%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SEU339+1 : TPTP v8.1.2. Released v3.3.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n012.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 17:44:10 EDT 2023 % Result : Theorem 18.96s 4.38s % Output : Proof 76.37s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.05/0.16 % Problem : SEU339+1 : TPTP v8.1.2. Released v3.3.0. % 0.05/0.16 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.11/0.36 % Computer : n012.cluster.edu % 0.11/0.36 % Model : x86_64 x86_64 % 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.11/0.36 % Memory : 8042.1875MB % 0.11/0.36 % OS : Linux 3.10.0-693.el7.x86_64 % 0.11/0.37 % CPULimit : 300 % 0.11/0.37 % WCLimit : 300 % 0.11/0.37 % DateTime : Wed Aug 23 20:22:27 EDT 2023 % 0.11/0.37 % CPUTime : % 0.16/0.63 ________ _____ % 0.16/0.63 ___ __ \_________(_)________________________________ % 0.16/0.63 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.16/0.63 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.16/0.63 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.16/0.63 % 0.16/0.63 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.16/0.63 (2023-06-19) % 0.16/0.63 % 0.16/0.63 (c) Philipp Rümmer, 2009-2023 % 0.16/0.63 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.16/0.63 Amanda Stjerna. % 0.16/0.63 Free software under BSD-3-Clause. % 0.16/0.63 % 0.16/0.63 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.16/0.63 % 0.16/0.63 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.16/0.65 Running up to 7 provers in parallel. % 0.16/0.70 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.16/0.70 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.16/0.70 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.16/0.70 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.16/0.70 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.16/0.70 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.16/0.71 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.63/1.21 Prover 4: Preprocessing ... % 2.63/1.21 Prover 1: Preprocessing ... % 2.93/1.28 Prover 0: Preprocessing ... % 2.93/1.28 Prover 3: Preprocessing ... % 2.93/1.28 Prover 5: Preprocessing ... % 2.93/1.28 Prover 2: Preprocessing ... % 2.93/1.30 Prover 6: Preprocessing ... % 6.72/2.11 Prover 1: Warning: ignoring some quantifiers % 6.72/2.13 Prover 2: Proving ... % 6.72/2.14 Prover 5: Proving ... % 6.72/2.14 Prover 6: Proving ... % 7.57/2.19 Prover 4: Warning: ignoring some quantifiers % 7.57/2.19 Prover 3: Warning: ignoring some quantifiers % 7.57/2.22 Prover 1: Constructing countermodel ... % 7.57/2.25 Prover 3: Constructing countermodel ... % 8.20/2.31 Prover 4: Constructing countermodel ... % 9.07/2.54 Prover 0: Proving ... % 10.57/2.86 Prover 1: gave up % 11.43/2.89 Prover 3: gave up % 11.43/2.91 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 11.43/2.92 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 11.73/3.00 Prover 7: Preprocessing ... % 12.02/3.01 Prover 8: Preprocessing ... % 13.09/3.20 Prover 7: Warning: ignoring some quantifiers % 13.09/3.21 Prover 8: Warning: ignoring some quantifiers % 13.40/3.25 Prover 8: Constructing countermodel ... % 13.40/3.26 Prover 7: Constructing countermodel ... % 14.50/3.65 Prover 8: gave up % 14.50/3.66 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889 % 14.50/3.71 Prover 9: Preprocessing ... % 16.83/3.86 Prover 7: gave up % 17.00/3.88 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 17.34/3.94 Prover 10: Preprocessing ... % 17.92/4.07 Prover 9: Warning: ignoring some quantifiers % 17.92/4.07 Prover 10: Warning: ignoring some quantifiers % 18.25/4.10 Prover 10: Constructing countermodel ... % 18.25/4.10 Prover 9: Constructing countermodel ... % 18.78/4.16 Prover 10: gave up % 18.78/4.16 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 18.96/4.20 Prover 11: Preprocessing ... % 18.96/4.38 Prover 0: proved (3728ms) % 18.96/4.38 % 18.96/4.38 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 18.96/4.38 % 18.96/4.38 Prover 5: stopped % 18.96/4.40 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 18.96/4.40 Prover 9: stopped % 18.96/4.41 Prover 2: stopped % 18.96/4.41 Prover 6: stopped % 18.96/4.41 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 18.96/4.41 Prover 13: Preprocessing ... % 18.96/4.41 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085 % 18.96/4.43 Prover 16: Preprocessing ... % 18.96/4.44 Prover 11: Warning: ignoring some quantifiers % 18.96/4.44 Prover 19: Preprocessing ... % 18.96/4.46 Prover 11: Constructing countermodel ... % 21.04/4.50 Prover 16: Warning: ignoring some quantifiers % 21.04/4.51 Prover 16: Constructing countermodel ... % 21.56/4.58 Prover 13: Warning: ignoring some quantifiers % 21.56/4.60 Prover 13: Constructing countermodel ... % 21.56/4.62 Prover 19: Warning: ignoring some quantifiers % 21.56/4.65 Prover 19: Constructing countermodel ... % 24.11/5.04 Prover 19: gave up % 27.67/5.56 Prover 16: gave up % 56.15/10.58 Prover 13: stopped % 73.58/15.77 Prover 4: Found proof (size 868) % 73.58/15.77 Prover 4: proved (15076ms) % 73.58/15.77 Prover 11: stopped % 73.58/15.77 % 73.58/15.77 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 73.58/15.77 % 73.58/15.84 % SZS output start Proof for theBenchmark % 73.58/15.85 Assumptions after simplification: % 73.58/15.85 --------------------------------- % 73.58/15.85 % 73.58/15.85 (cc1_relset_1) % 74.05/15.88 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 74.05/15.88 (cartesian_product2(v0, v1) = v3) | ~ (powerset(v3) = v4) | ~ (element(v2, % 74.05/15.88 v4) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | relation(v2) = 0) % 74.05/15.88 % 74.05/15.88 (commutativity_k2_tarski) % 74.05/15.89 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (unordered_pair(v1, v0) = v2) | % 74.05/15.89 ~ $i(v1) | ~ $i(v0) | (unordered_pair(v0, v1) = v2 & $i(v2))) & ! [v0: $i] % 74.05/15.89 : ! [v1: $i] : ! [v2: $i] : ( ~ (unordered_pair(v0, v1) = v2) | ~ $i(v1) | % 74.05/15.89 ~ $i(v0) | (unordered_pair(v1, v0) = v2 & $i(v2))) % 74.05/15.89 % 74.05/15.89 (d4_relat_2) % 74.05/15.90 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v3 = v2 % 74.05/15.90 | ~ (is_antisymmetric_in(v0, v1) = 0) | ~ (ordered_pair(v3, v2) = v4) | ~ % 74.05/15.90 (relation(v0) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: % 74.05/15.90 any] : ? [v6: any] : ? [v7: $i] : ? [v8: any] : ? [v9: any] : % 74.05/15.90 (ordered_pair(v2, v3) = v7 & in(v7, v0) = v8 & in(v4, v0) = v9 & in(v3, v1) % 74.05/15.90 = v6 & in(v2, v1) = v5 & $i(v7) & ( ~ (v9 = 0) | ~ (v8 = 0) | ~ (v6 = 0) % 74.05/15.90 | ~ (v5 = 0)))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] % 74.05/15.90 : ! [v4: $i] : (v3 = v2 | ~ (is_antisymmetric_in(v0, v1) = 0) | ~ % 74.05/15.90 (ordered_pair(v2, v3) = v4) | ~ (relation(v0) = 0) | ~ $i(v3) | ~ $i(v2) % 74.05/15.90 | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : ? [v7: any] : ? % 74.05/15.90 [v8: $i] : ? [v9: any] : (ordered_pair(v3, v2) = v8 & in(v8, v0) = v9 & % 74.05/15.90 in(v4, v0) = v7 & in(v3, v1) = v6 & in(v2, v1) = v5 & $i(v8) & ( ~ (v9 = % 74.05/15.90 0) | ~ (v7 = 0) | ~ (v6 = 0) | ~ (v5 = 0)))) & ! [v0: $i] : ! % 74.05/15.90 [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (is_antisymmetric_in(v0, v1) = v2) | ~ % 74.05/15.90 (relation(v0) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : ? % 74.05/15.90 [v5: $i] : ? [v6: $i] : ( ~ (v4 = v3) & ordered_pair(v4, v3) = v6 & % 74.05/15.90 ordered_pair(v3, v4) = v5 & in(v6, v0) = 0 & in(v5, v0) = 0 & in(v4, v1) = % 74.05/15.90 0 & in(v3, v1) = 0 & $i(v6) & $i(v5) & $i(v4) & $i(v3))) % 74.05/15.90 % 74.05/15.90 (d5_tarski) % 74.05/15.90 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (ordered_pair(v0, v1) = v2) | ~ % 74.05/15.90 $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : (singleton(v0) = v4 & % 74.05/15.90 unordered_pair(v3, v4) = v2 & unordered_pair(v0, v1) = v3 & $i(v4) & % 74.05/15.90 $i(v3) & $i(v2))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 74.05/15.90 (unordered_pair(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? % 74.05/15.90 [v4: $i] : (singleton(v0) = v4 & ordered_pair(v0, v1) = v3 & % 74.05/15.90 unordered_pair(v2, v4) = v3 & $i(v4) & $i(v3))) % 74.05/15.90 % 74.05/15.90 (d6_orders_2) % 74.05/15.91 ! [v0: $i] : ! [v1: $i] : ( ~ (the_InternalRel(v0) = v1) | ~ $i(v0) | ? % 74.05/15.91 [v2: any] : ? [v3: any] : ? [v4: $i] : ? [v5: any] : (rel_str(v0) = v2 & % 74.05/15.91 antisymmetric_relstr(v0) = v3 & the_carrier(v0) = v4 & % 74.05/15.91 is_antisymmetric_in(v1, v4) = v5 & $i(v4) & ( ~ (v2 = 0) | (( ~ (v5 = 0) | % 74.05/15.92 v3 = 0) & ( ~ (v3 = 0) | v5 = 0))))) & ! [v0: $i] : ! [v1: any] : % 74.05/15.92 ( ~ (antisymmetric_relstr(v0) = v1) | ~ $i(v0) | ? [v2: any] : ? [v3: $i] : % 74.05/15.92 ? [v4: $i] : ? [v5: any] : (the_InternalRel(v0) = v3 & rel_str(v0) = v2 & % 74.05/15.92 the_carrier(v0) = v4 & is_antisymmetric_in(v3, v4) = v5 & $i(v4) & $i(v3) % 74.05/15.92 & ( ~ (v2 = 0) | (( ~ (v5 = 0) | v1 = 0) & ( ~ (v1 = 0) | v5 = 0))))) & ! % 74.05/15.92 [v0: $i] : ! [v1: $i] : ( ~ (the_carrier(v0) = v1) | ~ $i(v0) | ? [v2: any] % 74.05/15.92 : ? [v3: any] : ? [v4: $i] : ? [v5: any] : (the_InternalRel(v0) = v4 & % 74.05/15.92 rel_str(v0) = v2 & antisymmetric_relstr(v0) = v3 & is_antisymmetric_in(v4, % 74.05/15.92 v1) = v5 & $i(v4) & ( ~ (v2 = 0) | (( ~ (v5 = 0) | v3 = 0) & ( ~ (v3 = % 74.05/15.92 0) | v5 = 0))))) & ! [v0: $i] : ( ~ (rel_str(v0) = 0) | ~ $i(v0) % 74.05/15.92 | ? [v1: any] : ? [v2: $i] : ? [v3: $i] : ? [v4: any] : % 74.05/15.92 (the_InternalRel(v0) = v2 & antisymmetric_relstr(v0) = v1 & the_carrier(v0) % 74.05/15.92 = v3 & is_antisymmetric_in(v2, v3) = v4 & $i(v3) & $i(v2) & ( ~ (v4 = 0) | % 74.05/15.92 v1 = 0) & ( ~ (v1 = 0) | v4 = 0))) % 74.05/15.92 % 74.05/15.92 (d9_orders_2) % 74.57/15.94 ! [v0: $i] : ! [v1: $i] : ( ~ (the_InternalRel(v0) = v1) | ~ $i(v0) | ? % 74.57/15.94 [v2: any] : ? [v3: $i] : (rel_str(v0) = v2 & the_carrier(v0) = v3 & $i(v3) % 74.57/15.94 & ( ~ (v2 = 0) | ( ! [v4: $i] : ! [v5: $i] : ! [v6: any] : ( ~ % 74.57/15.94 (related(v0, v4, v5) = v6) | ~ (element(v4, v3) = 0) | ~ $i(v5) | % 74.57/15.94 ~ $i(v4) | ? [v7: any] : ? [v8: $i] : ? [v9: any] : % 74.57/15.94 (ordered_pair(v4, v5) = v8 & element(v5, v3) = v7 & in(v8, v1) = v9 % 74.57/15.94 & $i(v8) & ( ~ (v7 = 0) | (( ~ (v9 = 0) | v6 = 0) & ( ~ (v6 = 0) | % 74.57/15.94 v9 = 0))))) & ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~ % 74.57/15.94 (ordered_pair(v4, v5) = v6) | ~ (element(v4, v3) = 0) | ~ $i(v5) | % 74.57/15.94 ~ $i(v4) | ? [v7: any] : ? [v8: any] : ? [v9: any] : % 74.57/15.94 (related(v0, v4, v5) = v8 & element(v5, v3) = v7 & in(v6, v1) = v9 & % 74.57/15.94 ( ~ (v7 = 0) | (( ~ (v9 = 0) | v8 = 0) & ( ~ (v8 = 0) | v9 = % 74.57/15.94 0))))) & ! [v4: $i] : ! [v5: $i] : ( ~ (element(v5, v3) = % 74.57/15.94 0) | ~ (element(v4, v3) = 0) | ~ $i(v5) | ~ $i(v4) | ? [v6: % 74.57/15.94 any] : ? [v7: $i] : ? [v8: any] : (related(v0, v4, v5) = v6 & % 74.57/15.94 ordered_pair(v4, v5) = v7 & in(v7, v1) = v8 & $i(v7) & ( ~ (v8 = % 74.57/15.94 0) | v6 = 0) & ( ~ (v6 = 0) | v8 = 0))))))) & ! [v0: $i] : ! % 74.57/15.94 [v1: $i] : ( ~ (the_carrier(v0) = v1) | ~ $i(v0) | ? [v2: any] : ? [v3: $i] % 74.57/15.94 : (the_InternalRel(v0) = v3 & rel_str(v0) = v2 & $i(v3) & ( ~ (v2 = 0) | ( ! % 74.57/15.94 [v4: $i] : ! [v5: $i] : ! [v6: any] : ( ~ (related(v0, v4, v5) = v6) % 74.57/15.94 | ~ (element(v4, v1) = 0) | ~ $i(v5) | ~ $i(v4) | ? [v7: any] : % 74.57/15.94 ? [v8: $i] : ? [v9: any] : (ordered_pair(v4, v5) = v8 & element(v5, % 74.57/15.94 v1) = v7 & in(v8, v3) = v9 & $i(v8) & ( ~ (v7 = 0) | (( ~ (v9 = % 74.57/15.94 0) | v6 = 0) & ( ~ (v6 = 0) | v9 = 0))))) & ! [v4: $i] : % 74.57/15.94 ! [v5: $i] : ! [v6: $i] : ( ~ (ordered_pair(v4, v5) = v6) | ~ % 74.57/15.94 (element(v4, v1) = 0) | ~ $i(v5) | ~ $i(v4) | ? [v7: any] : ? % 74.57/15.94 [v8: any] : ? [v9: any] : (related(v0, v4, v5) = v8 & element(v5, % 74.57/15.94 v1) = v7 & in(v6, v3) = v9 & ( ~ (v7 = 0) | (( ~ (v9 = 0) | v8 = % 74.57/15.94 0) & ( ~ (v8 = 0) | v9 = 0))))) & ! [v4: $i] : ! [v5: $i] % 74.57/15.94 : ( ~ (element(v5, v1) = 0) | ~ (element(v4, v1) = 0) | ~ $i(v5) | % 74.57/15.94 ~ $i(v4) | ? [v6: any] : ? [v7: $i] : ? [v8: any] : (related(v0, % 74.57/15.94 v4, v5) = v6 & ordered_pair(v4, v5) = v7 & in(v7, v3) = v8 & % 74.57/15.94 $i(v7) & ( ~ (v8 = 0) | v6 = 0) & ( ~ (v6 = 0) | v8 = 0))))))) & % 74.57/15.94 ! [v0: $i] : ( ~ (rel_str(v0) = 0) | ~ $i(v0) | ? [v1: $i] : ? [v2: $i] : % 74.57/15.94 (the_InternalRel(v0) = v2 & the_carrier(v0) = v1 & $i(v2) & $i(v1) & ! [v3: % 74.57/15.94 $i] : ! [v4: $i] : ! [v5: any] : ( ~ (related(v0, v3, v4) = v5) | ~ % 74.57/15.94 (element(v3, v1) = 0) | ~ $i(v4) | ~ $i(v3) | ? [v6: any] : ? [v7: % 74.57/15.94 $i] : ? [v8: any] : (ordered_pair(v3, v4) = v7 & element(v4, v1) = v6 % 74.57/15.94 & in(v7, v2) = v8 & $i(v7) & ( ~ (v6 = 0) | (( ~ (v8 = 0) | v5 = 0) & % 74.57/15.94 ( ~ (v5 = 0) | v8 = 0))))) & ! [v3: $i] : ! [v4: $i] : ! [v5: % 74.57/15.94 $i] : ( ~ (ordered_pair(v3, v4) = v5) | ~ (element(v3, v1) = 0) | ~ % 74.57/15.94 $i(v4) | ~ $i(v3) | ? [v6: any] : ? [v7: any] : ? [v8: any] : % 74.57/15.94 (related(v0, v3, v4) = v7 & element(v4, v1) = v6 & in(v5, v2) = v8 & ( ~ % 74.57/15.94 (v6 = 0) | (( ~ (v8 = 0) | v7 = 0) & ( ~ (v7 = 0) | v8 = 0))))) & ! % 74.57/15.94 [v3: $i] : ! [v4: $i] : ( ~ (element(v4, v1) = 0) | ~ (element(v3, v1) = % 74.57/15.94 0) | ~ $i(v4) | ~ $i(v3) | ? [v5: any] : ? [v6: $i] : ? [v7: any] % 74.57/15.94 : (related(v0, v3, v4) = v5 & ordered_pair(v3, v4) = v6 & in(v6, v2) = % 74.57/15.94 v7 & $i(v6) & ( ~ (v7 = 0) | v5 = 0) & ( ~ (v5 = 0) | v7 = 0))))) % 74.57/15.94 % 74.57/15.94 (dt_m2_relset_1) % 74.57/15.95 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 74.57/15.95 int] : (v5 = 0 | ~ (cartesian_product2(v0, v1) = v3) | ~ (powerset(v3) = % 74.57/15.95 v4) | ~ (element(v2, v4) = v5) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 74.57/15.95 [v6: int] : ( ~ (v6 = 0) & relation_of2_as_subset(v2, v0, v1) = v6)) & ! % 74.57/15.95 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (relation_of2_as_subset(v2, v0, v1) % 74.57/15.95 = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : % 74.57/15.95 (cartesian_product2(v0, v1) = v3 & powerset(v3) = v4 & element(v2, v4) = 0 & % 74.57/15.95 $i(v4) & $i(v3))) % 74.57/15.95 % 74.57/15.95 (dt_u1_orders_2) % 74.57/15.95 ! [v0: $i] : ! [v1: $i] : ( ~ (the_InternalRel(v0) = v1) | ~ $i(v0) | ? % 74.57/15.95 [v2: any] : ? [v3: $i] : ? [v4: any] : (relation_of2_as_subset(v1, v3, v3) % 74.57/15.95 = v4 & rel_str(v0) = v2 & the_carrier(v0) = v3 & $i(v3) & ( ~ (v2 = 0) | % 74.57/15.95 v4 = 0))) & ! [v0: $i] : ! [v1: $i] : ( ~ (the_carrier(v0) = v1) | ~ % 74.57/15.95 $i(v0) | ? [v2: any] : ? [v3: $i] : ? [v4: any] : % 74.57/15.95 (relation_of2_as_subset(v3, v1, v1) = v4 & the_InternalRel(v0) = v3 & % 74.57/15.95 rel_str(v0) = v2 & $i(v3) & ( ~ (v2 = 0) | v4 = 0))) & ! [v0: $i] : ( ~ % 74.57/15.95 (rel_str(v0) = 0) | ~ $i(v0) | ? [v1: $i] : ? [v2: $i] : % 74.57/15.95 (relation_of2_as_subset(v1, v2, v2) = 0 & the_InternalRel(v0) = v1 & % 74.57/15.95 the_carrier(v0) = v2 & $i(v2) & $i(v1))) % 74.57/15.95 % 74.57/15.95 (existence_l1_orders_2) % 74.57/15.95 ? [v0: $i] : (rel_str(v0) = 0 & $i(v0)) % 74.57/15.95 % 74.57/15.95 (fc1_subset_1) % 74.57/15.95 ! [v0: $i] : ! [v1: $i] : ( ~ (powerset(v0) = v1) | ~ $i(v0) | ? [v2: int] % 74.57/15.95 : ( ~ (v2 = 0) & empty(v1) = v2)) % 74.57/15.95 % 74.57/15.95 (fc4_subset_1) % 74.57/15.96 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (cartesian_product2(v0, v1) = % 74.57/15.96 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ? [v5: any] : % 74.57/15.96 (empty(v2) = v5 & empty(v1) = v4 & empty(v0) = v3 & ( ~ (v5 = 0) | v4 = 0 | % 74.57/15.96 v3 = 0))) % 74.57/15.96 % 74.57/15.96 (rc1_subset_1) % 74.57/15.96 ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (empty(v0) = v1) | ~ $i(v0) | ? % 74.57/15.96 [v2: $i] : ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & empty(v3) = v4 & % 74.57/15.96 powerset(v0) = v2 & element(v3, v2) = 0 & $i(v3) & $i(v2))) & ! [v0: $i] % 74.57/15.96 : ! [v1: $i] : ( ~ (powerset(v0) = v1) | ~ $i(v0) | ? [v2: int] : ? [v3: % 74.57/15.96 $i] : ? [v4: int] : ? [v5: int] : ($i(v3) & ((v4 = 0 & ~ (v5 = 0) & % 74.57/15.96 empty(v3) = v5 & element(v3, v1) = 0) | (v2 = 0 & empty(v0) = 0)))) % 74.57/15.96 % 74.57/15.96 (rc1_xboole_0) % 74.57/15.96 ? [v0: $i] : (empty(v0) = 0 & $i(v0)) % 74.57/15.96 % 74.57/15.96 (rc2_subset_1) % 74.57/15.96 ! [v0: $i] : ! [v1: $i] : ( ~ (powerset(v0) = v1) | ~ $i(v0) | ? [v2: $i] % 74.57/15.96 : (empty(v2) = 0 & element(v2, v1) = 0 & $i(v2))) % 74.57/15.96 % 74.57/15.96 (rc2_xboole_0) % 74.57/15.96 ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & empty(v0) = v1 & $i(v0)) % 74.57/15.96 % 74.57/15.96 (t106_zfmisc_1) % 74.57/15.97 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 74.57/15.97 $i] : ! [v6: int] : (v6 = 0 | ~ (ordered_pair(v0, v1) = v4) | ~ % 74.57/15.97 (cartesian_product2(v2, v3) = v5) | ~ (in(v4, v5) = v6) | ~ $i(v3) | ~ % 74.57/15.97 $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v7: any] : ? [v8: any] : (in(v1, v3) = % 74.57/15.97 v8 & in(v0, v2) = v7 & ( ~ (v8 = 0) | ~ (v7 = 0)))) & ! [v0: $i] : ! % 74.57/15.97 [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ % 74.57/15.97 (ordered_pair(v0, v1) = v4) | ~ (cartesian_product2(v2, v3) = v5) | ~ % 74.57/15.97 (in(v4, v5) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | (in(v1, % 74.57/15.97 v3) = 0 & in(v0, v2) = 0)) % 74.57/15.97 % 74.57/15.97 (t1_subset) % 74.57/15.97 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (element(v0, v1) = v2) % 74.57/15.97 | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ( ~ (v3 = 0) & in(v0, v1) = v3)) & % 74.57/15.97 ! [v0: $i] : ! [v1: $i] : ( ~ (in(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | % 74.57/15.97 element(v0, v1) = 0) % 74.57/15.97 % 74.57/15.97 (t25_orders_2) % 74.57/15.97 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ( ~ (v3 = v2) & % 74.57/15.97 related(v0, v3, v2) = 0 & related(v0, v2, v3) = 0 & rel_str(v0) = 0 & % 74.57/15.97 antisymmetric_relstr(v0) = 0 & the_carrier(v0) = v1 & element(v3, v1) = 0 & % 74.57/15.97 element(v2, v1) = 0 & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 74.57/15.97 % 74.57/15.97 (t2_subset) % 74.57/15.97 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (in(v0, v1) = v2) | ~ % 74.57/15.97 $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : (empty(v1) = v4 & % 74.57/15.97 element(v0, v1) = v3 & ( ~ (v3 = 0) | v4 = 0))) & ! [v0: $i] : ! [v1: % 74.57/15.97 $i] : ( ~ (element(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: any] : ? % 74.57/15.97 [v3: any] : (empty(v1) = v2 & in(v0, v1) = v3 & (v3 = 0 | v2 = 0))) % 74.57/15.97 % 74.57/15.97 (t4_subset) % 74.57/15.98 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0 % 74.57/15.98 | ~ (powerset(v2) = v3) | ~ (element(v1, v3) = 0) | ~ (element(v0, v2) = % 74.57/15.98 v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ( ~ (v5 = 0) & % 74.57/15.98 in(v0, v1) = v5)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] % 74.57/15.98 : (v3 = 0 | ~ (element(v0, v2) = v3) | ~ (in(v0, v1) = 0) | ~ $i(v2) | ~ % 74.57/15.98 $i(v1) | ~ $i(v0) | ? [v4: $i] : ? [v5: int] : ( ~ (v5 = 0) & % 74.57/15.98 powerset(v2) = v4 & element(v1, v4) = v5 & $i(v4))) & ! [v0: $i] : ! % 74.57/15.98 [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (powerset(v2) = v3) | ~ % 74.57/15.98 (element(v1, v3) = 0) | ~ (in(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ % 74.57/15.98 $i(v0) | element(v0, v2) = 0) % 74.57/15.98 % 74.57/15.98 (t5_subset) % 74.57/15.98 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (powerset(v2) = % 74.57/15.98 v3) | ~ (element(v1, v3) = 0) | ~ (in(v0, v1) = 0) | ~ $i(v2) | ~ % 74.57/15.98 $i(v1) | ~ $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & empty(v2) = v4)) & ! % 74.57/15.98 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (empty(v2) = 0) | ~ (in(v0, v1) = % 74.57/15.98 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ % 74.57/15.98 (v4 = 0) & powerset(v2) = v3 & element(v1, v3) = v4 & $i(v3))) % 74.57/15.98 % 74.57/15.98 (t6_boole) % 74.57/15.98 $i(empty_set) & ! [v0: $i] : (v0 = empty_set | ~ (empty(v0) = 0) | ~ % 74.57/15.98 $i(v0)) % 74.57/15.98 % 74.57/15.98 (t7_boole) % 74.57/15.98 ! [v0: $i] : ! [v1: $i] : ( ~ (in(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? % 74.57/15.98 [v2: int] : ( ~ (v2 = 0) & empty(v1) = v2)) % 74.57/15.98 % 74.57/15.98 (t8_boole) % 74.57/15.98 ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (empty(v1) = 0) | ~ (empty(v0) = 0) % 74.57/15.98 | ~ $i(v1) | ~ $i(v0)) % 74.57/15.98 % 74.57/15.98 (function-axioms) % 74.57/15.99 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 74.57/15.99 [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (relation_of2(v4, v3, v2) = v1) | ~ % 74.57/15.99 (relation_of2(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 74.57/15.99 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ % 74.57/15.99 (relation_of2_as_subset(v4, v3, v2) = v1) | ~ (relation_of2_as_subset(v4, % 74.57/15.99 v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] % 74.57/15.99 : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (related(v4, v3, v2) % 74.57/15.99 = v1) | ~ (related(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! % 74.57/15.99 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 74.57/15.99 (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0: % 74.57/15.99 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 74.57/15.99 : (v1 = v0 | ~ (is_antisymmetric_in(v3, v2) = v1) | ~ % 74.57/15.99 (is_antisymmetric_in(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 74.57/15.99 $i] : ! [v3: $i] : (v1 = v0 | ~ (ordered_pair(v3, v2) = v1) | ~ % 74.57/15.99 (ordered_pair(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 74.57/15.99 [v3: $i] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ % 74.57/15.99 (unordered_pair(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 74.57/15.99 ! [v3: $i] : (v1 = v0 | ~ (cartesian_product2(v3, v2) = v1) | ~ % 74.57/15.99 (cartesian_product2(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 74.57/15.99 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (element(v3, % 74.57/15.99 v2) = v1) | ~ (element(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! % 74.57/15.99 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (in(v3, % 74.57/15.99 v2) = v1) | ~ (in(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 74.57/15.99 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (empty(v2) = v1) | ~ % 74.57/15.99 (empty(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] % 74.57/15.99 : ! [v2: $i] : (v1 = v0 | ~ (one_sorted_str(v2) = v1) | ~ % 74.57/15.99 (one_sorted_str(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = % 74.57/15.99 v0 | ~ (the_InternalRel(v2) = v1) | ~ (the_InternalRel(v2) = v0)) & ! % 74.57/15.99 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 % 74.57/15.99 | ~ (rel_str(v2) = v1) | ~ (rel_str(v2) = v0)) & ! [v0: % 74.57/15.99 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 74.57/15.99 ~ (antisymmetric_relstr(v2) = v1) | ~ (antisymmetric_relstr(v2) = v0)) & ! % 74.57/15.99 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (the_carrier(v2) = v1) | % 74.57/15.99 ~ (the_carrier(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = % 74.57/15.99 v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ! [v0: $i] : ! % 74.57/15.99 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) % 74.57/15.99 = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 74.57/15.99 $i] : (v1 = v0 | ~ (relation(v2) = v1) | ~ (relation(v2) = v0)) % 74.57/15.99 % 74.57/15.99 Further assumptions not needed in the proof: % 74.57/15.99 -------------------------------------------- % 74.57/15.99 antisymmetry_r2_hidden, dt_k1_tarski, dt_k1_xboole_0, dt_k1_zfmisc_1, % 74.57/15.99 dt_k2_tarski, dt_k2_zfmisc_1, dt_k4_tarski, dt_l1_orders_2, dt_l1_struct_0, % 74.57/15.99 dt_m1_relset_1, dt_m1_subset_1, dt_u1_struct_0, existence_l1_struct_0, % 74.57/15.99 existence_m1_relset_1, existence_m1_subset_1, existence_m2_relset_1, % 74.57/15.99 fc1_xboole_0, fc2_subset_1, fc3_subset_1, redefinition_m2_relset_1, % 74.57/15.99 reflexivity_r1_tarski, t3_subset % 74.57/15.99 % 74.57/15.99 Those formulas are unsatisfiable: % 74.57/15.99 --------------------------------- % 74.57/15.99 % 74.57/15.99 Begin of proof % 74.57/15.99 | % 74.57/15.99 | ALPHA: (commutativity_k2_tarski) implies: % 74.57/15.99 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (unordered_pair(v1, v0) = % 74.57/15.99 | v2) | ~ $i(v1) | ~ $i(v0) | (unordered_pair(v0, v1) = v2 & % 74.57/15.99 | $i(v2))) % 74.57/16.00 | % 74.57/16.00 | ALPHA: (d4_relat_2) implies: % 74.57/16.00 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 74.57/16.00 | (v3 = v2 | ~ (is_antisymmetric_in(v0, v1) = 0) | ~ (ordered_pair(v2, % 74.57/16.00 | v3) = v4) | ~ (relation(v0) = 0) | ~ $i(v3) | ~ $i(v2) | ~ % 74.57/16.00 | $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : ? [v7: any] : ? % 74.57/16.00 | [v8: $i] : ? [v9: any] : (ordered_pair(v3, v2) = v8 & in(v8, v0) = % 74.57/16.00 | v9 & in(v4, v0) = v7 & in(v3, v1) = v6 & in(v2, v1) = v5 & $i(v8) & % 74.57/16.00 | ( ~ (v9 = 0) | ~ (v7 = 0) | ~ (v6 = 0) | ~ (v5 = 0)))) % 74.57/16.00 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 74.57/16.00 | (v3 = v2 | ~ (is_antisymmetric_in(v0, v1) = 0) | ~ (ordered_pair(v3, % 74.57/16.00 | v2) = v4) | ~ (relation(v0) = 0) | ~ $i(v3) | ~ $i(v2) | ~ % 74.57/16.00 | $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : ? [v7: $i] : ? % 74.57/16.00 | [v8: any] : ? [v9: any] : (ordered_pair(v2, v3) = v7 & in(v7, v0) = % 74.57/16.00 | v8 & in(v4, v0) = v9 & in(v3, v1) = v6 & in(v2, v1) = v5 & $i(v7) & % 74.57/16.00 | ( ~ (v9 = 0) | ~ (v8 = 0) | ~ (v6 = 0) | ~ (v5 = 0)))) % 74.57/16.00 | % 74.57/16.00 | ALPHA: (d5_tarski) implies: % 74.57/16.00 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (ordered_pair(v0, v1) = % 74.57/16.00 | v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : % 74.57/16.00 | (singleton(v0) = v4 & unordered_pair(v3, v4) = v2 & % 74.57/16.00 | unordered_pair(v0, v1) = v3 & $i(v4) & $i(v3) & $i(v2))) % 74.57/16.00 | % 74.57/16.00 | ALPHA: (d6_orders_2) implies: % 74.57/16.00 | (5) ! [v0: $i] : ( ~ (rel_str(v0) = 0) | ~ $i(v0) | ? [v1: any] : ? % 74.57/16.00 | [v2: $i] : ? [v3: $i] : ? [v4: any] : (the_InternalRel(v0) = v2 & % 74.57/16.00 | antisymmetric_relstr(v0) = v1 & the_carrier(v0) = v3 & % 74.57/16.00 | is_antisymmetric_in(v2, v3) = v4 & $i(v3) & $i(v2) & ( ~ (v4 = 0) | % 74.57/16.00 | v1 = 0) & ( ~ (v1 = 0) | v4 = 0))) % 74.57/16.00 | (6) ! [v0: $i] : ! [v1: $i] : ( ~ (the_carrier(v0) = v1) | ~ $i(v0) | ? % 74.57/16.00 | [v2: any] : ? [v3: any] : ? [v4: $i] : ? [v5: any] : % 74.57/16.00 | (the_InternalRel(v0) = v4 & rel_str(v0) = v2 & % 74.57/16.00 | antisymmetric_relstr(v0) = v3 & is_antisymmetric_in(v4, v1) = v5 & % 74.57/16.00 | $i(v4) & ( ~ (v2 = 0) | (( ~ (v5 = 0) | v3 = 0) & ( ~ (v3 = 0) | v5 % 74.57/16.00 | = 0))))) % 74.57/16.01 | (7) ! [v0: $i] : ! [v1: any] : ( ~ (antisymmetric_relstr(v0) = v1) | ~ % 74.57/16.01 | $i(v0) | ? [v2: any] : ? [v3: $i] : ? [v4: $i] : ? [v5: any] : % 74.57/16.01 | (the_InternalRel(v0) = v3 & rel_str(v0) = v2 & the_carrier(v0) = v4 & % 74.57/16.01 | is_antisymmetric_in(v3, v4) = v5 & $i(v4) & $i(v3) & ( ~ (v2 = 0) | % 74.57/16.01 | (( ~ (v5 = 0) | v1 = 0) & ( ~ (v1 = 0) | v5 = 0))))) % 75.00/16.01 | (8) ! [v0: $i] : ! [v1: $i] : ( ~ (the_InternalRel(v0) = v1) | ~ $i(v0) % 75.00/16.01 | | ? [v2: any] : ? [v3: any] : ? [v4: $i] : ? [v5: any] : % 75.00/16.01 | (rel_str(v0) = v2 & antisymmetric_relstr(v0) = v3 & the_carrier(v0) = % 75.00/16.01 | v4 & is_antisymmetric_in(v1, v4) = v5 & $i(v4) & ( ~ (v2 = 0) | (( % 75.00/16.01 | ~ (v5 = 0) | v3 = 0) & ( ~ (v3 = 0) | v5 = 0))))) % 75.00/16.01 | % 75.00/16.01 | ALPHA: (d9_orders_2) implies: % 75.00/16.01 | (9) ! [v0: $i] : ( ~ (rel_str(v0) = 0) | ~ $i(v0) | ? [v1: $i] : ? [v2: % 75.00/16.01 | $i] : (the_InternalRel(v0) = v2 & the_carrier(v0) = v1 & $i(v2) & % 75.00/16.01 | $i(v1) & ! [v3: $i] : ! [v4: $i] : ! [v5: any] : ( ~ % 75.00/16.01 | (related(v0, v3, v4) = v5) | ~ (element(v3, v1) = 0) | ~ $i(v4) % 75.00/16.01 | | ~ $i(v3) | ? [v6: any] : ? [v7: $i] : ? [v8: any] : % 75.00/16.01 | (ordered_pair(v3, v4) = v7 & element(v4, v1) = v6 & in(v7, v2) = % 75.00/16.01 | v8 & $i(v7) & ( ~ (v6 = 0) | (( ~ (v8 = 0) | v5 = 0) & ( ~ (v5 % 75.00/16.01 | = 0) | v8 = 0))))) & ! [v3: $i] : ! [v4: $i] : ! % 75.00/16.01 | [v5: $i] : ( ~ (ordered_pair(v3, v4) = v5) | ~ (element(v3, v1) = % 75.00/16.01 | 0) | ~ $i(v4) | ~ $i(v3) | ? [v6: any] : ? [v7: any] : ? % 75.00/16.01 | [v8: any] : (related(v0, v3, v4) = v7 & element(v4, v1) = v6 & % 75.00/16.01 | in(v5, v2) = v8 & ( ~ (v6 = 0) | (( ~ (v8 = 0) | v7 = 0) & ( ~ % 75.00/16.01 | (v7 = 0) | v8 = 0))))) & ! [v3: $i] : ! [v4: $i] : ( ~ % 75.00/16.01 | (element(v4, v1) = 0) | ~ (element(v3, v1) = 0) | ~ $i(v4) | ~ % 75.00/16.01 | $i(v3) | ? [v5: any] : ? [v6: $i] : ? [v7: any] : (related(v0, % 75.00/16.01 | v3, v4) = v5 & ordered_pair(v3, v4) = v6 & in(v6, v2) = v7 & % 75.00/16.01 | $i(v6) & ( ~ (v7 = 0) | v5 = 0) & ( ~ (v5 = 0) | v7 = 0))))) % 75.00/16.02 | (10) ! [v0: $i] : ! [v1: $i] : ( ~ (the_carrier(v0) = v1) | ~ $i(v0) | % 75.00/16.02 | ? [v2: any] : ? [v3: $i] : (the_InternalRel(v0) = v3 & rel_str(v0) % 75.00/16.02 | = v2 & $i(v3) & ( ~ (v2 = 0) | ( ! [v4: $i] : ! [v5: $i] : ! % 75.00/16.02 | [v6: any] : ( ~ (related(v0, v4, v5) = v6) | ~ (element(v4, % 75.00/16.02 | v1) = 0) | ~ $i(v5) | ~ $i(v4) | ? [v7: any] : ? % 75.00/16.02 | [v8: $i] : ? [v9: any] : (ordered_pair(v4, v5) = v8 & % 75.00/16.02 | element(v5, v1) = v7 & in(v8, v3) = v9 & $i(v8) & ( ~ (v7 % 75.00/16.02 | = 0) | (( ~ (v9 = 0) | v6 = 0) & ( ~ (v6 = 0) | v9 = % 75.00/16.02 | 0))))) & ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( % 75.00/16.02 | ~ (ordered_pair(v4, v5) = v6) | ~ (element(v4, v1) = 0) | % 75.00/16.02 | ~ $i(v5) | ~ $i(v4) | ? [v7: any] : ? [v8: any] : ? [v9: % 75.00/16.02 | any] : (related(v0, v4, v5) = v8 & element(v5, v1) = v7 & % 75.00/16.02 | in(v6, v3) = v9 & ( ~ (v7 = 0) | (( ~ (v9 = 0) | v8 = 0) & % 75.00/16.02 | ( ~ (v8 = 0) | v9 = 0))))) & ! [v4: $i] : ! [v5: $i] % 75.00/16.02 | : ( ~ (element(v5, v1) = 0) | ~ (element(v4, v1) = 0) | ~ % 75.00/16.02 | $i(v5) | ~ $i(v4) | ? [v6: any] : ? [v7: $i] : ? [v8: % 75.00/16.02 | any] : (related(v0, v4, v5) = v6 & ordered_pair(v4, v5) = % 75.00/16.02 | v7 & in(v7, v3) = v8 & $i(v7) & ( ~ (v8 = 0) | v6 = 0) & ( % 75.00/16.02 | ~ (v6 = 0) | v8 = 0))))))) % 75.00/16.02 | (11) ! [v0: $i] : ! [v1: $i] : ( ~ (the_InternalRel(v0) = v1) | ~ $i(v0) % 75.00/16.02 | | ? [v2: any] : ? [v3: $i] : (rel_str(v0) = v2 & the_carrier(v0) = % 75.00/16.02 | v3 & $i(v3) & ( ~ (v2 = 0) | ( ! [v4: $i] : ! [v5: $i] : ! [v6: % 75.00/16.02 | any] : ( ~ (related(v0, v4, v5) = v6) | ~ (element(v4, v3) % 75.00/16.02 | = 0) | ~ $i(v5) | ~ $i(v4) | ? [v7: any] : ? [v8: $i] % 75.00/16.02 | : ? [v9: any] : (ordered_pair(v4, v5) = v8 & element(v5, % 75.00/16.02 | v3) = v7 & in(v8, v1) = v9 & $i(v8) & ( ~ (v7 = 0) | (( % 75.00/16.02 | ~ (v9 = 0) | v6 = 0) & ( ~ (v6 = 0) | v9 = 0))))) & % 75.00/16.02 | ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~ (ordered_pair(v4, % 75.00/16.02 | v5) = v6) | ~ (element(v4, v3) = 0) | ~ $i(v5) | ~ % 75.00/16.02 | $i(v4) | ? [v7: any] : ? [v8: any] : ? [v9: any] : % 75.00/16.02 | (related(v0, v4, v5) = v8 & element(v5, v3) = v7 & in(v6, % 75.00/16.02 | v1) = v9 & ( ~ (v7 = 0) | (( ~ (v9 = 0) | v8 = 0) & ( ~ % 75.00/16.02 | (v8 = 0) | v9 = 0))))) & ! [v4: $i] : ! [v5: $i] : % 75.00/16.02 | ( ~ (element(v5, v3) = 0) | ~ (element(v4, v3) = 0) | ~ % 75.00/16.02 | $i(v5) | ~ $i(v4) | ? [v6: any] : ? [v7: $i] : ? [v8: % 75.00/16.02 | any] : (related(v0, v4, v5) = v6 & ordered_pair(v4, v5) = % 75.00/16.02 | v7 & in(v7, v1) = v8 & $i(v7) & ( ~ (v8 = 0) | v6 = 0) & ( % 75.00/16.02 | ~ (v6 = 0) | v8 = 0))))))) % 75.00/16.02 | % 75.00/16.02 | ALPHA: (dt_m2_relset_1) implies: % 75.00/16.02 | (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 75.00/16.02 | (relation_of2_as_subset(v2, v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | % 75.00/16.02 | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : (cartesian_product2(v0, v1) = % 75.00/16.02 | v3 & powerset(v3) = v4 & element(v2, v4) = 0 & $i(v4) & $i(v3))) % 75.00/16.02 | % 75.00/16.02 | ALPHA: (dt_u1_orders_2) implies: % 75.00/16.03 | (13) ! [v0: $i] : ( ~ (rel_str(v0) = 0) | ~ $i(v0) | ? [v1: $i] : ? % 75.00/16.03 | [v2: $i] : (relation_of2_as_subset(v1, v2, v2) = 0 & % 75.00/16.03 | the_InternalRel(v0) = v1 & the_carrier(v0) = v2 & $i(v2) & % 75.00/16.03 | $i(v1))) % 75.00/16.03 | (14) ! [v0: $i] : ! [v1: $i] : ( ~ (the_carrier(v0) = v1) | ~ $i(v0) | % 75.00/16.03 | ? [v2: any] : ? [v3: $i] : ? [v4: any] : % 75.00/16.03 | (relation_of2_as_subset(v3, v1, v1) = v4 & the_InternalRel(v0) = v3 % 75.00/16.03 | & rel_str(v0) = v2 & $i(v3) & ( ~ (v2 = 0) | v4 = 0))) % 75.00/16.03 | % 75.00/16.03 | ALPHA: (rc1_subset_1) implies: % 75.00/16.03 | (15) ! [v0: $i] : ! [v1: $i] : ( ~ (powerset(v0) = v1) | ~ $i(v0) | ? % 75.00/16.03 | [v2: int] : ? [v3: $i] : ? [v4: int] : ? [v5: int] : ($i(v3) & % 75.00/16.03 | ((v4 = 0 & ~ (v5 = 0) & empty(v3) = v5 & element(v3, v1) = 0) | % 75.00/16.03 | (v2 = 0 & empty(v0) = 0)))) % 75.00/16.03 | (16) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (empty(v0) = v1) | ~ $i(v0) % 75.00/16.03 | | ? [v2: $i] : ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & % 75.00/16.03 | empty(v3) = v4 & powerset(v0) = v2 & element(v3, v2) = 0 & $i(v3) % 75.00/16.03 | & $i(v2))) % 75.00/16.03 | % 75.00/16.03 | ALPHA: (t106_zfmisc_1) implies: % 75.00/16.03 | (17) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 75.00/16.03 | ! [v5: $i] : ( ~ (ordered_pair(v0, v1) = v4) | ~ % 75.00/16.03 | (cartesian_product2(v2, v3) = v5) | ~ (in(v4, v5) = 0) | ~ $i(v3) % 75.00/16.03 | | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | (in(v1, v3) = 0 & in(v0, v2) = % 75.00/16.03 | 0)) % 75.00/16.03 | % 75.00/16.03 | ALPHA: (t1_subset) implies: % 75.00/16.03 | (18) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (element(v0, % 75.00/16.03 | v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ( ~ (v3 = 0) % 75.00/16.03 | & in(v0, v1) = v3)) % 75.00/16.03 | % 75.00/16.03 | ALPHA: (t2_subset) implies: % 75.00/16.03 | (19) ! [v0: $i] : ! [v1: $i] : ( ~ (element(v0, v1) = 0) | ~ $i(v1) | ~ % 75.00/16.03 | $i(v0) | ? [v2: any] : ? [v3: any] : (empty(v1) = v2 & in(v0, v1) % 75.00/16.03 | = v3 & (v3 = 0 | v2 = 0))) % 75.00/16.04 | (20) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (in(v0, v1) = % 75.00/16.04 | v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : % 75.00/16.04 | (empty(v1) = v4 & element(v0, v1) = v3 & ( ~ (v3 = 0) | v4 = 0))) % 75.00/16.04 | % 75.00/16.04 | ALPHA: (t4_subset) implies: % 75.00/16.04 | (21) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 75.00/16.04 | (powerset(v2) = v3) | ~ (element(v1, v3) = 0) | ~ (in(v0, v1) = 0) % 75.00/16.04 | | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | element(v0, v2) = 0) % 75.00/16.04 | % 75.00/16.04 | ALPHA: (t5_subset) implies: % 75.00/16.04 | (22) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (empty(v2) = 0) | ~ % 75.00/16.04 | (in(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : % 75.00/16.04 | ? [v4: int] : ( ~ (v4 = 0) & powerset(v2) = v3 & element(v1, v3) = % 75.00/16.04 | v4 & $i(v3))) % 75.00/16.04 | (23) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 75.00/16.04 | (powerset(v2) = v3) | ~ (element(v1, v3) = 0) | ~ (in(v0, v1) = 0) % 75.00/16.04 | | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & % 75.00/16.04 | empty(v2) = v4)) % 75.00/16.04 | % 75.00/16.04 | ALPHA: (t6_boole) implies: % 75.00/16.04 | (24) ! [v0: $i] : (v0 = empty_set | ~ (empty(v0) = 0) | ~ $i(v0)) % 75.00/16.04 | % 75.00/16.04 | ALPHA: (function-axioms) implies: % 75.00/16.04 | (25) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (singleton(v2) % 75.00/16.04 | = v1) | ~ (singleton(v2) = v0)) % 75.00/16.05 | (26) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 75.00/16.05 | (the_carrier(v2) = v1) | ~ (the_carrier(v2) = v0)) % 75.00/16.05 | (27) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 75.00/16.05 | : (v1 = v0 | ~ (antisymmetric_relstr(v2) = v1) | ~ % 75.00/16.05 | (antisymmetric_relstr(v2) = v0)) % 75.00/16.05 | (28) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 75.00/16.05 | : (v1 = v0 | ~ (rel_str(v2) = v1) | ~ (rel_str(v2) = v0)) % 75.00/16.05 | (29) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 75.00/16.05 | (the_InternalRel(v2) = v1) | ~ (the_InternalRel(v2) = v0)) % 75.00/16.05 | (30) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 75.00/16.05 | : (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0)) % 75.00/16.05 | (31) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 75.00/16.05 | : ! [v3: $i] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = % 75.00/16.05 | v0)) % 75.00/16.05 | (32) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 75.00/16.05 | (ordered_pair(v3, v2) = v1) | ~ (ordered_pair(v3, v2) = v0)) % 75.00/16.05 | (33) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 75.00/16.05 | : ! [v3: $i] : (v1 = v0 | ~ (is_antisymmetric_in(v3, v2) = v1) | ~ % 75.00/16.05 | (is_antisymmetric_in(v3, v2) = v0)) % 75.00/16.05 | (34) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 75.00/16.05 | : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (related(v4, v3, v2) = v1) % 75.00/16.05 | | ~ (related(v4, v3, v2) = v0)) % 75.00/16.05 | % 75.00/16.05 | DELTA: instantiating (rc1_xboole_0) with fresh symbol all_33_0 gives: % 75.00/16.05 | (35) empty(all_33_0) = 0 & $i(all_33_0) % 75.00/16.05 | % 75.00/16.05 | ALPHA: (35) implies: % 75.00/16.05 | (36) $i(all_33_0) % 75.00/16.05 | (37) empty(all_33_0) = 0 % 75.00/16.05 | % 75.00/16.05 | DELTA: instantiating (existence_l1_orders_2) with fresh symbol all_35_0 gives: % 75.00/16.05 | (38) rel_str(all_35_0) = 0 & $i(all_35_0) % 75.00/16.05 | % 75.00/16.05 | ALPHA: (38) implies: % 75.00/16.05 | (39) $i(all_35_0) % 75.00/16.05 | (40) rel_str(all_35_0) = 0 % 75.00/16.05 | % 75.00/16.05 | DELTA: instantiating (rc2_xboole_0) with fresh symbols all_38_0, all_38_1 % 75.00/16.05 | gives: % 75.00/16.06 | (41) ~ (all_38_0 = 0) & empty(all_38_1) = all_38_0 & $i(all_38_1) % 75.00/16.06 | % 75.00/16.06 | ALPHA: (41) implies: % 75.00/16.06 | (42) ~ (all_38_0 = 0) % 75.00/16.06 | (43) $i(all_38_1) % 75.00/16.06 | (44) empty(all_38_1) = all_38_0 % 75.00/16.06 | % 75.00/16.06 | DELTA: instantiating (t25_orders_2) with fresh symbols all_42_0, all_42_1, % 75.00/16.06 | all_42_2, all_42_3 gives: % 75.00/16.06 | (45) ~ (all_42_0 = all_42_1) & related(all_42_3, all_42_0, all_42_1) = 0 & % 75.00/16.06 | related(all_42_3, all_42_1, all_42_0) = 0 & rel_str(all_42_3) = 0 & % 75.00/16.06 | antisymmetric_relstr(all_42_3) = 0 & the_carrier(all_42_3) = all_42_2 % 75.00/16.06 | & element(all_42_0, all_42_2) = 0 & element(all_42_1, all_42_2) = 0 & % 75.00/16.06 | $i(all_42_0) & $i(all_42_1) & $i(all_42_2) & $i(all_42_3) % 75.00/16.06 | % 75.00/16.06 | ALPHA: (45) implies: % 75.00/16.06 | (46) ~ (all_42_0 = all_42_1) % 75.00/16.06 | (47) $i(all_42_3) % 75.00/16.06 | (48) $i(all_42_2) % 75.00/16.06 | (49) $i(all_42_1) % 75.00/16.06 | (50) $i(all_42_0) % 75.00/16.06 | (51) element(all_42_1, all_42_2) = 0 % 75.00/16.06 | (52) element(all_42_0, all_42_2) = 0 % 75.00/16.06 | (53) the_carrier(all_42_3) = all_42_2 % 75.00/16.06 | (54) antisymmetric_relstr(all_42_3) = 0 % 75.00/16.06 | (55) rel_str(all_42_3) = 0 % 75.00/16.06 | (56) related(all_42_3, all_42_1, all_42_0) = 0 % 75.00/16.06 | (57) related(all_42_3, all_42_0, all_42_1) = 0 % 75.00/16.06 | % 75.00/16.06 | GROUND_INST: instantiating (19) with all_42_1, all_42_2, simplifying with % 75.00/16.06 | (48), (49), (51) gives: % 75.00/16.06 | (58) ? [v0: any] : ? [v1: any] : (empty(all_42_2) = v0 & in(all_42_1, % 75.00/16.06 | all_42_2) = v1 & (v1 = 0 | v0 = 0)) % 75.00/16.06 | % 75.00/16.06 | GROUND_INST: instantiating (19) with all_42_0, all_42_2, simplifying with % 75.00/16.06 | (48), (50), (52) gives: % 75.00/16.06 | (59) ? [v0: any] : ? [v1: any] : (empty(all_42_2) = v0 & in(all_42_0, % 75.00/16.06 | all_42_2) = v1 & (v1 = 0 | v0 = 0)) % 75.00/16.06 | % 75.00/16.06 | GROUND_INST: instantiating (6) with all_42_3, all_42_2, simplifying with (47), % 75.00/16.06 | (53) gives: % 75.00/16.06 | (60) ? [v0: any] : ? [v1: any] : ? [v2: $i] : ? [v3: any] : % 75.00/16.06 | (the_InternalRel(all_42_3) = v2 & rel_str(all_42_3) = v0 & % 75.00/16.06 | antisymmetric_relstr(all_42_3) = v1 & is_antisymmetric_in(v2, % 75.00/16.06 | all_42_2) = v3 & $i(v2) & ( ~ (v0 = 0) | (( ~ (v3 = 0) | v1 = 0) & % 75.00/16.06 | ( ~ (v1 = 0) | v3 = 0)))) % 75.00/16.06 | % 75.00/16.06 | GROUND_INST: instantiating (14) with all_42_3, all_42_2, simplifying with % 75.00/16.06 | (47), (53) gives: % 75.00/16.07 | (61) ? [v0: any] : ? [v1: $i] : ? [v2: any] : % 75.00/16.07 | (relation_of2_as_subset(v1, all_42_2, all_42_2) = v2 & % 75.00/16.07 | the_InternalRel(all_42_3) = v1 & rel_str(all_42_3) = v0 & $i(v1) & ( % 75.00/16.07 | ~ (v0 = 0) | v2 = 0)) % 75.00/16.07 | % 75.00/16.07 | GROUND_INST: instantiating (10) with all_42_3, all_42_2, simplifying with % 75.00/16.07 | (47), (53) gives: % 75.00/16.07 | (62) ? [v0: any] : ? [v1: $i] : (the_InternalRel(all_42_3) = v1 & % 75.00/16.07 | rel_str(all_42_3) = v0 & $i(v1) & ( ~ (v0 = 0) | ( ! [v2: $i] : ! % 75.00/16.07 | [v3: $i] : ! [v4: any] : ( ~ (related(all_42_3, v2, v3) = v4) | % 75.00/16.07 | ~ (element(v2, all_42_2) = 0) | ~ $i(v3) | ~ $i(v2) | ? % 75.00/16.07 | [v5: any] : ? [v6: $i] : ? [v7: any] : (ordered_pair(v2, v3) % 75.00/16.07 | = v6 & element(v3, all_42_2) = v5 & in(v6, v1) = v7 & $i(v6) % 75.00/16.07 | & ( ~ (v5 = 0) | (( ~ (v7 = 0) | v4 = 0) & ( ~ (v4 = 0) | v7 % 75.00/16.07 | = 0))))) & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( % 75.00/16.07 | ~ (ordered_pair(v2, v3) = v4) | ~ (element(v2, all_42_2) = 0) % 75.00/16.07 | | ~ $i(v3) | ~ $i(v2) | ? [v5: any] : ? [v6: any] : ? % 75.00/16.07 | [v7: any] : (related(all_42_3, v2, v3) = v6 & element(v3, % 75.00/16.07 | all_42_2) = v5 & in(v4, v1) = v7 & ( ~ (v5 = 0) | (( ~ (v7 % 75.00/16.07 | = 0) | v6 = 0) & ( ~ (v6 = 0) | v7 = 0))))) & ! % 75.00/16.07 | [v2: $i] : ! [v3: $i] : ( ~ (element(v3, all_42_2) = 0) | ~ % 75.00/16.07 | (element(v2, all_42_2) = 0) | ~ $i(v3) | ~ $i(v2) | ? [v4: % 75.00/16.07 | any] : ? [v5: $i] : ? [v6: any] : (related(all_42_3, v2, % 75.00/16.07 | v3) = v4 & ordered_pair(v2, v3) = v5 & in(v5, v1) = v6 & % 75.00/16.07 | $i(v5) & ( ~ (v6 = 0) | v4 = 0) & ( ~ (v4 = 0) | v6 = % 75.00/16.07 | 0)))))) % 75.00/16.07 | % 75.00/16.07 | GROUND_INST: instantiating (7) with all_42_3, 0, simplifying with (47), (54) % 75.00/16.07 | gives: % 75.00/16.07 | (63) ? [v0: any] : ? [v1: $i] : ? [v2: $i] : ? [v3: any] : % 75.00/16.07 | (the_InternalRel(all_42_3) = v1 & rel_str(all_42_3) = v0 & % 75.00/16.07 | the_carrier(all_42_3) = v2 & is_antisymmetric_in(v1, v2) = v3 & % 75.00/16.07 | $i(v2) & $i(v1) & ( ~ (v0 = 0) | v3 = 0)) % 75.00/16.07 | % 75.00/16.07 | GROUND_INST: instantiating (5) with all_35_0, simplifying with (39), (40) % 75.00/16.07 | gives: % 75.00/16.07 | (64) ? [v0: any] : ? [v1: $i] : ? [v2: $i] : ? [v3: any] : % 75.00/16.07 | (the_InternalRel(all_35_0) = v1 & antisymmetric_relstr(all_35_0) = v0 % 75.00/16.07 | & the_carrier(all_35_0) = v2 & is_antisymmetric_in(v1, v2) = v3 & % 75.00/16.07 | $i(v2) & $i(v1) & ( ~ (v3 = 0) | v0 = 0) & ( ~ (v0 = 0) | v3 = 0)) % 75.00/16.07 | % 75.00/16.07 | GROUND_INST: instantiating (13) with all_35_0, simplifying with (39), (40) % 75.00/16.07 | gives: % 75.00/16.08 | (65) ? [v0: $i] : ? [v1: $i] : (relation_of2_as_subset(v0, v1, v1) = 0 & % 75.00/16.08 | the_InternalRel(all_35_0) = v0 & the_carrier(all_35_0) = v1 & $i(v1) % 75.00/16.08 | & $i(v0)) % 75.00/16.08 | % 75.00/16.08 | GROUND_INST: instantiating (9) with all_35_0, simplifying with (39), (40) % 75.00/16.08 | gives: % 75.00/16.08 | (66) ? [v0: $i] : ? [v1: $i] : (the_InternalRel(all_35_0) = v1 & % 75.00/16.08 | the_carrier(all_35_0) = v0 & $i(v1) & $i(v0) & ! [v2: $i] : ! [v3: % 75.00/16.08 | $i] : ! [v4: any] : ( ~ (related(all_35_0, v2, v3) = v4) | ~ % 75.00/16.08 | (element(v2, v0) = 0) | ~ $i(v3) | ~ $i(v2) | ? [v5: any] : ? % 75.00/16.08 | [v6: $i] : ? [v7: any] : (ordered_pair(v2, v3) = v6 & element(v3, % 75.00/16.08 | v0) = v5 & in(v6, v1) = v7 & $i(v6) & ( ~ (v5 = 0) | (( ~ (v7 % 75.00/16.08 | = 0) | v4 = 0) & ( ~ (v4 = 0) | v7 = 0))))) & ! [v2: % 75.00/16.08 | $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (ordered_pair(v2, v3) = v4) % 75.00/16.08 | | ~ (element(v2, v0) = 0) | ~ $i(v3) | ~ $i(v2) | ? [v5: any] % 75.00/16.08 | : ? [v6: any] : ? [v7: any] : (related(all_35_0, v2, v3) = v6 & % 75.00/16.08 | element(v3, v0) = v5 & in(v4, v1) = v7 & ( ~ (v5 = 0) | (( ~ (v7 % 75.00/16.08 | = 0) | v6 = 0) & ( ~ (v6 = 0) | v7 = 0))))) & ! [v2: % 75.00/16.08 | $i] : ! [v3: $i] : ( ~ (element(v3, v0) = 0) | ~ (element(v2, % 75.00/16.08 | v0) = 0) | ~ $i(v3) | ~ $i(v2) | ? [v4: any] : ? [v5: $i] % 75.00/16.08 | : ? [v6: any] : (related(all_35_0, v2, v3) = v4 & % 75.00/16.08 | ordered_pair(v2, v3) = v5 & in(v5, v1) = v6 & $i(v5) & ( ~ (v6 = % 75.00/16.08 | 0) | v4 = 0) & ( ~ (v4 = 0) | v6 = 0)))) % 75.00/16.08 | % 75.00/16.08 | GROUND_INST: instantiating (5) with all_42_3, simplifying with (47), (55) % 75.00/16.08 | gives: % 75.00/16.08 | (67) ? [v0: any] : ? [v1: $i] : ? [v2: $i] : ? [v3: any] : % 75.00/16.08 | (the_InternalRel(all_42_3) = v1 & antisymmetric_relstr(all_42_3) = v0 % 75.00/16.08 | & the_carrier(all_42_3) = v2 & is_antisymmetric_in(v1, v2) = v3 & % 75.00/16.08 | $i(v2) & $i(v1) & ( ~ (v3 = 0) | v0 = 0) & ( ~ (v0 = 0) | v3 = 0)) % 75.00/16.08 | % 75.00/16.08 | GROUND_INST: instantiating (13) with all_42_3, simplifying with (47), (55) % 75.00/16.08 | gives: % 75.00/16.08 | (68) ? [v0: $i] : ? [v1: $i] : (relation_of2_as_subset(v0, v1, v1) = 0 & % 75.00/16.08 | the_InternalRel(all_42_3) = v0 & the_carrier(all_42_3) = v1 & $i(v1) % 75.00/16.08 | & $i(v0)) % 75.00/16.08 | % 75.00/16.08 | GROUND_INST: instantiating (9) with all_42_3, simplifying with (47), (55) % 75.00/16.08 | gives: % 75.39/16.09 | (69) ? [v0: $i] : ? [v1: $i] : (the_InternalRel(all_42_3) = v1 & % 75.39/16.09 | the_carrier(all_42_3) = v0 & $i(v1) & $i(v0) & ! [v2: $i] : ! [v3: % 75.39/16.09 | $i] : ! [v4: any] : ( ~ (related(all_42_3, v2, v3) = v4) | ~ % 75.39/16.09 | (element(v2, v0) = 0) | ~ $i(v3) | ~ $i(v2) | ? [v5: any] : ? % 75.39/16.09 | [v6: $i] : ? [v7: any] : (ordered_pair(v2, v3) = v6 & element(v3, % 75.39/16.09 | v0) = v5 & in(v6, v1) = v7 & $i(v6) & ( ~ (v5 = 0) | (( ~ (v7 % 75.39/16.09 | = 0) | v4 = 0) & ( ~ (v4 = 0) | v7 = 0))))) & ! [v2: % 75.39/16.09 | $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (ordered_pair(v2, v3) = v4) % 75.39/16.09 | | ~ (element(v2, v0) = 0) | ~ $i(v3) | ~ $i(v2) | ? [v5: any] % 75.39/16.09 | : ? [v6: any] : ? [v7: any] : (related(all_42_3, v2, v3) = v6 & % 75.39/16.09 | element(v3, v0) = v5 & in(v4, v1) = v7 & ( ~ (v5 = 0) | (( ~ (v7 % 75.39/16.09 | = 0) | v6 = 0) & ( ~ (v6 = 0) | v7 = 0))))) & ! [v2: % 75.39/16.09 | $i] : ! [v3: $i] : ( ~ (element(v3, v0) = 0) | ~ (element(v2, % 75.39/16.09 | v0) = 0) | ~ $i(v3) | ~ $i(v2) | ? [v4: any] : ? [v5: $i] % 75.39/16.09 | : ? [v6: any] : (related(all_42_3, v2, v3) = v4 & % 75.39/16.09 | ordered_pair(v2, v3) = v5 & in(v5, v1) = v6 & $i(v5) & ( ~ (v6 = % 75.39/16.09 | 0) | v4 = 0) & ( ~ (v4 = 0) | v6 = 0)))) % 75.39/16.09 | % 75.39/16.09 | GROUND_INST: instantiating (24) with all_33_0, simplifying with (36), (37) % 75.39/16.09 | gives: % 75.39/16.09 | (70) all_33_0 = empty_set % 75.39/16.09 | % 75.39/16.09 | GROUND_INST: instantiating (16) with all_38_1, all_38_0, simplifying with % 75.39/16.09 | (43), (44) gives: % 75.39/16.09 | (71) all_38_0 = 0 | ? [v0: $i] : ? [v1: $i] : ? [v2: int] : ( ~ (v2 = 0) % 75.39/16.09 | & empty(v1) = v2 & powerset(all_38_1) = v0 & element(v1, v0) = 0 & % 75.39/16.09 | $i(v1) & $i(v0)) % 75.39/16.09 | % 75.39/16.09 | DELTA: instantiating (59) with fresh symbols all_50_0, all_50_1 gives: % 75.39/16.09 | (72) empty(all_42_2) = all_50_1 & in(all_42_0, all_42_2) = all_50_0 & % 75.39/16.09 | (all_50_0 = 0 | all_50_1 = 0) % 75.39/16.09 | % 75.39/16.09 | ALPHA: (72) implies: % 75.39/16.09 | (73) in(all_42_0, all_42_2) = all_50_0 % 75.39/16.09 | (74) empty(all_42_2) = all_50_1 % 75.39/16.09 | (75) all_50_0 = 0 | all_50_1 = 0 % 75.39/16.09 | % 75.39/16.09 | DELTA: instantiating (58) with fresh symbols all_52_0, all_52_1 gives: % 75.39/16.09 | (76) empty(all_42_2) = all_52_1 & in(all_42_1, all_42_2) = all_52_0 & % 75.39/16.09 | (all_52_0 = 0 | all_52_1 = 0) % 75.39/16.09 | % 75.39/16.09 | ALPHA: (76) implies: % 75.39/16.09 | (77) in(all_42_1, all_42_2) = all_52_0 % 75.39/16.09 | (78) empty(all_42_2) = all_52_1 % 75.39/16.09 | (79) all_52_0 = 0 | all_52_1 = 0 % 75.39/16.09 | % 75.39/16.09 | DELTA: instantiating (65) with fresh symbols all_54_0, all_54_1 gives: % 75.39/16.09 | (80) relation_of2_as_subset(all_54_1, all_54_0, all_54_0) = 0 & % 75.39/16.09 | the_InternalRel(all_35_0) = all_54_1 & the_carrier(all_35_0) = % 75.39/16.09 | all_54_0 & $i(all_54_0) & $i(all_54_1) % 75.39/16.09 | % 75.39/16.09 | ALPHA: (80) implies: % 75.39/16.09 | (81) the_carrier(all_35_0) = all_54_0 % 75.39/16.09 | (82) the_InternalRel(all_35_0) = all_54_1 % 75.39/16.09 | (83) relation_of2_as_subset(all_54_1, all_54_0, all_54_0) = 0 % 75.39/16.09 | % 75.39/16.09 | DELTA: instantiating (68) with fresh symbols all_56_0, all_56_1 gives: % 75.39/16.09 | (84) relation_of2_as_subset(all_56_1, all_56_0, all_56_0) = 0 & % 75.39/16.09 | the_InternalRel(all_42_3) = all_56_1 & the_carrier(all_42_3) = % 75.39/16.09 | all_56_0 & $i(all_56_0) & $i(all_56_1) % 75.39/16.09 | % 75.39/16.09 | ALPHA: (84) implies: % 75.39/16.09 | (85) $i(all_56_0) % 75.39/16.09 | (86) the_carrier(all_42_3) = all_56_0 % 75.39/16.09 | (87) the_InternalRel(all_42_3) = all_56_1 % 75.39/16.09 | (88) relation_of2_as_subset(all_56_1, all_56_0, all_56_0) = 0 % 75.39/16.09 | % 75.39/16.09 | DELTA: instantiating (61) with fresh symbols all_58_0, all_58_1, all_58_2 % 75.39/16.09 | gives: % 75.39/16.09 | (89) relation_of2_as_subset(all_58_1, all_42_2, all_42_2) = all_58_0 & % 75.39/16.09 | the_InternalRel(all_42_3) = all_58_1 & rel_str(all_42_3) = all_58_2 & % 75.39/16.09 | $i(all_58_1) & ( ~ (all_58_2 = 0) | all_58_0 = 0) % 75.39/16.09 | % 75.39/16.09 | ALPHA: (89) implies: % 75.39/16.10 | (90) $i(all_58_1) % 75.39/16.10 | (91) the_InternalRel(all_42_3) = all_58_1 % 75.39/16.10 | % 75.39/16.10 | DELTA: instantiating (63) with fresh symbols all_60_0, all_60_1, all_60_2, % 75.39/16.10 | all_60_3 gives: % 75.39/16.10 | (92) the_InternalRel(all_42_3) = all_60_2 & rel_str(all_42_3) = all_60_3 & % 75.39/16.10 | the_carrier(all_42_3) = all_60_1 & is_antisymmetric_in(all_60_2, % 75.39/16.10 | all_60_1) = all_60_0 & $i(all_60_1) & $i(all_60_2) & ( ~ (all_60_3 = % 75.39/16.10 | 0) | all_60_0 = 0) % 75.39/16.10 | % 75.39/16.10 | ALPHA: (92) implies: % 75.39/16.10 | (93) the_carrier(all_42_3) = all_60_1 % 75.39/16.10 | (94) rel_str(all_42_3) = all_60_3 % 75.39/16.10 | (95) the_InternalRel(all_42_3) = all_60_2 % 75.39/16.10 | % 75.39/16.10 | DELTA: instantiating (67) with fresh symbols all_62_0, all_62_1, all_62_2, % 75.39/16.10 | all_62_3 gives: % 75.39/16.10 | (96) the_InternalRel(all_42_3) = all_62_2 & antisymmetric_relstr(all_42_3) % 75.39/16.10 | = all_62_3 & the_carrier(all_42_3) = all_62_1 & % 75.39/16.10 | is_antisymmetric_in(all_62_2, all_62_1) = all_62_0 & $i(all_62_1) & % 75.39/16.10 | $i(all_62_2) & ( ~ (all_62_0 = 0) | all_62_3 = 0) & ( ~ (all_62_3 = 0) % 75.39/16.10 | | all_62_0 = 0) % 75.39/16.10 | % 75.39/16.10 | ALPHA: (96) implies: % 75.39/16.10 | (97) is_antisymmetric_in(all_62_2, all_62_1) = all_62_0 % 75.39/16.10 | (98) the_carrier(all_42_3) = all_62_1 % 75.39/16.10 | (99) antisymmetric_relstr(all_42_3) = all_62_3 % 75.39/16.10 | (100) the_InternalRel(all_42_3) = all_62_2 % 75.39/16.10 | (101) ~ (all_62_3 = 0) | all_62_0 = 0 % 75.39/16.10 | % 75.39/16.10 | DELTA: instantiating (64) with fresh symbols all_64_0, all_64_1, all_64_2, % 75.39/16.10 | all_64_3 gives: % 75.39/16.10 | (102) the_InternalRel(all_35_0) = all_64_2 & antisymmetric_relstr(all_35_0) % 75.39/16.10 | = all_64_3 & the_carrier(all_35_0) = all_64_1 & % 75.39/16.10 | is_antisymmetric_in(all_64_2, all_64_1) = all_64_0 & $i(all_64_1) & % 75.39/16.10 | $i(all_64_2) & ( ~ (all_64_0 = 0) | all_64_3 = 0) & ( ~ (all_64_3 = % 75.39/16.10 | 0) | all_64_0 = 0) % 75.39/16.10 | % 75.39/16.10 | ALPHA: (102) implies: % 75.39/16.10 | (103) $i(all_64_2) % 75.39/16.10 | (104) $i(all_64_1) % 75.39/16.10 | (105) is_antisymmetric_in(all_64_2, all_64_1) = all_64_0 % 75.39/16.10 | (106) the_carrier(all_35_0) = all_64_1 % 75.39/16.10 | (107) antisymmetric_relstr(all_35_0) = all_64_3 % 75.39/16.10 | (108) the_InternalRel(all_35_0) = all_64_2 % 75.39/16.10 | (109) ~ (all_64_3 = 0) | all_64_0 = 0 % 75.39/16.10 | (110) ~ (all_64_0 = 0) | all_64_3 = 0 % 75.39/16.10 | % 75.39/16.10 | DELTA: instantiating (60) with fresh symbols all_66_0, all_66_1, all_66_2, % 75.39/16.10 | all_66_3 gives: % 75.39/16.10 | (111) the_InternalRel(all_42_3) = all_66_1 & rel_str(all_42_3) = all_66_3 & % 75.39/16.10 | antisymmetric_relstr(all_42_3) = all_66_2 & % 75.39/16.10 | is_antisymmetric_in(all_66_1, all_42_2) = all_66_0 & $i(all_66_1) & ( % 75.39/16.10 | ~ (all_66_3 = 0) | (( ~ (all_66_0 = 0) | all_66_2 = 0) & ( ~ % 75.39/16.10 | (all_66_2 = 0) | all_66_0 = 0))) % 75.39/16.10 | % 75.39/16.10 | ALPHA: (111) implies: % 75.39/16.10 | (112) antisymmetric_relstr(all_42_3) = all_66_2 % 75.39/16.10 | (113) rel_str(all_42_3) = all_66_3 % 75.39/16.10 | (114) the_InternalRel(all_42_3) = all_66_1 % 75.39/16.10 | % 75.39/16.10 | DELTA: instantiating (62) with fresh symbols all_68_0, all_68_1 gives: % 75.39/16.11 | (115) the_InternalRel(all_42_3) = all_68_0 & rel_str(all_42_3) = all_68_1 & % 75.39/16.11 | $i(all_68_0) & ( ~ (all_68_1 = 0) | ( ! [v0: $i] : ! [v1: $i] : ! % 75.39/16.11 | [v2: any] : ( ~ (related(all_42_3, v0, v1) = v2) | ~ % 75.39/16.11 | (element(v0, all_42_2) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v3: % 75.39/16.11 | any] : ? [v4: $i] : ? [v5: any] : (ordered_pair(v0, v1) = % 75.39/16.11 | v4 & element(v1, all_42_2) = v3 & in(v4, all_68_0) = v5 & % 75.39/16.11 | $i(v4) & ( ~ (v3 = 0) | (( ~ (v5 = 0) | v2 = 0) & ( ~ (v2 = % 75.39/16.11 | 0) | v5 = 0))))) & ! [v0: $i] : ! [v1: $i] : ! % 75.39/16.11 | [v2: $i] : ( ~ (ordered_pair(v0, v1) = v2) | ~ (element(v0, % 75.39/16.11 | all_42_2) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? % 75.39/16.11 | [v4: any] : ? [v5: any] : (related(all_42_3, v0, v1) = v4 & % 75.39/16.11 | element(v1, all_42_2) = v3 & in(v2, all_68_0) = v5 & ( ~ (v3 % 75.39/16.11 | = 0) | (( ~ (v5 = 0) | v4 = 0) & ( ~ (v4 = 0) | v5 = % 75.39/16.11 | 0))))) & ! [v0: $i] : ! [v1: $i] : ( ~ (element(v1, % 75.39/16.11 | all_42_2) = 0) | ~ (element(v0, all_42_2) = 0) | ~ $i(v1) % 75.39/16.11 | | ~ $i(v0) | ? [v2: any] : ? [v3: $i] : ? [v4: any] : % 75.39/16.11 | (related(all_42_3, v0, v1) = v2 & ordered_pair(v0, v1) = v3 & % 75.39/16.11 | in(v3, all_68_0) = v4 & $i(v3) & ( ~ (v4 = 0) | v2 = 0) & ( ~ % 75.39/16.11 | (v2 = 0) | v4 = 0))))) % 75.39/16.11 | % 75.39/16.11 | ALPHA: (115) implies: % 75.39/16.11 | (116) rel_str(all_42_3) = all_68_1 % 75.39/16.11 | (117) the_InternalRel(all_42_3) = all_68_0 % 75.39/16.11 | (118) ~ (all_68_1 = 0) | ( ! [v0: $i] : ! [v1: $i] : ! [v2: any] : ( ~ % 75.39/16.11 | (related(all_42_3, v0, v1) = v2) | ~ (element(v0, all_42_2) = 0) % 75.39/16.11 | | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: $i] : ? [v5: % 75.39/16.11 | any] : (ordered_pair(v0, v1) = v4 & element(v1, all_42_2) = v3 % 75.39/16.11 | & in(v4, all_68_0) = v5 & $i(v4) & ( ~ (v3 = 0) | (( ~ (v5 = 0) % 75.39/16.11 | | v2 = 0) & ( ~ (v2 = 0) | v5 = 0))))) & ! [v0: $i] : ! % 75.39/16.11 | [v1: $i] : ! [v2: $i] : ( ~ (ordered_pair(v0, v1) = v2) | ~ % 75.39/16.11 | (element(v0, all_42_2) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v3: % 75.39/16.11 | any] : ? [v4: any] : ? [v5: any] : (related(all_42_3, v0, v1) % 75.39/16.11 | = v4 & element(v1, all_42_2) = v3 & in(v2, all_68_0) = v5 & ( ~ % 75.39/16.11 | (v3 = 0) | (( ~ (v5 = 0) | v4 = 0) & ( ~ (v4 = 0) | v5 = % 75.39/16.11 | 0))))) & ! [v0: $i] : ! [v1: $i] : ( ~ (element(v1, % 75.39/16.11 | all_42_2) = 0) | ~ (element(v0, all_42_2) = 0) | ~ $i(v1) | % 75.39/16.11 | ~ $i(v0) | ? [v2: any] : ? [v3: $i] : ? [v4: any] : % 75.39/16.11 | (related(all_42_3, v0, v1) = v2 & ordered_pair(v0, v1) = v3 & % 75.39/16.11 | in(v3, all_68_0) = v4 & $i(v3) & ( ~ (v4 = 0) | v2 = 0) & ( ~ % 75.39/16.11 | (v2 = 0) | v4 = 0)))) % 75.39/16.11 | % 75.39/16.11 | DELTA: instantiating (69) with fresh symbols all_70_0, all_70_1 gives: % 75.39/16.12 | (119) the_InternalRel(all_42_3) = all_70_0 & the_carrier(all_42_3) = % 75.39/16.12 | all_70_1 & $i(all_70_0) & $i(all_70_1) & ! [v0: $i] : ! [v1: $i] : % 75.39/16.12 | ! [v2: any] : ( ~ (related(all_42_3, v0, v1) = v2) | ~ (element(v0, % 75.39/16.12 | all_70_1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: % 75.39/16.12 | $i] : ? [v5: any] : (ordered_pair(v0, v1) = v4 & element(v1, % 75.39/16.12 | all_70_1) = v3 & in(v4, all_70_0) = v5 & $i(v4) & ( ~ (v3 = 0) % 75.39/16.12 | | (( ~ (v5 = 0) | v2 = 0) & ( ~ (v2 = 0) | v5 = 0))))) & ! % 75.39/16.12 | [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (ordered_pair(v0, v1) = % 75.39/16.12 | v2) | ~ (element(v0, all_70_1) = 0) | ~ $i(v1) | ~ $i(v0) | ? % 75.39/16.12 | [v3: any] : ? [v4: any] : ? [v5: any] : (related(all_42_3, v0, % 75.39/16.12 | v1) = v4 & element(v1, all_70_1) = v3 & in(v2, all_70_0) = v5 & % 75.39/16.12 | ( ~ (v3 = 0) | (( ~ (v5 = 0) | v4 = 0) & ( ~ (v4 = 0) | v5 = % 75.39/16.12 | 0))))) & ! [v0: $i] : ! [v1: $i] : ( ~ (element(v1, % 75.39/16.12 | all_70_1) = 0) | ~ (element(v0, all_70_1) = 0) | ~ $i(v1) | % 75.39/16.12 | ~ $i(v0) | ? [v2: any] : ? [v3: $i] : ? [v4: any] : % 75.39/16.12 | (related(all_42_3, v0, v1) = v2 & ordered_pair(v0, v1) = v3 & % 75.39/16.12 | in(v3, all_70_0) = v4 & $i(v3) & ( ~ (v4 = 0) | v2 = 0) & ( ~ (v2 % 75.39/16.12 | = 0) | v4 = 0))) % 75.39/16.12 | % 75.39/16.12 | ALPHA: (119) implies: % 75.39/16.12 | (120) the_carrier(all_42_3) = all_70_1 % 75.39/16.12 | (121) the_InternalRel(all_42_3) = all_70_0 % 75.39/16.12 | % 75.39/16.12 | DELTA: instantiating (66) with fresh symbols all_73_0, all_73_1 gives: % 75.39/16.12 | (122) the_InternalRel(all_35_0) = all_73_0 & the_carrier(all_35_0) = % 75.39/16.12 | all_73_1 & $i(all_73_0) & $i(all_73_1) & ! [v0: $i] : ! [v1: $i] : % 75.39/16.12 | ! [v2: any] : ( ~ (related(all_35_0, v0, v1) = v2) | ~ (element(v0, % 75.39/16.12 | all_73_1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: % 75.39/16.12 | $i] : ? [v5: any] : (ordered_pair(v0, v1) = v4 & element(v1, % 75.39/16.12 | all_73_1) = v3 & in(v4, all_73_0) = v5 & $i(v4) & ( ~ (v3 = 0) % 75.39/16.12 | | (( ~ (v5 = 0) | v2 = 0) & ( ~ (v2 = 0) | v5 = 0))))) & ! % 75.39/16.12 | [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (ordered_pair(v0, v1) = % 75.39/16.12 | v2) | ~ (element(v0, all_73_1) = 0) | ~ $i(v1) | ~ $i(v0) | ? % 75.39/16.12 | [v3: any] : ? [v4: any] : ? [v5: any] : (related(all_35_0, v0, % 75.39/16.12 | v1) = v4 & element(v1, all_73_1) = v3 & in(v2, all_73_0) = v5 & % 75.39/16.12 | ( ~ (v3 = 0) | (( ~ (v5 = 0) | v4 = 0) & ( ~ (v4 = 0) | v5 = % 75.39/16.12 | 0))))) & ! [v0: $i] : ! [v1: $i] : ( ~ (element(v1, % 75.39/16.12 | all_73_1) = 0) | ~ (element(v0, all_73_1) = 0) | ~ $i(v1) | % 75.39/16.12 | ~ $i(v0) | ? [v2: any] : ? [v3: $i] : ? [v4: any] : % 75.39/16.12 | (related(all_35_0, v0, v1) = v2 & ordered_pair(v0, v1) = v3 & % 75.39/16.12 | in(v3, all_73_0) = v4 & $i(v3) & ( ~ (v4 = 0) | v2 = 0) & ( ~ (v2 % 75.39/16.12 | = 0) | v4 = 0))) % 75.39/16.12 | % 75.39/16.12 | ALPHA: (122) implies: % 75.39/16.12 | (123) the_carrier(all_35_0) = all_73_1 % 75.39/16.12 | (124) the_InternalRel(all_35_0) = all_73_0 % 75.39/16.12 | % 75.39/16.12 | REDUCE: (37), (70) imply: % 75.39/16.12 | (125) empty(empty_set) = 0 % 75.39/16.12 | % 75.39/16.12 | REDUCE: (36), (70) imply: % 75.39/16.12 | (126) $i(empty_set) % 75.39/16.12 | % 75.39/16.12 | BETA: splitting (71) gives: % 75.39/16.12 | % 75.39/16.12 | Case 1: % 75.39/16.12 | | % 75.39/16.12 | | (127) all_38_0 = 0 % 75.39/16.12 | | % 75.39/16.12 | | REDUCE: (42), (127) imply: % 75.39/16.12 | | (128) $false % 75.39/16.13 | | % 75.39/16.13 | | CLOSE: (128) is inconsistent. % 75.39/16.13 | | % 75.39/16.13 | Case 2: % 75.39/16.13 | | % 75.39/16.13 | | (129) ? [v0: $i] : ? [v1: $i] : ? [v2: int] : ( ~ (v2 = 0) & empty(v1) % 75.39/16.13 | | = v2 & powerset(all_38_1) = v0 & element(v1, v0) = 0 & $i(v1) & % 75.39/16.13 | | $i(v0)) % 75.39/16.13 | | % 75.39/16.13 | | DELTA: instantiating (129) with fresh symbols all_80_0, all_80_1, all_80_2 % 75.39/16.13 | | gives: % 75.39/16.13 | | (130) ~ (all_80_0 = 0) & empty(all_80_1) = all_80_0 & powerset(all_38_1) % 75.39/16.13 | | = all_80_2 & element(all_80_1, all_80_2) = 0 & $i(all_80_1) & % 75.39/16.13 | | $i(all_80_2) % 75.39/16.13 | | % 75.39/16.13 | | ALPHA: (130) implies: % 75.39/16.13 | | (131) ~ (all_80_0 = 0) % 75.39/16.13 | | (132) $i(all_80_2) % 75.39/16.13 | | (133) $i(all_80_1) % 75.39/16.13 | | (134) element(all_80_1, all_80_2) = 0 % 75.39/16.13 | | (135) powerset(all_38_1) = all_80_2 % 75.39/16.13 | | (136) empty(all_80_1) = all_80_0 % 75.39/16.13 | | % 75.39/16.13 | | GROUND_INST: instantiating (26) with all_64_1, all_73_1, all_35_0, % 75.39/16.13 | | simplifying with (106), (123) gives: % 75.39/16.13 | | (137) all_73_1 = all_64_1 % 75.39/16.13 | | % 75.39/16.13 | | GROUND_INST: instantiating (26) with all_54_0, all_73_1, all_35_0, % 75.39/16.13 | | simplifying with (81), (123) gives: % 75.39/16.13 | | (138) all_73_1 = all_54_0 % 75.39/16.13 | | % 75.39/16.13 | | GROUND_INST: instantiating (26) with all_42_2, all_62_1, all_42_3, % 75.39/16.13 | | simplifying with (53), (98) gives: % 75.39/16.13 | | (139) all_62_1 = all_42_2 % 75.39/16.13 | | % 75.39/16.13 | | GROUND_INST: instantiating (26) with all_60_1, all_62_1, all_42_3, % 75.39/16.13 | | simplifying with (93), (98) gives: % 75.39/16.13 | | (140) all_62_1 = all_60_1 % 75.39/16.13 | | % 75.39/16.13 | | GROUND_INST: instantiating (26) with all_62_1, all_70_1, all_42_3, % 75.39/16.13 | | simplifying with (98), (120) gives: % 75.39/16.13 | | (141) all_70_1 = all_62_1 % 75.39/16.13 | | % 75.39/16.13 | | GROUND_INST: instantiating (26) with all_56_0, all_70_1, all_42_3, % 75.39/16.13 | | simplifying with (86), (120) gives: % 75.39/16.13 | | (142) all_70_1 = all_56_0 % 75.39/16.13 | | % 75.39/16.13 | | GROUND_INST: instantiating (27) with 0, all_66_2, all_42_3, simplifying with % 75.39/16.13 | | (54), (112) gives: % 75.39/16.13 | | (143) all_66_2 = 0 % 75.39/16.13 | | % 75.39/16.13 | | GROUND_INST: instantiating (27) with all_62_3, all_66_2, all_42_3, % 75.39/16.13 | | simplifying with (99), (112) gives: % 75.39/16.13 | | (144) all_66_2 = all_62_3 % 75.39/16.13 | | % 75.39/16.13 | | GROUND_INST: instantiating (28) with 0, all_68_1, all_42_3, simplifying with % 75.39/16.13 | | (55), (116) gives: % 75.39/16.13 | | (145) all_68_1 = 0 % 75.39/16.13 | | % 75.39/16.13 | | GROUND_INST: instantiating (28) with all_66_3, all_68_1, all_42_3, % 75.39/16.13 | | simplifying with (113), (116) gives: % 75.39/16.13 | | (146) all_68_1 = all_66_3 % 75.39/16.13 | | % 75.39/16.13 | | GROUND_INST: instantiating (28) with all_60_3, all_68_1, all_42_3, % 75.39/16.13 | | simplifying with (94), (116) gives: % 75.39/16.13 | | (147) all_68_1 = all_60_3 % 75.39/16.13 | | % 75.39/16.13 | | GROUND_INST: instantiating (29) with all_64_2, all_73_0, all_35_0, % 75.39/16.13 | | simplifying with (108), (124) gives: % 75.39/16.13 | | (148) all_73_0 = all_64_2 % 75.39/16.13 | | % 75.39/16.13 | | GROUND_INST: instantiating (29) with all_54_1, all_73_0, all_35_0, % 75.39/16.13 | | simplifying with (82), (124) gives: % 75.39/16.13 | | (149) all_73_0 = all_54_1 % 75.39/16.13 | | % 75.39/16.13 | | GROUND_INST: instantiating (29) with all_58_1, all_62_2, all_42_3, % 75.39/16.13 | | simplifying with (91), (100) gives: % 75.39/16.13 | | (150) all_62_2 = all_58_1 % 75.39/16.13 | | % 75.39/16.13 | | GROUND_INST: instantiating (29) with all_56_1, all_62_2, all_42_3, % 75.39/16.13 | | simplifying with (87), (100) gives: % 75.39/16.13 | | (151) all_62_2 = all_56_1 % 75.39/16.13 | | % 75.39/16.13 | | GROUND_INST: instantiating (29) with all_62_2, all_66_1, all_42_3, % 75.39/16.13 | | simplifying with (100), (114) gives: % 75.39/16.13 | | (152) all_66_1 = all_62_2 % 75.39/16.13 | | % 75.39/16.13 | | GROUND_INST: instantiating (29) with all_68_0, all_70_0, all_42_3, % 75.39/16.13 | | simplifying with (117), (121) gives: % 75.39/16.13 | | (153) all_70_0 = all_68_0 % 75.39/16.13 | | % 75.39/16.13 | | GROUND_INST: instantiating (29) with all_66_1, all_70_0, all_42_3, % 75.39/16.13 | | simplifying with (114), (121) gives: % 75.39/16.13 | | (154) all_70_0 = all_66_1 % 75.39/16.13 | | % 75.39/16.14 | | GROUND_INST: instantiating (29) with all_60_2, all_70_0, all_42_3, % 75.39/16.14 | | simplifying with (95), (121) gives: % 75.39/16.14 | | (155) all_70_0 = all_60_2 % 75.39/16.14 | | % 75.39/16.14 | | GROUND_INST: instantiating (30) with all_50_1, all_52_1, all_42_2, % 75.39/16.14 | | simplifying with (74), (78) gives: % 75.39/16.14 | | (156) all_52_1 = all_50_1 % 75.39/16.14 | | % 75.39/16.14 | | COMBINE_EQS: (148), (149) imply: % 75.39/16.14 | | (157) all_64_2 = all_54_1 % 75.39/16.14 | | % 75.39/16.14 | | SIMP: (157) implies: % 75.39/16.14 | | (158) all_64_2 = all_54_1 % 75.39/16.14 | | % 75.39/16.14 | | COMBINE_EQS: (137), (138) imply: % 75.39/16.14 | | (159) all_64_1 = all_54_0 % 75.39/16.14 | | % 75.39/16.14 | | COMBINE_EQS: (153), (154) imply: % 75.39/16.14 | | (160) all_68_0 = all_66_1 % 75.39/16.14 | | % 75.39/16.14 | | COMBINE_EQS: (153), (155) imply: % 75.39/16.14 | | (161) all_68_0 = all_60_2 % 75.39/16.14 | | % 75.39/16.14 | | COMBINE_EQS: (141), (142) imply: % 75.39/16.14 | | (162) all_62_1 = all_56_0 % 75.39/16.14 | | % 75.39/16.14 | | SIMP: (162) implies: % 75.39/16.14 | | (163) all_62_1 = all_56_0 % 75.39/16.14 | | % 75.39/16.14 | | COMBINE_EQS: (160), (161) imply: % 75.39/16.14 | | (164) all_66_1 = all_60_2 % 75.39/16.14 | | % 75.39/16.14 | | SIMP: (164) implies: % 75.39/16.14 | | (165) all_66_1 = all_60_2 % 75.39/16.14 | | % 75.39/16.14 | | COMBINE_EQS: (145), (146) imply: % 75.39/16.14 | | (166) all_66_3 = 0 % 75.39/16.14 | | % 75.39/16.14 | | COMBINE_EQS: (146), (147) imply: % 75.39/16.14 | | (167) all_66_3 = all_60_3 % 75.39/16.14 | | % 75.39/16.14 | | COMBINE_EQS: (152), (165) imply: % 75.39/16.14 | | (168) all_62_2 = all_60_2 % 75.39/16.14 | | % 75.39/16.14 | | SIMP: (168) implies: % 75.39/16.14 | | (169) all_62_2 = all_60_2 % 75.39/16.14 | | % 75.39/16.14 | | COMBINE_EQS: (143), (144) imply: % 75.39/16.14 | | (170) all_62_3 = 0 % 75.39/16.14 | | % 75.39/16.14 | | COMBINE_EQS: (166), (167) imply: % 75.39/16.14 | | (171) all_60_3 = 0 % 75.39/16.14 | | % 75.39/16.14 | | COMBINE_EQS: (139), (140) imply: % 75.39/16.14 | | (172) all_60_1 = all_42_2 % 75.39/16.14 | | % 75.39/16.14 | | COMBINE_EQS: (140), (163) imply: % 75.39/16.14 | | (173) all_60_1 = all_56_0 % 75.39/16.14 | | % 75.39/16.14 | | COMBINE_EQS: (150), (169) imply: % 75.39/16.14 | | (174) all_60_2 = all_58_1 % 75.39/16.14 | | % 75.39/16.14 | | COMBINE_EQS: (151), (169) imply: % 75.39/16.14 | | (175) all_60_2 = all_56_1 % 75.39/16.14 | | % 75.39/16.14 | | COMBINE_EQS: (172), (173) imply: % 75.39/16.14 | | (176) all_56_0 = all_42_2 % 75.39/16.14 | | % 75.39/16.14 | | COMBINE_EQS: (174), (175) imply: % 75.39/16.14 | | (177) all_58_1 = all_56_1 % 75.39/16.14 | | % 75.39/16.14 | | COMBINE_EQS: (161), (175) imply: % 75.39/16.14 | | (178) all_68_0 = all_56_1 % 75.39/16.14 | | % 75.39/16.14 | | REDUCE: (88), (176) imply: % 75.39/16.14 | | (179) relation_of2_as_subset(all_56_1, all_42_2, all_42_2) = 0 % 75.39/16.14 | | % 75.39/16.14 | | REDUCE: (105), (158), (159) imply: % 75.39/16.14 | | (180) is_antisymmetric_in(all_54_1, all_54_0) = all_64_0 % 75.39/16.14 | | % 75.39/16.14 | | REDUCE: (97), (139), (151) imply: % 75.39/16.14 | | (181) is_antisymmetric_in(all_56_1, all_42_2) = all_62_0 % 75.39/16.14 | | % 75.39/16.14 | | REDUCE: (104), (159) imply: % 75.39/16.14 | | (182) $i(all_54_0) % 75.39/16.14 | | % 75.39/16.14 | | REDUCE: (103), (158) imply: % 75.39/16.14 | | (183) $i(all_54_1) % 75.39/16.14 | | % 75.39/16.14 | | REDUCE: (90), (177) imply: % 75.39/16.14 | | (184) $i(all_56_1) % 75.39/16.14 | | % 75.39/16.14 | | BETA: splitting (101) gives: % 75.39/16.14 | | % 75.39/16.14 | | Case 1: % 75.39/16.14 | | | % 75.39/16.14 | | | (185) ~ (all_62_3 = 0) % 75.39/16.14 | | | % 75.39/16.14 | | | REDUCE: (170), (185) imply: % 75.39/16.14 | | | (186) $false % 75.39/16.14 | | | % 75.39/16.14 | | | CLOSE: (186) is inconsistent. % 75.39/16.14 | | | % 75.39/16.14 | | Case 2: % 75.39/16.14 | | | % 75.39/16.14 | | | (187) all_62_0 = 0 % 75.39/16.14 | | | % 75.39/16.14 | | | REDUCE: (181), (187) imply: % 75.39/16.14 | | | (188) is_antisymmetric_in(all_56_1, all_42_2) = 0 % 75.39/16.14 | | | % 75.39/16.14 | | | BETA: splitting (118) gives: % 75.39/16.14 | | | % 75.39/16.14 | | | Case 1: % 75.39/16.14 | | | | % 75.39/16.14 | | | | (189) ~ (all_68_1 = 0) % 75.39/16.14 | | | | % 75.39/16.14 | | | | REDUCE: (145), (189) imply: % 75.39/16.14 | | | | (190) $false % 75.39/16.14 | | | | % 75.39/16.14 | | | | CLOSE: (190) is inconsistent. % 75.39/16.14 | | | | % 75.39/16.14 | | | Case 2: % 75.39/16.14 | | | | % 75.39/16.14 | | | | (191) ! [v0: $i] : ! [v1: $i] : ! [v2: any] : ( ~ % 75.39/16.14 | | | | (related(all_42_3, v0, v1) = v2) | ~ (element(v0, all_42_2) % 75.39/16.14 | | | | = 0) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: $i] : % 75.39/16.14 | | | | ? [v5: any] : (ordered_pair(v0, v1) = v4 & element(v1, % 75.39/16.14 | | | | all_42_2) = v3 & in(v4, all_68_0) = v5 & $i(v4) & ( ~ (v3 % 75.39/16.14 | | | | = 0) | (( ~ (v5 = 0) | v2 = 0) & ( ~ (v2 = 0) | v5 = % 75.39/16.14 | | | | 0))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( % 75.39/16.14 | | | | ~ (ordered_pair(v0, v1) = v2) | ~ (element(v0, all_42_2) = % 75.39/16.14 | | | | 0) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : % 75.39/16.14 | | | | ? [v5: any] : (related(all_42_3, v0, v1) = v4 & element(v1, % 75.39/16.14 | | | | all_42_2) = v3 & in(v2, all_68_0) = v5 & ( ~ (v3 = 0) | % 75.39/16.14 | | | | (( ~ (v5 = 0) | v4 = 0) & ( ~ (v4 = 0) | v5 = 0))))) & ! % 75.39/16.14 | | | | [v0: $i] : ! [v1: $i] : ( ~ (element(v1, all_42_2) = 0) | ~ % 75.39/16.14 | | | | (element(v0, all_42_2) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: % 75.39/16.14 | | | | any] : ? [v3: $i] : ? [v4: any] : (related(all_42_3, v0, % 75.39/16.14 | | | | v1) = v2 & ordered_pair(v0, v1) = v3 & in(v3, all_68_0) = % 75.39/16.14 | | | | v4 & $i(v3) & ( ~ (v4 = 0) | v2 = 0) & ( ~ (v2 = 0) | v4 = % 75.39/16.14 | | | | 0))) % 75.39/16.14 | | | | % 75.39/16.14 | | | | ALPHA: (191) implies: % 75.39/16.14 | | | | (192) ! [v0: $i] : ! [v1: $i] : ( ~ (element(v1, all_42_2) = 0) | % 75.39/16.14 | | | | ~ (element(v0, all_42_2) = 0) | ~ $i(v1) | ~ $i(v0) | ? % 75.39/16.14 | | | | [v2: any] : ? [v3: $i] : ? [v4: any] : (related(all_42_3, % 75.39/16.14 | | | | v0, v1) = v2 & ordered_pair(v0, v1) = v3 & in(v3, % 75.39/16.14 | | | | all_68_0) = v4 & $i(v3) & ( ~ (v4 = 0) | v2 = 0) & ( ~ % 75.39/16.14 | | | | (v2 = 0) | v4 = 0))) % 75.39/16.15 | | | | (193) ! [v0: $i] : ! [v1: $i] : ! [v2: any] : ( ~ % 75.39/16.15 | | | | (related(all_42_3, v0, v1) = v2) | ~ (element(v0, all_42_2) % 75.39/16.15 | | | | = 0) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: $i] : % 75.39/16.15 | | | | ? [v5: any] : (ordered_pair(v0, v1) = v4 & element(v1, % 75.39/16.15 | | | | all_42_2) = v3 & in(v4, all_68_0) = v5 & $i(v4) & ( ~ (v3 % 75.39/16.15 | | | | = 0) | (( ~ (v5 = 0) | v2 = 0) & ( ~ (v2 = 0) | v5 = % 75.39/16.15 | | | | 0))))) % 75.39/16.15 | | | | % 75.39/16.15 | | | | GROUND_INST: instantiating (192) with all_42_1, all_42_1, simplifying % 75.39/16.15 | | | | with (49), (51) gives: % 75.39/16.15 | | | | (194) ? [v0: any] : ? [v1: $i] : ? [v2: any] : (related(all_42_3, % 75.39/16.15 | | | | all_42_1, all_42_1) = v0 & ordered_pair(all_42_1, all_42_1) % 75.39/16.15 | | | | = v1 & in(v1, all_68_0) = v2 & $i(v1) & ( ~ (v2 = 0) | v0 = % 75.39/16.15 | | | | 0) & ( ~ (v0 = 0) | v2 = 0)) % 75.39/16.15 | | | | % 75.39/16.15 | | | | GROUND_INST: instantiating (192) with all_42_0, all_42_0, simplifying % 75.39/16.15 | | | | with (50), (52) gives: % 75.39/16.15 | | | | (195) ? [v0: any] : ? [v1: $i] : ? [v2: any] : (related(all_42_3, % 75.39/16.15 | | | | all_42_0, all_42_0) = v0 & ordered_pair(all_42_0, all_42_0) % 75.39/16.15 | | | | = v1 & in(v1, all_68_0) = v2 & $i(v1) & ( ~ (v2 = 0) | v0 = % 75.39/16.15 | | | | 0) & ( ~ (v0 = 0) | v2 = 0)) % 75.39/16.15 | | | | % 75.39/16.15 | | | | GROUND_INST: instantiating (192) with all_42_1, all_42_0, simplifying % 75.39/16.15 | | | | with (49), (50), (51), (52) gives: % 75.39/16.15 | | | | (196) ? [v0: any] : ? [v1: $i] : ? [v2: any] : (related(all_42_3, % 75.39/16.15 | | | | all_42_1, all_42_0) = v0 & ordered_pair(all_42_1, all_42_0) % 75.39/16.15 | | | | = v1 & in(v1, all_68_0) = v2 & $i(v1) & ( ~ (v2 = 0) | v0 = % 75.39/16.15 | | | | 0) & ( ~ (v0 = 0) | v2 = 0)) % 75.39/16.15 | | | | % 75.39/16.15 | | | | GROUND_INST: instantiating (192) with all_42_0, all_42_1, simplifying % 75.39/16.15 | | | | with (49), (50), (51), (52) gives: % 75.39/16.15 | | | | (197) ? [v0: any] : ? [v1: $i] : ? [v2: any] : (related(all_42_3, % 75.39/16.15 | | | | all_42_0, all_42_1) = v0 & ordered_pair(all_42_0, all_42_1) % 75.39/16.15 | | | | = v1 & in(v1, all_68_0) = v2 & $i(v1) & ( ~ (v2 = 0) | v0 = % 75.39/16.15 | | | | 0) & ( ~ (v0 = 0) | v2 = 0)) % 75.39/16.15 | | | | % 75.39/16.15 | | | | GROUND_INST: instantiating (193) with all_42_1, all_42_0, 0, simplifying % 75.39/16.15 | | | | with (49), (50), (51), (56) gives: % 75.39/16.15 | | | | (198) ? [v0: any] : ? [v1: $i] : ? [v2: any] : % 75.39/16.15 | | | | (ordered_pair(all_42_1, all_42_0) = v1 & element(all_42_0, % 75.39/16.15 | | | | all_42_2) = v0 & in(v1, all_68_0) = v2 & $i(v1) & ( ~ (v0 = % 75.39/16.15 | | | | 0) | v2 = 0)) % 75.39/16.15 | | | | % 75.39/16.15 | | | | GROUND_INST: instantiating (193) with all_42_0, all_42_1, 0, simplifying % 75.39/16.15 | | | | with (49), (50), (52), (57) gives: % 75.39/16.15 | | | | (199) ? [v0: any] : ? [v1: $i] : ? [v2: any] : % 75.39/16.15 | | | | (ordered_pair(all_42_0, all_42_1) = v1 & element(all_42_1, % 75.39/16.15 | | | | all_42_2) = v0 & in(v1, all_68_0) = v2 & $i(v1) & ( ~ (v0 = % 75.39/16.15 | | | | 0) | v2 = 0)) % 75.39/16.15 | | | | % 75.39/16.15 | | | | DELTA: instantiating (199) with fresh symbols all_102_0, all_102_1, % 75.39/16.15 | | | | all_102_2 gives: % 75.39/16.15 | | | | (200) ordered_pair(all_42_0, all_42_1) = all_102_1 & % 75.39/16.15 | | | | element(all_42_1, all_42_2) = all_102_2 & in(all_102_1, % 75.39/16.15 | | | | all_68_0) = all_102_0 & $i(all_102_1) & ( ~ (all_102_2 = 0) | % 75.39/16.15 | | | | all_102_0 = 0) % 75.39/16.15 | | | | % 75.39/16.15 | | | | ALPHA: (200) implies: % 75.39/16.15 | | | | (201) ordered_pair(all_42_0, all_42_1) = all_102_1 % 75.39/16.15 | | | | % 75.39/16.15 | | | | DELTA: instantiating (198) with fresh symbols all_104_0, all_104_1, % 75.39/16.15 | | | | all_104_2 gives: % 75.39/16.15 | | | | (202) ordered_pair(all_42_1, all_42_0) = all_104_1 & % 75.39/16.15 | | | | element(all_42_0, all_42_2) = all_104_2 & in(all_104_1, % 75.39/16.15 | | | | all_68_0) = all_104_0 & $i(all_104_1) & ( ~ (all_104_2 = 0) | % 75.39/16.15 | | | | all_104_0 = 0) % 75.39/16.15 | | | | % 75.39/16.15 | | | | ALPHA: (202) implies: % 75.39/16.15 | | | | (203) ordered_pair(all_42_1, all_42_0) = all_104_1 % 75.39/16.15 | | | | % 75.39/16.15 | | | | DELTA: instantiating (197) with fresh symbols all_106_0, all_106_1, % 75.39/16.15 | | | | all_106_2 gives: % 75.39/16.15 | | | | (204) related(all_42_3, all_42_0, all_42_1) = all_106_2 & % 75.39/16.15 | | | | ordered_pair(all_42_0, all_42_1) = all_106_1 & in(all_106_1, % 75.39/16.15 | | | | all_68_0) = all_106_0 & $i(all_106_1) & ( ~ (all_106_0 = 0) | % 75.39/16.15 | | | | all_106_2 = 0) & ( ~ (all_106_2 = 0) | all_106_0 = 0) % 75.39/16.15 | | | | % 75.39/16.15 | | | | ALPHA: (204) implies: % 75.39/16.15 | | | | (205) in(all_106_1, all_68_0) = all_106_0 % 75.39/16.15 | | | | (206) ordered_pair(all_42_0, all_42_1) = all_106_1 % 75.39/16.15 | | | | (207) related(all_42_3, all_42_0, all_42_1) = all_106_2 % 75.39/16.15 | | | | (208) ~ (all_106_2 = 0) | all_106_0 = 0 % 75.39/16.15 | | | | % 75.39/16.15 | | | | DELTA: instantiating (195) with fresh symbols all_108_0, all_108_1, % 75.39/16.15 | | | | all_108_2 gives: % 75.39/16.15 | | | | (209) related(all_42_3, all_42_0, all_42_0) = all_108_2 & % 75.39/16.15 | | | | ordered_pair(all_42_0, all_42_0) = all_108_1 & in(all_108_1, % 75.39/16.15 | | | | all_68_0) = all_108_0 & $i(all_108_1) & ( ~ (all_108_0 = 0) | % 75.39/16.15 | | | | all_108_2 = 0) & ( ~ (all_108_2 = 0) | all_108_0 = 0) % 75.39/16.15 | | | | % 75.39/16.15 | | | | ALPHA: (209) implies: % 75.39/16.15 | | | | (210) $i(all_108_1) % 75.39/16.15 | | | | (211) in(all_108_1, all_68_0) = all_108_0 % 75.39/16.15 | | | | (212) ordered_pair(all_42_0, all_42_0) = all_108_1 % 75.39/16.15 | | | | (213) ~ (all_108_2 = 0) | all_108_0 = 0 % 75.39/16.15 | | | | (214) ~ (all_108_0 = 0) | all_108_2 = 0 % 75.39/16.15 | | | | % 75.39/16.15 | | | | DELTA: instantiating (194) with fresh symbols all_110_0, all_110_1, % 75.39/16.15 | | | | all_110_2 gives: % 75.39/16.15 | | | | (215) related(all_42_3, all_42_1, all_42_1) = all_110_2 & % 75.39/16.15 | | | | ordered_pair(all_42_1, all_42_1) = all_110_1 & in(all_110_1, % 75.39/16.15 | | | | all_68_0) = all_110_0 & $i(all_110_1) & ( ~ (all_110_0 = 0) | % 75.39/16.15 | | | | all_110_2 = 0) & ( ~ (all_110_2 = 0) | all_110_0 = 0) % 75.39/16.15 | | | | % 75.39/16.15 | | | | ALPHA: (215) implies: % 75.39/16.15 | | | | (216) $i(all_110_1) % 75.39/16.15 | | | | (217) in(all_110_1, all_68_0) = all_110_0 % 75.39/16.15 | | | | (218) ordered_pair(all_42_1, all_42_1) = all_110_1 % 75.39/16.15 | | | | (219) ~ (all_110_0 = 0) | all_110_2 = 0 % 75.39/16.15 | | | | % 75.39/16.15 | | | | DELTA: instantiating (196) with fresh symbols all_112_0, all_112_1, % 75.39/16.15 | | | | all_112_2 gives: % 75.39/16.15 | | | | (220) related(all_42_3, all_42_1, all_42_0) = all_112_2 & % 75.39/16.15 | | | | ordered_pair(all_42_1, all_42_0) = all_112_1 & in(all_112_1, % 75.39/16.15 | | | | all_68_0) = all_112_0 & $i(all_112_1) & ( ~ (all_112_0 = 0) | % 75.39/16.15 | | | | all_112_2 = 0) & ( ~ (all_112_2 = 0) | all_112_0 = 0) % 75.39/16.15 | | | | % 75.39/16.15 | | | | ALPHA: (220) implies: % 75.39/16.15 | | | | (221) $i(all_112_1) % 75.39/16.15 | | | | (222) in(all_112_1, all_68_0) = all_112_0 % 75.39/16.15 | | | | (223) ordered_pair(all_42_1, all_42_0) = all_112_1 % 75.39/16.15 | | | | (224) related(all_42_3, all_42_1, all_42_0) = all_112_2 % 75.39/16.15 | | | | (225) ~ (all_112_2 = 0) | all_112_0 = 0 % 75.39/16.15 | | | | % 75.39/16.15 | | | | REDUCE: (178), (222) imply: % 75.39/16.15 | | | | (226) in(all_112_1, all_56_1) = all_112_0 % 75.39/16.15 | | | | % 75.39/16.15 | | | | REDUCE: (178), (217) imply: % 75.39/16.15 | | | | (227) in(all_110_1, all_56_1) = all_110_0 % 75.39/16.15 | | | | % 75.39/16.15 | | | | REDUCE: (178), (211) imply: % 75.39/16.15 | | | | (228) in(all_108_1, all_56_1) = all_108_0 % 75.39/16.15 | | | | % 75.39/16.15 | | | | REDUCE: (178), (205) imply: % 75.39/16.16 | | | | (229) in(all_106_1, all_56_1) = all_106_0 % 75.39/16.16 | | | | % 75.39/16.16 | | | | GROUND_INST: instantiating (32) with all_104_1, all_112_1, all_42_0, % 75.39/16.16 | | | | all_42_1, simplifying with (203), (223) gives: % 75.39/16.16 | | | | (230) all_112_1 = all_104_1 % 75.39/16.16 | | | | % 75.39/16.16 | | | | GROUND_INST: instantiating (32) with all_102_1, all_106_1, all_42_1, % 75.39/16.16 | | | | all_42_0, simplifying with (201), (206) gives: % 75.39/16.16 | | | | (231) all_106_1 = all_102_1 % 75.39/16.16 | | | | % 75.39/16.16 | | | | GROUND_INST: instantiating (34) with 0, all_112_2, all_42_0, all_42_1, % 75.39/16.16 | | | | all_42_3, simplifying with (56), (224) gives: % 75.39/16.16 | | | | (232) all_112_2 = 0 % 75.39/16.16 | | | | % 75.39/16.16 | | | | GROUND_INST: instantiating (34) with 0, all_106_2, all_42_1, all_42_0, % 75.39/16.16 | | | | all_42_3, simplifying with (57), (207) gives: % 75.39/16.16 | | | | (233) all_106_2 = 0 % 75.39/16.16 | | | | % 75.39/16.16 | | | | REDUCE: (226), (230) imply: % 75.39/16.16 | | | | (234) in(all_104_1, all_56_1) = all_112_0 % 75.39/16.16 | | | | % 75.39/16.16 | | | | REDUCE: (229), (231) imply: % 75.39/16.16 | | | | (235) in(all_102_1, all_56_1) = all_106_0 % 75.39/16.16 | | | | % 75.39/16.16 | | | | REDUCE: (221), (230) imply: % 75.39/16.16 | | | | (236) $i(all_104_1) % 75.39/16.16 | | | | % 75.39/16.16 | | | | BETA: splitting (225) gives: % 75.39/16.16 | | | | % 75.39/16.16 | | | | Case 1: % 75.39/16.16 | | | | | % 75.39/16.16 | | | | | (237) ~ (all_112_2 = 0) % 75.39/16.16 | | | | | % 75.39/16.16 | | | | | REDUCE: (232), (237) imply: % 75.39/16.16 | | | | | (238) $false % 75.39/16.16 | | | | | % 75.39/16.16 | | | | | CLOSE: (238) is inconsistent. % 75.39/16.16 | | | | | % 75.39/16.16 | | | | Case 2: % 75.39/16.16 | | | | | % 75.39/16.16 | | | | | (239) all_112_0 = 0 % 75.39/16.16 | | | | | % 75.39/16.16 | | | | | REDUCE: (234), (239) imply: % 75.39/16.16 | | | | | (240) in(all_104_1, all_56_1) = 0 % 75.39/16.16 | | | | | % 75.39/16.16 | | | | | BETA: splitting (208) gives: % 75.39/16.16 | | | | | % 75.39/16.16 | | | | | Case 1: % 75.39/16.16 | | | | | | % 75.39/16.16 | | | | | | (241) ~ (all_106_2 = 0) % 75.39/16.16 | | | | | | % 75.39/16.16 | | | | | | REDUCE: (233), (241) imply: % 75.39/16.16 | | | | | | (242) $false % 75.39/16.16 | | | | | | % 75.39/16.16 | | | | | | CLOSE: (242) is inconsistent. % 75.39/16.16 | | | | | | % 75.39/16.16 | | | | | Case 2: % 75.39/16.16 | | | | | | % 75.39/16.16 | | | | | | (243) all_106_0 = 0 % 75.39/16.16 | | | | | | % 75.39/16.16 | | | | | | REDUCE: (235), (243) imply: % 75.39/16.16 | | | | | | (244) in(all_102_1, all_56_1) = 0 % 75.39/16.16 | | | | | | % 75.39/16.16 | | | | | | GROUND_INST: instantiating (22) with all_104_1, all_56_1, empty_set, % 75.39/16.16 | | | | | | simplifying with (125), (126), (184), (236), (240) % 75.39/16.16 | | | | | | gives: % 75.39/16.16 | | | | | | (245) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & % 75.39/16.16 | | | | | | powerset(empty_set) = v0 & element(all_56_1, v0) = v1 & % 75.39/16.16 | | | | | | $i(v0)) % 75.39/16.16 | | | | | | % 75.39/16.16 | | | | | | GROUND_INST: instantiating (t7_boole) with all_104_1, all_56_1, % 75.39/16.16 | | | | | | simplifying with (184), (236), (240) gives: % 75.39/16.16 | | | | | | (246) ? [v0: int] : ( ~ (v0 = 0) & empty(all_56_1) = v0) % 75.39/16.16 | | | | | | % 75.39/16.16 | | | | | | GROUND_INST: instantiating (20) with all_108_1, all_56_1, all_108_0, % 75.39/16.16 | | | | | | simplifying with (184), (210), (228) gives: % 75.39/16.16 | | | | | | (247) all_108_0 = 0 | ? [v0: any] : ? [v1: any] : % 75.39/16.16 | | | | | | (empty(all_56_1) = v1 & element(all_108_1, all_56_1) = v0 & % 75.39/16.16 | | | | | | ( ~ (v0 = 0) | v1 = 0)) % 75.39/16.16 | | | | | | % 75.39/16.16 | | | | | | GROUND_INST: instantiating (20) with all_110_1, all_56_1, all_110_0, % 75.39/16.16 | | | | | | simplifying with (184), (216), (227) gives: % 75.39/16.16 | | | | | | (248) all_110_0 = 0 | ? [v0: any] : ? [v1: any] : % 75.39/16.16 | | | | | | (empty(all_56_1) = v1 & element(all_110_1, all_56_1) = v0 & % 75.39/16.16 | | | | | | ( ~ (v0 = 0) | v1 = 0)) % 75.39/16.16 | | | | | | % 75.39/16.16 | | | | | | GROUND_INST: instantiating (19) with all_80_1, all_80_2, simplifying % 75.39/16.16 | | | | | | with (132), (133), (134) gives: % 75.39/16.16 | | | | | | (249) ? [v0: any] : ? [v1: any] : (empty(all_80_2) = v0 & % 75.39/16.16 | | | | | | in(all_80_1, all_80_2) = v1 & (v1 = 0 | v0 = 0)) % 75.39/16.16 | | | | | | % 75.39/16.16 | | | | | | GROUND_INST: instantiating (15) with all_38_1, all_80_2, simplifying % 75.39/16.16 | | | | | | with (43), (135) gives: % 75.39/16.16 | | | | | | (250) ? [v0: int] : ? [v1: $i] : ? [v2: int] : ? [v3: int] : % 75.39/16.16 | | | | | | ($i(v1) & ((v2 = 0 & ~ (v3 = 0) & empty(v1) = v3 & % 75.39/16.16 | | | | | | element(v1, all_80_2) = 0) | (v0 = 0 & % 75.39/16.16 | | | | | | empty(all_38_1) = 0))) % 75.39/16.16 | | | | | | % 75.39/16.16 | | | | | | GROUND_INST: instantiating (fc1_subset_1) with all_38_1, all_80_2, % 75.39/16.16 | | | | | | simplifying with (43), (135) gives: % 75.39/16.16 | | | | | | (251) ? [v0: int] : ( ~ (v0 = 0) & empty(all_80_2) = v0) % 75.39/16.16 | | | | | | % 75.39/16.16 | | | | | | GROUND_INST: instantiating (rc2_subset_1) with all_38_1, all_80_2, % 75.39/16.16 | | | | | | simplifying with (43), (135) gives: % 75.39/16.16 | | | | | | (252) ? [v0: $i] : (empty(v0) = 0 & element(v0, all_80_2) = 0 & % 75.39/16.16 | | | | | | $i(v0)) % 75.39/16.16 | | | | | | % 75.39/16.16 | | | | | | GROUND_INST: instantiating (4) with all_42_1, all_42_1, all_110_1, % 75.39/16.16 | | | | | | simplifying with (49), (218) gives: % 75.39/16.16 | | | | | | (253) ? [v0: $i] : ? [v1: $i] : (singleton(all_42_1) = v1 & % 75.39/16.16 | | | | | | unordered_pair(v0, v1) = all_110_1 & % 75.39/16.16 | | | | | | unordered_pair(all_42_1, all_42_1) = v0 & $i(v1) & $i(v0) % 75.39/16.16 | | | | | | & $i(all_110_1)) % 75.39/16.16 | | | | | | % 75.39/16.16 | | | | | | GROUND_INST: instantiating (4) with all_42_1, all_42_0, all_104_1, % 75.39/16.16 | | | | | | simplifying with (49), (50), (203) gives: % 75.39/16.16 | | | | | | (254) ? [v0: $i] : ? [v1: $i] : (singleton(all_42_1) = v1 & % 75.39/16.16 | | | | | | unordered_pair(v0, v1) = all_104_1 & % 75.39/16.16 | | | | | | unordered_pair(all_42_1, all_42_0) = v0 & $i(v1) & $i(v0) % 75.39/16.16 | | | | | | & $i(all_104_1)) % 75.39/16.16 | | | | | | % 75.39/16.16 | | | | | | GROUND_INST: instantiating (4) with all_42_0, all_42_1, all_102_1, % 75.39/16.16 | | | | | | simplifying with (49), (50), (201) gives: % 75.39/16.16 | | | | | | (255) ? [v0: $i] : ? [v1: $i] : (singleton(all_42_0) = v1 & % 75.39/16.16 | | | | | | unordered_pair(v0, v1) = all_102_1 & % 75.39/16.16 | | | | | | unordered_pair(all_42_0, all_42_1) = v0 & $i(v1) & $i(v0) % 75.39/16.16 | | | | | | & $i(all_102_1)) % 75.39/16.16 | | | | | | % 75.39/16.16 | | | | | | GROUND_INST: instantiating (4) with all_42_0, all_42_0, all_108_1, % 75.39/16.16 | | | | | | simplifying with (50), (212) gives: % 75.39/16.16 | | | | | | (256) ? [v0: $i] : ? [v1: $i] : (singleton(all_42_0) = v1 & % 75.39/16.16 | | | | | | unordered_pair(v0, v1) = all_108_1 & % 75.39/16.16 | | | | | | unordered_pair(all_42_0, all_42_0) = v0 & $i(v1) & $i(v0) % 75.39/16.16 | | | | | | & $i(all_108_1)) % 75.39/16.16 | | | | | | % 75.39/16.16 | | | | | | GROUND_INST: instantiating (6) with all_35_0, all_54_0, simplifying % 75.39/16.16 | | | | | | with (39), (81) gives: % 75.39/16.16 | | | | | | (257) ? [v0: any] : ? [v1: any] : ? [v2: $i] : ? [v3: any] : % 75.39/16.16 | | | | | | (the_InternalRel(all_35_0) = v2 & rel_str(all_35_0) = v0 & % 75.39/16.16 | | | | | | antisymmetric_relstr(all_35_0) = v1 & % 75.39/16.16 | | | | | | is_antisymmetric_in(v2, all_54_0) = v3 & $i(v2) & ( ~ (v0 % 75.39/16.16 | | | | | | = 0) | (( ~ (v3 = 0) | v1 = 0) & ( ~ (v1 = 0) | v3 = % 75.39/16.16 | | | | | | 0)))) % 75.39/16.16 | | | | | | % 75.39/16.17 | | | | | | GROUND_INST: instantiating (10) with all_35_0, all_54_0, simplifying % 75.39/16.17 | | | | | | with (39), (81) gives: % 75.39/16.17 | | | | | | (258) ? [v0: any] : ? [v1: $i] : (the_InternalRel(all_35_0) = % 75.39/16.17 | | | | | | v1 & rel_str(all_35_0) = v0 & $i(v1) & ( ~ (v0 = 0) | ( ! % 75.39/16.17 | | | | | | [v2: $i] : ! [v3: $i] : ! [v4: any] : ( ~ % 75.39/16.17 | | | | | | (related(all_35_0, v2, v3) = v4) | ~ (element(v2, % 75.39/16.17 | | | | | | all_54_0) = 0) | ~ $i(v3) | ~ $i(v2) | ? % 75.39/16.17 | | | | | | [v5: any] : ? [v6: $i] : ? [v7: any] : % 75.39/16.17 | | | | | | (ordered_pair(v2, v3) = v6 & element(v3, all_54_0) % 75.39/16.17 | | | | | | = v5 & in(v6, v1) = v7 & $i(v6) & ( ~ (v5 = 0) | % 75.39/16.17 | | | | | | (( ~ (v7 = 0) | v4 = 0) & ( ~ (v4 = 0) | v7 = % 75.39/16.17 | | | | | | 0))))) & ! [v2: $i] : ! [v3: $i] : ! % 75.39/16.17 | | | | | | [v4: $i] : ( ~ (ordered_pair(v2, v3) = v4) | ~ % 75.39/16.17 | | | | | | (element(v2, all_54_0) = 0) | ~ $i(v3) | ~ $i(v2) % 75.39/16.17 | | | | | | | ? [v5: any] : ? [v6: any] : ? [v7: any] : % 75.39/16.17 | | | | | | (related(all_35_0, v2, v3) = v6 & element(v3, % 75.39/16.17 | | | | | | all_54_0) = v5 & in(v4, v1) = v7 & ( ~ (v5 = 0) % 75.39/16.17 | | | | | | | (( ~ (v7 = 0) | v6 = 0) & ( ~ (v6 = 0) | v7 = % 75.39/16.17 | | | | | | 0))))) & ! [v2: $i] : ! [v3: $i] : ( ~ % 75.39/16.17 | | | | | | (element(v3, all_54_0) = 0) | ~ (element(v2, % 75.39/16.17 | | | | | | all_54_0) = 0) | ~ $i(v3) | ~ $i(v2) | ? % 75.39/16.17 | | | | | | [v4: any] : ? [v5: $i] : ? [v6: any] : % 75.39/16.17 | | | | | | (related(all_35_0, v2, v3) = v4 & ordered_pair(v2, % 75.39/16.17 | | | | | | v3) = v5 & in(v5, v1) = v6 & $i(v5) & ( ~ (v6 = % 75.39/16.17 | | | | | | 0) | v4 = 0) & ( ~ (v4 = 0) | v6 = 0)))))) % 75.39/16.17 | | | | | | % 75.39/16.17 | | | | | | GROUND_INST: instantiating (7) with all_35_0, all_64_3, simplifying % 75.39/16.17 | | | | | | with (39), (107) gives: % 75.39/16.17 | | | | | | (259) ? [v0: any] : ? [v1: $i] : ? [v2: $i] : ? [v3: any] : % 75.39/16.17 | | | | | | (the_InternalRel(all_35_0) = v1 & rel_str(all_35_0) = v0 & % 75.39/16.17 | | | | | | the_carrier(all_35_0) = v2 & is_antisymmetric_in(v1, v2) % 75.39/16.17 | | | | | | = v3 & $i(v2) & $i(v1) & ( ~ (v0 = 0) | (( ~ (v3 = 0) | % 75.39/16.17 | | | | | | all_64_3 = 0) & ( ~ (all_64_3 = 0) | v3 = 0)))) % 75.39/16.17 | | | | | | % 75.39/16.17 | | | | | | GROUND_INST: instantiating (8) with all_35_0, all_54_1, simplifying % 75.39/16.17 | | | | | | with (39), (82) gives: % 75.39/16.17 | | | | | | (260) ? [v0: any] : ? [v1: any] : ? [v2: $i] : ? [v3: any] : % 75.39/16.17 | | | | | | (rel_str(all_35_0) = v0 & antisymmetric_relstr(all_35_0) = % 75.39/16.17 | | | | | | v1 & the_carrier(all_35_0) = v2 & % 75.39/16.17 | | | | | | is_antisymmetric_in(all_54_1, v2) = v3 & $i(v2) & ( ~ (v0 % 75.39/16.17 | | | | | | = 0) | (( ~ (v3 = 0) | v1 = 0) & ( ~ (v1 = 0) | v3 = % 75.39/16.17 | | | | | | 0)))) % 75.39/16.17 | | | | | | % 75.39/16.17 | | | | | | GROUND_INST: instantiating (11) with all_35_0, all_54_1, simplifying % 75.39/16.17 | | | | | | with (39), (82) gives: % 75.39/16.17 | | | | | | (261) ? [v0: any] : ? [v1: $i] : (rel_str(all_35_0) = v0 & % 75.39/16.17 | | | | | | the_carrier(all_35_0) = v1 & $i(v1) & ( ~ (v0 = 0) | ( ! % 75.39/16.17 | | | | | | [v2: $i] : ! [v3: $i] : ! [v4: any] : ( ~ % 75.39/16.17 | | | | | | (related(all_35_0, v2, v3) = v4) | ~ (element(v2, % 75.39/16.17 | | | | | | v1) = 0) | ~ $i(v3) | ~ $i(v2) | ? [v5: any] % 75.39/16.17 | | | | | | : ? [v6: $i] : ? [v7: any] : (ordered_pair(v2, % 75.39/16.17 | | | | | | v3) = v6 & element(v3, v1) = v5 & in(v6, % 75.39/16.17 | | | | | | all_54_1) = v7 & $i(v6) & ( ~ (v5 = 0) | (( ~ % 75.39/16.17 | | | | | | (v7 = 0) | v4 = 0) & ( ~ (v4 = 0) | v7 = % 75.39/16.17 | | | | | | 0))))) & ! [v2: $i] : ! [v3: $i] : ! % 75.39/16.17 | | | | | | [v4: $i] : ( ~ (ordered_pair(v2, v3) = v4) | ~ % 75.39/16.17 | | | | | | (element(v2, v1) = 0) | ~ $i(v3) | ~ $i(v2) | ? % 75.39/16.17 | | | | | | [v5: any] : ? [v6: any] : ? [v7: any] : % 75.39/16.17 | | | | | | (related(all_35_0, v2, v3) = v6 & element(v3, v1) = % 75.39/16.17 | | | | | | v5 & in(v4, all_54_1) = v7 & ( ~ (v5 = 0) | (( ~ % 75.39/16.17 | | | | | | (v7 = 0) | v6 = 0) & ( ~ (v6 = 0) | v7 = % 75.39/16.17 | | | | | | 0))))) & ! [v2: $i] : ! [v3: $i] : ( ~ % 75.39/16.17 | | | | | | (element(v3, v1) = 0) | ~ (element(v2, v1) = 0) | % 75.39/16.17 | | | | | | ~ $i(v3) | ~ $i(v2) | ? [v4: any] : ? [v5: $i] : % 75.39/16.17 | | | | | | ? [v6: any] : (related(all_35_0, v2, v3) = v4 & % 75.39/16.17 | | | | | | ordered_pair(v2, v3) = v5 & in(v5, all_54_1) = v6 % 75.39/16.17 | | | | | | & $i(v5) & ( ~ (v6 = 0) | v4 = 0) & ( ~ (v4 = 0) % 75.39/16.17 | | | | | | | v6 = 0)))))) % 75.39/16.17 | | | | | | % 75.39/16.17 | | | | | | GROUND_INST: instantiating (11) with all_42_3, all_56_1, simplifying % 75.39/16.17 | | | | | | with (47), (87) gives: % 75.39/16.17 | | | | | | (262) ? [v0: any] : ? [v1: $i] : (rel_str(all_42_3) = v0 & % 75.39/16.17 | | | | | | the_carrier(all_42_3) = v1 & $i(v1) & ( ~ (v0 = 0) | ( ! % 75.39/16.17 | | | | | | [v2: $i] : ! [v3: $i] : ! [v4: any] : ( ~ % 75.39/16.17 | | | | | | (related(all_42_3, v2, v3) = v4) | ~ (element(v2, % 75.39/16.17 | | | | | | v1) = 0) | ~ $i(v3) | ~ $i(v2) | ? [v5: any] % 75.39/16.17 | | | | | | : ? [v6: $i] : ? [v7: any] : (ordered_pair(v2, % 75.39/16.17 | | | | | | v3) = v6 & element(v3, v1) = v5 & in(v6, % 75.39/16.17 | | | | | | all_56_1) = v7 & $i(v6) & ( ~ (v5 = 0) | (( ~ % 75.39/16.17 | | | | | | (v7 = 0) | v4 = 0) & ( ~ (v4 = 0) | v7 = % 75.39/16.17 | | | | | | 0))))) & ! [v2: $i] : ! [v3: $i] : ! % 75.39/16.17 | | | | | | [v4: $i] : ( ~ (ordered_pair(v2, v3) = v4) | ~ % 75.39/16.17 | | | | | | (element(v2, v1) = 0) | ~ $i(v3) | ~ $i(v2) | ? % 75.39/16.17 | | | | | | [v5: any] : ? [v6: any] : ? [v7: any] : % 75.39/16.17 | | | | | | (related(all_42_3, v2, v3) = v6 & element(v3, v1) = % 75.39/16.17 | | | | | | v5 & in(v4, all_56_1) = v7 & ( ~ (v5 = 0) | (( ~ % 75.39/16.17 | | | | | | (v7 = 0) | v6 = 0) & ( ~ (v6 = 0) | v7 = % 75.39/16.17 | | | | | | 0))))) & ! [v2: $i] : ! [v3: $i] : ( ~ % 75.39/16.17 | | | | | | (element(v3, v1) = 0) | ~ (element(v2, v1) = 0) | % 75.39/16.17 | | | | | | ~ $i(v3) | ~ $i(v2) | ? [v4: any] : ? [v5: $i] : % 75.39/16.17 | | | | | | ? [v6: any] : (related(all_42_3, v2, v3) = v4 & % 75.39/16.17 | | | | | | ordered_pair(v2, v3) = v5 & in(v5, all_56_1) = v6 % 75.39/16.17 | | | | | | & $i(v5) & ( ~ (v6 = 0) | v4 = 0) & ( ~ (v4 = 0) % 75.39/16.17 | | | | | | | v6 = 0)))))) % 75.39/16.17 | | | | | | % 75.39/16.17 | | | | | | GROUND_INST: instantiating (12) with all_54_0, all_54_0, all_54_1, % 75.39/16.17 | | | | | | simplifying with (83), (182), (183) gives: % 75.39/16.17 | | | | | | (263) ? [v0: $i] : ? [v1: $i] : (cartesian_product2(all_54_0, % 75.39/16.17 | | | | | | all_54_0) = v0 & powerset(v0) = v1 & element(all_54_1, % 75.39/16.17 | | | | | | v1) = 0 & $i(v1) & $i(v0)) % 75.39/16.17 | | | | | | % 75.39/16.17 | | | | | | GROUND_INST: instantiating (12) with all_42_2, all_42_2, all_56_1, % 75.39/16.17 | | | | | | simplifying with (48), (179), (184) gives: % 75.39/16.17 | | | | | | (264) ? [v0: $i] : ? [v1: $i] : (cartesian_product2(all_42_2, % 75.39/16.17 | | | | | | all_42_2) = v0 & powerset(v0) = v1 & element(all_56_1, % 75.39/16.17 | | | | | | v1) = 0 & $i(v1) & $i(v0)) % 75.39/16.17 | | | | | | % 75.39/16.17 | | | | | | GROUND_INST: instantiating (16) with all_42_2, all_50_1, simplifying % 75.39/16.17 | | | | | | with (48), (74) gives: % 75.39/16.18 | | | | | | (265) all_50_1 = 0 | ? [v0: $i] : ? [v1: $i] : ? [v2: int] : ( % 75.39/16.18 | | | | | | ~ (v2 = 0) & empty(v1) = v2 & powerset(all_42_2) = v0 & % 75.39/16.18 | | | | | | element(v1, v0) = 0 & $i(v1) & $i(v0)) % 75.39/16.18 | | | | | | % 75.39/16.18 | | | | | | GROUND_INST: instantiating (16) with all_80_1, all_80_0, simplifying % 75.39/16.18 | | | | | | with (133), (136) gives: % 75.39/16.18 | | | | | | (266) all_80_0 = 0 | ? [v0: $i] : ? [v1: $i] : ? [v2: int] : ( % 75.39/16.18 | | | | | | ~ (v2 = 0) & empty(v1) = v2 & powerset(all_80_1) = v0 & % 75.39/16.18 | | | | | | element(v1, v0) = 0 & $i(v1) & $i(v0)) % 75.39/16.18 | | | | | | % 75.39/16.18 | | | | | | DELTA: instantiating (251) with fresh symbol all_150_0 gives: % 75.39/16.18 | | | | | | (267) ~ (all_150_0 = 0) & empty(all_80_2) = all_150_0 % 75.39/16.18 | | | | | | % 75.39/16.18 | | | | | | ALPHA: (267) implies: % 75.39/16.18 | | | | | | (268) ~ (all_150_0 = 0) % 75.39/16.18 | | | | | | (269) empty(all_80_2) = all_150_0 % 75.39/16.18 | | | | | | % 75.39/16.18 | | | | | | DELTA: instantiating (246) with fresh symbol all_154_0 gives: % 75.39/16.18 | | | | | | (270) ~ (all_154_0 = 0) & empty(all_56_1) = all_154_0 % 75.39/16.18 | | | | | | % 75.39/16.18 | | | | | | ALPHA: (270) implies: % 75.39/16.18 | | | | | | (271) ~ (all_154_0 = 0) % 75.39/16.18 | | | | | | (272) empty(all_56_1) = all_154_0 % 75.39/16.18 | | | | | | % 75.39/16.18 | | | | | | DELTA: instantiating (252) with fresh symbol all_156_0 gives: % 75.39/16.18 | | | | | | (273) empty(all_156_0) = 0 & element(all_156_0, all_80_2) = 0 & % 75.39/16.18 | | | | | | $i(all_156_0) % 75.39/16.18 | | | | | | % 75.39/16.18 | | | | | | ALPHA: (273) implies: % 75.39/16.18 | | | | | | (274) $i(all_156_0) % 75.39/16.18 | | | | | | (275) element(all_156_0, all_80_2) = 0 % 75.39/16.18 | | | | | | % 75.39/16.18 | | | | | | DELTA: instantiating (249) with fresh symbols all_158_0, all_158_1 % 75.39/16.18 | | | | | | gives: % 75.39/16.18 | | | | | | (276) empty(all_80_2) = all_158_1 & in(all_80_1, all_80_2) = % 75.39/16.18 | | | | | | all_158_0 & (all_158_0 = 0 | all_158_1 = 0) % 75.39/16.18 | | | | | | % 75.39/16.18 | | | | | | ALPHA: (276) implies: % 75.79/16.18 | | | | | | (277) empty(all_80_2) = all_158_1 % 75.79/16.18 | | | | | | (278) all_158_0 = 0 | all_158_1 = 0 % 75.79/16.18 | | | | | | % 75.79/16.18 | | | | | | DELTA: instantiating (245) with fresh symbols all_160_0, all_160_1 % 75.79/16.18 | | | | | | gives: % 75.79/16.18 | | | | | | (279) ~ (all_160_0 = 0) & powerset(empty_set) = all_160_1 & % 75.79/16.18 | | | | | | element(all_56_1, all_160_1) = all_160_0 & $i(all_160_1) % 75.79/16.18 | | | | | | % 75.79/16.18 | | | | | | ALPHA: (279) implies: % 75.79/16.18 | | | | | | (280) ~ (all_160_0 = 0) % 75.79/16.18 | | | | | | (281) $i(all_160_1) % 75.79/16.18 | | | | | | (282) element(all_56_1, all_160_1) = all_160_0 % 75.79/16.18 | | | | | | (283) powerset(empty_set) = all_160_1 % 75.79/16.18 | | | | | | % 75.79/16.18 | | | | | | DELTA: instantiating (264) with fresh symbols all_162_0, all_162_1 % 75.79/16.18 | | | | | | gives: % 75.79/16.18 | | | | | | (284) cartesian_product2(all_42_2, all_42_2) = all_162_1 & % 75.79/16.18 | | | | | | powerset(all_162_1) = all_162_0 & element(all_56_1, % 75.79/16.18 | | | | | | all_162_0) = 0 & $i(all_162_0) & $i(all_162_1) % 75.79/16.18 | | | | | | % 75.79/16.18 | | | | | | ALPHA: (284) implies: % 75.79/16.18 | | | | | | (285) $i(all_162_1) % 75.79/16.18 | | | | | | (286) element(all_56_1, all_162_0) = 0 % 75.79/16.18 | | | | | | (287) powerset(all_162_1) = all_162_0 % 75.79/16.18 | | | | | | (288) cartesian_product2(all_42_2, all_42_2) = all_162_1 % 75.79/16.18 | | | | | | % 75.79/16.18 | | | | | | DELTA: instantiating (263) with fresh symbols all_164_0, all_164_1 % 75.79/16.18 | | | | | | gives: % 75.79/16.18 | | | | | | (289) cartesian_product2(all_54_0, all_54_0) = all_164_1 & % 75.79/16.18 | | | | | | powerset(all_164_1) = all_164_0 & element(all_54_1, % 75.79/16.18 | | | | | | all_164_0) = 0 & $i(all_164_0) & $i(all_164_1) % 75.79/16.18 | | | | | | % 75.79/16.18 | | | | | | ALPHA: (289) implies: % 75.79/16.18 | | | | | | (290) $i(all_164_1) % 75.79/16.18 | | | | | | (291) element(all_54_1, all_164_0) = 0 % 75.79/16.18 | | | | | | (292) powerset(all_164_1) = all_164_0 % 75.79/16.18 | | | | | | (293) cartesian_product2(all_54_0, all_54_0) = all_164_1 % 75.79/16.18 | | | | | | % 75.79/16.18 | | | | | | DELTA: instantiating (256) with fresh symbols all_166_0, all_166_1 % 75.79/16.18 | | | | | | gives: % 75.79/16.18 | | | | | | (294) singleton(all_42_0) = all_166_0 & unordered_pair(all_166_1, % 75.79/16.18 | | | | | | all_166_0) = all_108_1 & unordered_pair(all_42_0, % 75.79/16.18 | | | | | | all_42_0) = all_166_1 & $i(all_166_0) & $i(all_166_1) & % 75.79/16.18 | | | | | | $i(all_108_1) % 75.79/16.18 | | | | | | % 75.79/16.18 | | | | | | ALPHA: (294) implies: % 75.79/16.18 | | | | | | (295) singleton(all_42_0) = all_166_0 % 75.79/16.18 | | | | | | % 75.79/16.18 | | | | | | DELTA: instantiating (255) with fresh symbols all_168_0, all_168_1 % 75.79/16.18 | | | | | | gives: % 75.79/16.18 | | | | | | (296) singleton(all_42_0) = all_168_0 & unordered_pair(all_168_1, % 75.79/16.18 | | | | | | all_168_0) = all_102_1 & unordered_pair(all_42_0, % 75.79/16.18 | | | | | | all_42_1) = all_168_1 & $i(all_168_0) & $i(all_168_1) & % 75.79/16.18 | | | | | | $i(all_102_1) % 75.79/16.18 | | | | | | % 75.79/16.18 | | | | | | ALPHA: (296) implies: % 75.79/16.18 | | | | | | (297) $i(all_102_1) % 75.79/16.18 | | | | | | (298) $i(all_168_0) % 75.79/16.18 | | | | | | (299) unordered_pair(all_42_0, all_42_1) = all_168_1 % 75.79/16.18 | | | | | | (300) unordered_pair(all_168_1, all_168_0) = all_102_1 % 75.79/16.18 | | | | | | (301) singleton(all_42_0) = all_168_0 % 75.79/16.18 | | | | | | % 75.79/16.18 | | | | | | DELTA: instantiating (254) with fresh symbols all_170_0, all_170_1 % 75.79/16.18 | | | | | | gives: % 75.79/16.18 | | | | | | (302) singleton(all_42_1) = all_170_0 & unordered_pair(all_170_1, % 75.79/16.18 | | | | | | all_170_0) = all_104_1 & unordered_pair(all_42_1, % 75.79/16.18 | | | | | | all_42_0) = all_170_1 & $i(all_170_0) & $i(all_170_1) & % 75.79/16.18 | | | | | | $i(all_104_1) % 75.79/16.18 | | | | | | % 75.79/16.18 | | | | | | ALPHA: (302) implies: % 75.79/16.18 | | | | | | (303) unordered_pair(all_42_1, all_42_0) = all_170_1 % 75.79/16.18 | | | | | | (304) unordered_pair(all_170_1, all_170_0) = all_104_1 % 75.79/16.18 | | | | | | (305) singleton(all_42_1) = all_170_0 % 75.79/16.18 | | | | | | % 75.79/16.18 | | | | | | DELTA: instantiating (253) with fresh symbols all_172_0, all_172_1 % 75.79/16.18 | | | | | | gives: % 75.79/16.18 | | | | | | (306) singleton(all_42_1) = all_172_0 & unordered_pair(all_172_1, % 75.79/16.18 | | | | | | all_172_0) = all_110_1 & unordered_pair(all_42_1, % 75.79/16.18 | | | | | | all_42_1) = all_172_1 & $i(all_172_0) & $i(all_172_1) & % 75.79/16.18 | | | | | | $i(all_110_1) % 75.79/16.18 | | | | | | % 75.79/16.18 | | | | | | ALPHA: (306) implies: % 75.79/16.18 | | | | | | (307) $i(all_172_0) % 75.79/16.18 | | | | | | (308) singleton(all_42_1) = all_172_0 % 75.79/16.18 | | | | | | % 75.79/16.18 | | | | | | DELTA: instantiating (250) with fresh symbols all_174_0, all_174_1, % 75.79/16.18 | | | | | | all_174_2, all_174_3 gives: % 75.79/16.18 | | | | | | (309) $i(all_174_2) & ((all_174_1 = 0 & ~ (all_174_0 = 0) & % 75.79/16.18 | | | | | | empty(all_174_2) = all_174_0 & element(all_174_2, % 75.79/16.18 | | | | | | all_80_2) = 0) | (all_174_3 = 0 & empty(all_38_1) = % 75.79/16.18 | | | | | | 0)) % 75.79/16.18 | | | | | | % 75.79/16.18 | | | | | | ALPHA: (309) implies: % 75.79/16.18 | | | | | | (310) $i(all_174_2) % 75.79/16.18 | | | | | | (311) (all_174_1 = 0 & ~ (all_174_0 = 0) & empty(all_174_2) = % 75.79/16.18 | | | | | | all_174_0 & element(all_174_2, all_80_2) = 0) | % 75.79/16.18 | | | | | | (all_174_3 = 0 & empty(all_38_1) = 0) % 75.79/16.18 | | | | | | % 75.79/16.18 | | | | | | DELTA: instantiating (260) with fresh symbols all_184_0, all_184_1, % 75.79/16.18 | | | | | | all_184_2, all_184_3 gives: % 75.79/16.18 | | | | | | (312) rel_str(all_35_0) = all_184_3 & % 75.79/16.18 | | | | | | antisymmetric_relstr(all_35_0) = all_184_2 & % 75.79/16.18 | | | | | | the_carrier(all_35_0) = all_184_1 & % 75.79/16.18 | | | | | | is_antisymmetric_in(all_54_1, all_184_1) = all_184_0 & % 75.79/16.18 | | | | | | $i(all_184_1) & ( ~ (all_184_3 = 0) | (( ~ (all_184_0 = 0) % 75.79/16.18 | | | | | | | all_184_2 = 0) & ( ~ (all_184_2 = 0) | all_184_0 = % 75.79/16.18 | | | | | | 0))) % 75.79/16.18 | | | | | | % 75.79/16.18 | | | | | | ALPHA: (312) implies: % 75.79/16.18 | | | | | | (313) $i(all_184_1) % 75.79/16.18 | | | | | | (314) is_antisymmetric_in(all_54_1, all_184_1) = all_184_0 % 75.79/16.18 | | | | | | (315) the_carrier(all_35_0) = all_184_1 % 75.79/16.18 | | | | | | % 75.79/16.18 | | | | | | DELTA: instantiating (257) with fresh symbols all_186_0, all_186_1, % 75.79/16.18 | | | | | | all_186_2, all_186_3 gives: % 75.79/16.18 | | | | | | (316) the_InternalRel(all_35_0) = all_186_1 & rel_str(all_35_0) = % 75.79/16.18 | | | | | | all_186_3 & antisymmetric_relstr(all_35_0) = all_186_2 & % 75.79/16.18 | | | | | | is_antisymmetric_in(all_186_1, all_54_0) = all_186_0 & % 75.79/16.18 | | | | | | $i(all_186_1) & ( ~ (all_186_3 = 0) | (( ~ (all_186_0 = 0) % 75.79/16.18 | | | | | | | all_186_2 = 0) & ( ~ (all_186_2 = 0) | all_186_0 = % 75.79/16.18 | | | | | | 0))) % 75.79/16.18 | | | | | | % 75.79/16.18 | | | | | | ALPHA: (316) implies: % 75.79/16.19 | | | | | | (317) $i(all_186_1) % 75.79/16.19 | | | | | | (318) is_antisymmetric_in(all_186_1, all_54_0) = all_186_0 % 75.79/16.19 | | | | | | (319) the_InternalRel(all_35_0) = all_186_1 % 75.79/16.19 | | | | | | % 75.79/16.19 | | | | | | DELTA: instantiating (259) with fresh symbols all_188_0, all_188_1, % 75.79/16.19 | | | | | | all_188_2, all_188_3 gives: % 75.79/16.19 | | | | | | (320) the_InternalRel(all_35_0) = all_188_2 & rel_str(all_35_0) = % 75.79/16.19 | | | | | | all_188_3 & the_carrier(all_35_0) = all_188_1 & % 75.79/16.19 | | | | | | is_antisymmetric_in(all_188_2, all_188_1) = all_188_0 & % 75.79/16.19 | | | | | | $i(all_188_1) & $i(all_188_2) & ( ~ (all_188_3 = 0) | (( ~ % 75.79/16.19 | | | | | | (all_188_0 = 0) | all_64_3 = 0) & ( ~ (all_64_3 = 0) % 75.79/16.19 | | | | | | | all_188_0 = 0))) % 75.79/16.19 | | | | | | % 75.79/16.19 | | | | | | ALPHA: (320) implies: % 75.79/16.19 | | | | | | (321) is_antisymmetric_in(all_188_2, all_188_1) = all_188_0 % 75.79/16.19 | | | | | | (322) the_carrier(all_35_0) = all_188_1 % 75.79/16.19 | | | | | | (323) the_InternalRel(all_35_0) = all_188_2 % 75.79/16.19 | | | | | | % 75.79/16.19 | | | | | | DELTA: instantiating (258) with fresh symbols all_190_0, all_190_1 % 75.79/16.19 | | | | | | gives: % 75.79/16.19 | | | | | | (324) the_InternalRel(all_35_0) = all_190_0 & rel_str(all_35_0) = % 75.79/16.19 | | | | | | all_190_1 & $i(all_190_0) & ( ~ (all_190_1 = 0) | ( ! [v0: % 75.79/16.19 | | | | | | $i] : ! [v1: $i] : ! [v2: any] : ( ~ % 75.79/16.19 | | | | | | (related(all_35_0, v0, v1) = v2) | ~ (element(v0, % 75.79/16.19 | | | | | | all_54_0) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v3: % 75.79/16.19 | | | | | | any] : ? [v4: $i] : ? [v5: any] : % 75.79/16.19 | | | | | | (ordered_pair(v0, v1) = v4 & element(v1, all_54_0) = % 75.79/16.19 | | | | | | v3 & in(v4, all_190_0) = v5 & $i(v4) & ( ~ (v3 = 0) % 75.79/16.19 | | | | | | | (( ~ (v5 = 0) | v2 = 0) & ( ~ (v2 = 0) | v5 = % 75.79/16.19 | | | | | | 0))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 75.79/16.19 | | | | | | $i] : ( ~ (ordered_pair(v0, v1) = v2) | ~ % 75.79/16.19 | | | | | | (element(v0, all_54_0) = 0) | ~ $i(v1) | ~ $i(v0) | % 75.79/16.19 | | | | | | ? [v3: any] : ? [v4: any] : ? [v5: any] : % 75.79/16.19 | | | | | | (related(all_35_0, v0, v1) = v4 & element(v1, % 75.79/16.19 | | | | | | all_54_0) = v3 & in(v2, all_190_0) = v5 & ( ~ (v3 % 75.79/16.19 | | | | | | = 0) | (( ~ (v5 = 0) | v4 = 0) & ( ~ (v4 = 0) | % 75.79/16.19 | | | | | | v5 = 0))))) & ! [v0: $i] : ! [v1: $i] : ( ~ % 75.79/16.19 | | | | | | (element(v1, all_54_0) = 0) | ~ (element(v0, % 75.79/16.19 | | | | | | all_54_0) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: % 75.79/16.19 | | | | | | any] : ? [v3: $i] : ? [v4: any] : % 75.79/16.19 | | | | | | (related(all_35_0, v0, v1) = v2 & ordered_pair(v0, % 75.79/16.19 | | | | | | v1) = v3 & in(v3, all_190_0) = v4 & $i(v3) & ( ~ % 75.79/16.19 | | | | | | (v4 = 0) | v2 = 0) & ( ~ (v2 = 0) | v4 = 0))))) % 75.79/16.19 | | | | | | % 75.84/16.19 | | | | | | ALPHA: (324) implies: % 75.84/16.19 | | | | | | (325) the_InternalRel(all_35_0) = all_190_0 % 75.84/16.19 | | | | | | % 75.84/16.19 | | | | | | DELTA: instantiating (262) with fresh symbols all_192_0, all_192_1 % 75.84/16.19 | | | | | | gives: % 75.84/16.19 | | | | | | (326) rel_str(all_42_3) = all_192_1 & the_carrier(all_42_3) = % 75.84/16.19 | | | | | | all_192_0 & $i(all_192_0) & ( ~ (all_192_1 = 0) | ( ! [v0: % 75.84/16.19 | | | | | | $i] : ! [v1: $i] : ! [v2: any] : ( ~ % 75.84/16.19 | | | | | | (related(all_42_3, v0, v1) = v2) | ~ (element(v0, % 75.84/16.19 | | | | | | all_192_0) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v3: % 75.84/16.19 | | | | | | any] : ? [v4: $i] : ? [v5: any] : % 75.84/16.19 | | | | | | (ordered_pair(v0, v1) = v4 & element(v1, all_192_0) = % 75.84/16.19 | | | | | | v3 & in(v4, all_56_1) = v5 & $i(v4) & ( ~ (v3 = 0) % 75.84/16.19 | | | | | | | (( ~ (v5 = 0) | v2 = 0) & ( ~ (v2 = 0) | v5 = % 75.84/16.19 | | | | | | 0))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 75.84/16.19 | | | | | | $i] : ( ~ (ordered_pair(v0, v1) = v2) | ~ % 75.84/16.19 | | | | | | (element(v0, all_192_0) = 0) | ~ $i(v1) | ~ $i(v0) % 75.84/16.19 | | | | | | | ? [v3: any] : ? [v4: any] : ? [v5: any] : % 75.84/16.19 | | | | | | (related(all_42_3, v0, v1) = v4 & element(v1, % 75.84/16.19 | | | | | | all_192_0) = v3 & in(v2, all_56_1) = v5 & ( ~ (v3 % 75.84/16.19 | | | | | | = 0) | (( ~ (v5 = 0) | v4 = 0) & ( ~ (v4 = 0) | % 75.84/16.19 | | | | | | v5 = 0))))) & ! [v0: $i] : ! [v1: $i] : ( ~ % 75.84/16.19 | | | | | | (element(v1, all_192_0) = 0) | ~ (element(v0, % 75.84/16.19 | | | | | | all_192_0) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: % 75.84/16.19 | | | | | | any] : ? [v3: $i] : ? [v4: any] : % 75.84/16.19 | | | | | | (related(all_42_3, v0, v1) = v2 & ordered_pair(v0, % 75.84/16.19 | | | | | | v1) = v3 & in(v3, all_56_1) = v4 & $i(v3) & ( ~ % 75.84/16.19 | | | | | | (v4 = 0) | v2 = 0) & ( ~ (v2 = 0) | v4 = 0))))) % 75.84/16.19 | | | | | | % 75.84/16.19 | | | | | | ALPHA: (326) implies: % 75.84/16.19 | | | | | | (327) $i(all_192_0) % 75.84/16.19 | | | | | | (328) the_carrier(all_42_3) = all_192_0 % 75.84/16.19 | | | | | | % 75.84/16.19 | | | | | | DELTA: instantiating (261) with fresh symbols all_194_0, all_194_1 % 75.84/16.19 | | | | | | gives: % 75.84/16.19 | | | | | | (329) rel_str(all_35_0) = all_194_1 & the_carrier(all_35_0) = % 75.84/16.19 | | | | | | all_194_0 & $i(all_194_0) & ( ~ (all_194_1 = 0) | ( ! [v0: % 75.84/16.19 | | | | | | $i] : ! [v1: $i] : ! [v2: any] : ( ~ % 75.84/16.19 | | | | | | (related(all_35_0, v0, v1) = v2) | ~ (element(v0, % 75.84/16.19 | | | | | | all_194_0) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v3: % 75.84/16.19 | | | | | | any] : ? [v4: $i] : ? [v5: any] : % 75.84/16.19 | | | | | | (ordered_pair(v0, v1) = v4 & element(v1, all_194_0) = % 75.84/16.19 | | | | | | v3 & in(v4, all_54_1) = v5 & $i(v4) & ( ~ (v3 = 0) % 75.84/16.19 | | | | | | | (( ~ (v5 = 0) | v2 = 0) & ( ~ (v2 = 0) | v5 = % 75.84/16.19 | | | | | | 0))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 75.84/16.19 | | | | | | $i] : ( ~ (ordered_pair(v0, v1) = v2) | ~ % 75.84/16.19 | | | | | | (element(v0, all_194_0) = 0) | ~ $i(v1) | ~ $i(v0) % 75.84/16.19 | | | | | | | ? [v3: any] : ? [v4: any] : ? [v5: any] : % 75.84/16.19 | | | | | | (related(all_35_0, v0, v1) = v4 & element(v1, % 75.84/16.19 | | | | | | all_194_0) = v3 & in(v2, all_54_1) = v5 & ( ~ (v3 % 75.84/16.19 | | | | | | = 0) | (( ~ (v5 = 0) | v4 = 0) & ( ~ (v4 = 0) | % 75.84/16.19 | | | | | | v5 = 0))))) & ! [v0: $i] : ! [v1: $i] : ( ~ % 75.84/16.19 | | | | | | (element(v1, all_194_0) = 0) | ~ (element(v0, % 75.84/16.19 | | | | | | all_194_0) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: % 75.84/16.19 | | | | | | any] : ? [v3: $i] : ? [v4: any] : % 75.84/16.19 | | | | | | (related(all_35_0, v0, v1) = v2 & ordered_pair(v0, % 75.84/16.19 | | | | | | v1) = v3 & in(v3, all_54_1) = v4 & $i(v3) & ( ~ % 75.84/16.19 | | | | | | (v4 = 0) | v2 = 0) & ( ~ (v2 = 0) | v4 = 0))))) % 75.84/16.19 | | | | | | % 75.84/16.19 | | | | | | ALPHA: (329) implies: % 75.84/16.19 | | | | | | (330) the_carrier(all_35_0) = all_194_0 % 75.84/16.19 | | | | | | % 75.84/16.19 | | | | | | BETA: splitting (311) gives: % 75.84/16.19 | | | | | | % 75.84/16.19 | | | | | | Case 1: % 75.84/16.19 | | | | | | | % 75.84/16.19 | | | | | | | (331) all_174_1 = 0 & ~ (all_174_0 = 0) & empty(all_174_2) = % 75.84/16.19 | | | | | | | all_174_0 & element(all_174_2, all_80_2) = 0 % 75.84/16.19 | | | | | | | % 75.84/16.19 | | | | | | | ALPHA: (331) implies: % 75.84/16.19 | | | | | | | (332) element(all_174_2, all_80_2) = 0 % 75.84/16.19 | | | | | | | % 75.84/16.19 | | | | | | | BETA: splitting (266) gives: % 75.84/16.19 | | | | | | | % 75.84/16.19 | | | | | | | Case 1: % 75.84/16.19 | | | | | | | | % 75.84/16.19 | | | | | | | | (333) all_80_0 = 0 % 75.84/16.19 | | | | | | | | % 75.84/16.19 | | | | | | | | REDUCE: (131), (333) imply: % 75.84/16.19 | | | | | | | | (334) $false % 75.84/16.19 | | | | | | | | % 75.84/16.19 | | | | | | | | CLOSE: (334) is inconsistent. % 75.84/16.19 | | | | | | | | % 75.84/16.19 | | | | | | | Case 2: % 75.84/16.19 | | | | | | | | % 75.84/16.19 | | | | | | | | (335) ? [v0: $i] : ? [v1: $i] : ? [v2: int] : ( ~ (v2 = 0) % 75.84/16.19 | | | | | | | | & empty(v1) = v2 & powerset(all_80_1) = v0 & % 75.84/16.19 | | | | | | | | element(v1, v0) = 0 & $i(v1) & $i(v0)) % 75.84/16.20 | | | | | | | | % 75.84/16.20 | | | | | | | | DELTA: instantiating (335) with fresh symbols all_203_0, % 75.84/16.20 | | | | | | | | all_203_1, all_203_2 gives: % 75.84/16.20 | | | | | | | | (336) ~ (all_203_0 = 0) & empty(all_203_1) = all_203_0 & % 75.84/16.20 | | | | | | | | powerset(all_80_1) = all_203_2 & element(all_203_1, % 75.84/16.20 | | | | | | | | all_203_2) = 0 & $i(all_203_1) & $i(all_203_2) % 75.84/16.20 | | | | | | | | % 75.84/16.20 | | | | | | | | ALPHA: (336) implies: % 75.84/16.20 | | | | | | | | (337) $i(all_203_2) % 75.84/16.20 | | | | | | | | (338) $i(all_203_1) % 75.84/16.20 | | | | | | | | (339) element(all_203_1, all_203_2) = 0 % 75.84/16.20 | | | | | | | | (340) powerset(all_80_1) = all_203_2 % 75.84/16.20 | | | | | | | | % 75.84/16.20 | | | | | | | | GROUND_INST: instantiating (25) with all_170_0, all_172_0, % 75.84/16.20 | | | | | | | | all_42_1, simplifying with (305), (308) gives: % 75.84/16.20 | | | | | | | | (341) all_172_0 = all_170_0 % 75.84/16.20 | | | | | | | | % 75.84/16.20 | | | | | | | | GROUND_INST: instantiating (25) with all_166_0, all_168_0, % 75.84/16.20 | | | | | | | | all_42_0, simplifying with (295), (301) gives: % 75.84/16.20 | | | | | | | | (342) all_168_0 = all_166_0 % 75.84/16.20 | | | | | | | | % 75.84/16.20 | | | | | | | | GROUND_INST: instantiating (26) with all_184_1, all_188_1, % 75.84/16.20 | | | | | | | | all_35_0, simplifying with (315), (322) gives: % 75.84/16.20 | | | | | | | | (343) all_188_1 = all_184_1 % 75.84/16.20 | | | | | | | | % 75.84/16.20 | | | | | | | | GROUND_INST: instantiating (26) with all_54_0, all_194_0, % 75.84/16.20 | | | | | | | | all_35_0, simplifying with (81), (330) gives: % 75.84/16.20 | | | | | | | | (344) all_194_0 = all_54_0 % 75.84/16.20 | | | | | | | | % 75.84/16.20 | | | | | | | | GROUND_INST: instantiating (26) with all_188_1, all_194_0, % 75.84/16.20 | | | | | | | | all_35_0, simplifying with (322), (330) gives: % 75.84/16.20 | | | | | | | | (345) all_194_0 = all_188_1 % 75.84/16.20 | | | | | | | | % 75.84/16.20 | | | | | | | | GROUND_INST: instantiating (26) with all_42_2, all_192_0, % 75.84/16.20 | | | | | | | | all_42_3, simplifying with (53), (328) gives: % 75.84/16.20 | | | | | | | | (346) all_192_0 = all_42_2 % 75.84/16.20 | | | | | | | | % 75.84/16.20 | | | | | | | | GROUND_INST: instantiating (29) with all_186_1, all_188_2, % 75.84/16.20 | | | | | | | | all_35_0, simplifying with (319), (323) gives: % 75.84/16.20 | | | | | | | | (347) all_188_2 = all_186_1 % 75.84/16.20 | | | | | | | | % 75.84/16.20 | | | | | | | | GROUND_INST: instantiating (29) with all_54_1, all_190_0, % 75.84/16.20 | | | | | | | | all_35_0, simplifying with (82), (325) gives: % 75.84/16.20 | | | | | | | | (348) all_190_0 = all_54_1 % 75.84/16.20 | | | | | | | | % 75.84/16.20 | | | | | | | | GROUND_INST: instantiating (29) with all_188_2, all_190_0, % 75.84/16.20 | | | | | | | | all_35_0, simplifying with (323), (325) gives: % 75.84/16.20 | | | | | | | | (349) all_190_0 = all_188_2 % 75.84/16.20 | | | | | | | | % 75.84/16.20 | | | | | | | | GROUND_INST: instantiating (30) with all_150_0, all_158_1, % 75.84/16.20 | | | | | | | | all_80_2, simplifying with (269), (277) gives: % 75.84/16.20 | | | | | | | | (350) all_158_1 = all_150_0 % 75.84/16.20 | | | | | | | | % 75.84/16.20 | | | | | | | | COMBINE_EQS: (344), (345) imply: % 75.84/16.20 | | | | | | | | (351) all_188_1 = all_54_0 % 75.84/16.20 | | | | | | | | % 75.84/16.20 | | | | | | | | SIMP: (351) implies: % 75.84/16.20 | | | | | | | | (352) all_188_1 = all_54_0 % 75.84/16.20 | | | | | | | | % 75.84/16.20 | | | | | | | | COMBINE_EQS: (348), (349) imply: % 75.84/16.20 | | | | | | | | (353) all_188_2 = all_54_1 % 75.84/16.20 | | | | | | | | % 75.84/16.20 | | | | | | | | SIMP: (353) implies: % 75.84/16.20 | | | | | | | | (354) all_188_2 = all_54_1 % 75.84/16.20 | | | | | | | | % 75.84/16.20 | | | | | | | | COMBINE_EQS: (343), (352) imply: % 75.84/16.20 | | | | | | | | (355) all_184_1 = all_54_0 % 75.84/16.20 | | | | | | | | % 75.84/16.20 | | | | | | | | SIMP: (355) implies: % 75.84/16.20 | | | | | | | | (356) all_184_1 = all_54_0 % 75.84/16.20 | | | | | | | | % 75.84/16.20 | | | | | | | | COMBINE_EQS: (347), (354) imply: % 75.84/16.20 | | | | | | | | (357) all_186_1 = all_54_1 % 75.84/16.20 | | | | | | | | % 75.84/16.20 | | | | | | | | REDUCE: (321), (352), (354) imply: % 75.84/16.20 | | | | | | | | (358) is_antisymmetric_in(all_54_1, all_54_0) = all_188_0 % 75.84/16.20 | | | | | | | | % 75.84/16.20 | | | | | | | | REDUCE: (318), (357) imply: % 75.84/16.20 | | | | | | | | (359) is_antisymmetric_in(all_54_1, all_54_0) = all_186_0 % 75.84/16.20 | | | | | | | | % 75.84/16.20 | | | | | | | | REDUCE: (314), (356) imply: % 75.84/16.20 | | | | | | | | (360) is_antisymmetric_in(all_54_1, all_54_0) = all_184_0 % 75.84/16.20 | | | | | | | | % 75.84/16.20 | | | | | | | | REDUCE: (300), (342) imply: % 75.84/16.20 | | | | | | | | (361) unordered_pair(all_168_1, all_166_0) = all_102_1 % 75.84/16.20 | | | | | | | | % 75.84/16.20 | | | | | | | | REDUCE: (307), (341) imply: % 75.84/16.20 | | | | | | | | (362) $i(all_170_0) % 75.84/16.20 | | | | | | | | % 75.84/16.20 | | | | | | | | REDUCE: (298), (342) imply: % 75.84/16.20 | | | | | | | | (363) $i(all_166_0) % 75.84/16.20 | | | | | | | | % 75.84/16.20 | | | | | | | | BETA: splitting (278) gives: % 75.84/16.20 | | | | | | | | % 75.84/16.20 | | | | | | | | Case 1: % 75.84/16.20 | | | | | | | | | % 75.84/16.20 | | | | | | | | | % 75.84/16.20 | | | | | | | | | GROUND_INST: instantiating (33) with all_64_0, all_186_0, % 75.84/16.20 | | | | | | | | | all_54_0, all_54_1, simplifying with (180), (359) % 75.84/16.20 | | | | | | | | | gives: % 75.84/16.20 | | | | | | | | | (364) all_186_0 = all_64_0 % 75.84/16.20 | | | | | | | | | % 75.84/16.20 | | | | | | | | | GROUND_INST: instantiating (33) with all_186_0, all_188_0, % 75.84/16.20 | | | | | | | | | all_54_0, all_54_1, simplifying with (358), (359) % 75.84/16.20 | | | | | | | | | gives: % 75.84/16.20 | | | | | | | | | (365) all_188_0 = all_186_0 % 75.84/16.20 | | | | | | | | | % 75.84/16.20 | | | | | | | | | GROUND_INST: instantiating (33) with all_184_0, all_188_0, % 75.84/16.20 | | | | | | | | | all_54_0, all_54_1, simplifying with (358), (360) % 75.84/16.20 | | | | | | | | | gives: % 75.84/16.20 | | | | | | | | | (366) all_188_0 = all_184_0 % 75.84/16.20 | | | | | | | | | % 75.84/16.20 | | | | | | | | | COMBINE_EQS: (365), (366) imply: % 75.84/16.20 | | | | | | | | | (367) all_186_0 = all_184_0 % 75.84/16.20 | | | | | | | | | % 75.84/16.20 | | | | | | | | | SIMP: (367) implies: % 75.84/16.20 | | | | | | | | | (368) all_186_0 = all_184_0 % 75.84/16.20 | | | | | | | | | % 75.84/16.20 | | | | | | | | | COMBINE_EQS: (364), (368) imply: % 75.84/16.20 | | | | | | | | | (369) all_184_0 = all_64_0 % 75.84/16.20 | | | | | | | | | % 75.84/16.20 | | | | | | | | | GROUND_INST: instantiating (18) with all_56_1, all_160_1, % 75.84/16.20 | | | | | | | | | all_160_0, simplifying with (184), (281), (282) % 75.84/16.20 | | | | | | | | | gives: % 75.84/16.20 | | | | | | | | | (370) all_160_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & % 75.84/16.20 | | | | | | | | | in(all_56_1, all_160_1) = v0) % 75.84/16.20 | | | | | | | | | % 75.84/16.20 | | | | | | | | | GROUND_INST: instantiating (19) with all_156_0, all_80_2, % 75.84/16.20 | | | | | | | | | simplifying with (132), (274), (275) gives: % 75.84/16.20 | | | | | | | | | (371) ? [v0: any] : ? [v1: any] : (empty(all_80_2) = v0 & % 75.84/16.20 | | | | | | | | | in(all_156_0, all_80_2) = v1 & (v1 = 0 | v0 = 0)) % 75.84/16.20 | | | | | | | | | % 75.84/16.20 | | | | | | | | | GROUND_INST: instantiating (19) with all_174_2, all_80_2, % 75.84/16.20 | | | | | | | | | simplifying with (132), (310), (332) gives: % 75.84/16.20 | | | | | | | | | (372) ? [v0: any] : ? [v1: any] : (empty(all_80_2) = v0 & % 75.84/16.20 | | | | | | | | | in(all_174_2, all_80_2) = v1 & (v1 = 0 | v0 = 0)) % 75.84/16.20 | | | | | | | | | % 75.84/16.20 | | | | | | | | | GROUND_INST: instantiating (19) with all_203_1, all_203_2, % 75.84/16.20 | | | | | | | | | simplifying with (337), (338), (339) gives: % 75.84/16.20 | | | | | | | | | (373) ? [v0: any] : ? [v1: any] : (empty(all_203_2) = v0 % 75.84/16.20 | | | | | | | | | & in(all_203_1, all_203_2) = v1 & (v1 = 0 | v0 = % 75.84/16.20 | | | | | | | | | 0)) % 75.84/16.20 | | | | | | | | | % 75.84/16.20 | | | | | | | | | GROUND_INST: instantiating (rc2_subset_1) with empty_set, % 75.84/16.20 | | | | | | | | | all_160_1, simplifying with (126), (283) gives: % 75.84/16.20 | | | | | | | | | (374) ? [v0: $i] : (empty(v0) = 0 & element(v0, all_160_1) % 75.84/16.20 | | | | | | | | | = 0 & $i(v0)) % 75.84/16.20 | | | | | | | | | % 75.84/16.20 | | | | | | | | | GROUND_INST: instantiating (fc1_subset_1) with all_80_1, % 75.84/16.20 | | | | | | | | | all_203_2, simplifying with (133), (340) gives: % 75.84/16.20 | | | | | | | | | (375) ? [v0: int] : ( ~ (v0 = 0) & empty(all_203_2) = v0) % 75.84/16.20 | | | | | | | | | % 75.84/16.20 | | | | | | | | | GROUND_INST: instantiating (rc2_subset_1) with all_80_1, % 75.84/16.20 | | | | | | | | | all_203_2, simplifying with (133), (340) gives: % 75.84/16.20 | | | | | | | | | (376) ? [v0: $i] : (empty(v0) = 0 & element(v0, all_203_2) % 75.84/16.20 | | | | | | | | | = 0 & $i(v0)) % 75.84/16.20 | | | | | | | | | % 75.84/16.20 | | | | | | | | | GROUND_INST: instantiating (21) with all_104_1, all_56_1, % 75.84/16.20 | | | | | | | | | all_162_1, all_162_0, simplifying with (184), % 75.84/16.20 | | | | | | | | | (236), (240), (285), (286), (287) gives: % 75.84/16.20 | | | | | | | | | (377) element(all_104_1, all_162_1) = 0 % 75.84/16.20 | | | | | | | | | % 75.84/16.20 | | | | | | | | | GROUND_INST: instantiating (21) with all_102_1, all_56_1, % 75.84/16.20 | | | | | | | | | all_162_1, all_162_0, simplifying with (184), % 75.84/16.20 | | | | | | | | | (244), (285), (286), (287), (297) gives: % 75.84/16.20 | | | | | | | | | (378) element(all_102_1, all_162_1) = 0 % 75.84/16.20 | | | | | | | | | % 75.84/16.20 | | | | | | | | | GROUND_INST: instantiating (23) with all_102_1, all_56_1, % 75.84/16.20 | | | | | | | | | all_162_1, all_162_0, simplifying with (184), % 75.84/16.20 | | | | | | | | | (244), (285), (286), (287), (297) gives: % 75.84/16.20 | | | | | | | | | (379) ? [v0: int] : ( ~ (v0 = 0) & empty(all_162_1) = v0) % 75.84/16.21 | | | | | | | | | % 75.84/16.21 | | | | | | | | | GROUND_INST: instantiating (rc2_subset_1) with all_162_1, % 75.84/16.21 | | | | | | | | | all_162_0, simplifying with (285), (287) gives: % 75.84/16.21 | | | | | | | | | (380) ? [v0: $i] : (empty(v0) = 0 & element(v0, all_162_0) % 75.84/16.21 | | | | | | | | | = 0 & $i(v0)) % 75.84/16.21 | | | | | | | | | % 75.84/16.21 | | | | | | | | | GROUND_INST: instantiating (rc2_subset_1) with all_164_1, % 75.84/16.21 | | | | | | | | | all_164_0, simplifying with (290), (292) gives: % 75.84/16.21 | | | | | | | | | (381) ? [v0: $i] : (empty(v0) = 0 & element(v0, all_164_0) % 75.84/16.21 | | | | | | | | | = 0 & $i(v0)) % 75.84/16.21 | | | | | | | | | % 75.84/16.21 | | | | | | | | | GROUND_INST: instantiating (cc1_relset_1) with all_42_2, % 75.84/16.21 | | | | | | | | | all_42_2, all_56_1, all_162_1, all_162_0, % 75.84/16.21 | | | | | | | | | simplifying with (48), (184), (286), (287), (288) % 75.84/16.21 | | | | | | | | | gives: % 75.84/16.21 | | | | | | | | | (382) relation(all_56_1) = 0 % 75.84/16.21 | | | | | | | | | % 75.84/16.21 | | | | | | | | | GROUND_INST: instantiating (fc4_subset_1) with all_42_2, % 75.84/16.21 | | | | | | | | | all_42_2, all_162_1, simplifying with (48), (288) % 75.84/16.21 | | | | | | | | | gives: % 75.84/16.21 | | | | | | | | | (383) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 75.84/16.21 | | | | | | | | | (empty(all_162_1) = v2 & empty(all_42_2) = v1 & % 75.84/16.21 | | | | | | | | | empty(all_42_2) = v0 & ( ~ (v2 = 0) | v1 = 0 | v0 = % 75.84/16.21 | | | | | | | | | 0)) % 75.84/16.21 | | | | | | | | | % 75.84/16.21 | | | | | | | | | GROUND_INST: instantiating (cc1_relset_1) with all_54_0, % 75.84/16.21 | | | | | | | | | all_54_0, all_54_1, all_164_1, all_164_0, % 75.84/16.21 | | | | | | | | | simplifying with (182), (183), (291), (292), (293) % 75.84/16.21 | | | | | | | | | gives: % 75.84/16.21 | | | | | | | | | (384) relation(all_54_1) = 0 % 75.84/16.21 | | | | | | | | | % 75.84/16.21 | | | | | | | | | GROUND_INST: instantiating (fc4_subset_1) with all_54_0, % 75.84/16.21 | | | | | | | | | all_54_0, all_164_1, simplifying with (182), (293) % 75.84/16.21 | | | | | | | | | gives: % 75.84/16.21 | | | | | | | | | (385) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 75.84/16.21 | | | | | | | | | (empty(all_164_1) = v2 & empty(all_54_0) = v1 & % 75.84/16.21 | | | | | | | | | empty(all_54_0) = v0 & ( ~ (v2 = 0) | v1 = 0 | v0 = % 75.84/16.21 | | | | | | | | | 0)) % 75.84/16.21 | | | | | | | | | % 75.84/16.21 | | | | | | | | | GROUND_INST: instantiating (1) with all_42_0, all_42_1, % 75.84/16.21 | | | | | | | | | all_170_1, simplifying with (49), (50), (303) % 75.84/16.21 | | | | | | | | | gives: % 75.84/16.21 | | | | | | | | | (386) unordered_pair(all_42_0, all_42_1) = all_170_1 & % 75.84/16.21 | | | | | | | | | $i(all_170_1) % 75.84/16.21 | | | | | | | | | % 75.84/16.21 | | | | | | | | | ALPHA: (386) implies: % 75.84/16.21 | | | | | | | | | (387) $i(all_170_1) % 75.84/16.21 | | | | | | | | | % 75.84/16.21 | | | | | | | | | GROUND_INST: instantiating (1) with all_42_1, all_42_0, % 75.84/16.21 | | | | | | | | | all_168_1, simplifying with (49), (50), (299) % 75.84/16.21 | | | | | | | | | gives: % 75.84/16.21 | | | | | | | | | (388) unordered_pair(all_42_1, all_42_0) = all_168_1 & % 75.84/16.21 | | | | | | | | | $i(all_168_1) % 75.84/16.21 | | | | | | | | | % 75.84/16.21 | | | | | | | | | ALPHA: (388) implies: % 75.84/16.21 | | | | | | | | | (389) $i(all_168_1) % 75.84/16.21 | | | | | | | | | % 75.84/16.21 | | | | | | | | | GROUND_INST: instantiating (1) with all_166_0, all_168_1, % 75.84/16.21 | | | | | | | | | all_102_1, simplifying with (361), (363), (389) % 75.84/16.21 | | | | | | | | | gives: % 75.84/16.21 | | | | | | | | | (390) unordered_pair(all_166_0, all_168_1) = all_102_1 & % 75.84/16.21 | | | | | | | | | $i(all_102_1) % 75.84/16.21 | | | | | | | | | % 75.84/16.21 | | | | | | | | | GROUND_INST: instantiating (1) with all_170_0, all_170_1, % 75.84/16.21 | | | | | | | | | all_104_1, simplifying with (304), (362), (387) % 75.84/16.21 | | | | | | | | | gives: % 75.84/16.21 | | | | | | | | | (391) unordered_pair(all_170_0, all_170_1) = all_104_1 & % 75.84/16.21 | | | | | | | | | $i(all_104_1) % 75.84/16.21 | | | | | | | | | % 75.84/16.21 | | | | | | | | | GROUND_INST: instantiating (16) with all_80_2, all_150_0, % 75.84/16.21 | | | | | | | | | simplifying with (132), (269) gives: % 75.94/16.21 | | | | | | | | | (392) all_150_0 = 0 | ? [v0: $i] : ? [v1: $i] : ? [v2: % 75.94/16.21 | | | | | | | | | int] : ( ~ (v2 = 0) & empty(v1) = v2 & % 75.94/16.21 | | | | | | | | | powerset(all_80_2) = v0 & element(v1, v0) = 0 & % 75.94/16.21 | | | | | | | | | $i(v1) & $i(v0)) % 75.94/16.21 | | | | | | | | | % 75.94/16.21 | | | | | | | | | DELTA: instantiating (379) with fresh symbol all_256_0 gives: % 75.94/16.21 | | | | | | | | | (393) ~ (all_256_0 = 0) & empty(all_162_1) = all_256_0 % 75.94/16.21 | | | | | | | | | % 75.94/16.21 | | | | | | | | | ALPHA: (393) implies: % 75.94/16.21 | | | | | | | | | (394) ~ (all_256_0 = 0) % 75.94/16.21 | | | | | | | | | (395) empty(all_162_1) = all_256_0 % 75.94/16.21 | | | | | | | | | % 75.94/16.21 | | | | | | | | | DELTA: instantiating (375) with fresh symbol all_282_0 gives: % 75.94/16.21 | | | | | | | | | (396) ~ (all_282_0 = 0) & empty(all_203_2) = all_282_0 % 75.94/16.21 | | | | | | | | | % 75.94/16.21 | | | | | | | | | ALPHA: (396) implies: % 75.94/16.21 | | | | | | | | | (397) ~ (all_282_0 = 0) % 75.94/16.21 | | | | | | | | | (398) empty(all_203_2) = all_282_0 % 75.94/16.21 | | | | | | | | | % 75.94/16.21 | | | | | | | | | DELTA: instantiating (380) with fresh symbol all_288_0 gives: % 75.94/16.21 | | | | | | | | | (399) empty(all_288_0) = 0 & element(all_288_0, all_162_0) % 75.94/16.21 | | | | | | | | | = 0 & $i(all_288_0) % 75.94/16.21 | | | | | | | | | % 75.94/16.21 | | | | | | | | | ALPHA: (399) implies: % 75.94/16.21 | | | | | | | | | (400) $i(all_288_0) % 75.94/16.21 | | | | | | | | | (401) empty(all_288_0) = 0 % 75.94/16.21 | | | | | | | | | % 75.94/16.21 | | | | | | | | | DELTA: instantiating (374) with fresh symbol all_290_0 gives: % 75.94/16.21 | | | | | | | | | (402) empty(all_290_0) = 0 & element(all_290_0, all_160_1) % 75.94/16.21 | | | | | | | | | = 0 & $i(all_290_0) % 75.94/16.21 | | | | | | | | | % 75.94/16.21 | | | | | | | | | ALPHA: (402) implies: % 75.94/16.21 | | | | | | | | | (403) $i(all_290_0) % 75.94/16.21 | | | | | | | | | (404) empty(all_290_0) = 0 % 75.94/16.21 | | | | | | | | | % 75.94/16.21 | | | | | | | | | DELTA: instantiating (381) with fresh symbol all_292_0 gives: % 75.94/16.21 | | | | | | | | | (405) empty(all_292_0) = 0 & element(all_292_0, all_164_0) % 75.94/16.21 | | | | | | | | | = 0 & $i(all_292_0) % 75.94/16.21 | | | | | | | | | % 75.94/16.21 | | | | | | | | | ALPHA: (405) implies: % 75.94/16.21 | | | | | | | | | (406) $i(all_292_0) % 75.94/16.21 | | | | | | | | | (407) empty(all_292_0) = 0 % 75.94/16.21 | | | | | | | | | % 75.94/16.21 | | | | | | | | | DELTA: instantiating (376) with fresh symbol all_294_0 gives: % 75.94/16.21 | | | | | | | | | (408) empty(all_294_0) = 0 & element(all_294_0, all_203_2) % 75.94/16.21 | | | | | | | | | = 0 & $i(all_294_0) % 75.94/16.21 | | | | | | | | | % 75.94/16.21 | | | | | | | | | ALPHA: (408) implies: % 75.94/16.21 | | | | | | | | | (409) $i(all_294_0) % 75.94/16.21 | | | | | | | | | (410) empty(all_294_0) = 0 % 75.94/16.21 | | | | | | | | | % 75.94/16.21 | | | | | | | | | DELTA: instantiating (371) with fresh symbols all_300_0, % 75.94/16.21 | | | | | | | | | all_300_1 gives: % 75.94/16.21 | | | | | | | | | (411) empty(all_80_2) = all_300_1 & in(all_156_0, all_80_2) % 75.94/16.21 | | | | | | | | | = all_300_0 & (all_300_0 = 0 | all_300_1 = 0) % 75.94/16.21 | | | | | | | | | % 75.94/16.21 | | | | | | | | | ALPHA: (411) implies: % 75.94/16.21 | | | | | | | | | (412) empty(all_80_2) = all_300_1 % 75.94/16.21 | | | | | | | | | % 75.94/16.21 | | | | | | | | | DELTA: instantiating (373) with fresh symbols all_306_0, % 75.94/16.21 | | | | | | | | | all_306_1 gives: % 75.94/16.21 | | | | | | | | | (413) empty(all_203_2) = all_306_1 & in(all_203_1, % 75.94/16.21 | | | | | | | | | all_203_2) = all_306_0 & (all_306_0 = 0 | all_306_1 % 75.94/16.21 | | | | | | | | | = 0) % 75.94/16.21 | | | | | | | | | % 75.94/16.21 | | | | | | | | | ALPHA: (413) implies: % 75.94/16.21 | | | | | | | | | (414) empty(all_203_2) = all_306_1 % 75.94/16.21 | | | | | | | | | % 75.94/16.21 | | | | | | | | | DELTA: instantiating (372) with fresh symbols all_308_0, % 75.94/16.21 | | | | | | | | | all_308_1 gives: % 75.94/16.21 | | | | | | | | | (415) empty(all_80_2) = all_308_1 & in(all_174_2, all_80_2) % 75.94/16.21 | | | | | | | | | = all_308_0 & (all_308_0 = 0 | all_308_1 = 0) % 75.94/16.21 | | | | | | | | | % 75.94/16.21 | | | | | | | | | ALPHA: (415) implies: % 75.94/16.21 | | | | | | | | | (416) empty(all_80_2) = all_308_1 % 75.94/16.21 | | | | | | | | | % 75.94/16.21 | | | | | | | | | DELTA: instantiating (385) with fresh symbols all_322_0, % 75.94/16.21 | | | | | | | | | all_322_1, all_322_2 gives: % 75.94/16.21 | | | | | | | | | (417) empty(all_164_1) = all_322_0 & empty(all_54_0) = % 75.94/16.21 | | | | | | | | | all_322_1 & empty(all_54_0) = all_322_2 & ( ~ % 75.94/16.21 | | | | | | | | | (all_322_0 = 0) | all_322_1 = 0 | all_322_2 = 0) % 75.94/16.21 | | | | | | | | | % 75.94/16.21 | | | | | | | | | ALPHA: (417) implies: % 75.94/16.21 | | | | | | | | | (418) empty(all_54_0) = all_322_2 % 75.94/16.21 | | | | | | | | | (419) empty(all_54_0) = all_322_1 % 75.94/16.21 | | | | | | | | | (420) empty(all_164_1) = all_322_0 % 75.94/16.21 | | | | | | | | | (421) ~ (all_322_0 = 0) | all_322_1 = 0 | all_322_2 = 0 % 75.94/16.21 | | | | | | | | | % 75.94/16.21 | | | | | | | | | DELTA: instantiating (383) with fresh symbols all_324_0, % 75.94/16.21 | | | | | | | | | all_324_1, all_324_2 gives: % 75.94/16.21 | | | | | | | | | (422) empty(all_162_1) = all_324_0 & empty(all_42_2) = % 75.94/16.21 | | | | | | | | | all_324_1 & empty(all_42_2) = all_324_2 & ( ~ % 75.94/16.21 | | | | | | | | | (all_324_0 = 0) | all_324_1 = 0 | all_324_2 = 0) % 75.94/16.21 | | | | | | | | | % 75.94/16.21 | | | | | | | | | ALPHA: (422) implies: % 75.94/16.21 | | | | | | | | | (423) empty(all_42_2) = all_324_2 % 75.94/16.21 | | | | | | | | | (424) empty(all_42_2) = all_324_1 % 75.94/16.21 | | | | | | | | | (425) empty(all_162_1) = all_324_0 % 75.94/16.21 | | | | | | | | | % 75.94/16.21 | | | | | | | | | BETA: splitting (392) gives: % 75.94/16.21 | | | | | | | | | % 75.94/16.21 | | | | | | | | | Case 1: % 75.94/16.21 | | | | | | | | | | % 75.94/16.21 | | | | | | | | | | (426) all_150_0 = 0 % 75.94/16.21 | | | | | | | | | | % 75.94/16.21 | | | | | | | | | | REDUCE: (268), (426) imply: % 75.94/16.21 | | | | | | | | | | (427) $false % 75.94/16.21 | | | | | | | | | | % 75.94/16.21 | | | | | | | | | | CLOSE: (427) is inconsistent. % 75.94/16.21 | | | | | | | | | | % 75.94/16.21 | | | | | | | | | Case 2: % 75.94/16.21 | | | | | | | | | | % 75.94/16.21 | | | | | | | | | | (428) ? [v0: $i] : ? [v1: $i] : ? [v2: int] : ( ~ (v2 % 75.94/16.21 | | | | | | | | | | = 0) & empty(v1) = v2 & powerset(all_80_2) = v0 % 75.94/16.21 | | | | | | | | | | & element(v1, v0) = 0 & $i(v1) & $i(v0)) % 75.94/16.21 | | | | | | | | | | % 75.94/16.21 | | | | | | | | | | DELTA: instantiating (428) with fresh symbols all_350_0, % 75.94/16.21 | | | | | | | | | | all_350_1, all_350_2 gives: % 75.94/16.21 | | | | | | | | | | (429) ~ (all_350_0 = 0) & empty(all_350_1) = all_350_0 & % 75.94/16.22 | | | | | | | | | | powerset(all_80_2) = all_350_2 & element(all_350_1, % 75.94/16.22 | | | | | | | | | | all_350_2) = 0 & $i(all_350_1) & $i(all_350_2) % 75.94/16.22 | | | | | | | | | | % 75.94/16.22 | | | | | | | | | | ALPHA: (429) implies: % 75.94/16.22 | | | | | | | | | | (430) powerset(all_80_2) = all_350_2 % 75.94/16.22 | | | | | | | | | | % 75.94/16.22 | | | | | | | | | | BETA: splitting (370) gives: % 75.94/16.22 | | | | | | | | | | % 75.94/16.22 | | | | | | | | | | Case 1: % 75.94/16.22 | | | | | | | | | | | % 75.94/16.22 | | | | | | | | | | | (431) all_160_0 = 0 % 75.94/16.22 | | | | | | | | | | | % 75.94/16.22 | | | | | | | | | | | REDUCE: (280), (431) imply: % 75.94/16.22 | | | | | | | | | | | (432) $false % 75.94/16.22 | | | | | | | | | | | % 75.94/16.22 | | | | | | | | | | | CLOSE: (432) is inconsistent. % 75.94/16.22 | | | | | | | | | | | % 75.94/16.22 | | | | | | | | | | Case 2: % 75.94/16.22 | | | | | | | | | | | % 75.94/16.22 | | | | | | | | | | | % 75.94/16.22 | | | | | | | | | | | GROUND_INST: instantiating (30) with all_50_1, all_324_1, % 75.94/16.22 | | | | | | | | | | | all_42_2, simplifying with (74), (424) gives: % 75.94/16.22 | | | | | | | | | | | (433) all_324_1 = all_50_1 % 75.94/16.22 | | | | | | | | | | | % 75.94/16.22 | | | | | | | | | | | GROUND_INST: instantiating (30) with all_324_2, all_324_1, % 75.94/16.22 | | | | | | | | | | | all_42_2, simplifying with (423), (424) gives: % 75.94/16.22 | | | | | | | | | | | (434) all_324_1 = all_324_2 % 75.94/16.22 | | | | | | | | | | | % 75.94/16.22 | | | | | | | | | | | GROUND_INST: instantiating (30) with all_322_2, all_322_1, % 75.94/16.22 | | | | | | | | | | | all_54_0, simplifying with (418), (419) gives: % 75.94/16.22 | | | | | | | | | | | (435) all_322_1 = all_322_2 % 75.94/16.22 | | | | | | | | | | | % 75.94/16.22 | | | | | | | | | | | GROUND_INST: instantiating (30) with all_150_0, all_308_1, % 75.94/16.22 | | | | | | | | | | | all_80_2, simplifying with (269), (416) gives: % 75.94/16.22 | | | | | | | | | | | (436) all_308_1 = all_150_0 % 75.94/16.22 | | | | | | | | | | | % 75.94/16.22 | | | | | | | | | | | GROUND_INST: instantiating (30) with all_300_1, all_308_1, % 75.94/16.22 | | | | | | | | | | | all_80_2, simplifying with (412), (416) gives: % 75.94/16.22 | | | | | | | | | | | (437) all_308_1 = all_300_1 % 75.94/16.22 | | | | | | | | | | | % 75.94/16.22 | | | | | | | | | | | GROUND_INST: instantiating (30) with all_256_0, all_324_0, % 75.94/16.22 | | | | | | | | | | | all_162_1, simplifying with (395), (425) gives: % 75.94/16.22 | | | | | | | | | | | (438) all_324_0 = all_256_0 % 75.94/16.22 | | | | | | | | | | | % 75.94/16.22 | | | | | | | | | | | GROUND_INST: instantiating (30) with all_282_0, all_306_1, % 75.94/16.22 | | | | | | | | | | | all_203_2, simplifying with (398), (414) gives: % 75.97/16.22 | | | | | | | | | | | (439) all_306_1 = all_282_0 % 75.97/16.22 | | | | | | | | | | | % 75.97/16.22 | | | | | | | | | | | COMBINE_EQS: (433), (434) imply: % 75.97/16.22 | | | | | | | | | | | (440) all_324_2 = all_50_1 % 75.97/16.22 | | | | | | | | | | | % 75.97/16.22 | | | | | | | | | | | COMBINE_EQS: (436), (437) imply: % 75.97/16.22 | | | | | | | | | | | (441) all_300_1 = all_150_0 % 75.97/16.22 | | | | | | | | | | | % 75.97/16.22 | | | | | | | | | | | BETA: splitting (75) gives: % 75.97/16.22 | | | | | | | | | | | % 75.97/16.22 | | | | | | | | | | | Case 1: % 75.97/16.22 | | | | | | | | | | | | % 75.97/16.22 | | | | | | | | | | | | (442) all_50_0 = 0 % 75.97/16.22 | | | | | | | | | | | | % 75.97/16.22 | | | | | | | | | | | | REDUCE: (73), (442) imply: % 75.97/16.22 | | | | | | | | | | | | (443) in(all_42_0, all_42_2) = 0 % 75.97/16.22 | | | | | | | | | | | | % 75.97/16.22 | | | | | | | | | | | | BETA: splitting (79) gives: % 75.97/16.22 | | | | | | | | | | | | % 75.97/16.22 | | | | | | | | | | | | Case 1: % 75.97/16.22 | | | | | | | | | | | | | % 75.97/16.22 | | | | | | | | | | | | | (444) all_52_0 = 0 % 75.97/16.22 | | | | | | | | | | | | | % 75.97/16.22 | | | | | | | | | | | | | REDUCE: (77), (444) imply: % 75.97/16.22 | | | | | | | | | | | | | (445) in(all_42_1, all_42_2) = 0 % 75.97/16.22 | | | | | | | | | | | | | % 75.97/16.22 | | | | | | | | | | | | | BETA: splitting (265) gives: % 75.97/16.22 | | | | | | | | | | | | | % 75.97/16.22 | | | | | | | | | | | | | Case 1: % 75.97/16.22 | | | | | | | | | | | | | | % 75.97/16.22 | | | | | | | | | | | | | | (446) all_50_1 = 0 % 75.97/16.22 | | | | | | | | | | | | | | % 75.97/16.22 | | | | | | | | | | | | | | REDUCE: (74), (446) imply: % 75.97/16.22 | | | | | | | | | | | | | | (447) empty(all_42_2) = 0 % 75.97/16.22 | | | | | | | | | | | | | | % 75.97/16.22 | | | | | | | | | | | | | | REF_CLOSE: (24), (30), (48), (50), (219), (248), (271), % 75.97/16.22 | | | | | | | | | | | | | | (272), (400), (401), (403), (404), (406), (407), % 75.97/16.22 | | | | | | | | | | | | | | (409), (410), (443), (447), (t7_boole), (t8_boole) % 75.97/16.22 | | | | | | | | | | | | | | are inconsistent by sub-proof #3. % 75.97/16.22 | | | | | | | | | | | | | | % 75.97/16.22 | | | | | | | | | | | | | Case 2: % 75.97/16.22 | | | | | | | | | | | | | | % 75.97/16.22 | | | | | | | | | | | | | | % 75.97/16.22 | | | | | | | | | | | | | | GROUND_INST: instantiating (3) with all_56_1, all_42_2, % 75.97/16.22 | | | | | | | | | | | | | | all_42_1, all_42_0, all_102_1, simplifying with % 75.97/16.22 | | | | | | | | | | | | | | (48), (49), (50), (184), (188), (201), (382) % 75.97/16.22 | | | | | | | | | | | | | | gives: % 75.97/16.22 | | | | | | | | | | | | | | (448) all_42_0 = all_42_1 | ? [v0: any] : ? [v1: any] % 75.97/16.22 | | | | | | | | | | | | | | : ? [v2: $i] : ? [v3: any] : ? [v4: any] : % 75.97/16.22 | | | | | | | | | | | | | | (ordered_pair(all_42_1, all_42_0) = v2 & in(v2, % 75.97/16.22 | | | | | | | | | | | | | | all_56_1) = v3 & in(all_102_1, all_56_1) = v4 % 75.97/16.22 | | | | | | | | | | | | | | & in(all_42_0, all_42_2) = v1 & in(all_42_1, % 75.97/16.22 | | | | | | | | | | | | | | all_42_2) = v0 & $i(v2) & ( ~ (v4 = 0) | ~ % 75.97/16.22 | | | | | | | | | | | | | | (v3 = 0) | ~ (v1 = 0) | ~ (v0 = 0))) % 75.97/16.22 | | | | | | | | | | | | | | % 75.97/16.22 | | | | | | | | | | | | | | GROUND_INST: instantiating (2) with all_56_1, all_42_2, % 75.97/16.22 | | | | | | | | | | | | | | all_42_0, all_42_1, all_102_1, simplifying with % 75.97/16.22 | | | | | | | | | | | | | | (48), (49), (50), (184), (188), (201), (382) % 75.97/16.22 | | | | | | | | | | | | | | gives: % 75.97/16.22 | | | | | | | | | | | | | | (449) all_42_0 = all_42_1 | ? [v0: any] : ? [v1: any] % 75.97/16.22 | | | | | | | | | | | | | | : ? [v2: any] : ? [v3: $i] : ? [v4: any] : % 75.97/16.22 | | | | | | | | | | | | | | (ordered_pair(all_42_1, all_42_0) = v3 & in(v3, % 75.97/16.22 | | | | | | | | | | | | | | all_56_1) = v4 & in(all_102_1, all_56_1) = v2 % 75.97/16.22 | | | | | | | | | | | | | | & in(all_42_0, all_42_2) = v0 & in(all_42_1, % 75.97/16.22 | | | | | | | | | | | | | | all_42_2) = v1 & $i(v3) & ( ~ (v4 = 0) | ~ % 75.97/16.22 | | | | | | | | | | | | | | (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0))) % 75.97/16.22 | | | | | | | | | | | | | | % 75.97/16.22 | | | | | | | | | | | | | | GROUND_INST: instantiating (2) with all_56_1, all_42_2, % 75.97/16.22 | | | | | | | | | | | | | | all_42_1, all_42_0, all_104_1, simplifying with % 75.97/16.22 | | | | | | | | | | | | | | (48), (49), (50), (184), (188), (203), (382) % 75.97/16.22 | | | | | | | | | | | | | | gives: % 75.97/16.22 | | | | | | | | | | | | | | (450) all_42_0 = all_42_1 | ? [v0: any] : ? [v1: any] % 75.97/16.22 | | | | | | | | | | | | | | : ? [v2: any] : ? [v3: $i] : ? [v4: any] : % 75.97/16.22 | | | | | | | | | | | | | | (ordered_pair(all_42_0, all_42_1) = v3 & in(v3, % 75.97/16.22 | | | | | | | | | | | | | | all_56_1) = v4 & in(all_104_1, all_56_1) = v2 % 75.97/16.22 | | | | | | | | | | | | | | & in(all_42_0, all_42_2) = v1 & in(all_42_1, % 75.97/16.22 | | | | | | | | | | | | | | all_42_2) = v0 & $i(v3) & ( ~ (v4 = 0) | ~ % 75.97/16.22 | | | | | | | | | | | | | | (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0))) % 75.97/16.22 | | | | | | | | | | | | | | % 75.97/16.22 | | | | | | | | | | | | | | BETA: splitting (450) gives: % 75.97/16.22 | | | | | | | | | | | | | | % 75.97/16.22 | | | | | | | | | | | | | | Case 1: % 75.97/16.22 | | | | | | | | | | | | | | | % 75.97/16.22 | | | | | | | | | | | | | | | (451) all_42_0 = all_42_1 % 75.97/16.22 | | | | | | | | | | | | | | | % 75.97/16.22 | | | | | | | | | | | | | | | REDUCE: (46), (451) imply: % 75.97/16.22 | | | | | | | | | | | | | | | (452) $false % 75.97/16.22 | | | | | | | | | | | | | | | % 75.97/16.22 | | | | | | | | | | | | | | | CLOSE: (452) is inconsistent. % 75.97/16.22 | | | | | | | | | | | | | | | % 75.97/16.22 | | | | | | | | | | | | | | Case 2: % 75.97/16.22 | | | | | | | | | | | | | | | % 75.97/16.22 | | | | | | | | | | | | | | | (453) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? % 75.97/16.22 | | | | | | | | | | | | | | | [v3: $i] : ? [v4: any] : (ordered_pair(all_42_0, % 75.97/16.22 | | | | | | | | | | | | | | | all_42_1) = v3 & in(v3, all_56_1) = v4 & % 75.97/16.22 | | | | | | | | | | | | | | | in(all_104_1, all_56_1) = v2 & in(all_42_0, % 75.97/16.22 | | | | | | | | | | | | | | | all_42_2) = v1 & in(all_42_1, all_42_2) = v0 & % 75.97/16.22 | | | | | | | | | | | | | | | $i(v3) & ( ~ (v4 = 0) | ~ (v2 = 0) | ~ (v1 = % 75.97/16.22 | | | | | | | | | | | | | | | 0) | ~ (v0 = 0))) % 75.97/16.22 | | | | | | | | | | | | | | | % 75.97/16.22 | | | | | | | | | | | | | | | DELTA: instantiating (453) with fresh symbols all_650_0, % 75.97/16.22 | | | | | | | | | | | | | | | all_650_1, all_650_2, all_650_3, all_650_4 gives: % 75.97/16.22 | | | | | | | | | | | | | | | (454) ordered_pair(all_42_0, all_42_1) = all_650_1 & % 75.97/16.22 | | | | | | | | | | | | | | | in(all_650_1, all_56_1) = all_650_0 & % 75.97/16.22 | | | | | | | | | | | | | | | in(all_104_1, all_56_1) = all_650_2 & in(all_42_0, % 75.97/16.22 | | | | | | | | | | | | | | | all_42_2) = all_650_3 & in(all_42_1, all_42_2) = % 75.97/16.22 | | | | | | | | | | | | | | | all_650_4 & $i(all_650_1) & ( ~ (all_650_0 = 0) | % 75.97/16.22 | | | | | | | | | | | | | | | ~ (all_650_2 = 0) | ~ (all_650_3 = 0) | ~ % 75.97/16.22 | | | | | | | | | | | | | | | (all_650_4 = 0)) % 75.97/16.22 | | | | | | | | | | | | | | | % 75.97/16.22 | | | | | | | | | | | | | | | ALPHA: (454) implies: % 75.97/16.22 | | | | | | | | | | | | | | | (455) in(all_42_1, all_42_2) = all_650_4 % 75.97/16.22 | | | | | | | | | | | | | | | (456) in(all_42_0, all_42_2) = all_650_3 % 75.97/16.22 | | | | | | | | | | | | | | | (457) in(all_104_1, all_56_1) = all_650_2 % 75.97/16.22 | | | | | | | | | | | | | | | (458) in(all_650_1, all_56_1) = all_650_0 % 75.97/16.22 | | | | | | | | | | | | | | | (459) ordered_pair(all_42_0, all_42_1) = all_650_1 % 75.97/16.22 | | | | | | | | | | | | | | | (460) ~ (all_650_0 = 0) | ~ (all_650_2 = 0) | ~ % 75.97/16.22 | | | | | | | | | | | | | | | (all_650_3 = 0) | ~ (all_650_4 = 0) % 75.97/16.22 | | | | | | | | | | | | | | | % 75.97/16.22 | | | | | | | | | | | | | | | GROUND_INST: instantiating (31) with 0, all_650_4, all_42_2, % 75.97/16.22 | | | | | | | | | | | | | | | all_42_1, simplifying with (445), (455) gives: % 75.97/16.22 | | | | | | | | | | | | | | | (461) all_650_4 = 0 % 75.97/16.22 | | | | | | | | | | | | | | | % 75.97/16.22 | | | | | | | | | | | | | | | GROUND_INST: instantiating (31) with 0, all_650_3, all_42_2, % 75.97/16.22 | | | | | | | | | | | | | | | all_42_0, simplifying with (443), (456) gives: % 75.97/16.22 | | | | | | | | | | | | | | | (462) all_650_3 = 0 % 75.97/16.22 | | | | | | | | | | | | | | | % 75.97/16.22 | | | | | | | | | | | | | | | GROUND_INST: instantiating (31) with 0, all_650_2, all_56_1, % 75.97/16.22 | | | | | | | | | | | | | | | all_104_1, simplifying with (240), (457) gives: % 75.97/16.22 | | | | | | | | | | | | | | | (463) all_650_2 = 0 % 75.97/16.22 | | | | | | | | | | | | | | | % 75.97/16.22 | | | | | | | | | | | | | | | GROUND_INST: instantiating (32) with all_102_1, all_650_1, % 75.97/16.22 | | | | | | | | | | | | | | | all_42_1, all_42_0, simplifying with (201), (459) % 75.97/16.22 | | | | | | | | | | | | | | | gives: % 75.97/16.22 | | | | | | | | | | | | | | | (464) all_650_1 = all_102_1 % 75.97/16.22 | | | | | | | | | | | | | | | % 75.97/16.22 | | | | | | | | | | | | | | | REDUCE: (458), (464) imply: % 75.97/16.22 | | | | | | | | | | | | | | | (465) in(all_102_1, all_56_1) = all_650_0 % 75.97/16.22 | | | | | | | | | | | | | | | % 75.97/16.22 | | | | | | | | | | | | | | | BETA: splitting (460) gives: % 75.97/16.22 | | | | | | | | | | | | | | | % 75.97/16.22 | | | | | | | | | | | | | | | Case 1: % 75.97/16.22 | | | | | | | | | | | | | | | | % 75.97/16.22 | | | | | | | | | | | | | | | | (466) ~ (all_650_0 = 0) % 75.97/16.22 | | | | | | | | | | | | | | | | % 75.97/16.22 | | | | | | | | | | | | | | | | BETA: splitting (449) gives: % 75.97/16.22 | | | | | | | | | | | | | | | | % 75.97/16.22 | | | | | | | | | | | | | | | | Case 1: % 75.97/16.22 | | | | | | | | | | | | | | | | | % 75.97/16.22 | | | | | | | | | | | | | | | | | (467) all_42_0 = all_42_1 % 75.97/16.22 | | | | | | | | | | | | | | | | | % 75.97/16.22 | | | | | | | | | | | | | | | | | REDUCE: (46), (467) imply: % 75.97/16.22 | | | | | | | | | | | | | | | | | (468) $false % 75.97/16.22 | | | | | | | | | | | | | | | | | % 75.97/16.22 | | | | | | | | | | | | | | | | | CLOSE: (468) is inconsistent. % 75.97/16.22 | | | | | | | | | | | | | | | | | % 75.97/16.22 | | | | | | | | | | | | | | | | Case 2: % 75.97/16.22 | | | | | | | | | | | | | | | | | % 75.97/16.23 | | | | | | | | | | | | | | | | | (469) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? % 75.97/16.23 | | | | | | | | | | | | | | | | | [v3: $i] : ? [v4: any] : (ordered_pair(all_42_1, % 75.97/16.23 | | | | | | | | | | | | | | | | | all_42_0) = v3 & in(v3, all_56_1) = v4 & % 75.97/16.23 | | | | | | | | | | | | | | | | | in(all_102_1, all_56_1) = v2 & in(all_42_0, % 75.97/16.23 | | | | | | | | | | | | | | | | | all_42_2) = v0 & in(all_42_1, all_42_2) = v1 & % 75.97/16.23 | | | | | | | | | | | | | | | | | $i(v3) & ( ~ (v4 = 0) | ~ (v2 = 0) | ~ (v1 = % 75.97/16.23 | | | | | | | | | | | | | | | | | 0) | ~ (v0 = 0))) % 75.97/16.23 | | | | | | | | | | | | | | | | | % 75.97/16.23 | | | | | | | | | | | | | | | | | DELTA: instantiating (469) with fresh symbols all_834_0, % 75.97/16.23 | | | | | | | | | | | | | | | | | all_834_1, all_834_2, all_834_3, all_834_4 gives: % 75.97/16.23 | | | | | | | | | | | | | | | | | (470) ordered_pair(all_42_1, all_42_0) = all_834_1 & % 75.97/16.23 | | | | | | | | | | | | | | | | | in(all_834_1, all_56_1) = all_834_0 & % 75.97/16.23 | | | | | | | | | | | | | | | | | in(all_102_1, all_56_1) = all_834_2 & in(all_42_0, % 75.97/16.23 | | | | | | | | | | | | | | | | | all_42_2) = all_834_4 & in(all_42_1, all_42_2) = % 75.97/16.23 | | | | | | | | | | | | | | | | | all_834_3 & $i(all_834_1) & ( ~ (all_834_0 = 0) | % 75.97/16.23 | | | | | | | | | | | | | | | | | ~ (all_834_2 = 0) | ~ (all_834_3 = 0) | ~ % 75.97/16.23 | | | | | | | | | | | | | | | | | (all_834_4 = 0)) % 75.97/16.23 | | | | | | | | | | | | | | | | | % 75.97/16.23 | | | | | | | | | | | | | | | | | ALPHA: (470) implies: % 75.97/16.23 | | | | | | | | | | | | | | | | | (471) in(all_102_1, all_56_1) = all_834_2 % 75.97/16.23 | | | | | | | | | | | | | | | | | % 75.97/16.23 | | | | | | | | | | | | | | | | | BETA: splitting (448) gives: % 75.97/16.23 | | | | | | | | | | | | | | | | | % 75.97/16.23 | | | | | | | | | | | | | | | | | Case 1: % 75.97/16.23 | | | | | | | | | | | | | | | | | | % 75.97/16.23 | | | | | | | | | | | | | | | | | | (472) all_42_0 = all_42_1 % 75.97/16.23 | | | | | | | | | | | | | | | | | | % 75.97/16.23 | | | | | | | | | | | | | | | | | | REDUCE: (46), (472) imply: % 75.97/16.23 | | | | | | | | | | | | | | | | | | (473) $false % 75.97/16.23 | | | | | | | | | | | | | | | | | | % 75.97/16.23 | | | | | | | | | | | | | | | | | | CLOSE: (473) is inconsistent. % 75.97/16.23 | | | | | | | | | | | | | | | | | | % 75.97/16.23 | | | | | | | | | | | | | | | | | Case 2: % 75.97/16.23 | | | | | | | | | | | | | | | | | | % 75.97/16.23 | | | | | | | | | | | | | | | | | | (474) ? [v0: any] : ? [v1: any] : ? [v2: $i] : ? % 75.97/16.23 | | | | | | | | | | | | | | | | | | [v3: any] : ? [v4: any] : (ordered_pair(all_42_1, % 75.97/16.23 | | | | | | | | | | | | | | | | | | all_42_0) = v2 & in(v2, all_56_1) = v3 & % 75.97/16.23 | | | | | | | | | | | | | | | | | | in(all_102_1, all_56_1) = v4 & in(all_42_0, % 75.97/16.23 | | | | | | | | | | | | | | | | | | all_42_2) = v1 & in(all_42_1, all_42_2) = v0 & % 75.97/16.23 | | | | | | | | | | | | | | | | | | $i(v2) & ( ~ (v4 = 0) | ~ (v3 = 0) | ~ (v1 = % 75.97/16.23 | | | | | | | | | | | | | | | | | | 0) | ~ (v0 = 0))) % 75.97/16.23 | | | | | | | | | | | | | | | | | | % 75.97/16.23 | | | | | | | | | | | | | | | | | | DELTA: instantiating (474) with fresh symbols all_844_0, % 75.97/16.23 | | | | | | | | | | | | | | | | | | all_844_1, all_844_2, all_844_3, all_844_4 gives: % 75.97/16.23 | | | | | | | | | | | | | | | | | | (475) ordered_pair(all_42_1, all_42_0) = all_844_2 & % 75.97/16.23 | | | | | | | | | | | | | | | | | | in(all_844_2, all_56_1) = all_844_1 & % 75.97/16.23 | | | | | | | | | | | | | | | | | | in(all_102_1, all_56_1) = all_844_0 & in(all_42_0, % 75.97/16.23 | | | | | | | | | | | | | | | | | | all_42_2) = all_844_3 & in(all_42_1, all_42_2) = % 75.97/16.23 | | | | | | | | | | | | | | | | | | all_844_4 & $i(all_844_2) & ( ~ (all_844_0 = 0) | % 75.97/16.23 | | | | | | | | | | | | | | | | | | ~ (all_844_1 = 0) | ~ (all_844_3 = 0) | ~ % 75.97/16.23 | | | | | | | | | | | | | | | | | | (all_844_4 = 0)) % 75.97/16.23 | | | | | | | | | | | | | | | | | | % 75.97/16.23 | | | | | | | | | | | | | | | | | | ALPHA: (475) implies: % 75.97/16.23 | | | | | | | | | | | | | | | | | | (476) in(all_102_1, all_56_1) = all_844_0 % 75.97/16.23 | | | | | | | | | | | | | | | | | | % 75.97/16.23 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (31) with 0, all_834_2, all_56_1, % 75.97/16.23 | | | | | | | | | | | | | | | | | | all_102_1, simplifying with (244), (471) gives: % 75.97/16.23 | | | | | | | | | | | | | | | | | | (477) all_834_2 = 0 % 75.97/16.23 | | | | | | | | | | | | | | | | | | % 75.97/16.23 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (31) with all_834_2, all_844_0, % 75.97/16.23 | | | | | | | | | | | | | | | | | | all_56_1, all_102_1, simplifying with (471), (476) % 75.97/16.23 | | | | | | | | | | | | | | | | | | gives: % 75.97/16.23 | | | | | | | | | | | | | | | | | | (478) all_844_0 = all_834_2 % 75.97/16.23 | | | | | | | | | | | | | | | | | | % 75.97/16.23 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (31) with all_650_0, all_844_0, % 75.97/16.23 | | | | | | | | | | | | | | | | | | all_56_1, all_102_1, simplifying with (465), (476) % 75.97/16.23 | | | | | | | | | | | | | | | | | | gives: % 75.97/16.23 | | | | | | | | | | | | | | | | | | (479) all_844_0 = all_650_0 % 75.97/16.23 | | | | | | | | | | | | | | | | | | % 75.97/16.23 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (478), (479) imply: % 75.97/16.23 | | | | | | | | | | | | | | | | | | (480) all_834_2 = all_650_0 % 75.97/16.23 | | | | | | | | | | | | | | | | | | % 75.97/16.23 | | | | | | | | | | | | | | | | | | SIMP: (480) implies: % 75.97/16.23 | | | | | | | | | | | | | | | | | | (481) all_834_2 = all_650_0 % 75.97/16.23 | | | | | | | | | | | | | | | | | | % 75.97/16.23 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (477), (481) imply: % 75.97/16.23 | | | | | | | | | | | | | | | | | | (482) all_650_0 = 0 % 75.97/16.23 | | | | | | | | | | | | | | | | | | % 75.97/16.23 | | | | | | | | | | | | | | | | | | REDUCE: (466), (482) imply: % 75.97/16.23 | | | | | | | | | | | | | | | | | | (483) $false % 75.97/16.23 | | | | | | | | | | | | | | | | | | % 75.97/16.23 | | | | | | | | | | | | | | | | | | CLOSE: (483) is inconsistent. % 75.97/16.23 | | | | | | | | | | | | | | | | | | % 75.97/16.23 | | | | | | | | | | | | | | | | | End of split % 75.97/16.23 | | | | | | | | | | | | | | | | | % 75.97/16.23 | | | | | | | | | | | | | | | | End of split % 75.97/16.23 | | | | | | | | | | | | | | | | % 75.97/16.23 | | | | | | | | | | | | | | | Case 2: % 75.97/16.23 | | | | | | | | | | | | | | | | % 75.97/16.23 | | | | | | | | | | | | | | | | (484) ~ (all_650_2 = 0) | ~ (all_650_3 = 0) | ~ % 75.97/16.23 | | | | | | | | | | | | | | | | (all_650_4 = 0) % 75.97/16.23 | | | | | | | | | | | | | | | | % 75.97/16.23 | | | | | | | | | | | | | | | | BETA: splitting (484) gives: % 75.97/16.23 | | | | | | | | | | | | | | | | % 75.97/16.23 | | | | | | | | | | | | | | | | Case 1: % 75.97/16.23 | | | | | | | | | | | | | | | | | % 75.97/16.23 | | | | | | | | | | | | | | | | | (485) ~ (all_650_2 = 0) % 75.97/16.23 | | | | | | | | | | | | | | | | | % 75.97/16.23 | | | | | | | | | | | | | | | | | REDUCE: (463), (485) imply: % 75.97/16.23 | | | | | | | | | | | | | | | | | (486) $false % 75.97/16.23 | | | | | | | | | | | | | | | | | % 75.97/16.23 | | | | | | | | | | | | | | | | | CLOSE: (486) is inconsistent. % 75.97/16.23 | | | | | | | | | | | | | | | | | % 75.97/16.23 | | | | | | | | | | | | | | | | Case 2: % 75.97/16.23 | | | | | | | | | | | | | | | | | % 75.97/16.23 | | | | | | | | | | | | | | | | | (487) ~ (all_650_3 = 0) | ~ (all_650_4 = 0) % 75.97/16.23 | | | | | | | | | | | | | | | | | % 75.97/16.23 | | | | | | | | | | | | | | | | | BETA: splitting (487) gives: % 75.97/16.23 | | | | | | | | | | | | | | | | | % 75.97/16.23 | | | | | | | | | | | | | | | | | Case 1: % 75.97/16.23 | | | | | | | | | | | | | | | | | | % 75.97/16.23 | | | | | | | | | | | | | | | | | | (488) ~ (all_650_3 = 0) % 75.97/16.23 | | | | | | | | | | | | | | | | | | % 75.97/16.23 | | | | | | | | | | | | | | | | | | REDUCE: (462), (488) imply: % 75.97/16.23 | | | | | | | | | | | | | | | | | | (489) $false % 75.97/16.23 | | | | | | | | | | | | | | | | | | % 75.97/16.23 | | | | | | | | | | | | | | | | | | CLOSE: (489) is inconsistent. % 75.97/16.23 | | | | | | | | | | | | | | | | | | % 75.97/16.23 | | | | | | | | | | | | | | | | | Case 2: % 75.97/16.23 | | | | | | | | | | | | | | | | | | % 75.97/16.23 | | | | | | | | | | | | | | | | | | (490) ~ (all_650_4 = 0) % 75.97/16.23 | | | | | | | | | | | | | | | | | | % 75.97/16.23 | | | | | | | | | | | | | | | | | | REDUCE: (461), (490) imply: % 75.97/16.23 | | | | | | | | | | | | | | | | | | (491) $false % 75.97/16.23 | | | | | | | | | | | | | | | | | | % 75.97/16.23 | | | | | | | | | | | | | | | | | | CLOSE: (491) is inconsistent. % 75.97/16.23 | | | | | | | | | | | | | | | | | | % 75.97/16.23 | | | | | | | | | | | | | | | | | End of split % 75.97/16.23 | | | | | | | | | | | | | | | | | % 75.97/16.23 | | | | | | | | | | | | | | | | End of split % 75.97/16.23 | | | | | | | | | | | | | | | | % 75.97/16.23 | | | | | | | | | | | | | | | End of split % 75.97/16.23 | | | | | | | | | | | | | | | % 75.97/16.23 | | | | | | | | | | | | | | End of split % 75.97/16.23 | | | | | | | | | | | | | | % 75.97/16.23 | | | | | | | | | | | | | End of split % 75.97/16.23 | | | | | | | | | | | | | % 75.97/16.23 | | | | | | | | | | | | Case 2: % 75.97/16.23 | | | | | | | | | | | | | % 75.97/16.23 | | | | | | | | | | | | | (492) all_52_1 = 0 % 75.97/16.23 | | | | | | | | | | | | | % 75.97/16.23 | | | | | | | | | | | | | COMBINE_EQS: (156), (492) imply: % 75.97/16.23 | | | | | | | | | | | | | (493) all_50_1 = 0 % 75.97/16.23 | | | | | | | | | | | | | % 75.97/16.23 | | | | | | | | | | | | | SIMP: (493) implies: % 75.97/16.23 | | | | | | | | | | | | | (494) all_50_1 = 0 % 75.97/16.23 | | | | | | | | | | | | | % 75.97/16.23 | | | | | | | | | | | | | REDUCE: (74), (494) imply: % 75.97/16.23 | | | | | | | | | | | | | (495) empty(all_42_2) = 0 % 75.97/16.23 | | | | | | | | | | | | | % 75.97/16.23 | | | | | | | | | | | | | REF_CLOSE: (24), (30), (48), (50), (219), (248), (271), % 75.97/16.23 | | | | | | | | | | | | | (272), (400), (401), (403), (404), (406), (407), % 75.97/16.23 | | | | | | | | | | | | | (409), (410), (443), (495), (t7_boole), (t8_boole) % 75.97/16.23 | | | | | | | | | | | | | are inconsistent by sub-proof #3. % 75.97/16.23 | | | | | | | | | | | | | % 75.97/16.23 | | | | | | | | | | | | End of split % 75.97/16.23 | | | | | | | | | | | | % 75.97/16.23 | | | | | | | | | | | Case 2: % 75.97/16.23 | | | | | | | | | | | | % 75.97/16.23 | | | | | | | | | | | | (496) all_50_1 = 0 % 75.97/16.23 | | | | | | | | | | | | (497) ~ (all_50_0 = 0) % 75.97/16.23 | | | | | | | | | | | | % 75.97/16.23 | | | | | | | | | | | | REDUCE: (74), (496) imply: % 75.97/16.23 | | | | | | | | | | | | (498) empty(all_42_2) = 0 % 75.97/16.23 | | | | | | | | | | | | % 75.97/16.23 | | | | | | | | | | | | BETA: splitting (109) gives: % 75.97/16.23 | | | | | | | | | | | | % 75.97/16.23 | | | | | | | | | | | | Case 1: % 75.97/16.23 | | | | | | | | | | | | | % 75.97/16.23 | | | | | | | | | | | | | (499) ~ (all_64_3 = 0) % 75.97/16.23 | | | | | | | | | | | | | % 75.97/16.23 | | | | | | | | | | | | | BETA: splitting (110) gives: % 75.97/16.23 | | | | | | | | | | | | | % 75.97/16.23 | | | | | | | | | | | | | Case 1: % 75.97/16.23 | | | | | | | | | | | | | | % 75.97/16.23 | | | | | | | | | | | | | | % 75.97/16.23 | | | | | | | | | | | | | | GROUND_INST: instantiating (3) with all_56_1, all_42_2, % 75.97/16.23 | | | | | | | | | | | | | | all_42_1, all_42_0, all_102_1, simplifying with % 75.97/16.23 | | | | | | | | | | | | | | (48), (49), (50), (184), (188), (201), (382) % 75.97/16.23 | | | | | | | | | | | | | | gives: % 75.97/16.23 | | | | | | | | | | | | | | (500) all_42_0 = all_42_1 | ? [v0: any] : ? [v1: any] % 75.97/16.23 | | | | | | | | | | | | | | : ? [v2: $i] : ? [v3: any] : ? [v4: any] : % 75.97/16.23 | | | | | | | | | | | | | | (ordered_pair(all_42_1, all_42_0) = v2 & in(v2, % 75.97/16.23 | | | | | | | | | | | | | | all_56_1) = v3 & in(all_102_1, all_56_1) = v4 % 75.97/16.23 | | | | | | | | | | | | | | & in(all_42_0, all_42_2) = v1 & in(all_42_1, % 75.97/16.23 | | | | | | | | | | | | | | all_42_2) = v0 & $i(v2) & ( ~ (v4 = 0) | ~ % 75.97/16.23 | | | | | | | | | | | | | | (v3 = 0) | ~ (v1 = 0) | ~ (v0 = 0))) % 75.97/16.23 | | | | | | | | | | | | | | % 75.97/16.23 | | | | | | | | | | | | | | GROUND_INST: instantiating (2) with all_56_1, all_42_2, % 75.97/16.23 | | | | | | | | | | | | | | all_42_0, all_42_1, all_102_1, simplifying with % 75.97/16.23 | | | | | | | | | | | | | | (48), (49), (50), (184), (188), (201), (382) % 75.97/16.23 | | | | | | | | | | | | | | gives: % 75.97/16.23 | | | | | | | | | | | | | | (501) all_42_0 = all_42_1 | ? [v0: any] : ? [v1: any] % 75.97/16.23 | | | | | | | | | | | | | | : ? [v2: any] : ? [v3: $i] : ? [v4: any] : % 75.97/16.23 | | | | | | | | | | | | | | (ordered_pair(all_42_1, all_42_0) = v3 & in(v3, % 75.97/16.23 | | | | | | | | | | | | | | all_56_1) = v4 & in(all_102_1, all_56_1) = v2 % 75.97/16.23 | | | | | | | | | | | | | | & in(all_42_0, all_42_2) = v0 & in(all_42_1, % 75.97/16.23 | | | | | | | | | | | | | | all_42_2) = v1 & $i(v3) & ( ~ (v4 = 0) | ~ % 75.97/16.23 | | | | | | | | | | | | | | (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0))) % 75.97/16.23 | | | | | | | | | | | | | | % 75.97/16.23 | | | | | | | | | | | | | | GROUND_INST: instantiating (3) with all_56_1, all_42_2, % 75.97/16.23 | | | | | | | | | | | | | | all_42_0, all_42_1, all_104_1, simplifying with % 75.97/16.23 | | | | | | | | | | | | | | (48), (49), (50), (184), (188), (203), (382) % 75.97/16.23 | | | | | | | | | | | | | | gives: % 75.97/16.23 | | | | | | | | | | | | | | (502) all_42_0 = all_42_1 | ? [v0: any] : ? [v1: any] % 75.97/16.23 | | | | | | | | | | | | | | : ? [v2: $i] : ? [v3: any] : ? [v4: any] : % 75.97/16.23 | | | | | | | | | | | | | | (ordered_pair(all_42_0, all_42_1) = v2 & in(v2, % 75.97/16.23 | | | | | | | | | | | | | | all_56_1) = v3 & in(all_104_1, all_56_1) = v4 % 75.97/16.23 | | | | | | | | | | | | | | & in(all_42_0, all_42_2) = v0 & in(all_42_1, % 75.97/16.23 | | | | | | | | | | | | | | all_42_2) = v1 & $i(v2) & ( ~ (v4 = 0) | ~ % 75.97/16.23 | | | | | | | | | | | | | | (v3 = 0) | ~ (v1 = 0) | ~ (v0 = 0))) % 75.97/16.23 | | | | | | | | | | | | | | % 75.97/16.23 | | | | | | | | | | | | | | GROUND_INST: instantiating (2) with all_56_1, all_42_2, % 75.97/16.23 | | | | | | | | | | | | | | all_42_1, all_42_0, all_104_1, simplifying with % 75.97/16.23 | | | | | | | | | | | | | | (48), (49), (50), (184), (188), (203), (382) % 75.97/16.23 | | | | | | | | | | | | | | gives: % 75.97/16.23 | | | | | | | | | | | | | | (503) all_42_0 = all_42_1 | ? [v0: any] : ? [v1: any] % 75.97/16.23 | | | | | | | | | | | | | | : ? [v2: any] : ? [v3: $i] : ? [v4: any] : % 75.97/16.23 | | | | | | | | | | | | | | (ordered_pair(all_42_0, all_42_1) = v3 & in(v3, % 75.97/16.23 | | | | | | | | | | | | | | all_56_1) = v4 & in(all_104_1, all_56_1) = v2 % 75.97/16.23 | | | | | | | | | | | | | | & in(all_42_0, all_42_2) = v1 & in(all_42_1, % 75.97/16.23 | | | | | | | | | | | | | | all_42_2) = v0 & $i(v3) & ( ~ (v4 = 0) | ~ % 75.97/16.23 | | | | | | | | | | | | | | (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0))) % 75.97/16.23 | | | | | | | | | | | | | | % 75.97/16.24 | | | | | | | | | | | | | | GROUND_INST: instantiating (19) with all_102_1, all_162_1, % 75.97/16.24 | | | | | | | | | | | | | | simplifying with (285), (297), (378) gives: % 75.97/16.24 | | | | | | | | | | | | | | (504) ? [v0: any] : ? [v1: any] : (empty(all_162_1) = % 75.97/16.24 | | | | | | | | | | | | | | v0 & in(all_102_1, all_162_1) = v1 & (v1 = 0 | % 75.97/16.24 | | | | | | | | | | | | | | v0 = 0)) % 75.97/16.24 | | | | | | | | | | | | | | % 75.97/16.24 | | | | | | | | | | | | | | GROUND_INST: instantiating (19) with all_104_1, all_162_1, % 75.97/16.24 | | | | | | | | | | | | | | simplifying with (236), (285), (377) gives: % 75.97/16.24 | | | | | | | | | | | | | | (505) ? [v0: any] : ? [v1: any] : (empty(all_162_1) = % 75.97/16.24 | | | | | | | | | | | | | | v0 & in(all_104_1, all_162_1) = v1 & (v1 = 0 | % 75.97/16.24 | | | | | | | | | | | | | | v0 = 0)) % 75.97/16.24 | | | | | | | | | | | | | | % 75.97/16.24 | | | | | | | | | | | | | | GROUND_INST: instantiating (16) with all_164_1, all_322_0, % 75.97/16.24 | | | | | | | | | | | | | | simplifying with (290), (420) gives: % 75.97/16.24 | | | | | | | | | | | | | | (506) all_322_0 = 0 | ? [v0: $i] : ? [v1: $i] : ? % 75.97/16.24 | | | | | | | | | | | | | | [v2: int] : ( ~ (v2 = 0) & empty(v1) = v2 & % 75.97/16.24 | | | | | | | | | | | | | | powerset(all_164_1) = v0 & element(v1, v0) = 0 & % 75.97/16.24 | | | | | | | | | | | | | | $i(v1) & $i(v0)) % 75.97/16.24 | | | | | | | | | | | | | | % 75.97/16.24 | | | | | | | | | | | | | | GROUND_INST: instantiating (16) with all_203_2, all_282_0, % 75.97/16.24 | | | | | | | | | | | | | | simplifying with (337), (398) gives: % 75.97/16.24 | | | | | | | | | | | | | | (507) all_282_0 = 0 | ? [v0: $i] : ? [v1: $i] : ? % 75.97/16.24 | | | | | | | | | | | | | | [v2: int] : ( ~ (v2 = 0) & empty(v1) = v2 & % 75.97/16.24 | | | | | | | | | | | | | | powerset(all_203_2) = v0 & element(v1, v0) = 0 & % 75.97/16.24 | | | | | | | | | | | | | | $i(v1) & $i(v0)) % 75.97/16.24 | | | | | | | | | | | | | | % 75.97/16.24 | | | | | | | | | | | | | | GROUND_INST: instantiating (t8_boole) with all_288_0, % 75.97/16.24 | | | | | | | | | | | | | | all_290_0, simplifying with (400), (401), (403), % 75.97/16.24 | | | | | | | | | | | | | | (404) gives: % 75.97/16.24 | | | | | | | | | | | | | | (508) all_290_0 = all_288_0 % 75.97/16.24 | | | | | | | | | | | | | | % 75.97/16.24 | | | | | | | | | | | | | | GROUND_INST: instantiating (24) with all_290_0, simplifying % 75.97/16.24 | | | | | | | | | | | | | | with (403), (404) gives: % 75.97/16.24 | | | | | | | | | | | | | | (509) all_290_0 = empty_set % 75.97/16.24 | | | | | | | | | | | | | | % 75.97/16.24 | | | | | | | | | | | | | | GROUND_INST: instantiating (t8_boole) with all_288_0, % 75.97/16.24 | | | | | | | | | | | | | | all_292_0, simplifying with (400), (401), (406), % 75.97/16.24 | | | | | | | | | | | | | | (407) gives: % 75.97/16.24 | | | | | | | | | | | | | | (510) all_292_0 = all_288_0 % 75.97/16.24 | | | | | | | | | | | | | | % 75.97/16.24 | | | | | | | | | | | | | | GROUND_INST: instantiating (t8_boole) with all_292_0, % 75.97/16.24 | | | | | | | | | | | | | | all_294_0, simplifying with (406), (407), (409), % 75.97/16.24 | | | | | | | | | | | | | | (410) gives: % 75.97/16.24 | | | | | | | | | | | | | | (511) all_294_0 = all_292_0 % 75.97/16.24 | | | | | | | | | | | | | | % 75.97/16.24 | | | | | | | | | | | | | | GROUND_INST: instantiating (t8_boole) with all_42_2, all_294_0, % 75.97/16.24 | | | | | | | | | | | | | | simplifying with (48), (409), (410), (498) gives: % 75.97/16.24 | | | | | | | | | | | | | | (512) all_294_0 = all_42_2 % 75.97/16.24 | | | | | | | | | | | | | | % 75.97/16.24 | | | | | | | | | | | | | | COMBINE_EQS: (511), (512) imply: % 75.97/16.24 | | | | | | | | | | | | | | (513) all_292_0 = all_42_2 % 75.97/16.24 | | | | | | | | | | | | | | % 75.97/16.24 | | | | | | | | | | | | | | SIMP: (513) implies: % 75.97/16.24 | | | | | | | | | | | | | | (514) all_292_0 = all_42_2 % 75.97/16.24 | | | | | | | | | | | | | | % 75.97/16.24 | | | | | | | | | | | | | | COMBINE_EQS: (510), (514) imply: % 75.97/16.24 | | | | | | | | | | | | | | (515) all_288_0 = all_42_2 % 75.97/16.24 | | | | | | | | | | | | | | % 75.97/16.24 | | | | | | | | | | | | | | SIMP: (515) implies: % 75.97/16.24 | | | | | | | | | | | | | | (516) all_288_0 = all_42_2 % 75.97/16.24 | | | | | | | | | | | | | | % 75.97/16.24 | | | | | | | | | | | | | | COMBINE_EQS: (508), (509) imply: % 75.97/16.24 | | | | | | | | | | | | | | (517) all_288_0 = empty_set % 75.97/16.24 | | | | | | | | | | | | | | % 75.97/16.24 | | | | | | | | | | | | | | SIMP: (517) implies: % 75.97/16.24 | | | | | | | | | | | | | | (518) all_288_0 = empty_set % 75.97/16.24 | | | | | | | | | | | | | | % 75.97/16.24 | | | | | | | | | | | | | | COMBINE_EQS: (516), (518) imply: % 75.97/16.24 | | | | | | | | | | | | | | (519) all_42_2 = empty_set % 75.97/16.24 | | | | | | | | | | | | | | % 75.97/16.24 | | | | | | | | | | | | | | DELTA: instantiating (505) with fresh symbols all_502_0, % 75.97/16.24 | | | | | | | | | | | | | | all_502_1 gives: % 75.97/16.24 | | | | | | | | | | | | | | (520) empty(all_162_1) = all_502_1 & in(all_104_1, % 75.97/16.24 | | | | | | | | | | | | | | all_162_1) = all_502_0 & (all_502_0 = 0 | % 75.97/16.24 | | | | | | | | | | | | | | all_502_1 = 0) % 75.97/16.24 | | | | | | | | | | | | | | % 75.97/16.24 | | | | | | | | | | | | | | ALPHA: (520) implies: % 75.97/16.24 | | | | | | | | | | | | | | (521) in(all_104_1, all_162_1) = all_502_0 % 75.97/16.24 | | | | | | | | | | | | | | (522) empty(all_162_1) = all_502_1 % 75.97/16.24 | | | | | | | | | | | | | | (523) all_502_0 = 0 | all_502_1 = 0 % 75.97/16.24 | | | | | | | | | | | | | | % 75.97/16.24 | | | | | | | | | | | | | | DELTA: instantiating (504) with fresh symbols all_504_0, % 75.97/16.24 | | | | | | | | | | | | | | all_504_1 gives: % 75.97/16.24 | | | | | | | | | | | | | | (524) empty(all_162_1) = all_504_1 & in(all_102_1, % 75.97/16.24 | | | | | | | | | | | | | | all_162_1) = all_504_0 & (all_504_0 = 0 | % 75.97/16.24 | | | | | | | | | | | | | | all_504_1 = 0) % 75.97/16.24 | | | | | | | | | | | | | | % 75.97/16.24 | | | | | | | | | | | | | | ALPHA: (524) implies: % 75.97/16.24 | | | | | | | | | | | | | | (525) empty(all_162_1) = all_504_1 % 75.97/16.24 | | | | | | | | | | | | | | % 75.97/16.24 | | | | | | | | | | | | | | REDUCE: (288), (519) imply: % 75.97/16.24 | | | | | | | | | | | | | | (526) cartesian_product2(empty_set, empty_set) = % 75.97/16.24 | | | | | | | | | | | | | | all_162_1 % 75.97/16.24 | | | | | | | | | | | | | | % 75.97/16.24 | | | | | | | | | | | | | | REDUCE: (73), (519) imply: % 75.97/16.24 | | | | | | | | | | | | | | (527) in(all_42_0, empty_set) = all_50_0 % 75.97/16.24 | | | | | | | | | | | | | | % 75.97/16.24 | | | | | | | | | | | | | | BETA: splitting (501) gives: % 75.97/16.24 | | | | | | | | | | | | | | % 75.97/16.24 | | | | | | | | | | | | | | Case 1: % 75.97/16.24 | | | | | | | | | | | | | | | % 75.97/16.24 | | | | | | | | | | | | | | | (528) all_42_0 = all_42_1 % 75.97/16.24 | | | | | | | | | | | | | | | % 75.97/16.24 | | | | | | | | | | | | | | | REDUCE: (46), (528) imply: % 75.97/16.24 | | | | | | | | | | | | | | | (529) $false % 75.97/16.24 | | | | | | | | | | | | | | | % 75.97/16.24 | | | | | | | | | | | | | | | CLOSE: (529) is inconsistent. % 75.97/16.24 | | | | | | | | | | | | | | | % 75.97/16.24 | | | | | | | | | | | | | | Case 2: % 75.97/16.24 | | | | | | | | | | | | | | | % 75.97/16.24 | | | | | | | | | | | | | | | (530) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? % 75.97/16.24 | | | | | | | | | | | | | | | [v3: $i] : ? [v4: any] : (ordered_pair(all_42_1, % 75.97/16.24 | | | | | | | | | | | | | | | all_42_0) = v3 & in(v3, all_56_1) = v4 & % 75.97/16.24 | | | | | | | | | | | | | | | in(all_102_1, all_56_1) = v2 & in(all_42_0, % 75.97/16.24 | | | | | | | | | | | | | | | all_42_2) = v0 & in(all_42_1, all_42_2) = v1 & % 75.97/16.24 | | | | | | | | | | | | | | | $i(v3) & ( ~ (v4 = 0) | ~ (v2 = 0) | ~ (v1 = % 75.97/16.24 | | | | | | | | | | | | | | | 0) | ~ (v0 = 0))) % 75.97/16.24 | | | | | | | | | | | | | | | % 75.97/16.24 | | | | | | | | | | | | | | | DELTA: instantiating (530) with fresh symbols all_745_0, % 75.97/16.24 | | | | | | | | | | | | | | | all_745_1, all_745_2, all_745_3, all_745_4 gives: % 75.97/16.24 | | | | | | | | | | | | | | | (531) ordered_pair(all_42_1, all_42_0) = all_745_1 & % 75.97/16.24 | | | | | | | | | | | | | | | in(all_745_1, all_56_1) = all_745_0 & % 75.97/16.24 | | | | | | | | | | | | | | | in(all_102_1, all_56_1) = all_745_2 & in(all_42_0, % 75.97/16.24 | | | | | | | | | | | | | | | all_42_2) = all_745_4 & in(all_42_1, all_42_2) = % 75.97/16.24 | | | | | | | | | | | | | | | all_745_3 & $i(all_745_1) & ( ~ (all_745_0 = 0) | % 75.97/16.24 | | | | | | | | | | | | | | | ~ (all_745_2 = 0) | ~ (all_745_3 = 0) | ~ % 75.97/16.24 | | | | | | | | | | | | | | | (all_745_4 = 0)) % 75.97/16.24 | | | | | | | | | | | | | | | % 75.97/16.24 | | | | | | | | | | | | | | | ALPHA: (531) implies: % 75.97/16.24 | | | | | | | | | | | | | | | (532) in(all_42_0, all_42_2) = all_745_4 % 75.97/16.24 | | | | | | | | | | | | | | | (533) ordered_pair(all_42_1, all_42_0) = all_745_1 % 75.97/16.24 | | | | | | | | | | | | | | | % 75.97/16.24 | | | | | | | | | | | | | | | REDUCE: (519), (532) imply: % 75.97/16.24 | | | | | | | | | | | | | | | (534) in(all_42_0, empty_set) = all_745_4 % 75.97/16.24 | | | | | | | | | | | | | | | % 75.97/16.24 | | | | | | | | | | | | | | | BETA: splitting (500) gives: % 75.97/16.24 | | | | | | | | | | | | | | | % 75.97/16.24 | | | | | | | | | | | | | | | Case 1: % 75.97/16.24 | | | | | | | | | | | | | | | | % 75.97/16.24 | | | | | | | | | | | | | | | | (535) all_42_0 = all_42_1 % 75.97/16.24 | | | | | | | | | | | | | | | | % 75.97/16.24 | | | | | | | | | | | | | | | | REDUCE: (46), (535) imply: % 75.97/16.24 | | | | | | | | | | | | | | | | (536) $false % 75.97/16.24 | | | | | | | | | | | | | | | | % 75.97/16.24 | | | | | | | | | | | | | | | | CLOSE: (536) is inconsistent. % 75.97/16.24 | | | | | | | | | | | | | | | | % 75.97/16.24 | | | | | | | | | | | | | | | Case 2: % 75.97/16.24 | | | | | | | | | | | | | | | | % 75.97/16.24 | | | | | | | | | | | | | | | | (537) ? [v0: any] : ? [v1: any] : ? [v2: $i] : ? % 75.97/16.24 | | | | | | | | | | | | | | | | [v3: any] : ? [v4: any] : (ordered_pair(all_42_1, % 75.97/16.24 | | | | | | | | | | | | | | | | all_42_0) = v2 & in(v2, all_56_1) = v3 & % 75.97/16.24 | | | | | | | | | | | | | | | | in(all_102_1, all_56_1) = v4 & in(all_42_0, % 75.97/16.24 | | | | | | | | | | | | | | | | all_42_2) = v1 & in(all_42_1, all_42_2) = v0 & % 75.97/16.24 | | | | | | | | | | | | | | | | $i(v2) & ( ~ (v4 = 0) | ~ (v3 = 0) | ~ (v1 = % 75.97/16.24 | | | | | | | | | | | | | | | | 0) | ~ (v0 = 0))) % 75.97/16.24 | | | | | | | | | | | | | | | | % 75.97/16.24 | | | | | | | | | | | | | | | | DELTA: instantiating (537) with fresh symbols all_750_0, % 75.97/16.24 | | | | | | | | | | | | | | | | all_750_1, all_750_2, all_750_3, all_750_4 gives: % 75.97/16.24 | | | | | | | | | | | | | | | | (538) ordered_pair(all_42_1, all_42_0) = all_750_2 & % 75.97/16.24 | | | | | | | | | | | | | | | | in(all_750_2, all_56_1) = all_750_1 & % 75.97/16.24 | | | | | | | | | | | | | | | | in(all_102_1, all_56_1) = all_750_0 & in(all_42_0, % 75.97/16.24 | | | | | | | | | | | | | | | | all_42_2) = all_750_3 & in(all_42_1, all_42_2) = % 75.97/16.24 | | | | | | | | | | | | | | | | all_750_4 & $i(all_750_2) & ( ~ (all_750_0 = 0) | % 75.97/16.24 | | | | | | | | | | | | | | | | ~ (all_750_1 = 0) | ~ (all_750_3 = 0) | ~ % 75.97/16.24 | | | | | | | | | | | | | | | | (all_750_4 = 0)) % 75.97/16.24 | | | | | | | | | | | | | | | | % 75.97/16.24 | | | | | | | | | | | | | | | | ALPHA: (538) implies: % 75.97/16.24 | | | | | | | | | | | | | | | | (539) in(all_42_0, all_42_2) = all_750_3 % 75.97/16.24 | | | | | | | | | | | | | | | | (540) ordered_pair(all_42_1, all_42_0) = all_750_2 % 75.97/16.24 | | | | | | | | | | | | | | | | % 75.97/16.24 | | | | | | | | | | | | | | | | REDUCE: (519), (539) imply: % 75.97/16.24 | | | | | | | | | | | | | | | | (541) in(all_42_0, empty_set) = all_750_3 % 75.97/16.24 | | | | | | | | | | | | | | | | % 75.97/16.24 | | | | | | | | | | | | | | | | BETA: splitting (503) gives: % 75.97/16.24 | | | | | | | | | | | | | | | | % 75.97/16.24 | | | | | | | | | | | | | | | | Case 1: % 75.97/16.24 | | | | | | | | | | | | | | | | | % 75.97/16.24 | | | | | | | | | | | | | | | | | (542) all_42_0 = all_42_1 % 75.97/16.24 | | | | | | | | | | | | | | | | | % 75.97/16.24 | | | | | | | | | | | | | | | | | REDUCE: (46), (542) imply: % 75.97/16.24 | | | | | | | | | | | | | | | | | (543) $false % 75.97/16.24 | | | | | | | | | | | | | | | | | % 75.97/16.24 | | | | | | | | | | | | | | | | | CLOSE: (543) is inconsistent. % 75.97/16.24 | | | | | | | | | | | | | | | | | % 75.97/16.24 | | | | | | | | | | | | | | | | Case 2: % 75.97/16.24 | | | | | | | | | | | | | | | | | % 75.97/16.24 | | | | | | | | | | | | | | | | | (544) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? % 75.97/16.24 | | | | | | | | | | | | | | | | | [v3: $i] : ? [v4: any] : (ordered_pair(all_42_0, % 75.97/16.24 | | | | | | | | | | | | | | | | | all_42_1) = v3 & in(v3, all_56_1) = v4 & % 75.97/16.24 | | | | | | | | | | | | | | | | | in(all_104_1, all_56_1) = v2 & in(all_42_0, % 75.97/16.24 | | | | | | | | | | | | | | | | | all_42_2) = v1 & in(all_42_1, all_42_2) = v0 & % 75.97/16.24 | | | | | | | | | | | | | | | | | $i(v3) & ( ~ (v4 = 0) | ~ (v2 = 0) | ~ (v1 = % 75.97/16.24 | | | | | | | | | | | | | | | | | 0) | ~ (v0 = 0))) % 75.97/16.24 | | | | | | | | | | | | | | | | | % 75.97/16.24 | | | | | | | | | | | | | | | | | DELTA: instantiating (544) with fresh symbols all_755_0, % 75.97/16.24 | | | | | | | | | | | | | | | | | all_755_1, all_755_2, all_755_3, all_755_4 gives: % 75.97/16.24 | | | | | | | | | | | | | | | | | (545) ordered_pair(all_42_0, all_42_1) = all_755_1 & % 75.97/16.24 | | | | | | | | | | | | | | | | | in(all_755_1, all_56_1) = all_755_0 & % 75.97/16.24 | | | | | | | | | | | | | | | | | in(all_104_1, all_56_1) = all_755_2 & in(all_42_0, % 75.97/16.24 | | | | | | | | | | | | | | | | | all_42_2) = all_755_3 & in(all_42_1, all_42_2) = % 75.97/16.24 | | | | | | | | | | | | | | | | | all_755_4 & $i(all_755_1) & ( ~ (all_755_0 = 0) | % 75.97/16.24 | | | | | | | | | | | | | | | | | ~ (all_755_2 = 0) | ~ (all_755_3 = 0) | ~ % 75.97/16.24 | | | | | | | | | | | | | | | | | (all_755_4 = 0)) % 75.97/16.24 | | | | | | | | | | | | | | | | | % 75.97/16.24 | | | | | | | | | | | | | | | | | ALPHA: (545) implies: % 75.97/16.24 | | | | | | | | | | | | | | | | | (546) in(all_42_0, all_42_2) = all_755_3 % 75.97/16.24 | | | | | | | | | | | | | | | | | % 75.97/16.24 | | | | | | | | | | | | | | | | | REDUCE: (519), (546) imply: % 75.97/16.25 | | | | | | | | | | | | | | | | | (547) in(all_42_0, empty_set) = all_755_3 % 75.97/16.25 | | | | | | | | | | | | | | | | | % 75.97/16.25 | | | | | | | | | | | | | | | | | BETA: splitting (502) gives: % 75.97/16.25 | | | | | | | | | | | | | | | | | % 75.97/16.25 | | | | | | | | | | | | | | | | | Case 1: % 75.97/16.25 | | | | | | | | | | | | | | | | | | % 75.97/16.25 | | | | | | | | | | | | | | | | | | (548) all_42_0 = all_42_1 % 75.97/16.25 | | | | | | | | | | | | | | | | | | % 75.97/16.25 | | | | | | | | | | | | | | | | | | REDUCE: (46), (548) imply: % 75.97/16.25 | | | | | | | | | | | | | | | | | | (549) $false % 75.97/16.25 | | | | | | | | | | | | | | | | | | % 75.97/16.25 | | | | | | | | | | | | | | | | | | CLOSE: (549) is inconsistent. % 75.97/16.25 | | | | | | | | | | | | | | | | | | % 75.97/16.25 | | | | | | | | | | | | | | | | | Case 2: % 75.97/16.25 | | | | | | | | | | | | | | | | | | % 75.97/16.25 | | | | | | | | | | | | | | | | | | (550) ? [v0: any] : ? [v1: any] : ? [v2: $i] : ? % 75.97/16.25 | | | | | | | | | | | | | | | | | | [v3: any] : ? [v4: any] : (ordered_pair(all_42_0, % 75.97/16.25 | | | | | | | | | | | | | | | | | | all_42_1) = v2 & in(v2, all_56_1) = v3 & % 75.97/16.25 | | | | | | | | | | | | | | | | | | in(all_104_1, all_56_1) = v4 & in(all_42_0, % 75.97/16.25 | | | | | | | | | | | | | | | | | | all_42_2) = v0 & in(all_42_1, all_42_2) = v1 & % 75.97/16.25 | | | | | | | | | | | | | | | | | | $i(v2) & ( ~ (v4 = 0) | ~ (v3 = 0) | ~ (v1 = % 75.97/16.25 | | | | | | | | | | | | | | | | | | 0) | ~ (v0 = 0))) % 75.97/16.25 | | | | | | | | | | | | | | | | | | % 75.97/16.25 | | | | | | | | | | | | | | | | | | DELTA: instantiating (550) with fresh symbols all_760_0, % 75.97/16.25 | | | | | | | | | | | | | | | | | | all_760_1, all_760_2, all_760_3, all_760_4 gives: % 75.97/16.25 | | | | | | | | | | | | | | | | | | (551) ordered_pair(all_42_0, all_42_1) = all_760_2 & % 75.97/16.25 | | | | | | | | | | | | | | | | | | in(all_760_2, all_56_1) = all_760_1 & % 75.97/16.25 | | | | | | | | | | | | | | | | | | in(all_104_1, all_56_1) = all_760_0 & in(all_42_0, % 75.97/16.25 | | | | | | | | | | | | | | | | | | all_42_2) = all_760_4 & in(all_42_1, all_42_2) = % 75.97/16.25 | | | | | | | | | | | | | | | | | | all_760_3 & $i(all_760_2) & ( ~ (all_760_0 = 0) | % 75.97/16.25 | | | | | | | | | | | | | | | | | | ~ (all_760_1 = 0) | ~ (all_760_3 = 0) | ~ % 75.97/16.25 | | | | | | | | | | | | | | | | | | (all_760_4 = 0)) % 75.97/16.25 | | | | | | | | | | | | | | | | | | % 75.97/16.25 | | | | | | | | | | | | | | | | | | ALPHA: (551) implies: % 75.97/16.25 | | | | | | | | | | | | | | | | | | (552) in(all_42_0, all_42_2) = all_760_4 % 75.97/16.25 | | | | | | | | | | | | | | | | | | % 75.97/16.25 | | | | | | | | | | | | | | | | | | REDUCE: (519), (552) imply: % 75.97/16.25 | | | | | | | | | | | | | | | | | | (553) in(all_42_0, empty_set) = all_760_4 % 75.97/16.25 | | | | | | | | | | | | | | | | | | % 75.97/16.25 | | | | | | | | | | | | | | | | | | BETA: splitting (507) gives: % 75.97/16.25 | | | | | | | | | | | | | | | | | | % 75.97/16.25 | | | | | | | | | | | | | | | | | | Case 1: % 75.97/16.25 | | | | | | | | | | | | | | | | | | | % 75.97/16.25 | | | | | | | | | | | | | | | | | | | (554) all_282_0 = 0 % 75.97/16.25 | | | | | | | | | | | | | | | | | | | % 75.97/16.25 | | | | | | | | | | | | | | | | | | | REDUCE: (397), (554) imply: % 75.97/16.25 | | | | | | | | | | | | | | | | | | | (555) $false % 75.97/16.25 | | | | | | | | | | | | | | | | | | | % 75.97/16.25 | | | | | | | | | | | | | | | | | | | CLOSE: (555) is inconsistent. % 75.97/16.25 | | | | | | | | | | | | | | | | | | | % 75.97/16.25 | | | | | | | | | | | | | | | | | | Case 2: % 75.97/16.25 | | | | | | | | | | | | | | | | | | | % 75.97/16.25 | | | | | | | | | | | | | | | | | | | % 75.97/16.25 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (31) with all_750_3, all_755_3, % 75.97/16.25 | | | | | | | | | | | | | | | | | | | empty_set, all_42_0, simplifying with (541), (547) % 75.97/16.25 | | | | | | | | | | | | | | | | | | | gives: % 75.97/16.25 | | | | | | | | | | | | | | | | | | | (556) all_755_3 = all_750_3 % 75.97/16.25 | | | | | | | | | | | | | | | | | | | % 75.97/16.25 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (31) with all_745_4, all_755_3, % 75.97/16.25 | | | | | | | | | | | | | | | | | | | empty_set, all_42_0, simplifying with (534), (547) % 75.97/16.25 | | | | | | | | | | | | | | | | | | | gives: % 75.97/16.25 | | | | | | | | | | | | | | | | | | | (557) all_755_3 = all_745_4 % 75.97/16.25 | | | | | | | | | | | | | | | | | | | % 75.97/16.25 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (31) with all_755_3, all_760_4, % 75.97/16.25 | | | | | | | | | | | | | | | | | | | empty_set, all_42_0, simplifying with (547), (553) % 75.97/16.25 | | | | | | | | | | | | | | | | | | | gives: % 75.97/16.25 | | | | | | | | | | | | | | | | | | | (558) all_760_4 = all_755_3 % 75.97/16.25 | | | | | | | | | | | | | | | | | | | % 75.97/16.25 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (31) with all_50_0, all_760_4, % 75.97/16.25 | | | | | | | | | | | | | | | | | | | empty_set, all_42_0, simplifying with (527), (553) % 75.97/16.25 | | | | | | | | | | | | | | | | | | | gives: % 75.97/16.25 | | | | | | | | | | | | | | | | | | | (559) all_760_4 = all_50_0 % 75.97/16.25 | | | | | | | | | | | | | | | | | | | % 75.97/16.25 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (32) with all_104_1, all_750_2, % 75.97/16.25 | | | | | | | | | | | | | | | | | | | all_42_0, all_42_1, simplifying with (203), (540) % 75.97/16.25 | | | | | | | | | | | | | | | | | | | gives: % 75.97/16.25 | | | | | | | | | | | | | | | | | | | (560) all_750_2 = all_104_1 % 75.97/16.25 | | | | | | | | | | | | | | | | | | | % 75.97/16.25 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (32) with all_745_1, all_750_2, % 75.97/16.25 | | | | | | | | | | | | | | | | | | | all_42_0, all_42_1, simplifying with (533), (540) % 75.97/16.25 | | | | | | | | | | | | | | | | | | | gives: % 75.97/16.25 | | | | | | | | | | | | | | | | | | | (561) all_750_2 = all_745_1 % 75.97/16.25 | | | | | | | | | | | | | | | | | | | % 75.97/16.25 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (30) with all_256_0, all_504_1, % 75.97/16.25 | | | | | | | | | | | | | | | | | | | all_162_1, simplifying with (395), (525) gives: % 75.97/16.25 | | | | | | | | | | | | | | | | | | | (562) all_504_1 = all_256_0 % 75.97/16.25 | | | | | | | | | | | | | | | | | | | % 75.97/16.25 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (30) with all_502_1, all_504_1, % 75.97/16.25 | | | | | | | | | | | | | | | | | | | all_162_1, simplifying with (522), (525) gives: % 75.97/16.25 | | | | | | | | | | | | | | | | | | | (563) all_504_1 = all_502_1 % 75.97/16.25 | | | | | | | | | | | | | | | | | | | % 75.97/16.25 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (558), (559) imply: % 75.97/16.25 | | | | | | | | | | | | | | | | | | | (564) all_755_3 = all_50_0 % 75.97/16.25 | | | | | | | | | | | | | | | | | | | % 75.97/16.25 | | | | | | | | | | | | | | | | | | | SIMP: (564) implies: % 75.97/16.25 | | | | | | | | | | | | | | | | | | | (565) all_755_3 = all_50_0 % 75.97/16.25 | | | | | | | | | | | | | | | | | | | % 75.97/16.25 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (556), (557) imply: % 75.97/16.25 | | | | | | | | | | | | | | | | | | | (566) all_750_3 = all_745_4 % 75.97/16.25 | | | | | | | | | | | | | | | | | | | % 75.97/16.25 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (556), (565) imply: % 75.97/16.25 | | | | | | | | | | | | | | | | | | | (567) all_750_3 = all_50_0 % 75.97/16.25 | | | | | | | | | | | | | | | | | | | % 75.97/16.25 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (560), (561) imply: % 75.97/16.25 | | | | | | | | | | | | | | | | | | | (568) all_745_1 = all_104_1 % 75.97/16.25 | | | | | | | | | | | | | | | | | | | % 75.97/16.25 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (566), (567) imply: % 75.97/16.25 | | | | | | | | | | | | | | | | | | | (569) all_745_4 = all_50_0 % 75.97/16.25 | | | | | | | | | | | | | | | | | | | % 75.97/16.25 | | | | | | | | | | | | | | | | | | | SIMP: (569) implies: % 75.97/16.25 | | | | | | | | | | | | | | | | | | | (570) all_745_4 = all_50_0 % 75.97/16.25 | | | | | | | | | | | | | | | | | | | % 75.97/16.25 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (562), (563) imply: % 75.97/16.25 | | | | | | | | | | | | | | | | | | | (571) all_502_1 = all_256_0 % 75.97/16.25 | | | | | | | | | | | | | | | | | | | % 75.97/16.25 | | | | | | | | | | | | | | | | | | | SIMP: (571) implies: % 75.97/16.25 | | | | | | | | | | | | | | | | | | | (572) all_502_1 = all_256_0 % 75.97/16.25 | | | | | | | | | | | | | | | | | | | % 75.97/16.25 | | | | | | | | | | | | | | | | | | | BETA: splitting (523) gives: % 75.97/16.25 | | | | | | | | | | | | | | | | | | | % 75.97/16.25 | | | | | | | | | | | | | | | | | | | Case 1: % 75.97/16.25 | | | | | | | | | | | | | | | | | | | | % 75.97/16.25 | | | | | | | | | | | | | | | | | | | | (573) all_502_0 = 0 % 75.97/16.25 | | | | | | | | | | | | | | | | | | | | % 75.97/16.25 | | | | | | | | | | | | | | | | | | | | REDUCE: (521), (573) imply: % 75.97/16.25 | | | | | | | | | | | | | | | | | | | | (574) in(all_104_1, all_162_1) = 0 % 75.97/16.25 | | | | | | | | | | | | | | | | | | | | % 75.97/16.25 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (31), (49), (50), (126), (203), (421), % 75.97/16.25 | | | | | | | | | | | | | | | | | | | | (435), (497), (506), (526), (527), (574) are % 75.97/16.25 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1. % 75.97/16.25 | | | | | | | | | | | | | | | | | | | | % 75.97/16.25 | | | | | | | | | | | | | | | | | | | Case 2: % 75.97/16.25 | | | | | | | | | | | | | | | | | | | | % 75.97/16.25 | | | | | | | | | | | | | | | | | | | | (575) all_502_1 = 0 % 75.97/16.25 | | | | | | | | | | | | | | | | | | | | % 75.97/16.25 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (572), (575) imply: % 75.97/16.25 | | | | | | | | | | | | | | | | | | | | (576) all_256_0 = 0 % 75.97/16.25 | | | | | | | | | | | | | | | | | | | | % 75.97/16.25 | | | | | | | | | | | | | | | | | | | | REDUCE: (394), (576) imply: % 75.97/16.25 | | | | | | | | | | | | | | | | | | | | (577) $false % 75.97/16.25 | | | | | | | | | | | | | | | | | | | | % 75.97/16.25 | | | | | | | | | | | | | | | | | | | | CLOSE: (577) is inconsistent. % 75.97/16.25 | | | | | | | | | | | | | | | | | | | | % 75.97/16.25 | | | | | | | | | | | | | | | | | | | End of split % 75.97/16.25 | | | | | | | | | | | | | | | | | | | % 75.97/16.25 | | | | | | | | | | | | | | | | | | End of split % 75.97/16.25 | | | | | | | | | | | | | | | | | | % 75.97/16.25 | | | | | | | | | | | | | | | | | End of split % 75.97/16.25 | | | | | | | | | | | | | | | | | % 75.97/16.25 | | | | | | | | | | | | | | | | End of split % 75.97/16.25 | | | | | | | | | | | | | | | | % 75.97/16.25 | | | | | | | | | | | | | | | End of split % 75.97/16.25 | | | | | | | | | | | | | | | % 75.97/16.25 | | | | | | | | | | | | | | End of split % 75.97/16.25 | | | | | | | | | | | | | | % 75.97/16.25 | | | | | | | | | | | | | Case 2: % 75.97/16.25 | | | | | | | | | | | | | | % 75.97/16.25 | | | | | | | | | | | | | | (578) all_64_3 = 0 % 75.97/16.25 | | | | | | | | | | | | | | % 75.97/16.25 | | | | | | | | | | | | | | REDUCE: (499), (578) imply: % 75.97/16.25 | | | | | | | | | | | | | | (579) $false % 75.97/16.25 | | | | | | | | | | | | | | % 75.97/16.25 | | | | | | | | | | | | | | CLOSE: (579) is inconsistent. % 75.97/16.25 | | | | | | | | | | | | | | % 75.97/16.25 | | | | | | | | | | | | | End of split % 75.97/16.25 | | | | | | | | | | | | | % 75.97/16.25 | | | | | | | | | | | | Case 2: % 75.97/16.25 | | | | | | | | | | | | | % 75.97/16.25 | | | | | | | | | | | | | (580) all_64_0 = 0 % 75.97/16.25 | | | | | | | | | | | | | % 75.97/16.25 | | | | | | | | | | | | | REDUCE: (180), (580) imply: % 75.97/16.25 | | | | | | | | | | | | | (581) is_antisymmetric_in(all_54_1, all_54_0) = 0 % 75.97/16.25 | | | | | | | | | | | | | % 75.97/16.25 | | | | | | | | | | | | | BETA: splitting (213) gives: % 75.97/16.25 | | | | | | | | | | | | | % 75.97/16.25 | | | | | | | | | | | | | Case 1: % 75.97/16.25 | | | | | | | | | | | | | | % 75.97/16.25 | | | | | | | | | | | | | | (582) ~ (all_108_2 = 0) % 75.97/16.25 | | | | | | | | | | | | | | % 75.97/16.25 | | | | | | | | | | | | | | BETA: splitting (214) gives: % 75.97/16.25 | | | | | | | | | | | | | | % 75.97/16.25 | | | | | | | | | | | | | | Case 1: % 75.97/16.25 | | | | | | | | | | | | | | | % 75.97/16.25 | | | | | | | | | | | | | | | (583) ~ (all_108_0 = 0) % 75.97/16.25 | | | | | | | | | | | | | | | % 75.97/16.25 | | | | | | | | | | | | | | | BETA: splitting (247) gives: % 75.97/16.25 | | | | | | | | | | | | | | | % 75.97/16.25 | | | | | | | | | | | | | | | Case 1: % 75.97/16.25 | | | | | | | | | | | | | | | | % 75.97/16.25 | | | | | | | | | | | | | | | | (584) all_108_0 = 0 % 75.97/16.25 | | | | | | | | | | | | | | | | % 75.97/16.25 | | | | | | | | | | | | | | | | REDUCE: (583), (584) imply: % 75.97/16.25 | | | | | | | | | | | | | | | | (585) $false % 75.97/16.25 | | | | | | | | | | | | | | | | % 75.97/16.25 | | | | | | | | | | | | | | | | CLOSE: (585) is inconsistent. % 75.97/16.25 | | | | | | | | | | | | | | | | % 75.97/16.25 | | | | | | | | | | | | | | | Case 2: % 75.97/16.25 | | | | | | | | | | | | | | | | % 75.97/16.25 | | | | | | | | | | | | | | | | (586) ? [v0: any] : ? [v1: any] : (empty(all_56_1) = % 75.97/16.25 | | | | | | | | | | | | | | | | v1 & element(all_108_1, all_56_1) = v0 & ( ~ (v0 % 75.97/16.25 | | | | | | | | | | | | | | | | = 0) | v1 = 0)) % 75.97/16.25 | | | | | | | | | | | | | | | | % 75.97/16.25 | | | | | | | | | | | | | | | | DELTA: instantiating (586) with fresh symbols all_444_0, % 75.97/16.25 | | | | | | | | | | | | | | | | all_444_1 gives: % 75.97/16.25 | | | | | | | | | | | | | | | | (587) empty(all_56_1) = all_444_0 & element(all_108_1, % 75.97/16.25 | | | | | | | | | | | | | | | | all_56_1) = all_444_1 & ( ~ (all_444_1 = 0) | % 75.97/16.25 | | | | | | | | | | | | | | | | all_444_0 = 0) % 75.97/16.25 | | | | | | | | | | | | | | | | % 75.97/16.25 | | | | | | | | | | | | | | | | ALPHA: (587) implies: % 75.97/16.25 | | | | | | | | | | | | | | | | (588) empty(all_56_1) = all_444_0 % 75.97/16.25 | | | | | | | | | | | | | | | | (589) ~ (all_444_1 = 0) | all_444_0 = 0 % 75.97/16.25 | | | | | | | | | | | | | | | | % 75.97/16.25 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (30) with all_154_0, all_444_0, % 75.97/16.25 | | | | | | | | | | | | | | | | all_56_1, simplifying with (272), (588) gives: % 75.97/16.25 | | | | | | | | | | | | | | | | (590) all_444_0 = all_154_0 % 75.97/16.25 | | | | | | | | | | | | | | | | % 75.97/16.25 | | | | | | | | | | | | | | | | BETA: splitting (589) gives: % 75.97/16.25 | | | | | | | | | | | | | | | | % 75.97/16.25 | | | | | | | | | | | | | | | | Case 1: % 75.97/16.25 | | | | | | | | | | | | | | | | | % 75.97/16.25 | | | | | | | | | | | | | | | | | % 75.97/16.25 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (2) with all_56_1, all_42_2, % 75.97/16.25 | | | | | | | | | | | | | | | | | all_42_1, all_42_0, all_104_1, simplifying with % 75.97/16.25 | | | | | | | | | | | | | | | | | (48), (49), (50), (184), (188), (203), (382) % 75.97/16.25 | | | | | | | | | | | | | | | | | gives: % 75.97/16.26 | | | | | | | | | | | | | | | | | (591) all_42_0 = all_42_1 | ? [v0: any] : ? [v1: any] % 75.97/16.26 | | | | | | | | | | | | | | | | | : ? [v2: any] : ? [v3: $i] : ? [v4: any] : % 75.97/16.26 | | | | | | | | | | | | | | | | | (ordered_pair(all_42_0, all_42_1) = v3 & in(v3, % 75.97/16.26 | | | | | | | | | | | | | | | | | all_56_1) = v4 & in(all_104_1, all_56_1) = v2 % 75.97/16.26 | | | | | | | | | | | | | | | | | & in(all_42_0, all_42_2) = v1 & in(all_42_1, % 75.97/16.26 | | | | | | | | | | | | | | | | | all_42_2) = v0 & $i(v3) & ( ~ (v4 = 0) | ~ % 75.97/16.26 | | | | | | | | | | | | | | | | | (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0))) % 75.97/16.26 | | | | | | | | | | | | | | | | | % 75.97/16.26 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (19) with all_102_1, all_162_1, % 75.97/16.26 | | | | | | | | | | | | | | | | | simplifying with (285), (297), (378) gives: % 75.97/16.26 | | | | | | | | | | | | | | | | | (592) ? [v0: any] : ? [v1: any] : (empty(all_162_1) = % 75.97/16.26 | | | | | | | | | | | | | | | | | v0 & in(all_102_1, all_162_1) = v1 & (v1 = 0 | % 75.97/16.26 | | | | | | | | | | | | | | | | | v0 = 0)) % 75.97/16.26 | | | | | | | | | | | | | | | | | % 75.97/16.26 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (19) with all_104_1, all_162_1, % 75.97/16.26 | | | | | | | | | | | | | | | | | simplifying with (236), (285), (377) gives: % 75.97/16.26 | | | | | | | | | | | | | | | | | (593) ? [v0: any] : ? [v1: any] : (empty(all_162_1) = % 75.97/16.26 | | | | | | | | | | | | | | | | | v0 & in(all_104_1, all_162_1) = v1 & (v1 = 0 | % 75.97/16.26 | | | | | | | | | | | | | | | | | v0 = 0)) % 75.97/16.26 | | | | | | | | | | | | | | | | | % 75.97/16.26 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (3) with all_54_1, all_54_0, % 75.97/16.26 | | | | | | | | | | | | | | | | | all_42_1, all_42_0, all_102_1, simplifying with % 75.97/16.26 | | | | | | | | | | | | | | | | | (49), (50), (182), (183), (201), (384), (581) % 75.97/16.26 | | | | | | | | | | | | | | | | | gives: % 75.97/16.26 | | | | | | | | | | | | | | | | | (594) all_42_0 = all_42_1 | ? [v0: any] : ? [v1: any] % 75.97/16.26 | | | | | | | | | | | | | | | | | : ? [v2: $i] : ? [v3: any] : ? [v4: any] : % 75.97/16.26 | | | | | | | | | | | | | | | | | (ordered_pair(all_42_1, all_42_0) = v2 & in(v2, % 75.97/16.26 | | | | | | | | | | | | | | | | | all_54_1) = v3 & in(all_102_1, all_54_1) = v4 % 75.97/16.26 | | | | | | | | | | | | | | | | | & in(all_42_0, all_54_0) = v1 & in(all_42_1, % 75.97/16.26 | | | | | | | | | | | | | | | | | all_54_0) = v0 & $i(v2) & ( ~ (v4 = 0) | ~ % 75.97/16.26 | | | | | | | | | | | | | | | | | (v3 = 0) | ~ (v1 = 0) | ~ (v0 = 0))) % 75.97/16.26 | | | | | | | | | | | | | | | | | % 75.97/16.26 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (2) with all_54_1, all_54_0, % 75.97/16.26 | | | | | | | | | | | | | | | | | all_42_0, all_42_1, all_102_1, simplifying with % 75.97/16.26 | | | | | | | | | | | | | | | | | (49), (50), (182), (183), (201), (384), (581) % 75.97/16.26 | | | | | | | | | | | | | | | | | gives: % 75.97/16.26 | | | | | | | | | | | | | | | | | (595) all_42_0 = all_42_1 | ? [v0: any] : ? [v1: any] % 75.97/16.26 | | | | | | | | | | | | | | | | | : ? [v2: any] : ? [v3: $i] : ? [v4: any] : % 75.97/16.26 | | | | | | | | | | | | | | | | | (ordered_pair(all_42_1, all_42_0) = v3 & in(v3, % 75.97/16.26 | | | | | | | | | | | | | | | | | all_54_1) = v4 & in(all_102_1, all_54_1) = v2 % 75.97/16.26 | | | | | | | | | | | | | | | | | & in(all_42_0, all_54_0) = v0 & in(all_42_1, % 75.97/16.26 | | | | | | | | | | | | | | | | | all_54_0) = v1 & $i(v3) & ( ~ (v4 = 0) | ~ % 75.97/16.26 | | | | | | | | | | | | | | | | | (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0))) % 75.97/16.26 | | | | | | | | | | | | | | | | | % 75.97/16.26 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (16) with all_164_1, all_322_0, % 75.97/16.26 | | | | | | | | | | | | | | | | | simplifying with (290), (420) gives: % 75.97/16.26 | | | | | | | | | | | | | | | | | (596) all_322_0 = 0 | ? [v0: $i] : ? [v1: $i] : ? % 75.97/16.26 | | | | | | | | | | | | | | | | | [v2: int] : ( ~ (v2 = 0) & empty(v1) = v2 & % 75.97/16.26 | | | | | | | | | | | | | | | | | powerset(all_164_1) = v0 & element(v1, v0) = 0 & % 75.97/16.26 | | | | | | | | | | | | | | | | | $i(v1) & $i(v0)) % 75.97/16.26 | | | | | | | | | | | | | | | | | % 75.97/16.26 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (t8_boole) with all_288_0, % 75.97/16.26 | | | | | | | | | | | | | | | | | all_290_0, simplifying with (400), (401), (403), % 75.97/16.26 | | | | | | | | | | | | | | | | | (404) gives: % 75.97/16.26 | | | | | | | | | | | | | | | | | (597) all_290_0 = all_288_0 % 75.97/16.26 | | | | | | | | | | | | | | | | | % 75.97/16.26 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (t8_boole) with all_290_0, % 75.97/16.26 | | | | | | | | | | | | | | | | | all_292_0, simplifying with (403), (404), (406), % 75.97/16.26 | | | | | | | | | | | | | | | | | (407) gives: % 75.97/16.26 | | | | | | | | | | | | | | | | | (598) all_292_0 = all_290_0 % 75.97/16.26 | | | | | | | | | | | | | | | | | % 75.97/16.26 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (24) with all_292_0, simplifying % 75.97/16.26 | | | | | | | | | | | | | | | | | with (406), (407) gives: % 75.97/16.26 | | | | | | | | | | | | | | | | | (599) all_292_0 = empty_set % 75.97/16.26 | | | | | | | | | | | | | | | | | % 75.97/16.26 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (t8_boole) with all_290_0, % 75.97/16.26 | | | | | | | | | | | | | | | | | all_294_0, simplifying with (403), (404), (409), % 75.97/16.26 | | | | | | | | | | | | | | | | | (410) gives: % 75.97/16.26 | | | | | | | | | | | | | | | | | (600) all_294_0 = all_290_0 % 75.97/16.26 | | | | | | | | | | | | | | | | | % 75.97/16.26 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (t8_boole) with all_42_2, all_294_0, % 75.97/16.26 | | | | | | | | | | | | | | | | | simplifying with (48), (409), (410), (498) gives: % 75.97/16.26 | | | | | | | | | | | | | | | | | (601) all_294_0 = all_42_2 % 75.97/16.26 | | | | | | | | | | | | | | | | | % 75.97/16.26 | | | | | | | | | | | | | | | | | COMBINE_EQS: (600), (601) imply: % 75.97/16.26 | | | | | | | | | | | | | | | | | (602) all_290_0 = all_42_2 % 75.97/16.26 | | | | | | | | | | | | | | | | | % 75.97/16.26 | | | | | | | | | | | | | | | | | SIMP: (602) implies: % 75.97/16.26 | | | | | | | | | | | | | | | | | (603) all_290_0 = all_42_2 % 75.97/16.26 | | | | | | | | | | | | | | | | | % 75.97/16.26 | | | | | | | | | | | | | | | | | COMBINE_EQS: (598), (599) imply: % 75.97/16.26 | | | | | | | | | | | | | | | | | (604) all_290_0 = empty_set % 75.97/16.26 | | | | | | | | | | | | | | | | | % 75.97/16.26 | | | | | | | | | | | | | | | | | SIMP: (604) implies: % 75.97/16.26 | | | | | | | | | | | | | | | | | (605) all_290_0 = empty_set % 75.97/16.26 | | | | | | | | | | | | | | | | | % 75.97/16.26 | | | | | | | | | | | | | | | | | COMBINE_EQS: (597), (605) imply: % 75.97/16.26 | | | | | | | | | | | | | | | | | (606) all_288_0 = empty_set % 75.97/16.26 | | | | | | | | | | | | | | | | | % 75.97/16.26 | | | | | | | | | | | | | | | | | COMBINE_EQS: (597), (603) imply: % 75.97/16.26 | | | | | | | | | | | | | | | | | (607) all_288_0 = all_42_2 % 75.97/16.26 | | | | | | | | | | | | | | | | | % 75.97/16.26 | | | | | | | | | | | | | | | | | COMBINE_EQS: (606), (607) imply: % 75.97/16.26 | | | | | | | | | | | | | | | | | (608) all_42_2 = empty_set % 75.97/16.26 | | | | | | | | | | | | | | | | | % 75.97/16.26 | | | | | | | | | | | | | | | | | SIMP: (608) implies: % 75.97/16.26 | | | | | | | | | | | | | | | | | (609) all_42_2 = empty_set % 75.97/16.26 | | | | | | | | | | | | | | | | | % 75.97/16.26 | | | | | | | | | | | | | | | | | DELTA: instantiating (593) with fresh symbols all_512_0, % 75.97/16.26 | | | | | | | | | | | | | | | | | all_512_1 gives: % 75.97/16.26 | | | | | | | | | | | | | | | | | (610) empty(all_162_1) = all_512_1 & in(all_104_1, % 75.97/16.26 | | | | | | | | | | | | | | | | | all_162_1) = all_512_0 & (all_512_0 = 0 | % 75.97/16.26 | | | | | | | | | | | | | | | | | all_512_1 = 0) % 75.97/16.26 | | | | | | | | | | | | | | | | | % 75.97/16.26 | | | | | | | | | | | | | | | | | ALPHA: (610) implies: % 75.97/16.26 | | | | | | | | | | | | | | | | | (611) in(all_104_1, all_162_1) = all_512_0 % 75.97/16.26 | | | | | | | | | | | | | | | | | (612) empty(all_162_1) = all_512_1 % 75.97/16.26 | | | | | | | | | | | | | | | | | (613) all_512_0 = 0 | all_512_1 = 0 % 75.97/16.26 | | | | | | | | | | | | | | | | | % 75.97/16.26 | | | | | | | | | | | | | | | | | DELTA: instantiating (592) with fresh symbols all_520_0, % 75.97/16.26 | | | | | | | | | | | | | | | | | all_520_1 gives: % 75.97/16.26 | | | | | | | | | | | | | | | | | (614) empty(all_162_1) = all_520_1 & in(all_102_1, % 75.97/16.26 | | | | | | | | | | | | | | | | | all_162_1) = all_520_0 & (all_520_0 = 0 | % 75.97/16.26 | | | | | | | | | | | | | | | | | all_520_1 = 0) % 75.97/16.26 | | | | | | | | | | | | | | | | | % 75.97/16.26 | | | | | | | | | | | | | | | | | ALPHA: (614) implies: % 75.97/16.26 | | | | | | | | | | | | | | | | | (615) empty(all_162_1) = all_520_1 % 75.97/16.26 | | | | | | | | | | | | | | | | | % 75.97/16.26 | | | | | | | | | | | | | | | | | REDUCE: (288), (609) imply: % 75.97/16.26 | | | | | | | | | | | | | | | | | (616) cartesian_product2(empty_set, empty_set) = % 75.97/16.26 | | | | | | | | | | | | | | | | | all_162_1 % 75.97/16.26 | | | | | | | | | | | | | | | | | % 75.97/16.26 | | | | | | | | | | | | | | | | | REDUCE: (73), (609) imply: % 75.97/16.26 | | | | | | | | | | | | | | | | | (617) in(all_42_0, empty_set) = all_50_0 % 75.97/16.26 | | | | | | | | | | | | | | | | | % 75.97/16.26 | | | | | | | | | | | | | | | | | BETA: splitting (591) gives: % 75.97/16.26 | | | | | | | | | | | | | | | | | % 75.97/16.26 | | | | | | | | | | | | | | | | | Case 1: % 75.97/16.26 | | | | | | | | | | | | | | | | | | % 75.97/16.26 | | | | | | | | | | | | | | | | | | (618) all_42_0 = all_42_1 % 75.97/16.26 | | | | | | | | | | | | | | | | | | % 75.97/16.26 | | | | | | | | | | | | | | | | | | REDUCE: (46), (618) imply: % 75.97/16.26 | | | | | | | | | | | | | | | | | | (619) $false % 75.97/16.26 | | | | | | | | | | | | | | | | | | % 75.97/16.26 | | | | | | | | | | | | | | | | | | CLOSE: (619) is inconsistent. % 75.97/16.26 | | | | | | | | | | | | | | | | | | % 75.97/16.26 | | | | | | | | | | | | | | | | | Case 2: % 75.97/16.26 | | | | | | | | | | | | | | | | | | % 75.97/16.26 | | | | | | | | | | | | | | | | | | (620) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? % 75.97/16.26 | | | | | | | | | | | | | | | | | | [v3: $i] : ? [v4: any] : (ordered_pair(all_42_0, % 75.97/16.26 | | | | | | | | | | | | | | | | | | all_42_1) = v3 & in(v3, all_56_1) = v4 & % 75.97/16.26 | | | | | | | | | | | | | | | | | | in(all_104_1, all_56_1) = v2 & in(all_42_0, % 75.97/16.26 | | | | | | | | | | | | | | | | | | all_42_2) = v1 & in(all_42_1, all_42_2) = v0 & % 75.97/16.26 | | | | | | | | | | | | | | | | | | $i(v3) & ( ~ (v4 = 0) | ~ (v2 = 0) | ~ (v1 = % 75.97/16.26 | | | | | | | | | | | | | | | | | | 0) | ~ (v0 = 0))) % 75.97/16.26 | | | | | | | | | | | | | | | | | | % 75.97/16.26 | | | | | | | | | | | | | | | | | | DELTA: instantiating (620) with fresh symbols all_633_0, % 75.97/16.26 | | | | | | | | | | | | | | | | | | all_633_1, all_633_2, all_633_3, all_633_4 gives: % 75.97/16.26 | | | | | | | | | | | | | | | | | | (621) ordered_pair(all_42_0, all_42_1) = all_633_1 & % 75.97/16.26 | | | | | | | | | | | | | | | | | | in(all_633_1, all_56_1) = all_633_0 & % 75.97/16.26 | | | | | | | | | | | | | | | | | | in(all_104_1, all_56_1) = all_633_2 & in(all_42_0, % 75.97/16.26 | | | | | | | | | | | | | | | | | | all_42_2) = all_633_3 & in(all_42_1, all_42_2) = % 75.97/16.26 | | | | | | | | | | | | | | | | | | all_633_4 & $i(all_633_1) & ( ~ (all_633_0 = 0) | % 75.97/16.26 | | | | | | | | | | | | | | | | | | ~ (all_633_2 = 0) | ~ (all_633_3 = 0) | ~ % 75.97/16.26 | | | | | | | | | | | | | | | | | | (all_633_4 = 0)) % 75.97/16.26 | | | | | | | | | | | | | | | | | | % 75.97/16.26 | | | | | | | | | | | | | | | | | | ALPHA: (621) implies: % 75.97/16.26 | | | | | | | | | | | | | | | | | | (622) in(all_42_0, all_42_2) = all_633_3 % 75.97/16.26 | | | | | | | | | | | | | | | | | | % 75.97/16.26 | | | | | | | | | | | | | | | | | | REDUCE: (609), (622) imply: % 75.97/16.26 | | | | | | | | | | | | | | | | | | (623) in(all_42_0, empty_set) = all_633_3 % 75.97/16.26 | | | | | | | | | | | | | | | | | | % 75.97/16.26 | | | | | | | | | | | | | | | | | | BETA: splitting (595) gives: % 75.97/16.26 | | | | | | | | | | | | | | | | | | % 75.97/16.26 | | | | | | | | | | | | | | | | | | Case 1: % 75.97/16.26 | | | | | | | | | | | | | | | | | | | % 75.97/16.26 | | | | | | | | | | | | | | | | | | | (624) all_42_0 = all_42_1 % 75.97/16.26 | | | | | | | | | | | | | | | | | | | % 75.97/16.26 | | | | | | | | | | | | | | | | | | | REDUCE: (46), (624) imply: % 75.97/16.26 | | | | | | | | | | | | | | | | | | | (625) $false % 75.97/16.26 | | | | | | | | | | | | | | | | | | | % 75.97/16.26 | | | | | | | | | | | | | | | | | | | CLOSE: (625) is inconsistent. % 75.97/16.26 | | | | | | | | | | | | | | | | | | | % 75.97/16.26 | | | | | | | | | | | | | | | | | | Case 2: % 75.97/16.26 | | | | | | | | | | | | | | | | | | | % 75.97/16.26 | | | | | | | | | | | | | | | | | | | (626) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? % 75.97/16.26 | | | | | | | | | | | | | | | | | | | [v3: $i] : ? [v4: any] : (ordered_pair(all_42_1, % 75.97/16.26 | | | | | | | | | | | | | | | | | | | all_42_0) = v3 & in(v3, all_54_1) = v4 & % 75.97/16.26 | | | | | | | | | | | | | | | | | | | in(all_102_1, all_54_1) = v2 & in(all_42_0, % 75.97/16.26 | | | | | | | | | | | | | | | | | | | all_54_0) = v0 & in(all_42_1, all_54_0) = v1 & % 75.97/16.26 | | | | | | | | | | | | | | | | | | | $i(v3) & ( ~ (v4 = 0) | ~ (v2 = 0) | ~ (v1 = % 75.97/16.26 | | | | | | | | | | | | | | | | | | | 0) | ~ (v0 = 0))) % 75.97/16.26 | | | | | | | | | | | | | | | | | | | % 75.97/16.26 | | | | | | | | | | | | | | | | | | | DELTA: instantiating (626) with fresh symbols all_777_0, % 75.97/16.26 | | | | | | | | | | | | | | | | | | | all_777_1, all_777_2, all_777_3, all_777_4 gives: % 75.97/16.26 | | | | | | | | | | | | | | | | | | | (627) ordered_pair(all_42_1, all_42_0) = all_777_1 & % 75.97/16.26 | | | | | | | | | | | | | | | | | | | in(all_777_1, all_54_1) = all_777_0 & % 75.97/16.26 | | | | | | | | | | | | | | | | | | | in(all_102_1, all_54_1) = all_777_2 & in(all_42_0, % 75.97/16.26 | | | | | | | | | | | | | | | | | | | all_54_0) = all_777_4 & in(all_42_1, all_54_0) = % 75.97/16.26 | | | | | | | | | | | | | | | | | | | all_777_3 & $i(all_777_1) & ( ~ (all_777_0 = 0) | % 75.97/16.26 | | | | | | | | | | | | | | | | | | | ~ (all_777_2 = 0) | ~ (all_777_3 = 0) | ~ % 75.97/16.26 | | | | | | | | | | | | | | | | | | | (all_777_4 = 0)) % 75.97/16.26 | | | | | | | | | | | | | | | | | | | % 75.97/16.26 | | | | | | | | | | | | | | | | | | | ALPHA: (627) implies: % 75.97/16.26 | | | | | | | | | | | | | | | | | | | (628) ordered_pair(all_42_1, all_42_0) = all_777_1 % 75.97/16.26 | | | | | | | | | | | | | | | | | | | % 75.97/16.26 | | | | | | | | | | | | | | | | | | | BETA: splitting (594) gives: % 75.97/16.26 | | | | | | | | | | | | | | | | | | | % 75.97/16.26 | | | | | | | | | | | | | | | | | | | Case 1: % 75.97/16.26 | | | | | | | | | | | | | | | | | | | | % 75.97/16.26 | | | | | | | | | | | | | | | | | | | | (629) all_42_0 = all_42_1 % 75.97/16.26 | | | | | | | | | | | | | | | | | | | | % 75.97/16.26 | | | | | | | | | | | | | | | | | | | | REDUCE: (46), (629) imply: % 75.97/16.26 | | | | | | | | | | | | | | | | | | | | (630) $false % 75.97/16.26 | | | | | | | | | | | | | | | | | | | | % 75.97/16.26 | | | | | | | | | | | | | | | | | | | | CLOSE: (630) is inconsistent. % 75.97/16.26 | | | | | | | | | | | | | | | | | | | | % 75.97/16.27 | | | | | | | | | | | | | | | | | | | Case 2: % 75.97/16.27 | | | | | | | | | | | | | | | | | | | | % 75.97/16.27 | | | | | | | | | | | | | | | | | | | | (631) ? [v0: any] : ? [v1: any] : ? [v2: $i] : ? % 75.97/16.27 | | | | | | | | | | | | | | | | | | | | [v3: any] : ? [v4: any] : (ordered_pair(all_42_1, % 75.97/16.27 | | | | | | | | | | | | | | | | | | | | all_42_0) = v2 & in(v2, all_54_1) = v3 & % 75.97/16.27 | | | | | | | | | | | | | | | | | | | | in(all_102_1, all_54_1) = v4 & in(all_42_0, % 75.97/16.27 | | | | | | | | | | | | | | | | | | | | all_54_0) = v1 & in(all_42_1, all_54_0) = v0 & % 75.97/16.27 | | | | | | | | | | | | | | | | | | | | $i(v2) & ( ~ (v4 = 0) | ~ (v3 = 0) | ~ (v1 = % 75.97/16.27 | | | | | | | | | | | | | | | | | | | | 0) | ~ (v0 = 0))) % 75.97/16.27 | | | | | | | | | | | | | | | | | | | | % 75.97/16.27 | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (631) with fresh symbols all_782_0, % 75.97/16.27 | | | | | | | | | | | | | | | | | | | | all_782_1, all_782_2, all_782_3, all_782_4 gives: % 75.97/16.27 | | | | | | | | | | | | | | | | | | | | (632) ordered_pair(all_42_1, all_42_0) = all_782_2 & % 75.97/16.27 | | | | | | | | | | | | | | | | | | | | in(all_782_2, all_54_1) = all_782_1 & % 75.97/16.27 | | | | | | | | | | | | | | | | | | | | in(all_102_1, all_54_1) = all_782_0 & in(all_42_0, % 75.97/16.27 | | | | | | | | | | | | | | | | | | | | all_54_0) = all_782_3 & in(all_42_1, all_54_0) = % 75.97/16.27 | | | | | | | | | | | | | | | | | | | | all_782_4 & $i(all_782_2) & ( ~ (all_782_0 = 0) | % 75.97/16.27 | | | | | | | | | | | | | | | | | | | | ~ (all_782_1 = 0) | ~ (all_782_3 = 0) | ~ % 75.97/16.27 | | | | | | | | | | | | | | | | | | | | (all_782_4 = 0)) % 75.97/16.27 | | | | | | | | | | | | | | | | | | | | % 75.97/16.27 | | | | | | | | | | | | | | | | | | | | ALPHA: (632) implies: % 75.97/16.27 | | | | | | | | | | | | | | | | | | | | (633) ordered_pair(all_42_1, all_42_0) = all_782_2 % 75.97/16.27 | | | | | | | | | | | | | | | | | | | | % 75.97/16.27 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (31) with all_50_0, all_633_3, % 75.97/16.27 | | | | | | | | | | | | | | | | | | | | empty_set, all_42_0, simplifying with (617), (623) % 75.97/16.27 | | | | | | | | | | | | | | | | | | | | gives: % 75.97/16.27 | | | | | | | | | | | | | | | | | | | | (634) all_633_3 = all_50_0 % 75.97/16.27 | | | | | | | | | | | | | | | | | | | | % 75.97/16.27 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (32) with all_104_1, all_782_2, % 75.97/16.27 | | | | | | | | | | | | | | | | | | | | all_42_0, all_42_1, simplifying with (203), (633) % 75.97/16.27 | | | | | | | | | | | | | | | | | | | | gives: % 75.97/16.27 | | | | | | | | | | | | | | | | | | | | (635) all_782_2 = all_104_1 % 75.97/16.27 | | | | | | | | | | | | | | | | | | | | % 75.97/16.27 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (32) with all_777_1, all_782_2, % 75.97/16.27 | | | | | | | | | | | | | | | | | | | | all_42_0, all_42_1, simplifying with (628), (633) % 75.97/16.27 | | | | | | | | | | | | | | | | | | | | gives: % 75.97/16.27 | | | | | | | | | | | | | | | | | | | | (636) all_782_2 = all_777_1 % 75.97/16.27 | | | | | | | | | | | | | | | | | | | | % 75.97/16.27 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (30) with all_256_0, all_520_1, % 75.97/16.27 | | | | | | | | | | | | | | | | | | | | all_162_1, simplifying with (395), (615) gives: % 75.97/16.27 | | | | | | | | | | | | | | | | | | | | (637) all_520_1 = all_256_0 % 75.97/16.27 | | | | | | | | | | | | | | | | | | | | % 75.97/16.27 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (30) with all_512_1, all_520_1, % 75.97/16.27 | | | | | | | | | | | | | | | | | | | | all_162_1, simplifying with (612), (615) gives: % 75.97/16.27 | | | | | | | | | | | | | | | | | | | | (638) all_520_1 = all_512_1 % 75.97/16.27 | | | | | | | | | | | | | | | | | | | | % 75.97/16.27 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (635), (636) imply: % 75.97/16.27 | | | | | | | | | | | | | | | | | | | | (639) all_777_1 = all_104_1 % 75.97/16.27 | | | | | | | | | | | | | | | | | | | | % 75.97/16.27 | | | | | | | | | | | | | | | | | | | | SIMP: (639) implies: % 75.97/16.27 | | | | | | | | | | | | | | | | | | | | (640) all_777_1 = all_104_1 % 75.97/16.27 | | | | | | | | | | | | | | | | | | | | % 75.97/16.27 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (637), (638) imply: % 75.97/16.27 | | | | | | | | | | | | | | | | | | | | (641) all_512_1 = all_256_0 % 75.97/16.27 | | | | | | | | | | | | | | | | | | | | % 75.97/16.27 | | | | | | | | | | | | | | | | | | | | SIMP: (641) implies: % 75.97/16.27 | | | | | | | | | | | | | | | | | | | | (642) all_512_1 = all_256_0 % 75.97/16.27 | | | | | | | | | | | | | | | | | | | | % 75.97/16.27 | | | | | | | | | | | | | | | | | | | | BETA: splitting (613) gives: % 75.97/16.27 | | | | | | | | | | | | | | | | | | | | % 75.97/16.27 | | | | | | | | | | | | | | | | | | | | Case 1: % 75.97/16.27 | | | | | | | | | | | | | | | | | | | | | % 75.97/16.27 | | | | | | | | | | | | | | | | | | | | | (643) all_512_0 = 0 % 75.97/16.27 | | | | | | | | | | | | | | | | | | | | | % 75.97/16.27 | | | | | | | | | | | | | | | | | | | | | REDUCE: (611), (643) imply: % 75.97/16.27 | | | | | | | | | | | | | | | | | | | | | (644) in(all_104_1, all_162_1) = 0 % 75.97/16.27 | | | | | | | | | | | | | | | | | | | | | % 75.97/16.27 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (31), (49), (50), (126), (203), (421), % 75.97/16.27 | | | | | | | | | | | | | | | | | | | | | (435), (497), (596), (616), (617), (644) are % 75.97/16.27 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1. % 75.97/16.27 | | | | | | | | | | | | | | | | | | | | | % 75.97/16.27 | | | | | | | | | | | | | | | | | | | | Case 2: % 75.97/16.27 | | | | | | | | | | | | | | | | | | | | | % 75.97/16.27 | | | | | | | | | | | | | | | | | | | | | (645) all_512_1 = 0 % 75.97/16.27 | | | | | | | | | | | | | | | | | | | | | % 75.97/16.27 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (642), (645) imply: % 75.97/16.27 | | | | | | | | | | | | | | | | | | | | | (646) all_256_0 = 0 % 75.97/16.27 | | | | | | | | | | | | | | | | | | | | | % 75.97/16.27 | | | | | | | | | | | | | | | | | | | | | SIMP: (646) implies: % 75.97/16.27 | | | | | | | | | | | | | | | | | | | | | (647) all_256_0 = 0 % 75.97/16.27 | | | | | | | | | | | | | | | | | | | | | % 75.97/16.27 | | | | | | | | | | | | | | | | | | | | | REDUCE: (394), (647) imply: % 75.97/16.27 | | | | | | | | | | | | | | | | | | | | | (648) $false % 75.97/16.27 | | | | | | | | | | | | | | | | | | | | | % 75.97/16.27 | | | | | | | | | | | | | | | | | | | | | CLOSE: (648) is inconsistent. % 75.97/16.27 | | | | | | | | | | | | | | | | | | | | | % 75.97/16.27 | | | | | | | | | | | | | | | | | | | | End of split % 75.97/16.27 | | | | | | | | | | | | | | | | | | | | % 75.97/16.27 | | | | | | | | | | | | | | | | | | | End of split % 75.97/16.27 | | | | | | | | | | | | | | | | | | | % 75.97/16.27 | | | | | | | | | | | | | | | | | | End of split % 75.97/16.27 | | | | | | | | | | | | | | | | | | % 75.97/16.27 | | | | | | | | | | | | | | | | | End of split % 75.97/16.27 | | | | | | | | | | | | | | | | | % 75.97/16.27 | | | | | | | | | | | | | | | | Case 2: % 75.97/16.27 | | | | | | | | | | | | | | | | | % 75.97/16.27 | | | | | | | | | | | | | | | | | (649) all_444_0 = 0 % 75.97/16.27 | | | | | | | | | | | | | | | | | % 75.97/16.27 | | | | | | | | | | | | | | | | | COMBINE_EQS: (590), (649) imply: % 75.97/16.27 | | | | | | | | | | | | | | | | | (650) all_154_0 = 0 % 75.97/16.27 | | | | | | | | | | | | | | | | | % 75.97/16.27 | | | | | | | | | | | | | | | | | REDUCE: (271), (650) imply: % 75.97/16.27 | | | | | | | | | | | | | | | | | (651) $false % 75.97/16.27 | | | | | | | | | | | | | | | | | % 75.97/16.27 | | | | | | | | | | | | | | | | | CLOSE: (651) is inconsistent. % 75.97/16.27 | | | | | | | | | | | | | | | | | % 75.97/16.27 | | | | | | | | | | | | | | | | End of split % 75.97/16.27 | | | | | | | | | | | | | | | | % 75.97/16.27 | | | | | | | | | | | | | | | End of split % 75.97/16.27 | | | | | | | | | | | | | | | % 75.97/16.27 | | | | | | | | | | | | | | Case 2: % 75.97/16.27 | | | | | | | | | | | | | | | % 75.97/16.27 | | | | | | | | | | | | | | | (652) all_108_2 = 0 % 75.97/16.27 | | | | | | | | | | | | | | | % 75.97/16.27 | | | | | | | | | | | | | | | REDUCE: (582), (652) imply: % 75.97/16.27 | | | | | | | | | | | | | | | (653) $false % 75.97/16.27 | | | | | | | | | | | | | | | % 75.97/16.27 | | | | | | | | | | | | | | | CLOSE: (653) is inconsistent. % 75.97/16.27 | | | | | | | | | | | | | | | % 75.97/16.27 | | | | | | | | | | | | | | End of split % 75.97/16.27 | | | | | | | | | | | | | | % 75.97/16.27 | | | | | | | | | | | | | Case 2: % 75.97/16.27 | | | | | | | | | | | | | | % 75.97/16.27 | | | | | | | | | | | | | | % 75.97/16.27 | | | | | | | | | | | | | | GROUND_INST: instantiating (3) with all_56_1, all_42_2, % 75.97/16.27 | | | | | | | | | | | | | | all_42_1, all_42_0, all_102_1, simplifying with % 75.97/16.27 | | | | | | | | | | | | | | (48), (49), (50), (184), (188), (201), (382) % 75.97/16.27 | | | | | | | | | | | | | | gives: % 75.97/16.27 | | | | | | | | | | | | | | (654) all_42_0 = all_42_1 | ? [v0: any] : ? [v1: any] % 75.97/16.27 | | | | | | | | | | | | | | : ? [v2: $i] : ? [v3: any] : ? [v4: any] : % 75.97/16.27 | | | | | | | | | | | | | | (ordered_pair(all_42_1, all_42_0) = v2 & in(v2, % 75.97/16.27 | | | | | | | | | | | | | | all_56_1) = v3 & in(all_102_1, all_56_1) = v4 % 75.97/16.27 | | | | | | | | | | | | | | & in(all_42_0, all_42_2) = v1 & in(all_42_1, % 75.97/16.27 | | | | | | | | | | | | | | all_42_2) = v0 & $i(v2) & ( ~ (v4 = 0) | ~ % 75.97/16.27 | | | | | | | | | | | | | | (v3 = 0) | ~ (v1 = 0) | ~ (v0 = 0))) % 75.97/16.27 | | | | | | | | | | | | | | % 75.97/16.27 | | | | | | | | | | | | | | GROUND_INST: instantiating (2) with all_56_1, all_42_2, % 75.97/16.27 | | | | | | | | | | | | | | all_42_0, all_42_1, all_102_1, simplifying with % 75.97/16.27 | | | | | | | | | | | | | | (48), (49), (50), (184), (188), (201), (382) % 75.97/16.27 | | | | | | | | | | | | | | gives: % 75.97/16.27 | | | | | | | | | | | | | | (655) all_42_0 = all_42_1 | ? [v0: any] : ? [v1: any] % 75.97/16.27 | | | | | | | | | | | | | | : ? [v2: any] : ? [v3: $i] : ? [v4: any] : % 75.97/16.27 | | | | | | | | | | | | | | (ordered_pair(all_42_1, all_42_0) = v3 & in(v3, % 75.97/16.27 | | | | | | | | | | | | | | all_56_1) = v4 & in(all_102_1, all_56_1) = v2 % 75.97/16.27 | | | | | | | | | | | | | | & in(all_42_0, all_42_2) = v0 & in(all_42_1, % 75.97/16.27 | | | | | | | | | | | | | | all_42_2) = v1 & $i(v3) & ( ~ (v4 = 0) | ~ % 75.97/16.27 | | | | | | | | | | | | | | (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0))) % 75.97/16.27 | | | | | | | | | | | | | | % 75.97/16.27 | | | | | | | | | | | | | | GROUND_INST: instantiating (3) with all_56_1, all_42_2, % 75.97/16.27 | | | | | | | | | | | | | | all_42_0, all_42_1, all_104_1, simplifying with % 75.97/16.27 | | | | | | | | | | | | | | (48), (49), (50), (184), (188), (203), (382) % 75.97/16.27 | | | | | | | | | | | | | | gives: % 75.97/16.27 | | | | | | | | | | | | | | (656) all_42_0 = all_42_1 | ? [v0: any] : ? [v1: any] % 75.97/16.27 | | | | | | | | | | | | | | : ? [v2: $i] : ? [v3: any] : ? [v4: any] : % 75.97/16.27 | | | | | | | | | | | | | | (ordered_pair(all_42_0, all_42_1) = v2 & in(v2, % 75.97/16.27 | | | | | | | | | | | | | | all_56_1) = v3 & in(all_104_1, all_56_1) = v4 % 75.97/16.27 | | | | | | | | | | | | | | & in(all_42_0, all_42_2) = v0 & in(all_42_1, % 75.97/16.27 | | | | | | | | | | | | | | all_42_2) = v1 & $i(v2) & ( ~ (v4 = 0) | ~ % 75.97/16.27 | | | | | | | | | | | | | | (v3 = 0) | ~ (v1 = 0) | ~ (v0 = 0))) % 75.97/16.27 | | | | | | | | | | | | | | % 75.97/16.27 | | | | | | | | | | | | | | GROUND_INST: instantiating (2) with all_56_1, all_42_2, % 75.97/16.27 | | | | | | | | | | | | | | all_42_1, all_42_0, all_104_1, simplifying with % 75.97/16.27 | | | | | | | | | | | | | | (48), (49), (50), (184), (188), (203), (382) % 75.97/16.27 | | | | | | | | | | | | | | gives: % 75.97/16.27 | | | | | | | | | | | | | | (657) all_42_0 = all_42_1 | ? [v0: any] : ? [v1: any] % 75.97/16.27 | | | | | | | | | | | | | | : ? [v2: any] : ? [v3: $i] : ? [v4: any] : % 75.97/16.27 | | | | | | | | | | | | | | (ordered_pair(all_42_0, all_42_1) = v3 & in(v3, % 75.97/16.27 | | | | | | | | | | | | | | all_56_1) = v4 & in(all_104_1, all_56_1) = v2 % 75.97/16.27 | | | | | | | | | | | | | | & in(all_42_0, all_42_2) = v1 & in(all_42_1, % 75.97/16.27 | | | | | | | | | | | | | | all_42_2) = v0 & $i(v3) & ( ~ (v4 = 0) | ~ % 75.97/16.27 | | | | | | | | | | | | | | (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0))) % 75.97/16.27 | | | | | | | | | | | | | | % 75.97/16.27 | | | | | | | | | | | | | | GROUND_INST: instantiating (19) with all_102_1, all_162_1, % 75.97/16.27 | | | | | | | | | | | | | | simplifying with (285), (297), (378) gives: % 75.97/16.27 | | | | | | | | | | | | | | (658) ? [v0: any] : ? [v1: any] : (empty(all_162_1) = % 75.97/16.27 | | | | | | | | | | | | | | v0 & in(all_102_1, all_162_1) = v1 & (v1 = 0 | % 75.97/16.27 | | | | | | | | | | | | | | v0 = 0)) % 75.97/16.27 | | | | | | | | | | | | | | % 75.97/16.27 | | | | | | | | | | | | | | GROUND_INST: instantiating (19) with all_104_1, all_162_1, % 75.97/16.27 | | | | | | | | | | | | | | simplifying with (236), (285), (377) gives: % 75.97/16.27 | | | | | | | | | | | | | | (659) ? [v0: any] : ? [v1: any] : (empty(all_162_1) = % 75.97/16.27 | | | | | | | | | | | | | | v0 & in(all_104_1, all_162_1) = v1 & (v1 = 0 | % 75.97/16.27 | | | | | | | | | | | | | | v0 = 0)) % 75.97/16.27 | | | | | | | | | | | | | | % 75.97/16.27 | | | | | | | | | | | | | | GROUND_INST: instantiating (15) with all_80_2, all_350_2, % 75.97/16.27 | | | | | | | | | | | | | | simplifying with (132), (430) gives: % 75.97/16.27 | | | | | | | | | | | | | | (660) ? [v0: int] : ? [v1: $i] : ? [v2: int] : ? % 75.97/16.27 | | | | | | | | | | | | | | [v3: int] : ($i(v1) & ((v2 = 0 & ~ (v3 = 0) & % 75.97/16.27 | | | | | | | | | | | | | | empty(v1) = v3 & element(v1, all_350_2) = 0) % 75.97/16.27 | | | | | | | | | | | | | | | (v0 = 0 & empty(all_80_2) = 0))) % 75.97/16.27 | | | | | | | | | | | | | | % 75.97/16.28 | | | | | | | | | | | | | | GROUND_INST: instantiating (3) with all_54_1, all_54_0, % 75.97/16.28 | | | | | | | | | | | | | | all_42_1, all_42_0, all_102_1, simplifying with % 75.97/16.28 | | | | | | | | | | | | | | (49), (50), (182), (183), (201), (384), (581) % 75.97/16.28 | | | | | | | | | | | | | | gives: % 75.97/16.28 | | | | | | | | | | | | | | (661) all_42_0 = all_42_1 | ? [v0: any] : ? [v1: any] % 75.97/16.28 | | | | | | | | | | | | | | : ? [v2: $i] : ? [v3: any] : ? [v4: any] : % 75.97/16.28 | | | | | | | | | | | | | | (ordered_pair(all_42_1, all_42_0) = v2 & in(v2, % 75.97/16.28 | | | | | | | | | | | | | | all_54_1) = v3 & in(all_102_1, all_54_1) = v4 % 75.97/16.28 | | | | | | | | | | | | | | & in(all_42_0, all_54_0) = v1 & in(all_42_1, % 75.97/16.28 | | | | | | | | | | | | | | all_54_0) = v0 & $i(v2) & ( ~ (v4 = 0) | ~ % 75.97/16.28 | | | | | | | | | | | | | | (v3 = 0) | ~ (v1 = 0) | ~ (v0 = 0))) % 75.97/16.28 | | | | | | | | | | | | | | % 75.97/16.28 | | | | | | | | | | | | | | GROUND_INST: instantiating (2) with all_54_1, all_54_0, % 75.97/16.28 | | | | | | | | | | | | | | all_42_0, all_42_1, all_102_1, simplifying with % 75.97/16.28 | | | | | | | | | | | | | | (49), (50), (182), (183), (201), (384), (581) % 75.97/16.28 | | | | | | | | | | | | | | gives: % 75.97/16.28 | | | | | | | | | | | | | | (662) all_42_0 = all_42_1 | ? [v0: any] : ? [v1: any] % 75.97/16.28 | | | | | | | | | | | | | | : ? [v2: any] : ? [v3: $i] : ? [v4: any] : % 75.97/16.28 | | | | | | | | | | | | | | (ordered_pair(all_42_1, all_42_0) = v3 & in(v3, % 75.97/16.28 | | | | | | | | | | | | | | all_54_1) = v4 & in(all_102_1, all_54_1) = v2 % 75.97/16.28 | | | | | | | | | | | | | | & in(all_42_0, all_54_0) = v0 & in(all_42_1, % 75.97/16.28 | | | | | | | | | | | | | | all_54_0) = v1 & $i(v3) & ( ~ (v4 = 0) | ~ % 75.97/16.28 | | | | | | | | | | | | | | (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0))) % 75.97/16.28 | | | | | | | | | | | | | | % 75.97/16.28 | | | | | | | | | | | | | | GROUND_INST: instantiating (16) with all_164_1, all_322_0, % 75.97/16.28 | | | | | | | | | | | | | | simplifying with (290), (420) gives: % 75.97/16.28 | | | | | | | | | | | | | | (663) all_322_0 = 0 | ? [v0: $i] : ? [v1: $i] : ? % 75.97/16.28 | | | | | | | | | | | | | | [v2: int] : ( ~ (v2 = 0) & empty(v1) = v2 & % 75.97/16.28 | | | | | | | | | | | | | | powerset(all_164_1) = v0 & element(v1, v0) = 0 & % 75.97/16.28 | | | | | | | | | | | | | | $i(v1) & $i(v0)) % 75.97/16.28 | | | | | | | | | | | | | | % 75.97/16.28 | | | | | | | | | | | | | | GROUND_INST: instantiating (t8_boole) with all_290_0, % 75.97/16.28 | | | | | | | | | | | | | | all_292_0, simplifying with (403), (404), (406), % 75.97/16.28 | | | | | | | | | | | | | | (407) gives: % 75.97/16.28 | | | | | | | | | | | | | | (664) all_292_0 = all_290_0 % 75.97/16.28 | | | | | | | | | | | | | | % 75.97/16.28 | | | | | | | | | | | | | | GROUND_INST: instantiating (t8_boole) with all_288_0, % 75.97/16.28 | | | | | | | | | | | | | | all_292_0, simplifying with (400), (401), (406), % 75.97/16.28 | | | | | | | | | | | | | | (407) gives: % 75.97/16.28 | | | | | | | | | | | | | | (665) all_292_0 = all_288_0 % 75.97/16.28 | | | | | | | | | | | | | | % 75.97/16.28 | | | | | | | | | | | | | | GROUND_INST: instantiating (24) with all_292_0, simplifying % 75.97/16.28 | | | | | | | | | | | | | | with (406), (407) gives: % 75.97/16.28 | | | | | | | | | | | | | | (666) all_292_0 = empty_set % 75.97/16.28 | | | | | | | | | | | | | | % 75.97/16.28 | | | | | | | | | | | | | | GROUND_INST: instantiating (t8_boole) with all_290_0, % 75.97/16.28 | | | | | | | | | | | | | | all_294_0, simplifying with (403), (404), (409), % 75.97/16.28 | | | | | | | | | | | | | | (410) gives: % 75.97/16.28 | | | | | | | | | | | | | | (667) all_294_0 = all_290_0 % 75.97/16.28 | | | | | | | | | | | | | | % 75.97/16.28 | | | | | | | | | | | | | | GROUND_INST: instantiating (t8_boole) with all_42_2, all_294_0, % 75.97/16.28 | | | | | | | | | | | | | | simplifying with (48), (409), (410), (498) gives: % 75.97/16.28 | | | | | | | | | | | | | | (668) all_294_0 = all_42_2 % 75.97/16.28 | | | | | | | | | | | | | | % 75.97/16.28 | | | | | | | | | | | | | | COMBINE_EQS: (667), (668) imply: % 75.97/16.28 | | | | | | | | | | | | | | (669) all_290_0 = all_42_2 % 75.97/16.28 | | | | | | | | | | | | | | % 75.97/16.28 | | | | | | | | | | | | | | SIMP: (669) implies: % 75.97/16.28 | | | | | | | | | | | | | | (670) all_290_0 = all_42_2 % 75.97/16.28 | | | | | | | | | | | | | | % 75.97/16.28 | | | | | | | | | | | | | | COMBINE_EQS: (664), (665) imply: % 75.97/16.28 | | | | | | | | | | | | | | (671) all_290_0 = all_288_0 % 75.97/16.28 | | | | | | | | | | | | | | % 75.97/16.28 | | | | | | | | | | | | | | SIMP: (671) implies: % 75.97/16.28 | | | | | | | | | | | | | | (672) all_290_0 = all_288_0 % 75.97/16.28 | | | | | | | | | | | | | | % 75.97/16.28 | | | | | | | | | | | | | | COMBINE_EQS: (665), (666) imply: % 75.97/16.28 | | | | | | | | | | | | | | (673) all_288_0 = empty_set % 75.97/16.28 | | | | | | | | | | | | | | % 75.97/16.28 | | | | | | | | | | | | | | COMBINE_EQS: (670), (672) imply: % 75.97/16.28 | | | | | | | | | | | | | | (674) all_288_0 = all_42_2 % 75.97/16.28 | | | | | | | | | | | | | | % 75.97/16.28 | | | | | | | | | | | | | | SIMP: (674) implies: % 75.97/16.28 | | | | | | | | | | | | | | (675) all_288_0 = all_42_2 % 75.97/16.28 | | | | | | | | | | | | | | % 75.97/16.28 | | | | | | | | | | | | | | COMBINE_EQS: (673), (675) imply: % 75.97/16.28 | | | | | | | | | | | | | | (676) all_42_2 = empty_set % 75.97/16.28 | | | | | | | | | | | | | | % 75.97/16.28 | | | | | | | | | | | | | | DELTA: instantiating (658) with fresh symbols all_506_0, % 75.97/16.28 | | | | | | | | | | | | | | all_506_1 gives: % 75.97/16.28 | | | | | | | | | | | | | | (677) empty(all_162_1) = all_506_1 & in(all_102_1, % 75.97/16.28 | | | | | | | | | | | | | | all_162_1) = all_506_0 & (all_506_0 = 0 | % 75.97/16.28 | | | | | | | | | | | | | | all_506_1 = 0) % 75.97/16.28 | | | | | | | | | | | | | | % 75.97/16.28 | | | | | | | | | | | | | | ALPHA: (677) implies: % 75.97/16.28 | | | | | | | | | | | | | | (678) empty(all_162_1) = all_506_1 % 75.97/16.28 | | | | | | | | | | | | | | % 75.97/16.28 | | | | | | | | | | | | | | DELTA: instantiating (659) with fresh symbols all_516_0, % 75.97/16.28 | | | | | | | | | | | | | | all_516_1 gives: % 75.97/16.28 | | | | | | | | | | | | | | (679) empty(all_162_1) = all_516_1 & in(all_104_1, % 75.97/16.28 | | | | | | | | | | | | | | all_162_1) = all_516_0 & (all_516_0 = 0 | % 75.97/16.28 | | | | | | | | | | | | | | all_516_1 = 0) % 75.97/16.28 | | | | | | | | | | | | | | % 75.97/16.28 | | | | | | | | | | | | | | ALPHA: (679) implies: % 75.97/16.28 | | | | | | | | | | | | | | (680) in(all_104_1, all_162_1) = all_516_0 % 75.97/16.28 | | | | | | | | | | | | | | (681) empty(all_162_1) = all_516_1 % 75.97/16.28 | | | | | | | | | | | | | | (682) all_516_0 = 0 | all_516_1 = 0 % 75.97/16.28 | | | | | | | | | | | | | | % 75.97/16.28 | | | | | | | | | | | | | | DELTA: instantiating (660) with fresh symbols all_590_0, % 75.97/16.28 | | | | | | | | | | | | | | all_590_1, all_590_2, all_590_3 gives: % 75.97/16.28 | | | | | | | | | | | | | | (683) $i(all_590_2) & ((all_590_1 = 0 & ~ (all_590_0 = % 75.97/16.28 | | | | | | | | | | | | | | 0) & empty(all_590_2) = all_590_0 & % 75.97/16.28 | | | | | | | | | | | | | | element(all_590_2, all_350_2) = 0) | % 75.97/16.28 | | | | | | | | | | | | | | (all_590_3 = 0 & empty(all_80_2) = 0)) % 75.97/16.28 | | | | | | | | | | | | | | % 75.97/16.28 | | | | | | | | | | | | | | ALPHA: (683) implies: % 75.97/16.28 | | | | | | | | | | | | | | (684) (all_590_1 = 0 & ~ (all_590_0 = 0) & % 75.97/16.28 | | | | | | | | | | | | | | empty(all_590_2) = all_590_0 & % 75.97/16.28 | | | | | | | | | | | | | | element(all_590_2, all_350_2) = 0) | (all_590_3 % 75.97/16.28 | | | | | | | | | | | | | | = 0 & empty(all_80_2) = 0) % 75.97/16.28 | | | | | | | | | | | | | | % 75.97/16.28 | | | | | | | | | | | | | | REDUCE: (288), (676) imply: % 75.97/16.28 | | | | | | | | | | | | | | (685) cartesian_product2(empty_set, empty_set) = % 75.97/16.28 | | | | | | | | | | | | | | all_162_1 % 75.97/16.28 | | | | | | | | | | | | | | % 75.97/16.28 | | | | | | | | | | | | | | REDUCE: (73), (676) imply: % 75.97/16.28 | | | | | | | | | | | | | | (686) in(all_42_0, empty_set) = all_50_0 % 75.97/16.28 | | | | | | | | | | | | | | % 75.97/16.28 | | | | | | | | | | | | | | BETA: splitting (654) gives: % 75.97/16.28 | | | | | | | | | | | | | | % 75.97/16.28 | | | | | | | | | | | | | | Case 1: % 75.97/16.28 | | | | | | | | | | | | | | | % 75.97/16.28 | | | | | | | | | | | | | | | (687) all_42_0 = all_42_1 % 75.97/16.28 | | | | | | | | | | | | | | | % 75.97/16.28 | | | | | | | | | | | | | | | REDUCE: (46), (687) imply: % 75.97/16.28 | | | | | | | | | | | | | | | (688) $false % 75.97/16.28 | | | | | | | | | | | | | | | % 75.97/16.28 | | | | | | | | | | | | | | | CLOSE: (688) is inconsistent. % 75.97/16.28 | | | | | | | | | | | | | | | % 75.97/16.28 | | | | | | | | | | | | | | Case 2: % 75.97/16.28 | | | | | | | | | | | | | | | % 75.97/16.28 | | | | | | | | | | | | | | | (689) ? [v0: any] : ? [v1: any] : ? [v2: $i] : ? % 75.97/16.28 | | | | | | | | | | | | | | | [v3: any] : ? [v4: any] : (ordered_pair(all_42_1, % 75.97/16.28 | | | | | | | | | | | | | | | all_42_0) = v2 & in(v2, all_56_1) = v3 & % 75.97/16.28 | | | | | | | | | | | | | | | in(all_102_1, all_56_1) = v4 & in(all_42_0, % 75.97/16.28 | | | | | | | | | | | | | | | all_42_2) = v1 & in(all_42_1, all_42_2) = v0 & % 75.97/16.28 | | | | | | | | | | | | | | | $i(v2) & ( ~ (v4 = 0) | ~ (v3 = 0) | ~ (v1 = % 75.97/16.28 | | | | | | | | | | | | | | | 0) | ~ (v0 = 0))) % 75.97/16.28 | | | | | | | | | | | | | | | % 75.97/16.28 | | | | | | | | | | | | | | | DELTA: instantiating (689) with fresh symbols all_641_0, % 75.97/16.28 | | | | | | | | | | | | | | | all_641_1, all_641_2, all_641_3, all_641_4 gives: % 75.97/16.28 | | | | | | | | | | | | | | | (690) ordered_pair(all_42_1, all_42_0) = all_641_2 & % 75.97/16.28 | | | | | | | | | | | | | | | in(all_641_2, all_56_1) = all_641_1 & % 75.97/16.28 | | | | | | | | | | | | | | | in(all_102_1, all_56_1) = all_641_0 & in(all_42_0, % 75.97/16.28 | | | | | | | | | | | | | | | all_42_2) = all_641_3 & in(all_42_1, all_42_2) = % 75.97/16.28 | | | | | | | | | | | | | | | all_641_4 & $i(all_641_2) & ( ~ (all_641_0 = 0) | % 75.97/16.28 | | | | | | | | | | | | | | | ~ (all_641_1 = 0) | ~ (all_641_3 = 0) | ~ % 75.97/16.28 | | | | | | | | | | | | | | | (all_641_4 = 0)) % 75.97/16.28 | | | | | | | | | | | | | | | % 75.97/16.28 | | | | | | | | | | | | | | | ALPHA: (690) implies: % 75.97/16.28 | | | | | | | | | | | | | | | (691) in(all_42_0, all_42_2) = all_641_3 % 75.97/16.28 | | | | | | | | | | | | | | | (692) ordered_pair(all_42_1, all_42_0) = all_641_2 % 75.97/16.28 | | | | | | | | | | | | | | | % 75.97/16.28 | | | | | | | | | | | | | | | REDUCE: (676), (691) imply: % 75.97/16.28 | | | | | | | | | | | | | | | (693) in(all_42_0, empty_set) = all_641_3 % 75.97/16.28 | | | | | | | | | | | | | | | % 75.97/16.28 | | | | | | | | | | | | | | | BETA: splitting (655) gives: % 75.97/16.28 | | | | | | | | | | | | | | | % 75.97/16.28 | | | | | | | | | | | | | | | Case 1: % 75.97/16.28 | | | | | | | | | | | | | | | | % 75.97/16.28 | | | | | | | | | | | | | | | | (694) all_42_0 = all_42_1 % 75.97/16.28 | | | | | | | | | | | | | | | | % 75.97/16.28 | | | | | | | | | | | | | | | | REDUCE: (46), (694) imply: % 75.97/16.28 | | | | | | | | | | | | | | | | (695) $false % 75.97/16.28 | | | | | | | | | | | | | | | | % 75.97/16.28 | | | | | | | | | | | | | | | | CLOSE: (695) is inconsistent. % 75.97/16.28 | | | | | | | | | | | | | | | | % 75.97/16.28 | | | | | | | | | | | | | | | Case 2: % 75.97/16.28 | | | | | | | | | | | | | | | | % 75.97/16.28 | | | | | | | | | | | | | | | | (696) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? % 75.97/16.28 | | | | | | | | | | | | | | | | [v3: $i] : ? [v4: any] : (ordered_pair(all_42_1, % 75.97/16.28 | | | | | | | | | | | | | | | | all_42_0) = v3 & in(v3, all_56_1) = v4 & % 75.97/16.28 | | | | | | | | | | | | | | | | in(all_102_1, all_56_1) = v2 & in(all_42_0, % 75.97/16.28 | | | | | | | | | | | | | | | | all_42_2) = v0 & in(all_42_1, all_42_2) = v1 & % 75.97/16.28 | | | | | | | | | | | | | | | | $i(v3) & ( ~ (v4 = 0) | ~ (v2 = 0) | ~ (v1 = % 75.97/16.28 | | | | | | | | | | | | | | | | 0) | ~ (v0 = 0))) % 75.97/16.28 | | | | | | | | | | | | | | | | % 75.97/16.29 | | | | | | | | | | | | | | | | DELTA: instantiating (696) with fresh symbols all_646_0, % 75.97/16.29 | | | | | | | | | | | | | | | | all_646_1, all_646_2, all_646_3, all_646_4 gives: % 75.97/16.29 | | | | | | | | | | | | | | | | (697) ordered_pair(all_42_1, all_42_0) = all_646_1 & % 75.97/16.29 | | | | | | | | | | | | | | | | in(all_646_1, all_56_1) = all_646_0 & % 75.97/16.29 | | | | | | | | | | | | | | | | in(all_102_1, all_56_1) = all_646_2 & in(all_42_0, % 75.97/16.29 | | | | | | | | | | | | | | | | all_42_2) = all_646_4 & in(all_42_1, all_42_2) = % 75.97/16.29 | | | | | | | | | | | | | | | | all_646_3 & $i(all_646_1) & ( ~ (all_646_0 = 0) | % 75.97/16.29 | | | | | | | | | | | | | | | | ~ (all_646_2 = 0) | ~ (all_646_3 = 0) | ~ % 75.97/16.29 | | | | | | | | | | | | | | | | (all_646_4 = 0)) % 75.97/16.29 | | | | | | | | | | | | | | | | % 75.97/16.29 | | | | | | | | | | | | | | | | ALPHA: (697) implies: % 75.97/16.29 | | | | | | | | | | | | | | | | (698) in(all_42_0, all_42_2) = all_646_4 % 75.97/16.29 | | | | | | | | | | | | | | | | (699) ordered_pair(all_42_1, all_42_0) = all_646_1 % 75.97/16.29 | | | | | | | | | | | | | | | | % 75.97/16.29 | | | | | | | | | | | | | | | | REDUCE: (676), (698) imply: % 75.97/16.29 | | | | | | | | | | | | | | | | (700) in(all_42_0, empty_set) = all_646_4 % 75.97/16.29 | | | | | | | | | | | | | | | | % 75.97/16.29 | | | | | | | | | | | | | | | | BETA: splitting (656) gives: % 75.97/16.29 | | | | | | | | | | | | | | | | % 75.97/16.29 | | | | | | | | | | | | | | | | Case 1: % 75.97/16.29 | | | | | | | | | | | | | | | | | % 75.97/16.29 | | | | | | | | | | | | | | | | | (701) all_42_0 = all_42_1 % 75.97/16.29 | | | | | | | | | | | | | | | | | % 75.97/16.29 | | | | | | | | | | | | | | | | | REDUCE: (46), (701) imply: % 75.97/16.29 | | | | | | | | | | | | | | | | | (702) $false % 75.97/16.29 | | | | | | | | | | | | | | | | | % 75.97/16.29 | | | | | | | | | | | | | | | | | CLOSE: (702) is inconsistent. % 75.97/16.29 | | | | | | | | | | | | | | | | | % 75.97/16.29 | | | | | | | | | | | | | | | | Case 2: % 75.97/16.29 | | | | | | | | | | | | | | | | | % 75.97/16.29 | | | | | | | | | | | | | | | | | (703) ? [v0: any] : ? [v1: any] : ? [v2: $i] : ? % 75.97/16.29 | | | | | | | | | | | | | | | | | [v3: any] : ? [v4: any] : (ordered_pair(all_42_0, % 75.97/16.29 | | | | | | | | | | | | | | | | | all_42_1) = v2 & in(v2, all_56_1) = v3 & % 75.97/16.29 | | | | | | | | | | | | | | | | | in(all_104_1, all_56_1) = v4 & in(all_42_0, % 75.97/16.29 | | | | | | | | | | | | | | | | | all_42_2) = v0 & in(all_42_1, all_42_2) = v1 & % 75.97/16.29 | | | | | | | | | | | | | | | | | $i(v2) & ( ~ (v4 = 0) | ~ (v3 = 0) | ~ (v1 = % 75.97/16.29 | | | | | | | | | | | | | | | | | 0) | ~ (v0 = 0))) % 75.97/16.29 | | | | | | | | | | | | | | | | | % 75.97/16.29 | | | | | | | | | | | | | | | | | DELTA: instantiating (703) with fresh symbols all_656_0, % 75.97/16.29 | | | | | | | | | | | | | | | | | all_656_1, all_656_2, all_656_3, all_656_4 gives: % 75.97/16.29 | | | | | | | | | | | | | | | | | (704) ordered_pair(all_42_0, all_42_1) = all_656_2 & % 75.97/16.29 | | | | | | | | | | | | | | | | | in(all_656_2, all_56_1) = all_656_1 & % 75.97/16.29 | | | | | | | | | | | | | | | | | in(all_104_1, all_56_1) = all_656_0 & in(all_42_0, % 75.97/16.29 | | | | | | | | | | | | | | | | | all_42_2) = all_656_4 & in(all_42_1, all_42_2) = % 75.97/16.29 | | | | | | | | | | | | | | | | | all_656_3 & $i(all_656_2) & ( ~ (all_656_0 = 0) | % 75.97/16.29 | | | | | | | | | | | | | | | | | ~ (all_656_1 = 0) | ~ (all_656_3 = 0) | ~ % 75.97/16.29 | | | | | | | | | | | | | | | | | (all_656_4 = 0)) % 75.97/16.29 | | | | | | | | | | | | | | | | | % 75.97/16.29 | | | | | | | | | | | | | | | | | ALPHA: (704) implies: % 75.97/16.29 | | | | | | | | | | | | | | | | | (705) in(all_42_0, all_42_2) = all_656_4 % 75.97/16.29 | | | | | | | | | | | | | | | | | % 75.97/16.29 | | | | | | | | | | | | | | | | | REDUCE: (676), (705) imply: % 75.97/16.29 | | | | | | | | | | | | | | | | | (706) in(all_42_0, empty_set) = all_656_4 % 75.97/16.29 | | | | | | | | | | | | | | | | | % 75.97/16.29 | | | | | | | | | | | | | | | | | BETA: splitting (657) gives: % 75.97/16.29 | | | | | | | | | | | | | | | | | % 75.97/16.29 | | | | | | | | | | | | | | | | | Case 1: % 75.97/16.29 | | | | | | | | | | | | | | | | | | % 75.97/16.29 | | | | | | | | | | | | | | | | | | (707) all_42_0 = all_42_1 % 75.97/16.29 | | | | | | | | | | | | | | | | | | % 75.97/16.29 | | | | | | | | | | | | | | | | | | REDUCE: (46), (707) imply: % 75.97/16.29 | | | | | | | | | | | | | | | | | | (708) $false % 75.97/16.29 | | | | | | | | | | | | | | | | | | % 75.97/16.29 | | | | | | | | | | | | | | | | | | CLOSE: (708) is inconsistent. % 75.97/16.29 | | | | | | | | | | | | | | | | | | % 75.97/16.29 | | | | | | | | | | | | | | | | | Case 2: % 75.97/16.29 | | | | | | | | | | | | | | | | | | % 75.97/16.29 | | | | | | | | | | | | | | | | | | (709) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? % 75.97/16.29 | | | | | | | | | | | | | | | | | | [v3: $i] : ? [v4: any] : (ordered_pair(all_42_0, % 75.97/16.29 | | | | | | | | | | | | | | | | | | all_42_1) = v3 & in(v3, all_56_1) = v4 & % 75.97/16.29 | | | | | | | | | | | | | | | | | | in(all_104_1, all_56_1) = v2 & in(all_42_0, % 75.97/16.29 | | | | | | | | | | | | | | | | | | all_42_2) = v1 & in(all_42_1, all_42_2) = v0 & % 75.97/16.29 | | | | | | | | | | | | | | | | | | $i(v3) & ( ~ (v4 = 0) | ~ (v2 = 0) | ~ (v1 = % 75.97/16.29 | | | | | | | | | | | | | | | | | | 0) | ~ (v0 = 0))) % 75.97/16.29 | | | | | | | | | | | | | | | | | | % 75.97/16.29 | | | | | | | | | | | | | | | | | | DELTA: instantiating (709) with fresh symbols all_661_0, % 75.97/16.29 | | | | | | | | | | | | | | | | | | all_661_1, all_661_2, all_661_3, all_661_4 gives: % 75.97/16.29 | | | | | | | | | | | | | | | | | | (710) ordered_pair(all_42_0, all_42_1) = all_661_1 & % 75.97/16.29 | | | | | | | | | | | | | | | | | | in(all_661_1, all_56_1) = all_661_0 & % 75.97/16.29 | | | | | | | | | | | | | | | | | | in(all_104_1, all_56_1) = all_661_2 & in(all_42_0, % 75.97/16.29 | | | | | | | | | | | | | | | | | | all_42_2) = all_661_3 & in(all_42_1, all_42_2) = % 75.97/16.29 | | | | | | | | | | | | | | | | | | all_661_4 & $i(all_661_1) & ( ~ (all_661_0 = 0) | % 75.97/16.29 | | | | | | | | | | | | | | | | | | ~ (all_661_2 = 0) | ~ (all_661_3 = 0) | ~ % 75.97/16.29 | | | | | | | | | | | | | | | | | | (all_661_4 = 0)) % 75.97/16.29 | | | | | | | | | | | | | | | | | | % 75.97/16.29 | | | | | | | | | | | | | | | | | | ALPHA: (710) implies: % 75.97/16.29 | | | | | | | | | | | | | | | | | | (711) in(all_42_0, all_42_2) = all_661_3 % 75.97/16.29 | | | | | | | | | | | | | | | | | | % 75.97/16.29 | | | | | | | | | | | | | | | | | | REDUCE: (676), (711) imply: % 75.97/16.29 | | | | | | | | | | | | | | | | | | (712) in(all_42_0, empty_set) = all_661_3 % 75.97/16.29 | | | | | | | | | | | | | | | | | | % 75.97/16.29 | | | | | | | | | | | | | | | | | | BETA: splitting (662) gives: % 75.97/16.29 | | | | | | | | | | | | | | | | | | % 75.97/16.29 | | | | | | | | | | | | | | | | | | Case 1: % 75.97/16.29 | | | | | | | | | | | | | | | | | | | % 75.97/16.29 | | | | | | | | | | | | | | | | | | | (713) all_42_0 = all_42_1 % 75.97/16.29 | | | | | | | | | | | | | | | | | | | % 75.97/16.29 | | | | | | | | | | | | | | | | | | | REDUCE: (46), (713) imply: % 75.97/16.29 | | | | | | | | | | | | | | | | | | | (714) $false % 75.97/16.29 | | | | | | | | | | | | | | | | | | | % 75.97/16.29 | | | | | | | | | | | | | | | | | | | CLOSE: (714) is inconsistent. % 75.97/16.29 | | | | | | | | | | | | | | | | | | | % 75.97/16.29 | | | | | | | | | | | | | | | | | | Case 2: % 75.97/16.29 | | | | | | | | | | | | | | | | | | | % 75.97/16.29 | | | | | | | | | | | | | | | | | | | (715) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? % 75.97/16.29 | | | | | | | | | | | | | | | | | | | [v3: $i] : ? [v4: any] : (ordered_pair(all_42_1, % 75.97/16.29 | | | | | | | | | | | | | | | | | | | all_42_0) = v3 & in(v3, all_54_1) = v4 & % 75.97/16.29 | | | | | | | | | | | | | | | | | | | in(all_102_1, all_54_1) = v2 & in(all_42_0, % 75.97/16.29 | | | | | | | | | | | | | | | | | | | all_54_0) = v0 & in(all_42_1, all_54_0) = v1 & % 75.97/16.29 | | | | | | | | | | | | | | | | | | | $i(v3) & ( ~ (v4 = 0) | ~ (v2 = 0) | ~ (v1 = % 75.97/16.29 | | | | | | | | | | | | | | | | | | | 0) | ~ (v0 = 0))) % 75.97/16.29 | | | | | | | | | | | | | | | | | | | % 75.97/16.29 | | | | | | | | | | | | | | | | | | | DELTA: instantiating (715) with fresh symbols all_671_0, % 75.97/16.29 | | | | | | | | | | | | | | | | | | | all_671_1, all_671_2, all_671_3, all_671_4 gives: % 75.97/16.29 | | | | | | | | | | | | | | | | | | | (716) ordered_pair(all_42_1, all_42_0) = all_671_1 & % 75.97/16.29 | | | | | | | | | | | | | | | | | | | in(all_671_1, all_54_1) = all_671_0 & % 75.97/16.29 | | | | | | | | | | | | | | | | | | | in(all_102_1, all_54_1) = all_671_2 & in(all_42_0, % 75.97/16.29 | | | | | | | | | | | | | | | | | | | all_54_0) = all_671_4 & in(all_42_1, all_54_0) = % 75.97/16.29 | | | | | | | | | | | | | | | | | | | all_671_3 & $i(all_671_1) & ( ~ (all_671_0 = 0) | % 75.97/16.29 | | | | | | | | | | | | | | | | | | | ~ (all_671_2 = 0) | ~ (all_671_3 = 0) | ~ % 75.97/16.29 | | | | | | | | | | | | | | | | | | | (all_671_4 = 0)) % 75.97/16.29 | | | | | | | | | | | | | | | | | | | % 75.97/16.29 | | | | | | | | | | | | | | | | | | | ALPHA: (716) implies: % 75.97/16.29 | | | | | | | | | | | | | | | | | | | (717) ordered_pair(all_42_1, all_42_0) = all_671_1 % 75.97/16.29 | | | | | | | | | | | | | | | | | | | % 75.97/16.29 | | | | | | | | | | | | | | | | | | | BETA: splitting (661) gives: % 75.97/16.29 | | | | | | | | | | | | | | | | | | | % 75.97/16.29 | | | | | | | | | | | | | | | | | | | Case 1: % 75.97/16.29 | | | | | | | | | | | | | | | | | | | | % 75.97/16.29 | | | | | | | | | | | | | | | | | | | | (718) all_42_0 = all_42_1 % 75.97/16.29 | | | | | | | | | | | | | | | | | | | | % 75.97/16.29 | | | | | | | | | | | | | | | | | | | | REDUCE: (46), (718) imply: % 75.97/16.29 | | | | | | | | | | | | | | | | | | | | (719) $false % 75.97/16.29 | | | | | | | | | | | | | | | | | | | | % 75.97/16.29 | | | | | | | | | | | | | | | | | | | | CLOSE: (719) is inconsistent. % 75.97/16.29 | | | | | | | | | | | | | | | | | | | | % 75.97/16.29 | | | | | | | | | | | | | | | | | | | Case 2: % 75.97/16.29 | | | | | | | | | | | | | | | | | | | | % 75.97/16.29 | | | | | | | | | | | | | | | | | | | | (720) ? [v0: any] : ? [v1: any] : ? [v2: $i] : ? % 75.97/16.29 | | | | | | | | | | | | | | | | | | | | [v3: any] : ? [v4: any] : (ordered_pair(all_42_1, % 75.97/16.29 | | | | | | | | | | | | | | | | | | | | all_42_0) = v2 & in(v2, all_54_1) = v3 & % 75.97/16.29 | | | | | | | | | | | | | | | | | | | | in(all_102_1, all_54_1) = v4 & in(all_42_0, % 75.97/16.29 | | | | | | | | | | | | | | | | | | | | all_54_0) = v1 & in(all_42_1, all_54_0) = v0 & % 75.97/16.29 | | | | | | | | | | | | | | | | | | | | $i(v2) & ( ~ (v4 = 0) | ~ (v3 = 0) | ~ (v1 = % 75.97/16.29 | | | | | | | | | | | | | | | | | | | | 0) | ~ (v0 = 0))) % 75.97/16.29 | | | | | | | | | | | | | | | | | | | | % 75.97/16.29 | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (720) with fresh symbols all_676_0, % 75.97/16.29 | | | | | | | | | | | | | | | | | | | | all_676_1, all_676_2, all_676_3, all_676_4 gives: % 75.97/16.30 | | | | | | | | | | | | | | | | | | | | (721) ordered_pair(all_42_1, all_42_0) = all_676_2 & % 75.97/16.30 | | | | | | | | | | | | | | | | | | | | in(all_676_2, all_54_1) = all_676_1 & % 75.97/16.30 | | | | | | | | | | | | | | | | | | | | in(all_102_1, all_54_1) = all_676_0 & in(all_42_0, % 75.97/16.30 | | | | | | | | | | | | | | | | | | | | all_54_0) = all_676_3 & in(all_42_1, all_54_0) = % 75.97/16.30 | | | | | | | | | | | | | | | | | | | | all_676_4 & $i(all_676_2) & ( ~ (all_676_0 = 0) | % 75.97/16.30 | | | | | | | | | | | | | | | | | | | | ~ (all_676_1 = 0) | ~ (all_676_3 = 0) | ~ % 75.97/16.30 | | | | | | | | | | | | | | | | | | | | (all_676_4 = 0)) % 75.97/16.30 | | | | | | | | | | | | | | | | | | | | % 75.97/16.30 | | | | | | | | | | | | | | | | | | | | ALPHA: (721) implies: % 75.97/16.30 | | | | | | | | | | | | | | | | | | | | (722) ordered_pair(all_42_1, all_42_0) = all_676_2 % 75.97/16.30 | | | | | | | | | | | | | | | | | | | | % 75.97/16.30 | | | | | | | | | | | | | | | | | | | | BETA: splitting (684) gives: % 75.97/16.30 | | | | | | | | | | | | | | | | | | | | % 75.97/16.30 | | | | | | | | | | | | | | | | | | | | Case 1: % 75.97/16.30 | | | | | | | | | | | | | | | | | | | | | % 75.97/16.30 | | | | | | | | | | | | | | | | | | | | | % 75.97/16.30 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (31) with all_641_3, all_646_4, % 75.97/16.30 | | | | | | | | | | | | | | | | | | | | | empty_set, all_42_0, simplifying with (693), (700) % 75.97/16.30 | | | | | | | | | | | | | | | | | | | | | gives: % 75.97/16.30 | | | | | | | | | | | | | | | | | | | | | (723) all_646_4 = all_641_3 % 75.97/16.30 | | | | | | | | | | | | | | | | | | | | | % 75.97/16.30 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (31) with all_646_4, all_656_4, % 75.97/16.30 | | | | | | | | | | | | | | | | | | | | | empty_set, all_42_0, simplifying with (700), (706) % 75.97/16.30 | | | | | | | | | | | | | | | | | | | | | gives: % 75.97/16.30 | | | | | | | | | | | | | | | | | | | | | (724) all_656_4 = all_646_4 % 75.97/16.30 | | | | | | | | | | | | | | | | | | | | | % 75.97/16.30 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (31) with all_656_4, all_661_3, % 75.97/16.30 | | | | | | | | | | | | | | | | | | | | | empty_set, all_42_0, simplifying with (706), (712) % 75.97/16.30 | | | | | | | | | | | | | | | | | | | | | gives: % 75.97/16.30 | | | | | | | | | | | | | | | | | | | | | (725) all_661_3 = all_656_4 % 75.97/16.30 | | | | | | | | | | | | | | | | | | | | | % 75.97/16.30 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (31) with all_50_0, all_661_3, % 75.97/16.30 | | | | | | | | | | | | | | | | | | | | | empty_set, all_42_0, simplifying with (686), (712) % 75.97/16.30 | | | | | | | | | | | | | | | | | | | | | gives: % 75.97/16.30 | | | | | | | | | | | | | | | | | | | | | (726) all_661_3 = all_50_0 % 75.97/16.30 | | | | | | | | | | | | | | | | | | | | | % 75.97/16.30 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (32) with all_104_1, all_646_1, % 75.97/16.30 | | | | | | | | | | | | | | | | | | | | | all_42_0, all_42_1, simplifying with (203), (699) % 75.97/16.30 | | | | | | | | | | | | | | | | | | | | | gives: % 75.97/16.30 | | | | | | | | | | | | | | | | | | | | | (727) all_646_1 = all_104_1 % 75.97/16.30 | | | | | | | | | | | | | | | | | | | | | % 75.97/16.30 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (32) with all_646_1, all_671_1, % 75.97/16.30 | | | | | | | | | | | | | | | | | | | | | all_42_0, all_42_1, simplifying with (699), (717) % 75.97/16.30 | | | | | | | | | | | | | | | | | | | | | gives: % 75.97/16.30 | | | | | | | | | | | | | | | | | | | | | (728) all_671_1 = all_646_1 % 75.97/16.30 | | | | | | | | | | | | | | | | | | | | | % 75.97/16.30 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (32) with all_671_1, all_676_2, % 75.97/16.30 | | | | | | | | | | | | | | | | | | | | | all_42_0, all_42_1, simplifying with (717), (722) % 75.97/16.30 | | | | | | | | | | | | | | | | | | | | | gives: % 75.97/16.30 | | | | | | | | | | | | | | | | | | | | | (729) all_676_2 = all_671_1 % 75.97/16.30 | | | | | | | | | | | | | | | | | | | | | % 75.97/16.30 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (32) with all_641_2, all_676_2, % 75.97/16.30 | | | | | | | | | | | | | | | | | | | | | all_42_0, all_42_1, simplifying with (692), (722) % 75.97/16.30 | | | | | | | | | | | | | | | | | | | | | gives: % 75.97/16.30 | | | | | | | | | | | | | | | | | | | | | (730) all_676_2 = all_641_2 % 75.97/16.30 | | | | | | | | | | | | | | | | | | | | | % 75.97/16.30 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (30) with all_256_0, all_516_1, % 75.97/16.30 | | | | | | | | | | | | | | | | | | | | | all_162_1, simplifying with (395), (681) gives: % 75.97/16.30 | | | | | | | | | | | | | | | | | | | | | (731) all_516_1 = all_256_0 % 75.97/16.30 | | | | | | | | | | | | | | | | | | | | | % 75.97/16.30 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (30) with all_506_1, all_516_1, % 75.97/16.30 | | | | | | | | | | | | | | | | | | | | | all_162_1, simplifying with (678), (681) gives: % 75.97/16.30 | | | | | | | | | | | | | | | | | | | | | (732) all_516_1 = all_506_1 % 75.97/16.30 | | | | | | | | | | | | | | | | | | | | | % 75.97/16.30 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (729), (730) imply: % 75.97/16.30 | | | | | | | | | | | | | | | | | | | | | (733) all_671_1 = all_641_2 % 75.97/16.30 | | | | | | | | | | | | | | | | | | | | | % 75.97/16.30 | | | | | | | | | | | | | | | | | | | | | SIMP: (733) implies: % 75.97/16.30 | | | | | | | | | | | | | | | | | | | | | (734) all_671_1 = all_641_2 % 75.97/16.30 | | | | | | | | | | | | | | | | | | | | | % 75.97/16.30 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (728), (734) imply: % 75.97/16.30 | | | | | | | | | | | | | | | | | | | | | (735) all_646_1 = all_641_2 % 75.97/16.30 | | | | | | | | | | | | | | | | | | | | | % 75.97/16.30 | | | | | | | | | | | | | | | | | | | | | SIMP: (735) implies: % 75.97/16.30 | | | | | | | | | | | | | | | | | | | | | (736) all_646_1 = all_641_2 % 75.97/16.30 | | | | | | | | | | | | | | | | | | | | | % 75.97/16.30 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (725), (726) imply: % 75.97/16.30 | | | | | | | | | | | | | | | | | | | | | (737) all_656_4 = all_50_0 % 75.97/16.30 | | | | | | | | | | | | | | | | | | | | | % 75.97/16.30 | | | | | | | | | | | | | | | | | | | | | SIMP: (737) implies: % 75.97/16.30 | | | | | | | | | | | | | | | | | | | | | (738) all_656_4 = all_50_0 % 75.97/16.30 | | | | | | | | | | | | | | | | | | | | | % 75.97/16.30 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (724), (738) imply: % 75.97/16.30 | | | | | | | | | | | | | | | | | | | | | (739) all_646_4 = all_50_0 % 75.97/16.30 | | | | | | | | | | | | | | | | | | | | | % 75.97/16.30 | | | | | | | | | | | | | | | | | | | | | SIMP: (739) implies: % 75.97/16.30 | | | | | | | | | | | | | | | | | | | | | (740) all_646_4 = all_50_0 % 75.97/16.30 | | | | | | | | | | | | | | | | | | | | | % 75.97/16.30 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (727), (736) imply: % 75.97/16.30 | | | | | | | | | | | | | | | | | | | | | (741) all_641_2 = all_104_1 % 75.97/16.30 | | | | | | | | | | | | | | | | | | | | | % 75.97/16.30 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (723), (740) imply: % 75.97/16.30 | | | | | | | | | | | | | | | | | | | | | (742) all_641_3 = all_50_0 % 75.97/16.30 | | | | | | | | | | | | | | | | | | | | | % 75.97/16.30 | | | | | | | | | | | | | | | | | | | | | SIMP: (742) implies: % 75.97/16.30 | | | | | | | | | | | | | | | | | | | | | (743) all_641_3 = all_50_0 % 75.97/16.30 | | | | | | | | | | | | | | | | | | | | | % 75.97/16.30 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (731), (732) imply: % 75.97/16.30 | | | | | | | | | | | | | | | | | | | | | (744) all_506_1 = all_256_0 % 75.97/16.30 | | | | | | | | | | | | | | | | | | | | | % 75.97/16.30 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (682) gives: % 75.97/16.30 | | | | | | | | | | | | | | | | | | | | | % 75.97/16.30 | | | | | | | | | | | | | | | | | | | | | Case 1: % 75.97/16.30 | | | | | | | | | | | | | | | | | | | | | | % 75.97/16.30 | | | | | | | | | | | | | | | | | | | | | | (745) all_516_0 = 0 % 75.97/16.30 | | | | | | | | | | | | | | | | | | | | | | % 75.97/16.30 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (680), (745) imply: % 75.97/16.30 | | | | | | | | | | | | | | | | | | | | | | (746) in(all_104_1, all_162_1) = 0 % 75.97/16.30 | | | | | | | | | | | | | | | | | | | | | | % 75.97/16.30 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (31), (49), (50), (126), (203), (421), % 75.97/16.30 | | | | | | | | | | | | | | | | | | | | | | (435), (497), (663), (685), (686), (746) are % 75.97/16.30 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1. % 75.97/16.30 | | | | | | | | | | | | | | | | | | | | | | % 75.97/16.30 | | | | | | | | | | | | | | | | | | | | | Case 2: % 75.97/16.30 | | | | | | | | | | | | | | | | | | | | | | % 75.97/16.30 | | | | | | | | | | | | | | | | | | | | | | (747) all_516_1 = 0 % 75.97/16.30 | | | | | | | | | | | | | | | | | | | | | | % 75.97/16.30 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (731), (747) imply: % 75.97/16.30 | | | | | | | | | | | | | | | | | | | | | | (748) all_256_0 = 0 % 75.97/16.30 | | | | | | | | | | | | | | | | | | | | | | % 75.97/16.30 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (394), (748) imply: % 75.97/16.30 | | | | | | | | | | | | | | | | | | | | | | (749) $false % 75.97/16.30 | | | | | | | | | | | | | | | | | | | | | | % 75.97/16.30 | | | | | | | | | | | | | | | | | | | | | | CLOSE: (749) is inconsistent. % 75.97/16.30 | | | | | | | | | | | | | | | | | | | | | | % 75.97/16.30 | | | | | | | | | | | | | | | | | | | | | End of split % 75.97/16.30 | | | | | | | | | | | | | | | | | | | | | % 75.97/16.30 | | | | | | | | | | | | | | | | | | | | Case 2: % 75.97/16.30 | | | | | | | | | | | | | | | | | | | | | % 75.97/16.30 | | | | | | | | | | | | | | | | | | | | | (750) all_590_3 = 0 & empty(all_80_2) = 0 % 75.97/16.30 | | | | | | | | | | | | | | | | | | | | | % 75.97/16.30 | | | | | | | | | | | | | | | | | | | | | ALPHA: (750) implies: % 75.97/16.30 | | | | | | | | | | | | | | | | | | | | | (751) empty(all_80_2) = 0 % 75.97/16.30 | | | | | | | | | | | | | | | | | | | | | % 75.97/16.30 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (30) with all_150_0, 0, all_80_2, % 75.97/16.30 | | | | | | | | | | | | | | | | | | | | | simplifying with (269), (751) gives: % 75.97/16.30 | | | | | | | | | | | | | | | | | | | | | (752) all_150_0 = 0 % 75.97/16.30 | | | | | | | | | | | | | | | | | | | | | % 75.97/16.30 | | | | | | | | | | | | | | | | | | | | | REDUCE: (268), (752) imply: % 75.97/16.30 | | | | | | | | | | | | | | | | | | | | | (753) $false % 75.97/16.30 | | | | | | | | | | | | | | | | | | | | | % 75.97/16.30 | | | | | | | | | | | | | | | | | | | | | CLOSE: (753) is inconsistent. % 75.97/16.30 | | | | | | | | | | | | | | | | | | | | | % 75.97/16.30 | | | | | | | | | | | | | | | | | | | | End of split % 75.97/16.30 | | | | | | | | | | | | | | | | | | | | % 75.97/16.30 | | | | | | | | | | | | | | | | | | | End of split % 75.97/16.30 | | | | | | | | | | | | | | | | | | | % 75.97/16.30 | | | | | | | | | | | | | | | | | | End of split % 75.97/16.30 | | | | | | | | | | | | | | | | | | % 75.97/16.30 | | | | | | | | | | | | | | | | | End of split % 75.97/16.30 | | | | | | | | | | | | | | | | | % 75.97/16.30 | | | | | | | | | | | | | | | | End of split % 75.97/16.30 | | | | | | | | | | | | | | | | % 75.97/16.30 | | | | | | | | | | | | | | | End of split % 75.97/16.30 | | | | | | | | | | | | | | | % 75.97/16.30 | | | | | | | | | | | | | | End of split % 75.97/16.30 | | | | | | | | | | | | | | % 75.97/16.30 | | | | | | | | | | | | | End of split % 75.97/16.30 | | | | | | | | | | | | | % 75.97/16.30 | | | | | | | | | | | | End of split % 75.97/16.30 | | | | | | | | | | | | % 75.97/16.30 | | | | | | | | | | | End of split % 75.97/16.30 | | | | | | | | | | | % 75.97/16.30 | | | | | | | | | | End of split % 75.97/16.30 | | | | | | | | | | % 75.97/16.30 | | | | | | | | | End of split % 75.97/16.30 | | | | | | | | | % 76.37/16.31 | | | | | | | | Case 2: % 76.37/16.31 | | | | | | | | | % 76.37/16.31 | | | | | | | | | (754) all_158_1 = 0 % 76.37/16.31 | | | | | | | | | % 76.37/16.31 | | | | | | | | | COMBINE_EQS: (350), (754) imply: % 76.37/16.31 | | | | | | | | | (755) all_150_0 = 0 % 76.37/16.31 | | | | | | | | | % 76.37/16.31 | | | | | | | | | SIMP: (755) implies: % 76.37/16.31 | | | | | | | | | (756) all_150_0 = 0 % 76.37/16.31 | | | | | | | | | % 76.37/16.31 | | | | | | | | | REDUCE: (268), (756) imply: % 76.37/16.31 | | | | | | | | | (757) $false % 76.37/16.31 | | | | | | | | | % 76.37/16.31 | | | | | | | | | CLOSE: (757) is inconsistent. % 76.37/16.31 | | | | | | | | | % 76.37/16.31 | | | | | | | | End of split % 76.37/16.31 | | | | | | | | % 76.37/16.31 | | | | | | | End of split % 76.37/16.31 | | | | | | | % 76.37/16.31 | | | | | | Case 2: % 76.37/16.31 | | | | | | | % 76.37/16.31 | | | | | | | (758) all_174_3 = 0 & empty(all_38_1) = 0 % 76.37/16.31 | | | | | | | % 76.37/16.31 | | | | | | | ALPHA: (758) implies: % 76.37/16.31 | | | | | | | (759) empty(all_38_1) = 0 % 76.37/16.31 | | | | | | | % 76.37/16.31 | | | | | | | GROUND_INST: instantiating (30) with all_38_0, 0, all_38_1, % 76.37/16.31 | | | | | | | simplifying with (44), (759) gives: % 76.37/16.31 | | | | | | | (760) all_38_0 = 0 % 76.37/16.31 | | | | | | | % 76.37/16.31 | | | | | | | REDUCE: (42), (760) imply: % 76.37/16.31 | | | | | | | (761) $false % 76.37/16.31 | | | | | | | % 76.37/16.31 | | | | | | | CLOSE: (761) is inconsistent. % 76.37/16.31 | | | | | | | % 76.37/16.31 | | | | | | End of split % 76.37/16.31 | | | | | | % 76.37/16.31 | | | | | End of split % 76.37/16.31 | | | | | % 76.37/16.31 | | | | End of split % 76.37/16.31 | | | | % 76.37/16.31 | | | End of split % 76.37/16.31 | | | % 76.37/16.31 | | End of split % 76.37/16.31 | | % 76.37/16.31 | End of split % 76.37/16.31 | % 76.37/16.31 End of proof % 76.37/16.31 % 76.37/16.31 Sub-proof #1 shows that the following formulas are inconsistent: % 76.37/16.31 ---------------------------------------------------------------- % 76.37/16.31 (1) ordered_pair(all_42_1, all_42_0) = all_104_1 % 76.37/16.31 (2) ~ (all_322_0 = 0) | all_322_1 = 0 | all_322_2 = 0 % 76.37/16.31 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! % 76.37/16.31 [v5: $i] : ( ~ (ordered_pair(v0, v1) = v4) | ~ (cartesian_product2(v2, % 76.37/16.31 v3) = v5) | ~ (in(v4, v5) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) % 76.37/16.31 | ~ $i(v0) | (in(v1, v3) = 0 & in(v0, v2) = 0)) % 76.37/16.31 (4) $i(empty_set) % 76.37/16.31 (5) $i(all_42_0) % 76.37/16.31 (6) ~ (all_50_0 = 0) % 76.37/16.31 (7) $i(all_42_1) % 76.37/16.31 (8) all_322_1 = all_322_2 % 76.37/16.31 (9) all_322_0 = 0 | ? [v0: $i] : ? [v1: $i] : ? [v2: int] : ( ~ (v2 = 0) & % 76.37/16.32 empty(v1) = v2 & powerset(all_164_1) = v0 & element(v1, v0) = 0 & % 76.37/16.32 $i(v1) & $i(v0)) % 76.37/16.32 (10) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 76.37/16.32 ! [v3: $i] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) % 76.37/16.32 (11) in(all_104_1, all_162_1) = 0 % 76.37/16.32 (12) cartesian_product2(empty_set, empty_set) = all_162_1 % 76.37/16.32 (13) in(all_42_0, empty_set) = all_50_0 % 76.37/16.32 % 76.37/16.32 Begin of proof % 76.37/16.32 | % 76.37/16.32 | BETA: splitting (2) gives: % 76.37/16.32 | % 76.37/16.32 | Case 1: % 76.37/16.32 | | % 76.37/16.32 | | (14) ~ (all_322_0 = 0) % 76.37/16.32 | | % 76.37/16.32 | | BETA: splitting (9) gives: % 76.37/16.32 | | % 76.37/16.32 | | Case 1: % 76.37/16.32 | | | % 76.37/16.32 | | | (15) all_322_0 = 0 % 76.37/16.32 | | | % 76.37/16.32 | | | REDUCE: (14), (15) imply: % 76.37/16.32 | | | (16) $false % 76.37/16.32 | | | % 76.37/16.32 | | | CLOSE: (16) is inconsistent. % 76.37/16.32 | | | % 76.37/16.32 | | Case 2: % 76.37/16.32 | | | % 76.37/16.32 | | | % 76.37/16.32 | | | GROUND_INST: instantiating (3) with all_42_1, all_42_0, empty_set, % 76.37/16.32 | | | empty_set, all_104_1, all_162_1, simplifying with (1), (4), % 76.37/16.32 | | | (5), (7), (11), (12) gives: % 76.37/16.32 | | | (17) in(all_42_0, empty_set) = 0 & in(all_42_1, empty_set) = 0 % 76.37/16.32 | | | % 76.37/16.32 | | | REF_CLOSE: (6), (10), (13), (17) are inconsistent by sub-proof #2. % 76.37/16.32 | | | % 76.37/16.32 | | End of split % 76.37/16.32 | | % 76.37/16.32 | Case 2: % 76.37/16.32 | | % 76.37/16.32 | | (18) all_322_1 = 0 | all_322_2 = 0 % 76.37/16.32 | | % 76.37/16.32 | | BETA: splitting (18) gives: % 76.37/16.32 | | % 76.37/16.32 | | Case 1: % 76.37/16.32 | | | % 76.37/16.32 | | | % 76.37/16.32 | | | GROUND_INST: instantiating (3) with all_42_1, all_42_0, empty_set, % 76.37/16.32 | | | empty_set, all_104_1, all_162_1, simplifying with (1), (4), % 76.37/16.32 | | | (5), (7), (11), (12) gives: % 76.37/16.32 | | | (19) in(all_42_0, empty_set) = 0 & in(all_42_1, empty_set) = 0 % 76.37/16.32 | | | % 76.37/16.32 | | | REF_CLOSE: (6), (10), (13), (19) are inconsistent by sub-proof #2. % 76.37/16.32 | | | % 76.37/16.32 | | Case 2: % 76.37/16.32 | | | % 76.37/16.32 | | | (20) all_322_2 = 0 % 76.37/16.32 | | | (21) ~ (all_322_1 = 0) % 76.37/16.32 | | | % 76.37/16.32 | | | COMBINE_EQS: (8), (20) imply: % 76.37/16.32 | | | (22) all_322_1 = 0 % 76.37/16.32 | | | % 76.37/16.32 | | | REDUCE: (21), (22) imply: % 76.37/16.32 | | | (23) $false % 76.37/16.32 | | | % 76.37/16.32 | | | CLOSE: (23) is inconsistent. % 76.37/16.32 | | | % 76.37/16.32 | | End of split % 76.37/16.32 | | % 76.37/16.32 | End of split % 76.37/16.32 | % 76.37/16.32 End of proof % 76.37/16.32 % 76.37/16.32 Sub-proof #2 shows that the following formulas are inconsistent: % 76.37/16.32 ---------------------------------------------------------------- % 76.37/16.32 (1) in(all_42_0, empty_set) = 0 & in(all_42_1, empty_set) = 0 % 76.37/16.32 (2) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 76.37/16.32 ! [v3: $i] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) % 76.37/16.32 (3) in(all_42_0, empty_set) = all_50_0 % 76.37/16.32 (4) ~ (all_50_0 = 0) % 76.37/16.32 % 76.37/16.32 Begin of proof % 76.37/16.32 | % 76.37/16.32 | ALPHA: (1) implies: % 76.37/16.32 | (5) in(all_42_0, empty_set) = 0 % 76.37/16.32 | % 76.37/16.32 | GROUND_INST: instantiating (2) with all_50_0, 0, empty_set, all_42_0, % 76.37/16.32 | simplifying with (3), (5) gives: % 76.37/16.32 | (6) all_50_0 = 0 % 76.37/16.32 | % 76.37/16.32 | REDUCE: (4), (6) imply: % 76.37/16.32 | (7) $false % 76.37/16.32 | % 76.37/16.32 | CLOSE: (7) is inconsistent. % 76.37/16.32 | % 76.37/16.32 End of proof % 76.37/16.32 % 76.37/16.32 Sub-proof #3 shows that the following formulas are inconsistent: % 76.37/16.32 ---------------------------------------------------------------- % 76.37/16.32 (1) $i(all_288_0) % 76.37/16.32 (2) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (empty(v1) = 0) | ~ (empty(v0) % 76.37/16.32 = 0) | ~ $i(v1) | ~ $i(v0)) % 76.37/16.32 (3) empty(all_56_1) = all_154_0 % 76.37/16.32 (4) ~ (all_154_0 = 0) % 76.37/16.32 (5) all_110_0 = 0 | ? [v0: any] : ? [v1: any] : (empty(all_56_1) = v1 & % 76.37/16.32 element(all_110_1, all_56_1) = v0 & ( ~ (v0 = 0) | v1 = 0)) % 76.37/16.32 (6) ! [v0: $i] : ! [v1: $i] : ( ~ (in(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) % 76.37/16.32 | ? [v2: int] : ( ~ (v2 = 0) & empty(v1) = v2)) % 76.37/16.32 (7) ! [v0: $i] : (v0 = empty_set | ~ (empty(v0) = 0) | ~ $i(v0)) % 76.37/16.32 (8) empty(all_290_0) = 0 % 76.37/16.32 (9) $i(all_42_2) % 76.37/16.32 (10) empty(all_292_0) = 0 % 76.37/16.32 (11) $i(all_42_0) % 76.37/16.32 (12) ~ (all_110_0 = 0) | all_110_2 = 0 % 76.37/16.32 (13) $i(all_290_0) % 76.37/16.32 (14) empty(all_42_2) = 0 % 76.37/16.32 (15) $i(all_292_0) % 76.37/16.32 (16) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 76.37/16.32 (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0)) % 76.37/16.32 (17) $i(all_294_0) % 76.37/16.32 (18) empty(all_288_0) = 0 % 76.37/16.32 (19) empty(all_294_0) = 0 % 76.37/16.32 (20) in(all_42_0, all_42_2) = 0 % 76.37/16.32 % 76.37/16.32 Begin of proof % 76.37/16.32 | % 76.37/16.32 | BETA: splitting (12) gives: % 76.37/16.32 | % 76.37/16.32 | Case 1: % 76.37/16.32 | | % 76.37/16.32 | | (21) ~ (all_110_0 = 0) % 76.37/16.32 | | % 76.37/16.32 | | BETA: splitting (5) gives: % 76.37/16.32 | | % 76.37/16.32 | | Case 1: % 76.37/16.32 | | | % 76.37/16.32 | | | (22) all_110_0 = 0 % 76.37/16.32 | | | % 76.37/16.33 | | | REDUCE: (21), (22) imply: % 76.37/16.33 | | | (23) $false % 76.37/16.33 | | | % 76.37/16.33 | | | CLOSE: (23) is inconsistent. % 76.37/16.33 | | | % 76.37/16.33 | | Case 2: % 76.37/16.33 | | | % 76.37/16.33 | | | (24) ? [v0: any] : ? [v1: any] : (empty(all_56_1) = v1 & % 76.37/16.33 | | | element(all_110_1, all_56_1) = v0 & ( ~ (v0 = 0) | v1 = 0)) % 76.37/16.33 | | | % 76.37/16.33 | | | DELTA: instantiating (24) with fresh symbols all_474_0, all_474_1 gives: % 76.37/16.33 | | | (25) empty(all_56_1) = all_474_0 & element(all_110_1, all_56_1) = % 76.37/16.33 | | | all_474_1 & ( ~ (all_474_1 = 0) | all_474_0 = 0) % 76.37/16.33 | | | % 76.37/16.33 | | | ALPHA: (25) implies: % 76.37/16.33 | | | (26) empty(all_56_1) = all_474_0 % 76.37/16.33 | | | (27) ~ (all_474_1 = 0) | all_474_0 = 0 % 76.37/16.33 | | | % 76.37/16.33 | | | GROUND_INST: instantiating (16) with all_154_0, all_474_0, all_56_1, % 76.37/16.33 | | | simplifying with (3), (26) gives: % 76.37/16.33 | | | (28) all_474_0 = all_154_0 % 76.37/16.33 | | | % 76.37/16.33 | | | BETA: splitting (27) gives: % 76.37/16.33 | | | % 76.37/16.33 | | | Case 1: % 76.37/16.33 | | | | % 76.37/16.33 | | | | % 76.37/16.33 | | | | GROUND_INST: instantiating (6) with all_42_0, all_42_2, simplifying with % 76.37/16.33 | | | | (9), (11), (20) gives: % 76.37/16.33 | | | | (29) ? [v0: int] : ( ~ (v0 = 0) & empty(all_42_2) = v0) % 76.37/16.33 | | | | % 76.37/16.33 | | | | GROUND_INST: instantiating (7) with all_290_0, simplifying with (8), % 76.37/16.33 | | | | (13) gives: % 76.37/16.33 | | | | (30) all_290_0 = empty_set % 76.37/16.33 | | | | % 76.37/16.33 | | | | GROUND_INST: instantiating (2) with all_290_0, all_292_0, simplifying % 76.37/16.33 | | | | with (8), (10), (13), (15) gives: % 76.37/16.33 | | | | (31) all_292_0 = all_290_0 % 76.37/16.33 | | | | % 76.37/16.33 | | | | GROUND_INST: instantiating (2) with all_288_0, all_292_0, simplifying % 76.37/16.33 | | | | with (1), (10), (15), (18) gives: % 76.37/16.33 | | | | (32) all_292_0 = all_288_0 % 76.37/16.33 | | | | % 76.37/16.33 | | | | GROUND_INST: instantiating (2) with all_292_0, all_294_0, simplifying % 76.37/16.33 | | | | with (10), (15), (17), (19) gives: % 76.37/16.33 | | | | (33) all_294_0 = all_292_0 % 76.37/16.33 | | | | % 76.37/16.33 | | | | GROUND_INST: instantiating (2) with all_42_2, all_294_0, simplifying % 76.37/16.33 | | | | with (9), (14), (17), (19) gives: % 76.37/16.33 | | | | (34) all_294_0 = all_42_2 % 76.37/16.33 | | | | % 76.37/16.33 | | | | COMBINE_EQS: (33), (34) imply: % 76.37/16.33 | | | | (35) all_292_0 = all_42_2 % 76.37/16.33 | | | | % 76.37/16.33 | | | | SIMP: (35) implies: % 76.37/16.33 | | | | (36) all_292_0 = all_42_2 % 76.37/16.33 | | | | % 76.37/16.33 | | | | COMBINE_EQS: (31), (32) imply: % 76.37/16.33 | | | | (37) all_290_0 = all_288_0 % 76.37/16.33 | | | | % 76.37/16.33 | | | | SIMP: (37) implies: % 76.37/16.33 | | | | (38) all_290_0 = all_288_0 % 76.37/16.33 | | | | % 76.37/16.33 | | | | COMBINE_EQS: (32), (36) imply: % 76.37/16.33 | | | | (39) all_288_0 = all_42_2 % 76.37/16.33 | | | | % 76.37/16.33 | | | | COMBINE_EQS: (30), (38) imply: % 76.37/16.33 | | | | (40) all_288_0 = empty_set % 76.37/16.33 | | | | % 76.37/16.33 | | | | SIMP: (40) implies: % 76.37/16.33 | | | | (41) all_288_0 = empty_set % 76.37/16.33 | | | | % 76.37/16.33 | | | | COMBINE_EQS: (39), (41) imply: % 76.37/16.33 | | | | (42) all_42_2 = empty_set % 76.37/16.33 | | | | % 76.37/16.33 | | | | SIMP: (42) implies: % 76.37/16.33 | | | | (43) all_42_2 = empty_set % 76.37/16.33 | | | | % 76.37/16.33 | | | | DELTA: instantiating (29) with fresh symbol all_510_0 gives: % 76.37/16.33 | | | | (44) ~ (all_510_0 = 0) & empty(all_42_2) = all_510_0 % 76.37/16.33 | | | | % 76.37/16.33 | | | | ALPHA: (44) implies: % 76.37/16.33 | | | | (45) ~ (all_510_0 = 0) % 76.37/16.33 | | | | (46) empty(all_42_2) = all_510_0 % 76.37/16.33 | | | | % 76.37/16.33 | | | | REDUCE: (43), (46) imply: % 76.37/16.33 | | | | (47) empty(empty_set) = all_510_0 % 76.37/16.33 | | | | % 76.37/16.33 | | | | REDUCE: (14), (43) imply: % 76.37/16.33 | | | | (48) empty(empty_set) = 0 % 76.37/16.33 | | | | % 76.37/16.33 | | | | GROUND_INST: instantiating (16) with 0, all_510_0, empty_set, % 76.37/16.33 | | | | simplifying with (47), (48) gives: % 76.37/16.33 | | | | (49) all_510_0 = 0 % 76.37/16.33 | | | | % 76.37/16.33 | | | | REDUCE: (45), (49) imply: % 76.37/16.33 | | | | (50) $false % 76.37/16.33 | | | | % 76.37/16.33 | | | | CLOSE: (50) is inconsistent. % 76.37/16.33 | | | | % 76.37/16.33 | | | Case 2: % 76.37/16.33 | | | | % 76.37/16.33 | | | | (51) all_474_0 = 0 % 76.37/16.33 | | | | % 76.37/16.33 | | | | COMBINE_EQS: (28), (51) imply: % 76.37/16.33 | | | | (52) all_154_0 = 0 % 76.37/16.33 | | | | % 76.37/16.33 | | | | REDUCE: (4), (52) imply: % 76.37/16.33 | | | | (53) $false % 76.37/16.33 | | | | % 76.37/16.33 | | | | CLOSE: (53) is inconsistent. % 76.37/16.33 | | | | % 76.37/16.33 | | | End of split % 76.37/16.33 | | | % 76.37/16.33 | | End of split % 76.37/16.33 | | % 76.37/16.33 | Case 2: % 76.37/16.33 | | % 76.37/16.33 | | % 76.37/16.33 | | GROUND_INST: instantiating (6) with all_42_0, all_42_2, simplifying with % 76.37/16.33 | | (9), (11), (20) gives: % 76.37/16.33 | | (54) ? [v0: int] : ( ~ (v0 = 0) & empty(all_42_2) = v0) % 76.37/16.33 | | % 76.37/16.33 | | GROUND_INST: instantiating (7) with all_288_0, simplifying with (1), (18) % 76.37/16.33 | | gives: % 76.37/16.33 | | (55) all_288_0 = empty_set % 76.37/16.33 | | % 76.37/16.33 | | GROUND_INST: instantiating (2) with all_290_0, all_292_0, simplifying with % 76.37/16.33 | | (8), (10), (13), (15) gives: % 76.37/16.33 | | (56) all_292_0 = all_290_0 % 76.37/16.33 | | % 76.37/16.33 | | GROUND_INST: instantiating (2) with all_288_0, all_292_0, simplifying with % 76.37/16.33 | | (1), (10), (15), (18) gives: % 76.37/16.33 | | (57) all_292_0 = all_288_0 % 76.37/16.33 | | % 76.37/16.33 | | GROUND_INST: instantiating (2) with all_292_0, all_294_0, simplifying with % 76.37/16.34 | | (10), (15), (17), (19) gives: % 76.37/16.34 | | (58) all_294_0 = all_292_0 % 76.37/16.34 | | % 76.37/16.34 | | GROUND_INST: instantiating (2) with all_42_2, all_294_0, simplifying with % 76.37/16.34 | | (9), (14), (17), (19) gives: % 76.37/16.34 | | (59) all_294_0 = all_42_2 % 76.37/16.34 | | % 76.37/16.34 | | COMBINE_EQS: (58), (59) imply: % 76.37/16.34 | | (60) all_292_0 = all_42_2 % 76.37/16.34 | | % 76.37/16.34 | | SIMP: (60) implies: % 76.37/16.34 | | (61) all_292_0 = all_42_2 % 76.37/16.34 | | % 76.37/16.34 | | COMBINE_EQS: (56), (61) imply: % 76.37/16.34 | | (62) all_290_0 = all_42_2 % 76.37/16.34 | | % 76.37/16.34 | | COMBINE_EQS: (56), (57) imply: % 76.37/16.34 | | (63) all_290_0 = all_288_0 % 76.37/16.34 | | % 76.37/16.34 | | COMBINE_EQS: (62), (63) imply: % 76.37/16.34 | | (64) all_288_0 = all_42_2 % 76.37/16.34 | | % 76.37/16.34 | | SIMP: (64) implies: % 76.37/16.34 | | (65) all_288_0 = all_42_2 % 76.37/16.34 | | % 76.37/16.34 | | COMBINE_EQS: (55), (65) imply: % 76.37/16.34 | | (66) all_42_2 = empty_set % 76.37/16.34 | | % 76.37/16.34 | | SIMP: (66) implies: % 76.37/16.34 | | (67) all_42_2 = empty_set % 76.37/16.34 | | % 76.37/16.34 | | DELTA: instantiating (54) with fresh symbol all_486_0 gives: % 76.37/16.34 | | (68) ~ (all_486_0 = 0) & empty(all_42_2) = all_486_0 % 76.37/16.34 | | % 76.37/16.34 | | ALPHA: (68) implies: % 76.37/16.34 | | (69) ~ (all_486_0 = 0) % 76.37/16.34 | | (70) empty(all_42_2) = all_486_0 % 76.37/16.34 | | % 76.37/16.34 | | REDUCE: (67), (70) imply: % 76.37/16.34 | | (71) empty(empty_set) = all_486_0 % 76.37/16.34 | | % 76.37/16.34 | | REDUCE: (14), (67) imply: % 76.37/16.34 | | (72) empty(empty_set) = 0 % 76.37/16.34 | | % 76.37/16.34 | | GROUND_INST: instantiating (16) with 0, all_486_0, empty_set, simplifying % 76.37/16.34 | | with (71), (72) gives: % 76.37/16.34 | | (73) all_486_0 = 0 % 76.37/16.34 | | % 76.37/16.34 | | REDUCE: (69), (73) imply: % 76.37/16.34 | | (74) $false % 76.37/16.34 | | % 76.37/16.34 | | CLOSE: (74) is inconsistent. % 76.37/16.34 | | % 76.37/16.34 | End of split % 76.37/16.34 | % 76.37/16.34 End of proof % 76.37/16.34 % SZS output end Proof for theBenchmark % 76.37/16.34 % 76.37/16.34 15708ms %------------------------------------------------------------------------------