%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SYN036+2 : TPTP v8.1.2. Released v2.0.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n005.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 : Fri Sep 1 03:26:14 EDT 2023 % Result : Theorem 8.50s 1.88s % Output : Proof 13.12s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.13 % Problem : SYN036+2 : TPTP v8.1.2. Released v2.0.0. % 0.07/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.14/0.35 % Computer : n005.cluster.edu % 0.14/0.35 % Model : x86_64 x86_64 % 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.35 % Memory : 8042.1875MB % 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.35 % CPULimit : 300 % 0.14/0.35 % WCLimit : 300 % 0.14/0.35 % DateTime : Sat Aug 26 18:53:38 EDT 2023 % 0.14/0.35 % CPUTime : % 0.20/0.61 ________ _____ % 0.20/0.61 ___ __ \_________(_)________________________________ % 0.20/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.20/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.20/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.20/0.61 % 0.20/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.20/0.61 (2023-06-19) % 0.20/0.61 % 0.20/0.61 (c) Philipp Rümmer, 2009-2023 % 0.20/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.20/0.61 Amanda Stjerna. % 0.20/0.61 Free software under BSD-3-Clause. % 0.20/0.61 % 0.20/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.20/0.61 % 0.20/0.61 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.20/0.62 Running up to 7 provers in parallel. % 0.20/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.20/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.20/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.20/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.20/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.20/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.20/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 1.55/0.95 Prover 1: Preprocessing ... % 1.55/0.95 Prover 4: Preprocessing ... % 2.26/1.00 Prover 6: Preprocessing ... % 2.26/1.00 Prover 5: Preprocessing ... % 2.26/1.00 Prover 2: Preprocessing ... % 2.26/1.00 Prover 0: Preprocessing ... % 2.26/1.00 Prover 3: Preprocessing ... % 3.54/1.20 Prover 5: Proving ... % 3.54/1.22 Prover 2: Proving ... % 4.19/1.27 Prover 3: Constructing countermodel ... % 4.19/1.28 Prover 1: Constructing countermodel ... % 4.19/1.28 Prover 4: Constructing countermodel ... % 4.19/1.29 Prover 6: Proving ... % 4.19/1.29 Prover 0: Proving ... % 8.50/1.88 Prover 3: proved (1243ms) % 8.50/1.88 % 8.50/1.88 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 8.50/1.88 % 8.50/1.89 Prover 5: stopped % 8.50/1.89 Prover 0: stopped % 8.50/1.89 Prover 6: stopped % 8.50/1.89 Prover 2: stopped % 8.50/1.89 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 8.50/1.89 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 8.50/1.89 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 8.50/1.89 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 8.50/1.89 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 8.50/1.91 Prover 8: Preprocessing ... % 8.50/1.91 Prover 7: Preprocessing ... % 8.50/1.91 Prover 13: Preprocessing ... % 8.50/1.91 Prover 11: Preprocessing ... % 8.50/1.92 Prover 10: Preprocessing ... % 8.50/1.94 Prover 13: Warning: ignoring some quantifiers % 8.50/1.94 Prover 13: Constructing countermodel ... % 8.50/1.95 Prover 10: Warning: ignoring some quantifiers % 8.50/1.95 Prover 10: Constructing countermodel ... % 9.22/1.96 Prover 7: Warning: ignoring some quantifiers % 9.22/1.96 Prover 7: Constructing countermodel ... % 9.22/1.99 Prover 11: Constructing countermodel ... % 9.22/1.99 Prover 10: gave up % 9.22/2.00 Prover 8: Warning: ignoring some quantifiers % 9.22/2.00 Prover 13: gave up % 9.22/2.00 Prover 8: Constructing countermodel ... % 9.22/2.00 Prover 7: gave up % 9.22/2.00 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 9.22/2.00 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085 % 9.22/2.01 Prover 19: Preprocessing ... % 9.22/2.01 Prover 16: Preprocessing ... % 9.22/2.04 Prover 16: Warning: ignoring some quantifiers % 9.22/2.04 Prover 16: Constructing countermodel ... % 9.91/2.07 Prover 16: gave up % 9.91/2.07 Prover 19: Constructing countermodel ... % 11.42/2.33 Prover 1: Found proof (size 546) % 11.42/2.33 Prover 1: proved (1695ms) % 11.42/2.33 Prover 19: stopped % 11.42/2.33 Prover 4: stopped % 11.42/2.33 Prover 11: stopped % 11.42/2.33 Prover 8: stopped % 11.42/2.33 % 11.42/2.33 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 11.42/2.33 % 11.42/2.35 % SZS output start Proof for theBenchmark % 11.42/2.35 Assumptions after simplification: % 11.42/2.35 --------------------------------- % 12.12/2.35 % 12.12/2.35 (pel34) % 12.32/2.40 ((( ! [v0: $i] : ! [v1: any] : ( ~ (big_q(v0) = v1) | ~ $i(v0) | ? [v2: $i] % 12.32/2.40 : ? [v3: any] : (big_q(v2) = v3 & $i(v2) & ( ~ (v3 = 0) | ~ (v1 = % 12.32/2.40 0)) & (v3 = 0 | v1 = 0))) & (( ! [v0: $i] : ! [v1: int] : (v1 = % 12.32/2.40 0 | ~ (big_q(v0) = v1) | ~ $i(v0)) & ! [v0: $i] : ( ~ % 12.32/2.40 (big_p(v0) = 0) | ~ $i(v0))) | ( ? [v0: $i] : ? [v1: int] : ( ~ % 12.32/2.40 (v1 = 0) & big_q(v0) = v1 & $i(v0)) & ? [v0: $i] : (big_p(v0) = 0 % 12.32/2.40 & $i(v0))))) | ( ? [v0: $i] : ? [v1: any] : (big_q(v0) = v1 & % 12.32/2.40 $i(v0) & ! [v2: $i] : ! [v3: int] : ( ~ (v1 = 0) | v3 = 0 | ~ % 12.32/2.40 (big_q(v2) = v3) | ~ $i(v2)) & ! [v2: $i] : (v1 = 0 | ~ % 12.32/2.40 (big_q(v2) = 0) | ~ $i(v2))) & (( ! [v0: $i] : ! [v1: int] : (v1 = % 12.32/2.40 0 | ~ (big_q(v0) = v1) | ~ $i(v0)) & ? [v0: $i] : (big_p(v0) = % 12.32/2.40 0 & $i(v0))) | ( ! [v0: $i] : ( ~ (big_p(v0) = 0) | ~ $i(v0)) & % 12.32/2.40 ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & big_q(v0) = v1 & % 12.32/2.40 $i(v0)))))) & (( ! [v0: $i] : ! [v1: any] : ( ~ (big_p(v0) = v1) % 12.32/2.40 | ~ $i(v0) | ? [v2: $i] : ? [v3: any] : (big_p(v2) = v3 & $i(v2) & % 12.32/2.40 ( ~ (v3 = 0) | ~ (v1 = 0)) & (v3 = 0 | v1 = 0))) & (( ! [v0: $i] : % 12.32/2.40 ! [v1: int] : (v1 = 0 | ~ (big_p(v0) = v1) | ~ $i(v0)) & ? [v0: % 12.32/2.40 $i] : (big_q(v0) = 0 & $i(v0))) | ( ! [v0: $i] : ( ~ (big_q(v0) = % 12.32/2.40 0) | ~ $i(v0)) & ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & % 12.32/2.40 big_p(v0) = v1 & $i(v0))))) | ( ? [v0: $i] : ? [v1: any] : % 12.32/2.40 (big_p(v0) = v1 & $i(v0) & ! [v2: $i] : ! [v3: int] : ( ~ (v1 = 0) | % 12.32/2.40 v3 = 0 | ~ (big_p(v2) = v3) | ~ $i(v2)) & ! [v2: $i] : (v1 = 0 | % 12.32/2.40 ~ (big_p(v2) = 0) | ~ $i(v2))) & (( ! [v0: $i] : ! [v1: int] : (v1 % 12.32/2.40 = 0 | ~ (big_p(v0) = v1) | ~ $i(v0)) & ! [v0: $i] : ( ~ % 12.32/2.40 (big_q(v0) = 0) | ~ $i(v0))) | ( ? [v0: $i] : ? [v1: int] : ( ~ % 12.32/2.40 (v1 = 0) & big_p(v0) = v1 & $i(v0)) & ? [v0: $i] : (big_q(v0) = 0 % 12.32/2.40 & $i(v0))))))) | ((( ! [v0: $i] : ! [v1: any] : ( ~ (big_q(v0) = % 12.32/2.40 v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: any] : (big_q(v2) = v3 & % 12.32/2.40 $i(v2) & ( ~ (v3 = 0) | ~ (v1 = 0)) & (v3 = 0 | v1 = 0))) & (( ! % 12.32/2.40 [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (big_q(v0) = v1) | ~ $i(v0)) % 12.32/2.40 & ? [v0: $i] : (big_p(v0) = 0 & $i(v0))) | ( ! [v0: $i] : ( ~ % 12.32/2.40 (big_p(v0) = 0) | ~ $i(v0)) & ? [v0: $i] : ? [v1: int] : ( ~ % 12.32/2.40 (v1 = 0) & big_q(v0) = v1 & $i(v0))))) | ( ? [v0: $i] : ? [v1: % 12.32/2.40 any] : (big_q(v0) = v1 & $i(v0) & ! [v2: $i] : ! [v3: int] : ( ~ (v1 % 12.32/2.40 = 0) | v3 = 0 | ~ (big_q(v2) = v3) | ~ $i(v2)) & ! [v2: $i] : % 12.32/2.40 (v1 = 0 | ~ (big_q(v2) = 0) | ~ $i(v2))) & (( ! [v0: $i] : ! [v1: % 12.32/2.40 int] : (v1 = 0 | ~ (big_q(v0) = v1) | ~ $i(v0)) & ! [v0: $i] : % 12.32/2.40 ( ~ (big_p(v0) = 0) | ~ $i(v0))) | ( ? [v0: $i] : ? [v1: int] : ( % 12.32/2.40 ~ (v1 = 0) & big_q(v0) = v1 & $i(v0)) & ? [v0: $i] : (big_p(v0) = % 12.32/2.40 0 & $i(v0)))))) & (( ! [v0: $i] : ! [v1: any] : ( ~ (big_p(v0) = % 12.32/2.40 v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: any] : (big_p(v2) = v3 & % 12.32/2.40 $i(v2) & ( ~ (v3 = 0) | ~ (v1 = 0)) & (v3 = 0 | v1 = 0))) & (( ! % 12.32/2.40 [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (big_p(v0) = v1) | ~ $i(v0)) % 12.32/2.40 & ! [v0: $i] : ( ~ (big_q(v0) = 0) | ~ $i(v0))) | ( ? [v0: $i] : % 12.32/2.40 ? [v1: int] : ( ~ (v1 = 0) & big_p(v0) = v1 & $i(v0)) & ? [v0: $i] % 12.32/2.40 : (big_q(v0) = 0 & $i(v0))))) | ( ? [v0: $i] : ? [v1: any] : % 12.32/2.40 (big_p(v0) = v1 & $i(v0) & ! [v2: $i] : ! [v3: int] : ( ~ (v1 = 0) | % 12.32/2.40 v3 = 0 | ~ (big_p(v2) = v3) | ~ $i(v2)) & ! [v2: $i] : (v1 = 0 | % 12.32/2.40 ~ (big_p(v2) = 0) | ~ $i(v2))) & (( ! [v0: $i] : ! [v1: int] : (v1 % 12.32/2.40 = 0 | ~ (big_p(v0) = v1) | ~ $i(v0)) & ? [v0: $i] : (big_q(v0) % 12.32/2.40 = 0 & $i(v0))) | ( ! [v0: $i] : ( ~ (big_q(v0) = 0) | ~ $i(v0)) & % 12.32/2.40 ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & big_p(v0) = v1 & % 12.32/2.40 $i(v0))))))) % 12.32/2.40 % 12.32/2.40 Those formulas are unsatisfiable: % 12.32/2.40 --------------------------------- % 12.32/2.40 % 12.32/2.40 Begin of proof % 12.32/2.40 | % 12.32/2.40 | BETA: splitting (pel34) gives: % 12.32/2.40 | % 12.32/2.40 | Case 1: % 12.32/2.40 | | % 12.32/2.41 | | (1) (( ! [v0: $i] : ! [v1: any] : ( ~ (big_q(v0) = v1) | ~ $i(v0) | ? % 12.32/2.41 | | [v2: $i] : ? [v3: any] : (big_q(v2) = v3 & $i(v2) & ( ~ (v3 = % 12.32/2.41 | | 0) | ~ (v1 = 0)) & (v3 = 0 | v1 = 0))) & (( ! [v0: $i] : % 12.32/2.41 | | ! [v1: int] : (v1 = 0 | ~ (big_q(v0) = v1) | ~ $i(v0)) & % 12.32/2.41 | | ! [v0: $i] : ( ~ (big_p(v0) = 0) | ~ $i(v0))) | ( ? [v0: $i] % 12.32/2.41 | | : ? [v1: int] : ( ~ (v1 = 0) & big_q(v0) = v1 & $i(v0)) & ? % 12.32/2.41 | | [v0: $i] : (big_p(v0) = 0 & $i(v0))))) | ( ? [v0: $i] : ? % 12.32/2.41 | | [v1: any] : (big_q(v0) = v1 & $i(v0) & ! [v2: $i] : ! [v3: int] % 12.32/2.41 | | : ( ~ (v1 = 0) | v3 = 0 | ~ (big_q(v2) = v3) | ~ $i(v2)) & ! % 12.32/2.41 | | [v2: $i] : (v1 = 0 | ~ (big_q(v2) = 0) | ~ $i(v2))) & (( ! % 12.32/2.41 | | [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (big_q(v0) = v1) | ~ % 12.32/2.41 | | $i(v0)) & ? [v0: $i] : (big_p(v0) = 0 & $i(v0))) | ( ! % 12.32/2.41 | | [v0: $i] : ( ~ (big_p(v0) = 0) | ~ $i(v0)) & ? [v0: $i] : % 12.32/2.41 | | ? [v1: int] : ( ~ (v1 = 0) & big_q(v0) = v1 & $i(v0)))))) & % 12.32/2.41 | | (( ! [v0: $i] : ! [v1: any] : ( ~ (big_p(v0) = v1) | ~ $i(v0) | ? % 12.32/2.41 | | [v2: $i] : ? [v3: any] : (big_p(v2) = v3 & $i(v2) & ( ~ (v3 = % 12.32/2.41 | | 0) | ~ (v1 = 0)) & (v3 = 0 | v1 = 0))) & (( ! [v0: $i] : % 12.32/2.41 | | ! [v1: int] : (v1 = 0 | ~ (big_p(v0) = v1) | ~ $i(v0)) & % 12.32/2.41 | | ? [v0: $i] : (big_q(v0) = 0 & $i(v0))) | ( ! [v0: $i] : ( ~ % 12.32/2.41 | | (big_q(v0) = 0) | ~ $i(v0)) & ? [v0: $i] : ? [v1: int] : % 12.32/2.41 | | ( ~ (v1 = 0) & big_p(v0) = v1 & $i(v0))))) | ( ? [v0: $i] : % 12.32/2.41 | | ? [v1: any] : (big_p(v0) = v1 & $i(v0) & ! [v2: $i] : ! [v3: % 12.32/2.41 | | int] : ( ~ (v1 = 0) | v3 = 0 | ~ (big_p(v2) = v3) | ~ % 12.32/2.41 | | $i(v2)) & ! [v2: $i] : (v1 = 0 | ~ (big_p(v2) = 0) | ~ % 12.32/2.41 | | $i(v2))) & (( ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ % 12.32/2.41 | | (big_p(v0) = v1) | ~ $i(v0)) & ! [v0: $i] : ( ~ % 12.32/2.41 | | (big_q(v0) = 0) | ~ $i(v0))) | ( ? [v0: $i] : ? [v1: int] % 12.32/2.41 | | : ( ~ (v1 = 0) & big_p(v0) = v1 & $i(v0)) & ? [v0: $i] : % 12.32/2.41 | | (big_q(v0) = 0 & $i(v0)))))) % 12.32/2.41 | | % 12.32/2.41 | | ALPHA: (1) implies: % 12.32/2.41 | | (2) ( ! [v0: $i] : ! [v1: any] : ( ~ (big_p(v0) = v1) | ~ $i(v0) | ? % 12.32/2.41 | | [v2: $i] : ? [v3: any] : (big_p(v2) = v3 & $i(v2) & ( ~ (v3 = 0) % 12.32/2.41 | | | ~ (v1 = 0)) & (v3 = 0 | v1 = 0))) & (( ! [v0: $i] : ! % 12.32/2.41 | | [v1: int] : (v1 = 0 | ~ (big_p(v0) = v1) | ~ $i(v0)) & ? % 12.32/2.41 | | [v0: $i] : (big_q(v0) = 0 & $i(v0))) | ( ! [v0: $i] : ( ~ % 12.32/2.41 | | (big_q(v0) = 0) | ~ $i(v0)) & ? [v0: $i] : ? [v1: int] : ( % 12.32/2.41 | | ~ (v1 = 0) & big_p(v0) = v1 & $i(v0))))) | ( ? [v0: $i] : ? % 12.32/2.41 | | [v1: any] : (big_p(v0) = v1 & $i(v0) & ! [v2: $i] : ! [v3: int] : % 12.32/2.41 | | ( ~ (v1 = 0) | v3 = 0 | ~ (big_p(v2) = v3) | ~ $i(v2)) & ! % 12.32/2.41 | | [v2: $i] : (v1 = 0 | ~ (big_p(v2) = 0) | ~ $i(v2))) & (( ! [v0: % 12.32/2.41 | | $i] : ! [v1: int] : (v1 = 0 | ~ (big_p(v0) = v1) | ~ % 12.32/2.41 | | $i(v0)) & ! [v0: $i] : ( ~ (big_q(v0) = 0) | ~ $i(v0))) | ( % 12.32/2.41 | | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & big_p(v0) = v1 & % 12.32/2.41 | | $i(v0)) & ? [v0: $i] : (big_q(v0) = 0 & $i(v0))))) % 12.32/2.41 | | (3) ( ! [v0: $i] : ! [v1: any] : ( ~ (big_q(v0) = v1) | ~ $i(v0) | ? % 12.32/2.41 | | [v2: $i] : ? [v3: any] : (big_q(v2) = v3 & $i(v2) & ( ~ (v3 = 0) % 12.32/2.41 | | | ~ (v1 = 0)) & (v3 = 0 | v1 = 0))) & (( ! [v0: $i] : ! % 12.32/2.41 | | [v1: int] : (v1 = 0 | ~ (big_q(v0) = v1) | ~ $i(v0)) & ! % 12.32/2.41 | | [v0: $i] : ( ~ (big_p(v0) = 0) | ~ $i(v0))) | ( ? [v0: $i] : % 12.32/2.41 | | ? [v1: int] : ( ~ (v1 = 0) & big_q(v0) = v1 & $i(v0)) & ? [v0: % 12.32/2.41 | | $i] : (big_p(v0) = 0 & $i(v0))))) | ( ? [v0: $i] : ? [v1: % 12.32/2.41 | | any] : (big_q(v0) = v1 & $i(v0) & ! [v2: $i] : ! [v3: int] : ( % 12.32/2.41 | | ~ (v1 = 0) | v3 = 0 | ~ (big_q(v2) = v3) | ~ $i(v2)) & ! % 12.32/2.41 | | [v2: $i] : (v1 = 0 | ~ (big_q(v2) = 0) | ~ $i(v2))) & (( ! [v0: % 12.32/2.41 | | $i] : ! [v1: int] : (v1 = 0 | ~ (big_q(v0) = v1) | ~ % 12.32/2.41 | | $i(v0)) & ? [v0: $i] : (big_p(v0) = 0 & $i(v0))) | ( ! [v0: % 12.32/2.41 | | $i] : ( ~ (big_p(v0) = 0) | ~ $i(v0)) & ? [v0: $i] : ? % 12.32/2.41 | | [v1: int] : ( ~ (v1 = 0) & big_q(v0) = v1 & $i(v0))))) % 12.32/2.41 | | % 12.32/2.41 | | BETA: splitting (2) gives: % 12.32/2.41 | | % 12.32/2.41 | | Case 1: % 12.32/2.41 | | | % 12.32/2.42 | | | (4) ! [v0: $i] : ! [v1: any] : ( ~ (big_p(v0) = v1) | ~ $i(v0) | ? % 12.32/2.42 | | | [v2: $i] : ? [v3: any] : (big_p(v2) = v3 & $i(v2) & ( ~ (v3 = 0) % 12.32/2.42 | | | | ~ (v1 = 0)) & (v3 = 0 | v1 = 0))) & (( ! [v0: $i] : ! % 12.32/2.42 | | | [v1: int] : (v1 = 0 | ~ (big_p(v0) = v1) | ~ $i(v0)) & ? % 12.32/2.42 | | | [v0: $i] : (big_q(v0) = 0 & $i(v0))) | ( ! [v0: $i] : ( ~ % 12.32/2.42 | | | (big_q(v0) = 0) | ~ $i(v0)) & ? [v0: $i] : ? [v1: int] : ( % 12.32/2.42 | | | ~ (v1 = 0) & big_p(v0) = v1 & $i(v0)))) % 12.32/2.42 | | | % 12.32/2.42 | | | ALPHA: (4) implies: % 12.32/2.42 | | | (5) ( ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (big_p(v0) = v1) | ~ % 12.32/2.42 | | | $i(v0)) & ? [v0: $i] : (big_q(v0) = 0 & $i(v0))) | ( ! [v0: % 12.32/2.42 | | | $i] : ( ~ (big_q(v0) = 0) | ~ $i(v0)) & ? [v0: $i] : ? [v1: % 12.32/2.42 | | | int] : ( ~ (v1 = 0) & big_p(v0) = v1 & $i(v0))) % 12.32/2.42 | | | (6) ! [v0: $i] : ! [v1: any] : ( ~ (big_p(v0) = v1) | ~ $i(v0) | ? % 12.32/2.42 | | | [v2: $i] : ? [v3: any] : (big_p(v2) = v3 & $i(v2) & ( ~ (v3 = 0) % 12.32/2.42 | | | | ~ (v1 = 0)) & (v3 = 0 | v1 = 0))) % 12.32/2.42 | | | % 12.32/2.42 | | | BETA: splitting (3) gives: % 12.32/2.42 | | | % 12.32/2.42 | | | Case 1: % 12.32/2.42 | | | | % 12.32/2.42 | | | | (7) ! [v0: $i] : ! [v1: any] : ( ~ (big_q(v0) = v1) | ~ $i(v0) | % 12.32/2.42 | | | | ? [v2: $i] : ? [v3: any] : (big_q(v2) = v3 & $i(v2) & ( ~ (v3 % 12.32/2.42 | | | | = 0) | ~ (v1 = 0)) & (v3 = 0 | v1 = 0))) & (( ! [v0: $i] % 12.32/2.42 | | | | : ! [v1: int] : (v1 = 0 | ~ (big_q(v0) = v1) | ~ $i(v0)) & % 12.32/2.42 | | | | ! [v0: $i] : ( ~ (big_p(v0) = 0) | ~ $i(v0))) | ( ? [v0: % 12.32/2.42 | | | | $i] : ? [v1: int] : ( ~ (v1 = 0) & big_q(v0) = v1 & % 12.32/2.42 | | | | $i(v0)) & ? [v0: $i] : (big_p(v0) = 0 & $i(v0)))) % 12.32/2.42 | | | | % 12.32/2.42 | | | | ALPHA: (7) implies: % 12.32/2.42 | | | | (8) ( ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (big_q(v0) = v1) | ~ % 12.32/2.42 | | | | $i(v0)) & ! [v0: $i] : ( ~ (big_p(v0) = 0) | ~ $i(v0))) | ( % 12.32/2.42 | | | | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & big_q(v0) = v1 & % 12.32/2.42 | | | | $i(v0)) & ? [v0: $i] : (big_p(v0) = 0 & $i(v0))) % 12.32/2.42 | | | | (9) ! [v0: $i] : ! [v1: any] : ( ~ (big_q(v0) = v1) | ~ $i(v0) | % 12.32/2.42 | | | | ? [v2: $i] : ? [v3: any] : (big_q(v2) = v3 & $i(v2) & ( ~ (v3 % 12.32/2.42 | | | | = 0) | ~ (v1 = 0)) & (v3 = 0 | v1 = 0))) % 12.32/2.42 | | | | % 12.32/2.42 | | | | BETA: splitting (5) gives: % 12.32/2.42 | | | | % 12.32/2.42 | | | | Case 1: % 12.32/2.42 | | | | | % 12.32/2.42 | | | | | (10) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (big_p(v0) = v1) | % 12.32/2.42 | | | | | ~ $i(v0)) & ? [v0: $i] : (big_q(v0) = 0 & $i(v0)) % 12.32/2.42 | | | | | % 12.32/2.42 | | | | | ALPHA: (10) implies: % 12.32/2.42 | | | | | (11) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (big_p(v0) = v1) | % 12.32/2.42 | | | | | ~ $i(v0)) % 12.32/2.42 | | | | | (12) ? [v0: $i] : (big_q(v0) = 0 & $i(v0)) % 12.32/2.42 | | | | | % 12.32/2.42 | | | | | DELTA: instantiating (12) with fresh symbol all_19_0 gives: % 12.32/2.42 | | | | | (13) big_q(all_19_0) = 0 & $i(all_19_0) % 12.32/2.42 | | | | | % 12.32/2.42 | | | | | ALPHA: (13) implies: % 12.32/2.42 | | | | | (14) $i(all_19_0) % 12.32/2.42 | | | | | (15) big_q(all_19_0) = 0 % 12.32/2.42 | | | | | % 12.32/2.42 | | | | | GROUND_INST: instantiating (9) with all_19_0, 0, simplifying with % 12.32/2.42 | | | | | (14), (15) gives: % 12.32/2.42 | | | | | (16) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & big_q(v0) = v1 & % 12.32/2.42 | | | | | $i(v0)) % 12.32/2.42 | | | | | % 12.32/2.42 | | | | | DELTA: instantiating (16) with fresh symbols all_26_0, all_26_1 gives: % 12.32/2.42 | | | | | (17) ~ (all_26_0 = 0) & big_q(all_26_1) = all_26_0 & $i(all_26_1) % 12.32/2.42 | | | | | % 12.32/2.42 | | | | | ALPHA: (17) implies: % 12.32/2.42 | | | | | (18) ~ (all_26_0 = 0) % 12.32/2.42 | | | | | (19) $i(all_26_1) % 12.32/2.42 | | | | | (20) big_q(all_26_1) = all_26_0 % 12.32/2.42 | | | | | % 12.32/2.42 | | | | | BETA: splitting (8) gives: % 12.32/2.42 | | | | | % 12.32/2.42 | | | | | Case 1: % 12.32/2.42 | | | | | | % 12.32/2.43 | | | | | | (21) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (big_q(v0) = v1) | % 12.32/2.43 | | | | | | ~ $i(v0)) & ! [v0: $i] : ( ~ (big_p(v0) = 0) | ~ % 12.32/2.43 | | | | | | $i(v0)) % 12.32/2.43 | | | | | | % 12.32/2.43 | | | | | | ALPHA: (21) implies: % 12.32/2.43 | | | | | | (22) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (big_q(v0) = v1) | % 12.32/2.43 | | | | | | ~ $i(v0)) % 12.32/2.43 | | | | | | % 12.32/2.43 | | | | | | GROUND_INST: instantiating (22) with all_26_1, all_26_0, simplifying % 12.32/2.43 | | | | | | with (19), (20) gives: % 12.32/2.43 | | | | | | (23) all_26_0 = 0 % 12.32/2.43 | | | | | | % 12.32/2.43 | | | | | | REDUCE: (18), (23) imply: % 12.32/2.43 | | | | | | (24) $false % 12.32/2.43 | | | | | | % 12.32/2.43 | | | | | | CLOSE: (24) is inconsistent. % 12.32/2.43 | | | | | | % 12.32/2.43 | | | | | Case 2: % 12.32/2.43 | | | | | | % 12.32/2.43 | | | | | | (25) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & big_q(v0) = v1 & % 12.32/2.43 | | | | | | $i(v0)) & ? [v0: $i] : (big_p(v0) = 0 & $i(v0)) % 12.32/2.43 | | | | | | % 12.32/2.43 | | | | | | ALPHA: (25) implies: % 12.32/2.43 | | | | | | (26) ? [v0: $i] : (big_p(v0) = 0 & $i(v0)) % 12.32/2.43 | | | | | | % 12.32/2.43 | | | | | | REF_CLOSE: (6), (11), (26) are inconsistent by sub-proof #3. % 12.32/2.43 | | | | | | % 12.32/2.43 | | | | | End of split % 12.32/2.43 | | | | | % 12.32/2.43 | | | | Case 2: % 12.32/2.43 | | | | | % 12.32/2.43 | | | | | (27) ! [v0: $i] : ( ~ (big_q(v0) = 0) | ~ $i(v0)) & ? [v0: $i] : % 12.32/2.43 | | | | | ? [v1: int] : ( ~ (v1 = 0) & big_p(v0) = v1 & $i(v0)) % 12.32/2.43 | | | | | % 12.32/2.43 | | | | | ALPHA: (27) implies: % 12.32/2.43 | | | | | (28) ! [v0: $i] : ( ~ (big_q(v0) = 0) | ~ $i(v0)) % 12.32/2.43 | | | | | (29) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & big_p(v0) = v1 & % 12.32/2.43 | | | | | $i(v0)) % 12.32/2.43 | | | | | % 12.32/2.43 | | | | | DELTA: instantiating (29) with fresh symbols all_19_0, all_19_1 gives: % 12.32/2.43 | | | | | (30) ~ (all_19_0 = 0) & big_p(all_19_1) = all_19_0 & $i(all_19_1) % 12.32/2.43 | | | | | % 12.32/2.43 | | | | | ALPHA: (30) implies: % 12.32/2.43 | | | | | (31) ~ (all_19_0 = 0) % 12.32/2.43 | | | | | (32) $i(all_19_1) % 12.32/2.43 | | | | | (33) big_p(all_19_1) = all_19_0 % 12.32/2.43 | | | | | % 12.32/2.43 | | | | | GROUND_INST: instantiating (6) with all_19_1, all_19_0, simplifying % 12.32/2.43 | | | | | with (32), (33) gives: % 12.32/2.43 | | | | | (34) ? [v0: $i] : ? [v1: any] : (big_p(v0) = v1 & $i(v0) & ( ~ % 12.32/2.43 | | | | | (v1 = 0) | ~ (all_19_0 = 0)) & (v1 = 0 | all_19_0 = 0)) % 12.32/2.43 | | | | | % 12.32/2.43 | | | | | DELTA: instantiating (34) with fresh symbols all_26_0, all_26_1 gives: % 12.32/2.43 | | | | | (35) big_p(all_26_1) = all_26_0 & $i(all_26_1) & ( ~ (all_26_0 = 0) % 12.32/2.43 | | | | | | ~ (all_19_0 = 0)) & (all_26_0 = 0 | all_19_0 = 0) % 12.32/2.43 | | | | | % 12.32/2.43 | | | | | ALPHA: (35) implies: % 12.32/2.43 | | | | | (36) $i(all_26_1) % 12.32/2.43 | | | | | (37) big_p(all_26_1) = all_26_0 % 12.32/2.43 | | | | | (38) all_26_0 = 0 | all_19_0 = 0 % 12.32/2.43 | | | | | % 12.32/2.43 | | | | | BETA: splitting (38) gives: % 12.32/2.43 | | | | | % 12.32/2.43 | | | | | Case 1: % 12.32/2.43 | | | | | | % 12.32/2.43 | | | | | | (39) all_26_0 = 0 % 12.32/2.43 | | | | | | % 12.32/2.43 | | | | | | REDUCE: (37), (39) imply: % 12.32/2.43 | | | | | | (40) big_p(all_26_1) = 0 % 12.32/2.43 | | | | | | % 12.32/2.43 | | | | | | DELTA: instantiating (29) with fresh symbols all_37_0, all_37_1 % 12.32/2.43 | | | | | | gives: % 12.32/2.43 | | | | | | (41) ~ (all_37_0 = 0) & big_p(all_37_1) = all_37_0 & % 12.32/2.43 | | | | | | $i(all_37_1) % 12.32/2.43 | | | | | | % 12.32/2.43 | | | | | | ALPHA: (41) implies: % 12.32/2.43 | | | | | | (42) ~ (all_37_0 = 0) % 12.32/2.43 | | | | | | (43) $i(all_37_1) % 12.32/2.43 | | | | | | (44) big_p(all_37_1) = all_37_0 % 12.32/2.43 | | | | | | % 12.32/2.43 | | | | | | GROUND_INST: instantiating (6) with all_37_1, all_37_0, simplifying % 12.32/2.43 | | | | | | with (43), (44) gives: % 12.32/2.43 | | | | | | (45) ? [v0: $i] : ? [v1: any] : (big_p(v0) = v1 & $i(v0) & ( ~ % 12.32/2.43 | | | | | | (v1 = 0) | ~ (all_37_0 = 0)) & (v1 = 0 | all_37_0 = 0)) % 12.32/2.43 | | | | | | % 12.32/2.43 | | | | | | DELTA: instantiating (45) with fresh symbols all_44_0, all_44_1 % 12.32/2.43 | | | | | | gives: % 12.32/2.43 | | | | | | (46) big_p(all_44_1) = all_44_0 & $i(all_44_1) & ( ~ (all_44_0 = % 12.32/2.43 | | | | | | 0) | ~ (all_37_0 = 0)) & (all_44_0 = 0 | all_37_0 = 0) % 12.32/2.43 | | | | | | % 12.32/2.43 | | | | | | ALPHA: (46) implies: % 12.32/2.44 | | | | | | (47) $i(all_44_1) % 12.32/2.44 | | | | | | (48) big_p(all_44_1) = all_44_0 % 12.32/2.44 | | | | | | (49) all_44_0 = 0 | all_37_0 = 0 % 12.32/2.44 | | | | | | % 12.32/2.44 | | | | | | BETA: splitting (49) gives: % 12.32/2.44 | | | | | | % 12.32/2.44 | | | | | | Case 1: % 12.32/2.44 | | | | | | | % 12.32/2.44 | | | | | | | (50) all_44_0 = 0 % 12.32/2.44 | | | | | | | % 12.32/2.44 | | | | | | | REDUCE: (48), (50) imply: % 12.32/2.44 | | | | | | | (51) big_p(all_44_1) = 0 % 12.32/2.44 | | | | | | | % 12.32/2.44 | | | | | | | DELTA: instantiating (29) with fresh symbols all_55_0, all_55_1 % 12.32/2.44 | | | | | | | gives: % 12.32/2.44 | | | | | | | (52) ~ (all_55_0 = 0) & big_p(all_55_1) = all_55_0 & % 12.32/2.44 | | | | | | | $i(all_55_1) % 12.32/2.44 | | | | | | | % 12.32/2.44 | | | | | | | ALPHA: (52) implies: % 12.32/2.44 | | | | | | | (53) ~ (all_55_0 = 0) % 12.32/2.44 | | | | | | | (54) $i(all_55_1) % 12.32/2.44 | | | | | | | (55) big_p(all_55_1) = all_55_0 % 12.32/2.44 | | | | | | | % 12.32/2.44 | | | | | | | GROUND_INST: instantiating (6) with all_55_1, all_55_0, % 12.32/2.44 | | | | | | | simplifying with (54), (55) gives: % 12.54/2.44 | | | | | | | (56) ? [v0: $i] : ? [v1: any] : (big_p(v0) = v1 & $i(v0) & ( % 12.54/2.44 | | | | | | | ~ (v1 = 0) | ~ (all_55_0 = 0)) & (v1 = 0 | all_55_0 = % 12.54/2.44 | | | | | | | 0)) % 12.54/2.44 | | | | | | | % 12.54/2.44 | | | | | | | DELTA: instantiating (56) with fresh symbols all_62_0, all_62_1 % 12.54/2.44 | | | | | | | gives: % 12.54/2.44 | | | | | | | (57) big_p(all_62_1) = all_62_0 & $i(all_62_1) & ( ~ (all_62_0 % 12.54/2.44 | | | | | | | = 0) | ~ (all_55_0 = 0)) & (all_62_0 = 0 | all_55_0 = % 12.54/2.44 | | | | | | | 0) % 12.54/2.44 | | | | | | | % 12.54/2.44 | | | | | | | ALPHA: (57) implies: % 12.54/2.44 | | | | | | | (58) $i(all_62_1) % 12.54/2.44 | | | | | | | (59) big_p(all_62_1) = all_62_0 % 12.54/2.44 | | | | | | | (60) all_62_0 = 0 | all_55_0 = 0 % 12.54/2.44 | | | | | | | % 12.54/2.44 | | | | | | | BETA: splitting (60) gives: % 12.54/2.44 | | | | | | | % 12.54/2.45 | | | | | | | Case 1: % 12.54/2.45 | | | | | | | | % 12.54/2.45 | | | | | | | | (61) all_62_0 = 0 % 12.54/2.45 | | | | | | | | % 12.54/2.45 | | | | | | | | REDUCE: (59), (61) imply: % 12.54/2.45 | | | | | | | | (62) big_p(all_62_1) = 0 % 12.54/2.45 | | | | | | | | % 12.54/2.45 | | | | | | | | DELTA: instantiating (29) with fresh symbols all_73_0, all_73_1 % 12.54/2.45 | | | | | | | | gives: % 12.54/2.45 | | | | | | | | (63) ~ (all_73_0 = 0) & big_p(all_73_1) = all_73_0 & % 12.54/2.45 | | | | | | | | $i(all_73_1) % 12.54/2.45 | | | | | | | | % 12.54/2.45 | | | | | | | | ALPHA: (63) implies: % 12.54/2.45 | | | | | | | | (64) ~ (all_73_0 = 0) % 12.54/2.45 | | | | | | | | (65) $i(all_73_1) % 12.54/2.45 | | | | | | | | (66) big_p(all_73_1) = all_73_0 % 12.54/2.45 | | | | | | | | % 12.54/2.46 | | | | | | | | GROUND_INST: instantiating (6) with all_73_1, all_73_0, % 12.54/2.46 | | | | | | | | simplifying with (65), (66) gives: % 12.54/2.46 | | | | | | | | (67) ? [v0: $i] : ? [v1: any] : (big_p(v0) = v1 & $i(v0) & % 12.54/2.46 | | | | | | | | ( ~ (v1 = 0) | ~ (all_73_0 = 0)) & (v1 = 0 | all_73_0 % 12.54/2.46 | | | | | | | | = 0)) % 12.54/2.46 | | | | | | | | % 12.54/2.46 | | | | | | | | DELTA: instantiating (67) with fresh symbols all_80_0, all_80_1 % 12.54/2.46 | | | | | | | | gives: % 12.54/2.46 | | | | | | | | (68) big_p(all_80_1) = all_80_0 & $i(all_80_1) & ( ~ % 12.54/2.46 | | | | | | | | (all_80_0 = 0) | ~ (all_73_0 = 0)) & (all_80_0 = 0 | % 12.54/2.46 | | | | | | | | all_73_0 = 0) % 12.54/2.46 | | | | | | | | % 12.54/2.46 | | | | | | | | ALPHA: (68) implies: % 12.54/2.46 | | | | | | | | (69) $i(all_80_1) % 12.54/2.46 | | | | | | | | (70) big_p(all_80_1) = all_80_0 % 12.54/2.46 | | | | | | | | (71) all_80_0 = 0 | all_73_0 = 0 % 12.54/2.46 | | | | | | | | % 12.54/2.46 | | | | | | | | BETA: splitting (71) gives: % 12.54/2.46 | | | | | | | | % 12.54/2.46 | | | | | | | | Case 1: % 12.54/2.46 | | | | | | | | | % 12.54/2.46 | | | | | | | | | (72) all_80_0 = 0 % 12.54/2.46 | | | | | | | | | % 12.54/2.46 | | | | | | | | | REDUCE: (70), (72) imply: % 12.54/2.46 | | | | | | | | | (73) big_p(all_80_1) = 0 % 12.54/2.46 | | | | | | | | | % 12.54/2.46 | | | | | | | | | DELTA: instantiating (29) with fresh symbols all_91_0, % 12.54/2.46 | | | | | | | | | all_91_1 gives: % 12.54/2.46 | | | | | | | | | (74) ~ (all_91_0 = 0) & big_p(all_91_1) = all_91_0 & % 12.54/2.46 | | | | | | | | | $i(all_91_1) % 12.54/2.46 | | | | | | | | | % 12.54/2.46 | | | | | | | | | ALPHA: (74) implies: % 12.54/2.46 | | | | | | | | | (75) ~ (all_91_0 = 0) % 12.54/2.46 | | | | | | | | | (76) $i(all_91_1) % 12.54/2.46 | | | | | | | | | (77) big_p(all_91_1) = all_91_0 % 12.54/2.46 | | | | | | | | | % 12.54/2.46 | | | | | | | | | GROUND_INST: instantiating (6) with all_91_1, all_91_0, % 12.54/2.46 | | | | | | | | | simplifying with (76), (77) gives: % 12.54/2.46 | | | | | | | | | (78) ? [v0: $i] : ? [v1: any] : (big_p(v0) = v1 & $i(v0) % 12.54/2.46 | | | | | | | | | & ( ~ (v1 = 0) | ~ (all_91_0 = 0)) & (v1 = 0 | % 12.54/2.46 | | | | | | | | | all_91_0 = 0)) % 12.54/2.46 | | | | | | | | | % 12.54/2.46 | | | | | | | | | DELTA: instantiating (78) with fresh symbols all_98_0, % 12.54/2.46 | | | | | | | | | all_98_1 gives: % 12.54/2.46 | | | | | | | | | (79) big_p(all_98_1) = all_98_0 & $i(all_98_1) & ( ~ % 12.54/2.46 | | | | | | | | | (all_98_0 = 0) | ~ (all_91_0 = 0)) & (all_98_0 = 0 % 12.54/2.46 | | | | | | | | | | all_91_0 = 0) % 12.54/2.46 | | | | | | | | | % 12.54/2.46 | | | | | | | | | ALPHA: (79) implies: % 12.54/2.46 | | | | | | | | | (80) $i(all_98_1) % 12.54/2.46 | | | | | | | | | (81) big_p(all_98_1) = all_98_0 % 12.54/2.46 | | | | | | | | | (82) all_98_0 = 0 | all_91_0 = 0 % 12.54/2.46 | | | | | | | | | % 12.54/2.46 | | | | | | | | | BETA: splitting (82) gives: % 12.54/2.46 | | | | | | | | | % 12.54/2.46 | | | | | | | | | Case 1: % 12.54/2.46 | | | | | | | | | | % 12.54/2.46 | | | | | | | | | | (83) all_98_0 = 0 % 12.54/2.46 | | | | | | | | | | % 12.54/2.46 | | | | | | | | | | REDUCE: (81), (83) imply: % 12.54/2.46 | | | | | | | | | | (84) big_p(all_98_1) = 0 % 12.54/2.46 | | | | | | | | | | % 12.54/2.46 | | | | | | | | | | BETA: splitting (8) gives: % 12.54/2.46 | | | | | | | | | | % 12.54/2.46 | | | | | | | | | | Case 1: % 12.54/2.46 | | | | | | | | | | | % 12.54/2.46 | | | | | | | | | | | (85) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ % 12.54/2.46 | | | | | | | | | | | (big_q(v0) = v1) | ~ $i(v0)) & ! [v0: $i] : ( % 12.54/2.46 | | | | | | | | | | | ~ (big_p(v0) = 0) | ~ $i(v0)) % 12.54/2.46 | | | | | | | | | | | % 12.54/2.46 | | | | | | | | | | | ALPHA: (85) implies: % 12.54/2.46 | | | | | | | | | | | (86) ! [v0: $i] : ( ~ (big_p(v0) = 0) | ~ $i(v0)) % 12.54/2.46 | | | | | | | | | | | % 12.54/2.46 | | | | | | | | | | | GROUND_INST: instantiating (86) with all_98_1, simplifying with % 12.54/2.46 | | | | | | | | | | | (80), (84) gives: % 12.54/2.46 | | | | | | | | | | | (87) $false % 12.54/2.46 | | | | | | | | | | | % 12.54/2.46 | | | | | | | | | | | CLOSE: (87) is inconsistent. % 12.54/2.46 | | | | | | | | | | | % 12.54/2.46 | | | | | | | | | | Case 2: % 12.54/2.46 | | | | | | | | | | | % 12.54/2.46 | | | | | | | | | | | (88) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & % 12.54/2.46 | | | | | | | | | | | big_q(v0) = v1 & $i(v0)) & ? [v0: $i] : % 12.54/2.46 | | | | | | | | | | | (big_p(v0) = 0 & $i(v0)) % 12.54/2.46 | | | | | | | | | | | % 12.54/2.46 | | | | | | | | | | | ALPHA: (88) implies: % 12.54/2.46 | | | | | | | | | | | (89) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & % 12.54/2.46 | | | | | | | | | | | big_q(v0) = v1 & $i(v0)) % 12.54/2.46 | | | | | | | | | | | % 12.54/2.46 | | | | | | | | | | | REF_CLOSE: (9), (28), (89) are inconsistent by sub-proof #2. % 12.54/2.46 | | | | | | | | | | | % 12.54/2.46 | | | | | | | | | | End of split % 12.54/2.46 | | | | | | | | | | % 12.54/2.46 | | | | | | | | | Case 2: % 12.54/2.46 | | | | | | | | | | % 12.54/2.46 | | | | | | | | | | (90) all_91_0 = 0 % 12.54/2.46 | | | | | | | | | | % 12.54/2.46 | | | | | | | | | | REDUCE: (75), (90) imply: % 12.54/2.46 | | | | | | | | | | (91) $false % 12.54/2.46 | | | | | | | | | | % 12.54/2.46 | | | | | | | | | | CLOSE: (91) is inconsistent. % 12.54/2.46 | | | | | | | | | | % 12.54/2.46 | | | | | | | | | End of split % 12.54/2.46 | | | | | | | | | % 12.54/2.46 | | | | | | | | Case 2: % 12.54/2.46 | | | | | | | | | % 12.54/2.46 | | | | | | | | | (92) all_73_0 = 0 % 12.54/2.46 | | | | | | | | | % 12.54/2.46 | | | | | | | | | REDUCE: (64), (92) imply: % 12.54/2.46 | | | | | | | | | (93) $false % 12.54/2.46 | | | | | | | | | % 12.54/2.46 | | | | | | | | | CLOSE: (93) is inconsistent. % 12.54/2.46 | | | | | | | | | % 12.54/2.46 | | | | | | | | End of split % 12.54/2.46 | | | | | | | | % 12.54/2.46 | | | | | | | Case 2: % 12.54/2.46 | | | | | | | | % 12.54/2.46 | | | | | | | | (94) all_55_0 = 0 % 12.54/2.46 | | | | | | | | % 12.54/2.46 | | | | | | | | REDUCE: (53), (94) imply: % 12.54/2.46 | | | | | | | | (95) $false % 12.54/2.46 | | | | | | | | % 12.54/2.46 | | | | | | | | CLOSE: (95) is inconsistent. % 12.54/2.46 | | | | | | | | % 12.54/2.46 | | | | | | | End of split % 12.54/2.46 | | | | | | | % 12.54/2.46 | | | | | | Case 2: % 12.54/2.46 | | | | | | | % 12.54/2.46 | | | | | | | (96) all_37_0 = 0 % 12.54/2.46 | | | | | | | % 12.54/2.46 | | | | | | | REDUCE: (42), (96) imply: % 12.54/2.46 | | | | | | | (97) $false % 12.54/2.46 | | | | | | | % 12.54/2.46 | | | | | | | CLOSE: (97) is inconsistent. % 12.54/2.46 | | | | | | | % 12.54/2.46 | | | | | | End of split % 12.54/2.46 | | | | | | % 12.54/2.46 | | | | | Case 2: % 12.54/2.46 | | | | | | % 12.54/2.46 | | | | | | (98) all_19_0 = 0 % 12.54/2.46 | | | | | | % 12.54/2.46 | | | | | | REDUCE: (31), (98) imply: % 12.54/2.46 | | | | | | (99) $false % 12.54/2.46 | | | | | | % 12.54/2.46 | | | | | | CLOSE: (99) is inconsistent. % 12.54/2.46 | | | | | | % 12.54/2.46 | | | | | End of split % 12.54/2.46 | | | | | % 12.54/2.46 | | | | End of split % 12.54/2.46 | | | | % 12.54/2.46 | | | Case 2: % 12.54/2.46 | | | | % 12.54/2.46 | | | | (100) ? [v0: $i] : ? [v1: any] : (big_q(v0) = v1 & $i(v0) & ! [v2: % 12.54/2.47 | | | | $i] : ! [v3: int] : ( ~ (v1 = 0) | v3 = 0 | ~ (big_q(v2) % 12.54/2.47 | | | | = v3) | ~ $i(v2)) & ! [v2: $i] : (v1 = 0 | ~ % 12.54/2.47 | | | | (big_q(v2) = 0) | ~ $i(v2))) & (( ! [v0: $i] : ! [v1: % 12.54/2.47 | | | | int] : (v1 = 0 | ~ (big_q(v0) = v1) | ~ $i(v0)) & ? % 12.54/2.47 | | | | [v0: $i] : (big_p(v0) = 0 & $i(v0))) | ( ! [v0: $i] : ( ~ % 12.54/2.47 | | | | (big_p(v0) = 0) | ~ $i(v0)) & ? [v0: $i] : ? [v1: int] % 12.54/2.47 | | | | : ( ~ (v1 = 0) & big_q(v0) = v1 & $i(v0)))) % 12.54/2.47 | | | | % 12.54/2.47 | | | | ALPHA: (100) implies: % 12.54/2.47 | | | | (101) ( ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (big_q(v0) = v1) | % 12.54/2.47 | | | | ~ $i(v0)) & ? [v0: $i] : (big_p(v0) = 0 & $i(v0))) | ( ! % 12.54/2.47 | | | | [v0: $i] : ( ~ (big_p(v0) = 0) | ~ $i(v0)) & ? [v0: $i] : % 12.54/2.47 | | | | ? [v1: int] : ( ~ (v1 = 0) & big_q(v0) = v1 & $i(v0))) % 12.54/2.47 | | | | (102) ? [v0: $i] : ? [v1: any] : (big_q(v0) = v1 & $i(v0) & ! [v2: % 12.54/2.47 | | | | $i] : ! [v3: int] : ( ~ (v1 = 0) | v3 = 0 | ~ (big_q(v2) % 12.54/2.47 | | | | = v3) | ~ $i(v2)) & ! [v2: $i] : (v1 = 0 | ~ % 12.54/2.47 | | | | (big_q(v2) = 0) | ~ $i(v2))) % 12.54/2.47 | | | | % 12.54/2.47 | | | | DELTA: instantiating (102) with fresh symbols all_14_0, all_14_1 gives: % 12.54/2.47 | | | | (103) big_q(all_14_1) = all_14_0 & $i(all_14_1) & ! [v0: $i] : ! % 12.54/2.47 | | | | [v1: int] : ( ~ (all_14_0 = 0) | v1 = 0 | ~ (big_q(v0) = v1) | % 12.54/2.47 | | | | ~ $i(v0)) & ! [v0: $i] : (all_14_0 = 0 | ~ (big_q(v0) = 0) % 12.54/2.47 | | | | | ~ $i(v0)) % 12.54/2.47 | | | | % 12.54/2.47 | | | | ALPHA: (103) implies: % 12.54/2.47 | | | | (104) $i(all_14_1) % 12.54/2.47 | | | | (105) big_q(all_14_1) = all_14_0 % 12.54/2.47 | | | | (106) ! [v0: $i] : (all_14_0 = 0 | ~ (big_q(v0) = 0) | ~ $i(v0)) % 12.54/2.47 | | | | (107) ! [v0: $i] : ! [v1: int] : ( ~ (all_14_0 = 0) | v1 = 0 | ~ % 12.54/2.47 | | | | (big_q(v0) = v1) | ~ $i(v0)) % 12.54/2.47 | | | | % 12.54/2.47 | | | | BETA: splitting (5) gives: % 12.54/2.47 | | | | % 12.54/2.47 | | | | Case 1: % 12.54/2.47 | | | | | % 12.54/2.47 | | | | | (108) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (big_p(v0) = v1) | % 12.54/2.47 | | | | | ~ $i(v0)) & ? [v0: $i] : (big_q(v0) = 0 & $i(v0)) % 12.54/2.47 | | | | | % 12.54/2.47 | | | | | ALPHA: (108) implies: % 12.54/2.47 | | | | | (109) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (big_p(v0) = v1) | % 12.54/2.47 | | | | | ~ $i(v0)) % 12.54/2.47 | | | | | (110) ? [v0: $i] : (big_q(v0) = 0 & $i(v0)) % 12.54/2.47 | | | | | % 12.54/2.47 | | | | | DELTA: instantiating (110) with fresh symbol all_24_0 gives: % 12.54/2.47 | | | | | (111) big_q(all_24_0) = 0 & $i(all_24_0) % 12.54/2.47 | | | | | % 12.54/2.47 | | | | | ALPHA: (111) implies: % 12.54/2.47 | | | | | (112) $i(all_24_0) % 12.54/2.47 | | | | | (113) big_q(all_24_0) = 0 % 12.54/2.47 | | | | | % 12.54/2.47 | | | | | GROUND_INST: instantiating (106) with all_24_0, simplifying with % 12.54/2.47 | | | | | (112), (113) gives: % 12.54/2.47 | | | | | (114) all_14_0 = 0 % 12.54/2.47 | | | | | % 12.54/2.47 | | | | | BETA: splitting (101) gives: % 12.54/2.47 | | | | | % 12.54/2.47 | | | | | Case 1: % 12.54/2.47 | | | | | | % 12.54/2.47 | | | | | | (115) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (big_q(v0) = v1) % 12.54/2.47 | | | | | | | ~ $i(v0)) & ? [v0: $i] : (big_p(v0) = 0 & $i(v0)) % 12.54/2.47 | | | | | | % 12.54/2.47 | | | | | | ALPHA: (115) implies: % 12.54/2.47 | | | | | | (116) ? [v0: $i] : (big_p(v0) = 0 & $i(v0)) % 12.54/2.47 | | | | | | % 12.54/2.47 | | | | | | REF_CLOSE: (6), (109), (116) are inconsistent by sub-proof #3. % 12.54/2.47 | | | | | | % 12.54/2.47 | | | | | Case 2: % 12.54/2.47 | | | | | | % 12.54/2.47 | | | | | | (117) ! [v0: $i] : ( ~ (big_p(v0) = 0) | ~ $i(v0)) & ? [v0: % 12.54/2.47 | | | | | | $i] : ? [v1: int] : ( ~ (v1 = 0) & big_q(v0) = v1 & % 12.54/2.47 | | | | | | $i(v0)) % 12.54/2.47 | | | | | | % 12.54/2.47 | | | | | | ALPHA: (117) implies: % 12.54/2.47 | | | | | | (118) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & big_q(v0) = v1 % 12.54/2.47 | | | | | | & $i(v0)) % 12.54/2.47 | | | | | | % 12.54/2.47 | | | | | | DELTA: instantiating (118) with fresh symbols all_39_0, all_39_1 % 12.54/2.47 | | | | | | gives: % 12.54/2.47 | | | | | | (119) ~ (all_39_0 = 0) & big_q(all_39_1) = all_39_0 & % 12.54/2.47 | | | | | | $i(all_39_1) % 12.54/2.47 | | | | | | % 12.54/2.47 | | | | | | ALPHA: (119) implies: % 12.54/2.47 | | | | | | (120) ~ (all_39_0 = 0) % 12.54/2.47 | | | | | | (121) $i(all_39_1) % 12.54/2.47 | | | | | | (122) big_q(all_39_1) = all_39_0 % 12.54/2.47 | | | | | | % 12.54/2.47 | | | | | | GROUND_INST: instantiating (107) with all_39_1, all_39_0, % 12.54/2.47 | | | | | | simplifying with (121), (122) gives: % 12.54/2.47 | | | | | | (123) ~ (all_14_0 = 0) | all_39_0 = 0 % 12.54/2.47 | | | | | | % 12.54/2.47 | | | | | | BETA: splitting (123) gives: % 12.54/2.47 | | | | | | % 12.54/2.47 | | | | | | Case 1: % 12.54/2.47 | | | | | | | % 12.54/2.47 | | | | | | | (124) ~ (all_14_0 = 0) % 12.54/2.47 | | | | | | | % 12.54/2.47 | | | | | | | REDUCE: (114), (124) imply: % 12.54/2.47 | | | | | | | (125) $false % 12.54/2.47 | | | | | | | % 12.54/2.47 | | | | | | | CLOSE: (125) is inconsistent. % 12.54/2.47 | | | | | | | % 12.54/2.47 | | | | | | Case 2: % 12.54/2.47 | | | | | | | % 12.54/2.47 | | | | | | | (126) all_39_0 = 0 % 12.54/2.47 | | | | | | | % 12.54/2.47 | | | | | | | REDUCE: (120), (126) imply: % 12.54/2.47 | | | | | | | (127) $false % 12.54/2.47 | | | | | | | % 12.54/2.47 | | | | | | | CLOSE: (127) is inconsistent. % 12.54/2.47 | | | | | | | % 12.54/2.47 | | | | | | End of split % 12.54/2.47 | | | | | | % 12.54/2.47 | | | | | End of split % 12.54/2.47 | | | | | % 12.54/2.47 | | | | Case 2: % 12.54/2.47 | | | | | % 12.54/2.47 | | | | | (128) ! [v0: $i] : ( ~ (big_q(v0) = 0) | ~ $i(v0)) & ? [v0: $i] % 12.54/2.47 | | | | | : ? [v1: int] : ( ~ (v1 = 0) & big_p(v0) = v1 & $i(v0)) % 12.54/2.47 | | | | | % 12.54/2.47 | | | | | ALPHA: (128) implies: % 12.54/2.47 | | | | | (129) ! [v0: $i] : ( ~ (big_q(v0) = 0) | ~ $i(v0)) % 12.54/2.47 | | | | | (130) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & big_p(v0) = v1 & % 12.54/2.47 | | | | | $i(v0)) % 12.54/2.47 | | | | | % 12.54/2.47 | | | | | DELTA: instantiating (130) with fresh symbols all_24_0, all_24_1 % 12.54/2.47 | | | | | gives: % 12.54/2.47 | | | | | (131) ~ (all_24_0 = 0) & big_p(all_24_1) = all_24_0 & $i(all_24_1) % 12.54/2.47 | | | | | % 12.54/2.47 | | | | | ALPHA: (131) implies: % 12.54/2.47 | | | | | (132) ~ (all_24_0 = 0) % 12.54/2.47 | | | | | (133) $i(all_24_1) % 12.54/2.47 | | | | | (134) big_p(all_24_1) = all_24_0 % 12.54/2.47 | | | | | % 12.54/2.47 | | | | | GROUND_INST: instantiating (6) with all_24_1, all_24_0, simplifying % 12.54/2.47 | | | | | with (133), (134) gives: % 12.54/2.48 | | | | | (135) ? [v0: $i] : ? [v1: any] : (big_p(v0) = v1 & $i(v0) & ( ~ % 12.54/2.48 | | | | | (v1 = 0) | ~ (all_24_0 = 0)) & (v1 = 0 | all_24_0 = 0)) % 12.54/2.48 | | | | | % 12.54/2.48 | | | | | DELTA: instantiating (135) with fresh symbols all_31_0, all_31_1 % 12.54/2.48 | | | | | gives: % 12.54/2.48 | | | | | (136) big_p(all_31_1) = all_31_0 & $i(all_31_1) & ( ~ (all_31_0 = % 12.54/2.48 | | | | | 0) | ~ (all_24_0 = 0)) & (all_31_0 = 0 | all_24_0 = 0) % 12.54/2.48 | | | | | % 12.54/2.48 | | | | | ALPHA: (136) implies: % 12.54/2.48 | | | | | (137) $i(all_31_1) % 12.54/2.48 | | | | | (138) big_p(all_31_1) = all_31_0 % 12.54/2.48 | | | | | (139) all_31_0 = 0 | all_24_0 = 0 % 12.54/2.48 | | | | | % 12.54/2.48 | | | | | BETA: splitting (139) gives: % 12.54/2.48 | | | | | % 12.54/2.48 | | | | | Case 1: % 12.54/2.48 | | | | | | % 12.54/2.48 | | | | | | (140) all_31_0 = 0 % 12.54/2.48 | | | | | | % 12.54/2.48 | | | | | | REDUCE: (138), (140) imply: % 12.54/2.48 | | | | | | (141) big_p(all_31_1) = 0 % 12.54/2.48 | | | | | | % 12.54/2.48 | | | | | | DELTA: instantiating (130) with fresh symbols all_42_0, all_42_1 % 12.54/2.48 | | | | | | gives: % 12.54/2.48 | | | | | | (142) ~ (all_42_0 = 0) & big_p(all_42_1) = all_42_0 & % 12.54/2.48 | | | | | | $i(all_42_1) % 12.54/2.48 | | | | | | % 12.54/2.48 | | | | | | ALPHA: (142) implies: % 12.54/2.48 | | | | | | (143) ~ (all_42_0 = 0) % 12.54/2.48 | | | | | | (144) $i(all_42_1) % 12.54/2.48 | | | | | | (145) big_p(all_42_1) = all_42_0 % 12.54/2.48 | | | | | | % 12.54/2.48 | | | | | | GROUND_INST: instantiating (6) with all_42_1, all_42_0, simplifying % 12.54/2.48 | | | | | | with (144), (145) gives: % 12.54/2.48 | | | | | | (146) ? [v0: $i] : ? [v1: any] : (big_p(v0) = v1 & $i(v0) & ( ~ % 12.54/2.48 | | | | | | (v1 = 0) | ~ (all_42_0 = 0)) & (v1 = 0 | all_42_0 = % 12.54/2.48 | | | | | | 0)) % 12.54/2.48 | | | | | | % 12.54/2.48 | | | | | | DELTA: instantiating (146) with fresh symbols all_49_0, all_49_1 % 12.54/2.48 | | | | | | gives: % 12.54/2.48 | | | | | | (147) big_p(all_49_1) = all_49_0 & $i(all_49_1) & ( ~ (all_49_0 = % 12.54/2.48 | | | | | | 0) | ~ (all_42_0 = 0)) & (all_49_0 = 0 | all_42_0 = 0) % 12.54/2.48 | | | | | | % 12.54/2.48 | | | | | | ALPHA: (147) implies: % 12.54/2.48 | | | | | | (148) $i(all_49_1) % 12.54/2.48 | | | | | | (149) big_p(all_49_1) = all_49_0 % 12.54/2.48 | | | | | | (150) all_49_0 = 0 | all_42_0 = 0 % 12.54/2.48 | | | | | | % 12.54/2.48 | | | | | | BETA: splitting (150) gives: % 12.54/2.48 | | | | | | % 12.54/2.48 | | | | | | Case 1: % 12.54/2.48 | | | | | | | % 12.54/2.48 | | | | | | | (151) all_49_0 = 0 % 12.54/2.48 | | | | | | | % 12.54/2.48 | | | | | | | REDUCE: (149), (151) imply: % 12.54/2.48 | | | | | | | (152) big_p(all_49_1) = 0 % 12.54/2.48 | | | | | | | % 12.54/2.48 | | | | | | | DELTA: instantiating (130) with fresh symbols all_60_0, all_60_1 % 12.54/2.48 | | | | | | | gives: % 12.54/2.48 | | | | | | | (153) ~ (all_60_0 = 0) & big_p(all_60_1) = all_60_0 & % 12.54/2.48 | | | | | | | $i(all_60_1) % 12.54/2.48 | | | | | | | % 12.54/2.48 | | | | | | | ALPHA: (153) implies: % 12.54/2.48 | | | | | | | (154) ~ (all_60_0 = 0) % 12.54/2.48 | | | | | | | (155) $i(all_60_1) % 12.54/2.48 | | | | | | | (156) big_p(all_60_1) = all_60_0 % 12.54/2.48 | | | | | | | % 12.54/2.48 | | | | | | | GROUND_INST: instantiating (6) with all_60_1, all_60_0, % 12.54/2.48 | | | | | | | simplifying with (155), (156) gives: % 12.54/2.48 | | | | | | | (157) ? [v0: $i] : ? [v1: any] : (big_p(v0) = v1 & $i(v0) & ( % 12.54/2.48 | | | | | | | ~ (v1 = 0) | ~ (all_60_0 = 0)) & (v1 = 0 | all_60_0 % 12.54/2.48 | | | | | | | = 0)) % 12.54/2.48 | | | | | | | % 12.54/2.48 | | | | | | | DELTA: instantiating (157) with fresh symbols all_67_0, all_67_1 % 12.54/2.48 | | | | | | | gives: % 12.54/2.48 | | | | | | | (158) big_p(all_67_1) = all_67_0 & $i(all_67_1) & ( ~ (all_67_0 % 12.54/2.48 | | | | | | | = 0) | ~ (all_60_0 = 0)) & (all_67_0 = 0 | all_60_0 % 12.54/2.48 | | | | | | | = 0) % 12.54/2.48 | | | | | | | % 12.54/2.48 | | | | | | | ALPHA: (158) implies: % 12.54/2.48 | | | | | | | (159) $i(all_67_1) % 12.54/2.48 | | | | | | | (160) big_p(all_67_1) = all_67_0 % 12.54/2.48 | | | | | | | (161) all_67_0 = 0 | all_60_0 = 0 % 12.54/2.48 | | | | | | | % 12.54/2.48 | | | | | | | BETA: splitting (161) gives: % 12.54/2.48 | | | | | | | % 12.54/2.48 | | | | | | | Case 1: % 12.54/2.48 | | | | | | | | % 12.54/2.48 | | | | | | | | (162) all_67_0 = 0 % 12.54/2.48 | | | | | | | | % 12.54/2.48 | | | | | | | | REDUCE: (160), (162) imply: % 12.54/2.48 | | | | | | | | (163) big_p(all_67_1) = 0 % 12.54/2.48 | | | | | | | | % 12.54/2.48 | | | | | | | | DELTA: instantiating (130) with fresh symbols all_78_0, all_78_1 % 12.54/2.48 | | | | | | | | gives: % 12.54/2.48 | | | | | | | | (164) ~ (all_78_0 = 0) & big_p(all_78_1) = all_78_0 & % 12.54/2.48 | | | | | | | | $i(all_78_1) % 12.54/2.48 | | | | | | | | % 12.54/2.48 | | | | | | | | ALPHA: (164) implies: % 12.54/2.48 | | | | | | | | (165) ~ (all_78_0 = 0) % 12.54/2.48 | | | | | | | | (166) $i(all_78_1) % 12.54/2.48 | | | | | | | | (167) big_p(all_78_1) = all_78_0 % 12.54/2.48 | | | | | | | | % 12.54/2.48 | | | | | | | | GROUND_INST: instantiating (6) with all_78_1, all_78_0, % 12.54/2.48 | | | | | | | | simplifying with (166), (167) gives: % 12.54/2.48 | | | | | | | | (168) ? [v0: $i] : ? [v1: any] : (big_p(v0) = v1 & $i(v0) & % 12.54/2.48 | | | | | | | | ( ~ (v1 = 0) | ~ (all_78_0 = 0)) & (v1 = 0 | % 12.54/2.48 | | | | | | | | all_78_0 = 0)) % 12.54/2.48 | | | | | | | | % 12.54/2.48 | | | | | | | | DELTA: instantiating (168) with fresh symbols all_85_0, all_85_1 % 12.54/2.48 | | | | | | | | gives: % 12.54/2.48 | | | | | | | | (169) big_p(all_85_1) = all_85_0 & $i(all_85_1) & ( ~ % 12.54/2.48 | | | | | | | | (all_85_0 = 0) | ~ (all_78_0 = 0)) & (all_85_0 = 0 | % 12.54/2.48 | | | | | | | | all_78_0 = 0) % 12.54/2.48 | | | | | | | | % 12.54/2.48 | | | | | | | | ALPHA: (169) implies: % 12.54/2.48 | | | | | | | | (170) $i(all_85_1) % 12.54/2.48 | | | | | | | | (171) big_p(all_85_1) = all_85_0 % 12.54/2.48 | | | | | | | | (172) all_85_0 = 0 | all_78_0 = 0 % 12.54/2.48 | | | | | | | | % 12.54/2.48 | | | | | | | | BETA: splitting (172) gives: % 12.54/2.48 | | | | | | | | % 12.54/2.48 | | | | | | | | Case 1: % 12.54/2.48 | | | | | | | | | % 12.54/2.48 | | | | | | | | | (173) all_85_0 = 0 % 12.54/2.48 | | | | | | | | | % 12.54/2.48 | | | | | | | | | REDUCE: (171), (173) imply: % 12.54/2.48 | | | | | | | | | (174) big_p(all_85_1) = 0 % 12.54/2.48 | | | | | | | | | % 12.54/2.48 | | | | | | | | | DELTA: instantiating (130) with fresh symbols all_96_0, % 12.54/2.48 | | | | | | | | | all_96_1 gives: % 12.54/2.48 | | | | | | | | | (175) ~ (all_96_0 = 0) & big_p(all_96_1) = all_96_0 & % 12.54/2.48 | | | | | | | | | $i(all_96_1) % 12.54/2.48 | | | | | | | | | % 12.54/2.48 | | | | | | | | | ALPHA: (175) implies: % 12.54/2.48 | | | | | | | | | (176) ~ (all_96_0 = 0) % 12.54/2.48 | | | | | | | | | (177) $i(all_96_1) % 12.54/2.48 | | | | | | | | | (178) big_p(all_96_1) = all_96_0 % 12.54/2.48 | | | | | | | | | % 12.54/2.48 | | | | | | | | | GROUND_INST: instantiating (6) with all_96_1, all_96_0, % 12.54/2.48 | | | | | | | | | simplifying with (177), (178) gives: % 12.54/2.48 | | | | | | | | | (179) ? [v0: $i] : ? [v1: any] : (big_p(v0) = v1 & $i(v0) % 12.54/2.48 | | | | | | | | | & ( ~ (v1 = 0) | ~ (all_96_0 = 0)) & (v1 = 0 | % 12.54/2.48 | | | | | | | | | all_96_0 = 0)) % 12.54/2.48 | | | | | | | | | % 12.54/2.48 | | | | | | | | | DELTA: instantiating (179) with fresh symbols all_103_0, % 12.54/2.48 | | | | | | | | | all_103_1 gives: % 12.54/2.48 | | | | | | | | | (180) big_p(all_103_1) = all_103_0 & $i(all_103_1) & ( ~ % 12.54/2.48 | | | | | | | | | (all_103_0 = 0) | ~ (all_96_0 = 0)) & (all_103_0 = % 12.54/2.48 | | | | | | | | | 0 | all_96_0 = 0) % 12.54/2.48 | | | | | | | | | % 12.54/2.48 | | | | | | | | | ALPHA: (180) implies: % 12.54/2.48 | | | | | | | | | (181) $i(all_103_1) % 12.54/2.48 | | | | | | | | | (182) big_p(all_103_1) = all_103_0 % 12.54/2.48 | | | | | | | | | (183) all_103_0 = 0 | all_96_0 = 0 % 12.54/2.48 | | | | | | | | | % 12.54/2.48 | | | | | | | | | BETA: splitting (183) gives: % 12.54/2.48 | | | | | | | | | % 12.54/2.48 | | | | | | | | | Case 1: % 12.54/2.48 | | | | | | | | | | % 12.54/2.48 | | | | | | | | | | (184) all_103_0 = 0 % 12.54/2.48 | | | | | | | | | | % 12.54/2.48 | | | | | | | | | | REDUCE: (182), (184) imply: % 12.54/2.48 | | | | | | | | | | (185) big_p(all_103_1) = 0 % 12.54/2.48 | | | | | | | | | | % 12.54/2.48 | | | | | | | | | | BETA: splitting (101) gives: % 12.54/2.48 | | | | | | | | | | % 12.54/2.48 | | | | | | | | | | Case 1: % 12.54/2.48 | | | | | | | | | | | % 12.54/2.49 | | | | | | | | | | | (186) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ % 12.54/2.49 | | | | | | | | | | | (big_q(v0) = v1) | ~ $i(v0)) & ? [v0: $i] : % 12.54/2.49 | | | | | | | | | | | (big_p(v0) = 0 & $i(v0)) % 12.54/2.49 | | | | | | | | | | | % 12.54/2.49 | | | | | | | | | | | ALPHA: (186) implies: % 12.54/2.49 | | | | | | | | | | | (187) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ % 12.54/2.49 | | | | | | | | | | | (big_q(v0) = v1) | ~ $i(v0)) % 12.54/2.49 | | | | | | | | | | | % 12.54/2.49 | | | | | | | | | | | GROUND_INST: instantiating (187) with all_14_1, all_14_0, % 12.54/2.49 | | | | | | | | | | | simplifying with (104), (105) gives: % 12.54/2.49 | | | | | | | | | | | (188) all_14_0 = 0 % 12.54/2.49 | | | | | | | | | | | % 12.54/2.49 | | | | | | | | | | | REDUCE: (105), (188) imply: % 12.54/2.49 | | | | | | | | | | | (189) big_q(all_14_1) = 0 % 12.54/2.49 | | | | | | | | | | | % 12.54/2.49 | | | | | | | | | | | GROUND_INST: instantiating (129) with all_14_1, simplifying % 12.54/2.49 | | | | | | | | | | | with (104), (189) gives: % 12.54/2.49 | | | | | | | | | | | (190) $false % 12.54/2.49 | | | | | | | | | | | % 12.54/2.49 | | | | | | | | | | | CLOSE: (190) is inconsistent. % 12.54/2.49 | | | | | | | | | | | % 12.54/2.49 | | | | | | | | | | Case 2: % 12.54/2.49 | | | | | | | | | | | % 12.54/2.49 | | | | | | | | | | | (191) ! [v0: $i] : ( ~ (big_p(v0) = 0) | ~ $i(v0)) & % 12.54/2.49 | | | | | | | | | | | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & % 12.54/2.49 | | | | | | | | | | | big_q(v0) = v1 & $i(v0)) % 12.54/2.49 | | | | | | | | | | | % 12.54/2.49 | | | | | | | | | | | ALPHA: (191) implies: % 12.54/2.49 | | | | | | | | | | | (192) ! [v0: $i] : ( ~ (big_p(v0) = 0) | ~ $i(v0)) % 12.54/2.49 | | | | | | | | | | | % 12.54/2.49 | | | | | | | | | | | GROUND_INST: instantiating (192) with all_103_1, simplifying % 12.54/2.49 | | | | | | | | | | | with (181), (185) gives: % 12.54/2.49 | | | | | | | | | | | (193) $false % 12.54/2.49 | | | | | | | | | | | % 12.54/2.49 | | | | | | | | | | | CLOSE: (193) is inconsistent. % 12.54/2.49 | | | | | | | | | | | % 12.54/2.49 | | | | | | | | | | End of split % 12.54/2.49 | | | | | | | | | | % 12.54/2.49 | | | | | | | | | Case 2: % 12.54/2.49 | | | | | | | | | | % 12.54/2.49 | | | | | | | | | | (194) all_96_0 = 0 % 12.54/2.49 | | | | | | | | | | % 12.54/2.49 | | | | | | | | | | REDUCE: (176), (194) imply: % 12.54/2.49 | | | | | | | | | | (195) $false % 12.54/2.49 | | | | | | | | | | % 12.54/2.49 | | | | | | | | | | CLOSE: (195) is inconsistent. % 12.54/2.49 | | | | | | | | | | % 12.54/2.49 | | | | | | | | | End of split % 12.54/2.49 | | | | | | | | | % 12.54/2.49 | | | | | | | | Case 2: % 12.54/2.49 | | | | | | | | | % 12.54/2.49 | | | | | | | | | (196) all_78_0 = 0 % 12.54/2.49 | | | | | | | | | % 12.54/2.49 | | | | | | | | | REDUCE: (165), (196) imply: % 12.54/2.49 | | | | | | | | | (197) $false % 12.54/2.49 | | | | | | | | | % 12.54/2.49 | | | | | | | | | CLOSE: (197) is inconsistent. % 12.54/2.49 | | | | | | | | | % 12.54/2.49 | | | | | | | | End of split % 12.54/2.49 | | | | | | | | % 12.54/2.49 | | | | | | | Case 2: % 12.54/2.49 | | | | | | | | % 12.54/2.49 | | | | | | | | (198) all_60_0 = 0 % 12.54/2.49 | | | | | | | | % 12.54/2.49 | | | | | | | | REDUCE: (154), (198) imply: % 12.54/2.49 | | | | | | | | (199) $false % 12.54/2.49 | | | | | | | | % 12.54/2.49 | | | | | | | | CLOSE: (199) is inconsistent. % 12.54/2.49 | | | | | | | | % 12.54/2.49 | | | | | | | End of split % 12.54/2.49 | | | | | | | % 12.54/2.49 | | | | | | Case 2: % 12.54/2.49 | | | | | | | % 12.54/2.49 | | | | | | | (200) all_42_0 = 0 % 12.54/2.49 | | | | | | | % 12.54/2.49 | | | | | | | REDUCE: (143), (200) imply: % 12.54/2.49 | | | | | | | (201) $false % 12.54/2.49 | | | | | | | % 12.54/2.49 | | | | | | | CLOSE: (201) is inconsistent. % 12.54/2.49 | | | | | | | % 12.54/2.49 | | | | | | End of split % 12.54/2.49 | | | | | | % 12.54/2.49 | | | | | Case 2: % 12.54/2.49 | | | | | | % 12.54/2.49 | | | | | | (202) all_24_0 = 0 % 12.54/2.49 | | | | | | % 12.54/2.49 | | | | | | REDUCE: (132), (202) imply: % 12.54/2.49 | | | | | | (203) $false % 12.54/2.49 | | | | | | % 12.54/2.49 | | | | | | CLOSE: (203) is inconsistent. % 12.54/2.49 | | | | | | % 12.54/2.49 | | | | | End of split % 12.54/2.49 | | | | | % 12.54/2.49 | | | | End of split % 12.54/2.49 | | | | % 12.54/2.49 | | | End of split % 12.54/2.49 | | | % 12.54/2.49 | | Case 2: % 12.54/2.49 | | | % 12.54/2.49 | | | (204) ? [v0: $i] : ? [v1: any] : (big_p(v0) = v1 & $i(v0) & ! [v2: % 12.54/2.49 | | | $i] : ! [v3: int] : ( ~ (v1 = 0) | v3 = 0 | ~ (big_p(v2) = % 12.54/2.49 | | | v3) | ~ $i(v2)) & ! [v2: $i] : (v1 = 0 | ~ (big_p(v2) = % 12.54/2.49 | | | 0) | ~ $i(v2))) & (( ! [v0: $i] : ! [v1: int] : (v1 = 0 | % 12.54/2.49 | | | ~ (big_p(v0) = v1) | ~ $i(v0)) & ! [v0: $i] : ( ~ % 12.54/2.49 | | | (big_q(v0) = 0) | ~ $i(v0))) | ( ? [v0: $i] : ? [v1: int] % 12.54/2.49 | | | : ( ~ (v1 = 0) & big_p(v0) = v1 & $i(v0)) & ? [v0: $i] : % 12.54/2.49 | | | (big_q(v0) = 0 & $i(v0)))) % 12.54/2.49 | | | % 12.54/2.49 | | | ALPHA: (204) implies: % 12.54/2.49 | | | (205) ( ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (big_p(v0) = v1) | ~ % 12.54/2.49 | | | $i(v0)) & ! [v0: $i] : ( ~ (big_q(v0) = 0) | ~ $i(v0))) | ( % 12.54/2.49 | | | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & big_p(v0) = v1 & % 12.54/2.49 | | | $i(v0)) & ? [v0: $i] : (big_q(v0) = 0 & $i(v0))) % 12.54/2.49 | | | (206) ? [v0: $i] : ? [v1: any] : (big_p(v0) = v1 & $i(v0) & ! [v2: % 12.54/2.49 | | | $i] : ! [v3: int] : ( ~ (v1 = 0) | v3 = 0 | ~ (big_p(v2) = % 12.54/2.49 | | | v3) | ~ $i(v2)) & ! [v2: $i] : (v1 = 0 | ~ (big_p(v2) = % 12.54/2.49 | | | 0) | ~ $i(v2))) % 12.54/2.49 | | | % 12.54/2.49 | | | DELTA: instantiating (206) with fresh symbols all_10_0, all_10_1 gives: % 12.54/2.49 | | | (207) big_p(all_10_1) = all_10_0 & $i(all_10_1) & ! [v0: $i] : ! [v1: % 12.54/2.49 | | | int] : ( ~ (all_10_0 = 0) | v1 = 0 | ~ (big_p(v0) = v1) | ~ % 12.54/2.49 | | | $i(v0)) & ! [v0: $i] : (all_10_0 = 0 | ~ (big_p(v0) = 0) | ~ % 12.54/2.49 | | | $i(v0)) % 12.54/2.49 | | | % 12.54/2.49 | | | ALPHA: (207) implies: % 12.54/2.49 | | | (208) $i(all_10_1) % 12.54/2.49 | | | (209) big_p(all_10_1) = all_10_0 % 12.54/2.49 | | | (210) ! [v0: $i] : (all_10_0 = 0 | ~ (big_p(v0) = 0) | ~ $i(v0)) % 12.54/2.49 | | | (211) ! [v0: $i] : ! [v1: int] : ( ~ (all_10_0 = 0) | v1 = 0 | ~ % 12.54/2.49 | | | (big_p(v0) = v1) | ~ $i(v0)) % 12.54/2.49 | | | % 12.54/2.49 | | | BETA: splitting (3) gives: % 12.54/2.49 | | | % 12.54/2.49 | | | Case 1: % 12.54/2.49 | | | | % 12.54/2.49 | | | | (212) ! [v0: $i] : ! [v1: any] : ( ~ (big_q(v0) = v1) | ~ $i(v0) | % 12.54/2.49 | | | | ? [v2: $i] : ? [v3: any] : (big_q(v2) = v3 & $i(v2) & ( ~ % 12.54/2.49 | | | | (v3 = 0) | ~ (v1 = 0)) & (v3 = 0 | v1 = 0))) & (( ! [v0: % 12.54/2.49 | | | | $i] : ! [v1: int] : (v1 = 0 | ~ (big_q(v0) = v1) | ~ % 12.54/2.49 | | | | $i(v0)) & ! [v0: $i] : ( ~ (big_p(v0) = 0) | ~ $i(v0))) % 12.54/2.49 | | | | | ( ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & big_q(v0) = v1 % 12.54/2.49 | | | | & $i(v0)) & ? [v0: $i] : (big_p(v0) = 0 & $i(v0)))) % 12.54/2.49 | | | | % 12.54/2.49 | | | | ALPHA: (212) implies: % 12.54/2.49 | | | | (213) ( ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (big_q(v0) = v1) | % 12.54/2.49 | | | | ~ $i(v0)) & ! [v0: $i] : ( ~ (big_p(v0) = 0) | ~ $i(v0))) % 12.54/2.49 | | | | | ( ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & big_q(v0) = v1 & % 12.54/2.49 | | | | $i(v0)) & ? [v0: $i] : (big_p(v0) = 0 & $i(v0))) % 12.54/2.49 | | | | (214) ! [v0: $i] : ! [v1: any] : ( ~ (big_q(v0) = v1) | ~ $i(v0) | % 12.54/2.49 | | | | ? [v2: $i] : ? [v3: any] : (big_q(v2) = v3 & $i(v2) & ( ~ % 12.54/2.49 | | | | (v3 = 0) | ~ (v1 = 0)) & (v3 = 0 | v1 = 0))) % 12.54/2.49 | | | | % 12.54/2.49 | | | | BETA: splitting (205) gives: % 12.54/2.49 | | | | % 12.54/2.49 | | | | Case 1: % 12.54/2.49 | | | | | % 12.54/2.49 | | | | | (215) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (big_p(v0) = v1) | % 12.54/2.49 | | | | | ~ $i(v0)) & ! [v0: $i] : ( ~ (big_q(v0) = 0) | ~ $i(v0)) % 12.54/2.49 | | | | | % 12.54/2.49 | | | | | ALPHA: (215) implies: % 12.54/2.49 | | | | | (216) ! [v0: $i] : ( ~ (big_q(v0) = 0) | ~ $i(v0)) % 12.54/2.49 | | | | | (217) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (big_p(v0) = v1) | % 12.54/2.49 | | | | | ~ $i(v0)) % 12.54/2.49 | | | | | % 12.54/2.49 | | | | | GROUND_INST: instantiating (217) with all_10_1, all_10_0, simplifying % 12.54/2.49 | | | | | with (208), (209) gives: % 12.54/2.49 | | | | | (218) all_10_0 = 0 % 12.54/2.49 | | | | | % 12.54/2.49 | | | | | REDUCE: (209), (218) imply: % 12.54/2.49 | | | | | (219) big_p(all_10_1) = 0 % 12.54/2.49 | | | | | % 12.54/2.49 | | | | | BETA: splitting (213) gives: % 12.54/2.49 | | | | | % 12.54/2.49 | | | | | Case 1: % 12.54/2.49 | | | | | | % 12.54/2.49 | | | | | | (220) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (big_q(v0) = v1) % 12.54/2.49 | | | | | | | ~ $i(v0)) & ! [v0: $i] : ( ~ (big_p(v0) = 0) | ~ % 12.54/2.49 | | | | | | $i(v0)) % 12.54/2.49 | | | | | | % 12.54/2.49 | | | | | | ALPHA: (220) implies: % 12.54/2.50 | | | | | | (221) ! [v0: $i] : ( ~ (big_p(v0) = 0) | ~ $i(v0)) % 12.54/2.50 | | | | | | % 12.54/2.50 | | | | | | GROUND_INST: instantiating (221) with all_10_1, simplifying with % 12.54/2.50 | | | | | | (208), (219) gives: % 12.54/2.50 | | | | | | (222) $false % 12.54/2.50 | | | | | | % 12.54/2.50 | | | | | | CLOSE: (222) is inconsistent. % 12.54/2.50 | | | | | | % 12.54/2.50 | | | | | Case 2: % 12.54/2.50 | | | | | | % 12.54/2.50 | | | | | | (223) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & big_q(v0) = v1 % 12.54/2.50 | | | | | | & $i(v0)) & ? [v0: $i] : (big_p(v0) = 0 & $i(v0)) % 12.54/2.50 | | | | | | % 12.54/2.50 | | | | | | ALPHA: (223) implies: % 12.54/2.50 | | | | | | (224) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & big_q(v0) = v1 % 12.54/2.50 | | | | | | & $i(v0)) % 12.54/2.50 | | | | | | % 12.54/2.50 | | | | | | REF_CLOSE: (214), (216), (224) are inconsistent by sub-proof #2. % 12.54/2.50 | | | | | | % 12.54/2.50 | | | | | End of split % 12.54/2.50 | | | | | % 12.54/2.50 | | | | Case 2: % 12.54/2.50 | | | | | % 12.54/2.50 | | | | | (225) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & big_p(v0) = v1 & % 12.54/2.50 | | | | | $i(v0)) & ? [v0: $i] : (big_q(v0) = 0 & $i(v0)) % 12.54/2.50 | | | | | % 12.54/2.50 | | | | | ALPHA: (225) implies: % 12.54/2.50 | | | | | (226) ? [v0: $i] : (big_q(v0) = 0 & $i(v0)) % 12.54/2.50 | | | | | (227) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & big_p(v0) = v1 & % 12.54/2.50 | | | | | $i(v0)) % 12.54/2.50 | | | | | % 12.54/2.50 | | | | | DELTA: instantiating (226) with fresh symbol all_23_0 gives: % 12.54/2.50 | | | | | (228) big_q(all_23_0) = 0 & $i(all_23_0) % 12.54/2.50 | | | | | % 12.54/2.50 | | | | | ALPHA: (228) implies: % 12.54/2.50 | | | | | (229) $i(all_23_0) % 12.54/2.50 | | | | | (230) big_q(all_23_0) = 0 % 12.54/2.50 | | | | | % 12.54/2.50 | | | | | DELTA: instantiating (227) with fresh symbols all_25_0, all_25_1 % 12.54/2.50 | | | | | gives: % 12.54/2.50 | | | | | (231) ~ (all_25_0 = 0) & big_p(all_25_1) = all_25_0 & $i(all_25_1) % 12.54/2.50 | | | | | % 12.54/2.50 | | | | | ALPHA: (231) implies: % 12.54/2.50 | | | | | (232) ~ (all_25_0 = 0) % 12.54/2.50 | | | | | (233) $i(all_25_1) % 12.54/2.50 | | | | | (234) big_p(all_25_1) = all_25_0 % 12.54/2.50 | | | | | % 12.54/2.50 | | | | | GROUND_INST: instantiating (211) with all_25_1, all_25_0, simplifying % 12.54/2.50 | | | | | with (233), (234) gives: % 12.54/2.50 | | | | | (235) ~ (all_10_0 = 0) | all_25_0 = 0 % 12.54/2.50 | | | | | % 12.54/2.50 | | | | | GROUND_INST: instantiating (214) with all_23_0, 0, simplifying with % 12.54/2.50 | | | | | (229), (230) gives: % 12.54/2.50 | | | | | (236) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & big_q(v0) = v1 & % 12.54/2.50 | | | | | $i(v0)) % 12.54/2.50 | | | | | % 12.54/2.50 | | | | | DELTA: instantiating (236) with fresh symbols all_32_0, all_32_1 % 12.54/2.50 | | | | | gives: % 12.54/2.50 | | | | | (237) ~ (all_32_0 = 0) & big_q(all_32_1) = all_32_0 & $i(all_32_1) % 12.54/2.50 | | | | | % 12.54/2.50 | | | | | ALPHA: (237) implies: % 12.54/2.50 | | | | | (238) ~ (all_32_0 = 0) % 12.54/2.50 | | | | | (239) $i(all_32_1) % 12.54/2.50 | | | | | (240) big_q(all_32_1) = all_32_0 % 12.54/2.50 | | | | | % 12.54/2.50 | | | | | BETA: splitting (235) gives: % 12.54/2.50 | | | | | % 12.54/2.50 | | | | | Case 1: % 12.54/2.50 | | | | | | % 12.54/2.50 | | | | | | (241) ~ (all_10_0 = 0) % 12.54/2.50 | | | | | | % 12.54/2.50 | | | | | | BETA: splitting (213) gives: % 12.54/2.50 | | | | | | % 12.54/2.50 | | | | | | Case 1: % 12.54/2.50 | | | | | | | % 12.54/2.50 | | | | | | | (242) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (big_q(v0) = % 12.54/2.50 | | | | | | | v1) | ~ $i(v0)) & ! [v0: $i] : ( ~ (big_p(v0) = 0) % 12.54/2.50 | | | | | | | | ~ $i(v0)) % 12.54/2.50 | | | | | | | % 12.54/2.50 | | | | | | | ALPHA: (242) implies: % 12.54/2.50 | | | | | | | (243) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (big_q(v0) = % 12.54/2.50 | | | | | | | v1) | ~ $i(v0)) % 12.54/2.50 | | | | | | | % 12.54/2.50 | | | | | | | GROUND_INST: instantiating (243) with all_32_1, all_32_0, % 12.54/2.50 | | | | | | | simplifying with (239), (240) gives: % 12.54/2.50 | | | | | | | (244) all_32_0 = 0 % 12.54/2.50 | | | | | | | % 12.54/2.50 | | | | | | | REDUCE: (238), (244) imply: % 12.54/2.50 | | | | | | | (245) $false % 12.54/2.50 | | | | | | | % 12.54/2.50 | | | | | | | CLOSE: (245) is inconsistent. % 12.54/2.50 | | | | | | | % 12.54/2.50 | | | | | | Case 2: % 12.54/2.50 | | | | | | | % 12.54/2.50 | | | | | | | (246) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & big_q(v0) = % 12.54/2.50 | | | | | | | v1 & $i(v0)) & ? [v0: $i] : (big_p(v0) = 0 & $i(v0)) % 12.54/2.50 | | | | | | | % 12.54/2.50 | | | | | | | ALPHA: (246) implies: % 12.54/2.50 | | | | | | | (247) ? [v0: $i] : (big_p(v0) = 0 & $i(v0)) % 12.54/2.50 | | | | | | | % 12.54/2.50 | | | | | | | REF_CLOSE: (210), (241), (247) are inconsistent by sub-proof #1. % 12.54/2.50 | | | | | | | % 12.54/2.50 | | | | | | End of split % 12.54/2.50 | | | | | | % 12.54/2.50 | | | | | Case 2: % 12.54/2.50 | | | | | | % 12.54/2.50 | | | | | | (248) all_25_0 = 0 % 12.54/2.50 | | | | | | % 12.54/2.50 | | | | | | REDUCE: (232), (248) imply: % 12.54/2.50 | | | | | | (249) $false % 12.54/2.50 | | | | | | % 12.54/2.50 | | | | | | CLOSE: (249) is inconsistent. % 12.54/2.50 | | | | | | % 12.54/2.50 | | | | | End of split % 12.54/2.50 | | | | | % 12.54/2.50 | | | | End of split % 12.54/2.50 | | | | % 12.54/2.50 | | | Case 2: % 12.54/2.50 | | | | % 12.54/2.50 | | | | (250) ? [v0: $i] : ? [v1: any] : (big_q(v0) = v1 & $i(v0) & ! [v2: % 12.54/2.50 | | | | $i] : ! [v3: int] : ( ~ (v1 = 0) | v3 = 0 | ~ (big_q(v2) % 12.54/2.50 | | | | = v3) | ~ $i(v2)) & ! [v2: $i] : (v1 = 0 | ~ % 12.54/2.50 | | | | (big_q(v2) = 0) | ~ $i(v2))) & (( ! [v0: $i] : ! [v1: % 12.54/2.50 | | | | int] : (v1 = 0 | ~ (big_q(v0) = v1) | ~ $i(v0)) & ? % 12.54/2.50 | | | | [v0: $i] : (big_p(v0) = 0 & $i(v0))) | ( ! [v0: $i] : ( ~ % 12.54/2.50 | | | | (big_p(v0) = 0) | ~ $i(v0)) & ? [v0: $i] : ? [v1: int] % 12.54/2.50 | | | | : ( ~ (v1 = 0) & big_q(v0) = v1 & $i(v0)))) % 12.54/2.50 | | | | % 12.54/2.50 | | | | ALPHA: (250) implies: % 12.54/2.50 | | | | (251) ( ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (big_q(v0) = v1) | % 12.54/2.50 | | | | ~ $i(v0)) & ? [v0: $i] : (big_p(v0) = 0 & $i(v0))) | ( ! % 12.54/2.50 | | | | [v0: $i] : ( ~ (big_p(v0) = 0) | ~ $i(v0)) & ? [v0: $i] : % 12.54/2.50 | | | | ? [v1: int] : ( ~ (v1 = 0) & big_q(v0) = v1 & $i(v0))) % 12.54/2.50 | | | | (252) ? [v0: $i] : ? [v1: any] : (big_q(v0) = v1 & $i(v0) & ! [v2: % 12.54/2.50 | | | | $i] : ! [v3: int] : ( ~ (v1 = 0) | v3 = 0 | ~ (big_q(v2) % 12.54/2.50 | | | | = v3) | ~ $i(v2)) & ! [v2: $i] : (v1 = 0 | ~ % 12.54/2.50 | | | | (big_q(v2) = 0) | ~ $i(v2))) % 12.54/2.50 | | | | % 12.54/2.50 | | | | DELTA: instantiating (252) with fresh symbols all_19_0, all_19_1 gives: % 12.54/2.50 | | | | (253) big_q(all_19_1) = all_19_0 & $i(all_19_1) & ! [v0: $i] : ! % 12.54/2.50 | | | | [v1: int] : ( ~ (all_19_0 = 0) | v1 = 0 | ~ (big_q(v0) = v1) | % 12.54/2.50 | | | | ~ $i(v0)) & ! [v0: $i] : (all_19_0 = 0 | ~ (big_q(v0) = 0) % 12.54/2.50 | | | | | ~ $i(v0)) % 12.54/2.50 | | | | % 12.54/2.50 | | | | ALPHA: (253) implies: % 12.54/2.50 | | | | (254) $i(all_19_1) % 12.54/2.50 | | | | (255) big_q(all_19_1) = all_19_0 % 12.54/2.50 | | | | (256) ! [v0: $i] : (all_19_0 = 0 | ~ (big_q(v0) = 0) | ~ $i(v0)) % 12.54/2.50 | | | | (257) ! [v0: $i] : ! [v1: int] : ( ~ (all_19_0 = 0) | v1 = 0 | ~ % 12.54/2.50 | | | | (big_q(v0) = v1) | ~ $i(v0)) % 12.54/2.50 | | | | % 12.54/2.50 | | | | BETA: splitting (205) gives: % 12.54/2.50 | | | | % 12.54/2.50 | | | | Case 1: % 12.54/2.50 | | | | | % 12.54/2.50 | | | | | (258) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (big_p(v0) = v1) | % 12.54/2.50 | | | | | ~ $i(v0)) & ! [v0: $i] : ( ~ (big_q(v0) = 0) | ~ $i(v0)) % 12.54/2.50 | | | | | % 12.54/2.50 | | | | | ALPHA: (258) implies: % 12.54/2.50 | | | | | (259) ! [v0: $i] : ( ~ (big_q(v0) = 0) | ~ $i(v0)) % 12.54/2.50 | | | | | (260) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (big_p(v0) = v1) | % 12.54/2.50 | | | | | ~ $i(v0)) % 12.54/2.50 | | | | | % 12.54/2.50 | | | | | GROUND_INST: instantiating (260) with all_10_1, all_10_0, simplifying % 12.54/2.50 | | | | | with (208), (209) gives: % 12.54/2.50 | | | | | (261) all_10_0 = 0 % 12.54/2.50 | | | | | % 12.54/2.50 | | | | | REDUCE: (209), (261) imply: % 12.54/2.50 | | | | | (262) big_p(all_10_1) = 0 % 12.54/2.50 | | | | | % 12.54/2.50 | | | | | BETA: splitting (251) gives: % 12.54/2.50 | | | | | % 12.54/2.50 | | | | | Case 1: % 12.54/2.50 | | | | | | % 12.54/2.51 | | | | | | (263) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (big_q(v0) = v1) % 12.54/2.51 | | | | | | | ~ $i(v0)) & ? [v0: $i] : (big_p(v0) = 0 & $i(v0)) % 12.54/2.51 | | | | | | % 12.54/2.51 | | | | | | ALPHA: (263) implies: % 12.54/2.51 | | | | | | (264) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (big_q(v0) = v1) % 12.54/2.51 | | | | | | | ~ $i(v0)) % 12.54/2.51 | | | | | | % 12.54/2.51 | | | | | | GROUND_INST: instantiating (264) with all_19_1, all_19_0, % 12.54/2.51 | | | | | | simplifying with (254), (255) gives: % 12.54/2.51 | | | | | | (265) all_19_0 = 0 % 12.82/2.51 | | | | | | % 12.82/2.51 | | | | | | REDUCE: (255), (265) imply: % 12.82/2.51 | | | | | | (266) big_q(all_19_1) = 0 % 12.82/2.51 | | | | | | % 12.82/2.51 | | | | | | GROUND_INST: instantiating (259) with all_19_1, simplifying with % 12.82/2.51 | | | | | | (254), (266) gives: % 12.82/2.51 | | | | | | (267) $false % 12.82/2.51 | | | | | | % 12.82/2.51 | | | | | | CLOSE: (267) is inconsistent. % 12.82/2.51 | | | | | | % 12.82/2.51 | | | | | Case 2: % 12.82/2.51 | | | | | | % 12.82/2.51 | | | | | | (268) ! [v0: $i] : ( ~ (big_p(v0) = 0) | ~ $i(v0)) & ? [v0: % 12.82/2.51 | | | | | | $i] : ? [v1: int] : ( ~ (v1 = 0) & big_q(v0) = v1 & % 12.82/2.51 | | | | | | $i(v0)) % 12.82/2.51 | | | | | | % 12.82/2.51 | | | | | | ALPHA: (268) implies: % 12.82/2.51 | | | | | | (269) ! [v0: $i] : ( ~ (big_p(v0) = 0) | ~ $i(v0)) % 12.82/2.51 | | | | | | % 12.82/2.51 | | | | | | GROUND_INST: instantiating (269) with all_10_1, simplifying with % 12.82/2.51 | | | | | | (208), (262) gives: % 12.82/2.51 | | | | | | (270) $false % 12.82/2.51 | | | | | | % 12.82/2.51 | | | | | | CLOSE: (270) is inconsistent. % 12.82/2.51 | | | | | | % 12.82/2.51 | | | | | End of split % 12.82/2.51 | | | | | % 12.82/2.51 | | | | Case 2: % 12.82/2.51 | | | | | % 12.82/2.51 | | | | | (271) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & big_p(v0) = v1 & % 12.82/2.51 | | | | | $i(v0)) & ? [v0: $i] : (big_q(v0) = 0 & $i(v0)) % 12.82/2.51 | | | | | % 12.82/2.51 | | | | | ALPHA: (271) implies: % 12.82/2.51 | | | | | (272) ? [v0: $i] : (big_q(v0) = 0 & $i(v0)) % 12.82/2.51 | | | | | (273) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & big_p(v0) = v1 & % 12.82/2.51 | | | | | $i(v0)) % 12.82/2.51 | | | | | % 12.82/2.51 | | | | | DELTA: instantiating (272) with fresh symbol all_28_0 gives: % 12.82/2.51 | | | | | (274) big_q(all_28_0) = 0 & $i(all_28_0) % 12.82/2.51 | | | | | % 12.82/2.51 | | | | | ALPHA: (274) implies: % 12.82/2.51 | | | | | (275) $i(all_28_0) % 12.82/2.51 | | | | | (276) big_q(all_28_0) = 0 % 12.82/2.51 | | | | | % 12.82/2.51 | | | | | DELTA: instantiating (273) with fresh symbols all_30_0, all_30_1 % 12.82/2.51 | | | | | gives: % 12.82/2.51 | | | | | (277) ~ (all_30_0 = 0) & big_p(all_30_1) = all_30_0 & $i(all_30_1) % 12.82/2.51 | | | | | % 12.82/2.51 | | | | | ALPHA: (277) implies: % 12.82/2.51 | | | | | (278) ~ (all_30_0 = 0) % 12.82/2.51 | | | | | (279) $i(all_30_1) % 12.82/2.51 | | | | | (280) big_p(all_30_1) = all_30_0 % 12.82/2.51 | | | | | % 12.82/2.51 | | | | | GROUND_INST: instantiating (211) with all_30_1, all_30_0, simplifying % 12.82/2.51 | | | | | with (279), (280) gives: % 12.82/2.51 | | | | | (281) ~ (all_10_0 = 0) | all_30_0 = 0 % 12.82/2.51 | | | | | % 12.82/2.51 | | | | | GROUND_INST: instantiating (256) with all_28_0, simplifying with % 12.82/2.51 | | | | | (275), (276) gives: % 12.82/2.51 | | | | | (282) all_19_0 = 0 % 12.82/2.51 | | | | | % 12.82/2.51 | | | | | BETA: splitting (281) gives: % 12.82/2.51 | | | | | % 12.82/2.51 | | | | | Case 1: % 12.82/2.51 | | | | | | % 12.82/2.51 | | | | | | (283) ~ (all_10_0 = 0) % 12.82/2.51 | | | | | | % 12.82/2.51 | | | | | | BETA: splitting (251) gives: % 12.82/2.51 | | | | | | % 12.82/2.51 | | | | | | Case 1: % 12.82/2.51 | | | | | | | % 12.82/2.51 | | | | | | | (284) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (big_q(v0) = % 12.82/2.51 | | | | | | | v1) | ~ $i(v0)) & ? [v0: $i] : (big_p(v0) = 0 & % 12.82/2.51 | | | | | | | $i(v0)) % 12.82/2.51 | | | | | | | % 12.82/2.51 | | | | | | | ALPHA: (284) implies: % 12.82/2.51 | | | | | | | (285) ? [v0: $i] : (big_p(v0) = 0 & $i(v0)) % 12.82/2.51 | | | | | | | % 12.82/2.51 | | | | | | | REF_CLOSE: (210), (283), (285) are inconsistent by sub-proof #1. % 12.82/2.51 | | | | | | | % 12.82/2.51 | | | | | | Case 2: % 12.82/2.51 | | | | | | | % 12.82/2.51 | | | | | | | (286) ! [v0: $i] : ( ~ (big_p(v0) = 0) | ~ $i(v0)) & ? [v0: % 12.82/2.51 | | | | | | | $i] : ? [v1: int] : ( ~ (v1 = 0) & big_q(v0) = v1 & % 12.82/2.51 | | | | | | | $i(v0)) % 12.82/2.51 | | | | | | | % 12.82/2.51 | | | | | | | ALPHA: (286) implies: % 12.82/2.51 | | | | | | | (287) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & big_q(v0) = % 12.82/2.51 | | | | | | | v1 & $i(v0)) % 12.82/2.51 | | | | | | | % 12.82/2.51 | | | | | | | DELTA: instantiating (287) with fresh symbols all_49_0, all_49_1 % 12.82/2.51 | | | | | | | gives: % 12.82/2.51 | | | | | | | (288) ~ (all_49_0 = 0) & big_q(all_49_1) = all_49_0 & % 12.82/2.51 | | | | | | | $i(all_49_1) % 12.82/2.51 | | | | | | | % 12.82/2.51 | | | | | | | ALPHA: (288) implies: % 12.82/2.51 | | | | | | | (289) ~ (all_49_0 = 0) % 12.82/2.51 | | | | | | | (290) $i(all_49_1) % 12.82/2.51 | | | | | | | (291) big_q(all_49_1) = all_49_0 % 12.82/2.51 | | | | | | | % 12.82/2.51 | | | | | | | GROUND_INST: instantiating (257) with all_49_1, all_49_0, % 12.82/2.51 | | | | | | | simplifying with (290), (291) gives: % 12.82/2.51 | | | | | | | (292) ~ (all_19_0 = 0) | all_49_0 = 0 % 12.82/2.51 | | | | | | | % 12.82/2.51 | | | | | | | BETA: splitting (292) gives: % 12.82/2.51 | | | | | | | % 12.82/2.51 | | | | | | | Case 1: % 12.82/2.51 | | | | | | | | % 12.82/2.51 | | | | | | | | (293) ~ (all_19_0 = 0) % 12.82/2.51 | | | | | | | | % 12.82/2.51 | | | | | | | | REDUCE: (282), (293) imply: % 12.82/2.51 | | | | | | | | (294) $false % 12.82/2.51 | | | | | | | | % 12.82/2.51 | | | | | | | | CLOSE: (294) is inconsistent. % 12.82/2.51 | | | | | | | | % 12.82/2.51 | | | | | | | Case 2: % 12.82/2.51 | | | | | | | | % 12.82/2.51 | | | | | | | | (295) all_49_0 = 0 % 12.82/2.51 | | | | | | | | % 12.82/2.51 | | | | | | | | REDUCE: (289), (295) imply: % 12.82/2.51 | | | | | | | | (296) $false % 12.82/2.51 | | | | | | | | % 12.82/2.51 | | | | | | | | CLOSE: (296) is inconsistent. % 12.82/2.51 | | | | | | | | % 12.82/2.51 | | | | | | | End of split % 12.82/2.51 | | | | | | | % 12.82/2.51 | | | | | | End of split % 12.82/2.51 | | | | | | % 12.82/2.51 | | | | | Case 2: % 12.82/2.51 | | | | | | % 12.82/2.51 | | | | | | (297) all_30_0 = 0 % 12.82/2.51 | | | | | | % 12.82/2.51 | | | | | | REDUCE: (278), (297) imply: % 12.82/2.51 | | | | | | (298) $false % 12.82/2.51 | | | | | | % 12.82/2.51 | | | | | | CLOSE: (298) is inconsistent. % 12.82/2.51 | | | | | | % 12.82/2.51 | | | | | End of split % 12.82/2.51 | | | | | % 12.82/2.51 | | | | End of split % 12.82/2.51 | | | | % 12.82/2.51 | | | End of split % 12.82/2.51 | | | % 12.82/2.51 | | End of split % 12.82/2.51 | | % 12.82/2.51 | Case 2: % 12.82/2.51 | | % 12.82/2.51 | | (299) (( ! [v0: $i] : ! [v1: any] : ( ~ (big_q(v0) = v1) | ~ $i(v0) | % 12.82/2.51 | | ? [v2: $i] : ? [v3: any] : (big_q(v2) = v3 & $i(v2) & ( ~ % 12.82/2.51 | | (v3 = 0) | ~ (v1 = 0)) & (v3 = 0 | v1 = 0))) & (( ! [v0: % 12.82/2.51 | | $i] : ! [v1: int] : (v1 = 0 | ~ (big_q(v0) = v1) | ~ % 12.82/2.51 | | $i(v0)) & ? [v0: $i] : (big_p(v0) = 0 & $i(v0))) | ( ! % 12.82/2.51 | | [v0: $i] : ( ~ (big_p(v0) = 0) | ~ $i(v0)) & ? [v0: $i] : % 12.82/2.51 | | ? [v1: int] : ( ~ (v1 = 0) & big_q(v0) = v1 & $i(v0))))) | % 12.82/2.51 | | ( ? [v0: $i] : ? [v1: any] : (big_q(v0) = v1 & $i(v0) & ! [v2: % 12.82/2.51 | | $i] : ! [v3: int] : ( ~ (v1 = 0) | v3 = 0 | ~ (big_q(v2) % 12.82/2.51 | | = v3) | ~ $i(v2)) & ! [v2: $i] : (v1 = 0 | ~ % 12.82/2.51 | | (big_q(v2) = 0) | ~ $i(v2))) & (( ! [v0: $i] : ! [v1: % 12.82/2.51 | | int] : (v1 = 0 | ~ (big_q(v0) = v1) | ~ $i(v0)) & ! % 12.82/2.51 | | [v0: $i] : ( ~ (big_p(v0) = 0) | ~ $i(v0))) | ( ? [v0: $i] % 12.82/2.51 | | : ? [v1: int] : ( ~ (v1 = 0) & big_q(v0) = v1 & $i(v0)) & % 12.82/2.51 | | ? [v0: $i] : (big_p(v0) = 0 & $i(v0)))))) & (( ! [v0: $i] : % 12.82/2.51 | | ! [v1: any] : ( ~ (big_p(v0) = v1) | ~ $i(v0) | ? [v2: $i] : % 12.82/2.51 | | ? [v3: any] : (big_p(v2) = v3 & $i(v2) & ( ~ (v3 = 0) | ~ % 12.82/2.51 | | (v1 = 0)) & (v3 = 0 | v1 = 0))) & (( ! [v0: $i] : ! [v1: % 12.82/2.51 | | int] : (v1 = 0 | ~ (big_p(v0) = v1) | ~ $i(v0)) & ! % 12.82/2.51 | | [v0: $i] : ( ~ (big_q(v0) = 0) | ~ $i(v0))) | ( ? [v0: $i] % 12.82/2.51 | | : ? [v1: int] : ( ~ (v1 = 0) & big_p(v0) = v1 & $i(v0)) & % 12.82/2.51 | | ? [v0: $i] : (big_q(v0) = 0 & $i(v0))))) | ( ? [v0: $i] : % 12.82/2.51 | | ? [v1: any] : (big_p(v0) = v1 & $i(v0) & ! [v2: $i] : ! [v3: % 12.82/2.51 | | int] : ( ~ (v1 = 0) | v3 = 0 | ~ (big_p(v2) = v3) | ~ % 12.82/2.51 | | $i(v2)) & ! [v2: $i] : (v1 = 0 | ~ (big_p(v2) = 0) | ~ % 12.82/2.51 | | $i(v2))) & (( ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ % 12.82/2.51 | | (big_p(v0) = v1) | ~ $i(v0)) & ? [v0: $i] : (big_q(v0) % 12.82/2.51 | | = 0 & $i(v0))) | ( ! [v0: $i] : ( ~ (big_q(v0) = 0) | ~ % 12.82/2.51 | | $i(v0)) & ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & % 12.82/2.51 | | big_p(v0) = v1 & $i(v0)))))) % 12.82/2.51 | | % 12.82/2.51 | | ALPHA: (299) implies: % 12.82/2.51 | | (300) ( ! [v0: $i] : ! [v1: any] : ( ~ (big_p(v0) = v1) | ~ $i(v0) | ? % 12.82/2.51 | | [v2: $i] : ? [v3: any] : (big_p(v2) = v3 & $i(v2) & ( ~ (v3 = % 12.82/2.51 | | 0) | ~ (v1 = 0)) & (v3 = 0 | v1 = 0))) & (( ! [v0: $i] : % 12.82/2.51 | | ! [v1: int] : (v1 = 0 | ~ (big_p(v0) = v1) | ~ $i(v0)) & % 12.82/2.51 | | ! [v0: $i] : ( ~ (big_q(v0) = 0) | ~ $i(v0))) | ( ? [v0: $i] % 12.82/2.51 | | : ? [v1: int] : ( ~ (v1 = 0) & big_p(v0) = v1 & $i(v0)) & ? % 12.82/2.51 | | [v0: $i] : (big_q(v0) = 0 & $i(v0))))) | ( ? [v0: $i] : ? % 12.82/2.51 | | [v1: any] : (big_p(v0) = v1 & $i(v0) & ! [v2: $i] : ! [v3: int] % 12.82/2.51 | | : ( ~ (v1 = 0) | v3 = 0 | ~ (big_p(v2) = v3) | ~ $i(v2)) & ! % 12.82/2.51 | | [v2: $i] : (v1 = 0 | ~ (big_p(v2) = 0) | ~ $i(v2))) & (( ! % 12.82/2.51 | | [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (big_p(v0) = v1) | ~ % 12.82/2.51 | | $i(v0)) & ? [v0: $i] : (big_q(v0) = 0 & $i(v0))) | ( ! % 12.82/2.51 | | [v0: $i] : ( ~ (big_q(v0) = 0) | ~ $i(v0)) & ? [v0: $i] : % 12.82/2.51 | | ? [v1: int] : ( ~ (v1 = 0) & big_p(v0) = v1 & $i(v0))))) % 12.82/2.52 | | (301) ( ! [v0: $i] : ! [v1: any] : ( ~ (big_q(v0) = v1) | ~ $i(v0) | ? % 12.82/2.52 | | [v2: $i] : ? [v3: any] : (big_q(v2) = v3 & $i(v2) & ( ~ (v3 = % 12.82/2.52 | | 0) | ~ (v1 = 0)) & (v3 = 0 | v1 = 0))) & (( ! [v0: $i] : % 12.82/2.52 | | ! [v1: int] : (v1 = 0 | ~ (big_q(v0) = v1) | ~ $i(v0)) & % 12.82/2.52 | | ? [v0: $i] : (big_p(v0) = 0 & $i(v0))) | ( ! [v0: $i] : ( ~ % 12.82/2.52 | | (big_p(v0) = 0) | ~ $i(v0)) & ? [v0: $i] : ? [v1: int] : % 12.82/2.52 | | ( ~ (v1 = 0) & big_q(v0) = v1 & $i(v0))))) | ( ? [v0: $i] : % 12.82/2.52 | | ? [v1: any] : (big_q(v0) = v1 & $i(v0) & ! [v2: $i] : ! [v3: % 12.82/2.52 | | int] : ( ~ (v1 = 0) | v3 = 0 | ~ (big_q(v2) = v3) | ~ % 12.82/2.52 | | $i(v2)) & ! [v2: $i] : (v1 = 0 | ~ (big_q(v2) = 0) | ~ % 12.82/2.52 | | $i(v2))) & (( ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ % 12.82/2.52 | | (big_q(v0) = v1) | ~ $i(v0)) & ! [v0: $i] : ( ~ % 12.82/2.52 | | (big_p(v0) = 0) | ~ $i(v0))) | ( ? [v0: $i] : ? [v1: int] % 12.82/2.52 | | : ( ~ (v1 = 0) & big_q(v0) = v1 & $i(v0)) & ? [v0: $i] : % 12.82/2.52 | | (big_p(v0) = 0 & $i(v0))))) % 12.82/2.52 | | % 12.82/2.52 | | BETA: splitting (300) gives: % 12.82/2.52 | | % 12.82/2.52 | | Case 1: % 12.82/2.52 | | | % 12.82/2.52 | | | (302) ! [v0: $i] : ! [v1: any] : ( ~ (big_p(v0) = v1) | ~ $i(v0) | % 12.82/2.52 | | | ? [v2: $i] : ? [v3: any] : (big_p(v2) = v3 & $i(v2) & ( ~ (v3 % 12.82/2.52 | | | = 0) | ~ (v1 = 0)) & (v3 = 0 | v1 = 0))) & (( ! [v0: $i] % 12.82/2.52 | | | : ! [v1: int] : (v1 = 0 | ~ (big_p(v0) = v1) | ~ $i(v0)) & % 12.82/2.52 | | | ! [v0: $i] : ( ~ (big_q(v0) = 0) | ~ $i(v0))) | ( ? [v0: % 12.82/2.52 | | | $i] : ? [v1: int] : ( ~ (v1 = 0) & big_p(v0) = v1 & % 12.82/2.52 | | | $i(v0)) & ? [v0: $i] : (big_q(v0) = 0 & $i(v0)))) % 12.82/2.52 | | | % 12.82/2.52 | | | ALPHA: (302) implies: % 12.82/2.52 | | | (303) ( ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (big_p(v0) = v1) | ~ % 12.82/2.52 | | | $i(v0)) & ! [v0: $i] : ( ~ (big_q(v0) = 0) | ~ $i(v0))) | ( % 12.82/2.52 | | | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & big_p(v0) = v1 & % 12.82/2.52 | | | $i(v0)) & ? [v0: $i] : (big_q(v0) = 0 & $i(v0))) % 12.82/2.52 | | | (304) ! [v0: $i] : ! [v1: any] : ( ~ (big_p(v0) = v1) | ~ $i(v0) | % 12.82/2.52 | | | ? [v2: $i] : ? [v3: any] : (big_p(v2) = v3 & $i(v2) & ( ~ (v3 % 12.82/2.52 | | | = 0) | ~ (v1 = 0)) & (v3 = 0 | v1 = 0))) % 12.82/2.52 | | | % 12.82/2.52 | | | BETA: splitting (301) gives: % 12.82/2.52 | | | % 12.82/2.52 | | | Case 1: % 12.82/2.52 | | | | % 12.82/2.52 | | | | (305) ! [v0: $i] : ! [v1: any] : ( ~ (big_q(v0) = v1) | ~ $i(v0) | % 12.82/2.52 | | | | ? [v2: $i] : ? [v3: any] : (big_q(v2) = v3 & $i(v2) & ( ~ % 12.82/2.52 | | | | (v3 = 0) | ~ (v1 = 0)) & (v3 = 0 | v1 = 0))) & (( ! [v0: % 12.82/2.52 | | | | $i] : ! [v1: int] : (v1 = 0 | ~ (big_q(v0) = v1) | ~ % 12.82/2.52 | | | | $i(v0)) & ? [v0: $i] : (big_p(v0) = 0 & $i(v0))) | ( ! % 12.82/2.52 | | | | [v0: $i] : ( ~ (big_p(v0) = 0) | ~ $i(v0)) & ? [v0: $i] : % 12.82/2.52 | | | | ? [v1: int] : ( ~ (v1 = 0) & big_q(v0) = v1 & $i(v0)))) % 12.82/2.52 | | | | % 12.82/2.52 | | | | ALPHA: (305) implies: % 12.82/2.52 | | | | (306) ( ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (big_q(v0) = v1) | % 12.82/2.52 | | | | ~ $i(v0)) & ? [v0: $i] : (big_p(v0) = 0 & $i(v0))) | ( ! % 12.82/2.52 | | | | [v0: $i] : ( ~ (big_p(v0) = 0) | ~ $i(v0)) & ? [v0: $i] : % 12.82/2.52 | | | | ? [v1: int] : ( ~ (v1 = 0) & big_q(v0) = v1 & $i(v0))) % 12.82/2.52 | | | | (307) ! [v0: $i] : ! [v1: any] : ( ~ (big_q(v0) = v1) | ~ $i(v0) | % 12.82/2.52 | | | | ? [v2: $i] : ? [v3: any] : (big_q(v2) = v3 & $i(v2) & ( ~ % 12.82/2.52 | | | | (v3 = 0) | ~ (v1 = 0)) & (v3 = 0 | v1 = 0))) % 12.82/2.52 | | | | % 12.82/2.52 | | | | BETA: splitting (303) gives: % 12.82/2.52 | | | | % 12.82/2.52 | | | | Case 1: % 12.82/2.52 | | | | | % 12.82/2.52 | | | | | (308) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (big_p(v0) = v1) | % 12.82/2.52 | | | | | ~ $i(v0)) & ! [v0: $i] : ( ~ (big_q(v0) = 0) | ~ $i(v0)) % 12.82/2.52 | | | | | % 12.82/2.52 | | | | | ALPHA: (308) implies: % 12.82/2.52 | | | | | (309) ! [v0: $i] : ( ~ (big_q(v0) = 0) | ~ $i(v0)) % 12.82/2.52 | | | | | (310) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (big_p(v0) = v1) | % 12.82/2.52 | | | | | ~ $i(v0)) % 12.82/2.52 | | | | | % 12.82/2.52 | | | | | BETA: splitting (306) gives: % 12.82/2.52 | | | | | % 12.82/2.52 | | | | | Case 1: % 12.82/2.52 | | | | | | % 12.82/2.52 | | | | | | (311) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (big_q(v0) = v1) % 12.82/2.52 | | | | | | | ~ $i(v0)) & ? [v0: $i] : (big_p(v0) = 0 & $i(v0)) % 12.82/2.52 | | | | | | % 12.82/2.52 | | | | | | ALPHA: (311) implies: % 12.82/2.52 | | | | | | (312) ? [v0: $i] : (big_p(v0) = 0 & $i(v0)) % 12.82/2.52 | | | | | | % 12.82/2.52 | | | | | | REF_CLOSE: (304), (310), (312) are inconsistent by sub-proof #3. % 12.82/2.52 | | | | | | % 12.82/2.52 | | | | | Case 2: % 12.82/2.52 | | | | | | % 12.82/2.52 | | | | | | (313) ! [v0: $i] : ( ~ (big_p(v0) = 0) | ~ $i(v0)) & ? [v0: % 12.82/2.52 | | | | | | $i] : ? [v1: int] : ( ~ (v1 = 0) & big_q(v0) = v1 & % 12.82/2.52 | | | | | | $i(v0)) % 12.82/2.52 | | | | | | % 12.82/2.52 | | | | | | ALPHA: (313) implies: % 12.82/2.52 | | | | | | (314) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & big_q(v0) = v1 % 12.82/2.52 | | | | | | & $i(v0)) % 12.82/2.52 | | | | | | % 12.82/2.52 | | | | | | REF_CLOSE: (307), (309), (314) are inconsistent by sub-proof #2. % 12.82/2.52 | | | | | | % 12.82/2.52 | | | | | End of split % 12.82/2.52 | | | | | % 12.82/2.52 | | | | Case 2: % 12.82/2.52 | | | | | % 12.82/2.52 | | | | | (315) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & big_p(v0) = v1 & % 12.82/2.52 | | | | | $i(v0)) & ? [v0: $i] : (big_q(v0) = 0 & $i(v0)) % 12.82/2.52 | | | | | % 12.82/2.52 | | | | | ALPHA: (315) implies: % 12.82/2.52 | | | | | (316) ? [v0: $i] : (big_q(v0) = 0 & $i(v0)) % 12.82/2.52 | | | | | (317) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & big_p(v0) = v1 & % 12.82/2.52 | | | | | $i(v0)) % 12.82/2.52 | | | | | % 12.82/2.52 | | | | | DELTA: instantiating (316) with fresh symbol all_18_0 gives: % 12.82/2.52 | | | | | (318) big_q(all_18_0) = 0 & $i(all_18_0) % 12.82/2.52 | | | | | % 12.82/2.52 | | | | | ALPHA: (318) implies: % 12.82/2.52 | | | | | (319) $i(all_18_0) % 12.82/2.52 | | | | | (320) big_q(all_18_0) = 0 % 12.82/2.52 | | | | | % 12.82/2.52 | | | | | DELTA: instantiating (317) with fresh symbols all_20_0, all_20_1 % 12.82/2.52 | | | | | gives: % 12.82/2.52 | | | | | (321) ~ (all_20_0 = 0) & big_p(all_20_1) = all_20_0 & $i(all_20_1) % 12.82/2.52 | | | | | % 12.82/2.52 | | | | | ALPHA: (321) implies: % 12.82/2.52 | | | | | (322) ~ (all_20_0 = 0) % 12.82/2.52 | | | | | (323) $i(all_20_1) % 12.82/2.52 | | | | | (324) big_p(all_20_1) = all_20_0 % 12.82/2.52 | | | | | % 12.82/2.52 | | | | | GROUND_INST: instantiating (304) with all_20_1, all_20_0, simplifying % 12.82/2.52 | | | | | with (323), (324) gives: % 12.82/2.52 | | | | | (325) ? [v0: $i] : ? [v1: any] : (big_p(v0) = v1 & $i(v0) & ( ~ % 12.82/2.52 | | | | | (v1 = 0) | ~ (all_20_0 = 0)) & (v1 = 0 | all_20_0 = 0)) % 12.82/2.52 | | | | | % 12.82/2.52 | | | | | GROUND_INST: instantiating (307) with all_18_0, 0, simplifying with % 12.82/2.52 | | | | | (319), (320) gives: % 12.82/2.52 | | | | | (326) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & big_q(v0) = v1 & % 12.82/2.52 | | | | | $i(v0)) % 12.82/2.52 | | | | | % 12.82/2.52 | | | | | DELTA: instantiating (326) with fresh symbols all_27_0, all_27_1 % 12.82/2.52 | | | | | gives: % 12.82/2.52 | | | | | (327) ~ (all_27_0 = 0) & big_q(all_27_1) = all_27_0 & $i(all_27_1) % 12.82/2.52 | | | | | % 12.82/2.52 | | | | | ALPHA: (327) implies: % 12.82/2.52 | | | | | (328) ~ (all_27_0 = 0) % 12.82/2.52 | | | | | (329) $i(all_27_1) % 12.82/2.52 | | | | | (330) big_q(all_27_1) = all_27_0 % 12.82/2.52 | | | | | % 12.82/2.52 | | | | | DELTA: instantiating (325) with fresh symbols all_29_0, all_29_1 % 12.82/2.52 | | | | | gives: % 12.82/2.52 | | | | | (331) big_p(all_29_1) = all_29_0 & $i(all_29_1) & ( ~ (all_29_0 = % 12.82/2.52 | | | | | 0) | ~ (all_20_0 = 0)) & (all_29_0 = 0 | all_20_0 = 0) % 12.82/2.52 | | | | | % 12.82/2.52 | | | | | ALPHA: (331) implies: % 12.82/2.52 | | | | | (332) $i(all_29_1) % 12.82/2.52 | | | | | (333) big_p(all_29_1) = all_29_0 % 12.82/2.52 | | | | | (334) all_29_0 = 0 | all_20_0 = 0 % 12.82/2.52 | | | | | % 12.82/2.52 | | | | | BETA: splitting (334) gives: % 12.82/2.52 | | | | | % 12.82/2.52 | | | | | Case 1: % 12.82/2.52 | | | | | | % 12.82/2.52 | | | | | | (335) all_29_0 = 0 % 12.82/2.52 | | | | | | % 12.82/2.52 | | | | | | REDUCE: (333), (335) imply: % 12.82/2.52 | | | | | | (336) big_p(all_29_1) = 0 % 12.82/2.52 | | | | | | % 12.82/2.52 | | | | | | DELTA: instantiating (317) with fresh symbols all_40_0, all_40_1 % 12.82/2.52 | | | | | | gives: % 12.82/2.52 | | | | | | (337) ~ (all_40_0 = 0) & big_p(all_40_1) = all_40_0 & % 12.82/2.52 | | | | | | $i(all_40_1) % 12.82/2.52 | | | | | | % 12.82/2.52 | | | | | | ALPHA: (337) implies: % 12.82/2.52 | | | | | | (338) ~ (all_40_0 = 0) % 12.82/2.52 | | | | | | (339) $i(all_40_1) % 12.82/2.52 | | | | | | (340) big_p(all_40_1) = all_40_0 % 12.82/2.52 | | | | | | % 12.82/2.52 | | | | | | GROUND_INST: instantiating (304) with all_40_1, all_40_0, % 12.82/2.52 | | | | | | simplifying with (339), (340) gives: % 12.82/2.52 | | | | | | (341) ? [v0: $i] : ? [v1: any] : (big_p(v0) = v1 & $i(v0) & ( ~ % 12.82/2.52 | | | | | | (v1 = 0) | ~ (all_40_0 = 0)) & (v1 = 0 | all_40_0 = % 12.82/2.52 | | | | | | 0)) % 12.82/2.52 | | | | | | % 12.82/2.52 | | | | | | DELTA: instantiating (341) with fresh symbols all_55_0, all_55_1 % 12.82/2.52 | | | | | | gives: % 12.82/2.52 | | | | | | (342) big_p(all_55_1) = all_55_0 & $i(all_55_1) & ( ~ (all_55_0 = % 12.82/2.52 | | | | | | 0) | ~ (all_40_0 = 0)) & (all_55_0 = 0 | all_40_0 = 0) % 12.82/2.52 | | | | | | % 12.82/2.52 | | | | | | ALPHA: (342) implies: % 12.82/2.52 | | | | | | (343) $i(all_55_1) % 12.82/2.52 | | | | | | (344) big_p(all_55_1) = all_55_0 % 12.82/2.52 | | | | | | (345) all_55_0 = 0 | all_40_0 = 0 % 12.82/2.52 | | | | | | % 12.82/2.52 | | | | | | BETA: splitting (345) gives: % 12.82/2.52 | | | | | | % 12.82/2.52 | | | | | | Case 1: % 12.82/2.52 | | | | | | | % 12.82/2.52 | | | | | | | (346) all_55_0 = 0 % 12.82/2.52 | | | | | | | % 12.82/2.52 | | | | | | | REDUCE: (344), (346) imply: % 12.82/2.52 | | | | | | | (347) big_p(all_55_1) = 0 % 12.82/2.52 | | | | | | | % 12.82/2.52 | | | | | | | DELTA: instantiating (317) with fresh symbols all_66_0, all_66_1 % 12.82/2.52 | | | | | | | gives: % 12.82/2.52 | | | | | | | (348) ~ (all_66_0 = 0) & big_p(all_66_1) = all_66_0 & % 12.82/2.52 | | | | | | | $i(all_66_1) % 12.82/2.52 | | | | | | | % 12.82/2.52 | | | | | | | ALPHA: (348) implies: % 12.82/2.52 | | | | | | | (349) ~ (all_66_0 = 0) % 12.82/2.53 | | | | | | | (350) $i(all_66_1) % 12.82/2.53 | | | | | | | (351) big_p(all_66_1) = all_66_0 % 12.82/2.53 | | | | | | | % 12.82/2.53 | | | | | | | GROUND_INST: instantiating (304) with all_66_1, all_66_0, % 12.82/2.53 | | | | | | | simplifying with (350), (351) gives: % 12.82/2.53 | | | | | | | (352) ? [v0: $i] : ? [v1: any] : (big_p(v0) = v1 & $i(v0) & ( % 12.82/2.53 | | | | | | | ~ (v1 = 0) | ~ (all_66_0 = 0)) & (v1 = 0 | all_66_0 % 12.82/2.53 | | | | | | | = 0)) % 12.82/2.53 | | | | | | | % 12.82/2.53 | | | | | | | DELTA: instantiating (352) with fresh symbols all_81_0, all_81_1 % 12.82/2.53 | | | | | | | gives: % 12.82/2.53 | | | | | | | (353) big_p(all_81_1) = all_81_0 & $i(all_81_1) & ( ~ (all_81_0 % 12.82/2.53 | | | | | | | = 0) | ~ (all_66_0 = 0)) & (all_81_0 = 0 | all_66_0 % 12.82/2.53 | | | | | | | = 0) % 12.82/2.53 | | | | | | | % 12.82/2.53 | | | | | | | ALPHA: (353) implies: % 12.82/2.53 | | | | | | | (354) $i(all_81_1) % 12.82/2.53 | | | | | | | (355) big_p(all_81_1) = all_81_0 % 12.82/2.53 | | | | | | | (356) all_81_0 = 0 | all_66_0 = 0 % 12.82/2.53 | | | | | | | % 12.82/2.53 | | | | | | | BETA: splitting (356) gives: % 12.82/2.53 | | | | | | | % 12.82/2.53 | | | | | | | Case 1: % 12.82/2.53 | | | | | | | | % 12.82/2.53 | | | | | | | | (357) all_81_0 = 0 % 12.82/2.53 | | | | | | | | % 12.82/2.53 | | | | | | | | REDUCE: (355), (357) imply: % 12.82/2.53 | | | | | | | | (358) big_p(all_81_1) = 0 % 12.82/2.53 | | | | | | | | % 12.82/2.53 | | | | | | | | DELTA: instantiating (317) with fresh symbols all_92_0, all_92_1 % 12.82/2.53 | | | | | | | | gives: % 12.82/2.53 | | | | | | | | (359) ~ (all_92_0 = 0) & big_p(all_92_1) = all_92_0 & % 12.82/2.53 | | | | | | | | $i(all_92_1) % 12.82/2.53 | | | | | | | | % 12.82/2.53 | | | | | | | | ALPHA: (359) implies: % 12.82/2.53 | | | | | | | | (360) ~ (all_92_0 = 0) % 12.82/2.53 | | | | | | | | (361) $i(all_92_1) % 12.82/2.53 | | | | | | | | (362) big_p(all_92_1) = all_92_0 % 12.82/2.53 | | | | | | | | % 12.82/2.53 | | | | | | | | GROUND_INST: instantiating (304) with all_92_1, all_92_0, % 12.82/2.53 | | | | | | | | simplifying with (361), (362) gives: % 12.82/2.53 | | | | | | | | (363) ? [v0: $i] : ? [v1: any] : (big_p(v0) = v1 & $i(v0) & % 12.82/2.53 | | | | | | | | ( ~ (v1 = 0) | ~ (all_92_0 = 0)) & (v1 = 0 | % 12.82/2.53 | | | | | | | | all_92_0 = 0)) % 12.82/2.53 | | | | | | | | % 12.82/2.53 | | | | | | | | DELTA: instantiating (363) with fresh symbols all_107_0, % 12.82/2.53 | | | | | | | | all_107_1 gives: % 12.82/2.53 | | | | | | | | (364) big_p(all_107_1) = all_107_0 & $i(all_107_1) & ( ~ % 12.82/2.53 | | | | | | | | (all_107_0 = 0) | ~ (all_92_0 = 0)) & (all_107_0 = 0 % 12.82/2.53 | | | | | | | | | all_92_0 = 0) % 12.82/2.53 | | | | | | | | % 12.82/2.53 | | | | | | | | ALPHA: (364) implies: % 12.82/2.53 | | | | | | | | (365) $i(all_107_1) % 12.82/2.53 | | | | | | | | (366) big_p(all_107_1) = all_107_0 % 12.82/2.53 | | | | | | | | (367) all_107_0 = 0 | all_92_0 = 0 % 12.82/2.53 | | | | | | | | % 12.82/2.53 | | | | | | | | BETA: splitting (367) gives: % 12.82/2.53 | | | | | | | | % 12.82/2.53 | | | | | | | | Case 1: % 12.82/2.53 | | | | | | | | | % 12.82/2.53 | | | | | | | | | (368) all_107_0 = 0 % 12.82/2.53 | | | | | | | | | % 12.82/2.53 | | | | | | | | | REDUCE: (366), (368) imply: % 12.82/2.53 | | | | | | | | | (369) big_p(all_107_1) = 0 % 12.82/2.53 | | | | | | | | | % 12.82/2.53 | | | | | | | | | BETA: splitting (306) gives: % 12.82/2.53 | | | | | | | | | % 12.82/2.53 | | | | | | | | | Case 1: % 12.82/2.53 | | | | | | | | | | % 12.82/2.53 | | | | | | | | | | (370) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ % 12.82/2.53 | | | | | | | | | | (big_q(v0) = v1) | ~ $i(v0)) & ? [v0: $i] : % 12.82/2.53 | | | | | | | | | | (big_p(v0) = 0 & $i(v0)) % 12.82/2.53 | | | | | | | | | | % 12.82/2.53 | | | | | | | | | | ALPHA: (370) implies: % 12.82/2.53 | | | | | | | | | | (371) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ % 12.82/2.53 | | | | | | | | | | (big_q(v0) = v1) | ~ $i(v0)) % 12.82/2.53 | | | | | | | | | | % 12.82/2.53 | | | | | | | | | | GROUND_INST: instantiating (371) with all_27_1, all_27_0, % 12.82/2.53 | | | | | | | | | | simplifying with (329), (330) gives: % 12.82/2.53 | | | | | | | | | | (372) all_27_0 = 0 % 12.82/2.53 | | | | | | | | | | % 12.82/2.53 | | | | | | | | | | REDUCE: (328), (372) imply: % 12.82/2.53 | | | | | | | | | | (373) $false % 12.82/2.53 | | | | | | | | | | % 12.82/2.53 | | | | | | | | | | CLOSE: (373) is inconsistent. % 12.82/2.53 | | | | | | | | | | % 12.82/2.53 | | | | | | | | | Case 2: % 12.82/2.53 | | | | | | | | | | % 12.82/2.53 | | | | | | | | | | (374) ! [v0: $i] : ( ~ (big_p(v0) = 0) | ~ $i(v0)) & ? % 12.82/2.53 | | | | | | | | | | [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & big_q(v0) % 12.82/2.53 | | | | | | | | | | = v1 & $i(v0)) % 12.82/2.53 | | | | | | | | | | % 12.82/2.53 | | | | | | | | | | ALPHA: (374) implies: % 12.82/2.53 | | | | | | | | | | (375) ! [v0: $i] : ( ~ (big_p(v0) = 0) | ~ $i(v0)) % 12.82/2.53 | | | | | | | | | | % 12.82/2.53 | | | | | | | | | | GROUND_INST: instantiating (375) with all_107_1, simplifying % 12.82/2.53 | | | | | | | | | | with (365), (369) gives: % 12.82/2.53 | | | | | | | | | | (376) $false % 12.82/2.53 | | | | | | | | | | % 12.82/2.53 | | | | | | | | | | CLOSE: (376) is inconsistent. % 12.82/2.53 | | | | | | | | | | % 12.82/2.53 | | | | | | | | | End of split % 12.82/2.53 | | | | | | | | | % 12.82/2.53 | | | | | | | | Case 2: % 12.82/2.53 | | | | | | | | | % 12.82/2.53 | | | | | | | | | (377) all_92_0 = 0 % 12.82/2.53 | | | | | | | | | % 12.82/2.53 | | | | | | | | | REDUCE: (360), (377) imply: % 12.82/2.53 | | | | | | | | | (378) $false % 12.82/2.53 | | | | | | | | | % 12.82/2.53 | | | | | | | | | CLOSE: (378) is inconsistent. % 12.82/2.53 | | | | | | | | | % 12.82/2.53 | | | | | | | | End of split % 12.82/2.53 | | | | | | | | % 12.82/2.53 | | | | | | | Case 2: % 12.82/2.53 | | | | | | | | % 12.82/2.53 | | | | | | | | (379) all_66_0 = 0 % 12.82/2.53 | | | | | | | | % 12.82/2.53 | | | | | | | | REDUCE: (349), (379) imply: % 12.82/2.53 | | | | | | | | (380) $false % 12.82/2.53 | | | | | | | | % 12.82/2.53 | | | | | | | | CLOSE: (380) is inconsistent. % 12.82/2.53 | | | | | | | | % 12.82/2.53 | | | | | | | End of split % 12.82/2.53 | | | | | | | % 12.82/2.53 | | | | | | Case 2: % 12.82/2.53 | | | | | | | % 12.82/2.53 | | | | | | | (381) all_40_0 = 0 % 12.82/2.53 | | | | | | | % 12.82/2.53 | | | | | | | REDUCE: (338), (381) imply: % 12.82/2.53 | | | | | | | (382) $false % 12.82/2.53 | | | | | | | % 12.82/2.53 | | | | | | | CLOSE: (382) is inconsistent. % 12.82/2.53 | | | | | | | % 12.82/2.53 | | | | | | End of split % 12.82/2.53 | | | | | | % 12.82/2.53 | | | | | Case 2: % 12.82/2.53 | | | | | | % 12.82/2.53 | | | | | | (383) all_20_0 = 0 % 12.82/2.53 | | | | | | % 12.82/2.53 | | | | | | REDUCE: (322), (383) imply: % 12.82/2.53 | | | | | | (384) $false % 12.82/2.53 | | | | | | % 12.82/2.53 | | | | | | CLOSE: (384) is inconsistent. % 12.82/2.53 | | | | | | % 12.82/2.53 | | | | | End of split % 12.82/2.53 | | | | | % 12.82/2.53 | | | | End of split % 12.82/2.53 | | | | % 12.82/2.53 | | | Case 2: % 12.82/2.53 | | | | % 12.82/2.53 | | | | (385) ? [v0: $i] : ? [v1: any] : (big_q(v0) = v1 & $i(v0) & ! [v2: % 12.82/2.53 | | | | $i] : ! [v3: int] : ( ~ (v1 = 0) | v3 = 0 | ~ (big_q(v2) % 12.82/2.53 | | | | = v3) | ~ $i(v2)) & ! [v2: $i] : (v1 = 0 | ~ % 12.82/2.53 | | | | (big_q(v2) = 0) | ~ $i(v2))) & (( ! [v0: $i] : ! [v1: % 12.82/2.53 | | | | int] : (v1 = 0 | ~ (big_q(v0) = v1) | ~ $i(v0)) & ! % 12.82/2.53 | | | | [v0: $i] : ( ~ (big_p(v0) = 0) | ~ $i(v0))) | ( ? [v0: $i] % 12.82/2.53 | | | | : ? [v1: int] : ( ~ (v1 = 0) & big_q(v0) = v1 & $i(v0)) & % 12.82/2.53 | | | | ? [v0: $i] : (big_p(v0) = 0 & $i(v0)))) % 12.82/2.53 | | | | % 12.82/2.53 | | | | ALPHA: (385) implies: % 12.82/2.53 | | | | (386) ( ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (big_q(v0) = v1) | % 12.82/2.53 | | | | ~ $i(v0)) & ! [v0: $i] : ( ~ (big_p(v0) = 0) | ~ $i(v0))) % 12.82/2.53 | | | | | ( ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & big_q(v0) = v1 & % 12.82/2.53 | | | | $i(v0)) & ? [v0: $i] : (big_p(v0) = 0 & $i(v0))) % 12.82/2.53 | | | | (387) ? [v0: $i] : ? [v1: any] : (big_q(v0) = v1 & $i(v0) & ! [v2: % 12.82/2.53 | | | | $i] : ! [v3: int] : ( ~ (v1 = 0) | v3 = 0 | ~ (big_q(v2) % 12.82/2.53 | | | | = v3) | ~ $i(v2)) & ! [v2: $i] : (v1 = 0 | ~ % 12.82/2.53 | | | | (big_q(v2) = 0) | ~ $i(v2))) % 12.82/2.53 | | | | % 12.82/2.53 | | | | DELTA: instantiating (387) with fresh symbols all_14_0, all_14_1 gives: % 12.82/2.53 | | | | (388) big_q(all_14_1) = all_14_0 & $i(all_14_1) & ! [v0: $i] : ! % 12.82/2.53 | | | | [v1: int] : ( ~ (all_14_0 = 0) | v1 = 0 | ~ (big_q(v0) = v1) | % 12.82/2.53 | | | | ~ $i(v0)) & ! [v0: $i] : (all_14_0 = 0 | ~ (big_q(v0) = 0) % 12.82/2.53 | | | | | ~ $i(v0)) % 12.82/2.53 | | | | % 12.82/2.53 | | | | ALPHA: (388) implies: % 12.82/2.53 | | | | (389) $i(all_14_1) % 12.82/2.53 | | | | (390) big_q(all_14_1) = all_14_0 % 12.82/2.53 | | | | (391) ! [v0: $i] : (all_14_0 = 0 | ~ (big_q(v0) = 0) | ~ $i(v0)) % 12.82/2.53 | | | | (392) ! [v0: $i] : ! [v1: int] : ( ~ (all_14_0 = 0) | v1 = 0 | ~ % 12.82/2.53 | | | | (big_q(v0) = v1) | ~ $i(v0)) % 12.82/2.53 | | | | % 12.82/2.53 | | | | BETA: splitting (303) gives: % 12.82/2.53 | | | | % 12.82/2.53 | | | | Case 1: % 12.82/2.53 | | | | | % 12.82/2.53 | | | | | (393) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (big_p(v0) = v1) | % 12.82/2.53 | | | | | ~ $i(v0)) & ! [v0: $i] : ( ~ (big_q(v0) = 0) | ~ $i(v0)) % 12.82/2.53 | | | | | % 12.82/2.53 | | | | | ALPHA: (393) implies: % 12.82/2.53 | | | | | (394) ! [v0: $i] : ( ~ (big_q(v0) = 0) | ~ $i(v0)) % 12.82/2.53 | | | | | (395) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (big_p(v0) = v1) | % 12.82/2.53 | | | | | ~ $i(v0)) % 12.82/2.53 | | | | | % 12.82/2.53 | | | | | BETA: splitting (386) gives: % 12.82/2.53 | | | | | % 12.82/2.53 | | | | | Case 1: % 12.82/2.53 | | | | | | % 12.82/2.53 | | | | | | (396) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (big_q(v0) = v1) % 12.82/2.53 | | | | | | | ~ $i(v0)) & ! [v0: $i] : ( ~ (big_p(v0) = 0) | ~ % 12.82/2.53 | | | | | | $i(v0)) % 12.82/2.53 | | | | | | % 12.82/2.53 | | | | | | ALPHA: (396) implies: % 12.82/2.53 | | | | | | (397) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (big_q(v0) = v1) % 12.82/2.53 | | | | | | | ~ $i(v0)) % 12.82/2.53 | | | | | | % 12.82/2.53 | | | | | | GROUND_INST: instantiating (397) with all_14_1, all_14_0, % 12.82/2.53 | | | | | | simplifying with (389), (390) gives: % 12.82/2.53 | | | | | | (398) all_14_0 = 0 % 12.82/2.53 | | | | | | % 12.82/2.53 | | | | | | REDUCE: (390), (398) imply: % 12.82/2.53 | | | | | | (399) big_q(all_14_1) = 0 % 12.82/2.53 | | | | | | % 12.82/2.53 | | | | | | GROUND_INST: instantiating (394) with all_14_1, simplifying with % 12.82/2.53 | | | | | | (389), (399) gives: % 12.82/2.53 | | | | | | (400) $false % 12.82/2.53 | | | | | | % 12.82/2.53 | | | | | | CLOSE: (400) is inconsistent. % 12.82/2.53 | | | | | | % 12.82/2.53 | | | | | Case 2: % 12.82/2.53 | | | | | | % 12.82/2.53 | | | | | | (401) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & big_q(v0) = v1 % 12.82/2.53 | | | | | | & $i(v0)) & ? [v0: $i] : (big_p(v0) = 0 & $i(v0)) % 12.82/2.53 | | | | | | % 12.82/2.53 | | | | | | ALPHA: (401) implies: % 12.82/2.53 | | | | | | (402) ? [v0: $i] : (big_p(v0) = 0 & $i(v0)) % 12.82/2.53 | | | | | | % 12.82/2.53 | | | | | | DELTA: instantiating (402) with fresh symbol all_27_0 gives: % 12.82/2.53 | | | | | | (403) big_p(all_27_0) = 0 & $i(all_27_0) % 12.82/2.53 | | | | | | % 12.82/2.53 | | | | | | ALPHA: (403) implies: % 12.82/2.53 | | | | | | (404) $i(all_27_0) % 12.82/2.53 | | | | | | (405) big_p(all_27_0) = 0 % 12.82/2.53 | | | | | | % 12.82/2.53 | | | | | | GROUND_INST: instantiating (304) with all_27_0, 0, simplifying with % 12.82/2.53 | | | | | | (404), (405) gives: % 12.82/2.53 | | | | | | (406) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & big_p(v0) = v1 % 12.82/2.53 | | | | | | & $i(v0)) % 12.82/2.53 | | | | | | % 12.82/2.53 | | | | | | DELTA: instantiating (406) with fresh symbols all_36_0, all_36_1 % 12.82/2.53 | | | | | | gives: % 12.82/2.53 | | | | | | (407) ~ (all_36_0 = 0) & big_p(all_36_1) = all_36_0 & % 12.82/2.53 | | | | | | $i(all_36_1) % 12.82/2.53 | | | | | | % 12.82/2.53 | | | | | | ALPHA: (407) implies: % 12.82/2.53 | | | | | | (408) ~ (all_36_0 = 0) % 12.82/2.53 | | | | | | (409) $i(all_36_1) % 12.82/2.53 | | | | | | (410) big_p(all_36_1) = all_36_0 % 12.82/2.53 | | | | | | % 12.82/2.53 | | | | | | GROUND_INST: instantiating (395) with all_36_1, all_36_0, % 12.82/2.53 | | | | | | simplifying with (409), (410) gives: % 12.82/2.53 | | | | | | (411) all_36_0 = 0 % 12.82/2.53 | | | | | | % 12.82/2.53 | | | | | | REDUCE: (408), (411) imply: % 12.82/2.53 | | | | | | (412) $false % 12.82/2.53 | | | | | | % 12.82/2.53 | | | | | | CLOSE: (412) is inconsistent. % 12.82/2.53 | | | | | | % 12.82/2.54 | | | | | End of split % 12.82/2.54 | | | | | % 12.82/2.54 | | | | Case 2: % 12.82/2.54 | | | | | % 12.82/2.54 | | | | | (413) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & big_p(v0) = v1 & % 12.82/2.54 | | | | | $i(v0)) & ? [v0: $i] : (big_q(v0) = 0 & $i(v0)) % 12.82/2.54 | | | | | % 12.82/2.54 | | | | | ALPHA: (413) implies: % 12.82/2.54 | | | | | (414) ? [v0: $i] : (big_q(v0) = 0 & $i(v0)) % 12.82/2.54 | | | | | (415) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & big_p(v0) = v1 & % 12.82/2.54 | | | | | $i(v0)) % 12.82/2.54 | | | | | % 12.82/2.54 | | | | | DELTA: instantiating (414) with fresh symbol all_23_0 gives: % 12.82/2.54 | | | | | (416) big_q(all_23_0) = 0 & $i(all_23_0) % 12.82/2.54 | | | | | % 12.82/2.54 | | | | | ALPHA: (416) implies: % 12.82/2.54 | | | | | (417) $i(all_23_0) % 12.82/2.54 | | | | | (418) big_q(all_23_0) = 0 % 12.82/2.54 | | | | | % 12.82/2.54 | | | | | DELTA: instantiating (415) with fresh symbols all_25_0, all_25_1 % 12.82/2.54 | | | | | gives: % 12.82/2.54 | | | | | (419) ~ (all_25_0 = 0) & big_p(all_25_1) = all_25_0 & $i(all_25_1) % 12.82/2.54 | | | | | % 12.82/2.54 | | | | | ALPHA: (419) implies: % 12.82/2.54 | | | | | (420) ~ (all_25_0 = 0) % 12.82/2.54 | | | | | (421) $i(all_25_1) % 12.82/2.54 | | | | | (422) big_p(all_25_1) = all_25_0 % 12.82/2.54 | | | | | % 12.82/2.54 | | | | | GROUND_INST: instantiating (304) with all_25_1, all_25_0, simplifying % 12.82/2.54 | | | | | with (421), (422) gives: % 12.82/2.54 | | | | | (423) ? [v0: $i] : ? [v1: any] : (big_p(v0) = v1 & $i(v0) & ( ~ % 12.82/2.54 | | | | | (v1 = 0) | ~ (all_25_0 = 0)) & (v1 = 0 | all_25_0 = 0)) % 12.82/2.54 | | | | | % 12.82/2.54 | | | | | GROUND_INST: instantiating (391) with all_23_0, simplifying with % 12.82/2.54 | | | | | (417), (418) gives: % 12.82/2.54 | | | | | (424) all_14_0 = 0 % 12.82/2.54 | | | | | % 12.82/2.54 | | | | | DELTA: instantiating (423) with fresh symbols all_33_0, all_33_1 % 12.82/2.54 | | | | | gives: % 12.82/2.54 | | | | | (425) big_p(all_33_1) = all_33_0 & $i(all_33_1) & ( ~ (all_33_0 = % 12.82/2.54 | | | | | 0) | ~ (all_25_0 = 0)) & (all_33_0 = 0 | all_25_0 = 0) % 12.82/2.54 | | | | | % 12.82/2.54 | | | | | ALPHA: (425) implies: % 12.82/2.54 | | | | | (426) $i(all_33_1) % 12.82/2.54 | | | | | (427) big_p(all_33_1) = all_33_0 % 12.82/2.54 | | | | | (428) all_33_0 = 0 | all_25_0 = 0 % 12.82/2.54 | | | | | % 12.82/2.54 | | | | | BETA: splitting (428) gives: % 12.82/2.54 | | | | | % 12.82/2.54 | | | | | Case 1: % 12.82/2.54 | | | | | | % 12.82/2.54 | | | | | | (429) all_33_0 = 0 % 12.82/2.54 | | | | | | % 12.82/2.54 | | | | | | REDUCE: (427), (429) imply: % 12.82/2.54 | | | | | | (430) big_p(all_33_1) = 0 % 12.82/2.54 | | | | | | % 12.82/2.54 | | | | | | DELTA: instantiating (415) with fresh symbols all_44_0, all_44_1 % 12.82/2.54 | | | | | | gives: % 12.82/2.54 | | | | | | (431) ~ (all_44_0 = 0) & big_p(all_44_1) = all_44_0 & % 12.82/2.54 | | | | | | $i(all_44_1) % 12.82/2.54 | | | | | | % 12.82/2.54 | | | | | | ALPHA: (431) implies: % 12.82/2.54 | | | | | | (432) ~ (all_44_0 = 0) % 12.82/2.54 | | | | | | (433) $i(all_44_1) % 12.82/2.54 | | | | | | (434) big_p(all_44_1) = all_44_0 % 12.82/2.54 | | | | | | % 12.82/2.54 | | | | | | GROUND_INST: instantiating (304) with all_44_1, all_44_0, % 12.82/2.54 | | | | | | simplifying with (433), (434) gives: % 12.82/2.54 | | | | | | (435) ? [v0: $i] : ? [v1: any] : (big_p(v0) = v1 & $i(v0) & ( ~ % 12.82/2.54 | | | | | | (v1 = 0) | ~ (all_44_0 = 0)) & (v1 = 0 | all_44_0 = % 12.82/2.54 | | | | | | 0)) % 12.82/2.54 | | | | | | % 12.82/2.54 | | | | | | DELTA: instantiating (435) with fresh symbols all_51_0, all_51_1 % 12.82/2.54 | | | | | | gives: % 12.82/2.54 | | | | | | (436) big_p(all_51_1) = all_51_0 & $i(all_51_1) & ( ~ (all_51_0 = % 12.82/2.54 | | | | | | 0) | ~ (all_44_0 = 0)) & (all_51_0 = 0 | all_44_0 = 0) % 12.82/2.54 | | | | | | % 12.82/2.54 | | | | | | ALPHA: (436) implies: % 12.82/2.54 | | | | | | (437) $i(all_51_1) % 12.82/2.54 | | | | | | (438) big_p(all_51_1) = all_51_0 % 12.82/2.54 | | | | | | (439) all_51_0 = 0 | all_44_0 = 0 % 12.82/2.54 | | | | | | % 12.82/2.54 | | | | | | BETA: splitting (439) gives: % 12.82/2.54 | | | | | | % 12.82/2.54 | | | | | | Case 1: % 12.82/2.54 | | | | | | | % 12.82/2.54 | | | | | | | (440) all_51_0 = 0 % 12.82/2.54 | | | | | | | % 12.82/2.54 | | | | | | | REDUCE: (438), (440) imply: % 12.82/2.54 | | | | | | | (441) big_p(all_51_1) = 0 % 12.82/2.54 | | | | | | | % 12.82/2.54 | | | | | | | DELTA: instantiating (415) with fresh symbols all_62_0, all_62_1 % 12.82/2.54 | | | | | | | gives: % 12.82/2.54 | | | | | | | (442) ~ (all_62_0 = 0) & big_p(all_62_1) = all_62_0 & % 12.82/2.54 | | | | | | | $i(all_62_1) % 12.82/2.54 | | | | | | | % 12.82/2.54 | | | | | | | ALPHA: (442) implies: % 12.82/2.54 | | | | | | | (443) ~ (all_62_0 = 0) % 12.82/2.54 | | | | | | | (444) $i(all_62_1) % 12.82/2.54 | | | | | | | (445) big_p(all_62_1) = all_62_0 % 12.82/2.54 | | | | | | | % 12.82/2.54 | | | | | | | GROUND_INST: instantiating (304) with all_62_1, all_62_0, % 12.82/2.54 | | | | | | | simplifying with (444), (445) gives: % 12.82/2.54 | | | | | | | (446) ? [v0: $i] : ? [v1: any] : (big_p(v0) = v1 & $i(v0) & ( % 12.82/2.54 | | | | | | | ~ (v1 = 0) | ~ (all_62_0 = 0)) & (v1 = 0 | all_62_0 % 12.82/2.54 | | | | | | | = 0)) % 12.82/2.54 | | | | | | | % 12.82/2.54 | | | | | | | DELTA: instantiating (446) with fresh symbols all_69_0, all_69_1 % 12.82/2.54 | | | | | | | gives: % 12.82/2.54 | | | | | | | (447) big_p(all_69_1) = all_69_0 & $i(all_69_1) & ( ~ (all_69_0 % 12.82/2.54 | | | | | | | = 0) | ~ (all_62_0 = 0)) & (all_69_0 = 0 | all_62_0 % 12.82/2.54 | | | | | | | = 0) % 12.82/2.54 | | | | | | | % 12.82/2.54 | | | | | | | ALPHA: (447) implies: % 12.82/2.54 | | | | | | | (448) $i(all_69_1) % 12.82/2.54 | | | | | | | (449) big_p(all_69_1) = all_69_0 % 12.82/2.54 | | | | | | | (450) all_69_0 = 0 | all_62_0 = 0 % 12.82/2.54 | | | | | | | % 12.82/2.54 | | | | | | | BETA: splitting (450) gives: % 12.82/2.54 | | | | | | | % 12.82/2.54 | | | | | | | Case 1: % 12.82/2.54 | | | | | | | | % 12.82/2.54 | | | | | | | | (451) all_69_0 = 0 % 12.82/2.54 | | | | | | | | % 12.82/2.54 | | | | | | | | REDUCE: (449), (451) imply: % 12.82/2.54 | | | | | | | | (452) big_p(all_69_1) = 0 % 12.82/2.54 | | | | | | | | % 12.82/2.54 | | | | | | | | DELTA: instantiating (415) with fresh symbols all_80_0, all_80_1 % 12.82/2.54 | | | | | | | | gives: % 12.82/2.54 | | | | | | | | (453) ~ (all_80_0 = 0) & big_p(all_80_1) = all_80_0 & % 12.82/2.54 | | | | | | | | $i(all_80_1) % 12.82/2.54 | | | | | | | | % 12.82/2.54 | | | | | | | | ALPHA: (453) implies: % 12.82/2.54 | | | | | | | | (454) ~ (all_80_0 = 0) % 12.82/2.54 | | | | | | | | (455) $i(all_80_1) % 12.82/2.54 | | | | | | | | (456) big_p(all_80_1) = all_80_0 % 12.82/2.54 | | | | | | | | % 12.82/2.54 | | | | | | | | GROUND_INST: instantiating (304) with all_80_1, all_80_0, % 12.82/2.54 | | | | | | | | simplifying with (455), (456) gives: % 12.82/2.54 | | | | | | | | (457) ? [v0: $i] : ? [v1: any] : (big_p(v0) = v1 & $i(v0) & % 12.82/2.54 | | | | | | | | ( ~ (v1 = 0) | ~ (all_80_0 = 0)) & (v1 = 0 | % 12.82/2.54 | | | | | | | | all_80_0 = 0)) % 12.82/2.54 | | | | | | | | % 12.82/2.54 | | | | | | | | DELTA: instantiating (457) with fresh symbols all_87_0, all_87_1 % 12.82/2.54 | | | | | | | | gives: % 12.82/2.54 | | | | | | | | (458) big_p(all_87_1) = all_87_0 & $i(all_87_1) & ( ~ % 12.82/2.54 | | | | | | | | (all_87_0 = 0) | ~ (all_80_0 = 0)) & (all_87_0 = 0 | % 12.82/2.54 | | | | | | | | all_80_0 = 0) % 12.82/2.54 | | | | | | | | % 12.82/2.54 | | | | | | | | ALPHA: (458) implies: % 12.82/2.54 | | | | | | | | (459) $i(all_87_1) % 12.82/2.54 | | | | | | | | (460) big_p(all_87_1) = all_87_0 % 12.82/2.54 | | | | | | | | (461) all_87_0 = 0 | all_80_0 = 0 % 12.82/2.54 | | | | | | | | % 12.82/2.54 | | | | | | | | BETA: splitting (461) gives: % 12.82/2.54 | | | | | | | | % 12.82/2.54 | | | | | | | | Case 1: % 12.82/2.54 | | | | | | | | | % 12.82/2.54 | | | | | | | | | (462) all_87_0 = 0 % 12.82/2.54 | | | | | | | | | % 12.82/2.54 | | | | | | | | | REDUCE: (460), (462) imply: % 12.82/2.54 | | | | | | | | | (463) big_p(all_87_1) = 0 % 12.82/2.54 | | | | | | | | | % 12.82/2.54 | | | | | | | | | DELTA: instantiating (415) with fresh symbols all_98_0, % 12.82/2.54 | | | | | | | | | all_98_1 gives: % 12.82/2.54 | | | | | | | | | (464) ~ (all_98_0 = 0) & big_p(all_98_1) = all_98_0 & % 12.82/2.54 | | | | | | | | | $i(all_98_1) % 12.82/2.54 | | | | | | | | | % 12.82/2.54 | | | | | | | | | ALPHA: (464) implies: % 12.82/2.54 | | | | | | | | | (465) ~ (all_98_0 = 0) % 12.82/2.54 | | | | | | | | | (466) $i(all_98_1) % 12.82/2.54 | | | | | | | | | (467) big_p(all_98_1) = all_98_0 % 12.82/2.54 | | | | | | | | | % 12.82/2.54 | | | | | | | | | GROUND_INST: instantiating (304) with all_98_1, all_98_0, % 12.82/2.54 | | | | | | | | | simplifying with (466), (467) gives: % 12.82/2.54 | | | | | | | | | (468) ? [v0: $i] : ? [v1: any] : (big_p(v0) = v1 & $i(v0) % 12.82/2.54 | | | | | | | | | & ( ~ (v1 = 0) | ~ (all_98_0 = 0)) & (v1 = 0 | % 12.82/2.54 | | | | | | | | | all_98_0 = 0)) % 12.82/2.54 | | | | | | | | | % 12.82/2.54 | | | | | | | | | DELTA: instantiating (468) with fresh symbols all_105_0, % 12.82/2.54 | | | | | | | | | all_105_1 gives: % 12.82/2.54 | | | | | | | | | (469) big_p(all_105_1) = all_105_0 & $i(all_105_1) & ( ~ % 12.82/2.54 | | | | | | | | | (all_105_0 = 0) | ~ (all_98_0 = 0)) & (all_105_0 = % 12.82/2.54 | | | | | | | | | 0 | all_98_0 = 0) % 12.82/2.54 | | | | | | | | | % 12.82/2.54 | | | | | | | | | ALPHA: (469) implies: % 12.82/2.54 | | | | | | | | | (470) $i(all_105_1) % 12.82/2.54 | | | | | | | | | (471) big_p(all_105_1) = all_105_0 % 12.82/2.54 | | | | | | | | | (472) all_105_0 = 0 | all_98_0 = 0 % 12.82/2.54 | | | | | | | | | % 12.82/2.54 | | | | | | | | | BETA: splitting (472) gives: % 12.82/2.54 | | | | | | | | | % 12.82/2.54 | | | | | | | | | Case 1: % 12.82/2.54 | | | | | | | | | | % 12.82/2.54 | | | | | | | | | | (473) all_105_0 = 0 % 12.82/2.54 | | | | | | | | | | % 12.82/2.54 | | | | | | | | | | REDUCE: (471), (473) imply: % 12.82/2.54 | | | | | | | | | | (474) big_p(all_105_1) = 0 % 12.82/2.54 | | | | | | | | | | % 12.82/2.54 | | | | | | | | | | BETA: splitting (386) gives: % 12.82/2.54 | | | | | | | | | | % 12.82/2.54 | | | | | | | | | | Case 1: % 12.82/2.54 | | | | | | | | | | | % 12.82/2.54 | | | | | | | | | | | (475) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ % 12.82/2.54 | | | | | | | | | | | (big_q(v0) = v1) | ~ $i(v0)) & ! [v0: $i] : ( % 12.82/2.54 | | | | | | | | | | | ~ (big_p(v0) = 0) | ~ $i(v0)) % 12.82/2.54 | | | | | | | | | | | % 12.82/2.54 | | | | | | | | | | | ALPHA: (475) implies: % 12.82/2.54 | | | | | | | | | | | (476) ! [v0: $i] : ( ~ (big_p(v0) = 0) | ~ $i(v0)) % 12.82/2.54 | | | | | | | | | | | % 12.82/2.54 | | | | | | | | | | | GROUND_INST: instantiating (476) with all_105_1, simplifying % 12.82/2.54 | | | | | | | | | | | with (470), (474) gives: % 12.82/2.54 | | | | | | | | | | | (477) $false % 12.82/2.54 | | | | | | | | | | | % 12.82/2.54 | | | | | | | | | | | CLOSE: (477) is inconsistent. % 12.82/2.54 | | | | | | | | | | | % 12.82/2.54 | | | | | | | | | | Case 2: % 12.82/2.54 | | | | | | | | | | | % 12.82/2.54 | | | | | | | | | | | (478) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & % 12.82/2.54 | | | | | | | | | | | big_q(v0) = v1 & $i(v0)) & ? [v0: $i] : % 12.82/2.54 | | | | | | | | | | | (big_p(v0) = 0 & $i(v0)) % 12.82/2.54 | | | | | | | | | | | % 12.82/2.54 | | | | | | | | | | | ALPHA: (478) implies: % 12.82/2.54 | | | | | | | | | | | (479) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & % 12.82/2.54 | | | | | | | | | | | big_q(v0) = v1 & $i(v0)) % 12.82/2.54 | | | | | | | | | | | % 12.82/2.54 | | | | | | | | | | | DELTA: instantiating (479) with fresh symbols all_125_0, % 12.82/2.54 | | | | | | | | | | | all_125_1 gives: % 12.82/2.54 | | | | | | | | | | | (480) ~ (all_125_0 = 0) & big_q(all_125_1) = all_125_0 % 12.82/2.54 | | | | | | | | | | | & $i(all_125_1) % 12.82/2.54 | | | | | | | | | | | % 12.82/2.54 | | | | | | | | | | | ALPHA: (480) implies: % 12.82/2.54 | | | | | | | | | | | (481) ~ (all_125_0 = 0) % 12.82/2.54 | | | | | | | | | | | (482) $i(all_125_1) % 12.82/2.54 | | | | | | | | | | | (483) big_q(all_125_1) = all_125_0 % 12.82/2.54 | | | | | | | | | | | % 12.82/2.54 | | | | | | | | | | | GROUND_INST: instantiating (392) with all_125_1, all_125_0, % 12.82/2.54 | | | | | | | | | | | simplifying with (482), (483) gives: % 12.82/2.54 | | | | | | | | | | | (484) ~ (all_14_0 = 0) | all_125_0 = 0 % 12.82/2.54 | | | | | | | | | | | % 12.82/2.54 | | | | | | | | | | | BETA: splitting (484) gives: % 12.82/2.54 | | | | | | | | | | | % 12.82/2.54 | | | | | | | | | | | Case 1: % 12.82/2.54 | | | | | | | | | | | | % 12.82/2.54 | | | | | | | | | | | | (485) ~ (all_14_0 = 0) % 12.82/2.54 | | | | | | | | | | | | % 12.82/2.54 | | | | | | | | | | | | REDUCE: (424), (485) imply: % 12.82/2.54 | | | | | | | | | | | | (486) $false % 12.82/2.54 | | | | | | | | | | | | % 12.82/2.54 | | | | | | | | | | | | CLOSE: (486) is inconsistent. % 12.82/2.54 | | | | | | | | | | | | % 12.82/2.55 | | | | | | | | | | | Case 2: % 12.82/2.55 | | | | | | | | | | | | % 12.82/2.55 | | | | | | | | | | | | (487) all_125_0 = 0 % 12.82/2.55 | | | | | | | | | | | | % 12.82/2.55 | | | | | | | | | | | | REDUCE: (481), (487) imply: % 12.82/2.55 | | | | | | | | | | | | (488) $false % 12.82/2.55 | | | | | | | | | | | | % 12.82/2.55 | | | | | | | | | | | | CLOSE: (488) is inconsistent. % 12.82/2.55 | | | | | | | | | | | | % 12.82/2.55 | | | | | | | | | | | End of split % 12.82/2.55 | | | | | | | | | | | % 12.82/2.55 | | | | | | | | | | End of split % 12.82/2.55 | | | | | | | | | | % 12.82/2.55 | | | | | | | | | Case 2: % 12.82/2.55 | | | | | | | | | | % 12.82/2.55 | | | | | | | | | | (489) all_98_0 = 0 % 12.82/2.55 | | | | | | | | | | % 12.82/2.55 | | | | | | | | | | REDUCE: (465), (489) imply: % 12.82/2.55 | | | | | | | | | | (490) $false % 12.82/2.55 | | | | | | | | | | % 12.82/2.55 | | | | | | | | | | CLOSE: (490) is inconsistent. % 12.82/2.55 | | | | | | | | | | % 12.82/2.55 | | | | | | | | | End of split % 12.82/2.55 | | | | | | | | | % 12.82/2.55 | | | | | | | | Case 2: % 12.82/2.55 | | | | | | | | | % 12.82/2.55 | | | | | | | | | (491) all_80_0 = 0 % 12.82/2.55 | | | | | | | | | % 12.82/2.55 | | | | | | | | | REDUCE: (454), (491) imply: % 12.82/2.55 | | | | | | | | | (492) $false % 12.82/2.55 | | | | | | | | | % 12.82/2.55 | | | | | | | | | CLOSE: (492) is inconsistent. % 12.82/2.55 | | | | | | | | | % 12.82/2.55 | | | | | | | | End of split % 12.82/2.55 | | | | | | | | % 12.82/2.55 | | | | | | | Case 2: % 12.82/2.55 | | | | | | | | % 12.82/2.55 | | | | | | | | (493) all_62_0 = 0 % 12.82/2.55 | | | | | | | | % 12.82/2.55 | | | | | | | | REDUCE: (443), (493) imply: % 12.82/2.55 | | | | | | | | (494) $false % 12.82/2.55 | | | | | | | | % 12.82/2.55 | | | | | | | | CLOSE: (494) is inconsistent. % 12.82/2.55 | | | | | | | | % 12.82/2.55 | | | | | | | End of split % 12.82/2.55 | | | | | | | % 12.82/2.55 | | | | | | Case 2: % 12.82/2.55 | | | | | | | % 12.82/2.55 | | | | | | | (495) all_44_0 = 0 % 12.82/2.55 | | | | | | | % 12.82/2.55 | | | | | | | REDUCE: (432), (495) imply: % 12.82/2.55 | | | | | | | (496) $false % 12.82/2.55 | | | | | | | % 12.82/2.55 | | | | | | | CLOSE: (496) is inconsistent. % 12.82/2.55 | | | | | | | % 12.82/2.55 | | | | | | End of split % 12.82/2.55 | | | | | | % 12.82/2.55 | | | | | Case 2: % 12.82/2.55 | | | | | | % 12.82/2.55 | | | | | | (497) all_25_0 = 0 % 12.82/2.55 | | | | | | % 12.82/2.55 | | | | | | REDUCE: (420), (497) imply: % 12.82/2.55 | | | | | | (498) $false % 12.82/2.55 | | | | | | % 12.82/2.55 | | | | | | CLOSE: (498) is inconsistent. % 12.82/2.55 | | | | | | % 12.82/2.55 | | | | | End of split % 12.82/2.55 | | | | | % 12.82/2.55 | | | | End of split % 12.82/2.55 | | | | % 12.82/2.55 | | | End of split % 12.82/2.55 | | | % 12.82/2.55 | | Case 2: % 12.82/2.55 | | | % 12.82/2.55 | | | (499) ? [v0: $i] : ? [v1: any] : (big_p(v0) = v1 & $i(v0) & ! [v2: % 12.82/2.55 | | | $i] : ! [v3: int] : ( ~ (v1 = 0) | v3 = 0 | ~ (big_p(v2) = % 12.82/2.55 | | | v3) | ~ $i(v2)) & ! [v2: $i] : (v1 = 0 | ~ (big_p(v2) = % 12.82/2.55 | | | 0) | ~ $i(v2))) & (( ! [v0: $i] : ! [v1: int] : (v1 = 0 | % 12.82/2.55 | | | ~ (big_p(v0) = v1) | ~ $i(v0)) & ? [v0: $i] : (big_q(v0) % 12.82/2.55 | | | = 0 & $i(v0))) | ( ! [v0: $i] : ( ~ (big_q(v0) = 0) | ~ % 12.82/2.55 | | | $i(v0)) & ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & % 12.82/2.55 | | | big_p(v0) = v1 & $i(v0)))) % 12.82/2.55 | | | % 12.82/2.55 | | | ALPHA: (499) implies: % 12.82/2.55 | | | (500) ( ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (big_p(v0) = v1) | ~ % 12.82/2.55 | | | $i(v0)) & ? [v0: $i] : (big_q(v0) = 0 & $i(v0))) | ( ! [v0: % 12.82/2.55 | | | $i] : ( ~ (big_q(v0) = 0) | ~ $i(v0)) & ? [v0: $i] : ? % 12.82/2.55 | | | [v1: int] : ( ~ (v1 = 0) & big_p(v0) = v1 & $i(v0))) % 12.82/2.55 | | | (501) ? [v0: $i] : ? [v1: any] : (big_p(v0) = v1 & $i(v0) & ! [v2: % 12.82/2.55 | | | $i] : ! [v3: int] : ( ~ (v1 = 0) | v3 = 0 | ~ (big_p(v2) = % 12.82/2.55 | | | v3) | ~ $i(v2)) & ! [v2: $i] : (v1 = 0 | ~ (big_p(v2) = % 12.82/2.55 | | | 0) | ~ $i(v2))) % 12.82/2.55 | | | % 12.82/2.55 | | | DELTA: instantiating (501) with fresh symbols all_10_0, all_10_1 gives: % 12.82/2.55 | | | (502) big_p(all_10_1) = all_10_0 & $i(all_10_1) & ! [v0: $i] : ! [v1: % 12.82/2.55 | | | int] : ( ~ (all_10_0 = 0) | v1 = 0 | ~ (big_p(v0) = v1) | ~ % 12.82/2.55 | | | $i(v0)) & ! [v0: $i] : (all_10_0 = 0 | ~ (big_p(v0) = 0) | ~ % 12.82/2.55 | | | $i(v0)) % 12.82/2.55 | | | % 12.82/2.55 | | | ALPHA: (502) implies: % 12.82/2.55 | | | (503) $i(all_10_1) % 12.82/2.55 | | | (504) big_p(all_10_1) = all_10_0 % 12.82/2.55 | | | (505) ! [v0: $i] : (all_10_0 = 0 | ~ (big_p(v0) = 0) | ~ $i(v0)) % 12.82/2.55 | | | (506) ! [v0: $i] : ! [v1: int] : ( ~ (all_10_0 = 0) | v1 = 0 | ~ % 12.82/2.55 | | | (big_p(v0) = v1) | ~ $i(v0)) % 12.82/2.55 | | | % 12.82/2.55 | | | BETA: splitting (301) gives: % 12.82/2.55 | | | % 12.82/2.55 | | | Case 1: % 12.82/2.55 | | | | % 12.82/2.55 | | | | (507) ! [v0: $i] : ! [v1: any] : ( ~ (big_q(v0) = v1) | ~ $i(v0) | % 12.82/2.55 | | | | ? [v2: $i] : ? [v3: any] : (big_q(v2) = v3 & $i(v2) & ( ~ % 12.82/2.55 | | | | (v3 = 0) | ~ (v1 = 0)) & (v3 = 0 | v1 = 0))) & (( ! [v0: % 12.82/2.55 | | | | $i] : ! [v1: int] : (v1 = 0 | ~ (big_q(v0) = v1) | ~ % 12.82/2.55 | | | | $i(v0)) & ? [v0: $i] : (big_p(v0) = 0 & $i(v0))) | ( ! % 12.82/2.55 | | | | [v0: $i] : ( ~ (big_p(v0) = 0) | ~ $i(v0)) & ? [v0: $i] : % 12.82/2.55 | | | | ? [v1: int] : ( ~ (v1 = 0) & big_q(v0) = v1 & $i(v0)))) % 12.82/2.55 | | | | % 12.82/2.55 | | | | ALPHA: (507) implies: % 12.82/2.55 | | | | (508) ( ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (big_q(v0) = v1) | % 12.82/2.55 | | | | ~ $i(v0)) & ? [v0: $i] : (big_p(v0) = 0 & $i(v0))) | ( ! % 12.82/2.55 | | | | [v0: $i] : ( ~ (big_p(v0) = 0) | ~ $i(v0)) & ? [v0: $i] : % 12.82/2.55 | | | | ? [v1: int] : ( ~ (v1 = 0) & big_q(v0) = v1 & $i(v0))) % 12.82/2.55 | | | | (509) ! [v0: $i] : ! [v1: any] : ( ~ (big_q(v0) = v1) | ~ $i(v0) | % 12.82/2.55 | | | | ? [v2: $i] : ? [v3: any] : (big_q(v2) = v3 & $i(v2) & ( ~ % 12.82/2.55 | | | | (v3 = 0) | ~ (v1 = 0)) & (v3 = 0 | v1 = 0))) % 12.82/2.55 | | | | % 12.82/2.55 | | | | BETA: splitting (500) gives: % 12.82/2.55 | | | | % 12.82/2.55 | | | | Case 1: % 12.82/2.55 | | | | | % 12.82/2.55 | | | | | (510) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (big_p(v0) = v1) | % 12.82/2.55 | | | | | ~ $i(v0)) & ? [v0: $i] : (big_q(v0) = 0 & $i(v0)) % 12.82/2.55 | | | | | % 12.82/2.55 | | | | | ALPHA: (510) implies: % 12.82/2.55 | | | | | (511) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (big_p(v0) = v1) | % 12.82/2.55 | | | | | ~ $i(v0)) % 12.82/2.55 | | | | | (512) ? [v0: $i] : (big_q(v0) = 0 & $i(v0)) % 12.82/2.55 | | | | | % 12.82/2.55 | | | | | GROUND_INST: instantiating (511) with all_10_1, all_10_0, simplifying % 12.82/2.55 | | | | | with (503), (504) gives: % 12.82/2.55 | | | | | (513) all_10_0 = 0 % 12.82/2.55 | | | | | % 12.82/2.55 | | | | | DELTA: instantiating (512) with fresh symbol all_25_0 gives: % 12.82/2.55 | | | | | (514) big_q(all_25_0) = 0 & $i(all_25_0) % 12.82/2.55 | | | | | % 12.82/2.55 | | | | | ALPHA: (514) implies: % 12.82/2.55 | | | | | (515) $i(all_25_0) % 12.82/2.55 | | | | | (516) big_q(all_25_0) = 0 % 12.82/2.55 | | | | | % 12.82/2.55 | | | | | REDUCE: (504), (513) imply: % 12.82/2.55 | | | | | (517) big_p(all_10_1) = 0 % 12.82/2.55 | | | | | % 12.82/2.55 | | | | | GROUND_INST: instantiating (509) with all_25_0, 0, simplifying with % 12.82/2.55 | | | | | (515), (516) gives: % 12.82/2.55 | | | | | (518) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & big_q(v0) = v1 & % 12.82/2.55 | | | | | $i(v0)) % 12.82/2.55 | | | | | % 12.82/2.55 | | | | | DELTA: instantiating (518) with fresh symbols all_32_0, all_32_1 % 12.82/2.55 | | | | | gives: % 12.82/2.55 | | | | | (519) ~ (all_32_0 = 0) & big_q(all_32_1) = all_32_0 & $i(all_32_1) % 12.82/2.55 | | | | | % 12.82/2.55 | | | | | ALPHA: (519) implies: % 12.82/2.55 | | | | | (520) ~ (all_32_0 = 0) % 12.82/2.55 | | | | | (521) $i(all_32_1) % 12.82/2.55 | | | | | (522) big_q(all_32_1) = all_32_0 % 12.82/2.55 | | | | | % 12.82/2.55 | | | | | BETA: splitting (508) gives: % 12.82/2.55 | | | | | % 12.82/2.55 | | | | | Case 1: % 12.82/2.55 | | | | | | % 12.82/2.55 | | | | | | (523) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (big_q(v0) = v1) % 12.82/2.55 | | | | | | | ~ $i(v0)) & ? [v0: $i] : (big_p(v0) = 0 & $i(v0)) % 12.82/2.55 | | | | | | % 12.82/2.55 | | | | | | ALPHA: (523) implies: % 12.82/2.55 | | | | | | (524) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (big_q(v0) = v1) % 12.82/2.55 | | | | | | | ~ $i(v0)) % 12.82/2.55 | | | | | | % 12.82/2.55 | | | | | | GROUND_INST: instantiating (524) with all_32_1, all_32_0, % 12.82/2.55 | | | | | | simplifying with (521), (522) gives: % 12.82/2.55 | | | | | | (525) all_32_0 = 0 % 12.82/2.55 | | | | | | % 12.82/2.55 | | | | | | REDUCE: (520), (525) imply: % 12.82/2.55 | | | | | | (526) $false % 12.82/2.55 | | | | | | % 12.82/2.55 | | | | | | CLOSE: (526) is inconsistent. % 12.82/2.55 | | | | | | % 12.82/2.55 | | | | | Case 2: % 12.82/2.55 | | | | | | % 12.82/2.55 | | | | | | (527) ! [v0: $i] : ( ~ (big_p(v0) = 0) | ~ $i(v0)) & ? [v0: % 12.82/2.55 | | | | | | $i] : ? [v1: int] : ( ~ (v1 = 0) & big_q(v0) = v1 & % 12.82/2.55 | | | | | | $i(v0)) % 12.82/2.55 | | | | | | % 12.82/2.55 | | | | | | ALPHA: (527) implies: % 12.82/2.55 | | | | | | (528) ! [v0: $i] : ( ~ (big_p(v0) = 0) | ~ $i(v0)) % 12.82/2.55 | | | | | | % 12.82/2.55 | | | | | | GROUND_INST: instantiating (528) with all_10_1, simplifying with % 12.82/2.55 | | | | | | (503), (517) gives: % 12.82/2.55 | | | | | | (529) $false % 12.82/2.55 | | | | | | % 12.82/2.55 | | | | | | CLOSE: (529) is inconsistent. % 12.82/2.55 | | | | | | % 12.82/2.55 | | | | | End of split % 12.82/2.55 | | | | | % 12.82/2.55 | | | | Case 2: % 12.82/2.55 | | | | | % 12.82/2.55 | | | | | (530) ! [v0: $i] : ( ~ (big_q(v0) = 0) | ~ $i(v0)) & ? [v0: $i] % 12.82/2.55 | | | | | : ? [v1: int] : ( ~ (v1 = 0) & big_p(v0) = v1 & $i(v0)) % 12.82/2.55 | | | | | % 12.82/2.55 | | | | | ALPHA: (530) implies: % 12.82/2.55 | | | | | (531) ! [v0: $i] : ( ~ (big_q(v0) = 0) | ~ $i(v0)) % 12.82/2.55 | | | | | (532) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & big_p(v0) = v1 & % 12.82/2.55 | | | | | $i(v0)) % 12.82/2.55 | | | | | % 12.82/2.55 | | | | | DELTA: instantiating (532) with fresh symbols all_24_0, all_24_1 % 12.82/2.55 | | | | | gives: % 12.82/2.55 | | | | | (533) ~ (all_24_0 = 0) & big_p(all_24_1) = all_24_0 & $i(all_24_1) % 12.82/2.55 | | | | | % 12.82/2.55 | | | | | ALPHA: (533) implies: % 12.82/2.55 | | | | | (534) ~ (all_24_0 = 0) % 12.82/2.55 | | | | | (535) $i(all_24_1) % 12.82/2.55 | | | | | (536) big_p(all_24_1) = all_24_0 % 12.82/2.55 | | | | | % 12.82/2.55 | | | | | GROUND_INST: instantiating (506) with all_24_1, all_24_0, simplifying % 12.82/2.55 | | | | | with (535), (536) gives: % 12.82/2.55 | | | | | (537) ~ (all_10_0 = 0) | all_24_0 = 0 % 12.82/2.55 | | | | | % 12.82/2.55 | | | | | BETA: splitting (508) gives: % 12.82/2.55 | | | | | % 12.82/2.55 | | | | | Case 1: % 12.82/2.55 | | | | | | % 12.82/2.55 | | | | | | (538) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (big_q(v0) = v1) % 12.82/2.55 | | | | | | | ~ $i(v0)) & ? [v0: $i] : (big_p(v0) = 0 & $i(v0)) % 12.82/2.55 | | | | | | % 12.82/2.55 | | | | | | ALPHA: (538) implies: % 12.82/2.55 | | | | | | (539) ? [v0: $i] : (big_p(v0) = 0 & $i(v0)) % 12.82/2.55 | | | | | | % 12.82/2.55 | | | | | | DELTA: instantiating (539) with fresh symbol all_33_0 gives: % 12.82/2.55 | | | | | | (540) big_p(all_33_0) = 0 & $i(all_33_0) % 12.82/2.55 | | | | | | % 12.82/2.55 | | | | | | ALPHA: (540) implies: % 12.82/2.55 | | | | | | (541) $i(all_33_0) % 12.82/2.55 | | | | | | (542) big_p(all_33_0) = 0 % 12.82/2.55 | | | | | | % 12.82/2.55 | | | | | | BETA: splitting (537) gives: % 12.82/2.55 | | | | | | % 12.82/2.55 | | | | | | Case 1: % 12.82/2.55 | | | | | | | % 12.82/2.55 | | | | | | | (543) ~ (all_10_0 = 0) % 12.82/2.55 | | | | | | | % 12.82/2.55 | | | | | | | GROUND_INST: instantiating (505) with all_33_0, simplifying with % 12.82/2.55 | | | | | | | (541), (542) gives: % 12.82/2.55 | | | | | | | (544) all_10_0 = 0 % 12.82/2.55 | | | | | | | % 12.82/2.55 | | | | | | | REDUCE: (543), (544) imply: % 12.82/2.55 | | | | | | | (545) $false % 12.82/2.55 | | | | | | | % 12.82/2.55 | | | | | | | CLOSE: (545) is inconsistent. % 12.82/2.55 | | | | | | | % 12.82/2.55 | | | | | | Case 2: % 12.82/2.55 | | | | | | | % 12.82/2.55 | | | | | | | (546) all_24_0 = 0 % 12.82/2.55 | | | | | | | % 12.82/2.55 | | | | | | | REDUCE: (534), (546) imply: % 12.82/2.55 | | | | | | | (547) $false % 12.82/2.55 | | | | | | | % 12.82/2.55 | | | | | | | CLOSE: (547) is inconsistent. % 12.82/2.55 | | | | | | | % 12.82/2.55 | | | | | | End of split % 12.82/2.55 | | | | | | % 12.82/2.55 | | | | | Case 2: % 12.82/2.55 | | | | | | % 12.82/2.55 | | | | | | (548) ! [v0: $i] : ( ~ (big_p(v0) = 0) | ~ $i(v0)) & ? [v0: % 12.82/2.55 | | | | | | $i] : ? [v1: int] : ( ~ (v1 = 0) & big_q(v0) = v1 & % 12.82/2.55 | | | | | | $i(v0)) % 12.82/2.55 | | | | | | % 12.82/2.55 | | | | | | ALPHA: (548) implies: % 12.82/2.56 | | | | | | (549) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & big_q(v0) = v1 % 12.82/2.56 | | | | | | & $i(v0)) % 12.82/2.56 | | | | | | % 12.82/2.56 | | | | | | REF_CLOSE: (509), (531), (549) are inconsistent by sub-proof #2. % 12.82/2.56 | | | | | | % 12.82/2.56 | | | | | End of split % 12.82/2.56 | | | | | % 12.82/2.56 | | | | End of split % 12.82/2.56 | | | | % 12.82/2.56 | | | Case 2: % 12.82/2.56 | | | | % 12.82/2.56 | | | | (550) ? [v0: $i] : ? [v1: any] : (big_q(v0) = v1 & $i(v0) & ! [v2: % 12.82/2.56 | | | | $i] : ! [v3: int] : ( ~ (v1 = 0) | v3 = 0 | ~ (big_q(v2) % 12.82/2.56 | | | | = v3) | ~ $i(v2)) & ! [v2: $i] : (v1 = 0 | ~ % 12.82/2.56 | | | | (big_q(v2) = 0) | ~ $i(v2))) & (( ! [v0: $i] : ! [v1: % 12.82/2.56 | | | | int] : (v1 = 0 | ~ (big_q(v0) = v1) | ~ $i(v0)) & ! % 12.82/2.56 | | | | [v0: $i] : ( ~ (big_p(v0) = 0) | ~ $i(v0))) | ( ? [v0: $i] % 12.82/2.56 | | | | : ? [v1: int] : ( ~ (v1 = 0) & big_q(v0) = v1 & $i(v0)) & % 12.82/2.56 | | | | ? [v0: $i] : (big_p(v0) = 0 & $i(v0)))) % 12.82/2.56 | | | | % 12.82/2.56 | | | | ALPHA: (550) implies: % 12.82/2.56 | | | | (551) ( ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (big_q(v0) = v1) | % 12.82/2.56 | | | | ~ $i(v0)) & ! [v0: $i] : ( ~ (big_p(v0) = 0) | ~ $i(v0))) % 12.82/2.56 | | | | | ( ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & big_q(v0) = v1 & % 12.82/2.56 | | | | $i(v0)) & ? [v0: $i] : (big_p(v0) = 0 & $i(v0))) % 12.82/2.56 | | | | (552) ? [v0: $i] : ? [v1: any] : (big_q(v0) = v1 & $i(v0) & ! [v2: % 12.82/2.56 | | | | $i] : ! [v3: int] : ( ~ (v1 = 0) | v3 = 0 | ~ (big_q(v2) % 12.82/2.56 | | | | = v3) | ~ $i(v2)) & ! [v2: $i] : (v1 = 0 | ~ % 12.82/2.56 | | | | (big_q(v2) = 0) | ~ $i(v2))) % 12.82/2.56 | | | | % 12.82/2.56 | | | | DELTA: instantiating (552) with fresh symbols all_19_0, all_19_1 gives: % 12.82/2.56 | | | | (553) big_q(all_19_1) = all_19_0 & $i(all_19_1) & ! [v0: $i] : ! % 12.82/2.56 | | | | [v1: int] : ( ~ (all_19_0 = 0) | v1 = 0 | ~ (big_q(v0) = v1) | % 12.82/2.56 | | | | ~ $i(v0)) & ! [v0: $i] : (all_19_0 = 0 | ~ (big_q(v0) = 0) % 12.82/2.56 | | | | | ~ $i(v0)) % 12.82/2.56 | | | | % 12.82/2.56 | | | | ALPHA: (553) implies: % 12.82/2.56 | | | | (554) $i(all_19_1) % 12.82/2.56 | | | | (555) big_q(all_19_1) = all_19_0 % 12.82/2.56 | | | | (556) ! [v0: $i] : (all_19_0 = 0 | ~ (big_q(v0) = 0) | ~ $i(v0)) % 12.82/2.56 | | | | (557) ! [v0: $i] : ! [v1: int] : ( ~ (all_19_0 = 0) | v1 = 0 | ~ % 12.82/2.56 | | | | (big_q(v0) = v1) | ~ $i(v0)) % 12.82/2.56 | | | | % 12.82/2.56 | | | | BETA: splitting (500) gives: % 12.82/2.56 | | | | % 12.82/2.56 | | | | Case 1: % 12.82/2.56 | | | | | % 12.82/2.56 | | | | | (558) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (big_p(v0) = v1) | % 12.82/2.56 | | | | | ~ $i(v0)) & ? [v0: $i] : (big_q(v0) = 0 & $i(v0)) % 12.82/2.56 | | | | | % 12.82/2.56 | | | | | ALPHA: (558) implies: % 12.82/2.56 | | | | | (559) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (big_p(v0) = v1) | % 12.82/2.56 | | | | | ~ $i(v0)) % 12.82/2.56 | | | | | (560) ? [v0: $i] : (big_q(v0) = 0 & $i(v0)) % 12.82/2.56 | | | | | % 12.82/2.56 | | | | | GROUND_INST: instantiating (559) with all_10_1, all_10_0, simplifying % 12.82/2.56 | | | | | with (503), (504) gives: % 12.82/2.56 | | | | | (561) all_10_0 = 0 % 12.82/2.56 | | | | | % 12.82/2.56 | | | | | DELTA: instantiating (560) with fresh symbol all_30_0 gives: % 12.82/2.56 | | | | | (562) big_q(all_30_0) = 0 & $i(all_30_0) % 12.82/2.56 | | | | | % 12.82/2.56 | | | | | ALPHA: (562) implies: % 12.82/2.56 | | | | | (563) $i(all_30_0) % 12.82/2.56 | | | | | (564) big_q(all_30_0) = 0 % 12.82/2.56 | | | | | % 12.82/2.56 | | | | | REDUCE: (504), (561) imply: % 12.82/2.56 | | | | | (565) big_p(all_10_1) = 0 % 12.82/2.56 | | | | | % 12.82/2.56 | | | | | GROUND_INST: instantiating (556) with all_30_0, simplifying with % 12.82/2.56 | | | | | (563), (564) gives: % 12.82/2.56 | | | | | (566) all_19_0 = 0 % 12.82/2.56 | | | | | % 12.82/2.56 | | | | | BETA: splitting (551) gives: % 12.82/2.56 | | | | | % 12.82/2.56 | | | | | Case 1: % 12.82/2.56 | | | | | | % 12.82/2.56 | | | | | | (567) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (big_q(v0) = v1) % 12.82/2.56 | | | | | | | ~ $i(v0)) & ! [v0: $i] : ( ~ (big_p(v0) = 0) | ~ % 12.82/2.56 | | | | | | $i(v0)) % 12.82/2.56 | | | | | | % 12.82/2.56 | | | | | | ALPHA: (567) implies: % 12.82/2.56 | | | | | | (568) ! [v0: $i] : ( ~ (big_p(v0) = 0) | ~ $i(v0)) % 12.82/2.56 | | | | | | % 12.82/2.56 | | | | | | GROUND_INST: instantiating (568) with all_10_1, simplifying with % 12.82/2.56 | | | | | | (503), (565) gives: % 12.82/2.56 | | | | | | (569) $false % 12.82/2.56 | | | | | | % 12.82/2.56 | | | | | | CLOSE: (569) is inconsistent. % 12.82/2.56 | | | | | | % 12.82/2.56 | | | | | Case 2: % 12.82/2.56 | | | | | | % 12.82/2.56 | | | | | | (570) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & big_q(v0) = v1 % 12.82/2.56 | | | | | | & $i(v0)) & ? [v0: $i] : (big_p(v0) = 0 & $i(v0)) % 12.82/2.56 | | | | | | % 12.82/2.56 | | | | | | ALPHA: (570) implies: % 12.82/2.56 | | | | | | (571) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & big_q(v0) = v1 % 12.82/2.56 | | | | | | & $i(v0)) % 12.82/2.56 | | | | | | % 12.82/2.56 | | | | | | DELTA: instantiating (571) with fresh symbols all_46_0, all_46_1 % 12.82/2.56 | | | | | | gives: % 12.82/2.56 | | | | | | (572) ~ (all_46_0 = 0) & big_q(all_46_1) = all_46_0 & % 12.82/2.56 | | | | | | $i(all_46_1) % 12.82/2.56 | | | | | | % 12.82/2.56 | | | | | | ALPHA: (572) implies: % 12.82/2.56 | | | | | | (573) ~ (all_46_0 = 0) % 12.82/2.56 | | | | | | (574) $i(all_46_1) % 12.82/2.56 | | | | | | (575) big_q(all_46_1) = all_46_0 % 12.82/2.56 | | | | | | % 12.82/2.56 | | | | | | GROUND_INST: instantiating (557) with all_46_1, all_46_0, % 12.82/2.56 | | | | | | simplifying with (574), (575) gives: % 12.82/2.56 | | | | | | (576) ~ (all_19_0 = 0) | all_46_0 = 0 % 12.82/2.56 | | | | | | % 12.82/2.56 | | | | | | BETA: splitting (576) gives: % 12.82/2.56 | | | | | | % 12.82/2.56 | | | | | | Case 1: % 12.82/2.56 | | | | | | | % 12.82/2.56 | | | | | | | (577) ~ (all_19_0 = 0) % 12.82/2.56 | | | | | | | % 12.82/2.56 | | | | | | | REDUCE: (566), (577) imply: % 12.82/2.56 | | | | | | | (578) $false % 12.82/2.56 | | | | | | | % 12.82/2.56 | | | | | | | CLOSE: (578) is inconsistent. % 12.82/2.56 | | | | | | | % 12.82/2.56 | | | | | | Case 2: % 12.82/2.56 | | | | | | | % 12.82/2.56 | | | | | | | (579) all_46_0 = 0 % 12.82/2.56 | | | | | | | % 12.82/2.56 | | | | | | | REDUCE: (573), (579) imply: % 12.82/2.56 | | | | | | | (580) $false % 12.82/2.56 | | | | | | | % 12.82/2.56 | | | | | | | CLOSE: (580) is inconsistent. % 12.82/2.56 | | | | | | | % 12.82/2.56 | | | | | | End of split % 12.82/2.56 | | | | | | % 12.82/2.56 | | | | | End of split % 12.82/2.56 | | | | | % 12.82/2.56 | | | | Case 2: % 12.82/2.56 | | | | | % 12.82/2.56 | | | | | (581) ! [v0: $i] : ( ~ (big_q(v0) = 0) | ~ $i(v0)) & ? [v0: $i] % 12.82/2.56 | | | | | : ? [v1: int] : ( ~ (v1 = 0) & big_p(v0) = v1 & $i(v0)) % 12.82/2.56 | | | | | % 12.82/2.56 | | | | | ALPHA: (581) implies: % 12.82/2.56 | | | | | (582) ! [v0: $i] : ( ~ (big_q(v0) = 0) | ~ $i(v0)) % 12.82/2.56 | | | | | (583) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & big_p(v0) = v1 & % 12.82/2.56 | | | | | $i(v0)) % 12.82/2.56 | | | | | % 12.82/2.56 | | | | | DELTA: instantiating (583) with fresh symbols all_29_0, all_29_1 % 12.82/2.56 | | | | | gives: % 12.82/2.56 | | | | | (584) ~ (all_29_0 = 0) & big_p(all_29_1) = all_29_0 & $i(all_29_1) % 12.82/2.56 | | | | | % 12.82/2.56 | | | | | ALPHA: (584) implies: % 12.82/2.56 | | | | | (585) ~ (all_29_0 = 0) % 12.82/2.56 | | | | | (586) $i(all_29_1) % 12.82/2.56 | | | | | (587) big_p(all_29_1) = all_29_0 % 12.82/2.56 | | | | | % 12.82/2.56 | | | | | GROUND_INST: instantiating (506) with all_29_1, all_29_0, simplifying % 12.82/2.56 | | | | | with (586), (587) gives: % 12.82/2.56 | | | | | (588) ~ (all_10_0 = 0) | all_29_0 = 0 % 12.82/2.56 | | | | | % 12.82/2.56 | | | | | BETA: splitting (551) gives: % 12.82/2.56 | | | | | % 12.82/2.56 | | | | | Case 1: % 12.82/2.56 | | | | | | % 12.82/2.56 | | | | | | (589) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (big_q(v0) = v1) % 12.82/2.56 | | | | | | | ~ $i(v0)) & ! [v0: $i] : ( ~ (big_p(v0) = 0) | ~ % 12.82/2.56 | | | | | | $i(v0)) % 12.82/2.56 | | | | | | % 12.82/2.56 | | | | | | ALPHA: (589) implies: % 12.82/2.56 | | | | | | (590) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (big_q(v0) = v1) % 12.82/2.56 | | | | | | | ~ $i(v0)) % 12.82/2.56 | | | | | | % 12.82/2.56 | | | | | | GROUND_INST: instantiating (590) with all_19_1, all_19_0, % 12.82/2.56 | | | | | | simplifying with (554), (555) gives: % 12.82/2.56 | | | | | | (591) all_19_0 = 0 % 12.82/2.56 | | | | | | % 12.82/2.56 | | | | | | REDUCE: (555), (591) imply: % 12.82/2.56 | | | | | | (592) big_q(all_19_1) = 0 % 12.82/2.56 | | | | | | % 12.82/2.56 | | | | | | GROUND_INST: instantiating (582) with all_19_1, simplifying with % 12.82/2.56 | | | | | | (554), (592) gives: % 12.82/2.56 | | | | | | (593) $false % 12.82/2.56 | | | | | | % 12.82/2.56 | | | | | | CLOSE: (593) is inconsistent. % 12.82/2.56 | | | | | | % 12.82/2.56 | | | | | Case 2: % 12.82/2.56 | | | | | | % 12.82/2.56 | | | | | | (594) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & big_q(v0) = v1 % 12.82/2.56 | | | | | | & $i(v0)) & ? [v0: $i] : (big_p(v0) = 0 & $i(v0)) % 12.82/2.56 | | | | | | % 12.82/2.56 | | | | | | ALPHA: (594) implies: % 12.82/2.56 | | | | | | (595) ? [v0: $i] : (big_p(v0) = 0 & $i(v0)) % 12.82/2.56 | | | | | | % 12.82/2.56 | | | | | | DELTA: instantiating (595) with fresh symbol all_37_0 gives: % 12.82/2.56 | | | | | | (596) big_p(all_37_0) = 0 & $i(all_37_0) % 12.82/2.56 | | | | | | % 12.82/2.56 | | | | | | ALPHA: (596) implies: % 12.82/2.56 | | | | | | (597) $i(all_37_0) % 12.82/2.56 | | | | | | (598) big_p(all_37_0) = 0 % 12.82/2.56 | | | | | | % 12.82/2.56 | | | | | | BETA: splitting (588) gives: % 12.82/2.56 | | | | | | % 12.82/2.56 | | | | | | Case 1: % 12.82/2.56 | | | | | | | % 12.82/2.56 | | | | | | | (599) ~ (all_10_0 = 0) % 12.82/2.56 | | | | | | | % 12.82/2.56 | | | | | | | GROUND_INST: instantiating (505) with all_37_0, simplifying with % 12.82/2.56 | | | | | | | (597), (598) gives: % 12.82/2.56 | | | | | | | (600) all_10_0 = 0 % 12.82/2.56 | | | | | | | % 12.82/2.56 | | | | | | | REDUCE: (599), (600) imply: % 12.82/2.56 | | | | | | | (601) $false % 12.82/2.56 | | | | | | | % 12.82/2.56 | | | | | | | CLOSE: (601) is inconsistent. % 12.82/2.56 | | | | | | | % 12.82/2.56 | | | | | | Case 2: % 12.82/2.56 | | | | | | | % 12.82/2.56 | | | | | | | (602) all_29_0 = 0 % 12.82/2.56 | | | | | | | % 12.82/2.56 | | | | | | | REDUCE: (585), (602) imply: % 12.82/2.56 | | | | | | | (603) $false % 12.82/2.56 | | | | | | | % 12.82/2.56 | | | | | | | CLOSE: (603) is inconsistent. % 12.82/2.56 | | | | | | | % 12.82/2.56 | | | | | | End of split % 12.82/2.56 | | | | | | % 12.82/2.56 | | | | | End of split % 12.82/2.56 | | | | | % 12.82/2.56 | | | | End of split % 12.82/2.56 | | | | % 12.82/2.56 | | | End of split % 12.82/2.56 | | | % 12.82/2.56 | | End of split % 12.82/2.56 | | % 12.82/2.56 | End of split % 12.82/2.56 | % 12.82/2.56 End of proof % 12.82/2.56 % 12.82/2.56 Sub-proof #1 shows that the following formulas are inconsistent: % 12.82/2.56 ---------------------------------------------------------------- % 12.82/2.56 (1) ? [v0: $i] : (big_p(v0) = 0 & $i(v0)) % 13.12/2.56 (2) ! [v0: $i] : (all_10_0 = 0 | ~ (big_p(v0) = 0) | ~ $i(v0)) % 13.12/2.56 (3) ~ (all_10_0 = 0) % 13.12/2.56 % 13.12/2.56 Begin of proof % 13.12/2.56 | % 13.12/2.56 | DELTA: instantiating (1) with fresh symbol all_133_0 gives: % 13.12/2.56 | (4) big_p(all_133_0) = 0 & $i(all_133_0) % 13.12/2.56 | % 13.12/2.56 | ALPHA: (4) implies: % 13.12/2.56 | (5) $i(all_133_0) % 13.12/2.56 | (6) big_p(all_133_0) = 0 % 13.12/2.56 | % 13.12/2.56 | GROUND_INST: instantiating (2) with all_133_0, simplifying with (5), (6) % 13.12/2.56 | gives: % 13.12/2.56 | (7) all_10_0 = 0 % 13.12/2.56 | % 13.12/2.56 | REDUCE: (3), (7) imply: % 13.12/2.56 | (8) $false % 13.12/2.56 | % 13.12/2.56 | CLOSE: (8) is inconsistent. % 13.12/2.56 | % 13.12/2.56 End of proof % 13.12/2.56 % 13.12/2.56 Sub-proof #2 shows that the following formulas are inconsistent: % 13.12/2.56 ---------------------------------------------------------------- % 13.12/2.56 (1) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & big_q(v0) = v1 & $i(v0)) % 13.12/2.56 (2) ! [v0: $i] : ! [v1: any] : ( ~ (big_q(v0) = v1) | ~ $i(v0) | ? [v2: % 13.12/2.56 $i] : ? [v3: any] : (big_q(v2) = v3 & $i(v2) & ( ~ (v3 = 0) | ~ (v1 % 13.12/2.56 = 0)) & (v3 = 0 | v1 = 0))) % 13.12/2.56 (3) ! [v0: $i] : ( ~ (big_q(v0) = 0) | ~ $i(v0)) % 13.12/2.56 % 13.12/2.56 Begin of proof % 13.12/2.57 | % 13.12/2.57 | DELTA: instantiating (1) with fresh symbols all_23_0, all_23_1 gives: % 13.12/2.57 | (4) ~ (all_23_0 = 0) & big_q(all_23_1) = all_23_0 & $i(all_23_1) % 13.12/2.57 | % 13.12/2.57 | ALPHA: (4) implies: % 13.12/2.57 | (5) ~ (all_23_0 = 0) % 13.12/2.57 | (6) $i(all_23_1) % 13.12/2.57 | (7) big_q(all_23_1) = all_23_0 % 13.12/2.57 | % 13.12/2.57 | GROUND_INST: instantiating (2) with all_23_1, all_23_0, simplifying with (6), % 13.12/2.57 | (7) gives: % 13.12/2.57 | (8) ? [v0: $i] : ? [v1: any] : (big_q(v0) = v1 & $i(v0) & ( ~ (v1 = 0) | % 13.12/2.57 | ~ (all_23_0 = 0)) & (v1 = 0 | all_23_0 = 0)) % 13.12/2.57 | % 13.12/2.57 | DELTA: instantiating (8) with fresh symbols all_30_0, all_30_1 gives: % 13.12/2.57 | (9) big_q(all_30_1) = all_30_0 & $i(all_30_1) & ( ~ (all_30_0 = 0) | ~ % 13.12/2.57 | (all_23_0 = 0)) & (all_30_0 = 0 | all_23_0 = 0) % 13.12/2.57 | % 13.12/2.57 | ALPHA: (9) implies: % 13.12/2.57 | (10) $i(all_30_1) % 13.12/2.57 | (11) big_q(all_30_1) = all_30_0 % 13.12/2.57 | (12) all_30_0 = 0 | all_23_0 = 0 % 13.12/2.57 | % 13.12/2.57 | BETA: splitting (12) gives: % 13.12/2.57 | % 13.12/2.57 | Case 1: % 13.12/2.57 | | % 13.12/2.57 | | (13) all_30_0 = 0 % 13.12/2.57 | | % 13.12/2.57 | | REDUCE: (11), (13) imply: % 13.12/2.57 | | (14) big_q(all_30_1) = 0 % 13.12/2.57 | | % 13.12/2.57 | | GROUND_INST: instantiating (3) with all_30_1, simplifying with (10), (14) % 13.12/2.57 | | gives: % 13.12/2.57 | | (15) $false % 13.12/2.57 | | % 13.12/2.57 | | CLOSE: (15) is inconsistent. % 13.12/2.57 | | % 13.12/2.57 | Case 2: % 13.12/2.57 | | % 13.12/2.57 | | (16) all_23_0 = 0 % 13.12/2.57 | | % 13.12/2.57 | | REDUCE: (5), (16) imply: % 13.12/2.57 | | (17) $false % 13.12/2.57 | | % 13.12/2.57 | | CLOSE: (17) is inconsistent. % 13.12/2.57 | | % 13.12/2.57 | End of split % 13.12/2.57 | % 13.12/2.57 End of proof % 13.12/2.57 % 13.12/2.57 Sub-proof #3 shows that the following formulas are inconsistent: % 13.12/2.57 ---------------------------------------------------------------- % 13.12/2.57 (1) ? [v0: $i] : (big_p(v0) = 0 & $i(v0)) % 13.12/2.57 (2) ! [v0: $i] : ! [v1: any] : ( ~ (big_p(v0) = v1) | ~ $i(v0) | ? [v2: % 13.12/2.57 $i] : ? [v3: any] : (big_p(v2) = v3 & $i(v2) & ( ~ (v3 = 0) | ~ (v1 % 13.12/2.57 = 0)) & (v3 = 0 | v1 = 0))) % 13.12/2.57 (3) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (big_p(v0) = v1) | ~ $i(v0)) % 13.12/2.57 % 13.12/2.57 Begin of proof % 13.12/2.57 | % 13.12/2.57 | DELTA: instantiating (1) with fresh symbol all_23_0 gives: % 13.12/2.57 | (4) big_p(all_23_0) = 0 & $i(all_23_0) % 13.12/2.57 | % 13.12/2.57 | ALPHA: (4) implies: % 13.12/2.57 | (5) $i(all_23_0) % 13.12/2.57 | (6) big_p(all_23_0) = 0 % 13.12/2.57 | % 13.12/2.57 | GROUND_INST: instantiating (2) with all_23_0, 0, simplifying with (5), (6) % 13.12/2.57 | gives: % 13.12/2.57 | (7) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & big_p(v0) = v1 & $i(v0)) % 13.12/2.57 | % 13.12/2.57 | DELTA: instantiating (7) with fresh symbols all_30_0, all_30_1 gives: % 13.12/2.57 | (8) ~ (all_30_0 = 0) & big_p(all_30_1) = all_30_0 & $i(all_30_1) % 13.12/2.57 | % 13.12/2.57 | ALPHA: (8) implies: % 13.12/2.57 | (9) ~ (all_30_0 = 0) % 13.12/2.57 | (10) $i(all_30_1) % 13.12/2.57 | (11) big_p(all_30_1) = all_30_0 % 13.12/2.57 | % 13.12/2.57 | GROUND_INST: instantiating (3) with all_30_1, all_30_0, simplifying with (10), % 13.12/2.57 | (11) gives: % 13.12/2.57 | (12) all_30_0 = 0 % 13.12/2.57 | % 13.12/2.57 | REDUCE: (9), (12) imply: % 13.12/2.57 | (13) $false % 13.12/2.57 | % 13.12/2.57 | CLOSE: (13) is inconsistent. % 13.12/2.57 | % 13.12/2.57 End of proof % 13.12/2.57 % SZS output end Proof for theBenchmark % 13.12/2.57 % 13.12/2.57 1956ms %------------------------------------------------------------------------------