%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SWC094+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 : n014.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 20:49:37 EDT 2023 % Result : Theorem 29.92s 4.75s % Output : Proof 41.21s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SWC094+1 : TPTP v8.1.2. Released v2.4.0. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.16/0.34 % Computer : n014.cluster.edu % 0.16/0.34 % Model : x86_64 x86_64 % 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.16/0.34 % Memory : 8042.1875MB % 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.16/0.34 % CPULimit : 300 % 0.16/0.34 % WCLimit : 300 % 0.16/0.34 % DateTime : Mon Aug 28 14:41:31 EDT 2023 % 0.16/0.34 % CPUTime : % 0.19/0.57 ________ _____ % 0.19/0.57 ___ __ \_________(_)________________________________ % 0.19/0.57 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.19/0.57 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.19/0.57 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.19/0.57 % 0.19/0.57 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.19/0.57 (2023-06-19) % 0.19/0.57 % 0.19/0.57 (c) Philipp Rümmer, 2009-2023 % 0.19/0.57 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.19/0.57 Amanda Stjerna. % 0.19/0.57 Free software under BSD-3-Clause. % 0.19/0.57 % 0.19/0.57 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.19/0.57 % 0.19/0.57 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.19/0.58 Running up to 7 provers in parallel. % 0.19/0.60 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.19/0.60 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.19/0.60 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.19/0.60 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.19/0.60 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.19/0.60 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.19/0.60 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 4.71/1.36 Prover 4: Preprocessing ... % 4.71/1.36 Prover 1: Preprocessing ... % 5.24/1.41 Prover 6: Preprocessing ... % 5.24/1.41 Prover 5: Preprocessing ... % 5.24/1.41 Prover 2: Preprocessing ... % 5.24/1.41 Prover 3: Preprocessing ... % 5.24/1.41 Prover 0: Preprocessing ... % 16.34/2.89 Prover 2: Proving ... % 16.34/2.92 Prover 5: Constructing countermodel ... % 16.92/2.97 Prover 6: Proving ... % 17.05/2.99 Prover 1: Constructing countermodel ... % 17.05/2.99 Prover 3: Constructing countermodel ... % 23.90/3.91 Prover 4: Constructing countermodel ... % 23.90/3.95 Prover 0: Proving ... % 29.92/4.73 Prover 2: proved (4139ms) % 29.92/4.75 % 29.92/4.75 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 29.92/4.75 % 29.92/4.75 Prover 6: stopped % 29.92/4.76 Prover 5: stopped % 29.92/4.76 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 29.92/4.76 Prover 0: stopped % 29.92/4.77 Prover 3: stopped % 29.92/4.78 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 29.92/4.78 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 29.92/4.78 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 29.92/4.78 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 32.07/5.06 Prover 11: Preprocessing ... % 32.07/5.06 Prover 7: Preprocessing ... % 32.07/5.06 Prover 10: Preprocessing ... % 32.72/5.09 Prover 8: Preprocessing ... % 32.88/5.11 Prover 13: Preprocessing ... % 33.74/5.22 Prover 10: Constructing countermodel ... % 34.29/5.37 Prover 7: Constructing countermodel ... % 34.93/5.46 Prover 13: Constructing countermodel ... % 36.28/5.58 Prover 8: Warning: ignoring some quantifiers % 36.28/5.61 Prover 8: Constructing countermodel ... % 39.30/6.02 Prover 10: Found proof (size 86) % 39.30/6.02 Prover 10: proved (1250ms) % 39.30/6.02 Prover 13: stopped % 39.30/6.02 Prover 8: stopped % 39.30/6.02 Prover 7: stopped % 39.30/6.02 Prover 4: stopped % 39.30/6.02 Prover 1: stopped % 40.58/6.23 Prover 11: Constructing countermodel ... % 40.58/6.25 Prover 11: stopped % 40.58/6.25 % 40.58/6.25 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 40.58/6.25 % 40.87/6.27 % SZS output start Proof for theBenchmark % 40.87/6.27 Assumptions after simplification: % 40.87/6.27 --------------------------------- % 40.87/6.27 % 40.87/6.27 (ax17) % 40.87/6.28 $i(nil) & ssList(nil) % 40.87/6.28 % 40.87/6.28 (ax26) % 40.87/6.30 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (app(v0, v1) = v2) | ~ $i(v1) | % 40.87/6.30 ~ $i(v0) | ~ ssList(v1) | ~ ssList(v0) | ssList(v2)) % 40.87/6.30 % 40.87/6.30 (ax28) % 40.87/6.30 $i(nil) & ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (app(nil, v0) = v1) | ~ % 40.87/6.30 $i(v0) | ~ ssList(v0)) % 40.87/6.30 % 40.87/6.30 (ax45) % 41.05/6.30 $i(nil) & ! [v0: $i] : ( ~ $i(v0) | ~ ssList(v0) | frontsegP(v0, nil)) % 41.05/6.30 % 41.05/6.30 (ax46) % 41.05/6.30 $i(nil) & ! [v0: $i] : (v0 = nil | ~ $i(v0) | ~ frontsegP(nil, v0) | ~ % 41.05/6.30 ssList(v0)) & ( ~ ssList(nil) | frontsegP(nil, nil)) % 41.05/6.30 % 41.05/6.30 (ax5) % 41.05/6.30 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (app(v1, v2) = v0) | ~ $i(v2) | % 41.05/6.30 ~ $i(v1) | ~ $i(v0) | ~ ssList(v2) | ~ ssList(v1) | ~ ssList(v0) | % 41.05/6.30 frontsegP(v0, v1)) & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ % 41.05/6.30 frontsegP(v0, v1) | ~ ssList(v1) | ~ ssList(v0) | ? [v2: $i] : (app(v1, % 41.05/6.30 v2) = v0 & $i(v2) & ssList(v2))) % 41.05/6.30 % 41.05/6.30 (ax52) % 41.05/6.30 $i(nil) & ! [v0: $i] : (v0 = nil | ~ $i(v0) | ~ rearsegP(nil, v0) | ~ % 41.05/6.30 ssList(v0)) & ( ~ ssList(nil) | rearsegP(nil, nil)) % 41.05/6.30 % 41.05/6.30 (ax58) % 41.05/6.31 $i(nil) & ! [v0: $i] : (v0 = nil | ~ $i(v0) | ~ segmentP(nil, v0) | ~ % 41.05/6.31 ssList(v0)) & ( ~ ssList(nil) | segmentP(nil, nil)) % 41.05/6.31 % 41.05/6.31 (ax6) % 41.05/6.31 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (app(v2, v1) = v0) | ~ $i(v2) | % 41.05/6.31 ~ $i(v1) | ~ $i(v0) | ~ ssList(v2) | ~ ssList(v1) | ~ ssList(v0) | % 41.05/6.31 rearsegP(v0, v1)) & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ % 41.05/6.31 rearsegP(v0, v1) | ~ ssList(v1) | ~ ssList(v0) | ? [v2: $i] : (app(v2, % 41.05/6.31 v1) = v0 & $i(v2) & ssList(v2))) % 41.05/6.31 % 41.05/6.31 (ax7) % 41.05/6.31 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 41.05/6.31 (app(v3, v4) = v0) | ~ (app(v2, v1) = v3) | ~ $i(v4) | ~ $i(v2) | ~ % 41.05/6.31 $i(v1) | ~ $i(v0) | ~ ssList(v4) | ~ ssList(v2) | ~ ssList(v1) | ~ % 41.05/6.31 ssList(v0) | segmentP(v0, v1)) & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ % 41.05/6.31 $i(v0) | ~ segmentP(v0, v1) | ~ ssList(v1) | ~ ssList(v0) | ? [v2: $i] : % 41.05/6.31 ? [v3: $i] : ? [v4: $i] : (app(v3, v4) = v0 & app(v2, v1) = v3 & $i(v4) & % 41.05/6.31 $i(v3) & $i(v2) & ssList(v4) & ssList(v2))) % 41.05/6.31 % 41.05/6.31 (ax82) % 41.05/6.31 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 41.05/6.31 (app(v2, v3) = v4) | ~ (app(v0, v1) = v2) | ~ $i(v3) | ~ $i(v1) | ~ % 41.05/6.31 $i(v0) | ~ ssList(v3) | ~ ssList(v1) | ~ ssList(v0) | ? [v5: $i] : % 41.05/6.31 (app(v1, v3) = v5 & app(v0, v5) = v4 & $i(v5) & $i(v4))) % 41.05/6.31 % 41.05/6.31 (ax83) % 41.05/6.31 $i(nil) & ! [v0: $i] : ! [v1: $i] : (v1 = nil | ~ (app(v0, v1) = nil) | ~ % 41.05/6.31 $i(v1) | ~ $i(v0) | ~ ssList(v1) | ~ ssList(v0)) & ! [v0: $i] : ! [v1: % 41.05/6.31 $i] : (v0 = nil | ~ (app(v0, v1) = nil) | ~ $i(v1) | ~ $i(v0) | ~ % 41.05/6.31 ssList(v1) | ~ ssList(v0)) & ! [v0: $i] : (v0 = nil | ~ (app(nil, nil) = % 41.05/6.31 v0) | ~ ssList(nil)) % 41.05/6.31 % 41.05/6.31 (ax84) % 41.05/6.32 $i(nil) & ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (app(v0, nil) = v1) | ~ % 41.05/6.32 $i(v0) | ~ ssList(v0)) % 41.05/6.32 % 41.05/6.32 (ax86) % 41.05/6.32 $i(nil) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v0 = nil | % 41.05/6.32 ~ (tl(v0) = v1) | ~ (app(v1, v2) = v3) | ~ $i(v2) | ~ $i(v0) | ~ % 41.05/6.32 ssList(v2) | ~ ssList(v0) | ? [v4: $i] : (tl(v4) = v3 & app(v0, v2) = v4 & % 41.05/6.32 $i(v4) & $i(v3))) % 41.05/6.32 % 41.05/6.32 (co1) % 41.05/6.32 ? [v0: $i] : ($i(v0) & ssList(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : % 41.05/6.32 ! [v4: $i] : ( ~ (app(v3, v4) = v0) | ~ (app(v1, v2) = v3) | ~ $i(v4) | % 41.05/6.32 ~ $i(v2) | ~ $i(v1) | ~ ssList(v4) | ~ ssList(v2) | ~ ssList(v1) | ? % 41.05/6.32 [v5: $i] : ( ~ (v5 = v0) & app(v1, v4) = v5 & $i(v5)))) % 41.05/6.32 % 41.05/6.32 (function-axioms) % 41.05/6.32 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 41.05/6.32 (cons(v3, v2) = v1) | ~ (cons(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : % 41.05/6.32 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (app(v3, v2) = v1) | ~ (app(v3, v2) % 41.05/6.32 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (tl(v2) = % 41.05/6.32 v1) | ~ (tl(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = % 41.05/6.32 v0 | ~ (hd(v2) = v1) | ~ (hd(v2) = v0)) % 41.05/6.32 % 41.05/6.32 Further assumptions not needed in the proof: % 41.05/6.32 -------------------------------------------- % 41.05/6.32 ax1, ax10, ax11, ax12, ax13, ax14, ax15, ax16, ax18, ax19, ax2, ax20, ax21, % 41.05/6.32 ax22, ax23, ax24, ax25, ax27, ax29, ax3, ax30, ax31, ax32, ax33, ax34, ax35, % 41.05/6.32 ax36, ax37, ax38, ax39, ax4, ax40, ax41, ax42, ax43, ax44, ax47, ax48, ax49, % 41.05/6.32 ax50, ax51, ax53, ax54, ax55, ax56, ax57, ax59, ax60, ax61, ax62, ax63, ax64, % 41.05/6.32 ax65, ax66, ax67, ax68, ax69, ax70, ax71, ax72, ax73, ax74, ax75, ax76, ax77, % 41.05/6.32 ax78, ax79, ax8, ax80, ax81, ax85, ax87, ax88, ax89, ax9, ax90, ax91, ax92, % 41.05/6.32 ax93, ax94, ax95 % 41.05/6.32 % 41.05/6.32 Those formulas are unsatisfiable: % 41.05/6.32 --------------------------------- % 41.05/6.32 % 41.05/6.32 Begin of proof % 41.05/6.32 | % 41.05/6.32 | ALPHA: (ax5) implies: % 41.05/6.32 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ frontsegP(v0, % 41.05/6.32 | v1) | ~ ssList(v1) | ~ ssList(v0) | ? [v2: $i] : (app(v1, v2) = % 41.05/6.32 | v0 & $i(v2) & ssList(v2))) % 41.05/6.32 | % 41.05/6.32 | ALPHA: (ax6) implies: % 41.05/6.32 | (2) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ rearsegP(v0, % 41.05/6.32 | v1) | ~ ssList(v1) | ~ ssList(v0) | ? [v2: $i] : (app(v2, v1) = % 41.05/6.32 | v0 & $i(v2) & ssList(v2))) % 41.05/6.32 | % 41.05/6.33 | ALPHA: (ax7) implies: % 41.05/6.33 | (3) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ segmentP(v0, % 41.05/6.33 | v1) | ~ ssList(v1) | ~ ssList(v0) | ? [v2: $i] : ? [v3: $i] : % 41.05/6.33 | ? [v4: $i] : (app(v3, v4) = v0 & app(v2, v1) = v3 & $i(v4) & $i(v3) & % 41.05/6.33 | $i(v2) & ssList(v4) & ssList(v2))) % 41.05/6.33 | % 41.05/6.33 | ALPHA: (ax17) implies: % 41.05/6.33 | (4) ssList(nil) % 41.05/6.33 | % 41.05/6.33 | ALPHA: (ax28) implies: % 41.05/6.33 | (5) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (app(nil, v0) = v1) | ~ % 41.05/6.33 | $i(v0) | ~ ssList(v0)) % 41.05/6.33 | % 41.05/6.33 | ALPHA: (ax45) implies: % 41.05/6.33 | (6) ! [v0: $i] : ( ~ $i(v0) | ~ ssList(v0) | frontsegP(v0, nil)) % 41.05/6.33 | % 41.05/6.33 | ALPHA: (ax46) implies: % 41.05/6.33 | (7) ~ ssList(nil) | frontsegP(nil, nil) % 41.05/6.33 | % 41.05/6.33 | ALPHA: (ax52) implies: % 41.05/6.33 | (8) ~ ssList(nil) | rearsegP(nil, nil) % 41.05/6.33 | % 41.05/6.33 | ALPHA: (ax58) implies: % 41.05/6.33 | (9) ~ ssList(nil) | segmentP(nil, nil) % 41.05/6.33 | % 41.05/6.33 | ALPHA: (ax83) implies: % 41.05/6.33 | (10) ! [v0: $i] : (v0 = nil | ~ (app(nil, nil) = v0) | ~ ssList(nil)) % 41.05/6.33 | (11) ! [v0: $i] : ! [v1: $i] : (v0 = nil | ~ (app(v0, v1) = nil) | ~ % 41.05/6.33 | $i(v1) | ~ $i(v0) | ~ ssList(v1) | ~ ssList(v0)) % 41.05/6.33 | (12) ! [v0: $i] : ! [v1: $i] : (v1 = nil | ~ (app(v0, v1) = nil) | ~ % 41.05/6.33 | $i(v1) | ~ $i(v0) | ~ ssList(v1) | ~ ssList(v0)) % 41.05/6.33 | % 41.05/6.33 | ALPHA: (ax84) implies: % 41.05/6.33 | (13) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (app(v0, nil) = v1) | ~ % 41.05/6.33 | $i(v0) | ~ ssList(v0)) % 41.05/6.33 | % 41.05/6.33 | ALPHA: (ax86) implies: % 41.05/6.33 | (14) $i(nil) % 41.05/6.33 | % 41.05/6.33 | ALPHA: (function-axioms) implies: % 41.05/6.33 | (15) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 41.05/6.33 | (app(v3, v2) = v1) | ~ (app(v3, v2) = v0)) % 41.05/6.33 | % 41.21/6.33 | DELTA: instantiating (co1) with fresh symbol all_91_0 gives: % 41.21/6.33 | (16) $i(all_91_0) & ssList(all_91_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 41.21/6.33 | $i] : ! [v3: $i] : ( ~ (app(v2, v3) = all_91_0) | ~ (app(v0, v1) = % 41.21/6.33 | v2) | ~ $i(v3) | ~ $i(v1) | ~ $i(v0) | ~ ssList(v3) | ~ % 41.21/6.33 | ssList(v1) | ~ ssList(v0) | ? [v4: any] : ( ~ (v4 = all_91_0) & % 41.21/6.33 | app(v0, v3) = v4 & $i(v4))) % 41.21/6.33 | % 41.21/6.33 | ALPHA: (16) implies: % 41.21/6.33 | (17) ssList(all_91_0) % 41.21/6.33 | (18) $i(all_91_0) % 41.21/6.34 | (19) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (app(v2, % 41.21/6.34 | v3) = all_91_0) | ~ (app(v0, v1) = v2) | ~ $i(v3) | ~ $i(v1) % 41.21/6.34 | | ~ $i(v0) | ~ ssList(v3) | ~ ssList(v1) | ~ ssList(v0) | ? % 41.21/6.34 | [v4: any] : ( ~ (v4 = all_91_0) & app(v0, v3) = v4 & $i(v4))) % 41.21/6.34 | % 41.21/6.34 | BETA: splitting (7) gives: % 41.21/6.34 | % 41.21/6.34 | Case 1: % 41.21/6.34 | | % 41.21/6.34 | | (20) ~ ssList(nil) % 41.21/6.34 | | % 41.21/6.34 | | PRED_UNIFY: (4), (20) imply: % 41.21/6.34 | | (21) $false % 41.21/6.34 | | % 41.21/6.34 | | CLOSE: (21) is inconsistent. % 41.21/6.34 | | % 41.21/6.34 | Case 2: % 41.21/6.34 | | % 41.21/6.34 | | (22) frontsegP(nil, nil) % 41.21/6.34 | | % 41.21/6.34 | | BETA: splitting (8) gives: % 41.21/6.34 | | % 41.21/6.34 | | Case 1: % 41.21/6.34 | | | % 41.21/6.34 | | | (23) ~ ssList(nil) % 41.21/6.34 | | | % 41.21/6.34 | | | PRED_UNIFY: (4), (23) imply: % 41.21/6.34 | | | (24) $false % 41.21/6.34 | | | % 41.21/6.34 | | | CLOSE: (24) is inconsistent. % 41.21/6.34 | | | % 41.21/6.34 | | Case 2: % 41.21/6.34 | | | % 41.21/6.34 | | | (25) rearsegP(nil, nil) % 41.21/6.34 | | | % 41.21/6.34 | | | BETA: splitting (9) gives: % 41.21/6.34 | | | % 41.21/6.34 | | | Case 1: % 41.21/6.34 | | | | % 41.21/6.34 | | | | (26) ~ ssList(nil) % 41.21/6.34 | | | | % 41.21/6.34 | | | | PRED_UNIFY: (4), (26) imply: % 41.21/6.34 | | | | (27) $false % 41.21/6.34 | | | | % 41.21/6.34 | | | | CLOSE: (27) is inconsistent. % 41.21/6.34 | | | | % 41.21/6.34 | | | Case 2: % 41.21/6.34 | | | | % 41.21/6.34 | | | | (28) segmentP(nil, nil) % 41.21/6.34 | | | | % 41.21/6.34 | | | | GROUND_INST: instantiating (6) with all_91_0, simplifying with (17), % 41.21/6.34 | | | | (18) gives: % 41.21/6.34 | | | | (29) frontsegP(all_91_0, nil) % 41.21/6.34 | | | | % 41.21/6.34 | | | | GROUND_INST: instantiating (1) with nil, nil, simplifying with (4), % 41.21/6.34 | | | | (14), (22) gives: % 41.21/6.34 | | | | (30) ? [v0: $i] : (app(nil, v0) = nil & $i(v0) & ssList(v0)) % 41.21/6.34 | | | | % 41.21/6.34 | | | | GROUND_INST: instantiating (2) with nil, nil, simplifying with (4), % 41.21/6.34 | | | | (14), (25) gives: % 41.21/6.34 | | | | (31) ? [v0: $i] : (app(v0, nil) = nil & $i(v0) & ssList(v0)) % 41.21/6.34 | | | | % 41.21/6.34 | | | | GROUND_INST: instantiating (3) with nil, nil, simplifying with (4), % 41.21/6.34 | | | | (14), (28) gives: % 41.21/6.34 | | | | (32) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (app(v1, v2) = nil & % 41.21/6.34 | | | | app(v0, nil) = v1 & $i(v2) & $i(v1) & $i(v0) & ssList(v2) & % 41.21/6.34 | | | | ssList(v0)) % 41.21/6.34 | | | | % 41.21/6.34 | | | | DELTA: instantiating (31) with fresh symbol all_112_0 gives: % 41.21/6.34 | | | | (33) app(all_112_0, nil) = nil & $i(all_112_0) & ssList(all_112_0) % 41.21/6.34 | | | | % 41.21/6.34 | | | | ALPHA: (33) implies: % 41.21/6.34 | | | | (34) ssList(all_112_0) % 41.21/6.34 | | | | (35) $i(all_112_0) % 41.21/6.34 | | | | (36) app(all_112_0, nil) = nil % 41.21/6.34 | | | | % 41.21/6.34 | | | | DELTA: instantiating (30) with fresh symbol all_114_0 gives: % 41.21/6.34 | | | | (37) app(nil, all_114_0) = nil & $i(all_114_0) & ssList(all_114_0) % 41.21/6.34 | | | | % 41.21/6.34 | | | | ALPHA: (37) implies: % 41.21/6.34 | | | | (38) ssList(all_114_0) % 41.21/6.34 | | | | (39) $i(all_114_0) % 41.21/6.34 | | | | (40) app(nil, all_114_0) = nil % 41.21/6.34 | | | | % 41.21/6.34 | | | | DELTA: instantiating (32) with fresh symbols all_116_0, all_116_1, % 41.21/6.34 | | | | all_116_2 gives: % 41.21/6.35 | | | | (41) app(all_116_1, all_116_0) = nil & app(all_116_2, nil) = % 41.21/6.35 | | | | all_116_1 & $i(all_116_0) & $i(all_116_1) & $i(all_116_2) & % 41.21/6.35 | | | | ssList(all_116_0) & ssList(all_116_2) % 41.21/6.35 | | | | % 41.21/6.35 | | | | ALPHA: (41) implies: % 41.21/6.35 | | | | (42) ssList(all_116_2) % 41.21/6.35 | | | | (43) ssList(all_116_0) % 41.21/6.35 | | | | (44) $i(all_116_2) % 41.21/6.35 | | | | (45) $i(all_116_1) % 41.21/6.35 | | | | (46) $i(all_116_0) % 41.21/6.35 | | | | (47) app(all_116_2, nil) = all_116_1 % 41.21/6.35 | | | | (48) app(all_116_1, all_116_0) = nil % 41.21/6.35 | | | | % 41.21/6.35 | | | | GROUND_INST: instantiating (1) with all_91_0, nil, simplifying with (4), % 41.21/6.35 | | | | (14), (17), (18), (29) gives: % 41.21/6.35 | | | | (49) ? [v0: $i] : (app(nil, v0) = all_91_0 & $i(v0) & ssList(v0)) % 41.21/6.35 | | | | % 41.21/6.35 | | | | GROUND_INST: instantiating (ax82) with nil, all_114_0, nil, all_114_0, % 41.21/6.35 | | | | nil, simplifying with (4), (14), (38), (39), (40) gives: % 41.21/6.35 | | | | (50) ? [v0: $i] : (app(all_114_0, all_114_0) = v0 & app(nil, v0) = % 41.21/6.35 | | | | nil & $i(v0)) % 41.21/6.35 | | | | % 41.21/6.35 | | | | GROUND_INST: instantiating (5) with all_114_0, nil, simplifying with % 41.21/6.35 | | | | (38), (39), (40) gives: % 41.21/6.35 | | | | (51) all_114_0 = nil % 41.21/6.35 | | | | % 41.21/6.35 | | | | GROUND_INST: instantiating (13) with all_112_0, nil, simplifying with % 41.21/6.35 | | | | (34), (35), (36) gives: % 41.21/6.35 | | | | (52) all_112_0 = nil % 41.21/6.35 | | | | % 41.21/6.35 | | | | GROUND_INST: instantiating (ax26) with all_116_2, nil, all_116_1, % 41.21/6.35 | | | | simplifying with (4), (14), (42), (44), (47) gives: % 41.21/6.35 | | | | (53) ssList(all_116_1) % 41.21/6.35 | | | | % 41.21/6.35 | | | | GROUND_INST: instantiating (13) with all_116_2, all_116_1, simplifying % 41.21/6.35 | | | | with (42), (44), (47) gives: % 41.21/6.35 | | | | (54) all_116_1 = all_116_2 % 41.21/6.35 | | | | % 41.21/6.35 | | | | DELTA: instantiating (50) with fresh symbol all_140_0 gives: % 41.21/6.35 | | | | (55) app(all_114_0, all_114_0) = all_140_0 & app(nil, all_140_0) = % 41.21/6.35 | | | | nil & $i(all_140_0) % 41.21/6.35 | | | | % 41.21/6.35 | | | | ALPHA: (55) implies: % 41.21/6.35 | | | | (56) $i(all_140_0) % 41.21/6.35 | | | | (57) app(all_114_0, all_114_0) = all_140_0 % 41.21/6.35 | | | | % 41.21/6.35 | | | | DELTA: instantiating (49) with fresh symbol all_142_0 gives: % 41.21/6.35 | | | | (58) app(nil, all_142_0) = all_91_0 & $i(all_142_0) & % 41.21/6.35 | | | | ssList(all_142_0) % 41.21/6.35 | | | | % 41.21/6.35 | | | | ALPHA: (58) implies: % 41.21/6.35 | | | | (59) ssList(all_142_0) % 41.21/6.35 | | | | (60) $i(all_142_0) % 41.21/6.35 | | | | (61) app(nil, all_142_0) = all_91_0 % 41.21/6.35 | | | | % 41.21/6.35 | | | | REDUCE: (48), (54) imply: % 41.21/6.35 | | | | (62) app(all_116_2, all_116_0) = nil % 41.21/6.35 | | | | % 41.21/6.35 | | | | REDUCE: (51), (57) imply: % 41.21/6.35 | | | | (63) app(nil, nil) = all_140_0 % 41.21/6.35 | | | | % 41.21/6.35 | | | | GROUND_INST: instantiating (10) with all_140_0, simplifying with (4), % 41.21/6.35 | | | | (63) gives: % 41.21/6.35 | | | | (64) all_140_0 = nil % 41.21/6.35 | | | | % 41.21/6.35 | | | | REDUCE: (63), (64) imply: % 41.21/6.35 | | | | (65) app(nil, nil) = nil % 41.21/6.35 | | | | % 41.21/6.35 | | | | GROUND_INST: instantiating (ax82) with nil, nil, nil, all_142_0, % 41.21/6.35 | | | | all_91_0, simplifying with (4), (14), (59), (60), (61), % 41.21/6.35 | | | | (65) gives: % 41.21/6.35 | | | | (66) ? [v0: $i] : (app(nil, v0) = all_91_0 & app(nil, all_142_0) = % 41.21/6.35 | | | | v0 & $i(v0) & $i(all_91_0)) % 41.21/6.35 | | | | % 41.21/6.36 | | | | GROUND_INST: instantiating (19) with nil, nil, nil, all_142_0, % 41.21/6.36 | | | | simplifying with (4), (14), (59), (60), (61), (65) gives: % 41.21/6.36 | | | | (67) ? [v0: any] : ( ~ (v0 = all_91_0) & app(nil, all_142_0) = v0 & % 41.21/6.36 | | | | $i(v0)) % 41.21/6.36 | | | | % 41.21/6.36 | | | | GROUND_INST: instantiating (5) with all_142_0, all_91_0, simplifying % 41.21/6.36 | | | | with (59), (60), (61) gives: % 41.21/6.36 | | | | (68) all_142_0 = all_91_0 % 41.21/6.36 | | | | % 41.21/6.36 | | | | GROUND_INST: instantiating (ax82) with all_116_2, all_116_0, nil, % 41.21/6.36 | | | | all_142_0, all_91_0, simplifying with (42), (43), (44), % 41.21/6.36 | | | | (46), (59), (60), (61), (62) gives: % 41.21/6.36 | | | | (69) ? [v0: $i] : (app(all_116_0, all_142_0) = v0 & app(all_116_2, % 41.21/6.36 | | | | v0) = all_91_0 & $i(v0) & $i(all_91_0)) % 41.21/6.36 | | | | % 41.21/6.36 | | | | GROUND_INST: instantiating (19) with all_116_2, all_116_0, nil, % 41.21/6.36 | | | | all_142_0, simplifying with (42), (43), (44), (46), (59), % 41.21/6.36 | | | | (60), (61), (62) gives: % 41.21/6.36 | | | | (70) ? [v0: any] : ( ~ (v0 = all_91_0) & app(all_116_2, all_142_0) = % 41.21/6.36 | | | | v0 & $i(v0)) % 41.21/6.36 | | | | % 41.21/6.36 | | | | GROUND_INST: instantiating (12) with all_116_2, all_116_0, simplifying % 41.21/6.36 | | | | with (42), (43), (44), (46), (62) gives: % 41.21/6.36 | | | | (71) all_116_0 = nil % 41.21/6.36 | | | | % 41.21/6.36 | | | | GROUND_INST: instantiating (11) with all_116_2, all_116_0, simplifying % 41.21/6.36 | | | | with (42), (43), (44), (46), (62) gives: % 41.21/6.36 | | | | (72) all_116_2 = nil % 41.21/6.36 | | | | % 41.21/6.36 | | | | DELTA: instantiating (70) with fresh symbol all_158_0 gives: % 41.21/6.36 | | | | (73) ~ (all_158_0 = all_91_0) & app(all_116_2, all_142_0) = % 41.21/6.36 | | | | all_158_0 & $i(all_158_0) % 41.21/6.36 | | | | % 41.21/6.36 | | | | ALPHA: (73) implies: % 41.21/6.36 | | | | (74) ~ (all_158_0 = all_91_0) % 41.21/6.36 | | | | (75) app(all_116_2, all_142_0) = all_158_0 % 41.21/6.36 | | | | % 41.21/6.36 | | | | DELTA: instantiating (67) with fresh symbol all_170_0 gives: % 41.21/6.36 | | | | (76) ~ (all_170_0 = all_91_0) & app(nil, all_142_0) = all_170_0 & % 41.21/6.36 | | | | $i(all_170_0) % 41.21/6.36 | | | | % 41.21/6.36 | | | | ALPHA: (76) implies: % 41.21/6.36 | | | | (77) app(nil, all_142_0) = all_170_0 % 41.21/6.36 | | | | % 41.21/6.36 | | | | DELTA: instantiating (66) with fresh symbol all_196_0 gives: % 41.21/6.36 | | | | (78) app(nil, all_196_0) = all_91_0 & app(nil, all_142_0) = all_196_0 % 41.21/6.36 | | | | & $i(all_196_0) & $i(all_91_0) % 41.21/6.36 | | | | % 41.21/6.36 | | | | ALPHA: (78) implies: % 41.21/6.36 | | | | (79) app(nil, all_142_0) = all_196_0 % 41.21/6.36 | | | | % 41.21/6.36 | | | | DELTA: instantiating (69) with fresh symbol all_200_0 gives: % 41.21/6.36 | | | | (80) app(all_116_0, all_142_0) = all_200_0 & app(all_116_2, % 41.21/6.36 | | | | all_200_0) = all_91_0 & $i(all_200_0) & $i(all_91_0) % 41.21/6.36 | | | | % 41.21/6.36 | | | | ALPHA: (80) implies: % 41.21/6.36 | | | | (81) app(all_116_0, all_142_0) = all_200_0 % 41.21/6.36 | | | | % 41.21/6.36 | | | | REDUCE: (68), (71), (81) imply: % 41.21/6.36 | | | | (82) app(nil, all_91_0) = all_200_0 % 41.21/6.36 | | | | % 41.21/6.36 | | | | REDUCE: (68), (72), (75) imply: % 41.21/6.36 | | | | (83) app(nil, all_91_0) = all_158_0 % 41.21/6.36 | | | | % 41.21/6.36 | | | | REDUCE: (68), (79) imply: % 41.21/6.36 | | | | (84) app(nil, all_91_0) = all_196_0 % 41.21/6.36 | | | | % 41.21/6.36 | | | | REDUCE: (68), (77) imply: % 41.21/6.36 | | | | (85) app(nil, all_91_0) = all_170_0 % 41.21/6.36 | | | | % 41.21/6.36 | | | | REDUCE: (61), (68) imply: % 41.21/6.36 | | | | (86) app(nil, all_91_0) = all_91_0 % 41.21/6.36 | | | | % 41.21/6.36 | | | | GROUND_INST: instantiating (15) with all_91_0, all_170_0, all_91_0, nil, % 41.21/6.36 | | | | simplifying with (85), (86) gives: % 41.21/6.36 | | | | (87) all_170_0 = all_91_0 % 41.21/6.36 | | | | % 41.21/6.36 | | | | GROUND_INST: instantiating (15) with all_196_0, all_200_0, all_91_0, % 41.21/6.36 | | | | nil, simplifying with (82), (84) gives: % 41.21/6.36 | | | | (88) all_200_0 = all_196_0 % 41.21/6.36 | | | | % 41.21/6.36 | | | | GROUND_INST: instantiating (15) with all_170_0, all_200_0, all_91_0, % 41.21/6.36 | | | | nil, simplifying with (82), (85) gives: % 41.21/6.37 | | | | (89) all_200_0 = all_170_0 % 41.21/6.37 | | | | % 41.21/6.37 | | | | GROUND_INST: instantiating (15) with all_158_0, all_200_0, all_91_0, % 41.21/6.37 | | | | nil, simplifying with (82), (83) gives: % 41.21/6.37 | | | | (90) all_200_0 = all_158_0 % 41.21/6.37 | | | | % 41.21/6.37 | | | | COMBINE_EQS: (88), (90) imply: % 41.21/6.37 | | | | (91) all_196_0 = all_158_0 % 41.21/6.37 | | | | % 41.21/6.37 | | | | COMBINE_EQS: (88), (89) imply: % 41.21/6.37 | | | | (92) all_196_0 = all_170_0 % 41.21/6.37 | | | | % 41.21/6.37 | | | | COMBINE_EQS: (91), (92) imply: % 41.21/6.37 | | | | (93) all_170_0 = all_158_0 % 41.21/6.37 | | | | % 41.21/6.37 | | | | SIMP: (93) implies: % 41.21/6.37 | | | | (94) all_170_0 = all_158_0 % 41.21/6.37 | | | | % 41.21/6.37 | | | | COMBINE_EQS: (87), (94) imply: % 41.21/6.37 | | | | (95) all_158_0 = all_91_0 % 41.21/6.37 | | | | % 41.21/6.37 | | | | REDUCE: (74), (95) imply: % 41.21/6.37 | | | | (96) $false % 41.21/6.37 | | | | % 41.21/6.37 | | | | CLOSE: (96) is inconsistent. % 41.21/6.37 | | | | % 41.21/6.37 | | | End of split % 41.21/6.37 | | | % 41.21/6.37 | | End of split % 41.21/6.37 | | % 41.21/6.37 | End of split % 41.21/6.37 | % 41.21/6.37 End of proof % 41.21/6.37 % SZS output end Proof for theBenchmark % 41.21/6.37 % 41.21/6.37 5794ms %------------------------------------------------------------------------------