TSTP Solution File: SWC008+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SWC008+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 : n025.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 20:49:09 EDT 2023
% Result : Theorem 158.88s 21.97s
% Output : Proof 159.87s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SWC008+1 : TPTP v8.1.2. Released v2.4.0.
% 0.12/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.14/0.34 % Computer : n025.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Mon Aug 28 16:37:10 EDT 2023
% 0.14/0.34 % CPUTime :
% 0.20/0.54 ________ _____
% 0.20/0.54 ___ __ \_________(_)________________________________
% 0.20/0.54 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.20/0.54 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.20/0.54 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.20/0.54
% 0.20/0.54 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.54 (2023-06-19)
% 0.20/0.54
% 0.20/0.54 (c) Philipp Rümmer, 2009-2023
% 0.20/0.54 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.54 Amanda Stjerna.
% 0.20/0.54 Free software under BSD-3-Clause.
% 0.20/0.54
% 0.20/0.54 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.54
% 0.20/0.54 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.20/0.55 Running up to 7 provers in parallel.
% 0.20/0.57 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.57 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.57 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.57 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.57 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.57 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.20/0.57 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 5.53/1.44 Prover 1: Preprocessing ...
% 5.53/1.44 Prover 4: Preprocessing ...
% 6.01/1.50 Prover 0: Preprocessing ...
% 6.01/1.50 Prover 5: Preprocessing ...
% 6.01/1.50 Prover 6: Preprocessing ...
% 6.01/1.50 Prover 2: Preprocessing ...
% 6.01/1.50 Prover 3: Preprocessing ...
% 15.95/2.89 Prover 5: Constructing countermodel ...
% 15.95/2.90 Prover 2: Proving ...
% 15.95/2.91 Prover 6: Proving ...
% 17.00/3.00 Prover 1: Constructing countermodel ...
% 17.36/3.05 Prover 3: Constructing countermodel ...
% 24.54/3.99 Prover 4: Constructing countermodel ...
% 24.54/4.20 Prover 0: Proving ...
% 72.50/10.35 Prover 2: stopped
% 72.50/10.37 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 74.28/10.61 Prover 7: Preprocessing ...
% 75.86/10.81 Prover 7: Constructing countermodel ...
% 98.46/13.89 Prover 5: stopped
% 99.09/13.91 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 99.65/14.08 Prover 8: Preprocessing ...
% 102.06/14.34 Prover 8: Warning: ignoring some quantifiers
% 102.06/14.35 Prover 8: Constructing countermodel ...
% 113.64/15.92 Prover 1: stopped
% 113.64/15.93 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889
% 113.64/16.06 Prover 9: Preprocessing ...
% 121.84/16.98 Prover 9: Constructing countermodel ...
% 127.98/17.81 Prover 6: stopped
% 127.98/17.83 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 128.83/17.90 Prover 10: Preprocessing ...
% 129.29/18.08 Prover 10: Constructing countermodel ...
% 158.88/21.95 Prover 10: Found proof (size 249)
% 158.88/21.97 Prover 10: proved (4125ms)
% 158.88/21.97 Prover 3: stopped
% 158.88/21.97 Prover 8: stopped
% 158.88/21.97 Prover 9: stopped
% 158.88/21.97 Prover 7: stopped
% 158.88/21.97 Prover 4: stopped
% 158.88/21.97 Prover 0: stopped
% 158.88/21.97
% 158.88/21.97 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 158.88/21.97
% 158.88/22.02 % SZS output start Proof for theBenchmark
% 158.88/22.03 Assumptions after simplification:
% 158.88/22.03 ---------------------------------
% 158.88/22.03
% 158.88/22.03 (ax1)
% 158.88/22.03 ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ $i(v1) | ~ $i(v0) | ~ ssItem(v1) |
% 158.88/22.03 ~ ssItem(v0) | neq(v0, v1)) & ! [v0: $i] : ( ~ $i(v0) | ~ neq(v0, v0) |
% 158.88/22.03 ~ ssItem(v0))
% 158.88/22.03
% 158.88/22.03 (ax15)
% 159.34/22.04 ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ $i(v1) | ~ $i(v0) | ~ ssList(v1) |
% 159.34/22.04 ~ ssList(v0) | neq(v0, v1)) & ! [v0: $i] : ( ~ $i(v0) | ~ ssList(v0) | ~
% 159.34/22.04 neq(v0, v0))
% 159.34/22.04
% 159.34/22.04 (ax17)
% 159.34/22.04 $i(nil) & ssList(nil)
% 159.34/22.04
% 159.34/22.04 (ax2)
% 159.34/22.04 ? [v0: $i] : ? [v1: $i] : ( ~ (v1 = v0) & $i(v1) & $i(v0) & ssItem(v1) &
% 159.34/22.04 ssItem(v0))
% 159.34/22.04
% 159.34/22.04 (ax26)
% 159.34/22.06 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (app(v0, v1) = v2) | ~ $i(v1) |
% 159.34/22.06 ~ $i(v0) | ~ ssList(v1) | ~ ssList(v0) | ssList(v2))
% 159.34/22.06
% 159.34/22.06 (ax28)
% 159.34/22.06 $i(nil) & ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (app(nil, v0) = v1) | ~
% 159.34/22.06 $i(v0) | ~ ssList(v0))
% 159.34/22.06
% 159.34/22.06 (ax42)
% 159.34/22.06 ! [v0: $i] : ( ~ $i(v0) | ~ ssList(v0) | frontsegP(v0, v0))
% 159.34/22.06
% 159.34/22.06 (ax45)
% 159.34/22.06 $i(nil) & ! [v0: $i] : ( ~ $i(v0) | ~ ssList(v0) | frontsegP(v0, nil))
% 159.34/22.06
% 159.34/22.06 (ax46)
% 159.34/22.06 $i(nil) & ! [v0: $i] : (v0 = nil | ~ $i(v0) | ~ frontsegP(nil, v0) | ~
% 159.34/22.06 ssList(v0)) & ( ~ ssList(nil) | frontsegP(nil, nil))
% 159.34/22.06
% 159.34/22.06 (ax49)
% 159.34/22.06 ! [v0: $i] : ( ~ $i(v0) | ~ ssList(v0) | rearsegP(v0, v0))
% 159.34/22.06
% 159.34/22.06 (ax5)
% 159.34/22.07 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (app(v1, v2) = v0) | ~ $i(v2) |
% 159.34/22.07 ~ $i(v1) | ~ $i(v0) | ~ ssList(v2) | ~ ssList(v1) | ~ ssList(v0) |
% 159.34/22.07 frontsegP(v0, v1)) & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~
% 159.34/22.07 frontsegP(v0, v1) | ~ ssList(v1) | ~ ssList(v0) | ? [v2: $i] : (app(v1,
% 159.34/22.07 v2) = v0 & $i(v2) & ssList(v2)))
% 159.34/22.07
% 159.34/22.07 (ax51)
% 159.34/22.07 $i(nil) & ! [v0: $i] : ( ~ $i(v0) | ~ ssList(v0) | rearsegP(v0, nil))
% 159.34/22.07
% 159.34/22.07 (ax52)
% 159.34/22.07 $i(nil) & ! [v0: $i] : (v0 = nil | ~ $i(v0) | ~ rearsegP(nil, v0) | ~
% 159.34/22.07 ssList(v0)) & ( ~ ssList(nil) | rearsegP(nil, nil))
% 159.34/22.07
% 159.34/22.07 (ax58)
% 159.34/22.07 $i(nil) & ! [v0: $i] : (v0 = nil | ~ $i(v0) | ~ segmentP(nil, v0) | ~
% 159.34/22.07 ssList(v0)) & ( ~ ssList(nil) | segmentP(nil, nil))
% 159.34/22.07
% 159.34/22.07 (ax6)
% 159.34/22.07 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (app(v2, v1) = v0) | ~ $i(v2) |
% 159.34/22.07 ~ $i(v1) | ~ $i(v0) | ~ ssList(v2) | ~ ssList(v1) | ~ ssList(v0) |
% 159.34/22.07 rearsegP(v0, v1)) & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~
% 159.34/22.07 rearsegP(v0, v1) | ~ ssList(v1) | ~ ssList(v0) | ? [v2: $i] : (app(v2,
% 159.34/22.07 v1) = v0 & $i(v2) & ssList(v2)))
% 159.34/22.07
% 159.34/22.07 (ax7)
% 159.34/22.07 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 159.34/22.07 (app(v3, v4) = v0) | ~ (app(v2, v1) = v3) | ~ $i(v4) | ~ $i(v2) | ~
% 159.34/22.07 $i(v1) | ~ $i(v0) | ~ ssList(v4) | ~ ssList(v2) | ~ ssList(v1) | ~
% 159.34/22.07 ssList(v0) | segmentP(v0, v1)) & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~
% 159.34/22.08 $i(v0) | ~ segmentP(v0, v1) | ~ ssList(v1) | ~ ssList(v0) | ? [v2: $i] :
% 159.34/22.08 ? [v3: $i] : ? [v4: $i] : (app(v3, v4) = v0 & app(v2, v1) = v3 & $i(v4) &
% 159.34/22.08 $i(v3) & $i(v2) & ssList(v4) & ssList(v2)))
% 159.34/22.08
% 159.34/22.08 (ax79)
% 159.34/22.08 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v0 | ~ (app(v3,
% 159.34/22.08 v1) = v2) | ~ (app(v0, v1) = v2) | ~ $i(v3) | ~ $i(v1) | ~ $i(v0) |
% 159.34/22.08 ~ ssList(v3) | ~ ssList(v1) | ~ ssList(v0))
% 159.34/22.08
% 159.34/22.08 (ax80)
% 159.34/22.08 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v0 | ~ (app(v1,
% 159.34/22.08 v3) = v2) | ~ (app(v1, v0) = v2) | ~ $i(v3) | ~ $i(v1) | ~ $i(v0) |
% 159.34/22.08 ~ ssList(v3) | ~ ssList(v1) | ~ ssList(v0))
% 159.34/22.08
% 159.34/22.08 (ax82)
% 159.34/22.08 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 159.34/22.08 (app(v2, v3) = v4) | ~ (app(v0, v1) = v2) | ~ $i(v3) | ~ $i(v1) | ~
% 159.34/22.08 $i(v0) | ~ ssList(v3) | ~ ssList(v1) | ~ ssList(v0) | ? [v5: $i] :
% 159.34/22.08 (app(v1, v3) = v5 & app(v0, v5) = v4 & $i(v5) & $i(v4)))
% 159.34/22.08
% 159.34/22.08 (ax83)
% 159.34/22.08 $i(nil) & ! [v0: $i] : ! [v1: $i] : (v1 = nil | ~ (app(v0, v1) = nil) | ~
% 159.34/22.08 $i(v1) | ~ $i(v0) | ~ ssList(v1) | ~ ssList(v0)) & ! [v0: $i] : ! [v1:
% 159.34/22.08 $i] : (v0 = nil | ~ (app(v0, v1) = nil) | ~ $i(v1) | ~ $i(v0) | ~
% 159.34/22.08 ssList(v1) | ~ ssList(v0)) & ! [v0: $i] : (v0 = nil | ~ (app(nil, nil) =
% 159.34/22.08 v0) | ~ ssList(nil))
% 159.34/22.08
% 159.34/22.08 (ax84)
% 159.34/22.08 $i(nil) & ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (app(v0, nil) = v1) | ~
% 159.34/22.08 $i(v0) | ~ ssList(v0))
% 159.34/22.08
% 159.34/22.08 (ax86)
% 159.34/22.09 $i(nil) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v0 = nil |
% 159.57/22.09 ~ (tl(v0) = v1) | ~ (app(v1, v2) = v3) | ~ $i(v2) | ~ $i(v0) | ~
% 159.57/22.09 ssList(v2) | ~ ssList(v0) | ? [v4: $i] : (tl(v4) = v3 & app(v0, v2) = v4 &
% 159.57/22.09 $i(v4) & $i(v3)))
% 159.57/22.09
% 159.57/22.09 (co1)
% 159.57/22.09 ? [v0: $i] : ? [v1: $i] : ($i(v1) & $i(v0) & equalelemsP(v0) & frontsegP(v1,
% 159.57/22.09 v0) & ssList(v1) & ssList(v0) & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 159.57/22.09 ! [v5: $i] : ( ~ (app(v4, v5) = v1) | ~ (app(v2, v3) = v4) | ~ $i(v5) | ~
% 159.57/22.09 $i(v3) | ~ $i(v2) | ~ ssList(v5) | ~ ssList(v3) | ~ ssList(v2) | ?
% 159.57/22.09 [v6: $i] : ( ~ (v6 = v0) & app(v2, v5) = v6 & $i(v6))) & ! [v2: $i] : ( ~
% 159.57/22.09 $i(v2) | ~ equalelemsP(v2) | ~ segmentP(v2, v0) | ~ frontsegP(v1, v2) |
% 159.57/22.09 ~ ssList(v2) | ~ neq(v0, v2)))
% 159.57/22.09
% 159.57/22.09 (function-axioms)
% 159.57/22.09 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 159.57/22.09 (cons(v3, v2) = v1) | ~ (cons(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] :
% 159.57/22.09 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (app(v3, v2) = v1) | ~ (app(v3, v2)
% 159.57/22.09 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (tl(v2) =
% 159.57/22.09 v1) | ~ (tl(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 =
% 159.57/22.09 v0 | ~ (hd(v2) = v1) | ~ (hd(v2) = v0))
% 159.57/22.09
% 159.57/22.09 Further assumptions not needed in the proof:
% 159.57/22.09 --------------------------------------------
% 159.57/22.09 ax10, ax11, ax12, ax13, ax14, ax16, ax18, ax19, ax20, ax21, ax22, ax23, ax24,
% 159.57/22.09 ax25, ax27, ax29, ax3, ax30, ax31, ax32, ax33, ax34, ax35, ax36, ax37, ax38,
% 159.57/22.09 ax39, ax4, ax40, ax41, ax43, ax44, ax47, ax48, ax50, ax53, ax54, ax55, ax56,
% 159.57/22.09 ax57, ax59, ax60, ax61, ax62, ax63, ax64, ax65, ax66, ax67, ax68, ax69, ax70,
% 159.57/22.09 ax71, ax72, ax73, ax74, ax75, ax76, ax77, ax78, ax8, ax81, ax85, ax87, ax88,
% 159.57/22.09 ax89, ax9, ax90, ax91, ax92, ax93, ax94, ax95
% 159.57/22.09
% 159.57/22.09 Those formulas are unsatisfiable:
% 159.57/22.09 ---------------------------------
% 159.57/22.09
% 159.57/22.09 Begin of proof
% 159.57/22.09 |
% 159.57/22.09 | ALPHA: (ax1) implies:
% 159.57/22.09 | (1) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ $i(v1) | ~ $i(v0) | ~
% 159.57/22.09 | ssItem(v1) | ~ ssItem(v0) | neq(v0, v1))
% 159.57/22.09 |
% 159.57/22.09 | ALPHA: (ax5) implies:
% 159.57/22.10 | (2) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ frontsegP(v0,
% 159.57/22.10 | v1) | ~ ssList(v1) | ~ ssList(v0) | ? [v2: $i] : (app(v1, v2) =
% 159.57/22.10 | v0 & $i(v2) & ssList(v2)))
% 159.57/22.10 |
% 159.57/22.10 | ALPHA: (ax6) implies:
% 159.57/22.10 | (3) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ rearsegP(v0,
% 159.57/22.10 | v1) | ~ ssList(v1) | ~ ssList(v0) | ? [v2: $i] : (app(v2, v1) =
% 159.57/22.10 | v0 & $i(v2) & ssList(v2)))
% 159.57/22.10 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (app(v2, v1) = v0) | ~
% 159.57/22.10 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ ssList(v2) | ~ ssList(v1) | ~
% 159.57/22.10 | ssList(v0) | rearsegP(v0, v1))
% 159.57/22.10 |
% 159.57/22.10 | ALPHA: (ax7) implies:
% 159.57/22.10 | (5) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ segmentP(v0,
% 159.57/22.10 | v1) | ~ ssList(v1) | ~ ssList(v0) | ? [v2: $i] : ? [v3: $i] :
% 159.57/22.10 | ? [v4: $i] : (app(v3, v4) = v0 & app(v2, v1) = v3 & $i(v4) & $i(v3) &
% 159.57/22.10 | $i(v2) & ssList(v4) & ssList(v2)))
% 159.57/22.10 |
% 159.57/22.10 | ALPHA: (ax15) implies:
% 159.57/22.10 | (6) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ $i(v1) | ~ $i(v0) | ~
% 159.57/22.10 | ssList(v1) | ~ ssList(v0) | neq(v0, v1))
% 159.57/22.10 |
% 159.57/22.10 | ALPHA: (ax17) implies:
% 159.57/22.10 | (7) ssList(nil)
% 159.57/22.10 |
% 159.57/22.10 | ALPHA: (ax28) implies:
% 159.57/22.10 | (8) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (app(nil, v0) = v1) | ~
% 159.57/22.10 | $i(v0) | ~ ssList(v0))
% 159.57/22.10 |
% 159.57/22.10 | ALPHA: (ax45) implies:
% 159.57/22.10 | (9) ! [v0: $i] : ( ~ $i(v0) | ~ ssList(v0) | frontsegP(v0, nil))
% 159.57/22.10 |
% 159.57/22.10 | ALPHA: (ax46) implies:
% 159.57/22.10 | (10) ~ ssList(nil) | frontsegP(nil, nil)
% 159.57/22.10 |
% 159.57/22.10 | ALPHA: (ax51) implies:
% 159.57/22.10 | (11) ! [v0: $i] : ( ~ $i(v0) | ~ ssList(v0) | rearsegP(v0, nil))
% 159.57/22.10 |
% 159.57/22.10 | ALPHA: (ax52) implies:
% 159.57/22.10 | (12) ~ ssList(nil) | rearsegP(nil, nil)
% 159.57/22.10 |
% 159.57/22.10 | ALPHA: (ax58) implies:
% 159.57/22.10 | (13) ~ ssList(nil) | segmentP(nil, nil)
% 159.57/22.10 |
% 159.57/22.10 | ALPHA: (ax83) implies:
% 159.57/22.10 | (14) ! [v0: $i] : (v0 = nil | ~ (app(nil, nil) = v0) | ~ ssList(nil))
% 159.57/22.10 | (15) ! [v0: $i] : ! [v1: $i] : (v0 = nil | ~ (app(v0, v1) = nil) | ~
% 159.57/22.10 | $i(v1) | ~ $i(v0) | ~ ssList(v1) | ~ ssList(v0))
% 159.57/22.10 | (16) ! [v0: $i] : ! [v1: $i] : (v1 = nil | ~ (app(v0, v1) = nil) | ~
% 159.57/22.10 | $i(v1) | ~ $i(v0) | ~ ssList(v1) | ~ ssList(v0))
% 159.57/22.10 |
% 159.57/22.10 | ALPHA: (ax84) implies:
% 159.57/22.10 | (17) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (app(v0, nil) = v1) | ~
% 159.57/22.10 | $i(v0) | ~ ssList(v0))
% 159.57/22.10 |
% 159.57/22.10 | ALPHA: (ax86) implies:
% 159.57/22.10 | (18) $i(nil)
% 159.57/22.10 |
% 159.57/22.10 | ALPHA: (function-axioms) implies:
% 159.57/22.10 | (19) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 159.57/22.10 | (app(v3, v2) = v1) | ~ (app(v3, v2) = v0))
% 159.57/22.10 |
% 159.57/22.11 | DELTA: instantiating (ax2) with fresh symbols all_89_0, all_89_1 gives:
% 159.57/22.11 | (20) ~ (all_89_0 = all_89_1) & $i(all_89_0) & $i(all_89_1) &
% 159.57/22.11 | ssItem(all_89_0) & ssItem(all_89_1)
% 159.57/22.11 |
% 159.57/22.11 | ALPHA: (20) implies:
% 159.57/22.11 | (21) ~ (all_89_0 = all_89_1)
% 159.57/22.11 | (22) ssItem(all_89_1)
% 159.57/22.11 | (23) ssItem(all_89_0)
% 159.57/22.11 | (24) $i(all_89_1)
% 159.57/22.11 | (25) $i(all_89_0)
% 159.57/22.11 |
% 159.57/22.11 | DELTA: instantiating (co1) with fresh symbols all_91_0, all_91_1 gives:
% 159.57/22.11 | (26) $i(all_91_0) & $i(all_91_1) & equalelemsP(all_91_1) &
% 159.57/22.11 | frontsegP(all_91_0, all_91_1) & ssList(all_91_0) & ssList(all_91_1) &
% 159.57/22.11 | ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (app(v2,
% 159.57/22.11 | v3) = all_91_0) | ~ (app(v0, v1) = v2) | ~ $i(v3) | ~ $i(v1)
% 159.57/22.11 | | ~ $i(v0) | ~ ssList(v3) | ~ ssList(v1) | ~ ssList(v0) | ?
% 159.57/22.11 | [v4: any] : ( ~ (v4 = all_91_1) & app(v0, v3) = v4 & $i(v4))) & !
% 159.57/22.11 | [v0: $i] : ( ~ $i(v0) | ~ equalelemsP(v0) | ~ segmentP(v0, all_91_1)
% 159.57/22.11 | | ~ frontsegP(all_91_0, v0) | ~ ssList(v0) | ~ neq(all_91_1, v0))
% 159.57/22.11 |
% 159.57/22.11 | ALPHA: (26) implies:
% 159.57/22.11 | (27) ssList(all_91_1)
% 159.57/22.11 | (28) ssList(all_91_0)
% 159.57/22.11 | (29) frontsegP(all_91_0, all_91_1)
% 159.57/22.11 | (30) $i(all_91_1)
% 159.57/22.11 | (31) $i(all_91_0)
% 159.57/22.11 | (32) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (app(v2,
% 159.57/22.11 | v3) = all_91_0) | ~ (app(v0, v1) = v2) | ~ $i(v3) | ~ $i(v1)
% 159.57/22.11 | | ~ $i(v0) | ~ ssList(v3) | ~ ssList(v1) | ~ ssList(v0) | ?
% 159.57/22.11 | [v4: any] : ( ~ (v4 = all_91_1) & app(v0, v3) = v4 & $i(v4)))
% 159.57/22.11 |
% 159.57/22.11 | BETA: splitting (10) gives:
% 159.57/22.11 |
% 159.57/22.11 | Case 1:
% 159.57/22.11 | |
% 159.57/22.11 | | (33) ~ ssList(nil)
% 159.57/22.11 | |
% 159.57/22.11 | | PRED_UNIFY: (7), (33) imply:
% 159.57/22.11 | | (34) $false
% 159.57/22.11 | |
% 159.57/22.11 | | CLOSE: (34) is inconsistent.
% 159.57/22.11 | |
% 159.57/22.11 | Case 2:
% 159.57/22.11 | |
% 159.57/22.11 | | (35) frontsegP(nil, nil)
% 159.57/22.11 | |
% 159.57/22.11 | | BETA: splitting (12) gives:
% 159.57/22.11 | |
% 159.57/22.11 | | Case 1:
% 159.57/22.11 | | |
% 159.57/22.11 | | | (36) ~ ssList(nil)
% 159.57/22.11 | | |
% 159.57/22.11 | | | PRED_UNIFY: (7), (36) imply:
% 159.57/22.11 | | | (37) $false
% 159.57/22.11 | | |
% 159.57/22.11 | | | CLOSE: (37) is inconsistent.
% 159.57/22.11 | | |
% 159.57/22.11 | | Case 2:
% 159.57/22.11 | | |
% 159.57/22.11 | | | (38) rearsegP(nil, nil)
% 159.57/22.11 | | |
% 159.57/22.11 | | | BETA: splitting (13) gives:
% 159.57/22.11 | | |
% 159.57/22.11 | | | Case 1:
% 159.57/22.11 | | | |
% 159.57/22.11 | | | | (39) ~ ssList(nil)
% 159.57/22.11 | | | |
% 159.57/22.11 | | | | PRED_UNIFY: (7), (39) imply:
% 159.57/22.11 | | | | (40) $false
% 159.57/22.11 | | | |
% 159.57/22.11 | | | | CLOSE: (40) is inconsistent.
% 159.57/22.11 | | | |
% 159.57/22.11 | | | Case 2:
% 159.57/22.11 | | | |
% 159.57/22.11 | | | | (41) segmentP(nil, nil)
% 159.57/22.11 | | | |
% 159.57/22.12 | | | | GROUND_INST: instantiating (1) with all_89_1, all_89_0, simplifying with
% 159.57/22.12 | | | | (22), (23), (24), (25) gives:
% 159.57/22.12 | | | | (42) all_89_0 = all_89_1 | neq(all_89_1, all_89_0)
% 159.57/22.12 | | | |
% 159.57/22.12 | | | | GROUND_INST: instantiating (ax49) with all_91_1, simplifying with (27),
% 159.57/22.12 | | | | (30) gives:
% 159.57/22.12 | | | | (43) rearsegP(all_91_1, all_91_1)
% 159.57/22.12 | | | |
% 159.57/22.12 | | | | GROUND_INST: instantiating (11) with all_91_1, simplifying with (27),
% 159.57/22.12 | | | | (30) gives:
% 159.57/22.12 | | | | (44) rearsegP(all_91_1, nil)
% 159.57/22.12 | | | |
% 159.57/22.12 | | | | GROUND_INST: instantiating (ax42) with all_91_1, simplifying with (27),
% 159.57/22.12 | | | | (30) gives:
% 159.57/22.12 | | | | (45) frontsegP(all_91_1, all_91_1)
% 159.57/22.12 | | | |
% 159.57/22.12 | | | | GROUND_INST: instantiating (9) with all_91_1, simplifying with (27),
% 159.57/22.12 | | | | (30) gives:
% 159.57/22.12 | | | | (46) frontsegP(all_91_1, nil)
% 159.57/22.12 | | | |
% 159.57/22.12 | | | | GROUND_INST: instantiating (11) with all_91_0, simplifying with (28),
% 159.57/22.12 | | | | (31) gives:
% 159.57/22.12 | | | | (47) rearsegP(all_91_0, nil)
% 159.57/22.12 | | | |
% 159.57/22.12 | | | | GROUND_INST: instantiating (ax42) with all_91_0, simplifying with (28),
% 159.57/22.12 | | | | (31) gives:
% 159.57/22.12 | | | | (48) frontsegP(all_91_0, all_91_0)
% 159.57/22.12 | | | |
% 159.57/22.12 | | | | GROUND_INST: instantiating (9) with all_91_0, simplifying with (28),
% 159.57/22.12 | | | | (31) gives:
% 159.57/22.12 | | | | (49) frontsegP(all_91_0, nil)
% 159.57/22.12 | | | |
% 159.57/22.12 | | | | GROUND_INST: instantiating (2) with nil, nil, simplifying with (7),
% 159.57/22.12 | | | | (18), (35) gives:
% 159.57/22.12 | | | | (50) ? [v0: $i] : (app(nil, v0) = nil & $i(v0) & ssList(v0))
% 159.57/22.12 | | | |
% 159.57/22.12 | | | | GROUND_INST: instantiating (2) with all_91_0, all_91_1, simplifying with
% 159.57/22.12 | | | | (27), (28), (29), (30), (31) gives:
% 159.57/22.12 | | | | (51) ? [v0: $i] : (app(all_91_1, v0) = all_91_0 & $i(v0) &
% 159.57/22.12 | | | | ssList(v0))
% 159.57/22.12 | | | |
% 159.57/22.12 | | | | GROUND_INST: instantiating (3) with nil, nil, simplifying with (7),
% 159.57/22.12 | | | | (18), (38) gives:
% 159.57/22.12 | | | | (52) ? [v0: $i] : (app(v0, nil) = nil & $i(v0) & ssList(v0))
% 159.57/22.12 | | | |
% 159.57/22.12 | | | | GROUND_INST: instantiating (5) with nil, nil, simplifying with (7),
% 159.57/22.12 | | | | (18), (41) gives:
% 159.57/22.12 | | | | (53) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (app(v1, v2) = nil &
% 159.57/22.12 | | | | app(v0, nil) = v1 & $i(v2) & $i(v1) & $i(v0) & ssList(v2) &
% 159.57/22.12 | | | | ssList(v0))
% 159.57/22.12 | | | |
% 159.57/22.12 | | | | DELTA: instantiating (52) with fresh symbol all_112_0 gives:
% 159.57/22.12 | | | | (54) app(all_112_0, nil) = nil & $i(all_112_0) & ssList(all_112_0)
% 159.57/22.12 | | | |
% 159.57/22.12 | | | | ALPHA: (54) implies:
% 159.57/22.12 | | | | (55) ssList(all_112_0)
% 159.57/22.12 | | | | (56) $i(all_112_0)
% 159.57/22.12 | | | | (57) app(all_112_0, nil) = nil
% 159.57/22.12 | | | |
% 159.57/22.12 | | | | DELTA: instantiating (51) with fresh symbol all_114_0 gives:
% 159.57/22.12 | | | | (58) app(all_91_1, all_114_0) = all_91_0 & $i(all_114_0) &
% 159.57/22.12 | | | | ssList(all_114_0)
% 159.57/22.12 | | | |
% 159.57/22.12 | | | | ALPHA: (58) implies:
% 159.57/22.12 | | | | (59) ssList(all_114_0)
% 159.57/22.12 | | | | (60) $i(all_114_0)
% 159.57/22.12 | | | | (61) app(all_91_1, all_114_0) = all_91_0
% 159.57/22.12 | | | |
% 159.57/22.12 | | | | DELTA: instantiating (50) with fresh symbol all_116_0 gives:
% 159.57/22.12 | | | | (62) app(nil, all_116_0) = nil & $i(all_116_0) & ssList(all_116_0)
% 159.57/22.12 | | | |
% 159.57/22.12 | | | | ALPHA: (62) implies:
% 159.57/22.12 | | | | (63) ssList(all_116_0)
% 159.57/22.12 | | | | (64) $i(all_116_0)
% 159.57/22.12 | | | | (65) app(nil, all_116_0) = nil
% 159.57/22.12 | | | |
% 159.57/22.12 | | | | DELTA: instantiating (53) with fresh symbols all_118_0, all_118_1,
% 159.57/22.12 | | | | all_118_2 gives:
% 159.57/22.12 | | | | (66) app(all_118_1, all_118_0) = nil & app(all_118_2, nil) =
% 159.57/22.12 | | | | all_118_1 & $i(all_118_0) & $i(all_118_1) & $i(all_118_2) &
% 159.57/22.12 | | | | ssList(all_118_0) & ssList(all_118_2)
% 159.57/22.12 | | | |
% 159.57/22.12 | | | | ALPHA: (66) implies:
% 159.57/22.12 | | | | (67) ssList(all_118_2)
% 159.57/22.13 | | | | (68) ssList(all_118_0)
% 159.57/22.13 | | | | (69) $i(all_118_2)
% 159.57/22.13 | | | | (70) $i(all_118_1)
% 159.57/22.13 | | | | (71) $i(all_118_0)
% 159.57/22.13 | | | | (72) app(all_118_2, nil) = all_118_1
% 159.57/22.13 | | | | (73) app(all_118_1, all_118_0) = nil
% 159.57/22.13 | | | |
% 159.57/22.13 | | | | BETA: splitting (42) gives:
% 159.57/22.13 | | | |
% 159.57/22.13 | | | | Case 1:
% 159.57/22.13 | | | | |
% 159.57/22.13 | | | | |
% 159.57/22.13 | | | | | GROUND_INST: instantiating (2) with all_91_1, nil, simplifying with
% 159.57/22.13 | | | | | (7), (18), (27), (30), (46) gives:
% 159.57/22.13 | | | | | (74) ? [v0: $i] : (app(nil, v0) = all_91_1 & $i(v0) & ssList(v0))
% 159.57/22.13 | | | | |
% 159.57/22.13 | | | | | GROUND_INST: instantiating (2) with all_91_1, all_91_1, simplifying
% 159.57/22.13 | | | | | with (27), (30), (45) gives:
% 159.57/22.13 | | | | | (75) ? [v0: $i] : (app(all_91_1, v0) = all_91_1 & $i(v0) &
% 159.57/22.13 | | | | | ssList(v0))
% 159.57/22.13 | | | | |
% 159.57/22.13 | | | | | GROUND_INST: instantiating (2) with all_91_0, nil, simplifying with
% 159.57/22.13 | | | | | (7), (18), (28), (31), (49) gives:
% 159.57/22.13 | | | | | (76) ? [v0: $i] : (app(nil, v0) = all_91_0 & $i(v0) & ssList(v0))
% 159.57/22.13 | | | | |
% 159.57/22.13 | | | | | GROUND_INST: instantiating (2) with all_91_0, all_91_0, simplifying
% 159.57/22.13 | | | | | with (28), (31), (48) gives:
% 159.57/22.13 | | | | | (77) ? [v0: $i] : (app(all_91_0, v0) = all_91_0 & $i(v0) &
% 159.57/22.13 | | | | | ssList(v0))
% 159.57/22.13 | | | | |
% 159.57/22.13 | | | | | GROUND_INST: instantiating (3) with all_91_1, nil, simplifying with
% 159.57/22.13 | | | | | (7), (18), (27), (30), (44) gives:
% 159.57/22.13 | | | | | (78) ? [v0: $i] : (app(v0, nil) = all_91_1 & $i(v0) & ssList(v0))
% 159.57/22.13 | | | | |
% 159.57/22.13 | | | | | GROUND_INST: instantiating (3) with all_91_1, all_91_1, simplifying
% 159.57/22.13 | | | | | with (27), (30), (43) gives:
% 159.57/22.13 | | | | | (79) ? [v0: $i] : (app(v0, all_91_1) = all_91_1 & $i(v0) &
% 159.57/22.13 | | | | | ssList(v0))
% 159.57/22.13 | | | | |
% 159.57/22.13 | | | | | GROUND_INST: instantiating (3) with all_91_0, nil, simplifying with
% 159.57/22.13 | | | | | (7), (18), (28), (31), (47) gives:
% 159.57/22.13 | | | | | (80) ? [v0: $i] : (app(v0, nil) = all_91_0 & $i(v0) & ssList(v0))
% 159.57/22.13 | | | | |
% 159.57/22.13 | | | | | GROUND_INST: instantiating (ax82) with nil, all_116_0, nil, all_116_0,
% 159.57/22.13 | | | | | nil, simplifying with (7), (18), (63), (64), (65) gives:
% 159.57/22.13 | | | | | (81) ? [v0: $i] : (app(all_116_0, all_116_0) = v0 & app(nil, v0) =
% 159.57/22.13 | | | | | nil & $i(v0))
% 159.57/22.13 | | | | |
% 159.57/22.13 | | | | | GROUND_INST: instantiating (8) with all_116_0, nil, simplifying with
% 159.57/22.13 | | | | | (63), (64), (65) gives:
% 159.57/22.13 | | | | | (82) all_116_0 = nil
% 159.57/22.13 | | | | |
% 159.57/22.14 | | | | | GROUND_INST: instantiating (4) with all_91_0, all_114_0, all_91_1,
% 159.57/22.14 | | | | | simplifying with (27), (28), (30), (31), (59), (60), (61)
% 159.57/22.14 | | | | | gives:
% 159.57/22.14 | | | | | (83) rearsegP(all_91_0, all_114_0)
% 159.57/22.14 | | | | |
% 159.57/22.14 | | | | | GROUND_INST: instantiating (17) with all_112_0, nil, simplifying with
% 159.57/22.14 | | | | | (55), (56), (57) gives:
% 159.57/22.14 | | | | | (84) all_112_0 = nil
% 159.57/22.14 | | | | |
% 159.57/22.14 | | | | | GROUND_INST: instantiating (ax26) with all_118_2, nil, all_118_1,
% 159.57/22.14 | | | | | simplifying with (7), (18), (67), (69), (72) gives:
% 159.57/22.14 | | | | | (85) ssList(all_118_1)
% 159.57/22.14 | | | | |
% 159.57/22.14 | | | | | GROUND_INST: instantiating (17) with all_118_2, all_118_1, simplifying
% 159.57/22.14 | | | | | with (67), (69), (72) gives:
% 159.57/22.14 | | | | | (86) all_118_1 = all_118_2
% 159.57/22.14 | | | | |
% 159.57/22.14 | | | | | GROUND_INST: instantiating (ax82) with all_118_2, nil, all_118_1,
% 159.57/22.14 | | | | | all_118_0, nil, simplifying with (7), (18), (67), (68),
% 159.57/22.14 | | | | | (69), (71), (72), (73) gives:
% 159.57/22.14 | | | | | (87) ? [v0: $i] : (app(all_118_2, v0) = nil & app(nil, all_118_0)
% 159.57/22.14 | | | | | = v0 & $i(v0))
% 159.57/22.14 | | | | |
% 159.57/22.14 | | | | | DELTA: instantiating (87) with fresh symbol all_134_0 gives:
% 159.57/22.14 | | | | | (88) app(all_118_2, all_134_0) = nil & app(nil, all_118_0) =
% 159.57/22.14 | | | | | all_134_0 & $i(all_134_0)
% 159.57/22.14 | | | | |
% 159.57/22.14 | | | | | ALPHA: (88) implies:
% 159.57/22.14 | | | | | (89) app(nil, all_118_0) = all_134_0
% 159.57/22.14 | | | | |
% 159.57/22.14 | | | | | DELTA: instantiating (79) with fresh symbol all_138_0 gives:
% 159.57/22.14 | | | | | (90) app(all_138_0, all_91_1) = all_91_1 & $i(all_138_0) &
% 159.57/22.14 | | | | | ssList(all_138_0)
% 159.57/22.14 | | | | |
% 159.57/22.14 | | | | | ALPHA: (90) implies:
% 159.57/22.14 | | | | | (91) ssList(all_138_0)
% 159.57/22.14 | | | | | (92) $i(all_138_0)
% 159.57/22.14 | | | | | (93) app(all_138_0, all_91_1) = all_91_1
% 159.57/22.14 | | | | |
% 159.57/22.14 | | | | | DELTA: instantiating (78) with fresh symbol all_140_0 gives:
% 159.57/22.14 | | | | | (94) app(all_140_0, nil) = all_91_1 & $i(all_140_0) &
% 159.57/22.14 | | | | | ssList(all_140_0)
% 159.57/22.14 | | | | |
% 159.57/22.14 | | | | | ALPHA: (94) implies:
% 159.57/22.14 | | | | | (95) ssList(all_140_0)
% 159.57/22.14 | | | | | (96) $i(all_140_0)
% 159.57/22.14 | | | | | (97) app(all_140_0, nil) = all_91_1
% 159.57/22.14 | | | | |
% 159.57/22.14 | | | | | DELTA: instantiating (80) with fresh symbol all_142_0 gives:
% 159.57/22.14 | | | | | (98) app(all_142_0, nil) = all_91_0 & $i(all_142_0) &
% 159.57/22.14 | | | | | ssList(all_142_0)
% 159.57/22.14 | | | | |
% 159.57/22.14 | | | | | ALPHA: (98) implies:
% 159.57/22.14 | | | | | (99) ssList(all_142_0)
% 159.57/22.14 | | | | | (100) $i(all_142_0)
% 159.57/22.14 | | | | | (101) app(all_142_0, nil) = all_91_0
% 159.57/22.14 | | | | |
% 159.57/22.14 | | | | | DELTA: instantiating (77) with fresh symbol all_144_0 gives:
% 159.57/22.14 | | | | | (102) app(all_91_0, all_144_0) = all_91_0 & $i(all_144_0) &
% 159.57/22.14 | | | | | ssList(all_144_0)
% 159.57/22.14 | | | | |
% 159.57/22.14 | | | | | ALPHA: (102) implies:
% 159.57/22.14 | | | | | (103) ssList(all_144_0)
% 159.57/22.14 | | | | | (104) $i(all_144_0)
% 159.57/22.14 | | | | | (105) app(all_91_0, all_144_0) = all_91_0
% 159.57/22.14 | | | | |
% 159.57/22.14 | | | | | DELTA: instantiating (75) with fresh symbol all_146_0 gives:
% 159.57/22.14 | | | | | (106) app(all_91_1, all_146_0) = all_91_1 & $i(all_146_0) &
% 159.57/22.14 | | | | | ssList(all_146_0)
% 159.57/22.14 | | | | |
% 159.57/22.14 | | | | | ALPHA: (106) implies:
% 159.57/22.14 | | | | | (107) ssList(all_146_0)
% 159.57/22.14 | | | | | (108) $i(all_146_0)
% 159.57/22.14 | | | | | (109) app(all_91_1, all_146_0) = all_91_1
% 159.57/22.14 | | | | |
% 159.57/22.14 | | | | | DELTA: instantiating (74) with fresh symbol all_148_0 gives:
% 159.57/22.14 | | | | | (110) app(nil, all_148_0) = all_91_1 & $i(all_148_0) &
% 159.57/22.14 | | | | | ssList(all_148_0)
% 159.57/22.14 | | | | |
% 159.57/22.14 | | | | | ALPHA: (110) implies:
% 159.57/22.14 | | | | | (111) ssList(all_148_0)
% 159.57/22.14 | | | | | (112) $i(all_148_0)
% 159.57/22.14 | | | | | (113) app(nil, all_148_0) = all_91_1
% 159.57/22.14 | | | | |
% 159.57/22.14 | | | | | DELTA: instantiating (76) with fresh symbol all_150_0 gives:
% 159.57/22.14 | | | | | (114) app(nil, all_150_0) = all_91_0 & $i(all_150_0) &
% 159.57/22.14 | | | | | ssList(all_150_0)
% 159.57/22.14 | | | | |
% 159.57/22.14 | | | | | ALPHA: (114) implies:
% 159.57/22.14 | | | | | (115) ssList(all_150_0)
% 159.57/22.14 | | | | | (116) $i(all_150_0)
% 159.57/22.14 | | | | | (117) app(nil, all_150_0) = all_91_0
% 159.57/22.14 | | | | |
% 159.57/22.14 | | | | | DELTA: instantiating (81) with fresh symbol all_152_0 gives:
% 159.57/22.15 | | | | | (118) app(all_116_0, all_116_0) = all_152_0 & app(nil, all_152_0) =
% 159.57/22.15 | | | | | nil & $i(all_152_0)
% 159.57/22.15 | | | | |
% 159.57/22.15 | | | | | ALPHA: (118) implies:
% 159.57/22.15 | | | | | (119) $i(all_152_0)
% 159.57/22.15 | | | | | (120) app(all_116_0, all_116_0) = all_152_0
% 159.57/22.15 | | | | |
% 159.57/22.15 | | | | | REDUCE: (73), (86) imply:
% 159.57/22.15 | | | | | (121) app(all_118_2, all_118_0) = nil
% 159.57/22.15 | | | | |
% 159.57/22.15 | | | | | REDUCE: (82), (120) imply:
% 159.87/22.15 | | | | | (122) app(nil, nil) = all_152_0
% 159.87/22.15 | | | | |
% 159.87/22.15 | | | | | GROUND_INST: instantiating (14) with all_152_0, simplifying with (7),
% 159.87/22.15 | | | | | (122) gives:
% 159.87/22.15 | | | | | (123) all_152_0 = nil
% 159.87/22.15 | | | | |
% 159.87/22.15 | | | | | REDUCE: (122), (123) imply:
% 159.87/22.15 | | | | | (124) app(nil, nil) = nil
% 159.87/22.15 | | | | |
% 159.87/22.15 | | | | | GROUND_INST: instantiating (6) with all_140_0, all_142_0, simplifying
% 159.87/22.15 | | | | | with (95), (96), (99), (100) gives:
% 159.87/22.15 | | | | | (125) all_142_0 = all_140_0 | neq(all_140_0, all_142_0)
% 159.87/22.15 | | | | |
% 159.87/22.15 | | | | | GROUND_INST: instantiating (3) with all_91_0, all_114_0, simplifying
% 159.87/22.15 | | | | | with (28), (31), (59), (60), (83) gives:
% 159.87/22.15 | | | | | (126) ? [v0: $i] : (app(v0, all_114_0) = all_91_0 & $i(v0) &
% 159.87/22.15 | | | | | ssList(v0))
% 159.87/22.15 | | | | |
% 159.87/22.15 | | | | | GROUND_INST: instantiating (ax82) with nil, nil, nil, all_118_0,
% 159.87/22.15 | | | | | all_134_0, simplifying with (7), (18), (68), (71), (89),
% 159.87/22.15 | | | | | (124) gives:
% 159.87/22.15 | | | | | (127) ? [v0: $i] : (app(nil, v0) = all_134_0 & app(nil, all_118_0)
% 159.87/22.15 | | | | | = v0 & $i(v0) & $i(all_134_0))
% 159.87/22.15 | | | | |
% 159.87/22.15 | | | | | GROUND_INST: instantiating (8) with all_118_0, all_134_0, simplifying
% 159.87/22.15 | | | | | with (68), (71), (89) gives:
% 159.87/22.15 | | | | | (128) all_134_0 = all_118_0
% 159.87/22.15 | | | | |
% 159.87/22.15 | | | | | GROUND_INST: instantiating (ax82) with nil, all_148_0, all_91_1,
% 159.87/22.15 | | | | | all_114_0, all_91_0, simplifying with (7), (18), (59),
% 159.87/22.15 | | | | | (60), (61), (111), (112), (113) gives:
% 159.87/22.15 | | | | | (129) ? [v0: $i] : (app(all_148_0, all_114_0) = v0 & app(nil, v0)
% 159.87/22.15 | | | | | = all_91_0 & $i(v0) & $i(all_91_0))
% 159.87/22.15 | | | | |
% 159.87/22.15 | | | | | GROUND_INST: instantiating (ax82) with nil, nil, nil, all_148_0,
% 159.87/22.15 | | | | | all_91_1, simplifying with (7), (18), (111), (112),
% 159.87/22.15 | | | | | (113), (124) gives:
% 159.87/22.15 | | | | | (130) ? [v0: $i] : (app(nil, v0) = all_91_1 & app(nil, all_148_0)
% 159.87/22.15 | | | | | = v0 & $i(v0) & $i(all_91_1))
% 159.87/22.15 | | | | |
% 159.87/22.15 | | | | | GROUND_INST: instantiating (8) with all_148_0, all_91_1, simplifying
% 159.87/22.15 | | | | | with (111), (112), (113) gives:
% 159.87/22.15 | | | | | (131) all_148_0 = all_91_1
% 159.87/22.15 | | | | |
% 159.87/22.15 | | | | | GROUND_INST: instantiating (8) with all_150_0, all_91_0, simplifying
% 159.87/22.15 | | | | | with (115), (116), (117) gives:
% 159.87/22.15 | | | | | (132) all_150_0 = all_91_0
% 159.87/22.15 | | | | |
% 159.87/22.15 | | | | | GROUND_INST: instantiating (32) with all_91_1, all_146_0, all_91_1,
% 159.87/22.15 | | | | | all_114_0, simplifying with (27), (30), (59), (60), (61),
% 159.87/22.15 | | | | | (107), (108), (109) gives:
% 159.87/22.16 | | | | | (133) ? [v0: any] : ( ~ (v0 = all_91_1) & app(all_91_1, all_114_0)
% 159.87/22.16 | | | | | = v0 & $i(v0))
% 159.87/22.16 | | | | |
% 159.87/22.16 | | | | | GROUND_INST: instantiating (ax82) with nil, all_148_0, all_91_1,
% 159.87/22.16 | | | | | all_146_0, all_91_1, simplifying with (7), (18), (107),
% 159.87/22.16 | | | | | (108), (109), (111), (112), (113) gives:
% 159.87/22.16 | | | | | (134) ? [v0: $i] : (app(all_148_0, all_146_0) = v0 & app(nil, v0)
% 159.87/22.16 | | | | | = all_91_1 & $i(v0) & $i(all_91_1))
% 159.87/22.16 | | | | |
% 159.87/22.16 | | | | | GROUND_INST: instantiating (32) with all_91_0, all_144_0, all_91_0,
% 159.87/22.16 | | | | | all_144_0, simplifying with (28), (31), (103), (104),
% 159.87/22.16 | | | | | (105) gives:
% 159.87/22.16 | | | | | (135) ? [v0: any] : ( ~ (v0 = all_91_1) & app(all_91_0, all_144_0)
% 159.87/22.16 | | | | | = v0 & $i(v0))
% 159.87/22.16 | | | | |
% 159.87/22.16 | | | | | GROUND_INST: instantiating (ax82) with nil, all_150_0, all_91_0,
% 159.87/22.16 | | | | | all_144_0, all_91_0, simplifying with (7), (18), (103),
% 159.87/22.16 | | | | | (104), (105), (115), (116), (117) gives:
% 159.87/22.16 | | | | | (136) ? [v0: $i] : (app(all_150_0, all_144_0) = v0 & app(nil, v0)
% 159.87/22.16 | | | | | = all_91_0 & $i(v0) & $i(all_91_0))
% 159.87/22.16 | | | | |
% 159.87/22.17 | | | | | GROUND_INST: instantiating (32) with all_91_1, all_114_0, all_91_0,
% 159.87/22.17 | | | | | all_144_0, simplifying with (27), (30), (59), (60), (61),
% 159.87/22.17 | | | | | (103), (104), (105) gives:
% 159.87/22.17 | | | | | (137) ? [v0: any] : ( ~ (v0 = all_91_1) & app(all_91_1, all_144_0)
% 159.87/22.17 | | | | | = v0 & $i(v0))
% 159.87/22.17 | | | | |
% 159.87/22.17 | | | | | GROUND_INST: instantiating (ax82) with all_118_2, all_118_0, nil,
% 159.87/22.17 | | | | | all_148_0, all_91_1, simplifying with (67), (68), (69),
% 159.87/22.17 | | | | | (71), (111), (112), (113), (121) gives:
% 159.87/22.17 | | | | | (138) ? [v0: $i] : (app(all_118_0, all_148_0) = v0 &
% 159.87/22.17 | | | | | app(all_118_2, v0) = all_91_1 & $i(v0) & $i(all_91_1))
% 159.87/22.17 | | | | |
% 159.87/22.17 | | | | | GROUND_INST: instantiating (ax82) with all_118_2, all_118_0, nil,
% 159.87/22.17 | | | | | all_118_0, all_134_0, simplifying with (67), (68), (69),
% 159.87/22.17 | | | | | (71), (89), (121) gives:
% 159.87/22.17 | | | | | (139) ? [v0: $i] : (app(all_118_0, all_118_0) = v0 &
% 159.87/22.17 | | | | | app(all_118_2, v0) = all_134_0 & $i(v0) & $i(all_134_0))
% 159.87/22.17 | | | | |
% 159.87/22.17 | | | | | GROUND_INST: instantiating (ax82) with all_118_2, all_118_0, nil, nil,
% 159.87/22.17 | | | | | nil, simplifying with (7), (18), (67), (68), (69), (71),
% 159.87/22.17 | | | | | (121), (124) gives:
% 159.87/22.17 | | | | | (140) ? [v0: $i] : (app(all_118_0, nil) = v0 & app(all_118_2, v0)
% 159.87/22.17 | | | | | = nil & $i(v0))
% 159.87/22.17 | | | | |
% 159.87/22.17 | | | | | GROUND_INST: instantiating (16) with all_118_2, all_118_0, simplifying
% 159.87/22.17 | | | | | with (67), (68), (69), (71), (121) gives:
% 159.87/22.17 | | | | | (141) all_118_0 = nil
% 159.87/22.17 | | | | |
% 159.87/22.17 | | | | | GROUND_INST: instantiating (15) with all_118_2, all_118_0, simplifying
% 159.87/22.17 | | | | | with (67), (68), (69), (71), (121) gives:
% 159.87/22.17 | | | | | (142) all_118_2 = nil
% 159.87/22.17 | | | | |
% 159.87/22.17 | | | | | GROUND_INST: instantiating (ax82) with all_138_0, all_91_1, all_91_1,
% 159.87/22.17 | | | | | all_114_0, all_91_0, simplifying with (27), (30), (59),
% 159.87/22.17 | | | | | (60), (61), (91), (92), (93) gives:
% 159.87/22.17 | | | | | (143) ? [v0: $i] : (app(all_138_0, v0) = all_91_0 & app(all_91_1,
% 159.87/22.17 | | | | | all_114_0) = v0 & $i(v0) & $i(all_91_0))
% 159.87/22.17 | | | | |
% 159.87/22.17 | | | | | GROUND_INST: instantiating (32) with all_140_0, nil, all_91_1,
% 159.87/22.17 | | | | | all_114_0, simplifying with (7), (18), (59), (60), (61),
% 159.87/22.17 | | | | | (95), (96), (97) gives:
% 159.87/22.17 | | | | | (144) ? [v0: any] : ( ~ (v0 = all_91_1) & app(all_140_0,
% 159.87/22.17 | | | | | all_114_0) = v0 & $i(v0))
% 159.87/22.17 | | | | |
% 159.87/22.17 | | | | | GROUND_INST: instantiating (17) with all_140_0, all_91_1, simplifying
% 159.87/22.17 | | | | | with (95), (96), (97) gives:
% 159.87/22.17 | | | | | (145) all_140_0 = all_91_1
% 159.87/22.17 | | | | |
% 159.87/22.18 | | | | | GROUND_INST: instantiating (32) with all_142_0, nil, all_91_0,
% 159.87/22.18 | | | | | all_144_0, simplifying with (7), (18), (99), (100),
% 159.87/22.18 | | | | | (101), (103), (104), (105) gives:
% 159.87/22.18 | | | | | (146) ? [v0: any] : ( ~ (v0 = all_91_1) & app(all_142_0,
% 159.87/22.18 | | | | | all_144_0) = v0 & $i(v0))
% 159.87/22.18 | | | | |
% 159.87/22.18 | | | | | GROUND_INST: instantiating (17) with all_142_0, all_91_0, simplifying
% 159.87/22.18 | | | | | with (99), (100), (101) gives:
% 159.87/22.18 | | | | | (147) all_142_0 = all_91_0
% 159.87/22.18 | | | | |
% 159.87/22.18 | | | | | COMBINE_EQS: (128), (141) imply:
% 159.87/22.18 | | | | | (148) all_134_0 = nil
% 159.87/22.18 | | | | |
% 159.87/22.18 | | | | | DELTA: instantiating (146) with fresh symbol all_172_0 gives:
% 159.87/22.18 | | | | | (149) ~ (all_172_0 = all_91_1) & app(all_142_0, all_144_0) =
% 159.87/22.18 | | | | | all_172_0 & $i(all_172_0)
% 159.87/22.18 | | | | |
% 159.87/22.18 | | | | | ALPHA: (149) implies:
% 159.87/22.18 | | | | | (150) ~ (all_172_0 = all_91_1)
% 159.87/22.18 | | | | | (151) $i(all_172_0)
% 159.87/22.18 | | | | | (152) app(all_142_0, all_144_0) = all_172_0
% 159.87/22.18 | | | | |
% 159.87/22.18 | | | | | DELTA: instantiating (140) with fresh symbol all_176_0 gives:
% 159.87/22.18 | | | | | (153) app(all_118_0, nil) = all_176_0 & app(all_118_2, all_176_0) =
% 159.87/22.18 | | | | | nil & $i(all_176_0)
% 159.87/22.18 | | | | |
% 159.87/22.18 | | | | | ALPHA: (153) implies:
% 159.87/22.18 | | | | | (154) $i(all_176_0)
% 159.87/22.18 | | | | | (155) app(all_118_0, nil) = all_176_0
% 159.87/22.18 | | | | |
% 159.87/22.18 | | | | | DELTA: instantiating (133) with fresh symbol all_182_0 gives:
% 159.87/22.18 | | | | | (156) ~ (all_182_0 = all_91_1) & app(all_91_1, all_114_0) =
% 159.87/22.18 | | | | | all_182_0 & $i(all_182_0)
% 159.87/22.18 | | | | |
% 159.87/22.18 | | | | | ALPHA: (156) implies:
% 159.87/22.18 | | | | | (157) app(all_91_1, all_114_0) = all_182_0
% 159.87/22.18 | | | | |
% 159.87/22.18 | | | | | DELTA: instantiating (137) with fresh symbol all_188_0 gives:
% 159.87/22.18 | | | | | (158) ~ (all_188_0 = all_91_1) & app(all_91_1, all_144_0) =
% 159.87/22.18 | | | | | all_188_0 & $i(all_188_0)
% 159.87/22.18 | | | | |
% 159.87/22.18 | | | | | ALPHA: (158) implies:
% 159.87/22.18 | | | | | (159) ~ (all_188_0 = all_91_1)
% 159.87/22.18 | | | | | (160) app(all_91_1, all_144_0) = all_188_0
% 159.87/22.18 | | | | |
% 159.87/22.18 | | | | | DELTA: instantiating (144) with fresh symbol all_200_0 gives:
% 159.87/22.18 | | | | | (161) ~ (all_200_0 = all_91_1) & app(all_140_0, all_114_0) =
% 159.87/22.18 | | | | | all_200_0 & $i(all_200_0)
% 159.87/22.18 | | | | |
% 159.87/22.18 | | | | | ALPHA: (161) implies:
% 159.87/22.18 | | | | | (162) app(all_140_0, all_114_0) = all_200_0
% 159.87/22.18 | | | | |
% 159.87/22.18 | | | | | DELTA: instantiating (135) with fresh symbol all_222_0 gives:
% 159.87/22.18 | | | | | (163) ~ (all_222_0 = all_91_1) & app(all_91_0, all_144_0) =
% 159.87/22.18 | | | | | all_222_0 & $i(all_222_0)
% 159.87/22.18 | | | | |
% 159.87/22.18 | | | | | ALPHA: (163) implies:
% 159.87/22.18 | | | | | (164) app(all_91_0, all_144_0) = all_222_0
% 159.87/22.18 | | | | |
% 159.87/22.18 | | | | | DELTA: instantiating (126) with fresh symbol all_224_0 gives:
% 159.87/22.18 | | | | | (165) app(all_224_0, all_114_0) = all_91_0 & $i(all_224_0) &
% 159.87/22.18 | | | | | ssList(all_224_0)
% 159.87/22.18 | | | | |
% 159.87/22.18 | | | | | ALPHA: (165) implies:
% 159.87/22.18 | | | | | (166) ssList(all_224_0)
% 159.87/22.18 | | | | | (167) $i(all_224_0)
% 159.87/22.18 | | | | | (168) app(all_224_0, all_114_0) = all_91_0
% 159.87/22.18 | | | | |
% 159.87/22.18 | | | | | DELTA: instantiating (143) with fresh symbol all_234_0 gives:
% 159.87/22.18 | | | | | (169) app(all_138_0, all_234_0) = all_91_0 & app(all_91_1,
% 159.87/22.18 | | | | | all_114_0) = all_234_0 & $i(all_234_0) & $i(all_91_0)
% 159.87/22.18 | | | | |
% 159.87/22.18 | | | | | ALPHA: (169) implies:
% 159.87/22.18 | | | | | (170) app(all_91_1, all_114_0) = all_234_0
% 159.87/22.18 | | | | |
% 159.87/22.18 | | | | | DELTA: instantiating (136) with fresh symbol all_240_0 gives:
% 159.87/22.18 | | | | | (171) app(all_150_0, all_144_0) = all_240_0 & app(nil, all_240_0) =
% 159.87/22.18 | | | | | all_91_0 & $i(all_240_0) & $i(all_91_0)
% 159.87/22.18 | | | | |
% 159.87/22.18 | | | | | ALPHA: (171) implies:
% 159.87/22.18 | | | | | (172) app(all_150_0, all_144_0) = all_240_0
% 159.87/22.18 | | | | |
% 159.87/22.18 | | | | | DELTA: instantiating (138) with fresh symbol all_248_0 gives:
% 159.87/22.18 | | | | | (173) app(all_118_0, all_148_0) = all_248_0 & app(all_118_2,
% 159.87/22.18 | | | | | all_248_0) = all_91_1 & $i(all_248_0) & $i(all_91_1)
% 159.87/22.18 | | | | |
% 159.87/22.18 | | | | | ALPHA: (173) implies:
% 159.87/22.18 | | | | | (174) $i(all_248_0)
% 159.87/22.18 | | | | | (175) app(all_118_0, all_148_0) = all_248_0
% 159.87/22.18 | | | | |
% 159.87/22.18 | | | | | DELTA: instantiating (134) with fresh symbol all_250_0 gives:
% 159.87/22.18 | | | | | (176) app(all_148_0, all_146_0) = all_250_0 & app(nil, all_250_0) =
% 159.87/22.18 | | | | | all_91_1 & $i(all_250_0) & $i(all_91_1)
% 159.87/22.18 | | | | |
% 159.87/22.18 | | | | | ALPHA: (176) implies:
% 159.87/22.18 | | | | | (177) app(all_148_0, all_146_0) = all_250_0
% 159.87/22.18 | | | | |
% 159.87/22.18 | | | | | DELTA: instantiating (127) with fresh symbol all_252_0 gives:
% 159.87/22.18 | | | | | (178) app(nil, all_252_0) = all_134_0 & app(nil, all_118_0) =
% 159.87/22.18 | | | | | all_252_0 & $i(all_252_0) & $i(all_134_0)
% 159.87/22.18 | | | | |
% 159.87/22.18 | | | | | ALPHA: (178) implies:
% 159.87/22.18 | | | | | (179) app(nil, all_118_0) = all_252_0
% 159.87/22.18 | | | | |
% 159.87/22.18 | | | | | DELTA: instantiating (129) with fresh symbol all_254_0 gives:
% 159.87/22.18 | | | | | (180) app(all_148_0, all_114_0) = all_254_0 & app(nil, all_254_0) =
% 159.87/22.18 | | | | | all_91_0 & $i(all_254_0) & $i(all_91_0)
% 159.87/22.18 | | | | |
% 159.87/22.18 | | | | | ALPHA: (180) implies:
% 159.87/22.19 | | | | | (181) app(all_148_0, all_114_0) = all_254_0
% 159.87/22.19 | | | | |
% 159.87/22.19 | | | | | DELTA: instantiating (139) with fresh symbol all_256_0 gives:
% 159.87/22.19 | | | | | (182) app(all_118_0, all_118_0) = all_256_0 & app(all_118_2,
% 159.87/22.19 | | | | | all_256_0) = all_134_0 & $i(all_256_0) & $i(all_134_0)
% 159.87/22.19 | | | | |
% 159.87/22.19 | | | | | ALPHA: (182) implies:
% 159.87/22.19 | | | | | (183) app(all_118_0, all_118_0) = all_256_0
% 159.87/22.19 | | | | |
% 159.87/22.19 | | | | | DELTA: instantiating (130) with fresh symbol all_260_0 gives:
% 159.87/22.19 | | | | | (184) app(nil, all_260_0) = all_91_1 & app(nil, all_148_0) =
% 159.87/22.19 | | | | | all_260_0 & $i(all_260_0) & $i(all_91_1)
% 159.87/22.19 | | | | |
% 159.87/22.19 | | | | | ALPHA: (184) implies:
% 159.87/22.19 | | | | | (185) app(nil, all_148_0) = all_260_0
% 159.87/22.19 | | | | |
% 159.87/22.19 | | | | | REDUCE: (132), (172) imply:
% 159.87/22.19 | | | | | (186) app(all_91_0, all_144_0) = all_240_0
% 159.87/22.19 | | | | |
% 159.87/22.19 | | | | | REDUCE: (131), (177) imply:
% 159.87/22.19 | | | | | (187) app(all_91_1, all_146_0) = all_250_0
% 159.87/22.19 | | | | |
% 159.87/22.19 | | | | | REDUCE: (131), (181) imply:
% 159.87/22.19 | | | | | (188) app(all_91_1, all_114_0) = all_254_0
% 159.87/22.19 | | | | |
% 159.87/22.19 | | | | | REDUCE: (147), (152) imply:
% 159.87/22.19 | | | | | (189) app(all_91_0, all_144_0) = all_172_0
% 159.87/22.19 | | | | |
% 159.87/22.19 | | | | | REDUCE: (101), (147) imply:
% 159.87/22.19 | | | | | (190) app(all_91_0, nil) = all_91_0
% 159.87/22.19 | | | | |
% 159.87/22.19 | | | | | REDUCE: (145), (162) imply:
% 159.87/22.19 | | | | | (191) app(all_91_1, all_114_0) = all_200_0
% 159.87/22.19 | | | | |
% 159.87/22.19 | | | | | REDUCE: (97), (145) imply:
% 159.87/22.19 | | | | | (192) app(all_91_1, nil) = all_91_1
% 159.87/22.19 | | | | |
% 159.87/22.19 | | | | | REDUCE: (131), (141), (175) imply:
% 159.87/22.19 | | | | | (193) app(nil, all_91_1) = all_248_0
% 159.87/22.19 | | | | |
% 159.87/22.19 | | | | | REDUCE: (141), (183) imply:
% 159.87/22.19 | | | | | (194) app(nil, nil) = all_256_0
% 159.87/22.19 | | | | |
% 159.87/22.19 | | | | | REDUCE: (141), (155) imply:
% 159.87/22.19 | | | | | (195) app(nil, nil) = all_176_0
% 159.87/22.19 | | | | |
% 159.87/22.19 | | | | | REDUCE: (131), (185) imply:
% 159.87/22.19 | | | | | (196) app(nil, all_91_1) = all_260_0
% 159.87/22.19 | | | | |
% 159.87/22.19 | | | | | REDUCE: (113), (131) imply:
% 159.87/22.19 | | | | | (197) app(nil, all_91_1) = all_91_1
% 159.87/22.19 | | | | |
% 159.87/22.19 | | | | | REDUCE: (141), (179) imply:
% 159.87/22.19 | | | | | (198) app(nil, nil) = all_252_0
% 159.87/22.19 | | | | |
% 159.87/22.19 | | | | | GROUND_INST: instantiating (19) with nil, all_252_0, nil, nil,
% 159.87/22.19 | | | | | simplifying with (124), (198) gives:
% 159.87/22.19 | | | | | (199) all_252_0 = nil
% 159.87/22.19 | | | | |
% 159.87/22.19 | | | | | GROUND_INST: instantiating (19) with all_252_0, all_256_0, nil, nil,
% 159.87/22.19 | | | | | simplifying with (194), (198) gives:
% 159.87/22.19 | | | | | (200) all_256_0 = all_252_0
% 159.87/22.19 | | | | |
% 159.87/22.19 | | | | | GROUND_INST: instantiating (19) with all_176_0, all_256_0, nil, nil,
% 159.87/22.19 | | | | | simplifying with (194), (195) gives:
% 159.87/22.19 | | | | | (201) all_256_0 = all_176_0
% 159.87/22.19 | | | | |
% 159.87/22.19 | | | | | GROUND_INST: instantiating (19) with all_248_0, all_260_0, all_91_1,
% 159.87/22.19 | | | | | nil, simplifying with (193), (196) gives:
% 159.87/22.19 | | | | | (202) all_260_0 = all_248_0
% 159.87/22.19 | | | | |
% 159.87/22.19 | | | | | GROUND_INST: instantiating (19) with all_91_1, all_260_0, all_91_1,
% 159.87/22.19 | | | | | nil, simplifying with (196), (197) gives:
% 159.87/22.19 | | | | | (203) all_260_0 = all_91_1
% 159.87/22.19 | | | | |
% 159.87/22.19 | | | | | GROUND_INST: instantiating (19) with all_91_0, all_200_0, all_114_0,
% 159.87/22.19 | | | | | all_91_1, simplifying with (61), (191) gives:
% 159.87/22.19 | | | | | (204) all_200_0 = all_91_0
% 159.87/22.19 | | | | |
% 159.87/22.19 | | | | | GROUND_INST: instantiating (19) with all_200_0, all_234_0, all_114_0,
% 159.87/22.19 | | | | | all_91_1, simplifying with (170), (191) gives:
% 159.87/22.19 | | | | | (205) all_234_0 = all_200_0
% 159.87/22.19 | | | | |
% 159.87/22.19 | | | | | GROUND_INST: instantiating (19) with all_234_0, all_254_0, all_114_0,
% 159.87/22.19 | | | | | all_91_1, simplifying with (170), (188) gives:
% 159.87/22.19 | | | | | (206) all_254_0 = all_234_0
% 159.87/22.19 | | | | |
% 159.87/22.19 | | | | | GROUND_INST: instantiating (19) with all_182_0, all_254_0, all_114_0,
% 159.87/22.19 | | | | | all_91_1, simplifying with (157), (188) gives:
% 159.87/22.19 | | | | | (207) all_254_0 = all_182_0
% 159.87/22.19 | | | | |
% 159.87/22.19 | | | | | GROUND_INST: instantiating (19) with all_91_1, all_250_0, all_146_0,
% 159.87/22.19 | | | | | all_91_1, simplifying with (109), (187) gives:
% 159.87/22.19 | | | | | (208) all_250_0 = all_91_1
% 159.87/22.19 | | | | |
% 159.87/22.19 | | | | | GROUND_INST: instantiating (19) with all_172_0, all_222_0, all_144_0,
% 159.87/22.19 | | | | | all_91_0, simplifying with (164), (189) gives:
% 159.87/22.19 | | | | | (209) all_222_0 = all_172_0
% 159.87/22.19 | | | | |
% 159.87/22.19 | | | | | GROUND_INST: instantiating (19) with all_91_0, all_240_0, all_144_0,
% 159.87/22.19 | | | | | all_91_0, simplifying with (105), (186) gives:
% 159.87/22.19 | | | | | (210) all_240_0 = all_91_0
% 159.87/22.19 | | | | |
% 159.87/22.19 | | | | | GROUND_INST: instantiating (19) with all_222_0, all_240_0, all_144_0,
% 159.87/22.19 | | | | | all_91_0, simplifying with (164), (186) gives:
% 159.87/22.19 | | | | | (211) all_240_0 = all_222_0
% 159.87/22.19 | | | | |
% 159.87/22.19 | | | | | COMBINE_EQS: (202), (203) imply:
% 159.87/22.19 | | | | | (212) all_248_0 = all_91_1
% 159.87/22.19 | | | | |
% 159.87/22.19 | | | | | COMBINE_EQS: (200), (201) imply:
% 159.87/22.19 | | | | | (213) all_252_0 = all_176_0
% 159.87/22.19 | | | | |
% 159.87/22.19 | | | | | SIMP: (213) implies:
% 159.87/22.20 | | | | | (214) all_252_0 = all_176_0
% 159.87/22.20 | | | | |
% 159.87/22.20 | | | | | COMBINE_EQS: (206), (207) imply:
% 159.87/22.20 | | | | | (215) all_234_0 = all_182_0
% 159.87/22.20 | | | | |
% 159.87/22.20 | | | | | SIMP: (215) implies:
% 159.87/22.20 | | | | | (216) all_234_0 = all_182_0
% 159.87/22.20 | | | | |
% 159.87/22.20 | | | | | COMBINE_EQS: (199), (214) imply:
% 159.87/22.20 | | | | | (217) all_176_0 = nil
% 159.87/22.20 | | | | |
% 159.87/22.20 | | | | | SIMP: (217) implies:
% 159.87/22.20 | | | | | (218) all_176_0 = nil
% 159.87/22.20 | | | | |
% 159.87/22.20 | | | | | COMBINE_EQS: (210), (211) imply:
% 159.87/22.20 | | | | | (219) all_222_0 = all_91_0
% 159.87/22.20 | | | | |
% 159.87/22.20 | | | | | SIMP: (219) implies:
% 159.87/22.20 | | | | | (220) all_222_0 = all_91_0
% 159.87/22.20 | | | | |
% 159.87/22.20 | | | | | COMBINE_EQS: (205), (216) imply:
% 159.87/22.20 | | | | | (221) all_200_0 = all_182_0
% 159.87/22.20 | | | | |
% 159.87/22.20 | | | | | SIMP: (221) implies:
% 159.87/22.20 | | | | | (222) all_200_0 = all_182_0
% 159.87/22.20 | | | | |
% 159.87/22.20 | | | | | COMBINE_EQS: (209), (220) imply:
% 159.87/22.20 | | | | | (223) all_172_0 = all_91_0
% 159.87/22.20 | | | | |
% 159.87/22.20 | | | | | COMBINE_EQS: (204), (222) imply:
% 159.87/22.20 | | | | | (224) all_182_0 = all_91_0
% 159.87/22.20 | | | | |
% 159.87/22.20 | | | | | REDUCE: (150), (223) imply:
% 159.87/22.20 | | | | | (225) ~ (all_91_0 = all_91_1)
% 159.87/22.20 | | | | |
% 159.87/22.20 | | | | | BETA: splitting (125) gives:
% 159.87/22.20 | | | | |
% 159.87/22.20 | | | | | Case 1:
% 159.87/22.20 | | | | | |
% 159.87/22.20 | | | | | |
% 159.87/22.20 | | | | | | GROUND_INST: instantiating (ax80) with nil, all_91_1, all_91_1,
% 159.87/22.20 | | | | | | all_146_0, simplifying with (7), (18), (27), (30),
% 159.87/22.20 | | | | | | (107), (108), (109), (192) gives:
% 159.87/22.20 | | | | | | (226) all_146_0 = nil
% 159.87/22.20 | | | | | |
% 159.87/22.20 | | | | | | GROUND_INST: instantiating (ax82) with all_138_0, all_91_1,
% 159.87/22.20 | | | | | | all_91_1, all_144_0, all_188_0, simplifying with (27),
% 159.87/22.20 | | | | | | (30), (91), (92), (93), (103), (104), (160) gives:
% 159.87/22.20 | | | | | | (227) ? [v0: $i] : (app(all_138_0, v0) = all_188_0 &
% 159.87/22.20 | | | | | | app(all_91_1, all_144_0) = v0 & $i(v0) & $i(all_188_0))
% 159.87/22.20 | | | | | |
% 159.87/22.20 | | | | | | GROUND_INST: instantiating (ax82) with nil, all_91_1, all_91_1,
% 159.87/22.20 | | | | | | all_144_0, all_188_0, simplifying with (7), (18), (27),
% 159.87/22.20 | | | | | | (30), (103), (104), (160), (197) gives:
% 159.87/22.20 | | | | | | (228) ? [v0: $i] : (app(all_91_1, all_144_0) = v0 & app(nil, v0)
% 159.87/22.20 | | | | | | = all_188_0 & $i(v0) & $i(all_188_0))
% 159.87/22.20 | | | | | |
% 159.87/22.20 | | | | | | GROUND_INST: instantiating (ax80) with nil, all_91_0, all_91_0,
% 159.87/22.20 | | | | | | all_144_0, simplifying with (7), (18), (28), (31),
% 159.87/22.20 | | | | | | (103), (104), (105), (190) gives:
% 159.87/22.20 | | | | | | (229) all_144_0 = nil
% 159.87/22.20 | | | | | |
% 159.87/22.20 | | | | | | GROUND_INST: instantiating (32) with all_91_1, all_114_0, all_91_0,
% 159.87/22.20 | | | | | | nil, simplifying with (7), (18), (27), (30), (59),
% 159.87/22.20 | | | | | | (60), (61), (190) gives:
% 159.87/22.20 | | | | | | (230) ? [v0: any] : ( ~ (v0 = all_91_1) & app(all_91_1, nil) =
% 159.87/22.20 | | | | | | v0 & $i(v0))
% 159.87/22.20 | | | | | |
% 159.87/22.20 | | | | | | GROUND_INST: instantiating (32) with all_224_0, all_114_0, all_91_0,
% 159.87/22.20 | | | | | | all_144_0, simplifying with (59), (60), (103), (104),
% 159.87/22.20 | | | | | | (105), (166), (167), (168) gives:
% 159.87/22.20 | | | | | | (231) ? [v0: any] : ( ~ (v0 = all_91_1) & app(all_224_0,
% 159.87/22.20 | | | | | | all_144_0) = v0 & $i(v0))
% 159.87/22.20 | | | | | |
% 159.87/22.20 | | | | | | GROUND_INST: instantiating (ax79) with all_224_0, all_114_0,
% 159.87/22.20 | | | | | | all_91_0, all_91_1, simplifying with (27), (30), (59),
% 159.87/22.20 | | | | | | (60), (61), (166), (167), (168) gives:
% 159.87/22.20 | | | | | | (232) all_224_0 = all_91_1
% 159.87/22.20 | | | | | |
% 159.87/22.20 | | | | | | GROUND_INST: instantiating (32) with all_224_0, all_114_0, all_91_0,
% 159.87/22.20 | | | | | | nil, simplifying with (7), (18), (59), (60), (166),
% 159.87/22.20 | | | | | | (167), (168), (190) gives:
% 159.87/22.20 | | | | | | (233) ? [v0: any] : ( ~ (v0 = all_91_1) & app(all_224_0, nil) =
% 159.87/22.20 | | | | | | v0 & $i(v0))
% 159.87/22.20 | | | | | |
% 159.87/22.20 | | | | | | DELTA: instantiating (233) with fresh symbol all_322_0 gives:
% 159.87/22.20 | | | | | | (234) ~ (all_322_0 = all_91_1) & app(all_224_0, nil) = all_322_0
% 159.87/22.20 | | | | | | & $i(all_322_0)
% 159.87/22.20 | | | | | |
% 159.87/22.20 | | | | | | ALPHA: (234) implies:
% 159.87/22.20 | | | | | | (235) app(all_224_0, nil) = all_322_0
% 159.87/22.20 | | | | | |
% 159.87/22.20 | | | | | | DELTA: instantiating (231) with fresh symbol all_324_0 gives:
% 159.87/22.20 | | | | | | (236) ~ (all_324_0 = all_91_1) & app(all_224_0, all_144_0) =
% 159.87/22.20 | | | | | | all_324_0 & $i(all_324_0)
% 159.87/22.20 | | | | | |
% 159.87/22.20 | | | | | | ALPHA: (236) implies:
% 159.87/22.20 | | | | | | (237) app(all_224_0, all_144_0) = all_324_0
% 159.87/22.20 | | | | | |
% 159.87/22.20 | | | | | | DELTA: instantiating (230) with fresh symbol all_370_0 gives:
% 159.87/22.20 | | | | | | (238) ~ (all_370_0 = all_91_1) & app(all_91_1, nil) = all_370_0
% 159.87/22.20 | | | | | | & $i(all_370_0)
% 159.87/22.20 | | | | | |
% 159.87/22.20 | | | | | | ALPHA: (238) implies:
% 159.87/22.20 | | | | | | (239) app(all_91_1, nil) = all_370_0
% 159.87/22.20 | | | | | |
% 159.87/22.20 | | | | | | DELTA: instantiating (228) with fresh symbol all_552_0 gives:
% 159.87/22.20 | | | | | | (240) app(all_91_1, all_144_0) = all_552_0 & app(nil, all_552_0)
% 159.87/22.20 | | | | | | = all_188_0 & $i(all_552_0) & $i(all_188_0)
% 159.87/22.20 | | | | | |
% 159.87/22.20 | | | | | | ALPHA: (240) implies:
% 159.87/22.20 | | | | | | (241) app(all_91_1, all_144_0) = all_552_0
% 159.87/22.20 | | | | | |
% 159.87/22.20 | | | | | | DELTA: instantiating (227) with fresh symbol all_580_0 gives:
% 159.87/22.20 | | | | | | (242) app(all_138_0, all_580_0) = all_188_0 & app(all_91_1,
% 159.87/22.20 | | | | | | all_144_0) = all_580_0 & $i(all_580_0) & $i(all_188_0)
% 159.87/22.20 | | | | | |
% 159.87/22.20 | | | | | | ALPHA: (242) implies:
% 159.87/22.21 | | | | | | (243) app(all_91_1, all_144_0) = all_580_0
% 159.87/22.21 | | | | | |
% 159.87/22.21 | | | | | | REDUCE: (229), (232), (237) imply:
% 159.87/22.21 | | | | | | (244) app(all_91_1, nil) = all_324_0
% 159.87/22.21 | | | | | |
% 159.87/22.21 | | | | | | REDUCE: (232), (235) imply:
% 159.87/22.21 | | | | | | (245) app(all_91_1, nil) = all_322_0
% 159.87/22.21 | | | | | |
% 159.87/22.21 | | | | | | REDUCE: (229), (243) imply:
% 159.87/22.21 | | | | | | (246) app(all_91_1, nil) = all_580_0
% 159.87/22.21 | | | | | |
% 159.87/22.21 | | | | | | REDUCE: (229), (241) imply:
% 159.87/22.21 | | | | | | (247) app(all_91_1, nil) = all_552_0
% 159.87/22.21 | | | | | |
% 159.87/22.21 | | | | | | REDUCE: (160), (229) imply:
% 159.87/22.21 | | | | | | (248) app(all_91_1, nil) = all_188_0
% 159.87/22.21 | | | | | |
% 159.87/22.21 | | | | | | GROUND_INST: instantiating (19) with all_91_1, all_322_0, nil,
% 159.87/22.21 | | | | | | all_91_1, simplifying with (192), (245) gives:
% 159.87/22.21 | | | | | | (249) all_322_0 = all_91_1
% 159.87/22.21 | | | | | |
% 159.87/22.21 | | | | | | GROUND_INST: instantiating (19) with all_322_0, all_324_0, nil,
% 159.87/22.21 | | | | | | all_91_1, simplifying with (244), (245) gives:
% 159.87/22.21 | | | | | | (250) all_324_0 = all_322_0
% 159.87/22.21 | | | | | |
% 159.87/22.21 | | | | | | GROUND_INST: instantiating (19) with all_324_0, all_370_0, nil,
% 159.87/22.21 | | | | | | all_91_1, simplifying with (239), (244) gives:
% 159.87/22.21 | | | | | | (251) all_370_0 = all_324_0
% 159.87/22.21 | | | | | |
% 159.87/22.21 | | | | | | GROUND_INST: instantiating (19) with all_370_0, all_552_0, nil,
% 159.87/22.21 | | | | | | all_91_1, simplifying with (239), (247) gives:
% 159.87/22.21 | | | | | | (252) all_552_0 = all_370_0
% 159.87/22.21 | | | | | |
% 159.87/22.21 | | | | | | GROUND_INST: instantiating (19) with all_552_0, all_580_0, nil,
% 159.87/22.21 | | | | | | all_91_1, simplifying with (246), (247) gives:
% 159.87/22.21 | | | | | | (253) all_580_0 = all_552_0
% 159.87/22.21 | | | | | |
% 159.87/22.21 | | | | | | GROUND_INST: instantiating (19) with all_188_0, all_580_0, nil,
% 159.87/22.21 | | | | | | all_91_1, simplifying with (246), (248) gives:
% 159.87/22.21 | | | | | | (254) all_580_0 = all_188_0
% 159.87/22.21 | | | | | |
% 159.87/22.21 | | | | | | COMBINE_EQS: (253), (254) imply:
% 159.87/22.21 | | | | | | (255) all_552_0 = all_188_0
% 159.87/22.21 | | | | | |
% 159.87/22.21 | | | | | | SIMP: (255) implies:
% 159.87/22.21 | | | | | | (256) all_552_0 = all_188_0
% 159.87/22.21 | | | | | |
% 159.87/22.21 | | | | | | COMBINE_EQS: (252), (256) imply:
% 159.87/22.21 | | | | | | (257) all_370_0 = all_188_0
% 159.87/22.21 | | | | | |
% 159.87/22.21 | | | | | | SIMP: (257) implies:
% 159.87/22.21 | | | | | | (258) all_370_0 = all_188_0
% 159.87/22.21 | | | | | |
% 159.87/22.21 | | | | | | COMBINE_EQS: (251), (258) imply:
% 159.87/22.21 | | | | | | (259) all_324_0 = all_188_0
% 159.87/22.21 | | | | | |
% 159.87/22.21 | | | | | | SIMP: (259) implies:
% 159.87/22.21 | | | | | | (260) all_324_0 = all_188_0
% 159.87/22.21 | | | | | |
% 159.87/22.21 | | | | | | COMBINE_EQS: (250), (260) imply:
% 159.87/22.21 | | | | | | (261) all_322_0 = all_188_0
% 159.87/22.21 | | | | | |
% 159.87/22.21 | | | | | | SIMP: (261) implies:
% 159.87/22.21 | | | | | | (262) all_322_0 = all_188_0
% 159.87/22.21 | | | | | |
% 159.87/22.21 | | | | | | COMBINE_EQS: (249), (262) imply:
% 159.87/22.21 | | | | | | (263) all_188_0 = all_91_1
% 159.87/22.21 | | | | | |
% 159.87/22.21 | | | | | | REDUCE: (159), (263) imply:
% 159.87/22.21 | | | | | | (264) $false
% 159.87/22.21 | | | | | |
% 159.87/22.21 | | | | | | CLOSE: (264) is inconsistent.
% 159.87/22.21 | | | | | |
% 159.87/22.21 | | | | | Case 2:
% 159.87/22.21 | | | | | |
% 159.87/22.21 | | | | | | (265) all_142_0 = all_140_0
% 159.87/22.21 | | | | | |
% 159.87/22.21 | | | | | | COMBINE_EQS: (147), (265) imply:
% 159.87/22.21 | | | | | | (266) all_140_0 = all_91_0
% 159.87/22.21 | | | | | |
% 159.87/22.21 | | | | | | COMBINE_EQS: (145), (266) imply:
% 159.87/22.21 | | | | | | (267) all_91_0 = all_91_1
% 159.87/22.21 | | | | | |
% 159.87/22.21 | | | | | | SIMP: (267) implies:
% 159.87/22.21 | | | | | | (268) all_91_0 = all_91_1
% 159.87/22.21 | | | | | |
% 159.87/22.21 | | | | | | REDUCE: (225), (268) imply:
% 159.87/22.21 | | | | | | (269) $false
% 159.87/22.21 | | | | | |
% 159.87/22.21 | | | | | | CLOSE: (269) is inconsistent.
% 159.87/22.21 | | | | | |
% 159.87/22.21 | | | | | End of split
% 159.87/22.21 | | | | |
% 159.87/22.21 | | | | Case 2:
% 159.87/22.21 | | | | |
% 159.87/22.21 | | | | | (270) all_89_0 = all_89_1
% 159.87/22.21 | | | | |
% 159.87/22.21 | | | | | REDUCE: (21), (270) imply:
% 159.87/22.21 | | | | | (271) $false
% 159.87/22.21 | | | | |
% 159.87/22.21 | | | | | CLOSE: (271) is inconsistent.
% 159.87/22.21 | | | | |
% 159.87/22.21 | | | | End of split
% 159.87/22.21 | | | |
% 159.87/22.21 | | | End of split
% 159.87/22.21 | | |
% 159.87/22.21 | | End of split
% 159.87/22.21 | |
% 159.87/22.21 | End of split
% 159.87/22.21 |
% 159.87/22.21 End of proof
% 159.87/22.21 % SZS output end Proof for theBenchmark
% 159.87/22.21
% 159.87/22.21 21668ms
%------------------------------------------------------------------------------