%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SEV551+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 : n009.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 13.17s 2.51s % Output : Proof 16.31s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : SEV551+1 : TPTP v9.1.0. Released v9.1.0. % 0.03/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.34 % Computer : n009.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 300 % 0.13/0.34 % DateTime : Mon Mar 31 11:52:58 EDT 2025 % 0.13/0.34 % CPUTime : % 0.58/0.60 ________ _____ % 0.58/0.60 ___ __ \_________(_)________________________________ % 0.58/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.58/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.58/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.58/0.60 % 0.58/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.58/0.60 (2023-06-19) % 0.58/0.60 % 0.58/0.60 (c) Philipp Rümmer, 2009-2023 % 0.58/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.58/0.60 Amanda Stjerna. % 0.58/0.60 Free software under BSD-3-Clause. % 0.58/0.60 % 0.58/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.58/0.60 % 0.58/0.60 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.58/0.61 Running up to 7 provers in parallel. % 0.58/0.62 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.58/0.62 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.58/0.62 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.58/0.62 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.58/0.62 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.58/0.62 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.58/0.62 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.63/1.07 Prover 1: Preprocessing ... % 3.02/1.09 Prover 4: Preprocessing ... % 3.02/1.12 Prover 0: Preprocessing ... % 3.02/1.12 Prover 2: Preprocessing ... % 3.02/1.12 Prover 3: Preprocessing ... % 3.02/1.12 Prover 5: Preprocessing ... % 3.02/1.14 Prover 6: Preprocessing ... % 6.50/1.60 Prover 5: Proving ... % 7.05/1.62 Prover 2: Proving ... % 7.48/1.72 Prover 6: Proving ... % 7.48/1.73 Prover 3: Constructing countermodel ... % 7.48/1.73 Prover 1: Constructing countermodel ... % 8.31/1.79 Prover 4: Constructing countermodel ... % 8.31/1.80 Prover 0: Proving ... % 9.17/1.95 Prover 3: gave up % 9.64/1.98 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 9.64/2.00 Prover 1: gave up % 9.64/2.02 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 9.64/2.05 Prover 8: Preprocessing ... % 9.64/2.06 Prover 7: Preprocessing ... % 10.93/2.17 Prover 7: Warning: ignoring some quantifiers % 10.93/2.18 Prover 7: Constructing countermodel ... % 12.00/2.31 Prover 8: Warning: ignoring some quantifiers % 12.00/2.33 Prover 8: Constructing countermodel ... % 13.17/2.51 Prover 0: proved (1890ms) % 13.17/2.51 % 13.17/2.51 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 13.17/2.51 % 13.17/2.51 Prover 6: stopped % 13.17/2.51 Prover 2: stopped % 13.81/2.52 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 13.81/2.52 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 13.81/2.52 Prover 8: gave up % 13.81/2.52 Prover 5: stopped % 13.81/2.55 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 13.81/2.55 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 13.81/2.55 Prover 10: Preprocessing ... % 13.81/2.55 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085 % 13.81/2.57 Prover 16: Preprocessing ... % 14.28/2.58 Prover 11: Preprocessing ... % 14.28/2.59 Prover 19: Preprocessing ... % 14.28/2.60 Prover 13: Preprocessing ... % 14.28/2.62 Prover 4: Found proof (size 172) % 14.28/2.62 Prover 4: proved (2002ms) % 14.28/2.62 Prover 7: stopped % 14.28/2.63 Prover 13: stopped % 14.28/2.64 Prover 10: Warning: ignoring some quantifiers % 14.28/2.65 Prover 16: stopped % 14.28/2.65 Prover 10: Constructing countermodel ... % 14.28/2.65 Prover 11: stopped % 14.28/2.66 Prover 10: stopped % 15.24/2.81 Prover 19: Warning: ignoring some quantifiers % 15.61/2.82 Prover 19: Constructing countermodel ... % 15.61/2.83 Prover 19: stopped % 15.61/2.84 % 15.61/2.84 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 15.61/2.84 % 15.61/2.87 % SZS output start Proof for theBenchmark % 15.61/2.87 Assumptions after simplification: % 15.61/2.87 --------------------------------- % 15.61/2.87 % 15.61/2.87 (a_def) % 15.87/2.91 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (u(v0, v2) = v3) | % 15.87/2.91 ~ (s(v1) = v2) | ~ $i(v1) | ~ $i(v0) | (a(v0, v1) = v3 & $i(v3))) & ! % 15.87/2.91 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (a(v0, v1) = v2) | ~ $i(v1) | ~ % 15.87/2.91 $i(v0) | ? [v3: $i] : (u(v0, v3) = v2 & s(v1) = v3 & $i(v3) & $i(v2))) % 15.87/2.91 % 15.87/2.91 (atleast2p_def) % 15.87/2.91 ! [v0: $i] : ! [v1: int] : ! [v2: $i] : ! [v3: $i] : (v1 = 0 | ~ % 15.87/2.91 (atleast2p(v0) = v1) | ~ (p(v2) = v3) | ~ $i(v2) | ~ $i(v0) | ? [v4: % 15.87/2.91 any] : ? [v5: any] : (subq(v0, v3) = v5 & mem(v2, v0) = v4 & ( ~ (v4 = 0) % 15.87/2.91 | v5 = 0))) & ! [v0: $i] : ! [v1: int] : ! [v2: $i] : (v1 = 0 | ~ % 15.87/2.91 (atleast2p(v0) = v1) | ~ (mem(v2, v0) = 0) | ~ $i(v2) | ~ $i(v0) | ? % 15.87/2.91 [v3: $i] : (p(v2) = v3 & subq(v0, v3) = 0 & $i(v3))) & ! [v0: $i] : ( ~ % 15.87/2.91 (atleast2p(v0) = 0) | ~ $i(v0) | ? [v1: $i] : ? [v2: $i] : ? [v3: int] : % 15.87/2.91 ( ~ (v3 = 0) & p(v1) = v2 & subq(v0, v2) = v3 & mem(v1, v0) = 0 & $i(v2) & % 15.87/2.91 $i(v1))) % 15.87/2.91 % 15.87/2.91 (atleast3p_def) % 15.87/2.91 ! [v0: $i] : ! [v1: int] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | v1 = 0 | % 15.87/2.91 ~ (atleast3p(v0) = v1) | ~ (subq(v0, v2) = v3) | ~ $i(v2) | ~ $i(v0) | ? % 15.87/2.91 [v4: any] : ? [v5: any] : (atleast2p(v2) = v5 & subq(v2, v0) = v4 & ( ~ (v5 % 15.87/2.91 = 0) | ~ (v4 = 0)))) & ! [v0: $i] : ! [v1: int] : ! [v2: $i] : (v1 % 15.87/2.91 = 0 | ~ (atleast3p(v0) = v1) | ~ (atleast2p(v2) = 0) | ~ $i(v2) | ~ % 15.87/2.91 $i(v0) | ? [v3: any] : ? [v4: any] : (subq(v2, v0) = v3 & subq(v0, v2) = % 15.87/2.91 v4 & ( ~ (v3 = 0) | v4 = 0))) & ! [v0: $i] : ! [v1: int] : ! [v2: $i] : % 15.87/2.92 (v1 = 0 | ~ (atleast3p(v0) = v1) | ~ (subq(v2, v0) = 0) | ~ $i(v2) | ~ % 15.87/2.92 $i(v0) | ? [v3: any] : ? [v4: any] : (atleast2p(v2) = v3 & subq(v0, v2) = % 15.87/2.92 v4 & ( ~ (v3 = 0) | v4 = 0))) & ! [v0: $i] : ( ~ (atleast3p(v0) = 0) | ~ % 15.87/2.92 $i(v0) | ? [v1: $i] : ? [v2: int] : ( ~ (v2 = 0) & atleast2p(v1) = 0 & % 15.87/2.92 subq(v1, v0) = 0 & subq(v0, v1) = v2 & $i(v1))) % 15.87/2.92 % 15.87/2.92 (atmost2_2560) % 15.87/2.92 $i(e) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 15.87/2.92 ? [v5: $i] : (atleast3p(v5) = 0 & n(v1) = v4 & n(v0) = v1 & n(e) = v0 & a(v3, % 15.87/2.92 v4) = v5 & a(v0, v1) = v2 & s(v2) = v3 & $i(v5) & $i(v4) & $i(v3) & $i(v2) % 15.87/2.92 & $i(v1) & $i(v0)) % 15.87/2.92 % 15.87/2.92 (n_def) % 15.87/2.92 ! [v0: $i] : ! [v1: $i] : ( ~ (n(v0) = v1) | ~ $i(v0) | (a(v0, v0) = v1 & % 15.87/2.92 $i(v1))) & ! [v0: $i] : ! [v1: $i] : ( ~ (a(v0, v0) = v1) | ~ $i(v0) | % 15.87/2.92 (n(v0) = v1 & $i(v1))) % 15.87/2.92 % 15.87/2.92 (p_ax) % 15.87/2.92 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (p(v1) = % 15.87/2.92 v2) | ~ (mem(v0, v2) = v3) | ~ $i(v1) | ~ $i(v0) | ? [v4: int] : ( ~ % 15.87/2.92 (v4 = 0) & subq(v0, v1) = v4)) & ! [v0: $i] : ! [v1: $i] : ! [v2: int] % 15.87/2.92 : (v2 = 0 | ~ (subq(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? % 15.87/2.92 [v4: int] : ( ~ (v4 = 0) & p(v1) = v3 & mem(v0, v3) = v4 & $i(v3))) & ! % 15.87/2.92 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (p(v1) = v2) | ~ (mem(v0, v2) = 0) % 15.87/2.92 | ~ $i(v1) | ~ $i(v0) | subq(v0, v1) = 0) & ! [v0: $i] : ! [v1: $i] : ( % 15.87/2.92 ~ (subq(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: $i] : (p(v1) = v2 & % 15.87/2.92 mem(v0, v2) = 0 & $i(v2))) % 15.87/2.92 % 15.87/2.92 (s_ax) % 15.87/2.92 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (s(v0) = v1) | ~ % 15.87/2.92 (mem(v0, v1) = v2) | ~ $i(v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 15.87/2.92 (v1 = v0 | ~ (s(v1) = v2) | ~ (mem(v0, v2) = 0) | ~ $i(v1) | ~ $i(v0)) % 15.87/2.92 % 15.87/2.92 (subq_def) % 15.87/2.92 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 15.87/2.92 (subq(v0, v1) = 0) | ~ (mem(v2, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ % 15.87/2.92 $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & mem(v2, v0) = v4)) & ! [v0: $i] : ! % 15.87/2.92 [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subq(v0, v1) = v2) | ~ $i(v1) | ~ % 15.87/2.92 $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & mem(v3, v1) = v4 & % 15.87/2.92 mem(v3, v0) = 0 & $i(v3))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 15.87/2.92 (subq(v0, v1) = 0) | ~ (mem(v2, v0) = 0) | ~ $i(v2) | ~ $i(v1) | ~ % 15.87/2.92 $i(v0) | mem(v2, v1) = 0) % 15.87/2.92 % 15.87/2.92 (u_ax) % 15.87/2.92 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0 % 15.87/2.92 | ~ (u(v1, v2) = v3) | ~ (mem(v0, v3) = v4) | ~ $i(v2) | ~ $i(v1) | ~ % 15.87/2.92 $i(v0) | ? [v5: int] : ? [v6: int] : ( ~ (v6 = 0) & ~ (v5 = 0) & mem(v0, % 15.87/2.92 v2) = v6 & mem(v0, v1) = v5)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 15.87/2.92 : ! [v3: $i] : ( ~ (u(v1, v2) = v3) | ~ (mem(v0, v3) = 0) | ~ $i(v2) | ~ % 15.87/2.92 $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] : (mem(v0, v2) = v5 & % 15.87/2.92 mem(v0, v1) = v4 & (v5 = 0 | v4 = 0))) % 15.87/2.92 % 15.87/2.93 (function-axioms) % 15.87/2.93 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (a(v3, % 15.87/2.93 v2) = v1) | ~ (a(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 15.87/2.93 $i] : ! [v3: $i] : (v1 = v0 | ~ (m(v3, v2) = v1) | ~ (m(v3, v2) = v0)) & % 15.87/2.93 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (u(v3, % 15.87/2.93 v2) = v1) | ~ (u(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 15.87/2.93 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (disj(v3, v2) % 15.87/2.93 = v1) | ~ (disj(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 15.87/2.93 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (subq(v3, v2) % 15.87/2.93 = v1) | ~ (subq(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 15.87/2.93 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (mem(v3, v2) % 15.87/2.93 = v1) | ~ (mem(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 15.87/2.93 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (atleast16p(v2) = v1) | ~ % 15.87/2.93 (atleast16p(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 15.87/2.93 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (atleast15p(v2) = v1) | ~ % 15.87/2.93 (atleast15p(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 15.87/2.93 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (atleast14p(v2) = v1) | ~ % 15.87/2.93 (atleast14p(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 15.87/2.93 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (atleast13p(v2) = v1) | ~ % 15.87/2.93 (atleast13p(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 15.87/2.93 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (atleast12p(v2) = v1) | ~ % 15.87/2.93 (atleast12p(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 15.87/2.93 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (atleast11p(v2) = v1) | ~ % 15.87/2.93 (atleast11p(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 15.87/2.93 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (atleast10p(v2) = v1) | ~ % 15.87/2.93 (atleast10p(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 15.87/2.93 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (atleast9p(v2) = v1) | ~ % 15.87/2.93 (atleast9p(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 15.87/2.93 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (atleast8p(v2) = v1) | ~ % 15.87/2.93 (atleast8p(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 15.87/2.93 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (atleast7p(v2) = v1) | ~ % 15.87/2.93 (atleast7p(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 15.87/2.93 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (atleast6p(v2) = v1) | ~ % 15.87/2.93 (atleast6p(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 15.87/2.93 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (atleast5p(v2) = v1) | ~ % 15.87/2.93 (atleast5p(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 15.87/2.93 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (atleast4p(v2) = v1) | ~ % 15.87/2.93 (atleast4p(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 15.87/2.93 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (atleast3p(v2) = v1) | ~ % 15.87/2.93 (atleast3p(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 15.87/2.93 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (atleast2p(v2) = v1) | ~ % 15.87/2.93 (atleast2p(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | % 15.87/2.93 ~ (p(v2) = v1) | ~ (p(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 15.87/2.93 : (v1 = v0 | ~ (n(v2) = v1) | ~ (n(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : % 15.87/2.93 ! [v2: $i] : (v1 = v0 | ~ (s(v2) = v1) | ~ (s(v2) = v0)) % 15.87/2.93 % 15.87/2.93 Further assumptions not needed in the proof: % 15.87/2.93 -------------------------------------------- % 15.87/2.93 atleast10p_def, atleast11p_def, atleast12p_def, atleast13p_def, atleast14p_def, % 15.87/2.93 atleast15p_def, atleast16p_def, atleast4p_def, atleast5p_def, atleast6p_def, % 15.87/2.93 atleast7p_def, atleast8p_def, atleast9p_def, disj_def, e_ax, m_ax, setext % 15.87/2.93 % 15.87/2.93 Those formulas are unsatisfiable: % 15.87/2.93 --------------------------------- % 15.87/2.93 % 15.87/2.93 Begin of proof % 15.87/2.93 | % 15.87/2.93 | ALPHA: (subq_def) implies: % 15.87/2.94 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (subq(v0, v1) = 0) | ~ % 15.87/2.94 | (mem(v2, v0) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | mem(v2, v1) = % 15.87/2.94 | 0) % 15.87/2.94 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subq(v0, v1) = % 15.87/2.94 | v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 % 15.87/2.94 | = 0) & mem(v3, v1) = v4 & mem(v3, v0) = 0 & $i(v3))) % 15.87/2.94 | % 15.87/2.94 | ALPHA: (s_ax) implies: % 15.87/2.94 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (s(v1) = v2) | % 15.87/2.94 | ~ (mem(v0, v2) = 0) | ~ $i(v1) | ~ $i(v0)) % 15.87/2.94 | % 15.87/2.94 | ALPHA: (u_ax) implies: % 15.87/2.94 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (u(v1, v2) % 15.87/2.94 | = v3) | ~ (mem(v0, v3) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 15.87/2.94 | ? [v4: any] : ? [v5: any] : (mem(v0, v2) = v5 & mem(v0, v1) = v4 & % 15.87/2.94 | (v5 = 0 | v4 = 0))) % 15.87/2.94 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : % 15.87/2.94 | (v4 = 0 | ~ (u(v1, v2) = v3) | ~ (mem(v0, v3) = v4) | ~ $i(v2) | ~ % 15.87/2.94 | $i(v1) | ~ $i(v0) | ? [v5: int] : ? [v6: int] : ( ~ (v6 = 0) & ~ % 15.87/2.94 | (v5 = 0) & mem(v0, v2) = v6 & mem(v0, v1) = v5)) % 15.87/2.94 | % 15.87/2.94 | ALPHA: (a_def) implies: % 15.87/2.94 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (a(v0, v1) = v2) | ~ % 15.87/2.94 | $i(v1) | ~ $i(v0) | ? [v3: $i] : (u(v0, v3) = v2 & s(v1) = v3 & % 15.87/2.94 | $i(v3) & $i(v2))) % 15.87/2.94 | % 15.87/2.94 | ALPHA: (n_def) implies: % 15.87/2.94 | (7) ! [v0: $i] : ! [v1: $i] : ( ~ (n(v0) = v1) | ~ $i(v0) | (a(v0, v0) = % 15.87/2.94 | v1 & $i(v1))) % 15.87/2.94 | % 15.87/2.94 | ALPHA: (p_ax) implies: % 15.87/2.94 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 15.87/2.94 | (p(v1) = v2) | ~ (mem(v0, v2) = v3) | ~ $i(v1) | ~ $i(v0) | ? % 15.87/2.94 | [v4: int] : ( ~ (v4 = 0) & subq(v0, v1) = v4)) % 15.87/2.94 | % 15.87/2.94 | ALPHA: (atleast2p_def) implies: % 15.87/2.94 | (9) ! [v0: $i] : ( ~ (atleast2p(v0) = 0) | ~ $i(v0) | ? [v1: $i] : ? % 15.87/2.94 | [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) & p(v1) = v2 & subq(v0, v2) = % 15.87/2.94 | v3 & mem(v1, v0) = 0 & $i(v2) & $i(v1))) % 15.87/2.94 | % 15.87/2.94 | ALPHA: (atleast3p_def) implies: % 15.87/2.94 | (10) ! [v0: $i] : ( ~ (atleast3p(v0) = 0) | ~ $i(v0) | ? [v1: $i] : ? % 15.87/2.94 | [v2: int] : ( ~ (v2 = 0) & atleast2p(v1) = 0 & subq(v1, v0) = 0 & % 15.87/2.94 | subq(v0, v1) = v2 & $i(v1))) % 15.87/2.94 | % 15.87/2.94 | ALPHA: (atmost2_2560) implies: % 15.87/2.94 | (11) $i(e) % 15.87/2.94 | (12) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 15.87/2.94 | ? [v5: $i] : (atleast3p(v5) = 0 & n(v1) = v4 & n(v0) = v1 & n(e) = v0 % 15.87/2.94 | & a(v3, v4) = v5 & a(v0, v1) = v2 & s(v2) = v3 & $i(v5) & $i(v4) & % 15.87/2.94 | $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 15.87/2.94 | % 15.87/2.94 | ALPHA: (function-axioms) implies: % 15.87/2.94 | (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (s(v2) = v1) | % 15.87/2.94 | ~ (s(v2) = v0)) % 15.87/2.94 | (14) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 15.87/2.94 | : ! [v3: $i] : (v1 = v0 | ~ (mem(v3, v2) = v1) | ~ (mem(v3, v2) = % 15.87/2.94 | v0)) % 15.87/2.94 | % 15.87/2.94 | DELTA: instantiating (12) with fresh symbols all_29_0, all_29_1, all_29_2, % 15.87/2.94 | all_29_3, all_29_4, all_29_5 gives: % 15.87/2.95 | (15) atleast3p(all_29_0) = 0 & n(all_29_4) = all_29_1 & n(all_29_5) = % 15.87/2.95 | all_29_4 & n(e) = all_29_5 & a(all_29_2, all_29_1) = all_29_0 & % 15.87/2.95 | a(all_29_5, all_29_4) = all_29_3 & s(all_29_3) = all_29_2 & % 15.87/2.95 | $i(all_29_0) & $i(all_29_1) & $i(all_29_2) & $i(all_29_3) & % 15.87/2.95 | $i(all_29_4) & $i(all_29_5) % 15.87/2.95 | % 15.87/2.95 | ALPHA: (15) implies: % 15.87/2.95 | (16) $i(all_29_5) % 15.87/2.95 | (17) $i(all_29_4) % 15.87/2.95 | (18) $i(all_29_2) % 15.87/2.95 | (19) $i(all_29_1) % 15.87/2.95 | (20) $i(all_29_0) % 15.87/2.95 | (21) s(all_29_3) = all_29_2 % 15.87/2.95 | (22) a(all_29_5, all_29_4) = all_29_3 % 15.87/2.95 | (23) a(all_29_2, all_29_1) = all_29_0 % 15.87/2.95 | (24) n(e) = all_29_5 % 15.87/2.95 | (25) n(all_29_5) = all_29_4 % 15.87/2.95 | (26) n(all_29_4) = all_29_1 % 15.87/2.95 | (27) atleast3p(all_29_0) = 0 % 15.87/2.95 | % 15.87/2.95 | GROUND_INST: instantiating (6) with all_29_5, all_29_4, all_29_3, simplifying % 15.87/2.95 | with (16), (17), (22) gives: % 15.87/2.95 | (28) ? [v0: $i] : (u(all_29_5, v0) = all_29_3 & s(all_29_4) = v0 & $i(v0) % 15.87/2.95 | & $i(all_29_3)) % 15.87/2.95 | % 15.87/2.95 | GROUND_INST: instantiating (6) with all_29_2, all_29_1, all_29_0, simplifying % 15.87/2.95 | with (18), (19), (23) gives: % 15.87/2.95 | (29) ? [v0: $i] : (u(all_29_2, v0) = all_29_0 & s(all_29_1) = v0 & $i(v0) % 15.87/2.95 | & $i(all_29_0)) % 15.87/2.95 | % 15.87/2.95 | GROUND_INST: instantiating (7) with e, all_29_5, simplifying with (11), (24) % 15.87/2.95 | gives: % 15.87/2.95 | (30) a(e, e) = all_29_5 & $i(all_29_5) % 15.87/2.95 | % 15.87/2.95 | ALPHA: (30) implies: % 15.87/2.95 | (31) a(e, e) = all_29_5 % 15.87/2.95 | % 15.87/2.95 | GROUND_INST: instantiating (7) with all_29_5, all_29_4, simplifying with (16), % 15.87/2.95 | (25) gives: % 15.87/2.95 | (32) a(all_29_5, all_29_5) = all_29_4 & $i(all_29_4) % 15.87/2.95 | % 15.87/2.95 | ALPHA: (32) implies: % 15.87/2.95 | (33) a(all_29_5, all_29_5) = all_29_4 % 15.87/2.95 | % 15.87/2.95 | GROUND_INST: instantiating (7) with all_29_4, all_29_1, simplifying with (17), % 15.87/2.95 | (26) gives: % 15.87/2.95 | (34) a(all_29_4, all_29_4) = all_29_1 & $i(all_29_1) % 15.87/2.95 | % 15.87/2.95 | ALPHA: (34) implies: % 15.87/2.95 | (35) a(all_29_4, all_29_4) = all_29_1 % 15.87/2.95 | % 15.87/2.95 | GROUND_INST: instantiating (10) with all_29_0, simplifying with (20), (27) % 15.87/2.95 | gives: % 15.87/2.95 | (36) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & atleast2p(v0) = 0 & % 15.87/2.95 | subq(v0, all_29_0) = 0 & subq(all_29_0, v0) = v1 & $i(v0)) % 15.87/2.95 | % 15.87/2.95 | DELTA: instantiating (29) with fresh symbol all_37_0 gives: % 15.87/2.95 | (37) u(all_29_2, all_37_0) = all_29_0 & s(all_29_1) = all_37_0 & % 15.87/2.95 | $i(all_37_0) & $i(all_29_0) % 15.87/2.95 | % 15.87/2.95 | ALPHA: (37) implies: % 15.87/2.95 | (38) $i(all_37_0) % 16.23/2.95 | (39) s(all_29_1) = all_37_0 % 16.23/2.95 | (40) u(all_29_2, all_37_0) = all_29_0 % 16.23/2.95 | % 16.23/2.95 | DELTA: instantiating (28) with fresh symbol all_39_0 gives: % 16.23/2.95 | (41) u(all_29_5, all_39_0) = all_29_3 & s(all_29_4) = all_39_0 & % 16.23/2.95 | $i(all_39_0) & $i(all_29_3) % 16.23/2.95 | % 16.23/2.95 | ALPHA: (41) implies: % 16.23/2.95 | (42) $i(all_29_3) % 16.23/2.95 | (43) s(all_29_4) = all_39_0 % 16.23/2.95 | (44) u(all_29_5, all_39_0) = all_29_3 % 16.23/2.95 | % 16.23/2.95 | DELTA: instantiating (36) with fresh symbols all_41_0, all_41_1 gives: % 16.23/2.95 | (45) ~ (all_41_0 = 0) & atleast2p(all_41_1) = 0 & subq(all_41_1, all_29_0) % 16.23/2.95 | = 0 & subq(all_29_0, all_41_1) = all_41_0 & $i(all_41_1) % 16.23/2.95 | % 16.23/2.95 | ALPHA: (45) implies: % 16.23/2.95 | (46) ~ (all_41_0 = 0) % 16.23/2.95 | (47) $i(all_41_1) % 16.23/2.95 | (48) subq(all_29_0, all_41_1) = all_41_0 % 16.23/2.96 | (49) subq(all_41_1, all_29_0) = 0 % 16.23/2.96 | (50) atleast2p(all_41_1) = 0 % 16.23/2.96 | % 16.23/2.96 | GROUND_INST: instantiating (2) with all_29_0, all_41_1, all_41_0, simplifying % 16.23/2.96 | with (20), (47), (48) gives: % 16.23/2.96 | (51) all_41_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & mem(v0, % 16.23/2.96 | all_41_1) = v1 & mem(v0, all_29_0) = 0 & $i(v0)) % 16.23/2.96 | % 16.23/2.96 | GROUND_INST: instantiating (6) with e, e, all_29_5, simplifying with (11), % 16.23/2.96 | (31) gives: % 16.23/2.96 | (52) ? [v0: $i] : (u(e, v0) = all_29_5 & s(e) = v0 & $i(v0) & % 16.23/2.96 | $i(all_29_5)) % 16.23/2.96 | % 16.23/2.96 | GROUND_INST: instantiating (6) with all_29_5, all_29_5, all_29_4, simplifying % 16.23/2.96 | with (16), (33) gives: % 16.23/2.96 | (53) ? [v0: $i] : (u(all_29_5, v0) = all_29_4 & s(all_29_5) = v0 & $i(v0) % 16.23/2.96 | & $i(all_29_4)) % 16.23/2.96 | % 16.23/2.96 | GROUND_INST: instantiating (6) with all_29_4, all_29_4, all_29_1, simplifying % 16.23/2.96 | with (17), (35) gives: % 16.23/2.96 | (54) ? [v0: $i] : (u(all_29_4, v0) = all_29_1 & s(all_29_4) = v0 & $i(v0) % 16.23/2.96 | & $i(all_29_1)) % 16.23/2.96 | % 16.23/2.96 | GROUND_INST: instantiating (9) with all_41_1, simplifying with (47), (50) % 16.23/2.96 | gives: % 16.23/2.96 | (55) ? [v0: $i] : ? [v1: $i] : ? [v2: int] : ( ~ (v2 = 0) & p(v0) = v1 & % 16.23/2.96 | subq(all_41_1, v1) = v2 & mem(v0, all_41_1) = 0 & $i(v1) & $i(v0)) % 16.23/2.96 | % 16.23/2.96 | DELTA: instantiating (54) with fresh symbol all_50_0 gives: % 16.23/2.96 | (56) u(all_29_4, all_50_0) = all_29_1 & s(all_29_4) = all_50_0 & % 16.23/2.96 | $i(all_50_0) & $i(all_29_1) % 16.23/2.96 | % 16.23/2.96 | ALPHA: (56) implies: % 16.23/2.96 | (57) $i(all_50_0) % 16.23/2.96 | (58) s(all_29_4) = all_50_0 % 16.23/2.96 | (59) u(all_29_4, all_50_0) = all_29_1 % 16.23/2.96 | % 16.23/2.96 | DELTA: instantiating (53) with fresh symbol all_52_0 gives: % 16.23/2.96 | (60) u(all_29_5, all_52_0) = all_29_4 & s(all_29_5) = all_52_0 & % 16.23/2.96 | $i(all_52_0) & $i(all_29_4) % 16.23/2.96 | % 16.23/2.96 | ALPHA: (60) implies: % 16.23/2.96 | (61) $i(all_52_0) % 16.23/2.96 | (62) u(all_29_5, all_52_0) = all_29_4 % 16.23/2.96 | % 16.23/2.96 | DELTA: instantiating (52) with fresh symbol all_54_0 gives: % 16.23/2.96 | (63) u(e, all_54_0) = all_29_5 & s(e) = all_54_0 & $i(all_54_0) & % 16.23/2.96 | $i(all_29_5) % 16.23/2.96 | % 16.23/2.96 | DELTA: instantiating (55) with fresh symbols all_56_0, all_56_1, all_56_2 % 16.23/2.96 | gives: % 16.23/2.96 | (64) ~ (all_56_0 = 0) & p(all_56_2) = all_56_1 & subq(all_41_1, all_56_1) % 16.23/2.96 | = all_56_0 & mem(all_56_2, all_41_1) = 0 & $i(all_56_1) & $i(all_56_2) % 16.23/2.96 | % 16.23/2.96 | ALPHA: (64) implies: % 16.23/2.96 | (65) ~ (all_56_0 = 0) % 16.23/2.96 | (66) $i(all_56_2) % 16.23/2.96 | (67) $i(all_56_1) % 16.23/2.96 | (68) mem(all_56_2, all_41_1) = 0 % 16.23/2.96 | (69) subq(all_41_1, all_56_1) = all_56_0 % 16.23/2.96 | (70) p(all_56_2) = all_56_1 % 16.23/2.96 | % 16.23/2.96 | BETA: splitting (51) gives: % 16.23/2.96 | % 16.23/2.96 | Case 1: % 16.23/2.96 | | % 16.23/2.96 | | (71) all_41_0 = 0 % 16.23/2.96 | | % 16.23/2.96 | | REDUCE: (46), (71) imply: % 16.23/2.96 | | (72) $false % 16.23/2.97 | | % 16.23/2.97 | | CLOSE: (72) is inconsistent. % 16.23/2.97 | | % 16.23/2.97 | Case 2: % 16.23/2.97 | | % 16.23/2.97 | | (73) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & mem(v0, all_41_1) = v1 & % 16.23/2.97 | | mem(v0, all_29_0) = 0 & $i(v0)) % 16.23/2.97 | | % 16.23/2.97 | | DELTA: instantiating (73) with fresh symbols all_62_0, all_62_1 gives: % 16.23/2.97 | | (74) ~ (all_62_0 = 0) & mem(all_62_1, all_41_1) = all_62_0 & % 16.23/2.97 | | mem(all_62_1, all_29_0) = 0 & $i(all_62_1) % 16.23/2.97 | | % 16.23/2.97 | | ALPHA: (74) implies: % 16.23/2.97 | | (75) ~ (all_62_0 = 0) % 16.23/2.97 | | (76) $i(all_62_1) % 16.23/2.97 | | (77) mem(all_62_1, all_29_0) = 0 % 16.23/2.97 | | (78) mem(all_62_1, all_41_1) = all_62_0 % 16.23/2.97 | | % 16.23/2.97 | | GROUND_INST: instantiating (13) with all_39_0, all_50_0, all_29_4, % 16.23/2.97 | | simplifying with (43), (58) gives: % 16.23/2.97 | | (79) all_50_0 = all_39_0 % 16.23/2.97 | | % 16.23/2.97 | | REDUCE: (59), (79) imply: % 16.23/2.97 | | (80) u(all_29_4, all_39_0) = all_29_1 % 16.23/2.97 | | % 16.23/2.97 | | REDUCE: (57), (79) imply: % 16.23/2.97 | | (81) $i(all_39_0) % 16.23/2.97 | | % 16.23/2.97 | | GROUND_INST: instantiating (1) with all_41_1, all_29_0, all_56_2, % 16.23/2.97 | | simplifying with (20), (47), (49), (66), (68) gives: % 16.23/2.97 | | (82) mem(all_56_2, all_29_0) = 0 % 16.23/2.97 | | % 16.23/2.97 | | GROUND_INST: instantiating (4) with all_62_1, all_29_2, all_37_0, all_29_0, % 16.23/2.97 | | simplifying with (18), (38), (40), (76), (77) gives: % 16.31/2.97 | | (83) ? [v0: any] : ? [v1: any] : (mem(all_62_1, all_37_0) = v1 & % 16.31/2.97 | | mem(all_62_1, all_29_2) = v0 & (v1 = 0 | v0 = 0)) % 16.31/2.97 | | % 16.31/2.97 | | GROUND_INST: instantiating (2) with all_41_1, all_56_1, all_56_0, % 16.31/2.97 | | simplifying with (47), (67), (69) gives: % 16.31/2.97 | | (84) all_56_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & mem(v0, % 16.31/2.97 | | all_56_1) = v1 & mem(v0, all_41_1) = 0 & $i(v0)) % 16.31/2.97 | | % 16.31/2.97 | | DELTA: instantiating (83) with fresh symbols all_79_0, all_79_1 gives: % 16.31/2.97 | | (85) mem(all_62_1, all_37_0) = all_79_0 & mem(all_62_1, all_29_2) = % 16.31/2.97 | | all_79_1 & (all_79_0 = 0 | all_79_1 = 0) % 16.31/2.97 | | % 16.31/2.97 | | ALPHA: (85) implies: % 16.31/2.97 | | (86) mem(all_62_1, all_29_2) = all_79_1 % 16.31/2.97 | | (87) mem(all_62_1, all_37_0) = all_79_0 % 16.31/2.97 | | (88) all_79_0 = 0 | all_79_1 = 0 % 16.31/2.97 | | % 16.31/2.97 | | BETA: splitting (84) gives: % 16.31/2.97 | | % 16.31/2.97 | | Case 1: % 16.31/2.97 | | | % 16.31/2.97 | | | (89) all_56_0 = 0 % 16.31/2.97 | | | % 16.31/2.97 | | | REDUCE: (65), (89) imply: % 16.31/2.97 | | | (90) $false % 16.31/2.97 | | | % 16.31/2.97 | | | CLOSE: (90) is inconsistent. % 16.31/2.97 | | | % 16.31/2.97 | | Case 2: % 16.31/2.97 | | | % 16.31/2.97 | | | (91) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & mem(v0, all_56_1) = v1 % 16.31/2.97 | | | & mem(v0, all_41_1) = 0 & $i(v0)) % 16.31/2.97 | | | % 16.31/2.97 | | | DELTA: instantiating (91) with fresh symbols all_85_0, all_85_1 gives: % 16.31/2.97 | | | (92) ~ (all_85_0 = 0) & mem(all_85_1, all_56_1) = all_85_0 & % 16.31/2.97 | | | mem(all_85_1, all_41_1) = 0 & $i(all_85_1) % 16.31/2.97 | | | % 16.31/2.97 | | | ALPHA: (92) implies: % 16.31/2.97 | | | (93) ~ (all_85_0 = 0) % 16.31/2.97 | | | (94) $i(all_85_1) % 16.31/2.97 | | | (95) mem(all_85_1, all_41_1) = 0 % 16.31/2.97 | | | (96) mem(all_85_1, all_56_1) = all_85_0 % 16.31/2.97 | | | % 16.31/2.97 | | | GROUND_INST: instantiating (4) with all_56_2, all_29_2, all_37_0, % 16.31/2.97 | | | all_29_0, simplifying with (18), (38), (40), (66), (82) % 16.31/2.97 | | | gives: % 16.31/2.97 | | | (97) ? [v0: any] : ? [v1: any] : (mem(all_56_2, all_37_0) = v1 & % 16.31/2.98 | | | mem(all_56_2, all_29_2) = v0 & (v1 = 0 | v0 = 0)) % 16.31/2.98 | | | % 16.31/2.98 | | | GROUND_INST: instantiating (1) with all_41_1, all_29_0, all_85_1, % 16.31/2.98 | | | simplifying with (20), (47), (49), (94), (95) gives: % 16.31/2.98 | | | (98) mem(all_85_1, all_29_0) = 0 % 16.31/2.98 | | | % 16.31/2.98 | | | GROUND_INST: instantiating (8) with all_85_1, all_56_2, all_56_1, % 16.31/2.98 | | | all_85_0, simplifying with (66), (70), (94), (96) gives: % 16.31/2.98 | | | (99) all_85_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & subq(all_85_1, % 16.31/2.98 | | | all_56_2) = v0) % 16.31/2.98 | | | % 16.31/2.98 | | | DELTA: instantiating (97) with fresh symbols all_98_0, all_98_1 gives: % 16.31/2.98 | | | (100) mem(all_56_2, all_37_0) = all_98_0 & mem(all_56_2, all_29_2) = % 16.31/2.98 | | | all_98_1 & (all_98_0 = 0 | all_98_1 = 0) % 16.31/2.98 | | | % 16.31/2.98 | | | ALPHA: (100) implies: % 16.31/2.98 | | | (101) mem(all_56_2, all_29_2) = all_98_1 % 16.31/2.98 | | | (102) mem(all_56_2, all_37_0) = all_98_0 % 16.31/2.98 | | | (103) all_98_0 = 0 | all_98_1 = 0 % 16.31/2.98 | | | % 16.31/2.98 | | | BETA: splitting (99) gives: % 16.31/2.98 | | | % 16.31/2.98 | | | Case 1: % 16.31/2.98 | | | | % 16.31/2.98 | | | | (104) all_85_0 = 0 % 16.31/2.98 | | | | % 16.31/2.98 | | | | REDUCE: (93), (104) imply: % 16.31/2.98 | | | | (105) $false % 16.31/2.98 | | | | % 16.31/2.98 | | | | CLOSE: (105) is inconsistent. % 16.31/2.98 | | | | % 16.31/2.98 | | | Case 2: % 16.31/2.98 | | | | % 16.31/2.98 | | | | (106) ? [v0: int] : ( ~ (v0 = 0) & subq(all_85_1, all_56_2) = v0) % 16.31/2.98 | | | | % 16.31/2.98 | | | | DELTA: instantiating (106) with fresh symbol all_104_0 gives: % 16.31/2.98 | | | | (107) ~ (all_104_0 = 0) & subq(all_85_1, all_56_2) = all_104_0 % 16.31/2.98 | | | | % 16.31/2.98 | | | | ALPHA: (107) implies: % 16.31/2.98 | | | | (108) ~ (all_104_0 = 0) % 16.31/2.98 | | | | (109) subq(all_85_1, all_56_2) = all_104_0 % 16.31/2.98 | | | | % 16.31/2.98 | | | | GROUND_INST: instantiating (4) with all_85_1, all_29_2, all_37_0, % 16.31/2.98 | | | | all_29_0, simplifying with (18), (38), (40), (94), (98) % 16.31/2.98 | | | | gives: % 16.31/2.98 | | | | (110) ? [v0: any] : ? [v1: any] : (mem(all_85_1, all_37_0) = v1 & % 16.31/2.98 | | | | mem(all_85_1, all_29_2) = v0 & (v1 = 0 | v0 = 0)) % 16.31/2.98 | | | | % 16.31/2.98 | | | | GROUND_INST: instantiating (2) with all_85_1, all_56_2, all_104_0, % 16.31/2.98 | | | | simplifying with (66), (94), (109) gives: % 16.31/2.98 | | | | (111) all_104_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & % 16.31/2.98 | | | | mem(v0, all_85_1) = 0 & mem(v0, all_56_2) = v1 & $i(v0)) % 16.31/2.98 | | | | % 16.31/2.98 | | | | DELTA: instantiating (110) with fresh symbols all_111_0, all_111_1 % 16.31/2.98 | | | | gives: % 16.31/2.98 | | | | (112) mem(all_85_1, all_37_0) = all_111_0 & mem(all_85_1, all_29_2) = % 16.31/2.98 | | | | all_111_1 & (all_111_0 = 0 | all_111_1 = 0) % 16.31/2.98 | | | | % 16.31/2.98 | | | | ALPHA: (112) implies: % 16.31/2.98 | | | | (113) mem(all_85_1, all_29_2) = all_111_1 % 16.31/2.98 | | | | (114) mem(all_85_1, all_37_0) = all_111_0 % 16.31/2.98 | | | | (115) all_111_0 = 0 | all_111_1 = 0 % 16.31/2.98 | | | | % 16.31/2.98 | | | | BETA: splitting (111) gives: % 16.31/2.98 | | | | % 16.31/2.98 | | | | Case 1: % 16.31/2.98 | | | | | % 16.31/2.98 | | | | | (116) all_104_0 = 0 % 16.31/2.98 | | | | | % 16.31/2.98 | | | | | REDUCE: (108), (116) imply: % 16.31/2.98 | | | | | (117) $false % 16.31/2.98 | | | | | % 16.31/2.98 | | | | | CLOSE: (117) is inconsistent. % 16.31/2.98 | | | | | % 16.31/2.98 | | | | Case 2: % 16.31/2.98 | | | | | % 16.31/2.98 | | | | | (118) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & mem(v0, all_85_1) % 16.31/2.98 | | | | | = 0 & mem(v0, all_56_2) = v1 & $i(v0)) % 16.31/2.98 | | | | | % 16.31/2.98 | | | | | DELTA: instantiating (118) with fresh symbols all_117_0, all_117_1 % 16.31/2.98 | | | | | gives: % 16.31/2.98 | | | | | (119) ~ (all_117_0 = 0) & mem(all_117_1, all_85_1) = 0 & % 16.31/2.98 | | | | | mem(all_117_1, all_56_2) = all_117_0 & $i(all_117_1) % 16.31/2.98 | | | | | % 16.31/2.98 | | | | | ALPHA: (119) implies: % 16.31/2.98 | | | | | (120) ~ (all_117_0 = 0) % 16.31/2.98 | | | | | (121) $i(all_117_1) % 16.31/2.98 | | | | | (122) mem(all_117_1, all_56_2) = all_117_0 % 16.31/2.98 | | | | | (123) mem(all_117_1, all_85_1) = 0 % 16.31/2.98 | | | | | % 16.31/2.98 | | | | | BETA: splitting (88) gives: % 16.31/2.98 | | | | | % 16.31/2.98 | | | | | Case 1: % 16.31/2.98 | | | | | | % 16.31/2.98 | | | | | | (124) all_79_0 = 0 % 16.31/2.98 | | | | | | % 16.31/2.98 | | | | | | REDUCE: (87), (124) imply: % 16.31/2.98 | | | | | | (125) mem(all_62_1, all_37_0) = 0 % 16.31/2.98 | | | | | | % 16.31/2.98 | | | | | | GROUND_INST: instantiating (3) with all_62_1, all_29_1, all_37_0, % 16.31/2.98 | | | | | | simplifying with (19), (39), (76), (125) gives: % 16.31/2.98 | | | | | | (126) all_62_1 = all_29_1 % 16.31/2.98 | | | | | | % 16.31/2.98 | | | | | | REDUCE: (78), (126) imply: % 16.31/2.98 | | | | | | (127) mem(all_29_1, all_41_1) = all_62_0 % 16.31/2.98 | | | | | | % 16.31/2.98 | | | | | | BETA: splitting (103) gives: % 16.31/2.98 | | | | | | % 16.31/2.98 | | | | | | Case 1: % 16.31/2.98 | | | | | | | % 16.31/2.98 | | | | | | | (128) all_98_0 = 0 % 16.31/2.98 | | | | | | | % 16.31/2.98 | | | | | | | REDUCE: (102), (128) imply: % 16.31/2.98 | | | | | | | (129) mem(all_56_2, all_37_0) = 0 % 16.31/2.98 | | | | | | | % 16.31/2.99 | | | | | | | GROUND_INST: instantiating (3) with all_56_2, all_29_1, all_37_0, % 16.31/2.99 | | | | | | | simplifying with (19), (39), (66), (129) gives: % 16.31/2.99 | | | | | | | (130) all_56_2 = all_29_1 % 16.31/2.99 | | | | | | | % 16.31/2.99 | | | | | | | REDUCE: (68), (130) imply: % 16.31/2.99 | | | | | | | (131) mem(all_29_1, all_41_1) = 0 % 16.31/2.99 | | | | | | | % 16.31/2.99 | | | | | | | GROUND_INST: instantiating (14) with all_62_0, 0, all_41_1, % 16.31/2.99 | | | | | | | all_29_1, simplifying with (127), (131) gives: % 16.31/2.99 | | | | | | | (132) all_62_0 = 0 % 16.31/2.99 | | | | | | | % 16.31/2.99 | | | | | | | REDUCE: (75), (132) imply: % 16.31/2.99 | | | | | | | (133) $false % 16.31/2.99 | | | | | | | % 16.31/2.99 | | | | | | | CLOSE: (133) is inconsistent. % 16.31/2.99 | | | | | | | % 16.31/2.99 | | | | | | Case 2: % 16.31/2.99 | | | | | | | % 16.31/2.99 | | | | | | | (134) all_98_1 = 0 % 16.31/2.99 | | | | | | | % 16.31/2.99 | | | | | | | REDUCE: (101), (134) imply: % 16.31/2.99 | | | | | | | (135) mem(all_56_2, all_29_2) = 0 % 16.31/2.99 | | | | | | | % 16.31/2.99 | | | | | | | GROUND_INST: instantiating (3) with all_56_2, all_29_3, all_29_2, % 16.31/2.99 | | | | | | | simplifying with (21), (42), (66), (135) gives: % 16.31/2.99 | | | | | | | (136) all_56_2 = all_29_3 % 16.31/2.99 | | | | | | | % 16.31/2.99 | | | | | | | REDUCE: (109), (136) imply: % 16.31/2.99 | | | | | | | (137) subq(all_85_1, all_29_3) = all_104_0 % 16.31/2.99 | | | | | | | % 16.31/2.99 | | | | | | | REDUCE: (122), (136) imply: % 16.31/2.99 | | | | | | | (138) mem(all_117_1, all_29_3) = all_117_0 % 16.31/2.99 | | | | | | | % 16.31/2.99 | | | | | | | GROUND_INST: instantiating (5) with all_117_1, all_29_5, all_39_0, % 16.31/2.99 | | | | | | | all_29_3, all_117_0, simplifying with (16), (44), % 16.31/2.99 | | | | | | | (81), (121), (138) gives: % 16.31/2.99 | | | | | | | (139) all_117_0 = 0 | ? [v0: int] : ? [v1: int] : ( ~ (v1 = % 16.31/2.99 | | | | | | | 0) & ~ (v0 = 0) & mem(all_117_1, all_39_0) = v1 & % 16.31/2.99 | | | | | | | mem(all_117_1, all_29_5) = v0) % 16.31/2.99 | | | | | | | % 16.31/2.99 | | | | | | | GROUND_INST: instantiating (2) with all_85_1, all_29_3, all_104_0, % 16.31/2.99 | | | | | | | simplifying with (42), (94), (137) gives: % 16.31/2.99 | | | | | | | (140) all_104_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) % 16.31/2.99 | | | | | | | & mem(v0, all_85_1) = 0 & mem(v0, all_29_3) = v1 & % 16.31/2.99 | | | | | | | $i(v0)) % 16.31/2.99 | | | | | | | % 16.31/2.99 | | | | | | | BETA: splitting (115) gives: % 16.31/2.99 | | | | | | | % 16.31/2.99 | | | | | | | Case 1: % 16.31/2.99 | | | | | | | | % 16.31/2.99 | | | | | | | | (141) all_111_0 = 0 % 16.31/2.99 | | | | | | | | % 16.31/2.99 | | | | | | | | REDUCE: (114), (141) imply: % 16.31/2.99 | | | | | | | | (142) mem(all_85_1, all_37_0) = 0 % 16.31/2.99 | | | | | | | | % 16.31/2.99 | | | | | | | | BETA: splitting (140) gives: % 16.31/2.99 | | | | | | | | % 16.31/2.99 | | | | | | | | Case 1: % 16.31/2.99 | | | | | | | | | % 16.31/2.99 | | | | | | | | | (143) all_104_0 = 0 % 16.31/2.99 | | | | | | | | | % 16.31/2.99 | | | | | | | | | REDUCE: (108), (143) imply: % 16.31/2.99 | | | | | | | | | (144) $false % 16.31/2.99 | | | | | | | | | % 16.31/2.99 | | | | | | | | | CLOSE: (144) is inconsistent. % 16.31/2.99 | | | | | | | | | % 16.31/2.99 | | | | | | | | Case 2: % 16.31/2.99 | | | | | | | | | % 16.31/2.99 | | | | | | | | | % 16.31/2.99 | | | | | | | | | GROUND_INST: instantiating (3) with all_85_1, all_29_1, % 16.31/2.99 | | | | | | | | | all_37_0, simplifying with (19), (39), (94), (142) % 16.31/2.99 | | | | | | | | | gives: % 16.31/2.99 | | | | | | | | | (145) all_85_1 = all_29_1 % 16.31/2.99 | | | | | | | | | % 16.31/2.99 | | | | | | | | | REDUCE: (95), (145) imply: % 16.31/2.99 | | | | | | | | | (146) mem(all_29_1, all_41_1) = 0 % 16.31/2.99 | | | | | | | | | % 16.31/2.99 | | | | | | | | | GROUND_INST: instantiating (14) with all_62_0, 0, all_41_1, % 16.31/2.99 | | | | | | | | | all_29_1, simplifying with (127), (146) gives: % 16.31/2.99 | | | | | | | | | (147) all_62_0 = 0 % 16.31/2.99 | | | | | | | | | % 16.31/2.99 | | | | | | | | | REDUCE: (75), (147) imply: % 16.31/2.99 | | | | | | | | | (148) $false % 16.31/2.99 | | | | | | | | | % 16.31/2.99 | | | | | | | | | CLOSE: (148) is inconsistent. % 16.31/2.99 | | | | | | | | | % 16.31/2.99 | | | | | | | | End of split % 16.31/2.99 | | | | | | | | % 16.31/2.99 | | | | | | | Case 2: % 16.31/2.99 | | | | | | | | % 16.31/2.99 | | | | | | | | (149) all_111_1 = 0 % 16.31/2.99 | | | | | | | | % 16.31/2.99 | | | | | | | | REDUCE: (113), (149) imply: % 16.31/2.99 | | | | | | | | (150) mem(all_85_1, all_29_2) = 0 % 16.31/2.99 | | | | | | | | % 16.31/2.99 | | | | | | | | BETA: splitting (139) gives: % 16.31/2.99 | | | | | | | | % 16.31/2.99 | | | | | | | | Case 1: % 16.31/2.99 | | | | | | | | | % 16.31/2.99 | | | | | | | | | (151) all_117_0 = 0 % 16.31/2.99 | | | | | | | | | % 16.31/2.99 | | | | | | | | | REDUCE: (120), (151) imply: % 16.31/2.99 | | | | | | | | | (152) $false % 16.31/2.99 | | | | | | | | | % 16.31/2.99 | | | | | | | | | CLOSE: (152) is inconsistent. % 16.31/2.99 | | | | | | | | | % 16.31/2.99 | | | | | | | | Case 2: % 16.31/2.99 | | | | | | | | | % 16.31/2.99 | | | | | | | | | % 16.31/2.99 | | | | | | | | | GROUND_INST: instantiating (3) with all_85_1, all_29_3, % 16.31/2.99 | | | | | | | | | all_29_2, simplifying with (21), (42), (94), (150) % 16.31/2.99 | | | | | | | | | gives: % 16.31/2.99 | | | | | | | | | (153) all_85_1 = all_29_3 % 16.31/2.99 | | | | | | | | | % 16.31/2.99 | | | | | | | | | REDUCE: (123), (153) imply: % 16.31/2.99 | | | | | | | | | (154) mem(all_117_1, all_29_3) = 0 % 16.31/2.99 | | | | | | | | | % 16.31/2.99 | | | | | | | | | GROUND_INST: instantiating (14) with all_117_0, 0, all_29_3, % 16.31/2.99 | | | | | | | | | all_117_1, simplifying with (138), (154) gives: % 16.31/2.99 | | | | | | | | | (155) all_117_0 = 0 % 16.31/2.99 | | | | | | | | | % 16.31/2.99 | | | | | | | | | REDUCE: (120), (155) imply: % 16.31/2.99 | | | | | | | | | (156) $false % 16.31/2.99 | | | | | | | | | % 16.31/2.99 | | | | | | | | | CLOSE: (156) is inconsistent. % 16.31/2.99 | | | | | | | | | % 16.31/2.99 | | | | | | | | End of split % 16.31/2.99 | | | | | | | | % 16.31/2.99 | | | | | | | End of split % 16.31/2.99 | | | | | | | % 16.31/2.99 | | | | | | End of split % 16.31/2.99 | | | | | | % 16.31/2.99 | | | | | Case 2: % 16.31/2.99 | | | | | | % 16.31/2.99 | | | | | | (157) all_79_1 = 0 % 16.31/2.99 | | | | | | % 16.31/2.99 | | | | | | REDUCE: (86), (157) imply: % 16.31/2.99 | | | | | | (158) mem(all_62_1, all_29_2) = 0 % 16.31/2.99 | | | | | | % 16.31/2.99 | | | | | | GROUND_INST: instantiating (3) with all_62_1, all_29_3, all_29_2, % 16.31/2.99 | | | | | | simplifying with (21), (42), (76), (158) gives: % 16.31/2.99 | | | | | | (159) all_62_1 = all_29_3 % 16.31/2.99 | | | | | | % 16.31/2.99 | | | | | | REDUCE: (78), (159) imply: % 16.31/2.99 | | | | | | (160) mem(all_29_3, all_41_1) = all_62_0 % 16.31/2.99 | | | | | | % 16.31/2.99 | | | | | | BETA: splitting (103) gives: % 16.31/2.99 | | | | | | % 16.31/2.99 | | | | | | Case 1: % 16.31/2.99 | | | | | | | % 16.31/2.99 | | | | | | | (161) all_98_0 = 0 % 16.31/2.99 | | | | | | | % 16.31/2.99 | | | | | | | REDUCE: (102), (161) imply: % 16.31/2.99 | | | | | | | (162) mem(all_56_2, all_37_0) = 0 % 16.31/2.99 | | | | | | | % 16.31/2.99 | | | | | | | GROUND_INST: instantiating (3) with all_56_2, all_29_1, all_37_0, % 16.31/2.99 | | | | | | | simplifying with (19), (39), (66), (162) gives: % 16.31/2.99 | | | | | | | (163) all_56_2 = all_29_1 % 16.31/2.99 | | | | | | | % 16.31/2.99 | | | | | | | REDUCE: (109), (163) imply: % 16.31/2.99 | | | | | | | (164) subq(all_85_1, all_29_1) = all_104_0 % 16.31/2.99 | | | | | | | % 16.31/2.99 | | | | | | | REDUCE: (122), (163) imply: % 16.31/2.99 | | | | | | | (165) mem(all_117_1, all_29_1) = all_117_0 % 16.31/2.99 | | | | | | | % 16.31/2.99 | | | | | | | GROUND_INST: instantiating (5) with all_117_1, all_29_4, all_39_0, % 16.31/2.99 | | | | | | | all_29_1, all_117_0, simplifying with (17), (80), % 16.31/2.99 | | | | | | | (81), (121), (165) gives: % 16.31/3.00 | | | | | | | (166) all_117_0 = 0 | ? [v0: int] : ? [v1: int] : ( ~ (v1 = % 16.31/3.00 | | | | | | | 0) & ~ (v0 = 0) & mem(all_117_1, all_39_0) = v1 & % 16.31/3.00 | | | | | | | mem(all_117_1, all_29_4) = v0) % 16.31/3.00 | | | | | | | % 16.31/3.00 | | | | | | | GROUND_INST: instantiating (2) with all_85_1, all_29_1, all_104_0, % 16.31/3.00 | | | | | | | simplifying with (19), (94), (164) gives: % 16.31/3.00 | | | | | | | (167) all_104_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) % 16.31/3.00 | | | | | | | & mem(v0, all_85_1) = 0 & mem(v0, all_29_1) = v1 & % 16.31/3.00 | | | | | | | $i(v0)) % 16.31/3.00 | | | | | | | % 16.31/3.00 | | | | | | | BETA: splitting (167) gives: % 16.31/3.00 | | | | | | | % 16.31/3.00 | | | | | | | Case 1: % 16.31/3.00 | | | | | | | | % 16.31/3.00 | | | | | | | | (168) all_104_0 = 0 % 16.31/3.00 | | | | | | | | % 16.31/3.00 | | | | | | | | REDUCE: (108), (168) imply: % 16.31/3.00 | | | | | | | | (169) $false % 16.31/3.00 | | | | | | | | % 16.31/3.00 | | | | | | | | CLOSE: (169) is inconsistent. % 16.31/3.00 | | | | | | | | % 16.31/3.00 | | | | | | | Case 2: % 16.31/3.00 | | | | | | | | % 16.31/3.00 | | | | | | | | (170) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & mem(v0, % 16.31/3.00 | | | | | | | | all_85_1) = 0 & mem(v0, all_29_1) = v1 & $i(v0)) % 16.31/3.00 | | | | | | | | % 16.31/3.00 | | | | | | | | DELTA: instantiating (170) with fresh symbols all_156_0, % 16.31/3.00 | | | | | | | | all_156_1 gives: % 16.31/3.00 | | | | | | | | (171) ~ (all_156_0 = 0) & mem(all_156_1, all_85_1) = 0 & % 16.31/3.00 | | | | | | | | mem(all_156_1, all_29_1) = all_156_0 & $i(all_156_1) % 16.31/3.00 | | | | | | | | % 16.31/3.00 | | | | | | | | ALPHA: (171) implies: % 16.31/3.00 | | | | | | | | (172) ~ (all_156_0 = 0) % 16.31/3.00 | | | | | | | | (173) $i(all_156_1) % 16.31/3.00 | | | | | | | | (174) mem(all_156_1, all_29_1) = all_156_0 % 16.31/3.00 | | | | | | | | % 16.31/3.00 | | | | | | | | BETA: splitting (166) gives: % 16.31/3.00 | | | | | | | | % 16.31/3.00 | | | | | | | | Case 1: % 16.31/3.00 | | | | | | | | | % 16.31/3.00 | | | | | | | | | (175) all_117_0 = 0 % 16.31/3.00 | | | | | | | | | % 16.31/3.00 | | | | | | | | | REDUCE: (120), (175) imply: % 16.31/3.00 | | | | | | | | | (176) $false % 16.31/3.00 | | | | | | | | | % 16.31/3.00 | | | | | | | | | CLOSE: (176) is inconsistent. % 16.31/3.00 | | | | | | | | | % 16.31/3.00 | | | | | | | | Case 2: % 16.31/3.00 | | | | | | | | | % 16.31/3.00 | | | | | | | | | (177) ? [v0: int] : ? [v1: int] : ( ~ (v1 = 0) & ~ (v0 = % 16.31/3.00 | | | | | | | | | 0) & mem(all_117_1, all_39_0) = v1 & % 16.31/3.00 | | | | | | | | | mem(all_117_1, all_29_4) = v0) % 16.31/3.00 | | | | | | | | | % 16.31/3.00 | | | | | | | | | DELTA: instantiating (177) with fresh symbols all_161_0, % 16.31/3.00 | | | | | | | | | all_161_1 gives: % 16.31/3.00 | | | | | | | | | (178) ~ (all_161_0 = 0) & ~ (all_161_1 = 0) & % 16.31/3.00 | | | | | | | | | mem(all_117_1, all_39_0) = all_161_0 & mem(all_117_1, % 16.31/3.00 | | | | | | | | | all_29_4) = all_161_1 % 16.31/3.00 | | | | | | | | | % 16.31/3.00 | | | | | | | | | ALPHA: (178) implies: % 16.31/3.00 | | | | | | | | | (179) ~ (all_161_1 = 0) % 16.31/3.00 | | | | | | | | | (180) mem(all_117_1, all_29_4) = all_161_1 % 16.31/3.00 | | | | | | | | | % 16.31/3.00 | | | | | | | | | GROUND_INST: instantiating (5) with all_117_1, all_29_5, % 16.31/3.00 | | | | | | | | | all_52_0, all_29_4, all_161_1, simplifying with % 16.31/3.00 | | | | | | | | | (16), (61), (62), (121), (180) gives: % 16.31/3.00 | | | | | | | | | (181) all_161_1 = 0 | ? [v0: int] : ? [v1: int] : ( ~ (v1 % 16.31/3.00 | | | | | | | | | = 0) & ~ (v0 = 0) & mem(all_117_1, all_52_0) = % 16.31/3.00 | | | | | | | | | v1 & mem(all_117_1, all_29_5) = v0) % 16.31/3.00 | | | | | | | | | % 16.31/3.00 | | | | | | | | | GROUND_INST: instantiating (5) with all_156_1, all_29_4, % 16.31/3.00 | | | | | | | | | all_39_0, all_29_1, all_156_0, simplifying with % 16.31/3.00 | | | | | | | | | (17), (80), (81), (173), (174) gives: % 16.31/3.00 | | | | | | | | | (182) all_156_0 = 0 | ? [v0: int] : ? [v1: int] : ( ~ (v1 % 16.31/3.00 | | | | | | | | | = 0) & ~ (v0 = 0) & mem(all_156_1, all_39_0) = % 16.31/3.00 | | | | | | | | | v1 & mem(all_156_1, all_29_4) = v0) % 16.31/3.00 | | | | | | | | | % 16.31/3.00 | | | | | | | | | BETA: splitting (115) gives: % 16.31/3.00 | | | | | | | | | % 16.31/3.00 | | | | | | | | | Case 1: % 16.31/3.00 | | | | | | | | | | % 16.31/3.00 | | | | | | | | | | (183) all_111_0 = 0 % 16.31/3.00 | | | | | | | | | | % 16.31/3.00 | | | | | | | | | | REDUCE: (114), (183) imply: % 16.31/3.00 | | | | | | | | | | (184) mem(all_85_1, all_37_0) = 0 % 16.31/3.00 | | | | | | | | | | % 16.31/3.00 | | | | | | | | | | BETA: splitting (182) gives: % 16.31/3.00 | | | | | | | | | | % 16.31/3.00 | | | | | | | | | | Case 1: % 16.31/3.00 | | | | | | | | | | | % 16.31/3.00 | | | | | | | | | | | (185) all_156_0 = 0 % 16.31/3.00 | | | | | | | | | | | % 16.31/3.00 | | | | | | | | | | | REDUCE: (172), (185) imply: % 16.31/3.00 | | | | | | | | | | | (186) $false % 16.31/3.00 | | | | | | | | | | | % 16.31/3.00 | | | | | | | | | | | CLOSE: (186) is inconsistent. % 16.31/3.00 | | | | | | | | | | | % 16.31/3.00 | | | | | | | | | | Case 2: % 16.31/3.00 | | | | | | | | | | | % 16.31/3.00 | | | | | | | | | | | % 16.31/3.00 | | | | | | | | | | | GROUND_INST: instantiating (3) with all_85_1, all_29_1, % 16.31/3.00 | | | | | | | | | | | all_37_0, simplifying with (19), (39), (94), (184) % 16.31/3.00 | | | | | | | | | | | gives: % 16.31/3.00 | | | | | | | | | | | (187) all_85_1 = all_29_1 % 16.31/3.00 | | | | | | | | | | | % 16.31/3.00 | | | | | | | | | | | REDUCE: (123), (187) imply: % 16.31/3.00 | | | | | | | | | | | (188) mem(all_117_1, all_29_1) = 0 % 16.31/3.00 | | | | | | | | | | | % 16.31/3.00 | | | | | | | | | | | GROUND_INST: instantiating (14) with all_117_0, 0, all_29_1, % 16.31/3.00 | | | | | | | | | | | all_117_1, simplifying with (165), (188) gives: % 16.31/3.00 | | | | | | | | | | | (189) all_117_0 = 0 % 16.31/3.00 | | | | | | | | | | | % 16.31/3.00 | | | | | | | | | | | REDUCE: (120), (189) imply: % 16.31/3.00 | | | | | | | | | | | (190) $false % 16.31/3.00 | | | | | | | | | | | % 16.31/3.00 | | | | | | | | | | | CLOSE: (190) is inconsistent. % 16.31/3.00 | | | | | | | | | | | % 16.31/3.00 | | | | | | | | | | End of split % 16.31/3.00 | | | | | | | | | | % 16.31/3.00 | | | | | | | | | Case 2: % 16.31/3.00 | | | | | | | | | | % 16.31/3.00 | | | | | | | | | | (191) all_111_1 = 0 % 16.31/3.00 | | | | | | | | | | % 16.31/3.00 | | | | | | | | | | REDUCE: (113), (191) imply: % 16.31/3.00 | | | | | | | | | | (192) mem(all_85_1, all_29_2) = 0 % 16.31/3.00 | | | | | | | | | | % 16.31/3.00 | | | | | | | | | | BETA: splitting (181) gives: % 16.31/3.00 | | | | | | | | | | % 16.31/3.00 | | | | | | | | | | Case 1: % 16.31/3.00 | | | | | | | | | | | % 16.31/3.00 | | | | | | | | | | | (193) all_161_1 = 0 % 16.31/3.00 | | | | | | | | | | | % 16.31/3.00 | | | | | | | | | | | REDUCE: (179), (193) imply: % 16.31/3.00 | | | | | | | | | | | (194) $false % 16.31/3.00 | | | | | | | | | | | % 16.31/3.00 | | | | | | | | | | | CLOSE: (194) is inconsistent. % 16.31/3.00 | | | | | | | | | | | % 16.31/3.00 | | | | | | | | | | Case 2: % 16.31/3.00 | | | | | | | | | | | % 16.31/3.00 | | | | | | | | | | | % 16.31/3.00 | | | | | | | | | | | GROUND_INST: instantiating (3) with all_85_1, all_29_3, % 16.31/3.00 | | | | | | | | | | | all_29_2, simplifying with (21), (42), (94), (192) % 16.31/3.00 | | | | | | | | | | | gives: % 16.31/3.00 | | | | | | | | | | | (195) all_85_1 = all_29_3 % 16.31/3.00 | | | | | | | | | | | % 16.31/3.00 | | | | | | | | | | | REDUCE: (95), (195) imply: % 16.31/3.00 | | | | | | | | | | | (196) mem(all_29_3, all_41_1) = 0 % 16.31/3.00 | | | | | | | | | | | % 16.31/3.00 | | | | | | | | | | | GROUND_INST: instantiating (14) with all_62_0, 0, all_41_1, % 16.31/3.00 | | | | | | | | | | | all_29_3, simplifying with (160), (196) gives: % 16.31/3.00 | | | | | | | | | | | (197) all_62_0 = 0 % 16.31/3.00 | | | | | | | | | | | % 16.31/3.00 | | | | | | | | | | | REDUCE: (75), (197) imply: % 16.31/3.00 | | | | | | | | | | | (198) $false % 16.31/3.00 | | | | | | | | | | | % 16.31/3.00 | | | | | | | | | | | CLOSE: (198) is inconsistent. % 16.31/3.00 | | | | | | | | | | | % 16.31/3.00 | | | | | | | | | | End of split % 16.31/3.00 | | | | | | | | | | % 16.31/3.00 | | | | | | | | | End of split % 16.31/3.00 | | | | | | | | | % 16.31/3.00 | | | | | | | | End of split % 16.31/3.00 | | | | | | | | % 16.31/3.00 | | | | | | | End of split % 16.31/3.00 | | | | | | | % 16.31/3.00 | | | | | | Case 2: % 16.31/3.00 | | | | | | | % 16.31/3.00 | | | | | | | (199) all_98_1 = 0 % 16.31/3.00 | | | | | | | % 16.31/3.00 | | | | | | | REDUCE: (101), (199) imply: % 16.31/3.00 | | | | | | | (200) mem(all_56_2, all_29_2) = 0 % 16.31/3.00 | | | | | | | % 16.31/3.00 | | | | | | | GROUND_INST: instantiating (3) with all_56_2, all_29_3, all_29_2, % 16.31/3.00 | | | | | | | simplifying with (21), (42), (66), (200) gives: % 16.31/3.00 | | | | | | | (201) all_56_2 = all_29_3 % 16.31/3.00 | | | | | | | % 16.31/3.00 | | | | | | | REDUCE: (68), (201) imply: % 16.31/3.00 | | | | | | | (202) mem(all_29_3, all_41_1) = 0 % 16.31/3.00 | | | | | | | % 16.31/3.00 | | | | | | | GROUND_INST: instantiating (14) with all_62_0, 0, all_41_1, % 16.31/3.00 | | | | | | | all_29_3, simplifying with (160), (202) gives: % 16.31/3.00 | | | | | | | (203) all_62_0 = 0 % 16.31/3.00 | | | | | | | % 16.31/3.00 | | | | | | | REDUCE: (75), (203) imply: % 16.31/3.00 | | | | | | | (204) $false % 16.31/3.00 | | | | | | | % 16.31/3.00 | | | | | | | CLOSE: (204) is inconsistent. % 16.31/3.00 | | | | | | | % 16.31/3.00 | | | | | | End of split % 16.31/3.00 | | | | | | % 16.31/3.00 | | | | | End of split % 16.31/3.00 | | | | | % 16.31/3.00 | | | | End of split % 16.31/3.00 | | | | % 16.31/3.00 | | | End of split % 16.31/3.00 | | | % 16.31/3.00 | | End of split % 16.31/3.00 | | % 16.31/3.00 | End of split % 16.31/3.00 | % 16.31/3.00 End of proof % 16.31/3.00 % SZS output end Proof for theBenchmark % 16.31/3.00 % 16.31/3.00 2405ms %------------------------------------------------------------------------------