%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SET710+4 : TPTP v8.1.2. Bugfixed v2.2.1. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n012.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 15:26:05 EDT 2023 % Result : Theorem 13.22s 2.55s % Output : Proof 23.50s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SET710+4 : TPTP v8.1.2. Bugfixed v2.2.1. % 0.13/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.34 % Computer : n012.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 : Sat Aug 26 15:00:40 EDT 2023 % 0.13/0.34 % CPUTime : % 0.19/0.61 ________ _____ % 0.19/0.61 ___ __ \_________(_)________________________________ % 0.19/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.19/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.19/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.19/0.61 % 0.19/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.19/0.61 (2023-06-19) % 0.19/0.61 % 0.19/0.61 (c) Philipp Rümmer, 2009-2023 % 0.19/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.19/0.61 Amanda Stjerna. % 0.19/0.61 Free software under BSD-3-Clause. % 0.19/0.61 % 0.19/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.19/0.61 % 0.19/0.61 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.19/0.62 Running up to 7 provers in parallel. % 0.19/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.19/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.19/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.19/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.19/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.19/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.19/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 3.96/1.23 Prover 4: Preprocessing ... % 3.96/1.23 Prover 1: Preprocessing ... % 3.96/1.27 Prover 0: Preprocessing ... % 3.96/1.27 Prover 5: Preprocessing ... % 3.96/1.27 Prover 6: Preprocessing ... % 3.96/1.27 Prover 3: Preprocessing ... % 3.96/1.28 Prover 2: Preprocessing ... % 9.93/2.06 Prover 2: Proving ... % 9.93/2.06 Prover 6: Proving ... % 9.93/2.06 Prover 5: Proving ... % 9.93/2.18 Prover 1: Constructing countermodel ... % 9.93/2.24 Prover 3: Constructing countermodel ... % 13.22/2.55 Prover 3: proved (1916ms) % 13.22/2.55 % 13.22/2.55 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 13.22/2.55 % 13.22/2.55 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 13.22/2.56 Prover 2: stopped % 13.22/2.56 Prover 5: stopped % 13.22/2.56 Prover 6: stopped % 13.22/2.57 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 13.22/2.57 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 13.22/2.57 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 13.93/2.59 Prover 4: Constructing countermodel ... % 14.13/2.65 Prover 8: Preprocessing ... % 14.13/2.65 Prover 10: Preprocessing ... % 14.13/2.66 Prover 11: Preprocessing ... % 14.13/2.67 Prover 7: Preprocessing ... % 14.79/2.71 Prover 0: Proving ... % 14.79/2.71 Prover 0: stopped % 14.79/2.74 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 15.44/2.80 Prover 10: Warning: ignoring some quantifiers % 15.44/2.81 Prover 13: Preprocessing ... % 15.44/2.81 Prover 7: Warning: ignoring some quantifiers % 15.44/2.84 Prover 10: Constructing countermodel ... % 15.44/2.84 Prover 7: Constructing countermodel ... % 16.22/2.92 Prover 8: Warning: ignoring some quantifiers % 16.22/2.95 Prover 8: Constructing countermodel ... % 16.22/2.99 Prover 13: Warning: ignoring some quantifiers % 16.83/3.01 Prover 13: Constructing countermodel ... % 17.18/3.07 Prover 10: gave up % 17.18/3.07 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 17.76/3.14 Prover 16: Preprocessing ... % 18.35/3.27 Prover 11: Constructing countermodel ... % 19.10/3.28 Prover 16: Warning: ignoring some quantifiers % 19.26/3.31 Prover 16: Constructing countermodel ... % 22.58/3.76 Prover 1: Found proof (size 286) % 22.58/3.76 Prover 1: proved (3126ms) % 22.58/3.76 Prover 13: stopped % 22.58/3.76 Prover 11: stopped % 22.58/3.76 Prover 7: stopped % 22.58/3.76 Prover 4: stopped % 22.58/3.76 Prover 8: stopped % 22.58/3.76 Prover 16: stopped % 22.58/3.76 % 22.58/3.76 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 22.58/3.76 % 22.72/3.77 % SZS output start Proof for theBenchmark % 22.72/3.78 Assumptions after simplification: % 22.72/3.78 --------------------------------- % 22.72/3.78 % 22.72/3.78 (compose_function) % 22.72/3.81 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 22.72/3.81 $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: any] : ( ~ (compose_function(v0, % 22.72/3.81 v1, v2, v3, v4) = v7) | ~ (apply(v7, v5, v6) = v8) | ~ $i(v6) | ~ % 22.72/3.81 $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v9: % 22.72/3.81 any] : ? [v10: any] : (member(v6, v4) = v10 & member(v5, v2) = v9 & ( ~ % 22.72/3.81 (v10 = 0) | ~ (v9 = 0))) | (( ~ (v8 = 0) | ? [v9: $i] : (apply(v1, v5, % 22.72/3.81 v9) = 0 & apply(v0, v9, v6) = 0 & member(v9, v3) = 0 & $i(v9))) & % 22.72/3.81 (v8 = 0 | ! [v9: $i] : ( ~ (apply(v0, v9, v6) = 0) | ~ $i(v9) | ? [v10: % 22.72/3.81 any] : ? [v11: any] : (apply(v1, v5, v9) = v11 & member(v9, v3) = % 22.72/3.81 v10 & ( ~ (v11 = 0) | ~ (v10 = 0))))))) % 22.72/3.81 % 22.72/3.81 (equal_maps) % 22.72/3.81 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0 % 22.72/3.81 | ~ (equal_maps(v0, v1, v2, v3) = v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | % 22.72/3.81 ~ $i(v0) | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ( ~ (v7 = v6) & % 22.72/3.81 apply(v1, v5, v7) = 0 & apply(v0, v5, v6) = 0 & member(v7, v3) = 0 & % 22.72/3.81 member(v6, v3) = 0 & member(v5, v2) = 0 & $i(v7) & $i(v6) & $i(v5))) & ! % 22.72/3.81 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (equal_maps(v0, v1, % 22.72/3.81 v2, v3) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ! [v4: % 22.72/3.81 $i] : ! [v5: $i] : ! [v6: $i] : (v6 = v5 | ~ (apply(v1, v4, v6) = 0) | % 22.72/3.81 ~ (apply(v0, v4, v5) = 0) | ~ $i(v6) | ~ $i(v5) | ~ $i(v4) | ? [v7: % 22.72/3.81 any] : ? [v8: any] : ? [v9: any] : (member(v6, v3) = v9 & member(v5, % 22.72/3.81 v3) = v8 & member(v4, v2) = v7 & ( ~ (v9 = 0) | ~ (v8 = 0) | ~ (v7 = % 22.72/3.81 0))))) % 22.72/3.81 % 22.72/3.81 (maps) % 22.72/3.82 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 22.72/3.82 (maps(v0, v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: $i] : % 22.72/3.82 ? [v5: $i] : ? [v6: $i] : ( ~ (v6 = v5) & apply(v0, v4, v6) = 0 & apply(v0, % 22.72/3.82 v4, v5) = 0 & member(v6, v2) = 0 & member(v5, v2) = 0 & member(v4, v1) = % 22.72/3.82 0 & $i(v6) & $i(v5) & $i(v4)) | ? [v4: $i] : (member(v4, v1) = 0 & $i(v4) % 22.72/3.82 & ! [v5: $i] : ( ~ (apply(v0, v4, v5) = 0) | ~ $i(v5) | ? [v6: int] : ( % 22.72/3.82 ~ (v6 = 0) & member(v5, v2) = v6)))) & ! [v0: $i] : ! [v1: $i] : ! % 22.72/3.82 [v2: $i] : ( ~ (maps(v0, v1, v2) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ( % 22.72/3.82 ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v5 = v4 | ~ (apply(v0, v3, v5) % 22.72/3.82 = 0) | ~ (apply(v0, v3, v4) = 0) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) % 22.72/3.82 | ? [v6: any] : ? [v7: any] : ? [v8: any] : (member(v5, v2) = v8 & % 22.72/3.82 member(v4, v2) = v7 & member(v3, v1) = v6 & ( ~ (v8 = 0) | ~ (v7 = 0) % 22.72/3.82 | ~ (v6 = 0)))) & ! [v3: $i] : ( ~ (member(v3, v1) = 0) | ~ % 22.72/3.82 $i(v3) | ? [v4: $i] : (apply(v0, v3, v4) = 0 & member(v4, v2) = 0 & % 22.72/3.82 $i(v4))))) % 22.72/3.82 % 22.72/3.82 (thII02) % 22.97/3.82 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: % 22.97/3.82 $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ? [v10: $i] : % 22.97/3.82 ? [v11: int] : ( ~ (v11 = 0) & equal_maps(v8, v10, v3, v6) = v11 & % 22.97/3.82 compose_function(v9, v0, v3, v4, v6) = v10 & compose_function(v2, v7, v3, % 22.97/3.82 v5, v6) = v8 & compose_function(v2, v1, v4, v5, v6) = v9 & % 22.97/3.82 compose_function(v1, v0, v3, v4, v5) = v7 & maps(v2, v5, v6) = 0 & maps(v1, % 22.97/3.82 v4, v5) = 0 & maps(v0, v3, v4) = 0 & $i(v10) & $i(v9) & $i(v8) & $i(v7) & % 22.97/3.82 $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 22.97/3.82 % 22.97/3.82 (function-axioms) % 22.97/3.83 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 22.97/3.83 [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : (v1 = v0 | % 22.97/3.83 ~ (compose_predicate(v7, v6, v5, v4, v3, v2) = v1) | ~ % 22.97/3.83 (compose_predicate(v7, v6, v5, v4, v3, v2) = v0)) & ! [v0: % 22.97/3.83 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 22.97/3.83 : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v1 = v0 | ~ (isomorphism(v6, v5, % 22.97/3.83 v4, v3, v2) = v1) | ~ (isomorphism(v6, v5, v4, v3, v2) = v0)) & ! [v0: % 22.97/3.83 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 22.97/3.83 : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v1 = v0 | ~ (decreasing(v6, v5, % 22.97/3.83 v4, v3, v2) = v1) | ~ (decreasing(v6, v5, v4, v3, v2) = v0)) & ! [v0: % 22.97/3.83 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 22.97/3.83 : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v1 = v0 | ~ (increasing(v6, v5, % 22.97/3.83 v4, v3, v2) = v1) | ~ (increasing(v6, v5, v4, v3, v2) = v0)) & ! [v0: % 22.97/3.83 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : % 22.97/3.83 ! [v6: $i] : (v1 = v0 | ~ (compose_function(v6, v5, v4, v3, v2) = v1) | ~ % 22.97/3.83 (compose_function(v6, v5, v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : % 22.97/3.83 ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 22.97/3.83 $i] : (v1 = v0 | ~ (inverse_predicate(v5, v4, v3, v2) = v1) | ~ % 22.97/3.83 (inverse_predicate(v5, v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! % 22.97/3.83 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 22.97/3.83 $i] : (v1 = v0 | ~ (equal_maps(v5, v4, v3, v2) = v1) | ~ (equal_maps(v5, % 22.97/3.83 v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 22.97/3.83 $i] : ! [v4: $i] : (v1 = v0 | ~ (inverse_image3(v4, v3, v2) = v1) | ~ % 22.97/3.83 (inverse_image3(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 22.97/3.83 : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (image3(v4, v3, v2) = v1) | ~ % 22.97/3.83 (image3(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 22.97/3.83 [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (inverse_function(v4, v3, v2) = v1) | % 22.97/3.83 ~ (inverse_function(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! % 22.97/3.83 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | % 22.97/3.83 ~ (one_to_one(v4, v3, v2) = v1) | ~ (one_to_one(v4, v3, v2) = v0)) & ! % 22.97/3.83 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 22.97/3.83 $i] : ! [v4: $i] : (v1 = v0 | ~ (surjective(v4, v3, v2) = v1) | ~ % 22.97/3.83 (surjective(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 22.97/3.83 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ % 22.97/3.83 (injective(v4, v3, v2) = v1) | ~ (injective(v4, v3, v2) = v0)) & ! [v0: % 22.97/3.83 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 22.97/3.83 : ! [v4: $i] : (v1 = v0 | ~ (maps(v4, v3, v2) = v1) | ~ (maps(v4, v3, v2) = % 22.97/3.83 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 22.97/3.83 $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (apply(v4, v3, v2) = v1) | % 22.97/3.83 ~ (apply(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 22.97/3.83 [v3: $i] : (v1 = v0 | ~ (inverse_image2(v3, v2) = v1) | ~ % 22.97/3.83 (inverse_image2(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 22.97/3.83 ! [v3: $i] : (v1 = v0 | ~ (image2(v3, v2) = v1) | ~ (image2(v3, v2) = v0)) & % 22.97/3.83 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 22.97/3.83 [v3: $i] : (v1 = v0 | ~ (identity(v3, v2) = v1) | ~ (identity(v3, v2) = v0)) % 22.97/3.83 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 22.97/3.83 (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) & ! [v0: % 22.97/3.83 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 22.97/3.83 (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0)) & ! [v0: $i] : ! % 22.97/3.83 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (union(v3, v2) = v1) | ~ % 22.97/3.83 (union(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 22.97/3.83 $i] : (v1 = v0 | ~ (intersection(v3, v2) = v1) | ~ (intersection(v3, v2) = % 22.97/3.83 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 22.97/3.83 $i] : ! [v3: $i] : (v1 = v0 | ~ (equal_set(v3, v2) = v1) | ~ % 22.97/3.83 (equal_set(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 22.97/3.83 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (subset(v3, % 22.97/3.83 v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! % 22.97/3.83 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 22.97/3.83 (member(v3, v2) = v1) | ~ (member(v3, v2) = v0)) & ! [v0: $i] : ! [v1: % 22.97/3.83 $i] : ! [v2: $i] : (v1 = v0 | ~ (product(v2) = v1) | ~ (product(v2) = % 22.97/3.83 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (sum(v2) = % 22.97/3.83 v1) | ~ (sum(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = % 22.97/3.83 v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ! [v0: $i] : ! % 22.97/3.83 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (power_set(v2) = v1) | ~ % 22.97/3.83 (power_set(v2) = v0)) % 22.97/3.83 % 22.97/3.83 Further assumptions not needed in the proof: % 22.97/3.83 -------------------------------------------- % 22.97/3.83 compose_predicate, decreasing_function, difference, empty_set, equal_set, % 22.97/3.83 identity, image2, image3, increasing_function, injective, intersection, % 22.97/3.83 inverse_function, inverse_image2, inverse_image3, inverse_predicate, % 22.97/3.83 isomorphism, one_to_one, power_set, product, singleton, subset, sum, surjective, % 22.97/3.83 union, unordered_pair % 22.97/3.83 % 22.97/3.83 Those formulas are unsatisfiable: % 22.97/3.83 --------------------------------- % 22.97/3.83 % 22.97/3.83 Begin of proof % 22.97/3.83 | % 22.97/3.83 | ALPHA: (maps) implies: % 22.97/3.84 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (maps(v0, v1, v2) = 0) | % 22.97/3.84 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ( ! [v3: $i] : ! [v4: $i] : ! % 22.97/3.84 | [v5: $i] : (v5 = v4 | ~ (apply(v0, v3, v5) = 0) | ~ (apply(v0, % 22.97/3.84 | v3, v4) = 0) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ? [v6: % 22.97/3.84 | any] : ? [v7: any] : ? [v8: any] : (member(v5, v2) = v8 & % 22.97/3.84 | member(v4, v2) = v7 & member(v3, v1) = v6 & ( ~ (v8 = 0) | ~ % 22.97/3.84 | (v7 = 0) | ~ (v6 = 0)))) & ! [v3: $i] : ( ~ (member(v3, v1) % 22.97/3.84 | = 0) | ~ $i(v3) | ? [v4: $i] : (apply(v0, v3, v4) = 0 & % 22.97/3.84 | member(v4, v2) = 0 & $i(v4))))) % 22.97/3.84 | % 22.97/3.84 | ALPHA: (equal_maps) implies: % 22.97/3.84 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : % 22.97/3.84 | (v4 = 0 | ~ (equal_maps(v0, v1, v2, v3) = v4) | ~ $i(v3) | ~ $i(v2) % 22.97/3.84 | | ~ $i(v1) | ~ $i(v0) | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ( % 22.97/3.84 | ~ (v7 = v6) & apply(v1, v5, v7) = 0 & apply(v0, v5, v6) = 0 & % 22.97/3.84 | member(v7, v3) = 0 & member(v6, v3) = 0 & member(v5, v2) = 0 & % 22.97/3.84 | $i(v7) & $i(v6) & $i(v5))) % 22.97/3.84 | % 22.97/3.84 | ALPHA: (function-axioms) implies: % 22.97/3.84 | (3) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 22.97/3.84 | ! [v3: $i] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) % 22.97/3.84 | = v0)) % 22.97/3.84 | % 22.97/3.84 | DELTA: instantiating (thII02) with fresh symbols all_32_0, all_32_1, all_32_2, % 22.97/3.84 | all_32_3, all_32_4, all_32_5, all_32_6, all_32_7, all_32_8, all_32_9, % 22.97/3.84 | all_32_10, all_32_11 gives: % 22.97/3.84 | (4) ~ (all_32_0 = 0) & equal_maps(all_32_3, all_32_1, all_32_8, all_32_5) % 22.97/3.84 | = all_32_0 & compose_function(all_32_2, all_32_11, all_32_8, all_32_7, % 22.97/3.84 | all_32_5) = all_32_1 & compose_function(all_32_9, all_32_4, all_32_8, % 22.97/3.84 | all_32_6, all_32_5) = all_32_3 & compose_function(all_32_9, % 22.97/3.84 | all_32_10, all_32_7, all_32_6, all_32_5) = all_32_2 & % 22.97/3.84 | compose_function(all_32_10, all_32_11, all_32_8, all_32_7, all_32_6) = % 22.97/3.84 | all_32_4 & maps(all_32_9, all_32_6, all_32_5) = 0 & maps(all_32_10, % 22.97/3.84 | all_32_7, all_32_6) = 0 & maps(all_32_11, all_32_8, all_32_7) = 0 & % 22.97/3.84 | $i(all_32_1) & $i(all_32_2) & $i(all_32_3) & $i(all_32_4) & % 22.97/3.84 | $i(all_32_5) & $i(all_32_6) & $i(all_32_7) & $i(all_32_8) & % 22.97/3.84 | $i(all_32_9) & $i(all_32_10) & $i(all_32_11) % 22.97/3.84 | % 22.97/3.84 | ALPHA: (4) implies: % 22.97/3.84 | (5) ~ (all_32_0 = 0) % 22.97/3.84 | (6) $i(all_32_11) % 22.97/3.84 | (7) $i(all_32_10) % 22.97/3.84 | (8) $i(all_32_9) % 22.97/3.84 | (9) $i(all_32_8) % 22.97/3.84 | (10) $i(all_32_7) % 22.97/3.84 | (11) $i(all_32_6) % 22.97/3.84 | (12) $i(all_32_5) % 22.97/3.84 | (13) $i(all_32_4) % 22.97/3.84 | (14) $i(all_32_3) % 22.97/3.84 | (15) $i(all_32_2) % 22.97/3.84 | (16) $i(all_32_1) % 22.97/3.84 | (17) maps(all_32_11, all_32_8, all_32_7) = 0 % 22.97/3.84 | (18) maps(all_32_10, all_32_7, all_32_6) = 0 % 22.97/3.84 | (19) maps(all_32_9, all_32_6, all_32_5) = 0 % 22.97/3.84 | (20) compose_function(all_32_10, all_32_11, all_32_8, all_32_7, all_32_6) = % 22.97/3.84 | all_32_4 % 22.97/3.84 | (21) compose_function(all_32_9, all_32_10, all_32_7, all_32_6, all_32_5) = % 22.97/3.84 | all_32_2 % 22.97/3.84 | (22) compose_function(all_32_9, all_32_4, all_32_8, all_32_6, all_32_5) = % 22.97/3.84 | all_32_3 % 22.97/3.84 | (23) compose_function(all_32_2, all_32_11, all_32_8, all_32_7, all_32_5) = % 22.97/3.84 | all_32_1 % 22.97/3.84 | (24) equal_maps(all_32_3, all_32_1, all_32_8, all_32_5) = all_32_0 % 22.97/3.84 | % 22.97/3.84 | GROUND_INST: instantiating (1) with all_32_11, all_32_8, all_32_7, simplifying % 22.97/3.84 | with (6), (9), (10), (17) gives: % 22.97/3.85 | (25) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v1 | ~ % 22.97/3.85 | (apply(all_32_11, v0, v2) = 0) | ~ (apply(all_32_11, v0, v1) = 0) | % 22.97/3.85 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ? % 22.97/3.85 | [v5: any] : (member(v2, all_32_7) = v5 & member(v1, all_32_7) = v4 & % 22.97/3.85 | member(v0, all_32_8) = v3 & ( ~ (v5 = 0) | ~ (v4 = 0) | ~ (v3 = % 22.97/3.85 | 0)))) & ! [v0: $i] : ( ~ (member(v0, all_32_8) = 0) | ~ % 22.97/3.85 | $i(v0) | ? [v1: $i] : (apply(all_32_11, v0, v1) = 0 & member(v1, % 22.97/3.85 | all_32_7) = 0 & $i(v1))) % 22.97/3.85 | % 22.97/3.85 | ALPHA: (25) implies: % 22.97/3.85 | (26) ! [v0: $i] : ( ~ (member(v0, all_32_8) = 0) | ~ $i(v0) | ? [v1: $i] % 22.97/3.85 | : (apply(all_32_11, v0, v1) = 0 & member(v1, all_32_7) = 0 & % 22.97/3.85 | $i(v1))) % 22.97/3.85 | (27) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v1 | ~ % 22.97/3.85 | (apply(all_32_11, v0, v2) = 0) | ~ (apply(all_32_11, v0, v1) = 0) | % 22.97/3.85 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ? % 22.97/3.85 | [v5: any] : (member(v2, all_32_7) = v5 & member(v1, all_32_7) = v4 & % 22.97/3.85 | member(v0, all_32_8) = v3 & ( ~ (v5 = 0) | ~ (v4 = 0) | ~ (v3 = % 22.97/3.85 | 0)))) % 22.97/3.85 | % 22.97/3.85 | GROUND_INST: instantiating (1) with all_32_10, all_32_7, all_32_6, simplifying % 22.97/3.85 | with (7), (10), (11), (18) gives: % 23.11/3.85 | (28) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v1 | ~ % 23.11/3.85 | (apply(all_32_10, v0, v2) = 0) | ~ (apply(all_32_10, v0, v1) = 0) | % 23.11/3.85 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ? % 23.11/3.85 | [v5: any] : (member(v2, all_32_6) = v5 & member(v1, all_32_6) = v4 & % 23.11/3.85 | member(v0, all_32_7) = v3 & ( ~ (v5 = 0) | ~ (v4 = 0) | ~ (v3 = % 23.11/3.85 | 0)))) & ! [v0: $i] : ( ~ (member(v0, all_32_7) = 0) | ~ % 23.11/3.85 | $i(v0) | ? [v1: $i] : (apply(all_32_10, v0, v1) = 0 & member(v1, % 23.11/3.85 | all_32_6) = 0 & $i(v1))) % 23.11/3.85 | % 23.11/3.85 | ALPHA: (28) implies: % 23.11/3.85 | (29) ! [v0: $i] : ( ~ (member(v0, all_32_7) = 0) | ~ $i(v0) | ? [v1: $i] % 23.11/3.85 | : (apply(all_32_10, v0, v1) = 0 & member(v1, all_32_6) = 0 & % 23.11/3.85 | $i(v1))) % 23.11/3.85 | (30) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v1 | ~ % 23.11/3.85 | (apply(all_32_10, v0, v2) = 0) | ~ (apply(all_32_10, v0, v1) = 0) | % 23.11/3.85 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ? % 23.11/3.85 | [v5: any] : (member(v2, all_32_6) = v5 & member(v1, all_32_6) = v4 & % 23.11/3.85 | member(v0, all_32_7) = v3 & ( ~ (v5 = 0) | ~ (v4 = 0) | ~ (v3 = % 23.11/3.85 | 0)))) % 23.11/3.85 | % 23.11/3.85 | GROUND_INST: instantiating (1) with all_32_9, all_32_6, all_32_5, simplifying % 23.11/3.85 | with (8), (11), (12), (19) gives: % 23.11/3.85 | (31) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v1 | ~ % 23.11/3.85 | (apply(all_32_9, v0, v2) = 0) | ~ (apply(all_32_9, v0, v1) = 0) | % 23.11/3.85 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ? % 23.11/3.85 | [v5: any] : (member(v2, all_32_5) = v5 & member(v1, all_32_5) = v4 & % 23.11/3.85 | member(v0, all_32_6) = v3 & ( ~ (v5 = 0) | ~ (v4 = 0) | ~ (v3 = % 23.11/3.85 | 0)))) & ! [v0: $i] : ( ~ (member(v0, all_32_6) = 0) | ~ % 23.11/3.85 | $i(v0) | ? [v1: $i] : (apply(all_32_9, v0, v1) = 0 & member(v1, % 23.11/3.85 | all_32_5) = 0 & $i(v1))) % 23.11/3.85 | % 23.11/3.85 | ALPHA: (31) implies: % 23.11/3.85 | (32) ! [v0: $i] : ( ~ (member(v0, all_32_6) = 0) | ~ $i(v0) | ? [v1: $i] % 23.11/3.85 | : (apply(all_32_9, v0, v1) = 0 & member(v1, all_32_5) = 0 & $i(v1))) % 23.11/3.86 | (33) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v1 | ~ % 23.11/3.86 | (apply(all_32_9, v0, v2) = 0) | ~ (apply(all_32_9, v0, v1) = 0) | % 23.11/3.86 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ? % 23.11/3.86 | [v5: any] : (member(v2, all_32_5) = v5 & member(v1, all_32_5) = v4 & % 23.11/3.86 | member(v0, all_32_6) = v3 & ( ~ (v5 = 0) | ~ (v4 = 0) | ~ (v3 = % 23.11/3.86 | 0)))) % 23.11/3.86 | % 23.11/3.86 | GROUND_INST: instantiating (2) with all_32_3, all_32_1, all_32_8, all_32_5, % 23.11/3.86 | all_32_0, simplifying with (9), (12), (14), (16), (24) gives: % 23.11/3.86 | (34) all_32_0 = 0 | ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ( ~ (v2 = v1) % 23.11/3.86 | & apply(all_32_1, v0, v2) = 0 & apply(all_32_3, v0, v1) = 0 & % 23.11/3.86 | member(v2, all_32_5) = 0 & member(v1, all_32_5) = 0 & member(v0, % 23.11/3.86 | all_32_8) = 0 & $i(v2) & $i(v1) & $i(v0)) % 23.11/3.86 | % 23.11/3.86 | BETA: splitting (34) gives: % 23.11/3.86 | % 23.11/3.86 | Case 1: % 23.11/3.86 | | % 23.11/3.86 | | (35) all_32_0 = 0 % 23.11/3.86 | | % 23.11/3.86 | | REDUCE: (5), (35) imply: % 23.11/3.86 | | (36) $false % 23.11/3.86 | | % 23.11/3.86 | | CLOSE: (36) is inconsistent. % 23.11/3.86 | | % 23.11/3.86 | Case 2: % 23.11/3.86 | | % 23.11/3.86 | | (37) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ( ~ (v2 = v1) & % 23.11/3.86 | | apply(all_32_1, v0, v2) = 0 & apply(all_32_3, v0, v1) = 0 & % 23.11/3.86 | | member(v2, all_32_5) = 0 & member(v1, all_32_5) = 0 & member(v0, % 23.11/3.86 | | all_32_8) = 0 & $i(v2) & $i(v1) & $i(v0)) % 23.11/3.86 | | % 23.11/3.86 | | DELTA: instantiating (37) with fresh symbols all_45_0, all_45_1, all_45_2 % 23.11/3.86 | | gives: % 23.11/3.86 | | (38) ~ (all_45_0 = all_45_1) & apply(all_32_1, all_45_2, all_45_0) = 0 & % 23.11/3.86 | | apply(all_32_3, all_45_2, all_45_1) = 0 & member(all_45_0, all_32_5) % 23.11/3.86 | | = 0 & member(all_45_1, all_32_5) = 0 & member(all_45_2, all_32_8) = % 23.11/3.86 | | 0 & $i(all_45_0) & $i(all_45_1) & $i(all_45_2) % 23.11/3.86 | | % 23.11/3.86 | | ALPHA: (38) implies: % 23.11/3.86 | | (39) ~ (all_45_0 = all_45_1) % 23.11/3.86 | | (40) $i(all_45_2) % 23.11/3.86 | | (41) $i(all_45_1) % 23.11/3.86 | | (42) $i(all_45_0) % 23.11/3.86 | | (43) member(all_45_2, all_32_8) = 0 % 23.11/3.86 | | (44) member(all_45_1, all_32_5) = 0 % 23.11/3.86 | | (45) member(all_45_0, all_32_5) = 0 % 23.11/3.86 | | (46) apply(all_32_3, all_45_2, all_45_1) = 0 % 23.11/3.86 | | (47) apply(all_32_1, all_45_2, all_45_0) = 0 % 23.11/3.86 | | % 23.11/3.86 | | GROUND_INST: instantiating (26) with all_45_2, simplifying with (40), (43) % 23.11/3.86 | | gives: % 23.11/3.86 | | (48) ? [v0: $i] : (apply(all_32_11, all_45_2, v0) = 0 & member(v0, % 23.11/3.86 | | all_32_7) = 0 & $i(v0)) % 23.11/3.86 | | % 23.11/3.86 | | GROUND_INST: instantiating (compose_function) with all_32_9, all_32_4, % 23.11/3.86 | | all_32_8, all_32_6, all_32_5, all_45_2, all_45_1, all_32_3, 0, % 23.11/3.86 | | simplifying with (8), (9), (11), (12), (13), (22), (40), (41), % 23.11/3.86 | | (46) gives: % 23.11/3.86 | | (49) ? [v0: any] : ? [v1: any] : (member(all_45_1, all_32_5) = v1 & % 23.11/3.86 | | member(all_45_2, all_32_8) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) | % 23.11/3.86 | | ? [v0: $i] : (apply(all_32_4, all_45_2, v0) = 0 & apply(all_32_9, % 23.11/3.86 | | v0, all_45_1) = 0 & member(v0, all_32_6) = 0 & $i(v0)) % 23.11/3.86 | | % 23.11/3.87 | | GROUND_INST: instantiating (compose_function) with all_32_2, all_32_11, % 23.11/3.87 | | all_32_8, all_32_7, all_32_5, all_45_2, all_45_0, all_32_1, 0, % 23.11/3.87 | | simplifying with (6), (9), (10), (12), (15), (23), (40), (42), % 23.11/3.87 | | (47) gives: % 23.11/3.87 | | (50) ? [v0: any] : ? [v1: any] : (member(all_45_0, all_32_5) = v1 & % 23.11/3.87 | | member(all_45_2, all_32_8) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) | % 23.11/3.87 | | ? [v0: $i] : (apply(all_32_2, v0, all_45_0) = 0 & apply(all_32_11, % 23.11/3.87 | | all_45_2, v0) = 0 & member(v0, all_32_7) = 0 & $i(v0)) % 23.11/3.87 | | % 23.11/3.87 | | DELTA: instantiating (48) with fresh symbol all_52_0 gives: % 23.11/3.87 | | (51) apply(all_32_11, all_45_2, all_52_0) = 0 & member(all_52_0, % 23.11/3.87 | | all_32_7) = 0 & $i(all_52_0) % 23.11/3.87 | | % 23.11/3.87 | | ALPHA: (51) implies: % 23.11/3.87 | | (52) $i(all_52_0) % 23.11/3.87 | | (53) member(all_52_0, all_32_7) = 0 % 23.11/3.87 | | (54) apply(all_32_11, all_45_2, all_52_0) = 0 % 23.11/3.87 | | % 23.11/3.87 | | BETA: splitting (50) gives: % 23.11/3.87 | | % 23.11/3.87 | | Case 1: % 23.11/3.87 | | | % 23.11/3.87 | | | (55) ? [v0: any] : ? [v1: any] : (member(all_45_0, all_32_5) = v1 & % 23.11/3.87 | | | member(all_45_2, all_32_8) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 23.11/3.87 | | | % 23.11/3.87 | | | DELTA: instantiating (55) with fresh symbols all_57_0, all_57_1 gives: % 23.11/3.87 | | | (56) member(all_45_0, all_32_5) = all_57_0 & member(all_45_2, all_32_8) % 23.11/3.87 | | | = all_57_1 & ( ~ (all_57_0 = 0) | ~ (all_57_1 = 0)) % 23.11/3.87 | | | % 23.11/3.87 | | | ALPHA: (56) implies: % 23.11/3.87 | | | (57) member(all_45_2, all_32_8) = all_57_1 % 23.11/3.87 | | | (58) member(all_45_0, all_32_5) = all_57_0 % 23.11/3.87 | | | (59) ~ (all_57_0 = 0) | ~ (all_57_1 = 0) % 23.11/3.87 | | | % 23.11/3.87 | | | GROUND_INST: instantiating (3) with 0, all_57_1, all_32_8, all_45_2, % 23.11/3.87 | | | simplifying with (43), (57) gives: % 23.11/3.87 | | | (60) all_57_1 = 0 % 23.11/3.87 | | | % 23.11/3.87 | | | GROUND_INST: instantiating (3) with 0, all_57_0, all_32_5, all_45_0, % 23.11/3.87 | | | simplifying with (45), (58) gives: % 23.11/3.87 | | | (61) all_57_0 = 0 % 23.11/3.87 | | | % 23.11/3.87 | | | BETA: splitting (59) gives: % 23.11/3.87 | | | % 23.11/3.87 | | | Case 1: % 23.11/3.87 | | | | % 23.11/3.87 | | | | (62) ~ (all_57_0 = 0) % 23.11/3.87 | | | | % 23.11/3.87 | | | | REDUCE: (61), (62) imply: % 23.11/3.87 | | | | (63) $false % 23.11/3.87 | | | | % 23.11/3.87 | | | | CLOSE: (63) is inconsistent. % 23.11/3.87 | | | | % 23.11/3.87 | | | Case 2: % 23.11/3.87 | | | | % 23.11/3.87 | | | | (64) ~ (all_57_1 = 0) % 23.11/3.87 | | | | % 23.11/3.87 | | | | REDUCE: (60), (64) imply: % 23.11/3.87 | | | | (65) $false % 23.11/3.87 | | | | % 23.11/3.87 | | | | CLOSE: (65) is inconsistent. % 23.11/3.87 | | | | % 23.11/3.87 | | | End of split % 23.11/3.87 | | | % 23.11/3.87 | | Case 2: % 23.11/3.87 | | | % 23.11/3.87 | | | (66) ? [v0: $i] : (apply(all_32_2, v0, all_45_0) = 0 & % 23.11/3.87 | | | apply(all_32_11, all_45_2, v0) = 0 & member(v0, all_32_7) = 0 & % 23.11/3.87 | | | $i(v0)) % 23.11/3.87 | | | % 23.11/3.87 | | | DELTA: instantiating (66) with fresh symbol all_57_0 gives: % 23.11/3.87 | | | (67) apply(all_32_2, all_57_0, all_45_0) = 0 & apply(all_32_11, % 23.11/3.87 | | | all_45_2, all_57_0) = 0 & member(all_57_0, all_32_7) = 0 & % 23.11/3.87 | | | $i(all_57_0) % 23.11/3.87 | | | % 23.11/3.87 | | | ALPHA: (67) implies: % 23.11/3.87 | | | (68) $i(all_57_0) % 23.11/3.87 | | | (69) member(all_57_0, all_32_7) = 0 % 23.11/3.87 | | | (70) apply(all_32_11, all_45_2, all_57_0) = 0 % 23.11/3.87 | | | (71) apply(all_32_2, all_57_0, all_45_0) = 0 % 23.11/3.87 | | | % 23.11/3.87 | | | BETA: splitting (49) gives: % 23.11/3.87 | | | % 23.11/3.87 | | | Case 1: % 23.11/3.87 | | | | % 23.11/3.87 | | | | (72) ? [v0: any] : ? [v1: any] : (member(all_45_1, all_32_5) = v1 & % 23.11/3.87 | | | | member(all_45_2, all_32_8) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 23.11/3.87 | | | | % 23.11/3.87 | | | | DELTA: instantiating (72) with fresh symbols all_61_0, all_61_1 gives: % 23.11/3.87 | | | | (73) member(all_45_1, all_32_5) = all_61_0 & member(all_45_2, % 23.11/3.87 | | | | all_32_8) = all_61_1 & ( ~ (all_61_0 = 0) | ~ (all_61_1 = 0)) % 23.11/3.87 | | | | % 23.11/3.87 | | | | ALPHA: (73) implies: % 23.11/3.87 | | | | (74) member(all_45_2, all_32_8) = all_61_1 % 23.11/3.87 | | | | (75) member(all_45_1, all_32_5) = all_61_0 % 23.11/3.87 | | | | (76) ~ (all_61_0 = 0) | ~ (all_61_1 = 0) % 23.11/3.87 | | | | % 23.11/3.87 | | | | GROUND_INST: instantiating (3) with 0, all_61_1, all_32_8, all_45_2, % 23.11/3.87 | | | | simplifying with (43), (74) gives: % 23.11/3.88 | | | | (77) all_61_1 = 0 % 23.11/3.88 | | | | % 23.11/3.88 | | | | GROUND_INST: instantiating (3) with 0, all_61_0, all_32_5, all_45_1, % 23.11/3.88 | | | | simplifying with (44), (75) gives: % 23.11/3.88 | | | | (78) all_61_0 = 0 % 23.11/3.88 | | | | % 23.11/3.88 | | | | BETA: splitting (76) gives: % 23.11/3.88 | | | | % 23.11/3.88 | | | | Case 1: % 23.11/3.88 | | | | | % 23.11/3.88 | | | | | (79) ~ (all_61_0 = 0) % 23.11/3.88 | | | | | % 23.11/3.88 | | | | | REDUCE: (78), (79) imply: % 23.11/3.88 | | | | | (80) $false % 23.11/3.88 | | | | | % 23.11/3.88 | | | | | CLOSE: (80) is inconsistent. % 23.11/3.88 | | | | | % 23.11/3.88 | | | | Case 2: % 23.11/3.88 | | | | | % 23.11/3.88 | | | | | (81) ~ (all_61_1 = 0) % 23.11/3.88 | | | | | % 23.11/3.88 | | | | | REDUCE: (77), (81) imply: % 23.11/3.88 | | | | | (82) $false % 23.11/3.88 | | | | | % 23.11/3.88 | | | | | CLOSE: (82) is inconsistent. % 23.11/3.88 | | | | | % 23.11/3.88 | | | | End of split % 23.11/3.88 | | | | % 23.11/3.88 | | | Case 2: % 23.11/3.88 | | | | % 23.11/3.88 | | | | (83) ? [v0: $i] : (apply(all_32_4, all_45_2, v0) = 0 & % 23.11/3.88 | | | | apply(all_32_9, v0, all_45_1) = 0 & member(v0, all_32_6) = 0 & % 23.11/3.88 | | | | $i(v0)) % 23.11/3.88 | | | | % 23.11/3.88 | | | | DELTA: instantiating (83) with fresh symbol all_61_0 gives: % 23.11/3.88 | | | | (84) apply(all_32_4, all_45_2, all_61_0) = 0 & apply(all_32_9, % 23.11/3.88 | | | | all_61_0, all_45_1) = 0 & member(all_61_0, all_32_6) = 0 & % 23.11/3.88 | | | | $i(all_61_0) % 23.11/3.88 | | | | % 23.11/3.88 | | | | ALPHA: (84) implies: % 23.11/3.88 | | | | (85) $i(all_61_0) % 23.11/3.88 | | | | (86) member(all_61_0, all_32_6) = 0 % 23.11/3.88 | | | | (87) apply(all_32_9, all_61_0, all_45_1) = 0 % 23.11/3.88 | | | | (88) apply(all_32_4, all_45_2, all_61_0) = 0 % 23.11/3.88 | | | | % 23.11/3.88 | | | | GROUND_INST: instantiating (29) with all_57_0, simplifying with (68), % 23.11/3.88 | | | | (69) gives: % 23.11/3.88 | | | | (89) ? [v0: $i] : (apply(all_32_10, all_57_0, v0) = 0 & member(v0, % 23.11/3.88 | | | | all_32_6) = 0 & $i(v0)) % 23.11/3.88 | | | | % 23.11/3.88 | | | | GROUND_INST: instantiating (32) with all_61_0, simplifying with (85), % 23.11/3.88 | | | | (86) gives: % 23.11/3.88 | | | | (90) ? [v0: $i] : (apply(all_32_9, all_61_0, v0) = 0 & member(v0, % 23.11/3.88 | | | | all_32_5) = 0 & $i(v0)) % 23.11/3.88 | | | | % 23.11/3.88 | | | | GROUND_INST: instantiating (27) with all_45_2, all_52_0, all_57_0, % 23.11/3.88 | | | | simplifying with (40), (52), (54), (68), (70) gives: % 23.11/3.88 | | | | (91) all_57_0 = all_52_0 | ? [v0: any] : ? [v1: any] : ? [v2: any] % 23.11/3.88 | | | | : (member(all_57_0, all_32_7) = v2 & member(all_52_0, all_32_7) % 23.11/3.88 | | | | = v1 & member(all_45_2, all_32_8) = v0 & ( ~ (v2 = 0) | ~ (v1 % 23.11/3.88 | | | | = 0) | ~ (v0 = 0))) % 23.11/3.88 | | | | % 23.11/3.88 | | | | GROUND_INST: instantiating (compose_function) with all_32_10, all_32_11, % 23.11/3.88 | | | | all_32_8, all_32_7, all_32_6, all_45_2, all_61_0, all_32_4, % 23.11/3.88 | | | | 0, simplifying with (6), (7), (9), (10), (11), (20), (40), % 23.11/3.88 | | | | (85), (88) gives: % 23.11/3.88 | | | | (92) ? [v0: any] : ? [v1: any] : (member(all_61_0, all_32_6) = v1 & % 23.11/3.88 | | | | member(all_45_2, all_32_8) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 23.11/3.88 | | | | | ? [v0: $i] : (apply(all_32_10, v0, all_61_0) = 0 & % 23.11/3.88 | | | | apply(all_32_11, all_45_2, v0) = 0 & member(v0, all_32_7) = 0 % 23.11/3.88 | | | | & $i(v0)) % 23.11/3.88 | | | | % 23.11/3.88 | | | | GROUND_INST: instantiating (compose_function) with all_32_9, all_32_10, % 23.11/3.88 | | | | all_32_7, all_32_6, all_32_5, all_57_0, all_45_0, all_32_2, % 23.11/3.88 | | | | 0, simplifying with (7), (8), (10), (11), (12), (21), (42), % 23.11/3.88 | | | | (68), (71) gives: % 23.11/3.88 | | | | (93) ? [v0: any] : ? [v1: any] : (member(all_57_0, all_32_7) = v0 & % 23.11/3.88 | | | | member(all_45_0, all_32_5) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 23.11/3.88 | | | | | ? [v0: $i] : (apply(all_32_9, v0, all_45_0) = 0 & % 23.11/3.88 | | | | apply(all_32_10, all_57_0, v0) = 0 & member(v0, all_32_6) = 0 % 23.11/3.88 | | | | & $i(v0)) % 23.11/3.88 | | | | % 23.11/3.88 | | | | DELTA: instantiating (90) with fresh symbol all_68_0 gives: % 23.11/3.88 | | | | (94) apply(all_32_9, all_61_0, all_68_0) = 0 & member(all_68_0, % 23.11/3.88 | | | | all_32_5) = 0 & $i(all_68_0) % 23.11/3.88 | | | | % 23.11/3.88 | | | | ALPHA: (94) implies: % 23.11/3.88 | | | | (95) $i(all_68_0) % 23.11/3.88 | | | | (96) member(all_68_0, all_32_5) = 0 % 23.11/3.88 | | | | (97) apply(all_32_9, all_61_0, all_68_0) = 0 % 23.11/3.88 | | | | % 23.11/3.88 | | | | DELTA: instantiating (89) with fresh symbol all_70_0 gives: % 23.11/3.88 | | | | (98) apply(all_32_10, all_57_0, all_70_0) = 0 & member(all_70_0, % 23.11/3.88 | | | | all_32_6) = 0 & $i(all_70_0) % 23.11/3.88 | | | | % 23.11/3.88 | | | | ALPHA: (98) implies: % 23.11/3.88 | | | | (99) $i(all_70_0) % 23.11/3.88 | | | | (100) member(all_70_0, all_32_6) = 0 % 23.11/3.88 | | | | (101) apply(all_32_10, all_57_0, all_70_0) = 0 % 23.11/3.88 | | | | % 23.11/3.88 | | | | BETA: splitting (91) gives: % 23.11/3.88 | | | | % 23.11/3.88 | | | | Case 1: % 23.11/3.88 | | | | | % 23.11/3.88 | | | | | (102) all_57_0 = all_52_0 % 23.11/3.88 | | | | | % 23.11/3.88 | | | | | REDUCE: (101), (102) imply: % 23.11/3.88 | | | | | (103) apply(all_32_10, all_52_0, all_70_0) = 0 % 23.11/3.88 | | | | | % 23.11/3.88 | | | | | BETA: splitting (93) gives: % 23.11/3.88 | | | | | % 23.11/3.88 | | | | | Case 1: % 23.11/3.88 | | | | | | % 23.11/3.89 | | | | | | (104) ? [v0: any] : ? [v1: any] : (member(all_57_0, all_32_7) = % 23.11/3.89 | | | | | | v0 & member(all_45_0, all_32_5) = v1 & ( ~ (v1 = 0) | ~ % 23.11/3.89 | | | | | | (v0 = 0))) % 23.11/3.89 | | | | | | % 23.11/3.89 | | | | | | DELTA: instantiating (104) with fresh symbols all_80_0, all_80_1 % 23.11/3.89 | | | | | | gives: % 23.11/3.89 | | | | | | (105) member(all_57_0, all_32_7) = all_80_1 & member(all_45_0, % 23.11/3.89 | | | | | | all_32_5) = all_80_0 & ( ~ (all_80_0 = 0) | ~ (all_80_1 % 23.11/3.89 | | | | | | = 0)) % 23.11/3.89 | | | | | | % 23.11/3.89 | | | | | | ALPHA: (105) implies: % 23.11/3.89 | | | | | | (106) member(all_45_0, all_32_5) = all_80_0 % 23.11/3.89 | | | | | | (107) member(all_57_0, all_32_7) = all_80_1 % 23.11/3.89 | | | | | | (108) ~ (all_80_0 = 0) | ~ (all_80_1 = 0) % 23.11/3.89 | | | | | | % 23.11/3.89 | | | | | | REDUCE: (102), (107) imply: % 23.11/3.89 | | | | | | (109) member(all_52_0, all_32_7) = all_80_1 % 23.11/3.89 | | | | | | % 23.11/3.89 | | | | | | GROUND_INST: instantiating (3) with 0, all_80_0, all_32_5, all_45_0, % 23.11/3.89 | | | | | | simplifying with (45), (106) gives: % 23.11/3.89 | | | | | | (110) all_80_0 = 0 % 23.11/3.89 | | | | | | % 23.11/3.89 | | | | | | GROUND_INST: instantiating (3) with 0, all_80_1, all_32_7, all_52_0, % 23.11/3.89 | | | | | | simplifying with (53), (109) gives: % 23.11/3.89 | | | | | | (111) all_80_1 = 0 % 23.11/3.89 | | | | | | % 23.11/3.89 | | | | | | BETA: splitting (108) gives: % 23.11/3.89 | | | | | | % 23.11/3.89 | | | | | | Case 1: % 23.11/3.89 | | | | | | | % 23.11/3.89 | | | | | | | (112) ~ (all_80_0 = 0) % 23.11/3.89 | | | | | | | % 23.11/3.89 | | | | | | | REDUCE: (110), (112) imply: % 23.11/3.89 | | | | | | | (113) $false % 23.11/3.89 | | | | | | | % 23.11/3.89 | | | | | | | CLOSE: (113) is inconsistent. % 23.11/3.89 | | | | | | | % 23.11/3.89 | | | | | | Case 2: % 23.11/3.89 | | | | | | | % 23.11/3.89 | | | | | | | (114) ~ (all_80_1 = 0) % 23.11/3.89 | | | | | | | % 23.11/3.89 | | | | | | | REDUCE: (111), (114) imply: % 23.11/3.89 | | | | | | | (115) $false % 23.11/3.89 | | | | | | | % 23.11/3.89 | | | | | | | CLOSE: (115) is inconsistent. % 23.11/3.89 | | | | | | | % 23.11/3.89 | | | | | | End of split % 23.11/3.89 | | | | | | % 23.11/3.89 | | | | | Case 2: % 23.11/3.89 | | | | | | % 23.11/3.89 | | | | | | (116) ? [v0: $i] : (apply(all_32_9, v0, all_45_0) = 0 & % 23.11/3.89 | | | | | | apply(all_32_10, all_57_0, v0) = 0 & member(v0, all_32_6) % 23.11/3.89 | | | | | | = 0 & $i(v0)) % 23.11/3.89 | | | | | | % 23.11/3.89 | | | | | | DELTA: instantiating (116) with fresh symbol all_80_0 gives: % 23.11/3.89 | | | | | | (117) apply(all_32_9, all_80_0, all_45_0) = 0 & apply(all_32_10, % 23.11/3.89 | | | | | | all_57_0, all_80_0) = 0 & member(all_80_0, all_32_6) = 0 % 23.11/3.89 | | | | | | & $i(all_80_0) % 23.11/3.89 | | | | | | % 23.11/3.89 | | | | | | ALPHA: (117) implies: % 23.11/3.89 | | | | | | (118) $i(all_80_0) % 23.11/3.89 | | | | | | (119) member(all_80_0, all_32_6) = 0 % 23.11/3.89 | | | | | | (120) apply(all_32_10, all_57_0, all_80_0) = 0 % 23.11/3.89 | | | | | | (121) apply(all_32_9, all_80_0, all_45_0) = 0 % 23.11/3.89 | | | | | | % 23.11/3.89 | | | | | | REDUCE: (102), (120) imply: % 23.11/3.89 | | | | | | (122) apply(all_32_10, all_52_0, all_80_0) = 0 % 23.11/3.89 | | | | | | % 23.11/3.89 | | | | | | BETA: splitting (92) gives: % 23.11/3.89 | | | | | | % 23.11/3.89 | | | | | | Case 1: % 23.11/3.89 | | | | | | | % 23.11/3.89 | | | | | | | (123) ? [v0: any] : ? [v1: any] : (member(all_61_0, all_32_6) % 23.11/3.89 | | | | | | | = v1 & member(all_45_2, all_32_8) = v0 & ( ~ (v1 = 0) | % 23.11/3.89 | | | | | | | ~ (v0 = 0))) % 23.11/3.89 | | | | | | | % 23.11/3.89 | | | | | | | DELTA: instantiating (123) with fresh symbols all_85_0, all_85_1 % 23.11/3.89 | | | | | | | gives: % 23.11/3.89 | | | | | | | (124) member(all_61_0, all_32_6) = all_85_0 & member(all_45_2, % 23.11/3.89 | | | | | | | all_32_8) = all_85_1 & ( ~ (all_85_0 = 0) | ~ % 23.11/3.89 | | | | | | | (all_85_1 = 0)) % 23.11/3.89 | | | | | | | % 23.11/3.89 | | | | | | | ALPHA: (124) implies: % 23.11/3.89 | | | | | | | (125) member(all_45_2, all_32_8) = all_85_1 % 23.11/3.89 | | | | | | | (126) member(all_61_0, all_32_6) = all_85_0 % 23.11/3.89 | | | | | | | (127) ~ (all_85_0 = 0) | ~ (all_85_1 = 0) % 23.11/3.89 | | | | | | | % 23.11/3.89 | | | | | | | GROUND_INST: instantiating (3) with 0, all_85_1, all_32_8, % 23.11/3.89 | | | | | | | all_45_2, simplifying with (43), (125) gives: % 23.11/3.89 | | | | | | | (128) all_85_1 = 0 % 23.11/3.89 | | | | | | | % 23.11/3.89 | | | | | | | GROUND_INST: instantiating (3) with 0, all_85_0, all_32_6, % 23.11/3.89 | | | | | | | all_61_0, simplifying with (86), (126) gives: % 23.11/3.89 | | | | | | | (129) all_85_0 = 0 % 23.11/3.89 | | | | | | | % 23.11/3.89 | | | | | | | BETA: splitting (127) gives: % 23.11/3.89 | | | | | | | % 23.11/3.89 | | | | | | | Case 1: % 23.11/3.89 | | | | | | | | % 23.11/3.89 | | | | | | | | (130) ~ (all_85_0 = 0) % 23.11/3.89 | | | | | | | | % 23.11/3.89 | | | | | | | | REDUCE: (129), (130) imply: % 23.11/3.89 | | | | | | | | (131) $false % 23.11/3.89 | | | | | | | | % 23.11/3.89 | | | | | | | | CLOSE: (131) is inconsistent. % 23.11/3.89 | | | | | | | | % 23.11/3.89 | | | | | | | Case 2: % 23.11/3.89 | | | | | | | | % 23.11/3.89 | | | | | | | | (132) ~ (all_85_1 = 0) % 23.11/3.89 | | | | | | | | % 23.11/3.89 | | | | | | | | REDUCE: (128), (132) imply: % 23.11/3.89 | | | | | | | | (133) $false % 23.11/3.89 | | | | | | | | % 23.11/3.89 | | | | | | | | CLOSE: (133) is inconsistent. % 23.11/3.89 | | | | | | | | % 23.11/3.89 | | | | | | | End of split % 23.11/3.89 | | | | | | | % 23.11/3.89 | | | | | | Case 2: % 23.11/3.89 | | | | | | | % 23.11/3.89 | | | | | | | (134) ? [v0: $i] : (apply(all_32_10, v0, all_61_0) = 0 & % 23.11/3.89 | | | | | | | apply(all_32_11, all_45_2, v0) = 0 & member(v0, % 23.11/3.89 | | | | | | | all_32_7) = 0 & $i(v0)) % 23.11/3.89 | | | | | | | % 23.11/3.89 | | | | | | | DELTA: instantiating (134) with fresh symbol all_85_0 gives: % 23.11/3.89 | | | | | | | (135) apply(all_32_10, all_85_0, all_61_0) = 0 & % 23.11/3.89 | | | | | | | apply(all_32_11, all_45_2, all_85_0) = 0 & % 23.11/3.89 | | | | | | | member(all_85_0, all_32_7) = 0 & $i(all_85_0) % 23.11/3.89 | | | | | | | % 23.11/3.89 | | | | | | | ALPHA: (135) implies: % 23.11/3.89 | | | | | | | (136) $i(all_85_0) % 23.11/3.89 | | | | | | | (137) member(all_85_0, all_32_7) = 0 % 23.11/3.89 | | | | | | | (138) apply(all_32_11, all_45_2, all_85_0) = 0 % 23.11/3.89 | | | | | | | (139) apply(all_32_10, all_85_0, all_61_0) = 0 % 23.11/3.89 | | | | | | | % 23.11/3.89 | | | | | | | GROUND_INST: instantiating (32) with all_70_0, simplifying with % 23.11/3.89 | | | | | | | (99), (100) gives: % 23.11/3.89 | | | | | | | (140) ? [v0: $i] : (apply(all_32_9, all_70_0, v0) = 0 & % 23.11/3.89 | | | | | | | member(v0, all_32_5) = 0 & $i(v0)) % 23.11/3.89 | | | | | | | % 23.11/3.89 | | | | | | | GROUND_INST: instantiating (32) with all_80_0, simplifying with % 23.11/3.89 | | | | | | | (118), (119) gives: % 23.11/3.89 | | | | | | | (141) ? [v0: $i] : (apply(all_32_9, all_80_0, v0) = 0 & % 23.11/3.89 | | | | | | | member(v0, all_32_5) = 0 & $i(v0)) % 23.11/3.89 | | | | | | | % 23.11/3.89 | | | | | | | GROUND_INST: instantiating (29) with all_85_0, simplifying with % 23.11/3.89 | | | | | | | (136), (137) gives: % 23.11/3.89 | | | | | | | (142) ? [v0: $i] : (apply(all_32_10, all_85_0, v0) = 0 & % 23.11/3.89 | | | | | | | member(v0, all_32_6) = 0 & $i(v0)) % 23.11/3.89 | | | | | | | % 23.11/3.89 | | | | | | | GROUND_INST: instantiating (27) with all_45_2, all_85_0, all_52_0, % 23.11/3.89 | | | | | | | simplifying with (40), (52), (54), (136), (138) % 23.11/3.89 | | | | | | | gives: % 23.11/3.89 | | | | | | | (143) all_85_0 = all_52_0 | ? [v0: any] : ? [v1: any] : ? % 23.11/3.89 | | | | | | | [v2: any] : (member(all_85_0, all_32_7) = v1 & % 23.11/3.89 | | | | | | | member(all_52_0, all_32_7) = v2 & member(all_45_2, % 23.11/3.89 | | | | | | | all_32_8) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 % 23.11/3.89 | | | | | | | = 0))) % 23.11/3.89 | | | | | | | % 23.11/3.89 | | | | | | | GROUND_INST: instantiating (30) with all_52_0, all_80_0, all_70_0, % 23.11/3.89 | | | | | | | simplifying with (52), (99), (103), (118), (122) % 23.11/3.89 | | | | | | | gives: % 23.11/3.89 | | | | | | | (144) all_80_0 = all_70_0 | ? [v0: any] : ? [v1: any] : ? % 23.11/3.89 | | | | | | | [v2: any] : (member(all_80_0, all_32_6) = v1 & % 23.11/3.89 | | | | | | | member(all_70_0, all_32_6) = v2 & member(all_52_0, % 23.11/3.89 | | | | | | | all_32_7) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 % 23.11/3.89 | | | | | | | = 0))) % 23.11/3.89 | | | | | | | % 23.11/3.90 | | | | | | | GROUND_INST: instantiating (33) with all_61_0, all_68_0, all_45_1, % 23.11/3.90 | | | | | | | simplifying with (41), (85), (87), (95), (97) gives: % 23.11/3.90 | | | | | | | (145) all_68_0 = all_45_1 | ? [v0: any] : ? [v1: any] : ? % 23.11/3.90 | | | | | | | [v2: any] : (member(all_68_0, all_32_5) = v1 & % 23.11/3.90 | | | | | | | member(all_61_0, all_32_6) = v0 & member(all_45_1, % 23.11/3.90 | | | | | | | all_32_5) = v2 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 % 23.11/3.90 | | | | | | | = 0))) % 23.11/3.90 | | | | | | | % 23.11/3.90 | | | | | | | DELTA: instantiating (142) with fresh symbol all_92_0 gives: % 23.11/3.90 | | | | | | | (146) apply(all_32_10, all_85_0, all_92_0) = 0 & % 23.11/3.90 | | | | | | | member(all_92_0, all_32_6) = 0 & $i(all_92_0) % 23.11/3.90 | | | | | | | % 23.11/3.90 | | | | | | | ALPHA: (146) implies: % 23.11/3.90 | | | | | | | (147) $i(all_92_0) % 23.11/3.90 | | | | | | | (148) member(all_92_0, all_32_6) = 0 % 23.11/3.90 | | | | | | | (149) apply(all_32_10, all_85_0, all_92_0) = 0 % 23.11/3.90 | | | | | | | % 23.11/3.90 | | | | | | | DELTA: instantiating (140) with fresh symbol all_96_0 gives: % 23.11/3.90 | | | | | | | (150) apply(all_32_9, all_70_0, all_96_0) = 0 & % 23.11/3.90 | | | | | | | member(all_96_0, all_32_5) = 0 & $i(all_96_0) % 23.11/3.90 | | | | | | | % 23.11/3.90 | | | | | | | ALPHA: (150) implies: % 23.11/3.90 | | | | | | | (151) $i(all_96_0) % 23.11/3.90 | | | | | | | (152) member(all_96_0, all_32_5) = 0 % 23.11/3.90 | | | | | | | (153) apply(all_32_9, all_70_0, all_96_0) = 0 % 23.11/3.90 | | | | | | | % 23.11/3.90 | | | | | | | DELTA: instantiating (141) with fresh symbol all_98_0 gives: % 23.11/3.90 | | | | | | | (154) apply(all_32_9, all_80_0, all_98_0) = 0 & % 23.11/3.90 | | | | | | | member(all_98_0, all_32_5) = 0 & $i(all_98_0) % 23.11/3.90 | | | | | | | % 23.11/3.90 | | | | | | | ALPHA: (154) implies: % 23.11/3.90 | | | | | | | (155) $i(all_98_0) % 23.11/3.90 | | | | | | | (156) member(all_98_0, all_32_5) = 0 % 23.11/3.90 | | | | | | | (157) apply(all_32_9, all_80_0, all_98_0) = 0 % 23.11/3.90 | | | | | | | % 23.11/3.90 | | | | | | | BETA: splitting (144) gives: % 23.11/3.90 | | | | | | | % 23.11/3.90 | | | | | | | Case 1: % 23.11/3.90 | | | | | | | | % 23.11/3.90 | | | | | | | | (158) all_80_0 = all_70_0 % 23.11/3.90 | | | | | | | | % 23.11/3.90 | | | | | | | | REDUCE: (157), (158) imply: % 23.11/3.90 | | | | | | | | (159) apply(all_32_9, all_70_0, all_98_0) = 0 % 23.11/3.90 | | | | | | | | % 23.11/3.90 | | | | | | | | REDUCE: (121), (158) imply: % 23.11/3.90 | | | | | | | | (160) apply(all_32_9, all_70_0, all_45_0) = 0 % 23.11/3.90 | | | | | | | | % 23.11/3.90 | | | | | | | | BETA: splitting (143) gives: % 23.11/3.90 | | | | | | | | % 23.11/3.90 | | | | | | | | Case 1: % 23.11/3.90 | | | | | | | | | % 23.11/3.90 | | | | | | | | | (161) all_85_0 = all_52_0 % 23.11/3.90 | | | | | | | | | % 23.11/3.90 | | | | | | | | | REDUCE: (149), (161) imply: % 23.11/3.90 | | | | | | | | | (162) apply(all_32_10, all_52_0, all_92_0) = 0 % 23.11/3.90 | | | | | | | | | % 23.11/3.90 | | | | | | | | | REDUCE: (139), (161) imply: % 23.11/3.90 | | | | | | | | | (163) apply(all_32_10, all_52_0, all_61_0) = 0 % 23.11/3.90 | | | | | | | | | % 23.11/3.90 | | | | | | | | | GROUND_INST: instantiating (32) with all_92_0, simplifying with % 23.11/3.90 | | | | | | | | | (147), (148) gives: % 23.11/3.90 | | | | | | | | | (164) ? [v0: $i] : (apply(all_32_9, all_92_0, v0) = 0 & % 23.11/3.90 | | | | | | | | | member(v0, all_32_5) = 0 & $i(v0)) % 23.11/3.90 | | | | | | | | | % 23.11/3.90 | | | | | | | | | GROUND_INST: instantiating (30) with all_52_0, all_92_0, % 23.11/3.90 | | | | | | | | | all_70_0, simplifying with (52), (99), (103), % 23.11/3.90 | | | | | | | | | (147), (162) gives: % 23.11/3.90 | | | | | | | | | (165) all_92_0 = all_70_0 | ? [v0: any] : ? [v1: any] : % 23.11/3.90 | | | | | | | | | ? [v2: any] : (member(all_92_0, all_32_6) = v1 & % 23.11/3.90 | | | | | | | | | member(all_70_0, all_32_6) = v2 & member(all_52_0, % 23.11/3.90 | | | | | | | | | all_32_7) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ % 23.11/3.90 | | | | | | | | | (v0 = 0))) % 23.11/3.90 | | | | | | | | | % 23.11/3.90 | | | | | | | | | GROUND_INST: instantiating (30) with all_52_0, all_92_0, % 23.11/3.90 | | | | | | | | | all_61_0, simplifying with (52), (85), (147), % 23.11/3.90 | | | | | | | | | (162), (163) gives: % 23.11/3.90 | | | | | | | | | (166) all_92_0 = all_61_0 | ? [v0: any] : ? [v1: any] : % 23.11/3.90 | | | | | | | | | ? [v2: any] : (member(all_92_0, all_32_6) = v1 & % 23.11/3.90 | | | | | | | | | member(all_61_0, all_32_6) = v2 & member(all_52_0, % 23.11/3.90 | | | | | | | | | all_32_7) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ % 23.11/3.90 | | | | | | | | | (v0 = 0))) % 23.11/3.90 | | | | | | | | | % 23.11/3.90 | | | | | | | | | GROUND_INST: instantiating (33) with all_70_0, all_98_0, % 23.11/3.90 | | | | | | | | | all_96_0, simplifying with (99), (151), (153), % 23.11/3.90 | | | | | | | | | (155), (159) gives: % 23.11/3.90 | | | | | | | | | (167) all_98_0 = all_96_0 | ? [v0: any] : ? [v1: any] : % 23.11/3.90 | | | | | | | | | ? [v2: any] : (member(all_98_0, all_32_5) = v1 & % 23.11/3.90 | | | | | | | | | member(all_96_0, all_32_5) = v2 & member(all_70_0, % 23.11/3.90 | | | | | | | | | all_32_6) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ % 23.11/3.90 | | | | | | | | | (v0 = 0))) % 23.11/3.90 | | | | | | | | | % 23.11/3.90 | | | | | | | | | GROUND_INST: instantiating (33) with all_70_0, all_98_0, % 23.11/3.90 | | | | | | | | | all_45_0, simplifying with (42), (99), (155), % 23.11/3.90 | | | | | | | | | (159), (160) gives: % 23.11/3.90 | | | | | | | | | (168) all_98_0 = all_45_0 | ? [v0: any] : ? [v1: any] : % 23.11/3.90 | | | | | | | | | ? [v2: any] : (member(all_98_0, all_32_5) = v1 & % 23.11/3.90 | | | | | | | | | member(all_70_0, all_32_6) = v0 & member(all_45_0, % 23.11/3.90 | | | | | | | | | all_32_5) = v2 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ % 23.11/3.90 | | | | | | | | | (v0 = 0))) % 23.11/3.90 | | | | | | | | | % 23.11/3.90 | | | | | | | | | DELTA: instantiating (164) with fresh symbol all_127_0 gives: % 23.11/3.90 | | | | | | | | | (169) apply(all_32_9, all_92_0, all_127_0) = 0 & % 23.11/3.90 | | | | | | | | | member(all_127_0, all_32_5) = 0 & $i(all_127_0) % 23.11/3.90 | | | | | | | | | % 23.11/3.90 | | | | | | | | | ALPHA: (169) implies: % 23.11/3.90 | | | | | | | | | (170) $i(all_127_0) % 23.11/3.90 | | | | | | | | | (171) member(all_127_0, all_32_5) = 0 % 23.11/3.90 | | | | | | | | | (172) apply(all_32_9, all_92_0, all_127_0) = 0 % 23.11/3.90 | | | | | | | | | % 23.11/3.90 | | | | | | | | | BETA: splitting (166) gives: % 23.11/3.90 | | | | | | | | | % 23.11/3.90 | | | | | | | | | Case 1: % 23.11/3.90 | | | | | | | | | | % 23.11/3.90 | | | | | | | | | | (173) all_92_0 = all_61_0 % 23.11/3.90 | | | | | | | | | | % 23.11/3.90 | | | | | | | | | | REDUCE: (172), (173) imply: % 23.11/3.90 | | | | | | | | | | (174) apply(all_32_9, all_61_0, all_127_0) = 0 % 23.11/3.90 | | | | | | | | | | % 23.11/3.90 | | | | | | | | | | BETA: splitting (165) gives: % 23.11/3.90 | | | | | | | | | | % 23.11/3.90 | | | | | | | | | | Case 1: % 23.11/3.90 | | | | | | | | | | | % 23.11/3.90 | | | | | | | | | | | (175) all_92_0 = all_70_0 % 23.11/3.90 | | | | | | | | | | | % 23.11/3.90 | | | | | | | | | | | COMBINE_EQS: (173), (175) imply: % 23.11/3.90 | | | | | | | | | | | (176) all_70_0 = all_61_0 % 23.11/3.90 | | | | | | | | | | | % 23.11/3.90 | | | | | | | | | | | SIMP: (176) implies: % 23.11/3.90 | | | | | | | | | | | (177) all_70_0 = all_61_0 % 23.11/3.90 | | | | | | | | | | | % 23.11/3.90 | | | | | | | | | | | REDUCE: (160), (177) imply: % 23.11/3.90 | | | | | | | | | | | (178) apply(all_32_9, all_61_0, all_45_0) = 0 % 23.11/3.90 | | | | | | | | | | | % 23.11/3.90 | | | | | | | | | | | GROUND_INST: instantiating (33) with all_61_0, all_127_0, % 23.11/3.90 | | | | | | | | | | | all_45_1, simplifying with (41), (85), (87), % 23.11/3.90 | | | | | | | | | | | (170), (174) gives: % 23.11/3.90 | | | | | | | | | | | (179) all_127_0 = all_45_1 | ? [v0: any] : ? [v1: any] % 23.11/3.90 | | | | | | | | | | | : ? [v2: any] : (member(all_127_0, all_32_5) = v1 % 23.11/3.90 | | | | | | | | | | | & member(all_61_0, all_32_6) = v0 & % 23.11/3.90 | | | | | | | | | | | member(all_45_1, all_32_5) = v2 & ( ~ (v2 = 0) | % 23.11/3.90 | | | | | | | | | | | ~ (v1 = 0) | ~ (v0 = 0))) % 23.11/3.90 | | | | | | | | | | | % 23.11/3.90 | | | | | | | | | | | GROUND_INST: instantiating (33) with all_61_0, all_127_0, % 23.11/3.90 | | | | | | | | | | | all_45_0, simplifying with (42), (85), (170), % 23.11/3.90 | | | | | | | | | | | (174), (178) gives: % 23.11/3.90 | | | | | | | | | | | (180) all_127_0 = all_45_0 | ? [v0: any] : ? [v1: any] % 23.11/3.90 | | | | | | | | | | | : ? [v2: any] : (member(all_127_0, all_32_5) = v1 % 23.11/3.90 | | | | | | | | | | | & member(all_61_0, all_32_6) = v0 & % 23.11/3.90 | | | | | | | | | | | member(all_45_0, all_32_5) = v2 & ( ~ (v2 = 0) | % 23.11/3.90 | | | | | | | | | | | ~ (v1 = 0) | ~ (v0 = 0))) % 23.11/3.90 | | | | | | | | | | | % 23.11/3.90 | | | | | | | | | | | BETA: splitting (180) gives: % 23.11/3.90 | | | | | | | | | | | % 23.11/3.90 | | | | | | | | | | | Case 1: % 23.11/3.90 | | | | | | | | | | | | % 23.11/3.90 | | | | | | | | | | | | (181) all_127_0 = all_45_0 % 23.11/3.90 | | | | | | | | | | | | % 23.11/3.90 | | | | | | | | | | | | BETA: splitting (179) gives: % 23.11/3.90 | | | | | | | | | | | | % 23.11/3.90 | | | | | | | | | | | | Case 1: % 23.11/3.90 | | | | | | | | | | | | | % 23.11/3.90 | | | | | | | | | | | | | (182) all_127_0 = all_45_1 % 23.11/3.90 | | | | | | | | | | | | | % 23.11/3.90 | | | | | | | | | | | | | COMBINE_EQS: (181), (182) imply: % 23.11/3.90 | | | | | | | | | | | | | (183) all_45_0 = all_45_1 % 23.11/3.90 | | | | | | | | | | | | | % 23.11/3.90 | | | | | | | | | | | | | REDUCE: (39), (183) imply: % 23.11/3.90 | | | | | | | | | | | | | (184) $false % 23.11/3.90 | | | | | | | | | | | | | % 23.11/3.90 | | | | | | | | | | | | | CLOSE: (184) is inconsistent. % 23.11/3.90 | | | | | | | | | | | | | % 23.11/3.90 | | | | | | | | | | | | Case 2: % 23.11/3.90 | | | | | | | | | | | | | % 23.11/3.90 | | | | | | | | | | | | | (185) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 23.11/3.90 | | | | | | | | | | | | | (member(all_127_0, all_32_5) = v1 & % 23.11/3.90 | | | | | | | | | | | | | member(all_61_0, all_32_6) = v0 & % 23.11/3.90 | | | | | | | | | | | | | member(all_45_1, all_32_5) = v2 & ( ~ (v2 = 0) | % 23.11/3.90 | | | | | | | | | | | | | ~ (v1 = 0) | ~ (v0 = 0))) % 23.11/3.91 | | | | | | | | | | | | | % 23.11/3.91 | | | | | | | | | | | | | DELTA: instantiating (185) with fresh symbols all_164_0, % 23.11/3.91 | | | | | | | | | | | | | all_164_1, all_164_2 gives: % 23.11/3.91 | | | | | | | | | | | | | (186) member(all_127_0, all_32_5) = all_164_1 & % 23.11/3.91 | | | | | | | | | | | | | member(all_61_0, all_32_6) = all_164_2 & % 23.11/3.91 | | | | | | | | | | | | | member(all_45_1, all_32_5) = all_164_0 & ( ~ % 23.11/3.91 | | | | | | | | | | | | | (all_164_0 = 0) | ~ (all_164_1 = 0) | ~ % 23.11/3.91 | | | | | | | | | | | | | (all_164_2 = 0)) % 23.11/3.91 | | | | | | | | | | | | | % 23.11/3.91 | | | | | | | | | | | | | ALPHA: (186) implies: % 23.11/3.91 | | | | | | | | | | | | | (187) member(all_45_1, all_32_5) = all_164_0 % 23.11/3.91 | | | | | | | | | | | | | (188) member(all_61_0, all_32_6) = all_164_2 % 23.11/3.91 | | | | | | | | | | | | | (189) member(all_127_0, all_32_5) = all_164_1 % 23.11/3.91 | | | | | | | | | | | | | (190) ~ (all_164_0 = 0) | ~ (all_164_1 = 0) | ~ % 23.11/3.91 | | | | | | | | | | | | | (all_164_2 = 0) % 23.11/3.91 | | | | | | | | | | | | | % 23.11/3.91 | | | | | | | | | | | | | REDUCE: (181), (189) imply: % 23.11/3.91 | | | | | | | | | | | | | (191) member(all_45_0, all_32_5) = all_164_1 % 23.11/3.91 | | | | | | | | | | | | | % 23.11/3.91 | | | | | | | | | | | | | GROUND_INST: instantiating (3) with 0, all_164_0, all_32_5, % 23.11/3.91 | | | | | | | | | | | | | all_45_1, simplifying with (44), (187) gives: % 23.11/3.91 | | | | | | | | | | | | | (192) all_164_0 = 0 % 23.11/3.91 | | | | | | | | | | | | | % 23.11/3.91 | | | | | | | | | | | | | GROUND_INST: instantiating (3) with 0, all_164_1, all_32_5, % 23.11/3.91 | | | | | | | | | | | | | all_45_0, simplifying with (45), (191) gives: % 23.11/3.91 | | | | | | | | | | | | | (193) all_164_1 = 0 % 23.11/3.91 | | | | | | | | | | | | | % 23.11/3.91 | | | | | | | | | | | | | GROUND_INST: instantiating (3) with 0, all_164_2, all_32_6, % 23.11/3.91 | | | | | | | | | | | | | all_61_0, simplifying with (86), (188) gives: % 23.11/3.91 | | | | | | | | | | | | | (194) all_164_2 = 0 % 23.11/3.91 | | | | | | | | | | | | | % 23.11/3.91 | | | | | | | | | | | | | BETA: splitting (190) gives: % 23.11/3.91 | | | | | | | | | | | | | % 23.11/3.91 | | | | | | | | | | | | | Case 1: % 23.11/3.91 | | | | | | | | | | | | | | % 23.11/3.91 | | | | | | | | | | | | | | (195) ~ (all_164_0 = 0) % 23.11/3.91 | | | | | | | | | | | | | | % 23.11/3.91 | | | | | | | | | | | | | | REDUCE: (192), (195) imply: % 23.11/3.91 | | | | | | | | | | | | | | (196) $false % 23.11/3.91 | | | | | | | | | | | | | | % 23.11/3.91 | | | | | | | | | | | | | | CLOSE: (196) is inconsistent. % 23.11/3.91 | | | | | | | | | | | | | | % 23.11/3.91 | | | | | | | | | | | | | Case 2: % 23.11/3.91 | | | | | | | | | | | | | | % 23.11/3.91 | | | | | | | | | | | | | | (197) ~ (all_164_1 = 0) | ~ (all_164_2 = 0) % 23.11/3.91 | | | | | | | | | | | | | | % 23.11/3.91 | | | | | | | | | | | | | | BETA: splitting (197) gives: % 23.11/3.91 | | | | | | | | | | | | | | % 23.11/3.91 | | | | | | | | | | | | | | Case 1: % 23.11/3.91 | | | | | | | | | | | | | | | % 23.11/3.91 | | | | | | | | | | | | | | | (198) ~ (all_164_1 = 0) % 23.11/3.91 | | | | | | | | | | | | | | | % 23.11/3.91 | | | | | | | | | | | | | | | REDUCE: (193), (198) imply: % 23.11/3.91 | | | | | | | | | | | | | | | (199) $false % 23.11/3.91 | | | | | | | | | | | | | | | % 23.11/3.91 | | | | | | | | | | | | | | | CLOSE: (199) is inconsistent. % 23.11/3.91 | | | | | | | | | | | | | | | % 23.11/3.91 | | | | | | | | | | | | | | Case 2: % 23.11/3.91 | | | | | | | | | | | | | | | % 23.11/3.91 | | | | | | | | | | | | | | | (200) ~ (all_164_2 = 0) % 23.11/3.91 | | | | | | | | | | | | | | | % 23.11/3.91 | | | | | | | | | | | | | | | REDUCE: (194), (200) imply: % 23.11/3.91 | | | | | | | | | | | | | | | (201) $false % 23.11/3.91 | | | | | | | | | | | | | | | % 23.11/3.91 | | | | | | | | | | | | | | | CLOSE: (201) is inconsistent. % 23.11/3.91 | | | | | | | | | | | | | | | % 23.11/3.91 | | | | | | | | | | | | | | End of split % 23.11/3.91 | | | | | | | | | | | | | | % 23.11/3.91 | | | | | | | | | | | | | End of split % 23.11/3.91 | | | | | | | | | | | | | % 23.11/3.91 | | | | | | | | | | | | End of split % 23.11/3.91 | | | | | | | | | | | | % 23.11/3.91 | | | | | | | | | | | Case 2: % 23.11/3.91 | | | | | | | | | | | | % 23.11/3.91 | | | | | | | | | | | | (202) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 23.11/3.91 | | | | | | | | | | | | (member(all_127_0, all_32_5) = v1 & % 23.11/3.91 | | | | | | | | | | | | member(all_61_0, all_32_6) = v0 & % 23.11/3.91 | | | | | | | | | | | | member(all_45_0, all_32_5) = v2 & ( ~ (v2 = 0) | % 23.11/3.91 | | | | | | | | | | | | ~ (v1 = 0) | ~ (v0 = 0))) % 23.11/3.91 | | | | | | | | | | | | % 23.11/3.91 | | | | | | | | | | | | DELTA: instantiating (202) with fresh symbols all_160_0, % 23.11/3.91 | | | | | | | | | | | | all_160_1, all_160_2 gives: % 23.11/3.91 | | | | | | | | | | | | (203) member(all_127_0, all_32_5) = all_160_1 & % 23.11/3.91 | | | | | | | | | | | | member(all_61_0, all_32_6) = all_160_2 & % 23.11/3.91 | | | | | | | | | | | | member(all_45_0, all_32_5) = all_160_0 & ( ~ % 23.11/3.91 | | | | | | | | | | | | (all_160_0 = 0) | ~ (all_160_1 = 0) | ~ % 23.11/3.91 | | | | | | | | | | | | (all_160_2 = 0)) % 23.11/3.91 | | | | | | | | | | | | % 23.11/3.91 | | | | | | | | | | | | ALPHA: (203) implies: % 23.11/3.91 | | | | | | | | | | | | (204) member(all_45_0, all_32_5) = all_160_0 % 23.11/3.91 | | | | | | | | | | | | (205) member(all_61_0, all_32_6) = all_160_2 % 23.11/3.91 | | | | | | | | | | | | (206) member(all_127_0, all_32_5) = all_160_1 % 23.11/3.91 | | | | | | | | | | | | (207) ~ (all_160_0 = 0) | ~ (all_160_1 = 0) | ~ % 23.11/3.91 | | | | | | | | | | | | (all_160_2 = 0) % 23.11/3.91 | | | | | | | | | | | | % 23.11/3.91 | | | | | | | | | | | | GROUND_INST: instantiating (3) with 0, all_160_0, all_32_5, % 23.11/3.91 | | | | | | | | | | | | all_45_0, simplifying with (45), (204) gives: % 23.11/3.91 | | | | | | | | | | | | (208) all_160_0 = 0 % 23.11/3.91 | | | | | | | | | | | | % 23.11/3.91 | | | | | | | | | | | | GROUND_INST: instantiating (3) with 0, all_160_2, all_32_6, % 23.11/3.91 | | | | | | | | | | | | all_61_0, simplifying with (86), (205) gives: % 23.11/3.91 | | | | | | | | | | | | (209) all_160_2 = 0 % 23.11/3.91 | | | | | | | | | | | | % 23.11/3.91 | | | | | | | | | | | | GROUND_INST: instantiating (3) with 0, all_160_1, all_32_5, % 23.11/3.91 | | | | | | | | | | | | all_127_0, simplifying with (171), (206) gives: % 23.11/3.91 | | | | | | | | | | | | (210) all_160_1 = 0 % 23.11/3.91 | | | | | | | | | | | | % 23.11/3.91 | | | | | | | | | | | | BETA: splitting (207) gives: % 23.11/3.91 | | | | | | | | | | | | % 23.11/3.91 | | | | | | | | | | | | Case 1: % 23.11/3.91 | | | | | | | | | | | | | % 23.11/3.91 | | | | | | | | | | | | | (211) ~ (all_160_0 = 0) % 23.11/3.91 | | | | | | | | | | | | | % 23.11/3.91 | | | | | | | | | | | | | REDUCE: (208), (211) imply: % 23.11/3.91 | | | | | | | | | | | | | (212) $false % 23.11/3.91 | | | | | | | | | | | | | % 23.11/3.91 | | | | | | | | | | | | | CLOSE: (212) is inconsistent. % 23.11/3.91 | | | | | | | | | | | | | % 23.11/3.91 | | | | | | | | | | | | Case 2: % 23.11/3.91 | | | | | | | | | | | | | % 23.11/3.91 | | | | | | | | | | | | | (213) ~ (all_160_1 = 0) | ~ (all_160_2 = 0) % 23.11/3.91 | | | | | | | | | | | | | % 23.11/3.91 | | | | | | | | | | | | | BETA: splitting (213) gives: % 23.11/3.91 | | | | | | | | | | | | | % 23.11/3.91 | | | | | | | | | | | | | Case 1: % 23.11/3.91 | | | | | | | | | | | | | | % 23.11/3.91 | | | | | | | | | | | | | | (214) ~ (all_160_1 = 0) % 23.11/3.91 | | | | | | | | | | | | | | % 23.11/3.91 | | | | | | | | | | | | | | REDUCE: (210), (214) imply: % 23.11/3.91 | | | | | | | | | | | | | | (215) $false % 23.11/3.91 | | | | | | | | | | | | | | % 23.11/3.91 | | | | | | | | | | | | | | CLOSE: (215) is inconsistent. % 23.11/3.91 | | | | | | | | | | | | | | % 23.11/3.91 | | | | | | | | | | | | | Case 2: % 23.11/3.91 | | | | | | | | | | | | | | % 23.11/3.91 | | | | | | | | | | | | | | (216) ~ (all_160_2 = 0) % 23.11/3.91 | | | | | | | | | | | | | | % 23.11/3.91 | | | | | | | | | | | | | | REDUCE: (209), (216) imply: % 23.11/3.91 | | | | | | | | | | | | | | (217) $false % 23.11/3.91 | | | | | | | | | | | | | | % 23.11/3.91 | | | | | | | | | | | | | | CLOSE: (217) is inconsistent. % 23.11/3.91 | | | | | | | | | | | | | | % 23.11/3.91 | | | | | | | | | | | | | End of split % 23.11/3.91 | | | | | | | | | | | | | % 23.11/3.91 | | | | | | | | | | | | End of split % 23.11/3.91 | | | | | | | | | | | | % 23.11/3.91 | | | | | | | | | | | End of split % 23.11/3.91 | | | | | | | | | | | % 23.11/3.91 | | | | | | | | | | Case 2: % 23.11/3.91 | | | | | | | | | | | % 23.11/3.91 | | | | | | | | | | | (218) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 23.11/3.91 | | | | | | | | | | | (member(all_92_0, all_32_6) = v1 & % 23.11/3.91 | | | | | | | | | | | member(all_70_0, all_32_6) = v2 & % 23.11/3.91 | | | | | | | | | | | member(all_52_0, all_32_7) = v0 & ( ~ (v2 = 0) | % 23.11/3.91 | | | | | | | | | | | ~ (v1 = 0) | ~ (v0 = 0))) % 23.11/3.91 | | | | | | | | | | | % 23.11/3.91 | | | | | | | | | | | DELTA: instantiating (218) with fresh symbols all_137_0, % 23.11/3.91 | | | | | | | | | | | all_137_1, all_137_2 gives: % 23.11/3.91 | | | | | | | | | | | (219) member(all_92_0, all_32_6) = all_137_1 & % 23.11/3.91 | | | | | | | | | | | member(all_70_0, all_32_6) = all_137_0 & % 23.11/3.91 | | | | | | | | | | | member(all_52_0, all_32_7) = all_137_2 & ( ~ % 23.11/3.91 | | | | | | | | | | | (all_137_0 = 0) | ~ (all_137_1 = 0) | ~ % 23.11/3.91 | | | | | | | | | | | (all_137_2 = 0)) % 23.11/3.91 | | | | | | | | | | | % 23.11/3.91 | | | | | | | | | | | ALPHA: (219) implies: % 23.11/3.91 | | | | | | | | | | | (220) member(all_52_0, all_32_7) = all_137_2 % 23.11/3.91 | | | | | | | | | | | (221) member(all_70_0, all_32_6) = all_137_0 % 23.11/3.91 | | | | | | | | | | | (222) member(all_92_0, all_32_6) = all_137_1 % 23.11/3.91 | | | | | | | | | | | (223) ~ (all_137_0 = 0) | ~ (all_137_1 = 0) | ~ % 23.11/3.91 | | | | | | | | | | | (all_137_2 = 0) % 23.11/3.91 | | | | | | | | | | | % 23.11/3.91 | | | | | | | | | | | REDUCE: (173), (222) imply: % 23.11/3.91 | | | | | | | | | | | (224) member(all_61_0, all_32_6) = all_137_1 % 23.11/3.91 | | | | | | | | | | | % 23.11/3.91 | | | | | | | | | | | GROUND_INST: instantiating (3) with 0, all_137_2, all_32_7, % 23.11/3.91 | | | | | | | | | | | all_52_0, simplifying with (53), (220) gives: % 23.11/3.91 | | | | | | | | | | | (225) all_137_2 = 0 % 23.11/3.91 | | | | | | | | | | | % 23.11/3.91 | | | | | | | | | | | GROUND_INST: instantiating (3) with 0, all_137_1, all_32_6, % 23.11/3.91 | | | | | | | | | | | all_61_0, simplifying with (86), (224) gives: % 23.11/3.91 | | | | | | | | | | | (226) all_137_1 = 0 % 23.11/3.91 | | | | | | | | | | | % 23.11/3.91 | | | | | | | | | | | GROUND_INST: instantiating (3) with 0, all_137_0, all_32_6, % 23.11/3.91 | | | | | | | | | | | all_70_0, simplifying with (100), (221) gives: % 23.11/3.91 | | | | | | | | | | | (227) all_137_0 = 0 % 23.11/3.91 | | | | | | | | | | | % 23.11/3.91 | | | | | | | | | | | BETA: splitting (223) gives: % 23.11/3.91 | | | | | | | | | | | % 23.11/3.91 | | | | | | | | | | | Case 1: % 23.11/3.91 | | | | | | | | | | | | % 23.11/3.91 | | | | | | | | | | | | (228) ~ (all_137_0 = 0) % 23.11/3.91 | | | | | | | | | | | | % 23.11/3.91 | | | | | | | | | | | | REDUCE: (227), (228) imply: % 23.11/3.91 | | | | | | | | | | | | (229) $false % 23.11/3.91 | | | | | | | | | | | | % 23.11/3.91 | | | | | | | | | | | | CLOSE: (229) is inconsistent. % 23.11/3.91 | | | | | | | | | | | | % 23.11/3.91 | | | | | | | | | | | Case 2: % 23.11/3.91 | | | | | | | | | | | | % 23.11/3.91 | | | | | | | | | | | | (230) ~ (all_137_1 = 0) | ~ (all_137_2 = 0) % 23.11/3.91 | | | | | | | | | | | | % 23.11/3.91 | | | | | | | | | | | | BETA: splitting (230) gives: % 23.11/3.91 | | | | | | | | | | | | % 23.11/3.91 | | | | | | | | | | | | Case 1: % 23.11/3.91 | | | | | | | | | | | | | % 23.11/3.91 | | | | | | | | | | | | | (231) ~ (all_137_1 = 0) % 23.11/3.91 | | | | | | | | | | | | | % 23.11/3.91 | | | | | | | | | | | | | REDUCE: (226), (231) imply: % 23.11/3.91 | | | | | | | | | | | | | (232) $false % 23.11/3.91 | | | | | | | | | | | | | % 23.11/3.91 | | | | | | | | | | | | | CLOSE: (232) is inconsistent. % 23.11/3.91 | | | | | | | | | | | | | % 23.11/3.91 | | | | | | | | | | | | Case 2: % 23.11/3.91 | | | | | | | | | | | | | % 23.11/3.91 | | | | | | | | | | | | | (233) ~ (all_137_2 = 0) % 23.11/3.91 | | | | | | | | | | | | | % 23.11/3.91 | | | | | | | | | | | | | REDUCE: (225), (233) imply: % 23.11/3.91 | | | | | | | | | | | | | (234) $false % 23.11/3.91 | | | | | | | | | | | | | % 23.11/3.91 | | | | | | | | | | | | | CLOSE: (234) is inconsistent. % 23.11/3.91 | | | | | | | | | | | | | % 23.11/3.91 | | | | | | | | | | | | End of split % 23.11/3.91 | | | | | | | | | | | | % 23.11/3.91 | | | | | | | | | | | End of split % 23.11/3.91 | | | | | | | | | | | % 23.11/3.91 | | | | | | | | | | End of split % 23.11/3.91 | | | | | | | | | | % 23.11/3.91 | | | | | | | | | Case 2: % 23.11/3.91 | | | | | | | | | | % 23.11/3.91 | | | | | | | | | | (235) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 23.11/3.91 | | | | | | | | | | (member(all_92_0, all_32_6) = v1 & member(all_61_0, % 23.11/3.91 | | | | | | | | | | all_32_6) = v2 & member(all_52_0, all_32_7) = % 23.11/3.91 | | | | | | | | | | v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0))) % 23.11/3.91 | | | | | | | | | | % 23.11/3.91 | | | | | | | | | | DELTA: instantiating (235) with fresh symbols all_133_0, % 23.11/3.91 | | | | | | | | | | all_133_1, all_133_2 gives: % 23.11/3.91 | | | | | | | | | | (236) member(all_92_0, all_32_6) = all_133_1 & % 23.11/3.91 | | | | | | | | | | member(all_61_0, all_32_6) = all_133_0 & % 23.11/3.91 | | | | | | | | | | member(all_52_0, all_32_7) = all_133_2 & ( ~ % 23.11/3.91 | | | | | | | | | | (all_133_0 = 0) | ~ (all_133_1 = 0) | ~ % 23.11/3.91 | | | | | | | | | | (all_133_2 = 0)) % 23.11/3.91 | | | | | | | | | | % 23.11/3.91 | | | | | | | | | | ALPHA: (236) implies: % 23.11/3.91 | | | | | | | | | | (237) member(all_52_0, all_32_7) = all_133_2 % 23.11/3.91 | | | | | | | | | | (238) member(all_61_0, all_32_6) = all_133_0 % 23.11/3.91 | | | | | | | | | | (239) member(all_92_0, all_32_6) = all_133_1 % 23.11/3.91 | | | | | | | | | | (240) ~ (all_133_0 = 0) | ~ (all_133_1 = 0) | ~ % 23.11/3.91 | | | | | | | | | | (all_133_2 = 0) % 23.11/3.91 | | | | | | | | | | % 23.11/3.91 | | | | | | | | | | BETA: splitting (168) gives: % 23.11/3.91 | | | | | | | | | | % 23.11/3.91 | | | | | | | | | | Case 1: % 23.11/3.92 | | | | | | | | | | | % 23.11/3.92 | | | | | | | | | | | (241) all_98_0 = all_45_0 % 23.11/3.92 | | | | | | | | | | | % 23.11/3.92 | | | | | | | | | | | BETA: splitting (167) gives: % 23.11/3.92 | | | | | | | | | | | % 23.11/3.92 | | | | | | | | | | | Case 1: % 23.11/3.92 | | | | | | | | | | | | % 23.11/3.92 | | | | | | | | | | | | % 23.11/3.92 | | | | | | | | | | | | GROUND_INST: instantiating (3) with 0, all_133_2, all_32_7, % 23.11/3.92 | | | | | | | | | | | | all_52_0, simplifying with (53), (237) gives: % 23.11/3.92 | | | | | | | | | | | | (242) all_133_2 = 0 % 23.11/3.92 | | | | | | | | | | | | % 23.11/3.92 | | | | | | | | | | | | GROUND_INST: instantiating (3) with 0, all_133_0, all_32_6, % 23.11/3.92 | | | | | | | | | | | | all_61_0, simplifying with (86), (238) gives: % 23.11/3.92 | | | | | | | | | | | | (243) all_133_0 = 0 % 23.11/3.92 | | | | | | | | | | | | % 23.11/3.92 | | | | | | | | | | | | GROUND_INST: instantiating (3) with 0, all_133_1, all_32_6, % 23.11/3.92 | | | | | | | | | | | | all_92_0, simplifying with (148), (239) gives: % 23.11/3.92 | | | | | | | | | | | | (244) all_133_1 = 0 % 23.11/3.92 | | | | | | | | | | | | % 23.11/3.92 | | | | | | | | | | | | REF_CLOSE: (240), (242), (243), (244) are inconsistent by % 23.11/3.92 | | | | | | | | | | | | sub-proof #1. % 23.11/3.92 | | | | | | | | | | | | % 23.11/3.92 | | | | | | | | | | | Case 2: % 23.11/3.92 | | | | | | | | | | | | % 23.11/3.92 | | | | | | | | | | | | (245) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 23.11/3.92 | | | | | | | | | | | | (member(all_98_0, all_32_5) = v1 & % 23.11/3.92 | | | | | | | | | | | | member(all_96_0, all_32_5) = v2 & % 23.11/3.92 | | | | | | | | | | | | member(all_70_0, all_32_6) = v0 & ( ~ (v2 = 0) | % 23.11/3.92 | | | | | | | | | | | | ~ (v1 = 0) | ~ (v0 = 0))) % 23.11/3.92 | | | | | | | | | | | | % 23.11/3.92 | | | | | | | | | | | | DELTA: instantiating (245) with fresh symbols all_147_0, % 23.11/3.92 | | | | | | | | | | | | all_147_1, all_147_2 gives: % 23.11/3.92 | | | | | | | | | | | | (246) member(all_98_0, all_32_5) = all_147_1 & % 23.11/3.92 | | | | | | | | | | | | member(all_96_0, all_32_5) = all_147_0 & % 23.11/3.92 | | | | | | | | | | | | member(all_70_0, all_32_6) = all_147_2 & ( ~ % 23.11/3.92 | | | | | | | | | | | | (all_147_0 = 0) | ~ (all_147_1 = 0) | ~ % 23.11/3.92 | | | | | | | | | | | | (all_147_2 = 0)) % 23.11/3.92 | | | | | | | | | | | | % 23.11/3.92 | | | | | | | | | | | | ALPHA: (246) implies: % 23.11/3.92 | | | | | | | | | | | | (247) member(all_70_0, all_32_6) = all_147_2 % 23.11/3.92 | | | | | | | | | | | | (248) member(all_96_0, all_32_5) = all_147_0 % 23.11/3.92 | | | | | | | | | | | | (249) member(all_98_0, all_32_5) = all_147_1 % 23.11/3.92 | | | | | | | | | | | | (250) ~ (all_147_0 = 0) | ~ (all_147_1 = 0) | ~ % 23.11/3.92 | | | | | | | | | | | | (all_147_2 = 0) % 23.11/3.92 | | | | | | | | | | | | % 23.11/3.92 | | | | | | | | | | | | REDUCE: (241), (249) imply: % 23.11/3.92 | | | | | | | | | | | | (251) member(all_45_0, all_32_5) = all_147_1 % 23.11/3.92 | | | | | | | | | | | | % 23.11/3.92 | | | | | | | | | | | | GROUND_INST: instantiating (3) with 0, all_147_1, all_32_5, % 23.11/3.92 | | | | | | | | | | | | all_45_0, simplifying with (45), (251) gives: % 23.11/3.92 | | | | | | | | | | | | (252) all_147_1 = 0 % 23.11/3.92 | | | | | | | | | | | | % 23.11/3.92 | | | | | | | | | | | | GROUND_INST: instantiating (3) with 0, all_147_2, all_32_6, % 23.11/3.92 | | | | | | | | | | | | all_70_0, simplifying with (100), (247) gives: % 23.11/3.92 | | | | | | | | | | | | (253) all_147_2 = 0 % 23.11/3.92 | | | | | | | | | | | | % 23.11/3.92 | | | | | | | | | | | | GROUND_INST: instantiating (3) with 0, all_147_0, all_32_5, % 23.11/3.92 | | | | | | | | | | | | all_96_0, simplifying with (152), (248) gives: % 23.11/3.92 | | | | | | | | | | | | (254) all_147_0 = 0 % 23.11/3.92 | | | | | | | | | | | | % 23.11/3.92 | | | | | | | | | | | | BETA: splitting (250) gives: % 23.11/3.92 | | | | | | | | | | | | % 23.11/3.92 | | | | | | | | | | | | Case 1: % 23.11/3.92 | | | | | | | | | | | | | % 23.11/3.92 | | | | | | | | | | | | | (255) ~ (all_147_0 = 0) % 23.11/3.92 | | | | | | | | | | | | | % 23.11/3.92 | | | | | | | | | | | | | REDUCE: (254), (255) imply: % 23.11/3.92 | | | | | | | | | | | | | (256) $false % 23.11/3.92 | | | | | | | | | | | | | % 23.11/3.92 | | | | | | | | | | | | | CLOSE: (256) is inconsistent. % 23.11/3.92 | | | | | | | | | | | | | % 23.11/3.92 | | | | | | | | | | | | Case 2: % 23.11/3.92 | | | | | | | | | | | | | % 23.11/3.92 | | | | | | | | | | | | | (257) ~ (all_147_1 = 0) | ~ (all_147_2 = 0) % 23.11/3.92 | | | | | | | | | | | | | % 23.11/3.92 | | | | | | | | | | | | | BETA: splitting (257) gives: % 23.11/3.92 | | | | | | | | | | | | | % 23.11/3.92 | | | | | | | | | | | | | Case 1: % 23.11/3.92 | | | | | | | | | | | | | | % 23.11/3.92 | | | | | | | | | | | | | | (258) ~ (all_147_1 = 0) % 23.11/3.92 | | | | | | | | | | | | | | % 23.11/3.92 | | | | | | | | | | | | | | REDUCE: (252), (258) imply: % 23.11/3.92 | | | | | | | | | | | | | | (259) $false % 23.11/3.92 | | | | | | | | | | | | | | % 23.11/3.92 | | | | | | | | | | | | | | CLOSE: (259) is inconsistent. % 23.11/3.92 | | | | | | | | | | | | | | % 23.11/3.92 | | | | | | | | | | | | | Case 2: % 23.11/3.92 | | | | | | | | | | | | | | % 23.11/3.92 | | | | | | | | | | | | | | (260) ~ (all_147_2 = 0) % 23.11/3.92 | | | | | | | | | | | | | | % 23.11/3.92 | | | | | | | | | | | | | | REDUCE: (253), (260) imply: % 23.11/3.92 | | | | | | | | | | | | | | (261) $false % 23.11/3.92 | | | | | | | | | | | | | | % 23.11/3.92 | | | | | | | | | | | | | | CLOSE: (261) is inconsistent. % 23.11/3.92 | | | | | | | | | | | | | | % 23.11/3.92 | | | | | | | | | | | | | End of split % 23.11/3.92 | | | | | | | | | | | | | % 23.11/3.92 | | | | | | | | | | | | End of split % 23.11/3.92 | | | | | | | | | | | | % 23.11/3.92 | | | | | | | | | | | End of split % 23.11/3.92 | | | | | | | | | | | % 23.11/3.92 | | | | | | | | | | Case 2: % 23.11/3.92 | | | | | | | | | | | % 23.11/3.92 | | | | | | | | | | | % 23.11/3.92 | | | | | | | | | | | GROUND_INST: instantiating (3) with 0, all_133_2, all_32_7, % 23.11/3.92 | | | | | | | | | | | all_52_0, simplifying with (53), (237) gives: % 23.11/3.92 | | | | | | | | | | | (262) all_133_2 = 0 % 23.11/3.92 | | | | | | | | | | | % 23.11/3.92 | | | | | | | | | | | GROUND_INST: instantiating (3) with 0, all_133_0, all_32_6, % 23.11/3.92 | | | | | | | | | | | all_61_0, simplifying with (86), (238) gives: % 23.11/3.92 | | | | | | | | | | | (263) all_133_0 = 0 % 23.11/3.92 | | | | | | | | | | | % 23.11/3.92 | | | | | | | | | | | GROUND_INST: instantiating (3) with 0, all_133_1, all_32_6, % 23.11/3.92 | | | | | | | | | | | all_92_0, simplifying with (148), (239) gives: % 23.11/3.92 | | | | | | | | | | | (264) all_133_1 = 0 % 23.11/3.92 | | | | | | | | | | | % 23.11/3.92 | | | | | | | | | | | REF_CLOSE: (240), (262), (263), (264) are inconsistent by % 23.11/3.92 | | | | | | | | | | | sub-proof #1. % 23.11/3.92 | | | | | | | | | | | % 23.11/3.92 | | | | | | | | | | End of split % 23.11/3.92 | | | | | | | | | | % 23.11/3.92 | | | | | | | | | End of split % 23.11/3.92 | | | | | | | | | % 23.11/3.92 | | | | | | | | Case 2: % 23.11/3.92 | | | | | | | | | % 23.11/3.92 | | | | | | | | | (265) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 23.11/3.92 | | | | | | | | | (member(all_85_0, all_32_7) = v1 & member(all_52_0, % 23.11/3.92 | | | | | | | | | all_32_7) = v2 & member(all_45_2, all_32_8) = v0 % 23.11/3.92 | | | | | | | | | & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0))) % 23.11/3.92 | | | | | | | | | % 23.11/3.92 | | | | | | | | | DELTA: instantiating (265) with fresh symbols all_116_0, % 23.11/3.92 | | | | | | | | | all_116_1, all_116_2 gives: % 23.11/3.92 | | | | | | | | | (266) member(all_85_0, all_32_7) = all_116_1 & % 23.11/3.92 | | | | | | | | | member(all_52_0, all_32_7) = all_116_0 & % 23.11/3.92 | | | | | | | | | member(all_45_2, all_32_8) = all_116_2 & ( ~ % 23.11/3.92 | | | | | | | | | (all_116_0 = 0) | ~ (all_116_1 = 0) | ~ % 23.11/3.92 | | | | | | | | | (all_116_2 = 0)) % 23.11/3.92 | | | | | | | | | % 23.11/3.92 | | | | | | | | | ALPHA: (266) implies: % 23.11/3.92 | | | | | | | | | (267) member(all_45_2, all_32_8) = all_116_2 % 23.11/3.92 | | | | | | | | | (268) member(all_52_0, all_32_7) = all_116_0 % 23.11/3.92 | | | | | | | | | (269) member(all_85_0, all_32_7) = all_116_1 % 23.11/3.92 | | | | | | | | | (270) ~ (all_116_0 = 0) | ~ (all_116_1 = 0) | ~ % 23.11/3.92 | | | | | | | | | (all_116_2 = 0) % 23.11/3.92 | | | | | | | | | % 23.11/3.92 | | | | | | | | | BETA: splitting (145) gives: % 23.11/3.92 | | | | | | | | | % 23.11/3.92 | | | | | | | | | Case 1: % 23.11/3.92 | | | | | | | | | | % 23.11/3.92 | | | | | | | | | | % 23.11/3.92 | | | | | | | | | | GROUND_INST: instantiating (3) with 0, all_116_2, all_32_8, % 23.11/3.92 | | | | | | | | | | all_45_2, simplifying with (43), (267) gives: % 23.11/3.92 | | | | | | | | | | (271) all_116_2 = 0 % 23.11/3.92 | | | | | | | | | | % 23.11/3.92 | | | | | | | | | | GROUND_INST: instantiating (3) with 0, all_116_0, all_32_7, % 23.11/3.92 | | | | | | | | | | all_52_0, simplifying with (53), (268) gives: % 23.11/3.92 | | | | | | | | | | (272) all_116_0 = 0 % 23.11/3.92 | | | | | | | | | | % 23.11/3.92 | | | | | | | | | | GROUND_INST: instantiating (3) with 0, all_116_1, all_32_7, % 23.11/3.92 | | | | | | | | | | all_85_0, simplifying with (137), (269) gives: % 23.11/3.92 | | | | | | | | | | (273) all_116_1 = 0 % 23.11/3.92 | | | | | | | | | | % 23.11/3.92 | | | | | | | | | | BETA: splitting (270) gives: % 23.11/3.92 | | | | | | | | | | % 23.11/3.92 | | | | | | | | | | Case 1: % 23.11/3.92 | | | | | | | | | | | % 23.11/3.92 | | | | | | | | | | | (274) ~ (all_116_0 = 0) % 23.11/3.92 | | | | | | | | | | | % 23.11/3.92 | | | | | | | | | | | REDUCE: (272), (274) imply: % 23.11/3.92 | | | | | | | | | | | (275) $false % 23.11/3.92 | | | | | | | | | | | % 23.11/3.92 | | | | | | | | | | | CLOSE: (275) is inconsistent. % 23.11/3.92 | | | | | | | | | | | % 23.11/3.92 | | | | | | | | | | Case 2: % 23.11/3.92 | | | | | | | | | | | % 23.11/3.92 | | | | | | | | | | | (276) ~ (all_116_1 = 0) | ~ (all_116_2 = 0) % 23.11/3.92 | | | | | | | | | | | % 23.11/3.92 | | | | | | | | | | | BETA: splitting (276) gives: % 23.11/3.92 | | | | | | | | | | | % 23.11/3.92 | | | | | | | | | | | Case 1: % 23.11/3.92 | | | | | | | | | | | | % 23.11/3.92 | | | | | | | | | | | | (277) ~ (all_116_1 = 0) % 23.11/3.92 | | | | | | | | | | | | % 23.11/3.92 | | | | | | | | | | | | REDUCE: (273), (277) imply: % 23.11/3.92 | | | | | | | | | | | | (278) $false % 23.11/3.92 | | | | | | | | | | | | % 23.11/3.92 | | | | | | | | | | | | CLOSE: (278) is inconsistent. % 23.11/3.92 | | | | | | | | | | | | % 23.11/3.92 | | | | | | | | | | | Case 2: % 23.11/3.92 | | | | | | | | | | | | % 23.11/3.92 | | | | | | | | | | | | (279) ~ (all_116_2 = 0) % 23.11/3.92 | | | | | | | | | | | | % 23.11/3.92 | | | | | | | | | | | | REDUCE: (271), (279) imply: % 23.11/3.92 | | | | | | | | | | | | (280) $false % 23.11/3.92 | | | | | | | | | | | | % 23.11/3.92 | | | | | | | | | | | | CLOSE: (280) is inconsistent. % 23.11/3.92 | | | | | | | | | | | | % 23.11/3.92 | | | | | | | | | | | End of split % 23.11/3.92 | | | | | | | | | | | % 23.11/3.92 | | | | | | | | | | End of split % 23.11/3.92 | | | | | | | | | | % 23.11/3.92 | | | | | | | | | Case 2: % 23.11/3.92 | | | | | | | | | | % 23.11/3.92 | | | | | | | | | | (281) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 23.11/3.92 | | | | | | | | | | (member(all_68_0, all_32_5) = v1 & member(all_61_0, % 23.11/3.92 | | | | | | | | | | all_32_6) = v0 & member(all_45_1, all_32_5) = % 23.11/3.92 | | | | | | | | | | v2 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0))) % 23.11/3.92 | | | | | | | | | | % 23.11/3.92 | | | | | | | | | | DELTA: instantiating (281) with fresh symbols all_122_0, % 23.11/3.92 | | | | | | | | | | all_122_1, all_122_2 gives: % 23.11/3.92 | | | | | | | | | | (282) member(all_68_0, all_32_5) = all_122_1 & % 23.11/3.92 | | | | | | | | | | member(all_61_0, all_32_6) = all_122_2 & % 23.11/3.92 | | | | | | | | | | member(all_45_1, all_32_5) = all_122_0 & ( ~ % 23.11/3.92 | | | | | | | | | | (all_122_0 = 0) | ~ (all_122_1 = 0) | ~ % 23.11/3.92 | | | | | | | | | | (all_122_2 = 0)) % 23.11/3.92 | | | | | | | | | | % 23.11/3.92 | | | | | | | | | | ALPHA: (282) implies: % 23.11/3.92 | | | | | | | | | | (283) member(all_45_1, all_32_5) = all_122_0 % 23.11/3.92 | | | | | | | | | | (284) member(all_61_0, all_32_6) = all_122_2 % 23.11/3.92 | | | | | | | | | | (285) member(all_68_0, all_32_5) = all_122_1 % 23.11/3.92 | | | | | | | | | | (286) ~ (all_122_0 = 0) | ~ (all_122_1 = 0) | ~ % 23.11/3.92 | | | | | | | | | | (all_122_2 = 0) % 23.11/3.92 | | | | | | | | | | % 23.11/3.92 | | | | | | | | | | GROUND_INST: instantiating (3) with 0, all_122_0, all_32_5, % 23.11/3.92 | | | | | | | | | | all_45_1, simplifying with (44), (283) gives: % 23.11/3.92 | | | | | | | | | | (287) all_122_0 = 0 % 23.11/3.92 | | | | | | | | | | % 23.11/3.92 | | | | | | | | | | GROUND_INST: instantiating (3) with 0, all_122_2, all_32_6, % 23.11/3.92 | | | | | | | | | | all_61_0, simplifying with (86), (284) gives: % 23.11/3.92 | | | | | | | | | | (288) all_122_2 = 0 % 23.11/3.92 | | | | | | | | | | % 23.11/3.92 | | | | | | | | | | GROUND_INST: instantiating (3) with 0, all_122_1, all_32_5, % 23.11/3.92 | | | | | | | | | | all_68_0, simplifying with (96), (285) gives: % 23.11/3.92 | | | | | | | | | | (289) all_122_1 = 0 % 23.11/3.92 | | | | | | | | | | % 23.11/3.92 | | | | | | | | | | BETA: splitting (286) gives: % 23.11/3.92 | | | | | | | | | | % 23.11/3.92 | | | | | | | | | | Case 1: % 23.11/3.92 | | | | | | | | | | | % 23.11/3.92 | | | | | | | | | | | (290) ~ (all_122_0 = 0) % 23.11/3.92 | | | | | | | | | | | % 23.11/3.92 | | | | | | | | | | | REDUCE: (287), (290) imply: % 23.11/3.92 | | | | | | | | | | | (291) $false % 23.11/3.92 | | | | | | | | | | | % 23.11/3.92 | | | | | | | | | | | CLOSE: (291) is inconsistent. % 23.11/3.92 | | | | | | | | | | | % 23.11/3.92 | | | | | | | | | | Case 2: % 23.11/3.92 | | | | | | | | | | | % 23.11/3.92 | | | | | | | | | | | (292) ~ (all_122_1 = 0) | ~ (all_122_2 = 0) % 23.11/3.92 | | | | | | | | | | | % 23.11/3.92 | | | | | | | | | | | BETA: splitting (292) gives: % 23.11/3.92 | | | | | | | | | | | % 23.11/3.92 | | | | | | | | | | | Case 1: % 23.11/3.92 | | | | | | | | | | | | % 23.11/3.92 | | | | | | | | | | | | (293) ~ (all_122_1 = 0) % 23.11/3.92 | | | | | | | | | | | | % 23.11/3.92 | | | | | | | | | | | | REDUCE: (289), (293) imply: % 23.11/3.92 | | | | | | | | | | | | (294) $false % 23.11/3.92 | | | | | | | | | | | | % 23.11/3.92 | | | | | | | | | | | | CLOSE: (294) is inconsistent. % 23.11/3.92 | | | | | | | | | | | | % 23.11/3.92 | | | | | | | | | | | Case 2: % 23.11/3.92 | | | | | | | | | | | | % 23.11/3.92 | | | | | | | | | | | | (295) ~ (all_122_2 = 0) % 23.11/3.92 | | | | | | | | | | | | % 23.11/3.92 | | | | | | | | | | | | REDUCE: (288), (295) imply: % 23.11/3.92 | | | | | | | | | | | | (296) $false % 23.11/3.92 | | | | | | | | | | | | % 23.11/3.92 | | | | | | | | | | | | CLOSE: (296) is inconsistent. % 23.11/3.92 | | | | | | | | | | | | % 23.11/3.92 | | | | | | | | | | | End of split % 23.11/3.92 | | | | | | | | | | | % 23.11/3.92 | | | | | | | | | | End of split % 23.11/3.92 | | | | | | | | | | % 23.11/3.92 | | | | | | | | | End of split % 23.11/3.92 | | | | | | | | | % 23.11/3.92 | | | | | | | | End of split % 23.11/3.92 | | | | | | | | % 23.11/3.93 | | | | | | | Case 2: % 23.11/3.93 | | | | | | | | % 23.11/3.93 | | | | | | | | (297) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 23.11/3.93 | | | | | | | | (member(all_80_0, all_32_6) = v1 & member(all_70_0, % 23.11/3.93 | | | | | | | | all_32_6) = v2 & member(all_52_0, all_32_7) = v0 & % 23.11/3.93 | | | | | | | | ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0))) % 23.11/3.93 | | | | | | | | % 23.11/3.93 | | | | | | | | DELTA: instantiating (297) with fresh symbols all_104_0, % 23.11/3.93 | | | | | | | | all_104_1, all_104_2 gives: % 23.11/3.93 | | | | | | | | (298) member(all_80_0, all_32_6) = all_104_1 & % 23.11/3.93 | | | | | | | | member(all_70_0, all_32_6) = all_104_0 & % 23.11/3.93 | | | | | | | | member(all_52_0, all_32_7) = all_104_2 & ( ~ (all_104_0 % 23.11/3.93 | | | | | | | | = 0) | ~ (all_104_1 = 0) | ~ (all_104_2 = 0)) % 23.11/3.93 | | | | | | | | % 23.11/3.93 | | | | | | | | ALPHA: (298) implies: % 23.11/3.93 | | | | | | | | (299) member(all_52_0, all_32_7) = all_104_2 % 23.50/3.93 | | | | | | | | (300) member(all_70_0, all_32_6) = all_104_0 % 23.50/3.93 | | | | | | | | (301) member(all_80_0, all_32_6) = all_104_1 % 23.50/3.93 | | | | | | | | (302) ~ (all_104_0 = 0) | ~ (all_104_1 = 0) | ~ (all_104_2 % 23.50/3.93 | | | | | | | | = 0) % 23.50/3.93 | | | | | | | | % 23.50/3.93 | | | | | | | | GROUND_INST: instantiating (3) with 0, all_104_2, all_32_7, % 23.50/3.93 | | | | | | | | all_52_0, simplifying with (53), (299) gives: % 23.50/3.93 | | | | | | | | (303) all_104_2 = 0 % 23.50/3.93 | | | | | | | | % 23.50/3.93 | | | | | | | | GROUND_INST: instantiating (3) with 0, all_104_0, all_32_6, % 23.50/3.93 | | | | | | | | all_70_0, simplifying with (100), (300) gives: % 23.50/3.93 | | | | | | | | (304) all_104_0 = 0 % 23.50/3.93 | | | | | | | | % 23.50/3.93 | | | | | | | | GROUND_INST: instantiating (3) with 0, all_104_1, all_32_6, % 23.50/3.93 | | | | | | | | all_80_0, simplifying with (119), (301) gives: % 23.50/3.93 | | | | | | | | (305) all_104_1 = 0 % 23.50/3.93 | | | | | | | | % 23.50/3.93 | | | | | | | | BETA: splitting (302) gives: % 23.50/3.93 | | | | | | | | % 23.50/3.93 | | | | | | | | Case 1: % 23.50/3.93 | | | | | | | | | % 23.50/3.93 | | | | | | | | | (306) ~ (all_104_0 = 0) % 23.50/3.93 | | | | | | | | | % 23.50/3.93 | | | | | | | | | REDUCE: (304), (306) imply: % 23.50/3.93 | | | | | | | | | (307) $false % 23.50/3.93 | | | | | | | | | % 23.50/3.93 | | | | | | | | | CLOSE: (307) is inconsistent. % 23.50/3.93 | | | | | | | | | % 23.50/3.93 | | | | | | | | Case 2: % 23.50/3.93 | | | | | | | | | % 23.50/3.93 | | | | | | | | | (308) ~ (all_104_1 = 0) | ~ (all_104_2 = 0) % 23.50/3.93 | | | | | | | | | % 23.50/3.93 | | | | | | | | | BETA: splitting (308) gives: % 23.50/3.93 | | | | | | | | | % 23.50/3.93 | | | | | | | | | Case 1: % 23.50/3.93 | | | | | | | | | | % 23.50/3.93 | | | | | | | | | | (309) ~ (all_104_1 = 0) % 23.50/3.93 | | | | | | | | | | % 23.50/3.93 | | | | | | | | | | REDUCE: (305), (309) imply: % 23.50/3.93 | | | | | | | | | | (310) $false % 23.50/3.93 | | | | | | | | | | % 23.50/3.93 | | | | | | | | | | CLOSE: (310) is inconsistent. % 23.50/3.93 | | | | | | | | | | % 23.50/3.93 | | | | | | | | | Case 2: % 23.50/3.93 | | | | | | | | | | % 23.50/3.93 | | | | | | | | | | (311) ~ (all_104_2 = 0) % 23.50/3.93 | | | | | | | | | | % 23.50/3.93 | | | | | | | | | | REDUCE: (303), (311) imply: % 23.50/3.93 | | | | | | | | | | (312) $false % 23.50/3.93 | | | | | | | | | | % 23.50/3.93 | | | | | | | | | | CLOSE: (312) is inconsistent. % 23.50/3.93 | | | | | | | | | | % 23.50/3.93 | | | | | | | | | End of split % 23.50/3.93 | | | | | | | | | % 23.50/3.93 | | | | | | | | End of split % 23.50/3.93 | | | | | | | | % 23.50/3.93 | | | | | | | End of split % 23.50/3.93 | | | | | | | % 23.50/3.93 | | | | | | End of split % 23.50/3.93 | | | | | | % 23.50/3.93 | | | | | End of split % 23.50/3.93 | | | | | % 23.50/3.93 | | | | Case 2: % 23.50/3.93 | | | | | % 23.50/3.93 | | | | | (313) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 23.50/3.93 | | | | | (member(all_57_0, all_32_7) = v2 & member(all_52_0, all_32_7) % 23.50/3.93 | | | | | = v1 & member(all_45_2, all_32_8) = v0 & ( ~ (v2 = 0) | ~ % 23.50/3.93 | | | | | (v1 = 0) | ~ (v0 = 0))) % 23.50/3.93 | | | | | % 23.50/3.93 | | | | | DELTA: instantiating (313) with fresh symbols all_78_0, all_78_1, % 23.50/3.93 | | | | | all_78_2 gives: % 23.50/3.93 | | | | | (314) member(all_57_0, all_32_7) = all_78_0 & member(all_52_0, % 23.50/3.93 | | | | | all_32_7) = all_78_1 & member(all_45_2, all_32_8) = % 23.50/3.93 | | | | | all_78_2 & ( ~ (all_78_0 = 0) | ~ (all_78_1 = 0) | ~ % 23.50/3.93 | | | | | (all_78_2 = 0)) % 23.50/3.93 | | | | | % 23.50/3.93 | | | | | ALPHA: (314) implies: % 23.50/3.93 | | | | | (315) member(all_45_2, all_32_8) = all_78_2 % 23.50/3.93 | | | | | (316) member(all_52_0, all_32_7) = all_78_1 % 23.50/3.93 | | | | | (317) member(all_57_0, all_32_7) = all_78_0 % 23.50/3.93 | | | | | (318) ~ (all_78_0 = 0) | ~ (all_78_1 = 0) | ~ (all_78_2 = 0) % 23.50/3.93 | | | | | % 23.50/3.93 | | | | | GROUND_INST: instantiating (3) with 0, all_78_2, all_32_8, all_45_2, % 23.50/3.93 | | | | | simplifying with (43), (315) gives: % 23.50/3.93 | | | | | (319) all_78_2 = 0 % 23.50/3.93 | | | | | % 23.50/3.93 | | | | | GROUND_INST: instantiating (3) with 0, all_78_1, all_32_7, all_52_0, % 23.50/3.93 | | | | | simplifying with (53), (316) gives: % 23.50/3.93 | | | | | (320) all_78_1 = 0 % 23.50/3.93 | | | | | % 23.50/3.93 | | | | | GROUND_INST: instantiating (3) with 0, all_78_0, all_32_7, all_57_0, % 23.50/3.93 | | | | | simplifying with (69), (317) gives: % 23.50/3.93 | | | | | (321) all_78_0 = 0 % 23.50/3.93 | | | | | % 23.50/3.93 | | | | | BETA: splitting (318) gives: % 23.50/3.93 | | | | | % 23.50/3.93 | | | | | Case 1: % 23.50/3.93 | | | | | | % 23.50/3.93 | | | | | | (322) ~ (all_78_0 = 0) % 23.50/3.93 | | | | | | % 23.50/3.93 | | | | | | REDUCE: (321), (322) imply: % 23.50/3.93 | | | | | | (323) $false % 23.50/3.93 | | | | | | % 23.50/3.93 | | | | | | CLOSE: (323) is inconsistent. % 23.50/3.93 | | | | | | % 23.50/3.93 | | | | | Case 2: % 23.50/3.93 | | | | | | % 23.50/3.93 | | | | | | (324) ~ (all_78_1 = 0) | ~ (all_78_2 = 0) % 23.50/3.93 | | | | | | % 23.50/3.93 | | | | | | BETA: splitting (324) gives: % 23.50/3.93 | | | | | | % 23.50/3.93 | | | | | | Case 1: % 23.50/3.93 | | | | | | | % 23.50/3.93 | | | | | | | (325) ~ (all_78_1 = 0) % 23.50/3.93 | | | | | | | % 23.50/3.93 | | | | | | | REDUCE: (320), (325) imply: % 23.50/3.93 | | | | | | | (326) $false % 23.50/3.93 | | | | | | | % 23.50/3.93 | | | | | | | CLOSE: (326) is inconsistent. % 23.50/3.93 | | | | | | | % 23.50/3.93 | | | | | | Case 2: % 23.50/3.93 | | | | | | | % 23.50/3.93 | | | | | | | (327) ~ (all_78_2 = 0) % 23.50/3.93 | | | | | | | % 23.50/3.93 | | | | | | | REDUCE: (319), (327) imply: % 23.50/3.93 | | | | | | | (328) $false % 23.50/3.93 | | | | | | | % 23.50/3.93 | | | | | | | CLOSE: (328) is inconsistent. % 23.50/3.93 | | | | | | | % 23.50/3.93 | | | | | | End of split % 23.50/3.93 | | | | | | % 23.50/3.93 | | | | | End of split % 23.50/3.93 | | | | | % 23.50/3.93 | | | | End of split % 23.50/3.93 | | | | % 23.50/3.93 | | | End of split % 23.50/3.93 | | | % 23.50/3.93 | | End of split % 23.50/3.93 | | % 23.50/3.93 | End of split % 23.50/3.93 | % 23.50/3.93 End of proof % 23.50/3.93 % 23.50/3.93 Sub-proof #1 shows that the following formulas are inconsistent: % 23.50/3.93 ---------------------------------------------------------------- % 23.50/3.93 (1) ~ (all_133_0 = 0) | ~ (all_133_1 = 0) | ~ (all_133_2 = 0) % 23.50/3.93 (2) all_133_0 = 0 % 23.50/3.93 (3) all_133_1 = 0 % 23.50/3.93 (4) all_133_2 = 0 % 23.50/3.93 % 23.50/3.93 Begin of proof % 23.50/3.93 | % 23.50/3.93 | BETA: splitting (1) gives: % 23.50/3.93 | % 23.50/3.93 | Case 1: % 23.50/3.93 | | % 23.50/3.93 | | (5) ~ (all_133_0 = 0) % 23.50/3.93 | | % 23.50/3.93 | | REDUCE: (2), (5) imply: % 23.50/3.93 | | (6) $false % 23.50/3.93 | | % 23.50/3.93 | | CLOSE: (6) is inconsistent. % 23.50/3.93 | | % 23.50/3.93 | Case 2: % 23.50/3.93 | | % 23.50/3.93 | | (7) ~ (all_133_1 = 0) | ~ (all_133_2 = 0) % 23.50/3.93 | | % 23.50/3.93 | | BETA: splitting (7) gives: % 23.50/3.93 | | % 23.50/3.93 | | Case 1: % 23.50/3.93 | | | % 23.50/3.93 | | | (8) ~ (all_133_1 = 0) % 23.50/3.93 | | | % 23.50/3.93 | | | REDUCE: (3), (8) imply: % 23.50/3.93 | | | (9) $false % 23.50/3.93 | | | % 23.50/3.93 | | | CLOSE: (9) is inconsistent. % 23.50/3.93 | | | % 23.50/3.93 | | Case 2: % 23.50/3.93 | | | % 23.50/3.93 | | | (10) ~ (all_133_2 = 0) % 23.50/3.93 | | | % 23.50/3.93 | | | REDUCE: (4), (10) imply: % 23.50/3.93 | | | (11) $false % 23.50/3.93 | | | % 23.50/3.93 | | | CLOSE: (11) is inconsistent. % 23.50/3.93 | | | % 23.50/3.93 | | End of split % 23.50/3.93 | | % 23.50/3.93 | End of split % 23.50/3.93 | % 23.50/3.93 End of proof % 23.50/3.93 % SZS output end Proof for theBenchmark % 23.50/3.93 % 23.50/3.93 3321ms %------------------------------------------------------------------------------