%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SYN036+1 : TPTP v8.1.2. Released v2.0.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n032.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 7.68s 1.78s % Output : Proof 9.52s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.10 % Problem : SYN036+1 : TPTP v8.1.2. Released v2.0.0. % 0.00/0.10 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.10/0.30 % Computer : n032.cluster.edu % 0.10/0.30 % Model : x86_64 x86_64 % 0.10/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.10/0.30 % Memory : 8042.1875MB % 0.10/0.30 % OS : Linux 3.10.0-693.el7.x86_64 % 0.10/0.30 % CPULimit : 300 % 0.10/0.30 % WCLimit : 300 % 0.10/0.30 % DateTime : Sat Aug 26 16:53:29 EDT 2023 % 0.10/0.30 % CPUTime : % 0.15/0.51 ________ _____ % 0.15/0.51 ___ __ \_________(_)________________________________ % 0.15/0.51 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.15/0.51 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.15/0.51 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.15/0.51 % 0.15/0.51 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.15/0.51 (2023-06-19) % 0.15/0.51 % 0.15/0.51 (c) Philipp Rümmer, 2009-2023 % 0.15/0.51 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.15/0.51 Amanda Stjerna. % 0.15/0.51 Free software under BSD-3-Clause. % 0.15/0.51 % 0.15/0.51 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.15/0.51 % 0.15/0.51 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.15/0.52 Running up to 7 provers in parallel. % 0.15/0.53 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.15/0.53 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.15/0.53 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.15/0.53 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.15/0.53 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.15/0.53 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.15/0.53 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 1.50/0.86 Prover 4: Preprocessing ... % 1.50/0.86 Prover 1: Preprocessing ... % 1.92/0.91 Prover 3: Preprocessing ... % 1.92/0.91 Prover 2: Preprocessing ... % 1.92/0.91 Prover 6: Preprocessing ... % 1.92/0.91 Prover 5: Preprocessing ... % 1.92/0.91 Prover 0: Preprocessing ... % 3.59/1.13 Prover 2: Proving ... % 3.59/1.17 Prover 5: Proving ... % 3.59/1.17 Prover 0: Proving ... % 3.59/1.18 Prover 1: Constructing countermodel ... % 3.59/1.18 Prover 3: Constructing countermodel ... % 3.59/1.19 Prover 4: Constructing countermodel ... % 3.59/1.20 Prover 6: Proving ... % 7.68/1.78 Prover 3: proved (1250ms) % 7.68/1.78 % 7.68/1.78 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 7.68/1.78 % 7.68/1.78 Prover 6: stopped % 7.68/1.78 Prover 2: stopped % 7.68/1.78 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 7.68/1.78 Prover 0: stopped % 8.36/1.80 Prover 5: stopped % 8.36/1.80 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 8.36/1.80 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 8.36/1.80 Prover 8: Preprocessing ... % 8.36/1.80 Prover 7: Preprocessing ... % 8.36/1.80 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 8.36/1.80 Prover 10: Preprocessing ... % 8.36/1.80 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 8.36/1.81 Prover 11: Preprocessing ... % 8.36/1.81 Prover 13: Preprocessing ... % 8.36/1.82 Prover 4: Found proof (size 157) % 8.36/1.82 Prover 4: proved (1295ms) % 8.36/1.82 Prover 1: stopped % 8.36/1.83 Prover 7: Warning: ignoring some quantifiers % 8.36/1.83 Prover 7: Constructing countermodel ... % 8.36/1.84 Prover 7: stopped % 8.36/1.84 Prover 13: Warning: ignoring some quantifiers % 8.36/1.84 Prover 13: Constructing countermodel ... % 8.36/1.84 Prover 10: Warning: ignoring some quantifiers % 8.36/1.84 Prover 13: stopped % 8.36/1.84 Prover 10: Constructing countermodel ... % 8.36/1.85 Prover 10: stopped % 8.36/1.85 Prover 11: stopped % 8.36/1.88 Prover 8: Warning: ignoring some quantifiers % 8.36/1.88 Prover 8: Constructing countermodel ... % 8.36/1.89 Prover 8: stopped % 8.36/1.89 % 8.36/1.89 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 8.36/1.89 % 9.01/1.90 % SZS output start Proof for theBenchmark % 9.03/1.90 Assumptions after simplification: % 9.03/1.90 --------------------------------- % 9.03/1.90 % 9.03/1.90 (pel34) % 9.03/1.96 ? [v0: $i] : ? [v1: int] : ? [v2: $i] : ? [v3: int] : ? [v4: $i] : ? % 9.03/1.96 [v5: int] : ? [v6: $i] : ? [v7: int] : ? [v8: $i] : ? [v9: any] : ? [v10: % 9.03/1.96 $i] : ? [v11: int] : ? [v12: $i] : ? [v13: int] : ? [v14: $i] : ? [v15: % 9.03/1.96 int] : ? [v16: $i] : ? [v17: int] : ? [v18: $i] : ? [v19: any] : ? % 9.03/1.96 [v20: $i] : ? [v21: int] : ? [v22: $i] : ? [v23: int] : ? [v24: $i] : ? % 9.03/1.96 [v25: int] : ? [v26: $i] : ? [v27: int] : ? [v28: $i] : ? [v29: any] : ? % 9.03/1.96 [v30: $i] : ? [v31: int] : ? [v32: $i] : ? [v33: int] : ? [v34: $i] : ? % 9.03/1.96 [v35: int] : ? [v36: $i] : ? [v37: int] : ? [v38: $i] : ? [v39: any] : % 9.03/1.96 ($i(v38) & $i(v36) & $i(v34) & $i(v32) & $i(v30) & $i(v28) & $i(v26) & $i(v24) % 9.03/1.96 & $i(v22) & $i(v20) & $i(v18) & $i(v16) & $i(v14) & $i(v12) & $i(v10) & % 9.03/1.96 $i(v8) & $i(v6) & $i(v4) & $i(v2) & $i(v0) & ((((big_q(v28) = v29 & ! [v40: % 9.03/1.96 $i] : ! [v41: int] : ( ~ (v29 = 0) | v41 = 0 | ~ (big_q(v40) = % 9.03/1.96 v41) | ~ $i(v40)) & ! [v40: $i] : (v29 = 0 | ~ (big_q(v40) = % 9.03/1.96 0) | ~ $i(v40)) & ((v27 = 0 & ~ (v25 = 0) & big_p(v26) = 0 & % 9.03/1.96 big_p(v24) = v25) | ( ! [v40: $i] : ! [v41: int] : (v41 = 0 | % 9.03/1.96 ~ (big_p(v40) = v41) | ~ $i(v40)) & ! [v40: $i] : ( ~ % 9.03/1.96 (big_p(v40) = 0) | ~ $i(v40))))) | ( ! [v40: $i] : ! [v41: % 9.03/1.96 any] : ( ~ (big_q(v40) = v41) | ~ $i(v40) | ? [v42: $i] : ? % 9.03/1.96 [v43: any] : (big_q(v42) = v43 & $i(v42) & ( ~ (v43 = 0) | ~ (v41 % 9.03/1.96 = 0)) & (v43 = 0 | v41 = 0))) & ((v23 = 0 & big_p(v22) = 0 & % 9.03/1.96 ! [v40: $i] : ! [v41: int] : (v41 = 0 | ~ (big_p(v40) = v41) % 9.03/1.96 | ~ $i(v40))) | ( ~ (v21 = 0) & big_p(v20) = v21 & ! [v40: % 9.03/1.96 $i] : ( ~ (big_p(v40) = 0) | ~ $i(v40)))))) & ((big_p(v38) = % 9.03/1.96 v39 & ! [v40: $i] : ! [v41: int] : ( ~ (v39 = 0) | v41 = 0 | ~ % 9.03/1.96 (big_p(v40) = v41) | ~ $i(v40)) & ! [v40: $i] : (v39 = 0 | ~ % 9.03/1.96 (big_p(v40) = 0) | ~ $i(v40)) & ((v37 = 0 & big_q(v36) = 0 & ! % 9.03/1.96 [v40: $i] : ! [v41: int] : (v41 = 0 | ~ (big_q(v40) = v41) | % 9.03/1.96 ~ $i(v40))) | ( ~ (v35 = 0) & big_q(v34) = v35 & ! [v40: $i] % 9.03/1.96 : ( ~ (big_q(v40) = 0) | ~ $i(v40))))) | ( ! [v40: $i] : ! % 9.03/1.96 [v41: any] : ( ~ (big_p(v40) = v41) | ~ $i(v40) | ? [v42: $i] : ? % 9.03/1.96 [v43: any] : (big_p(v42) = v43 & $i(v42) & ( ~ (v43 = 0) | ~ (v41 % 9.03/1.96 = 0)) & (v43 = 0 | v41 = 0))) & ((v33 = 0 & ~ (v31 = 0) & % 9.03/1.96 big_q(v32) = 0 & big_q(v30) = v31) | ( ! [v40: $i] : ! [v41: % 9.03/1.96 int] : (v41 = 0 | ~ (big_q(v40) = v41) | ~ $i(v40)) & ! % 9.03/1.96 [v40: $i] : ( ~ (big_q(v40) = 0) | ~ $i(v40))))))) | % 9.03/1.96 (((big_q(v18) = v19 & ! [v40: $i] : ! [v41: int] : ( ~ (v19 = 0) | v41 = % 9.03/1.96 0 | ~ (big_q(v40) = v41) | ~ $i(v40)) & ! [v40: $i] : (v19 = 0 % 9.03/1.96 | ~ (big_q(v40) = 0) | ~ $i(v40)) & ((v17 = 0 & big_p(v16) = 0 & % 9.03/1.96 ! [v40: $i] : ! [v41: int] : (v41 = 0 | ~ (big_p(v40) = v41) % 9.03/1.96 | ~ $i(v40))) | ( ~ (v15 = 0) & big_p(v14) = v15 & ! [v40: % 9.03/1.96 $i] : ( ~ (big_p(v40) = 0) | ~ $i(v40))))) | ( ! [v40: $i] : % 9.03/1.96 ! [v41: any] : ( ~ (big_q(v40) = v41) | ~ $i(v40) | ? [v42: $i] : % 9.03/1.96 ? [v43: any] : (big_q(v42) = v43 & $i(v42) & ( ~ (v43 = 0) | ~ % 9.03/1.96 (v41 = 0)) & (v43 = 0 | v41 = 0))) & ((v13 = 0 & ~ (v11 = 0) % 9.03/1.96 & big_p(v12) = 0 & big_p(v10) = v11) | ( ! [v40: $i] : ! [v41: % 9.03/1.96 int] : (v41 = 0 | ~ (big_p(v40) = v41) | ~ $i(v40)) & ! % 9.03/1.96 [v40: $i] : ( ~ (big_p(v40) = 0) | ~ $i(v40)))))) & ((big_p(v8) % 9.03/1.96 = v9 & ! [v40: $i] : ! [v41: int] : ( ~ (v9 = 0) | v41 = 0 | ~ % 9.03/1.96 (big_p(v40) = v41) | ~ $i(v40)) & ! [v40: $i] : (v9 = 0 | ~ % 9.03/1.96 (big_p(v40) = 0) | ~ $i(v40)) & ((v7 = 0 & ~ (v5 = 0) & % 9.03/1.96 big_q(v6) = 0 & big_q(v4) = v5) | ( ! [v40: $i] : ! [v41: int] % 9.03/1.96 : (v41 = 0 | ~ (big_q(v40) = v41) | ~ $i(v40)) & ! [v40: $i] % 9.03/1.96 : ( ~ (big_q(v40) = 0) | ~ $i(v40))))) | ( ! [v40: $i] : ! % 9.03/1.96 [v41: any] : ( ~ (big_p(v40) = v41) | ~ $i(v40) | ? [v42: $i] : ? % 9.03/1.96 [v43: any] : (big_p(v42) = v43 & $i(v42) & ( ~ (v43 = 0) | ~ (v41 % 9.03/1.96 = 0)) & (v43 = 0 | v41 = 0))) & ((v3 = 0 & big_q(v2) = 0 & % 9.03/1.96 ! [v40: $i] : ! [v41: int] : (v41 = 0 | ~ (big_q(v40) = v41) | % 9.03/1.96 ~ $i(v40))) | ( ~ (v1 = 0) & big_q(v0) = v1 & ! [v40: $i] : % 9.03/1.96 ( ~ (big_q(v40) = 0) | ~ $i(v40))))))))) % 9.03/1.96 % 9.03/1.96 Those formulas are unsatisfiable: % 9.03/1.96 --------------------------------- % 9.03/1.96 % 9.03/1.96 Begin of proof % 9.03/1.96 | % 9.03/1.96 | DELTA: instantiating (pel34) with fresh symbols all_3_0, all_3_1, all_3_2, % 9.03/1.96 | all_3_3, all_3_4, all_3_5, all_3_6, all_3_7, all_3_8, all_3_9, % 9.03/1.96 | all_3_10, all_3_11, all_3_12, all_3_13, all_3_14, all_3_15, all_3_16, % 9.03/1.96 | all_3_17, all_3_18, all_3_19, all_3_20, all_3_21, all_3_22, all_3_23, % 9.03/1.96 | all_3_24, all_3_25, all_3_26, all_3_27, all_3_28, all_3_29, all_3_30, % 9.03/1.96 | all_3_31, all_3_32, all_3_33, all_3_34, all_3_35, all_3_36, all_3_37, % 9.03/1.96 | all_3_38, all_3_39 gives: % 9.03/1.97 | (1) $i(all_3_1) & $i(all_3_3) & $i(all_3_5) & $i(all_3_7) & $i(all_3_9) & % 9.03/1.97 | $i(all_3_11) & $i(all_3_13) & $i(all_3_15) & $i(all_3_17) & % 9.03/1.97 | $i(all_3_19) & $i(all_3_21) & $i(all_3_23) & $i(all_3_25) & % 9.03/1.97 | $i(all_3_27) & $i(all_3_29) & $i(all_3_31) & $i(all_3_33) & % 9.03/1.97 | $i(all_3_35) & $i(all_3_37) & $i(all_3_39) & ((((big_q(all_3_11) = % 9.03/1.97 | all_3_10 & ! [v0: $i] : ! [v1: int] : ( ~ (all_3_10 = 0) | v1 % 9.03/1.97 | = 0 | ~ (big_q(v0) = v1) | ~ $i(v0)) & ! [v0: $i] : % 9.03/1.97 | (all_3_10 = 0 | ~ (big_q(v0) = 0) | ~ $i(v0)) & ((all_3_12 = % 9.03/1.97 | 0 & ~ (all_3_14 = 0) & big_p(all_3_13) = 0 & % 9.03/1.97 | big_p(all_3_15) = all_3_14) | ( ! [v0: $i] : ! [v1: int] : % 9.03/1.97 | (v1 = 0 | ~ (big_p(v0) = v1) | ~ $i(v0)) & ! [v0: $i] : % 9.03/1.97 | ( ~ (big_p(v0) = 0) | ~ $i(v0))))) | ( ! [v0: $i] : ! % 9.03/1.97 | [v1: any] : ( ~ (big_q(v0) = v1) | ~ $i(v0) | ? [v2: $i] : ? % 9.03/1.97 | [v3: any] : (big_q(v2) = v3 & $i(v2) & ( ~ (v3 = 0) | ~ (v1 % 9.03/1.97 | = 0)) & (v3 = 0 | v1 = 0))) & ((all_3_16 = 0 & % 9.03/1.97 | big_p(all_3_17) = 0 & ! [v0: $i] : ! [v1: int] : (v1 = 0 % 9.03/1.97 | | ~ (big_p(v0) = v1) | ~ $i(v0))) | ( ~ (all_3_18 = 0) % 9.03/1.97 | & big_p(all_3_19) = all_3_18 & ! [v0: $i] : ( ~ (big_p(v0) % 9.03/1.97 | = 0) | ~ $i(v0)))))) & ((big_p(all_3_1) = all_3_0 & ! % 9.03/1.97 | [v0: $i] : ! [v1: int] : ( ~ (all_3_0 = 0) | v1 = 0 | ~ % 9.03/1.97 | (big_p(v0) = v1) | ~ $i(v0)) & ! [v0: $i] : (all_3_0 = 0 | % 9.03/1.97 | ~ (big_p(v0) = 0) | ~ $i(v0)) & ((all_3_2 = 0 & % 9.03/1.97 | big_q(all_3_3) = 0 & ! [v0: $i] : ! [v1: int] : (v1 = 0 | % 9.03/1.97 | ~ (big_q(v0) = v1) | ~ $i(v0))) | ( ~ (all_3_4 = 0) & % 9.03/1.97 | big_q(all_3_5) = all_3_4 & ! [v0: $i] : ( ~ (big_q(v0) = % 9.03/1.97 | 0) | ~ $i(v0))))) | ( ! [v0: $i] : ! [v1: any] : ( ~ % 9.03/1.97 | (big_p(v0) = v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: any] : % 9.03/1.97 | (big_p(v2) = v3 & $i(v2) & ( ~ (v3 = 0) | ~ (v1 = 0)) & (v3 % 9.03/1.97 | = 0 | v1 = 0))) & ((all_3_6 = 0 & ~ (all_3_8 = 0) & % 9.03/1.97 | big_q(all_3_7) = 0 & big_q(all_3_9) = all_3_8) | ( ! [v0: % 9.03/1.97 | $i] : ! [v1: int] : (v1 = 0 | ~ (big_q(v0) = v1) | ~ % 9.03/1.97 | $i(v0)) & ! [v0: $i] : ( ~ (big_q(v0) = 0) | ~ % 9.03/1.97 | $i(v0))))))) | (((big_q(all_3_21) = all_3_20 & ! [v0: % 9.03/1.97 | $i] : ! [v1: int] : ( ~ (all_3_20 = 0) | v1 = 0 | ~ % 9.03/1.97 | (big_q(v0) = v1) | ~ $i(v0)) & ! [v0: $i] : (all_3_20 = 0 | % 9.03/1.97 | ~ (big_q(v0) = 0) | ~ $i(v0)) & ((all_3_22 = 0 & % 9.03/1.97 | big_p(all_3_23) = 0 & ! [v0: $i] : ! [v1: int] : (v1 = 0 % 9.03/1.97 | | ~ (big_p(v0) = v1) | ~ $i(v0))) | ( ~ (all_3_24 = 0) % 9.03/1.97 | & big_p(all_3_25) = all_3_24 & ! [v0: $i] : ( ~ (big_p(v0) % 9.03/1.97 | = 0) | ~ $i(v0))))) | ( ! [v0: $i] : ! [v1: any] : ( % 9.03/1.97 | ~ (big_q(v0) = v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: any] : % 9.03/1.97 | (big_q(v2) = v3 & $i(v2) & ( ~ (v3 = 0) | ~ (v1 = 0)) & (v3 % 9.03/1.97 | = 0 | v1 = 0))) & ((all_3_26 = 0 & ~ (all_3_28 = 0) & % 9.03/1.97 | big_p(all_3_27) = 0 & big_p(all_3_29) = all_3_28) | ( ! % 9.03/1.97 | [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (big_p(v0) = v1) | % 9.03/1.97 | ~ $i(v0)) & ! [v0: $i] : ( ~ (big_p(v0) = 0) | ~ % 9.03/1.97 | $i(v0)))))) & ((big_p(all_3_31) = all_3_30 & ! [v0: $i] % 9.03/1.97 | : ! [v1: int] : ( ~ (all_3_30 = 0) | v1 = 0 | ~ (big_p(v0) = % 9.03/1.97 | v1) | ~ $i(v0)) & ! [v0: $i] : (all_3_30 = 0 | ~ % 9.03/1.97 | (big_p(v0) = 0) | ~ $i(v0)) & ((all_3_32 = 0 & ~ (all_3_34 % 9.03/1.97 | = 0) & big_q(all_3_33) = 0 & big_q(all_3_35) = all_3_34) % 9.03/1.97 | | ( ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (big_q(v0) = v1) % 9.03/1.97 | | ~ $i(v0)) & ! [v0: $i] : ( ~ (big_q(v0) = 0) | ~ % 9.03/1.97 | $i(v0))))) | ( ! [v0: $i] : ! [v1: any] : ( ~ (big_p(v0) % 9.03/1.97 | = v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: any] : (big_p(v2) % 9.03/1.97 | = v3 & $i(v2) & ( ~ (v3 = 0) | ~ (v1 = 0)) & (v3 = 0 | v1 % 9.03/1.97 | = 0))) & ((all_3_36 = 0 & big_q(all_3_37) = 0 & ! [v0: % 9.03/1.97 | $i] : ! [v1: int] : (v1 = 0 | ~ (big_q(v0) = v1) | ~ % 9.03/1.97 | $i(v0))) | ( ~ (all_3_38 = 0) & big_q(all_3_39) = % 9.03/1.97 | all_3_38 & ! [v0: $i] : ( ~ (big_q(v0) = 0) | ~ % 9.03/1.97 | $i(v0)))))))) % 9.03/1.97 | % 9.03/1.97 | ALPHA: (1) implies: % 9.03/1.98 | (2) $i(all_3_39) % 9.03/1.98 | (3) $i(all_3_37) % 9.03/1.98 | (4) $i(all_3_35) % 9.03/1.98 | (5) $i(all_3_33) % 9.03/1.98 | (6) $i(all_3_31) % 9.03/1.98 | (7) $i(all_3_29) % 9.03/1.98 | (8) $i(all_3_27) % 9.03/1.98 | (9) $i(all_3_25) % 9.03/1.98 | (10) $i(all_3_23) % 9.03/1.98 | (11) $i(all_3_21) % 9.03/1.98 | (12) $i(all_3_19) % 9.03/1.98 | (13) $i(all_3_17) % 9.03/1.98 | (14) $i(all_3_15) % 9.03/1.98 | (15) $i(all_3_13) % 9.03/1.98 | (16) $i(all_3_11) % 9.03/1.98 | (17) $i(all_3_9) % 9.03/1.98 | (18) $i(all_3_7) % 9.03/1.98 | (19) $i(all_3_5) % 9.03/1.98 | (20) $i(all_3_3) % 9.03/1.98 | (21) $i(all_3_1) % 9.03/1.99 | (22) (((big_q(all_3_11) = all_3_10 & ! [v0: $i] : ! [v1: int] : ( ~ % 9.03/1.99 | (all_3_10 = 0) | v1 = 0 | ~ (big_q(v0) = v1) | ~ $i(v0)) & % 9.03/1.99 | ! [v0: $i] : (all_3_10 = 0 | ~ (big_q(v0) = 0) | ~ $i(v0)) & % 9.03/1.99 | ((all_3_12 = 0 & ~ (all_3_14 = 0) & big_p(all_3_13) = 0 & % 9.03/1.99 | big_p(all_3_15) = all_3_14) | ( ! [v0: $i] : ! [v1: int] : % 9.03/1.99 | (v1 = 0 | ~ (big_p(v0) = v1) | ~ $i(v0)) & ! [v0: $i] : ( % 9.03/1.99 | ~ (big_p(v0) = 0) | ~ $i(v0))))) | ( ! [v0: $i] : ! [v1: % 9.03/1.99 | any] : ( ~ (big_q(v0) = v1) | ~ $i(v0) | ? [v2: $i] : ? % 9.03/1.99 | [v3: any] : (big_q(v2) = v3 & $i(v2) & ( ~ (v3 = 0) | ~ (v1 = % 9.03/1.99 | 0)) & (v3 = 0 | v1 = 0))) & ((all_3_16 = 0 & % 9.03/1.99 | big_p(all_3_17) = 0 & ! [v0: $i] : ! [v1: int] : (v1 = 0 | % 9.03/1.99 | ~ (big_p(v0) = v1) | ~ $i(v0))) | ( ~ (all_3_18 = 0) & % 9.03/1.99 | big_p(all_3_19) = all_3_18 & ! [v0: $i] : ( ~ (big_p(v0) = % 9.03/1.99 | 0) | ~ $i(v0)))))) & ((big_p(all_3_1) = all_3_0 & ! % 9.03/1.99 | [v0: $i] : ! [v1: int] : ( ~ (all_3_0 = 0) | v1 = 0 | ~ % 9.03/1.99 | (big_p(v0) = v1) | ~ $i(v0)) & ! [v0: $i] : (all_3_0 = 0 | % 9.03/1.99 | ~ (big_p(v0) = 0) | ~ $i(v0)) & ((all_3_2 = 0 & % 9.03/1.99 | big_q(all_3_3) = 0 & ! [v0: $i] : ! [v1: int] : (v1 = 0 | % 9.03/1.99 | ~ (big_q(v0) = v1) | ~ $i(v0))) | ( ~ (all_3_4 = 0) & % 9.03/1.99 | big_q(all_3_5) = all_3_4 & ! [v0: $i] : ( ~ (big_q(v0) = 0) % 9.03/1.99 | | ~ $i(v0))))) | ( ! [v0: $i] : ! [v1: any] : ( ~ % 9.03/1.99 | (big_p(v0) = v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: any] : % 9.03/1.99 | (big_p(v2) = v3 & $i(v2) & ( ~ (v3 = 0) | ~ (v1 = 0)) & (v3 = % 9.03/1.99 | 0 | v1 = 0))) & ((all_3_6 = 0 & ~ (all_3_8 = 0) & % 9.03/1.99 | big_q(all_3_7) = 0 & big_q(all_3_9) = all_3_8) | ( ! [v0: % 9.03/1.99 | $i] : ! [v1: int] : (v1 = 0 | ~ (big_q(v0) = v1) | ~ % 9.03/1.99 | $i(v0)) & ! [v0: $i] : ( ~ (big_q(v0) = 0) | ~ % 9.03/1.99 | $i(v0))))))) | (((big_q(all_3_21) = all_3_20 & ! [v0: $i] % 9.03/1.99 | : ! [v1: int] : ( ~ (all_3_20 = 0) | v1 = 0 | ~ (big_q(v0) = % 9.03/1.99 | v1) | ~ $i(v0)) & ! [v0: $i] : (all_3_20 = 0 | ~ % 9.03/1.99 | (big_q(v0) = 0) | ~ $i(v0)) & ((all_3_22 = 0 & % 9.03/1.99 | big_p(all_3_23) = 0 & ! [v0: $i] : ! [v1: int] : (v1 = 0 | % 9.03/1.99 | ~ (big_p(v0) = v1) | ~ $i(v0))) | ( ~ (all_3_24 = 0) & % 9.03/1.99 | big_p(all_3_25) = all_3_24 & ! [v0: $i] : ( ~ (big_p(v0) = % 9.03/1.99 | 0) | ~ $i(v0))))) | ( ! [v0: $i] : ! [v1: any] : ( ~ % 9.03/1.99 | (big_q(v0) = v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: any] : % 9.03/1.99 | (big_q(v2) = v3 & $i(v2) & ( ~ (v3 = 0) | ~ (v1 = 0)) & (v3 = % 9.03/1.99 | 0 | v1 = 0))) & ((all_3_26 = 0 & ~ (all_3_28 = 0) & % 9.03/1.99 | big_p(all_3_27) = 0 & big_p(all_3_29) = all_3_28) | ( ! [v0: % 9.03/1.99 | $i] : ! [v1: int] : (v1 = 0 | ~ (big_p(v0) = v1) | ~ % 9.03/1.99 | $i(v0)) & ! [v0: $i] : ( ~ (big_p(v0) = 0) | ~ % 9.03/1.99 | $i(v0)))))) & ((big_p(all_3_31) = all_3_30 & ! [v0: $i] : % 9.03/1.99 | ! [v1: int] : ( ~ (all_3_30 = 0) | v1 = 0 | ~ (big_p(v0) = v1) % 9.03/1.99 | | ~ $i(v0)) & ! [v0: $i] : (all_3_30 = 0 | ~ (big_p(v0) = % 9.03/1.99 | 0) | ~ $i(v0)) & ((all_3_32 = 0 & ~ (all_3_34 = 0) & % 9.03/1.99 | big_q(all_3_33) = 0 & big_q(all_3_35) = all_3_34) | ( ! [v0: % 9.03/1.99 | $i] : ! [v1: int] : (v1 = 0 | ~ (big_q(v0) = v1) | ~ % 9.03/1.99 | $i(v0)) & ! [v0: $i] : ( ~ (big_q(v0) = 0) | ~ % 9.03/1.99 | $i(v0))))) | ( ! [v0: $i] : ! [v1: any] : ( ~ (big_p(v0) % 9.03/1.99 | = v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: any] : (big_p(v2) % 9.03/1.99 | = v3 & $i(v2) & ( ~ (v3 = 0) | ~ (v1 = 0)) & (v3 = 0 | v1 = % 9.03/1.99 | 0))) & ((all_3_36 = 0 & big_q(all_3_37) = 0 & ! [v0: $i] % 9.03/1.99 | : ! [v1: int] : (v1 = 0 | ~ (big_q(v0) = v1) | ~ $i(v0))) % 9.03/1.99 | | ( ~ (all_3_38 = 0) & big_q(all_3_39) = all_3_38 & ! [v0: % 9.03/1.99 | $i] : ( ~ (big_q(v0) = 0) | ~ $i(v0))))))) % 9.03/1.99 | % 9.03/1.99 | BETA: splitting (22) gives: % 9.03/1.99 | % 9.03/1.99 | Case 1: % 9.03/1.99 | | % 9.03/1.99 | | (23) ((big_q(all_3_11) = all_3_10 & ! [v0: $i] : ! [v1: int] : ( ~ % 9.03/1.99 | | (all_3_10 = 0) | v1 = 0 | ~ (big_q(v0) = v1) | ~ $i(v0)) & % 9.03/1.99 | | ! [v0: $i] : (all_3_10 = 0 | ~ (big_q(v0) = 0) | ~ $i(v0)) & % 9.03/1.99 | | ((all_3_12 = 0 & ~ (all_3_14 = 0) & big_p(all_3_13) = 0 & % 9.03/1.99 | | big_p(all_3_15) = all_3_14) | ( ! [v0: $i] : ! [v1: int] : % 9.03/1.99 | | (v1 = 0 | ~ (big_p(v0) = v1) | ~ $i(v0)) & ! [v0: $i] : ( % 9.03/1.99 | | ~ (big_p(v0) = 0) | ~ $i(v0))))) | ( ! [v0: $i] : ! [v1: % 9.03/1.99 | | any] : ( ~ (big_q(v0) = v1) | ~ $i(v0) | ? [v2: $i] : ? % 9.03/1.99 | | [v3: any] : (big_q(v2) = v3 & $i(v2) & ( ~ (v3 = 0) | ~ (v1 = % 9.03/1.99 | | 0)) & (v3 = 0 | v1 = 0))) & ((all_3_16 = 0 & % 9.03/1.99 | | big_p(all_3_17) = 0 & ! [v0: $i] : ! [v1: int] : (v1 = 0 | % 9.03/1.99 | | ~ (big_p(v0) = v1) | ~ $i(v0))) | ( ~ (all_3_18 = 0) & % 9.03/1.99 | | big_p(all_3_19) = all_3_18 & ! [v0: $i] : ( ~ (big_p(v0) = % 9.03/1.99 | | 0) | ~ $i(v0)))))) & ((big_p(all_3_1) = all_3_0 & ! % 9.03/1.99 | | [v0: $i] : ! [v1: int] : ( ~ (all_3_0 = 0) | v1 = 0 | ~ % 9.03/1.99 | | (big_p(v0) = v1) | ~ $i(v0)) & ! [v0: $i] : (all_3_0 = 0 | % 9.03/1.99 | | ~ (big_p(v0) = 0) | ~ $i(v0)) & ((all_3_2 = 0 & % 9.03/1.99 | | big_q(all_3_3) = 0 & ! [v0: $i] : ! [v1: int] : (v1 = 0 | % 9.03/1.99 | | ~ (big_q(v0) = v1) | ~ $i(v0))) | ( ~ (all_3_4 = 0) & % 9.03/1.99 | | big_q(all_3_5) = all_3_4 & ! [v0: $i] : ( ~ (big_q(v0) = 0) % 9.03/1.99 | | | ~ $i(v0))))) | ( ! [v0: $i] : ! [v1: any] : ( ~ % 9.03/1.99 | | (big_p(v0) = v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: any] : % 9.03/1.99 | | (big_p(v2) = v3 & $i(v2) & ( ~ (v3 = 0) | ~ (v1 = 0)) & (v3 = % 9.03/1.99 | | 0 | v1 = 0))) & ((all_3_6 = 0 & ~ (all_3_8 = 0) & % 9.03/1.99 | | big_q(all_3_7) = 0 & big_q(all_3_9) = all_3_8) | ( ! [v0: % 9.03/1.99 | | $i] : ! [v1: int] : (v1 = 0 | ~ (big_q(v0) = v1) | ~ % 9.03/1.99 | | $i(v0)) & ! [v0: $i] : ( ~ (big_q(v0) = 0) | ~ % 9.03/1.99 | | $i(v0)))))) % 9.03/1.99 | | % 9.03/1.99 | | ALPHA: (23) implies: % 9.03/2.00 | | (24) (big_p(all_3_1) = all_3_0 & ! [v0: $i] : ! [v1: int] : ( ~ % 9.03/2.00 | | (all_3_0 = 0) | v1 = 0 | ~ (big_p(v0) = v1) | ~ $i(v0)) & ! % 9.03/2.00 | | [v0: $i] : (all_3_0 = 0 | ~ (big_p(v0) = 0) | ~ $i(v0)) & % 9.03/2.00 | | ((all_3_2 = 0 & big_q(all_3_3) = 0 & ! [v0: $i] : ! [v1: int] : % 9.03/2.00 | | (v1 = 0 | ~ (big_q(v0) = v1) | ~ $i(v0))) | ( ~ (all_3_4 = % 9.03/2.00 | | 0) & big_q(all_3_5) = all_3_4 & ! [v0: $i] : ( ~ (big_q(v0) % 9.03/2.00 | | = 0) | ~ $i(v0))))) | ( ! [v0: $i] : ! [v1: any] : ( ~ % 9.03/2.00 | | (big_p(v0) = v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: any] : % 9.03/2.00 | | (big_p(v2) = v3 & $i(v2) & ( ~ (v3 = 0) | ~ (v1 = 0)) & (v3 = 0 % 9.03/2.00 | | | v1 = 0))) & ((all_3_6 = 0 & ~ (all_3_8 = 0) & % 9.03/2.00 | | big_q(all_3_7) = 0 & big_q(all_3_9) = all_3_8) | ( ! [v0: $i] % 9.03/2.00 | | : ! [v1: int] : (v1 = 0 | ~ (big_q(v0) = v1) | ~ $i(v0)) & % 9.03/2.00 | | ! [v0: $i] : ( ~ (big_q(v0) = 0) | ~ $i(v0))))) % 9.03/2.00 | | (25) (big_q(all_3_11) = all_3_10 & ! [v0: $i] : ! [v1: int] : ( ~ % 9.03/2.00 | | (all_3_10 = 0) | v1 = 0 | ~ (big_q(v0) = v1) | ~ $i(v0)) & ! % 9.03/2.00 | | [v0: $i] : (all_3_10 = 0 | ~ (big_q(v0) = 0) | ~ $i(v0)) & % 9.03/2.00 | | ((all_3_12 = 0 & ~ (all_3_14 = 0) & big_p(all_3_13) = 0 & % 9.03/2.00 | | big_p(all_3_15) = all_3_14) | ( ! [v0: $i] : ! [v1: int] : % 9.03/2.00 | | (v1 = 0 | ~ (big_p(v0) = v1) | ~ $i(v0)) & ! [v0: $i] : ( ~ % 9.03/2.00 | | (big_p(v0) = 0) | ~ $i(v0))))) | ( ! [v0: $i] : ! [v1: % 9.03/2.00 | | any] : ( ~ (big_q(v0) = v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: % 9.03/2.00 | | any] : (big_q(v2) = v3 & $i(v2) & ( ~ (v3 = 0) | ~ (v1 = 0)) % 9.03/2.00 | | & (v3 = 0 | v1 = 0))) & ((all_3_16 = 0 & big_p(all_3_17) = 0 & % 9.03/2.00 | | ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (big_p(v0) = v1) | % 9.03/2.00 | | ~ $i(v0))) | ( ~ (all_3_18 = 0) & big_p(all_3_19) = all_3_18 % 9.03/2.00 | | & ! [v0: $i] : ( ~ (big_p(v0) = 0) | ~ $i(v0))))) % 9.03/2.00 | | % 9.03/2.00 | | BETA: splitting (24) gives: % 9.03/2.00 | | % 9.03/2.00 | | Case 1: % 9.03/2.00 | | | % 9.52/2.00 | | | (26) big_p(all_3_1) = all_3_0 & ! [v0: $i] : ! [v1: int] : ( ~ % 9.52/2.00 | | | (all_3_0 = 0) | v1 = 0 | ~ (big_p(v0) = v1) | ~ $i(v0)) & ! % 9.52/2.00 | | | [v0: $i] : (all_3_0 = 0 | ~ (big_p(v0) = 0) | ~ $i(v0)) & % 9.52/2.00 | | | ((all_3_2 = 0 & big_q(all_3_3) = 0 & ! [v0: $i] : ! [v1: int] : % 9.52/2.00 | | | (v1 = 0 | ~ (big_q(v0) = v1) | ~ $i(v0))) | ( ~ (all_3_4 = % 9.52/2.00 | | | 0) & big_q(all_3_5) = all_3_4 & ! [v0: $i] : ( ~ (big_q(v0) % 9.52/2.00 | | | = 0) | ~ $i(v0)))) % 9.52/2.00 | | | % 9.52/2.00 | | | ALPHA: (26) implies: % 9.52/2.00 | | | (27) big_p(all_3_1) = all_3_0 % 9.52/2.00 | | | (28) (all_3_2 = 0 & big_q(all_3_3) = 0 & ! [v0: $i] : ! [v1: int] : % 9.52/2.00 | | | (v1 = 0 | ~ (big_q(v0) = v1) | ~ $i(v0))) | ( ~ (all_3_4 = 0) % 9.52/2.00 | | | & big_q(all_3_5) = all_3_4 & ! [v0: $i] : ( ~ (big_q(v0) = 0) | % 9.52/2.00 | | | ~ $i(v0))) % 9.52/2.00 | | | (29) ! [v0: $i] : (all_3_0 = 0 | ~ (big_p(v0) = 0) | ~ $i(v0)) % 9.52/2.00 | | | (30) ! [v0: $i] : ! [v1: int] : ( ~ (all_3_0 = 0) | v1 = 0 | ~ % 9.52/2.00 | | | (big_p(v0) = v1) | ~ $i(v0)) % 9.52/2.00 | | | % 9.52/2.00 | | | BETA: splitting (25) gives: % 9.52/2.00 | | | % 9.52/2.00 | | | Case 1: % 9.52/2.00 | | | | % 9.52/2.00 | | | | (31) big_q(all_3_11) = all_3_10 & ! [v0: $i] : ! [v1: int] : ( ~ % 9.52/2.00 | | | | (all_3_10 = 0) | v1 = 0 | ~ (big_q(v0) = v1) | ~ $i(v0)) & % 9.52/2.00 | | | | ! [v0: $i] : (all_3_10 = 0 | ~ (big_q(v0) = 0) | ~ $i(v0)) & % 9.52/2.00 | | | | ((all_3_12 = 0 & ~ (all_3_14 = 0) & big_p(all_3_13) = 0 & % 9.52/2.00 | | | | big_p(all_3_15) = all_3_14) | ( ! [v0: $i] : ! [v1: int] : % 9.52/2.00 | | | | (v1 = 0 | ~ (big_p(v0) = v1) | ~ $i(v0)) & ! [v0: $i] : ( % 9.52/2.00 | | | | ~ (big_p(v0) = 0) | ~ $i(v0)))) % 9.52/2.00 | | | | % 9.52/2.00 | | | | ALPHA: (31) implies: % 9.52/2.01 | | | | (32) (all_3_12 = 0 & ~ (all_3_14 = 0) & big_p(all_3_13) = 0 & % 9.52/2.01 | | | | big_p(all_3_15) = all_3_14) | ( ! [v0: $i] : ! [v1: int] : % 9.52/2.01 | | | | (v1 = 0 | ~ (big_p(v0) = v1) | ~ $i(v0)) & ! [v0: $i] : ( ~ % 9.52/2.01 | | | | (big_p(v0) = 0) | ~ $i(v0))) % 9.52/2.01 | | | | % 9.52/2.01 | | | | BETA: splitting (32) gives: % 9.52/2.01 | | | | % 9.52/2.01 | | | | Case 1: % 9.52/2.01 | | | | | % 9.52/2.01 | | | | | (33) all_3_12 = 0 & ~ (all_3_14 = 0) & big_p(all_3_13) = 0 & % 9.52/2.01 | | | | | big_p(all_3_15) = all_3_14 % 9.52/2.01 | | | | | % 9.52/2.01 | | | | | ALPHA: (33) implies: % 9.52/2.01 | | | | | (34) ~ (all_3_14 = 0) % 9.52/2.01 | | | | | (35) big_p(all_3_15) = all_3_14 % 9.52/2.01 | | | | | (36) big_p(all_3_13) = 0 % 9.52/2.01 | | | | | % 9.52/2.01 | | | | | GROUND_INST: instantiating (30) with all_3_15, all_3_14, simplifying % 9.52/2.01 | | | | | with (14), (35) gives: % 9.52/2.01 | | | | | (37) ~ (all_3_0 = 0) | all_3_14 = 0 % 9.52/2.01 | | | | | % 9.52/2.01 | | | | | GROUND_INST: instantiating (29) with all_3_13, simplifying with (15), % 9.52/2.01 | | | | | (36) gives: % 9.52/2.01 | | | | | (38) all_3_0 = 0 % 9.52/2.01 | | | | | % 9.52/2.01 | | | | | BETA: splitting (37) gives: % 9.52/2.01 | | | | | % 9.52/2.01 | | | | | Case 1: % 9.52/2.01 | | | | | | % 9.52/2.01 | | | | | | (39) ~ (all_3_0 = 0) % 9.52/2.01 | | | | | | % 9.52/2.01 | | | | | | REDUCE: (38), (39) imply: % 9.52/2.01 | | | | | | (40) $false % 9.52/2.01 | | | | | | % 9.52/2.01 | | | | | | CLOSE: (40) is inconsistent. % 9.52/2.01 | | | | | | % 9.52/2.01 | | | | | Case 2: % 9.52/2.01 | | | | | | % 9.52/2.01 | | | | | | (41) all_3_14 = 0 % 9.52/2.01 | | | | | | % 9.52/2.01 | | | | | | REDUCE: (34), (41) imply: % 9.52/2.01 | | | | | | (42) $false % 9.52/2.01 | | | | | | % 9.52/2.01 | | | | | | CLOSE: (42) is inconsistent. % 9.52/2.01 | | | | | | % 9.52/2.01 | | | | | End of split % 9.52/2.01 | | | | | % 9.52/2.01 | | | | Case 2: % 9.52/2.01 | | | | | % 9.52/2.01 | | | | | (43) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (big_p(v0) = v1) | % 9.52/2.01 | | | | | ~ $i(v0)) & ! [v0: $i] : ( ~ (big_p(v0) = 0) | ~ $i(v0)) % 9.52/2.01 | | | | | % 9.52/2.01 | | | | | ALPHA: (43) implies: % 9.52/2.01 | | | | | (44) ! [v0: $i] : ( ~ (big_p(v0) = 0) | ~ $i(v0)) % 9.52/2.01 | | | | | (45) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (big_p(v0) = v1) | % 9.52/2.01 | | | | | ~ $i(v0)) % 9.52/2.01 | | | | | % 9.52/2.01 | | | | | GROUND_INST: instantiating (45) with all_3_1, all_3_0, simplifying % 9.52/2.01 | | | | | with (21), (27) gives: % 9.52/2.01 | | | | | (46) all_3_0 = 0 % 9.52/2.01 | | | | | % 9.52/2.01 | | | | | REDUCE: (27), (46) imply: % 9.52/2.01 | | | | | (47) big_p(all_3_1) = 0 % 9.52/2.01 | | | | | % 9.52/2.01 | | | | | GROUND_INST: instantiating (44) with all_3_1, simplifying with (21), % 9.52/2.01 | | | | | (47) gives: % 9.52/2.01 | | | | | (48) $false % 9.52/2.01 | | | | | % 9.52/2.01 | | | | | CLOSE: (48) is inconsistent. % 9.52/2.01 | | | | | % 9.52/2.01 | | | | End of split % 9.52/2.01 | | | | % 9.52/2.01 | | | Case 2: % 9.52/2.01 | | | | % 9.52/2.01 | | | | (49) ! [v0: $i] : ! [v1: any] : ( ~ (big_q(v0) = v1) | ~ $i(v0) | % 9.52/2.01 | | | | ? [v2: $i] : ? [v3: any] : (big_q(v2) = v3 & $i(v2) & ( ~ (v3 % 9.52/2.01 | | | | = 0) | ~ (v1 = 0)) & (v3 = 0 | v1 = 0))) & ((all_3_16 = % 9.52/2.01 | | | | 0 & big_p(all_3_17) = 0 & ! [v0: $i] : ! [v1: int] : (v1 = % 9.52/2.01 | | | | 0 | ~ (big_p(v0) = v1) | ~ $i(v0))) | ( ~ (all_3_18 = 0) % 9.52/2.01 | | | | & big_p(all_3_19) = all_3_18 & ! [v0: $i] : ( ~ (big_p(v0) % 9.52/2.01 | | | | = 0) | ~ $i(v0)))) % 9.52/2.01 | | | | % 9.52/2.01 | | | | ALPHA: (49) implies: % 9.52/2.01 | | | | (50) ! [v0: $i] : ! [v1: any] : ( ~ (big_q(v0) = v1) | ~ $i(v0) | % 9.52/2.01 | | | | ? [v2: $i] : ? [v3: any] : (big_q(v2) = v3 & $i(v2) & ( ~ (v3 % 9.52/2.01 | | | | = 0) | ~ (v1 = 0)) & (v3 = 0 | v1 = 0))) % 9.52/2.01 | | | | % 9.52/2.01 | | | | BETA: splitting (28) gives: % 9.52/2.01 | | | | % 9.52/2.01 | | | | Case 1: % 9.52/2.01 | | | | | % 9.52/2.01 | | | | | (51) all_3_2 = 0 & big_q(all_3_3) = 0 & ! [v0: $i] : ! [v1: int] % 9.52/2.01 | | | | | : (v1 = 0 | ~ (big_q(v0) = v1) | ~ $i(v0)) % 9.52/2.02 | | | | | % 9.52/2.02 | | | | | ALPHA: (51) implies: % 9.52/2.02 | | | | | (52) big_q(all_3_3) = 0 % 9.52/2.02 | | | | | (53) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (big_q(v0) = v1) | % 9.52/2.02 | | | | | ~ $i(v0)) % 9.52/2.02 | | | | | % 9.52/2.02 | | | | | GROUND_INST: instantiating (50) with all_3_3, 0, simplifying with % 9.52/2.02 | | | | | (20), (52) gives: % 9.52/2.02 | | | | | (54) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & big_q(v0) = v1 & % 9.52/2.02 | | | | | $i(v0)) % 9.52/2.02 | | | | | % 9.52/2.02 | | | | | DELTA: instantiating (54) with fresh symbols all_31_0, all_31_1 gives: % 9.52/2.02 | | | | | (55) ~ (all_31_0 = 0) & big_q(all_31_1) = all_31_0 & $i(all_31_1) % 9.52/2.02 | | | | | % 9.52/2.02 | | | | | ALPHA: (55) implies: % 9.52/2.02 | | | | | (56) ~ (all_31_0 = 0) % 9.52/2.02 | | | | | (57) $i(all_31_1) % 9.52/2.02 | | | | | (58) big_q(all_31_1) = all_31_0 % 9.52/2.02 | | | | | % 9.52/2.02 | | | | | GROUND_INST: instantiating (53) with all_31_1, all_31_0, simplifying % 9.52/2.02 | | | | | with (57), (58) gives: % 9.52/2.02 | | | | | (59) all_31_0 = 0 % 9.52/2.02 | | | | | % 9.52/2.02 | | | | | REDUCE: (56), (59) imply: % 9.52/2.02 | | | | | (60) $false % 9.52/2.02 | | | | | % 9.52/2.02 | | | | | CLOSE: (60) is inconsistent. % 9.52/2.02 | | | | | % 9.52/2.02 | | | | Case 2: % 9.52/2.02 | | | | | % 9.52/2.02 | | | | | (61) ~ (all_3_4 = 0) & big_q(all_3_5) = all_3_4 & ! [v0: $i] : ( % 9.52/2.02 | | | | | ~ (big_q(v0) = 0) | ~ $i(v0)) % 9.52/2.02 | | | | | % 9.52/2.02 | | | | | ALPHA: (61) implies: % 9.52/2.02 | | | | | (62) ~ (all_3_4 = 0) % 9.52/2.02 | | | | | (63) big_q(all_3_5) = all_3_4 % 9.52/2.02 | | | | | (64) ! [v0: $i] : ( ~ (big_q(v0) = 0) | ~ $i(v0)) % 9.52/2.02 | | | | | % 9.52/2.02 | | | | | GROUND_INST: instantiating (50) with all_3_5, all_3_4, simplifying % 9.52/2.02 | | | | | with (19), (63) gives: % 9.52/2.02 | | | | | (65) ? [v0: $i] : ? [v1: any] : (big_q(v0) = v1 & $i(v0) & ( ~ % 9.52/2.02 | | | | | (v1 = 0) | ~ (all_3_4 = 0)) & (v1 = 0 | all_3_4 = 0)) % 9.52/2.02 | | | | | % 9.52/2.02 | | | | | DELTA: instantiating (65) with fresh symbols all_31_0, all_31_1 gives: % 9.52/2.02 | | | | | (66) big_q(all_31_1) = all_31_0 & $i(all_31_1) & ( ~ (all_31_0 = 0) % 9.52/2.02 | | | | | | ~ (all_3_4 = 0)) & (all_31_0 = 0 | all_3_4 = 0) % 9.52/2.02 | | | | | % 9.52/2.02 | | | | | ALPHA: (66) implies: % 9.52/2.02 | | | | | (67) $i(all_31_1) % 9.52/2.02 | | | | | (68) big_q(all_31_1) = all_31_0 % 9.52/2.02 | | | | | (69) all_31_0 = 0 | all_3_4 = 0 % 9.52/2.02 | | | | | % 9.52/2.02 | | | | | BETA: splitting (69) gives: % 9.52/2.02 | | | | | % 9.52/2.02 | | | | | Case 1: % 9.52/2.02 | | | | | | % 9.52/2.02 | | | | | | (70) all_31_0 = 0 % 9.52/2.02 | | | | | | % 9.52/2.02 | | | | | | REDUCE: (68), (70) imply: % 9.52/2.02 | | | | | | (71) big_q(all_31_1) = 0 % 9.52/2.02 | | | | | | % 9.52/2.02 | | | | | | GROUND_INST: instantiating (64) with all_31_1, simplifying with % 9.52/2.02 | | | | | | (67), (71) gives: % 9.52/2.02 | | | | | | (72) $false % 9.52/2.02 | | | | | | % 9.52/2.02 | | | | | | CLOSE: (72) is inconsistent. % 9.52/2.02 | | | | | | % 9.52/2.02 | | | | | Case 2: % 9.52/2.02 | | | | | | % 9.52/2.02 | | | | | | (73) all_3_4 = 0 % 9.52/2.02 | | | | | | % 9.52/2.02 | | | | | | REDUCE: (62), (73) imply: % 9.52/2.02 | | | | | | (74) $false % 9.52/2.02 | | | | | | % 9.52/2.02 | | | | | | CLOSE: (74) is inconsistent. % 9.52/2.02 | | | | | | % 9.52/2.02 | | | | | End of split % 9.52/2.02 | | | | | % 9.52/2.02 | | | | End of split % 9.52/2.02 | | | | % 9.52/2.02 | | | End of split % 9.52/2.02 | | | % 9.52/2.02 | | Case 2: % 9.52/2.02 | | | % 9.52/2.02 | | | (75) ! [v0: $i] : ! [v1: any] : ( ~ (big_p(v0) = v1) | ~ $i(v0) | ? % 9.52/2.02 | | | [v2: $i] : ? [v3: any] : (big_p(v2) = v3 & $i(v2) & ( ~ (v3 = % 9.52/2.02 | | | 0) | ~ (v1 = 0)) & (v3 = 0 | v1 = 0))) & ((all_3_6 = 0 & % 9.52/2.02 | | | ~ (all_3_8 = 0) & big_q(all_3_7) = 0 & big_q(all_3_9) = % 9.52/2.02 | | | all_3_8) | ( ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ % 9.52/2.02 | | | (big_q(v0) = v1) | ~ $i(v0)) & ! [v0: $i] : ( ~ (big_q(v0) % 9.52/2.02 | | | = 0) | ~ $i(v0)))) % 9.52/2.02 | | | % 9.52/2.02 | | | ALPHA: (75) implies: % 9.52/2.02 | | | (76) (all_3_6 = 0 & ~ (all_3_8 = 0) & big_q(all_3_7) = 0 & % 9.52/2.02 | | | big_q(all_3_9) = all_3_8) | ( ! [v0: $i] : ! [v1: int] : (v1 = % 9.52/2.02 | | | 0 | ~ (big_q(v0) = v1) | ~ $i(v0)) & ! [v0: $i] : ( ~ % 9.52/2.02 | | | (big_q(v0) = 0) | ~ $i(v0))) % 9.52/2.02 | | | (77) ! [v0: $i] : ! [v1: any] : ( ~ (big_p(v0) = v1) | ~ $i(v0) | ? % 9.52/2.02 | | | [v2: $i] : ? [v3: any] : (big_p(v2) = v3 & $i(v2) & ( ~ (v3 = % 9.52/2.02 | | | 0) | ~ (v1 = 0)) & (v3 = 0 | v1 = 0))) % 9.52/2.02 | | | % 9.52/2.02 | | | BETA: splitting (25) gives: % 9.52/2.02 | | | % 9.52/2.02 | | | Case 1: % 9.52/2.02 | | | | % 9.52/2.02 | | | | (78) big_q(all_3_11) = all_3_10 & ! [v0: $i] : ! [v1: int] : ( ~ % 9.52/2.02 | | | | (all_3_10 = 0) | v1 = 0 | ~ (big_q(v0) = v1) | ~ $i(v0)) & % 9.52/2.02 | | | | ! [v0: $i] : (all_3_10 = 0 | ~ (big_q(v0) = 0) | ~ $i(v0)) & % 9.52/2.02 | | | | ((all_3_12 = 0 & ~ (all_3_14 = 0) & big_p(all_3_13) = 0 & % 9.52/2.02 | | | | big_p(all_3_15) = all_3_14) | ( ! [v0: $i] : ! [v1: int] : % 9.52/2.02 | | | | (v1 = 0 | ~ (big_p(v0) = v1) | ~ $i(v0)) & ! [v0: $i] : ( % 9.52/2.02 | | | | ~ (big_p(v0) = 0) | ~ $i(v0)))) % 9.52/2.02 | | | | % 9.52/2.02 | | | | ALPHA: (78) implies: % 9.52/2.03 | | | | (79) big_q(all_3_11) = all_3_10 % 9.52/2.03 | | | | (80) ! [v0: $i] : (all_3_10 = 0 | ~ (big_q(v0) = 0) | ~ $i(v0)) % 9.52/2.03 | | | | (81) ! [v0: $i] : ! [v1: int] : ( ~ (all_3_10 = 0) | v1 = 0 | ~ % 9.52/2.03 | | | | (big_q(v0) = v1) | ~ $i(v0)) % 9.52/2.03 | | | | % 9.52/2.03 | | | | BETA: splitting (76) gives: % 9.52/2.03 | | | | % 9.52/2.03 | | | | Case 1: % 9.52/2.03 | | | | | % 9.52/2.03 | | | | | (82) all_3_6 = 0 & ~ (all_3_8 = 0) & big_q(all_3_7) = 0 & % 9.52/2.03 | | | | | big_q(all_3_9) = all_3_8 % 9.52/2.03 | | | | | % 9.52/2.03 | | | | | ALPHA: (82) implies: % 9.52/2.03 | | | | | (83) ~ (all_3_8 = 0) % 9.52/2.03 | | | | | (84) big_q(all_3_9) = all_3_8 % 9.52/2.03 | | | | | (85) big_q(all_3_7) = 0 % 9.52/2.03 | | | | | % 9.52/2.03 | | | | | GROUND_INST: instantiating (81) with all_3_9, all_3_8, simplifying % 9.52/2.03 | | | | | with (17), (84) gives: % 9.52/2.03 | | | | | (86) ~ (all_3_10 = 0) | all_3_8 = 0 % 9.52/2.03 | | | | | % 9.52/2.03 | | | | | GROUND_INST: instantiating (80) with all_3_7, simplifying with (18), % 9.52/2.03 | | | | | (85) gives: % 9.52/2.03 | | | | | (87) all_3_10 = 0 % 9.52/2.03 | | | | | % 9.52/2.03 | | | | | BETA: splitting (86) gives: % 9.52/2.03 | | | | | % 9.52/2.03 | | | | | Case 1: % 9.52/2.03 | | | | | | % 9.52/2.03 | | | | | | (88) ~ (all_3_10 = 0) % 9.52/2.03 | | | | | | % 9.52/2.03 | | | | | | REDUCE: (87), (88) imply: % 9.52/2.03 | | | | | | (89) $false % 9.52/2.03 | | | | | | % 9.52/2.03 | | | | | | CLOSE: (89) is inconsistent. % 9.52/2.03 | | | | | | % 9.52/2.03 | | | | | Case 2: % 9.52/2.03 | | | | | | % 9.52/2.03 | | | | | | (90) all_3_8 = 0 % 9.52/2.03 | | | | | | % 9.52/2.03 | | | | | | REDUCE: (83), (90) imply: % 9.52/2.03 | | | | | | (91) $false % 9.52/2.03 | | | | | | % 9.52/2.03 | | | | | | CLOSE: (91) is inconsistent. % 9.52/2.03 | | | | | | % 9.52/2.03 | | | | | End of split % 9.52/2.03 | | | | | % 9.52/2.03 | | | | Case 2: % 9.52/2.03 | | | | | % 9.52/2.03 | | | | | (92) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (big_q(v0) = v1) | % 9.52/2.03 | | | | | ~ $i(v0)) & ! [v0: $i] : ( ~ (big_q(v0) = 0) | ~ $i(v0)) % 9.52/2.03 | | | | | % 9.52/2.03 | | | | | ALPHA: (92) implies: % 9.52/2.03 | | | | | (93) ! [v0: $i] : ( ~ (big_q(v0) = 0) | ~ $i(v0)) % 9.52/2.03 | | | | | (94) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (big_q(v0) = v1) | % 9.52/2.03 | | | | | ~ $i(v0)) % 9.52/2.03 | | | | | % 9.52/2.03 | | | | | GROUND_INST: instantiating (94) with all_3_11, all_3_10, simplifying % 9.52/2.03 | | | | | with (16), (79) gives: % 9.52/2.03 | | | | | (95) all_3_10 = 0 % 9.52/2.03 | | | | | % 9.52/2.03 | | | | | REDUCE: (79), (95) imply: % 9.52/2.03 | | | | | (96) big_q(all_3_11) = 0 % 9.52/2.03 | | | | | % 9.52/2.03 | | | | | GROUND_INST: instantiating (93) with all_3_11, simplifying with (16), % 9.52/2.03 | | | | | (96) gives: % 9.52/2.03 | | | | | (97) $false % 9.52/2.03 | | | | | % 9.52/2.03 | | | | | CLOSE: (97) is inconsistent. % 9.52/2.03 | | | | | % 9.52/2.03 | | | | End of split % 9.52/2.03 | | | | % 9.52/2.03 | | | Case 2: % 9.52/2.03 | | | | % 9.52/2.03 | | | | (98) ! [v0: $i] : ! [v1: any] : ( ~ (big_q(v0) = v1) | ~ $i(v0) | % 9.52/2.03 | | | | ? [v2: $i] : ? [v3: any] : (big_q(v2) = v3 & $i(v2) & ( ~ (v3 % 9.52/2.03 | | | | = 0) | ~ (v1 = 0)) & (v3 = 0 | v1 = 0))) & ((all_3_16 = % 9.52/2.03 | | | | 0 & big_p(all_3_17) = 0 & ! [v0: $i] : ! [v1: int] : (v1 = % 9.52/2.03 | | | | 0 | ~ (big_p(v0) = v1) | ~ $i(v0))) | ( ~ (all_3_18 = 0) % 9.52/2.03 | | | | & big_p(all_3_19) = all_3_18 & ! [v0: $i] : ( ~ (big_p(v0) % 9.52/2.03 | | | | = 0) | ~ $i(v0)))) % 9.52/2.03 | | | | % 9.52/2.03 | | | | ALPHA: (98) implies: % 9.52/2.03 | | | | (99) (all_3_16 = 0 & big_p(all_3_17) = 0 & ! [v0: $i] : ! [v1: int] % 9.52/2.03 | | | | : (v1 = 0 | ~ (big_p(v0) = v1) | ~ $i(v0))) | ( ~ (all_3_18 % 9.52/2.03 | | | | = 0) & big_p(all_3_19) = all_3_18 & ! [v0: $i] : ( ~ % 9.52/2.03 | | | | (big_p(v0) = 0) | ~ $i(v0))) % 9.52/2.03 | | | | % 9.52/2.03 | | | | BETA: splitting (99) gives: % 9.52/2.03 | | | | % 9.52/2.03 | | | | Case 1: % 9.52/2.03 | | | | | % 9.52/2.03 | | | | | (100) all_3_16 = 0 & big_p(all_3_17) = 0 & ! [v0: $i] : ! [v1: % 9.52/2.03 | | | | | int] : (v1 = 0 | ~ (big_p(v0) = v1) | ~ $i(v0)) % 9.52/2.03 | | | | | % 9.52/2.03 | | | | | ALPHA: (100) implies: % 9.52/2.03 | | | | | (101) big_p(all_3_17) = 0 % 9.52/2.03 | | | | | (102) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (big_p(v0) = v1) | % 9.52/2.03 | | | | | ~ $i(v0)) % 9.52/2.03 | | | | | % 9.52/2.03 | | | | | GROUND_INST: instantiating (77) with all_3_17, 0, simplifying with % 9.52/2.03 | | | | | (13), (101) gives: % 9.52/2.03 | | | | | (103) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & big_p(v0) = v1 & % 9.52/2.03 | | | | | $i(v0)) % 9.52/2.03 | | | | | % 9.52/2.03 | | | | | DELTA: instantiating (103) with fresh symbols all_31_0, all_31_1 % 9.52/2.03 | | | | | gives: % 9.52/2.03 | | | | | (104) ~ (all_31_0 = 0) & big_p(all_31_1) = all_31_0 & $i(all_31_1) % 9.52/2.03 | | | | | % 9.52/2.03 | | | | | ALPHA: (104) implies: % 9.52/2.03 | | | | | (105) ~ (all_31_0 = 0) % 9.52/2.03 | | | | | (106) $i(all_31_1) % 9.52/2.03 | | | | | (107) big_p(all_31_1) = all_31_0 % 9.52/2.03 | | | | | % 9.52/2.03 | | | | | GROUND_INST: instantiating (102) with all_31_1, all_31_0, simplifying % 9.52/2.03 | | | | | with (106), (107) gives: % 9.52/2.03 | | | | | (108) all_31_0 = 0 % 9.52/2.03 | | | | | % 9.52/2.03 | | | | | REDUCE: (105), (108) imply: % 9.52/2.03 | | | | | (109) $false % 9.52/2.03 | | | | | % 9.52/2.03 | | | | | CLOSE: (109) is inconsistent. % 9.52/2.03 | | | | | % 9.52/2.03 | | | | Case 2: % 9.52/2.03 | | | | | % 9.52/2.03 | | | | | (110) ~ (all_3_18 = 0) & big_p(all_3_19) = all_3_18 & ! [v0: $i] % 9.52/2.03 | | | | | : ( ~ (big_p(v0) = 0) | ~ $i(v0)) % 9.52/2.03 | | | | | % 9.52/2.03 | | | | | ALPHA: (110) implies: % 9.52/2.03 | | | | | (111) ~ (all_3_18 = 0) % 9.52/2.03 | | | | | (112) big_p(all_3_19) = all_3_18 % 9.52/2.03 | | | | | (113) ! [v0: $i] : ( ~ (big_p(v0) = 0) | ~ $i(v0)) % 9.52/2.03 | | | | | % 9.52/2.04 | | | | | GROUND_INST: instantiating (77) with all_3_19, all_3_18, simplifying % 9.52/2.04 | | | | | with (12), (112) gives: % 9.52/2.04 | | | | | (114) ? [v0: $i] : ? [v1: any] : (big_p(v0) = v1 & $i(v0) & ( ~ % 9.52/2.04 | | | | | (v1 = 0) | ~ (all_3_18 = 0)) & (v1 = 0 | all_3_18 = 0)) % 9.52/2.04 | | | | | % 9.52/2.04 | | | | | DELTA: instantiating (114) with fresh symbols all_31_0, all_31_1 % 9.52/2.04 | | | | | gives: % 9.52/2.04 | | | | | (115) big_p(all_31_1) = all_31_0 & $i(all_31_1) & ( ~ (all_31_0 = % 9.52/2.04 | | | | | 0) | ~ (all_3_18 = 0)) & (all_31_0 = 0 | all_3_18 = 0) % 9.52/2.04 | | | | | % 9.52/2.04 | | | | | ALPHA: (115) implies: % 9.52/2.04 | | | | | (116) $i(all_31_1) % 9.52/2.04 | | | | | (117) big_p(all_31_1) = all_31_0 % 9.52/2.04 | | | | | (118) all_31_0 = 0 | all_3_18 = 0 % 9.52/2.04 | | | | | % 9.52/2.04 | | | | | BETA: splitting (118) gives: % 9.52/2.04 | | | | | % 9.52/2.04 | | | | | Case 1: % 9.52/2.04 | | | | | | % 9.52/2.04 | | | | | | (119) all_31_0 = 0 % 9.52/2.04 | | | | | | % 9.52/2.04 | | | | | | REDUCE: (117), (119) imply: % 9.52/2.04 | | | | | | (120) big_p(all_31_1) = 0 % 9.52/2.04 | | | | | | % 9.52/2.04 | | | | | | GROUND_INST: instantiating (113) with all_31_1, simplifying with % 9.52/2.04 | | | | | | (116), (120) gives: % 9.52/2.04 | | | | | | (121) $false % 9.52/2.04 | | | | | | % 9.52/2.04 | | | | | | CLOSE: (121) is inconsistent. % 9.52/2.04 | | | | | | % 9.52/2.04 | | | | | Case 2: % 9.52/2.04 | | | | | | % 9.52/2.04 | | | | | | (122) all_3_18 = 0 % 9.52/2.04 | | | | | | % 9.52/2.04 | | | | | | REDUCE: (111), (122) imply: % 9.52/2.04 | | | | | | (123) $false % 9.52/2.04 | | | | | | % 9.52/2.04 | | | | | | CLOSE: (123) is inconsistent. % 9.52/2.04 | | | | | | % 9.52/2.04 | | | | | End of split % 9.52/2.04 | | | | | % 9.52/2.04 | | | | End of split % 9.52/2.04 | | | | % 9.52/2.04 | | | End of split % 9.52/2.04 | | | % 9.52/2.04 | | End of split % 9.52/2.04 | | % 9.52/2.04 | Case 2: % 9.52/2.04 | | % 9.52/2.04 | | (124) ((big_q(all_3_21) = all_3_20 & ! [v0: $i] : ! [v1: int] : ( ~ % 9.52/2.04 | | (all_3_20 = 0) | v1 = 0 | ~ (big_q(v0) = v1) | ~ $i(v0)) & % 9.52/2.04 | | ! [v0: $i] : (all_3_20 = 0 | ~ (big_q(v0) = 0) | ~ $i(v0)) & % 9.52/2.04 | | ((all_3_22 = 0 & big_p(all_3_23) = 0 & ! [v0: $i] : ! [v1: % 9.52/2.04 | | int] : (v1 = 0 | ~ (big_p(v0) = v1) | ~ $i(v0))) | ( ~ % 9.52/2.04 | | (all_3_24 = 0) & big_p(all_3_25) = all_3_24 & ! [v0: $i] : % 9.52/2.04 | | ( ~ (big_p(v0) = 0) | ~ $i(v0))))) | ( ! [v0: $i] : ! % 9.52/2.04 | | [v1: any] : ( ~ (big_q(v0) = v1) | ~ $i(v0) | ? [v2: $i] : ? % 9.52/2.04 | | [v3: any] : (big_q(v2) = v3 & $i(v2) & ( ~ (v3 = 0) | ~ (v1 % 9.52/2.04 | | = 0)) & (v3 = 0 | v1 = 0))) & ((all_3_26 = 0 & ~ % 9.52/2.04 | | (all_3_28 = 0) & big_p(all_3_27) = 0 & big_p(all_3_29) = % 9.52/2.04 | | all_3_28) | ( ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ % 9.52/2.04 | | (big_p(v0) = v1) | ~ $i(v0)) & ! [v0: $i] : ( ~ % 9.52/2.04 | | (big_p(v0) = 0) | ~ $i(v0)))))) & ((big_p(all_3_31) = % 9.52/2.04 | | all_3_30 & ! [v0: $i] : ! [v1: int] : ( ~ (all_3_30 = 0) | v1 % 9.52/2.04 | | = 0 | ~ (big_p(v0) = v1) | ~ $i(v0)) & ! [v0: $i] : % 9.52/2.04 | | (all_3_30 = 0 | ~ (big_p(v0) = 0) | ~ $i(v0)) & ((all_3_32 = % 9.52/2.04 | | 0 & ~ (all_3_34 = 0) & big_q(all_3_33) = 0 & % 9.52/2.04 | | big_q(all_3_35) = all_3_34) | ( ! [v0: $i] : ! [v1: int] : % 9.52/2.04 | | (v1 = 0 | ~ (big_q(v0) = v1) | ~ $i(v0)) & ! [v0: $i] : % 9.52/2.04 | | ( ~ (big_q(v0) = 0) | ~ $i(v0))))) | ( ! [v0: $i] : ! % 9.52/2.04 | | [v1: any] : ( ~ (big_p(v0) = v1) | ~ $i(v0) | ? [v2: $i] : ? % 9.52/2.04 | | [v3: any] : (big_p(v2) = v3 & $i(v2) & ( ~ (v3 = 0) | ~ (v1 % 9.52/2.04 | | = 0)) & (v3 = 0 | v1 = 0))) & ((all_3_36 = 0 & % 9.52/2.04 | | big_q(all_3_37) = 0 & ! [v0: $i] : ! [v1: int] : (v1 = 0 % 9.52/2.04 | | | ~ (big_q(v0) = v1) | ~ $i(v0))) | ( ~ (all_3_38 = 0) % 9.52/2.04 | | & big_q(all_3_39) = all_3_38 & ! [v0: $i] : ( ~ (big_q(v0) % 9.52/2.04 | | = 0) | ~ $i(v0)))))) % 9.52/2.04 | | % 9.52/2.04 | | ALPHA: (124) implies: % 9.52/2.04 | | (125) (big_p(all_3_31) = all_3_30 & ! [v0: $i] : ! [v1: int] : ( ~ % 9.52/2.04 | | (all_3_30 = 0) | v1 = 0 | ~ (big_p(v0) = v1) | ~ $i(v0)) & ! % 9.52/2.04 | | [v0: $i] : (all_3_30 = 0 | ~ (big_p(v0) = 0) | ~ $i(v0)) & % 9.52/2.04 | | ((all_3_32 = 0 & ~ (all_3_34 = 0) & big_q(all_3_33) = 0 & % 9.52/2.04 | | big_q(all_3_35) = all_3_34) | ( ! [v0: $i] : ! [v1: int] : % 9.52/2.04 | | (v1 = 0 | ~ (big_q(v0) = v1) | ~ $i(v0)) & ! [v0: $i] : ( % 9.52/2.04 | | ~ (big_q(v0) = 0) | ~ $i(v0))))) | ( ! [v0: $i] : ! [v1: % 9.52/2.04 | | any] : ( ~ (big_p(v0) = v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: % 9.52/2.04 | | any] : (big_p(v2) = v3 & $i(v2) & ( ~ (v3 = 0) | ~ (v1 = 0)) % 9.52/2.04 | | & (v3 = 0 | v1 = 0))) & ((all_3_36 = 0 & big_q(all_3_37) = 0 % 9.52/2.04 | | & ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (big_q(v0) = v1) % 9.52/2.04 | | | ~ $i(v0))) | ( ~ (all_3_38 = 0) & big_q(all_3_39) = % 9.52/2.04 | | all_3_38 & ! [v0: $i] : ( ~ (big_q(v0) = 0) | ~ $i(v0))))) % 9.52/2.04 | | (126) (big_q(all_3_21) = all_3_20 & ! [v0: $i] : ! [v1: int] : ( ~ % 9.52/2.04 | | (all_3_20 = 0) | v1 = 0 | ~ (big_q(v0) = v1) | ~ $i(v0)) & ! % 9.52/2.04 | | [v0: $i] : (all_3_20 = 0 | ~ (big_q(v0) = 0) | ~ $i(v0)) & % 9.52/2.04 | | ((all_3_22 = 0 & big_p(all_3_23) = 0 & ! [v0: $i] : ! [v1: int] % 9.52/2.04 | | : (v1 = 0 | ~ (big_p(v0) = v1) | ~ $i(v0))) | ( ~ (all_3_24 % 9.52/2.04 | | = 0) & big_p(all_3_25) = all_3_24 & ! [v0: $i] : ( ~ % 9.52/2.04 | | (big_p(v0) = 0) | ~ $i(v0))))) | ( ! [v0: $i] : ! [v1: % 9.52/2.04 | | any] : ( ~ (big_q(v0) = v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: % 9.52/2.04 | | any] : (big_q(v2) = v3 & $i(v2) & ( ~ (v3 = 0) | ~ (v1 = 0)) % 9.52/2.04 | | & (v3 = 0 | v1 = 0))) & ((all_3_26 = 0 & ~ (all_3_28 = 0) & % 9.52/2.04 | | big_p(all_3_27) = 0 & big_p(all_3_29) = all_3_28) | ( ! [v0: % 9.52/2.04 | | $i] : ! [v1: int] : (v1 = 0 | ~ (big_p(v0) = v1) | ~ % 9.52/2.04 | | $i(v0)) & ! [v0: $i] : ( ~ (big_p(v0) = 0) | ~ $i(v0))))) % 9.52/2.04 | | % 9.52/2.04 | | BETA: splitting (125) gives: % 9.52/2.04 | | % 9.52/2.04 | | Case 1: % 9.52/2.04 | | | % 9.52/2.04 | | | (127) big_p(all_3_31) = all_3_30 & ! [v0: $i] : ! [v1: int] : ( ~ % 9.52/2.04 | | | (all_3_30 = 0) | v1 = 0 | ~ (big_p(v0) = v1) | ~ $i(v0)) & ! % 9.52/2.04 | | | [v0: $i] : (all_3_30 = 0 | ~ (big_p(v0) = 0) | ~ $i(v0)) & % 9.52/2.04 | | | ((all_3_32 = 0 & ~ (all_3_34 = 0) & big_q(all_3_33) = 0 & % 9.52/2.04 | | | big_q(all_3_35) = all_3_34) | ( ! [v0: $i] : ! [v1: int] : % 9.52/2.04 | | | (v1 = 0 | ~ (big_q(v0) = v1) | ~ $i(v0)) & ! [v0: $i] : ( % 9.52/2.04 | | | ~ (big_q(v0) = 0) | ~ $i(v0)))) % 9.52/2.04 | | | % 9.52/2.04 | | | ALPHA: (127) implies: % 9.52/2.04 | | | (128) big_p(all_3_31) = all_3_30 % 9.52/2.04 | | | (129) (all_3_32 = 0 & ~ (all_3_34 = 0) & big_q(all_3_33) = 0 & % 9.52/2.04 | | | big_q(all_3_35) = all_3_34) | ( ! [v0: $i] : ! [v1: int] : (v1 % 9.52/2.04 | | | = 0 | ~ (big_q(v0) = v1) | ~ $i(v0)) & ! [v0: $i] : ( ~ % 9.52/2.04 | | | (big_q(v0) = 0) | ~ $i(v0))) % 9.52/2.04 | | | (130) ! [v0: $i] : (all_3_30 = 0 | ~ (big_p(v0) = 0) | ~ $i(v0)) % 9.52/2.04 | | | (131) ! [v0: $i] : ! [v1: int] : ( ~ (all_3_30 = 0) | v1 = 0 | ~ % 9.52/2.04 | | | (big_p(v0) = v1) | ~ $i(v0)) % 9.52/2.04 | | | % 9.52/2.04 | | | BETA: splitting (126) gives: % 9.52/2.04 | | | % 9.52/2.04 | | | Case 1: % 9.52/2.04 | | | | % 9.52/2.04 | | | | (132) big_q(all_3_21) = all_3_20 & ! [v0: $i] : ! [v1: int] : ( ~ % 9.52/2.04 | | | | (all_3_20 = 0) | v1 = 0 | ~ (big_q(v0) = v1) | ~ $i(v0)) & % 9.52/2.04 | | | | ! [v0: $i] : (all_3_20 = 0 | ~ (big_q(v0) = 0) | ~ $i(v0)) & % 9.52/2.04 | | | | ((all_3_22 = 0 & big_p(all_3_23) = 0 & ! [v0: $i] : ! [v1: % 9.52/2.04 | | | | int] : (v1 = 0 | ~ (big_p(v0) = v1) | ~ $i(v0))) | ( ~ % 9.52/2.04 | | | | (all_3_24 = 0) & big_p(all_3_25) = all_3_24 & ! [v0: $i] : % 9.52/2.04 | | | | ( ~ (big_p(v0) = 0) | ~ $i(v0)))) % 9.52/2.04 | | | | % 9.52/2.05 | | | | ALPHA: (132) implies: % 9.52/2.05 | | | | (133) big_q(all_3_21) = all_3_20 % 9.52/2.05 | | | | (134) ! [v0: $i] : (all_3_20 = 0 | ~ (big_q(v0) = 0) | ~ $i(v0)) % 9.52/2.05 | | | | (135) ! [v0: $i] : ! [v1: int] : ( ~ (all_3_20 = 0) | v1 = 0 | ~ % 9.52/2.05 | | | | (big_q(v0) = v1) | ~ $i(v0)) % 9.52/2.05 | | | | % 9.52/2.05 | | | | BETA: splitting (129) gives: % 9.52/2.05 | | | | % 9.52/2.05 | | | | Case 1: % 9.52/2.05 | | | | | % 9.52/2.05 | | | | | (136) all_3_32 = 0 & ~ (all_3_34 = 0) & big_q(all_3_33) = 0 & % 9.52/2.05 | | | | | big_q(all_3_35) = all_3_34 % 9.52/2.05 | | | | | % 9.52/2.05 | | | | | ALPHA: (136) implies: % 9.52/2.05 | | | | | (137) ~ (all_3_34 = 0) % 9.52/2.05 | | | | | (138) big_q(all_3_35) = all_3_34 % 9.52/2.05 | | | | | (139) big_q(all_3_33) = 0 % 9.52/2.05 | | | | | % 9.52/2.05 | | | | | GROUND_INST: instantiating (135) with all_3_35, all_3_34, simplifying % 9.52/2.05 | | | | | with (4), (138) gives: % 9.52/2.05 | | | | | (140) ~ (all_3_20 = 0) | all_3_34 = 0 % 9.52/2.05 | | | | | % 9.52/2.05 | | | | | GROUND_INST: instantiating (134) with all_3_33, simplifying with (5), % 9.52/2.05 | | | | | (139) gives: % 9.52/2.05 | | | | | (141) all_3_20 = 0 % 9.52/2.05 | | | | | % 9.52/2.05 | | | | | BETA: splitting (140) gives: % 9.52/2.05 | | | | | % 9.52/2.05 | | | | | Case 1: % 9.52/2.05 | | | | | | % 9.52/2.05 | | | | | | (142) ~ (all_3_20 = 0) % 9.52/2.05 | | | | | | % 9.52/2.05 | | | | | | REDUCE: (141), (142) imply: % 9.52/2.05 | | | | | | (143) $false % 9.52/2.05 | | | | | | % 9.52/2.05 | | | | | | CLOSE: (143) is inconsistent. % 9.52/2.05 | | | | | | % 9.52/2.05 | | | | | Case 2: % 9.52/2.05 | | | | | | % 9.52/2.05 | | | | | | (144) all_3_34 = 0 % 9.52/2.05 | | | | | | % 9.52/2.05 | | | | | | REDUCE: (137), (144) imply: % 9.52/2.05 | | | | | | (145) $false % 9.52/2.05 | | | | | | % 9.52/2.05 | | | | | | CLOSE: (145) is inconsistent. % 9.52/2.05 | | | | | | % 9.52/2.05 | | | | | End of split % 9.52/2.05 | | | | | % 9.52/2.05 | | | | Case 2: % 9.52/2.05 | | | | | % 9.52/2.05 | | | | | (146) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (big_q(v0) = v1) | % 9.52/2.05 | | | | | ~ $i(v0)) & ! [v0: $i] : ( ~ (big_q(v0) = 0) | ~ $i(v0)) % 9.52/2.05 | | | | | % 9.52/2.05 | | | | | ALPHA: (146) implies: % 9.52/2.05 | | | | | (147) ! [v0: $i] : ( ~ (big_q(v0) = 0) | ~ $i(v0)) % 9.52/2.05 | | | | | (148) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (big_q(v0) = v1) | % 9.52/2.05 | | | | | ~ $i(v0)) % 9.52/2.05 | | | | | % 9.52/2.05 | | | | | GROUND_INST: instantiating (148) with all_3_21, all_3_20, simplifying % 9.52/2.05 | | | | | with (11), (133) gives: % 9.52/2.05 | | | | | (149) all_3_20 = 0 % 9.52/2.05 | | | | | % 9.52/2.05 | | | | | REDUCE: (133), (149) imply: % 9.52/2.05 | | | | | (150) big_q(all_3_21) = 0 % 9.52/2.05 | | | | | % 9.52/2.05 | | | | | GROUND_INST: instantiating (147) with all_3_21, simplifying with (11), % 9.52/2.05 | | | | | (150) gives: % 9.52/2.05 | | | | | (151) $false % 9.52/2.05 | | | | | % 9.52/2.05 | | | | | CLOSE: (151) is inconsistent. % 9.52/2.05 | | | | | % 9.52/2.05 | | | | End of split % 9.52/2.05 | | | | % 9.52/2.05 | | | Case 2: % 9.52/2.05 | | | | % 9.52/2.05 | | | | (152) ! [v0: $i] : ! [v1: any] : ( ~ (big_q(v0) = v1) | ~ $i(v0) | % 9.52/2.05 | | | | ? [v2: $i] : ? [v3: any] : (big_q(v2) = v3 & $i(v2) & ( ~ % 9.52/2.05 | | | | (v3 = 0) | ~ (v1 = 0)) & (v3 = 0 | v1 = 0))) & % 9.52/2.05 | | | | ((all_3_26 = 0 & ~ (all_3_28 = 0) & big_p(all_3_27) = 0 & % 9.52/2.05 | | | | big_p(all_3_29) = all_3_28) | ( ! [v0: $i] : ! [v1: int] : % 9.52/2.05 | | | | (v1 = 0 | ~ (big_p(v0) = v1) | ~ $i(v0)) & ! [v0: $i] : % 9.52/2.05 | | | | ( ~ (big_p(v0) = 0) | ~ $i(v0)))) % 9.52/2.05 | | | | % 9.52/2.05 | | | | ALPHA: (152) implies: % 9.52/2.05 | | | | (153) (all_3_26 = 0 & ~ (all_3_28 = 0) & big_p(all_3_27) = 0 & % 9.52/2.05 | | | | big_p(all_3_29) = all_3_28) | ( ! [v0: $i] : ! [v1: int] : % 9.52/2.05 | | | | (v1 = 0 | ~ (big_p(v0) = v1) | ~ $i(v0)) & ! [v0: $i] : ( % 9.52/2.05 | | | | ~ (big_p(v0) = 0) | ~ $i(v0))) % 9.52/2.05 | | | | % 9.52/2.05 | | | | BETA: splitting (153) gives: % 9.52/2.05 | | | | % 9.52/2.05 | | | | Case 1: % 9.52/2.05 | | | | | % 9.52/2.05 | | | | | (154) all_3_26 = 0 & ~ (all_3_28 = 0) & big_p(all_3_27) = 0 & % 9.52/2.05 | | | | | big_p(all_3_29) = all_3_28 % 9.52/2.05 | | | | | % 9.52/2.05 | | | | | ALPHA: (154) implies: % 9.52/2.05 | | | | | (155) ~ (all_3_28 = 0) % 9.52/2.05 | | | | | (156) big_p(all_3_29) = all_3_28 % 9.52/2.05 | | | | | (157) big_p(all_3_27) = 0 % 9.52/2.05 | | | | | % 9.52/2.05 | | | | | GROUND_INST: instantiating (131) with all_3_29, all_3_28, simplifying % 9.52/2.05 | | | | | with (7), (156) gives: % 9.52/2.05 | | | | | (158) ~ (all_3_30 = 0) | all_3_28 = 0 % 9.52/2.05 | | | | | % 9.52/2.05 | | | | | GROUND_INST: instantiating (130) with all_3_27, simplifying with (8), % 9.52/2.05 | | | | | (157) gives: % 9.52/2.05 | | | | | (159) all_3_30 = 0 % 9.52/2.05 | | | | | % 9.52/2.05 | | | | | BETA: splitting (158) gives: % 9.52/2.05 | | | | | % 9.52/2.05 | | | | | Case 1: % 9.52/2.05 | | | | | | % 9.52/2.05 | | | | | | (160) ~ (all_3_30 = 0) % 9.52/2.05 | | | | | | % 9.52/2.05 | | | | | | REDUCE: (159), (160) imply: % 9.52/2.05 | | | | | | (161) $false % 9.52/2.05 | | | | | | % 9.52/2.05 | | | | | | CLOSE: (161) is inconsistent. % 9.52/2.05 | | | | | | % 9.52/2.05 | | | | | Case 2: % 9.52/2.05 | | | | | | % 9.52/2.05 | | | | | | (162) all_3_28 = 0 % 9.52/2.05 | | | | | | % 9.52/2.05 | | | | | | REDUCE: (155), (162) imply: % 9.52/2.05 | | | | | | (163) $false % 9.52/2.05 | | | | | | % 9.52/2.05 | | | | | | CLOSE: (163) is inconsistent. % 9.52/2.05 | | | | | | % 9.52/2.05 | | | | | End of split % 9.52/2.05 | | | | | % 9.52/2.05 | | | | Case 2: % 9.52/2.05 | | | | | % 9.52/2.05 | | | | | (164) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (big_p(v0) = v1) | % 9.52/2.05 | | | | | ~ $i(v0)) & ! [v0: $i] : ( ~ (big_p(v0) = 0) | ~ $i(v0)) % 9.52/2.05 | | | | | % 9.52/2.05 | | | | | ALPHA: (164) implies: % 9.52/2.05 | | | | | (165) ! [v0: $i] : ( ~ (big_p(v0) = 0) | ~ $i(v0)) % 9.52/2.05 | | | | | (166) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (big_p(v0) = v1) | % 9.52/2.05 | | | | | ~ $i(v0)) % 9.52/2.05 | | | | | % 9.52/2.05 | | | | | GROUND_INST: instantiating (166) with all_3_31, all_3_30, simplifying % 9.52/2.05 | | | | | with (6), (128) gives: % 9.52/2.05 | | | | | (167) all_3_30 = 0 % 9.52/2.05 | | | | | % 9.52/2.05 | | | | | REDUCE: (128), (167) imply: % 9.52/2.05 | | | | | (168) big_p(all_3_31) = 0 % 9.52/2.05 | | | | | % 9.52/2.05 | | | | | GROUND_INST: instantiating (165) with all_3_31, simplifying with (6), % 9.52/2.05 | | | | | (168) gives: % 9.52/2.05 | | | | | (169) $false % 9.52/2.05 | | | | | % 9.52/2.05 | | | | | CLOSE: (169) is inconsistent. % 9.52/2.05 | | | | | % 9.52/2.05 | | | | End of split % 9.52/2.05 | | | | % 9.52/2.05 | | | End of split % 9.52/2.05 | | | % 9.52/2.05 | | Case 2: % 9.52/2.05 | | | % 9.52/2.05 | | | (170) ! [v0: $i] : ! [v1: any] : ( ~ (big_p(v0) = v1) | ~ $i(v0) | % 9.52/2.05 | | | ? [v2: $i] : ? [v3: any] : (big_p(v2) = v3 & $i(v2) & ( ~ (v3 % 9.52/2.05 | | | = 0) | ~ (v1 = 0)) & (v3 = 0 | v1 = 0))) & ((all_3_36 = % 9.52/2.05 | | | 0 & big_q(all_3_37) = 0 & ! [v0: $i] : ! [v1: int] : (v1 = % 9.52/2.05 | | | 0 | ~ (big_q(v0) = v1) | ~ $i(v0))) | ( ~ (all_3_38 = 0) % 9.52/2.05 | | | & big_q(all_3_39) = all_3_38 & ! [v0: $i] : ( ~ (big_q(v0) = % 9.52/2.05 | | | 0) | ~ $i(v0)))) % 9.52/2.05 | | | % 9.52/2.05 | | | ALPHA: (170) implies: % 9.52/2.05 | | | (171) (all_3_36 = 0 & big_q(all_3_37) = 0 & ! [v0: $i] : ! [v1: int] % 9.52/2.05 | | | : (v1 = 0 | ~ (big_q(v0) = v1) | ~ $i(v0))) | ( ~ (all_3_38 = % 9.52/2.05 | | | 0) & big_q(all_3_39) = all_3_38 & ! [v0: $i] : ( ~ % 9.52/2.05 | | | (big_q(v0) = 0) | ~ $i(v0))) % 9.52/2.06 | | | (172) ! [v0: $i] : ! [v1: any] : ( ~ (big_p(v0) = v1) | ~ $i(v0) | % 9.52/2.06 | | | ? [v2: $i] : ? [v3: any] : (big_p(v2) = v3 & $i(v2) & ( ~ (v3 % 9.52/2.06 | | | = 0) | ~ (v1 = 0)) & (v3 = 0 | v1 = 0))) % 9.52/2.06 | | | % 9.52/2.06 | | | BETA: splitting (126) gives: % 9.52/2.06 | | | % 9.52/2.06 | | | Case 1: % 9.52/2.06 | | | | % 9.52/2.06 | | | | (173) big_q(all_3_21) = all_3_20 & ! [v0: $i] : ! [v1: int] : ( ~ % 9.52/2.06 | | | | (all_3_20 = 0) | v1 = 0 | ~ (big_q(v0) = v1) | ~ $i(v0)) & % 9.52/2.06 | | | | ! [v0: $i] : (all_3_20 = 0 | ~ (big_q(v0) = 0) | ~ $i(v0)) & % 9.52/2.06 | | | | ((all_3_22 = 0 & big_p(all_3_23) = 0 & ! [v0: $i] : ! [v1: % 9.52/2.06 | | | | int] : (v1 = 0 | ~ (big_p(v0) = v1) | ~ $i(v0))) | ( ~ % 9.52/2.06 | | | | (all_3_24 = 0) & big_p(all_3_25) = all_3_24 & ! [v0: $i] : % 9.52/2.06 | | | | ( ~ (big_p(v0) = 0) | ~ $i(v0)))) % 9.52/2.06 | | | | % 9.52/2.06 | | | | ALPHA: (173) implies: % 9.52/2.06 | | | | (174) (all_3_22 = 0 & big_p(all_3_23) = 0 & ! [v0: $i] : ! [v1: % 9.52/2.06 | | | | int] : (v1 = 0 | ~ (big_p(v0) = v1) | ~ $i(v0))) | ( ~ % 9.52/2.06 | | | | (all_3_24 = 0) & big_p(all_3_25) = all_3_24 & ! [v0: $i] : ( % 9.52/2.06 | | | | ~ (big_p(v0) = 0) | ~ $i(v0))) % 9.52/2.06 | | | | % 9.52/2.06 | | | | BETA: splitting (174) gives: % 9.52/2.06 | | | | % 9.52/2.06 | | | | Case 1: % 9.52/2.06 | | | | | % 9.52/2.06 | | | | | (175) all_3_22 = 0 & big_p(all_3_23) = 0 & ! [v0: $i] : ! [v1: % 9.52/2.06 | | | | | int] : (v1 = 0 | ~ (big_p(v0) = v1) | ~ $i(v0)) % 9.52/2.06 | | | | | % 9.52/2.06 | | | | | ALPHA: (175) implies: % 9.52/2.06 | | | | | (176) big_p(all_3_23) = 0 % 9.52/2.06 | | | | | (177) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (big_p(v0) = v1) | % 9.52/2.06 | | | | | ~ $i(v0)) % 9.52/2.06 | | | | | % 9.52/2.06 | | | | | GROUND_INST: instantiating (172) with all_3_23, 0, simplifying with % 9.52/2.06 | | | | | (10), (176) gives: % 9.52/2.06 | | | | | (178) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & big_p(v0) = v1 & % 9.52/2.06 | | | | | $i(v0)) % 9.52/2.06 | | | | | % 9.52/2.06 | | | | | DELTA: instantiating (178) with fresh symbols all_40_0, all_40_1 % 9.52/2.06 | | | | | gives: % 9.52/2.06 | | | | | (179) ~ (all_40_0 = 0) & big_p(all_40_1) = all_40_0 & $i(all_40_1) % 9.52/2.06 | | | | | % 9.52/2.06 | | | | | ALPHA: (179) implies: % 9.52/2.06 | | | | | (180) ~ (all_40_0 = 0) % 9.52/2.06 | | | | | (181) $i(all_40_1) % 9.52/2.06 | | | | | (182) big_p(all_40_1) = all_40_0 % 9.52/2.06 | | | | | % 9.52/2.06 | | | | | GROUND_INST: instantiating (177) with all_40_1, all_40_0, simplifying % 9.52/2.06 | | | | | with (181), (182) gives: % 9.52/2.06 | | | | | (183) all_40_0 = 0 % 9.52/2.06 | | | | | % 9.52/2.06 | | | | | REDUCE: (180), (183) imply: % 9.52/2.06 | | | | | (184) $false % 9.52/2.06 | | | | | % 9.52/2.06 | | | | | CLOSE: (184) is inconsistent. % 9.52/2.06 | | | | | % 9.52/2.06 | | | | Case 2: % 9.52/2.06 | | | | | % 9.52/2.06 | | | | | (185) ~ (all_3_24 = 0) & big_p(all_3_25) = all_3_24 & ! [v0: $i] % 9.52/2.06 | | | | | : ( ~ (big_p(v0) = 0) | ~ $i(v0)) % 9.52/2.06 | | | | | % 9.52/2.06 | | | | | ALPHA: (185) implies: % 9.52/2.06 | | | | | (186) ~ (all_3_24 = 0) % 9.52/2.06 | | | | | (187) big_p(all_3_25) = all_3_24 % 9.52/2.06 | | | | | (188) ! [v0: $i] : ( ~ (big_p(v0) = 0) | ~ $i(v0)) % 9.52/2.06 | | | | | % 9.52/2.06 | | | | | GROUND_INST: instantiating (172) with all_3_25, all_3_24, simplifying % 9.52/2.06 | | | | | with (9), (187) gives: % 9.52/2.06 | | | | | (189) ? [v0: $i] : ? [v1: any] : (big_p(v0) = v1 & $i(v0) & ( ~ % 9.52/2.06 | | | | | (v1 = 0) | ~ (all_3_24 = 0)) & (v1 = 0 | all_3_24 = 0)) % 9.52/2.06 | | | | | % 9.52/2.06 | | | | | DELTA: instantiating (189) with fresh symbols all_40_0, all_40_1 % 9.52/2.06 | | | | | gives: % 9.52/2.06 | | | | | (190) big_p(all_40_1) = all_40_0 & $i(all_40_1) & ( ~ (all_40_0 = % 9.52/2.06 | | | | | 0) | ~ (all_3_24 = 0)) & (all_40_0 = 0 | all_3_24 = 0) % 9.52/2.06 | | | | | % 9.52/2.06 | | | | | ALPHA: (190) implies: % 9.52/2.06 | | | | | (191) $i(all_40_1) % 9.52/2.06 | | | | | (192) big_p(all_40_1) = all_40_0 % 9.52/2.06 | | | | | (193) all_40_0 = 0 | all_3_24 = 0 % 9.52/2.06 | | | | | % 9.52/2.06 | | | | | BETA: splitting (193) gives: % 9.52/2.06 | | | | | % 9.52/2.06 | | | | | Case 1: % 9.52/2.06 | | | | | | % 9.52/2.06 | | | | | | (194) all_40_0 = 0 % 9.52/2.06 | | | | | | % 9.52/2.06 | | | | | | REDUCE: (192), (194) imply: % 9.52/2.06 | | | | | | (195) big_p(all_40_1) = 0 % 9.52/2.06 | | | | | | % 9.52/2.06 | | | | | | GROUND_INST: instantiating (188) with all_40_1, simplifying with % 9.52/2.06 | | | | | | (191), (195) gives: % 9.52/2.06 | | | | | | (196) $false % 9.52/2.06 | | | | | | % 9.52/2.06 | | | | | | CLOSE: (196) is inconsistent. % 9.52/2.06 | | | | | | % 9.52/2.06 | | | | | Case 2: % 9.52/2.06 | | | | | | % 9.52/2.06 | | | | | | (197) all_3_24 = 0 % 9.52/2.06 | | | | | | % 9.52/2.06 | | | | | | REDUCE: (186), (197) imply: % 9.52/2.06 | | | | | | (198) $false % 9.52/2.06 | | | | | | % 9.52/2.06 | | | | | | CLOSE: (198) is inconsistent. % 9.52/2.06 | | | | | | % 9.52/2.06 | | | | | End of split % 9.52/2.06 | | | | | % 9.52/2.06 | | | | End of split % 9.52/2.06 | | | | % 9.52/2.06 | | | Case 2: % 9.52/2.06 | | | | % 9.52/2.06 | | | | (199) ! [v0: $i] : ! [v1: any] : ( ~ (big_q(v0) = v1) | ~ $i(v0) | % 9.52/2.06 | | | | ? [v2: $i] : ? [v3: any] : (big_q(v2) = v3 & $i(v2) & ( ~ % 9.52/2.06 | | | | (v3 = 0) | ~ (v1 = 0)) & (v3 = 0 | v1 = 0))) & % 9.52/2.06 | | | | ((all_3_26 = 0 & ~ (all_3_28 = 0) & big_p(all_3_27) = 0 & % 9.52/2.06 | | | | big_p(all_3_29) = all_3_28) | ( ! [v0: $i] : ! [v1: int] : % 9.52/2.06 | | | | (v1 = 0 | ~ (big_p(v0) = v1) | ~ $i(v0)) & ! [v0: $i] : % 9.52/2.06 | | | | ( ~ (big_p(v0) = 0) | ~ $i(v0)))) % 9.52/2.06 | | | | % 9.52/2.06 | | | | ALPHA: (199) implies: % 9.52/2.06 | | | | (200) ! [v0: $i] : ! [v1: any] : ( ~ (big_q(v0) = v1) | ~ $i(v0) | % 9.52/2.06 | | | | ? [v2: $i] : ? [v3: any] : (big_q(v2) = v3 & $i(v2) & ( ~ % 9.52/2.06 | | | | (v3 = 0) | ~ (v1 = 0)) & (v3 = 0 | v1 = 0))) % 9.52/2.06 | | | | % 9.52/2.06 | | | | BETA: splitting (171) gives: % 9.52/2.06 | | | | % 9.52/2.06 | | | | Case 1: % 9.52/2.06 | | | | | % 9.52/2.06 | | | | | (201) all_3_36 = 0 & big_q(all_3_37) = 0 & ! [v0: $i] : ! [v1: % 9.52/2.06 | | | | | int] : (v1 = 0 | ~ (big_q(v0) = v1) | ~ $i(v0)) % 9.52/2.06 | | | | | % 9.52/2.06 | | | | | ALPHA: (201) implies: % 9.52/2.06 | | | | | (202) big_q(all_3_37) = 0 % 9.52/2.06 | | | | | (203) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (big_q(v0) = v1) | % 9.52/2.06 | | | | | ~ $i(v0)) % 9.52/2.06 | | | | | % 9.52/2.06 | | | | | GROUND_INST: instantiating (200) with all_3_37, 0, simplifying with % 9.52/2.06 | | | | | (3), (202) gives: % 9.52/2.06 | | | | | (204) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & big_q(v0) = v1 & % 9.52/2.06 | | | | | $i(v0)) % 9.52/2.06 | | | | | % 9.52/2.06 | | | | | DELTA: instantiating (204) with fresh symbols all_27_0, all_27_1 % 9.52/2.06 | | | | | gives: % 9.52/2.06 | | | | | (205) ~ (all_27_0 = 0) & big_q(all_27_1) = all_27_0 & $i(all_27_1) % 9.52/2.06 | | | | | % 9.52/2.06 | | | | | ALPHA: (205) implies: % 9.52/2.06 | | | | | (206) ~ (all_27_0 = 0) % 9.52/2.06 | | | | | (207) $i(all_27_1) % 9.52/2.06 | | | | | (208) big_q(all_27_1) = all_27_0 % 9.52/2.06 | | | | | % 9.52/2.06 | | | | | GROUND_INST: instantiating (203) with all_27_1, all_27_0, simplifying % 9.52/2.06 | | | | | with (207), (208) gives: % 9.52/2.06 | | | | | (209) all_27_0 = 0 % 9.52/2.06 | | | | | % 9.52/2.06 | | | | | REDUCE: (206), (209) imply: % 9.52/2.06 | | | | | (210) $false % 9.52/2.06 | | | | | % 9.52/2.06 | | | | | CLOSE: (210) is inconsistent. % 9.52/2.06 | | | | | % 9.52/2.06 | | | | Case 2: % 9.52/2.06 | | | | | % 9.52/2.06 | | | | | (211) ~ (all_3_38 = 0) & big_q(all_3_39) = all_3_38 & ! [v0: $i] % 9.52/2.06 | | | | | : ( ~ (big_q(v0) = 0) | ~ $i(v0)) % 9.52/2.06 | | | | | % 9.52/2.06 | | | | | ALPHA: (211) implies: % 9.52/2.06 | | | | | (212) ~ (all_3_38 = 0) % 9.52/2.06 | | | | | (213) big_q(all_3_39) = all_3_38 % 9.52/2.06 | | | | | (214) ! [v0: $i] : ( ~ (big_q(v0) = 0) | ~ $i(v0)) % 9.52/2.06 | | | | | % 9.52/2.07 | | | | | GROUND_INST: instantiating (200) with all_3_39, all_3_38, simplifying % 9.52/2.07 | | | | | with (2), (213) gives: % 9.52/2.07 | | | | | (215) ? [v0: $i] : ? [v1: any] : (big_q(v0) = v1 & $i(v0) & ( ~ % 9.52/2.07 | | | | | (v1 = 0) | ~ (all_3_38 = 0)) & (v1 = 0 | all_3_38 = 0)) % 9.52/2.07 | | | | | % 9.52/2.07 | | | | | DELTA: instantiating (215) with fresh symbols all_27_0, all_27_1 % 9.52/2.07 | | | | | gives: % 9.52/2.07 | | | | | (216) big_q(all_27_1) = all_27_0 & $i(all_27_1) & ( ~ (all_27_0 = % 9.52/2.07 | | | | | 0) | ~ (all_3_38 = 0)) & (all_27_0 = 0 | all_3_38 = 0) % 9.52/2.07 | | | | | % 9.52/2.07 | | | | | ALPHA: (216) implies: % 9.52/2.07 | | | | | (217) $i(all_27_1) % 9.52/2.07 | | | | | (218) big_q(all_27_1) = all_27_0 % 9.52/2.07 | | | | | (219) all_27_0 = 0 | all_3_38 = 0 % 9.52/2.07 | | | | | % 9.52/2.07 | | | | | BETA: splitting (219) gives: % 9.52/2.07 | | | | | % 9.52/2.07 | | | | | Case 1: % 9.52/2.07 | | | | | | % 9.52/2.07 | | | | | | (220) all_27_0 = 0 % 9.52/2.07 | | | | | | % 9.52/2.07 | | | | | | REDUCE: (218), (220) imply: % 9.52/2.07 | | | | | | (221) big_q(all_27_1) = 0 % 9.52/2.07 | | | | | | % 9.52/2.07 | | | | | | GROUND_INST: instantiating (214) with all_27_1, simplifying with % 9.52/2.07 | | | | | | (217), (221) gives: % 9.52/2.07 | | | | | | (222) $false % 9.52/2.07 | | | | | | % 9.52/2.07 | | | | | | CLOSE: (222) is inconsistent. % 9.52/2.07 | | | | | | % 9.52/2.07 | | | | | Case 2: % 9.52/2.07 | | | | | | % 9.52/2.07 | | | | | | (223) all_3_38 = 0 % 9.52/2.07 | | | | | | % 9.52/2.07 | | | | | | REDUCE: (212), (223) imply: % 9.52/2.07 | | | | | | (224) $false % 9.52/2.07 | | | | | | % 9.52/2.07 | | | | | | CLOSE: (224) is inconsistent. % 9.52/2.07 | | | | | | % 9.52/2.07 | | | | | End of split % 9.52/2.07 | | | | | % 9.52/2.07 | | | | End of split % 9.52/2.07 | | | | % 9.52/2.07 | | | End of split % 9.52/2.07 | | | % 9.52/2.07 | | End of split % 9.52/2.07 | | % 9.52/2.07 | End of split % 9.52/2.07 | % 9.52/2.07 End of proof % 9.52/2.07 % SZS output end Proof for theBenchmark % 9.52/2.07 % 9.52/2.07 1560ms %------------------------------------------------------------------------------