%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SET724+4 : TPTP v8.1.2. Bugfixed v2.2.1. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n018.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 : Thu Aug 31 15:26:09 EDT 2023 % Result : Theorem 25.80s 4.26s % Output : Proof 26.89s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SET724+4 : TPTP v8.1.2. Bugfixed v2.2.1. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.34 % Computer : n018.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 300 % 0.13/0.34 % DateTime : Sat Aug 26 09:59:30 EDT 2023 % 0.13/0.34 % 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. % 0.20/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.20/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.20/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.20/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.20/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.20/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.20/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 3.77/1.30 Prover 1: Preprocessing ... % 3.77/1.30 Prover 4: Preprocessing ... % 4.31/1.32 Prover 0: Preprocessing ... % 4.31/1.32 Prover 5: Preprocessing ... % 4.31/1.32 Prover 6: Preprocessing ... % 4.31/1.32 Prover 2: Preprocessing ... % 4.31/1.32 Prover 3: Preprocessing ... % 9.52/2.04 Prover 5: Proving ... % 9.52/2.05 Prover 2: Proving ... % 9.76/2.14 Prover 6: Proving ... % 9.76/2.17 Prover 3: Constructing countermodel ... % 9.76/2.21 Prover 1: Constructing countermodel ... % 13.99/2.66 Prover 4: Constructing countermodel ... % 14.16/2.70 Prover 0: Proving ... % 25.80/4.25 Prover 4: Found proof (size 559) % 25.80/4.25 Prover 4: proved (3623ms) % 25.80/4.25 Prover 2: stopped % 25.80/4.25 Prover 6: stopped % 25.80/4.25 Prover 5: stopped % 25.80/4.25 Prover 1: stopped % 25.80/4.26 Prover 0: stopped % 25.80/4.26 Prover 3: stopped % 25.80/4.26 % 25.80/4.26 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 25.80/4.26 % 26.12/4.27 % SZS output start Proof for theBenchmark % 26.12/4.28 Assumptions after simplification: % 26.12/4.28 --------------------------------- % 26.12/4.28 % 26.12/4.28 (compose_function) % 26.12/4.31 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 26.12/4.31 $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: int] : ! [v9: $i] : (v8 = 0 | ~ % 26.12/4.31 (compose_function(v0, v1, v2, v3, v4) = v7) | ~ (apply(v7, v5, v6) = v8) | % 26.12/4.31 ~ (apply(v1, v5, v9) = 0) | ~ $i(v9) | ~ $i(v6) | ~ $i(v5) | ~ $i(v4) | % 26.12/4.31 ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v10: any] : ? [v11: any] % 26.12/4.31 : ((apply(v0, v9, v6) = v11 & member(v9, v3) = v10 & ( ~ (v11 = 0) | ~ (v10 % 26.12/4.31 = 0))) | (member(v6, v4) = v11 & member(v5, v2) = v10 & ( ~ (v11 = % 26.12/4.31 0) | ~ (v10 = 0))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 26.12/4.31 [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: % 26.12/4.31 int] : ! [v9: $i] : (v8 = 0 | ~ (compose_function(v0, v1, v2, v3, v4) = % 26.12/4.31 v7) | ~ (apply(v7, v5, v6) = v8) | ~ (apply(v0, v9, v6) = 0) | ~ $i(v9) % 26.12/4.31 | ~ $i(v6) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 26.12/4.31 $i(v0) | ? [v10: any] : ? [v11: any] : ((apply(v1, v5, v9) = v11 & % 26.12/4.31 member(v9, v3) = v10 & ( ~ (v11 = 0) | ~ (v10 = 0))) | (member(v6, v4) % 26.12/4.32 = v11 & member(v5, v2) = v10 & ( ~ (v11 = 0) | ~ (v10 = 0))))) & ! % 26.12/4.32 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] % 26.12/4.32 : ! [v6: $i] : ! [v7: $i] : ! [v8: int] : ! [v9: $i] : (v8 = 0 | ~ % 26.12/4.32 (compose_function(v0, v1, v2, v3, v4) = v7) | ~ (apply(v7, v5, v6) = v8) | % 26.12/4.32 ~ (member(v9, v3) = 0) | ~ $i(v9) | ~ $i(v6) | ~ $i(v5) | ~ $i(v4) | ~ % 26.12/4.32 $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v10: any] : ? [v11: any] : % 26.12/4.32 ((apply(v1, v5, v9) = v10 & apply(v0, v9, v6) = v11 & ( ~ (v11 = 0) | ~ % 26.12/4.32 (v10 = 0))) | (member(v6, v4) = v11 & member(v5, v2) = v10 & ( ~ (v11 % 26.12/4.32 = 0) | ~ (v10 = 0))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 26.12/4.32 ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ( ~ % 26.12/4.32 (compose_function(v0, v1, v2, v3, v4) = v7) | ~ (apply(v7, v5, v6) = 0) | % 26.12/4.32 ~ $i(v6) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 26.12/4.32 $i(v0) | ? [v8: any] : ? [v9: any] : ? [v10: $i] : ? [v11: int] : ? % 26.12/4.32 [v12: int] : ? [v13: int] : ($i(v10) & ((v13 = 0 & v12 = 0 & v11 = 0 & % 26.12/4.32 apply(v1, v5, v10) = 0 & apply(v0, v10, v6) = 0 & member(v10, v3) = 0) % 26.12/4.32 | (member(v6, v4) = v9 & member(v5, v2) = v8 & ( ~ (v9 = 0) | ~ (v8 = % 26.12/4.32 0)))))) % 26.12/4.32 % 26.12/4.32 (equal_maps) % 26.12/4.32 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 26.12/4.32 $i] : ! [v6: $i] : (v6 = v5 | ~ (equal_maps(v0, v1, v2, v3) = 0) | ~ % 26.12/4.32 (apply(v1, v4, v6) = 0) | ~ (apply(v0, v4, v5) = 0) | ~ $i(v6) | ~ $i(v5) % 26.12/4.32 | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v7: any] : % 26.12/4.32 ? [v8: any] : ? [v9: any] : (member(v6, v3) = v9 & member(v5, v3) = v8 & % 26.12/4.32 member(v4, v2) = v7 & ( ~ (v9 = 0) | ~ (v8 = 0) | ~ (v7 = 0)))) & ! % 26.12/4.32 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] % 26.12/4.32 : ! [v6: $i] : (v6 = v5 | ~ (equal_maps(v0, v1, v2, v3) = 0) | ~ (apply(v1, % 26.12/4.32 v4, v6) = 0) | ~ (member(v5, v3) = 0) | ~ $i(v6) | ~ $i(v5) | ~ % 26.12/4.32 $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v7: any] : ? % 26.12/4.32 [v8: any] : ? [v9: any] : (apply(v0, v4, v5) = v9 & member(v6, v3) = v8 & % 26.12/4.32 member(v4, v2) = v7 & ( ~ (v9 = 0) | ~ (v8 = 0) | ~ (v7 = 0)))) & ! % 26.12/4.32 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] % 26.12/4.32 : ! [v6: $i] : (v6 = v5 | ~ (equal_maps(v0, v1, v2, v3) = 0) | ~ (apply(v0, % 26.12/4.32 v4, v5) = 0) | ~ (member(v6, v3) = 0) | ~ $i(v6) | ~ $i(v5) | ~ % 26.12/4.32 $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v7: any] : ? % 26.12/4.32 [v8: any] : ? [v9: any] : (apply(v1, v4, v6) = v9 & member(v5, v3) = v8 & % 26.12/4.32 member(v4, v2) = v7 & ( ~ (v9 = 0) | ~ (v8 = 0) | ~ (v7 = 0)))) & ! % 26.12/4.32 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] % 26.12/4.32 : ! [v6: $i] : (v6 = v5 | ~ (equal_maps(v0, v1, v2, v3) = 0) | ~ % 26.12/4.32 (member(v6, v3) = 0) | ~ (member(v5, v3) = 0) | ~ (member(v4, v2) = 0) | % 26.12/4.32 ~ $i(v6) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 26.12/4.32 $i(v0) | ? [v7: any] : ? [v8: any] : (apply(v1, v4, v6) = v8 & apply(v0, % 26.12/4.32 v4, v5) = v7 & ( ~ (v8 = 0) | ~ (v7 = 0)))) & ! [v0: $i] : ! [v1: $i] % 26.12/4.32 : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0 | ~ (equal_maps(v0, v1, % 26.12/4.32 v2, v3) = v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: % 26.12/4.32 $i] : ? [v6: $i] : ? [v7: $i] : ( ~ (v7 = v6) & apply(v1, v5, v7) = 0 & % 26.12/4.32 apply(v0, v5, v6) = 0 & member(v7, v3) = 0 & member(v6, v3) = 0 & % 26.12/4.32 member(v5, v2) = 0 & $i(v7) & $i(v6) & $i(v5))) % 26.12/4.32 % 26.12/4.32 (maps) % 26.12/4.33 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 26.12/4.33 $i] : (v5 = v4 | ~ (maps(v0, v1, v2) = 0) | ~ (apply(v0, v3, v5) = 0) | ~ % 26.12/4.33 (apply(v0, v3, v4) = 0) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ % 26.12/4.33 $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: any] : ? [v8: any] : % 26.12/4.33 (member(v5, v2) = v8 & member(v4, v2) = v7 & member(v3, v1) = v6 & ( ~ (v8 = % 26.12/4.33 0) | ~ (v7 = 0) | ~ (v6 = 0)))) & ! [v0: $i] : ! [v1: $i] : ! % 26.12/4.33 [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v5 = v4 | ~ (maps(v0, % 26.12/4.33 v1, v2) = 0) | ~ (apply(v0, v3, v5) = 0) | ~ (member(v4, v2) = 0) | ~ % 26.12/4.33 $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: % 26.12/4.33 any] : ? [v7: any] : ? [v8: any] : (apply(v0, v3, v4) = v8 & member(v5, % 26.12/4.33 v2) = v7 & member(v3, v1) = v6 & ( ~ (v8 = 0) | ~ (v7 = 0) | ~ (v6 = % 26.12/4.33 0)))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! % 26.12/4.33 [v4: $i] : ! [v5: $i] : (v5 = v4 | ~ (maps(v0, v1, v2) = 0) | ~ (apply(v0, % 26.12/4.33 v3, v4) = 0) | ~ (member(v5, v2) = 0) | ~ $i(v5) | ~ $i(v4) | ~ % 26.12/4.33 $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: any] : % 26.12/4.33 ? [v8: any] : (apply(v0, v3, v5) = v8 & member(v4, v2) = v7 & member(v3, v1) % 26.12/4.33 = v6 & ( ~ (v8 = 0) | ~ (v7 = 0) | ~ (v6 = 0)))) & ! [v0: $i] : ! [v1: % 26.12/4.33 $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v5 = v4 | ~ % 26.12/4.33 (maps(v0, v1, v2) = 0) | ~ (member(v5, v2) = 0) | ~ (member(v4, v2) = 0) | % 26.12/4.33 ~ (member(v3, v1) = 0) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ % 26.12/4.33 $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: any] : (apply(v0, v3, v5) = v7 & % 26.12/4.33 apply(v0, v3, v4) = v6 & ( ~ (v7 = 0) | ~ (v6 = 0)))) & ! [v0: $i] : ! % 26.12/4.33 [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (maps(v0, v1, v2) = v3) | % 26.12/4.33 ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: $i] : ? [v5: $i] : ? [v6: $i] % 26.12/4.33 : ? [v7: int] : ? [v8: int] : ? [v9: int] : ? [v10: int] : ? [v11: int] % 26.12/4.33 : ? [v12: $i] : ? [v13: int] : ($i(v12) & $i(v6) & $i(v5) & $i(v4) & ((v13 % 26.12/4.33 = 0 & member(v12, v1) = 0 & ! [v14: $i] : ( ~ (apply(v0, v12, v14) = % 26.12/4.33 0) | ~ $i(v14) | ? [v15: int] : ( ~ (v15 = 0) & member(v14, v2) % 26.12/4.33 = v15)) & ! [v14: $i] : ( ~ (member(v14, v2) = 0) | ~ $i(v14) | % 26.12/4.33 ? [v15: int] : ( ~ (v15 = 0) & apply(v0, v12, v14) = v15))) | (v11 = % 26.12/4.33 0 & v10 = 0 & v9 = 0 & v8 = 0 & v7 = 0 & ~ (v6 = v5) & apply(v0, v4, % 26.12/4.33 v6) = 0 & apply(v0, v4, v5) = 0 & member(v6, v2) = 0 & member(v5, % 26.12/4.33 v2) = 0 & member(v4, v1) = 0)))) & ! [v0: $i] : ! [v1: $i] : ! % 26.12/4.33 [v2: $i] : ! [v3: $i] : ( ~ (maps(v0, v1, v2) = 0) | ~ (member(v3, v1) = 0) % 26.12/4.33 | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: $i] : (apply(v0, % 26.12/4.33 v3, v4) = 0 & member(v4, v2) = 0 & $i(v4))) % 26.12/4.33 % 26.12/4.33 (surjective) % 26.12/4.33 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 26.12/4.33 (surjective(v0, v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: % 26.12/4.33 $i] : (member(v4, v2) = 0 & $i(v4) & ! [v5: $i] : ( ~ (apply(v0, v5, v4) % 26.12/4.33 = 0) | ~ $i(v5) | ? [v6: int] : ( ~ (v6 = 0) & member(v5, v1) = v6)) % 26.12/4.33 & ! [v5: $i] : ( ~ (member(v5, v1) = 0) | ~ $i(v5) | ? [v6: int] : ( ~ % 26.12/4.33 (v6 = 0) & apply(v0, v5, v4) = v6)))) & ! [v0: $i] : ! [v1: $i] : ! % 26.12/4.33 [v2: $i] : ! [v3: $i] : ( ~ (surjective(v0, v1, v2) = 0) | ~ (member(v3, v2) % 26.12/4.33 = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: $i] : % 26.12/4.33 (apply(v0, v4, v3) = 0 & member(v4, v1) = 0 & $i(v4))) % 26.12/4.33 % 26.12/4.33 (thII15) % 26.12/4.33 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: % 26.12/4.33 $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: int] : ( ~ (v8 = 0) & % 26.12/4.33 surjective(v0, v3, v4) = 0 & equal_maps(v6, v7, v3, v5) = 0 & equal_maps(v1, % 26.12/4.33 v2, v4, v5) = v8 & compose_function(v2, v0, v3, v4, v5) = v7 & % 26.12/4.33 compose_function(v1, v0, v3, v4, v5) = v6 & maps(v2, v4, v5) = 0 & maps(v1, % 26.12/4.33 v4, v5) = 0 & maps(v0, v3, v4) = 0 & $i(v7) & $i(v6) & $i(v5) & $i(v4) & % 26.12/4.33 $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 26.12/4.33 % 26.12/4.33 (function-axioms) % 26.48/4.34 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 26.48/4.34 [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : (v1 = v0 | % 26.48/4.34 ~ (compose_predicate(v7, v6, v5, v4, v3, v2) = v1) | ~ % 26.48/4.34 (compose_predicate(v7, v6, v5, v4, v3, v2) = v0)) & ! [v0: % 26.48/4.34 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 26.48/4.34 : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v1 = v0 | ~ (isomorphism(v6, v5, % 26.48/4.34 v4, v3, v2) = v1) | ~ (isomorphism(v6, v5, v4, v3, v2) = v0)) & ! [v0: % 26.48/4.34 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 26.48/4.34 : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v1 = v0 | ~ (decreasing(v6, v5, % 26.48/4.34 v4, v3, v2) = v1) | ~ (decreasing(v6, v5, v4, v3, v2) = v0)) & ! [v0: % 26.48/4.34 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 26.48/4.34 : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v1 = v0 | ~ (increasing(v6, v5, % 26.48/4.34 v4, v3, v2) = v1) | ~ (increasing(v6, v5, v4, v3, v2) = v0)) & ! [v0: % 26.48/4.34 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : % 26.48/4.34 ! [v6: $i] : (v1 = v0 | ~ (compose_function(v6, v5, v4, v3, v2) = v1) | ~ % 26.48/4.34 (compose_function(v6, v5, v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : % 26.48/4.34 ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 26.48/4.34 $i] : (v1 = v0 | ~ (inverse_predicate(v5, v4, v3, v2) = v1) | ~ % 26.48/4.34 (inverse_predicate(v5, v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! % 26.48/4.34 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 26.48/4.34 $i] : (v1 = v0 | ~ (equal_maps(v5, v4, v3, v2) = v1) | ~ (equal_maps(v5, % 26.48/4.34 v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 26.48/4.34 $i] : ! [v4: $i] : (v1 = v0 | ~ (inverse_image3(v4, v3, v2) = v1) | ~ % 26.48/4.34 (inverse_image3(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 26.48/4.34 : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (image3(v4, v3, v2) = v1) | ~ % 26.48/4.34 (image3(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 26.48/4.34 [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (inverse_function(v4, v3, v2) = v1) | % 26.48/4.34 ~ (inverse_function(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! % 26.48/4.34 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | % 26.48/4.34 ~ (one_to_one(v4, v3, v2) = v1) | ~ (one_to_one(v4, v3, v2) = v0)) & ! % 26.48/4.34 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 26.48/4.34 $i] : ! [v4: $i] : (v1 = v0 | ~ (surjective(v4, v3, v2) = v1) | ~ % 26.48/4.34 (surjective(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 26.48/4.34 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ % 26.48/4.34 (injective(v4, v3, v2) = v1) | ~ (injective(v4, v3, v2) = v0)) & ! [v0: % 26.48/4.34 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 26.48/4.34 : ! [v4: $i] : (v1 = v0 | ~ (maps(v4, v3, v2) = v1) | ~ (maps(v4, v3, v2) = % 26.48/4.34 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 26.48/4.34 $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (apply(v4, v3, v2) = v1) | % 26.48/4.34 ~ (apply(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 26.48/4.34 [v3: $i] : (v1 = v0 | ~ (inverse_image2(v3, v2) = v1) | ~ % 26.48/4.34 (inverse_image2(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 26.48/4.34 ! [v3: $i] : (v1 = v0 | ~ (image2(v3, v2) = v1) | ~ (image2(v3, v2) = v0)) & % 26.48/4.34 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 26.48/4.34 [v3: $i] : (v1 = v0 | ~ (identity(v3, v2) = v1) | ~ (identity(v3, v2) = v0)) % 26.48/4.34 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 26.48/4.34 (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) & ! [v0: % 26.48/4.34 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 26.48/4.34 (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0)) & ! [v0: $i] : ! % 26.48/4.34 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (union(v3, v2) = v1) | ~ % 26.48/4.34 (union(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 26.48/4.34 $i] : (v1 = v0 | ~ (intersection(v3, v2) = v1) | ~ (intersection(v3, v2) = % 26.48/4.34 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 26.48/4.34 $i] : ! [v3: $i] : (v1 = v0 | ~ (equal_set(v3, v2) = v1) | ~ % 26.48/4.34 (equal_set(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 26.48/4.34 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (subset(v3, % 26.48/4.34 v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! % 26.48/4.34 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 26.48/4.34 (member(v3, v2) = v1) | ~ (member(v3, v2) = v0)) & ! [v0: $i] : ! [v1: % 26.48/4.34 $i] : ! [v2: $i] : (v1 = v0 | ~ (product(v2) = v1) | ~ (product(v2) = % 26.48/4.34 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (sum(v2) = % 26.48/4.34 v1) | ~ (sum(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = % 26.48/4.34 v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ! [v0: $i] : ! % 26.48/4.34 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (power_set(v2) = v1) | ~ % 26.48/4.34 (power_set(v2) = v0)) % 26.48/4.34 % 26.48/4.34 Further assumptions not needed in the proof: % 26.48/4.34 -------------------------------------------- % 26.48/4.34 compose_predicate, decreasing_function, difference, empty_set, equal_set, % 26.48/4.34 identity, image2, image3, increasing_function, injective, intersection, % 26.48/4.34 inverse_function, inverse_image2, inverse_image3, inverse_predicate, % 26.48/4.34 isomorphism, one_to_one, power_set, product, singleton, subset, sum, union, % 26.48/4.34 unordered_pair % 26.48/4.34 % 26.48/4.34 Those formulas are unsatisfiable: % 26.48/4.34 --------------------------------- % 26.48/4.34 % 26.48/4.34 Begin of proof % 26.48/4.34 | % 26.48/4.35 | ALPHA: (maps) implies: % 26.48/4.35 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (maps(v0, % 26.48/4.35 | v1, v2) = 0) | ~ (member(v3, v1) = 0) | ~ $i(v3) | ~ $i(v2) | % 26.48/4.35 | ~ $i(v1) | ~ $i(v0) | ? [v4: $i] : (apply(v0, v3, v4) = 0 & % 26.48/4.35 | member(v4, v2) = 0 & $i(v4))) % 26.48/4.35 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 26.48/4.35 | ! [v5: $i] : (v5 = v4 | ~ (maps(v0, v1, v2) = 0) | ~ (member(v5, v2) % 26.48/4.35 | = 0) | ~ (member(v4, v2) = 0) | ~ (member(v3, v1) = 0) | ~ % 26.48/4.35 | $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 26.48/4.35 | ? [v6: any] : ? [v7: any] : (apply(v0, v3, v5) = v7 & apply(v0, v3, % 26.48/4.35 | v4) = v6 & ( ~ (v7 = 0) | ~ (v6 = 0)))) % 26.48/4.35 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 26.48/4.35 | ! [v5: $i] : (v5 = v4 | ~ (maps(v0, v1, v2) = 0) | ~ (apply(v0, v3, % 26.48/4.35 | v5) = 0) | ~ (member(v4, v2) = 0) | ~ $i(v5) | ~ $i(v4) | ~ % 26.48/4.35 | $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: % 26.48/4.35 | any] : ? [v8: any] : (apply(v0, v3, v4) = v8 & member(v5, v2) = v7 % 26.48/4.35 | & member(v3, v1) = v6 & ( ~ (v8 = 0) | ~ (v7 = 0) | ~ (v6 = 0)))) % 26.48/4.35 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 26.48/4.35 | ! [v5: $i] : (v5 = v4 | ~ (maps(v0, v1, v2) = 0) | ~ (apply(v0, v3, % 26.48/4.35 | v5) = 0) | ~ (apply(v0, v3, v4) = 0) | ~ $i(v5) | ~ $i(v4) | % 26.48/4.35 | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: % 26.48/4.35 | any] : ? [v8: any] : (member(v5, v2) = v8 & member(v4, v2) = v7 & % 26.48/4.35 | member(v3, v1) = v6 & ( ~ (v8 = 0) | ~ (v7 = 0) | ~ (v6 = 0)))) % 26.48/4.35 | % 26.48/4.35 | ALPHA: (compose_function) implies: % 26.48/4.35 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 26.48/4.35 | ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: int] : ! [v9: $i] : % 26.48/4.35 | (v8 = 0 | ~ (compose_function(v0, v1, v2, v3, v4) = v7) | ~ % 26.48/4.35 | (apply(v7, v5, v6) = v8) | ~ (member(v9, v3) = 0) | ~ $i(v9) | ~ % 26.48/4.35 | $i(v6) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | % 26.48/4.35 | ~ $i(v0) | ? [v10: any] : ? [v11: any] : ((apply(v1, v5, v9) = v10 % 26.48/4.35 | & apply(v0, v9, v6) = v11 & ( ~ (v11 = 0) | ~ (v10 = 0))) | % 26.48/4.35 | (member(v6, v4) = v11 & member(v5, v2) = v10 & ( ~ (v11 = 0) | ~ % 26.48/4.35 | (v10 = 0))))) % 26.48/4.36 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 26.48/4.36 | ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: int] : ! [v9: $i] : % 26.48/4.36 | (v8 = 0 | ~ (compose_function(v0, v1, v2, v3, v4) = v7) | ~ % 26.48/4.36 | (apply(v7, v5, v6) = v8) | ~ (apply(v0, v9, v6) = 0) | ~ $i(v9) | % 26.48/4.36 | ~ $i(v6) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) % 26.48/4.36 | | ~ $i(v0) | ? [v10: any] : ? [v11: any] : ((apply(v1, v5, v9) = % 26.48/4.36 | v11 & member(v9, v3) = v10 & ( ~ (v11 = 0) | ~ (v10 = 0))) | % 26.48/4.36 | (member(v6, v4) = v11 & member(v5, v2) = v10 & ( ~ (v11 = 0) | ~ % 26.48/4.36 | (v10 = 0))))) % 26.48/4.36 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 26.48/4.36 | ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: int] : ! [v9: $i] : % 26.48/4.36 | (v8 = 0 | ~ (compose_function(v0, v1, v2, v3, v4) = v7) | ~ % 26.48/4.36 | (apply(v7, v5, v6) = v8) | ~ (apply(v1, v5, v9) = 0) | ~ $i(v9) | % 26.48/4.36 | ~ $i(v6) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) % 26.48/4.36 | | ~ $i(v0) | ? [v10: any] : ? [v11: any] : ((apply(v0, v9, v6) = % 26.48/4.36 | v11 & member(v9, v3) = v10 & ( ~ (v11 = 0) | ~ (v10 = 0))) | % 26.48/4.36 | (member(v6, v4) = v11 & member(v5, v2) = v10 & ( ~ (v11 = 0) | ~ % 26.48/4.36 | (v10 = 0))))) % 26.48/4.36 | % 26.48/4.36 | ALPHA: (equal_maps) implies: % 26.48/4.36 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : % 26.48/4.36 | (v4 = 0 | ~ (equal_maps(v0, v1, v2, v3) = v4) | ~ $i(v3) | ~ $i(v2) % 26.48/4.36 | | ~ $i(v1) | ~ $i(v0) | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ( % 26.48/4.36 | ~ (v7 = v6) & apply(v1, v5, v7) = 0 & apply(v0, v5, v6) = 0 & % 26.48/4.36 | member(v7, v3) = 0 & member(v6, v3) = 0 & member(v5, v2) = 0 & % 26.48/4.36 | $i(v7) & $i(v6) & $i(v5))) % 26.48/4.36 | (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 26.48/4.36 | ! [v5: $i] : ! [v6: $i] : (v6 = v5 | ~ (equal_maps(v0, v1, v2, v3) = % 26.48/4.36 | 0) | ~ (member(v6, v3) = 0) | ~ (member(v5, v3) = 0) | ~ % 26.48/4.36 | (member(v4, v2) = 0) | ~ $i(v6) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) % 26.48/4.36 | | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v7: any] : ? [v8: any] : % 26.48/4.36 | (apply(v1, v4, v6) = v8 & apply(v0, v4, v5) = v7 & ( ~ (v8 = 0) | ~ % 26.48/4.36 | (v7 = 0)))) % 26.48/4.36 | % 26.48/4.36 | ALPHA: (surjective) implies: % 26.48/4.36 | (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 26.48/4.36 | (surjective(v0, v1, v2) = 0) | ~ (member(v3, v2) = 0) | ~ $i(v3) | % 26.48/4.36 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: $i] : (apply(v0, v4, v3) % 26.48/4.36 | = 0 & member(v4, v1) = 0 & $i(v4))) % 26.48/4.36 | % 26.48/4.36 | ALPHA: (function-axioms) implies: % 26.48/4.36 | (11) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 26.48/4.36 | : ! [v3: $i] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, % 26.48/4.36 | v2) = v0)) % 26.48/4.36 | (12) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 26.48/4.36 | : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (apply(v4, v3, v2) = v1) | % 26.48/4.36 | ~ (apply(v4, v3, v2) = v0)) % 26.48/4.36 | % 26.48/4.36 | DELTA: instantiating (thII15) with fresh symbols all_32_0, all_32_1, all_32_2, % 26.48/4.36 | all_32_3, all_32_4, all_32_5, all_32_6, all_32_7, all_32_8 gives: % 26.48/4.36 | (13) ~ (all_32_0 = 0) & surjective(all_32_8, all_32_5, all_32_4) = 0 & % 26.48/4.36 | equal_maps(all_32_2, all_32_1, all_32_5, all_32_3) = 0 & % 26.48/4.36 | equal_maps(all_32_7, all_32_6, all_32_4, all_32_3) = all_32_0 & % 26.48/4.36 | compose_function(all_32_6, all_32_8, all_32_5, all_32_4, all_32_3) = % 26.48/4.36 | all_32_1 & compose_function(all_32_7, all_32_8, all_32_5, all_32_4, % 26.48/4.36 | all_32_3) = all_32_2 & maps(all_32_6, all_32_4, all_32_3) = 0 & % 26.48/4.36 | maps(all_32_7, all_32_4, all_32_3) = 0 & maps(all_32_8, all_32_5, % 26.48/4.36 | all_32_4) = 0 & $i(all_32_1) & $i(all_32_2) & $i(all_32_3) & % 26.48/4.36 | $i(all_32_4) & $i(all_32_5) & $i(all_32_6) & $i(all_32_7) & % 26.48/4.36 | $i(all_32_8) % 26.48/4.36 | % 26.48/4.36 | ALPHA: (13) implies: % 26.48/4.36 | (14) ~ (all_32_0 = 0) % 26.48/4.36 | (15) $i(all_32_8) % 26.48/4.36 | (16) $i(all_32_7) % 26.48/4.36 | (17) $i(all_32_6) % 26.48/4.36 | (18) $i(all_32_5) % 26.48/4.36 | (19) $i(all_32_4) % 26.48/4.37 | (20) $i(all_32_3) % 26.48/4.37 | (21) $i(all_32_2) % 26.48/4.37 | (22) $i(all_32_1) % 26.48/4.37 | (23) maps(all_32_8, all_32_5, all_32_4) = 0 % 26.48/4.37 | (24) maps(all_32_7, all_32_4, all_32_3) = 0 % 26.48/4.37 | (25) maps(all_32_6, all_32_4, all_32_3) = 0 % 26.48/4.37 | (26) compose_function(all_32_7, all_32_8, all_32_5, all_32_4, all_32_3) = % 26.48/4.37 | all_32_2 % 26.48/4.37 | (27) compose_function(all_32_6, all_32_8, all_32_5, all_32_4, all_32_3) = % 26.48/4.37 | all_32_1 % 26.48/4.37 | (28) equal_maps(all_32_7, all_32_6, all_32_4, all_32_3) = all_32_0 % 26.48/4.37 | (29) equal_maps(all_32_2, all_32_1, all_32_5, all_32_3) = 0 % 26.48/4.37 | (30) surjective(all_32_8, all_32_5, all_32_4) = 0 % 26.48/4.37 | % 26.48/4.37 | GROUND_INST: instantiating (8) with all_32_7, all_32_6, all_32_4, all_32_3, % 26.48/4.37 | all_32_0, simplifying with (16), (17), (19), (20), (28) gives: % 26.48/4.37 | (31) all_32_0 = 0 | ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ( ~ (v2 = v1) % 26.48/4.37 | & apply(all_32_6, v0, v2) = 0 & apply(all_32_7, v0, v1) = 0 & % 26.48/4.37 | member(v2, all_32_3) = 0 & member(v1, all_32_3) = 0 & member(v0, % 26.48/4.37 | all_32_4) = 0 & $i(v2) & $i(v1) & $i(v0)) % 26.48/4.37 | % 26.48/4.37 | BETA: splitting (31) gives: % 26.48/4.37 | % 26.48/4.37 | Case 1: % 26.48/4.37 | | % 26.48/4.37 | | (32) all_32_0 = 0 % 26.48/4.37 | | % 26.48/4.37 | | REDUCE: (14), (32) imply: % 26.48/4.37 | | (33) $false % 26.48/4.37 | | % 26.48/4.37 | | CLOSE: (33) is inconsistent. % 26.48/4.37 | | % 26.48/4.37 | Case 2: % 26.48/4.37 | | % 26.48/4.37 | | (34) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ( ~ (v2 = v1) & % 26.48/4.37 | | apply(all_32_6, v0, v2) = 0 & apply(all_32_7, v0, v1) = 0 & % 26.48/4.37 | | member(v2, all_32_3) = 0 & member(v1, all_32_3) = 0 & member(v0, % 26.48/4.37 | | all_32_4) = 0 & $i(v2) & $i(v1) & $i(v0)) % 26.48/4.37 | | % 26.48/4.37 | | DELTA: instantiating (34) with fresh symbols all_47_0, all_47_1, all_47_2 % 26.48/4.37 | | gives: % 26.48/4.37 | | (35) ~ (all_47_0 = all_47_1) & apply(all_32_6, all_47_2, all_47_0) = 0 & % 26.48/4.37 | | apply(all_32_7, all_47_2, all_47_1) = 0 & member(all_47_0, all_32_3) % 26.48/4.37 | | = 0 & member(all_47_1, all_32_3) = 0 & member(all_47_2, all_32_4) = % 26.48/4.37 | | 0 & $i(all_47_0) & $i(all_47_1) & $i(all_47_2) % 26.48/4.37 | | % 26.48/4.37 | | ALPHA: (35) implies: % 26.48/4.37 | | (36) ~ (all_47_0 = all_47_1) % 26.48/4.37 | | (37) $i(all_47_2) % 26.48/4.37 | | (38) $i(all_47_1) % 26.48/4.37 | | (39) $i(all_47_0) % 26.48/4.37 | | (40) member(all_47_2, all_32_4) = 0 % 26.62/4.37 | | (41) member(all_47_1, all_32_3) = 0 % 26.62/4.37 | | (42) member(all_47_0, all_32_3) = 0 % 26.62/4.37 | | (43) apply(all_32_7, all_47_2, all_47_1) = 0 % 26.62/4.37 | | (44) apply(all_32_6, all_47_2, all_47_0) = 0 % 26.62/4.37 | | % 26.62/4.37 | | GROUND_INST: instantiating (1) with all_32_6, all_32_4, all_32_3, all_47_2, % 26.62/4.37 | | simplifying with (17), (19), (20), (25), (37), (40) gives: % 26.62/4.37 | | (45) ? [v0: $i] : (apply(all_32_6, all_47_2, v0) = 0 & member(v0, % 26.62/4.37 | | all_32_3) = 0 & $i(v0)) % 26.62/4.37 | | % 26.62/4.37 | | GROUND_INST: instantiating (1) with all_32_7, all_32_4, all_32_3, all_47_2, % 26.62/4.37 | | simplifying with (16), (19), (20), (24), (37), (40) gives: % 26.62/4.37 | | (46) ? [v0: $i] : (apply(all_32_7, all_47_2, v0) = 0 & member(v0, % 26.62/4.37 | | all_32_3) = 0 & $i(v0)) % 26.62/4.37 | | % 26.62/4.37 | | GROUND_INST: instantiating (10) with all_32_8, all_32_5, all_32_4, all_47_2, % 26.62/4.37 | | simplifying with (15), (18), (19), (30), (37), (40) gives: % 26.62/4.38 | | (47) ? [v0: $i] : (apply(all_32_8, v0, all_47_2) = 0 & member(v0, % 26.62/4.38 | | all_32_5) = 0 & $i(v0)) % 26.62/4.38 | | % 26.62/4.38 | | DELTA: instantiating (47) with fresh symbol all_58_0 gives: % 26.62/4.38 | | (48) apply(all_32_8, all_58_0, all_47_2) = 0 & member(all_58_0, all_32_5) % 26.62/4.38 | | = 0 & $i(all_58_0) % 26.62/4.38 | | % 26.62/4.38 | | ALPHA: (48) implies: % 26.62/4.38 | | (49) $i(all_58_0) % 26.62/4.38 | | (50) member(all_58_0, all_32_5) = 0 % 26.62/4.38 | | (51) apply(all_32_8, all_58_0, all_47_2) = 0 % 26.62/4.38 | | % 26.62/4.38 | | DELTA: instantiating (46) with fresh symbol all_60_0 gives: % 26.62/4.38 | | (52) apply(all_32_7, all_47_2, all_60_0) = 0 & member(all_60_0, all_32_3) % 26.62/4.38 | | = 0 & $i(all_60_0) % 26.62/4.38 | | % 26.62/4.38 | | ALPHA: (52) implies: % 26.62/4.38 | | (53) $i(all_60_0) % 26.62/4.38 | | (54) member(all_60_0, all_32_3) = 0 % 26.62/4.38 | | (55) apply(all_32_7, all_47_2, all_60_0) = 0 % 26.62/4.38 | | % 26.62/4.38 | | DELTA: instantiating (45) with fresh symbol all_62_0 gives: % 26.62/4.38 | | (56) apply(all_32_6, all_47_2, all_62_0) = 0 & member(all_62_0, all_32_3) % 26.62/4.38 | | = 0 & $i(all_62_0) % 26.62/4.38 | | % 26.62/4.38 | | ALPHA: (56) implies: % 26.62/4.38 | | (57) $i(all_62_0) % 26.62/4.38 | | (58) member(all_62_0, all_32_3) = 0 % 26.62/4.38 | | (59) apply(all_32_6, all_47_2, all_62_0) = 0 % 26.62/4.38 | | % 26.62/4.38 | | GROUND_INST: instantiating (9) with all_32_2, all_32_1, all_32_5, all_32_3, % 26.62/4.38 | | all_58_0, all_47_1, all_47_0, simplifying with (18), (20), % 26.62/4.38 | | (21), (22), (29), (38), (39), (41), (42), (49), (50) gives: % 26.62/4.38 | | (60) all_47_0 = all_47_1 | ? [v0: any] : ? [v1: any] : (apply(all_32_1, % 26.62/4.38 | | all_58_0, all_47_0) = v1 & apply(all_32_2, all_58_0, all_47_1) = % 26.62/4.38 | | v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 26.62/4.38 | | % 26.62/4.38 | | GROUND_INST: instantiating (1) with all_32_8, all_32_5, all_32_4, all_58_0, % 26.62/4.38 | | simplifying with (15), (18), (19), (23), (49), (50) gives: % 26.62/4.38 | | (61) ? [v0: $i] : (apply(all_32_8, all_58_0, v0) = 0 & member(v0, % 26.62/4.38 | | all_32_4) = 0 & $i(v0)) % 26.62/4.38 | | % 26.62/4.38 | | GROUND_INST: instantiating (9) with all_32_2, all_32_1, all_32_5, all_32_3, % 26.62/4.38 | | all_58_0, all_60_0, all_47_0, simplifying with (18), (20), % 26.62/4.38 | | (21), (22), (29), (39), (42), (49), (50), (53), (54) gives: % 26.62/4.38 | | (62) all_60_0 = all_47_0 | ? [v0: any] : ? [v1: any] : (apply(all_32_1, % 26.62/4.38 | | all_58_0, all_47_0) = v1 & apply(all_32_2, all_58_0, all_60_0) = % 26.62/4.38 | | v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 26.62/4.38 | | % 26.62/4.38 | | GROUND_INST: instantiating (9) with all_32_2, all_32_1, all_32_5, all_32_3, % 26.62/4.38 | | all_58_0, all_47_1, all_60_0, simplifying with (18), (20), % 26.62/4.38 | | (21), (22), (29), (38), (41), (49), (50), (53), (54) gives: % 26.62/4.38 | | (63) all_60_0 = all_47_1 | ? [v0: any] : ? [v1: any] : (apply(all_32_1, % 26.62/4.38 | | all_58_0, all_60_0) = v1 & apply(all_32_2, all_58_0, all_47_1) = % 26.62/4.38 | | v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 26.62/4.38 | | % 26.62/4.38 | | GROUND_INST: instantiating (2) with all_32_7, all_32_4, all_32_3, all_47_2, % 26.62/4.38 | | all_60_0, all_47_1, simplifying with (16), (19), (20), (24), % 26.62/4.38 | | (37), (38), (40), (41), (53), (54) gives: % 26.62/4.38 | | (64) all_60_0 = all_47_1 | ? [v0: any] : ? [v1: any] : (apply(all_32_7, % 26.62/4.38 | | all_47_2, all_60_0) = v0 & apply(all_32_7, all_47_2, all_47_1) = % 26.62/4.38 | | v1 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 26.62/4.38 | | % 26.62/4.38 | | GROUND_INST: instantiating (9) with all_32_2, all_32_1, all_32_5, all_32_3, % 26.62/4.38 | | all_58_0, all_47_1, all_62_0, simplifying with (18), (20), % 26.62/4.38 | | (21), (22), (29), (38), (41), (49), (50), (57), (58) gives: % 26.62/4.38 | | (65) all_62_0 = all_47_1 | ? [v0: any] : ? [v1: any] : (apply(all_32_1, % 26.62/4.38 | | all_58_0, all_62_0) = v1 & apply(all_32_2, all_58_0, all_47_1) = % 26.62/4.38 | | v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 26.62/4.38 | | % 26.62/4.38 | | GROUND_INST: instantiating (9) with all_32_2, all_32_1, all_32_5, all_32_3, % 26.62/4.38 | | all_58_0, all_62_0, all_47_1, simplifying with (18), (20), % 26.62/4.38 | | (21), (22), (29), (38), (41), (49), (50), (57), (58) gives: % 26.62/4.38 | | (66) all_62_0 = all_47_1 | ? [v0: any] : ? [v1: any] : (apply(all_32_1, % 26.62/4.38 | | all_58_0, all_47_1) = v1 & apply(all_32_2, all_58_0, all_62_0) = % 26.62/4.38 | | v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 26.62/4.38 | | % 26.62/4.38 | | GROUND_INST: instantiating (9) with all_32_2, all_32_1, all_32_5, all_32_3, % 26.62/4.38 | | all_58_0, all_60_0, all_62_0, simplifying with (18), (20), % 26.62/4.38 | | (21), (22), (29), (49), (50), (53), (54), (57), (58) gives: % 26.62/4.39 | | (67) all_62_0 = all_60_0 | ? [v0: any] : ? [v1: any] : (apply(all_32_1, % 26.62/4.39 | | all_58_0, all_62_0) = v1 & apply(all_32_2, all_58_0, all_60_0) = % 26.62/4.39 | | v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 26.62/4.39 | | % 26.62/4.39 | | GROUND_INST: instantiating (2) with all_32_6, all_32_4, all_32_3, all_47_2, % 26.62/4.39 | | all_62_0, all_47_0, simplifying with (17), (19), (20), (25), % 26.62/4.39 | | (37), (39), (40), (42), (57), (58) gives: % 26.62/4.39 | | (68) all_62_0 = all_47_0 | ? [v0: any] : ? [v1: any] : (apply(all_32_6, % 26.62/4.39 | | all_47_2, all_62_0) = v0 & apply(all_32_6, all_47_2, all_47_0) = % 26.62/4.39 | | v1 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 26.62/4.39 | | % 26.62/4.39 | | GROUND_INST: instantiating (3) with all_32_7, all_32_4, all_32_3, all_47_2, % 26.62/4.39 | | all_47_1, all_60_0, simplifying with (16), (19), (20), (24), % 26.62/4.39 | | (37), (38), (41), (53), (55) gives: % 26.62/4.39 | | (69) all_60_0 = all_47_1 | ? [v0: any] : ? [v1: any] : ? [v2: any] : % 26.62/4.39 | | (apply(all_32_7, all_47_2, all_47_1) = v2 & member(all_60_0, % 26.62/4.39 | | all_32_3) = v1 & member(all_47_2, all_32_4) = v0 & ( ~ (v2 = 0) % 26.62/4.39 | | | ~ (v1 = 0) | ~ (v0 = 0))) % 26.62/4.39 | | % 26.62/4.39 | | GROUND_INST: instantiating (3) with all_32_6, all_32_4, all_32_3, all_47_2, % 26.62/4.39 | | all_47_0, all_62_0, simplifying with (17), (19), (20), (25), % 26.62/4.39 | | (37), (39), (42), (57), (59) gives: % 26.62/4.39 | | (70) all_62_0 = all_47_0 | ? [v0: any] : ? [v1: any] : ? [v2: any] : % 26.62/4.39 | | (apply(all_32_6, all_47_2, all_47_0) = v2 & member(all_62_0, % 26.62/4.39 | | all_32_3) = v1 & member(all_47_2, all_32_4) = v0 & ( ~ (v2 = 0) % 26.62/4.39 | | | ~ (v1 = 0) | ~ (v0 = 0))) % 26.62/4.39 | | % 26.62/4.39 | | DELTA: instantiating (61) with fresh symbol all_114_0 gives: % 26.62/4.39 | | (71) apply(all_32_8, all_58_0, all_114_0) = 0 & member(all_114_0, % 26.62/4.39 | | all_32_4) = 0 & $i(all_114_0) % 26.62/4.39 | | % 26.62/4.39 | | ALPHA: (71) implies: % 26.62/4.39 | | (72) $i(all_114_0) % 26.62/4.39 | | (73) member(all_114_0, all_32_4) = 0 % 26.62/4.39 | | (74) apply(all_32_8, all_58_0, all_114_0) = 0 % 26.62/4.39 | | % 26.62/4.39 | | BETA: splitting (68) gives: % 26.62/4.39 | | % 26.62/4.39 | | Case 1: % 26.62/4.39 | | | % 26.62/4.39 | | | (75) all_62_0 = all_47_0 % 26.62/4.39 | | | % 26.62/4.39 | | | BETA: splitting (69) gives: % 26.62/4.39 | | | % 26.62/4.39 | | | Case 1: % 26.62/4.39 | | | | % 26.62/4.39 | | | | (76) all_60_0 = all_47_1 % 26.62/4.39 | | | | % 26.62/4.39 | | | | REF_CLOSE: (2), (4), (5), (6), (7), (11), (12), (15), (16), (17), (18), % 26.62/4.39 | | | | (19), (20), (23), (26), (27), (36), (37), (38), (39), (40), % 26.62/4.39 | | | | (41), (42), (43), (44), (49), (50), (51), (60), (62), (65), % 26.62/4.39 | | | | (67), (72), (73), (74), (75), (76) are inconsistent by % 26.62/4.39 | | | | sub-proof #2. % 26.62/4.39 | | | | % 26.62/4.39 | | | Case 2: % 26.62/4.39 | | | | % 26.62/4.39 | | | | (77) ? [v0: any] : ? [v1: any] : ? [v2: any] : (apply(all_32_7, % 26.62/4.39 | | | | all_47_2, all_47_1) = v2 & member(all_60_0, all_32_3) = v1 & % 26.62/4.39 | | | | member(all_47_2, all_32_4) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | % 26.62/4.39 | | | | ~ (v0 = 0))) % 26.62/4.39 | | | | % 26.62/4.39 | | | | DELTA: instantiating (77) with fresh symbols all_124_0, all_124_1, % 26.62/4.39 | | | | all_124_2 gives: % 26.62/4.39 | | | | (78) apply(all_32_7, all_47_2, all_47_1) = all_124_0 & % 26.62/4.39 | | | | member(all_60_0, all_32_3) = all_124_1 & member(all_47_2, % 26.62/4.39 | | | | all_32_4) = all_124_2 & ( ~ (all_124_0 = 0) | ~ (all_124_1 = % 26.62/4.39 | | | | 0) | ~ (all_124_2 = 0)) % 26.62/4.39 | | | | % 26.62/4.39 | | | | ALPHA: (78) implies: % 26.62/4.39 | | | | (79) member(all_47_2, all_32_4) = all_124_2 % 26.62/4.39 | | | | (80) member(all_60_0, all_32_3) = all_124_1 % 26.62/4.39 | | | | (81) apply(all_32_7, all_47_2, all_47_1) = all_124_0 % 26.62/4.39 | | | | (82) ~ (all_124_0 = 0) | ~ (all_124_1 = 0) | ~ (all_124_2 = 0) % 26.62/4.39 | | | | % 26.62/4.39 | | | | BETA: splitting (64) gives: % 26.62/4.39 | | | | % 26.62/4.39 | | | | Case 1: % 26.62/4.39 | | | | | % 26.62/4.39 | | | | | (83) all_60_0 = all_47_1 % 26.62/4.39 | | | | | % 26.62/4.39 | | | | | REF_CLOSE: (2), (4), (5), (6), (7), (11), (12), (15), (16), (17), % 26.62/4.39 | | | | | (18), (19), (20), (23), (26), (27), (36), (37), (38), (39), % 26.62/4.39 | | | | | (40), (41), (42), (43), (44), (49), (50), (51), (60), (62), % 26.62/4.39 | | | | | (65), (67), (72), (73), (74), (75), (83) are inconsistent % 26.62/4.39 | | | | | by sub-proof #2. % 26.62/4.39 | | | | | % 26.62/4.39 | | | | Case 2: % 26.62/4.39 | | | | | % 26.62/4.39 | | | | | (84) ? [v0: any] : ? [v1: any] : (apply(all_32_7, all_47_2, % 26.62/4.39 | | | | | all_60_0) = v0 & apply(all_32_7, all_47_2, all_47_1) = v1 % 26.62/4.39 | | | | | & ( ~ (v1 = 0) | ~ (v0 = 0))) % 26.62/4.39 | | | | | % 26.62/4.39 | | | | | DELTA: instantiating (84) with fresh symbols all_130_0, all_130_1 % 26.62/4.39 | | | | | gives: % 26.62/4.39 | | | | | (85) apply(all_32_7, all_47_2, all_60_0) = all_130_1 & % 26.62/4.39 | | | | | apply(all_32_7, all_47_2, all_47_1) = all_130_0 & ( ~ % 26.62/4.39 | | | | | (all_130_0 = 0) | ~ (all_130_1 = 0)) % 26.62/4.39 | | | | | % 26.62/4.39 | | | | | ALPHA: (85) implies: % 26.62/4.39 | | | | | (86) apply(all_32_7, all_47_2, all_47_1) = all_130_0 % 26.62/4.39 | | | | | % 26.62/4.39 | | | | | BETA: splitting (66) gives: % 26.62/4.39 | | | | | % 26.62/4.39 | | | | | Case 1: % 26.62/4.39 | | | | | | % 26.62/4.39 | | | | | | (87) all_62_0 = all_47_1 % 26.62/4.39 | | | | | | % 26.62/4.39 | | | | | | COMBINE_EQS: (75), (87) imply: % 26.62/4.39 | | | | | | (88) all_47_0 = all_47_1 % 26.62/4.39 | | | | | | % 26.62/4.39 | | | | | | SIMP: (88) implies: % 26.62/4.39 | | | | | | (89) all_47_0 = all_47_1 % 26.62/4.39 | | | | | | % 26.62/4.39 | | | | | | REDUCE: (36), (89) imply: % 26.62/4.39 | | | | | | (90) $false % 26.62/4.39 | | | | | | % 26.62/4.39 | | | | | | CLOSE: (90) is inconsistent. % 26.62/4.39 | | | | | | % 26.62/4.39 | | | | | Case 2: % 26.62/4.39 | | | | | | % 26.62/4.39 | | | | | | % 26.62/4.39 | | | | | | GROUND_INST: instantiating (11) with 0, all_124_2, all_32_4, % 26.62/4.39 | | | | | | all_47_2, simplifying with (40), (79) gives: % 26.62/4.39 | | | | | | (91) all_124_2 = 0 % 26.62/4.39 | | | | | | % 26.62/4.39 | | | | | | GROUND_INST: instantiating (11) with 0, all_124_1, all_32_3, % 26.62/4.39 | | | | | | all_60_0, simplifying with (54), (80) gives: % 26.62/4.39 | | | | | | (92) all_124_1 = 0 % 26.62/4.39 | | | | | | % 26.62/4.39 | | | | | | GROUND_INST: instantiating (12) with 0, all_130_0, all_47_1, % 26.62/4.39 | | | | | | all_47_2, all_32_7, simplifying with (43), (86) gives: % 26.62/4.39 | | | | | | (93) all_130_0 = 0 % 26.62/4.39 | | | | | | % 26.62/4.39 | | | | | | GROUND_INST: instantiating (12) with all_124_0, all_130_0, all_47_1, % 26.62/4.39 | | | | | | all_47_2, all_32_7, simplifying with (81), (86) gives: % 26.62/4.39 | | | | | | (94) all_130_0 = all_124_0 % 26.62/4.39 | | | | | | % 26.62/4.39 | | | | | | COMBINE_EQS: (93), (94) imply: % 26.62/4.39 | | | | | | (95) all_124_0 = 0 % 26.62/4.39 | | | | | | % 26.62/4.39 | | | | | | SIMP: (95) implies: % 26.62/4.39 | | | | | | (96) all_124_0 = 0 % 26.62/4.39 | | | | | | % 26.62/4.39 | | | | | | BETA: splitting (82) gives: % 26.62/4.39 | | | | | | % 26.62/4.39 | | | | | | Case 1: % 26.62/4.39 | | | | | | | % 26.62/4.39 | | | | | | | (97) ~ (all_124_0 = 0) % 26.62/4.39 | | | | | | | % 26.62/4.39 | | | | | | | REDUCE: (96), (97) imply: % 26.62/4.39 | | | | | | | (98) $false % 26.62/4.39 | | | | | | | % 26.62/4.39 | | | | | | | CLOSE: (98) is inconsistent. % 26.62/4.39 | | | | | | | % 26.62/4.39 | | | | | | Case 2: % 26.62/4.39 | | | | | | | % 26.62/4.39 | | | | | | | (99) ~ (all_124_1 = 0) | ~ (all_124_2 = 0) % 26.62/4.39 | | | | | | | % 26.62/4.39 | | | | | | | BETA: splitting (99) gives: % 26.62/4.39 | | | | | | | % 26.62/4.39 | | | | | | | Case 1: % 26.62/4.39 | | | | | | | | % 26.62/4.39 | | | | | | | | (100) ~ (all_124_1 = 0) % 26.62/4.39 | | | | | | | | % 26.62/4.39 | | | | | | | | REDUCE: (92), (100) imply: % 26.62/4.39 | | | | | | | | (101) $false % 26.62/4.39 | | | | | | | | % 26.62/4.39 | | | | | | | | CLOSE: (101) is inconsistent. % 26.62/4.39 | | | | | | | | % 26.62/4.40 | | | | | | | Case 2: % 26.62/4.40 | | | | | | | | % 26.62/4.40 | | | | | | | | (102) ~ (all_124_2 = 0) % 26.62/4.40 | | | | | | | | % 26.62/4.40 | | | | | | | | REDUCE: (91), (102) imply: % 26.62/4.40 | | | | | | | | (103) $false % 26.62/4.40 | | | | | | | | % 26.62/4.40 | | | | | | | | CLOSE: (103) is inconsistent. % 26.62/4.40 | | | | | | | | % 26.62/4.40 | | | | | | | End of split % 26.62/4.40 | | | | | | | % 26.62/4.40 | | | | | | End of split % 26.62/4.40 | | | | | | % 26.62/4.40 | | | | | End of split % 26.62/4.40 | | | | | % 26.62/4.40 | | | | End of split % 26.62/4.40 | | | | % 26.62/4.40 | | | End of split % 26.62/4.40 | | | % 26.62/4.40 | | Case 2: % 26.62/4.40 | | | % 26.62/4.40 | | | (104) ~ (all_62_0 = all_47_0) % 26.62/4.40 | | | (105) ? [v0: any] : ? [v1: any] : (apply(all_32_6, all_47_2, % 26.62/4.40 | | | all_62_0) = v0 & apply(all_32_6, all_47_2, all_47_0) = v1 & ( % 26.62/4.40 | | | ~ (v1 = 0) | ~ (v0 = 0))) % 26.62/4.40 | | | % 26.62/4.40 | | | DELTA: instantiating (105) with fresh symbols all_120_0, all_120_1 gives: % 26.62/4.40 | | | (106) apply(all_32_6, all_47_2, all_62_0) = all_120_1 & apply(all_32_6, % 26.62/4.40 | | | all_47_2, all_47_0) = all_120_0 & ( ~ (all_120_0 = 0) | ~ % 26.62/4.40 | | | (all_120_1 = 0)) % 26.62/4.40 | | | % 26.62/4.40 | | | ALPHA: (106) implies: % 26.62/4.40 | | | (107) apply(all_32_6, all_47_2, all_47_0) = all_120_0 % 26.62/4.40 | | | (108) apply(all_32_6, all_47_2, all_62_0) = all_120_1 % 26.62/4.40 | | | (109) ~ (all_120_0 = 0) | ~ (all_120_1 = 0) % 26.62/4.40 | | | % 26.62/4.40 | | | BETA: splitting (70) gives: % 26.62/4.40 | | | % 26.62/4.40 | | | Case 1: % 26.62/4.40 | | | | % 26.62/4.40 | | | | (110) all_62_0 = all_47_0 % 26.62/4.40 | | | | % 26.62/4.40 | | | | REDUCE: (104), (110) imply: % 26.62/4.40 | | | | (111) $false % 26.62/4.40 | | | | % 26.62/4.40 | | | | CLOSE: (111) is inconsistent. % 26.62/4.40 | | | | % 26.62/4.40 | | | Case 2: % 26.62/4.40 | | | | % 26.62/4.40 | | | | (112) ? [v0: any] : ? [v1: any] : ? [v2: any] : (apply(all_32_6, % 26.62/4.40 | | | | all_47_2, all_47_0) = v2 & member(all_62_0, all_32_3) = v1 % 26.62/4.40 | | | | & member(all_47_2, all_32_4) = v0 & ( ~ (v2 = 0) | ~ (v1 = % 26.62/4.40 | | | | 0) | ~ (v0 = 0))) % 26.62/4.40 | | | | % 26.62/4.40 | | | | DELTA: instantiating (112) with fresh symbols all_126_0, all_126_1, % 26.62/4.40 | | | | all_126_2 gives: % 26.62/4.40 | | | | (113) apply(all_32_6, all_47_2, all_47_0) = all_126_0 & % 26.62/4.40 | | | | member(all_62_0, all_32_3) = all_126_1 & member(all_47_2, % 26.62/4.40 | | | | all_32_4) = all_126_2 & ( ~ (all_126_0 = 0) | ~ (all_126_1 = % 26.62/4.40 | | | | 0) | ~ (all_126_2 = 0)) % 26.62/4.40 | | | | % 26.62/4.40 | | | | ALPHA: (113) implies: % 26.62/4.40 | | | | (114) apply(all_32_6, all_47_2, all_47_0) = all_126_0 % 26.62/4.40 | | | | % 26.62/4.40 | | | | BETA: splitting (64) gives: % 26.62/4.40 | | | | % 26.62/4.40 | | | | Case 1: % 26.62/4.40 | | | | | % 26.62/4.40 | | | | | (115) all_60_0 = all_47_1 % 26.62/4.40 | | | | | % 26.62/4.40 | | | | | BETA: splitting (62) gives: % 26.62/4.40 | | | | | % 26.62/4.40 | | | | | Case 1: % 26.62/4.40 | | | | | | % 26.62/4.40 | | | | | | (116) all_60_0 = all_47_0 % 26.62/4.40 | | | | | | % 26.62/4.40 | | | | | | COMBINE_EQS: (115), (116) imply: % 26.62/4.40 | | | | | | (117) all_47_0 = all_47_1 % 26.62/4.40 | | | | | | % 26.62/4.40 | | | | | | REDUCE: (36), (117) imply: % 26.62/4.40 | | | | | | (118) $false % 26.62/4.40 | | | | | | % 26.62/4.40 | | | | | | CLOSE: (118) is inconsistent. % 26.62/4.40 | | | | | | % 26.62/4.40 | | | | | Case 2: % 26.62/4.40 | | | | | | % 26.62/4.40 | | | | | | % 26.62/4.40 | | | | | | GROUND_INST: instantiating (12) with 0, all_120_0, all_47_0, % 26.62/4.40 | | | | | | all_47_2, all_32_6, simplifying with (44), (107) gives: % 26.62/4.40 | | | | | | (119) all_120_0 = 0 % 26.62/4.40 | | | | | | % 26.62/4.40 | | | | | | GROUND_INST: instantiating (12) with 0, all_120_1, all_62_0, % 26.62/4.40 | | | | | | all_47_2, all_32_6, simplifying with (59), (108) gives: % 26.62/4.40 | | | | | | (120) all_120_1 = 0 % 26.62/4.40 | | | | | | % 26.62/4.40 | | | | | | REF_CLOSE: (109), (119), (120) are inconsistent by sub-proof #1. % 26.62/4.40 | | | | | | % 26.62/4.40 | | | | | End of split % 26.62/4.40 | | | | | % 26.62/4.40 | | | | Case 2: % 26.62/4.40 | | | | | % 26.62/4.40 | | | | | (121) ~ (all_60_0 = all_47_1) % 26.62/4.40 | | | | | % 26.62/4.40 | | | | | BETA: splitting (63) gives: % 26.62/4.40 | | | | | % 26.62/4.40 | | | | | Case 1: % 26.62/4.40 | | | | | | % 26.62/4.40 | | | | | | (122) all_60_0 = all_47_1 % 26.62/4.40 | | | | | | % 26.62/4.40 | | | | | | REDUCE: (121), (122) imply: % 26.62/4.40 | | | | | | (123) $false % 26.62/4.40 | | | | | | % 26.62/4.40 | | | | | | CLOSE: (123) is inconsistent. % 26.62/4.40 | | | | | | % 26.62/4.40 | | | | | Case 2: % 26.62/4.40 | | | | | | % 26.62/4.40 | | | | | | % 26.62/4.40 | | | | | | GROUND_INST: instantiating (12) with 0, all_126_0, all_47_0, % 26.62/4.40 | | | | | | all_47_2, all_32_6, simplifying with (44), (114) gives: % 26.62/4.40 | | | | | | (124) all_126_0 = 0 % 26.62/4.40 | | | | | | % 26.62/4.40 | | | | | | GROUND_INST: instantiating (12) with all_120_0, all_126_0, all_47_0, % 26.62/4.40 | | | | | | all_47_2, all_32_6, simplifying with (107), (114) % 26.62/4.40 | | | | | | gives: % 26.62/4.40 | | | | | | (125) all_126_0 = all_120_0 % 26.62/4.40 | | | | | | % 26.62/4.40 | | | | | | GROUND_INST: instantiating (12) with 0, all_120_1, all_62_0, % 26.62/4.40 | | | | | | all_47_2, all_32_6, simplifying with (59), (108) gives: % 26.62/4.40 | | | | | | (126) all_120_1 = 0 % 26.62/4.40 | | | | | | % 26.62/4.40 | | | | | | COMBINE_EQS: (124), (125) imply: % 26.62/4.40 | | | | | | (127) all_120_0 = 0 % 26.62/4.40 | | | | | | % 26.62/4.40 | | | | | | REF_CLOSE: (109), (126), (127) are inconsistent by sub-proof #1. % 26.62/4.40 | | | | | | % 26.62/4.40 | | | | | End of split % 26.62/4.40 | | | | | % 26.62/4.40 | | | | End of split % 26.62/4.40 | | | | % 26.62/4.40 | | | End of split % 26.62/4.40 | | | % 26.62/4.40 | | End of split % 26.62/4.40 | | % 26.62/4.40 | End of split % 26.62/4.40 | % 26.62/4.40 End of proof % 26.62/4.40 % 26.62/4.40 Sub-proof #1 shows that the following formulas are inconsistent: % 26.62/4.40 ---------------------------------------------------------------- % 26.62/4.40 (1) ~ (all_120_0 = 0) | ~ (all_120_1 = 0) % 26.62/4.40 (2) all_120_0 = 0 % 26.62/4.40 (3) all_120_1 = 0 % 26.62/4.40 % 26.62/4.40 Begin of proof % 26.62/4.40 | % 26.62/4.40 | BETA: splitting (1) gives: % 26.62/4.40 | % 26.62/4.40 | Case 1: % 26.62/4.40 | | % 26.62/4.40 | | (4) ~ (all_120_0 = 0) % 26.62/4.40 | | % 26.62/4.40 | | REDUCE: (2), (4) imply: % 26.62/4.40 | | (5) $false % 26.62/4.40 | | % 26.62/4.40 | | CLOSE: (5) is inconsistent. % 26.62/4.40 | | % 26.62/4.40 | Case 2: % 26.62/4.40 | | % 26.62/4.40 | | (6) ~ (all_120_1 = 0) % 26.62/4.40 | | % 26.62/4.40 | | REDUCE: (3), (6) imply: % 26.62/4.40 | | (7) $false % 26.62/4.40 | | % 26.62/4.40 | | CLOSE: (7) is inconsistent. % 26.62/4.40 | | % 26.62/4.40 | End of split % 26.62/4.40 | % 26.62/4.40 End of proof % 26.62/4.40 % 26.62/4.40 Sub-proof #2 shows that the following formulas are inconsistent: % 26.62/4.40 ---------------------------------------------------------------- % 26.62/4.40 (1) $i(all_32_6) % 26.62/4.40 (2) all_62_0 = all_47_0 % 26.62/4.40 (3) all_60_0 = all_47_1 % 26.62/4.40 (4) $i(all_47_2) % 26.62/4.40 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! % 26.62/4.40 [v5: $i] : (v5 = v4 | ~ (maps(v0, v1, v2) = 0) | ~ (apply(v0, v3, v5) = % 26.62/4.40 0) | ~ (apply(v0, v3, v4) = 0) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | % 26.62/4.40 ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: any] : ? % 26.62/4.40 [v8: any] : (member(v5, v2) = v8 & member(v4, v2) = v7 & member(v3, v1) % 26.62/4.40 = v6 & ( ~ (v8 = 0) | ~ (v7 = 0) | ~ (v6 = 0)))) % 26.62/4.40 (6) $i(all_32_3) % 26.62/4.40 (7) ~ (all_47_0 = all_47_1) % 26.62/4.40 (8) $i(all_32_8) % 26.62/4.40 (9) member(all_47_1, all_32_3) = 0 % 26.62/4.40 (10) member(all_58_0, all_32_5) = 0 % 26.62/4.40 (11) all_62_0 = all_60_0 | ? [v0: any] : ? [v1: any] : (apply(all_32_1, % 26.62/4.40 all_58_0, all_62_0) = v1 & apply(all_32_2, all_58_0, all_60_0) = v0 % 26.62/4.40 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 26.62/4.40 (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! % 26.62/4.40 [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: int] : ! [v9: $i] : (v8 % 26.62/4.40 = 0 | ~ (compose_function(v0, v1, v2, v3, v4) = v7) | ~ (apply(v7, % 26.62/4.40 v5, v6) = v8) | ~ (apply(v0, v9, v6) = 0) | ~ $i(v9) | ~ $i(v6) % 26.62/4.40 | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 26.62/4.40 $i(v0) | ? [v10: any] : ? [v11: any] : ((apply(v1, v5, v9) = v11 & % 26.62/4.40 member(v9, v3) = v10 & ( ~ (v11 = 0) | ~ (v10 = 0))) | % 26.62/4.40 (member(v6, v4) = v11 & member(v5, v2) = v10 & ( ~ (v11 = 0) | ~ % 26.62/4.40 (v10 = 0))))) % 26.62/4.40 (13) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 26.62/4.40 ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (apply(v4, v3, v2) = v1) | ~ % 26.62/4.40 (apply(v4, v3, v2) = v0)) % 26.62/4.41 (14) all_47_0 = all_47_1 | ? [v0: any] : ? [v1: any] : (apply(all_32_1, % 26.62/4.41 all_58_0, all_47_0) = v1 & apply(all_32_2, all_58_0, all_47_1) = v0 % 26.62/4.41 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 26.62/4.41 (15) member(all_114_0, all_32_4) = 0 % 26.62/4.41 (16) all_60_0 = all_47_0 | ? [v0: any] : ? [v1: any] : (apply(all_32_1, % 26.62/4.41 all_58_0, all_47_0) = v1 & apply(all_32_2, all_58_0, all_60_0) = v0 % 26.62/4.41 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 26.62/4.41 (17) compose_function(all_32_6, all_32_8, all_32_5, all_32_4, all_32_3) = % 26.62/4.41 all_32_1 % 26.62/4.41 (18) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! % 26.62/4.41 [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: int] : ! [v9: $i] : (v8 % 26.62/4.41 = 0 | ~ (compose_function(v0, v1, v2, v3, v4) = v7) | ~ (apply(v7, % 26.62/4.41 v5, v6) = v8) | ~ (apply(v1, v5, v9) = 0) | ~ $i(v9) | ~ $i(v6) % 26.62/4.41 | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 26.62/4.41 $i(v0) | ? [v10: any] : ? [v11: any] : ((apply(v0, v9, v6) = v11 & % 26.62/4.41 member(v9, v3) = v10 & ( ~ (v11 = 0) | ~ (v10 = 0))) | % 26.62/4.41 (member(v6, v4) = v11 & member(v5, v2) = v10 & ( ~ (v11 = 0) | ~ % 26.62/4.41 (v10 = 0))))) % 26.62/4.41 (19) apply(all_32_6, all_47_2, all_47_0) = 0 % 26.62/4.41 (20) apply(all_32_7, all_47_2, all_47_1) = 0 % 26.62/4.41 (21) member(all_47_0, all_32_3) = 0 % 26.62/4.41 (22) $i(all_47_1) % 26.62/4.41 (23) $i(all_32_4) % 26.62/4.41 (24) $i(all_47_0) % 26.62/4.41 (25) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! % 26.62/4.41 [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: int] : ! [v9: $i] : (v8 % 26.62/4.41 = 0 | ~ (compose_function(v0, v1, v2, v3, v4) = v7) | ~ (apply(v7, % 26.62/4.41 v5, v6) = v8) | ~ (member(v9, v3) = 0) | ~ $i(v9) | ~ $i(v6) | % 26.62/4.41 ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 26.62/4.41 ? [v10: any] : ? [v11: any] : ((apply(v1, v5, v9) = v10 & apply(v0, % 26.62/4.41 v9, v6) = v11 & ( ~ (v11 = 0) | ~ (v10 = 0))) | (member(v6, v4) % 26.62/4.41 = v11 & member(v5, v2) = v10 & ( ~ (v11 = 0) | ~ (v10 = 0))))) % 26.62/4.41 (26) apply(all_32_8, all_58_0, all_47_2) = 0 % 26.62/4.41 (27) compose_function(all_32_7, all_32_8, all_32_5, all_32_4, all_32_3) = % 26.62/4.41 all_32_2 % 26.62/4.41 (28) $i(all_32_5) % 26.62/4.41 (29) $i(all_58_0) % 26.62/4.41 (30) all_62_0 = all_47_1 | ? [v0: any] : ? [v1: any] : (apply(all_32_1, % 26.62/4.41 all_58_0, all_62_0) = v1 & apply(all_32_2, all_58_0, all_47_1) = v0 % 26.62/4.41 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 26.62/4.41 (31) member(all_47_2, all_32_4) = 0 % 26.62/4.41 (32) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! % 26.62/4.41 [v5: $i] : (v5 = v4 | ~ (maps(v0, v1, v2) = 0) | ~ (member(v5, v2) = % 26.62/4.41 0) | ~ (member(v4, v2) = 0) | ~ (member(v3, v1) = 0) | ~ $i(v5) | % 26.62/4.41 ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: % 26.62/4.41 any] : ? [v7: any] : (apply(v0, v3, v5) = v7 & apply(v0, v3, v4) = % 26.62/4.41 v6 & ( ~ (v7 = 0) | ~ (v6 = 0)))) % 26.62/4.41 (33) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 26.62/4.41 ! [v3: $i] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) = % 26.62/4.41 v0)) % 26.62/4.41 (34) maps(all_32_8, all_32_5, all_32_4) = 0 % 26.62/4.41 (35) $i(all_114_0) % 26.62/4.41 (36) apply(all_32_8, all_58_0, all_114_0) = 0 % 26.62/4.41 (37) $i(all_32_7) % 26.62/4.41 % 26.62/4.41 Begin of proof % 26.62/4.41 | % 26.62/4.41 | BETA: splitting (16) gives: % 26.62/4.41 | % 26.62/4.41 | Case 1: % 26.62/4.41 | | % 26.62/4.41 | | (38) all_60_0 = all_47_0 % 26.62/4.41 | | % 26.62/4.41 | | COMBINE_EQS: (3), (38) imply: % 26.62/4.41 | | (39) all_47_0 = all_47_1 % 26.62/4.41 | | % 26.62/4.41 | | REDUCE: (7), (39) imply: % 26.62/4.41 | | (40) $false % 26.62/4.41 | | % 26.62/4.41 | | CLOSE: (40) is inconsistent. % 26.62/4.41 | | % 26.62/4.41 | Case 2: % 26.62/4.41 | | % 26.62/4.41 | | (41) ~ (all_60_0 = all_47_0) % 26.62/4.41 | | (42) ? [v0: any] : ? [v1: any] : (apply(all_32_1, all_58_0, all_47_0) = % 26.62/4.41 | | v1 & apply(all_32_2, all_58_0, all_60_0) = v0 & ( ~ (v1 = 0) | ~ % 26.62/4.41 | | (v0 = 0))) % 26.62/4.41 | | % 26.62/4.41 | | DELTA: instantiating (42) with fresh symbols all_133_0, all_133_1 gives: % 26.62/4.41 | | (43) apply(all_32_1, all_58_0, all_47_0) = all_133_0 & apply(all_32_2, % 26.62/4.41 | | all_58_0, all_60_0) = all_133_1 & ( ~ (all_133_0 = 0) | ~ % 26.62/4.41 | | (all_133_1 = 0)) % 26.62/4.41 | | % 26.62/4.41 | | ALPHA: (43) implies: % 26.62/4.41 | | (44) apply(all_32_2, all_58_0, all_60_0) = all_133_1 % 26.62/4.41 | | (45) apply(all_32_1, all_58_0, all_47_0) = all_133_0 % 26.62/4.41 | | (46) ~ (all_133_0 = 0) | ~ (all_133_1 = 0) % 26.62/4.41 | | % 26.62/4.41 | | REDUCE: (3), (41) imply: % 26.62/4.41 | | (47) ~ (all_47_0 = all_47_1) % 26.62/4.41 | | % 26.62/4.41 | | REDUCE: (3), (44) imply: % 26.62/4.41 | | (48) apply(all_32_2, all_58_0, all_47_1) = all_133_1 % 26.62/4.41 | | % 26.62/4.41 | | BETA: splitting (14) gives: % 26.62/4.41 | | % 26.62/4.41 | | Case 1: % 26.62/4.41 | | | % 26.62/4.41 | | | (49) all_47_0 = all_47_1 % 26.62/4.41 | | | % 26.62/4.41 | | | REDUCE: (7), (49) imply: % 26.62/4.41 | | | (50) $false % 26.62/4.41 | | | % 26.62/4.41 | | | CLOSE: (50) is inconsistent. % 26.62/4.41 | | | % 26.62/4.41 | | Case 2: % 26.62/4.41 | | | % 26.62/4.41 | | | (51) ? [v0: any] : ? [v1: any] : (apply(all_32_1, all_58_0, all_47_0) % 26.62/4.41 | | | = v1 & apply(all_32_2, all_58_0, all_47_1) = v0 & ( ~ (v1 = 0) | % 26.62/4.41 | | | ~ (v0 = 0))) % 26.62/4.41 | | | % 26.62/4.41 | | | DELTA: instantiating (51) with fresh symbols all_148_0, all_148_1 gives: % 26.62/4.41 | | | (52) apply(all_32_1, all_58_0, all_47_0) = all_148_0 & apply(all_32_2, % 26.62/4.41 | | | all_58_0, all_47_1) = all_148_1 & ( ~ (all_148_0 = 0) | ~ % 26.62/4.41 | | | (all_148_1 = 0)) % 26.62/4.41 | | | % 26.62/4.41 | | | ALPHA: (52) implies: % 26.62/4.41 | | | (53) apply(all_32_2, all_58_0, all_47_1) = all_148_1 % 26.62/4.41 | | | (54) apply(all_32_1, all_58_0, all_47_0) = all_148_0 % 26.62/4.41 | | | % 26.62/4.41 | | | BETA: splitting (11) gives: % 26.62/4.41 | | | % 26.62/4.41 | | | Case 1: % 26.62/4.41 | | | | % 26.62/4.41 | | | | (55) all_62_0 = all_60_0 % 26.62/4.41 | | | | % 26.62/4.41 | | | | COMBINE_EQS: (2), (55) imply: % 26.62/4.41 | | | | (56) all_60_0 = all_47_0 % 26.62/4.41 | | | | % 26.62/4.41 | | | | COMBINE_EQS: (3), (56) imply: % 26.62/4.41 | | | | (57) all_47_0 = all_47_1 % 26.62/4.41 | | | | % 26.62/4.41 | | | | SIMP: (57) implies: % 26.62/4.41 | | | | (58) all_47_0 = all_47_1 % 26.62/4.41 | | | | % 26.62/4.41 | | | | REDUCE: (7), (58) imply: % 26.62/4.41 | | | | (59) $false % 26.62/4.41 | | | | % 26.62/4.41 | | | | CLOSE: (59) is inconsistent. % 26.62/4.41 | | | | % 26.62/4.41 | | | Case 2: % 26.62/4.41 | | | | % 26.62/4.41 | | | | (60) ~ (all_62_0 = all_60_0) % 26.62/4.41 | | | | (61) ? [v0: any] : ? [v1: any] : (apply(all_32_1, all_58_0, % 26.62/4.41 | | | | all_62_0) = v1 & apply(all_32_2, all_58_0, all_60_0) = v0 & % 26.62/4.41 | | | | ( ~ (v1 = 0) | ~ (v0 = 0))) % 26.62/4.41 | | | | % 26.62/4.41 | | | | DELTA: instantiating (61) with fresh symbols all_153_0, all_153_1 gives: % 26.62/4.41 | | | | (62) apply(all_32_1, all_58_0, all_62_0) = all_153_0 & % 26.62/4.41 | | | | apply(all_32_2, all_58_0, all_60_0) = all_153_1 & ( ~ (all_153_0 % 26.62/4.41 | | | | = 0) | ~ (all_153_1 = 0)) % 26.62/4.41 | | | | % 26.62/4.41 | | | | ALPHA: (62) implies: % 26.62/4.41 | | | | (63) apply(all_32_2, all_58_0, all_60_0) = all_153_1 % 26.62/4.41 | | | | (64) apply(all_32_1, all_58_0, all_62_0) = all_153_0 % 26.62/4.41 | | | | % 26.62/4.41 | | | | REDUCE: (2), (64) imply: % 26.62/4.41 | | | | (65) apply(all_32_1, all_58_0, all_47_0) = all_153_0 % 26.62/4.41 | | | | % 26.62/4.41 | | | | REDUCE: (3), (63) imply: % 26.62/4.41 | | | | (66) apply(all_32_2, all_58_0, all_47_1) = all_153_1 % 26.62/4.41 | | | | % 26.62/4.41 | | | | BETA: splitting (30) gives: % 26.62/4.41 | | | | % 26.62/4.41 | | | | Case 1: % 26.62/4.41 | | | | | % 26.62/4.41 | | | | | (67) all_62_0 = all_47_1 % 26.62/4.41 | | | | | % 26.62/4.41 | | | | | COMBINE_EQS: (2), (67) imply: % 26.62/4.41 | | | | | (68) all_47_0 = all_47_1 % 26.62/4.41 | | | | | % 26.62/4.41 | | | | | SIMP: (68) implies: % 26.62/4.41 | | | | | (69) all_47_0 = all_47_1 % 26.62/4.41 | | | | | % 26.62/4.41 | | | | | REDUCE: (7), (69) imply: % 26.62/4.41 | | | | | (70) $false % 26.62/4.41 | | | | | % 26.62/4.41 | | | | | CLOSE: (70) is inconsistent. % 26.62/4.41 | | | | | % 26.62/4.41 | | | | Case 2: % 26.62/4.41 | | | | | % 26.62/4.42 | | | | | (71) ? [v0: any] : ? [v1: any] : (apply(all_32_1, all_58_0, % 26.62/4.42 | | | | | all_62_0) = v1 & apply(all_32_2, all_58_0, all_47_1) = v0 % 26.62/4.42 | | | | | & ( ~ (v1 = 0) | ~ (v0 = 0))) % 26.62/4.42 | | | | | % 26.62/4.42 | | | | | DELTA: instantiating (71) with fresh symbols all_158_0, all_158_1 % 26.62/4.42 | | | | | gives: % 26.62/4.42 | | | | | (72) apply(all_32_1, all_58_0, all_62_0) = all_158_0 & % 26.62/4.42 | | | | | apply(all_32_2, all_58_0, all_47_1) = all_158_1 & ( ~ % 26.62/4.42 | | | | | (all_158_0 = 0) | ~ (all_158_1 = 0)) % 26.62/4.42 | | | | | % 26.62/4.42 | | | | | ALPHA: (72) implies: % 26.62/4.42 | | | | | (73) apply(all_32_2, all_58_0, all_47_1) = all_158_1 % 26.62/4.42 | | | | | (74) apply(all_32_1, all_58_0, all_62_0) = all_158_0 % 26.62/4.42 | | | | | % 26.62/4.42 | | | | | REDUCE: (2), (74) imply: % 26.62/4.42 | | | | | (75) apply(all_32_1, all_58_0, all_47_0) = all_158_0 % 26.62/4.42 | | | | | % 26.62/4.42 | | | | | GROUND_INST: instantiating (13) with all_148_1, all_153_1, all_47_1, % 26.62/4.42 | | | | | all_58_0, all_32_2, simplifying with (53), (66) gives: % 26.62/4.42 | | | | | (76) all_153_1 = all_148_1 % 26.62/4.42 | | | | | % 26.62/4.42 | | | | | GROUND_INST: instantiating (13) with all_153_1, all_158_1, all_47_1, % 26.62/4.42 | | | | | all_58_0, all_32_2, simplifying with (66), (73) gives: % 26.62/4.42 | | | | | (77) all_158_1 = all_153_1 % 26.62/4.42 | | | | | % 26.62/4.42 | | | | | GROUND_INST: instantiating (13) with all_133_1, all_158_1, all_47_1, % 26.62/4.42 | | | | | all_58_0, all_32_2, simplifying with (48), (73) gives: % 26.62/4.42 | | | | | (78) all_158_1 = all_133_1 % 26.62/4.42 | | | | | % 26.62/4.42 | | | | | GROUND_INST: instantiating (13) with all_153_0, all_158_0, all_47_0, % 26.62/4.42 | | | | | all_58_0, all_32_1, simplifying with (65), (75) gives: % 26.62/4.42 | | | | | (79) all_158_0 = all_153_0 % 26.62/4.42 | | | | | % 26.62/4.42 | | | | | GROUND_INST: instantiating (13) with all_148_0, all_158_0, all_47_0, % 26.62/4.42 | | | | | all_58_0, all_32_1, simplifying with (54), (75) gives: % 26.62/4.42 | | | | | (80) all_158_0 = all_148_0 % 26.62/4.42 | | | | | % 26.62/4.42 | | | | | GROUND_INST: instantiating (13) with all_133_0, all_158_0, all_47_0, % 26.62/4.42 | | | | | all_58_0, all_32_1, simplifying with (45), (75) gives: % 26.62/4.42 | | | | | (81) all_158_0 = all_133_0 % 26.62/4.42 | | | | | % 26.62/4.42 | | | | | COMBINE_EQS: (79), (80) imply: % 26.62/4.42 | | | | | (82) all_153_0 = all_148_0 % 26.62/4.42 | | | | | % 26.62/4.42 | | | | | COMBINE_EQS: (79), (81) imply: % 26.62/4.42 | | | | | (83) all_153_0 = all_133_0 % 26.62/4.42 | | | | | % 26.62/4.42 | | | | | COMBINE_EQS: (77), (78) imply: % 26.62/4.42 | | | | | (84) all_153_1 = all_133_1 % 26.62/4.42 | | | | | % 26.62/4.42 | | | | | SIMP: (84) implies: % 26.62/4.42 | | | | | (85) all_153_1 = all_133_1 % 26.62/4.42 | | | | | % 26.62/4.42 | | | | | COMBINE_EQS: (82), (83) imply: % 26.62/4.42 | | | | | (86) all_148_0 = all_133_0 % 26.62/4.42 | | | | | % 26.62/4.42 | | | | | SIMP: (86) implies: % 26.62/4.42 | | | | | (87) all_148_0 = all_133_0 % 26.62/4.42 | | | | | % 26.62/4.42 | | | | | COMBINE_EQS: (76), (85) imply: % 26.62/4.42 | | | | | (88) all_148_1 = all_133_1 % 26.62/4.42 | | | | | % 26.62/4.42 | | | | | GROUND_INST: instantiating (32) with all_32_8, all_32_5, all_32_4, % 26.62/4.42 | | | | | all_58_0, all_47_2, all_114_0, simplifying with (4), (8), % 26.62/4.42 | | | | | (10), (15), (23), (28), (29), (31), (34), (35) gives: % 26.62/4.42 | | | | | (89) all_114_0 = all_47_2 | ? [v0: any] : ? [v1: any] : % 26.62/4.42 | | | | | (apply(all_32_8, all_58_0, all_114_0) = v1 & apply(all_32_8, % 26.62/4.42 | | | | | all_58_0, all_47_2) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 26.62/4.42 | | | | | % 26.62/4.42 | | | | | GROUND_INST: instantiating (5) with all_32_8, all_32_5, all_32_4, % 26.62/4.42 | | | | | all_58_0, all_114_0, all_47_2, simplifying with (4), (8), % 26.62/4.42 | | | | | (23), (26), (28), (29), (34), (35), (36) gives: % 26.62/4.42 | | | | | (90) all_114_0 = all_47_2 | ? [v0: any] : ? [v1: any] : ? [v2: % 26.62/4.42 | | | | | any] : (member(all_114_0, all_32_4) = v1 & member(all_58_0, % 26.62/4.42 | | | | | all_32_5) = v0 & member(all_47_2, all_32_4) = v2 & ( ~ (v2 % 26.62/4.42 | | | | | = 0) | ~ (v1 = 0) | ~ (v0 = 0))) % 26.62/4.42 | | | | | % 26.62/4.42 | | | | | GROUND_INST: instantiating (12) with all_32_7, all_32_8, all_32_5, % 26.62/4.42 | | | | | all_32_4, all_32_3, all_58_0, all_47_1, all_32_2, % 26.62/4.42 | | | | | all_133_1, all_47_2, simplifying with (4), (6), (8), % 26.62/4.42 | | | | | (20), (22), (23), (27), (28), (29), (37), (48) gives: % 26.62/4.42 | | | | | (91) all_133_1 = 0 | ? [v0: any] : ? [v1: any] : % 26.62/4.42 | | | | | ((apply(all_32_8, all_58_0, all_47_2) = v1 & member(all_47_2, % 26.62/4.42 | | | | | all_32_4) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) | % 26.62/4.42 | | | | | (member(all_58_0, all_32_5) = v0 & member(all_47_1, % 26.62/4.42 | | | | | all_32_3) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0)))) % 26.62/4.42 | | | | | % 26.62/4.42 | | | | | GROUND_INST: instantiating (25) with all_32_7, all_32_8, all_32_5, % 26.62/4.42 | | | | | all_32_4, all_32_3, all_58_0, all_47_1, all_32_2, % 26.62/4.42 | | | | | all_133_1, all_47_2, simplifying with (4), (6), (8), % 26.62/4.42 | | | | | (22), (23), (27), (28), (29), (31), (37), (48) gives: % 26.62/4.42 | | | | | (92) all_133_1 = 0 | ? [v0: any] : ? [v1: any] : % 26.62/4.42 | | | | | ((apply(all_32_7, all_47_2, all_47_1) = v1 & apply(all_32_8, % 26.62/4.42 | | | | | all_58_0, all_47_2) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 26.62/4.42 | | | | | | (member(all_58_0, all_32_5) = v0 & member(all_47_1, % 26.62/4.42 | | | | | all_32_3) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0)))) % 26.62/4.42 | | | | | % 26.62/4.42 | | | | | GROUND_INST: instantiating (12) with all_32_6, all_32_8, all_32_5, % 26.62/4.42 | | | | | all_32_4, all_32_3, all_58_0, all_47_0, all_32_1, % 26.62/4.42 | | | | | all_133_0, all_47_2, simplifying with (1), (4), (6), (8), % 26.62/4.42 | | | | | (17), (19), (23), (24), (28), (29), (45) gives: % 26.62/4.42 | | | | | (93) all_133_0 = 0 | ? [v0: any] : ? [v1: any] : % 26.62/4.42 | | | | | ((apply(all_32_8, all_58_0, all_47_2) = v1 & member(all_47_2, % 26.62/4.42 | | | | | all_32_4) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) | % 26.62/4.42 | | | | | (member(all_58_0, all_32_5) = v0 & member(all_47_0, % 26.62/4.42 | | | | | all_32_3) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0)))) % 26.62/4.42 | | | | | % 26.62/4.42 | | | | | GROUND_INST: instantiating (18) with all_32_6, all_32_8, all_32_5, % 26.62/4.42 | | | | | all_32_4, all_32_3, all_58_0, all_47_0, all_32_1, % 26.62/4.42 | | | | | all_133_0, all_47_2, simplifying with (1), (4), (6), (8), % 26.62/4.42 | | | | | (17), (23), (24), (26), (28), (29), (45) gives: % 26.62/4.42 | | | | | (94) all_133_0 = 0 | ? [v0: any] : ? [v1: any] : % 26.62/4.42 | | | | | ((apply(all_32_6, all_47_2, all_47_0) = v1 & member(all_47_2, % 26.62/4.42 | | | | | all_32_4) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) | % 26.62/4.42 | | | | | (member(all_58_0, all_32_5) = v0 & member(all_47_0, % 26.62/4.42 | | | | | all_32_3) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0)))) % 26.62/4.42 | | | | | % 26.62/4.42 | | | | | GROUND_INST: instantiating (25) with all_32_6, all_32_8, all_32_5, % 26.62/4.42 | | | | | all_32_4, all_32_3, all_58_0, all_47_0, all_32_1, % 26.62/4.42 | | | | | all_133_0, all_47_2, simplifying with (1), (4), (6), (8), % 26.62/4.42 | | | | | (17), (23), (24), (28), (29), (31), (45) gives: % 26.62/4.42 | | | | | (95) all_133_0 = 0 | ? [v0: any] : ? [v1: any] : % 26.62/4.42 | | | | | ((apply(all_32_6, all_47_2, all_47_0) = v1 & apply(all_32_8, % 26.62/4.42 | | | | | all_58_0, all_47_2) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 26.62/4.42 | | | | | | (member(all_58_0, all_32_5) = v0 & member(all_47_0, % 26.62/4.42 | | | | | all_32_3) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0)))) % 26.62/4.42 | | | | | % 26.62/4.42 | | | | | GROUND_INST: instantiating (25) with all_32_6, all_32_8, all_32_5, % 26.62/4.42 | | | | | all_32_4, all_32_3, all_58_0, all_47_0, all_32_1, % 26.62/4.42 | | | | | all_133_0, all_114_0, simplifying with (1), (6), (8), % 26.62/4.42 | | | | | (15), (17), (23), (24), (28), (29), (35), (45) gives: % 26.62/4.42 | | | | | (96) all_133_0 = 0 | ? [v0: any] : ? [v1: any] : % 26.62/4.42 | | | | | ((apply(all_32_6, all_114_0, all_47_0) = v1 & apply(all_32_8, % 26.62/4.42 | | | | | all_58_0, all_114_0) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 26.62/4.42 | | | | | | (member(all_58_0, all_32_5) = v0 & member(all_47_0, % 26.62/4.42 | | | | | all_32_3) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0)))) % 26.62/4.42 | | | | | % 26.62/4.42 | | | | | BETA: splitting (95) gives: % 26.62/4.42 | | | | | % 26.62/4.42 | | | | | Case 1: % 26.62/4.42 | | | | | | % 26.62/4.42 | | | | | | (97) all_133_0 = 0 % 26.62/4.42 | | | | | | % 26.62/4.42 | | | | | | BETA: splitting (91) gives: % 26.62/4.42 | | | | | | % 26.62/4.42 | | | | | | Case 1: % 26.62/4.42 | | | | | | | % 26.62/4.42 | | | | | | | (98) all_133_1 = 0 % 26.62/4.42 | | | | | | | % 26.62/4.42 | | | | | | | REF_CLOSE: (46), (97), (98) are inconsistent by sub-proof #7. % 26.62/4.42 | | | | | | | % 26.62/4.42 | | | | | | Case 2: % 26.62/4.42 | | | | | | | % 26.62/4.42 | | | | | | | (99) ? [v0: any] : ? [v1: any] : ((apply(all_32_8, all_58_0, % 26.62/4.42 | | | | | | | all_47_2) = v1 & member(all_47_2, all_32_4) = v0 & ( % 26.62/4.42 | | | | | | | ~ (v1 = 0) | ~ (v0 = 0))) | (member(all_58_0, % 26.62/4.42 | | | | | | | all_32_5) = v0 & member(all_47_1, all_32_3) = v1 & ( % 26.62/4.42 | | | | | | | ~ (v1 = 0) | ~ (v0 = 0)))) % 26.62/4.42 | | | | | | | % 26.62/4.42 | | | | | | | DELTA: instantiating (99) with fresh symbols all_197_0, all_197_1 % 26.62/4.42 | | | | | | | gives: % 26.62/4.42 | | | | | | | (100) (apply(all_32_8, all_58_0, all_47_2) = all_197_0 & % 26.62/4.42 | | | | | | | member(all_47_2, all_32_4) = all_197_1 & ( ~ (all_197_0 % 26.62/4.42 | | | | | | | = 0) | ~ (all_197_1 = 0))) | (member(all_58_0, % 26.62/4.42 | | | | | | | all_32_5) = all_197_1 & member(all_47_1, all_32_3) = % 26.62/4.42 | | | | | | | all_197_0 & ( ~ (all_197_0 = 0) | ~ (all_197_1 = 0))) % 26.62/4.42 | | | | | | | % 26.62/4.42 | | | | | | | BETA: splitting (100) gives: % 26.62/4.42 | | | | | | | % 26.62/4.42 | | | | | | | Case 1: % 26.62/4.42 | | | | | | | | % 26.62/4.42 | | | | | | | | (101) apply(all_32_8, all_58_0, all_47_2) = all_197_0 & % 26.62/4.42 | | | | | | | | member(all_47_2, all_32_4) = all_197_1 & ( ~ (all_197_0 % 26.62/4.42 | | | | | | | | = 0) | ~ (all_197_1 = 0)) % 26.62/4.42 | | | | | | | | % 26.62/4.42 | | | | | | | | ALPHA: (101) implies: % 26.62/4.42 | | | | | | | | (102) member(all_47_2, all_32_4) = all_197_1 % 26.62/4.42 | | | | | | | | (103) apply(all_32_8, all_58_0, all_47_2) = all_197_0 % 26.62/4.43 | | | | | | | | (104) ~ (all_197_0 = 0) | ~ (all_197_1 = 0) % 26.62/4.43 | | | | | | | | % 26.62/4.43 | | | | | | | | BETA: splitting (92) gives: % 26.62/4.43 | | | | | | | | % 26.62/4.43 | | | | | | | | Case 1: % 26.62/4.43 | | | | | | | | | % 26.62/4.43 | | | | | | | | | (105) all_133_1 = 0 % 26.62/4.43 | | | | | | | | | % 26.62/4.43 | | | | | | | | | REF_CLOSE: (46), (97), (105) are inconsistent by sub-proof #7. % 26.62/4.43 | | | | | | | | | % 26.62/4.43 | | | | | | | | Case 2: % 26.62/4.43 | | | | | | | | | % 26.62/4.43 | | | | | | | | | (106) ? [v0: any] : ? [v1: any] : ((apply(all_32_7, % 26.62/4.43 | | | | | | | | | all_47_2, all_47_1) = v1 & apply(all_32_8, % 26.62/4.43 | | | | | | | | | all_58_0, all_47_2) = v0 & ( ~ (v1 = 0) | ~ % 26.62/4.43 | | | | | | | | | (v0 = 0))) | (member(all_58_0, all_32_5) = v0 & % 26.62/4.43 | | | | | | | | | member(all_47_1, all_32_3) = v1 & ( ~ (v1 = 0) | % 26.62/4.43 | | | | | | | | | ~ (v0 = 0)))) % 26.62/4.43 | | | | | | | | | % 26.62/4.43 | | | | | | | | | DELTA: instantiating (106) with fresh symbols all_220_0, % 26.62/4.43 | | | | | | | | | all_220_1 gives: % 26.62/4.43 | | | | | | | | | (107) (apply(all_32_7, all_47_2, all_47_1) = all_220_0 & % 26.62/4.43 | | | | | | | | | apply(all_32_8, all_58_0, all_47_2) = all_220_1 & ( % 26.62/4.43 | | | | | | | | | ~ (all_220_0 = 0) | ~ (all_220_1 = 0))) | % 26.62/4.43 | | | | | | | | | (member(all_58_0, all_32_5) = all_220_1 & % 26.62/4.43 | | | | | | | | | member(all_47_1, all_32_3) = all_220_0 & ( ~ % 26.62/4.43 | | | | | | | | | (all_220_0 = 0) | ~ (all_220_1 = 0))) % 26.62/4.43 | | | | | | | | | % 26.62/4.43 | | | | | | | | | BETA: splitting (107) gives: % 26.62/4.43 | | | | | | | | | % 26.62/4.43 | | | | | | | | | Case 1: % 26.62/4.43 | | | | | | | | | | % 26.62/4.43 | | | | | | | | | | (108) apply(all_32_7, all_47_2, all_47_1) = all_220_0 & % 26.62/4.43 | | | | | | | | | | apply(all_32_8, all_58_0, all_47_2) = all_220_1 & ( % 26.62/4.43 | | | | | | | | | | ~ (all_220_0 = 0) | ~ (all_220_1 = 0)) % 26.62/4.43 | | | | | | | | | | % 26.62/4.43 | | | | | | | | | | ALPHA: (108) implies: % 26.62/4.43 | | | | | | | | | | (109) apply(all_32_8, all_58_0, all_47_2) = all_220_1 % 26.62/4.43 | | | | | | | | | | % 26.62/4.43 | | | | | | | | | | GROUND_INST: instantiating (33) with 0, all_197_1, all_32_4, % 26.62/4.43 | | | | | | | | | | all_47_2, simplifying with (31), (102) gives: % 26.62/4.43 | | | | | | | | | | (110) all_197_1 = 0 % 26.62/4.43 | | | | | | | | | | % 26.62/4.43 | | | | | | | | | | GROUND_INST: instantiating (13) with 0, all_220_1, all_47_2, % 26.62/4.43 | | | | | | | | | | all_58_0, all_32_8, simplifying with (26), (109) % 26.62/4.43 | | | | | | | | | | gives: % 26.62/4.43 | | | | | | | | | | (111) all_220_1 = 0 % 26.62/4.43 | | | | | | | | | | % 26.89/4.43 | | | | | | | | | | GROUND_INST: instantiating (13) with all_197_0, all_220_1, % 26.89/4.43 | | | | | | | | | | all_47_2, all_58_0, all_32_8, simplifying with % 26.89/4.43 | | | | | | | | | | (103), (109) gives: % 26.89/4.43 | | | | | | | | | | (112) all_220_1 = all_197_0 % 26.89/4.43 | | | | | | | | | | % 26.89/4.43 | | | | | | | | | | COMBINE_EQS: (111), (112) imply: % 26.89/4.43 | | | | | | | | | | (113) all_197_0 = 0 % 26.89/4.43 | | | | | | | | | | % 26.89/4.43 | | | | | | | | | | REF_CLOSE: (104), (110), (113) are inconsistent by sub-proof % 26.89/4.43 | | | | | | | | | | #6. % 26.89/4.43 | | | | | | | | | | % 26.89/4.43 | | | | | | | | | Case 2: % 26.89/4.43 | | | | | | | | | | % 26.89/4.43 | | | | | | | | | | % 26.89/4.43 | | | | | | | | | | GROUND_INST: instantiating (33) with 0, all_197_1, all_32_4, % 26.89/4.43 | | | | | | | | | | all_47_2, simplifying with (31), (102) gives: % 26.89/4.43 | | | | | | | | | | (114) all_197_1 = 0 % 26.89/4.43 | | | | | | | | | | % 26.89/4.43 | | | | | | | | | | GROUND_INST: instantiating (13) with 0, all_197_0, all_47_2, % 26.89/4.43 | | | | | | | | | | all_58_0, all_32_8, simplifying with (26), (103) % 26.89/4.43 | | | | | | | | | | gives: % 26.89/4.43 | | | | | | | | | | (115) all_197_0 = 0 % 26.89/4.43 | | | | | | | | | | % 26.89/4.43 | | | | | | | | | | REF_CLOSE: (104), (114), (115) are inconsistent by sub-proof % 26.89/4.43 | | | | | | | | | | #6. % 26.89/4.43 | | | | | | | | | | % 26.89/4.43 | | | | | | | | | End of split % 26.89/4.43 | | | | | | | | | % 26.89/4.43 | | | | | | | | End of split % 26.89/4.43 | | | | | | | | % 26.89/4.43 | | | | | | | Case 2: % 26.89/4.43 | | | | | | | | % 26.89/4.43 | | | | | | | | (116) member(all_58_0, all_32_5) = all_197_1 & % 26.89/4.43 | | | | | | | | member(all_47_1, all_32_3) = all_197_0 & ( ~ (all_197_0 % 26.89/4.43 | | | | | | | | = 0) | ~ (all_197_1 = 0)) % 26.89/4.43 | | | | | | | | % 26.89/4.43 | | | | | | | | ALPHA: (116) implies: % 26.89/4.43 | | | | | | | | (117) member(all_47_1, all_32_3) = all_197_0 % 26.89/4.43 | | | | | | | | (118) member(all_58_0, all_32_5) = all_197_1 % 26.89/4.43 | | | | | | | | (119) ~ (all_197_0 = 0) | ~ (all_197_1 = 0) % 26.89/4.43 | | | | | | | | % 26.89/4.43 | | | | | | | | GROUND_INST: instantiating (33) with 0, all_197_0, all_32_3, % 26.89/4.43 | | | | | | | | all_47_1, simplifying with (9), (117) gives: % 26.89/4.43 | | | | | | | | (120) all_197_0 = 0 % 26.89/4.43 | | | | | | | | % 26.89/4.43 | | | | | | | | GROUND_INST: instantiating (33) with 0, all_197_1, all_32_5, % 26.89/4.43 | | | | | | | | all_58_0, simplifying with (10), (118) gives: % 26.89/4.43 | | | | | | | | (121) all_197_1 = 0 % 26.89/4.43 | | | | | | | | % 26.89/4.43 | | | | | | | | BETA: splitting (119) gives: % 26.89/4.43 | | | | | | | | % 26.89/4.43 | | | | | | | | Case 1: % 26.89/4.43 | | | | | | | | | % 26.89/4.43 | | | | | | | | | (122) ~ (all_197_0 = 0) % 26.89/4.43 | | | | | | | | | % 26.89/4.43 | | | | | | | | | REDUCE: (120), (122) imply: % 26.89/4.43 | | | | | | | | | (123) $false % 26.89/4.43 | | | | | | | | | % 26.89/4.43 | | | | | | | | | CLOSE: (123) is inconsistent. % 26.89/4.43 | | | | | | | | | % 26.89/4.43 | | | | | | | | Case 2: % 26.89/4.43 | | | | | | | | | % 26.89/4.43 | | | | | | | | | (124) ~ (all_197_1 = 0) % 26.89/4.43 | | | | | | | | | % 26.89/4.43 | | | | | | | | | REDUCE: (121), (124) imply: % 26.89/4.43 | | | | | | | | | (125) $false % 26.89/4.43 | | | | | | | | | % 26.89/4.43 | | | | | | | | | CLOSE: (125) is inconsistent. % 26.89/4.43 | | | | | | | | | % 26.89/4.43 | | | | | | | | End of split % 26.89/4.43 | | | | | | | | % 26.89/4.43 | | | | | | | End of split % 26.89/4.43 | | | | | | | % 26.89/4.43 | | | | | | End of split % 26.89/4.43 | | | | | | % 26.89/4.43 | | | | | Case 2: % 26.89/4.43 | | | | | | % 26.89/4.43 | | | | | | (126) ~ (all_133_0 = 0) % 26.89/4.43 | | | | | | (127) ? [v0: any] : ? [v1: any] : ((apply(all_32_6, all_47_2, % 26.89/4.43 | | | | | | all_47_0) = v1 & apply(all_32_8, all_58_0, all_47_2) % 26.89/4.43 | | | | | | = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) | (member(all_58_0, % 26.89/4.43 | | | | | | all_32_5) = v0 & member(all_47_0, all_32_3) = v1 & ( % 26.89/4.43 | | | | | | ~ (v1 = 0) | ~ (v0 = 0)))) % 26.89/4.43 | | | | | | % 26.89/4.43 | | | | | | DELTA: instantiating (127) with fresh symbols all_184_0, all_184_1 % 26.89/4.43 | | | | | | gives: % 26.89/4.43 | | | | | | (128) (apply(all_32_6, all_47_2, all_47_0) = all_184_0 & % 26.89/4.43 | | | | | | apply(all_32_8, all_58_0, all_47_2) = all_184_1 & ( ~ % 26.89/4.43 | | | | | | (all_184_0 = 0) | ~ (all_184_1 = 0))) | % 26.89/4.43 | | | | | | (member(all_58_0, all_32_5) = all_184_1 & member(all_47_0, % 26.89/4.43 | | | | | | all_32_3) = all_184_0 & ( ~ (all_184_0 = 0) | ~ % 26.89/4.43 | | | | | | (all_184_1 = 0))) % 26.89/4.43 | | | | | | % 26.89/4.43 | | | | | | BETA: splitting (128) gives: % 26.89/4.43 | | | | | | % 26.89/4.43 | | | | | | Case 1: % 26.89/4.43 | | | | | | | % 26.89/4.43 | | | | | | | (129) apply(all_32_6, all_47_2, all_47_0) = all_184_0 & % 26.89/4.43 | | | | | | | apply(all_32_8, all_58_0, all_47_2) = all_184_1 & ( ~ % 26.89/4.43 | | | | | | | (all_184_0 = 0) | ~ (all_184_1 = 0)) % 26.89/4.43 | | | | | | | % 26.89/4.43 | | | | | | | ALPHA: (129) implies: % 26.89/4.43 | | | | | | | (130) apply(all_32_8, all_58_0, all_47_2) = all_184_1 % 26.89/4.43 | | | | | | | % 26.89/4.43 | | | | | | | BETA: splitting (96) gives: % 26.89/4.43 | | | | | | | % 26.89/4.43 | | | | | | | Case 1: % 26.89/4.43 | | | | | | | | % 26.89/4.43 | | | | | | | | (131) all_133_0 = 0 % 26.89/4.43 | | | | | | | | % 26.89/4.43 | | | | | | | | REDUCE: (126), (131) imply: % 26.89/4.43 | | | | | | | | (132) $false % 26.89/4.43 | | | | | | | | % 26.89/4.43 | | | | | | | | CLOSE: (132) is inconsistent. % 26.89/4.43 | | | | | | | | % 26.89/4.43 | | | | | | | Case 2: % 26.89/4.43 | | | | | | | | % 26.89/4.43 | | | | | | | | (133) ? [v0: any] : ? [v1: any] : ((apply(all_32_6, % 26.89/4.43 | | | | | | | | all_114_0, all_47_0) = v1 & apply(all_32_8, % 26.89/4.43 | | | | | | | | all_58_0, all_114_0) = v0 & ( ~ (v1 = 0) | ~ (v0 % 26.89/4.43 | | | | | | | | = 0))) | (member(all_58_0, all_32_5) = v0 & % 26.89/4.43 | | | | | | | | member(all_47_0, all_32_3) = v1 & ( ~ (v1 = 0) | ~ % 26.89/4.43 | | | | | | | | (v0 = 0)))) % 26.89/4.43 | | | | | | | | % 26.89/4.43 | | | | | | | | DELTA: instantiating (133) with fresh symbols all_192_0, % 26.89/4.43 | | | | | | | | all_192_1 gives: % 26.89/4.43 | | | | | | | | (134) (apply(all_32_6, all_114_0, all_47_0) = all_192_0 & % 26.89/4.43 | | | | | | | | apply(all_32_8, all_58_0, all_114_0) = all_192_1 & ( % 26.89/4.43 | | | | | | | | ~ (all_192_0 = 0) | ~ (all_192_1 = 0))) | % 26.89/4.43 | | | | | | | | (member(all_58_0, all_32_5) = all_192_1 & % 26.89/4.43 | | | | | | | | member(all_47_0, all_32_3) = all_192_0 & ( ~ % 26.89/4.43 | | | | | | | | (all_192_0 = 0) | ~ (all_192_1 = 0))) % 26.89/4.43 | | | | | | | | % 26.89/4.43 | | | | | | | | BETA: splitting (90) gives: % 26.89/4.43 | | | | | | | | % 26.89/4.43 | | | | | | | | Case 1: % 26.89/4.43 | | | | | | | | | % 26.89/4.43 | | | | | | | | | (135) all_114_0 = all_47_2 % 26.89/4.43 | | | | | | | | | % 26.89/4.43 | | | | | | | | | BETA: splitting (134) gives: % 26.89/4.43 | | | | | | | | | % 26.89/4.43 | | | | | | | | | Case 1: % 26.89/4.43 | | | | | | | | | | % 26.89/4.43 | | | | | | | | | | (136) apply(all_32_6, all_114_0, all_47_0) = all_192_0 & % 26.89/4.43 | | | | | | | | | | apply(all_32_8, all_58_0, all_114_0) = all_192_1 & % 26.89/4.43 | | | | | | | | | | ( ~ (all_192_0 = 0) | ~ (all_192_1 = 0)) % 26.89/4.43 | | | | | | | | | | % 26.89/4.43 | | | | | | | | | | ALPHA: (136) implies: % 26.89/4.43 | | | | | | | | | | (137) apply(all_32_8, all_58_0, all_114_0) = all_192_1 % 26.89/4.43 | | | | | | | | | | (138) apply(all_32_6, all_114_0, all_47_0) = all_192_0 % 26.89/4.43 | | | | | | | | | | (139) ~ (all_192_0 = 0) | ~ (all_192_1 = 0) % 26.89/4.43 | | | | | | | | | | % 26.89/4.43 | | | | | | | | | | REDUCE: (135), (138) imply: % 26.89/4.43 | | | | | | | | | | (140) apply(all_32_6, all_47_2, all_47_0) = all_192_0 % 26.89/4.43 | | | | | | | | | | % 26.89/4.43 | | | | | | | | | | REDUCE: (135), (137) imply: % 26.89/4.43 | | | | | | | | | | (141) apply(all_32_8, all_58_0, all_47_2) = all_192_1 % 26.89/4.43 | | | | | | | | | | % 26.89/4.43 | | | | | | | | | | GROUND_INST: instantiating (13) with 0, all_192_1, all_47_2, % 26.89/4.43 | | | | | | | | | | all_58_0, all_32_8, simplifying with (26), (141) % 26.89/4.43 | | | | | | | | | | gives: % 26.89/4.43 | | | | | | | | | | (142) all_192_1 = 0 % 26.89/4.43 | | | | | | | | | | % 26.89/4.43 | | | | | | | | | | GROUND_INST: instantiating (13) with 0, all_192_0, all_47_0, % 26.89/4.43 | | | | | | | | | | all_47_2, all_32_6, simplifying with (19), (140) % 26.89/4.43 | | | | | | | | | | gives: % 26.89/4.43 | | | | | | | | | | (143) all_192_0 = 0 % 26.89/4.43 | | | | | | | | | | % 26.89/4.43 | | | | | | | | | | REF_CLOSE: (139), (142), (143) are inconsistent by sub-proof % 26.89/4.43 | | | | | | | | | | #5. % 26.89/4.43 | | | | | | | | | | % 26.89/4.43 | | | | | | | | | Case 2: % 26.89/4.43 | | | | | | | | | | % 26.89/4.43 | | | | | | | | | | (144) member(all_58_0, all_32_5) = all_192_1 & % 26.89/4.43 | | | | | | | | | | member(all_47_0, all_32_3) = all_192_0 & ( ~ % 26.89/4.43 | | | | | | | | | | (all_192_0 = 0) | ~ (all_192_1 = 0)) % 26.89/4.43 | | | | | | | | | | % 26.89/4.43 | | | | | | | | | | ALPHA: (144) implies: % 26.89/4.43 | | | | | | | | | | (145) member(all_47_0, all_32_3) = all_192_0 % 26.89/4.43 | | | | | | | | | | (146) member(all_58_0, all_32_5) = all_192_1 % 26.89/4.43 | | | | | | | | | | (147) ~ (all_192_0 = 0) | ~ (all_192_1 = 0) % 26.89/4.43 | | | | | | | | | | % 26.89/4.43 | | | | | | | | | | BETA: splitting (94) gives: % 26.89/4.43 | | | | | | | | | | % 26.89/4.43 | | | | | | | | | | Case 1: % 26.89/4.43 | | | | | | | | | | | % 26.89/4.43 | | | | | | | | | | | (148) all_133_0 = 0 % 26.89/4.43 | | | | | | | | | | | % 26.89/4.43 | | | | | | | | | | | REDUCE: (126), (148) imply: % 26.89/4.43 | | | | | | | | | | | (149) $false % 26.89/4.43 | | | | | | | | | | | % 26.89/4.43 | | | | | | | | | | | CLOSE: (149) is inconsistent. % 26.89/4.43 | | | | | | | | | | | % 26.89/4.43 | | | | | | | | | | Case 2: % 26.89/4.43 | | | | | | | | | | | % 26.89/4.43 | | | | | | | | | | | (150) ? [v0: any] : ? [v1: any] : ((apply(all_32_6, % 26.89/4.43 | | | | | | | | | | | all_47_2, all_47_0) = v1 & member(all_47_2, % 26.89/4.43 | | | | | | | | | | | all_32_4) = v0 & ( ~ (v1 = 0) | ~ (v0 = % 26.89/4.43 | | | | | | | | | | | 0))) | (member(all_58_0, all_32_5) = v0 & % 26.89/4.43 | | | | | | | | | | | member(all_47_0, all_32_3) = v1 & ( ~ (v1 = 0) % 26.89/4.43 | | | | | | | | | | | | ~ (v0 = 0)))) % 26.89/4.43 | | | | | | | | | | | % 26.89/4.43 | | | | | | | | | | | DELTA: instantiating (150) with fresh symbols all_224_0, % 26.89/4.43 | | | | | | | | | | | all_224_1 gives: % 26.89/4.43 | | | | | | | | | | | (151) (apply(all_32_6, all_47_2, all_47_0) = all_224_0 & % 26.89/4.43 | | | | | | | | | | | member(all_47_2, all_32_4) = all_224_1 & ( ~ % 26.89/4.43 | | | | | | | | | | | (all_224_0 = 0) | ~ (all_224_1 = 0))) | % 26.89/4.43 | | | | | | | | | | | (member(all_58_0, all_32_5) = all_224_1 & % 26.89/4.43 | | | | | | | | | | | member(all_47_0, all_32_3) = all_224_0 & ( ~ % 26.89/4.43 | | | | | | | | | | | (all_224_0 = 0) | ~ (all_224_1 = 0))) % 26.89/4.43 | | | | | | | | | | | % 26.89/4.43 | | | | | | | | | | | BETA: splitting (151) gives: % 26.89/4.43 | | | | | | | | | | | % 26.89/4.43 | | | | | | | | | | | Case 1: % 26.89/4.43 | | | | | | | | | | | | % 26.89/4.43 | | | | | | | | | | | | % 26.89/4.43 | | | | | | | | | | | | GROUND_INST: instantiating (33) with 0, all_192_0, all_32_3, % 26.89/4.43 | | | | | | | | | | | | all_47_0, simplifying with (21), (145) gives: % 26.89/4.43 | | | | | | | | | | | | (152) all_192_0 = 0 % 26.89/4.43 | | | | | | | | | | | | % 26.89/4.43 | | | | | | | | | | | | GROUND_INST: instantiating (33) with 0, all_192_1, all_32_5, % 26.89/4.43 | | | | | | | | | | | | all_58_0, simplifying with (10), (146) gives: % 26.89/4.43 | | | | | | | | | | | | (153) all_192_1 = 0 % 26.89/4.43 | | | | | | | | | | | | % 26.89/4.43 | | | | | | | | | | | | REF_CLOSE: (147), (152), (153) are inconsistent by sub-proof % 26.89/4.43 | | | | | | | | | | | | #5. % 26.89/4.43 | | | | | | | | | | | | % 26.89/4.43 | | | | | | | | | | | Case 2: % 26.89/4.43 | | | | | | | | | | | | % 26.89/4.44 | | | | | | | | | | | | (154) member(all_58_0, all_32_5) = all_224_1 & % 26.89/4.44 | | | | | | | | | | | | member(all_47_0, all_32_3) = all_224_0 & ( ~ % 26.89/4.44 | | | | | | | | | | | | (all_224_0 = 0) | ~ (all_224_1 = 0)) % 26.89/4.44 | | | | | | | | | | | | % 26.89/4.44 | | | | | | | | | | | | ALPHA: (154) implies: % 26.89/4.44 | | | | | | | | | | | | (155) member(all_47_0, all_32_3) = all_224_0 % 26.89/4.44 | | | | | | | | | | | | (156) member(all_58_0, all_32_5) = all_224_1 % 26.89/4.44 | | | | | | | | | | | | % 26.89/4.44 | | | | | | | | | | | | GROUND_INST: instantiating (33) with 0, all_224_0, all_32_3, % 26.89/4.44 | | | | | | | | | | | | all_47_0, simplifying with (21), (155) gives: % 26.89/4.44 | | | | | | | | | | | | (157) all_224_0 = 0 % 26.89/4.44 | | | | | | | | | | | | % 26.89/4.44 | | | | | | | | | | | | GROUND_INST: instantiating (33) with all_192_0, all_224_0, % 26.89/4.44 | | | | | | | | | | | | all_32_3, all_47_0, simplifying with (145), (155) % 26.89/4.44 | | | | | | | | | | | | gives: % 26.89/4.44 | | | | | | | | | | | | (158) all_224_0 = all_192_0 % 26.89/4.44 | | | | | | | | | | | | % 26.89/4.44 | | | | | | | | | | | | GROUND_INST: instantiating (33) with 0, all_224_1, all_32_5, % 26.89/4.44 | | | | | | | | | | | | all_58_0, simplifying with (10), (156) gives: % 26.89/4.44 | | | | | | | | | | | | (159) all_224_1 = 0 % 26.89/4.44 | | | | | | | | | | | | % 26.89/4.44 | | | | | | | | | | | | GROUND_INST: instantiating (33) with all_192_1, all_224_1, % 26.89/4.44 | | | | | | | | | | | | all_32_5, all_58_0, simplifying with (146), (156) % 26.89/4.44 | | | | | | | | | | | | gives: % 26.89/4.44 | | | | | | | | | | | | (160) all_224_1 = all_192_1 % 26.89/4.44 | | | | | | | | | | | | % 26.89/4.44 | | | | | | | | | | | | COMBINE_EQS: (157), (158) imply: % 26.89/4.44 | | | | | | | | | | | | (161) all_192_0 = 0 % 26.89/4.44 | | | | | | | | | | | | % 26.89/4.44 | | | | | | | | | | | | COMBINE_EQS: (159), (160) imply: % 26.89/4.44 | | | | | | | | | | | | (162) all_192_1 = 0 % 26.89/4.44 | | | | | | | | | | | | % 26.89/4.44 | | | | | | | | | | | | SIMP: (162) implies: % 26.89/4.44 | | | | | | | | | | | | (163) all_192_1 = 0 % 26.89/4.44 | | | | | | | | | | | | % 26.89/4.44 | | | | | | | | | | | | REF_CLOSE: (147), (161), (163) are inconsistent by sub-proof % 26.89/4.44 | | | | | | | | | | | | #5. % 26.89/4.44 | | | | | | | | | | | | % 26.89/4.44 | | | | | | | | | | | End of split % 26.89/4.44 | | | | | | | | | | | % 26.89/4.44 | | | | | | | | | | End of split % 26.89/4.44 | | | | | | | | | | % 26.89/4.44 | | | | | | | | | End of split % 26.89/4.44 | | | | | | | | | % 26.89/4.44 | | | | | | | | Case 2: % 26.89/4.44 | | | | | | | | | % 26.89/4.44 | | | | | | | | | (164) ~ (all_114_0 = all_47_2) % 26.89/4.44 | | | | | | | | | (165) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 26.89/4.44 | | | | | | | | | (member(all_114_0, all_32_4) = v1 & member(all_58_0, % 26.89/4.44 | | | | | | | | | all_32_5) = v0 & member(all_47_2, all_32_4) = v2 % 26.89/4.44 | | | | | | | | | & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0))) % 26.89/4.44 | | | | | | | | | % 26.89/4.44 | | | | | | | | | DELTA: instantiating (165) with fresh symbols all_197_0, % 26.89/4.44 | | | | | | | | | all_197_1, all_197_2 gives: % 26.89/4.44 | | | | | | | | | (166) member(all_114_0, all_32_4) = all_197_1 & % 26.89/4.44 | | | | | | | | | member(all_58_0, all_32_5) = all_197_2 & % 26.89/4.44 | | | | | | | | | member(all_47_2, all_32_4) = all_197_0 & ( ~ % 26.89/4.44 | | | | | | | | | (all_197_0 = 0) | ~ (all_197_1 = 0) | ~ % 26.89/4.44 | | | | | | | | | (all_197_2 = 0)) % 26.89/4.44 | | | | | | | | | % 26.89/4.44 | | | | | | | | | ALPHA: (166) implies: % 26.89/4.44 | | | | | | | | | (167) member(all_58_0, all_32_5) = all_197_2 % 26.89/4.44 | | | | | | | | | % 26.89/4.44 | | | | | | | | | BETA: splitting (89) gives: % 26.89/4.44 | | | | | | | | | % 26.89/4.44 | | | | | | | | | Case 1: % 26.89/4.44 | | | | | | | | | | % 26.89/4.44 | | | | | | | | | | (168) all_114_0 = all_47_2 % 26.89/4.44 | | | | | | | | | | % 26.89/4.44 | | | | | | | | | | REDUCE: (164), (168) imply: % 26.89/4.44 | | | | | | | | | | (169) $false % 26.89/4.44 | | | | | | | | | | % 26.89/4.44 | | | | | | | | | | CLOSE: (169) is inconsistent. % 26.89/4.44 | | | | | | | | | | % 26.89/4.44 | | | | | | | | | Case 2: % 26.89/4.44 | | | | | | | | | | % 26.89/4.44 | | | | | | | | | | (170) ? [v0: any] : ? [v1: any] : (apply(all_32_8, % 26.89/4.44 | | | | | | | | | | all_58_0, all_114_0) = v1 & apply(all_32_8, % 26.89/4.44 | | | | | | | | | | all_58_0, all_47_2) = v0 & ( ~ (v1 = 0) | ~ % 26.89/4.44 | | | | | | | | | | (v0 = 0))) % 26.89/4.44 | | | | | | | | | | % 26.89/4.44 | | | | | | | | | | DELTA: instantiating (170) with fresh symbols all_213_0, % 26.89/4.44 | | | | | | | | | | all_213_1 gives: % 26.89/4.44 | | | | | | | | | | (171) apply(all_32_8, all_58_0, all_114_0) = all_213_0 & % 26.89/4.44 | | | | | | | | | | apply(all_32_8, all_58_0, all_47_2) = all_213_1 & ( % 26.89/4.44 | | | | | | | | | | ~ (all_213_0 = 0) | ~ (all_213_1 = 0)) % 26.89/4.44 | | | | | | | | | | % 26.89/4.44 | | | | | | | | | | ALPHA: (171) implies: % 26.89/4.44 | | | | | | | | | | (172) apply(all_32_8, all_58_0, all_47_2) = all_213_1 % 26.89/4.44 | | | | | | | | | | % 26.89/4.44 | | | | | | | | | | BETA: splitting (93) gives: % 26.89/4.44 | | | | | | | | | | % 26.89/4.44 | | | | | | | | | | Case 1: % 26.89/4.44 | | | | | | | | | | | % 26.89/4.44 | | | | | | | | | | | (173) all_133_0 = 0 % 26.89/4.44 | | | | | | | | | | | % 26.89/4.44 | | | | | | | | | | | REDUCE: (126), (173) imply: % 26.89/4.44 | | | | | | | | | | | (174) $false % 26.89/4.44 | | | | | | | | | | | % 26.89/4.44 | | | | | | | | | | | CLOSE: (174) is inconsistent. % 26.89/4.44 | | | | | | | | | | | % 26.89/4.44 | | | | | | | | | | Case 2: % 26.89/4.44 | | | | | | | | | | | % 26.89/4.44 | | | | | | | | | | | (175) ? [v0: any] : ? [v1: any] : ((apply(all_32_8, % 26.89/4.44 | | | | | | | | | | | all_58_0, all_47_2) = v1 & member(all_47_2, % 26.89/4.44 | | | | | | | | | | | all_32_4) = v0 & ( ~ (v1 = 0) | ~ (v0 = % 26.89/4.44 | | | | | | | | | | | 0))) | (member(all_58_0, all_32_5) = v0 & % 26.89/4.44 | | | | | | | | | | | member(all_47_0, all_32_3) = v1 & ( ~ (v1 = 0) % 26.89/4.44 | | | | | | | | | | | | ~ (v0 = 0)))) % 26.89/4.44 | | | | | | | | | | | % 26.89/4.44 | | | | | | | | | | | DELTA: instantiating (175) with fresh symbols all_237_0, % 26.89/4.44 | | | | | | | | | | | all_237_1 gives: % 26.89/4.44 | | | | | | | | | | | (176) (apply(all_32_8, all_58_0, all_47_2) = all_237_0 & % 26.89/4.44 | | | | | | | | | | | member(all_47_2, all_32_4) = all_237_1 & ( ~ % 26.89/4.44 | | | | | | | | | | | (all_237_0 = 0) | ~ (all_237_1 = 0))) | % 26.89/4.44 | | | | | | | | | | | (member(all_58_0, all_32_5) = all_237_1 & % 26.89/4.44 | | | | | | | | | | | member(all_47_0, all_32_3) = all_237_0 & ( ~ % 26.89/4.44 | | | | | | | | | | | (all_237_0 = 0) | ~ (all_237_1 = 0))) % 26.89/4.44 | | | | | | | | | | | % 26.89/4.44 | | | | | | | | | | | BETA: splitting (176) gives: % 26.89/4.44 | | | | | | | | | | | % 26.89/4.44 | | | | | | | | | | | Case 1: % 26.89/4.44 | | | | | | | | | | | | % 26.89/4.44 | | | | | | | | | | | | (177) apply(all_32_8, all_58_0, all_47_2) = all_237_0 & % 26.89/4.44 | | | | | | | | | | | | member(all_47_2, all_32_4) = all_237_1 & ( ~ % 26.89/4.44 | | | | | | | | | | | | (all_237_0 = 0) | ~ (all_237_1 = 0)) % 26.89/4.44 | | | | | | | | | | | | % 26.89/4.44 | | | | | | | | | | | | ALPHA: (177) implies: % 26.89/4.44 | | | | | | | | | | | | (178) member(all_47_2, all_32_4) = all_237_1 % 26.89/4.44 | | | | | | | | | | | | (179) apply(all_32_8, all_58_0, all_47_2) = all_237_0 % 26.89/4.44 | | | | | | | | | | | | (180) ~ (all_237_0 = 0) | ~ (all_237_1 = 0) % 26.89/4.44 | | | | | | | | | | | | % 26.89/4.44 | | | | | | | | | | | | GROUND_INST: instantiating (33) with 0, all_237_1, all_32_4, % 26.89/4.44 | | | | | | | | | | | | all_47_2, simplifying with (31), (178) gives: % 26.89/4.44 | | | | | | | | | | | | (181) all_237_1 = 0 % 26.89/4.44 | | | | | | | | | | | | % 26.89/4.44 | | | | | | | | | | | | GROUND_INST: instantiating (13) with 0, all_213_1, all_47_2, % 26.89/4.44 | | | | | | | | | | | | all_58_0, all_32_8, simplifying with (26), (172) % 26.89/4.44 | | | | | | | | | | | | gives: % 26.89/4.44 | | | | | | | | | | | | (182) all_213_1 = 0 % 26.89/4.44 | | | | | | | | | | | | % 26.89/4.44 | | | | | | | | | | | | GROUND_INST: instantiating (13) with all_213_1, all_237_0, % 26.89/4.44 | | | | | | | | | | | | all_47_2, all_58_0, all_32_8, simplifying with % 26.89/4.44 | | | | | | | | | | | | (172), (179) gives: % 26.89/4.44 | | | | | | | | | | | | (183) all_237_0 = all_213_1 % 26.89/4.44 | | | | | | | | | | | | % 26.89/4.44 | | | | | | | | | | | | GROUND_INST: instantiating (13) with all_184_1, all_237_0, % 26.89/4.44 | | | | | | | | | | | | all_47_2, all_58_0, all_32_8, simplifying with % 26.89/4.44 | | | | | | | | | | | | (130), (179) gives: % 26.89/4.44 | | | | | | | | | | | | (184) all_237_0 = all_184_1 % 26.89/4.44 | | | | | | | | | | | | % 26.89/4.44 | | | | | | | | | | | | COMBINE_EQS: (183), (184) imply: % 26.89/4.44 | | | | | | | | | | | | (185) all_213_1 = all_184_1 % 26.89/4.44 | | | | | | | | | | | | % 26.89/4.44 | | | | | | | | | | | | SIMP: (185) implies: % 26.89/4.44 | | | | | | | | | | | | (186) all_213_1 = all_184_1 % 26.89/4.44 | | | | | | | | | | | | % 26.89/4.44 | | | | | | | | | | | | COMBINE_EQS: (182), (186) imply: % 26.89/4.44 | | | | | | | | | | | | (187) all_184_1 = 0 % 26.89/4.44 | | | | | | | | | | | | % 26.89/4.44 | | | | | | | | | | | | COMBINE_EQS: (184), (187) imply: % 26.89/4.44 | | | | | | | | | | | | (188) all_237_0 = 0 % 26.89/4.44 | | | | | | | | | | | | % 26.89/4.44 | | | | | | | | | | | | REF_CLOSE: (180), (181), (188) are inconsistent by sub-proof % 26.89/4.44 | | | | | | | | | | | | #4. % 26.89/4.44 | | | | | | | | | | | | % 26.89/4.44 | | | | | | | | | | | Case 2: % 26.89/4.44 | | | | | | | | | | | | % 26.89/4.44 | | | | | | | | | | | | (189) member(all_58_0, all_32_5) = all_237_1 & % 26.89/4.44 | | | | | | | | | | | | member(all_47_0, all_32_3) = all_237_0 & ( ~ % 26.89/4.44 | | | | | | | | | | | | (all_237_0 = 0) | ~ (all_237_1 = 0)) % 26.89/4.44 | | | | | | | | | | | | % 26.89/4.44 | | | | | | | | | | | | ALPHA: (189) implies: % 26.89/4.44 | | | | | | | | | | | | (190) member(all_47_0, all_32_3) = all_237_0 % 26.89/4.44 | | | | | | | | | | | | (191) member(all_58_0, all_32_5) = all_237_1 % 26.89/4.44 | | | | | | | | | | | | (192) ~ (all_237_0 = 0) | ~ (all_237_1 = 0) % 26.89/4.44 | | | | | | | | | | | | % 26.89/4.44 | | | | | | | | | | | | GROUND_INST: instantiating (33) with 0, all_237_0, all_32_3, % 26.89/4.44 | | | | | | | | | | | | all_47_0, simplifying with (21), (190) gives: % 26.89/4.44 | | | | | | | | | | | | (193) all_237_0 = 0 % 26.89/4.44 | | | | | | | | | | | | % 26.89/4.44 | | | | | | | | | | | | GROUND_INST: instantiating (33) with 0, all_237_1, all_32_5, % 26.89/4.44 | | | | | | | | | | | | all_58_0, simplifying with (10), (191) gives: % 26.89/4.44 | | | | | | | | | | | | (194) all_237_1 = 0 % 26.89/4.44 | | | | | | | | | | | | % 26.89/4.44 | | | | | | | | | | | | GROUND_INST: instantiating (33) with all_197_2, all_237_1, % 26.89/4.44 | | | | | | | | | | | | all_32_5, all_58_0, simplifying with (167), (191) % 26.89/4.44 | | | | | | | | | | | | gives: % 26.89/4.44 | | | | | | | | | | | | (195) all_237_1 = all_197_2 % 26.89/4.44 | | | | | | | | | | | | % 26.89/4.44 | | | | | | | | | | | | COMBINE_EQS: (194), (195) imply: % 26.89/4.44 | | | | | | | | | | | | (196) all_197_2 = 0 % 26.89/4.44 | | | | | | | | | | | | % 26.89/4.44 | | | | | | | | | | | | REF_CLOSE: (192), (193), (194) are inconsistent by sub-proof % 26.89/4.44 | | | | | | | | | | | | #4. % 26.89/4.44 | | | | | | | | | | | | % 26.89/4.44 | | | | | | | | | | | End of split % 26.89/4.44 | | | | | | | | | | | % 26.89/4.44 | | | | | | | | | | End of split % 26.89/4.44 | | | | | | | | | | % 26.89/4.44 | | | | | | | | | End of split % 26.89/4.44 | | | | | | | | | % 26.89/4.44 | | | | | | | | End of split % 26.89/4.44 | | | | | | | | % 26.89/4.44 | | | | | | | End of split % 26.89/4.44 | | | | | | | % 26.89/4.44 | | | | | | Case 2: % 26.89/4.44 | | | | | | | % 26.89/4.44 | | | | | | | (197) member(all_58_0, all_32_5) = all_184_1 & member(all_47_0, % 26.89/4.44 | | | | | | | all_32_3) = all_184_0 & ( ~ (all_184_0 = 0) | ~ % 26.89/4.44 | | | | | | | (all_184_1 = 0)) % 26.89/4.44 | | | | | | | % 26.89/4.44 | | | | | | | ALPHA: (197) implies: % 26.89/4.44 | | | | | | | (198) member(all_47_0, all_32_3) = all_184_0 % 26.89/4.44 | | | | | | | (199) member(all_58_0, all_32_5) = all_184_1 % 26.89/4.44 | | | | | | | (200) ~ (all_184_0 = 0) | ~ (all_184_1 = 0) % 26.89/4.44 | | | | | | | % 26.89/4.44 | | | | | | | BETA: splitting (96) gives: % 26.89/4.44 | | | | | | | % 26.89/4.44 | | | | | | | Case 1: % 26.89/4.44 | | | | | | | | % 26.89/4.44 | | | | | | | | (201) all_133_0 = 0 % 26.89/4.44 | | | | | | | | % 26.89/4.44 | | | | | | | | REDUCE: (126), (201) imply: % 26.89/4.44 | | | | | | | | (202) $false % 26.89/4.44 | | | | | | | | % 26.89/4.44 | | | | | | | | CLOSE: (202) is inconsistent. % 26.89/4.44 | | | | | | | | % 26.89/4.44 | | | | | | | Case 2: % 26.89/4.44 | | | | | | | | % 26.89/4.44 | | | | | | | | (203) ? [v0: any] : ? [v1: any] : ((apply(all_32_6, % 26.89/4.44 | | | | | | | | all_114_0, all_47_0) = v1 & apply(all_32_8, % 26.89/4.44 | | | | | | | | all_58_0, all_114_0) = v0 & ( ~ (v1 = 0) | ~ (v0 % 26.89/4.44 | | | | | | | | = 0))) | (member(all_58_0, all_32_5) = v0 & % 26.89/4.44 | | | | | | | | member(all_47_0, all_32_3) = v1 & ( ~ (v1 = 0) | ~ % 26.89/4.44 | | | | | | | | (v0 = 0)))) % 26.89/4.44 | | | | | | | | % 26.89/4.44 | | | | | | | | DELTA: instantiating (203) with fresh symbols all_192_0, % 26.89/4.44 | | | | | | | | all_192_1 gives: % 26.89/4.44 | | | | | | | | (204) (apply(all_32_6, all_114_0, all_47_0) = all_192_0 & % 26.89/4.44 | | | | | | | | apply(all_32_8, all_58_0, all_114_0) = all_192_1 & ( % 26.89/4.44 | | | | | | | | ~ (all_192_0 = 0) | ~ (all_192_1 = 0))) | % 26.89/4.44 | | | | | | | | (member(all_58_0, all_32_5) = all_192_1 & % 26.89/4.44 | | | | | | | | member(all_47_0, all_32_3) = all_192_0 & ( ~ % 26.89/4.44 | | | | | | | | (all_192_0 = 0) | ~ (all_192_1 = 0))) % 26.89/4.44 | | | | | | | | % 26.89/4.44 | | | | | | | | BETA: splitting (204) gives: % 26.89/4.44 | | | | | | | | % 26.89/4.44 | | | | | | | | Case 1: % 26.89/4.44 | | | | | | | | | % 26.89/4.44 | | | | | | | | | % 26.89/4.44 | | | | | | | | | GROUND_INST: instantiating (33) with 0, all_184_0, all_32_3, % 26.89/4.44 | | | | | | | | | all_47_0, simplifying with (21), (198) gives: % 26.89/4.44 | | | | | | | | | (205) all_184_0 = 0 % 26.89/4.44 | | | | | | | | | % 26.89/4.44 | | | | | | | | | GROUND_INST: instantiating (33) with 0, all_184_1, all_32_5, % 26.89/4.44 | | | | | | | | | all_58_0, simplifying with (10), (199) gives: % 26.89/4.44 | | | | | | | | | (206) all_184_1 = 0 % 26.89/4.44 | | | | | | | | | % 26.89/4.44 | | | | | | | | | REF_CLOSE: (200), (205), (206) are inconsistent by sub-proof % 26.89/4.44 | | | | | | | | | #3. % 26.89/4.44 | | | | | | | | | % 26.89/4.44 | | | | | | | | Case 2: % 26.89/4.44 | | | | | | | | | % 26.89/4.44 | | | | | | | | | (207) member(all_58_0, all_32_5) = all_192_1 & % 26.89/4.44 | | | | | | | | | member(all_47_0, all_32_3) = all_192_0 & ( ~ % 26.89/4.44 | | | | | | | | | (all_192_0 = 0) | ~ (all_192_1 = 0)) % 26.89/4.44 | | | | | | | | | % 26.89/4.44 | | | | | | | | | ALPHA: (207) implies: % 26.89/4.44 | | | | | | | | | (208) member(all_47_0, all_32_3) = all_192_0 % 26.89/4.44 | | | | | | | | | (209) member(all_58_0, all_32_5) = all_192_1 % 26.89/4.44 | | | | | | | | | % 26.89/4.44 | | | | | | | | | GROUND_INST: instantiating (33) with 0, all_192_0, all_32_3, % 26.89/4.44 | | | | | | | | | all_47_0, simplifying with (21), (208) gives: % 26.89/4.44 | | | | | | | | | (210) all_192_0 = 0 % 26.89/4.44 | | | | | | | | | % 26.89/4.44 | | | | | | | | | GROUND_INST: instantiating (33) with all_184_0, all_192_0, % 26.89/4.44 | | | | | | | | | all_32_3, all_47_0, simplifying with (198), (208) % 26.89/4.44 | | | | | | | | | gives: % 26.89/4.44 | | | | | | | | | (211) all_192_0 = all_184_0 % 26.89/4.45 | | | | | | | | | % 26.89/4.45 | | | | | | | | | GROUND_INST: instantiating (33) with 0, all_192_1, all_32_5, % 26.89/4.45 | | | | | | | | | all_58_0, simplifying with (10), (209) gives: % 26.89/4.45 | | | | | | | | | (212) all_192_1 = 0 % 26.89/4.45 | | | | | | | | | % 26.89/4.45 | | | | | | | | | GROUND_INST: instantiating (33) with all_184_1, all_192_1, % 26.89/4.45 | | | | | | | | | all_32_5, all_58_0, simplifying with (199), (209) % 26.89/4.45 | | | | | | | | | gives: % 26.89/4.45 | | | | | | | | | (213) all_192_1 = all_184_1 % 26.89/4.45 | | | | | | | | | % 26.89/4.45 | | | | | | | | | COMBINE_EQS: (210), (211) imply: % 26.89/4.45 | | | | | | | | | (214) all_184_0 = 0 % 26.89/4.45 | | | | | | | | | % 26.89/4.45 | | | | | | | | | COMBINE_EQS: (212), (213) imply: % 26.89/4.45 | | | | | | | | | (215) all_184_1 = 0 % 26.89/4.45 | | | | | | | | | % 26.89/4.45 | | | | | | | | | REF_CLOSE: (200), (214), (215) are inconsistent by sub-proof % 26.89/4.45 | | | | | | | | | #3. % 26.89/4.45 | | | | | | | | | % 26.89/4.45 | | | | | | | | End of split % 26.89/4.45 | | | | | | | | % 26.89/4.45 | | | | | | | End of split % 26.89/4.45 | | | | | | | % 26.89/4.45 | | | | | | End of split % 26.89/4.45 | | | | | | % 26.89/4.45 | | | | | End of split % 26.89/4.45 | | | | | % 26.89/4.45 | | | | End of split % 26.89/4.45 | | | | % 26.89/4.45 | | | End of split % 26.89/4.45 | | | % 26.89/4.45 | | End of split % 26.89/4.45 | | % 26.89/4.45 | End of split % 26.89/4.45 | % 26.89/4.45 End of proof % 26.89/4.45 % 26.89/4.45 Sub-proof #3 shows that the following formulas are inconsistent: % 26.89/4.45 ---------------------------------------------------------------- % 26.89/4.45 (1) ~ (all_184_0 = 0) | ~ (all_184_1 = 0) % 26.89/4.45 (2) all_184_0 = 0 % 26.89/4.45 (3) all_184_1 = 0 % 26.89/4.45 % 26.89/4.45 Begin of proof % 26.89/4.45 | % 26.89/4.45 | BETA: splitting (1) gives: % 26.89/4.45 | % 26.89/4.45 | Case 1: % 26.89/4.45 | | % 26.89/4.45 | | (4) ~ (all_184_0 = 0) % 26.89/4.45 | | % 26.89/4.45 | | REDUCE: (2), (4) imply: % 26.89/4.45 | | (5) $false % 26.89/4.45 | | % 26.89/4.45 | | CLOSE: (5) is inconsistent. % 26.89/4.45 | | % 26.89/4.45 | Case 2: % 26.89/4.45 | | % 26.89/4.45 | | (6) ~ (all_184_1 = 0) % 26.89/4.45 | | % 26.89/4.45 | | REDUCE: (3), (6) imply: % 26.89/4.45 | | (7) $false % 26.89/4.45 | | % 26.89/4.45 | | CLOSE: (7) is inconsistent. % 26.89/4.45 | | % 26.89/4.45 | End of split % 26.89/4.45 | % 26.89/4.45 End of proof % 26.89/4.45 % 26.89/4.45 Sub-proof #4 shows that the following formulas are inconsistent: % 26.89/4.45 ---------------------------------------------------------------- % 26.89/4.45 (1) ~ (all_237_0 = 0) | ~ (all_237_1 = 0) % 26.89/4.45 (2) all_237_0 = 0 % 26.89/4.45 (3) all_237_1 = 0 % 26.89/4.45 % 26.89/4.45 Begin of proof % 26.89/4.45 | % 26.89/4.45 | BETA: splitting (1) gives: % 26.89/4.45 | % 26.89/4.45 | Case 1: % 26.89/4.45 | | % 26.89/4.45 | | (4) ~ (all_237_0 = 0) % 26.89/4.45 | | % 26.89/4.45 | | REDUCE: (2), (4) imply: % 26.89/4.45 | | (5) $false % 26.89/4.45 | | % 26.89/4.45 | | CLOSE: (5) is inconsistent. % 26.89/4.45 | | % 26.89/4.45 | Case 2: % 26.89/4.45 | | % 26.89/4.45 | | (6) ~ (all_237_1 = 0) % 26.89/4.45 | | % 26.89/4.45 | | REDUCE: (3), (6) imply: % 26.89/4.45 | | (7) $false % 26.89/4.45 | | % 26.89/4.45 | | CLOSE: (7) is inconsistent. % 26.89/4.45 | | % 26.89/4.45 | End of split % 26.89/4.45 | % 26.89/4.45 End of proof % 26.89/4.45 % 26.89/4.45 Sub-proof #5 shows that the following formulas are inconsistent: % 26.89/4.45 ---------------------------------------------------------------- % 26.89/4.45 (1) ~ (all_192_0 = 0) | ~ (all_192_1 = 0) % 26.89/4.45 (2) all_192_0 = 0 % 26.89/4.45 (3) all_192_1 = 0 % 26.89/4.45 % 26.89/4.45 Begin of proof % 26.89/4.45 | % 26.89/4.45 | BETA: splitting (1) gives: % 26.89/4.45 | % 26.89/4.45 | Case 1: % 26.89/4.45 | | % 26.89/4.45 | | (4) ~ (all_192_0 = 0) % 26.89/4.45 | | % 26.89/4.45 | | REDUCE: (2), (4) imply: % 26.89/4.45 | | (5) $false % 26.89/4.45 | | % 26.89/4.45 | | CLOSE: (5) is inconsistent. % 26.89/4.45 | | % 26.89/4.45 | Case 2: % 26.89/4.45 | | % 26.89/4.45 | | (6) ~ (all_192_1 = 0) % 26.89/4.45 | | % 26.89/4.45 | | REDUCE: (3), (6) imply: % 26.89/4.45 | | (7) $false % 26.89/4.45 | | % 26.89/4.45 | | CLOSE: (7) is inconsistent. % 26.89/4.45 | | % 26.89/4.45 | End of split % 26.89/4.45 | % 26.89/4.45 End of proof % 26.89/4.45 % 26.89/4.45 Sub-proof #6 shows that the following formulas are inconsistent: % 26.89/4.45 ---------------------------------------------------------------- % 26.89/4.45 (1) ~ (all_197_0 = 0) | ~ (all_197_1 = 0) % 26.89/4.45 (2) all_197_0 = 0 % 26.89/4.45 (3) all_197_1 = 0 % 26.89/4.45 % 26.89/4.45 Begin of proof % 26.89/4.45 | % 26.89/4.45 | BETA: splitting (1) gives: % 26.89/4.45 | % 26.89/4.45 | Case 1: % 26.89/4.45 | | % 26.89/4.45 | | (4) ~ (all_197_0 = 0) % 26.89/4.45 | | % 26.89/4.45 | | REDUCE: (2), (4) imply: % 26.89/4.45 | | (5) $false % 26.89/4.45 | | % 26.89/4.45 | | CLOSE: (5) is inconsistent. % 26.89/4.45 | | % 26.89/4.45 | Case 2: % 26.89/4.45 | | % 26.89/4.45 | | (6) ~ (all_197_1 = 0) % 26.89/4.45 | | % 26.89/4.45 | | REDUCE: (3), (6) imply: % 26.89/4.45 | | (7) $false % 26.89/4.45 | | % 26.89/4.45 | | CLOSE: (7) is inconsistent. % 26.89/4.45 | | % 26.89/4.45 | End of split % 26.89/4.45 | % 26.89/4.45 End of proof % 26.89/4.45 % 26.89/4.45 Sub-proof #7 shows that the following formulas are inconsistent: % 26.89/4.45 ---------------------------------------------------------------- % 26.89/4.45 (1) ~ (all_133_0 = 0) | ~ (all_133_1 = 0) % 26.89/4.45 (2) all_133_0 = 0 % 26.89/4.45 (3) all_133_1 = 0 % 26.89/4.45 % 26.89/4.45 Begin of proof % 26.89/4.45 | % 26.89/4.45 | BETA: splitting (1) gives: % 26.89/4.45 | % 26.89/4.45 | Case 1: % 26.89/4.45 | | % 26.89/4.45 | | (4) ~ (all_133_0 = 0) % 26.89/4.45 | | % 26.89/4.45 | | REDUCE: (2), (4) imply: % 26.89/4.45 | | (5) $false % 26.89/4.45 | | % 26.89/4.45 | | CLOSE: (5) is inconsistent. % 26.89/4.45 | | % 26.89/4.45 | Case 2: % 26.89/4.45 | | % 26.89/4.45 | | (6) ~ (all_133_1 = 0) % 26.89/4.45 | | % 26.89/4.45 | | REDUCE: (3), (6) imply: % 26.89/4.45 | | (7) $false % 26.89/4.45 | | % 26.89/4.45 | | CLOSE: (7) is inconsistent. % 26.89/4.45 | | % 26.89/4.45 | End of split % 26.89/4.45 | % 26.89/4.45 End of proof % 26.89/4.45 % SZS output end Proof for theBenchmark % 26.89/4.45 % 26.89/4.45 3842ms %------------------------------------------------------------------------------