%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SET721+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 : n011.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 15:26:08 EDT 2023 % Result : Theorem 21.26s 3.67s % Output : Proof 21.85s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.13 % Problem : SET721+4 : TPTP v8.1.2. Bugfixed v2.2.1. % 0.07/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.35 % Computer : n011.cluster.edu % 0.13/0.35 % Model : x86_64 x86_64 % 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.35 % Memory : 8042.1875MB % 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.35 % CPULimit : 300 % 0.13/0.35 % WCLimit : 300 % 0.13/0.35 % DateTime : Sat Aug 26 10:01:24 EDT 2023 % 0.13/0.35 % CPUTime : % 0.20/0.62 ________ _____ % 0.20/0.62 ___ __ \_________(_)________________________________ % 0.20/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.20/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.20/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.20/0.62 % 0.20/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.20/0.62 (2023-06-19) % 0.20/0.62 % 0.20/0.62 (c) Philipp Rümmer, 2009-2023 % 0.20/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.20/0.62 Amanda Stjerna. % 0.20/0.62 Free software under BSD-3-Clause. % 0.20/0.62 % 0.20/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.20/0.62 % 0.20/0.62 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.20/0.63 Running up to 7 provers in parallel. % 0.20/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.20/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.20/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.20/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.20/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.20/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.20/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 3.84/1.28 Prover 1: Preprocessing ... % 3.84/1.28 Prover 4: Preprocessing ... % 3.84/1.31 Prover 6: Preprocessing ... % 3.84/1.31 Prover 5: Preprocessing ... % 3.84/1.31 Prover 0: Preprocessing ... % 3.84/1.31 Prover 3: Preprocessing ... % 3.84/1.31 Prover 2: Preprocessing ... % 8.51/2.05 Prover 5: Proving ... % 9.86/2.10 Prover 2: Proving ... % 10.16/2.14 Prover 6: Proving ... % 10.16/2.16 Prover 3: Constructing countermodel ... % 10.16/2.19 Prover 1: Constructing countermodel ... % 12.45/2.42 Prover 3: gave up % 12.45/2.42 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 12.45/2.45 Prover 4: Constructing countermodel ... % 12.45/2.52 Prover 7: Preprocessing ... % 12.45/2.54 Prover 0: Proving ... % 13.34/2.64 Prover 1: gave up % 13.34/2.64 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 13.34/2.66 Prover 7: Warning: ignoring some quantifiers % 14.20/2.69 Prover 7: Constructing countermodel ... % 14.20/2.69 Prover 8: Preprocessing ... % 15.39/2.89 Prover 8: Warning: ignoring some quantifiers % 15.39/2.90 Prover 8: Constructing countermodel ... % 17.54/3.14 Prover 8: gave up % 17.54/3.15 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889 % 17.86/3.23 Prover 9: Preprocessing ... % 20.57/3.56 Prover 4: Found proof (size 109) % 20.57/3.56 Prover 4: proved (2916ms) % 20.57/3.56 Prover 7: stopped % 20.57/3.56 Prover 2: stopped % 20.57/3.56 Prover 6: stopped % 20.57/3.56 Prover 5: stopped % 20.57/3.56 Prover 0: stopped % 20.98/3.66 Prover 9: Constructing countermodel ... % 21.26/3.67 Prover 9: stopped % 21.26/3.67 % 21.26/3.67 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 21.26/3.67 % 21.26/3.68 % SZS output start Proof for theBenchmark % 21.26/3.69 Assumptions after simplification: % 21.26/3.69 --------------------------------- % 21.26/3.69 % 21.26/3.69 (compose_function) % 21.26/3.73 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 21.26/3.73 $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: int] : ! [v9: $i] : (v8 = 0 | ~ % 21.26/3.73 (compose_function(v0, v1, v2, v3, v4) = v7) | ~ (apply(v7, v5, v6) = v8) | % 21.26/3.73 ~ (apply(v1, v5, v9) = 0) | ~ $i(v9) | ~ $i(v6) | ~ $i(v5) | ~ $i(v4) | % 21.26/3.73 ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v10: any] : ? [v11: any] % 21.26/3.73 : ((apply(v0, v9, v6) = v11 & member(v9, v3) = v10 & ( ~ (v11 = 0) | ~ (v10 % 21.26/3.73 = 0))) | (member(v6, v4) = v11 & member(v5, v2) = v10 & ( ~ (v11 = % 21.26/3.73 0) | ~ (v10 = 0))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 21.26/3.73 [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: % 21.26/3.73 int] : ! [v9: $i] : (v8 = 0 | ~ (compose_function(v0, v1, v2, v3, v4) = % 21.26/3.73 v7) | ~ (apply(v7, v5, v6) = v8) | ~ (apply(v0, v9, v6) = 0) | ~ $i(v9) % 21.26/3.73 | ~ $i(v6) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 21.26/3.73 $i(v0) | ? [v10: any] : ? [v11: any] : ((apply(v1, v5, v9) = v11 & % 21.26/3.73 member(v9, v3) = v10 & ( ~ (v11 = 0) | ~ (v10 = 0))) | (member(v6, v4) % 21.26/3.73 = v11 & member(v5, v2) = v10 & ( ~ (v11 = 0) | ~ (v10 = 0))))) & ! % 21.26/3.73 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] % 21.26/3.73 : ! [v6: $i] : ! [v7: $i] : ! [v8: int] : ! [v9: $i] : (v8 = 0 | ~ % 21.26/3.73 (compose_function(v0, v1, v2, v3, v4) = v7) | ~ (apply(v7, v5, v6) = v8) | % 21.26/3.73 ~ (member(v9, v3) = 0) | ~ $i(v9) | ~ $i(v6) | ~ $i(v5) | ~ $i(v4) | ~ % 21.26/3.73 $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v10: any] : ? [v11: any] : % 21.26/3.73 ((apply(v1, v5, v9) = v10 & apply(v0, v9, v6) = v11 & ( ~ (v11 = 0) | ~ % 21.26/3.73 (v10 = 0))) | (member(v6, v4) = v11 & member(v5, v2) = v10 & ( ~ (v11 % 21.26/3.73 = 0) | ~ (v10 = 0))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 21.26/3.73 ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ( ~ % 21.26/3.73 (compose_function(v0, v1, v2, v3, v4) = v7) | ~ (apply(v7, v5, v6) = 0) | % 21.26/3.73 ~ $i(v6) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 21.26/3.73 $i(v0) | ? [v8: any] : ? [v9: any] : ? [v10: $i] : ? [v11: int] : ? % 21.26/3.73 [v12: int] : ? [v13: int] : ($i(v10) & ((v13 = 0 & v12 = 0 & v11 = 0 & % 21.26/3.73 apply(v1, v5, v10) = 0 & apply(v0, v10, v6) = 0 & member(v10, v3) = 0) % 21.26/3.73 | (member(v6, v4) = v9 & member(v5, v2) = v8 & ( ~ (v9 = 0) | ~ (v8 = % 21.26/3.73 0)))))) % 21.26/3.73 % 21.26/3.73 (injective) % 21.26/3.74 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 21.26/3.74 $i] : (v4 = v3 | ~ (injective(v0, v1, v2) = 0) | ~ (apply(v0, v4, v5) = 0) % 21.26/3.74 | ~ (apply(v0, v3, v5) = 0) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) % 21.26/3.74 | ~ $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: any] : ? [v8: any] : % 21.26/3.74 (member(v5, v2) = v8 & member(v4, v1) = v7 & member(v3, v1) = v6 & ( ~ (v8 = % 21.26/3.74 0) | ~ (v7 = 0) | ~ (v6 = 0)))) & ! [v0: $i] : ! [v1: $i] : ! % 21.26/3.74 [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v4 = v3 | ~ % 21.26/3.74 (injective(v0, v1, v2) = 0) | ~ (apply(v0, v4, v5) = 0) | ~ (member(v3, % 21.26/3.74 v1) = 0) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | % 21.26/3.74 ~ $i(v0) | ? [v6: any] : ? [v7: any] : ? [v8: any] : (apply(v0, v3, v5) = % 21.26/3.74 v8 & member(v5, v2) = v7 & member(v4, v1) = v6 & ( ~ (v8 = 0) | ~ (v7 = % 21.26/3.74 0) | ~ (v6 = 0)))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 21.26/3.74 [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v4 = v3 | ~ (injective(v0, v1, v2) = % 21.26/3.74 0) | ~ (apply(v0, v3, v5) = 0) | ~ (member(v4, v1) = 0) | ~ $i(v5) | ~ % 21.26/3.74 $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any] : ? % 21.26/3.74 [v7: any] : ? [v8: any] : (apply(v0, v4, v5) = v8 & member(v5, v2) = v7 & % 21.26/3.74 member(v3, v1) = v6 & ( ~ (v8 = 0) | ~ (v7 = 0) | ~ (v6 = 0)))) & ! % 21.26/3.74 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] % 21.26/3.74 : (v4 = v3 | ~ (injective(v0, v1, v2) = 0) | ~ (member(v5, v2) = 0) | ~ % 21.26/3.74 (member(v4, v1) = 0) | ~ (member(v3, v1) = 0) | ~ $i(v5) | ~ $i(v4) | ~ % 21.26/3.74 $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: any] : % 21.26/3.74 (apply(v0, v4, v5) = v7 & apply(v0, v3, v5) = v6 & ( ~ (v7 = 0) | ~ (v6 = % 21.26/3.74 0)))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = % 21.26/3.74 0 | ~ (injective(v0, v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 21.26/3.74 [v4: $i] : ? [v5: $i] : ? [v6: $i] : ( ~ (v5 = v4) & apply(v0, v5, v6) = 0 % 21.26/3.74 & apply(v0, v4, v6) = 0 & member(v6, v2) = 0 & member(v5, v1) = 0 & % 21.26/3.74 member(v4, v1) = 0 & $i(v6) & $i(v5) & $i(v4))) % 21.26/3.74 % 21.26/3.74 (maps) % 21.26/3.74 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 21.26/3.74 $i] : (v5 = v4 | ~ (maps(v0, v1, v2) = 0) | ~ (apply(v0, v3, v5) = 0) | ~ % 21.26/3.74 (apply(v0, v3, v4) = 0) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ % 21.26/3.74 $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: any] : ? [v8: any] : % 21.26/3.74 (member(v5, v2) = v8 & member(v4, v2) = v7 & member(v3, v1) = v6 & ( ~ (v8 = % 21.26/3.74 0) | ~ (v7 = 0) | ~ (v6 = 0)))) & ! [v0: $i] : ! [v1: $i] : ! % 21.26/3.75 [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v5 = v4 | ~ (maps(v0, % 21.26/3.75 v1, v2) = 0) | ~ (apply(v0, v3, v5) = 0) | ~ (member(v4, v2) = 0) | ~ % 21.26/3.75 $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: % 21.26/3.75 any] : ? [v7: any] : ? [v8: any] : (apply(v0, v3, v4) = v8 & member(v5, % 21.26/3.75 v2) = v7 & member(v3, v1) = v6 & ( ~ (v8 = 0) | ~ (v7 = 0) | ~ (v6 = % 21.26/3.75 0)))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! % 21.26/3.75 [v4: $i] : ! [v5: $i] : (v5 = v4 | ~ (maps(v0, v1, v2) = 0) | ~ (apply(v0, % 21.26/3.75 v3, v4) = 0) | ~ (member(v5, v2) = 0) | ~ $i(v5) | ~ $i(v4) | ~ % 21.26/3.75 $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: any] : % 21.26/3.75 ? [v8: any] : (apply(v0, v3, v5) = v8 & member(v4, v2) = v7 & member(v3, v1) % 21.26/3.75 = v6 & ( ~ (v8 = 0) | ~ (v7 = 0) | ~ (v6 = 0)))) & ! [v0: $i] : ! [v1: % 21.26/3.75 $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v5 = v4 | ~ % 21.26/3.75 (maps(v0, v1, v2) = 0) | ~ (member(v5, v2) = 0) | ~ (member(v4, v2) = 0) | % 21.26/3.75 ~ (member(v3, v1) = 0) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ % 21.26/3.75 $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: any] : (apply(v0, v3, v5) = v7 & % 21.26/3.75 apply(v0, v3, v4) = v6 & ( ~ (v7 = 0) | ~ (v6 = 0)))) & ! [v0: $i] : ! % 21.26/3.75 [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (maps(v0, v1, v2) = v3) | % 21.26/3.75 ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: $i] : ? [v5: $i] : ? [v6: $i] % 21.26/3.75 : ? [v7: int] : ? [v8: int] : ? [v9: int] : ? [v10: int] : ? [v11: int] % 21.26/3.75 : ? [v12: $i] : ? [v13: int] : ($i(v12) & $i(v6) & $i(v5) & $i(v4) & ((v13 % 21.26/3.75 = 0 & member(v12, v1) = 0 & ! [v14: $i] : ( ~ (apply(v0, v12, v14) = % 21.26/3.75 0) | ~ $i(v14) | ? [v15: int] : ( ~ (v15 = 0) & member(v14, v2) % 21.26/3.75 = v15)) & ! [v14: $i] : ( ~ (member(v14, v2) = 0) | ~ $i(v14) | % 21.26/3.75 ? [v15: int] : ( ~ (v15 = 0) & apply(v0, v12, v14) = v15))) | (v11 = % 21.26/3.75 0 & v10 = 0 & v9 = 0 & v8 = 0 & v7 = 0 & ~ (v6 = v5) & apply(v0, v4, % 21.26/3.75 v6) = 0 & apply(v0, v4, v5) = 0 & member(v6, v2) = 0 & member(v5, % 21.26/3.75 v2) = 0 & member(v4, v1) = 0)))) & ! [v0: $i] : ! [v1: $i] : ! % 21.26/3.75 [v2: $i] : ! [v3: $i] : ( ~ (maps(v0, v1, v2) = 0) | ~ (member(v3, v1) = 0) % 21.26/3.75 | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: $i] : (apply(v0, % 21.26/3.75 v3, v4) = 0 & member(v4, v2) = 0 & $i(v4))) % 21.26/3.75 % 21.26/3.75 (one_to_one) % 21.26/3.75 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 21.26/3.75 (one_to_one(v0, v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: % 21.26/3.75 any] : ? [v5: any] : (surjective(v0, v1, v2) = v5 & injective(v0, v1, v2) % 21.26/3.75 = v4 & ( ~ (v5 = 0) | ~ (v4 = 0)))) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 21.26/3.75 $i] : ! [v3: any] : ( ~ (surjective(v0, v1, v2) = v3) | ~ $i(v2) | ~ % 21.26/3.75 $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] : (one_to_one(v0, v1, v2) = % 21.26/3.75 v4 & injective(v0, v1, v2) = v5 & ( ~ (v4 = 0) | (v5 = 0 & v3 = 0)))) & ! % 21.26/3.75 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ( ~ (injective(v0, v1, % 21.26/3.75 v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: % 21.26/3.75 any] : (one_to_one(v0, v1, v2) = v4 & surjective(v0, v1, v2) = v5 & ( ~ % 21.26/3.75 (v4 = 0) | (v5 = 0 & v3 = 0)))) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 21.26/3.75 $i] : ( ~ (one_to_one(v0, v1, v2) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 21.26/3.75 (surjective(v0, v1, v2) = 0 & injective(v0, v1, v2) = 0)) & ! [v0: $i] : ! % 21.26/3.75 [v1: $i] : ! [v2: $i] : ( ~ (surjective(v0, v1, v2) = 0) | ~ $i(v2) | ~ % 21.26/3.75 $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : (one_to_one(v0, v1, v2) = % 21.26/3.75 v4 & injective(v0, v1, v2) = v3 & ( ~ (v3 = 0) | v4 = 0))) & ! [v0: $i] : % 21.26/3.75 ! [v1: $i] : ! [v2: $i] : ( ~ (injective(v0, v1, v2) = 0) | ~ $i(v2) | ~ % 21.26/3.75 $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : (one_to_one(v0, v1, v2) = % 21.26/3.75 v4 & surjective(v0, v1, v2) = v3 & ( ~ (v3 = 0) | v4 = 0))) % 21.26/3.75 % 21.26/3.75 (thII12) % 21.26/3.75 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: % 21.26/3.75 $i] : ? [v6: int] : ( ~ (v6 = 0) & injective(v5, v2, v4) = 0 & % 21.26/3.75 injective(v0, v2, v3) = v6 & compose_function(v1, v0, v2, v3, v4) = v5 & % 21.26/3.75 maps(v1, v3, v4) = 0 & maps(v0, v2, v3) = 0 & $i(v5) & $i(v4) & $i(v3) & % 21.26/3.75 $i(v2) & $i(v1) & $i(v0)) % 21.26/3.75 % 21.26/3.75 (function-axioms) % 21.26/3.76 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 21.26/3.76 [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : (v1 = v0 | % 21.26/3.76 ~ (compose_predicate(v7, v6, v5, v4, v3, v2) = v1) | ~ % 21.26/3.76 (compose_predicate(v7, v6, v5, v4, v3, v2) = v0)) & ! [v0: % 21.26/3.76 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 21.26/3.76 : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v1 = v0 | ~ (isomorphism(v6, v5, % 21.26/3.76 v4, v3, v2) = v1) | ~ (isomorphism(v6, v5, v4, v3, v2) = v0)) & ! [v0: % 21.26/3.76 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 21.26/3.76 : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v1 = v0 | ~ (decreasing(v6, v5, % 21.26/3.76 v4, v3, v2) = v1) | ~ (decreasing(v6, v5, v4, v3, v2) = v0)) & ! [v0: % 21.26/3.76 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 21.26/3.76 : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v1 = v0 | ~ (increasing(v6, v5, % 21.26/3.76 v4, v3, v2) = v1) | ~ (increasing(v6, v5, v4, v3, v2) = v0)) & ! [v0: % 21.26/3.76 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : % 21.26/3.76 ! [v6: $i] : (v1 = v0 | ~ (compose_function(v6, v5, v4, v3, v2) = v1) | ~ % 21.26/3.76 (compose_function(v6, v5, v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : % 21.26/3.76 ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 21.26/3.76 $i] : (v1 = v0 | ~ (inverse_predicate(v5, v4, v3, v2) = v1) | ~ % 21.26/3.76 (inverse_predicate(v5, v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! % 21.26/3.76 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 21.26/3.76 $i] : (v1 = v0 | ~ (equal_maps(v5, v4, v3, v2) = v1) | ~ (equal_maps(v5, % 21.26/3.76 v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 21.26/3.76 $i] : ! [v4: $i] : (v1 = v0 | ~ (inverse_image3(v4, v3, v2) = v1) | ~ % 21.26/3.76 (inverse_image3(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 21.26/3.76 : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (image3(v4, v3, v2) = v1) | ~ % 21.26/3.76 (image3(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 21.26/3.76 [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (inverse_function(v4, v3, v2) = v1) | % 21.26/3.76 ~ (inverse_function(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! % 21.26/3.76 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | % 21.26/3.76 ~ (one_to_one(v4, v3, v2) = v1) | ~ (one_to_one(v4, v3, v2) = v0)) & ! % 21.26/3.76 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 21.26/3.76 $i] : ! [v4: $i] : (v1 = v0 | ~ (surjective(v4, v3, v2) = v1) | ~ % 21.26/3.76 (surjective(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 21.26/3.76 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ % 21.26/3.76 (injective(v4, v3, v2) = v1) | ~ (injective(v4, v3, v2) = v0)) & ! [v0: % 21.26/3.76 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 21.26/3.76 : ! [v4: $i] : (v1 = v0 | ~ (maps(v4, v3, v2) = v1) | ~ (maps(v4, v3, v2) = % 21.69/3.76 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 21.69/3.76 $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (apply(v4, v3, v2) = v1) | % 21.69/3.76 ~ (apply(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 21.69/3.76 [v3: $i] : (v1 = v0 | ~ (inverse_image2(v3, v2) = v1) | ~ % 21.69/3.76 (inverse_image2(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 21.69/3.76 ! [v3: $i] : (v1 = v0 | ~ (image2(v3, v2) = v1) | ~ (image2(v3, v2) = v0)) & % 21.69/3.76 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 21.69/3.76 [v3: $i] : (v1 = v0 | ~ (identity(v3, v2) = v1) | ~ (identity(v3, v2) = v0)) % 21.69/3.76 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 21.69/3.76 (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) & ! [v0: % 21.69/3.76 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 21.69/3.76 (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0)) & ! [v0: $i] : ! % 21.69/3.76 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (union(v3, v2) = v1) | ~ % 21.69/3.76 (union(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 21.69/3.76 $i] : (v1 = v0 | ~ (intersection(v3, v2) = v1) | ~ (intersection(v3, v2) = % 21.69/3.76 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 21.69/3.76 $i] : ! [v3: $i] : (v1 = v0 | ~ (equal_set(v3, v2) = v1) | ~ % 21.69/3.76 (equal_set(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 21.69/3.76 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (subset(v3, % 21.69/3.76 v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! % 21.69/3.76 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 21.69/3.76 (member(v3, v2) = v1) | ~ (member(v3, v2) = v0)) & ! [v0: $i] : ! [v1: % 21.69/3.76 $i] : ! [v2: $i] : (v1 = v0 | ~ (product(v2) = v1) | ~ (product(v2) = % 21.69/3.76 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (sum(v2) = % 21.69/3.76 v1) | ~ (sum(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = % 21.69/3.76 v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ! [v0: $i] : ! % 21.69/3.76 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (power_set(v2) = v1) | ~ % 21.69/3.76 (power_set(v2) = v0)) % 21.69/3.76 % 21.69/3.76 Further assumptions not needed in the proof: % 21.69/3.76 -------------------------------------------- % 21.69/3.76 compose_predicate, decreasing_function, difference, empty_set, equal_maps, % 21.69/3.76 equal_set, identity, image2, image3, increasing_function, intersection, % 21.69/3.76 inverse_function, inverse_image2, inverse_image3, inverse_predicate, % 21.69/3.76 isomorphism, power_set, product, singleton, subset, sum, surjective, union, % 21.69/3.76 unordered_pair % 21.69/3.76 % 21.69/3.76 Those formulas are unsatisfiable: % 21.69/3.76 --------------------------------- % 21.69/3.76 % 21.69/3.76 Begin of proof % 21.69/3.76 | % 21.69/3.76 | ALPHA: (maps) implies: % 21.69/3.76 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (maps(v0, % 21.69/3.76 | v1, v2) = 0) | ~ (member(v3, v1) = 0) | ~ $i(v3) | ~ $i(v2) | % 21.69/3.76 | ~ $i(v1) | ~ $i(v0) | ? [v4: $i] : (apply(v0, v3, v4) = 0 & % 21.69/3.76 | member(v4, v2) = 0 & $i(v4))) % 21.69/3.76 | % 21.69/3.76 | ALPHA: (compose_function) implies: % 21.69/3.77 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 21.69/3.77 | ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: int] : ! [v9: $i] : % 21.69/3.77 | (v8 = 0 | ~ (compose_function(v0, v1, v2, v3, v4) = v7) | ~ % 21.69/3.77 | (apply(v7, v5, v6) = v8) | ~ (member(v9, v3) = 0) | ~ $i(v9) | ~ % 21.69/3.77 | $i(v6) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | % 21.69/3.77 | ~ $i(v0) | ? [v10: any] : ? [v11: any] : ((apply(v1, v5, v9) = v10 % 21.69/3.77 | & apply(v0, v9, v6) = v11 & ( ~ (v11 = 0) | ~ (v10 = 0))) | % 21.69/3.77 | (member(v6, v4) = v11 & member(v5, v2) = v10 & ( ~ (v11 = 0) | ~ % 21.69/3.77 | (v10 = 0))))) % 21.69/3.77 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 21.69/3.77 | ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: int] : ! [v9: $i] : % 21.69/3.77 | (v8 = 0 | ~ (compose_function(v0, v1, v2, v3, v4) = v7) | ~ % 21.69/3.77 | (apply(v7, v5, v6) = v8) | ~ (apply(v0, v9, v6) = 0) | ~ $i(v9) | % 21.69/3.77 | ~ $i(v6) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) % 21.69/3.77 | | ~ $i(v0) | ? [v10: any] : ? [v11: any] : ((apply(v1, v5, v9) = % 21.69/3.77 | v11 & member(v9, v3) = v10 & ( ~ (v11 = 0) | ~ (v10 = 0))) | % 21.69/3.77 | (member(v6, v4) = v11 & member(v5, v2) = v10 & ( ~ (v11 = 0) | ~ % 21.69/3.77 | (v10 = 0))))) % 21.69/3.77 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 21.69/3.77 | ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: int] : ! [v9: $i] : % 21.69/3.77 | (v8 = 0 | ~ (compose_function(v0, v1, v2, v3, v4) = v7) | ~ % 21.69/3.77 | (apply(v7, v5, v6) = v8) | ~ (apply(v1, v5, v9) = 0) | ~ $i(v9) | % 21.69/3.77 | ~ $i(v6) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) % 21.69/3.77 | | ~ $i(v0) | ? [v10: any] : ? [v11: any] : ((apply(v0, v9, v6) = % 21.69/3.77 | v11 & member(v9, v3) = v10 & ( ~ (v11 = 0) | ~ (v10 = 0))) | % 21.69/3.77 | (member(v6, v4) = v11 & member(v5, v2) = v10 & ( ~ (v11 = 0) | ~ % 21.69/3.77 | (v10 = 0))))) % 21.69/3.77 | % 21.69/3.77 | ALPHA: (injective) implies: % 21.69/3.77 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 21.69/3.77 | (injective(v0, v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 21.69/3.77 | [v4: $i] : ? [v5: $i] : ? [v6: $i] : ( ~ (v5 = v4) & apply(v0, v5, % 21.69/3.77 | v6) = 0 & apply(v0, v4, v6) = 0 & member(v6, v2) = 0 & member(v5, % 21.69/3.77 | v1) = 0 & member(v4, v1) = 0 & $i(v6) & $i(v5) & $i(v4))) % 21.69/3.77 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 21.69/3.77 | ! [v5: $i] : (v4 = v3 | ~ (injective(v0, v1, v2) = 0) | ~ (member(v5, % 21.69/3.77 | v2) = 0) | ~ (member(v4, v1) = 0) | ~ (member(v3, v1) = 0) | ~ % 21.69/3.77 | $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 21.69/3.77 | ? [v6: any] : ? [v7: any] : (apply(v0, v4, v5) = v7 & apply(v0, v3, % 21.69/3.77 | v5) = v6 & ( ~ (v7 = 0) | ~ (v6 = 0)))) % 21.69/3.77 | % 21.69/3.77 | ALPHA: (one_to_one) implies: % 21.69/3.77 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (injective(v0, v1, v2) = % 21.69/3.77 | 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: % 21.69/3.77 | any] : (one_to_one(v0, v1, v2) = v4 & surjective(v0, v1, v2) = v3 & % 21.69/3.77 | ( ~ (v3 = 0) | v4 = 0))) % 21.69/3.77 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ( ~ % 21.69/3.77 | (injective(v0, v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 21.69/3.77 | [v4: any] : ? [v5: any] : (one_to_one(v0, v1, v2) = v4 & % 21.69/3.77 | surjective(v0, v1, v2) = v5 & ( ~ (v4 = 0) | (v5 = 0 & v3 = 0)))) % 21.69/3.77 | (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ( ~ % 21.69/3.77 | (surjective(v0, v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 21.69/3.77 | ? [v4: any] : ? [v5: any] : (one_to_one(v0, v1, v2) = v4 & % 21.69/3.77 | injective(v0, v1, v2) = v5 & ( ~ (v4 = 0) | (v5 = 0 & v3 = 0)))) % 21.69/3.77 | % 21.69/3.77 | ALPHA: (function-axioms) implies: % 21.69/3.78 | (10) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 21.69/3.78 | : ! [v3: $i] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, % 21.69/3.78 | v2) = v0)) % 21.69/3.78 | (11) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 21.69/3.78 | : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (apply(v4, v3, v2) = v1) | % 21.69/3.78 | ~ (apply(v4, v3, v2) = v0)) % 21.69/3.78 | (12) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 21.69/3.78 | : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (injective(v4, v3, v2) = % 21.69/3.78 | v1) | ~ (injective(v4, v3, v2) = v0)) % 21.69/3.78 | (13) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 21.69/3.78 | : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (surjective(v4, v3, v2) = % 21.69/3.78 | v1) | ~ (surjective(v4, v3, v2) = v0)) % 21.69/3.78 | % 21.69/3.78 | DELTA: instantiating (thII12) with fresh symbols all_32_0, all_32_1, all_32_2, % 21.69/3.78 | all_32_3, all_32_4, all_32_5, all_32_6 gives: % 21.69/3.78 | (14) ~ (all_32_0 = 0) & injective(all_32_1, all_32_4, all_32_2) = 0 & % 21.69/3.78 | injective(all_32_6, all_32_4, all_32_3) = all_32_0 & % 21.69/3.78 | compose_function(all_32_5, all_32_6, all_32_4, all_32_3, all_32_2) = % 21.69/3.78 | all_32_1 & maps(all_32_5, all_32_3, all_32_2) = 0 & maps(all_32_6, % 21.69/3.78 | all_32_4, all_32_3) = 0 & $i(all_32_1) & $i(all_32_2) & $i(all_32_3) % 21.69/3.78 | & $i(all_32_4) & $i(all_32_5) & $i(all_32_6) % 21.69/3.78 | % 21.69/3.78 | ALPHA: (14) implies: % 21.69/3.78 | (15) ~ (all_32_0 = 0) % 21.69/3.78 | (16) $i(all_32_6) % 21.69/3.78 | (17) $i(all_32_5) % 21.69/3.78 | (18) $i(all_32_4) % 21.69/3.78 | (19) $i(all_32_3) % 21.69/3.78 | (20) $i(all_32_2) % 21.69/3.78 | (21) $i(all_32_1) % 21.69/3.78 | (22) maps(all_32_5, all_32_3, all_32_2) = 0 % 21.69/3.78 | (23) compose_function(all_32_5, all_32_6, all_32_4, all_32_3, all_32_2) = % 21.69/3.78 | all_32_1 % 21.69/3.78 | (24) injective(all_32_6, all_32_4, all_32_3) = all_32_0 % 21.69/3.78 | (25) injective(all_32_1, all_32_4, all_32_2) = 0 % 21.69/3.78 | % 21.69/3.78 | GROUND_INST: instantiating (5) with all_32_6, all_32_4, all_32_3, all_32_0, % 21.69/3.78 | simplifying with (16), (18), (19), (24) gives: % 21.69/3.78 | (26) all_32_0 = 0 | ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ( ~ (v1 = v0) % 21.69/3.78 | & apply(all_32_6, v1, v2) = 0 & apply(all_32_6, v0, v2) = 0 & % 21.69/3.78 | member(v2, all_32_3) = 0 & member(v1, all_32_4) = 0 & member(v0, % 21.69/3.78 | all_32_4) = 0 & $i(v2) & $i(v1) & $i(v0)) % 21.69/3.78 | % 21.69/3.78 | GROUND_INST: instantiating (7) with all_32_1, all_32_4, all_32_2, simplifying % 21.69/3.78 | with (18), (20), (21), (25) gives: % 21.69/3.78 | (27) ? [v0: any] : ? [v1: any] : (one_to_one(all_32_1, all_32_4, % 21.69/3.78 | all_32_2) = v1 & surjective(all_32_1, all_32_4, all_32_2) = v0 & ( % 21.69/3.78 | ~ (v0 = 0) | v1 = 0)) % 21.69/3.78 | % 21.69/3.78 | GROUND_INST: instantiating (8) with all_32_1, all_32_4, all_32_2, 0, % 21.69/3.78 | simplifying with (18), (20), (21), (25) gives: % 21.69/3.78 | (28) ? [v0: any] : ? [v1: any] : (one_to_one(all_32_1, all_32_4, % 21.69/3.78 | all_32_2) = v0 & surjective(all_32_1, all_32_4, all_32_2) = v1 & ( % 21.69/3.78 | ~ (v0 = 0) | v1 = 0)) % 21.69/3.78 | % 21.69/3.78 | DELTA: instantiating (28) with fresh symbols all_39_0, all_39_1 gives: % 21.69/3.79 | (29) one_to_one(all_32_1, all_32_4, all_32_2) = all_39_1 & % 21.69/3.79 | surjective(all_32_1, all_32_4, all_32_2) = all_39_0 & ( ~ (all_39_1 = % 21.69/3.79 | 0) | all_39_0 = 0) % 21.69/3.79 | % 21.69/3.79 | ALPHA: (29) implies: % 21.69/3.79 | (30) surjective(all_32_1, all_32_4, all_32_2) = all_39_0 % 21.69/3.79 | % 21.69/3.79 | DELTA: instantiating (27) with fresh symbols all_41_0, all_41_1 gives: % 21.69/3.79 | (31) one_to_one(all_32_1, all_32_4, all_32_2) = all_41_0 & % 21.69/3.79 | surjective(all_32_1, all_32_4, all_32_2) = all_41_1 & ( ~ (all_41_1 = % 21.69/3.79 | 0) | all_41_0 = 0) % 21.69/3.79 | % 21.69/3.79 | ALPHA: (31) implies: % 21.69/3.79 | (32) surjective(all_32_1, all_32_4, all_32_2) = all_41_1 % 21.69/3.79 | % 21.69/3.79 | BETA: splitting (26) gives: % 21.69/3.79 | % 21.69/3.79 | Case 1: % 21.69/3.79 | | % 21.69/3.79 | | (33) all_32_0 = 0 % 21.69/3.79 | | % 21.69/3.79 | | REDUCE: (15), (33) imply: % 21.69/3.79 | | (34) $false % 21.69/3.79 | | % 21.69/3.79 | | CLOSE: (34) is inconsistent. % 21.69/3.79 | | % 21.69/3.79 | Case 2: % 21.69/3.79 | | % 21.69/3.79 | | (35) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ( ~ (v1 = v0) & % 21.69/3.79 | | apply(all_32_6, v1, v2) = 0 & apply(all_32_6, v0, v2) = 0 & % 21.69/3.79 | | member(v2, all_32_3) = 0 & member(v1, all_32_4) = 0 & member(v0, % 21.69/3.79 | | all_32_4) = 0 & $i(v2) & $i(v1) & $i(v0)) % 21.69/3.79 | | % 21.69/3.79 | | DELTA: instantiating (35) with fresh symbols all_53_0, all_53_1, all_53_2 % 21.69/3.79 | | gives: % 21.69/3.79 | | (36) ~ (all_53_1 = all_53_2) & apply(all_32_6, all_53_1, all_53_0) = 0 & % 21.69/3.79 | | apply(all_32_6, all_53_2, all_53_0) = 0 & member(all_53_0, all_32_3) % 21.69/3.79 | | = 0 & member(all_53_1, all_32_4) = 0 & member(all_53_2, all_32_4) = % 21.69/3.79 | | 0 & $i(all_53_0) & $i(all_53_1) & $i(all_53_2) % 21.69/3.79 | | % 21.69/3.79 | | ALPHA: (36) implies: % 21.85/3.79 | | (37) ~ (all_53_1 = all_53_2) % 21.85/3.79 | | (38) $i(all_53_2) % 21.85/3.79 | | (39) $i(all_53_1) % 21.85/3.79 | | (40) $i(all_53_0) % 21.85/3.79 | | (41) member(all_53_2, all_32_4) = 0 % 21.85/3.79 | | (42) member(all_53_1, all_32_4) = 0 % 21.85/3.79 | | (43) member(all_53_0, all_32_3) = 0 % 21.85/3.79 | | (44) apply(all_32_6, all_53_2, all_53_0) = 0 % 21.85/3.79 | | (45) apply(all_32_6, all_53_1, all_53_0) = 0 % 21.85/3.79 | | % 21.85/3.79 | | GROUND_INST: instantiating (13) with all_39_0, all_41_1, all_32_2, all_32_4, % 21.85/3.79 | | all_32_1, simplifying with (30), (32) gives: % 21.85/3.79 | | (46) all_41_1 = all_39_0 % 21.85/3.79 | | % 21.85/3.79 | | GROUND_INST: instantiating (1) with all_32_5, all_32_3, all_32_2, all_53_0, % 21.85/3.79 | | simplifying with (17), (19), (20), (22), (40), (43) gives: % 21.85/3.79 | | (47) ? [v0: $i] : (apply(all_32_5, all_53_0, v0) = 0 & member(v0, % 21.85/3.79 | | all_32_2) = 0 & $i(v0)) % 21.85/3.79 | | % 21.85/3.79 | | GROUND_INST: instantiating (9) with all_32_1, all_32_4, all_32_2, all_39_0, % 21.85/3.79 | | simplifying with (18), (20), (21), (30) gives: % 21.85/3.79 | | (48) ? [v0: any] : ? [v1: any] : (one_to_one(all_32_1, all_32_4, % 21.85/3.79 | | all_32_2) = v0 & injective(all_32_1, all_32_4, all_32_2) = v1 & % 21.85/3.79 | | ( ~ (v0 = 0) | (v1 = 0 & all_39_0 = 0))) % 21.85/3.79 | | % 21.85/3.79 | | DELTA: instantiating (47) with fresh symbol all_64_0 gives: % 21.85/3.79 | | (49) apply(all_32_5, all_53_0, all_64_0) = 0 & member(all_64_0, all_32_2) % 21.85/3.79 | | = 0 & $i(all_64_0) % 21.85/3.79 | | % 21.85/3.79 | | ALPHA: (49) implies: % 21.85/3.79 | | (50) $i(all_64_0) % 21.85/3.79 | | (51) member(all_64_0, all_32_2) = 0 % 21.85/3.79 | | (52) apply(all_32_5, all_53_0, all_64_0) = 0 % 21.85/3.79 | | % 21.85/3.79 | | DELTA: instantiating (48) with fresh symbols all_70_0, all_70_1 gives: % 21.85/3.79 | | (53) one_to_one(all_32_1, all_32_4, all_32_2) = all_70_1 & % 21.85/3.79 | | injective(all_32_1, all_32_4, all_32_2) = all_70_0 & ( ~ (all_70_1 = % 21.85/3.79 | | 0) | (all_70_0 = 0 & all_39_0 = 0)) % 21.85/3.79 | | % 21.85/3.79 | | ALPHA: (53) implies: % 21.85/3.79 | | (54) injective(all_32_1, all_32_4, all_32_2) = all_70_0 % 21.85/3.79 | | % 21.85/3.79 | | GROUND_INST: instantiating (12) with 0, all_70_0, all_32_2, all_32_4, % 21.85/3.79 | | all_32_1, simplifying with (25), (54) gives: % 21.85/3.79 | | (55) all_70_0 = 0 % 21.85/3.79 | | % 21.85/3.80 | | GROUND_INST: instantiating (6) with all_32_1, all_32_4, all_32_2, all_53_2, % 21.85/3.80 | | all_53_1, all_64_0, simplifying with (18), (20), (21), (25), % 21.85/3.80 | | (38), (39), (41), (42), (50), (51) gives: % 21.85/3.80 | | (56) all_53_1 = all_53_2 | ? [v0: any] : ? [v1: any] : (apply(all_32_1, % 21.85/3.80 | | all_53_1, all_64_0) = v1 & apply(all_32_1, all_53_2, all_64_0) = % 21.85/3.80 | | v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 21.85/3.80 | | % 21.85/3.80 | | GROUND_INST: instantiating (6) with all_32_1, all_32_4, all_32_2, all_53_1, % 21.85/3.80 | | all_53_2, all_64_0, simplifying with (18), (20), (21), (25), % 21.85/3.80 | | (38), (39), (41), (42), (50), (51) gives: % 21.85/3.80 | | (57) all_53_1 = all_53_2 | ? [v0: any] : ? [v1: any] : (apply(all_32_1, % 21.85/3.80 | | all_53_1, all_64_0) = v0 & apply(all_32_1, all_53_2, all_64_0) = % 21.85/3.80 | | v1 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 21.85/3.80 | | % 21.85/3.80 | | BETA: splitting (57) gives: % 21.85/3.80 | | % 21.85/3.80 | | Case 1: % 21.85/3.80 | | | % 21.85/3.80 | | | (58) all_53_1 = all_53_2 % 21.85/3.80 | | | % 21.85/3.80 | | | REDUCE: (37), (58) imply: % 21.85/3.80 | | | (59) $false % 21.85/3.80 | | | % 21.85/3.80 | | | CLOSE: (59) is inconsistent. % 21.85/3.80 | | | % 21.85/3.80 | | Case 2: % 21.85/3.80 | | | % 21.85/3.80 | | | (60) ? [v0: any] : ? [v1: any] : (apply(all_32_1, all_53_1, all_64_0) % 21.85/3.80 | | | = v0 & apply(all_32_1, all_53_2, all_64_0) = v1 & ( ~ (v1 = 0) | % 21.85/3.80 | | | ~ (v0 = 0))) % 21.85/3.80 | | | % 21.85/3.80 | | | DELTA: instantiating (60) with fresh symbols all_103_0, all_103_1 gives: % 21.85/3.80 | | | (61) apply(all_32_1, all_53_1, all_64_0) = all_103_1 & apply(all_32_1, % 21.85/3.80 | | | all_53_2, all_64_0) = all_103_0 & ( ~ (all_103_0 = 0) | ~ % 21.85/3.80 | | | (all_103_1 = 0)) % 21.85/3.80 | | | % 21.85/3.80 | | | ALPHA: (61) implies: % 21.85/3.80 | | | (62) apply(all_32_1, all_53_2, all_64_0) = all_103_0 % 21.85/3.80 | | | (63) apply(all_32_1, all_53_1, all_64_0) = all_103_1 % 21.85/3.80 | | | (64) ~ (all_103_0 = 0) | ~ (all_103_1 = 0) % 21.85/3.80 | | | % 21.85/3.80 | | | BETA: splitting (56) gives: % 21.85/3.80 | | | % 21.85/3.80 | | | Case 1: % 21.85/3.80 | | | | % 21.85/3.80 | | | | (65) all_53_1 = all_53_2 % 21.85/3.80 | | | | % 21.85/3.80 | | | | REDUCE: (37), (65) imply: % 21.85/3.80 | | | | (66) $false % 21.85/3.80 | | | | % 21.85/3.80 | | | | CLOSE: (66) is inconsistent. % 21.85/3.80 | | | | % 21.85/3.80 | | | Case 2: % 21.85/3.80 | | | | % 21.85/3.80 | | | | (67) ? [v0: any] : ? [v1: any] : (apply(all_32_1, all_53_1, % 21.85/3.80 | | | | all_64_0) = v1 & apply(all_32_1, all_53_2, all_64_0) = v0 & % 21.85/3.80 | | | | ( ~ (v1 = 0) | ~ (v0 = 0))) % 21.85/3.80 | | | | % 21.85/3.80 | | | | DELTA: instantiating (67) with fresh symbols all_108_0, all_108_1 gives: % 21.85/3.80 | | | | (68) apply(all_32_1, all_53_1, all_64_0) = all_108_0 & % 21.85/3.80 | | | | apply(all_32_1, all_53_2, all_64_0) = all_108_1 & ( ~ (all_108_0 % 21.85/3.80 | | | | = 0) | ~ (all_108_1 = 0)) % 21.85/3.80 | | | | % 21.85/3.80 | | | | ALPHA: (68) implies: % 21.85/3.80 | | | | (69) apply(all_32_1, all_53_2, all_64_0) = all_108_1 % 21.85/3.80 | | | | (70) apply(all_32_1, all_53_1, all_64_0) = all_108_0 % 21.85/3.80 | | | | % 21.85/3.80 | | | | GROUND_INST: instantiating (11) with all_103_0, all_108_1, all_64_0, % 21.85/3.80 | | | | all_53_2, all_32_1, simplifying with (62), (69) gives: % 21.85/3.80 | | | | (71) all_108_1 = all_103_0 % 21.85/3.80 | | | | % 21.85/3.80 | | | | GROUND_INST: instantiating (11) with all_103_1, all_108_0, all_64_0, % 21.85/3.80 | | | | all_53_1, all_32_1, simplifying with (63), (70) gives: % 21.85/3.80 | | | | (72) all_108_0 = all_103_1 % 21.85/3.80 | | | | % 21.85/3.80 | | | | GROUND_INST: instantiating (4) with all_32_5, all_32_6, all_32_4, % 21.85/3.80 | | | | all_32_3, all_32_2, all_53_2, all_64_0, all_32_1, % 21.85/3.80 | | | | all_103_0, all_53_0, simplifying with (16), (17), (18), % 21.85/3.80 | | | | (19), (20), (23), (38), (40), (44), (50), (62) gives: % 21.85/3.80 | | | | (73) all_103_0 = 0 | ? [v0: any] : ? [v1: any] : ((apply(all_32_5, % 21.85/3.80 | | | | all_53_0, all_64_0) = v1 & member(all_53_0, all_32_3) = v0 % 21.85/3.80 | | | | & ( ~ (v1 = 0) | ~ (v0 = 0))) | (member(all_64_0, all_32_2) % 21.85/3.80 | | | | = v1 & member(all_53_2, all_32_4) = v0 & ( ~ (v1 = 0) | ~ % 21.85/3.80 | | | | (v0 = 0)))) % 21.85/3.80 | | | | % 21.85/3.80 | | | | GROUND_INST: instantiating (2) with all_32_5, all_32_6, all_32_4, % 21.85/3.80 | | | | all_32_3, all_32_2, all_53_2, all_64_0, all_32_1, % 21.85/3.80 | | | | all_103_0, all_53_0, simplifying with (16), (17), (18), % 21.85/3.80 | | | | (19), (20), (23), (38), (40), (43), (50), (62) gives: % 21.85/3.80 | | | | (74) all_103_0 = 0 | ? [v0: any] : ? [v1: any] : ((apply(all_32_5, % 21.85/3.80 | | | | all_53_0, all_64_0) = v1 & apply(all_32_6, all_53_2, % 21.85/3.80 | | | | all_53_0) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) | % 21.85/3.80 | | | | (member(all_64_0, all_32_2) = v1 & member(all_53_2, all_32_4) % 21.85/3.80 | | | | = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))) % 21.85/3.80 | | | | % 21.85/3.80 | | | | GROUND_INST: instantiating (3) with all_32_5, all_32_6, all_32_4, % 21.85/3.80 | | | | all_32_3, all_32_2, all_53_1, all_64_0, all_32_1, % 21.85/3.80 | | | | all_103_1, all_53_0, simplifying with (16), (17), (18), % 21.85/3.80 | | | | (19), (20), (23), (39), (40), (50), (52), (63) gives: % 21.85/3.81 | | | | (75) all_103_1 = 0 | ? [v0: any] : ? [v1: any] : ((apply(all_32_6, % 21.85/3.81 | | | | all_53_1, all_53_0) = v1 & member(all_53_0, all_32_3) = v0 % 21.85/3.81 | | | | & ( ~ (v1 = 0) | ~ (v0 = 0))) | (member(all_64_0, all_32_2) % 21.85/3.81 | | | | = v1 & member(all_53_1, all_32_4) = v0 & ( ~ (v1 = 0) | ~ % 21.85/3.81 | | | | (v0 = 0)))) % 21.85/3.81 | | | | % 21.85/3.81 | | | | BETA: splitting (73) gives: % 21.85/3.81 | | | | % 21.85/3.81 | | | | Case 1: % 21.85/3.81 | | | | | % 21.85/3.81 | | | | | (76) all_103_0 = 0 % 21.85/3.81 | | | | | % 21.85/3.81 | | | | | BETA: splitting (64) gives: % 21.85/3.81 | | | | | % 21.85/3.81 | | | | | Case 1: % 21.85/3.81 | | | | | | % 21.85/3.81 | | | | | | (77) ~ (all_103_0 = 0) % 21.85/3.81 | | | | | | % 21.85/3.81 | | | | | | REDUCE: (76), (77) imply: % 21.85/3.81 | | | | | | (78) $false % 21.85/3.81 | | | | | | % 21.85/3.81 | | | | | | CLOSE: (78) is inconsistent. % 21.85/3.81 | | | | | | % 21.85/3.81 | | | | | Case 2: % 21.85/3.81 | | | | | | % 21.85/3.81 | | | | | | (79) ~ (all_103_1 = 0) % 21.85/3.81 | | | | | | % 21.85/3.81 | | | | | | BETA: splitting (75) gives: % 21.85/3.81 | | | | | | % 21.85/3.81 | | | | | | Case 1: % 21.85/3.81 | | | | | | | % 21.85/3.81 | | | | | | | (80) all_103_1 = 0 % 21.85/3.81 | | | | | | | % 21.85/3.81 | | | | | | | REDUCE: (79), (80) imply: % 21.85/3.81 | | | | | | | (81) $false % 21.85/3.81 | | | | | | | % 21.85/3.81 | | | | | | | CLOSE: (81) is inconsistent. % 21.85/3.81 | | | | | | | % 21.85/3.81 | | | | | | Case 2: % 21.85/3.81 | | | | | | | % 21.85/3.81 | | | | | | | (82) ? [v0: any] : ? [v1: any] : ((apply(all_32_6, all_53_1, % 21.85/3.81 | | | | | | | all_53_0) = v1 & member(all_53_0, all_32_3) = v0 & ( % 21.85/3.81 | | | | | | | ~ (v1 = 0) | ~ (v0 = 0))) | (member(all_64_0, % 21.85/3.81 | | | | | | | all_32_2) = v1 & member(all_53_1, all_32_4) = v0 & ( % 21.85/3.81 | | | | | | | ~ (v1 = 0) | ~ (v0 = 0)))) % 21.85/3.81 | | | | | | | % 21.85/3.81 | | | | | | | DELTA: instantiating (82) with fresh symbols all_158_0, all_158_1 % 21.85/3.81 | | | | | | | gives: % 21.85/3.81 | | | | | | | (83) (apply(all_32_6, all_53_1, all_53_0) = all_158_0 & % 21.85/3.81 | | | | | | | member(all_53_0, all_32_3) = all_158_1 & ( ~ (all_158_0 % 21.85/3.81 | | | | | | | = 0) | ~ (all_158_1 = 0))) | (member(all_64_0, % 21.85/3.81 | | | | | | | all_32_2) = all_158_0 & member(all_53_1, all_32_4) = % 21.85/3.81 | | | | | | | all_158_1 & ( ~ (all_158_0 = 0) | ~ (all_158_1 = 0))) % 21.85/3.81 | | | | | | | % 21.85/3.81 | | | | | | | BETA: splitting (83) gives: % 21.85/3.81 | | | | | | | % 21.85/3.81 | | | | | | | Case 1: % 21.85/3.81 | | | | | | | | % 21.85/3.81 | | | | | | | | (84) apply(all_32_6, all_53_1, all_53_0) = all_158_0 & % 21.85/3.81 | | | | | | | | member(all_53_0, all_32_3) = all_158_1 & ( ~ (all_158_0 % 21.85/3.81 | | | | | | | | = 0) | ~ (all_158_1 = 0)) % 21.85/3.81 | | | | | | | | % 21.85/3.81 | | | | | | | | ALPHA: (84) implies: % 21.85/3.81 | | | | | | | | (85) member(all_53_0, all_32_3) = all_158_1 % 21.85/3.81 | | | | | | | | (86) apply(all_32_6, all_53_1, all_53_0) = all_158_0 % 21.85/3.81 | | | | | | | | (87) ~ (all_158_0 = 0) | ~ (all_158_1 = 0) % 21.85/3.81 | | | | | | | | % 21.85/3.81 | | | | | | | | GROUND_INST: instantiating (10) with 0, all_158_1, all_32_3, % 21.85/3.81 | | | | | | | | all_53_0, simplifying with (43), (85) gives: % 21.85/3.81 | | | | | | | | (88) all_158_1 = 0 % 21.85/3.81 | | | | | | | | % 21.85/3.81 | | | | | | | | GROUND_INST: instantiating (11) with 0, all_158_0, all_53_0, % 21.85/3.81 | | | | | | | | all_53_1, all_32_6, simplifying with (45), (86) % 21.85/3.81 | | | | | | | | gives: % 21.85/3.81 | | | | | | | | (89) all_158_0 = 0 % 21.85/3.81 | | | | | | | | % 21.85/3.81 | | | | | | | | REF_CLOSE: (87), (88), (89) are inconsistent by sub-proof #2. % 21.85/3.81 | | | | | | | | % 21.85/3.81 | | | | | | | Case 2: % 21.85/3.81 | | | | | | | | % 21.85/3.81 | | | | | | | | (90) member(all_64_0, all_32_2) = all_158_0 & % 21.85/3.81 | | | | | | | | member(all_53_1, all_32_4) = all_158_1 & ( ~ (all_158_0 % 21.85/3.81 | | | | | | | | = 0) | ~ (all_158_1 = 0)) % 21.85/3.81 | | | | | | | | % 21.85/3.81 | | | | | | | | ALPHA: (90) implies: % 21.85/3.81 | | | | | | | | (91) member(all_53_1, all_32_4) = all_158_1 % 21.85/3.81 | | | | | | | | (92) member(all_64_0, all_32_2) = all_158_0 % 21.85/3.81 | | | | | | | | (93) ~ (all_158_0 = 0) | ~ (all_158_1 = 0) % 21.85/3.81 | | | | | | | | % 21.85/3.81 | | | | | | | | GROUND_INST: instantiating (10) with 0, all_158_1, all_32_4, % 21.85/3.81 | | | | | | | | all_53_1, simplifying with (42), (91) gives: % 21.85/3.81 | | | | | | | | (94) all_158_1 = 0 % 21.85/3.81 | | | | | | | | % 21.85/3.81 | | | | | | | | GROUND_INST: instantiating (10) with 0, all_158_0, all_32_2, % 21.85/3.81 | | | | | | | | all_64_0, simplifying with (51), (92) gives: % 21.85/3.81 | | | | | | | | (95) all_158_0 = 0 % 21.85/3.81 | | | | | | | | % 21.85/3.81 | | | | | | | | REF_CLOSE: (93), (94), (95) are inconsistent by sub-proof #2. % 21.85/3.81 | | | | | | | | % 21.85/3.81 | | | | | | | End of split % 21.85/3.81 | | | | | | | % 21.85/3.81 | | | | | | End of split % 21.85/3.81 | | | | | | % 21.85/3.81 | | | | | End of split % 21.85/3.81 | | | | | % 21.85/3.81 | | | | Case 2: % 21.85/3.81 | | | | | % 21.85/3.81 | | | | | (96) ~ (all_103_0 = 0) % 21.85/3.81 | | | | | (97) ? [v0: any] : ? [v1: any] : ((apply(all_32_5, all_53_0, % 21.85/3.81 | | | | | all_64_0) = v1 & member(all_53_0, all_32_3) = v0 & ( ~ % 21.85/3.81 | | | | | (v1 = 0) | ~ (v0 = 0))) | (member(all_64_0, all_32_2) = % 21.85/3.81 | | | | | v1 & member(all_53_2, all_32_4) = v0 & ( ~ (v1 = 0) | ~ % 21.85/3.81 | | | | | (v0 = 0)))) % 21.85/3.81 | | | | | % 21.85/3.81 | | | | | DELTA: instantiating (97) with fresh symbols all_125_0, all_125_1 % 21.85/3.81 | | | | | gives: % 21.85/3.81 | | | | | (98) (apply(all_32_5, all_53_0, all_64_0) = all_125_0 & % 21.85/3.81 | | | | | member(all_53_0, all_32_3) = all_125_1 & ( ~ (all_125_0 = 0) % 21.85/3.81 | | | | | | ~ (all_125_1 = 0))) | (member(all_64_0, all_32_2) = % 21.85/3.81 | | | | | all_125_0 & member(all_53_2, all_32_4) = all_125_1 & ( ~ % 21.85/3.81 | | | | | (all_125_0 = 0) | ~ (all_125_1 = 0))) % 21.85/3.81 | | | | | % 21.85/3.81 | | | | | BETA: splitting (98) gives: % 21.85/3.81 | | | | | % 21.85/3.81 | | | | | Case 1: % 21.85/3.81 | | | | | | % 21.85/3.81 | | | | | | (99) apply(all_32_5, all_53_0, all_64_0) = all_125_0 & % 21.85/3.81 | | | | | | member(all_53_0, all_32_3) = all_125_1 & ( ~ (all_125_0 = 0) % 21.85/3.81 | | | | | | | ~ (all_125_1 = 0)) % 21.85/3.81 | | | | | | % 21.85/3.81 | | | | | | ALPHA: (99) implies: % 21.85/3.81 | | | | | | (100) member(all_53_0, all_32_3) = all_125_1 % 21.85/3.81 | | | | | | (101) apply(all_32_5, all_53_0, all_64_0) = all_125_0 % 21.85/3.81 | | | | | | (102) ~ (all_125_0 = 0) | ~ (all_125_1 = 0) % 21.85/3.81 | | | | | | % 21.85/3.81 | | | | | | BETA: splitting (74) gives: % 21.85/3.81 | | | | | | % 21.85/3.81 | | | | | | Case 1: % 21.85/3.81 | | | | | | | % 21.85/3.81 | | | | | | | (103) all_103_0 = 0 % 21.85/3.81 | | | | | | | % 21.85/3.81 | | | | | | | REDUCE: (96), (103) imply: % 21.85/3.81 | | | | | | | (104) $false % 21.85/3.81 | | | | | | | % 21.85/3.81 | | | | | | | CLOSE: (104) is inconsistent. % 21.85/3.81 | | | | | | | % 21.85/3.81 | | | | | | Case 2: % 21.85/3.81 | | | | | | | % 21.85/3.81 | | | | | | | % 21.85/3.81 | | | | | | | GROUND_INST: instantiating (10) with 0, all_125_1, all_32_3, % 21.85/3.81 | | | | | | | all_53_0, simplifying with (43), (100) gives: % 21.85/3.81 | | | | | | | (105) all_125_1 = 0 % 21.85/3.81 | | | | | | | % 21.85/3.81 | | | | | | | GROUND_INST: instantiating (11) with 0, all_125_0, all_64_0, % 21.85/3.81 | | | | | | | all_53_0, all_32_5, simplifying with (52), (101) % 21.85/3.81 | | | | | | | gives: % 21.85/3.81 | | | | | | | (106) all_125_0 = 0 % 21.85/3.81 | | | | | | | % 21.85/3.81 | | | | | | | REF_CLOSE: (102), (105), (106) are inconsistent by sub-proof #1. % 21.85/3.81 | | | | | | | % 21.85/3.81 | | | | | | End of split % 21.85/3.81 | | | | | | % 21.85/3.81 | | | | | Case 2: % 21.85/3.81 | | | | | | % 21.85/3.81 | | | | | | (107) member(all_64_0, all_32_2) = all_125_0 & member(all_53_2, % 21.85/3.81 | | | | | | all_32_4) = all_125_1 & ( ~ (all_125_0 = 0) | ~ % 21.85/3.81 | | | | | | (all_125_1 = 0)) % 21.85/3.81 | | | | | | % 21.85/3.81 | | | | | | ALPHA: (107) implies: % 21.85/3.81 | | | | | | (108) member(all_53_2, all_32_4) = all_125_1 % 21.85/3.81 | | | | | | (109) member(all_64_0, all_32_2) = all_125_0 % 21.85/3.81 | | | | | | (110) ~ (all_125_0 = 0) | ~ (all_125_1 = 0) % 21.85/3.81 | | | | | | % 21.85/3.81 | | | | | | BETA: splitting (74) gives: % 21.85/3.81 | | | | | | % 21.85/3.81 | | | | | | Case 1: % 21.85/3.81 | | | | | | | % 21.85/3.81 | | | | | | | (111) all_103_0 = 0 % 21.85/3.81 | | | | | | | % 21.85/3.81 | | | | | | | REDUCE: (96), (111) imply: % 21.85/3.81 | | | | | | | (112) $false % 21.85/3.81 | | | | | | | % 21.85/3.81 | | | | | | | CLOSE: (112) is inconsistent. % 21.85/3.81 | | | | | | | % 21.85/3.81 | | | | | | Case 2: % 21.85/3.81 | | | | | | | % 21.85/3.81 | | | | | | | % 21.85/3.81 | | | | | | | GROUND_INST: instantiating (10) with 0, all_125_1, all_32_4, % 21.85/3.81 | | | | | | | all_53_2, simplifying with (41), (108) gives: % 21.85/3.82 | | | | | | | (113) all_125_1 = 0 % 21.85/3.82 | | | | | | | % 21.85/3.82 | | | | | | | GROUND_INST: instantiating (10) with 0, all_125_0, all_32_2, % 21.85/3.82 | | | | | | | all_64_0, simplifying with (51), (109) gives: % 21.85/3.82 | | | | | | | (114) all_125_0 = 0 % 21.85/3.82 | | | | | | | % 21.85/3.82 | | | | | | | REF_CLOSE: (110), (113), (114) are inconsistent by sub-proof #1. % 21.85/3.82 | | | | | | | % 21.85/3.82 | | | | | | End of split % 21.85/3.82 | | | | | | % 21.85/3.82 | | | | | End of split % 21.85/3.82 | | | | | % 21.85/3.82 | | | | End of split % 21.85/3.82 | | | | % 21.85/3.82 | | | End of split % 21.85/3.82 | | | % 21.85/3.82 | | End of split % 21.85/3.82 | | % 21.85/3.82 | End of split % 21.85/3.82 | % 21.85/3.82 End of proof % 21.85/3.82 % 21.85/3.82 Sub-proof #1 shows that the following formulas are inconsistent: % 21.85/3.82 ---------------------------------------------------------------- % 21.85/3.82 (1) ~ (all_125_0 = 0) | ~ (all_125_1 = 0) % 21.85/3.82 (2) all_125_0 = 0 % 21.85/3.82 (3) all_125_1 = 0 % 21.85/3.82 % 21.85/3.82 Begin of proof % 21.85/3.82 | % 21.85/3.82 | BETA: splitting (1) gives: % 21.85/3.82 | % 21.85/3.82 | Case 1: % 21.85/3.82 | | % 21.85/3.82 | | (4) ~ (all_125_0 = 0) % 21.85/3.82 | | % 21.85/3.82 | | REDUCE: (2), (4) imply: % 21.85/3.82 | | (5) $false % 21.85/3.82 | | % 21.85/3.82 | | CLOSE: (5) is inconsistent. % 21.85/3.82 | | % 21.85/3.82 | Case 2: % 21.85/3.82 | | % 21.85/3.82 | | (6) ~ (all_125_1 = 0) % 21.85/3.82 | | % 21.85/3.82 | | REDUCE: (3), (6) imply: % 21.85/3.82 | | (7) $false % 21.85/3.82 | | % 21.85/3.82 | | CLOSE: (7) is inconsistent. % 21.85/3.82 | | % 21.85/3.82 | End of split % 21.85/3.82 | % 21.85/3.82 End of proof % 21.85/3.82 % 21.85/3.82 Sub-proof #2 shows that the following formulas are inconsistent: % 21.85/3.82 ---------------------------------------------------------------- % 21.85/3.82 (1) ~ (all_158_0 = 0) | ~ (all_158_1 = 0) % 21.85/3.82 (2) all_158_0 = 0 % 21.85/3.82 (3) all_158_1 = 0 % 21.85/3.82 % 21.85/3.82 Begin of proof % 21.85/3.82 | % 21.85/3.82 | BETA: splitting (1) gives: % 21.85/3.82 | % 21.85/3.82 | Case 1: % 21.85/3.82 | | % 21.85/3.82 | | (4) ~ (all_158_0 = 0) % 21.85/3.82 | | % 21.85/3.82 | | REDUCE: (2), (4) imply: % 21.85/3.82 | | (5) $false % 21.85/3.82 | | % 21.85/3.82 | | CLOSE: (5) is inconsistent. % 21.85/3.82 | | % 21.85/3.82 | Case 2: % 21.85/3.82 | | % 21.85/3.82 | | (6) ~ (all_158_1 = 0) % 21.85/3.82 | | % 21.85/3.82 | | REDUCE: (3), (6) imply: % 21.85/3.82 | | (7) $false % 21.85/3.82 | | % 21.85/3.82 | | CLOSE: (7) is inconsistent. % 21.85/3.82 | | % 21.85/3.82 | End of split % 21.85/3.82 | % 21.85/3.82 End of proof % 21.85/3.82 % SZS output end Proof for theBenchmark % 21.85/3.82 % 21.85/3.82 3201ms %------------------------------------------------------------------------------