%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SWC060+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 : n009.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 20:49:26 EDT 2023 % Result : Theorem 33.52s 5.12s % Output : Proof 256.93s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.12 % Problem : SWC060+1 : TPTP v8.1.2. Released v2.4.0. % 0.11/0.12 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.12/0.33 % Computer : n009.cluster.edu % 0.12/0.33 % Model : x86_64 x86_64 % 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.33 % Memory : 8042.1875MB % 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.33 % CPULimit : 300 % 0.12/0.33 % WCLimit : 300 % 0.12/0.33 % DateTime : Mon Aug 28 18:32:05 EDT 2023 % 0.12/0.33 % CPUTime : % 0.67/0.64 ________ _____ % 0.67/0.64 ___ __ \_________(_)________________________________ % 0.67/0.64 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.67/0.64 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.67/0.64 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.67/0.64 % 0.67/0.64 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.67/0.64 (2023-06-19) % 0.67/0.64 % 0.67/0.64 (c) Philipp Rümmer, 2009-2023 % 0.67/0.64 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.67/0.64 Amanda Stjerna. % 0.67/0.64 Free software under BSD-3-Clause. % 0.67/0.64 % 0.67/0.64 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.67/0.64 % 0.67/0.64 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.67/0.66 Running up to 7 provers in parallel. % 0.67/0.67 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.67/0.67 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.67/0.67 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.67/0.67 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.67/0.67 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.67/0.67 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 0.67/0.67 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 5.70/1.47 Prover 1: Preprocessing ... % 5.70/1.47 Prover 4: Preprocessing ... % 6.04/1.52 Prover 5: Preprocessing ... % 6.04/1.52 Prover 3: Preprocessing ... % 6.04/1.54 Prover 0: Preprocessing ... % 6.04/1.54 Prover 6: Preprocessing ... % 6.04/1.54 Prover 2: Preprocessing ... % 15.00/2.75 Prover 2: Proving ... % 15.67/2.80 Prover 5: Constructing countermodel ... % 16.03/2.85 Prover 1: Constructing countermodel ... % 16.03/2.86 Prover 6: Proving ... % 16.03/2.90 Prover 3: Constructing countermodel ... % 22.50/3.70 Prover 4: Constructing countermodel ... % 23.71/3.87 Prover 0: Proving ... % 33.52/5.12 Prover 3: proved (4446ms) % 33.52/5.12 % 33.52/5.12 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 33.52/5.12 % 33.52/5.12 Prover 5: stopped % 33.52/5.13 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 33.52/5.13 Prover 6: stopped % 33.52/5.13 Prover 0: stopped % 33.52/5.13 Prover 2: stopped % 33.52/5.13 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 33.52/5.13 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 33.52/5.15 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 33.52/5.15 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 35.25/5.37 Prover 7: Preprocessing ... % 35.25/5.39 Prover 8: Preprocessing ... % 35.87/5.41 Prover 10: Preprocessing ... % 35.87/5.42 Prover 11: Preprocessing ... % 35.87/5.43 Prover 13: Preprocessing ... % 36.93/5.59 Prover 10: Constructing countermodel ... % 36.93/5.61 Prover 7: Constructing countermodel ... % 37.65/5.66 Prover 13: Constructing countermodel ... % 38.90/5.80 Prover 8: Warning: ignoring some quantifiers % 38.90/5.83 Prover 8: Constructing countermodel ... % 45.37/6.60 Prover 11: Constructing countermodel ... % 73.16/10.20 Prover 13: stopped % 73.47/10.21 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 73.80/10.32 Prover 16: Preprocessing ... % 74.91/10.42 Prover 16: Constructing countermodel ... % 115.61/15.73 Prover 16: stopped % 115.61/15.74 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085 % 116.36/15.85 Prover 19: Preprocessing ... % 118.14/16.03 Prover 1: stopped % 118.92/16.22 Prover 19: Warning: ignoring some quantifiers % 119.58/16.25 Prover 19: Constructing countermodel ... % 142.76/19.46 Prover 19: stopped % 186.85/27.71 Prover 7: stopped % 188.10/28.00 Prover 4: stopped % 230.99/39.85 Prover 8: stopped % 231.51/40.01 Prover 11: stopped % 255.71/60.60 Prover 10: Found proof (size 253) % 255.71/60.60 Prover 10: proved (55475ms) % 255.71/60.60 % 255.71/60.60 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 255.71/60.60 % 256.28/60.75 % SZS output start Proof for theBenchmark % 256.39/60.75 Assumptions after simplification: % 256.39/60.75 --------------------------------- % 256.39/60.75 % 256.39/60.75 (ax15) % 256.39/60.76 ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ $i(v1) | ~ $i(v0) | ~ ssList(v1) | % 256.39/60.76 ~ ssList(v0) | neq(v0, v1)) & ! [v0: $i] : ( ~ $i(v0) | ~ ssList(v0) | ~ % 256.39/60.76 neq(v0, v0)) % 256.39/60.76 % 256.39/60.76 (ax17) % 256.39/60.76 $i(nil) & ssList(nil) % 256.39/60.76 % 256.39/60.76 (ax26) % 256.39/60.79 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (app(v0, v1) = v2) | ~ $i(v1) | % 256.39/60.79 ~ $i(v0) | ~ ssList(v1) | ~ ssList(v0) | ssList(v2)) % 256.39/60.79 % 256.39/60.79 (ax28) % 256.39/60.79 $i(nil) & ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (app(nil, v0) = v1) | ~ % 256.39/60.79 $i(v0) | ~ ssList(v0)) % 256.39/60.79 % 256.39/60.79 (ax42) % 256.39/60.79 ! [v0: $i] : ( ~ $i(v0) | ~ ssList(v0) | frontsegP(v0, v0)) % 256.39/60.79 % 256.39/60.79 (ax45) % 256.39/60.79 $i(nil) & ! [v0: $i] : ( ~ $i(v0) | ~ ssList(v0) | frontsegP(v0, nil)) % 256.39/60.79 % 256.39/60.79 (ax46) % 256.39/60.79 $i(nil) & ! [v0: $i] : (v0 = nil | ~ $i(v0) | ~ frontsegP(nil, v0) | ~ % 256.39/60.79 ssList(v0)) & ( ~ ssList(nil) | frontsegP(nil, nil)) % 256.39/60.79 % 256.39/60.79 (ax49) % 256.39/60.79 ! [v0: $i] : ( ~ $i(v0) | ~ ssList(v0) | rearsegP(v0, v0)) % 256.39/60.79 % 256.39/60.79 (ax5) % 256.39/60.79 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (app(v1, v2) = v0) | ~ $i(v2) | % 256.39/60.79 ~ $i(v1) | ~ $i(v0) | ~ ssList(v2) | ~ ssList(v1) | ~ ssList(v0) | % 256.39/60.79 frontsegP(v0, v1)) & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ % 256.39/60.79 frontsegP(v0, v1) | ~ ssList(v1) | ~ ssList(v0) | ? [v2: $i] : (app(v1, % 256.39/60.79 v2) = v0 & $i(v2) & ssList(v2))) % 256.39/60.79 % 256.39/60.79 (ax50) % 256.39/60.80 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (app(v2, v0) = v3) % 256.39/60.80 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ rearsegP(v0, v1) | ~ ssList(v2) | % 256.39/60.80 ~ ssList(v1) | ~ ssList(v0) | rearsegP(v3, v1)) % 256.39/60.80 % 256.39/60.80 (ax51) % 256.39/60.80 $i(nil) & ! [v0: $i] : ( ~ $i(v0) | ~ ssList(v0) | rearsegP(v0, nil)) % 256.39/60.80 % 256.39/60.80 (ax52) % 256.39/60.80 $i(nil) & ! [v0: $i] : (v0 = nil | ~ $i(v0) | ~ rearsegP(nil, v0) | ~ % 256.39/60.80 ssList(v0)) & ( ~ ssList(nil) | rearsegP(nil, nil)) % 256.39/60.80 % 256.39/60.80 (ax58) % 256.39/60.80 $i(nil) & ! [v0: $i] : (v0 = nil | ~ $i(v0) | ~ segmentP(nil, v0) | ~ % 256.39/60.80 ssList(v0)) & ( ~ ssList(nil) | segmentP(nil, nil)) % 256.39/60.80 % 256.39/60.80 (ax6) % 256.39/60.80 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (app(v2, v1) = v0) | ~ $i(v2) | % 256.39/60.80 ~ $i(v1) | ~ $i(v0) | ~ ssList(v2) | ~ ssList(v1) | ~ ssList(v0) | % 256.39/60.80 rearsegP(v0, v1)) & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ % 256.39/60.80 rearsegP(v0, v1) | ~ ssList(v1) | ~ ssList(v0) | ? [v2: $i] : (app(v2, % 256.39/60.80 v1) = v0 & $i(v2) & ssList(v2))) % 256.39/60.80 % 256.39/60.80 (ax7) % 256.39/60.81 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 256.39/60.81 (app(v3, v4) = v0) | ~ (app(v2, v1) = v3) | ~ $i(v4) | ~ $i(v2) | ~ % 256.39/60.81 $i(v1) | ~ $i(v0) | ~ ssList(v4) | ~ ssList(v2) | ~ ssList(v1) | ~ % 256.39/60.81 ssList(v0) | segmentP(v0, v1)) & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ % 256.39/60.81 $i(v0) | ~ segmentP(v0, v1) | ~ ssList(v1) | ~ ssList(v0) | ? [v2: $i] : % 256.39/60.81 ? [v3: $i] : ? [v4: $i] : (app(v3, v4) = v0 & app(v2, v1) = v3 & $i(v4) & % 256.39/60.81 $i(v3) & $i(v2) & ssList(v4) & ssList(v2))) % 256.39/60.81 % 256.39/60.81 (ax79) % 256.39/60.81 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v0 | ~ (app(v3, % 256.39/60.81 v1) = v2) | ~ (app(v0, v1) = v2) | ~ $i(v3) | ~ $i(v1) | ~ $i(v0) | % 256.39/60.81 ~ ssList(v3) | ~ ssList(v1) | ~ ssList(v0)) % 256.39/60.81 % 256.39/60.81 (ax80) % 256.39/60.81 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v0 | ~ (app(v1, % 256.39/60.81 v3) = v2) | ~ (app(v1, v0) = v2) | ~ $i(v3) | ~ $i(v1) | ~ $i(v0) | % 256.39/60.81 ~ ssList(v3) | ~ ssList(v1) | ~ ssList(v0)) % 256.39/60.81 % 256.39/60.81 (ax82) % 256.39/60.81 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 256.39/60.81 (app(v2, v3) = v4) | ~ (app(v0, v1) = v2) | ~ $i(v3) | ~ $i(v1) | ~ % 256.39/60.81 $i(v0) | ~ ssList(v3) | ~ ssList(v1) | ~ ssList(v0) | ? [v5: $i] : % 256.39/60.81 (app(v1, v3) = v5 & app(v0, v5) = v4 & $i(v5) & $i(v4))) % 256.39/60.81 % 256.39/60.81 (ax83) % 256.39/60.82 $i(nil) & ! [v0: $i] : ! [v1: $i] : (v1 = nil | ~ (app(v0, v1) = nil) | ~ % 256.39/60.82 $i(v1) | ~ $i(v0) | ~ ssList(v1) | ~ ssList(v0)) & ! [v0: $i] : ! [v1: % 256.39/60.82 $i] : (v0 = nil | ~ (app(v0, v1) = nil) | ~ $i(v1) | ~ $i(v0) | ~ % 256.39/60.82 ssList(v1) | ~ ssList(v0)) & ! [v0: $i] : (v0 = nil | ~ (app(nil, nil) = % 256.39/60.82 v0) | ~ ssList(nil)) % 256.39/60.82 % 256.39/60.82 (ax84) % 256.39/60.82 $i(nil) & ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (app(v0, nil) = v1) | ~ % 256.39/60.82 $i(v0) | ~ ssList(v0)) % 256.39/60.82 % 256.39/60.82 (co1) % 256.39/60.82 $i(nil) & ? [v0: $i] : ? [v1: $i] : ($i(v1) & $i(v0) & ssList(v1) & % 256.39/60.82 ssList(v0) & ((v1 = nil & v0 = nil) | (segmentP(v1, v0) & neq(v0, nil))) & % 256.39/60.82 ((v1 = nil & ~ (v0 = nil)) | (neq(v1, nil) & ! [v2: $i] : ( ~ $i(v2) | ~ % 256.39/60.82 segmentP(v1, v2) | ~ segmentP(v0, v2) | ~ ssList(v2) | ~ neq(v2, % 256.39/60.82 nil))))) % 256.39/60.82 % 256.39/60.82 (function-axioms) % 256.39/60.82 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 256.39/60.82 (cons(v3, v2) = v1) | ~ (cons(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : % 256.39/60.82 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (app(v3, v2) = v1) | ~ (app(v3, v2) % 256.39/60.82 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (tl(v2) = % 256.39/60.82 v1) | ~ (tl(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = % 256.39/60.82 v0 | ~ (hd(v2) = v1) | ~ (hd(v2) = v0)) % 256.39/60.82 % 256.39/60.82 Further assumptions not needed in the proof: % 256.39/60.82 -------------------------------------------- % 256.39/60.82 ax1, ax10, ax11, ax12, ax13, ax14, ax16, ax18, ax19, ax2, ax20, ax21, ax22, % 256.39/60.82 ax23, ax24, ax25, ax27, ax29, ax3, ax30, ax31, ax32, ax33, ax34, ax35, ax36, % 256.39/60.82 ax37, ax38, ax39, ax4, ax40, ax41, ax43, ax44, ax47, ax48, ax53, ax54, ax55, % 256.39/60.82 ax56, ax57, ax59, ax60, ax61, ax62, ax63, ax64, ax65, ax66, ax67, ax68, ax69, % 256.72/60.82 ax70, ax71, ax72, ax73, ax74, ax75, ax76, ax77, ax78, ax8, ax81, ax85, ax86, % 256.72/60.82 ax87, ax88, ax89, ax9, ax90, ax91, ax92, ax93, ax94, ax95 % 256.72/60.82 % 256.72/60.82 Those formulas are unsatisfiable: % 256.72/60.82 --------------------------------- % 256.72/60.82 % 256.72/60.82 Begin of proof % 256.72/60.83 | % 256.72/60.83 | ALPHA: (ax5) implies: % 256.72/60.83 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ frontsegP(v0, % 256.72/60.83 | v1) | ~ ssList(v1) | ~ ssList(v0) | ? [v2: $i] : (app(v1, v2) = % 256.72/60.83 | v0 & $i(v2) & ssList(v2))) % 256.72/60.83 | % 256.72/60.83 | ALPHA: (ax6) implies: % 256.72/60.83 | (2) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ rearsegP(v0, % 256.72/60.83 | v1) | ~ ssList(v1) | ~ ssList(v0) | ? [v2: $i] : (app(v2, v1) = % 256.72/60.83 | v0 & $i(v2) & ssList(v2))) % 256.72/60.83 | % 256.72/60.83 | ALPHA: (ax7) implies: % 256.72/60.83 | (3) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ segmentP(v0, % 256.72/60.83 | v1) | ~ ssList(v1) | ~ ssList(v0) | ? [v2: $i] : ? [v3: $i] : % 256.72/60.83 | ? [v4: $i] : (app(v3, v4) = v0 & app(v2, v1) = v3 & $i(v4) & $i(v3) & % 256.72/60.83 | $i(v2) & ssList(v4) & ssList(v2))) % 256.72/60.83 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( % 256.72/60.83 | ~ (app(v3, v4) = v0) | ~ (app(v2, v1) = v3) | ~ $i(v4) | ~ $i(v2) % 256.72/60.83 | | ~ $i(v1) | ~ $i(v0) | ~ ssList(v4) | ~ ssList(v2) | ~ % 256.72/60.83 | ssList(v1) | ~ ssList(v0) | segmentP(v0, v1)) % 256.72/60.83 | % 256.72/60.83 | ALPHA: (ax15) implies: % 256.72/60.83 | (5) ! [v0: $i] : ( ~ $i(v0) | ~ ssList(v0) | ~ neq(v0, v0)) % 256.72/60.83 | % 256.72/60.83 | ALPHA: (ax17) implies: % 256.72/60.83 | (6) ssList(nil) % 256.72/60.83 | % 256.72/60.83 | ALPHA: (ax28) implies: % 256.72/60.84 | (7) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (app(nil, v0) = v1) | ~ % 256.72/60.84 | $i(v0) | ~ ssList(v0)) % 256.72/60.84 | % 256.72/60.84 | ALPHA: (ax45) implies: % 256.72/60.84 | (8) ! [v0: $i] : ( ~ $i(v0) | ~ ssList(v0) | frontsegP(v0, nil)) % 256.72/60.84 | % 256.72/60.84 | ALPHA: (ax46) implies: % 256.72/60.84 | (9) ~ ssList(nil) | frontsegP(nil, nil) % 256.72/60.84 | % 256.72/60.84 | ALPHA: (ax51) implies: % 256.72/60.84 | (10) ! [v0: $i] : ( ~ $i(v0) | ~ ssList(v0) | rearsegP(v0, nil)) % 256.72/60.84 | % 256.72/60.84 | ALPHA: (ax52) implies: % 256.72/60.84 | (11) ~ ssList(nil) | rearsegP(nil, nil) % 256.72/60.84 | % 256.72/60.84 | ALPHA: (ax58) implies: % 256.72/60.84 | (12) ~ ssList(nil) | segmentP(nil, nil) % 256.72/60.84 | (13) ! [v0: $i] : (v0 = nil | ~ $i(v0) | ~ segmentP(nil, v0) | ~ % 256.72/60.84 | ssList(v0)) % 256.72/60.84 | % 256.72/60.84 | ALPHA: (ax83) implies: % 256.72/60.84 | (14) ! [v0: $i] : (v0 = nil | ~ (app(nil, nil) = v0) | ~ ssList(nil)) % 256.72/60.84 | (15) ! [v0: $i] : ! [v1: $i] : (v0 = nil | ~ (app(v0, v1) = nil) | ~ % 256.72/60.84 | $i(v1) | ~ $i(v0) | ~ ssList(v1) | ~ ssList(v0)) % 256.72/60.84 | (16) ! [v0: $i] : ! [v1: $i] : (v1 = nil | ~ (app(v0, v1) = nil) | ~ % 256.72/60.84 | $i(v1) | ~ $i(v0) | ~ ssList(v1) | ~ ssList(v0)) % 256.72/60.84 | % 256.72/60.84 | ALPHA: (ax84) implies: % 256.72/60.84 | (17) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (app(v0, nil) = v1) | ~ % 256.72/60.84 | $i(v0) | ~ ssList(v0)) % 256.72/60.84 | % 256.72/60.84 | ALPHA: (co1) implies: % 256.72/60.84 | (18) $i(nil) % 256.72/60.84 | (19) ? [v0: $i] : ? [v1: $i] : ($i(v1) & $i(v0) & ssList(v1) & ssList(v0) % 256.72/60.84 | & ((v1 = nil & v0 = nil) | (segmentP(v1, v0) & neq(v0, nil))) & ((v1 % 256.72/60.84 | = nil & ~ (v0 = nil)) | (neq(v1, nil) & ! [v2: $i] : ( ~ % 256.72/60.84 | $i(v2) | ~ segmentP(v1, v2) | ~ segmentP(v0, v2) | ~ % 256.72/60.84 | ssList(v2) | ~ neq(v2, nil))))) % 256.72/60.84 | % 256.72/60.84 | ALPHA: (function-axioms) implies: % 256.72/60.84 | (20) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 256.72/60.84 | (app(v3, v2) = v1) | ~ (app(v3, v2) = v0)) % 256.72/60.84 | % 256.72/60.85 | DELTA: instantiating (19) with fresh symbols all_91_0, all_91_1 gives: % 256.72/60.85 | (21) $i(all_91_0) & $i(all_91_1) & ssList(all_91_0) & ssList(all_91_1) & % 256.72/60.85 | ((all_91_0 = nil & all_91_1 = nil) | (segmentP(all_91_0, all_91_1) & % 256.72/60.85 | neq(all_91_1, nil))) & ((all_91_0 = nil & ~ (all_91_1 = nil)) | % 256.72/60.85 | (neq(all_91_0, nil) & ! [v0: $i] : ( ~ $i(v0) | ~ % 256.72/60.85 | segmentP(all_91_0, v0) | ~ segmentP(all_91_1, v0) | ~ % 256.72/60.85 | ssList(v0) | ~ neq(v0, nil)))) % 256.72/60.85 | % 256.72/60.85 | ALPHA: (21) implies: % 256.72/60.85 | (22) ssList(all_91_1) % 256.72/60.85 | (23) $i(all_91_1) % 256.72/60.85 | (24) (all_91_0 = nil & ~ (all_91_1 = nil)) | (neq(all_91_0, nil) & ! [v0: % 256.72/60.85 | $i] : ( ~ $i(v0) | ~ segmentP(all_91_0, v0) | ~ % 256.72/60.85 | segmentP(all_91_1, v0) | ~ ssList(v0) | ~ neq(v0, nil))) % 256.72/60.85 | (25) (all_91_0 = nil & all_91_1 = nil) | (segmentP(all_91_0, all_91_1) & % 256.72/60.85 | neq(all_91_1, nil)) % 256.72/60.85 | % 256.72/60.85 | BETA: splitting (11) gives: % 256.72/60.85 | % 256.72/60.85 | Case 1: % 256.72/60.85 | | % 256.72/60.85 | | (26) ~ ssList(nil) % 256.72/60.85 | | % 256.72/60.85 | | PRED_UNIFY: (6), (26) imply: % 256.72/60.85 | | (27) $false % 256.72/60.85 | | % 256.72/60.85 | | CLOSE: (27) is inconsistent. % 256.72/60.85 | | % 256.72/60.85 | Case 2: % 256.72/60.85 | | % 256.72/60.85 | | (28) rearsegP(nil, nil) % 256.72/60.85 | | % 256.72/60.85 | | BETA: splitting (9) gives: % 256.72/60.85 | | % 256.72/60.85 | | Case 1: % 256.72/60.85 | | | % 256.72/60.85 | | | (29) ~ ssList(nil) % 256.72/60.85 | | | % 256.72/60.85 | | | PRED_UNIFY: (6), (29) imply: % 256.72/60.85 | | | (30) $false % 256.72/60.85 | | | % 256.72/60.85 | | | CLOSE: (30) is inconsistent. % 256.72/60.85 | | | % 256.72/60.85 | | Case 2: % 256.72/60.85 | | | % 256.72/60.85 | | | (31) frontsegP(nil, nil) % 256.72/60.85 | | | % 256.72/60.85 | | | BETA: splitting (12) gives: % 256.72/60.85 | | | % 256.72/60.85 | | | Case 1: % 256.72/60.85 | | | | % 256.72/60.85 | | | | (32) ~ ssList(nil) % 256.72/60.85 | | | | % 256.72/60.85 | | | | PRED_UNIFY: (6), (32) imply: % 256.72/60.85 | | | | (33) $false % 256.72/60.85 | | | | % 256.72/60.85 | | | | CLOSE: (33) is inconsistent. % 256.72/60.85 | | | | % 256.72/60.85 | | | Case 2: % 256.72/60.85 | | | | % 256.72/60.85 | | | | (34) segmentP(nil, nil) % 256.72/60.85 | | | | % 256.72/60.86 | | | | GROUND_INST: instantiating (ax49) with all_91_1, simplifying with (22), % 256.72/60.86 | | | | (23) gives: % 256.72/60.86 | | | | (35) rearsegP(all_91_1, all_91_1) % 256.72/60.86 | | | | % 256.72/60.86 | | | | GROUND_INST: instantiating (10) with all_91_1, simplifying with (22), % 256.72/60.86 | | | | (23) gives: % 256.72/60.86 | | | | (36) rearsegP(all_91_1, nil) % 256.72/60.86 | | | | % 256.72/60.86 | | | | GROUND_INST: instantiating (ax42) with all_91_1, simplifying with (22), % 256.72/60.86 | | | | (23) gives: % 256.72/60.86 | | | | (37) frontsegP(all_91_1, all_91_1) % 256.72/60.86 | | | | % 256.72/60.86 | | | | GROUND_INST: instantiating (8) with all_91_1, simplifying with (22), % 256.72/60.86 | | | | (23) gives: % 256.72/60.86 | | | | (38) frontsegP(all_91_1, nil) % 256.72/60.86 | | | | % 256.72/60.86 | | | | GROUND_INST: instantiating (1) with nil, nil, simplifying with (6), % 256.72/60.86 | | | | (18), (31) gives: % 256.72/60.86 | | | | (39) ? [v0: $i] : (app(nil, v0) = nil & $i(v0) & ssList(v0)) % 256.72/60.86 | | | | % 256.72/60.86 | | | | GROUND_INST: instantiating (2) with nil, nil, simplifying with (6), % 256.72/60.86 | | | | (18), (28) gives: % 256.72/60.86 | | | | (40) ? [v0: $i] : (app(v0, nil) = nil & $i(v0) & ssList(v0)) % 256.72/60.86 | | | | % 256.72/60.86 | | | | GROUND_INST: instantiating (3) with nil, nil, simplifying with (6), % 256.72/60.86 | | | | (18), (34) gives: % 256.72/60.86 | | | | (41) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (app(v1, v2) = nil & % 256.72/60.86 | | | | app(v0, nil) = v1 & $i(v2) & $i(v1) & $i(v0) & ssList(v2) & % 256.72/60.86 | | | | ssList(v0)) % 256.72/60.86 | | | | % 256.72/60.86 | | | | DELTA: instantiating (40) with fresh symbol all_111_0 gives: % 256.72/60.86 | | | | (42) app(all_111_0, nil) = nil & $i(all_111_0) & ssList(all_111_0) % 256.72/60.86 | | | | % 256.72/60.86 | | | | ALPHA: (42) implies: % 256.72/60.86 | | | | (43) ssList(all_111_0) % 256.72/60.86 | | | | (44) $i(all_111_0) % 256.72/60.86 | | | | (45) app(all_111_0, nil) = nil % 256.72/60.86 | | | | % 256.72/60.86 | | | | DELTA: instantiating (39) with fresh symbol all_113_0 gives: % 256.72/60.86 | | | | (46) app(nil, all_113_0) = nil & $i(all_113_0) & ssList(all_113_0) % 256.72/60.86 | | | | % 256.72/60.86 | | | | ALPHA: (46) implies: % 256.72/60.86 | | | | (47) ssList(all_113_0) % 256.72/60.86 | | | | (48) $i(all_113_0) % 256.72/60.86 | | | | (49) app(nil, all_113_0) = nil % 256.72/60.86 | | | | % 256.72/60.86 | | | | DELTA: instantiating (41) with fresh symbols all_115_0, all_115_1, % 256.72/60.86 | | | | all_115_2 gives: % 256.72/60.86 | | | | (50) app(all_115_1, all_115_0) = nil & app(all_115_2, nil) = % 256.72/60.86 | | | | all_115_1 & $i(all_115_0) & $i(all_115_1) & $i(all_115_2) & % 256.72/60.86 | | | | ssList(all_115_0) & ssList(all_115_2) % 256.72/60.86 | | | | % 256.72/60.86 | | | | ALPHA: (50) implies: % 256.72/60.86 | | | | (51) ssList(all_115_2) % 256.72/60.86 | | | | (52) ssList(all_115_0) % 256.72/60.86 | | | | (53) $i(all_115_2) % 256.72/60.86 | | | | (54) $i(all_115_1) % 256.72/60.86 | | | | (55) $i(all_115_0) % 256.72/60.86 | | | | (56) app(all_115_2, nil) = all_115_1 % 256.72/60.86 | | | | (57) app(all_115_1, all_115_0) = nil % 256.72/60.86 | | | | % 256.72/60.86 | | | | GROUND_INST: instantiating (ax49) with all_115_2, simplifying with (51), % 256.72/60.86 | | | | (53) gives: % 256.72/60.86 | | | | (58) rearsegP(all_115_2, all_115_2) % 256.72/60.86 | | | | % 256.72/60.86 | | | | GROUND_INST: instantiating (ax42) with all_115_2, simplifying with (51), % 256.72/60.86 | | | | (53) gives: % 256.72/60.86 | | | | (59) frontsegP(all_115_2, all_115_2) % 256.72/60.86 | | | | % 256.72/60.86 | | | | GROUND_INST: instantiating (8) with all_115_2, simplifying with (51), % 256.72/60.86 | | | | (53) gives: % 256.72/60.86 | | | | (60) frontsegP(all_115_2, nil) % 256.72/60.86 | | | | % 256.72/60.86 | | | | GROUND_INST: instantiating (ax49) with all_115_0, simplifying with (52), % 256.72/60.86 | | | | (55) gives: % 256.72/60.86 | | | | (61) rearsegP(all_115_0, all_115_0) % 256.72/60.86 | | | | % 256.72/60.86 | | | | GROUND_INST: instantiating (10) with all_115_0, simplifying with (52), % 256.72/60.86 | | | | (55) gives: % 256.72/60.86 | | | | (62) rearsegP(all_115_0, nil) % 256.72/60.86 | | | | % 256.72/60.86 | | | | GROUND_INST: instantiating (ax42) with all_115_0, simplifying with (52), % 256.72/60.86 | | | | (55) gives: % 256.72/60.87 | | | | (63) frontsegP(all_115_0, all_115_0) % 256.72/60.87 | | | | % 256.72/60.87 | | | | GROUND_INST: instantiating (8) with all_115_0, simplifying with (52), % 256.72/60.87 | | | | (55) gives: % 256.72/60.87 | | | | (64) frontsegP(all_115_0, nil) % 256.72/60.87 | | | | % 256.72/60.87 | | | | GROUND_INST: instantiating (1) with all_91_1, nil, simplifying with (6), % 256.72/60.87 | | | | (18), (22), (23), (38) gives: % 256.72/60.87 | | | | (65) ? [v0: $i] : (app(nil, v0) = all_91_1 & $i(v0) & ssList(v0)) % 256.72/60.87 | | | | % 256.72/60.87 | | | | GROUND_INST: instantiating (1) with all_91_1, all_91_1, simplifying with % 256.72/60.87 | | | | (22), (23), (37) gives: % 256.72/60.87 | | | | (66) ? [v0: $i] : (app(all_91_1, v0) = all_91_1 & $i(v0) & % 256.72/60.87 | | | | ssList(v0)) % 256.72/60.87 | | | | % 256.72/60.87 | | | | GROUND_INST: instantiating (2) with all_91_1, nil, simplifying with (6), % 256.72/60.87 | | | | (18), (22), (23), (36) gives: % 256.72/60.87 | | | | (67) ? [v0: $i] : (app(v0, nil) = all_91_1 & $i(v0) & ssList(v0)) % 256.72/60.87 | | | | % 256.72/60.87 | | | | GROUND_INST: instantiating (2) with all_91_1, all_91_1, simplifying with % 256.72/60.87 | | | | (22), (23), (35) gives: % 256.72/60.87 | | | | (68) ? [v0: $i] : (app(v0, all_91_1) = all_91_1 & $i(v0) & % 256.72/60.87 | | | | ssList(v0)) % 256.72/60.87 | | | | % 256.72/60.87 | | | | GROUND_INST: instantiating (ax82) with nil, all_113_0, nil, all_113_0, % 256.72/60.87 | | | | nil, simplifying with (6), (18), (47), (48), (49) gives: % 256.72/60.87 | | | | (69) ? [v0: $i] : (app(all_113_0, all_113_0) = v0 & app(nil, v0) = % 256.72/60.87 | | | | nil & $i(v0)) % 256.72/60.87 | | | | % 256.72/60.87 | | | | GROUND_INST: instantiating (7) with all_113_0, nil, simplifying with % 256.72/60.87 | | | | (47), (48), (49) gives: % 256.72/60.87 | | | | (70) all_113_0 = nil % 256.72/60.87 | | | | % 256.72/60.87 | | | | GROUND_INST: instantiating (17) with all_111_0, nil, simplifying with % 256.72/60.87 | | | | (43), (44), (45) gives: % 256.72/60.87 | | | | (71) all_111_0 = nil % 256.72/60.87 | | | | % 256.72/60.87 | | | | GROUND_INST: instantiating (ax50) with nil, nil, all_115_2, all_115_1, % 256.72/60.87 | | | | simplifying with (6), (18), (28), (51), (53), (56) gives: % 256.72/60.87 | | | | (72) rearsegP(all_115_1, nil) % 256.72/60.87 | | | | % 256.72/60.87 | | | | GROUND_INST: instantiating (ax26) with all_115_2, nil, all_115_1, % 256.72/60.87 | | | | simplifying with (6), (18), (51), (53), (56) gives: % 256.72/60.87 | | | | (73) ssList(all_115_1) % 256.72/60.87 | | | | % 256.72/60.87 | | | | GROUND_INST: instantiating (17) with all_115_2, all_115_1, simplifying % 256.72/60.87 | | | | with (51), (53), (56) gives: % 256.72/60.87 | | | | (74) all_115_1 = all_115_2 % 256.72/60.87 | | | | % 256.72/60.87 | | | | GROUND_INST: instantiating (ax82) with all_115_2, nil, all_115_1, % 256.72/60.87 | | | | all_115_0, nil, simplifying with (6), (18), (51), (52), % 256.72/60.87 | | | | (53), (55), (56), (57) gives: % 256.72/60.87 | | | | (75) ? [v0: $i] : (app(all_115_2, v0) = nil & app(nil, all_115_0) = % 256.72/60.87 | | | | v0 & $i(v0)) % 256.72/60.87 | | | | % 256.72/60.87 | | | | DELTA: instantiating (68) with fresh symbol all_135_0 gives: % 256.93/60.88 | | | | (76) app(all_135_0, all_91_1) = all_91_1 & $i(all_135_0) & % 256.93/60.88 | | | | ssList(all_135_0) % 256.93/60.88 | | | | % 256.93/60.88 | | | | ALPHA: (76) implies: % 256.93/60.88 | | | | (77) ssList(all_135_0) % 256.93/60.88 | | | | (78) $i(all_135_0) % 256.93/60.88 | | | | (79) app(all_135_0, all_91_1) = all_91_1 % 256.93/60.88 | | | | % 256.93/60.88 | | | | DELTA: instantiating (67) with fresh symbol all_137_0 gives: % 256.93/60.88 | | | | (80) app(all_137_0, nil) = all_91_1 & $i(all_137_0) & % 256.93/60.88 | | | | ssList(all_137_0) % 256.93/60.88 | | | | % 256.93/60.88 | | | | ALPHA: (80) implies: % 256.93/60.88 | | | | (81) ssList(all_137_0) % 256.93/60.88 | | | | (82) $i(all_137_0) % 256.93/60.88 | | | | (83) app(all_137_0, nil) = all_91_1 % 256.93/60.88 | | | | % 256.93/60.88 | | | | DELTA: instantiating (75) with fresh symbol all_139_0 gives: % 256.93/60.88 | | | | (84) app(all_115_2, all_139_0) = nil & app(nil, all_115_0) = % 256.93/60.88 | | | | all_139_0 & $i(all_139_0) % 256.93/60.88 | | | | % 256.93/60.88 | | | | ALPHA: (84) implies: % 256.93/60.88 | | | | (85) app(nil, all_115_0) = all_139_0 % 256.93/60.88 | | | | % 256.93/60.88 | | | | DELTA: instantiating (69) with fresh symbol all_145_0 gives: % 256.93/60.88 | | | | (86) app(all_113_0, all_113_0) = all_145_0 & app(nil, all_145_0) = % 256.93/60.88 | | | | nil & $i(all_145_0) % 256.93/60.88 | | | | % 256.93/60.88 | | | | ALPHA: (86) implies: % 256.93/60.88 | | | | (87) $i(all_145_0) % 256.93/60.88 | | | | (88) app(all_113_0, all_113_0) = all_145_0 % 256.93/60.88 | | | | % 256.93/60.88 | | | | DELTA: instantiating (66) with fresh symbol all_147_0 gives: % 256.93/60.88 | | | | (89) app(all_91_1, all_147_0) = all_91_1 & $i(all_147_0) & % 256.93/60.88 | | | | ssList(all_147_0) % 256.93/60.88 | | | | % 256.93/60.88 | | | | ALPHA: (89) implies: % 256.93/60.88 | | | | (90) ssList(all_147_0) % 256.93/60.88 | | | | (91) $i(all_147_0) % 256.93/60.88 | | | | (92) app(all_91_1, all_147_0) = all_91_1 % 256.93/60.88 | | | | % 256.93/60.88 | | | | DELTA: instantiating (65) with fresh symbol all_149_0 gives: % 256.93/60.88 | | | | (93) app(nil, all_149_0) = all_91_1 & $i(all_149_0) & % 256.93/60.88 | | | | ssList(all_149_0) % 256.93/60.88 | | | | % 256.93/60.88 | | | | ALPHA: (93) implies: % 256.93/60.88 | | | | (94) ssList(all_149_0) % 256.93/60.88 | | | | (95) $i(all_149_0) % 256.93/60.88 | | | | (96) app(nil, all_149_0) = all_91_1 % 256.93/60.88 | | | | % 256.93/60.88 | | | | REDUCE: (57), (74) imply: % 256.93/60.88 | | | | (97) app(all_115_2, all_115_0) = nil % 256.93/60.88 | | | | % 256.93/60.88 | | | | REDUCE: (70), (88) imply: % 256.93/60.88 | | | | (98) app(nil, nil) = all_145_0 % 256.93/60.88 | | | | % 256.93/60.88 | | | | REDUCE: (72), (74) imply: % 256.93/60.88 | | | | (99) rearsegP(all_115_2, nil) % 256.93/60.88 | | | | % 256.93/60.88 | | | | GROUND_INST: instantiating (14) with all_145_0, simplifying with (6), % 256.93/60.88 | | | | (98) gives: % 256.93/60.88 | | | | (100) all_145_0 = nil % 256.93/60.88 | | | | % 256.93/60.88 | | | | REDUCE: (98), (100) imply: % 256.93/60.88 | | | | (101) app(nil, nil) = nil % 256.93/60.88 | | | | % 256.93/60.88 | | | | GROUND_INST: instantiating (1) with all_115_2, nil, simplifying with % 256.93/60.88 | | | | (6), (18), (51), (53), (60) gives: % 256.93/60.88 | | | | (102) ? [v0: $i] : (app(nil, v0) = all_115_2 & $i(v0) & ssList(v0)) % 256.93/60.88 | | | | % 256.93/60.88 | | | | GROUND_INST: instantiating (1) with all_115_2, all_115_2, simplifying % 256.93/60.88 | | | | with (51), (53), (59) gives: % 256.93/60.88 | | | | (103) ? [v0: $i] : (app(all_115_2, v0) = all_115_2 & $i(v0) & % 256.93/60.88 | | | | ssList(v0)) % 256.93/60.88 | | | | % 256.93/60.88 | | | | GROUND_INST: instantiating (1) with all_115_0, nil, simplifying with % 256.93/60.88 | | | | (6), (18), (52), (55), (64) gives: % 256.93/60.88 | | | | (104) ? [v0: $i] : (app(nil, v0) = all_115_0 & $i(v0) & ssList(v0)) % 256.93/60.88 | | | | % 256.93/60.88 | | | | GROUND_INST: instantiating (1) with all_115_0, all_115_0, simplifying % 256.93/60.88 | | | | with (52), (55), (63) gives: % 256.93/60.89 | | | | (105) ? [v0: $i] : (app(all_115_0, v0) = all_115_0 & $i(v0) & % 256.93/60.89 | | | | ssList(v0)) % 256.93/60.89 | | | | % 256.93/60.89 | | | | GROUND_INST: instantiating (2) with all_115_2, nil, simplifying with % 256.93/60.89 | | | | (6), (18), (51), (53), (99) gives: % 256.93/60.89 | | | | (106) ? [v0: $i] : (app(v0, nil) = all_115_2 & $i(v0) & ssList(v0)) % 256.93/60.89 | | | | % 256.93/60.89 | | | | GROUND_INST: instantiating (2) with all_115_2, all_115_2, simplifying % 256.93/60.89 | | | | with (51), (53), (58) gives: % 256.93/60.89 | | | | (107) ? [v0: $i] : (app(v0, all_115_2) = all_115_2 & $i(v0) & % 256.93/60.89 | | | | ssList(v0)) % 256.93/60.89 | | | | % 256.93/60.89 | | | | GROUND_INST: instantiating (2) with all_115_0, nil, simplifying with % 256.93/60.89 | | | | (6), (18), (52), (55), (62) gives: % 256.93/60.89 | | | | (108) ? [v0: $i] : (app(v0, nil) = all_115_0 & $i(v0) & ssList(v0)) % 256.93/60.89 | | | | % 256.93/60.89 | | | | GROUND_INST: instantiating (2) with all_115_0, all_115_0, simplifying % 256.93/60.89 | | | | with (52), (55), (61) gives: % 256.93/60.89 | | | | (109) ? [v0: $i] : (app(v0, all_115_0) = all_115_0 & $i(v0) & % 256.93/60.89 | | | | ssList(v0)) % 256.93/60.89 | | | | % 256.93/60.89 | | | | GROUND_INST: instantiating (ax82) with nil, nil, nil, all_115_0, % 256.93/60.89 | | | | all_139_0, simplifying with (6), (18), (52), (55), (85), % 256.93/60.89 | | | | (101) gives: % 256.93/60.89 | | | | (110) ? [v0: $i] : (app(nil, v0) = all_139_0 & app(nil, all_115_0) = % 256.93/60.89 | | | | v0 & $i(v0) & $i(all_139_0)) % 256.93/60.89 | | | | % 256.93/60.89 | | | | GROUND_INST: instantiating (7) with all_115_0, all_139_0, simplifying % 256.93/60.89 | | | | with (52), (55), (85) gives: % 256.93/60.89 | | | | (111) all_139_0 = all_115_0 % 256.93/60.89 | | | | % 256.93/60.89 | | | | GROUND_INST: instantiating (ax82) with nil, nil, nil, all_149_0, % 256.93/60.89 | | | | all_91_1, simplifying with (6), (18), (94), (95), (96), % 256.93/60.89 | | | | (101) gives: % 256.93/60.89 | | | | (112) ? [v0: $i] : (app(nil, v0) = all_91_1 & app(nil, all_149_0) = % 256.93/60.89 | | | | v0 & $i(v0) & $i(all_91_1)) % 256.93/60.89 | | | | % 256.93/60.89 | | | | GROUND_INST: instantiating (7) with all_149_0, all_91_1, simplifying % 256.93/60.89 | | | | with (94), (95), (96) gives: % 256.93/60.89 | | | | (113) all_149_0 = all_91_1 % 256.93/60.89 | | | | % 256.93/60.89 | | | | GROUND_INST: instantiating (4) with all_91_1, all_149_0, nil, all_91_1, % 256.93/60.89 | | | | all_147_0, simplifying with (6), (18), (22), (23), (90), % 256.93/60.89 | | | | (91), (92), (94), (95), (96) gives: % 256.93/60.89 | | | | (114) segmentP(all_91_1, all_149_0) % 256.93/60.89 | | | | % 256.93/60.90 | | | | GROUND_INST: instantiating (ax82) with nil, all_149_0, all_91_1, % 256.93/60.90 | | | | all_147_0, all_91_1, simplifying with (6), (18), (90), % 256.93/60.90 | | | | (91), (92), (94), (95), (96) gives: % 256.93/60.90 | | | | (115) ? [v0: $i] : (app(all_149_0, all_147_0) = v0 & app(nil, v0) = % 256.93/60.90 | | | | all_91_1 & $i(v0) & $i(all_91_1)) % 256.93/60.90 | | | | % 256.93/60.90 | | | | GROUND_INST: instantiating (ax82) with all_115_2, all_115_0, nil, % 256.93/60.90 | | | | all_149_0, all_91_1, simplifying with (51), (52), (53), % 256.93/60.90 | | | | (55), (94), (95), (96), (97) gives: % 256.93/60.90 | | | | (116) ? [v0: $i] : (app(all_115_0, all_149_0) = v0 & app(all_115_2, % 256.93/60.90 | | | | v0) = all_91_1 & $i(v0) & $i(all_91_1)) % 256.93/60.90 | | | | % 256.93/60.90 | | | | GROUND_INST: instantiating (ax82) with all_115_2, all_115_0, nil, % 256.93/60.90 | | | | all_115_0, all_139_0, simplifying with (51), (52), (53), % 256.93/60.90 | | | | (55), (85), (97) gives: % 256.93/60.90 | | | | (117) ? [v0: $i] : (app(all_115_0, all_115_0) = v0 & app(all_115_2, % 256.93/60.90 | | | | v0) = all_139_0 & $i(v0) & $i(all_139_0)) % 256.93/60.90 | | | | % 256.93/60.90 | | | | GROUND_INST: instantiating (ax82) with all_115_2, all_115_0, nil, nil, % 256.93/60.90 | | | | nil, simplifying with (6), (18), (51), (52), (53), (55), % 256.93/60.90 | | | | (97), (101) gives: % 256.93/60.90 | | | | (118) ? [v0: $i] : (app(all_115_0, nil) = v0 & app(all_115_2, v0) = % 256.93/60.90 | | | | nil & $i(v0)) % 256.93/60.90 | | | | % 256.93/60.90 | | | | GROUND_INST: instantiating (16) with all_115_2, all_115_0, simplifying % 256.93/60.90 | | | | with (51), (52), (53), (55), (97) gives: % 256.93/60.90 | | | | (119) all_115_0 = nil % 256.93/60.90 | | | | % 256.93/60.90 | | | | GROUND_INST: instantiating (15) with all_115_2, all_115_0, simplifying % 256.93/60.90 | | | | with (51), (52), (53), (55), (97) gives: % 256.93/60.90 | | | | (120) all_115_2 = nil % 256.93/60.90 | | | | % 256.93/60.90 | | | | GROUND_INST: instantiating (17) with all_137_0, all_91_1, simplifying % 256.93/60.90 | | | | with (81), (82), (83) gives: % 256.93/60.90 | | | | (121) all_137_0 = all_91_1 % 256.93/60.90 | | | | % 256.93/60.90 | | | | COMBINE_EQS: (111), (119) imply: % 256.93/60.90 | | | | (122) all_139_0 = nil % 256.93/60.90 | | | | % 256.93/60.90 | | | | DELTA: instantiating (118) with fresh symbol all_169_0 gives: % 256.93/60.90 | | | | (123) app(all_115_0, nil) = all_169_0 & app(all_115_2, all_169_0) = % 256.93/60.90 | | | | nil & $i(all_169_0) % 256.93/60.90 | | | | % 256.93/60.90 | | | | ALPHA: (123) implies: % 256.93/60.90 | | | | (124) $i(all_169_0) % 256.93/60.90 | | | | (125) app(all_115_0, nil) = all_169_0 % 256.93/60.90 | | | | % 256.93/60.90 | | | | DELTA: instantiating (109) with fresh symbol all_171_0 gives: % 256.93/60.90 | | | | (126) app(all_171_0, all_115_0) = all_115_0 & $i(all_171_0) & % 256.93/60.90 | | | | ssList(all_171_0) % 256.93/60.90 | | | | % 256.93/60.90 | | | | ALPHA: (126) implies: % 256.93/60.90 | | | | (127) ssList(all_171_0) % 256.93/60.90 | | | | (128) $i(all_171_0) % 256.93/60.90 | | | | (129) app(all_171_0, all_115_0) = all_115_0 % 256.93/60.90 | | | | % 256.93/60.90 | | | | DELTA: instantiating (107) with fresh symbol all_173_0 gives: % 256.93/60.90 | | | | (130) app(all_173_0, all_115_2) = all_115_2 & $i(all_173_0) & % 256.93/60.90 | | | | ssList(all_173_0) % 256.93/60.90 | | | | % 256.93/60.90 | | | | ALPHA: (130) implies: % 256.93/60.90 | | | | (131) ssList(all_173_0) % 256.93/60.90 | | | | (132) $i(all_173_0) % 256.93/60.90 | | | | (133) app(all_173_0, all_115_2) = all_115_2 % 256.93/60.90 | | | | % 256.93/60.90 | | | | DELTA: instantiating (106) with fresh symbol all_175_0 gives: % 256.93/60.90 | | | | (134) app(all_175_0, nil) = all_115_2 & $i(all_175_0) & % 256.93/60.90 | | | | ssList(all_175_0) % 256.93/60.90 | | | | % 256.93/60.90 | | | | ALPHA: (134) implies: % 256.93/60.90 | | | | (135) ssList(all_175_0) % 256.93/60.91 | | | | (136) $i(all_175_0) % 256.93/60.91 | | | | (137) app(all_175_0, nil) = all_115_2 % 256.93/60.91 | | | | % 256.93/60.91 | | | | DELTA: instantiating (108) with fresh symbol all_181_0 gives: % 256.93/60.91 | | | | (138) app(all_181_0, nil) = all_115_0 & $i(all_181_0) & % 256.93/60.91 | | | | ssList(all_181_0) % 256.93/60.91 | | | | % 256.93/60.91 | | | | ALPHA: (138) implies: % 256.93/60.91 | | | | (139) ssList(all_181_0) % 256.93/60.91 | | | | (140) $i(all_181_0) % 256.93/60.91 | | | | (141) app(all_181_0, nil) = all_115_0 % 256.93/60.91 | | | | % 256.93/60.91 | | | | DELTA: instantiating (105) with fresh symbol all_183_0 gives: % 256.93/60.91 | | | | (142) app(all_115_0, all_183_0) = all_115_0 & $i(all_183_0) & % 256.93/60.91 | | | | ssList(all_183_0) % 256.93/60.91 | | | | % 256.93/60.91 | | | | ALPHA: (142) implies: % 256.93/60.91 | | | | (143) ssList(all_183_0) % 256.93/60.91 | | | | (144) $i(all_183_0) % 256.93/60.91 | | | | (145) app(all_115_0, all_183_0) = all_115_0 % 256.93/60.91 | | | | % 256.93/60.91 | | | | DELTA: instantiating (104) with fresh symbol all_185_0 gives: % 256.93/60.91 | | | | (146) app(nil, all_185_0) = all_115_0 & $i(all_185_0) & % 256.93/60.91 | | | | ssList(all_185_0) % 256.93/60.91 | | | | % 256.93/60.91 | | | | ALPHA: (146) implies: % 256.93/60.91 | | | | (147) ssList(all_185_0) % 256.93/60.91 | | | | (148) $i(all_185_0) % 256.93/60.91 | | | | (149) app(nil, all_185_0) = all_115_0 % 256.93/60.91 | | | | % 256.93/60.91 | | | | DELTA: instantiating (103) with fresh symbol all_187_0 gives: % 256.93/60.91 | | | | (150) app(all_115_2, all_187_0) = all_115_2 & $i(all_187_0) & % 256.93/60.91 | | | | ssList(all_187_0) % 256.93/60.91 | | | | % 256.93/60.91 | | | | ALPHA: (150) implies: % 256.93/60.91 | | | | (151) ssList(all_187_0) % 256.93/60.91 | | | | (152) $i(all_187_0) % 256.93/60.91 | | | | (153) app(all_115_2, all_187_0) = all_115_2 % 256.93/60.91 | | | | % 256.93/60.91 | | | | DELTA: instantiating (102) with fresh symbol all_189_0 gives: % 256.93/60.91 | | | | (154) app(nil, all_189_0) = all_115_2 & $i(all_189_0) & % 256.93/60.91 | | | | ssList(all_189_0) % 256.93/60.91 | | | | % 256.93/60.91 | | | | ALPHA: (154) implies: % 256.93/60.91 | | | | (155) ssList(all_189_0) % 256.93/60.91 | | | | (156) $i(all_189_0) % 256.93/60.91 | | | | (157) app(nil, all_189_0) = all_115_2 % 256.93/60.91 | | | | % 256.93/60.91 | | | | DELTA: instantiating (115) with fresh symbol all_195_0 gives: % 256.93/60.91 | | | | (158) app(all_149_0, all_147_0) = all_195_0 & app(nil, all_195_0) = % 256.93/60.91 | | | | all_91_1 & $i(all_195_0) & $i(all_91_1) % 256.93/60.91 | | | | % 256.93/60.91 | | | | ALPHA: (158) implies: % 256.93/60.91 | | | | (159) $i(all_195_0) % 256.93/60.91 | | | | (160) app(all_149_0, all_147_0) = all_195_0 % 256.93/60.91 | | | | % 256.93/60.91 | | | | DELTA: instantiating (117) with fresh symbol all_197_0 gives: % 256.93/60.91 | | | | (161) app(all_115_0, all_115_0) = all_197_0 & app(all_115_2, % 256.93/60.91 | | | | all_197_0) = all_139_0 & $i(all_197_0) & $i(all_139_0) % 256.93/60.91 | | | | % 256.93/60.91 | | | | ALPHA: (161) implies: % 256.93/60.91 | | | | (162) app(all_115_0, all_115_0) = all_197_0 % 256.93/60.91 | | | | % 256.93/60.91 | | | | DELTA: instantiating (112) with fresh symbol all_201_0 gives: % 256.93/60.91 | | | | (163) app(nil, all_201_0) = all_91_1 & app(nil, all_149_0) = % 256.93/60.91 | | | | all_201_0 & $i(all_201_0) & $i(all_91_1) % 256.93/60.91 | | | | % 256.93/60.91 | | | | ALPHA: (163) implies: % 256.93/60.91 | | | | (164) app(nil, all_149_0) = all_201_0 % 256.93/60.91 | | | | % 256.93/60.91 | | | | DELTA: instantiating (116) with fresh symbol all_215_0 gives: % 256.93/60.91 | | | | (165) app(all_115_0, all_149_0) = all_215_0 & app(all_115_2, % 256.93/60.91 | | | | all_215_0) = all_91_1 & $i(all_215_0) & $i(all_91_1) % 256.93/60.91 | | | | % 256.93/60.91 | | | | ALPHA: (165) implies: % 256.93/60.91 | | | | (166) app(all_115_0, all_149_0) = all_215_0 % 256.93/60.91 | | | | % 256.93/60.91 | | | | DELTA: instantiating (110) with fresh symbol all_217_0 gives: % 256.93/60.91 | | | | (167) app(nil, all_217_0) = all_139_0 & app(nil, all_115_0) = % 256.93/60.91 | | | | all_217_0 & $i(all_217_0) & $i(all_139_0) % 256.93/60.91 | | | | % 256.93/60.91 | | | | ALPHA: (167) implies: % 256.93/60.91 | | | | (168) app(nil, all_115_0) = all_217_0 % 256.93/60.91 | | | | % 256.93/60.91 | | | | REDUCE: (119), (141) imply: % 256.93/60.91 | | | | (169) app(all_181_0, nil) = nil % 256.93/60.91 | | | | % 256.93/60.91 | | | | REDUCE: (120), (137) imply: % 256.93/60.91 | | | | (170) app(all_175_0, nil) = nil % 256.93/60.91 | | | | % 256.93/60.91 | | | | REDUCE: (120), (133) imply: % 256.93/60.91 | | | | (171) app(all_173_0, nil) = nil % 256.93/60.91 | | | | % 256.93/60.91 | | | | REDUCE: (119), (129) imply: % 256.93/60.91 | | | | (172) app(all_171_0, nil) = nil % 256.93/60.91 | | | | % 256.93/60.91 | | | | REDUCE: (113), (160) imply: % 256.93/60.91 | | | | (173) app(all_91_1, all_147_0) = all_195_0 % 256.93/60.91 | | | | % 256.93/60.92 | | | | REDUCE: (119), (145) imply: % 256.93/60.92 | | | | (174) app(nil, all_183_0) = nil % 256.93/60.92 | | | | % 256.93/60.92 | | | | REDUCE: (113), (119), (166) imply: % 256.93/60.92 | | | | (175) app(nil, all_91_1) = all_215_0 % 256.93/60.92 | | | | % 256.93/60.92 | | | | REDUCE: (119), (162) imply: % 256.93/60.92 | | | | (176) app(nil, nil) = all_197_0 % 256.93/60.92 | | | | % 256.93/60.92 | | | | REDUCE: (119), (125) imply: % 256.93/60.92 | | | | (177) app(nil, nil) = all_169_0 % 256.93/60.92 | | | | % 256.93/60.92 | | | | REDUCE: (120), (153) imply: % 256.93/60.92 | | | | (178) app(nil, all_187_0) = nil % 256.93/60.92 | | | | % 256.93/60.92 | | | | REDUCE: (120), (157) imply: % 256.93/60.92 | | | | (179) app(nil, all_189_0) = nil % 256.93/60.92 | | | | % 256.93/60.92 | | | | REDUCE: (119), (149) imply: % 256.93/60.92 | | | | (180) app(nil, all_185_0) = nil % 256.93/60.92 | | | | % 256.93/60.92 | | | | REDUCE: (113), (164) imply: % 256.93/60.92 | | | | (181) app(nil, all_91_1) = all_201_0 % 256.93/60.92 | | | | % 256.93/60.92 | | | | REDUCE: (96), (113) imply: % 256.93/60.92 | | | | (182) app(nil, all_91_1) = all_91_1 % 256.93/60.92 | | | | % 256.93/60.92 | | | | REDUCE: (119), (168) imply: % 256.93/60.92 | | | | (183) app(nil, nil) = all_217_0 % 256.93/60.92 | | | | % 256.93/60.92 | | | | REDUCE: (113), (114) imply: % 256.93/60.92 | | | | (184) segmentP(all_91_1, all_91_1) % 256.93/60.92 | | | | % 256.93/60.92 | | | | GROUND_INST: instantiating (20) with nil, all_197_0, nil, nil, % 256.93/60.92 | | | | simplifying with (101), (176) gives: % 256.93/60.92 | | | | (185) all_197_0 = nil % 256.93/60.92 | | | | % 256.93/60.92 | | | | GROUND_INST: instantiating (20) with all_197_0, all_217_0, nil, nil, % 256.93/60.92 | | | | simplifying with (176), (183) gives: % 256.93/60.92 | | | | (186) all_217_0 = all_197_0 % 256.93/60.92 | | | | % 256.93/60.92 | | | | GROUND_INST: instantiating (20) with all_169_0, all_217_0, nil, nil, % 256.93/60.92 | | | | simplifying with (177), (183) gives: % 256.93/60.92 | | | | (187) all_217_0 = all_169_0 % 256.93/60.92 | | | | % 256.93/60.92 | | | | GROUND_INST: instantiating (20) with all_201_0, all_215_0, all_91_1, % 256.93/60.92 | | | | nil, simplifying with (175), (181) gives: % 256.93/60.92 | | | | (188) all_215_0 = all_201_0 % 256.93/60.92 | | | | % 256.93/60.92 | | | | GROUND_INST: instantiating (20) with all_91_1, all_215_0, all_91_1, nil, % 256.93/60.92 | | | | simplifying with (175), (182) gives: % 256.93/60.92 | | | | (189) all_215_0 = all_91_1 % 256.93/60.92 | | | | % 256.93/60.92 | | | | GROUND_INST: instantiating (20) with all_91_1, all_195_0, all_147_0, % 256.93/60.92 | | | | all_91_1, simplifying with (92), (173) gives: % 256.93/60.92 | | | | (190) all_195_0 = all_91_1 % 256.93/60.92 | | | | % 256.93/60.92 | | | | COMBINE_EQS: (186), (187) imply: % 256.93/60.92 | | | | (191) all_197_0 = all_169_0 % 256.93/60.92 | | | | % 256.93/60.92 | | | | SIMP: (191) implies: % 256.93/60.92 | | | | (192) all_197_0 = all_169_0 % 256.93/60.92 | | | | % 256.93/60.92 | | | | COMBINE_EQS: (188), (189) imply: % 256.93/60.92 | | | | (193) all_201_0 = all_91_1 % 256.93/60.92 | | | | % 256.93/60.92 | | | | COMBINE_EQS: (185), (192) imply: % 256.93/60.92 | | | | (194) all_169_0 = nil % 256.93/60.92 | | | | % 256.93/60.92 | | | | SIMP: (194) implies: % 256.93/60.92 | | | | (195) all_169_0 = nil % 256.93/60.92 | | | | % 256.93/60.92 | | | | GROUND_INST: instantiating (ax79) with nil, all_91_1, all_91_1, % 256.93/60.92 | | | | all_135_0, simplifying with (6), (18), (22), (23), (77), % 256.93/60.92 | | | | (78), (79), (182) gives: % 256.93/60.92 | | | | (196) all_135_0 = nil % 256.93/60.92 | | | | % 256.93/60.92 | | | | GROUND_INST: instantiating (ax82) with nil, all_183_0, nil, all_91_1, % 256.93/60.92 | | | | all_91_1, simplifying with (6), (18), (22), (23), (143), % 256.93/60.92 | | | | (144), (174), (182) gives: % 256.93/60.92 | | | | (197) ? [v0: $i] : (app(all_183_0, all_91_1) = v0 & app(nil, v0) = % 256.93/60.92 | | | | all_91_1 & $i(v0)) % 256.93/60.92 | | | | % 256.93/60.93 | | | | GROUND_INST: instantiating (ax82) with nil, all_185_0, nil, all_91_1, % 256.93/60.93 | | | | all_91_1, simplifying with (6), (18), (22), (23), (147), % 256.93/60.93 | | | | (148), (180), (182) gives: % 256.93/60.93 | | | | (198) ? [v0: $i] : (app(all_185_0, all_91_1) = v0 & app(nil, v0) = % 256.93/60.93 | | | | all_91_1 & $i(v0)) % 256.93/60.93 | | | | % 256.93/60.93 | | | | GROUND_INST: instantiating (7) with all_185_0, nil, simplifying with % 256.93/60.93 | | | | (147), (148), (180) gives: % 256.93/60.93 | | | | (199) all_185_0 = nil % 256.93/60.93 | | | | % 256.93/60.93 | | | | GROUND_INST: instantiating (ax80) with all_185_0, nil, nil, all_187_0, % 256.93/60.93 | | | | simplifying with (6), (18), (147), (148), (151), (152), % 256.93/60.93 | | | | (178), (180) gives: % 256.93/60.93 | | | | (200) all_187_0 = all_185_0 % 256.93/60.93 | | | | % 256.93/60.93 | | | | GROUND_INST: instantiating (ax82) with nil, all_187_0, nil, all_91_1, % 256.93/60.93 | | | | all_91_1, simplifying with (6), (18), (22), (23), (151), % 256.93/60.93 | | | | (152), (178), (182) gives: % 256.93/60.93 | | | | (201) ? [v0: $i] : (app(all_187_0, all_91_1) = v0 & app(nil, v0) = % 256.93/60.93 | | | | all_91_1 & $i(v0)) % 256.93/60.93 | | | | % 256.93/60.93 | | | | GROUND_INST: instantiating (ax80) with all_187_0, nil, nil, all_189_0, % 256.93/60.93 | | | | simplifying with (6), (18), (151), (152), (155), (156), % 256.93/60.93 | | | | (178), (179) gives: % 256.93/60.93 | | | | (202) all_189_0 = all_187_0 % 256.93/60.93 | | | | % 256.93/60.93 | | | | GROUND_INST: instantiating (ax80) with all_183_0, nil, nil, all_189_0, % 256.93/60.93 | | | | simplifying with (6), (18), (143), (144), (155), (156), % 256.93/60.93 | | | | (174), (179) gives: % 256.93/60.93 | | | | (203) all_189_0 = all_183_0 % 256.93/60.93 | | | | % 256.93/60.93 | | | | GROUND_INST: instantiating (ax82) with nil, all_189_0, nil, all_91_1, % 256.93/60.93 | | | | all_91_1, simplifying with (6), (18), (22), (23), (155), % 256.93/60.93 | | | | (156), (179), (182) gives: % 256.93/60.93 | | | | (204) ? [v0: $i] : (app(all_189_0, all_91_1) = v0 & app(nil, v0) = % 256.93/60.93 | | | | all_91_1 & $i(v0)) % 256.93/60.93 | | | | % 256.93/60.93 | | | | GROUND_INST: instantiating (ax82) with all_171_0, nil, nil, all_91_1, % 256.93/60.93 | | | | all_91_1, simplifying with (6), (18), (22), (23), (127), % 256.93/60.93 | | | | (128), (172), (182) gives: % 256.93/60.93 | | | | (205) ? [v0: $i] : (app(all_171_0, v0) = all_91_1 & app(nil, % 256.93/60.93 | | | | all_91_1) = v0 & $i(v0)) % 256.93/60.93 | | | | % 256.93/60.94 | | | | GROUND_INST: instantiating (ax82) with all_173_0, nil, nil, all_91_1, % 256.93/60.94 | | | | all_91_1, simplifying with (6), (18), (22), (23), (131), % 256.93/60.94 | | | | (132), (171), (182) gives: % 256.93/60.94 | | | | (206) ? [v0: $i] : (app(all_173_0, v0) = all_91_1 & app(nil, % 256.93/60.94 | | | | all_91_1) = v0 & $i(v0)) % 256.93/60.94 | | | | % 256.93/60.94 | | | | GROUND_INST: instantiating (ax82) with all_175_0, nil, nil, all_91_1, % 256.93/60.94 | | | | all_91_1, simplifying with (6), (18), (22), (23), (135), % 256.93/60.94 | | | | (136), (170), (182) gives: % 256.93/60.94 | | | | (207) ? [v0: $i] : (app(all_175_0, v0) = all_91_1 & app(nil, % 256.93/60.94 | | | | all_91_1) = v0 & $i(v0)) % 256.93/60.94 | | | | % 256.93/60.94 | | | | GROUND_INST: instantiating (ax82) with all_181_0, nil, nil, all_91_1, % 256.93/60.94 | | | | all_91_1, simplifying with (6), (18), (22), (23), (139), % 256.93/60.94 | | | | (140), (169), (182) gives: % 256.93/60.94 | | | | (208) ? [v0: $i] : (app(all_181_0, v0) = all_91_1 & app(nil, % 256.93/60.94 | | | | all_91_1) = v0 & $i(v0)) % 256.93/60.94 | | | | % 256.93/60.94 | | | | COMBINE_EQS: (202), (203) imply: % 256.93/60.94 | | | | (209) all_187_0 = all_183_0 % 256.93/60.94 | | | | % 256.93/60.94 | | | | SIMP: (209) implies: % 256.93/60.94 | | | | (210) all_187_0 = all_183_0 % 256.93/60.94 | | | | % 256.93/60.94 | | | | COMBINE_EQS: (200), (210) imply: % 256.93/60.94 | | | | (211) all_185_0 = all_183_0 % 256.93/60.94 | | | | % 256.93/60.94 | | | | SIMP: (211) implies: % 256.93/60.94 | | | | (212) all_185_0 = all_183_0 % 256.93/60.94 | | | | % 256.93/60.94 | | | | COMBINE_EQS: (199), (212) imply: % 256.93/60.94 | | | | (213) all_183_0 = nil % 256.93/60.94 | | | | % 256.93/60.94 | | | | COMBINE_EQS: (210), (213) imply: % 256.93/60.94 | | | | (214) all_187_0 = nil % 256.93/60.94 | | | | % 256.93/60.94 | | | | COMBINE_EQS: (203), (213) imply: % 256.93/60.94 | | | | (215) all_189_0 = nil % 256.93/60.94 | | | | % 256.93/60.94 | | | | DELTA: instantiating (198) with fresh symbol all_239_0 gives: % 256.93/60.94 | | | | (216) app(all_185_0, all_91_1) = all_239_0 & app(nil, all_239_0) = % 256.93/60.94 | | | | all_91_1 & $i(all_239_0) % 256.93/60.94 | | | | % 256.93/60.94 | | | | ALPHA: (216) implies: % 256.93/60.94 | | | | (217) $i(all_239_0) % 256.93/60.94 | | | | (218) app(all_185_0, all_91_1) = all_239_0 % 256.93/60.94 | | | | % 256.93/60.94 | | | | DELTA: instantiating (206) with fresh symbol all_253_0 gives: % 256.93/60.94 | | | | (219) app(all_173_0, all_253_0) = all_91_1 & app(nil, all_91_1) = % 256.93/60.94 | | | | all_253_0 & $i(all_253_0) % 256.93/60.94 | | | | % 256.93/60.94 | | | | ALPHA: (219) implies: % 256.93/60.94 | | | | (220) app(nil, all_91_1) = all_253_0 % 256.93/60.94 | | | | % 256.93/60.94 | | | | DELTA: instantiating (208) with fresh symbol all_265_0 gives: % 256.93/60.94 | | | | (221) app(all_181_0, all_265_0) = all_91_1 & app(nil, all_91_1) = % 256.93/60.94 | | | | all_265_0 & $i(all_265_0) % 256.93/60.94 | | | | % 256.93/60.94 | | | | ALPHA: (221) implies: % 256.93/60.94 | | | | (222) app(nil, all_91_1) = all_265_0 % 256.93/60.94 | | | | % 256.93/60.94 | | | | DELTA: instantiating (201) with fresh symbol all_273_0 gives: % 256.93/60.94 | | | | (223) app(all_187_0, all_91_1) = all_273_0 & app(nil, all_273_0) = % 256.93/60.94 | | | | all_91_1 & $i(all_273_0) % 256.93/60.94 | | | | % 256.93/60.94 | | | | ALPHA: (223) implies: % 256.93/60.94 | | | | (224) app(all_187_0, all_91_1) = all_273_0 % 256.93/60.94 | | | | % 256.93/60.94 | | | | DELTA: instantiating (205) with fresh symbol all_343_0 gives: % 256.93/60.94 | | | | (225) app(all_171_0, all_343_0) = all_91_1 & app(nil, all_91_1) = % 256.93/60.94 | | | | all_343_0 & $i(all_343_0) % 256.93/60.94 | | | | % 256.93/60.94 | | | | ALPHA: (225) implies: % 256.93/60.94 | | | | (226) app(nil, all_91_1) = all_343_0 % 256.93/60.94 | | | | % 256.93/60.94 | | | | DELTA: instantiating (204) with fresh symbol all_375_0 gives: % 256.93/60.95 | | | | (227) app(all_189_0, all_91_1) = all_375_0 & app(nil, all_375_0) = % 256.93/60.95 | | | | all_91_1 & $i(all_375_0) % 256.93/60.95 | | | | % 256.93/60.95 | | | | ALPHA: (227) implies: % 256.93/60.95 | | | | (228) app(all_189_0, all_91_1) = all_375_0 % 256.93/60.95 | | | | % 256.93/60.95 | | | | DELTA: instantiating (197) with fresh symbol all_383_0 gives: % 256.93/60.95 | | | | (229) app(all_183_0, all_91_1) = all_383_0 & app(nil, all_383_0) = % 256.93/60.95 | | | | all_91_1 & $i(all_383_0) % 256.93/60.95 | | | | % 256.93/60.95 | | | | ALPHA: (229) implies: % 256.93/60.95 | | | | (230) app(all_183_0, all_91_1) = all_383_0 % 256.93/60.95 | | | | % 256.93/60.95 | | | | DELTA: instantiating (207) with fresh symbol all_393_0 gives: % 256.93/60.95 | | | | (231) app(all_175_0, all_393_0) = all_91_1 & app(nil, all_91_1) = % 256.93/60.95 | | | | all_393_0 & $i(all_393_0) % 256.93/60.95 | | | | % 256.93/60.95 | | | | ALPHA: (231) implies: % 256.93/60.95 | | | | (232) app(nil, all_91_1) = all_393_0 % 256.93/60.95 | | | | % 256.93/60.95 | | | | REDUCE: (215), (228) imply: % 256.93/60.95 | | | | (233) app(nil, all_91_1) = all_375_0 % 256.93/60.95 | | | | % 256.93/60.95 | | | | REDUCE: (214), (224) imply: % 256.93/60.95 | | | | (234) app(nil, all_91_1) = all_273_0 % 256.93/60.95 | | | | % 256.93/60.95 | | | | REDUCE: (199), (218) imply: % 256.93/60.95 | | | | (235) app(nil, all_91_1) = all_239_0 % 256.93/60.95 | | | | % 256.93/60.95 | | | | REDUCE: (213), (230) imply: % 256.93/60.95 | | | | (236) app(nil, all_91_1) = all_383_0 % 256.93/60.95 | | | | % 256.93/60.95 | | | | GROUND_INST: instantiating (20) with all_91_1, all_253_0, all_91_1, nil, % 256.93/60.95 | | | | simplifying with (182), (220) gives: % 256.93/60.95 | | | | (237) all_253_0 = all_91_1 % 256.93/60.95 | | | | % 256.93/60.95 | | | | GROUND_INST: instantiating (20) with all_343_0, all_375_0, all_91_1, % 256.93/60.95 | | | | nil, simplifying with (226), (233) gives: % 256.93/60.95 | | | | (238) all_375_0 = all_343_0 % 256.93/60.95 | | | | % 256.93/60.95 | | | | GROUND_INST: instantiating (20) with all_265_0, all_375_0, all_91_1, % 256.93/60.95 | | | | nil, simplifying with (222), (233) gives: % 256.93/60.95 | | | | (239) all_375_0 = all_265_0 % 256.93/60.95 | | | | % 256.93/60.95 | | | | GROUND_INST: instantiating (20) with all_253_0, all_375_0, all_91_1, % 256.93/60.95 | | | | nil, simplifying with (220), (233) gives: % 256.93/60.95 | | | | (240) all_375_0 = all_253_0 % 256.93/60.95 | | | | % 256.93/60.95 | | | | GROUND_INST: instantiating (20) with all_375_0, all_383_0, all_91_1, % 256.93/60.95 | | | | nil, simplifying with (233), (236) gives: % 256.93/60.95 | | | | (241) all_383_0 = all_375_0 % 256.93/60.95 | | | | % 256.93/60.95 | | | | GROUND_INST: instantiating (20) with all_273_0, all_383_0, all_91_1, % 256.93/60.95 | | | | nil, simplifying with (234), (236) gives: % 256.93/60.95 | | | | (242) all_383_0 = all_273_0 % 256.93/60.95 | | | | % 256.93/60.95 | | | | GROUND_INST: instantiating (20) with all_343_0, all_393_0, all_91_1, % 256.93/60.95 | | | | nil, simplifying with (226), (232) gives: % 256.93/60.95 | | | | (243) all_393_0 = all_343_0 % 256.93/60.95 | | | | % 256.93/60.95 | | | | GROUND_INST: instantiating (20) with all_239_0, all_393_0, all_91_1, % 256.93/60.95 | | | | nil, simplifying with (232), (235) gives: % 256.93/60.95 | | | | (244) all_393_0 = all_239_0 % 256.93/60.95 | | | | % 256.93/60.95 | | | | COMBINE_EQS: (243), (244) imply: % 256.93/60.95 | | | | (245) all_343_0 = all_239_0 % 256.93/60.95 | | | | % 256.93/60.95 | | | | SIMP: (245) implies: % 256.93/60.95 | | | | (246) all_343_0 = all_239_0 % 256.93/60.95 | | | | % 256.93/60.95 | | | | COMBINE_EQS: (241), (242) imply: % 256.93/60.95 | | | | (247) all_375_0 = all_273_0 % 256.93/60.95 | | | | % 256.93/60.95 | | | | SIMP: (247) implies: % 256.93/60.95 | | | | (248) all_375_0 = all_273_0 % 256.93/60.95 | | | | % 256.93/60.95 | | | | COMBINE_EQS: (240), (248) imply: % 256.93/60.95 | | | | (249) all_273_0 = all_253_0 % 256.93/60.95 | | | | % 256.93/60.95 | | | | COMBINE_EQS: (238), (248) imply: % 256.93/60.95 | | | | (250) all_343_0 = all_273_0 % 256.93/60.95 | | | | % 256.93/60.95 | | | | SIMP: (250) implies: % 256.93/60.95 | | | | (251) all_343_0 = all_273_0 % 256.93/60.95 | | | | % 256.93/60.95 | | | | COMBINE_EQS: (239), (248) imply: % 256.93/60.95 | | | | (252) all_273_0 = all_265_0 % 256.93/60.95 | | | | % 256.93/60.95 | | | | COMBINE_EQS: (246), (251) imply: % 256.93/60.95 | | | | (253) all_273_0 = all_239_0 % 256.93/60.95 | | | | % 256.93/60.95 | | | | SIMP: (253) implies: % 256.93/60.95 | | | | (254) all_273_0 = all_239_0 % 256.93/60.95 | | | | % 256.93/60.95 | | | | COMBINE_EQS: (252), (254) imply: % 256.93/60.95 | | | | (255) all_265_0 = all_239_0 % 256.93/60.95 | | | | % 256.93/60.95 | | | | COMBINE_EQS: (249), (252) imply: % 256.93/60.95 | | | | (256) all_265_0 = all_253_0 % 256.93/60.95 | | | | % 256.93/60.95 | | | | COMBINE_EQS: (255), (256) imply: % 256.93/60.95 | | | | (257) all_253_0 = all_239_0 % 256.93/60.95 | | | | % 256.93/60.95 | | | | SIMP: (257) implies: % 256.93/60.95 | | | | (258) all_253_0 = all_239_0 % 256.93/60.95 | | | | % 256.93/60.95 | | | | COMBINE_EQS: (237), (258) imply: % 256.93/60.95 | | | | (259) all_239_0 = all_91_1 % 256.93/60.95 | | | | % 256.93/60.95 | | | | BETA: splitting (24) gives: % 256.93/60.95 | | | | % 256.93/60.95 | | | | Case 1: % 256.93/60.95 | | | | | % 256.93/60.95 | | | | | (260) all_91_0 = nil & ~ (all_91_1 = nil) % 256.93/60.95 | | | | | % 256.93/60.95 | | | | | ALPHA: (260) implies: % 256.93/60.95 | | | | | (261) all_91_0 = nil % 256.93/60.95 | | | | | (262) ~ (all_91_1 = nil) % 256.93/60.95 | | | | | % 256.93/60.95 | | | | | BETA: splitting (25) gives: % 256.93/60.95 | | | | | % 256.93/60.95 | | | | | Case 1: % 256.93/60.95 | | | | | | % 256.93/60.95 | | | | | | (263) all_91_0 = nil & all_91_1 = nil % 256.93/60.95 | | | | | | % 256.93/60.95 | | | | | | ALPHA: (263) implies: % 256.93/60.96 | | | | | | (264) all_91_1 = nil % 256.93/60.96 | | | | | | % 256.93/60.96 | | | | | | REDUCE: (262), (264) imply: % 256.93/60.96 | | | | | | (265) $false % 256.93/60.96 | | | | | | % 256.93/60.96 | | | | | | CLOSE: (265) is inconsistent. % 256.93/60.96 | | | | | | % 256.93/60.96 | | | | | Case 2: % 256.93/60.96 | | | | | | % 256.93/60.96 | | | | | | (266) segmentP(all_91_0, all_91_1) & neq(all_91_1, nil) % 256.93/60.96 | | | | | | % 256.93/60.96 | | | | | | ALPHA: (266) implies: % 256.93/60.96 | | | | | | (267) segmentP(all_91_0, all_91_1) % 256.93/60.96 | | | | | | % 256.93/60.96 | | | | | | REDUCE: (261), (267) imply: % 256.93/60.96 | | | | | | (268) segmentP(nil, all_91_1) % 256.93/60.96 | | | | | | % 256.93/60.96 | | | | | | GROUND_INST: instantiating (13) with all_91_1, simplifying with % 256.93/60.96 | | | | | | (22), (23), (268) gives: % 256.93/60.96 | | | | | | (269) all_91_1 = nil % 256.93/60.96 | | | | | | % 256.93/60.96 | | | | | | REDUCE: (262), (269) imply: % 256.93/60.96 | | | | | | (270) $false % 256.93/60.96 | | | | | | % 256.93/60.96 | | | | | | CLOSE: (270) is inconsistent. % 256.93/60.96 | | | | | | % 256.93/60.96 | | | | | End of split % 256.93/60.96 | | | | | % 256.93/60.96 | | | | Case 2: % 256.93/60.96 | | | | | % 256.93/60.96 | | | | | (271) neq(all_91_0, nil) & ! [v0: $i] : ( ~ $i(v0) | ~ % 256.93/60.96 | | | | | segmentP(all_91_0, v0) | ~ segmentP(all_91_1, v0) | ~ % 256.93/60.96 | | | | | ssList(v0) | ~ neq(v0, nil)) % 256.93/60.96 | | | | | % 256.93/60.96 | | | | | ALPHA: (271) implies: % 256.93/60.96 | | | | | (272) neq(all_91_0, nil) % 256.93/60.96 | | | | | (273) ! [v0: $i] : ( ~ $i(v0) | ~ segmentP(all_91_0, v0) | ~ % 256.93/60.96 | | | | | segmentP(all_91_1, v0) | ~ ssList(v0) | ~ neq(v0, nil)) % 256.93/60.96 | | | | | % 256.93/60.96 | | | | | BETA: splitting (25) gives: % 256.93/60.96 | | | | | % 256.93/60.96 | | | | | Case 1: % 256.93/60.96 | | | | | | % 256.93/60.96 | | | | | | (274) all_91_0 = nil & all_91_1 = nil % 256.93/60.96 | | | | | | % 256.93/60.96 | | | | | | ALPHA: (274) implies: % 256.93/60.96 | | | | | | (275) all_91_1 = nil % 256.93/60.96 | | | | | | (276) all_91_0 = nil % 256.93/60.96 | | | | | | % 256.93/60.96 | | | | | | REDUCE: (272), (276) imply: % 256.93/60.96 | | | | | | (277) neq(nil, nil) % 256.93/60.96 | | | | | | % 256.93/60.96 | | | | | | GROUND_INST: instantiating (5) with nil, simplifying with (6), (18), % 256.93/60.96 | | | | | | (277) gives: % 256.93/60.96 | | | | | | (278) $false % 256.93/60.96 | | | | | | % 256.93/60.96 | | | | | | CLOSE: (278) is inconsistent. % 256.93/60.96 | | | | | | % 256.93/60.96 | | | | | Case 2: % 256.93/60.96 | | | | | | % 256.93/60.96 | | | | | | (279) segmentP(all_91_0, all_91_1) & neq(all_91_1, nil) % 256.93/60.96 | | | | | | % 256.93/60.96 | | | | | | ALPHA: (279) implies: % 256.93/60.96 | | | | | | (280) neq(all_91_1, nil) % 256.93/60.96 | | | | | | (281) segmentP(all_91_0, all_91_1) % 256.93/60.96 | | | | | | % 256.93/60.96 | | | | | | GROUND_INST: instantiating (273) with all_91_1, simplifying with % 256.93/60.96 | | | | | | (22), (23), (184), (280), (281) gives: % 256.93/60.96 | | | | | | (282) $false % 256.93/60.96 | | | | | | % 256.93/60.96 | | | | | | CLOSE: (282) is inconsistent. % 256.93/60.96 | | | | | | % 256.93/60.96 | | | | | End of split % 256.93/60.96 | | | | | % 256.93/60.96 | | | | End of split % 256.93/60.96 | | | | % 256.93/60.96 | | | End of split % 256.93/60.96 | | | % 256.93/60.96 | | End of split % 256.93/60.96 | | % 256.93/60.96 | End of split % 256.93/60.96 | % 256.93/60.96 End of proof % 256.93/60.96 % SZS output end Proof for theBenchmark % 256.93/60.96 % 256.93/60.96 60325ms %------------------------------------------------------------------------------