%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SEV578+1 : TPTP v9.1.0. Released v9.1.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n004.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 : Tue Apr 1 02:02:57 AM UTC 2025 % Result : Theorem 12.15s 2.32s % Output : Proof 15.15s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.06/0.11 % Problem : SEV578+1 : TPTP v9.1.0. Released v9.1.0. % 0.06/0.12 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.33 % Computer : n004.cluster.edu % 0.13/0.33 % Model : x86_64 x86_64 % 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.33 % Memory : 8042.1875MB % 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.33 % CPULimit : 300 % 0.13/0.33 % WCLimit : 300 % 0.13/0.33 % DateTime : Mon Mar 31 13:06:25 EDT 2025 % 0.13/0.33 % CPUTime : % 0.51/0.59 ________ _____ % 0.51/0.59 ___ __ \_________(_)________________________________ % 0.51/0.59 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.51/0.59 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.51/0.59 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.51/0.59 % 0.51/0.59 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.51/0.59 (2023-06-19) % 0.51/0.59 % 0.51/0.59 (c) Philipp Rümmer, 2009-2023 % 0.51/0.59 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.51/0.59 Amanda Stjerna. % 0.51/0.59 Free software under BSD-3-Clause. % 0.51/0.59 % 0.51/0.59 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.51/0.59 % 0.51/0.59 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.51/0.60 Running up to 7 provers in parallel. % 0.51/0.61 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.51/0.61 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.51/0.61 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.51/0.61 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.51/0.61 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.51/0.61 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.51/0.61 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.55/1.04 Prover 4: Preprocessing ... % 2.55/1.05 Prover 1: Preprocessing ... % 3.15/1.08 Prover 2: Preprocessing ... % 3.15/1.08 Prover 0: Preprocessing ... % 3.15/1.08 Prover 5: Preprocessing ... % 3.15/1.08 Prover 3: Preprocessing ... % 3.15/1.08 Prover 6: Preprocessing ... % 6.87/1.60 Prover 2: Proving ... % 6.87/1.61 Prover 5: Proving ... % 6.87/1.65 Prover 6: Proving ... % 7.44/1.66 Prover 1: Constructing countermodel ... % 7.60/1.68 Prover 3: Constructing countermodel ... % 7.97/1.74 Prover 4: Constructing countermodel ... % 8.13/1.75 Prover 0: Proving ... % 9.05/1.93 Prover 3: gave up % 9.60/1.95 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 9.60/1.97 Prover 1: gave up % 9.60/1.97 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 9.82/2.01 Prover 7: Preprocessing ... % 10.19/2.03 Prover 8: Preprocessing ... % 10.37/2.11 Prover 7: Warning: ignoring some quantifiers % 10.93/2.12 Prover 7: Constructing countermodel ... % 10.93/2.17 Prover 8: Warning: ignoring some quantifiers % 11.35/2.18 Prover 8: Constructing countermodel ... % 12.15/2.32 Prover 0: proved (1710ms) % 12.15/2.32 % 12.15/2.32 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 12.15/2.32 % 12.15/2.32 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 12.15/2.32 Prover 5: stopped % 12.48/2.33 Prover 6: stopped % 12.59/2.34 Prover 2: stopped % 12.59/2.35 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 12.59/2.35 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 12.59/2.36 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 12.59/2.37 Prover 11: Preprocessing ... % 12.59/2.37 Prover 10: Preprocessing ... % 12.59/2.38 Prover 8: gave up % 12.59/2.38 Prover 13: Preprocessing ... % 12.59/2.40 Prover 16: Preprocessing ... % 12.59/2.40 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085 % 13.12/2.46 Prover 13: Warning: ignoring some quantifiers % 13.12/2.46 Prover 19: Preprocessing ... % 13.12/2.47 Prover 13: Constructing countermodel ... % 13.51/2.48 Prover 10: Warning: ignoring some quantifiers % 13.51/2.49 Prover 10: Constructing countermodel ... % 13.51/2.51 Prover 16: Warning: ignoring some quantifiers % 13.51/2.52 Prover 4: Found proof (size 226) % 13.51/2.52 Prover 4: proved (1906ms) % 13.51/2.52 Prover 16: Constructing countermodel ... % 13.51/2.52 Prover 7: stopped % 13.51/2.52 Prover 13: stopped % 13.51/2.52 Prover 11: stopped % 13.51/2.52 Prover 10: stopped % 13.51/2.52 Prover 16: stopped % 14.22/2.62 Prover 19: Warning: ignoring some quantifiers % 14.47/2.64 Prover 19: Constructing countermodel ... % 14.47/2.65 Prover 19: stopped % 14.47/2.65 % 14.47/2.65 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 14.47/2.65 % 14.47/2.67 % SZS output start Proof for theBenchmark % 14.47/2.67 Assumptions after simplification: % 14.47/2.67 --------------------------------- % 14.47/2.67 % 14.47/2.67 (a_def) % 14.47/2.70 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (u(v0, v2) = v3) | % 14.47/2.70 ~ (s(v1) = v2) | ~ $i(v1) | ~ $i(v0) | (a(v0, v1) = v3 & $i(v3))) & ! % 14.47/2.70 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (a(v0, v1) = v2) | ~ $i(v1) | ~ % 14.47/2.70 $i(v0) | ? [v3: $i] : (u(v0, v3) = v2 & s(v1) = v3 & $i(v3) & $i(v2))) % 14.47/2.70 % 14.47/2.70 (n_def) % 14.47/2.70 ! [v0: $i] : ! [v1: $i] : ( ~ (n(v0) = v1) | ~ $i(v0) | (a(v0, v0) = v1 & % 14.47/2.70 $i(v1))) & ! [v0: $i] : ! [v1: $i] : ( ~ (a(v0, v0) = v1) | ~ $i(v0) | % 14.47/2.70 (n(v0) = v1 & $i(v1))) % 14.47/2.70 % 14.47/2.70 (p_ax) % 14.47/2.70 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (p(v1) = % 14.47/2.70 v2) | ~ (mem(v0, v2) = v3) | ~ $i(v1) | ~ $i(v0) | ? [v4: int] : ( ~ % 14.47/2.70 (v4 = 0) & subq(v0, v1) = v4)) & ! [v0: $i] : ! [v1: $i] : ! [v2: int] % 14.47/2.70 : (v2 = 0 | ~ (subq(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? % 14.47/2.70 [v4: int] : ( ~ (v4 = 0) & p(v1) = v3 & mem(v0, v3) = v4 & $i(v3))) & ! % 14.47/2.70 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (p(v1) = v2) | ~ (mem(v0, v2) = 0) % 14.47/2.70 | ~ $i(v1) | ~ $i(v0) | subq(v0, v1) = 0) & ! [v0: $i] : ! [v1: $i] : ( % 14.47/2.70 ~ (subq(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: $i] : (p(v1) = v2 & % 14.47/2.70 mem(v0, v2) = 0 & $i(v2))) % 14.47/2.70 % 14.47/2.70 (s_ax) % 14.47/2.71 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (s(v0) = v1) | ~ % 14.47/2.71 (mem(v0, v1) = v2) | ~ $i(v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 14.47/2.71 (v1 = v0 | ~ (s(v1) = v2) | ~ (mem(v0, v2) = 0) | ~ $i(v1) | ~ $i(v0)) % 14.47/2.71 % 14.47/2.71 (subq_1462_1463) % 14.47/2.71 $i(e) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 14.47/2.71 ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ? [v10: % 14.47/2.71 $i] : ? [v11: $i] : ? [v12: $i] : ? [v13: $i] : ? [v14: $i] : ? [v15: % 14.47/2.71 $i] : ? [v16: $i] : ? [v17: $i] : ? [v18: $i] : ? [v19: $i] : ? [v20: % 14.47/2.71 $i] : ? [v21: $i] : ? [v22: $i] : ? [v23: int] : ( ~ (v23 = 0) & p(v5) = % 14.47/2.71 v18 & p(v1) = v5 & n(v11) = v12 & n(v3) = v17 & n(v1) = v2 & n(v0) = v7 & % 14.47/2.71 n(e) = v0 & a(v18, v8) = v19 & a(v13, v14) = v15 & a(v6, v8) = v9 & a(v1, % 14.47/2.71 v7) = v14 & u(v20, v21) = v22 & u(v17, v19) = v20 & u(v10, v15) = v16 & % 14.47/2.71 u(v4, v9) = v10 & u(v1, v12) = v13 & u(v0, v2) = v3 & s(v14) = v21 & s(v7) = % 14.47/2.71 v8 & s(v5) = v6 & s(v3) = v4 & s(v1) = v11 & s(v0) = v1 & subq(v16, v22) = % 14.47/2.71 v23 & $i(v22) & $i(v21) & $i(v20) & $i(v19) & $i(v18) & $i(v17) & $i(v16) & % 14.47/2.71 $i(v15) & $i(v14) & $i(v13) & $i(v12) & $i(v11) & $i(v10) & $i(v9) & $i(v8) % 14.47/2.71 & $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 14.47/2.71 % 14.47/2.71 (subq_def) % 14.47/2.71 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 14.47/2.71 (subq(v0, v1) = 0) | ~ (mem(v2, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ % 14.47/2.71 $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & mem(v2, v0) = v4)) & ! [v0: $i] : ! % 14.47/2.71 [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subq(v0, v1) = v2) | ~ $i(v1) | ~ % 14.47/2.71 $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & mem(v3, v1) = v4 & % 14.47/2.71 mem(v3, v0) = 0 & $i(v3))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 14.47/2.71 (subq(v0, v1) = 0) | ~ (mem(v2, v0) = 0) | ~ $i(v2) | ~ $i(v1) | ~ % 14.47/2.71 $i(v0) | mem(v2, v1) = 0) % 14.47/2.71 % 14.47/2.71 (u_ax) % 14.47/2.71 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0 % 14.47/2.71 | ~ (u(v1, v2) = v3) | ~ (mem(v0, v3) = v4) | ~ $i(v2) | ~ $i(v1) | ~ % 14.47/2.71 $i(v0) | ? [v5: int] : ? [v6: int] : ( ~ (v6 = 0) & ~ (v5 = 0) & mem(v0, % 14.47/2.72 v2) = v6 & mem(v0, v1) = v5)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 14.47/2.72 : ! [v3: $i] : ( ~ (u(v1, v2) = v3) | ~ (mem(v0, v3) = 0) | ~ $i(v2) | ~ % 14.47/2.72 $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] : (mem(v0, v2) = v5 & % 14.47/2.72 mem(v0, v1) = v4 & (v5 = 0 | v4 = 0))) % 14.47/2.72 % 14.47/2.72 (function-axioms) % 14.86/2.72 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (a(v3, % 14.86/2.72 v2) = v1) | ~ (a(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 14.86/2.72 $i] : ! [v3: $i] : (v1 = v0 | ~ (m(v3, v2) = v1) | ~ (m(v3, v2) = v0)) & % 14.86/2.72 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (u(v3, % 14.86/2.72 v2) = v1) | ~ (u(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 14.86/2.72 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (disj(v3, v2) % 14.86/2.72 = v1) | ~ (disj(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 14.86/2.72 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (subq(v3, v2) % 14.86/2.72 = v1) | ~ (subq(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 14.86/2.72 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (mem(v3, v2) % 14.86/2.72 = v1) | ~ (mem(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 14.86/2.72 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (atleast16p(v2) = v1) | ~ % 14.86/2.72 (atleast16p(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 14.86/2.72 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (atleast15p(v2) = v1) | ~ % 14.86/2.72 (atleast15p(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 14.86/2.72 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (atleast14p(v2) = v1) | ~ % 14.86/2.72 (atleast14p(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 14.86/2.72 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (atleast13p(v2) = v1) | ~ % 14.86/2.72 (atleast13p(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 14.86/2.72 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (atleast12p(v2) = v1) | ~ % 14.86/2.72 (atleast12p(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 14.86/2.72 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (atleast11p(v2) = v1) | ~ % 14.86/2.72 (atleast11p(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 14.86/2.72 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (atleast10p(v2) = v1) | ~ % 14.86/2.72 (atleast10p(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 14.86/2.72 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (atleast9p(v2) = v1) | ~ % 14.86/2.72 (atleast9p(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 14.86/2.72 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (atleast8p(v2) = v1) | ~ % 14.86/2.72 (atleast8p(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 14.86/2.72 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (atleast7p(v2) = v1) | ~ % 14.86/2.72 (atleast7p(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 14.86/2.72 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (atleast6p(v2) = v1) | ~ % 14.86/2.72 (atleast6p(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 14.86/2.72 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (atleast5p(v2) = v1) | ~ % 14.86/2.72 (atleast5p(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 14.86/2.72 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (atleast4p(v2) = v1) | ~ % 14.86/2.72 (atleast4p(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 14.86/2.72 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (atleast3p(v2) = v1) | ~ % 14.86/2.72 (atleast3p(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 14.86/2.72 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (atleast2p(v2) = v1) | ~ % 14.86/2.72 (atleast2p(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | % 14.86/2.72 ~ (p(v2) = v1) | ~ (p(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 14.86/2.72 : (v1 = v0 | ~ (n(v2) = v1) | ~ (n(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : % 14.86/2.72 ! [v2: $i] : (v1 = v0 | ~ (s(v2) = v1) | ~ (s(v2) = v0)) % 14.86/2.72 % 14.86/2.72 Further assumptions not needed in the proof: % 14.86/2.72 -------------------------------------------- % 14.86/2.72 atleast10p_def, atleast11p_def, atleast12p_def, atleast13p_def, atleast14p_def, % 14.86/2.72 atleast15p_def, atleast16p_def, atleast2p_def, atleast3p_def, atleast4p_def, % 14.86/2.72 atleast5p_def, atleast6p_def, atleast7p_def, atleast8p_def, atleast9p_def, % 14.86/2.72 disj_def, e_ax, m_ax, setext % 14.86/2.72 % 14.86/2.72 Those formulas are unsatisfiable: % 14.86/2.72 --------------------------------- % 14.86/2.72 % 14.86/2.72 Begin of proof % 14.86/2.72 | % 14.86/2.72 | ALPHA: (subq_def) implies: % 14.86/2.73 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subq(v0, v1) = % 14.86/2.73 | v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 % 14.86/2.73 | = 0) & mem(v3, v1) = v4 & mem(v3, v0) = 0 & $i(v3))) % 14.86/2.73 | % 14.86/2.73 | ALPHA: (s_ax) implies: % 14.86/2.73 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (s(v1) = v2) | % 14.86/2.73 | ~ (mem(v0, v2) = 0) | ~ $i(v1) | ~ $i(v0)) % 14.86/2.73 | % 14.86/2.73 | ALPHA: (u_ax) implies: % 14.86/2.73 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (u(v1, v2) % 14.86/2.73 | = v3) | ~ (mem(v0, v3) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 14.86/2.73 | ? [v4: any] : ? [v5: any] : (mem(v0, v2) = v5 & mem(v0, v1) = v4 & % 14.86/2.73 | (v5 = 0 | v4 = 0))) % 14.86/2.73 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : % 14.86/2.73 | (v4 = 0 | ~ (u(v1, v2) = v3) | ~ (mem(v0, v3) = v4) | ~ $i(v2) | ~ % 14.86/2.73 | $i(v1) | ~ $i(v0) | ? [v5: int] : ? [v6: int] : ( ~ (v6 = 0) & ~ % 14.86/2.73 | (v5 = 0) & mem(v0, v2) = v6 & mem(v0, v1) = v5)) % 14.86/2.73 | % 14.86/2.73 | ALPHA: (a_def) implies: % 14.86/2.73 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (a(v0, v1) = v2) | ~ % 14.86/2.73 | $i(v1) | ~ $i(v0) | ? [v3: $i] : (u(v0, v3) = v2 & s(v1) = v3 & % 14.86/2.73 | $i(v3) & $i(v2))) % 14.86/2.73 | % 14.86/2.73 | ALPHA: (n_def) implies: % 14.86/2.73 | (6) ! [v0: $i] : ! [v1: $i] : ( ~ (n(v0) = v1) | ~ $i(v0) | (a(v0, v0) = % 14.86/2.73 | v1 & $i(v1))) % 14.86/2.73 | % 14.86/2.73 | ALPHA: (p_ax) implies: % 14.86/2.73 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 14.86/2.73 | (p(v1) = v2) | ~ (mem(v0, v2) = v3) | ~ $i(v1) | ~ $i(v0) | ? % 14.86/2.73 | [v4: int] : ( ~ (v4 = 0) & subq(v0, v1) = v4)) % 14.86/2.73 | % 14.86/2.73 | ALPHA: (subq_1462_1463) implies: % 14.86/2.73 | (8) $i(e) % 14.86/2.74 | (9) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 14.86/2.74 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ? % 14.86/2.74 | [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13: $i] : ? [v14: $i] : % 14.86/2.74 | ? [v15: $i] : ? [v16: $i] : ? [v17: $i] : ? [v18: $i] : ? [v19: % 14.86/2.74 | $i] : ? [v20: $i] : ? [v21: $i] : ? [v22: $i] : ? [v23: int] : ( % 14.86/2.74 | ~ (v23 = 0) & p(v5) = v18 & p(v1) = v5 & n(v11) = v12 & n(v3) = v17 & % 14.86/2.74 | n(v1) = v2 & n(v0) = v7 & n(e) = v0 & a(v18, v8) = v19 & a(v13, v14) % 14.86/2.74 | = v15 & a(v6, v8) = v9 & a(v1, v7) = v14 & u(v20, v21) = v22 & u(v17, % 14.86/2.74 | v19) = v20 & u(v10, v15) = v16 & u(v4, v9) = v10 & u(v1, v12) = v13 % 14.86/2.74 | & u(v0, v2) = v3 & s(v14) = v21 & s(v7) = v8 & s(v5) = v6 & s(v3) = % 14.86/2.74 | v4 & s(v1) = v11 & s(v0) = v1 & subq(v16, v22) = v23 & $i(v22) & % 14.86/2.74 | $i(v21) & $i(v20) & $i(v19) & $i(v18) & $i(v17) & $i(v16) & $i(v15) & % 14.86/2.74 | $i(v14) & $i(v13) & $i(v12) & $i(v11) & $i(v10) & $i(v9) & $i(v8) & % 14.86/2.74 | $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & % 14.86/2.74 | $i(v0)) % 14.86/2.74 | % 14.86/2.74 | ALPHA: (function-axioms) implies: % 14.86/2.74 | (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (s(v2) = v1) | % 14.86/2.74 | ~ (s(v2) = v0)) % 14.86/2.74 | (11) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 14.86/2.74 | : ! [v3: $i] : (v1 = v0 | ~ (mem(v3, v2) = v1) | ~ (mem(v3, v2) = % 14.86/2.74 | v0)) % 14.86/2.74 | % 14.86/2.74 | DELTA: instantiating (9) with fresh symbols all_29_0, all_29_1, all_29_2, % 14.86/2.74 | all_29_3, all_29_4, all_29_5, all_29_6, all_29_7, all_29_8, all_29_9, % 14.86/2.74 | all_29_10, all_29_11, all_29_12, all_29_13, all_29_14, all_29_15, % 14.86/2.74 | all_29_16, all_29_17, all_29_18, all_29_19, all_29_20, all_29_21, % 14.86/2.74 | all_29_22, all_29_23 gives: % 14.86/2.74 | (12) ~ (all_29_0 = 0) & p(all_29_18) = all_29_5 & p(all_29_22) = all_29_18 % 14.86/2.74 | & n(all_29_12) = all_29_11 & n(all_29_20) = all_29_6 & n(all_29_22) = % 14.86/2.74 | all_29_21 & n(all_29_23) = all_29_16 & n(e) = all_29_23 & a(all_29_5, % 14.86/2.74 | all_29_15) = all_29_4 & a(all_29_10, all_29_9) = all_29_8 & % 14.86/2.74 | a(all_29_17, all_29_15) = all_29_14 & a(all_29_22, all_29_16) = % 14.86/2.74 | all_29_9 & u(all_29_3, all_29_2) = all_29_1 & u(all_29_6, all_29_4) = % 14.86/2.74 | all_29_3 & u(all_29_13, all_29_8) = all_29_7 & u(all_29_19, all_29_14) % 14.86/2.74 | = all_29_13 & u(all_29_22, all_29_11) = all_29_10 & u(all_29_23, % 14.86/2.74 | all_29_21) = all_29_20 & s(all_29_9) = all_29_2 & s(all_29_16) = % 14.86/2.74 | all_29_15 & s(all_29_18) = all_29_17 & s(all_29_20) = all_29_19 & % 14.86/2.74 | s(all_29_22) = all_29_12 & s(all_29_23) = all_29_22 & subq(all_29_7, % 14.86/2.74 | all_29_1) = all_29_0 & $i(all_29_1) & $i(all_29_2) & $i(all_29_3) & % 14.86/2.74 | $i(all_29_4) & $i(all_29_5) & $i(all_29_6) & $i(all_29_7) & % 14.86/2.74 | $i(all_29_8) & $i(all_29_9) & $i(all_29_10) & $i(all_29_11) & % 14.86/2.74 | $i(all_29_12) & $i(all_29_13) & $i(all_29_14) & $i(all_29_15) & % 14.86/2.74 | $i(all_29_16) & $i(all_29_17) & $i(all_29_18) & $i(all_29_19) & % 14.86/2.74 | $i(all_29_20) & $i(all_29_21) & $i(all_29_22) & $i(all_29_23) % 14.86/2.74 | % 14.86/2.74 | ALPHA: (12) implies: % 14.86/2.74 | (13) ~ (all_29_0 = 0) % 14.86/2.74 | (14) $i(all_29_22) % 14.86/2.74 | (15) $i(all_29_20) % 14.86/2.74 | (16) $i(all_29_18) % 14.86/2.74 | (17) $i(all_29_17) % 14.86/2.74 | (18) $i(all_29_15) % 14.86/2.74 | (19) $i(all_29_13) % 14.86/2.74 | (20) $i(all_29_12) % 14.86/2.74 | (21) $i(all_29_10) % 14.86/2.74 | (22) $i(all_29_9) % 14.86/2.74 | (23) $i(all_29_7) % 14.86/2.74 | (24) $i(all_29_5) % 14.86/2.74 | (25) $i(all_29_3) % 14.86/2.74 | (26) $i(all_29_1) % 14.86/2.74 | (27) subq(all_29_7, all_29_1) = all_29_0 % 14.86/2.74 | (28) s(all_29_23) = all_29_22 % 14.86/2.74 | (29) s(all_29_22) = all_29_12 % 14.86/2.74 | (30) s(all_29_20) = all_29_19 % 14.86/2.74 | (31) s(all_29_18) = all_29_17 % 14.86/2.74 | (32) s(all_29_9) = all_29_2 % 14.86/2.75 | (33) u(all_29_23, all_29_21) = all_29_20 % 14.86/2.75 | (34) u(all_29_22, all_29_11) = all_29_10 % 14.86/2.75 | (35) u(all_29_19, all_29_14) = all_29_13 % 14.86/2.75 | (36) u(all_29_13, all_29_8) = all_29_7 % 14.86/2.75 | (37) u(all_29_6, all_29_4) = all_29_3 % 14.86/2.75 | (38) u(all_29_3, all_29_2) = all_29_1 % 14.86/2.75 | (39) a(all_29_17, all_29_15) = all_29_14 % 14.86/2.75 | (40) a(all_29_10, all_29_9) = all_29_8 % 14.86/2.75 | (41) a(all_29_5, all_29_15) = all_29_4 % 14.86/2.75 | (42) n(e) = all_29_23 % 14.86/2.75 | (43) n(all_29_23) = all_29_16 % 14.86/2.75 | (44) n(all_29_22) = all_29_21 % 14.86/2.75 | (45) n(all_29_20) = all_29_6 % 14.86/2.75 | (46) n(all_29_12) = all_29_11 % 14.86/2.75 | (47) p(all_29_22) = all_29_18 % 14.86/2.75 | (48) p(all_29_18) = all_29_5 % 14.86/2.75 | % 14.86/2.75 | GROUND_INST: instantiating (1) with all_29_7, all_29_1, all_29_0, simplifying % 14.86/2.75 | with (23), (26), (27) gives: % 14.86/2.75 | (49) all_29_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & mem(v0, % 14.86/2.75 | all_29_1) = v1 & mem(v0, all_29_7) = 0 & $i(v0)) % 14.86/2.75 | % 14.86/2.75 | GROUND_INST: instantiating (5) with all_29_17, all_29_15, all_29_14, % 14.86/2.75 | simplifying with (17), (18), (39) gives: % 14.86/2.75 | (50) ? [v0: $i] : (u(all_29_17, v0) = all_29_14 & s(all_29_15) = v0 & % 14.86/2.75 | $i(v0) & $i(all_29_14)) % 14.86/2.75 | % 14.86/2.75 | GROUND_INST: instantiating (5) with all_29_10, all_29_9, all_29_8, simplifying % 14.86/2.75 | with (21), (22), (40) gives: % 14.86/2.75 | (51) ? [v0: $i] : (u(all_29_10, v0) = all_29_8 & s(all_29_9) = v0 & $i(v0) % 14.86/2.75 | & $i(all_29_8)) % 14.86/2.75 | % 14.86/2.75 | GROUND_INST: instantiating (5) with all_29_5, all_29_15, all_29_4, simplifying % 14.86/2.75 | with (18), (24), (41) gives: % 14.86/2.75 | (52) ? [v0: $i] : (u(all_29_5, v0) = all_29_4 & s(all_29_15) = v0 & $i(v0) % 14.86/2.75 | & $i(all_29_4)) % 14.86/2.75 | % 14.86/2.75 | GROUND_INST: instantiating (6) with e, all_29_23, simplifying with (8), (42) % 14.86/2.75 | gives: % 14.86/2.75 | (53) a(e, e) = all_29_23 & $i(all_29_23) % 14.86/2.75 | % 14.86/2.75 | ALPHA: (53) implies: % 14.86/2.75 | (54) $i(all_29_23) % 14.86/2.75 | (55) a(e, e) = all_29_23 % 14.86/2.75 | % 14.86/2.75 | GROUND_INST: instantiating (6) with all_29_23, all_29_16, simplifying with % 14.86/2.75 | (43), (54) gives: % 14.86/2.75 | (56) a(all_29_23, all_29_23) = all_29_16 & $i(all_29_16) % 14.86/2.75 | % 14.86/2.75 | ALPHA: (56) implies: % 14.86/2.75 | (57) a(all_29_23, all_29_23) = all_29_16 % 14.86/2.75 | % 14.86/2.76 | GROUND_INST: instantiating (6) with all_29_22, all_29_21, simplifying with % 14.86/2.76 | (14), (44) gives: % 14.86/2.76 | (58) a(all_29_22, all_29_22) = all_29_21 & $i(all_29_21) % 14.86/2.76 | % 14.86/2.76 | ALPHA: (58) implies: % 14.86/2.76 | (59) a(all_29_22, all_29_22) = all_29_21 % 14.86/2.76 | % 14.86/2.76 | GROUND_INST: instantiating (6) with all_29_20, all_29_6, simplifying with % 14.86/2.76 | (15), (45) gives: % 14.86/2.76 | (60) a(all_29_20, all_29_20) = all_29_6 & $i(all_29_6) % 14.86/2.76 | % 14.86/2.76 | ALPHA: (60) implies: % 14.86/2.76 | (61) a(all_29_20, all_29_20) = all_29_6 % 14.86/2.76 | % 14.86/2.76 | GROUND_INST: instantiating (6) with all_29_12, all_29_11, simplifying with % 14.86/2.76 | (20), (46) gives: % 14.86/2.76 | (62) a(all_29_12, all_29_12) = all_29_11 & $i(all_29_11) % 14.86/2.76 | % 14.86/2.76 | ALPHA: (62) implies: % 14.86/2.76 | (63) a(all_29_12, all_29_12) = all_29_11 % 14.86/2.76 | % 14.86/2.76 | DELTA: instantiating (51) with fresh symbol all_37_0 gives: % 14.86/2.76 | (64) u(all_29_10, all_37_0) = all_29_8 & s(all_29_9) = all_37_0 & % 14.86/2.76 | $i(all_37_0) & $i(all_29_8) % 14.86/2.76 | % 14.86/2.76 | ALPHA: (64) implies: % 14.86/2.76 | (65) $i(all_29_8) % 14.86/2.76 | (66) $i(all_37_0) % 14.86/2.76 | (67) s(all_29_9) = all_37_0 % 14.86/2.76 | (68) u(all_29_10, all_37_0) = all_29_8 % 14.86/2.76 | % 14.86/2.76 | DELTA: instantiating (50) with fresh symbol all_39_0 gives: % 14.86/2.76 | (69) u(all_29_17, all_39_0) = all_29_14 & s(all_29_15) = all_39_0 & % 14.86/2.76 | $i(all_39_0) & $i(all_29_14) % 14.86/2.76 | % 14.86/2.76 | ALPHA: (69) implies: % 14.86/2.76 | (70) $i(all_29_14) % 14.86/2.76 | (71) s(all_29_15) = all_39_0 % 14.86/2.76 | (72) u(all_29_17, all_39_0) = all_29_14 % 14.86/2.76 | % 14.86/2.76 | DELTA: instantiating (52) with fresh symbol all_41_0 gives: % 14.86/2.76 | (73) u(all_29_5, all_41_0) = all_29_4 & s(all_29_15) = all_41_0 & % 14.86/2.76 | $i(all_41_0) & $i(all_29_4) % 14.86/2.76 | % 14.86/2.76 | ALPHA: (73) implies: % 14.86/2.76 | (74) $i(all_29_4) % 14.86/2.76 | (75) $i(all_41_0) % 14.86/2.76 | (76) s(all_29_15) = all_41_0 % 14.86/2.76 | (77) u(all_29_5, all_41_0) = all_29_4 % 14.86/2.76 | % 14.86/2.76 | BETA: splitting (49) gives: % 14.86/2.76 | % 14.86/2.76 | Case 1: % 14.86/2.76 | | % 14.86/2.76 | | (78) all_29_0 = 0 % 14.86/2.76 | | % 14.86/2.76 | | REDUCE: (13), (78) imply: % 14.86/2.76 | | (79) $false % 14.86/2.76 | | % 14.86/2.76 | | CLOSE: (79) is inconsistent. % 14.86/2.76 | | % 14.86/2.76 | Case 2: % 14.86/2.76 | | % 14.86/2.76 | | (80) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & mem(v0, all_29_1) = v1 & % 14.86/2.76 | | mem(v0, all_29_7) = 0 & $i(v0)) % 14.86/2.76 | | % 14.86/2.76 | | DELTA: instantiating (80) with fresh symbols all_49_0, all_49_1 gives: % 14.86/2.76 | | (81) ~ (all_49_0 = 0) & mem(all_49_1, all_29_1) = all_49_0 & % 14.86/2.76 | | mem(all_49_1, all_29_7) = 0 & $i(all_49_1) % 14.86/2.76 | | % 14.86/2.76 | | ALPHA: (81) implies: % 14.86/2.76 | | (82) ~ (all_49_0 = 0) % 14.86/2.76 | | (83) $i(all_49_1) % 14.86/2.76 | | (84) mem(all_49_1, all_29_7) = 0 % 14.86/2.76 | | (85) mem(all_49_1, all_29_1) = all_49_0 % 14.86/2.76 | | % 14.86/2.76 | | GROUND_INST: instantiating (10) with all_39_0, all_41_0, all_29_15, % 14.86/2.76 | | simplifying with (71), (76) gives: % 14.86/2.76 | | (86) all_41_0 = all_39_0 % 14.86/2.76 | | % 14.86/2.76 | | GROUND_INST: instantiating (10) with all_29_2, all_37_0, all_29_9, % 14.86/2.76 | | simplifying with (32), (67) gives: % 14.86/2.76 | | (87) all_37_0 = all_29_2 % 14.86/2.76 | | % 14.86/2.76 | | REDUCE: (77), (86) imply: % 14.86/2.76 | | (88) u(all_29_5, all_39_0) = all_29_4 % 14.86/2.76 | | % 14.86/2.76 | | REDUCE: (68), (87) imply: % 14.86/2.76 | | (89) u(all_29_10, all_29_2) = all_29_8 % 14.86/2.76 | | % 14.86/2.77 | | REDUCE: (75), (86) imply: % 14.86/2.77 | | (90) $i(all_39_0) % 14.86/2.77 | | % 14.86/2.77 | | REDUCE: (66), (87) imply: % 14.86/2.77 | | (91) $i(all_29_2) % 14.86/2.77 | | % 14.86/2.77 | | GROUND_INST: instantiating (3) with all_49_1, all_29_13, all_29_8, all_29_7, % 14.86/2.77 | | simplifying with (19), (36), (65), (83), (84) gives: % 14.86/2.77 | | (92) ? [v0: any] : ? [v1: any] : (mem(all_49_1, all_29_8) = v1 & % 14.86/2.77 | | mem(all_49_1, all_29_13) = v0 & (v1 = 0 | v0 = 0)) % 14.86/2.77 | | % 14.86/2.77 | | GROUND_INST: instantiating (4) with all_49_1, all_29_3, all_29_2, all_29_1, % 14.86/2.77 | | all_49_0, simplifying with (25), (38), (83), (85), (91) gives: % 14.86/2.77 | | (93) all_49_0 = 0 | ? [v0: int] : ? [v1: int] : ( ~ (v1 = 0) & ~ (v0 = % 14.86/2.77 | | 0) & mem(all_49_1, all_29_2) = v1 & mem(all_49_1, all_29_3) = % 14.86/2.77 | | v0) % 14.86/2.77 | | % 14.86/2.77 | | GROUND_INST: instantiating (5) with e, e, all_29_23, simplifying with (8), % 14.86/2.77 | | (55) gives: % 14.86/2.77 | | (94) ? [v0: $i] : (u(e, v0) = all_29_23 & s(e) = v0 & $i(v0) & % 14.86/2.77 | | $i(all_29_23)) % 14.86/2.77 | | % 14.86/2.77 | | GROUND_INST: instantiating (5) with all_29_23, all_29_23, all_29_16, % 14.86/2.77 | | simplifying with (54), (57) gives: % 14.86/2.77 | | (95) ? [v0: $i] : (u(all_29_23, v0) = all_29_16 & s(all_29_23) = v0 & % 14.86/2.77 | | $i(v0) & $i(all_29_16)) % 14.86/2.77 | | % 14.86/2.77 | | GROUND_INST: instantiating (5) with all_29_22, all_29_22, all_29_21, % 14.86/2.77 | | simplifying with (14), (59) gives: % 14.86/2.77 | | (96) ? [v0: $i] : (u(all_29_22, v0) = all_29_21 & s(all_29_22) = v0 & % 14.86/2.77 | | $i(v0) & $i(all_29_21)) % 14.86/2.77 | | % 14.86/2.77 | | GROUND_INST: instantiating (5) with all_29_20, all_29_20, all_29_6, % 14.86/2.77 | | simplifying with (15), (61) gives: % 14.86/2.77 | | (97) ? [v0: $i] : (u(all_29_20, v0) = all_29_6 & s(all_29_20) = v0 & % 14.86/2.77 | | $i(v0) & $i(all_29_6)) % 14.86/2.77 | | % 14.86/2.77 | | GROUND_INST: instantiating (5) with all_29_12, all_29_12, all_29_11, % 14.86/2.77 | | simplifying with (20), (63) gives: % 14.86/2.77 | | (98) ? [v0: $i] : (u(all_29_12, v0) = all_29_11 & s(all_29_12) = v0 & % 14.86/2.77 | | $i(v0) & $i(all_29_11)) % 14.86/2.77 | | % 14.86/2.77 | | DELTA: instantiating (98) with fresh symbol all_65_0 gives: % 14.86/2.77 | | (99) u(all_29_12, all_65_0) = all_29_11 & s(all_29_12) = all_65_0 & % 14.86/2.77 | | $i(all_65_0) & $i(all_29_11) % 14.86/2.77 | | % 14.86/2.77 | | ALPHA: (99) implies: % 14.86/2.77 | | (100) $i(all_29_11) % 14.86/2.77 | | (101) $i(all_65_0) % 14.86/2.77 | | (102) s(all_29_12) = all_65_0 % 14.86/2.77 | | (103) u(all_29_12, all_65_0) = all_29_11 % 14.86/2.77 | | % 14.86/2.77 | | DELTA: instantiating (95) with fresh symbol all_67_0 gives: % 14.86/2.77 | | (104) u(all_29_23, all_67_0) = all_29_16 & s(all_29_23) = all_67_0 & % 14.86/2.77 | | $i(all_67_0) & $i(all_29_16) % 14.86/2.77 | | % 14.86/2.77 | | ALPHA: (104) implies: % 14.86/2.77 | | (105) $i(all_67_0) % 14.86/2.77 | | (106) s(all_29_23) = all_67_0 % 14.86/2.77 | | % 14.86/2.77 | | DELTA: instantiating (92) with fresh symbols all_69_0, all_69_1 gives: % 14.86/2.77 | | (107) mem(all_49_1, all_29_8) = all_69_0 & mem(all_49_1, all_29_13) = % 14.86/2.77 | | all_69_1 & (all_69_0 = 0 | all_69_1 = 0) % 14.86/2.77 | | % 14.86/2.77 | | ALPHA: (107) implies: % 14.86/2.77 | | (108) mem(all_49_1, all_29_13) = all_69_1 % 14.86/2.77 | | (109) mem(all_49_1, all_29_8) = all_69_0 % 14.86/2.77 | | (110) all_69_0 = 0 | all_69_1 = 0 % 14.86/2.77 | | % 14.86/2.77 | | DELTA: instantiating (94) with fresh symbol all_71_0 gives: % 14.86/2.77 | | (111) u(e, all_71_0) = all_29_23 & s(e) = all_71_0 & $i(all_71_0) & % 14.86/2.77 | | $i(all_29_23) % 14.86/2.77 | | % 14.86/2.77 | | DELTA: instantiating (97) with fresh symbol all_73_0 gives: % 14.86/2.77 | | (112) u(all_29_20, all_73_0) = all_29_6 & s(all_29_20) = all_73_0 & % 14.86/2.77 | | $i(all_73_0) & $i(all_29_6) % 14.86/2.77 | | % 14.86/2.77 | | ALPHA: (112) implies: % 14.86/2.77 | | (113) $i(all_29_6) % 14.86/2.77 | | (114) $i(all_73_0) % 14.86/2.77 | | (115) s(all_29_20) = all_73_0 % 14.86/2.77 | | (116) u(all_29_20, all_73_0) = all_29_6 % 14.86/2.77 | | % 14.86/2.77 | | DELTA: instantiating (96) with fresh symbol all_75_0 gives: % 14.86/2.78 | | (117) u(all_29_22, all_75_0) = all_29_21 & s(all_29_22) = all_75_0 & % 14.86/2.78 | | $i(all_75_0) & $i(all_29_21) % 14.86/2.78 | | % 14.86/2.78 | | ALPHA: (117) implies: % 14.86/2.78 | | (118) $i(all_29_21) % 14.86/2.78 | | (119) $i(all_75_0) % 14.86/2.78 | | (120) s(all_29_22) = all_75_0 % 14.86/2.78 | | (121) u(all_29_22, all_75_0) = all_29_21 % 14.86/2.78 | | % 14.86/2.78 | | BETA: splitting (93) gives: % 14.86/2.78 | | % 15.15/2.78 | | Case 1: % 15.15/2.78 | | | % 15.15/2.78 | | | (122) all_49_0 = 0 % 15.15/2.78 | | | % 15.15/2.78 | | | REDUCE: (82), (122) imply: % 15.15/2.78 | | | (123) $false % 15.15/2.78 | | | % 15.15/2.78 | | | CLOSE: (123) is inconsistent. % 15.15/2.78 | | | % 15.15/2.78 | | Case 2: % 15.15/2.78 | | | % 15.15/2.78 | | | (124) ? [v0: int] : ? [v1: int] : ( ~ (v1 = 0) & ~ (v0 = 0) & % 15.15/2.78 | | | mem(all_49_1, all_29_2) = v1 & mem(all_49_1, all_29_3) = v0) % 15.15/2.78 | | | % 15.15/2.78 | | | DELTA: instantiating (124) with fresh symbols all_81_0, all_81_1 gives: % 15.15/2.78 | | | (125) ~ (all_81_0 = 0) & ~ (all_81_1 = 0) & mem(all_49_1, all_29_2) = % 15.15/2.78 | | | all_81_0 & mem(all_49_1, all_29_3) = all_81_1 % 15.15/2.78 | | | % 15.15/2.78 | | | ALPHA: (125) implies: % 15.15/2.78 | | | (126) ~ (all_81_1 = 0) % 15.15/2.78 | | | (127) ~ (all_81_0 = 0) % 15.15/2.78 | | | (128) mem(all_49_1, all_29_3) = all_81_1 % 15.15/2.78 | | | (129) mem(all_49_1, all_29_2) = all_81_0 % 15.15/2.78 | | | % 15.15/2.78 | | | GROUND_INST: instantiating (10) with all_29_22, all_67_0, all_29_23, % 15.15/2.78 | | | simplifying with (28), (106) gives: % 15.15/2.78 | | | (130) all_67_0 = all_29_22 % 15.15/2.78 | | | % 15.15/2.78 | | | GROUND_INST: instantiating (10) with all_29_12, all_75_0, all_29_22, % 15.15/2.78 | | | simplifying with (29), (120) gives: % 15.15/2.78 | | | (131) all_75_0 = all_29_12 % 15.15/2.78 | | | % 15.15/2.78 | | | GROUND_INST: instantiating (10) with all_29_19, all_73_0, all_29_20, % 15.15/2.78 | | | simplifying with (30), (115) gives: % 15.15/2.78 | | | (132) all_73_0 = all_29_19 % 15.15/2.78 | | | % 15.15/2.78 | | | REDUCE: (116), (132) imply: % 15.15/2.78 | | | (133) u(all_29_20, all_29_19) = all_29_6 % 15.15/2.78 | | | % 15.15/2.78 | | | REDUCE: (121), (131) imply: % 15.15/2.78 | | | (134) u(all_29_22, all_29_12) = all_29_21 % 15.15/2.78 | | | % 15.15/2.78 | | | REDUCE: (114), (132) imply: % 15.15/2.78 | | | (135) $i(all_29_19) % 15.15/2.78 | | | % 15.15/2.78 | | | GROUND_INST: instantiating (4) with all_49_1, all_29_6, all_29_4, % 15.15/2.78 | | | all_29_3, all_81_1, simplifying with (37), (74), (83), (113), % 15.15/2.78 | | | (128) gives: % 15.15/2.78 | | | (136) all_81_1 = 0 | ? [v0: int] : ? [v1: int] : ( ~ (v1 = 0) & ~ % 15.15/2.78 | | | (v0 = 0) & mem(all_49_1, all_29_4) = v1 & mem(all_49_1, % 15.15/2.78 | | | all_29_6) = v0) % 15.15/2.78 | | | % 15.15/2.78 | | | BETA: splitting (110) gives: % 15.15/2.78 | | | % 15.15/2.78 | | | Case 1: % 15.15/2.78 | | | | % 15.15/2.78 | | | | (137) all_69_0 = 0 % 15.15/2.78 | | | | % 15.15/2.78 | | | | REDUCE: (109), (137) imply: % 15.15/2.78 | | | | (138) mem(all_49_1, all_29_8) = 0 % 15.15/2.78 | | | | % 15.15/2.78 | | | | BETA: splitting (136) gives: % 15.15/2.78 | | | | % 15.15/2.78 | | | | Case 1: % 15.15/2.78 | | | | | % 15.15/2.78 | | | | | (139) all_81_1 = 0 % 15.15/2.78 | | | | | % 15.15/2.78 | | | | | REDUCE: (126), (139) imply: % 15.15/2.78 | | | | | (140) $false % 15.15/2.78 | | | | | % 15.15/2.78 | | | | | CLOSE: (140) is inconsistent. % 15.15/2.78 | | | | | % 15.15/2.78 | | | | Case 2: % 15.15/2.78 | | | | | % 15.15/2.78 | | | | | (141) ? [v0: int] : ? [v1: int] : ( ~ (v1 = 0) & ~ (v0 = 0) & % 15.15/2.78 | | | | | mem(all_49_1, all_29_4) = v1 & mem(all_49_1, all_29_6) = % 15.15/2.78 | | | | | v0) % 15.15/2.78 | | | | | % 15.15/2.78 | | | | | DELTA: instantiating (141) with fresh symbols all_98_0, all_98_1 % 15.15/2.78 | | | | | gives: % 15.15/2.78 | | | | | (142) ~ (all_98_0 = 0) & ~ (all_98_1 = 0) & mem(all_49_1, % 15.15/2.78 | | | | | all_29_4) = all_98_0 & mem(all_49_1, all_29_6) = all_98_1 % 15.15/2.78 | | | | | % 15.15/2.78 | | | | | ALPHA: (142) implies: % 15.15/2.78 | | | | | (143) ~ (all_98_1 = 0) % 15.15/2.78 | | | | | (144) ~ (all_98_0 = 0) % 15.15/2.78 | | | | | (145) mem(all_49_1, all_29_6) = all_98_1 % 15.15/2.78 | | | | | (146) mem(all_49_1, all_29_4) = all_98_0 % 15.15/2.78 | | | | | % 15.15/2.78 | | | | | GROUND_INST: instantiating (3) with all_49_1, all_29_10, all_29_2, % 15.15/2.78 | | | | | all_29_8, simplifying with (21), (83), (89), (91), (138) % 15.15/2.78 | | | | | gives: % 15.15/2.78 | | | | | (147) ? [v0: any] : ? [v1: any] : (mem(all_49_1, all_29_2) = v1 & % 15.15/2.78 | | | | | mem(all_49_1, all_29_10) = v0 & (v1 = 0 | v0 = 0)) % 15.15/2.78 | | | | | % 15.15/2.78 | | | | | GROUND_INST: instantiating (4) with all_49_1, all_29_20, all_29_19, % 15.15/2.78 | | | | | all_29_6, all_98_1, simplifying with (15), (83), (133), % 15.15/2.78 | | | | | (135), (145) gives: % 15.15/2.78 | | | | | (148) all_98_1 = 0 | ? [v0: int] : ? [v1: int] : ( ~ (v1 = 0) & % 15.15/2.78 | | | | | ~ (v0 = 0) & mem(all_49_1, all_29_19) = v1 & mem(all_49_1, % 15.15/2.78 | | | | | all_29_20) = v0) % 15.15/2.78 | | | | | % 15.15/2.78 | | | | | GROUND_INST: instantiating (4) with all_49_1, all_29_5, all_39_0, % 15.15/2.78 | | | | | all_29_4, all_98_0, simplifying with (24), (83), (88), % 15.15/2.78 | | | | | (90), (146) gives: % 15.15/2.78 | | | | | (149) all_98_0 = 0 | ? [v0: int] : ? [v1: int] : ( ~ (v1 = 0) & % 15.15/2.78 | | | | | ~ (v0 = 0) & mem(all_49_1, all_39_0) = v1 & mem(all_49_1, % 15.15/2.78 | | | | | all_29_5) = v0) % 15.15/2.78 | | | | | % 15.15/2.78 | | | | | DELTA: instantiating (147) with fresh symbols all_105_0, all_105_1 % 15.15/2.78 | | | | | gives: % 15.15/2.79 | | | | | (150) mem(all_49_1, all_29_2) = all_105_0 & mem(all_49_1, % 15.15/2.79 | | | | | all_29_10) = all_105_1 & (all_105_0 = 0 | all_105_1 = 0) % 15.15/2.79 | | | | | % 15.15/2.79 | | | | | ALPHA: (150) implies: % 15.15/2.79 | | | | | (151) mem(all_49_1, all_29_10) = all_105_1 % 15.15/2.79 | | | | | (152) mem(all_49_1, all_29_2) = all_105_0 % 15.15/2.79 | | | | | (153) all_105_0 = 0 | all_105_1 = 0 % 15.15/2.79 | | | | | % 15.15/2.79 | | | | | BETA: splitting (149) gives: % 15.15/2.79 | | | | | % 15.15/2.79 | | | | | Case 1: % 15.15/2.79 | | | | | | % 15.15/2.79 | | | | | | (154) all_98_0 = 0 % 15.15/2.79 | | | | | | % 15.15/2.79 | | | | | | REDUCE: (144), (154) imply: % 15.15/2.79 | | | | | | (155) $false % 15.15/2.79 | | | | | | % 15.15/2.79 | | | | | | CLOSE: (155) is inconsistent. % 15.15/2.79 | | | | | | % 15.15/2.79 | | | | | Case 2: % 15.15/2.79 | | | | | | % 15.15/2.79 | | | | | | (156) ? [v0: int] : ? [v1: int] : ( ~ (v1 = 0) & ~ (v0 = 0) & % 15.15/2.79 | | | | | | mem(all_49_1, all_39_0) = v1 & mem(all_49_1, all_29_5) = % 15.15/2.79 | | | | | | v0) % 15.15/2.79 | | | | | | % 15.15/2.79 | | | | | | DELTA: instantiating (156) with fresh symbols all_111_0, all_111_1 % 15.15/2.79 | | | | | | gives: % 15.15/2.79 | | | | | | (157) ~ (all_111_0 = 0) & ~ (all_111_1 = 0) & mem(all_49_1, % 15.15/2.79 | | | | | | all_39_0) = all_111_0 & mem(all_49_1, all_29_5) = % 15.15/2.79 | | | | | | all_111_1 % 15.15/2.79 | | | | | | % 15.15/2.79 | | | | | | ALPHA: (157) implies: % 15.15/2.79 | | | | | | (158) ~ (all_111_1 = 0) % 15.15/2.79 | | | | | | (159) mem(all_49_1, all_29_5) = all_111_1 % 15.15/2.79 | | | | | | % 15.15/2.79 | | | | | | BETA: splitting (148) gives: % 15.15/2.79 | | | | | | % 15.15/2.79 | | | | | | Case 1: % 15.15/2.79 | | | | | | | % 15.15/2.79 | | | | | | | (160) all_98_1 = 0 % 15.15/2.79 | | | | | | | % 15.15/2.79 | | | | | | | REDUCE: (143), (160) imply: % 15.15/2.79 | | | | | | | (161) $false % 15.15/2.79 | | | | | | | % 15.15/2.79 | | | | | | | CLOSE: (161) is inconsistent. % 15.15/2.79 | | | | | | | % 15.15/2.79 | | | | | | Case 2: % 15.15/2.79 | | | | | | | % 15.15/2.79 | | | | | | | (162) ? [v0: int] : ? [v1: int] : ( ~ (v1 = 0) & ~ (v0 = 0) % 15.15/2.79 | | | | | | | & mem(all_49_1, all_29_19) = v1 & mem(all_49_1, % 15.15/2.79 | | | | | | | all_29_20) = v0) % 15.15/2.79 | | | | | | | % 15.15/2.79 | | | | | | | DELTA: instantiating (162) with fresh symbols all_116_0, all_116_1 % 15.15/2.79 | | | | | | | gives: % 15.15/2.79 | | | | | | | (163) ~ (all_116_0 = 0) & ~ (all_116_1 = 0) & mem(all_49_1, % 15.15/2.79 | | | | | | | all_29_19) = all_116_0 & mem(all_49_1, all_29_20) = % 15.15/2.79 | | | | | | | all_116_1 % 15.15/2.79 | | | | | | | % 15.15/2.79 | | | | | | | ALPHA: (163) implies: % 15.15/2.79 | | | | | | | (164) ~ (all_116_1 = 0) % 15.15/2.79 | | | | | | | (165) mem(all_49_1, all_29_20) = all_116_1 % 15.15/2.79 | | | | | | | % 15.15/2.79 | | | | | | | GROUND_INST: instantiating (11) with all_81_0, all_105_0, % 15.15/2.79 | | | | | | | all_29_2, all_49_1, simplifying with (129), (152) % 15.15/2.79 | | | | | | | gives: % 15.15/2.79 | | | | | | | (166) all_105_0 = all_81_0 % 15.15/2.79 | | | | | | | % 15.15/2.79 | | | | | | | BETA: splitting (153) gives: % 15.15/2.79 | | | | | | | % 15.15/2.79 | | | | | | | Case 1: % 15.15/2.79 | | | | | | | | % 15.15/2.79 | | | | | | | | (167) all_105_0 = 0 % 15.15/2.79 | | | | | | | | % 15.15/2.79 | | | | | | | | COMBINE_EQS: (166), (167) imply: % 15.15/2.79 | | | | | | | | (168) all_81_0 = 0 % 15.15/2.79 | | | | | | | | % 15.15/2.79 | | | | | | | | REDUCE: (127), (168) imply: % 15.15/2.79 | | | | | | | | (169) $false % 15.15/2.79 | | | | | | | | % 15.15/2.79 | | | | | | | | CLOSE: (169) is inconsistent. % 15.15/2.79 | | | | | | | | % 15.15/2.79 | | | | | | | Case 2: % 15.15/2.79 | | | | | | | | % 15.15/2.79 | | | | | | | | (170) all_105_1 = 0 % 15.15/2.79 | | | | | | | | % 15.15/2.79 | | | | | | | | REDUCE: (151), (170) imply: % 15.15/2.79 | | | | | | | | (171) mem(all_49_1, all_29_10) = 0 % 15.15/2.79 | | | | | | | | % 15.15/2.79 | | | | | | | | GROUND_INST: instantiating (4) with all_49_1, all_29_23, % 15.15/2.79 | | | | | | | | all_29_21, all_29_20, all_116_1, simplifying with % 15.15/2.79 | | | | | | | | (33), (54), (83), (118), (165) gives: % 15.15/2.79 | | | | | | | | (172) all_116_1 = 0 | ? [v0: int] : ? [v1: int] : ( ~ (v1 = % 15.15/2.79 | | | | | | | | 0) & ~ (v0 = 0) & mem(all_49_1, all_29_21) = v1 & % 15.15/2.79 | | | | | | | | mem(all_49_1, all_29_23) = v0) % 15.15/2.79 | | | | | | | | % 15.15/2.79 | | | | | | | | GROUND_INST: instantiating (3) with all_49_1, all_29_22, % 15.15/2.79 | | | | | | | | all_29_11, all_29_10, simplifying with (14), (34), % 15.15/2.79 | | | | | | | | (83), (100), (171) gives: % 15.15/2.79 | | | | | | | | (173) ? [v0: any] : ? [v1: any] : (mem(all_49_1, all_29_11) % 15.15/2.79 | | | | | | | | = v1 & mem(all_49_1, all_29_22) = v0 & (v1 = 0 | v0 = % 15.15/2.79 | | | | | | | | 0)) % 15.15/2.79 | | | | | | | | % 15.15/2.79 | | | | | | | | GROUND_INST: instantiating (7) with all_49_1, all_29_18, % 15.15/2.79 | | | | | | | | all_29_5, all_111_1, simplifying with (16), (48), % 15.15/2.79 | | | | | | | | (83), (159) gives: % 15.15/2.79 | | | | | | | | (174) all_111_1 = 0 | ? [v0: int] : ( ~ (v0 = 0) & % 15.15/2.79 | | | | | | | | subq(all_49_1, all_29_18) = v0) % 15.15/2.79 | | | | | | | | % 15.15/2.79 | | | | | | | | DELTA: instantiating (173) with fresh symbols all_131_0, % 15.15/2.79 | | | | | | | | all_131_1 gives: % 15.15/2.79 | | | | | | | | (175) mem(all_49_1, all_29_11) = all_131_0 & mem(all_49_1, % 15.15/2.79 | | | | | | | | all_29_22) = all_131_1 & (all_131_0 = 0 | all_131_1 = % 15.15/2.79 | | | | | | | | 0) % 15.15/2.79 | | | | | | | | % 15.15/2.79 | | | | | | | | ALPHA: (175) implies: % 15.15/2.79 | | | | | | | | (176) mem(all_49_1, all_29_22) = all_131_1 % 15.15/2.79 | | | | | | | | (177) mem(all_49_1, all_29_11) = all_131_0 % 15.15/2.79 | | | | | | | | (178) all_131_0 = 0 | all_131_1 = 0 % 15.15/2.79 | | | | | | | | % 15.15/2.79 | | | | | | | | BETA: splitting (174) gives: % 15.15/2.79 | | | | | | | | % 15.15/2.79 | | | | | | | | Case 1: % 15.15/2.79 | | | | | | | | | % 15.15/2.79 | | | | | | | | | (179) all_111_1 = 0 % 15.15/2.79 | | | | | | | | | % 15.15/2.79 | | | | | | | | | REDUCE: (158), (179) imply: % 15.15/2.79 | | | | | | | | | (180) $false % 15.15/2.79 | | | | | | | | | % 15.15/2.79 | | | | | | | | | CLOSE: (180) is inconsistent. % 15.15/2.79 | | | | | | | | | % 15.15/2.79 | | | | | | | | Case 2: % 15.15/2.79 | | | | | | | | | % 15.15/2.79 | | | | | | | | | (181) ? [v0: int] : ( ~ (v0 = 0) & subq(all_49_1, % 15.15/2.79 | | | | | | | | | all_29_18) = v0) % 15.15/2.79 | | | | | | | | | % 15.15/2.79 | | | | | | | | | DELTA: instantiating (181) with fresh symbol all_137_0 gives: % 15.15/2.79 | | | | | | | | | (182) ~ (all_137_0 = 0) & subq(all_49_1, all_29_18) = % 15.15/2.79 | | | | | | | | | all_137_0 % 15.15/2.79 | | | | | | | | | % 15.15/2.79 | | | | | | | | | ALPHA: (182) implies: % 15.15/2.79 | | | | | | | | | (183) ~ (all_137_0 = 0) % 15.15/2.79 | | | | | | | | | (184) subq(all_49_1, all_29_18) = all_137_0 % 15.15/2.79 | | | | | | | | | % 15.15/2.79 | | | | | | | | | BETA: splitting (172) gives: % 15.15/2.79 | | | | | | | | | % 15.15/2.79 | | | | | | | | | Case 1: % 15.15/2.79 | | | | | | | | | | % 15.15/2.79 | | | | | | | | | | (185) all_116_1 = 0 % 15.15/2.79 | | | | | | | | | | % 15.15/2.79 | | | | | | | | | | REDUCE: (164), (185) imply: % 15.15/2.79 | | | | | | | | | | (186) $false % 15.15/2.79 | | | | | | | | | | % 15.15/2.79 | | | | | | | | | | CLOSE: (186) is inconsistent. % 15.15/2.79 | | | | | | | | | | % 15.15/2.79 | | | | | | | | | Case 2: % 15.15/2.79 | | | | | | | | | | % 15.15/2.79 | | | | | | | | | | (187) ? [v0: int] : ? [v1: int] : ( ~ (v1 = 0) & ~ (v0 % 15.15/2.79 | | | | | | | | | | = 0) & mem(all_49_1, all_29_21) = v1 & % 15.15/2.79 | | | | | | | | | | mem(all_49_1, all_29_23) = v0) % 15.15/2.79 | | | | | | | | | | % 15.15/2.79 | | | | | | | | | | DELTA: instantiating (187) with fresh symbols all_142_0, % 15.15/2.79 | | | | | | | | | | all_142_1 gives: % 15.15/2.80 | | | | | | | | | | (188) ~ (all_142_0 = 0) & ~ (all_142_1 = 0) & % 15.15/2.80 | | | | | | | | | | mem(all_49_1, all_29_21) = all_142_0 & % 15.15/2.80 | | | | | | | | | | mem(all_49_1, all_29_23) = all_142_1 % 15.15/2.80 | | | | | | | | | | % 15.15/2.80 | | | | | | | | | | ALPHA: (188) implies: % 15.15/2.80 | | | | | | | | | | (189) ~ (all_142_0 = 0) % 15.15/2.80 | | | | | | | | | | (190) mem(all_49_1, all_29_21) = all_142_0 % 15.15/2.80 | | | | | | | | | | % 15.15/2.80 | | | | | | | | | | GROUND_INST: instantiating (4) with all_49_1, all_29_22, % 15.15/2.80 | | | | | | | | | | all_29_12, all_29_21, all_142_0, simplifying with % 15.15/2.80 | | | | | | | | | | (14), (20), (83), (134), (190) gives: % 15.15/2.80 | | | | | | | | | | (191) all_142_0 = 0 | ? [v0: int] : ? [v1: int] : ( ~ % 15.15/2.80 | | | | | | | | | | (v1 = 0) & ~ (v0 = 0) & mem(all_49_1, all_29_12) % 15.15/2.80 | | | | | | | | | | = v1 & mem(all_49_1, all_29_22) = v0) % 15.15/2.80 | | | | | | | | | | % 15.15/2.80 | | | | | | | | | | GROUND_INST: instantiating (1) with all_49_1, all_29_18, % 15.15/2.80 | | | | | | | | | | all_137_0, simplifying with (16), (83), (184) % 15.15/2.80 | | | | | | | | | | gives: % 15.15/2.80 | | | | | | | | | | (192) all_137_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ % 15.15/2.80 | | | | | | | | | | (v1 = 0) & mem(v0, all_49_1) = 0 & mem(v0, % 15.15/2.80 | | | | | | | | | | all_29_18) = v1 & $i(v0)) % 15.15/2.80 | | | | | | | | | | % 15.15/2.80 | | | | | | | | | | BETA: splitting (192) gives: % 15.15/2.80 | | | | | | | | | | % 15.15/2.80 | | | | | | | | | | Case 1: % 15.15/2.80 | | | | | | | | | | | % 15.15/2.80 | | | | | | | | | | | (193) all_137_0 = 0 % 15.15/2.80 | | | | | | | | | | | % 15.15/2.80 | | | | | | | | | | | REDUCE: (183), (193) imply: % 15.15/2.80 | | | | | | | | | | | (194) $false % 15.15/2.80 | | | | | | | | | | | % 15.15/2.80 | | | | | | | | | | | CLOSE: (194) is inconsistent. % 15.15/2.80 | | | | | | | | | | | % 15.15/2.80 | | | | | | | | | | Case 2: % 15.15/2.80 | | | | | | | | | | | % 15.15/2.80 | | | | | | | | | | | (195) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & % 15.15/2.80 | | | | | | | | | | | mem(v0, all_49_1) = 0 & mem(v0, all_29_18) = v1 % 15.15/2.80 | | | | | | | | | | | & $i(v0)) % 15.15/2.80 | | | | | | | | | | | % 15.15/2.80 | | | | | | | | | | | DELTA: instantiating (195) with fresh symbols all_162_0, % 15.15/2.80 | | | | | | | | | | | all_162_1 gives: % 15.15/2.80 | | | | | | | | | | | (196) ~ (all_162_0 = 0) & mem(all_162_1, all_49_1) = 0 % 15.15/2.80 | | | | | | | | | | | & mem(all_162_1, all_29_18) = all_162_0 & % 15.15/2.80 | | | | | | | | | | | $i(all_162_1) % 15.15/2.80 | | | | | | | | | | | % 15.15/2.80 | | | | | | | | | | | ALPHA: (196) implies: % 15.15/2.80 | | | | | | | | | | | (197) ~ (all_162_0 = 0) % 15.15/2.80 | | | | | | | | | | | (198) $i(all_162_1) % 15.15/2.80 | | | | | | | | | | | (199) mem(all_162_1, all_29_18) = all_162_0 % 15.15/2.80 | | | | | | | | | | | (200) mem(all_162_1, all_49_1) = 0 % 15.15/2.80 | | | | | | | | | | | % 15.15/2.80 | | | | | | | | | | | BETA: splitting (191) gives: % 15.15/2.80 | | | | | | | | | | | % 15.15/2.80 | | | | | | | | | | | Case 1: % 15.15/2.80 | | | | | | | | | | | | % 15.15/2.80 | | | | | | | | | | | | (201) all_142_0 = 0 % 15.15/2.80 | | | | | | | | | | | | % 15.15/2.80 | | | | | | | | | | | | REDUCE: (189), (201) imply: % 15.15/2.80 | | | | | | | | | | | | (202) $false % 15.15/2.80 | | | | | | | | | | | | % 15.15/2.80 | | | | | | | | | | | | CLOSE: (202) is inconsistent. % 15.15/2.80 | | | | | | | | | | | | % 15.15/2.80 | | | | | | | | | | | Case 2: % 15.15/2.80 | | | | | | | | | | | | % 15.15/2.80 | | | | | | | | | | | | (203) ? [v0: int] : ? [v1: int] : ( ~ (v1 = 0) & ~ % 15.15/2.80 | | | | | | | | | | | | (v0 = 0) & mem(all_49_1, all_29_12) = v1 & % 15.15/2.80 | | | | | | | | | | | | mem(all_49_1, all_29_22) = v0) % 15.15/2.80 | | | | | | | | | | | | % 15.15/2.80 | | | | | | | | | | | | DELTA: instantiating (203) with fresh symbols all_167_0, % 15.15/2.80 | | | | | | | | | | | | all_167_1 gives: % 15.15/2.80 | | | | | | | | | | | | (204) ~ (all_167_0 = 0) & ~ (all_167_1 = 0) & % 15.15/2.80 | | | | | | | | | | | | mem(all_49_1, all_29_12) = all_167_0 & % 15.15/2.80 | | | | | | | | | | | | mem(all_49_1, all_29_22) = all_167_1 % 15.15/2.80 | | | | | | | | | | | | % 15.15/2.80 | | | | | | | | | | | | ALPHA: (204) implies: % 15.15/2.80 | | | | | | | | | | | | (205) ~ (all_167_1 = 0) % 15.15/2.80 | | | | | | | | | | | | (206) ~ (all_167_0 = 0) % 15.15/2.80 | | | | | | | | | | | | (207) mem(all_49_1, all_29_22) = all_167_1 % 15.15/2.80 | | | | | | | | | | | | (208) mem(all_49_1, all_29_12) = all_167_0 % 15.15/2.80 | | | | | | | | | | | | % 15.15/2.80 | | | | | | | | | | | | GROUND_INST: instantiating (11) with all_131_1, all_167_1, % 15.15/2.80 | | | | | | | | | | | | all_29_22, all_49_1, simplifying with (176), (207) % 15.15/2.80 | | | | | | | | | | | | gives: % 15.15/2.80 | | | | | | | | | | | | (209) all_167_1 = all_131_1 % 15.15/2.80 | | | | | | | | | | | | % 15.15/2.80 | | | | | | | | | | | | REDUCE: (205), (209) imply: % 15.15/2.80 | | | | | | | | | | | | (210) ~ (all_131_1 = 0) % 15.15/2.80 | | | | | | | | | | | | % 15.15/2.80 | | | | | | | | | | | | BETA: splitting (178) gives: % 15.15/2.80 | | | | | | | | | | | | % 15.15/2.80 | | | | | | | | | | | | Case 1: % 15.15/2.80 | | | | | | | | | | | | | % 15.15/2.80 | | | | | | | | | | | | | (211) all_131_0 = 0 % 15.15/2.80 | | | | | | | | | | | | | % 15.15/2.80 | | | | | | | | | | | | | REDUCE: (177), (211) imply: % 15.15/2.80 | | | | | | | | | | | | | (212) mem(all_49_1, all_29_11) = 0 % 15.15/2.80 | | | | | | | | | | | | | % 15.15/2.80 | | | | | | | | | | | | | GROUND_INST: instantiating (3) with all_49_1, all_29_12, % 15.15/2.80 | | | | | | | | | | | | | all_65_0, all_29_11, simplifying with (20), (83), % 15.15/2.80 | | | | | | | | | | | | | (101), (103), (212) gives: % 15.15/2.80 | | | | | | | | | | | | | (213) ? [v0: any] : ? [v1: any] : (mem(all_49_1, % 15.15/2.80 | | | | | | | | | | | | | all_65_0) = v1 & mem(all_49_1, all_29_12) = v0 % 15.15/2.80 | | | | | | | | | | | | | & (v1 = 0 | v0 = 0)) % 15.15/2.80 | | | | | | | | | | | | | % 15.15/2.80 | | | | | | | | | | | | | GROUND_INST: instantiating (7) with all_162_1, all_29_22, % 15.15/2.80 | | | | | | | | | | | | | all_29_18, all_162_0, simplifying with (14), (47), % 15.15/2.80 | | | | | | | | | | | | | (198), (199) gives: % 15.15/2.80 | | | | | | | | | | | | | (214) all_162_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & % 15.15/2.80 | | | | | | | | | | | | | subq(all_162_1, all_29_22) = v0) % 15.15/2.80 | | | | | | | | | | | | | % 15.15/2.80 | | | | | | | | | | | | | DELTA: instantiating (213) with fresh symbols all_182_0, % 15.15/2.80 | | | | | | | | | | | | | all_182_1 gives: % 15.15/2.80 | | | | | | | | | | | | | (215) mem(all_49_1, all_65_0) = all_182_0 & % 15.15/2.80 | | | | | | | | | | | | | mem(all_49_1, all_29_12) = all_182_1 & (all_182_0 % 15.15/2.80 | | | | | | | | | | | | | = 0 | all_182_1 = 0) % 15.15/2.80 | | | | | | | | | | | | | % 15.15/2.80 | | | | | | | | | | | | | ALPHA: (215) implies: % 15.15/2.80 | | | | | | | | | | | | | (216) mem(all_49_1, all_29_12) = all_182_1 % 15.15/2.80 | | | | | | | | | | | | | (217) mem(all_49_1, all_65_0) = all_182_0 % 15.15/2.80 | | | | | | | | | | | | | (218) all_182_0 = 0 | all_182_1 = 0 % 15.15/2.80 | | | | | | | | | | | | | % 15.15/2.80 | | | | | | | | | | | | | BETA: splitting (214) gives: % 15.15/2.80 | | | | | | | | | | | | | % 15.15/2.80 | | | | | | | | | | | | | Case 1: % 15.15/2.80 | | | | | | | | | | | | | | % 15.15/2.80 | | | | | | | | | | | | | | (219) all_162_0 = 0 % 15.15/2.80 | | | | | | | | | | | | | | % 15.15/2.80 | | | | | | | | | | | | | | REDUCE: (197), (219) imply: % 15.15/2.80 | | | | | | | | | | | | | | (220) $false % 15.15/2.80 | | | | | | | | | | | | | | % 15.15/2.80 | | | | | | | | | | | | | | CLOSE: (220) is inconsistent. % 15.15/2.80 | | | | | | | | | | | | | | % 15.15/2.80 | | | | | | | | | | | | | Case 2: % 15.15/2.80 | | | | | | | | | | | | | | % 15.15/2.80 | | | | | | | | | | | | | | (221) ? [v0: int] : ( ~ (v0 = 0) & subq(all_162_1, % 15.15/2.80 | | | | | | | | | | | | | | all_29_22) = v0) % 15.15/2.80 | | | | | | | | | | | | | | % 15.15/2.80 | | | | | | | | | | | | | | DELTA: instantiating (221) with fresh symbol all_188_0 % 15.15/2.80 | | | | | | | | | | | | | | gives: % 15.15/2.80 | | | | | | | | | | | | | | (222) ~ (all_188_0 = 0) & subq(all_162_1, all_29_22) = % 15.15/2.80 | | | | | | | | | | | | | | all_188_0 % 15.15/2.80 | | | | | | | | | | | | | | % 15.15/2.80 | | | | | | | | | | | | | | ALPHA: (222) implies: % 15.15/2.80 | | | | | | | | | | | | | | (223) ~ (all_188_0 = 0) % 15.15/2.80 | | | | | | | | | | | | | | (224) subq(all_162_1, all_29_22) = all_188_0 % 15.15/2.80 | | | | | | | | | | | | | | % 15.15/2.80 | | | | | | | | | | | | | | GROUND_INST: instantiating (11) with all_167_0, all_182_1, % 15.15/2.80 | | | | | | | | | | | | | | all_29_12, all_49_1, simplifying with (208), (216) % 15.15/2.80 | | | | | | | | | | | | | | gives: % 15.15/2.80 | | | | | | | | | | | | | | (225) all_182_1 = all_167_0 % 15.15/2.80 | | | | | | | | | | | | | | % 15.15/2.80 | | | | | | | | | | | | | | BETA: splitting (218) gives: % 15.15/2.80 | | | | | | | | | | | | | | % 15.15/2.80 | | | | | | | | | | | | | | Case 1: % 15.15/2.80 | | | | | | | | | | | | | | | % 15.15/2.80 | | | | | | | | | | | | | | | (226) all_182_0 = 0 % 15.15/2.80 | | | | | | | | | | | | | | | % 15.15/2.80 | | | | | | | | | | | | | | | REDUCE: (217), (226) imply: % 15.15/2.80 | | | | | | | | | | | | | | | (227) mem(all_49_1, all_65_0) = 0 % 15.15/2.80 | | | | | | | | | | | | | | | % 15.15/2.81 | | | | | | | | | | | | | | | GROUND_INST: instantiating (2) with all_49_1, all_29_12, % 15.15/2.81 | | | | | | | | | | | | | | | all_65_0, simplifying with (20), (83), (102), % 15.15/2.81 | | | | | | | | | | | | | | | (227) gives: % 15.15/2.81 | | | | | | | | | | | | | | | (228) all_49_1 = all_29_12 % 15.15/2.81 | | | | | | | | | | | | | | | % 15.15/2.81 | | | | | | | | | | | | | | | GROUND_INST: instantiating (1) with all_162_1, all_29_22, % 15.15/2.81 | | | | | | | | | | | | | | | all_188_0, simplifying with (14), (198), (224) % 15.15/2.81 | | | | | | | | | | | | | | | gives: % 15.15/2.81 | | | | | | | | | | | | | | | (229) all_188_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ % 15.15/2.81 | | | | | | | | | | | | | | | (v1 = 0) & mem(v0, all_162_1) = 0 & mem(v0, % 15.15/2.81 | | | | | | | | | | | | | | | all_29_22) = v1 & $i(v0)) % 15.15/2.81 | | | | | | | | | | | | | | | % 15.15/2.81 | | | | | | | | | | | | | | | REDUCE: (200), (228) imply: % 15.15/2.81 | | | | | | | | | | | | | | | (230) mem(all_162_1, all_29_12) = 0 % 15.15/2.81 | | | | | | | | | | | | | | | % 15.15/2.81 | | | | | | | | | | | | | | | BETA: splitting (229) gives: % 15.15/2.81 | | | | | | | | | | | | | | | % 15.15/2.81 | | | | | | | | | | | | | | | Case 1: % 15.15/2.81 | | | | | | | | | | | | | | | | % 15.15/2.81 | | | | | | | | | | | | | | | | (231) all_188_0 = 0 % 15.15/2.81 | | | | | | | | | | | | | | | | % 15.15/2.81 | | | | | | | | | | | | | | | | REDUCE: (223), (231) imply: % 15.15/2.81 | | | | | | | | | | | | | | | | (232) $false % 15.15/2.81 | | | | | | | | | | | | | | | | % 15.15/2.81 | | | | | | | | | | | | | | | | CLOSE: (232) is inconsistent. % 15.15/2.81 | | | | | | | | | | | | | | | | % 15.15/2.81 | | | | | | | | | | | | | | | Case 2: % 15.15/2.81 | | | | | | | | | | | | | | | | % 15.15/2.81 | | | | | | | | | | | | | | | | (233) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & % 15.15/2.81 | | | | | | | | | | | | | | | | mem(v0, all_162_1) = 0 & mem(v0, all_29_22) = v1 % 15.15/2.81 | | | | | | | | | | | | | | | | & $i(v0)) % 15.15/2.81 | | | | | | | | | | | | | | | | % 15.15/2.81 | | | | | | | | | | | | | | | | DELTA: instantiating (233) with fresh symbols all_213_0, % 15.15/2.81 | | | | | | | | | | | | | | | | all_213_1 gives: % 15.15/2.81 | | | | | | | | | | | | | | | | (234) ~ (all_213_0 = 0) & mem(all_213_1, all_162_1) = 0 % 15.15/2.81 | | | | | | | | | | | | | | | | & mem(all_213_1, all_29_22) = all_213_0 & % 15.15/2.81 | | | | | | | | | | | | | | | | $i(all_213_1) % 15.15/2.81 | | | | | | | | | | | | | | | | % 15.15/2.81 | | | | | | | | | | | | | | | | ALPHA: (234) implies: % 15.15/2.81 | | | | | | | | | | | | | | | | (235) ~ (all_213_0 = 0) % 15.15/2.81 | | | | | | | | | | | | | | | | (236) mem(all_213_1, all_29_22) = all_213_0 % 15.15/2.81 | | | | | | | | | | | | | | | | (237) mem(all_213_1, all_162_1) = 0 % 15.15/2.81 | | | | | | | | | | | | | | | | % 15.15/2.81 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (2) with all_162_1, all_29_22, % 15.15/2.81 | | | | | | | | | | | | | | | | all_29_12, simplifying with (14), (29), (198), % 15.15/2.81 | | | | | | | | | | | | | | | | (230) gives: % 15.15/2.81 | | | | | | | | | | | | | | | | (238) all_162_1 = all_29_22 % 15.15/2.81 | | | | | | | | | | | | | | | | % 15.15/2.81 | | | | | | | | | | | | | | | | REDUCE: (237), (238) imply: % 15.15/2.81 | | | | | | | | | | | | | | | | (239) mem(all_213_1, all_29_22) = 0 % 15.15/2.81 | | | | | | | | | | | | | | | | % 15.15/2.81 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (11) with all_213_0, 0, all_29_22, % 15.15/2.81 | | | | | | | | | | | | | | | | all_213_1, simplifying with (236), (239) gives: % 15.15/2.81 | | | | | | | | | | | | | | | | (240) all_213_0 = 0 % 15.15/2.81 | | | | | | | | | | | | | | | | % 15.15/2.81 | | | | | | | | | | | | | | | | REDUCE: (235), (240) imply: % 15.15/2.81 | | | | | | | | | | | | | | | | (241) $false % 15.15/2.81 | | | | | | | | | | | | | | | | % 15.15/2.81 | | | | | | | | | | | | | | | | CLOSE: (241) is inconsistent. % 15.15/2.81 | | | | | | | | | | | | | | | | % 15.15/2.81 | | | | | | | | | | | | | | | End of split % 15.15/2.81 | | | | | | | | | | | | | | | % 15.15/2.81 | | | | | | | | | | | | | | Case 2: % 15.15/2.81 | | | | | | | | | | | | | | | % 15.15/2.81 | | | | | | | | | | | | | | | (242) all_182_1 = 0 % 15.15/2.81 | | | | | | | | | | | | | | | % 15.15/2.81 | | | | | | | | | | | | | | | COMBINE_EQS: (225), (242) imply: % 15.15/2.81 | | | | | | | | | | | | | | | (243) all_167_0 = 0 % 15.15/2.81 | | | | | | | | | | | | | | | % 15.15/2.81 | | | | | | | | | | | | | | | SIMP: (243) implies: % 15.15/2.81 | | | | | | | | | | | | | | | (244) all_167_0 = 0 % 15.15/2.81 | | | | | | | | | | | | | | | % 15.15/2.81 | | | | | | | | | | | | | | | REDUCE: (206), (244) imply: % 15.15/2.81 | | | | | | | | | | | | | | | (245) $false % 15.15/2.81 | | | | | | | | | | | | | | | % 15.15/2.81 | | | | | | | | | | | | | | | CLOSE: (245) is inconsistent. % 15.15/2.81 | | | | | | | | | | | | | | | % 15.15/2.81 | | | | | | | | | | | | | | End of split % 15.15/2.81 | | | | | | | | | | | | | | % 15.15/2.81 | | | | | | | | | | | | | End of split % 15.15/2.81 | | | | | | | | | | | | | % 15.15/2.81 | | | | | | | | | | | | Case 2: % 15.15/2.81 | | | | | | | | | | | | | % 15.15/2.81 | | | | | | | | | | | | | (246) all_131_1 = 0 % 15.15/2.81 | | | | | | | | | | | | | % 15.15/2.81 | | | | | | | | | | | | | REDUCE: (210), (246) imply: % 15.15/2.81 | | | | | | | | | | | | | (247) $false % 15.15/2.81 | | | | | | | | | | | | | % 15.15/2.81 | | | | | | | | | | | | | CLOSE: (247) is inconsistent. % 15.15/2.81 | | | | | | | | | | | | | % 15.15/2.81 | | | | | | | | | | | | End of split % 15.15/2.81 | | | | | | | | | | | | % 15.15/2.81 | | | | | | | | | | | End of split % 15.15/2.81 | | | | | | | | | | | % 15.15/2.81 | | | | | | | | | | End of split % 15.15/2.81 | | | | | | | | | | % 15.15/2.81 | | | | | | | | | End of split % 15.15/2.81 | | | | | | | | | % 15.15/2.81 | | | | | | | | End of split % 15.15/2.81 | | | | | | | | % 15.15/2.81 | | | | | | | End of split % 15.15/2.81 | | | | | | | % 15.15/2.81 | | | | | | End of split % 15.15/2.81 | | | | | | % 15.15/2.81 | | | | | End of split % 15.15/2.81 | | | | | % 15.15/2.81 | | | | End of split % 15.15/2.81 | | | | % 15.15/2.81 | | | Case 2: % 15.15/2.81 | | | | % 15.15/2.81 | | | | (248) all_69_1 = 0 % 15.15/2.81 | | | | % 15.15/2.81 | | | | REDUCE: (108), (248) imply: % 15.15/2.81 | | | | (249) mem(all_49_1, all_29_13) = 0 % 15.15/2.81 | | | | % 15.15/2.81 | | | | BETA: splitting (136) gives: % 15.15/2.81 | | | | % 15.15/2.81 | | | | Case 1: % 15.15/2.81 | | | | | % 15.15/2.81 | | | | | (250) all_81_1 = 0 % 15.15/2.81 | | | | | % 15.15/2.81 | | | | | REDUCE: (126), (250) imply: % 15.15/2.81 | | | | | (251) $false % 15.15/2.81 | | | | | % 15.15/2.81 | | | | | CLOSE: (251) is inconsistent. % 15.15/2.81 | | | | | % 15.15/2.81 | | | | Case 2: % 15.15/2.81 | | | | | % 15.15/2.81 | | | | | (252) ? [v0: int] : ? [v1: int] : ( ~ (v1 = 0) & ~ (v0 = 0) & % 15.15/2.81 | | | | | mem(all_49_1, all_29_4) = v1 & mem(all_49_1, all_29_6) = % 15.15/2.81 | | | | | v0) % 15.15/2.81 | | | | | % 15.15/2.81 | | | | | DELTA: instantiating (252) with fresh symbols all_103_0, all_103_1 % 15.15/2.81 | | | | | gives: % 15.15/2.81 | | | | | (253) ~ (all_103_0 = 0) & ~ (all_103_1 = 0) & mem(all_49_1, % 15.15/2.81 | | | | | all_29_4) = all_103_0 & mem(all_49_1, all_29_6) = all_103_1 % 15.15/2.81 | | | | | % 15.15/2.81 | | | | | ALPHA: (253) implies: % 15.15/2.81 | | | | | (254) ~ (all_103_1 = 0) % 15.15/2.81 | | | | | (255) ~ (all_103_0 = 0) % 15.15/2.81 | | | | | (256) mem(all_49_1, all_29_6) = all_103_1 % 15.15/2.81 | | | | | (257) mem(all_49_1, all_29_4) = all_103_0 % 15.15/2.81 | | | | | % 15.15/2.81 | | | | | GROUND_INST: instantiating (3) with all_49_1, all_29_19, all_29_14, % 15.15/2.81 | | | | | all_29_13, simplifying with (35), (70), (83), (135), % 15.15/2.81 | | | | | (249) gives: % 15.15/2.81 | | | | | (258) ? [v0: any] : ? [v1: any] : (mem(all_49_1, all_29_14) = v1 % 15.15/2.81 | | | | | & mem(all_49_1, all_29_19) = v0 & (v1 = 0 | v0 = 0)) % 15.15/2.81 | | | | | % 15.15/2.81 | | | | | GROUND_INST: instantiating (4) with all_49_1, all_29_20, all_29_19, % 15.15/2.81 | | | | | all_29_6, all_103_1, simplifying with (15), (83), (133), % 15.15/2.81 | | | | | (135), (256) gives: % 15.15/2.81 | | | | | (259) all_103_1 = 0 | ? [v0: int] : ? [v1: int] : ( ~ (v1 = 0) & % 15.15/2.81 | | | | | ~ (v0 = 0) & mem(all_49_1, all_29_19) = v1 & mem(all_49_1, % 15.15/2.81 | | | | | all_29_20) = v0) % 15.15/2.81 | | | | | % 15.15/2.81 | | | | | GROUND_INST: instantiating (4) with all_49_1, all_29_5, all_39_0, % 15.15/2.81 | | | | | all_29_4, all_103_0, simplifying with (24), (83), (88), % 15.15/2.81 | | | | | (90), (257) gives: % 15.15/2.81 | | | | | (260) all_103_0 = 0 | ? [v0: int] : ? [v1: int] : ( ~ (v1 = 0) & % 15.15/2.81 | | | | | ~ (v0 = 0) & mem(all_49_1, all_39_0) = v1 & mem(all_49_1, % 15.15/2.81 | | | | | all_29_5) = v0) % 15.15/2.81 | | | | | % 15.15/2.81 | | | | | DELTA: instantiating (258) with fresh symbols all_114_0, all_114_1 % 15.15/2.81 | | | | | gives: % 15.15/2.81 | | | | | (261) mem(all_49_1, all_29_14) = all_114_0 & mem(all_49_1, % 15.15/2.81 | | | | | all_29_19) = all_114_1 & (all_114_0 = 0 | all_114_1 = 0) % 15.15/2.81 | | | | | % 15.15/2.81 | | | | | ALPHA: (261) implies: % 15.15/2.81 | | | | | (262) mem(all_49_1, all_29_19) = all_114_1 % 15.15/2.81 | | | | | (263) mem(all_49_1, all_29_14) = all_114_0 % 15.15/2.81 | | | | | (264) all_114_0 = 0 | all_114_1 = 0 % 15.15/2.81 | | | | | % 15.15/2.81 | | | | | BETA: splitting (259) gives: % 15.15/2.81 | | | | | % 15.15/2.81 | | | | | Case 1: % 15.15/2.81 | | | | | | % 15.15/2.81 | | | | | | (265) all_103_1 = 0 % 15.15/2.82 | | | | | | % 15.15/2.82 | | | | | | REDUCE: (254), (265) imply: % 15.15/2.82 | | | | | | (266) $false % 15.15/2.82 | | | | | | % 15.15/2.82 | | | | | | CLOSE: (266) is inconsistent. % 15.15/2.82 | | | | | | % 15.15/2.82 | | | | | Case 2: % 15.15/2.82 | | | | | | % 15.15/2.82 | | | | | | (267) ? [v0: int] : ? [v1: int] : ( ~ (v1 = 0) & ~ (v0 = 0) & % 15.15/2.82 | | | | | | mem(all_49_1, all_29_19) = v1 & mem(all_49_1, all_29_20) % 15.15/2.82 | | | | | | = v0) % 15.15/2.82 | | | | | | % 15.15/2.82 | | | | | | DELTA: instantiating (267) with fresh symbols all_120_0, all_120_1 % 15.15/2.82 | | | | | | gives: % 15.15/2.82 | | | | | | (268) ~ (all_120_0 = 0) & ~ (all_120_1 = 0) & mem(all_49_1, % 15.15/2.82 | | | | | | all_29_19) = all_120_0 & mem(all_49_1, all_29_20) = % 15.15/2.82 | | | | | | all_120_1 % 15.15/2.82 | | | | | | % 15.15/2.82 | | | | | | ALPHA: (268) implies: % 15.15/2.82 | | | | | | (269) ~ (all_120_0 = 0) % 15.15/2.82 | | | | | | (270) mem(all_49_1, all_29_19) = all_120_0 % 15.15/2.82 | | | | | | % 15.15/2.82 | | | | | | BETA: splitting (260) gives: % 15.15/2.82 | | | | | | % 15.15/2.82 | | | | | | Case 1: % 15.15/2.82 | | | | | | | % 15.15/2.82 | | | | | | | (271) all_103_0 = 0 % 15.15/2.82 | | | | | | | % 15.15/2.82 | | | | | | | REDUCE: (255), (271) imply: % 15.15/2.82 | | | | | | | (272) $false % 15.15/2.82 | | | | | | | % 15.15/2.82 | | | | | | | CLOSE: (272) is inconsistent. % 15.15/2.82 | | | | | | | % 15.15/2.82 | | | | | | Case 2: % 15.15/2.82 | | | | | | | % 15.15/2.82 | | | | | | | (273) ? [v0: int] : ? [v1: int] : ( ~ (v1 = 0) & ~ (v0 = 0) % 15.15/2.82 | | | | | | | & mem(all_49_1, all_39_0) = v1 & mem(all_49_1, % 15.15/2.82 | | | | | | | all_29_5) = v0) % 15.15/2.82 | | | | | | | % 15.15/2.82 | | | | | | | DELTA: instantiating (273) with fresh symbols all_130_0, all_130_1 % 15.15/2.82 | | | | | | | gives: % 15.15/2.82 | | | | | | | (274) ~ (all_130_0 = 0) & ~ (all_130_1 = 0) & mem(all_49_1, % 15.15/2.82 | | | | | | | all_39_0) = all_130_0 & mem(all_49_1, all_29_5) = % 15.15/2.82 | | | | | | | all_130_1 % 15.15/2.82 | | | | | | | % 15.15/2.82 | | | | | | | ALPHA: (274) implies: % 15.15/2.82 | | | | | | | (275) ~ (all_130_1 = 0) % 15.15/2.82 | | | | | | | (276) ~ (all_130_0 = 0) % 15.15/2.82 | | | | | | | (277) mem(all_49_1, all_29_5) = all_130_1 % 15.15/2.82 | | | | | | | (278) mem(all_49_1, all_39_0) = all_130_0 % 15.15/2.82 | | | | | | | % 15.15/2.82 | | | | | | | GROUND_INST: instantiating (11) with all_114_1, all_120_0, % 15.15/2.82 | | | | | | | all_29_19, all_49_1, simplifying with (262), (270) % 15.15/2.82 | | | | | | | gives: % 15.15/2.82 | | | | | | | (279) all_120_0 = all_114_1 % 15.15/2.82 | | | | | | | % 15.15/2.82 | | | | | | | REDUCE: (269), (279) imply: % 15.15/2.82 | | | | | | | (280) ~ (all_114_1 = 0) % 15.15/2.82 | | | | | | | % 15.15/2.82 | | | | | | | BETA: splitting (264) gives: % 15.15/2.82 | | | | | | | % 15.15/2.82 | | | | | | | Case 1: % 15.15/2.82 | | | | | | | | % 15.15/2.82 | | | | | | | | (281) all_114_0 = 0 % 15.15/2.82 | | | | | | | | % 15.15/2.82 | | | | | | | | REDUCE: (263), (281) imply: % 15.15/2.82 | | | | | | | | (282) mem(all_49_1, all_29_14) = 0 % 15.15/2.82 | | | | | | | | % 15.15/2.82 | | | | | | | | GROUND_INST: instantiating (3) with all_49_1, all_29_17, % 15.15/2.82 | | | | | | | | all_39_0, all_29_14, simplifying with (17), (72), % 15.15/2.82 | | | | | | | | (83), (90), (282) gives: % 15.15/2.82 | | | | | | | | (283) ? [v0: any] : ? [v1: any] : (mem(all_49_1, all_39_0) % 15.15/2.82 | | | | | | | | = v1 & mem(all_49_1, all_29_17) = v0 & (v1 = 0 | v0 = % 15.15/2.82 | | | | | | | | 0)) % 15.15/2.82 | | | | | | | | % 15.15/2.82 | | | | | | | | GROUND_INST: instantiating (7) with all_49_1, all_29_18, % 15.15/2.82 | | | | | | | | all_29_5, all_130_1, simplifying with (16), (48), % 15.15/2.82 | | | | | | | | (83), (277) gives: % 15.15/2.82 | | | | | | | | (284) all_130_1 = 0 | ? [v0: int] : ( ~ (v0 = 0) & % 15.15/2.82 | | | | | | | | subq(all_49_1, all_29_18) = v0) % 15.15/2.82 | | | | | | | | % 15.15/2.82 | | | | | | | | DELTA: instantiating (283) with fresh symbols all_145_0, % 15.15/2.82 | | | | | | | | all_145_1 gives: % 15.15/2.82 | | | | | | | | (285) mem(all_49_1, all_39_0) = all_145_0 & mem(all_49_1, % 15.15/2.82 | | | | | | | | all_29_17) = all_145_1 & (all_145_0 = 0 | all_145_1 = % 15.15/2.82 | | | | | | | | 0) % 15.15/2.82 | | | | | | | | % 15.15/2.82 | | | | | | | | ALPHA: (285) implies: % 15.15/2.82 | | | | | | | | (286) mem(all_49_1, all_29_17) = all_145_1 % 15.15/2.82 | | | | | | | | (287) mem(all_49_1, all_39_0) = all_145_0 % 15.15/2.82 | | | | | | | | (288) all_145_0 = 0 | all_145_1 = 0 % 15.15/2.82 | | | | | | | | % 15.15/2.82 | | | | | | | | BETA: splitting (284) gives: % 15.15/2.82 | | | | | | | | % 15.15/2.82 | | | | | | | | Case 1: % 15.15/2.82 | | | | | | | | | % 15.15/2.82 | | | | | | | | | (289) all_130_1 = 0 % 15.15/2.82 | | | | | | | | | % 15.15/2.82 | | | | | | | | | REDUCE: (275), (289) imply: % 15.15/2.82 | | | | | | | | | (290) $false % 15.15/2.82 | | | | | | | | | % 15.15/2.82 | | | | | | | | | CLOSE: (290) is inconsistent. % 15.15/2.82 | | | | | | | | | % 15.15/2.82 | | | | | | | | Case 2: % 15.15/2.82 | | | | | | | | | % 15.15/2.82 | | | | | | | | | (291) ? [v0: int] : ( ~ (v0 = 0) & subq(all_49_1, % 15.15/2.82 | | | | | | | | | all_29_18) = v0) % 15.15/2.82 | | | | | | | | | % 15.15/2.82 | | | | | | | | | DELTA: instantiating (291) with fresh symbol all_151_0 gives: % 15.15/2.82 | | | | | | | | | (292) ~ (all_151_0 = 0) & subq(all_49_1, all_29_18) = % 15.15/2.82 | | | | | | | | | all_151_0 % 15.15/2.82 | | | | | | | | | % 15.15/2.82 | | | | | | | | | ALPHA: (292) implies: % 15.15/2.82 | | | | | | | | | (293) ~ (all_151_0 = 0) % 15.15/2.82 | | | | | | | | | (294) subq(all_49_1, all_29_18) = all_151_0 % 15.15/2.82 | | | | | | | | | % 15.15/2.82 | | | | | | | | | GROUND_INST: instantiating (11) with all_130_0, all_145_0, % 15.15/2.82 | | | | | | | | | all_39_0, all_49_1, simplifying with (278), (287) % 15.15/2.82 | | | | | | | | | gives: % 15.15/2.82 | | | | | | | | | (295) all_145_0 = all_130_0 % 15.15/2.82 | | | | | | | | | % 15.15/2.82 | | | | | | | | | BETA: splitting (288) gives: % 15.15/2.82 | | | | | | | | | % 15.15/2.82 | | | | | | | | | Case 1: % 15.15/2.82 | | | | | | | | | | % 15.15/2.82 | | | | | | | | | | (296) all_145_0 = 0 % 15.15/2.82 | | | | | | | | | | % 15.15/2.82 | | | | | | | | | | COMBINE_EQS: (295), (296) imply: % 15.15/2.82 | | | | | | | | | | (297) all_130_0 = 0 % 15.15/2.82 | | | | | | | | | | % 15.15/2.82 | | | | | | | | | | REDUCE: (276), (297) imply: % 15.15/2.82 | | | | | | | | | | (298) $false % 15.15/2.82 | | | | | | | | | | % 15.15/2.82 | | | | | | | | | | CLOSE: (298) is inconsistent. % 15.15/2.82 | | | | | | | | | | % 15.15/2.82 | | | | | | | | | Case 2: % 15.15/2.82 | | | | | | | | | | % 15.15/2.82 | | | | | | | | | | (299) all_145_1 = 0 % 15.15/2.82 | | | | | | | | | | % 15.15/2.82 | | | | | | | | | | REDUCE: (286), (299) imply: % 15.15/2.82 | | | | | | | | | | (300) mem(all_49_1, all_29_17) = 0 % 15.15/2.82 | | | | | | | | | | % 15.15/2.82 | | | | | | | | | | GROUND_INST: instantiating (2) with all_49_1, all_29_18, % 15.15/2.82 | | | | | | | | | | all_29_17, simplifying with (16), (31), (83), % 15.15/2.82 | | | | | | | | | | (300) gives: % 15.15/2.82 | | | | | | | | | | (301) all_49_1 = all_29_18 % 15.15/2.82 | | | | | | | | | | % 15.15/2.82 | | | | | | | | | | GROUND_INST: instantiating (1) with all_49_1, all_29_18, % 15.15/2.82 | | | | | | | | | | all_151_0, simplifying with (16), (83), (294) % 15.15/2.82 | | | | | | | | | | gives: % 15.15/2.82 | | | | | | | | | | (302) all_151_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ % 15.15/2.82 | | | | | | | | | | (v1 = 0) & mem(v0, all_49_1) = 0 & mem(v0, % 15.15/2.82 | | | | | | | | | | all_29_18) = v1 & $i(v0)) % 15.15/2.82 | | | | | | | | | | % 15.15/2.82 | | | | | | | | | | BETA: splitting (302) gives: % 15.15/2.82 | | | | | | | | | | % 15.15/2.82 | | | | | | | | | | Case 1: % 15.15/2.82 | | | | | | | | | | | % 15.15/2.82 | | | | | | | | | | | (303) all_151_0 = 0 % 15.15/2.82 | | | | | | | | | | | % 15.15/2.82 | | | | | | | | | | | REDUCE: (293), (303) imply: % 15.15/2.82 | | | | | | | | | | | (304) $false % 15.15/2.82 | | | | | | | | | | | % 15.15/2.82 | | | | | | | | | | | CLOSE: (304) is inconsistent. % 15.15/2.82 | | | | | | | | | | | % 15.15/2.82 | | | | | | | | | | Case 2: % 15.15/2.82 | | | | | | | | | | | % 15.15/2.82 | | | | | | | | | | | (305) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & % 15.15/2.82 | | | | | | | | | | | mem(v0, all_49_1) = 0 & mem(v0, all_29_18) = v1 % 15.15/2.82 | | | | | | | | | | | & $i(v0)) % 15.15/2.82 | | | | | | | | | | | % 15.15/2.82 | | | | | | | | | | | DELTA: instantiating (305) with fresh symbols all_181_0, % 15.15/2.82 | | | | | | | | | | | all_181_1 gives: % 15.15/2.82 | | | | | | | | | | | (306) ~ (all_181_0 = 0) & mem(all_181_1, all_49_1) = 0 % 15.15/2.82 | | | | | | | | | | | & mem(all_181_1, all_29_18) = all_181_0 & % 15.15/2.82 | | | | | | | | | | | $i(all_181_1) % 15.15/2.82 | | | | | | | | | | | % 15.15/2.82 | | | | | | | | | | | ALPHA: (306) implies: % 15.15/2.82 | | | | | | | | | | | (307) ~ (all_181_0 = 0) % 15.15/2.82 | | | | | | | | | | | (308) mem(all_181_1, all_29_18) = all_181_0 % 15.15/2.82 | | | | | | | | | | | (309) mem(all_181_1, all_49_1) = 0 % 15.15/2.82 | | | | | | | | | | | % 15.15/2.82 | | | | | | | | | | | REDUCE: (301), (309) imply: % 15.15/2.83 | | | | | | | | | | | (310) mem(all_181_1, all_29_18) = 0 % 15.15/2.83 | | | | | | | | | | | % 15.15/2.83 | | | | | | | | | | | GROUND_INST: instantiating (11) with 0, all_181_0, all_29_18, % 15.15/2.83 | | | | | | | | | | | all_181_1, simplifying with (308), (310) gives: % 15.15/2.83 | | | | | | | | | | | (311) all_181_0 = 0 % 15.15/2.83 | | | | | | | | | | | % 15.15/2.83 | | | | | | | | | | | REDUCE: (307), (311) imply: % 15.15/2.83 | | | | | | | | | | | (312) $false % 15.15/2.83 | | | | | | | | | | | % 15.15/2.83 | | | | | | | | | | | CLOSE: (312) is inconsistent. % 15.15/2.83 | | | | | | | | | | | % 15.15/2.83 | | | | | | | | | | End of split % 15.15/2.83 | | | | | | | | | | % 15.15/2.83 | | | | | | | | | End of split % 15.15/2.83 | | | | | | | | | % 15.15/2.83 | | | | | | | | End of split % 15.15/2.83 | | | | | | | | % 15.15/2.83 | | | | | | | Case 2: % 15.15/2.83 | | | | | | | | % 15.15/2.83 | | | | | | | | (313) all_114_1 = 0 % 15.15/2.83 | | | | | | | | % 15.15/2.83 | | | | | | | | REDUCE: (280), (313) imply: % 15.15/2.83 | | | | | | | | (314) $false % 15.15/2.83 | | | | | | | | % 15.15/2.83 | | | | | | | | CLOSE: (314) is inconsistent. % 15.15/2.83 | | | | | | | | % 15.15/2.83 | | | | | | | End of split % 15.15/2.83 | | | | | | | % 15.15/2.83 | | | | | | End of split % 15.15/2.83 | | | | | | % 15.15/2.83 | | | | | End of split % 15.15/2.83 | | | | | % 15.15/2.83 | | | | End of split % 15.15/2.83 | | | | % 15.15/2.83 | | | End of split % 15.15/2.83 | | | % 15.15/2.83 | | End of split % 15.15/2.83 | | % 15.15/2.83 | End of split % 15.15/2.83 | % 15.15/2.83 End of proof % 15.15/2.83 % SZS output end Proof for theBenchmark % 15.15/2.83 % 15.15/2.83 2238ms %------------------------------------------------------------------------------