%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SEV550+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 : n019.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 02:02:55 AM UTC 2025 % Result : Theorem 34.41s 5.19s % Output : Proof 35.32s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.12 % Problem : SEV550+1 : TPTP v9.1.0. Released v9.1.0. % 0.11/0.12 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.12/0.33 % Computer : n019.cluster.edu % 0.12/0.33 % Model : x86_64 x86_64 % 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.33 % Memory : 8042.1875MB % 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.33 % CPULimit : 300 % 0.12/0.33 % WCLimit : 300 % 0.12/0.33 % DateTime : Mon Mar 31 11:50:17 EDT 2025 % 0.12/0.33 % CPUTime : % 0.62/0.59 ________ _____ % 0.62/0.59 ___ __ \_________(_)________________________________ % 0.62/0.59 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.62/0.59 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.62/0.59 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.62/0.59 % 0.62/0.59 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.62/0.59 (2023-06-19) % 0.62/0.59 % 0.62/0.59 (c) Philipp Rümmer, 2009-2023 % 0.62/0.59 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.62/0.59 Amanda Stjerna. % 0.62/0.59 Free software under BSD-3-Clause. % 0.62/0.59 % 0.62/0.59 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.62/0.59 % 0.62/0.59 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.65/0.60 Running up to 7 provers in parallel. % 0.65/0.62 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.65/0.62 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.65/0.62 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.65/0.62 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.65/0.62 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.65/0.62 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.65/0.62 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.80/1.07 Prover 4: Preprocessing ... % 2.80/1.07 Prover 1: Preprocessing ... % 3.26/1.10 Prover 5: Preprocessing ... % 3.26/1.10 Prover 2: Preprocessing ... % 3.26/1.10 Prover 0: Preprocessing ... % 3.26/1.10 Prover 3: Preprocessing ... % 3.26/1.10 Prover 6: Preprocessing ... % 6.47/1.59 Prover 5: Proving ... % 6.47/1.60 Prover 2: Proving ... % 7.08/1.67 Prover 1: Constructing countermodel ... % 7.57/1.70 Prover 3: Constructing countermodel ... % 7.57/1.71 Prover 6: Proving ... % 8.28/1.81 Prover 4: Constructing countermodel ... % 8.49/1.88 Prover 0: Proving ... % 10.49/2.10 Prover 3: gave up % 10.49/2.11 Prover 1: gave up % 10.72/2.12 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 10.72/2.12 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 10.72/2.18 Prover 7: Preprocessing ... % 10.72/2.18 Prover 8: Preprocessing ... % 11.43/2.28 Prover 7: Warning: ignoring some quantifiers % 12.04/2.31 Prover 7: Constructing countermodel ... % 12.04/2.34 Prover 8: Warning: ignoring some quantifiers % 12.04/2.37 Prover 8: Constructing countermodel ... % 14.35/2.68 Prover 8: gave up % 15.06/2.69 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889 % 15.26/2.76 Prover 9: Preprocessing ... % 17.32/3.01 Prover 9: Constructing countermodel ... % 34.29/5.19 Prover 4: Found proof (size 595) % 34.29/5.19 Prover 4: proved (4570ms) % 34.29/5.19 Prover 6: stopped % 34.29/5.19 Prover 5: stopped % 34.29/5.19 Prover 9: stopped % 34.41/5.19 Prover 0: stopped % 34.41/5.19 Prover 2: stopped % 34.41/5.19 Prover 7: stopped % 34.41/5.19 % 34.41/5.19 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 34.41/5.19 % 34.51/5.21 % SZS output start Proof for theBenchmark % 34.51/5.22 Assumptions after simplification: % 34.51/5.22 --------------------------------- % 34.53/5.22 % 34.53/5.22 (a_def) % 34.53/5.24 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (u(v0, v2) = v3) | % 34.53/5.24 ~ (s(v1) = v2) | ~ $i(v1) | ~ $i(v0) | (a(v0, v1) = v3 & $i(v3))) & ! % 34.53/5.25 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (a(v0, v1) = v2) | ~ $i(v1) | ~ % 34.53/5.25 $i(v0) | ? [v3: $i] : (u(v0, v3) = v2 & s(v1) = v3 & $i(v3) & $i(v2))) % 34.53/5.25 % 34.53/5.25 (atleast2p_def) % 34.53/5.25 ! [v0: $i] : ! [v1: int] : ! [v2: $i] : ! [v3: $i] : (v1 = 0 | ~ % 34.53/5.25 (atleast2p(v0) = v1) | ~ (p(v2) = v3) | ~ $i(v2) | ~ $i(v0) | ? [v4: % 34.53/5.25 any] : ? [v5: any] : (subq(v0, v3) = v5 & mem(v2, v0) = v4 & ( ~ (v4 = 0) % 34.53/5.25 | v5 = 0))) & ! [v0: $i] : ! [v1: int] : ! [v2: $i] : (v1 = 0 | ~ % 34.53/5.25 (atleast2p(v0) = v1) | ~ (mem(v2, v0) = 0) | ~ $i(v2) | ~ $i(v0) | ? % 34.53/5.25 [v3: $i] : (p(v2) = v3 & subq(v0, v3) = 0 & $i(v3))) & ! [v0: $i] : ( ~ % 34.53/5.25 (atleast2p(v0) = 0) | ~ $i(v0) | ? [v1: $i] : ? [v2: $i] : ? [v3: int] : % 34.53/5.25 ( ~ (v3 = 0) & p(v1) = v2 & subq(v0, v2) = v3 & mem(v1, v0) = 0 & $i(v2) & % 34.53/5.25 $i(v1))) % 34.53/5.25 % 34.53/5.25 (atleast3p_def) % 34.53/5.25 ! [v0: $i] : ! [v1: int] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | v1 = 0 | % 34.53/5.25 ~ (atleast3p(v0) = v1) | ~ (subq(v0, v2) = v3) | ~ $i(v2) | ~ $i(v0) | ? % 34.53/5.25 [v4: any] : ? [v5: any] : (atleast2p(v2) = v5 & subq(v2, v0) = v4 & ( ~ (v5 % 34.53/5.25 = 0) | ~ (v4 = 0)))) & ! [v0: $i] : ! [v1: int] : ! [v2: $i] : (v1 % 34.53/5.25 = 0 | ~ (atleast3p(v0) = v1) | ~ (atleast2p(v2) = 0) | ~ $i(v2) | ~ % 34.53/5.25 $i(v0) | ? [v3: any] : ? [v4: any] : (subq(v2, v0) = v3 & subq(v0, v2) = % 34.53/5.25 v4 & ( ~ (v3 = 0) | v4 = 0))) & ! [v0: $i] : ! [v1: int] : ! [v2: $i] : % 34.53/5.25 (v1 = 0 | ~ (atleast3p(v0) = v1) | ~ (subq(v2, v0) = 0) | ~ $i(v2) | ~ % 34.53/5.25 $i(v0) | ? [v3: any] : ? [v4: any] : (atleast2p(v2) = v3 & subq(v0, v2) = % 34.53/5.25 v4 & ( ~ (v3 = 0) | v4 = 0))) & ! [v0: $i] : ( ~ (atleast3p(v0) = 0) | ~ % 34.53/5.25 $i(v0) | ? [v1: $i] : ? [v2: int] : ( ~ (v2 = 0) & atleast2p(v1) = 0 & % 34.53/5.25 subq(v1, v0) = 0 & subq(v0, v1) = v2 & $i(v1))) % 34.53/5.25 % 34.53/5.25 (atleast4p_def) % 34.53/5.26 ! [v0: $i] : ! [v1: int] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | v1 = 0 | % 34.53/5.26 ~ (atleast4p(v0) = v1) | ~ (subq(v0, v2) = v3) | ~ $i(v2) | ~ $i(v0) | ? % 34.53/5.26 [v4: any] : ? [v5: any] : (atleast3p(v2) = v5 & subq(v2, v0) = v4 & ( ~ (v5 % 34.53/5.26 = 0) | ~ (v4 = 0)))) & ! [v0: $i] : ! [v1: int] : ! [v2: $i] : (v1 % 34.53/5.26 = 0 | ~ (atleast4p(v0) = v1) | ~ (atleast3p(v2) = 0) | ~ $i(v2) | ~ % 34.53/5.26 $i(v0) | ? [v3: any] : ? [v4: any] : (subq(v2, v0) = v3 & subq(v0, v2) = % 34.53/5.26 v4 & ( ~ (v3 = 0) | v4 = 0))) & ! [v0: $i] : ! [v1: int] : ! [v2: $i] : % 34.53/5.26 (v1 = 0 | ~ (atleast4p(v0) = v1) | ~ (subq(v2, v0) = 0) | ~ $i(v2) | ~ % 34.53/5.26 $i(v0) | ? [v3: any] : ? [v4: any] : (atleast3p(v2) = v3 & subq(v0, v2) = % 34.53/5.26 v4 & ( ~ (v3 = 0) | v4 = 0))) & ! [v0: $i] : ( ~ (atleast4p(v0) = 0) | ~ % 34.53/5.26 $i(v0) | ? [v1: $i] : ? [v2: int] : ( ~ (v2 = 0) & atleast3p(v1) = 0 & % 34.53/5.26 subq(v1, v0) = 0 & subq(v0, v1) = v2 & $i(v1))) % 34.53/5.26 % 34.53/5.26 (atmost3_7) % 34.53/5.26 $i(e) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : (atleast4p(v3) % 34.53/5.26 = 0 & n(v1) = v2 & n(e) = v0 & u(v0, v2) = v3 & s(v0) = v1 & $i(v3) & $i(v2) % 34.53/5.26 & $i(v1) & $i(v0)) % 34.53/5.26 % 34.53/5.26 (e_ax) % 34.53/5.26 $i(e) & ! [v0: $i] : ( ~ (mem(v0, e) = 0) | ~ $i(v0)) % 34.53/5.26 % 34.53/5.26 (n_def) % 34.53/5.26 ! [v0: $i] : ! [v1: $i] : ( ~ (n(v0) = v1) | ~ $i(v0) | (a(v0, v0) = v1 & % 34.53/5.26 $i(v1))) & ! [v0: $i] : ! [v1: $i] : ( ~ (a(v0, v0) = v1) | ~ $i(v0) | % 34.53/5.26 (n(v0) = v1 & $i(v1))) % 34.53/5.26 % 34.53/5.26 (p_ax) % 34.53/5.26 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (p(v1) = % 34.53/5.26 v2) | ~ (mem(v0, v2) = v3) | ~ $i(v1) | ~ $i(v0) | ? [v4: int] : ( ~ % 34.53/5.26 (v4 = 0) & subq(v0, v1) = v4)) & ! [v0: $i] : ! [v1: $i] : ! [v2: int] % 34.53/5.26 : (v2 = 0 | ~ (subq(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? % 34.53/5.26 [v4: int] : ( ~ (v4 = 0) & p(v1) = v3 & mem(v0, v3) = v4 & $i(v3))) & ! % 34.53/5.26 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (p(v1) = v2) | ~ (mem(v0, v2) = 0) % 34.53/5.26 | ~ $i(v1) | ~ $i(v0) | subq(v0, v1) = 0) & ! [v0: $i] : ! [v1: $i] : ( % 34.53/5.26 ~ (subq(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: $i] : (p(v1) = v2 & % 34.53/5.26 mem(v0, v2) = 0 & $i(v2))) % 34.53/5.26 % 34.53/5.26 (s_ax) % 34.53/5.26 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (s(v0) = v1) | ~ % 34.53/5.26 (mem(v0, v1) = v2) | ~ $i(v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 34.53/5.26 (v1 = v0 | ~ (s(v1) = v2) | ~ (mem(v0, v2) = 0) | ~ $i(v1) | ~ $i(v0)) % 34.53/5.26 % 34.53/5.26 (subq_def) % 34.53/5.26 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 34.53/5.26 (subq(v0, v1) = 0) | ~ (mem(v2, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ % 34.53/5.26 $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & mem(v2, v0) = v4)) & ! [v0: $i] : ! % 34.53/5.26 [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subq(v0, v1) = v2) | ~ $i(v1) | ~ % 34.53/5.26 $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & mem(v3, v1) = v4 & % 34.53/5.26 mem(v3, v0) = 0 & $i(v3))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 34.53/5.26 (subq(v0, v1) = 0) | ~ (mem(v2, v0) = 0) | ~ $i(v2) | ~ $i(v1) | ~ % 34.53/5.26 $i(v0) | mem(v2, v1) = 0) % 34.53/5.26 % 34.53/5.26 (u_ax) % 34.53/5.27 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0 % 34.53/5.27 | ~ (u(v1, v2) = v3) | ~ (mem(v0, v3) = v4) | ~ $i(v2) | ~ $i(v1) | ~ % 34.53/5.27 $i(v0) | ? [v5: int] : ? [v6: int] : ( ~ (v6 = 0) & ~ (v5 = 0) & mem(v0, % 34.53/5.27 v2) = v6 & mem(v0, v1) = v5)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 34.53/5.27 : ! [v3: $i] : ( ~ (u(v1, v2) = v3) | ~ (mem(v0, v3) = 0) | ~ $i(v2) | ~ % 34.53/5.27 $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] : (mem(v0, v2) = v5 & % 34.53/5.27 mem(v0, v1) = v4 & (v5 = 0 | v4 = 0))) % 34.53/5.27 % 34.53/5.27 (function-axioms) % 34.53/5.27 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (a(v3, % 34.53/5.27 v2) = v1) | ~ (a(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 34.53/5.27 $i] : ! [v3: $i] : (v1 = v0 | ~ (m(v3, v2) = v1) | ~ (m(v3, v2) = v0)) & % 34.53/5.27 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (u(v3, % 34.53/5.27 v2) = v1) | ~ (u(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 34.53/5.27 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (disj(v3, v2) % 34.53/5.27 = v1) | ~ (disj(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 34.53/5.27 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (subq(v3, v2) % 34.53/5.27 = v1) | ~ (subq(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 34.53/5.27 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (mem(v3, v2) % 34.53/5.27 = v1) | ~ (mem(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 34.53/5.27 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (atleast16p(v2) = v1) | ~ % 34.53/5.27 (atleast16p(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 34.53/5.27 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (atleast15p(v2) = v1) | ~ % 34.53/5.27 (atleast15p(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 34.53/5.27 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (atleast14p(v2) = v1) | ~ % 34.53/5.27 (atleast14p(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 34.53/5.27 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (atleast13p(v2) = v1) | ~ % 34.53/5.27 (atleast13p(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 34.53/5.27 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (atleast12p(v2) = v1) | ~ % 34.53/5.27 (atleast12p(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 34.53/5.27 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (atleast11p(v2) = v1) | ~ % 34.53/5.27 (atleast11p(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 34.53/5.27 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (atleast10p(v2) = v1) | ~ % 34.53/5.27 (atleast10p(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 34.53/5.27 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (atleast9p(v2) = v1) | ~ % 34.53/5.27 (atleast9p(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 34.53/5.27 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (atleast8p(v2) = v1) | ~ % 34.53/5.27 (atleast8p(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 34.53/5.27 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (atleast7p(v2) = v1) | ~ % 34.53/5.27 (atleast7p(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 34.53/5.27 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (atleast6p(v2) = v1) | ~ % 34.53/5.27 (atleast6p(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 34.53/5.27 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (atleast5p(v2) = v1) | ~ % 34.53/5.27 (atleast5p(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 34.53/5.27 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (atleast4p(v2) = v1) | ~ % 34.53/5.27 (atleast4p(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 34.53/5.27 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (atleast3p(v2) = v1) | ~ % 34.53/5.27 (atleast3p(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 34.53/5.27 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (atleast2p(v2) = v1) | ~ % 34.53/5.27 (atleast2p(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | % 34.53/5.27 ~ (p(v2) = v1) | ~ (p(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 34.53/5.27 : (v1 = v0 | ~ (n(v2) = v1) | ~ (n(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : % 34.53/5.27 ! [v2: $i] : (v1 = v0 | ~ (s(v2) = v1) | ~ (s(v2) = v0)) % 34.53/5.27 % 34.53/5.27 Further assumptions not needed in the proof: % 34.53/5.27 -------------------------------------------- % 34.53/5.27 atleast10p_def, atleast11p_def, atleast12p_def, atleast13p_def, atleast14p_def, % 34.53/5.27 atleast15p_def, atleast16p_def, atleast5p_def, atleast6p_def, atleast7p_def, % 34.53/5.27 atleast8p_def, atleast9p_def, disj_def, m_ax, setext % 34.53/5.27 % 34.53/5.27 Those formulas are unsatisfiable: % 34.53/5.27 --------------------------------- % 34.53/5.27 % 34.53/5.27 Begin of proof % 34.53/5.27 | % 34.53/5.27 | ALPHA: (subq_def) implies: % 34.53/5.27 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (subq(v0, v1) = 0) | ~ % 34.53/5.27 | (mem(v2, v0) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | mem(v2, v1) = % 34.53/5.27 | 0) % 34.53/5.28 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subq(v0, v1) = % 34.53/5.28 | v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 % 34.53/5.28 | = 0) & mem(v3, v1) = v4 & mem(v3, v0) = 0 & $i(v3))) % 34.53/5.28 | % 34.53/5.28 | ALPHA: (e_ax) implies: % 34.53/5.28 | (3) ! [v0: $i] : ( ~ (mem(v0, e) = 0) | ~ $i(v0)) % 34.53/5.28 | % 34.53/5.28 | ALPHA: (s_ax) implies: % 34.53/5.28 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (s(v1) = v2) | % 34.53/5.28 | ~ (mem(v0, v2) = 0) | ~ $i(v1) | ~ $i(v0)) % 34.53/5.28 | % 34.53/5.28 | ALPHA: (u_ax) implies: % 34.53/5.28 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (u(v1, v2) % 34.53/5.28 | = v3) | ~ (mem(v0, v3) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 34.53/5.28 | ? [v4: any] : ? [v5: any] : (mem(v0, v2) = v5 & mem(v0, v1) = v4 & % 34.53/5.28 | (v5 = 0 | v4 = 0))) % 34.53/5.28 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : % 34.53/5.28 | (v4 = 0 | ~ (u(v1, v2) = v3) | ~ (mem(v0, v3) = v4) | ~ $i(v2) | ~ % 34.53/5.28 | $i(v1) | ~ $i(v0) | ? [v5: int] : ? [v6: int] : ( ~ (v6 = 0) & ~ % 34.53/5.28 | (v5 = 0) & mem(v0, v2) = v6 & mem(v0, v1) = v5)) % 34.53/5.28 | % 34.53/5.28 | ALPHA: (a_def) implies: % 34.53/5.28 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (a(v0, v1) = v2) | ~ % 34.53/5.28 | $i(v1) | ~ $i(v0) | ? [v3: $i] : (u(v0, v3) = v2 & s(v1) = v3 & % 34.53/5.28 | $i(v3) & $i(v2))) % 34.53/5.28 | % 34.53/5.28 | ALPHA: (n_def) implies: % 34.53/5.28 | (8) ! [v0: $i] : ! [v1: $i] : ( ~ (n(v0) = v1) | ~ $i(v0) | (a(v0, v0) = % 34.53/5.28 | v1 & $i(v1))) % 34.53/5.28 | % 34.53/5.28 | ALPHA: (p_ax) implies: % 34.53/5.28 | (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 34.53/5.28 | (p(v1) = v2) | ~ (mem(v0, v2) = v3) | ~ $i(v1) | ~ $i(v0) | ? % 34.53/5.28 | [v4: int] : ( ~ (v4 = 0) & subq(v0, v1) = v4)) % 34.53/5.28 | % 34.53/5.28 | ALPHA: (atleast2p_def) implies: % 34.53/5.28 | (10) ! [v0: $i] : ( ~ (atleast2p(v0) = 0) | ~ $i(v0) | ? [v1: $i] : ? % 34.53/5.28 | [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) & p(v1) = v2 & subq(v0, v2) = % 34.53/5.28 | v3 & mem(v1, v0) = 0 & $i(v2) & $i(v1))) % 34.53/5.28 | % 34.53/5.28 | ALPHA: (atleast3p_def) implies: % 34.53/5.28 | (11) ! [v0: $i] : ( ~ (atleast3p(v0) = 0) | ~ $i(v0) | ? [v1: $i] : ? % 34.53/5.28 | [v2: int] : ( ~ (v2 = 0) & atleast2p(v1) = 0 & subq(v1, v0) = 0 & % 34.53/5.28 | subq(v0, v1) = v2 & $i(v1))) % 34.53/5.28 | % 34.53/5.28 | ALPHA: (atleast4p_def) implies: % 34.53/5.28 | (12) ! [v0: $i] : ( ~ (atleast4p(v0) = 0) | ~ $i(v0) | ? [v1: $i] : ? % 34.53/5.28 | [v2: int] : ( ~ (v2 = 0) & atleast3p(v1) = 0 & subq(v1, v0) = 0 & % 34.53/5.28 | subq(v0, v1) = v2 & $i(v1))) % 34.53/5.28 | % 34.53/5.28 | ALPHA: (atmost3_7) implies: % 34.53/5.28 | (13) $i(e) % 34.53/5.28 | (14) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : (atleast4p(v3) % 34.53/5.28 | = 0 & n(v1) = v2 & n(e) = v0 & u(v0, v2) = v3 & s(v0) = v1 & $i(v3) % 34.53/5.28 | & $i(v2) & $i(v1) & $i(v0)) % 34.53/5.28 | % 34.53/5.28 | ALPHA: (function-axioms) implies: % 34.53/5.28 | (15) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 34.53/5.28 | : ! [v3: $i] : (v1 = v0 | ~ (mem(v3, v2) = v1) | ~ (mem(v3, v2) = % 34.53/5.28 | v0)) % 34.53/5.28 | % 34.53/5.28 | DELTA: instantiating (14) with fresh symbols all_29_0, all_29_1, all_29_2, % 34.53/5.28 | all_29_3 gives: % 34.53/5.28 | (16) atleast4p(all_29_0) = 0 & n(all_29_2) = all_29_1 & n(e) = all_29_3 & % 34.53/5.28 | u(all_29_3, all_29_1) = all_29_0 & s(all_29_3) = all_29_2 & % 34.53/5.28 | $i(all_29_0) & $i(all_29_1) & $i(all_29_2) & $i(all_29_3) % 34.53/5.28 | % 34.53/5.28 | ALPHA: (16) implies: % 34.53/5.28 | (17) $i(all_29_2) % 34.53/5.28 | (18) $i(all_29_0) % 34.53/5.28 | (19) s(all_29_3) = all_29_2 % 34.53/5.28 | (20) u(all_29_3, all_29_1) = all_29_0 % 34.53/5.29 | (21) n(e) = all_29_3 % 34.53/5.29 | (22) n(all_29_2) = all_29_1 % 34.53/5.29 | (23) atleast4p(all_29_0) = 0 % 34.53/5.29 | % 34.53/5.29 | GROUND_INST: instantiating (8) with e, all_29_3, simplifying with (13), (21) % 34.53/5.29 | gives: % 34.53/5.29 | (24) a(e, e) = all_29_3 & $i(all_29_3) % 34.53/5.29 | % 34.53/5.29 | ALPHA: (24) implies: % 34.53/5.29 | (25) a(e, e) = all_29_3 % 34.53/5.29 | % 34.53/5.29 | GROUND_INST: instantiating (8) with all_29_2, all_29_1, simplifying with (17), % 34.53/5.29 | (22) gives: % 34.53/5.29 | (26) a(all_29_2, all_29_2) = all_29_1 & $i(all_29_1) % 34.53/5.29 | % 34.53/5.29 | ALPHA: (26) implies: % 34.53/5.29 | (27) a(all_29_2, all_29_2) = all_29_1 % 34.53/5.29 | % 34.53/5.29 | GROUND_INST: instantiating (12) with all_29_0, simplifying with (18), (23) % 34.53/5.29 | gives: % 34.53/5.29 | (28) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & atleast3p(v0) = 0 & % 34.53/5.29 | subq(v0, all_29_0) = 0 & subq(all_29_0, v0) = v1 & $i(v0)) % 34.53/5.29 | % 34.53/5.29 | DELTA: instantiating (28) with fresh symbols all_37_0, all_37_1 gives: % 34.53/5.29 | (29) ~ (all_37_0 = 0) & atleast3p(all_37_1) = 0 & subq(all_37_1, all_29_0) % 34.53/5.29 | = 0 & subq(all_29_0, all_37_1) = all_37_0 & $i(all_37_1) % 34.53/5.29 | % 34.53/5.29 | ALPHA: (29) implies: % 34.53/5.29 | (30) ~ (all_37_0 = 0) % 34.53/5.29 | (31) $i(all_37_1) % 34.53/5.29 | (32) subq(all_29_0, all_37_1) = all_37_0 % 34.53/5.29 | (33) subq(all_37_1, all_29_0) = 0 % 34.53/5.29 | (34) atleast3p(all_37_1) = 0 % 34.53/5.29 | % 34.53/5.29 | GROUND_INST: instantiating (2) with all_29_0, all_37_1, all_37_0, simplifying % 34.53/5.29 | with (18), (31), (32) gives: % 34.53/5.29 | (35) all_37_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & mem(v0, % 34.53/5.29 | all_37_1) = v1 & mem(v0, all_29_0) = 0 & $i(v0)) % 34.53/5.29 | % 34.53/5.29 | GROUND_INST: instantiating (7) with e, e, all_29_3, simplifying with (13), % 34.53/5.29 | (25) gives: % 34.53/5.29 | (36) ? [v0: $i] : (u(e, v0) = all_29_3 & s(e) = v0 & $i(v0) & % 34.53/5.29 | $i(all_29_3)) % 34.53/5.29 | % 34.53/5.29 | GROUND_INST: instantiating (7) with all_29_2, all_29_2, all_29_1, simplifying % 34.53/5.29 | with (17), (27) gives: % 34.53/5.29 | (37) ? [v0: $i] : (u(all_29_2, v0) = all_29_1 & s(all_29_2) = v0 & $i(v0) % 34.53/5.29 | & $i(all_29_1)) % 34.53/5.29 | % 34.53/5.29 | GROUND_INST: instantiating (11) with all_37_1, simplifying with (31), (34) % 34.53/5.29 | gives: % 34.53/5.29 | (38) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & atleast2p(v0) = 0 & % 34.53/5.29 | subq(v0, all_37_1) = 0 & subq(all_37_1, v0) = v1 & $i(v0)) % 34.53/5.29 | % 34.53/5.29 | DELTA: instantiating (37) with fresh symbol all_46_0 gives: % 34.53/5.29 | (39) u(all_29_2, all_46_0) = all_29_1 & s(all_29_2) = all_46_0 & % 34.53/5.29 | $i(all_46_0) & $i(all_29_1) % 34.53/5.29 | % 34.53/5.29 | ALPHA: (39) implies: % 34.53/5.29 | (40) $i(all_29_1) % 34.53/5.29 | (41) $i(all_46_0) % 34.53/5.29 | (42) s(all_29_2) = all_46_0 % 34.53/5.29 | (43) u(all_29_2, all_46_0) = all_29_1 % 34.53/5.29 | % 34.53/5.29 | DELTA: instantiating (36) with fresh symbol all_48_0 gives: % 34.53/5.29 | (44) u(e, all_48_0) = all_29_3 & s(e) = all_48_0 & $i(all_48_0) & % 34.53/5.29 | $i(all_29_3) % 34.53/5.29 | % 34.53/5.29 | ALPHA: (44) implies: % 34.53/5.29 | (45) $i(all_29_3) % 34.53/5.29 | (46) $i(all_48_0) % 34.53/5.29 | (47) s(e) = all_48_0 % 34.53/5.29 | (48) u(e, all_48_0) = all_29_3 % 34.53/5.29 | % 34.53/5.29 | DELTA: instantiating (38) with fresh symbols all_50_0, all_50_1 gives: % 34.53/5.29 | (49) ~ (all_50_0 = 0) & atleast2p(all_50_1) = 0 & subq(all_50_1, all_37_1) % 34.53/5.29 | = 0 & subq(all_37_1, all_50_1) = all_50_0 & $i(all_50_1) % 34.53/5.29 | % 34.53/5.29 | ALPHA: (49) implies: % 34.53/5.29 | (50) ~ (all_50_0 = 0) % 34.53/5.29 | (51) $i(all_50_1) % 34.53/5.29 | (52) subq(all_37_1, all_50_1) = all_50_0 % 34.53/5.29 | (53) subq(all_50_1, all_37_1) = 0 % 34.53/5.29 | (54) atleast2p(all_50_1) = 0 % 34.53/5.29 | % 34.53/5.29 | BETA: splitting (35) gives: % 34.53/5.29 | % 34.53/5.29 | Case 1: % 34.53/5.29 | | % 34.53/5.30 | | (55) all_37_0 = 0 % 34.53/5.30 | | % 34.53/5.30 | | REDUCE: (30), (55) imply: % 34.53/5.30 | | (56) $false % 34.53/5.30 | | % 34.53/5.30 | | CLOSE: (56) is inconsistent. % 34.53/5.30 | | % 34.53/5.30 | Case 2: % 34.53/5.30 | | % 34.53/5.30 | | (57) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & mem(v0, all_37_1) = v1 & % 34.53/5.30 | | mem(v0, all_29_0) = 0 & $i(v0)) % 34.53/5.30 | | % 34.53/5.30 | | DELTA: instantiating (57) with fresh symbols all_56_0, all_56_1 gives: % 34.53/5.30 | | (58) ~ (all_56_0 = 0) & mem(all_56_1, all_37_1) = all_56_0 & % 34.53/5.30 | | mem(all_56_1, all_29_0) = 0 & $i(all_56_1) % 34.53/5.30 | | % 34.53/5.30 | | ALPHA: (58) implies: % 34.53/5.30 | | (59) ~ (all_56_0 = 0) % 34.53/5.30 | | (60) $i(all_56_1) % 34.53/5.30 | | (61) mem(all_56_1, all_29_0) = 0 % 34.53/5.30 | | (62) mem(all_56_1, all_37_1) = all_56_0 % 34.53/5.30 | | % 34.53/5.30 | | GROUND_INST: instantiating (5) with all_56_1, all_29_3, all_29_1, all_29_0, % 34.53/5.30 | | simplifying with (20), (40), (45), (60), (61) gives: % 34.53/5.30 | | (63) ? [v0: any] : ? [v1: any] : (mem(all_56_1, all_29_1) = v1 & % 34.53/5.30 | | mem(all_56_1, all_29_3) = v0 & (v1 = 0 | v0 = 0)) % 34.53/5.30 | | % 34.53/5.30 | | GROUND_INST: instantiating (2) with all_37_1, all_50_1, all_50_0, % 34.53/5.30 | | simplifying with (31), (51), (52) gives: % 34.53/5.30 | | (64) all_50_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & mem(v0, % 34.53/5.30 | | all_50_1) = v1 & mem(v0, all_37_1) = 0 & $i(v0)) % 34.53/5.30 | | % 34.53/5.30 | | GROUND_INST: instantiating (10) with all_50_1, simplifying with (51), (54) % 34.53/5.30 | | gives: % 34.53/5.30 | | (65) ? [v0: $i] : ? [v1: $i] : ? [v2: int] : ( ~ (v2 = 0) & p(v0) = v1 % 34.53/5.30 | | & subq(all_50_1, v1) = v2 & mem(v0, all_50_1) = 0 & $i(v1) & % 34.53/5.30 | | $i(v0)) % 34.53/5.30 | | % 34.53/5.30 | | DELTA: instantiating (63) with fresh symbols all_70_0, all_70_1 gives: % 34.53/5.30 | | (66) mem(all_56_1, all_29_1) = all_70_0 & mem(all_56_1, all_29_3) = % 34.53/5.30 | | all_70_1 & (all_70_0 = 0 | all_70_1 = 0) % 34.53/5.30 | | % 34.53/5.30 | | ALPHA: (66) implies: % 34.53/5.30 | | (67) mem(all_56_1, all_29_3) = all_70_1 % 34.53/5.30 | | (68) mem(all_56_1, all_29_1) = all_70_0 % 34.53/5.30 | | (69) all_70_0 = 0 | all_70_1 = 0 % 34.53/5.30 | | % 34.53/5.30 | | DELTA: instantiating (65) with fresh symbols all_72_0, all_72_1, all_72_2 % 34.53/5.30 | | gives: % 34.53/5.30 | | (70) ~ (all_72_0 = 0) & p(all_72_2) = all_72_1 & subq(all_50_1, % 34.53/5.30 | | all_72_1) = all_72_0 & mem(all_72_2, all_50_1) = 0 & $i(all_72_1) % 34.53/5.30 | | & $i(all_72_2) % 34.53/5.30 | | % 34.53/5.30 | | ALPHA: (70) implies: % 34.53/5.30 | | (71) ~ (all_72_0 = 0) % 34.53/5.30 | | (72) $i(all_72_2) % 34.53/5.30 | | (73) $i(all_72_1) % 34.53/5.30 | | (74) mem(all_72_2, all_50_1) = 0 % 34.95/5.30 | | (75) subq(all_50_1, all_72_1) = all_72_0 % 34.95/5.30 | | (76) p(all_72_2) = all_72_1 % 34.95/5.30 | | % 34.95/5.30 | | BETA: splitting (64) gives: % 34.95/5.30 | | % 34.95/5.30 | | Case 1: % 34.95/5.30 | | | % 34.95/5.30 | | | (77) all_50_0 = 0 % 34.95/5.30 | | | % 34.95/5.30 | | | REDUCE: (50), (77) imply: % 34.95/5.30 | | | (78) $false % 34.95/5.30 | | | % 34.95/5.30 | | | CLOSE: (78) is inconsistent. % 34.95/5.30 | | | % 34.95/5.30 | | Case 2: % 34.95/5.30 | | | % 34.95/5.30 | | | (79) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & mem(v0, all_50_1) = v1 % 34.95/5.30 | | | & mem(v0, all_37_1) = 0 & $i(v0)) % 34.95/5.30 | | | % 34.95/5.30 | | | DELTA: instantiating (79) with fresh symbols all_83_0, all_83_1 gives: % 34.95/5.30 | | | (80) ~ (all_83_0 = 0) & mem(all_83_1, all_50_1) = all_83_0 & % 34.95/5.30 | | | mem(all_83_1, all_37_1) = 0 & $i(all_83_1) % 34.95/5.30 | | | % 34.95/5.30 | | | ALPHA: (80) implies: % 34.95/5.30 | | | (81) ~ (all_83_0 = 0) % 34.95/5.30 | | | (82) $i(all_83_1) % 34.95/5.31 | | | (83) mem(all_83_1, all_37_1) = 0 % 34.95/5.31 | | | (84) mem(all_83_1, all_50_1) = all_83_0 % 34.95/5.31 | | | % 34.95/5.31 | | | GROUND_INST: instantiating (1) with all_50_1, all_37_1, all_72_2, % 34.95/5.31 | | | simplifying with (31), (51), (53), (72), (74) gives: % 34.95/5.31 | | | (85) mem(all_72_2, all_37_1) = 0 % 34.95/5.31 | | | % 34.95/5.31 | | | GROUND_INST: instantiating (1) with all_37_1, all_29_0, all_83_1, % 34.95/5.31 | | | simplifying with (18), (31), (33), (82), (83) gives: % 34.95/5.31 | | | (86) mem(all_83_1, all_29_0) = 0 % 34.95/5.31 | | | % 34.95/5.31 | | | GROUND_INST: instantiating (2) with all_50_1, all_72_1, all_72_0, % 34.95/5.31 | | | simplifying with (51), (73), (75) gives: % 34.95/5.31 | | | (87) all_72_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & mem(v0, % 34.95/5.31 | | | all_72_1) = v1 & mem(v0, all_50_1) = 0 & $i(v0)) % 34.95/5.31 | | | % 34.95/5.31 | | | BETA: splitting (87) gives: % 34.95/5.31 | | | % 34.95/5.31 | | | Case 1: % 34.95/5.31 | | | | % 34.95/5.31 | | | | (88) all_72_0 = 0 % 34.95/5.31 | | | | % 34.95/5.31 | | | | REDUCE: (71), (88) imply: % 34.95/5.31 | | | | (89) $false % 34.95/5.31 | | | | % 34.95/5.31 | | | | CLOSE: (89) is inconsistent. % 34.95/5.31 | | | | % 34.95/5.31 | | | Case 2: % 34.95/5.31 | | | | % 34.95/5.31 | | | | (90) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & mem(v0, all_72_1) = % 34.95/5.31 | | | | v1 & mem(v0, all_50_1) = 0 & $i(v0)) % 34.95/5.31 | | | | % 34.95/5.31 | | | | DELTA: instantiating (90) with fresh symbols all_109_0, all_109_1 gives: % 34.95/5.31 | | | | (91) ~ (all_109_0 = 0) & mem(all_109_1, all_72_1) = all_109_0 & % 34.95/5.31 | | | | mem(all_109_1, all_50_1) = 0 & $i(all_109_1) % 34.95/5.31 | | | | % 34.95/5.31 | | | | ALPHA: (91) implies: % 34.95/5.31 | | | | (92) ~ (all_109_0 = 0) % 34.95/5.31 | | | | (93) $i(all_109_1) % 34.95/5.31 | | | | (94) mem(all_109_1, all_50_1) = 0 % 34.95/5.31 | | | | (95) mem(all_109_1, all_72_1) = all_109_0 % 34.95/5.31 | | | | % 34.95/5.31 | | | | GROUND_INST: instantiating (1) with all_37_1, all_29_0, all_72_2, % 34.95/5.31 | | | | simplifying with (18), (31), (33), (72), (85) gives: % 34.95/5.31 | | | | (96) mem(all_72_2, all_29_0) = 0 % 34.95/5.31 | | | | % 34.95/5.31 | | | | GROUND_INST: instantiating (5) with all_83_1, all_29_3, all_29_1, % 34.95/5.31 | | | | all_29_0, simplifying with (20), (40), (45), (82), (86) % 34.95/5.31 | | | | gives: % 34.95/5.31 | | | | (97) ? [v0: any] : ? [v1: any] : (mem(all_83_1, all_29_1) = v1 & % 34.95/5.31 | | | | mem(all_83_1, all_29_3) = v0 & (v1 = 0 | v0 = 0)) % 34.95/5.31 | | | | % 34.95/5.31 | | | | GROUND_INST: instantiating (1) with all_50_1, all_37_1, all_109_1, % 34.95/5.31 | | | | simplifying with (31), (51), (53), (93), (94) gives: % 34.95/5.31 | | | | (98) mem(all_109_1, all_37_1) = 0 % 34.95/5.31 | | | | % 34.95/5.31 | | | | GROUND_INST: instantiating (9) with all_109_1, all_72_2, all_72_1, % 34.95/5.31 | | | | all_109_0, simplifying with (72), (76), (93), (95) gives: % 34.95/5.31 | | | | (99) all_109_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & subq(all_109_1, % 34.95/5.31 | | | | all_72_2) = v0) % 34.95/5.31 | | | | % 34.95/5.31 | | | | DELTA: instantiating (97) with fresh symbols all_117_0, all_117_1 gives: % 34.95/5.31 | | | | (100) mem(all_83_1, all_29_1) = all_117_0 & mem(all_83_1, all_29_3) = % 34.95/5.31 | | | | all_117_1 & (all_117_0 = 0 | all_117_1 = 0) % 34.95/5.31 | | | | % 34.95/5.31 | | | | ALPHA: (100) implies: % 34.95/5.31 | | | | (101) mem(all_83_1, all_29_3) = all_117_1 % 34.95/5.31 | | | | (102) mem(all_83_1, all_29_1) = all_117_0 % 34.95/5.31 | | | | (103) all_117_0 = 0 | all_117_1 = 0 % 34.95/5.31 | | | | % 34.95/5.31 | | | | BETA: splitting (99) gives: % 34.95/5.31 | | | | % 34.95/5.31 | | | | Case 1: % 34.95/5.31 | | | | | % 34.95/5.31 | | | | | (104) all_109_0 = 0 % 34.95/5.31 | | | | | % 34.95/5.31 | | | | | REDUCE: (92), (104) imply: % 34.95/5.31 | | | | | (105) $false % 34.95/5.31 | | | | | % 34.95/5.31 | | | | | CLOSE: (105) is inconsistent. % 34.95/5.31 | | | | | % 34.95/5.31 | | | | Case 2: % 34.95/5.31 | | | | | % 34.95/5.31 | | | | | (106) ? [v0: int] : ( ~ (v0 = 0) & subq(all_109_1, all_72_2) = v0) % 34.95/5.31 | | | | | % 34.95/5.31 | | | | | DELTA: instantiating (106) with fresh symbol all_123_0 gives: % 34.95/5.31 | | | | | (107) ~ (all_123_0 = 0) & subq(all_109_1, all_72_2) = all_123_0 % 34.95/5.31 | | | | | % 34.95/5.31 | | | | | ALPHA: (107) implies: % 34.95/5.31 | | | | | (108) ~ (all_123_0 = 0) % 34.95/5.31 | | | | | (109) subq(all_109_1, all_72_2) = all_123_0 % 34.95/5.31 | | | | | % 34.95/5.32 | | | | | GROUND_INST: instantiating (5) with all_72_2, all_29_3, all_29_1, % 34.95/5.32 | | | | | all_29_0, simplifying with (20), (40), (45), (72), (96) % 34.95/5.32 | | | | | gives: % 34.95/5.32 | | | | | (110) ? [v0: any] : ? [v1: any] : (mem(all_72_2, all_29_1) = v1 & % 34.95/5.32 | | | | | mem(all_72_2, all_29_3) = v0 & (v1 = 0 | v0 = 0)) % 34.95/5.32 | | | | | % 34.95/5.32 | | | | | GROUND_INST: instantiating (6) with all_83_1, all_29_2, all_46_0, % 34.95/5.32 | | | | | all_29_1, all_117_0, simplifying with (17), (41), (43), % 34.95/5.32 | | | | | (82), (102) gives: % 34.95/5.32 | | | | | (111) all_117_0 = 0 | ? [v0: int] : ? [v1: int] : ( ~ (v1 = 0) & % 34.95/5.32 | | | | | ~ (v0 = 0) & mem(all_83_1, all_46_0) = v1 & mem(all_83_1, % 34.95/5.32 | | | | | all_29_2) = v0) % 34.95/5.32 | | | | | % 34.95/5.32 | | | | | GROUND_INST: instantiating (1) with all_37_1, all_29_0, all_109_1, % 34.95/5.32 | | | | | simplifying with (18), (31), (33), (93), (98) gives: % 34.95/5.32 | | | | | (112) mem(all_109_1, all_29_0) = 0 % 34.95/5.32 | | | | | % 34.95/5.32 | | | | | GROUND_INST: instantiating (2) with all_109_1, all_72_2, all_123_0, % 34.95/5.32 | | | | | simplifying with (72), (93), (109) gives: % 34.95/5.32 | | | | | (113) all_123_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & % 34.95/5.32 | | | | | mem(v0, all_109_1) = 0 & mem(v0, all_72_2) = v1 & $i(v0)) % 34.95/5.32 | | | | | % 34.95/5.32 | | | | | DELTA: instantiating (110) with fresh symbols all_131_0, all_131_1 % 34.95/5.32 | | | | | gives: % 34.95/5.32 | | | | | (114) mem(all_72_2, all_29_1) = all_131_0 & mem(all_72_2, all_29_3) % 34.95/5.32 | | | | | = all_131_1 & (all_131_0 = 0 | all_131_1 = 0) % 34.95/5.32 | | | | | % 34.95/5.32 | | | | | ALPHA: (114) implies: % 34.95/5.32 | | | | | (115) mem(all_72_2, all_29_3) = all_131_1 % 34.95/5.32 | | | | | (116) mem(all_72_2, all_29_1) = all_131_0 % 34.95/5.32 | | | | | (117) all_131_0 = 0 | all_131_1 = 0 % 34.95/5.32 | | | | | % 34.95/5.32 | | | | | BETA: splitting (113) gives: % 34.95/5.32 | | | | | % 34.95/5.32 | | | | | Case 1: % 34.95/5.32 | | | | | | % 34.95/5.32 | | | | | | (118) all_123_0 = 0 % 34.95/5.32 | | | | | | % 34.95/5.32 | | | | | | REDUCE: (108), (118) imply: % 34.95/5.32 | | | | | | (119) $false % 34.95/5.32 | | | | | | % 34.95/5.32 | | | | | | CLOSE: (119) is inconsistent. % 34.95/5.32 | | | | | | % 34.95/5.32 | | | | | Case 2: % 34.95/5.32 | | | | | | % 34.95/5.32 | | | | | | (120) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & mem(v0, % 34.95/5.32 | | | | | | all_109_1) = 0 & mem(v0, all_72_2) = v1 & $i(v0)) % 34.95/5.32 | | | | | | % 34.95/5.32 | | | | | | DELTA: instantiating (120) with fresh symbols all_137_0, all_137_1 % 34.95/5.32 | | | | | | gives: % 34.95/5.32 | | | | | | (121) ~ (all_137_0 = 0) & mem(all_137_1, all_109_1) = 0 & % 34.95/5.32 | | | | | | mem(all_137_1, all_72_2) = all_137_0 & $i(all_137_1) % 34.95/5.32 | | | | | | % 34.95/5.32 | | | | | | ALPHA: (121) implies: % 34.95/5.32 | | | | | | (122) ~ (all_137_0 = 0) % 34.95/5.32 | | | | | | (123) $i(all_137_1) % 34.95/5.32 | | | | | | (124) mem(all_137_1, all_72_2) = all_137_0 % 34.95/5.32 | | | | | | (125) mem(all_137_1, all_109_1) = 0 % 34.95/5.32 | | | | | | % 34.95/5.32 | | | | | | GROUND_INST: instantiating (5) with all_109_1, all_29_3, all_29_1, % 34.95/5.32 | | | | | | all_29_0, simplifying with (20), (40), (45), (93), % 34.95/5.32 | | | | | | (112) gives: % 34.95/5.32 | | | | | | (126) ? [v0: any] : ? [v1: any] : (mem(all_109_1, all_29_1) = % 34.95/5.32 | | | | | | v1 & mem(all_109_1, all_29_3) = v0 & (v1 = 0 | v0 = 0)) % 34.95/5.32 | | | | | | % 34.95/5.32 | | | | | | DELTA: instantiating (126) with fresh symbols all_144_0, all_144_1 % 34.95/5.32 | | | | | | gives: % 34.95/5.32 | | | | | | (127) mem(all_109_1, all_29_1) = all_144_0 & mem(all_109_1, % 34.95/5.32 | | | | | | all_29_3) = all_144_1 & (all_144_0 = 0 | all_144_1 = 0) % 34.95/5.32 | | | | | | % 34.95/5.32 | | | | | | ALPHA: (127) implies: % 34.95/5.32 | | | | | | (128) mem(all_109_1, all_29_3) = all_144_1 % 34.95/5.32 | | | | | | (129) mem(all_109_1, all_29_1) = all_144_0 % 34.95/5.32 | | | | | | (130) all_144_0 = 0 | all_144_1 = 0 % 34.95/5.32 | | | | | | % 34.95/5.32 | | | | | | GROUND_INST: instantiating (6) with all_109_1, all_29_2, all_46_0, % 34.95/5.32 | | | | | | all_29_1, all_144_0, simplifying with (17), (41), (43), % 34.95/5.32 | | | | | | (93), (129) gives: % 34.95/5.32 | | | | | | (131) all_144_0 = 0 | ? [v0: int] : ? [v1: int] : ( ~ (v1 = 0) % 34.95/5.32 | | | | | | & ~ (v0 = 0) & mem(all_109_1, all_46_0) = v1 & % 34.95/5.32 | | | | | | mem(all_109_1, all_29_2) = v0) % 34.95/5.32 | | | | | | % 34.95/5.32 | | | | | | BETA: splitting (69) gives: % 34.95/5.32 | | | | | | % 34.95/5.32 | | | | | | Case 1: % 34.95/5.32 | | | | | | | % 34.95/5.32 | | | | | | | (132) all_70_0 = 0 % 34.95/5.32 | | | | | | | % 34.95/5.32 | | | | | | | REDUCE: (68), (132) imply: % 34.95/5.32 | | | | | | | (133) mem(all_56_1, all_29_1) = 0 % 34.95/5.32 | | | | | | | % 34.95/5.32 | | | | | | | GROUND_INST: instantiating (5) with all_56_1, all_29_2, all_46_0, % 34.95/5.32 | | | | | | | all_29_1, simplifying with (17), (41), (43), (60), % 34.95/5.32 | | | | | | | (133) gives: % 34.95/5.32 | | | | | | | (134) ? [v0: any] : ? [v1: any] : (mem(all_56_1, all_46_0) = % 34.95/5.32 | | | | | | | v1 & mem(all_56_1, all_29_2) = v0 & (v1 = 0 | v0 = 0)) % 34.95/5.32 | | | | | | | % 34.95/5.32 | | | | | | | DELTA: instantiating (134) with fresh symbols all_158_0, all_158_1 % 34.95/5.32 | | | | | | | gives: % 34.95/5.32 | | | | | | | (135) mem(all_56_1, all_46_0) = all_158_0 & mem(all_56_1, % 34.95/5.32 | | | | | | | all_29_2) = all_158_1 & (all_158_0 = 0 | all_158_1 = 0) % 34.95/5.32 | | | | | | | % 34.95/5.32 | | | | | | | ALPHA: (135) implies: % 34.95/5.32 | | | | | | | (136) mem(all_56_1, all_29_2) = all_158_1 % 34.95/5.32 | | | | | | | (137) mem(all_56_1, all_46_0) = all_158_0 % 34.95/5.32 | | | | | | | (138) all_158_0 = 0 | all_158_1 = 0 % 34.95/5.32 | | | | | | | % 34.95/5.32 | | | | | | | BETA: splitting (103) gives: % 34.95/5.32 | | | | | | | % 34.95/5.32 | | | | | | | Case 1: % 34.95/5.32 | | | | | | | | % 34.95/5.32 | | | | | | | | (139) all_117_0 = 0 % 34.95/5.32 | | | | | | | | % 34.95/5.32 | | | | | | | | REDUCE: (102), (139) imply: % 34.95/5.32 | | | | | | | | (140) mem(all_83_1, all_29_1) = 0 % 34.95/5.32 | | | | | | | | % 34.95/5.32 | | | | | | | | GROUND_INST: instantiating (5) with all_83_1, all_29_2, % 34.95/5.32 | | | | | | | | all_46_0, all_29_1, simplifying with (17), (41), % 34.95/5.32 | | | | | | | | (43), (82), (140) gives: % 34.95/5.32 | | | | | | | | (141) ? [v0: any] : ? [v1: any] : (mem(all_83_1, all_46_0) % 34.95/5.32 | | | | | | | | = v1 & mem(all_83_1, all_29_2) = v0 & (v1 = 0 | v0 = % 34.95/5.32 | | | | | | | | 0)) % 34.95/5.32 | | | | | | | | % 34.95/5.32 | | | | | | | | DELTA: instantiating (141) with fresh symbols all_181_0, % 34.95/5.32 | | | | | | | | all_181_1 gives: % 34.95/5.32 | | | | | | | | (142) mem(all_83_1, all_46_0) = all_181_0 & mem(all_83_1, % 34.95/5.32 | | | | | | | | all_29_2) = all_181_1 & (all_181_0 = 0 | all_181_1 = % 34.95/5.32 | | | | | | | | 0) % 34.95/5.32 | | | | | | | | % 34.95/5.32 | | | | | | | | ALPHA: (142) implies: % 34.95/5.33 | | | | | | | | (143) mem(all_83_1, all_29_2) = all_181_1 % 34.95/5.33 | | | | | | | | (144) mem(all_83_1, all_46_0) = all_181_0 % 34.95/5.33 | | | | | | | | (145) all_181_0 = 0 | all_181_1 = 0 % 34.95/5.33 | | | | | | | | % 34.95/5.33 | | | | | | | | BETA: splitting (117) gives: % 34.95/5.33 | | | | | | | | % 34.95/5.33 | | | | | | | | Case 1: % 34.95/5.33 | | | | | | | | | % 34.95/5.33 | | | | | | | | | (146) all_131_0 = 0 % 34.95/5.33 | | | | | | | | | % 34.95/5.33 | | | | | | | | | REDUCE: (116), (146) imply: % 34.95/5.33 | | | | | | | | | (147) mem(all_72_2, all_29_1) = 0 % 34.95/5.33 | | | | | | | | | % 34.95/5.33 | | | | | | | | | GROUND_INST: instantiating (5) with all_72_2, all_29_2, % 34.95/5.33 | | | | | | | | | all_46_0, all_29_1, simplifying with (17), (41), % 34.95/5.33 | | | | | | | | | (43), (72), (147) gives: % 34.95/5.33 | | | | | | | | | (148) ? [v0: any] : ? [v1: any] : (mem(all_72_2, % 34.95/5.33 | | | | | | | | | all_46_0) = v1 & mem(all_72_2, all_29_2) = v0 & % 34.95/5.33 | | | | | | | | | (v1 = 0 | v0 = 0)) % 34.95/5.33 | | | | | | | | | % 34.95/5.33 | | | | | | | | | DELTA: instantiating (148) with fresh symbols all_204_0, % 34.95/5.33 | | | | | | | | | all_204_1 gives: % 34.95/5.33 | | | | | | | | | (149) mem(all_72_2, all_46_0) = all_204_0 & mem(all_72_2, % 34.95/5.33 | | | | | | | | | all_29_2) = all_204_1 & (all_204_0 = 0 | all_204_1 % 34.95/5.33 | | | | | | | | | = 0) % 34.95/5.33 | | | | | | | | | % 34.95/5.33 | | | | | | | | | ALPHA: (149) implies: % 34.95/5.33 | | | | | | | | | (150) mem(all_72_2, all_29_2) = all_204_1 % 34.95/5.33 | | | | | | | | | (151) mem(all_72_2, all_46_0) = all_204_0 % 34.95/5.33 | | | | | | | | | (152) all_204_0 = 0 | all_204_1 = 0 % 34.95/5.33 | | | | | | | | | % 34.95/5.33 | | | | | | | | | BETA: splitting (138) gives: % 34.95/5.33 | | | | | | | | | % 34.95/5.33 | | | | | | | | | Case 1: % 34.95/5.33 | | | | | | | | | | % 34.95/5.33 | | | | | | | | | | (153) all_158_0 = 0 % 34.95/5.33 | | | | | | | | | | % 34.95/5.33 | | | | | | | | | | REDUCE: (137), (153) imply: % 34.95/5.33 | | | | | | | | | | (154) mem(all_56_1, all_46_0) = 0 % 34.95/5.33 | | | | | | | | | | % 34.95/5.33 | | | | | | | | | | GROUND_INST: instantiating (4) with all_56_1, all_29_2, % 34.95/5.33 | | | | | | | | | | all_46_0, simplifying with (17), (42), (60), (154) % 34.95/5.33 | | | | | | | | | | gives: % 34.95/5.33 | | | | | | | | | | (155) all_56_1 = all_29_2 % 34.95/5.33 | | | | | | | | | | % 34.95/5.33 | | | | | | | | | | REDUCE: (62), (155) imply: % 34.95/5.33 | | | | | | | | | | (156) mem(all_29_2, all_37_1) = all_56_0 % 34.95/5.33 | | | | | | | | | | % 34.95/5.33 | | | | | | | | | | BETA: splitting (145) gives: % 34.95/5.33 | | | | | | | | | | % 34.95/5.33 | | | | | | | | | | Case 1: % 34.95/5.33 | | | | | | | | | | | % 34.95/5.33 | | | | | | | | | | | (157) all_181_0 = 0 % 34.95/5.33 | | | | | | | | | | | % 34.95/5.33 | | | | | | | | | | | REDUCE: (144), (157) imply: % 34.95/5.33 | | | | | | | | | | | (158) mem(all_83_1, all_46_0) = 0 % 34.95/5.33 | | | | | | | | | | | % 34.95/5.33 | | | | | | | | | | | GROUND_INST: instantiating (4) with all_83_1, all_29_2, % 34.95/5.33 | | | | | | | | | | | all_46_0, simplifying with (17), (42), (82), (158) % 34.95/5.33 | | | | | | | | | | | gives: % 34.95/5.33 | | | | | | | | | | | (159) all_83_1 = all_29_2 % 34.95/5.33 | | | | | | | | | | | % 34.95/5.33 | | | | | | | | | | | REDUCE: (83), (159) imply: % 34.95/5.33 | | | | | | | | | | | (160) mem(all_29_2, all_37_1) = 0 % 34.95/5.33 | | | | | | | | | | | % 34.95/5.33 | | | | | | | | | | | REF_CLOSE: (15), (59), (156), (160) are inconsistent by % 34.95/5.33 | | | | | | | | | | | sub-proof #12. % 34.95/5.33 | | | | | | | | | | | % 34.95/5.33 | | | | | | | | | | Case 2: % 34.95/5.33 | | | | | | | | | | | % 34.95/5.33 | | | | | | | | | | | (161) all_181_1 = 0 % 34.95/5.33 | | | | | | | | | | | % 34.95/5.33 | | | | | | | | | | | REDUCE: (143), (161) imply: % 34.95/5.33 | | | | | | | | | | | (162) mem(all_83_1, all_29_2) = 0 % 34.95/5.33 | | | | | | | | | | | % 34.95/5.33 | | | | | | | | | | | GROUND_INST: instantiating (4) with all_83_1, all_29_3, % 34.95/5.33 | | | | | | | | | | | all_29_2, simplifying with (19), (45), (82), (162) % 34.95/5.33 | | | | | | | | | | | gives: % 34.95/5.33 | | | | | | | | | | | (163) all_83_1 = all_29_3 % 34.95/5.33 | | | | | | | | | | | % 34.95/5.33 | | | | | | | | | | | REDUCE: (84), (163) imply: % 34.95/5.33 | | | | | | | | | | | (164) mem(all_29_3, all_50_1) = all_83_0 % 34.95/5.33 | | | | | | | | | | | % 34.95/5.33 | | | | | | | | | | | BETA: splitting (152) gives: % 34.95/5.33 | | | | | | | | | | | % 34.95/5.33 | | | | | | | | | | | Case 1: % 34.95/5.33 | | | | | | | | | | | | % 34.95/5.33 | | | | | | | | | | | | (165) all_204_0 = 0 % 34.95/5.33 | | | | | | | | | | | | % 34.95/5.33 | | | | | | | | | | | | REDUCE: (151), (165) imply: % 34.95/5.33 | | | | | | | | | | | | (166) mem(all_72_2, all_46_0) = 0 % 34.95/5.33 | | | | | | | | | | | | % 34.95/5.33 | | | | | | | | | | | | REF_CLOSE: (4), (15), (17), (42), (59), (72), (85), (156), % 34.95/5.33 | | | | | | | | | | | | (166) are inconsistent by sub-proof #11. % 34.95/5.33 | | | | | | | | | | | | % 34.95/5.33 | | | | | | | | | | | Case 2: % 34.95/5.33 | | | | | | | | | | | | % 34.95/5.33 | | | | | | | | | | | | (167) all_204_1 = 0 % 34.95/5.33 | | | | | | | | | | | | % 34.95/5.33 | | | | | | | | | | | | REDUCE: (150), (167) imply: % 34.95/5.33 | | | | | | | | | | | | (168) mem(all_72_2, all_29_2) = 0 % 34.95/5.33 | | | | | | | | | | | | % 34.95/5.33 | | | | | | | | | | | | REF_CLOSE: (4), (15), (19), (45), (72), (74), (81), (164), % 34.95/5.33 | | | | | | | | | | | | (168) are inconsistent by sub-proof #10. % 34.95/5.33 | | | | | | | | | | | | % 34.95/5.33 | | | | | | | | | | | End of split % 34.95/5.33 | | | | | | | | | | | % 34.95/5.33 | | | | | | | | | | End of split % 34.95/5.33 | | | | | | | | | | % 34.95/5.33 | | | | | | | | | Case 2: % 34.95/5.33 | | | | | | | | | | % 34.95/5.33 | | | | | | | | | | (169) all_158_1 = 0 % 34.95/5.33 | | | | | | | | | | % 34.95/5.33 | | | | | | | | | | REDUCE: (136), (169) imply: % 34.95/5.33 | | | | | | | | | | (170) mem(all_56_1, all_29_2) = 0 % 34.95/5.33 | | | | | | | | | | % 34.95/5.33 | | | | | | | | | | GROUND_INST: instantiating (4) with all_56_1, all_29_3, % 34.95/5.33 | | | | | | | | | | all_29_2, simplifying with (19), (45), (60), (170) % 34.95/5.33 | | | | | | | | | | gives: % 34.95/5.33 | | | | | | | | | | (171) all_56_1 = all_29_3 % 34.95/5.33 | | | | | | | | | | % 34.95/5.33 | | | | | | | | | | REDUCE: (62), (171) imply: % 34.95/5.33 | | | | | | | | | | (172) mem(all_29_3, all_37_1) = all_56_0 % 34.95/5.33 | | | | | | | | | | % 34.95/5.33 | | | | | | | | | | BETA: splitting (145) gives: % 34.95/5.33 | | | | | | | | | | % 34.95/5.33 | | | | | | | | | | Case 1: % 34.95/5.33 | | | | | | | | | | | % 34.95/5.33 | | | | | | | | | | | (173) all_181_0 = 0 % 34.95/5.33 | | | | | | | | | | | % 34.95/5.33 | | | | | | | | | | | REDUCE: (144), (173) imply: % 34.95/5.33 | | | | | | | | | | | (174) mem(all_83_1, all_46_0) = 0 % 34.95/5.33 | | | | | | | | | | | % 34.95/5.33 | | | | | | | | | | | GROUND_INST: instantiating (4) with all_83_1, all_29_2, % 34.95/5.33 | | | | | | | | | | | all_46_0, simplifying with (17), (42), (82), (174) % 34.95/5.33 | | | | | | | | | | | gives: % 34.95/5.33 | | | | | | | | | | | (175) all_83_1 = all_29_2 % 34.95/5.33 | | | | | | | | | | | % 34.95/5.33 | | | | | | | | | | | REDUCE: (84), (175) imply: % 34.95/5.33 | | | | | | | | | | | (176) mem(all_29_2, all_50_1) = all_83_0 % 34.95/5.33 | | | | | | | | | | | % 34.95/5.33 | | | | | | | | | | | BETA: splitting (152) gives: % 34.95/5.33 | | | | | | | | | | | % 34.95/5.33 | | | | | | | | | | | Case 1: % 34.95/5.33 | | | | | | | | | | | | % 34.95/5.33 | | | | | | | | | | | | (177) all_204_0 = 0 % 34.95/5.33 | | | | | | | | | | | | % 34.95/5.33 | | | | | | | | | | | | REDUCE: (151), (177) imply: % 34.95/5.33 | | | | | | | | | | | | (178) mem(all_72_2, all_46_0) = 0 % 34.95/5.33 | | | | | | | | | | | | % 34.95/5.33 | | | | | | | | | | | | REF_CLOSE: (4), (15), (17), (42), (72), (74), (81), (176), % 34.95/5.33 | | | | | | | | | | | | (178) are inconsistent by sub-proof #9. % 34.95/5.33 | | | | | | | | | | | | % 34.95/5.33 | | | | | | | | | | | Case 2: % 34.95/5.33 | | | | | | | | | | | | % 34.95/5.33 | | | | | | | | | | | | (179) all_204_1 = 0 % 34.95/5.33 | | | | | | | | | | | | % 34.95/5.33 | | | | | | | | | | | | REDUCE: (150), (179) imply: % 34.95/5.33 | | | | | | | | | | | | (180) mem(all_72_2, all_29_2) = 0 % 34.95/5.33 | | | | | | | | | | | | % 34.95/5.33 | | | | | | | | | | | | REF_CLOSE: (4), (15), (19), (45), (59), (72), (85), (172), % 34.95/5.33 | | | | | | | | | | | | (180) are inconsistent by sub-proof #8. % 34.95/5.33 | | | | | | | | | | | | % 34.95/5.33 | | | | | | | | | | | End of split % 34.95/5.33 | | | | | | | | | | | % 34.95/5.33 | | | | | | | | | | Case 2: % 34.95/5.33 | | | | | | | | | | | % 34.95/5.33 | | | | | | | | | | | (181) all_181_1 = 0 % 34.95/5.33 | | | | | | | | | | | % 34.95/5.33 | | | | | | | | | | | REDUCE: (143), (181) imply: % 34.95/5.33 | | | | | | | | | | | (182) mem(all_83_1, all_29_2) = 0 % 34.95/5.33 | | | | | | | | | | | % 34.95/5.33 | | | | | | | | | | | REF_CLOSE: (4), (15), (19), (45), (59), (82), (83), (172), % 34.95/5.33 | | | | | | | | | | | (182) are inconsistent by sub-proof #7. % 34.95/5.33 | | | | | | | | | | | % 34.95/5.33 | | | | | | | | | | End of split % 34.95/5.33 | | | | | | | | | | % 34.95/5.33 | | | | | | | | | End of split % 34.95/5.33 | | | | | | | | | % 34.95/5.33 | | | | | | | | Case 2: % 34.95/5.33 | | | | | | | | | % 34.95/5.33 | | | | | | | | | (183) all_131_1 = 0 % 34.95/5.33 | | | | | | | | | % 34.95/5.33 | | | | | | | | | REDUCE: (115), (183) imply: % 34.95/5.33 | | | | | | | | | (184) mem(all_72_2, all_29_3) = 0 % 34.95/5.33 | | | | | | | | | % 34.95/5.33 | | | | | | | | | GROUND_INST: instantiating (5) with all_72_2, e, all_48_0, % 34.95/5.33 | | | | | | | | | all_29_3, simplifying with (13), (46), (48), (72), % 34.95/5.33 | | | | | | | | | (184) gives: % 34.95/5.34 | | | | | | | | | (185) ? [v0: any] : ? [v1: any] : (mem(all_72_2, % 34.95/5.34 | | | | | | | | | all_48_0) = v1 & mem(all_72_2, e) = v0 & (v1 = 0 % 34.95/5.34 | | | | | | | | | | v0 = 0)) % 34.95/5.34 | | | | | | | | | % 34.95/5.34 | | | | | | | | | DELTA: instantiating (185) with fresh symbols all_210_0, % 34.95/5.34 | | | | | | | | | all_210_1 gives: % 34.95/5.34 | | | | | | | | | (186) mem(all_72_2, all_48_0) = all_210_0 & mem(all_72_2, % 34.95/5.34 | | | | | | | | | e) = all_210_1 & (all_210_0 = 0 | all_210_1 = 0) % 34.95/5.34 | | | | | | | | | % 34.95/5.34 | | | | | | | | | ALPHA: (186) implies: % 34.95/5.34 | | | | | | | | | (187) mem(all_72_2, e) = all_210_1 % 34.95/5.34 | | | | | | | | | (188) mem(all_72_2, all_48_0) = all_210_0 % 34.95/5.34 | | | | | | | | | (189) all_210_0 = 0 | all_210_1 = 0 % 34.95/5.34 | | | | | | | | | % 34.95/5.34 | | | | | | | | | BETA: splitting (130) gives: % 34.95/5.34 | | | | | | | | | % 34.95/5.34 | | | | | | | | | Case 1: % 34.95/5.34 | | | | | | | | | | % 34.95/5.34 | | | | | | | | | | (190) all_144_0 = 0 % 34.95/5.34 | | | | | | | | | | % 34.95/5.34 | | | | | | | | | | REDUCE: (129), (190) imply: % 34.95/5.34 | | | | | | | | | | (191) mem(all_109_1, all_29_1) = 0 % 34.95/5.34 | | | | | | | | | | % 34.95/5.34 | | | | | | | | | | GROUND_INST: instantiating (5) with all_109_1, all_29_2, % 34.95/5.34 | | | | | | | | | | all_46_0, all_29_1, simplifying with (17), (41), % 34.95/5.34 | | | | | | | | | | (43), (93), (191) gives: % 34.95/5.34 | | | | | | | | | | (192) ? [v0: any] : ? [v1: any] : (mem(all_109_1, % 34.95/5.34 | | | | | | | | | | all_46_0) = v1 & mem(all_109_1, all_29_2) = v0 % 34.95/5.34 | | | | | | | | | | & (v1 = 0 | v0 = 0)) % 34.95/5.34 | | | | | | | | | | % 34.95/5.34 | | | | | | | | | | DELTA: instantiating (192) with fresh symbols all_224_0, % 34.95/5.34 | | | | | | | | | | all_224_1 gives: % 34.95/5.34 | | | | | | | | | | (193) mem(all_109_1, all_46_0) = all_224_0 & % 34.95/5.34 | | | | | | | | | | mem(all_109_1, all_29_2) = all_224_1 & (all_224_0 = % 34.95/5.34 | | | | | | | | | | 0 | all_224_1 = 0) % 34.95/5.34 | | | | | | | | | | % 34.95/5.34 | | | | | | | | | | ALPHA: (193) implies: % 34.95/5.34 | | | | | | | | | | (194) mem(all_109_1, all_29_2) = all_224_1 % 34.95/5.34 | | | | | | | | | | (195) mem(all_109_1, all_46_0) = all_224_0 % 34.95/5.34 | | | | | | | | | | (196) all_224_0 = 0 | all_224_1 = 0 % 34.95/5.34 | | | | | | | | | | % 34.95/5.34 | | | | | | | | | | BETA: splitting (138) gives: % 34.95/5.34 | | | | | | | | | | % 34.95/5.34 | | | | | | | | | | Case 1: % 34.95/5.34 | | | | | | | | | | | % 34.95/5.34 | | | | | | | | | | | (197) all_158_0 = 0 % 34.95/5.34 | | | | | | | | | | | % 34.95/5.34 | | | | | | | | | | | REDUCE: (137), (197) imply: % 34.95/5.34 | | | | | | | | | | | (198) mem(all_56_1, all_46_0) = 0 % 34.95/5.34 | | | | | | | | | | | % 34.95/5.34 | | | | | | | | | | | GROUND_INST: instantiating (4) with all_56_1, all_29_2, % 34.95/5.34 | | | | | | | | | | | all_46_0, simplifying with (17), (42), (60), (198) % 34.95/5.34 | | | | | | | | | | | gives: % 34.95/5.34 | | | | | | | | | | | (199) all_56_1 = all_29_2 % 34.95/5.34 | | | | | | | | | | | % 34.95/5.34 | | | | | | | | | | | REDUCE: (62), (199) imply: % 34.95/5.34 | | | | | | | | | | | (200) mem(all_29_2, all_37_1) = all_56_0 % 34.95/5.34 | | | | | | | | | | | % 34.95/5.34 | | | | | | | | | | | BETA: splitting (145) gives: % 34.95/5.34 | | | | | | | | | | | % 34.95/5.34 | | | | | | | | | | | Case 1: % 34.95/5.34 | | | | | | | | | | | | % 34.95/5.34 | | | | | | | | | | | | (201) all_181_0 = 0 % 34.95/5.34 | | | | | | | | | | | | % 34.95/5.34 | | | | | | | | | | | | REDUCE: (144), (201) imply: % 34.95/5.34 | | | | | | | | | | | | (202) mem(all_83_1, all_46_0) = 0 % 34.95/5.34 | | | | | | | | | | | | % 34.95/5.34 | | | | | | | | | | | | GROUND_INST: instantiating (4) with all_83_1, all_29_2, % 34.95/5.34 | | | | | | | | | | | | all_46_0, simplifying with (17), (42), (82), (202) % 34.95/5.34 | | | | | | | | | | | | gives: % 34.95/5.34 | | | | | | | | | | | | (203) all_83_1 = all_29_2 % 34.95/5.34 | | | | | | | | | | | | % 34.95/5.34 | | | | | | | | | | | | REDUCE: (83), (203) imply: % 34.95/5.34 | | | | | | | | | | | | (204) mem(all_29_2, all_37_1) = 0 % 34.95/5.34 | | | | | | | | | | | | % 34.95/5.34 | | | | | | | | | | | | REF_CLOSE: (15), (59), (200), (204) are inconsistent by % 34.95/5.34 | | | | | | | | | | | | sub-proof #12. % 34.95/5.34 | | | | | | | | | | | | % 34.95/5.34 | | | | | | | | | | | Case 2: % 34.95/5.34 | | | | | | | | | | | | % 34.95/5.34 | | | | | | | | | | | | (205) all_181_1 = 0 % 34.95/5.34 | | | | | | | | | | | | % 34.95/5.34 | | | | | | | | | | | | REDUCE: (143), (205) imply: % 34.95/5.34 | | | | | | | | | | | | (206) mem(all_83_1, all_29_2) = 0 % 34.95/5.34 | | | | | | | | | | | | % 34.95/5.34 | | | | | | | | | | | | GROUND_INST: instantiating (4) with all_83_1, all_29_3, % 34.95/5.34 | | | | | | | | | | | | all_29_2, simplifying with (19), (45), (82), (206) % 34.95/5.34 | | | | | | | | | | | | gives: % 34.95/5.34 | | | | | | | | | | | | (207) all_83_1 = all_29_3 % 34.95/5.34 | | | | | | | | | | | | % 34.95/5.34 | | | | | | | | | | | | REDUCE: (84), (207) imply: % 34.95/5.34 | | | | | | | | | | | | (208) mem(all_29_3, all_50_1) = all_83_0 % 34.95/5.34 | | | | | | | | | | | | % 34.95/5.34 | | | | | | | | | | | | BETA: splitting (196) gives: % 34.95/5.34 | | | | | | | | | | | | % 34.95/5.34 | | | | | | | | | | | | Case 1: % 34.95/5.34 | | | | | | | | | | | | | % 34.95/5.34 | | | | | | | | | | | | | (209) all_224_0 = 0 % 34.95/5.34 | | | | | | | | | | | | | % 34.95/5.34 | | | | | | | | | | | | | REDUCE: (195), (209) imply: % 34.95/5.34 | | | | | | | | | | | | | (210) mem(all_109_1, all_46_0) = 0 % 34.95/5.34 | | | | | | | | | | | | | % 34.95/5.34 | | | | | | | | | | | | | GROUND_INST: instantiating (4) with all_109_1, all_29_2, % 34.95/5.34 | | | | | | | | | | | | | all_46_0, simplifying with (17), (42), (93), (210) % 34.95/5.34 | | | | | | | | | | | | | gives: % 34.95/5.34 | | | | | | | | | | | | | (211) all_109_1 = all_29_2 % 34.95/5.34 | | | | | | | | | | | | | % 34.95/5.34 | | | | | | | | | | | | | REDUCE: (98), (211) imply: % 34.95/5.34 | | | | | | | | | | | | | (212) mem(all_29_2, all_37_1) = 0 % 34.95/5.34 | | | | | | | | | | | | | % 34.95/5.34 | | | | | | | | | | | | | REF_CLOSE: (15), (59), (200), (212) are inconsistent by % 34.95/5.34 | | | | | | | | | | | | | sub-proof #12. % 34.95/5.34 | | | | | | | | | | | | | % 34.95/5.34 | | | | | | | | | | | | Case 2: % 34.95/5.34 | | | | | | | | | | | | | % 34.95/5.34 | | | | | | | | | | | | | (213) all_224_1 = 0 % 34.95/5.34 | | | | | | | | | | | | | % 34.95/5.34 | | | | | | | | | | | | | REDUCE: (194), (213) imply: % 34.95/5.34 | | | | | | | | | | | | | (214) mem(all_109_1, all_29_2) = 0 % 34.95/5.34 | | | | | | | | | | | | | % 34.95/5.34 | | | | | | | | | | | | | REF_CLOSE: (4), (15), (19), (45), (81), (93), (94), (208), % 34.95/5.34 | | | | | | | | | | | | | (214) are inconsistent by sub-proof #6. % 34.95/5.34 | | | | | | | | | | | | | % 34.95/5.34 | | | | | | | | | | | | End of split % 34.95/5.34 | | | | | | | | | | | | % 34.95/5.34 | | | | | | | | | | | End of split % 34.95/5.34 | | | | | | | | | | | % 34.95/5.34 | | | | | | | | | | Case 2: % 34.95/5.34 | | | | | | | | | | | % 34.95/5.34 | | | | | | | | | | | (215) all_158_1 = 0 % 34.95/5.34 | | | | | | | | | | | % 34.95/5.34 | | | | | | | | | | | REDUCE: (136), (215) imply: % 34.95/5.34 | | | | | | | | | | | (216) mem(all_56_1, all_29_2) = 0 % 34.95/5.34 | | | | | | | | | | | % 34.95/5.34 | | | | | | | | | | | GROUND_INST: instantiating (4) with all_56_1, all_29_3, % 34.95/5.34 | | | | | | | | | | | all_29_2, simplifying with (19), (45), (60), (216) % 34.95/5.34 | | | | | | | | | | | gives: % 34.95/5.34 | | | | | | | | | | | (217) all_56_1 = all_29_3 % 34.95/5.34 | | | | | | | | | | | % 34.95/5.34 | | | | | | | | | | | REDUCE: (62), (217) imply: % 34.95/5.34 | | | | | | | | | | | (218) mem(all_29_3, all_37_1) = all_56_0 % 34.95/5.34 | | | | | | | | | | | % 34.95/5.34 | | | | | | | | | | | BETA: splitting (145) gives: % 34.95/5.34 | | | | | | | | | | | % 34.95/5.34 | | | | | | | | | | | Case 1: % 34.95/5.34 | | | | | | | | | | | | % 34.95/5.34 | | | | | | | | | | | | (219) all_181_0 = 0 % 34.95/5.34 | | | | | | | | | | | | % 34.95/5.34 | | | | | | | | | | | | REDUCE: (144), (219) imply: % 34.95/5.34 | | | | | | | | | | | | (220) mem(all_83_1, all_46_0) = 0 % 34.95/5.34 | | | | | | | | | | | | % 34.95/5.34 | | | | | | | | | | | | GROUND_INST: instantiating (4) with all_83_1, all_29_2, % 34.95/5.34 | | | | | | | | | | | | all_46_0, simplifying with (17), (42), (82), (220) % 34.95/5.34 | | | | | | | | | | | | gives: % 34.95/5.34 | | | | | | | | | | | | (221) all_83_1 = all_29_2 % 34.95/5.34 | | | | | | | | | | | | % 34.95/5.34 | | | | | | | | | | | | REDUCE: (84), (221) imply: % 34.95/5.34 | | | | | | | | | | | | (222) mem(all_29_2, all_50_1) = all_83_0 % 34.95/5.34 | | | | | | | | | | | | % 34.95/5.34 | | | | | | | | | | | | BETA: splitting (196) gives: % 34.95/5.34 | | | | | | | | | | | | % 34.95/5.34 | | | | | | | | | | | | Case 1: % 34.95/5.34 | | | | | | | | | | | | | % 34.95/5.34 | | | | | | | | | | | | | (223) all_224_0 = 0 % 34.95/5.34 | | | | | | | | | | | | | % 34.95/5.34 | | | | | | | | | | | | | REDUCE: (195), (223) imply: % 34.95/5.34 | | | | | | | | | | | | | (224) mem(all_109_1, all_46_0) = 0 % 34.95/5.34 | | | | | | | | | | | | | % 34.95/5.34 | | | | | | | | | | | | | GROUND_INST: instantiating (4) with all_109_1, all_29_2, % 34.95/5.34 | | | | | | | | | | | | | all_46_0, simplifying with (17), (42), (93), (224) % 34.95/5.34 | | | | | | | | | | | | | gives: % 34.95/5.34 | | | | | | | | | | | | | (225) all_109_1 = all_29_2 % 34.95/5.34 | | | | | | | | | | | | | % 34.95/5.34 | | | | | | | | | | | | | REDUCE: (94), (225) imply: % 34.95/5.34 | | | | | | | | | | | | | (226) mem(all_29_2, all_50_1) = 0 % 34.95/5.34 | | | | | | | | | | | | | % 34.95/5.34 | | | | | | | | | | | | | REF_CLOSE: (15), (81), (222), (226) are inconsistent by % 34.95/5.34 | | | | | | | | | | | | | sub-proof #5. % 34.95/5.34 | | | | | | | | | | | | | % 34.95/5.34 | | | | | | | | | | | | Case 2: % 34.95/5.34 | | | | | | | | | | | | | % 34.95/5.34 | | | | | | | | | | | | | (227) all_224_1 = 0 % 34.95/5.34 | | | | | | | | | | | | | % 34.95/5.34 | | | | | | | | | | | | | REDUCE: (194), (227) imply: % 34.95/5.34 | | | | | | | | | | | | | (228) mem(all_109_1, all_29_2) = 0 % 34.95/5.34 | | | | | | | | | | | | | % 34.95/5.34 | | | | | | | | | | | | | REF_CLOSE: (4), (15), (19), (45), (59), (93), (98), (218), % 34.95/5.34 | | | | | | | | | | | | | (228) are inconsistent by sub-proof #4. % 34.95/5.34 | | | | | | | | | | | | | % 34.95/5.34 | | | | | | | | | | | | End of split % 34.95/5.34 | | | | | | | | | | | | % 34.95/5.34 | | | | | | | | | | | Case 2: % 34.95/5.34 | | | | | | | | | | | | % 34.95/5.34 | | | | | | | | | | | | (229) all_181_1 = 0 % 34.95/5.34 | | | | | | | | | | | | % 34.95/5.34 | | | | | | | | | | | | REDUCE: (143), (229) imply: % 34.95/5.34 | | | | | | | | | | | | (230) mem(all_83_1, all_29_2) = 0 % 34.95/5.34 | | | | | | | | | | | | % 34.95/5.34 | | | | | | | | | | | | REF_CLOSE: (4), (15), (19), (45), (59), (82), (83), (218), % 34.95/5.34 | | | | | | | | | | | | (230) are inconsistent by sub-proof #7. % 34.95/5.34 | | | | | | | | | | | | % 34.95/5.34 | | | | | | | | | | | End of split % 34.95/5.34 | | | | | | | | | | | % 34.95/5.34 | | | | | | | | | | End of split % 34.95/5.34 | | | | | | | | | | % 34.95/5.34 | | | | | | | | | Case 2: % 34.95/5.34 | | | | | | | | | | % 34.95/5.34 | | | | | | | | | | (231) all_144_1 = 0 % 34.95/5.34 | | | | | | | | | | % 34.95/5.34 | | | | | | | | | | REDUCE: (128), (231) imply: % 34.95/5.34 | | | | | | | | | | (232) mem(all_109_1, all_29_3) = 0 % 34.95/5.34 | | | | | | | | | | % 34.95/5.34 | | | | | | | | | | GROUND_INST: instantiating (5) with all_109_1, e, all_48_0, % 34.95/5.34 | | | | | | | | | | all_29_3, simplifying with (13), (46), (48), (93), % 34.95/5.34 | | | | | | | | | | (232) gives: % 34.95/5.34 | | | | | | | | | | (233) ? [v0: any] : ? [v1: any] : (mem(all_109_1, % 34.95/5.34 | | | | | | | | | | all_48_0) = v1 & mem(all_109_1, e) = v0 & (v1 = % 34.95/5.34 | | | | | | | | | | 0 | v0 = 0)) % 34.95/5.34 | | | | | | | | | | % 34.95/5.34 | | | | | | | | | | DELTA: instantiating (233) with fresh symbols all_230_0, % 34.95/5.34 | | | | | | | | | | all_230_1 gives: % 34.95/5.35 | | | | | | | | | | (234) mem(all_109_1, all_48_0) = all_230_0 & % 34.95/5.35 | | | | | | | | | | mem(all_109_1, e) = all_230_1 & (all_230_0 = 0 | % 34.95/5.35 | | | | | | | | | | all_230_1 = 0) % 34.95/5.35 | | | | | | | | | | % 34.95/5.35 | | | | | | | | | | ALPHA: (234) implies: % 34.95/5.35 | | | | | | | | | | (235) mem(all_109_1, e) = all_230_1 % 34.95/5.35 | | | | | | | | | | (236) mem(all_109_1, all_48_0) = all_230_0 % 34.95/5.35 | | | | | | | | | | (237) all_230_0 = 0 | all_230_1 = 0 % 34.95/5.35 | | | | | | | | | | % 34.95/5.35 | | | | | | | | | | BETA: splitting (189) gives: % 34.95/5.35 | | | | | | | | | | % 34.95/5.35 | | | | | | | | | | Case 1: % 34.95/5.35 | | | | | | | | | | | % 34.95/5.35 | | | | | | | | | | | (238) all_210_0 = 0 % 34.95/5.35 | | | | | | | | | | | % 34.95/5.35 | | | | | | | | | | | REDUCE: (188), (238) imply: % 34.95/5.35 | | | | | | | | | | | (239) mem(all_72_2, all_48_0) = 0 % 34.95/5.35 | | | | | | | | | | | % 34.95/5.35 | | | | | | | | | | | GROUND_INST: instantiating (4) with all_72_2, e, all_48_0, % 34.95/5.35 | | | | | | | | | | | simplifying with (13), (47), (72), (239) gives: % 34.95/5.35 | | | | | | | | | | | (240) all_72_2 = e % 34.95/5.35 | | | | | | | | | | | % 34.95/5.35 | | | | | | | | | | | REDUCE: (124), (240) imply: % 34.95/5.35 | | | | | | | | | | | (241) mem(all_137_1, e) = all_137_0 % 34.95/5.35 | | | | | | | | | | | % 34.95/5.35 | | | | | | | | | | | BETA: splitting (237) gives: % 34.95/5.35 | | | | | | | | | | | % 34.95/5.35 | | | | | | | | | | | Case 1: % 34.95/5.35 | | | | | | | | | | | | % 34.95/5.35 | | | | | | | | | | | | (242) all_230_0 = 0 % 34.95/5.35 | | | | | | | | | | | | % 34.95/5.35 | | | | | | | | | | | | REDUCE: (236), (242) imply: % 34.95/5.35 | | | | | | | | | | | | (243) mem(all_109_1, all_48_0) = 0 % 34.95/5.35 | | | | | | | | | | | | % 34.95/5.35 | | | | | | | | | | | | GROUND_INST: instantiating (4) with all_109_1, e, all_48_0, % 34.95/5.35 | | | | | | | | | | | | simplifying with (13), (47), (93), (243) gives: % 34.95/5.35 | | | | | | | | | | | | (244) all_109_1 = e % 34.95/5.35 | | | | | | | | | | | | % 34.95/5.35 | | | | | | | | | | | | REDUCE: (125), (244) imply: % 34.95/5.35 | | | | | | | | | | | | (245) mem(all_137_1, e) = 0 % 34.95/5.35 | | | | | | | | | | | | % 34.95/5.35 | | | | | | | | | | | | GROUND_INST: instantiating (15) with all_137_0, 0, e, % 34.95/5.35 | | | | | | | | | | | | all_137_1, simplifying with (241), (245) gives: % 34.95/5.35 | | | | | | | | | | | | (246) all_137_0 = 0 % 34.95/5.35 | | | | | | | | | | | | % 34.95/5.35 | | | | | | | | | | | | REDUCE: (122), (246) imply: % 34.95/5.35 | | | | | | | | | | | | (247) $false % 34.95/5.35 | | | | | | | | | | | | % 34.95/5.35 | | | | | | | | | | | | CLOSE: (247) is inconsistent. % 34.95/5.35 | | | | | | | | | | | | % 34.95/5.35 | | | | | | | | | | | Case 2: % 34.95/5.35 | | | | | | | | | | | | % 34.95/5.35 | | | | | | | | | | | | (248) all_230_1 = 0 % 34.95/5.35 | | | | | | | | | | | | % 34.95/5.35 | | | | | | | | | | | | REDUCE: (235), (248) imply: % 34.95/5.35 | | | | | | | | | | | | (249) mem(all_109_1, e) = 0 % 34.95/5.35 | | | | | | | | | | | | % 34.95/5.35 | | | | | | | | | | | | GROUND_INST: instantiating (3) with all_109_1, simplifying with % 34.95/5.35 | | | | | | | | | | | | (93), (249) gives: % 34.95/5.35 | | | | | | | | | | | | (250) $false % 34.95/5.35 | | | | | | | | | | | | % 34.95/5.35 | | | | | | | | | | | | CLOSE: (250) is inconsistent. % 34.95/5.35 | | | | | | | | | | | | % 34.95/5.35 | | | | | | | | | | | End of split % 34.95/5.35 | | | | | | | | | | | % 34.95/5.35 | | | | | | | | | | Case 2: % 34.95/5.35 | | | | | | | | | | | % 34.95/5.35 | | | | | | | | | | | (251) all_210_1 = 0 % 34.95/5.35 | | | | | | | | | | | % 34.95/5.35 | | | | | | | | | | | REDUCE: (187), (251) imply: % 34.95/5.35 | | | | | | | | | | | (252) mem(all_72_2, e) = 0 % 34.95/5.35 | | | | | | | | | | | % 34.95/5.35 | | | | | | | | | | | GROUND_INST: instantiating (3) with all_72_2, simplifying with % 34.95/5.35 | | | | | | | | | | | (72), (252) gives: % 34.95/5.35 | | | | | | | | | | | (253) $false % 34.95/5.35 | | | | | | | | | | | % 34.95/5.35 | | | | | | | | | | | CLOSE: (253) is inconsistent. % 34.95/5.35 | | | | | | | | | | | % 34.95/5.35 | | | | | | | | | | End of split % 34.95/5.35 | | | | | | | | | | % 34.95/5.35 | | | | | | | | | End of split % 34.95/5.35 | | | | | | | | | % 34.95/5.35 | | | | | | | | End of split % 34.95/5.35 | | | | | | | | % 34.95/5.35 | | | | | | | Case 2: % 34.95/5.35 | | | | | | | | % 34.95/5.35 | | | | | | | | (254) all_117_1 = 0 % 34.95/5.35 | | | | | | | | % 34.95/5.35 | | | | | | | | REDUCE: (101), (254) imply: % 34.95/5.35 | | | | | | | | (255) mem(all_83_1, all_29_3) = 0 % 34.95/5.35 | | | | | | | | % 34.95/5.35 | | | | | | | | GROUND_INST: instantiating (5) with all_83_1, e, all_48_0, % 34.95/5.35 | | | | | | | | all_29_3, simplifying with (13), (46), (48), (82), % 34.95/5.35 | | | | | | | | (255) gives: % 34.95/5.35 | | | | | | | | (256) ? [v0: any] : ? [v1: any] : (mem(all_83_1, all_48_0) % 34.95/5.35 | | | | | | | | = v1 & mem(all_83_1, e) = v0 & (v1 = 0 | v0 = 0)) % 34.95/5.35 | | | | | | | | % 34.95/5.35 | | | | | | | | DELTA: instantiating (256) with fresh symbols all_187_0, % 34.95/5.35 | | | | | | | | all_187_1 gives: % 34.95/5.35 | | | | | | | | (257) mem(all_83_1, all_48_0) = all_187_0 & mem(all_83_1, e) % 34.95/5.35 | | | | | | | | = all_187_1 & (all_187_0 = 0 | all_187_1 = 0) % 34.95/5.35 | | | | | | | | % 34.95/5.35 | | | | | | | | ALPHA: (257) implies: % 34.95/5.35 | | | | | | | | (258) mem(all_83_1, e) = all_187_1 % 34.95/5.35 | | | | | | | | (259) mem(all_83_1, all_48_0) = all_187_0 % 34.95/5.35 | | | | | | | | (260) all_187_0 = 0 | all_187_1 = 0 % 34.95/5.35 | | | | | | | | % 34.95/5.35 | | | | | | | | BETA: splitting (117) gives: % 34.95/5.35 | | | | | | | | % 34.95/5.35 | | | | | | | | Case 1: % 34.95/5.35 | | | | | | | | | % 34.95/5.35 | | | | | | | | | (261) all_131_0 = 0 % 34.95/5.35 | | | | | | | | | % 34.95/5.35 | | | | | | | | | REDUCE: (116), (261) imply: % 34.95/5.35 | | | | | | | | | (262) mem(all_72_2, all_29_1) = 0 % 34.95/5.35 | | | | | | | | | % 34.95/5.35 | | | | | | | | | GROUND_INST: instantiating (5) with all_72_2, all_29_2, % 34.95/5.35 | | | | | | | | | all_46_0, all_29_1, simplifying with (17), (41), % 34.95/5.35 | | | | | | | | | (43), (72), (262) gives: % 34.95/5.35 | | | | | | | | | (263) ? [v0: any] : ? [v1: any] : (mem(all_72_2, % 34.95/5.35 | | | | | | | | | all_46_0) = v1 & mem(all_72_2, all_29_2) = v0 & % 34.95/5.35 | | | | | | | | | (v1 = 0 | v0 = 0)) % 34.95/5.35 | | | | | | | | | % 34.95/5.35 | | | | | | | | | DELTA: instantiating (263) with fresh symbols all_201_0, % 34.95/5.35 | | | | | | | | | all_201_1 gives: % 34.95/5.35 | | | | | | | | | (264) mem(all_72_2, all_46_0) = all_201_0 & mem(all_72_2, % 34.95/5.35 | | | | | | | | | all_29_2) = all_201_1 & (all_201_0 = 0 | all_201_1 % 34.95/5.35 | | | | | | | | | = 0) % 34.95/5.35 | | | | | | | | | % 34.95/5.35 | | | | | | | | | ALPHA: (264) implies: % 34.95/5.35 | | | | | | | | | (265) mem(all_72_2, all_29_2) = all_201_1 % 34.95/5.35 | | | | | | | | | (266) mem(all_72_2, all_46_0) = all_201_0 % 34.95/5.35 | | | | | | | | | (267) all_201_0 = 0 | all_201_1 = 0 % 34.95/5.35 | | | | | | | | | % 34.95/5.35 | | | | | | | | | BETA: splitting (130) gives: % 34.95/5.35 | | | | | | | | | % 34.95/5.35 | | | | | | | | | Case 1: % 34.95/5.35 | | | | | | | | | | % 34.95/5.35 | | | | | | | | | | (268) all_144_0 = 0 % 34.95/5.35 | | | | | | | | | | % 34.95/5.35 | | | | | | | | | | REDUCE: (129), (268) imply: % 34.95/5.35 | | | | | | | | | | (269) mem(all_109_1, all_29_1) = 0 % 34.95/5.35 | | | | | | | | | | % 34.95/5.35 | | | | | | | | | | GROUND_INST: instantiating (5) with all_109_1, all_29_2, % 34.95/5.35 | | | | | | | | | | all_46_0, all_29_1, simplifying with (17), (41), % 34.95/5.35 | | | | | | | | | | (43), (93), (269) gives: % 34.95/5.35 | | | | | | | | | | (270) ? [v0: any] : ? [v1: any] : (mem(all_109_1, % 34.95/5.35 | | | | | | | | | | all_46_0) = v1 & mem(all_109_1, all_29_2) = v0 % 34.95/5.35 | | | | | | | | | | & (v1 = 0 | v0 = 0)) % 34.95/5.35 | | | | | | | | | | % 34.95/5.35 | | | | | | | | | | DELTA: instantiating (270) with fresh symbols all_224_0, % 34.95/5.35 | | | | | | | | | | all_224_1 gives: % 34.95/5.35 | | | | | | | | | | (271) mem(all_109_1, all_46_0) = all_224_0 & % 34.95/5.35 | | | | | | | | | | mem(all_109_1, all_29_2) = all_224_1 & (all_224_0 = % 34.95/5.35 | | | | | | | | | | 0 | all_224_1 = 0) % 34.95/5.35 | | | | | | | | | | % 34.95/5.35 | | | | | | | | | | ALPHA: (271) implies: % 34.95/5.35 | | | | | | | | | | (272) mem(all_109_1, all_29_2) = all_224_1 % 34.95/5.35 | | | | | | | | | | (273) mem(all_109_1, all_46_0) = all_224_0 % 34.95/5.35 | | | | | | | | | | (274) all_224_0 = 0 | all_224_1 = 0 % 34.95/5.35 | | | | | | | | | | % 34.95/5.35 | | | | | | | | | | BETA: splitting (138) gives: % 34.95/5.35 | | | | | | | | | | % 34.95/5.35 | | | | | | | | | | Case 1: % 34.95/5.35 | | | | | | | | | | | % 34.95/5.35 | | | | | | | | | | | (275) all_158_0 = 0 % 34.95/5.35 | | | | | | | | | | | % 34.95/5.35 | | | | | | | | | | | REDUCE: (137), (275) imply: % 34.95/5.35 | | | | | | | | | | | (276) mem(all_56_1, all_46_0) = 0 % 34.95/5.35 | | | | | | | | | | | % 34.95/5.35 | | | | | | | | | | | GROUND_INST: instantiating (4) with all_56_1, all_29_2, % 34.95/5.35 | | | | | | | | | | | all_46_0, simplifying with (17), (42), (60), (276) % 34.95/5.35 | | | | | | | | | | | gives: % 34.95/5.35 | | | | | | | | | | | (277) all_56_1 = all_29_2 % 34.95/5.35 | | | | | | | | | | | % 34.95/5.35 | | | | | | | | | | | REDUCE: (62), (277) imply: % 34.95/5.35 | | | | | | | | | | | (278) mem(all_29_2, all_37_1) = all_56_0 % 34.95/5.35 | | | | | | | | | | | % 34.95/5.35 | | | | | | | | | | | BETA: splitting (260) gives: % 34.95/5.35 | | | | | | | | | | | % 34.95/5.35 | | | | | | | | | | | Case 1: % 34.95/5.35 | | | | | | | | | | | | % 34.95/5.35 | | | | | | | | | | | | (279) all_187_0 = 0 % 34.95/5.35 | | | | | | | | | | | | % 34.95/5.35 | | | | | | | | | | | | REDUCE: (259), (279) imply: % 34.95/5.35 | | | | | | | | | | | | (280) mem(all_83_1, all_48_0) = 0 % 34.95/5.35 | | | | | | | | | | | | % 34.95/5.35 | | | | | | | | | | | | GROUND_INST: instantiating (4) with all_83_1, e, all_48_0, % 34.95/5.35 | | | | | | | | | | | | simplifying with (13), (47), (82), (280) gives: % 34.95/5.35 | | | | | | | | | | | | (281) all_83_1 = e % 34.95/5.35 | | | | | | | | | | | | % 34.95/5.35 | | | | | | | | | | | | BETA: splitting (267) gives: % 34.95/5.35 | | | | | | | | | | | | % 34.95/5.35 | | | | | | | | | | | | Case 1: % 34.95/5.35 | | | | | | | | | | | | | % 34.95/5.35 | | | | | | | | | | | | | (282) all_201_0 = 0 % 34.95/5.35 | | | | | | | | | | | | | % 34.95/5.35 | | | | | | | | | | | | | REDUCE: (266), (282) imply: % 34.95/5.35 | | | | | | | | | | | | | (283) mem(all_72_2, all_46_0) = 0 % 34.95/5.35 | | | | | | | | | | | | | % 34.95/5.35 | | | | | | | | | | | | | REF_CLOSE: (4), (15), (17), (42), (59), (72), (85), (278), % 34.95/5.35 | | | | | | | | | | | | | (283) are inconsistent by sub-proof #11. % 34.95/5.35 | | | | | | | | | | | | | % 34.95/5.35 | | | | | | | | | | | | Case 2: % 34.95/5.35 | | | | | | | | | | | | | % 34.95/5.35 | | | | | | | | | | | | | (284) all_201_1 = 0 % 34.95/5.35 | | | | | | | | | | | | | % 34.95/5.35 | | | | | | | | | | | | | REDUCE: (265), (284) imply: % 34.95/5.35 | | | | | | | | | | | | | (285) mem(all_72_2, all_29_2) = 0 % 34.95/5.35 | | | | | | | | | | | | | % 34.95/5.35 | | | | | | | | | | | | | GROUND_INST: instantiating (4) with all_72_2, all_29_3, % 34.95/5.35 | | | | | | | | | | | | | all_29_2, simplifying with (19), (45), (72), (285) % 34.95/5.35 | | | | | | | | | | | | | gives: % 34.95/5.35 | | | | | | | | | | | | | (286) all_72_2 = all_29_3 % 34.95/5.35 | | | | | | | | | | | | | % 34.95/5.35 | | | | | | | | | | | | | REDUCE: (124), (286) imply: % 34.95/5.35 | | | | | | | | | | | | | (287) mem(all_137_1, all_29_3) = all_137_0 % 34.95/5.35 | | | | | | | | | | | | | % 34.95/5.35 | | | | | | | | | | | | | GROUND_INST: instantiating (6) with all_137_1, e, all_48_0, % 34.95/5.35 | | | | | | | | | | | | | all_29_3, all_137_0, simplifying with (13), (46), % 34.95/5.35 | | | | | | | | | | | | | (48), (123), (287) gives: % 34.95/5.35 | | | | | | | | | | | | | (288) all_137_0 = 0 | ? [v0: int] : ? [v1: int] : ( ~ % 34.95/5.35 | | | | | | | | | | | | | (v1 = 0) & ~ (v0 = 0) & mem(all_137_1, % 34.95/5.35 | | | | | | | | | | | | | all_48_0) = v1 & mem(all_137_1, e) = v0) % 34.95/5.35 | | | | | | | | | | | | | % 34.95/5.35 | | | | | | | | | | | | | BETA: splitting (274) gives: % 34.95/5.35 | | | | | | | | | | | | | % 34.95/5.35 | | | | | | | | | | | | | Case 1: % 34.95/5.35 | | | | | | | | | | | | | | % 34.95/5.35 | | | | | | | | | | | | | | (289) all_224_0 = 0 % 34.95/5.35 | | | | | | | | | | | | | | % 34.95/5.35 | | | | | | | | | | | | | | REDUCE: (273), (289) imply: % 34.95/5.35 | | | | | | | | | | | | | | (290) mem(all_109_1, all_46_0) = 0 % 34.95/5.35 | | | | | | | | | | | | | | % 34.95/5.35 | | | | | | | | | | | | | | BETA: splitting (288) gives: % 34.95/5.35 | | | | | | | | | | | | | | % 34.95/5.35 | | | | | | | | | | | | | | Case 1: % 34.95/5.35 | | | | | | | | | | | | | | | % 34.95/5.35 | | | | | | | | | | | | | | | (291) all_137_0 = 0 % 34.95/5.35 | | | | | | | | | | | | | | | % 34.95/5.35 | | | | | | | | | | | | | | | REDUCE: (122), (291) imply: % 34.95/5.35 | | | | | | | | | | | | | | | (292) $false % 34.95/5.35 | | | | | | | | | | | | | | | % 34.95/5.35 | | | | | | | | | | | | | | | CLOSE: (292) is inconsistent. % 34.95/5.35 | | | | | | | | | | | | | | | % 34.95/5.35 | | | | | | | | | | | | | | Case 2: % 34.95/5.35 | | | | | | | | | | | | | | | % 34.95/5.36 | | | | | | | | | | | | | | | % 34.95/5.36 | | | | | | | | | | | | | | | GROUND_INST: instantiating (4) with all_109_1, all_29_2, % 34.95/5.36 | | | | | | | | | | | | | | | all_46_0, simplifying with (17), (42), (93), (290) % 34.95/5.36 | | | | | | | | | | | | | | | gives: % 34.95/5.36 | | | | | | | | | | | | | | | (293) all_109_1 = all_29_2 % 34.95/5.36 | | | | | | | | | | | | | | | % 34.95/5.36 | | | | | | | | | | | | | | | REDUCE: (98), (293) imply: % 34.95/5.36 | | | | | | | | | | | | | | | (294) mem(all_29_2, all_37_1) = 0 % 34.95/5.36 | | | | | | | | | | | | | | | % 34.95/5.36 | | | | | | | | | | | | | | | REF_CLOSE: (15), (59), (278), (294) are inconsistent by % 34.95/5.36 | | | | | | | | | | | | | | | sub-proof #12. % 34.95/5.36 | | | | | | | | | | | | | | | % 34.95/5.36 | | | | | | | | | | | | | | End of split % 34.95/5.36 | | | | | | | | | | | | | | % 34.95/5.36 | | | | | | | | | | | | | Case 2: % 34.95/5.36 | | | | | | | | | | | | | | % 34.95/5.36 | | | | | | | | | | | | | | (295) all_224_1 = 0 % 34.95/5.36 | | | | | | | | | | | | | | % 34.95/5.36 | | | | | | | | | | | | | | REDUCE: (272), (295) imply: % 34.95/5.36 | | | | | | | | | | | | | | (296) mem(all_109_1, all_29_2) = 0 % 34.95/5.36 | | | | | | | | | | | | | | % 34.95/5.36 | | | | | | | | | | | | | | REF_CLOSE: (4), (15), (19), (45), (93), (122), (125), (287), % 34.95/5.36 | | | | | | | | | | | | | | (288), (296) are inconsistent by sub-proof #3. % 34.95/5.36 | | | | | | | | | | | | | | % 34.95/5.36 | | | | | | | | | | | | | End of split % 34.95/5.36 | | | | | | | | | | | | | % 34.95/5.36 | | | | | | | | | | | | End of split % 34.95/5.36 | | | | | | | | | | | | % 34.95/5.36 | | | | | | | | | | | Case 2: % 34.95/5.36 | | | | | | | | | | | | % 34.95/5.36 | | | | | | | | | | | | (297) all_187_1 = 0 % 34.95/5.36 | | | | | | | | | | | | % 34.95/5.36 | | | | | | | | | | | | REDUCE: (258), (297) imply: % 34.95/5.36 | | | | | | | | | | | | (298) mem(all_83_1, e) = 0 % 34.95/5.36 | | | | | | | | | | | | % 34.95/5.36 | | | | | | | | | | | | GROUND_INST: instantiating (3) with all_83_1, simplifying with % 34.95/5.36 | | | | | | | | | | | | (82), (298) gives: % 34.95/5.36 | | | | | | | | | | | | (299) $false % 34.95/5.36 | | | | | | | | | | | | % 34.95/5.36 | | | | | | | | | | | | CLOSE: (299) is inconsistent. % 34.95/5.36 | | | | | | | | | | | | % 34.95/5.36 | | | | | | | | | | | End of split % 34.95/5.36 | | | | | | | | | | | % 34.95/5.36 | | | | | | | | | | Case 2: % 34.95/5.36 | | | | | | | | | | | % 34.95/5.36 | | | | | | | | | | | (300) all_158_1 = 0 % 34.95/5.36 | | | | | | | | | | | % 34.95/5.36 | | | | | | | | | | | REDUCE: (136), (300) imply: % 34.95/5.36 | | | | | | | | | | | (301) mem(all_56_1, all_29_2) = 0 % 34.95/5.36 | | | | | | | | | | | % 34.95/5.36 | | | | | | | | | | | GROUND_INST: instantiating (4) with all_56_1, all_29_3, % 34.95/5.36 | | | | | | | | | | | all_29_2, simplifying with (19), (45), (60), (301) % 34.95/5.36 | | | | | | | | | | | gives: % 34.95/5.36 | | | | | | | | | | | (302) all_56_1 = all_29_3 % 34.95/5.36 | | | | | | | | | | | % 34.95/5.36 | | | | | | | | | | | REDUCE: (62), (302) imply: % 34.95/5.36 | | | | | | | | | | | (303) mem(all_29_3, all_37_1) = all_56_0 % 34.95/5.36 | | | | | | | | | | | % 34.95/5.36 | | | | | | | | | | | BETA: splitting (267) gives: % 34.95/5.36 | | | | | | | | | | | % 34.95/5.36 | | | | | | | | | | | Case 1: % 34.95/5.36 | | | | | | | | | | | | % 34.95/5.36 | | | | | | | | | | | | (304) all_201_0 = 0 % 34.95/5.36 | | | | | | | | | | | | % 34.95/5.36 | | | | | | | | | | | | REDUCE: (266), (304) imply: % 34.95/5.36 | | | | | | | | | | | | (305) mem(all_72_2, all_46_0) = 0 % 34.95/5.36 | | | | | | | | | | | | % 34.95/5.36 | | | | | | | | | | | | GROUND_INST: instantiating (4) with all_72_2, all_29_2, % 34.95/5.36 | | | | | | | | | | | | all_46_0, simplifying with (17), (42), (72), (305) % 34.95/5.36 | | | | | | | | | | | | gives: % 34.95/5.36 | | | | | | | | | | | | (306) all_72_2 = all_29_2 % 34.95/5.36 | | | | | | | | | | | | % 34.95/5.36 | | | | | | | | | | | | REDUCE: (124), (306) imply: % 34.95/5.36 | | | | | | | | | | | | (307) mem(all_137_1, all_29_2) = all_137_0 % 34.95/5.36 | | | | | | | | | | | | % 34.95/5.36 | | | | | | | | | | | | BETA: splitting (274) gives: % 34.95/5.36 | | | | | | | | | | | | % 34.95/5.36 | | | | | | | | | | | | Case 1: % 34.95/5.36 | | | | | | | | | | | | | % 34.95/5.36 | | | | | | | | | | | | | (308) all_224_0 = 0 % 34.95/5.36 | | | | | | | | | | | | | % 34.95/5.36 | | | | | | | | | | | | | REDUCE: (273), (308) imply: % 34.95/5.36 | | | | | | | | | | | | | (309) mem(all_109_1, all_46_0) = 0 % 34.95/5.36 | | | | | | | | | | | | | % 34.95/5.36 | | | | | | | | | | | | | REF_CLOSE: (4), (15), (17), (42), (93), (122), (125), (307), % 34.95/5.36 | | | | | | | | | | | | | (309) are inconsistent by sub-proof #2. % 34.95/5.36 | | | | | | | | | | | | | % 34.95/5.36 | | | | | | | | | | | | Case 2: % 34.95/5.36 | | | | | | | | | | | | | % 34.95/5.36 | | | | | | | | | | | | | (310) all_224_1 = 0 % 34.95/5.36 | | | | | | | | | | | | | % 34.95/5.36 | | | | | | | | | | | | | REDUCE: (272), (310) imply: % 34.95/5.36 | | | | | | | | | | | | | (311) mem(all_109_1, all_29_2) = 0 % 34.95/5.36 | | | | | | | | | | | | | % 34.95/5.36 | | | | | | | | | | | | | REF_CLOSE: (4), (15), (19), (45), (59), (93), (98), (303), % 34.95/5.36 | | | | | | | | | | | | | (311) are inconsistent by sub-proof #4. % 34.95/5.36 | | | | | | | | | | | | | % 34.95/5.36 | | | | | | | | | | | | End of split % 34.95/5.36 | | | | | | | | | | | | % 34.95/5.36 | | | | | | | | | | | Case 2: % 34.95/5.36 | | | | | | | | | | | | % 34.95/5.36 | | | | | | | | | | | | (312) all_201_1 = 0 % 34.95/5.36 | | | | | | | | | | | | % 34.95/5.36 | | | | | | | | | | | | REDUCE: (265), (312) imply: % 34.95/5.36 | | | | | | | | | | | | (313) mem(all_72_2, all_29_2) = 0 % 34.95/5.36 | | | | | | | | | | | | % 34.95/5.36 | | | | | | | | | | | | REF_CLOSE: (4), (15), (19), (45), (59), (72), (85), (303), % 34.95/5.36 | | | | | | | | | | | | (313) are inconsistent by sub-proof #8. % 34.95/5.36 | | | | | | | | | | | | % 34.95/5.36 | | | | | | | | | | | End of split % 34.95/5.36 | | | | | | | | | | | % 34.95/5.36 | | | | | | | | | | End of split % 34.95/5.36 | | | | | | | | | | % 34.95/5.36 | | | | | | | | | Case 2: % 34.95/5.36 | | | | | | | | | | % 34.95/5.36 | | | | | | | | | | (314) all_144_1 = 0 % 34.95/5.36 | | | | | | | | | | (315) ~ (all_144_0 = 0) % 34.95/5.36 | | | | | | | | | | % 34.95/5.36 | | | | | | | | | | REDUCE: (128), (314) imply: % 34.95/5.36 | | | | | | | | | | (316) mem(all_109_1, all_29_3) = 0 % 34.95/5.36 | | | | | | | | | | % 34.95/5.36 | | | | | | | | | | BETA: splitting (131) gives: % 34.95/5.36 | | | | | | | | | | % 34.95/5.36 | | | | | | | | | | Case 1: % 34.95/5.36 | | | | | | | | | | | % 34.95/5.36 | | | | | | | | | | | (317) all_144_0 = 0 % 34.95/5.36 | | | | | | | | | | | % 34.95/5.36 | | | | | | | | | | | REDUCE: (315), (317) imply: % 34.95/5.36 | | | | | | | | | | | (318) $false % 34.95/5.36 | | | | | | | | | | | % 34.95/5.36 | | | | | | | | | | | CLOSE: (318) is inconsistent. % 34.95/5.36 | | | | | | | | | | | % 34.95/5.36 | | | | | | | | | | Case 2: % 34.95/5.36 | | | | | | | | | | | % 34.95/5.36 | | | | | | | | | | | % 34.95/5.36 | | | | | | | | | | | GROUND_INST: instantiating (5) with all_109_1, e, all_48_0, % 34.95/5.36 | | | | | | | | | | | all_29_3, simplifying with (13), (46), (48), (93), % 34.95/5.36 | | | | | | | | | | | (316) gives: % 34.95/5.36 | | | | | | | | | | | (319) ? [v0: any] : ? [v1: any] : (mem(all_109_1, % 34.95/5.36 | | | | | | | | | | | all_48_0) = v1 & mem(all_109_1, e) = v0 & (v1 % 34.95/5.36 | | | | | | | | | | | = 0 | v0 = 0)) % 34.95/5.36 | | | | | | | | | | | % 34.95/5.36 | | | | | | | | | | | DELTA: instantiating (319) with fresh symbols all_230_0, % 34.95/5.36 | | | | | | | | | | | all_230_1 gives: % 34.95/5.36 | | | | | | | | | | | (320) mem(all_109_1, all_48_0) = all_230_0 & % 34.95/5.36 | | | | | | | | | | | mem(all_109_1, e) = all_230_1 & (all_230_0 = 0 | % 34.95/5.36 | | | | | | | | | | | all_230_1 = 0) % 34.95/5.36 | | | | | | | | | | | % 34.95/5.36 | | | | | | | | | | | ALPHA: (320) implies: % 34.95/5.36 | | | | | | | | | | | (321) mem(all_109_1, e) = all_230_1 % 34.95/5.36 | | | | | | | | | | | (322) mem(all_109_1, all_48_0) = all_230_0 % 34.95/5.36 | | | | | | | | | | | (323) all_230_0 = 0 | all_230_1 = 0 % 34.95/5.36 | | | | | | | | | | | % 34.95/5.36 | | | | | | | | | | | BETA: splitting (260) gives: % 34.95/5.36 | | | | | | | | | | | % 34.95/5.36 | | | | | | | | | | | Case 1: % 34.95/5.36 | | | | | | | | | | | | % 34.95/5.36 | | | | | | | | | | | | (324) all_187_0 = 0 % 34.95/5.36 | | | | | | | | | | | | % 34.95/5.36 | | | | | | | | | | | | REDUCE: (259), (324) imply: % 34.95/5.36 | | | | | | | | | | | | (325) mem(all_83_1, all_48_0) = 0 % 34.95/5.36 | | | | | | | | | | | | % 34.95/5.36 | | | | | | | | | | | | GROUND_INST: instantiating (4) with all_83_1, e, all_48_0, % 34.95/5.36 | | | | | | | | | | | | simplifying with (13), (47), (82), (325) gives: % 34.95/5.36 | | | | | | | | | | | | (326) all_83_1 = e % 34.95/5.36 | | | | | | | | | | | | % 34.95/5.36 | | | | | | | | | | | | REDUCE: (84), (326) imply: % 34.95/5.36 | | | | | | | | | | | | (327) mem(e, all_50_1) = all_83_0 % 34.95/5.36 | | | | | | | | | | | | % 34.95/5.36 | | | | | | | | | | | | BETA: splitting (323) gives: % 34.95/5.36 | | | | | | | | | | | | % 34.95/5.36 | | | | | | | | | | | | Case 1: % 34.95/5.36 | | | | | | | | | | | | | % 34.95/5.36 | | | | | | | | | | | | | (328) all_230_0 = 0 % 34.95/5.36 | | | | | | | | | | | | | % 34.95/5.36 | | | | | | | | | | | | | REDUCE: (322), (328) imply: % 34.95/5.36 | | | | | | | | | | | | | (329) mem(all_109_1, all_48_0) = 0 % 34.95/5.36 | | | | | | | | | | | | | % 34.95/5.36 | | | | | | | | | | | | | GROUND_INST: instantiating (4) with all_109_1, e, all_48_0, % 34.95/5.36 | | | | | | | | | | | | | simplifying with (13), (47), (93), (329) gives: % 34.95/5.36 | | | | | | | | | | | | | (330) all_109_1 = e % 34.95/5.36 | | | | | | | | | | | | | % 34.95/5.36 | | | | | | | | | | | | | REDUCE: (94), (330) imply: % 34.95/5.36 | | | | | | | | | | | | | (331) mem(e, all_50_1) = 0 % 34.95/5.36 | | | | | | | | | | | | | % 34.95/5.36 | | | | | | | | | | | | | GROUND_INST: instantiating (15) with all_83_0, 0, all_50_1, e, % 34.95/5.36 | | | | | | | | | | | | | simplifying with (327), (331) gives: % 34.95/5.36 | | | | | | | | | | | | | (332) all_83_0 = 0 % 34.95/5.36 | | | | | | | | | | | | | % 34.95/5.36 | | | | | | | | | | | | | REDUCE: (81), (332) imply: % 34.95/5.36 | | | | | | | | | | | | | (333) $false % 34.95/5.36 | | | | | | | | | | | | | % 34.95/5.36 | | | | | | | | | | | | | CLOSE: (333) is inconsistent. % 34.95/5.36 | | | | | | | | | | | | | % 34.95/5.36 | | | | | | | | | | | | Case 2: % 34.95/5.36 | | | | | | | | | | | | | % 34.95/5.36 | | | | | | | | | | | | | (334) all_230_1 = 0 % 34.95/5.36 | | | | | | | | | | | | | % 34.95/5.36 | | | | | | | | | | | | | REDUCE: (321), (334) imply: % 34.95/5.36 | | | | | | | | | | | | | (335) mem(all_109_1, e) = 0 % 34.95/5.36 | | | | | | | | | | | | | % 34.95/5.36 | | | | | | | | | | | | | GROUND_INST: instantiating (3) with all_109_1, simplifying with % 34.95/5.36 | | | | | | | | | | | | | (93), (335) gives: % 34.95/5.36 | | | | | | | | | | | | | (336) $false % 34.95/5.36 | | | | | | | | | | | | | % 34.95/5.36 | | | | | | | | | | | | | CLOSE: (336) is inconsistent. % 34.95/5.36 | | | | | | | | | | | | | % 34.95/5.36 | | | | | | | | | | | | End of split % 34.95/5.36 | | | | | | | | | | | | % 34.95/5.36 | | | | | | | | | | | Case 2: % 34.95/5.36 | | | | | | | | | | | | % 34.95/5.36 | | | | | | | | | | | | (337) all_187_1 = 0 % 34.95/5.36 | | | | | | | | | | | | % 34.95/5.36 | | | | | | | | | | | | REDUCE: (258), (337) imply: % 34.95/5.36 | | | | | | | | | | | | (338) mem(all_83_1, e) = 0 % 34.95/5.36 | | | | | | | | | | | | % 34.95/5.36 | | | | | | | | | | | | GROUND_INST: instantiating (3) with all_83_1, simplifying with % 34.95/5.36 | | | | | | | | | | | | (82), (338) gives: % 34.95/5.36 | | | | | | | | | | | | (339) $false % 34.95/5.36 | | | | | | | | | | | | % 34.95/5.36 | | | | | | | | | | | | CLOSE: (339) is inconsistent. % 34.95/5.36 | | | | | | | | | | | | % 34.95/5.36 | | | | | | | | | | | End of split % 34.95/5.36 | | | | | | | | | | | % 34.95/5.36 | | | | | | | | | | End of split % 34.95/5.36 | | | | | | | | | | % 34.95/5.36 | | | | | | | | | End of split % 34.95/5.36 | | | | | | | | | % 34.95/5.36 | | | | | | | | Case 2: % 34.95/5.36 | | | | | | | | | % 34.95/5.36 | | | | | | | | | (340) all_131_1 = 0 % 34.95/5.36 | | | | | | | | | % 34.95/5.36 | | | | | | | | | REDUCE: (115), (340) imply: % 34.95/5.36 | | | | | | | | | (341) mem(all_72_2, all_29_3) = 0 % 34.95/5.36 | | | | | | | | | % 34.95/5.36 | | | | | | | | | GROUND_INST: instantiating (5) with all_72_2, e, all_48_0, % 34.95/5.36 | | | | | | | | | all_29_3, simplifying with (13), (46), (48), (72), % 34.95/5.36 | | | | | | | | | (341) gives: % 34.95/5.36 | | | | | | | | | (342) ? [v0: any] : ? [v1: any] : (mem(all_72_2, % 34.95/5.36 | | | | | | | | | all_48_0) = v1 & mem(all_72_2, e) = v0 & (v1 = 0 % 34.95/5.36 | | | | | | | | | | v0 = 0)) % 34.95/5.36 | | | | | | | | | % 34.95/5.36 | | | | | | | | | DELTA: instantiating (342) with fresh symbols all_207_0, % 34.95/5.36 | | | | | | | | | all_207_1 gives: % 34.95/5.36 | | | | | | | | | (343) mem(all_72_2, all_48_0) = all_207_0 & mem(all_72_2, % 34.95/5.36 | | | | | | | | | e) = all_207_1 & (all_207_0 = 0 | all_207_1 = 0) % 34.95/5.36 | | | | | | | | | % 34.95/5.36 | | | | | | | | | ALPHA: (343) implies: % 34.95/5.36 | | | | | | | | | (344) mem(all_72_2, e) = all_207_1 % 34.95/5.36 | | | | | | | | | (345) mem(all_72_2, all_48_0) = all_207_0 % 34.95/5.36 | | | | | | | | | (346) all_207_0 = 0 | all_207_1 = 0 % 34.95/5.36 | | | | | | | | | % 34.95/5.36 | | | | | | | | | BETA: splitting (260) gives: % 34.95/5.36 | | | | | | | | | % 34.95/5.36 | | | | | | | | | Case 1: % 34.95/5.36 | | | | | | | | | | % 34.95/5.36 | | | | | | | | | | (347) all_187_0 = 0 % 34.95/5.36 | | | | | | | | | | % 34.95/5.36 | | | | | | | | | | REDUCE: (259), (347) imply: % 34.95/5.36 | | | | | | | | | | (348) mem(all_83_1, all_48_0) = 0 % 34.95/5.36 | | | | | | | | | | % 34.95/5.36 | | | | | | | | | | GROUND_INST: instantiating (4) with all_83_1, e, all_48_0, % 34.95/5.36 | | | | | | | | | | simplifying with (13), (47), (82), (348) gives: % 34.95/5.36 | | | | | | | | | | (349) all_83_1 = e % 34.95/5.36 | | | | | | | | | | % 34.95/5.36 | | | | | | | | | | REDUCE: (84), (349) imply: % 34.95/5.36 | | | | | | | | | | (350) mem(e, all_50_1) = all_83_0 % 34.95/5.36 | | | | | | | | | | % 34.95/5.36 | | | | | | | | | | BETA: splitting (346) gives: % 34.95/5.36 | | | | | | | | | | % 34.95/5.36 | | | | | | | | | | Case 1: % 34.95/5.36 | | | | | | | | | | | % 34.95/5.36 | | | | | | | | | | | (351) all_207_0 = 0 % 34.95/5.36 | | | | | | | | | | | % 34.95/5.36 | | | | | | | | | | | REDUCE: (345), (351) imply: % 34.95/5.36 | | | | | | | | | | | (352) mem(all_72_2, all_48_0) = 0 % 34.95/5.36 | | | | | | | | | | | % 34.95/5.36 | | | | | | | | | | | GROUND_INST: instantiating (4) with all_72_2, e, all_48_0, % 34.95/5.36 | | | | | | | | | | | simplifying with (13), (47), (72), (352) gives: % 34.95/5.36 | | | | | | | | | | | (353) all_72_2 = e % 34.95/5.36 | | | | | | | | | | | % 34.95/5.36 | | | | | | | | | | | REDUCE: (74), (353) imply: % 34.95/5.36 | | | | | | | | | | | (354) mem(e, all_50_1) = 0 % 34.95/5.36 | | | | | | | | | | | % 34.95/5.36 | | | | | | | | | | | GROUND_INST: instantiating (15) with all_83_0, 0, all_50_1, e, % 34.95/5.36 | | | | | | | | | | | simplifying with (350), (354) gives: % 34.95/5.37 | | | | | | | | | | | (355) all_83_0 = 0 % 34.95/5.37 | | | | | | | | | | | % 34.95/5.37 | | | | | | | | | | | REDUCE: (81), (355) imply: % 34.95/5.37 | | | | | | | | | | | (356) $false % 34.95/5.37 | | | | | | | | | | | % 34.95/5.37 | | | | | | | | | | | CLOSE: (356) is inconsistent. % 34.95/5.37 | | | | | | | | | | | % 34.95/5.37 | | | | | | | | | | Case 2: % 34.95/5.37 | | | | | | | | | | | % 34.95/5.37 | | | | | | | | | | | (357) all_207_1 = 0 % 34.95/5.37 | | | | | | | | | | | % 34.95/5.37 | | | | | | | | | | | REDUCE: (344), (357) imply: % 34.95/5.37 | | | | | | | | | | | (358) mem(all_72_2, e) = 0 % 34.95/5.37 | | | | | | | | | | | % 34.95/5.37 | | | | | | | | | | | GROUND_INST: instantiating (3) with all_72_2, simplifying with % 34.95/5.37 | | | | | | | | | | | (72), (358) gives: % 34.95/5.37 | | | | | | | | | | | (359) $false % 34.95/5.37 | | | | | | | | | | | % 34.95/5.37 | | | | | | | | | | | CLOSE: (359) is inconsistent. % 34.95/5.37 | | | | | | | | | | | % 34.95/5.37 | | | | | | | | | | End of split % 34.95/5.37 | | | | | | | | | | % 34.95/5.37 | | | | | | | | | Case 2: % 34.95/5.37 | | | | | | | | | | % 34.95/5.37 | | | | | | | | | | (360) all_187_1 = 0 % 34.95/5.37 | | | | | | | | | | % 34.95/5.37 | | | | | | | | | | REDUCE: (258), (360) imply: % 34.95/5.37 | | | | | | | | | | (361) mem(all_83_1, e) = 0 % 34.95/5.37 | | | | | | | | | | % 34.95/5.37 | | | | | | | | | | GROUND_INST: instantiating (3) with all_83_1, simplifying with % 34.95/5.37 | | | | | | | | | | (82), (361) gives: % 34.95/5.37 | | | | | | | | | | (362) $false % 34.95/5.37 | | | | | | | | | | % 34.95/5.37 | | | | | | | | | | CLOSE: (362) is inconsistent. % 34.95/5.37 | | | | | | | | | | % 34.95/5.37 | | | | | | | | | End of split % 34.95/5.37 | | | | | | | | | % 34.95/5.37 | | | | | | | | End of split % 34.95/5.37 | | | | | | | | % 34.95/5.37 | | | | | | | End of split % 34.95/5.37 | | | | | | | % 34.95/5.37 | | | | | | Case 2: % 34.95/5.37 | | | | | | | % 34.95/5.37 | | | | | | | (363) all_70_1 = 0 % 34.95/5.37 | | | | | | | % 34.95/5.37 | | | | | | | REDUCE: (67), (363) imply: % 34.95/5.37 | | | | | | | (364) mem(all_56_1, all_29_3) = 0 % 34.95/5.37 | | | | | | | % 34.95/5.37 | | | | | | | GROUND_INST: instantiating (5) with all_56_1, e, all_48_0, % 34.95/5.37 | | | | | | | all_29_3, simplifying with (13), (46), (48), (60), % 34.95/5.37 | | | | | | | (364) gives: % 34.95/5.37 | | | | | | | (365) ? [v0: any] : ? [v1: any] : (mem(all_56_1, all_48_0) = % 34.95/5.37 | | | | | | | v1 & mem(all_56_1, e) = v0 & (v1 = 0 | v0 = 0)) % 34.95/5.37 | | | | | | | % 34.95/5.37 | | | | | | | DELTA: instantiating (365) with fresh symbols all_164_0, all_164_1 % 34.95/5.37 | | | | | | | gives: % 34.95/5.37 | | | | | | | (366) mem(all_56_1, all_48_0) = all_164_0 & mem(all_56_1, e) = % 34.95/5.37 | | | | | | | all_164_1 & (all_164_0 = 0 | all_164_1 = 0) % 34.95/5.37 | | | | | | | % 34.95/5.37 | | | | | | | ALPHA: (366) implies: % 34.95/5.37 | | | | | | | (367) mem(all_56_1, e) = all_164_1 % 34.95/5.37 | | | | | | | (368) mem(all_56_1, all_48_0) = all_164_0 % 34.95/5.37 | | | | | | | (369) all_164_0 = 0 | all_164_1 = 0 % 34.95/5.37 | | | | | | | % 34.95/5.37 | | | | | | | BETA: splitting (103) gives: % 34.95/5.37 | | | | | | | % 34.95/5.37 | | | | | | | Case 1: % 34.95/5.37 | | | | | | | | % 34.95/5.37 | | | | | | | | (370) all_117_0 = 0 % 34.95/5.37 | | | | | | | | % 34.95/5.37 | | | | | | | | REDUCE: (102), (370) imply: % 34.95/5.37 | | | | | | | | (371) mem(all_83_1, all_29_1) = 0 % 34.95/5.37 | | | | | | | | % 34.95/5.37 | | | | | | | | GROUND_INST: instantiating (5) with all_83_1, all_29_2, % 34.95/5.37 | | | | | | | | all_46_0, all_29_1, simplifying with (17), (41), % 34.95/5.37 | | | | | | | | (43), (82), (371) gives: % 34.95/5.37 | | | | | | | | (372) ? [v0: any] : ? [v1: any] : (mem(all_83_1, all_46_0) % 34.95/5.37 | | | | | | | | = v1 & mem(all_83_1, all_29_2) = v0 & (v1 = 0 | v0 = % 34.95/5.37 | | | | | | | | 0)) % 34.95/5.37 | | | | | | | | % 34.95/5.37 | | | | | | | | DELTA: instantiating (372) with fresh symbols all_178_0, % 34.95/5.37 | | | | | | | | all_178_1 gives: % 34.95/5.37 | | | | | | | | (373) mem(all_83_1, all_46_0) = all_178_0 & mem(all_83_1, % 34.95/5.37 | | | | | | | | all_29_2) = all_178_1 & (all_178_0 = 0 | all_178_1 = % 34.95/5.37 | | | | | | | | 0) % 34.95/5.37 | | | | | | | | % 34.95/5.37 | | | | | | | | ALPHA: (373) implies: % 34.95/5.37 | | | | | | | | (374) mem(all_83_1, all_29_2) = all_178_1 % 34.95/5.37 | | | | | | | | (375) mem(all_83_1, all_46_0) = all_178_0 % 34.95/5.37 | | | | | | | | (376) all_178_0 = 0 | all_178_1 = 0 % 34.95/5.37 | | | | | | | | % 34.95/5.37 | | | | | | | | BETA: splitting (117) gives: % 34.95/5.37 | | | | | | | | % 34.95/5.37 | | | | | | | | Case 1: % 34.95/5.37 | | | | | | | | | % 34.95/5.37 | | | | | | | | | (377) all_131_0 = 0 % 34.95/5.37 | | | | | | | | | % 34.95/5.37 | | | | | | | | | REDUCE: (116), (377) imply: % 34.95/5.37 | | | | | | | | | (378) mem(all_72_2, all_29_1) = 0 % 34.95/5.37 | | | | | | | | | % 34.95/5.37 | | | | | | | | | GROUND_INST: instantiating (5) with all_72_2, all_29_2, % 34.95/5.37 | | | | | | | | | all_46_0, all_29_1, simplifying with (17), (41), % 34.95/5.37 | | | | | | | | | (43), (72), (378) gives: % 34.95/5.37 | | | | | | | | | (379) ? [v0: any] : ? [v1: any] : (mem(all_72_2, % 34.95/5.37 | | | | | | | | | all_46_0) = v1 & mem(all_72_2, all_29_2) = v0 & % 34.95/5.37 | | | | | | | | | (v1 = 0 | v0 = 0)) % 34.95/5.37 | | | | | | | | | % 34.95/5.37 | | | | | | | | | DELTA: instantiating (379) with fresh symbols all_201_0, % 34.95/5.37 | | | | | | | | | all_201_1 gives: % 34.95/5.37 | | | | | | | | | (380) mem(all_72_2, all_46_0) = all_201_0 & mem(all_72_2, % 34.95/5.37 | | | | | | | | | all_29_2) = all_201_1 & (all_201_0 = 0 | all_201_1 % 34.95/5.37 | | | | | | | | | = 0) % 34.95/5.37 | | | | | | | | | % 34.95/5.37 | | | | | | | | | ALPHA: (380) implies: % 34.95/5.37 | | | | | | | | | (381) mem(all_72_2, all_29_2) = all_201_1 % 34.95/5.37 | | | | | | | | | (382) mem(all_72_2, all_46_0) = all_201_0 % 34.95/5.37 | | | | | | | | | (383) all_201_0 = 0 | all_201_1 = 0 % 34.95/5.37 | | | | | | | | | % 34.95/5.37 | | | | | | | | | BETA: splitting (130) gives: % 34.95/5.37 | | | | | | | | | % 34.95/5.37 | | | | | | | | | Case 1: % 34.95/5.37 | | | | | | | | | | % 34.95/5.37 | | | | | | | | | | (384) all_144_0 = 0 % 34.95/5.37 | | | | | | | | | | % 34.95/5.37 | | | | | | | | | | REDUCE: (129), (384) imply: % 34.95/5.37 | | | | | | | | | | (385) mem(all_109_1, all_29_1) = 0 % 34.95/5.37 | | | | | | | | | | % 34.95/5.37 | | | | | | | | | | GROUND_INST: instantiating (5) with all_109_1, all_29_2, % 34.95/5.37 | | | | | | | | | | all_46_0, all_29_1, simplifying with (17), (41), % 34.95/5.37 | | | | | | | | | | (43), (93), (385) gives: % 34.95/5.37 | | | | | | | | | | (386) ? [v0: any] : ? [v1: any] : (mem(all_109_1, % 34.95/5.37 | | | | | | | | | | all_46_0) = v1 & mem(all_109_1, all_29_2) = v0 % 34.95/5.37 | | | | | | | | | | & (v1 = 0 | v0 = 0)) % 34.95/5.37 | | | | | | | | | | % 34.95/5.37 | | | | | | | | | | DELTA: instantiating (386) with fresh symbols all_224_0, % 34.95/5.37 | | | | | | | | | | all_224_1 gives: % 34.95/5.37 | | | | | | | | | | (387) mem(all_109_1, all_46_0) = all_224_0 & % 34.95/5.37 | | | | | | | | | | mem(all_109_1, all_29_2) = all_224_1 & (all_224_0 = % 34.95/5.37 | | | | | | | | | | 0 | all_224_1 = 0) % 34.95/5.37 | | | | | | | | | | % 34.95/5.37 | | | | | | | | | | ALPHA: (387) implies: % 34.95/5.37 | | | | | | | | | | (388) mem(all_109_1, all_29_2) = all_224_1 % 34.95/5.37 | | | | | | | | | | (389) mem(all_109_1, all_46_0) = all_224_0 % 34.95/5.37 | | | | | | | | | | (390) all_224_0 = 0 | all_224_1 = 0 % 34.95/5.37 | | | | | | | | | | % 34.95/5.37 | | | | | | | | | | BETA: splitting (369) gives: % 34.95/5.37 | | | | | | | | | | % 34.95/5.37 | | | | | | | | | | Case 1: % 34.95/5.37 | | | | | | | | | | | % 34.95/5.37 | | | | | | | | | | | (391) all_164_0 = 0 % 34.95/5.37 | | | | | | | | | | | % 34.95/5.37 | | | | | | | | | | | REDUCE: (368), (391) imply: % 34.95/5.37 | | | | | | | | | | | (392) mem(all_56_1, all_48_0) = 0 % 34.95/5.37 | | | | | | | | | | | % 34.95/5.37 | | | | | | | | | | | GROUND_INST: instantiating (4) with all_56_1, e, all_48_0, % 34.95/5.37 | | | | | | | | | | | simplifying with (13), (47), (60), (392) gives: % 34.95/5.37 | | | | | | | | | | | (393) all_56_1 = e % 34.95/5.37 | | | | | | | | | | | % 34.95/5.37 | | | | | | | | | | | BETA: splitting (376) gives: % 34.95/5.37 | | | | | | | | | | | % 34.95/5.37 | | | | | | | | | | | Case 1: % 34.95/5.37 | | | | | | | | | | | | % 34.95/5.37 | | | | | | | | | | | | (394) all_178_0 = 0 % 34.95/5.37 | | | | | | | | | | | | % 34.95/5.37 | | | | | | | | | | | | REDUCE: (375), (394) imply: % 34.95/5.37 | | | | | | | | | | | | (395) mem(all_83_1, all_46_0) = 0 % 34.95/5.37 | | | | | | | | | | | | % 34.95/5.37 | | | | | | | | | | | | GROUND_INST: instantiating (4) with all_83_1, all_29_2, % 34.95/5.37 | | | | | | | | | | | | all_46_0, simplifying with (17), (42), (82), (395) % 34.95/5.37 | | | | | | | | | | | | gives: % 34.95/5.37 | | | | | | | | | | | | (396) all_83_1 = all_29_2 % 34.95/5.37 | | | | | | | | | | | | % 34.95/5.37 | | | | | | | | | | | | REDUCE: (84), (396) imply: % 34.95/5.37 | | | | | | | | | | | | (397) mem(all_29_2, all_50_1) = all_83_0 % 34.95/5.37 | | | | | | | | | | | | % 34.95/5.37 | | | | | | | | | | | | BETA: splitting (383) gives: % 34.95/5.37 | | | | | | | | | | | | % 34.95/5.37 | | | | | | | | | | | | Case 1: % 34.95/5.37 | | | | | | | | | | | | | % 34.95/5.37 | | | | | | | | | | | | | (398) all_201_0 = 0 % 34.95/5.37 | | | | | | | | | | | | | % 34.95/5.37 | | | | | | | | | | | | | REDUCE: (382), (398) imply: % 34.95/5.37 | | | | | | | | | | | | | (399) mem(all_72_2, all_46_0) = 0 % 34.95/5.37 | | | | | | | | | | | | | % 34.95/5.37 | | | | | | | | | | | | | REF_CLOSE: (4), (15), (17), (42), (72), (74), (81), (397), % 34.95/5.37 | | | | | | | | | | | | | (399) are inconsistent by sub-proof #9. % 34.95/5.37 | | | | | | | | | | | | | % 34.95/5.37 | | | | | | | | | | | | Case 2: % 34.95/5.37 | | | | | | | | | | | | | % 34.95/5.37 | | | | | | | | | | | | | (400) all_201_1 = 0 % 34.95/5.37 | | | | | | | | | | | | | % 34.95/5.37 | | | | | | | | | | | | | REDUCE: (381), (400) imply: % 34.95/5.37 | | | | | | | | | | | | | (401) mem(all_72_2, all_29_2) = 0 % 34.95/5.37 | | | | | | | | | | | | | % 34.95/5.37 | | | | | | | | | | | | | GROUND_INST: instantiating (4) with all_72_2, all_29_3, % 34.95/5.37 | | | | | | | | | | | | | all_29_2, simplifying with (19), (45), (72), (401) % 34.95/5.37 | | | | | | | | | | | | | gives: % 34.95/5.37 | | | | | | | | | | | | | (402) all_72_2 = all_29_3 % 34.95/5.37 | | | | | | | | | | | | | % 34.95/5.37 | | | | | | | | | | | | | REDUCE: (124), (402) imply: % 34.95/5.37 | | | | | | | | | | | | | (403) mem(all_137_1, all_29_3) = all_137_0 % 34.95/5.37 | | | | | | | | | | | | | % 34.95/5.37 | | | | | | | | | | | | | GROUND_INST: instantiating (6) with all_137_1, e, all_48_0, % 34.95/5.37 | | | | | | | | | | | | | all_29_3, all_137_0, simplifying with (13), (46), % 34.95/5.37 | | | | | | | | | | | | | (48), (123), (403) gives: % 34.95/5.37 | | | | | | | | | | | | | (404) all_137_0 = 0 | ? [v0: int] : ? [v1: int] : ( ~ % 34.95/5.37 | | | | | | | | | | | | | (v1 = 0) & ~ (v0 = 0) & mem(all_137_1, % 34.95/5.37 | | | | | | | | | | | | | all_48_0) = v1 & mem(all_137_1, e) = v0) % 34.95/5.37 | | | | | | | | | | | | | % 34.95/5.37 | | | | | | | | | | | | | BETA: splitting (390) gives: % 34.95/5.37 | | | | | | | | | | | | | % 34.95/5.37 | | | | | | | | | | | | | Case 1: % 34.95/5.37 | | | | | | | | | | | | | | % 34.95/5.37 | | | | | | | | | | | | | | (405) all_224_0 = 0 % 34.95/5.37 | | | | | | | | | | | | | | % 34.95/5.37 | | | | | | | | | | | | | | REDUCE: (389), (405) imply: % 34.95/5.37 | | | | | | | | | | | | | | (406) mem(all_109_1, all_46_0) = 0 % 34.95/5.37 | | | | | | | | | | | | | | % 34.95/5.37 | | | | | | | | | | | | | | GROUND_INST: instantiating (4) with all_109_1, all_29_2, % 34.95/5.37 | | | | | | | | | | | | | | all_46_0, simplifying with (17), (42), (93), (406) % 34.95/5.37 | | | | | | | | | | | | | | gives: % 34.95/5.37 | | | | | | | | | | | | | | (407) all_109_1 = all_29_2 % 34.95/5.37 | | | | | | | | | | | | | | % 34.95/5.37 | | | | | | | | | | | | | | REDUCE: (94), (407) imply: % 34.95/5.37 | | | | | | | | | | | | | | (408) mem(all_29_2, all_50_1) = 0 % 34.95/5.37 | | | | | | | | | | | | | | % 34.95/5.37 | | | | | | | | | | | | | | REF_CLOSE: (15), (81), (397), (408) are inconsistent by % 34.95/5.37 | | | | | | | | | | | | | | sub-proof #5. % 34.95/5.37 | | | | | | | | | | | | | | % 34.95/5.37 | | | | | | | | | | | | | Case 2: % 34.95/5.37 | | | | | | | | | | | | | | % 34.95/5.37 | | | | | | | | | | | | | | (409) all_224_1 = 0 % 34.95/5.37 | | | | | | | | | | | | | | % 34.95/5.37 | | | | | | | | | | | | | | REDUCE: (388), (409) imply: % 34.95/5.37 | | | | | | | | | | | | | | (410) mem(all_109_1, all_29_2) = 0 % 34.95/5.37 | | | | | | | | | | | | | | % 34.95/5.37 | | | | | | | | | | | | | | REF_CLOSE: (4), (15), (19), (45), (93), (122), (125), (403), % 34.95/5.37 | | | | | | | | | | | | | | (404), (410) are inconsistent by sub-proof #3. % 34.95/5.37 | | | | | | | | | | | | | | % 34.95/5.37 | | | | | | | | | | | | | End of split % 34.95/5.37 | | | | | | | | | | | | | % 34.95/5.37 | | | | | | | | | | | | End of split % 34.95/5.37 | | | | | | | | | | | | % 34.95/5.37 | | | | | | | | | | | Case 2: % 34.95/5.37 | | | | | | | | | | | | % 34.95/5.37 | | | | | | | | | | | | (411) all_178_1 = 0 % 34.95/5.37 | | | | | | | | | | | | % 34.95/5.37 | | | | | | | | | | | | REDUCE: (374), (411) imply: % 34.95/5.37 | | | | | | | | | | | | (412) mem(all_83_1, all_29_2) = 0 % 34.95/5.37 | | | | | | | | | | | | % 34.95/5.37 | | | | | | | | | | | | GROUND_INST: instantiating (4) with all_83_1, all_29_3, % 34.95/5.37 | | | | | | | | | | | | all_29_2, simplifying with (19), (45), (82), (412) % 34.95/5.37 | | | | | | | | | | | | gives: % 34.95/5.37 | | | | | | | | | | | | (413) all_83_1 = all_29_3 % 34.95/5.37 | | | | | | | | | | | | % 34.95/5.37 | | | | | | | | | | | | REDUCE: (84), (413) imply: % 34.95/5.37 | | | | | | | | | | | | (414) mem(all_29_3, all_50_1) = all_83_0 % 34.95/5.37 | | | | | | | | | | | | % 34.95/5.37 | | | | | | | | | | | | BETA: splitting (383) gives: % 34.95/5.37 | | | | | | | | | | | | % 34.95/5.37 | | | | | | | | | | | | Case 1: % 34.95/5.37 | | | | | | | | | | | | | % 34.95/5.37 | | | | | | | | | | | | | (415) all_201_0 = 0 % 34.95/5.37 | | | | | | | | | | | | | % 34.95/5.37 | | | | | | | | | | | | | REDUCE: (382), (415) imply: % 34.95/5.37 | | | | | | | | | | | | | (416) mem(all_72_2, all_46_0) = 0 % 34.95/5.37 | | | | | | | | | | | | | % 34.95/5.37 | | | | | | | | | | | | | GROUND_INST: instantiating (4) with all_72_2, all_29_2, % 34.95/5.37 | | | | | | | | | | | | | all_46_0, simplifying with (17), (42), (72), (416) % 34.95/5.37 | | | | | | | | | | | | | gives: % 34.95/5.37 | | | | | | | | | | | | | (417) all_72_2 = all_29_2 % 34.95/5.37 | | | | | | | | | | | | | % 34.95/5.37 | | | | | | | | | | | | | REDUCE: (124), (417) imply: % 34.95/5.37 | | | | | | | | | | | | | (418) mem(all_137_1, all_29_2) = all_137_0 % 34.95/5.37 | | | | | | | | | | | | | % 34.95/5.37 | | | | | | | | | | | | | BETA: splitting (390) gives: % 34.95/5.37 | | | | | | | | | | | | | % 34.95/5.37 | | | | | | | | | | | | | Case 1: % 34.95/5.37 | | | | | | | | | | | | | | % 34.95/5.37 | | | | | | | | | | | | | | (419) all_224_0 = 0 % 34.95/5.37 | | | | | | | | | | | | | | % 34.95/5.37 | | | | | | | | | | | | | | REDUCE: (389), (419) imply: % 34.95/5.37 | | | | | | | | | | | | | | (420) mem(all_109_1, all_46_0) = 0 % 34.95/5.37 | | | | | | | | | | | | | | % 34.95/5.37 | | | | | | | | | | | | | | REF_CLOSE: (4), (15), (17), (42), (93), (122), (125), (418), % 34.95/5.37 | | | | | | | | | | | | | | (420) are inconsistent by sub-proof #2. % 34.95/5.37 | | | | | | | | | | | | | | % 34.95/5.37 | | | | | | | | | | | | | Case 2: % 34.95/5.37 | | | | | | | | | | | | | | % 34.95/5.37 | | | | | | | | | | | | | | (421) all_224_1 = 0 % 34.95/5.38 | | | | | | | | | | | | | | % 34.95/5.38 | | | | | | | | | | | | | | REDUCE: (388), (421) imply: % 34.95/5.38 | | | | | | | | | | | | | | (422) mem(all_109_1, all_29_2) = 0 % 34.95/5.38 | | | | | | | | | | | | | | % 34.95/5.38 | | | | | | | | | | | | | | REF_CLOSE: (4), (15), (19), (45), (81), (93), (94), (414), % 34.95/5.38 | | | | | | | | | | | | | | (422) are inconsistent by sub-proof #6. % 34.95/5.38 | | | | | | | | | | | | | | % 34.95/5.38 | | | | | | | | | | | | | End of split % 34.95/5.38 | | | | | | | | | | | | | % 34.95/5.38 | | | | | | | | | | | | Case 2: % 34.95/5.38 | | | | | | | | | | | | | % 34.95/5.38 | | | | | | | | | | | | | (423) all_201_1 = 0 % 34.95/5.38 | | | | | | | | | | | | | % 34.95/5.38 | | | | | | | | | | | | | REDUCE: (381), (423) imply: % 34.95/5.38 | | | | | | | | | | | | | (424) mem(all_72_2, all_29_2) = 0 % 34.95/5.38 | | | | | | | | | | | | | % 34.95/5.38 | | | | | | | | | | | | | REF_CLOSE: (4), (15), (19), (45), (72), (74), (81), (414), % 34.95/5.38 | | | | | | | | | | | | | (424) are inconsistent by sub-proof #10. % 34.95/5.38 | | | | | | | | | | | | | % 34.95/5.38 | | | | | | | | | | | | End of split % 34.95/5.38 | | | | | | | | | | | | % 34.95/5.38 | | | | | | | | | | | End of split % 34.95/5.38 | | | | | | | | | | | % 34.95/5.38 | | | | | | | | | | Case 2: % 34.95/5.38 | | | | | | | | | | | % 34.95/5.38 | | | | | | | | | | | (425) all_164_1 = 0 % 34.95/5.38 | | | | | | | | | | | % 34.95/5.38 | | | | | | | | | | | REDUCE: (367), (425) imply: % 34.95/5.38 | | | | | | | | | | | (426) mem(all_56_1, e) = 0 % 34.95/5.38 | | | | | | | | | | | % 34.95/5.38 | | | | | | | | | | | GROUND_INST: instantiating (3) with all_56_1, simplifying with % 34.95/5.38 | | | | | | | | | | | (60), (426) gives: % 34.95/5.38 | | | | | | | | | | | (427) $false % 34.95/5.38 | | | | | | | | | | | % 34.95/5.38 | | | | | | | | | | | CLOSE: (427) is inconsistent. % 34.95/5.38 | | | | | | | | | | | % 34.95/5.38 | | | | | | | | | | End of split % 34.95/5.38 | | | | | | | | | | % 34.95/5.38 | | | | | | | | | Case 2: % 34.95/5.38 | | | | | | | | | | % 34.95/5.38 | | | | | | | | | | (428) all_144_1 = 0 % 34.95/5.38 | | | | | | | | | | % 34.95/5.38 | | | | | | | | | | REDUCE: (128), (428) imply: % 34.95/5.38 | | | | | | | | | | (429) mem(all_109_1, all_29_3) = 0 % 34.95/5.38 | | | | | | | | | | % 34.95/5.38 | | | | | | | | | | GROUND_INST: instantiating (5) with all_109_1, e, all_48_0, % 34.95/5.38 | | | | | | | | | | all_29_3, simplifying with (13), (46), (48), (93), % 34.95/5.38 | | | | | | | | | | (429) gives: % 34.95/5.38 | | | | | | | | | | (430) ? [v0: any] : ? [v1: any] : (mem(all_109_1, % 34.95/5.38 | | | | | | | | | | all_48_0) = v1 & mem(all_109_1, e) = v0 & (v1 = % 34.95/5.38 | | | | | | | | | | 0 | v0 = 0)) % 34.95/5.38 | | | | | | | | | | % 34.95/5.38 | | | | | | | | | | DELTA: instantiating (430) with fresh symbols all_230_0, % 34.95/5.38 | | | | | | | | | | all_230_1 gives: % 34.95/5.38 | | | | | | | | | | (431) mem(all_109_1, all_48_0) = all_230_0 & % 34.95/5.38 | | | | | | | | | | mem(all_109_1, e) = all_230_1 & (all_230_0 = 0 | % 34.95/5.38 | | | | | | | | | | all_230_1 = 0) % 34.95/5.38 | | | | | | | | | | % 34.95/5.38 | | | | | | | | | | ALPHA: (431) implies: % 34.95/5.38 | | | | | | | | | | (432) mem(all_109_1, e) = all_230_1 % 34.95/5.38 | | | | | | | | | | (433) mem(all_109_1, all_48_0) = all_230_0 % 34.95/5.38 | | | | | | | | | | (434) all_230_0 = 0 | all_230_1 = 0 % 34.95/5.38 | | | | | | | | | | % 34.95/5.38 | | | | | | | | | | BETA: splitting (369) gives: % 34.95/5.38 | | | | | | | | | | % 34.95/5.38 | | | | | | | | | | Case 1: % 34.95/5.38 | | | | | | | | | | | % 34.95/5.38 | | | | | | | | | | | (435) all_164_0 = 0 % 34.95/5.38 | | | | | | | | | | | % 34.95/5.38 | | | | | | | | | | | REDUCE: (368), (435) imply: % 34.95/5.38 | | | | | | | | | | | (436) mem(all_56_1, all_48_0) = 0 % 34.95/5.38 | | | | | | | | | | | % 34.95/5.38 | | | | | | | | | | | GROUND_INST: instantiating (4) with all_56_1, e, all_48_0, % 34.95/5.38 | | | | | | | | | | | simplifying with (13), (47), (60), (436) gives: % 34.95/5.38 | | | | | | | | | | | (437) all_56_1 = e % 34.95/5.38 | | | | | | | | | | | % 34.95/5.38 | | | | | | | | | | | REDUCE: (62), (437) imply: % 34.95/5.38 | | | | | | | | | | | (438) mem(e, all_37_1) = all_56_0 % 34.95/5.38 | | | | | | | | | | | % 34.95/5.38 | | | | | | | | | | | BETA: splitting (434) gives: % 34.95/5.38 | | | | | | | | | | | % 34.95/5.38 | | | | | | | | | | | Case 1: % 34.95/5.38 | | | | | | | | | | | | % 34.95/5.38 | | | | | | | | | | | | (439) all_230_0 = 0 % 34.95/5.38 | | | | | | | | | | | | % 34.95/5.38 | | | | | | | | | | | | REDUCE: (433), (439) imply: % 34.95/5.38 | | | | | | | | | | | | (440) mem(all_109_1, all_48_0) = 0 % 34.95/5.38 | | | | | | | | | | | | % 34.95/5.38 | | | | | | | | | | | | GROUND_INST: instantiating (4) with all_109_1, e, all_48_0, % 34.95/5.38 | | | | | | | | | | | | simplifying with (13), (47), (93), (440) gives: % 34.95/5.38 | | | | | | | | | | | | (441) all_109_1 = e % 34.95/5.38 | | | | | | | | | | | | % 34.95/5.38 | | | | | | | | | | | | REDUCE: (98), (441) imply: % 34.95/5.38 | | | | | | | | | | | | (442) mem(e, all_37_1) = 0 % 34.95/5.38 | | | | | | | | | | | | % 34.95/5.38 | | | | | | | | | | | | REF_CLOSE: (15), (59), (438), (442) are inconsistent by % 34.95/5.38 | | | | | | | | | | | | sub-proof #1. % 34.95/5.38 | | | | | | | | | | | | % 34.95/5.38 | | | | | | | | | | | Case 2: % 34.95/5.38 | | | | | | | | | | | | % 34.95/5.38 | | | | | | | | | | | | (443) all_230_1 = 0 % 34.95/5.38 | | | | | | | | | | | | % 34.95/5.38 | | | | | | | | | | | | REDUCE: (432), (443) imply: % 34.95/5.38 | | | | | | | | | | | | (444) mem(all_109_1, e) = 0 % 34.95/5.38 | | | | | | | | | | | | % 34.95/5.38 | | | | | | | | | | | | GROUND_INST: instantiating (3) with all_109_1, simplifying with % 34.95/5.38 | | | | | | | | | | | | (93), (444) gives: % 34.95/5.38 | | | | | | | | | | | | (445) $false % 34.95/5.38 | | | | | | | | | | | | % 34.95/5.38 | | | | | | | | | | | | CLOSE: (445) is inconsistent. % 34.95/5.38 | | | | | | | | | | | | % 34.95/5.38 | | | | | | | | | | | End of split % 34.95/5.38 | | | | | | | | | | | % 34.95/5.38 | | | | | | | | | | Case 2: % 34.95/5.38 | | | | | | | | | | | % 34.95/5.38 | | | | | | | | | | | (446) all_164_1 = 0 % 34.95/5.38 | | | | | | | | | | | % 34.95/5.38 | | | | | | | | | | | REDUCE: (367), (446) imply: % 34.95/5.38 | | | | | | | | | | | (447) mem(all_56_1, e) = 0 % 34.95/5.38 | | | | | | | | | | | % 34.95/5.38 | | | | | | | | | | | GROUND_INST: instantiating (3) with all_56_1, simplifying with % 34.95/5.38 | | | | | | | | | | | (60), (447) gives: % 34.95/5.38 | | | | | | | | | | | (448) $false % 34.95/5.38 | | | | | | | | | | | % 34.95/5.38 | | | | | | | | | | | CLOSE: (448) is inconsistent. % 34.95/5.38 | | | | | | | | | | | % 34.95/5.38 | | | | | | | | | | End of split % 34.95/5.38 | | | | | | | | | | % 34.95/5.38 | | | | | | | | | End of split % 34.95/5.38 | | | | | | | | | % 34.95/5.38 | | | | | | | | Case 2: % 34.95/5.38 | | | | | | | | | % 34.95/5.38 | | | | | | | | | (449) all_131_1 = 0 % 34.95/5.38 | | | | | | | | | % 34.95/5.38 | | | | | | | | | REDUCE: (115), (449) imply: % 34.95/5.38 | | | | | | | | | (450) mem(all_72_2, all_29_3) = 0 % 34.95/5.38 | | | | | | | | | % 34.95/5.38 | | | | | | | | | GROUND_INST: instantiating (5) with all_72_2, e, all_48_0, % 34.95/5.38 | | | | | | | | | all_29_3, simplifying with (13), (46), (48), (72), % 34.95/5.38 | | | | | | | | | (450) gives: % 34.95/5.38 | | | | | | | | | (451) ? [v0: any] : ? [v1: any] : (mem(all_72_2, % 34.95/5.38 | | | | | | | | | all_48_0) = v1 & mem(all_72_2, e) = v0 & (v1 = 0 % 34.95/5.38 | | | | | | | | | | v0 = 0)) % 34.95/5.38 | | | | | | | | | % 34.95/5.38 | | | | | | | | | DELTA: instantiating (451) with fresh symbols all_207_0, % 34.95/5.38 | | | | | | | | | all_207_1 gives: % 34.95/5.38 | | | | | | | | | (452) mem(all_72_2, all_48_0) = all_207_0 & mem(all_72_2, % 34.95/5.38 | | | | | | | | | e) = all_207_1 & (all_207_0 = 0 | all_207_1 = 0) % 34.95/5.38 | | | | | | | | | % 34.95/5.38 | | | | | | | | | ALPHA: (452) implies: % 34.95/5.38 | | | | | | | | | (453) mem(all_72_2, e) = all_207_1 % 34.95/5.38 | | | | | | | | | (454) mem(all_72_2, all_48_0) = all_207_0 % 34.95/5.38 | | | | | | | | | (455) all_207_0 = 0 | all_207_1 = 0 % 34.95/5.38 | | | | | | | | | % 34.95/5.38 | | | | | | | | | BETA: splitting (369) gives: % 34.95/5.38 | | | | | | | | | % 34.95/5.38 | | | | | | | | | Case 1: % 34.95/5.38 | | | | | | | | | | % 34.95/5.38 | | | | | | | | | | (456) all_164_0 = 0 % 34.95/5.38 | | | | | | | | | | % 34.95/5.38 | | | | | | | | | | REDUCE: (368), (456) imply: % 34.95/5.38 | | | | | | | | | | (457) mem(all_56_1, all_48_0) = 0 % 34.95/5.38 | | | | | | | | | | % 34.95/5.38 | | | | | | | | | | GROUND_INST: instantiating (4) with all_56_1, e, all_48_0, % 34.95/5.38 | | | | | | | | | | simplifying with (13), (47), (60), (457) gives: % 34.95/5.38 | | | | | | | | | | (458) all_56_1 = e % 34.95/5.38 | | | | | | | | | | % 34.95/5.38 | | | | | | | | | | REDUCE: (62), (458) imply: % 34.95/5.38 | | | | | | | | | | (459) mem(e, all_37_1) = all_56_0 % 34.95/5.38 | | | | | | | | | | % 34.95/5.38 | | | | | | | | | | BETA: splitting (455) gives: % 34.95/5.38 | | | | | | | | | | % 34.95/5.38 | | | | | | | | | | Case 1: % 34.95/5.38 | | | | | | | | | | | % 34.95/5.38 | | | | | | | | | | | (460) all_207_0 = 0 % 34.95/5.38 | | | | | | | | | | | % 34.95/5.38 | | | | | | | | | | | REDUCE: (454), (460) imply: % 34.95/5.38 | | | | | | | | | | | (461) mem(all_72_2, all_48_0) = 0 % 34.95/5.38 | | | | | | | | | | | % 35.32/5.38 | | | | | | | | | | | GROUND_INST: instantiating (4) with all_72_2, e, all_48_0, % 35.32/5.38 | | | | | | | | | | | simplifying with (13), (47), (72), (461) gives: % 35.32/5.38 | | | | | | | | | | | (462) all_72_2 = e % 35.32/5.38 | | | | | | | | | | | % 35.32/5.38 | | | | | | | | | | | REDUCE: (85), (462) imply: % 35.32/5.38 | | | | | | | | | | | (463) mem(e, all_37_1) = 0 % 35.32/5.38 | | | | | | | | | | | % 35.32/5.38 | | | | | | | | | | | REF_CLOSE: (15), (59), (459), (463) are inconsistent by % 35.32/5.38 | | | | | | | | | | | sub-proof #1. % 35.32/5.38 | | | | | | | | | | | % 35.32/5.38 | | | | | | | | | | Case 2: % 35.32/5.38 | | | | | | | | | | | % 35.32/5.38 | | | | | | | | | | | (464) all_207_1 = 0 % 35.32/5.38 | | | | | | | | | | | % 35.32/5.38 | | | | | | | | | | | REDUCE: (453), (464) imply: % 35.32/5.38 | | | | | | | | | | | (465) mem(all_72_2, e) = 0 % 35.32/5.38 | | | | | | | | | | | % 35.32/5.38 | | | | | | | | | | | GROUND_INST: instantiating (3) with all_72_2, simplifying with % 35.32/5.38 | | | | | | | | | | | (72), (465) gives: % 35.32/5.38 | | | | | | | | | | | (466) $false % 35.32/5.38 | | | | | | | | | | | % 35.32/5.38 | | | | | | | | | | | CLOSE: (466) is inconsistent. % 35.32/5.38 | | | | | | | | | | | % 35.32/5.38 | | | | | | | | | | End of split % 35.32/5.38 | | | | | | | | | | % 35.32/5.38 | | | | | | | | | Case 2: % 35.32/5.38 | | | | | | | | | | % 35.32/5.38 | | | | | | | | | | (467) all_164_1 = 0 % 35.32/5.38 | | | | | | | | | | % 35.32/5.38 | | | | | | | | | | REDUCE: (367), (467) imply: % 35.32/5.38 | | | | | | | | | | (468) mem(all_56_1, e) = 0 % 35.32/5.38 | | | | | | | | | | % 35.32/5.38 | | | | | | | | | | GROUND_INST: instantiating (3) with all_56_1, simplifying with % 35.32/5.38 | | | | | | | | | | (60), (468) gives: % 35.32/5.38 | | | | | | | | | | (469) $false % 35.32/5.38 | | | | | | | | | | % 35.32/5.38 | | | | | | | | | | CLOSE: (469) is inconsistent. % 35.32/5.38 | | | | | | | | | | % 35.32/5.38 | | | | | | | | | End of split % 35.32/5.38 | | | | | | | | | % 35.32/5.38 | | | | | | | | End of split % 35.32/5.38 | | | | | | | | % 35.32/5.38 | | | | | | | Case 2: % 35.32/5.38 | | | | | | | | % 35.32/5.38 | | | | | | | | (470) all_117_1 = 0 % 35.32/5.38 | | | | | | | | (471) ~ (all_117_0 = 0) % 35.32/5.38 | | | | | | | | % 35.32/5.38 | | | | | | | | REDUCE: (101), (470) imply: % 35.32/5.38 | | | | | | | | (472) mem(all_83_1, all_29_3) = 0 % 35.32/5.38 | | | | | | | | % 35.32/5.38 | | | | | | | | BETA: splitting (111) gives: % 35.32/5.38 | | | | | | | | % 35.32/5.38 | | | | | | | | Case 1: % 35.32/5.38 | | | | | | | | | % 35.32/5.38 | | | | | | | | | (473) all_117_0 = 0 % 35.32/5.38 | | | | | | | | | % 35.32/5.38 | | | | | | | | | REDUCE: (471), (473) imply: % 35.32/5.38 | | | | | | | | | (474) $false % 35.32/5.38 | | | | | | | | | % 35.32/5.38 | | | | | | | | | CLOSE: (474) is inconsistent. % 35.32/5.38 | | | | | | | | | % 35.32/5.38 | | | | | | | | Case 2: % 35.32/5.38 | | | | | | | | | % 35.32/5.38 | | | | | | | | | % 35.32/5.38 | | | | | | | | | GROUND_INST: instantiating (5) with all_83_1, e, all_48_0, % 35.32/5.38 | | | | | | | | | all_29_3, simplifying with (13), (46), (48), (82), % 35.32/5.38 | | | | | | | | | (472) gives: % 35.32/5.38 | | | | | | | | | (475) ? [v0: any] : ? [v1: any] : (mem(all_83_1, % 35.32/5.38 | | | | | | | | | all_48_0) = v1 & mem(all_83_1, e) = v0 & (v1 = 0 % 35.32/5.38 | | | | | | | | | | v0 = 0)) % 35.32/5.38 | | | | | | | | | % 35.32/5.38 | | | | | | | | | DELTA: instantiating (475) with fresh symbols all_184_0, % 35.32/5.38 | | | | | | | | | all_184_1 gives: % 35.32/5.38 | | | | | | | | | (476) mem(all_83_1, all_48_0) = all_184_0 & mem(all_83_1, % 35.32/5.38 | | | | | | | | | e) = all_184_1 & (all_184_0 = 0 | all_184_1 = 0) % 35.32/5.38 | | | | | | | | | % 35.32/5.38 | | | | | | | | | ALPHA: (476) implies: % 35.32/5.38 | | | | | | | | | (477) mem(all_83_1, e) = all_184_1 % 35.32/5.38 | | | | | | | | | (478) mem(all_83_1, all_48_0) = all_184_0 % 35.32/5.38 | | | | | | | | | (479) all_184_0 = 0 | all_184_1 = 0 % 35.32/5.38 | | | | | | | | | % 35.32/5.38 | | | | | | | | | BETA: splitting (369) gives: % 35.32/5.38 | | | | | | | | | % 35.32/5.38 | | | | | | | | | Case 1: % 35.32/5.38 | | | | | | | | | | % 35.32/5.38 | | | | | | | | | | (480) all_164_0 = 0 % 35.32/5.38 | | | | | | | | | | % 35.32/5.38 | | | | | | | | | | REDUCE: (368), (480) imply: % 35.32/5.38 | | | | | | | | | | (481) mem(all_56_1, all_48_0) = 0 % 35.32/5.38 | | | | | | | | | | % 35.32/5.38 | | | | | | | | | | GROUND_INST: instantiating (4) with all_56_1, e, all_48_0, % 35.32/5.38 | | | | | | | | | | simplifying with (13), (47), (60), (481) gives: % 35.32/5.38 | | | | | | | | | | (482) all_56_1 = e % 35.32/5.38 | | | | | | | | | | % 35.32/5.38 | | | | | | | | | | REDUCE: (62), (482) imply: % 35.32/5.38 | | | | | | | | | | (483) mem(e, all_37_1) = all_56_0 % 35.32/5.38 | | | | | | | | | | % 35.32/5.38 | | | | | | | | | | BETA: splitting (479) gives: % 35.32/5.38 | | | | | | | | | | % 35.32/5.38 | | | | | | | | | | Case 1: % 35.32/5.38 | | | | | | | | | | | % 35.32/5.38 | | | | | | | | | | | (484) all_184_0 = 0 % 35.32/5.38 | | | | | | | | | | | % 35.32/5.38 | | | | | | | | | | | REDUCE: (478), (484) imply: % 35.32/5.38 | | | | | | | | | | | (485) mem(all_83_1, all_48_0) = 0 % 35.32/5.38 | | | | | | | | | | | % 35.32/5.38 | | | | | | | | | | | GROUND_INST: instantiating (4) with all_83_1, e, all_48_0, % 35.32/5.38 | | | | | | | | | | | simplifying with (13), (47), (82), (485) gives: % 35.32/5.39 | | | | | | | | | | | (486) all_83_1 = e % 35.32/5.39 | | | | | | | | | | | % 35.32/5.39 | | | | | | | | | | | REDUCE: (83), (486) imply: % 35.32/5.39 | | | | | | | | | | | (487) mem(e, all_37_1) = 0 % 35.32/5.39 | | | | | | | | | | | % 35.32/5.39 | | | | | | | | | | | GROUND_INST: instantiating (15) with all_56_0, 0, all_37_1, e, % 35.32/5.39 | | | | | | | | | | | simplifying with (483), (487) gives: % 35.32/5.39 | | | | | | | | | | | (488) all_56_0 = 0 % 35.32/5.39 | | | | | | | | | | | % 35.32/5.39 | | | | | | | | | | | REDUCE: (59), (488) imply: % 35.32/5.39 | | | | | | | | | | | (489) $false % 35.32/5.39 | | | | | | | | | | | % 35.32/5.39 | | | | | | | | | | | CLOSE: (489) is inconsistent. % 35.32/5.39 | | | | | | | | | | | % 35.32/5.39 | | | | | | | | | | Case 2: % 35.32/5.39 | | | | | | | | | | | % 35.32/5.39 | | | | | | | | | | | (490) all_184_1 = 0 % 35.32/5.39 | | | | | | | | | | | % 35.32/5.39 | | | | | | | | | | | REDUCE: (477), (490) imply: % 35.32/5.39 | | | | | | | | | | | (491) mem(all_83_1, e) = 0 % 35.32/5.39 | | | | | | | | | | | % 35.32/5.39 | | | | | | | | | | | GROUND_INST: instantiating (3) with all_83_1, simplifying with % 35.32/5.39 | | | | | | | | | | | (82), (491) gives: % 35.32/5.39 | | | | | | | | | | | (492) $false % 35.32/5.39 | | | | | | | | | | | % 35.32/5.39 | | | | | | | | | | | CLOSE: (492) is inconsistent. % 35.32/5.39 | | | | | | | | | | | % 35.32/5.39 | | | | | | | | | | End of split % 35.32/5.39 | | | | | | | | | | % 35.32/5.39 | | | | | | | | | Case 2: % 35.32/5.39 | | | | | | | | | | % 35.32/5.39 | | | | | | | | | | (493) all_164_1 = 0 % 35.32/5.39 | | | | | | | | | | % 35.32/5.39 | | | | | | | | | | REDUCE: (367), (493) imply: % 35.32/5.39 | | | | | | | | | | (494) mem(all_56_1, e) = 0 % 35.32/5.39 | | | | | | | | | | % 35.32/5.39 | | | | | | | | | | GROUND_INST: instantiating (3) with all_56_1, simplifying with % 35.32/5.39 | | | | | | | | | | (60), (494) gives: % 35.32/5.39 | | | | | | | | | | (495) $false % 35.32/5.39 | | | | | | | | | | % 35.32/5.39 | | | | | | | | | | CLOSE: (495) is inconsistent. % 35.32/5.39 | | | | | | | | | | % 35.32/5.39 | | | | | | | | | End of split % 35.32/5.39 | | | | | | | | | % 35.32/5.39 | | | | | | | | End of split % 35.32/5.39 | | | | | | | | % 35.32/5.39 | | | | | | | End of split % 35.32/5.39 | | | | | | | % 35.32/5.39 | | | | | | End of split % 35.32/5.39 | | | | | | % 35.32/5.39 | | | | | End of split % 35.32/5.39 | | | | | % 35.32/5.39 | | | | End of split % 35.32/5.39 | | | | % 35.32/5.39 | | | End of split % 35.32/5.39 | | | % 35.32/5.39 | | End of split % 35.32/5.39 | | % 35.32/5.39 | End of split % 35.32/5.39 | % 35.32/5.39 End of proof % 35.32/5.39 % 35.32/5.39 Sub-proof #1 shows that the following formulas are inconsistent: % 35.32/5.39 ---------------------------------------------------------------- % 35.32/5.39 (1) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 35.32/5.39 ! [v3: $i] : (v1 = v0 | ~ (mem(v3, v2) = v1) | ~ (mem(v3, v2) = v0)) % 35.32/5.39 (2) mem(e, all_37_1) = all_56_0 % 35.32/5.39 (3) mem(e, all_37_1) = 0 % 35.32/5.39 (4) ~ (all_56_0 = 0) % 35.32/5.39 % 35.32/5.39 Begin of proof % 35.32/5.39 | % 35.32/5.39 | GROUND_INST: instantiating (1) with all_56_0, 0, all_37_1, e, simplifying with % 35.32/5.39 | (2), (3) gives: % 35.32/5.39 | (5) all_56_0 = 0 % 35.32/5.39 | % 35.32/5.39 | REDUCE: (4), (5) imply: % 35.32/5.39 | (6) $false % 35.32/5.39 | % 35.32/5.39 | CLOSE: (6) is inconsistent. % 35.32/5.39 | % 35.32/5.39 End of proof % 35.32/5.39 % 35.32/5.39 Sub-proof #2 shows that the following formulas are inconsistent: % 35.32/5.39 ---------------------------------------------------------------- % 35.32/5.39 (1) s(all_29_2) = all_46_0 % 35.32/5.39 (2) mem(all_109_1, all_46_0) = 0 % 35.32/5.39 (3) ~ (all_137_0 = 0) % 35.32/5.39 (4) $i(all_109_1) % 35.32/5.39 (5) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 35.32/5.39 ! [v3: $i] : (v1 = v0 | ~ (mem(v3, v2) = v1) | ~ (mem(v3, v2) = v0)) % 35.32/5.39 (6) mem(all_137_1, all_29_2) = all_137_0 % 35.32/5.39 (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (s(v1) = v2) | ~ % 35.32/5.39 (mem(v0, v2) = 0) | ~ $i(v1) | ~ $i(v0)) % 35.32/5.39 (8) $i(all_29_2) % 35.32/5.39 (9) mem(all_137_1, all_109_1) = 0 % 35.32/5.39 % 35.32/5.39 Begin of proof % 35.32/5.39 | % 35.32/5.39 | GROUND_INST: instantiating (7) with all_109_1, all_29_2, all_46_0, simplifying % 35.32/5.39 | with (1), (2), (4), (8) gives: % 35.32/5.39 | (10) all_109_1 = all_29_2 % 35.32/5.39 | % 35.32/5.39 | REDUCE: (9), (10) imply: % 35.32/5.39 | (11) mem(all_137_1, all_29_2) = 0 % 35.32/5.39 | % 35.32/5.39 | GROUND_INST: instantiating (5) with all_137_0, 0, all_29_2, all_137_1, % 35.32/5.39 | simplifying with (6), (11) gives: % 35.32/5.39 | (12) all_137_0 = 0 % 35.32/5.39 | % 35.32/5.39 | REDUCE: (3), (12) imply: % 35.32/5.39 | (13) $false % 35.32/5.39 | % 35.32/5.39 | CLOSE: (13) is inconsistent. % 35.32/5.39 | % 35.32/5.39 End of proof % 35.32/5.39 % 35.32/5.39 Sub-proof #3 shows that the following formulas are inconsistent: % 35.32/5.39 ---------------------------------------------------------------- % 35.32/5.39 (1) mem(all_137_1, all_29_3) = all_137_0 % 35.32/5.39 (2) s(all_29_3) = all_29_2 % 35.32/5.39 (3) all_137_0 = 0 | ? [v0: int] : ? [v1: int] : ( ~ (v1 = 0) & ~ (v0 = 0) % 35.32/5.39 & mem(all_137_1, all_48_0) = v1 & mem(all_137_1, e) = v0) % 35.32/5.39 (4) $i(all_29_3) % 35.32/5.39 (5) ~ (all_137_0 = 0) % 35.32/5.39 (6) $i(all_109_1) % 35.32/5.39 (7) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 35.32/5.39 ! [v3: $i] : (v1 = v0 | ~ (mem(v3, v2) = v1) | ~ (mem(v3, v2) = v0)) % 35.32/5.39 (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (s(v1) = v2) | ~ % 35.32/5.39 (mem(v0, v2) = 0) | ~ $i(v1) | ~ $i(v0)) % 35.32/5.39 (9) mem(all_109_1, all_29_2) = 0 % 35.32/5.39 (10) mem(all_137_1, all_109_1) = 0 % 35.32/5.39 % 35.32/5.39 Begin of proof % 35.32/5.39 | % 35.32/5.39 | BETA: splitting (3) gives: % 35.32/5.39 | % 35.32/5.39 | Case 1: % 35.32/5.39 | | % 35.32/5.39 | | (11) all_137_0 = 0 % 35.32/5.39 | | % 35.32/5.39 | | REDUCE: (5), (11) imply: % 35.32/5.39 | | (12) $false % 35.32/5.39 | | % 35.32/5.39 | | CLOSE: (12) is inconsistent. % 35.32/5.39 | | % 35.32/5.39 | Case 2: % 35.32/5.39 | | % 35.32/5.39 | | % 35.32/5.39 | | GROUND_INST: instantiating (8) with all_109_1, all_29_3, all_29_2, % 35.32/5.39 | | simplifying with (2), (4), (6), (9) gives: % 35.32/5.39 | | (13) all_109_1 = all_29_3 % 35.32/5.39 | | % 35.32/5.39 | | REDUCE: (10), (13) imply: % 35.32/5.39 | | (14) mem(all_137_1, all_29_3) = 0 % 35.32/5.39 | | % 35.32/5.39 | | GROUND_INST: instantiating (7) with all_137_0, 0, all_29_3, all_137_1, % 35.32/5.39 | | simplifying with (1), (14) gives: % 35.32/5.39 | | (15) all_137_0 = 0 % 35.32/5.39 | | % 35.32/5.39 | | REDUCE: (5), (15) imply: % 35.32/5.39 | | (16) $false % 35.32/5.39 | | % 35.32/5.39 | | CLOSE: (16) is inconsistent. % 35.32/5.39 | | % 35.32/5.39 | End of split % 35.32/5.39 | % 35.32/5.39 End of proof % 35.32/5.39 % 35.32/5.39 Sub-proof #4 shows that the following formulas are inconsistent: % 35.32/5.39 ---------------------------------------------------------------- % 35.32/5.39 (1) s(all_29_3) = all_29_2 % 35.32/5.39 (2) $i(all_29_3) % 35.32/5.39 (3) $i(all_109_1) % 35.32/5.39 (4) ~ (all_56_0 = 0) % 35.32/5.39 (5) mem(all_29_3, all_37_1) = all_56_0 % 35.32/5.39 (6) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 35.32/5.39 ! [v3: $i] : (v1 = v0 | ~ (mem(v3, v2) = v1) | ~ (mem(v3, v2) = v0)) % 35.32/5.39 (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (s(v1) = v2) | ~ % 35.32/5.39 (mem(v0, v2) = 0) | ~ $i(v1) | ~ $i(v0)) % 35.32/5.39 (8) mem(all_109_1, all_29_2) = 0 % 35.32/5.39 (9) mem(all_109_1, all_37_1) = 0 % 35.32/5.39 % 35.32/5.39 Begin of proof % 35.32/5.39 | % 35.32/5.39 | GROUND_INST: instantiating (7) with all_109_1, all_29_3, all_29_2, simplifying % 35.32/5.39 | with (1), (2), (3), (8) gives: % 35.32/5.39 | (10) all_109_1 = all_29_3 % 35.32/5.39 | % 35.32/5.39 | REDUCE: (9), (10) imply: % 35.32/5.39 | (11) mem(all_29_3, all_37_1) = 0 % 35.32/5.39 | % 35.32/5.39 | GROUND_INST: instantiating (6) with all_56_0, 0, all_37_1, all_29_3, % 35.32/5.39 | simplifying with (5), (11) gives: % 35.32/5.39 | (12) all_56_0 = 0 % 35.32/5.39 | % 35.32/5.39 | REDUCE: (4), (12) imply: % 35.32/5.39 | (13) $false % 35.32/5.39 | % 35.32/5.39 | CLOSE: (13) is inconsistent. % 35.32/5.39 | % 35.32/5.39 End of proof % 35.32/5.39 % 35.32/5.39 Sub-proof #5 shows that the following formulas are inconsistent: % 35.32/5.39 ---------------------------------------------------------------- % 35.32/5.39 (1) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 35.32/5.39 ! [v3: $i] : (v1 = v0 | ~ (mem(v3, v2) = v1) | ~ (mem(v3, v2) = v0)) % 35.32/5.39 (2) mem(all_29_2, all_50_1) = all_83_0 % 35.32/5.39 (3) mem(all_29_2, all_50_1) = 0 % 35.32/5.39 (4) ~ (all_83_0 = 0) % 35.32/5.39 % 35.32/5.39 Begin of proof % 35.32/5.39 | % 35.32/5.39 | GROUND_INST: instantiating (1) with all_83_0, 0, all_50_1, all_29_2, % 35.32/5.39 | simplifying with (2), (3) gives: % 35.32/5.39 | (5) all_83_0 = 0 % 35.32/5.39 | % 35.32/5.39 | REDUCE: (4), (5) imply: % 35.32/5.39 | (6) $false % 35.32/5.39 | % 35.32/5.39 | CLOSE: (6) is inconsistent. % 35.32/5.39 | % 35.32/5.39 End of proof % 35.32/5.39 % 35.32/5.39 Sub-proof #6 shows that the following formulas are inconsistent: % 35.32/5.39 ---------------------------------------------------------------- % 35.32/5.39 (1) mem(all_109_1, all_50_1) = 0 % 35.32/5.39 (2) s(all_29_3) = all_29_2 % 35.32/5.39 (3) $i(all_29_3) % 35.32/5.39 (4) $i(all_109_1) % 35.32/5.39 (5) mem(all_29_3, all_50_1) = all_83_0 % 35.32/5.39 (6) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 35.32/5.39 ! [v3: $i] : (v1 = v0 | ~ (mem(v3, v2) = v1) | ~ (mem(v3, v2) = v0)) % 35.32/5.39 (7) ~ (all_83_0 = 0) % 35.32/5.39 (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (s(v1) = v2) | ~ % 35.32/5.39 (mem(v0, v2) = 0) | ~ $i(v1) | ~ $i(v0)) % 35.32/5.39 (9) mem(all_109_1, all_29_2) = 0 % 35.32/5.39 % 35.32/5.39 Begin of proof % 35.32/5.39 | % 35.32/5.39 | GROUND_INST: instantiating (8) with all_109_1, all_29_3, all_29_2, simplifying % 35.32/5.39 | with (2), (3), (4), (9) gives: % 35.32/5.39 | (10) all_109_1 = all_29_3 % 35.32/5.39 | % 35.32/5.39 | REDUCE: (1), (10) imply: % 35.32/5.39 | (11) mem(all_29_3, all_50_1) = 0 % 35.32/5.39 | % 35.32/5.39 | GROUND_INST: instantiating (6) with all_83_0, 0, all_50_1, all_29_3, % 35.32/5.39 | simplifying with (5), (11) gives: % 35.32/5.39 | (12) all_83_0 = 0 % 35.32/5.39 | % 35.32/5.39 | REDUCE: (7), (12) imply: % 35.32/5.39 | (13) $false % 35.32/5.39 | % 35.32/5.39 | CLOSE: (13) is inconsistent. % 35.32/5.39 | % 35.32/5.39 End of proof % 35.32/5.39 % 35.32/5.39 Sub-proof #7 shows that the following formulas are inconsistent: % 35.32/5.39 ---------------------------------------------------------------- % 35.32/5.39 (1) $i(all_83_1) % 35.32/5.39 (2) s(all_29_3) = all_29_2 % 35.32/5.39 (3) mem(all_83_1, all_37_1) = 0 % 35.32/5.39 (4) $i(all_29_3) % 35.32/5.39 (5) ~ (all_56_0 = 0) % 35.32/5.39 (6) mem(all_83_1, all_29_2) = 0 % 35.32/5.39 (7) mem(all_29_3, all_37_1) = all_56_0 % 35.32/5.40 (8) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 35.32/5.40 ! [v3: $i] : (v1 = v0 | ~ (mem(v3, v2) = v1) | ~ (mem(v3, v2) = v0)) % 35.32/5.40 (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (s(v1) = v2) | ~ % 35.32/5.40 (mem(v0, v2) = 0) | ~ $i(v1) | ~ $i(v0)) % 35.32/5.40 % 35.32/5.40 Begin of proof % 35.32/5.40 | % 35.32/5.40 | GROUND_INST: instantiating (9) with all_83_1, all_29_3, all_29_2, simplifying % 35.32/5.40 | with (1), (2), (4), (6) gives: % 35.32/5.40 | (10) all_83_1 = all_29_3 % 35.32/5.40 | % 35.32/5.40 | REDUCE: (3), (10) imply: % 35.32/5.40 | (11) mem(all_29_3, all_37_1) = 0 % 35.32/5.40 | % 35.32/5.40 | GROUND_INST: instantiating (8) with all_56_0, 0, all_37_1, all_29_3, % 35.32/5.40 | simplifying with (7), (11) gives: % 35.32/5.40 | (12) all_56_0 = 0 % 35.32/5.40 | % 35.32/5.40 | REDUCE: (5), (12) imply: % 35.32/5.40 | (13) $false % 35.32/5.40 | % 35.32/5.40 | CLOSE: (13) is inconsistent. % 35.32/5.40 | % 35.32/5.40 End of proof % 35.32/5.40 % 35.32/5.40 Sub-proof #8 shows that the following formulas are inconsistent: % 35.32/5.40 ---------------------------------------------------------------- % 35.32/5.40 (1) mem(all_72_2, all_37_1) = 0 % 35.32/5.40 (2) s(all_29_3) = all_29_2 % 35.32/5.40 (3) mem(all_72_2, all_29_2) = 0 % 35.32/5.40 (4) $i(all_72_2) % 35.32/5.40 (5) $i(all_29_3) % 35.32/5.40 (6) ~ (all_56_0 = 0) % 35.32/5.40 (7) mem(all_29_3, all_37_1) = all_56_0 % 35.32/5.40 (8) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 35.32/5.40 ! [v3: $i] : (v1 = v0 | ~ (mem(v3, v2) = v1) | ~ (mem(v3, v2) = v0)) % 35.32/5.40 (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (s(v1) = v2) | ~ % 35.32/5.40 (mem(v0, v2) = 0) | ~ $i(v1) | ~ $i(v0)) % 35.32/5.40 % 35.32/5.40 Begin of proof % 35.32/5.40 | % 35.32/5.40 | GROUND_INST: instantiating (9) with all_72_2, all_29_3, all_29_2, simplifying % 35.32/5.40 | with (2), (3), (4), (5) gives: % 35.32/5.40 | (10) all_72_2 = all_29_3 % 35.32/5.40 | % 35.32/5.40 | REDUCE: (1), (10) imply: % 35.32/5.40 | (11) mem(all_29_3, all_37_1) = 0 % 35.32/5.40 | % 35.32/5.40 | GROUND_INST: instantiating (8) with all_56_0, 0, all_37_1, all_29_3, % 35.32/5.40 | simplifying with (7), (11) gives: % 35.32/5.40 | (12) all_56_0 = 0 % 35.32/5.40 | % 35.32/5.40 | REDUCE: (6), (12) imply: % 35.32/5.40 | (13) $false % 35.32/5.40 | % 35.32/5.40 | CLOSE: (13) is inconsistent. % 35.32/5.40 | % 35.32/5.40 End of proof % 35.32/5.40 % 35.32/5.40 Sub-proof #9 shows that the following formulas are inconsistent: % 35.32/5.40 ---------------------------------------------------------------- % 35.32/5.40 (1) mem(all_72_2, all_50_1) = 0 % 35.32/5.40 (2) s(all_29_2) = all_46_0 % 35.32/5.40 (3) mem(all_72_2, all_46_0) = 0 % 35.32/5.40 (4) $i(all_72_2) % 35.32/5.40 (5) mem(all_29_2, all_50_1) = all_83_0 % 35.32/5.40 (6) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 35.32/5.40 ! [v3: $i] : (v1 = v0 | ~ (mem(v3, v2) = v1) | ~ (mem(v3, v2) = v0)) % 35.32/5.40 (7) ~ (all_83_0 = 0) % 35.32/5.40 (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (s(v1) = v2) | ~ % 35.32/5.40 (mem(v0, v2) = 0) | ~ $i(v1) | ~ $i(v0)) % 35.32/5.40 (9) $i(all_29_2) % 35.32/5.40 % 35.32/5.40 Begin of proof % 35.32/5.40 | % 35.32/5.40 | GROUND_INST: instantiating (8) with all_72_2, all_29_2, all_46_0, simplifying % 35.32/5.40 | with (2), (3), (4), (9) gives: % 35.32/5.40 | (10) all_72_2 = all_29_2 % 35.32/5.40 | % 35.32/5.40 | REDUCE: (1), (10) imply: % 35.32/5.40 | (11) mem(all_29_2, all_50_1) = 0 % 35.32/5.40 | % 35.32/5.40 | GROUND_INST: instantiating (6) with all_83_0, 0, all_50_1, all_29_2, % 35.32/5.40 | simplifying with (5), (11) gives: % 35.32/5.40 | (12) all_83_0 = 0 % 35.32/5.40 | % 35.32/5.40 | REDUCE: (7), (12) imply: % 35.32/5.40 | (13) $false % 35.32/5.40 | % 35.32/5.40 | CLOSE: (13) is inconsistent. % 35.32/5.40 | % 35.32/5.40 End of proof % 35.32/5.40 % 35.32/5.40 Sub-proof #10 shows that the following formulas are inconsistent: % 35.32/5.40 ---------------------------------------------------------------- % 35.32/5.40 (1) mem(all_72_2, all_50_1) = 0 % 35.32/5.40 (2) s(all_29_3) = all_29_2 % 35.32/5.40 (3) mem(all_72_2, all_29_2) = 0 % 35.32/5.40 (4) $i(all_72_2) % 35.32/5.40 (5) $i(all_29_3) % 35.32/5.40 (6) mem(all_29_3, all_50_1) = all_83_0 % 35.32/5.40 (7) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 35.32/5.40 ! [v3: $i] : (v1 = v0 | ~ (mem(v3, v2) = v1) | ~ (mem(v3, v2) = v0)) % 35.32/5.40 (8) ~ (all_83_0 = 0) % 35.32/5.40 (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (s(v1) = v2) | ~ % 35.32/5.40 (mem(v0, v2) = 0) | ~ $i(v1) | ~ $i(v0)) % 35.32/5.40 % 35.32/5.40 Begin of proof % 35.32/5.40 | % 35.32/5.40 | GROUND_INST: instantiating (9) with all_72_2, all_29_3, all_29_2, simplifying % 35.32/5.40 | with (2), (3), (4), (5) gives: % 35.32/5.40 | (10) all_72_2 = all_29_3 % 35.32/5.40 | % 35.32/5.40 | REDUCE: (1), (10) imply: % 35.32/5.40 | (11) mem(all_29_3, all_50_1) = 0 % 35.32/5.40 | % 35.32/5.40 | GROUND_INST: instantiating (7) with all_83_0, 0, all_50_1, all_29_3, % 35.32/5.40 | simplifying with (6), (11) gives: % 35.32/5.40 | (12) all_83_0 = 0 % 35.32/5.40 | % 35.32/5.40 | REDUCE: (8), (12) imply: % 35.32/5.40 | (13) $false % 35.32/5.40 | % 35.32/5.40 | CLOSE: (13) is inconsistent. % 35.32/5.40 | % 35.32/5.40 End of proof % 35.32/5.40 % 35.32/5.40 Sub-proof #11 shows that the following formulas are inconsistent: % 35.32/5.40 ---------------------------------------------------------------- % 35.32/5.40 (1) s(all_29_2) = all_46_0 % 35.32/5.40 (2) mem(all_72_2, all_46_0) = 0 % 35.32/5.40 (3) mem(all_72_2, all_37_1) = 0 % 35.32/5.40 (4) $i(all_72_2) % 35.32/5.40 (5) ~ (all_56_0 = 0) % 35.32/5.40 (6) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 35.32/5.40 ! [v3: $i] : (v1 = v0 | ~ (mem(v3, v2) = v1) | ~ (mem(v3, v2) = v0)) % 35.32/5.40 (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (s(v1) = v2) | ~ % 35.32/5.40 (mem(v0, v2) = 0) | ~ $i(v1) | ~ $i(v0)) % 35.32/5.40 (8) $i(all_29_2) % 35.32/5.40 (9) mem(all_29_2, all_37_1) = all_56_0 % 35.32/5.40 % 35.32/5.40 Begin of proof % 35.32/5.40 | % 35.32/5.40 | GROUND_INST: instantiating (7) with all_72_2, all_29_2, all_46_0, simplifying % 35.32/5.40 | with (1), (2), (4), (8) gives: % 35.32/5.40 | (10) all_72_2 = all_29_2 % 35.32/5.40 | % 35.32/5.40 | REDUCE: (3), (10) imply: % 35.32/5.40 | (11) mem(all_29_2, all_37_1) = 0 % 35.32/5.40 | % 35.32/5.40 | GROUND_INST: instantiating (6) with all_56_0, 0, all_37_1, all_29_2, % 35.32/5.40 | simplifying with (9), (11) gives: % 35.32/5.40 | (12) all_56_0 = 0 % 35.32/5.40 | % 35.32/5.40 | REDUCE: (5), (12) imply: % 35.32/5.40 | (13) $false % 35.32/5.40 | % 35.32/5.40 | CLOSE: (13) is inconsistent. % 35.32/5.40 | % 35.32/5.40 End of proof % 35.32/5.40 % 35.32/5.40 Sub-proof #12 shows that the following formulas are inconsistent: % 35.32/5.40 ---------------------------------------------------------------- % 35.32/5.40 (1) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 35.32/5.40 ! [v3: $i] : (v1 = v0 | ~ (mem(v3, v2) = v1) | ~ (mem(v3, v2) = v0)) % 35.32/5.40 (2) mem(all_29_2, all_37_1) = all_56_0 % 35.32/5.40 (3) mem(all_29_2, all_37_1) = 0 % 35.32/5.40 (4) ~ (all_56_0 = 0) % 35.32/5.40 % 35.32/5.40 Begin of proof % 35.32/5.40 | % 35.32/5.40 | GROUND_INST: instantiating (1) with all_56_0, 0, all_37_1, all_29_2, % 35.32/5.40 | simplifying with (2), (3) gives: % 35.32/5.40 | (5) all_56_0 = 0 % 35.32/5.40 | % 35.32/5.40 | REDUCE: (4), (5) imply: % 35.32/5.40 | (6) $false % 35.32/5.40 | % 35.32/5.40 | CLOSE: (6) is inconsistent. % 35.32/5.40 | % 35.32/5.40 End of proof % 35.32/5.40 % SZS output end Proof for theBenchmark % 35.32/5.40 % 35.32/5.40 4811ms %------------------------------------------------------------------------------