%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SEV552+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 13.59s 2.63s % Output : Proof 16.30s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : SEV552+1 : TPTP v9.1.0. Released v9.1.0. % 0.07/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.34 % Computer : n019.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 11:55:47 EDT 2025 % 0.13/0.34 % CPUTime : % 0.66/0.65 ________ _____ % 0.66/0.65 ___ __ \_________(_)________________________________ % 0.66/0.65 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.66/0.65 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.66/0.65 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.66/0.65 % 0.66/0.65 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.66/0.65 (2023-06-19) % 0.66/0.65 % 0.66/0.65 (c) Philipp Rümmer, 2009-2023 % 0.66/0.65 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.66/0.65 Amanda Stjerna. % 0.66/0.65 Free software under BSD-3-Clause. % 0.66/0.65 % 0.66/0.65 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.66/0.65 % 0.66/0.65 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.66/0.67 Running up to 7 provers in parallel. % 0.66/0.69 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.66/0.69 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.66/0.69 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.66/0.69 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.66/0.69 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.66/0.69 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.66/0.69 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.82/1.14 Prover 4: Preprocessing ... % 2.82/1.14 Prover 1: Preprocessing ... % 2.82/1.18 Prover 6: Preprocessing ... % 2.82/1.18 Prover 0: Preprocessing ... % 2.82/1.18 Prover 5: Preprocessing ... % 2.82/1.18 Prover 2: Preprocessing ... % 3.32/1.18 Prover 3: Preprocessing ... % 6.52/1.66 Prover 5: Proving ... % 7.15/1.72 Prover 2: Proving ... % 7.15/1.78 Prover 1: Constructing countermodel ... % 7.74/1.82 Prover 3: Constructing countermodel ... % 7.74/1.82 Prover 6: Proving ... % 8.65/1.99 Prover 4: Constructing countermodel ... % 9.35/2.01 Prover 1: gave up % 9.35/2.02 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 9.35/2.04 Prover 0: Proving ... % 9.35/2.05 Prover 3: gave up % 9.35/2.06 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 9.92/2.09 Prover 7: Preprocessing ... % 9.92/2.16 Prover 8: Preprocessing ... % 10.80/2.23 Prover 7: Warning: ignoring some quantifiers % 10.80/2.24 Prover 7: Constructing countermodel ... % 11.60/2.39 Prover 8: Warning: ignoring some quantifiers % 12.23/2.41 Prover 8: Constructing countermodel ... % 12.91/2.58 Prover 8: gave up % 12.91/2.58 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889 % 13.59/2.63 Prover 0: proved (1957ms) % 13.59/2.63 % 13.59/2.63 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 13.59/2.63 % 13.59/2.63 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 13.59/2.63 Prover 9: Preprocessing ... % 13.59/2.64 Prover 5: stopped % 13.59/2.64 Prover 2: stopped % 13.59/2.65 Prover 6: stopped % 13.59/2.66 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 13.59/2.66 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 13.59/2.66 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 13.59/2.67 Prover 10: Preprocessing ... % 14.35/2.69 Prover 13: Preprocessing ... % 14.48/2.71 Prover 11: Preprocessing ... % 14.48/2.73 Prover 16: Preprocessing ... % 14.48/2.79 Prover 10: Warning: ignoring some quantifiers % 15.15/2.80 Prover 16: Warning: ignoring some quantifiers % 15.15/2.81 Prover 16: Constructing countermodel ... % 15.15/2.81 Prover 10: Constructing countermodel ... % 15.15/2.82 Prover 4: Found proof (size 124) % 15.15/2.82 Prover 4: proved (2134ms) % 15.15/2.82 Prover 7: stopped % 15.15/2.82 Prover 16: stopped % 15.15/2.82 Prover 10: stopped % 15.15/2.83 Prover 9: Constructing countermodel ... % 15.15/2.84 Prover 13: Warning: ignoring some quantifiers % 15.15/2.84 Prover 9: stopped % 15.15/2.85 Prover 13: Constructing countermodel ... % 15.15/2.86 Prover 13: stopped % 15.70/2.93 Prover 11: Constructing countermodel ... % 15.70/2.95 Prover 11: stopped % 15.70/2.95 % 15.70/2.95 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 15.70/2.95 % 15.70/2.96 % SZS output start Proof for theBenchmark % 15.70/2.96 Assumptions after simplification: % 15.70/2.96 --------------------------------- % 15.70/2.96 % 15.70/2.96 (a_def) % 16.16/2.99 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (u(v0, v2) = v3) | % 16.16/2.99 ~ (s(v1) = v2) | ~ $i(v1) | ~ $i(v0) | (a(v0, v1) = v3 & $i(v3))) & ! % 16.16/2.99 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (a(v0, v1) = v2) | ~ $i(v1) | ~ % 16.16/2.99 $i(v0) | ? [v3: $i] : (u(v0, v3) = v2 & s(v1) = v3 & $i(v3) & $i(v2))) % 16.16/2.99 % 16.16/2.99 (atleast2p_def) % 16.16/2.99 ! [v0: $i] : ! [v1: int] : ! [v2: $i] : ! [v3: $i] : (v1 = 0 | ~ % 16.16/2.99 (atleast2p(v0) = v1) | ~ (p(v2) = v3) | ~ $i(v2) | ~ $i(v0) | ? [v4: % 16.16/2.99 any] : ? [v5: any] : (subq(v0, v3) = v5 & mem(v2, v0) = v4 & ( ~ (v4 = 0) % 16.16/2.99 | v5 = 0))) & ! [v0: $i] : ! [v1: int] : ! [v2: $i] : (v1 = 0 | ~ % 16.16/2.99 (atleast2p(v0) = v1) | ~ (mem(v2, v0) = 0) | ~ $i(v2) | ~ $i(v0) | ? % 16.16/2.99 [v3: $i] : (p(v2) = v3 & subq(v0, v3) = 0 & $i(v3))) & ! [v0: $i] : ( ~ % 16.16/2.99 (atleast2p(v0) = 0) | ~ $i(v0) | ? [v1: $i] : ? [v2: $i] : ? [v3: int] : % 16.16/2.99 ( ~ (v3 = 0) & p(v1) = v2 & subq(v0, v2) = v3 & mem(v1, v0) = 0 & $i(v2) & % 16.16/2.99 $i(v1))) % 16.16/2.99 % 16.16/3.00 (atleast3p_def) % 16.16/3.00 ! [v0: $i] : ! [v1: int] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | v1 = 0 | % 16.16/3.00 ~ (atleast3p(v0) = v1) | ~ (subq(v0, v2) = v3) | ~ $i(v2) | ~ $i(v0) | ? % 16.16/3.00 [v4: any] : ? [v5: any] : (atleast2p(v2) = v5 & subq(v2, v0) = v4 & ( ~ (v5 % 16.16/3.00 = 0) | ~ (v4 = 0)))) & ! [v0: $i] : ! [v1: int] : ! [v2: $i] : (v1 % 16.16/3.00 = 0 | ~ (atleast3p(v0) = v1) | ~ (atleast2p(v2) = 0) | ~ $i(v2) | ~ % 16.16/3.00 $i(v0) | ? [v3: any] : ? [v4: any] : (subq(v2, v0) = v3 & subq(v0, v2) = % 16.16/3.00 v4 & ( ~ (v3 = 0) | v4 = 0))) & ! [v0: $i] : ! [v1: int] : ! [v2: $i] : % 16.16/3.00 (v1 = 0 | ~ (atleast3p(v0) = v1) | ~ (subq(v2, v0) = 0) | ~ $i(v2) | ~ % 16.16/3.00 $i(v0) | ? [v3: any] : ? [v4: any] : (atleast2p(v2) = v3 & subq(v0, v2) = % 16.16/3.00 v4 & ( ~ (v3 = 0) | v4 = 0))) & ! [v0: $i] : ( ~ (atleast3p(v0) = 0) | ~ % 16.16/3.00 $i(v0) | ? [v1: $i] : ? [v2: int] : ( ~ (v2 = 0) & atleast2p(v1) = 0 & % 16.16/3.00 subq(v1, v0) = 0 & subq(v0, v1) = v2 & $i(v1))) % 16.16/3.00 % 16.16/3.00 (atmost2_4352) % 16.16/3.01 $i(e) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 16.16/3.01 ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : (atleast3p(v7) = 0 & n(v0) = v1 & % 16.16/3.01 n(e) = v0 & a(v5, v1) = v6 & a(v3, v6) = v7 & s(v4) = v5 & s(v2) = v3 & % 16.16/3.01 s(v1) = v2 & s(v0) = v4 & $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) & % 16.16/3.01 $i(v2) & $i(v1) & $i(v0)) % 16.16/3.01 % 16.16/3.01 (p_ax) % 16.25/3.01 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (p(v1) = % 16.25/3.01 v2) | ~ (mem(v0, v2) = v3) | ~ $i(v1) | ~ $i(v0) | ? [v4: int] : ( ~ % 16.25/3.01 (v4 = 0) & subq(v0, v1) = v4)) & ! [v0: $i] : ! [v1: $i] : ! [v2: int] % 16.25/3.01 : (v2 = 0 | ~ (subq(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? % 16.25/3.01 [v4: int] : ( ~ (v4 = 0) & p(v1) = v3 & mem(v0, v3) = v4 & $i(v3))) & ! % 16.25/3.01 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (p(v1) = v2) | ~ (mem(v0, v2) = 0) % 16.25/3.01 | ~ $i(v1) | ~ $i(v0) | subq(v0, v1) = 0) & ! [v0: $i] : ! [v1: $i] : ( % 16.25/3.01 ~ (subq(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: $i] : (p(v1) = v2 & % 16.25/3.01 mem(v0, v2) = 0 & $i(v2))) % 16.25/3.01 % 16.25/3.01 (s_ax) % 16.25/3.01 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (s(v0) = v1) | ~ % 16.25/3.01 (mem(v0, v1) = v2) | ~ $i(v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 16.25/3.01 (v1 = v0 | ~ (s(v1) = v2) | ~ (mem(v0, v2) = 0) | ~ $i(v1) | ~ $i(v0)) % 16.25/3.01 % 16.25/3.01 (subq_def) % 16.25/3.01 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 16.25/3.01 (subq(v0, v1) = 0) | ~ (mem(v2, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ % 16.25/3.01 $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & mem(v2, v0) = v4)) & ! [v0: $i] : ! % 16.25/3.01 [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subq(v0, v1) = v2) | ~ $i(v1) | ~ % 16.25/3.01 $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & mem(v3, v1) = v4 & % 16.25/3.01 mem(v3, v0) = 0 & $i(v3))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 16.25/3.01 (subq(v0, v1) = 0) | ~ (mem(v2, v0) = 0) | ~ $i(v2) | ~ $i(v1) | ~ % 16.25/3.01 $i(v0) | mem(v2, v1) = 0) % 16.25/3.01 % 16.25/3.01 (u_ax) % 16.30/3.02 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0 % 16.30/3.02 | ~ (u(v1, v2) = v3) | ~ (mem(v0, v3) = v4) | ~ $i(v2) | ~ $i(v1) | ~ % 16.30/3.02 $i(v0) | ? [v5: int] : ? [v6: int] : ( ~ (v6 = 0) & ~ (v5 = 0) & mem(v0, % 16.30/3.02 v2) = v6 & mem(v0, v1) = v5)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 16.30/3.02 : ! [v3: $i] : ( ~ (u(v1, v2) = v3) | ~ (mem(v0, v3) = 0) | ~ $i(v2) | ~ % 16.30/3.02 $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] : (mem(v0, v2) = v5 & % 16.30/3.02 mem(v0, v1) = v4 & (v5 = 0 | v4 = 0))) % 16.30/3.02 % 16.30/3.02 (function-axioms) % 16.30/3.02 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (a(v3, % 16.30/3.02 v2) = v1) | ~ (a(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 16.30/3.02 $i] : ! [v3: $i] : (v1 = v0 | ~ (m(v3, v2) = v1) | ~ (m(v3, v2) = v0)) & % 16.30/3.02 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (u(v3, % 16.30/3.02 v2) = v1) | ~ (u(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 16.30/3.02 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (disj(v3, v2) % 16.30/3.02 = v1) | ~ (disj(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 16.30/3.02 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (subq(v3, v2) % 16.30/3.02 = v1) | ~ (subq(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 16.30/3.02 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (mem(v3, v2) % 16.30/3.02 = v1) | ~ (mem(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 16.30/3.02 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (atleast16p(v2) = v1) | ~ % 16.30/3.02 (atleast16p(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 16.30/3.02 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (atleast15p(v2) = v1) | ~ % 16.30/3.02 (atleast15p(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 16.30/3.02 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (atleast14p(v2) = v1) | ~ % 16.30/3.02 (atleast14p(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 16.30/3.02 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (atleast13p(v2) = v1) | ~ % 16.30/3.02 (atleast13p(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 16.30/3.02 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (atleast12p(v2) = v1) | ~ % 16.30/3.02 (atleast12p(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 16.30/3.02 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (atleast11p(v2) = v1) | ~ % 16.30/3.02 (atleast11p(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 16.30/3.02 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (atleast10p(v2) = v1) | ~ % 16.30/3.02 (atleast10p(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 16.30/3.02 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (atleast9p(v2) = v1) | ~ % 16.30/3.02 (atleast9p(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 16.30/3.02 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (atleast8p(v2) = v1) | ~ % 16.30/3.02 (atleast8p(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 16.30/3.02 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (atleast7p(v2) = v1) | ~ % 16.30/3.02 (atleast7p(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 16.30/3.02 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (atleast6p(v2) = v1) | ~ % 16.30/3.02 (atleast6p(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 16.30/3.02 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (atleast5p(v2) = v1) | ~ % 16.30/3.02 (atleast5p(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 16.30/3.02 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (atleast4p(v2) = v1) | ~ % 16.30/3.02 (atleast4p(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 16.30/3.02 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (atleast3p(v2) = v1) | ~ % 16.30/3.02 (atleast3p(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 16.30/3.02 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (atleast2p(v2) = v1) | ~ % 16.30/3.02 (atleast2p(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | % 16.30/3.02 ~ (p(v2) = v1) | ~ (p(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 16.30/3.02 : (v1 = v0 | ~ (n(v2) = v1) | ~ (n(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : % 16.30/3.02 ! [v2: $i] : (v1 = v0 | ~ (s(v2) = v1) | ~ (s(v2) = v0)) % 16.30/3.02 % 16.30/3.02 Further assumptions not needed in the proof: % 16.30/3.02 -------------------------------------------- % 16.30/3.02 atleast10p_def, atleast11p_def, atleast12p_def, atleast13p_def, atleast14p_def, % 16.30/3.02 atleast15p_def, atleast16p_def, atleast4p_def, atleast5p_def, atleast6p_def, % 16.30/3.02 atleast7p_def, atleast8p_def, atleast9p_def, disj_def, e_ax, m_ax, n_def, setext % 16.30/3.02 % 16.30/3.02 Those formulas are unsatisfiable: % 16.30/3.02 --------------------------------- % 16.30/3.02 % 16.30/3.02 Begin of proof % 16.30/3.02 | % 16.30/3.02 | ALPHA: (subq_def) implies: % 16.30/3.03 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (subq(v0, v1) = 0) | ~ % 16.30/3.03 | (mem(v2, v0) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | mem(v2, v1) = % 16.30/3.03 | 0) % 16.30/3.03 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subq(v0, v1) = % 16.30/3.03 | v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 % 16.30/3.03 | = 0) & mem(v3, v1) = v4 & mem(v3, v0) = 0 & $i(v3))) % 16.30/3.03 | % 16.30/3.03 | ALPHA: (s_ax) implies: % 16.30/3.03 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (s(v1) = v2) | % 16.30/3.03 | ~ (mem(v0, v2) = 0) | ~ $i(v1) | ~ $i(v0)) % 16.30/3.03 | % 16.30/3.03 | ALPHA: (u_ax) implies: % 16.30/3.03 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (u(v1, v2) % 16.30/3.03 | = v3) | ~ (mem(v0, v3) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 16.30/3.03 | ? [v4: any] : ? [v5: any] : (mem(v0, v2) = v5 & mem(v0, v1) = v4 & % 16.30/3.03 | (v5 = 0 | v4 = 0))) % 16.30/3.03 | % 16.30/3.03 | ALPHA: (a_def) implies: % 16.30/3.03 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (a(v0, v1) = v2) | ~ % 16.30/3.03 | $i(v1) | ~ $i(v0) | ? [v3: $i] : (u(v0, v3) = v2 & s(v1) = v3 & % 16.30/3.03 | $i(v3) & $i(v2))) % 16.30/3.03 | % 16.30/3.03 | ALPHA: (p_ax) implies: % 16.30/3.03 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 16.30/3.03 | (p(v1) = v2) | ~ (mem(v0, v2) = v3) | ~ $i(v1) | ~ $i(v0) | ? % 16.30/3.03 | [v4: int] : ( ~ (v4 = 0) & subq(v0, v1) = v4)) % 16.30/3.03 | % 16.30/3.03 | ALPHA: (atleast2p_def) implies: % 16.30/3.03 | (7) ! [v0: $i] : ( ~ (atleast2p(v0) = 0) | ~ $i(v0) | ? [v1: $i] : ? % 16.30/3.03 | [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) & p(v1) = v2 & subq(v0, v2) = % 16.30/3.03 | v3 & mem(v1, v0) = 0 & $i(v2) & $i(v1))) % 16.30/3.03 | % 16.30/3.03 | ALPHA: (atleast3p_def) implies: % 16.30/3.03 | (8) ! [v0: $i] : ( ~ (atleast3p(v0) = 0) | ~ $i(v0) | ? [v1: $i] : ? % 16.30/3.03 | [v2: int] : ( ~ (v2 = 0) & atleast2p(v1) = 0 & subq(v1, v0) = 0 & % 16.30/3.03 | subq(v0, v1) = v2 & $i(v1))) % 16.30/3.03 | % 16.30/3.03 | ALPHA: (atmost2_4352) implies: % 16.30/3.03 | (9) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 16.30/3.03 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : (atleast3p(v7) = 0 & n(v0) = % 16.30/3.03 | v1 & n(e) = v0 & a(v5, v1) = v6 & a(v3, v6) = v7 & s(v4) = v5 & s(v2) % 16.30/3.03 | = v3 & s(v1) = v2 & s(v0) = v4 & $i(v7) & $i(v6) & $i(v5) & $i(v4) & % 16.30/3.03 | $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 16.30/3.03 | % 16.30/3.03 | ALPHA: (function-axioms) implies: % 16.30/3.03 | (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (s(v2) = v1) | % 16.30/3.03 | ~ (s(v2) = v0)) % 16.30/3.03 | (11) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 16.30/3.03 | : ! [v3: $i] : (v1 = v0 | ~ (mem(v3, v2) = v1) | ~ (mem(v3, v2) = % 16.30/3.03 | v0)) % 16.30/3.03 | % 16.30/3.04 | DELTA: instantiating (9) with fresh symbols all_29_0, all_29_1, all_29_2, % 16.30/3.04 | all_29_3, all_29_4, all_29_5, all_29_6, all_29_7 gives: % 16.30/3.04 | (12) atleast3p(all_29_0) = 0 & n(all_29_7) = all_29_6 & n(e) = all_29_7 & % 16.30/3.04 | a(all_29_2, all_29_6) = all_29_1 & a(all_29_4, all_29_1) = all_29_0 & % 16.30/3.04 | s(all_29_3) = all_29_2 & s(all_29_5) = all_29_4 & s(all_29_6) = % 16.30/3.04 | all_29_5 & s(all_29_7) = all_29_3 & $i(all_29_0) & $i(all_29_1) & % 16.30/3.04 | $i(all_29_2) & $i(all_29_3) & $i(all_29_4) & $i(all_29_5) & % 16.30/3.04 | $i(all_29_6) & $i(all_29_7) % 16.30/3.04 | % 16.30/3.04 | ALPHA: (12) implies: % 16.30/3.04 | (13) $i(all_29_6) % 16.30/3.04 | (14) $i(all_29_4) % 16.30/3.04 | (15) $i(all_29_2) % 16.30/3.04 | (16) $i(all_29_1) % 16.30/3.04 | (17) $i(all_29_0) % 16.30/3.04 | (18) s(all_29_6) = all_29_5 % 16.30/3.04 | (19) s(all_29_5) = all_29_4 % 16.30/3.04 | (20) a(all_29_4, all_29_1) = all_29_0 % 16.30/3.04 | (21) a(all_29_2, all_29_6) = all_29_1 % 16.30/3.04 | (22) atleast3p(all_29_0) = 0 % 16.30/3.04 | % 16.30/3.04 | GROUND_INST: instantiating (5) with all_29_4, all_29_1, all_29_0, simplifying % 16.30/3.04 | with (14), (16), (20) gives: % 16.30/3.04 | (23) ? [v0: $i] : (u(all_29_4, v0) = all_29_0 & s(all_29_1) = v0 & $i(v0) % 16.30/3.04 | & $i(all_29_0)) % 16.30/3.04 | % 16.30/3.04 | GROUND_INST: instantiating (5) with all_29_2, all_29_6, all_29_1, simplifying % 16.30/3.04 | with (13), (15), (21) gives: % 16.30/3.04 | (24) ? [v0: $i] : (u(all_29_2, v0) = all_29_1 & s(all_29_6) = v0 & $i(v0) % 16.30/3.04 | & $i(all_29_1)) % 16.30/3.04 | % 16.30/3.04 | GROUND_INST: instantiating (8) with all_29_0, simplifying with (17), (22) % 16.30/3.04 | gives: % 16.30/3.04 | (25) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & atleast2p(v0) = 0 & % 16.30/3.04 | subq(v0, all_29_0) = 0 & subq(all_29_0, v0) = v1 & $i(v0)) % 16.30/3.04 | % 16.30/3.04 | DELTA: instantiating (24) with fresh symbol all_37_0 gives: % 16.30/3.04 | (26) u(all_29_2, all_37_0) = all_29_1 & s(all_29_6) = all_37_0 & % 16.30/3.04 | $i(all_37_0) & $i(all_29_1) % 16.30/3.04 | % 16.30/3.04 | ALPHA: (26) implies: % 16.30/3.04 | (27) $i(all_37_0) % 16.30/3.04 | (28) s(all_29_6) = all_37_0 % 16.30/3.04 | % 16.30/3.04 | DELTA: instantiating (23) with fresh symbol all_39_0 gives: % 16.30/3.04 | (29) u(all_29_4, all_39_0) = all_29_0 & s(all_29_1) = all_39_0 & % 16.30/3.04 | $i(all_39_0) & $i(all_29_0) % 16.30/3.04 | % 16.30/3.04 | ALPHA: (29) implies: % 16.30/3.04 | (30) $i(all_39_0) % 16.30/3.04 | (31) s(all_29_1) = all_39_0 % 16.30/3.04 | (32) u(all_29_4, all_39_0) = all_29_0 % 16.30/3.04 | % 16.30/3.04 | DELTA: instantiating (25) with fresh symbols all_41_0, all_41_1 gives: % 16.30/3.04 | (33) ~ (all_41_0 = 0) & atleast2p(all_41_1) = 0 & subq(all_41_1, all_29_0) % 16.30/3.04 | = 0 & subq(all_29_0, all_41_1) = all_41_0 & $i(all_41_1) % 16.30/3.04 | % 16.30/3.04 | ALPHA: (33) implies: % 16.30/3.04 | (34) ~ (all_41_0 = 0) % 16.30/3.04 | (35) $i(all_41_1) % 16.30/3.04 | (36) subq(all_29_0, all_41_1) = all_41_0 % 16.30/3.04 | (37) subq(all_41_1, all_29_0) = 0 % 16.30/3.04 | (38) atleast2p(all_41_1) = 0 % 16.30/3.04 | % 16.30/3.04 | GROUND_INST: instantiating (10) with all_29_5, all_37_0, all_29_6, simplifying % 16.30/3.04 | with (18), (28) gives: % 16.30/3.04 | (39) all_37_0 = all_29_5 % 16.30/3.04 | % 16.30/3.04 | REDUCE: (27), (39) imply: % 16.30/3.04 | (40) $i(all_29_5) % 16.30/3.05 | % 16.30/3.05 | GROUND_INST: instantiating (2) with all_29_0, all_41_1, all_41_0, simplifying % 16.30/3.05 | with (17), (35), (36) gives: % 16.30/3.05 | (41) all_41_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & mem(v0, % 16.30/3.05 | all_41_1) = v1 & mem(v0, all_29_0) = 0 & $i(v0)) % 16.30/3.05 | % 16.30/3.05 | GROUND_INST: instantiating (7) with all_41_1, simplifying with (35), (38) % 16.30/3.05 | gives: % 16.30/3.05 | (42) ? [v0: $i] : ? [v1: $i] : ? [v2: int] : ( ~ (v2 = 0) & p(v0) = v1 & % 16.30/3.05 | subq(all_41_1, v1) = v2 & mem(v0, all_41_1) = 0 & $i(v1) & $i(v0)) % 16.30/3.05 | % 16.30/3.05 | DELTA: instantiating (42) with fresh symbols all_58_0, all_58_1, all_58_2 % 16.30/3.05 | gives: % 16.30/3.05 | (43) ~ (all_58_0 = 0) & p(all_58_2) = all_58_1 & subq(all_41_1, all_58_1) % 16.30/3.05 | = all_58_0 & mem(all_58_2, all_41_1) = 0 & $i(all_58_1) & $i(all_58_2) % 16.30/3.05 | % 16.30/3.05 | ALPHA: (43) implies: % 16.30/3.05 | (44) ~ (all_58_0 = 0) % 16.30/3.05 | (45) $i(all_58_2) % 16.30/3.05 | (46) $i(all_58_1) % 16.30/3.05 | (47) mem(all_58_2, all_41_1) = 0 % 16.30/3.05 | (48) subq(all_41_1, all_58_1) = all_58_0 % 16.30/3.05 | (49) p(all_58_2) = all_58_1 % 16.30/3.05 | % 16.30/3.05 | BETA: splitting (41) gives: % 16.30/3.05 | % 16.30/3.05 | Case 1: % 16.30/3.05 | | % 16.30/3.05 | | (50) all_41_0 = 0 % 16.30/3.05 | | % 16.30/3.05 | | REDUCE: (34), (50) imply: % 16.30/3.05 | | (51) $false % 16.30/3.05 | | % 16.30/3.05 | | CLOSE: (51) is inconsistent. % 16.30/3.05 | | % 16.30/3.05 | Case 2: % 16.30/3.05 | | % 16.30/3.05 | | (52) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & mem(v0, all_41_1) = v1 & % 16.30/3.05 | | mem(v0, all_29_0) = 0 & $i(v0)) % 16.30/3.05 | | % 16.30/3.05 | | DELTA: instantiating (52) with fresh symbols all_64_0, all_64_1 gives: % 16.30/3.05 | | (53) ~ (all_64_0 = 0) & mem(all_64_1, all_41_1) = all_64_0 & % 16.30/3.05 | | mem(all_64_1, all_29_0) = 0 & $i(all_64_1) % 16.30/3.05 | | % 16.30/3.05 | | ALPHA: (53) implies: % 16.30/3.05 | | (54) ~ (all_64_0 = 0) % 16.30/3.05 | | (55) $i(all_64_1) % 16.30/3.05 | | (56) mem(all_64_1, all_29_0) = 0 % 16.30/3.05 | | (57) mem(all_64_1, all_41_1) = all_64_0 % 16.30/3.05 | | % 16.30/3.05 | | GROUND_INST: instantiating (1) with all_41_1, all_29_0, all_58_2, % 16.30/3.05 | | simplifying with (17), (35), (37), (45), (47) gives: % 16.30/3.05 | | (58) mem(all_58_2, all_29_0) = 0 % 16.30/3.05 | | % 16.30/3.05 | | GROUND_INST: instantiating (4) with all_64_1, all_29_4, all_39_0, all_29_0, % 16.30/3.05 | | simplifying with (14), (30), (32), (55), (56) gives: % 16.30/3.05 | | (59) ? [v0: any] : ? [v1: any] : (mem(all_64_1, all_39_0) = v1 & % 16.30/3.05 | | mem(all_64_1, all_29_4) = v0 & (v1 = 0 | v0 = 0)) % 16.30/3.05 | | % 16.30/3.05 | | GROUND_INST: instantiating (2) with all_41_1, all_58_1, all_58_0, % 16.30/3.05 | | simplifying with (35), (46), (48) gives: % 16.30/3.05 | | (60) all_58_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & mem(v0, % 16.30/3.05 | | all_58_1) = v1 & mem(v0, all_41_1) = 0 & $i(v0)) % 16.30/3.05 | | % 16.30/3.06 | | DELTA: instantiating (59) with fresh symbols all_81_0, all_81_1 gives: % 16.30/3.06 | | (61) mem(all_64_1, all_39_0) = all_81_0 & mem(all_64_1, all_29_4) = % 16.30/3.06 | | all_81_1 & (all_81_0 = 0 | all_81_1 = 0) % 16.30/3.06 | | % 16.30/3.06 | | ALPHA: (61) implies: % 16.30/3.06 | | (62) mem(all_64_1, all_29_4) = all_81_1 % 16.30/3.06 | | (63) mem(all_64_1, all_39_0) = all_81_0 % 16.30/3.06 | | (64) all_81_0 = 0 | all_81_1 = 0 % 16.30/3.06 | | % 16.30/3.06 | | BETA: splitting (60) gives: % 16.30/3.06 | | % 16.30/3.06 | | Case 1: % 16.30/3.06 | | | % 16.30/3.06 | | | (65) all_58_0 = 0 % 16.30/3.06 | | | % 16.30/3.06 | | | REDUCE: (44), (65) imply: % 16.30/3.06 | | | (66) $false % 16.30/3.06 | | | % 16.30/3.06 | | | CLOSE: (66) is inconsistent. % 16.30/3.06 | | | % 16.30/3.06 | | Case 2: % 16.30/3.06 | | | % 16.30/3.06 | | | (67) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & mem(v0, all_58_1) = v1 % 16.30/3.06 | | | & mem(v0, all_41_1) = 0 & $i(v0)) % 16.30/3.06 | | | % 16.30/3.06 | | | DELTA: instantiating (67) with fresh symbols all_87_0, all_87_1 gives: % 16.30/3.06 | | | (68) ~ (all_87_0 = 0) & mem(all_87_1, all_58_1) = all_87_0 & % 16.30/3.06 | | | mem(all_87_1, all_41_1) = 0 & $i(all_87_1) % 16.30/3.06 | | | % 16.30/3.06 | | | ALPHA: (68) implies: % 16.30/3.06 | | | (69) ~ (all_87_0 = 0) % 16.30/3.06 | | | (70) $i(all_87_1) % 16.30/3.06 | | | (71) mem(all_87_1, all_41_1) = 0 % 16.30/3.06 | | | (72) mem(all_87_1, all_58_1) = all_87_0 % 16.30/3.06 | | | % 16.30/3.06 | | | GROUND_INST: instantiating (4) with all_58_2, all_29_4, all_39_0, % 16.30/3.06 | | | all_29_0, simplifying with (14), (30), (32), (45), (58) % 16.30/3.06 | | | gives: % 16.30/3.06 | | | (73) ? [v0: any] : ? [v1: any] : (mem(all_58_2, all_39_0) = v1 & % 16.30/3.06 | | | mem(all_58_2, all_29_4) = v0 & (v1 = 0 | v0 = 0)) % 16.30/3.06 | | | % 16.30/3.06 | | | GROUND_INST: instantiating (1) with all_41_1, all_29_0, all_87_1, % 16.30/3.06 | | | simplifying with (17), (35), (37), (70), (71) gives: % 16.30/3.06 | | | (74) mem(all_87_1, all_29_0) = 0 % 16.30/3.06 | | | % 16.30/3.06 | | | GROUND_INST: instantiating (6) with all_87_1, all_58_2, all_58_1, % 16.30/3.06 | | | all_87_0, simplifying with (45), (49), (70), (72) gives: % 16.30/3.06 | | | (75) all_87_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & subq(all_87_1, % 16.30/3.06 | | | all_58_2) = v0) % 16.30/3.06 | | | % 16.30/3.06 | | | DELTA: instantiating (73) with fresh symbols all_100_0, all_100_1 gives: % 16.30/3.06 | | | (76) mem(all_58_2, all_39_0) = all_100_0 & mem(all_58_2, all_29_4) = % 16.30/3.06 | | | all_100_1 & (all_100_0 = 0 | all_100_1 = 0) % 16.30/3.06 | | | % 16.30/3.06 | | | ALPHA: (76) implies: % 16.30/3.06 | | | (77) mem(all_58_2, all_29_4) = all_100_1 % 16.30/3.06 | | | (78) mem(all_58_2, all_39_0) = all_100_0 % 16.30/3.06 | | | (79) all_100_0 = 0 | all_100_1 = 0 % 16.30/3.06 | | | % 16.30/3.06 | | | BETA: splitting (75) gives: % 16.30/3.06 | | | % 16.30/3.06 | | | Case 1: % 16.30/3.06 | | | | % 16.30/3.06 | | | | (80) all_87_0 = 0 % 16.30/3.06 | | | | % 16.30/3.06 | | | | REDUCE: (69), (80) imply: % 16.30/3.06 | | | | (81) $false % 16.30/3.06 | | | | % 16.30/3.06 | | | | CLOSE: (81) is inconsistent. % 16.30/3.06 | | | | % 16.30/3.06 | | | Case 2: % 16.30/3.06 | | | | % 16.30/3.06 | | | | (82) ? [v0: int] : ( ~ (v0 = 0) & subq(all_87_1, all_58_2) = v0) % 16.30/3.06 | | | | % 16.30/3.06 | | | | DELTA: instantiating (82) with fresh symbol all_106_0 gives: % 16.30/3.06 | | | | (83) ~ (all_106_0 = 0) & subq(all_87_1, all_58_2) = all_106_0 % 16.30/3.06 | | | | % 16.30/3.06 | | | | ALPHA: (83) implies: % 16.30/3.07 | | | | (84) ~ (all_106_0 = 0) % 16.30/3.07 | | | | (85) subq(all_87_1, all_58_2) = all_106_0 % 16.30/3.07 | | | | % 16.30/3.07 | | | | GROUND_INST: instantiating (4) with all_87_1, all_29_4, all_39_0, % 16.30/3.07 | | | | all_29_0, simplifying with (14), (30), (32), (70), (74) % 16.30/3.07 | | | | gives: % 16.30/3.07 | | | | (86) ? [v0: any] : ? [v1: any] : (mem(all_87_1, all_39_0) = v1 & % 16.30/3.07 | | | | mem(all_87_1, all_29_4) = v0 & (v1 = 0 | v0 = 0)) % 16.30/3.07 | | | | % 16.30/3.07 | | | | GROUND_INST: instantiating (2) with all_87_1, all_58_2, all_106_0, % 16.30/3.07 | | | | simplifying with (45), (70), (85) gives: % 16.30/3.07 | | | | (87) all_106_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & % 16.30/3.07 | | | | mem(v0, all_87_1) = 0 & mem(v0, all_58_2) = v1 & $i(v0)) % 16.30/3.07 | | | | % 16.30/3.07 | | | | DELTA: instantiating (86) with fresh symbols all_113_0, all_113_1 gives: % 16.30/3.07 | | | | (88) mem(all_87_1, all_39_0) = all_113_0 & mem(all_87_1, all_29_4) = % 16.30/3.07 | | | | all_113_1 & (all_113_0 = 0 | all_113_1 = 0) % 16.30/3.07 | | | | % 16.30/3.07 | | | | ALPHA: (88) implies: % 16.30/3.07 | | | | (89) mem(all_87_1, all_29_4) = all_113_1 % 16.30/3.07 | | | | (90) mem(all_87_1, all_39_0) = all_113_0 % 16.30/3.07 | | | | (91) all_113_0 = 0 | all_113_1 = 0 % 16.30/3.07 | | | | % 16.30/3.07 | | | | BETA: splitting (87) gives: % 16.30/3.07 | | | | % 16.30/3.07 | | | | Case 1: % 16.30/3.07 | | | | | % 16.30/3.07 | | | | | (92) all_106_0 = 0 % 16.30/3.07 | | | | | % 16.30/3.07 | | | | | REDUCE: (84), (92) imply: % 16.30/3.07 | | | | | (93) $false % 16.30/3.07 | | | | | % 16.30/3.07 | | | | | CLOSE: (93) is inconsistent. % 16.30/3.07 | | | | | % 16.30/3.07 | | | | Case 2: % 16.30/3.07 | | | | | % 16.30/3.07 | | | | | (94) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & mem(v0, all_87_1) % 16.30/3.07 | | | | | = 0 & mem(v0, all_58_2) = v1 & $i(v0)) % 16.30/3.07 | | | | | % 16.30/3.07 | | | | | DELTA: instantiating (94) with fresh symbols all_119_0, all_119_1 % 16.30/3.07 | | | | | gives: % 16.30/3.07 | | | | | (95) ~ (all_119_0 = 0) & mem(all_119_1, all_87_1) = 0 & % 16.30/3.07 | | | | | mem(all_119_1, all_58_2) = all_119_0 & $i(all_119_1) % 16.30/3.07 | | | | | % 16.30/3.07 | | | | | ALPHA: (95) implies: % 16.30/3.07 | | | | | (96) ~ (all_119_0 = 0) % 16.30/3.07 | | | | | (97) mem(all_119_1, all_58_2) = all_119_0 % 16.30/3.07 | | | | | (98) mem(all_119_1, all_87_1) = 0 % 16.30/3.07 | | | | | % 16.30/3.07 | | | | | BETA: splitting (64) gives: % 16.30/3.07 | | | | | % 16.30/3.07 | | | | | Case 1: % 16.30/3.07 | | | | | | % 16.30/3.07 | | | | | | (99) all_81_0 = 0 % 16.30/3.07 | | | | | | % 16.30/3.07 | | | | | | REDUCE: (63), (99) imply: % 16.30/3.07 | | | | | | (100) mem(all_64_1, all_39_0) = 0 % 16.30/3.07 | | | | | | % 16.30/3.07 | | | | | | GROUND_INST: instantiating (3) with all_64_1, all_29_1, all_39_0, % 16.30/3.07 | | | | | | simplifying with (16), (31), (55), (100) gives: % 16.30/3.07 | | | | | | (101) all_64_1 = all_29_1 % 16.30/3.07 | | | | | | % 16.30/3.07 | | | | | | REDUCE: (57), (101) imply: % 16.30/3.07 | | | | | | (102) mem(all_29_1, all_41_1) = all_64_0 % 16.30/3.07 | | | | | | % 16.30/3.07 | | | | | | BETA: splitting (79) gives: % 16.30/3.07 | | | | | | % 16.30/3.07 | | | | | | Case 1: % 16.30/3.07 | | | | | | | % 16.30/3.07 | | | | | | | (103) all_100_0 = 0 % 16.30/3.07 | | | | | | | % 16.30/3.07 | | | | | | | REDUCE: (78), (103) imply: % 16.30/3.07 | | | | | | | (104) mem(all_58_2, all_39_0) = 0 % 16.30/3.07 | | | | | | | % 16.30/3.07 | | | | | | | GROUND_INST: instantiating (3) with all_58_2, all_29_1, all_39_0, % 16.30/3.07 | | | | | | | simplifying with (16), (31), (45), (104) gives: % 16.30/3.07 | | | | | | | (105) all_58_2 = all_29_1 % 16.30/3.07 | | | | | | | % 16.30/3.07 | | | | | | | REDUCE: (47), (105) imply: % 16.30/3.07 | | | | | | | (106) mem(all_29_1, all_41_1) = 0 % 16.30/3.07 | | | | | | | % 16.30/3.07 | | | | | | | GROUND_INST: instantiating (11) with all_64_0, 0, all_41_1, % 16.30/3.07 | | | | | | | all_29_1, simplifying with (102), (106) gives: % 16.30/3.07 | | | | | | | (107) all_64_0 = 0 % 16.30/3.07 | | | | | | | % 16.30/3.07 | | | | | | | REDUCE: (54), (107) imply: % 16.30/3.07 | | | | | | | (108) $false % 16.30/3.07 | | | | | | | % 16.30/3.07 | | | | | | | CLOSE: (108) is inconsistent. % 16.30/3.07 | | | | | | | % 16.30/3.07 | | | | | | Case 2: % 16.30/3.07 | | | | | | | % 16.30/3.07 | | | | | | | (109) all_100_1 = 0 % 16.30/3.07 | | | | | | | % 16.30/3.07 | | | | | | | REDUCE: (77), (109) imply: % 16.30/3.07 | | | | | | | (110) mem(all_58_2, all_29_4) = 0 % 16.30/3.07 | | | | | | | % 16.30/3.07 | | | | | | | GROUND_INST: instantiating (3) with all_58_2, all_29_5, all_29_4, % 16.30/3.07 | | | | | | | simplifying with (19), (40), (45), (110) gives: % 16.30/3.08 | | | | | | | (111) all_58_2 = all_29_5 % 16.30/3.08 | | | | | | | % 16.30/3.08 | | | | | | | REDUCE: (97), (111) imply: % 16.30/3.08 | | | | | | | (112) mem(all_119_1, all_29_5) = all_119_0 % 16.30/3.08 | | | | | | | % 16.30/3.08 | | | | | | | BETA: splitting (91) gives: % 16.30/3.08 | | | | | | | % 16.30/3.08 | | | | | | | Case 1: % 16.30/3.08 | | | | | | | | % 16.30/3.08 | | | | | | | | (113) all_113_0 = 0 % 16.30/3.08 | | | | | | | | % 16.30/3.08 | | | | | | | | REDUCE: (90), (113) imply: % 16.30/3.08 | | | | | | | | (114) mem(all_87_1, all_39_0) = 0 % 16.30/3.08 | | | | | | | | % 16.30/3.08 | | | | | | | | GROUND_INST: instantiating (3) with all_87_1, all_29_1, % 16.30/3.08 | | | | | | | | all_39_0, simplifying with (16), (31), (70), (114) % 16.30/3.08 | | | | | | | | gives: % 16.30/3.08 | | | | | | | | (115) all_87_1 = all_29_1 % 16.30/3.08 | | | | | | | | % 16.30/3.08 | | | | | | | | REDUCE: (71), (115) imply: % 16.30/3.08 | | | | | | | | (116) mem(all_29_1, all_41_1) = 0 % 16.30/3.08 | | | | | | | | % 16.30/3.08 | | | | | | | | GROUND_INST: instantiating (11) with all_64_0, 0, all_41_1, % 16.30/3.08 | | | | | | | | all_29_1, simplifying with (102), (116) gives: % 16.30/3.08 | | | | | | | | (117) all_64_0 = 0 % 16.30/3.08 | | | | | | | | % 16.30/3.08 | | | | | | | | REDUCE: (54), (117) imply: % 16.30/3.08 | | | | | | | | (118) $false % 16.30/3.08 | | | | | | | | % 16.30/3.08 | | | | | | | | CLOSE: (118) is inconsistent. % 16.30/3.08 | | | | | | | | % 16.30/3.08 | | | | | | | Case 2: % 16.30/3.08 | | | | | | | | % 16.30/3.08 | | | | | | | | (119) all_113_1 = 0 % 16.30/3.08 | | | | | | | | % 16.30/3.08 | | | | | | | | REDUCE: (89), (119) imply: % 16.30/3.08 | | | | | | | | (120) mem(all_87_1, all_29_4) = 0 % 16.30/3.08 | | | | | | | | % 16.30/3.08 | | | | | | | | GROUND_INST: instantiating (3) with all_87_1, all_29_5, % 16.30/3.08 | | | | | | | | all_29_4, simplifying with (19), (40), (70), (120) % 16.30/3.08 | | | | | | | | gives: % 16.30/3.08 | | | | | | | | (121) all_87_1 = all_29_5 % 16.30/3.08 | | | | | | | | % 16.30/3.08 | | | | | | | | REDUCE: (98), (121) imply: % 16.30/3.08 | | | | | | | | (122) mem(all_119_1, all_29_5) = 0 % 16.30/3.08 | | | | | | | | % 16.30/3.08 | | | | | | | | GROUND_INST: instantiating (11) with all_119_0, 0, all_29_5, % 16.30/3.08 | | | | | | | | all_119_1, simplifying with (112), (122) gives: % 16.30/3.08 | | | | | | | | (123) all_119_0 = 0 % 16.30/3.08 | | | | | | | | % 16.30/3.08 | | | | | | | | REDUCE: (96), (123) imply: % 16.30/3.08 | | | | | | | | (124) $false % 16.30/3.08 | | | | | | | | % 16.30/3.08 | | | | | | | | CLOSE: (124) is inconsistent. % 16.30/3.08 | | | | | | | | % 16.30/3.08 | | | | | | | End of split % 16.30/3.08 | | | | | | | % 16.30/3.08 | | | | | | End of split % 16.30/3.08 | | | | | | % 16.30/3.08 | | | | | Case 2: % 16.30/3.08 | | | | | | % 16.30/3.08 | | | | | | (125) all_81_1 = 0 % 16.30/3.08 | | | | | | % 16.30/3.08 | | | | | | REDUCE: (62), (125) imply: % 16.30/3.08 | | | | | | (126) mem(all_64_1, all_29_4) = 0 % 16.30/3.08 | | | | | | % 16.30/3.08 | | | | | | GROUND_INST: instantiating (3) with all_64_1, all_29_5, all_29_4, % 16.30/3.08 | | | | | | simplifying with (19), (40), (55), (126) gives: % 16.30/3.08 | | | | | | (127) all_64_1 = all_29_5 % 16.30/3.08 | | | | | | % 16.30/3.08 | | | | | | REDUCE: (57), (127) imply: % 16.30/3.08 | | | | | | (128) mem(all_29_5, all_41_1) = all_64_0 % 16.30/3.08 | | | | | | % 16.30/3.08 | | | | | | BETA: splitting (79) gives: % 16.30/3.08 | | | | | | % 16.30/3.08 | | | | | | Case 1: % 16.30/3.08 | | | | | | | % 16.30/3.08 | | | | | | | (129) all_100_0 = 0 % 16.30/3.08 | | | | | | | % 16.30/3.08 | | | | | | | REDUCE: (78), (129) imply: % 16.30/3.08 | | | | | | | (130) mem(all_58_2, all_39_0) = 0 % 16.30/3.08 | | | | | | | % 16.30/3.08 | | | | | | | GROUND_INST: instantiating (3) with all_58_2, all_29_1, all_39_0, % 16.30/3.08 | | | | | | | simplifying with (16), (31), (45), (130) gives: % 16.30/3.08 | | | | | | | (131) all_58_2 = all_29_1 % 16.30/3.08 | | | | | | | % 16.30/3.08 | | | | | | | REDUCE: (97), (131) imply: % 16.30/3.08 | | | | | | | (132) mem(all_119_1, all_29_1) = all_119_0 % 16.30/3.08 | | | | | | | % 16.30/3.08 | | | | | | | BETA: splitting (91) gives: % 16.30/3.08 | | | | | | | % 16.30/3.08 | | | | | | | Case 1: % 16.30/3.08 | | | | | | | | % 16.30/3.08 | | | | | | | | (133) all_113_0 = 0 % 16.30/3.08 | | | | | | | | % 16.30/3.08 | | | | | | | | REDUCE: (90), (133) imply: % 16.30/3.08 | | | | | | | | (134) mem(all_87_1, all_39_0) = 0 % 16.30/3.08 | | | | | | | | % 16.30/3.08 | | | | | | | | GROUND_INST: instantiating (3) with all_87_1, all_29_1, % 16.30/3.08 | | | | | | | | all_39_0, simplifying with (16), (31), (70), (134) % 16.30/3.08 | | | | | | | | gives: % 16.30/3.08 | | | | | | | | (135) all_87_1 = all_29_1 % 16.30/3.08 | | | | | | | | % 16.30/3.08 | | | | | | | | REDUCE: (98), (135) imply: % 16.30/3.08 | | | | | | | | (136) mem(all_119_1, all_29_1) = 0 % 16.30/3.08 | | | | | | | | % 16.30/3.08 | | | | | | | | GROUND_INST: instantiating (11) with all_119_0, 0, all_29_1, % 16.30/3.08 | | | | | | | | all_119_1, simplifying with (132), (136) gives: % 16.30/3.08 | | | | | | | | (137) all_119_0 = 0 % 16.30/3.08 | | | | | | | | % 16.30/3.08 | | | | | | | | REDUCE: (96), (137) imply: % 16.30/3.08 | | | | | | | | (138) $false % 16.30/3.08 | | | | | | | | % 16.30/3.08 | | | | | | | | CLOSE: (138) is inconsistent. % 16.30/3.08 | | | | | | | | % 16.30/3.08 | | | | | | | Case 2: % 16.30/3.08 | | | | | | | | % 16.30/3.08 | | | | | | | | (139) all_113_1 = 0 % 16.30/3.08 | | | | | | | | % 16.30/3.08 | | | | | | | | REDUCE: (89), (139) imply: % 16.30/3.08 | | | | | | | | (140) mem(all_87_1, all_29_4) = 0 % 16.30/3.08 | | | | | | | | % 16.30/3.08 | | | | | | | | GROUND_INST: instantiating (3) with all_87_1, all_29_5, % 16.30/3.08 | | | | | | | | all_29_4, simplifying with (19), (40), (70), (140) % 16.30/3.08 | | | | | | | | gives: % 16.30/3.08 | | | | | | | | (141) all_87_1 = all_29_5 % 16.30/3.08 | | | | | | | | % 16.30/3.08 | | | | | | | | REDUCE: (71), (141) imply: % 16.30/3.09 | | | | | | | | (142) mem(all_29_5, all_41_1) = 0 % 16.30/3.09 | | | | | | | | % 16.30/3.09 | | | | | | | | GROUND_INST: instantiating (11) with all_64_0, 0, all_41_1, % 16.30/3.09 | | | | | | | | all_29_5, simplifying with (128), (142) gives: % 16.30/3.09 | | | | | | | | (143) all_64_0 = 0 % 16.30/3.09 | | | | | | | | % 16.30/3.09 | | | | | | | | REDUCE: (54), (143) imply: % 16.30/3.09 | | | | | | | | (144) $false % 16.30/3.09 | | | | | | | | % 16.30/3.09 | | | | | | | | CLOSE: (144) is inconsistent. % 16.30/3.09 | | | | | | | | % 16.30/3.09 | | | | | | | End of split % 16.30/3.09 | | | | | | | % 16.30/3.09 | | | | | | Case 2: % 16.30/3.09 | | | | | | | % 16.30/3.09 | | | | | | | (145) all_100_1 = 0 % 16.30/3.09 | | | | | | | % 16.30/3.09 | | | | | | | REDUCE: (77), (145) imply: % 16.30/3.09 | | | | | | | (146) mem(all_58_2, all_29_4) = 0 % 16.30/3.09 | | | | | | | % 16.30/3.09 | | | | | | | GROUND_INST: instantiating (3) with all_58_2, all_29_5, all_29_4, % 16.30/3.09 | | | | | | | simplifying with (19), (40), (45), (146) gives: % 16.30/3.09 | | | | | | | (147) all_58_2 = all_29_5 % 16.30/3.09 | | | | | | | % 16.30/3.09 | | | | | | | REDUCE: (47), (147) imply: % 16.30/3.09 | | | | | | | (148) mem(all_29_5, all_41_1) = 0 % 16.30/3.09 | | | | | | | % 16.30/3.09 | | | | | | | GROUND_INST: instantiating (11) with all_64_0, 0, all_41_1, % 16.30/3.09 | | | | | | | all_29_5, simplifying with (128), (148) gives: % 16.30/3.09 | | | | | | | (149) all_64_0 = 0 % 16.30/3.09 | | | | | | | % 16.30/3.09 | | | | | | | REDUCE: (54), (149) imply: % 16.30/3.09 | | | | | | | (150) $false % 16.30/3.09 | | | | | | | % 16.30/3.09 | | | | | | | CLOSE: (150) is inconsistent. % 16.30/3.09 | | | | | | | % 16.30/3.09 | | | | | | End of split % 16.30/3.09 | | | | | | % 16.30/3.09 | | | | | End of split % 16.30/3.09 | | | | | % 16.30/3.09 | | | | End of split % 16.30/3.09 | | | | % 16.30/3.09 | | | End of split % 16.30/3.09 | | | % 16.30/3.09 | | End of split % 16.30/3.09 | | % 16.30/3.09 | End of split % 16.30/3.09 | % 16.30/3.09 End of proof % 16.30/3.09 % SZS output end Proof for theBenchmark % 16.30/3.09 % 16.30/3.09 2439ms %------------------------------------------------------------------------------