%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SWC016+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 : n002.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 20:49:11 EDT 2023 % Result : Theorem 32.14s 5.29s % Output : Proof 69.25s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.12 % Problem : SWC016+1 : TPTP v8.1.2. Released v2.4.0. % 0.11/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.34 % Computer : n002.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % 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 16:08:49 EDT 2023 % 0.13/0.34 % CPUTime : % 0.20/0.64 ________ _____ % 0.20/0.64 ___ __ \_________(_)________________________________ % 0.20/0.64 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.20/0.64 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.20/0.64 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.20/0.64 % 0.20/0.64 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.20/0.64 (2023-06-19) % 0.20/0.64 % 0.20/0.64 (c) Philipp Rümmer, 2009-2023 % 0.20/0.64 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.20/0.64 Amanda Stjerna. % 0.20/0.64 Free software under BSD-3-Clause. % 0.20/0.64 % 0.20/0.64 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.20/0.64 % 0.20/0.64 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.20/0.65 Running up to 7 provers in parallel. % 0.20/0.67 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.20/0.67 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.20/0.67 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.20/0.67 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.20/0.67 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.20/0.67 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.20/0.67 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 6.20/1.67 Prover 1: Preprocessing ... % 6.20/1.67 Prover 4: Preprocessing ... % 6.36/1.72 Prover 2: Preprocessing ... % 6.36/1.72 Prover 5: Preprocessing ... % 6.36/1.72 Prover 6: Preprocessing ... % 6.36/1.72 Prover 3: Preprocessing ... % 6.61/1.73 Prover 0: Preprocessing ... % 19.74/3.51 Prover 2: Proving ... % 21.04/3.70 Prover 5: Constructing countermodel ... % 21.04/3.70 Prover 3: Constructing countermodel ... % 21.04/3.71 Prover 1: Constructing countermodel ... % 22.01/3.90 Prover 6: Proving ... % 30.21/4.98 Prover 4: Constructing countermodel ... % 32.14/5.28 Prover 3: proved (4617ms) % 32.14/5.29 % 32.14/5.29 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 32.14/5.29 % 32.14/5.29 Prover 5: stopped % 32.14/5.29 Prover 2: stopped % 32.14/5.29 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 32.14/5.29 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 32.14/5.30 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 32.14/5.33 Prover 6: stopped % 32.14/5.34 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 33.99/5.44 Prover 0: Proving ... % 33.99/5.46 Prover 0: stopped % 33.99/5.47 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 35.40/5.65 Prover 10: Preprocessing ... % 36.57/5.78 Prover 8: Preprocessing ... % 36.57/5.78 Prover 7: Preprocessing ... % 36.57/5.79 Prover 11: Preprocessing ... % 36.57/5.82 Prover 13: Preprocessing ... % 37.61/6.02 Prover 10: Constructing countermodel ... % 40.31/6.30 Prover 7: Constructing countermodel ... % 41.60/6.47 Prover 13: Constructing countermodel ... % 41.60/6.48 Prover 8: Warning: ignoring some quantifiers % 41.60/6.55 Prover 8: Constructing countermodel ... % 49.91/7.53 Prover 11: Constructing countermodel ... % 68.58/10.00 Prover 1: Found proof (size 87) % 68.58/10.00 Prover 1: proved (9330ms) % 68.58/10.00 Prover 7: stopped % 68.58/10.00 Prover 11: stopped % 68.58/10.00 Prover 13: stopped % 68.58/10.00 Prover 10: stopped % 68.58/10.00 Prover 8: stopped % 68.58/10.00 Prover 4: stopped % 68.58/10.00 % 68.58/10.00 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 68.58/10.00 % 68.58/10.01 % SZS output start Proof for theBenchmark % 68.58/10.02 Assumptions after simplification: % 68.58/10.02 --------------------------------- % 68.58/10.02 % 68.58/10.02 (ax15) % 69.03/10.06 ! [v0: $i] : ( ~ (ssList(v0) = 0) | ~ $i(v0) | ! [v1: $i] : ! [v2: any] : % 69.03/10.06 ( ~ (neq(v0, v1) = v2) | ~ $i(v1) | ? [v3: int] : ( ~ (v3 = 0) & % 69.03/10.06 ssList(v1) = v3) | (( ~ (v2 = 0) | ~ (v1 = v0)) & (v2 = 0 | v1 = v0)))) % 69.03/10.06 % 69.03/10.06 (ax17) % 69.03/10.06 ssList(nil) = 0 & $i(nil) % 69.03/10.06 % 69.03/10.06 (ax2) % 69.03/10.07 ? [v0: $i] : (ssItem(v0) = 0 & $i(v0) & ? [v1: $i] : ( ~ (v1 = v0) & % 69.03/10.07 ssItem(v1) = 0 & $i(v1))) % 69.03/10.07 % 69.03/10.07 (ax20) % 69.03/10.07 $i(nil) & ! [v0: $i] : (v0 = nil | ~ (ssList(v0) = 0) | ~ $i(v0) | ? [v1: % 69.03/10.07 $i] : (ssList(v1) = 0 & $i(v1) & ? [v2: $i] : (cons(v2, v1) = v0 & % 69.03/10.07 ssItem(v2) = 0 & $i(v2)))) % 69.03/10.07 % 69.03/10.07 (ax44) % 69.03/10.07 ! [v0: $i] : ( ~ (ssItem(v0) = 0) | ~ $i(v0) | ! [v1: $i] : ( ~ (ssItem(v1) % 69.03/10.07 = 0) | ~ $i(v1) | ! [v2: $i] : ! [v3: $i] : ( ~ (cons(v0, v2) = v3) | % 69.03/10.07 ~ $i(v2) | ? [v4: int] : ( ~ (v4 = 0) & ssList(v2) = v4) | ! [v4: $i] % 69.03/10.07 : ! [v5: $i] : ! [v6: any] : ( ~ (frontsegP(v3, v5) = v6) | ~ % 69.03/10.07 (cons(v1, v4) = v5) | ~ $i(v4) | ? [v7: any] : ? [v8: any] : % 69.03/10.07 (frontsegP(v2, v4) = v8 & ssList(v4) = v7 & ( ~ (v7 = 0) | (( ~ (v8 = % 69.03/10.07 0) | ~ (v1 = v0) | v6 = 0) & ( ~ (v6 = 0) | (v8 = 0 & v1 = % 69.03/10.07 v0))))))))) % 69.03/10.07 % 69.03/10.07 (co1) % 69.03/10.08 $i(nil) & ? [v0: $i] : (ssList(v0) = 0 & $i(v0) & ? [v1: $i] : ? [v2: any] % 69.03/10.08 : (ssList(v1) = 0 & neq(v1, nil) = v2 & $i(v1) & ( ~ (v2 = 0) | ? [v3: $i] % 69.03/10.08 : (frontsegP(v1, v3) = 0 & frontsegP(v0, v3) = 0 & ssList(v3) = 0 & % 69.03/10.08 neq(v3, nil) = 0 & $i(v3))) & ( ~ (v1 = nil) | v0 = nil) & ((v2 = 0 & % 69.03/10.08 ! [v3: $i] : ( ~ (neq(v3, nil) = 0) | ~ $i(v3) | ? [v4: any] : ? % 69.03/10.08 [v5: any] : ? [v6: any] : (frontsegP(v1, v3) = v5 & frontsegP(v0, % 69.03/10.08 v3) = v6 & ssList(v3) = v4 & ( ~ (v6 = 0) | ~ (v5 = 0) | ~ (v4 % 69.03/10.08 = 0))))) | (v1 = nil & ~ (v0 = nil))))) % 69.03/10.08 % 69.03/10.08 (function-axioms) % 69.03/10.08 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 69.03/10.08 [v3: $i] : (v1 = v0 | ~ (gt(v3, v2) = v1) | ~ (gt(v3, v2) = v0)) & ! [v0: % 69.03/10.08 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 69.03/10.08 : (v1 = v0 | ~ (geq(v3, v2) = v1) | ~ (geq(v3, v2) = v0)) & ! [v0: % 69.03/10.08 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 69.03/10.08 : (v1 = v0 | ~ (lt(v3, v2) = v1) | ~ (lt(v3, v2) = v0)) & ! [v0: % 69.03/10.08 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 69.03/10.09 : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0)) & ! [v0: % 69.03/10.09 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 69.03/10.09 : (v1 = v0 | ~ (segmentP(v3, v2) = v1) | ~ (segmentP(v3, v2) = v0)) & ! % 69.03/10.09 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 69.03/10.09 $i] : (v1 = v0 | ~ (rearsegP(v3, v2) = v1) | ~ (rearsegP(v3, v2) = v0)) & % 69.03/10.09 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 69.03/10.09 $i] : (v1 = v0 | ~ (frontsegP(v3, v2) = v1) | ~ (frontsegP(v3, v2) = v0)) % 69.03/10.09 & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 69.03/10.09 [v3: $i] : (v1 = v0 | ~ (memberP(v3, v2) = v1) | ~ (memberP(v3, v2) = v0)) & % 69.03/10.09 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 69.03/10.09 (cons(v3, v2) = v1) | ~ (cons(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : % 69.03/10.09 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (app(v3, v2) = v1) | ~ (app(v3, v2) % 69.03/10.09 = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 69.03/10.09 $i] : ! [v3: $i] : (v1 = v0 | ~ (neq(v3, v2) = v1) | ~ (neq(v3, v2) = % 69.03/10.09 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (tl(v2) = % 69.03/10.09 v1) | ~ (tl(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = % 69.03/10.09 v0 | ~ (hd(v2) = v1) | ~ (hd(v2) = v0)) & ! [v0: MultipleValueBool] : ! % 69.03/10.09 [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (equalelemsP(v2) = v1) | % 69.03/10.09 ~ (equalelemsP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 69.03/10.09 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (duplicatefreeP(v2) = v1) | % 69.03/10.09 ~ (duplicatefreeP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 69.03/10.09 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (strictorderedP(v2) = v1) | % 69.03/10.09 ~ (strictorderedP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 69.03/10.09 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (totalorderedP(v2) = v1) | % 69.03/10.09 ~ (totalorderedP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 69.03/10.09 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (strictorderP(v2) = v1) | % 69.03/10.09 ~ (strictorderP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 69.03/10.09 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (totalorderP(v2) = v1) | ~ % 69.03/10.09 (totalorderP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 69.03/10.09 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (cyclefreeP(v2) = v1) | ~ % 69.03/10.09 (cyclefreeP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 69.03/10.09 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (singletonP(v2) = v1) | ~ % 69.03/10.09 (singletonP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 69.03/10.09 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (ssList(v2) = v1) | ~ % 69.03/10.09 (ssList(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] % 69.03/10.09 : ! [v2: $i] : (v1 = v0 | ~ (ssItem(v2) = v1) | ~ (ssItem(v2) = v0)) % 69.03/10.09 % 69.03/10.09 Further assumptions not needed in the proof: % 69.03/10.09 -------------------------------------------- % 69.03/10.09 ax1, ax10, ax11, ax12, ax13, ax14, ax16, ax18, ax19, ax21, ax22, ax23, ax24, % 69.03/10.09 ax25, ax26, ax27, ax28, ax29, ax3, ax30, ax31, ax32, ax33, ax34, ax35, ax36, % 69.03/10.09 ax37, ax38, ax39, ax4, ax40, ax41, ax42, ax43, ax45, ax46, ax47, ax48, ax49, % 69.03/10.09 ax5, ax50, ax51, ax52, ax53, ax54, ax55, ax56, ax57, ax58, ax59, ax6, ax60, % 69.03/10.09 ax61, ax62, ax63, ax64, ax65, ax66, ax67, ax68, ax69, ax7, ax70, ax71, ax72, % 69.03/10.09 ax73, ax74, ax75, ax76, ax77, ax78, ax79, ax8, ax80, ax81, ax82, ax83, ax84, % 69.03/10.09 ax85, ax86, ax87, ax88, ax89, ax9, ax90, ax91, ax92, ax93, ax94, ax95 % 69.03/10.09 % 69.03/10.09 Those formulas are unsatisfiable: % 69.03/10.09 --------------------------------- % 69.03/10.09 % 69.03/10.09 Begin of proof % 69.03/10.09 | % 69.03/10.09 | ALPHA: (ax17) implies: % 69.03/10.09 | (1) ssList(nil) = 0 % 69.03/10.09 | % 69.03/10.09 | ALPHA: (ax20) implies: % 69.03/10.09 | (2) ! [v0: $i] : (v0 = nil | ~ (ssList(v0) = 0) | ~ $i(v0) | ? [v1: $i] % 69.03/10.09 | : (ssList(v1) = 0 & $i(v1) & ? [v2: $i] : (cons(v2, v1) = v0 & % 69.03/10.09 | ssItem(v2) = 0 & $i(v2)))) % 69.03/10.09 | % 69.03/10.09 | ALPHA: (co1) implies: % 69.03/10.09 | (3) $i(nil) % 69.03/10.10 | (4) ? [v0: $i] : (ssList(v0) = 0 & $i(v0) & ? [v1: $i] : ? [v2: any] : % 69.03/10.10 | (ssList(v1) = 0 & neq(v1, nil) = v2 & $i(v1) & ( ~ (v2 = 0) | ? [v3: % 69.03/10.10 | $i] : (frontsegP(v1, v3) = 0 & frontsegP(v0, v3) = 0 & % 69.03/10.10 | ssList(v3) = 0 & neq(v3, nil) = 0 & $i(v3))) & ( ~ (v1 = nil) | % 69.03/10.10 | v0 = nil) & ((v2 = 0 & ! [v3: $i] : ( ~ (neq(v3, nil) = 0) | ~ % 69.03/10.10 | $i(v3) | ? [v4: any] : ? [v5: any] : ? [v6: any] : % 69.03/10.10 | (frontsegP(v1, v3) = v5 & frontsegP(v0, v3) = v6 & ssList(v3) % 69.03/10.10 | = v4 & ( ~ (v6 = 0) | ~ (v5 = 0) | ~ (v4 = 0))))) | (v1 = % 69.03/10.10 | nil & ~ (v0 = nil))))) % 69.03/10.10 | % 69.03/10.10 | ALPHA: (function-axioms) implies: % 69.03/10.10 | (5) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 69.03/10.10 | (v1 = v0 | ~ (ssList(v2) = v1) | ~ (ssList(v2) = v0)) % 69.03/10.10 | (6) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 69.03/10.10 | ! [v3: $i] : (v1 = v0 | ~ (frontsegP(v3, v2) = v1) | ~ % 69.03/10.10 | (frontsegP(v3, v2) = v0)) % 69.03/10.10 | % 69.03/10.10 | DELTA: instantiating (ax2) with fresh symbol all_91_0 gives: % 69.03/10.10 | (7) ssItem(all_91_0) = 0 & $i(all_91_0) & ? [v0: any] : ( ~ (v0 = % 69.03/10.10 | all_91_0) & ssItem(v0) = 0 & $i(v0)) % 69.03/10.10 | % 69.03/10.10 | ALPHA: (7) implies: % 69.03/10.10 | (8) ? [v0: any] : ( ~ (v0 = all_91_0) & ssItem(v0) = 0 & $i(v0)) % 69.03/10.10 | % 69.03/10.10 | DELTA: instantiating (4) with fresh symbol all_93_0 gives: % 69.03/10.10 | (9) ssList(all_93_0) = 0 & $i(all_93_0) & ? [v0: $i] : ? [v1: any] : % 69.03/10.10 | (ssList(v0) = 0 & neq(v0, nil) = v1 & $i(v0) & ( ~ (v1 = 0) | ? [v2: % 69.03/10.10 | $i] : (frontsegP(v0, v2) = 0 & frontsegP(all_93_0, v2) = 0 & % 69.03/10.10 | ssList(v2) = 0 & neq(v2, nil) = 0 & $i(v2))) & ( ~ (v0 = nil) | % 69.03/10.10 | all_93_0 = nil) & ((v1 = 0 & ! [v2: $i] : ( ~ (neq(v2, nil) = 0) | % 69.03/10.10 | ~ $i(v2) | ? [v3: any] : ? [v4: any] : ? [v5: any] : % 69.03/10.10 | (frontsegP(v0, v2) = v4 & frontsegP(all_93_0, v2) = v5 & % 69.03/10.10 | ssList(v2) = v3 & ( ~ (v5 = 0) | ~ (v4 = 0) | ~ (v3 = % 69.03/10.10 | 0))))) | (v0 = nil & ~ (all_93_0 = nil)))) % 69.03/10.10 | % 69.03/10.10 | ALPHA: (9) implies: % 69.03/10.10 | (10) ? [v0: $i] : ? [v1: any] : (ssList(v0) = 0 & neq(v0, nil) = v1 & % 69.03/10.10 | $i(v0) & ( ~ (v1 = 0) | ? [v2: $i] : (frontsegP(v0, v2) = 0 & % 69.03/10.10 | frontsegP(all_93_0, v2) = 0 & ssList(v2) = 0 & neq(v2, nil) = 0 % 69.03/10.10 | & $i(v2))) & ( ~ (v0 = nil) | all_93_0 = nil) & ((v1 = 0 & ! % 69.03/10.10 | [v2: $i] : ( ~ (neq(v2, nil) = 0) | ~ $i(v2) | ? [v3: any] : % 69.03/10.10 | ? [v4: any] : ? [v5: any] : (frontsegP(v0, v2) = v4 & % 69.03/10.10 | frontsegP(all_93_0, v2) = v5 & ssList(v2) = v3 & ( ~ (v5 = % 69.03/10.11 | 0) | ~ (v4 = 0) | ~ (v3 = 0))))) | (v0 = nil & ~ % 69.03/10.11 | (all_93_0 = nil)))) % 69.03/10.11 | % 69.03/10.11 | DELTA: instantiating (8) with fresh symbol all_95_0 gives: % 69.03/10.11 | (11) ~ (all_95_0 = all_91_0) & ssItem(all_95_0) = 0 & $i(all_95_0) % 69.03/10.11 | % 69.03/10.11 | ALPHA: (11) implies: % 69.03/10.11 | (12) $i(all_95_0) % 69.03/10.11 | (13) ssItem(all_95_0) = 0 % 69.03/10.11 | % 69.03/10.11 | DELTA: instantiating (10) with fresh symbols all_97_0, all_97_1 gives: % 69.03/10.11 | (14) ssList(all_97_1) = 0 & neq(all_97_1, nil) = all_97_0 & $i(all_97_1) & % 69.03/10.11 | ( ~ (all_97_0 = 0) | ? [v0: $i] : (frontsegP(all_97_1, v0) = 0 & % 69.03/10.11 | frontsegP(all_93_0, v0) = 0 & ssList(v0) = 0 & neq(v0, nil) = 0 & % 69.03/10.11 | $i(v0))) & ( ~ (all_97_1 = nil) | all_93_0 = nil) & ((all_97_0 = 0 % 69.03/10.11 | & ! [v0: $i] : ( ~ (neq(v0, nil) = 0) | ~ $i(v0) | ? [v1: any] % 69.03/10.11 | : ? [v2: any] : ? [v3: any] : (frontsegP(all_97_1, v0) = v2 & % 69.03/10.11 | frontsegP(all_93_0, v0) = v3 & ssList(v0) = v1 & ( ~ (v3 = 0) % 69.03/10.11 | | ~ (v2 = 0) | ~ (v1 = 0))))) | (all_97_1 = nil & ~ % 69.03/10.11 | (all_93_0 = nil))) % 69.03/10.11 | % 69.03/10.11 | ALPHA: (14) implies: % 69.03/10.11 | (15) $i(all_97_1) % 69.03/10.11 | (16) neq(all_97_1, nil) = all_97_0 % 69.03/10.11 | (17) ssList(all_97_1) = 0 % 69.03/10.11 | (18) (all_97_0 = 0 & ! [v0: $i] : ( ~ (neq(v0, nil) = 0) | ~ $i(v0) | ? % 69.03/10.11 | [v1: any] : ? [v2: any] : ? [v3: any] : (frontsegP(all_97_1, v0) % 69.03/10.11 | = v2 & frontsegP(all_93_0, v0) = v3 & ssList(v0) = v1 & ( ~ (v3 % 69.03/10.11 | = 0) | ~ (v2 = 0) | ~ (v1 = 0))))) | (all_97_1 = nil & ~ % 69.03/10.11 | (all_93_0 = nil)) % 69.03/10.11 | (19) ~ (all_97_1 = nil) | all_93_0 = nil % 69.03/10.11 | (20) ~ (all_97_0 = 0) | ? [v0: $i] : (frontsegP(all_97_1, v0) = 0 & % 69.03/10.11 | frontsegP(all_93_0, v0) = 0 & ssList(v0) = 0 & neq(v0, nil) = 0 & % 69.03/10.11 | $i(v0)) % 69.03/10.11 | % 69.03/10.11 | GROUND_INST: instantiating (2) with all_97_1, simplifying with (15), (17) % 69.03/10.11 | gives: % 69.03/10.11 | (21) all_97_1 = nil | ? [v0: $i] : (ssList(v0) = 0 & $i(v0) & ? [v1: $i] % 69.03/10.11 | : (cons(v1, v0) = all_97_1 & ssItem(v1) = 0 & $i(v1))) % 69.03/10.11 | % 69.03/10.11 | GROUND_INST: instantiating (ax15) with all_97_1, simplifying with (15), (17) % 69.03/10.11 | gives: % 69.03/10.11 | (22) ! [v0: $i] : ! [v1: any] : ( ~ (neq(all_97_1, v0) = v1) | ~ $i(v0) % 69.03/10.11 | | ? [v2: int] : ( ~ (v2 = 0) & ssList(v0) = v2) | (( ~ (v1 = 0) | % 69.03/10.11 | ~ (v0 = all_97_1)) & (v1 = 0 | v0 = all_97_1))) % 69.03/10.11 | % 69.03/10.11 | GROUND_INST: instantiating (22) with nil, all_97_0, simplifying with (3), (16) % 69.03/10.11 | gives: % 69.03/10.11 | (23) ? [v0: int] : ( ~ (v0 = 0) & ssList(nil) = v0) | (( ~ (all_97_0 = 0) % 69.03/10.11 | | ~ (all_97_1 = nil)) & (all_97_0 = 0 | all_97_1 = nil)) % 69.03/10.11 | % 69.03/10.11 | BETA: splitting (18) gives: % 69.03/10.11 | % 69.03/10.11 | Case 1: % 69.03/10.11 | | % 69.03/10.11 | | (24) all_97_0 = 0 & ! [v0: $i] : ( ~ (neq(v0, nil) = 0) | ~ $i(v0) | ? % 69.03/10.11 | | [v1: any] : ? [v2: any] : ? [v3: any] : (frontsegP(all_97_1, v0) % 69.03/10.11 | | = v2 & frontsegP(all_93_0, v0) = v3 & ssList(v0) = v1 & ( ~ (v3 % 69.03/10.11 | | = 0) | ~ (v2 = 0) | ~ (v1 = 0)))) % 69.03/10.11 | | % 69.03/10.11 | | ALPHA: (24) implies: % 69.03/10.12 | | (25) all_97_0 = 0 % 69.03/10.12 | | (26) ! [v0: $i] : ( ~ (neq(v0, nil) = 0) | ~ $i(v0) | ? [v1: any] : ? % 69.03/10.12 | | [v2: any] : ? [v3: any] : (frontsegP(all_97_1, v0) = v2 & % 69.03/10.12 | | frontsegP(all_93_0, v0) = v3 & ssList(v0) = v1 & ( ~ (v3 = 0) | % 69.03/10.12 | | ~ (v2 = 0) | ~ (v1 = 0)))) % 69.03/10.12 | | % 69.03/10.12 | | BETA: splitting (23) gives: % 69.03/10.12 | | % 69.03/10.12 | | Case 1: % 69.03/10.12 | | | % 69.03/10.12 | | | (27) ? [v0: int] : ( ~ (v0 = 0) & ssList(nil) = v0) % 69.03/10.12 | | | % 69.03/10.12 | | | DELTA: instantiating (27) with fresh symbol all_274_0 gives: % 69.03/10.12 | | | (28) ~ (all_274_0 = 0) & ssList(nil) = all_274_0 % 69.03/10.12 | | | % 69.03/10.12 | | | ALPHA: (28) implies: % 69.03/10.12 | | | (29) ~ (all_274_0 = 0) % 69.03/10.12 | | | (30) ssList(nil) = all_274_0 % 69.03/10.12 | | | % 69.03/10.12 | | | DELTA: instantiating (27) with fresh symbol all_276_0 gives: % 69.03/10.12 | | | (31) ~ (all_276_0 = 0) & ssList(nil) = all_276_0 % 69.03/10.12 | | | % 69.03/10.12 | | | ALPHA: (31) implies: % 69.03/10.12 | | | (32) ssList(nil) = all_276_0 % 69.03/10.12 | | | % 69.03/10.12 | | | GROUND_INST: instantiating (5) with 0, all_276_0, nil, simplifying with % 69.03/10.12 | | | (1), (32) gives: % 69.03/10.12 | | | (33) all_276_0 = 0 % 69.03/10.12 | | | % 69.03/10.12 | | | GROUND_INST: instantiating (5) with all_274_0, all_276_0, nil, simplifying % 69.03/10.12 | | | with (30), (32) gives: % 69.03/10.12 | | | (34) all_276_0 = all_274_0 % 69.03/10.12 | | | % 69.03/10.12 | | | COMBINE_EQS: (33), (34) imply: % 69.03/10.12 | | | (35) all_274_0 = 0 % 69.03/10.12 | | | % 69.03/10.12 | | | REDUCE: (29), (35) imply: % 69.03/10.12 | | | (36) $false % 69.03/10.12 | | | % 69.03/10.12 | | | CLOSE: (36) is inconsistent. % 69.03/10.12 | | | % 69.03/10.12 | | Case 2: % 69.03/10.12 | | | % 69.03/10.12 | | | (37) ( ~ (all_97_0 = 0) | ~ (all_97_1 = nil)) & (all_97_0 = 0 | % 69.03/10.12 | | | all_97_1 = nil) % 69.03/10.12 | | | % 69.03/10.12 | | | ALPHA: (37) implies: % 69.03/10.12 | | | (38) ~ (all_97_0 = 0) | ~ (all_97_1 = nil) % 69.03/10.12 | | | % 69.03/10.12 | | | BETA: splitting (20) gives: % 69.03/10.12 | | | % 69.03/10.12 | | | Case 1: % 69.03/10.12 | | | | % 69.03/10.12 | | | | (39) ~ (all_97_0 = 0) % 69.03/10.12 | | | | % 69.03/10.12 | | | | REDUCE: (25), (39) imply: % 69.03/10.12 | | | | (40) $false % 69.03/10.12 | | | | % 69.03/10.12 | | | | CLOSE: (40) is inconsistent. % 69.03/10.12 | | | | % 69.03/10.12 | | | Case 2: % 69.03/10.12 | | | | % 69.03/10.12 | | | | (41) ? [v0: $i] : (frontsegP(all_97_1, v0) = 0 & frontsegP(all_93_0, % 69.03/10.12 | | | | v0) = 0 & ssList(v0) = 0 & neq(v0, nil) = 0 & $i(v0)) % 69.03/10.12 | | | | % 69.03/10.12 | | | | DELTA: instantiating (41) with fresh symbol all_301_0 gives: % 69.03/10.12 | | | | (42) frontsegP(all_97_1, all_301_0) = 0 & frontsegP(all_93_0, % 69.03/10.12 | | | | all_301_0) = 0 & ssList(all_301_0) = 0 & neq(all_301_0, nil) = % 69.03/10.12 | | | | 0 & $i(all_301_0) % 69.03/10.12 | | | | % 69.03/10.12 | | | | ALPHA: (42) implies: % 69.03/10.12 | | | | (43) $i(all_301_0) % 69.03/10.12 | | | | (44) neq(all_301_0, nil) = 0 % 69.03/10.12 | | | | (45) ssList(all_301_0) = 0 % 69.03/10.12 | | | | (46) frontsegP(all_93_0, all_301_0) = 0 % 69.03/10.12 | | | | (47) frontsegP(all_97_1, all_301_0) = 0 % 69.03/10.12 | | | | % 69.03/10.12 | | | | BETA: splitting (38) gives: % 69.03/10.12 | | | | % 69.03/10.12 | | | | Case 1: % 69.03/10.12 | | | | | % 69.03/10.12 | | | | | (48) ~ (all_97_1 = nil) % 69.03/10.12 | | | | | % 69.03/10.12 | | | | | BETA: splitting (21) gives: % 69.03/10.12 | | | | | % 69.03/10.12 | | | | | Case 1: % 69.03/10.12 | | | | | | % 69.03/10.12 | | | | | | (49) all_97_1 = nil % 69.03/10.12 | | | | | | % 69.03/10.12 | | | | | | REDUCE: (48), (49) imply: % 69.03/10.12 | | | | | | (50) $false % 69.03/10.12 | | | | | | % 69.03/10.12 | | | | | | CLOSE: (50) is inconsistent. % 69.03/10.12 | | | | | | % 69.03/10.12 | | | | | Case 2: % 69.03/10.12 | | | | | | % 69.03/10.12 | | | | | | (51) ? [v0: $i] : (ssList(v0) = 0 & $i(v0) & ? [v1: $i] : % 69.03/10.12 | | | | | | (cons(v1, v0) = all_97_1 & ssItem(v1) = 0 & $i(v1))) % 69.03/10.12 | | | | | | % 69.03/10.12 | | | | | | DELTA: instantiating (51) with fresh symbol all_311_0 gives: % 69.03/10.12 | | | | | | (52) ssList(all_311_0) = 0 & $i(all_311_0) & ? [v0: $i] : % 69.03/10.12 | | | | | | (cons(v0, all_311_0) = all_97_1 & ssItem(v0) = 0 & $i(v0)) % 69.03/10.12 | | | | | | % 69.03/10.12 | | | | | | ALPHA: (52) implies: % 69.03/10.12 | | | | | | (53) $i(all_311_0) % 69.03/10.12 | | | | | | (54) ssList(all_311_0) = 0 % 69.03/10.13 | | | | | | (55) ? [v0: $i] : (cons(v0, all_311_0) = all_97_1 & ssItem(v0) = % 69.03/10.13 | | | | | | 0 & $i(v0)) % 69.03/10.13 | | | | | | % 69.03/10.13 | | | | | | DELTA: instantiating (55) with fresh symbol all_313_0 gives: % 69.03/10.13 | | | | | | (56) cons(all_313_0, all_311_0) = all_97_1 & ssItem(all_313_0) = % 69.03/10.13 | | | | | | 0 & $i(all_313_0) % 69.03/10.13 | | | | | | % 69.03/10.13 | | | | | | ALPHA: (56) implies: % 69.03/10.13 | | | | | | (57) $i(all_313_0) % 69.03/10.13 | | | | | | (58) ssItem(all_313_0) = 0 % 69.03/10.13 | | | | | | (59) cons(all_313_0, all_311_0) = all_97_1 % 69.03/10.13 | | | | | | % 69.03/10.13 | | | | | | GROUND_INST: instantiating (ax44) with all_313_0, simplifying with % 69.03/10.13 | | | | | | (57), (58) gives: % 69.03/10.13 | | | | | | (60) ! [v0: $i] : ( ~ (ssItem(v0) = 0) | ~ $i(v0) | ! [v1: $i] % 69.03/10.13 | | | | | | : ! [v2: $i] : ( ~ (cons(all_313_0, v1) = v2) | ~ $i(v1) % 69.03/10.13 | | | | | | | ? [v3: int] : ( ~ (v3 = 0) & ssList(v1) = v3) | ! % 69.03/10.13 | | | | | | [v3: $i] : ! [v4: $i] : ! [v5: any] : ( ~ % 69.03/10.13 | | | | | | (frontsegP(v2, v4) = v5) | ~ (cons(v0, v3) = v4) | ~ % 69.03/10.13 | | | | | | $i(v3) | ? [v6: any] : ? [v7: any] : (frontsegP(v1, % 69.03/10.13 | | | | | | v3) = v7 & ssList(v3) = v6 & ( ~ (v6 = 0) | (( ~ % 69.03/10.13 | | | | | | (v7 = 0) | ~ (v0 = all_313_0) | v5 = 0) & ( ~ % 69.03/10.13 | | | | | | (v5 = 0) | (v7 = 0 & v0 = all_313_0)))))))) % 69.03/10.13 | | | | | | % 69.03/10.13 | | | | | | GROUND_INST: instantiating (26) with all_301_0, simplifying with % 69.03/10.13 | | | | | | (43), (44) gives: % 69.03/10.13 | | | | | | (61) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 69.03/10.13 | | | | | | (frontsegP(all_97_1, all_301_0) = v1 & frontsegP(all_93_0, % 69.03/10.13 | | | | | | all_301_0) = v2 & ssList(all_301_0) = v0 & ( ~ (v2 = 0) % 69.03/10.13 | | | | | | | ~ (v1 = 0) | ~ (v0 = 0))) % 69.03/10.13 | | | | | | % 69.03/10.13 | | | | | | GROUND_INST: instantiating (60) with all_95_0, simplifying with % 69.03/10.13 | | | | | | (12), (13) gives: % 69.03/10.13 | | | | | | (62) ! [v0: $i] : ! [v1: $i] : ( ~ (cons(all_313_0, v0) = v1) | % 69.03/10.13 | | | | | | ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & ssList(v0) = v2) % 69.03/10.13 | | | | | | | ! [v2: $i] : ! [v3: $i] : ! [v4: any] : ( ~ % 69.03/10.13 | | | | | | (frontsegP(v1, v3) = v4) | ~ (cons(all_95_0, v2) = v3) % 69.03/10.13 | | | | | | | ~ $i(v2) | ? [v5: any] : ? [v6: any] : % 69.03/10.13 | | | | | | (frontsegP(v0, v2) = v6 & ssList(v2) = v5 & ( ~ (v5 = 0) % 69.03/10.13 | | | | | | | (( ~ (v6 = 0) | ~ (all_313_0 = all_95_0) | v4 = % 69.03/10.13 | | | | | | 0) & ( ~ (v4 = 0) | (v6 = 0 & all_313_0 = % 69.03/10.13 | | | | | | all_95_0))))))) % 69.03/10.13 | | | | | | % 69.03/10.13 | | | | | | GROUND_INST: instantiating (62) with all_311_0, all_97_1, % 69.03/10.13 | | | | | | simplifying with (53), (59) gives: % 69.03/10.13 | | | | | | (63) ? [v0: int] : ( ~ (v0 = 0) & ssList(all_311_0) = v0) | ! % 69.03/10.13 | | | | | | [v0: $i] : ! [v1: $i] : ! [v2: any] : ( ~ % 69.03/10.13 | | | | | | (frontsegP(all_97_1, v1) = v2) | ~ (cons(all_95_0, v0) = % 69.03/10.13 | | | | | | v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : % 69.03/10.13 | | | | | | (frontsegP(all_311_0, v0) = v4 & ssList(v0) = v3 & ( ~ (v3 % 69.03/10.13 | | | | | | = 0) | (( ~ (v4 = 0) | ~ (all_313_0 = all_95_0) | % 69.03/10.13 | | | | | | v2 = 0) & ( ~ (v2 = 0) | (v4 = 0 & all_313_0 = % 69.03/10.13 | | | | | | all_95_0)))))) % 69.03/10.13 | | | | | | % 69.03/10.13 | | | | | | DELTA: instantiating (61) with fresh symbols all_680_0, all_680_1, % 69.03/10.13 | | | | | | all_680_2 gives: % 69.03/10.13 | | | | | | (64) frontsegP(all_97_1, all_301_0) = all_680_1 & % 69.03/10.13 | | | | | | frontsegP(all_93_0, all_301_0) = all_680_0 & % 69.03/10.13 | | | | | | ssList(all_301_0) = all_680_2 & ( ~ (all_680_0 = 0) | ~ % 69.03/10.13 | | | | | | (all_680_1 = 0) | ~ (all_680_2 = 0)) % 69.03/10.13 | | | | | | % 69.03/10.13 | | | | | | ALPHA: (64) implies: % 69.03/10.13 | | | | | | (65) ssList(all_301_0) = all_680_2 % 69.03/10.13 | | | | | | (66) frontsegP(all_93_0, all_301_0) = all_680_0 % 69.03/10.13 | | | | | | (67) frontsegP(all_97_1, all_301_0) = all_680_1 % 69.03/10.13 | | | | | | (68) ~ (all_680_0 = 0) | ~ (all_680_1 = 0) | ~ (all_680_2 = 0) % 69.03/10.13 | | | | | | % 69.03/10.13 | | | | | | BETA: splitting (63) gives: % 69.03/10.13 | | | | | | % 69.03/10.13 | | | | | | Case 1: % 69.03/10.13 | | | | | | | % 69.03/10.13 | | | | | | | (69) ? [v0: int] : ( ~ (v0 = 0) & ssList(all_311_0) = v0) % 69.03/10.13 | | | | | | | % 69.03/10.13 | | | | | | | DELTA: instantiating (69) with fresh symbol all_707_0 gives: % 69.03/10.13 | | | | | | | (70) ~ (all_707_0 = 0) & ssList(all_311_0) = all_707_0 % 69.03/10.13 | | | | | | | % 69.03/10.13 | | | | | | | ALPHA: (70) implies: % 69.03/10.13 | | | | | | | (71) ~ (all_707_0 = 0) % 69.03/10.13 | | | | | | | (72) ssList(all_311_0) = all_707_0 % 69.03/10.13 | | | | | | | % 69.03/10.13 | | | | | | | DELTA: instantiating (69) with fresh symbol all_709_0 gives: % 69.03/10.13 | | | | | | | (73) ~ (all_709_0 = 0) & ssList(all_311_0) = all_709_0 % 69.03/10.13 | | | | | | | % 69.03/10.13 | | | | | | | ALPHA: (73) implies: % 69.03/10.13 | | | | | | | (74) ssList(all_311_0) = all_709_0 % 69.03/10.13 | | | | | | | % 69.03/10.13 | | | | | | | DELTA: instantiating (69) with fresh symbol all_711_0 gives: % 69.03/10.13 | | | | | | | (75) ~ (all_711_0 = 0) & ssList(all_311_0) = all_711_0 % 69.03/10.13 | | | | | | | % 69.03/10.13 | | | | | | | ALPHA: (75) implies: % 69.03/10.13 | | | | | | | (76) ssList(all_311_0) = all_711_0 % 69.03/10.13 | | | | | | | % 69.03/10.13 | | | | | | | GROUND_INST: instantiating (5) with all_707_0, all_709_0, % 69.03/10.13 | | | | | | | all_311_0, simplifying with (72), (74) gives: % 69.03/10.14 | | | | | | | (77) all_709_0 = all_707_0 % 69.03/10.14 | | | | | | | % 69.03/10.14 | | | | | | | GROUND_INST: instantiating (5) with 0, all_711_0, all_311_0, % 69.03/10.14 | | | | | | | simplifying with (54), (76) gives: % 69.03/10.14 | | | | | | | (78) all_711_0 = 0 % 69.03/10.14 | | | | | | | % 69.03/10.14 | | | | | | | GROUND_INST: instantiating (5) with all_709_0, all_711_0, % 69.03/10.14 | | | | | | | all_311_0, simplifying with (74), (76) gives: % 69.03/10.14 | | | | | | | (79) all_711_0 = all_709_0 % 69.03/10.14 | | | | | | | % 69.03/10.14 | | | | | | | COMBINE_EQS: (78), (79) imply: % 69.03/10.14 | | | | | | | (80) all_709_0 = 0 % 69.03/10.14 | | | | | | | % 69.03/10.14 | | | | | | | SIMP: (80) implies: % 69.03/10.14 | | | | | | | (81) all_709_0 = 0 % 69.03/10.14 | | | | | | | % 69.03/10.14 | | | | | | | COMBINE_EQS: (77), (81) imply: % 69.03/10.14 | | | | | | | (82) all_707_0 = 0 % 69.03/10.14 | | | | | | | % 69.03/10.14 | | | | | | | SIMP: (82) implies: % 69.03/10.14 | | | | | | | (83) all_707_0 = 0 % 69.03/10.14 | | | | | | | % 69.03/10.14 | | | | | | | REDUCE: (71), (83) imply: % 69.03/10.14 | | | | | | | (84) $false % 69.03/10.14 | | | | | | | % 69.03/10.14 | | | | | | | CLOSE: (84) is inconsistent. % 69.03/10.14 | | | | | | | % 69.03/10.14 | | | | | | Case 2: % 69.03/10.14 | | | | | | | % 69.03/10.14 | | | | | | | % 69.03/10.14 | | | | | | | GROUND_INST: instantiating (5) with 0, all_680_2, all_301_0, % 69.03/10.14 | | | | | | | simplifying with (45), (65) gives: % 69.03/10.14 | | | | | | | (85) all_680_2 = 0 % 69.03/10.14 | | | | | | | % 69.03/10.14 | | | | | | | GROUND_INST: instantiating (6) with 0, all_680_0, all_301_0, % 69.03/10.14 | | | | | | | all_93_0, simplifying with (46), (66) gives: % 69.03/10.14 | | | | | | | (86) all_680_0 = 0 % 69.03/10.14 | | | | | | | % 69.03/10.14 | | | | | | | GROUND_INST: instantiating (6) with 0, all_680_1, all_301_0, % 69.03/10.14 | | | | | | | all_97_1, simplifying with (47), (67) gives: % 69.03/10.14 | | | | | | | (87) all_680_1 = 0 % 69.03/10.14 | | | | | | | % 69.03/10.14 | | | | | | | BETA: splitting (68) gives: % 69.03/10.14 | | | | | | | % 69.03/10.14 | | | | | | | Case 1: % 69.03/10.14 | | | | | | | | % 69.03/10.14 | | | | | | | | (88) ~ (all_680_0 = 0) % 69.03/10.14 | | | | | | | | % 69.03/10.14 | | | | | | | | REDUCE: (86), (88) imply: % 69.03/10.14 | | | | | | | | (89) $false % 69.03/10.14 | | | | | | | | % 69.03/10.14 | | | | | | | | CLOSE: (89) is inconsistent. % 69.03/10.14 | | | | | | | | % 69.03/10.14 | | | | | | | Case 2: % 69.03/10.14 | | | | | | | | % 69.03/10.14 | | | | | | | | (90) ~ (all_680_1 = 0) | ~ (all_680_2 = 0) % 69.03/10.14 | | | | | | | | % 69.03/10.14 | | | | | | | | BETA: splitting (90) gives: % 69.03/10.14 | | | | | | | | % 69.03/10.14 | | | | | | | | Case 1: % 69.03/10.14 | | | | | | | | | % 69.25/10.14 | | | | | | | | | (91) ~ (all_680_1 = 0) % 69.25/10.14 | | | | | | | | | % 69.25/10.14 | | | | | | | | | REDUCE: (87), (91) imply: % 69.25/10.14 | | | | | | | | | (92) $false % 69.25/10.14 | | | | | | | | | % 69.25/10.14 | | | | | | | | | CLOSE: (92) is inconsistent. % 69.25/10.14 | | | | | | | | | % 69.25/10.14 | | | | | | | | Case 2: % 69.25/10.14 | | | | | | | | | % 69.25/10.14 | | | | | | | | | (93) ~ (all_680_2 = 0) % 69.25/10.14 | | | | | | | | | % 69.25/10.14 | | | | | | | | | REDUCE: (85), (93) imply: % 69.25/10.14 | | | | | | | | | (94) $false % 69.25/10.14 | | | | | | | | | % 69.25/10.14 | | | | | | | | | CLOSE: (94) is inconsistent. % 69.25/10.14 | | | | | | | | | % 69.25/10.14 | | | | | | | | End of split % 69.25/10.14 | | | | | | | | % 69.25/10.14 | | | | | | | End of split % 69.25/10.14 | | | | | | | % 69.25/10.14 | | | | | | End of split % 69.25/10.14 | | | | | | % 69.25/10.14 | | | | | End of split % 69.25/10.14 | | | | | % 69.25/10.14 | | | | Case 2: % 69.25/10.14 | | | | | % 69.25/10.14 | | | | | (95) ~ (all_97_0 = 0) % 69.25/10.14 | | | | | % 69.25/10.14 | | | | | REDUCE: (25), (95) imply: % 69.25/10.14 | | | | | (96) $false % 69.25/10.14 | | | | | % 69.25/10.14 | | | | | CLOSE: (96) is inconsistent. % 69.25/10.14 | | | | | % 69.25/10.14 | | | | End of split % 69.25/10.14 | | | | % 69.25/10.14 | | | End of split % 69.25/10.14 | | | % 69.25/10.14 | | End of split % 69.25/10.14 | | % 69.25/10.14 | Case 2: % 69.25/10.14 | | % 69.25/10.14 | | (97) all_97_1 = nil & ~ (all_93_0 = nil) % 69.25/10.14 | | % 69.25/10.14 | | ALPHA: (97) implies: % 69.25/10.14 | | (98) all_97_1 = nil % 69.25/10.14 | | (99) ~ (all_93_0 = nil) % 69.25/10.14 | | % 69.25/10.14 | | BETA: splitting (19) gives: % 69.25/10.14 | | % 69.25/10.14 | | Case 1: % 69.25/10.14 | | | % 69.25/10.14 | | | (100) ~ (all_97_1 = nil) % 69.25/10.14 | | | % 69.25/10.14 | | | REDUCE: (98), (100) imply: % 69.25/10.14 | | | (101) $false % 69.25/10.14 | | | % 69.25/10.14 | | | CLOSE: (101) is inconsistent. % 69.25/10.14 | | | % 69.25/10.14 | | Case 2: % 69.25/10.14 | | | % 69.25/10.14 | | | (102) all_93_0 = nil % 69.25/10.14 | | | % 69.25/10.14 | | | REDUCE: (99), (102) imply: % 69.25/10.14 | | | (103) $false % 69.25/10.14 | | | % 69.25/10.14 | | | CLOSE: (103) is inconsistent. % 69.25/10.14 | | | % 69.25/10.14 | | End of split % 69.25/10.14 | | % 69.25/10.14 | End of split % 69.25/10.14 | % 69.25/10.14 End of proof % 69.25/10.14 % SZS output end Proof for theBenchmark % 69.25/10.14 % 69.25/10.14 9505ms %------------------------------------------------------------------------------