%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SWC068+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 20:49:29 EDT 2023 % Result : Theorem 119.29s 16.44s % Output : Proof 289.11s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SWC068+1 : TPTP v8.1.2. Released v2.4.0. % 0.00/0.12 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.16/0.33 % Computer : n025.cluster.edu % 0.16/0.33 % Model : x86_64 x86_64 % 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.16/0.33 % Memory : 8042.1875MB % 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.16/0.33 % CPULimit : 300 % 0.16/0.33 % WCLimit : 300 % 0.16/0.33 % DateTime : Mon Aug 28 17:27:54 EDT 2023 % 0.16/0.34 % 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/sandbox/benchmark/theBenchmark.p ... % 0.20/0.61 Running up to 7 provers in parallel. % 0.20/0.62 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.20/0.62 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.20/0.62 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.20/0.62 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.20/0.62 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.20/0.62 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 0.20/0.62 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 4.95/1.43 Prover 4: Preprocessing ... % 4.95/1.44 Prover 1: Preprocessing ... % 5.84/1.51 Prover 0: Preprocessing ... % 5.84/1.51 Prover 2: Preprocessing ... % 5.84/1.51 Prover 3: Preprocessing ... % 5.84/1.51 Prover 6: Preprocessing ... % 5.84/1.51 Prover 5: Preprocessing ... % 15.99/2.92 Prover 2: Proving ... % 16.69/2.97 Prover 5: Constructing countermodel ... % 16.69/2.98 Prover 1: Constructing countermodel ... % 17.00/2.99 Prover 6: Proving ... % 17.00/3.03 Prover 3: Constructing countermodel ... % 22.75/3.78 Prover 0: Proving ... % 23.65/3.87 Prover 4: Constructing countermodel ... % 72.24/10.32 Prover 2: stopped % 72.24/10.34 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 74.54/10.51 Prover 7: Preprocessing ... % 75.44/10.65 Prover 7: Constructing countermodel ... % 77.09/10.84 Prover 3: gave up % 77.09/10.84 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 77.72/10.96 Prover 8: Preprocessing ... % 79.03/11.17 Prover 8: Warning: ignoring some quantifiers % 79.03/11.17 Prover 8: Constructing countermodel ... % 100.57/13.95 Prover 5: stopped % 100.57/13.95 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889 % 100.57/14.04 Prover 9: Preprocessing ... % 108.42/14.96 Prover 9: Constructing countermodel ... % 116.15/15.97 Prover 1: stopped % 116.15/15.98 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 116.81/16.12 Prover 10: Preprocessing ... % 116.81/16.22 Prover 10: Constructing countermodel ... % 119.29/16.42 Prover 9: proved (2468ms) % 119.29/16.44 % 119.29/16.44 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 119.29/16.44 % 119.29/16.44 Prover 0: stopped % 119.29/16.45 Prover 6: stopped % 119.79/16.46 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 119.79/16.46 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 119.79/16.47 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 120.12/16.53 Prover 11: Preprocessing ... % 120.36/16.55 Prover 16: Preprocessing ... % 121.07/16.63 Prover 13: Preprocessing ... % 121.07/16.67 Prover 16: Constructing countermodel ... % 122.13/16.77 Prover 13: Constructing countermodel ... % 125.39/17.26 Prover 11: Constructing countermodel ... % 146.48/20.06 Prover 13: stopped % 146.48/20.06 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085 % 147.43/20.16 Prover 19: Preprocessing ... % 150.83/20.63 Prover 16: stopped % 150.83/20.66 Prover 19: Warning: ignoring some quantifiers % 151.24/20.69 Prover 19: Constructing countermodel ... % 168.50/23.21 Prover 19: stopped % 195.71/27.96 Prover 4: stopped % 204.14/29.85 Prover 7: stopped % 250.92/42.63 Prover 8: stopped % 253.50/43.73 Prover 11: stopped % 287.55/71.59 Prover 10: Found proof (size 400) % 287.55/71.59 Prover 10: proved (55609ms) % 287.55/71.59 % 287.55/71.59 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 287.55/71.59 % 288.04/71.80 % SZS output start Proof for theBenchmark % 288.04/71.81 Assumptions after simplification: % 288.04/71.81 --------------------------------- % 288.04/71.81 % 288.04/71.81 (ax15) % 288.04/71.81 ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ $i(v1) | ~ $i(v0) | ~ ssList(v1) | % 288.04/71.81 ~ ssList(v0) | neq(v0, v1)) & ! [v0: $i] : ( ~ $i(v0) | ~ ssList(v0) | ~ % 288.04/71.81 neq(v0, v0)) % 288.04/71.81 % 288.04/71.82 (ax17) % 288.04/71.82 $i(nil) & ssList(nil) % 288.04/71.82 % 288.04/71.82 (ax26) % 288.04/71.84 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (app(v0, v1) = v2) | ~ $i(v1) | % 288.04/71.84 ~ $i(v0) | ~ ssList(v1) | ~ ssList(v0) | ssList(v2)) % 288.04/71.84 % 288.04/71.84 (ax28) % 288.04/71.84 $i(nil) & ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (app(nil, v0) = v1) | ~ % 288.04/71.84 $i(v0) | ~ ssList(v0)) % 288.04/71.84 % 288.04/71.84 (ax42) % 288.04/71.85 ! [v0: $i] : ( ~ $i(v0) | ~ ssList(v0) | frontsegP(v0, v0)) % 288.04/71.85 % 288.04/71.85 (ax45) % 288.04/71.85 $i(nil) & ! [v0: $i] : ( ~ $i(v0) | ~ ssList(v0) | frontsegP(v0, nil)) % 288.04/71.85 % 288.04/71.85 (ax46) % 288.04/71.85 $i(nil) & ! [v0: $i] : (v0 = nil | ~ $i(v0) | ~ frontsegP(nil, v0) | ~ % 288.04/71.85 ssList(v0)) & ( ~ ssList(nil) | frontsegP(nil, nil)) % 288.04/71.85 % 288.04/71.85 (ax49) % 288.04/71.85 ! [v0: $i] : ( ~ $i(v0) | ~ ssList(v0) | rearsegP(v0, v0)) % 288.04/71.85 % 288.04/71.85 (ax5) % 288.04/71.85 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (app(v1, v2) = v0) | ~ $i(v2) | % 288.04/71.85 ~ $i(v1) | ~ $i(v0) | ~ ssList(v2) | ~ ssList(v1) | ~ ssList(v0) | % 288.04/71.85 frontsegP(v0, v1)) & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ % 288.04/71.85 frontsegP(v0, v1) | ~ ssList(v1) | ~ ssList(v0) | ? [v2: $i] : (app(v1, % 288.04/71.85 v2) = v0 & $i(v2) & ssList(v2))) % 288.04/71.85 % 288.04/71.85 (ax50) % 288.04/71.85 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (app(v2, v0) = v3) % 288.04/71.85 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ rearsegP(v0, v1) | ~ ssList(v2) | % 288.04/71.85 ~ ssList(v1) | ~ ssList(v0) | rearsegP(v3, v1)) % 288.04/71.85 % 288.04/71.85 (ax51) % 288.04/71.85 $i(nil) & ! [v0: $i] : ( ~ $i(v0) | ~ ssList(v0) | rearsegP(v0, nil)) % 288.04/71.85 % 288.04/71.85 (ax52) % 288.04/71.85 $i(nil) & ! [v0: $i] : (v0 = nil | ~ $i(v0) | ~ rearsegP(nil, v0) | ~ % 288.04/71.85 ssList(v0)) & ( ~ ssList(nil) | rearsegP(nil, nil)) % 288.04/71.85 % 288.04/71.85 (ax56) % 288.04/71.86 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 288.04/71.86 $i] : ( ~ (app(v3, v4) = v5) | ~ (app(v2, v0) = v3) | ~ $i(v4) | ~ $i(v2) % 288.04/71.86 | ~ $i(v1) | ~ $i(v0) | ~ segmentP(v0, v1) | ~ ssList(v4) | ~ % 288.04/71.86 ssList(v2) | ~ ssList(v1) | ~ ssList(v0) | segmentP(v5, v1)) % 288.04/71.86 % 288.04/71.86 (ax57) % 288.04/71.86 $i(nil) & ! [v0: $i] : ( ~ $i(v0) | ~ ssList(v0) | segmentP(v0, nil)) % 288.04/71.86 % 288.04/71.86 (ax58) % 288.04/71.86 $i(nil) & ! [v0: $i] : (v0 = nil | ~ $i(v0) | ~ segmentP(nil, v0) | ~ % 288.04/71.86 ssList(v0)) & ( ~ ssList(nil) | segmentP(nil, nil)) % 288.04/71.86 % 288.04/71.86 (ax6) % 288.04/71.86 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (app(v2, v1) = v0) | ~ $i(v2) | % 288.04/71.86 ~ $i(v1) | ~ $i(v0) | ~ ssList(v2) | ~ ssList(v1) | ~ ssList(v0) | % 288.04/71.86 rearsegP(v0, v1)) & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ % 288.04/71.86 rearsegP(v0, v1) | ~ ssList(v1) | ~ ssList(v0) | ? [v2: $i] : (app(v2, % 288.04/71.86 v1) = v0 & $i(v2) & ssList(v2))) % 288.04/71.86 % 288.04/71.86 (ax7) % 288.04/71.86 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 288.04/71.86 (app(v3, v4) = v0) | ~ (app(v2, v1) = v3) | ~ $i(v4) | ~ $i(v2) | ~ % 288.04/71.86 $i(v1) | ~ $i(v0) | ~ ssList(v4) | ~ ssList(v2) | ~ ssList(v1) | ~ % 288.04/71.86 ssList(v0) | segmentP(v0, v1)) & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ % 288.04/71.86 $i(v0) | ~ segmentP(v0, v1) | ~ ssList(v1) | ~ ssList(v0) | ? [v2: $i] : % 288.04/71.86 ? [v3: $i] : ? [v4: $i] : (app(v3, v4) = v0 & app(v2, v1) = v3 & $i(v4) & % 288.04/71.86 $i(v3) & $i(v2) & ssList(v4) & ssList(v2))) % 288.04/71.86 % 288.04/71.86 (ax79) % 288.04/71.87 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v0 | ~ (app(v3, % 288.04/71.87 v1) = v2) | ~ (app(v0, v1) = v2) | ~ $i(v3) | ~ $i(v1) | ~ $i(v0) | % 288.04/71.87 ~ ssList(v3) | ~ ssList(v1) | ~ ssList(v0)) % 288.04/71.87 % 288.04/71.87 (ax80) % 288.04/71.87 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v0 | ~ (app(v1, % 288.04/71.87 v3) = v2) | ~ (app(v1, v0) = v2) | ~ $i(v3) | ~ $i(v1) | ~ $i(v0) | % 288.04/71.87 ~ ssList(v3) | ~ ssList(v1) | ~ ssList(v0)) % 288.04/71.87 % 288.04/71.87 (ax82) % 288.04/71.87 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 288.04/71.87 (app(v2, v3) = v4) | ~ (app(v0, v1) = v2) | ~ $i(v3) | ~ $i(v1) | ~ % 288.04/71.87 $i(v0) | ~ ssList(v3) | ~ ssList(v1) | ~ ssList(v0) | ? [v5: $i] : % 288.04/71.87 (app(v1, v3) = v5 & app(v0, v5) = v4 & $i(v5) & $i(v4))) % 288.04/71.87 % 288.04/71.87 (ax83) % 288.04/71.87 $i(nil) & ! [v0: $i] : ! [v1: $i] : (v1 = nil | ~ (app(v0, v1) = nil) | ~ % 288.04/71.87 $i(v1) | ~ $i(v0) | ~ ssList(v1) | ~ ssList(v0)) & ! [v0: $i] : ! [v1: % 288.04/71.87 $i] : (v0 = nil | ~ (app(v0, v1) = nil) | ~ $i(v1) | ~ $i(v0) | ~ % 288.04/71.87 ssList(v1) | ~ ssList(v0)) & ! [v0: $i] : (v0 = nil | ~ (app(nil, nil) = % 288.04/71.87 v0) | ~ ssList(nil)) % 288.04/71.87 % 288.04/71.87 (ax84) % 288.04/71.87 $i(nil) & ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (app(v0, nil) = v1) | ~ % 288.04/71.87 $i(v0) | ~ ssList(v0)) % 288.04/71.87 % 288.04/71.87 (co1) % 288.04/71.88 $i(nil) & ? [v0: $i] : ? [v1: $i] : (app(v1, v1) = v0 & $i(v1) & $i(v0) & % 288.04/71.88 ssList(v1) & ssList(v0) & ! [v2: $i] : ( ~ $i(v2) | ~ segmentP(v1, v2) | % 288.04/71.88 ~ segmentP(v0, v2) | ~ ssList(v2) | ~ neq(v2, nil)) & ( ~ (v1 = nil) | % 288.04/71.88 ~ (v0 = nil))) % 288.04/71.88 % 288.04/71.88 (function-axioms) % 288.04/71.88 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 288.04/71.88 (cons(v3, v2) = v1) | ~ (cons(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : % 288.04/71.88 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (app(v3, v2) = v1) | ~ (app(v3, v2) % 288.04/71.88 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (tl(v2) = % 288.04/71.88 v1) | ~ (tl(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = % 288.04/71.88 v0 | ~ (hd(v2) = v1) | ~ (hd(v2) = v0)) % 288.04/71.88 % 288.04/71.88 Further assumptions not needed in the proof: % 288.04/71.88 -------------------------------------------- % 288.04/71.88 ax1, ax10, ax11, ax12, ax13, ax14, ax16, ax18, ax19, ax2, ax20, ax21, ax22, % 288.04/71.88 ax23, ax24, ax25, ax27, ax29, ax3, ax30, ax31, ax32, ax33, ax34, ax35, ax36, % 288.04/71.88 ax37, ax38, ax39, ax4, ax40, ax41, ax43, ax44, ax47, ax48, ax53, ax54, ax55, % 288.04/71.88 ax59, ax60, ax61, ax62, ax63, ax64, ax65, ax66, ax67, ax68, ax69, ax70, ax71, % 288.04/71.88 ax72, ax73, ax74, ax75, ax76, ax77, ax78, ax8, ax81, ax85, ax86, ax87, ax88, % 288.04/71.88 ax89, ax9, ax90, ax91, ax92, ax93, ax94, ax95 % 288.04/71.88 % 288.04/71.88 Those formulas are unsatisfiable: % 288.04/71.88 --------------------------------- % 288.04/71.88 % 288.04/71.88 Begin of proof % 288.04/71.88 | % 288.04/71.88 | ALPHA: (ax5) implies: % 288.04/71.88 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ frontsegP(v0, % 288.04/71.88 | v1) | ~ ssList(v1) | ~ ssList(v0) | ? [v2: $i] : (app(v1, v2) = % 288.04/71.88 | v0 & $i(v2) & ssList(v2))) % 288.04/71.89 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (app(v1, v2) = v0) | ~ % 288.04/71.89 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ ssList(v2) | ~ ssList(v1) | ~ % 288.04/71.89 | ssList(v0) | frontsegP(v0, v1)) % 288.04/71.89 | % 288.04/71.89 | ALPHA: (ax6) implies: % 288.04/71.89 | (3) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ rearsegP(v0, % 288.04/71.89 | v1) | ~ ssList(v1) | ~ ssList(v0) | ? [v2: $i] : (app(v2, v1) = % 288.04/71.89 | v0 & $i(v2) & ssList(v2))) % 288.04/71.89 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (app(v2, v1) = v0) | ~ % 288.04/71.89 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ ssList(v2) | ~ ssList(v1) | ~ % 288.04/71.89 | ssList(v0) | rearsegP(v0, v1)) % 288.04/71.89 | % 288.04/71.89 | ALPHA: (ax7) implies: % 288.04/71.89 | (5) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ segmentP(v0, % 288.04/71.89 | v1) | ~ ssList(v1) | ~ ssList(v0) | ? [v2: $i] : ? [v3: $i] : % 288.04/71.89 | ? [v4: $i] : (app(v3, v4) = v0 & app(v2, v1) = v3 & $i(v4) & $i(v3) & % 288.04/71.89 | $i(v2) & ssList(v4) & ssList(v2))) % 288.04/71.89 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( % 288.04/71.89 | ~ (app(v3, v4) = v0) | ~ (app(v2, v1) = v3) | ~ $i(v4) | ~ $i(v2) % 288.04/71.89 | | ~ $i(v1) | ~ $i(v0) | ~ ssList(v4) | ~ ssList(v2) | ~ % 288.04/71.89 | ssList(v1) | ~ ssList(v0) | segmentP(v0, v1)) % 288.04/71.89 | % 288.04/71.89 | ALPHA: (ax15) implies: % 288.04/71.89 | (7) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ $i(v1) | ~ $i(v0) | ~ % 288.04/71.89 | ssList(v1) | ~ ssList(v0) | neq(v0, v1)) % 288.04/71.89 | % 288.04/71.89 | ALPHA: (ax17) implies: % 288.04/71.89 | (8) ssList(nil) % 288.04/71.89 | % 288.04/71.89 | ALPHA: (ax28) implies: % 288.04/71.89 | (9) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (app(nil, v0) = v1) | ~ % 288.04/71.89 | $i(v0) | ~ ssList(v0)) % 288.04/71.89 | % 288.04/71.89 | ALPHA: (ax45) implies: % 288.04/71.89 | (10) ! [v0: $i] : ( ~ $i(v0) | ~ ssList(v0) | frontsegP(v0, nil)) % 288.04/71.89 | % 288.04/71.89 | ALPHA: (ax46) implies: % 288.04/71.90 | (11) ~ ssList(nil) | frontsegP(nil, nil) % 288.04/71.90 | % 288.04/71.90 | ALPHA: (ax51) implies: % 288.04/71.90 | (12) ! [v0: $i] : ( ~ $i(v0) | ~ ssList(v0) | rearsegP(v0, nil)) % 288.04/71.90 | % 288.04/71.90 | ALPHA: (ax52) implies: % 288.04/71.90 | (13) ~ ssList(nil) | rearsegP(nil, nil) % 288.04/71.90 | % 288.04/71.90 | ALPHA: (ax57) implies: % 288.04/71.90 | (14) ! [v0: $i] : ( ~ $i(v0) | ~ ssList(v0) | segmentP(v0, nil)) % 288.04/71.90 | % 288.04/71.90 | ALPHA: (ax58) implies: % 288.04/71.90 | (15) ~ ssList(nil) | segmentP(nil, nil) % 288.04/71.90 | % 288.04/71.90 | ALPHA: (ax83) implies: % 288.04/71.90 | (16) ! [v0: $i] : (v0 = nil | ~ (app(nil, nil) = v0) | ~ ssList(nil)) % 288.04/71.90 | (17) ! [v0: $i] : ! [v1: $i] : (v0 = nil | ~ (app(v0, v1) = nil) | ~ % 288.04/71.90 | $i(v1) | ~ $i(v0) | ~ ssList(v1) | ~ ssList(v0)) % 288.04/71.90 | (18) ! [v0: $i] : ! [v1: $i] : (v1 = nil | ~ (app(v0, v1) = nil) | ~ % 288.04/71.90 | $i(v1) | ~ $i(v0) | ~ ssList(v1) | ~ ssList(v0)) % 288.04/71.90 | % 288.04/71.90 | ALPHA: (ax84) implies: % 288.04/71.90 | (19) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (app(v0, nil) = v1) | ~ % 288.04/71.90 | $i(v0) | ~ ssList(v0)) % 288.04/71.90 | % 288.04/71.90 | ALPHA: (co1) implies: % 288.04/71.90 | (20) $i(nil) % 288.04/71.90 | (21) ? [v0: $i] : ? [v1: $i] : (app(v1, v1) = v0 & $i(v1) & $i(v0) & % 288.04/71.90 | ssList(v1) & ssList(v0) & ! [v2: $i] : ( ~ $i(v2) | ~ segmentP(v1, % 288.04/71.90 | v2) | ~ segmentP(v0, v2) | ~ ssList(v2) | ~ neq(v2, nil)) & ( % 288.04/71.90 | ~ (v1 = nil) | ~ (v0 = nil))) % 288.04/71.90 | % 288.04/71.90 | ALPHA: (function-axioms) implies: % 288.04/71.90 | (22) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 288.04/71.90 | (app(v3, v2) = v1) | ~ (app(v3, v2) = v0)) % 288.04/71.90 | % 288.04/71.90 | DELTA: instantiating (21) with fresh symbols all_91_0, all_91_1 gives: % 288.04/71.90 | (23) app(all_91_0, all_91_0) = all_91_1 & $i(all_91_0) & $i(all_91_1) & % 288.04/71.90 | ssList(all_91_0) & ssList(all_91_1) & ! [v0: $i] : ( ~ $i(v0) | ~ % 288.04/71.90 | segmentP(all_91_0, v0) | ~ segmentP(all_91_1, v0) | ~ ssList(v0) | % 288.04/71.90 | ~ neq(v0, nil)) & ( ~ (all_91_0 = nil) | ~ (all_91_1 = nil)) % 288.04/71.90 | % 288.04/71.90 | ALPHA: (23) implies: % 288.04/71.90 | (24) ssList(all_91_1) % 288.04/71.90 | (25) ssList(all_91_0) % 288.04/71.90 | (26) $i(all_91_1) % 288.04/71.91 | (27) $i(all_91_0) % 288.04/71.91 | (28) app(all_91_0, all_91_0) = all_91_1 % 288.04/71.91 | (29) ~ (all_91_0 = nil) | ~ (all_91_1 = nil) % 288.04/71.91 | (30) ! [v0: $i] : ( ~ $i(v0) | ~ segmentP(all_91_0, v0) | ~ % 288.04/71.91 | segmentP(all_91_1, v0) | ~ ssList(v0) | ~ neq(v0, nil)) % 288.04/71.91 | % 288.04/71.91 | BETA: splitting (13) gives: % 288.04/71.91 | % 288.04/71.91 | Case 1: % 288.04/71.91 | | % 288.04/71.91 | | (31) ~ ssList(nil) % 288.04/71.91 | | % 288.04/71.91 | | PRED_UNIFY: (8), (31) imply: % 288.04/71.91 | | (32) $false % 288.04/71.91 | | % 288.04/71.91 | | CLOSE: (32) is inconsistent. % 288.04/71.91 | | % 288.04/71.91 | Case 2: % 288.04/71.91 | | % 288.04/71.91 | | (33) rearsegP(nil, nil) % 288.04/71.91 | | % 288.04/71.91 | | BETA: splitting (11) gives: % 288.04/71.91 | | % 288.04/71.91 | | Case 1: % 288.04/71.91 | | | % 288.04/71.91 | | | (34) ~ ssList(nil) % 288.04/71.91 | | | % 288.04/71.91 | | | PRED_UNIFY: (8), (34) imply: % 288.04/71.91 | | | (35) $false % 288.04/71.91 | | | % 288.04/71.91 | | | CLOSE: (35) is inconsistent. % 288.04/71.91 | | | % 288.04/71.91 | | Case 2: % 288.04/71.91 | | | % 288.04/71.91 | | | (36) frontsegP(nil, nil) % 288.04/71.91 | | | % 288.04/71.91 | | | BETA: splitting (15) gives: % 288.04/71.91 | | | % 288.04/71.91 | | | Case 1: % 288.04/71.91 | | | | % 288.04/71.91 | | | | (37) ~ ssList(nil) % 288.04/71.91 | | | | % 288.04/71.91 | | | | PRED_UNIFY: (8), (37) imply: % 288.04/71.91 | | | | (38) $false % 288.04/71.91 | | | | % 288.04/71.91 | | | | CLOSE: (38) is inconsistent. % 288.04/71.91 | | | | % 288.04/71.91 | | | Case 2: % 288.04/71.91 | | | | % 288.04/71.91 | | | | (39) segmentP(nil, nil) % 288.04/71.91 | | | | % 288.04/71.91 | | | | GROUND_INST: instantiating (ax49) with all_91_1, simplifying with (24), % 288.04/71.91 | | | | (26) gives: % 288.04/71.91 | | | | (40) rearsegP(all_91_1, all_91_1) % 288.04/71.91 | | | | % 288.04/71.91 | | | | GROUND_INST: instantiating (12) with all_91_1, simplifying with (24), % 288.04/71.91 | | | | (26) gives: % 288.04/71.92 | | | | (41) rearsegP(all_91_1, nil) % 288.04/71.92 | | | | % 288.04/71.92 | | | | GROUND_INST: instantiating (ax42) with all_91_1, simplifying with (24), % 288.04/71.92 | | | | (26) gives: % 288.04/71.92 | | | | (42) frontsegP(all_91_1, all_91_1) % 288.04/71.92 | | | | % 288.04/71.92 | | | | GROUND_INST: instantiating (10) with all_91_1, simplifying with (24), % 288.04/71.92 | | | | (26) gives: % 288.04/71.92 | | | | (43) frontsegP(all_91_1, nil) % 288.04/71.92 | | | | % 288.04/71.92 | | | | GROUND_INST: instantiating (7) with all_91_0, nil, simplifying with (8), % 288.04/71.92 | | | | (20), (25), (27) gives: % 288.04/71.92 | | | | (44) all_91_0 = nil | neq(all_91_0, nil) % 288.04/71.92 | | | | % 288.04/71.92 | | | | GROUND_INST: instantiating (14) with all_91_0, simplifying with (25), % 288.04/71.92 | | | | (27) gives: % 288.04/71.92 | | | | (45) segmentP(all_91_0, nil) % 288.04/71.92 | | | | % 288.04/71.92 | | | | GROUND_INST: instantiating (ax49) with all_91_0, simplifying with (25), % 288.04/71.92 | | | | (27) gives: % 288.04/71.92 | | | | (46) rearsegP(all_91_0, all_91_0) % 288.04/71.92 | | | | % 288.04/71.92 | | | | GROUND_INST: instantiating (12) with all_91_0, simplifying with (25), % 288.04/71.92 | | | | (27) gives: % 288.04/71.92 | | | | (47) rearsegP(all_91_0, nil) % 288.04/71.92 | | | | % 288.04/71.92 | | | | GROUND_INST: instantiating (ax42) with all_91_0, simplifying with (25), % 288.04/71.92 | | | | (27) gives: % 288.04/71.92 | | | | (48) frontsegP(all_91_0, all_91_0) % 288.04/71.92 | | | | % 288.04/71.92 | | | | GROUND_INST: instantiating (10) with all_91_0, simplifying with (25), % 288.04/71.92 | | | | (27) gives: % 288.04/71.92 | | | | (49) frontsegP(all_91_0, nil) % 288.04/71.92 | | | | % 288.04/71.92 | | | | GROUND_INST: instantiating (1) with nil, nil, simplifying with (8), % 288.04/71.92 | | | | (20), (36) gives: % 288.04/71.92 | | | | (50) ? [v0: $i] : (app(nil, v0) = nil & $i(v0) & ssList(v0)) % 288.04/71.92 | | | | % 288.04/71.92 | | | | GROUND_INST: instantiating (5) with nil, nil, simplifying with (8), % 288.04/71.92 | | | | (20), (39) gives: % 288.04/71.92 | | | | (51) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (app(v1, v2) = nil & % 288.04/71.92 | | | | app(v0, nil) = v1 & $i(v2) & $i(v1) & $i(v0) & ssList(v2) & % 288.04/71.92 | | | | ssList(v0)) % 288.04/71.92 | | | | % 288.04/71.92 | | | | GROUND_INST: instantiating (2) with all_91_1, all_91_0, all_91_0, % 288.04/71.92 | | | | simplifying with (24), (25), (26), (27), (28) gives: % 288.04/71.92 | | | | (52) frontsegP(all_91_1, all_91_0) % 288.04/71.92 | | | | % 288.04/71.92 | | | | GROUND_INST: instantiating (4) with all_91_1, all_91_0, all_91_0, % 288.04/71.92 | | | | simplifying with (24), (25), (26), (27), (28) gives: % 288.04/71.92 | | | | (53) rearsegP(all_91_1, all_91_0) % 288.04/71.92 | | | | % 288.04/71.92 | | | | DELTA: instantiating (50) with fresh symbol all_112_0 gives: % 288.04/71.92 | | | | (54) app(nil, all_112_0) = nil & $i(all_112_0) & ssList(all_112_0) % 288.04/71.92 | | | | % 288.04/71.92 | | | | ALPHA: (54) implies: % 288.04/71.92 | | | | (55) ssList(all_112_0) % 288.04/71.92 | | | | (56) $i(all_112_0) % 288.04/71.92 | | | | (57) app(nil, all_112_0) = nil % 288.04/71.92 | | | | % 288.04/71.92 | | | | DELTA: instantiating (51) with fresh symbols all_116_0, all_116_1, % 288.04/71.92 | | | | all_116_2 gives: % 288.04/71.92 | | | | (58) app(all_116_1, all_116_0) = nil & app(all_116_2, nil) = % 288.04/71.92 | | | | all_116_1 & $i(all_116_0) & $i(all_116_1) & $i(all_116_2) & % 288.04/71.92 | | | | ssList(all_116_0) & ssList(all_116_2) % 288.04/71.92 | | | | % 288.04/71.92 | | | | ALPHA: (58) implies: % 288.04/71.92 | | | | (59) ssList(all_116_2) % 288.04/71.92 | | | | (60) ssList(all_116_0) % 288.04/71.92 | | | | (61) $i(all_116_2) % 288.04/71.92 | | | | (62) $i(all_116_1) % 288.04/71.92 | | | | (63) $i(all_116_0) % 288.04/71.92 | | | | (64) app(all_116_2, nil) = all_116_1 % 288.04/71.92 | | | | (65) app(all_116_1, all_116_0) = nil % 288.04/71.92 | | | | % 288.04/71.92 | | | | GROUND_INST: instantiating (ax49) with all_116_2, simplifying with (59), % 288.04/71.92 | | | | (61) gives: % 288.04/71.92 | | | | (66) rearsegP(all_116_2, all_116_2) % 288.04/71.92 | | | | % 288.04/71.92 | | | | GROUND_INST: instantiating (ax42) with all_116_2, simplifying with (59), % 288.04/71.93 | | | | (61) gives: % 288.04/71.93 | | | | (67) frontsegP(all_116_2, all_116_2) % 288.04/71.93 | | | | % 288.04/71.93 | | | | GROUND_INST: instantiating (10) with all_116_2, simplifying with (59), % 288.04/71.93 | | | | (61) gives: % 288.04/71.93 | | | | (68) frontsegP(all_116_2, nil) % 288.04/71.93 | | | | % 288.04/71.93 | | | | GROUND_INST: instantiating (ax49) with all_116_0, simplifying with (60), % 288.04/71.93 | | | | (63) gives: % 288.04/71.93 | | | | (69) rearsegP(all_116_0, all_116_0) % 288.04/71.93 | | | | % 288.04/71.93 | | | | GROUND_INST: instantiating (12) with all_116_0, simplifying with (60), % 288.04/71.93 | | | | (63) gives: % 288.04/71.93 | | | | (70) rearsegP(all_116_0, nil) % 288.04/71.93 | | | | % 288.04/71.93 | | | | GROUND_INST: instantiating (ax42) with all_116_0, simplifying with (60), % 288.04/71.93 | | | | (63) gives: % 288.04/71.93 | | | | (71) frontsegP(all_116_0, all_116_0) % 288.04/71.93 | | | | % 288.04/71.93 | | | | GROUND_INST: instantiating (10) with all_116_0, simplifying with (60), % 288.04/71.93 | | | | (63) gives: % 288.04/71.93 | | | | (72) frontsegP(all_116_0, nil) % 288.04/71.93 | | | | % 288.04/71.93 | | | | GROUND_INST: instantiating (1) with all_91_1, nil, simplifying with (8), % 288.04/71.93 | | | | (20), (24), (26), (43) gives: % 288.04/71.93 | | | | (73) ? [v0: $i] : (app(nil, v0) = all_91_1 & $i(v0) & ssList(v0)) % 288.04/71.93 | | | | % 288.04/71.93 | | | | GROUND_INST: instantiating (1) with all_91_1, all_91_1, simplifying with % 288.04/71.93 | | | | (24), (26), (42) gives: % 288.04/71.93 | | | | (74) ? [v0: $i] : (app(all_91_1, v0) = all_91_1 & $i(v0) & % 288.04/71.93 | | | | ssList(v0)) % 288.04/71.93 | | | | % 288.04/71.93 | | | | GROUND_INST: instantiating (1) with all_91_1, all_91_0, simplifying with % 288.04/71.93 | | | | (24), (25), (26), (27), (52) gives: % 288.04/71.93 | | | | (75) ? [v0: $i] : (app(all_91_0, v0) = all_91_1 & $i(v0) & % 288.04/71.93 | | | | ssList(v0)) % 288.04/71.93 | | | | % 288.04/71.93 | | | | GROUND_INST: instantiating (1) with all_91_0, nil, simplifying with (8), % 288.04/71.93 | | | | (20), (25), (27), (49) gives: % 288.04/71.93 | | | | (76) ? [v0: $i] : (app(nil, v0) = all_91_0 & $i(v0) & ssList(v0)) % 288.04/71.93 | | | | % 288.04/71.93 | | | | GROUND_INST: instantiating (1) with all_91_0, all_91_0, simplifying with % 288.04/71.93 | | | | (25), (27), (48) gives: % 288.04/71.93 | | | | (77) ? [v0: $i] : (app(all_91_0, v0) = all_91_0 & $i(v0) & % 288.04/71.93 | | | | ssList(v0)) % 288.04/71.93 | | | | % 288.04/71.93 | | | | GROUND_INST: instantiating (3) with all_91_1, nil, simplifying with (8), % 288.04/71.93 | | | | (20), (24), (26), (41) gives: % 288.04/71.93 | | | | (78) ? [v0: $i] : (app(v0, nil) = all_91_1 & $i(v0) & ssList(v0)) % 288.04/71.93 | | | | % 288.04/71.93 | | | | GROUND_INST: instantiating (3) with all_91_1, all_91_1, simplifying with % 288.04/71.93 | | | | (24), (26), (40) gives: % 288.04/71.93 | | | | (79) ? [v0: $i] : (app(v0, all_91_1) = all_91_1 & $i(v0) & % 288.04/71.93 | | | | ssList(v0)) % 288.04/71.93 | | | | % 288.04/71.93 | | | | GROUND_INST: instantiating (3) with all_91_1, all_91_0, simplifying with % 288.04/71.93 | | | | (24), (25), (26), (27), (53) gives: % 288.04/71.93 | | | | (80) ? [v0: $i] : (app(v0, all_91_0) = all_91_1 & $i(v0) & % 288.04/71.93 | | | | ssList(v0)) % 288.04/71.93 | | | | % 288.04/71.94 | | | | GROUND_INST: instantiating (3) with all_91_0, nil, simplifying with (8), % 288.04/71.94 | | | | (20), (25), (27), (47) gives: % 288.04/71.94 | | | | (81) ? [v0: $i] : (app(v0, nil) = all_91_0 & $i(v0) & ssList(v0)) % 288.04/71.94 | | | | % 288.04/71.94 | | | | GROUND_INST: instantiating (3) with all_91_0, all_91_0, simplifying with % 288.04/71.94 | | | | (25), (27), (46) gives: % 288.04/71.94 | | | | (82) ? [v0: $i] : (app(v0, all_91_0) = all_91_0 & $i(v0) & % 288.04/71.94 | | | | ssList(v0)) % 288.04/71.94 | | | | % 288.04/71.94 | | | | GROUND_INST: instantiating (5) with all_91_0, nil, simplifying with (8), % 288.04/71.94 | | | | (20), (25), (27), (45) gives: % 288.04/71.94 | | | | (83) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (app(v1, v2) = % 288.04/71.94 | | | | all_91_0 & app(v0, nil) = v1 & $i(v2) & $i(v1) & $i(v0) & % 288.04/71.94 | | | | ssList(v2) & ssList(v0)) % 288.04/71.94 | | | | % 288.04/71.94 | | | | GROUND_INST: instantiating (ax82) with nil, all_112_0, nil, all_112_0, % 288.04/71.94 | | | | nil, simplifying with (8), (20), (55), (56), (57) gives: % 288.04/71.94 | | | | (84) ? [v0: $i] : (app(all_112_0, all_112_0) = v0 & app(nil, v0) = % 288.04/71.94 | | | | nil & $i(v0)) % 288.04/71.94 | | | | % 288.04/71.94 | | | | GROUND_INST: instantiating (9) with all_112_0, nil, simplifying with % 288.04/71.94 | | | | (55), (56), (57) gives: % 288.04/71.94 | | | | (85) all_112_0 = nil % 288.04/71.94 | | | | % 288.04/71.94 | | | | GROUND_INST: instantiating (ax50) with nil, nil, all_116_2, all_116_1, % 288.04/71.94 | | | | simplifying with (8), (20), (33), (59), (61), (64) gives: % 288.04/71.94 | | | | (86) rearsegP(all_116_1, nil) % 288.04/71.94 | | | | % 288.04/71.94 | | | | GROUND_INST: instantiating (ax26) with all_116_2, nil, all_116_1, % 288.04/71.94 | | | | simplifying with (8), (20), (59), (61), (64) gives: % 288.04/71.94 | | | | (87) ssList(all_116_1) % 288.04/71.94 | | | | % 288.04/71.94 | | | | GROUND_INST: instantiating (19) with all_116_2, all_116_1, simplifying % 288.04/71.94 | | | | with (59), (61), (64) gives: % 288.04/71.94 | | | | (88) all_116_1 = all_116_2 % 288.04/71.94 | | | | % 288.74/71.94 | | | | GROUND_INST: instantiating (ax82) with all_116_2, nil, all_116_1, % 288.74/71.94 | | | | all_116_0, nil, simplifying with (8), (20), (59), (60), % 288.74/71.94 | | | | (61), (63), (64), (65) gives: % 288.74/71.94 | | | | (89) ? [v0: $i] : (app(all_116_2, v0) = nil & app(nil, all_116_0) = % 288.74/71.94 | | | | v0 & $i(v0)) % 288.74/71.94 | | | | % 288.74/71.94 | | | | DELTA: instantiating (76) with fresh symbol all_132_0 gives: % 288.74/71.94 | | | | (90) app(nil, all_132_0) = all_91_0 & $i(all_132_0) & % 288.74/71.94 | | | | ssList(all_132_0) % 288.74/71.94 | | | | % 288.74/71.94 | | | | ALPHA: (90) implies: % 288.74/71.94 | | | | (91) ssList(all_132_0) % 288.74/71.94 | | | | (92) $i(all_132_0) % 288.74/71.94 | | | | (93) app(nil, all_132_0) = all_91_0 % 288.74/71.94 | | | | % 288.74/71.94 | | | | DELTA: instantiating (75) with fresh symbol all_134_0 gives: % 288.74/71.94 | | | | (94) app(all_91_0, all_134_0) = all_91_1 & $i(all_134_0) & % 288.74/71.94 | | | | ssList(all_134_0) % 288.74/71.94 | | | | % 288.74/71.94 | | | | ALPHA: (94) implies: % 288.74/71.94 | | | | (95) ssList(all_134_0) % 288.74/71.94 | | | | (96) $i(all_134_0) % 288.74/71.94 | | | | (97) app(all_91_0, all_134_0) = all_91_1 % 288.74/71.94 | | | | % 288.74/71.94 | | | | DELTA: instantiating (82) with fresh symbol all_136_0 gives: % 288.74/71.95 | | | | (98) app(all_136_0, all_91_0) = all_91_0 & $i(all_136_0) & % 288.74/71.95 | | | | ssList(all_136_0) % 288.74/71.95 | | | | % 288.74/71.95 | | | | ALPHA: (98) implies: % 288.74/71.95 | | | | (99) ssList(all_136_0) % 288.74/71.95 | | | | (100) $i(all_136_0) % 288.74/71.95 | | | | (101) app(all_136_0, all_91_0) = all_91_0 % 288.74/71.95 | | | | % 288.74/71.95 | | | | DELTA: instantiating (84) with fresh symbol all_138_0 gives: % 288.74/71.95 | | | | (102) app(all_112_0, all_112_0) = all_138_0 & app(nil, all_138_0) = % 288.74/71.95 | | | | nil & $i(all_138_0) % 288.74/71.95 | | | | % 288.74/71.95 | | | | ALPHA: (102) implies: % 288.74/71.95 | | | | (103) $i(all_138_0) % 288.74/71.95 | | | | (104) app(all_112_0, all_112_0) = all_138_0 % 288.74/71.95 | | | | % 288.74/71.95 | | | | DELTA: instantiating (89) with fresh symbol all_140_0 gives: % 288.74/71.95 | | | | (105) app(all_116_2, all_140_0) = nil & app(nil, all_116_0) = % 288.74/71.95 | | | | all_140_0 & $i(all_140_0) % 288.74/71.95 | | | | % 288.74/71.95 | | | | ALPHA: (105) implies: % 288.74/71.95 | | | | (106) app(nil, all_116_0) = all_140_0 % 288.74/71.95 | | | | % 288.74/71.95 | | | | DELTA: instantiating (81) with fresh symbol all_142_0 gives: % 288.74/71.95 | | | | (107) app(all_142_0, nil) = all_91_0 & $i(all_142_0) & % 288.74/71.95 | | | | ssList(all_142_0) % 288.74/71.95 | | | | % 288.74/71.95 | | | | ALPHA: (107) implies: % 288.74/71.95 | | | | (108) ssList(all_142_0) % 288.74/71.95 | | | | (109) $i(all_142_0) % 288.74/71.95 | | | | (110) app(all_142_0, nil) = all_91_0 % 288.74/71.95 | | | | % 288.74/71.95 | | | | DELTA: instantiating (74) with fresh symbol all_144_0 gives: % 288.74/71.95 | | | | (111) app(all_91_1, all_144_0) = all_91_1 & $i(all_144_0) & % 288.74/71.95 | | | | ssList(all_144_0) % 288.74/71.95 | | | | % 288.74/71.95 | | | | ALPHA: (111) implies: % 288.74/71.95 | | | | (112) ssList(all_144_0) % 288.74/71.95 | | | | (113) $i(all_144_0) % 288.74/71.95 | | | | (114) app(all_91_1, all_144_0) = all_91_1 % 288.74/71.95 | | | | % 288.74/71.95 | | | | DELTA: instantiating (73) with fresh symbol all_146_0 gives: % 288.74/71.95 | | | | (115) app(nil, all_146_0) = all_91_1 & $i(all_146_0) & % 288.74/71.95 | | | | ssList(all_146_0) % 288.74/71.95 | | | | % 288.74/71.95 | | | | ALPHA: (115) implies: % 288.74/71.95 | | | | (116) ssList(all_146_0) % 288.74/71.95 | | | | (117) $i(all_146_0) % 288.74/71.95 | | | | (118) app(nil, all_146_0) = all_91_1 % 288.74/71.95 | | | | % 288.74/71.95 | | | | DELTA: instantiating (80) with fresh symbol all_148_0 gives: % 288.74/71.95 | | | | (119) app(all_148_0, all_91_0) = all_91_1 & $i(all_148_0) & % 288.74/71.95 | | | | ssList(all_148_0) % 288.74/71.95 | | | | % 288.74/71.95 | | | | ALPHA: (119) implies: % 288.74/71.95 | | | | (120) ssList(all_148_0) % 288.74/71.95 | | | | (121) $i(all_148_0) % 288.74/71.95 | | | | (122) app(all_148_0, all_91_0) = all_91_1 % 288.74/71.95 | | | | % 288.74/71.95 | | | | DELTA: instantiating (79) with fresh symbol all_150_0 gives: % 288.74/71.95 | | | | (123) app(all_150_0, all_91_1) = all_91_1 & $i(all_150_0) & % 288.74/71.95 | | | | ssList(all_150_0) % 288.74/71.95 | | | | % 288.74/71.95 | | | | ALPHA: (123) implies: % 288.74/71.95 | | | | (124) ssList(all_150_0) % 288.74/71.95 | | | | (125) $i(all_150_0) % 288.74/71.95 | | | | (126) app(all_150_0, all_91_1) = all_91_1 % 288.74/71.95 | | | | % 288.74/71.95 | | | | DELTA: instantiating (78) with fresh symbol all_152_0 gives: % 288.74/71.95 | | | | (127) app(all_152_0, nil) = all_91_1 & $i(all_152_0) & % 288.74/71.95 | | | | ssList(all_152_0) % 288.74/71.95 | | | | % 288.74/71.95 | | | | ALPHA: (127) implies: % 288.74/71.95 | | | | (128) ssList(all_152_0) % 288.74/71.95 | | | | (129) $i(all_152_0) % 288.74/71.95 | | | | (130) app(all_152_0, nil) = all_91_1 % 288.74/71.95 | | | | % 288.74/71.95 | | | | DELTA: instantiating (77) with fresh symbol all_154_0 gives: % 288.74/71.95 | | | | (131) app(all_91_0, all_154_0) = all_91_0 & $i(all_154_0) & % 288.74/71.95 | | | | ssList(all_154_0) % 288.74/71.95 | | | | % 288.74/71.95 | | | | ALPHA: (131) implies: % 288.74/71.95 | | | | (132) ssList(all_154_0) % 288.74/71.95 | | | | (133) $i(all_154_0) % 288.74/71.95 | | | | (134) app(all_91_0, all_154_0) = all_91_0 % 288.74/71.95 | | | | % 288.74/71.95 | | | | DELTA: instantiating (83) with fresh symbols all_162_0, all_162_1, % 288.74/71.95 | | | | all_162_2 gives: % 288.74/71.95 | | | | (135) app(all_162_1, all_162_0) = all_91_0 & app(all_162_2, nil) = % 288.74/71.95 | | | | all_162_1 & $i(all_162_0) & $i(all_162_1) & $i(all_162_2) & % 288.74/71.95 | | | | ssList(all_162_0) & ssList(all_162_2) % 288.74/71.95 | | | | % 288.74/71.95 | | | | ALPHA: (135) implies: % 288.74/71.95 | | | | (136) ssList(all_162_2) % 288.74/71.96 | | | | (137) ssList(all_162_0) % 288.74/71.96 | | | | (138) $i(all_162_2) % 288.74/71.96 | | | | (139) $i(all_162_1) % 288.74/71.96 | | | | (140) $i(all_162_0) % 288.74/71.96 | | | | (141) app(all_162_2, nil) = all_162_1 % 288.74/71.96 | | | | (142) app(all_162_1, all_162_0) = all_91_0 % 288.74/71.96 | | | | % 288.74/71.96 | | | | REDUCE: (65), (88) imply: % 288.74/71.96 | | | | (143) app(all_116_2, all_116_0) = nil % 288.74/71.96 | | | | % 288.74/71.96 | | | | REDUCE: (85), (104) imply: % 288.74/71.96 | | | | (144) app(nil, nil) = all_138_0 % 288.74/71.96 | | | | % 288.74/71.96 | | | | REDUCE: (86), (88) imply: % 288.74/71.96 | | | | (145) rearsegP(all_116_2, nil) % 288.74/71.96 | | | | % 288.74/71.96 | | | | GROUND_INST: instantiating (16) with all_138_0, simplifying with (8), % 288.74/71.96 | | | | (144) gives: % 288.74/71.96 | | | | (146) all_138_0 = nil % 288.74/71.96 | | | | % 288.74/71.96 | | | | REDUCE: (144), (146) imply: % 288.74/71.96 | | | | (147) app(nil, nil) = nil % 288.74/71.96 | | | | % 288.74/71.96 | | | | GROUND_INST: instantiating (1) with all_116_2, nil, simplifying with % 288.74/71.96 | | | | (8), (20), (59), (61), (68) gives: % 288.74/71.96 | | | | (148) ? [v0: $i] : (app(nil, v0) = all_116_2 & $i(v0) & ssList(v0)) % 288.74/71.96 | | | | % 288.74/71.96 | | | | GROUND_INST: instantiating (1) with all_116_2, all_116_2, simplifying % 288.74/71.96 | | | | with (59), (61), (67) gives: % 288.74/71.96 | | | | (149) ? [v0: $i] : (app(all_116_2, v0) = all_116_2 & $i(v0) & % 288.74/71.96 | | | | ssList(v0)) % 288.74/71.96 | | | | % 288.74/71.96 | | | | GROUND_INST: instantiating (1) with all_116_0, nil, simplifying with % 288.74/71.96 | | | | (8), (20), (60), (63), (72) gives: % 288.74/71.96 | | | | (150) ? [v0: $i] : (app(nil, v0) = all_116_0 & $i(v0) & ssList(v0)) % 288.74/71.96 | | | | % 288.74/71.96 | | | | GROUND_INST: instantiating (1) with all_116_0, all_116_0, simplifying % 288.74/71.96 | | | | with (60), (63), (71) gives: % 288.74/71.96 | | | | (151) ? [v0: $i] : (app(all_116_0, v0) = all_116_0 & $i(v0) & % 288.74/71.96 | | | | ssList(v0)) % 288.74/71.96 | | | | % 288.74/71.96 | | | | GROUND_INST: instantiating (3) with all_116_2, nil, simplifying with % 288.74/71.96 | | | | (8), (20), (59), (61), (145) gives: % 288.74/71.96 | | | | (152) ? [v0: $i] : (app(v0, nil) = all_116_2 & $i(v0) & ssList(v0)) % 288.74/71.96 | | | | % 288.74/71.96 | | | | GROUND_INST: instantiating (3) with all_116_2, all_116_2, simplifying % 288.74/71.96 | | | | with (59), (61), (66) gives: % 288.74/71.96 | | | | (153) ? [v0: $i] : (app(v0, all_116_2) = all_116_2 & $i(v0) & % 288.74/71.96 | | | | ssList(v0)) % 288.74/71.96 | | | | % 288.74/71.96 | | | | GROUND_INST: instantiating (3) with all_116_0, nil, simplifying with % 288.74/71.96 | | | | (8), (20), (60), (63), (70) gives: % 288.74/71.96 | | | | (154) ? [v0: $i] : (app(v0, nil) = all_116_0 & $i(v0) & ssList(v0)) % 288.74/71.96 | | | | % 288.74/71.97 | | | | GROUND_INST: instantiating (3) with all_116_0, all_116_0, simplifying % 288.74/71.97 | | | | with (60), (63), (69) gives: % 288.74/71.97 | | | | (155) ? [v0: $i] : (app(v0, all_116_0) = all_116_0 & $i(v0) & % 288.74/71.97 | | | | ssList(v0)) % 288.74/71.97 | | | | % 288.74/71.97 | | | | GROUND_INST: instantiating (ax82) with nil, nil, nil, all_116_0, % 288.74/71.97 | | | | all_140_0, simplifying with (8), (20), (60), (63), (106), % 288.74/71.97 | | | | (147) gives: % 288.74/71.97 | | | | (156) ? [v0: $i] : (app(nil, v0) = all_140_0 & app(nil, all_116_0) = % 288.74/71.97 | | | | v0 & $i(v0) & $i(all_140_0)) % 288.74/71.97 | | | | % 288.74/71.97 | | | | GROUND_INST: instantiating (9) with all_116_0, all_140_0, simplifying % 288.74/71.97 | | | | with (60), (63), (106) gives: % 288.74/71.97 | | | | (157) all_140_0 = all_116_0 % 288.74/71.97 | | | | % 288.74/71.97 | | | | GROUND_INST: instantiating (ax82) with nil, all_132_0, all_91_0, % 288.74/71.97 | | | | all_91_0, all_91_1, simplifying with (8), (20), (25), (27), % 288.74/71.97 | | | | (28), (91), (92), (93) gives: % 288.74/71.97 | | | | (158) ? [v0: $i] : (app(all_132_0, all_91_0) = v0 & app(nil, v0) = % 288.74/71.97 | | | | all_91_1 & $i(v0) & $i(all_91_1)) % 288.74/71.97 | | | | % 288.74/71.97 | | | | GROUND_INST: instantiating (ax82) with nil, nil, nil, all_132_0, % 288.74/71.97 | | | | all_91_0, simplifying with (8), (20), (91), (92), (93), % 288.74/71.97 | | | | (147) gives: % 288.74/71.97 | | | | (159) ? [v0: $i] : (app(nil, v0) = all_91_0 & app(nil, all_132_0) = % 288.74/71.97 | | | | v0 & $i(v0) & $i(all_91_0)) % 288.74/71.97 | | | | % 288.74/71.97 | | | | GROUND_INST: instantiating (9) with all_132_0, all_91_0, simplifying % 288.74/71.97 | | | | with (91), (92), (93) gives: % 288.74/71.97 | | | | (160) all_132_0 = all_91_0 % 288.74/71.97 | | | | % 288.74/71.97 | | | | GROUND_INST: instantiating (ax82) with nil, nil, nil, all_146_0, % 288.74/71.97 | | | | all_91_1, simplifying with (8), (20), (116), (117), (118), % 288.74/71.97 | | | | (147) gives: % 288.74/71.97 | | | | (161) ? [v0: $i] : (app(nil, v0) = all_91_1 & app(nil, all_146_0) = % 288.74/71.97 | | | | v0 & $i(v0) & $i(all_91_1)) % 288.74/71.97 | | | | % 288.74/71.97 | | | | GROUND_INST: instantiating (9) with all_146_0, all_91_1, simplifying % 288.74/71.97 | | | | with (116), (117), (118) gives: % 288.74/71.97 | | | | (162) all_146_0 = all_91_1 % 288.74/71.97 | | | | % 288.74/71.97 | | | | GROUND_INST: instantiating (ax82) with all_91_0, all_91_0, all_91_1, % 288.74/71.97 | | | | all_144_0, all_91_1, simplifying with (25), (27), (28), % 288.74/71.97 | | | | (112), (113), (114) gives: % 288.74/71.97 | | | | (163) ? [v0: $i] : (app(all_91_0, v0) = all_91_1 & app(all_91_0, % 288.74/71.97 | | | | all_144_0) = v0 & $i(v0) & $i(all_91_1)) % 288.74/71.97 | | | | % 288.74/71.97 | | | | GROUND_INST: instantiating (ax82) with nil, all_146_0, all_91_1, % 288.74/71.97 | | | | all_144_0, all_91_1, simplifying with (8), (20), (112), % 288.74/71.97 | | | | (113), (114), (116), (117), (118) gives: % 288.74/71.97 | | | | (164) ? [v0: $i] : (app(all_146_0, all_144_0) = v0 & app(nil, v0) = % 288.74/71.97 | | | | all_91_1 & $i(v0) & $i(all_91_1)) % 288.74/71.97 | | | | % 288.74/71.97 | | | | GROUND_INST: instantiating (ax80) with all_134_0, all_91_0, all_91_1, % 288.74/71.97 | | | | all_91_0, simplifying with (25), (27), (28), (95), (96), % 288.74/71.97 | | | | (97) gives: % 288.74/71.97 | | | | (165) all_134_0 = all_91_0 % 288.74/71.97 | | | | % 288.74/71.98 | | | | GROUND_INST: instantiating (ax82) with all_91_0, all_134_0, all_91_1, % 288.74/71.98 | | | | all_144_0, all_91_1, simplifying with (25), (27), (95), % 288.74/71.98 | | | | (96), (97), (112), (113), (114) gives: % 288.74/71.98 | | | | (166) ? [v0: $i] : (app(all_134_0, all_144_0) = v0 & app(all_91_0, % 288.74/71.98 | | | | v0) = all_91_1 & $i(v0) & $i(all_91_1)) % 288.74/71.98 | | | | % 288.74/71.98 | | | | GROUND_INST: instantiating (6) with all_91_1, all_132_0, nil, all_91_0, % 288.74/71.98 | | | | all_134_0, simplifying with (8), (20), (24), (26), (91), % 288.74/71.98 | | | | (92), (93), (95), (96), (97) gives: % 288.74/71.98 | | | | (167) segmentP(all_91_1, all_132_0) % 288.74/71.98 | | | | % 288.74/71.98 | | | | GROUND_INST: instantiating (ax82) with nil, all_132_0, all_91_0, % 288.74/71.98 | | | | all_134_0, all_91_1, simplifying with (8), (20), (91), % 288.74/71.98 | | | | (92), (93), (95), (96), (97) gives: % 288.74/71.98 | | | | (168) ? [v0: $i] : (app(all_132_0, all_134_0) = v0 & app(nil, v0) = % 288.74/71.98 | | | | all_91_1 & $i(v0) & $i(all_91_1)) % 288.74/71.98 | | | | % 288.74/71.98 | | | | GROUND_INST: instantiating (ax82) with all_91_0, all_154_0, all_91_0, % 288.74/71.98 | | | | all_91_0, all_91_1, simplifying with (25), (27), (28), % 288.74/71.98 | | | | (132), (133), (134) gives: % 288.74/71.98 | | | | (169) ? [v0: $i] : (app(all_154_0, all_91_0) = v0 & app(all_91_0, % 288.74/71.98 | | | | v0) = all_91_1 & $i(v0) & $i(all_91_1)) % 288.74/71.98 | | | | % 288.74/71.98 | | | | GROUND_INST: instantiating (ax82) with all_91_0, all_154_0, all_91_0, % 288.74/71.98 | | | | all_134_0, all_91_1, simplifying with (25), (27), (95), % 288.74/71.98 | | | | (96), (97), (132), (133), (134) gives: % 288.74/71.98 | | | | (170) ? [v0: $i] : (app(all_154_0, all_134_0) = v0 & app(all_91_0, % 288.74/71.98 | | | | v0) = all_91_1 & $i(v0) & $i(all_91_1)) % 288.74/71.98 | | | | % 288.74/71.98 | | | | GROUND_INST: instantiating (6) with all_91_0, all_132_0, nil, all_91_0, % 288.74/71.98 | | | | all_154_0, simplifying with (8), (20), (25), (27), (91), % 288.74/71.98 | | | | (92), (93), (132), (133), (134) gives: % 288.74/71.98 | | | | (171) segmentP(all_91_0, all_132_0) % 288.74/71.98 | | | | % 288.74/71.98 | | | | GROUND_INST: instantiating (ax82) with nil, all_132_0, all_91_0, % 288.74/71.98 | | | | all_154_0, all_91_0, simplifying with (8), (20), (91), % 288.74/71.98 | | | | (92), (93), (132), (133), (134) gives: % 288.74/71.98 | | | | (172) ? [v0: $i] : (app(all_132_0, all_154_0) = v0 & app(nil, v0) = % 288.74/71.98 | | | | all_91_0 & $i(v0) & $i(all_91_0)) % 288.74/71.98 | | | | % 288.74/71.98 | | | | GROUND_INST: instantiating (ax82) with all_116_2, all_116_0, nil, % 288.74/71.98 | | | | all_146_0, all_91_1, simplifying with (59), (60), (61), % 288.74/71.98 | | | | (63), (116), (117), (118), (143) gives: % 288.74/71.98 | | | | (173) ? [v0: $i] : (app(all_116_0, all_146_0) = v0 & app(all_116_2, % 288.74/71.98 | | | | v0) = all_91_1 & $i(v0) & $i(all_91_1)) % 288.74/71.98 | | | | % 288.74/71.98 | | | | GROUND_INST: instantiating (ax82) with all_116_2, all_116_0, nil, % 288.74/71.98 | | | | all_132_0, all_91_0, simplifying with (59), (60), (61), % 288.74/71.98 | | | | (63), (91), (92), (93), (143) gives: % 288.74/71.98 | | | | (174) ? [v0: $i] : (app(all_116_0, all_132_0) = v0 & app(all_116_2, % 288.74/71.98 | | | | v0) = all_91_0 & $i(v0) & $i(all_91_0)) % 288.74/71.98 | | | | % 288.74/71.98 | | | | GROUND_INST: instantiating (ax82) with all_116_2, all_116_0, nil, % 288.74/71.98 | | | | all_116_0, all_140_0, simplifying with (59), (60), (61), % 288.74/71.98 | | | | (63), (106), (143) gives: % 288.74/71.98 | | | | (175) ? [v0: $i] : (app(all_116_0, all_116_0) = v0 & app(all_116_2, % 288.74/71.98 | | | | v0) = all_140_0 & $i(v0) & $i(all_140_0)) % 288.74/71.98 | | | | % 288.74/71.98 | | | | GROUND_INST: instantiating (ax82) with all_116_2, all_116_0, nil, nil, % 288.74/71.98 | | | | nil, simplifying with (8), (20), (59), (60), (61), (63), % 288.74/71.98 | | | | (143), (147) gives: % 288.74/71.98 | | | | (176) ? [v0: $i] : (app(all_116_0, nil) = v0 & app(all_116_2, v0) = % 288.74/71.98 | | | | nil & $i(v0)) % 288.74/71.98 | | | | % 288.74/71.99 | | | | GROUND_INST: instantiating (18) with all_116_2, all_116_0, simplifying % 288.74/71.99 | | | | with (59), (60), (61), (63), (143) gives: % 288.74/71.99 | | | | (177) all_116_0 = nil % 288.74/71.99 | | | | % 288.74/71.99 | | | | GROUND_INST: instantiating (17) with all_116_2, all_116_0, simplifying % 288.74/71.99 | | | | with (59), (60), (61), (63), (143) gives: % 288.74/71.99 | | | | (178) all_116_2 = nil % 288.74/71.99 | | | | % 288.74/71.99 | | | | GROUND_INST: instantiating (ax82) with all_136_0, all_91_0, all_91_0, % 288.74/71.99 | | | | all_91_0, all_91_1, simplifying with (25), (27), (28), % 288.74/71.99 | | | | (99), (100), (101) gives: % 288.74/71.99 | | | | (179) ? [v0: $i] : (app(all_136_0, v0) = all_91_1 & app(all_91_0, % 288.74/71.99 | | | | all_91_0) = v0 & $i(v0) & $i(all_91_1)) % 288.74/71.99 | | | | % 288.74/71.99 | | | | GROUND_INST: instantiating (ax82) with all_136_0, all_91_0, all_91_0, % 288.74/71.99 | | | | all_134_0, all_91_1, simplifying with (25), (27), (95), % 288.74/71.99 | | | | (96), (97), (99), (100), (101) gives: % 288.74/71.99 | | | | (180) ? [v0: $i] : (app(all_136_0, v0) = all_91_1 & app(all_91_0, % 288.74/71.99 | | | | all_134_0) = v0 & $i(v0) & $i(all_91_1)) % 288.74/71.99 | | | | % 288.74/71.99 | | | | GROUND_INST: instantiating (ax82) with all_142_0, nil, all_91_0, % 288.74/71.99 | | | | all_91_0, all_91_1, simplifying with (8), (20), (25), (27), % 288.74/71.99 | | | | (28), (108), (109), (110) gives: % 288.74/71.99 | | | | (181) ? [v0: $i] : (app(all_142_0, v0) = all_91_1 & app(nil, % 288.74/71.99 | | | | all_91_0) = v0 & $i(v0) & $i(all_91_1)) % 288.74/71.99 | | | | % 288.74/71.99 | | | | GROUND_INST: instantiating (ax82) with all_142_0, nil, all_91_0, % 288.74/71.99 | | | | all_134_0, all_91_1, simplifying with (8), (20), (95), % 288.74/71.99 | | | | (96), (97), (108), (109), (110) gives: % 288.74/71.99 | | | | (182) ? [v0: $i] : (app(all_142_0, v0) = all_91_1 & app(nil, % 288.74/71.99 | | | | all_134_0) = v0 & $i(v0) & $i(all_91_1)) % 288.74/71.99 | | | | % 288.74/71.99 | | | | GROUND_INST: instantiating (19) with all_142_0, all_91_0, simplifying % 288.74/71.99 | | | | with (108), (109), (110) gives: % 288.74/71.99 | | | | (183) all_142_0 = all_91_0 % 288.74/71.99 | | | | % 288.74/71.99 | | | | GROUND_INST: instantiating (ax82) with all_148_0, all_91_0, all_91_1, % 288.74/71.99 | | | | all_144_0, all_91_1, simplifying with (25), (27), (112), % 288.74/71.99 | | | | (113), (114), (120), (121), (122) gives: % 288.74/71.99 | | | | (184) ? [v0: $i] : (app(all_148_0, v0) = all_91_1 & app(all_91_0, % 288.74/71.99 | | | | all_144_0) = v0 & $i(v0) & $i(all_91_1)) % 288.74/71.99 | | | | % 288.74/71.99 | | | | GROUND_INST: instantiating (19) with all_152_0, all_91_1, simplifying % 288.74/71.99 | | | | with (128), (129), (130) gives: % 288.74/71.99 | | | | (185) all_152_0 = all_91_1 % 288.74/71.99 | | | | % 288.74/71.99 | | | | GROUND_INST: instantiating (ax26) with all_162_2, nil, all_162_1, % 288.74/71.99 | | | | simplifying with (8), (20), (136), (138), (141) gives: % 288.74/71.99 | | | | (186) ssList(all_162_1) % 288.74/71.99 | | | | % 288.74/71.99 | | | | GROUND_INST: instantiating (19) with all_162_2, all_162_1, simplifying % 288.74/71.99 | | | | with (136), (138), (141) gives: % 288.74/71.99 | | | | (187) all_162_1 = all_162_2 % 288.74/71.99 | | | | % 288.74/71.99 | | | | COMBINE_EQS: (157), (177) imply: % 288.74/71.99 | | | | (188) all_140_0 = nil % 288.74/71.99 | | | | % 288.74/71.99 | | | | DELTA: instantiating (153) with fresh symbol all_174_0 gives: % 288.74/71.99 | | | | (189) app(all_174_0, all_116_2) = all_116_2 & $i(all_174_0) & % 288.74/71.99 | | | | ssList(all_174_0) % 288.74/71.99 | | | | % 288.74/71.99 | | | | ALPHA: (189) implies: % 288.74/71.99 | | | | (190) ssList(all_174_0) % 288.74/71.99 | | | | (191) $i(all_174_0) % 288.74/71.99 | | | | (192) app(all_174_0, all_116_2) = all_116_2 % 288.74/71.99 | | | | % 288.74/71.99 | | | | DELTA: instantiating (152) with fresh symbol all_176_0 gives: % 288.74/71.99 | | | | (193) app(all_176_0, nil) = all_116_2 & $i(all_176_0) & % 288.74/71.99 | | | | ssList(all_176_0) % 288.74/71.99 | | | | % 288.74/71.99 | | | | ALPHA: (193) implies: % 288.74/71.99 | | | | (194) ssList(all_176_0) % 288.74/71.99 | | | | (195) $i(all_176_0) % 288.74/71.99 | | | | (196) app(all_176_0, nil) = all_116_2 % 288.74/71.99 | | | | % 288.74/71.99 | | | | DELTA: instantiating (155) with fresh symbol all_178_0 gives: % 288.74/71.99 | | | | (197) app(all_178_0, all_116_0) = all_116_0 & $i(all_178_0) & % 288.74/71.99 | | | | ssList(all_178_0) % 288.74/71.99 | | | | % 288.74/71.99 | | | | ALPHA: (197) implies: % 288.74/71.99 | | | | (198) ssList(all_178_0) % 288.74/71.99 | | | | (199) $i(all_178_0) % 288.74/71.99 | | | | (200) app(all_178_0, all_116_0) = all_116_0 % 288.74/71.99 | | | | % 288.74/71.99 | | | | DELTA: instantiating (154) with fresh symbol all_180_0 gives: % 288.74/71.99 | | | | (201) app(all_180_0, nil) = all_116_0 & $i(all_180_0) & % 288.74/71.99 | | | | ssList(all_180_0) % 288.74/71.99 | | | | % 288.74/71.99 | | | | ALPHA: (201) implies: % 288.74/71.99 | | | | (202) ssList(all_180_0) % 288.74/71.99 | | | | (203) $i(all_180_0) % 288.74/71.99 | | | | (204) app(all_180_0, nil) = all_116_0 % 288.74/71.99 | | | | % 288.74/71.99 | | | | DELTA: instantiating (176) with fresh symbol all_184_0 gives: % 288.74/71.99 | | | | (205) app(all_116_0, nil) = all_184_0 & app(all_116_2, all_184_0) = % 288.74/71.99 | | | | nil & $i(all_184_0) % 288.74/71.99 | | | | % 288.74/71.99 | | | | ALPHA: (205) implies: % 288.74/71.99 | | | | (206) $i(all_184_0) % 288.74/71.99 | | | | (207) app(all_116_0, nil) = all_184_0 % 288.74/71.99 | | | | % 288.74/71.99 | | | | DELTA: instantiating (151) with fresh symbol all_186_0 gives: % 288.74/71.99 | | | | (208) app(all_116_0, all_186_0) = all_116_0 & $i(all_186_0) & % 288.74/71.99 | | | | ssList(all_186_0) % 288.74/71.99 | | | | % 288.74/71.99 | | | | ALPHA: (208) implies: % 288.74/71.99 | | | | (209) ssList(all_186_0) % 288.74/71.99 | | | | (210) $i(all_186_0) % 288.74/71.99 | | | | (211) app(all_116_0, all_186_0) = all_116_0 % 288.74/71.99 | | | | % 288.74/71.99 | | | | DELTA: instantiating (150) with fresh symbol all_188_0 gives: % 288.74/71.99 | | | | (212) app(nil, all_188_0) = all_116_0 & $i(all_188_0) & % 288.74/71.99 | | | | ssList(all_188_0) % 288.74/71.99 | | | | % 288.74/71.99 | | | | ALPHA: (212) implies: % 288.74/71.99 | | | | (213) ssList(all_188_0) % 288.74/71.99 | | | | (214) $i(all_188_0) % 288.74/71.99 | | | | (215) app(nil, all_188_0) = all_116_0 % 288.74/71.99 | | | | % 288.74/71.99 | | | | DELTA: instantiating (149) with fresh symbol all_192_0 gives: % 288.74/71.99 | | | | (216) app(all_116_2, all_192_0) = all_116_2 & $i(all_192_0) & % 288.74/71.99 | | | | ssList(all_192_0) % 288.74/71.99 | | | | % 288.74/71.99 | | | | ALPHA: (216) implies: % 288.74/71.99 | | | | (217) ssList(all_192_0) % 288.74/71.99 | | | | (218) $i(all_192_0) % 288.74/71.99 | | | | (219) app(all_116_2, all_192_0) = all_116_2 % 288.74/71.99 | | | | % 288.74/71.99 | | | | DELTA: instantiating (148) with fresh symbol all_194_0 gives: % 288.74/71.99 | | | | (220) app(nil, all_194_0) = all_116_2 & $i(all_194_0) & % 288.74/71.99 | | | | ssList(all_194_0) % 288.74/71.99 | | | | % 288.74/71.99 | | | | ALPHA: (220) implies: % 288.74/71.99 | | | | (221) ssList(all_194_0) % 288.74/71.99 | | | | (222) $i(all_194_0) % 288.74/71.99 | | | | (223) app(nil, all_194_0) = all_116_2 % 288.74/71.99 | | | | % 288.74/71.99 | | | | DELTA: instantiating (156) with fresh symbol all_202_0 gives: % 288.74/72.00 | | | | (224) app(nil, all_202_0) = all_140_0 & app(nil, all_116_0) = % 288.74/72.00 | | | | all_202_0 & $i(all_202_0) & $i(all_140_0) % 288.74/72.00 | | | | % 288.74/72.00 | | | | ALPHA: (224) implies: % 288.74/72.00 | | | | (225) app(nil, all_116_0) = all_202_0 % 288.74/72.00 | | | | % 288.74/72.00 | | | | DELTA: instantiating (179) with fresh symbol all_204_0 gives: % 288.74/72.00 | | | | (226) app(all_136_0, all_204_0) = all_91_1 & app(all_91_0, all_91_0) % 288.74/72.00 | | | | = all_204_0 & $i(all_204_0) & $i(all_91_1) % 288.74/72.00 | | | | % 288.74/72.00 | | | | ALPHA: (226) implies: % 288.74/72.00 | | | | (227) $i(all_204_0) % 288.74/72.00 | | | | (228) app(all_91_0, all_91_0) = all_204_0 % 288.74/72.00 | | | | (229) app(all_136_0, all_204_0) = all_91_1 % 288.74/72.00 | | | | % 288.74/72.00 | | | | DELTA: instantiating (181) with fresh symbol all_208_0 gives: % 288.74/72.00 | | | | (230) app(all_142_0, all_208_0) = all_91_1 & app(nil, all_91_0) = % 288.74/72.00 | | | | all_208_0 & $i(all_208_0) & $i(all_91_1) % 288.74/72.00 | | | | % 288.74/72.00 | | | | ALPHA: (230) implies: % 288.74/72.00 | | | | (231) $i(all_208_0) % 288.74/72.00 | | | | (232) app(nil, all_91_0) = all_208_0 % 288.74/72.00 | | | | % 288.74/72.00 | | | | DELTA: instantiating (184) with fresh symbol all_210_0 gives: % 288.74/72.00 | | | | (233) app(all_148_0, all_210_0) = all_91_1 & app(all_91_0, all_144_0) % 288.74/72.00 | | | | = all_210_0 & $i(all_210_0) & $i(all_91_1) % 288.74/72.00 | | | | % 288.74/72.00 | | | | ALPHA: (233) implies: % 288.74/72.00 | | | | (234) app(all_91_0, all_144_0) = all_210_0 % 288.74/72.00 | | | | % 288.74/72.00 | | | | DELTA: instantiating (175) with fresh symbol all_216_0 gives: % 288.74/72.00 | | | | (235) app(all_116_0, all_116_0) = all_216_0 & app(all_116_2, % 288.74/72.00 | | | | all_216_0) = all_140_0 & $i(all_216_0) & $i(all_140_0) % 288.74/72.00 | | | | % 288.74/72.00 | | | | ALPHA: (235) implies: % 288.74/72.00 | | | | (236) app(all_116_0, all_116_0) = all_216_0 % 288.74/72.00 | | | | % 288.74/72.00 | | | | DELTA: instantiating (173) with fresh symbol all_218_0 gives: % 288.74/72.00 | | | | (237) app(all_116_0, all_146_0) = all_218_0 & app(all_116_2, % 288.74/72.00 | | | | all_218_0) = all_91_1 & $i(all_218_0) & $i(all_91_1) % 288.74/72.00 | | | | % 288.74/72.00 | | | | ALPHA: (237) implies: % 288.74/72.00 | | | | (238) app(all_116_0, all_146_0) = all_218_0 % 288.74/72.00 | | | | % 288.74/72.00 | | | | DELTA: instantiating (174) with fresh symbol all_220_0 gives: % 288.74/72.00 | | | | (239) app(all_116_0, all_132_0) = all_220_0 & app(all_116_2, % 288.74/72.00 | | | | all_220_0) = all_91_0 & $i(all_220_0) & $i(all_91_0) % 288.74/72.00 | | | | % 288.74/72.00 | | | | ALPHA: (239) implies: % 288.74/72.00 | | | | (240) app(all_116_0, all_132_0) = all_220_0 % 288.74/72.00 | | | | % 288.74/72.00 | | | | DELTA: instantiating (182) with fresh symbol all_222_0 gives: % 288.74/72.00 | | | | (241) app(all_142_0, all_222_0) = all_91_1 & app(nil, all_134_0) = % 288.74/72.00 | | | | all_222_0 & $i(all_222_0) & $i(all_91_1) % 288.74/72.00 | | | | % 288.74/72.00 | | | | ALPHA: (241) implies: % 288.74/72.00 | | | | (242) app(nil, all_134_0) = all_222_0 % 288.74/72.00 | | | | % 288.74/72.00 | | | | DELTA: instantiating (163) with fresh symbol all_224_0 gives: % 288.74/72.00 | | | | (243) app(all_91_0, all_224_0) = all_91_1 & app(all_91_0, all_144_0) % 288.74/72.00 | | | | = all_224_0 & $i(all_224_0) & $i(all_91_1) % 288.74/72.00 | | | | % 288.74/72.00 | | | | ALPHA: (243) implies: % 288.74/72.00 | | | | (244) app(all_91_0, all_144_0) = all_224_0 % 288.74/72.00 | | | | (245) app(all_91_0, all_224_0) = all_91_1 % 288.74/72.00 | | | | % 288.74/72.00 | | | | DELTA: instantiating (161) with fresh symbol all_226_0 gives: % 288.74/72.00 | | | | (246) app(nil, all_226_0) = all_91_1 & app(nil, all_146_0) = % 288.74/72.00 | | | | all_226_0 & $i(all_226_0) & $i(all_91_1) % 288.74/72.00 | | | | % 288.74/72.00 | | | | ALPHA: (246) implies: % 288.74/72.00 | | | | (247) app(nil, all_146_0) = all_226_0 % 288.74/72.00 | | | | % 288.74/72.00 | | | | DELTA: instantiating (159) with fresh symbol all_228_0 gives: % 288.74/72.00 | | | | (248) app(nil, all_228_0) = all_91_0 & app(nil, all_132_0) = % 288.74/72.00 | | | | all_228_0 & $i(all_228_0) & $i(all_91_0) % 288.74/72.00 | | | | % 288.74/72.00 | | | | ALPHA: (248) implies: % 288.74/72.00 | | | | (249) app(nil, all_132_0) = all_228_0 % 288.74/72.00 | | | | % 288.74/72.00 | | | | DELTA: instantiating (170) with fresh symbol all_230_0 gives: % 288.74/72.00 | | | | (250) app(all_154_0, all_134_0) = all_230_0 & app(all_91_0, % 288.74/72.00 | | | | all_230_0) = all_91_1 & $i(all_230_0) & $i(all_91_1) % 288.74/72.00 | | | | % 288.74/72.00 | | | | ALPHA: (250) implies: % 288.74/72.00 | | | | (251) app(all_154_0, all_134_0) = all_230_0 % 288.74/72.00 | | | | % 288.74/72.00 | | | | DELTA: instantiating (164) with fresh symbol all_232_0 gives: % 288.74/72.00 | | | | (252) app(all_146_0, all_144_0) = all_232_0 & app(nil, all_232_0) = % 288.74/72.00 | | | | all_91_1 & $i(all_232_0) & $i(all_91_1) % 288.74/72.00 | | | | % 288.74/72.00 | | | | ALPHA: (252) implies: % 288.74/72.00 | | | | (253) app(all_146_0, all_144_0) = all_232_0 % 288.74/72.00 | | | | % 288.74/72.00 | | | | DELTA: instantiating (168) with fresh symbol all_234_0 gives: % 288.74/72.00 | | | | (254) app(all_132_0, all_134_0) = all_234_0 & app(nil, all_234_0) = % 288.74/72.00 | | | | all_91_1 & $i(all_234_0) & $i(all_91_1) % 288.74/72.00 | | | | % 288.74/72.00 | | | | ALPHA: (254) implies: % 288.74/72.00 | | | | (255) app(all_132_0, all_134_0) = all_234_0 % 288.74/72.00 | | | | % 288.74/72.00 | | | | DELTA: instantiating (166) with fresh symbol all_236_0 gives: % 288.74/72.00 | | | | (256) app(all_134_0, all_144_0) = all_236_0 & app(all_91_0, % 288.74/72.00 | | | | all_236_0) = all_91_1 & $i(all_236_0) & $i(all_91_1) % 288.74/72.00 | | | | % 288.74/72.00 | | | | ALPHA: (256) implies: % 288.74/72.00 | | | | (257) app(all_134_0, all_144_0) = all_236_0 % 288.74/72.00 | | | | % 288.74/72.00 | | | | DELTA: instantiating (180) with fresh symbol all_238_0 gives: % 288.74/72.00 | | | | (258) app(all_136_0, all_238_0) = all_91_1 & app(all_91_0, all_134_0) % 288.74/72.00 | | | | = all_238_0 & $i(all_238_0) & $i(all_91_1) % 288.74/72.00 | | | | % 288.74/72.00 | | | | ALPHA: (258) implies: % 289.06/72.00 | | | | (259) app(all_91_0, all_134_0) = all_238_0 % 289.06/72.00 | | | | % 289.06/72.00 | | | | DELTA: instantiating (172) with fresh symbol all_240_0 gives: % 289.06/72.00 | | | | (260) app(all_132_0, all_154_0) = all_240_0 & app(nil, all_240_0) = % 289.06/72.00 | | | | all_91_0 & $i(all_240_0) & $i(all_91_0) % 289.06/72.00 | | | | % 289.06/72.00 | | | | ALPHA: (260) implies: % 289.06/72.00 | | | | (261) app(all_132_0, all_154_0) = all_240_0 % 289.06/72.00 | | | | % 289.06/72.00 | | | | DELTA: instantiating (169) with fresh symbol all_242_0 gives: % 289.06/72.00 | | | | (262) app(all_154_0, all_91_0) = all_242_0 & app(all_91_0, all_242_0) % 289.06/72.00 | | | | = all_91_1 & $i(all_242_0) & $i(all_91_1) % 289.06/72.00 | | | | % 289.06/72.00 | | | | ALPHA: (262) implies: % 289.06/72.00 | | | | (263) app(all_154_0, all_91_0) = all_242_0 % 289.06/72.00 | | | | % 289.06/72.00 | | | | DELTA: instantiating (158) with fresh symbol all_244_0 gives: % 289.06/72.00 | | | | (264) app(all_132_0, all_91_0) = all_244_0 & app(nil, all_244_0) = % 289.06/72.00 | | | | all_91_1 & $i(all_244_0) & $i(all_91_1) % 289.06/72.00 | | | | % 289.06/72.00 | | | | ALPHA: (264) implies: % 289.06/72.00 | | | | (265) app(all_132_0, all_91_0) = all_244_0 % 289.06/72.00 | | | | % 289.06/72.00 | | | | REDUCE: (177), (204) imply: % 289.06/72.00 | | | | (266) app(all_180_0, nil) = nil % 289.06/72.00 | | | | % 289.06/72.00 | | | | REDUCE: (177), (200) imply: % 289.06/72.00 | | | | (267) app(all_178_0, nil) = nil % 289.06/72.00 | | | | % 289.06/72.00 | | | | REDUCE: (178), (196) imply: % 289.06/72.00 | | | | (268) app(all_176_0, nil) = nil % 289.06/72.00 | | | | % 289.06/72.00 | | | | REDUCE: (178), (192) imply: % 289.06/72.00 | | | | (269) app(all_174_0, nil) = nil % 289.06/72.00 | | | | % 289.06/72.00 | | | | REDUCE: (142), (187) imply: % 289.06/72.00 | | | | (270) app(all_162_2, all_162_0) = all_91_0 % 289.06/72.00 | | | | % 289.06/72.00 | | | | REDUCE: (165), (251) imply: % 289.06/72.00 | | | | (271) app(all_154_0, all_91_0) = all_230_0 % 289.06/72.00 | | | | % 289.06/72.00 | | | | REDUCE: (130), (185) imply: % 289.06/72.00 | | | | (272) app(all_91_1, nil) = all_91_1 % 289.06/72.00 | | | | % 289.06/72.00 | | | | REDUCE: (162), (253) imply: % 289.06/72.00 | | | | (273) app(all_91_1, all_144_0) = all_232_0 % 289.06/72.00 | | | | % 289.06/72.00 | | | | REDUCE: (110), (183) imply: % 289.06/72.01 | | | | (274) app(all_91_0, nil) = all_91_0 % 289.06/72.01 | | | | % 289.06/72.01 | | | | REDUCE: (165), (257) imply: % 289.06/72.01 | | | | (275) app(all_91_0, all_144_0) = all_236_0 % 289.06/72.01 | | | | % 289.06/72.01 | | | | REDUCE: (160), (261) imply: % 289.06/72.01 | | | | (276) app(all_91_0, all_154_0) = all_240_0 % 289.06/72.01 | | | | % 289.06/72.01 | | | | REDUCE: (160), (165), (255) imply: % 289.06/72.01 | | | | (277) app(all_91_0, all_91_0) = all_234_0 % 289.06/72.01 | | | | % 289.06/72.01 | | | | REDUCE: (160), (265) imply: % 289.06/72.01 | | | | (278) app(all_91_0, all_91_0) = all_244_0 % 289.06/72.01 | | | | % 289.06/72.01 | | | | REDUCE: (177), (211) imply: % 289.06/72.01 | | | | (279) app(nil, all_186_0) = nil % 289.06/72.01 | | | | % 289.06/72.01 | | | | REDUCE: (162), (177), (238) imply: % 289.06/72.01 | | | | (280) app(nil, all_91_1) = all_218_0 % 289.06/72.01 | | | | % 289.06/72.01 | | | | REDUCE: (160), (177), (240) imply: % 289.06/72.01 | | | | (281) app(nil, all_91_0) = all_220_0 % 289.06/72.01 | | | | % 289.06/72.01 | | | | REDUCE: (177), (236) imply: % 289.06/72.01 | | | | (282) app(nil, nil) = all_216_0 % 289.06/72.01 | | | | % 289.06/72.01 | | | | REDUCE: (177), (207) imply: % 289.06/72.01 | | | | (283) app(nil, nil) = all_184_0 % 289.06/72.01 | | | | % 289.06/72.01 | | | | REDUCE: (178), (219) imply: % 289.06/72.01 | | | | (284) app(nil, all_192_0) = nil % 289.06/72.01 | | | | % 289.06/72.01 | | | | REDUCE: (165), (259) imply: % 289.06/72.01 | | | | (285) app(all_91_0, all_91_0) = all_238_0 % 289.06/72.01 | | | | % 289.06/72.01 | | | | REDUCE: (178), (223) imply: % 289.06/72.01 | | | | (286) app(nil, all_194_0) = nil % 289.06/72.01 | | | | % 289.06/72.01 | | | | REDUCE: (177), (215) imply: % 289.06/72.01 | | | | (287) app(nil, all_188_0) = nil % 289.06/72.01 | | | | % 289.06/72.01 | | | | REDUCE: (162), (247) imply: % 289.06/72.01 | | | | (288) app(nil, all_91_1) = all_226_0 % 289.06/72.01 | | | | % 289.06/72.01 | | | | REDUCE: (118), (162) imply: % 289.06/72.01 | | | | (289) app(nil, all_91_1) = all_91_1 % 289.06/72.01 | | | | % 289.06/72.01 | | | | REDUCE: (165), (242) imply: % 289.06/72.01 | | | | (290) app(nil, all_91_0) = all_222_0 % 289.06/72.01 | | | | % 289.06/72.01 | | | | REDUCE: (160), (249) imply: % 289.06/72.01 | | | | (291) app(nil, all_91_0) = all_228_0 % 289.06/72.01 | | | | % 289.06/72.01 | | | | REDUCE: (93), (160) imply: % 289.06/72.01 | | | | (292) app(nil, all_91_0) = all_91_0 % 289.06/72.01 | | | | % 289.06/72.01 | | | | REDUCE: (177), (225) imply: % 289.06/72.01 | | | | (293) app(nil, nil) = all_202_0 % 289.06/72.01 | | | | % 289.06/72.01 | | | | REDUCE: (160), (171) imply: % 289.06/72.01 | | | | (294) segmentP(all_91_0, all_91_0) % 289.06/72.01 | | | | % 289.06/72.01 | | | | REDUCE: (160), (167) imply: % 289.06/72.01 | | | | (295) segmentP(all_91_1, all_91_0) % 289.06/72.01 | | | | % 289.06/72.01 | | | | GROUND_INST: instantiating (22) with all_184_0, all_202_0, nil, nil, % 289.06/72.01 | | | | simplifying with (283), (293) gives: % 289.06/72.01 | | | | (296) all_202_0 = all_184_0 % 289.06/72.01 | | | | % 289.06/72.01 | | | | GROUND_INST: instantiating (22) with nil, all_216_0, nil, nil, % 289.06/72.01 | | | | simplifying with (147), (282) gives: % 289.06/72.01 | | | | (297) all_216_0 = nil % 289.06/72.01 | | | | % 289.06/72.01 | | | | GROUND_INST: instantiating (22) with all_202_0, all_216_0, nil, nil, % 289.06/72.01 | | | | simplifying with (282), (293) gives: % 289.06/72.01 | | | | (298) all_216_0 = all_202_0 % 289.06/72.01 | | | | % 289.06/72.01 | | | | GROUND_INST: instantiating (22) with all_218_0, all_226_0, all_91_1, % 289.06/72.01 | | | | nil, simplifying with (280), (288) gives: % 289.06/72.01 | | | | (299) all_226_0 = all_218_0 % 289.06/72.01 | | | | % 289.06/72.01 | | | | GROUND_INST: instantiating (22) with all_91_1, all_226_0, all_91_1, nil, % 289.06/72.01 | | | | simplifying with (288), (289) gives: % 289.06/72.01 | | | | (300) all_226_0 = all_91_1 % 289.06/72.01 | | | | % 289.06/72.01 | | | | GROUND_INST: instantiating (22) with all_91_0, all_220_0, all_91_0, nil, % 289.06/72.01 | | | | simplifying with (281), (292) gives: % 289.06/72.01 | | | | (301) all_220_0 = all_91_0 % 289.06/72.01 | | | | % 289.06/72.01 | | | | GROUND_INST: instantiating (22) with all_220_0, all_222_0, all_91_0, % 289.06/72.01 | | | | nil, simplifying with (281), (290) gives: % 289.06/72.01 | | | | (302) all_222_0 = all_220_0 % 289.06/72.01 | | | | % 289.06/72.01 | | | | GROUND_INST: instantiating (22) with all_222_0, all_228_0, all_91_0, % 289.06/72.01 | | | | nil, simplifying with (290), (291) gives: % 289.06/72.01 | | | | (303) all_228_0 = all_222_0 % 289.06/72.01 | | | | % 289.06/72.01 | | | | GROUND_INST: instantiating (22) with all_208_0, all_228_0, all_91_0, % 289.06/72.01 | | | | nil, simplifying with (232), (291) gives: % 289.06/72.01 | | | | (304) all_228_0 = all_208_0 % 289.06/72.01 | | | | % 289.06/72.01 | | | | GROUND_INST: instantiating (22) with all_91_1, all_232_0, all_144_0, % 289.06/72.01 | | | | all_91_1, simplifying with (114), (273) gives: % 289.06/72.01 | | | | (305) all_232_0 = all_91_1 % 289.06/72.01 | | | | % 289.06/72.01 | | | | GROUND_INST: instantiating (22) with all_91_1, all_234_0, all_91_0, % 289.06/72.01 | | | | all_91_0, simplifying with (28), (277) gives: % 289.06/72.01 | | | | (306) all_234_0 = all_91_1 % 289.06/72.01 | | | | % 289.11/72.01 | | | | GROUND_INST: instantiating (22) with all_238_0, all_244_0, all_91_0, % 289.11/72.01 | | | | all_91_0, simplifying with (278), (285) gives: % 289.11/72.01 | | | | (307) all_244_0 = all_238_0 % 289.11/72.01 | | | | % 289.11/72.01 | | | | GROUND_INST: instantiating (22) with all_234_0, all_244_0, all_91_0, % 289.11/72.01 | | | | all_91_0, simplifying with (277), (278) gives: % 289.11/72.01 | | | | (308) all_244_0 = all_234_0 % 289.11/72.01 | | | | % 289.11/72.01 | | | | GROUND_INST: instantiating (22) with all_204_0, all_244_0, all_91_0, % 289.11/72.01 | | | | all_91_0, simplifying with (228), (278) gives: % 289.11/72.01 | | | | (309) all_244_0 = all_204_0 % 289.11/72.01 | | | | % 289.11/72.01 | | | | GROUND_INST: instantiating (22) with all_224_0, all_236_0, all_144_0, % 289.11/72.01 | | | | all_91_0, simplifying with (244), (275) gives: % 289.11/72.01 | | | | (310) all_236_0 = all_224_0 % 289.11/72.01 | | | | % 289.11/72.01 | | | | GROUND_INST: instantiating (22) with all_210_0, all_236_0, all_144_0, % 289.11/72.01 | | | | all_91_0, simplifying with (234), (275) gives: % 289.11/72.01 | | | | (311) all_236_0 = all_210_0 % 289.11/72.01 | | | | % 289.11/72.01 | | | | GROUND_INST: instantiating (22) with all_91_0, all_240_0, all_154_0, % 289.11/72.01 | | | | all_91_0, simplifying with (134), (276) gives: % 289.11/72.01 | | | | (312) all_240_0 = all_91_0 % 289.11/72.01 | | | | % 289.11/72.01 | | | | GROUND_INST: instantiating (22) with all_230_0, all_242_0, all_91_0, % 289.11/72.01 | | | | all_154_0, simplifying with (263), (271) gives: % 289.11/72.01 | | | | (313) all_242_0 = all_230_0 % 289.11/72.01 | | | | % 289.11/72.01 | | | | COMBINE_EQS: (307), (309) imply: % 289.11/72.01 | | | | (314) all_238_0 = all_204_0 % 289.11/72.01 | | | | % 289.11/72.01 | | | | COMBINE_EQS: (307), (308) imply: % 289.11/72.01 | | | | (315) all_238_0 = all_234_0 % 289.11/72.01 | | | | % 289.11/72.01 | | | | COMBINE_EQS: (314), (315) imply: % 289.11/72.01 | | | | (316) all_234_0 = all_204_0 % 289.11/72.01 | | | | % 289.11/72.01 | | | | SIMP: (316) implies: % 289.11/72.01 | | | | (317) all_234_0 = all_204_0 % 289.11/72.01 | | | | % 289.11/72.01 | | | | COMBINE_EQS: (310), (311) imply: % 289.11/72.01 | | | | (318) all_224_0 = all_210_0 % 289.11/72.01 | | | | % 289.11/72.01 | | | | COMBINE_EQS: (306), (317) imply: % 289.11/72.01 | | | | (319) all_204_0 = all_91_1 % 289.11/72.01 | | | | % 289.11/72.01 | | | | COMBINE_EQS: (303), (304) imply: % 289.11/72.01 | | | | (320) all_222_0 = all_208_0 % 289.11/72.01 | | | | % 289.11/72.01 | | | | SIMP: (320) implies: % 289.11/72.01 | | | | (321) all_222_0 = all_208_0 % 289.11/72.01 | | | | % 289.11/72.01 | | | | COMBINE_EQS: (299), (300) imply: % 289.11/72.01 | | | | (322) all_218_0 = all_91_1 % 289.11/72.01 | | | | % 289.11/72.01 | | | | SIMP: (322) implies: % 289.11/72.01 | | | | (323) all_218_0 = all_91_1 % 289.11/72.01 | | | | % 289.11/72.01 | | | | COMBINE_EQS: (302), (321) imply: % 289.11/72.01 | | | | (324) all_220_0 = all_208_0 % 289.11/72.01 | | | | % 289.11/72.01 | | | | SIMP: (324) implies: % 289.11/72.01 | | | | (325) all_220_0 = all_208_0 % 289.11/72.01 | | | | % 289.11/72.01 | | | | COMBINE_EQS: (301), (325) imply: % 289.11/72.01 | | | | (326) all_208_0 = all_91_0 % 289.11/72.01 | | | | % 289.11/72.01 | | | | SIMP: (326) implies: % 289.11/72.01 | | | | (327) all_208_0 = all_91_0 % 289.11/72.01 | | | | % 289.11/72.01 | | | | COMBINE_EQS: (297), (298) imply: % 289.11/72.01 | | | | (328) all_202_0 = nil % 289.11/72.01 | | | | % 289.11/72.01 | | | | SIMP: (328) implies: % 289.11/72.01 | | | | (329) all_202_0 = nil % 289.11/72.01 | | | | % 289.11/72.01 | | | | COMBINE_EQS: (296), (329) imply: % 289.11/72.01 | | | | (330) all_184_0 = nil % 289.11/72.01 | | | | % 289.11/72.01 | | | | SIMP: (330) implies: % 289.11/72.01 | | | | (331) all_184_0 = nil % 289.11/72.01 | | | | % 289.11/72.01 | | | | REDUCE: (229), (319) imply: % 289.11/72.01 | | | | (332) app(all_136_0, all_91_1) = all_91_1 % 289.11/72.01 | | | | % 289.11/72.01 | | | | REDUCE: (245), (318) imply: % 289.11/72.01 | | | | (333) app(all_91_0, all_210_0) = all_91_1 % 289.11/72.01 | | | | % 289.11/72.01 | | | | GROUND_INST: instantiating (ax79) with nil, all_91_1, all_91_1, % 289.11/72.01 | | | | all_150_0, simplifying with (8), (20), (24), (26), (124), % 289.11/72.01 | | | | (125), (126), (289) gives: % 289.11/72.01 | | | | (334) all_150_0 = nil % 289.11/72.01 | | | | % 289.11/72.01 | | | | GROUND_INST: instantiating (ax82) with nil, all_186_0, nil, all_91_0, % 289.11/72.01 | | | | all_91_0, simplifying with (8), (20), (25), (27), (209), % 289.11/72.01 | | | | (210), (279), (292) gives: % 289.11/72.02 | | | | (335) ? [v0: $i] : (app(all_186_0, all_91_0) = v0 & app(nil, v0) = % 289.11/72.02 | | | | all_91_0 & $i(v0)) % 289.11/72.02 | | | | % 289.11/72.02 | | | | GROUND_INST: instantiating (ax82) with nil, all_188_0, nil, all_91_0, % 289.11/72.02 | | | | all_91_0, simplifying with (8), (20), (25), (27), (213), % 289.11/72.02 | | | | (214), (287), (292) gives: % 289.11/72.02 | | | | (336) ? [v0: $i] : (app(all_188_0, all_91_0) = v0 & app(nil, v0) = % 289.11/72.02 | | | | all_91_0 & $i(v0)) % 289.11/72.02 | | | | % 289.11/72.02 | | | | GROUND_INST: instantiating (9) with all_188_0, nil, simplifying with % 289.11/72.02 | | | | (213), (214), (287) gives: % 289.11/72.02 | | | | (337) all_188_0 = nil % 289.11/72.02 | | | | % 289.11/72.02 | | | | GROUND_INST: instantiating (ax82) with nil, all_192_0, nil, all_91_0, % 289.11/72.02 | | | | all_91_0, simplifying with (8), (20), (25), (27), (217), % 289.11/72.02 | | | | (218), (284), (292) gives: % 289.11/72.02 | | | | (338) ? [v0: $i] : (app(all_192_0, all_91_0) = v0 & app(nil, v0) = % 289.11/72.02 | | | | all_91_0 & $i(v0)) % 289.11/72.02 | | | | % 289.11/72.02 | | | | GROUND_INST: instantiating (ax80) with all_192_0, nil, nil, all_194_0, % 289.11/72.02 | | | | simplifying with (8), (20), (217), (218), (221), (222), % 289.11/72.02 | | | | (284), (286) gives: % 289.11/72.02 | | | | (339) all_194_0 = all_192_0 % 289.11/72.02 | | | | % 289.11/72.02 | | | | GROUND_INST: instantiating (ax80) with all_188_0, nil, nil, all_194_0, % 289.11/72.02 | | | | simplifying with (8), (20), (213), (214), (221), (222), % 289.11/72.02 | | | | (286), (287) gives: % 289.11/72.02 | | | | (340) all_194_0 = all_188_0 % 289.11/72.02 | | | | % 289.11/72.02 | | | | GROUND_INST: instantiating (ax80) with all_186_0, nil, nil, all_194_0, % 289.11/72.02 | | | | simplifying with (8), (20), (209), (210), (221), (222), % 289.11/72.02 | | | | (279), (286) gives: % 289.11/72.02 | | | | (341) all_194_0 = all_186_0 % 289.11/72.02 | | | | % 289.11/72.02 | | | | GROUND_INST: instantiating (ax82) with nil, all_194_0, nil, all_91_0, % 289.11/72.02 | | | | all_91_0, simplifying with (8), (20), (25), (27), (221), % 289.11/72.02 | | | | (222), (286), (292) gives: % 289.11/72.02 | | | | (342) ? [v0: $i] : (app(all_194_0, all_91_0) = v0 & app(nil, v0) = % 289.11/72.02 | | | | all_91_0 & $i(v0)) % 289.11/72.02 | | | | % 289.11/72.02 | | | | GROUND_INST: instantiating (ax80) with nil, all_91_1, all_91_1, % 289.11/72.02 | | | | all_144_0, simplifying with (8), (20), (24), (26), (112), % 289.11/72.02 | | | | (113), (114), (272) gives: % 289.11/72.02 | | | | (343) all_144_0 = nil % 289.11/72.02 | | | | % 289.11/72.02 | | | | GROUND_INST: instantiating (ax80) with nil, all_91_0, all_91_0, % 289.11/72.02 | | | | all_154_0, simplifying with (8), (20), (25), (27), (132), % 289.11/72.02 | | | | (133), (134), (274) gives: % 289.11/72.02 | | | | (344) all_154_0 = nil % 289.11/72.02 | | | | % 289.11/72.02 | | | | GROUND_INST: instantiating (ax82) with all_136_0, all_91_0, all_91_0, % 289.11/72.02 | | | | all_144_0, all_210_0, simplifying with (25), (27), (99), % 289.11/72.02 | | | | (100), (101), (112), (113), (234) gives: % 289.11/72.02 | | | | (345) ? [v0: $i] : (app(all_136_0, v0) = all_210_0 & app(all_91_0, % 289.11/72.02 | | | | all_144_0) = v0 & $i(v0) & $i(all_210_0)) % 289.11/72.02 | | | | % 289.11/72.02 | | | | GROUND_INST: instantiating (ax56) with all_91_0, all_91_0, nil, % 289.11/72.02 | | | | all_91_0, all_144_0, all_210_0, simplifying with (8), (20), % 289.11/72.02 | | | | (25), (27), (112), (113), (234), (292), (294) gives: % 289.11/72.02 | | | | (346) segmentP(all_210_0, all_91_0) % 289.11/72.02 | | | | % 289.11/72.02 | | | | GROUND_INST: instantiating (ax82) with nil, all_91_0, all_91_0, % 289.11/72.02 | | | | all_144_0, all_210_0, simplifying with (8), (20), (25), % 289.11/72.02 | | | | (27), (112), (113), (234), (292) gives: % 289.11/72.02 | | | | (347) ? [v0: $i] : (app(all_91_0, all_144_0) = v0 & app(nil, v0) = % 289.11/72.02 | | | | all_210_0 & $i(v0) & $i(all_210_0)) % 289.11/72.02 | | | | % 289.11/72.02 | | | | GROUND_INST: instantiating (ax26) with all_91_0, all_144_0, all_210_0, % 289.11/72.02 | | | | simplifying with (25), (27), (112), (113), (234) gives: % 289.11/72.02 | | | | (348) ssList(all_210_0) % 289.11/72.02 | | | | % 289.11/72.02 | | | | GROUND_INST: instantiating (ax79) with all_136_0, all_91_1, all_91_1, % 289.11/72.02 | | | | all_150_0, simplifying with (24), (26), (99), (100), (124), % 289.11/72.02 | | | | (125), (126), (332) gives: % 289.11/72.02 | | | | (349) all_150_0 = all_136_0 % 289.11/72.02 | | | | % 289.11/72.02 | | | | GROUND_INST: instantiating (ax82) with all_162_2, all_162_0, all_91_0, % 289.11/72.02 | | | | all_144_0, all_210_0, simplifying with (112), (113), (136), % 289.11/72.02 | | | | (137), (138), (140), (234), (270) gives: % 289.11/72.02 | | | | (350) ? [v0: $i] : (app(all_162_0, all_144_0) = v0 & app(all_162_2, % 289.11/72.02 | | | | v0) = all_210_0 & $i(v0) & $i(all_210_0)) % 289.11/72.02 | | | | % 289.11/72.02 | | | | GROUND_INST: instantiating (ax82) with all_174_0, nil, nil, all_91_0, % 289.11/72.02 | | | | all_91_0, simplifying with (8), (20), (25), (27), (190), % 289.11/72.02 | | | | (191), (269), (292) gives: % 289.11/72.02 | | | | (351) ? [v0: $i] : (app(all_174_0, v0) = all_91_0 & app(nil, % 289.11/72.02 | | | | all_91_0) = v0 & $i(v0)) % 289.11/72.02 | | | | % 289.11/72.02 | | | | GROUND_INST: instantiating (ax82) with all_176_0, nil, nil, all_91_0, % 289.11/72.02 | | | | all_91_0, simplifying with (8), (20), (25), (27), (194), % 289.11/72.02 | | | | (195), (268), (292) gives: % 289.11/72.02 | | | | (352) ? [v0: $i] : (app(all_176_0, v0) = all_91_0 & app(nil, % 289.11/72.02 | | | | all_91_0) = v0 & $i(v0)) % 289.11/72.02 | | | | % 289.11/72.02 | | | | GROUND_INST: instantiating (ax82) with all_178_0, nil, nil, all_91_0, % 289.11/72.02 | | | | all_91_0, simplifying with (8), (20), (25), (27), (198), % 289.11/72.02 | | | | (199), (267), (292) gives: % 289.11/72.02 | | | | (353) ? [v0: $i] : (app(all_178_0, v0) = all_91_0 & app(nil, % 289.11/72.02 | | | | all_91_0) = v0 & $i(v0)) % 289.11/72.02 | | | | % 289.11/72.02 | | | | GROUND_INST: instantiating (ax82) with all_180_0, nil, nil, all_91_0, % 289.11/72.02 | | | | all_91_0, simplifying with (8), (20), (25), (27), (202), % 289.11/72.02 | | | | (203), (266), (292) gives: % 289.11/72.02 | | | | (354) ? [v0: $i] : (app(all_180_0, v0) = all_91_0 & app(nil, % 289.11/72.02 | | | | all_91_0) = v0 & $i(v0)) % 289.11/72.02 | | | | % 289.11/72.02 | | | | COMBINE_EQS: (339), (340) imply: % 289.11/72.02 | | | | (355) all_192_0 = all_188_0 % 289.11/72.02 | | | | % 289.11/72.02 | | | | COMBINE_EQS: (339), (341) imply: % 289.11/72.02 | | | | (356) all_192_0 = all_186_0 % 289.11/72.02 | | | | % 289.11/72.02 | | | | COMBINE_EQS: (355), (356) imply: % 289.11/72.02 | | | | (357) all_188_0 = all_186_0 % 289.11/72.02 | | | | % 289.11/72.02 | | | | SIMP: (357) implies: % 289.11/72.02 | | | | (358) all_188_0 = all_186_0 % 289.11/72.02 | | | | % 289.11/72.02 | | | | COMBINE_EQS: (337), (358) imply: % 289.11/72.02 | | | | (359) all_186_0 = nil % 289.11/72.02 | | | | % 289.11/72.02 | | | | SIMP: (359) implies: % 289.11/72.02 | | | | (360) all_186_0 = nil % 289.11/72.02 | | | | % 289.11/72.02 | | | | COMBINE_EQS: (334), (349) imply: % 289.11/72.02 | | | | (361) all_136_0 = nil % 289.11/72.02 | | | | % 289.11/72.02 | | | | SIMP: (361) implies: % 289.11/72.02 | | | | (362) all_136_0 = nil % 289.11/72.02 | | | | % 289.11/72.02 | | | | COMBINE_EQS: (356), (360) imply: % 289.11/72.02 | | | | (363) all_192_0 = nil % 289.11/72.02 | | | | % 289.11/72.02 | | | | COMBINE_EQS: (339), (363) imply: % 289.11/72.02 | | | | (364) all_194_0 = nil % 289.11/72.02 | | | | % 289.11/72.02 | | | | DELTA: instantiating (335) with fresh symbol all_264_0 gives: % 289.11/72.02 | | | | (365) app(all_186_0, all_91_0) = all_264_0 & app(nil, all_264_0) = % 289.11/72.02 | | | | all_91_0 & $i(all_264_0) % 289.11/72.02 | | | | % 289.11/72.02 | | | | ALPHA: (365) implies: % 289.11/72.02 | | | | (366) app(all_186_0, all_91_0) = all_264_0 % 289.11/72.02 | | | | % 289.11/72.02 | | | | DELTA: instantiating (351) with fresh symbol all_294_0 gives: % 289.11/72.02 | | | | (367) app(all_174_0, all_294_0) = all_91_0 & app(nil, all_91_0) = % 289.11/72.02 | | | | all_294_0 & $i(all_294_0) % 289.11/72.02 | | | | % 289.11/72.02 | | | | ALPHA: (367) implies: % 289.11/72.02 | | | | (368) app(nil, all_91_0) = all_294_0 % 289.11/72.02 | | | | % 289.11/72.02 | | | | DELTA: instantiating (352) with fresh symbol all_296_0 gives: % 289.11/72.02 | | | | (369) app(all_176_0, all_296_0) = all_91_0 & app(nil, all_91_0) = % 289.11/72.02 | | | | all_296_0 & $i(all_296_0) % 289.11/72.02 | | | | % 289.11/72.02 | | | | ALPHA: (369) implies: % 289.11/72.02 | | | | (370) app(nil, all_91_0) = all_296_0 % 289.11/72.02 | | | | % 289.11/72.02 | | | | DELTA: instantiating (342) with fresh symbol all_304_0 gives: % 289.11/72.02 | | | | (371) app(all_194_0, all_91_0) = all_304_0 & app(nil, all_304_0) = % 289.11/72.02 | | | | all_91_0 & $i(all_304_0) % 289.11/72.02 | | | | % 289.11/72.02 | | | | ALPHA: (371) implies: % 289.11/72.02 | | | | (372) app(all_194_0, all_91_0) = all_304_0 % 289.11/72.02 | | | | % 289.11/72.02 | | | | DELTA: instantiating (338) with fresh symbol all_306_0 gives: % 289.11/72.02 | | | | (373) app(all_192_0, all_91_0) = all_306_0 & app(nil, all_306_0) = % 289.11/72.02 | | | | all_91_0 & $i(all_306_0) % 289.11/72.03 | | | | % 289.11/72.03 | | | | ALPHA: (373) implies: % 289.11/72.03 | | | | (374) app(all_192_0, all_91_0) = all_306_0 % 289.11/72.03 | | | | % 289.11/72.03 | | | | DELTA: instantiating (354) with fresh symbol all_312_0 gives: % 289.11/72.03 | | | | (375) app(all_180_0, all_312_0) = all_91_0 & app(nil, all_91_0) = % 289.11/72.03 | | | | all_312_0 & $i(all_312_0) % 289.11/72.03 | | | | % 289.11/72.03 | | | | ALPHA: (375) implies: % 289.11/72.03 | | | | (376) app(nil, all_91_0) = all_312_0 % 289.11/72.03 | | | | % 289.11/72.03 | | | | DELTA: instantiating (353) with fresh symbol all_414_0 gives: % 289.11/72.03 | | | | (377) app(all_178_0, all_414_0) = all_91_0 & app(nil, all_91_0) = % 289.11/72.03 | | | | all_414_0 & $i(all_414_0) % 289.11/72.03 | | | | % 289.11/72.03 | | | | ALPHA: (377) implies: % 289.11/72.03 | | | | (378) app(nil, all_91_0) = all_414_0 % 289.11/72.03 | | | | % 289.11/72.03 | | | | DELTA: instantiating (336) with fresh symbol all_418_0 gives: % 289.11/72.03 | | | | (379) app(all_188_0, all_91_0) = all_418_0 & app(nil, all_418_0) = % 289.11/72.03 | | | | all_91_0 & $i(all_418_0) % 289.11/72.03 | | | | % 289.11/72.03 | | | | ALPHA: (379) implies: % 289.11/72.03 | | | | (380) app(all_188_0, all_91_0) = all_418_0 % 289.11/72.03 | | | | % 289.11/72.03 | | | | DELTA: instantiating (347) with fresh symbol all_562_0 gives: % 289.11/72.03 | | | | (381) app(all_91_0, all_144_0) = all_562_0 & app(nil, all_562_0) = % 289.11/72.03 | | | | all_210_0 & $i(all_562_0) & $i(all_210_0) % 289.11/72.03 | | | | % 289.11/72.03 | | | | ALPHA: (381) implies: % 289.11/72.03 | | | | (382) app(all_91_0, all_144_0) = all_562_0 % 289.11/72.03 | | | | % 289.11/72.03 | | | | DELTA: instantiating (345) with fresh symbol all_590_0 gives: % 289.11/72.03 | | | | (383) app(all_136_0, all_590_0) = all_210_0 & app(all_91_0, % 289.11/72.03 | | | | all_144_0) = all_590_0 & $i(all_590_0) & $i(all_210_0) % 289.11/72.03 | | | | % 289.11/72.03 | | | | ALPHA: (383) implies: % 289.11/72.03 | | | | (384) app(all_91_0, all_144_0) = all_590_0 % 289.11/72.03 | | | | % 289.11/72.03 | | | | DELTA: instantiating (350) with fresh symbol all_592_0 gives: % 289.11/72.03 | | | | (385) app(all_162_0, all_144_0) = all_592_0 & app(all_162_2, % 289.11/72.03 | | | | all_592_0) = all_210_0 & $i(all_592_0) & $i(all_210_0) % 289.11/72.03 | | | | % 289.11/72.03 | | | | ALPHA: (385) implies: % 289.11/72.03 | | | | (386) $i(all_210_0) % 289.11/72.03 | | | | % 289.11/72.03 | | | | REDUCE: (364), (372) imply: % 289.11/72.03 | | | | (387) app(nil, all_91_0) = all_304_0 % 289.11/72.03 | | | | % 289.11/72.03 | | | | REDUCE: (363), (374) imply: % 289.11/72.03 | | | | (388) app(nil, all_91_0) = all_306_0 % 289.11/72.03 | | | | % 289.11/72.03 | | | | REDUCE: (337), (380) imply: % 289.11/72.03 | | | | (389) app(nil, all_91_0) = all_418_0 % 289.11/72.03 | | | | % 289.11/72.03 | | | | REDUCE: (360), (366) imply: % 289.11/72.03 | | | | (390) app(nil, all_91_0) = all_264_0 % 289.11/72.03 | | | | % 289.11/72.03 | | | | REDUCE: (271), (344) imply: % 289.11/72.03 | | | | (391) app(nil, all_91_0) = all_230_0 % 289.11/72.03 | | | | % 289.11/72.03 | | | | REDUCE: (343), (384) imply: % 289.11/72.03 | | | | (392) app(all_91_0, nil) = all_590_0 % 289.11/72.03 | | | | % 289.11/72.03 | | | | REDUCE: (343), (382) imply: % 289.11/72.03 | | | | (393) app(all_91_0, nil) = all_562_0 % 289.11/72.03 | | | | % 289.11/72.03 | | | | REDUCE: (234), (343) imply: % 289.11/72.03 | | | | (394) app(all_91_0, nil) = all_210_0 % 289.11/72.03 | | | | % 289.11/72.03 | | | | GROUND_INST: instantiating (22) with all_91_0, all_296_0, all_91_0, nil, % 289.11/72.03 | | | | simplifying with (292), (370) gives: % 289.11/72.03 | | | | (395) all_296_0 = all_91_0 % 289.11/72.03 | | | | % 289.11/72.03 | | | | GROUND_INST: instantiating (22) with all_264_0, all_296_0, all_91_0, % 289.11/72.03 | | | | nil, simplifying with (370), (390) gives: % 289.11/72.03 | | | | (396) all_296_0 = all_264_0 % 289.11/72.03 | | | | % 289.11/72.03 | | | | GROUND_INST: instantiating (22) with all_230_0, all_296_0, all_91_0, % 289.11/72.03 | | | | nil, simplifying with (370), (391) gives: % 289.11/72.03 | | | | (397) all_296_0 = all_230_0 % 289.11/72.03 | | | | % 289.11/72.03 | | | | GROUND_INST: instantiating (22) with all_296_0, all_304_0, all_91_0, % 289.11/72.03 | | | | nil, simplifying with (370), (387) gives: % 289.11/72.03 | | | | (398) all_304_0 = all_296_0 % 289.11/72.03 | | | | % 289.11/72.03 | | | | GROUND_INST: instantiating (22) with all_304_0, all_306_0, all_91_0, % 289.11/72.03 | | | | nil, simplifying with (387), (388) gives: % 289.11/72.03 | | | | (399) all_306_0 = all_304_0 % 289.11/72.03 | | | | % 289.11/72.03 | | | | GROUND_INST: instantiating (22) with all_306_0, all_312_0, all_91_0, % 289.11/72.03 | | | | nil, simplifying with (376), (388) gives: % 289.11/72.03 | | | | (400) all_312_0 = all_306_0 % 289.11/72.03 | | | | % 289.11/72.03 | | | | GROUND_INST: instantiating (22) with all_312_0, all_414_0, all_91_0, % 289.11/72.03 | | | | nil, simplifying with (376), (378) gives: % 289.11/72.03 | | | | (401) all_414_0 = all_312_0 % 289.11/72.03 | | | | % 289.11/72.03 | | | | GROUND_INST: instantiating (22) with all_414_0, all_418_0, all_91_0, % 289.11/72.03 | | | | nil, simplifying with (378), (389) gives: % 289.11/72.03 | | | | (402) all_418_0 = all_414_0 % 289.11/72.03 | | | | % 289.11/72.03 | | | | GROUND_INST: instantiating (22) with all_294_0, all_418_0, all_91_0, % 289.11/72.03 | | | | nil, simplifying with (368), (389) gives: % 289.11/72.03 | | | | (403) all_418_0 = all_294_0 % 289.11/72.03 | | | | % 289.11/72.03 | | | | GROUND_INST: instantiating (22) with all_91_0, all_562_0, nil, all_91_0, % 289.11/72.03 | | | | simplifying with (274), (393) gives: % 289.11/72.03 | | | | (404) all_562_0 = all_91_0 % 289.11/72.03 | | | | % 289.11/72.03 | | | | GROUND_INST: instantiating (22) with all_562_0, all_590_0, nil, % 289.11/72.03 | | | | all_91_0, simplifying with (392), (393) gives: % 289.11/72.03 | | | | (405) all_590_0 = all_562_0 % 289.11/72.03 | | | | % 289.11/72.03 | | | | GROUND_INST: instantiating (22) with all_210_0, all_590_0, nil, % 289.11/72.03 | | | | all_91_0, simplifying with (392), (394) gives: % 289.11/72.03 | | | | (406) all_590_0 = all_210_0 % 289.11/72.03 | | | | % 289.11/72.03 | | | | COMBINE_EQS: (405), (406) imply: % 289.11/72.03 | | | | (407) all_562_0 = all_210_0 % 289.11/72.03 | | | | % 289.11/72.03 | | | | SIMP: (407) implies: % 289.11/72.03 | | | | (408) all_562_0 = all_210_0 % 289.11/72.03 | | | | % 289.11/72.03 | | | | COMBINE_EQS: (404), (408) imply: % 289.11/72.03 | | | | (409) all_210_0 = all_91_0 % 289.11/72.03 | | | | % 289.11/72.03 | | | | COMBINE_EQS: (402), (403) imply: % 289.11/72.03 | | | | (410) all_414_0 = all_294_0 % 289.11/72.03 | | | | % 289.11/72.03 | | | | SIMP: (410) implies: % 289.11/72.03 | | | | (411) all_414_0 = all_294_0 % 289.11/72.03 | | | | % 289.11/72.03 | | | | COMBINE_EQS: (401), (411) imply: % 289.11/72.03 | | | | (412) all_312_0 = all_294_0 % 289.11/72.03 | | | | % 289.11/72.03 | | | | SIMP: (412) implies: % 289.11/72.03 | | | | (413) all_312_0 = all_294_0 % 289.11/72.03 | | | | % 289.11/72.03 | | | | COMBINE_EQS: (400), (413) imply: % 289.11/72.03 | | | | (414) all_306_0 = all_294_0 % 289.11/72.03 | | | | % 289.11/72.03 | | | | SIMP: (414) implies: % 289.11/72.03 | | | | (415) all_306_0 = all_294_0 % 289.11/72.03 | | | | % 289.11/72.03 | | | | COMBINE_EQS: (399), (415) imply: % 289.11/72.03 | | | | (416) all_304_0 = all_294_0 % 289.11/72.03 | | | | % 289.11/72.03 | | | | SIMP: (416) implies: % 289.11/72.03 | | | | (417) all_304_0 = all_294_0 % 289.11/72.03 | | | | % 289.11/72.03 | | | | COMBINE_EQS: (398), (417) imply: % 289.11/72.03 | | | | (418) all_296_0 = all_294_0 % 289.11/72.03 | | | | % 289.11/72.03 | | | | SIMP: (418) implies: % 289.11/72.03 | | | | (419) all_296_0 = all_294_0 % 289.11/72.03 | | | | % 289.11/72.03 | | | | COMBINE_EQS: (395), (419) imply: % 289.11/72.03 | | | | (420) all_294_0 = all_91_0 % 289.11/72.03 | | | | % 289.11/72.03 | | | | COMBINE_EQS: (397), (419) imply: % 289.11/72.03 | | | | (421) all_294_0 = all_230_0 % 289.11/72.03 | | | | % 289.11/72.03 | | | | COMBINE_EQS: (396), (419) imply: % 289.11/72.03 | | | | (422) all_294_0 = all_264_0 % 289.11/72.03 | | | | % 289.11/72.03 | | | | COMBINE_EQS: (420), (422) imply: % 289.11/72.03 | | | | (423) all_264_0 = all_91_0 % 289.11/72.03 | | | | % 289.11/72.03 | | | | COMBINE_EQS: (421), (422) imply: % 289.11/72.03 | | | | (424) all_264_0 = all_230_0 % 289.11/72.03 | | | | % 289.11/72.03 | | | | COMBINE_EQS: (423), (424) imply: % 289.11/72.03 | | | | (425) all_230_0 = all_91_0 % 289.11/72.03 | | | | % 289.11/72.03 | | | | BETA: splitting (29) gives: % 289.11/72.03 | | | | % 289.11/72.03 | | | | Case 1: % 289.11/72.03 | | | | | % 289.11/72.03 | | | | | (426) ~ (all_91_0 = nil) % 289.11/72.03 | | | | | % 289.11/72.03 | | | | | BETA: splitting (44) gives: % 289.11/72.03 | | | | | % 289.11/72.03 | | | | | Case 1: % 289.11/72.03 | | | | | | % 289.11/72.03 | | | | | | (427) neq(all_91_0, nil) % 289.11/72.03 | | | | | | % 289.11/72.03 | | | | | | GROUND_INST: instantiating (30) with all_91_0, simplifying with % 289.11/72.03 | | | | | | (25), (27), (294), (295), (427) gives: % 289.11/72.03 | | | | | | (428) $false % 289.11/72.03 | | | | | | % 289.11/72.03 | | | | | | CLOSE: (428) is inconsistent. % 289.11/72.03 | | | | | | % 289.11/72.03 | | | | | Case 2: % 289.11/72.03 | | | | | | % 289.11/72.03 | | | | | | (429) all_91_0 = nil % 289.11/72.03 | | | | | | % 289.11/72.03 | | | | | | REDUCE: (426), (429) imply: % 289.11/72.03 | | | | | | (430) $false % 289.11/72.03 | | | | | | % 289.11/72.03 | | | | | | CLOSE: (430) is inconsistent. % 289.11/72.03 | | | | | | % 289.11/72.03 | | | | | End of split % 289.11/72.03 | | | | | % 289.11/72.03 | | | | Case 2: % 289.11/72.03 | | | | | % 289.11/72.03 | | | | | (431) all_91_0 = nil % 289.11/72.03 | | | | | (432) ~ (all_91_1 = nil) % 289.11/72.03 | | | | | % 289.11/72.03 | | | | | REDUCE: (28), (431) imply: % 289.11/72.03 | | | | | (433) app(nil, nil) = all_91_1 % 289.11/72.03 | | | | | % 289.11/72.03 | | | | | GROUND_INST: instantiating (22) with nil, all_91_1, nil, nil, % 289.11/72.03 | | | | | simplifying with (147), (433) gives: % 289.11/72.03 | | | | | (434) all_91_1 = nil % 289.11/72.03 | | | | | % 289.11/72.03 | | | | | REDUCE: (432), (434) imply: % 289.11/72.03 | | | | | (435) $false % 289.11/72.03 | | | | | % 289.11/72.03 | | | | | CLOSE: (435) is inconsistent. % 289.11/72.03 | | | | | % 289.11/72.03 | | | | End of split % 289.11/72.03 | | | | % 289.11/72.04 | | | End of split % 289.11/72.04 | | | % 289.11/72.04 | | End of split % 289.11/72.04 | | % 289.11/72.04 | End of split % 289.11/72.04 | % 289.11/72.04 End of proof % 289.11/72.04 % SZS output end Proof for theBenchmark % 289.11/72.04 % 289.11/72.04 71437ms %------------------------------------------------------------------------------