TSTP Solution File: SWC012+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SWC012+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 : n002.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 20:49:10 EDT 2023
% Result : Theorem 47.86s 7.04s
% Output : Proof 104.53s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SWC012+1 : TPTP v8.1.2. Released v2.4.0.
% 0.06/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.14/0.33 % Computer : n002.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 16:34:04 EDT 2023
% 0.14/0.34 % CPUTime :
% 0.20/0.60 ________ _____
% 0.20/0.60 ___ __ \_________(_)________________________________
% 0.20/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.20/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.20/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.20/0.60
% 0.20/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.60 (2023-06-19)
% 0.20/0.60
% 0.20/0.60 (c) Philipp Rümmer, 2009-2023
% 0.20/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.60 Amanda Stjerna.
% 0.20/0.60 Free software under BSD-3-Clause.
% 0.20/0.60
% 0.20/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.60
% 0.20/0.60 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.20/0.61 Running up to 7 provers in parallel.
% 0.20/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.20/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 5.60/1.48 Prover 1: Preprocessing ...
% 5.60/1.49 Prover 4: Preprocessing ...
% 5.83/1.51 Prover 0: Preprocessing ...
% 5.83/1.51 Prover 2: Preprocessing ...
% 5.83/1.51 Prover 5: Preprocessing ...
% 5.83/1.51 Prover 6: Preprocessing ...
% 5.83/1.51 Prover 3: Preprocessing ...
% 15.48/2.81 Prover 2: Proving ...
% 16.04/2.88 Prover 5: Constructing countermodel ...
% 16.04/2.89 Prover 6: Proving ...
% 16.04/2.89 Prover 1: Constructing countermodel ...
% 16.28/2.92 Prover 3: Constructing countermodel ...
% 21.86/3.63 Prover 4: Constructing countermodel ...
% 23.26/3.85 Prover 0: Proving ...
% 47.86/7.04 Prover 5: proved (6418ms)
% 47.86/7.04
% 47.86/7.04 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 47.86/7.04
% 47.86/7.05 Prover 6: stopped
% 47.86/7.05 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 47.86/7.05 Prover 2: stopped
% 47.86/7.06 Prover 0: stopped
% 47.86/7.07 Prover 3: stopped
% 48.26/7.09 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 48.26/7.09 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 48.26/7.09 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 48.26/7.09 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 50.20/7.35 Prover 8: Preprocessing ...
% 50.20/7.36 Prover 7: Preprocessing ...
% 50.20/7.36 Prover 11: Preprocessing ...
% 50.20/7.37 Prover 10: Preprocessing ...
% 50.20/7.37 Prover 13: Preprocessing ...
% 51.74/7.59 Prover 7: Constructing countermodel ...
% 51.74/7.61 Prover 10: Constructing countermodel ...
% 52.26/7.65 Prover 13: Constructing countermodel ...
% 52.95/7.77 Prover 8: Warning: ignoring some quantifiers
% 53.65/7.79 Prover 8: Constructing countermodel ...
% 57.39/8.32 Prover 11: Constructing countermodel ...
% 83.94/11.70 Prover 13: stopped
% 83.94/11.72 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 84.49/11.83 Prover 16: Preprocessing ...
% 85.59/11.97 Prover 16: Constructing countermodel ...
% 103.42/14.26 Prover 10: Found proof (size 285)
% 103.42/14.26 Prover 10: proved (7196ms)
% 103.42/14.26 Prover 7: stopped
% 103.42/14.26 Prover 16: stopped
% 103.42/14.26 Prover 1: stopped
% 103.42/14.26 Prover 8: stopped
% 103.42/14.26 Prover 11: stopped
% 103.42/14.26 Prover 4: stopped
% 103.42/14.26
% 103.42/14.26 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 103.42/14.26
% 103.71/14.32 % SZS output start Proof for theBenchmark
% 103.71/14.33 Assumptions after simplification:
% 103.71/14.33 ---------------------------------
% 103.71/14.33
% 103.71/14.33 (ax16)
% 103.82/14.35 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (cons(v1, v0) = v2) | ~ $i(v1)
% 103.82/14.36 | ~ $i(v0) | ~ ssList(v0) | ~ ssItem(v1) | ssList(v2))
% 103.82/14.36
% 103.82/14.36 (ax17)
% 103.82/14.36 $i(nil) & ssList(nil)
% 103.82/14.36
% 103.82/14.36 (ax23)
% 103.82/14.36 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (cons(v1, v0) = v2) | ~ $i(v1)
% 103.82/14.36 | ~ $i(v0) | ~ ssList(v0) | ~ ssItem(v1) | hd(v2) = v1)
% 103.82/14.36
% 103.82/14.36 (ax25)
% 103.82/14.36 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (cons(v1, v0) = v2) | ~ $i(v1)
% 103.82/14.36 | ~ $i(v0) | ~ ssList(v0) | ~ ssItem(v1) | tl(v2) = v0)
% 103.82/14.36
% 103.82/14.36 (ax26)
% 103.82/14.36 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (app(v0, v1) = v2) | ~ $i(v1) |
% 103.82/14.36 ~ $i(v0) | ~ ssList(v1) | ~ ssList(v0) | ssList(v2))
% 103.82/14.36
% 103.82/14.36 (ax27)
% 103.82/14.36 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 103.82/14.36 (cons(v3, v2) = v4) | ~ (app(v1, v0) = v2) | ~ $i(v3) | ~ $i(v1) | ~
% 103.82/14.36 $i(v0) | ~ ssList(v1) | ~ ssList(v0) | ~ ssItem(v3) | ? [v5: $i] :
% 103.82/14.36 (cons(v3, v1) = v5 & app(v5, v0) = v4 & $i(v5) & $i(v4)))
% 103.82/14.36
% 103.82/14.36 (ax28)
% 103.82/14.36 $i(nil) & ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (app(nil, v0) = v1) | ~
% 103.82/14.36 $i(v0) | ~ ssList(v0))
% 103.82/14.36
% 103.82/14.36 (ax31)
% 103.82/14.36 ! [v0: $i] : ( ~ $i(v0) | ~ ssItem(v0) | leq(v0, v0))
% 103.82/14.36
% 103.82/14.36 (ax4)
% 103.82/14.37 $i(nil) & ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v1, nil) = v0) | ~ $i(v1) |
% 103.82/14.37 ~ $i(v0) | ~ ssList(v0) | ~ ssItem(v1) | singletonP(v0)) & ! [v0: $i] : (
% 103.82/14.37 ~ $i(v0) | ~ singletonP(v0) | ~ ssList(v0) | ? [v1: $i] : (cons(v1, nil)
% 103.82/14.37 = v0 & $i(v1) & ssItem(v1)))
% 103.82/14.37
% 103.82/14.37 (ax42)
% 103.82/14.37 ! [v0: $i] : ( ~ $i(v0) | ~ ssList(v0) | frontsegP(v0, v0))
% 103.82/14.37
% 103.82/14.37 (ax44)
% 103.82/14.37 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 103.82/14.37 $i] : (v1 = v0 | ~ (cons(v1, v4) = v5) | ~ (cons(v0, v2) = v3) | ~ $i(v4)
% 103.82/14.37 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ frontsegP(v3, v5) | ~ ssList(v4) |
% 103.82/14.37 ~ ssList(v2) | ~ ssItem(v1) | ~ ssItem(v0)) & ! [v0: $i] : ! [v1: $i] :
% 103.82/14.37 ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (cons(v1, v4) =
% 103.82/14.37 v5) | ~ (cons(v0, v2) = v3) | ~ $i(v4) | ~ $i(v2) | ~ $i(v1) | ~
% 103.82/14.37 $i(v0) | ~ frontsegP(v3, v5) | ~ ssList(v4) | ~ ssList(v2) | ~
% 103.82/14.37 ssItem(v1) | ~ ssItem(v0) | frontsegP(v2, v4)) & ! [v0: $i] : ! [v1: $i]
% 103.82/14.37 : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (cons(v0, v3) = v4) | ~
% 103.82/14.37 (cons(v0, v1) = v2) | ~ $i(v3) | ~ $i(v1) | ~ $i(v0) | ~ frontsegP(v1,
% 103.82/14.37 v3) | ~ ssList(v3) | ~ ssList(v1) | ~ ssItem(v0) | frontsegP(v2, v4))
% 103.82/14.37
% 103.82/14.37 (ax45)
% 103.82/14.37 $i(nil) & ! [v0: $i] : ( ~ $i(v0) | ~ ssList(v0) | frontsegP(v0, nil))
% 103.82/14.37
% 103.82/14.37 (ax46)
% 103.82/14.37 $i(nil) & ! [v0: $i] : (v0 = nil | ~ $i(v0) | ~ frontsegP(nil, v0) | ~
% 103.82/14.37 ssList(v0)) & ( ~ ssList(nil) | frontsegP(nil, nil))
% 103.82/14.37
% 103.82/14.37 (ax49)
% 103.82/14.38 ! [v0: $i] : ( ~ $i(v0) | ~ ssList(v0) | rearsegP(v0, v0))
% 103.82/14.38
% 103.82/14.38 (ax5)
% 103.82/14.38 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (app(v1, v2) = v0) | ~ $i(v2) |
% 103.82/14.38 ~ $i(v1) | ~ $i(v0) | ~ ssList(v2) | ~ ssList(v1) | ~ ssList(v0) |
% 103.82/14.38 frontsegP(v0, v1)) & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~
% 103.82/14.38 frontsegP(v0, v1) | ~ ssList(v1) | ~ ssList(v0) | ? [v2: $i] : (app(v1,
% 103.82/14.38 v2) = v0 & $i(v2) & ssList(v2)))
% 103.82/14.38
% 103.82/14.38 (ax51)
% 103.82/14.38 $i(nil) & ! [v0: $i] : ( ~ $i(v0) | ~ ssList(v0) | rearsegP(v0, nil))
% 103.82/14.38
% 103.82/14.38 (ax52)
% 103.82/14.38 $i(nil) & ! [v0: $i] : (v0 = nil | ~ $i(v0) | ~ rearsegP(nil, v0) | ~
% 103.82/14.38 ssList(v0)) & ( ~ ssList(nil) | rearsegP(nil, nil))
% 103.82/14.38
% 103.82/14.38 (ax58)
% 103.82/14.38 $i(nil) & ! [v0: $i] : (v0 = nil | ~ $i(v0) | ~ segmentP(nil, v0) | ~
% 103.82/14.38 ssList(v0)) & ( ~ ssList(nil) | segmentP(nil, nil))
% 103.82/14.38
% 103.82/14.38 (ax6)
% 103.82/14.38 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (app(v2, v1) = v0) | ~ $i(v2) |
% 103.82/14.38 ~ $i(v1) | ~ $i(v0) | ~ ssList(v2) | ~ ssList(v1) | ~ ssList(v0) |
% 103.82/14.38 rearsegP(v0, v1)) & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~
% 103.82/14.38 rearsegP(v0, v1) | ~ ssList(v1) | ~ ssList(v0) | ? [v2: $i] : (app(v2,
% 103.82/14.38 v1) = v0 & $i(v2) & ssList(v2)))
% 103.82/14.38
% 103.82/14.38 (ax65)
% 103.82/14.38 $i(nil) & ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) |
% 103.82/14.38 ~ ssItem(v0) | totalorderedP(v1))
% 103.82/14.38
% 103.82/14.38 (ax67)
% 103.82/14.38 $i(nil) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (hd(v1) = v2) | ~
% 103.82/14.38 $i(v1) | ~ $i(v0) | ~ ssList(v1) | ~ ssItem(v0) | ? [v3: $i] : ((v1 =
% 103.82/14.38 nil | (cons(v0, v1) = v3 & $i(v3) & ~ totalorderedP(v3)) |
% 103.82/14.38 (totalorderedP(v1) & leq(v0, v2))) & (( ~ (v1 = nil) & ( ~
% 103.82/14.38 totalorderedP(v1) | ~ leq(v0, v2))) | (cons(v0, v1) = v3 & $i(v3) &
% 103.82/14.38 totalorderedP(v3)))))
% 103.82/14.38
% 103.82/14.38 (ax7)
% 103.82/14.39 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 103.82/14.39 (app(v3, v4) = v0) | ~ (app(v2, v1) = v3) | ~ $i(v4) | ~ $i(v2) | ~
% 103.82/14.39 $i(v1) | ~ $i(v0) | ~ ssList(v4) | ~ ssList(v2) | ~ ssList(v1) | ~
% 103.82/14.39 ssList(v0) | segmentP(v0, v1)) & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~
% 103.82/14.39 $i(v0) | ~ segmentP(v0, v1) | ~ ssList(v1) | ~ ssList(v0) | ? [v2: $i] :
% 103.82/14.39 ? [v3: $i] : ? [v4: $i] : (app(v3, v4) = v0 & app(v2, v1) = v3 & $i(v4) &
% 103.82/14.39 $i(v3) & $i(v2) & ssList(v4) & ssList(v2)))
% 103.82/14.39
% 103.82/14.39 (ax77)
% 103.82/14.39 $i(nil) & ! [v0: $i] : ! [v1: $i] : ( ~ (tl(v0) = v1) | ~ $i(v0) | ~
% 103.82/14.39 ssList(v0) | ? [v2: $i] : (hd(v0) = v2 & $i(v2) & ! [v3: $i] : (v3 = v0 |
% 103.82/14.39 v3 = nil | v0 = nil | ~ (tl(v3) = v1) | ~ $i(v3) | ~ ssList(v3) | ?
% 103.82/14.39 [v4: $i] : ( ~ (v4 = v2) & hd(v3) = v4 & $i(v4)))))
% 103.82/14.39
% 103.82/14.39 (ax79)
% 103.82/14.39 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v0 | ~ (app(v3,
% 103.82/14.39 v1) = v2) | ~ (app(v0, v1) = v2) | ~ $i(v3) | ~ $i(v1) | ~ $i(v0) |
% 103.82/14.39 ~ ssList(v3) | ~ ssList(v1) | ~ ssList(v0))
% 103.82/14.39
% 103.82/14.39 (ax80)
% 103.82/14.39 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v0 | ~ (app(v1,
% 103.82/14.39 v3) = v2) | ~ (app(v1, v0) = v2) | ~ $i(v3) | ~ $i(v1) | ~ $i(v0) |
% 103.82/14.39 ~ ssList(v3) | ~ ssList(v1) | ~ ssList(v0))
% 103.82/14.39
% 103.82/14.39 (ax81)
% 103.82/14.39 $i(nil) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 103.82/14.39 (cons(v1, nil) = v2) | ~ (app(v2, v0) = v3) | ~ $i(v1) | ~ $i(v0) | ~
% 103.82/14.39 ssList(v0) | ~ ssItem(v1) | (cons(v1, v0) = v3 & $i(v3)))
% 103.82/14.39
% 103.82/14.39 (ax82)
% 103.82/14.39 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 103.82/14.39 (app(v2, v3) = v4) | ~ (app(v0, v1) = v2) | ~ $i(v3) | ~ $i(v1) | ~
% 103.82/14.39 $i(v0) | ~ ssList(v3) | ~ ssList(v1) | ~ ssList(v0) | ? [v5: $i] :
% 103.82/14.39 (app(v1, v3) = v5 & app(v0, v5) = v4 & $i(v5) & $i(v4)))
% 103.82/14.39
% 103.82/14.39 (ax83)
% 103.82/14.39 $i(nil) & ! [v0: $i] : ! [v1: $i] : (v1 = nil | ~ (app(v0, v1) = nil) | ~
% 103.82/14.39 $i(v1) | ~ $i(v0) | ~ ssList(v1) | ~ ssList(v0)) & ! [v0: $i] : ! [v1:
% 103.82/14.39 $i] : (v0 = nil | ~ (app(v0, v1) = nil) | ~ $i(v1) | ~ $i(v0) | ~
% 103.82/14.39 ssList(v1) | ~ ssList(v0)) & ! [v0: $i] : (v0 = nil | ~ (app(nil, nil) =
% 103.82/14.39 v0) | ~ ssList(nil))
% 103.82/14.39
% 103.82/14.39 (ax84)
% 103.82/14.39 $i(nil) & ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (app(v0, nil) = v1) | ~
% 103.82/14.39 $i(v0) | ~ ssList(v0))
% 103.82/14.39
% 103.82/14.39 (co1)
% 103.82/14.39 $i(nil) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : (cons(v2,
% 103.82/14.39 nil) = v3 & app(v0, v3) = v1 & $i(v3) & $i(v2) & $i(v1) & $i(v0) &
% 103.82/14.39 ssList(v1) & ssList(v0) & neq(v1, nil) & ssItem(v2) & ! [v4: $i] : ! [v5:
% 103.82/14.39 $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ( ~ (cons(v4, nil) = v5) |
% 103.82/14.39 ~ (app(v7, v8) = v1) | ~ (app(v6, v5) = v7) | ~ $i(v8) | ~ $i(v6) | ~
% 103.82/14.39 $i(v4) | ~ ssList(v8) | ~ ssList(v6) | ~ ssItem(v4) | ? [v9: $i] : ( ~
% 103.82/14.40 (v9 = v0) & app(v6, v8) = v9 & $i(v9))))
% 103.82/14.40
% 103.82/14.40 (function-axioms)
% 103.82/14.40 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 103.82/14.40 (cons(v3, v2) = v1) | ~ (cons(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] :
% 103.82/14.40 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (app(v3, v2) = v1) | ~ (app(v3, v2)
% 103.82/14.40 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (tl(v2) =
% 103.82/14.40 v1) | ~ (tl(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 =
% 103.82/14.40 v0 | ~ (hd(v2) = v1) | ~ (hd(v2) = v0))
% 103.82/14.40
% 103.82/14.40 Further assumptions not needed in the proof:
% 103.82/14.40 --------------------------------------------
% 103.82/14.40 ax1, ax10, ax11, ax12, ax13, ax14, ax15, ax18, ax19, ax2, ax20, ax21, ax22,
% 103.82/14.40 ax24, ax29, ax3, ax30, ax32, ax33, ax34, ax35, ax36, ax37, ax38, ax39, ax40,
% 103.82/14.40 ax41, ax43, ax47, ax48, ax50, ax53, ax54, ax55, ax56, ax57, ax59, ax60, ax61,
% 103.82/14.40 ax62, ax63, ax64, ax66, ax68, ax69, ax70, ax71, ax72, ax73, ax74, ax75, ax76,
% 103.82/14.40 ax78, ax8, ax85, ax86, ax87, ax88, ax89, ax9, ax90, ax91, ax92, ax93, ax94, ax95
% 103.82/14.40
% 103.82/14.40 Those formulas are unsatisfiable:
% 103.82/14.40 ---------------------------------
% 103.82/14.40
% 103.82/14.40 Begin of proof
% 103.82/14.40 |
% 103.82/14.40 | ALPHA: (ax4) implies:
% 103.82/14.40 | (1) ! [v0: $i] : ( ~ $i(v0) | ~ singletonP(v0) | ~ ssList(v0) | ? [v1:
% 103.82/14.40 | $i] : (cons(v1, nil) = v0 & $i(v1) & ssItem(v1)))
% 103.82/14.40 | (2) ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v1, nil) = v0) | ~ $i(v1) | ~
% 103.82/14.40 | $i(v0) | ~ ssList(v0) | ~ ssItem(v1) | singletonP(v0))
% 103.82/14.40 |
% 103.82/14.40 | ALPHA: (ax5) implies:
% 103.82/14.40 | (3) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ frontsegP(v0,
% 103.82/14.40 | v1) | ~ ssList(v1) | ~ ssList(v0) | ? [v2: $i] : (app(v1, v2) =
% 103.82/14.40 | v0 & $i(v2) & ssList(v2)))
% 103.82/14.40 |
% 103.82/14.40 | ALPHA: (ax6) implies:
% 103.82/14.40 | (4) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ rearsegP(v0,
% 103.82/14.40 | v1) | ~ ssList(v1) | ~ ssList(v0) | ? [v2: $i] : (app(v2, v1) =
% 103.82/14.40 | v0 & $i(v2) & ssList(v2)))
% 103.82/14.40 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (app(v2, v1) = v0) | ~
% 103.82/14.40 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ ssList(v2) | ~ ssList(v1) | ~
% 103.82/14.40 | ssList(v0) | rearsegP(v0, v1))
% 103.82/14.40 |
% 103.82/14.40 | ALPHA: (ax7) implies:
% 103.82/14.40 | (6) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ segmentP(v0,
% 103.82/14.40 | v1) | ~ ssList(v1) | ~ ssList(v0) | ? [v2: $i] : ? [v3: $i] :
% 103.82/14.40 | ? [v4: $i] : (app(v3, v4) = v0 & app(v2, v1) = v3 & $i(v4) & $i(v3) &
% 103.82/14.40 | $i(v2) & ssList(v4) & ssList(v2)))
% 103.82/14.40 |
% 103.82/14.40 | ALPHA: (ax17) implies:
% 103.82/14.40 | (7) ssList(nil)
% 103.82/14.40 |
% 103.82/14.40 | ALPHA: (ax28) implies:
% 103.82/14.41 | (8) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (app(nil, v0) = v1) | ~
% 103.82/14.41 | $i(v0) | ~ ssList(v0))
% 103.82/14.41 |
% 103.82/14.41 | ALPHA: (ax44) implies:
% 103.82/14.41 | (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (
% 103.82/14.41 | ~ (cons(v0, v3) = v4) | ~ (cons(v0, v1) = v2) | ~ $i(v3) | ~
% 103.82/14.41 | $i(v1) | ~ $i(v0) | ~ frontsegP(v1, v3) | ~ ssList(v3) | ~
% 103.82/14.41 | ssList(v1) | ~ ssItem(v0) | frontsegP(v2, v4))
% 103.82/14.41 |
% 103.82/14.41 | ALPHA: (ax45) implies:
% 103.82/14.41 | (10) ! [v0: $i] : ( ~ $i(v0) | ~ ssList(v0) | frontsegP(v0, nil))
% 103.82/14.41 |
% 103.82/14.41 | ALPHA: (ax46) implies:
% 103.82/14.41 | (11) ~ ssList(nil) | frontsegP(nil, nil)
% 103.82/14.41 |
% 103.82/14.41 | ALPHA: (ax51) implies:
% 103.82/14.41 | (12) ! [v0: $i] : ( ~ $i(v0) | ~ ssList(v0) | rearsegP(v0, nil))
% 103.82/14.41 |
% 103.82/14.41 | ALPHA: (ax52) implies:
% 103.82/14.41 | (13) ~ ssList(nil) | rearsegP(nil, nil)
% 103.82/14.41 |
% 103.82/14.41 | ALPHA: (ax58) implies:
% 103.82/14.41 | (14) ~ ssList(nil) | segmentP(nil, nil)
% 103.82/14.41 |
% 103.82/14.41 | ALPHA: (ax65) implies:
% 103.82/14.41 | (15) ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | ~
% 103.82/14.41 | ssItem(v0) | totalorderedP(v1))
% 103.82/14.41 |
% 103.82/14.41 | ALPHA: (ax67) implies:
% 103.82/14.41 | (16) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (hd(v1) = v2) | ~
% 103.82/14.41 | $i(v1) | ~ $i(v0) | ~ ssList(v1) | ~ ssItem(v0) | ? [v3: $i] :
% 103.82/14.41 | ((v1 = nil | (cons(v0, v1) = v3 & $i(v3) & ~ totalorderedP(v3)) |
% 103.82/14.41 | (totalorderedP(v1) & leq(v0, v2))) & (( ~ (v1 = nil) & ( ~
% 103.82/14.41 | totalorderedP(v1) | ~ leq(v0, v2))) | (cons(v0, v1) = v3 &
% 103.82/14.41 | $i(v3) & totalorderedP(v3)))))
% 103.82/14.41 |
% 103.82/14.41 | ALPHA: (ax77) implies:
% 103.82/14.41 | (17) ! [v0: $i] : ! [v1: $i] : ( ~ (tl(v0) = v1) | ~ $i(v0) | ~
% 103.82/14.41 | ssList(v0) | ? [v2: $i] : (hd(v0) = v2 & $i(v2) & ! [v3: $i] : (v3
% 103.82/14.41 | = v0 | v3 = nil | v0 = nil | ~ (tl(v3) = v1) | ~ $i(v3) | ~
% 103.82/14.41 | ssList(v3) | ? [v4: $i] : ( ~ (v4 = v2) & hd(v3) = v4 &
% 103.82/14.41 | $i(v4)))))
% 103.82/14.41 |
% 103.82/14.41 | ALPHA: (ax81) implies:
% 103.82/14.41 | (18) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (cons(v1,
% 103.82/14.41 | nil) = v2) | ~ (app(v2, v0) = v3) | ~ $i(v1) | ~ $i(v0) | ~
% 103.82/14.41 | ssList(v0) | ~ ssItem(v1) | (cons(v1, v0) = v3 & $i(v3)))
% 103.82/14.41 |
% 103.82/14.41 | ALPHA: (ax83) implies:
% 103.82/14.41 | (19) ! [v0: $i] : (v0 = nil | ~ (app(nil, nil) = v0) | ~ ssList(nil))
% 103.82/14.41 | (20) ! [v0: $i] : ! [v1: $i] : (v0 = nil | ~ (app(v0, v1) = nil) | ~
% 103.82/14.41 | $i(v1) | ~ $i(v0) | ~ ssList(v1) | ~ ssList(v0))
% 103.82/14.41 | (21) ! [v0: $i] : ! [v1: $i] : (v1 = nil | ~ (app(v0, v1) = nil) | ~
% 103.82/14.41 | $i(v1) | ~ $i(v0) | ~ ssList(v1) | ~ ssList(v0))
% 103.82/14.41 |
% 103.82/14.41 | ALPHA: (ax84) implies:
% 103.82/14.41 | (22) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (app(v0, nil) = v1) | ~
% 103.82/14.41 | $i(v0) | ~ ssList(v0))
% 103.82/14.41 |
% 103.82/14.41 | ALPHA: (co1) implies:
% 103.82/14.41 | (23) $i(nil)
% 103.82/14.42 | (24) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : (cons(v2, nil)
% 103.82/14.42 | = v3 & app(v0, v3) = v1 & $i(v3) & $i(v2) & $i(v1) & $i(v0) &
% 103.82/14.42 | ssList(v1) & ssList(v0) & neq(v1, nil) & ssItem(v2) & ! [v4: $i] :
% 103.82/14.42 | ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ( ~ (cons(v4,
% 103.82/14.42 | nil) = v5) | ~ (app(v7, v8) = v1) | ~ (app(v6, v5) = v7) |
% 103.82/14.42 | ~ $i(v8) | ~ $i(v6) | ~ $i(v4) | ~ ssList(v8) | ~ ssList(v6) |
% 103.82/14.42 | ~ ssItem(v4) | ? [v9: $i] : ( ~ (v9 = v0) & app(v6, v8) = v9 &
% 103.82/14.42 | $i(v9))))
% 103.82/14.42 |
% 103.82/14.42 | ALPHA: (function-axioms) implies:
% 103.82/14.42 | (25) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (hd(v2) = v1)
% 103.82/14.42 | | ~ (hd(v2) = v0))
% 103.82/14.42 | (26) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 103.82/14.42 | (app(v3, v2) = v1) | ~ (app(v3, v2) = v0))
% 103.82/14.42 | (27) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 103.82/14.42 | (cons(v3, v2) = v1) | ~ (cons(v3, v2) = v0))
% 103.82/14.42 |
% 103.82/14.42 | DELTA: instantiating (24) with fresh symbols all_91_0, all_91_1, all_91_2,
% 103.82/14.42 | all_91_3 gives:
% 103.82/14.42 | (28) cons(all_91_1, nil) = all_91_0 & app(all_91_3, all_91_0) = all_91_2 &
% 103.82/14.42 | $i(all_91_0) & $i(all_91_1) & $i(all_91_2) & $i(all_91_3) &
% 103.82/14.42 | ssList(all_91_2) & ssList(all_91_3) & neq(all_91_2, nil) &
% 103.82/14.42 | ssItem(all_91_1) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 103.82/14.42 | $i] : ! [v4: $i] : ( ~ (cons(v0, nil) = v1) | ~ (app(v3, v4) =
% 103.82/14.42 | all_91_2) | ~ (app(v2, v1) = v3) | ~ $i(v4) | ~ $i(v2) | ~
% 103.82/14.42 | $i(v0) | ~ ssList(v4) | ~ ssList(v2) | ~ ssItem(v0) | ? [v5:
% 103.82/14.42 | any] : ( ~ (v5 = all_91_3) & app(v2, v4) = v5 & $i(v5)))
% 103.82/14.42 |
% 103.82/14.42 | ALPHA: (28) implies:
% 103.82/14.42 | (29) ssItem(all_91_1)
% 103.82/14.42 | (30) ssList(all_91_3)
% 103.82/14.42 | (31) ssList(all_91_2)
% 103.82/14.42 | (32) $i(all_91_3)
% 103.82/14.42 | (33) $i(all_91_2)
% 104.24/14.42 | (34) $i(all_91_1)
% 104.24/14.42 | (35) $i(all_91_0)
% 104.24/14.42 | (36) app(all_91_3, all_91_0) = all_91_2
% 104.24/14.42 | (37) cons(all_91_1, nil) = all_91_0
% 104.24/14.42 | (38) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 104.24/14.42 | ( ~ (cons(v0, nil) = v1) | ~ (app(v3, v4) = all_91_2) | ~ (app(v2,
% 104.24/14.42 | v1) = v3) | ~ $i(v4) | ~ $i(v2) | ~ $i(v0) | ~ ssList(v4) |
% 104.24/14.42 | ~ ssList(v2) | ~ ssItem(v0) | ? [v5: any] : ( ~ (v5 = all_91_3) &
% 104.24/14.42 | app(v2, v4) = v5 & $i(v5)))
% 104.24/14.42 |
% 104.24/14.42 | BETA: splitting (11) gives:
% 104.24/14.42 |
% 104.24/14.42 | Case 1:
% 104.24/14.42 | |
% 104.24/14.42 | | (39) ~ ssList(nil)
% 104.24/14.42 | |
% 104.24/14.43 | | PRED_UNIFY: (7), (39) imply:
% 104.24/14.43 | | (40) $false
% 104.24/14.43 | |
% 104.24/14.43 | | CLOSE: (40) is inconsistent.
% 104.24/14.43 | |
% 104.24/14.43 | Case 2:
% 104.24/14.43 | |
% 104.24/14.43 | | (41) frontsegP(nil, nil)
% 104.24/14.43 | |
% 104.24/14.43 | | BETA: splitting (13) gives:
% 104.24/14.43 | |
% 104.24/14.43 | | Case 1:
% 104.24/14.43 | | |
% 104.24/14.43 | | | (42) ~ ssList(nil)
% 104.24/14.43 | | |
% 104.24/14.43 | | | PRED_UNIFY: (7), (42) imply:
% 104.24/14.43 | | | (43) $false
% 104.24/14.43 | | |
% 104.24/14.43 | | | CLOSE: (43) is inconsistent.
% 104.24/14.43 | | |
% 104.24/14.43 | | Case 2:
% 104.24/14.43 | | |
% 104.24/14.43 | | | (44) rearsegP(nil, nil)
% 104.24/14.43 | | |
% 104.24/14.43 | | | BETA: splitting (14) gives:
% 104.24/14.43 | | |
% 104.24/14.43 | | | Case 1:
% 104.24/14.43 | | | |
% 104.24/14.43 | | | | (45) ~ ssList(nil)
% 104.24/14.43 | | | |
% 104.24/14.43 | | | | PRED_UNIFY: (7), (45) imply:
% 104.24/14.43 | | | | (46) $false
% 104.24/14.43 | | | |
% 104.24/14.43 | | | | CLOSE: (46) is inconsistent.
% 104.24/14.43 | | | |
% 104.24/14.43 | | | Case 2:
% 104.24/14.43 | | | |
% 104.24/14.43 | | | | (47) segmentP(nil, nil)
% 104.24/14.43 | | | |
% 104.24/14.43 | | | | GROUND_INST: instantiating (ax31) with all_91_1, simplifying with (29),
% 104.24/14.43 | | | | (34) gives:
% 104.24/14.43 | | | | (48) leq(all_91_1, all_91_1)
% 104.24/14.43 | | | |
% 104.24/14.43 | | | | GROUND_INST: instantiating (ax49) with all_91_3, simplifying with (30),
% 104.24/14.43 | | | | (32) gives:
% 104.24/14.43 | | | | (49) rearsegP(all_91_3, all_91_3)
% 104.24/14.43 | | | |
% 104.24/14.43 | | | | GROUND_INST: instantiating (12) with all_91_3, simplifying with (30),
% 104.24/14.43 | | | | (32) gives:
% 104.24/14.43 | | | | (50) rearsegP(all_91_3, nil)
% 104.24/14.43 | | | |
% 104.24/14.43 | | | | GROUND_INST: instantiating (ax42) with all_91_3, simplifying with (30),
% 104.24/14.43 | | | | (32) gives:
% 104.24/14.43 | | | | (51) frontsegP(all_91_3, all_91_3)
% 104.24/14.43 | | | |
% 104.24/14.43 | | | | GROUND_INST: instantiating (10) with all_91_3, simplifying with (30),
% 104.24/14.43 | | | | (32) gives:
% 104.24/14.43 | | | | (52) frontsegP(all_91_3, nil)
% 104.24/14.43 | | | |
% 104.24/14.43 | | | | GROUND_INST: instantiating (12) with all_91_2, simplifying with (31),
% 104.24/14.43 | | | | (33) gives:
% 104.24/14.43 | | | | (53) rearsegP(all_91_2, nil)
% 104.24/14.43 | | | |
% 104.24/14.43 | | | | GROUND_INST: instantiating (ax42) with all_91_2, simplifying with (31),
% 104.24/14.43 | | | | (33) gives:
% 104.24/14.43 | | | | (54) frontsegP(all_91_2, all_91_2)
% 104.24/14.43 | | | |
% 104.24/14.43 | | | | GROUND_INST: instantiating (10) with all_91_2, simplifying with (31),
% 104.24/14.43 | | | | (33) gives:
% 104.24/14.43 | | | | (55) frontsegP(all_91_2, nil)
% 104.24/14.43 | | | |
% 104.24/14.43 | | | | GROUND_INST: instantiating (3) with nil, nil, simplifying with (7),
% 104.24/14.43 | | | | (23), (41) gives:
% 104.24/14.43 | | | | (56) ? [v0: $i] : (app(nil, v0) = nil & $i(v0) & ssList(v0))
% 104.24/14.43 | | | |
% 104.24/14.43 | | | | GROUND_INST: instantiating (4) with nil, nil, simplifying with (7),
% 104.24/14.43 | | | | (23), (44) gives:
% 104.24/14.43 | | | | (57) ? [v0: $i] : (app(v0, nil) = nil & $i(v0) & ssList(v0))
% 104.24/14.43 | | | |
% 104.24/14.43 | | | | GROUND_INST: instantiating (6) with nil, nil, simplifying with (7),
% 104.24/14.43 | | | | (23), (47) gives:
% 104.24/14.43 | | | | (58) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (app(v1, v2) = nil &
% 104.24/14.43 | | | | app(v0, nil) = v1 & $i(v2) & $i(v1) & $i(v0) & ssList(v2) &
% 104.24/14.43 | | | | ssList(v0))
% 104.24/14.43 | | | |
% 104.24/14.43 | | | | GROUND_INST: instantiating (9) with all_91_1, nil, all_91_0, nil,
% 104.24/14.43 | | | | all_91_0, simplifying with (7), (23), (29), (34), (37),
% 104.24/14.44 | | | | (41) gives:
% 104.24/14.44 | | | | (59) frontsegP(all_91_0, all_91_0)
% 104.24/14.44 | | | |
% 104.24/14.44 | | | | GROUND_INST: instantiating (ax25) with nil, all_91_1, all_91_0,
% 104.24/14.44 | | | | simplifying with (7), (23), (29), (34), (37) gives:
% 104.24/14.44 | | | | (60) tl(all_91_0) = nil
% 104.24/14.44 | | | |
% 104.24/14.44 | | | | GROUND_INST: instantiating (ax23) with nil, all_91_1, all_91_0,
% 104.24/14.44 | | | | simplifying with (7), (23), (29), (34), (37) gives:
% 104.24/14.44 | | | | (61) hd(all_91_0) = all_91_1
% 104.24/14.44 | | | |
% 104.24/14.44 | | | | GROUND_INST: instantiating (ax16) with nil, all_91_1, all_91_0,
% 104.24/14.44 | | | | simplifying with (7), (23), (29), (34), (37) gives:
% 104.24/14.44 | | | | (62) ssList(all_91_0)
% 104.24/14.44 | | | |
% 104.24/14.44 | | | | GROUND_INST: instantiating (15) with all_91_1, all_91_0, simplifying
% 104.24/14.44 | | | | with (29), (34), (37) gives:
% 104.24/14.44 | | | | (63) totalorderedP(all_91_0)
% 104.24/14.44 | | | |
% 104.24/14.44 | | | | DELTA: instantiating (57) with fresh symbol all_112_0 gives:
% 104.24/14.44 | | | | (64) app(all_112_0, nil) = nil & $i(all_112_0) & ssList(all_112_0)
% 104.24/14.44 | | | |
% 104.24/14.44 | | | | ALPHA: (64) implies:
% 104.24/14.44 | | | | (65) ssList(all_112_0)
% 104.24/14.44 | | | | (66) $i(all_112_0)
% 104.24/14.44 | | | | (67) app(all_112_0, nil) = nil
% 104.24/14.44 | | | |
% 104.24/14.44 | | | | DELTA: instantiating (56) with fresh symbol all_114_0 gives:
% 104.24/14.44 | | | | (68) app(nil, all_114_0) = nil & $i(all_114_0) & ssList(all_114_0)
% 104.24/14.44 | | | |
% 104.24/14.44 | | | | ALPHA: (68) implies:
% 104.24/14.44 | | | | (69) ssList(all_114_0)
% 104.24/14.44 | | | | (70) $i(all_114_0)
% 104.24/14.44 | | | | (71) app(nil, all_114_0) = nil
% 104.24/14.44 | | | |
% 104.24/14.44 | | | | DELTA: instantiating (58) with fresh symbols all_116_0, all_116_1,
% 104.24/14.44 | | | | all_116_2 gives:
% 104.24/14.44 | | | | (72) app(all_116_1, all_116_0) = nil & app(all_116_2, nil) =
% 104.24/14.44 | | | | all_116_1 & $i(all_116_0) & $i(all_116_1) & $i(all_116_2) &
% 104.24/14.44 | | | | ssList(all_116_0) & ssList(all_116_2)
% 104.24/14.44 | | | |
% 104.24/14.44 | | | | ALPHA: (72) implies:
% 104.24/14.44 | | | | (73) ssList(all_116_2)
% 104.24/14.44 | | | | (74) ssList(all_116_0)
% 104.24/14.44 | | | | (75) $i(all_116_2)
% 104.24/14.44 | | | | (76) $i(all_116_1)
% 104.24/14.44 | | | | (77) $i(all_116_0)
% 104.24/14.44 | | | | (78) app(all_116_2, nil) = all_116_1
% 104.24/14.44 | | | | (79) app(all_116_1, all_116_0) = nil
% 104.24/14.44 | | | |
% 104.24/14.44 | | | | GROUND_INST: instantiating (2) with all_91_0, all_91_1, simplifying with
% 104.24/14.44 | | | | (29), (34), (35), (37), (62) gives:
% 104.24/14.44 | | | | (80) singletonP(all_91_0)
% 104.24/14.44 | | | |
% 104.24/14.44 | | | | GROUND_INST: instantiating (5) with all_91_2, all_91_0, all_91_3,
% 104.24/14.44 | | | | simplifying with (30), (31), (32), (33), (35), (36), (62)
% 104.24/14.44 | | | | gives:
% 104.24/14.44 | | | | (81) rearsegP(all_91_2, all_91_0)
% 104.24/14.44 | | | |
% 104.24/14.44 | | | | GROUND_INST: instantiating (3) with all_91_3, nil, simplifying with (7),
% 104.24/14.44 | | | | (23), (30), (32), (52) gives:
% 104.24/14.44 | | | | (82) ? [v0: $i] : (app(nil, v0) = all_91_3 & $i(v0) & ssList(v0))
% 104.24/14.44 | | | |
% 104.24/14.44 | | | | GROUND_INST: instantiating (3) with all_91_3, all_91_3, simplifying with
% 104.24/14.44 | | | | (30), (32), (51) gives:
% 104.24/14.44 | | | | (83) ? [v0: $i] : (app(all_91_3, v0) = all_91_3 & $i(v0) &
% 104.24/14.44 | | | | ssList(v0))
% 104.24/14.44 | | | |
% 104.24/14.44 | | | | GROUND_INST: instantiating (3) with all_91_2, nil, simplifying with (7),
% 104.24/14.44 | | | | (23), (31), (33), (55) gives:
% 104.24/14.45 | | | | (84) ? [v0: $i] : (app(nil, v0) = all_91_2 & $i(v0) & ssList(v0))
% 104.24/14.45 | | | |
% 104.24/14.45 | | | | GROUND_INST: instantiating (3) with all_91_2, all_91_2, simplifying with
% 104.24/14.45 | | | | (31), (33), (54) gives:
% 104.24/14.45 | | | | (85) ? [v0: $i] : (app(all_91_2, v0) = all_91_2 & $i(v0) &
% 104.24/14.45 | | | | ssList(v0))
% 104.24/14.45 | | | |
% 104.24/14.45 | | | | GROUND_INST: instantiating (3) with all_91_0, all_91_0, simplifying with
% 104.24/14.45 | | | | (35), (59), (62) gives:
% 104.24/14.45 | | | | (86) ? [v0: $i] : (app(all_91_0, v0) = all_91_0 & $i(v0) &
% 104.24/14.45 | | | | ssList(v0))
% 104.24/14.45 | | | |
% 104.24/14.45 | | | | GROUND_INST: instantiating (4) with all_91_3, nil, simplifying with (7),
% 104.24/14.45 | | | | (23), (30), (32), (50) gives:
% 104.24/14.45 | | | | (87) ? [v0: $i] : (app(v0, nil) = all_91_3 & $i(v0) & ssList(v0))
% 104.24/14.45 | | | |
% 104.24/14.45 | | | | GROUND_INST: instantiating (4) with all_91_3, all_91_3, simplifying with
% 104.24/14.45 | | | | (30), (32), (49) gives:
% 104.24/14.45 | | | | (88) ? [v0: $i] : (app(v0, all_91_3) = all_91_3 & $i(v0) &
% 104.24/14.45 | | | | ssList(v0))
% 104.24/14.45 | | | |
% 104.24/14.45 | | | | GROUND_INST: instantiating (4) with all_91_2, nil, simplifying with (7),
% 104.24/14.45 | | | | (23), (31), (33), (53) gives:
% 104.24/14.45 | | | | (89) ? [v0: $i] : (app(v0, nil) = all_91_2 & $i(v0) & ssList(v0))
% 104.24/14.45 | | | |
% 104.24/14.45 | | | | GROUND_INST: instantiating (ax27) with all_114_0, nil, nil, all_91_1,
% 104.24/14.45 | | | | all_91_0, simplifying with (7), (23), (29), (34), (37),
% 104.24/14.45 | | | | (69), (70), (71) gives:
% 104.24/14.45 | | | | (90) ? [v0: $i] : (cons(all_91_1, nil) = v0 & app(v0, all_114_0) =
% 104.24/14.45 | | | | all_91_0 & $i(v0) & $i(all_91_0))
% 104.24/14.45 | | | |
% 104.24/14.45 | | | | GROUND_INST: instantiating (ax82) with nil, all_114_0, nil, all_114_0,
% 104.24/14.45 | | | | nil, simplifying with (7), (23), (69), (70), (71) gives:
% 104.24/14.45 | | | | (91) ? [v0: $i] : (app(all_114_0, all_114_0) = v0 & app(nil, v0) =
% 104.24/14.45 | | | | nil & $i(v0))
% 104.24/14.45 | | | |
% 104.24/14.45 | | | | GROUND_INST: instantiating (8) with all_114_0, nil, simplifying with
% 104.24/14.45 | | | | (69), (70), (71) gives:
% 104.24/14.45 | | | | (92) all_114_0 = nil
% 104.24/14.45 | | | |
% 104.24/14.45 | | | | GROUND_INST: instantiating (ax27) with nil, all_112_0, nil, all_91_1,
% 104.24/14.45 | | | | all_91_0, simplifying with (7), (23), (29), (34), (37),
% 104.24/14.45 | | | | (65), (66), (67) gives:
% 104.24/14.45 | | | | (93) ? [v0: $i] : (cons(all_91_1, all_112_0) = v0 & app(v0, nil) =
% 104.24/14.45 | | | | all_91_0 & $i(v0) & $i(all_91_0))
% 104.24/14.45 | | | |
% 104.24/14.45 | | | | GROUND_INST: instantiating (22) with all_112_0, nil, simplifying with
% 104.24/14.45 | | | | (65), (66), (67) gives:
% 104.24/14.45 | | | | (94) all_112_0 = nil
% 104.24/14.45 | | | |
% 104.24/14.46 | | | | GROUND_INST: instantiating (ax26) with all_116_2, nil, all_116_1,
% 104.24/14.46 | | | | simplifying with (7), (23), (73), (75), (78) gives:
% 104.24/14.46 | | | | (95) ssList(all_116_1)
% 104.24/14.46 | | | |
% 104.24/14.46 | | | | GROUND_INST: instantiating (22) with all_116_2, all_116_1, simplifying
% 104.24/14.46 | | | | with (73), (75), (78) gives:
% 104.24/14.46 | | | | (96) all_116_1 = all_116_2
% 104.24/14.46 | | | |
% 104.24/14.46 | | | | GROUND_INST: instantiating (ax82) with all_116_2, nil, all_116_1,
% 104.24/14.46 | | | | all_116_0, nil, simplifying with (7), (23), (73), (74),
% 104.24/14.46 | | | | (75), (77), (78), (79) gives:
% 104.24/14.46 | | | | (97) ? [v0: $i] : (app(all_116_2, v0) = nil & app(nil, all_116_0) =
% 104.24/14.46 | | | | v0 & $i(v0))
% 104.24/14.46 | | | |
% 104.24/14.46 | | | | GROUND_INST: instantiating (16) with all_91_1, all_91_0, all_91_1,
% 104.24/14.46 | | | | simplifying with (29), (34), (35), (61), (62) gives:
% 104.24/14.46 | | | | (98) ? [v0: $i] : ((all_91_0 = nil | (cons(all_91_1, all_91_0) = v0
% 104.24/14.46 | | | | & $i(v0) & ~ totalorderedP(v0)) |
% 104.24/14.46 | | | | (totalorderedP(all_91_0) & leq(all_91_1, all_91_1))) & (( ~
% 104.24/14.46 | | | | (all_91_0 = nil) & ( ~ totalorderedP(all_91_0) | ~
% 104.24/14.46 | | | | leq(all_91_1, all_91_1))) | (cons(all_91_1, all_91_0) =
% 104.24/14.46 | | | | v0 & $i(v0) & totalorderedP(v0))))
% 104.24/14.46 | | | |
% 104.24/14.46 | | | | GROUND_INST: instantiating (17) with all_91_0, nil, simplifying with
% 104.24/14.46 | | | | (35), (60), (62) gives:
% 104.24/14.46 | | | | (99) ? [v0: $i] : (hd(all_91_0) = v0 & $i(v0) & ! [v1: any] : (v1 =
% 104.24/14.46 | | | | all_91_0 | v1 = nil | all_91_0 = nil | ~ (tl(v1) = nil) |
% 104.24/14.46 | | | | ~ $i(v1) | ~ ssList(v1) | ? [v2: $i] : ( ~ (v2 = v0) &
% 104.24/14.46 | | | | hd(v1) = v2 & $i(v2))))
% 104.24/14.46 | | | |
% 104.24/14.46 | | | | DELTA: instantiating (97) with fresh symbol all_132_0 gives:
% 104.24/14.46 | | | | (100) app(all_116_2, all_132_0) = nil & app(nil, all_116_0) =
% 104.24/14.46 | | | | all_132_0 & $i(all_132_0)
% 104.24/14.46 | | | |
% 104.24/14.46 | | | | ALPHA: (100) implies:
% 104.24/14.46 | | | | (101) app(nil, all_116_0) = all_132_0
% 104.24/14.46 | | | |
% 104.24/14.46 | | | | DELTA: instantiating (84) with fresh symbol all_134_0 gives:
% 104.24/14.46 | | | | (102) app(nil, all_134_0) = all_91_2 & $i(all_134_0) &
% 104.24/14.46 | | | | ssList(all_134_0)
% 104.24/14.46 | | | |
% 104.24/14.46 | | | | ALPHA: (102) implies:
% 104.24/14.46 | | | | (103) ssList(all_134_0)
% 104.24/14.46 | | | | (104) $i(all_134_0)
% 104.24/14.46 | | | | (105) app(nil, all_134_0) = all_91_2
% 104.24/14.46 | | | |
% 104.24/14.46 | | | | DELTA: instantiating (82) with fresh symbol all_136_0 gives:
% 104.24/14.46 | | | | (106) app(nil, all_136_0) = all_91_3 & $i(all_136_0) &
% 104.24/14.46 | | | | ssList(all_136_0)
% 104.24/14.46 | | | |
% 104.24/14.46 | | | | ALPHA: (106) implies:
% 104.24/14.46 | | | | (107) ssList(all_136_0)
% 104.24/14.46 | | | | (108) $i(all_136_0)
% 104.24/14.46 | | | | (109) app(nil, all_136_0) = all_91_3
% 104.24/14.46 | | | |
% 104.24/14.46 | | | | DELTA: instantiating (83) with fresh symbol all_138_0 gives:
% 104.24/14.46 | | | | (110) app(all_91_3, all_138_0) = all_91_3 & $i(all_138_0) &
% 104.24/14.46 | | | | ssList(all_138_0)
% 104.24/14.46 | | | |
% 104.24/14.46 | | | | ALPHA: (110) implies:
% 104.24/14.46 | | | | (111) ssList(all_138_0)
% 104.24/14.46 | | | | (112) $i(all_138_0)
% 104.24/14.46 | | | | (113) app(all_91_3, all_138_0) = all_91_3
% 104.24/14.46 | | | |
% 104.24/14.46 | | | | DELTA: instantiating (91) with fresh symbol all_140_0 gives:
% 104.24/14.46 | | | | (114) app(all_114_0, all_114_0) = all_140_0 & app(nil, all_140_0) =
% 104.24/14.46 | | | | nil & $i(all_140_0)
% 104.24/14.46 | | | |
% 104.24/14.46 | | | | ALPHA: (114) implies:
% 104.24/14.46 | | | | (115) $i(all_140_0)
% 104.24/14.46 | | | | (116) app(all_114_0, all_114_0) = all_140_0
% 104.24/14.46 | | | |
% 104.24/14.46 | | | | DELTA: instantiating (89) with fresh symbol all_144_0 gives:
% 104.24/14.46 | | | | (117) app(all_144_0, nil) = all_91_2 & $i(all_144_0) &
% 104.24/14.46 | | | | ssList(all_144_0)
% 104.24/14.46 | | | |
% 104.24/14.46 | | | | ALPHA: (117) implies:
% 104.24/14.46 | | | | (118) ssList(all_144_0)
% 104.24/14.46 | | | | (119) $i(all_144_0)
% 104.24/14.46 | | | | (120) app(all_144_0, nil) = all_91_2
% 104.24/14.46 | | | |
% 104.24/14.46 | | | | DELTA: instantiating (88) with fresh symbol all_146_0 gives:
% 104.24/14.46 | | | | (121) app(all_146_0, all_91_3) = all_91_3 & $i(all_146_0) &
% 104.24/14.46 | | | | ssList(all_146_0)
% 104.24/14.46 | | | |
% 104.24/14.46 | | | | ALPHA: (121) implies:
% 104.24/14.46 | | | | (122) ssList(all_146_0)
% 104.24/14.46 | | | | (123) $i(all_146_0)
% 104.24/14.46 | | | | (124) app(all_146_0, all_91_3) = all_91_3
% 104.24/14.46 | | | |
% 104.24/14.46 | | | | DELTA: instantiating (87) with fresh symbol all_148_0 gives:
% 104.24/14.46 | | | | (125) app(all_148_0, nil) = all_91_3 & $i(all_148_0) &
% 104.24/14.46 | | | | ssList(all_148_0)
% 104.24/14.47 | | | |
% 104.24/14.47 | | | | ALPHA: (125) implies:
% 104.24/14.47 | | | | (126) ssList(all_148_0)
% 104.24/14.47 | | | | (127) $i(all_148_0)
% 104.24/14.47 | | | | (128) app(all_148_0, nil) = all_91_3
% 104.24/14.47 | | | |
% 104.24/14.47 | | | | DELTA: instantiating (86) with fresh symbol all_150_0 gives:
% 104.24/14.47 | | | | (129) app(all_91_0, all_150_0) = all_91_0 & $i(all_150_0) &
% 104.24/14.47 | | | | ssList(all_150_0)
% 104.24/14.47 | | | |
% 104.24/14.47 | | | | ALPHA: (129) implies:
% 104.24/14.47 | | | | (130) ssList(all_150_0)
% 104.24/14.47 | | | | (131) $i(all_150_0)
% 104.24/14.47 | | | | (132) app(all_91_0, all_150_0) = all_91_0
% 104.24/14.47 | | | |
% 104.24/14.47 | | | | DELTA: instantiating (85) with fresh symbol all_152_0 gives:
% 104.24/14.47 | | | | (133) app(all_91_2, all_152_0) = all_91_2 & $i(all_152_0) &
% 104.24/14.47 | | | | ssList(all_152_0)
% 104.24/14.47 | | | |
% 104.24/14.47 | | | | ALPHA: (133) implies:
% 104.24/14.47 | | | | (134) ssList(all_152_0)
% 104.24/14.47 | | | | (135) $i(all_152_0)
% 104.24/14.47 | | | | (136) app(all_91_2, all_152_0) = all_91_2
% 104.24/14.47 | | | |
% 104.24/14.47 | | | | DELTA: instantiating (93) with fresh symbol all_154_0 gives:
% 104.24/14.47 | | | | (137) cons(all_91_1, all_112_0) = all_154_0 & app(all_154_0, nil) =
% 104.24/14.47 | | | | all_91_0 & $i(all_154_0) & $i(all_91_0)
% 104.24/14.47 | | | |
% 104.24/14.47 | | | | ALPHA: (137) implies:
% 104.24/14.47 | | | | (138) $i(all_154_0)
% 104.24/14.47 | | | | (139) app(all_154_0, nil) = all_91_0
% 104.24/14.47 | | | | (140) cons(all_91_1, all_112_0) = all_154_0
% 104.24/14.47 | | | |
% 104.24/14.47 | | | | DELTA: instantiating (90) with fresh symbol all_156_0 gives:
% 104.24/14.47 | | | | (141) cons(all_91_1, nil) = all_156_0 & app(all_156_0, all_114_0) =
% 104.24/14.47 | | | | all_91_0 & $i(all_156_0) & $i(all_91_0)
% 104.24/14.47 | | | |
% 104.24/14.47 | | | | ALPHA: (141) implies:
% 104.24/14.47 | | | | (142) cons(all_91_1, nil) = all_156_0
% 104.24/14.47 | | | |
% 104.24/14.47 | | | | DELTA: instantiating (99) with fresh symbol all_170_0 gives:
% 104.24/14.47 | | | | (143) hd(all_91_0) = all_170_0 & $i(all_170_0) & ! [v0: any] : (v0 =
% 104.24/14.47 | | | | all_91_0 | v0 = nil | all_91_0 = nil | ~ (tl(v0) = nil) | ~
% 104.24/14.47 | | | | $i(v0) | ~ ssList(v0) | ? [v1: any] : ( ~ (v1 = all_170_0)
% 104.24/14.47 | | | | & hd(v0) = v1 & $i(v1)))
% 104.24/14.47 | | | |
% 104.24/14.47 | | | | ALPHA: (143) implies:
% 104.24/14.47 | | | | (144) $i(all_170_0)
% 104.24/14.47 | | | | (145) hd(all_91_0) = all_170_0
% 104.24/14.47 | | | |
% 104.24/14.47 | | | | DELTA: instantiating (98) with fresh symbol all_173_0 gives:
% 104.24/14.47 | | | | (146) (all_91_0 = nil | (cons(all_91_1, all_91_0) = all_173_0 &
% 104.24/14.47 | | | | $i(all_173_0) & ~ totalorderedP(all_173_0)) |
% 104.24/14.47 | | | | (totalorderedP(all_91_0) & leq(all_91_1, all_91_1))) & (( ~
% 104.24/14.47 | | | | (all_91_0 = nil) & ( ~ totalorderedP(all_91_0) | ~
% 104.24/14.47 | | | | leq(all_91_1, all_91_1))) | (cons(all_91_1, all_91_0) =
% 104.24/14.47 | | | | all_173_0 & $i(all_173_0) & totalorderedP(all_173_0)))
% 104.24/14.47 | | | |
% 104.24/14.47 | | | | ALPHA: (146) implies:
% 104.24/14.47 | | | | (147) ( ~ (all_91_0 = nil) & ( ~ totalorderedP(all_91_0) | ~
% 104.24/14.47 | | | | leq(all_91_1, all_91_1))) | (cons(all_91_1, all_91_0) =
% 104.24/14.47 | | | | all_173_0 & $i(all_173_0) & totalorderedP(all_173_0))
% 104.24/14.47 | | | |
% 104.24/14.47 | | | | REDUCE: (94), (140) imply:
% 104.24/14.47 | | | | (148) cons(all_91_1, nil) = all_154_0
% 104.24/14.47 | | | |
% 104.24/14.47 | | | | REDUCE: (79), (96) imply:
% 104.24/14.47 | | | | (149) app(all_116_2, all_116_0) = nil
% 104.24/14.47 | | | |
% 104.24/14.47 | | | | REDUCE: (92), (116) imply:
% 104.24/14.47 | | | | (150) app(nil, nil) = all_140_0
% 104.24/14.47 | | | |
% 104.24/14.47 | | | | BETA: splitting (147) gives:
% 104.24/14.47 | | | |
% 104.24/14.47 | | | | Case 1:
% 104.24/14.47 | | | | |
% 104.24/14.47 | | | | | (151) ~ (all_91_0 = nil) & ( ~ totalorderedP(all_91_0) | ~
% 104.24/14.47 | | | | | leq(all_91_1, all_91_1))
% 104.24/14.47 | | | | |
% 104.24/14.47 | | | | | ALPHA: (151) implies:
% 104.24/14.47 | | | | | (152) ~ totalorderedP(all_91_0) | ~ leq(all_91_1, all_91_1)
% 104.24/14.47 | | | | |
% 104.24/14.47 | | | | | BETA: splitting (152) gives:
% 104.24/14.47 | | | | |
% 104.24/14.47 | | | | | Case 1:
% 104.24/14.47 | | | | | |
% 104.24/14.47 | | | | | | (153) ~ totalorderedP(all_91_0)
% 104.24/14.47 | | | | | |
% 104.24/14.47 | | | | | | PRED_UNIFY: (63), (153) imply:
% 104.24/14.47 | | | | | | (154) $false
% 104.24/14.47 | | | | | |
% 104.24/14.47 | | | | | | CLOSE: (154) is inconsistent.
% 104.24/14.47 | | | | | |
% 104.24/14.47 | | | | | Case 2:
% 104.24/14.47 | | | | | |
% 104.24/14.47 | | | | | | (155) ~ leq(all_91_1, all_91_1)
% 104.24/14.47 | | | | | |
% 104.24/14.47 | | | | | | PRED_UNIFY: (48), (155) imply:
% 104.24/14.47 | | | | | | (156) $false
% 104.24/14.47 | | | | | |
% 104.24/14.47 | | | | | | CLOSE: (156) is inconsistent.
% 104.24/14.47 | | | | | |
% 104.24/14.47 | | | | | End of split
% 104.24/14.47 | | | | |
% 104.24/14.47 | | | | Case 2:
% 104.24/14.47 | | | | |
% 104.24/14.47 | | | | |
% 104.24/14.47 | | | | | GROUND_INST: instantiating (19) with all_140_0, simplifying with (7),
% 104.24/14.47 | | | | | (150) gives:
% 104.24/14.47 | | | | | (157) all_140_0 = nil
% 104.24/14.47 | | | | |
% 104.24/14.47 | | | | | GROUND_INST: instantiating (27) with all_91_0, all_156_0, nil,
% 104.24/14.47 | | | | | all_91_1, simplifying with (37), (142) gives:
% 104.24/14.47 | | | | | (158) all_156_0 = all_91_0
% 104.24/14.47 | | | | |
% 104.24/14.47 | | | | | GROUND_INST: instantiating (27) with all_154_0, all_156_0, nil,
% 104.24/14.47 | | | | | all_91_1, simplifying with (142), (148) gives:
% 104.24/14.47 | | | | | (159) all_156_0 = all_154_0
% 104.24/14.47 | | | | |
% 104.24/14.47 | | | | | GROUND_INST: instantiating (25) with all_91_1, all_170_0, all_91_0,
% 104.24/14.47 | | | | | simplifying with (61), (145) gives:
% 104.24/14.47 | | | | | (160) all_170_0 = all_91_1
% 104.24/14.47 | | | | |
% 104.24/14.47 | | | | | COMBINE_EQS: (158), (159) imply:
% 104.24/14.47 | | | | | (161) all_154_0 = all_91_0
% 104.24/14.47 | | | | |
% 104.24/14.47 | | | | | REDUCE: (139), (161) imply:
% 104.24/14.47 | | | | | (162) app(all_91_0, nil) = all_91_0
% 104.24/14.47 | | | | |
% 104.24/14.47 | | | | | REDUCE: (150), (157) imply:
% 104.24/14.47 | | | | | (163) app(nil, nil) = nil
% 104.24/14.47 | | | | |
% 104.24/14.47 | | | | | GROUND_INST: instantiating (1) with all_91_0, simplifying with (35),
% 104.24/14.47 | | | | | (62), (80) gives:
% 104.24/14.48 | | | | | (164) ? [v0: $i] : (cons(v0, nil) = all_91_0 & $i(v0) &
% 104.24/14.48 | | | | | ssItem(v0))
% 104.24/14.48 | | | | |
% 104.24/14.48 | | | | | GROUND_INST: instantiating (4) with all_91_2, all_91_0, simplifying
% 104.24/14.48 | | | | | with (31), (33), (35), (62), (81) gives:
% 104.24/14.48 | | | | | (165) ? [v0: $i] : (app(v0, all_91_0) = all_91_2 & $i(v0) &
% 104.24/14.48 | | | | | ssList(v0))
% 104.24/14.48 | | | | |
% 104.24/14.48 | | | | | GROUND_INST: instantiating (ax82) with nil, nil, nil, all_116_0,
% 104.24/14.48 | | | | | all_132_0, simplifying with (7), (23), (74), (77), (101),
% 104.24/14.48 | | | | | (163) gives:
% 104.24/14.48 | | | | | (166) ? [v0: $i] : (app(nil, v0) = all_132_0 & app(nil, all_116_0)
% 104.24/14.48 | | | | | = v0 & $i(v0) & $i(all_132_0))
% 104.24/14.48 | | | | |
% 104.24/14.48 | | | | | GROUND_INST: instantiating (8) with all_116_0, all_132_0, simplifying
% 104.24/14.48 | | | | | with (74), (77), (101) gives:
% 104.24/14.48 | | | | | (167) all_132_0 = all_116_0
% 104.24/14.48 | | | | |
% 104.24/14.48 | | | | | GROUND_INST: instantiating (8) with all_134_0, all_91_2, simplifying
% 104.24/14.48 | | | | | with (103), (104), (105) gives:
% 104.24/14.48 | | | | | (168) all_134_0 = all_91_2
% 104.24/14.48 | | | | |
% 104.24/14.48 | | | | | GROUND_INST: instantiating (ax82) with nil, all_136_0, all_91_3,
% 104.24/14.48 | | | | | all_91_0, all_91_2, simplifying with (7), (23), (35),
% 104.24/14.48 | | | | | (36), (62), (107), (108), (109) gives:
% 104.24/14.48 | | | | | (169) ? [v0: $i] : (app(all_136_0, all_91_0) = v0 & app(nil, v0) =
% 104.24/14.48 | | | | | all_91_2 & $i(v0) & $i(all_91_2))
% 104.24/14.48 | | | | |
% 104.24/14.48 | | | | | GROUND_INST: instantiating (ax82) with nil, nil, nil, all_136_0,
% 104.24/14.48 | | | | | all_91_3, simplifying with (7), (23), (107), (108),
% 104.24/14.48 | | | | | (109), (163) gives:
% 104.24/14.48 | | | | | (170) ? [v0: $i] : (app(nil, v0) = all_91_3 & app(nil, all_136_0)
% 104.24/14.48 | | | | | = v0 & $i(v0) & $i(all_91_3))
% 104.24/14.48 | | | | |
% 104.24/14.48 | | | | | GROUND_INST: instantiating (8) with all_136_0, all_91_3, simplifying
% 104.24/14.48 | | | | | with (107), (108), (109) gives:
% 104.24/14.48 | | | | | (171) all_136_0 = all_91_3
% 104.24/14.48 | | | | |
% 104.24/14.48 | | | | | GROUND_INST: instantiating (ax82) with nil, all_136_0, all_91_3,
% 104.24/14.48 | | | | | all_138_0, all_91_3, simplifying with (7), (23), (107),
% 104.24/14.48 | | | | | (108), (109), (111), (112), (113) gives:
% 104.24/14.48 | | | | | (172) ? [v0: $i] : (app(all_136_0, all_138_0) = v0 & app(nil, v0)
% 104.24/14.48 | | | | | = all_91_3 & $i(v0) & $i(all_91_3))
% 104.24/14.48 | | | | |
% 104.24/14.48 | | | | | GROUND_INST: instantiating (ax82) with nil, all_134_0, all_91_2,
% 104.24/14.48 | | | | | all_152_0, all_91_2, simplifying with (7), (23), (103),
% 104.24/14.48 | | | | | (104), (105), (134), (135), (136) gives:
% 104.24/14.48 | | | | | (173) ? [v0: $i] : (app(all_134_0, all_152_0) = v0 & app(nil, v0)
% 104.24/14.48 | | | | | = all_91_2 & $i(v0) & $i(all_91_2))
% 104.24/14.48 | | | | |
% 104.24/14.48 | | | | | GROUND_INST: instantiating (38) with all_91_1, all_91_0, all_91_3,
% 104.24/14.48 | | | | | all_91_2, all_152_0, simplifying with (29), (30), (32),
% 104.24/14.48 | | | | | (34), (36), (37), (134), (135), (136) gives:
% 104.53/14.48 | | | | | (174) ? [v0: any] : ( ~ (v0 = all_91_3) & app(all_91_3, all_152_0)
% 104.53/14.48 | | | | | = v0 & $i(v0))
% 104.53/14.48 | | | | |
% 104.53/14.48 | | | | | GROUND_INST: instantiating (18) with all_150_0, all_91_1, all_91_0,
% 104.53/14.48 | | | | | all_91_0, simplifying with (29), (34), (37), (130),
% 104.53/14.48 | | | | | (131), (132) gives:
% 104.53/14.48 | | | | | (175) cons(all_91_1, all_150_0) = all_91_0 & $i(all_91_0)
% 104.53/14.48 | | | | |
% 104.53/14.48 | | | | | ALPHA: (175) implies:
% 104.53/14.48 | | | | | (176) cons(all_91_1, all_150_0) = all_91_0
% 104.53/14.48 | | | | |
% 104.53/14.48 | | | | | GROUND_INST: instantiating (ax82) with all_91_0, all_150_0, all_91_0,
% 104.53/14.48 | | | | | all_150_0, all_91_0, simplifying with (35), (62), (130),
% 104.53/14.48 | | | | | (131), (132) gives:
% 104.53/14.48 | | | | | (177) ? [v0: $i] : (app(all_150_0, all_150_0) = v0 & app(all_91_0,
% 104.53/14.48 | | | | | v0) = all_91_0 & $i(v0))
% 104.53/14.48 | | | | |
% 104.53/14.48 | | | | | GROUND_INST: instantiating (ax80) with all_150_0, all_91_0, all_91_0,
% 104.53/14.48 | | | | | nil, simplifying with (7), (23), (35), (62), (130),
% 104.53/14.48 | | | | | (131), (132), (162) gives:
% 104.53/14.48 | | | | | (178) all_150_0 = nil
% 104.53/14.48 | | | | |
% 104.53/14.48 | | | | | GROUND_INST: instantiating (ax82) with all_91_0, nil, all_91_0,
% 104.53/14.48 | | | | | all_150_0, all_91_0, simplifying with (7), (23), (35),
% 104.53/14.48 | | | | | (62), (130), (131), (132), (162) gives:
% 104.53/14.48 | | | | | (179) ? [v0: $i] : (app(all_91_0, v0) = all_91_0 & app(nil,
% 104.53/14.48 | | | | | all_150_0) = v0 & $i(v0))
% 104.53/14.48 | | | | |
% 104.53/14.48 | | | | | GROUND_INST: instantiating (ax82) with all_91_0, all_150_0, all_91_0,
% 104.53/14.48 | | | | | nil, all_91_0, simplifying with (7), (23), (35), (62),
% 104.53/14.48 | | | | | (130), (131), (132), (162) gives:
% 104.53/14.48 | | | | | (180) ? [v0: $i] : (app(all_150_0, nil) = v0 & app(all_91_0, v0) =
% 104.53/14.48 | | | | | all_91_0 & $i(v0))
% 104.53/14.48 | | | | |
% 104.53/14.48 | | | | | GROUND_INST: instantiating (ax27) with all_116_0, all_116_2, nil,
% 104.53/14.48 | | | | | all_91_1, all_91_0, simplifying with (29), (34), (37),
% 104.53/14.48 | | | | | (73), (74), (75), (77), (149) gives:
% 104.53/14.48 | | | | | (181) ? [v0: $i] : (cons(all_91_1, all_116_2) = v0 & app(v0,
% 104.53/14.48 | | | | | all_116_0) = all_91_0 & $i(v0) & $i(all_91_0))
% 104.53/14.48 | | | | |
% 104.53/14.48 | | | | | GROUND_INST: instantiating (ax82) with all_116_2, all_116_0, nil,
% 104.53/14.48 | | | | | all_136_0, all_91_3, simplifying with (73), (74), (75),
% 104.53/14.48 | | | | | (77), (107), (108), (109), (149) gives:
% 104.53/14.49 | | | | | (182) ? [v0: $i] : (app(all_116_0, all_136_0) = v0 &
% 104.53/14.49 | | | | | app(all_116_2, v0) = all_91_3 & $i(v0) & $i(all_91_3))
% 104.53/14.49 | | | | |
% 104.53/14.49 | | | | | GROUND_INST: instantiating (ax82) with all_116_2, all_116_0, nil,
% 104.53/14.49 | | | | | all_116_0, all_132_0, simplifying with (73), (74), (75),
% 104.53/14.49 | | | | | (77), (101), (149) gives:
% 104.53/14.49 | | | | | (183) ? [v0: $i] : (app(all_116_0, all_116_0) = v0 &
% 104.53/14.49 | | | | | app(all_116_2, v0) = all_132_0 & $i(v0) & $i(all_132_0))
% 104.53/14.49 | | | | |
% 104.53/14.49 | | | | | GROUND_INST: instantiating (ax82) with all_116_2, all_116_0, nil, nil,
% 104.53/14.49 | | | | | nil, simplifying with (7), (23), (73), (74), (75), (77),
% 104.53/14.49 | | | | | (149), (163) gives:
% 104.53/14.49 | | | | | (184) ? [v0: $i] : (app(all_116_0, nil) = v0 & app(all_116_2, v0)
% 104.53/14.49 | | | | | = nil & $i(v0))
% 104.53/14.49 | | | | |
% 104.53/14.49 | | | | | GROUND_INST: instantiating (21) with all_116_2, all_116_0, simplifying
% 104.53/14.49 | | | | | with (73), (74), (75), (77), (149) gives:
% 104.53/14.49 | | | | | (185) all_116_0 = nil
% 104.53/14.49 | | | | |
% 104.53/14.49 | | | | | GROUND_INST: instantiating (20) with all_116_2, all_116_0, simplifying
% 104.53/14.49 | | | | | with (73), (74), (75), (77), (149) gives:
% 104.53/14.49 | | | | | (186) all_116_2 = nil
% 104.53/14.49 | | | | |
% 104.53/14.49 | | | | | GROUND_INST: instantiating (22) with all_144_0, all_91_2, simplifying
% 104.53/14.49 | | | | | with (118), (119), (120) gives:
% 104.53/14.49 | | | | | (187) all_144_0 = all_91_2
% 104.53/14.49 | | | | |
% 104.53/14.49 | | | | | GROUND_INST: instantiating (ax82) with all_146_0, all_91_3, all_91_3,
% 104.53/14.49 | | | | | all_91_0, all_91_2, simplifying with (30), (32), (35),
% 104.53/14.49 | | | | | (36), (62), (122), (123), (124) gives:
% 104.53/14.49 | | | | | (188) ? [v0: $i] : (app(all_146_0, v0) = all_91_2 & app(all_91_3,
% 104.53/14.49 | | | | | all_91_0) = v0 & $i(v0) & $i(all_91_2))
% 104.53/14.49 | | | | |
% 104.53/14.49 | | | | | GROUND_INST: instantiating (22) with all_148_0, all_91_3, simplifying
% 104.53/14.49 | | | | | with (126), (127), (128) gives:
% 104.53/14.49 | | | | | (189) all_148_0 = all_91_3
% 104.53/14.49 | | | | |
% 104.53/14.49 | | | | | COMBINE_EQS: (167), (185) imply:
% 104.53/14.49 | | | | | (190) all_132_0 = nil
% 104.53/14.49 | | | | |
% 104.53/14.49 | | | | | DELTA: instantiating (177) with fresh symbol all_193_0 gives:
% 104.53/14.49 | | | | | (191) app(all_150_0, all_150_0) = all_193_0 & app(all_91_0,
% 104.53/14.49 | | | | | all_193_0) = all_91_0 & $i(all_193_0)
% 104.53/14.49 | | | | |
% 104.53/14.49 | | | | | ALPHA: (191) implies:
% 104.53/14.49 | | | | | (192) $i(all_193_0)
% 104.53/14.49 | | | | | (193) app(all_150_0, all_150_0) = all_193_0
% 104.53/14.49 | | | | |
% 104.53/14.49 | | | | | DELTA: instantiating (174) with fresh symbol all_197_0 gives:
% 104.53/14.49 | | | | | (194) ~ (all_197_0 = all_91_3) & app(all_91_3, all_152_0) =
% 104.53/14.49 | | | | | all_197_0 & $i(all_197_0)
% 104.53/14.49 | | | | |
% 104.53/14.49 | | | | | ALPHA: (194) implies:
% 104.53/14.49 | | | | | (195) ~ (all_197_0 = all_91_3)
% 104.53/14.49 | | | | | (196) app(all_91_3, all_152_0) = all_197_0
% 104.53/14.49 | | | | |
% 104.53/14.49 | | | | | DELTA: instantiating (165) with fresh symbol all_205_0 gives:
% 104.53/14.49 | | | | | (197) app(all_205_0, all_91_0) = all_91_2 & $i(all_205_0) &
% 104.53/14.49 | | | | | ssList(all_205_0)
% 104.53/14.49 | | | | |
% 104.53/14.49 | | | | | ALPHA: (197) implies:
% 104.53/14.49 | | | | | (198) ssList(all_205_0)
% 104.53/14.49 | | | | | (199) $i(all_205_0)
% 104.53/14.49 | | | | | (200) app(all_205_0, all_91_0) = all_91_2
% 104.53/14.49 | | | | |
% 104.53/14.49 | | | | | DELTA: instantiating (164) with fresh symbol all_213_0 gives:
% 104.53/14.49 | | | | | (201) cons(all_213_0, nil) = all_91_0 & $i(all_213_0) &
% 104.53/14.49 | | | | | ssItem(all_213_0)
% 104.53/14.49 | | | | |
% 104.53/14.49 | | | | | ALPHA: (201) implies:
% 104.53/14.49 | | | | | (202) ssItem(all_213_0)
% 104.53/14.49 | | | | | (203) $i(all_213_0)
% 104.53/14.49 | | | | | (204) cons(all_213_0, nil) = all_91_0
% 104.53/14.49 | | | | |
% 104.53/14.49 | | | | | DELTA: instantiating (180) with fresh symbol all_217_0 gives:
% 104.53/14.49 | | | | | (205) app(all_150_0, nil) = all_217_0 & app(all_91_0, all_217_0) =
% 104.53/14.49 | | | | | all_91_0 & $i(all_217_0)
% 104.53/14.49 | | | | |
% 104.53/14.49 | | | | | ALPHA: (205) implies:
% 104.53/14.49 | | | | | (206) app(all_150_0, nil) = all_217_0
% 104.53/14.49 | | | | |
% 104.53/14.49 | | | | | DELTA: instantiating (184) with fresh symbol all_219_0 gives:
% 104.53/14.49 | | | | | (207) app(all_116_0, nil) = all_219_0 & app(all_116_2, all_219_0) =
% 104.53/14.49 | | | | | nil & $i(all_219_0)
% 104.53/14.49 | | | | |
% 104.53/14.49 | | | | | ALPHA: (207) implies:
% 104.53/14.49 | | | | | (208) app(all_116_0, nil) = all_219_0
% 104.53/14.49 | | | | |
% 104.53/14.49 | | | | | DELTA: instantiating (179) with fresh symbol all_229_0 gives:
% 104.53/14.49 | | | | | (209) app(all_91_0, all_229_0) = all_91_0 & app(nil, all_150_0) =
% 104.53/14.49 | | | | | all_229_0 & $i(all_229_0)
% 104.53/14.49 | | | | |
% 104.53/14.49 | | | | | ALPHA: (209) implies:
% 104.53/14.49 | | | | | (210) app(nil, all_150_0) = all_229_0
% 104.53/14.49 | | | | |
% 104.53/14.49 | | | | | DELTA: instantiating (183) with fresh symbol all_247_0 gives:
% 104.53/14.49 | | | | | (211) app(all_116_0, all_116_0) = all_247_0 & app(all_116_2,
% 104.53/14.49 | | | | | all_247_0) = all_132_0 & $i(all_247_0) & $i(all_132_0)
% 104.53/14.49 | | | | |
% 104.53/14.49 | | | | | ALPHA: (211) implies:
% 104.53/14.49 | | | | | (212) app(all_116_0, all_116_0) = all_247_0
% 104.53/14.49 | | | | |
% 104.53/14.49 | | | | | DELTA: instantiating (173) with fresh symbol all_253_0 gives:
% 104.53/14.49 | | | | | (213) app(all_134_0, all_152_0) = all_253_0 & app(nil, all_253_0) =
% 104.53/14.49 | | | | | all_91_2 & $i(all_253_0) & $i(all_91_2)
% 104.53/14.49 | | | | |
% 104.53/14.49 | | | | | ALPHA: (213) implies:
% 104.53/14.49 | | | | | (214) $i(all_253_0)
% 104.53/14.49 | | | | | (215) app(all_134_0, all_152_0) = all_253_0
% 104.53/14.49 | | | | |
% 104.53/14.49 | | | | | DELTA: instantiating (188) with fresh symbol all_257_0 gives:
% 104.53/14.49 | | | | | (216) app(all_146_0, all_257_0) = all_91_2 & app(all_91_3,
% 104.53/14.49 | | | | | all_91_0) = all_257_0 & $i(all_257_0) & $i(all_91_2)
% 104.53/14.49 | | | | |
% 104.53/14.49 | | | | | ALPHA: (216) implies:
% 104.53/14.49 | | | | | (217) app(all_91_3, all_91_0) = all_257_0
% 104.53/14.49 | | | | |
% 104.53/14.49 | | | | | DELTA: instantiating (166) with fresh symbol all_259_0 gives:
% 104.53/14.49 | | | | | (218) app(nil, all_259_0) = all_132_0 & app(nil, all_116_0) =
% 104.53/14.49 | | | | | all_259_0 & $i(all_259_0) & $i(all_132_0)
% 104.53/14.49 | | | | |
% 104.53/14.49 | | | | | ALPHA: (218) implies:
% 104.53/14.49 | | | | | (219) app(nil, all_116_0) = all_259_0
% 104.53/14.49 | | | | |
% 104.53/14.49 | | | | | DELTA: instantiating (182) with fresh symbol all_269_0 gives:
% 104.53/14.49 | | | | | (220) app(all_116_0, all_136_0) = all_269_0 & app(all_116_2,
% 104.53/14.49 | | | | | all_269_0) = all_91_3 & $i(all_269_0) & $i(all_91_3)
% 104.53/14.49 | | | | |
% 104.53/14.49 | | | | | ALPHA: (220) implies:
% 104.53/14.49 | | | | | (221) $i(all_269_0)
% 104.53/14.49 | | | | | (222) app(all_116_0, all_136_0) = all_269_0
% 104.53/14.49 | | | | |
% 104.53/14.49 | | | | | DELTA: instantiating (172) with fresh symbol all_271_0 gives:
% 104.53/14.49 | | | | | (223) app(all_136_0, all_138_0) = all_271_0 & app(nil, all_271_0) =
% 104.53/14.49 | | | | | all_91_3 & $i(all_271_0) & $i(all_91_3)
% 104.53/14.49 | | | | |
% 104.53/14.49 | | | | | ALPHA: (223) implies:
% 104.53/14.49 | | | | | (224) app(all_136_0, all_138_0) = all_271_0
% 104.53/14.49 | | | | |
% 104.53/14.49 | | | | | DELTA: instantiating (181) with fresh symbol all_273_0 gives:
% 104.53/14.49 | | | | | (225) cons(all_91_1, all_116_2) = all_273_0 & app(all_273_0,
% 104.53/14.49 | | | | | all_116_0) = all_91_0 & $i(all_273_0) & $i(all_91_0)
% 104.53/14.49 | | | | |
% 104.53/14.49 | | | | | ALPHA: (225) implies:
% 104.53/14.49 | | | | | (226) $i(all_273_0)
% 104.53/14.49 | | | | | (227) cons(all_91_1, all_116_2) = all_273_0
% 104.53/14.49 | | | | |
% 104.53/14.49 | | | | | DELTA: instantiating (170) with fresh symbol all_275_0 gives:
% 104.53/14.49 | | | | | (228) app(nil, all_275_0) = all_91_3 & app(nil, all_136_0) =
% 104.53/14.49 | | | | | all_275_0 & $i(all_275_0) & $i(all_91_3)
% 104.53/14.49 | | | | |
% 104.53/14.49 | | | | | ALPHA: (228) implies:
% 104.53/14.49 | | | | | (229) app(nil, all_136_0) = all_275_0
% 104.53/14.49 | | | | |
% 104.53/14.49 | | | | | DELTA: instantiating (169) with fresh symbol all_277_0 gives:
% 104.53/14.49 | | | | | (230) app(all_136_0, all_91_0) = all_277_0 & app(nil, all_277_0) =
% 104.53/14.49 | | | | | all_91_2 & $i(all_277_0) & $i(all_91_2)
% 104.53/14.49 | | | | |
% 104.53/14.49 | | | | | ALPHA: (230) implies:
% 104.53/14.50 | | | | | (231) app(all_136_0, all_91_0) = all_277_0
% 104.53/14.50 | | | | |
% 104.53/14.50 | | | | | REDUCE: (186), (227) imply:
% 104.53/14.50 | | | | | (232) cons(all_91_1, nil) = all_273_0
% 104.53/14.50 | | | | |
% 104.53/14.50 | | | | | REDUCE: (178), (193) imply:
% 104.53/14.50 | | | | | (233) app(nil, nil) = all_193_0
% 104.53/14.50 | | | | |
% 104.53/14.50 | | | | | REDUCE: (178), (206) imply:
% 104.53/14.50 | | | | | (234) app(nil, nil) = all_217_0
% 104.53/14.50 | | | | |
% 104.53/14.50 | | | | | REDUCE: (128), (189) imply:
% 104.53/14.50 | | | | | (235) app(all_91_3, nil) = all_91_3
% 104.53/14.50 | | | | |
% 104.53/14.50 | | | | | REDUCE: (120), (187) imply:
% 104.53/14.50 | | | | | (236) app(all_91_2, nil) = all_91_2
% 104.53/14.50 | | | | |
% 104.53/14.50 | | | | | REDUCE: (171), (224) imply:
% 104.53/14.50 | | | | | (237) app(all_91_3, all_138_0) = all_271_0
% 104.53/14.50 | | | | |
% 104.53/14.50 | | | | | REDUCE: (171), (231) imply:
% 104.53/14.50 | | | | | (238) app(all_91_3, all_91_0) = all_277_0
% 104.53/14.50 | | | | |
% 104.53/14.50 | | | | | REDUCE: (168), (215) imply:
% 104.53/14.50 | | | | | (239) app(all_91_2, all_152_0) = all_253_0
% 104.53/14.50 | | | | |
% 104.53/14.50 | | | | | REDUCE: (171), (185), (222) imply:
% 104.53/14.50 | | | | | (240) app(nil, all_91_3) = all_269_0
% 104.53/14.50 | | | | |
% 104.53/14.50 | | | | | REDUCE: (185), (212) imply:
% 104.53/14.50 | | | | | (241) app(nil, nil) = all_247_0
% 104.53/14.50 | | | | |
% 104.53/14.50 | | | | | REDUCE: (185), (208) imply:
% 104.53/14.50 | | | | | (242) app(nil, nil) = all_219_0
% 104.53/14.50 | | | | |
% 104.53/14.50 | | | | | REDUCE: (178), (210) imply:
% 104.53/14.50 | | | | | (243) app(nil, nil) = all_229_0
% 104.53/14.50 | | | | |
% 104.53/14.50 | | | | | REDUCE: (171), (229) imply:
% 104.53/14.50 | | | | | (244) app(nil, all_91_3) = all_275_0
% 104.53/14.50 | | | | |
% 104.53/14.50 | | | | | REDUCE: (109), (171) imply:
% 104.53/14.50 | | | | | (245) app(nil, all_91_3) = all_91_3
% 104.53/14.50 | | | | |
% 104.53/14.50 | | | | | REDUCE: (185), (219) imply:
% 104.53/14.50 | | | | | (246) app(nil, nil) = all_259_0
% 104.53/14.50 | | | | |
% 104.53/14.50 | | | | | GROUND_INST: instantiating (26) with nil, all_217_0, nil, nil,
% 104.53/14.50 | | | | | simplifying with (163), (234) gives:
% 104.53/14.50 | | | | | (247) all_217_0 = nil
% 104.53/14.50 | | | | |
% 104.53/14.50 | | | | | GROUND_INST: instantiating (26) with all_217_0, all_229_0, nil, nil,
% 104.53/14.50 | | | | | simplifying with (234), (243) gives:
% 104.53/14.50 | | | | | (248) all_229_0 = all_217_0
% 104.53/14.50 | | | | |
% 104.53/14.50 | | | | | GROUND_INST: instantiating (26) with all_193_0, all_229_0, nil, nil,
% 104.53/14.50 | | | | | simplifying with (233), (243) gives:
% 104.53/14.50 | | | | | (249) all_229_0 = all_193_0
% 104.53/14.50 | | | | |
% 104.53/14.50 | | | | | GROUND_INST: instantiating (26) with all_229_0, all_247_0, nil, nil,
% 104.53/14.50 | | | | | simplifying with (241), (243) gives:
% 104.53/14.50 | | | | | (250) all_247_0 = all_229_0
% 104.53/14.50 | | | | |
% 104.53/14.50 | | | | | GROUND_INST: instantiating (26) with all_247_0, all_259_0, nil, nil,
% 104.53/14.50 | | | | | simplifying with (241), (246) gives:
% 104.53/14.50 | | | | | (251) all_259_0 = all_247_0
% 104.53/14.50 | | | | |
% 104.53/14.50 | | | | | GROUND_INST: instantiating (26) with all_219_0, all_259_0, nil, nil,
% 104.53/14.50 | | | | | simplifying with (242), (246) gives:
% 104.53/14.50 | | | | | (252) all_259_0 = all_219_0
% 104.53/14.50 | | | | |
% 104.53/14.50 | | | | | GROUND_INST: instantiating (26) with all_269_0, all_275_0, all_91_3,
% 104.53/14.50 | | | | | nil, simplifying with (240), (244) gives:
% 104.53/14.50 | | | | | (253) all_275_0 = all_269_0
% 104.53/14.50 | | | | |
% 104.53/14.50 | | | | | GROUND_INST: instantiating (26) with all_91_3, all_275_0, all_91_3,
% 104.53/14.50 | | | | | nil, simplifying with (244), (245) gives:
% 104.53/14.50 | | | | | (254) all_275_0 = all_91_3
% 104.53/14.50 | | | | |
% 104.53/14.50 | | | | | GROUND_INST: instantiating (26) with all_91_2, all_277_0, all_91_0,
% 104.53/14.50 | | | | | all_91_3, simplifying with (36), (238) gives:
% 104.53/14.50 | | | | | (255) all_277_0 = all_91_2
% 104.53/14.50 | | | | |
% 104.53/14.50 | | | | | GROUND_INST: instantiating (26) with all_257_0, all_277_0, all_91_0,
% 104.53/14.50 | | | | | all_91_3, simplifying with (217), (238) gives:
% 104.53/14.50 | | | | | (256) all_277_0 = all_257_0
% 104.53/14.50 | | | | |
% 104.53/14.50 | | | | | GROUND_INST: instantiating (26) with all_91_3, all_271_0, all_138_0,
% 104.53/14.50 | | | | | all_91_3, simplifying with (113), (237) gives:
% 104.53/14.50 | | | | | (257) all_271_0 = all_91_3
% 104.53/14.50 | | | | |
% 104.53/14.50 | | | | | GROUND_INST: instantiating (26) with all_91_2, all_253_0, all_152_0,
% 104.53/14.50 | | | | | all_91_2, simplifying with (136), (239) gives:
% 104.53/14.50 | | | | | (258) all_253_0 = all_91_2
% 104.53/14.50 | | | | |
% 104.53/14.50 | | | | | GROUND_INST: instantiating (27) with all_91_0, all_273_0, nil,
% 104.53/14.50 | | | | | all_91_1, simplifying with (37), (232) gives:
% 104.53/14.50 | | | | | (259) all_273_0 = all_91_0
% 104.53/14.50 | | | | |
% 104.53/14.50 | | | | | COMBINE_EQS: (255), (256) imply:
% 104.53/14.50 | | | | | (260) all_257_0 = all_91_2
% 104.53/14.50 | | | | |
% 104.53/14.50 | | | | | COMBINE_EQS: (253), (254) imply:
% 104.53/14.50 | | | | | (261) all_269_0 = all_91_3
% 104.53/14.50 | | | | |
% 104.53/14.50 | | | | | SIMP: (261) implies:
% 104.53/14.50 | | | | | (262) all_269_0 = all_91_3
% 104.53/14.50 | | | | |
% 104.53/14.50 | | | | | COMBINE_EQS: (251), (252) imply:
% 104.53/14.50 | | | | | (263) all_247_0 = all_219_0
% 104.53/14.50 | | | | |
% 104.53/14.50 | | | | | SIMP: (263) implies:
% 104.53/14.50 | | | | | (264) all_247_0 = all_219_0
% 104.53/14.50 | | | | |
% 104.53/14.50 | | | | | COMBINE_EQS: (250), (264) imply:
% 104.53/14.50 | | | | | (265) all_229_0 = all_219_0
% 104.53/14.50 | | | | |
% 104.53/14.50 | | | | | SIMP: (265) implies:
% 104.53/14.50 | | | | | (266) all_229_0 = all_219_0
% 104.53/14.50 | | | | |
% 104.53/14.50 | | | | | COMBINE_EQS: (248), (266) imply:
% 104.53/14.50 | | | | | (267) all_219_0 = all_217_0
% 104.53/14.50 | | | | |
% 104.53/14.50 | | | | | COMBINE_EQS: (249), (266) imply:
% 104.53/14.50 | | | | | (268) all_219_0 = all_193_0
% 104.53/14.50 | | | | |
% 104.53/14.50 | | | | | COMBINE_EQS: (267), (268) imply:
% 104.53/14.50 | | | | | (269) all_217_0 = all_193_0
% 104.53/14.50 | | | | |
% 104.53/14.50 | | | | | SIMP: (269) implies:
% 104.53/14.50 | | | | | (270) all_217_0 = all_193_0
% 104.53/14.50 | | | | |
% 104.53/14.50 | | | | | COMBINE_EQS: (247), (270) imply:
% 104.53/14.50 | | | | | (271) all_193_0 = nil
% 104.53/14.50 | | | | |
% 104.53/14.50 | | | | | SIMP: (271) implies:
% 104.53/14.50 | | | | | (272) all_193_0 = nil
% 104.53/14.50 | | | | |
% 104.53/14.50 | | | | | GROUND_INST: instantiating (ax80) with nil, all_91_3, all_91_3,
% 104.53/14.50 | | | | | all_138_0, simplifying with (7), (23), (30), (32), (111),
% 104.53/14.50 | | | | | (112), (113), (235) gives:
% 104.53/14.50 | | | | | (273) all_138_0 = nil
% 104.53/14.50 | | | | |
% 104.53/14.50 | | | | | GROUND_INST: instantiating (ax82) with all_146_0, all_91_3, all_91_3,
% 104.53/14.50 | | | | | all_152_0, all_197_0, simplifying with (30), (32), (122),
% 104.53/14.50 | | | | | (123), (124), (134), (135), (196) gives:
% 104.53/14.50 | | | | | (274) ? [v0: $i] : (app(all_146_0, v0) = all_197_0 & app(all_91_3,
% 104.53/14.50 | | | | | all_152_0) = v0 & $i(v0) & $i(all_197_0))
% 104.53/14.50 | | | | |
% 104.53/14.50 | | | | | GROUND_INST: instantiating (ax82) with nil, all_91_3, all_91_3,
% 104.53/14.50 | | | | | all_152_0, all_197_0, simplifying with (7), (23), (30),
% 104.53/14.50 | | | | | (32), (134), (135), (196), (245) gives:
% 104.53/14.50 | | | | | (275) ? [v0: $i] : (app(all_91_3, all_152_0) = v0 & app(nil, v0) =
% 104.53/14.50 | | | | | all_197_0 & $i(v0) & $i(all_197_0))
% 104.53/14.50 | | | | |
% 104.53/14.50 | | | | | GROUND_INST: instantiating (ax80) with nil, all_91_2, all_91_2,
% 104.53/14.50 | | | | | all_152_0, simplifying with (7), (23), (31), (33), (134),
% 104.53/14.50 | | | | | (135), (136), (236) gives:
% 104.53/14.50 | | | | | (276) all_152_0 = nil
% 104.53/14.50 | | | | |
% 104.53/14.50 | | | | | GROUND_INST: instantiating (ax79) with all_205_0, all_91_0, all_91_2,
% 104.53/14.50 | | | | | all_91_3, simplifying with (30), (32), (35), (36), (62),
% 104.53/14.50 | | | | | (198), (199), (200) gives:
% 104.53/14.50 | | | | | (277) all_205_0 = all_91_3
% 104.53/14.50 | | | | |
% 104.53/14.50 | | | | | GROUND_INST: instantiating (38) with all_213_0, all_91_0, all_205_0,
% 104.53/14.50 | | | | | all_91_2, all_152_0, simplifying with (134), (135),
% 104.53/14.50 | | | | | (136), (198), (199), (200), (202), (203), (204) gives:
% 104.53/14.50 | | | | | (278) ? [v0: any] : ( ~ (v0 = all_91_3) & app(all_205_0,
% 104.53/14.50 | | | | | all_152_0) = v0 & $i(v0))
% 104.53/14.50 | | | | |
% 104.53/14.50 | | | | | GROUND_INST: instantiating (38) with all_213_0, all_91_0, all_91_3,
% 104.53/14.50 | | | | | all_91_2, nil, simplifying with (7), (23), (30), (32),
% 104.53/14.50 | | | | | (36), (202), (203), (204), (236) gives:
% 104.53/14.50 | | | | | (279) ? [v0: any] : ( ~ (v0 = all_91_3) & app(all_91_3, nil) = v0
% 104.53/14.50 | | | | | & $i(v0))
% 104.53/14.50 | | | | |
% 104.53/14.51 | | | | | GROUND_INST: instantiating (38) with all_213_0, all_91_0, all_205_0,
% 104.53/14.51 | | | | | all_91_2, nil, simplifying with (7), (23), (198), (199),
% 104.53/14.51 | | | | | (200), (202), (203), (204), (236) gives:
% 104.53/14.51 | | | | | (280) ? [v0: any] : ( ~ (v0 = all_91_3) & app(all_205_0, nil) = v0
% 104.53/14.51 | | | | | & $i(v0))
% 104.53/14.51 | | | | |
% 104.53/14.51 | | | | | DELTA: instantiating (280) with fresh symbol all_323_0 gives:
% 104.53/14.51 | | | | | (281) ~ (all_323_0 = all_91_3) & app(all_205_0, nil) = all_323_0 &
% 104.53/14.51 | | | | | $i(all_323_0)
% 104.53/14.51 | | | | |
% 104.53/14.51 | | | | | ALPHA: (281) implies:
% 104.53/14.51 | | | | | (282) app(all_205_0, nil) = all_323_0
% 104.53/14.51 | | | | |
% 104.53/14.51 | | | | | DELTA: instantiating (279) with fresh symbol all_347_0 gives:
% 104.53/14.51 | | | | | (283) ~ (all_347_0 = all_91_3) & app(all_91_3, nil) = all_347_0 &
% 104.53/14.51 | | | | | $i(all_347_0)
% 104.53/14.51 | | | | |
% 104.53/14.51 | | | | | ALPHA: (283) implies:
% 104.53/14.51 | | | | | (284) app(all_91_3, nil) = all_347_0
% 104.53/14.51 | | | | |
% 104.53/14.51 | | | | | DELTA: instantiating (278) with fresh symbol all_349_0 gives:
% 104.53/14.51 | | | | | (285) ~ (all_349_0 = all_91_3) & app(all_205_0, all_152_0) =
% 104.53/14.51 | | | | | all_349_0 & $i(all_349_0)
% 104.53/14.51 | | | | |
% 104.53/14.51 | | | | | ALPHA: (285) implies:
% 104.53/14.51 | | | | | (286) app(all_205_0, all_152_0) = all_349_0
% 104.53/14.51 | | | | |
% 104.53/14.51 | | | | | DELTA: instantiating (275) with fresh symbol all_745_0 gives:
% 104.53/14.51 | | | | | (287) app(all_91_3, all_152_0) = all_745_0 & app(nil, all_745_0) =
% 104.53/14.51 | | | | | all_197_0 & $i(all_745_0) & $i(all_197_0)
% 104.53/14.51 | | | | |
% 104.53/14.51 | | | | | ALPHA: (287) implies:
% 104.53/14.51 | | | | | (288) app(all_91_3, all_152_0) = all_745_0
% 104.53/14.51 | | | | |
% 104.53/14.51 | | | | | DELTA: instantiating (274) with fresh symbol all_747_0 gives:
% 104.53/14.51 | | | | | (289) app(all_146_0, all_747_0) = all_197_0 & app(all_91_3,
% 104.53/14.51 | | | | | all_152_0) = all_747_0 & $i(all_747_0) & $i(all_197_0)
% 104.53/14.51 | | | | |
% 104.53/14.51 | | | | | ALPHA: (289) implies:
% 104.53/14.51 | | | | | (290) app(all_91_3, all_152_0) = all_747_0
% 104.53/14.51 | | | | |
% 104.53/14.51 | | | | | REDUCE: (276), (277), (286) imply:
% 104.53/14.51 | | | | | (291) app(all_91_3, nil) = all_349_0
% 104.53/14.51 | | | | |
% 104.53/14.51 | | | | | REDUCE: (277), (282) imply:
% 104.53/14.51 | | | | | (292) app(all_91_3, nil) = all_323_0
% 104.53/14.51 | | | | |
% 104.53/14.51 | | | | | REDUCE: (276), (290) imply:
% 104.53/14.51 | | | | | (293) app(all_91_3, nil) = all_747_0
% 104.53/14.51 | | | | |
% 104.53/14.51 | | | | | REDUCE: (276), (288) imply:
% 104.53/14.51 | | | | | (294) app(all_91_3, nil) = all_745_0
% 104.53/14.51 | | | | |
% 104.53/14.51 | | | | | REDUCE: (196), (276) imply:
% 104.53/14.51 | | | | | (295) app(all_91_3, nil) = all_197_0
% 104.53/14.51 | | | | |
% 104.53/14.51 | | | | | GROUND_INST: instantiating (26) with all_347_0, all_349_0, nil,
% 104.53/14.51 | | | | | all_91_3, simplifying with (284), (291) gives:
% 104.53/14.51 | | | | | (296) all_349_0 = all_347_0
% 104.53/14.51 | | | | |
% 104.53/14.51 | | | | | GROUND_INST: instantiating (26) with all_323_0, all_349_0, nil,
% 104.53/14.51 | | | | | all_91_3, simplifying with (291), (292) gives:
% 104.53/14.51 | | | | | (297) all_349_0 = all_323_0
% 104.53/14.51 | | | | |
% 104.53/14.51 | | | | | GROUND_INST: instantiating (26) with all_347_0, all_745_0, nil,
% 104.53/14.51 | | | | | all_91_3, simplifying with (284), (294) gives:
% 104.53/14.51 | | | | | (298) all_745_0 = all_347_0
% 104.53/14.51 | | | | |
% 104.53/14.51 | | | | | GROUND_INST: instantiating (26) with all_197_0, all_745_0, nil,
% 104.53/14.51 | | | | | all_91_3, simplifying with (294), (295) gives:
% 104.53/14.51 | | | | | (299) all_745_0 = all_197_0
% 104.53/14.51 | | | | |
% 104.53/14.51 | | | | | GROUND_INST: instantiating (26) with all_91_3, all_747_0, nil,
% 104.53/14.51 | | | | | all_91_3, simplifying with (235), (293) gives:
% 104.53/14.51 | | | | | (300) all_747_0 = all_91_3
% 104.53/14.51 | | | | |
% 104.53/14.51 | | | | | GROUND_INST: instantiating (26) with all_349_0, all_747_0, nil,
% 104.53/14.51 | | | | | all_91_3, simplifying with (291), (293) gives:
% 104.53/14.51 | | | | | (301) all_747_0 = all_349_0
% 104.53/14.51 | | | | |
% 104.53/14.51 | | | | | COMBINE_EQS: (300), (301) imply:
% 104.53/14.51 | | | | | (302) all_349_0 = all_91_3
% 104.53/14.51 | | | | |
% 104.53/14.51 | | | | | SIMP: (302) implies:
% 104.53/14.51 | | | | | (303) all_349_0 = all_91_3
% 104.53/14.51 | | | | |
% 104.53/14.51 | | | | | COMBINE_EQS: (298), (299) imply:
% 104.53/14.51 | | | | | (304) all_347_0 = all_197_0
% 104.53/14.51 | | | | |
% 104.53/14.51 | | | | | SIMP: (304) implies:
% 104.53/14.51 | | | | | (305) all_347_0 = all_197_0
% 104.53/14.51 | | | | |
% 104.53/14.51 | | | | | COMBINE_EQS: (297), (303) imply:
% 104.53/14.51 | | | | | (306) all_323_0 = all_91_3
% 104.53/14.51 | | | | |
% 104.53/14.51 | | | | | COMBINE_EQS: (296), (297) imply:
% 104.53/14.51 | | | | | (307) all_347_0 = all_323_0
% 104.53/14.51 | | | | |
% 104.53/14.51 | | | | | SIMP: (307) implies:
% 104.53/14.51 | | | | | (308) all_347_0 = all_323_0
% 104.53/14.51 | | | | |
% 104.53/14.51 | | | | | COMBINE_EQS: (305), (308) imply:
% 104.53/14.51 | | | | | (309) all_323_0 = all_197_0
% 104.53/14.51 | | | | |
% 104.53/14.51 | | | | | SIMP: (309) implies:
% 104.53/14.51 | | | | | (310) all_323_0 = all_197_0
% 104.53/14.51 | | | | |
% 104.53/14.51 | | | | | COMBINE_EQS: (306), (310) imply:
% 104.53/14.51 | | | | | (311) all_197_0 = all_91_3
% 104.53/14.51 | | | | |
% 104.53/14.51 | | | | | REDUCE: (195), (311) imply:
% 104.53/14.51 | | | | | (312) $false
% 104.53/14.51 | | | | |
% 104.53/14.51 | | | | | CLOSE: (312) is inconsistent.
% 104.53/14.51 | | | | |
% 104.53/14.51 | | | | End of split
% 104.53/14.51 | | | |
% 104.53/14.51 | | | End of split
% 104.53/14.51 | | |
% 104.53/14.51 | | End of split
% 104.53/14.51 | |
% 104.53/14.51 | End of split
% 104.53/14.51 |
% 104.53/14.51 End of proof
% 104.53/14.51 % SZS output end Proof for theBenchmark
% 104.53/14.51
% 104.53/14.51 13914ms
%------------------------------------------------------------------------------