41.25/6.57 | | | | | | | | REDUCE: (673), (685) imply:
% 41.25/6.57 | | | | | | | | (688) f2(true, true, all_42_1) = all_301_2
% 41.25/6.57 | | | | | | | |
% 41.25/6.57 | | | | | | | | REDUCE: (684), (685) imply:
% 41.25/6.57 | | | | | | | | (689) f2(true, true, true) = err
% 41.25/6.57 | | | | | | | |
% 41.25/6.57 | | | | | | | | BETA: splitting (667) gives:
% 41.25/6.57 | | | | | | | |
% 41.25/6.57 | | | | | | | | Case 1:
% 41.25/6.57 | | | | | | | | |
% 41.25/6.57 | | | | | | | | | (690) all_289_0 = all_42_1 & all_237_0 = 0
% 41.25/6.57 | | | | | | | | |
% 41.25/6.57 | | | | | | | | | ALPHA: (690) implies:
% 41.25/6.57 | | | | | | | | | (691) all_289_0 = all_42_1
% 41.25/6.57 | | | | | | | | |
% 41.25/6.57 | | | | | | | | | COMBINE_EQS: (686), (691) imply:
% 41.25/6.57 | | | | | | | | | (692) all_42_1 = true
% 41.25/6.57 | | | | | | | | |
% 41.25/6.57 | | | | | | | | | REDUCE: (669), (692) imply:
% 41.25/6.57 | | | | | | | | | (693) f2(true, true, true) = all_293_2
% 41.25/6.57 | | | | | | | | |
% 41.25/6.57 | | | | | | | | | REDUCE: (688), (692) imply:
% 41.25/6.57 | | | | | | | | | (694) f2(true, true, true) = all_301_2
% 41.25/6.57 | | | | | | | | |
% 41.25/6.57 | | | | | | | | | REDUCE: (531), (692) imply:
% 41.25/6.57 | | | | | | | | | (695) f2(true, true, true) = all_253_2
% 41.25/6.57 | | | | | | | | |
% 41.25/6.57 | | | | | | | | | GROUND_INST: instantiating (46) with true, all_293_2, true,
% 41.25/6.57 | | | | | | | | | true, true, simplifying with (403), (693) gives:
% 41.25/6.57 | | | | | | | | | (696) all_293_2 = true
% 41.25/6.57 | | | | | | | | |
% 41.25/6.57 | | | | | | | | | GROUND_INST: instantiating (46) with all_293_2, all_295_2,
% 41.25/6.57 | | | | | | | | | true, true, true, simplifying with (687), (693)
% 41.25/6.57 | | | | | | | | | gives:
% 41.25/6.57 | | | | | | | | | (697) all_295_2 = all_293_2
% 41.25/6.57 | | | | | | | | |
% 41.25/6.57 | | | | | | | | | GROUND_INST: instantiating (46) with err, all_295_2, true,
% 41.25/6.57 | | | | | | | | | true, true, simplifying with (687), (689) gives:
% 41.25/6.57 | | | | | | | | | (698) all_295_2 = err
% 41.25/6.57 | | | | | | | | |
% 41.25/6.57 | | | | | | | | | GROUND_INST: instantiating (46) with all_295_2, all_301_2,
% 41.25/6.57 | | | | | | | | | true, true, true, simplifying with (687), (694)
% 41.25/6.57 | | | | | | | | | gives:
% 41.25/6.57 | | | | | | | | | (699) all_301_2 = all_295_2
% 41.25/6.57 | | | | | | | | |
% 41.25/6.57 | | | | | | | | | GROUND_INST: instantiating (46) with all_253_2, all_301_2,
% 41.25/6.57 | | | | | | | | | true, true, true, simplifying with (694), (695)
% 41.25/6.57 | | | | | | | | | gives:
% 41.25/6.57 | | | | | | | | | (700) all_301_2 = all_253_2
% 41.25/6.57 | | | | | | | | |
% 41.25/6.57 | | | | | | | | | COMBINE_EQS: (699), (700) imply:
% 41.25/6.57 | | | | | | | | | (701) all_295_2 = all_253_2
% 41.25/6.57 | | | | | | | | |
% 41.25/6.57 | | | | | | | | | SIMP: (701) implies:
% 41.25/6.57 | | | | | | | | | (702) all_295_2 = all_253_2
% 41.25/6.57 | | | | | | | | |
% 41.25/6.57 | | | | | | | | | COMBINE_EQS: (698), (702) imply:
% 41.25/6.57 | | | | | | | | | (703) all_253_2 = err
% 41.25/6.57 | | | | | | | | |
% 41.25/6.57 | | | | | | | | | COMBINE_EQS: (697), (702) imply:
% 41.25/6.57 | | | | | | | | | (704) all_293_2 = all_253_2
% 41.25/6.57 | | | | | | | | |
% 41.25/6.57 | | | | | | | | | SIMP: (704) implies:
% 41.25/6.57 | | | | | | | | | (705) all_293_2 = all_253_2
% 41.25/6.57 | | | | | | | | |
% 41.25/6.57 | | | | | | | | | COMBINE_EQS: (696), (705) imply:
% 41.25/6.57 | | | | | | | | | (706) all_253_2 = true
% 41.25/6.57 | | | | | | | | |
% 41.25/6.57 | | | | | | | | | SIMP: (706) implies:
% 41.25/6.57 | | | | | | | | | (707) all_253_2 = true
% 41.25/6.57 | | | | | | | | |
% 41.25/6.57 | | | | | | | | | COMBINE_EQS: (703), (707) imply:
% 41.25/6.57 | | | | | | | | | (708) err = true
% 41.25/6.57 | | | | | | | | |
% 41.25/6.57 | | | | | | | | | SIMP: (708) implies:
% 41.25/6.57 | | | | | | | | | (709) err = true
% 41.25/6.57 | | | | | | | | |
% 41.25/6.57 | | | | | | | | | REDUCE: (4), (709) imply:
% 41.25/6.57 | | | | | | | | | (710) $false
% 41.25/6.57 | | | | | | | | |
% 41.25/6.57 | | | | | | | | | CLOSE: (710) is inconsistent.
% 41.25/6.57 | | | | | | | | |
% 41.25/6.57 | | | | | | | | Case 2:
% 41.25/6.57 | | | | | | | | |
% 41.25/6.57 | | | | | | | | | (711) all_289_0 = err & ~ (all_237_0 = 0)
% 41.25/6.57 | | | | | | | | |
% 41.25/6.57 | | | | | | | | | ALPHA: (711) implies:
% 41.25/6.57 | | | | | | | | | (712) all_289_0 = err
% 41.25/6.57 | | | | | | | | |
% 41.25/6.57 | | | | | | | | | COMBINE_EQS: (686), (712) imply:
% 41.25/6.57 | | | | | | | | | (713) err = true
% 41.25/6.57 | | | | | | | | |
% 41.25/6.57 | | | | | | | | | SIMP: (713) implies:
% 41.25/6.57 | | | | | | | | | (714) err = true
% 41.25/6.57 | | | | | | | | |
% 41.25/6.57 | | | | | | | | | REDUCE: (4), (714) imply:
% 41.25/6.57 | | | | | | | | | (715) $false
% 41.25/6.57 | | | | | | | | |
% 41.25/6.57 | | | | | | | | | CLOSE: (715) is inconsistent.
% 41.25/6.57 | | | | | | | | |
% 41.25/6.57 | | | | | | | | End of split
% 41.25/6.57 | | | | | | | |
% 41.25/6.57 | | | | | | | Case 2:
% 41.25/6.57 | | | | | | | |
% 41.25/6.57 | | | | | | | | (716) all_42_0 = false
% 41.25/6.57 | | | | | | | |
% 41.25/6.57 | | | | | | | | REDUCE: (684), (716) imply:
% 41.25/6.57 | | | | | | | | (717) f2(true, true, false) = err
% 41.25/6.57 | | | | | | | |
% 41.25/6.57 | | | | | | | | REF_CLOSE: (4), (46), (404), (717) are inconsistent by sub-proof
% 41.25/6.57 | | | | | | | | #3.
% 41.25/6.57 | | | | | | | |
% 41.25/6.57 | | | | | | | End of split
% 41.25/6.57 | | | | | | |
% 41.25/6.57 | | | | | | End of split
% 41.25/6.57 | | | | | |
% 41.25/6.58 | | | | | End of split
% 41.25/6.58 | | | | |
% 41.25/6.58 | | | | Case 2:
% 41.25/6.58 | | | | |
% 41.25/6.58 | | | | | (718) ? [v0: int] : ( ~ (v0 = 0) & bool(all_42_1) = v0)
% 41.25/6.58 | | | | |
% 41.25/6.58 | | | | | DELTA: instantiating (718) with fresh symbol all_197_0 gives:
% 41.25/6.58 | | | | | (719) ~ (all_197_0 = 0) & bool(all_42_1) = all_197_0
% 41.25/6.58 | | | | |
% 41.25/6.58 | | | | | REF_CLOSE: (39), (441), (719) are inconsistent by sub-proof #2.
% 41.25/6.58 | | | | |
% 41.25/6.58 | | | | End of split
% 41.25/6.58 | | | |
% 41.25/6.58 | | | Case 2:
% 41.25/6.58 | | | |
% 41.25/6.58 | | | | (720) all_53_0 = false
% 41.25/6.58 | | | |
% 41.25/6.58 | | | | REDUCE: (70), (720) imply:
% 41.25/6.58 | | | | (721) lazy_impl(false, all_42_1) = all_42_0
% 41.25/6.58 | | | |
% 41.25/6.58 | | | | BETA: splitting (139) gives:
% 41.25/6.58 | | | |
% 41.25/6.58 | | | | Case 1:
% 41.25/6.58 | | | | |
% 41.25/6.58 | | | | | (722) prop(all_53_0) = false
% 41.25/6.58 | | | | |
% 41.25/6.58 | | | | | REDUCE: (720), (722) imply:
% 41.25/6.58 | | | | | (723) prop(false) = false
% 41.25/6.58 | | | | |
% 41.25/6.58 | | | | | GROUND_INST: instantiating (41) with true, false, false, simplifying
% 41.25/6.58 | | | | | with (94), (723) gives:
% 41.25/6.58 | | | | | (724) true = false
% 41.25/6.58 | | | | |
% 41.25/6.58 | | | | | REDUCE: (137), (724) imply:
% 41.25/6.58 | | | | | (725) $false
% 41.25/6.58 | | | | |
% 41.25/6.58 | | | | | CLOSE: (725) is inconsistent.
% 41.25/6.58 | | | | |
% 41.25/6.58 | | | | Case 2:
% 41.25/6.58 | | | | |
% 41.25/6.58 | | | | |
% 41.25/6.58 | | | | | GROUND_INST: instantiating (20) with all_42_1, all_42_0, simplifying
% 41.25/6.58 | | | | | with (48), (721) gives:
% 41.25/6.58 | | | | | (726) all_42_0 = true
% 41.25/6.58 | | | | |
% 41.25/6.58 | | | | | REDUCE: (439), (726) imply:
% 41.25/6.58 | | | | | (727) lazy_and1(true, true) = err
% 41.25/6.58 | | | | |
% 41.25/6.58 | | | | | GROUND_INST: instantiating (45) with true, err, true, true,
% 41.25/6.58 | | | | | simplifying with (103), (727) gives:
% 41.25/6.58 | | | | | (728) err = true
% 41.25/6.58 | | | | |
% 41.25/6.58 | | | | | REDUCE: (4), (728) imply:
% 41.25/6.58 | | | | | (729) $false
% 41.25/6.58 | | | | |
% 41.25/6.58 | | | | | CLOSE: (729) is inconsistent.
% 41.25/6.58 | | | | |
% 41.25/6.58 | | | | End of split
% 41.25/6.58 | | | |
% 41.25/6.58 | | | End of split
% 41.25/6.58 | | |
% 41.25/6.58 | | End of split
% 41.25/6.58 | |
% 41.25/6.58 | Case 2:
% 41.25/6.58 | |
% 41.25/6.58 | | (730) all_55_0 = false2
% 41.25/6.58 | | (731) ~ (all_55_1 = 0)
% 41.25/6.58 | |
% 41.25/6.58 | | REDUCE: (73), (730) imply:
% 41.25/6.58 | | (732) not1(all_42_0) = false2
% 41.25/6.58 | |
% 41.25/6.58 | | BETA: splitting (81) gives:
% 41.25/6.58 | |
% 41.25/6.58 | | Case 1:
% 41.25/6.58 | | |
% 41.25/6.58 | | | (733) all_59_0 = 0 & all_42_0 = false2
% 41.25/6.58 | | |
% 41.25/6.58 | | | ALPHA: (733) implies:
% 41.25/6.58 | | | (734) all_42_0 = false2
% 41.25/6.58 | | |
% 41.25/6.58 | | | REDUCE: (732), (734) imply:
% 41.25/6.58 | | | (735) not1(false2) = false2
% 41.25/6.58 | | |
% 41.25/6.58 | | | REDUCE: (70), (734) imply:
% 41.25/6.58 | | | (736) lazy_impl(all_53_0, all_42_1) = false2
% 41.25/6.58 | | |
% 41.25/6.58 | | | REDUCE: (63), (734) imply:
% 41.25/6.58 | | | (737) lazy_impl(true, false2) = false2
% 41.25/6.58 | | |
% 41.25/6.58 | | | REDUCE: (50), (734) imply:
% 41.25/6.58 | | | (738) phi(false2) = false2
% 41.25/6.58 | | |
% 41.25/6.58 | | | REDUCE: (72), (734) imply:
% 41.25/6.58 | | | (739) bool(false2) = all_55_1
% 41.25/6.58 | | |
% 41.25/6.58 | | | BETA: splitting (108) gives:
% 41.25/6.58 | | |
% 41.25/6.58 | | | Case 1:
% 41.25/6.58 | | | |
% 41.25/6.58 | | | | (740) bool(all_42_1) = 0
% 41.25/6.58 | | | |
% 41.25/6.58 | | | | BETA: splitting (107) gives:
% 41.25/6.58 | | | |
% 41.25/6.58 | | | | Case 1:
% 41.25/6.58 | | | | |
% 41.25/6.58 | | | | | (741) all_53_0 = true
% 41.25/6.58 | | | | |
% 41.25/6.58 | | | | | REDUCE: (187), (741) imply:
% 41.25/6.58 | | | | | (742) not1(true) = all_105_0
% 41.25/6.58 | | | | |
% 41.25/6.58 | | | | | REDUCE: (145), (741) imply:
% 41.25/6.58 | | | | | (743) lazy_and1(true, true) = all_79_0
% 41.25/6.58 | | | | |
% 41.25/6.58 | | | | | REDUCE: (736), (741) imply:
% 41.25/6.58 | | | | | (744) lazy_impl(true, all_42_1) = false2
% 41.25/6.58 | | | | |
% 41.25/6.58 | | | | | REDUCE: (147), (741) imply:
% 41.25/6.58 | | | | | (745) lazy_impl(true, true) = all_79_0
% 41.25/6.58 | | | | |
% 41.25/6.58 | | | | | REDUCE: (69), (741) imply:
% 41.25/6.58 | | | | | (746) prop(all_42_1) = true
% 41.25/6.58 | | | | |
% 41.25/6.58 | | | | | GROUND_INST: instantiating (45) with true, all_79_0, true, true,
% 41.25/6.58 | | | | | simplifying with (103), (743) gives:
% 41.25/6.58 | | | | | (747) all_79_0 = true
% 41.25/6.58 | | | | |
% 41.25/6.58 | | | | | GROUND_INST: instantiating (42) with false, all_105_0, true,
% 41.25/6.58 | | | | | simplifying with (36), (742) gives:
% 41.25/6.58 | | | | | (748) all_105_0 = false
% 41.25/6.58 | | | | |
% 41.25/6.58 | | | | | GROUND_INST: instantiating (3) with all_42_1, simplifying with (48),
% 41.25/6.58 | | | | | (740) gives:
% 41.25/6.58 | | | | | (749) all_42_1 = true | all_42_1 = false
% 41.25/6.58 | | | | |
% 41.25/6.58 | | | | | GROUND_INST: instantiating (19) with all_42_1, simplifying with (48),
% 41.25/6.58 | | | | | (740) gives:
% 41.25/6.58 | | | | | (750) impl(true, all_42_1) = all_42_1
% 41.25/6.58 | | | | |
% 41.25/6.58 | | | | | GROUND_INST: instantiating (18) with all_42_1, simplifying with (48),
% 41.25/6.58 | | | | | (740) gives:
% 41.25/6.58 | | | | | (751) impl(false, all_42_1) = true
% 41.25/6.58 | | | | |
% 41.25/6.58 | | | | | GROUND_INST: instantiating (22) with all_42_1, false2, simplifying
% 41.25/6.58 | | | | | with (48), (744) gives:
% 41.25/6.58 | | | | | (752) phi(all_42_1) = false2 & $i(false2)
% 41.25/6.58 | | | | |
% 41.25/6.58 | | | | | ALPHA: (752) implies:
% 41.25/6.58 | | | | | (753) phi(all_42_1) = false2
% 41.25/6.58 | | | | |
% 41.25/6.58 | | | | | GROUND_INST: instantiating (31) with all_42_1, false2, simplifying
% 41.25/6.58 | | | | | with (48), (753) gives:
% 41.25/6.58 | | | | | (754) ? [v0: any] : ? [v1: $i] : (not1(all_42_1) = v1 &
% 41.25/6.58 | | | | | bool(all_42_1) = v0 & $i(v1) & (v1 = false2 | v0 = 0))
% 41.25/6.58 | | | | |
% 41.25/6.58 | | | | | GROUND_INST: instantiating (11) with all_42_1, false2, simplifying
% 41.25/6.58 | | | | | with (48), (753) gives:
% 41.25/6.58 | | | | | (755) ? [v0: any] : (d(all_42_1) = v0 & ((v0 = 0 & all_42_1 =
% 41.25/6.58 | | | | | false2) | (false2 = err & ~ (v0 = 0))))
% 41.25/6.58 | | | | |
% 41.25/6.58 | | | | | GROUND_INST: instantiating (23) with true, false, all_42_1, true,
% 41.25/6.58 | | | | | true, simplifying with (35), (48), (54), (96), (751)
% 41.25/6.58 | | | | | gives:
% 41.25/6.58 | | | | | (756) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (f1(true, false,
% 41.25/6.58 | | | | | all_42_1) = v0 & lazy_impl(v1, v2) = v0 & impl(true,
% 41.25/6.58 | | | | | all_42_1) = v2 & prop(all_42_1) = v1 & $i(v2) & $i(v1) &
% 41.25/6.58 | | | | | $i(v0))
% 41.25/6.58 | | | | |
% 41.25/6.58 | | | | | GROUND_INST: instantiating (23) with false, false, all_42_1, true,
% 41.25/6.58 | | | | | true, simplifying with (48), (54), (97), (751) gives:
% 41.25/6.58 | | | | | (757) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (f1(false, false,
% 41.25/6.58 | | | | | all_42_1) = v0 & lazy_impl(v1, v2) = v0 & impl(true,
% 41.25/6.58 | | | | | all_42_1) = v2 & prop(all_42_1) = v1 & $i(v2) & $i(v1) &
% 41.25/6.58 | | | | | $i(v0))
% 41.25/6.58 | | | | |
% 41.25/6.58 | | | | | GROUND_INST: instantiating (25) with true, false, all_42_1, true,
% 41.25/6.58 | | | | | true, simplifying with (35), (48), (54), (104), (751)
% 41.25/6.58 | | | | | gives:
% 41.25/6.58 | | | | | (758) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (f2(true, false,
% 41.25/6.58 | | | | | all_42_1) = v0 & lazy_impl(v1, v2) = v0 & impl(true,
% 41.25/6.58 | | | | | all_42_1) = v2 & prop(all_42_1) = v1 & $i(v2) & $i(v1) &
% 41.25/6.58 | | | | | $i(v0))
% 41.25/6.58 | | | | |
% 41.25/6.58 | | | | | GROUND_INST: instantiating (26) with false, false, all_42_1, true,
% 41.25/6.58 | | | | | true, all_42_1, all_42_1, simplifying with (48), (54),
% 41.25/6.58 | | | | | (750), (751) gives:
% 41.25/6.58 | | | | | (759) ? [v0: $i] : ? [v1: $i] : (f3(false, false, all_42_1) = v0
% 41.25/6.58 | | | | | & lazy_impl(v1, all_42_1) = v0 & prop(all_42_1) = v1 &
% 41.25/6.58 | | | | | $i(v1) & $i(v0))
% 41.25/6.58 | | | | |
% 41.25/6.58 | | | | | GROUND_INST: instantiating (23) with true, true, all_42_1, all_42_1,
% 41.25/6.58 | | | | | all_42_1, simplifying with (35), (48), (750) gives:
% 41.25/6.59 | | | | | (760) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (f1(true, true,
% 41.25/6.59 | | | | | all_42_1) = v0 & lazy_impl(v1, v2) = v0 & impl(all_42_1,
% 41.25/6.59 | | | | | all_42_1) = v2 & prop(all_42_1) = v1 & $i(v2) & $i(v1) &
% 41.25/6.59 | | | | | $i(v0))
% 41.25/6.59 | | | | |
% 41.25/6.59 | | | | | GROUND_INST: instantiating (23) with false, true, all_42_1, all_42_1,
% 41.25/6.59 | | | | | true, simplifying with (35), (48), (54), (750), (751)
% 41.25/6.59 | | | | | gives:
% 41.25/6.59 | | | | | (761) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (f1(false, true,
% 41.25/6.59 | | | | | all_42_1) = v0 & lazy_impl(v1, v2) = v0 & impl(true,
% 41.25/6.59 | | | | | all_42_1) = v2 & prop(all_42_1) = v1 & $i(v2) & $i(v1) &
% 41.25/6.59 | | | | | $i(v0))
% 41.25/6.59 | | | | |
% 41.25/6.59 | | | | | GROUND_INST: instantiating (25) with true, true, all_42_1, all_42_1,
% 41.25/6.59 | | | | | false2, simplifying with (35), (48), (744), (750) gives:
% 41.25/6.59 | | | | | (762) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (f2(true, true,
% 41.25/6.59 | | | | | all_42_1) = v0 & lazy_impl(v1, v2) = v0 & impl(false2,
% 41.25/6.59 | | | | | all_42_1) = v2 & prop(all_42_1) = v1 & $i(v2) & $i(v1) &
% 41.25/6.59 | | | | | $i(v0))
% 41.25/6.59 | | | | |
% 41.25/6.59 | | | | | DELTA: instantiating (759) with fresh symbols all_233_0, all_233_1
% 41.25/6.59 | | | | | gives:
% 41.25/6.59 | | | | | (763) f3(false, false, all_42_1) = all_233_1 & lazy_impl(all_233_0,
% 41.25/6.59 | | | | | all_42_1) = all_233_1 & prop(all_42_1) = all_233_0 &
% 41.25/6.59 | | | | | $i(all_233_0) & $i(all_233_1)
% 41.25/6.59 | | | | |
% 41.25/6.59 | | | | | ALPHA: (763) implies:
% 41.25/6.59 | | | | | (764) $i(all_233_1)
% 41.25/6.59 | | | | | (765) $i(all_233_0)
% 41.25/6.59 | | | | | (766) prop(all_42_1) = all_233_0
% 41.25/6.59 | | | | | (767) lazy_impl(all_233_0, all_42_1) = all_233_1
% 41.25/6.59 | | | | |
% 41.25/6.59 | | | | | DELTA: instantiating (754) with fresh symbols all_235_0, all_235_1
% 41.25/6.59 | | | | | gives:
% 41.25/6.59 | | | | | (768) not1(all_42_1) = all_235_0 & bool(all_42_1) = all_235_1 &
% 41.25/6.59 | | | | | $i(all_235_0) & (all_235_0 = false2 | all_235_1 = 0)
% 41.25/6.59 | | | | |
% 41.25/6.59 | | | | | ALPHA: (768) implies:
% 41.25/6.59 | | | | | (769) not1(all_42_1) = all_235_0
% 41.25/6.59 | | | | |
% 41.25/6.59 | | | | | DELTA: instantiating (755) with fresh symbol all_237_0 gives:
% 41.25/6.59 | | | | | (770) d(all_42_1) = all_237_0 & ((all_237_0 = 0 & all_42_1 =
% 41.25/6.59 | | | | | false2) | (false2 = err & ~ (all_237_0 = 0)))
% 41.25/6.59 | | | | |
% 41.25/6.59 | | | | | ALPHA: (770) implies:
% 41.25/6.59 | | | | | (771) (all_237_0 = 0 & all_42_1 = false2) | (false2 = err & ~
% 41.25/6.59 | | | | | (all_237_0 = 0))
% 41.25/6.59 | | | | |
% 41.25/6.59 | | | | | DELTA: instantiating (758) with fresh symbols all_239_0, all_239_1,
% 41.25/6.59 | | | | | all_239_2 gives:
% 41.25/6.59 | | | | | (772) f2(true, false, all_42_1) = all_239_2 & lazy_impl(all_239_1,
% 41.25/6.59 | | | | | all_239_0) = all_239_2 & impl(true, all_42_1) = all_239_0 &
% 41.25/6.59 | | | | | prop(all_42_1) = all_239_1 & $i(all_239_0) & $i(all_239_1) &
% 41.25/6.59 | | | | | $i(all_239_2)
% 41.25/6.59 | | | | |
% 41.25/6.59 | | | | | ALPHA: (772) implies:
% 41.25/6.59 | | | | | (773) $i(all_239_0)
% 41.25/6.59 | | | | | (774) prop(all_42_1) = all_239_1
% 41.25/6.59 | | | | | (775) impl(true, all_42_1) = all_239_0
% 41.25/6.59 | | | | | (776) lazy_impl(all_239_1, all_239_0) = all_239_2
% 41.25/6.59 | | | | |
% 41.25/6.59 | | | | | DELTA: instantiating (757) with fresh symbols all_241_0, all_241_1,
% 41.25/6.59 | | | | | all_241_2 gives:
% 41.25/6.59 | | | | | (777) f1(false, false, all_42_1) = all_241_2 & lazy_impl(all_241_1,
% 41.25/6.59 | | | | | all_241_0) = all_241_2 & impl(true, all_42_1) = all_241_0 &
% 41.25/6.59 | | | | | prop(all_42_1) = all_241_1 & $i(all_241_0) & $i(all_241_1) &
% 41.25/6.59 | | | | | $i(all_241_2)
% 41.25/6.59 | | | | |
% 41.25/6.59 | | | | | ALPHA: (777) implies:
% 41.25/6.59 | | | | | (778) prop(all_42_1) = all_241_1
% 41.25/6.59 | | | | | (779) impl(true, all_42_1) = all_241_0
% 41.25/6.59 | | | | | (780) lazy_impl(all_241_1, all_241_0) = all_241_2
% 41.25/6.59 | | | | |
% 41.25/6.59 | | | | | DELTA: instantiating (756) with fresh symbols all_243_0, all_243_1,
% 41.25/6.59 | | | | | all_243_2 gives:
% 41.25/6.59 | | | | | (781) f1(true, false, all_42_1) = all_243_2 & lazy_impl(all_243_1,
% 41.25/6.59 | | | | | all_243_0) = all_243_2 & impl(true, all_42_1) = all_243_0 &
% 41.25/6.59 | | | | | prop(all_42_1) = all_243_1 & $i(all_243_0) & $i(all_243_1) &
% 41.25/6.59 | | | | | $i(all_243_2)
% 41.25/6.59 | | | | |
% 41.25/6.59 | | | | | ALPHA: (781) implies:
% 41.25/6.59 | | | | | (782) prop(all_42_1) = all_243_1
% 41.25/6.59 | | | | | (783) impl(true, all_42_1) = all_243_0
% 41.25/6.59 | | | | | (784) lazy_impl(all_243_1, all_243_0) = all_243_2
% 41.25/6.59 | | | | |
% 41.25/6.59 | | | | | DELTA: instantiating (762) with fresh symbols all_245_0, all_245_1,
% 41.25/6.59 | | | | | all_245_2 gives:
% 41.25/6.59 | | | | | (785) f2(true, true, all_42_1) = all_245_2 & lazy_impl(all_245_1,
% 41.25/6.59 | | | | | all_245_0) = all_245_2 & impl(false2, all_42_1) = all_245_0
% 41.25/6.59 | | | | | & prop(all_42_1) = all_245_1 & $i(all_245_0) & $i(all_245_1)
% 41.25/6.59 | | | | | & $i(all_245_2)
% 41.25/6.59 | | | | |
% 41.25/6.59 | | | | | ALPHA: (785) implies:
% 41.25/6.59 | | | | | (786) prop(all_42_1) = all_245_1
% 41.25/6.59 | | | | | (787) impl(false2, all_42_1) = all_245_0
% 41.25/6.59 | | | | | (788) lazy_impl(all_245_1, all_245_0) = all_245_2
% 41.25/6.59 | | | | | (789) f2(true, true, all_42_1) = all_245_2
% 41.25/6.59 | | | | |
% 41.25/6.59 | | | | | DELTA: instantiating (760) with fresh symbols all_247_0, all_247_1,
% 41.25/6.59 | | | | | all_247_2 gives:
% 41.25/6.59 | | | | | (790) f1(true, true, all_42_1) = all_247_2 & lazy_impl(all_247_1,
% 41.25/6.59 | | | | | all_247_0) = all_247_2 & impl(all_42_1, all_42_1) =
% 41.25/6.59 | | | | | all_247_0 & prop(all_42_1) = all_247_1 & $i(all_247_0) &
% 41.25/6.59 | | | | | $i(all_247_1) & $i(all_247_2)
% 41.25/6.59 | | | | |
% 41.25/6.59 | | | | | ALPHA: (790) implies:
% 41.25/6.59 | | | | | (791) prop(all_42_1) = all_247_1
% 41.25/6.59 | | | | | (792) impl(all_42_1, all_42_1) = all_247_0
% 41.25/6.59 | | | | | (793) lazy_impl(all_247_1, all_247_0) = all_247_2
% 41.25/6.59 | | | | |
% 41.25/6.59 | | | | | DELTA: instantiating (761) with fresh symbols all_249_0, all_249_1,
% 41.25/6.59 | | | | | all_249_2 gives:
% 41.25/6.59 | | | | | (794) f1(false, true, all_42_1) = all_249_2 & lazy_impl(all_249_1,
% 41.25/6.59 | | | | | all_249_0) = all_249_2 & impl(true, all_42_1) = all_249_0 &
% 41.25/6.59 | | | | | prop(all_42_1) = all_249_1 & $i(all_249_0) & $i(all_249_1) &
% 41.25/6.59 | | | | | $i(all_249_2)
% 41.25/6.59 | | | | |
% 41.25/6.59 | | | | | ALPHA: (794) implies:
% 41.25/6.59 | | | | | (795) prop(all_42_1) = all_249_1
% 41.25/6.59 | | | | | (796) impl(true, all_42_1) = all_249_0
% 41.25/6.59 | | | | | (797) lazy_impl(all_249_1, all_249_0) = all_249_2
% 41.25/6.59 | | | | |
% 41.25/6.59 | | | | | GROUND_INST: instantiating (41) with all_233_0, all_241_1, all_42_1,
% 41.25/6.59 | | | | | simplifying with (766), (778) gives:
% 41.25/6.59 | | | | | (798) all_241_1 = all_233_0
% 41.25/6.59 | | | | |
% 41.25/6.59 | | | | | GROUND_INST: instantiating (41) with all_241_1, all_243_1, all_42_1,
% 41.25/6.59 | | | | | simplifying with (778), (782) gives:
% 41.25/6.59 | | | | | (799) all_243_1 = all_241_1
% 41.25/6.59 | | | | |
% 41.25/6.59 | | | | | GROUND_INST: instantiating (41) with all_239_1, all_243_1, all_42_1,
% 41.25/6.59 | | | | | simplifying with (774), (782) gives:
% 41.25/6.59 | | | | | (800) all_243_1 = all_239_1
% 41.25/6.59 | | | | |
% 41.25/6.59 | | | | | GROUND_INST: instantiating (41) with all_243_1, all_245_1, all_42_1,
% 41.25/6.59 | | | | | simplifying with (782), (786) gives:
% 41.25/6.59 | | | | | (801) all_245_1 = all_243_1
% 41.25/6.59 | | | | |
% 41.25/6.59 | | | | | GROUND_INST: instantiating (41) with true, all_249_1, all_42_1,
% 41.25/6.59 | | | | | simplifying with (746), (795) gives:
% 41.25/6.59 | | | | | (802) all_249_1 = true
% 41.25/6.59 | | | | |
% 41.25/6.59 | | | | | GROUND_INST: instantiating (41) with all_247_1, all_249_1, all_42_1,
% 41.25/6.59 | | | | | simplifying with (791), (795) gives:
% 41.25/6.59 | | | | | (803) all_249_1 = all_247_1
% 41.25/6.59 | | | | |
% 41.25/6.59 | | | | | GROUND_INST: instantiating (41) with all_245_1, all_249_1, all_42_1,
% 41.25/6.59 | | | | | simplifying with (786), (795) gives:
% 41.25/6.59 | | | | | (804) all_249_1 = all_245_1
% 41.25/6.59 | | | | |
% 41.25/6.59 | | | | | GROUND_INST: instantiating (43) with all_42_1, all_241_0, all_42_1,
% 41.25/6.59 | | | | | true, simplifying with (750), (779) gives:
% 41.25/6.59 | | | | | (805) all_241_0 = all_42_1
% 41.25/6.59 | | | | |
% 41.25/6.59 | | | | | GROUND_INST: instantiating (43) with all_241_0, all_243_0, all_42_1,
% 41.25/6.59 | | | | | true, simplifying with (779), (783) gives:
% 41.25/6.59 | | | | | (806) all_243_0 = all_241_0
% 41.25/6.59 | | | | |
% 41.25/6.59 | | | | | GROUND_INST: instantiating (43) with all_243_0, all_249_0, all_42_1,
% 41.25/6.59 | | | | | true, simplifying with (783), (796) gives:
% 41.25/6.59 | | | | | (807) all_249_0 = all_243_0
% 41.25/6.59 | | | | |
% 41.25/6.59 | | | | | GROUND_INST: instantiating (43) with all_239_0, all_249_0, all_42_1,
% 41.25/6.59 | | | | | true, simplifying with (775), (796) gives:
% 41.25/6.59 | | | | | (808) all_249_0 = all_239_0
% 41.25/6.59 | | | | |
% 41.25/6.59 | | | | | COMBINE_EQS: (807), (808) imply:
% 41.25/6.59 | | | | | (809) all_243_0 = all_239_0
% 41.25/6.59 | | | | |
% 41.25/6.59 | | | | | SIMP: (809) implies:
% 41.25/6.59 | | | | | (810) all_243_0 = all_239_0
% 41.25/6.59 | | | | |
% 41.25/6.59 | | | | | COMBINE_EQS: (803), (804) imply:
% 41.25/6.59 | | | | | (811) all_247_1 = all_245_1
% 41.25/6.59 | | | | |
% 41.25/6.59 | | | | | COMBINE_EQS: (802), (803) imply:
% 41.25/6.59 | | | | | (812) all_247_1 = true
% 41.25/6.59 | | | | |
% 41.25/6.59 | | | | | COMBINE_EQS: (811), (812) imply:
% 41.25/6.59 | | | | | (813) all_245_1 = true
% 41.25/6.59 | | | | |
% 41.25/6.59 | | | | | SIMP: (813) implies:
% 41.25/6.59 | | | | | (814) all_245_1 = true
% 41.25/6.59 | | | | |
% 41.25/6.59 | | | | | COMBINE_EQS: (801), (814) imply:
% 41.25/6.59 | | | | | (815) all_243_1 = true
% 41.25/6.59 | | | | |
% 41.25/6.59 | | | | | SIMP: (815) implies:
% 41.25/6.59 | | | | | (816) all_243_1 = true
% 41.25/6.59 | | | | |
% 41.25/6.59 | | | | | COMBINE_EQS: (806), (810) imply:
% 41.25/6.59 | | | | | (817) all_241_0 = all_239_0
% 41.25/6.59 | | | | |
% 41.25/6.59 | | | | | SIMP: (817) implies:
% 41.25/6.59 | | | | | (818) all_241_0 = all_239_0
% 41.25/6.59 | | | | |
% 41.25/6.59 | | | | | COMBINE_EQS: (799), (800) imply:
% 41.25/6.59 | | | | | (819) all_241_1 = all_239_1
% 41.25/6.59 | | | | |
% 41.25/6.59 | | | | | SIMP: (819) implies:
% 41.25/6.59 | | | | | (820) all_241_1 = all_239_1
% 41.25/6.59 | | | | |
% 41.25/6.59 | | | | | COMBINE_EQS: (800), (816) imply:
% 41.25/6.59 | | | | | (821) all_239_1 = true
% 41.25/6.59 | | | | |
% 41.25/6.59 | | | | | COMBINE_EQS: (805), (818) imply:
% 41.25/6.59 | | | | | (822) all_239_0 = all_42_1
% 41.25/6.59 | | | | |
% 41.25/6.59 | | | | | COMBINE_EQS: (798), (820) imply:
% 41.25/6.59 | | | | | (823) all_239_1 = all_233_0
% 41.25/6.59 | | | | |
% 41.25/6.59 | | | | | SIMP: (823) implies:
% 41.25/6.59 | | | | | (824) all_239_1 = all_233_0
% 41.25/6.59 | | | | |
% 41.25/6.59 | | | | | COMBINE_EQS: (821), (824) imply:
% 41.25/6.59 | | | | | (825) all_233_0 = true
% 41.25/6.59 | | | | |
% 41.25/6.59 | | | | | SIMP: (825) implies:
% 41.25/6.59 | | | | | (826) all_233_0 = true
% 41.25/6.59 | | | | |
% 41.25/6.59 | | | | | COMBINE_EQS: (798), (826) imply:
% 41.25/6.59 | | | | | (827) all_241_1 = true
% 41.25/6.59 | | | | |
% 41.25/6.59 | | | | | COMBINE_EQS: (810), (822) imply:
% 41.25/6.59 | | | | | (828) all_243_0 = all_42_1
% 41.25/6.59 | | | | |
% 41.25/6.59 | | | | | COMBINE_EQS: (808), (822) imply:
% 41.25/6.59 | | | | | (829) all_249_0 = all_42_1
% 41.25/6.59 | | | | |
% 41.25/6.59 | | | | | REDUCE: (797), (802), (829) imply:
% 41.25/6.59 | | | | | (830) lazy_impl(true, all_42_1) = all_249_2
% 41.25/6.59 | | | | |
% 41.25/6.59 | | | | | REDUCE: (793), (812) imply:
% 41.25/6.59 | | | | | (831) lazy_impl(true, all_247_0) = all_247_2
% 41.25/6.59 | | | | |
% 41.25/6.59 | | | | | REDUCE: (788), (814) imply:
% 41.25/6.59 | | | | | (832) lazy_impl(true, all_245_0) = all_245_2
% 41.25/6.59 | | | | |
% 41.25/6.59 | | | | | REDUCE: (784), (816), (828) imply:
% 41.25/6.59 | | | | | (833) lazy_impl(true, all_42_1) = all_243_2
% 41.25/6.59 | | | | |
% 41.25/6.59 | | | | | REDUCE: (780), (805), (827) imply:
% 41.25/6.59 | | | | | (834) lazy_impl(true, all_42_1) = all_241_2
% 41.25/6.59 | | | | |
% 41.25/6.59 | | | | | REDUCE: (776), (821), (822) imply:
% 41.25/6.59 | | | | | (835) lazy_impl(true, all_42_1) = all_239_2
% 41.25/6.59 | | | | |
% 41.25/6.59 | | | | | REDUCE: (767), (826) imply:
% 41.25/6.59 | | | | | (836) lazy_impl(true, all_42_1) = all_233_1
% 41.25/6.59 | | | | |
% 41.25/6.59 | | | | | GROUND_INST: instantiating (44) with false2, all_239_2, all_42_1,
% 41.25/6.59 | | | | | true, simplifying with (744), (835) gives:
% 41.25/6.59 | | | | | (837) all_239_2 = false2
% 41.25/6.59 | | | | |
% 41.25/6.59 | | | | | GROUND_INST: instantiating (44) with all_241_2, all_243_2, all_42_1,
% 41.25/6.59 | | | | | true, simplifying with (833), (834) gives:
% 41.25/6.59 | | | | | (838) all_243_2 = all_241_2
% 41.25/6.59 | | | | |
% 41.25/6.59 | | | | | GROUND_INST: instantiating (44) with all_239_2, all_243_2, all_42_1,
% 41.25/6.59 | | | | | true, simplifying with (833), (835) gives:
% 41.25/6.59 | | | | | (839) all_243_2 = all_239_2
% 41.25/6.59 | | | | |
% 41.25/6.59 | | | | | GROUND_INST: instantiating (44) with all_243_2, all_249_2, all_42_1,
% 41.25/6.59 | | | | | true, simplifying with (830), (833) gives:
% 41.25/6.59 | | | | | (840) all_249_2 = all_243_2
% 41.25/6.59 | | | | |
% 41.25/6.59 | | | | | GROUND_INST: instantiating (44) with all_233_1, all_249_2, all_42_1,
% 41.25/6.59 | | | | | true, simplifying with (830), (836) gives:
% 41.25/6.59 | | | | | (841) all_249_2 = all_233_1
% 41.25/6.59 | | | | |
% 41.25/6.59 | | | | | COMBINE_EQS: (840), (841) imply:
% 41.25/6.59 | | | | | (842) all_243_2 = all_233_1
% 41.25/6.59 | | | | |
% 41.25/6.59 | | | | | SIMP: (842) implies:
% 41.25/6.59 | | | | | (843) all_243_2 = all_233_1
% 41.25/6.59 | | | | |
% 41.25/6.59 | | | | | COMBINE_EQS: (838), (839) imply:
% 41.25/6.59 | | | | | (844) all_241_2 = all_239_2
% 41.25/6.59 | | | | |
% 41.25/6.59 | | | | | COMBINE_EQS: (838), (843) imply:
% 41.25/6.59 | | | | | (845) all_241_2 = all_233_1
% 41.25/6.59 | | | | |
% 41.25/6.59 | | | | | COMBINE_EQS: (844), (845) imply:
% 41.25/6.59 | | | | | (846) all_239_2 = all_233_1
% 41.25/6.59 | | | | |
% 41.25/6.59 | | | | | SIMP: (846) implies:
% 41.25/6.59 | | | | | (847) all_239_2 = all_233_1
% 41.25/6.59 | | | | |
% 41.25/6.59 | | | | | COMBINE_EQS: (837), (847) imply:
% 41.25/6.59 | | | | | (848) all_233_1 = false2
% 41.25/6.59 | | | | |
% 41.25/6.59 | | | | | GROUND_INST: instantiating (impl_axiom1) with false2, all_42_1,
% 41.25/6.59 | | | | | all_245_0, simplifying with (48), (138), (787) gives:
% 41.25/6.59 | | | | | (849) ? [v0: any] : ? [v1: $i] : (phi(false2) = v1 & bool(false2)
% 41.25/6.59 | | | | | = v0 & $i(v1) & (v1 = all_245_0 | v0 = 0))
% 41.25/6.59 | | | | |
% 41.25/6.59 | | | | | GROUND_INST: instantiating (25) with true, all_42_1, all_42_1,
% 41.25/6.59 | | | | | all_247_0, all_247_2, simplifying with (35), (48), (792),
% 41.25/6.59 | | | | | (831) gives:
% 41.25/6.59 | | | | | (850) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (f2(true, all_42_1,
% 41.25/6.59 | | | | | all_42_1) = v0 & lazy_impl(v1, v2) = v0 & impl(all_247_2,
% 41.25/6.59 | | | | | all_42_1) = v2 & prop(all_42_1) = v1 & $i(v2) & $i(v1) &
% 41.25/6.59 | | | | | $i(v0))
% 41.25/6.59 | | | | |
% 41.25/6.59 | | | | | DELTA: instantiating (849) with fresh symbols all_269_0, all_269_1
% 41.25/6.59 | | | | | gives:
% 41.25/6.59 | | | | | (851) phi(false2) = all_269_0 & bool(false2) = all_269_1 &
% 41.25/6.59 | | | | | $i(all_269_0) & (all_269_0 = all_245_0 | all_269_1 = 0)
% 41.25/6.59 | | | | |
% 41.25/6.59 | | | | | ALPHA: (851) implies:
% 41.25/6.59 | | | | | (852) bool(false2) = all_269_1
% 41.25/6.59 | | | | | (853) phi(false2) = all_269_0
% 41.25/6.59 | | | | | (854) all_269_0 = all_245_0 | all_269_1 = 0
% 41.25/6.59 | | | | |
% 41.25/6.59 | | | | | DELTA: instantiating (850) with fresh symbols all_273_0, all_273_1,
% 41.25/6.59 | | | | | all_273_2 gives:
% 41.25/6.59 | | | | | (855) f2(true, all_42_1, all_42_1) = all_273_2 &
% 41.25/6.59 | | | | | lazy_impl(all_273_1, all_273_0) = all_273_2 & impl(all_247_2,
% 41.25/6.59 | | | | | all_42_1) = all_273_0 & prop(all_42_1) = all_273_1 &
% 41.25/6.59 | | | | | $i(all_273_0) & $i(all_273_1) & $i(all_273_2)
% 41.25/6.59 | | | | |
% 41.25/6.59 | | | | | ALPHA: (855) implies:
% 41.25/6.59 | | | | | (856) f2(true, all_42_1, all_42_1) = all_273_2
% 41.25/6.59 | | | | |
% 41.25/6.59 | | | | | GROUND_INST: instantiating (39) with all_55_1, all_269_1, false2,
% 41.25/6.59 | | | | | simplifying with (739), (852) gives:
% 41.25/6.59 | | | | | (857) all_269_1 = all_55_1
% 41.25/6.59 | | | | |
% 41.25/6.59 | | | | | GROUND_INST: instantiating (40) with false2, all_269_0, false2,
% 41.25/6.59 | | | | | simplifying with (738), (853) gives:
% 41.25/6.59 | | | | | (858) all_269_0 = false2
% 41.25/6.59 | | | | |
% 41.25/6.59 | | | | | BETA: splitting (854) gives:
% 41.25/6.59 | | | | |
% 41.25/6.59 | | | | | Case 1:
% 41.25/6.59 | | | | | |
% 41.25/6.59 | | | | | | (859) all_269_1 = 0
% 41.25/6.59 | | | | | |
% 41.25/6.59 | | | | | | COMBINE_EQS: (857), (859) imply:
% 41.25/6.60 | | | | | | (860) all_55_1 = 0
% 41.25/6.60 | | | | | |
% 41.25/6.60 | | | | | | SIMP: (860) implies:
% 41.25/6.60 | | | | | | (861) all_55_1 = 0
% 41.25/6.60 | | | | | |
% 41.25/6.60 | | | | | | REDUCE: (731), (861) imply:
% 41.25/6.60 | | | | | | (862) $false
% 41.25/6.60 | | | | | |
% 41.25/6.60 | | | | | | CLOSE: (862) is inconsistent.
% 41.25/6.60 | | | | | |
% 41.25/6.60 | | | | | Case 2:
% 41.25/6.60 | | | | | |
% 41.25/6.60 | | | | | | (863) all_269_0 = all_245_0
% 41.25/6.60 | | | | | |
% 41.25/6.60 | | | | | | COMBINE_EQS: (858), (863) imply:
% 41.25/6.60 | | | | | | (864) all_245_0 = false2
% 41.25/6.60 | | | | | |
% 41.25/6.60 | | | | | | REDUCE: (832), (864) imply:
% 41.25/6.60 | | | | | | (865) lazy_impl(true, false2) = all_245_2
% 41.25/6.60 | | | | | |
% 41.25/6.60 | | | | | | GROUND_INST: instantiating (44) with false2, all_245_2, false2,
% 41.25/6.60 | | | | | | true, simplifying with (737), (865) gives:
% 41.25/6.60 | | | | | | (866) all_245_2 = false2
% 41.25/6.60 | | | | | |
% 41.25/6.60 | | | | | | REDUCE: (789), (866) imply:
% 41.25/6.60 | | | | | | (867) f2(true, true, all_42_1) = false2
% 41.25/6.60 | | | | | |
% 41.25/6.60 | | | | | | BETA: splitting (749) gives:
% 41.25/6.60 | | | | | |
% 41.25/6.60 | | | | | | Case 1:
% 41.25/6.60 | | | | | | |
% 41.25/6.60 | | | | | | | (868) all_42_1 = true
% 41.25/6.60 | | | | | | |
% 41.25/6.60 | | | | | | | REDUCE: (769), (868) imply:
% 41.25/6.60 | | | | | | | (869) not1(true) = all_235_0
% 41.25/6.60 | | | | | | |
% 41.25/6.60 | | | | | | | REDUCE: (856), (868) imply:
% 41.25/6.60 | | | | | | | (870) f2(true, true, true) = all_273_2
% 41.25/6.60 | | | | | | |
% 41.25/6.60 | | | | | | | REDUCE: (867), (868) imply:
% 41.25/6.60 | | | | | | | (871) f2(true, true, true) = false2
% 41.25/6.60 | | | | | | |
% 41.25/6.60 | | | | | | | GROUND_INST: instantiating (46) with true, all_273_2, true, true,
% 41.25/6.60 | | | | | | | true, simplifying with (403), (870) gives:
% 41.25/6.60 | | | | | | | (872) all_273_2 = true
% 41.25/6.60 | | | | | | |
% 41.25/6.60 | | | | | | | GROUND_INST: instantiating (46) with false2, all_273_2, true,
% 41.25/6.60 | | | | | | | true, true, simplifying with (870), (871) gives:
% 41.25/6.60 | | | | | | | (873) all_273_2 = false2
% 41.25/6.60 | | | | | | |
% 41.25/6.60 | | | | | | | GROUND_INST: instantiating (42) with false, all_235_0, true,
% 41.25/6.60 | | | | | | | simplifying with (36), (869) gives:
% 41.25/6.60 | | | | | | | (874) all_235_0 = false
% 41.25/6.60 | | | | | | |
% 41.25/6.60 | | | | | | | COMBINE_EQS: (872), (873) imply:
% 41.25/6.60 | | | | | | | (875) false2 = true
% 41.25/6.60 | | | | | | |
% 41.25/6.60 | | | | | | | SIMP: (875) implies:
% 41.25/6.60 | | | | | | | (876) false2 = true
% 41.25/6.60 | | | | | | |
% 41.25/6.60 | | | | | | | REDUCE: (735), (876) imply:
% 41.25/6.60 | | | | | | | (877) not1(true) = true
% 41.25/6.60 | | | | | | |
% 41.25/6.60 | | | | | | | REF_CLOSE: (36), (42), (137), (877) are inconsistent by sub-proof
% 41.25/6.60 | | | | | | | #1.
% 41.25/6.60 | | | | | | |
% 41.25/6.60 | | | | | | Case 2:
% 41.25/6.60 | | | | | | |
% 41.25/6.60 | | | | | | | (878) all_42_1 = false
% 41.25/6.60 | | | | | | |
% 41.25/6.60 | | | | | | | REDUCE: (867), (878) imply:
% 41.25/6.60 | | | | | | | (879) f2(true, true, false) = false2
% 41.25/6.60 | | | | | | |
% 41.25/6.60 | | | | | | | BETA: splitting (771) gives:
% 41.25/6.60 | | | | | | |
% 41.25/6.60 | | | | | | | Case 1:
% 41.25/6.60 | | | | | | | |
% 41.25/6.60 | | | | | | | | (880) all_237_0 = 0 & all_42_1 = false2
% 41.25/6.60 | | | | | | | |
% 41.25/6.60 | | | | | | | | ALPHA: (880) implies:
% 41.25/6.60 | | | | | | | | (881) all_42_1 = false2
% 41.25/6.60 | | | | | | | |
% 41.25/6.60 | | | | | | | | COMBINE_EQS: (878), (881) imply:
% 41.25/6.60 | | | | | | | | (882) false2 = false
% 41.25/6.60 | | | | | | | |
% 41.25/6.60 | | | | | | | | REDUCE: (53), (882) imply:
% 41.25/6.60 | | | | | | | | (883) $false
% 41.25/6.60 | | | | | | | |
% 41.25/6.60 | | | | | | | | CLOSE: (883) is inconsistent.
% 41.25/6.60 | | | | | | | |
% 41.25/6.60 | | | | | | | Case 2:
% 41.25/6.60 | | | | | | | |
% 41.25/6.60 | | | | | | | | (884) false2 = err & ~ (all_237_0 = 0)
% 41.25/6.60 | | | | | | | |
% 41.25/6.60 | | | | | | | | ALPHA: (884) implies:
% 41.25/6.60 | | | | | | | | (885) false2 = err
% 41.25/6.60 | | | | | | | |
% 41.25/6.60 | | | | | | | | REDUCE: (879), (885) imply:
% 41.25/6.60 | | | | | | | | (886) f2(true, true, false) = err
% 41.25/6.60 | | | | | | | |
% 41.25/6.60 | | | | | | | | REF_CLOSE: (4), (46), (404), (886) are inconsistent by sub-proof
% 41.25/6.60 | | | | | | | | #3.
% 41.25/6.60 | | | | | | | |
% 41.25/6.60 | | | | | | | End of split
% 41.25/6.60 | | | | | | |
% 41.25/6.60 | | | | | | End of split
% 41.25/6.60 | | | | | |
% 41.25/6.60 | | | | | End of split
% 41.25/6.60 | | | | |
% 41.25/6.60 | | | | Case 2:
% 41.25/6.60 | | | | |
% 41.25/6.60 | | | | | (887) ? [v0: int] : ( ~ (v0 = 0) & bool(all_42_1) = v0)
% 41.25/6.60 | | | | |
% 41.25/6.60 | | | | | DELTA: instantiating (887) with fresh symbol all_197_0 gives:
% 41.25/6.60 | | | | | (888) ~ (all_197_0 = 0) & bool(all_42_1) = all_197_0
% 41.25/6.60 | | | | |
% 41.25/6.60 | | | | | REF_CLOSE: (39), (740), (888) are inconsistent by sub-proof #2.
% 41.25/6.60 | | | | |
% 41.25/6.60 | | | | End of split
% 41.25/6.60 | | | |
% 41.25/6.60 | | | Case 2:
% 41.25/6.60 | | | |
% 41.25/6.60 | | | | (889) all_53_0 = false
% 41.25/6.60 | | | |
% 41.25/6.60 | | | | REDUCE: (187), (889) imply:
% 41.25/6.60 | | | | (890) not1(false) = all_105_0
% 41.25/6.60 | | | |
% 41.25/6.60 | | | | REDUCE: (145), (889) imply:
% 41.25/6.60 | | | | (891) lazy_and1(true, false) = all_79_0
% 41.25/6.60 | | | |
% 41.25/6.60 | | | | REDUCE: (736), (889) imply:
% 41.25/6.60 | | | | (892) lazy_impl(false, all_42_1) = false2
% 41.25/6.60 | | | |
% 41.25/6.60 | | | | BETA: splitting (140) gives:
% 41.25/6.60 | | | |
% 41.25/6.60 | | | | Case 1:
% 41.25/6.60 | | | | |
% 41.25/6.60 | | | | |
% 41.25/6.60 | | | | | GROUND_INST: instantiating (20) with all_42_1, false2, simplifying
% 41.25/6.60 | | | | | with (48), (892) gives:
% 41.25/6.60 | | | | | (893) false2 = true
% 41.25/6.60 | | | | |
% 41.25/6.60 | | | | | REDUCE: (735), (893) imply:
% 41.25/6.60 | | | | | (894) not1(true) = true
% 41.25/6.60 | | | | |
% 41.25/6.60 | | | | | REF_CLOSE: (36), (42), (137), (894) are inconsistent by sub-proof #1.
% 41.25/6.60 | | | | |
% 41.25/6.60 | | | | Case 2:
% 41.25/6.60 | | | | |
% 41.25/6.60 | | | | | (895) ~ (all_79_1 = 0)
% 41.25/6.60 | | | | |
% 41.25/6.60 | | | | | BETA: splitting (124) gives:
% 41.25/6.60 | | | | |
% 41.25/6.60 | | | | | Case 1:
% 41.25/6.60 | | | | | |
% 41.25/6.60 | | | | | | (896) all_79_1 = 0
% 41.25/6.60 | | | | | |
% 41.25/6.60 | | | | | | REDUCE: (895), (896) imply:
% 41.25/6.60 | | | | | | (897) $false
% 41.25/6.60 | | | | | |
% 41.25/6.60 | | | | | | CLOSE: (897) is inconsistent.
% 41.25/6.60 | | | | | |
% 41.25/6.60 | | | | | Case 2:
% 41.25/6.60 | | | | | |
% 41.25/6.60 | | | | | | (898) all_79_0 = all_42_0
% 41.25/6.60 | | | | | |
% 41.25/6.60 | | | | | | COMBINE_EQS: (734), (898) imply:
% 41.25/6.60 | | | | | | (899) all_79_0 = false2
% 41.25/6.60 | | | | | |
% 41.25/6.60 | | | | | | COMBINE_EQS: (421), (899) imply:
% 41.25/6.60 | | | | | | (900) all_162_0 = false2
% 41.25/6.60 | | | | | |
% 41.25/6.60 | | | | | | REDUCE: (891), (899) imply:
% 41.25/6.60 | | | | | | (901) lazy_and1(true, false) = false2
% 41.25/6.60 | | | | | |
% 41.25/6.60 | | | | | | BETA: splitting (141) gives:
% 41.25/6.60 | | | | | |
% 41.25/6.60 | | | | | | Case 1:
% 41.25/6.60 | | | | | | |
% 41.25/6.60 | | | | | | | (902) all_79_1 = 0
% 41.25/6.60 | | | | | | |
% 41.25/6.60 | | | | | | | REDUCE: (895), (902) imply:
% 41.25/6.60 | | | | | | | (903) $false
% 41.25/6.60 | | | | | | |
% 41.25/6.60 | | | | | | | CLOSE: (903) is inconsistent.
% 41.25/6.60 | | | | | | |
% 41.25/6.60 | | | | | | Case 2:
% 41.25/6.60 | | | | | | |
% 41.25/6.60 | | | | | | | (904) ? [v0: $i] : (not1(all_53_0) = v0 & phi(all_53_0) = v0 &
% 41.25/6.60 | | | | | | | $i(v0))
% 41.25/6.60 | | | | | | |
% 41.25/6.60 | | | | | | | DELTA: instantiating (904) with fresh symbol all_212_0 gives:
% 41.25/6.60 | | | | | | | (905) not1(all_53_0) = all_212_0 & phi(all_53_0) = all_212_0 &
% 41.25/6.60 | | | | | | | $i(all_212_0)
% 41.25/6.60 | | | | | | |
% 41.25/6.60 | | | | | | | ALPHA: (905) implies:
% 41.25/6.60 | | | | | | | (906) not1(all_53_0) = all_212_0
% 41.25/6.60 | | | | | | |
% 41.25/6.60 | | | | | | | REDUCE: (889), (906) imply:
% 41.25/6.60 | | | | | | | (907) not1(false) = all_212_0
% 41.25/6.60 | | | | | | |
% 41.25/6.60 | | | | | | | BETA: splitting (176) gives:
% 41.25/6.60 | | | | | | |
% 41.25/6.60 | | | | | | | Case 1:
% 41.25/6.60 | | | | | | | |
% 41.25/6.60 | | | | | | | | (908) all_99_0 = 0 & all_79_0 = all_53_0
% 41.25/6.60 | | | | | | | |
% 41.25/6.60 | | | | | | | | ALPHA: (908) implies:
% 41.25/6.60 | | | | | | | | (909) all_79_0 = all_53_0
% 41.25/6.60 | | | | | | | |
% 41.25/6.60 | | | | | | | | COMBINE_EQS: (899), (909) imply:
% 41.25/6.60 | | | | | | | | (910) all_53_0 = false2
% 41.25/6.60 | | | | | | | |
% 41.25/6.60 | | | | | | | | COMBINE_EQS: (889), (910) imply:
% 41.25/6.60 | | | | | | | | (911) false2 = false
% 41.25/6.60 | | | | | | | |
% 41.25/6.60 | | | | | | | | SIMP: (911) implies:
% 41.25/6.60 | | | | | | | | (912) false2 = false
% 41.25/6.60 | | | | | | | |
% 41.25/6.60 | | | | | | | | REDUCE: (53), (912) imply:
% 41.25/6.60 | | | | | | | | (913) $false
% 41.25/6.60 | | | | | | | |
% 41.25/6.60 | | | | | | | | CLOSE: (913) is inconsistent.
% 41.25/6.60 | | | | | | | |
% 41.25/6.60 | | | | | | | Case 2:
% 41.25/6.60 | | | | | | | |
% 41.25/6.60 | | | | | | | | (914) all_79_0 = err & ~ (all_99_0 = 0)
% 41.25/6.60 | | | | | | | |
% 41.25/6.60 | | | | | | | | ALPHA: (914) implies:
% 41.25/6.60 | | | | | | | | (915) all_79_0 = err
% 41.25/6.60 | | | | | | | |
% 41.25/6.60 | | | | | | | | COMBINE_EQS: (899), (915) imply:
% 41.25/6.60 | | | | | | | | (916) false2 = err
% 41.25/6.60 | | | | | | | |
% 41.25/6.60 | | | | | | | | COMBINE_EQS: (900), (916) imply:
% 41.25/6.60 | | | | | | | | (917) all_162_0 = err
% 41.25/6.60 | | | | | | | |
% 41.25/6.60 | | | | | | | | REDUCE: (901), (916) imply:
% 41.25/6.60 | | | | | | | | (918) lazy_and1(true, false) = err
% 41.25/6.60 | | | | | | | |
% 41.25/6.60 | | | | | | | | BETA: splitting (415) gives:
% 41.25/6.60 | | | | | | | |
% 41.25/6.60 | | | | | | | | Case 1:
% 41.25/6.60 | | | | | | | | |
% 41.25/6.60 | | | | | | | | | (919) all_162_1 = 0
% 41.25/6.60 | | | | | | | | |
% 41.25/6.60 | | | | | | | | | COMBINE_EQS: (418), (919) imply:
% 41.25/6.60 | | | | | | | | | (920) all_79_1 = 0
% 41.25/6.60 | | | | | | | | |
% 41.25/6.60 | | | | | | | | | SIMP: (920) implies:
% 41.25/6.60 | | | | | | | | | (921) all_79_1 = 0
% 41.25/6.60 | | | | | | | | |
% 41.25/6.60 | | | | | | | | | REDUCE: (895), (921) imply:
% 41.25/6.60 | | | | | | | | | (922) $false
% 41.25/6.60 | | | | | | | | |
% 41.25/6.60 | | | | | | | | | CLOSE: (922) is inconsistent.
% 41.25/6.60 | | | | | | | | |
% 41.25/6.60 | | | | | | | | Case 2:
% 41.25/6.60 | | | | | | | | |
% 41.25/6.60 | | | | | | | | | (923) all_162_0 = all_105_0
% 41.25/6.60 | | | | | | | | |
% 41.25/6.60 | | | | | | | | | COMBINE_EQS: (917), (923) imply:
% 41.25/6.60 | | | | | | | | | (924) all_105_0 = err
% 41.25/6.60 | | | | | | | | |
% 41.25/6.60 | | | | | | | | | SIMP: (924) implies:
% 41.25/6.60 | | | | | | | | | (925) all_105_0 = err
% 41.25/6.60 | | | | | | | | |
% 41.25/6.60 | | | | | | | | | REDUCE: (890), (925) imply:
% 41.25/6.60 | | | | | | | | | (926) not1(false) = err
% 41.25/6.60 | | | | | | | | |
% 41.25/6.60 | | | | | | | | | GROUND_INST: instantiating (45) with false, err, false, true,
% 41.25/6.60 | | | | | | | | | simplifying with (101), (918) gives:
% 41.25/6.60 | | | | | | | | | (927) err = false
% 41.25/6.60 | | | | | | | | |
% 41.25/6.60 | | | | | | | | | GROUND_INST: instantiating (42) with true, all_212_0, false,
% 41.25/6.60 | | | | | | | | | simplifying with (34), (907) gives:
% 41.25/6.60 | | | | | | | | | (928) all_212_0 = true
% 41.25/6.60 | | | | | | | | |
% 41.25/6.60 | | | | | | | | | GROUND_INST: instantiating (42) with err, all_212_0, false,
% 41.25/6.60 | | | | | | | | | simplifying with (907), (926) gives:
% 41.25/6.60 | | | | | | | | | (929) all_212_0 = err
% 41.25/6.60 | | | | | | | | |
% 41.25/6.60 | | | | | | | | | COMBINE_EQS: (928), (929) imply:
% 41.25/6.60 | | | | | | | | | (930) err = true
% 41.25/6.60 | | | | | | | | |
% 41.25/6.60 | | | | | | | | | SIMP: (930) implies:
% 41.25/6.60 | | | | | | | | | (931) err = true
% 41.25/6.60 | | | | | | | | |
% 41.25/6.60 | | | | | | | | | COMBINE_EQS: (927), (931) imply:
% 41.25/6.60 | | | | | | | | | (932) true = false
% 41.25/6.60 | | | | | | | | |
% 41.25/6.60 | | | | | | | | | SIMP: (932) implies:
% 41.25/6.60 | | | | | | | | | (933) true = false
% 41.25/6.60 | | | | | | | | |
% 41.25/6.60 | | | | | | | | | REDUCE: (137), (933) imply:
% 41.25/6.60 | | | | | | | | | (934) $false
% 41.25/6.60 | | | | | | | | |
% 41.25/6.60 | | | | | | | | | CLOSE: (934) is inconsistent.
% 41.25/6.60 | | | | | | | | |
% 41.25/6.60 | | | | | | | | End of split
% 41.25/6.60 | | | | | | | |
% 41.25/6.60 | | | | | | | End of split
% 41.25/6.60 | | | | | | |
% 41.25/6.60 | | | | | | End of split
% 41.25/6.60 | | | | | |
% 41.25/6.60 | | | | | End of split
% 41.25/6.60 | | | | |
% 41.25/6.60 | | | | End of split
% 41.25/6.60 | | | |
% 41.25/6.60 | | | End of split
% 41.25/6.60 | | |
% 41.25/6.60 | | Case 2:
% 41.25/6.60 | | |
% 41.25/6.60 | | | (935) false2 = err & ~ (all_59_0 = 0)
% 41.25/6.60 | | |
% 41.25/6.60 | | | ALPHA: (935) implies:
% 41.25/6.60 | | | (936) false2 = err
% 41.25/6.60 | | |
% 41.25/6.60 | | | REDUCE: (732), (936) imply:
% 41.25/6.60 | | | (937) not1(all_42_0) = err
% 41.25/6.60 | | |
% 41.25/6.60 | | | REDUCE: (61), (936) imply:
% 41.25/6.60 | | | (938) lazy_and1(true, all_42_0) = err
% 41.25/6.60 | | |
% 41.25/6.60 | | | REDUCE: (50), (936) imply:
% 41.25/6.60 | | | (939) phi(all_42_0) = err
% 41.25/6.60 | | |
% 41.25/6.60 | | | BETA: splitting (108) gives:
% 41.25/6.60 | | |
% 41.25/6.60 | | | Case 1:
% 41.25/6.60 | | | |
% 41.25/6.60 | | | | (940) bool(all_42_1) = 0
% 41.25/6.60 | | | |
% 41.25/6.61 | | | | BETA: splitting (107) gives:
% 41.25/6.61 | | | |
% 41.25/6.61 | | | | Case 1:
% 41.25/6.61 | | | | |
% 41.25/6.61 | | | | | (941) all_53_0 = true
% 41.25/6.61 | | | | |
% 41.25/6.61 | | | | | REDUCE: (187), (941) imply:
% 41.25/6.61 | | | | | (942) not1(true) = all_105_0
% 41.25/6.61 | | | | |
% 41.25/6.61 | | | | | REDUCE: (145), (941) imply:
% 41.25/6.61 | | | | | (943) lazy_and1(true, true) = all_79_0
% 41.25/6.61 | | | | |
% 41.25/6.61 | | | | | REDUCE: (70), (941) imply:
% 41.25/6.61 | | | | | (944) lazy_impl(true, all_42_1) = all_42_0
% 41.25/6.61 | | | | |
% 41.25/6.61 | | | | | REDUCE: (147), (941) imply:
% 41.25/6.61 | | | | | (945) lazy_impl(true, true) = all_79_0
% 41.25/6.61 | | | | |
% 41.25/6.61 | | | | | REDUCE: (69), (941) imply:
% 41.25/6.61 | | | | | (946) prop(all_42_1) = true
% 41.25/6.61 | | | | |
% 41.25/6.61 | | | | | GROUND_INST: instantiating (45) with true, all_79_0, true, true,
% 41.25/6.61 | | | | | simplifying with (103), (943) gives:
% 41.25/6.61 | | | | | (947) all_79_0 = true
% 41.25/6.61 | | | | |
% 41.25/6.61 | | | | | GROUND_INST: instantiating (42) with false, all_105_0, true,
% 41.25/6.61 | | | | | simplifying with (36), (942) gives:
% 41.25/6.61 | | | | | (948) all_105_0 = false
% 41.25/6.61 | | | | |
% 41.25/6.61 | | | | | GROUND_INST: instantiating (3) with all_42_1, simplifying with (48),
% 41.25/6.61 | | | | | (940) gives:
% 41.25/6.61 | | | | | (949) all_42_1 = true | all_42_1 = false
% 41.25/6.61 | | | | |
% 41.25/6.61 | | | | | GROUND_INST: instantiating (19) with all_42_1, simplifying with (48),
% 41.25/6.61 | | | | | (940) gives:
% 41.25/6.61 | | | | | (950) impl(true, all_42_1) = all_42_1
% 41.25/6.61 | | | | |
% 41.25/6.61 | | | | | GROUND_INST: instantiating (18) with all_42_1, simplifying with (48),
% 41.25/6.61 | | | | | (940) gives:
% 41.25/6.61 | | | | | (951) impl(false, all_42_1) = true
% 41.25/6.61 | | | | |
% 41.25/6.61 | | | | | GROUND_INST: instantiating (23) with true, false, all_42_1, true,
% 41.25/6.61 | | | | | true, simplifying with (35), (48), (54), (96), (951)
% 41.25/6.61 | | | | | gives:
% 41.25/6.61 | | | | | (952) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (f1(true, false,
% 41.25/6.61 | | | | | all_42_1) = v0 & lazy_impl(v1, v2) = v0 & impl(true,
% 41.25/6.61 | | | | | all_42_1) = v2 & prop(all_42_1) = v1 & $i(v2) & $i(v1) &
% 41.25/6.61 | | | | | $i(v0))
% 41.25/6.61 | | | | |
% 41.25/6.61 | | | | | GROUND_INST: instantiating (23) with false, false, all_42_1, true,
% 41.25/6.61 | | | | | true, simplifying with (48), (54), (97), (951) gives:
% 41.25/6.61 | | | | | (953) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (f1(false, false,
% 41.25/6.61 | | | | | all_42_1) = v0 & lazy_impl(v1, v2) = v0 & impl(true,
% 41.25/6.61 | | | | | all_42_1) = v2 & prop(all_42_1) = v1 & $i(v2) & $i(v1) &
% 41.25/6.61 | | | | | $i(v0))
% 41.25/6.61 | | | | |
% 41.25/6.61 | | | | | GROUND_INST: instantiating (25) with true, false, all_42_1, true,
% 41.25/6.61 | | | | | true, simplifying with (35), (48), (54), (104), (951)
% 41.25/6.61 | | | | | gives:
% 41.25/6.61 | | | | | (954) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (f2(true, false,
% 41.25/6.61 | | | | | all_42_1) = v0 & lazy_impl(v1, v2) = v0 & impl(true,
% 41.25/6.61 | | | | | all_42_1) = v2 & prop(all_42_1) = v1 & $i(v2) & $i(v1) &
% 41.25/6.61 | | | | | $i(v0))
% 41.25/6.61 | | | | |
% 41.25/6.61 | | | | | GROUND_INST: instantiating (26) with false, false, all_42_1, true,
% 41.25/6.61 | | | | | true, all_42_1, all_42_1, simplifying with (48), (54),
% 41.25/6.61 | | | | | (950), (951) gives:
% 41.25/6.61 | | | | | (955) ? [v0: $i] : ? [v1: $i] : (f3(false, false, all_42_1) = v0
% 41.25/6.61 | | | | | & lazy_impl(v1, all_42_1) = v0 & prop(all_42_1) = v1 &
% 41.25/6.61 | | | | | $i(v1) & $i(v0))
% 41.25/6.61 | | | | |
% 41.25/6.61 | | | | | GROUND_INST: instantiating (23) with true, true, all_42_1, all_42_1,
% 41.25/6.61 | | | | | all_42_1, simplifying with (35), (48), (950) gives:
% 41.25/6.61 | | | | | (956) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (f1(true, true,
% 41.25/6.61 | | | | | all_42_1) = v0 & lazy_impl(v1, v2) = v0 & impl(all_42_1,
% 41.25/6.61 | | | | | all_42_1) = v2 & prop(all_42_1) = v1 & $i(v2) & $i(v1) &
% 41.25/6.61 | | | | | $i(v0))
% 41.25/6.61 | | | | |
% 41.25/6.61 | | | | | GROUND_INST: instantiating (23) with false, true, all_42_1, all_42_1,
% 41.25/6.61 | | | | | true, simplifying with (35), (48), (54), (950), (951)
% 41.25/6.61 | | | | | gives:
% 41.25/6.61 | | | | | (957) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (f1(false, true,
% 41.25/6.61 | | | | | all_42_1) = v0 & lazy_impl(v1, v2) = v0 & impl(true,
% 41.25/6.61 | | | | | all_42_1) = v2 & prop(all_42_1) = v1 & $i(v2) & $i(v1) &
% 41.25/6.61 | | | | | $i(v0))
% 41.25/6.61 | | | | |
% 41.25/6.61 | | | | | GROUND_INST: instantiating (25) with true, true, all_42_1, all_42_1,
% 41.25/6.61 | | | | | all_42_0, simplifying with (35), (48), (944), (950)
% 41.25/6.61 | | | | | gives:
% 41.25/6.61 | | | | | (958) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (f2(true, true,
% 41.25/6.61 | | | | | all_42_1) = v0 & lazy_impl(v1, v2) = v0 & impl(all_42_0,
% 41.25/6.61 | | | | | all_42_1) = v2 & prop(all_42_1) = v1 & $i(v2) & $i(v1) &
% 41.25/6.61 | | | | | $i(v0))
% 41.25/6.61 | | | | |
% 41.25/6.61 | | | | | DELTA: instantiating (955) with fresh symbols all_233_0, all_233_1
% 41.25/6.61 | | | | | gives:
% 41.25/6.61 | | | | | (959) f3(false, false, all_42_1) = all_233_1 & lazy_impl(all_233_0,
% 41.25/6.61 | | | | | all_42_1) = all_233_1 & prop(all_42_1) = all_233_0 &
% 41.25/6.61 | | | | | $i(all_233_0) & $i(all_233_1)
% 41.25/6.61 | | | | |
% 41.25/6.61 | | | | | ALPHA: (959) implies:
% 41.25/6.61 | | | | | (960) $i(all_233_1)
% 41.25/6.61 | | | | | (961) $i(all_233_0)
% 41.25/6.61 | | | | | (962) prop(all_42_1) = all_233_0
% 41.25/6.61 | | | | | (963) lazy_impl(all_233_0, all_42_1) = all_233_1
% 41.25/6.61 | | | | |
% 41.25/6.61 | | | | | DELTA: instantiating (954) with fresh symbols all_239_0, all_239_1,
% 41.25/6.61 | | | | | all_239_2 gives:
% 41.25/6.61 | | | | | (964) f2(true, false, all_42_1) = all_239_2 & lazy_impl(all_239_1,
% 41.25/6.61 | | | | | all_239_0) = all_239_2 & impl(true, all_42_1) = all_239_0 &
% 41.25/6.61 | | | | | prop(all_42_1) = all_239_1 & $i(all_239_0) & $i(all_239_1) &
% 41.25/6.61 | | | | | $i(all_239_2)
% 41.25/6.61 | | | | |
% 41.25/6.61 | | | | | ALPHA: (964) implies:
% 41.25/6.61 | | | | | (965) $i(all_239_0)
% 41.25/6.61 | | | | | (966) prop(all_42_1) = all_239_1
% 41.25/6.61 | | | | | (967) impl(true, all_42_1) = all_239_0
% 41.25/6.61 | | | | | (968) lazy_impl(all_239_1, all_239_0) = all_239_2
% 41.25/6.61 | | | | |
% 41.25/6.61 | | | | | DELTA: instantiating (953) with fresh symbols all_241_0, all_241_1,
% 41.25/6.61 | | | | | all_241_2 gives:
% 41.25/6.61 | | | | | (969) f1(false, false, all_42_1) = all_241_2 & lazy_impl(all_241_1,
% 41.25/6.61 | | | | | all_241_0) = all_241_2 & impl(true, all_42_1) = all_241_0 &
% 41.25/6.61 | | | | | prop(all_42_1) = all_241_1 & $i(all_241_0) & $i(all_241_1) &
% 41.25/6.61 | | | | | $i(all_241_2)
% 41.25/6.61 | | | | |
% 41.25/6.61 | | | | | ALPHA: (969) implies:
% 41.25/6.61 | | | | | (970) prop(all_42_1) = all_241_1
% 41.25/6.61 | | | | | (971) impl(true, all_42_1) = all_241_0
% 41.25/6.61 | | | | | (972) lazy_impl(all_241_1, all_241_0) = all_241_2
% 41.25/6.61 | | | | |
% 41.25/6.61 | | | | | DELTA: instantiating (952) with fresh symbols all_243_0, all_243_1,
% 41.25/6.61 | | | | | all_243_2 gives:
% 41.25/6.61 | | | | | (973) f1(true, false, all_42_1) = all_243_2 & lazy_impl(all_243_1,
% 41.25/6.61 | | | | | all_243_0) = all_243_2 & impl(true, all_42_1) = all_243_0 &
% 41.25/6.61 | | | | | prop(all_42_1) = all_243_1 & $i(all_243_0) & $i(all_243_1) &
% 41.25/6.61 | | | | | $i(all_243_2)
% 41.25/6.61 | | | | |
% 41.25/6.61 | | | | | ALPHA: (973) implies:
% 41.25/6.61 | | | | | (974) prop(all_42_1) = all_243_1
% 41.25/6.61 | | | | | (975) impl(true, all_42_1) = all_243_0
% 41.25/6.61 | | | | | (976) lazy_impl(all_243_1, all_243_0) = all_243_2
% 41.25/6.61 | | | | |
% 41.25/6.61 | | | | | DELTA: instantiating (958) with fresh symbols all_245_0, all_245_1,
% 41.25/6.61 | | | | | all_245_2 gives:
% 41.25/6.61 | | | | | (977) f2(true, true, all_42_1) = all_245_2 & lazy_impl(all_245_1,
% 41.25/6.61 | | | | | all_245_0) = all_245_2 & impl(all_42_0, all_42_1) =
% 41.25/6.61 | | | | | all_245_0 & prop(all_42_1) = all_245_1 & $i(all_245_0) &
% 41.25/6.61 | | | | | $i(all_245_1) & $i(all_245_2)
% 41.25/6.61 | | | | |
% 41.25/6.61 | | | | | ALPHA: (977) implies:
% 41.25/6.61 | | | | | (978) prop(all_42_1) = all_245_1
% 41.25/6.61 | | | | | (979) impl(all_42_0, all_42_1) = all_245_0
% 41.25/6.61 | | | | | (980) lazy_impl(all_245_1, all_245_0) = all_245_2
% 41.25/6.61 | | | | | (981) f2(true, true, all_42_1) = all_245_2
% 41.25/6.61 | | | | |
% 41.25/6.61 | | | | | DELTA: instantiating (956) with fresh symbols all_247_0, all_247_1,
% 41.25/6.61 | | | | | all_247_2 gives:
% 41.25/6.61 | | | | | (982) f1(true, true, all_42_1) = all_247_2 & lazy_impl(all_247_1,
% 41.25/6.61 | | | | | all_247_0) = all_247_2 & impl(all_42_1, all_42_1) =
% 41.25/6.61 | | | | | all_247_0 & prop(all_42_1) = all_247_1 & $i(all_247_0) &
% 41.25/6.61 | | | | | $i(all_247_1) & $i(all_247_2)
% 41.25/6.61 | | | | |
% 41.25/6.61 | | | | | ALPHA: (982) implies:
% 41.25/6.61 | | | | | (983) prop(all_42_1) = all_247_1
% 41.25/6.61 | | | | | (984) impl(all_42_1, all_42_1) = all_247_0
% 41.25/6.61 | | | | | (985) lazy_impl(all_247_1, all_247_0) = all_247_2
% 41.25/6.61 | | | | |
% 41.25/6.61 | | | | | DELTA: instantiating (957) with fresh symbols all_249_0, all_249_1,
% 41.25/6.61 | | | | | all_249_2 gives:
% 41.25/6.61 | | | | | (986) f1(false, true, all_42_1) = all_249_2 & lazy_impl(all_249_1,
% 41.25/6.61 | | | | | all_249_0) = all_249_2 & impl(true, all_42_1) = all_249_0 &
% 41.25/6.61 | | | | | prop(all_42_1) = all_249_1 & $i(all_249_0) & $i(all_249_1) &
% 41.25/6.61 | | | | | $i(all_249_2)
% 41.25/6.61 | | | | |
% 41.25/6.61 | | | | | ALPHA: (986) implies:
% 41.25/6.61 | | | | | (987) prop(all_42_1) = all_249_1
% 41.25/6.61 | | | | | (988) impl(true, all_42_1) = all_249_0
% 41.25/6.61 | | | | | (989) lazy_impl(all_249_1, all_249_0) = all_249_2
% 41.25/6.61 | | | | |
% 41.25/6.61 | | | | | GROUND_INST: instantiating (41) with all_233_0, all_241_1, all_42_1,
% 41.25/6.61 | | | | | simplifying with (962), (970) gives:
% 41.25/6.61 | | | | | (990) all_241_1 = all_233_0
% 41.25/6.61 | | | | |
% 41.25/6.61 | | | | | GROUND_INST: instantiating (41) with all_241_1, all_243_1, all_42_1,
% 41.25/6.61 | | | | | simplifying with (970), (974) gives:
% 41.25/6.61 | | | | | (991) all_243_1 = all_241_1
% 41.25/6.61 | | | | |
% 41.25/6.61 | | | | | GROUND_INST: instantiating (41) with all_239_1, all_243_1, all_42_1,
% 41.25/6.61 | | | | | simplifying with (966), (974) gives:
% 41.25/6.61 | | | | | (992) all_243_1 = all_239_1
% 41.25/6.61 | | | | |
% 41.25/6.61 | | | | | GROUND_INST: instantiating (41) with all_243_1, all_245_1, all_42_1,
% 41.25/6.61 | | | | | simplifying with (974), (978) gives:
% 41.25/6.61 | | | | | (993) all_245_1 = all_243_1
% 41.25/6.61 | | | | |
% 41.25/6.61 | | | | | GROUND_INST: instantiating (41) with true, all_249_1, all_42_1,
% 41.25/6.61 | | | | | simplifying with (946), (987) gives:
% 41.25/6.61 | | | | | (994) all_249_1 = true
% 41.25/6.61 | | | | |
% 41.25/6.61 | | | | | GROUND_INST: instantiating (41) with all_247_1, all_249_1, all_42_1,
% 41.25/6.61 | | | | | simplifying with (983), (987) gives:
% 41.25/6.61 | | | | | (995) all_249_1 = all_247_1
% 41.25/6.61 | | | | |
% 41.25/6.61 | | | | | GROUND_INST: instantiating (41) with all_245_1, all_249_1, all_42_1,
% 41.25/6.61 | | | | | simplifying with (978), (987) gives:
% 41.25/6.61 | | | | | (996) all_249_1 = all_245_1
% 41.25/6.61 | | | | |
% 41.25/6.61 | | | | | GROUND_INST: instantiating (43) with all_42_1, all_241_0, all_42_1,
% 41.25/6.61 | | | | | true, simplifying with (950), (971) gives:
% 41.25/6.61 | | | | | (997) all_241_0 = all_42_1
% 41.25/6.61 | | | | |
% 41.25/6.61 | | | | | GROUND_INST: instantiating (43) with all_241_0, all_243_0, all_42_1,
% 41.25/6.61 | | | | | true, simplifying with (971), (975) gives:
% 41.25/6.61 | | | | | (998) all_243_0 = all_241_0
% 41.25/6.61 | | | | |
% 41.25/6.61 | | | | | GROUND_INST: instantiating (43) with all_243_0, all_249_0, all_42_1,
% 41.25/6.61 | | | | | true, simplifying with (975), (988) gives:
% 41.25/6.61 | | | | | (999) all_249_0 = all_243_0
% 41.25/6.61 | | | | |
% 41.25/6.61 | | | | | GROUND_INST: instantiating (43) with all_239_0, all_249_0, all_42_1,
% 41.25/6.61 | | | | | true, simplifying with (967), (988) gives:
% 41.25/6.61 | | | | | (1000) all_249_0 = all_239_0
% 41.25/6.61 | | | | |
% 41.25/6.61 | | | | | COMBINE_EQS: (999), (1000) imply:
% 41.25/6.61 | | | | | (1001) all_243_0 = all_239_0
% 41.25/6.61 | | | | |
% 41.25/6.61 | | | | | SIMP: (1001) implies:
% 41.25/6.61 | | | | | (1002) all_243_0 = all_239_0
% 41.25/6.61 | | | | |
% 41.25/6.61 | | | | | COMBINE_EQS: (995), (996) imply:
% 41.25/6.61 | | | | | (1003) all_247_1 = all_245_1
% 41.25/6.61 | | | | |
% 41.25/6.61 | | | | | COMBINE_EQS: (994), (995) imply:
% 41.25/6.61 | | | | | (1004) all_247_1 = true
% 41.25/6.61 | | | | |
% 41.25/6.61 | | | | | COMBINE_EQS: (1003), (1004) imply:
% 41.25/6.61 | | | | | (1005) all_245_1 = true
% 41.25/6.61 | | | | |
% 41.25/6.61 | | | | | SIMP: (1005) implies:
% 41.25/6.61 | | | | | (1006) all_245_1 = true
% 41.25/6.61 | | | | |
% 41.25/6.61 | | | | | COMBINE_EQS: (993), (1006) imply:
% 41.25/6.61 | | | | | (1007) all_243_1 = true
% 41.25/6.61 | | | | |
% 41.25/6.61 | | | | | SIMP: (1007) implies:
% 41.25/6.61 | | | | | (1008) all_243_1 = true
% 41.25/6.61 | | | | |
% 41.25/6.61 | | | | | COMBINE_EQS: (998), (1002) imply:
% 41.25/6.61 | | | | | (1009) all_241_0 = all_239_0
% 41.25/6.61 | | | | |
% 41.25/6.61 | | | | | SIMP: (1009) implies:
% 41.25/6.61 | | | | | (1010) all_241_0 = all_239_0
% 41.25/6.61 | | | | |
% 41.25/6.61 | | | | | COMBINE_EQS: (991), (992) imply:
% 41.25/6.61 | | | | | (1011) all_241_1 = all_239_1
% 41.25/6.61 | | | | |
% 41.25/6.61 | | | | | SIMP: (1011) implies:
% 41.25/6.61 | | | | | (1012) all_241_1 = all_239_1
% 41.25/6.61 | | | | |
% 41.25/6.61 | | | | | COMBINE_EQS: (992), (1008) imply:
% 41.25/6.61 | | | | | (1013) all_239_1 = true
% 41.25/6.61 | | | | |
% 41.25/6.61 | | | | | COMBINE_EQS: (997), (1010) imply:
% 41.25/6.61 | | | | | (1014) all_239_0 = all_42_1
% 41.25/6.61 | | | | |
% 41.25/6.61 | | | | | COMBINE_EQS: (990), (1012) imply:
% 41.25/6.61 | | | | | (1015) all_239_1 = all_233_0
% 41.25/6.61 | | | | |
% 41.25/6.61 | | | | | SIMP: (1015) implies:
% 41.25/6.61 | | | | | (1016) all_239_1 = all_233_0
% 41.25/6.61 | | | | |
% 41.25/6.61 | | | | | COMBINE_EQS: (1013), (1016) imply:
% 41.25/6.61 | | | | | (1017) all_233_0 = true
% 41.25/6.61 | | | | |
% 41.25/6.61 | | | | | SIMP: (1017) implies:
% 41.25/6.61 | | | | | (1018) all_233_0 = true
% 41.25/6.61 | | | | |
% 41.25/6.61 | | | | | COMBINE_EQS: (990), (1018) imply:
% 41.25/6.61 | | | | | (1019) all_241_1 = true
% 41.25/6.61 | | | | |
% 41.25/6.61 | | | | | COMBINE_EQS: (1002), (1014) imply:
% 41.25/6.61 | | | | | (1020) all_243_0 = all_42_1
% 41.25/6.61 | | | | |
% 41.25/6.61 | | | | | COMBINE_EQS: (1000), (1014) imply:
% 41.25/6.61 | | | | | (1021) all_249_0 = all_42_1
% 41.25/6.61 | | | | |
% 41.25/6.61 | | | | | REDUCE: (989), (994), (1021) imply:
% 41.25/6.61 | | | | | (1022) lazy_impl(true, all_42_1) = all_249_2
% 41.25/6.61 | | | | |
% 41.25/6.61 | | | | | REDUCE: (985), (1004) imply:
% 41.25/6.61 | | | | | (1023) lazy_impl(true, all_247_0) = all_247_2
% 41.25/6.61 | | | | |
% 41.25/6.61 | | | | | REDUCE: (980), (1006) imply:
% 41.25/6.61 | | | | | (1024) lazy_impl(true, all_245_0) = all_245_2
% 41.25/6.61 | | | | |
% 41.25/6.61 | | | | | REDUCE: (976), (1008), (1020) imply:
% 41.25/6.61 | | | | | (1025) lazy_impl(true, all_42_1) = all_243_2
% 41.25/6.61 | | | | |
% 41.25/6.61 | | | | | REDUCE: (972), (997), (1019) imply:
% 41.25/6.61 | | | | | (1026) lazy_impl(true, all_42_1) = all_241_2
% 41.25/6.61 | | | | |
% 41.25/6.61 | | | | | REDUCE: (968), (1013), (1014) imply:
% 41.25/6.61 | | | | | (1027) lazy_impl(true, all_42_1) = all_239_2
% 41.25/6.61 | | | | |
% 41.25/6.61 | | | | | REDUCE: (963), (1018) imply:
% 41.25/6.61 | | | | | (1028) lazy_impl(true, all_42_1) = all_233_1
% 41.25/6.61 | | | | |
% 41.25/6.61 | | | | | GROUND_INST: instantiating (44) with all_42_0, all_239_2, all_42_1,
% 41.25/6.61 | | | | | true, simplifying with (944), (1027) gives:
% 41.25/6.61 | | | | | (1029) all_239_2 = all_42_0
% 41.25/6.61 | | | | |
% 41.25/6.61 | | | | | GROUND_INST: instantiating (44) with all_241_2, all_243_2, all_42_1,
% 41.25/6.61 | | | | | true, simplifying with (1025), (1026) gives:
% 41.25/6.61 | | | | | (1030) all_243_2 = all_241_2
% 41.25/6.61 | | | | |
% 41.25/6.61 | | | | | GROUND_INST: instantiating (44) with all_239_2, all_243_2, all_42_1,
% 41.25/6.61 | | | | | true, simplifying with (1025), (1027) gives:
% 41.25/6.61 | | | | | (1031) all_243_2 = all_239_2
% 41.25/6.61 | | | | |
% 41.25/6.61 | | | | | GROUND_INST: instantiating (44) with all_243_2, all_249_2, all_42_1,
% 41.25/6.61 | | | | | true, simplifying with (1022), (1025) gives:
% 41.25/6.61 | | | | | (1032) all_249_2 = all_243_2
% 41.25/6.61 | | | | |
% 41.25/6.61 | | | | | GROUND_INST: instantiating (44) with all_233_1, all_249_2, all_42_1,
% 41.25/6.61 | | | | | true, simplifying with (1022), (1028) gives:
% 41.25/6.61 | | | | | (1033) all_249_2 = all_233_1
% 41.25/6.61 | | | | |
% 41.25/6.61 | | | | | COMBINE_EQS: (1032), (1033) imply:
% 41.25/6.61 | | | | | (1034) all_243_2 = all_233_1
% 41.25/6.61 | | | | |
% 41.25/6.61 | | | | | SIMP: (1034) implies:
% 41.25/6.61 | | | | | (1035) all_243_2 = all_233_1
% 41.25/6.61 | | | | |
% 41.25/6.61 | | | | | COMBINE_EQS: (1030), (1031) imply:
% 41.25/6.61 | | | | | (1036) all_241_2 = all_239_2
% 41.25/6.61 | | | | |
% 41.25/6.61 | | | | | COMBINE_EQS: (1030), (1035) imply:
% 41.25/6.61 | | | | | (1037) all_241_2 = all_233_1
% 41.25/6.61 | | | | |
% 41.25/6.61 | | | | | COMBINE_EQS: (1036), (1037) imply:
% 41.25/6.61 | | | | | (1038) all_239_2 = all_233_1
% 41.25/6.61 | | | | |
% 41.25/6.61 | | | | | SIMP: (1038) implies:
% 41.25/6.61 | | | | | (1039) all_239_2 = all_233_1
% 41.25/6.61 | | | | |
% 41.25/6.61 | | | | | COMBINE_EQS: (1029), (1039) imply:
% 41.25/6.61 | | | | | (1040) all_233_1 = all_42_0
% 41.25/6.61 | | | | |
% 41.25/6.61 | | | | | GROUND_INST: instantiating (impl_axiom1) with all_42_0, all_42_1,
% 41.25/6.61 | | | | | all_245_0, simplifying with (48), (49), (979) gives:
% 41.25/6.62 | | | | | (1041) ? [v0: any] : ? [v1: $i] : (phi(all_42_0) = v1 &
% 41.25/6.62 | | | | | bool(all_42_0) = v0 & $i(v1) & (v1 = all_245_0 | v0 = 0))
% 41.25/6.62 | | | | |
% 41.25/6.62 | | | | | GROUND_INST: instantiating (25) with true, all_42_1, all_42_1,
% 41.25/6.62 | | | | | all_247_0, all_247_2, simplifying with (35), (48), (984),
% 41.25/6.62 | | | | | (1023) gives:
% 41.25/6.62 | | | | | (1042) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (f2(true,
% 41.25/6.62 | | | | | all_42_1, all_42_1) = v0 & lazy_impl(v1, v2) = v0 &
% 41.25/6.62 | | | | | impl(all_247_2, all_42_1) = v2 & prop(all_42_1) = v1 &
% 41.25/6.62 | | | | | $i(v2) & $i(v1) & $i(v0))
% 41.25/6.62 | | | | |
% 41.25/6.62 | | | | | DELTA: instantiating (1041) with fresh symbols all_267_0, all_267_1
% 41.25/6.62 | | | | | gives:
% 41.25/6.62 | | | | | (1043) phi(all_42_0) = all_267_0 & bool(all_42_0) = all_267_1 &
% 41.25/6.62 | | | | | $i(all_267_0) & (all_267_0 = all_245_0 | all_267_1 = 0)
% 41.25/6.62 | | | | |
% 41.25/6.62 | | | | | ALPHA: (1043) implies:
% 41.25/6.62 | | | | | (1044) bool(all_42_0) = all_267_1
% 41.25/6.62 | | | | | (1045) phi(all_42_0) = all_267_0
% 41.25/6.62 | | | | | (1046) all_267_0 = all_245_0 | all_267_1 = 0
% 41.25/6.62 | | | | |
% 41.25/6.62 | | | | | DELTA: instantiating (1042) with fresh symbols all_273_0, all_273_1,
% 41.25/6.62 | | | | | all_273_2 gives:
% 41.25/6.62 | | | | | (1047) f2(true, all_42_1, all_42_1) = all_273_2 &
% 41.25/6.62 | | | | | lazy_impl(all_273_1, all_273_0) = all_273_2 &
% 41.25/6.62 | | | | | impl(all_247_2, all_42_1) = all_273_0 & prop(all_42_1) =
% 41.25/6.62 | | | | | all_273_1 & $i(all_273_0) & $i(all_273_1) & $i(all_273_2)
% 41.25/6.62 | | | | |
% 41.25/6.62 | | | | | ALPHA: (1047) implies:
% 41.25/6.62 | | | | | (1048) f2(true, all_42_1, all_42_1) = all_273_2
% 41.25/6.62 | | | | |
% 41.25/6.62 | | | | | GROUND_INST: instantiating (39) with all_55_1, all_267_1, all_42_0,
% 41.25/6.62 | | | | | simplifying with (72), (1044) gives:
% 41.25/6.62 | | | | | (1049) all_267_1 = all_55_1
% 41.25/6.62 | | | | |
% 41.25/6.62 | | | | | GROUND_INST: instantiating (40) with err, all_267_0, all_42_0,
% 41.25/6.62 | | | | | simplifying with (939), (1045) gives:
% 41.25/6.62 | | | | | (1050) all_267_0 = err
% 41.25/6.62 | | | | |
% 41.25/6.62 | | | | | BETA: splitting (1046) gives:
% 41.25/6.62 | | | | |
% 41.25/6.62 | | | | | Case 1:
% 41.25/6.62 | | | | | |
% 41.25/6.62 | | | | | | (1051) all_267_1 = 0
% 41.25/6.62 | | | | | |
% 41.25/6.62 | | | | | | COMBINE_EQS: (1049), (1051) imply:
% 41.25/6.62 | | | | | | (1052) all_55_1 = 0
% 41.25/6.62 | | | | | |
% 41.25/6.62 | | | | | | SIMP: (1052) implies:
% 41.25/6.62 | | | | | | (1053) all_55_1 = 0
% 41.25/6.62 | | | | | |
% 41.25/6.62 | | | | | | REDUCE: (731), (1053) imply:
% 41.25/6.62 | | | | | | (1054) $false
% 41.25/6.62 | | | | | |
% 41.25/6.62 | | | | | | CLOSE: (1054) is inconsistent.
% 41.25/6.62 | | | | | |
% 41.25/6.62 | | | | | Case 2:
% 41.25/6.62 | | | | | |
% 41.25/6.62 | | | | | | (1055) all_267_0 = all_245_0
% 41.25/6.62 | | | | | |
% 41.25/6.62 | | | | | | COMBINE_EQS: (1050), (1055) imply:
% 41.25/6.62 | | | | | | (1056) all_245_0 = err
% 41.25/6.62 | | | | | |
% 41.25/6.62 | | | | | | REDUCE: (1024), (1056) imply:
% 41.25/6.62 | | | | | | (1057) lazy_impl(true, err) = all_245_2
% 41.25/6.62 | | | | | |
% 41.25/6.62 | | | | | | GROUND_INST: instantiating (44) with err, all_245_2, err, true,
% 41.25/6.62 | | | | | | simplifying with (106), (1057) gives:
% 41.25/6.62 | | | | | | (1058) all_245_2 = err
% 41.25/6.62 | | | | | |
% 41.25/6.62 | | | | | | REDUCE: (981), (1058) imply:
% 41.25/6.62 | | | | | | (1059) f2(true, true, all_42_1) = err
% 41.25/6.62 | | | | | |
% 41.25/6.62 | | | | | | BETA: splitting (949) gives:
% 41.25/6.62 | | | | | |
% 41.25/6.62 | | | | | | Case 1:
% 41.25/6.62 | | | | | | |
% 41.25/6.62 | | | | | | | (1060) all_42_1 = true
% 41.25/6.62 | | | | | | |
% 41.25/6.62 | | | | | | | REDUCE: (1048), (1060) imply:
% 41.25/6.62 | | | | | | | (1061) f2(true, true, true) = all_273_2
% 41.25/6.62 | | | | | | |
% 41.25/6.62 | | | | | | | REDUCE: (1059), (1060) imply:
% 41.25/6.62 | | | | | | | (1062) f2(true, true, true) = err
% 41.25/6.62 | | | | | | |
% 41.25/6.62 | | | | | | | GROUND_INST: instantiating (46) with true, all_273_2, true, true,
% 41.25/6.62 | | | | | | | true, simplifying with (403), (1061) gives:
% 41.25/6.62 | | | | | | | (1063) all_273_2 = true
% 41.25/6.62 | | | | | | |
% 41.25/6.62 | | | | | | | GROUND_INST: instantiating (46) with err, all_273_2, true, true,
% 41.25/6.62 | | | | | | | true, simplifying with (1061), (1062) gives:
% 41.25/6.62 | | | | | | | (1064) all_273_2 = err
% 41.25/6.62 | | | | | | |
% 41.25/6.62 | | | | | | | COMBINE_EQS: (1063), (1064) imply:
% 41.25/6.62 | | | | | | | (1065) err = true
% 41.25/6.62 | | | | | | |
% 41.25/6.62 | | | | | | | REDUCE: (4), (1065) imply:
% 41.25/6.62 | | | | | | | (1066) $false
% 41.25/6.62 | | | | | | |
% 41.25/6.62 | | | | | | | CLOSE: (1066) is inconsistent.
% 41.25/6.62 | | | | | | |
% 41.25/6.62 | | | | | | Case 2:
% 41.25/6.62 | | | | | | |
% 41.25/6.62 | | | | | | | (1067) all_42_1 = false
% 41.25/6.62 | | | | | | |
% 41.25/6.62 | | | | | | | REDUCE: (1059), (1067) imply:
% 41.25/6.62 | | | | | | | (1068) f2(true, true, false) = err
% 41.25/6.62 | | | | | | |
% 41.25/6.62 | | | | | | | GROUND_INST: instantiating (46) with true, err, false, true, true,
% 41.25/6.62 | | | | | | | simplifying with (404), (1068) gives:
% 41.25/6.62 | | | | | | | (1069) err = true
% 41.25/6.62 | | | | | | |
% 41.25/6.62 | | | | | | | REDUCE: (4), (1069) imply:
% 41.25/6.62 | | | | | | | (1070) $false
% 41.25/6.62 | | | | | | |
% 41.25/6.62 | | | | | | | CLOSE: (1070) is inconsistent.
% 41.25/6.62 | | | | | | |
% 41.25/6.62 | | | | | | End of split
% 41.25/6.62 | | | | | |
% 41.25/6.62 | | | | | End of split
% 41.25/6.62 | | | | |
% 41.25/6.62 | | | | Case 2:
% 41.25/6.62 | | | | |
% 41.25/6.62 | | | | | (1071) ? [v0: int] : ( ~ (v0 = 0) & bool(all_42_1) = v0)
% 41.25/6.62 | | | | |
% 41.25/6.62 | | | | | DELTA: instantiating (1071) with fresh symbol all_197_0 gives:
% 41.25/6.62 | | | | | (1072) ~ (all_197_0 = 0) & bool(all_42_1) = all_197_0
% 41.25/6.62 | | | | |
% 41.25/6.62 | | | | | REF_CLOSE: (39), (940), (1072) are inconsistent by sub-proof #2.
% 41.25/6.62 | | | | |
% 41.25/6.62 | | | | End of split
% 41.25/6.62 | | | |
% 41.25/6.62 | | | Case 2:
% 41.25/6.62 | | | |
% 41.25/6.62 | | | | (1073) all_53_0 = false
% 41.25/6.62 | | | |
% 41.25/6.62 | | | | REDUCE: (70), (1073) imply:
% 41.25/6.62 | | | | (1074) lazy_impl(false, all_42_1) = all_42_0
% 41.25/6.62 | | | |
% 41.25/6.62 | | | | BETA: splitting (107) gives:
% 41.25/6.62 | | | |
% 41.25/6.62 | | | | Case 1:
% 41.25/6.62 | | | | |
% 41.25/6.62 | | | | | (1075) all_53_0 = true
% 41.25/6.62 | | | | |
% 41.25/6.62 | | | | | COMBINE_EQS: (1073), (1075) imply:
% 41.25/6.62 | | | | | (1076) true = false
% 41.25/6.62 | | | | |
% 41.25/6.62 | | | | | REDUCE: (137), (1076) imply:
% 41.25/6.62 | | | | | (1077) $false
% 41.25/6.62 | | | | |
% 41.25/6.62 | | | | | CLOSE: (1077) is inconsistent.
% 41.25/6.62 | | | | |
% 41.25/6.62 | | | | Case 2:
% 41.25/6.62 | | | | |
% 41.25/6.62 | | | | | (1078) ~ (all_53_0 = true)
% 41.25/6.62 | | | | |
% 41.25/6.62 | | | | | REDUCE: (1073), (1078) imply:
% 41.25/6.62 | | | | | (1079) ~ (true = false)
% 41.25/6.62 | | | | |
% 41.25/6.62 | | | | | GROUND_INST: instantiating (20) with all_42_1, all_42_0, simplifying
% 41.25/6.62 | | | | | with (48), (1074) gives:
% 41.25/6.62 | | | | | (1080) all_42_0 = true
% 41.25/6.62 | | | | |
% 41.25/6.62 | | | | | REDUCE: (937), (1080) imply:
% 41.25/6.62 | | | | | (1081) not1(true) = err
% 41.25/6.62 | | | | |
% 41.25/6.62 | | | | | REDUCE: (938), (1080) imply:
% 41.25/6.62 | | | | | (1082) lazy_and1(true, true) = err
% 41.25/6.62 | | | | |
% 41.25/6.62 | | | | | GROUND_INST: instantiating (45) with true, err, true, true,
% 41.25/6.62 | | | | | simplifying with (103), (1082) gives:
% 41.25/6.62 | | | | | (1083) err = true
% 41.25/6.62 | | | | |
% 41.25/6.62 | | | | | GROUND_INST: instantiating (42) with false, err, true, simplifying
% 41.25/6.62 | | | | | with (36), (1081) gives:
% 41.25/6.62 | | | | | (1084) err = false
% 41.25/6.62 | | | | |
% 41.25/6.62 | | | | | COMBINE_EQS: (1083), (1084) imply:
% 41.25/6.62 | | | | | (1085) true = false
% 41.25/6.62 | | | | |
% 41.25/6.62 | | | | | SIMP: (1085) implies:
% 41.25/6.62 | | | | | (1086) true = false
% 41.25/6.62 | | | | |
% 41.25/6.62 | | | | | REDUCE: (137), (1086) imply:
% 41.25/6.62 | | | | | (1087) $false
% 41.25/6.62 | | | | |
% 41.25/6.62 | | | | | CLOSE: (1087) is inconsistent.
% 41.25/6.62 | | | | |
% 41.25/6.62 | | | | End of split
% 41.25/6.62 | | | |
% 41.25/6.62 | | | End of split
% 41.25/6.62 | | |
% 41.25/6.62 | | End of split
% 41.25/6.62 | |
% 41.25/6.62 | End of split
% 41.25/6.62 |
% 41.25/6.62 End of proof
% 41.25/6.62
% 41.25/6.62 Sub-proof #1 shows that the following formulas are inconsistent:
% 41.25/6.62 ----------------------------------------------------------------
% 41.50/6.62 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (not1(v2) = v1) |
% 41.50/6.62 ~ (not1(v2) = v0))
% 41.50/6.62 (2) not1(true) = true
% 41.50/6.62 (3) not1(true) = false
% 41.50/6.62 (4) ~ (true = false)
% 41.50/6.62
% 41.50/6.62 Begin of proof
% 41.50/6.62 |
% 41.50/6.62 | GROUND_INST: instantiating (1) with false, true, true, simplifying with (2),
% 41.50/6.62 | (3) gives:
% 41.50/6.62 | (5) true = false
% 41.50/6.62 |
% 41.50/6.62 | REDUCE: (4), (5) imply:
% 41.50/6.62 | (6) $false
% 41.50/6.62 |
% 41.50/6.62 | CLOSE: (6) is inconsistent.
% 41.50/6.62 |
% 41.50/6.62 End of proof
% 41.50/6.62
% 41.50/6.62 Sub-proof #2 shows that the following formulas are inconsistent:
% 41.50/6.62 ----------------------------------------------------------------
% 41.50/6.62 (1) ~ (all_197_0 = 0) & bool(all_42_1) = all_197_0
% 41.50/6.62 (2) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 41.50/6.62 (v1 = v0 | ~ (bool(v2) = v1) | ~ (bool(v2) = v0))
% 41.50/6.62 (3) bool(all_42_1) = 0
% 41.50/6.62
% 41.50/6.62 Begin of proof
% 41.50/6.62 |
% 41.50/6.62 | ALPHA: (1) implies:
% 41.50/6.62 | (4) ~ (all_197_0 = 0)
% 41.50/6.62 | (5) bool(all_42_1) = all_197_0
% 41.50/6.62 |
% 41.50/6.62 | GROUND_INST: instantiating (2) with 0, all_197_0, all_42_1, simplifying with
% 41.50/6.62 | (3), (5) gives:
% 41.50/6.62 | (6) all_197_0 = 0
% 41.50/6.62 |
% 41.50/6.62 | REDUCE: (4), (6) imply:
% 41.50/6.62 | (7) $false
% 41.50/6.62 |
% 41.50/6.62 | CLOSE: (7) is inconsistent.
% 41.50/6.62 |
% 41.50/6.62 End of proof
% 41.50/6.62
% 41.50/6.62 Sub-proof #3 shows that the following formulas are inconsistent:
% 41.50/6.62 ----------------------------------------------------------------
% 41.50/6.62 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1
% 41.50/6.62 = v0 | ~ (f2(v4, v3, v2) = v1) | ~ (f2(v4, v3, v2) = v0))
% 41.50/6.62 (2) f2(true, true, false) = err
% 41.50/6.62 (3) f2(true, true, false) = true
% 41.50/6.62 (4) ~ (err = true)
% 41.50/6.62
% 41.50/6.62 Begin of proof
% 41.50/6.62 |
% 41.50/6.62 | GROUND_INST: instantiating (1) with true, err, false, true, true, simplifying
% 41.50/6.62 | with (2), (3) gives:
% 41.50/6.62 | (5) err = true
% 41.50/6.62 |
% 41.50/6.62 | REDUCE: (4), (5) imply:
% 41.50/6.62 | (6) $false
% 41.50/6.62 |
% 41.50/6.62 | CLOSE: (6) is inconsistent.
% 41.50/6.62 |
% 41.50/6.62 End of proof
% 41.50/6.62 % SZS output end Proof for theBenchmark
% 41.50/6.62
% 41.50/6.62 6005ms
%------------------------------------------------------------------------------