TSTP Solution File: SWC277+1 by Princess---230619
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- Process Solution
%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SWC277+1 : TPTP v8.1.2. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n018.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 20:50:36 EDT 2023
% Result : Theorem 71.96s 10.17s
% Output : Proof 225.46s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWC277+1 : TPTP v8.1.2. Released v2.4.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.14/0.33 % Computer : n018.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 300
% 0.14/0.33 % DateTime : Mon Aug 28 17:57:02 EDT 2023
% 0.14/0.33 % CPUTime :
% 0.19/0.59 ________ _____
% 0.19/0.59 ___ __ \_________(_)________________________________
% 0.19/0.59 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.19/0.59 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.19/0.59 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.19/0.59
% 0.19/0.59 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.19/0.59 (2023-06-19)
% 0.19/0.59
% 0.19/0.59 (c) Philipp Rümmer, 2009-2023
% 0.19/0.59 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.19/0.59 Amanda Stjerna.
% 0.19/0.59 Free software under BSD-3-Clause.
% 0.19/0.59
% 0.19/0.59 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.19/0.59
% 0.19/0.60 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.19/0.61 Running up to 7 provers in parallel.
% 0.19/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.19/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.19/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.19/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.19/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.19/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.19/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 6.69/1.64 Prover 1: Preprocessing ...
% 6.69/1.65 Prover 0: Preprocessing ...
% 6.69/1.67 Prover 3: Preprocessing ...
% 6.69/1.67 Prover 2: Preprocessing ...
% 6.69/1.67 Prover 5: Preprocessing ...
% 7.11/1.70 Prover 4: Preprocessing ...
% 7.11/1.70 Prover 6: Preprocessing ...
% 16.33/2.95 Prover 2: Proving ...
% 16.65/2.98 Prover 5: Constructing countermodel ...
% 16.65/2.99 Prover 1: Constructing countermodel ...
% 17.25/3.07 Prover 6: Proving ...
% 17.62/3.10 Prover 3: Constructing countermodel ...
% 22.50/3.74 Prover 0: Proving ...
% 22.50/3.74 Prover 4: Constructing countermodel ...
% 71.96/10.17 Prover 3: proved (9545ms)
% 71.96/10.17
% 71.96/10.17 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 71.96/10.17
% 71.96/10.17 Prover 2: stopped
% 71.96/10.17 Prover 6: stopped
% 71.96/10.17 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 71.96/10.17 Prover 5: stopped
% 71.96/10.17 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 71.96/10.17 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 71.96/10.17 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 71.96/10.18 Prover 0: stopped
% 71.96/10.18 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 73.29/10.38 Prover 11: Preprocessing ...
% 73.29/10.39 Prover 13: Preprocessing ...
% 73.72/10.39 Prover 10: Preprocessing ...
% 73.72/10.39 Prover 8: Preprocessing ...
% 73.72/10.44 Prover 7: Preprocessing ...
% 74.58/10.59 Prover 10: Constructing countermodel ...
% 75.11/10.66 Prover 7: Constructing countermodel ...
% 75.11/10.69 Prover 13: Constructing countermodel ...
% 76.43/10.78 Prover 8: Warning: ignoring some quantifiers
% 76.43/10.79 Prover 8: Constructing countermodel ...
% 81.16/11.37 Prover 11: Constructing countermodel ...
% 104.07/14.42 Prover 13: stopped
% 104.70/14.45 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 105.51/14.60 Prover 16: Preprocessing ...
% 106.36/14.70 Prover 16: Constructing countermodel ...
% 116.11/15.98 Prover 1: stopped
% 116.64/16.00 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085
% 117.21/16.10 Prover 19: Preprocessing ...
% 119.76/16.46 Prover 19: Warning: ignoring some quantifiers
% 120.24/16.50 Prover 19: Constructing countermodel ...
% 142.98/19.55 Prover 16: stopped
% 144.40/19.76 Prover 19: stopped
% 188.66/27.97 Prover 4: stopped
% 198.57/30.14 Prover 7: stopped
% 224.06/37.79 Prover 8: Found proof (size 419)
% 224.06/37.79 Prover 8: proved (27518ms)
% 224.06/37.80 Prover 11: stopped
% 224.06/37.81 Prover 10: stopped
% 224.06/37.81
% 224.06/37.81 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 224.06/37.81
% 224.36/37.85 % SZS output start Proof for theBenchmark
% 224.36/37.86 Assumptions after simplification:
% 224.36/37.86 ---------------------------------
% 224.36/37.86
% 224.36/37.86 (ax11)
% 224.56/37.92 ! [v0: $i] : ! [v1: any] : ( ~ (totalorderedP(v0) = v1) | ~ $i(v0) | ?
% 224.56/37.92 [v2: int] : ( ~ (v2 = 0) & ssList(v0) = v2) | (( ~ (v1 = 0) | ! [v2: $i] :
% 224.56/37.92 ( ~ (ssItem(v2) = 0) | ~ $i(v2) | ! [v3: $i] : ! [v4: any] : ( ~
% 224.56/37.92 (leq(v2, v3) = v4) | ~ $i(v3) | ? [v5: int] : ( ~ (v5 = 0) &
% 224.56/37.92 ssItem(v3) = v5) | ! [v5: $i] : ( ~ (ssList(v5) = 0) | ~ $i(v5)
% 224.56/37.92 | ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ( ~ (cons(v2, v6) =
% 224.56/37.92 v7) | ~ (app(v5, v7) = v8) | ~ $i(v6) | ? [v9: int] : ( ~
% 224.56/37.92 (v9 = 0) & ssList(v6) = v9) | ! [v9: $i] : ! [v10: $i] : (v4
% 224.56/37.92 = 0 | ~ (cons(v3, v9) = v10) | ~ (app(v8, v10) = v0) | ~
% 224.56/37.92 $i(v9) | ? [v11: int] : ( ~ (v11 = 0) & ssList(v9) =
% 224.56/37.92 v11))))))) & (v1 = 0 | ? [v2: $i] : (ssItem(v2) = 0 &
% 224.56/37.92 $i(v2) & ? [v3: $i] : ? [v4: any] : (leq(v2, v3) = v4 & ssItem(v3) =
% 224.56/37.92 0 & $i(v3) & ? [v5: $i] : (ssList(v5) = 0 & $i(v5) & ? [v6: $i] :
% 224.56/37.92 ? [v7: $i] : ? [v8: $i] : (ssList(v6) = 0 & cons(v2, v6) = v7 &
% 224.56/37.92 app(v5, v7) = v8 & $i(v8) & $i(v7) & $i(v6) & ? [v9: $i] : ?
% 224.56/37.92 [v10: $i] : ( ~ (v4 = 0) & ssList(v9) = 0 & cons(v3, v9) = v10 &
% 224.56/37.92 app(v8, v10) = v0 & $i(v10) & $i(v9)))))))))
% 224.56/37.92
% 224.56/37.92 (ax13)
% 224.56/37.93 ! [v0: $i] : ! [v1: any] : ( ~ (duplicatefreeP(v0) = v1) | ~ $i(v0) | ?
% 224.56/37.93 [v2: int] : ( ~ (v2 = 0) & ssList(v0) = v2) | (( ~ (v1 = 0) | ! [v2: $i] :
% 224.56/37.93 ( ~ (ssItem(v2) = 0) | ~ $i(v2) | ! [v3: $i] : ( ~ (ssItem(v3) = 0) |
% 224.56/37.93 ~ $i(v3) | ! [v4: $i] : ( ~ (ssList(v4) = 0) | ~ $i(v4) | ! [v5:
% 224.56/37.93 $i] : ! [v6: $i] : ! [v7: $i] : ( ~ (cons(v2, v5) = v6) | ~
% 224.56/37.93 (app(v4, v6) = v7) | ~ $i(v5) | ? [v8: int] : ( ~ (v8 = 0) &
% 224.56/37.93 ssList(v5) = v8) | ! [v8: $i] : ! [v9: $i] : ( ~ (v3 = v2) |
% 224.56/37.93 ~ (cons(v2, v8) = v9) | ~ (app(v7, v9) = v0) | ~ $i(v8) |
% 224.56/37.93 ? [v10: int] : ( ~ (v10 = 0) & ssList(v8) = v10))))))) & (v1 =
% 224.56/37.93 0 | ? [v2: $i] : (ssItem(v2) = 0 & $i(v2) & ? [v3: $i] : (ssItem(v3) =
% 224.56/37.93 0 & $i(v3) & ? [v4: $i] : (ssList(v4) = 0 & $i(v4) & ? [v5: $i] :
% 224.56/37.93 ? [v6: $i] : ? [v7: $i] : (ssList(v5) = 0 & cons(v2, v5) = v6 &
% 224.56/37.93 app(v4, v6) = v7 & $i(v7) & $i(v6) & $i(v5) & ? [v8: $i] : ?
% 224.56/37.93 [v9: $i] : (v3 = v2 & ssList(v8) = 0 & cons(v2, v8) = v9 &
% 224.56/37.93 app(v7, v9) = v0 & $i(v9) & $i(v8)))))))))
% 224.56/37.93
% 224.56/37.93 (ax15)
% 224.56/37.94 ! [v0: $i] : ( ~ (ssList(v0) = 0) | ~ $i(v0) | ! [v1: $i] : ! [v2: any] :
% 224.56/37.94 ( ~ (neq(v0, v1) = v2) | ~ $i(v1) | ? [v3: int] : ( ~ (v3 = 0) &
% 224.56/37.94 ssList(v1) = v3) | (( ~ (v2 = 0) | ~ (v1 = v0)) & (v2 = 0 | v1 = v0))))
% 224.56/37.94
% 224.56/37.94 (ax17)
% 224.56/37.94 ssList(nil) = 0 & $i(nil)
% 224.56/37.94
% 224.56/37.94 (ax20)
% 224.56/37.94 $i(nil) & ! [v0: $i] : (v0 = nil | ~ (ssList(v0) = 0) | ~ $i(v0) | ? [v1:
% 224.56/37.94 $i] : (ssList(v1) = 0 & $i(v1) & ? [v2: $i] : (cons(v2, v1) = v0 &
% 224.56/37.94 ssItem(v2) = 0 & $i(v2))))
% 224.56/37.94
% 224.56/37.94 (ax23)
% 224.56/37.94 ! [v0: $i] : ( ~ (ssList(v0) = 0) | ~ $i(v0) | ! [v1: $i] : ! [v2: $i] : (
% 224.56/37.94 ~ (cons(v1, v0) = v2) | ~ $i(v1) | ? [v3: any] : ? [v4: $i] : (hd(v2) =
% 224.56/37.94 v4 & ssItem(v1) = v3 & $i(v4) & ( ~ (v3 = 0) | v4 = v1))))
% 224.56/37.94
% 224.56/37.94 (ax25)
% 224.56/37.94 ! [v0: $i] : ( ~ (ssList(v0) = 0) | ~ $i(v0) | ! [v1: $i] : ! [v2: $i] : (
% 224.56/37.94 ~ (cons(v1, v0) = v2) | ~ $i(v1) | ? [v3: any] : ? [v4: $i] : (tl(v2) =
% 224.56/37.94 v4 & ssItem(v1) = v3 & $i(v4) & ( ~ (v3 = 0) | v4 = v0))))
% 224.56/37.94
% 224.56/37.94 (ax39)
% 224.56/37.94 $i(nil) & ? [v0: int] : ( ~ (v0 = 0) & singletonP(nil) = v0)
% 224.56/37.94
% 224.56/37.94 (ax4)
% 224.56/37.94 $i(nil) & ! [v0: $i] : ! [v1: any] : ( ~ (singletonP(v0) = v1) | ~ $i(v0) |
% 224.56/37.94 ? [v2: int] : ( ~ (v2 = 0) & ssList(v0) = v2) | (( ~ (v1 = 0) | ? [v2: $i]
% 224.56/37.94 : (cons(v2, nil) = v0 & ssItem(v2) = 0 & $i(v2))) & (v1 = 0 | ! [v2:
% 224.56/37.94 $i] : ( ~ (cons(v2, nil) = v0) | ~ $i(v2) | ? [v3: int] : ( ~ (v3 =
% 224.56/37.94 0) & ssItem(v2) = v3)))))
% 224.56/37.94
% 224.56/37.94 (ax54)
% 224.56/37.94 ! [v0: $i] : ( ~ (ssList(v0) = 0) | ~ $i(v0) | ! [v1: $i] : (v1 = v0 | ~
% 224.56/37.94 (segmentP(v0, v1) = 0) | ~ $i(v1) | ? [v2: any] : ? [v3: any] :
% 224.56/37.94 (segmentP(v1, v0) = v3 & ssList(v1) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0)))))
% 224.56/37.94
% 224.56/37.94 (ax58)
% 224.83/37.95 $i(nil) & ! [v0: $i] : ! [v1: any] : ( ~ (segmentP(nil, v0) = v1) | ~
% 224.83/37.95 $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & ssList(v0) = v2) | (( ~ (v1 = 0) | v0
% 224.83/37.95 = nil) & ( ~ (v0 = nil) | v1 = 0)))
% 224.83/37.95
% 224.83/37.95 (ax59)
% 224.83/37.95 $i(nil) & ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) |
% 224.83/37.95 ? [v2: any] : ? [v3: any] : (cyclefreeP(v1) = v3 & ssItem(v0) = v2 & ( ~
% 224.83/37.95 (v2 = 0) | v3 = 0)))
% 224.83/37.95
% 224.83/37.95 (ax61)
% 224.83/37.95 $i(nil) & ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) |
% 224.83/37.95 ? [v2: any] : ? [v3: any] : (totalorderP(v1) = v3 & ssItem(v0) = v2 & ( ~
% 224.83/37.95 (v2 = 0) | v3 = 0)))
% 224.83/37.95
% 224.83/37.95 (ax63)
% 224.83/37.95 $i(nil) & ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) |
% 224.83/37.95 ? [v2: any] : ? [v3: any] : (strictorderP(v1) = v3 & ssItem(v0) = v2 & ( ~
% 224.83/37.95 (v2 = 0) | v3 = 0)))
% 224.83/37.95
% 224.83/37.95 (ax65)
% 224.83/37.95 $i(nil) & ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) |
% 224.83/37.95 ? [v2: any] : ? [v3: any] : (totalorderedP(v1) = v3 & ssItem(v0) = v2 & ( ~
% 224.83/37.95 (v2 = 0) | v3 = 0)))
% 224.83/37.95
% 224.83/37.95 (ax66)
% 224.83/37.95 totalorderedP(nil) = 0 & $i(nil)
% 224.83/37.95
% 224.83/37.95 (ax68)
% 224.83/37.95 $i(nil) & ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) |
% 224.83/37.95 ? [v2: any] : ? [v3: any] : (strictorderedP(v1) = v3 & ssItem(v0) = v2 & (
% 224.83/37.95 ~ (v2 = 0) | v3 = 0)))
% 224.83/37.95
% 224.83/37.95 (ax7)
% 224.83/37.95 ! [v0: $i] : ( ~ (ssList(v0) = 0) | ~ $i(v0) | ! [v1: $i] : ! [v2: any] :
% 224.83/37.95 ( ~ (segmentP(v0, v1) = v2) | ~ $i(v1) | ? [v3: int] : ( ~ (v3 = 0) &
% 224.83/37.95 ssList(v1) = v3) | (( ~ (v2 = 0) | ? [v3: $i] : ? [v4: $i] :
% 224.83/37.95 (ssList(v3) = 0 & app(v3, v1) = v4 & $i(v4) & $i(v3) & ? [v5: $i] :
% 224.83/37.95 (ssList(v5) = 0 & app(v4, v5) = v0 & $i(v5)))) & (v2 = 0 | ! [v3:
% 224.83/37.95 $i] : ! [v4: $i] : ( ~ (app(v3, v1) = v4) | ~ $i(v3) | ? [v5:
% 224.83/37.95 int] : ( ~ (v5 = 0) & ssList(v3) = v5) | ! [v5: $i] : ( ~
% 224.83/37.95 (app(v4, v5) = v0) | ~ $i(v5) | ? [v6: int] : ( ~ (v6 = 0) &
% 224.83/37.95 ssList(v5) = v6)))))))
% 224.83/37.95
% 224.83/37.95 (ax71)
% 224.83/37.96 $i(nil) & ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) |
% 224.83/37.96 ? [v2: any] : ? [v3: any] : (duplicatefreeP(v1) = v3 & ssItem(v0) = v2 & (
% 224.83/37.96 ~ (v2 = 0) | v3 = 0)))
% 224.83/37.96
% 224.83/37.96 (ax72)
% 224.88/37.96 duplicatefreeP(nil) = 0 & $i(nil)
% 224.88/37.96
% 224.88/37.96 (ax73)
% 224.88/37.96 $i(nil) & ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) |
% 224.88/37.96 ? [v2: any] : ? [v3: any] : (equalelemsP(v1) = v3 & ssItem(v0) = v2 & ( ~
% 224.88/37.96 (v2 = 0) | v3 = 0)))
% 224.88/37.96
% 224.88/37.96 (co1)
% 224.88/37.96 $i(nil) & ? [v0: $i] : ? [v1: any] : (totalorderedP(v0) = v1 & ssList(v0) =
% 224.88/37.96 0 & $i(v0) & ? [v2: $i] : (ssList(v2) = 0 & $i(v2) & ? [v3: $i] : ? [v4:
% 224.88/37.96 any] : (singletonP(v3) = v4 & ssList(v3) = 0 & $i(v3) & ? [v5: any] :
% 224.88/37.96 (v3 = v0 & ~ (v1 = 0) & segmentP(v2, v0) = 0 & neq(v2, nil) = v5 & ( ~
% 224.88/37.96 (v5 = 0) | v4 = 0)))))
% 224.88/37.96
% 224.88/37.96 (function-axioms)
% 224.88/37.97 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 224.88/37.97 [v3: $i] : (v1 = v0 | ~ (gt(v3, v2) = v1) | ~ (gt(v3, v2) = v0)) & ! [v0:
% 224.88/37.97 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 224.88/37.97 : (v1 = v0 | ~ (geq(v3, v2) = v1) | ~ (geq(v3, v2) = v0)) & ! [v0:
% 224.88/37.97 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 224.88/37.97 : (v1 = v0 | ~ (lt(v3, v2) = v1) | ~ (lt(v3, v2) = v0)) & ! [v0:
% 224.88/37.97 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 224.88/37.97 : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0)) & ! [v0:
% 224.88/37.97 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 224.88/37.97 : (v1 = v0 | ~ (segmentP(v3, v2) = v1) | ~ (segmentP(v3, v2) = v0)) & !
% 224.88/37.97 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 224.88/37.97 $i] : (v1 = v0 | ~ (rearsegP(v3, v2) = v1) | ~ (rearsegP(v3, v2) = v0)) &
% 224.88/37.97 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 224.88/37.97 $i] : (v1 = v0 | ~ (frontsegP(v3, v2) = v1) | ~ (frontsegP(v3, v2) = v0))
% 224.88/37.97 & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 224.88/37.97 [v3: $i] : (v1 = v0 | ~ (memberP(v3, v2) = v1) | ~ (memberP(v3, v2) = v0)) &
% 224.88/37.97 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 224.88/37.97 (cons(v3, v2) = v1) | ~ (cons(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] :
% 224.88/37.97 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (app(v3, v2) = v1) | ~ (app(v3, v2)
% 224.88/37.97 = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 224.88/37.97 $i] : ! [v3: $i] : (v1 = v0 | ~ (neq(v3, v2) = v1) | ~ (neq(v3, v2) =
% 224.88/37.97 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (tl(v2) =
% 224.88/37.97 v1) | ~ (tl(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 =
% 224.88/37.97 v0 | ~ (hd(v2) = v1) | ~ (hd(v2) = v0)) & ! [v0: MultipleValueBool] : !
% 224.88/37.97 [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (equalelemsP(v2) = v1) |
% 224.88/37.97 ~ (equalelemsP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 224.88/37.97 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (duplicatefreeP(v2) = v1) |
% 224.88/37.97 ~ (duplicatefreeP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 224.88/37.97 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (strictorderedP(v2) = v1) |
% 224.88/37.97 ~ (strictorderedP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 224.88/37.97 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (totalorderedP(v2) = v1) |
% 224.88/37.97 ~ (totalorderedP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 224.88/37.97 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (strictorderP(v2) = v1) |
% 224.88/37.97 ~ (strictorderP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 224.88/37.97 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (totalorderP(v2) = v1) | ~
% 224.88/37.97 (totalorderP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 224.88/37.97 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (cyclefreeP(v2) = v1) | ~
% 224.88/37.97 (cyclefreeP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 224.88/37.97 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (singletonP(v2) = v1) | ~
% 224.88/37.97 (singletonP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 224.88/37.97 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (ssList(v2) = v1) | ~
% 224.88/37.97 (ssList(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool]
% 224.88/37.97 : ! [v2: $i] : (v1 = v0 | ~ (ssItem(v2) = v1) | ~ (ssItem(v2) = v0)) & ?
% 224.88/37.97 [v0: $i] : ? [v1: $i] : ? [v2: MultipleValueBool] : (gt(v1, v0) = v2) & ?
% 224.88/37.97 [v0: $i] : ? [v1: $i] : ? [v2: MultipleValueBool] : (geq(v1, v0) = v2) & ?
% 224.88/37.97 [v0: $i] : ? [v1: $i] : ? [v2: MultipleValueBool] : (lt(v1, v0) = v2) & ?
% 224.88/37.97 [v0: $i] : ? [v1: $i] : ? [v2: MultipleValueBool] : (leq(v1, v0) = v2) & ?
% 224.88/37.97 [v0: $i] : ? [v1: $i] : ? [v2: MultipleValueBool] : (segmentP(v1, v0) = v2)
% 224.88/37.97 & ? [v0: $i] : ? [v1: $i] : ? [v2: MultipleValueBool] : (rearsegP(v1, v0) =
% 224.88/37.97 v2) & ? [v0: $i] : ? [v1: $i] : ? [v2: MultipleValueBool] :
% 224.88/37.97 (frontsegP(v1, v0) = v2) & ? [v0: $i] : ? [v1: $i] : ? [v2:
% 224.88/37.97 MultipleValueBool] : (memberP(v1, v0) = v2) & ? [v0: $i] : ? [v1: $i] : ?
% 224.88/37.97 [v2: MultipleValueBool] : (neq(v1, v0) = v2) & ? [v0: $i] : ? [v1: $i] : ?
% 224.88/37.97 [v2: $i] : (cons(v1, v0) = v2 & $i(v2)) & ? [v0: $i] : ? [v1: $i] : ? [v2:
% 224.88/37.97 $i] : (app(v1, v0) = v2 & $i(v2)) & ? [v0: $i] : ? [v1: MultipleValueBool]
% 224.88/37.97 : (equalelemsP(v0) = v1) & ? [v0: $i] : ? [v1: MultipleValueBool] :
% 224.88/37.97 (duplicatefreeP(v0) = v1) & ? [v0: $i] : ? [v1: MultipleValueBool] :
% 224.88/37.97 (strictorderedP(v0) = v1) & ? [v0: $i] : ? [v1: MultipleValueBool] :
% 224.88/37.97 (totalorderedP(v0) = v1) & ? [v0: $i] : ? [v1: MultipleValueBool] :
% 224.88/37.97 (strictorderP(v0) = v1) & ? [v0: $i] : ? [v1: MultipleValueBool] :
% 224.88/37.97 (totalorderP(v0) = v1) & ? [v0: $i] : ? [v1: MultipleValueBool] :
% 224.88/37.97 (cyclefreeP(v0) = v1) & ? [v0: $i] : ? [v1: MultipleValueBool] :
% 224.88/37.97 (singletonP(v0) = v1) & ? [v0: $i] : ? [v1: MultipleValueBool] : (ssList(v0)
% 224.88/37.97 = v1) & ? [v0: $i] : ? [v1: MultipleValueBool] : (ssItem(v0) = v1) & ?
% 224.88/37.97 [v0: $i] : ? [v1: $i] : (tl(v0) = v1 & $i(v1)) & ? [v0: $i] : ? [v1: $i] :
% 224.88/37.97 (hd(v0) = v1 & $i(v1))
% 224.88/37.97
% 224.88/37.97 Further assumptions not needed in the proof:
% 224.88/37.97 --------------------------------------------
% 224.88/37.97 ax1, ax10, ax12, ax14, ax16, ax18, ax19, ax2, ax21, ax22, ax24, ax26, ax27,
% 224.88/37.97 ax28, ax29, ax3, ax30, ax31, ax32, ax33, ax34, ax35, ax36, ax37, ax38, ax40,
% 224.88/37.97 ax41, ax42, ax43, ax44, ax45, ax46, ax47, ax48, ax49, ax5, ax50, ax51, ax52,
% 224.88/37.97 ax53, ax55, ax56, ax57, ax6, ax60, ax62, ax64, ax67, ax69, ax70, ax74, ax75,
% 224.88/37.97 ax76, ax77, ax78, ax79, ax8, ax80, ax81, ax82, ax83, ax84, ax85, ax86, ax87,
% 224.88/37.97 ax88, ax89, ax9, ax90, ax91, ax92, ax93, ax94, ax95
% 224.88/37.97
% 224.88/37.97 Those formulas are unsatisfiable:
% 224.88/37.97 ---------------------------------
% 224.88/37.97
% 224.88/37.97 Begin of proof
% 224.88/37.98 |
% 224.88/37.98 | ALPHA: (ax4) implies:
% 224.88/37.98 | (1) ! [v0: $i] : ! [v1: any] : ( ~ (singletonP(v0) = v1) | ~ $i(v0) | ?
% 224.88/37.98 | [v2: int] : ( ~ (v2 = 0) & ssList(v0) = v2) | (( ~ (v1 = 0) | ? [v2:
% 224.88/37.98 | $i] : (cons(v2, nil) = v0 & ssItem(v2) = 0 & $i(v2))) & (v1 = 0
% 224.88/37.98 | | ! [v2: $i] : ( ~ (cons(v2, nil) = v0) | ~ $i(v2) | ? [v3:
% 224.88/37.98 | int] : ( ~ (v3 = 0) & ssItem(v2) = v3)))))
% 224.88/37.98 |
% 224.88/37.98 | ALPHA: (ax17) implies:
% 224.88/37.98 | (2) ssList(nil) = 0
% 224.88/37.98 |
% 224.88/37.98 | ALPHA: (ax20) implies:
% 224.88/37.98 | (3) ! [v0: $i] : (v0 = nil | ~ (ssList(v0) = 0) | ~ $i(v0) | ? [v1: $i]
% 224.88/37.98 | : (ssList(v1) = 0 & $i(v1) & ? [v2: $i] : (cons(v2, v1) = v0 &
% 224.88/37.98 | ssItem(v2) = 0 & $i(v2))))
% 224.88/37.98 |
% 224.88/37.98 | ALPHA: (ax39) implies:
% 224.88/37.98 | (4) ? [v0: int] : ( ~ (v0 = 0) & singletonP(nil) = v0)
% 224.88/37.98 |
% 224.88/37.98 | ALPHA: (ax58) implies:
% 224.88/37.98 | (5) ! [v0: $i] : ! [v1: any] : ( ~ (segmentP(nil, v0) = v1) | ~ $i(v0) |
% 224.88/37.98 | ? [v2: int] : ( ~ (v2 = 0) & ssList(v0) = v2) | (( ~ (v1 = 0) | v0 =
% 224.88/37.98 | nil) & ( ~ (v0 = nil) | v1 = 0)))
% 224.88/37.98 |
% 224.88/37.98 | ALPHA: (ax59) implies:
% 224.88/37.98 | (6) ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | ?
% 224.88/37.98 | [v2: any] : ? [v3: any] : (cyclefreeP(v1) = v3 & ssItem(v0) = v2 & (
% 224.88/37.98 | ~ (v2 = 0) | v3 = 0)))
% 224.88/37.98 |
% 224.88/37.98 | ALPHA: (ax61) implies:
% 224.88/37.98 | (7) ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | ?
% 224.88/37.98 | [v2: any] : ? [v3: any] : (totalorderP(v1) = v3 & ssItem(v0) = v2 &
% 224.88/37.98 | ( ~ (v2 = 0) | v3 = 0)))
% 224.88/37.98 |
% 224.88/37.98 | ALPHA: (ax63) implies:
% 224.88/37.98 | (8) ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | ?
% 224.88/37.98 | [v2: any] : ? [v3: any] : (strictorderP(v1) = v3 & ssItem(v0) = v2 &
% 224.88/37.98 | ( ~ (v2 = 0) | v3 = 0)))
% 224.88/37.98 |
% 224.88/37.98 | ALPHA: (ax65) implies:
% 224.88/37.99 | (9) ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | ?
% 224.88/37.99 | [v2: any] : ? [v3: any] : (totalorderedP(v1) = v3 & ssItem(v0) = v2
% 224.88/37.99 | & ( ~ (v2 = 0) | v3 = 0)))
% 224.88/37.99 |
% 224.88/37.99 | ALPHA: (ax66) implies:
% 224.88/37.99 | (10) totalorderedP(nil) = 0
% 224.88/37.99 |
% 224.88/37.99 | ALPHA: (ax68) implies:
% 224.88/37.99 | (11) ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | ?
% 224.88/37.99 | [v2: any] : ? [v3: any] : (strictorderedP(v1) = v3 & ssItem(v0) =
% 224.88/37.99 | v2 & ( ~ (v2 = 0) | v3 = 0)))
% 224.88/37.99 |
% 224.88/37.99 | ALPHA: (ax71) implies:
% 224.88/37.99 | (12) ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | ?
% 224.88/37.99 | [v2: any] : ? [v3: any] : (duplicatefreeP(v1) = v3 & ssItem(v0) =
% 224.88/37.99 | v2 & ( ~ (v2 = 0) | v3 = 0)))
% 224.88/37.99 |
% 224.88/37.99 | ALPHA: (ax72) implies:
% 224.88/37.99 | (13) duplicatefreeP(nil) = 0
% 224.88/37.99 |
% 224.88/37.99 | ALPHA: (ax73) implies:
% 224.88/37.99 | (14) ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | ?
% 224.88/37.99 | [v2: any] : ? [v3: any] : (equalelemsP(v1) = v3 & ssItem(v0) = v2 &
% 224.88/37.99 | ( ~ (v2 = 0) | v3 = 0)))
% 224.88/37.99 |
% 224.88/37.99 | ALPHA: (co1) implies:
% 224.88/37.99 | (15) $i(nil)
% 224.88/37.99 | (16) ? [v0: $i] : ? [v1: any] : (totalorderedP(v0) = v1 & ssList(v0) = 0
% 224.88/37.99 | & $i(v0) & ? [v2: $i] : (ssList(v2) = 0 & $i(v2) & ? [v3: $i] : ?
% 224.88/37.99 | [v4: any] : (singletonP(v3) = v4 & ssList(v3) = 0 & $i(v3) & ?
% 224.88/37.99 | [v5: any] : (v3 = v0 & ~ (v1 = 0) & segmentP(v2, v0) = 0 &
% 224.88/37.99 | neq(v2, nil) = v5 & ( ~ (v5 = 0) | v4 = 0)))))
% 224.88/37.99 |
% 224.88/37.99 | ALPHA: (function-axioms) implies:
% 224.88/37.99 | (17) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 224.88/37.99 | : (v1 = v0 | ~ (ssItem(v2) = v1) | ~ (ssItem(v2) = v0))
% 224.88/37.99 | (18) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 224.88/37.99 | : (v1 = v0 | ~ (ssList(v2) = v1) | ~ (ssList(v2) = v0))
% 224.88/37.99 | (19) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 224.88/37.99 | : (v1 = v0 | ~ (singletonP(v2) = v1) | ~ (singletonP(v2) = v0))
% 224.88/37.99 | (20) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 224.88/37.99 | : (v1 = v0 | ~ (totalorderedP(v2) = v1) | ~ (totalorderedP(v2) =
% 224.88/37.99 | v0))
% 224.88/37.99 |
% 224.88/38.00 | DELTA: instantiating (4) with fresh symbol all_127_0 gives:
% 224.88/38.00 | (21) ~ (all_127_0 = 0) & singletonP(nil) = all_127_0
% 224.88/38.00 |
% 224.88/38.00 | ALPHA: (21) implies:
% 224.88/38.00 | (22) ~ (all_127_0 = 0)
% 224.88/38.00 | (23) singletonP(nil) = all_127_0
% 224.88/38.00 |
% 224.88/38.00 | DELTA: instantiating (16) with fresh symbols all_139_0, all_139_1 gives:
% 224.88/38.00 | (24) totalorderedP(all_139_1) = all_139_0 & ssList(all_139_1) = 0 &
% 224.88/38.00 | $i(all_139_1) & ? [v0: $i] : (ssList(v0) = 0 & $i(v0) & ? [v1: $i] :
% 224.88/38.00 | ? [v2: any] : (singletonP(v1) = v2 & ssList(v1) = 0 & $i(v1) & ?
% 224.88/38.00 | [v3: any] : (v1 = all_139_1 & ~ (all_139_0 = 0) & segmentP(v0,
% 224.88/38.00 | all_139_1) = 0 & neq(v0, nil) = v3 & ( ~ (v3 = 0) | v2 = 0))))
% 224.88/38.00 |
% 224.88/38.00 | ALPHA: (24) implies:
% 224.88/38.00 | (25) totalorderedP(all_139_1) = all_139_0
% 224.88/38.00 | (26) ? [v0: $i] : (ssList(v0) = 0 & $i(v0) & ? [v1: $i] : ? [v2: any] :
% 224.88/38.00 | (singletonP(v1) = v2 & ssList(v1) = 0 & $i(v1) & ? [v3: any] : (v1
% 224.88/38.00 | = all_139_1 & ~ (all_139_0 = 0) & segmentP(v0, all_139_1) = 0 &
% 224.88/38.00 | neq(v0, nil) = v3 & ( ~ (v3 = 0) | v2 = 0))))
% 224.88/38.00 |
% 224.88/38.00 | DELTA: instantiating (26) with fresh symbol all_143_0 gives:
% 224.88/38.00 | (27) ssList(all_143_0) = 0 & $i(all_143_0) & ? [v0: $i] : ? [v1: any] :
% 224.88/38.00 | (singletonP(v0) = v1 & ssList(v0) = 0 & $i(v0) & ? [v2: any] : (v0 =
% 224.88/38.00 | all_139_1 & ~ (all_139_0 = 0) & segmentP(all_143_0, all_139_1) =
% 224.88/38.00 | 0 & neq(all_143_0, nil) = v2 & ( ~ (v2 = 0) | v1 = 0)))
% 224.88/38.00 |
% 224.88/38.00 | ALPHA: (27) implies:
% 224.88/38.00 | (28) $i(all_143_0)
% 224.88/38.00 | (29) ssList(all_143_0) = 0
% 224.88/38.00 | (30) ? [v0: $i] : ? [v1: any] : (singletonP(v0) = v1 & ssList(v0) = 0 &
% 224.88/38.00 | $i(v0) & ? [v2: any] : (v0 = all_139_1 & ~ (all_139_0 = 0) &
% 224.88/38.00 | segmentP(all_143_0, all_139_1) = 0 & neq(all_143_0, nil) = v2 & (
% 224.88/38.00 | ~ (v2 = 0) | v1 = 0)))
% 224.88/38.00 |
% 224.88/38.00 | DELTA: instantiating (30) with fresh symbols all_145_0, all_145_1 gives:
% 224.88/38.01 | (31) singletonP(all_145_1) = all_145_0 & ssList(all_145_1) = 0 &
% 224.88/38.01 | $i(all_145_1) & ? [v0: any] : (all_145_1 = all_139_1 & ~ (all_139_0
% 224.88/38.01 | = 0) & segmentP(all_143_0, all_139_1) = 0 & neq(all_143_0, nil) =
% 224.88/38.01 | v0 & ( ~ (v0 = 0) | all_145_0 = 0))
% 224.88/38.01 |
% 224.88/38.01 | ALPHA: (31) implies:
% 224.88/38.01 | (32) $i(all_145_1)
% 224.88/38.01 | (33) ssList(all_145_1) = 0
% 224.88/38.01 | (34) singletonP(all_145_1) = all_145_0
% 224.88/38.01 | (35) ? [v0: any] : (all_145_1 = all_139_1 & ~ (all_139_0 = 0) &
% 224.88/38.01 | segmentP(all_143_0, all_139_1) = 0 & neq(all_143_0, nil) = v0 & ( ~
% 224.88/38.01 | (v0 = 0) | all_145_0 = 0))
% 224.88/38.01 |
% 224.88/38.01 | DELTA: instantiating (35) with fresh symbol all_147_0 gives:
% 224.88/38.01 | (36) all_145_1 = all_139_1 & ~ (all_139_0 = 0) & segmentP(all_143_0,
% 224.88/38.01 | all_139_1) = 0 & neq(all_143_0, nil) = all_147_0 & ( ~ (all_147_0 =
% 224.88/38.01 | 0) | all_145_0 = 0)
% 224.88/38.01 |
% 224.88/38.01 | ALPHA: (36) implies:
% 224.88/38.01 | (37) all_145_1 = all_139_1
% 224.88/38.01 | (38) ~ (all_139_0 = 0)
% 224.88/38.01 | (39) neq(all_143_0, nil) = all_147_0
% 224.88/38.01 | (40) segmentP(all_143_0, all_139_1) = 0
% 224.88/38.01 | (41) ~ (all_147_0 = 0) | all_145_0 = 0
% 224.88/38.01 |
% 224.88/38.01 | REDUCE: (34), (37) imply:
% 224.88/38.01 | (42) singletonP(all_139_1) = all_145_0
% 224.88/38.01 |
% 224.88/38.01 | REDUCE: (33), (37) imply:
% 224.88/38.01 | (43) ssList(all_139_1) = 0
% 224.88/38.01 |
% 224.88/38.01 | REDUCE: (32), (37) imply:
% 224.88/38.01 | (44) $i(all_139_1)
% 224.88/38.01 |
% 224.88/38.01 | GROUND_INST: instantiating (ax25) with nil, simplifying with (2), (15) gives:
% 224.88/38.01 | (45) ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | ?
% 224.88/38.01 | [v2: any] : ? [v3: $i] : (tl(v1) = v3 & ssItem(v0) = v2 & $i(v3) &
% 224.88/38.01 | ( ~ (v2 = 0) | v3 = nil)))
% 224.88/38.01 |
% 224.88/38.01 | GROUND_INST: instantiating (ax23) with nil, simplifying with (2), (15) gives:
% 224.88/38.01 | (46) ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | ?
% 224.88/38.01 | [v2: any] : ? [v3: $i] : (hd(v1) = v3 & ssItem(v0) = v2 & $i(v3) &
% 224.88/38.01 | ( ~ (v2 = 0) | v3 = v0)))
% 224.88/38.01 |
% 224.88/38.01 | GROUND_INST: instantiating (3) with all_139_1, simplifying with (43), (44)
% 224.88/38.01 | gives:
% 224.88/38.01 | (47) all_139_1 = nil | ? [v0: $i] : (ssList(v0) = 0 & $i(v0) & ? [v1: $i]
% 224.88/38.01 | : (cons(v1, v0) = all_139_1 & ssItem(v1) = 0 & $i(v1)))
% 224.88/38.01 |
% 224.88/38.01 | GROUND_INST: instantiating (3) with all_143_0, simplifying with (28), (29)
% 224.88/38.01 | gives:
% 224.88/38.01 | (48) all_143_0 = nil | ? [v0: $i] : (ssList(v0) = 0 & $i(v0) & ? [v1: $i]
% 224.88/38.01 | : (cons(v1, v0) = all_143_0 & ssItem(v1) = 0 & $i(v1)))
% 224.88/38.01 |
% 224.88/38.01 | GROUND_INST: instantiating (ax7) with all_143_0, simplifying with (28), (29)
% 224.88/38.01 | gives:
% 224.88/38.02 | (49) ! [v0: $i] : ! [v1: any] : ( ~ (segmentP(all_143_0, v0) = v1) | ~
% 224.88/38.02 | $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & ssList(v0) = v2) | (( ~ (v1 =
% 224.88/38.02 | 0) | ? [v2: $i] : ? [v3: $i] : (ssList(v2) = 0 & app(v2, v0)
% 224.88/38.02 | = v3 & $i(v3) & $i(v2) & ? [v4: $i] : (ssList(v4) = 0 &
% 224.88/38.02 | app(v3, v4) = all_143_0 & $i(v4)))) & (v1 = 0 | ! [v2: $i]
% 224.88/38.02 | : ! [v3: $i] : ( ~ (app(v2, v0) = v3) | ~ $i(v2) | ? [v4:
% 224.88/38.02 | int] : ( ~ (v4 = 0) & ssList(v2) = v4) | ! [v4: $i] : ( ~
% 224.88/38.02 | (app(v3, v4) = all_143_0) | ~ $i(v4) | ? [v5: int] : ( ~
% 224.88/38.02 | (v5 = 0) & ssList(v4) = v5))))))
% 224.88/38.02 |
% 224.88/38.02 | GROUND_INST: instantiating (ax15) with all_143_0, simplifying with (28), (29)
% 224.88/38.02 | gives:
% 224.88/38.02 | (50) ! [v0: $i] : ! [v1: any] : ( ~ (neq(all_143_0, v0) = v1) | ~ $i(v0)
% 224.88/38.02 | | ? [v2: int] : ( ~ (v2 = 0) & ssList(v0) = v2) | (( ~ (v1 = 0) |
% 224.88/38.02 | ~ (v0 = all_143_0)) & (v1 = 0 | v0 = all_143_0)))
% 224.88/38.02 |
% 224.88/38.02 | GROUND_INST: instantiating (ax54) with all_143_0, simplifying with (28), (29)
% 224.88/38.02 | gives:
% 224.88/38.02 | (51) ! [v0: any] : (v0 = all_143_0 | ~ (segmentP(all_143_0, v0) = 0) | ~
% 224.88/38.02 | $i(v0) | ? [v1: any] : ? [v2: any] : (segmentP(v0, all_143_0) = v2
% 224.88/38.02 | & ssList(v0) = v1 & ( ~ (v2 = 0) | ~ (v1 = 0))))
% 224.88/38.02 |
% 224.88/38.02 | GROUND_INST: instantiating (1) with all_139_1, all_145_0, simplifying with
% 224.88/38.02 | (42), (44) gives:
% 224.88/38.02 | (52) ? [v0: int] : ( ~ (v0 = 0) & ssList(all_139_1) = v0) | (( ~
% 224.88/38.02 | (all_145_0 = 0) | ? [v0: $i] : (cons(v0, nil) = all_139_1 &
% 224.88/38.02 | ssItem(v0) = 0 & $i(v0))) & (all_145_0 = 0 | ! [v0: $i] : ( ~
% 224.88/38.02 | (cons(v0, nil) = all_139_1) | ~ $i(v0) | ? [v1: int] : ( ~ (v1
% 224.88/38.02 | = 0) & ssItem(v0) = v1))))
% 224.88/38.02 |
% 224.88/38.02 | GROUND_INST: instantiating (ax11) with all_139_1, all_139_0, simplifying with
% 224.88/38.02 | (25), (44) gives:
% 224.88/38.02 | (53) ? [v0: int] : ( ~ (v0 = 0) & ssList(all_139_1) = v0) | (( ~
% 224.88/38.02 | (all_139_0 = 0) | ! [v0: $i] : ( ~ (ssItem(v0) = 0) | ~ $i(v0) |
% 224.88/38.02 | ! [v1: $i] : ! [v2: any] : ( ~ (leq(v0, v1) = v2) | ~ $i(v1)
% 224.88/38.02 | | ? [v3: int] : ( ~ (v3 = 0) & ssItem(v1) = v3) | ! [v3: $i]
% 224.88/38.02 | : ( ~ (ssList(v3) = 0) | ~ $i(v3) | ! [v4: $i] : ! [v5: $i]
% 224.88/38.02 | : ! [v6: $i] : ( ~ (cons(v0, v4) = v5) | ~ (app(v3, v5) =
% 224.88/38.02 | v6) | ~ $i(v4) | ? [v7: int] : ( ~ (v7 = 0) &
% 224.88/38.02 | ssList(v4) = v7) | ! [v7: $i] : ! [v8: $i] : (v2 = 0 |
% 224.88/38.02 | ~ (cons(v1, v7) = v8) | ~ (app(v6, v8) = all_139_1) |
% 224.88/38.02 | ~ $i(v7) | ? [v9: int] : ( ~ (v9 = 0) & ssList(v7) =
% 224.88/38.02 | v9))))))) & (all_139_0 = 0 | ? [v0: $i] : (ssItem(v0)
% 224.88/38.02 | = 0 & $i(v0) & ? [v1: $i] : ? [v2: any] : (leq(v0, v1) = v2 &
% 224.88/38.02 | ssItem(v1) = 0 & $i(v1) & ? [v3: $i] : (ssList(v3) = 0 &
% 224.88/38.02 | $i(v3) & ? [v4: $i] : ? [v5: $i] : ? [v6: $i] :
% 224.88/38.02 | (ssList(v4) = 0 & cons(v0, v4) = v5 & app(v3, v5) = v6 &
% 224.88/38.02 | $i(v6) & $i(v5) & $i(v4) & ? [v7: $i] : ? [v8: $i] : ( ~
% 224.88/38.02 | (v2 = 0) & ssList(v7) = 0 & cons(v1, v7) = v8 & app(v6,
% 224.88/38.02 | v8) = all_139_1 & $i(v8) & $i(v7))))))))
% 224.88/38.02 |
% 224.88/38.03 | GROUND_INST: instantiating (ax13) with nil, 0, simplifying with (13), (15)
% 224.88/38.03 | gives:
% 224.88/38.03 | (54) ? [v0: int] : ( ~ (v0 = 0) & ssList(nil) = v0) | ! [v0: $i] : ( ~
% 224.88/38.03 | (ssItem(v0) = 0) | ~ $i(v0) | ! [v1: $i] : ( ~ (ssItem(v1) = 0) |
% 224.88/38.03 | ~ $i(v1) | ! [v2: $i] : ( ~ (ssList(v2) = 0) | ~ $i(v2) | !
% 224.88/38.03 | [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (cons(v0, v3) = v4) |
% 224.88/38.03 | ~ (app(v2, v4) = v5) | ~ $i(v3) | ? [v6: int] : ( ~ (v6 =
% 224.88/38.03 | 0) & ssList(v3) = v6) | ! [v6: $i] : ! [v7: $i] : ( ~
% 224.88/38.03 | (v1 = v0) | ~ (cons(v0, v6) = v7) | ~ (app(v5, v7) = nil)
% 224.88/38.03 | | ~ $i(v6) | ? [v8: int] : ( ~ (v8 = 0) & ssList(v6) =
% 224.88/38.03 | v8))))))
% 224.88/38.03 |
% 224.88/38.03 | GROUND_INST: instantiating (51) with all_139_1, simplifying with (40), (44)
% 224.88/38.03 | gives:
% 224.88/38.03 | (55) all_143_0 = all_139_1 | ? [v0: any] : ? [v1: any] :
% 224.88/38.03 | (segmentP(all_139_1, all_143_0) = v1 & ssList(all_139_1) = v0 & ( ~
% 224.88/38.03 | (v1 = 0) | ~ (v0 = 0)))
% 224.88/38.03 |
% 224.88/38.03 | GROUND_INST: instantiating (50) with nil, all_147_0, simplifying with (15),
% 224.88/38.03 | (39) gives:
% 224.88/38.03 | (56) ? [v0: int] : ( ~ (v0 = 0) & ssList(nil) = v0) | (( ~ (all_147_0 = 0)
% 224.88/38.03 | | ~ (all_143_0 = nil)) & (all_147_0 = 0 | all_143_0 = nil))
% 224.88/38.03 |
% 224.88/38.03 | GROUND_INST: instantiating (49) with all_139_1, 0, simplifying with (40), (44)
% 224.88/38.03 | gives:
% 224.88/38.03 | (57) ? [v0: $i] : ? [v1: $i] : (ssList(v0) = 0 & app(v0, all_139_1) = v1
% 224.88/38.03 | & $i(v1) & $i(v0) & ? [v2: $i] : (ssList(v2) = 0 & app(v1, v2) =
% 224.88/38.03 | all_143_0 & $i(v2))) | ? [v0: int] : ( ~ (v0 = 0) &
% 224.88/38.03 | ssList(all_139_1) = v0)
% 224.88/38.03 |
% 224.88/38.03 | BETA: splitting (54) gives:
% 224.88/38.03 |
% 224.88/38.03 | Case 1:
% 224.88/38.03 | |
% 224.88/38.03 | | (58) ? [v0: int] : ( ~ (v0 = 0) & ssList(nil) = v0)
% 224.88/38.03 | |
% 224.88/38.03 | | REF_CLOSE: (2), (18), (58) are inconsistent by sub-proof #1.
% 224.88/38.03 | |
% 224.88/38.03 | Case 2:
% 224.88/38.03 | |
% 224.88/38.03 | | (59) ! [v0: $i] : ( ~ (ssItem(v0) = 0) | ~ $i(v0) | ! [v1: $i] : ( ~
% 224.88/38.03 | | (ssItem(v1) = 0) | ~ $i(v1) | ! [v2: $i] : ( ~ (ssList(v2) =
% 224.88/38.03 | | 0) | ~ $i(v2) | ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (
% 224.88/38.03 | | ~ (cons(v0, v3) = v4) | ~ (app(v2, v4) = v5) | ~ $i(v3) |
% 224.88/38.03 | | ? [v6: int] : ( ~ (v6 = 0) & ssList(v3) = v6) | ! [v6: $i]
% 224.88/38.03 | | : ! [v7: $i] : ( ~ (v1 = v0) | ~ (cons(v0, v6) = v7) | ~
% 224.88/38.03 | | (app(v5, v7) = nil) | ~ $i(v6) | ? [v8: int] : ( ~ (v8 =
% 224.88/38.03 | | 0) & ssList(v6) = v8))))))
% 224.88/38.03 | |
% 224.88/38.03 | | BETA: splitting (53) gives:
% 224.88/38.03 | |
% 224.88/38.03 | | Case 1:
% 224.88/38.03 | | |
% 224.88/38.03 | | | (60) ? [v0: int] : ( ~ (v0 = 0) & ssList(all_139_1) = v0)
% 224.88/38.03 | | |
% 224.88/38.03 | | | DELTA: instantiating (60) with fresh symbol all_340_0 gives:
% 224.88/38.03 | | | (61) ~ (all_340_0 = 0) & ssList(all_139_1) = all_340_0
% 224.88/38.03 | | |
% 224.88/38.03 | | | ALPHA: (61) implies:
% 224.88/38.03 | | | (62) ~ (all_340_0 = 0)
% 224.88/38.03 | | | (63) ssList(all_139_1) = all_340_0
% 224.88/38.03 | | |
% 224.88/38.03 | | | DELTA: instantiating (60) with fresh symbol all_344_0 gives:
% 224.88/38.04 | | | (64) ~ (all_344_0 = 0) & ssList(all_139_1) = all_344_0
% 224.88/38.04 | | |
% 224.88/38.04 | | | ALPHA: (64) implies:
% 224.88/38.04 | | | (65) ssList(all_139_1) = all_344_0
% 224.88/38.04 | | |
% 224.88/38.04 | | | GROUND_INST: instantiating (18) with 0, all_344_0, all_139_1, simplifying
% 224.88/38.04 | | | with (43), (65) gives:
% 224.88/38.04 | | | (66) all_344_0 = 0
% 224.88/38.04 | | |
% 224.88/38.04 | | | GROUND_INST: instantiating (18) with all_340_0, all_344_0, all_139_1,
% 224.88/38.04 | | | simplifying with (63), (65) gives:
% 224.88/38.04 | | | (67) all_344_0 = all_340_0
% 224.88/38.04 | | |
% 224.88/38.04 | | | COMBINE_EQS: (66), (67) imply:
% 224.88/38.04 | | | (68) all_340_0 = 0
% 224.88/38.04 | | |
% 224.88/38.04 | | | REDUCE: (62), (68) imply:
% 224.88/38.04 | | | (69) $false
% 224.88/38.04 | | |
% 224.88/38.04 | | | CLOSE: (69) is inconsistent.
% 224.88/38.04 | | |
% 224.88/38.04 | | Case 2:
% 224.88/38.04 | | |
% 224.88/38.04 | | | (70) ( ~ (all_139_0 = 0) | ! [v0: $i] : ( ~ (ssItem(v0) = 0) | ~
% 224.88/38.04 | | | $i(v0) | ! [v1: $i] : ! [v2: any] : ( ~ (leq(v0, v1) = v2) |
% 224.88/38.04 | | | ~ $i(v1) | ? [v3: int] : ( ~ (v3 = 0) & ssItem(v1) = v3) |
% 224.88/38.04 | | | ! [v3: $i] : ( ~ (ssList(v3) = 0) | ~ $i(v3) | ! [v4: $i]
% 224.88/38.04 | | | : ! [v5: $i] : ! [v6: $i] : ( ~ (cons(v0, v4) = v5) | ~
% 224.88/38.04 | | | (app(v3, v5) = v6) | ~ $i(v4) | ? [v7: int] : ( ~ (v7
% 224.88/38.04 | | | = 0) & ssList(v4) = v7) | ! [v7: $i] : ! [v8: $i]
% 224.88/38.04 | | | : (v2 = 0 | ~ (cons(v1, v7) = v8) | ~ (app(v6, v8) =
% 224.88/38.04 | | | all_139_1) | ~ $i(v7) | ? [v9: int] : ( ~ (v9 = 0)
% 224.88/38.04 | | | & ssList(v7) = v9))))))) & (all_139_0 = 0 | ? [v0:
% 224.88/38.04 | | | $i] : (ssItem(v0) = 0 & $i(v0) & ? [v1: $i] : ? [v2: any] :
% 224.88/38.04 | | | (leq(v0, v1) = v2 & ssItem(v1) = 0 & $i(v1) & ? [v3: $i] :
% 224.88/38.04 | | | (ssList(v3) = 0 & $i(v3) & ? [v4: $i] : ? [v5: $i] : ?
% 224.88/38.04 | | | [v6: $i] : (ssList(v4) = 0 & cons(v0, v4) = v5 & app(v3,
% 224.88/38.04 | | | v5) = v6 & $i(v6) & $i(v5) & $i(v4) & ? [v7: $i] : ?
% 224.88/38.04 | | | [v8: $i] : ( ~ (v2 = 0) & ssList(v7) = 0 & cons(v1, v7)
% 224.88/38.04 | | | = v8 & app(v6, v8) = all_139_1 & $i(v8) & $i(v7)))))))
% 224.88/38.04 | | |
% 224.88/38.04 | | | ALPHA: (70) implies:
% 224.88/38.04 | | | (71) all_139_0 = 0 | ? [v0: $i] : (ssItem(v0) = 0 & $i(v0) & ? [v1:
% 224.88/38.04 | | | $i] : ? [v2: any] : (leq(v0, v1) = v2 & ssItem(v1) = 0 &
% 224.88/38.04 | | | $i(v1) & ? [v3: $i] : (ssList(v3) = 0 & $i(v3) & ? [v4: $i]
% 224.88/38.04 | | | : ? [v5: $i] : ? [v6: $i] : (ssList(v4) = 0 & cons(v0, v4)
% 224.88/38.04 | | | = v5 & app(v3, v5) = v6 & $i(v6) & $i(v5) & $i(v4) & ?
% 224.88/38.04 | | | [v7: $i] : ? [v8: $i] : ( ~ (v2 = 0) & ssList(v7) = 0 &
% 224.88/38.04 | | | cons(v1, v7) = v8 & app(v6, v8) = all_139_1 & $i(v8) &
% 224.88/38.04 | | | $i(v7))))))
% 224.88/38.04 | | |
% 224.88/38.04 | | | BETA: splitting (57) gives:
% 224.88/38.04 | | |
% 224.88/38.04 | | | Case 1:
% 224.88/38.04 | | | |
% 224.88/38.04 | | | | (72) ? [v0: $i] : ? [v1: $i] : (ssList(v0) = 0 & app(v0, all_139_1)
% 224.88/38.04 | | | | = v1 & $i(v1) & $i(v0) & ? [v2: $i] : (ssList(v2) = 0 &
% 224.88/38.04 | | | | app(v1, v2) = all_143_0 & $i(v2)))
% 224.88/38.04 | | | |
% 224.88/38.04 | | | | DELTA: instantiating (72) with fresh symbols all_341_0, all_341_1 gives:
% 224.88/38.04 | | | | (73) ssList(all_341_1) = 0 & app(all_341_1, all_139_1) = all_341_0 &
% 224.88/38.04 | | | | $i(all_341_0) & $i(all_341_1) & ? [v0: $i] : (ssList(v0) = 0 &
% 224.88/38.04 | | | | app(all_341_0, v0) = all_143_0 & $i(v0))
% 224.88/38.04 | | | |
% 224.88/38.04 | | | | ALPHA: (73) implies:
% 224.88/38.04 | | | | (74) $i(all_341_1)
% 224.88/38.04 | | | | (75) app(all_341_1, all_139_1) = all_341_0
% 224.88/38.04 | | | | (76) ssList(all_341_1) = 0
% 224.88/38.04 | | | |
% 224.88/38.04 | | | | BETA: splitting (71) gives:
% 224.88/38.04 | | | |
% 224.88/38.04 | | | | Case 1:
% 224.88/38.04 | | | | |
% 224.88/38.04 | | | | | (77) all_139_0 = 0
% 224.88/38.04 | | | | |
% 224.88/38.04 | | | | | REDUCE: (38), (77) imply:
% 224.88/38.04 | | | | | (78) $false
% 224.88/38.04 | | | | |
% 224.88/38.04 | | | | | CLOSE: (78) is inconsistent.
% 224.88/38.04 | | | | |
% 224.88/38.04 | | | | Case 2:
% 224.88/38.04 | | | | |
% 224.88/38.05 | | | | | (79) ? [v0: $i] : (ssItem(v0) = 0 & $i(v0) & ? [v1: $i] : ? [v2:
% 224.88/38.05 | | | | | any] : (leq(v0, v1) = v2 & ssItem(v1) = 0 & $i(v1) & ?
% 224.88/38.05 | | | | | [v3: $i] : (ssList(v3) = 0 & $i(v3) & ? [v4: $i] : ?
% 224.88/38.05 | | | | | [v5: $i] : ? [v6: $i] : (ssList(v4) = 0 & cons(v0, v4)
% 224.88/38.05 | | | | | = v5 & app(v3, v5) = v6 & $i(v6) & $i(v5) & $i(v4) &
% 224.88/38.05 | | | | | ? [v7: $i] : ? [v8: $i] : ( ~ (v2 = 0) & ssList(v7) =
% 224.88/38.05 | | | | | 0 & cons(v1, v7) = v8 & app(v6, v8) = all_139_1 &
% 224.88/38.05 | | | | | $i(v8) & $i(v7))))))
% 224.88/38.05 | | | | |
% 224.88/38.05 | | | | | DELTA: instantiating (79) with fresh symbol all_353_0 gives:
% 224.88/38.05 | | | | | (80) ssItem(all_353_0) = 0 & $i(all_353_0) & ? [v0: $i] : ? [v1:
% 224.88/38.05 | | | | | any] : (leq(all_353_0, v0) = v1 & ssItem(v0) = 0 & $i(v0) &
% 224.88/38.05 | | | | | ? [v2: $i] : (ssList(v2) = 0 & $i(v2) & ? [v3: $i] : ?
% 224.88/38.05 | | | | | [v4: $i] : ? [v5: $i] : (ssList(v3) = 0 & cons(all_353_0,
% 224.88/38.05 | | | | | v3) = v4 & app(v2, v4) = v5 & $i(v5) & $i(v4) & $i(v3)
% 224.88/38.05 | | | | | & ? [v6: $i] : ? [v7: $i] : ( ~ (v1 = 0) & ssList(v6)
% 224.88/38.05 | | | | | = 0 & cons(v0, v6) = v7 & app(v5, v7) = all_139_1 &
% 224.88/38.05 | | | | | $i(v7) & $i(v6)))))
% 224.88/38.05 | | | | |
% 224.88/38.05 | | | | | ALPHA: (80) implies:
% 224.88/38.05 | | | | | (81) $i(all_353_0)
% 224.88/38.05 | | | | | (82) ssItem(all_353_0) = 0
% 224.88/38.05 | | | | |
% 224.88/38.05 | | | | | BETA: splitting (41) gives:
% 224.88/38.05 | | | | |
% 224.88/38.05 | | | | | Case 1:
% 224.88/38.05 | | | | | |
% 224.88/38.05 | | | | | | (83) ~ (all_147_0 = 0)
% 224.88/38.05 | | | | | |
% 224.88/38.05 | | | | | | BETA: splitting (56) gives:
% 224.88/38.05 | | | | | |
% 224.88/38.05 | | | | | | Case 1:
% 224.88/38.05 | | | | | | |
% 224.88/38.05 | | | | | | | (84) ? [v0: int] : ( ~ (v0 = 0) & ssList(nil) = v0)
% 224.88/38.05 | | | | | | |
% 224.88/38.05 | | | | | | | REF_CLOSE: (2), (18), (84) are inconsistent by sub-proof #1.
% 224.88/38.05 | | | | | | |
% 224.88/38.05 | | | | | | Case 2:
% 224.88/38.05 | | | | | | |
% 224.88/38.05 | | | | | | | (85) ( ~ (all_147_0 = 0) | ~ (all_143_0 = nil)) & (all_147_0 =
% 224.88/38.05 | | | | | | | 0 | all_143_0 = nil)
% 224.88/38.05 | | | | | | |
% 224.88/38.05 | | | | | | | ALPHA: (85) implies:
% 224.88/38.05 | | | | | | | (86) all_147_0 = 0 | all_143_0 = nil
% 224.88/38.05 | | | | | | |
% 224.88/38.05 | | | | | | | BETA: splitting (86) gives:
% 224.88/38.05 | | | | | | |
% 224.88/38.05 | | | | | | | Case 1:
% 224.88/38.05 | | | | | | | |
% 224.88/38.05 | | | | | | | | (87) all_143_0 = nil
% 224.88/38.05 | | | | | | | |
% 224.88/38.05 | | | | | | | | REDUCE: (40), (87) imply:
% 224.88/38.05 | | | | | | | | (88) segmentP(nil, all_139_1) = 0
% 224.88/38.05 | | | | | | | |
% 224.88/38.05 | | | | | | | | BETA: splitting (47) gives:
% 224.88/38.05 | | | | | | | |
% 224.88/38.05 | | | | | | | | Case 1:
% 224.88/38.05 | | | | | | | | |
% 224.88/38.05 | | | | | | | | | (89) all_139_1 = nil
% 224.88/38.05 | | | | | | | | |
% 224.88/38.05 | | | | | | | | | REDUCE: (25), (89) imply:
% 224.88/38.05 | | | | | | | | | (90) totalorderedP(nil) = all_139_0
% 224.88/38.05 | | | | | | | | |
% 224.88/38.05 | | | | | | | | | GROUND_INST: instantiating (20) with 0, all_139_0, nil,
% 224.88/38.05 | | | | | | | | | simplifying with (10), (90) gives:
% 224.88/38.05 | | | | | | | | | (91) all_139_0 = 0
% 224.88/38.05 | | | | | | | | |
% 224.88/38.05 | | | | | | | | | REDUCE: (38), (91) imply:
% 224.88/38.05 | | | | | | | | | (92) $false
% 224.88/38.05 | | | | | | | | |
% 224.88/38.05 | | | | | | | | | CLOSE: (92) is inconsistent.
% 224.88/38.05 | | | | | | | | |
% 224.88/38.05 | | | | | | | | Case 2:
% 224.88/38.05 | | | | | | | | |
% 224.88/38.05 | | | | | | | | | (93) ~ (all_139_1 = nil)
% 224.88/38.05 | | | | | | | | |
% 224.88/38.05 | | | | | | | | | GROUND_INST: instantiating (5) with all_139_1, 0, simplifying
% 224.88/38.05 | | | | | | | | | with (44), (88) gives:
% 224.88/38.05 | | | | | | | | | (94) all_139_1 = nil | ? [v0: int] : ( ~ (v0 = 0) &
% 224.88/38.05 | | | | | | | | | ssList(all_139_1) = v0)
% 224.88/38.05 | | | | | | | | |
% 224.88/38.05 | | | | | | | | | BETA: splitting (94) gives:
% 224.88/38.05 | | | | | | | | |
% 224.88/38.05 | | | | | | | | | Case 1:
% 224.88/38.05 | | | | | | | | | |
% 224.88/38.05 | | | | | | | | | | (95) all_139_1 = nil
% 224.88/38.05 | | | | | | | | | |
% 224.88/38.05 | | | | | | | | | | REDUCE: (93), (95) imply:
% 224.88/38.05 | | | | | | | | | | (96) $false
% 224.88/38.05 | | | | | | | | | |
% 224.88/38.05 | | | | | | | | | | CLOSE: (96) is inconsistent.
% 224.88/38.05 | | | | | | | | | |
% 224.88/38.05 | | | | | | | | | Case 2:
% 224.88/38.05 | | | | | | | | | |
% 224.88/38.05 | | | | | | | | | | (97) ? [v0: int] : ( ~ (v0 = 0) & ssList(all_139_1) =
% 224.88/38.05 | | | | | | | | | | v0)
% 224.88/38.05 | | | | | | | | | |
% 224.88/38.05 | | | | | | | | | | DELTA: instantiating (97) with fresh symbol all_416_0 gives:
% 224.88/38.05 | | | | | | | | | | (98) ~ (all_416_0 = 0) & ssList(all_139_1) = all_416_0
% 224.88/38.05 | | | | | | | | | |
% 224.88/38.05 | | | | | | | | | | ALPHA: (98) implies:
% 224.88/38.05 | | | | | | | | | | (99) ~ (all_416_0 = 0)
% 224.88/38.05 | | | | | | | | | | (100) ssList(all_139_1) = all_416_0
% 224.88/38.05 | | | | | | | | | |
% 224.88/38.05 | | | | | | | | | | GROUND_INST: instantiating (18) with 0, all_416_0, all_139_1,
% 224.88/38.05 | | | | | | | | | | simplifying with (43), (100) gives:
% 224.88/38.05 | | | | | | | | | | (101) all_416_0 = 0
% 224.88/38.05 | | | | | | | | | |
% 224.88/38.05 | | | | | | | | | | REDUCE: (99), (101) imply:
% 224.88/38.05 | | | | | | | | | | (102) $false
% 224.88/38.05 | | | | | | | | | |
% 224.88/38.05 | | | | | | | | | | CLOSE: (102) is inconsistent.
% 224.88/38.05 | | | | | | | | | |
% 224.88/38.05 | | | | | | | | | End of split
% 224.88/38.05 | | | | | | | | |
% 224.88/38.05 | | | | | | | | End of split
% 224.88/38.05 | | | | | | | |
% 224.88/38.05 | | | | | | | Case 2:
% 224.88/38.05 | | | | | | | |
% 224.88/38.05 | | | | | | | | (103) all_147_0 = 0
% 224.88/38.05 | | | | | | | |
% 224.88/38.05 | | | | | | | | REDUCE: (83), (103) imply:
% 224.88/38.05 | | | | | | | | (104) $false
% 224.88/38.05 | | | | | | | |
% 224.88/38.05 | | | | | | | | CLOSE: (104) is inconsistent.
% 224.88/38.05 | | | | | | | |
% 224.88/38.05 | | | | | | | End of split
% 224.88/38.05 | | | | | | |
% 224.88/38.05 | | | | | | End of split
% 224.88/38.05 | | | | | |
% 224.88/38.05 | | | | | Case 2:
% 224.88/38.05 | | | | | |
% 224.88/38.05 | | | | | | (105) all_145_0 = 0
% 224.88/38.05 | | | | | | (106) all_147_0 = 0
% 224.88/38.05 | | | | | |
% 224.88/38.05 | | | | | | REDUCE: (42), (105) imply:
% 224.88/38.05 | | | | | | (107) singletonP(all_139_1) = 0
% 224.88/38.05 | | | | | |
% 224.88/38.05 | | | | | | BETA: splitting (56) gives:
% 224.88/38.05 | | | | | |
% 224.88/38.05 | | | | | | Case 1:
% 224.88/38.05 | | | | | | |
% 224.88/38.05 | | | | | | | (108) ? [v0: int] : ( ~ (v0 = 0) & ssList(nil) = v0)
% 224.88/38.05 | | | | | | |
% 224.88/38.05 | | | | | | | DELTA: instantiating (108) with fresh symbol all_378_0 gives:
% 224.88/38.05 | | | | | | | (109) ~ (all_378_0 = 0) & ssList(nil) = all_378_0
% 224.88/38.05 | | | | | | |
% 224.88/38.05 | | | | | | | ALPHA: (109) implies:
% 224.88/38.05 | | | | | | | (110) ~ (all_378_0 = 0)
% 224.88/38.05 | | | | | | | (111) ssList(nil) = all_378_0
% 224.88/38.06 | | | | | | |
% 224.88/38.06 | | | | | | | GROUND_INST: instantiating (18) with 0, all_378_0, nil,
% 224.88/38.06 | | | | | | | simplifying with (2), (111) gives:
% 224.88/38.06 | | | | | | | (112) all_378_0 = 0
% 224.88/38.06 | | | | | | |
% 224.88/38.06 | | | | | | | REDUCE: (110), (112) imply:
% 224.88/38.06 | | | | | | | (113) $false
% 224.88/38.06 | | | | | | |
% 224.88/38.06 | | | | | | | CLOSE: (113) is inconsistent.
% 224.88/38.06 | | | | | | |
% 224.88/38.06 | | | | | | Case 2:
% 224.88/38.06 | | | | | | |
% 224.88/38.06 | | | | | | | (114) ( ~ (all_147_0 = 0) | ~ (all_143_0 = nil)) & (all_147_0
% 224.88/38.06 | | | | | | | = 0 | all_143_0 = nil)
% 224.88/38.06 | | | | | | |
% 224.88/38.06 | | | | | | | ALPHA: (114) implies:
% 224.88/38.06 | | | | | | | (115) ~ (all_147_0 = 0) | ~ (all_143_0 = nil)
% 224.88/38.06 | | | | | | |
% 224.88/38.06 | | | | | | | BETA: splitting (52) gives:
% 224.88/38.06 | | | | | | |
% 224.88/38.06 | | | | | | | Case 1:
% 224.88/38.06 | | | | | | | |
% 224.88/38.06 | | | | | | | | (116) ? [v0: int] : ( ~ (v0 = 0) & ssList(all_139_1) = v0)
% 224.88/38.06 | | | | | | | |
% 224.88/38.06 | | | | | | | | DELTA: instantiating (116) with fresh symbol all_379_0 gives:
% 224.88/38.06 | | | | | | | | (117) ~ (all_379_0 = 0) & ssList(all_139_1) = all_379_0
% 224.88/38.06 | | | | | | | |
% 224.88/38.06 | | | | | | | | ALPHA: (117) implies:
% 224.88/38.06 | | | | | | | | (118) ~ (all_379_0 = 0)
% 224.88/38.06 | | | | | | | | (119) ssList(all_139_1) = all_379_0
% 224.88/38.06 | | | | | | | |
% 224.88/38.06 | | | | | | | | GROUND_INST: instantiating (18) with 0, all_379_0, all_139_1,
% 224.88/38.06 | | | | | | | | simplifying with (43), (119) gives:
% 224.88/38.06 | | | | | | | | (120) all_379_0 = 0
% 224.88/38.06 | | | | | | | |
% 224.88/38.06 | | | | | | | | REDUCE: (118), (120) imply:
% 224.88/38.06 | | | | | | | | (121) $false
% 224.88/38.06 | | | | | | | |
% 224.88/38.06 | | | | | | | | CLOSE: (121) is inconsistent.
% 224.88/38.06 | | | | | | | |
% 224.88/38.06 | | | | | | | Case 2:
% 224.88/38.06 | | | | | | | |
% 224.88/38.06 | | | | | | | | (122) ( ~ (all_145_0 = 0) | ? [v0: $i] : (cons(v0, nil) =
% 224.88/38.06 | | | | | | | | all_139_1 & ssItem(v0) = 0 & $i(v0))) & (all_145_0
% 224.88/38.06 | | | | | | | | = 0 | ! [v0: $i] : ( ~ (cons(v0, nil) = all_139_1) |
% 224.88/38.06 | | | | | | | | ~ $i(v0) | ? [v1: int] : ( ~ (v1 = 0) &
% 224.88/38.06 | | | | | | | | ssItem(v0) = v1)))
% 224.88/38.06 | | | | | | | |
% 224.88/38.06 | | | | | | | | ALPHA: (122) implies:
% 224.88/38.06 | | | | | | | | (123) ~ (all_145_0 = 0) | ? [v0: $i] : (cons(v0, nil) =
% 224.88/38.06 | | | | | | | | all_139_1 & ssItem(v0) = 0 & $i(v0))
% 224.88/38.06 | | | | | | | |
% 224.88/38.06 | | | | | | | | BETA: splitting (115) gives:
% 224.88/38.06 | | | | | | | |
% 224.88/38.06 | | | | | | | | Case 1:
% 224.88/38.06 | | | | | | | | |
% 224.88/38.06 | | | | | | | | | (124) ~ (all_143_0 = nil)
% 224.88/38.06 | | | | | | | | |
% 224.88/38.06 | | | | | | | | | BETA: splitting (123) gives:
% 224.88/38.06 | | | | | | | | |
% 224.88/38.06 | | | | | | | | | Case 1:
% 224.88/38.06 | | | | | | | | | |
% 224.88/38.06 | | | | | | | | | | (125) ~ (all_145_0 = 0)
% 224.88/38.06 | | | | | | | | | |
% 224.88/38.06 | | | | | | | | | | REDUCE: (105), (125) imply:
% 224.88/38.06 | | | | | | | | | | (126) $false
% 224.88/38.06 | | | | | | | | | |
% 224.88/38.06 | | | | | | | | | | CLOSE: (126) is inconsistent.
% 224.88/38.06 | | | | | | | | | |
% 224.88/38.06 | | | | | | | | | Case 2:
% 224.88/38.06 | | | | | | | | | |
% 224.88/38.06 | | | | | | | | | | (127) ? [v0: $i] : (cons(v0, nil) = all_139_1 &
% 224.88/38.06 | | | | | | | | | | ssItem(v0) = 0 & $i(v0))
% 224.88/38.06 | | | | | | | | | |
% 224.88/38.06 | | | | | | | | | | DELTA: instantiating (127) with fresh symbol all_385_0
% 224.88/38.06 | | | | | | | | | | gives:
% 224.88/38.06 | | | | | | | | | | (128) cons(all_385_0, nil) = all_139_1 &
% 224.88/38.06 | | | | | | | | | | ssItem(all_385_0) = 0 & $i(all_385_0)
% 224.88/38.06 | | | | | | | | | |
% 224.88/38.06 | | | | | | | | | | ALPHA: (128) implies:
% 224.88/38.06 | | | | | | | | | | (129) $i(all_385_0)
% 224.88/38.06 | | | | | | | | | | (130) ssItem(all_385_0) = 0
% 224.88/38.06 | | | | | | | | | | (131) cons(all_385_0, nil) = all_139_1
% 224.88/38.06 | | | | | | | | | |
% 224.88/38.06 | | | | | | | | | | BETA: splitting (48) gives:
% 224.88/38.06 | | | | | | | | | |
% 224.88/38.06 | | | | | | | | | | Case 1:
% 224.88/38.06 | | | | | | | | | | |
% 224.88/38.06 | | | | | | | | | | | (132) all_143_0 = nil
% 224.88/38.06 | | | | | | | | | | |
% 224.88/38.06 | | | | | | | | | | | REDUCE: (124), (132) imply:
% 224.88/38.06 | | | | | | | | | | | (133) $false
% 224.88/38.06 | | | | | | | | | | |
% 224.88/38.06 | | | | | | | | | | | CLOSE: (133) is inconsistent.
% 224.88/38.06 | | | | | | | | | | |
% 224.88/38.06 | | | | | | | | | | Case 2:
% 224.88/38.06 | | | | | | | | | | |
% 224.88/38.06 | | | | | | | | | | | (134) ? [v0: $i] : (ssList(v0) = 0 & $i(v0) & ? [v1:
% 224.88/38.06 | | | | | | | | | | | $i] : (cons(v1, v0) = all_143_0 & ssItem(v1) =
% 224.88/38.06 | | | | | | | | | | | 0 & $i(v1)))
% 224.88/38.06 | | | | | | | | | | |
% 224.88/38.06 | | | | | | | | | | | DELTA: instantiating (134) with fresh symbol all_391_0
% 224.88/38.06 | | | | | | | | | | | gives:
% 224.88/38.06 | | | | | | | | | | | (135) ssList(all_391_0) = 0 & $i(all_391_0) & ? [v0:
% 224.88/38.06 | | | | | | | | | | | $i] : (cons(v0, all_391_0) = all_143_0 &
% 224.88/38.06 | | | | | | | | | | | ssItem(v0) = 0 & $i(v0))
% 224.88/38.06 | | | | | | | | | | |
% 224.88/38.06 | | | | | | | | | | | ALPHA: (135) implies:
% 224.88/38.06 | | | | | | | | | | | (136) $i(all_391_0)
% 224.88/38.06 | | | | | | | | | | | (137) ssList(all_391_0) = 0
% 224.88/38.06 | | | | | | | | | | | (138) ? [v0: $i] : (cons(v0, all_391_0) = all_143_0 &
% 224.88/38.06 | | | | | | | | | | | ssItem(v0) = 0 & $i(v0))
% 224.88/38.06 | | | | | | | | | | |
% 224.88/38.06 | | | | | | | | | | | DELTA: instantiating (138) with fresh symbol all_393_0
% 224.88/38.06 | | | | | | | | | | | gives:
% 224.88/38.06 | | | | | | | | | | | (139) cons(all_393_0, all_391_0) = all_143_0 &
% 224.88/38.06 | | | | | | | | | | | ssItem(all_393_0) = 0 & $i(all_393_0)
% 224.88/38.06 | | | | | | | | | | |
% 224.88/38.06 | | | | | | | | | | | ALPHA: (139) implies:
% 224.88/38.06 | | | | | | | | | | | (140) $i(all_393_0)
% 224.88/38.06 | | | | | | | | | | | (141) ssItem(all_393_0) = 0
% 224.88/38.06 | | | | | | | | | | | (142) cons(all_393_0, all_391_0) = all_143_0
% 224.88/38.06 | | | | | | | | | | |
% 224.88/38.06 | | | | | | | | | | | BETA: splitting (47) gives:
% 224.88/38.06 | | | | | | | | | | |
% 224.88/38.06 | | | | | | | | | | | Case 1:
% 224.88/38.06 | | | | | | | | | | | |
% 224.88/38.06 | | | | | | | | | | | | (143) all_139_1 = nil
% 224.88/38.06 | | | | | | | | | | | |
% 224.88/38.06 | | | | | | | | | | | | REDUCE: (107), (143) imply:
% 224.88/38.06 | | | | | | | | | | | | (144) singletonP(nil) = 0
% 224.88/38.06 | | | | | | | | | | | |
% 224.88/38.06 | | | | | | | | | | | | GROUND_INST: instantiating (19) with all_127_0, 0, nil,
% 224.88/38.06 | | | | | | | | | | | | simplifying with (23), (144) gives:
% 224.88/38.06 | | | | | | | | | | | | (145) all_127_0 = 0
% 224.88/38.06 | | | | | | | | | | | |
% 224.88/38.06 | | | | | | | | | | | | REDUCE: (22), (145) imply:
% 224.88/38.06 | | | | | | | | | | | | (146) $false
% 224.88/38.06 | | | | | | | | | | | |
% 224.88/38.06 | | | | | | | | | | | | CLOSE: (146) is inconsistent.
% 224.88/38.06 | | | | | | | | | | | |
% 224.88/38.06 | | | | | | | | | | | Case 2:
% 224.88/38.06 | | | | | | | | | | | |
% 224.88/38.06 | | | | | | | | | | | | (147) ? [v0: $i] : (ssList(v0) = 0 & $i(v0) & ? [v1:
% 224.88/38.06 | | | | | | | | | | | | $i] : (cons(v1, v0) = all_139_1 & ssItem(v1) =
% 224.88/38.06 | | | | | | | | | | | | 0 & $i(v1)))
% 224.88/38.06 | | | | | | | | | | | |
% 224.88/38.06 | | | | | | | | | | | | DELTA: instantiating (147) with fresh symbol all_401_0
% 224.88/38.06 | | | | | | | | | | | | gives:
% 224.88/38.07 | | | | | | | | | | | | (148) ssList(all_401_0) = 0 & $i(all_401_0) & ? [v0:
% 224.88/38.07 | | | | | | | | | | | | $i] : (cons(v0, all_401_0) = all_139_1 &
% 224.88/38.07 | | | | | | | | | | | | ssItem(v0) = 0 & $i(v0))
% 224.88/38.07 | | | | | | | | | | | |
% 224.88/38.07 | | | | | | | | | | | | ALPHA: (148) implies:
% 224.88/38.07 | | | | | | | | | | | | (149) $i(all_401_0)
% 224.88/38.07 | | | | | | | | | | | | (150) ssList(all_401_0) = 0
% 224.88/38.07 | | | | | | | | | | | | (151) ? [v0: $i] : (cons(v0, all_401_0) = all_139_1 &
% 224.88/38.07 | | | | | | | | | | | | ssItem(v0) = 0 & $i(v0))
% 224.88/38.07 | | | | | | | | | | | |
% 224.88/38.07 | | | | | | | | | | | | DELTA: instantiating (151) with fresh symbol all_403_0
% 224.88/38.07 | | | | | | | | | | | | gives:
% 224.88/38.07 | | | | | | | | | | | | (152) cons(all_403_0, all_401_0) = all_139_1 &
% 224.88/38.07 | | | | | | | | | | | | ssItem(all_403_0) = 0 & $i(all_403_0)
% 224.88/38.07 | | | | | | | | | | | |
% 224.88/38.07 | | | | | | | | | | | | ALPHA: (152) implies:
% 224.88/38.07 | | | | | | | | | | | | (153) $i(all_403_0)
% 224.88/38.07 | | | | | | | | | | | | (154) ssItem(all_403_0) = 0
% 224.88/38.07 | | | | | | | | | | | | (155) cons(all_403_0, all_401_0) = all_139_1
% 224.88/38.07 | | | | | | | | | | | |
% 224.88/38.07 | | | | | | | | | | | | BETA: splitting (55) gives:
% 224.88/38.07 | | | | | | | | | | | |
% 224.88/38.07 | | | | | | | | | | | | Case 1:
% 224.88/38.07 | | | | | | | | | | | | |
% 224.88/38.07 | | | | | | | | | | | | | (156) all_143_0 = all_139_1
% 224.88/38.07 | | | | | | | | | | | | |
% 224.88/38.07 | | | | | | | | | | | | | REDUCE: (142), (156) imply:
% 224.88/38.07 | | | | | | | | | | | | | (157) cons(all_393_0, all_391_0) = all_139_1
% 224.88/38.07 | | | | | | | | | | | | |
% 224.88/38.07 | | | | | | | | | | | | | GROUND_INST: instantiating (59) with all_393_0, simplifying
% 224.88/38.07 | | | | | | | | | | | | | with (140), (141) gives:
% 224.88/38.07 | | | | | | | | | | | | | (158) ! [v0: $i] : ( ~ (ssItem(v0) = 0) | ~ $i(v0) |
% 224.88/38.07 | | | | | | | | | | | | | ! [v1: $i] : ( ~ (ssList(v1) = 0) | ~ $i(v1) |
% 224.88/38.07 | | | | | | | | | | | | | ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 224.88/38.07 | | | | | | | | | | | | | (cons(all_393_0, v2) = v3) | ~ (app(v1, v3)
% 224.88/38.07 | | | | | | | | | | | | | = v4) | ~ $i(v2) | ? [v5: int] : ( ~ (v5
% 224.88/38.07 | | | | | | | | | | | | | = 0) & ssList(v2) = v5) | ! [v5: $i] :
% 224.88/38.07 | | | | | | | | | | | | | ! [v6: $i] : ( ~ (v0 = all_393_0) | ~
% 224.88/38.07 | | | | | | | | | | | | | (cons(all_393_0, v5) = v6) | ~ (app(v4,
% 224.88/38.07 | | | | | | | | | | | | | v6) = nil) | ~ $i(v5) | ? [v7: int]
% 224.88/38.07 | | | | | | | | | | | | | : ( ~ (v7 = 0) & ssList(v5) = v7)))))
% 224.88/38.07 | | | | | | | | | | | | |
% 224.88/38.07 | | | | | | | | | | | | | GROUND_INST: instantiating (45) with all_385_0, all_139_1,
% 224.88/38.07 | | | | | | | | | | | | | simplifying with (129), (131) gives:
% 224.88/38.07 | | | | | | | | | | | | | (159) ? [v0: any] : ? [v1: $i] : (tl(all_139_1) = v1 &
% 224.88/38.07 | | | | | | | | | | | | | ssItem(all_385_0) = v0 & $i(v1) & ( ~ (v0 = 0) |
% 224.88/38.07 | | | | | | | | | | | | | v1 = nil))
% 224.88/38.07 | | | | | | | | | | | | |
% 224.88/38.07 | | | | | | | | | | | | | GROUND_INST: instantiating (46) with all_385_0, all_139_1,
% 224.88/38.07 | | | | | | | | | | | | | simplifying with (129), (131) gives:
% 224.88/38.07 | | | | | | | | | | | | | (160) ? [v0: any] : ? [v1: $i] : (hd(all_139_1) = v1 &
% 224.88/38.07 | | | | | | | | | | | | | ssItem(all_385_0) = v0 & $i(v1) & ( ~ (v0 = 0) |
% 224.88/38.07 | | | | | | | | | | | | | v1 = all_385_0))
% 224.88/38.07 | | | | | | | | | | | | |
% 224.88/38.07 | | | | | | | | | | | | | GROUND_INST: instantiating (11) with all_385_0, all_139_1,
% 224.88/38.07 | | | | | | | | | | | | | simplifying with (129), (131) gives:
% 224.88/38.07 | | | | | | | | | | | | | (161) ? [v0: any] : ? [v1: any] :
% 224.88/38.07 | | | | | | | | | | | | | (strictorderedP(all_139_1) = v1 &
% 224.88/38.07 | | | | | | | | | | | | | ssItem(all_385_0) = v0 & ( ~ (v0 = 0) | v1 = 0))
% 224.88/38.07 | | | | | | | | | | | | |
% 224.88/38.07 | | | | | | | | | | | | | GROUND_INST: instantiating (9) with all_385_0, all_139_1,
% 224.88/38.07 | | | | | | | | | | | | | simplifying with (129), (131) gives:
% 224.88/38.07 | | | | | | | | | | | | | (162) ? [v0: any] : ? [v1: any] :
% 224.88/38.07 | | | | | | | | | | | | | (totalorderedP(all_139_1) = v1 & ssItem(all_385_0)
% 224.88/38.07 | | | | | | | | | | | | | = v0 & ( ~ (v0 = 0) | v1 = 0))
% 224.88/38.07 | | | | | | | | | | | | |
% 224.88/38.07 | | | | | | | | | | | | | GROUND_INST: instantiating (8) with all_385_0, all_139_1,
% 224.88/38.07 | | | | | | | | | | | | | simplifying with (129), (131) gives:
% 224.88/38.07 | | | | | | | | | | | | | (163) ? [v0: any] : ? [v1: any] :
% 224.88/38.07 | | | | | | | | | | | | | (strictorderP(all_139_1) = v1 & ssItem(all_385_0)
% 224.88/38.07 | | | | | | | | | | | | | = v0 & ( ~ (v0 = 0) | v1 = 0))
% 224.88/38.07 | | | | | | | | | | | | |
% 224.88/38.07 | | | | | | | | | | | | | GROUND_INST: instantiating (7) with all_385_0, all_139_1,
% 224.88/38.07 | | | | | | | | | | | | | simplifying with (129), (131) gives:
% 224.88/38.07 | | | | | | | | | | | | | (164) ? [v0: any] : ? [v1: any] :
% 224.88/38.07 | | | | | | | | | | | | | (totalorderP(all_139_1) = v1 & ssItem(all_385_0) =
% 224.88/38.07 | | | | | | | | | | | | | v0 & ( ~ (v0 = 0) | v1 = 0))
% 224.88/38.07 | | | | | | | | | | | | |
% 224.88/38.07 | | | | | | | | | | | | | GROUND_INST: instantiating (158) with all_353_0, simplifying
% 224.88/38.07 | | | | | | | | | | | | | with (81), (82) gives:
% 224.88/38.07 | | | | | | | | | | | | | (165) ! [v0: $i] : ( ~ (ssList(v0) = 0) | ~ $i(v0) |
% 224.88/38.07 | | | | | | | | | | | | | ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 224.88/38.07 | | | | | | | | | | | | | (cons(all_393_0, v1) = v2) | ~ (app(v0, v2) =
% 224.88/38.07 | | | | | | | | | | | | | v3) | ~ $i(v1) | ? [v4: int] : ( ~ (v4 =
% 224.88/38.07 | | | | | | | | | | | | | 0) & ssList(v1) = v4) | ! [v4: $i] : !
% 224.88/38.07 | | | | | | | | | | | | | [v5: $i] : ( ~ (all_393_0 = all_353_0) | ~
% 224.88/38.07 | | | | | | | | | | | | | (cons(all_353_0, v4) = v5) | ~ (app(v3, v5)
% 224.88/38.07 | | | | | | | | | | | | | = nil) | ~ $i(v4) | ? [v6: int] : ( ~
% 224.88/38.07 | | | | | | | | | | | | | (v6 = 0) & ssList(v4) = v6))))
% 224.88/38.07 | | | | | | | | | | | | |
% 224.88/38.07 | | | | | | | | | | | | | GROUND_INST: instantiating (165) with all_341_1, simplifying
% 224.88/38.07 | | | | | | | | | | | | | with (74), (76) gives:
% 224.88/38.07 | | | | | | | | | | | | | (166) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 224.88/38.07 | | | | | | | | | | | | | (cons(all_393_0, v0) = v1) | ~ (app(all_341_1,
% 224.88/38.07 | | | | | | | | | | | | | v1) = v2) | ~ $i(v0) | ? [v3: int] : ( ~
% 224.88/38.07 | | | | | | | | | | | | | (v3 = 0) & ssList(v0) = v3) | ! [v3: $i] : !
% 224.88/38.08 | | | | | | | | | | | | | [v4: $i] : ( ~ (all_393_0 = all_353_0) | ~
% 224.88/38.08 | | | | | | | | | | | | | (cons(all_353_0, v3) = v4) | ~ (app(v2, v4) =
% 224.88/38.08 | | | | | | | | | | | | | nil) | ~ $i(v3) | ? [v5: int] : ( ~ (v5 =
% 224.88/38.08 | | | | | | | | | | | | | 0) & ssList(v3) = v5)))
% 224.88/38.08 | | | | | | | | | | | | |
% 224.88/38.08 | | | | | | | | | | | | | GROUND_INST: instantiating (166) with all_391_0, all_139_1,
% 224.88/38.08 | | | | | | | | | | | | | all_341_0, simplifying with (75), (136), (157)
% 224.88/38.08 | | | | | | | | | | | | | gives:
% 224.88/38.08 | | | | | | | | | | | | | (167) ? [v0: int] : ( ~ (v0 = 0) & ssList(all_391_0) =
% 224.88/38.08 | | | | | | | | | | | | | v0) | ! [v0: $i] : ! [v1: $i] : ( ~ (all_393_0
% 224.88/38.08 | | | | | | | | | | | | | = all_353_0) | ~ (cons(all_353_0, v0) = v1) |
% 224.88/38.08 | | | | | | | | | | | | | ~ (app(all_341_0, v1) = nil) | ~ $i(v0) | ?
% 224.88/38.08 | | | | | | | | | | | | | [v2: int] : ( ~ (v2 = 0) & ssList(v0) = v2))
% 224.88/38.08 | | | | | | | | | | | | |
% 224.88/38.08 | | | | | | | | | | | | | DELTA: instantiating (164) with fresh symbols all_1799_0,
% 224.88/38.08 | | | | | | | | | | | | | all_1799_1 gives:
% 224.88/38.08 | | | | | | | | | | | | | (168) totalorderP(all_139_1) = all_1799_0 &
% 224.88/38.08 | | | | | | | | | | | | | ssItem(all_385_0) = all_1799_1 & ( ~ (all_1799_1 =
% 224.88/38.08 | | | | | | | | | | | | | 0) | all_1799_0 = 0)
% 224.88/38.08 | | | | | | | | | | | | |
% 224.88/38.08 | | | | | | | | | | | | | ALPHA: (168) implies:
% 224.88/38.08 | | | | | | | | | | | | | (169) ssItem(all_385_0) = all_1799_1
% 224.88/38.08 | | | | | | | | | | | | |
% 224.88/38.08 | | | | | | | | | | | | | DELTA: instantiating (163) with fresh symbols all_1801_0,
% 224.88/38.08 | | | | | | | | | | | | | all_1801_1 gives:
% 224.88/38.08 | | | | | | | | | | | | | (170) strictorderP(all_139_1) = all_1801_0 &
% 224.88/38.08 | | | | | | | | | | | | | ssItem(all_385_0) = all_1801_1 & ( ~ (all_1801_1 =
% 224.88/38.08 | | | | | | | | | | | | | 0) | all_1801_0 = 0)
% 224.88/38.08 | | | | | | | | | | | | |
% 224.88/38.08 | | | | | | | | | | | | | ALPHA: (170) implies:
% 224.88/38.08 | | | | | | | | | | | | | (171) ssItem(all_385_0) = all_1801_1
% 224.88/38.08 | | | | | | | | | | | | |
% 224.88/38.08 | | | | | | | | | | | | | DELTA: instantiating (162) with fresh symbols all_1803_0,
% 224.88/38.08 | | | | | | | | | | | | | all_1803_1 gives:
% 224.88/38.08 | | | | | | | | | | | | | (172) totalorderedP(all_139_1) = all_1803_0 &
% 224.88/38.08 | | | | | | | | | | | | | ssItem(all_385_0) = all_1803_1 & ( ~ (all_1803_1 =
% 224.88/38.08 | | | | | | | | | | | | | 0) | all_1803_0 = 0)
% 224.88/38.08 | | | | | | | | | | | | |
% 224.88/38.08 | | | | | | | | | | | | | ALPHA: (172) implies:
% 224.88/38.08 | | | | | | | | | | | | | (173) ssItem(all_385_0) = all_1803_1
% 224.88/38.08 | | | | | | | | | | | | | (174) totalorderedP(all_139_1) = all_1803_0
% 224.88/38.08 | | | | | | | | | | | | | (175) ~ (all_1803_1 = 0) | all_1803_0 = 0
% 224.88/38.08 | | | | | | | | | | | | |
% 224.88/38.08 | | | | | | | | | | | | | DELTA: instantiating (161) with fresh symbols all_1805_0,
% 224.88/38.08 | | | | | | | | | | | | | all_1805_1 gives:
% 224.88/38.08 | | | | | | | | | | | | | (176) strictorderedP(all_139_1) = all_1805_0 &
% 224.88/38.08 | | | | | | | | | | | | | ssItem(all_385_0) = all_1805_1 & ( ~ (all_1805_1 =
% 224.88/38.08 | | | | | | | | | | | | | 0) | all_1805_0 = 0)
% 224.88/38.08 | | | | | | | | | | | | |
% 224.88/38.08 | | | | | | | | | | | | | ALPHA: (176) implies:
% 224.88/38.08 | | | | | | | | | | | | | (177) ssItem(all_385_0) = all_1805_1
% 224.88/38.08 | | | | | | | | | | | | |
% 224.88/38.08 | | | | | | | | | | | | | DELTA: instantiating (160) with fresh symbols all_1807_0,
% 224.88/38.08 | | | | | | | | | | | | | all_1807_1 gives:
% 224.88/38.08 | | | | | | | | | | | | | (178) hd(all_139_1) = all_1807_0 & ssItem(all_385_0) =
% 224.88/38.08 | | | | | | | | | | | | | all_1807_1 & $i(all_1807_0) & ( ~ (all_1807_1 = 0)
% 224.88/38.08 | | | | | | | | | | | | | | all_1807_0 = all_385_0)
% 224.88/38.08 | | | | | | | | | | | | |
% 224.88/38.08 | | | | | | | | | | | | | ALPHA: (178) implies:
% 224.88/38.08 | | | | | | | | | | | | | (179) ssItem(all_385_0) = all_1807_1
% 224.88/38.08 | | | | | | | | | | | | |
% 224.88/38.08 | | | | | | | | | | | | | DELTA: instantiating (159) with fresh symbols all_1809_0,
% 224.88/38.08 | | | | | | | | | | | | | all_1809_1 gives:
% 224.88/38.08 | | | | | | | | | | | | | (180) tl(all_139_1) = all_1809_0 & ssItem(all_385_0) =
% 224.88/38.08 | | | | | | | | | | | | | all_1809_1 & $i(all_1809_0) & ( ~ (all_1809_1 = 0)
% 224.88/38.08 | | | | | | | | | | | | | | all_1809_0 = nil)
% 224.88/38.08 | | | | | | | | | | | | |
% 224.88/38.08 | | | | | | | | | | | | | ALPHA: (180) implies:
% 224.88/38.08 | | | | | | | | | | | | | (181) ssItem(all_385_0) = all_1809_1
% 224.88/38.08 | | | | | | | | | | | | |
% 224.88/38.08 | | | | | | | | | | | | | BETA: splitting (167) gives:
% 224.88/38.08 | | | | | | | | | | | | |
% 224.88/38.08 | | | | | | | | | | | | | Case 1:
% 224.88/38.08 | | | | | | | | | | | | | |
% 224.88/38.08 | | | | | | | | | | | | | | (182) ? [v0: int] : ( ~ (v0 = 0) & ssList(all_391_0) =
% 224.88/38.08 | | | | | | | | | | | | | | v0)
% 224.88/38.08 | | | | | | | | | | | | | |
% 224.88/38.08 | | | | | | | | | | | | | | DELTA: instantiating (182) with fresh symbol all_1963_0
% 224.88/38.08 | | | | | | | | | | | | | | gives:
% 224.88/38.08 | | | | | | | | | | | | | | (183) ~ (all_1963_0 = 0) & ssList(all_391_0) =
% 224.88/38.08 | | | | | | | | | | | | | | all_1963_0
% 224.88/38.08 | | | | | | | | | | | | | |
% 224.88/38.08 | | | | | | | | | | | | | | ALPHA: (183) implies:
% 224.88/38.08 | | | | | | | | | | | | | | (184) ~ (all_1963_0 = 0)
% 224.88/38.08 | | | | | | | | | | | | | | (185) ssList(all_391_0) = all_1963_0
% 224.88/38.08 | | | | | | | | | | | | | |
% 224.88/38.08 | | | | | | | | | | | | | | DELTA: instantiating (182) with fresh symbol all_1965_0
% 224.88/38.08 | | | | | | | | | | | | | | gives:
% 224.88/38.08 | | | | | | | | | | | | | | (186) ~ (all_1965_0 = 0) & ssList(all_391_0) =
% 224.88/38.08 | | | | | | | | | | | | | | all_1965_0
% 224.88/38.08 | | | | | | | | | | | | | |
% 224.88/38.08 | | | | | | | | | | | | | | ALPHA: (186) implies:
% 224.88/38.08 | | | | | | | | | | | | | | (187) ssList(all_391_0) = all_1965_0
% 224.88/38.08 | | | | | | | | | | | | | |
% 224.88/38.08 | | | | | | | | | | | | | | DELTA: instantiating (182) with fresh symbol all_1967_0
% 224.88/38.08 | | | | | | | | | | | | | | gives:
% 224.88/38.08 | | | | | | | | | | | | | | (188) ~ (all_1967_0 = 0) & ssList(all_391_0) =
% 224.88/38.08 | | | | | | | | | | | | | | all_1967_0
% 224.88/38.08 | | | | | | | | | | | | | |
% 224.88/38.08 | | | | | | | | | | | | | | ALPHA: (188) implies:
% 224.88/38.08 | | | | | | | | | | | | | | (189) ssList(all_391_0) = all_1967_0
% 224.88/38.08 | | | | | | | | | | | | | |
% 224.88/38.08 | | | | | | | | | | | | | | DELTA: instantiating (182) with fresh symbol all_1969_0
% 224.88/38.08 | | | | | | | | | | | | | | gives:
% 224.88/38.08 | | | | | | | | | | | | | | (190) ~ (all_1969_0 = 0) & ssList(all_391_0) =
% 224.88/38.08 | | | | | | | | | | | | | | all_1969_0
% 224.88/38.08 | | | | | | | | | | | | | |
% 224.88/38.08 | | | | | | | | | | | | | | ALPHA: (190) implies:
% 224.88/38.08 | | | | | | | | | | | | | | (191) ssList(all_391_0) = all_1969_0
% 224.88/38.08 | | | | | | | | | | | | | |
% 224.88/38.08 | | | | | | | | | | | | | | DELTA: instantiating (182) with fresh symbol all_1971_0
% 224.88/38.08 | | | | | | | | | | | | | | gives:
% 224.88/38.08 | | | | | | | | | | | | | | (192) ~ (all_1971_0 = 0) & ssList(all_391_0) =
% 224.88/38.08 | | | | | | | | | | | | | | all_1971_0
% 224.88/38.08 | | | | | | | | | | | | | |
% 224.88/38.08 | | | | | | | | | | | | | | ALPHA: (192) implies:
% 224.88/38.08 | | | | | | | | | | | | | | (193) ssList(all_391_0) = all_1971_0
% 224.88/38.08 | | | | | | | | | | | | | |
% 224.88/38.08 | | | | | | | | | | | | | | DELTA: instantiating (182) with fresh symbol all_1973_0
% 224.88/38.08 | | | | | | | | | | | | | | gives:
% 224.88/38.08 | | | | | | | | | | | | | | (194) ~ (all_1973_0 = 0) & ssList(all_391_0) =
% 224.88/38.08 | | | | | | | | | | | | | | all_1973_0
% 224.88/38.08 | | | | | | | | | | | | | |
% 224.88/38.08 | | | | | | | | | | | | | | ALPHA: (194) implies:
% 224.88/38.08 | | | | | | | | | | | | | | (195) ssList(all_391_0) = all_1973_0
% 224.88/38.08 | | | | | | | | | | | | | |
% 224.88/38.08 | | | | | | | | | | | | | | DELTA: instantiating (182) with fresh symbol all_1975_0
% 224.88/38.08 | | | | | | | | | | | | | | gives:
% 224.88/38.08 | | | | | | | | | | | | | | (196) ~ (all_1975_0 = 0) & ssList(all_391_0) =
% 224.88/38.08 | | | | | | | | | | | | | | all_1975_0
% 224.88/38.08 | | | | | | | | | | | | | |
% 224.88/38.08 | | | | | | | | | | | | | | ALPHA: (196) implies:
% 224.88/38.08 | | | | | | | | | | | | | | (197) ssList(all_391_0) = all_1975_0
% 224.88/38.08 | | | | | | | | | | | | | |
% 224.88/38.08 | | | | | | | | | | | | | | DELTA: instantiating (182) with fresh symbol all_1977_0
% 224.88/38.08 | | | | | | | | | | | | | | gives:
% 224.88/38.08 | | | | | | | | | | | | | | (198) ~ (all_1977_0 = 0) & ssList(all_391_0) =
% 224.88/38.08 | | | | | | | | | | | | | | all_1977_0
% 224.88/38.08 | | | | | | | | | | | | | |
% 224.88/38.08 | | | | | | | | | | | | | | ALPHA: (198) implies:
% 224.88/38.08 | | | | | | | | | | | | | | (199) ssList(all_391_0) = all_1977_0
% 224.88/38.08 | | | | | | | | | | | | | |
% 224.88/38.08 | | | | | | | | | | | | | | GROUND_INST: instantiating (18) with 0, all_1969_0, all_391_0,
% 224.88/38.08 | | | | | | | | | | | | | | simplifying with (137), (191) gives:
% 224.88/38.08 | | | | | | | | | | | | | | (200) all_1969_0 = 0
% 224.88/38.08 | | | | | | | | | | | | | |
% 224.88/38.08 | | | | | | | | | | | | | | GROUND_INST: instantiating (18) with all_1969_0, all_1971_0,
% 224.88/38.08 | | | | | | | | | | | | | | all_391_0, simplifying with (191), (193) gives:
% 224.88/38.08 | | | | | | | | | | | | | | (201) all_1971_0 = all_1969_0
% 224.88/38.08 | | | | | | | | | | | | | |
% 224.88/38.08 | | | | | | | | | | | | | | GROUND_INST: instantiating (18) with all_1963_0, all_1971_0,
% 224.88/38.08 | | | | | | | | | | | | | | all_391_0, simplifying with (185), (193) gives:
% 224.88/38.08 | | | | | | | | | | | | | | (202) all_1971_0 = all_1963_0
% 224.88/38.08 | | | | | | | | | | | | | |
% 224.88/38.08 | | | | | | | | | | | | | | GROUND_INST: instantiating (18) with all_1969_0, all_1973_0,
% 224.88/38.08 | | | | | | | | | | | | | | all_391_0, simplifying with (191), (195) gives:
% 224.88/38.09 | | | | | | | | | | | | | | (203) all_1973_0 = all_1969_0
% 224.88/38.09 | | | | | | | | | | | | | |
% 224.88/38.09 | | | | | | | | | | | | | | GROUND_INST: instantiating (18) with all_1965_0, all_1973_0,
% 224.88/38.09 | | | | | | | | | | | | | | all_391_0, simplifying with (187), (195) gives:
% 224.88/38.09 | | | | | | | | | | | | | | (204) all_1973_0 = all_1965_0
% 224.88/38.09 | | | | | | | | | | | | | |
% 224.88/38.09 | | | | | | | | | | | | | | GROUND_INST: instantiating (18) with all_1969_0, all_1975_0,
% 224.88/38.09 | | | | | | | | | | | | | | all_391_0, simplifying with (191), (197) gives:
% 224.88/38.09 | | | | | | | | | | | | | | (205) all_1975_0 = all_1969_0
% 224.88/38.09 | | | | | | | | | | | | | |
% 224.88/38.09 | | | | | | | | | | | | | | GROUND_INST: instantiating (18) with all_1975_0, all_1977_0,
% 224.88/38.09 | | | | | | | | | | | | | | all_391_0, simplifying with (197), (199) gives:
% 224.88/38.09 | | | | | | | | | | | | | | (206) all_1977_0 = all_1975_0
% 224.88/38.09 | | | | | | | | | | | | | |
% 224.88/38.09 | | | | | | | | | | | | | | GROUND_INST: instantiating (18) with all_1967_0, all_1977_0,
% 224.88/38.09 | | | | | | | | | | | | | | all_391_0, simplifying with (189), (199) gives:
% 224.88/38.09 | | | | | | | | | | | | | | (207) all_1977_0 = all_1967_0
% 224.88/38.09 | | | | | | | | | | | | | |
% 224.88/38.09 | | | | | | | | | | | | | | COMBINE_EQS: (206), (207) imply:
% 224.88/38.09 | | | | | | | | | | | | | | (208) all_1975_0 = all_1967_0
% 224.88/38.09 | | | | | | | | | | | | | |
% 224.88/38.09 | | | | | | | | | | | | | | SIMP: (208) implies:
% 224.88/38.09 | | | | | | | | | | | | | | (209) all_1975_0 = all_1967_0
% 224.88/38.09 | | | | | | | | | | | | | |
% 224.88/38.09 | | | | | | | | | | | | | | COMBINE_EQS: (205), (209) imply:
% 224.88/38.09 | | | | | | | | | | | | | | (210) all_1969_0 = all_1967_0
% 224.88/38.09 | | | | | | | | | | | | | |
% 224.88/38.09 | | | | | | | | | | | | | | SIMP: (210) implies:
% 224.88/38.09 | | | | | | | | | | | | | | (211) all_1969_0 = all_1967_0
% 224.88/38.09 | | | | | | | | | | | | | |
% 224.88/38.09 | | | | | | | | | | | | | | COMBINE_EQS: (203), (204) imply:
% 224.88/38.09 | | | | | | | | | | | | | | (212) all_1969_0 = all_1965_0
% 224.88/38.09 | | | | | | | | | | | | | |
% 224.88/38.09 | | | | | | | | | | | | | | SIMP: (212) implies:
% 224.88/38.09 | | | | | | | | | | | | | | (213) all_1969_0 = all_1965_0
% 224.88/38.09 | | | | | | | | | | | | | |
% 224.88/38.09 | | | | | | | | | | | | | | COMBINE_EQS: (201), (202) imply:
% 224.88/38.09 | | | | | | | | | | | | | | (214) all_1969_0 = all_1963_0
% 224.88/38.09 | | | | | | | | | | | | | |
% 224.88/38.09 | | | | | | | | | | | | | | SIMP: (214) implies:
% 224.88/38.09 | | | | | | | | | | | | | | (215) all_1969_0 = all_1963_0
% 224.88/38.09 | | | | | | | | | | | | | |
% 224.88/38.09 | | | | | | | | | | | | | | COMBINE_EQS: (211), (215) imply:
% 224.88/38.09 | | | | | | | | | | | | | | (216) all_1967_0 = all_1963_0
% 224.88/38.09 | | | | | | | | | | | | | |
% 224.88/38.09 | | | | | | | | | | | | | | COMBINE_EQS: (200), (211) imply:
% 224.88/38.09 | | | | | | | | | | | | | | (217) all_1967_0 = 0
% 224.88/38.09 | | | | | | | | | | | | | |
% 224.88/38.09 | | | | | | | | | | | | | | COMBINE_EQS: (211), (213) imply:
% 224.88/38.09 | | | | | | | | | | | | | | (218) all_1967_0 = all_1965_0
% 224.88/38.09 | | | | | | | | | | | | | |
% 224.88/38.09 | | | | | | | | | | | | | | COMBINE_EQS: (217), (218) imply:
% 224.88/38.09 | | | | | | | | | | | | | | (219) all_1965_0 = 0
% 224.88/38.09 | | | | | | | | | | | | | |
% 224.88/38.09 | | | | | | | | | | | | | | COMBINE_EQS: (216), (218) imply:
% 224.88/38.09 | | | | | | | | | | | | | | (220) all_1965_0 = all_1963_0
% 224.88/38.09 | | | | | | | | | | | | | |
% 224.88/38.09 | | | | | | | | | | | | | | COMBINE_EQS: (219), (220) imply:
% 224.88/38.09 | | | | | | | | | | | | | | (221) all_1963_0 = 0
% 224.88/38.09 | | | | | | | | | | | | | |
% 224.88/38.09 | | | | | | | | | | | | | | REDUCE: (184), (221) imply:
% 224.88/38.09 | | | | | | | | | | | | | | (222) $false
% 224.88/38.09 | | | | | | | | | | | | | |
% 224.88/38.09 | | | | | | | | | | | | | | CLOSE: (222) is inconsistent.
% 224.88/38.09 | | | | | | | | | | | | | |
% 224.88/38.09 | | | | | | | | | | | | | Case 2:
% 224.88/38.09 | | | | | | | | | | | | | |
% 224.88/38.09 | | | | | | | | | | | | | |
% 224.88/38.09 | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with 0, all_1801_1, all_385_0,
% 224.88/38.09 | | | | | | | | | | | | | | simplifying with (130), (171) gives:
% 224.88/38.09 | | | | | | | | | | | | | | (223) all_1801_1 = 0
% 224.88/38.09 | | | | | | | | | | | | | |
% 224.88/38.09 | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with all_1801_1, all_1803_1,
% 224.88/38.09 | | | | | | | | | | | | | | all_385_0, simplifying with (171), (173) gives:
% 224.88/38.09 | | | | | | | | | | | | | | (224) all_1803_1 = all_1801_1
% 224.88/38.09 | | | | | | | | | | | | | |
% 224.88/38.09 | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with all_1799_1, all_1807_1,
% 224.88/38.09 | | | | | | | | | | | | | | all_385_0, simplifying with (169), (179) gives:
% 224.88/38.09 | | | | | | | | | | | | | | (225) all_1807_1 = all_1799_1
% 224.88/38.09 | | | | | | | | | | | | | |
% 224.88/38.09 | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with all_1807_1, all_1809_1,
% 224.88/38.09 | | | | | | | | | | | | | | all_385_0, simplifying with (179), (181) gives:
% 224.88/38.09 | | | | | | | | | | | | | | (226) all_1809_1 = all_1807_1
% 224.88/38.09 | | | | | | | | | | | | | |
% 224.88/38.09 | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with all_1805_1, all_1809_1,
% 224.88/38.09 | | | | | | | | | | | | | | all_385_0, simplifying with (177), (181) gives:
% 224.88/38.09 | | | | | | | | | | | | | | (227) all_1809_1 = all_1805_1
% 224.88/38.09 | | | | | | | | | | | | | |
% 224.88/38.09 | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with all_1803_1, all_1809_1,
% 224.88/38.09 | | | | | | | | | | | | | | all_385_0, simplifying with (173), (181) gives:
% 224.88/38.09 | | | | | | | | | | | | | | (228) all_1809_1 = all_1803_1
% 224.88/38.09 | | | | | | | | | | | | | |
% 224.88/38.09 | | | | | | | | | | | | | | GROUND_INST: instantiating (20) with all_139_0, all_1803_0,
% 224.88/38.09 | | | | | | | | | | | | | | all_139_1, simplifying with (25), (174) gives:
% 224.88/38.09 | | | | | | | | | | | | | | (229) all_1803_0 = all_139_0
% 224.88/38.09 | | | | | | | | | | | | | |
% 224.88/38.09 | | | | | | | | | | | | | | COMBINE_EQS: (227), (228) imply:
% 224.88/38.09 | | | | | | | | | | | | | | (230) all_1805_1 = all_1803_1
% 224.88/38.09 | | | | | | | | | | | | | |
% 224.88/38.09 | | | | | | | | | | | | | | COMBINE_EQS: (226), (227) imply:
% 224.88/38.09 | | | | | | | | | | | | | | (231) all_1807_1 = all_1805_1
% 224.88/38.09 | | | | | | | | | | | | | |
% 224.88/38.09 | | | | | | | | | | | | | | SIMP: (231) implies:
% 224.88/38.09 | | | | | | | | | | | | | | (232) all_1807_1 = all_1805_1
% 224.88/38.09 | | | | | | | | | | | | | |
% 224.88/38.09 | | | | | | | | | | | | | | COMBINE_EQS: (225), (232) imply:
% 224.88/38.09 | | | | | | | | | | | | | | (233) all_1805_1 = all_1799_1
% 224.88/38.09 | | | | | | | | | | | | | |
% 224.88/38.09 | | | | | | | | | | | | | | SIMP: (233) implies:
% 224.88/38.09 | | | | | | | | | | | | | | (234) all_1805_1 = all_1799_1
% 224.88/38.09 | | | | | | | | | | | | | |
% 224.88/38.09 | | | | | | | | | | | | | | COMBINE_EQS: (230), (234) imply:
% 224.88/38.09 | | | | | | | | | | | | | | (235) all_1803_1 = all_1799_1
% 224.88/38.09 | | | | | | | | | | | | | |
% 224.88/38.09 | | | | | | | | | | | | | | SIMP: (235) implies:
% 224.88/38.09 | | | | | | | | | | | | | | (236) all_1803_1 = all_1799_1
% 224.88/38.09 | | | | | | | | | | | | | |
% 224.88/38.09 | | | | | | | | | | | | | | COMBINE_EQS: (224), (236) imply:
% 224.88/38.09 | | | | | | | | | | | | | | (237) all_1801_1 = all_1799_1
% 224.88/38.09 | | | | | | | | | | | | | |
% 224.88/38.09 | | | | | | | | | | | | | | SIMP: (237) implies:
% 224.88/38.09 | | | | | | | | | | | | | | (238) all_1801_1 = all_1799_1
% 224.88/38.09 | | | | | | | | | | | | | |
% 224.88/38.09 | | | | | | | | | | | | | | COMBINE_EQS: (223), (238) imply:
% 224.88/38.09 | | | | | | | | | | | | | | (239) all_1799_1 = 0
% 224.88/38.09 | | | | | | | | | | | | | |
% 224.88/38.09 | | | | | | | | | | | | | | COMBINE_EQS: (236), (239) imply:
% 224.88/38.09 | | | | | | | | | | | | | | (240) all_1803_1 = 0
% 224.88/38.09 | | | | | | | | | | | | | |
% 224.88/38.09 | | | | | | | | | | | | | | BETA: splitting (175) gives:
% 224.88/38.09 | | | | | | | | | | | | | |
% 224.88/38.09 | | | | | | | | | | | | | | Case 1:
% 224.88/38.09 | | | | | | | | | | | | | | |
% 224.88/38.09 | | | | | | | | | | | | | | | (241) ~ (all_1803_1 = 0)
% 224.88/38.09 | | | | | | | | | | | | | | |
% 224.88/38.09 | | | | | | | | | | | | | | | REDUCE: (240), (241) imply:
% 224.88/38.09 | | | | | | | | | | | | | | | (242) $false
% 224.88/38.09 | | | | | | | | | | | | | | |
% 224.88/38.09 | | | | | | | | | | | | | | | CLOSE: (242) is inconsistent.
% 224.88/38.09 | | | | | | | | | | | | | | |
% 224.88/38.09 | | | | | | | | | | | | | | Case 2:
% 224.88/38.09 | | | | | | | | | | | | | | |
% 224.88/38.09 | | | | | | | | | | | | | | | (243) all_1803_0 = 0
% 224.88/38.09 | | | | | | | | | | | | | | |
% 224.88/38.09 | | | | | | | | | | | | | | | COMBINE_EQS: (229), (243) imply:
% 224.88/38.09 | | | | | | | | | | | | | | | (244) all_139_0 = 0
% 224.88/38.09 | | | | | | | | | | | | | | |
% 224.88/38.09 | | | | | | | | | | | | | | | SIMP: (244) implies:
% 224.88/38.09 | | | | | | | | | | | | | | | (245) all_139_0 = 0
% 224.88/38.09 | | | | | | | | | | | | | | |
% 224.88/38.09 | | | | | | | | | | | | | | | REDUCE: (38), (245) imply:
% 224.88/38.09 | | | | | | | | | | | | | | | (246) $false
% 224.88/38.09 | | | | | | | | | | | | | | |
% 224.88/38.09 | | | | | | | | | | | | | | | CLOSE: (246) is inconsistent.
% 224.88/38.09 | | | | | | | | | | | | | | |
% 224.88/38.09 | | | | | | | | | | | | | | End of split
% 224.88/38.09 | | | | | | | | | | | | | |
% 224.88/38.09 | | | | | | | | | | | | | End of split
% 224.88/38.09 | | | | | | | | | | | | |
% 224.88/38.09 | | | | | | | | | | | | Case 2:
% 224.88/38.09 | | | | | | | | | | | | |
% 224.88/38.09 | | | | | | | | | | | | | (247) ? [v0: any] : ? [v1: any] : (segmentP(all_139_1,
% 224.88/38.09 | | | | | | | | | | | | | all_143_0) = v1 & ssList(all_139_1) = v0 & ( ~
% 224.88/38.09 | | | | | | | | | | | | | (v1 = 0) | ~ (v0 = 0)))
% 224.88/38.09 | | | | | | | | | | | | |
% 224.88/38.09 | | | | | | | | | | | | | DELTA: instantiating (247) with fresh symbols all_417_0,
% 224.88/38.09 | | | | | | | | | | | | | all_417_1 gives:
% 224.88/38.09 | | | | | | | | | | | | | (248) segmentP(all_139_1, all_143_0) = all_417_0 &
% 224.88/38.09 | | | | | | | | | | | | | ssList(all_139_1) = all_417_1 & ( ~ (all_417_0 =
% 224.88/38.09 | | | | | | | | | | | | | 0) | ~ (all_417_1 = 0))
% 224.88/38.09 | | | | | | | | | | | | |
% 224.88/38.09 | | | | | | | | | | | | | ALPHA: (248) implies:
% 224.88/38.09 | | | | | | | | | | | | | (249) ssList(all_139_1) = all_417_1
% 224.88/38.10 | | | | | | | | | | | | | (250) ~ (all_417_0 = 0) | ~ (all_417_1 = 0)
% 224.88/38.10 | | | | | | | | | | | | |
% 224.88/38.10 | | | | | | | | | | | | | GROUND_INST: instantiating (18) with 0, all_417_1, all_139_1,
% 224.88/38.10 | | | | | | | | | | | | | simplifying with (43), (249) gives:
% 224.88/38.10 | | | | | | | | | | | | | (251) all_417_1 = 0
% 224.88/38.10 | | | | | | | | | | | | |
% 224.88/38.10 | | | | | | | | | | | | | BETA: splitting (250) gives:
% 224.88/38.10 | | | | | | | | | | | | |
% 224.88/38.10 | | | | | | | | | | | | | Case 1:
% 224.88/38.10 | | | | | | | | | | | | | |
% 224.88/38.10 | | | | | | | | | | | | | |
% 224.88/38.10 | | | | | | | | | | | | | | GROUND_INST: instantiating (59) with all_403_0, simplifying
% 224.88/38.10 | | | | | | | | | | | | | | with (153), (154) gives:
% 224.88/38.10 | | | | | | | | | | | | | | (252) ! [v0: $i] : ( ~ (ssItem(v0) = 0) | ~ $i(v0) |
% 224.88/38.10 | | | | | | | | | | | | | | ! [v1: $i] : ( ~ (ssList(v1) = 0) | ~ $i(v1) |
% 224.88/38.10 | | | | | | | | | | | | | | ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 224.88/38.10 | | | | | | | | | | | | | | (cons(all_403_0, v2) = v3) | ~ (app(v1, v3)
% 224.88/38.10 | | | | | | | | | | | | | | = v4) | ~ $i(v2) | ? [v5: int] : ( ~ (v5
% 224.88/38.10 | | | | | | | | | | | | | | = 0) & ssList(v2) = v5) | ! [v5: $i] :
% 224.88/38.10 | | | | | | | | | | | | | | ! [v6: $i] : ( ~ (v0 = all_403_0) | ~
% 224.88/38.10 | | | | | | | | | | | | | | (cons(all_403_0, v5) = v6) | ~ (app(v4,
% 224.88/38.10 | | | | | | | | | | | | | | v6) = nil) | ~ $i(v5) | ? [v7: int]
% 224.88/38.10 | | | | | | | | | | | | | | : ( ~ (v7 = 0) & ssList(v5) = v7)))))
% 224.88/38.10 | | | | | | | | | | | | | |
% 224.88/38.10 | | | | | | | | | | | | | | GROUND_INST: instantiating (45) with all_385_0, all_139_1,
% 224.88/38.10 | | | | | | | | | | | | | | simplifying with (129), (131) gives:
% 224.88/38.10 | | | | | | | | | | | | | | (253) ? [v0: any] : ? [v1: $i] : (tl(all_139_1) = v1 &
% 224.88/38.10 | | | | | | | | | | | | | | ssItem(all_385_0) = v0 & $i(v1) & ( ~ (v0 = 0) |
% 224.88/38.10 | | | | | | | | | | | | | | v1 = nil))
% 224.88/38.10 | | | | | | | | | | | | | |
% 224.88/38.10 | | | | | | | | | | | | | | GROUND_INST: instantiating (46) with all_385_0, all_139_1,
% 224.88/38.10 | | | | | | | | | | | | | | simplifying with (129), (131) gives:
% 224.88/38.10 | | | | | | | | | | | | | | (254) ? [v0: any] : ? [v1: $i] : (hd(all_139_1) = v1 &
% 224.88/38.10 | | | | | | | | | | | | | | ssItem(all_385_0) = v0 & $i(v1) & ( ~ (v0 = 0) |
% 224.88/38.10 | | | | | | | | | | | | | | v1 = all_385_0))
% 224.88/38.10 | | | | | | | | | | | | | |
% 224.88/38.10 | | | | | | | | | | | | | | GROUND_INST: instantiating (14) with all_385_0, all_139_1,
% 224.88/38.10 | | | | | | | | | | | | | | simplifying with (129), (131) gives:
% 224.88/38.10 | | | | | | | | | | | | | | (255) ? [v0: any] : ? [v1: any] :
% 224.88/38.10 | | | | | | | | | | | | | | (equalelemsP(all_139_1) = v1 & ssItem(all_385_0) =
% 224.88/38.10 | | | | | | | | | | | | | | v0 & ( ~ (v0 = 0) | v1 = 0))
% 224.88/38.10 | | | | | | | | | | | | | |
% 224.88/38.10 | | | | | | | | | | | | | | GROUND_INST: instantiating (12) with all_385_0, all_139_1,
% 224.88/38.10 | | | | | | | | | | | | | | simplifying with (129), (131) gives:
% 224.88/38.10 | | | | | | | | | | | | | | (256) ? [v0: any] : ? [v1: any] :
% 224.88/38.10 | | | | | | | | | | | | | | (duplicatefreeP(all_139_1) = v1 &
% 224.88/38.10 | | | | | | | | | | | | | | ssItem(all_385_0) = v0 & ( ~ (v0 = 0) | v1 = 0))
% 224.88/38.10 | | | | | | | | | | | | | |
% 224.88/38.10 | | | | | | | | | | | | | | GROUND_INST: instantiating (11) with all_385_0, all_139_1,
% 224.88/38.10 | | | | | | | | | | | | | | simplifying with (129), (131) gives:
% 224.88/38.10 | | | | | | | | | | | | | | (257) ? [v0: any] : ? [v1: any] :
% 224.88/38.10 | | | | | | | | | | | | | | (strictorderedP(all_139_1) = v1 &
% 224.88/38.10 | | | | | | | | | | | | | | ssItem(all_385_0) = v0 & ( ~ (v0 = 0) | v1 = 0))
% 224.88/38.10 | | | | | | | | | | | | | |
% 224.88/38.10 | | | | | | | | | | | | | | GROUND_INST: instantiating (9) with all_385_0, all_139_1,
% 224.88/38.10 | | | | | | | | | | | | | | simplifying with (129), (131) gives:
% 224.88/38.10 | | | | | | | | | | | | | | (258) ? [v0: any] : ? [v1: any] :
% 224.88/38.10 | | | | | | | | | | | | | | (totalorderedP(all_139_1) = v1 & ssItem(all_385_0)
% 224.88/38.10 | | | | | | | | | | | | | | = v0 & ( ~ (v0 = 0) | v1 = 0))
% 224.88/38.10 | | | | | | | | | | | | | |
% 224.88/38.10 | | | | | | | | | | | | | | GROUND_INST: instantiating (8) with all_385_0, all_139_1,
% 224.88/38.10 | | | | | | | | | | | | | | simplifying with (129), (131) gives:
% 224.88/38.10 | | | | | | | | | | | | | | (259) ? [v0: any] : ? [v1: any] :
% 224.88/38.10 | | | | | | | | | | | | | | (strictorderP(all_139_1) = v1 & ssItem(all_385_0)
% 224.88/38.10 | | | | | | | | | | | | | | = v0 & ( ~ (v0 = 0) | v1 = 0))
% 224.88/38.10 | | | | | | | | | | | | | |
% 224.88/38.10 | | | | | | | | | | | | | | GROUND_INST: instantiating (7) with all_385_0, all_139_1,
% 224.88/38.10 | | | | | | | | | | | | | | simplifying with (129), (131) gives:
% 224.88/38.10 | | | | | | | | | | | | | | (260) ? [v0: any] : ? [v1: any] :
% 224.88/38.10 | | | | | | | | | | | | | | (totalorderP(all_139_1) = v1 & ssItem(all_385_0) =
% 224.88/38.10 | | | | | | | | | | | | | | v0 & ( ~ (v0 = 0) | v1 = 0))
% 224.88/38.10 | | | | | | | | | | | | | |
% 224.88/38.10 | | | | | | | | | | | | | | GROUND_INST: instantiating (6) with all_385_0, all_139_1,
% 224.88/38.10 | | | | | | | | | | | | | | simplifying with (129), (131) gives:
% 224.88/38.10 | | | | | | | | | | | | | | (261) ? [v0: any] : ? [v1: any] :
% 224.88/38.10 | | | | | | | | | | | | | | (cyclefreeP(all_139_1) = v1 & ssItem(all_385_0) =
% 224.88/38.10 | | | | | | | | | | | | | | v0 & ( ~ (v0 = 0) | v1 = 0))
% 224.88/38.10 | | | | | | | | | | | | | |
% 224.88/38.10 | | | | | | | | | | | | | | GROUND_INST: instantiating (252) with all_385_0, simplifying
% 224.88/38.10 | | | | | | | | | | | | | | with (129), (130) gives:
% 224.88/38.10 | | | | | | | | | | | | | | (262) ! [v0: $i] : ( ~ (ssList(v0) = 0) | ~ $i(v0) |
% 224.88/38.10 | | | | | | | | | | | | | | ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 224.88/38.10 | | | | | | | | | | | | | | (cons(all_403_0, v1) = v2) | ~ (app(v0, v2) =
% 224.88/38.10 | | | | | | | | | | | | | | v3) | ~ $i(v1) | ? [v4: int] : ( ~ (v4 =
% 224.88/38.10 | | | | | | | | | | | | | | 0) & ssList(v1) = v4) | ! [v4: $i] : !
% 224.88/38.10 | | | | | | | | | | | | | | [v5: $i] : ( ~ (all_403_0 = all_385_0) | ~
% 224.88/38.10 | | | | | | | | | | | | | | (cons(all_385_0, v4) = v5) | ~ (app(v3, v5)
% 224.88/38.10 | | | | | | | | | | | | | | = nil) | ~ $i(v4) | ? [v6: int] : ( ~
% 224.88/38.10 | | | | | | | | | | | | | | (v6 = 0) & ssList(v4) = v6))))
% 224.88/38.10 | | | | | | | | | | | | | |
% 224.88/38.10 | | | | | | | | | | | | | | GROUND_INST: instantiating (262) with all_341_1, simplifying
% 224.88/38.10 | | | | | | | | | | | | | | with (74), (76) gives:
% 224.88/38.10 | | | | | | | | | | | | | | (263) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 224.88/38.10 | | | | | | | | | | | | | | (cons(all_403_0, v0) = v1) | ~ (app(all_341_1,
% 224.88/38.10 | | | | | | | | | | | | | | v1) = v2) | ~ $i(v0) | ? [v3: int] : ( ~
% 224.88/38.10 | | | | | | | | | | | | | | (v3 = 0) & ssList(v0) = v3) | ! [v3: $i] : !
% 224.88/38.10 | | | | | | | | | | | | | | [v4: $i] : ( ~ (all_403_0 = all_385_0) | ~
% 224.88/38.10 | | | | | | | | | | | | | | (cons(all_385_0, v3) = v4) | ~ (app(v2, v4) =
% 224.88/38.10 | | | | | | | | | | | | | | nil) | ~ $i(v3) | ? [v5: int] : ( ~ (v5 =
% 224.88/38.10 | | | | | | | | | | | | | | 0) & ssList(v3) = v5)))
% 224.88/38.10 | | | | | | | | | | | | | |
% 224.88/38.10 | | | | | | | | | | | | | | GROUND_INST: instantiating (263) with all_401_0, all_139_1,
% 224.88/38.10 | | | | | | | | | | | | | | all_341_0, simplifying with (75), (149), (155)
% 224.88/38.10 | | | | | | | | | | | | | | gives:
% 224.88/38.11 | | | | | | | | | | | | | | (264) ? [v0: int] : ( ~ (v0 = 0) & ssList(all_401_0) =
% 224.88/38.11 | | | | | | | | | | | | | | v0) | ! [v0: $i] : ! [v1: $i] : ( ~ (all_403_0
% 224.88/38.11 | | | | | | | | | | | | | | = all_385_0) | ~ (cons(all_385_0, v0) = v1) |
% 224.88/38.11 | | | | | | | | | | | | | | ~ (app(all_341_0, v1) = nil) | ~ $i(v0) | ?
% 224.88/38.11 | | | | | | | | | | | | | | [v2: int] : ( ~ (v2 = 0) & ssList(v0) = v2))
% 224.88/38.11 | | | | | | | | | | | | | |
% 224.88/38.11 | | | | | | | | | | | | | | DELTA: instantiating (256) with fresh symbols all_1895_0,
% 224.88/38.11 | | | | | | | | | | | | | | all_1895_1 gives:
% 224.88/38.11 | | | | | | | | | | | | | | (265) duplicatefreeP(all_139_1) = all_1895_0 &
% 224.88/38.11 | | | | | | | | | | | | | | ssItem(all_385_0) = all_1895_1 & ( ~ (all_1895_1 =
% 224.88/38.11 | | | | | | | | | | | | | | 0) | all_1895_0 = 0)
% 224.88/38.11 | | | | | | | | | | | | | |
% 224.88/38.11 | | | | | | | | | | | | | | ALPHA: (265) implies:
% 224.88/38.11 | | | | | | | | | | | | | | (266) ssItem(all_385_0) = all_1895_1
% 224.88/38.11 | | | | | | | | | | | | | |
% 224.88/38.11 | | | | | | | | | | | | | | DELTA: instantiating (255) with fresh symbols all_1897_0,
% 224.88/38.11 | | | | | | | | | | | | | | all_1897_1 gives:
% 224.88/38.11 | | | | | | | | | | | | | | (267) equalelemsP(all_139_1) = all_1897_0 &
% 224.88/38.11 | | | | | | | | | | | | | | ssItem(all_385_0) = all_1897_1 & ( ~ (all_1897_1 =
% 224.88/38.11 | | | | | | | | | | | | | | 0) | all_1897_0 = 0)
% 224.88/38.11 | | | | | | | | | | | | | |
% 224.88/38.11 | | | | | | | | | | | | | | ALPHA: (267) implies:
% 224.88/38.11 | | | | | | | | | | | | | | (268) ssItem(all_385_0) = all_1897_1
% 224.88/38.11 | | | | | | | | | | | | | |
% 224.88/38.11 | | | | | | | | | | | | | | DELTA: instantiating (261) with fresh symbols all_1899_0,
% 224.88/38.11 | | | | | | | | | | | | | | all_1899_1 gives:
% 224.88/38.11 | | | | | | | | | | | | | | (269) cyclefreeP(all_139_1) = all_1899_0 &
% 224.88/38.11 | | | | | | | | | | | | | | ssItem(all_385_0) = all_1899_1 & ( ~ (all_1899_1 =
% 224.88/38.11 | | | | | | | | | | | | | | 0) | all_1899_0 = 0)
% 224.88/38.11 | | | | | | | | | | | | | |
% 224.88/38.11 | | | | | | | | | | | | | | ALPHA: (269) implies:
% 224.88/38.11 | | | | | | | | | | | | | | (270) ssItem(all_385_0) = all_1899_1
% 224.88/38.11 | | | | | | | | | | | | | |
% 224.88/38.11 | | | | | | | | | | | | | | DELTA: instantiating (260) with fresh symbols all_1901_0,
% 224.88/38.11 | | | | | | | | | | | | | | all_1901_1 gives:
% 224.88/38.11 | | | | | | | | | | | | | | (271) totalorderP(all_139_1) = all_1901_0 &
% 224.88/38.11 | | | | | | | | | | | | | | ssItem(all_385_0) = all_1901_1 & ( ~ (all_1901_1 =
% 224.88/38.11 | | | | | | | | | | | | | | 0) | all_1901_0 = 0)
% 224.88/38.11 | | | | | | | | | | | | | |
% 224.88/38.11 | | | | | | | | | | | | | | ALPHA: (271) implies:
% 224.88/38.11 | | | | | | | | | | | | | | (272) ssItem(all_385_0) = all_1901_1
% 224.88/38.11 | | | | | | | | | | | | | |
% 224.88/38.11 | | | | | | | | | | | | | | DELTA: instantiating (259) with fresh symbols all_1903_0,
% 224.88/38.11 | | | | | | | | | | | | | | all_1903_1 gives:
% 224.88/38.11 | | | | | | | | | | | | | | (273) strictorderP(all_139_1) = all_1903_0 &
% 224.88/38.11 | | | | | | | | | | | | | | ssItem(all_385_0) = all_1903_1 & ( ~ (all_1903_1 =
% 224.88/38.11 | | | | | | | | | | | | | | 0) | all_1903_0 = 0)
% 224.88/38.11 | | | | | | | | | | | | | |
% 224.88/38.11 | | | | | | | | | | | | | | ALPHA: (273) implies:
% 224.88/38.11 | | | | | | | | | | | | | | (274) ssItem(all_385_0) = all_1903_1
% 224.88/38.11 | | | | | | | | | | | | | |
% 224.88/38.11 | | | | | | | | | | | | | | DELTA: instantiating (258) with fresh symbols all_1905_0,
% 224.88/38.11 | | | | | | | | | | | | | | all_1905_1 gives:
% 224.88/38.11 | | | | | | | | | | | | | | (275) totalorderedP(all_139_1) = all_1905_0 &
% 224.88/38.11 | | | | | | | | | | | | | | ssItem(all_385_0) = all_1905_1 & ( ~ (all_1905_1 =
% 224.88/38.11 | | | | | | | | | | | | | | 0) | all_1905_0 = 0)
% 224.88/38.11 | | | | | | | | | | | | | |
% 224.88/38.11 | | | | | | | | | | | | | | ALPHA: (275) implies:
% 224.88/38.11 | | | | | | | | | | | | | | (276) ssItem(all_385_0) = all_1905_1
% 224.88/38.11 | | | | | | | | | | | | | | (277) totalorderedP(all_139_1) = all_1905_0
% 224.88/38.11 | | | | | | | | | | | | | | (278) ~ (all_1905_1 = 0) | all_1905_0 = 0
% 224.88/38.11 | | | | | | | | | | | | | |
% 224.88/38.11 | | | | | | | | | | | | | | DELTA: instantiating (257) with fresh symbols all_1907_0,
% 224.88/38.11 | | | | | | | | | | | | | | all_1907_1 gives:
% 224.88/38.11 | | | | | | | | | | | | | | (279) strictorderedP(all_139_1) = all_1907_0 &
% 224.88/38.11 | | | | | | | | | | | | | | ssItem(all_385_0) = all_1907_1 & ( ~ (all_1907_1 =
% 224.88/38.11 | | | | | | | | | | | | | | 0) | all_1907_0 = 0)
% 224.88/38.11 | | | | | | | | | | | | | |
% 224.88/38.11 | | | | | | | | | | | | | | ALPHA: (279) implies:
% 224.88/38.11 | | | | | | | | | | | | | | (280) ssItem(all_385_0) = all_1907_1
% 224.88/38.11 | | | | | | | | | | | | | |
% 224.88/38.11 | | | | | | | | | | | | | | DELTA: instantiating (254) with fresh symbols all_1909_0,
% 224.88/38.11 | | | | | | | | | | | | | | all_1909_1 gives:
% 224.88/38.11 | | | | | | | | | | | | | | (281) hd(all_139_1) = all_1909_0 & ssItem(all_385_0) =
% 224.88/38.11 | | | | | | | | | | | | | | all_1909_1 & $i(all_1909_0) & ( ~ (all_1909_1 = 0)
% 224.88/38.11 | | | | | | | | | | | | | | | all_1909_0 = all_385_0)
% 224.88/38.11 | | | | | | | | | | | | | |
% 224.88/38.11 | | | | | | | | | | | | | | ALPHA: (281) implies:
% 224.88/38.11 | | | | | | | | | | | | | | (282) ssItem(all_385_0) = all_1909_1
% 224.88/38.11 | | | | | | | | | | | | | |
% 224.88/38.11 | | | | | | | | | | | | | | DELTA: instantiating (253) with fresh symbols all_1911_0,
% 224.88/38.11 | | | | | | | | | | | | | | all_1911_1 gives:
% 224.88/38.11 | | | | | | | | | | | | | | (283) tl(all_139_1) = all_1911_0 & ssItem(all_385_0) =
% 224.88/38.11 | | | | | | | | | | | | | | all_1911_1 & $i(all_1911_0) & ( ~ (all_1911_1 = 0)
% 224.88/38.11 | | | | | | | | | | | | | | | all_1911_0 = nil)
% 224.88/38.11 | | | | | | | | | | | | | |
% 224.88/38.11 | | | | | | | | | | | | | | ALPHA: (283) implies:
% 224.88/38.11 | | | | | | | | | | | | | | (284) ssItem(all_385_0) = all_1911_1
% 224.88/38.11 | | | | | | | | | | | | | |
% 224.88/38.11 | | | | | | | | | | | | | | BETA: splitting (264) gives:
% 224.88/38.11 | | | | | | | | | | | | | |
% 224.88/38.11 | | | | | | | | | | | | | | Case 1:
% 224.88/38.11 | | | | | | | | | | | | | | |
% 224.88/38.11 | | | | | | | | | | | | | | | (285) ? [v0: int] : ( ~ (v0 = 0) & ssList(all_401_0) =
% 224.88/38.11 | | | | | | | | | | | | | | | v0)
% 224.88/38.11 | | | | | | | | | | | | | | |
% 224.88/38.11 | | | | | | | | | | | | | | | DELTA: instantiating (285) with fresh symbol all_1956_0
% 224.88/38.11 | | | | | | | | | | | | | | | gives:
% 224.88/38.11 | | | | | | | | | | | | | | | (286) ~ (all_1956_0 = 0) & ssList(all_401_0) =
% 224.88/38.11 | | | | | | | | | | | | | | | all_1956_0
% 224.88/38.11 | | | | | | | | | | | | | | |
% 224.88/38.11 | | | | | | | | | | | | | | | ALPHA: (286) implies:
% 224.88/38.11 | | | | | | | | | | | | | | | (287) ~ (all_1956_0 = 0)
% 224.88/38.11 | | | | | | | | | | | | | | | (288) ssList(all_401_0) = all_1956_0
% 224.88/38.11 | | | | | | | | | | | | | | |
% 224.88/38.11 | | | | | | | | | | | | | | | DELTA: instantiating (285) with fresh symbol all_1958_0
% 224.88/38.11 | | | | | | | | | | | | | | | gives:
% 224.88/38.11 | | | | | | | | | | | | | | | (289) ~ (all_1958_0 = 0) & ssList(all_401_0) =
% 224.88/38.11 | | | | | | | | | | | | | | | all_1958_0
% 224.88/38.11 | | | | | | | | | | | | | | |
% 224.88/38.11 | | | | | | | | | | | | | | | ALPHA: (289) implies:
% 224.88/38.11 | | | | | | | | | | | | | | | (290) ssList(all_401_0) = all_1958_0
% 224.88/38.11 | | | | | | | | | | | | | | |
% 224.88/38.11 | | | | | | | | | | | | | | | DELTA: instantiating (285) with fresh symbol all_1960_0
% 224.88/38.11 | | | | | | | | | | | | | | | gives:
% 224.88/38.11 | | | | | | | | | | | | | | | (291) ~ (all_1960_0 = 0) & ssList(all_401_0) =
% 224.88/38.11 | | | | | | | | | | | | | | | all_1960_0
% 224.88/38.11 | | | | | | | | | | | | | | |
% 224.88/38.11 | | | | | | | | | | | | | | | ALPHA: (291) implies:
% 224.88/38.11 | | | | | | | | | | | | | | | (292) ssList(all_401_0) = all_1960_0
% 224.88/38.11 | | | | | | | | | | | | | | |
% 224.88/38.11 | | | | | | | | | | | | | | | DELTA: instantiating (285) with fresh symbol all_1972_0
% 224.88/38.11 | | | | | | | | | | | | | | | gives:
% 224.88/38.11 | | | | | | | | | | | | | | | (293) ~ (all_1972_0 = 0) & ssList(all_401_0) =
% 224.88/38.11 | | | | | | | | | | | | | | | all_1972_0
% 224.88/38.11 | | | | | | | | | | | | | | |
% 224.88/38.11 | | | | | | | | | | | | | | | ALPHA: (293) implies:
% 224.88/38.11 | | | | | | | | | | | | | | | (294) ssList(all_401_0) = all_1972_0
% 224.88/38.11 | | | | | | | | | | | | | | |
% 224.88/38.11 | | | | | | | | | | | | | | | DELTA: instantiating (285) with fresh symbol all_1974_0
% 224.88/38.11 | | | | | | | | | | | | | | | gives:
% 224.88/38.11 | | | | | | | | | | | | | | | (295) ~ (all_1974_0 = 0) & ssList(all_401_0) =
% 224.88/38.11 | | | | | | | | | | | | | | | all_1974_0
% 224.88/38.11 | | | | | | | | | | | | | | |
% 224.88/38.11 | | | | | | | | | | | | | | | ALPHA: (295) implies:
% 224.88/38.11 | | | | | | | | | | | | | | | (296) ssList(all_401_0) = all_1974_0
% 224.88/38.11 | | | | | | | | | | | | | | |
% 224.88/38.11 | | | | | | | | | | | | | | | DELTA: instantiating (285) with fresh symbol all_1976_0
% 224.88/38.11 | | | | | | | | | | | | | | | gives:
% 224.88/38.11 | | | | | | | | | | | | | | | (297) ~ (all_1976_0 = 0) & ssList(all_401_0) =
% 224.88/38.11 | | | | | | | | | | | | | | | all_1976_0
% 224.88/38.11 | | | | | | | | | | | | | | |
% 224.88/38.11 | | | | | | | | | | | | | | | ALPHA: (297) implies:
% 224.88/38.11 | | | | | | | | | | | | | | | (298) ssList(all_401_0) = all_1976_0
% 224.88/38.11 | | | | | | | | | | | | | | |
% 224.88/38.11 | | | | | | | | | | | | | | | DELTA: instantiating (285) with fresh symbol all_1978_0
% 224.88/38.11 | | | | | | | | | | | | | | | gives:
% 224.88/38.11 | | | | | | | | | | | | | | | (299) ~ (all_1978_0 = 0) & ssList(all_401_0) =
% 224.88/38.11 | | | | | | | | | | | | | | | all_1978_0
% 224.88/38.11 | | | | | | | | | | | | | | |
% 224.88/38.11 | | | | | | | | | | | | | | | ALPHA: (299) implies:
% 224.88/38.11 | | | | | | | | | | | | | | | (300) ssList(all_401_0) = all_1978_0
% 224.88/38.11 | | | | | | | | | | | | | | |
% 224.88/38.11 | | | | | | | | | | | | | | | GROUND_INST: instantiating (18) with 0, all_1972_0, all_401_0,
% 224.88/38.11 | | | | | | | | | | | | | | | simplifying with (150), (294) gives:
% 224.88/38.11 | | | | | | | | | | | | | | | (301) all_1972_0 = 0
% 224.88/38.11 | | | | | | | | | | | | | | |
% 224.88/38.11 | | | | | | | | | | | | | | | GROUND_INST: instantiating (18) with all_1958_0, all_1972_0,
% 224.88/38.11 | | | | | | | | | | | | | | | all_401_0, simplifying with (290), (294) gives:
% 224.88/38.11 | | | | | | | | | | | | | | | (302) all_1972_0 = all_1958_0
% 224.88/38.11 | | | | | | | | | | | | | | |
% 224.88/38.11 | | | | | | | | | | | | | | | GROUND_INST: instantiating (18) with all_1974_0, all_1976_0,
% 224.88/38.11 | | | | | | | | | | | | | | | all_401_0, simplifying with (296), (298) gives:
% 224.88/38.11 | | | | | | | | | | | | | | | (303) all_1976_0 = all_1974_0
% 224.88/38.11 | | | | | | | | | | | | | | |
% 224.88/38.11 | | | | | | | | | | | | | | | GROUND_INST: instantiating (18) with all_1956_0, all_1976_0,
% 224.88/38.11 | | | | | | | | | | | | | | | all_401_0, simplifying with (288), (298) gives:
% 224.88/38.11 | | | | | | | | | | | | | | | (304) all_1976_0 = all_1956_0
% 224.88/38.11 | | | | | | | | | | | | | | |
% 224.88/38.11 | | | | | | | | | | | | | | | GROUND_INST: instantiating (18) with all_1976_0, all_1978_0,
% 224.88/38.11 | | | | | | | | | | | | | | | all_401_0, simplifying with (298), (300) gives:
% 224.88/38.11 | | | | | | | | | | | | | | | (305) all_1978_0 = all_1976_0
% 224.88/38.11 | | | | | | | | | | | | | | |
% 224.88/38.11 | | | | | | | | | | | | | | | GROUND_INST: instantiating (18) with all_1972_0, all_1978_0,
% 224.88/38.11 | | | | | | | | | | | | | | | all_401_0, simplifying with (294), (300) gives:
% 224.88/38.11 | | | | | | | | | | | | | | | (306) all_1978_0 = all_1972_0
% 224.88/38.11 | | | | | | | | | | | | | | |
% 224.88/38.11 | | | | | | | | | | | | | | | GROUND_INST: instantiating (18) with all_1960_0, all_1978_0,
% 224.88/38.11 | | | | | | | | | | | | | | | all_401_0, simplifying with (292), (300) gives:
% 224.88/38.11 | | | | | | | | | | | | | | | (307) all_1978_0 = all_1960_0
% 224.88/38.11 | | | | | | | | | | | | | | |
% 224.88/38.11 | | | | | | | | | | | | | | | COMBINE_EQS: (306), (307) imply:
% 224.88/38.11 | | | | | | | | | | | | | | | (308) all_1972_0 = all_1960_0
% 224.88/38.11 | | | | | | | | | | | | | | |
% 224.88/38.11 | | | | | | | | | | | | | | | SIMP: (308) implies:
% 224.88/38.11 | | | | | | | | | | | | | | | (309) all_1972_0 = all_1960_0
% 224.88/38.11 | | | | | | | | | | | | | | |
% 224.88/38.11 | | | | | | | | | | | | | | | COMBINE_EQS: (305), (307) imply:
% 224.88/38.12 | | | | | | | | | | | | | | | (310) all_1976_0 = all_1960_0
% 224.88/38.12 | | | | | | | | | | | | | | |
% 224.88/38.12 | | | | | | | | | | | | | | | SIMP: (310) implies:
% 224.88/38.12 | | | | | | | | | | | | | | | (311) all_1976_0 = all_1960_0
% 224.88/38.12 | | | | | | | | | | | | | | |
% 224.88/38.12 | | | | | | | | | | | | | | | COMBINE_EQS: (303), (311) imply:
% 224.88/38.12 | | | | | | | | | | | | | | | (312) all_1974_0 = all_1960_0
% 224.88/38.12 | | | | | | | | | | | | | | |
% 224.88/38.12 | | | | | | | | | | | | | | | COMBINE_EQS: (303), (304) imply:
% 224.88/38.12 | | | | | | | | | | | | | | | (313) all_1974_0 = all_1956_0
% 224.88/38.12 | | | | | | | | | | | | | | |
% 224.88/38.12 | | | | | | | | | | | | | | | COMBINE_EQS: (312), (313) imply:
% 224.88/38.12 | | | | | | | | | | | | | | | (314) all_1960_0 = all_1956_0
% 224.88/38.12 | | | | | | | | | | | | | | |
% 224.88/38.12 | | | | | | | | | | | | | | | SIMP: (314) implies:
% 224.88/38.12 | | | | | | | | | | | | | | | (315) all_1960_0 = all_1956_0
% 224.88/38.12 | | | | | | | | | | | | | | |
% 224.88/38.12 | | | | | | | | | | | | | | | COMBINE_EQS: (302), (309) imply:
% 224.88/38.12 | | | | | | | | | | | | | | | (316) all_1960_0 = all_1958_0
% 224.88/38.12 | | | | | | | | | | | | | | |
% 224.88/38.12 | | | | | | | | | | | | | | | SIMP: (316) implies:
% 224.88/38.12 | | | | | | | | | | | | | | | (317) all_1960_0 = all_1958_0
% 224.88/38.12 | | | | | | | | | | | | | | |
% 224.88/38.12 | | | | | | | | | | | | | | | COMBINE_EQS: (301), (302) imply:
% 224.88/38.12 | | | | | | | | | | | | | | | (318) all_1958_0 = 0
% 224.88/38.12 | | | | | | | | | | | | | | |
% 224.88/38.12 | | | | | | | | | | | | | | | COMBINE_EQS: (315), (317) imply:
% 224.88/38.12 | | | | | | | | | | | | | | | (319) all_1958_0 = all_1956_0
% 224.88/38.12 | | | | | | | | | | | | | | |
% 224.88/38.12 | | | | | | | | | | | | | | | SIMP: (319) implies:
% 224.88/38.12 | | | | | | | | | | | | | | | (320) all_1958_0 = all_1956_0
% 224.88/38.12 | | | | | | | | | | | | | | |
% 224.88/38.12 | | | | | | | | | | | | | | | COMBINE_EQS: (318), (320) imply:
% 224.88/38.12 | | | | | | | | | | | | | | | (321) all_1956_0 = 0
% 224.88/38.12 | | | | | | | | | | | | | | |
% 224.88/38.12 | | | | | | | | | | | | | | | REDUCE: (287), (321) imply:
% 224.88/38.12 | | | | | | | | | | | | | | | (322) $false
% 224.88/38.12 | | | | | | | | | | | | | | |
% 224.88/38.12 | | | | | | | | | | | | | | | CLOSE: (322) is inconsistent.
% 224.88/38.12 | | | | | | | | | | | | | | |
% 224.88/38.12 | | | | | | | | | | | | | | Case 2:
% 224.88/38.12 | | | | | | | | | | | | | | |
% 224.88/38.12 | | | | | | | | | | | | | | |
% 224.88/38.12 | | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with all_1899_1, all_1901_1,
% 224.88/38.12 | | | | | | | | | | | | | | | all_385_0, simplifying with (270), (272) gives:
% 224.88/38.12 | | | | | | | | | | | | | | | (323) all_1901_1 = all_1899_1
% 224.88/38.12 | | | | | | | | | | | | | | |
% 224.88/38.12 | | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with all_1903_1, all_1905_1,
% 224.88/38.12 | | | | | | | | | | | | | | | all_385_0, simplifying with (274), (276) gives:
% 224.88/38.12 | | | | | | | | | | | | | | | (324) all_1905_1 = all_1903_1
% 224.88/38.12 | | | | | | | | | | | | | | |
% 224.88/38.12 | | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with all_1899_1, all_1905_1,
% 224.88/38.12 | | | | | | | | | | | | | | | all_385_0, simplifying with (270), (276) gives:
% 224.88/38.12 | | | | | | | | | | | | | | | (325) all_1905_1 = all_1899_1
% 224.88/38.12 | | | | | | | | | | | | | | |
% 224.88/38.12 | | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with all_1899_1, all_1907_1,
% 224.88/38.12 | | | | | | | | | | | | | | | all_385_0, simplifying with (270), (280) gives:
% 224.88/38.12 | | | | | | | | | | | | | | | (326) all_1907_1 = all_1899_1
% 224.88/38.12 | | | | | | | | | | | | | | |
% 224.88/38.12 | | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with all_1897_1, all_1907_1,
% 224.88/38.12 | | | | | | | | | | | | | | | all_385_0, simplifying with (268), (280) gives:
% 224.88/38.12 | | | | | | | | | | | | | | | (327) all_1907_1 = all_1897_1
% 224.88/38.12 | | | | | | | | | | | | | | |
% 224.88/38.12 | | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with 0, all_1909_1, all_385_0,
% 224.88/38.12 | | | | | | | | | | | | | | | simplifying with (130), (282) gives:
% 224.88/38.12 | | | | | | | | | | | | | | | (328) all_1909_1 = 0
% 224.88/38.12 | | | | | | | | | | | | | | |
% 224.88/38.12 | | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with all_1901_1, all_1909_1,
% 224.88/38.12 | | | | | | | | | | | | | | | all_385_0, simplifying with (272), (282) gives:
% 224.88/38.12 | | | | | | | | | | | | | | | (329) all_1909_1 = all_1901_1
% 224.88/38.12 | | | | | | | | | | | | | | |
% 224.88/38.12 | | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with all_1905_1, all_1911_1,
% 224.88/38.12 | | | | | | | | | | | | | | | all_385_0, simplifying with (276), (284) gives:
% 224.88/38.12 | | | | | | | | | | | | | | | (330) all_1911_1 = all_1905_1
% 224.88/38.12 | | | | | | | | | | | | | | |
% 224.88/38.12 | | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with all_1895_1, all_1911_1,
% 224.88/38.12 | | | | | | | | | | | | | | | all_385_0, simplifying with (266), (284) gives:
% 224.88/38.12 | | | | | | | | | | | | | | | (331) all_1911_1 = all_1895_1
% 224.88/38.12 | | | | | | | | | | | | | | |
% 224.88/38.12 | | | | | | | | | | | | | | | GROUND_INST: instantiating (20) with all_139_0, all_1905_0,
% 224.88/38.12 | | | | | | | | | | | | | | | all_139_1, simplifying with (25), (277) gives:
% 224.88/38.12 | | | | | | | | | | | | | | | (332) all_1905_0 = all_139_0
% 224.88/38.12 | | | | | | | | | | | | | | |
% 224.88/38.12 | | | | | | | | | | | | | | | COMBINE_EQS: (330), (331) imply:
% 224.88/38.12 | | | | | | | | | | | | | | | (333) all_1905_1 = all_1895_1
% 224.88/38.12 | | | | | | | | | | | | | | |
% 224.88/38.12 | | | | | | | | | | | | | | | SIMP: (333) implies:
% 224.88/38.12 | | | | | | | | | | | | | | | (334) all_1905_1 = all_1895_1
% 224.88/38.12 | | | | | | | | | | | | | | |
% 224.88/38.12 | | | | | | | | | | | | | | | COMBINE_EQS: (328), (329) imply:
% 224.88/38.12 | | | | | | | | | | | | | | | (335) all_1901_1 = 0
% 224.88/38.12 | | | | | | | | | | | | | | |
% 224.88/38.12 | | | | | | | | | | | | | | | SIMP: (335) implies:
% 224.88/38.12 | | | | | | | | | | | | | | | (336) all_1901_1 = 0
% 224.88/38.12 | | | | | | | | | | | | | | |
% 224.88/38.12 | | | | | | | | | | | | | | | COMBINE_EQS: (326), (327) imply:
% 224.88/38.12 | | | | | | | | | | | | | | | (337) all_1899_1 = all_1897_1
% 224.88/38.12 | | | | | | | | | | | | | | |
% 224.88/38.12 | | | | | | | | | | | | | | | SIMP: (337) implies:
% 224.88/38.12 | | | | | | | | | | | | | | | (338) all_1899_1 = all_1897_1
% 224.88/38.12 | | | | | | | | | | | | | | |
% 224.88/38.12 | | | | | | | | | | | | | | | COMBINE_EQS: (324), (325) imply:
% 224.88/38.12 | | | | | | | | | | | | | | | (339) all_1903_1 = all_1899_1
% 224.88/38.12 | | | | | | | | | | | | | | |
% 224.88/38.12 | | | | | | | | | | | | | | | COMBINE_EQS: (324), (334) imply:
% 224.88/38.12 | | | | | | | | | | | | | | | (340) all_1903_1 = all_1895_1
% 224.88/38.12 | | | | | | | | | | | | | | |
% 224.88/38.12 | | | | | | | | | | | | | | | COMBINE_EQS: (339), (340) imply:
% 224.88/38.12 | | | | | | | | | | | | | | | (341) all_1899_1 = all_1895_1
% 224.88/38.12 | | | | | | | | | | | | | | |
% 224.88/38.12 | | | | | | | | | | | | | | | SIMP: (341) implies:
% 224.88/38.12 | | | | | | | | | | | | | | | (342) all_1899_1 = all_1895_1
% 224.88/38.12 | | | | | | | | | | | | | | |
% 224.88/38.12 | | | | | | | | | | | | | | | COMBINE_EQS: (323), (336) imply:
% 224.88/38.12 | | | | | | | | | | | | | | | (343) all_1899_1 = 0
% 224.88/38.12 | | | | | | | | | | | | | | |
% 224.88/38.12 | | | | | | | | | | | | | | | SIMP: (343) implies:
% 224.88/38.12 | | | | | | | | | | | | | | | (344) all_1899_1 = 0
% 224.88/38.12 | | | | | | | | | | | | | | |
% 224.88/38.12 | | | | | | | | | | | | | | | COMBINE_EQS: (338), (344) imply:
% 224.88/38.12 | | | | | | | | | | | | | | | (345) all_1897_1 = 0
% 224.88/38.12 | | | | | | | | | | | | | | |
% 224.88/38.12 | | | | | | | | | | | | | | | COMBINE_EQS: (338), (342) imply:
% 224.88/38.12 | | | | | | | | | | | | | | | (346) all_1897_1 = all_1895_1
% 224.88/38.12 | | | | | | | | | | | | | | |
% 224.88/38.12 | | | | | | | | | | | | | | | COMBINE_EQS: (345), (346) imply:
% 224.88/38.12 | | | | | | | | | | | | | | | (347) all_1895_1 = 0
% 224.88/38.12 | | | | | | | | | | | | | | |
% 224.88/38.12 | | | | | | | | | | | | | | | SIMP: (347) implies:
% 224.88/38.12 | | | | | | | | | | | | | | | (348) all_1895_1 = 0
% 224.88/38.12 | | | | | | | | | | | | | | |
% 224.88/38.12 | | | | | | | | | | | | | | | COMBINE_EQS: (340), (348) imply:
% 224.88/38.12 | | | | | | | | | | | | | | | (349) all_1903_1 = 0
% 224.88/38.12 | | | | | | | | | | | | | | |
% 224.88/38.12 | | | | | | | | | | | | | | | COMBINE_EQS: (324), (349) imply:
% 224.88/38.12 | | | | | | | | | | | | | | | (350) all_1905_1 = 0
% 224.88/38.12 | | | | | | | | | | | | | | |
% 224.88/38.12 | | | | | | | | | | | | | | | BETA: splitting (278) gives:
% 224.88/38.12 | | | | | | | | | | | | | | |
% 224.88/38.12 | | | | | | | | | | | | | | | Case 1:
% 224.88/38.12 | | | | | | | | | | | | | | | |
% 224.88/38.12 | | | | | | | | | | | | | | | | (351) ~ (all_1905_1 = 0)
% 224.88/38.12 | | | | | | | | | | | | | | | |
% 224.88/38.12 | | | | | | | | | | | | | | | | REDUCE: (350), (351) imply:
% 224.88/38.12 | | | | | | | | | | | | | | | | (352) $false
% 224.88/38.12 | | | | | | | | | | | | | | | |
% 224.88/38.12 | | | | | | | | | | | | | | | | CLOSE: (352) is inconsistent.
% 224.88/38.12 | | | | | | | | | | | | | | | |
% 224.88/38.12 | | | | | | | | | | | | | | | Case 2:
% 224.88/38.12 | | | | | | | | | | | | | | | |
% 224.88/38.12 | | | | | | | | | | | | | | | | (353) all_1905_0 = 0
% 224.88/38.12 | | | | | | | | | | | | | | | |
% 224.88/38.12 | | | | | | | | | | | | | | | | COMBINE_EQS: (332), (353) imply:
% 224.88/38.12 | | | | | | | | | | | | | | | | (354) all_139_0 = 0
% 224.88/38.12 | | | | | | | | | | | | | | | |
% 224.88/38.12 | | | | | | | | | | | | | | | | SIMP: (354) implies:
% 224.88/38.12 | | | | | | | | | | | | | | | | (355) all_139_0 = 0
% 224.88/38.12 | | | | | | | | | | | | | | | |
% 224.88/38.12 | | | | | | | | | | | | | | | | REDUCE: (38), (355) imply:
% 224.88/38.12 | | | | | | | | | | | | | | | | (356) $false
% 224.88/38.12 | | | | | | | | | | | | | | | |
% 224.88/38.12 | | | | | | | | | | | | | | | | CLOSE: (356) is inconsistent.
% 224.88/38.12 | | | | | | | | | | | | | | | |
% 224.88/38.12 | | | | | | | | | | | | | | | End of split
% 224.88/38.12 | | | | | | | | | | | | | | |
% 224.88/38.12 | | | | | | | | | | | | | | End of split
% 224.88/38.12 | | | | | | | | | | | | | |
% 224.88/38.12 | | | | | | | | | | | | | Case 2:
% 224.88/38.12 | | | | | | | | | | | | | |
% 224.88/38.12 | | | | | | | | | | | | | | (357) ~ (all_417_1 = 0)
% 224.88/38.12 | | | | | | | | | | | | | |
% 224.88/38.12 | | | | | | | | | | | | | | REDUCE: (251), (357) imply:
% 224.88/38.12 | | | | | | | | | | | | | | (358) $false
% 224.88/38.12 | | | | | | | | | | | | | |
% 224.88/38.12 | | | | | | | | | | | | | | CLOSE: (358) is inconsistent.
% 224.88/38.12 | | | | | | | | | | | | | |
% 224.88/38.12 | | | | | | | | | | | | | End of split
% 224.88/38.12 | | | | | | | | | | | | |
% 224.88/38.12 | | | | | | | | | | | | End of split
% 224.88/38.12 | | | | | | | | | | | |
% 224.88/38.12 | | | | | | | | | | | End of split
% 224.88/38.12 | | | | | | | | | | |
% 224.88/38.12 | | | | | | | | | | End of split
% 224.88/38.12 | | | | | | | | | |
% 224.88/38.12 | | | | | | | | | End of split
% 224.88/38.12 | | | | | | | | |
% 224.88/38.12 | | | | | | | | Case 2:
% 224.88/38.12 | | | | | | | | |
% 224.88/38.12 | | | | | | | | | (359) ~ (all_147_0 = 0)
% 224.88/38.12 | | | | | | | | |
% 224.88/38.12 | | | | | | | | | REDUCE: (106), (359) imply:
% 224.88/38.12 | | | | | | | | | (360) $false
% 224.88/38.12 | | | | | | | | |
% 224.88/38.12 | | | | | | | | | CLOSE: (360) is inconsistent.
% 224.88/38.12 | | | | | | | | |
% 224.88/38.12 | | | | | | | | End of split
% 224.88/38.12 | | | | | | | |
% 224.88/38.12 | | | | | | | End of split
% 224.88/38.12 | | | | | | |
% 224.88/38.12 | | | | | | End of split
% 224.88/38.12 | | | | | |
% 224.88/38.12 | | | | | End of split
% 224.88/38.12 | | | | |
% 224.88/38.12 | | | | End of split
% 224.88/38.12 | | | |
% 224.88/38.12 | | | Case 2:
% 224.88/38.12 | | | |
% 224.88/38.12 | | | | (361) ? [v0: int] : ( ~ (v0 = 0) & ssList(all_139_1) = v0)
% 224.88/38.12 | | | |
% 224.88/38.12 | | | | DELTA: instantiating (361) with fresh symbol all_341_0 gives:
% 224.88/38.12 | | | | (362) ~ (all_341_0 = 0) & ssList(all_139_1) = all_341_0
% 224.88/38.12 | | | |
% 224.88/38.12 | | | | ALPHA: (362) implies:
% 224.88/38.12 | | | | (363) ~ (all_341_0 = 0)
% 224.88/38.12 | | | | (364) ssList(all_139_1) = all_341_0
% 224.88/38.12 | | | |
% 224.88/38.12 | | | | GROUND_INST: instantiating (18) with 0, all_341_0, all_139_1,
% 224.88/38.12 | | | | simplifying with (43), (364) gives:
% 224.88/38.12 | | | | (365) all_341_0 = 0
% 224.88/38.12 | | | |
% 224.88/38.12 | | | | REDUCE: (363), (365) imply:
% 224.88/38.12 | | | | (366) $false
% 224.88/38.12 | | | |
% 224.88/38.12 | | | | CLOSE: (366) is inconsistent.
% 224.88/38.12 | | | |
% 224.88/38.12 | | | End of split
% 224.88/38.12 | | |
% 224.88/38.12 | | End of split
% 224.88/38.12 | |
% 224.88/38.12 | End of split
% 224.88/38.12 |
% 224.88/38.12 End of proof
% 224.88/38.12
% 224.88/38.12 Sub-proof #1 shows that the following formulas are inconsistent:
% 224.88/38.12 ----------------------------------------------------------------
% 224.88/38.13 (1) ? [v0: int] : ( ~ (v0 = 0) & ssList(nil) = v0)
% 224.88/38.13 (2) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 224.88/38.13 (v1 = v0 | ~ (ssList(v2) = v1) | ~ (ssList(v2) = v0))
% 224.88/38.13 (3) ssList(nil) = 0
% 224.88/38.13
% 224.88/38.13 Begin of proof
% 224.88/38.13 |
% 224.88/38.13 | DELTA: instantiating (1) with fresh symbol all_1950_0 gives:
% 224.88/38.13 | (4) ~ (all_1950_0 = 0) & ssList(nil) = all_1950_0
% 224.88/38.13 |
% 224.88/38.13 | ALPHA: (4) implies:
% 224.88/38.13 | (5) ~ (all_1950_0 = 0)
% 224.88/38.13 | (6) ssList(nil) = all_1950_0
% 224.88/38.13 |
% 224.88/38.13 | DELTA: instantiating (1) with fresh symbol all_1952_0 gives:
% 224.88/38.13 | (7) ~ (all_1952_0 = 0) & ssList(nil) = all_1952_0
% 224.88/38.13 |
% 224.88/38.13 | ALPHA: (7) implies:
% 224.88/38.13 | (8) ssList(nil) = all_1952_0
% 224.88/38.13 |
% 224.88/38.13 | DELTA: instantiating (1) with fresh symbol all_1970_0 gives:
% 225.46/38.13 | (9) ~ (all_1970_0 = 0) & ssList(nil) = all_1970_0
% 225.46/38.13 |
% 225.46/38.13 | ALPHA: (9) implies:
% 225.46/38.13 | (10) ssList(nil) = all_1970_0
% 225.46/38.13 |
% 225.46/38.13 | DELTA: instantiating (1) with fresh symbol all_1972_0 gives:
% 225.46/38.13 | (11) ~ (all_1972_0 = 0) & ssList(nil) = all_1972_0
% 225.46/38.13 |
% 225.46/38.13 | ALPHA: (11) implies:
% 225.46/38.13 | (12) ssList(nil) = all_1972_0
% 225.46/38.13 |
% 225.46/38.13 | DELTA: instantiating (1) with fresh symbol all_1974_0 gives:
% 225.46/38.13 | (13) ~ (all_1974_0 = 0) & ssList(nil) = all_1974_0
% 225.46/38.13 |
% 225.46/38.13 | ALPHA: (13) implies:
% 225.46/38.13 | (14) ssList(nil) = all_1974_0
% 225.46/38.13 |
% 225.46/38.13 | DELTA: instantiating (1) with fresh symbol all_1976_0 gives:
% 225.46/38.13 | (15) ~ (all_1976_0 = 0) & ssList(nil) = all_1976_0
% 225.46/38.13 |
% 225.46/38.13 | ALPHA: (15) implies:
% 225.46/38.13 | (16) ssList(nil) = all_1976_0
% 225.46/38.13 |
% 225.46/38.13 | DELTA: instantiating (1) with fresh symbol all_1978_0 gives:
% 225.46/38.13 | (17) ~ (all_1978_0 = 0) & ssList(nil) = all_1978_0
% 225.46/38.13 |
% 225.46/38.13 | ALPHA: (17) implies:
% 225.46/38.13 | (18) ssList(nil) = all_1978_0
% 225.46/38.13 |
% 225.46/38.13 | GROUND_INST: instantiating (2) with all_1950_0, all_1952_0, nil, simplifying
% 225.46/38.13 | with (6), (8) gives:
% 225.46/38.13 | (19) all_1952_0 = all_1950_0
% 225.46/38.13 |
% 225.46/38.13 | GROUND_INST: instantiating (2) with all_1952_0, all_1970_0, nil, simplifying
% 225.46/38.13 | with (8), (10) gives:
% 225.46/38.13 | (20) all_1970_0 = all_1952_0
% 225.46/38.13 |
% 225.46/38.13 | GROUND_INST: instantiating (2) with all_1974_0, all_1976_0, nil, simplifying
% 225.46/38.13 | with (14), (16) gives:
% 225.46/38.13 | (21) all_1976_0 = all_1974_0
% 225.46/38.13 |
% 225.46/38.13 | GROUND_INST: instantiating (2) with all_1972_0, all_1976_0, nil, simplifying
% 225.46/38.13 | with (12), (16) gives:
% 225.46/38.13 | (22) all_1976_0 = all_1972_0
% 225.46/38.13 |
% 225.46/38.13 | GROUND_INST: instantiating (2) with all_1970_0, all_1976_0, nil, simplifying
% 225.46/38.13 | with (10), (16) gives:
% 225.46/38.13 | (23) all_1976_0 = all_1970_0
% 225.46/38.13 |
% 225.46/38.13 | GROUND_INST: instantiating (2) with 0, all_1978_0, nil, simplifying with (3),
% 225.46/38.13 | (18) gives:
% 225.46/38.13 | (24) all_1978_0 = 0
% 225.46/38.13 |
% 225.46/38.13 | GROUND_INST: instantiating (2) with all_1974_0, all_1978_0, nil, simplifying
% 225.46/38.13 | with (14), (18) gives:
% 225.46/38.13 | (25) all_1978_0 = all_1974_0
% 225.46/38.13 |
% 225.46/38.13 | COMBINE_EQS: (24), (25) imply:
% 225.46/38.13 | (26) all_1974_0 = 0
% 225.46/38.13 |
% 225.46/38.13 | SIMP: (26) implies:
% 225.46/38.13 | (27) all_1974_0 = 0
% 225.46/38.13 |
% 225.46/38.13 | COMBINE_EQS: (21), (22) imply:
% 225.46/38.13 | (28) all_1974_0 = all_1972_0
% 225.46/38.13 |
% 225.46/38.13 | SIMP: (28) implies:
% 225.46/38.13 | (29) all_1974_0 = all_1972_0
% 225.46/38.13 |
% 225.46/38.13 | COMBINE_EQS: (22), (23) imply:
% 225.46/38.13 | (30) all_1972_0 = all_1970_0
% 225.46/38.13 |
% 225.46/38.13 | COMBINE_EQS: (27), (29) imply:
% 225.46/38.13 | (31) all_1972_0 = 0
% 225.46/38.13 |
% 225.46/38.13 | SIMP: (31) implies:
% 225.46/38.13 | (32) all_1972_0 = 0
% 225.46/38.13 |
% 225.46/38.13 | COMBINE_EQS: (30), (32) imply:
% 225.46/38.13 | (33) all_1970_0 = 0
% 225.46/38.13 |
% 225.46/38.13 | SIMP: (33) implies:
% 225.46/38.13 | (34) all_1970_0 = 0
% 225.46/38.13 |
% 225.46/38.13 | COMBINE_EQS: (20), (34) imply:
% 225.46/38.13 | (35) all_1952_0 = 0
% 225.46/38.13 |
% 225.46/38.13 | SIMP: (35) implies:
% 225.46/38.13 | (36) all_1952_0 = 0
% 225.46/38.13 |
% 225.46/38.13 | COMBINE_EQS: (19), (36) imply:
% 225.46/38.13 | (37) all_1950_0 = 0
% 225.46/38.13 |
% 225.46/38.13 | SIMP: (37) implies:
% 225.46/38.13 | (38) all_1950_0 = 0
% 225.46/38.13 |
% 225.46/38.13 | REDUCE: (5), (38) imply:
% 225.46/38.13 | (39) $false
% 225.46/38.13 |
% 225.46/38.13 | CLOSE: (39) is inconsistent.
% 225.46/38.13 |
% 225.46/38.13 End of proof
% 225.46/38.13 % SZS output end Proof for theBenchmark
% 225.46/38.13
% 225.46/38.13 37535ms
%------------------------------------------------------------------------------