%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SEV582+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 : n010.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 10.53s 2.20s % Output : Proof 12.91s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : SEV582+1 : TPTP v9.1.0. Released v9.1.0. % 0.03/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.12/0.34 % Computer : n010.cluster.edu % 0.12/0.34 % Model : x86_64 x86_64 % 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.34 % Memory : 8042.1875MB % 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.34 % CPULimit : 300 % 0.12/0.34 % WCLimit : 300 % 0.12/0.34 % DateTime : Mon Mar 31 13:17:11 EDT 2025 % 0.12/0.34 % CPUTime : % 0.67/0.63 ________ _____ % 0.67/0.63 ___ __ \_________(_)________________________________ % 0.67/0.63 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.67/0.63 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.67/0.63 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.67/0.63 % 0.67/0.63 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.67/0.63 (2023-06-19) % 0.67/0.63 % 0.67/0.63 (c) Philipp Rümmer, 2009-2023 % 0.67/0.63 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.67/0.63 Amanda Stjerna. % 0.67/0.63 Free software under BSD-3-Clause. % 0.67/0.63 % 0.67/0.63 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.67/0.63 % 0.67/0.63 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.71/0.65 Running up to 7 provers in parallel. % 0.71/0.67 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.71/0.67 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.71/0.67 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.71/0.67 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.71/0.67 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.71/0.67 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.71/0.67 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.85/1.12 Prover 1: Preprocessing ... % 2.85/1.13 Prover 4: Preprocessing ... % 3.34/1.16 Prover 2: Preprocessing ... % 3.34/1.16 Prover 3: Preprocessing ... % 3.34/1.16 Prover 6: Preprocessing ... % 3.34/1.16 Prover 0: Preprocessing ... % 3.34/1.16 Prover 5: Preprocessing ... % 6.73/1.64 Prover 2: Proving ... % 6.73/1.65 Prover 5: Proving ... % 7.18/1.69 Prover 6: Proving ... % 7.18/1.71 Prover 3: Constructing countermodel ... % 7.18/1.74 Prover 1: Constructing countermodel ... % 7.93/1.79 Prover 4: Constructing countermodel ... % 8.17/1.83 Prover 0: Proving ... % 8.91/1.93 Prover 3: gave up % 8.91/1.96 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 8.91/1.97 Prover 1: gave up % 8.91/1.97 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 9.42/2.02 Prover 7: Preprocessing ... % 9.42/2.02 Prover 8: Preprocessing ... % 10.53/2.14 Prover 7: Warning: ignoring some quantifiers % 10.53/2.16 Prover 7: Constructing countermodel ... % 10.53/2.19 Prover 0: proved (1537ms) % 10.53/2.19 % 10.53/2.20 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 10.53/2.20 % 10.53/2.20 Prover 5: stopped % 10.53/2.20 Prover 6: stopped % 10.53/2.21 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 10.53/2.21 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 10.53/2.21 Prover 2: stopped % 11.15/2.22 Prover 8: Warning: ignoring some quantifiers % 11.15/2.22 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 11.15/2.22 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 11.15/2.22 Prover 8: Constructing countermodel ... % 11.15/2.25 Prover 10: Preprocessing ... % 11.15/2.25 Prover 11: Preprocessing ... % 11.15/2.27 Prover 13: Preprocessing ... % 11.69/2.30 Prover 4: Found proof (size 118) % 11.69/2.30 Prover 4: proved (1636ms) % 11.69/2.30 Prover 8: stopped % 11.69/2.30 Prover 7: stopped % 11.69/2.30 Prover 10: Warning: ignoring some quantifiers % 11.69/2.30 Prover 11: stopped % 11.69/2.31 Prover 16: Preprocessing ... % 11.69/2.31 Prover 10: Constructing countermodel ... % 11.69/2.32 Prover 10: stopped % 11.69/2.33 Prover 16: stopped % 11.69/2.34 Prover 13: Warning: ignoring some quantifiers % 11.69/2.35 Prover 13: Constructing countermodel ... % 11.69/2.36 Prover 13: stopped % 11.69/2.36 % 11.69/2.36 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 11.69/2.36 % 12.20/2.38 % SZS output start Proof for theBenchmark % 12.20/2.39 Assumptions after simplification: % 12.20/2.39 --------------------------------- % 12.20/2.39 % 12.20/2.39 (a_def) % 12.35/2.42 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (u(v0, v2) = v3) | % 12.35/2.42 ~ (s(v1) = v2) | ~ $i(v1) | ~ $i(v0) | (a(v0, v1) = v3 & $i(v3))) & ! % 12.35/2.42 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (a(v0, v1) = v2) | ~ $i(v1) | ~ % 12.35/2.42 $i(v0) | ? [v3: $i] : (u(v0, v3) = v2 & s(v1) = v3 & $i(v3) & $i(v2))) % 12.35/2.42 % 12.35/2.42 (n_def) % 12.35/2.42 ! [v0: $i] : ! [v1: $i] : ( ~ (n(v0) = v1) | ~ $i(v0) | (a(v0, v0) = v1 & % 12.35/2.42 $i(v1))) & ! [v0: $i] : ! [v1: $i] : ( ~ (a(v0, v0) = v1) | ~ $i(v0) | % 12.35/2.42 (n(v0) = v1 & $i(v1))) % 12.35/2.42 % 12.35/2.42 (s_ax) % 12.35/2.43 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (s(v0) = v1) | ~ % 12.35/2.43 (mem(v0, v1) = v2) | ~ $i(v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 12.35/2.43 (v1 = v0 | ~ (s(v1) = v2) | ~ (mem(v0, v2) = 0) | ~ $i(v1) | ~ $i(v0)) % 12.35/2.43 % 12.35/2.43 (subq_402_33170) % 12.45/2.43 $i(e) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 12.45/2.43 ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ? [v10: % 12.45/2.43 $i] : ? [v11: $i] : ? [v12: $i] : ? [v13: $i] : ? [v14: $i] : ? [v15: % 12.45/2.43 $i] : ? [v16: $i] : ? [v17: $i] : ? [v18: int] : ( ~ (v18 = 0) & p(v7) = % 12.45/2.43 v15 & n(v1) = v4 & n(v0) = v7 & n(e) = v0 & a(v12, v8) = v13 & a(v3, v5) = % 12.45/2.43 v6 & a(v1, v15) = v16 & a(v1, v2) = v3 & u(v14, v16) = v17 & u(v11, v13) = % 12.45/2.43 v14 & u(v6, v9) = v10 & u(v0, v4) = v5 & s(v8) = v9 & s(v7) = v8 & s(v5) = % 12.45/2.43 v11 & s(v2) = v12 & s(v1) = v2 & s(v0) = v1 & subq(v10, v17) = v18 & $i(v17) % 12.45/2.43 & $i(v16) & $i(v15) & $i(v14) & $i(v13) & $i(v12) & $i(v11) & $i(v10) & % 12.45/2.43 $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & % 12.45/2.43 $i(v1) & $i(v0)) % 12.45/2.43 % 12.45/2.43 (subq_def) % 12.45/2.44 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 12.45/2.44 (subq(v0, v1) = 0) | ~ (mem(v2, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ % 12.45/2.44 $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & mem(v2, v0) = v4)) & ! [v0: $i] : ! % 12.45/2.44 [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subq(v0, v1) = v2) | ~ $i(v1) | ~ % 12.45/2.44 $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & mem(v3, v1) = v4 & % 12.45/2.44 mem(v3, v0) = 0 & $i(v3))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 12.45/2.44 (subq(v0, v1) = 0) | ~ (mem(v2, v0) = 0) | ~ $i(v2) | ~ $i(v1) | ~ % 12.45/2.44 $i(v0) | mem(v2, v1) = 0) % 12.45/2.44 % 12.45/2.44 (u_ax) % 12.45/2.44 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0 % 12.45/2.44 | ~ (u(v1, v2) = v3) | ~ (mem(v0, v3) = v4) | ~ $i(v2) | ~ $i(v1) | ~ % 12.45/2.44 $i(v0) | ? [v5: int] : ? [v6: int] : ( ~ (v6 = 0) & ~ (v5 = 0) & mem(v0, % 12.45/2.44 v2) = v6 & mem(v0, v1) = v5)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 12.45/2.44 : ! [v3: $i] : ( ~ (u(v1, v2) = v3) | ~ (mem(v0, v3) = 0) | ~ $i(v2) | ~ % 12.45/2.44 $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] : (mem(v0, v2) = v5 & % 12.45/2.44 mem(v0, v1) = v4 & (v5 = 0 | v4 = 0))) % 12.45/2.44 % 12.45/2.44 (function-axioms) % 12.45/2.45 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (a(v3, % 12.45/2.45 v2) = v1) | ~ (a(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 12.45/2.45 $i] : ! [v3: $i] : (v1 = v0 | ~ (m(v3, v2) = v1) | ~ (m(v3, v2) = v0)) & % 12.45/2.45 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (u(v3, % 12.45/2.45 v2) = v1) | ~ (u(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 12.45/2.45 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (disj(v3, v2) % 12.45/2.45 = v1) | ~ (disj(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 12.45/2.45 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (subq(v3, v2) % 12.45/2.45 = v1) | ~ (subq(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 12.45/2.45 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (mem(v3, v2) % 12.45/2.45 = v1) | ~ (mem(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 12.45/2.45 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (atleast16p(v2) = v1) | ~ % 12.45/2.45 (atleast16p(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 12.45/2.45 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (atleast15p(v2) = v1) | ~ % 12.45/2.45 (atleast15p(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 12.45/2.45 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (atleast14p(v2) = v1) | ~ % 12.45/2.45 (atleast14p(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 12.45/2.45 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (atleast13p(v2) = v1) | ~ % 12.45/2.45 (atleast13p(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 12.45/2.45 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (atleast12p(v2) = v1) | ~ % 12.45/2.45 (atleast12p(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 12.45/2.45 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (atleast11p(v2) = v1) | ~ % 12.45/2.45 (atleast11p(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 12.45/2.45 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (atleast10p(v2) = v1) | ~ % 12.45/2.45 (atleast10p(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 12.45/2.45 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (atleast9p(v2) = v1) | ~ % 12.45/2.45 (atleast9p(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 12.45/2.45 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (atleast8p(v2) = v1) | ~ % 12.45/2.45 (atleast8p(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 12.45/2.45 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (atleast7p(v2) = v1) | ~ % 12.45/2.45 (atleast7p(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 12.45/2.45 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (atleast6p(v2) = v1) | ~ % 12.45/2.45 (atleast6p(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 12.45/2.45 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (atleast5p(v2) = v1) | ~ % 12.45/2.45 (atleast5p(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 12.45/2.45 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (atleast4p(v2) = v1) | ~ % 12.45/2.45 (atleast4p(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 12.45/2.45 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (atleast3p(v2) = v1) | ~ % 12.45/2.45 (atleast3p(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 12.45/2.45 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (atleast2p(v2) = v1) | ~ % 12.45/2.45 (atleast2p(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | % 12.45/2.45 ~ (p(v2) = v1) | ~ (p(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 12.45/2.45 : (v1 = v0 | ~ (n(v2) = v1) | ~ (n(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : % 12.45/2.45 ! [v2: $i] : (v1 = v0 | ~ (s(v2) = v1) | ~ (s(v2) = v0)) % 12.45/2.45 % 12.45/2.45 Further assumptions not needed in the proof: % 12.45/2.45 -------------------------------------------- % 12.45/2.45 atleast10p_def, atleast11p_def, atleast12p_def, atleast13p_def, atleast14p_def, % 12.45/2.45 atleast15p_def, atleast16p_def, atleast2p_def, atleast3p_def, atleast4p_def, % 12.45/2.45 atleast5p_def, atleast6p_def, atleast7p_def, atleast8p_def, atleast9p_def, % 12.45/2.45 disj_def, e_ax, m_ax, p_ax, setext % 12.45/2.45 % 12.45/2.45 Those formulas are unsatisfiable: % 12.45/2.45 --------------------------------- % 12.45/2.45 % 12.45/2.45 Begin of proof % 12.45/2.45 | % 12.45/2.45 | ALPHA: (subq_def) implies: % 12.45/2.45 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subq(v0, v1) = % 12.45/2.45 | v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 % 12.45/2.45 | = 0) & mem(v3, v1) = v4 & mem(v3, v0) = 0 & $i(v3))) % 12.45/2.45 | % 12.45/2.45 | ALPHA: (s_ax) implies: % 12.45/2.45 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (s(v1) = v2) | % 12.45/2.45 | ~ (mem(v0, v2) = 0) | ~ $i(v1) | ~ $i(v0)) % 12.45/2.45 | % 12.45/2.45 | ALPHA: (u_ax) implies: % 12.45/2.45 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (u(v1, v2) % 12.45/2.45 | = v3) | ~ (mem(v0, v3) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 12.45/2.45 | ? [v4: any] : ? [v5: any] : (mem(v0, v2) = v5 & mem(v0, v1) = v4 & % 12.45/2.45 | (v5 = 0 | v4 = 0))) % 12.45/2.46 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : % 12.45/2.46 | (v4 = 0 | ~ (u(v1, v2) = v3) | ~ (mem(v0, v3) = v4) | ~ $i(v2) | ~ % 12.45/2.46 | $i(v1) | ~ $i(v0) | ? [v5: int] : ? [v6: int] : ( ~ (v6 = 0) & ~ % 12.45/2.46 | (v5 = 0) & mem(v0, v2) = v6 & mem(v0, v1) = v5)) % 12.45/2.46 | % 12.45/2.46 | ALPHA: (a_def) implies: % 12.45/2.46 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (a(v0, v1) = v2) | ~ % 12.45/2.46 | $i(v1) | ~ $i(v0) | ? [v3: $i] : (u(v0, v3) = v2 & s(v1) = v3 & % 12.45/2.46 | $i(v3) & $i(v2))) % 12.45/2.46 | % 12.45/2.46 | ALPHA: (n_def) implies: % 12.45/2.46 | (6) ! [v0: $i] : ! [v1: $i] : ( ~ (n(v0) = v1) | ~ $i(v0) | (a(v0, v0) = % 12.45/2.46 | v1 & $i(v1))) % 12.45/2.46 | % 12.45/2.46 | ALPHA: (subq_402_33170) implies: % 12.45/2.46 | (7) $i(e) % 12.45/2.46 | (8) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 12.45/2.46 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ? % 12.45/2.46 | [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13: $i] : ? [v14: $i] : % 12.45/2.46 | ? [v15: $i] : ? [v16: $i] : ? [v17: $i] : ? [v18: int] : ( ~ (v18 = % 12.45/2.46 | 0) & p(v7) = v15 & n(v1) = v4 & n(v0) = v7 & n(e) = v0 & a(v12, v8) % 12.45/2.46 | = v13 & a(v3, v5) = v6 & a(v1, v15) = v16 & a(v1, v2) = v3 & u(v14, % 12.45/2.46 | v16) = v17 & u(v11, v13) = v14 & u(v6, v9) = v10 & u(v0, v4) = v5 & % 12.45/2.46 | s(v8) = v9 & s(v7) = v8 & s(v5) = v11 & s(v2) = v12 & s(v1) = v2 & % 12.45/2.46 | s(v0) = v1 & subq(v10, v17) = v18 & $i(v17) & $i(v16) & $i(v15) & % 12.45/2.46 | $i(v14) & $i(v13) & $i(v12) & $i(v11) & $i(v10) & $i(v9) & $i(v8) & % 12.45/2.46 | $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & % 12.45/2.46 | $i(v0)) % 12.45/2.46 | % 12.45/2.46 | ALPHA: (function-axioms) implies: % 12.45/2.46 | (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (s(v2) = v1) | % 12.45/2.46 | ~ (s(v2) = v0)) % 12.45/2.46 | (10) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 12.45/2.46 | : ! [v3: $i] : (v1 = v0 | ~ (mem(v3, v2) = v1) | ~ (mem(v3, v2) = % 12.45/2.46 | v0)) % 12.45/2.46 | % 12.45/2.46 | DELTA: instantiating (8) with fresh symbols all_29_0, all_29_1, all_29_2, % 12.45/2.46 | all_29_3, all_29_4, all_29_5, all_29_6, all_29_7, all_29_8, all_29_9, % 12.45/2.46 | all_29_10, all_29_11, all_29_12, all_29_13, all_29_14, all_29_15, % 12.45/2.46 | all_29_16, all_29_17, all_29_18 gives: % 12.45/2.47 | (11) ~ (all_29_0 = 0) & p(all_29_11) = all_29_3 & n(all_29_17) = all_29_14 % 12.45/2.47 | & n(all_29_18) = all_29_11 & n(e) = all_29_18 & a(all_29_6, all_29_10) % 12.45/2.47 | = all_29_5 & a(all_29_15, all_29_13) = all_29_12 & a(all_29_17, % 12.45/2.47 | all_29_3) = all_29_2 & a(all_29_17, all_29_16) = all_29_15 & % 12.45/2.47 | u(all_29_4, all_29_2) = all_29_1 & u(all_29_7, all_29_5) = all_29_4 & % 12.45/2.47 | u(all_29_12, all_29_9) = all_29_8 & u(all_29_18, all_29_14) = % 12.45/2.47 | all_29_13 & s(all_29_10) = all_29_9 & s(all_29_11) = all_29_10 & % 12.45/2.47 | s(all_29_13) = all_29_7 & s(all_29_16) = all_29_6 & s(all_29_17) = % 12.45/2.47 | all_29_16 & s(all_29_18) = all_29_17 & subq(all_29_8, all_29_1) = % 12.45/2.47 | all_29_0 & $i(all_29_1) & $i(all_29_2) & $i(all_29_3) & $i(all_29_4) & % 12.45/2.47 | $i(all_29_5) & $i(all_29_6) & $i(all_29_7) & $i(all_29_8) & % 12.45/2.47 | $i(all_29_9) & $i(all_29_10) & $i(all_29_11) & $i(all_29_12) & % 12.45/2.47 | $i(all_29_13) & $i(all_29_14) & $i(all_29_15) & $i(all_29_16) & % 12.45/2.47 | $i(all_29_17) & $i(all_29_18) % 12.45/2.47 | % 12.45/2.47 | ALPHA: (11) implies: % 12.45/2.47 | (12) ~ (all_29_0 = 0) % 12.45/2.47 | (13) $i(all_29_17) % 12.45/2.47 | (14) $i(all_29_16) % 12.45/2.47 | (15) $i(all_29_15) % 12.45/2.47 | (16) $i(all_29_13) % 12.45/2.47 | (17) $i(all_29_10) % 12.45/2.47 | (18) $i(all_29_8) % 12.45/2.47 | (19) $i(all_29_6) % 12.45/2.47 | (20) $i(all_29_4) % 12.45/2.47 | (21) $i(all_29_3) % 12.45/2.47 | (22) $i(all_29_1) % 12.45/2.47 | (23) subq(all_29_8, all_29_1) = all_29_0 % 12.45/2.47 | (24) s(all_29_18) = all_29_17 % 12.45/2.47 | (25) s(all_29_16) = all_29_6 % 12.45/2.47 | (26) s(all_29_13) = all_29_7 % 12.45/2.47 | (27) s(all_29_10) = all_29_9 % 12.45/2.47 | (28) u(all_29_12, all_29_9) = all_29_8 % 12.45/2.47 | (29) u(all_29_7, all_29_5) = all_29_4 % 12.45/2.47 | (30) u(all_29_4, all_29_2) = all_29_1 % 12.45/2.47 | (31) a(all_29_17, all_29_16) = all_29_15 % 12.45/2.47 | (32) a(all_29_17, all_29_3) = all_29_2 % 12.45/2.47 | (33) a(all_29_15, all_29_13) = all_29_12 % 12.45/2.47 | (34) a(all_29_6, all_29_10) = all_29_5 % 12.45/2.47 | (35) n(e) = all_29_18 % 12.45/2.47 | (36) n(all_29_18) = all_29_11 % 12.45/2.47 | % 12.45/2.47 | GROUND_INST: instantiating (1) with all_29_8, all_29_1, all_29_0, simplifying % 12.45/2.47 | with (18), (22), (23) gives: % 12.45/2.47 | (37) all_29_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & mem(v0, % 12.45/2.47 | all_29_1) = v1 & mem(v0, all_29_8) = 0 & $i(v0)) % 12.45/2.47 | % 12.45/2.47 | GROUND_INST: instantiating (5) with all_29_17, all_29_16, all_29_15, % 12.45/2.47 | simplifying with (13), (14), (31) gives: % 12.45/2.48 | (38) ? [v0: $i] : (u(all_29_17, v0) = all_29_15 & s(all_29_16) = v0 & % 12.45/2.48 | $i(v0) & $i(all_29_15)) % 12.45/2.48 | % 12.45/2.48 | GROUND_INST: instantiating (5) with all_29_17, all_29_3, all_29_2, simplifying % 12.45/2.48 | with (13), (21), (32) gives: % 12.45/2.48 | (39) ? [v0: $i] : (u(all_29_17, v0) = all_29_2 & s(all_29_3) = v0 & $i(v0) % 12.45/2.48 | & $i(all_29_2)) % 12.45/2.48 | % 12.45/2.48 | GROUND_INST: instantiating (5) with all_29_15, all_29_13, all_29_12, % 12.45/2.48 | simplifying with (15), (16), (33) gives: % 12.45/2.48 | (40) ? [v0: $i] : (u(all_29_15, v0) = all_29_12 & s(all_29_13) = v0 & % 12.45/2.48 | $i(v0) & $i(all_29_12)) % 12.45/2.48 | % 12.45/2.48 | GROUND_INST: instantiating (5) with all_29_6, all_29_10, all_29_5, simplifying % 12.45/2.48 | with (17), (19), (34) gives: % 12.45/2.48 | (41) ? [v0: $i] : (u(all_29_6, v0) = all_29_5 & s(all_29_10) = v0 & $i(v0) % 12.45/2.48 | & $i(all_29_5)) % 12.45/2.48 | % 12.45/2.48 | GROUND_INST: instantiating (6) with e, all_29_18, simplifying with (7), (35) % 12.45/2.48 | gives: % 12.45/2.48 | (42) a(e, e) = all_29_18 & $i(all_29_18) % 12.45/2.48 | % 12.45/2.48 | ALPHA: (42) implies: % 12.45/2.48 | (43) $i(all_29_18) % 12.45/2.48 | % 12.45/2.48 | GROUND_INST: instantiating (6) with all_29_18, all_29_11, simplifying with % 12.45/2.48 | (36), (43) gives: % 12.45/2.48 | (44) a(all_29_18, all_29_18) = all_29_11 & $i(all_29_11) % 12.45/2.48 | % 12.45/2.48 | ALPHA: (44) implies: % 12.45/2.48 | (45) a(all_29_18, all_29_18) = all_29_11 % 12.45/2.48 | % 12.45/2.48 | DELTA: instantiating (40) with fresh symbol all_37_0 gives: % 12.45/2.48 | (46) u(all_29_15, all_37_0) = all_29_12 & s(all_29_13) = all_37_0 & % 12.45/2.48 | $i(all_37_0) & $i(all_29_12) % 12.45/2.48 | % 12.45/2.48 | ALPHA: (46) implies: % 12.45/2.48 | (47) $i(all_29_12) % 12.45/2.48 | (48) $i(all_37_0) % 12.45/2.48 | (49) s(all_29_13) = all_37_0 % 12.45/2.48 | (50) u(all_29_15, all_37_0) = all_29_12 % 12.45/2.48 | % 12.45/2.48 | DELTA: instantiating (41) with fresh symbol all_39_0 gives: % 12.45/2.48 | (51) u(all_29_6, all_39_0) = all_29_5 & s(all_29_10) = all_39_0 & % 12.45/2.48 | $i(all_39_0) & $i(all_29_5) % 12.45/2.48 | % 12.45/2.48 | ALPHA: (51) implies: % 12.45/2.48 | (52) $i(all_29_5) % 12.45/2.48 | (53) $i(all_39_0) % 12.45/2.48 | (54) s(all_29_10) = all_39_0 % 12.45/2.48 | (55) u(all_29_6, all_39_0) = all_29_5 % 12.45/2.48 | % 12.45/2.48 | DELTA: instantiating (38) with fresh symbol all_41_0 gives: % 12.45/2.48 | (56) u(all_29_17, all_41_0) = all_29_15 & s(all_29_16) = all_41_0 & % 12.45/2.48 | $i(all_41_0) & $i(all_29_15) % 12.45/2.48 | % 12.45/2.48 | ALPHA: (56) implies: % 12.45/2.48 | (57) $i(all_41_0) % 12.45/2.48 | (58) s(all_29_16) = all_41_0 % 12.45/2.48 | (59) u(all_29_17, all_41_0) = all_29_15 % 12.45/2.48 | % 12.45/2.48 | DELTA: instantiating (39) with fresh symbol all_43_0 gives: % 12.45/2.48 | (60) u(all_29_17, all_43_0) = all_29_2 & s(all_29_3) = all_43_0 & % 12.45/2.48 | $i(all_43_0) & $i(all_29_2) % 12.45/2.48 | % 12.45/2.48 | ALPHA: (60) implies: % 12.45/2.48 | (61) $i(all_29_2) % 12.45/2.48 | (62) $i(all_43_0) % 12.45/2.48 | (63) u(all_29_17, all_43_0) = all_29_2 % 12.45/2.48 | % 12.45/2.48 | BETA: splitting (37) gives: % 12.45/2.48 | % 12.45/2.49 | Case 1: % 12.45/2.49 | | % 12.45/2.49 | | (64) all_29_0 = 0 % 12.45/2.49 | | % 12.45/2.49 | | REDUCE: (12), (64) imply: % 12.45/2.49 | | (65) $false % 12.45/2.49 | | % 12.45/2.49 | | CLOSE: (65) is inconsistent. % 12.45/2.49 | | % 12.45/2.49 | Case 2: % 12.45/2.49 | | % 12.45/2.49 | | (66) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & mem(v0, all_29_1) = v1 & % 12.45/2.49 | | mem(v0, all_29_8) = 0 & $i(v0)) % 12.45/2.49 | | % 12.45/2.49 | | DELTA: instantiating (66) with fresh symbols all_49_0, all_49_1 gives: % 12.45/2.49 | | (67) ~ (all_49_0 = 0) & mem(all_49_1, all_29_1) = all_49_0 & % 12.45/2.49 | | mem(all_49_1, all_29_8) = 0 & $i(all_49_1) % 12.45/2.49 | | % 12.45/2.49 | | ALPHA: (67) implies: % 12.45/2.49 | | (68) ~ (all_49_0 = 0) % 12.45/2.49 | | (69) $i(all_49_1) % 12.45/2.49 | | (70) mem(all_49_1, all_29_8) = 0 % 12.45/2.49 | | (71) mem(all_49_1, all_29_1) = all_49_0 % 12.45/2.49 | | % 12.45/2.49 | | GROUND_INST: instantiating (9) with all_29_6, all_41_0, all_29_16, % 12.45/2.49 | | simplifying with (25), (58) gives: % 12.45/2.49 | | (72) all_41_0 = all_29_6 % 12.45/2.49 | | % 12.45/2.49 | | GROUND_INST: instantiating (9) with all_29_7, all_37_0, all_29_13, % 12.45/2.49 | | simplifying with (26), (49) gives: % 12.45/2.49 | | (73) all_37_0 = all_29_7 % 12.45/2.49 | | % 12.45/2.49 | | GROUND_INST: instantiating (9) with all_29_9, all_39_0, all_29_10, % 12.45/2.49 | | simplifying with (27), (54) gives: % 12.45/2.49 | | (74) all_39_0 = all_29_9 % 12.45/2.49 | | % 12.45/2.49 | | REDUCE: (55), (74) imply: % 12.45/2.49 | | (75) u(all_29_6, all_29_9) = all_29_5 % 12.45/2.49 | | % 12.45/2.49 | | REDUCE: (50), (73) imply: % 12.45/2.49 | | (76) u(all_29_15, all_29_7) = all_29_12 % 12.45/2.49 | | % 12.45/2.49 | | REDUCE: (59), (72) imply: % 12.45/2.49 | | (77) u(all_29_17, all_29_6) = all_29_15 % 12.45/2.49 | | % 12.45/2.49 | | REDUCE: (53), (74) imply: % 12.45/2.49 | | (78) $i(all_29_9) % 12.45/2.49 | | % 12.45/2.49 | | REDUCE: (48), (73) imply: % 12.45/2.49 | | (79) $i(all_29_7) % 12.45/2.49 | | % 12.45/2.49 | | GROUND_INST: instantiating (3) with all_49_1, all_29_12, all_29_9, all_29_8, % 12.45/2.49 | | simplifying with (28), (47), (69), (70), (78) gives: % 12.45/2.49 | | (80) ? [v0: any] : ? [v1: any] : (mem(all_49_1, all_29_9) = v1 & % 12.45/2.49 | | mem(all_49_1, all_29_12) = v0 & (v1 = 0 | v0 = 0)) % 12.45/2.49 | | % 12.45/2.49 | | GROUND_INST: instantiating (4) with all_49_1, all_29_4, all_29_2, all_29_1, % 12.45/2.49 | | all_49_0, simplifying with (20), (30), (61), (69), (71) gives: % 12.45/2.50 | | (81) all_49_0 = 0 | ? [v0: int] : ? [v1: int] : ( ~ (v1 = 0) & ~ (v0 = % 12.45/2.50 | | 0) & mem(all_49_1, all_29_2) = v1 & mem(all_49_1, all_29_4) = % 12.45/2.50 | | v0) % 12.45/2.50 | | % 12.45/2.50 | | GROUND_INST: instantiating (5) with all_29_18, all_29_18, all_29_11, % 12.45/2.50 | | simplifying with (43), (45) gives: % 12.45/2.50 | | (82) ? [v0: $i] : (u(all_29_18, v0) = all_29_11 & s(all_29_18) = v0 & % 12.45/2.50 | | $i(v0) & $i(all_29_11)) % 12.45/2.50 | | % 12.45/2.50 | | DELTA: instantiating (82) with fresh symbol all_67_0 gives: % 12.45/2.50 | | (83) u(all_29_18, all_67_0) = all_29_11 & s(all_29_18) = all_67_0 & % 12.45/2.50 | | $i(all_67_0) & $i(all_29_11) % 12.45/2.50 | | % 12.45/2.50 | | ALPHA: (83) implies: % 12.45/2.50 | | (84) $i(all_67_0) % 12.45/2.50 | | (85) s(all_29_18) = all_67_0 % 12.45/2.50 | | % 12.45/2.50 | | DELTA: instantiating (80) with fresh symbols all_71_0, all_71_1 gives: % 12.45/2.50 | | (86) mem(all_49_1, all_29_9) = all_71_0 & mem(all_49_1, all_29_12) = % 12.45/2.50 | | all_71_1 & (all_71_0 = 0 | all_71_1 = 0) % 12.45/2.50 | | % 12.45/2.50 | | ALPHA: (86) implies: % 12.45/2.50 | | (87) mem(all_49_1, all_29_12) = all_71_1 % 12.45/2.50 | | (88) mem(all_49_1, all_29_9) = all_71_0 % 12.45/2.50 | | (89) all_71_0 = 0 | all_71_1 = 0 % 12.45/2.50 | | % 12.45/2.50 | | BETA: splitting (81) gives: % 12.45/2.50 | | % 12.45/2.50 | | Case 1: % 12.45/2.50 | | | % 12.45/2.50 | | | (90) all_49_0 = 0 % 12.45/2.50 | | | % 12.45/2.50 | | | REDUCE: (68), (90) imply: % 12.45/2.50 | | | (91) $false % 12.45/2.50 | | | % 12.45/2.50 | | | CLOSE: (91) is inconsistent. % 12.45/2.50 | | | % 12.45/2.50 | | Case 2: % 12.45/2.50 | | | % 12.45/2.50 | | | (92) ? [v0: int] : ? [v1: int] : ( ~ (v1 = 0) & ~ (v0 = 0) & % 12.45/2.50 | | | mem(all_49_1, all_29_2) = v1 & mem(all_49_1, all_29_4) = v0) % 12.45/2.50 | | | % 12.45/2.50 | | | DELTA: instantiating (92) with fresh symbols all_77_0, all_77_1 gives: % 12.45/2.50 | | | (93) ~ (all_77_0 = 0) & ~ (all_77_1 = 0) & mem(all_49_1, all_29_2) = % 12.45/2.50 | | | all_77_0 & mem(all_49_1, all_29_4) = all_77_1 % 12.45/2.50 | | | % 12.45/2.50 | | | ALPHA: (93) implies: % 12.45/2.50 | | | (94) ~ (all_77_1 = 0) % 12.45/2.50 | | | (95) ~ (all_77_0 = 0) % 12.45/2.50 | | | (96) mem(all_49_1, all_29_4) = all_77_1 % 12.45/2.50 | | | (97) mem(all_49_1, all_29_2) = all_77_0 % 12.45/2.50 | | | % 12.45/2.50 | | | GROUND_INST: instantiating (9) with all_29_17, all_67_0, all_29_18, % 12.45/2.50 | | | simplifying with (24), (85) gives: % 12.45/2.50 | | | (98) all_67_0 = all_29_17 % 12.45/2.50 | | | % 12.45/2.50 | | | GROUND_INST: instantiating (4) with all_49_1, all_29_7, all_29_5, % 12.45/2.50 | | | all_29_4, all_77_1, simplifying with (29), (52), (69), (79), % 12.45/2.50 | | | (96) gives: % 12.45/2.50 | | | (99) all_77_1 = 0 | ? [v0: int] : ? [v1: int] : ( ~ (v1 = 0) & ~ (v0 % 12.45/2.50 | | | = 0) & mem(all_49_1, all_29_5) = v1 & mem(all_49_1, all_29_7) % 12.45/2.50 | | | = v0) % 12.45/2.50 | | | % 12.45/2.50 | | | GROUND_INST: instantiating (4) with all_49_1, all_29_17, all_43_0, % 12.45/2.50 | | | all_29_2, all_77_0, simplifying with (13), (62), (63), (69), % 12.45/2.50 | | | (97) gives: % 12.45/2.50 | | | (100) all_77_0 = 0 | ? [v0: int] : ? [v1: int] : ( ~ (v1 = 0) & ~ % 12.45/2.50 | | | (v0 = 0) & mem(all_49_1, all_43_0) = v1 & mem(all_49_1, % 12.45/2.50 | | | all_29_17) = v0) % 12.45/2.50 | | | % 12.45/2.50 | | | BETA: splitting (89) gives: % 12.45/2.50 | | | % 12.45/2.50 | | | Case 1: % 12.45/2.50 | | | | % 12.45/2.50 | | | | (101) all_71_0 = 0 % 12.45/2.50 | | | | % 12.45/2.50 | | | | REDUCE: (88), (101) imply: % 12.45/2.50 | | | | (102) mem(all_49_1, all_29_9) = 0 % 12.45/2.50 | | | | % 12.45/2.50 | | | | BETA: splitting (99) gives: % 12.45/2.50 | | | | % 12.45/2.50 | | | | Case 1: % 12.45/2.50 | | | | | % 12.45/2.50 | | | | | (103) all_77_1 = 0 % 12.45/2.50 | | | | | % 12.45/2.50 | | | | | REDUCE: (94), (103) imply: % 12.45/2.50 | | | | | (104) $false % 12.45/2.50 | | | | | % 12.45/2.50 | | | | | CLOSE: (104) is inconsistent. % 12.45/2.50 | | | | | % 12.45/2.50 | | | | Case 2: % 12.45/2.50 | | | | | % 12.45/2.50 | | | | | (105) ? [v0: int] : ? [v1: int] : ( ~ (v1 = 0) & ~ (v0 = 0) & % 12.45/2.50 | | | | | mem(all_49_1, all_29_5) = v1 & mem(all_49_1, all_29_7) = % 12.45/2.50 | | | | | v0) % 12.45/2.50 | | | | | % 12.45/2.50 | | | | | DELTA: instantiating (105) with fresh symbols all_99_0, all_99_1 % 12.45/2.50 | | | | | gives: % 12.45/2.50 | | | | | (106) ~ (all_99_0 = 0) & ~ (all_99_1 = 0) & mem(all_49_1, % 12.45/2.50 | | | | | all_29_5) = all_99_0 & mem(all_49_1, all_29_7) = all_99_1 % 12.45/2.50 | | | | | % 12.45/2.50 | | | | | ALPHA: (106) implies: % 12.45/2.51 | | | | | (107) ~ (all_99_0 = 0) % 12.45/2.51 | | | | | (108) mem(all_49_1, all_29_5) = all_99_0 % 12.45/2.51 | | | | | % 12.45/2.51 | | | | | GROUND_INST: instantiating (2) with all_49_1, all_29_10, all_29_9, % 12.45/2.51 | | | | | simplifying with (17), (27), (69), (102) gives: % 12.45/2.51 | | | | | (109) all_49_1 = all_29_10 % 12.45/2.51 | | | | | % 12.45/2.51 | | | | | GROUND_INST: instantiating (4) with all_49_1, all_29_6, all_29_9, % 12.45/2.51 | | | | | all_29_5, all_99_0, simplifying with (19), (69), (75), % 12.45/2.51 | | | | | (78), (108) gives: % 12.45/2.51 | | | | | (110) all_99_0 = 0 | ? [v0: int] : ? [v1: int] : ( ~ (v1 = 0) & % 12.45/2.51 | | | | | ~ (v0 = 0) & mem(all_49_1, all_29_6) = v0 & mem(all_49_1, % 12.45/2.51 | | | | | all_29_9) = v1) % 12.45/2.51 | | | | | % 12.45/2.51 | | | | | REDUCE: (102), (109) imply: % 12.45/2.51 | | | | | (111) mem(all_29_10, all_29_9) = 0 % 12.45/2.51 | | | | | % 12.45/2.51 | | | | | BETA: splitting (110) gives: % 12.45/2.51 | | | | | % 12.45/2.51 | | | | | Case 1: % 12.45/2.51 | | | | | | % 12.45/2.51 | | | | | | (112) all_99_0 = 0 % 12.45/2.51 | | | | | | % 12.45/2.51 | | | | | | REDUCE: (107), (112) imply: % 12.45/2.51 | | | | | | (113) $false % 12.45/2.51 | | | | | | % 12.45/2.51 | | | | | | CLOSE: (113) is inconsistent. % 12.45/2.51 | | | | | | % 12.45/2.51 | | | | | Case 2: % 12.45/2.51 | | | | | | % 12.45/2.51 | | | | | | (114) ? [v0: int] : ? [v1: int] : ( ~ (v1 = 0) & ~ (v0 = 0) & % 12.45/2.51 | | | | | | mem(all_49_1, all_29_6) = v0 & mem(all_49_1, all_29_9) = % 12.45/2.51 | | | | | | v1) % 12.45/2.51 | | | | | | % 12.45/2.51 | | | | | | DELTA: instantiating (114) with fresh symbols all_111_0, all_111_1 % 12.45/2.51 | | | | | | gives: % 12.45/2.51 | | | | | | (115) ~ (all_111_0 = 0) & ~ (all_111_1 = 0) & mem(all_49_1, % 12.45/2.51 | | | | | | all_29_6) = all_111_1 & mem(all_49_1, all_29_9) = % 12.45/2.51 | | | | | | all_111_0 % 12.45/2.51 | | | | | | % 12.45/2.51 | | | | | | ALPHA: (115) implies: % 12.45/2.51 | | | | | | (116) ~ (all_111_0 = 0) % 12.45/2.51 | | | | | | (117) mem(all_49_1, all_29_9) = all_111_0 % 12.45/2.51 | | | | | | % 12.45/2.51 | | | | | | REDUCE: (109), (117) imply: % 12.45/2.51 | | | | | | (118) mem(all_29_10, all_29_9) = all_111_0 % 12.45/2.51 | | | | | | % 12.45/2.51 | | | | | | GROUND_INST: instantiating (10) with 0, all_111_0, all_29_9, % 12.45/2.51 | | | | | | all_29_10, simplifying with (111), (118) gives: % 12.45/2.51 | | | | | | (119) all_111_0 = 0 % 12.45/2.51 | | | | | | % 12.45/2.51 | | | | | | REDUCE: (116), (119) imply: % 12.45/2.51 | | | | | | (120) $false % 12.45/2.51 | | | | | | % 12.45/2.51 | | | | | | CLOSE: (120) is inconsistent. % 12.45/2.51 | | | | | | % 12.45/2.51 | | | | | End of split % 12.45/2.51 | | | | | % 12.45/2.51 | | | | End of split % 12.45/2.51 | | | | % 12.45/2.51 | | | Case 2: % 12.45/2.51 | | | | % 12.45/2.51 | | | | (121) all_71_1 = 0 % 12.45/2.51 | | | | % 12.45/2.51 | | | | REDUCE: (87), (121) imply: % 12.45/2.51 | | | | (122) mem(all_49_1, all_29_12) = 0 % 12.45/2.51 | | | | % 12.45/2.51 | | | | BETA: splitting (100) gives: % 12.45/2.51 | | | | % 12.45/2.51 | | | | Case 1: % 12.45/2.51 | | | | | % 12.45/2.51 | | | | | (123) all_77_0 = 0 % 12.45/2.51 | | | | | % 12.45/2.51 | | | | | REDUCE: (95), (123) imply: % 12.45/2.51 | | | | | (124) $false % 12.45/2.51 | | | | | % 12.45/2.51 | | | | | CLOSE: (124) is inconsistent. % 12.45/2.51 | | | | | % 12.45/2.51 | | | | Case 2: % 12.45/2.51 | | | | | % 12.45/2.51 | | | | | (125) ? [v0: int] : ? [v1: int] : ( ~ (v1 = 0) & ~ (v0 = 0) & % 12.45/2.51 | | | | | mem(all_49_1, all_43_0) = v1 & mem(all_49_1, all_29_17) = % 12.45/2.51 | | | | | v0) % 12.45/2.51 | | | | | % 12.45/2.51 | | | | | DELTA: instantiating (125) with fresh symbols all_94_0, all_94_1 % 12.45/2.51 | | | | | gives: % 12.45/2.51 | | | | | (126) ~ (all_94_0 = 0) & ~ (all_94_1 = 0) & mem(all_49_1, % 12.45/2.51 | | | | | all_43_0) = all_94_0 & mem(all_49_1, all_29_17) = all_94_1 % 12.45/2.51 | | | | | % 12.45/2.51 | | | | | ALPHA: (126) implies: % 12.45/2.51 | | | | | (127) ~ (all_94_1 = 0) % 12.45/2.51 | | | | | (128) mem(all_49_1, all_29_17) = all_94_1 % 12.45/2.51 | | | | | % 12.45/2.51 | | | | | BETA: splitting (99) gives: % 12.45/2.51 | | | | | % 12.45/2.51 | | | | | Case 1: % 12.45/2.51 | | | | | | % 12.45/2.51 | | | | | | (129) all_77_1 = 0 % 12.45/2.51 | | | | | | % 12.45/2.51 | | | | | | REDUCE: (94), (129) imply: % 12.45/2.51 | | | | | | (130) $false % 12.45/2.51 | | | | | | % 12.45/2.51 | | | | | | CLOSE: (130) is inconsistent. % 12.45/2.51 | | | | | | % 12.45/2.51 | | | | | Case 2: % 12.45/2.51 | | | | | | % 12.45/2.51 | | | | | | (131) ? [v0: int] : ? [v1: int] : ( ~ (v1 = 0) & ~ (v0 = 0) & % 12.45/2.51 | | | | | | mem(all_49_1, all_29_5) = v1 & mem(all_49_1, all_29_7) = % 12.45/2.51 | | | | | | v0) % 12.45/2.51 | | | | | | % 12.45/2.51 | | | | | | DELTA: instantiating (131) with fresh symbols all_99_0, all_99_1 % 12.45/2.51 | | | | | | gives: % 12.45/2.51 | | | | | | (132) ~ (all_99_0 = 0) & ~ (all_99_1 = 0) & mem(all_49_1, % 12.45/2.51 | | | | | | all_29_5) = all_99_0 & mem(all_49_1, all_29_7) = all_99_1 % 12.45/2.51 | | | | | | % 12.45/2.51 | | | | | | ALPHA: (132) implies: % 12.45/2.51 | | | | | | (133) ~ (all_99_1 = 0) % 12.45/2.51 | | | | | | (134) ~ (all_99_0 = 0) % 12.45/2.51 | | | | | | (135) mem(all_49_1, all_29_7) = all_99_1 % 12.45/2.51 | | | | | | (136) mem(all_49_1, all_29_5) = all_99_0 % 12.45/2.51 | | | | | | % 12.45/2.51 | | | | | | GROUND_INST: instantiating (3) with all_49_1, all_29_15, all_29_7, % 12.45/2.51 | | | | | | all_29_12, simplifying with (15), (69), (76), (79), % 12.45/2.51 | | | | | | (122) gives: % 12.45/2.51 | | | | | | (137) ? [v0: any] : ? [v1: any] : (mem(all_49_1, all_29_7) = v1 % 12.45/2.51 | | | | | | & mem(all_49_1, all_29_15) = v0 & (v1 = 0 | v0 = 0)) % 12.45/2.51 | | | | | | % 12.45/2.51 | | | | | | GROUND_INST: instantiating (4) with all_49_1, all_29_6, all_29_9, % 12.45/2.51 | | | | | | all_29_5, all_99_0, simplifying with (19), (69), (75), % 12.45/2.51 | | | | | | (78), (136) gives: % 12.45/2.52 | | | | | | (138) all_99_0 = 0 | ? [v0: int] : ? [v1: int] : ( ~ (v1 = 0) & % 12.45/2.52 | | | | | | ~ (v0 = 0) & mem(all_49_1, all_29_6) = v0 & % 12.45/2.52 | | | | | | mem(all_49_1, all_29_9) = v1) % 12.45/2.52 | | | | | | % 12.45/2.52 | | | | | | DELTA: instantiating (137) with fresh symbols all_106_0, all_106_1 % 12.45/2.52 | | | | | | gives: % 12.45/2.52 | | | | | | (139) mem(all_49_1, all_29_7) = all_106_0 & mem(all_49_1, % 12.45/2.52 | | | | | | all_29_15) = all_106_1 & (all_106_0 = 0 | all_106_1 = 0) % 12.45/2.52 | | | | | | % 12.45/2.52 | | | | | | ALPHA: (139) implies: % 12.45/2.52 | | | | | | (140) mem(all_49_1, all_29_15) = all_106_1 % 12.45/2.52 | | | | | | (141) mem(all_49_1, all_29_7) = all_106_0 % 12.45/2.52 | | | | | | (142) all_106_0 = 0 | all_106_1 = 0 % 12.45/2.52 | | | | | | % 12.45/2.52 | | | | | | BETA: splitting (138) gives: % 12.45/2.52 | | | | | | % 12.45/2.52 | | | | | | Case 1: % 12.45/2.52 | | | | | | | % 12.45/2.52 | | | | | | | (143) all_99_0 = 0 % 12.45/2.52 | | | | | | | % 12.45/2.52 | | | | | | | REDUCE: (134), (143) imply: % 12.45/2.52 | | | | | | | (144) $false % 12.45/2.52 | | | | | | | % 12.45/2.52 | | | | | | | CLOSE: (144) is inconsistent. % 12.45/2.52 | | | | | | | % 12.45/2.52 | | | | | | Case 2: % 12.45/2.52 | | | | | | | % 12.45/2.52 | | | | | | | (145) ? [v0: int] : ? [v1: int] : ( ~ (v1 = 0) & ~ (v0 = 0) % 12.45/2.52 | | | | | | | & mem(all_49_1, all_29_6) = v0 & mem(all_49_1, % 12.45/2.52 | | | | | | | all_29_9) = v1) % 12.45/2.52 | | | | | | | % 12.45/2.52 | | | | | | | DELTA: instantiating (145) with fresh symbols all_112_0, all_112_1 % 12.45/2.52 | | | | | | | gives: % 12.45/2.52 | | | | | | | (146) ~ (all_112_0 = 0) & ~ (all_112_1 = 0) & mem(all_49_1, % 12.45/2.52 | | | | | | | all_29_6) = all_112_1 & mem(all_49_1, all_29_9) = % 12.45/2.52 | | | | | | | all_112_0 % 12.45/2.52 | | | | | | | % 12.45/2.52 | | | | | | | ALPHA: (146) implies: % 12.45/2.52 | | | | | | | (147) ~ (all_112_1 = 0) % 12.45/2.52 | | | | | | | (148) mem(all_49_1, all_29_6) = all_112_1 % 12.45/2.52 | | | | | | | % 12.45/2.52 | | | | | | | GROUND_INST: instantiating (10) with all_99_1, all_106_0, % 12.45/2.52 | | | | | | | all_29_7, all_49_1, simplifying with (135), (141) % 12.45/2.52 | | | | | | | gives: % 12.45/2.52 | | | | | | | (149) all_106_0 = all_99_1 % 12.45/2.52 | | | | | | | % 12.45/2.52 | | | | | | | BETA: splitting (142) gives: % 12.45/2.52 | | | | | | | % 12.45/2.52 | | | | | | | Case 1: % 12.45/2.52 | | | | | | | | % 12.45/2.52 | | | | | | | | (150) all_106_0 = 0 % 12.45/2.52 | | | | | | | | % 12.45/2.52 | | | | | | | | COMBINE_EQS: (149), (150) imply: % 12.45/2.52 | | | | | | | | (151) all_99_1 = 0 % 12.45/2.52 | | | | | | | | % 12.45/2.52 | | | | | | | | SIMP: (151) implies: % 12.45/2.52 | | | | | | | | (152) all_99_1 = 0 % 12.45/2.52 | | | | | | | | % 12.45/2.52 | | | | | | | | REDUCE: (133), (152) imply: % 12.45/2.52 | | | | | | | | (153) $false % 12.45/2.52 | | | | | | | | % 12.45/2.52 | | | | | | | | CLOSE: (153) is inconsistent. % 12.45/2.52 | | | | | | | | % 12.45/2.52 | | | | | | | Case 2: % 12.45/2.52 | | | | | | | | % 12.45/2.52 | | | | | | | | (154) all_106_1 = 0 % 12.45/2.52 | | | | | | | | % 12.45/2.52 | | | | | | | | REDUCE: (140), (154) imply: % 12.45/2.52 | | | | | | | | (155) mem(all_49_1, all_29_15) = 0 % 12.45/2.52 | | | | | | | | % 12.91/2.52 | | | | | | | | GROUND_INST: instantiating (3) with all_49_1, all_29_17, % 12.91/2.52 | | | | | | | | all_29_6, all_29_15, simplifying with (13), (19), % 12.91/2.52 | | | | | | | | (69), (77), (155) gives: % 12.91/2.52 | | | | | | | | (156) ? [v0: any] : ? [v1: any] : (mem(all_49_1, all_29_6) % 12.91/2.52 | | | | | | | | = v1 & mem(all_49_1, all_29_17) = v0 & (v1 = 0 | v0 = % 12.91/2.52 | | | | | | | | 0)) % 12.91/2.52 | | | | | | | | % 12.91/2.52 | | | | | | | | DELTA: instantiating (156) with fresh symbols all_127_0, % 12.91/2.52 | | | | | | | | all_127_1 gives: % 12.91/2.52 | | | | | | | | (157) mem(all_49_1, all_29_6) = all_127_0 & mem(all_49_1, % 12.91/2.52 | | | | | | | | all_29_17) = all_127_1 & (all_127_0 = 0 | all_127_1 = % 12.91/2.52 | | | | | | | | 0) % 12.91/2.52 | | | | | | | | % 12.91/2.52 | | | | | | | | ALPHA: (157) implies: % 12.91/2.52 | | | | | | | | (158) mem(all_49_1, all_29_17) = all_127_1 % 12.91/2.52 | | | | | | | | (159) mem(all_49_1, all_29_6) = all_127_0 % 12.91/2.52 | | | | | | | | (160) all_127_0 = 0 | all_127_1 = 0 % 12.91/2.52 | | | | | | | | % 12.91/2.52 | | | | | | | | GROUND_INST: instantiating (10) with all_94_1, all_127_1, % 12.91/2.52 | | | | | | | | all_29_17, all_49_1, simplifying with (128), (158) % 12.91/2.52 | | | | | | | | gives: % 12.91/2.52 | | | | | | | | (161) all_127_1 = all_94_1 % 12.91/2.52 | | | | | | | | % 12.91/2.52 | | | | | | | | GROUND_INST: instantiating (10) with all_112_1, all_127_0, % 12.91/2.52 | | | | | | | | all_29_6, all_49_1, simplifying with (148), (159) % 12.91/2.52 | | | | | | | | gives: % 12.91/2.52 | | | | | | | | (162) all_127_0 = all_112_1 % 12.91/2.52 | | | | | | | | % 12.91/2.52 | | | | | | | | BETA: splitting (160) gives: % 12.91/2.52 | | | | | | | | % 12.91/2.52 | | | | | | | | Case 1: % 12.91/2.52 | | | | | | | | | % 12.91/2.52 | | | | | | | | | (163) all_127_0 = 0 % 12.91/2.52 | | | | | | | | | % 12.91/2.52 | | | | | | | | | COMBINE_EQS: (162), (163) imply: % 12.91/2.52 | | | | | | | | | (164) all_112_1 = 0 % 12.91/2.52 | | | | | | | | | % 12.91/2.52 | | | | | | | | | REDUCE: (147), (164) imply: % 12.91/2.52 | | | | | | | | | (165) $false % 12.91/2.52 | | | | | | | | | % 12.91/2.52 | | | | | | | | | CLOSE: (165) is inconsistent. % 12.91/2.52 | | | | | | | | | % 12.91/2.52 | | | | | | | | Case 2: % 12.91/2.52 | | | | | | | | | % 12.91/2.52 | | | | | | | | | (166) all_127_1 = 0 % 12.91/2.52 | | | | | | | | | % 12.91/2.52 | | | | | | | | | COMBINE_EQS: (161), (166) imply: % 12.91/2.52 | | | | | | | | | (167) all_94_1 = 0 % 12.91/2.52 | | | | | | | | | % 12.91/2.52 | | | | | | | | | SIMP: (167) implies: % 12.91/2.52 | | | | | | | | | (168) all_94_1 = 0 % 12.91/2.52 | | | | | | | | | % 12.91/2.52 | | | | | | | | | REDUCE: (127), (168) imply: % 12.91/2.52 | | | | | | | | | (169) $false % 12.91/2.52 | | | | | | | | | % 12.91/2.52 | | | | | | | | | CLOSE: (169) is inconsistent. % 12.91/2.52 | | | | | | | | | % 12.91/2.52 | | | | | | | | End of split % 12.91/2.52 | | | | | | | | % 12.91/2.52 | | | | | | | End of split % 12.91/2.52 | | | | | | | % 12.91/2.52 | | | | | | End of split % 12.91/2.52 | | | | | | % 12.91/2.52 | | | | | End of split % 12.91/2.52 | | | | | % 12.91/2.52 | | | | End of split % 12.91/2.52 | | | | % 12.91/2.52 | | | End of split % 12.91/2.52 | | | % 12.91/2.52 | | End of split % 12.91/2.52 | | % 12.91/2.52 | End of split % 12.91/2.52 | % 12.91/2.52 End of proof % 12.91/2.52 % SZS output end Proof for theBenchmark % 12.91/2.52 % 12.91/2.52 1896ms %------------------------------------------------------------------------------