%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SWC080+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 : n022.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 20:49:32 EDT 2023 % Result : Theorem 155.55s 21.03s % Output : Proof 156.38s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : SWC080+1 : TPTP v8.1.2. Released v2.4.0. % 0.07/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.33 % Computer : n022.cluster.edu % 0.13/0.33 % Model : x86_64 x86_64 % 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.33 % Memory : 8042.1875MB % 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 300 % 0.13/0.34 % DateTime : Mon Aug 28 16:41:39 EDT 2023 % 0.13/0.34 % CPUTime : % 0.20/0.59 ________ _____ % 0.20/0.59 ___ __ \_________(_)________________________________ % 0.20/0.59 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.20/0.59 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.20/0.59 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.20/0.59 % 0.20/0.59 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.20/0.59 (2023-06-19) % 0.20/0.59 % 0.20/0.59 (c) Philipp Rümmer, 2009-2023 % 0.20/0.59 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.20/0.59 Amanda Stjerna. % 0.20/0.59 Free software under BSD-3-Clause. % 0.20/0.59 % 0.20/0.59 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.20/0.59 % 0.20/0.59 Loading /export/starexec/sandbox2/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 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 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 % 5.70/1.47 Prover 1: Preprocessing ... % 5.70/1.47 Prover 4: Preprocessing ... % 5.70/1.49 Prover 2: Preprocessing ... % 5.70/1.49 Prover 3: Preprocessing ... % 5.70/1.49 Prover 0: Preprocessing ... % 5.70/1.50 Prover 5: Preprocessing ... % 5.70/1.50 Prover 6: Preprocessing ... % 14.92/2.68 Prover 2: Proving ... % 15.32/2.75 Prover 5: Constructing countermodel ... % 15.43/2.76 Prover 1: Constructing countermodel ... % 15.86/2.83 Prover 3: Constructing countermodel ... % 15.86/2.85 Prover 6: Proving ... % 20.48/3.47 Prover 4: Constructing countermodel ... % 21.32/3.56 Prover 0: Proving ... % 73.53/10.35 Prover 2: stopped % 73.53/10.35 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 74.92/10.54 Prover 7: Preprocessing ... % 77.03/10.77 Prover 7: Constructing countermodel ... % 100.69/13.95 Prover 5: stopped % 100.69/13.95 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 102.90/14.16 Prover 8: Preprocessing ... % 105.27/14.45 Prover 8: Warning: ignoring some quantifiers % 105.27/14.46 Prover 8: Constructing countermodel ... % 116.62/15.97 Prover 1: stopped % 116.62/15.99 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889 % 118.09/16.11 Prover 9: Preprocessing ... % 122.82/16.80 Prover 9: Constructing countermodel ... % 131.56/17.86 Prover 6: stopped % 131.56/17.86 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 132.31/17.99 Prover 10: Preprocessing ... % 132.96/18.11 Prover 10: Constructing countermodel ... % 155.55/21.01 Prover 10: Found proof (size 89) % 155.55/21.02 Prover 10: proved (3149ms) % 155.55/21.02 Prover 3: stopped % 155.55/21.02 Prover 0: stopped % 155.55/21.02 Prover 7: stopped % 155.55/21.02 Prover 8: stopped % 155.55/21.02 Prover 4: stopped % 155.55/21.03 Prover 9: stopped % 155.55/21.03 % 155.55/21.03 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 155.55/21.03 % 155.55/21.04 % SZS output start Proof for theBenchmark % 155.55/21.05 Assumptions after simplification: % 155.55/21.05 --------------------------------- % 155.55/21.05 % 155.55/21.05 (ax17) % 155.55/21.05 $i(nil) & ssList(nil) % 155.55/21.05 % 155.55/21.05 (ax26) % 156.10/21.07 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (app(v0, v1) = v2) | ~ $i(v1) | % 156.10/21.07 ~ $i(v0) | ~ ssList(v1) | ~ ssList(v0) | ssList(v2)) % 156.10/21.07 % 156.10/21.07 (ax28) % 156.10/21.08 $i(nil) & ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (app(nil, v0) = v1) | ~ % 156.10/21.08 $i(v0) | ~ ssList(v0)) % 156.10/21.08 % 156.10/21.08 (ax45) % 156.10/21.08 $i(nil) & ! [v0: $i] : ( ~ $i(v0) | ~ ssList(v0) | frontsegP(v0, nil)) % 156.10/21.08 % 156.10/21.08 (ax46) % 156.10/21.08 $i(nil) & ! [v0: $i] : (v0 = nil | ~ $i(v0) | ~ frontsegP(nil, v0) | ~ % 156.10/21.08 ssList(v0)) & ( ~ ssList(nil) | frontsegP(nil, nil)) % 156.10/21.08 % 156.10/21.08 (ax5) % 156.10/21.08 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (app(v1, v2) = v0) | ~ $i(v2) | % 156.10/21.08 ~ $i(v1) | ~ $i(v0) | ~ ssList(v2) | ~ ssList(v1) | ~ ssList(v0) | % 156.10/21.08 frontsegP(v0, v1)) & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ % 156.10/21.08 frontsegP(v0, v1) | ~ ssList(v1) | ~ ssList(v0) | ? [v2: $i] : (app(v1, % 156.10/21.08 v2) = v0 & $i(v2) & ssList(v2))) % 156.10/21.08 % 156.10/21.08 (ax51) % 156.10/21.08 $i(nil) & ! [v0: $i] : ( ~ $i(v0) | ~ ssList(v0) | rearsegP(v0, nil)) % 156.10/21.08 % 156.10/21.08 (ax52) % 156.10/21.08 $i(nil) & ! [v0: $i] : (v0 = nil | ~ $i(v0) | ~ rearsegP(nil, v0) | ~ % 156.10/21.08 ssList(v0)) & ( ~ ssList(nil) | rearsegP(nil, nil)) % 156.10/21.08 % 156.10/21.08 (ax58) % 156.10/21.08 $i(nil) & ! [v0: $i] : (v0 = nil | ~ $i(v0) | ~ segmentP(nil, v0) | ~ % 156.10/21.08 ssList(v0)) & ( ~ ssList(nil) | segmentP(nil, nil)) % 156.10/21.08 % 156.10/21.08 (ax6) % 156.10/21.09 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (app(v2, v1) = v0) | ~ $i(v2) | % 156.10/21.09 ~ $i(v1) | ~ $i(v0) | ~ ssList(v2) | ~ ssList(v1) | ~ ssList(v0) | % 156.10/21.09 rearsegP(v0, v1)) & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ % 156.10/21.09 rearsegP(v0, v1) | ~ ssList(v1) | ~ ssList(v0) | ? [v2: $i] : (app(v2, % 156.10/21.09 v1) = v0 & $i(v2) & ssList(v2))) % 156.10/21.09 % 156.10/21.09 (ax7) % 156.21/21.09 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 156.21/21.09 (app(v3, v4) = v0) | ~ (app(v2, v1) = v3) | ~ $i(v4) | ~ $i(v2) | ~ % 156.21/21.09 $i(v1) | ~ $i(v0) | ~ ssList(v4) | ~ ssList(v2) | ~ ssList(v1) | ~ % 156.21/21.09 ssList(v0) | segmentP(v0, v1)) & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ % 156.21/21.09 $i(v0) | ~ segmentP(v0, v1) | ~ ssList(v1) | ~ ssList(v0) | ? [v2: $i] : % 156.21/21.09 ? [v3: $i] : ? [v4: $i] : (app(v3, v4) = v0 & app(v2, v1) = v3 & $i(v4) & % 156.21/21.09 $i(v3) & $i(v2) & ssList(v4) & ssList(v2))) % 156.21/21.09 % 156.21/21.09 (ax82) % 156.21/21.09 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 156.21/21.09 (app(v2, v3) = v4) | ~ (app(v0, v1) = v2) | ~ $i(v3) | ~ $i(v1) | ~ % 156.21/21.09 $i(v0) | ~ ssList(v3) | ~ ssList(v1) | ~ ssList(v0) | ? [v5: $i] : % 156.21/21.09 (app(v1, v3) = v5 & app(v0, v5) = v4 & $i(v5) & $i(v4))) % 156.21/21.09 % 156.21/21.09 (ax83) % 156.21/21.09 $i(nil) & ! [v0: $i] : ! [v1: $i] : (v1 = nil | ~ (app(v0, v1) = nil) | ~ % 156.21/21.09 $i(v1) | ~ $i(v0) | ~ ssList(v1) | ~ ssList(v0)) & ! [v0: $i] : ! [v1: % 156.21/21.09 $i] : (v0 = nil | ~ (app(v0, v1) = nil) | ~ $i(v1) | ~ $i(v0) | ~ % 156.21/21.09 ssList(v1) | ~ ssList(v0)) & ! [v0: $i] : (v0 = nil | ~ (app(nil, nil) = % 156.21/21.09 v0) | ~ ssList(nil)) % 156.21/21.09 % 156.21/21.09 (ax84) % 156.21/21.09 $i(nil) & ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (app(v0, nil) = v1) | ~ % 156.21/21.09 $i(v0) | ~ ssList(v0)) % 156.21/21.09 % 156.21/21.09 (co1) % 156.21/21.10 $i(nil) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ($i(v2) & $i(v1) & $i(v0) % 156.21/21.10 & frontsegP(v1, v2) & frontsegP(v0, v2) & ssList(v2) & ssList(v1) & % 156.21/21.10 ssList(v0) & neq(v2, nil) & neq(v1, nil) & ! [v3: $i] : ( ~ $i(v3) | ~ % 156.21/21.10 segmentP(v1, v3) | ~ segmentP(v0, v3) | ~ ssList(v3) | ~ neq(v3, nil))) % 156.21/21.10 % 156.21/21.10 (function-axioms) % 156.21/21.10 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 156.21/21.10 (cons(v3, v2) = v1) | ~ (cons(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : % 156.21/21.10 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (app(v3, v2) = v1) | ~ (app(v3, v2) % 156.21/21.10 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (tl(v2) = % 156.21/21.10 v1) | ~ (tl(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = % 156.21/21.10 v0 | ~ (hd(v2) = v1) | ~ (hd(v2) = v0)) % 156.21/21.10 % 156.21/21.10 Further assumptions not needed in the proof: % 156.21/21.10 -------------------------------------------- % 156.21/21.10 ax1, ax10, ax11, ax12, ax13, ax14, ax15, ax16, ax18, ax19, ax2, ax20, ax21, % 156.21/21.10 ax22, ax23, ax24, ax25, ax27, ax29, ax3, ax30, ax31, ax32, ax33, ax34, ax35, % 156.21/21.10 ax36, ax37, ax38, ax39, ax4, ax40, ax41, ax42, ax43, ax44, ax47, ax48, ax49, % 156.21/21.10 ax50, ax53, ax54, ax55, ax56, ax57, ax59, ax60, ax61, ax62, ax63, ax64, ax65, % 156.21/21.10 ax66, ax67, ax68, ax69, ax70, ax71, ax72, ax73, ax74, ax75, ax76, ax77, ax78, % 156.21/21.10 ax79, ax8, ax80, ax81, ax85, ax86, ax87, ax88, ax89, ax9, ax90, ax91, ax92, % 156.21/21.10 ax93, ax94, ax95 % 156.21/21.10 % 156.21/21.10 Those formulas are unsatisfiable: % 156.21/21.10 --------------------------------- % 156.21/21.10 % 156.21/21.10 Begin of proof % 156.21/21.10 | % 156.21/21.10 | ALPHA: (ax5) implies: % 156.21/21.10 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ frontsegP(v0, % 156.21/21.10 | v1) | ~ ssList(v1) | ~ ssList(v0) | ? [v2: $i] : (app(v1, v2) = % 156.21/21.10 | v0 & $i(v2) & ssList(v2))) % 156.21/21.10 | % 156.21/21.10 | ALPHA: (ax6) implies: % 156.21/21.10 | (2) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ rearsegP(v0, % 156.21/21.10 | v1) | ~ ssList(v1) | ~ ssList(v0) | ? [v2: $i] : (app(v2, v1) = % 156.21/21.10 | v0 & $i(v2) & ssList(v2))) % 156.21/21.10 | % 156.21/21.10 | ALPHA: (ax7) implies: % 156.21/21.10 | (3) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ segmentP(v0, % 156.21/21.10 | v1) | ~ ssList(v1) | ~ ssList(v0) | ? [v2: $i] : ? [v3: $i] : % 156.21/21.10 | ? [v4: $i] : (app(v3, v4) = v0 & app(v2, v1) = v3 & $i(v4) & $i(v3) & % 156.21/21.10 | $i(v2) & ssList(v4) & ssList(v2))) % 156.21/21.10 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( % 156.21/21.10 | ~ (app(v3, v4) = v0) | ~ (app(v2, v1) = v3) | ~ $i(v4) | ~ $i(v2) % 156.21/21.10 | | ~ $i(v1) | ~ $i(v0) | ~ ssList(v4) | ~ ssList(v2) | ~ % 156.21/21.10 | ssList(v1) | ~ ssList(v0) | segmentP(v0, v1)) % 156.21/21.10 | % 156.21/21.10 | ALPHA: (ax17) implies: % 156.21/21.10 | (5) ssList(nil) % 156.21/21.10 | % 156.21/21.10 | ALPHA: (ax28) implies: % 156.21/21.11 | (6) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (app(nil, v0) = v1) | ~ % 156.21/21.11 | $i(v0) | ~ ssList(v0)) % 156.21/21.11 | % 156.21/21.11 | ALPHA: (ax45) implies: % 156.21/21.11 | (7) ! [v0: $i] : ( ~ $i(v0) | ~ ssList(v0) | frontsegP(v0, nil)) % 156.21/21.11 | % 156.21/21.11 | ALPHA: (ax46) implies: % 156.21/21.11 | (8) ~ ssList(nil) | frontsegP(nil, nil) % 156.21/21.11 | % 156.21/21.11 | ALPHA: (ax51) implies: % 156.21/21.11 | (9) ! [v0: $i] : ( ~ $i(v0) | ~ ssList(v0) | rearsegP(v0, nil)) % 156.21/21.11 | % 156.21/21.11 | ALPHA: (ax52) implies: % 156.21/21.11 | (10) ~ ssList(nil) | rearsegP(nil, nil) % 156.21/21.11 | % 156.21/21.11 | ALPHA: (ax58) implies: % 156.21/21.11 | (11) ~ ssList(nil) | segmentP(nil, nil) % 156.21/21.11 | % 156.21/21.11 | ALPHA: (ax83) implies: % 156.21/21.11 | (12) ! [v0: $i] : (v0 = nil | ~ (app(nil, nil) = v0) | ~ ssList(nil)) % 156.21/21.11 | (13) ! [v0: $i] : ! [v1: $i] : (v1 = nil | ~ (app(v0, v1) = nil) | ~ % 156.21/21.11 | $i(v1) | ~ $i(v0) | ~ ssList(v1) | ~ ssList(v0)) % 156.21/21.11 | % 156.21/21.11 | ALPHA: (ax84) implies: % 156.21/21.11 | (14) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (app(v0, nil) = v1) | ~ % 156.21/21.11 | $i(v0) | ~ ssList(v0)) % 156.21/21.11 | % 156.21/21.11 | ALPHA: (co1) implies: % 156.21/21.11 | (15) $i(nil) % 156.21/21.11 | (16) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ($i(v2) & $i(v1) & $i(v0) & % 156.21/21.11 | frontsegP(v1, v2) & frontsegP(v0, v2) & ssList(v2) & ssList(v1) & % 156.21/21.11 | ssList(v0) & neq(v2, nil) & neq(v1, nil) & ! [v3: $i] : ( ~ $i(v3) % 156.21/21.11 | | ~ segmentP(v1, v3) | ~ segmentP(v0, v3) | ~ ssList(v3) | ~ % 156.21/21.11 | neq(v3, nil))) % 156.21/21.11 | % 156.21/21.11 | ALPHA: (function-axioms) implies: % 156.21/21.11 | (17) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 156.21/21.11 | (app(v3, v2) = v1) | ~ (app(v3, v2) = v0)) % 156.21/21.11 | % 156.21/21.11 | DELTA: instantiating (16) with fresh symbols all_91_0, all_91_1, all_91_2 % 156.21/21.11 | gives: % 156.21/21.11 | (18) $i(all_91_0) & $i(all_91_1) & $i(all_91_2) & frontsegP(all_91_1, % 156.21/21.11 | all_91_0) & frontsegP(all_91_2, all_91_0) & ssList(all_91_0) & % 156.21/21.11 | ssList(all_91_1) & ssList(all_91_2) & neq(all_91_0, nil) & % 156.21/21.11 | neq(all_91_1, nil) & ! [v0: $i] : ( ~ $i(v0) | ~ segmentP(all_91_1, % 156.21/21.11 | v0) | ~ segmentP(all_91_2, v0) | ~ ssList(v0) | ~ neq(v0, nil)) % 156.21/21.11 | % 156.21/21.11 | ALPHA: (18) implies: % 156.21/21.11 | (19) neq(all_91_0, nil) % 156.21/21.11 | (20) ssList(all_91_2) % 156.21/21.11 | (21) ssList(all_91_1) % 156.21/21.11 | (22) ssList(all_91_0) % 156.21/21.11 | (23) frontsegP(all_91_2, all_91_0) % 156.21/21.11 | (24) frontsegP(all_91_1, all_91_0) % 156.21/21.11 | (25) $i(all_91_2) % 156.21/21.11 | (26) $i(all_91_1) % 156.21/21.11 | (27) $i(all_91_0) % 156.21/21.11 | (28) ! [v0: $i] : ( ~ $i(v0) | ~ segmentP(all_91_1, v0) | ~ % 156.21/21.11 | segmentP(all_91_2, v0) | ~ ssList(v0) | ~ neq(v0, nil)) % 156.21/21.11 | % 156.21/21.11 | BETA: splitting (8) gives: % 156.21/21.11 | % 156.21/21.11 | Case 1: % 156.21/21.11 | | % 156.21/21.11 | | (29) ~ ssList(nil) % 156.21/21.11 | | % 156.21/21.12 | | PRED_UNIFY: (5), (29) imply: % 156.21/21.12 | | (30) $false % 156.21/21.12 | | % 156.21/21.12 | | CLOSE: (30) is inconsistent. % 156.21/21.12 | | % 156.21/21.12 | Case 2: % 156.21/21.12 | | % 156.21/21.12 | | (31) frontsegP(nil, nil) % 156.21/21.12 | | % 156.21/21.12 | | BETA: splitting (10) gives: % 156.21/21.12 | | % 156.21/21.12 | | Case 1: % 156.21/21.12 | | | % 156.21/21.12 | | | (32) ~ ssList(nil) % 156.21/21.12 | | | % 156.21/21.12 | | | PRED_UNIFY: (5), (32) imply: % 156.21/21.12 | | | (33) $false % 156.21/21.12 | | | % 156.21/21.12 | | | CLOSE: (33) is inconsistent. % 156.21/21.12 | | | % 156.21/21.12 | | Case 2: % 156.21/21.12 | | | % 156.21/21.12 | | | (34) rearsegP(nil, nil) % 156.21/21.12 | | | % 156.21/21.12 | | | BETA: splitting (11) gives: % 156.21/21.12 | | | % 156.21/21.12 | | | Case 1: % 156.21/21.12 | | | | % 156.21/21.12 | | | | (35) ~ ssList(nil) % 156.21/21.12 | | | | % 156.21/21.12 | | | | PRED_UNIFY: (5), (35) imply: % 156.21/21.12 | | | | (36) $false % 156.21/21.12 | | | | % 156.21/21.12 | | | | CLOSE: (36) is inconsistent. % 156.21/21.12 | | | | % 156.21/21.12 | | | Case 2: % 156.21/21.12 | | | | % 156.21/21.12 | | | | (37) segmentP(nil, nil) % 156.21/21.12 | | | | % 156.21/21.12 | | | | GROUND_INST: instantiating (9) with all_91_0, simplifying with (22), % 156.21/21.12 | | | | (27) gives: % 156.21/21.12 | | | | (38) rearsegP(all_91_0, nil) % 156.21/21.12 | | | | % 156.21/21.12 | | | | GROUND_INST: instantiating (7) with all_91_0, simplifying with (22), % 156.21/21.12 | | | | (27) gives: % 156.21/21.12 | | | | (39) frontsegP(all_91_0, nil) % 156.21/21.12 | | | | % 156.21/21.12 | | | | GROUND_INST: instantiating (1) with nil, nil, simplifying with (5), % 156.21/21.12 | | | | (15), (31) gives: % 156.38/21.12 | | | | (40) ? [v0: $i] : (app(nil, v0) = nil & $i(v0) & ssList(v0)) % 156.38/21.12 | | | | % 156.38/21.12 | | | | GROUND_INST: instantiating (1) with all_91_2, all_91_0, simplifying with % 156.38/21.12 | | | | (20), (22), (23), (25), (27) gives: % 156.38/21.12 | | | | (41) ? [v0: $i] : (app(all_91_0, v0) = all_91_2 & $i(v0) & % 156.38/21.12 | | | | ssList(v0)) % 156.38/21.12 | | | | % 156.38/21.12 | | | | GROUND_INST: instantiating (1) with all_91_1, all_91_0, simplifying with % 156.38/21.12 | | | | (21), (22), (24), (26), (27) gives: % 156.38/21.12 | | | | (42) ? [v0: $i] : (app(all_91_0, v0) = all_91_1 & $i(v0) & % 156.38/21.12 | | | | ssList(v0)) % 156.38/21.12 | | | | % 156.38/21.12 | | | | GROUND_INST: instantiating (2) with nil, nil, simplifying with (5), % 156.38/21.12 | | | | (15), (34) gives: % 156.38/21.12 | | | | (43) ? [v0: $i] : (app(v0, nil) = nil & $i(v0) & ssList(v0)) % 156.38/21.12 | | | | % 156.38/21.12 | | | | GROUND_INST: instantiating (3) with nil, nil, simplifying with (5), % 156.38/21.12 | | | | (15), (37) gives: % 156.38/21.12 | | | | (44) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (app(v1, v2) = nil & % 156.38/21.12 | | | | app(v0, nil) = v1 & $i(v2) & $i(v1) & $i(v0) & ssList(v2) & % 156.38/21.12 | | | | ssList(v0)) % 156.38/21.12 | | | | % 156.38/21.12 | | | | DELTA: instantiating (43) with fresh symbol all_112_0 gives: % 156.38/21.12 | | | | (45) app(all_112_0, nil) = nil & $i(all_112_0) & ssList(all_112_0) % 156.38/21.12 | | | | % 156.38/21.12 | | | | ALPHA: (45) implies: % 156.38/21.12 | | | | (46) ssList(all_112_0) % 156.38/21.12 | | | | (47) $i(all_112_0) % 156.38/21.12 | | | | (48) app(all_112_0, nil) = nil % 156.38/21.12 | | | | % 156.38/21.12 | | | | DELTA: instantiating (41) with fresh symbol all_114_0 gives: % 156.38/21.12 | | | | (49) app(all_91_0, all_114_0) = all_91_2 & $i(all_114_0) & % 156.38/21.12 | | | | ssList(all_114_0) % 156.38/21.12 | | | | % 156.38/21.12 | | | | ALPHA: (49) implies: % 156.38/21.13 | | | | (50) ssList(all_114_0) % 156.38/21.13 | | | | (51) $i(all_114_0) % 156.38/21.13 | | | | (52) app(all_91_0, all_114_0) = all_91_2 % 156.38/21.13 | | | | % 156.38/21.13 | | | | DELTA: instantiating (42) with fresh symbol all_116_0 gives: % 156.38/21.13 | | | | (53) app(all_91_0, all_116_0) = all_91_1 & $i(all_116_0) & % 156.38/21.13 | | | | ssList(all_116_0) % 156.38/21.13 | | | | % 156.38/21.13 | | | | ALPHA: (53) implies: % 156.38/21.13 | | | | (54) ssList(all_116_0) % 156.38/21.13 | | | | (55) $i(all_116_0) % 156.38/21.13 | | | | (56) app(all_91_0, all_116_0) = all_91_1 % 156.38/21.13 | | | | % 156.38/21.13 | | | | DELTA: instantiating (40) with fresh symbol all_118_0 gives: % 156.38/21.13 | | | | (57) app(nil, all_118_0) = nil & $i(all_118_0) & ssList(all_118_0) % 156.38/21.13 | | | | % 156.38/21.13 | | | | ALPHA: (57) implies: % 156.38/21.13 | | | | (58) ssList(all_118_0) % 156.38/21.13 | | | | (59) $i(all_118_0) % 156.38/21.13 | | | | (60) app(nil, all_118_0) = nil % 156.38/21.13 | | | | % 156.38/21.13 | | | | DELTA: instantiating (44) with fresh symbols all_120_0, all_120_1, % 156.38/21.13 | | | | all_120_2 gives: % 156.38/21.13 | | | | (61) app(all_120_1, all_120_0) = nil & app(all_120_2, nil) = % 156.38/21.13 | | | | all_120_1 & $i(all_120_0) & $i(all_120_1) & $i(all_120_2) & % 156.38/21.13 | | | | ssList(all_120_0) & ssList(all_120_2) % 156.38/21.13 | | | | % 156.38/21.13 | | | | ALPHA: (61) implies: % 156.38/21.13 | | | | (62) ssList(all_120_2) % 156.38/21.13 | | | | (63) ssList(all_120_0) % 156.38/21.13 | | | | (64) $i(all_120_2) % 156.38/21.13 | | | | (65) $i(all_120_1) % 156.38/21.13 | | | | (66) $i(all_120_0) % 156.38/21.13 | | | | (67) app(all_120_2, nil) = all_120_1 % 156.38/21.13 | | | | (68) app(all_120_1, all_120_0) = nil % 156.38/21.13 | | | | % 156.38/21.13 | | | | GROUND_INST: instantiating (1) with all_91_0, nil, simplifying with (5), % 156.38/21.13 | | | | (15), (22), (27), (39) gives: % 156.38/21.13 | | | | (69) ? [v0: $i] : (app(nil, v0) = all_91_0 & $i(v0) & ssList(v0)) % 156.38/21.13 | | | | % 156.38/21.13 | | | | GROUND_INST: instantiating (2) with all_91_0, nil, simplifying with (5), % 156.38/21.13 | | | | (15), (22), (27), (38) gives: % 156.38/21.13 | | | | (70) ? [v0: $i] : (app(v0, nil) = all_91_0 & $i(v0) & ssList(v0)) % 156.38/21.13 | | | | % 156.38/21.13 | | | | GROUND_INST: instantiating (ax82) with nil, all_118_0, nil, all_118_0, % 156.38/21.13 | | | | nil, simplifying with (5), (15), (58), (59), (60) gives: % 156.38/21.13 | | | | (71) ? [v0: $i] : (app(all_118_0, all_118_0) = v0 & app(nil, v0) = % 156.38/21.13 | | | | nil & $i(v0)) % 156.38/21.13 | | | | % 156.38/21.13 | | | | GROUND_INST: instantiating (6) with all_118_0, nil, simplifying with % 156.38/21.13 | | | | (58), (59), (60) gives: % 156.38/21.13 | | | | (72) all_118_0 = nil % 156.38/21.13 | | | | % 156.38/21.13 | | | | GROUND_INST: instantiating (14) with all_112_0, nil, simplifying with % 156.38/21.13 | | | | (46), (47), (48) gives: % 156.38/21.13 | | | | (73) all_112_0 = nil % 156.38/21.13 | | | | % 156.38/21.13 | | | | GROUND_INST: instantiating (ax26) with all_120_2, nil, all_120_1, % 156.38/21.13 | | | | simplifying with (5), (15), (62), (64), (67) gives: % 156.38/21.13 | | | | (74) ssList(all_120_1) % 156.38/21.13 | | | | % 156.38/21.13 | | | | GROUND_INST: instantiating (14) with all_120_2, all_120_1, simplifying % 156.38/21.13 | | | | with (62), (64), (67) gives: % 156.38/21.13 | | | | (75) all_120_1 = all_120_2 % 156.38/21.13 | | | | % 156.38/21.13 | | | | DELTA: instantiating (70) with fresh symbol all_142_0 gives: % 156.38/21.13 | | | | (76) app(all_142_0, nil) = all_91_0 & $i(all_142_0) & % 156.38/21.13 | | | | ssList(all_142_0) % 156.38/21.13 | | | | % 156.38/21.13 | | | | ALPHA: (76) implies: % 156.38/21.13 | | | | (77) ssList(all_142_0) % 156.38/21.13 | | | | (78) $i(all_142_0) % 156.38/21.13 | | | | (79) app(all_142_0, nil) = all_91_0 % 156.38/21.13 | | | | % 156.38/21.13 | | | | DELTA: instantiating (69) with fresh symbol all_150_0 gives: % 156.38/21.14 | | | | (80) app(nil, all_150_0) = all_91_0 & $i(all_150_0) & % 156.38/21.14 | | | | ssList(all_150_0) % 156.38/21.14 | | | | % 156.38/21.14 | | | | ALPHA: (80) implies: % 156.38/21.14 | | | | (81) ssList(all_150_0) % 156.38/21.14 | | | | (82) $i(all_150_0) % 156.38/21.14 | | | | (83) app(nil, all_150_0) = all_91_0 % 156.38/21.14 | | | | % 156.38/21.14 | | | | DELTA: instantiating (71) with fresh symbol all_162_0 gives: % 156.38/21.14 | | | | (84) app(all_118_0, all_118_0) = all_162_0 & app(nil, all_162_0) = % 156.38/21.14 | | | | nil & $i(all_162_0) % 156.38/21.14 | | | | % 156.38/21.14 | | | | ALPHA: (84) implies: % 156.38/21.14 | | | | (85) $i(all_162_0) % 156.38/21.14 | | | | (86) app(all_118_0, all_118_0) = all_162_0 % 156.38/21.14 | | | | % 156.38/21.14 | | | | REDUCE: (68), (75) imply: % 156.38/21.14 | | | | (87) app(all_120_2, all_120_0) = nil % 156.38/21.14 | | | | % 156.38/21.14 | | | | REDUCE: (72), (86) imply: % 156.38/21.14 | | | | (88) app(nil, nil) = all_162_0 % 156.38/21.14 | | | | % 156.38/21.14 | | | | GROUND_INST: instantiating (12) with all_162_0, simplifying with (5), % 156.38/21.14 | | | | (88) gives: % 156.38/21.14 | | | | (89) all_162_0 = nil % 156.38/21.14 | | | | % 156.38/21.14 | | | | REDUCE: (88), (89) imply: % 156.38/21.14 | | | | (90) app(nil, nil) = nil % 156.38/21.14 | | | | % 156.38/21.14 | | | | GROUND_INST: instantiating (4) with all_91_1, all_150_0, nil, all_91_0, % 156.38/21.14 | | | | all_116_0, simplifying with (5), (15), (21), (26), (54), % 156.38/21.14 | | | | (55), (56), (81), (82), (83) gives: % 156.38/21.14 | | | | (91) segmentP(all_91_1, all_150_0) % 156.38/21.14 | | | | % 156.38/21.14 | | | | GROUND_INST: instantiating (4) with all_91_2, all_150_0, nil, all_91_0, % 156.38/21.14 | | | | all_114_0, simplifying with (5), (15), (20), (25), (50), % 156.38/21.14 | | | | (51), (52), (81), (82), (83) gives: % 156.38/21.14 | | | | (92) segmentP(all_91_2, all_150_0) % 156.38/21.14 | | | | % 156.38/21.14 | | | | GROUND_INST: instantiating (ax82) with nil, nil, nil, all_150_0, % 156.38/21.14 | | | | all_91_0, simplifying with (5), (15), (81), (82), (83), % 156.38/21.14 | | | | (90) gives: % 156.38/21.14 | | | | (93) ? [v0: $i] : (app(nil, v0) = all_91_0 & app(nil, all_150_0) = % 156.38/21.14 | | | | v0 & $i(v0) & $i(all_91_0)) % 156.38/21.14 | | | | % 156.38/21.14 | | | | GROUND_INST: instantiating (6) with all_150_0, all_91_0, simplifying % 156.38/21.14 | | | | with (81), (82), (83) gives: % 156.38/21.14 | | | | (94) all_150_0 = all_91_0 % 156.38/21.14 | | | | % 156.38/21.14 | | | | GROUND_INST: instantiating (ax82) with all_120_2, all_120_0, nil, % 156.38/21.14 | | | | all_150_0, all_91_0, simplifying with (62), (63), (64), % 156.38/21.14 | | | | (66), (81), (82), (83), (87) gives: % 156.38/21.14 | | | | (95) ? [v0: $i] : (app(all_120_0, all_150_0) = v0 & app(all_120_2, % 156.38/21.14 | | | | v0) = all_91_0 & $i(v0) & $i(all_91_0)) % 156.38/21.14 | | | | % 156.38/21.14 | | | | GROUND_INST: instantiating (13) with all_120_2, all_120_0, simplifying % 156.38/21.14 | | | | with (62), (63), (64), (66), (87) gives: % 156.38/21.14 | | | | (96) all_120_0 = nil % 156.38/21.14 | | | | % 156.38/21.15 | | | | GROUND_INST: instantiating (14) with all_142_0, all_91_0, simplifying % 156.38/21.15 | | | | with (77), (78), (79) gives: % 156.38/21.15 | | | | (97) all_142_0 = all_91_0 % 156.38/21.15 | | | | % 156.38/21.15 | | | | DELTA: instantiating (95) with fresh symbol all_236_0 gives: % 156.38/21.15 | | | | (98) app(all_120_0, all_150_0) = all_236_0 & app(all_120_2, % 156.38/21.15 | | | | all_236_0) = all_91_0 & $i(all_236_0) & $i(all_91_0) % 156.38/21.15 | | | | % 156.38/21.15 | | | | ALPHA: (98) implies: % 156.38/21.15 | | | | (99) $i(all_236_0) % 156.38/21.15 | | | | (100) app(all_120_0, all_150_0) = all_236_0 % 156.38/21.15 | | | | % 156.38/21.15 | | | | DELTA: instantiating (93) with fresh symbol all_250_0 gives: % 156.38/21.15 | | | | (101) app(nil, all_250_0) = all_91_0 & app(nil, all_150_0) = % 156.38/21.15 | | | | all_250_0 & $i(all_250_0) & $i(all_91_0) % 156.38/21.15 | | | | % 156.38/21.15 | | | | ALPHA: (101) implies: % 156.38/21.15 | | | | (102) app(nil, all_150_0) = all_250_0 % 156.38/21.15 | | | | % 156.38/21.15 | | | | REDUCE: (94), (96), (100) imply: % 156.38/21.15 | | | | (103) app(nil, all_91_0) = all_236_0 % 156.38/21.15 | | | | % 156.38/21.15 | | | | REDUCE: (94), (102) imply: % 156.38/21.15 | | | | (104) app(nil, all_91_0) = all_250_0 % 156.38/21.15 | | | | % 156.38/21.15 | | | | REDUCE: (83), (94) imply: % 156.38/21.15 | | | | (105) app(nil, all_91_0) = all_91_0 % 156.38/21.15 | | | | % 156.38/21.15 | | | | REDUCE: (91), (94) imply: % 156.38/21.15 | | | | (106) segmentP(all_91_1, all_91_0) % 156.38/21.15 | | | | % 156.38/21.15 | | | | REDUCE: (92), (94) imply: % 156.38/21.15 | | | | (107) segmentP(all_91_2, all_91_0) % 156.38/21.15 | | | | % 156.38/21.15 | | | | GROUND_INST: instantiating (17) with all_236_0, all_250_0, all_91_0, % 156.38/21.15 | | | | nil, simplifying with (103), (104) gives: % 156.38/21.15 | | | | (108) all_250_0 = all_236_0 % 156.38/21.15 | | | | % 156.38/21.15 | | | | GROUND_INST: instantiating (17) with all_91_0, all_250_0, all_91_0, nil, % 156.38/21.15 | | | | simplifying with (104), (105) gives: % 156.38/21.15 | | | | (109) all_250_0 = all_91_0 % 156.38/21.15 | | | | % 156.38/21.15 | | | | COMBINE_EQS: (108), (109) imply: % 156.38/21.15 | | | | (110) all_236_0 = all_91_0 % 156.38/21.15 | | | | % 156.38/21.15 | | | | GROUND_INST: instantiating (28) with all_91_0, simplifying with (19), % 156.38/21.15 | | | | (22), (27), (106), (107) gives: % 156.38/21.15 | | | | (111) $false % 156.38/21.15 | | | | % 156.38/21.15 | | | | CLOSE: (111) is inconsistent. % 156.38/21.15 | | | | % 156.38/21.15 | | | End of split % 156.38/21.15 | | | % 156.38/21.15 | | End of split % 156.38/21.15 | | % 156.38/21.15 | End of split % 156.38/21.15 | % 156.38/21.15 End of proof % 156.38/21.15 % SZS output end Proof for theBenchmark % 156.38/21.15 % 156.38/21.15 20556ms %------------------------------------------------------------------------------