%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SEU176+2 : TPTP v8.1.2. Released v3.3.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n029.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 17:43:04 EDT 2023 % Result : Theorem 24.24s 4.09s % Output : Proof 56.88s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.13 % Problem : SEU176+2 : TPTP v8.1.2. Released v3.3.0. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.35 % Computer : n029.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 : Wed Aug 23 17:55:52 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/sandbox/benchmark/theBenchmark.p ... % 0.20/0.63 Running up to 7 provers in parallel. % 0.20/0.65 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.20/0.65 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.20/0.65 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.20/0.65 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.20/0.65 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.20/0.65 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.20/0.65 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 4.18/1.38 Prover 4: Preprocessing ... % 4.18/1.38 Prover 1: Preprocessing ... % 4.18/1.45 Prover 3: Preprocessing ... % 4.18/1.45 Prover 6: Preprocessing ... % 4.18/1.45 Prover 5: Preprocessing ... % 4.18/1.45 Prover 2: Preprocessing ... % 4.18/1.48 Prover 0: Preprocessing ... % 13.12/2.57 Prover 5: Proving ... % 13.12/2.57 Prover 1: Warning: ignoring some quantifiers % 13.51/2.61 Prover 6: Proving ... % 13.51/2.63 Prover 3: Warning: ignoring some quantifiers % 13.86/2.66 Prover 3: Constructing countermodel ... % 13.86/2.69 Prover 1: Constructing countermodel ... % 13.86/2.74 Prover 4: Warning: ignoring some quantifiers % 14.57/2.74 Prover 2: Proving ... % 14.96/2.82 Prover 4: Constructing countermodel ... % 14.96/2.97 Prover 0: Proving ... % 24.24/4.08 Prover 0: proved (3441ms) % 24.24/4.09 % 24.24/4.09 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 24.24/4.09 % 24.24/4.09 Prover 3: stopped % 24.24/4.09 Prover 5: stopped % 24.24/4.10 Prover 6: stopped % 24.24/4.10 Prover 2: stopped % 24.57/4.11 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 24.57/4.11 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 24.57/4.11 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 24.57/4.11 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 24.57/4.11 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 24.57/4.22 Prover 7: Preprocessing ... % 24.57/4.31 Prover 8: Preprocessing ... % 25.81/4.37 Prover 13: Preprocessing ... % 25.81/4.39 Prover 11: Preprocessing ... % 25.81/4.39 Prover 10: Preprocessing ... % 27.31/4.54 Prover 7: Warning: ignoring some quantifiers % 28.00/4.57 Prover 7: Constructing countermodel ... % 28.39/4.64 Prover 10: Warning: ignoring some quantifiers % 28.61/4.66 Prover 13: Warning: ignoring some quantifiers % 28.61/4.67 Prover 8: Warning: ignoring some quantifiers % 28.61/4.69 Prover 13: Constructing countermodel ... % 28.61/4.70 Prover 10: Constructing countermodel ... % 28.61/4.71 Prover 8: Constructing countermodel ... % 30.28/4.93 Prover 11: Warning: ignoring some quantifiers % 30.28/4.98 Prover 11: Constructing countermodel ... % 54.72/8.14 Prover 4: Found proof (size 647) % 54.72/8.15 Prover 4: proved (7500ms) % 54.72/8.15 Prover 7: stopped % 54.72/8.15 Prover 1: stopped % 54.72/8.15 Prover 10: stopped % 54.72/8.15 Prover 8: stopped % 54.72/8.15 Prover 11: stopped % 54.72/8.15 Prover 13: stopped % 54.72/8.15 % 54.72/8.15 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 54.72/8.15 % 55.52/8.27 % SZS output start Proof for theBenchmark % 55.52/8.28 Assumptions after simplification: % 55.52/8.28 --------------------------------- % 55.52/8.28 % 55.52/8.28 (d2_subset_1) % 55.87/8.31 ! [v0: $i] : ! [v1: $i] : ! [v2: any] : ( ~ (element(v1, v0) = v2) | ~ % 55.87/8.31 $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : (empty(v1) = v4 & % 55.87/8.31 empty(v0) = v3 & ( ~ (v3 = 0) | (( ~ (v4 = 0) | v2 = 0) & ( ~ (v2 = 0) | % 55.87/8.31 v4 = 0))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: any] : ( ~ % 55.87/8.31 (element(v1, v0) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] % 55.87/8.31 : (empty(v0) = v3 & in(v1, v0) = v4 & (v3 = 0 | (( ~ (v4 = 0) | v2 = 0) & ( % 55.87/8.31 ~ (v2 = 0) | v4 = 0))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: any] % 55.87/8.31 : ( ~ (in(v1, v0) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] % 55.87/8.31 : (empty(v0) = v3 & element(v1, v0) = v4 & (v3 = 0 | (( ~ (v4 = 0) | v2 = 0) % 55.87/8.31 & ( ~ (v2 = 0) | v4 = 0))))) % 55.87/8.31 % 55.87/8.31 (d4_subset_1) % 55.87/8.31 ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (cast_to_subset(v0) = v1) | ~ % 55.87/8.31 $i(v0)) % 55.87/8.31 % 55.87/8.31 (d5_subset_1) % 55.87/8.32 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (subset_complement(v0, v1) = v2) % 55.87/8.32 | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: any] : ? [v5: $i] : % 55.87/8.32 (set_difference(v0, v1) = v5 & element(v1, v3) = v4 & powerset(v0) = v3 & % 55.87/8.32 $i(v5) & $i(v3) & ( ~ (v4 = 0) | v5 = v2))) & ! [v0: $i] : ! [v1: $i] : % 55.87/8.32 ! [v2: $i] : ( ~ (set_difference(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? % 55.87/8.32 [v3: $i] : ? [v4: any] : ? [v5: $i] : (subset_complement(v0, v1) = v5 & % 55.87/8.32 element(v1, v3) = v4 & powerset(v0) = v3 & $i(v5) & $i(v3) & ( ~ (v4 = 0) % 55.87/8.32 | v5 = v2))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 55.87/8.32 (element(v1, v2) = 0) | ~ (powerset(v0) = v2) | ~ $i(v1) | ~ $i(v0) | ? % 55.87/8.32 [v3: $i] : (subset_complement(v0, v1) = v3 & set_difference(v0, v1) = v3 & % 55.87/8.32 $i(v3))) % 55.87/8.32 % 55.87/8.32 (d8_setfam_1) % 55.87/8.33 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (element(v1, v3) = % 55.87/8.33 0) | ~ (powerset(v2) = v3) | ~ (powerset(v0) = v2) | ~ $i(v1) | ~ % 55.87/8.33 $i(v0) | ? [v4: $i] : (complements_of_subsets(v0, v1) = v4 & $i(v4) & ! % 55.87/8.33 [v5: $i] : ! [v6: $i] : ( ~ (subset_complement(v0, v5) = v6) | ~ % 55.87/8.33 (element(v4, v3) = 0) | ~ $i(v5) | ? [v7: any] : ? [v8: any] : ? % 55.87/8.33 [v9: any] : (element(v5, v2) = v7 & in(v6, v1) = v9 & in(v5, v4) = v8 & % 55.87/8.33 ( ~ (v7 = 0) | (( ~ (v9 = 0) | v8 = 0) & ( ~ (v8 = 0) | v9 = 0))))) & % 55.87/8.33 ! [v5: $i] : ! [v6: any] : ( ~ (element(v4, v3) = 0) | ~ (in(v5, v4) = % 55.87/8.33 v6) | ~ $i(v5) | ? [v7: any] : ? [v8: $i] : ? [v9: any] : % 55.87/8.33 (subset_complement(v0, v5) = v8 & element(v5, v2) = v7 & in(v8, v1) = v9 % 55.87/8.33 & $i(v8) & ( ~ (v7 = 0) | (( ~ (v9 = 0) | v6 = 0) & ( ~ (v6 = 0) | v9 % 55.87/8.33 = 0))))) & ! [v5: $i] : (v5 = v4 | ~ (element(v5, v3) = 0) | % 55.87/8.33 ~ $i(v5) | ? [v6: $i] : ? [v7: any] : ? [v8: $i] : ? [v9: any] : % 55.87/8.33 (subset_complement(v0, v6) = v8 & element(v6, v2) = 0 & in(v8, v1) = v9 % 55.87/8.33 & in(v6, v5) = v7 & $i(v8) & $i(v6) & ( ~ (v9 = 0) | ~ (v7 = 0)) & % 55.87/8.33 (v9 = 0 | v7 = 0))) & ! [v5: $i] : ( ~ (element(v5, v2) = 0) | ~ % 55.87/8.33 (element(v4, v3) = 0) | ~ $i(v5) | ? [v6: any] : ? [v7: $i] : ? [v8: % 55.87/8.33 any] : (subset_complement(v0, v5) = v7 & in(v7, v1) = v8 & in(v5, v4) % 55.87/8.33 = v6 & $i(v7) & ( ~ (v8 = 0) | v6 = 0) & ( ~ (v6 = 0) | v8 = 0))))) & % 55.87/8.33 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (complements_of_subsets(v0, v1) = % 55.87/8.33 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : ? [v5: any] : % 55.87/8.33 (element(v1, v4) = v5 & powerset(v3) = v4 & powerset(v0) = v3 & $i(v4) & % 55.87/8.33 $i(v3) & ( ~ (v5 = 0) | ( ! [v6: $i] : ! [v7: $i] : ( ~ % 55.87/8.33 (subset_complement(v0, v6) = v7) | ~ (element(v2, v4) = 0) | ~ % 55.87/8.33 $i(v6) | ~ $i(v2) | ? [v8: any] : ? [v9: any] : ? [v10: any] : % 55.87/8.33 (element(v6, v3) = v8 & in(v7, v1) = v10 & in(v6, v2) = v9 & ( ~ (v8 % 55.87/8.33 = 0) | (( ~ (v10 = 0) | v9 = 0) & ( ~ (v9 = 0) | v10 = 0))))) % 55.87/8.33 & ! [v6: $i] : ! [v7: any] : ( ~ (element(v2, v4) = 0) | ~ (in(v6, % 55.87/8.33 v2) = v7) | ~ $i(v6) | ~ $i(v2) | ? [v8: any] : ? [v9: $i] : % 55.87/8.33 ? [v10: any] : (subset_complement(v0, v6) = v9 & element(v6, v3) = % 55.87/8.33 v8 & in(v9, v1) = v10 & $i(v9) & ( ~ (v8 = 0) | (( ~ (v10 = 0) | % 55.87/8.33 v7 = 0) & ( ~ (v7 = 0) | v10 = 0))))) & ! [v6: $i] : (v6 = % 55.87/8.33 v2 | ~ (element(v6, v4) = 0) | ~ $i(v6) | ? [v7: $i] : ? [v8: % 55.87/8.33 any] : ? [v9: $i] : ? [v10: any] : (subset_complement(v0, v7) = % 55.87/8.33 v9 & element(v7, v3) = 0 & in(v9, v1) = v10 & in(v7, v6) = v8 & % 55.87/8.33 $i(v9) & $i(v7) & ( ~ (v10 = 0) | ~ (v8 = 0)) & (v10 = 0 | v8 = % 55.87/8.33 0))) & ! [v6: $i] : ( ~ (element(v6, v3) = 0) | ~ (element(v2, % 55.87/8.33 v4) = 0) | ~ $i(v6) | ~ $i(v2) | ? [v7: any] : ? [v8: $i] : % 55.87/8.33 ? [v9: any] : (subset_complement(v0, v6) = v8 & in(v8, v1) = v9 & % 55.87/8.33 in(v6, v2) = v7 & $i(v8) & ( ~ (v9 = 0) | v7 = 0) & ( ~ (v7 = 0) | % 55.87/8.33 v9 = 0))))))) % 55.87/8.33 % 55.87/8.33 (dt_k2_subset_1) % 55.87/8.33 ! [v0: $i] : ! [v1: $i] : ( ~ (cast_to_subset(v0) = v1) | ~ $i(v0) | ? % 55.87/8.33 [v2: $i] : (element(v1, v2) = 0 & powerset(v0) = v2 & $i(v2))) & ! [v0: $i] % 55.87/8.33 : ! [v1: $i] : ( ~ (powerset(v0) = v1) | ~ $i(v0) | ? [v2: $i] : % 55.87/8.33 (cast_to_subset(v0) = v2 & element(v2, v1) = 0 & $i(v2))) % 55.87/8.33 % 55.87/8.33 (dt_k3_subset_1) % 55.87/8.33 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (subset_complement(v0, v1) = v2) % 55.87/8.33 | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: any] : ? [v5: any] : % 55.87/8.33 (element(v2, v3) = v5 & element(v1, v3) = v4 & powerset(v0) = v3 & $i(v3) & % 55.87/8.33 ( ~ (v4 = 0) | v5 = 0))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 55.87/8.33 (element(v1, v2) = 0) | ~ (powerset(v0) = v2) | ~ $i(v1) | ~ $i(v0) | ? % 55.87/8.33 [v3: $i] : (subset_complement(v0, v1) = v3 & element(v3, v2) = 0 & $i(v3))) % 55.87/8.33 % 55.87/8.33 (dt_k5_setfam_1) % 55.87/8.33 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (element(v1, v3) = % 55.87/8.33 0) | ~ (powerset(v2) = v3) | ~ (powerset(v0) = v2) | ~ $i(v1) | ~ % 55.87/8.33 $i(v0) | ? [v4: $i] : (union_of_subsets(v0, v1) = v4 & element(v4, v2) = 0 % 55.87/8.33 & $i(v4))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 55.87/8.33 (union_of_subsets(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? % 55.87/8.33 [v4: $i] : ? [v5: any] : ? [v6: any] : (element(v2, v3) = v6 & element(v1, % 55.87/8.33 v4) = v5 & powerset(v3) = v4 & powerset(v0) = v3 & $i(v4) & $i(v3) & ( ~ % 55.87/8.33 (v5 = 0) | v6 = 0))) % 55.87/8.33 % 55.87/8.33 (dt_k6_setfam_1) % 55.87/8.33 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (element(v1, v3) = % 55.87/8.33 0) | ~ (powerset(v2) = v3) | ~ (powerset(v0) = v2) | ~ $i(v1) | ~ % 55.87/8.33 $i(v0) | ? [v4: $i] : (meet_of_subsets(v0, v1) = v4 & element(v4, v2) = 0 & % 55.87/8.33 $i(v4))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 55.87/8.33 (meet_of_subsets(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? % 55.87/8.33 [v4: $i] : ? [v5: any] : ? [v6: any] : (element(v2, v3) = v6 & element(v1, % 55.87/8.33 v4) = v5 & powerset(v3) = v4 & powerset(v0) = v3 & $i(v4) & $i(v3) & ( ~ % 55.87/8.33 (v5 = 0) | v6 = 0))) % 55.87/8.33 % 55.87/8.33 (dt_k6_subset_1) % 55.87/8.34 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 55.87/8.34 (subset_difference(v0, v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 55.87/8.34 ? [v4: $i] : ? [v5: any] : ? [v6: any] : ? [v7: any] : (element(v3, v4) = % 55.87/8.34 v7 & element(v2, v4) = v6 & element(v1, v4) = v5 & powerset(v0) = v4 & % 55.87/8.34 $i(v4) & ( ~ (v6 = 0) | ~ (v5 = 0) | v7 = 0))) % 55.87/8.34 % 55.87/8.34 (dt_k7_setfam_1) % 55.87/8.34 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (element(v1, v3) = % 55.87/8.34 0) | ~ (powerset(v2) = v3) | ~ (powerset(v0) = v2) | ~ $i(v1) | ~ % 55.87/8.34 $i(v0) | ? [v4: $i] : (complements_of_subsets(v0, v1) = v4 & element(v4, % 55.87/8.34 v3) = 0 & $i(v4))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 55.87/8.34 (complements_of_subsets(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] % 55.87/8.34 : ? [v4: $i] : ? [v5: any] : ? [v6: any] : (element(v2, v4) = v6 & % 55.87/8.34 element(v1, v4) = v5 & powerset(v3) = v4 & powerset(v0) = v3 & $i(v4) & % 55.87/8.34 $i(v3) & ( ~ (v5 = 0) | v6 = 0))) % 55.87/8.34 % 55.87/8.34 (fc1_subset_1) % 55.87/8.34 ! [v0: $i] : ! [v1: $i] : ( ~ (powerset(v0) = v1) | ~ $i(v0) | ? [v2: int] % 55.87/8.34 : ( ~ (v2 = 0) & empty(v1) = v2)) % 55.87/8.34 % 55.87/8.34 (involutiveness_k3_subset_1) % 55.87/8.34 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (subset_complement(v0, v1) = v2) % 55.87/8.34 | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: any] : ? [v5: $i] : % 55.87/8.34 (subset_complement(v0, v2) = v5 & element(v1, v3) = v4 & powerset(v0) = v3 & % 55.87/8.34 $i(v5) & $i(v3) & ( ~ (v4 = 0) | v5 = v1))) & ! [v0: $i] : ! [v1: $i] : % 55.87/8.34 ! [v2: $i] : ( ~ (element(v1, v2) = 0) | ~ (powerset(v0) = v2) | ~ $i(v1) | % 55.87/8.34 ~ $i(v0) | ? [v3: $i] : (subset_complement(v0, v3) = v1 & % 55.87/8.34 subset_complement(v0, v1) = v3 & $i(v3))) % 55.87/8.34 % 55.87/8.34 (involutiveness_k7_setfam_1) % 55.87/8.34 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (element(v1, v3) = % 55.87/8.34 0) | ~ (powerset(v2) = v3) | ~ (powerset(v0) = v2) | ~ $i(v1) | ~ % 55.87/8.34 $i(v0) | ? [v4: $i] : (complements_of_subsets(v0, v4) = v1 & % 55.87/8.34 complements_of_subsets(v0, v1) = v4 & $i(v4))) & ! [v0: $i] : ! [v1: $i] % 55.87/8.34 : ! [v2: $i] : ( ~ (complements_of_subsets(v0, v1) = v2) | ~ $i(v1) | ~ % 55.87/8.34 $i(v0) | ? [v3: $i] : ? [v4: $i] : ? [v5: any] : ? [v6: $i] : % 55.87/8.34 (complements_of_subsets(v0, v2) = v6 & element(v1, v4) = v5 & powerset(v3) = % 55.87/8.34 v4 & powerset(v0) = v3 & $i(v6) & $i(v4) & $i(v3) & ( ~ (v5 = 0) | v6 = % 55.87/8.34 v1))) % 55.87/8.34 % 55.87/8.34 (rc2_subset_1) % 55.87/8.34 ! [v0: $i] : ! [v1: $i] : ( ~ (powerset(v0) = v1) | ~ $i(v0) | ? [v2: $i] % 55.87/8.34 : (empty(v2) = 0 & element(v2, v1) = 0 & $i(v2))) % 55.87/8.34 % 55.87/8.34 (redefinition_k5_setfam_1) % 55.87/8.35 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (element(v1, v3) = % 55.87/8.35 0) | ~ (powerset(v2) = v3) | ~ (powerset(v0) = v2) | ~ $i(v1) | ~ % 55.87/8.35 $i(v0) | ? [v4: $i] : (union_of_subsets(v0, v1) = v4 & union(v1) = v4 & % 55.87/8.35 $i(v4))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 55.87/8.35 (union_of_subsets(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? % 55.87/8.35 [v4: $i] : ? [v5: any] : ? [v6: $i] : (union(v1) = v6 & element(v1, v4) = % 55.87/8.35 v5 & powerset(v3) = v4 & powerset(v0) = v3 & $i(v6) & $i(v4) & $i(v3) & ( % 55.87/8.35 ~ (v5 = 0) | v6 = v2))) % 55.87/8.35 % 55.87/8.35 (redefinition_k6_setfam_1) % 55.87/8.35 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (element(v1, v3) = % 55.87/8.35 0) | ~ (powerset(v2) = v3) | ~ (powerset(v0) = v2) | ~ $i(v1) | ~ % 55.87/8.35 $i(v0) | ? [v4: $i] : (meet_of_subsets(v0, v1) = v4 & set_meet(v1) = v4 & % 55.87/8.35 $i(v4))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 55.87/8.35 (meet_of_subsets(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? % 55.87/8.35 [v4: $i] : ? [v5: any] : ? [v6: $i] : (element(v1, v4) = v5 & powerset(v3) % 55.87/8.35 = v4 & powerset(v0) = v3 & set_meet(v1) = v6 & $i(v6) & $i(v4) & $i(v3) & % 55.87/8.35 ( ~ (v5 = 0) | v6 = v2))) % 55.87/8.35 % 55.87/8.35 (redefinition_k6_subset_1) % 55.87/8.35 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 55.87/8.35 (subset_difference(v0, v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 55.87/8.35 ? [v4: $i] : ? [v5: any] : ? [v6: any] : ? [v7: $i] : (set_difference(v1, % 55.87/8.35 v2) = v7 & element(v2, v4) = v6 & element(v1, v4) = v5 & powerset(v0) = % 55.87/8.35 v4 & $i(v7) & $i(v4) & ( ~ (v6 = 0) | ~ (v5 = 0) | v7 = v3))) % 55.87/8.35 % 55.87/8.35 (t1_zfmisc_1) % 55.87/8.35 $i(empty_set) & ? [v0: $i] : (powerset(empty_set) = v0 & singleton(empty_set) % 55.87/8.35 = v0 & $i(v0)) % 55.87/8.35 % 55.87/8.35 (t2_subset) % 55.87/8.35 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (in(v0, v1) = v2) | ~ % 55.87/8.35 $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : (empty(v1) = v4 & % 55.87/8.35 element(v0, v1) = v3 & ( ~ (v3 = 0) | v4 = 0))) & ! [v0: $i] : ! [v1: % 55.87/8.35 $i] : ( ~ (element(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: any] : ? % 55.87/8.35 [v3: any] : (empty(v1) = v2 & in(v0, v1) = v3 & (v3 = 0 | v2 = 0))) % 55.87/8.35 % 55.87/8.35 (t43_subset_1) % 55.87/8.35 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: any] : ( ~ % 55.87/8.35 (disjoint(v1, v3) = v4) | ~ (element(v1, v2) = 0) | ~ (powerset(v0) = v2) % 55.87/8.35 | ~ $i(v3) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: $i] : ? [v7: % 55.87/8.35 any] : (subset_complement(v0, v3) = v6 & element(v3, v2) = v5 & subset(v1, % 55.87/8.35 v6) = v7 & $i(v6) & ( ~ (v5 = 0) | (( ~ (v7 = 0) | v4 = 0) & ( ~ (v4 = % 55.87/8.35 0) | v7 = 0))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 55.87/8.35 [v3: $i] : ! [v4: $i] : ( ~ (subset_complement(v0, v3) = v4) | ~ % 55.87/8.35 (element(v1, v2) = 0) | ~ (powerset(v0) = v2) | ~ $i(v3) | ~ $i(v1) | ~ % 55.87/8.35 $i(v0) | ? [v5: any] : ? [v6: any] : ? [v7: any] : (disjoint(v1, v3) = v6 % 55.87/8.35 & element(v3, v2) = v5 & subset(v1, v4) = v7 & ( ~ (v5 = 0) | (( ~ (v7 = % 55.87/8.35 0) | v6 = 0) & ( ~ (v6 = 0) | v7 = 0))))) & ! [v0: $i] : ! [v1: % 55.87/8.35 $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (element(v3, v2) = 0) | ~ % 55.87/8.35 (element(v1, v2) = 0) | ~ (powerset(v0) = v2) | ~ $i(v3) | ~ $i(v1) | ~ % 55.87/8.35 $i(v0) | ? [v4: any] : ? [v5: $i] : ? [v6: any] : (disjoint(v1, v3) = v4 % 55.87/8.35 & subset_complement(v0, v3) = v5 & subset(v1, v5) = v6 & $i(v5) & ( ~ (v6 % 55.87/8.35 = 0) | v4 = 0) & ( ~ (v4 = 0) | v6 = 0))) % 55.87/8.35 % 55.87/8.36 (t46_setfam_1) % 55.87/8.36 $i(empty_set) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = % 55.87/8.36 empty_set | ~ (element(v1, v3) = 0) | ~ (powerset(v2) = v3) | ~ % 55.87/8.36 (powerset(v0) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: $i] : ( ~ (v4 = % 55.87/8.36 empty_set) & complements_of_subsets(v0, v1) = v4 & $i(v4))) & ! [v0: % 55.87/8.36 $i] : ! [v1: $i] : (v1 = empty_set | ~ (complements_of_subsets(v0, v1) = % 55.87/8.36 empty_set) | ~ $i(v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: $i] : ? [v4: % 55.87/8.36 int] : ( ~ (v4 = 0) & element(v1, v3) = v4 & powerset(v2) = v3 & % 55.87/8.36 powerset(v0) = v2 & $i(v3) & $i(v2))) % 55.87/8.36 % 55.87/8.36 (t47_setfam_1) % 55.87/8.36 $i(empty_set) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = % 55.87/8.36 empty_set | ~ (element(v1, v3) = 0) | ~ (powerset(v2) = v3) | ~ % 55.87/8.36 (powerset(v0) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: $i] : ? [v5: $i] : ? % 55.87/8.36 [v6: $i] : ? [v7: $i] : (subset_difference(v0, v4, v5) = v6 & % 55.87/8.36 meet_of_subsets(v0, v7) = v6 & union_of_subsets(v0, v1) = v5 & % 55.87/8.36 complements_of_subsets(v0, v1) = v7 & cast_to_subset(v0) = v4 & $i(v7) & % 55.87/8.36 $i(v6) & $i(v5) & $i(v4))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 % 55.87/8.36 = empty_set | ~ (union_of_subsets(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | % 55.87/8.36 ? [v3: $i] : ? [v4: $i] : ? [v5: any] : ? [v6: $i] : ? [v7: $i] : ? % 55.87/8.36 [v8: $i] : ? [v9: $i] : (subset_difference(v0, v6, v2) = v7 & % 55.87/8.36 meet_of_subsets(v0, v8) = v9 & complements_of_subsets(v0, v1) = v8 & % 55.87/8.36 cast_to_subset(v0) = v6 & element(v1, v4) = v5 & powerset(v3) = v4 & % 55.87/8.36 powerset(v0) = v3 & $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v4) & $i(v3) & % 55.87/8.36 ( ~ (v5 = 0) | v9 = v7))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 % 55.87/8.36 = empty_set | ~ (complements_of_subsets(v0, v1) = v2) | ~ $i(v1) | ~ % 55.87/8.36 $i(v0) | ? [v3: $i] : ? [v4: $i] : ? [v5: any] : ? [v6: $i] : ? [v7: % 55.87/8.36 $i] : ? [v8: $i] : ? [v9: $i] : (subset_difference(v0, v6, v7) = v8 & % 55.87/8.36 meet_of_subsets(v0, v2) = v9 & union_of_subsets(v0, v1) = v7 & % 55.87/8.36 cast_to_subset(v0) = v6 & element(v1, v4) = v5 & powerset(v3) = v4 & % 55.87/8.36 powerset(v0) = v3 & $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v4) & $i(v3) & % 55.87/8.36 ( ~ (v5 = 0) | v9 = v8))) % 55.87/8.36 % 55.87/8.36 (t48_setfam_1) % 55.87/8.36 $i(empty_set) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? % 55.87/8.36 [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ( ~ (v8 = % 55.87/8.36 v5) & ~ (v1 = empty_set) & subset_difference(v0, v6, v7) = v8 & % 55.87/8.36 meet_of_subsets(v0, v1) = v7 & union_of_subsets(v0, v4) = v5 & % 55.87/8.36 complements_of_subsets(v0, v1) = v4 & cast_to_subset(v0) = v6 & element(v1, % 55.87/8.36 v3) = 0 & powerset(v2) = v3 & powerset(v0) = v2 & $i(v8) & $i(v7) & $i(v6) % 55.87/8.36 & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 55.87/8.36 % 55.87/8.36 (t6_boole) % 55.87/8.36 $i(empty_set) & ! [v0: $i] : (v0 = empty_set | ~ (empty(v0) = 0) | ~ % 55.87/8.36 $i(v0)) % 55.87/8.36 % 55.87/8.36 (t8_boole) % 55.87/8.36 ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (empty(v1) = 0) | ~ (empty(v0) = 0) % 55.87/8.36 | ~ $i(v1) | ~ $i(v0)) % 55.87/8.36 % 55.87/8.36 (t99_zfmisc_1) % 55.87/8.37 ! [v0: $i] : ! [v1: $i] : ( ~ (powerset(v0) = v1) | ~ $i(v0) | union(v1) = % 55.87/8.37 v0) % 55.87/8.37 % 55.87/8.37 (function-axioms) % 55.87/8.37 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 % 55.87/8.37 | ~ (subset_difference(v4, v3, v2) = v1) | ~ (subset_difference(v4, v3, % 55.87/8.37 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : % 55.87/8.37 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (are_equipotent(v3, v2) = v1) | ~ % 55.87/8.37 (are_equipotent(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 55.87/8.37 ! [v3: $i] : (v1 = v0 | ~ (meet_of_subsets(v3, v2) = v1) | ~ % 55.87/8.37 (meet_of_subsets(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 55.87/8.37 ! [v3: $i] : (v1 = v0 | ~ (union_of_subsets(v3, v2) = v1) | ~ % 55.87/8.37 (union_of_subsets(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 55.87/8.37 ! [v3: $i] : (v1 = v0 | ~ (complements_of_subsets(v3, v2) = v1) | ~ % 55.87/8.37 (complements_of_subsets(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! % 55.87/8.37 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 55.87/8.37 (disjoint(v3, v2) = v1) | ~ (disjoint(v3, v2) = v0)) & ! [v0: $i] : ! % 55.87/8.37 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (subset_complement(v3, % 55.87/8.37 v2) = v1) | ~ (subset_complement(v3, v2) = v0)) & ! [v0: $i] : ! [v1: % 55.87/8.37 $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (set_difference(v3, v2) = % 55.87/8.37 v1) | ~ (set_difference(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 55.87/8.37 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (cartesian_product2(v3, v2) = v1) | ~ % 55.87/8.37 (cartesian_product2(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 55.87/8.37 : ! [v3: $i] : (v1 = v0 | ~ (ordered_pair(v3, v2) = v1) | ~ % 55.87/8.37 (ordered_pair(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 55.87/8.37 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (element(v3, % 55.87/8.37 v2) = v1) | ~ (element(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! % 55.87/8.37 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 55.87/8.37 (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0: $i] : ! [v1: % 55.87/8.37 $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (set_intersection2(v3, v2) = % 55.87/8.37 v1) | ~ (set_intersection2(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : % 55.87/8.37 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (set_union2(v3, v2) = v1) | ~ % 55.87/8.37 (set_union2(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 55.87/8.37 [v3: $i] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ % 55.87/8.37 (unordered_pair(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 55.87/8.37 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 55.87/8.37 (proper_subset(v3, v2) = v1) | ~ (proper_subset(v3, v2) = v0)) & ! [v0: % 55.87/8.37 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 55.87/8.37 : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) & ! [v0: $i] : ! % 55.87/8.37 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (union(v2) = v1) | ~ (union(v2) = v0)) % 55.87/8.37 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (cast_to_subset(v2) % 55.87/8.37 = v1) | ~ (cast_to_subset(v2) = v0)) & ! [v0: MultipleValueBool] : ! % 55.87/8.37 [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (empty(v2) = v1) | ~ % 55.87/8.37 (empty(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 55.87/8.37 (powerset(v2) = v1) | ~ (powerset(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : % 55.87/8.37 ! [v2: $i] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & % 55.87/8.37 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (set_meet(v2) = v1) | % 55.87/8.37 ~ (set_meet(v2) = v0)) % 55.87/8.37 % 55.87/8.37 Further assumptions not needed in the proof: % 55.87/8.37 -------------------------------------------- % 55.87/8.37 antisymmetry_r2_hidden, antisymmetry_r2_xboole_0, commutativity_k2_tarski, % 55.87/8.37 commutativity_k2_xboole_0, commutativity_k3_xboole_0, d10_xboole_0, d1_setfam_1, % 55.87/8.37 d1_tarski, d1_xboole_0, d1_zfmisc_1, d2_tarski, d2_xboole_0, d2_zfmisc_1, % 55.87/8.37 d3_tarski, d3_xboole_0, d4_tarski, d4_xboole_0, d5_tarski, d7_xboole_0, % 55.87/8.37 d8_xboole_0, dt_k1_setfam_1, dt_k1_tarski, dt_k1_xboole_0, dt_k1_zfmisc_1, % 55.87/8.37 dt_k2_tarski, dt_k2_xboole_0, dt_k2_zfmisc_1, dt_k3_tarski, dt_k3_xboole_0, % 55.87/8.37 dt_k4_tarski, dt_k4_xboole_0, dt_m1_subset_1, existence_m1_subset_1, % 55.87/8.37 fc1_xboole_0, fc1_zfmisc_1, fc2_xboole_0, fc3_xboole_0, idempotence_k2_xboole_0, % 55.87/8.37 idempotence_k3_xboole_0, irreflexivity_r2_xboole_0, l1_zfmisc_1, l23_zfmisc_1, % 55.87/8.37 l25_zfmisc_1, l28_zfmisc_1, l2_zfmisc_1, l32_xboole_1, l3_subset_1, l3_zfmisc_1, % 55.87/8.37 l4_zfmisc_1, l50_zfmisc_1, l55_zfmisc_1, l71_subset_1, rc1_subset_1, % 55.87/8.37 rc1_xboole_0, rc2_xboole_0, reflexivity_r1_tarski, symmetry_r1_xboole_0, % 55.87/8.37 t106_zfmisc_1, t10_zfmisc_1, t118_zfmisc_1, t119_zfmisc_1, t12_xboole_1, % 55.87/8.37 t136_zfmisc_1, t17_xboole_1, t19_xboole_1, t1_boole, t1_subset, t1_xboole_1, % 55.87/8.37 t26_xboole_1, t28_xboole_1, t2_boole, t2_tarski, t2_xboole_1, t33_xboole_1, % 55.87/8.37 t33_zfmisc_1, t36_xboole_1, t37_xboole_1, t37_zfmisc_1, t38_zfmisc_1, % 55.87/8.37 t39_xboole_1, t39_zfmisc_1, t3_boole, t3_subset, t3_xboole_0, t3_xboole_1, % 55.87/8.37 t40_xboole_1, t45_xboole_1, t46_zfmisc_1, t48_xboole_1, t4_boole, t4_subset, % 55.87/8.37 t4_xboole_0, t50_subset_1, t54_subset_1, t5_subset, t60_xboole_1, t63_xboole_1, % 55.87/8.37 t65_zfmisc_1, t69_enumset1, t6_zfmisc_1, t7_boole, t7_xboole_1, t83_xboole_1, % 55.87/8.37 t8_xboole_1, t8_zfmisc_1, t92_zfmisc_1, t9_tarski, t9_zfmisc_1 % 55.87/8.37 % 55.87/8.37 Those formulas are unsatisfiable: % 55.87/8.37 --------------------------------- % 55.87/8.37 % 55.87/8.37 Begin of proof % 55.87/8.38 | % 55.87/8.38 | ALPHA: (d2_subset_1) implies: % 55.87/8.38 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: any] : ( ~ (element(v1, v0) = v2) | % 55.87/8.38 | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : (empty(v1) = v4 % 55.87/8.38 | & empty(v0) = v3 & ( ~ (v3 = 0) | (( ~ (v4 = 0) | v2 = 0) & ( ~ (v2 % 55.87/8.38 | = 0) | v4 = 0))))) % 55.87/8.38 | % 55.87/8.38 | ALPHA: (d5_subset_1) implies: % 56.26/8.38 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (element(v1, v2) = 0) | % 56.26/8.38 | ~ (powerset(v0) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : % 56.26/8.38 | (subset_complement(v0, v1) = v3 & set_difference(v0, v1) = v3 & % 56.26/8.38 | $i(v3))) % 56.26/8.38 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (set_difference(v0, v1) = % 56.26/8.38 | v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: any] : ? [v5: % 56.26/8.38 | $i] : (subset_complement(v0, v1) = v5 & element(v1, v3) = v4 & % 56.26/8.38 | powerset(v0) = v3 & $i(v5) & $i(v3) & ( ~ (v4 = 0) | v5 = v2))) % 56.26/8.38 | % 56.26/8.38 | ALPHA: (d8_setfam_1) implies: % 56.26/8.38 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 56.26/8.38 | (complements_of_subsets(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? % 56.26/8.38 | [v3: $i] : ? [v4: $i] : ? [v5: any] : (element(v1, v4) = v5 & % 56.26/8.38 | powerset(v3) = v4 & powerset(v0) = v3 & $i(v4) & $i(v3) & ( ~ (v5 = % 56.26/8.38 | 0) | ( ! [v6: $i] : ! [v7: $i] : ( ~ (subset_complement(v0, % 56.26/8.38 | v6) = v7) | ~ (element(v2, v4) = 0) | ~ $i(v6) | ~ % 56.26/8.38 | $i(v2) | ? [v8: any] : ? [v9: any] : ? [v10: any] : % 56.26/8.38 | (element(v6, v3) = v8 & in(v7, v1) = v10 & in(v6, v2) = v9 & % 56.26/8.38 | ( ~ (v8 = 0) | (( ~ (v10 = 0) | v9 = 0) & ( ~ (v9 = 0) | % 56.26/8.38 | v10 = 0))))) & ! [v6: $i] : ! [v7: any] : ( ~ % 56.26/8.38 | (element(v2, v4) = 0) | ~ (in(v6, v2) = v7) | ~ $i(v6) | ~ % 56.26/8.38 | $i(v2) | ? [v8: any] : ? [v9: $i] : ? [v10: any] : % 56.26/8.38 | (subset_complement(v0, v6) = v9 & element(v6, v3) = v8 & % 56.26/8.38 | in(v9, v1) = v10 & $i(v9) & ( ~ (v8 = 0) | (( ~ (v10 = 0) | % 56.26/8.38 | v7 = 0) & ( ~ (v7 = 0) | v10 = 0))))) & ! [v6: $i] : % 56.26/8.38 | (v6 = v2 | ~ (element(v6, v4) = 0) | ~ $i(v6) | ? [v7: $i] : % 56.26/8.38 | ? [v8: any] : ? [v9: $i] : ? [v10: any] : % 56.26/8.38 | (subset_complement(v0, v7) = v9 & element(v7, v3) = 0 & % 56.26/8.38 | in(v9, v1) = v10 & in(v7, v6) = v8 & $i(v9) & $i(v7) & ( ~ % 56.26/8.38 | (v10 = 0) | ~ (v8 = 0)) & (v10 = 0 | v8 = 0))) & ! [v6: % 56.26/8.38 | $i] : ( ~ (element(v6, v3) = 0) | ~ (element(v2, v4) = 0) | % 56.26/8.38 | ~ $i(v6) | ~ $i(v2) | ? [v7: any] : ? [v8: $i] : ? [v9: % 56.26/8.38 | any] : (subset_complement(v0, v6) = v8 & in(v8, v1) = v9 & % 56.26/8.38 | in(v6, v2) = v7 & $i(v8) & ( ~ (v9 = 0) | v7 = 0) & ( ~ (v7 % 56.26/8.38 | = 0) | v9 = 0))))))) % 56.26/8.39 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 56.26/8.39 | (element(v1, v3) = 0) | ~ (powerset(v2) = v3) | ~ (powerset(v0) = % 56.26/8.39 | v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: $i] : % 56.26/8.39 | (complements_of_subsets(v0, v1) = v4 & $i(v4) & ! [v5: $i] : ! [v6: % 56.26/8.39 | $i] : ( ~ (subset_complement(v0, v5) = v6) | ~ (element(v4, v3) % 56.26/8.39 | = 0) | ~ $i(v5) | ? [v7: any] : ? [v8: any] : ? [v9: any] : % 56.26/8.39 | (element(v5, v2) = v7 & in(v6, v1) = v9 & in(v5, v4) = v8 & ( ~ % 56.26/8.39 | (v7 = 0) | (( ~ (v9 = 0) | v8 = 0) & ( ~ (v8 = 0) | v9 = % 56.26/8.39 | 0))))) & ! [v5: $i] : ! [v6: any] : ( ~ (element(v4, % 56.26/8.39 | v3) = 0) | ~ (in(v5, v4) = v6) | ~ $i(v5) | ? [v7: any] : % 56.26/8.39 | ? [v8: $i] : ? [v9: any] : (subset_complement(v0, v5) = v8 & % 56.26/8.39 | element(v5, v2) = v7 & in(v8, v1) = v9 & $i(v8) & ( ~ (v7 = 0) % 56.26/8.39 | | (( ~ (v9 = 0) | v6 = 0) & ( ~ (v6 = 0) | v9 = 0))))) & ! % 56.26/8.39 | [v5: $i] : (v5 = v4 | ~ (element(v5, v3) = 0) | ~ $i(v5) | ? % 56.26/8.39 | [v6: $i] : ? [v7: any] : ? [v8: $i] : ? [v9: any] : % 56.26/8.39 | (subset_complement(v0, v6) = v8 & element(v6, v2) = 0 & in(v8, % 56.26/8.39 | v1) = v9 & in(v6, v5) = v7 & $i(v8) & $i(v6) & ( ~ (v9 = 0) | % 56.26/8.39 | ~ (v7 = 0)) & (v9 = 0 | v7 = 0))) & ! [v5: $i] : ( ~ % 56.26/8.39 | (element(v5, v2) = 0) | ~ (element(v4, v3) = 0) | ~ $i(v5) | ? % 56.26/8.39 | [v6: any] : ? [v7: $i] : ? [v8: any] : (subset_complement(v0, % 56.26/8.39 | v5) = v7 & in(v7, v1) = v8 & in(v5, v4) = v6 & $i(v7) & ( ~ % 56.26/8.39 | (v8 = 0) | v6 = 0) & ( ~ (v6 = 0) | v8 = 0))))) % 56.26/8.39 | % 56.26/8.39 | ALPHA: (dt_k2_subset_1) implies: % 56.26/8.39 | (6) ! [v0: $i] : ! [v1: $i] : ( ~ (powerset(v0) = v1) | ~ $i(v0) | ? % 56.26/8.39 | [v2: $i] : (cast_to_subset(v0) = v2 & element(v2, v1) = 0 & $i(v2))) % 56.26/8.39 | (7) ! [v0: $i] : ! [v1: $i] : ( ~ (cast_to_subset(v0) = v1) | ~ $i(v0) | % 56.26/8.39 | ? [v2: $i] : (element(v1, v2) = 0 & powerset(v0) = v2 & $i(v2))) % 56.26/8.39 | % 56.26/8.39 | ALPHA: (dt_k3_subset_1) implies: % 56.26/8.39 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (element(v1, v2) = 0) | % 56.26/8.39 | ~ (powerset(v0) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : % 56.26/8.39 | (subset_complement(v0, v1) = v3 & element(v3, v2) = 0 & $i(v3))) % 56.26/8.39 | % 56.26/8.39 | ALPHA: (dt_k5_setfam_1) implies: % 56.26/8.39 | (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (union_of_subsets(v0, v1) % 56.26/8.39 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : ? [v5: % 56.26/8.39 | any] : ? [v6: any] : (element(v2, v3) = v6 & element(v1, v4) = v5 % 56.26/8.39 | & powerset(v3) = v4 & powerset(v0) = v3 & $i(v4) & $i(v3) & ( ~ (v5 % 56.26/8.39 | = 0) | v6 = 0))) % 56.26/8.39 | (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 56.26/8.39 | (element(v1, v3) = 0) | ~ (powerset(v2) = v3) | ~ (powerset(v0) = % 56.26/8.39 | v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: $i] : (union_of_subsets(v0, % 56.26/8.39 | v1) = v4 & element(v4, v2) = 0 & $i(v4))) % 56.26/8.39 | % 56.26/8.39 | ALPHA: (dt_k6_setfam_1) implies: % 56.26/8.39 | (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (meet_of_subsets(v0, v1) % 56.26/8.39 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : ? % 56.26/8.39 | [v5: any] : ? [v6: any] : (element(v2, v3) = v6 & element(v1, v4) = % 56.26/8.39 | v5 & powerset(v3) = v4 & powerset(v0) = v3 & $i(v4) & $i(v3) & ( ~ % 56.26/8.39 | (v5 = 0) | v6 = 0))) % 56.26/8.39 | (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 56.26/8.39 | (element(v1, v3) = 0) | ~ (powerset(v2) = v3) | ~ (powerset(v0) = % 56.26/8.39 | v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: $i] : (meet_of_subsets(v0, % 56.26/8.39 | v1) = v4 & element(v4, v2) = 0 & $i(v4))) % 56.26/8.39 | % 56.26/8.39 | ALPHA: (dt_k7_setfam_1) implies: % 56.26/8.39 | (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 56.26/8.39 | (complements_of_subsets(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? % 56.26/8.39 | [v3: $i] : ? [v4: $i] : ? [v5: any] : ? [v6: any] : (element(v2, % 56.26/8.39 | v4) = v6 & element(v1, v4) = v5 & powerset(v3) = v4 & % 56.26/8.39 | powerset(v0) = v3 & $i(v4) & $i(v3) & ( ~ (v5 = 0) | v6 = 0))) % 56.26/8.40 | (14) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 56.26/8.40 | (element(v1, v3) = 0) | ~ (powerset(v2) = v3) | ~ (powerset(v0) = % 56.26/8.40 | v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: $i] : % 56.26/8.40 | (complements_of_subsets(v0, v1) = v4 & element(v4, v3) = 0 & % 56.26/8.40 | $i(v4))) % 56.26/8.40 | % 56.26/8.40 | ALPHA: (involutiveness_k3_subset_1) implies: % 56.26/8.40 | (15) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (element(v1, v2) = 0) | % 56.26/8.40 | ~ (powerset(v0) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : % 56.26/8.40 | (subset_complement(v0, v3) = v1 & subset_complement(v0, v1) = v3 & % 56.26/8.40 | $i(v3))) % 56.26/8.40 | % 56.26/8.40 | ALPHA: (involutiveness_k7_setfam_1) implies: % 56.26/8.40 | (16) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 56.26/8.40 | (complements_of_subsets(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? % 56.26/8.40 | [v3: $i] : ? [v4: $i] : ? [v5: any] : ? [v6: $i] : % 56.26/8.40 | (complements_of_subsets(v0, v2) = v6 & element(v1, v4) = v5 & % 56.26/8.40 | powerset(v3) = v4 & powerset(v0) = v3 & $i(v6) & $i(v4) & $i(v3) & % 56.26/8.40 | ( ~ (v5 = 0) | v6 = v1))) % 56.26/8.40 | (17) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 56.26/8.40 | (element(v1, v3) = 0) | ~ (powerset(v2) = v3) | ~ (powerset(v0) = % 56.26/8.40 | v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: $i] : % 56.26/8.40 | (complements_of_subsets(v0, v4) = v1 & complements_of_subsets(v0, % 56.26/8.40 | v1) = v4 & $i(v4))) % 56.26/8.40 | % 56.26/8.40 | ALPHA: (redefinition_k5_setfam_1) implies: % 56.26/8.40 | (18) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (union_of_subsets(v0, % 56.26/8.40 | v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : % 56.26/8.40 | ? [v5: any] : ? [v6: $i] : (union(v1) = v6 & element(v1, v4) = v5 & % 56.26/8.40 | powerset(v3) = v4 & powerset(v0) = v3 & $i(v6) & $i(v4) & $i(v3) & % 56.26/8.40 | ( ~ (v5 = 0) | v6 = v2))) % 56.26/8.40 | (19) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 56.26/8.40 | (element(v1, v3) = 0) | ~ (powerset(v2) = v3) | ~ (powerset(v0) = % 56.26/8.40 | v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: $i] : (union_of_subsets(v0, % 56.26/8.40 | v1) = v4 & union(v1) = v4 & $i(v4))) % 56.26/8.40 | % 56.26/8.40 | ALPHA: (redefinition_k6_setfam_1) implies: % 56.26/8.40 | (20) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (meet_of_subsets(v0, v1) % 56.26/8.40 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : ? % 56.26/8.40 | [v5: any] : ? [v6: $i] : (element(v1, v4) = v5 & powerset(v3) = v4 % 56.26/8.40 | & powerset(v0) = v3 & set_meet(v1) = v6 & $i(v6) & $i(v4) & $i(v3) % 56.26/8.40 | & ( ~ (v5 = 0) | v6 = v2))) % 56.26/8.40 | (21) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 56.26/8.40 | (element(v1, v3) = 0) | ~ (powerset(v2) = v3) | ~ (powerset(v0) = % 56.26/8.40 | v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: $i] : (meet_of_subsets(v0, % 56.26/8.40 | v1) = v4 & set_meet(v1) = v4 & $i(v4))) % 56.26/8.40 | % 56.26/8.40 | ALPHA: (t1_zfmisc_1) implies: % 56.26/8.40 | (22) ? [v0: $i] : (powerset(empty_set) = v0 & singleton(empty_set) = v0 & % 56.26/8.40 | $i(v0)) % 56.26/8.40 | % 56.26/8.40 | ALPHA: (t2_subset) implies: % 56.26/8.40 | (23) ! [v0: $i] : ! [v1: $i] : ( ~ (element(v0, v1) = 0) | ~ $i(v1) | ~ % 56.26/8.40 | $i(v0) | ? [v2: any] : ? [v3: any] : (empty(v1) = v2 & in(v0, v1) % 56.26/8.40 | = v3 & (v3 = 0 | v2 = 0))) % 56.26/8.40 | % 56.26/8.40 | ALPHA: (t43_subset_1) implies: % 56.26/8.40 | (24) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 56.26/8.40 | (element(v3, v2) = 0) | ~ (element(v1, v2) = 0) | ~ (powerset(v0) % 56.26/8.40 | = v2) | ~ $i(v3) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: % 56.26/8.40 | $i] : ? [v6: any] : (disjoint(v1, v3) = v4 & % 56.26/8.40 | subset_complement(v0, v3) = v5 & subset(v1, v5) = v6 & $i(v5) & ( % 56.26/8.40 | ~ (v6 = 0) | v4 = 0) & ( ~ (v4 = 0) | v6 = 0))) % 56.26/8.40 | % 56.26/8.40 | ALPHA: (t46_setfam_1) implies: % 56.26/8.40 | (25) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = % 56.26/8.40 | empty_set | ~ (element(v1, v3) = 0) | ~ (powerset(v2) = v3) | ~ % 56.26/8.40 | (powerset(v0) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: $i] : ( ~ (v4 % 56.26/8.40 | = empty_set) & complements_of_subsets(v0, v1) = v4 & $i(v4))) % 56.26/8.40 | % 56.26/8.40 | ALPHA: (t47_setfam_1) implies: % 56.26/8.40 | (26) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = empty_set | ~ % 56.26/8.40 | (complements_of_subsets(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? % 56.26/8.40 | [v3: $i] : ? [v4: $i] : ? [v5: any] : ? [v6: $i] : ? [v7: $i] : % 56.26/8.40 | ? [v8: $i] : ? [v9: $i] : (subset_difference(v0, v6, v7) = v8 & % 56.26/8.40 | meet_of_subsets(v0, v2) = v9 & union_of_subsets(v0, v1) = v7 & % 56.26/8.40 | cast_to_subset(v0) = v6 & element(v1, v4) = v5 & powerset(v3) = v4 % 56.26/8.40 | & powerset(v0) = v3 & $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v4) & % 56.26/8.40 | $i(v3) & ( ~ (v5 = 0) | v9 = v8))) % 56.26/8.41 | (27) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = empty_set | ~ % 56.26/8.41 | (union_of_subsets(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: % 56.26/8.41 | $i] : ? [v4: $i] : ? [v5: any] : ? [v6: $i] : ? [v7: $i] : ? % 56.26/8.41 | [v8: $i] : ? [v9: $i] : (subset_difference(v0, v6, v2) = v7 & % 56.26/8.41 | meet_of_subsets(v0, v8) = v9 & complements_of_subsets(v0, v1) = v8 % 56.26/8.41 | & cast_to_subset(v0) = v6 & element(v1, v4) = v5 & powerset(v3) = % 56.26/8.41 | v4 & powerset(v0) = v3 & $i(v9) & $i(v8) & $i(v7) & $i(v6) & % 56.26/8.41 | $i(v4) & $i(v3) & ( ~ (v5 = 0) | v9 = v7))) % 56.26/8.41 | (28) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = % 56.26/8.41 | empty_set | ~ (element(v1, v3) = 0) | ~ (powerset(v2) = v3) | ~ % 56.26/8.41 | (powerset(v0) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: $i] : ? [v5: % 56.26/8.41 | $i] : ? [v6: $i] : ? [v7: $i] : (subset_difference(v0, v4, v5) = % 56.26/8.41 | v6 & meet_of_subsets(v0, v7) = v6 & union_of_subsets(v0, v1) = v5 % 56.26/8.41 | & complements_of_subsets(v0, v1) = v7 & cast_to_subset(v0) = v4 & % 56.26/8.41 | $i(v7) & $i(v6) & $i(v5) & $i(v4))) % 56.26/8.41 | % 56.26/8.41 | ALPHA: (t6_boole) implies: % 56.26/8.41 | (29) ! [v0: $i] : (v0 = empty_set | ~ (empty(v0) = 0) | ~ $i(v0)) % 56.26/8.41 | % 56.26/8.41 | ALPHA: (t48_setfam_1) implies: % 56.26/8.41 | (30) $i(empty_set) % 56.26/8.41 | (31) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 56.26/8.41 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ( ~ (v8 = v5) & % 56.26/8.41 | ~ (v1 = empty_set) & subset_difference(v0, v6, v7) = v8 & % 56.26/8.41 | meet_of_subsets(v0, v1) = v7 & union_of_subsets(v0, v4) = v5 & % 56.26/8.41 | complements_of_subsets(v0, v1) = v4 & cast_to_subset(v0) = v6 & % 56.26/8.41 | element(v1, v3) = 0 & powerset(v2) = v3 & powerset(v0) = v2 & $i(v8) % 56.26/8.41 | & $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & % 56.26/8.41 | $i(v0)) % 56.26/8.41 | % 56.26/8.41 | ALPHA: (function-axioms) implies: % 56.26/8.41 | (32) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (powerset(v2) % 56.26/8.41 | = v1) | ~ (powerset(v2) = v0)) % 56.26/8.41 | (33) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 56.26/8.41 | : (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0)) % 56.26/8.41 | (34) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 56.26/8.41 | (cast_to_subset(v2) = v1) | ~ (cast_to_subset(v2) = v0)) % 56.26/8.41 | (35) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (union(v2) = % 56.26/8.41 | v1) | ~ (union(v2) = v0)) % 56.26/8.41 | (36) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 56.26/8.41 | : ! [v3: $i] : (v1 = v0 | ~ (element(v3, v2) = v1) | ~ (element(v3, % 56.26/8.41 | v2) = v0)) % 56.26/8.41 | (37) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 56.26/8.41 | (set_difference(v3, v2) = v1) | ~ (set_difference(v3, v2) = v0)) % 56.26/8.41 | (38) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 56.26/8.41 | (subset_complement(v3, v2) = v1) | ~ (subset_complement(v3, v2) = % 56.26/8.41 | v0)) % 56.26/8.41 | (39) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 56.26/8.41 | (complements_of_subsets(v3, v2) = v1) | ~ % 56.26/8.41 | (complements_of_subsets(v3, v2) = v0)) % 56.26/8.41 | (40) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 56.26/8.41 | (union_of_subsets(v3, v2) = v1) | ~ (union_of_subsets(v3, v2) = % 56.26/8.41 | v0)) % 56.26/8.41 | (41) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 56.26/8.41 | (meet_of_subsets(v3, v2) = v1) | ~ (meet_of_subsets(v3, v2) = v0)) % 56.26/8.41 | (42) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 56.26/8.41 | (v1 = v0 | ~ (subset_difference(v4, v3, v2) = v1) | ~ % 56.26/8.41 | (subset_difference(v4, v3, v2) = v0)) % 56.26/8.41 | % 56.26/8.41 | DELTA: instantiating (22) with fresh symbol all_122_0 gives: % 56.26/8.41 | (43) powerset(empty_set) = all_122_0 & singleton(empty_set) = all_122_0 & % 56.26/8.41 | $i(all_122_0) % 56.26/8.41 | % 56.26/8.41 | ALPHA: (43) implies: % 56.26/8.41 | (44) powerset(empty_set) = all_122_0 % 56.26/8.41 | % 56.26/8.41 | DELTA: instantiating (31) with fresh symbols all_138_0, all_138_1, all_138_2, % 56.26/8.41 | all_138_3, all_138_4, all_138_5, all_138_6, all_138_7, all_138_8 gives: % 56.26/8.41 | (45) ~ (all_138_0 = all_138_3) & ~ (all_138_7 = empty_set) & % 56.26/8.41 | subset_difference(all_138_8, all_138_2, all_138_1) = all_138_0 & % 56.26/8.41 | meet_of_subsets(all_138_8, all_138_7) = all_138_1 & % 56.26/8.41 | union_of_subsets(all_138_8, all_138_4) = all_138_3 & % 56.26/8.41 | complements_of_subsets(all_138_8, all_138_7) = all_138_4 & % 56.26/8.41 | cast_to_subset(all_138_8) = all_138_2 & element(all_138_7, all_138_5) % 56.26/8.41 | = 0 & powerset(all_138_6) = all_138_5 & powerset(all_138_8) = % 56.26/8.41 | all_138_6 & $i(all_138_0) & $i(all_138_1) & $i(all_138_2) & % 56.26/8.41 | $i(all_138_3) & $i(all_138_4) & $i(all_138_5) & $i(all_138_6) & % 56.26/8.41 | $i(all_138_7) & $i(all_138_8) % 56.26/8.41 | % 56.26/8.41 | ALPHA: (45) implies: % 56.26/8.41 | (46) ~ (all_138_7 = empty_set) % 56.26/8.41 | (47) ~ (all_138_0 = all_138_3) % 56.26/8.41 | (48) $i(all_138_8) % 56.26/8.41 | (49) $i(all_138_7) % 56.26/8.41 | (50) $i(all_138_6) % 56.26/8.41 | (51) $i(all_138_5) % 56.26/8.41 | (52) $i(all_138_4) % 56.26/8.41 | (53) $i(all_138_3) % 56.26/8.41 | (54) $i(all_138_2) % 56.26/8.41 | (55) $i(all_138_1) % 56.26/8.42 | (56) powerset(all_138_8) = all_138_6 % 56.26/8.42 | (57) powerset(all_138_6) = all_138_5 % 56.26/8.42 | (58) element(all_138_7, all_138_5) = 0 % 56.26/8.42 | (59) cast_to_subset(all_138_8) = all_138_2 % 56.26/8.42 | (60) complements_of_subsets(all_138_8, all_138_7) = all_138_4 % 56.26/8.42 | (61) union_of_subsets(all_138_8, all_138_4) = all_138_3 % 56.26/8.42 | (62) meet_of_subsets(all_138_8, all_138_7) = all_138_1 % 56.26/8.42 | (63) subset_difference(all_138_8, all_138_2, all_138_1) = all_138_0 % 56.26/8.42 | % 56.26/8.42 | GROUND_INST: instantiating (rc2_subset_1) with empty_set, all_122_0, % 56.26/8.42 | simplifying with (30), (44) gives: % 56.26/8.42 | (64) ? [v0: $i] : (empty(v0) = 0 & element(v0, all_122_0) = 0 & $i(v0)) % 56.26/8.42 | % 56.26/8.42 | GROUND_INST: instantiating (t99_zfmisc_1) with all_138_8, all_138_6, % 56.26/8.42 | simplifying with (48), (56) gives: % 56.26/8.42 | (65) union(all_138_6) = all_138_8 % 56.26/8.42 | % 56.26/8.42 | GROUND_INST: instantiating (6) with all_138_8, all_138_6, simplifying with % 56.26/8.42 | (48), (56) gives: % 56.26/8.42 | (66) ? [v0: $i] : (cast_to_subset(all_138_8) = v0 & element(v0, all_138_6) % 56.26/8.42 | = 0 & $i(v0)) % 56.26/8.42 | % 56.26/8.42 | GROUND_INST: instantiating (rc2_subset_1) with all_138_8, all_138_6, % 56.26/8.42 | simplifying with (48), (56) gives: % 56.26/8.42 | (67) ? [v0: $i] : (empty(v0) = 0 & element(v0, all_138_6) = 0 & $i(v0)) % 56.26/8.42 | % 56.26/8.42 | GROUND_INST: instantiating (fc1_subset_1) with all_138_6, all_138_5, % 56.26/8.42 | simplifying with (50), (57) gives: % 56.26/8.42 | (68) ? [v0: int] : ( ~ (v0 = 0) & empty(all_138_5) = v0) % 56.26/8.42 | % 56.26/8.42 | GROUND_INST: instantiating (6) with all_138_6, all_138_5, simplifying with % 56.26/8.42 | (50), (57) gives: % 56.26/8.42 | (69) ? [v0: $i] : (cast_to_subset(all_138_6) = v0 & element(v0, all_138_5) % 56.26/8.42 | = 0 & $i(v0)) % 56.26/8.42 | % 56.26/8.42 | GROUND_INST: instantiating (rc2_subset_1) with all_138_6, all_138_5, % 56.26/8.42 | simplifying with (50), (57) gives: % 56.26/8.42 | (70) ? [v0: $i] : (empty(v0) = 0 & element(v0, all_138_5) = 0 & $i(v0)) % 56.26/8.42 | % 56.26/8.42 | GROUND_INST: instantiating (24) with all_138_6, all_138_7, all_138_5, % 56.26/8.42 | all_138_7, simplifying with (49), (50), (57), (58) gives: % 56.26/8.42 | (71) ? [v0: any] : ? [v1: $i] : ? [v2: any] : (disjoint(all_138_7, % 56.26/8.42 | all_138_7) = v0 & subset_complement(all_138_6, all_138_7) = v1 & % 56.26/8.42 | subset(all_138_7, v1) = v2 & $i(v1) & ( ~ (v2 = 0) | v0 = 0) & ( ~ % 56.26/8.42 | (v0 = 0) | v2 = 0)) % 56.26/8.42 | % 56.26/8.42 | GROUND_INST: instantiating (28) with all_138_8, all_138_7, all_138_6, % 56.26/8.42 | all_138_5, simplifying with (48), (49), (56), (57), (58) gives: % 56.26/8.42 | (72) all_138_7 = empty_set | ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? % 56.26/8.42 | [v3: $i] : (subset_difference(all_138_8, v0, v1) = v2 & % 56.26/8.42 | meet_of_subsets(all_138_8, v3) = v2 & union_of_subsets(all_138_8, % 56.26/8.42 | all_138_7) = v1 & complements_of_subsets(all_138_8, all_138_7) = % 56.26/8.42 | v3 & cast_to_subset(all_138_8) = v0 & $i(v3) & $i(v2) & $i(v1) & % 56.26/8.42 | $i(v0)) % 56.26/8.42 | % 56.26/8.42 | GROUND_INST: instantiating (25) with all_138_8, all_138_7, all_138_6, % 56.26/8.42 | all_138_5, simplifying with (48), (49), (56), (57), (58) gives: % 56.26/8.42 | (73) all_138_7 = empty_set | ? [v0: $i] : ( ~ (v0 = empty_set) & % 56.26/8.42 | complements_of_subsets(all_138_8, all_138_7) = v0 & $i(v0)) % 56.26/8.42 | % 56.26/8.42 | GROUND_INST: instantiating (12) with all_138_8, all_138_7, all_138_6, % 56.26/8.42 | all_138_5, simplifying with (48), (49), (56), (57), (58) gives: % 56.26/8.42 | (74) ? [v0: $i] : (meet_of_subsets(all_138_8, all_138_7) = v0 & % 56.26/8.42 | element(v0, all_138_6) = 0 & $i(v0)) % 56.26/8.42 | % 56.26/8.42 | GROUND_INST: instantiating (21) with all_138_8, all_138_7, all_138_6, % 56.26/8.42 | all_138_5, simplifying with (48), (49), (56), (57), (58) gives: % 56.26/8.42 | (75) ? [v0: $i] : (meet_of_subsets(all_138_8, all_138_7) = v0 & % 56.26/8.42 | set_meet(all_138_7) = v0 & $i(v0)) % 56.26/8.42 | % 56.26/8.42 | GROUND_INST: instantiating (19) with all_138_8, all_138_7, all_138_6, % 56.26/8.42 | all_138_5, simplifying with (48), (49), (56), (57), (58) gives: % 56.26/8.42 | (76) ? [v0: $i] : (union_of_subsets(all_138_8, all_138_7) = v0 & % 56.26/8.42 | union(all_138_7) = v0 & $i(v0)) % 56.26/8.42 | % 56.26/8.42 | GROUND_INST: instantiating (10) with all_138_8, all_138_7, all_138_6, % 56.26/8.42 | all_138_5, simplifying with (48), (49), (56), (57), (58) gives: % 56.26/8.42 | (77) ? [v0: $i] : (union_of_subsets(all_138_8, all_138_7) = v0 & % 56.26/8.42 | element(v0, all_138_6) = 0 & $i(v0)) % 56.26/8.42 | % 56.26/8.42 | GROUND_INST: instantiating (17) with all_138_8, all_138_7, all_138_6, % 56.26/8.42 | all_138_5, simplifying with (48), (49), (56), (57), (58) gives: % 56.26/8.42 | (78) ? [v0: $i] : (complements_of_subsets(all_138_8, v0) = all_138_7 & % 56.26/8.42 | complements_of_subsets(all_138_8, all_138_7) = v0 & $i(v0)) % 56.26/8.42 | % 56.26/8.42 | GROUND_INST: instantiating (14) with all_138_8, all_138_7, all_138_6, % 56.26/8.42 | all_138_5, simplifying with (48), (49), (56), (57), (58) gives: % 56.26/8.42 | (79) ? [v0: $i] : (complements_of_subsets(all_138_8, all_138_7) = v0 & % 56.26/8.42 | element(v0, all_138_5) = 0 & $i(v0)) % 56.26/8.42 | % 56.26/8.43 | GROUND_INST: instantiating (5) with all_138_8, all_138_7, all_138_6, % 56.26/8.43 | all_138_5, simplifying with (48), (49), (56), (57), (58) gives: % 56.26/8.43 | (80) ? [v0: $i] : (complements_of_subsets(all_138_8, all_138_7) = v0 & % 56.26/8.43 | $i(v0) & ! [v1: $i] : ! [v2: $i] : ( ~ % 56.26/8.43 | (subset_complement(all_138_8, v1) = v2) | ~ (element(v0, % 56.26/8.43 | all_138_5) = 0) | ~ $i(v1) | ? [v3: any] : ? [v4: any] : ? % 56.26/8.43 | [v5: any] : (element(v1, all_138_6) = v3 & in(v2, all_138_7) = v5 % 56.26/8.43 | & in(v1, v0) = v4 & ( ~ (v3 = 0) | (( ~ (v5 = 0) | v4 = 0) & ( ~ % 56.26/8.43 | (v4 = 0) | v5 = 0))))) & ! [v1: $i] : ! [v2: any] : ( ~ % 56.26/8.43 | (element(v0, all_138_5) = 0) | ~ (in(v1, v0) = v2) | ~ $i(v1) | % 56.26/8.43 | ? [v3: any] : ? [v4: $i] : ? [v5: any] : % 56.26/8.43 | (subset_complement(all_138_8, v1) = v4 & element(v1, all_138_6) = % 56.26/8.43 | v3 & in(v4, all_138_7) = v5 & $i(v4) & ( ~ (v3 = 0) | (( ~ (v5 = % 56.26/8.43 | 0) | v2 = 0) & ( ~ (v2 = 0) | v5 = 0))))) & ! [v1: $i] % 56.26/8.43 | : (v1 = v0 | ~ (element(v1, all_138_5) = 0) | ~ $i(v1) | ? [v2: % 56.26/8.43 | $i] : ? [v3: any] : ? [v4: $i] : ? [v5: any] : % 56.26/8.43 | (subset_complement(all_138_8, v2) = v4 & element(v2, all_138_6) = % 56.26/8.43 | 0 & in(v4, all_138_7) = v5 & in(v2, v1) = v3 & $i(v4) & $i(v2) & % 56.26/8.43 | ( ~ (v5 = 0) | ~ (v3 = 0)) & (v5 = 0 | v3 = 0))) & ! [v1: $i] % 56.26/8.43 | : ( ~ (element(v1, all_138_6) = 0) | ~ (element(v0, all_138_5) = 0) % 56.26/8.43 | | ~ $i(v1) | ? [v2: any] : ? [v3: $i] : ? [v4: any] : % 56.26/8.43 | (subset_complement(all_138_8, v1) = v3 & in(v3, all_138_7) = v4 & % 56.26/8.43 | in(v1, v0) = v2 & $i(v3) & ( ~ (v4 = 0) | v2 = 0) & ( ~ (v2 = 0) % 56.26/8.43 | | v4 = 0)))) % 56.26/8.43 | % 56.26/8.43 | GROUND_INST: instantiating (15) with all_138_6, all_138_7, all_138_5, % 56.26/8.43 | simplifying with (49), (50), (57), (58) gives: % 56.26/8.43 | (81) ? [v0: $i] : (subset_complement(all_138_6, v0) = all_138_7 & % 56.26/8.43 | subset_complement(all_138_6, all_138_7) = v0 & $i(v0)) % 56.26/8.43 | % 56.26/8.43 | GROUND_INST: instantiating (2) with all_138_6, all_138_7, all_138_5, % 56.26/8.43 | simplifying with (49), (50), (57), (58) gives: % 56.26/8.43 | (82) ? [v0: $i] : (subset_complement(all_138_6, all_138_7) = v0 & % 56.26/8.43 | set_difference(all_138_6, all_138_7) = v0 & $i(v0)) % 56.26/8.43 | % 56.26/8.43 | GROUND_INST: instantiating (8) with all_138_6, all_138_7, all_138_5, % 56.26/8.43 | simplifying with (49), (50), (57), (58) gives: % 56.26/8.43 | (83) ? [v0: $i] : (subset_complement(all_138_6, all_138_7) = v0 & % 56.26/8.43 | element(v0, all_138_5) = 0 & $i(v0)) % 56.26/8.43 | % 56.26/8.43 | GROUND_INST: instantiating (23) with all_138_7, all_138_5, simplifying with % 56.26/8.43 | (49), (51), (58) gives: % 56.26/8.43 | (84) ? [v0: any] : ? [v1: any] : (empty(all_138_5) = v0 & in(all_138_7, % 56.26/8.43 | all_138_5) = v1 & (v1 = 0 | v0 = 0)) % 56.26/8.43 | % 56.26/8.43 | GROUND_INST: instantiating (1) with all_138_5, all_138_7, 0, simplifying with % 56.26/8.43 | (49), (51), (58) gives: % 56.26/8.43 | (85) ? [v0: any] : ? [v1: any] : (empty(all_138_5) = v0 & % 56.26/8.43 | empty(all_138_7) = v1 & ( ~ (v0 = 0) | v1 = 0)) % 56.26/8.43 | % 56.26/8.43 | GROUND_INST: instantiating (d4_subset_1) with all_138_8, all_138_2, % 56.26/8.43 | simplifying with (48), (59) gives: % 56.26/8.43 | (86) all_138_2 = all_138_8 % 56.26/8.43 | % 56.26/8.43 | GROUND_INST: instantiating (7) with all_138_8, all_138_2, simplifying with % 56.26/8.43 | (48), (59) gives: % 56.26/8.43 | (87) ? [v0: $i] : (element(all_138_2, v0) = 0 & powerset(all_138_8) = v0 & % 56.26/8.43 | $i(v0)) % 56.26/8.43 | % 56.26/8.43 | GROUND_INST: instantiating (26) with all_138_8, all_138_7, all_138_4, % 56.26/8.43 | simplifying with (48), (49), (60) gives: % 56.26/8.43 | (88) all_138_7 = empty_set | ? [v0: $i] : ? [v1: $i] : ? [v2: any] : ? % 56.26/8.43 | [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : % 56.26/8.43 | (subset_difference(all_138_8, v3, v4) = v5 & % 56.26/8.43 | meet_of_subsets(all_138_8, all_138_4) = v6 & % 56.26/8.43 | union_of_subsets(all_138_8, all_138_7) = v4 & % 56.26/8.43 | cast_to_subset(all_138_8) = v3 & element(all_138_7, v1) = v2 & % 56.26/8.43 | powerset(v0) = v1 & powerset(all_138_8) = v0 & $i(v6) & $i(v5) & % 56.26/8.43 | $i(v4) & $i(v3) & $i(v1) & $i(v0) & ( ~ (v2 = 0) | v6 = v5)) % 56.26/8.43 | % 56.26/8.43 | GROUND_INST: instantiating (16) with all_138_8, all_138_7, all_138_4, % 56.26/8.43 | simplifying with (48), (49), (60) gives: % 56.26/8.43 | (89) ? [v0: $i] : ? [v1: $i] : ? [v2: any] : ? [v3: $i] : % 56.26/8.43 | (complements_of_subsets(all_138_8, all_138_4) = v3 & % 56.26/8.43 | element(all_138_7, v1) = v2 & powerset(v0) = v1 & % 56.26/8.43 | powerset(all_138_8) = v0 & $i(v3) & $i(v1) & $i(v0) & ( ~ (v2 = 0) | % 56.26/8.43 | v3 = all_138_7)) % 56.26/8.43 | % 56.26/8.43 | GROUND_INST: instantiating (13) with all_138_8, all_138_7, all_138_4, % 56.26/8.43 | simplifying with (48), (49), (60) gives: % 56.26/8.43 | (90) ? [v0: $i] : ? [v1: $i] : ? [v2: any] : ? [v3: any] : % 56.26/8.43 | (element(all_138_4, v1) = v3 & element(all_138_7, v1) = v2 & % 56.26/8.43 | powerset(v0) = v1 & powerset(all_138_8) = v0 & $i(v1) & $i(v0) & ( ~ % 56.26/8.43 | (v2 = 0) | v3 = 0)) % 56.26/8.43 | % 56.26/8.43 | GROUND_INST: instantiating (4) with all_138_8, all_138_7, all_138_4, % 56.26/8.43 | simplifying with (48), (49), (60) gives: % 56.26/8.44 | (91) ? [v0: $i] : ? [v1: $i] : ? [v2: any] : (element(all_138_7, v1) = % 56.26/8.44 | v2 & powerset(v0) = v1 & powerset(all_138_8) = v0 & $i(v1) & $i(v0) % 56.26/8.44 | & ( ~ (v2 = 0) | ( ! [v3: $i] : ! [v4: $i] : ( ~ % 56.26/8.44 | (subset_complement(all_138_8, v3) = v4) | ~ % 56.26/8.44 | (element(all_138_4, v1) = 0) | ~ $i(v3) | ~ $i(all_138_4) | % 56.26/8.44 | ? [v5: any] : ? [v6: any] : ? [v7: any] : (element(v3, v0) = % 56.26/8.44 | v5 & in(v4, all_138_7) = v7 & in(v3, all_138_4) = v6 & ( ~ % 56.26/8.44 | (v5 = 0) | (( ~ (v7 = 0) | v6 = 0) & ( ~ (v6 = 0) | v7 = % 56.26/8.44 | 0))))) & ! [v3: $i] : ! [v4: any] : ( ~ % 56.26/8.44 | (element(all_138_4, v1) = 0) | ~ (in(v3, all_138_4) = v4) | % 56.26/8.44 | ~ $i(v3) | ~ $i(all_138_4) | ? [v5: any] : ? [v6: $i] : ? % 56.26/8.44 | [v7: any] : (subset_complement(all_138_8, v3) = v6 & % 56.26/8.44 | element(v3, v0) = v5 & in(v6, all_138_7) = v7 & $i(v6) & ( ~ % 56.26/8.44 | (v5 = 0) | (( ~ (v7 = 0) | v4 = 0) & ( ~ (v4 = 0) | v7 = % 56.26/8.44 | 0))))) & ! [v3: any] : (v3 = all_138_4 | ~ % 56.26/8.44 | (element(v3, v1) = 0) | ~ $i(v3) | ? [v4: $i] : ? [v5: any] % 56.26/8.44 | : ? [v6: $i] : ? [v7: any] : (subset_complement(all_138_8, % 56.26/8.44 | v4) = v6 & element(v4, v0) = 0 & in(v6, all_138_7) = v7 & % 56.26/8.44 | in(v4, v3) = v5 & $i(v6) & $i(v4) & ( ~ (v7 = 0) | ~ (v5 = % 56.26/8.44 | 0)) & (v7 = 0 | v5 = 0))) & ! [v3: $i] : ( ~ % 56.26/8.44 | (element(v3, v0) = 0) | ~ (element(all_138_4, v1) = 0) | ~ % 56.26/8.44 | $i(v3) | ~ $i(all_138_4) | ? [v4: any] : ? [v5: $i] : ? % 56.26/8.44 | [v6: any] : (subset_complement(all_138_8, v3) = v5 & in(v5, % 56.26/8.44 | all_138_7) = v6 & in(v3, all_138_4) = v4 & $i(v5) & ( ~ % 56.26/8.44 | (v6 = 0) | v4 = 0) & ( ~ (v4 = 0) | v6 = 0)))))) % 56.26/8.44 | % 56.26/8.44 | GROUND_INST: instantiating (27) with all_138_8, all_138_4, all_138_3, % 56.26/8.44 | simplifying with (48), (52), (61) gives: % 56.26/8.44 | (92) all_138_4 = empty_set | ? [v0: $i] : ? [v1: $i] : ? [v2: any] : ? % 56.26/8.44 | [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : % 56.26/8.44 | (subset_difference(all_138_8, v3, all_138_3) = v4 & % 56.26/8.44 | meet_of_subsets(all_138_8, v5) = v6 & % 56.26/8.44 | complements_of_subsets(all_138_8, all_138_4) = v5 & % 56.26/8.44 | cast_to_subset(all_138_8) = v3 & element(all_138_4, v1) = v2 & % 56.26/8.44 | powerset(v0) = v1 & powerset(all_138_8) = v0 & $i(v6) & $i(v5) & % 56.26/8.44 | $i(v4) & $i(v3) & $i(v1) & $i(v0) & ( ~ (v2 = 0) | v6 = v4)) % 56.26/8.44 | % 56.26/8.44 | GROUND_INST: instantiating (18) with all_138_8, all_138_4, all_138_3, % 56.26/8.44 | simplifying with (48), (52), (61) gives: % 56.26/8.44 | (93) ? [v0: $i] : ? [v1: $i] : ? [v2: any] : ? [v3: $i] : % 56.26/8.44 | (union(all_138_4) = v3 & element(all_138_4, v1) = v2 & powerset(v0) = % 56.26/8.44 | v1 & powerset(all_138_8) = v0 & $i(v3) & $i(v1) & $i(v0) & ( ~ (v2 = % 56.26/8.44 | 0) | v3 = all_138_3)) % 56.26/8.44 | % 56.26/8.44 | GROUND_INST: instantiating (9) with all_138_8, all_138_4, all_138_3, % 56.26/8.44 | simplifying with (48), (52), (61) gives: % 56.26/8.44 | (94) ? [v0: $i] : ? [v1: $i] : ? [v2: any] : ? [v3: any] : % 56.26/8.44 | (element(all_138_3, v0) = v3 & element(all_138_4, v1) = v2 & % 56.26/8.44 | powerset(v0) = v1 & powerset(all_138_8) = v0 & $i(v1) & $i(v0) & ( ~ % 56.26/8.44 | (v2 = 0) | v3 = 0)) % 56.26/8.44 | % 56.26/8.44 | GROUND_INST: instantiating (11) with all_138_8, all_138_7, all_138_1, % 56.26/8.44 | simplifying with (48), (49), (62) gives: % 56.26/8.44 | (95) ? [v0: $i] : ? [v1: $i] : ? [v2: any] : ? [v3: any] : % 56.26/8.44 | (element(all_138_1, v0) = v3 & element(all_138_7, v1) = v2 & % 56.26/8.44 | powerset(v0) = v1 & powerset(all_138_8) = v0 & $i(v1) & $i(v0) & ( ~ % 56.26/8.44 | (v2 = 0) | v3 = 0)) % 56.26/8.44 | % 56.26/8.44 | GROUND_INST: instantiating (20) with all_138_8, all_138_7, all_138_1, % 56.26/8.44 | simplifying with (48), (49), (62) gives: % 56.26/8.44 | (96) ? [v0: $i] : ? [v1: $i] : ? [v2: any] : ? [v3: $i] : % 56.26/8.44 | (element(all_138_7, v1) = v2 & powerset(v0) = v1 & powerset(all_138_8) % 56.26/8.44 | = v0 & set_meet(all_138_7) = v3 & $i(v3) & $i(v1) & $i(v0) & ( ~ (v2 % 56.26/8.44 | = 0) | v3 = all_138_1)) % 56.26/8.44 | % 56.26/8.44 | GROUND_INST: instantiating (redefinition_k6_subset_1) with all_138_8, % 56.26/8.44 | all_138_2, all_138_1, all_138_0, simplifying with (48), (54), % 56.26/8.44 | (55), (63) gives: % 56.26/8.44 | (97) ? [v0: $i] : ? [v1: any] : ? [v2: any] : ? [v3: $i] : % 56.26/8.44 | (set_difference(all_138_2, all_138_1) = v3 & element(all_138_1, v0) = % 56.26/8.44 | v2 & element(all_138_2, v0) = v1 & powerset(all_138_8) = v0 & $i(v3) % 56.26/8.44 | & $i(v0) & ( ~ (v2 = 0) | ~ (v1 = 0) | v3 = all_138_0)) % 56.26/8.44 | % 56.26/8.44 | GROUND_INST: instantiating (dt_k6_subset_1) with all_138_8, all_138_2, % 56.26/8.44 | all_138_1, all_138_0, simplifying with (48), (54), (55), (63) % 56.26/8.44 | gives: % 56.26/8.44 | (98) ? [v0: $i] : ? [v1: any] : ? [v2: any] : ? [v3: any] : % 56.26/8.44 | (element(all_138_0, v0) = v3 & element(all_138_1, v0) = v2 & % 56.26/8.44 | element(all_138_2, v0) = v1 & powerset(all_138_8) = v0 & $i(v0) & ( % 56.26/8.44 | ~ (v2 = 0) | ~ (v1 = 0) | v3 = 0)) % 56.26/8.44 | % 56.26/8.44 | DELTA: instantiating (68) with fresh symbol all_158_0 gives: % 56.26/8.44 | (99) ~ (all_158_0 = 0) & empty(all_138_5) = all_158_0 % 56.26/8.44 | % 56.26/8.44 | ALPHA: (99) implies: % 56.26/8.44 | (100) ~ (all_158_0 = 0) % 56.26/8.44 | (101) empty(all_138_5) = all_158_0 % 56.26/8.44 | % 56.26/8.44 | DELTA: instantiating (87) with fresh symbol all_160_0 gives: % 56.26/8.44 | (102) element(all_138_2, all_160_0) = 0 & powerset(all_138_8) = all_160_0 & % 56.26/8.44 | $i(all_160_0) % 56.26/8.44 | % 56.26/8.44 | ALPHA: (102) implies: % 56.26/8.44 | (103) powerset(all_138_8) = all_160_0 % 56.26/8.44 | (104) element(all_138_2, all_160_0) = 0 % 56.26/8.44 | % 56.26/8.44 | DELTA: instantiating (70) with fresh symbol all_162_0 gives: % 56.26/8.44 | (105) empty(all_162_0) = 0 & element(all_162_0, all_138_5) = 0 & % 56.26/8.44 | $i(all_162_0) % 56.26/8.44 | % 56.26/8.44 | ALPHA: (105) implies: % 56.26/8.44 | (106) $i(all_162_0) % 56.26/8.44 | (107) element(all_162_0, all_138_5) = 0 % 56.26/8.44 | (108) empty(all_162_0) = 0 % 56.26/8.44 | % 56.26/8.44 | DELTA: instantiating (67) with fresh symbol all_164_0 gives: % 56.26/8.44 | (109) empty(all_164_0) = 0 & element(all_164_0, all_138_6) = 0 & % 56.26/8.44 | $i(all_164_0) % 56.26/8.44 | % 56.26/8.44 | ALPHA: (109) implies: % 56.26/8.44 | (110) $i(all_164_0) % 56.26/8.44 | (111) element(all_164_0, all_138_6) = 0 % 56.26/8.44 | (112) empty(all_164_0) = 0 % 56.26/8.44 | % 56.26/8.44 | DELTA: instantiating (66) with fresh symbol all_166_0 gives: % 56.26/8.45 | (113) cast_to_subset(all_138_8) = all_166_0 & element(all_166_0, all_138_6) % 56.26/8.45 | = 0 & $i(all_166_0) % 56.26/8.45 | % 56.26/8.45 | ALPHA: (113) implies: % 56.26/8.45 | (114) cast_to_subset(all_138_8) = all_166_0 % 56.26/8.45 | % 56.26/8.45 | DELTA: instantiating (69) with fresh symbol all_168_0 gives: % 56.26/8.45 | (115) cast_to_subset(all_138_6) = all_168_0 & element(all_168_0, all_138_5) % 56.26/8.45 | = 0 & $i(all_168_0) % 56.26/8.45 | % 56.26/8.45 | ALPHA: (115) implies: % 56.26/8.45 | (116) $i(all_168_0) % 56.26/8.45 | (117) element(all_168_0, all_138_5) = 0 % 56.26/8.45 | (118) cast_to_subset(all_138_6) = all_168_0 % 56.26/8.45 | % 56.26/8.45 | DELTA: instantiating (74) with fresh symbol all_170_0 gives: % 56.26/8.45 | (119) meet_of_subsets(all_138_8, all_138_7) = all_170_0 & % 56.26/8.45 | element(all_170_0, all_138_6) = 0 & $i(all_170_0) % 56.26/8.45 | % 56.26/8.45 | ALPHA: (119) implies: % 56.26/8.45 | (120) element(all_170_0, all_138_6) = 0 % 56.26/8.45 | (121) meet_of_subsets(all_138_8, all_138_7) = all_170_0 % 56.26/8.45 | % 56.26/8.45 | DELTA: instantiating (81) with fresh symbol all_172_0 gives: % 56.26/8.45 | (122) subset_complement(all_138_6, all_172_0) = all_138_7 & % 56.26/8.45 | subset_complement(all_138_6, all_138_7) = all_172_0 & $i(all_172_0) % 56.26/8.45 | % 56.26/8.45 | ALPHA: (122) implies: % 56.26/8.45 | (123) subset_complement(all_138_6, all_138_7) = all_172_0 % 56.26/8.45 | % 56.26/8.45 | DELTA: instantiating (78) with fresh symbol all_174_0 gives: % 56.26/8.45 | (124) complements_of_subsets(all_138_8, all_174_0) = all_138_7 & % 56.26/8.45 | complements_of_subsets(all_138_8, all_138_7) = all_174_0 & % 56.26/8.45 | $i(all_174_0) % 56.26/8.45 | % 56.26/8.45 | ALPHA: (124) implies: % 56.26/8.45 | (125) $i(all_174_0) % 56.26/8.45 | (126) complements_of_subsets(all_138_8, all_138_7) = all_174_0 % 56.26/8.45 | (127) complements_of_subsets(all_138_8, all_174_0) = all_138_7 % 56.26/8.45 | % 56.26/8.45 | DELTA: instantiating (76) with fresh symbol all_176_0 gives: % 56.26/8.45 | (128) union_of_subsets(all_138_8, all_138_7) = all_176_0 & union(all_138_7) % 56.26/8.45 | = all_176_0 & $i(all_176_0) % 56.26/8.45 | % 56.26/8.45 | ALPHA: (128) implies: % 56.26/8.45 | (129) union_of_subsets(all_138_8, all_138_7) = all_176_0 % 56.26/8.45 | % 56.26/8.45 | DELTA: instantiating (77) with fresh symbol all_178_0 gives: % 56.26/8.45 | (130) union_of_subsets(all_138_8, all_138_7) = all_178_0 & % 56.26/8.45 | element(all_178_0, all_138_6) = 0 & $i(all_178_0) % 56.26/8.45 | % 56.26/8.45 | ALPHA: (130) implies: % 56.26/8.45 | (131) $i(all_178_0) % 56.26/8.45 | (132) element(all_178_0, all_138_6) = 0 % 56.26/8.45 | (133) union_of_subsets(all_138_8, all_138_7) = all_178_0 % 56.26/8.45 | % 56.26/8.45 | DELTA: instantiating (75) with fresh symbol all_180_0 gives: % 56.26/8.45 | (134) meet_of_subsets(all_138_8, all_138_7) = all_180_0 & % 56.26/8.45 | set_meet(all_138_7) = all_180_0 & $i(all_180_0) % 56.26/8.45 | % 56.26/8.45 | ALPHA: (134) implies: % 56.26/8.45 | (135) meet_of_subsets(all_138_8, all_138_7) = all_180_0 % 56.26/8.45 | % 56.26/8.45 | DELTA: instantiating (79) with fresh symbol all_182_0 gives: % 56.26/8.45 | (136) complements_of_subsets(all_138_8, all_138_7) = all_182_0 & % 56.26/8.45 | element(all_182_0, all_138_5) = 0 & $i(all_182_0) % 56.26/8.45 | % 56.26/8.45 | ALPHA: (136) implies: % 56.26/8.45 | (137) element(all_182_0, all_138_5) = 0 % 56.26/8.45 | (138) complements_of_subsets(all_138_8, all_138_7) = all_182_0 % 56.26/8.45 | % 56.26/8.45 | DELTA: instantiating (83) with fresh symbol all_184_0 gives: % 56.26/8.45 | (139) subset_complement(all_138_6, all_138_7) = all_184_0 & % 56.26/8.45 | element(all_184_0, all_138_5) = 0 & $i(all_184_0) % 56.26/8.45 | % 56.26/8.45 | ALPHA: (139) implies: % 56.26/8.45 | (140) $i(all_184_0) % 56.26/8.45 | (141) element(all_184_0, all_138_5) = 0 % 56.26/8.45 | (142) subset_complement(all_138_6, all_138_7) = all_184_0 % 56.26/8.45 | % 56.26/8.45 | DELTA: instantiating (82) with fresh symbol all_186_0 gives: % 56.26/8.45 | (143) subset_complement(all_138_6, all_138_7) = all_186_0 & % 56.26/8.45 | set_difference(all_138_6, all_138_7) = all_186_0 & $i(all_186_0) % 56.26/8.45 | % 56.26/8.45 | ALPHA: (143) implies: % 56.26/8.45 | (144) subset_complement(all_138_6, all_138_7) = all_186_0 % 56.26/8.45 | % 56.26/8.45 | DELTA: instantiating (64) with fresh symbol all_188_0 gives: % 56.26/8.45 | (145) empty(all_188_0) = 0 & element(all_188_0, all_122_0) = 0 & % 56.26/8.45 | $i(all_188_0) % 56.26/8.45 | % 56.26/8.45 | ALPHA: (145) implies: % 56.26/8.45 | (146) $i(all_188_0) % 56.26/8.45 | (147) empty(all_188_0) = 0 % 56.26/8.45 | % 56.26/8.45 | DELTA: instantiating (85) with fresh symbols all_192_0, all_192_1 gives: % 56.26/8.45 | (148) empty(all_138_5) = all_192_1 & empty(all_138_7) = all_192_0 & ( ~ % 56.26/8.45 | (all_192_1 = 0) | all_192_0 = 0) % 56.26/8.45 | % 56.26/8.45 | ALPHA: (148) implies: % 56.26/8.45 | (149) empty(all_138_5) = all_192_1 % 56.26/8.45 | % 56.26/8.45 | DELTA: instantiating (84) with fresh symbols all_194_0, all_194_1 gives: % 56.26/8.45 | (150) empty(all_138_5) = all_194_1 & in(all_138_7, all_138_5) = all_194_0 & % 56.26/8.45 | (all_194_0 = 0 | all_194_1 = 0) % 56.26/8.45 | % 56.26/8.45 | ALPHA: (150) implies: % 56.26/8.45 | (151) empty(all_138_5) = all_194_1 % 56.26/8.45 | % 56.26/8.45 | DELTA: instantiating (98) with fresh symbols all_202_0, all_202_1, all_202_2, % 56.26/8.45 | all_202_3 gives: % 56.26/8.45 | (152) element(all_138_0, all_202_3) = all_202_0 & element(all_138_1, % 56.26/8.45 | all_202_3) = all_202_1 & element(all_138_2, all_202_3) = all_202_2 % 56.26/8.45 | & powerset(all_138_8) = all_202_3 & $i(all_202_3) & ( ~ (all_202_1 = % 56.26/8.45 | 0) | ~ (all_202_2 = 0) | all_202_0 = 0) % 56.26/8.45 | % 56.26/8.45 | ALPHA: (152) implies: % 56.26/8.45 | (153) powerset(all_138_8) = all_202_3 % 56.26/8.45 | (154) element(all_138_2, all_202_3) = all_202_2 % 56.26/8.45 | (155) element(all_138_1, all_202_3) = all_202_1 % 56.26/8.45 | (156) element(all_138_0, all_202_3) = all_202_0 % 56.26/8.45 | (157) ~ (all_202_1 = 0) | ~ (all_202_2 = 0) | all_202_0 = 0 % 56.26/8.45 | % 56.26/8.45 | DELTA: instantiating (90) with fresh symbols all_204_0, all_204_1, all_204_2, % 56.26/8.45 | all_204_3 gives: % 56.26/8.45 | (158) element(all_138_4, all_204_2) = all_204_0 & element(all_138_7, % 56.26/8.45 | all_204_2) = all_204_1 & powerset(all_204_3) = all_204_2 & % 56.26/8.45 | powerset(all_138_8) = all_204_3 & $i(all_204_2) & $i(all_204_3) & ( ~ % 56.26/8.45 | (all_204_1 = 0) | all_204_0 = 0) % 56.26/8.45 | % 56.26/8.45 | ALPHA: (158) implies: % 56.26/8.45 | (159) powerset(all_138_8) = all_204_3 % 56.26/8.45 | (160) powerset(all_204_3) = all_204_2 % 56.26/8.45 | (161) element(all_138_4, all_204_2) = all_204_0 % 56.26/8.45 | % 56.26/8.45 | DELTA: instantiating (94) with fresh symbols all_206_0, all_206_1, all_206_2, % 56.26/8.45 | all_206_3 gives: % 56.26/8.45 | (162) element(all_138_3, all_206_3) = all_206_0 & element(all_138_4, % 56.26/8.45 | all_206_2) = all_206_1 & powerset(all_206_3) = all_206_2 & % 56.26/8.45 | powerset(all_138_8) = all_206_3 & $i(all_206_2) & $i(all_206_3) & ( ~ % 56.26/8.45 | (all_206_1 = 0) | all_206_0 = 0) % 56.26/8.45 | % 56.26/8.45 | ALPHA: (162) implies: % 56.26/8.45 | (163) powerset(all_138_8) = all_206_3 % 56.26/8.45 | (164) powerset(all_206_3) = all_206_2 % 56.26/8.45 | (165) element(all_138_4, all_206_2) = all_206_1 % 56.26/8.45 | (166) element(all_138_3, all_206_3) = all_206_0 % 56.26/8.45 | (167) ~ (all_206_1 = 0) | all_206_0 = 0 % 56.26/8.45 | % 56.26/8.45 | DELTA: instantiating (71) with fresh symbols all_208_0, all_208_1, all_208_2 % 56.26/8.45 | gives: % 56.26/8.45 | (168) disjoint(all_138_7, all_138_7) = all_208_2 & % 56.26/8.45 | subset_complement(all_138_6, all_138_7) = all_208_1 & % 56.26/8.45 | subset(all_138_7, all_208_1) = all_208_0 & $i(all_208_1) & ( ~ % 56.26/8.45 | (all_208_0 = 0) | all_208_2 = 0) & ( ~ (all_208_2 = 0) | all_208_0 % 56.26/8.45 | = 0) % 56.26/8.45 | % 56.26/8.45 | ALPHA: (168) implies: % 56.26/8.45 | (169) subset_complement(all_138_6, all_138_7) = all_208_1 % 56.26/8.45 | % 56.26/8.45 | DELTA: instantiating (95) with fresh symbols all_210_0, all_210_1, all_210_2, % 56.26/8.45 | all_210_3 gives: % 56.26/8.46 | (170) element(all_138_1, all_210_3) = all_210_0 & element(all_138_7, % 56.26/8.46 | all_210_2) = all_210_1 & powerset(all_210_3) = all_210_2 & % 56.26/8.46 | powerset(all_138_8) = all_210_3 & $i(all_210_2) & $i(all_210_3) & ( ~ % 56.26/8.46 | (all_210_1 = 0) | all_210_0 = 0) % 56.26/8.46 | % 56.26/8.46 | ALPHA: (170) implies: % 56.26/8.46 | (171) powerset(all_138_8) = all_210_3 % 56.26/8.46 | (172) powerset(all_210_3) = all_210_2 % 56.26/8.46 | (173) element(all_138_1, all_210_3) = all_210_0 % 56.26/8.46 | % 56.26/8.46 | DELTA: instantiating (97) with fresh symbols all_212_0, all_212_1, all_212_2, % 56.26/8.46 | all_212_3 gives: % 56.26/8.46 | (174) set_difference(all_138_2, all_138_1) = all_212_0 & element(all_138_1, % 56.26/8.46 | all_212_3) = all_212_1 & element(all_138_2, all_212_3) = all_212_2 % 56.26/8.46 | & powerset(all_138_8) = all_212_3 & $i(all_212_0) & $i(all_212_3) & ( % 56.26/8.46 | ~ (all_212_1 = 0) | ~ (all_212_2 = 0) | all_212_0 = all_138_0) % 56.26/8.46 | % 56.26/8.46 | ALPHA: (174) implies: % 56.26/8.46 | (175) $i(all_212_0) % 56.26/8.46 | (176) powerset(all_138_8) = all_212_3 % 56.26/8.46 | (177) element(all_138_2, all_212_3) = all_212_2 % 56.26/8.46 | (178) element(all_138_1, all_212_3) = all_212_1 % 56.26/8.46 | (179) set_difference(all_138_2, all_138_1) = all_212_0 % 56.26/8.46 | (180) ~ (all_212_1 = 0) | ~ (all_212_2 = 0) | all_212_0 = all_138_0 % 56.26/8.46 | % 56.26/8.46 | DELTA: instantiating (93) with fresh symbols all_214_0, all_214_1, all_214_2, % 56.26/8.46 | all_214_3 gives: % 56.26/8.46 | (181) union(all_138_4) = all_214_0 & element(all_138_4, all_214_2) = % 56.26/8.46 | all_214_1 & powerset(all_214_3) = all_214_2 & powerset(all_138_8) = % 56.26/8.46 | all_214_3 & $i(all_214_0) & $i(all_214_2) & $i(all_214_3) & ( ~ % 56.26/8.46 | (all_214_1 = 0) | all_214_0 = all_138_3) % 56.26/8.46 | % 56.26/8.46 | ALPHA: (181) implies: % 56.26/8.46 | (182) powerset(all_138_8) = all_214_3 % 56.26/8.46 | (183) powerset(all_214_3) = all_214_2 % 56.26/8.46 | (184) element(all_138_4, all_214_2) = all_214_1 % 56.26/8.46 | % 56.26/8.46 | DELTA: instantiating (89) with fresh symbols all_216_0, all_216_1, all_216_2, % 56.26/8.46 | all_216_3 gives: % 56.26/8.46 | (185) complements_of_subsets(all_138_8, all_138_4) = all_216_0 & % 56.26/8.46 | element(all_138_7, all_216_2) = all_216_1 & powerset(all_216_3) = % 56.26/8.46 | all_216_2 & powerset(all_138_8) = all_216_3 & $i(all_216_0) & % 56.26/8.46 | $i(all_216_2) & $i(all_216_3) & ( ~ (all_216_1 = 0) | all_216_0 = % 56.26/8.46 | all_138_7) % 56.26/8.46 | % 56.26/8.46 | ALPHA: (185) implies: % 56.26/8.46 | (186) powerset(all_138_8) = all_216_3 % 56.26/8.46 | (187) powerset(all_216_3) = all_216_2 % 56.26/8.46 | (188) complements_of_subsets(all_138_8, all_138_4) = all_216_0 % 56.26/8.46 | % 56.26/8.46 | DELTA: instantiating (96) with fresh symbols all_218_0, all_218_1, all_218_2, % 56.26/8.46 | all_218_3 gives: % 56.26/8.46 | (189) element(all_138_7, all_218_2) = all_218_1 & powerset(all_218_3) = % 56.26/8.46 | all_218_2 & powerset(all_138_8) = all_218_3 & set_meet(all_138_7) = % 56.26/8.46 | all_218_0 & $i(all_218_0) & $i(all_218_2) & $i(all_218_3) & ( ~ % 56.26/8.46 | (all_218_1 = 0) | all_218_0 = all_138_1) % 56.26/8.46 | % 56.26/8.46 | ALPHA: (189) implies: % 56.26/8.46 | (190) powerset(all_138_8) = all_218_3 % 56.26/8.46 | (191) powerset(all_218_3) = all_218_2 % 56.26/8.46 | % 56.26/8.46 | DELTA: instantiating (80) with fresh symbol all_220_0 gives: % 56.26/8.46 | (192) complements_of_subsets(all_138_8, all_138_7) = all_220_0 & % 56.26/8.46 | $i(all_220_0) & ! [v0: $i] : ! [v1: $i] : ( ~ % 56.26/8.46 | (subset_complement(all_138_8, v0) = v1) | ~ (element(all_220_0, % 56.26/8.46 | all_138_5) = 0) | ~ $i(v0) | ? [v2: any] : ? [v3: any] : ? % 56.26/8.46 | [v4: any] : (element(v0, all_138_6) = v2 & in(v1, all_138_7) = v4 & % 56.26/8.46 | in(v0, all_220_0) = v3 & ( ~ (v2 = 0) | (( ~ (v4 = 0) | v3 = 0) & % 56.26/8.46 | ( ~ (v3 = 0) | v4 = 0))))) & ! [v0: $i] : ! [v1: any] : ( ~ % 56.26/8.46 | (element(all_220_0, all_138_5) = 0) | ~ (in(v0, all_220_0) = v1) | % 56.26/8.46 | ~ $i(v0) | ? [v2: any] : ? [v3: $i] : ? [v4: any] : % 56.26/8.46 | (subset_complement(all_138_8, v0) = v3 & element(v0, all_138_6) = % 56.26/8.46 | v2 & in(v3, all_138_7) = v4 & $i(v3) & ( ~ (v2 = 0) | (( ~ (v4 = % 56.26/8.46 | 0) | v1 = 0) & ( ~ (v1 = 0) | v4 = 0))))) & ! [v0: any] % 56.26/8.46 | : (v0 = all_220_0 | ~ (element(v0, all_138_5) = 0) | ~ $i(v0) | ? % 56.26/8.46 | [v1: $i] : ? [v2: any] : ? [v3: $i] : ? [v4: any] : % 56.26/8.46 | (subset_complement(all_138_8, v1) = v3 & element(v1, all_138_6) = 0 % 56.26/8.46 | & in(v3, all_138_7) = v4 & in(v1, v0) = v2 & $i(v3) & $i(v1) & ( % 56.26/8.46 | ~ (v4 = 0) | ~ (v2 = 0)) & (v4 = 0 | v2 = 0))) & ! [v0: $i] : % 56.26/8.46 | ( ~ (element(v0, all_138_6) = 0) | ~ (element(all_220_0, all_138_5) % 56.26/8.46 | = 0) | ~ $i(v0) | ? [v1: any] : ? [v2: $i] : ? [v3: any] : % 56.26/8.46 | (subset_complement(all_138_8, v0) = v2 & in(v2, all_138_7) = v3 & % 56.26/8.46 | in(v0, all_220_0) = v1 & $i(v2) & ( ~ (v3 = 0) | v1 = 0) & ( ~ % 56.26/8.46 | (v1 = 0) | v3 = 0))) % 56.26/8.46 | % 56.26/8.46 | ALPHA: (192) implies: % 56.26/8.46 | (193) complements_of_subsets(all_138_8, all_138_7) = all_220_0 % 56.26/8.46 | (194) ! [v0: any] : (v0 = all_220_0 | ~ (element(v0, all_138_5) = 0) | ~ % 56.26/8.46 | $i(v0) | ? [v1: $i] : ? [v2: any] : ? [v3: $i] : ? [v4: any] : % 56.26/8.46 | (subset_complement(all_138_8, v1) = v3 & element(v1, all_138_6) = 0 % 56.26/8.46 | & in(v3, all_138_7) = v4 & in(v1, v0) = v2 & $i(v3) & $i(v1) & ( % 56.26/8.46 | ~ (v4 = 0) | ~ (v2 = 0)) & (v4 = 0 | v2 = 0))) % 56.26/8.46 | % 56.26/8.46 | DELTA: instantiating (91) with fresh symbols all_223_0, all_223_1, all_223_2 % 56.26/8.46 | gives: % 56.26/8.47 | (195) element(all_138_7, all_223_1) = all_223_0 & powerset(all_223_2) = % 56.26/8.47 | all_223_1 & powerset(all_138_8) = all_223_2 & $i(all_223_1) & % 56.26/8.47 | $i(all_223_2) & ( ~ (all_223_0 = 0) | ( ! [v0: $i] : ! [v1: $i] : ( % 56.26/8.47 | ~ (subset_complement(all_138_8, v0) = v1) | ~ % 56.26/8.47 | (element(all_138_4, all_223_1) = 0) | ~ $i(v0) | ~ % 56.26/8.47 | $i(all_138_4) | ? [v2: any] : ? [v3: any] : ? [v4: any] : % 56.26/8.47 | (element(v0, all_223_2) = v2 & in(v1, all_138_7) = v4 & in(v0, % 56.26/8.47 | all_138_4) = v3 & ( ~ (v2 = 0) | (( ~ (v4 = 0) | v3 = 0) & % 56.26/8.47 | ( ~ (v3 = 0) | v4 = 0))))) & ! [v0: $i] : ! [v1: any] : % 56.26/8.47 | ( ~ (element(all_138_4, all_223_1) = 0) | ~ (in(v0, all_138_4) = % 56.26/8.47 | v1) | ~ $i(v0) | ~ $i(all_138_4) | ? [v2: any] : ? [v3: % 56.26/8.47 | $i] : ? [v4: any] : (subset_complement(all_138_8, v0) = v3 & % 56.26/8.47 | element(v0, all_223_2) = v2 & in(v3, all_138_7) = v4 & $i(v3) % 56.26/8.47 | & ( ~ (v2 = 0) | (( ~ (v4 = 0) | v1 = 0) & ( ~ (v1 = 0) | v4 % 56.26/8.47 | = 0))))) & ! [v0: any] : (v0 = all_138_4 | ~ % 56.26/8.47 | (element(v0, all_223_1) = 0) | ~ $i(v0) | ? [v1: $i] : ? % 56.26/8.47 | [v2: any] : ? [v3: $i] : ? [v4: any] : % 56.26/8.47 | (subset_complement(all_138_8, v1) = v3 & element(v1, all_223_2) % 56.26/8.47 | = 0 & in(v3, all_138_7) = v4 & in(v1, v0) = v2 & $i(v3) & % 56.26/8.47 | $i(v1) & ( ~ (v4 = 0) | ~ (v2 = 0)) & (v4 = 0 | v2 = 0))) & % 56.26/8.47 | ! [v0: $i] : ( ~ (element(v0, all_223_2) = 0) | ~ % 56.26/8.47 | (element(all_138_4, all_223_1) = 0) | ~ $i(v0) | ~ % 56.26/8.47 | $i(all_138_4) | ? [v1: any] : ? [v2: $i] : ? [v3: any] : % 56.26/8.47 | (subset_complement(all_138_8, v0) = v2 & in(v2, all_138_7) = v3 % 56.26/8.47 | & in(v0, all_138_4) = v1 & $i(v2) & ( ~ (v3 = 0) | v1 = 0) & % 56.26/8.47 | ( ~ (v1 = 0) | v3 = 0))))) % 56.26/8.47 | % 56.26/8.47 | ALPHA: (195) implies: % 56.26/8.47 | (196) powerset(all_138_8) = all_223_2 % 56.26/8.47 | (197) powerset(all_223_2) = all_223_1 % 56.26/8.47 | % 56.26/8.47 | REDUCE: (86), (179) imply: % 56.26/8.47 | (198) set_difference(all_138_8, all_138_1) = all_212_0 % 56.26/8.47 | % 56.26/8.47 | REDUCE: (59), (86) imply: % 56.26/8.47 | (199) cast_to_subset(all_138_8) = all_138_8 % 56.26/8.47 | % 56.26/8.47 | REDUCE: (86), (177) imply: % 56.26/8.47 | (200) element(all_138_8, all_212_3) = all_212_2 % 56.26/8.47 | % 56.26/8.47 | REDUCE: (86), (154) imply: % 56.26/8.47 | (201) element(all_138_8, all_202_3) = all_202_2 % 56.26/8.47 | % 56.26/8.47 | REDUCE: (86), (104) imply: % 56.26/8.47 | (202) element(all_138_8, all_160_0) = 0 % 56.26/8.47 | % 56.26/8.47 | BETA: splitting (73) gives: % 56.26/8.47 | % 56.26/8.47 | Case 1: % 56.26/8.47 | | % 56.26/8.47 | | (203) all_138_7 = empty_set % 56.26/8.47 | | % 56.26/8.47 | | REDUCE: (46), (203) imply: % 56.26/8.47 | | (204) $false % 56.26/8.47 | | % 56.26/8.47 | | CLOSE: (204) is inconsistent. % 56.26/8.47 | | % 56.26/8.47 | Case 2: % 56.26/8.47 | | % 56.26/8.47 | | (205) ? [v0: $i] : ( ~ (v0 = empty_set) & % 56.26/8.47 | | complements_of_subsets(all_138_8, all_138_7) = v0 & $i(v0)) % 56.26/8.47 | | % 56.26/8.47 | | DELTA: instantiating (205) with fresh symbol all_233_0 gives: % 56.26/8.47 | | (206) ~ (all_233_0 = empty_set) & complements_of_subsets(all_138_8, % 56.26/8.47 | | all_138_7) = all_233_0 & $i(all_233_0) % 56.26/8.47 | | % 56.26/8.47 | | ALPHA: (206) implies: % 56.26/8.47 | | (207) ~ (all_233_0 = empty_set) % 56.26/8.47 | | (208) complements_of_subsets(all_138_8, all_138_7) = all_233_0 % 56.26/8.47 | | % 56.26/8.47 | | BETA: splitting (72) gives: % 56.26/8.47 | | % 56.26/8.47 | | Case 1: % 56.26/8.47 | | | % 56.26/8.47 | | | (209) all_138_7 = empty_set % 56.26/8.47 | | | % 56.26/8.47 | | | REDUCE: (46), (209) imply: % 56.26/8.47 | | | (210) $false % 56.26/8.47 | | | % 56.26/8.47 | | | CLOSE: (210) is inconsistent. % 56.26/8.47 | | | % 56.26/8.47 | | Case 2: % 56.26/8.47 | | | % 56.26/8.47 | | | (211) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : % 56.26/8.47 | | | (subset_difference(all_138_8, v0, v1) = v2 & % 56.26/8.47 | | | meet_of_subsets(all_138_8, v3) = v2 & % 56.26/8.47 | | | union_of_subsets(all_138_8, all_138_7) = v1 & % 56.26/8.47 | | | complements_of_subsets(all_138_8, all_138_7) = v3 & % 56.26/8.47 | | | cast_to_subset(all_138_8) = v0 & $i(v3) & $i(v2) & $i(v1) & % 56.26/8.47 | | | $i(v0)) % 56.26/8.47 | | | % 56.26/8.47 | | | DELTA: instantiating (211) with fresh symbols all_238_0, all_238_1, % 56.26/8.47 | | | all_238_2, all_238_3 gives: % 56.26/8.47 | | | (212) subset_difference(all_138_8, all_238_3, all_238_2) = all_238_1 & % 56.26/8.47 | | | meet_of_subsets(all_138_8, all_238_0) = all_238_1 & % 56.26/8.47 | | | union_of_subsets(all_138_8, all_138_7) = all_238_2 & % 56.26/8.47 | | | complements_of_subsets(all_138_8, all_138_7) = all_238_0 & % 56.26/8.47 | | | cast_to_subset(all_138_8) = all_238_3 & $i(all_238_0) & % 56.26/8.47 | | | $i(all_238_1) & $i(all_238_2) & $i(all_238_3) % 56.26/8.47 | | | % 56.26/8.47 | | | ALPHA: (212) implies: % 56.26/8.47 | | | (213) cast_to_subset(all_138_8) = all_238_3 % 56.26/8.47 | | | (214) complements_of_subsets(all_138_8, all_138_7) = all_238_0 % 56.26/8.47 | | | (215) union_of_subsets(all_138_8, all_138_7) = all_238_2 % 56.26/8.47 | | | (216) meet_of_subsets(all_138_8, all_238_0) = all_238_1 % 56.26/8.47 | | | (217) subset_difference(all_138_8, all_238_3, all_238_2) = all_238_1 % 56.26/8.47 | | | % 56.26/8.47 | | | BETA: splitting (88) gives: % 56.26/8.47 | | | % 56.26/8.47 | | | Case 1: % 56.26/8.47 | | | | % 56.26/8.47 | | | | (218) all_138_7 = empty_set % 56.26/8.47 | | | | % 56.26/8.47 | | | | REDUCE: (46), (218) imply: % 56.26/8.47 | | | | (219) $false % 56.26/8.47 | | | | % 56.26/8.47 | | | | CLOSE: (219) is inconsistent. % 56.26/8.47 | | | | % 56.26/8.47 | | | Case 2: % 56.26/8.47 | | | | % 56.26/8.47 | | | | (220) ? [v0: $i] : ? [v1: $i] : ? [v2: any] : ? [v3: $i] : ? % 56.26/8.47 | | | | [v4: $i] : ? [v5: $i] : ? [v6: $i] : % 56.26/8.47 | | | | (subset_difference(all_138_8, v3, v4) = v5 & % 56.26/8.47 | | | | meet_of_subsets(all_138_8, all_138_4) = v6 & % 56.26/8.47 | | | | union_of_subsets(all_138_8, all_138_7) = v4 & % 56.26/8.47 | | | | cast_to_subset(all_138_8) = v3 & element(all_138_7, v1) = v2 % 56.26/8.47 | | | | & powerset(v0) = v1 & powerset(all_138_8) = v0 & $i(v6) & % 56.26/8.47 | | | | $i(v5) & $i(v4) & $i(v3) & $i(v1) & $i(v0) & ( ~ (v2 = 0) | % 56.26/8.47 | | | | v6 = v5)) % 56.26/8.47 | | | | % 56.26/8.47 | | | | DELTA: instantiating (220) with fresh symbols all_243_0, all_243_1, % 56.26/8.47 | | | | all_243_2, all_243_3, all_243_4, all_243_5, all_243_6 gives: % 56.26/8.47 | | | | (221) subset_difference(all_138_8, all_243_3, all_243_2) = all_243_1 % 56.26/8.47 | | | | & meet_of_subsets(all_138_8, all_138_4) = all_243_0 & % 56.26/8.47 | | | | union_of_subsets(all_138_8, all_138_7) = all_243_2 & % 56.26/8.47 | | | | cast_to_subset(all_138_8) = all_243_3 & element(all_138_7, % 56.26/8.47 | | | | all_243_5) = all_243_4 & powerset(all_243_6) = all_243_5 & % 56.26/8.47 | | | | powerset(all_138_8) = all_243_6 & $i(all_243_0) & $i(all_243_1) % 56.26/8.47 | | | | & $i(all_243_2) & $i(all_243_3) & $i(all_243_5) & $i(all_243_6) % 56.26/8.47 | | | | & ( ~ (all_243_4 = 0) | all_243_0 = all_243_1) % 56.26/8.47 | | | | % 56.26/8.47 | | | | ALPHA: (221) implies: % 56.26/8.47 | | | | (222) powerset(all_138_8) = all_243_6 % 56.26/8.47 | | | | (223) powerset(all_243_6) = all_243_5 % 56.26/8.47 | | | | (224) cast_to_subset(all_138_8) = all_243_3 % 56.26/8.47 | | | | (225) union_of_subsets(all_138_8, all_138_7) = all_243_2 % 56.26/8.47 | | | | (226) meet_of_subsets(all_138_8, all_138_4) = all_243_0 % 56.26/8.47 | | | | (227) subset_difference(all_138_8, all_243_3, all_243_2) = all_243_1 % 56.26/8.47 | | | | % 56.26/8.47 | | | | GROUND_INST: instantiating (32) with all_160_0, all_202_3, all_138_8, % 56.26/8.47 | | | | simplifying with (103), (153) gives: % 56.26/8.47 | | | | (228) all_202_3 = all_160_0 % 56.26/8.47 | | | | % 56.26/8.47 | | | | GROUND_INST: instantiating (32) with all_202_3, all_204_3, all_138_8, % 56.26/8.47 | | | | simplifying with (153), (159) gives: % 56.26/8.47 | | | | (229) all_204_3 = all_202_3 % 56.26/8.47 | | | | % 56.26/8.47 | | | | GROUND_INST: instantiating (32) with all_204_3, all_206_3, all_138_8, % 56.26/8.47 | | | | simplifying with (159), (163) gives: % 56.26/8.47 | | | | (230) all_206_3 = all_204_3 % 56.26/8.47 | | | | % 56.26/8.47 | | | | GROUND_INST: instantiating (32) with all_206_3, all_212_3, all_138_8, % 56.26/8.47 | | | | simplifying with (163), (176) gives: % 56.26/8.47 | | | | (231) all_212_3 = all_206_3 % 56.26/8.47 | | | | % 56.26/8.47 | | | | GROUND_INST: instantiating (32) with all_138_6, all_216_3, all_138_8, % 56.26/8.47 | | | | simplifying with (56), (186) gives: % 56.26/8.47 | | | | (232) all_216_3 = all_138_6 % 56.26/8.48 | | | | % 56.26/8.48 | | | | GROUND_INST: instantiating (32) with all_214_3, all_216_3, all_138_8, % 56.26/8.48 | | | | simplifying with (182), (186) gives: % 56.26/8.48 | | | | (233) all_216_3 = all_214_3 % 56.26/8.48 | | | | % 56.26/8.48 | | | | GROUND_INST: instantiating (32) with all_212_3, all_216_3, all_138_8, % 56.26/8.48 | | | | simplifying with (176), (186) gives: % 56.26/8.48 | | | | (234) all_216_3 = all_212_3 % 56.26/8.48 | | | | % 56.26/8.48 | | | | GROUND_INST: instantiating (32) with all_218_3, all_223_2, all_138_8, % 56.26/8.48 | | | | simplifying with (190), (196) gives: % 56.26/8.48 | | | | (235) all_223_2 = all_218_3 % 56.26/8.48 | | | | % 56.26/8.48 | | | | GROUND_INST: instantiating (32) with all_212_3, all_223_2, all_138_8, % 56.26/8.48 | | | | simplifying with (176), (196) gives: % 56.26/8.48 | | | | (236) all_223_2 = all_212_3 % 56.26/8.48 | | | | % 56.26/8.48 | | | | GROUND_INST: instantiating (32) with all_223_2, all_243_6, all_138_8, % 56.26/8.48 | | | | simplifying with (196), (222) gives: % 56.26/8.48 | | | | (237) all_243_6 = all_223_2 % 56.26/8.48 | | | | % 56.26/8.48 | | | | GROUND_INST: instantiating (32) with all_210_3, all_243_6, all_138_8, % 56.26/8.48 | | | | simplifying with (171), (222) gives: % 56.26/8.48 | | | | (238) all_243_6 = all_210_3 % 56.26/8.48 | | | | % 56.26/8.48 | | | | GROUND_INST: instantiating (33) with all_192_1, all_194_1, all_138_5, % 56.26/8.48 | | | | simplifying with (149), (151) gives: % 56.26/8.48 | | | | (239) all_194_1 = all_192_1 % 56.26/8.48 | | | | % 56.26/8.48 | | | | GROUND_INST: instantiating (33) with all_158_0, all_194_1, all_138_5, % 56.26/8.48 | | | | simplifying with (101), (151) gives: % 56.26/8.48 | | | | (240) all_194_1 = all_158_0 % 56.26/8.48 | | | | % 56.26/8.48 | | | | GROUND_INST: instantiating (34) with all_138_8, all_238_3, all_138_8, % 56.26/8.48 | | | | simplifying with (199), (213) gives: % 56.26/8.48 | | | | (241) all_238_3 = all_138_8 % 56.26/8.48 | | | | % 56.26/8.48 | | | | GROUND_INST: instantiating (34) with all_238_3, all_243_3, all_138_8, % 56.26/8.48 | | | | simplifying with (213), (224) gives: % 56.26/8.48 | | | | (242) all_243_3 = all_238_3 % 56.26/8.48 | | | | % 56.26/8.48 | | | | GROUND_INST: instantiating (34) with all_166_0, all_243_3, all_138_8, % 56.26/8.48 | | | | simplifying with (114), (224) gives: % 56.26/8.48 | | | | (243) all_243_3 = all_166_0 % 56.26/8.48 | | | | % 56.26/8.48 | | | | GROUND_INST: instantiating (38) with all_184_0, all_186_0, all_138_7, % 56.26/8.48 | | | | all_138_6, simplifying with (142), (144) gives: % 56.26/8.48 | | | | (244) all_186_0 = all_184_0 % 56.26/8.48 | | | | % 56.26/8.48 | | | | GROUND_INST: instantiating (38) with all_186_0, all_208_1, all_138_7, % 56.26/8.48 | | | | all_138_6, simplifying with (144), (169) gives: % 56.26/8.48 | | | | (245) all_208_1 = all_186_0 % 56.26/8.48 | | | | % 56.26/8.48 | | | | GROUND_INST: instantiating (38) with all_172_0, all_208_1, all_138_7, % 56.26/8.48 | | | | all_138_6, simplifying with (123), (169) gives: % 56.26/8.48 | | | | (246) all_208_1 = all_172_0 % 56.26/8.48 | | | | % 56.26/8.48 | | | | GROUND_INST: instantiating (39) with all_174_0, all_220_0, all_138_7, % 56.26/8.48 | | | | all_138_8, simplifying with (126), (193) gives: % 56.26/8.48 | | | | (247) all_220_0 = all_174_0 % 56.26/8.48 | | | | % 56.73/8.48 | | | | GROUND_INST: instantiating (39) with all_138_4, all_233_0, all_138_7, % 56.73/8.48 | | | | all_138_8, simplifying with (60), (208) gives: % 56.73/8.48 | | | | (248) all_233_0 = all_138_4 % 56.73/8.48 | | | | % 56.73/8.48 | | | | GROUND_INST: instantiating (39) with all_220_0, all_233_0, all_138_7, % 56.73/8.48 | | | | all_138_8, simplifying with (193), (208) gives: % 56.73/8.48 | | | | (249) all_233_0 = all_220_0 % 56.73/8.48 | | | | % 56.73/8.48 | | | | GROUND_INST: instantiating (39) with all_233_0, all_238_0, all_138_7, % 56.73/8.48 | | | | all_138_8, simplifying with (208), (214) gives: % 56.73/8.48 | | | | (250) all_238_0 = all_233_0 % 56.73/8.48 | | | | % 56.73/8.48 | | | | GROUND_INST: instantiating (39) with all_182_0, all_238_0, all_138_7, % 56.73/8.48 | | | | all_138_8, simplifying with (138), (214) gives: % 56.73/8.48 | | | | (251) all_238_0 = all_182_0 % 56.73/8.48 | | | | % 56.73/8.48 | | | | GROUND_INST: instantiating (40) with all_176_0, all_238_2, all_138_7, % 56.73/8.48 | | | | all_138_8, simplifying with (129), (215) gives: % 56.73/8.48 | | | | (252) all_238_2 = all_176_0 % 56.73/8.48 | | | | % 56.73/8.48 | | | | GROUND_INST: instantiating (40) with all_238_2, all_243_2, all_138_7, % 56.73/8.48 | | | | all_138_8, simplifying with (215), (225) gives: % 56.73/8.48 | | | | (253) all_243_2 = all_238_2 % 56.73/8.48 | | | | % 56.73/8.48 | | | | GROUND_INST: instantiating (40) with all_178_0, all_243_2, all_138_7, % 56.73/8.48 | | | | all_138_8, simplifying with (133), (225) gives: % 56.73/8.48 | | | | (254) all_243_2 = all_178_0 % 56.73/8.48 | | | | % 56.73/8.48 | | | | GROUND_INST: instantiating (41) with all_138_1, all_180_0, all_138_7, % 56.73/8.48 | | | | all_138_8, simplifying with (62), (135) gives: % 56.73/8.48 | | | | (255) all_180_0 = all_138_1 % 56.73/8.48 | | | | % 56.73/8.48 | | | | GROUND_INST: instantiating (41) with all_170_0, all_180_0, all_138_7, % 56.73/8.48 | | | | all_138_8, simplifying with (121), (135) gives: % 56.73/8.48 | | | | (256) all_180_0 = all_170_0 % 56.73/8.48 | | | | % 56.73/8.48 | | | | COMBINE_EQS: (253), (254) imply: % 56.73/8.48 | | | | (257) all_238_2 = all_178_0 % 56.73/8.48 | | | | % 56.73/8.48 | | | | SIMP: (257) implies: % 56.73/8.48 | | | | (258) all_238_2 = all_178_0 % 56.73/8.48 | | | | % 56.73/8.48 | | | | COMBINE_EQS: (242), (243) imply: % 56.73/8.48 | | | | (259) all_238_3 = all_166_0 % 56.73/8.48 | | | | % 56.73/8.48 | | | | SIMP: (259) implies: % 56.73/8.48 | | | | (260) all_238_3 = all_166_0 % 56.73/8.48 | | | | % 56.73/8.48 | | | | COMBINE_EQS: (237), (238) imply: % 56.73/8.48 | | | | (261) all_223_2 = all_210_3 % 56.73/8.48 | | | | % 56.73/8.48 | | | | SIMP: (261) implies: % 56.73/8.48 | | | | (262) all_223_2 = all_210_3 % 56.73/8.48 | | | | % 56.73/8.48 | | | | COMBINE_EQS: (250), (251) imply: % 56.73/8.48 | | | | (263) all_233_0 = all_182_0 % 56.73/8.48 | | | | % 56.73/8.48 | | | | SIMP: (263) implies: % 56.73/8.48 | | | | (264) all_233_0 = all_182_0 % 56.73/8.48 | | | | % 56.73/8.48 | | | | COMBINE_EQS: (252), (258) imply: % 56.73/8.48 | | | | (265) all_178_0 = all_176_0 % 56.73/8.48 | | | | % 56.73/8.48 | | | | SIMP: (265) implies: % 56.73/8.48 | | | | (266) all_178_0 = all_176_0 % 56.73/8.48 | | | | % 56.73/8.48 | | | | COMBINE_EQS: (241), (260) imply: % 56.73/8.48 | | | | (267) all_166_0 = all_138_8 % 56.73/8.48 | | | | % 56.73/8.48 | | | | COMBINE_EQS: (249), (264) imply: % 56.73/8.48 | | | | (268) all_220_0 = all_182_0 % 56.73/8.48 | | | | % 56.73/8.48 | | | | SIMP: (268) implies: % 56.73/8.48 | | | | (269) all_220_0 = all_182_0 % 56.73/8.48 | | | | % 56.73/8.48 | | | | COMBINE_EQS: (248), (264) imply: % 56.73/8.48 | | | | (270) all_182_0 = all_138_4 % 56.73/8.48 | | | | % 56.73/8.48 | | | | COMBINE_EQS: (235), (262) imply: % 56.73/8.48 | | | | (271) all_218_3 = all_210_3 % 56.73/8.48 | | | | % 56.73/8.48 | | | | COMBINE_EQS: (235), (236) imply: % 56.73/8.48 | | | | (272) all_218_3 = all_212_3 % 56.73/8.48 | | | | % 56.73/8.48 | | | | COMBINE_EQS: (247), (269) imply: % 56.73/8.48 | | | | (273) all_182_0 = all_174_0 % 56.73/8.48 | | | | % 56.73/8.48 | | | | SIMP: (273) implies: % 56.73/8.48 | | | | (274) all_182_0 = all_174_0 % 56.73/8.48 | | | | % 56.73/8.48 | | | | COMBINE_EQS: (271), (272) imply: % 56.73/8.48 | | | | (275) all_212_3 = all_210_3 % 56.73/8.48 | | | | % 56.73/8.48 | | | | SIMP: (275) implies: % 56.73/8.48 | | | | (276) all_212_3 = all_210_3 % 56.73/8.48 | | | | % 56.73/8.48 | | | | COMBINE_EQS: (233), (234) imply: % 56.73/8.48 | | | | (277) all_214_3 = all_212_3 % 56.73/8.48 | | | | % 56.73/8.48 | | | | COMBINE_EQS: (232), (233) imply: % 56.73/8.48 | | | | (278) all_214_3 = all_138_6 % 56.73/8.48 | | | | % 56.73/8.48 | | | | COMBINE_EQS: (277), (278) imply: % 56.73/8.48 | | | | (279) all_212_3 = all_138_6 % 56.73/8.48 | | | | % 56.73/8.48 | | | | SIMP: (279) implies: % 56.73/8.48 | | | | (280) all_212_3 = all_138_6 % 56.73/8.48 | | | | % 56.73/8.48 | | | | COMBINE_EQS: (231), (276) imply: % 56.73/8.48 | | | | (281) all_210_3 = all_206_3 % 56.73/8.48 | | | | % 56.73/8.48 | | | | COMBINE_EQS: (276), (280) imply: % 56.73/8.48 | | | | (282) all_210_3 = all_138_6 % 56.73/8.48 | | | | % 56.73/8.48 | | | | COMBINE_EQS: (281), (282) imply: % 56.73/8.48 | | | | (283) all_206_3 = all_138_6 % 56.73/8.48 | | | | % 56.73/8.48 | | | | SIMP: (283) implies: % 56.73/8.48 | | | | (284) all_206_3 = all_138_6 % 56.73/8.48 | | | | % 56.73/8.48 | | | | COMBINE_EQS: (245), (246) imply: % 56.73/8.48 | | | | (285) all_186_0 = all_172_0 % 56.73/8.48 | | | | % 56.73/8.48 | | | | SIMP: (285) implies: % 56.73/8.48 | | | | (286) all_186_0 = all_172_0 % 56.73/8.48 | | | | % 56.73/8.48 | | | | COMBINE_EQS: (230), (284) imply: % 56.73/8.48 | | | | (287) all_204_3 = all_138_6 % 56.73/8.48 | | | | % 56.73/8.48 | | | | SIMP: (287) implies: % 56.73/8.48 | | | | (288) all_204_3 = all_138_6 % 56.73/8.48 | | | | % 56.73/8.48 | | | | COMBINE_EQS: (229), (288) imply: % 56.73/8.48 | | | | (289) all_202_3 = all_138_6 % 56.73/8.48 | | | | % 56.73/8.48 | | | | SIMP: (289) implies: % 56.73/8.48 | | | | (290) all_202_3 = all_138_6 % 56.73/8.48 | | | | % 56.73/8.48 | | | | COMBINE_EQS: (228), (290) imply: % 56.73/8.48 | | | | (291) all_160_0 = all_138_6 % 56.73/8.48 | | | | % 56.73/8.48 | | | | COMBINE_EQS: (239), (240) imply: % 56.73/8.48 | | | | (292) all_192_1 = all_158_0 % 56.73/8.48 | | | | % 56.73/8.48 | | | | SIMP: (292) implies: % 56.73/8.48 | | | | (293) all_192_1 = all_158_0 % 56.73/8.48 | | | | % 56.73/8.48 | | | | COMBINE_EQS: (244), (286) imply: % 56.73/8.48 | | | | (294) all_184_0 = all_172_0 % 56.73/8.48 | | | | % 56.73/8.48 | | | | COMBINE_EQS: (270), (274) imply: % 56.73/8.48 | | | | (295) all_174_0 = all_138_4 % 56.73/8.48 | | | | % 56.73/8.48 | | | | COMBINE_EQS: (255), (256) imply: % 56.73/8.48 | | | | (296) all_170_0 = all_138_1 % 56.73/8.48 | | | | % 56.73/8.48 | | | | SIMP: (296) implies: % 56.73/8.48 | | | | (297) all_170_0 = all_138_1 % 56.73/8.48 | | | | % 56.73/8.48 | | | | COMBINE_EQS: (271), (282) imply: % 56.73/8.48 | | | | (298) all_218_3 = all_138_6 % 56.73/8.48 | | | | % 56.73/8.48 | | | | COMBINE_EQS: (247), (295) imply: % 56.73/8.48 | | | | (299) all_220_0 = all_138_4 % 56.73/8.48 | | | | % 56.73/8.48 | | | | COMBINE_EQS: (235), (298) imply: % 56.73/8.48 | | | | (300) all_223_2 = all_138_6 % 56.73/8.48 | | | | % 56.73/8.48 | | | | COMBINE_EQS: (251), (270) imply: % 56.73/8.49 | | | | (301) all_238_0 = all_138_4 % 56.73/8.49 | | | | % 56.73/8.49 | | | | COMBINE_EQS: (238), (282) imply: % 56.73/8.49 | | | | (302) all_243_6 = all_138_6 % 56.73/8.49 | | | | % 56.73/8.49 | | | | COMBINE_EQS: (243), (267) imply: % 56.73/8.49 | | | | (303) all_243_3 = all_138_8 % 56.73/8.49 | | | | % 56.73/8.49 | | | | COMBINE_EQS: (254), (266) imply: % 56.73/8.49 | | | | (304) all_243_2 = all_176_0 % 56.73/8.49 | | | | % 56.73/8.49 | | | | REDUCE: (207), (248) imply: % 56.73/8.49 | | | | (305) ~ (all_138_4 = empty_set) % 56.73/8.49 | | | | % 56.73/8.49 | | | | REDUCE: (227), (303), (304) imply: % 56.73/8.49 | | | | (306) subset_difference(all_138_8, all_138_8, all_176_0) = all_243_1 % 56.73/8.49 | | | | % 56.73/8.49 | | | | REDUCE: (217), (241), (252) imply: % 56.73/8.49 | | | | (307) subset_difference(all_138_8, all_138_8, all_176_0) = all_238_1 % 56.73/8.49 | | | | % 56.73/8.49 | | | | REDUCE: (216), (301) imply: % 56.73/8.49 | | | | (308) meet_of_subsets(all_138_8, all_138_4) = all_238_1 % 56.73/8.49 | | | | % 56.73/8.49 | | | | REDUCE: (127), (295) imply: % 56.73/8.49 | | | | (309) complements_of_subsets(all_138_8, all_138_4) = all_138_7 % 56.73/8.49 | | | | % 56.73/8.49 | | | | REDUCE: (141), (294) imply: % 56.73/8.49 | | | | (310) element(all_172_0, all_138_5) = 0 % 56.73/8.49 | | | | % 56.73/8.49 | | | | REDUCE: (137), (270) imply: % 56.73/8.49 | | | | (311) element(all_138_4, all_138_5) = 0 % 56.73/8.49 | | | | % 56.73/8.49 | | | | REDUCE: (132), (266) imply: % 56.73/8.49 | | | | (312) element(all_176_0, all_138_6) = 0 % 56.73/8.49 | | | | % 56.73/8.49 | | | | REDUCE: (120), (297) imply: % 56.73/8.49 | | | | (313) element(all_138_1, all_138_6) = 0 % 56.73/8.49 | | | | % 56.73/8.49 | | | | REDUCE: (156), (290) imply: % 56.73/8.49 | | | | (314) element(all_138_0, all_138_6) = all_202_0 % 56.73/8.49 | | | | % 56.73/8.49 | | | | REDUCE: (178), (280) imply: % 56.73/8.49 | | | | (315) element(all_138_1, all_138_6) = all_212_1 % 56.73/8.49 | | | | % 56.73/8.49 | | | | REDUCE: (173), (282) imply: % 56.73/8.49 | | | | (316) element(all_138_1, all_138_6) = all_210_0 % 56.73/8.49 | | | | % 56.73/8.49 | | | | REDUCE: (155), (290) imply: % 56.73/8.49 | | | | (317) element(all_138_1, all_138_6) = all_202_1 % 56.73/8.49 | | | | % 56.73/8.49 | | | | REDUCE: (166), (284) imply: % 56.73/8.49 | | | | (318) element(all_138_3, all_138_6) = all_206_0 % 56.73/8.49 | | | | % 56.73/8.49 | | | | REDUCE: (200), (280) imply: % 56.73/8.49 | | | | (319) element(all_138_8, all_138_6) = all_212_2 % 56.73/8.49 | | | | % 56.73/8.49 | | | | REDUCE: (201), (290) imply: % 56.73/8.49 | | | | (320) element(all_138_8, all_138_6) = all_202_2 % 56.73/8.49 | | | | % 56.73/8.49 | | | | REDUCE: (202), (291) imply: % 56.73/8.49 | | | | (321) element(all_138_8, all_138_6) = 0 % 56.73/8.49 | | | | % 56.73/8.49 | | | | REDUCE: (223), (302) imply: % 56.73/8.49 | | | | (322) powerset(all_138_6) = all_243_5 % 56.73/8.49 | | | | % 56.73/8.49 | | | | REDUCE: (197), (300) imply: % 56.73/8.49 | | | | (323) powerset(all_138_6) = all_223_1 % 56.73/8.49 | | | | % 56.73/8.49 | | | | REDUCE: (191), (298) imply: % 56.73/8.49 | | | | (324) powerset(all_138_6) = all_218_2 % 56.73/8.49 | | | | % 56.73/8.49 | | | | REDUCE: (187), (232) imply: % 56.73/8.49 | | | | (325) powerset(all_138_6) = all_216_2 % 56.73/8.49 | | | | % 56.73/8.49 | | | | REDUCE: (183), (278) imply: % 56.73/8.49 | | | | (326) powerset(all_138_6) = all_214_2 % 56.73/8.49 | | | | % 56.73/8.49 | | | | REDUCE: (172), (282) imply: % 56.73/8.49 | | | | (327) powerset(all_138_6) = all_210_2 % 56.73/8.49 | | | | % 56.73/8.49 | | | | REDUCE: (164), (284) imply: % 56.73/8.49 | | | | (328) powerset(all_138_6) = all_206_2 % 56.73/8.49 | | | | % 56.73/8.49 | | | | REDUCE: (160), (288) imply: % 56.73/8.49 | | | | (329) powerset(all_138_6) = all_204_2 % 56.73/8.49 | | | | % 56.73/8.49 | | | | REDUCE: (140), (294) imply: % 56.73/8.49 | | | | (330) $i(all_172_0) % 56.73/8.49 | | | | % 56.73/8.49 | | | | REDUCE: (131), (266) imply: % 56.73/8.49 | | | | (331) $i(all_176_0) % 56.73/8.49 | | | | % 56.73/8.49 | | | | BETA: splitting (92) gives: % 56.73/8.49 | | | | % 56.73/8.49 | | | | Case 1: % 56.73/8.49 | | | | | % 56.73/8.49 | | | | | (332) all_138_4 = empty_set % 56.73/8.49 | | | | | % 56.73/8.49 | | | | | REDUCE: (305), (332) imply: % 56.73/8.49 | | | | | (333) $false % 56.73/8.49 | | | | | % 56.73/8.49 | | | | | CLOSE: (333) is inconsistent. % 56.73/8.49 | | | | | % 56.73/8.49 | | | | Case 2: % 56.73/8.49 | | | | | % 56.73/8.49 | | | | | (334) ? [v0: $i] : ? [v1: $i] : ? [v2: any] : ? [v3: $i] : ? % 56.73/8.49 | | | | | [v4: $i] : ? [v5: $i] : ? [v6: $i] : % 56.73/8.49 | | | | | (subset_difference(all_138_8, v3, all_138_3) = v4 & % 56.73/8.49 | | | | | meet_of_subsets(all_138_8, v5) = v6 & % 56.73/8.49 | | | | | complements_of_subsets(all_138_8, all_138_4) = v5 & % 56.73/8.49 | | | | | cast_to_subset(all_138_8) = v3 & element(all_138_4, v1) = % 56.73/8.49 | | | | | v2 & powerset(v0) = v1 & powerset(all_138_8) = v0 & $i(v6) % 56.73/8.49 | | | | | & $i(v5) & $i(v4) & $i(v3) & $i(v1) & $i(v0) & ( ~ (v2 = 0) % 56.73/8.49 | | | | | | v6 = v4)) % 56.73/8.49 | | | | | % 56.73/8.49 | | | | | DELTA: instantiating (334) with fresh symbols all_262_0, all_262_1, % 56.73/8.49 | | | | | all_262_2, all_262_3, all_262_4, all_262_5, all_262_6 gives: % 56.73/8.49 | | | | | (335) subset_difference(all_138_8, all_262_3, all_138_3) = % 56.73/8.49 | | | | | all_262_2 & meet_of_subsets(all_138_8, all_262_1) = all_262_0 % 56.73/8.49 | | | | | & complements_of_subsets(all_138_8, all_138_4) = all_262_1 & % 56.73/8.49 | | | | | cast_to_subset(all_138_8) = all_262_3 & element(all_138_4, % 56.73/8.49 | | | | | all_262_5) = all_262_4 & powerset(all_262_6) = all_262_5 & % 56.73/8.49 | | | | | powerset(all_138_8) = all_262_6 & $i(all_262_0) & % 56.73/8.49 | | | | | $i(all_262_1) & $i(all_262_2) & $i(all_262_3) & $i(all_262_5) % 56.73/8.49 | | | | | & $i(all_262_6) & ( ~ (all_262_4 = 0) | all_262_0 = % 56.73/8.49 | | | | | all_262_2) % 56.73/8.49 | | | | | % 56.73/8.49 | | | | | ALPHA: (335) implies: % 56.73/8.49 | | | | | (336) $i(all_262_6) % 56.73/8.49 | | | | | (337) $i(all_262_5) % 56.73/8.49 | | | | | (338) $i(all_262_3) % 56.73/8.49 | | | | | (339) $i(all_262_2) % 56.73/8.49 | | | | | (340) powerset(all_138_8) = all_262_6 % 56.73/8.49 | | | | | (341) powerset(all_262_6) = all_262_5 % 56.73/8.49 | | | | | (342) element(all_138_4, all_262_5) = all_262_4 % 56.73/8.49 | | | | | (343) cast_to_subset(all_138_8) = all_262_3 % 56.73/8.49 | | | | | (344) complements_of_subsets(all_138_8, all_138_4) = all_262_1 % 56.73/8.49 | | | | | (345) meet_of_subsets(all_138_8, all_262_1) = all_262_0 % 56.73/8.49 | | | | | (346) subset_difference(all_138_8, all_262_3, all_138_3) = % 56.73/8.49 | | | | | all_262_2 % 56.73/8.49 | | | | | (347) ~ (all_262_4 = 0) | all_262_0 = all_262_2 % 56.73/8.49 | | | | | % 56.73/8.49 | | | | | GROUND_INST: instantiating (32) with all_138_6, all_262_6, all_138_8, % 56.73/8.49 | | | | | simplifying with (56), (340) gives: % 56.73/8.49 | | | | | (348) all_262_6 = all_138_6 % 56.73/8.49 | | | | | % 56.73/8.49 | | | | | GROUND_INST: instantiating (32) with all_210_2, all_214_2, all_138_6, % 56.73/8.49 | | | | | simplifying with (326), (327) gives: % 56.73/8.49 | | | | | (349) all_214_2 = all_210_2 % 56.73/8.49 | | | | | % 56.73/8.49 | | | | | GROUND_INST: instantiating (32) with all_214_2, all_218_2, all_138_6, % 56.73/8.49 | | | | | simplifying with (324), (326) gives: % 56.73/8.49 | | | | | (350) all_218_2 = all_214_2 % 56.73/8.49 | | | | | % 56.73/8.49 | | | | | GROUND_INST: instantiating (32) with all_138_5, all_223_1, all_138_6, % 56.73/8.49 | | | | | simplifying with (57), (323) gives: % 56.73/8.49 | | | | | (351) all_223_1 = all_138_5 % 56.73/8.49 | | | | | % 56.73/8.49 | | | | | GROUND_INST: instantiating (32) with all_216_2, all_223_1, all_138_6, % 56.73/8.49 | | | | | simplifying with (323), (325) gives: % 56.73/8.49 | | | | | (352) all_223_1 = all_216_2 % 56.73/8.49 | | | | | % 56.73/8.49 | | | | | GROUND_INST: instantiating (32) with all_210_2, all_223_1, all_138_6, % 56.73/8.49 | | | | | simplifying with (323), (327) gives: % 56.73/8.49 | | | | | (353) all_223_1 = all_210_2 % 56.73/8.49 | | | | | % 56.73/8.49 | | | | | GROUND_INST: instantiating (32) with all_206_2, all_223_1, all_138_6, % 56.73/8.49 | | | | | simplifying with (323), (328) gives: % 56.73/8.49 | | | | | (354) all_223_1 = all_206_2 % 56.73/8.49 | | | | | % 56.73/8.49 | | | | | GROUND_INST: instantiating (32) with all_218_2, all_243_5, all_138_6, % 56.73/8.49 | | | | | simplifying with (322), (324) gives: % 56.73/8.49 | | | | | (355) all_243_5 = all_218_2 % 56.73/8.49 | | | | | % 56.73/8.49 | | | | | GROUND_INST: instantiating (32) with all_204_2, all_243_5, all_138_6, % 56.73/8.49 | | | | | simplifying with (322), (329) gives: % 56.73/8.49 | | | | | (356) all_243_5 = all_204_2 % 56.73/8.49 | | | | | % 56.73/8.49 | | | | | GROUND_INST: instantiating (36) with all_202_2, all_212_2, all_138_6, % 56.73/8.49 | | | | | all_138_8, simplifying with (319), (320) gives: % 56.73/8.49 | | | | | (357) all_212_2 = all_202_2 % 56.73/8.49 | | | | | % 56.73/8.49 | | | | | GROUND_INST: instantiating (36) with 0, all_212_2, all_138_6, % 56.73/8.49 | | | | | all_138_8, simplifying with (319), (321) gives: % 56.73/8.49 | | | | | (358) all_212_2 = 0 % 56.73/8.49 | | | | | % 56.73/8.49 | | | | | GROUND_INST: instantiating (36) with all_210_0, all_212_1, all_138_6, % 56.73/8.49 | | | | | all_138_1, simplifying with (315), (316) gives: % 56.73/8.49 | | | | | (359) all_212_1 = all_210_0 % 56.73/8.49 | | | | | % 56.73/8.49 | | | | | GROUND_INST: instantiating (36) with all_202_1, all_212_1, all_138_6, % 56.73/8.49 | | | | | all_138_1, simplifying with (315), (317) gives: % 56.73/8.49 | | | | | (360) all_212_1 = all_202_1 % 56.73/8.49 | | | | | % 56.73/8.49 | | | | | GROUND_INST: instantiating (36) with 0, all_212_1, all_138_6, % 56.73/8.49 | | | | | all_138_1, simplifying with (313), (315) gives: % 56.73/8.50 | | | | | (361) all_212_1 = 0 % 56.73/8.50 | | | | | % 56.73/8.50 | | | | | GROUND_INST: instantiating (34) with all_138_8, all_262_3, all_138_8, % 56.73/8.50 | | | | | simplifying with (199), (343) gives: % 56.73/8.50 | | | | | (362) all_262_3 = all_138_8 % 56.73/8.50 | | | | | % 56.73/8.50 | | | | | GROUND_INST: instantiating (39) with all_216_0, all_262_1, all_138_4, % 56.73/8.50 | | | | | all_138_8, simplifying with (188), (344) gives: % 56.73/8.50 | | | | | (363) all_262_1 = all_216_0 % 56.73/8.50 | | | | | % 56.73/8.50 | | | | | GROUND_INST: instantiating (39) with all_138_7, all_262_1, all_138_4, % 56.73/8.50 | | | | | all_138_8, simplifying with (309), (344) gives: % 56.73/8.50 | | | | | (364) all_262_1 = all_138_7 % 56.73/8.50 | | | | | % 56.80/8.50 | | | | | GROUND_INST: instantiating (41) with all_243_0, all_238_1, all_138_4, % 56.80/8.50 | | | | | all_138_8, simplifying with (226), (308) gives: % 56.80/8.50 | | | | | (365) all_243_0 = all_238_1 % 56.80/8.50 | | | | | % 56.80/8.50 | | | | | GROUND_INST: instantiating (42) with all_238_1, all_243_1, all_176_0, % 56.80/8.50 | | | | | all_138_8, all_138_8, simplifying with (306), (307) % 56.80/8.50 | | | | | gives: % 56.80/8.50 | | | | | (366) all_243_1 = all_238_1 % 56.80/8.50 | | | | | % 56.80/8.50 | | | | | COMBINE_EQS: (363), (364) imply: % 56.80/8.50 | | | | | (367) all_216_0 = all_138_7 % 56.80/8.50 | | | | | % 56.80/8.50 | | | | | SIMP: (367) implies: % 56.80/8.50 | | | | | (368) all_216_0 = all_138_7 % 56.80/8.50 | | | | | % 56.80/8.50 | | | | | COMBINE_EQS: (355), (356) imply: % 56.80/8.50 | | | | | (369) all_218_2 = all_204_2 % 56.80/8.50 | | | | | % 56.80/8.50 | | | | | SIMP: (369) implies: % 56.80/8.50 | | | | | (370) all_218_2 = all_204_2 % 56.80/8.50 | | | | | % 56.80/8.50 | | | | | COMBINE_EQS: (352), (353) imply: % 56.80/8.50 | | | | | (371) all_216_2 = all_210_2 % 56.80/8.50 | | | | | % 56.80/8.50 | | | | | COMBINE_EQS: (351), (352) imply: % 56.80/8.50 | | | | | (372) all_216_2 = all_138_5 % 56.80/8.50 | | | | | % 56.80/8.50 | | | | | COMBINE_EQS: (352), (354) imply: % 56.80/8.50 | | | | | (373) all_216_2 = all_206_2 % 56.80/8.50 | | | | | % 56.80/8.50 | | | | | COMBINE_EQS: (350), (370) imply: % 56.80/8.50 | | | | | (374) all_214_2 = all_204_2 % 56.80/8.50 | | | | | % 56.80/8.50 | | | | | SIMP: (374) implies: % 56.80/8.50 | | | | | (375) all_214_2 = all_204_2 % 56.80/8.50 | | | | | % 56.80/8.50 | | | | | COMBINE_EQS: (371), (373) imply: % 56.80/8.50 | | | | | (376) all_210_2 = all_206_2 % 56.80/8.50 | | | | | % 56.80/8.50 | | | | | SIMP: (376) implies: % 56.80/8.50 | | | | | (377) all_210_2 = all_206_2 % 56.80/8.50 | | | | | % 56.80/8.50 | | | | | COMBINE_EQS: (372), (373) imply: % 56.80/8.50 | | | | | (378) all_206_2 = all_138_5 % 56.80/8.50 | | | | | % 56.80/8.50 | | | | | COMBINE_EQS: (349), (375) imply: % 56.80/8.50 | | | | | (379) all_210_2 = all_204_2 % 56.80/8.50 | | | | | % 56.80/8.50 | | | | | SIMP: (379) implies: % 56.80/8.50 | | | | | (380) all_210_2 = all_204_2 % 56.80/8.50 | | | | | % 56.80/8.50 | | | | | COMBINE_EQS: (359), (361) imply: % 56.80/8.50 | | | | | (381) all_210_0 = 0 % 56.80/8.50 | | | | | % 56.80/8.50 | | | | | COMBINE_EQS: (359), (360) imply: % 56.80/8.50 | | | | | (382) all_210_0 = all_202_1 % 56.80/8.50 | | | | | % 56.80/8.50 | | | | | COMBINE_EQS: (357), (358) imply: % 56.80/8.50 | | | | | (383) all_202_2 = 0 % 56.80/8.50 | | | | | % 56.80/8.50 | | | | | SIMP: (383) implies: % 56.80/8.50 | | | | | (384) all_202_2 = 0 % 56.80/8.50 | | | | | % 56.80/8.50 | | | | | COMBINE_EQS: (381), (382) imply: % 56.80/8.50 | | | | | (385) all_202_1 = 0 % 56.80/8.50 | | | | | % 56.80/8.50 | | | | | COMBINE_EQS: (377), (380) imply: % 56.80/8.50 | | | | | (386) all_206_2 = all_204_2 % 56.80/8.50 | | | | | % 56.80/8.50 | | | | | SIMP: (386) implies: % 56.80/8.50 | | | | | (387) all_206_2 = all_204_2 % 56.80/8.50 | | | | | % 56.80/8.50 | | | | | COMBINE_EQS: (378), (387) imply: % 56.80/8.50 | | | | | (388) all_204_2 = all_138_5 % 56.80/8.50 | | | | | % 56.80/8.50 | | | | | COMBINE_EQS: (375), (388) imply: % 56.80/8.50 | | | | | (389) all_214_2 = all_138_5 % 56.80/8.50 | | | | | % 56.80/8.50 | | | | | REDUCE: (346), (362) imply: % 56.80/8.50 | | | | | (390) subset_difference(all_138_8, all_138_8, all_138_3) = % 56.80/8.50 | | | | | all_262_2 % 56.80/8.50 | | | | | % 56.80/8.50 | | | | | REDUCE: (345), (364) imply: % 56.80/8.50 | | | | | (391) meet_of_subsets(all_138_8, all_138_7) = all_262_0 % 56.80/8.50 | | | | | % 56.80/8.50 | | | | | REDUCE: (184), (389) imply: % 56.80/8.50 | | | | | (392) element(all_138_4, all_138_5) = all_214_1 % 56.80/8.50 | | | | | % 56.80/8.50 | | | | | REDUCE: (165), (378) imply: % 56.80/8.50 | | | | | (393) element(all_138_4, all_138_5) = all_206_1 % 56.80/8.50 | | | | | % 56.80/8.50 | | | | | REDUCE: (161), (388) imply: % 56.80/8.50 | | | | | (394) element(all_138_4, all_138_5) = all_204_0 % 56.80/8.50 | | | | | % 56.80/8.50 | | | | | REDUCE: (341), (348) imply: % 56.80/8.50 | | | | | (395) powerset(all_138_6) = all_262_5 % 56.80/8.50 | | | | | % 56.80/8.50 | | | | | BETA: splitting (157) gives: % 56.80/8.50 | | | | | % 56.80/8.50 | | | | | Case 1: % 56.80/8.50 | | | | | | % 56.80/8.50 | | | | | | (396) ~ (all_202_1 = 0) % 56.80/8.50 | | | | | | % 56.80/8.50 | | | | | | REDUCE: (385), (396) imply: % 56.80/8.50 | | | | | | (397) $false % 56.80/8.50 | | | | | | % 56.80/8.50 | | | | | | CLOSE: (397) is inconsistent. % 56.80/8.50 | | | | | | % 56.80/8.50 | | | | | Case 2: % 56.80/8.50 | | | | | | % 56.80/8.50 | | | | | | (398) ~ (all_202_2 = 0) | all_202_0 = 0 % 56.80/8.50 | | | | | | % 56.80/8.50 | | | | | | BETA: splitting (398) gives: % 56.80/8.50 | | | | | | % 56.80/8.50 | | | | | | Case 1: % 56.80/8.50 | | | | | | | % 56.80/8.50 | | | | | | | (399) ~ (all_202_2 = 0) % 56.80/8.50 | | | | | | | % 56.80/8.50 | | | | | | | REDUCE: (384), (399) imply: % 56.80/8.50 | | | | | | | (400) $false % 56.80/8.50 | | | | | | | % 56.80/8.50 | | | | | | | CLOSE: (400) is inconsistent. % 56.80/8.50 | | | | | | | % 56.80/8.50 | | | | | | Case 2: % 56.80/8.50 | | | | | | | % 56.80/8.50 | | | | | | | (401) all_202_0 = 0 % 56.80/8.50 | | | | | | | % 56.80/8.50 | | | | | | | REDUCE: (314), (401) imply: % 56.80/8.50 | | | | | | | (402) element(all_138_0, all_138_6) = 0 % 56.80/8.50 | | | | | | | % 56.80/8.50 | | | | | | | BETA: splitting (180) gives: % 56.80/8.50 | | | | | | | % 56.80/8.50 | | | | | | | Case 1: % 56.80/8.50 | | | | | | | | % 56.80/8.50 | | | | | | | | (403) ~ (all_212_1 = 0) % 56.80/8.50 | | | | | | | | % 56.80/8.50 | | | | | | | | REDUCE: (361), (403) imply: % 56.80/8.50 | | | | | | | | (404) $false % 56.80/8.50 | | | | | | | | % 56.80/8.50 | | | | | | | | CLOSE: (404) is inconsistent. % 56.80/8.50 | | | | | | | | % 56.80/8.50 | | | | | | | Case 2: % 56.80/8.50 | | | | | | | | % 56.80/8.50 | | | | | | | | (405) ~ (all_212_2 = 0) | all_212_0 = all_138_0 % 56.80/8.50 | | | | | | | | % 56.80/8.50 | | | | | | | | BETA: splitting (405) gives: % 56.80/8.50 | | | | | | | | % 56.80/8.50 | | | | | | | | Case 1: % 56.80/8.50 | | | | | | | | | % 56.80/8.50 | | | | | | | | | (406) ~ (all_212_2 = 0) % 56.80/8.50 | | | | | | | | | % 56.80/8.50 | | | | | | | | | REDUCE: (358), (406) imply: % 56.80/8.50 | | | | | | | | | (407) $false % 56.80/8.50 | | | | | | | | | % 56.80/8.50 | | | | | | | | | CLOSE: (407) is inconsistent. % 56.80/8.50 | | | | | | | | | % 56.80/8.50 | | | | | | | | Case 2: % 56.80/8.50 | | | | | | | | | % 56.80/8.50 | | | | | | | | | (408) all_212_0 = all_138_0 % 56.80/8.50 | | | | | | | | | % 56.80/8.50 | | | | | | | | | REDUCE: (198), (408) imply: % 56.80/8.50 | | | | | | | | | (409) set_difference(all_138_8, all_138_1) = all_138_0 % 56.80/8.50 | | | | | | | | | % 56.80/8.50 | | | | | | | | | REDUCE: (175), (408) imply: % 56.80/8.50 | | | | | | | | | (410) $i(all_138_0) % 56.80/8.50 | | | | | | | | | % 56.80/8.50 | | | | | | | | | GROUND_INST: instantiating (32) with all_138_5, all_262_5, % 56.80/8.50 | | | | | | | | | all_138_6, simplifying with (57), (395) gives: % 56.80/8.50 | | | | | | | | | (411) all_262_5 = all_138_5 % 56.80/8.50 | | | | | | | | | % 56.80/8.50 | | | | | | | | | GROUND_INST: instantiating (36) with 0, all_214_1, all_138_5, % 56.80/8.50 | | | | | | | | | all_138_4, simplifying with (311), (392) gives: % 56.80/8.50 | | | | | | | | | (412) all_214_1 = 0 % 56.80/8.50 | | | | | | | | | % 56.80/8.50 | | | | | | | | | GROUND_INST: instantiating (36) with all_206_1, all_214_1, % 56.80/8.50 | | | | | | | | | all_138_5, all_138_4, simplifying with (392), % 56.80/8.50 | | | | | | | | | (393) gives: % 56.80/8.50 | | | | | | | | | (413) all_214_1 = all_206_1 % 56.80/8.50 | | | | | | | | | % 56.80/8.50 | | | | | | | | | GROUND_INST: instantiating (36) with all_204_0, all_214_1, % 56.80/8.50 | | | | | | | | | all_138_5, all_138_4, simplifying with (392), % 56.80/8.50 | | | | | | | | | (394) gives: % 56.80/8.50 | | | | | | | | | (414) all_214_1 = all_204_0 % 56.80/8.50 | | | | | | | | | % 56.80/8.50 | | | | | | | | | GROUND_INST: instantiating (41) with all_138_1, all_262_0, % 56.80/8.50 | | | | | | | | | all_138_7, all_138_8, simplifying with (62), (391) % 56.80/8.50 | | | | | | | | | gives: % 56.80/8.50 | | | | | | | | | (415) all_262_0 = all_138_1 % 56.80/8.50 | | | | | | | | | % 56.80/8.50 | | | | | | | | | COMBINE_EQS: (413), (414) imply: % 56.80/8.50 | | | | | | | | | (416) all_206_1 = all_204_0 % 56.80/8.50 | | | | | | | | | % 56.80/8.50 | | | | | | | | | COMBINE_EQS: (412), (413) imply: % 56.80/8.50 | | | | | | | | | (417) all_206_1 = 0 % 56.80/8.50 | | | | | | | | | % 56.80/8.50 | | | | | | | | | COMBINE_EQS: (416), (417) imply: % 56.80/8.50 | | | | | | | | | (418) all_204_0 = 0 % 56.80/8.50 | | | | | | | | | % 56.80/8.50 | | | | | | | | | REDUCE: (342), (411) imply: % 56.80/8.50 | | | | | | | | | (419) element(all_138_4, all_138_5) = all_262_4 % 56.80/8.50 | | | | | | | | | % 56.80/8.50 | | | | | | | | | BETA: splitting (167) gives: % 56.80/8.50 | | | | | | | | | % 56.80/8.50 | | | | | | | | | Case 1: % 56.80/8.50 | | | | | | | | | | % 56.80/8.50 | | | | | | | | | | (420) ~ (all_206_1 = 0) % 56.80/8.50 | | | | | | | | | | % 56.80/8.50 | | | | | | | | | | REDUCE: (417), (420) imply: % 56.80/8.50 | | | | | | | | | | (421) $false % 56.80/8.50 | | | | | | | | | | % 56.80/8.50 | | | | | | | | | | CLOSE: (421) is inconsistent. % 56.80/8.50 | | | | | | | | | | % 56.80/8.50 | | | | | | | | | Case 2: % 56.80/8.50 | | | | | | | | | | % 56.80/8.50 | | | | | | | | | | (422) all_206_0 = 0 % 56.80/8.50 | | | | | | | | | | % 56.80/8.50 | | | | | | | | | | REDUCE: (318), (422) imply: % 56.80/8.50 | | | | | | | | | | (423) element(all_138_3, all_138_6) = 0 % 56.80/8.50 | | | | | | | | | | % 56.80/8.50 | | | | | | | | | | GROUND_INST: instantiating (36) with 0, all_262_4, all_138_5, % 56.80/8.50 | | | | | | | | | | all_138_4, simplifying with (311), (419) gives: % 56.80/8.50 | | | | | | | | | | (424) all_262_4 = 0 % 56.80/8.50 | | | | | | | | | | % 56.80/8.50 | | | | | | | | | | BETA: splitting (347) gives: % 56.80/8.50 | | | | | | | | | | % 56.80/8.50 | | | | | | | | | | Case 1: % 56.80/8.50 | | | | | | | | | | | % 56.80/8.50 | | | | | | | | | | | (425) ~ (all_262_4 = 0) % 56.80/8.50 | | | | | | | | | | | % 56.80/8.50 | | | | | | | | | | | REDUCE: (424), (425) imply: % 56.80/8.50 | | | | | | | | | | | (426) $false % 56.80/8.50 | | | | | | | | | | | % 56.80/8.50 | | | | | | | | | | | CLOSE: (426) is inconsistent. % 56.80/8.50 | | | | | | | | | | | % 56.80/8.50 | | | | | | | | | | Case 2: % 56.80/8.50 | | | | | | | | | | | % 56.80/8.50 | | | | | | | | | | | (427) all_262_0 = all_262_2 % 56.80/8.50 | | | | | | | | | | | % 56.80/8.50 | | | | | | | | | | | COMBINE_EQS: (415), (427) imply: % 56.80/8.50 | | | | | | | | | | | (428) all_262_2 = all_138_1 % 56.80/8.50 | | | | | | | | | | | % 56.80/8.50 | | | | | | | | | | | SIMP: (428) implies: % 56.80/8.50 | | | | | | | | | | | (429) all_262_2 = all_138_1 % 56.80/8.51 | | | | | | | | | | | % 56.80/8.51 | | | | | | | | | | | REDUCE: (390), (429) imply: % 56.80/8.51 | | | | | | | | | | | (430) subset_difference(all_138_8, all_138_8, all_138_3) % 56.80/8.51 | | | | | | | | | | | = all_138_1 % 56.80/8.51 | | | | | | | | | | | % 56.80/8.51 | | | | | | | | | | | GROUND_INST: instantiating (23) with all_138_4, all_138_5, % 56.80/8.51 | | | | | | | | | | | simplifying with (51), (52), (311) gives: % 56.80/8.51 | | | | | | | | | | | (431) ? [v0: any] : ? [v1: any] : (empty(all_138_5) = % 56.80/8.51 | | | | | | | | | | | v0 & in(all_138_4, all_138_5) = v1 & (v1 = 0 | % 56.80/8.51 | | | | | | | | | | | v0 = 0)) % 56.80/8.51 | | | | | | | | | | | % 56.80/8.51 | | | | | | | | | | | GROUND_INST: instantiating (1) with all_138_5, all_138_4, 0, % 56.80/8.51 | | | | | | | | | | | simplifying with (51), (52), (311) gives: % 56.80/8.51 | | | | | | | | | | | (432) ? [v0: any] : ? [v1: any] : (empty(all_138_4) = % 56.80/8.51 | | | | | | | | | | | v1 & empty(all_138_5) = v0 & ( ~ (v0 = 0) | v1 = % 56.80/8.51 | | | | | | | | | | | 0)) % 56.80/8.51 | | | | | | | | | | | % 56.80/8.51 | | | | | | | | | | | GROUND_INST: instantiating (24) with all_138_8, all_138_3, % 56.80/8.51 | | | | | | | | | | | all_138_6, all_138_3, simplifying with (48), (53), % 56.80/8.51 | | | | | | | | | | | (56), (423) gives: % 56.80/8.51 | | | | | | | | | | | (433) ? [v0: any] : ? [v1: $i] : ? [v2: any] : % 56.80/8.51 | | | | | | | | | | | (disjoint(all_138_3, all_138_3) = v0 & % 56.80/8.51 | | | | | | | | | | | subset_complement(all_138_8, all_138_3) = v1 & % 56.80/8.51 | | | | | | | | | | | subset(all_138_3, v1) = v2 & $i(v1) & ( ~ (v2 = % 56.80/8.51 | | | | | | | | | | | 0) | v0 = 0) & ( ~ (v0 = 0) | v2 = 0)) % 56.80/8.51 | | | | | | | | | | | % 56.80/8.51 | | | | | | | | | | | GROUND_INST: instantiating (24) with all_138_8, all_138_8, % 56.80/8.51 | | | | | | | | | | | all_138_6, all_138_3, simplifying with (48), (53), % 56.80/8.51 | | | | | | | | | | | (56), (321), (423) gives: % 56.80/8.51 | | | | | | | | | | | (434) ? [v0: any] : ? [v1: $i] : ? [v2: any] : % 56.80/8.51 | | | | | | | | | | | (disjoint(all_138_8, all_138_3) = v0 & % 56.80/8.51 | | | | | | | | | | | subset_complement(all_138_8, all_138_3) = v1 & % 56.80/8.51 | | | | | | | | | | | subset(all_138_8, v1) = v2 & $i(v1) & ( ~ (v2 = % 56.80/8.51 | | | | | | | | | | | 0) | v0 = 0) & ( ~ (v0 = 0) | v2 = 0)) % 56.80/8.51 | | | | | | | | | | | % 56.80/8.51 | | | | | | | | | | | GROUND_INST: instantiating (15) with all_138_8, all_138_3, % 56.80/8.51 | | | | | | | | | | | all_138_6, simplifying with (48), (53), (56), % 56.80/8.51 | | | | | | | | | | | (423) gives: % 56.80/8.51 | | | | | | | | | | | (435) ? [v0: $i] : (subset_complement(all_138_8, v0) = % 56.80/8.51 | | | | | | | | | | | all_138_3 & subset_complement(all_138_8, % 56.80/8.51 | | | | | | | | | | | all_138_3) = v0 & $i(v0)) % 56.80/8.51 | | | | | | | | | | | % 56.80/8.51 | | | | | | | | | | | GROUND_INST: instantiating (2) with all_138_8, all_138_3, % 56.80/8.51 | | | | | | | | | | | all_138_6, simplifying with (48), (53), (56), % 56.80/8.51 | | | | | | | | | | | (423) gives: % 56.80/8.51 | | | | | | | | | | | (436) ? [v0: $i] : (subset_complement(all_138_8, % 56.80/8.51 | | | | | | | | | | | all_138_3) = v0 & set_difference(all_138_8, % 56.80/8.51 | | | | | | | | | | | all_138_3) = v0 & $i(v0)) % 56.80/8.51 | | | | | | | | | | | % 56.80/8.51 | | | | | | | | | | | GROUND_INST: instantiating (8) with all_138_8, all_138_3, % 56.80/8.51 | | | | | | | | | | | all_138_6, simplifying with (48), (53), (56), % 56.80/8.51 | | | | | | | | | | | (423) gives: % 56.80/8.51 | | | | | | | | | | | (437) ? [v0: $i] : (subset_complement(all_138_8, % 56.80/8.51 | | | | | | | | | | | all_138_3) = v0 & element(v0, all_138_6) = 0 & % 56.80/8.51 | | | | | | | | | | | $i(v0)) % 56.80/8.51 | | | | | | | | | | | % 56.80/8.51 | | | | | | | | | | | GROUND_INST: instantiating (24) with all_138_8, all_138_1, % 56.80/8.51 | | | | | | | | | | | all_138_6, all_138_1, simplifying with (48), (55), % 56.80/8.51 | | | | | | | | | | | (56), (313) gives: % 56.80/8.51 | | | | | | | | | | | (438) ? [v0: any] : ? [v1: $i] : ? [v2: any] : % 56.80/8.51 | | | | | | | | | | | (disjoint(all_138_1, all_138_1) = v0 & % 56.80/8.51 | | | | | | | | | | | subset_complement(all_138_8, all_138_1) = v1 & % 56.80/8.51 | | | | | | | | | | | subset(all_138_1, v1) = v2 & $i(v1) & ( ~ (v2 = % 56.80/8.51 | | | | | | | | | | | 0) | v0 = 0) & ( ~ (v0 = 0) | v2 = 0)) % 56.80/8.51 | | | | | | | | | | | % 56.80/8.51 | | | | | | | | | | | GROUND_INST: instantiating (24) with all_138_8, all_138_3, % 56.80/8.51 | | | | | | | | | | | all_138_6, all_138_1, simplifying with (48), (53), % 56.80/8.51 | | | | | | | | | | | (55), (56), (313), (423) gives: % 56.80/8.51 | | | | | | | | | | | (439) ? [v0: any] : ? [v1: $i] : ? [v2: any] : % 56.80/8.51 | | | | | | | | | | | (disjoint(all_138_3, all_138_1) = v0 & % 56.80/8.51 | | | | | | | | | | | subset_complement(all_138_8, all_138_1) = v1 & % 56.80/8.51 | | | | | | | | | | | subset(all_138_3, v1) = v2 & $i(v1) & ( ~ (v2 = % 56.80/8.51 | | | | | | | | | | | 0) | v0 = 0) & ( ~ (v0 = 0) | v2 = 0)) % 56.80/8.51 | | | | | | | | | | | % 56.80/8.51 | | | | | | | | | | | GROUND_INST: instantiating (24) with all_138_8, all_138_1, % 56.80/8.51 | | | | | | | | | | | all_138_6, all_138_3, simplifying with (48), (53), % 56.80/8.51 | | | | | | | | | | | (55), (56), (313), (423) gives: % 56.80/8.51 | | | | | | | | | | | (440) ? [v0: any] : ? [v1: $i] : ? [v2: any] : % 56.80/8.51 | | | | | | | | | | | (disjoint(all_138_1, all_138_3) = v0 & % 56.80/8.51 | | | | | | | | | | | subset_complement(all_138_8, all_138_3) = v1 & % 56.80/8.51 | | | | | | | | | | | subset(all_138_1, v1) = v2 & $i(v1) & ( ~ (v2 = % 56.80/8.51 | | | | | | | | | | | 0) | v0 = 0) & ( ~ (v0 = 0) | v2 = 0)) % 56.80/8.51 | | | | | | | | | | | % 56.80/8.51 | | | | | | | | | | | GROUND_INST: instantiating (24) with all_138_8, all_138_8, % 56.80/8.51 | | | | | | | | | | | all_138_6, all_138_1, simplifying with (48), (55), % 56.80/8.51 | | | | | | | | | | | (56), (313), (321) gives: % 56.80/8.51 | | | | | | | | | | | (441) ? [v0: any] : ? [v1: $i] : ? [v2: any] : % 56.80/8.51 | | | | | | | | | | | (disjoint(all_138_8, all_138_1) = v0 & % 56.80/8.51 | | | | | | | | | | | subset_complement(all_138_8, all_138_1) = v1 & % 56.80/8.51 | | | | | | | | | | | subset(all_138_8, v1) = v2 & $i(v1) & ( ~ (v2 = % 56.80/8.51 | | | | | | | | | | | 0) | v0 = 0) & ( ~ (v0 = 0) | v2 = 0)) % 56.80/8.51 | | | | | | | | | | | % 56.80/8.51 | | | | | | | | | | | GROUND_INST: instantiating (15) with all_138_8, all_138_1, % 56.80/8.51 | | | | | | | | | | | all_138_6, simplifying with (48), (55), (56), % 56.80/8.51 | | | | | | | | | | | (313) gives: % 56.80/8.51 | | | | | | | | | | | (442) ? [v0: $i] : (subset_complement(all_138_8, v0) = % 56.80/8.51 | | | | | | | | | | | all_138_1 & subset_complement(all_138_8, % 56.80/8.51 | | | | | | | | | | | all_138_1) = v0 & $i(v0)) % 56.80/8.51 | | | | | | | | | | | % 56.80/8.51 | | | | | | | | | | | GROUND_INST: instantiating (2) with all_138_8, all_138_1, % 56.80/8.51 | | | | | | | | | | | all_138_6, simplifying with (48), (55), (56), % 56.80/8.51 | | | | | | | | | | | (313) gives: % 56.80/8.51 | | | | | | | | | | | (443) ? [v0: $i] : (subset_complement(all_138_8, % 56.80/8.51 | | | | | | | | | | | all_138_1) = v0 & set_difference(all_138_8, % 56.80/8.51 | | | | | | | | | | | all_138_1) = v0 & $i(v0)) % 56.80/8.51 | | | | | | | | | | | % 56.80/8.51 | | | | | | | | | | | GROUND_INST: instantiating (8) with all_138_8, all_138_1, % 56.80/8.51 | | | | | | | | | | | all_138_6, simplifying with (48), (55), (56), % 56.80/8.51 | | | | | | | | | | | (313) gives: % 56.80/8.51 | | | | | | | | | | | (444) ? [v0: $i] : (subset_complement(all_138_8, % 56.80/8.51 | | | | | | | | | | | all_138_1) = v0 & element(v0, all_138_6) = 0 & % 56.80/8.51 | | | | | | | | | | | $i(v0)) % 56.80/8.51 | | | | | | | | | | | % 56.80/8.51 | | | | | | | | | | | GROUND_INST: instantiating (24) with all_138_8, all_138_0, % 56.80/8.51 | | | | | | | | | | | all_138_6, all_138_0, simplifying with (48), (56), % 56.80/8.51 | | | | | | | | | | | (402), (410) gives: % 56.80/8.51 | | | | | | | | | | | (445) ? [v0: any] : ? [v1: $i] : ? [v2: any] : % 56.80/8.51 | | | | | | | | | | | (disjoint(all_138_0, all_138_0) = v0 & % 56.80/8.51 | | | | | | | | | | | subset_complement(all_138_8, all_138_0) = v1 & % 56.80/8.51 | | | | | | | | | | | subset(all_138_0, v1) = v2 & $i(v1) & ( ~ (v2 = % 56.80/8.51 | | | | | | | | | | | 0) | v0 = 0) & ( ~ (v0 = 0) | v2 = 0)) % 56.80/8.51 | | | | | | | | | | | % 56.80/8.51 | | | | | | | | | | | GROUND_INST: instantiating (24) with all_138_8, all_138_1, % 56.80/8.51 | | | | | | | | | | | all_138_6, all_138_0, simplifying with (48), (55), % 56.80/8.51 | | | | | | | | | | | (56), (313), (402), (410) gives: % 56.80/8.51 | | | | | | | | | | | (446) ? [v0: any] : ? [v1: $i] : ? [v2: any] : % 56.80/8.51 | | | | | | | | | | | (disjoint(all_138_1, all_138_0) = v0 & % 56.80/8.51 | | | | | | | | | | | subset_complement(all_138_8, all_138_0) = v1 & % 56.80/8.51 | | | | | | | | | | | subset(all_138_1, v1) = v2 & $i(v1) & ( ~ (v2 = % 56.80/8.51 | | | | | | | | | | | 0) | v0 = 0) & ( ~ (v0 = 0) | v2 = 0)) % 56.80/8.51 | | | | | | | | | | | % 56.80/8.51 | | | | | | | | | | | GROUND_INST: instantiating (24) with all_138_8, all_138_0, % 56.80/8.51 | | | | | | | | | | | all_138_6, all_138_1, simplifying with (48), (55), % 56.80/8.51 | | | | | | | | | | | (56), (313), (402), (410) gives: % 56.80/8.51 | | | | | | | | | | | (447) ? [v0: any] : ? [v1: $i] : ? [v2: any] : % 56.80/8.51 | | | | | | | | | | | (disjoint(all_138_0, all_138_1) = v0 & % 56.80/8.51 | | | | | | | | | | | subset_complement(all_138_8, all_138_1) = v1 & % 56.80/8.51 | | | | | | | | | | | subset(all_138_0, v1) = v2 & $i(v1) & ( ~ (v2 = % 56.80/8.51 | | | | | | | | | | | 0) | v0 = 0) & ( ~ (v0 = 0) | v2 = 0)) % 56.80/8.51 | | | | | | | | | | | % 56.88/8.51 | | | | | | | | | | | GROUND_INST: instantiating (24) with all_138_8, all_138_3, % 56.88/8.51 | | | | | | | | | | | all_138_6, all_138_0, simplifying with (48), (53), % 56.88/8.51 | | | | | | | | | | | (56), (402), (410), (423) gives: % 56.88/8.51 | | | | | | | | | | | (448) ? [v0: any] : ? [v1: $i] : ? [v2: any] : % 56.88/8.51 | | | | | | | | | | | (disjoint(all_138_3, all_138_0) = v0 & % 56.88/8.51 | | | | | | | | | | | subset_complement(all_138_8, all_138_0) = v1 & % 56.88/8.51 | | | | | | | | | | | subset(all_138_3, v1) = v2 & $i(v1) & ( ~ (v2 = % 56.88/8.51 | | | | | | | | | | | 0) | v0 = 0) & ( ~ (v0 = 0) | v2 = 0)) % 56.88/8.51 | | | | | | | | | | | % 56.88/8.51 | | | | | | | | | | | GROUND_INST: instantiating (24) with all_138_8, all_138_0, % 56.88/8.51 | | | | | | | | | | | all_138_6, all_138_3, simplifying with (48), (53), % 56.88/8.51 | | | | | | | | | | | (56), (402), (410), (423) gives: % 56.88/8.52 | | | | | | | | | | | (449) ? [v0: any] : ? [v1: $i] : ? [v2: any] : % 56.88/8.52 | | | | | | | | | | | (disjoint(all_138_0, all_138_3) = v0 & % 56.88/8.52 | | | | | | | | | | | subset_complement(all_138_8, all_138_3) = v1 & % 56.88/8.52 | | | | | | | | | | | subset(all_138_0, v1) = v2 & $i(v1) & ( ~ (v2 = % 56.88/8.52 | | | | | | | | | | | 0) | v0 = 0) & ( ~ (v0 = 0) | v2 = 0)) % 56.88/8.52 | | | | | | | | | | | % 56.88/8.52 | | | | | | | | | | | GROUND_INST: instantiating (24) with all_138_8, all_138_8, % 56.88/8.52 | | | | | | | | | | | all_138_6, all_138_0, simplifying with (48), (56), % 56.88/8.52 | | | | | | | | | | | (321), (402), (410) gives: % 56.88/8.52 | | | | | | | | | | | (450) ? [v0: any] : ? [v1: $i] : ? [v2: any] : % 56.88/8.52 | | | | | | | | | | | (disjoint(all_138_8, all_138_0) = v0 & % 56.88/8.52 | | | | | | | | | | | subset_complement(all_138_8, all_138_0) = v1 & % 56.88/8.52 | | | | | | | | | | | subset(all_138_8, v1) = v2 & $i(v1) & ( ~ (v2 = % 56.88/8.52 | | | | | | | | | | | 0) | v0 = 0) & ( ~ (v0 = 0) | v2 = 0)) % 56.88/8.52 | | | | | | | | | | | % 56.88/8.52 | | | | | | | | | | | GROUND_INST: instantiating (15) with all_138_8, all_138_0, % 56.88/8.52 | | | | | | | | | | | all_138_6, simplifying with (48), (56), (402), % 56.88/8.52 | | | | | | | | | | | (410) gives: % 56.88/8.52 | | | | | | | | | | | (451) ? [v0: $i] : (subset_complement(all_138_8, v0) = % 56.88/8.52 | | | | | | | | | | | all_138_0 & subset_complement(all_138_8, % 56.88/8.52 | | | | | | | | | | | all_138_0) = v0 & $i(v0)) % 56.88/8.52 | | | | | | | | | | | % 56.88/8.52 | | | | | | | | | | | GROUND_INST: instantiating (2) with all_138_8, all_138_0, % 56.88/8.52 | | | | | | | | | | | all_138_6, simplifying with (48), (56), (402), % 56.88/8.52 | | | | | | | | | | | (410) gives: % 56.88/8.52 | | | | | | | | | | | (452) ? [v0: $i] : (subset_complement(all_138_8, % 56.88/8.52 | | | | | | | | | | | all_138_0) = v0 & set_difference(all_138_8, % 56.88/8.52 | | | | | | | | | | | all_138_0) = v0 & $i(v0)) % 56.88/8.52 | | | | | | | | | | | % 56.88/8.52 | | | | | | | | | | | GROUND_INST: instantiating (8) with all_138_8, all_138_0, % 56.88/8.52 | | | | | | | | | | | all_138_6, simplifying with (48), (56), (402), % 56.88/8.52 | | | | | | | | | | | (410) gives: % 56.88/8.52 | | | | | | | | | | | (453) ? [v0: $i] : (subset_complement(all_138_8, % 56.88/8.52 | | | | | | | | | | | all_138_0) = v0 & element(v0, all_138_6) = 0 & % 56.88/8.52 | | | | | | | | | | | $i(v0)) % 56.88/8.52 | | | | | | | | | | | % 56.88/8.52 | | | | | | | | | | | GROUND_INST: instantiating (194) with all_162_0, simplifying % 56.88/8.52 | | | | | | | | | | | with (106), (107) gives: % 56.88/8.52 | | | | | | | | | | | (454) all_220_0 = all_162_0 | ? [v0: $i] : ? [v1: any] % 56.88/8.52 | | | | | | | | | | | : ? [v2: $i] : ? [v3: any] : % 56.88/8.52 | | | | | | | | | | | (subset_complement(all_138_8, v0) = v2 & % 56.88/8.52 | | | | | | | | | | | element(v0, all_138_6) = 0 & in(v2, all_138_7) = % 56.88/8.52 | | | | | | | | | | | v3 & in(v0, all_162_0) = v1 & $i(v2) & $i(v0) & % 56.88/8.52 | | | | | | | | | | | ( ~ (v3 = 0) | ~ (v1 = 0)) & (v3 = 0 | v1 = 0)) % 56.88/8.52 | | | | | | | | | | | % 56.88/8.52 | | | | | | | | | | | GROUND_INST: instantiating (23) with all_162_0, all_138_5, % 56.88/8.52 | | | | | | | | | | | simplifying with (51), (106), (107) gives: % 56.88/8.52 | | | | | | | | | | | (455) ? [v0: any] : ? [v1: any] : (empty(all_138_5) = % 56.88/8.52 | | | | | | | | | | | v0 & in(all_162_0, all_138_5) = v1 & (v1 = 0 | % 56.88/8.52 | | | | | | | | | | | v0 = 0)) % 56.88/8.52 | | | | | | | | | | | % 56.88/8.52 | | | | | | | | | | | GROUND_INST: instantiating (24) with all_138_8, all_164_0, % 56.88/8.52 | | | | | | | | | | | all_138_6, all_138_0, simplifying with (48), (56), % 56.88/8.52 | | | | | | | | | | | (110), (111), (402), (410) gives: % 56.88/8.52 | | | | | | | | | | | (456) ? [v0: any] : ? [v1: $i] : ? [v2: any] : % 56.88/8.52 | | | | | | | | | | | (disjoint(all_164_0, all_138_0) = v0 & % 56.88/8.52 | | | | | | | | | | | subset_complement(all_138_8, all_138_0) = v1 & % 56.88/8.52 | | | | | | | | | | | subset(all_164_0, v1) = v2 & $i(v1) & ( ~ (v2 = % 56.88/8.52 | | | | | | | | | | | 0) | v0 = 0) & ( ~ (v0 = 0) | v2 = 0)) % 56.88/8.52 | | | | | | | | | | | % 56.88/8.52 | | | | | | | | | | | GROUND_INST: instantiating (24) with all_138_8, all_164_0, % 56.88/8.52 | | | | | | | | | | | all_138_6, all_138_1, simplifying with (48), (55), % 56.88/8.52 | | | | | | | | | | | (56), (110), (111), (313) gives: % 56.88/8.52 | | | | | | | | | | | (457) ? [v0: any] : ? [v1: $i] : ? [v2: any] : % 56.88/8.52 | | | | | | | | | | | (disjoint(all_164_0, all_138_1) = v0 & % 56.88/8.52 | | | | | | | | | | | subset_complement(all_138_8, all_138_1) = v1 & % 56.88/8.52 | | | | | | | | | | | subset(all_164_0, v1) = v2 & $i(v1) & ( ~ (v2 = % 56.88/8.52 | | | | | | | | | | | 0) | v0 = 0) & ( ~ (v0 = 0) | v2 = 0)) % 56.88/8.52 | | | | | | | | | | | % 56.88/8.52 | | | | | | | | | | | GROUND_INST: instantiating (24) with all_138_8, all_164_0, % 56.88/8.52 | | | | | | | | | | | all_138_6, all_138_3, simplifying with (48), (53), % 56.88/8.52 | | | | | | | | | | | (56), (110), (111), (423) gives: % 56.88/8.52 | | | | | | | | | | | (458) ? [v0: any] : ? [v1: $i] : ? [v2: any] : % 56.88/8.52 | | | | | | | | | | | (disjoint(all_164_0, all_138_3) = v0 & % 56.88/8.52 | | | | | | | | | | | subset_complement(all_138_8, all_138_3) = v1 & % 56.88/8.52 | | | | | | | | | | | subset(all_164_0, v1) = v2 & $i(v1) & ( ~ (v2 = % 56.88/8.52 | | | | | | | | | | | 0) | v0 = 0) & ( ~ (v0 = 0) | v2 = 0)) % 56.88/8.52 | | | | | | | | | | | % 56.88/8.52 | | | | | | | | | | | GROUND_INST: instantiating (19) with all_138_8, all_168_0, % 56.88/8.52 | | | | | | | | | | | all_138_6, all_138_5, simplifying with (48), (56), % 56.88/8.52 | | | | | | | | | | | (57), (116), (117) gives: % 56.88/8.52 | | | | | | | | | | | (459) ? [v0: $i] : (union_of_subsets(all_138_8, % 56.88/8.52 | | | | | | | | | | | all_168_0) = v0 & union(all_168_0) = v0 & % 56.88/8.52 | | | | | | | | | | | $i(v0)) % 56.88/8.52 | | | | | | | | | | | % 56.88/8.52 | | | | | | | | | | | GROUND_INST: instantiating (10) with all_138_8, all_168_0, % 56.88/8.52 | | | | | | | | | | | all_138_6, all_138_5, simplifying with (48), (56), % 56.88/8.52 | | | | | | | | | | | (57), (116), (117) gives: % 56.88/8.52 | | | | | | | | | | | (460) ? [v0: $i] : (union_of_subsets(all_138_8, % 56.88/8.52 | | | | | | | | | | | all_168_0) = v0 & element(v0, all_138_6) = 0 & % 56.88/8.52 | | | | | | | | | | | $i(v0)) % 56.88/8.52 | | | | | | | | | | | % 56.88/8.52 | | | | | | | | | | | GROUND_INST: instantiating (23) with all_168_0, all_138_5, % 56.88/8.52 | | | | | | | | | | | simplifying with (51), (116), (117) gives: % 56.88/8.52 | | | | | | | | | | | (461) ? [v0: any] : ? [v1: any] : (empty(all_138_5) = % 56.88/8.52 | | | | | | | | | | | v0 & in(all_168_0, all_138_5) = v1 & (v1 = 0 | % 56.88/8.52 | | | | | | | | | | | v0 = 0)) % 56.88/8.52 | | | | | | | | | | | % 56.88/8.52 | | | | | | | | | | | GROUND_INST: instantiating (23) with all_172_0, all_138_5, % 56.88/8.52 | | | | | | | | | | | simplifying with (51), (310), (330) gives: % 56.88/8.52 | | | | | | | | | | | (462) ? [v0: any] : ? [v1: any] : (empty(all_138_5) = % 56.88/8.52 | | | | | | | | | | | v0 & in(all_172_0, all_138_5) = v1 & (v1 = 0 | % 56.88/8.52 | | | | | | | | | | | v0 = 0)) % 56.88/8.52 | | | | | | | | | | | % 56.88/8.52 | | | | | | | | | | | GROUND_INST: instantiating (24) with all_138_8, all_176_0, % 56.88/8.52 | | | | | | | | | | | all_138_6, all_138_0, simplifying with (48), (56), % 56.88/8.52 | | | | | | | | | | | (312), (331), (402), (410) gives: % 56.88/8.52 | | | | | | | | | | | (463) ? [v0: any] : ? [v1: $i] : ? [v2: any] : % 56.88/8.52 | | | | | | | | | | | (disjoint(all_176_0, all_138_0) = v0 & % 56.88/8.52 | | | | | | | | | | | subset_complement(all_138_8, all_138_0) = v1 & % 56.88/8.52 | | | | | | | | | | | subset(all_176_0, v1) = v2 & $i(v1) & ( ~ (v2 = % 56.88/8.52 | | | | | | | | | | | 0) | v0 = 0) & ( ~ (v0 = 0) | v2 = 0)) % 56.88/8.52 | | | | | | | | | | | % 56.88/8.52 | | | | | | | | | | | GROUND_INST: instantiating (24) with all_138_8, all_176_0, % 56.88/8.52 | | | | | | | | | | | all_138_6, all_138_1, simplifying with (48), (55), % 56.88/8.52 | | | | | | | | | | | (56), (312), (313), (331) gives: % 56.88/8.52 | | | | | | | | | | | (464) ? [v0: any] : ? [v1: $i] : ? [v2: any] : % 56.88/8.52 | | | | | | | | | | | (disjoint(all_176_0, all_138_1) = v0 & % 56.88/8.52 | | | | | | | | | | | subset_complement(all_138_8, all_138_1) = v1 & % 56.88/8.52 | | | | | | | | | | | subset(all_176_0, v1) = v2 & $i(v1) & ( ~ (v2 = % 56.88/8.52 | | | | | | | | | | | 0) | v0 = 0) & ( ~ (v0 = 0) | v2 = 0)) % 56.88/8.52 | | | | | | | | | | | % 56.88/8.52 | | | | | | | | | | | GROUND_INST: instantiating (24) with all_138_8, all_176_0, % 56.88/8.52 | | | | | | | | | | | all_138_6, all_138_3, simplifying with (48), (53), % 56.88/8.52 | | | | | | | | | | | (56), (312), (331), (423) gives: % 56.88/8.52 | | | | | | | | | | | (465) ? [v0: any] : ? [v1: $i] : ? [v2: any] : % 56.88/8.52 | | | | | | | | | | | (disjoint(all_176_0, all_138_3) = v0 & % 56.88/8.52 | | | | | | | | | | | subset_complement(all_138_8, all_138_3) = v1 & % 56.88/8.52 | | | | | | | | | | | subset(all_176_0, v1) = v2 & $i(v1) & ( ~ (v2 = % 56.88/8.52 | | | | | | | | | | | 0) | v0 = 0) & ( ~ (v0 = 0) | v2 = 0)) % 56.88/8.52 | | | | | | | | | | | % 56.88/8.52 | | | | | | | | | | | GROUND_INST: instantiating (t8_boole) with all_164_0, % 56.88/8.52 | | | | | | | | | | | all_188_0, simplifying with (110), (112), (146), % 56.88/8.52 | | | | | | | | | | | (147) gives: % 56.88/8.52 | | | | | | | | | | | (466) all_188_0 = all_164_0 % 56.88/8.52 | | | | | | | | | | | % 56.88/8.52 | | | | | | | | | | | GROUND_INST: instantiating (t8_boole) with all_162_0, % 56.88/8.52 | | | | | | | | | | | all_188_0, simplifying with (106), (108), (146), % 56.88/8.52 | | | | | | | | | | | (147) gives: % 56.88/8.52 | | | | | | | | | | | (467) all_188_0 = all_162_0 % 56.88/8.52 | | | | | | | | | | | % 56.88/8.52 | | | | | | | | | | | GROUND_INST: instantiating (29) with all_188_0, simplifying % 56.88/8.52 | | | | | | | | | | | with (146), (147) gives: % 56.88/8.52 | | | | | | | | | | | (468) all_188_0 = empty_set % 56.88/8.52 | | | | | | | | | | | % 56.88/8.52 | | | | | | | | | | | GROUND_INST: instantiating (d4_subset_1) with all_138_6, % 56.88/8.52 | | | | | | | | | | | all_168_0, simplifying with (50), (118) gives: % 56.88/8.52 | | | | | | | | | | | (469) all_168_0 = all_138_6 % 56.88/8.52 | | | | | | | | | | | % 56.88/8.52 | | | | | | | | | | | GROUND_INST: instantiating (3) with all_138_8, all_138_1, % 56.88/8.52 | | | | | | | | | | | all_138_0, simplifying with (48), (55), (409) % 56.88/8.52 | | | | | | | | | | | gives: % 56.88/8.52 | | | | | | | | | | | (470) ? [v0: $i] : ? [v1: any] : ? [v2: $i] : % 56.88/8.52 | | | | | | | | | | | (subset_complement(all_138_8, all_138_1) = v2 & % 56.88/8.52 | | | | | | | | | | | element(all_138_1, v0) = v1 & % 56.88/8.52 | | | | | | | | | | | powerset(all_138_8) = v0 & $i(v2) & $i(v0) & ( ~ % 56.88/8.52 | | | | | | | | | | | (v1 = 0) | v2 = all_138_0)) % 56.88/8.52 | | | | | | | | | | | % 56.88/8.52 | | | | | | | | | | | GROUND_INST: instantiating (4) with all_138_8, all_138_4, % 56.88/8.52 | | | | | | | | | | | all_138_7, simplifying with (48), (52), (309) % 56.88/8.52 | | | | | | | | | | | gives: % 56.88/8.53 | | | | | | | | | | | (471) ? [v0: $i] : ? [v1: $i] : ? [v2: any] : % 56.88/8.53 | | | | | | | | | | | (element(all_138_4, v1) = v2 & powerset(v0) = v1 & % 56.88/8.53 | | | | | | | | | | | powerset(all_138_8) = v0 & $i(v1) & $i(v0) & ( ~ % 56.88/8.53 | | | | | | | | | | | (v2 = 0) | ( ! [v3: $i] : ! [v4: $i] : ( ~ % 56.88/8.53 | | | | | | | | | | | (subset_complement(all_138_8, v3) = v4) | % 56.88/8.53 | | | | | | | | | | | ~ (element(all_138_7, v1) = 0) | ~ $i(v3) % 56.88/8.53 | | | | | | | | | | | | ~ $i(all_138_7) | ? [v5: any] : ? % 56.88/8.53 | | | | | | | | | | | [v6: any] : ? [v7: any] : (element(v3, % 56.88/8.53 | | | | | | | | | | | v0) = v5 & in(v4, all_138_4) = v7 & % 56.88/8.53 | | | | | | | | | | | in(v3, all_138_7) = v6 & ( ~ (v5 = 0) | % 56.88/8.53 | | | | | | | | | | | (( ~ (v7 = 0) | v6 = 0) & ( ~ (v6 = 0) % 56.88/8.53 | | | | | | | | | | | | v7 = 0))))) & ! [v3: $i] : ! % 56.88/8.53 | | | | | | | | | | | [v4: any] : ( ~ (element(all_138_7, v1) = 0) % 56.88/8.53 | | | | | | | | | | | | ~ (in(v3, all_138_7) = v4) | ~ $i(v3) % 56.88/8.53 | | | | | | | | | | | | ~ $i(all_138_7) | ? [v5: any] : ? % 56.88/8.53 | | | | | | | | | | | [v6: $i] : ? [v7: any] : % 56.88/8.53 | | | | | | | | | | | (subset_complement(all_138_8, v3) = v6 & % 56.88/8.53 | | | | | | | | | | | element(v3, v0) = v5 & in(v6, all_138_4) % 56.88/8.53 | | | | | | | | | | | = v7 & $i(v6) & ( ~ (v5 = 0) | (( ~ (v7 % 56.88/8.53 | | | | | | | | | | | = 0) | v4 = 0) & ( ~ (v4 = 0) | % 56.88/8.53 | | | | | | | | | | | v7 = 0))))) & ! [v3: any] : (v3 = % 56.88/8.53 | | | | | | | | | | | all_138_7 | ~ (element(v3, v1) = 0) | ~ % 56.88/8.53 | | | | | | | | | | | $i(v3) | ? [v4: $i] : ? [v5: any] : ? % 56.88/8.53 | | | | | | | | | | | [v6: $i] : ? [v7: any] : % 56.88/8.53 | | | | | | | | | | | (subset_complement(all_138_8, v4) = v6 & % 56.88/8.53 | | | | | | | | | | | element(v4, v0) = 0 & in(v6, all_138_4) % 56.88/8.53 | | | | | | | | | | | = v7 & in(v4, v3) = v5 & $i(v6) & $i(v4) % 56.88/8.53 | | | | | | | | | | | & ( ~ (v7 = 0) | ~ (v5 = 0)) & (v7 = 0 % 56.88/8.53 | | | | | | | | | | | | v5 = 0))) & ! [v3: $i] : ( ~ % 56.88/8.53 | | | | | | | | | | | (element(v3, v0) = 0) | ~ % 56.88/8.53 | | | | | | | | | | | (element(all_138_7, v1) = 0) | ~ $i(v3) | % 56.88/8.53 | | | | | | | | | | | ~ $i(all_138_7) | ? [v4: any] : ? [v5: % 56.88/8.53 | | | | | | | | | | | $i] : ? [v6: any] : % 56.88/8.53 | | | | | | | | | | | (subset_complement(all_138_8, v3) = v5 & % 56.88/8.53 | | | | | | | | | | | in(v5, all_138_4) = v6 & in(v3, % 56.88/8.53 | | | | | | | | | | | all_138_7) = v4 & $i(v5) & ( ~ (v6 = % 56.88/8.53 | | | | | | | | | | | 0) | v4 = 0) & ( ~ (v4 = 0) | v6 = % 56.88/8.53 | | | | | | | | | | | 0)))))) % 56.88/8.53 | | | | | | | | | | | % 56.88/8.53 | | | | | | | | | | | GROUND_INST: instantiating (11) with all_138_8, all_138_4, % 56.88/8.53 | | | | | | | | | | | all_238_1, simplifying with (48), (52), (308) % 56.88/8.53 | | | | | | | | | | | gives: % 56.88/8.53 | | | | | | | | | | | (472) ? [v0: $i] : ? [v1: $i] : ? [v2: any] : ? [v3: % 56.88/8.53 | | | | | | | | | | | any] : (element(all_238_1, v0) = v3 & % 56.88/8.53 | | | | | | | | | | | element(all_138_4, v1) = v2 & powerset(v0) = v1 % 56.88/8.53 | | | | | | | | | | | & powerset(all_138_8) = v0 & $i(v1) & $i(v0) & ( % 56.88/8.53 | | | | | | | | | | | ~ (v2 = 0) | v3 = 0)) % 56.88/8.53 | | | | | | | | | | | % 56.88/8.53 | | | | | | | | | | | GROUND_INST: instantiating (20) with all_138_8, all_138_4, % 56.88/8.53 | | | | | | | | | | | all_238_1, simplifying with (48), (52), (308) % 56.88/8.53 | | | | | | | | | | | gives: % 56.88/8.53 | | | | | | | | | | | (473) ? [v0: $i] : ? [v1: $i] : ? [v2: any] : ? [v3: % 56.88/8.53 | | | | | | | | | | | $i] : (element(all_138_4, v1) = v2 & % 56.88/8.53 | | | | | | | | | | | powerset(v0) = v1 & powerset(all_138_8) = v0 & % 56.88/8.53 | | | | | | | | | | | set_meet(all_138_4) = v3 & $i(v3) & $i(v1) & % 56.88/8.53 | | | | | | | | | | | $i(v0) & ( ~ (v2 = 0) | v3 = all_238_1)) % 56.88/8.53 | | | | | | | | | | | % 56.88/8.53 | | | | | | | | | | | GROUND_INST: instantiating (redefinition_k6_subset_1) with % 56.88/8.53 | | | | | | | | | | | all_138_8, all_138_8, all_138_3, all_138_1, % 56.88/8.53 | | | | | | | | | | | simplifying with (48), (53), (430) gives: % 56.88/8.53 | | | | | | | | | | | (474) ? [v0: $i] : ? [v1: any] : ? [v2: any] : ? % 56.88/8.53 | | | | | | | | | | | [v3: $i] : (set_difference(all_138_8, all_138_3) = % 56.88/8.53 | | | | | | | | | | | v3 & element(all_138_3, v0) = v2 & % 56.88/8.53 | | | | | | | | | | | element(all_138_8, v0) = v1 & % 56.88/8.53 | | | | | | | | | | | powerset(all_138_8) = v0 & $i(v3) & $i(v0) & ( ~ % 56.88/8.53 | | | | | | | | | | | (v2 = 0) | ~ (v1 = 0) | v3 = all_138_1)) % 56.88/8.53 | | | | | | | | | | | % 56.88/8.53 | | | | | | | | | | | GROUND_INST: instantiating (redefinition_k6_subset_1) with % 56.88/8.53 | | | | | | | | | | | all_138_8, all_138_8, all_176_0, all_238_1, % 56.88/8.53 | | | | | | | | | | | simplifying with (48), (307), (331) gives: % 56.88/8.53 | | | | | | | | | | | (475) ? [v0: $i] : ? [v1: any] : ? [v2: any] : ? % 56.88/8.53 | | | | | | | | | | | [v3: $i] : (set_difference(all_138_8, all_176_0) = % 56.88/8.53 | | | | | | | | | | | v3 & element(all_176_0, v0) = v2 & % 56.88/8.53 | | | | | | | | | | | element(all_138_8, v0) = v1 & % 56.88/8.53 | | | | | | | | | | | powerset(all_138_8) = v0 & $i(v3) & $i(v0) & ( ~ % 56.88/8.53 | | | | | | | | | | | (v2 = 0) | ~ (v1 = 0) | v3 = all_238_1)) % 56.88/8.53 | | | | | | | | | | | % 56.88/8.53 | | | | | | | | | | | GROUND_INST: instantiating (dt_k6_subset_1) with all_138_8, % 56.88/8.53 | | | | | | | | | | | all_138_8, all_176_0, all_238_1, simplifying with % 56.88/8.53 | | | | | | | | | | | (48), (307), (331) gives: % 56.88/8.53 | | | | | | | | | | | (476) ? [v0: $i] : ? [v1: any] : ? [v2: any] : ? % 56.88/8.53 | | | | | | | | | | | [v3: any] : (element(all_238_1, v0) = v3 & % 56.88/8.53 | | | | | | | | | | | element(all_176_0, v0) = v2 & element(all_138_8, % 56.88/8.53 | | | | | | | | | | | v0) = v1 & powerset(all_138_8) = v0 & $i(v0) & % 56.88/8.53 | | | | | | | | | | | ( ~ (v2 = 0) | ~ (v1 = 0) | v3 = 0)) % 56.88/8.53 | | | | | | | | | | | % 56.88/8.53 | | | | | | | | | | | COMBINE_EQS: (466), (468) imply: % 56.88/8.53 | | | | | | | | | | | (477) all_164_0 = empty_set % 56.88/8.53 | | | | | | | | | | | % 56.88/8.53 | | | | | | | | | | | COMBINE_EQS: (466), (467) imply: % 56.88/8.53 | | | | | | | | | | | (478) all_164_0 = all_162_0 % 56.88/8.53 | | | | | | | | | | | % 56.88/8.53 | | | | | | | | | | | COMBINE_EQS: (477), (478) imply: % 56.88/8.53 | | | | | | | | | | | (479) all_162_0 = empty_set % 56.88/8.53 | | | | | | | | | | | % 56.88/8.53 | | | | | | | | | | | SIMP: (479) implies: % 56.88/8.53 | | | | | | | | | | | (480) all_162_0 = empty_set % 56.88/8.53 | | | | | | | | | | | % 56.88/8.53 | | | | | | | | | | | DELTA: instantiating (460) with fresh symbol all_324_0 % 56.88/8.53 | | | | | | | | | | | gives: % 56.88/8.53 | | | | | | | | | | | (481) union_of_subsets(all_138_8, all_168_0) = all_324_0 % 56.88/8.53 | | | | | | | | | | | & element(all_324_0, all_138_6) = 0 & % 56.88/8.53 | | | | | | | | | | | $i(all_324_0) % 56.88/8.53 | | | | | | | | | | | % 56.88/8.53 | | | | | | | | | | | ALPHA: (481) implies: % 56.88/8.53 | | | | | | | | | | | (482) element(all_324_0, all_138_6) = 0 % 56.88/8.53 | | | | | | | | | | | (483) union_of_subsets(all_138_8, all_168_0) = all_324_0 % 56.88/8.53 | | | | | | | | | | | % 56.88/8.53 | | | | | | | | | | | DELTA: instantiating (444) with fresh symbol all_326_0 % 56.88/8.53 | | | | | | | | | | | gives: % 56.88/8.53 | | | | | | | | | | | (484) subset_complement(all_138_8, all_138_1) = % 56.88/8.53 | | | | | | | | | | | all_326_0 & element(all_326_0, all_138_6) = 0 & % 56.88/8.53 | | | | | | | | | | | $i(all_326_0) % 56.88/8.53 | | | | | | | | | | | % 56.88/8.53 | | | | | | | | | | | ALPHA: (484) implies: % 56.88/8.53 | | | | | | | | | | | (485) subset_complement(all_138_8, all_138_1) = % 56.88/8.53 | | | | | | | | | | | all_326_0 % 56.88/8.53 | | | | | | | | | | | % 56.88/8.53 | | | | | | | | | | | DELTA: instantiating (459) with fresh symbol all_340_0 % 56.88/8.53 | | | | | | | | | | | gives: % 56.88/8.53 | | | | | | | | | | | (486) union_of_subsets(all_138_8, all_168_0) = all_340_0 % 56.88/8.53 | | | | | | | | | | | & union(all_168_0) = all_340_0 & $i(all_340_0) % 56.88/8.53 | | | | | | | | | | | % 56.88/8.53 | | | | | | | | | | | ALPHA: (486) implies: % 56.88/8.53 | | | | | | | | | | | (487) union(all_168_0) = all_340_0 % 56.88/8.53 | | | | | | | | | | | (488) union_of_subsets(all_138_8, all_168_0) = all_340_0 % 56.88/8.53 | | | | | | | | | | | % 56.88/8.53 | | | | | | | | | | | DELTA: instantiating (452) with fresh symbol all_350_0 % 56.88/8.53 | | | | | | | | | | | gives: % 56.88/8.53 | | | | | | | | | | | (489) subset_complement(all_138_8, all_138_0) = % 56.88/8.53 | | | | | | | | | | | all_350_0 & set_difference(all_138_8, all_138_0) = % 56.88/8.53 | | | | | | | | | | | all_350_0 & $i(all_350_0) % 56.88/8.53 | | | | | | | | | | | % 56.88/8.53 | | | | | | | | | | | ALPHA: (489) implies: % 56.88/8.53 | | | | | | | | | | | (490) subset_complement(all_138_8, all_138_0) = % 56.88/8.53 | | | | | | | | | | | all_350_0 % 56.88/8.53 | | | | | | | | | | | % 56.88/8.53 | | | | | | | | | | | DELTA: instantiating (451) with fresh symbol all_352_0 % 56.88/8.53 | | | | | | | | | | | gives: % 56.88/8.53 | | | | | | | | | | | (491) subset_complement(all_138_8, all_352_0) = % 56.88/8.53 | | | | | | | | | | | all_138_0 & subset_complement(all_138_8, % 56.88/8.53 | | | | | | | | | | | all_138_0) = all_352_0 & $i(all_352_0) % 56.88/8.53 | | | | | | | | | | | % 56.88/8.53 | | | | | | | | | | | ALPHA: (491) implies: % 56.88/8.53 | | | | | | | | | | | (492) subset_complement(all_138_8, all_138_0) = % 56.88/8.53 | | | | | | | | | | | all_352_0 % 56.88/8.53 | | | | | | | | | | | (493) subset_complement(all_138_8, all_352_0) = % 56.88/8.53 | | | | | | | | | | | all_138_0 % 56.88/8.53 | | | | | | | | | | | % 56.88/8.53 | | | | | | | | | | | DELTA: instantiating (443) with fresh symbol all_354_0 % 56.88/8.53 | | | | | | | | | | | gives: % 56.88/8.53 | | | | | | | | | | | (494) subset_complement(all_138_8, all_138_1) = % 56.88/8.53 | | | | | | | | | | | all_354_0 & set_difference(all_138_8, all_138_1) = % 56.88/8.53 | | | | | | | | | | | all_354_0 & $i(all_354_0) % 56.88/8.53 | | | | | | | | | | | % 56.88/8.53 | | | | | | | | | | | ALPHA: (494) implies: % 56.88/8.53 | | | | | | | | | | | (495) set_difference(all_138_8, all_138_1) = all_354_0 % 56.88/8.53 | | | | | | | | | | | (496) subset_complement(all_138_8, all_138_1) = % 56.88/8.53 | | | | | | | | | | | all_354_0 % 56.88/8.53 | | | | | | | | | | | % 56.88/8.53 | | | | | | | | | | | DELTA: instantiating (442) with fresh symbol all_356_0 % 56.88/8.53 | | | | | | | | | | | gives: % 56.88/8.53 | | | | | | | | | | | (497) subset_complement(all_138_8, all_356_0) = % 56.88/8.53 | | | | | | | | | | | all_138_1 & subset_complement(all_138_8, % 56.88/8.53 | | | | | | | | | | | all_138_1) = all_356_0 & $i(all_356_0) % 56.88/8.53 | | | | | | | | | | | % 56.88/8.53 | | | | | | | | | | | ALPHA: (497) implies: % 56.88/8.53 | | | | | | | | | | | (498) subset_complement(all_138_8, all_138_1) = % 56.88/8.53 | | | | | | | | | | | all_356_0 % 56.88/8.53 | | | | | | | | | | | (499) subset_complement(all_138_8, all_356_0) = % 56.88/8.53 | | | | | | | | | | | all_138_1 % 56.88/8.53 | | | | | | | | | | | % 56.88/8.53 | | | | | | | | | | | DELTA: instantiating (437) with fresh symbol all_442_0 % 56.88/8.53 | | | | | | | | | | | gives: % 56.88/8.54 | | | | | | | | | | | (500) subset_complement(all_138_8, all_138_3) = % 56.88/8.54 | | | | | | | | | | | all_442_0 & element(all_442_0, all_138_6) = 0 & % 56.88/8.54 | | | | | | | | | | | $i(all_442_0) % 56.88/8.54 | | | | | | | | | | | % 56.88/8.54 | | | | | | | | | | | ALPHA: (500) implies: % 56.88/8.54 | | | | | | | | | | | (501) subset_complement(all_138_8, all_138_3) = % 56.88/8.54 | | | | | | | | | | | all_442_0 % 56.88/8.54 | | | | | | | | | | | % 56.88/8.54 | | | | | | | | | | | DELTA: instantiating (436) with fresh symbol all_448_0 % 56.88/8.54 | | | | | | | | | | | gives: % 56.88/8.54 | | | | | | | | | | | (502) subset_complement(all_138_8, all_138_3) = % 56.88/8.54 | | | | | | | | | | | all_448_0 & set_difference(all_138_8, all_138_3) = % 56.88/8.54 | | | | | | | | | | | all_448_0 & $i(all_448_0) % 56.88/8.54 | | | | | | | | | | | % 56.88/8.54 | | | | | | | | | | | ALPHA: (502) implies: % 56.88/8.54 | | | | | | | | | | | (503) set_difference(all_138_8, all_138_3) = all_448_0 % 56.88/8.54 | | | | | | | | | | | (504) subset_complement(all_138_8, all_138_3) = % 56.88/8.54 | | | | | | | | | | | all_448_0 % 56.88/8.54 | | | | | | | | | | | % 56.88/8.54 | | | | | | | | | | | DELTA: instantiating (453) with fresh symbol all_450_0 % 56.88/8.54 | | | | | | | | | | | gives: % 56.88/8.54 | | | | | | | | | | | (505) subset_complement(all_138_8, all_138_0) = % 56.88/8.54 | | | | | | | | | | | all_450_0 & element(all_450_0, all_138_6) = 0 & % 56.88/8.54 | | | | | | | | | | | $i(all_450_0) % 56.88/8.54 | | | | | | | | | | | % 56.88/8.54 | | | | | | | | | | | ALPHA: (505) implies: % 56.88/8.54 | | | | | | | | | | | (506) subset_complement(all_138_8, all_138_0) = % 56.88/8.54 | | | | | | | | | | | all_450_0 % 56.88/8.54 | | | | | | | | | | | % 56.88/8.54 | | | | | | | | | | | DELTA: instantiating (435) with fresh symbol all_452_0 % 56.88/8.54 | | | | | | | | | | | gives: % 56.88/8.54 | | | | | | | | | | | (507) subset_complement(all_138_8, all_452_0) = % 56.88/8.54 | | | | | | | | | | | all_138_3 & subset_complement(all_138_8, % 56.88/8.54 | | | | | | | | | | | all_138_3) = all_452_0 & $i(all_452_0) % 56.88/8.54 | | | | | | | | | | | % 56.88/8.54 | | | | | | | | | | | ALPHA: (507) implies: % 56.88/8.54 | | | | | | | | | | | (508) subset_complement(all_138_8, all_138_3) = % 56.88/8.54 | | | | | | | | | | | all_452_0 % 56.88/8.54 | | | | | | | | | | | (509) subset_complement(all_138_8, all_452_0) = % 56.88/8.54 | | | | | | | | | | | all_138_3 % 56.88/8.54 | | | | | | | | | | | % 56.88/8.54 | | | | | | | | | | | DELTA: instantiating (461) with fresh symbols all_498_0, % 56.88/8.54 | | | | | | | | | | | all_498_1 gives: % 56.88/8.54 | | | | | | | | | | | (510) empty(all_138_5) = all_498_1 & in(all_168_0, % 56.88/8.54 | | | | | | | | | | | all_138_5) = all_498_0 & (all_498_0 = 0 | % 56.88/8.54 | | | | | | | | | | | all_498_1 = 0) % 56.88/8.54 | | | | | | | | | | | % 56.88/8.54 | | | | | | | | | | | ALPHA: (510) implies: % 56.88/8.54 | | | | | | | | | | | (511) empty(all_138_5) = all_498_1 % 56.88/8.54 | | | | | | | | | | | (512) all_498_0 = 0 | all_498_1 = 0 % 56.88/8.54 | | | | | | | | | | | % 56.88/8.54 | | | | | | | | | | | DELTA: instantiating (462) with fresh symbols all_504_0, % 56.88/8.54 | | | | | | | | | | | all_504_1 gives: % 56.88/8.54 | | | | | | | | | | | (513) empty(all_138_5) = all_504_1 & in(all_172_0, % 56.88/8.54 | | | | | | | | | | | all_138_5) = all_504_0 & (all_504_0 = 0 | % 56.88/8.54 | | | | | | | | | | | all_504_1 = 0) % 56.88/8.54 | | | | | | | | | | | % 56.88/8.54 | | | | | | | | | | | ALPHA: (513) implies: % 56.88/8.54 | | | | | | | | | | | (514) empty(all_138_5) = all_504_1 % 56.88/8.54 | | | | | | | | | | | % 56.88/8.54 | | | | | | | | | | | DELTA: instantiating (432) with fresh symbols all_516_0, % 56.88/8.54 | | | | | | | | | | | all_516_1 gives: % 56.88/8.54 | | | | | | | | | | | (515) empty(all_138_4) = all_516_0 & empty(all_138_5) = % 56.88/8.54 | | | | | | | | | | | all_516_1 & ( ~ (all_516_1 = 0) | all_516_0 = 0) % 56.88/8.54 | | | | | | | | | | | % 56.88/8.54 | | | | | | | | | | | ALPHA: (515) implies: % 56.88/8.54 | | | | | | | | | | | (516) empty(all_138_5) = all_516_1 % 56.88/8.54 | | | | | | | | | | | % 56.88/8.54 | | | | | | | | | | | DELTA: instantiating (431) with fresh symbols all_526_0, % 56.88/8.54 | | | | | | | | | | | all_526_1 gives: % 56.88/8.54 | | | | | | | | | | | (517) empty(all_138_5) = all_526_1 & in(all_138_4, % 56.88/8.54 | | | | | | | | | | | all_138_5) = all_526_0 & (all_526_0 = 0 | % 56.88/8.54 | | | | | | | | | | | all_526_1 = 0) % 56.88/8.54 | | | | | | | | | | | % 56.88/8.54 | | | | | | | | | | | ALPHA: (517) implies: % 56.88/8.54 | | | | | | | | | | | (518) empty(all_138_5) = all_526_1 % 56.88/8.54 | | | | | | | | | | | % 56.88/8.54 | | | | | | | | | | | DELTA: instantiating (455) with fresh symbols all_528_0, % 56.88/8.54 | | | | | | | | | | | all_528_1 gives: % 56.88/8.54 | | | | | | | | | | | (519) empty(all_138_5) = all_528_1 & in(all_162_0, % 56.88/8.54 | | | | | | | | | | | all_138_5) = all_528_0 & (all_528_0 = 0 | % 56.88/8.54 | | | | | | | | | | | all_528_1 = 0) % 56.88/8.54 | | | | | | | | | | | % 56.88/8.54 | | | | | | | | | | | ALPHA: (519) implies: % 56.88/8.54 | | | | | | | | | | | (520) empty(all_138_5) = all_528_1 % 56.88/8.54 | | | | | | | | | | | % 56.88/8.54 | | | | | | | | | | | DELTA: instantiating (470) with fresh symbols all_544_0, % 56.88/8.54 | | | | | | | | | | | all_544_1, all_544_2 gives: % 56.88/8.54 | | | | | | | | | | | (521) subset_complement(all_138_8, all_138_1) = % 56.88/8.54 | | | | | | | | | | | all_544_0 & element(all_138_1, all_544_2) = % 56.88/8.54 | | | | | | | | | | | all_544_1 & powerset(all_138_8) = all_544_2 & % 56.88/8.54 | | | | | | | | | | | $i(all_544_0) & $i(all_544_2) & ( ~ (all_544_1 = % 56.88/8.54 | | | | | | | | | | | 0) | all_544_0 = all_138_0) % 56.88/8.54 | | | | | | | | | | | % 56.88/8.54 | | | | | | | | | | | ALPHA: (521) implies: % 56.88/8.54 | | | | | | | | | | | (522) powerset(all_138_8) = all_544_2 % 56.88/8.54 | | | | | | | | | | | (523) subset_complement(all_138_8, all_138_1) = % 56.88/8.54 | | | | | | | | | | | all_544_0 % 56.88/8.54 | | | | | | | | | | | % 56.88/8.54 | | | | | | | | | | | DELTA: instantiating (450) with fresh symbols all_568_0, % 56.88/8.54 | | | | | | | | | | | all_568_1, all_568_2 gives: % 56.88/8.54 | | | | | | | | | | | (524) disjoint(all_138_8, all_138_0) = all_568_2 & % 56.88/8.54 | | | | | | | | | | | subset_complement(all_138_8, all_138_0) = % 56.88/8.54 | | | | | | | | | | | all_568_1 & subset(all_138_8, all_568_1) = % 56.88/8.54 | | | | | | | | | | | all_568_0 & $i(all_568_1) & ( ~ (all_568_0 = 0) | % 56.88/8.54 | | | | | | | | | | | all_568_2 = 0) & ( ~ (all_568_2 = 0) | all_568_0 % 56.88/8.54 | | | | | | | | | | | = 0) % 56.88/8.54 | | | | | | | | | | | % 56.88/8.54 | | | | | | | | | | | ALPHA: (524) implies: % 56.88/8.54 | | | | | | | | | | | (525) subset_complement(all_138_8, all_138_0) = % 56.88/8.54 | | | | | | | | | | | all_568_1 % 56.88/8.54 | | | | | | | | | | | % 56.88/8.54 | | | | | | | | | | | DELTA: instantiating (449) with fresh symbols all_570_0, % 56.88/8.54 | | | | | | | | | | | all_570_1, all_570_2 gives: % 56.88/8.54 | | | | | | | | | | | (526) disjoint(all_138_0, all_138_3) = all_570_2 & % 56.88/8.54 | | | | | | | | | | | subset_complement(all_138_8, all_138_3) = % 56.88/8.54 | | | | | | | | | | | all_570_1 & subset(all_138_0, all_570_1) = % 56.88/8.54 | | | | | | | | | | | all_570_0 & $i(all_570_1) & ( ~ (all_570_0 = 0) | % 56.88/8.54 | | | | | | | | | | | all_570_2 = 0) & ( ~ (all_570_2 = 0) | all_570_0 % 56.88/8.54 | | | | | | | | | | | = 0) % 56.88/8.54 | | | | | | | | | | | % 56.88/8.54 | | | | | | | | | | | ALPHA: (526) implies: % 56.88/8.54 | | | | | | | | | | | (527) subset_complement(all_138_8, all_138_3) = % 56.88/8.54 | | | | | | | | | | | all_570_1 % 56.88/8.54 | | | | | | | | | | | % 56.88/8.54 | | | | | | | | | | | DELTA: instantiating (448) with fresh symbols all_572_0, % 56.88/8.54 | | | | | | | | | | | all_572_1, all_572_2 gives: % 56.88/8.54 | | | | | | | | | | | (528) disjoint(all_138_3, all_138_0) = all_572_2 & % 56.88/8.54 | | | | | | | | | | | subset_complement(all_138_8, all_138_0) = % 56.88/8.54 | | | | | | | | | | | all_572_1 & subset(all_138_3, all_572_1) = % 56.88/8.54 | | | | | | | | | | | all_572_0 & $i(all_572_1) & ( ~ (all_572_0 = 0) | % 56.88/8.54 | | | | | | | | | | | all_572_2 = 0) & ( ~ (all_572_2 = 0) | all_572_0 % 56.88/8.54 | | | | | | | | | | | = 0) % 56.88/8.54 | | | | | | | | | | | % 56.88/8.54 | | | | | | | | | | | ALPHA: (528) implies: % 56.88/8.54 | | | | | | | | | | | (529) subset_complement(all_138_8, all_138_0) = % 56.88/8.54 | | | | | | | | | | | all_572_1 % 56.88/8.54 | | | | | | | | | | | % 56.88/8.54 | | | | | | | | | | | DELTA: instantiating (447) with fresh symbols all_574_0, % 56.88/8.54 | | | | | | | | | | | all_574_1, all_574_2 gives: % 56.88/8.54 | | | | | | | | | | | (530) disjoint(all_138_0, all_138_1) = all_574_2 & % 56.88/8.54 | | | | | | | | | | | subset_complement(all_138_8, all_138_1) = % 56.88/8.54 | | | | | | | | | | | all_574_1 & subset(all_138_0, all_574_1) = % 56.88/8.54 | | | | | | | | | | | all_574_0 & $i(all_574_1) & ( ~ (all_574_0 = 0) | % 56.88/8.54 | | | | | | | | | | | all_574_2 = 0) & ( ~ (all_574_2 = 0) | all_574_0 % 56.88/8.54 | | | | | | | | | | | = 0) % 56.88/8.54 | | | | | | | | | | | % 56.88/8.54 | | | | | | | | | | | ALPHA: (530) implies: % 56.88/8.54 | | | | | | | | | | | (531) subset_complement(all_138_8, all_138_1) = % 56.88/8.54 | | | | | | | | | | | all_574_1 % 56.88/8.54 | | | | | | | | | | | % 56.88/8.54 | | | | | | | | | | | DELTA: instantiating (476) with fresh symbols all_602_0, % 56.88/8.54 | | | | | | | | | | | all_602_1, all_602_2, all_602_3 gives: % 56.88/8.54 | | | | | | | | | | | (532) element(all_238_1, all_602_3) = all_602_0 & % 56.88/8.54 | | | | | | | | | | | element(all_176_0, all_602_3) = all_602_1 & % 56.88/8.54 | | | | | | | | | | | element(all_138_8, all_602_3) = all_602_2 & % 56.88/8.54 | | | | | | | | | | | powerset(all_138_8) = all_602_3 & $i(all_602_3) & % 56.88/8.54 | | | | | | | | | | | ( ~ (all_602_1 = 0) | ~ (all_602_2 = 0) | % 56.88/8.54 | | | | | | | | | | | all_602_0 = 0) % 56.88/8.54 | | | | | | | | | | | % 56.88/8.54 | | | | | | | | | | | ALPHA: (532) implies: % 56.88/8.54 | | | | | | | | | | | (533) powerset(all_138_8) = all_602_3 % 56.88/8.54 | | | | | | | | | | | % 56.88/8.54 | | | | | | | | | | | DELTA: instantiating (439) with fresh symbols all_606_0, % 56.88/8.54 | | | | | | | | | | | all_606_1, all_606_2 gives: % 56.88/8.54 | | | | | | | | | | | (534) disjoint(all_138_3, all_138_1) = all_606_2 & % 56.88/8.54 | | | | | | | | | | | subset_complement(all_138_8, all_138_1) = % 56.88/8.54 | | | | | | | | | | | all_606_1 & subset(all_138_3, all_606_1) = % 56.88/8.54 | | | | | | | | | | | all_606_0 & $i(all_606_1) & ( ~ (all_606_0 = 0) | % 56.88/8.54 | | | | | | | | | | | all_606_2 = 0) & ( ~ (all_606_2 = 0) | all_606_0 % 56.88/8.54 | | | | | | | | | | | = 0) % 56.88/8.54 | | | | | | | | | | | % 56.88/8.54 | | | | | | | | | | | ALPHA: (534) implies: % 56.88/8.54 | | | | | | | | | | | (535) subset_complement(all_138_8, all_138_1) = % 56.88/8.54 | | | | | | | | | | | all_606_1 % 56.88/8.54 | | | | | | | | | | | % 56.88/8.54 | | | | | | | | | | | DELTA: instantiating (438) with fresh symbols all_608_0, % 56.88/8.54 | | | | | | | | | | | all_608_1, all_608_2 gives: % 56.88/8.54 | | | | | | | | | | | (536) disjoint(all_138_1, all_138_1) = all_608_2 & % 56.88/8.54 | | | | | | | | | | | subset_complement(all_138_8, all_138_1) = % 56.88/8.54 | | | | | | | | | | | all_608_1 & subset(all_138_1, all_608_1) = % 56.88/8.54 | | | | | | | | | | | all_608_0 & $i(all_608_1) & ( ~ (all_608_0 = 0) | % 56.88/8.54 | | | | | | | | | | | all_608_2 = 0) & ( ~ (all_608_2 = 0) | all_608_0 % 56.88/8.54 | | | | | | | | | | | = 0) % 56.88/8.54 | | | | | | | | | | | % 56.88/8.54 | | | | | | | | | | | ALPHA: (536) implies: % 56.88/8.54 | | | | | | | | | | | (537) subset_complement(all_138_8, all_138_1) = % 56.88/8.54 | | | | | | | | | | | all_608_1 % 56.88/8.54 | | | | | | | | | | | % 56.88/8.54 | | | | | | | | | | | DELTA: instantiating (472) with fresh symbols all_612_0, % 56.88/8.54 | | | | | | | | | | | all_612_1, all_612_2, all_612_3 gives: % 56.88/8.54 | | | | | | | | | | | (538) element(all_238_1, all_612_3) = all_612_0 & % 56.88/8.54 | | | | | | | | | | | element(all_138_4, all_612_2) = all_612_1 & % 56.88/8.54 | | | | | | | | | | | powerset(all_612_3) = all_612_2 & % 56.88/8.54 | | | | | | | | | | | powerset(all_138_8) = all_612_3 & $i(all_612_2) & % 56.88/8.54 | | | | | | | | | | | $i(all_612_3) & ( ~ (all_612_1 = 0) | all_612_0 = % 56.88/8.54 | | | | | | | | | | | 0) % 56.88/8.54 | | | | | | | | | | | % 56.88/8.54 | | | | | | | | | | | ALPHA: (538) implies: % 56.88/8.54 | | | | | | | | | | | (539) powerset(all_138_8) = all_612_3 % 56.88/8.54 | | | | | | | | | | | % 56.88/8.54 | | | | | | | | | | | DELTA: instantiating (446) with fresh symbols all_616_0, % 56.88/8.54 | | | | | | | | | | | all_616_1, all_616_2 gives: % 56.88/8.54 | | | | | | | | | | | (540) disjoint(all_138_1, all_138_0) = all_616_2 & % 56.88/8.54 | | | | | | | | | | | subset_complement(all_138_8, all_138_0) = % 56.88/8.54 | | | | | | | | | | | all_616_1 & subset(all_138_1, all_616_1) = % 56.88/8.54 | | | | | | | | | | | all_616_0 & $i(all_616_1) & ( ~ (all_616_0 = 0) | % 56.88/8.54 | | | | | | | | | | | all_616_2 = 0) & ( ~ (all_616_2 = 0) | all_616_0 % 56.88/8.54 | | | | | | | | | | | = 0) % 56.88/8.54 | | | | | | | | | | | % 56.88/8.54 | | | | | | | | | | | ALPHA: (540) implies: % 56.88/8.54 | | | | | | | | | | | (541) subset_complement(all_138_8, all_138_0) = % 56.88/8.54 | | | | | | | | | | | all_616_1 % 56.88/8.54 | | | | | | | | | | | % 56.88/8.54 | | | | | | | | | | | DELTA: instantiating (445) with fresh symbols all_618_0, % 56.88/8.54 | | | | | | | | | | | all_618_1, all_618_2 gives: % 56.88/8.54 | | | | | | | | | | | (542) disjoint(all_138_0, all_138_0) = all_618_2 & % 56.88/8.54 | | | | | | | | | | | subset_complement(all_138_8, all_138_0) = % 56.88/8.54 | | | | | | | | | | | all_618_1 & subset(all_138_0, all_618_1) = % 56.88/8.54 | | | | | | | | | | | all_618_0 & $i(all_618_1) & ( ~ (all_618_0 = 0) | % 56.88/8.54 | | | | | | | | | | | all_618_2 = 0) & ( ~ (all_618_2 = 0) | all_618_0 % 56.88/8.54 | | | | | | | | | | | = 0) % 56.88/8.54 | | | | | | | | | | | % 56.88/8.54 | | | | | | | | | | | ALPHA: (542) implies: % 56.88/8.54 | | | | | | | | | | | (543) subset_complement(all_138_8, all_138_0) = % 56.88/8.54 | | | | | | | | | | | all_618_1 % 56.88/8.54 | | | | | | | | | | | % 56.88/8.54 | | | | | | | | | | | DELTA: instantiating (464) with fresh symbols all_628_0, % 56.88/8.54 | | | | | | | | | | | all_628_1, all_628_2 gives: % 56.88/8.54 | | | | | | | | | | | (544) disjoint(all_176_0, all_138_1) = all_628_2 & % 56.88/8.54 | | | | | | | | | | | subset_complement(all_138_8, all_138_1) = % 56.88/8.54 | | | | | | | | | | | all_628_1 & subset(all_176_0, all_628_1) = % 56.88/8.54 | | | | | | | | | | | all_628_0 & $i(all_628_1) & ( ~ (all_628_0 = 0) | % 56.88/8.54 | | | | | | | | | | | all_628_2 = 0) & ( ~ (all_628_2 = 0) | all_628_0 % 56.88/8.54 | | | | | | | | | | | = 0) % 56.88/8.54 | | | | | | | | | | | % 56.88/8.54 | | | | | | | | | | | ALPHA: (544) implies: % 56.88/8.54 | | | | | | | | | | | (545) subset_complement(all_138_8, all_138_1) = % 56.88/8.54 | | | | | | | | | | | all_628_1 % 56.88/8.54 | | | | | | | | | | | % 56.88/8.54 | | | | | | | | | | | DELTA: instantiating (463) with fresh symbols all_648_0, % 56.88/8.54 | | | | | | | | | | | all_648_1, all_648_2 gives: % 56.88/8.54 | | | | | | | | | | | (546) disjoint(all_176_0, all_138_0) = all_648_2 & % 56.88/8.54 | | | | | | | | | | | subset_complement(all_138_8, all_138_0) = % 56.88/8.54 | | | | | | | | | | | all_648_1 & subset(all_176_0, all_648_1) = % 56.88/8.54 | | | | | | | | | | | all_648_0 & $i(all_648_1) & ( ~ (all_648_0 = 0) | % 56.88/8.54 | | | | | | | | | | | all_648_2 = 0) & ( ~ (all_648_2 = 0) | all_648_0 % 56.88/8.54 | | | | | | | | | | | = 0) % 56.88/8.54 | | | | | | | | | | | % 56.88/8.54 | | | | | | | | | | | ALPHA: (546) implies: % 56.88/8.55 | | | | | | | | | | | (547) subset_complement(all_138_8, all_138_0) = % 56.88/8.55 | | | | | | | | | | | all_648_1 % 56.88/8.55 | | | | | | | | | | | % 56.88/8.55 | | | | | | | | | | | DELTA: instantiating (458) with fresh symbols all_658_0, % 56.88/8.55 | | | | | | | | | | | all_658_1, all_658_2 gives: % 56.88/8.55 | | | | | | | | | | | (548) disjoint(all_164_0, all_138_3) = all_658_2 & % 56.88/8.55 | | | | | | | | | | | subset_complement(all_138_8, all_138_3) = % 56.88/8.55 | | | | | | | | | | | all_658_1 & subset(all_164_0, all_658_1) = % 56.88/8.55 | | | | | | | | | | | all_658_0 & $i(all_658_1) & ( ~ (all_658_0 = 0) | % 56.88/8.55 | | | | | | | | | | | all_658_2 = 0) & ( ~ (all_658_2 = 0) | all_658_0 % 56.88/8.55 | | | | | | | | | | | = 0) % 56.88/8.55 | | | | | | | | | | | % 56.88/8.55 | | | | | | | | | | | ALPHA: (548) implies: % 56.88/8.55 | | | | | | | | | | | (549) subset_complement(all_138_8, all_138_3) = % 56.88/8.55 | | | | | | | | | | | all_658_1 % 56.88/8.55 | | | | | | | | | | | % 56.88/8.55 | | | | | | | | | | | DELTA: instantiating (434) with fresh symbols all_664_0, % 56.88/8.55 | | | | | | | | | | | all_664_1, all_664_2 gives: % 56.88/8.55 | | | | | | | | | | | (550) disjoint(all_138_8, all_138_3) = all_664_2 & % 56.88/8.55 | | | | | | | | | | | subset_complement(all_138_8, all_138_3) = % 56.88/8.55 | | | | | | | | | | | all_664_1 & subset(all_138_8, all_664_1) = % 56.88/8.55 | | | | | | | | | | | all_664_0 & $i(all_664_1) & ( ~ (all_664_0 = 0) | % 56.88/8.55 | | | | | | | | | | | all_664_2 = 0) & ( ~ (all_664_2 = 0) | all_664_0 % 56.88/8.55 | | | | | | | | | | | = 0) % 56.88/8.55 | | | | | | | | | | | % 56.88/8.55 | | | | | | | | | | | ALPHA: (550) implies: % 56.88/8.55 | | | | | | | | | | | (551) subset_complement(all_138_8, all_138_3) = % 56.88/8.55 | | | | | | | | | | | all_664_1 % 56.88/8.55 | | | | | | | | | | | % 56.88/8.55 | | | | | | | | | | | DELTA: instantiating (433) with fresh symbols all_666_0, % 56.88/8.55 | | | | | | | | | | | all_666_1, all_666_2 gives: % 56.88/8.55 | | | | | | | | | | | (552) disjoint(all_138_3, all_138_3) = all_666_2 & % 56.88/8.55 | | | | | | | | | | | subset_complement(all_138_8, all_138_3) = % 56.88/8.55 | | | | | | | | | | | all_666_1 & subset(all_138_3, all_666_1) = % 56.88/8.55 | | | | | | | | | | | all_666_0 & $i(all_666_1) & ( ~ (all_666_0 = 0) | % 56.88/8.55 | | | | | | | | | | | all_666_2 = 0) & ( ~ (all_666_2 = 0) | all_666_0 % 56.88/8.55 | | | | | | | | | | | = 0) % 56.88/8.55 | | | | | | | | | | | % 56.88/8.55 | | | | | | | | | | | ALPHA: (552) implies: % 56.88/8.55 | | | | | | | | | | | (553) subset_complement(all_138_8, all_138_3) = % 56.88/8.55 | | | | | | | | | | | all_666_1 % 56.88/8.55 | | | | | | | | | | | % 56.88/8.55 | | | | | | | | | | | DELTA: instantiating (457) with fresh symbols all_668_0, % 56.88/8.55 | | | | | | | | | | | all_668_1, all_668_2 gives: % 56.88/8.55 | | | | | | | | | | | (554) disjoint(all_164_0, all_138_1) = all_668_2 & % 56.88/8.55 | | | | | | | | | | | subset_complement(all_138_8, all_138_1) = % 56.88/8.55 | | | | | | | | | | | all_668_1 & subset(all_164_0, all_668_1) = % 56.88/8.55 | | | | | | | | | | | all_668_0 & $i(all_668_1) & ( ~ (all_668_0 = 0) | % 56.88/8.55 | | | | | | | | | | | all_668_2 = 0) & ( ~ (all_668_2 = 0) | all_668_0 % 56.88/8.55 | | | | | | | | | | | = 0) % 56.88/8.55 | | | | | | | | | | | % 56.88/8.55 | | | | | | | | | | | ALPHA: (554) implies: % 56.88/8.55 | | | | | | | | | | | (555) subset_complement(all_138_8, all_138_1) = % 56.88/8.55 | | | | | | | | | | | all_668_1 % 56.88/8.55 | | | | | | | | | | | % 56.88/8.55 | | | | | | | | | | | DELTA: instantiating (465) with fresh symbols all_684_0, % 56.88/8.55 | | | | | | | | | | | all_684_1, all_684_2 gives: % 56.88/8.55 | | | | | | | | | | | (556) disjoint(all_176_0, all_138_3) = all_684_2 & % 56.88/8.55 | | | | | | | | | | | subset_complement(all_138_8, all_138_3) = % 56.88/8.55 | | | | | | | | | | | all_684_1 & subset(all_176_0, all_684_1) = % 56.88/8.55 | | | | | | | | | | | all_684_0 & $i(all_684_1) & ( ~ (all_684_0 = 0) | % 56.88/8.55 | | | | | | | | | | | all_684_2 = 0) & ( ~ (all_684_2 = 0) | all_684_0 % 56.88/8.55 | | | | | | | | | | | = 0) % 56.88/8.55 | | | | | | | | | | | % 56.88/8.55 | | | | | | | | | | | ALPHA: (556) implies: % 56.88/8.55 | | | | | | | | | | | (557) subset_complement(all_138_8, all_138_3) = % 56.88/8.55 | | | | | | | | | | | all_684_1 % 56.88/8.55 | | | | | | | | | | | % 56.88/8.55 | | | | | | | | | | | DELTA: instantiating (456) with fresh symbols all_686_0, % 56.88/8.55 | | | | | | | | | | | all_686_1, all_686_2 gives: % 56.88/8.55 | | | | | | | | | | | (558) disjoint(all_164_0, all_138_0) = all_686_2 & % 56.88/8.55 | | | | | | | | | | | subset_complement(all_138_8, all_138_0) = % 56.88/8.55 | | | | | | | | | | | all_686_1 & subset(all_164_0, all_686_1) = % 56.88/8.55 | | | | | | | | | | | all_686_0 & $i(all_686_1) & ( ~ (all_686_0 = 0) | % 56.88/8.55 | | | | | | | | | | | all_686_2 = 0) & ( ~ (all_686_2 = 0) | all_686_0 % 56.88/8.55 | | | | | | | | | | | = 0) % 56.88/8.55 | | | | | | | | | | | % 56.88/8.55 | | | | | | | | | | | ALPHA: (558) implies: % 56.88/8.55 | | | | | | | | | | | (559) subset_complement(all_138_8, all_138_0) = % 56.88/8.55 | | | | | | | | | | | all_686_1 % 56.88/8.55 | | | | | | | | | | | % 56.88/8.55 | | | | | | | | | | | DELTA: instantiating (441) with fresh symbols all_700_0, % 56.88/8.55 | | | | | | | | | | | all_700_1, all_700_2 gives: % 56.88/8.55 | | | | | | | | | | | (560) disjoint(all_138_8, all_138_1) = all_700_2 & % 56.88/8.55 | | | | | | | | | | | subset_complement(all_138_8, all_138_1) = % 56.88/8.55 | | | | | | | | | | | all_700_1 & subset(all_138_8, all_700_1) = % 56.88/8.55 | | | | | | | | | | | all_700_0 & $i(all_700_1) & ( ~ (all_700_0 = 0) | % 56.88/8.55 | | | | | | | | | | | all_700_2 = 0) & ( ~ (all_700_2 = 0) | all_700_0 % 56.88/8.55 | | | | | | | | | | | = 0) % 56.88/8.55 | | | | | | | | | | | % 56.88/8.55 | | | | | | | | | | | ALPHA: (560) implies: % 56.88/8.55 | | | | | | | | | | | (561) subset_complement(all_138_8, all_138_1) = % 56.88/8.55 | | | | | | | | | | | all_700_1 % 56.88/8.55 | | | | | | | | | | | % 56.88/8.55 | | | | | | | | | | | DELTA: instantiating (440) with fresh symbols all_702_0, % 56.88/8.55 | | | | | | | | | | | all_702_1, all_702_2 gives: % 56.88/8.55 | | | | | | | | | | | (562) disjoint(all_138_1, all_138_3) = all_702_2 & % 56.88/8.55 | | | | | | | | | | | subset_complement(all_138_8, all_138_3) = % 56.88/8.55 | | | | | | | | | | | all_702_1 & subset(all_138_1, all_702_1) = % 56.88/8.55 | | | | | | | | | | | all_702_0 & $i(all_702_1) & ( ~ (all_702_0 = 0) | % 56.88/8.55 | | | | | | | | | | | all_702_2 = 0) & ( ~ (all_702_2 = 0) | all_702_0 % 56.88/8.55 | | | | | | | | | | | = 0) % 56.88/8.55 | | | | | | | | | | | % 56.88/8.55 | | | | | | | | | | | ALPHA: (562) implies: % 56.88/8.55 | | | | | | | | | | | (563) subset_complement(all_138_8, all_138_3) = % 56.88/8.55 | | | | | | | | | | | all_702_1 % 56.88/8.55 | | | | | | | | | | | % 56.88/8.55 | | | | | | | | | | | DELTA: instantiating (475) with fresh symbols all_726_0, % 56.88/8.55 | | | | | | | | | | | all_726_1, all_726_2, all_726_3 gives: % 56.88/8.55 | | | | | | | | | | | (564) set_difference(all_138_8, all_176_0) = all_726_0 & % 56.88/8.55 | | | | | | | | | | | element(all_176_0, all_726_3) = all_726_1 & % 56.88/8.55 | | | | | | | | | | | element(all_138_8, all_726_3) = all_726_2 & % 56.88/8.55 | | | | | | | | | | | powerset(all_138_8) = all_726_3 & $i(all_726_0) & % 56.88/8.55 | | | | | | | | | | | $i(all_726_3) & ( ~ (all_726_1 = 0) | ~ % 56.88/8.55 | | | | | | | | | | | (all_726_2 = 0) | all_726_0 = all_238_1) % 56.88/8.55 | | | | | | | | | | | % 56.88/8.55 | | | | | | | | | | | ALPHA: (564) implies: % 56.88/8.55 | | | | | | | | | | | (565) powerset(all_138_8) = all_726_3 % 56.88/8.55 | | | | | | | | | | | % 56.88/8.55 | | | | | | | | | | | DELTA: instantiating (473) with fresh symbols all_728_0, % 56.88/8.55 | | | | | | | | | | | all_728_1, all_728_2, all_728_3 gives: % 56.88/8.55 | | | | | | | | | | | (566) element(all_138_4, all_728_2) = all_728_1 & % 56.88/8.55 | | | | | | | | | | | powerset(all_728_3) = all_728_2 & % 56.88/8.55 | | | | | | | | | | | powerset(all_138_8) = all_728_3 & % 56.88/8.55 | | | | | | | | | | | set_meet(all_138_4) = all_728_0 & $i(all_728_0) & % 56.88/8.55 | | | | | | | | | | | $i(all_728_2) & $i(all_728_3) & ( ~ (all_728_1 = % 56.88/8.55 | | | | | | | | | | | 0) | all_728_0 = all_238_1) % 56.88/8.55 | | | | | | | | | | | % 56.88/8.55 | | | | | | | | | | | ALPHA: (566) implies: % 56.88/8.55 | | | | | | | | | | | (567) powerset(all_138_8) = all_728_3 % 56.88/8.55 | | | | | | | | | | | % 56.88/8.55 | | | | | | | | | | | DELTA: instantiating (474) with fresh symbols all_730_0, % 56.88/8.55 | | | | | | | | | | | all_730_1, all_730_2, all_730_3 gives: % 56.88/8.55 | | | | | | | | | | | (568) set_difference(all_138_8, all_138_3) = all_730_0 & % 56.88/8.55 | | | | | | | | | | | element(all_138_3, all_730_3) = all_730_1 & % 56.88/8.55 | | | | | | | | | | | element(all_138_8, all_730_3) = all_730_2 & % 56.88/8.55 | | | | | | | | | | | powerset(all_138_8) = all_730_3 & $i(all_730_0) & % 56.88/8.55 | | | | | | | | | | | $i(all_730_3) & ( ~ (all_730_1 = 0) | ~ % 56.88/8.55 | | | | | | | | | | | (all_730_2 = 0) | all_730_0 = all_138_1) % 56.88/8.55 | | | | | | | | | | | % 56.88/8.55 | | | | | | | | | | | ALPHA: (568) implies: % 56.88/8.55 | | | | | | | | | | | (569) powerset(all_138_8) = all_730_3 % 56.88/8.55 | | | | | | | | | | | (570) element(all_138_8, all_730_3) = all_730_2 % 56.88/8.55 | | | | | | | | | | | (571) element(all_138_3, all_730_3) = all_730_1 % 56.88/8.55 | | | | | | | | | | | (572) set_difference(all_138_8, all_138_3) = all_730_0 % 56.88/8.55 | | | | | | | | | | | (573) ~ (all_730_1 = 0) | ~ (all_730_2 = 0) | % 56.88/8.55 | | | | | | | | | | | all_730_0 = all_138_1 % 56.88/8.55 | | | | | | | | | | | % 56.88/8.55 | | | | | | | | | | | DELTA: instantiating (471) with fresh symbols all_749_0, % 56.88/8.55 | | | | | | | | | | | all_749_1, all_749_2 gives: % 56.88/8.55 | | | | | | | | | | | (574) element(all_138_4, all_749_1) = all_749_0 & % 56.88/8.55 | | | | | | | | | | | powerset(all_749_2) = all_749_1 & % 56.88/8.55 | | | | | | | | | | | powerset(all_138_8) = all_749_2 & $i(all_749_1) & % 56.88/8.55 | | | | | | | | | | | $i(all_749_2) & ( ~ (all_749_0 = 0) | ( ! [v0: $i] % 56.88/8.55 | | | | | | | | | | | : ! [v1: $i] : ( ~ % 56.88/8.55 | | | | | | | | | | | (subset_complement(all_138_8, v0) = v1) | ~ % 56.88/8.55 | | | | | | | | | | | (element(all_138_7, all_749_1) = 0) | ~ % 56.88/8.55 | | | | | | | | | | | $i(v0) | ~ $i(all_138_7) | ? [v2: any] : % 56.88/8.55 | | | | | | | | | | | ? [v3: any] : ? [v4: any] : (element(v0, % 56.88/8.55 | | | | | | | | | | | all_749_2) = v2 & in(v1, all_138_4) = v4 % 56.88/8.55 | | | | | | | | | | | & in(v0, all_138_7) = v3 & ( ~ (v2 = 0) | % 56.88/8.55 | | | | | | | | | | | (( ~ (v4 = 0) | v3 = 0) & ( ~ (v3 = 0) | % 56.88/8.55 | | | | | | | | | | | v4 = 0))))) & ! [v0: $i] : ! [v1: % 56.88/8.55 | | | | | | | | | | | any] : ( ~ (element(all_138_7, all_749_1) = % 56.88/8.55 | | | | | | | | | | | 0) | ~ (in(v0, all_138_7) = v1) | ~ % 56.88/8.55 | | | | | | | | | | | $i(v0) | ~ $i(all_138_7) | ? [v2: any] : % 56.88/8.55 | | | | | | | | | | | ? [v3: $i] : ? [v4: any] : % 56.88/8.55 | | | | | | | | | | | (subset_complement(all_138_8, v0) = v3 & % 56.88/8.55 | | | | | | | | | | | element(v0, all_749_2) = v2 & in(v3, % 56.88/8.55 | | | | | | | | | | | all_138_4) = v4 & $i(v3) & ( ~ (v2 = 0) % 56.88/8.55 | | | | | | | | | | | | (( ~ (v4 = 0) | v1 = 0) & ( ~ (v1 = 0) % 56.88/8.55 | | | | | | | | | | | | v4 = 0))))) & ! [v0: any] : (v0 = % 56.88/8.55 | | | | | | | | | | | all_138_7 | ~ (element(v0, all_749_1) = 0) % 56.88/8.55 | | | | | | | | | | | | ~ $i(v0) | ? [v1: $i] : ? [v2: any] : % 56.88/8.55 | | | | | | | | | | | ? [v3: $i] : ? [v4: any] : % 56.88/8.55 | | | | | | | | | | | (subset_complement(all_138_8, v1) = v3 & % 56.88/8.55 | | | | | | | | | | | element(v1, all_749_2) = 0 & in(v3, % 56.88/8.55 | | | | | | | | | | | all_138_4) = v4 & in(v1, v0) = v2 & % 56.88/8.55 | | | | | | | | | | | $i(v3) & $i(v1) & ( ~ (v4 = 0) | ~ (v2 = % 56.88/8.55 | | | | | | | | | | | 0)) & (v4 = 0 | v2 = 0))) & ! [v0: % 56.88/8.55 | | | | | | | | | | | $i] : ( ~ (element(v0, all_749_2) = 0) | ~ % 56.88/8.55 | | | | | | | | | | | (element(all_138_7, all_749_1) = 0) | ~ % 56.88/8.55 | | | | | | | | | | | $i(v0) | ~ $i(all_138_7) | ? [v1: any] : % 56.88/8.55 | | | | | | | | | | | ? [v2: $i] : ? [v3: any] : % 56.88/8.55 | | | | | | | | | | | (subset_complement(all_138_8, v0) = v2 & % 56.88/8.55 | | | | | | | | | | | in(v2, all_138_4) = v3 & in(v0, all_138_7) % 56.88/8.55 | | | | | | | | | | | = v1 & $i(v2) & ( ~ (v3 = 0) | v1 = 0) & ( % 56.88/8.55 | | | | | | | | | | | ~ (v1 = 0) | v3 = 0))))) % 56.88/8.55 | | | | | | | | | | | % 56.88/8.55 | | | | | | | | | | | ALPHA: (574) implies: % 56.88/8.55 | | | | | | | | | | | (575) powerset(all_138_8) = all_749_2 % 56.88/8.55 | | | | | | | | | | | % 56.88/8.55 | | | | | | | | | | | REDUCE: (469), (488) imply: % 56.88/8.55 | | | | | | | | | | | (576) union_of_subsets(all_138_8, all_138_6) = all_340_0 % 56.88/8.55 | | | | | | | | | | | % 56.88/8.55 | | | | | | | | | | | REDUCE: (469), (483) imply: % 56.88/8.55 | | | | | | | | | | | (577) union_of_subsets(all_138_8, all_138_6) = all_324_0 % 56.88/8.55 | | | | | | | | | | | % 56.88/8.55 | | | | | | | | | | | REDUCE: (469), (487) imply: % 56.88/8.55 | | | | | | | | | | | (578) union(all_138_6) = all_340_0 % 56.88/8.55 | | | | | | | | | | | % 56.88/8.55 | | | | | | | | | | | BETA: splitting (454) gives: % 56.88/8.55 | | | | | | | | | | | % 56.88/8.55 | | | | | | | | | | | Case 1: % 56.88/8.55 | | | | | | | | | | | | % 56.88/8.55 | | | | | | | | | | | | (579) all_220_0 = all_162_0 % 56.88/8.55 | | | | | | | | | | | | % 56.88/8.55 | | | | | | | | | | | | COMBINE_EQS: (299), (579) imply: % 56.88/8.55 | | | | | | | | | | | | (580) all_162_0 = all_138_4 % 56.88/8.55 | | | | | | | | | | | | % 56.88/8.55 | | | | | | | | | | | | SIMP: (580) implies: % 56.88/8.55 | | | | | | | | | | | | (581) all_162_0 = all_138_4 % 56.88/8.55 | | | | | | | | | | | | % 56.88/8.55 | | | | | | | | | | | | COMBINE_EQS: (480), (581) imply: % 56.88/8.55 | | | | | | | | | | | | (582) all_138_4 = empty_set % 56.88/8.55 | | | | | | | | | | | | % 56.88/8.55 | | | | | | | | | | | | REDUCE: (305), (582) imply: % 56.88/8.56 | | | | | | | | | | | | (583) $false % 56.88/8.56 | | | | | | | | | | | | % 56.88/8.56 | | | | | | | | | | | | CLOSE: (583) is inconsistent. % 56.88/8.56 | | | | | | | | | | | | % 56.88/8.56 | | | | | | | | | | | Case 2: % 56.88/8.56 | | | | | | | | | | | | % 56.88/8.56 | | | | | | | | | | | | % 56.88/8.56 | | | | | | | | | | | | GROUND_INST: instantiating (32) with all_138_6, all_726_3, % 56.88/8.56 | | | | | | | | | | | | all_138_8, simplifying with (56), (565) gives: % 56.88/8.56 | | | | | | | | | | | | (584) all_726_3 = all_138_6 % 56.88/8.56 | | | | | | | | | | | | % 56.88/8.56 | | | | | | | | | | | | GROUND_INST: instantiating (32) with all_602_3, all_726_3, % 56.88/8.56 | | | | | | | | | | | | all_138_8, simplifying with (533), (565) gives: % 56.88/8.56 | | | | | | | | | | | | (585) all_726_3 = all_602_3 % 56.88/8.56 | | | | | | | | | | | | % 56.88/8.56 | | | | | | | | | | | | GROUND_INST: instantiating (32) with all_726_3, all_728_3, % 56.88/8.56 | | | | | | | | | | | | all_138_8, simplifying with (565), (567) gives: % 56.88/8.56 | | | | | | | | | | | | (586) all_728_3 = all_726_3 % 56.88/8.56 | | | | | | | | | | | | % 56.88/8.56 | | | | | | | | | | | | GROUND_INST: instantiating (32) with all_726_3, all_730_3, % 56.88/8.56 | | | | | | | | | | | | all_138_8, simplifying with (565), (569) gives: % 56.88/8.56 | | | | | | | | | | | | (587) all_730_3 = all_726_3 % 56.88/8.56 | | | | | | | | | | | | % 56.88/8.56 | | | | | | | | | | | | GROUND_INST: instantiating (32) with all_544_2, all_730_3, % 56.88/8.56 | | | | | | | | | | | | all_138_8, simplifying with (522), (569) gives: % 56.88/8.56 | | | | | | | | | | | | (588) all_730_3 = all_544_2 % 56.88/8.56 | | | | | | | | | | | | % 56.88/8.56 | | | | | | | | | | | | GROUND_INST: instantiating (32) with all_728_3, all_749_2, % 56.88/8.56 | | | | | | | | | | | | all_138_8, simplifying with (567), (575) gives: % 56.88/8.56 | | | | | | | | | | | | (589) all_749_2 = all_728_3 % 56.88/8.56 | | | | | | | | | | | | % 56.88/8.56 | | | | | | | | | | | | GROUND_INST: instantiating (32) with all_612_3, all_749_2, % 56.88/8.56 | | | | | | | | | | | | all_138_8, simplifying with (539), (575) gives: % 56.88/8.56 | | | | | | | | | | | | (590) all_749_2 = all_612_3 % 56.88/8.56 | | | | | | | | | | | | % 56.88/8.56 | | | | | | | | | | | | GROUND_INST: instantiating (33) with all_504_1, all_516_1, % 56.88/8.56 | | | | | | | | | | | | all_138_5, simplifying with (514), (516) gives: % 56.88/8.56 | | | | | | | | | | | | (591) all_516_1 = all_504_1 % 56.88/8.56 | | | | | | | | | | | | % 56.88/8.56 | | | | | | | | | | | | GROUND_INST: instantiating (33) with all_516_1, all_526_1, % 56.88/8.56 | | | | | | | | | | | | all_138_5, simplifying with (516), (518) gives: % 56.88/8.56 | | | | | | | | | | | | (592) all_526_1 = all_516_1 % 56.88/8.56 | | | | | | | | | | | | % 56.88/8.56 | | | | | | | | | | | | GROUND_INST: instantiating (33) with all_498_1, all_526_1, % 56.88/8.56 | | | | | | | | | | | | all_138_5, simplifying with (511), (518) gives: % 56.88/8.56 | | | | | | | | | | | | (593) all_526_1 = all_498_1 % 56.88/8.56 | | | | | | | | | | | | % 56.88/8.56 | | | | | | | | | | | | GROUND_INST: instantiating (33) with all_158_0, all_528_1, % 56.88/8.56 | | | | | | | | | | | | all_138_5, simplifying with (101), (520) gives: % 56.88/8.56 | | | | | | | | | | | | (594) all_528_1 = all_158_0 % 56.88/8.56 | | | | | | | | | | | | % 56.88/8.56 | | | | | | | | | | | | GROUND_INST: instantiating (33) with all_504_1, all_528_1, % 56.88/8.56 | | | | | | | | | | | | all_138_5, simplifying with (514), (520) gives: % 56.88/8.56 | | | | | | | | | | | | (595) all_528_1 = all_504_1 % 56.88/8.56 | | | | | | | | | | | | % 56.88/8.56 | | | | | | | | | | | | GROUND_INST: instantiating (35) with all_138_8, all_340_0, % 56.88/8.56 | | | | | | | | | | | | all_138_6, simplifying with (65), (578) gives: % 56.88/8.56 | | | | | | | | | | | | (596) all_340_0 = all_138_8 % 56.88/8.56 | | | | | | | | | | | | % 56.88/8.56 | | | | | | | | | | | | GROUND_INST: instantiating (37) with all_448_0, all_730_0, % 56.88/8.56 | | | | | | | | | | | | all_138_3, all_138_8, simplifying with (503), % 56.88/8.56 | | | | | | | | | | | | (572) gives: % 56.88/8.56 | | | | | | | | | | | | (597) all_730_0 = all_448_0 % 56.88/8.56 | | | | | | | | | | | | % 56.88/8.56 | | | | | | | | | | | | GROUND_INST: instantiating (37) with all_138_0, all_354_0, % 56.88/8.56 | | | | | | | | | | | | all_138_1, all_138_8, simplifying with (409), % 56.88/8.56 | | | | | | | | | | | | (495) gives: % 56.88/8.56 | | | | | | | | | | | | (598) all_354_0 = all_138_0 % 56.88/8.56 | | | | | | | | | | | | % 56.88/8.56 | | | | | | | | | | | | GROUND_INST: instantiating (38) with all_570_1, all_664_1, % 56.88/8.56 | | | | | | | | | | | | all_138_3, all_138_8, simplifying with (527), % 56.88/8.56 | | | | | | | | | | | | (551) gives: % 56.88/8.56 | | | | | | | | | | | | (599) all_664_1 = all_570_1 % 56.88/8.56 | | | | | | | | | | | | % 56.88/8.56 | | | | | | | | | | | | GROUND_INST: instantiating (38) with all_452_0, all_664_1, % 56.88/8.56 | | | | | | | | | | | | all_138_3, all_138_8, simplifying with (508), % 56.88/8.56 | | | | | | | | | | | | (551) gives: % 56.88/8.56 | | | | | | | | | | | | (600) all_664_1 = all_452_0 % 56.88/8.56 | | | | | | | | | | | | % 56.88/8.56 | | | | | | | | | | | | GROUND_INST: instantiating (38) with all_442_0, all_664_1, % 56.88/8.56 | | | | | | | | | | | | all_138_3, all_138_8, simplifying with (501), % 56.88/8.56 | | | | | | | | | | | | (551) gives: % 56.88/8.56 | | | | | | | | | | | | (601) all_664_1 = all_442_0 % 56.88/8.56 | | | | | | | | | | | | % 56.88/8.56 | | | | | | | | | | | | GROUND_INST: instantiating (38) with all_658_1, all_684_1, % 56.88/8.56 | | | | | | | | | | | | all_138_3, all_138_8, simplifying with (549), % 56.88/8.56 | | | | | | | | | | | | (557) gives: % 56.88/8.56 | | | | | | | | | | | | (602) all_684_1 = all_658_1 % 56.88/8.56 | | | | | | | | | | | | % 56.88/8.56 | | | | | | | | | | | | GROUND_INST: instantiating (38) with all_570_1, all_684_1, % 56.88/8.56 | | | | | | | | | | | | all_138_3, all_138_8, simplifying with (527), % 56.88/8.56 | | | | | | | | | | | | (557) gives: % 56.88/8.56 | | | | | | | | | | | | (603) all_684_1 = all_570_1 % 56.88/8.56 | | | | | | | | | | | | % 56.88/8.56 | | | | | | | | | | | | GROUND_INST: instantiating (38) with all_448_0, all_684_1, % 56.88/8.56 | | | | | | | | | | | | all_138_3, all_138_8, simplifying with (504), % 56.88/8.56 | | | | | | | | | | | | (557) gives: % 56.88/8.56 | | | | | | | | | | | | (604) all_684_1 = all_448_0 % 56.88/8.56 | | | | | | | | | | | | % 56.88/8.56 | | | | | | | | | | | | GROUND_INST: instantiating (38) with all_684_1, all_702_1, % 56.88/8.56 | | | | | | | | | | | | all_138_3, all_138_8, simplifying with (557), % 56.88/8.56 | | | | | | | | | | | | (563) gives: % 56.88/8.56 | | | | | | | | | | | | (605) all_702_1 = all_684_1 % 56.88/8.56 | | | | | | | | | | | | % 56.88/8.56 | | | | | | | | | | | | GROUND_INST: instantiating (38) with all_666_1, all_702_1, % 56.88/8.56 | | | | | | | | | | | | all_138_3, all_138_8, simplifying with (553), % 56.88/8.56 | | | | | | | | | | | | (563) gives: % 56.88/8.56 | | | | | | | | | | | | (606) all_702_1 = all_666_1 % 56.88/8.56 | | | | | | | | | | | | % 56.88/8.56 | | | | | | | | | | | | GROUND_INST: instantiating (38) with all_544_0, all_606_1, % 56.88/8.56 | | | | | | | | | | | | all_138_1, all_138_8, simplifying with (523), % 56.88/8.56 | | | | | | | | | | | | (535) gives: % 56.88/8.56 | | | | | | | | | | | | (607) all_606_1 = all_544_0 % 56.88/8.56 | | | | | | | | | | | | % 56.88/8.56 | | | | | | | | | | | | GROUND_INST: instantiating (38) with all_326_0, all_606_1, % 56.88/8.56 | | | | | | | | | | | | all_138_1, all_138_8, simplifying with (485), % 56.88/8.56 | | | | | | | | | | | | (535) gives: % 56.88/8.56 | | | | | | | | | | | | (608) all_606_1 = all_326_0 % 56.88/8.56 | | | | | | | | | | | | % 56.88/8.56 | | | | | | | | | | | | GROUND_INST: instantiating (38) with all_606_1, all_608_1, % 56.88/8.56 | | | | | | | | | | | | all_138_1, all_138_8, simplifying with (535), % 56.88/8.56 | | | | | | | | | | | | (537) gives: % 56.88/8.56 | | | | | | | | | | | | (609) all_608_1 = all_606_1 % 56.88/8.56 | | | | | | | | | | | | % 56.88/8.56 | | | | | | | | | | | | GROUND_INST: instantiating (38) with all_608_1, all_628_1, % 56.88/8.56 | | | | | | | | | | | | all_138_1, all_138_8, simplifying with (537), % 56.88/8.56 | | | | | | | | | | | | (545) gives: % 56.88/8.56 | | | | | | | | | | | | (610) all_628_1 = all_608_1 % 56.88/8.56 | | | | | | | | | | | | % 56.88/8.56 | | | | | | | | | | | | GROUND_INST: instantiating (38) with all_356_0, all_628_1, % 56.88/8.56 | | | | | | | | | | | | all_138_1, all_138_8, simplifying with (498), % 56.88/8.56 | | | | | | | | | | | | (545) gives: % 56.88/8.56 | | | | | | | | | | | | (611) all_628_1 = all_356_0 % 56.88/8.56 | | | | | | | | | | | | % 56.88/8.56 | | | | | | | | | | | | GROUND_INST: instantiating (38) with all_354_0, all_668_1, % 56.88/8.56 | | | | | | | | | | | | all_138_1, all_138_8, simplifying with (496), % 56.88/8.56 | | | | | | | | | | | | (555) gives: % 56.88/8.56 | | | | | | | | | | | | (612) all_668_1 = all_354_0 % 56.88/8.56 | | | | | | | | | | | | % 56.88/8.56 | | | | | | | | | | | | GROUND_INST: instantiating (38) with all_668_1, all_700_1, % 56.88/8.56 | | | | | | | | | | | | all_138_1, all_138_8, simplifying with (555), % 56.88/8.56 | | | | | | | | | | | | (561) gives: % 56.88/8.56 | | | | | | | | | | | | (613) all_700_1 = all_668_1 % 56.88/8.56 | | | | | | | | | | | | % 56.88/8.56 | | | | | | | | | | | | GROUND_INST: instantiating (38) with all_574_1, all_700_1, % 56.88/8.56 | | | | | | | | | | | | all_138_1, all_138_8, simplifying with (531), % 56.88/8.56 | | | | | | | | | | | | (561) gives: % 56.88/8.56 | | | | | | | | | | | | (614) all_700_1 = all_574_1 % 56.88/8.56 | | | | | | | | | | | | % 56.88/8.56 | | | | | | | | | | | | GROUND_INST: instantiating (38) with all_544_0, all_700_1, % 56.88/8.56 | | | | | | | | | | | | all_138_1, all_138_8, simplifying with (523), % 56.88/8.56 | | | | | | | | | | | | (561) gives: % 56.88/8.56 | | | | | | | | | | | | (615) all_700_1 = all_544_0 % 56.88/8.56 | | | | | | | | | | | | % 56.88/8.56 | | | | | | | | | | | | GROUND_INST: instantiating (38) with all_350_0, all_450_0, % 56.88/8.56 | | | | | | | | | | | | all_138_0, all_138_8, simplifying with (490), % 56.88/8.56 | | | | | | | | | | | | (506) gives: % 56.88/8.56 | | | | | | | | | | | | (616) all_450_0 = all_350_0 % 56.88/8.56 | | | | | | | | | | | | % 56.88/8.56 | | | | | | | | | | | | GROUND_INST: instantiating (38) with all_450_0, all_568_1, % 56.88/8.56 | | | | | | | | | | | | all_138_0, all_138_8, simplifying with (506), % 56.88/8.56 | | | | | | | | | | | | (525) gives: % 56.88/8.56 | | | | | | | | | | | | (617) all_568_1 = all_450_0 % 56.88/8.56 | | | | | | | | | | | | % 56.88/8.56 | | | | | | | | | | | | GROUND_INST: instantiating (38) with all_568_1, all_572_1, % 56.88/8.56 | | | | | | | | | | | | all_138_0, all_138_8, simplifying with (525), % 56.88/8.56 | | | | | | | | | | | | (529) gives: % 56.88/8.56 | | | | | | | | | | | | (618) all_572_1 = all_568_1 % 56.88/8.56 | | | | | | | | | | | | % 56.88/8.56 | | | | | | | | | | | | GROUND_INST: instantiating (38) with all_572_1, all_616_1, % 56.88/8.56 | | | | | | | | | | | | all_138_0, all_138_8, simplifying with (529), % 56.88/8.56 | | | | | | | | | | | | (541) gives: % 56.88/8.56 | | | | | | | | | | | | (619) all_616_1 = all_572_1 % 56.88/8.56 | | | | | | | | | | | | % 56.88/8.56 | | | | | | | | | | | | GROUND_INST: instantiating (38) with all_616_1, all_618_1, % 56.88/8.56 | | | | | | | | | | | | all_138_0, all_138_8, simplifying with (541), % 56.88/8.56 | | | | | | | | | | | | (543) gives: % 56.88/8.56 | | | | | | | | | | | | (620) all_618_1 = all_616_1 % 56.88/8.56 | | | | | | | | | | | | % 56.88/8.56 | | | | | | | | | | | | GROUND_INST: instantiating (38) with all_618_1, all_648_1, % 56.88/8.56 | | | | | | | | | | | | all_138_0, all_138_8, simplifying with (543), % 56.88/8.56 | | | | | | | | | | | | (547) gives: % 56.88/8.56 | | | | | | | | | | | | (621) all_648_1 = all_618_1 % 56.88/8.56 | | | | | | | | | | | | % 56.88/8.56 | | | | | | | | | | | | GROUND_INST: instantiating (38) with all_648_1, all_686_1, % 56.88/8.56 | | | | | | | | | | | | all_138_0, all_138_8, simplifying with (547), % 56.88/8.56 | | | | | | | | | | | | (559) gives: % 56.88/8.56 | | | | | | | | | | | | (622) all_686_1 = all_648_1 % 56.88/8.56 | | | | | | | | | | | | % 56.88/8.56 | | | | | | | | | | | | GROUND_INST: instantiating (38) with all_352_0, all_686_1, % 56.88/8.56 | | | | | | | | | | | | all_138_0, all_138_8, simplifying with (492), % 56.88/8.56 | | | | | | | | | | | | (559) gives: % 56.88/8.56 | | | | | | | | | | | | (623) all_686_1 = all_352_0 % 56.88/8.56 | | | | | | | | | | | | % 56.88/8.56 | | | | | | | | | | | | GROUND_INST: instantiating (40) with all_324_0, all_340_0, % 56.88/8.56 | | | | | | | | | | | | all_138_6, all_138_8, simplifying with (576), % 56.88/8.56 | | | | | | | | | | | | (577) gives: % 56.88/8.56 | | | | | | | | | | | | (624) all_340_0 = all_324_0 % 56.88/8.56 | | | | | | | | | | | | % 56.88/8.56 | | | | | | | | | | | | COMBINE_EQS: (589), (590) imply: % 56.88/8.56 | | | | | | | | | | | | (625) all_728_3 = all_612_3 % 56.88/8.56 | | | | | | | | | | | | % 56.88/8.56 | | | | | | | | | | | | SIMP: (625) implies: % 56.88/8.56 | | | | | | | | | | | | (626) all_728_3 = all_612_3 % 56.88/8.56 | | | | | | | | | | | | % 56.88/8.56 | | | | | | | | | | | | COMBINE_EQS: (587), (588) imply: % 56.88/8.56 | | | | | | | | | | | | (627) all_726_3 = all_544_2 % 56.88/8.56 | | | | | | | | | | | | % 56.88/8.56 | | | | | | | | | | | | SIMP: (627) implies: % 56.88/8.56 | | | | | | | | | | | | (628) all_726_3 = all_544_2 % 56.88/8.56 | | | | | | | | | | | | % 56.88/8.56 | | | | | | | | | | | | COMBINE_EQS: (586), (626) imply: % 56.88/8.56 | | | | | | | | | | | | (629) all_726_3 = all_612_3 % 56.88/8.56 | | | | | | | | | | | | % 56.88/8.56 | | | | | | | | | | | | SIMP: (629) implies: % 56.88/8.56 | | | | | | | | | | | | (630) all_726_3 = all_612_3 % 56.88/8.56 | | | | | | | | | | | | % 56.88/8.56 | | | | | | | | | | | | COMBINE_EQS: (628), (630) imply: % 56.88/8.56 | | | | | | | | | | | | (631) all_612_3 = all_544_2 % 56.88/8.56 | | | | | | | | | | | | % 56.88/8.56 | | | | | | | | | | | | COMBINE_EQS: (585), (630) imply: % 56.88/8.56 | | | | | | | | | | | | (632) all_612_3 = all_602_3 % 56.88/8.56 | | | | | | | | | | | | % 56.88/8.56 | | | | | | | | | | | | COMBINE_EQS: (584), (630) imply: % 56.88/8.56 | | | | | | | | | | | | (633) all_612_3 = all_138_6 % 56.88/8.56 | | | | | | | | | | | | % 56.88/8.56 | | | | | | | | | | | | COMBINE_EQS: (605), (606) imply: % 56.88/8.56 | | | | | | | | | | | | (634) all_684_1 = all_666_1 % 56.88/8.56 | | | | | | | | | | | | % 56.88/8.56 | | | | | | | | | | | | SIMP: (634) implies: % 56.88/8.56 | | | | | | | | | | | | (635) all_684_1 = all_666_1 % 56.88/8.56 | | | | | | | | | | | | % 56.88/8.56 | | | | | | | | | | | | COMBINE_EQS: (613), (614) imply: % 56.88/8.56 | | | | | | | | | | | | (636) all_668_1 = all_574_1 % 56.88/8.56 | | | | | | | | | | | | % 56.88/8.56 | | | | | | | | | | | | SIMP: (636) implies: % 56.88/8.56 | | | | | | | | | | | | (637) all_668_1 = all_574_1 % 56.88/8.56 | | | | | | | | | | | | % 56.88/8.56 | | | | | | | | | | | | COMBINE_EQS: (614), (615) imply: % 56.88/8.56 | | | | | | | | | | | | (638) all_574_1 = all_544_0 % 56.88/8.56 | | | | | | | | | | | | % 56.88/8.56 | | | | | | | | | | | | COMBINE_EQS: (622), (623) imply: % 56.88/8.56 | | | | | | | | | | | | (639) all_648_1 = all_352_0 % 56.88/8.56 | | | | | | | | | | | | % 56.88/8.56 | | | | | | | | | | | | SIMP: (639) implies: % 56.88/8.56 | | | | | | | | | | | | (640) all_648_1 = all_352_0 % 56.88/8.56 | | | | | | | | | | | | % 56.88/8.56 | | | | | | | | | | | | COMBINE_EQS: (604), (635) imply: % 56.88/8.56 | | | | | | | | | | | | (641) all_666_1 = all_448_0 % 56.88/8.56 | | | | | | | | | | | | % 56.88/8.56 | | | | | | | | | | | | COMBINE_EQS: (603), (635) imply: % 56.88/8.56 | | | | | | | | | | | | (642) all_666_1 = all_570_1 % 56.88/8.56 | | | | | | | | | | | | % 56.88/8.56 | | | | | | | | | | | | COMBINE_EQS: (602), (635) imply: % 56.88/8.56 | | | | | | | | | | | | (643) all_666_1 = all_658_1 % 56.88/8.56 | | | | | | | | | | | | % 56.88/8.56 | | | | | | | | | | | | COMBINE_EQS: (612), (637) imply: % 56.88/8.56 | | | | | | | | | | | | (644) all_574_1 = all_354_0 % 56.88/8.56 | | | | | | | | | | | | % 56.88/8.56 | | | | | | | | | | | | SIMP: (644) implies: % 56.88/8.56 | | | | | | | | | | | | (645) all_574_1 = all_354_0 % 56.88/8.56 | | | | | | | | | | | | % 56.88/8.56 | | | | | | | | | | | | COMBINE_EQS: (642), (643) imply: % 56.88/8.56 | | | | | | | | | | | | (646) all_658_1 = all_570_1 % 56.88/8.56 | | | | | | | | | | | | % 56.88/8.56 | | | | | | | | | | | | COMBINE_EQS: (641), (643) imply: % 56.88/8.56 | | | | | | | | | | | | (647) all_658_1 = all_448_0 % 56.88/8.56 | | | | | | | | | | | | % 56.88/8.56 | | | | | | | | | | | | COMBINE_EQS: (599), (600) imply: % 56.88/8.56 | | | | | | | | | | | | (648) all_570_1 = all_452_0 % 56.88/8.56 | | | | | | | | | | | | % 56.88/8.56 | | | | | | | | | | | | SIMP: (648) implies: % 56.88/8.56 | | | | | | | | | | | | (649) all_570_1 = all_452_0 % 56.88/8.56 | | | | | | | | | | | | % 56.88/8.56 | | | | | | | | | | | | COMBINE_EQS: (600), (601) imply: % 56.88/8.56 | | | | | | | | | | | | (650) all_452_0 = all_442_0 % 56.88/8.56 | | | | | | | | | | | | % 56.88/8.56 | | | | | | | | | | | | COMBINE_EQS: (646), (647) imply: % 56.88/8.56 | | | | | | | | | | | | (651) all_570_1 = all_448_0 % 56.88/8.56 | | | | | | | | | | | | % 56.88/8.56 | | | | | | | | | | | | SIMP: (651) implies: % 56.88/8.56 | | | | | | | | | | | | (652) all_570_1 = all_448_0 % 56.88/8.56 | | | | | | | | | | | | % 56.88/8.56 | | | | | | | | | | | | COMBINE_EQS: (621), (640) imply: % 56.88/8.56 | | | | | | | | | | | | (653) all_618_1 = all_352_0 % 56.88/8.56 | | | | | | | | | | | | % 56.88/8.56 | | | | | | | | | | | | SIMP: (653) implies: % 56.88/8.56 | | | | | | | | | | | | (654) all_618_1 = all_352_0 % 56.88/8.56 | | | | | | | | | | | | % 56.88/8.56 | | | | | | | | | | | | COMBINE_EQS: (610), (611) imply: % 56.88/8.56 | | | | | | | | | | | | (655) all_608_1 = all_356_0 % 56.88/8.56 | | | | | | | | | | | | % 56.88/8.56 | | | | | | | | | | | | SIMP: (655) implies: % 56.88/8.56 | | | | | | | | | | | | (656) all_608_1 = all_356_0 % 56.88/8.56 | | | | | | | | | | | | % 56.88/8.56 | | | | | | | | | | | | COMBINE_EQS: (620), (654) imply: % 56.88/8.56 | | | | | | | | | | | | (657) all_616_1 = all_352_0 % 56.88/8.56 | | | | | | | | | | | | % 56.88/8.56 | | | | | | | | | | | | SIMP: (657) implies: % 56.88/8.56 | | | | | | | | | | | | (658) all_616_1 = all_352_0 % 56.88/8.56 | | | | | | | | | | | | % 56.88/8.56 | | | | | | | | | | | | COMBINE_EQS: (619), (658) imply: % 56.88/8.56 | | | | | | | | | | | | (659) all_572_1 = all_352_0 % 56.88/8.56 | | | | | | | | | | | | % 56.88/8.56 | | | | | | | | | | | | SIMP: (659) implies: % 56.88/8.56 | | | | | | | | | | | | (660) all_572_1 = all_352_0 % 56.88/8.56 | | | | | | | | | | | | % 56.88/8.56 | | | | | | | | | | | | COMBINE_EQS: (632), (633) imply: % 56.88/8.56 | | | | | | | | | | | | (661) all_602_3 = all_138_6 % 56.88/8.56 | | | | | | | | | | | | % 56.88/8.56 | | | | | | | | | | | | COMBINE_EQS: (631), (632) imply: % 56.88/8.56 | | | | | | | | | | | | (662) all_602_3 = all_544_2 % 56.88/8.56 | | | | | | | | | | | | % 56.88/8.56 | | | | | | | | | | | | COMBINE_EQS: (609), (656) imply: % 56.88/8.56 | | | | | | | | | | | | (663) all_606_1 = all_356_0 % 56.88/8.56 | | | | | | | | | | | | % 56.88/8.56 | | | | | | | | | | | | SIMP: (663) implies: % 56.88/8.56 | | | | | | | | | | | | (664) all_606_1 = all_356_0 % 56.88/8.56 | | | | | | | | | | | | % 56.88/8.56 | | | | | | | | | | | | COMBINE_EQS: (607), (664) imply: % 56.88/8.56 | | | | | | | | | | | | (665) all_544_0 = all_356_0 % 56.88/8.56 | | | | | | | | | | | | % 56.88/8.56 | | | | | | | | | | | | SIMP: (665) implies: % 56.88/8.56 | | | | | | | | | | | | (666) all_544_0 = all_356_0 % 56.88/8.56 | | | | | | | | | | | | % 56.88/8.56 | | | | | | | | | | | | COMBINE_EQS: (608), (664) imply: % 56.88/8.56 | | | | | | | | | | | | (667) all_356_0 = all_326_0 % 56.88/8.56 | | | | | | | | | | | | % 56.88/8.56 | | | | | | | | | | | | COMBINE_EQS: (661), (662) imply: % 56.88/8.56 | | | | | | | | | | | | (668) all_544_2 = all_138_6 % 56.88/8.56 | | | | | | | | | | | | % 56.88/8.56 | | | | | | | | | | | | COMBINE_EQS: (638), (645) imply: % 56.88/8.56 | | | | | | | | | | | | (669) all_544_0 = all_354_0 % 56.88/8.56 | | | | | | | | | | | | % 56.88/8.56 | | | | | | | | | | | | SIMP: (669) implies: % 56.88/8.56 | | | | | | | | | | | | (670) all_544_0 = all_354_0 % 56.88/8.56 | | | | | | | | | | | | % 56.88/8.56 | | | | | | | | | | | | COMBINE_EQS: (618), (660) imply: % 56.88/8.56 | | | | | | | | | | | | (671) all_568_1 = all_352_0 % 56.88/8.56 | | | | | | | | | | | | % 56.88/8.56 | | | | | | | | | | | | SIMP: (671) implies: % 56.88/8.56 | | | | | | | | | | | | (672) all_568_1 = all_352_0 % 56.88/8.56 | | | | | | | | | | | | % 56.88/8.56 | | | | | | | | | | | | COMBINE_EQS: (649), (652) imply: % 56.88/8.56 | | | | | | | | | | | | (673) all_452_0 = all_448_0 % 56.88/8.56 | | | | | | | | | | | | % 56.88/8.56 | | | | | | | | | | | | SIMP: (673) implies: % 56.88/8.57 | | | | | | | | | | | | (674) all_452_0 = all_448_0 % 56.88/8.57 | | | | | | | | | | | | % 56.88/8.57 | | | | | | | | | | | | COMBINE_EQS: (617), (672) imply: % 56.88/8.57 | | | | | | | | | | | | (675) all_450_0 = all_352_0 % 56.88/8.57 | | | | | | | | | | | | % 56.88/8.57 | | | | | | | | | | | | SIMP: (675) implies: % 56.88/8.57 | | | | | | | | | | | | (676) all_450_0 = all_352_0 % 56.88/8.57 | | | | | | | | | | | | % 56.88/8.57 | | | | | | | | | | | | COMBINE_EQS: (666), (670) imply: % 56.88/8.57 | | | | | | | | | | | | (677) all_356_0 = all_354_0 % 56.88/8.57 | | | | | | | | | | | | % 56.88/8.57 | | | | | | | | | | | | SIMP: (677) implies: % 56.88/8.57 | | | | | | | | | | | | (678) all_356_0 = all_354_0 % 56.88/8.57 | | | | | | | | | | | | % 56.88/8.57 | | | | | | | | | | | | COMBINE_EQS: (594), (595) imply: % 56.88/8.57 | | | | | | | | | | | | (679) all_504_1 = all_158_0 % 56.88/8.57 | | | | | | | | | | | | % 56.88/8.57 | | | | | | | | | | | | SIMP: (679) implies: % 56.88/8.57 | | | | | | | | | | | | (680) all_504_1 = all_158_0 % 56.88/8.57 | | | | | | | | | | | | % 56.88/8.57 | | | | | | | | | | | | COMBINE_EQS: (592), (593) imply: % 56.88/8.57 | | | | | | | | | | | | (681) all_516_1 = all_498_1 % 56.88/8.57 | | | | | | | | | | | | % 56.88/8.57 | | | | | | | | | | | | SIMP: (681) implies: % 56.88/8.57 | | | | | | | | | | | | (682) all_516_1 = all_498_1 % 56.88/8.57 | | | | | | | | | | | | % 56.88/8.57 | | | | | | | | | | | | COMBINE_EQS: (591), (682) imply: % 56.88/8.57 | | | | | | | | | | | | (683) all_504_1 = all_498_1 % 56.88/8.57 | | | | | | | | | | | | % 56.88/8.57 | | | | | | | | | | | | SIMP: (683) implies: % 56.88/8.57 | | | | | | | | | | | | (684) all_504_1 = all_498_1 % 56.88/8.57 | | | | | | | | | | | | % 56.88/8.57 | | | | | | | | | | | | COMBINE_EQS: (680), (684) imply: % 56.88/8.57 | | | | | | | | | | | | (685) all_498_1 = all_158_0 % 56.88/8.57 | | | | | | | | | | | | % 56.88/8.57 | | | | | | | | | | | | COMBINE_EQS: (650), (674) imply: % 56.88/8.57 | | | | | | | | | | | | (686) all_448_0 = all_442_0 % 56.88/8.57 | | | | | | | | | | | | % 56.88/8.57 | | | | | | | | | | | | COMBINE_EQS: (616), (676) imply: % 56.88/8.57 | | | | | | | | | | | | (687) all_352_0 = all_350_0 % 56.88/8.57 | | | | | | | | | | | | % 56.88/8.57 | | | | | | | | | | | | COMBINE_EQS: (667), (678) imply: % 56.88/8.57 | | | | | | | | | | | | (688) all_354_0 = all_326_0 % 56.88/8.57 | | | | | | | | | | | | % 56.88/8.57 | | | | | | | | | | | | SIMP: (688) implies: % 56.88/8.57 | | | | | | | | | | | | (689) all_354_0 = all_326_0 % 56.88/8.57 | | | | | | | | | | | | % 56.88/8.57 | | | | | | | | | | | | COMBINE_EQS: (598), (689) imply: % 56.88/8.57 | | | | | | | | | | | | (690) all_326_0 = all_138_0 % 56.88/8.57 | | | | | | | | | | | | % 56.88/8.57 | | | | | | | | | | | | COMBINE_EQS: (596), (624) imply: % 56.88/8.57 | | | | | | | | | | | | (691) all_324_0 = all_138_8 % 56.88/8.57 | | | | | | | | | | | | % 56.88/8.57 | | | | | | | | | | | | SIMP: (691) implies: % 56.88/8.57 | | | | | | | | | | | | (692) all_324_0 = all_138_8 % 56.88/8.57 | | | | | | | | | | | | % 56.88/8.57 | | | | | | | | | | | | COMBINE_EQS: (667), (690) imply: % 56.88/8.57 | | | | | | | | | | | | (693) all_356_0 = all_138_0 % 56.88/8.57 | | | | | | | | | | | | % 56.88/8.57 | | | | | | | | | | | | COMBINE_EQS: (588), (668) imply: % 56.88/8.57 | | | | | | | | | | | | (694) all_730_3 = all_138_6 % 56.88/8.57 | | | | | | | | | | | | % 56.88/8.57 | | | | | | | | | | | | COMBINE_EQS: (597), (686) imply: % 56.88/8.57 | | | | | | | | | | | | (695) all_730_0 = all_442_0 % 56.88/8.57 | | | | | | | | | | | | % 56.88/8.57 | | | | | | | | | | | | REDUCE: (509), (650) imply: % 56.88/8.57 | | | | | | | | | | | | (696) subset_complement(all_138_8, all_442_0) = % 56.88/8.57 | | | | | | | | | | | | all_138_3 % 56.88/8.57 | | | | | | | | | | | | % 56.88/8.57 | | | | | | | | | | | | REDUCE: (499), (693) imply: % 56.88/8.57 | | | | | | | | | | | | (697) subset_complement(all_138_8, all_138_0) = % 56.88/8.57 | | | | | | | | | | | | all_138_1 % 56.88/8.57 | | | | | | | | | | | | % 56.88/8.57 | | | | | | | | | | | | REDUCE: (493), (687) imply: % 56.88/8.57 | | | | | | | | | | | | (698) subset_complement(all_138_8, all_350_0) = % 56.88/8.57 | | | | | | | | | | | | all_138_0 % 56.88/8.57 | | | | | | | | | | | | % 56.88/8.57 | | | | | | | | | | | | REDUCE: (571), (694) imply: % 56.88/8.57 | | | | | | | | | | | | (699) element(all_138_3, all_138_6) = all_730_1 % 56.88/8.57 | | | | | | | | | | | | % 56.88/8.57 | | | | | | | | | | | | REDUCE: (570), (694) imply: % 56.88/8.57 | | | | | | | | | | | | (700) element(all_138_8, all_138_6) = all_730_2 % 56.88/8.57 | | | | | | | | | | | | % 56.88/8.57 | | | | | | | | | | | | BETA: splitting (512) gives: % 56.88/8.57 | | | | | | | | | | | | % 56.88/8.57 | | | | | | | | | | | | Case 1: % 56.88/8.57 | | | | | | | | | | | | | % 56.88/8.57 | | | | | | | | | | | | | % 56.88/8.57 | | | | | | | | | | | | | GROUND_INST: instantiating (36) with 0, all_730_2, all_138_6, % 56.88/8.57 | | | | | | | | | | | | | all_138_8, simplifying with (321), (700) gives: % 56.88/8.57 | | | | | | | | | | | | | (701) all_730_2 = 0 % 56.88/8.57 | | | | | | | | | | | | | % 56.88/8.57 | | | | | | | | | | | | | GROUND_INST: instantiating (36) with 0, all_730_1, all_138_6, % 56.88/8.57 | | | | | | | | | | | | | all_138_3, simplifying with (423), (699) gives: % 56.88/8.57 | | | | | | | | | | | | | (702) all_730_1 = 0 % 56.88/8.57 | | | | | | | | | | | | | % 56.88/8.57 | | | | | | | | | | | | | GROUND_INST: instantiating (38) with all_350_0, all_138_1, % 56.88/8.57 | | | | | | | | | | | | | all_138_0, all_138_8, simplifying with (490), % 56.88/8.57 | | | | | | | | | | | | | (697) gives: % 56.88/8.57 | | | | | | | | | | | | | (703) all_350_0 = all_138_1 % 56.88/8.57 | | | | | | | | | | | | | % 56.88/8.57 | | | | | | | | | | | | | REDUCE: (698), (703) imply: % 56.88/8.57 | | | | | | | | | | | | | (704) subset_complement(all_138_8, all_138_1) = % 56.88/8.57 | | | | | | | | | | | | | all_138_0 % 56.88/8.57 | | | | | | | | | | | | | % 56.88/8.57 | | | | | | | | | | | | | BETA: splitting (573) gives: % 56.88/8.57 | | | | | | | | | | | | | % 56.88/8.57 | | | | | | | | | | | | | Case 1: % 56.88/8.57 | | | | | | | | | | | | | | % 56.88/8.57 | | | | | | | | | | | | | | (705) ~ (all_730_1 = 0) % 56.88/8.57 | | | | | | | | | | | | | | % 56.88/8.57 | | | | | | | | | | | | | | REDUCE: (702), (705) imply: % 56.88/8.57 | | | | | | | | | | | | | | (706) $false % 56.88/8.57 | | | | | | | | | | | | | | % 56.88/8.57 | | | | | | | | | | | | | | CLOSE: (706) is inconsistent. % 56.88/8.57 | | | | | | | | | | | | | | % 56.88/8.57 | | | | | | | | | | | | | Case 2: % 56.88/8.57 | | | | | | | | | | | | | | % 56.88/8.57 | | | | | | | | | | | | | | (707) ~ (all_730_2 = 0) | all_730_0 = all_138_1 % 56.88/8.57 | | | | | | | | | | | | | | % 56.88/8.57 | | | | | | | | | | | | | | BETA: splitting (707) gives: % 56.88/8.57 | | | | | | | | | | | | | | % 56.88/8.57 | | | | | | | | | | | | | | Case 1: % 56.88/8.57 | | | | | | | | | | | | | | | % 56.88/8.57 | | | | | | | | | | | | | | | (708) ~ (all_730_2 = 0) % 56.88/8.57 | | | | | | | | | | | | | | | % 56.88/8.57 | | | | | | | | | | | | | | | REDUCE: (701), (708) imply: % 56.88/8.57 | | | | | | | | | | | | | | | (709) $false % 56.88/8.57 | | | | | | | | | | | | | | | % 56.88/8.57 | | | | | | | | | | | | | | | CLOSE: (709) is inconsistent. % 56.88/8.57 | | | | | | | | | | | | | | | % 56.88/8.57 | | | | | | | | | | | | | | Case 2: % 56.88/8.57 | | | | | | | | | | | | | | | % 56.88/8.57 | | | | | | | | | | | | | | | (710) all_730_0 = all_138_1 % 56.88/8.57 | | | | | | | | | | | | | | | % 56.88/8.57 | | | | | | | | | | | | | | | COMBINE_EQS: (695), (710) imply: % 56.88/8.57 | | | | | | | | | | | | | | | (711) all_442_0 = all_138_1 % 56.88/8.57 | | | | | | | | | | | | | | | % 56.88/8.57 | | | | | | | | | | | | | | | SIMP: (711) implies: % 56.88/8.57 | | | | | | | | | | | | | | | (712) all_442_0 = all_138_1 % 56.88/8.57 | | | | | | | | | | | | | | | % 56.88/8.57 | | | | | | | | | | | | | | | REDUCE: (696), (712) imply: % 56.88/8.57 | | | | | | | | | | | | | | | (713) subset_complement(all_138_8, all_138_1) = % 56.88/8.57 | | | | | | | | | | | | | | | all_138_3 % 56.88/8.57 | | | | | | | | | | | | | | | % 56.88/8.57 | | | | | | | | | | | | | | | GROUND_INST: instantiating (38) with all_138_0, all_138_3, % 56.88/8.57 | | | | | | | | | | | | | | | all_138_1, all_138_8, simplifying with (704), % 56.88/8.57 | | | | | | | | | | | | | | | (713) gives: % 56.88/8.57 | | | | | | | | | | | | | | | (714) all_138_0 = all_138_3 % 56.88/8.57 | | | | | | | | | | | | | | | % 56.88/8.57 | | | | | | | | | | | | | | | REDUCE: (47), (714) imply: % 56.88/8.57 | | | | | | | | | | | | | | | (715) $false % 56.88/8.57 | | | | | | | | | | | | | | | % 56.88/8.57 | | | | | | | | | | | | | | | CLOSE: (715) is inconsistent. % 56.88/8.57 | | | | | | | | | | | | | | | % 56.88/8.57 | | | | | | | | | | | | | | End of split % 56.88/8.57 | | | | | | | | | | | | | | % 56.88/8.57 | | | | | | | | | | | | | End of split % 56.88/8.57 | | | | | | | | | | | | | % 56.88/8.57 | | | | | | | | | | | | Case 2: % 56.88/8.57 | | | | | | | | | | | | | % 56.88/8.57 | | | | | | | | | | | | | (716) all_498_1 = 0 % 56.88/8.57 | | | | | | | | | | | | | % 56.88/8.57 | | | | | | | | | | | | | COMBINE_EQS: (685), (716) imply: % 56.88/8.57 | | | | | | | | | | | | | (717) all_158_0 = 0 % 56.88/8.57 | | | | | | | | | | | | | % 56.88/8.57 | | | | | | | | | | | | | SIMP: (717) implies: % 56.88/8.57 | | | | | | | | | | | | | (718) all_158_0 = 0 % 56.88/8.57 | | | | | | | | | | | | | % 56.88/8.57 | | | | | | | | | | | | | REDUCE: (100), (718) imply: % 56.88/8.57 | | | | | | | | | | | | | (719) $false % 56.88/8.57 | | | | | | | | | | | | | % 56.88/8.57 | | | | | | | | | | | | | CLOSE: (719) is inconsistent. % 56.88/8.57 | | | | | | | | | | | | | % 56.88/8.57 | | | | | | | | | | | | End of split % 56.88/8.57 | | | | | | | | | | | | % 56.88/8.57 | | | | | | | | | | | End of split % 56.88/8.57 | | | | | | | | | | | % 56.88/8.58 | | | | | | | | | | End of split % 56.88/8.58 | | | | | | | | | | % 56.88/8.58 | | | | | | | | | End of split % 56.88/8.58 | | | | | | | | | % 56.88/8.58 | | | | | | | | End of split % 56.88/8.58 | | | | | | | | % 56.88/8.58 | | | | | | | End of split % 56.88/8.58 | | | | | | | % 56.88/8.58 | | | | | | End of split % 56.88/8.58 | | | | | | % 56.88/8.58 | | | | | End of split % 56.88/8.58 | | | | | % 56.88/8.58 | | | | End of split % 56.88/8.58 | | | | % 56.88/8.58 | | | End of split % 56.88/8.58 | | | % 56.88/8.58 | | End of split % 56.88/8.58 | | % 56.88/8.58 | End of split % 56.88/8.58 | % 56.88/8.58 End of proof % 56.88/8.58 % SZS output end Proof for theBenchmark % 56.88/8.58 % 56.88/8.58 7957ms %------------------------------------------------------------------------------