%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SEU340+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 : n002.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 17:44:11 EDT 2023 % Result : Theorem 20.57s 3.44s % Output : Proof 81.38s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.10 % Problem : SEU340+1 : TPTP v8.1.2. Released v3.3.0. % 0.00/0.11 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.11/0.32 % Computer : n002.cluster.edu % 0.11/0.32 % Model : x86_64 x86_64 % 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.11/0.32 % Memory : 8042.1875MB % 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64 % 0.11/0.32 % CPULimit : 300 % 0.11/0.32 % WCLimit : 300 % 0.11/0.32 % DateTime : Wed Aug 23 20:01:31 EDT 2023 % 0.11/0.32 % CPUTime : % 0.18/0.56 ________ _____ % 0.18/0.56 ___ __ \_________(_)________________________________ % 0.18/0.56 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.18/0.56 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.18/0.56 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.18/0.56 % 0.18/0.56 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.18/0.56 (2023-06-19) % 0.18/0.56 % 0.18/0.56 (c) Philipp Rümmer, 2009-2023 % 0.18/0.56 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.18/0.56 Amanda Stjerna. % 0.18/0.56 Free software under BSD-3-Clause. % 0.18/0.56 % 0.18/0.56 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.18/0.56 % 0.18/0.57 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.18/0.58 Running up to 7 provers in parallel. % 0.18/0.59 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.18/0.59 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.18/0.59 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.18/0.59 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.18/0.59 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.18/0.59 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.18/0.59 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.74/1.03 Prover 4: Preprocessing ... % 2.74/1.04 Prover 1: Preprocessing ... % 2.74/1.07 Prover 3: Preprocessing ... % 2.74/1.07 Prover 6: Preprocessing ... % 2.74/1.07 Prover 5: Preprocessing ... % 2.74/1.07 Prover 0: Preprocessing ... % 2.74/1.07 Prover 2: Preprocessing ... % 6.54/1.62 Prover 1: Warning: ignoring some quantifiers % 6.54/1.62 Prover 5: Proving ... % 6.54/1.62 Prover 2: Proving ... % 6.54/1.63 Prover 6: Proving ... % 6.54/1.64 Prover 3: Warning: ignoring some quantifiers % 7.22/1.65 Prover 1: Constructing countermodel ... % 7.50/1.69 Prover 3: Constructing countermodel ... % 8.31/1.81 Prover 4: Warning: ignoring some quantifiers % 8.73/1.87 Prover 4: Constructing countermodel ... % 8.73/1.92 Prover 0: Proving ... % 9.43/1.99 Prover 3: gave up % 9.43/1.99 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 9.43/2.03 Prover 7: Preprocessing ... % 9.43/2.05 Prover 1: gave up % 9.43/2.06 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 10.38/2.11 Prover 8: Preprocessing ... % 10.38/2.14 Prover 7: Warning: ignoring some quantifiers % 10.90/2.15 Prover 7: Constructing countermodel ... % 11.29/2.23 Prover 8: Warning: ignoring some quantifiers % 11.58/2.24 Prover 8: Constructing countermodel ... % 13.27/2.48 Prover 8: gave up % 13.27/2.49 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889 % 13.56/2.51 Prover 9: Preprocessing ... % 15.33/2.77 Prover 7: gave up % 15.33/2.79 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 15.93/2.83 Prover 10: Preprocessing ... % 15.93/2.86 Prover 9: Warning: ignoring some quantifiers % 15.93/2.87 Prover 9: Constructing countermodel ... % 16.43/2.90 Prover 10: Warning: ignoring some quantifiers % 16.43/2.92 Prover 10: Constructing countermodel ... % 17.10/3.00 Prover 10: gave up % 17.10/3.00 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 17.38/3.03 Prover 11: Preprocessing ... % 18.71/3.24 Prover 11: Warning: ignoring some quantifiers % 19.33/3.27 Prover 11: Constructing countermodel ... % 20.57/3.44 Prover 0: proved (2860ms) % 20.57/3.44 % 20.57/3.44 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 20.57/3.44 % 20.57/3.44 Prover 9: stopped % 20.57/3.44 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 20.57/3.45 Prover 6: stopped % 20.57/3.46 Prover 5: stopped % 20.57/3.46 Prover 2: stopped % 20.57/3.46 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 20.57/3.46 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085 % 20.57/3.47 Prover 13: Preprocessing ... % 20.57/3.48 Prover 16: Preprocessing ... % 20.57/3.48 Prover 19: Preprocessing ... % 20.57/3.52 Prover 13: Warning: ignoring some quantifiers % 21.22/3.53 Prover 13: Constructing countermodel ... % 21.22/3.54 Prover 16: Warning: ignoring some quantifiers % 21.22/3.55 Prover 16: Constructing countermodel ... % 21.67/3.60 Prover 19: Warning: ignoring some quantifiers % 21.67/3.61 Prover 19: Constructing countermodel ... % 23.98/3.89 Prover 19: gave up % 37.29/5.86 Prover 16: gave up % 62.76/10.22 Prover 13: stopped % 78.93/15.60 Prover 4: Found proof (size 992) % 78.93/15.60 Prover 4: proved (15012ms) % 78.93/15.60 Prover 11: stopped % 78.93/15.60 % 78.93/15.60 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 78.93/15.60 % 79.29/15.70 % SZS output start Proof for theBenchmark % 79.43/15.71 Assumptions after simplification: % 79.43/15.71 --------------------------------- % 79.43/15.71 % 79.43/15.71 (cc1_relset_1) % 79.53/15.75 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 79.53/15.75 (cartesian_product2(v0, v1) = v3) | ~ (powerset(v3) = v4) | ~ (element(v2, % 79.53/15.75 v4) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | relation(v2) = 0) % 79.53/15.75 % 79.53/15.75 (commutativity_k2_tarski) % 79.53/15.75 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (unordered_pair(v1, v0) = v2) | % 79.53/15.75 ~ $i(v1) | ~ $i(v0) | (unordered_pair(v0, v1) = v2 & $i(v2))) & ! [v0: $i] % 79.53/15.75 : ! [v1: $i] : ! [v2: $i] : ( ~ (unordered_pair(v0, v1) = v2) | ~ $i(v1) | % 79.53/15.75 ~ $i(v0) | (unordered_pair(v1, v0) = v2 & $i(v2))) % 79.53/15.75 % 79.53/15.75 (d5_orders_2) % 79.53/15.76 ! [v0: $i] : ! [v1: $i] : ( ~ (the_InternalRel(v0) = v1) | ~ $i(v0) | ? % 79.53/15.76 [v2: any] : ? [v3: any] : ? [v4: $i] : ? [v5: any] : (rel_str(v0) = v2 & % 79.53/15.76 transitive_relstr(v0) = v3 & the_carrier(v0) = v4 & is_transitive_in(v1, % 79.53/15.76 v4) = v5 & $i(v4) & ( ~ (v2 = 0) | (( ~ (v5 = 0) | v3 = 0) & ( ~ (v3 = % 79.53/15.76 0) | v5 = 0))))) & ! [v0: $i] : ! [v1: any] : ( ~ % 79.53/15.76 (transitive_relstr(v0) = v1) | ~ $i(v0) | ? [v2: any] : ? [v3: $i] : ? % 79.53/15.76 [v4: $i] : ? [v5: any] : (the_InternalRel(v0) = v3 & rel_str(v0) = v2 & % 79.53/15.76 the_carrier(v0) = v4 & is_transitive_in(v3, v4) = v5 & $i(v4) & $i(v3) & ( % 79.53/15.76 ~ (v2 = 0) | (( ~ (v5 = 0) | v1 = 0) & ( ~ (v1 = 0) | v5 = 0))))) & ! % 79.53/15.76 [v0: $i] : ! [v1: $i] : ( ~ (the_carrier(v0) = v1) | ~ $i(v0) | ? [v2: any] % 79.53/15.76 : ? [v3: any] : ? [v4: $i] : ? [v5: any] : (the_InternalRel(v0) = v4 & % 79.53/15.76 rel_str(v0) = v2 & transitive_relstr(v0) = v3 & is_transitive_in(v4, v1) = % 79.53/15.76 v5 & $i(v4) & ( ~ (v2 = 0) | (( ~ (v5 = 0) | v3 = 0) & ( ~ (v3 = 0) | v5 = % 79.53/15.76 0))))) & ! [v0: $i] : ( ~ (rel_str(v0) = 0) | ~ $i(v0) | ? [v1: % 79.53/15.76 any] : ? [v2: $i] : ? [v3: $i] : ? [v4: any] : (the_InternalRel(v0) = % 79.53/15.76 v2 & transitive_relstr(v0) = v1 & the_carrier(v0) = v3 & % 79.53/15.76 is_transitive_in(v2, v3) = v4 & $i(v3) & $i(v2) & ( ~ (v4 = 0) | v1 = 0) & % 79.53/15.76 ( ~ (v1 = 0) | v4 = 0))) % 79.53/15.76 % 79.53/15.76 (d5_tarski) % 79.53/15.77 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (ordered_pair(v0, v1) = v2) | ~ % 79.53/15.77 $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : (singleton(v0) = v4 & % 79.53/15.77 unordered_pair(v3, v4) = v2 & unordered_pair(v0, v1) = v3 & $i(v4) & % 79.53/15.77 $i(v3) & $i(v2))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 79.53/15.77 (unordered_pair(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? % 79.53/15.77 [v4: $i] : (ordered_pair(v0, v1) = v3 & singleton(v0) = v4 & % 79.53/15.77 unordered_pair(v2, v4) = v3 & $i(v4) & $i(v3))) % 79.53/15.77 % 79.53/15.77 (d8_relat_2) % 79.53/15.80 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 79.53/15.80 $i] : ! [v6: $i] : ! [v7: int] : (v7 = 0 | ~ (ordered_pair(v3, v4) = v5) % 79.53/15.80 | ~ (ordered_pair(v2, v4) = v6) | ~ (is_transitive_in(v0, v1) = 0) | ~ % 79.53/15.80 (relation(v0) = 0) | ~ (in(v6, v0) = v7) | ~ (in(v5, v0) = 0) | ~ $i(v4) % 79.53/15.80 | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v8: any] : ? [v9: % 79.53/15.80 any] : ? [v10: any] : ? [v11: $i] : ? [v12: any] : (ordered_pair(v2, % 79.53/15.80 v3) = v11 & in(v11, v0) = v12 & in(v4, v1) = v10 & in(v3, v1) = v9 & % 79.53/15.80 in(v2, v1) = v8 & $i(v11) & ( ~ (v12 = 0) | ~ (v10 = 0) | ~ (v9 = 0) | % 79.53/15.80 ~ (v8 = 0)))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : % 79.53/15.80 ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: int] : (v7 = 0 | ~ % 79.53/15.80 (ordered_pair(v2, v4) = v6) | ~ (ordered_pair(v2, v3) = v5) | ~ % 79.53/15.80 (is_transitive_in(v0, v1) = 0) | ~ (relation(v0) = 0) | ~ (in(v6, v0) = % 79.53/15.80 v7) | ~ (in(v5, v0) = 0) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) % 79.53/15.80 | ~ $i(v0) | ? [v8: any] : ? [v9: any] : ? [v10: any] : ? [v11: $i] : % 79.53/15.80 ? [v12: any] : (ordered_pair(v3, v4) = v11 & in(v11, v0) = v12 & in(v4, v1) % 79.53/15.80 = v10 & in(v3, v1) = v9 & in(v2, v1) = v8 & $i(v11) & ( ~ (v12 = 0) | ~ % 79.53/15.80 (v10 = 0) | ~ (v9 = 0) | ~ (v8 = 0)))) & ! [v0: $i] : ! [v1: $i] : % 79.53/15.80 ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: int] : (v6 = 0 % 79.53/15.80 | ~ (ordered_pair(v2, v4) = v5) | ~ (is_transitive_in(v0, v1) = 0) | ~ % 79.53/15.80 (relation(v0) = 0) | ~ (in(v5, v0) = v6) | ~ (in(v3, v1) = 0) | ~ $i(v4) % 79.53/15.80 | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v7: any] : ? [v8: % 79.53/15.80 any] : ? [v9: $i] : ? [v10: any] : ? [v11: $i] : ? [v12: any] : % 79.53/15.80 (ordered_pair(v3, v4) = v11 & ordered_pair(v2, v3) = v9 & in(v11, v0) = v12 % 79.53/15.80 & in(v9, v0) = v10 & in(v4, v1) = v8 & in(v2, v1) = v7 & $i(v11) & $i(v9) % 79.53/15.80 & ( ~ (v12 = 0) | ~ (v10 = 0) | ~ (v8 = 0) | ~ (v7 = 0)))) & ! [v0: % 79.53/15.80 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : % 79.53/15.80 ! [v6: $i] : ( ~ (ordered_pair(v3, v4) = v6) | ~ (ordered_pair(v2, v3) = v5) % 79.53/15.80 | ~ (is_transitive_in(v0, v1) = 0) | ~ (relation(v0) = 0) | ~ (in(v6, v0) % 79.53/15.80 = 0) | ~ (in(v5, v0) = 0) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) % 79.53/15.80 | ~ $i(v0) | ? [v7: any] : ? [v8: any] : ? [v9: any] : ? [v10: $i] : ? % 79.53/15.80 [v11: any] : (ordered_pair(v2, v4) = v10 & in(v10, v0) = v11 & in(v4, v1) = % 79.53/15.80 v9 & in(v3, v1) = v8 & in(v2, v1) = v7 & $i(v10) & ( ~ (v9 = 0) | ~ (v8 = % 79.53/15.80 0) | ~ (v7 = 0) | v11 = 0))) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 79.53/15.80 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (ordered_pair(v3, v4) = % 79.53/15.80 v5) | ~ (is_transitive_in(v0, v1) = 0) | ~ (relation(v0) = 0) | ~ % 79.53/15.80 (in(v5, v0) = 0) | ~ (in(v2, v1) = 0) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | % 79.53/15.80 ~ $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: any] : ? [v8: $i] : ? [v9: % 79.53/15.80 any] : ? [v10: $i] : ? [v11: any] : (ordered_pair(v2, v4) = v10 & % 79.53/15.80 ordered_pair(v2, v3) = v8 & in(v10, v0) = v11 & in(v8, v0) = v9 & in(v4, % 79.53/15.80 v1) = v7 & in(v3, v1) = v6 & $i(v10) & $i(v8) & ( ~ (v9 = 0) | ~ (v7 = % 79.53/15.80 0) | ~ (v6 = 0) | v11 = 0))) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 79.53/15.80 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (ordered_pair(v2, v3) = % 79.53/15.80 v5) | ~ (is_transitive_in(v0, v1) = 0) | ~ (relation(v0) = 0) | ~ % 79.53/15.80 (in(v5, v0) = 0) | ~ (in(v4, v1) = 0) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | % 79.53/15.80 ~ $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: any] : ? [v8: $i] : ? [v9: % 79.53/15.80 any] : ? [v10: $i] : ? [v11: any] : (ordered_pair(v3, v4) = v8 & % 79.53/15.80 ordered_pair(v2, v4) = v10 & in(v10, v0) = v11 & in(v8, v0) = v9 & in(v3, % 79.53/15.80 v1) = v7 & in(v2, v1) = v6 & $i(v10) & $i(v8) & ( ~ (v9 = 0) | ~ (v7 = % 79.53/15.80 0) | ~ (v6 = 0) | v11 = 0))) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 79.53/15.80 $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (is_transitive_in(v0, v1) = 0) | ~ % 79.53/15.80 (relation(v0) = 0) | ~ (in(v4, v1) = 0) | ~ (in(v3, v1) = 0) | ~ (in(v2, % 79.53/15.80 v1) = 0) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 79.53/15.80 ? [v5: $i] : ? [v6: any] : ? [v7: $i] : ? [v8: any] : ? [v9: $i] : ? % 79.53/15.80 [v10: any] : (ordered_pair(v3, v4) = v7 & ordered_pair(v2, v4) = v9 & % 79.53/15.80 ordered_pair(v2, v3) = v5 & in(v9, v0) = v10 & in(v7, v0) = v8 & in(v5, % 79.53/15.80 v0) = v6 & $i(v9) & $i(v7) & $i(v5) & ( ~ (v8 = 0) | ~ (v6 = 0) | v10 = % 79.53/15.80 0))) & ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ % 79.53/15.80 (is_transitive_in(v0, v1) = v2) | ~ (relation(v0) = 0) | ~ $i(v1) | ~ % 79.53/15.80 $i(v0) | ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] % 79.53/15.80 : ? [v8: $i] : ? [v9: int] : ( ~ (v9 = 0) & ordered_pair(v4, v5) = v7 & % 79.53/15.80 ordered_pair(v3, v5) = v8 & ordered_pair(v3, v4) = v6 & in(v8, v0) = v9 & % 79.53/15.80 in(v7, v0) = 0 & in(v6, v0) = 0 & in(v5, v1) = 0 & in(v4, v1) = 0 & in(v3, % 79.53/15.80 v1) = 0 & $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3))) % 79.53/15.80 % 79.53/15.80 (d9_orders_2) % 79.53/15.82 ! [v0: $i] : ! [v1: $i] : ( ~ (the_InternalRel(v0) = v1) | ~ $i(v0) | ? % 79.53/15.82 [v2: any] : ? [v3: $i] : (rel_str(v0) = v2 & the_carrier(v0) = v3 & $i(v3) % 79.53/15.82 & ( ~ (v2 = 0) | ( ! [v4: $i] : ! [v5: $i] : ! [v6: any] : ( ~ % 79.53/15.82 (related(v0, v4, v5) = v6) | ~ (element(v4, v3) = 0) | ~ $i(v5) | % 79.53/15.82 ~ $i(v4) | ? [v7: any] : ? [v8: $i] : ? [v9: any] : % 79.53/15.82 (ordered_pair(v4, v5) = v8 & element(v5, v3) = v7 & in(v8, v1) = v9 % 79.53/15.82 & $i(v8) & ( ~ (v7 = 0) | (( ~ (v9 = 0) | v6 = 0) & ( ~ (v6 = 0) | % 79.53/15.82 v9 = 0))))) & ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~ % 79.53/15.82 (ordered_pair(v4, v5) = v6) | ~ (element(v4, v3) = 0) | ~ $i(v5) | % 79.53/15.82 ~ $i(v4) | ? [v7: any] : ? [v8: any] : ? [v9: any] : % 79.53/15.82 (related(v0, v4, v5) = v8 & element(v5, v3) = v7 & in(v6, v1) = v9 & % 79.53/15.82 ( ~ (v7 = 0) | (( ~ (v9 = 0) | v8 = 0) & ( ~ (v8 = 0) | v9 = % 79.53/15.82 0))))) & ! [v4: $i] : ! [v5: $i] : ( ~ (element(v5, v3) = % 79.53/15.82 0) | ~ (element(v4, v3) = 0) | ~ $i(v5) | ~ $i(v4) | ? [v6: % 79.53/15.82 any] : ? [v7: $i] : ? [v8: any] : (related(v0, v4, v5) = v6 & % 79.53/15.82 ordered_pair(v4, v5) = v7 & in(v7, v1) = v8 & $i(v7) & ( ~ (v8 = % 79.53/15.82 0) | v6 = 0) & ( ~ (v6 = 0) | v8 = 0))))))) & ! [v0: $i] : ! % 79.53/15.82 [v1: $i] : ( ~ (the_carrier(v0) = v1) | ~ $i(v0) | ? [v2: any] : ? [v3: $i] % 79.53/15.82 : (the_InternalRel(v0) = v3 & rel_str(v0) = v2 & $i(v3) & ( ~ (v2 = 0) | ( ! % 79.53/15.82 [v4: $i] : ! [v5: $i] : ! [v6: any] : ( ~ (related(v0, v4, v5) = v6) % 79.53/15.82 | ~ (element(v4, v1) = 0) | ~ $i(v5) | ~ $i(v4) | ? [v7: any] : % 79.53/15.82 ? [v8: $i] : ? [v9: any] : (ordered_pair(v4, v5) = v8 & element(v5, % 79.53/15.82 v1) = v7 & in(v8, v3) = v9 & $i(v8) & ( ~ (v7 = 0) | (( ~ (v9 = % 79.53/15.82 0) | v6 = 0) & ( ~ (v6 = 0) | v9 = 0))))) & ! [v4: $i] : % 79.53/15.82 ! [v5: $i] : ! [v6: $i] : ( ~ (ordered_pair(v4, v5) = v6) | ~ % 79.53/15.82 (element(v4, v1) = 0) | ~ $i(v5) | ~ $i(v4) | ? [v7: any] : ? % 79.53/15.82 [v8: any] : ? [v9: any] : (related(v0, v4, v5) = v8 & element(v5, % 79.53/15.82 v1) = v7 & in(v6, v3) = v9 & ( ~ (v7 = 0) | (( ~ (v9 = 0) | v8 = % 79.53/15.82 0) & ( ~ (v8 = 0) | v9 = 0))))) & ! [v4: $i] : ! [v5: $i] % 79.53/15.82 : ( ~ (element(v5, v1) = 0) | ~ (element(v4, v1) = 0) | ~ $i(v5) | % 79.53/15.82 ~ $i(v4) | ? [v6: any] : ? [v7: $i] : ? [v8: any] : (related(v0, % 79.53/15.82 v4, v5) = v6 & ordered_pair(v4, v5) = v7 & in(v7, v3) = v8 & % 79.53/15.82 $i(v7) & ( ~ (v8 = 0) | v6 = 0) & ( ~ (v6 = 0) | v8 = 0))))))) & % 79.53/15.82 ! [v0: $i] : ( ~ (rel_str(v0) = 0) | ~ $i(v0) | ? [v1: $i] : ? [v2: $i] : % 79.53/15.82 (the_InternalRel(v0) = v2 & the_carrier(v0) = v1 & $i(v2) & $i(v1) & ! [v3: % 79.53/15.82 $i] : ! [v4: $i] : ! [v5: any] : ( ~ (related(v0, v3, v4) = v5) | ~ % 79.53/15.82 (element(v3, v1) = 0) | ~ $i(v4) | ~ $i(v3) | ? [v6: any] : ? [v7: % 79.53/15.82 $i] : ? [v8: any] : (ordered_pair(v3, v4) = v7 & element(v4, v1) = v6 % 79.53/15.82 & in(v7, v2) = v8 & $i(v7) & ( ~ (v6 = 0) | (( ~ (v8 = 0) | v5 = 0) & % 79.53/15.82 ( ~ (v5 = 0) | v8 = 0))))) & ! [v3: $i] : ! [v4: $i] : ! [v5: % 79.53/15.82 $i] : ( ~ (ordered_pair(v3, v4) = v5) | ~ (element(v3, v1) = 0) | ~ % 79.53/15.82 $i(v4) | ~ $i(v3) | ? [v6: any] : ? [v7: any] : ? [v8: any] : % 79.53/15.82 (related(v0, v3, v4) = v7 & element(v4, v1) = v6 & in(v5, v2) = v8 & ( ~ % 79.53/15.82 (v6 = 0) | (( ~ (v8 = 0) | v7 = 0) & ( ~ (v7 = 0) | v8 = 0))))) & ! % 79.53/15.82 [v3: $i] : ! [v4: $i] : ( ~ (element(v4, v1) = 0) | ~ (element(v3, v1) = % 79.53/15.82 0) | ~ $i(v4) | ~ $i(v3) | ? [v5: any] : ? [v6: $i] : ? [v7: any] % 79.53/15.82 : (related(v0, v3, v4) = v5 & ordered_pair(v3, v4) = v6 & in(v6, v2) = % 79.53/15.82 v7 & $i(v6) & ( ~ (v7 = 0) | v5 = 0) & ( ~ (v5 = 0) | v7 = 0))))) % 79.53/15.82 % 79.53/15.82 (dt_m2_relset_1) % 79.53/15.82 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 79.53/15.82 int] : (v5 = 0 | ~ (cartesian_product2(v0, v1) = v3) | ~ (powerset(v3) = % 79.53/15.82 v4) | ~ (element(v2, v4) = v5) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 79.53/15.82 [v6: int] : ( ~ (v6 = 0) & relation_of2_as_subset(v2, v0, v1) = v6)) & ! % 79.53/15.82 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (relation_of2_as_subset(v2, v0, v1) % 79.53/15.82 = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : % 79.53/15.82 (cartesian_product2(v0, v1) = v3 & powerset(v3) = v4 & element(v2, v4) = 0 & % 79.53/15.82 $i(v4) & $i(v3))) % 79.53/15.82 % 79.53/15.82 (dt_u1_orders_2) % 79.53/15.82 ! [v0: $i] : ! [v1: $i] : ( ~ (the_InternalRel(v0) = v1) | ~ $i(v0) | ? % 79.53/15.82 [v2: any] : ? [v3: $i] : ? [v4: any] : (relation_of2_as_subset(v1, v3, v3) % 79.53/15.82 = v4 & rel_str(v0) = v2 & the_carrier(v0) = v3 & $i(v3) & ( ~ (v2 = 0) | % 79.53/15.82 v4 = 0))) & ! [v0: $i] : ! [v1: $i] : ( ~ (the_carrier(v0) = v1) | ~ % 79.53/15.82 $i(v0) | ? [v2: any] : ? [v3: $i] : ? [v4: any] : % 79.53/15.82 (relation_of2_as_subset(v3, v1, v1) = v4 & the_InternalRel(v0) = v3 & % 79.53/15.82 rel_str(v0) = v2 & $i(v3) & ( ~ (v2 = 0) | v4 = 0))) & ! [v0: $i] : ( ~ % 79.53/15.82 (rel_str(v0) = 0) | ~ $i(v0) | ? [v1: $i] : ? [v2: $i] : % 79.53/15.82 (relation_of2_as_subset(v1, v2, v2) = 0 & the_InternalRel(v0) = v1 & % 79.53/15.82 the_carrier(v0) = v2 & $i(v2) & $i(v1))) % 79.53/15.82 % 79.53/15.82 (existence_l1_orders_2) % 79.53/15.82 ? [v0: $i] : (rel_str(v0) = 0 & $i(v0)) % 79.53/15.82 % 79.53/15.82 (fc1_subset_1) % 79.53/15.83 ! [v0: $i] : ! [v1: $i] : ( ~ (powerset(v0) = v1) | ~ $i(v0) | ? [v2: int] % 79.53/15.83 : ( ~ (v2 = 0) & empty(v1) = v2)) % 79.53/15.83 % 79.53/15.83 (fc3_subset_1) % 79.53/15.83 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (unordered_pair(v0, v1) = v2) | % 79.53/15.83 ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ( ~ (v3 = 0) & empty(v2) = v3)) % 79.53/15.83 % 79.53/15.83 (fc4_subset_1) % 79.53/15.83 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (cartesian_product2(v0, v1) = % 79.53/15.83 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ? [v5: any] : % 79.53/15.83 (empty(v2) = v5 & empty(v1) = v4 & empty(v0) = v3 & ( ~ (v5 = 0) | v4 = 0 | % 79.53/15.83 v3 = 0))) % 79.53/15.83 % 79.53/15.83 (rc1_subset_1) % 79.53/15.83 ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (empty(v0) = v1) | ~ $i(v0) | ? % 79.53/15.83 [v2: $i] : ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & empty(v3) = v4 & % 79.53/15.83 powerset(v0) = v2 & element(v3, v2) = 0 & $i(v3) & $i(v2))) & ! [v0: $i] % 79.53/15.83 : ! [v1: $i] : ( ~ (powerset(v0) = v1) | ~ $i(v0) | ? [v2: int] : ? [v3: % 79.53/15.83 $i] : ? [v4: int] : ? [v5: int] : ($i(v3) & ((v4 = 0 & ~ (v5 = 0) & % 79.53/15.83 empty(v3) = v5 & element(v3, v1) = 0) | (v2 = 0 & empty(v0) = 0)))) % 79.53/15.83 % 79.53/15.83 (rc1_xboole_0) % 79.53/15.83 ? [v0: $i] : (empty(v0) = 0 & $i(v0)) % 79.53/15.83 % 79.53/15.83 (rc2_subset_1) % 79.53/15.83 ! [v0: $i] : ! [v1: $i] : ( ~ (powerset(v0) = v1) | ~ $i(v0) | ? [v2: $i] % 79.53/15.83 : (empty(v2) = 0 & element(v2, v1) = 0 & $i(v2))) % 79.53/15.83 % 79.53/15.83 (rc2_xboole_0) % 79.53/15.83 ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & empty(v0) = v1 & $i(v0)) % 79.53/15.83 % 79.53/15.83 (t106_zfmisc_1) % 79.53/15.84 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 79.53/15.84 $i] : ! [v6: int] : (v6 = 0 | ~ (ordered_pair(v0, v1) = v4) | ~ % 79.53/15.84 (cartesian_product2(v2, v3) = v5) | ~ (in(v4, v5) = v6) | ~ $i(v3) | ~ % 79.53/15.84 $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v7: any] : ? [v8: any] : (in(v1, v3) = % 79.53/15.84 v8 & in(v0, v2) = v7 & ( ~ (v8 = 0) | ~ (v7 = 0)))) & ! [v0: $i] : ! % 79.53/15.84 [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ % 79.53/15.84 (ordered_pair(v0, v1) = v4) | ~ (cartesian_product2(v2, v3) = v5) | ~ % 79.53/15.84 (in(v4, v5) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | (in(v1, % 79.53/15.84 v3) = 0 & in(v0, v2) = 0)) % 79.53/15.84 % 79.53/15.84 (t1_subset) % 79.53/15.84 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (element(v0, v1) = v2) % 79.53/15.84 | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ( ~ (v3 = 0) & in(v0, v1) = v3)) & % 79.53/15.84 ! [v0: $i] : ! [v1: $i] : ( ~ (in(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | % 79.53/15.84 element(v0, v1) = 0) % 79.53/15.84 % 79.53/15.84 (t26_orders_2) % 79.53/15.84 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: % 79.53/15.84 int] : ( ~ (v5 = 0) & related(v0, v3, v4) = 0 & related(v0, v2, v4) = v5 & % 79.53/15.84 related(v0, v2, v3) = 0 & rel_str(v0) = 0 & transitive_relstr(v0) = 0 & % 79.53/15.84 the_carrier(v0) = v1 & element(v4, v1) = 0 & element(v3, v1) = 0 & % 79.53/15.84 element(v2, v1) = 0 & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 79.53/15.84 % 79.53/15.84 (t2_subset) % 79.53/15.84 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (in(v0, v1) = v2) | ~ % 79.53/15.84 $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : (empty(v1) = v4 & % 79.53/15.84 element(v0, v1) = v3 & ( ~ (v3 = 0) | v4 = 0))) & ! [v0: $i] : ! [v1: % 79.53/15.84 $i] : ( ~ (element(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: any] : ? % 79.53/15.84 [v3: any] : (empty(v1) = v2 & in(v0, v1) = v3 & (v3 = 0 | v2 = 0))) % 79.53/15.84 % 79.53/15.84 (t4_subset) % 79.53/15.84 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0 % 79.53/15.84 | ~ (powerset(v2) = v3) | ~ (element(v1, v3) = 0) | ~ (element(v0, v2) = % 79.53/15.84 v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ( ~ (v5 = 0) & % 79.53/15.85 in(v0, v1) = v5)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] % 79.53/15.85 : (v3 = 0 | ~ (element(v0, v2) = v3) | ~ (in(v0, v1) = 0) | ~ $i(v2) | ~ % 79.53/15.85 $i(v1) | ~ $i(v0) | ? [v4: $i] : ? [v5: int] : ( ~ (v5 = 0) & % 79.53/15.85 powerset(v2) = v4 & element(v1, v4) = v5 & $i(v4))) & ! [v0: $i] : ! % 79.53/15.85 [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (powerset(v2) = v3) | ~ % 79.53/15.85 (element(v1, v3) = 0) | ~ (in(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ % 79.53/15.85 $i(v0) | element(v0, v2) = 0) % 79.53/15.85 % 79.53/15.85 (t5_subset) % 79.53/15.85 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (powerset(v2) = % 79.53/15.85 v3) | ~ (element(v1, v3) = 0) | ~ (in(v0, v1) = 0) | ~ $i(v2) | ~ % 79.53/15.85 $i(v1) | ~ $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & empty(v2) = v4)) & ! % 79.53/15.85 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (empty(v2) = 0) | ~ (in(v0, v1) = % 79.53/15.85 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ % 79.53/15.85 (v4 = 0) & powerset(v2) = v3 & element(v1, v3) = v4 & $i(v3))) % 79.53/15.85 % 79.53/15.85 (t6_boole) % 79.53/15.85 $i(empty_set) & ! [v0: $i] : (v0 = empty_set | ~ (empty(v0) = 0) | ~ % 79.53/15.85 $i(v0)) % 79.53/15.85 % 79.53/15.85 (t7_boole) % 79.53/15.85 ! [v0: $i] : ! [v1: $i] : ( ~ (in(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? % 79.53/15.85 [v2: int] : ( ~ (v2 = 0) & empty(v1) = v2)) % 79.53/15.85 % 79.53/15.85 (t8_boole) % 79.53/15.85 ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (empty(v1) = 0) | ~ (empty(v0) = 0) % 79.53/15.85 | ~ $i(v1) | ~ $i(v0)) % 79.53/15.85 % 79.53/15.85 (function-axioms) % 79.53/15.86 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 79.53/15.86 [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (relation_of2(v4, v3, v2) = v1) | ~ % 79.53/15.86 (relation_of2(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 79.53/15.86 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ % 79.53/15.86 (relation_of2_as_subset(v4, v3, v2) = v1) | ~ (relation_of2_as_subset(v4, % 79.53/15.86 v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] % 79.53/15.86 : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (related(v4, v3, v2) % 79.53/15.86 = v1) | ~ (related(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! % 79.53/15.86 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 79.53/15.86 (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0: $i] : ! [v1: % 79.53/15.86 $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (ordered_pair(v3, v2) = v1) % 79.53/15.86 | ~ (ordered_pair(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 79.53/15.86 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 79.53/15.86 (is_transitive_in(v3, v2) = v1) | ~ (is_transitive_in(v3, v2) = v0)) & ! % 79.53/15.86 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 79.53/15.86 (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) & ! [v0: % 79.53/15.86 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 79.53/15.86 (cartesian_product2(v3, v2) = v1) | ~ (cartesian_product2(v3, v2) = v0)) & % 79.53/15.86 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 79.53/15.86 $i] : (v1 = v0 | ~ (element(v3, v2) = v1) | ~ (element(v3, v2) = v0)) & ! % 79.53/15.86 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 79.53/15.86 $i] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) & ! [v0: % 79.53/15.86 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 79.53/15.86 ~ (empty(v2) = v1) | ~ (empty(v2) = v0)) & ! [v0: MultipleValueBool] : ! % 79.53/15.86 [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (one_sorted_str(v2) = % 79.53/15.86 v1) | ~ (one_sorted_str(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 79.53/15.86 $i] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ! % 79.53/15.86 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (the_InternalRel(v2) = % 79.53/15.86 v1) | ~ (the_InternalRel(v2) = v0)) & ! [v0: MultipleValueBool] : ! % 79.53/15.86 [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (rel_str(v2) = v1) | ~ % 79.53/15.86 (rel_str(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 79.53/15.86 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (transitive_relstr(v2) = % 79.53/15.86 v1) | ~ (transitive_relstr(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 79.53/15.86 [v2: $i] : (v1 = v0 | ~ (the_carrier(v2) = v1) | ~ (the_carrier(v2) = v0)) & % 79.53/15.86 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (powerset(v2) = v1) | % 79.53/15.86 ~ (powerset(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 79.53/15.86 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (relation(v2) = v1) | ~ % 79.53/15.86 (relation(v2) = v0)) % 79.53/15.86 % 79.53/15.86 Further assumptions not needed in the proof: % 79.53/15.86 -------------------------------------------- % 79.53/15.86 antisymmetry_r2_hidden, dt_k1_tarski, dt_k1_xboole_0, dt_k1_zfmisc_1, % 79.53/15.86 dt_k2_tarski, dt_k2_zfmisc_1, dt_k4_tarski, dt_l1_orders_2, dt_l1_struct_0, % 79.53/15.86 dt_m1_relset_1, dt_m1_subset_1, dt_u1_struct_0, existence_l1_struct_0, % 79.53/15.86 existence_m1_relset_1, existence_m1_subset_1, existence_m2_relset_1, % 79.53/15.86 fc1_xboole_0, fc2_subset_1, redefinition_m2_relset_1, reflexivity_r1_tarski, % 79.53/15.86 t3_subset % 79.53/15.86 % 79.53/15.86 Those formulas are unsatisfiable: % 79.53/15.86 --------------------------------- % 79.53/15.86 % 79.53/15.86 Begin of proof % 79.53/15.86 | % 79.53/15.86 | ALPHA: (commutativity_k2_tarski) implies: % 79.53/15.86 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (unordered_pair(v1, v0) = % 79.53/15.86 | v2) | ~ $i(v1) | ~ $i(v0) | (unordered_pair(v0, v1) = v2 & % 79.53/15.86 | $i(v2))) % 79.53/15.86 | % 79.53/15.86 | ALPHA: (d5_orders_2) implies: % 79.53/15.87 | (2) ! [v0: $i] : ( ~ (rel_str(v0) = 0) | ~ $i(v0) | ? [v1: any] : ? % 79.53/15.87 | [v2: $i] : ? [v3: $i] : ? [v4: any] : (the_InternalRel(v0) = v2 & % 79.53/15.87 | transitive_relstr(v0) = v1 & the_carrier(v0) = v3 & % 79.53/15.87 | is_transitive_in(v2, v3) = v4 & $i(v3) & $i(v2) & ( ~ (v4 = 0) | v1 % 79.53/15.87 | = 0) & ( ~ (v1 = 0) | v4 = 0))) % 79.53/15.87 | (3) ! [v0: $i] : ! [v1: $i] : ( ~ (the_carrier(v0) = v1) | ~ $i(v0) | ? % 79.53/15.87 | [v2: any] : ? [v3: any] : ? [v4: $i] : ? [v5: any] : % 79.53/15.87 | (the_InternalRel(v0) = v4 & rel_str(v0) = v2 & transitive_relstr(v0) % 79.53/15.87 | = v3 & is_transitive_in(v4, v1) = v5 & $i(v4) & ( ~ (v2 = 0) | (( ~ % 79.53/15.87 | (v5 = 0) | v3 = 0) & ( ~ (v3 = 0) | v5 = 0))))) % 79.53/15.87 | (4) ! [v0: $i] : ! [v1: any] : ( ~ (transitive_relstr(v0) = v1) | ~ % 79.53/15.87 | $i(v0) | ? [v2: any] : ? [v3: $i] : ? [v4: $i] : ? [v5: any] : % 79.53/15.87 | (the_InternalRel(v0) = v3 & rel_str(v0) = v2 & the_carrier(v0) = v4 & % 79.53/15.87 | is_transitive_in(v3, v4) = v5 & $i(v4) & $i(v3) & ( ~ (v2 = 0) | (( % 79.53/15.87 | ~ (v5 = 0) | v1 = 0) & ( ~ (v1 = 0) | v5 = 0))))) % 79.53/15.87 | (5) ! [v0: $i] : ! [v1: $i] : ( ~ (the_InternalRel(v0) = v1) | ~ $i(v0) % 79.53/15.87 | | ? [v2: any] : ? [v3: any] : ? [v4: $i] : ? [v5: any] : % 79.53/15.87 | (rel_str(v0) = v2 & transitive_relstr(v0) = v3 & the_carrier(v0) = v4 % 79.53/15.87 | & is_transitive_in(v1, v4) = v5 & $i(v4) & ( ~ (v2 = 0) | (( ~ (v5 % 79.53/15.87 | = 0) | v3 = 0) & ( ~ (v3 = 0) | v5 = 0))))) % 79.53/15.87 | % 79.53/15.87 | ALPHA: (d5_tarski) implies: % 79.53/15.87 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (ordered_pair(v0, v1) = % 79.53/15.87 | v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : % 79.53/15.87 | (singleton(v0) = v4 & unordered_pair(v3, v4) = v2 & % 79.53/15.87 | unordered_pair(v0, v1) = v3 & $i(v4) & $i(v3) & $i(v2))) % 79.53/15.87 | % 79.53/15.87 | ALPHA: (d8_relat_2) implies: % 79.53/15.88 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( % 79.53/15.88 | ~ (is_transitive_in(v0, v1) = 0) | ~ (relation(v0) = 0) | ~ (in(v4, % 79.53/15.88 | v1) = 0) | ~ (in(v3, v1) = 0) | ~ (in(v2, v1) = 0) | ~ $i(v4) % 79.53/15.88 | | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: $i] : ? % 79.53/15.88 | [v6: any] : ? [v7: $i] : ? [v8: any] : ? [v9: $i] : ? [v10: any] % 79.53/15.88 | : (ordered_pair(v3, v4) = v7 & ordered_pair(v2, v4) = v9 & % 79.53/15.88 | ordered_pair(v2, v3) = v5 & in(v9, v0) = v10 & in(v7, v0) = v8 & % 79.53/15.88 | in(v5, v0) = v6 & $i(v9) & $i(v7) & $i(v5) & ( ~ (v8 = 0) | ~ (v6 % 79.53/15.88 | = 0) | v10 = 0))) % 79.53/15.88 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 79.53/15.88 | ! [v5: $i] : ( ~ (ordered_pair(v2, v3) = v5) | ~ (is_transitive_in(v0, % 79.53/15.88 | v1) = 0) | ~ (relation(v0) = 0) | ~ (in(v5, v0) = 0) | ~ % 79.53/15.88 | (in(v4, v1) = 0) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 79.53/15.88 | $i(v0) | ? [v6: any] : ? [v7: any] : ? [v8: $i] : ? [v9: any] : % 79.53/15.88 | ? [v10: $i] : ? [v11: any] : (ordered_pair(v3, v4) = v8 & % 79.53/15.88 | ordered_pair(v2, v4) = v10 & in(v10, v0) = v11 & in(v8, v0) = v9 & % 79.53/15.88 | in(v3, v1) = v7 & in(v2, v1) = v6 & $i(v10) & $i(v8) & ( ~ (v9 = 0) % 79.53/15.88 | | ~ (v7 = 0) | ~ (v6 = 0) | v11 = 0))) % 79.53/15.88 | (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 79.53/15.88 | ! [v5: $i] : ( ~ (ordered_pair(v3, v4) = v5) | ~ (is_transitive_in(v0, % 79.53/15.88 | v1) = 0) | ~ (relation(v0) = 0) | ~ (in(v5, v0) = 0) | ~ % 79.53/15.88 | (in(v2, v1) = 0) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 79.53/15.88 | $i(v0) | ? [v6: any] : ? [v7: any] : ? [v8: $i] : ? [v9: any] : % 79.53/15.88 | ? [v10: $i] : ? [v11: any] : (ordered_pair(v2, v4) = v10 & % 79.53/15.88 | ordered_pair(v2, v3) = v8 & in(v10, v0) = v11 & in(v8, v0) = v9 & % 79.53/15.88 | in(v4, v1) = v7 & in(v3, v1) = v6 & $i(v10) & $i(v8) & ( ~ (v9 = 0) % 79.53/15.88 | | ~ (v7 = 0) | ~ (v6 = 0) | v11 = 0))) % 79.53/15.89 | (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 79.53/15.89 | ! [v5: $i] : ! [v6: $i] : ( ~ (ordered_pair(v3, v4) = v6) | ~ % 79.53/15.89 | (ordered_pair(v2, v3) = v5) | ~ (is_transitive_in(v0, v1) = 0) | ~ % 79.53/15.89 | (relation(v0) = 0) | ~ (in(v6, v0) = 0) | ~ (in(v5, v0) = 0) | ~ % 79.53/15.89 | $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v7: % 79.53/15.89 | any] : ? [v8: any] : ? [v9: any] : ? [v10: $i] : ? [v11: any] % 79.53/15.89 | : (ordered_pair(v2, v4) = v10 & in(v10, v0) = v11 & in(v4, v1) = v9 % 79.53/15.89 | & in(v3, v1) = v8 & in(v2, v1) = v7 & $i(v10) & ( ~ (v9 = 0) | ~ % 79.53/15.89 | (v8 = 0) | ~ (v7 = 0) | v11 = 0))) % 79.53/15.89 | % 79.53/15.89 | ALPHA: (d9_orders_2) implies: % 79.53/15.89 | (11) ! [v0: $i] : ( ~ (rel_str(v0) = 0) | ~ $i(v0) | ? [v1: $i] : ? % 79.53/15.89 | [v2: $i] : (the_InternalRel(v0) = v2 & the_carrier(v0) = v1 & $i(v2) % 79.53/15.89 | & $i(v1) & ! [v3: $i] : ! [v4: $i] : ! [v5: any] : ( ~ % 79.53/15.89 | (related(v0, v3, v4) = v5) | ~ (element(v3, v1) = 0) | ~ % 79.53/15.89 | $i(v4) | ~ $i(v3) | ? [v6: any] : ? [v7: $i] : ? [v8: any] : % 79.53/15.89 | (ordered_pair(v3, v4) = v7 & element(v4, v1) = v6 & in(v7, v2) = % 79.53/15.89 | v8 & $i(v7) & ( ~ (v6 = 0) | (( ~ (v8 = 0) | v5 = 0) & ( ~ (v5 % 79.53/15.89 | = 0) | v8 = 0))))) & ! [v3: $i] : ! [v4: $i] : ! % 79.53/15.89 | [v5: $i] : ( ~ (ordered_pair(v3, v4) = v5) | ~ (element(v3, v1) = % 79.53/15.89 | 0) | ~ $i(v4) | ~ $i(v3) | ? [v6: any] : ? [v7: any] : ? % 79.53/15.89 | [v8: any] : (related(v0, v3, v4) = v7 & element(v4, v1) = v6 & % 79.53/15.89 | in(v5, v2) = v8 & ( ~ (v6 = 0) | (( ~ (v8 = 0) | v7 = 0) & ( ~ % 79.53/15.89 | (v7 = 0) | v8 = 0))))) & ! [v3: $i] : ! [v4: $i] : ( ~ % 79.53/15.89 | (element(v4, v1) = 0) | ~ (element(v3, v1) = 0) | ~ $i(v4) | % 79.53/15.89 | ~ $i(v3) | ? [v5: any] : ? [v6: $i] : ? [v7: any] : % 79.53/15.89 | (related(v0, v3, v4) = v5 & ordered_pair(v3, v4) = v6 & in(v6, % 79.53/15.89 | v2) = v7 & $i(v6) & ( ~ (v7 = 0) | v5 = 0) & ( ~ (v5 = 0) | % 79.53/15.89 | v7 = 0))))) % 79.53/15.90 | (12) ! [v0: $i] : ! [v1: $i] : ( ~ (the_carrier(v0) = v1) | ~ $i(v0) | % 79.53/15.90 | ? [v2: any] : ? [v3: $i] : (the_InternalRel(v0) = v3 & rel_str(v0) % 79.53/15.90 | = v2 & $i(v3) & ( ~ (v2 = 0) | ( ! [v4: $i] : ! [v5: $i] : ! % 79.53/15.90 | [v6: any] : ( ~ (related(v0, v4, v5) = v6) | ~ (element(v4, % 79.53/15.90 | v1) = 0) | ~ $i(v5) | ~ $i(v4) | ? [v7: any] : ? % 79.53/15.90 | [v8: $i] : ? [v9: any] : (ordered_pair(v4, v5) = v8 & % 79.53/15.90 | element(v5, v1) = v7 & in(v8, v3) = v9 & $i(v8) & ( ~ (v7 % 79.53/15.90 | = 0) | (( ~ (v9 = 0) | v6 = 0) & ( ~ (v6 = 0) | v9 = % 79.53/15.90 | 0))))) & ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( % 79.53/15.90 | ~ (ordered_pair(v4, v5) = v6) | ~ (element(v4, v1) = 0) | % 79.53/15.90 | ~ $i(v5) | ~ $i(v4) | ? [v7: any] : ? [v8: any] : ? [v9: % 79.53/15.90 | any] : (related(v0, v4, v5) = v8 & element(v5, v1) = v7 & % 79.53/15.90 | in(v6, v3) = v9 & ( ~ (v7 = 0) | (( ~ (v9 = 0) | v8 = 0) & % 79.53/15.90 | ( ~ (v8 = 0) | v9 = 0))))) & ! [v4: $i] : ! [v5: $i] % 79.53/15.90 | : ( ~ (element(v5, v1) = 0) | ~ (element(v4, v1) = 0) | ~ % 79.53/15.90 | $i(v5) | ~ $i(v4) | ? [v6: any] : ? [v7: $i] : ? [v8: % 79.53/15.90 | any] : (related(v0, v4, v5) = v6 & ordered_pair(v4, v5) = % 79.53/15.90 | v7 & in(v7, v3) = v8 & $i(v7) & ( ~ (v8 = 0) | v6 = 0) & ( % 79.53/15.90 | ~ (v6 = 0) | v8 = 0))))))) % 79.53/15.90 | (13) ! [v0: $i] : ! [v1: $i] : ( ~ (the_InternalRel(v0) = v1) | ~ $i(v0) % 79.53/15.90 | | ? [v2: any] : ? [v3: $i] : (rel_str(v0) = v2 & the_carrier(v0) = % 79.53/15.90 | v3 & $i(v3) & ( ~ (v2 = 0) | ( ! [v4: $i] : ! [v5: $i] : ! [v6: % 79.53/15.90 | any] : ( ~ (related(v0, v4, v5) = v6) | ~ (element(v4, v3) % 79.53/15.90 | = 0) | ~ $i(v5) | ~ $i(v4) | ? [v7: any] : ? [v8: $i] % 79.53/15.90 | : ? [v9: any] : (ordered_pair(v4, v5) = v8 & element(v5, % 79.53/15.90 | v3) = v7 & in(v8, v1) = v9 & $i(v8) & ( ~ (v7 = 0) | (( % 79.53/15.90 | ~ (v9 = 0) | v6 = 0) & ( ~ (v6 = 0) | v9 = 0))))) & % 79.53/15.90 | ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~ (ordered_pair(v4, % 79.53/15.90 | v5) = v6) | ~ (element(v4, v3) = 0) | ~ $i(v5) | ~ % 79.53/15.90 | $i(v4) | ? [v7: any] : ? [v8: any] : ? [v9: any] : % 79.53/15.90 | (related(v0, v4, v5) = v8 & element(v5, v3) = v7 & in(v6, % 79.53/15.90 | v1) = v9 & ( ~ (v7 = 0) | (( ~ (v9 = 0) | v8 = 0) & ( ~ % 79.53/15.90 | (v8 = 0) | v9 = 0))))) & ! [v4: $i] : ! [v5: $i] : % 79.53/15.90 | ( ~ (element(v5, v3) = 0) | ~ (element(v4, v3) = 0) | ~ % 79.53/15.90 | $i(v5) | ~ $i(v4) | ? [v6: any] : ? [v7: $i] : ? [v8: % 79.53/15.90 | any] : (related(v0, v4, v5) = v6 & ordered_pair(v4, v5) = % 79.53/15.90 | v7 & in(v7, v1) = v8 & $i(v7) & ( ~ (v8 = 0) | v6 = 0) & ( % 79.53/15.90 | ~ (v6 = 0) | v8 = 0))))))) % 79.53/15.90 | % 79.53/15.90 | ALPHA: (dt_m2_relset_1) implies: % 79.53/15.90 | (14) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 79.53/15.90 | (relation_of2_as_subset(v2, v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | % 79.53/15.90 | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : (cartesian_product2(v0, v1) = % 79.53/15.90 | v3 & powerset(v3) = v4 & element(v2, v4) = 0 & $i(v4) & $i(v3))) % 79.53/15.90 | % 79.53/15.90 | ALPHA: (dt_u1_orders_2) implies: % 79.53/15.90 | (15) ! [v0: $i] : ( ~ (rel_str(v0) = 0) | ~ $i(v0) | ? [v1: $i] : ? % 79.53/15.90 | [v2: $i] : (relation_of2_as_subset(v1, v2, v2) = 0 & % 79.53/15.90 | the_InternalRel(v0) = v1 & the_carrier(v0) = v2 & $i(v2) & % 79.53/15.90 | $i(v1))) % 79.53/15.90 | (16) ! [v0: $i] : ! [v1: $i] : ( ~ (the_carrier(v0) = v1) | ~ $i(v0) | % 79.53/15.90 | ? [v2: any] : ? [v3: $i] : ? [v4: any] : % 79.53/15.90 | (relation_of2_as_subset(v3, v1, v1) = v4 & the_InternalRel(v0) = v3 % 79.53/15.91 | & rel_str(v0) = v2 & $i(v3) & ( ~ (v2 = 0) | v4 = 0))) % 79.53/15.91 | % 79.53/15.91 | ALPHA: (rc1_subset_1) implies: % 79.53/15.91 | (17) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (empty(v0) = v1) | ~ $i(v0) % 79.53/15.91 | | ? [v2: $i] : ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & % 79.53/15.91 | empty(v3) = v4 & powerset(v0) = v2 & element(v3, v2) = 0 & $i(v3) % 79.53/15.91 | & $i(v2))) % 79.53/15.91 | % 79.53/15.91 | ALPHA: (t106_zfmisc_1) implies: % 79.53/15.91 | (18) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 79.53/15.91 | ! [v5: $i] : ( ~ (ordered_pair(v0, v1) = v4) | ~ % 79.53/15.91 | (cartesian_product2(v2, v3) = v5) | ~ (in(v4, v5) = 0) | ~ $i(v3) % 79.53/15.91 | | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | (in(v1, v3) = 0 & in(v0, v2) = % 79.53/15.91 | 0)) % 79.53/15.91 | % 79.53/15.91 | ALPHA: (t1_subset) implies: % 79.53/15.91 | (19) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (element(v0, % 79.53/15.91 | v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ( ~ (v3 = 0) % 79.53/15.91 | & in(v0, v1) = v3)) % 79.53/15.91 | % 79.53/15.91 | ALPHA: (t2_subset) implies: % 79.53/15.91 | (20) ! [v0: $i] : ! [v1: $i] : ( ~ (element(v0, v1) = 0) | ~ $i(v1) | ~ % 79.53/15.91 | $i(v0) | ? [v2: any] : ? [v3: any] : (empty(v1) = v2 & in(v0, v1) % 79.53/15.91 | = v3 & (v3 = 0 | v2 = 0))) % 79.53/15.91 | (21) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (in(v0, v1) = % 79.53/15.91 | v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : % 79.53/15.91 | (empty(v1) = v4 & element(v0, v1) = v3 & ( ~ (v3 = 0) | v4 = 0))) % 79.53/15.91 | % 79.53/15.91 | ALPHA: (t4_subset) implies: % 79.53/15.91 | (22) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 79.53/15.91 | (powerset(v2) = v3) | ~ (element(v1, v3) = 0) | ~ (in(v0, v1) = 0) % 79.53/15.91 | | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | element(v0, v2) = 0) % 79.53/15.91 | (23) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : % 79.53/15.91 | (v4 = 0 | ~ (powerset(v2) = v3) | ~ (element(v1, v3) = 0) | ~ % 79.53/15.91 | (element(v0, v2) = v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: % 79.53/15.91 | int] : ( ~ (v5 = 0) & in(v0, v1) = v5)) % 79.53/15.91 | % 79.53/15.91 | ALPHA: (t5_subset) implies: % 79.53/15.91 | (24) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (empty(v2) = 0) | ~ % 79.53/15.91 | (in(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : % 79.53/15.91 | ? [v4: int] : ( ~ (v4 = 0) & powerset(v2) = v3 & element(v1, v3) = % 79.53/15.91 | v4 & $i(v3))) % 79.53/15.91 | (25) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 79.53/15.91 | (powerset(v2) = v3) | ~ (element(v1, v3) = 0) | ~ (in(v0, v1) = 0) % 79.53/15.91 | | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & % 79.53/15.91 | empty(v2) = v4)) % 79.53/15.91 | % 79.53/15.91 | ALPHA: (t6_boole) implies: % 79.53/15.91 | (26) ! [v0: $i] : (v0 = empty_set | ~ (empty(v0) = 0) | ~ $i(v0)) % 79.53/15.91 | % 79.53/15.91 | ALPHA: (function-axioms) implies: % 79.53/15.91 | (27) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (powerset(v2) % 79.53/15.91 | = v1) | ~ (powerset(v2) = v0)) % 79.53/15.92 | (28) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 79.53/15.92 | (the_carrier(v2) = v1) | ~ (the_carrier(v2) = v0)) % 79.53/15.92 | (29) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 79.53/15.92 | : (v1 = v0 | ~ (rel_str(v2) = v1) | ~ (rel_str(v2) = v0)) % 79.53/15.92 | (30) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 79.53/15.92 | (the_InternalRel(v2) = v1) | ~ (the_InternalRel(v2) = v0)) % 79.53/15.92 | (31) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (singleton(v2) % 79.53/15.92 | = v1) | ~ (singleton(v2) = v0)) % 79.53/15.92 | (32) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 79.53/15.92 | : (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0)) % 79.53/15.92 | (33) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 79.53/15.92 | : ! [v3: $i] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = % 79.53/15.92 | v0)) % 79.53/15.92 | (34) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 79.53/15.92 | : ! [v3: $i] : (v1 = v0 | ~ (element(v3, v2) = v1) | ~ (element(v3, % 79.53/15.92 | v2) = v0)) % 79.53/15.92 | (35) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 79.53/15.92 | (ordered_pair(v3, v2) = v1) | ~ (ordered_pair(v3, v2) = v0)) % 79.53/15.92 | (36) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 79.53/15.92 | : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (related(v4, v3, v2) = v1) % 79.53/15.92 | | ~ (related(v4, v3, v2) = v0)) % 79.53/15.92 | % 79.53/15.92 | DELTA: instantiating (rc1_xboole_0) with fresh symbol all_33_0 gives: % 79.53/15.92 | (37) empty(all_33_0) = 0 & $i(all_33_0) % 79.53/15.92 | % 79.53/15.92 | ALPHA: (37) implies: % 79.53/15.92 | (38) $i(all_33_0) % 79.53/15.92 | (39) empty(all_33_0) = 0 % 79.53/15.92 | % 79.53/15.92 | DELTA: instantiating (existence_l1_orders_2) with fresh symbol all_35_0 gives: % 79.53/15.92 | (40) rel_str(all_35_0) = 0 & $i(all_35_0) % 79.53/15.92 | % 79.53/15.92 | ALPHA: (40) implies: % 79.53/15.92 | (41) $i(all_35_0) % 79.53/15.92 | (42) rel_str(all_35_0) = 0 % 79.53/15.92 | % 79.53/15.92 | DELTA: instantiating (rc2_xboole_0) with fresh symbols all_38_0, all_38_1 % 79.53/15.92 | gives: % 79.53/15.92 | (43) ~ (all_38_0 = 0) & empty(all_38_1) = all_38_0 & $i(all_38_1) % 79.53/15.92 | % 79.53/15.92 | ALPHA: (43) implies: % 79.53/15.92 | (44) ~ (all_38_0 = 0) % 79.53/15.92 | (45) $i(all_38_1) % 79.53/15.92 | (46) empty(all_38_1) = all_38_0 % 79.53/15.92 | % 79.53/15.92 | DELTA: instantiating (t26_orders_2) with fresh symbols all_42_0, all_42_1, % 79.53/15.92 | all_42_2, all_42_3, all_42_4, all_42_5 gives: % 79.53/15.92 | (47) ~ (all_42_0 = 0) & related(all_42_5, all_42_2, all_42_1) = 0 & % 79.53/15.92 | related(all_42_5, all_42_3, all_42_1) = all_42_0 & related(all_42_5, % 79.53/15.92 | all_42_3, all_42_2) = 0 & rel_str(all_42_5) = 0 & % 79.53/15.92 | transitive_relstr(all_42_5) = 0 & the_carrier(all_42_5) = all_42_4 & % 79.53/15.92 | element(all_42_1, all_42_4) = 0 & element(all_42_2, all_42_4) = 0 & % 79.53/15.92 | element(all_42_3, all_42_4) = 0 & $i(all_42_1) & $i(all_42_2) & % 79.53/15.92 | $i(all_42_3) & $i(all_42_4) & $i(all_42_5) % 79.53/15.92 | % 79.53/15.92 | ALPHA: (47) implies: % 79.53/15.92 | (48) ~ (all_42_0 = 0) % 79.53/15.92 | (49) $i(all_42_5) % 79.53/15.92 | (50) $i(all_42_4) % 79.53/15.92 | (51) $i(all_42_3) % 79.53/15.92 | (52) $i(all_42_2) % 79.53/15.92 | (53) $i(all_42_1) % 79.53/15.92 | (54) element(all_42_3, all_42_4) = 0 % 79.53/15.92 | (55) element(all_42_2, all_42_4) = 0 % 79.53/15.92 | (56) element(all_42_1, all_42_4) = 0 % 79.53/15.92 | (57) the_carrier(all_42_5) = all_42_4 % 79.53/15.92 | (58) transitive_relstr(all_42_5) = 0 % 79.53/15.92 | (59) rel_str(all_42_5) = 0 % 79.53/15.92 | (60) related(all_42_5, all_42_3, all_42_2) = 0 % 79.53/15.92 | (61) related(all_42_5, all_42_3, all_42_1) = all_42_0 % 79.53/15.92 | (62) related(all_42_5, all_42_2, all_42_1) = 0 % 79.53/15.92 | % 79.53/15.93 | GROUND_INST: instantiating (20) with all_42_3, all_42_4, simplifying with % 79.53/15.93 | (50), (51), (54) gives: % 79.53/15.93 | (63) ? [v0: any] : ? [v1: any] : (empty(all_42_4) = v0 & in(all_42_3, % 79.53/15.93 | all_42_4) = v1 & (v1 = 0 | v0 = 0)) % 79.53/15.93 | % 79.53/15.93 | GROUND_INST: instantiating (20) with all_42_2, all_42_4, simplifying with % 79.53/15.93 | (50), (52), (55) gives: % 79.53/15.93 | (64) ? [v0: any] : ? [v1: any] : (empty(all_42_4) = v0 & in(all_42_2, % 79.53/15.93 | all_42_4) = v1 & (v1 = 0 | v0 = 0)) % 79.53/15.93 | % 79.53/15.93 | GROUND_INST: instantiating (20) with all_42_1, all_42_4, simplifying with % 79.53/15.93 | (50), (53), (56) gives: % 79.53/15.93 | (65) ? [v0: any] : ? [v1: any] : (empty(all_42_4) = v0 & in(all_42_1, % 79.53/15.93 | all_42_4) = v1 & (v1 = 0 | v0 = 0)) % 79.53/15.93 | % 79.53/15.93 | GROUND_INST: instantiating (3) with all_42_5, all_42_4, simplifying with (49), % 79.53/15.93 | (57) gives: % 79.53/15.93 | (66) ? [v0: any] : ? [v1: any] : ? [v2: $i] : ? [v3: any] : % 79.53/15.93 | (the_InternalRel(all_42_5) = v2 & rel_str(all_42_5) = v0 & % 79.53/15.93 | transitive_relstr(all_42_5) = v1 & is_transitive_in(v2, all_42_4) = % 79.53/15.93 | v3 & $i(v2) & ( ~ (v0 = 0) | (( ~ (v3 = 0) | v1 = 0) & ( ~ (v1 = 0) % 79.53/15.93 | | v3 = 0)))) % 79.53/15.93 | % 79.53/15.93 | GROUND_INST: instantiating (16) with all_42_5, all_42_4, simplifying with % 79.53/15.93 | (49), (57) gives: % 79.53/15.93 | (67) ? [v0: any] : ? [v1: $i] : ? [v2: any] : % 79.53/15.93 | (relation_of2_as_subset(v1, all_42_4, all_42_4) = v2 & % 79.53/15.93 | the_InternalRel(all_42_5) = v1 & rel_str(all_42_5) = v0 & $i(v1) & ( % 79.53/15.93 | ~ (v0 = 0) | v2 = 0)) % 79.53/15.93 | % 79.53/15.93 | GROUND_INST: instantiating (12) with all_42_5, all_42_4, simplifying with % 79.53/15.93 | (49), (57) gives: % 79.53/15.93 | (68) ? [v0: any] : ? [v1: $i] : (the_InternalRel(all_42_5) = v1 & % 79.53/15.93 | rel_str(all_42_5) = v0 & $i(v1) & ( ~ (v0 = 0) | ( ! [v2: $i] : ! % 79.53/15.93 | [v3: $i] : ! [v4: any] : ( ~ (related(all_42_5, v2, v3) = v4) | % 79.53/15.93 | ~ (element(v2, all_42_4) = 0) | ~ $i(v3) | ~ $i(v2) | ? % 79.53/15.93 | [v5: any] : ? [v6: $i] : ? [v7: any] : (ordered_pair(v2, v3) % 79.53/15.93 | = v6 & element(v3, all_42_4) = v5 & in(v6, v1) = v7 & $i(v6) % 79.53/15.93 | & ( ~ (v5 = 0) | (( ~ (v7 = 0) | v4 = 0) & ( ~ (v4 = 0) | v7 % 79.53/15.93 | = 0))))) & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( % 79.53/15.93 | ~ (ordered_pair(v2, v3) = v4) | ~ (element(v2, all_42_4) = 0) % 79.53/15.93 | | ~ $i(v3) | ~ $i(v2) | ? [v5: any] : ? [v6: any] : ? % 79.53/15.93 | [v7: any] : (related(all_42_5, v2, v3) = v6 & element(v3, % 79.53/15.93 | all_42_4) = v5 & in(v4, v1) = v7 & ( ~ (v5 = 0) | (( ~ (v7 % 79.53/15.93 | = 0) | v6 = 0) & ( ~ (v6 = 0) | v7 = 0))))) & ! % 79.53/15.93 | [v2: $i] : ! [v3: $i] : ( ~ (element(v3, all_42_4) = 0) | ~ % 79.53/15.93 | (element(v2, all_42_4) = 0) | ~ $i(v3) | ~ $i(v2) | ? [v4: % 79.53/15.93 | any] : ? [v5: $i] : ? [v6: any] : (related(all_42_5, v2, % 79.53/15.93 | v3) = v4 & ordered_pair(v2, v3) = v5 & in(v5, v1) = v6 & % 79.53/15.93 | $i(v5) & ( ~ (v6 = 0) | v4 = 0) & ( ~ (v4 = 0) | v6 = % 79.53/15.93 | 0)))))) % 79.53/15.93 | % 79.53/15.93 | GROUND_INST: instantiating (4) with all_42_5, 0, simplifying with (49), (58) % 79.53/15.93 | gives: % 79.53/15.93 | (69) ? [v0: any] : ? [v1: $i] : ? [v2: $i] : ? [v3: any] : % 79.53/15.93 | (the_InternalRel(all_42_5) = v1 & rel_str(all_42_5) = v0 & % 79.53/15.93 | the_carrier(all_42_5) = v2 & is_transitive_in(v1, v2) = v3 & $i(v2) % 79.53/15.93 | & $i(v1) & ( ~ (v0 = 0) | v3 = 0)) % 79.53/15.93 | % 79.53/15.93 | GROUND_INST: instantiating (2) with all_35_0, simplifying with (41), (42) % 79.53/15.93 | gives: % 79.53/15.93 | (70) ? [v0: any] : ? [v1: $i] : ? [v2: $i] : ? [v3: any] : % 79.53/15.93 | (the_InternalRel(all_35_0) = v1 & transitive_relstr(all_35_0) = v0 & % 79.53/15.93 | the_carrier(all_35_0) = v2 & is_transitive_in(v1, v2) = v3 & $i(v2) % 79.53/15.93 | & $i(v1) & ( ~ (v3 = 0) | v0 = 0) & ( ~ (v0 = 0) | v3 = 0)) % 79.53/15.93 | % 79.53/15.93 | GROUND_INST: instantiating (15) with all_35_0, simplifying with (41), (42) % 79.53/15.93 | gives: % 79.53/15.94 | (71) ? [v0: $i] : ? [v1: $i] : (relation_of2_as_subset(v0, v1, v1) = 0 & % 79.53/15.94 | the_InternalRel(all_35_0) = v0 & the_carrier(all_35_0) = v1 & $i(v1) % 79.53/15.94 | & $i(v0)) % 79.53/15.94 | % 79.53/15.94 | GROUND_INST: instantiating (11) with all_35_0, simplifying with (41), (42) % 79.53/15.94 | gives: % 79.53/15.94 | (72) ? [v0: $i] : ? [v1: $i] : (the_InternalRel(all_35_0) = v1 & % 79.53/15.94 | the_carrier(all_35_0) = v0 & $i(v1) & $i(v0) & ! [v2: $i] : ! [v3: % 79.53/15.94 | $i] : ! [v4: any] : ( ~ (related(all_35_0, v2, v3) = v4) | ~ % 79.53/15.94 | (element(v2, v0) = 0) | ~ $i(v3) | ~ $i(v2) | ? [v5: any] : ? % 79.53/15.94 | [v6: $i] : ? [v7: any] : (ordered_pair(v2, v3) = v6 & element(v3, % 79.53/15.94 | v0) = v5 & in(v6, v1) = v7 & $i(v6) & ( ~ (v5 = 0) | (( ~ (v7 % 79.53/15.94 | = 0) | v4 = 0) & ( ~ (v4 = 0) | v7 = 0))))) & ! [v2: % 79.53/15.94 | $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (ordered_pair(v2, v3) = v4) % 79.53/15.94 | | ~ (element(v2, v0) = 0) | ~ $i(v3) | ~ $i(v2) | ? [v5: any] % 79.53/15.94 | : ? [v6: any] : ? [v7: any] : (related(all_35_0, v2, v3) = v6 & % 79.53/15.94 | element(v3, v0) = v5 & in(v4, v1) = v7 & ( ~ (v5 = 0) | (( ~ (v7 % 79.53/15.94 | = 0) | v6 = 0) & ( ~ (v6 = 0) | v7 = 0))))) & ! [v2: % 79.53/15.94 | $i] : ! [v3: $i] : ( ~ (element(v3, v0) = 0) | ~ (element(v2, % 79.53/15.94 | v0) = 0) | ~ $i(v3) | ~ $i(v2) | ? [v4: any] : ? [v5: $i] % 79.53/15.94 | : ? [v6: any] : (related(all_35_0, v2, v3) = v4 & % 79.53/15.94 | ordered_pair(v2, v3) = v5 & in(v5, v1) = v6 & $i(v5) & ( ~ (v6 = % 79.53/15.94 | 0) | v4 = 0) & ( ~ (v4 = 0) | v6 = 0)))) % 79.53/15.94 | % 79.53/15.94 | GROUND_INST: instantiating (2) with all_42_5, simplifying with (49), (59) % 79.53/15.94 | gives: % 79.53/15.94 | (73) ? [v0: any] : ? [v1: $i] : ? [v2: $i] : ? [v3: any] : % 79.53/15.94 | (the_InternalRel(all_42_5) = v1 & transitive_relstr(all_42_5) = v0 & % 79.53/15.94 | the_carrier(all_42_5) = v2 & is_transitive_in(v1, v2) = v3 & $i(v2) % 79.53/15.94 | & $i(v1) & ( ~ (v3 = 0) | v0 = 0) & ( ~ (v0 = 0) | v3 = 0)) % 79.53/15.94 | % 79.53/15.94 | GROUND_INST: instantiating (15) with all_42_5, simplifying with (49), (59) % 79.53/15.94 | gives: % 79.53/15.94 | (74) ? [v0: $i] : ? [v1: $i] : (relation_of2_as_subset(v0, v1, v1) = 0 & % 79.53/15.94 | the_InternalRel(all_42_5) = v0 & the_carrier(all_42_5) = v1 & $i(v1) % 79.53/15.94 | & $i(v0)) % 79.53/15.94 | % 79.53/15.94 | GROUND_INST: instantiating (11) with all_42_5, simplifying with (49), (59) % 79.53/15.94 | gives: % 79.53/15.94 | (75) ? [v0: $i] : ? [v1: $i] : (the_InternalRel(all_42_5) = v1 & % 79.53/15.94 | the_carrier(all_42_5) = v0 & $i(v1) & $i(v0) & ! [v2: $i] : ! [v3: % 79.53/15.94 | $i] : ! [v4: any] : ( ~ (related(all_42_5, v2, v3) = v4) | ~ % 79.53/15.94 | (element(v2, v0) = 0) | ~ $i(v3) | ~ $i(v2) | ? [v5: any] : ? % 79.53/15.95 | [v6: $i] : ? [v7: any] : (ordered_pair(v2, v3) = v6 & element(v3, % 79.53/15.95 | v0) = v5 & in(v6, v1) = v7 & $i(v6) & ( ~ (v5 = 0) | (( ~ (v7 % 79.53/15.95 | = 0) | v4 = 0) & ( ~ (v4 = 0) | v7 = 0))))) & ! [v2: % 79.53/15.95 | $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (ordered_pair(v2, v3) = v4) % 79.53/15.95 | | ~ (element(v2, v0) = 0) | ~ $i(v3) | ~ $i(v2) | ? [v5: any] % 79.53/15.95 | : ? [v6: any] : ? [v7: any] : (related(all_42_5, v2, v3) = v6 & % 79.53/15.95 | element(v3, v0) = v5 & in(v4, v1) = v7 & ( ~ (v5 = 0) | (( ~ (v7 % 79.53/15.95 | = 0) | v6 = 0) & ( ~ (v6 = 0) | v7 = 0))))) & ! [v2: % 79.53/15.95 | $i] : ! [v3: $i] : ( ~ (element(v3, v0) = 0) | ~ (element(v2, % 79.53/15.95 | v0) = 0) | ~ $i(v3) | ~ $i(v2) | ? [v4: any] : ? [v5: $i] % 79.53/15.95 | : ? [v6: any] : (related(all_42_5, v2, v3) = v4 & % 79.53/15.95 | ordered_pair(v2, v3) = v5 & in(v5, v1) = v6 & $i(v5) & ( ~ (v6 = % 79.53/15.95 | 0) | v4 = 0) & ( ~ (v4 = 0) | v6 = 0)))) % 79.53/15.95 | % 79.53/15.95 | GROUND_INST: instantiating (26) with all_33_0, simplifying with (38), (39) % 79.53/15.95 | gives: % 79.53/15.95 | (76) all_33_0 = empty_set % 79.53/15.95 | % 79.53/15.95 | GROUND_INST: instantiating (17) with all_38_1, all_38_0, simplifying with % 79.53/15.95 | (45), (46) gives: % 79.53/15.95 | (77) all_38_0 = 0 | ? [v0: $i] : ? [v1: $i] : ? [v2: int] : ( ~ (v2 = 0) % 79.53/15.95 | & empty(v1) = v2 & powerset(all_38_1) = v0 & element(v1, v0) = 0 & % 79.53/15.95 | $i(v1) & $i(v0)) % 79.53/15.95 | % 79.53/15.95 | DELTA: instantiating (65) with fresh symbols all_50_0, all_50_1 gives: % 79.53/15.95 | (78) empty(all_42_4) = all_50_1 & in(all_42_1, all_42_4) = all_50_0 & % 79.53/15.95 | (all_50_0 = 0 | all_50_1 = 0) % 79.53/15.95 | % 79.53/15.95 | ALPHA: (78) implies: % 79.53/15.95 | (79) in(all_42_1, all_42_4) = all_50_0 % 79.53/15.95 | (80) empty(all_42_4) = all_50_1 % 79.53/15.95 | (81) all_50_0 = 0 | all_50_1 = 0 % 79.53/15.95 | % 79.53/15.95 | DELTA: instantiating (64) with fresh symbols all_52_0, all_52_1 gives: % 79.53/15.95 | (82) empty(all_42_4) = all_52_1 & in(all_42_2, all_42_4) = all_52_0 & % 79.53/15.95 | (all_52_0 = 0 | all_52_1 = 0) % 79.53/15.95 | % 79.53/15.95 | ALPHA: (82) implies: % 79.53/15.95 | (83) in(all_42_2, all_42_4) = all_52_0 % 79.53/15.95 | (84) empty(all_42_4) = all_52_1 % 79.53/15.95 | (85) all_52_0 = 0 | all_52_1 = 0 % 79.53/15.95 | % 79.53/15.95 | DELTA: instantiating (63) with fresh symbols all_54_0, all_54_1 gives: % 79.53/15.95 | (86) empty(all_42_4) = all_54_1 & in(all_42_3, all_42_4) = all_54_0 & % 79.53/15.95 | (all_54_0 = 0 | all_54_1 = 0) % 79.53/15.95 | % 79.53/15.95 | ALPHA: (86) implies: % 79.53/15.95 | (87) in(all_42_3, all_42_4) = all_54_0 % 79.53/15.95 | (88) empty(all_42_4) = all_54_1 % 79.53/15.95 | (89) all_54_0 = 0 | all_54_1 = 0 % 79.53/15.95 | % 79.53/15.95 | DELTA: instantiating (74) with fresh symbols all_56_0, all_56_1 gives: % 79.53/15.95 | (90) relation_of2_as_subset(all_56_1, all_56_0, all_56_0) = 0 & % 79.53/15.95 | the_InternalRel(all_42_5) = all_56_1 & the_carrier(all_42_5) = % 79.53/15.95 | all_56_0 & $i(all_56_0) & $i(all_56_1) % 79.53/15.95 | % 79.53/15.95 | ALPHA: (90) implies: % 79.53/15.95 | (91) $i(all_56_0) % 79.53/15.95 | (92) the_carrier(all_42_5) = all_56_0 % 79.53/15.95 | (93) the_InternalRel(all_42_5) = all_56_1 % 79.53/15.95 | (94) relation_of2_as_subset(all_56_1, all_56_0, all_56_0) = 0 % 79.53/15.95 | % 79.53/15.95 | DELTA: instantiating (71) with fresh symbols all_58_0, all_58_1 gives: % 79.53/15.95 | (95) relation_of2_as_subset(all_58_1, all_58_0, all_58_0) = 0 & % 79.53/15.95 | the_InternalRel(all_35_0) = all_58_1 & the_carrier(all_35_0) = % 79.53/15.95 | all_58_0 & $i(all_58_0) & $i(all_58_1) % 79.53/15.95 | % 79.53/15.95 | ALPHA: (95) implies: % 79.53/15.95 | (96) the_carrier(all_35_0) = all_58_0 % 79.53/15.95 | (97) the_InternalRel(all_35_0) = all_58_1 % 79.53/15.95 | (98) relation_of2_as_subset(all_58_1, all_58_0, all_58_0) = 0 % 79.53/15.95 | % 79.53/15.95 | DELTA: instantiating (67) with fresh symbols all_60_0, all_60_1, all_60_2 % 79.53/15.95 | gives: % 79.53/15.95 | (99) relation_of2_as_subset(all_60_1, all_42_4, all_42_4) = all_60_0 & % 79.53/15.95 | the_InternalRel(all_42_5) = all_60_1 & rel_str(all_42_5) = all_60_2 & % 79.53/15.95 | $i(all_60_1) & ( ~ (all_60_2 = 0) | all_60_0 = 0) % 79.53/15.95 | % 79.53/15.95 | ALPHA: (99) implies: % 79.53/15.95 | (100) $i(all_60_1) % 79.53/15.95 | (101) rel_str(all_42_5) = all_60_2 % 79.53/15.95 | (102) the_InternalRel(all_42_5) = all_60_1 % 79.53/15.95 | % 79.53/15.95 | DELTA: instantiating (69) with fresh symbols all_62_0, all_62_1, all_62_2, % 79.53/15.95 | all_62_3 gives: % 79.53/15.95 | (103) the_InternalRel(all_42_5) = all_62_2 & rel_str(all_42_5) = all_62_3 & % 79.53/15.95 | the_carrier(all_42_5) = all_62_1 & is_transitive_in(all_62_2, % 79.53/15.95 | all_62_1) = all_62_0 & $i(all_62_1) & $i(all_62_2) & ( ~ (all_62_3 % 79.53/15.95 | = 0) | all_62_0 = 0) % 79.53/15.95 | % 79.53/15.95 | ALPHA: (103) implies: % 79.53/15.95 | (104) is_transitive_in(all_62_2, all_62_1) = all_62_0 % 79.53/15.95 | (105) the_carrier(all_42_5) = all_62_1 % 79.53/15.95 | (106) rel_str(all_42_5) = all_62_3 % 79.53/15.95 | (107) the_InternalRel(all_42_5) = all_62_2 % 79.53/15.95 | (108) ~ (all_62_3 = 0) | all_62_0 = 0 % 79.53/15.95 | % 79.53/15.95 | DELTA: instantiating (66) with fresh symbols all_64_0, all_64_1, all_64_2, % 79.53/15.95 | all_64_3 gives: % 79.53/15.95 | (109) the_InternalRel(all_42_5) = all_64_1 & rel_str(all_42_5) = all_64_3 & % 79.53/15.95 | transitive_relstr(all_42_5) = all_64_2 & is_transitive_in(all_64_1, % 79.53/15.95 | all_42_4) = all_64_0 & $i(all_64_1) & ( ~ (all_64_3 = 0) | (( ~ % 79.53/15.95 | (all_64_0 = 0) | all_64_2 = 0) & ( ~ (all_64_2 = 0) | all_64_0 % 79.53/15.95 | = 0))) % 79.53/15.95 | % 79.53/15.95 | ALPHA: (109) implies: % 79.53/15.95 | (110) rel_str(all_42_5) = all_64_3 % 79.53/15.95 | (111) the_InternalRel(all_42_5) = all_64_1 % 79.53/15.95 | % 79.53/15.95 | DELTA: instantiating (70) with fresh symbols all_66_0, all_66_1, all_66_2, % 79.53/15.95 | all_66_3 gives: % 79.53/15.95 | (112) the_InternalRel(all_35_0) = all_66_2 & transitive_relstr(all_35_0) = % 79.53/15.95 | all_66_3 & the_carrier(all_35_0) = all_66_1 & % 79.53/15.95 | is_transitive_in(all_66_2, all_66_1) = all_66_0 & $i(all_66_1) & % 79.53/15.95 | $i(all_66_2) & ( ~ (all_66_0 = 0) | all_66_3 = 0) & ( ~ (all_66_3 = % 79.53/15.95 | 0) | all_66_0 = 0) % 79.53/15.95 | % 79.53/15.95 | ALPHA: (112) implies: % 79.53/15.95 | (113) $i(all_66_2) % 79.53/15.95 | (114) $i(all_66_1) % 79.53/15.95 | (115) the_carrier(all_35_0) = all_66_1 % 79.53/15.95 | (116) transitive_relstr(all_35_0) = all_66_3 % 79.53/15.95 | (117) the_InternalRel(all_35_0) = all_66_2 % 79.53/15.95 | % 79.53/15.95 | DELTA: instantiating (73) with fresh symbols all_68_0, all_68_1, all_68_2, % 79.53/15.95 | all_68_3 gives: % 79.53/15.95 | (118) the_InternalRel(all_42_5) = all_68_2 & transitive_relstr(all_42_5) = % 79.53/15.95 | all_68_3 & the_carrier(all_42_5) = all_68_1 & % 79.53/15.95 | is_transitive_in(all_68_2, all_68_1) = all_68_0 & $i(all_68_1) & % 79.53/15.95 | $i(all_68_2) & ( ~ (all_68_0 = 0) | all_68_3 = 0) & ( ~ (all_68_3 = % 79.53/15.95 | 0) | all_68_0 = 0) % 79.53/15.95 | % 79.53/15.95 | ALPHA: (118) implies: % 79.53/15.95 | (119) the_carrier(all_42_5) = all_68_1 % 79.53/15.95 | (120) the_InternalRel(all_42_5) = all_68_2 % 79.53/15.95 | % 79.53/15.95 | DELTA: instantiating (72) with fresh symbols all_70_0, all_70_1 gives: % 79.53/15.96 | (121) the_InternalRel(all_35_0) = all_70_0 & the_carrier(all_35_0) = % 79.53/15.96 | all_70_1 & $i(all_70_0) & $i(all_70_1) & ! [v0: $i] : ! [v1: $i] : % 79.53/15.96 | ! [v2: any] : ( ~ (related(all_35_0, v0, v1) = v2) | ~ (element(v0, % 79.53/15.96 | all_70_1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: % 79.53/15.96 | $i] : ? [v5: any] : (ordered_pair(v0, v1) = v4 & element(v1, % 79.53/15.96 | all_70_1) = v3 & in(v4, all_70_0) = v5 & $i(v4) & ( ~ (v3 = 0) % 79.53/15.96 | | (( ~ (v5 = 0) | v2 = 0) & ( ~ (v2 = 0) | v5 = 0))))) & ! % 79.53/15.96 | [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (ordered_pair(v0, v1) = % 79.53/15.96 | v2) | ~ (element(v0, all_70_1) = 0) | ~ $i(v1) | ~ $i(v0) | ? % 79.53/15.96 | [v3: any] : ? [v4: any] : ? [v5: any] : (related(all_35_0, v0, % 79.53/15.96 | v1) = v4 & element(v1, all_70_1) = v3 & in(v2, all_70_0) = v5 & % 79.53/15.96 | ( ~ (v3 = 0) | (( ~ (v5 = 0) | v4 = 0) & ( ~ (v4 = 0) | v5 = % 79.53/15.96 | 0))))) & ! [v0: $i] : ! [v1: $i] : ( ~ (element(v1, % 79.53/15.96 | all_70_1) = 0) | ~ (element(v0, all_70_1) = 0) | ~ $i(v1) | % 79.53/15.96 | ~ $i(v0) | ? [v2: any] : ? [v3: $i] : ? [v4: any] : % 79.53/15.96 | (related(all_35_0, v0, v1) = v2 & ordered_pair(v0, v1) = v3 & % 79.53/15.96 | in(v3, all_70_0) = v4 & $i(v3) & ( ~ (v4 = 0) | v2 = 0) & ( ~ (v2 % 79.53/15.96 | = 0) | v4 = 0))) % 79.53/15.96 | % 79.53/15.96 | ALPHA: (121) implies: % 79.53/15.96 | (122) the_carrier(all_35_0) = all_70_1 % 79.53/15.96 | (123) the_InternalRel(all_35_0) = all_70_0 % 79.53/15.96 | % 79.53/15.96 | DELTA: instantiating (75) with fresh symbols all_73_0, all_73_1 gives: % 79.53/15.96 | (124) the_InternalRel(all_42_5) = all_73_0 & the_carrier(all_42_5) = % 79.53/15.96 | all_73_1 & $i(all_73_0) & $i(all_73_1) & ! [v0: $i] : ! [v1: $i] : % 79.53/15.96 | ! [v2: any] : ( ~ (related(all_42_5, v0, v1) = v2) | ~ (element(v0, % 79.53/15.96 | all_73_1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: % 79.53/15.96 | $i] : ? [v5: any] : (ordered_pair(v0, v1) = v4 & element(v1, % 79.53/15.96 | all_73_1) = v3 & in(v4, all_73_0) = v5 & $i(v4) & ( ~ (v3 = 0) % 79.53/15.96 | | (( ~ (v5 = 0) | v2 = 0) & ( ~ (v2 = 0) | v5 = 0))))) & ! % 79.53/15.96 | [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (ordered_pair(v0, v1) = % 79.53/15.96 | v2) | ~ (element(v0, all_73_1) = 0) | ~ $i(v1) | ~ $i(v0) | ? % 79.53/15.96 | [v3: any] : ? [v4: any] : ? [v5: any] : (related(all_42_5, v0, % 79.53/15.96 | v1) = v4 & element(v1, all_73_1) = v3 & in(v2, all_73_0) = v5 & % 79.53/15.96 | ( ~ (v3 = 0) | (( ~ (v5 = 0) | v4 = 0) & ( ~ (v4 = 0) | v5 = % 79.53/15.96 | 0))))) & ! [v0: $i] : ! [v1: $i] : ( ~ (element(v1, % 79.53/15.96 | all_73_1) = 0) | ~ (element(v0, all_73_1) = 0) | ~ $i(v1) | % 79.53/15.96 | ~ $i(v0) | ? [v2: any] : ? [v3: $i] : ? [v4: any] : % 79.53/15.96 | (related(all_42_5, v0, v1) = v2 & ordered_pair(v0, v1) = v3 & % 79.53/15.96 | in(v3, all_73_0) = v4 & $i(v3) & ( ~ (v4 = 0) | v2 = 0) & ( ~ (v2 % 79.53/15.96 | = 0) | v4 = 0))) % 79.53/15.96 | % 79.53/15.96 | ALPHA: (124) implies: % 79.53/15.96 | (125) the_carrier(all_42_5) = all_73_1 % 79.53/15.96 | (126) the_InternalRel(all_42_5) = all_73_0 % 79.53/15.96 | % 79.53/15.96 | DELTA: instantiating (68) with fresh symbols all_76_0, all_76_1 gives: % 79.53/15.96 | (127) the_InternalRel(all_42_5) = all_76_0 & rel_str(all_42_5) = all_76_1 & % 79.53/15.96 | $i(all_76_0) & ( ~ (all_76_1 = 0) | ( ! [v0: $i] : ! [v1: $i] : ! % 79.53/15.96 | [v2: any] : ( ~ (related(all_42_5, v0, v1) = v2) | ~ % 79.53/15.96 | (element(v0, all_42_4) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v3: % 79.53/15.96 | any] : ? [v4: $i] : ? [v5: any] : (ordered_pair(v0, v1) = % 79.53/15.96 | v4 & element(v1, all_42_4) = v3 & in(v4, all_76_0) = v5 & % 79.53/15.96 | $i(v4) & ( ~ (v3 = 0) | (( ~ (v5 = 0) | v2 = 0) & ( ~ (v2 = % 79.53/15.96 | 0) | v5 = 0))))) & ! [v0: $i] : ! [v1: $i] : ! % 79.53/15.96 | [v2: $i] : ( ~ (ordered_pair(v0, v1) = v2) | ~ (element(v0, % 79.53/15.96 | all_42_4) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? % 79.53/15.96 | [v4: any] : ? [v5: any] : (related(all_42_5, v0, v1) = v4 & % 79.53/15.96 | element(v1, all_42_4) = v3 & in(v2, all_76_0) = v5 & ( ~ (v3 % 79.53/15.96 | = 0) | (( ~ (v5 = 0) | v4 = 0) & ( ~ (v4 = 0) | v5 = % 79.53/15.96 | 0))))) & ! [v0: $i] : ! [v1: $i] : ( ~ (element(v1, % 79.53/15.96 | all_42_4) = 0) | ~ (element(v0, all_42_4) = 0) | ~ $i(v1) % 79.53/15.96 | | ~ $i(v0) | ? [v2: any] : ? [v3: $i] : ? [v4: any] : % 79.53/15.96 | (related(all_42_5, v0, v1) = v2 & ordered_pair(v0, v1) = v3 & % 79.53/15.96 | in(v3, all_76_0) = v4 & $i(v3) & ( ~ (v4 = 0) | v2 = 0) & ( ~ % 79.53/15.96 | (v2 = 0) | v4 = 0))))) % 79.53/15.96 | % 79.53/15.96 | ALPHA: (127) implies: % 79.53/15.96 | (128) rel_str(all_42_5) = all_76_1 % 79.53/15.96 | (129) the_InternalRel(all_42_5) = all_76_0 % 79.53/15.97 | (130) ~ (all_76_1 = 0) | ( ! [v0: $i] : ! [v1: $i] : ! [v2: any] : ( ~ % 79.53/15.97 | (related(all_42_5, v0, v1) = v2) | ~ (element(v0, all_42_4) = 0) % 79.53/15.97 | | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: $i] : ? [v5: % 79.53/15.97 | any] : (ordered_pair(v0, v1) = v4 & element(v1, all_42_4) = v3 % 79.53/15.97 | & in(v4, all_76_0) = v5 & $i(v4) & ( ~ (v3 = 0) | (( ~ (v5 = 0) % 79.53/15.97 | | v2 = 0) & ( ~ (v2 = 0) | v5 = 0))))) & ! [v0: $i] : ! % 79.53/15.97 | [v1: $i] : ! [v2: $i] : ( ~ (ordered_pair(v0, v1) = v2) | ~ % 79.53/15.97 | (element(v0, all_42_4) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v3: % 79.53/15.97 | any] : ? [v4: any] : ? [v5: any] : (related(all_42_5, v0, v1) % 79.53/15.97 | = v4 & element(v1, all_42_4) = v3 & in(v2, all_76_0) = v5 & ( ~ % 79.53/15.97 | (v3 = 0) | (( ~ (v5 = 0) | v4 = 0) & ( ~ (v4 = 0) | v5 = % 79.53/15.97 | 0))))) & ! [v0: $i] : ! [v1: $i] : ( ~ (element(v1, % 79.53/15.97 | all_42_4) = 0) | ~ (element(v0, all_42_4) = 0) | ~ $i(v1) | % 79.53/15.97 | ~ $i(v0) | ? [v2: any] : ? [v3: $i] : ? [v4: any] : % 79.53/15.97 | (related(all_42_5, v0, v1) = v2 & ordered_pair(v0, v1) = v3 & % 79.53/15.97 | in(v3, all_76_0) = v4 & $i(v3) & ( ~ (v4 = 0) | v2 = 0) & ( ~ % 79.53/15.97 | (v2 = 0) | v4 = 0)))) % 79.53/15.97 | % 79.53/15.97 | REDUCE: (39), (76) imply: % 79.53/15.97 | (131) empty(empty_set) = 0 % 79.53/15.97 | % 79.53/15.97 | REDUCE: (38), (76) imply: % 79.53/15.97 | (132) $i(empty_set) % 79.53/15.97 | % 79.53/15.97 | BETA: splitting (77) gives: % 79.53/15.97 | % 79.53/15.97 | Case 1: % 79.53/15.97 | | % 79.53/15.97 | | (133) all_38_0 = 0 % 79.53/15.97 | | % 79.53/15.97 | | REDUCE: (44), (133) imply: % 79.53/15.97 | | (134) $false % 79.53/15.97 | | % 79.53/15.97 | | CLOSE: (134) is inconsistent. % 79.53/15.97 | | % 79.53/15.97 | Case 2: % 79.53/15.97 | | % 79.53/15.97 | | (135) ? [v0: $i] : ? [v1: $i] : ? [v2: int] : ( ~ (v2 = 0) & empty(v1) % 79.53/15.97 | | = v2 & powerset(all_38_1) = v0 & element(v1, v0) = 0 & $i(v1) & % 79.53/15.97 | | $i(v0)) % 79.53/15.97 | | % 79.53/15.97 | | DELTA: instantiating (135) with fresh symbols all_82_0, all_82_1, all_82_2 % 79.53/15.97 | | gives: % 79.53/15.97 | | (136) ~ (all_82_0 = 0) & empty(all_82_1) = all_82_0 & powerset(all_38_1) % 79.53/15.97 | | = all_82_2 & element(all_82_1, all_82_2) = 0 & $i(all_82_1) & % 79.53/15.97 | | $i(all_82_2) % 79.53/15.97 | | % 79.53/15.97 | | ALPHA: (136) implies: % 79.53/15.97 | | (137) ~ (all_82_0 = 0) % 79.53/15.97 | | (138) $i(all_82_2) % 79.53/15.97 | | (139) $i(all_82_1) % 79.53/15.97 | | (140) element(all_82_1, all_82_2) = 0 % 79.53/15.97 | | (141) powerset(all_38_1) = all_82_2 % 79.53/15.97 | | (142) empty(all_82_1) = all_82_0 % 79.53/15.97 | | % 79.53/15.97 | | GROUND_INST: instantiating (28) with all_66_1, all_70_1, all_35_0, % 79.53/15.97 | | simplifying with (115), (122) gives: % 79.53/15.97 | | (143) all_70_1 = all_66_1 % 79.53/15.97 | | % 79.53/15.97 | | GROUND_INST: instantiating (28) with all_58_0, all_70_1, all_35_0, % 79.53/15.97 | | simplifying with (96), (122) gives: % 79.53/15.97 | | (144) all_70_1 = all_58_0 % 79.53/15.97 | | % 79.53/15.97 | | GROUND_INST: instantiating (28) with all_56_0, all_68_1, all_42_5, % 79.53/15.97 | | simplifying with (92), (119) gives: % 79.53/15.97 | | (145) all_68_1 = all_56_0 % 79.53/15.97 | | % 79.53/15.97 | | GROUND_INST: instantiating (28) with all_42_4, all_73_1, all_42_5, % 79.53/15.97 | | simplifying with (57), (125) gives: % 79.53/15.97 | | (146) all_73_1 = all_42_4 % 79.53/15.97 | | % 79.53/15.97 | | GROUND_INST: instantiating (28) with all_68_1, all_73_1, all_42_5, % 79.53/15.97 | | simplifying with (119), (125) gives: % 79.53/15.97 | | (147) all_73_1 = all_68_1 % 79.53/15.97 | | % 79.53/15.97 | | GROUND_INST: instantiating (28) with all_62_1, all_73_1, all_42_5, % 79.53/15.97 | | simplifying with (105), (125) gives: % 79.53/15.97 | | (148) all_73_1 = all_62_1 % 79.53/15.97 | | % 79.53/15.97 | | GROUND_INST: instantiating (29) with 0, all_62_3, all_42_5, simplifying with % 79.53/15.97 | | (59), (106) gives: % 79.53/15.97 | | (149) all_62_3 = 0 % 79.53/15.97 | | % 79.53/15.97 | | GROUND_INST: instantiating (29) with all_62_3, all_64_3, all_42_5, % 79.53/15.97 | | simplifying with (106), (110) gives: % 79.53/15.97 | | (150) all_64_3 = all_62_3 % 79.53/15.97 | | % 79.53/15.97 | | GROUND_INST: instantiating (29) with all_64_3, all_76_1, all_42_5, % 79.53/15.97 | | simplifying with (110), (128) gives: % 79.53/15.97 | | (151) all_76_1 = all_64_3 % 79.53/15.97 | | % 79.53/15.97 | | GROUND_INST: instantiating (29) with all_60_2, all_76_1, all_42_5, % 79.53/15.97 | | simplifying with (101), (128) gives: % 79.53/15.97 | | (152) all_76_1 = all_60_2 % 79.53/15.97 | | % 79.53/15.97 | | GROUND_INST: instantiating (30) with all_66_2, all_70_0, all_35_0, % 79.53/15.97 | | simplifying with (117), (123) gives: % 79.53/15.97 | | (153) all_70_0 = all_66_2 % 79.53/15.97 | | % 79.53/15.97 | | GROUND_INST: instantiating (30) with all_58_1, all_70_0, all_35_0, % 79.53/15.97 | | simplifying with (97), (123) gives: % 79.53/15.97 | | (154) all_70_0 = all_58_1 % 79.53/15.97 | | % 79.53/15.97 | | GROUND_INST: instantiating (30) with all_56_1, all_64_1, all_42_5, % 79.53/15.97 | | simplifying with (93), (111) gives: % 79.53/15.97 | | (155) all_64_1 = all_56_1 % 79.53/15.97 | | % 79.53/15.97 | | GROUND_INST: instantiating (30) with all_68_2, all_73_0, all_42_5, % 79.53/15.97 | | simplifying with (120), (126) gives: % 79.53/15.97 | | (156) all_73_0 = all_68_2 % 79.53/15.97 | | % 79.53/15.97 | | GROUND_INST: instantiating (30) with all_64_1, all_73_0, all_42_5, % 79.53/15.97 | | simplifying with (111), (126) gives: % 79.53/15.97 | | (157) all_73_0 = all_64_1 % 79.53/15.97 | | % 79.53/15.97 | | GROUND_INST: instantiating (30) with all_60_1, all_73_0, all_42_5, % 79.53/15.97 | | simplifying with (102), (126) gives: % 79.53/15.97 | | (158) all_73_0 = all_60_1 % 79.53/15.97 | | % 79.53/15.97 | | GROUND_INST: instantiating (30) with all_64_1, all_76_0, all_42_5, % 79.53/15.97 | | simplifying with (111), (129) gives: % 79.53/15.97 | | (159) all_76_0 = all_64_1 % 79.53/15.97 | | % 79.53/15.97 | | GROUND_INST: instantiating (30) with all_62_2, all_76_0, all_42_5, % 79.53/15.97 | | simplifying with (107), (129) gives: % 79.53/15.98 | | (160) all_76_0 = all_62_2 % 79.53/15.98 | | % 79.53/15.98 | | GROUND_INST: instantiating (32) with all_52_1, all_54_1, all_42_4, % 79.53/15.98 | | simplifying with (84), (88) gives: % 79.53/15.98 | | (161) all_54_1 = all_52_1 % 79.53/15.98 | | % 79.53/15.98 | | GROUND_INST: instantiating (32) with all_50_1, all_54_1, all_42_4, % 79.53/15.98 | | simplifying with (80), (88) gives: % 79.53/15.98 | | (162) all_54_1 = all_50_1 % 79.53/15.98 | | % 79.53/15.98 | | COMBINE_EQS: (159), (160) imply: % 79.53/15.98 | | (163) all_64_1 = all_62_2 % 79.53/15.98 | | % 79.53/15.98 | | SIMP: (163) implies: % 79.53/15.98 | | (164) all_64_1 = all_62_2 % 79.53/15.98 | | % 79.53/15.98 | | COMBINE_EQS: (151), (152) imply: % 79.53/15.98 | | (165) all_64_3 = all_60_2 % 79.53/15.98 | | % 79.53/15.98 | | SIMP: (165) implies: % 79.53/15.98 | | (166) all_64_3 = all_60_2 % 79.53/15.98 | | % 79.53/15.98 | | COMBINE_EQS: (156), (157) imply: % 79.53/15.98 | | (167) all_68_2 = all_64_1 % 79.53/15.98 | | % 79.53/15.98 | | COMBINE_EQS: (156), (158) imply: % 79.53/15.98 | | (168) all_68_2 = all_60_1 % 79.53/15.98 | | % 79.53/15.98 | | COMBINE_EQS: (146), (148) imply: % 80.60/15.98 | | (169) all_62_1 = all_42_4 % 80.60/15.98 | | % 80.60/15.98 | | COMBINE_EQS: (147), (148) imply: % 80.60/15.98 | | (170) all_68_1 = all_62_1 % 80.60/15.98 | | % 80.60/15.98 | | SIMP: (170) implies: % 80.60/15.98 | | (171) all_68_1 = all_62_1 % 80.60/15.98 | | % 80.60/15.98 | | COMBINE_EQS: (153), (154) imply: % 80.60/15.98 | | (172) all_66_2 = all_58_1 % 80.60/15.98 | | % 80.60/15.98 | | SIMP: (172) implies: % 80.60/15.98 | | (173) all_66_2 = all_58_1 % 80.60/15.98 | | % 80.60/15.98 | | COMBINE_EQS: (143), (144) imply: % 80.60/15.98 | | (174) all_66_1 = all_58_0 % 80.60/15.98 | | % 80.60/15.98 | | SIMP: (174) implies: % 80.60/15.98 | | (175) all_66_1 = all_58_0 % 80.60/15.98 | | % 80.60/15.98 | | COMBINE_EQS: (145), (171) imply: % 80.60/15.98 | | (176) all_62_1 = all_56_0 % 80.60/15.98 | | % 80.60/15.98 | | SIMP: (176) implies: % 80.60/15.98 | | (177) all_62_1 = all_56_0 % 80.60/15.98 | | % 80.60/15.98 | | COMBINE_EQS: (167), (168) imply: % 80.60/15.98 | | (178) all_64_1 = all_60_1 % 80.60/15.98 | | % 80.60/15.98 | | SIMP: (178) implies: % 80.60/15.98 | | (179) all_64_1 = all_60_1 % 80.60/15.98 | | % 80.60/15.98 | | COMBINE_EQS: (164), (179) imply: % 80.60/15.98 | | (180) all_62_2 = all_60_1 % 80.60/15.98 | | % 80.60/15.98 | | COMBINE_EQS: (155), (164) imply: % 80.60/15.98 | | (181) all_62_2 = all_56_1 % 80.60/15.98 | | % 80.60/15.98 | | COMBINE_EQS: (150), (166) imply: % 80.60/15.98 | | (182) all_62_3 = all_60_2 % 80.60/15.98 | | % 80.60/15.98 | | SIMP: (182) implies: % 80.60/15.98 | | (183) all_62_3 = all_60_2 % 80.60/15.98 | | % 80.60/15.98 | | COMBINE_EQS: (169), (177) imply: % 80.60/15.98 | | (184) all_56_0 = all_42_4 % 80.60/15.98 | | % 80.60/15.98 | | COMBINE_EQS: (180), (181) imply: % 80.60/15.98 | | (185) all_60_1 = all_56_1 % 80.60/15.98 | | % 80.60/15.98 | | COMBINE_EQS: (149), (183) imply: % 80.60/15.98 | | (186) all_60_2 = 0 % 80.60/15.98 | | % 80.60/15.98 | | COMBINE_EQS: (161), (162) imply: % 80.60/15.98 | | (187) all_52_1 = all_50_1 % 80.60/15.98 | | % 80.60/15.98 | | COMBINE_EQS: (152), (186) imply: % 80.60/15.98 | | (188) all_76_1 = 0 % 80.60/15.98 | | % 80.60/15.98 | | COMBINE_EQS: (160), (181) imply: % 80.60/15.98 | | (189) all_76_0 = all_56_1 % 80.60/15.98 | | % 80.60/15.98 | | REDUCE: (94), (184) imply: % 80.60/15.98 | | (190) relation_of2_as_subset(all_56_1, all_42_4, all_42_4) = 0 % 80.60/15.98 | | % 80.60/15.98 | | REDUCE: (104), (169), (181) imply: % 80.60/15.98 | | (191) is_transitive_in(all_56_1, all_42_4) = all_62_0 % 80.60/15.98 | | % 80.60/15.98 | | REDUCE: (114), (175) imply: % 80.60/15.98 | | (192) $i(all_58_0) % 80.60/15.98 | | % 80.60/15.98 | | REDUCE: (113), (173) imply: % 80.60/15.98 | | (193) $i(all_58_1) % 80.60/15.98 | | % 80.60/15.98 | | REDUCE: (100), (185) imply: % 80.60/15.98 | | (194) $i(all_56_1) % 80.60/15.98 | | % 80.60/15.98 | | BETA: splitting (130) gives: % 80.60/15.98 | | % 80.60/15.98 | | Case 1: % 80.60/15.98 | | | % 80.60/15.98 | | | (195) ~ (all_76_1 = 0) % 80.60/15.98 | | | % 80.60/15.98 | | | REDUCE: (188), (195) imply: % 80.60/15.98 | | | (196) $false % 80.60/15.98 | | | % 80.60/15.98 | | | CLOSE: (196) is inconsistent. % 80.60/15.98 | | | % 80.60/15.98 | | Case 2: % 80.60/15.98 | | | % 80.60/15.98 | | | (197) ! [v0: $i] : ! [v1: $i] : ! [v2: any] : ( ~ (related(all_42_5, % 80.60/15.98 | | | v0, v1) = v2) | ~ (element(v0, all_42_4) = 0) | ~ $i(v1) % 80.60/15.98 | | | | ~ $i(v0) | ? [v3: any] : ? [v4: $i] : ? [v5: any] : % 80.60/15.98 | | | (ordered_pair(v0, v1) = v4 & element(v1, all_42_4) = v3 & % 80.60/15.98 | | | in(v4, all_76_0) = v5 & $i(v4) & ( ~ (v3 = 0) | (( ~ (v5 = 0) % 80.60/15.98 | | | | v2 = 0) & ( ~ (v2 = 0) | v5 = 0))))) & ! [v0: $i] : % 80.60/15.98 | | | ! [v1: $i] : ! [v2: $i] : ( ~ (ordered_pair(v0, v1) = v2) | ~ % 80.60/15.98 | | | (element(v0, all_42_4) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v3: % 80.60/15.98 | | | any] : ? [v4: any] : ? [v5: any] : (related(all_42_5, v0, % 80.60/15.98 | | | v1) = v4 & element(v1, all_42_4) = v3 & in(v2, all_76_0) = % 80.60/15.98 | | | v5 & ( ~ (v3 = 0) | (( ~ (v5 = 0) | v4 = 0) & ( ~ (v4 = 0) | % 80.60/15.98 | | | v5 = 0))))) & ! [v0: $i] : ! [v1: $i] : ( ~ % 80.60/15.98 | | | (element(v1, all_42_4) = 0) | ~ (element(v0, all_42_4) = 0) | % 80.60/15.98 | | | ~ $i(v1) | ~ $i(v0) | ? [v2: any] : ? [v3: $i] : ? [v4: % 80.60/15.98 | | | any] : (related(all_42_5, v0, v1) = v2 & ordered_pair(v0, v1) % 80.60/15.98 | | | = v3 & in(v3, all_76_0) = v4 & $i(v3) & ( ~ (v4 = 0) | v2 = % 80.60/15.98 | | | 0) & ( ~ (v2 = 0) | v4 = 0))) % 80.60/15.98 | | | % 80.60/15.98 | | | ALPHA: (197) implies: % 80.60/15.98 | | | (198) ! [v0: $i] : ! [v1: $i] : ( ~ (element(v1, all_42_4) = 0) | ~ % 80.60/15.98 | | | (element(v0, all_42_4) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: % 80.60/15.98 | | | any] : ? [v3: $i] : ? [v4: any] : (related(all_42_5, v0, % 80.60/15.98 | | | v1) = v2 & ordered_pair(v0, v1) = v3 & in(v3, all_76_0) = % 80.60/15.98 | | | v4 & $i(v3) & ( ~ (v4 = 0) | v2 = 0) & ( ~ (v2 = 0) | v4 = % 80.60/15.98 | | | 0))) % 80.60/15.98 | | | (199) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (ordered_pair(v0, % 80.60/15.98 | | | v1) = v2) | ~ (element(v0, all_42_4) = 0) | ~ $i(v1) | ~ % 80.60/15.98 | | | $i(v0) | ? [v3: any] : ? [v4: any] : ? [v5: any] : % 80.60/15.98 | | | (related(all_42_5, v0, v1) = v4 & element(v1, all_42_4) = v3 & % 80.60/15.98 | | | in(v2, all_76_0) = v5 & ( ~ (v3 = 0) | (( ~ (v5 = 0) | v4 = % 80.60/15.98 | | | 0) & ( ~ (v4 = 0) | v5 = 0))))) % 80.60/15.98 | | | (200) ! [v0: $i] : ! [v1: $i] : ! [v2: any] : ( ~ (related(all_42_5, % 80.60/15.98 | | | v0, v1) = v2) | ~ (element(v0, all_42_4) = 0) | ~ $i(v1) % 80.60/15.98 | | | | ~ $i(v0) | ? [v3: any] : ? [v4: $i] : ? [v5: any] : % 80.60/15.98 | | | (ordered_pair(v0, v1) = v4 & element(v1, all_42_4) = v3 & % 80.60/15.98 | | | in(v4, all_76_0) = v5 & $i(v4) & ( ~ (v3 = 0) | (( ~ (v5 = 0) % 80.60/15.98 | | | | v2 = 0) & ( ~ (v2 = 0) | v5 = 0))))) % 80.60/15.98 | | | % 80.60/15.98 | | | GROUND_INST: instantiating (198) with all_42_3, all_42_3, simplifying with % 80.60/15.98 | | | (51), (54) gives: % 80.60/15.98 | | | (201) ? [v0: any] : ? [v1: $i] : ? [v2: any] : (related(all_42_5, % 80.60/15.98 | | | all_42_3, all_42_3) = v0 & ordered_pair(all_42_3, all_42_3) = % 80.60/15.98 | | | v1 & in(v1, all_76_0) = v2 & $i(v1) & ( ~ (v2 = 0) | v0 = 0) & % 80.60/15.98 | | | ( ~ (v0 = 0) | v2 = 0)) % 80.60/15.98 | | | % 80.60/15.98 | | | GROUND_INST: instantiating (198) with all_42_2, all_42_2, simplifying with % 80.60/15.98 | | | (52), (55) gives: % 80.60/15.98 | | | (202) ? [v0: any] : ? [v1: $i] : ? [v2: any] : (related(all_42_5, % 80.60/15.98 | | | all_42_2, all_42_2) = v0 & ordered_pair(all_42_2, all_42_2) = % 80.60/15.98 | | | v1 & in(v1, all_76_0) = v2 & $i(v1) & ( ~ (v2 = 0) | v0 = 0) & % 80.60/15.98 | | | ( ~ (v0 = 0) | v2 = 0)) % 80.60/15.98 | | | % 80.60/15.98 | | | GROUND_INST: instantiating (198) with all_42_3, all_42_2, simplifying with % 80.60/15.98 | | | (51), (52), (54), (55) gives: % 80.60/15.98 | | | (203) ? [v0: any] : ? [v1: $i] : ? [v2: any] : (related(all_42_5, % 80.60/15.98 | | | all_42_3, all_42_2) = v0 & ordered_pair(all_42_3, all_42_2) = % 80.60/15.98 | | | v1 & in(v1, all_76_0) = v2 & $i(v1) & ( ~ (v2 = 0) | v0 = 0) & % 80.60/15.98 | | | ( ~ (v0 = 0) | v2 = 0)) % 80.60/15.98 | | | % 80.60/15.98 | | | GROUND_INST: instantiating (198) with all_42_2, all_42_3, simplifying with % 80.60/15.98 | | | (51), (52), (54), (55) gives: % 80.60/15.98 | | | (204) ? [v0: any] : ? [v1: $i] : ? [v2: any] : (related(all_42_5, % 80.60/15.98 | | | all_42_2, all_42_3) = v0 & ordered_pair(all_42_2, all_42_3) = % 80.60/15.98 | | | v1 & in(v1, all_76_0) = v2 & $i(v1) & ( ~ (v2 = 0) | v0 = 0) & % 80.60/15.98 | | | ( ~ (v0 = 0) | v2 = 0)) % 80.60/15.98 | | | % 80.60/15.98 | | | GROUND_INST: instantiating (198) with all_42_1, all_42_1, simplifying with % 80.60/15.98 | | | (53), (56) gives: % 80.60/15.99 | | | (205) ? [v0: any] : ? [v1: $i] : ? [v2: any] : (related(all_42_5, % 80.60/15.99 | | | all_42_1, all_42_1) = v0 & ordered_pair(all_42_1, all_42_1) = % 80.60/15.99 | | | v1 & in(v1, all_76_0) = v2 & $i(v1) & ( ~ (v2 = 0) | v0 = 0) & % 80.60/15.99 | | | ( ~ (v0 = 0) | v2 = 0)) % 80.60/15.99 | | | % 80.60/15.99 | | | GROUND_INST: instantiating (198) with all_42_2, all_42_1, simplifying with % 80.60/15.99 | | | (52), (53), (55), (56) gives: % 80.60/15.99 | | | (206) ? [v0: any] : ? [v1: $i] : ? [v2: any] : (related(all_42_5, % 80.60/15.99 | | | all_42_2, all_42_1) = v0 & ordered_pair(all_42_2, all_42_1) = % 80.60/15.99 | | | v1 & in(v1, all_76_0) = v2 & $i(v1) & ( ~ (v2 = 0) | v0 = 0) & % 80.60/15.99 | | | ( ~ (v0 = 0) | v2 = 0)) % 80.60/15.99 | | | % 80.60/15.99 | | | GROUND_INST: instantiating (198) with all_42_1, all_42_2, simplifying with % 80.60/15.99 | | | (52), (53), (55), (56) gives: % 80.60/15.99 | | | (207) ? [v0: any] : ? [v1: $i] : ? [v2: any] : (related(all_42_5, % 80.60/15.99 | | | all_42_1, all_42_2) = v0 & ordered_pair(all_42_1, all_42_2) = % 80.60/15.99 | | | v1 & in(v1, all_76_0) = v2 & $i(v1) & ( ~ (v2 = 0) | v0 = 0) & % 80.60/15.99 | | | ( ~ (v0 = 0) | v2 = 0)) % 80.60/15.99 | | | % 80.60/15.99 | | | GROUND_INST: instantiating (198) with all_42_3, all_42_1, simplifying with % 80.60/15.99 | | | (51), (53), (54), (56) gives: % 80.60/15.99 | | | (208) ? [v0: any] : ? [v1: $i] : ? [v2: any] : (related(all_42_5, % 80.60/15.99 | | | all_42_3, all_42_1) = v0 & ordered_pair(all_42_3, all_42_1) = % 80.60/15.99 | | | v1 & in(v1, all_76_0) = v2 & $i(v1) & ( ~ (v2 = 0) | v0 = 0) & % 80.60/15.99 | | | ( ~ (v0 = 0) | v2 = 0)) % 80.60/15.99 | | | % 80.60/15.99 | | | GROUND_INST: instantiating (198) with all_42_1, all_42_3, simplifying with % 80.60/15.99 | | | (51), (53), (54), (56) gives: % 80.60/15.99 | | | (209) ? [v0: any] : ? [v1: $i] : ? [v2: any] : (related(all_42_5, % 80.60/15.99 | | | all_42_1, all_42_3) = v0 & ordered_pair(all_42_1, all_42_3) = % 80.60/15.99 | | | v1 & in(v1, all_76_0) = v2 & $i(v1) & ( ~ (v2 = 0) | v0 = 0) & % 80.60/15.99 | | | ( ~ (v0 = 0) | v2 = 0)) % 80.60/15.99 | | | % 80.60/15.99 | | | GROUND_INST: instantiating (200) with all_42_3, all_42_2, 0, simplifying % 80.60/15.99 | | | with (51), (52), (54), (60) gives: % 80.60/15.99 | | | (210) ? [v0: any] : ? [v1: $i] : ? [v2: any] : % 80.60/15.99 | | | (ordered_pair(all_42_3, all_42_2) = v1 & element(all_42_2, % 80.60/15.99 | | | all_42_4) = v0 & in(v1, all_76_0) = v2 & $i(v1) & ( ~ (v0 = % 80.60/15.99 | | | 0) | v2 = 0)) % 80.60/15.99 | | | % 80.60/15.99 | | | GROUND_INST: instantiating (200) with all_42_3, all_42_1, all_42_0, % 80.60/15.99 | | | simplifying with (51), (53), (54), (61) gives: % 80.60/15.99 | | | (211) ? [v0: any] : ? [v1: $i] : ? [v2: any] : % 80.60/15.99 | | | (ordered_pair(all_42_3, all_42_1) = v1 & element(all_42_1, % 80.60/15.99 | | | all_42_4) = v0 & in(v1, all_76_0) = v2 & $i(v1) & ( ~ (v0 = % 80.60/15.99 | | | 0) | (( ~ (v2 = 0) | all_42_0 = 0) & ( ~ (all_42_0 = 0) | % 80.60/15.99 | | | v2 = 0)))) % 80.60/15.99 | | | % 80.60/15.99 | | | GROUND_INST: instantiating (200) with all_42_2, all_42_1, 0, simplifying % 80.60/15.99 | | | with (52), (53), (55), (62) gives: % 80.60/15.99 | | | (212) ? [v0: any] : ? [v1: $i] : ? [v2: any] : % 80.60/15.99 | | | (ordered_pair(all_42_2, all_42_1) = v1 & element(all_42_1, % 80.60/15.99 | | | all_42_4) = v0 & in(v1, all_76_0) = v2 & $i(v1) & ( ~ (v0 = % 80.60/15.99 | | | 0) | v2 = 0)) % 80.60/15.99 | | | % 80.60/15.99 | | | DELTA: instantiating (212) with fresh symbols all_108_0, all_108_1, % 80.60/15.99 | | | all_108_2 gives: % 80.60/15.99 | | | (213) ordered_pair(all_42_2, all_42_1) = all_108_1 & element(all_42_1, % 80.60/15.99 | | | all_42_4) = all_108_2 & in(all_108_1, all_76_0) = all_108_0 & % 80.60/15.99 | | | $i(all_108_1) & ( ~ (all_108_2 = 0) | all_108_0 = 0) % 80.60/15.99 | | | % 80.60/15.99 | | | ALPHA: (213) implies: % 80.60/15.99 | | | (214) element(all_42_1, all_42_4) = all_108_2 % 80.60/15.99 | | | (215) ordered_pair(all_42_2, all_42_1) = all_108_1 % 80.60/15.99 | | | % 80.60/15.99 | | | DELTA: instantiating (210) with fresh symbols all_110_0, all_110_1, % 80.60/15.99 | | | all_110_2 gives: % 80.60/15.99 | | | (216) ordered_pair(all_42_3, all_42_2) = all_110_1 & element(all_42_2, % 80.60/15.99 | | | all_42_4) = all_110_2 & in(all_110_1, all_76_0) = all_110_0 & % 80.60/15.99 | | | $i(all_110_1) & ( ~ (all_110_2 = 0) | all_110_0 = 0) % 80.60/15.99 | | | % 80.60/15.99 | | | ALPHA: (216) implies: % 80.60/15.99 | | | (217) in(all_110_1, all_76_0) = all_110_0 % 80.60/15.99 | | | (218) element(all_42_2, all_42_4) = all_110_2 % 80.60/15.99 | | | (219) ordered_pair(all_42_3, all_42_2) = all_110_1 % 80.60/15.99 | | | (220) ~ (all_110_2 = 0) | all_110_0 = 0 % 80.60/15.99 | | | % 80.60/15.99 | | | DELTA: instantiating (209) with fresh symbols all_112_0, all_112_1, % 80.60/15.99 | | | all_112_2 gives: % 80.60/15.99 | | | (221) related(all_42_5, all_42_1, all_42_3) = all_112_2 & % 80.60/15.99 | | | ordered_pair(all_42_1, all_42_3) = all_112_1 & in(all_112_1, % 80.60/15.99 | | | all_76_0) = all_112_0 & $i(all_112_1) & ( ~ (all_112_0 = 0) | % 80.60/15.99 | | | all_112_2 = 0) & ( ~ (all_112_2 = 0) | all_112_0 = 0) % 80.60/15.99 | | | % 80.60/15.99 | | | ALPHA: (221) implies: % 80.60/15.99 | | | (222) ordered_pair(all_42_1, all_42_3) = all_112_1 % 80.60/15.99 | | | % 80.60/15.99 | | | DELTA: instantiating (208) with fresh symbols all_114_0, all_114_1, % 80.60/15.99 | | | all_114_2 gives: % 80.60/15.99 | | | (223) related(all_42_5, all_42_3, all_42_1) = all_114_2 & % 80.60/15.99 | | | ordered_pair(all_42_3, all_42_1) = all_114_1 & in(all_114_1, % 80.60/15.99 | | | all_76_0) = all_114_0 & $i(all_114_1) & ( ~ (all_114_0 = 0) | % 80.60/15.99 | | | all_114_2 = 0) & ( ~ (all_114_2 = 0) | all_114_0 = 0) % 80.60/15.99 | | | % 80.60/15.99 | | | ALPHA: (223) implies: % 80.60/15.99 | | | (224) in(all_114_1, all_76_0) = all_114_0 % 80.60/15.99 | | | (225) ordered_pair(all_42_3, all_42_1) = all_114_1 % 80.60/15.99 | | | % 80.60/15.99 | | | DELTA: instantiating (207) with fresh symbols all_116_0, all_116_1, % 80.60/15.99 | | | all_116_2 gives: % 80.60/15.99 | | | (226) related(all_42_5, all_42_1, all_42_2) = all_116_2 & % 80.60/15.99 | | | ordered_pair(all_42_1, all_42_2) = all_116_1 & in(all_116_1, % 80.60/15.99 | | | all_76_0) = all_116_0 & $i(all_116_1) & ( ~ (all_116_0 = 0) | % 80.60/15.99 | | | all_116_2 = 0) & ( ~ (all_116_2 = 0) | all_116_0 = 0) % 80.60/15.99 | | | % 80.60/15.99 | | | ALPHA: (226) implies: % 80.60/15.99 | | | (227) $i(all_116_1) % 80.60/15.99 | | | (228) in(all_116_1, all_76_0) = all_116_0 % 80.60/15.99 | | | (229) ordered_pair(all_42_1, all_42_2) = all_116_1 % 80.60/15.99 | | | (230) related(all_42_5, all_42_1, all_42_2) = all_116_2 % 80.60/15.99 | | | (231) ~ (all_116_2 = 0) | all_116_0 = 0 % 80.60/15.99 | | | (232) ~ (all_116_0 = 0) | all_116_2 = 0 % 80.60/15.99 | | | % 80.60/15.99 | | | DELTA: instantiating (204) with fresh symbols all_118_0, all_118_1, % 80.60/15.99 | | | all_118_2 gives: % 80.60/15.99 | | | (233) related(all_42_5, all_42_2, all_42_3) = all_118_2 & % 80.60/15.99 | | | ordered_pair(all_42_2, all_42_3) = all_118_1 & in(all_118_1, % 80.60/15.99 | | | all_76_0) = all_118_0 & $i(all_118_1) & ( ~ (all_118_0 = 0) | % 80.60/15.99 | | | all_118_2 = 0) & ( ~ (all_118_2 = 0) | all_118_0 = 0) % 80.60/15.99 | | | % 80.60/15.99 | | | ALPHA: (233) implies: % 80.60/15.99 | | | (234) ordered_pair(all_42_2, all_42_3) = all_118_1 % 80.60/15.99 | | | % 80.60/15.99 | | | DELTA: instantiating (203) with fresh symbols all_120_0, all_120_1, % 80.60/15.99 | | | all_120_2 gives: % 80.60/15.99 | | | (235) related(all_42_5, all_42_3, all_42_2) = all_120_2 & % 80.60/15.99 | | | ordered_pair(all_42_3, all_42_2) = all_120_1 & in(all_120_1, % 80.60/15.99 | | | all_76_0) = all_120_0 & $i(all_120_1) & ( ~ (all_120_0 = 0) | % 80.60/15.99 | | | all_120_2 = 0) & ( ~ (all_120_2 = 0) | all_120_0 = 0) % 80.60/15.99 | | | % 80.60/15.99 | | | ALPHA: (235) implies: % 80.60/15.99 | | | (236) $i(all_120_1) % 80.60/15.99 | | | (237) ordered_pair(all_42_3, all_42_2) = all_120_1 % 80.60/15.99 | | | % 80.60/15.99 | | | DELTA: instantiating (202) with fresh symbols all_122_0, all_122_1, % 80.60/15.99 | | | all_122_2 gives: % 80.60/15.99 | | | (238) related(all_42_5, all_42_2, all_42_2) = all_122_2 & % 80.60/15.99 | | | ordered_pair(all_42_2, all_42_2) = all_122_1 & in(all_122_1, % 80.60/15.99 | | | all_76_0) = all_122_0 & $i(all_122_1) & ( ~ (all_122_0 = 0) | % 80.60/15.99 | | | all_122_2 = 0) & ( ~ (all_122_2 = 0) | all_122_0 = 0) % 80.60/15.99 | | | % 80.60/15.99 | | | ALPHA: (238) implies: % 80.60/15.99 | | | (239) $i(all_122_1) % 80.60/15.99 | | | (240) in(all_122_1, all_76_0) = all_122_0 % 80.60/15.99 | | | (241) ordered_pair(all_42_2, all_42_2) = all_122_1 % 80.60/15.99 | | | (242) ~ (all_122_2 = 0) | all_122_0 = 0 % 80.60/15.99 | | | (243) ~ (all_122_0 = 0) | all_122_2 = 0 % 80.60/15.99 | | | % 80.60/15.99 | | | DELTA: instantiating (206) with fresh symbols all_124_0, all_124_1, % 80.60/15.99 | | | all_124_2 gives: % 80.60/15.99 | | | (244) related(all_42_5, all_42_2, all_42_1) = all_124_2 & % 80.60/15.99 | | | ordered_pair(all_42_2, all_42_1) = all_124_1 & in(all_124_1, % 80.60/15.99 | | | all_76_0) = all_124_0 & $i(all_124_1) & ( ~ (all_124_0 = 0) | % 80.60/15.99 | | | all_124_2 = 0) & ( ~ (all_124_2 = 0) | all_124_0 = 0) % 80.60/15.99 | | | % 80.60/15.99 | | | ALPHA: (244) implies: % 80.60/15.99 | | | (245) in(all_124_1, all_76_0) = all_124_0 % 80.60/15.99 | | | (246) ordered_pair(all_42_2, all_42_1) = all_124_1 % 80.60/15.99 | | | (247) related(all_42_5, all_42_2, all_42_1) = all_124_2 % 80.60/15.99 | | | (248) ~ (all_124_2 = 0) | all_124_0 = 0 % 80.60/15.99 | | | % 80.60/15.99 | | | DELTA: instantiating (205) with fresh symbols all_126_0, all_126_1, % 80.60/15.99 | | | all_126_2 gives: % 80.60/15.99 | | | (249) related(all_42_5, all_42_1, all_42_1) = all_126_2 & % 80.60/15.99 | | | ordered_pair(all_42_1, all_42_1) = all_126_1 & in(all_126_1, % 80.60/15.99 | | | all_76_0) = all_126_0 & $i(all_126_1) & ( ~ (all_126_0 = 0) | % 80.60/15.99 | | | all_126_2 = 0) & ( ~ (all_126_2 = 0) | all_126_0 = 0) % 80.60/15.99 | | | % 80.60/15.99 | | | ALPHA: (249) implies: % 80.60/15.99 | | | (250) ordered_pair(all_42_1, all_42_1) = all_126_1 % 80.60/15.99 | | | (251) ~ (all_126_2 = 0) | all_126_0 = 0 % 80.60/15.99 | | | (252) ~ (all_126_0 = 0) | all_126_2 = 0 % 80.60/15.99 | | | % 80.60/15.99 | | | DELTA: instantiating (201) with fresh symbols all_128_0, all_128_1, % 80.60/15.99 | | | all_128_2 gives: % 80.60/15.99 | | | (253) related(all_42_5, all_42_3, all_42_3) = all_128_2 & % 80.60/15.99 | | | ordered_pair(all_42_3, all_42_3) = all_128_1 & in(all_128_1, % 80.60/15.99 | | | all_76_0) = all_128_0 & $i(all_128_1) & ( ~ (all_128_0 = 0) | % 80.60/15.99 | | | all_128_2 = 0) & ( ~ (all_128_2 = 0) | all_128_0 = 0) % 80.60/15.99 | | | % 80.60/15.99 | | | ALPHA: (253) implies: % 80.60/15.99 | | | (254) $i(all_128_1) % 80.60/15.99 | | | (255) in(all_128_1, all_76_0) = all_128_0 % 80.60/15.99 | | | (256) ordered_pair(all_42_3, all_42_3) = all_128_1 % 80.60/15.99 | | | (257) ~ (all_128_0 = 0) | all_128_2 = 0 % 80.60/15.99 | | | % 80.60/15.99 | | | DELTA: instantiating (211) with fresh symbols all_130_0, all_130_1, % 80.60/15.99 | | | all_130_2 gives: % 80.60/15.99 | | | (258) ordered_pair(all_42_3, all_42_1) = all_130_1 & element(all_42_1, % 80.60/15.99 | | | all_42_4) = all_130_2 & in(all_130_1, all_76_0) = all_130_0 & % 80.60/15.99 | | | $i(all_130_1) & ( ~ (all_130_2 = 0) | (( ~ (all_130_0 = 0) | % 80.60/15.99 | | | all_42_0 = 0) & ( ~ (all_42_0 = 0) | all_130_0 = 0))) % 80.60/15.99 | | | % 80.60/15.99 | | | ALPHA: (258) implies: % 80.60/16.00 | | | (259) $i(all_130_1) % 80.60/16.00 | | | (260) in(all_130_1, all_76_0) = all_130_0 % 80.60/16.00 | | | (261) element(all_42_1, all_42_4) = all_130_2 % 80.60/16.00 | | | (262) ordered_pair(all_42_3, all_42_1) = all_130_1 % 80.60/16.00 | | | (263) ~ (all_130_2 = 0) | (( ~ (all_130_0 = 0) | all_42_0 = 0) & ( ~ % 80.60/16.00 | | | (all_42_0 = 0) | all_130_0 = 0)) % 80.60/16.00 | | | % 80.60/16.00 | | | REDUCE: (189), (260) imply: % 80.60/16.00 | | | (264) in(all_130_1, all_56_1) = all_130_0 % 80.60/16.00 | | | % 80.60/16.00 | | | REDUCE: (189), (255) imply: % 80.60/16.00 | | | (265) in(all_128_1, all_56_1) = all_128_0 % 80.60/16.00 | | | % 80.60/16.00 | | | REDUCE: (189), (245) imply: % 80.60/16.00 | | | (266) in(all_124_1, all_56_1) = all_124_0 % 80.60/16.00 | | | % 80.60/16.00 | | | REDUCE: (189), (240) imply: % 80.60/16.00 | | | (267) in(all_122_1, all_56_1) = all_122_0 % 80.60/16.00 | | | % 80.60/16.00 | | | REDUCE: (189), (228) imply: % 80.60/16.00 | | | (268) in(all_116_1, all_56_1) = all_116_0 % 80.60/16.00 | | | % 80.60/16.00 | | | REDUCE: (189), (224) imply: % 80.60/16.00 | | | (269) in(all_114_1, all_56_1) = all_114_0 % 80.60/16.00 | | | % 80.60/16.00 | | | REDUCE: (189), (217) imply: % 80.60/16.00 | | | (270) in(all_110_1, all_56_1) = all_110_0 % 80.60/16.00 | | | % 80.60/16.00 | | | BETA: splitting (108) gives: % 80.60/16.00 | | | % 80.60/16.00 | | | Case 1: % 80.60/16.00 | | | | % 80.60/16.00 | | | | (271) ~ (all_62_3 = 0) % 80.60/16.00 | | | | % 80.60/16.00 | | | | REDUCE: (149), (271) imply: % 80.60/16.00 | | | | (272) $false % 80.60/16.00 | | | | % 80.60/16.00 | | | | CLOSE: (272) is inconsistent. % 80.60/16.00 | | | | % 80.60/16.00 | | | Case 2: % 80.60/16.00 | | | | % 80.60/16.00 | | | | (273) all_62_0 = 0 % 80.60/16.00 | | | | % 80.60/16.00 | | | | REDUCE: (191), (273) imply: % 80.60/16.00 | | | | (274) is_transitive_in(all_56_1, all_42_4) = 0 % 80.60/16.00 | | | | % 80.60/16.00 | | | | GROUND_INST: instantiating (34) with 0, all_110_2, all_42_4, all_42_2, % 80.60/16.00 | | | | simplifying with (55), (218) gives: % 80.60/16.00 | | | | (275) all_110_2 = 0 % 80.60/16.00 | | | | % 80.60/16.00 | | | | GROUND_INST: instantiating (34) with 0, all_130_2, all_42_4, all_42_1, % 80.60/16.00 | | | | simplifying with (56), (261) gives: % 80.60/16.00 | | | | (276) all_130_2 = 0 % 80.60/16.00 | | | | % 80.60/16.00 | | | | GROUND_INST: instantiating (34) with all_108_2, all_130_2, all_42_4, % 80.60/16.00 | | | | all_42_1, simplifying with (214), (261) gives: % 80.60/16.00 | | | | (277) all_130_2 = all_108_2 % 80.60/16.00 | | | | % 80.60/16.00 | | | | GROUND_INST: instantiating (35) with all_110_1, all_120_1, all_42_2, % 80.60/16.00 | | | | all_42_3, simplifying with (219), (237) gives: % 80.60/16.00 | | | | (278) all_120_1 = all_110_1 % 80.60/16.00 | | | | % 80.60/16.00 | | | | GROUND_INST: instantiating (35) with all_114_1, all_130_1, all_42_1, % 80.60/16.00 | | | | all_42_3, simplifying with (225), (262) gives: % 80.60/16.00 | | | | (279) all_130_1 = all_114_1 % 80.60/16.00 | | | | % 80.60/16.00 | | | | GROUND_INST: instantiating (35) with all_108_1, all_124_1, all_42_1, % 80.60/16.00 | | | | all_42_2, simplifying with (215), (246) gives: % 80.60/16.00 | | | | (280) all_124_1 = all_108_1 % 80.60/16.00 | | | | % 80.60/16.00 | | | | GROUND_INST: instantiating (36) with 0, all_124_2, all_42_1, all_42_2, % 80.60/16.00 | | | | all_42_5, simplifying with (62), (247) gives: % 80.60/16.00 | | | | (281) all_124_2 = 0 % 80.60/16.00 | | | | % 80.60/16.00 | | | | COMBINE_EQS: (276), (277) imply: % 80.60/16.00 | | | | (282) all_108_2 = 0 % 80.60/16.00 | | | | % 80.60/16.00 | | | | REDUCE: (264), (279) imply: % 80.60/16.00 | | | | (283) in(all_114_1, all_56_1) = all_130_0 % 80.60/16.00 | | | | % 80.60/16.00 | | | | REDUCE: (266), (280) imply: % 80.60/16.00 | | | | (284) in(all_108_1, all_56_1) = all_124_0 % 80.60/16.00 | | | | % 80.60/16.00 | | | | REDUCE: (259), (279) imply: % 80.60/16.00 | | | | (285) $i(all_114_1) % 80.60/16.00 | | | | % 80.60/16.00 | | | | REDUCE: (236), (278) imply: % 80.60/16.00 | | | | (286) $i(all_110_1) % 80.60/16.00 | | | | % 80.60/16.00 | | | | BETA: splitting (263) gives: % 80.60/16.00 | | | | % 80.60/16.00 | | | | Case 1: % 80.60/16.00 | | | | | % 80.60/16.00 | | | | | (287) ~ (all_130_2 = 0) % 80.60/16.00 | | | | | % 80.60/16.00 | | | | | REDUCE: (276), (287) imply: % 80.60/16.00 | | | | | (288) $false % 80.60/16.00 | | | | | % 80.60/16.00 | | | | | CLOSE: (288) is inconsistent. % 80.60/16.00 | | | | | % 80.60/16.00 | | | | Case 2: % 80.60/16.00 | | | | | % 80.60/16.00 | | | | | (289) ( ~ (all_130_0 = 0) | all_42_0 = 0) & ( ~ (all_42_0 = 0) | % 80.60/16.00 | | | | | all_130_0 = 0) % 80.60/16.00 | | | | | % 80.60/16.00 | | | | | ALPHA: (289) implies: % 80.60/16.00 | | | | | (290) ~ (all_130_0 = 0) | all_42_0 = 0 % 80.60/16.00 | | | | | % 80.60/16.00 | | | | | BETA: splitting (220) gives: % 80.60/16.00 | | | | | % 80.60/16.00 | | | | | Case 1: % 80.60/16.00 | | | | | | % 80.60/16.00 | | | | | | (291) ~ (all_110_2 = 0) % 80.60/16.00 | | | | | | % 80.60/16.00 | | | | | | REDUCE: (275), (291) imply: % 80.60/16.00 | | | | | | (292) $false % 80.60/16.00 | | | | | | % 80.60/16.00 | | | | | | CLOSE: (292) is inconsistent. % 80.60/16.00 | | | | | | % 80.60/16.00 | | | | | Case 2: % 80.60/16.00 | | | | | | % 80.60/16.00 | | | | | | (293) all_110_0 = 0 % 80.60/16.00 | | | | | | % 80.60/16.00 | | | | | | REDUCE: (270), (293) imply: % 80.60/16.00 | | | | | | (294) in(all_110_1, all_56_1) = 0 % 80.60/16.00 | | | | | | % 80.60/16.00 | | | | | | BETA: splitting (290) gives: % 80.60/16.00 | | | | | | % 80.60/16.00 | | | | | | Case 1: % 80.60/16.00 | | | | | | | % 80.60/16.00 | | | | | | | (295) ~ (all_130_0 = 0) % 80.60/16.00 | | | | | | | % 80.60/16.00 | | | | | | | BETA: splitting (248) gives: % 80.60/16.00 | | | | | | | % 80.60/16.00 | | | | | | | Case 1: % 80.60/16.00 | | | | | | | | % 80.60/16.00 | | | | | | | | (296) ~ (all_124_2 = 0) % 80.60/16.00 | | | | | | | | % 80.60/16.00 | | | | | | | | REDUCE: (281), (296) imply: % 80.60/16.00 | | | | | | | | (297) $false % 80.60/16.00 | | | | | | | | % 80.60/16.00 | | | | | | | | CLOSE: (297) is inconsistent. % 80.60/16.00 | | | | | | | | % 80.60/16.00 | | | | | | | Case 2: % 80.60/16.00 | | | | | | | | % 80.60/16.00 | | | | | | | | (298) all_124_0 = 0 % 80.60/16.00 | | | | | | | | % 80.60/16.00 | | | | | | | | REDUCE: (284), (298) imply: % 80.60/16.00 | | | | | | | | (299) in(all_108_1, all_56_1) = 0 % 80.60/16.00 | | | | | | | | % 80.60/16.00 | | | | | | | | GROUND_INST: instantiating (33) with all_114_0, all_130_0, % 80.60/16.00 | | | | | | | | all_56_1, all_114_1, simplifying with (269), (283) % 80.60/16.00 | | | | | | | | gives: % 80.60/16.00 | | | | | | | | (300) all_130_0 = all_114_0 % 80.60/16.00 | | | | | | | | % 80.60/16.00 | | | | | | | | REDUCE: (295), (300) imply: % 80.60/16.00 | | | | | | | | (301) ~ (all_114_0 = 0) % 80.60/16.00 | | | | | | | | % 80.60/16.00 | | | | | | | | GROUND_INST: instantiating (24) with all_110_1, all_56_1, % 80.60/16.00 | | | | | | | | empty_set, simplifying with (131), (132), (194), % 80.60/16.00 | | | | | | | | (286), (294) gives: % 80.60/16.00 | | | | | | | | (302) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & % 80.60/16.00 | | | | | | | | powerset(empty_set) = v0 & element(all_56_1, v0) = v1 % 80.60/16.00 | | | | | | | | & $i(v0)) % 80.60/16.00 | | | | | | | | % 80.60/16.00 | | | | | | | | GROUND_INST: instantiating (t7_boole) with all_110_1, all_56_1, % 80.60/16.00 | | | | | | | | simplifying with (194), (286), (294) gives: % 80.60/16.00 | | | | | | | | (303) ? [v0: int] : ( ~ (v0 = 0) & empty(all_56_1) = v0) % 80.60/16.00 | | | | | | | | % 80.60/16.00 | | | | | | | | GROUND_INST: instantiating (21) with all_114_1, all_56_1, % 80.60/16.00 | | | | | | | | all_114_0, simplifying with (194), (269), (285) % 80.60/16.00 | | | | | | | | gives: % 80.60/16.00 | | | | | | | | (304) all_114_0 = 0 | ? [v0: any] : ? [v1: any] : % 80.60/16.00 | | | | | | | | (empty(all_56_1) = v1 & element(all_114_1, all_56_1) = % 80.60/16.00 | | | | | | | | v0 & ( ~ (v0 = 0) | v1 = 0)) % 80.60/16.00 | | | | | | | | % 80.60/16.00 | | | | | | | | GROUND_INST: instantiating (21) with all_116_1, all_56_1, % 80.60/16.00 | | | | | | | | all_116_0, simplifying with (194), (227), (268) % 80.60/16.00 | | | | | | | | gives: % 80.60/16.00 | | | | | | | | (305) all_116_0 = 0 | ? [v0: any] : ? [v1: any] : % 80.60/16.00 | | | | | | | | (empty(all_56_1) = v1 & element(all_116_1, all_56_1) = % 80.60/16.00 | | | | | | | | v0 & ( ~ (v0 = 0) | v1 = 0)) % 80.60/16.00 | | | | | | | | % 80.60/16.00 | | | | | | | | GROUND_INST: instantiating (21) with all_122_1, all_56_1, % 80.60/16.00 | | | | | | | | all_122_0, simplifying with (194), (239), (267) % 80.60/16.00 | | | | | | | | gives: % 80.60/16.00 | | | | | | | | (306) all_122_0 = 0 | ? [v0: any] : ? [v1: any] : % 80.60/16.00 | | | | | | | | (empty(all_56_1) = v1 & element(all_122_1, all_56_1) = % 80.60/16.00 | | | | | | | | v0 & ( ~ (v0 = 0) | v1 = 0)) % 80.60/16.00 | | | | | | | | % 80.60/16.00 | | | | | | | | GROUND_INST: instantiating (21) with all_128_1, all_56_1, % 80.60/16.00 | | | | | | | | all_128_0, simplifying with (194), (254), (265) % 80.60/16.00 | | | | | | | | gives: % 80.60/16.00 | | | | | | | | (307) all_128_0 = 0 | ? [v0: any] : ? [v1: any] : % 80.60/16.00 | | | | | | | | (empty(all_56_1) = v1 & element(all_128_1, all_56_1) = % 80.60/16.00 | | | | | | | | v0 & ( ~ (v0 = 0) | v1 = 0)) % 80.60/16.00 | | | | | | | | % 80.60/16.00 | | | | | | | | GROUND_INST: instantiating (20) with all_82_1, all_82_2, % 80.60/16.00 | | | | | | | | simplifying with (138), (139), (140) gives: % 80.60/16.00 | | | | | | | | (308) ? [v0: any] : ? [v1: any] : (empty(all_82_2) = v0 & % 80.60/16.00 | | | | | | | | in(all_82_1, all_82_2) = v1 & (v1 = 0 | v0 = 0)) % 80.60/16.00 | | | | | | | | % 80.60/16.00 | | | | | | | | GROUND_INST: instantiating (fc1_subset_1) with all_38_1, % 80.60/16.00 | | | | | | | | all_82_2, simplifying with (45), (141) gives: % 80.60/16.00 | | | | | | | | (309) ? [v0: int] : ( ~ (v0 = 0) & empty(all_82_2) = v0) % 80.60/16.00 | | | | | | | | % 80.60/16.00 | | | | | | | | GROUND_INST: instantiating (rc2_subset_1) with all_38_1, % 80.60/16.00 | | | | | | | | all_82_2, simplifying with (45), (141) gives: % 80.60/16.00 | | | | | | | | (310) ? [v0: $i] : (empty(v0) = 0 & element(v0, all_82_2) = % 80.60/16.00 | | | | | | | | 0 & $i(v0)) % 80.60/16.00 | | | | | | | | % 80.60/16.00 | | | | | | | | GROUND_INST: instantiating (4) with all_35_0, all_66_3, % 80.60/16.01 | | | | | | | | simplifying with (41), (116) gives: % 80.60/16.01 | | | | | | | | (311) ? [v0: any] : ? [v1: $i] : ? [v2: $i] : ? [v3: any] % 80.60/16.01 | | | | | | | | : (the_InternalRel(all_35_0) = v1 & rel_str(all_35_0) = % 80.60/16.01 | | | | | | | | v0 & the_carrier(all_35_0) = v2 & % 80.60/16.01 | | | | | | | | is_transitive_in(v1, v2) = v3 & $i(v2) & $i(v1) & ( ~ % 80.60/16.01 | | | | | | | | (v0 = 0) | (( ~ (v3 = 0) | all_66_3 = 0) & ( ~ % 80.60/16.01 | | | | | | | | (all_66_3 = 0) | v3 = 0)))) % 80.60/16.01 | | | | | | | | % 80.60/16.01 | | | | | | | | GROUND_INST: instantiating (5) with all_35_0, all_58_1, % 80.60/16.01 | | | | | | | | simplifying with (41), (97) gives: % 80.60/16.01 | | | | | | | | (312) ? [v0: any] : ? [v1: any] : ? [v2: $i] : ? [v3: % 80.60/16.01 | | | | | | | | any] : (rel_str(all_35_0) = v0 & % 80.60/16.01 | | | | | | | | transitive_relstr(all_35_0) = v1 & % 80.60/16.01 | | | | | | | | the_carrier(all_35_0) = v2 & % 80.60/16.01 | | | | | | | | is_transitive_in(all_58_1, v2) = v3 & $i(v2) & ( ~ % 80.60/16.01 | | | | | | | | (v0 = 0) | (( ~ (v3 = 0) | v1 = 0) & ( ~ (v1 = 0) | % 80.60/16.01 | | | | | | | | v3 = 0)))) % 80.60/16.01 | | | | | | | | % 80.60/16.01 | | | | | | | | GROUND_INST: instantiating (13) with all_35_0, all_58_1, % 80.60/16.01 | | | | | | | | simplifying with (41), (97) gives: % 80.60/16.01 | | | | | | | | (313) ? [v0: any] : ? [v1: $i] : (rel_str(all_35_0) = v0 & % 80.60/16.01 | | | | | | | | the_carrier(all_35_0) = v1 & $i(v1) & ( ~ (v0 = 0) | % 80.60/16.01 | | | | | | | | ( ! [v2: $i] : ! [v3: $i] : ! [v4: any] : ( ~ % 80.60/16.01 | | | | | | | | (related(all_35_0, v2, v3) = v4) | ~ % 80.60/16.01 | | | | | | | | (element(v2, v1) = 0) | ~ $i(v3) | ~ $i(v2) | % 80.60/16.01 | | | | | | | | ? [v5: any] : ? [v6: $i] : ? [v7: any] : % 80.60/16.01 | | | | | | | | (ordered_pair(v2, v3) = v6 & element(v3, v1) = % 80.60/16.01 | | | | | | | | v5 & in(v6, all_58_1) = v7 & $i(v6) & ( ~ (v5 % 80.60/16.01 | | | | | | | | = 0) | (( ~ (v7 = 0) | v4 = 0) & ( ~ (v4 % 80.60/16.01 | | | | | | | | = 0) | v7 = 0))))) & ! [v2: $i] : ! % 80.60/16.01 | | | | | | | | [v3: $i] : ! [v4: $i] : ( ~ (ordered_pair(v2, % 80.60/16.01 | | | | | | | | v3) = v4) | ~ (element(v2, v1) = 0) | ~ % 80.60/16.01 | | | | | | | | $i(v3) | ~ $i(v2) | ? [v5: any] : ? [v6: % 80.60/16.01 | | | | | | | | any] : ? [v7: any] : (related(all_35_0, v2, % 80.60/16.01 | | | | | | | | v3) = v6 & element(v3, v1) = v5 & in(v4, % 80.60/16.01 | | | | | | | | all_58_1) = v7 & ( ~ (v5 = 0) | (( ~ (v7 = % 80.60/16.01 | | | | | | | | 0) | v6 = 0) & ( ~ (v6 = 0) | v7 = % 80.60/16.01 | | | | | | | | 0))))) & ! [v2: $i] : ! [v3: $i] : ( % 80.60/16.01 | | | | | | | | ~ (element(v3, v1) = 0) | ~ (element(v2, v1) = % 80.60/16.01 | | | | | | | | 0) | ~ $i(v3) | ~ $i(v2) | ? [v4: any] : % 80.60/16.01 | | | | | | | | ? [v5: $i] : ? [v6: any] : (related(all_35_0, % 80.60/16.01 | | | | | | | | v2, v3) = v4 & ordered_pair(v2, v3) = v5 & % 80.60/16.01 | | | | | | | | in(v5, all_58_1) = v6 & $i(v5) & ( ~ (v6 = 0) % 80.60/16.01 | | | | | | | | | v4 = 0) & ( ~ (v4 = 0) | v6 = 0)))))) % 80.60/16.01 | | | | | | | | % 80.60/16.01 | | | | | | | | GROUND_INST: instantiating (13) with all_42_5, all_56_1, % 80.60/16.01 | | | | | | | | simplifying with (49), (93) gives: % 80.60/16.01 | | | | | | | | (314) ? [v0: any] : ? [v1: $i] : (rel_str(all_42_5) = v0 & % 80.60/16.01 | | | | | | | | the_carrier(all_42_5) = v1 & $i(v1) & ( ~ (v0 = 0) | % 80.60/16.01 | | | | | | | | ( ! [v2: $i] : ! [v3: $i] : ! [v4: any] : ( ~ % 80.60/16.01 | | | | | | | | (related(all_42_5, v2, v3) = v4) | ~ % 80.60/16.01 | | | | | | | | (element(v2, v1) = 0) | ~ $i(v3) | ~ $i(v2) | % 80.60/16.01 | | | | | | | | ? [v5: any] : ? [v6: $i] : ? [v7: any] : % 80.60/16.01 | | | | | | | | (ordered_pair(v2, v3) = v6 & element(v3, v1) = % 80.60/16.01 | | | | | | | | v5 & in(v6, all_56_1) = v7 & $i(v6) & ( ~ (v5 % 80.60/16.01 | | | | | | | | = 0) | (( ~ (v7 = 0) | v4 = 0) & ( ~ (v4 % 80.60/16.01 | | | | | | | | = 0) | v7 = 0))))) & ! [v2: $i] : ! % 80.60/16.01 | | | | | | | | [v3: $i] : ! [v4: $i] : ( ~ (ordered_pair(v2, % 80.60/16.01 | | | | | | | | v3) = v4) | ~ (element(v2, v1) = 0) | ~ % 80.60/16.01 | | | | | | | | $i(v3) | ~ $i(v2) | ? [v5: any] : ? [v6: % 80.60/16.01 | | | | | | | | any] : ? [v7: any] : (related(all_42_5, v2, % 80.60/16.01 | | | | | | | | v3) = v6 & element(v3, v1) = v5 & in(v4, % 80.60/16.01 | | | | | | | | all_56_1) = v7 & ( ~ (v5 = 0) | (( ~ (v7 = % 80.60/16.01 | | | | | | | | 0) | v6 = 0) & ( ~ (v6 = 0) | v7 = % 80.60/16.01 | | | | | | | | 0))))) & ! [v2: $i] : ! [v3: $i] : ( % 80.60/16.01 | | | | | | | | ~ (element(v3, v1) = 0) | ~ (element(v2, v1) = % 80.60/16.01 | | | | | | | | 0) | ~ $i(v3) | ~ $i(v2) | ? [v4: any] : % 80.60/16.01 | | | | | | | | ? [v5: $i] : ? [v6: any] : (related(all_42_5, % 80.60/16.01 | | | | | | | | v2, v3) = v4 & ordered_pair(v2, v3) = v5 & % 80.60/16.01 | | | | | | | | in(v5, all_56_1) = v6 & $i(v5) & ( ~ (v6 = 0) % 80.60/16.01 | | | | | | | | | v4 = 0) & ( ~ (v4 = 0) | v6 = 0)))))) % 80.60/16.01 | | | | | | | | % 80.60/16.01 | | | | | | | | GROUND_INST: instantiating (6) with all_42_3, all_42_3, % 80.60/16.01 | | | | | | | | all_128_1, simplifying with (51), (256) gives: % 80.60/16.01 | | | | | | | | (315) ? [v0: $i] : ? [v1: $i] : (singleton(all_42_3) = v1 & % 80.60/16.01 | | | | | | | | unordered_pair(v0, v1) = all_128_1 & % 80.60/16.01 | | | | | | | | unordered_pair(all_42_3, all_42_3) = v0 & $i(v1) & % 80.60/16.01 | | | | | | | | $i(v0) & $i(all_128_1)) % 80.60/16.01 | | | | | | | | % 80.60/16.01 | | | | | | | | GROUND_INST: instantiating (6) with all_42_3, all_42_2, % 80.60/16.01 | | | | | | | | all_110_1, simplifying with (51), (52), (219) % 80.60/16.01 | | | | | | | | gives: % 80.60/16.01 | | | | | | | | (316) ? [v0: $i] : ? [v1: $i] : (singleton(all_42_3) = v1 & % 80.60/16.01 | | | | | | | | unordered_pair(v0, v1) = all_110_1 & % 80.60/16.01 | | | | | | | | unordered_pair(all_42_3, all_42_2) = v0 & $i(v1) & % 80.60/16.01 | | | | | | | | $i(v0) & $i(all_110_1)) % 80.60/16.01 | | | | | | | | % 80.60/16.01 | | | | | | | | GROUND_INST: instantiating (6) with all_42_3, all_42_1, % 80.60/16.01 | | | | | | | | all_114_1, simplifying with (51), (53), (225) % 80.60/16.01 | | | | | | | | gives: % 80.60/16.01 | | | | | | | | (317) ? [v0: $i] : ? [v1: $i] : (singleton(all_42_3) = v1 & % 80.60/16.01 | | | | | | | | unordered_pair(v0, v1) = all_114_1 & % 80.60/16.01 | | | | | | | | unordered_pair(all_42_3, all_42_1) = v0 & $i(v1) & % 80.60/16.01 | | | | | | | | $i(v0) & $i(all_114_1)) % 80.60/16.01 | | | | | | | | % 80.60/16.01 | | | | | | | | GROUND_INST: instantiating (6) with all_42_2, all_42_3, % 80.60/16.01 | | | | | | | | all_118_1, simplifying with (51), (52), (234) % 80.60/16.01 | | | | | | | | gives: % 80.60/16.01 | | | | | | | | (318) ? [v0: $i] : ? [v1: $i] : (singleton(all_42_2) = v1 & % 80.60/16.01 | | | | | | | | unordered_pair(v0, v1) = all_118_1 & % 80.60/16.01 | | | | | | | | unordered_pair(all_42_2, all_42_3) = v0 & $i(v1) & % 80.60/16.01 | | | | | | | | $i(v0) & $i(all_118_1)) % 80.60/16.01 | | | | | | | | % 80.60/16.01 | | | | | | | | GROUND_INST: instantiating (6) with all_42_2, all_42_2, % 80.60/16.01 | | | | | | | | all_122_1, simplifying with (52), (241) gives: % 80.60/16.01 | | | | | | | | (319) ? [v0: $i] : ? [v1: $i] : (singleton(all_42_2) = v1 & % 80.60/16.01 | | | | | | | | unordered_pair(v0, v1) = all_122_1 & % 80.60/16.01 | | | | | | | | unordered_pair(all_42_2, all_42_2) = v0 & $i(v1) & % 80.60/16.01 | | | | | | | | $i(v0) & $i(all_122_1)) % 80.60/16.01 | | | | | | | | % 80.60/16.01 | | | | | | | | GROUND_INST: instantiating (6) with all_42_2, all_42_1, % 80.60/16.01 | | | | | | | | all_108_1, simplifying with (52), (53), (215) % 80.60/16.01 | | | | | | | | gives: % 80.60/16.01 | | | | | | | | (320) ? [v0: $i] : ? [v1: $i] : (singleton(all_42_2) = v1 & % 80.60/16.01 | | | | | | | | unordered_pair(v0, v1) = all_108_1 & % 80.60/16.01 | | | | | | | | unordered_pair(all_42_2, all_42_1) = v0 & $i(v1) & % 80.60/16.01 | | | | | | | | $i(v0) & $i(all_108_1)) % 80.60/16.01 | | | | | | | | % 80.60/16.01 | | | | | | | | GROUND_INST: instantiating (6) with all_42_1, all_42_3, % 80.60/16.01 | | | | | | | | all_112_1, simplifying with (51), (53), (222) % 80.60/16.01 | | | | | | | | gives: % 80.60/16.01 | | | | | | | | (321) ? [v0: $i] : ? [v1: $i] : (singleton(all_42_1) = v1 & % 80.60/16.01 | | | | | | | | unordered_pair(v0, v1) = all_112_1 & % 80.60/16.01 | | | | | | | | unordered_pair(all_42_1, all_42_3) = v0 & $i(v1) & % 80.60/16.01 | | | | | | | | $i(v0) & $i(all_112_1)) % 80.60/16.01 | | | | | | | | % 80.60/16.01 | | | | | | | | GROUND_INST: instantiating (199) with all_42_1, all_42_2, % 80.60/16.01 | | | | | | | | all_116_1, simplifying with (52), (53), (56), (229) % 80.60/16.01 | | | | | | | | gives: % 80.60/16.01 | | | | | | | | (322) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 80.60/16.01 | | | | | | | | (related(all_42_5, all_42_1, all_42_2) = v1 & % 80.60/16.01 | | | | | | | | element(all_42_2, all_42_4) = v0 & in(all_116_1, % 80.60/16.01 | | | | | | | | all_76_0) = v2 & ( ~ (v0 = 0) | (( ~ (v2 = 0) | v1 % 80.60/16.01 | | | | | | | | = 0) & ( ~ (v1 = 0) | v2 = 0)))) % 80.60/16.01 | | | | | | | | % 80.60/16.01 | | | | | | | | GROUND_INST: instantiating (6) with all_42_1, all_42_2, % 80.60/16.01 | | | | | | | | all_116_1, simplifying with (52), (53), (229) % 80.60/16.01 | | | | | | | | gives: % 80.60/16.01 | | | | | | | | (323) ? [v0: $i] : ? [v1: $i] : (singleton(all_42_1) = v1 & % 80.60/16.01 | | | | | | | | unordered_pair(v0, v1) = all_116_1 & % 80.60/16.01 | | | | | | | | unordered_pair(all_42_1, all_42_2) = v0 & $i(v1) & % 80.60/16.01 | | | | | | | | $i(v0) & $i(all_116_1)) % 80.60/16.01 | | | | | | | | % 80.60/16.01 | | | | | | | | GROUND_INST: instantiating (6) with all_42_1, all_42_1, % 80.60/16.01 | | | | | | | | all_126_1, simplifying with (53), (250) gives: % 80.60/16.01 | | | | | | | | (324) ? [v0: $i] : ? [v1: $i] : (singleton(all_42_1) = v1 & % 80.60/16.01 | | | | | | | | unordered_pair(v0, v1) = all_126_1 & % 80.60/16.01 | | | | | | | | unordered_pair(all_42_1, all_42_1) = v0 & $i(v1) & % 80.60/16.01 | | | | | | | | $i(v0) & $i(all_126_1)) % 80.60/16.01 | | | | | | | | % 80.60/16.01 | | | | | | | | GROUND_INST: instantiating (200) with all_42_1, all_42_2, % 80.60/16.01 | | | | | | | | all_116_2, simplifying with (52), (53), (56), (230) % 80.60/16.01 | | | | | | | | gives: % 80.60/16.01 | | | | | | | | (325) ? [v0: any] : ? [v1: $i] : ? [v2: any] : % 80.60/16.01 | | | | | | | | (ordered_pair(all_42_1, all_42_2) = v1 & % 80.60/16.01 | | | | | | | | element(all_42_2, all_42_4) = v0 & in(v1, all_76_0) = % 80.60/16.01 | | | | | | | | v2 & $i(v1) & ( ~ (v0 = 0) | (( ~ (v2 = 0) | % 80.60/16.01 | | | | | | | | all_116_2 = 0) & ( ~ (all_116_2 = 0) | v2 = % 80.60/16.01 | | | | | | | | 0)))) % 80.60/16.01 | | | | | | | | % 80.60/16.01 | | | | | | | | GROUND_INST: instantiating (14) with all_42_4, all_42_4, % 80.60/16.01 | | | | | | | | all_56_1, simplifying with (50), (190), (194) % 80.60/16.01 | | | | | | | | gives: % 80.60/16.01 | | | | | | | | (326) ? [v0: $i] : ? [v1: $i] : % 80.60/16.01 | | | | | | | | (cartesian_product2(all_42_4, all_42_4) = v0 & % 80.60/16.01 | | | | | | | | powerset(v0) = v1 & element(all_56_1, v1) = 0 & % 80.60/16.01 | | | | | | | | $i(v1) & $i(v0)) % 80.60/16.01 | | | | | | | | % 80.60/16.01 | | | | | | | | GROUND_INST: instantiating (14) with all_58_0, all_58_0, % 80.60/16.01 | | | | | | | | all_58_1, simplifying with (98), (192), (193) % 80.60/16.01 | | | | | | | | gives: % 80.60/16.01 | | | | | | | | (327) ? [v0: $i] : ? [v1: $i] : % 80.60/16.01 | | | | | | | | (cartesian_product2(all_58_0, all_58_0) = v0 & % 80.60/16.01 | | | | | | | | powerset(v0) = v1 & element(all_58_1, v1) = 0 & % 80.60/16.01 | | | | | | | | $i(v1) & $i(v0)) % 80.60/16.01 | | | | | | | | % 80.60/16.01 | | | | | | | | GROUND_INST: instantiating (17) with all_82_1, all_82_0, % 80.60/16.01 | | | | | | | | simplifying with (139), (142) gives: % 80.60/16.01 | | | | | | | | (328) all_82_0 = 0 | ? [v0: $i] : ? [v1: $i] : ? [v2: int] % 80.60/16.01 | | | | | | | | : ( ~ (v2 = 0) & empty(v1) = v2 & powerset(all_82_1) = % 80.60/16.01 | | | | | | | | v0 & element(v1, v0) = 0 & $i(v1) & $i(v0)) % 80.60/16.01 | | | | | | | | % 80.60/16.01 | | | | | | | | DELTA: instantiating (309) with fresh symbol all_178_0 gives: % 80.60/16.01 | | | | | | | | (329) ~ (all_178_0 = 0) & empty(all_82_2) = all_178_0 % 80.60/16.01 | | | | | | | | % 80.60/16.01 | | | | | | | | ALPHA: (329) implies: % 80.60/16.01 | | | | | | | | (330) ~ (all_178_0 = 0) % 80.60/16.01 | | | | | | | | (331) empty(all_82_2) = all_178_0 % 80.60/16.01 | | | | | | | | % 80.60/16.01 | | | | | | | | DELTA: instantiating (303) with fresh symbol all_182_0 gives: % 80.60/16.01 | | | | | | | | (332) ~ (all_182_0 = 0) & empty(all_56_1) = all_182_0 % 80.60/16.01 | | | | | | | | % 80.60/16.01 | | | | | | | | ALPHA: (332) implies: % 80.60/16.01 | | | | | | | | (333) ~ (all_182_0 = 0) % 80.60/16.01 | | | | | | | | (334) empty(all_56_1) = all_182_0 % 80.60/16.01 | | | | | | | | % 80.60/16.01 | | | | | | | | DELTA: instantiating (310) with fresh symbol all_186_0 gives: % 80.60/16.01 | | | | | | | | (335) empty(all_186_0) = 0 & element(all_186_0, all_82_2) = 0 % 80.60/16.01 | | | | | | | | & $i(all_186_0) % 80.60/16.01 | | | | | | | | % 80.60/16.01 | | | | | | | | ALPHA: (335) implies: % 80.60/16.02 | | | | | | | | (336) $i(all_186_0) % 80.60/16.02 | | | | | | | | (337) empty(all_186_0) = 0 % 80.60/16.02 | | | | | | | | % 80.60/16.02 | | | | | | | | DELTA: instantiating (308) with fresh symbols all_188_0, % 80.60/16.02 | | | | | | | | all_188_1 gives: % 80.60/16.02 | | | | | | | | (338) empty(all_82_2) = all_188_1 & in(all_82_1, all_82_2) = % 80.60/16.02 | | | | | | | | all_188_0 & (all_188_0 = 0 | all_188_1 = 0) % 80.60/16.02 | | | | | | | | % 80.60/16.02 | | | | | | | | ALPHA: (338) implies: % 80.60/16.02 | | | | | | | | (339) in(all_82_1, all_82_2) = all_188_0 % 80.60/16.02 | | | | | | | | (340) empty(all_82_2) = all_188_1 % 80.60/16.02 | | | | | | | | (341) all_188_0 = 0 | all_188_1 = 0 % 80.60/16.02 | | | | | | | | % 80.60/16.02 | | | | | | | | DELTA: instantiating (302) with fresh symbols all_190_0, % 80.60/16.02 | | | | | | | | all_190_1 gives: % 80.60/16.02 | | | | | | | | (342) ~ (all_190_0 = 0) & powerset(empty_set) = all_190_1 & % 80.60/16.02 | | | | | | | | element(all_56_1, all_190_1) = all_190_0 & % 80.60/16.02 | | | | | | | | $i(all_190_1) % 80.60/16.02 | | | | | | | | % 80.60/16.02 | | | | | | | | ALPHA: (342) implies: % 80.60/16.02 | | | | | | | | (343) powerset(empty_set) = all_190_1 % 80.60/16.02 | | | | | | | | % 80.60/16.02 | | | | | | | | DELTA: instantiating (327) with fresh symbols all_192_0, % 80.60/16.02 | | | | | | | | all_192_1 gives: % 80.60/16.02 | | | | | | | | (344) cartesian_product2(all_58_0, all_58_0) = all_192_1 & % 80.60/16.02 | | | | | | | | powerset(all_192_1) = all_192_0 & element(all_58_1, % 80.60/16.02 | | | | | | | | all_192_0) = 0 & $i(all_192_0) & $i(all_192_1) % 80.60/16.02 | | | | | | | | % 80.60/16.02 | | | | | | | | ALPHA: (344) implies: % 80.60/16.02 | | | | | | | | (345) $i(all_192_1) % 80.60/16.02 | | | | | | | | (346) powerset(all_192_1) = all_192_0 % 80.60/16.02 | | | | | | | | (347) cartesian_product2(all_58_0, all_58_0) = all_192_1 % 80.60/16.02 | | | | | | | | % 80.60/16.02 | | | | | | | | DELTA: instantiating (326) with fresh symbols all_194_0, % 80.60/16.02 | | | | | | | | all_194_1 gives: % 80.60/16.02 | | | | | | | | (348) cartesian_product2(all_42_4, all_42_4) = all_194_1 & % 80.60/16.02 | | | | | | | | powerset(all_194_1) = all_194_0 & element(all_56_1, % 80.60/16.02 | | | | | | | | all_194_0) = 0 & $i(all_194_0) & $i(all_194_1) % 80.60/16.02 | | | | | | | | % 80.60/16.02 | | | | | | | | ALPHA: (348) implies: % 80.60/16.02 | | | | | | | | (349) $i(all_194_1) % 80.60/16.02 | | | | | | | | (350) element(all_56_1, all_194_0) = 0 % 80.60/16.02 | | | | | | | | (351) powerset(all_194_1) = all_194_0 % 80.60/16.02 | | | | | | | | (352) cartesian_product2(all_42_4, all_42_4) = all_194_1 % 80.60/16.02 | | | | | | | | % 80.60/16.02 | | | | | | | | DELTA: instantiating (317) with fresh symbols all_196_0, % 80.60/16.02 | | | | | | | | all_196_1 gives: % 80.60/16.02 | | | | | | | | (353) singleton(all_42_3) = all_196_0 & % 80.60/16.02 | | | | | | | | unordered_pair(all_196_1, all_196_0) = all_114_1 & % 80.60/16.02 | | | | | | | | unordered_pair(all_42_3, all_42_1) = all_196_1 & % 80.60/16.02 | | | | | | | | $i(all_196_0) & $i(all_196_1) & $i(all_114_1) % 80.60/16.02 | | | | | | | | % 80.60/16.02 | | | | | | | | ALPHA: (353) implies: % 80.60/16.02 | | | | | | | | (354) unordered_pair(all_42_3, all_42_1) = all_196_1 % 80.60/16.02 | | | | | | | | (355) unordered_pair(all_196_1, all_196_0) = all_114_1 % 80.60/16.02 | | | | | | | | (356) singleton(all_42_3) = all_196_0 % 80.60/16.02 | | | | | | | | % 80.60/16.02 | | | | | | | | DELTA: instantiating (324) with fresh symbols all_198_0, % 80.60/16.02 | | | | | | | | all_198_1 gives: % 80.60/16.02 | | | | | | | | (357) singleton(all_42_1) = all_198_0 & % 80.60/16.02 | | | | | | | | unordered_pair(all_198_1, all_198_0) = all_126_1 & % 80.60/16.02 | | | | | | | | unordered_pair(all_42_1, all_42_1) = all_198_1 & % 80.60/16.02 | | | | | | | | $i(all_198_0) & $i(all_198_1) & $i(all_126_1) % 80.60/16.02 | | | | | | | | % 80.60/16.02 | | | | | | | | ALPHA: (357) implies: % 80.60/16.02 | | | | | | | | (358) $i(all_198_1) % 80.60/16.02 | | | | | | | | (359) unordered_pair(all_42_1, all_42_1) = all_198_1 % 80.60/16.02 | | | | | | | | (360) singleton(all_42_1) = all_198_0 % 80.60/16.02 | | | | | | | | % 80.60/16.02 | | | | | | | | DELTA: instantiating (323) with fresh symbols all_200_0, % 80.60/16.02 | | | | | | | | all_200_1 gives: % 80.60/16.02 | | | | | | | | (361) singleton(all_42_1) = all_200_0 & % 80.60/16.02 | | | | | | | | unordered_pair(all_200_1, all_200_0) = all_116_1 & % 80.60/16.02 | | | | | | | | unordered_pair(all_42_1, all_42_2) = all_200_1 & % 80.60/16.02 | | | | | | | | $i(all_200_0) & $i(all_200_1) & $i(all_116_1) % 80.60/16.02 | | | | | | | | % 80.60/16.02 | | | | | | | | ALPHA: (361) implies: % 80.60/16.02 | | | | | | | | (362) $i(all_200_0) % 80.60/16.02 | | | | | | | | (363) unordered_pair(all_42_1, all_42_2) = all_200_1 % 80.60/16.02 | | | | | | | | (364) unordered_pair(all_200_1, all_200_0) = all_116_1 % 80.60/16.02 | | | | | | | | (365) singleton(all_42_1) = all_200_0 % 80.60/16.02 | | | | | | | | % 80.60/16.02 | | | | | | | | DELTA: instantiating (321) with fresh symbols all_202_0, % 80.60/16.02 | | | | | | | | all_202_1 gives: % 80.60/16.02 | | | | | | | | (366) singleton(all_42_1) = all_202_0 & % 80.60/16.02 | | | | | | | | unordered_pair(all_202_1, all_202_0) = all_112_1 & % 80.60/16.02 | | | | | | | | unordered_pair(all_42_1, all_42_3) = all_202_1 & % 80.60/16.02 | | | | | | | | $i(all_202_0) & $i(all_202_1) & $i(all_112_1) % 80.60/16.02 | | | | | | | | % 80.60/16.02 | | | | | | | | ALPHA: (366) implies: % 80.60/16.02 | | | | | | | | (367) singleton(all_42_1) = all_202_0 % 80.60/16.02 | | | | | | | | % 80.60/16.02 | | | | | | | | DELTA: instantiating (320) with fresh symbols all_204_0, % 80.60/16.02 | | | | | | | | all_204_1 gives: % 80.60/16.02 | | | | | | | | (368) singleton(all_42_2) = all_204_0 & % 80.60/16.02 | | | | | | | | unordered_pair(all_204_1, all_204_0) = all_108_1 & % 80.60/16.02 | | | | | | | | unordered_pair(all_42_2, all_42_1) = all_204_1 & % 80.60/16.02 | | | | | | | | $i(all_204_0) & $i(all_204_1) & $i(all_108_1) % 80.60/16.02 | | | | | | | | % 80.60/16.02 | | | | | | | | ALPHA: (368) implies: % 80.60/16.02 | | | | | | | | (369) $i(all_108_1) % 80.60/16.02 | | | | | | | | (370) unordered_pair(all_42_2, all_42_1) = all_204_1 % 80.60/16.02 | | | | | | | | (371) unordered_pair(all_204_1, all_204_0) = all_108_1 % 80.60/16.02 | | | | | | | | (372) singleton(all_42_2) = all_204_0 % 80.60/16.02 | | | | | | | | % 80.60/16.02 | | | | | | | | DELTA: instantiating (318) with fresh symbols all_206_0, % 80.60/16.02 | | | | | | | | all_206_1 gives: % 80.60/16.02 | | | | | | | | (373) singleton(all_42_2) = all_206_0 & % 80.60/16.02 | | | | | | | | unordered_pair(all_206_1, all_206_0) = all_118_1 & % 80.60/16.02 | | | | | | | | unordered_pair(all_42_2, all_42_3) = all_206_1 & % 80.60/16.02 | | | | | | | | $i(all_206_0) & $i(all_206_1) & $i(all_118_1) % 80.60/16.02 | | | | | | | | % 80.60/16.02 | | | | | | | | ALPHA: (373) implies: % 80.60/16.02 | | | | | | | | (374) $i(all_206_0) % 80.60/16.02 | | | | | | | | (375) unordered_pair(all_42_2, all_42_3) = all_206_1 % 80.60/16.02 | | | | | | | | (376) unordered_pair(all_206_1, all_206_0) = all_118_1 % 80.60/16.02 | | | | | | | | (377) singleton(all_42_2) = all_206_0 % 80.60/16.02 | | | | | | | | % 80.60/16.02 | | | | | | | | DELTA: instantiating (319) with fresh symbols all_208_0, % 80.60/16.02 | | | | | | | | all_208_1 gives: % 80.60/16.02 | | | | | | | | (378) singleton(all_42_2) = all_208_0 & % 80.60/16.02 | | | | | | | | unordered_pair(all_208_1, all_208_0) = all_122_1 & % 80.60/16.02 | | | | | | | | unordered_pair(all_42_2, all_42_2) = all_208_1 & % 80.60/16.02 | | | | | | | | $i(all_208_0) & $i(all_208_1) & $i(all_122_1) % 80.60/16.02 | | | | | | | | % 80.60/16.02 | | | | | | | | ALPHA: (378) implies: % 80.60/16.02 | | | | | | | | (379) singleton(all_42_2) = all_208_0 % 80.60/16.02 | | | | | | | | % 80.60/16.02 | | | | | | | | DELTA: instantiating (316) with fresh symbols all_210_0, % 80.60/16.02 | | | | | | | | all_210_1 gives: % 80.60/16.02 | | | | | | | | (380) singleton(all_42_3) = all_210_0 & % 80.60/16.02 | | | | | | | | unordered_pair(all_210_1, all_210_0) = all_110_1 & % 80.60/16.02 | | | | | | | | unordered_pair(all_42_3, all_42_2) = all_210_1 & % 80.60/16.02 | | | | | | | | $i(all_210_0) & $i(all_210_1) & $i(all_110_1) % 80.60/16.02 | | | | | | | | % 80.60/16.02 | | | | | | | | ALPHA: (380) implies: % 80.60/16.02 | | | | | | | | (381) $i(all_210_0) % 80.60/16.02 | | | | | | | | (382) unordered_pair(all_42_3, all_42_2) = all_210_1 % 80.60/16.02 | | | | | | | | (383) unordered_pair(all_210_1, all_210_0) = all_110_1 % 80.60/16.02 | | | | | | | | (384) singleton(all_42_3) = all_210_0 % 80.60/16.02 | | | | | | | | % 80.60/16.02 | | | | | | | | DELTA: instantiating (315) with fresh symbols all_212_0, % 80.60/16.02 | | | | | | | | all_212_1 gives: % 80.60/16.02 | | | | | | | | (385) singleton(all_42_3) = all_212_0 & % 80.60/16.02 | | | | | | | | unordered_pair(all_212_1, all_212_0) = all_128_1 & % 80.60/16.02 | | | | | | | | unordered_pair(all_42_3, all_42_3) = all_212_1 & % 80.60/16.02 | | | | | | | | $i(all_212_0) & $i(all_212_1) & $i(all_128_1) % 80.60/16.02 | | | | | | | | % 80.60/16.02 | | | | | | | | ALPHA: (385) implies: % 80.60/16.02 | | | | | | | | (386) singleton(all_42_3) = all_212_0 % 80.60/16.02 | | | | | | | | % 80.60/16.02 | | | | | | | | DELTA: instantiating (322) with fresh symbols all_218_0, % 80.60/16.02 | | | | | | | | all_218_1, all_218_2 gives: % 80.60/16.02 | | | | | | | | (387) related(all_42_5, all_42_1, all_42_2) = all_218_1 & % 80.60/16.02 | | | | | | | | element(all_42_2, all_42_4) = all_218_2 & in(all_116_1, % 80.60/16.02 | | | | | | | | all_76_0) = all_218_0 & ( ~ (all_218_2 = 0) | (( ~ % 80.60/16.02 | | | | | | | | (all_218_0 = 0) | all_218_1 = 0) & ( ~ (all_218_1 % 80.60/16.02 | | | | | | | | = 0) | all_218_0 = 0))) % 80.60/16.02 | | | | | | | | % 80.60/16.02 | | | | | | | | ALPHA: (387) implies: % 80.60/16.02 | | | | | | | | (388) in(all_116_1, all_76_0) = all_218_0 % 80.60/16.02 | | | | | | | | % 80.60/16.02 | | | | | | | | DELTA: instantiating (325) with fresh symbols all_238_0, % 80.60/16.02 | | | | | | | | all_238_1, all_238_2 gives: % 80.60/16.02 | | | | | | | | (389) ordered_pair(all_42_1, all_42_2) = all_238_1 & % 80.60/16.02 | | | | | | | | element(all_42_2, all_42_4) = all_238_2 & in(all_238_1, % 80.60/16.02 | | | | | | | | all_76_0) = all_238_0 & $i(all_238_1) & ( ~ % 80.60/16.02 | | | | | | | | (all_238_2 = 0) | (( ~ (all_238_0 = 0) | all_116_2 = % 80.60/16.02 | | | | | | | | 0) & ( ~ (all_116_2 = 0) | all_238_0 = 0))) % 80.60/16.02 | | | | | | | | % 80.60/16.02 | | | | | | | | ALPHA: (389) implies: % 80.60/16.02 | | | | | | | | (390) ordered_pair(all_42_1, all_42_2) = all_238_1 % 80.60/16.02 | | | | | | | | % 80.60/16.02 | | | | | | | | DELTA: instantiating (312) with fresh symbols all_240_0, % 80.60/16.02 | | | | | | | | all_240_1, all_240_2, all_240_3 gives: % 80.60/16.02 | | | | | | | | (391) rel_str(all_35_0) = all_240_3 & % 80.60/16.02 | | | | | | | | transitive_relstr(all_35_0) = all_240_2 & % 80.60/16.02 | | | | | | | | the_carrier(all_35_0) = all_240_1 & % 80.60/16.02 | | | | | | | | is_transitive_in(all_58_1, all_240_1) = all_240_0 & % 80.60/16.02 | | | | | | | | $i(all_240_1) & ( ~ (all_240_3 = 0) | (( ~ (all_240_0 = % 80.60/16.02 | | | | | | | | 0) | all_240_2 = 0) & ( ~ (all_240_2 = 0) | % 80.60/16.02 | | | | | | | | all_240_0 = 0))) % 80.60/16.02 | | | | | | | | % 80.60/16.02 | | | | | | | | ALPHA: (391) implies: % 80.60/16.02 | | | | | | | | (392) $i(all_240_1) % 80.60/16.02 | | | | | | | | (393) the_carrier(all_35_0) = all_240_1 % 80.60/16.02 | | | | | | | | % 80.60/16.02 | | | | | | | | DELTA: instantiating (311) with fresh symbols all_244_0, % 80.60/16.02 | | | | | | | | all_244_1, all_244_2, all_244_3 gives: % 80.60/16.02 | | | | | | | | (394) the_InternalRel(all_35_0) = all_244_2 & % 80.60/16.02 | | | | | | | | rel_str(all_35_0) = all_244_3 & the_carrier(all_35_0) = % 80.60/16.02 | | | | | | | | all_244_1 & is_transitive_in(all_244_2, all_244_1) = % 80.60/16.02 | | | | | | | | all_244_0 & $i(all_244_1) & $i(all_244_2) & ( ~ % 80.60/16.02 | | | | | | | | (all_244_3 = 0) | (( ~ (all_244_0 = 0) | all_66_3 = % 80.60/16.02 | | | | | | | | 0) & ( ~ (all_66_3 = 0) | all_244_0 = 0))) % 80.60/16.02 | | | | | | | | % 80.60/16.02 | | | | | | | | ALPHA: (394) implies: % 80.60/16.02 | | | | | | | | (395) the_carrier(all_35_0) = all_244_1 % 80.60/16.02 | | | | | | | | % 80.60/16.02 | | | | | | | | DELTA: instantiating (314) with fresh symbols all_246_0, % 80.60/16.02 | | | | | | | | all_246_1 gives: % 80.60/16.02 | | | | | | | | (396) rel_str(all_42_5) = all_246_1 & the_carrier(all_42_5) = % 80.60/16.02 | | | | | | | | all_246_0 & $i(all_246_0) & ( ~ (all_246_1 = 0) | ( ! % 80.60/16.02 | | | | | | | | [v0: $i] : ! [v1: $i] : ! [v2: any] : ( ~ % 80.60/16.02 | | | | | | | | (related(all_42_5, v0, v1) = v2) | ~ % 80.60/16.02 | | | | | | | | (element(v0, all_246_0) = 0) | ~ $i(v1) | ~ % 80.60/16.02 | | | | | | | | $i(v0) | ? [v3: any] : ? [v4: $i] : ? [v5: % 80.60/16.02 | | | | | | | | any] : (ordered_pair(v0, v1) = v4 & element(v1, % 80.60/16.02 | | | | | | | | all_246_0) = v3 & in(v4, all_56_1) = v5 & % 80.60/16.02 | | | | | | | | $i(v4) & ( ~ (v3 = 0) | (( ~ (v5 = 0) | v2 = 0) % 80.60/16.02 | | | | | | | | & ( ~ (v2 = 0) | v5 = 0))))) & ! [v0: $i] % 80.60/16.02 | | | | | | | | : ! [v1: $i] : ! [v2: $i] : ( ~ (ordered_pair(v0, % 80.60/16.02 | | | | | | | | v1) = v2) | ~ (element(v0, all_246_0) = 0) | % 80.60/16.02 | | | | | | | | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: % 80.60/16.02 | | | | | | | | any] : ? [v5: any] : (related(all_42_5, v0, % 80.60/16.02 | | | | | | | | v1) = v4 & element(v1, all_246_0) = v3 & % 80.60/16.02 | | | | | | | | in(v2, all_56_1) = v5 & ( ~ (v3 = 0) | (( ~ (v5 % 80.60/16.02 | | | | | | | | = 0) | v4 = 0) & ( ~ (v4 = 0) | v5 = % 80.60/16.02 | | | | | | | | 0))))) & ! [v0: $i] : ! [v1: $i] : ( ~ % 80.60/16.02 | | | | | | | | (element(v1, all_246_0) = 0) | ~ (element(v0, % 80.60/16.02 | | | | | | | | all_246_0) = 0) | ~ $i(v1) | ~ $i(v0) | ? % 80.60/16.02 | | | | | | | | [v2: any] : ? [v3: $i] : ? [v4: any] : % 80.60/16.02 | | | | | | | | (related(all_42_5, v0, v1) = v2 & % 80.60/16.02 | | | | | | | | ordered_pair(v0, v1) = v3 & in(v3, all_56_1) = % 80.60/16.02 | | | | | | | | v4 & $i(v3) & ( ~ (v4 = 0) | v2 = 0) & ( ~ (v2 % 80.60/16.02 | | | | | | | | = 0) | v4 = 0))))) % 80.60/16.02 | | | | | | | | % 80.60/16.02 | | | | | | | | ALPHA: (396) implies: % 80.60/16.02 | | | | | | | | (397) $i(all_246_0) % 80.60/16.02 | | | | | | | | (398) the_carrier(all_42_5) = all_246_0 % 80.60/16.02 | | | | | | | | % 80.60/16.02 | | | | | | | | DELTA: instantiating (313) with fresh symbols all_248_0, % 80.60/16.02 | | | | | | | | all_248_1 gives: % 80.60/16.03 | | | | | | | | (399) rel_str(all_35_0) = all_248_1 & the_carrier(all_35_0) = % 80.60/16.03 | | | | | | | | all_248_0 & $i(all_248_0) & ( ~ (all_248_1 = 0) | ( ! % 80.60/16.03 | | | | | | | | [v0: $i] : ! [v1: $i] : ! [v2: any] : ( ~ % 80.60/16.03 | | | | | | | | (related(all_35_0, v0, v1) = v2) | ~ % 80.60/16.03 | | | | | | | | (element(v0, all_248_0) = 0) | ~ $i(v1) | ~ % 80.60/16.03 | | | | | | | | $i(v0) | ? [v3: any] : ? [v4: $i] : ? [v5: % 80.60/16.03 | | | | | | | | any] : (ordered_pair(v0, v1) = v4 & element(v1, % 80.60/16.03 | | | | | | | | all_248_0) = v3 & in(v4, all_58_1) = v5 & % 80.60/16.03 | | | | | | | | $i(v4) & ( ~ (v3 = 0) | (( ~ (v5 = 0) | v2 = 0) % 80.60/16.03 | | | | | | | | & ( ~ (v2 = 0) | v5 = 0))))) & ! [v0: $i] % 80.60/16.03 | | | | | | | | : ! [v1: $i] : ! [v2: $i] : ( ~ (ordered_pair(v0, % 80.60/16.03 | | | | | | | | v1) = v2) | ~ (element(v0, all_248_0) = 0) | % 80.60/16.03 | | | | | | | | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: % 80.60/16.03 | | | | | | | | any] : ? [v5: any] : (related(all_35_0, v0, % 80.60/16.03 | | | | | | | | v1) = v4 & element(v1, all_248_0) = v3 & % 80.60/16.03 | | | | | | | | in(v2, all_58_1) = v5 & ( ~ (v3 = 0) | (( ~ (v5 % 80.60/16.03 | | | | | | | | = 0) | v4 = 0) & ( ~ (v4 = 0) | v5 = % 80.60/16.03 | | | | | | | | 0))))) & ! [v0: $i] : ! [v1: $i] : ( ~ % 80.60/16.03 | | | | | | | | (element(v1, all_248_0) = 0) | ~ (element(v0, % 80.60/16.03 | | | | | | | | all_248_0) = 0) | ~ $i(v1) | ~ $i(v0) | ? % 80.60/16.03 | | | | | | | | [v2: any] : ? [v3: $i] : ? [v4: any] : % 80.60/16.03 | | | | | | | | (related(all_35_0, v0, v1) = v2 & % 80.60/16.03 | | | | | | | | ordered_pair(v0, v1) = v3 & in(v3, all_58_1) = % 80.60/16.03 | | | | | | | | v4 & $i(v3) & ( ~ (v4 = 0) | v2 = 0) & ( ~ (v2 % 80.60/16.03 | | | | | | | | = 0) | v4 = 0))))) % 80.60/16.03 | | | | | | | | % 80.60/16.03 | | | | | | | | ALPHA: (399) implies: % 80.60/16.03 | | | | | | | | (400) the_carrier(all_35_0) = all_248_0 % 80.60/16.03 | | | | | | | | % 80.60/16.03 | | | | | | | | REDUCE: (189), (388) imply: % 80.60/16.03 | | | | | | | | (401) in(all_116_1, all_56_1) = all_218_0 % 80.60/16.03 | | | | | | | | % 80.60/16.03 | | | | | | | | BETA: splitting (328) gives: % 80.60/16.03 | | | | | | | | % 80.60/16.03 | | | | | | | | Case 1: % 80.60/16.03 | | | | | | | | | % 80.60/16.03 | | | | | | | | | (402) all_82_0 = 0 % 80.60/16.03 | | | | | | | | | % 80.60/16.03 | | | | | | | | | REDUCE: (137), (402) imply: % 80.60/16.03 | | | | | | | | | (403) $false % 80.60/16.03 | | | | | | | | | % 80.60/16.03 | | | | | | | | | CLOSE: (403) is inconsistent. % 80.60/16.03 | | | | | | | | | % 80.60/16.03 | | | | | | | | Case 2: % 80.60/16.03 | | | | | | | | | % 80.60/16.03 | | | | | | | | | (404) ? [v0: $i] : ? [v1: $i] : ? [v2: int] : ( ~ (v2 = % 80.60/16.03 | | | | | | | | | 0) & empty(v1) = v2 & powerset(all_82_1) = v0 & % 80.60/16.03 | | | | | | | | | element(v1, v0) = 0 & $i(v1) & $i(v0)) % 80.60/16.03 | | | | | | | | | % 80.60/16.03 | | | | | | | | | DELTA: instantiating (404) with fresh symbols all_259_0, % 80.60/16.03 | | | | | | | | | all_259_1, all_259_2 gives: % 80.60/16.03 | | | | | | | | | (405) ~ (all_259_0 = 0) & empty(all_259_1) = all_259_0 & % 80.60/16.03 | | | | | | | | | powerset(all_82_1) = all_259_2 & element(all_259_1, % 80.60/16.03 | | | | | | | | | all_259_2) = 0 & $i(all_259_1) & $i(all_259_2) % 80.60/16.03 | | | | | | | | | % 80.60/16.03 | | | | | | | | | ALPHA: (405) implies: % 80.60/16.03 | | | | | | | | | (406) ~ (all_259_0 = 0) % 80.60/16.03 | | | | | | | | | (407) $i(all_259_1) % 80.60/16.03 | | | | | | | | | (408) powerset(all_82_1) = all_259_2 % 80.60/16.03 | | | | | | | | | (409) empty(all_259_1) = all_259_0 % 80.60/16.03 | | | | | | | | | % 80.60/16.03 | | | | | | | | | BETA: splitting (304) gives: % 80.60/16.03 | | | | | | | | | % 80.60/16.03 | | | | | | | | | Case 1: % 80.60/16.03 | | | | | | | | | | % 80.60/16.03 | | | | | | | | | | (410) all_114_0 = 0 % 80.60/16.03 | | | | | | | | | | % 80.60/16.03 | | | | | | | | | | REDUCE: (301), (410) imply: % 80.60/16.03 | | | | | | | | | | (411) $false % 80.60/16.03 | | | | | | | | | | % 80.60/16.03 | | | | | | | | | | CLOSE: (411) is inconsistent. % 80.60/16.03 | | | | | | | | | | % 80.60/16.03 | | | | | | | | | Case 2: % 80.60/16.03 | | | | | | | | | | % 80.60/16.03 | | | | | | | | | | (412) ? [v0: any] : ? [v1: any] : (empty(all_56_1) = v1 % 80.60/16.03 | | | | | | | | | | & element(all_114_1, all_56_1) = v0 & ( ~ (v0 = % 80.60/16.03 | | | | | | | | | | 0) | v1 = 0)) % 80.60/16.03 | | | | | | | | | | % 80.60/16.03 | | | | | | | | | | DELTA: instantiating (412) with fresh symbols all_265_0, % 80.60/16.03 | | | | | | | | | | all_265_1 gives: % 80.60/16.03 | | | | | | | | | | (413) empty(all_56_1) = all_265_0 & element(all_114_1, % 80.60/16.03 | | | | | | | | | | all_56_1) = all_265_1 & ( ~ (all_265_1 = 0) | % 80.60/16.03 | | | | | | | | | | all_265_0 = 0) % 80.60/16.03 | | | | | | | | | | % 80.60/16.03 | | | | | | | | | | ALPHA: (413) implies: % 80.60/16.03 | | | | | | | | | | (414) empty(all_56_1) = all_265_0 % 80.60/16.03 | | | | | | | | | | % 80.60/16.03 | | | | | | | | | | GROUND_INST: instantiating (33) with all_116_0, all_218_0, % 80.60/16.03 | | | | | | | | | | all_56_1, all_116_1, simplifying with (268), (401) % 80.60/16.03 | | | | | | | | | | gives: % 80.60/16.03 | | | | | | | | | | (415) all_218_0 = all_116_0 % 80.60/16.03 | | | | | | | | | | % 80.60/16.03 | | | | | | | | | | GROUND_INST: instantiating (28) with all_240_1, all_244_1, % 80.60/16.03 | | | | | | | | | | all_35_0, simplifying with (393), (395) gives: % 80.60/16.03 | | | | | | | | | | (416) all_244_1 = all_240_1 % 80.60/16.03 | | | | | | | | | | % 80.60/16.03 | | | | | | | | | | GROUND_INST: instantiating (28) with all_58_0, all_248_0, % 80.60/16.03 | | | | | | | | | | all_35_0, simplifying with (96), (400) gives: % 80.60/16.03 | | | | | | | | | | (417) all_248_0 = all_58_0 % 80.60/16.03 | | | | | | | | | | % 80.60/16.03 | | | | | | | | | | GROUND_INST: instantiating (28) with all_244_1, all_248_0, % 80.60/16.03 | | | | | | | | | | all_35_0, simplifying with (395), (400) gives: % 80.60/16.03 | | | | | | | | | | (418) all_248_0 = all_244_1 % 80.60/16.03 | | | | | | | | | | % 80.60/16.03 | | | | | | | | | | GROUND_INST: instantiating (28) with all_42_4, all_246_0, % 80.60/16.03 | | | | | | | | | | all_42_5, simplifying with (57), (398) gives: % 80.60/16.03 | | | | | | | | | | (419) all_246_0 = all_42_4 % 80.60/16.03 | | | | | | | | | | % 80.60/16.03 | | | | | | | | | | GROUND_INST: instantiating (31) with all_210_0, all_212_0, % 80.60/16.03 | | | | | | | | | | all_42_3, simplifying with (384), (386) gives: % 80.60/16.03 | | | | | | | | | | (420) all_212_0 = all_210_0 % 80.60/16.03 | | | | | | | | | | % 80.60/16.03 | | | | | | | | | | GROUND_INST: instantiating (31) with all_196_0, all_212_0, % 80.60/16.03 | | | | | | | | | | all_42_3, simplifying with (356), (386) gives: % 80.60/16.03 | | | | | | | | | | (421) all_212_0 = all_196_0 % 80.60/16.03 | | | | | | | | | | % 80.60/16.03 | | | | | | | | | | GROUND_INST: instantiating (31) with all_206_0, all_208_0, % 80.60/16.03 | | | | | | | | | | all_42_2, simplifying with (377), (379) gives: % 80.60/16.03 | | | | | | | | | | (422) all_208_0 = all_206_0 % 80.60/16.03 | | | | | | | | | | % 80.60/16.03 | | | | | | | | | | GROUND_INST: instantiating (31) with all_204_0, all_208_0, % 80.60/16.03 | | | | | | | | | | all_42_2, simplifying with (372), (379) gives: % 80.60/16.03 | | | | | | | | | | (423) all_208_0 = all_204_0 % 80.60/16.03 | | | | | | | | | | % 80.60/16.03 | | | | | | | | | | GROUND_INST: instantiating (31) with all_200_0, all_202_0, % 80.60/16.03 | | | | | | | | | | all_42_1, simplifying with (365), (367) gives: % 80.60/16.03 | | | | | | | | | | (424) all_202_0 = all_200_0 % 80.60/16.03 | | | | | | | | | | % 80.60/16.03 | | | | | | | | | | GROUND_INST: instantiating (31) with all_198_0, all_202_0, % 80.60/16.03 | | | | | | | | | | all_42_1, simplifying with (360), (367) gives: % 80.60/16.03 | | | | | | | | | | (425) all_202_0 = all_198_0 % 80.60/16.03 | | | | | | | | | | % 80.60/16.03 | | | | | | | | | | GROUND_INST: instantiating (35) with all_116_1, all_238_1, % 80.60/16.03 | | | | | | | | | | all_42_2, all_42_1, simplifying with (229), (390) % 80.60/16.03 | | | | | | | | | | gives: % 80.60/16.03 | | | | | | | | | | (426) all_238_1 = all_116_1 % 80.60/16.03 | | | | | | | | | | % 80.60/16.03 | | | | | | | | | | GROUND_INST: instantiating (32) with all_182_0, all_265_0, % 80.60/16.03 | | | | | | | | | | all_56_1, simplifying with (334), (414) gives: % 80.60/16.03 | | | | | | | | | | (427) all_265_0 = all_182_0 % 80.60/16.03 | | | | | | | | | | % 80.60/16.03 | | | | | | | | | | GROUND_INST: instantiating (32) with all_178_0, all_188_1, % 80.60/16.03 | | | | | | | | | | all_82_2, simplifying with (331), (340) gives: % 80.60/16.03 | | | | | | | | | | (428) all_188_1 = all_178_0 % 80.60/16.03 | | | | | | | | | | % 80.60/16.03 | | | | | | | | | | COMBINE_EQS: (417), (418) imply: % 80.60/16.03 | | | | | | | | | | (429) all_244_1 = all_58_0 % 80.60/16.03 | | | | | | | | | | % 80.60/16.03 | | | | | | | | | | SIMP: (429) implies: % 80.60/16.03 | | | | | | | | | | (430) all_244_1 = all_58_0 % 80.60/16.03 | | | | | | | | | | % 80.60/16.03 | | | | | | | | | | COMBINE_EQS: (416), (430) imply: % 80.60/16.03 | | | | | | | | | | (431) all_240_1 = all_58_0 % 80.60/16.03 | | | | | | | | | | % 80.60/16.03 | | | | | | | | | | SIMP: (431) implies: % 80.60/16.03 | | | | | | | | | | (432) all_240_1 = all_58_0 % 80.60/16.03 | | | | | | | | | | % 80.60/16.03 | | | | | | | | | | COMBINE_EQS: (420), (421) imply: % 80.60/16.03 | | | | | | | | | | (433) all_210_0 = all_196_0 % 80.60/16.03 | | | | | | | | | | % 80.60/16.03 | | | | | | | | | | SIMP: (433) implies: % 80.60/16.03 | | | | | | | | | | (434) all_210_0 = all_196_0 % 80.60/16.03 | | | | | | | | | | % 80.60/16.03 | | | | | | | | | | COMBINE_EQS: (422), (423) imply: % 80.60/16.03 | | | | | | | | | | (435) all_206_0 = all_204_0 % 80.60/16.03 | | | | | | | | | | % 80.60/16.03 | | | | | | | | | | COMBINE_EQS: (424), (425) imply: % 80.60/16.03 | | | | | | | | | | (436) all_200_0 = all_198_0 % 80.60/16.03 | | | | | | | | | | % 80.60/16.03 | | | | | | | | | | SIMP: (436) implies: % 80.60/16.03 | | | | | | | | | | (437) all_200_0 = all_198_0 % 80.60/16.03 | | | | | | | | | | % 80.60/16.03 | | | | | | | | | | REDUCE: (383), (434) imply: % 80.60/16.03 | | | | | | | | | | (438) unordered_pair(all_210_1, all_196_0) = all_110_1 % 80.60/16.03 | | | | | | | | | | % 80.60/16.03 | | | | | | | | | | REDUCE: (376), (435) imply: % 80.60/16.03 | | | | | | | | | | (439) unordered_pair(all_206_1, all_204_0) = all_118_1 % 80.60/16.03 | | | | | | | | | | % 80.60/16.03 | | | | | | | | | | REDUCE: (364), (437) imply: % 80.60/16.03 | | | | | | | | | | (440) unordered_pair(all_200_1, all_198_0) = all_116_1 % 80.60/16.03 | | | | | | | | | | % 80.60/16.03 | | | | | | | | | | REDUCE: (381), (434) imply: % 80.60/16.03 | | | | | | | | | | (441) $i(all_196_0) % 80.60/16.03 | | | | | | | | | | % 80.60/16.03 | | | | | | | | | | REDUCE: (374), (435) imply: % 80.60/16.03 | | | | | | | | | | (442) $i(all_204_0) % 80.60/16.03 | | | | | | | | | | % 80.60/16.03 | | | | | | | | | | REDUCE: (362), (437) imply: % 80.60/16.03 | | | | | | | | | | (443) $i(all_198_0) % 80.60/16.03 | | | | | | | | | | % 80.60/16.03 | | | | | | | | | | BETA: splitting (341) gives: % 80.60/16.03 | | | | | | | | | | % 80.60/16.03 | | | | | | | | | | Case 1: % 80.60/16.03 | | | | | | | | | | | % 80.60/16.03 | | | | | | | | | | | (444) all_188_0 = 0 % 80.60/16.03 | | | | | | | | | | | % 80.60/16.03 | | | | | | | | | | | REDUCE: (339), (444) imply: % 80.60/16.03 | | | | | | | | | | | (445) in(all_82_1, all_82_2) = 0 % 80.60/16.03 | | | | | | | | | | | % 80.60/16.03 | | | | | | | | | | | BETA: splitting (81) gives: % 80.60/16.03 | | | | | | | | | | | % 80.60/16.03 | | | | | | | | | | | Case 1: % 80.60/16.03 | | | | | | | | | | | | % 80.60/16.03 | | | | | | | | | | | | (446) all_50_0 = 0 % 80.60/16.03 | | | | | | | | | | | | % 80.60/16.03 | | | | | | | | | | | | REDUCE: (79), (446) imply: % 80.60/16.03 | | | | | | | | | | | | (447) in(all_42_1, all_42_4) = 0 % 80.60/16.03 | | | | | | | | | | | | % 80.60/16.03 | | | | | | | | | | | | BETA: splitting (85) gives: % 80.60/16.03 | | | | | | | | | | | | % 80.60/16.03 | | | | | | | | | | | | Case 1: % 80.60/16.03 | | | | | | | | | | | | | % 80.60/16.03 | | | | | | | | | | | | | (448) all_52_0 = 0 % 80.60/16.03 | | | | | | | | | | | | | % 80.60/16.03 | | | | | | | | | | | | | REDUCE: (83), (448) imply: % 80.60/16.03 | | | | | | | | | | | | | (449) in(all_42_2, all_42_4) = 0 % 80.60/16.03 | | | | | | | | | | | | | % 80.60/16.03 | | | | | | | | | | | | | BETA: splitting (89) gives: % 80.60/16.03 | | | | | | | | | | | | | % 80.60/16.03 | | | | | | | | | | | | | Case 1: % 80.60/16.03 | | | | | | | | | | | | | | % 80.60/16.03 | | | | | | | | | | | | | | (450) all_54_0 = 0 % 80.60/16.03 | | | | | | | | | | | | | | % 80.60/16.03 | | | | | | | | | | | | | | REDUCE: (87), (450) imply: % 80.60/16.03 | | | | | | | | | | | | | | (451) in(all_42_3, all_42_4) = 0 % 80.60/16.03 | | | | | | | | | | | | | | % 80.60/16.03 | | | | | | | | | | | | | | GROUND_INST: instantiating (24) with all_42_1, all_42_4, % 80.60/16.03 | | | | | | | | | | | | | | empty_set, simplifying with (50), (53), (131), % 80.60/16.03 | | | | | | | | | | | | | | (132), (447) gives: % 80.60/16.03 | | | | | | | | | | | | | | (452) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & % 80.60/16.03 | | | | | | | | | | | | | | powerset(empty_set) = v0 & element(all_42_4, v0) % 80.60/16.03 | | | | | | | | | | | | | | = v1 & $i(v0)) % 80.60/16.03 | | | | | | | | | | | | | | % 80.60/16.03 | | | | | | | | | | | | | | GROUND_INST: instantiating (24) with all_82_1, all_82_2, % 80.60/16.03 | | | | | | | | | | | | | | empty_set, simplifying with (131), (132), (138), % 80.60/16.03 | | | | | | | | | | | | | | (139), (445) gives: % 80.60/16.03 | | | | | | | | | | | | | | (453) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & % 80.60/16.03 | | | | | | | | | | | | | | powerset(empty_set) = v0 & element(all_82_2, v0) % 80.60/16.03 | | | | | | | | | | | | | | = v1 & $i(v0)) % 80.60/16.03 | | | | | | | | | | | | | | % 80.60/16.03 | | | | | | | | | | | | | | GROUND_INST: instantiating (cc1_relset_1) with all_42_4, % 80.60/16.03 | | | | | | | | | | | | | | all_42_4, all_56_1, all_194_1, all_194_0, % 80.60/16.03 | | | | | | | | | | | | | | simplifying with (50), (194), (350), (351), (352) % 80.60/16.03 | | | | | | | | | | | | | | gives: % 80.60/16.03 | | | | | | | | | | | | | | (454) relation(all_56_1) = 0 % 80.60/16.03 | | | | | | | | | | | | | | % 80.60/16.03 | | | | | | | | | | | | | | GROUND_INST: instantiating (1) with all_42_3, all_42_2, % 80.60/16.03 | | | | | | | | | | | | | | all_206_1, simplifying with (51), (52), (375) % 80.60/16.03 | | | | | | | | | | | | | | gives: % 80.60/16.03 | | | | | | | | | | | | | | (455) unordered_pair(all_42_3, all_42_2) = all_206_1 & % 80.60/16.03 | | | | | | | | | | | | | | $i(all_206_1) % 80.60/16.03 | | | | | | | | | | | | | | % 80.60/16.03 | | | | | | | | | | | | | | ALPHA: (455) implies: % 80.60/16.03 | | | | | | | | | | | | | | (456) $i(all_206_1) % 80.60/16.03 | | | | | | | | | | | | | | % 80.60/16.03 | | | | | | | | | | | | | | GROUND_INST: instantiating (1) with all_42_1, all_42_2, % 80.60/16.03 | | | | | | | | | | | | | | all_204_1, simplifying with (52), (53), (370) % 80.60/16.03 | | | | | | | | | | | | | | gives: % 80.60/16.03 | | | | | | | | | | | | | | (457) unordered_pair(all_42_1, all_42_2) = all_204_1 & % 80.60/16.03 | | | | | | | | | | | | | | $i(all_204_1) % 80.60/16.03 | | | | | | | | | | | | | | % 80.60/16.03 | | | | | | | | | | | | | | ALPHA: (457) implies: % 80.60/16.03 | | | | | | | | | | | | | | (458) $i(all_204_1) % 80.60/16.03 | | | | | | | | | | | | | | % 80.60/16.03 | | | | | | | | | | | | | | GROUND_INST: instantiating (1) with all_42_2, all_42_1, % 80.60/16.03 | | | | | | | | | | | | | | all_200_1, simplifying with (52), (53), (363) % 80.60/16.03 | | | | | | | | | | | | | | gives: % 80.60/16.03 | | | | | | | | | | | | | | (459) unordered_pair(all_42_2, all_42_1) = all_200_1 & % 80.60/16.03 | | | | | | | | | | | | | | $i(all_200_1) % 80.60/16.03 | | | | | | | | | | | | | | % 80.60/16.03 | | | | | | | | | | | | | | ALPHA: (459) implies: % 80.60/16.03 | | | | | | | | | | | | | | (460) $i(all_200_1) % 80.60/16.03 | | | | | | | | | | | | | | % 80.60/16.03 | | | | | | | | | | | | | | GROUND_INST: instantiating (fc3_subset_1) with all_42_1, % 80.60/16.03 | | | | | | | | | | | | | | all_42_1, all_198_1, simplifying with (53), (359) % 80.60/16.03 | | | | | | | | | | | | | | gives: % 80.60/16.03 | | | | | | | | | | | | | | (461) ? [v0: int] : ( ~ (v0 = 0) & empty(all_198_1) = % 80.60/16.03 | | | | | | | | | | | | | | v0) % 80.60/16.03 | | | | | | | | | | | | | | % 80.60/16.03 | | | | | | | | | | | | | | GROUND_INST: instantiating (1) with all_198_0, all_200_1, % 80.60/16.03 | | | | | | | | | | | | | | all_116_1, simplifying with (440), (443), (460) % 80.60/16.03 | | | | | | | | | | | | | | gives: % 80.60/16.03 | | | | | | | | | | | | | | (462) unordered_pair(all_198_0, all_200_1) = all_116_1 & % 80.60/16.03 | | | | | | | | | | | | | | $i(all_116_1) % 80.60/16.03 | | | | | | | | | | | | | | % 80.60/16.03 | | | | | | | | | | | | | | GROUND_INST: instantiating (1) with all_204_0, all_204_1, % 80.60/16.03 | | | | | | | | | | | | | | all_108_1, simplifying with (371), (442), (458) % 80.60/16.03 | | | | | | | | | | | | | | gives: % 80.60/16.03 | | | | | | | | | | | | | | (463) unordered_pair(all_204_0, all_204_1) = all_108_1 & % 80.60/16.04 | | | | | | | | | | | | | | $i(all_108_1) % 80.60/16.04 | | | | | | | | | | | | | | % 80.60/16.04 | | | | | | | | | | | | | | GROUND_INST: instantiating (1) with all_204_0, all_206_1, % 80.60/16.04 | | | | | | | | | | | | | | all_118_1, simplifying with (439), (442), (456) % 80.60/16.04 | | | | | | | | | | | | | | gives: % 80.60/16.04 | | | | | | | | | | | | | | (464) unordered_pair(all_204_0, all_206_1) = all_118_1 & % 80.60/16.04 | | | | | | | | | | | | | | $i(all_118_1) % 80.60/16.04 | | | | | | | | | | | | | | % 80.60/16.04 | | | | | | | | | | | | | | ALPHA: (464) implies: % 80.60/16.04 | | | | | | | | | | | | | | (465) $i(all_118_1) % 80.60/16.04 | | | | | | | | | | | | | | % 80.60/16.04 | | | | | | | | | | | | | | GROUND_INST: instantiating (fc3_subset_1) with all_206_1, % 80.60/16.04 | | | | | | | | | | | | | | all_204_0, all_118_1, simplifying with (439), % 80.60/16.04 | | | | | | | | | | | | | | (442), (456) gives: % 80.60/16.04 | | | | | | | | | | | | | | (466) ? [v0: int] : ( ~ (v0 = 0) & empty(all_118_1) = % 80.60/16.04 | | | | | | | | | | | | | | v0) % 80.60/16.04 | | | | | | | | | | | | | | % 80.60/16.04 | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with all_56_1, all_182_0, % 80.60/16.04 | | | | | | | | | | | | | | simplifying with (194), (334) gives: % 80.60/16.04 | | | | | | | | | | | | | | (467) all_182_0 = 0 | ? [v0: $i] : ? [v1: $i] : ? % 80.60/16.04 | | | | | | | | | | | | | | [v2: int] : ( ~ (v2 = 0) & empty(v1) = v2 & % 80.60/16.04 | | | | | | | | | | | | | | powerset(all_56_1) = v0 & element(v1, v0) = 0 & % 80.60/16.04 | | | | | | | | | | | | | | $i(v1) & $i(v0)) % 80.60/16.04 | | | | | | | | | | | | | | % 80.60/16.04 | | | | | | | | | | | | | | GROUND_INST: instantiating (24) with all_108_1, all_56_1, % 80.60/16.04 | | | | | | | | | | | | | | all_186_0, simplifying with (194), (299), (336), % 80.60/16.04 | | | | | | | | | | | | | | (337), (369) gives: % 80.60/16.04 | | | | | | | | | | | | | | (468) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & % 80.60/16.04 | | | | | | | | | | | | | | powerset(all_186_0) = v0 & element(all_56_1, v0) % 80.60/16.04 | | | | | | | | | | | | | | = v1 & $i(v0)) % 80.60/16.04 | | | | | | | | | | | | | | % 80.60/16.04 | | | | | | | | | | | | | | GROUND_INST: instantiating (24) with all_82_1, all_82_2, % 80.60/16.04 | | | | | | | | | | | | | | all_186_0, simplifying with (138), (139), (336), % 80.60/16.04 | | | | | | | | | | | | | | (337), (445) gives: % 80.60/16.04 | | | | | | | | | | | | | | (469) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & % 80.60/16.04 | | | | | | | | | | | | | | powerset(all_186_0) = v0 & element(all_82_2, v0) % 80.60/16.04 | | | | | | | | | | | | | | = v1 & $i(v0)) % 80.60/16.04 | | | | | | | | | | | | | | % 80.60/16.04 | | | | | | | | | | | | | | GROUND_INST: instantiating (24) with all_42_3, all_42_4, % 80.60/16.04 | | | | | | | | | | | | | | all_186_0, simplifying with (50), (51), (336), % 80.60/16.04 | | | | | | | | | | | | | | (337), (451) gives: % 80.60/16.04 | | | | | | | | | | | | | | (470) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & % 80.60/16.04 | | | | | | | | | | | | | | powerset(all_186_0) = v0 & element(all_42_4, v0) % 80.60/16.04 | | | | | | | | | | | | | | = v1 & $i(v0)) % 80.60/16.04 | | | | | | | | | | | | | | % 80.60/16.04 | | | | | | | | | | | | | | GROUND_INST: instantiating (26) with all_186_0, simplifying % 80.60/16.04 | | | | | | | | | | | | | | with (336), (337) gives: % 80.60/16.04 | | | | | | | | | | | | | | (471) all_186_0 = empty_set % 80.60/16.04 | | | | | | | | | | | | | | % 80.60/16.04 | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with all_259_1, all_259_0, % 80.60/16.04 | | | | | | | | | | | | | | simplifying with (407), (409) gives: % 80.60/16.04 | | | | | | | | | | | | | | (472) all_259_0 = 0 | ? [v0: $i] : ? [v1: $i] : ? % 80.60/16.04 | | | | | | | | | | | | | | [v2: int] : ( ~ (v2 = 0) & empty(v1) = v2 & % 80.60/16.04 | | | | | | | | | | | | | | powerset(all_259_1) = v0 & element(v1, v0) = 0 & % 80.60/16.04 | | | | | | | | | | | | | | $i(v1) & $i(v0)) % 80.60/16.04 | | | | | | | | | | | | | | % 80.60/16.04 | | | | | | | | | | | | | | DELTA: instantiating (466) with fresh symbol all_350_0 % 80.60/16.04 | | | | | | | | | | | | | | gives: % 80.60/16.04 | | | | | | | | | | | | | | (473) ~ (all_350_0 = 0) & empty(all_118_1) = all_350_0 % 80.60/16.04 | | | | | | | | | | | | | | % 80.60/16.04 | | | | | | | | | | | | | | ALPHA: (473) implies: % 80.60/16.04 | | | | | | | | | | | | | | (474) ~ (all_350_0 = 0) % 80.60/16.04 | | | | | | | | | | | | | | (475) empty(all_118_1) = all_350_0 % 80.60/16.04 | | | | | | | | | | | | | | % 80.60/16.04 | | | | | | | | | | | | | | DELTA: instantiating (461) with fresh symbol all_398_0 % 80.60/16.04 | | | | | | | | | | | | | | gives: % 80.60/16.04 | | | | | | | | | | | | | | (476) ~ (all_398_0 = 0) & empty(all_198_1) = all_398_0 % 80.60/16.04 | | | | | | | | | | | | | | % 80.60/16.04 | | | | | | | | | | | | | | ALPHA: (476) implies: % 80.60/16.04 | | | | | | | | | | | | | | (477) ~ (all_398_0 = 0) % 80.60/16.04 | | | | | | | | | | | | | | (478) empty(all_198_1) = all_398_0 % 80.60/16.04 | | | | | | | | | | | | | | % 80.60/16.04 | | | | | | | | | | | | | | DELTA: instantiating (470) with fresh symbols all_416_0, % 80.60/16.04 | | | | | | | | | | | | | | all_416_1 gives: % 80.60/16.04 | | | | | | | | | | | | | | (479) ~ (all_416_0 = 0) & powerset(all_186_0) = % 80.60/16.04 | | | | | | | | | | | | | | all_416_1 & element(all_42_4, all_416_1) = % 80.60/16.04 | | | | | | | | | | | | | | all_416_0 & $i(all_416_1) % 80.60/16.04 | | | | | | | | | | | | | | % 80.60/16.04 | | | | | | | | | | | | | | ALPHA: (479) implies: % 80.60/16.04 | | | | | | | | | | | | | | (480) $i(all_416_1) % 80.60/16.04 | | | | | | | | | | | | | | (481) powerset(all_186_0) = all_416_1 % 80.60/16.04 | | | | | | | | | | | | | | % 80.60/16.04 | | | | | | | | | | | | | | DELTA: instantiating (453) with fresh symbols all_420_0, % 80.60/16.04 | | | | | | | | | | | | | | all_420_1 gives: % 80.60/16.04 | | | | | | | | | | | | | | (482) ~ (all_420_0 = 0) & powerset(empty_set) = % 80.60/16.04 | | | | | | | | | | | | | | all_420_1 & element(all_82_2, all_420_1) = % 80.60/16.04 | | | | | | | | | | | | | | all_420_0 & $i(all_420_1) % 80.60/16.04 | | | | | | | | | | | | | | % 80.60/16.04 | | | | | | | | | | | | | | ALPHA: (482) implies: % 80.60/16.04 | | | | | | | | | | | | | | (483) ~ (all_420_0 = 0) % 80.60/16.04 | | | | | | | | | | | | | | (484) element(all_82_2, all_420_1) = all_420_0 % 80.60/16.04 | | | | | | | | | | | | | | (485) powerset(empty_set) = all_420_1 % 80.60/16.04 | | | | | | | | | | | | | | % 80.60/16.04 | | | | | | | | | | | | | | DELTA: instantiating (469) with fresh symbols all_424_0, % 80.60/16.04 | | | | | | | | | | | | | | all_424_1 gives: % 80.60/16.04 | | | | | | | | | | | | | | (486) ~ (all_424_0 = 0) & powerset(all_186_0) = % 80.60/16.04 | | | | | | | | | | | | | | all_424_1 & element(all_82_2, all_424_1) = % 80.60/16.04 | | | | | | | | | | | | | | all_424_0 & $i(all_424_1) % 80.60/16.04 | | | | | | | | | | | | | | % 80.60/16.04 | | | | | | | | | | | | | | ALPHA: (486) implies: % 80.60/16.04 | | | | | | | | | | | | | | (487) powerset(all_186_0) = all_424_1 % 80.60/16.04 | | | | | | | | | | | | | | % 80.60/16.04 | | | | | | | | | | | | | | DELTA: instantiating (468) with fresh symbols all_426_0, % 80.60/16.04 | | | | | | | | | | | | | | all_426_1 gives: % 80.60/16.04 | | | | | | | | | | | | | | (488) ~ (all_426_0 = 0) & powerset(all_186_0) = % 80.60/16.04 | | | | | | | | | | | | | | all_426_1 & element(all_56_1, all_426_1) = % 80.60/16.04 | | | | | | | | | | | | | | all_426_0 & $i(all_426_1) % 80.60/16.04 | | | | | | | | | | | | | | % 80.60/16.04 | | | | | | | | | | | | | | ALPHA: (488) implies: % 80.60/16.04 | | | | | | | | | | | | | | (489) powerset(all_186_0) = all_426_1 % 80.60/16.04 | | | | | | | | | | | | | | % 80.60/16.04 | | | | | | | | | | | | | | DELTA: instantiating (452) with fresh symbols all_428_0, % 80.60/16.04 | | | | | | | | | | | | | | all_428_1 gives: % 80.60/16.04 | | | | | | | | | | | | | | (490) ~ (all_428_0 = 0) & powerset(empty_set) = % 80.60/16.04 | | | | | | | | | | | | | | all_428_1 & element(all_42_4, all_428_1) = % 80.60/16.04 | | | | | | | | | | | | | | all_428_0 & $i(all_428_1) % 80.60/16.04 | | | | | | | | | | | | | | % 80.60/16.04 | | | | | | | | | | | | | | ALPHA: (490) implies: % 80.60/16.04 | | | | | | | | | | | | | | (491) powerset(empty_set) = all_428_1 % 80.60/16.04 | | | | | | | | | | | | | | % 80.60/16.04 | | | | | | | | | | | | | | REDUCE: (471), (489) imply: % 80.60/16.04 | | | | | | | | | | | | | | (492) powerset(empty_set) = all_426_1 % 80.60/16.04 | | | | | | | | | | | | | | % 80.60/16.04 | | | | | | | | | | | | | | REDUCE: (471), (487) imply: % 80.60/16.04 | | | | | | | | | | | | | | (493) powerset(empty_set) = all_424_1 % 80.60/16.04 | | | | | | | | | | | | | | % 80.60/16.04 | | | | | | | | | | | | | | REDUCE: (471), (481) imply: % 80.60/16.04 | | | | | | | | | | | | | | (494) powerset(empty_set) = all_416_1 % 80.60/16.04 | | | | | | | | | | | | | | % 80.60/16.04 | | | | | | | | | | | | | | BETA: splitting (467) gives: % 80.60/16.04 | | | | | | | | | | | | | | % 80.60/16.04 | | | | | | | | | | | | | | Case 1: % 80.60/16.04 | | | | | | | | | | | | | | | % 80.60/16.04 | | | | | | | | | | | | | | | (495) all_182_0 = 0 % 80.60/16.04 | | | | | | | | | | | | | | | % 80.60/16.04 | | | | | | | | | | | | | | | REDUCE: (333), (495) imply: % 80.60/16.04 | | | | | | | | | | | | | | | (496) $false % 80.60/16.04 | | | | | | | | | | | | | | | % 80.60/16.04 | | | | | | | | | | | | | | | CLOSE: (496) is inconsistent. % 80.60/16.04 | | | | | | | | | | | | | | | % 80.60/16.04 | | | | | | | | | | | | | | Case 2: % 80.60/16.04 | | | | | | | | | | | | | | | % 80.60/16.04 | | | | | | | | | | | | | | | (497) ? [v0: $i] : ? [v1: $i] : ? [v2: int] : ( ~ (v2 % 80.60/16.04 | | | | | | | | | | | | | | | = 0) & empty(v1) = v2 & powerset(all_56_1) = % 80.60/16.04 | | | | | | | | | | | | | | | v0 & element(v1, v0) = 0 & $i(v1) & $i(v0)) % 80.60/16.04 | | | | | | | | | | | | | | | % 80.60/16.04 | | | | | | | | | | | | | | | DELTA: instantiating (497) with fresh symbols all_480_0, % 80.60/16.04 | | | | | | | | | | | | | | | all_480_1, all_480_2 gives: % 80.60/16.04 | | | | | | | | | | | | | | | (498) ~ (all_480_0 = 0) & empty(all_480_1) = all_480_0 % 80.60/16.04 | | | | | | | | | | | | | | | & powerset(all_56_1) = all_480_2 & % 80.60/16.04 | | | | | | | | | | | | | | | element(all_480_1, all_480_2) = 0 & $i(all_480_1) % 80.60/16.04 | | | | | | | | | | | | | | | & $i(all_480_2) % 80.60/16.04 | | | | | | | | | | | | | | | % 80.60/16.04 | | | | | | | | | | | | | | | ALPHA: (498) implies: % 80.60/16.04 | | | | | | | | | | | | | | | (499) $i(all_480_1) % 80.60/16.04 | | | | | | | | | | | | | | | (500) element(all_480_1, all_480_2) = 0 % 80.60/16.04 | | | | | | | | | | | | | | | (501) powerset(all_56_1) = all_480_2 % 80.60/16.04 | | | | | | | | | | | | | | | % 80.60/16.04 | | | | | | | | | | | | | | | BETA: splitting (472) gives: % 80.60/16.04 | | | | | | | | | | | | | | | % 80.60/16.04 | | | | | | | | | | | | | | | Case 1: % 80.60/16.04 | | | | | | | | | | | | | | | | % 80.60/16.04 | | | | | | | | | | | | | | | | (502) all_259_0 = 0 % 80.60/16.04 | | | | | | | | | | | | | | | | % 80.60/16.04 | | | | | | | | | | | | | | | | REDUCE: (406), (502) imply: % 80.60/16.04 | | | | | | | | | | | | | | | | (503) $false % 80.60/16.04 | | | | | | | | | | | | | | | | % 80.60/16.04 | | | | | | | | | | | | | | | | CLOSE: (503) is inconsistent. % 80.60/16.04 | | | | | | | | | | | | | | | | % 80.60/16.04 | | | | | | | | | | | | | | | Case 2: % 80.60/16.04 | | | | | | | | | | | | | | | | % 80.60/16.04 | | | | | | | | | | | | | | | | % 80.60/16.04 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (27) with all_190_1, all_424_1, % 80.60/16.04 | | | | | | | | | | | | | | | | empty_set, simplifying with (343), (493) gives: % 80.60/16.04 | | | | | | | | | | | | | | | | (504) all_424_1 = all_190_1 % 80.60/16.04 | | | | | | | | | | | | | | | | % 80.60/16.04 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (27) with all_420_1, all_424_1, % 80.60/16.04 | | | | | | | | | | | | | | | | empty_set, simplifying with (485), (493) gives: % 80.60/16.04 | | | | | | | | | | | | | | | | (505) all_424_1 = all_420_1 % 80.60/16.04 | | | | | | | | | | | | | | | | % 80.60/16.04 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (27) with all_426_1, all_428_1, % 80.60/16.04 | | | | | | | | | | | | | | | | empty_set, simplifying with (491), (492) gives: % 80.60/16.04 | | | | | | | | | | | | | | | | (506) all_428_1 = all_426_1 % 80.60/16.04 | | | | | | | | | | | | | | | | % 80.60/16.04 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (27) with all_424_1, all_428_1, % 80.60/16.04 | | | | | | | | | | | | | | | | empty_set, simplifying with (491), (493) gives: % 80.60/16.04 | | | | | | | | | | | | | | | | (507) all_428_1 = all_424_1 % 80.60/16.04 | | | | | | | | | | | | | | | | % 80.60/16.04 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (27) with all_416_1, all_428_1, % 80.60/16.04 | | | | | | | | | | | | | | | | empty_set, simplifying with (491), (494) gives: % 80.60/16.04 | | | | | | | | | | | | | | | | (508) all_428_1 = all_416_1 % 80.60/16.04 | | | | | | | | | | | | | | | | % 80.60/16.04 | | | | | | | | | | | | | | | | COMBINE_EQS: (506), (508) imply: % 80.60/16.04 | | | | | | | | | | | | | | | | (509) all_426_1 = all_416_1 % 80.60/16.04 | | | | | | | | | | | | | | | | % 80.60/16.04 | | | | | | | | | | | | | | | | COMBINE_EQS: (506), (507) imply: % 80.60/16.04 | | | | | | | | | | | | | | | | (510) all_426_1 = all_424_1 % 80.60/16.04 | | | | | | | | | | | | | | | | % 80.60/16.04 | | | | | | | | | | | | | | | | COMBINE_EQS: (509), (510) imply: % 80.60/16.04 | | | | | | | | | | | | | | | | (511) all_424_1 = all_416_1 % 80.60/16.04 | | | | | | | | | | | | | | | | % 80.60/16.04 | | | | | | | | | | | | | | | | SIMP: (511) implies: % 80.60/16.04 | | | | | | | | | | | | | | | | (512) all_424_1 = all_416_1 % 80.60/16.04 | | | | | | | | | | | | | | | | % 80.60/16.04 | | | | | | | | | | | | | | | | COMBINE_EQS: (504), (505) imply: % 80.60/16.04 | | | | | | | | | | | | | | | | (513) all_420_1 = all_190_1 % 80.60/16.04 | | | | | | | | | | | | | | | | % 80.60/16.04 | | | | | | | | | | | | | | | | COMBINE_EQS: (505), (512) imply: % 80.60/16.04 | | | | | | | | | | | | | | | | (514) all_420_1 = all_416_1 % 80.60/16.04 | | | | | | | | | | | | | | | | % 80.60/16.04 | | | | | | | | | | | | | | | | COMBINE_EQS: (513), (514) imply: % 80.60/16.04 | | | | | | | | | | | | | | | | (515) all_416_1 = all_190_1 % 80.60/16.04 | | | | | | | | | | | | | | | | % 80.60/16.04 | | | | | | | | | | | | | | | | REDUCE: (484), (513) imply: % 80.60/16.04 | | | | | | | | | | | | | | | | (516) element(all_82_2, all_190_1) = all_420_0 % 80.60/16.04 | | | | | | | | | | | | | | | | % 80.60/16.04 | | | | | | | | | | | | | | | | REDUCE: (480), (515) imply: % 80.60/16.04 | | | | | | | | | | | | | | | | (517) $i(all_190_1) % 80.60/16.04 | | | | | | | | | | | | | | | | % 80.60/16.04 | | | | | | | | | | | | | | | | BETA: splitting (231) gives: % 80.60/16.04 | | | | | | | | | | | | | | | | % 80.60/16.04 | | | | | | | | | | | | | | | | Case 1: % 80.60/16.04 | | | | | | | | | | | | | | | | | % 80.60/16.04 | | | | | | | | | | | | | | | | | (518) ~ (all_116_2 = 0) % 80.60/16.04 | | | | | | | | | | | | | | | | | % 80.60/16.04 | | | | | | | | | | | | | | | | | BETA: splitting (232) gives: % 80.60/16.04 | | | | | | | | | | | | | | | | | % 80.60/16.04 | | | | | | | | | | | | | | | | | Case 1: % 80.60/16.04 | | | | | | | | | | | | | | | | | | % 80.60/16.04 | | | | | | | | | | | | | | | | | | (519) ~ (all_116_0 = 0) % 80.60/16.04 | | | | | | | | | | | | | | | | | | % 80.60/16.04 | | | | | | | | | | | | | | | | | | BETA: splitting (305) gives: % 80.60/16.04 | | | | | | | | | | | | | | | | | | % 80.60/16.04 | | | | | | | | | | | | | | | | | | Case 1: % 80.60/16.04 | | | | | | | | | | | | | | | | | | | % 80.60/16.04 | | | | | | | | | | | | | | | | | | | (520) all_116_0 = 0 % 80.60/16.04 | | | | | | | | | | | | | | | | | | | % 80.60/16.04 | | | | | | | | | | | | | | | | | | | REDUCE: (519), (520) imply: % 80.60/16.04 | | | | | | | | | | | | | | | | | | | (521) $false % 80.60/16.04 | | | | | | | | | | | | | | | | | | | % 80.60/16.04 | | | | | | | | | | | | | | | | | | | CLOSE: (521) is inconsistent. % 80.60/16.04 | | | | | | | | | | | | | | | | | | | % 80.60/16.04 | | | | | | | | | | | | | | | | | | Case 2: % 80.60/16.04 | | | | | | | | | | | | | | | | | | | % 80.60/16.04 | | | | | | | | | | | | | | | | | | | (522) ? [v0: any] : ? [v1: any] : (empty(all_56_1) = % 80.60/16.04 | | | | | | | | | | | | | | | | | | | v1 & element(all_116_1, all_56_1) = v0 & ( ~ (v0 % 80.60/16.04 | | | | | | | | | | | | | | | | | | | = 0) | v1 = 0)) % 81.04/16.04 | | | | | | | | | | | | | | | | | | | % 81.04/16.04 | | | | | | | | | | | | | | | | | | | DELTA: instantiating (522) with fresh symbols all_596_0, % 81.04/16.04 | | | | | | | | | | | | | | | | | | | all_596_1 gives: % 81.04/16.04 | | | | | | | | | | | | | | | | | | | (523) empty(all_56_1) = all_596_0 & element(all_116_1, % 81.04/16.04 | | | | | | | | | | | | | | | | | | | all_56_1) = all_596_1 & ( ~ (all_596_1 = 0) | % 81.04/16.04 | | | | | | | | | | | | | | | | | | | all_596_0 = 0) % 81.04/16.04 | | | | | | | | | | | | | | | | | | | % 81.04/16.04 | | | | | | | | | | | | | | | | | | | ALPHA: (523) implies: % 81.04/16.04 | | | | | | | | | | | | | | | | | | | (524) element(all_116_1, all_56_1) = all_596_1 % 81.04/16.04 | | | | | | | | | | | | | | | | | | | (525) empty(all_56_1) = all_596_0 % 81.04/16.04 | | | | | | | | | | | | | | | | | | | (526) ~ (all_596_1 = 0) | all_596_0 = 0 % 81.04/16.04 | | | | | | | | | | | | | | | | | | | % 81.04/16.04 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (32) with all_182_0, all_596_0, % 81.04/16.04 | | | | | | | | | | | | | | | | | | | all_56_1, simplifying with (334), (525) gives: % 81.04/16.04 | | | | | | | | | | | | | | | | | | | (527) all_596_0 = all_182_0 % 81.04/16.04 | | | | | | | | | | | | | | | | | | | % 81.04/16.04 | | | | | | | | | | | | | | | | | | | BETA: splitting (526) gives: % 81.04/16.04 | | | | | | | | | | | | | | | | | | | % 81.04/16.04 | | | | | | | | | | | | | | | | | | | Case 1: % 81.04/16.04 | | | | | | | | | | | | | | | | | | | | % 81.04/16.04 | | | | | | | | | | | | | | | | | | | | (528) ~ (all_596_1 = 0) % 81.04/16.04 | | | | | | | | | | | | | | | | | | | | % 81.04/16.04 | | | | | | | | | | | | | | | | | | | | BETA: splitting (242) gives: % 81.04/16.04 | | | | | | | | | | | | | | | | | | | | % 81.04/16.04 | | | | | | | | | | | | | | | | | | | | Case 1: % 81.04/16.04 | | | | | | | | | | | | | | | | | | | | | % 81.04/16.04 | | | | | | | | | | | | | | | | | | | | | (529) ~ (all_122_2 = 0) % 81.04/16.04 | | | | | | | | | | | | | | | | | | | | | % 81.04/16.04 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (243) gives: % 81.04/16.04 | | | | | | | | | | | | | | | | | | | | | % 81.04/16.04 | | | | | | | | | | | | | | | | | | | | | Case 1: % 81.04/16.04 | | | | | | | | | | | | | | | | | | | | | | % 81.04/16.04 | | | | | | | | | | | | | | | | | | | | | | (530) ~ (all_122_0 = 0) % 81.04/16.04 | | | | | | | | | | | | | | | | | | | | | | % 81.04/16.04 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (306) gives: % 81.04/16.04 | | | | | | | | | | | | | | | | | | | | | | % 81.04/16.04 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 81.04/16.04 | | | | | | | | | | | | | | | | | | | | | | | % 81.04/16.04 | | | | | | | | | | | | | | | | | | | | | | | (531) all_122_0 = 0 % 81.04/16.04 | | | | | | | | | | | | | | | | | | | | | | | % 81.04/16.04 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (530), (531) imply: % 81.04/16.04 | | | | | | | | | | | | | | | | | | | | | | | (532) $false % 81.04/16.04 | | | | | | | | | | | | | | | | | | | | | | | % 81.04/16.04 | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (532) is inconsistent. % 81.04/16.04 | | | | | | | | | | | | | | | | | | | | | | | % 81.04/16.04 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 81.04/16.04 | | | | | | | | | | | | | | | | | | | | | | | % 81.04/16.04 | | | | | | | | | | | | | | | | | | | | | | | (533) ? [v0: any] : ? [v1: any] : (empty(all_56_1) = % 81.04/16.04 | | | | | | | | | | | | | | | | | | | | | | | v1 & element(all_122_1, all_56_1) = v0 & ( ~ (v0 % 81.04/16.04 | | | | | | | | | | | | | | | | | | | | | | | = 0) | v1 = 0)) % 81.04/16.04 | | | | | | | | | | | | | | | | | | | | | | | % 81.04/16.04 | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (533) with fresh symbols all_644_0, % 81.04/16.04 | | | | | | | | | | | | | | | | | | | | | | | all_644_1 gives: % 81.04/16.04 | | | | | | | | | | | | | | | | | | | | | | | (534) empty(all_56_1) = all_644_0 & element(all_122_1, % 81.04/16.04 | | | | | | | | | | | | | | | | | | | | | | | all_56_1) = all_644_1 & ( ~ (all_644_1 = 0) | % 81.04/16.04 | | | | | | | | | | | | | | | | | | | | | | | all_644_0 = 0) % 81.04/16.04 | | | | | | | | | | | | | | | | | | | | | | | % 81.04/16.04 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (534) implies: % 81.04/16.04 | | | | | | | | | | | | | | | | | | | | | | | (535) empty(all_56_1) = all_644_0 % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | (536) ~ (all_644_1 = 0) | all_644_0 = 0 % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (32) with all_182_0, all_644_0, % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | all_56_1, simplifying with (334), (535) gives: % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | (537) all_644_0 = all_182_0 % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (536) gives: % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (10) with all_56_1, all_42_4, % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | all_42_3, all_42_2, all_42_1, all_110_1, % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | all_108_1, simplifying with (50), (51), (52), % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | (53), (194), (215), (219), (274), (294), (299), % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | (454) gives: % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | (538) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | [v3: $i] : ? [v4: any] : (ordered_pair(all_42_3, % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | all_42_1) = v3 & in(v3, all_56_1) = v4 & % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | in(all_42_1, all_42_4) = v2 & in(all_42_2, % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | all_42_4) = v1 & in(all_42_3, all_42_4) = v0 & % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | $i(v3) & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | 0) | v4 = 0)) % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (9) with all_56_1, all_42_4, % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | all_42_3, all_42_2, all_42_1, all_108_1, % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (50), (51), (52), (53), (194), % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | (215), (274), (299), (451), (454) gives: % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | (539) ? [v0: any] : ? [v1: any] : ? [v2: $i] : ? % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | [v3: any] : ? [v4: $i] : ? [v5: any] : % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | (ordered_pair(all_42_3, all_42_1) = v4 & % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | ordered_pair(all_42_3, all_42_2) = v2 & in(v4, % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | all_56_1) = v5 & in(v2, all_56_1) = v3 & % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | in(all_42_1, all_42_4) = v1 & in(all_42_2, % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | all_42_4) = v0 & $i(v4) & $i(v2) & ( ~ (v3 = % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | 0) | ~ (v1 = 0) | ~ (v0 = 0) | v5 = 0)) % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (8) with all_56_1, all_42_4, % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | all_42_3, all_42_2, all_42_1, all_110_1, % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (50), (51), (52), (53), (194), % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | (219), (274), (294), (447), (454) gives: % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | (540) ? [v0: any] : ? [v1: any] : ? [v2: $i] : ? % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | [v3: any] : ? [v4: $i] : ? [v5: any] : % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | (ordered_pair(all_42_2, all_42_1) = v2 & % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | ordered_pair(all_42_3, all_42_1) = v4 & in(v4, % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | all_56_1) = v5 & in(v2, all_56_1) = v3 & % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | in(all_42_2, all_42_4) = v1 & in(all_42_3, % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | all_42_4) = v0 & $i(v4) & $i(v2) & ( ~ (v3 = % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | 0) | ~ (v1 = 0) | ~ (v0 = 0) | v5 = 0)) % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (7) with all_56_1, all_42_4, % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | all_42_3, all_42_2, all_42_1, simplifying with % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | (50), (51), (52), (53), (194), (274), (447), % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | (449), (451), (454) gives: % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | (541) ? [v0: $i] : ? [v1: any] : ? [v2: $i] : ? [v3: % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | any] : ? [v4: $i] : ? [v5: any] : % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | (ordered_pair(all_42_2, all_42_1) = v2 & % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | ordered_pair(all_42_3, all_42_1) = v4 & % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | ordered_pair(all_42_3, all_42_2) = v0 & in(v4, % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | all_56_1) = v5 & in(v2, all_56_1) = v3 & % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | in(v0, all_56_1) = v1 & $i(v4) & $i(v2) & $i(v0) % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | & ( ~ (v3 = 0) | ~ (v1 = 0) | v5 = 0)) % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with all_198_1, all_398_0, % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (358), (478) gives: % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | (542) all_398_0 = 0 | ? [v0: $i] : ? [v1: $i] : ? % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | [v2: int] : ( ~ (v2 = 0) & empty(v1) = v2 & % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | powerset(all_198_1) = v0 & element(v1, v0) = 0 & % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | $i(v1) & $i(v0)) % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (538) with fresh symbols all_862_0, % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | all_862_1, all_862_2, all_862_3, all_862_4 gives: % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | (543) ordered_pair(all_42_3, all_42_1) = all_862_1 & % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | in(all_862_1, all_56_1) = all_862_0 & in(all_42_1, % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | all_42_4) = all_862_2 & in(all_42_2, all_42_4) = % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | all_862_3 & in(all_42_3, all_42_4) = all_862_4 & % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_862_1) & ( ~ (all_862_2 = 0) | ~ % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | (all_862_3 = 0) | ~ (all_862_4 = 0) | all_862_0 % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | = 0) % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (543) implies: % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | (544) in(all_42_3, all_42_4) = all_862_4 % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | (545) in(all_42_2, all_42_4) = all_862_3 % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | (546) in(all_42_1, all_42_4) = all_862_2 % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | (547) in(all_862_1, all_56_1) = all_862_0 % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | (548) ordered_pair(all_42_3, all_42_1) = all_862_1 % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | (549) ~ (all_862_2 = 0) | ~ (all_862_3 = 0) | ~ % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | (all_862_4 = 0) | all_862_0 = 0 % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (541) with fresh symbols all_864_0, % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | all_864_1, all_864_2, all_864_3, all_864_4, % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | all_864_5 gives: % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | (550) ordered_pair(all_42_2, all_42_1) = all_864_3 & % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | ordered_pair(all_42_3, all_42_1) = all_864_1 & % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | ordered_pair(all_42_3, all_42_2) = all_864_5 & % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | in(all_864_1, all_56_1) = all_864_0 & % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | in(all_864_3, all_56_1) = all_864_2 & % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | in(all_864_5, all_56_1) = all_864_4 & % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_864_1) & $i(all_864_3) & $i(all_864_5) & ( % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_864_2 = 0) | ~ (all_864_4 = 0) | % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | all_864_0 = 0) % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (550) implies: % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | (551) in(all_864_1, all_56_1) = all_864_0 % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | (552) ordered_pair(all_42_3, all_42_1) = all_864_1 % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (539) with fresh symbols all_866_0, % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | all_866_1, all_866_2, all_866_3, all_866_4, % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | all_866_5 gives: % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | (553) ordered_pair(all_42_3, all_42_1) = all_866_1 & % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | ordered_pair(all_42_3, all_42_2) = all_866_3 & % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | in(all_866_1, all_56_1) = all_866_0 & % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | in(all_866_3, all_56_1) = all_866_2 & in(all_42_1, % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | all_42_4) = all_866_4 & in(all_42_2, all_42_4) = % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | all_866_5 & $i(all_866_1) & $i(all_866_3) & ( ~ % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | (all_866_2 = 0) | ~ (all_866_4 = 0) | ~ % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | (all_866_5 = 0) | all_866_0 = 0) % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (553) implies: % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | (554) in(all_42_2, all_42_4) = all_866_5 % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | (555) in(all_42_1, all_42_4) = all_866_4 % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | (556) in(all_866_1, all_56_1) = all_866_0 % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | (557) ordered_pair(all_42_3, all_42_1) = all_866_1 % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (540) with fresh symbols all_868_0, % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | all_868_1, all_868_2, all_868_3, all_868_4, % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | all_868_5 gives: % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | (558) ordered_pair(all_42_2, all_42_1) = all_868_3 & % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | ordered_pair(all_42_3, all_42_1) = all_868_1 & % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | in(all_868_1, all_56_1) = all_868_0 & % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | in(all_868_3, all_56_1) = all_868_2 & in(all_42_2, % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | all_42_4) = all_868_4 & in(all_42_3, all_42_4) = % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | all_868_5 & $i(all_868_1) & $i(all_868_3) & ( ~ % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | (all_868_2 = 0) | ~ (all_868_4 = 0) | ~ % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | (all_868_5 = 0) | all_868_0 = 0) % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (558) implies: % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | (559) in(all_42_3, all_42_4) = all_868_5 % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | (560) in(all_42_2, all_42_4) = all_868_4 % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | (561) in(all_868_1, all_56_1) = all_868_0 % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | (562) ordered_pair(all_42_3, all_42_1) = all_868_1 % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (542) gives: % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | | % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | | (563) all_398_0 = 0 % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | | % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (477), (563) imply: % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | | (564) $false % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | | % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (564) is inconsistent. % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | | % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | | % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | | % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (33) with 0, all_868_5, all_42_4, % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | | all_42_3, simplifying with (451), (559) gives: % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | | (565) all_868_5 = 0 % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | | % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (33) with all_862_4, all_868_5, % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | | all_42_4, all_42_3, simplifying with (544), (559) % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | | (566) all_868_5 = all_862_4 % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | | % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (33) with 0, all_868_4, all_42_4, % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | | all_42_2, simplifying with (449), (560) gives: % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | | (567) all_868_4 = 0 % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | | % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (33) with all_866_5, all_868_4, % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | | all_42_4, all_42_2, simplifying with (554), (560) % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | | (568) all_868_4 = all_866_5 % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | | % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (33) with all_862_3, all_868_4, % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | | all_42_4, all_42_2, simplifying with (545), (560) % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | | (569) all_868_4 = all_862_3 % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | | % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (33) with 0, all_866_4, all_42_4, % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | | all_42_1, simplifying with (447), (555) gives: % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | | (570) all_866_4 = 0 % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | | % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (33) with all_862_2, all_866_4, % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | | all_42_4, all_42_1, simplifying with (546), (555) % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | | (571) all_866_4 = all_862_2 % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | | % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (35) with all_114_1, all_864_1, % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | | all_42_1, all_42_3, simplifying with (225), (552) % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | | (572) all_864_1 = all_114_1 % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | | % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (35) with all_866_1, all_868_1, % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | | all_42_1, all_42_3, simplifying with (557), (562) % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | | (573) all_868_1 = all_866_1 % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | | % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (35) with all_864_1, all_868_1, % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | | all_42_1, all_42_3, simplifying with (552), (562) % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | | (574) all_868_1 = all_864_1 % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | | % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (35) with all_862_1, all_868_1, % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | | all_42_1, all_42_3, simplifying with (548), (562) % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | | (575) all_868_1 = all_862_1 % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | | % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (573), (574) imply: % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | | (576) all_866_1 = all_864_1 % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | | % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (573), (575) imply: % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | | (577) all_866_1 = all_862_1 % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | | % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (567), (568) imply: % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | | (578) all_866_5 = 0 % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | | % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (568), (569) imply: % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | | (579) all_866_5 = all_862_3 % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | | % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (565), (566) imply: % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | | (580) all_862_4 = 0 % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | | % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (580) implies: % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | | (581) all_862_4 = 0 % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | | % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (576), (577) imply: % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | | (582) all_864_1 = all_862_1 % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | | % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (582) implies: % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | | (583) all_864_1 = all_862_1 % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | | % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (570), (571) imply: % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | | (584) all_862_2 = 0 % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | | % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (584) implies: % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | | (585) all_862_2 = 0 % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | | % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (578), (579) imply: % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | | (586) all_862_3 = 0 % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | | % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (572), (583) imply: % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | | (587) all_862_1 = all_114_1 % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | | % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (587) implies: % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | | (588) all_862_1 = all_114_1 % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | | % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (577), (588) imply: % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | | (589) all_866_1 = all_114_1 % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | | % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (573), (589) imply: % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | | (590) all_868_1 = all_114_1 % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | | % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (561), (590) imply: % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | | (591) in(all_114_1, all_56_1) = all_868_0 % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | | % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (556), (589) imply: % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | | (592) in(all_114_1, all_56_1) = all_866_0 % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | | % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (551), (572) imply: % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | | (593) in(all_114_1, all_56_1) = all_864_0 % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | | % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (547), (588) imply: % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | | (594) in(all_114_1, all_56_1) = all_862_0 % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | | % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (549) gives: % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | | % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | | | % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | | | (595) ~ (all_862_2 = 0) % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | | | % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (585), (595) imply: % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | | | (596) $false % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | | | % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (596) is inconsistent. % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | | | % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | | | % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | | | (597) ~ (all_862_3 = 0) | ~ (all_862_4 = 0) | % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | | | all_862_0 = 0 % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | | | % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (597) gives: % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | | | % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | (598) ~ (all_862_3 = 0) % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (586), (598) imply: % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | (599) $false % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (599) is inconsistent. % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | (600) ~ (all_862_4 = 0) | all_862_0 = 0 % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (600) gives: % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (601) ~ (all_862_4 = 0) % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (581), (601) imply: % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (602) $false % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (602) is inconsistent. % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (603) all_862_0 = 0 % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (594), (603) imply: % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (604) in(all_114_1, all_56_1) = 0 % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (33) with all_114_0, all_866_0, % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_1, all_114_1, simplifying with (269), (592) % 81.04/16.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (605) all_866_0 = all_114_0 % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (33) with 0, all_866_0, all_56_1, % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_114_1, simplifying with (592), (604) gives: % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (606) all_866_0 = 0 % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (33) with all_866_0, all_868_0, % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_1, all_114_1, simplifying with (591), (592) % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (607) all_868_0 = all_866_0 % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (33) with all_864_0, all_868_0, % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_1, all_114_1, simplifying with (591), (593) % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (608) all_868_0 = all_864_0 % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (607), (608) imply: % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (609) all_866_0 = all_864_0 % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (609) implies: % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (610) all_866_0 = all_864_0 % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (605), (610) imply: % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (611) all_864_0 = all_114_0 % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (606), (610) imply: % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (612) all_864_0 = 0 % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (611), (612) imply: % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (613) all_114_0 = 0 % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (301), (613) imply: % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (614) $false % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (614) is inconsistent. % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | | | | | | % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | | | | | % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | | | | % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | | | | % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | | | | (615) all_644_0 = 0 % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | | | | % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (537), (615) imply: % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | | | | (616) all_182_0 = 0 % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | | | | % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (333), (616) imply: % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | | | | (617) $false % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | | | | % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (617) is inconsistent. % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | | | | % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | | | End of split % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | | | % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | | End of split % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | | % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | Case 2: % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | | % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | | (618) all_122_2 = 0 % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | | % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (529), (618) imply: % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | | (619) $false % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | | % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | | CLOSE: (619) is inconsistent. % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | | % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | End of split % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | Case 2: % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (10) with all_56_1, all_42_4, % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | all_42_3, all_42_2, all_42_1, all_110_1, % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | all_108_1, simplifying with (50), (51), (52), % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | (53), (194), (215), (219), (274), (294), (299), % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | (454) gives: % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | (620) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | [v3: $i] : ? [v4: any] : (ordered_pair(all_42_3, % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | all_42_1) = v3 & in(v3, all_56_1) = v4 & % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | in(all_42_1, all_42_4) = v2 & in(all_42_2, % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | all_42_4) = v1 & in(all_42_3, all_42_4) = v0 & % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | $i(v3) & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | 0) | v4 = 0)) % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (9) with all_56_1, all_42_4, % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | all_42_3, all_42_2, all_42_1, all_108_1, % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | simplifying with (50), (51), (52), (53), (194), % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | (215), (274), (299), (451), (454) gives: % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | (621) ? [v0: any] : ? [v1: any] : ? [v2: $i] : ? % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | [v3: any] : ? [v4: $i] : ? [v5: any] : % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | (ordered_pair(all_42_3, all_42_1) = v4 & % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | ordered_pair(all_42_3, all_42_2) = v2 & in(v4, % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | all_56_1) = v5 & in(v2, all_56_1) = v3 & % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | in(all_42_1, all_42_4) = v1 & in(all_42_2, % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | all_42_4) = v0 & $i(v4) & $i(v2) & ( ~ (v3 = % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | 0) | ~ (v1 = 0) | ~ (v0 = 0) | v5 = 0)) % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (8) with all_56_1, all_42_4, % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | all_42_3, all_42_2, all_42_1, all_110_1, % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | simplifying with (50), (51), (52), (53), (194), % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | (219), (274), (294), (447), (454) gives: % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | (622) ? [v0: any] : ? [v1: any] : ? [v2: $i] : ? % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | [v3: any] : ? [v4: $i] : ? [v5: any] : % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | (ordered_pair(all_42_2, all_42_1) = v2 & % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | ordered_pair(all_42_3, all_42_1) = v4 & in(v4, % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | all_56_1) = v5 & in(v2, all_56_1) = v3 & % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | in(all_42_2, all_42_4) = v1 & in(all_42_3, % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | all_42_4) = v0 & $i(v4) & $i(v2) & ( ~ (v3 = % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | 0) | ~ (v1 = 0) | ~ (v0 = 0) | v5 = 0)) % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (7) with all_56_1, all_42_4, % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | all_42_3, all_42_2, all_42_1, simplifying with % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | (50), (51), (52), (53), (194), (274), (447), % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | (449), (451), (454) gives: % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | (623) ? [v0: $i] : ? [v1: any] : ? [v2: $i] : ? [v3: % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | any] : ? [v4: $i] : ? [v5: any] : % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | (ordered_pair(all_42_2, all_42_1) = v2 & % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | ordered_pair(all_42_3, all_42_1) = v4 & % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | ordered_pair(all_42_3, all_42_2) = v0 & in(v4, % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | all_56_1) = v5 & in(v2, all_56_1) = v3 & % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | in(v0, all_56_1) = v1 & $i(v4) & $i(v2) & $i(v0) % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | & ( ~ (v3 = 0) | ~ (v1 = 0) | v5 = 0)) % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (23) with all_116_1, all_480_1, % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | all_56_1, all_480_2, all_596_1, simplifying with % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | (194), (227), (499), (500), (501), (524) gives: % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | (624) all_596_1 = 0 | ? [v0: int] : ( ~ (v0 = 0) & % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | in(all_116_1, all_480_1) = v0) % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (620) with fresh symbols all_846_0, % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | all_846_1, all_846_2, all_846_3, all_846_4 gives: % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | (625) ordered_pair(all_42_3, all_42_1) = all_846_1 & % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | in(all_846_1, all_56_1) = all_846_0 & in(all_42_1, % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | all_42_4) = all_846_2 & in(all_42_2, all_42_4) = % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | all_846_3 & in(all_42_3, all_42_4) = all_846_4 & % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | $i(all_846_1) & ( ~ (all_846_2 = 0) | ~ % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | (all_846_3 = 0) | ~ (all_846_4 = 0) | all_846_0 % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | = 0) % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | ALPHA: (625) implies: % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | (626) in(all_42_3, all_42_4) = all_846_4 % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | (627) in(all_42_2, all_42_4) = all_846_3 % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | (628) in(all_42_1, all_42_4) = all_846_2 % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | (629) in(all_846_1, all_56_1) = all_846_0 % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | (630) ordered_pair(all_42_3, all_42_1) = all_846_1 % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | (631) ~ (all_846_2 = 0) | ~ (all_846_3 = 0) | ~ % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | (all_846_4 = 0) | all_846_0 = 0 % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (623) with fresh symbols all_848_0, % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | all_848_1, all_848_2, all_848_3, all_848_4, % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | all_848_5 gives: % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | (632) ordered_pair(all_42_2, all_42_1) = all_848_3 & % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | ordered_pair(all_42_3, all_42_1) = all_848_1 & % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | ordered_pair(all_42_3, all_42_2) = all_848_5 & % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | in(all_848_1, all_56_1) = all_848_0 & % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | in(all_848_3, all_56_1) = all_848_2 & % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | in(all_848_5, all_56_1) = all_848_4 & % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | $i(all_848_1) & $i(all_848_3) & $i(all_848_5) & ( % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | ~ (all_848_2 = 0) | ~ (all_848_4 = 0) | % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | all_848_0 = 0) % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | ALPHA: (632) implies: % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | (633) in(all_848_1, all_56_1) = all_848_0 % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | (634) ordered_pair(all_42_3, all_42_1) = all_848_1 % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (622) with fresh symbols all_850_0, % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | all_850_1, all_850_2, all_850_3, all_850_4, % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | all_850_5 gives: % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | (635) ordered_pair(all_42_2, all_42_1) = all_850_3 & % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | ordered_pair(all_42_3, all_42_1) = all_850_1 & % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | in(all_850_1, all_56_1) = all_850_0 & % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | in(all_850_3, all_56_1) = all_850_2 & in(all_42_2, % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | all_42_4) = all_850_4 & in(all_42_3, all_42_4) = % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | all_850_5 & $i(all_850_1) & $i(all_850_3) & ( ~ % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | (all_850_2 = 0) | ~ (all_850_4 = 0) | ~ % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | (all_850_5 = 0) | all_850_0 = 0) % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | ALPHA: (635) implies: % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | (636) in(all_42_3, all_42_4) = all_850_5 % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | (637) in(all_42_2, all_42_4) = all_850_4 % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | (638) in(all_850_1, all_56_1) = all_850_0 % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | (639) ordered_pair(all_42_3, all_42_1) = all_850_1 % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (621) with fresh symbols all_852_0, % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | all_852_1, all_852_2, all_852_3, all_852_4, % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | all_852_5 gives: % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | (640) ordered_pair(all_42_3, all_42_1) = all_852_1 & % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | ordered_pair(all_42_3, all_42_2) = all_852_3 & % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | in(all_852_1, all_56_1) = all_852_0 & % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | in(all_852_3, all_56_1) = all_852_2 & in(all_42_1, % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | all_42_4) = all_852_4 & in(all_42_2, all_42_4) = % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | all_852_5 & $i(all_852_1) & $i(all_852_3) & ( ~ % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | (all_852_2 = 0) | ~ (all_852_4 = 0) | ~ % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | (all_852_5 = 0) | all_852_0 = 0) % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | ALPHA: (640) implies: % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | (641) in(all_42_2, all_42_4) = all_852_5 % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | (642) in(all_42_1, all_42_4) = all_852_4 % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | (643) in(all_852_1, all_56_1) = all_852_0 % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | (644) ordered_pair(all_42_3, all_42_1) = all_852_1 % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (624) gives: % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | Case 1: % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | | % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | | (645) all_596_1 = 0 % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | | % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (528), (645) imply: % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | | (646) $false % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | | % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | | CLOSE: (646) is inconsistent. % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | | % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | Case 2: % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | | % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | | % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (33) with 0, all_850_5, all_42_4, % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | | all_42_3, simplifying with (451), (636) gives: % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | | (647) all_850_5 = 0 % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | | % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (33) with all_846_4, all_850_5, % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | | all_42_4, all_42_3, simplifying with (626), (636) % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | | gives: % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | | (648) all_850_5 = all_846_4 % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | | % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (33) with 0, all_852_5, all_42_4, % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | | all_42_2, simplifying with (449), (641) gives: % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | | (649) all_852_5 = 0 % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | | % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (33) with all_850_4, all_852_5, % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | | all_42_4, all_42_2, simplifying with (637), (641) % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | | gives: % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | | (650) all_852_5 = all_850_4 % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | | % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (33) with all_846_3, all_852_5, % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | | all_42_4, all_42_2, simplifying with (627), (641) % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | | gives: % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | | (651) all_852_5 = all_846_3 % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | | % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (33) with 0, all_852_4, all_42_4, % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | | all_42_1, simplifying with (447), (642) gives: % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | | (652) all_852_4 = 0 % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | | % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (33) with all_846_2, all_852_4, % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | | all_42_4, all_42_1, simplifying with (628), (642) % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | | gives: % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | | (653) all_852_4 = all_846_2 % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | | % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (35) with all_114_1, all_848_1, % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | | all_42_1, all_42_3, simplifying with (225), (634) % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | | gives: % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | | (654) all_848_1 = all_114_1 % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | | % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (35) with all_850_1, all_852_1, % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | | all_42_1, all_42_3, simplifying with (639), (644) % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | | gives: % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | | (655) all_852_1 = all_850_1 % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | | % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (35) with all_848_1, all_852_1, % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | | all_42_1, all_42_3, simplifying with (634), (644) % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | | gives: % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | | (656) all_852_1 = all_848_1 % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | | % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (35) with all_846_1, all_852_1, % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | | all_42_1, all_42_3, simplifying with (630), (644) % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | | gives: % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | | (657) all_852_1 = all_846_1 % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | | % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (655), (656) imply: % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | | (658) all_850_1 = all_848_1 % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | | % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (655), (657) imply: % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | | (659) all_850_1 = all_846_1 % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | | % 81.04/16.06 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (652), (653) imply: % 81.04/16.07 | | | | | | | | | | | | | | | | | | | | | | (660) all_846_2 = 0 % 81.04/16.07 | | | | | | | | | | | | | | | | | | | | | | % 81.04/16.07 | | | | | | | | | | | | | | | | | | | | | | SIMP: (660) implies: % 81.04/16.07 | | | | | | | | | | | | | | | | | | | | | | (661) all_846_2 = 0 % 81.04/16.07 | | | | | | | | | | | | | | | | | | | | | | % 81.04/16.07 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (649), (650) imply: % 81.04/16.07 | | | | | | | | | | | | | | | | | | | | | | (662) all_850_4 = 0 % 81.04/16.07 | | | | | | | | | | | | | | | | | | | | | | % 81.04/16.07 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (650), (651) imply: % 81.04/16.07 | | | | | | | | | | | | | | | | | | | | | | (663) all_850_4 = all_846_3 % 81.04/16.07 | | | | | | | | | | | | | | | | | | | | | | % 81.04/16.07 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (658), (659) imply: % 81.04/16.07 | | | | | | | | | | | | | | | | | | | | | | (664) all_848_1 = all_846_1 % 81.04/16.07 | | | | | | | | | | | | | | | | | | | | | | % 81.04/16.07 | | | | | | | | | | | | | | | | | | | | | | SIMP: (664) implies: % 81.04/16.07 | | | | | | | | | | | | | | | | | | | | | | (665) all_848_1 = all_846_1 % 81.04/16.07 | | | | | | | | | | | | | | | | | | | | | | % 81.04/16.07 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (662), (663) imply: % 81.04/16.07 | | | | | | | | | | | | | | | | | | | | | | (666) all_846_3 = 0 % 81.04/16.07 | | | | | | | | | | | | | | | | | | | | | | % 81.04/16.07 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (647), (648) imply: % 81.04/16.07 | | | | | | | | | | | | | | | | | | | | | | (667) all_846_4 = 0 % 81.04/16.07 | | | | | | | | | | | | | | | | | | | | | | % 81.04/16.07 | | | | | | | | | | | | | | | | | | | | | | SIMP: (667) implies: % 81.04/16.07 | | | | | | | | | | | | | | | | | | | | | | (668) all_846_4 = 0 % 81.04/16.07 | | | | | | | | | | | | | | | | | | | | | | % 81.04/16.07 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (654), (665) imply: % 81.04/16.07 | | | | | | | | | | | | | | | | | | | | | | (669) all_846_1 = all_114_1 % 81.04/16.07 | | | | | | | | | | | | | | | | | | | | | | % 81.04/16.07 | | | | | | | | | | | | | | | | | | | | | | SIMP: (669) implies: % 81.04/16.07 | | | | | | | | | | | | | | | | | | | | | | (670) all_846_1 = all_114_1 % 81.04/16.07 | | | | | | | | | | | | | | | | | | | | | | % 81.04/16.07 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (659), (670) imply: % 81.04/16.07 | | | | | | | | | | | | | | | | | | | | | | (671) all_850_1 = all_114_1 % 81.04/16.07 | | | | | | | | | | | | | | | | | | | | | | % 81.04/16.07 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (655), (671) imply: % 81.04/16.07 | | | | | | | | | | | | | | | | | | | | | | (672) all_852_1 = all_114_1 % 81.04/16.07 | | | | | | | | | | | | | | | | | | | | | | % 81.04/16.07 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (643), (672) imply: % 81.04/16.07 | | | | | | | | | | | | | | | | | | | | | | (673) in(all_114_1, all_56_1) = all_852_0 % 81.04/16.07 | | | | | | | | | | | | | | | | | | | | | | % 81.04/16.07 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (638), (671) imply: % 81.04/16.07 | | | | | | | | | | | | | | | | | | | | | | (674) in(all_114_1, all_56_1) = all_850_0 % 81.04/16.07 | | | | | | | | | | | | | | | | | | | | | | % 81.04/16.07 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (633), (654) imply: % 81.04/16.07 | | | | | | | | | | | | | | | | | | | | | | (675) in(all_114_1, all_56_1) = all_848_0 % 81.04/16.07 | | | | | | | | | | | | | | | | | | | | | | % 81.04/16.07 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (629), (670) imply: % 81.04/16.07 | | | | | | | | | | | | | | | | | | | | | | (676) in(all_114_1, all_56_1) = all_846_0 % 81.04/16.07 | | | | | | | | | | | | | | | | | | | | | | % 81.04/16.07 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (631) gives: % 81.04/16.07 | | | | | | | | | | | | | | | | | | | | | | % 81.04/16.07 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 81.04/16.07 | | | | | | | | | | | | | | | | | | | | | | | % 81.04/16.07 | | | | | | | | | | | | | | | | | | | | | | | (677) ~ (all_846_2 = 0) % 81.04/16.07 | | | | | | | | | | | | | | | | | | | | | | | % 81.04/16.07 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (661), (677) imply: % 81.04/16.07 | | | | | | | | | | | | | | | | | | | | | | | (678) $false % 81.04/16.07 | | | | | | | | | | | | | | | | | | | | | | | % 81.04/16.07 | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (678) is inconsistent. % 81.04/16.07 | | | | | | | | | | | | | | | | | | | | | | | % 81.04/16.07 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 81.04/16.07 | | | | | | | | | | | | | | | | | | | | | | | % 81.04/16.07 | | | | | | | | | | | | | | | | | | | | | | | (679) ~ (all_846_3 = 0) | ~ (all_846_4 = 0) | % 81.04/16.07 | | | | | | | | | | | | | | | | | | | | | | | all_846_0 = 0 % 81.04/16.07 | | | | | | | | | | | | | | | | | | | | | | | % 81.04/16.07 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (679) gives: % 81.04/16.07 | | | | | | | | | | | | | | | | | | | | | | | % 81.04/16.07 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 81.04/16.07 | | | | | | | | | | | | | | | | | | | | | | | | % 81.04/16.07 | | | | | | | | | | | | | | | | | | | | | | | | (680) ~ (all_846_3 = 0) % 81.04/16.07 | | | | | | | | | | | | | | | | | | | | | | | | % 81.04/16.07 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (666), (680) imply: % 81.04/16.07 | | | | | | | | | | | | | | | | | | | | | | | | (681) $false % 81.04/16.07 | | | | | | | | | | | | | | | | | | | | | | | | % 81.04/16.07 | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (681) is inconsistent. % 81.04/16.07 | | | | | | | | | | | | | | | | | | | | | | | | % 81.04/16.07 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 81.04/16.07 | | | | | | | | | | | | | | | | | | | | | | | | % 81.04/16.07 | | | | | | | | | | | | | | | | | | | | | | | | (682) ~ (all_846_4 = 0) | all_846_0 = 0 % 81.04/16.07 | | | | | | | | | | | | | | | | | | | | | | | | % 81.04/16.07 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (682) gives: % 81.04/16.07 | | | | | | | | | | | | | | | | | | | | | | | | % 81.04/16.07 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 81.04/16.07 | | | | | | | | | | | | | | | | | | | | | | | | | % 81.04/16.07 | | | | | | | | | | | | | | | | | | | | | | | | | (683) ~ (all_846_4 = 0) % 81.04/16.07 | | | | | | | | | | | | | | | | | | | | | | | | | % 81.04/16.07 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (668), (683) imply: % 81.04/16.07 | | | | | | | | | | | | | | | | | | | | | | | | | (684) $false % 81.04/16.07 | | | | | | | | | | | | | | | | | | | | | | | | | % 81.04/16.07 | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (684) is inconsistent. % 81.04/16.07 | | | | | | | | | | | | | | | | | | | | | | | | | % 81.04/16.07 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 81.04/16.07 | | | | | | | | | | | | | | | | | | | | | | | | | % 81.04/16.07 | | | | | | | | | | | | | | | | | | | | | | | | | (685) all_846_0 = 0 % 81.04/16.07 | | | | | | | | | | | | | | | | | | | | | | | | | % 81.04/16.07 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (676), (685) imply: % 81.04/16.07 | | | | | | | | | | | | | | | | | | | | | | | | | (686) in(all_114_1, all_56_1) = 0 % 81.04/16.07 | | | | | | | | | | | | | | | | | | | | | | | | | % 81.04/16.07 | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (33) with all_114_0, all_850_0, % 81.04/16.07 | | | | | | | | | | | | | | | | | | | | | | | | | all_56_1, all_114_1, simplifying with (269), (674) % 81.04/16.07 | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 81.04/16.07 | | | | | | | | | | | | | | | | | | | | | | | | | (687) all_850_0 = all_114_0 % 81.04/16.07 | | | | | | | | | | | | | | | | | | | | | | | | | % 81.04/16.07 | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (33) with 0, all_850_0, all_56_1, % 81.04/16.07 | | | | | | | | | | | | | | | | | | | | | | | | | all_114_1, simplifying with (674), (686) gives: % 81.04/16.07 | | | | | | | | | | | | | | | | | | | | | | | | | (688) all_850_0 = 0 % 81.04/16.07 | | | | | | | | | | | | | | | | | | | | | | | | | % 81.04/16.07 | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (33) with all_850_0, all_852_0, % 81.04/16.07 | | | | | | | | | | | | | | | | | | | | | | | | | all_56_1, all_114_1, simplifying with (673), (674) % 81.04/16.07 | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 81.04/16.07 | | | | | | | | | | | | | | | | | | | | | | | | | (689) all_852_0 = all_850_0 % 81.04/16.07 | | | | | | | | | | | | | | | | | | | | | | | | | % 81.04/16.07 | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (33) with all_848_0, all_852_0, % 81.04/16.07 | | | | | | | | | | | | | | | | | | | | | | | | | all_56_1, all_114_1, simplifying with (673), (675) % 81.04/16.07 | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 81.04/16.07 | | | | | | | | | | | | | | | | | | | | | | | | | (690) all_852_0 = all_848_0 % 81.04/16.07 | | | | | | | | | | | | | | | | | | | | | | | | | % 81.04/16.07 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (689), (690) imply: % 81.04/16.07 | | | | | | | | | | | | | | | | | | | | | | | | | (691) all_850_0 = all_848_0 % 81.04/16.07 | | | | | | | | | | | | | | | | | | | | | | | | | % 81.04/16.07 | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (691) implies: % 81.04/16.07 | | | | | | | | | | | | | | | | | | | | | | | | | (692) all_850_0 = all_848_0 % 81.04/16.07 | | | | | | | | | | | | | | | | | | | | | | | | | % 81.04/16.07 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (687), (692) imply: % 81.04/16.07 | | | | | | | | | | | | | | | | | | | | | | | | | (693) all_848_0 = all_114_0 % 81.04/16.07 | | | | | | | | | | | | | | | | | | | | | | | | | % 81.04/16.07 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (688), (692) imply: % 81.04/16.07 | | | | | | | | | | | | | | | | | | | | | | | | | (694) all_848_0 = 0 % 81.04/16.07 | | | | | | | | | | | | | | | | | | | | | | | | | % 81.04/16.07 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (693), (694) imply: % 81.04/16.07 | | | | | | | | | | | | | | | | | | | | | | | | | (695) all_114_0 = 0 % 81.04/16.07 | | | | | | | | | | | | | | | | | | | | | | | | | % 81.04/16.07 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (301), (695) imply: % 81.04/16.07 | | | | | | | | | | | | | | | | | | | | | | | | | (696) $false % 81.04/16.07 | | | | | | | | | | | | | | | | | | | | | | | | | % 81.04/16.07 | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (696) is inconsistent. % 81.04/16.07 | | | | | | | | | | | | | | | | | | | | | | | | | % 81.04/16.07 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 81.04/16.07 | | | | | | | | | | | | | | | | | | | | | | | | % 81.04/16.07 | | | | | | | | | | | | | | | | | | | | | | | End of split % 81.04/16.07 | | | | | | | | | | | | | | | | | | | | | | | % 81.04/16.07 | | | | | | | | | | | | | | | | | | | | | | End of split % 81.04/16.07 | | | | | | | | | | | | | | | | | | | | | | % 81.04/16.07 | | | | | | | | | | | | | | | | | | | | | End of split % 81.04/16.07 | | | | | | | | | | | | | | | | | | | | | % 81.04/16.07 | | | | | | | | | | | | | | | | | | | | End of split % 81.04/16.07 | | | | | | | | | | | | | | | | | | | | % 81.04/16.07 | | | | | | | | | | | | | | | | | | | Case 2: % 81.04/16.07 | | | | | | | | | | | | | | | | | | | | % 81.04/16.07 | | | | | | | | | | | | | | | | | | | | (697) all_596_0 = 0 % 81.04/16.07 | | | | | | | | | | | | | | | | | | | | % 81.04/16.07 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (527), (697) imply: % 81.04/16.07 | | | | | | | | | | | | | | | | | | | | (698) all_182_0 = 0 % 81.04/16.07 | | | | | | | | | | | | | | | | | | | | % 81.04/16.07 | | | | | | | | | | | | | | | | | | | | REDUCE: (333), (698) imply: % 81.04/16.07 | | | | | | | | | | | | | | | | | | | | (699) $false % 81.04/16.07 | | | | | | | | | | | | | | | | | | | | % 81.04/16.07 | | | | | | | | | | | | | | | | | | | | CLOSE: (699) is inconsistent. % 81.04/16.07 | | | | | | | | | | | | | | | | | | | | % 81.04/16.07 | | | | | | | | | | | | | | | | | | | End of split % 81.04/16.07 | | | | | | | | | | | | | | | | | | | % 81.04/16.07 | | | | | | | | | | | | | | | | | | End of split % 81.04/16.07 | | | | | | | | | | | | | | | | | | % 81.04/16.07 | | | | | | | | | | | | | | | | | Case 2: % 81.04/16.07 | | | | | | | | | | | | | | | | | | % 81.04/16.07 | | | | | | | | | | | | | | | | | | (700) all_116_2 = 0 % 81.04/16.07 | | | | | | | | | | | | | | | | | | % 81.04/16.07 | | | | | | | | | | | | | | | | | | REDUCE: (518), (700) imply: % 81.04/16.07 | | | | | | | | | | | | | | | | | | (701) $false % 81.04/16.07 | | | | | | | | | | | | | | | | | | % 81.04/16.07 | | | | | | | | | | | | | | | | | | CLOSE: (701) is inconsistent. % 81.04/16.07 | | | | | | | | | | | | | | | | | | % 81.04/16.07 | | | | | | | | | | | | | | | | | End of split % 81.04/16.07 | | | | | | | | | | | | | | | | | % 81.04/16.07 | | | | | | | | | | | | | | | | Case 2: % 81.04/16.07 | | | | | | | | | | | | | | | | | % 81.04/16.07 | | | | | | | | | | | | | | | | | (702) all_116_0 = 0 % 81.04/16.07 | | | | | | | | | | | | | | | | | % 81.04/16.07 | | | | | | | | | | | | | | | | | REDUCE: (268), (702) imply: % 81.04/16.07 | | | | | | | | | | | | | | | | | (703) in(all_116_1, all_56_1) = 0 % 81.04/16.07 | | | | | | | | | | | | | | | | | % 81.04/16.07 | | | | | | | | | | | | | | | | | BETA: splitting (251) gives: % 81.04/16.07 | | | | | | | | | | | | | | | | | % 81.04/16.07 | | | | | | | | | | | | | | | | | Case 1: % 81.04/16.07 | | | | | | | | | | | | | | | | | | % 81.04/16.07 | | | | | | | | | | | | | | | | | | (704) ~ (all_126_2 = 0) % 81.04/16.07 | | | | | | | | | | | | | | | | | | % 81.04/16.07 | | | | | | | | | | | | | | | | | | BETA: splitting (252) gives: % 81.04/16.07 | | | | | | | | | | | | | | | | | | % 81.04/16.07 | | | | | | | | | | | | | | | | | | Case 1: % 81.04/16.07 | | | | | | | | | | | | | | | | | | | % 81.04/16.07 | | | | | | | | | | | | | | | | | | | % 81.04/16.07 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (8) with all_56_1, all_42_4, % 81.04/16.07 | | | | | | | | | | | | | | | | | | | all_42_1, all_42_2, all_42_1, all_116_1, % 81.04/16.07 | | | | | | | | | | | | | | | | | | | simplifying with (50), (52), (53), (194), (229), % 81.04/16.07 | | | | | | | | | | | | | | | | | | | (274), (447), (454), (703) gives: % 81.04/16.07 | | | | | | | | | | | | | | | | | | | (705) ? [v0: any] : ? [v1: any] : ? [v2: $i] : ? % 81.04/16.07 | | | | | | | | | | | | | | | | | | | [v3: any] : ? [v4: $i] : ? [v5: any] : % 81.04/16.07 | | | | | | | | | | | | | | | | | | | (ordered_pair(all_42_1, all_42_1) = v4 & % 81.04/16.07 | | | | | | | | | | | | | | | | | | | ordered_pair(all_42_2, all_42_1) = v2 & in(v4, % 81.04/16.07 | | | | | | | | | | | | | | | | | | | all_56_1) = v5 & in(v2, all_56_1) = v3 & % 81.04/16.07 | | | | | | | | | | | | | | | | | | | in(all_42_1, all_42_4) = v0 & in(all_42_2, % 81.04/16.07 | | | | | | | | | | | | | | | | | | | all_42_4) = v1 & $i(v4) & $i(v2) & ( ~ (v3 = % 81.04/16.07 | | | | | | | | | | | | | | | | | | | 0) | ~ (v1 = 0) | ~ (v0 = 0) | v5 = 0)) % 81.04/16.07 | | | | | | | | | | | | | | | | | | | % 81.04/16.07 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (10) with all_56_1, all_42_4, % 81.04/16.07 | | | | | | | | | | | | | | | | | | | all_42_1, all_42_2, all_42_1, all_116_1, % 81.04/16.07 | | | | | | | | | | | | | | | | | | | all_108_1, simplifying with (50), (52), (53), % 81.04/16.07 | | | | | | | | | | | | | | | | | | | (194), (215), (229), (274), (299), (454), (703) % 81.04/16.07 | | | | | | | | | | | | | | | | | | | gives: % 81.04/16.07 | | | | | | | | | | | | | | | | | | | (706) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? % 81.04/16.07 | | | | | | | | | | | | | | | | | | | [v3: $i] : ? [v4: any] : (ordered_pair(all_42_1, % 81.04/16.07 | | | | | | | | | | | | | | | | | | | all_42_1) = v3 & in(v3, all_56_1) = v4 & % 81.04/16.07 | | | | | | | | | | | | | | | | | | | in(all_42_1, all_42_4) = v2 & in(all_42_1, % 81.04/16.07 | | | | | | | | | | | | | | | | | | | all_42_4) = v0 & in(all_42_2, all_42_4) = v1 & % 81.04/16.07 | | | | | | | | | | | | | | | | | | | $i(v3) & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = % 81.04/16.07 | | | | | | | | | | | | | | | | | | | 0) | v4 = 0)) % 81.04/16.07 | | | | | | | | | | | | | | | | | | | % 81.04/16.07 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (10) with all_56_1, all_42_4, % 81.04/16.07 | | | | | | | | | | | | | | | | | | | all_42_3, all_42_2, all_42_1, all_110_1, % 81.04/16.07 | | | | | | | | | | | | | | | | | | | all_108_1, simplifying with (50), (51), (52), % 81.04/16.07 | | | | | | | | | | | | | | | | | | | (53), (194), (215), (219), (274), (294), (299), % 81.04/16.07 | | | | | | | | | | | | | | | | | | | (454) gives: % 81.04/16.07 | | | | | | | | | | | | | | | | | | | (707) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? % 81.04/16.07 | | | | | | | | | | | | | | | | | | | [v3: $i] : ? [v4: any] : (ordered_pair(all_42_3, % 81.04/16.07 | | | | | | | | | | | | | | | | | | | all_42_1) = v3 & in(v3, all_56_1) = v4 & % 81.04/16.07 | | | | | | | | | | | | | | | | | | | in(all_42_1, all_42_4) = v2 & in(all_42_2, % 81.04/16.07 | | | | | | | | | | | | | | | | | | | all_42_4) = v1 & in(all_42_3, all_42_4) = v0 & % 81.04/16.07 | | | | | | | | | | | | | | | | | | | $i(v3) & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = % 81.04/16.07 | | | | | | | | | | | | | | | | | | | 0) | v4 = 0)) % 81.04/16.07 | | | | | | | | | | | | | | | | | | | % 81.04/16.07 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (9) with all_56_1, all_42_4, % 81.04/16.07 | | | | | | | | | | | | | | | | | | | all_42_1, all_42_2, all_42_1, all_108_1, % 81.04/16.07 | | | | | | | | | | | | | | | | | | | simplifying with (50), (52), (53), (194), (215), % 81.04/16.07 | | | | | | | | | | | | | | | | | | | (274), (299), (447), (454) gives: % 81.04/16.07 | | | | | | | | | | | | | | | | | | | (708) ? [v0: any] : ? [v1: any] : ? [v2: $i] : ? % 81.04/16.07 | | | | | | | | | | | | | | | | | | | [v3: any] : ? [v4: $i] : ? [v5: any] : % 81.04/16.07 | | | | | | | | | | | | | | | | | | | (ordered_pair(all_42_1, all_42_1) = v4 & % 81.04/16.07 | | | | | | | | | | | | | | | | | | | ordered_pair(all_42_1, all_42_2) = v2 & in(v4, % 81.04/16.07 | | | | | | | | | | | | | | | | | | | all_56_1) = v5 & in(v2, all_56_1) = v3 & % 81.04/16.07 | | | | | | | | | | | | | | | | | | | in(all_42_1, all_42_4) = v1 & in(all_42_2, % 81.04/16.07 | | | | | | | | | | | | | | | | | | | all_42_4) = v0 & $i(v4) & $i(v2) & ( ~ (v3 = % 81.04/16.07 | | | | | | | | | | | | | | | | | | | 0) | ~ (v1 = 0) | ~ (v0 = 0) | v5 = 0)) % 81.04/16.07 | | | | | | | | | | | | | | | | | | | % 81.04/16.07 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (9) with all_56_1, all_42_4, % 81.04/16.07 | | | | | | | | | | | | | | | | | | | all_42_3, all_42_2, all_42_1, all_108_1, % 81.04/16.07 | | | | | | | | | | | | | | | | | | | simplifying with (50), (51), (52), (53), (194), % 81.04/16.07 | | | | | | | | | | | | | | | | | | | (215), (274), (299), (451), (454) gives: % 81.04/16.07 | | | | | | | | | | | | | | | | | | | (709) ? [v0: any] : ? [v1: any] : ? [v2: $i] : ? % 81.04/16.07 | | | | | | | | | | | | | | | | | | | [v3: any] : ? [v4: $i] : ? [v5: any] : % 81.04/16.07 | | | | | | | | | | | | | | | | | | | (ordered_pair(all_42_3, all_42_1) = v4 & % 81.04/16.07 | | | | | | | | | | | | | | | | | | | ordered_pair(all_42_3, all_42_2) = v2 & in(v4, % 81.04/16.07 | | | | | | | | | | | | | | | | | | | all_56_1) = v5 & in(v2, all_56_1) = v3 & % 81.04/16.07 | | | | | | | | | | | | | | | | | | | in(all_42_1, all_42_4) = v1 & in(all_42_2, % 81.04/16.07 | | | | | | | | | | | | | | | | | | | all_42_4) = v0 & $i(v4) & $i(v2) & ( ~ (v3 = % 81.04/16.07 | | | | | | | | | | | | | | | | | | | 0) | ~ (v1 = 0) | ~ (v0 = 0) | v5 = 0)) % 81.04/16.07 | | | | | | | | | | | | | | | | | | | % 81.04/16.07 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (8) with all_56_1, all_42_4, % 81.04/16.07 | | | | | | | | | | | | | | | | | | | all_42_3, all_42_2, all_42_1, all_110_1, % 81.04/16.07 | | | | | | | | | | | | | | | | | | | simplifying with (50), (51), (52), (53), (194), % 81.04/16.07 | | | | | | | | | | | | | | | | | | | (219), (274), (294), (447), (454) gives: % 81.04/16.07 | | | | | | | | | | | | | | | | | | | (710) ? [v0: any] : ? [v1: any] : ? [v2: $i] : ? % 81.04/16.07 | | | | | | | | | | | | | | | | | | | [v3: any] : ? [v4: $i] : ? [v5: any] : % 81.04/16.07 | | | | | | | | | | | | | | | | | | | (ordered_pair(all_42_2, all_42_1) = v2 & % 81.04/16.07 | | | | | | | | | | | | | | | | | | | ordered_pair(all_42_3, all_42_1) = v4 & in(v4, % 81.04/16.07 | | | | | | | | | | | | | | | | | | | all_56_1) = v5 & in(v2, all_56_1) = v3 & % 81.04/16.07 | | | | | | | | | | | | | | | | | | | in(all_42_2, all_42_4) = v1 & in(all_42_3, % 81.04/16.07 | | | | | | | | | | | | | | | | | | | all_42_4) = v0 & $i(v4) & $i(v2) & ( ~ (v3 = % 81.04/16.07 | | | | | | | | | | | | | | | | | | | 0) | ~ (v1 = 0) | ~ (v0 = 0) | v5 = 0)) % 81.04/16.07 | | | | | | | | | | | | | | | | | | | % 81.04/16.07 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (7) with all_56_1, all_42_4, % 81.04/16.07 | | | | | | | | | | | | | | | | | | | all_42_3, all_42_2, all_42_1, simplifying with % 81.04/16.07 | | | | | | | | | | | | | | | | | | | (50), (51), (52), (53), (194), (274), (447), % 81.04/16.07 | | | | | | | | | | | | | | | | | | | (449), (451), (454) gives: % 81.04/16.08 | | | | | | | | | | | | | | | | | | | (711) ? [v0: $i] : ? [v1: any] : ? [v2: $i] : ? [v3: % 81.04/16.08 | | | | | | | | | | | | | | | | | | | any] : ? [v4: $i] : ? [v5: any] : % 81.04/16.08 | | | | | | | | | | | | | | | | | | | (ordered_pair(all_42_2, all_42_1) = v2 & % 81.04/16.08 | | | | | | | | | | | | | | | | | | | ordered_pair(all_42_3, all_42_1) = v4 & % 81.04/16.08 | | | | | | | | | | | | | | | | | | | ordered_pair(all_42_3, all_42_2) = v0 & in(v4, % 81.04/16.08 | | | | | | | | | | | | | | | | | | | all_56_1) = v5 & in(v2, all_56_1) = v3 & % 81.04/16.08 | | | | | | | | | | | | | | | | | | | in(v0, all_56_1) = v1 & $i(v4) & $i(v2) & $i(v0) % 81.04/16.08 | | | | | | | | | | | | | | | | | | | & ( ~ (v3 = 0) | ~ (v1 = 0) | v5 = 0)) % 81.04/16.08 | | | | | | | | | | | | | | | | | | | % 81.04/16.08 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with all_118_1, all_350_0, % 81.04/16.08 | | | | | | | | | | | | | | | | | | | simplifying with (465), (475) gives: % 81.04/16.08 | | | | | | | | | | | | | | | | | | | (712) all_350_0 = 0 | ? [v0: $i] : ? [v1: $i] : ? % 81.04/16.08 | | | | | | | | | | | | | | | | | | | [v2: int] : ( ~ (v2 = 0) & empty(v1) = v2 & % 81.04/16.08 | | | | | | | | | | | | | | | | | | | powerset(all_118_1) = v0 & element(v1, v0) = 0 & % 81.04/16.08 | | | | | | | | | | | | | | | | | | | $i(v1) & $i(v0)) % 81.04/16.08 | | | | | | | | | | | | | | | | | | | % 81.04/16.08 | | | | | | | | | | | | | | | | | | | DELTA: instantiating (707) with fresh symbols all_814_0, % 81.04/16.08 | | | | | | | | | | | | | | | | | | | all_814_1, all_814_2, all_814_3, all_814_4 gives: % 81.04/16.08 | | | | | | | | | | | | | | | | | | | (713) ordered_pair(all_42_3, all_42_1) = all_814_1 & % 81.04/16.08 | | | | | | | | | | | | | | | | | | | in(all_814_1, all_56_1) = all_814_0 & in(all_42_1, % 81.04/16.08 | | | | | | | | | | | | | | | | | | | all_42_4) = all_814_2 & in(all_42_2, all_42_4) = % 81.04/16.08 | | | | | | | | | | | | | | | | | | | all_814_3 & in(all_42_3, all_42_4) = all_814_4 & % 81.04/16.08 | | | | | | | | | | | | | | | | | | | $i(all_814_1) & ( ~ (all_814_2 = 0) | ~ % 81.04/16.08 | | | | | | | | | | | | | | | | | | | (all_814_3 = 0) | ~ (all_814_4 = 0) | all_814_0 % 81.04/16.08 | | | | | | | | | | | | | | | | | | | = 0) % 81.04/16.08 | | | | | | | | | | | | | | | | | | | % 81.04/16.08 | | | | | | | | | | | | | | | | | | | ALPHA: (713) implies: % 81.04/16.08 | | | | | | | | | | | | | | | | | | | (714) in(all_42_3, all_42_4) = all_814_4 % 81.04/16.08 | | | | | | | | | | | | | | | | | | | (715) in(all_42_2, all_42_4) = all_814_3 % 81.04/16.08 | | | | | | | | | | | | | | | | | | | (716) in(all_42_1, all_42_4) = all_814_2 % 81.04/16.08 | | | | | | | | | | | | | | | | | | | (717) in(all_814_1, all_56_1) = all_814_0 % 81.04/16.08 | | | | | | | | | | | | | | | | | | | (718) ordered_pair(all_42_3, all_42_1) = all_814_1 % 81.04/16.08 | | | | | | | | | | | | | | | | | | | (719) ~ (all_814_2 = 0) | ~ (all_814_3 = 0) | ~ % 81.04/16.08 | | | | | | | | | | | | | | | | | | | (all_814_4 = 0) | all_814_0 = 0 % 81.04/16.08 | | | | | | | | | | | | | | | | | | | % 81.04/16.08 | | | | | | | | | | | | | | | | | | | DELTA: instantiating (706) with fresh symbols all_816_0, % 81.04/16.08 | | | | | | | | | | | | | | | | | | | all_816_1, all_816_2, all_816_3, all_816_4 gives: % 81.04/16.08 | | | | | | | | | | | | | | | | | | | (720) ordered_pair(all_42_1, all_42_1) = all_816_1 & % 81.04/16.08 | | | | | | | | | | | | | | | | | | | in(all_816_1, all_56_1) = all_816_0 & in(all_42_1, % 81.04/16.08 | | | | | | | | | | | | | | | | | | | all_42_4) = all_816_2 & in(all_42_1, all_42_4) = % 81.04/16.08 | | | | | | | | | | | | | | | | | | | all_816_4 & in(all_42_2, all_42_4) = all_816_3 & % 81.04/16.08 | | | | | | | | | | | | | | | | | | | $i(all_816_1) & ( ~ (all_816_2 = 0) | ~ % 81.04/16.08 | | | | | | | | | | | | | | | | | | | (all_816_3 = 0) | ~ (all_816_4 = 0) | all_816_0 % 81.04/16.08 | | | | | | | | | | | | | | | | | | | = 0) % 81.04/16.08 | | | | | | | | | | | | | | | | | | | % 81.04/16.08 | | | | | | | | | | | | | | | | | | | ALPHA: (720) implies: % 81.04/16.08 | | | | | | | | | | | | | | | | | | | (721) in(all_42_2, all_42_4) = all_816_3 % 81.04/16.08 | | | | | | | | | | | | | | | | | | | (722) in(all_42_1, all_42_4) = all_816_4 % 81.04/16.08 | | | | | | | | | | | | | | | | | | | (723) in(all_42_1, all_42_4) = all_816_2 % 81.04/16.08 | | | | | | | | | | | | | | | | | | | % 81.04/16.08 | | | | | | | | | | | | | | | | | | | DELTA: instantiating (705) with fresh symbols all_818_0, % 81.04/16.08 | | | | | | | | | | | | | | | | | | | all_818_1, all_818_2, all_818_3, all_818_4, % 81.04/16.08 | | | | | | | | | | | | | | | | | | | all_818_5 gives: % 81.04/16.08 | | | | | | | | | | | | | | | | | | | (724) ordered_pair(all_42_1, all_42_1) = all_818_1 & % 81.04/16.08 | | | | | | | | | | | | | | | | | | | ordered_pair(all_42_2, all_42_1) = all_818_3 & % 81.04/16.08 | | | | | | | | | | | | | | | | | | | in(all_818_1, all_56_1) = all_818_0 & % 81.04/16.08 | | | | | | | | | | | | | | | | | | | in(all_818_3, all_56_1) = all_818_2 & in(all_42_1, % 81.04/16.08 | | | | | | | | | | | | | | | | | | | all_42_4) = all_818_5 & in(all_42_2, all_42_4) = % 81.04/16.08 | | | | | | | | | | | | | | | | | | | all_818_4 & $i(all_818_1) & $i(all_818_3) & ( ~ % 81.04/16.08 | | | | | | | | | | | | | | | | | | | (all_818_2 = 0) | ~ (all_818_4 = 0) | ~ % 81.04/16.08 | | | | | | | | | | | | | | | | | | | (all_818_5 = 0) | all_818_0 = 0) % 81.04/16.08 | | | | | | | | | | | | | | | | | | | % 81.04/16.08 | | | | | | | | | | | | | | | | | | | ALPHA: (724) implies: % 81.04/16.08 | | | | | | | | | | | | | | | | | | | (725) in(all_42_2, all_42_4) = all_818_4 % 81.04/16.08 | | | | | | | | | | | | | | | | | | | (726) in(all_42_1, all_42_4) = all_818_5 % 81.04/16.08 | | | | | | | | | | | | | | | | | | | % 81.04/16.08 | | | | | | | | | | | | | | | | | | | DELTA: instantiating (711) with fresh symbols all_820_0, % 81.04/16.08 | | | | | | | | | | | | | | | | | | | all_820_1, all_820_2, all_820_3, all_820_4, % 81.04/16.08 | | | | | | | | | | | | | | | | | | | all_820_5 gives: % 81.04/16.08 | | | | | | | | | | | | | | | | | | | (727) ordered_pair(all_42_2, all_42_1) = all_820_3 & % 81.04/16.08 | | | | | | | | | | | | | | | | | | | ordered_pair(all_42_3, all_42_1) = all_820_1 & % 81.04/16.08 | | | | | | | | | | | | | | | | | | | ordered_pair(all_42_3, all_42_2) = all_820_5 & % 81.04/16.08 | | | | | | | | | | | | | | | | | | | in(all_820_1, all_56_1) = all_820_0 & % 81.04/16.08 | | | | | | | | | | | | | | | | | | | in(all_820_3, all_56_1) = all_820_2 & % 81.04/16.08 | | | | | | | | | | | | | | | | | | | in(all_820_5, all_56_1) = all_820_4 & % 81.04/16.08 | | | | | | | | | | | | | | | | | | | $i(all_820_1) & $i(all_820_3) & $i(all_820_5) & ( % 81.04/16.08 | | | | | | | | | | | | | | | | | | | ~ (all_820_2 = 0) | ~ (all_820_4 = 0) | % 81.04/16.08 | | | | | | | | | | | | | | | | | | | all_820_0 = 0) % 81.04/16.08 | | | | | | | | | | | | | | | | | | | % 81.04/16.08 | | | | | | | | | | | | | | | | | | | ALPHA: (727) implies: % 81.04/16.08 | | | | | | | | | | | | | | | | | | | (728) in(all_820_1, all_56_1) = all_820_0 % 81.04/16.08 | | | | | | | | | | | | | | | | | | | (729) ordered_pair(all_42_3, all_42_1) = all_820_1 % 81.04/16.08 | | | | | | | | | | | | | | | | | | | % 81.04/16.08 | | | | | | | | | | | | | | | | | | | DELTA: instantiating (710) with fresh symbols all_824_0, % 81.04/16.08 | | | | | | | | | | | | | | | | | | | all_824_1, all_824_2, all_824_3, all_824_4, % 81.04/16.08 | | | | | | | | | | | | | | | | | | | all_824_5 gives: % 81.04/16.08 | | | | | | | | | | | | | | | | | | | (730) ordered_pair(all_42_2, all_42_1) = all_824_3 & % 81.04/16.08 | | | | | | | | | | | | | | | | | | | ordered_pair(all_42_3, all_42_1) = all_824_1 & % 81.04/16.08 | | | | | | | | | | | | | | | | | | | in(all_824_1, all_56_1) = all_824_0 & % 81.04/16.08 | | | | | | | | | | | | | | | | | | | in(all_824_3, all_56_1) = all_824_2 & in(all_42_2, % 81.04/16.08 | | | | | | | | | | | | | | | | | | | all_42_4) = all_824_4 & in(all_42_3, all_42_4) = % 81.04/16.08 | | | | | | | | | | | | | | | | | | | all_824_5 & $i(all_824_1) & $i(all_824_3) & ( ~ % 81.04/16.08 | | | | | | | | | | | | | | | | | | | (all_824_2 = 0) | ~ (all_824_4 = 0) | ~ % 81.04/16.08 | | | | | | | | | | | | | | | | | | | (all_824_5 = 0) | all_824_0 = 0) % 81.04/16.08 | | | | | | | | | | | | | | | | | | | % 81.04/16.08 | | | | | | | | | | | | | | | | | | | ALPHA: (730) implies: % 81.04/16.08 | | | | | | | | | | | | | | | | | | | (731) in(all_42_3, all_42_4) = all_824_5 % 81.04/16.08 | | | | | | | | | | | | | | | | | | | (732) in(all_42_2, all_42_4) = all_824_4 % 81.04/16.08 | | | | | | | | | | | | | | | | | | | (733) in(all_824_1, all_56_1) = all_824_0 % 81.04/16.08 | | | | | | | | | | | | | | | | | | | (734) ordered_pair(all_42_3, all_42_1) = all_824_1 % 81.04/16.08 | | | | | | | | | | | | | | | | | | | % 81.04/16.08 | | | | | | | | | | | | | | | | | | | DELTA: instantiating (709) with fresh symbols all_826_0, % 81.04/16.08 | | | | | | | | | | | | | | | | | | | all_826_1, all_826_2, all_826_3, all_826_4, % 81.04/16.08 | | | | | | | | | | | | | | | | | | | all_826_5 gives: % 81.04/16.08 | | | | | | | | | | | | | | | | | | | (735) ordered_pair(all_42_3, all_42_1) = all_826_1 & % 81.04/16.08 | | | | | | | | | | | | | | | | | | | ordered_pair(all_42_3, all_42_2) = all_826_3 & % 81.04/16.08 | | | | | | | | | | | | | | | | | | | in(all_826_1, all_56_1) = all_826_0 & % 81.04/16.08 | | | | | | | | | | | | | | | | | | | in(all_826_3, all_56_1) = all_826_2 & in(all_42_1, % 81.04/16.08 | | | | | | | | | | | | | | | | | | | all_42_4) = all_826_4 & in(all_42_2, all_42_4) = % 81.04/16.08 | | | | | | | | | | | | | | | | | | | all_826_5 & $i(all_826_1) & $i(all_826_3) & ( ~ % 81.04/16.08 | | | | | | | | | | | | | | | | | | | (all_826_2 = 0) | ~ (all_826_4 = 0) | ~ % 81.04/16.08 | | | | | | | | | | | | | | | | | | | (all_826_5 = 0) | all_826_0 = 0) % 81.04/16.08 | | | | | | | | | | | | | | | | | | | % 81.04/16.08 | | | | | | | | | | | | | | | | | | | ALPHA: (735) implies: % 81.04/16.08 | | | | | | | | | | | | | | | | | | | (736) in(all_42_2, all_42_4) = all_826_5 % 81.04/16.08 | | | | | | | | | | | | | | | | | | | (737) in(all_42_1, all_42_4) = all_826_4 % 81.04/16.08 | | | | | | | | | | | | | | | | | | | (738) in(all_826_1, all_56_1) = all_826_0 % 81.04/16.08 | | | | | | | | | | | | | | | | | | | (739) ordered_pair(all_42_3, all_42_1) = all_826_1 % 81.04/16.08 | | | | | | | | | | | | | | | | | | | % 81.04/16.08 | | | | | | | | | | | | | | | | | | | DELTA: instantiating (708) with fresh symbols all_828_0, % 81.04/16.08 | | | | | | | | | | | | | | | | | | | all_828_1, all_828_2, all_828_3, all_828_4, % 81.04/16.08 | | | | | | | | | | | | | | | | | | | all_828_5 gives: % 81.04/16.08 | | | | | | | | | | | | | | | | | | | (740) ordered_pair(all_42_1, all_42_1) = all_828_1 & % 81.04/16.08 | | | | | | | | | | | | | | | | | | | ordered_pair(all_42_1, all_42_2) = all_828_3 & % 81.04/16.08 | | | | | | | | | | | | | | | | | | | in(all_828_1, all_56_1) = all_828_0 & % 81.04/16.08 | | | | | | | | | | | | | | | | | | | in(all_828_3, all_56_1) = all_828_2 & in(all_42_1, % 81.04/16.08 | | | | | | | | | | | | | | | | | | | all_42_4) = all_828_4 & in(all_42_2, all_42_4) = % 81.04/16.08 | | | | | | | | | | | | | | | | | | | all_828_5 & $i(all_828_1) & $i(all_828_3) & ( ~ % 81.04/16.08 | | | | | | | | | | | | | | | | | | | (all_828_2 = 0) | ~ (all_828_4 = 0) | ~ % 81.04/16.08 | | | | | | | | | | | | | | | | | | | (all_828_5 = 0) | all_828_0 = 0) % 81.04/16.08 | | | | | | | | | | | | | | | | | | | % 81.04/16.08 | | | | | | | | | | | | | | | | | | | ALPHA: (740) implies: % 81.04/16.08 | | | | | | | | | | | | | | | | | | | (741) in(all_42_2, all_42_4) = all_828_5 % 81.04/16.08 | | | | | | | | | | | | | | | | | | | (742) in(all_42_1, all_42_4) = all_828_4 % 81.04/16.08 | | | | | | | | | | | | | | | | | | | % 81.04/16.08 | | | | | | | | | | | | | | | | | | | BETA: splitting (712) gives: % 81.04/16.08 | | | | | | | | | | | | | | | | | | | % 81.04/16.08 | | | | | | | | | | | | | | | | | | | Case 1: % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | (743) all_350_0 = 0 % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | REDUCE: (474), (743) imply: % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | (744) $false % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | CLOSE: (744) is inconsistent. % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | % 81.04/16.08 | | | | | | | | | | | | | | | | | | | Case 2: % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (33) with 0, all_824_5, all_42_4, % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | all_42_3, simplifying with (451), (731) gives: % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | (745) all_824_5 = 0 % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (33) with all_814_4, all_824_5, % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | all_42_4, all_42_3, simplifying with (714), (731) % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | gives: % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | (746) all_824_5 = all_814_4 % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (33) with 0, all_824_4, all_42_4, % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | all_42_2, simplifying with (449), (732) gives: % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | (747) all_824_4 = 0 % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (33) with all_816_3, all_824_4, % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | all_42_4, all_42_2, simplifying with (721), (732) % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | gives: % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | (748) all_824_4 = all_816_3 % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (33) with all_824_4, all_826_5, % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | all_42_4, all_42_2, simplifying with (732), (736) % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | gives: % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | (749) all_826_5 = all_824_4 % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (33) with all_818_4, all_826_5, % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | all_42_4, all_42_2, simplifying with (725), (736) % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | gives: % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | (750) all_826_5 = all_818_4 % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (33) with all_826_5, all_828_5, % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | all_42_4, all_42_2, simplifying with (736), (741) % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | gives: % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | (751) all_828_5 = all_826_5 % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (33) with all_814_3, all_828_5, % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | all_42_4, all_42_2, simplifying with (715), (741) % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | gives: % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | (752) all_828_5 = all_814_3 % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (33) with all_816_4, all_816_2, % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | all_42_4, all_42_1, simplifying with (722), (723) % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | gives: % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | (753) all_816_2 = all_816_4 % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (33) with all_816_2, all_818_5, % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | all_42_4, all_42_1, simplifying with (723), (726) % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | gives: % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | (754) all_818_5 = all_816_2 % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (33) with all_816_4, all_826_4, % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | all_42_4, all_42_1, simplifying with (722), (737) % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | gives: % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | (755) all_826_4 = all_816_4 % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (33) with all_814_2, all_826_4, % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | all_42_4, all_42_1, simplifying with (716), (737) % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | gives: % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | (756) all_826_4 = all_814_2 % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (33) with 0, all_828_4, all_42_4, % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | all_42_1, simplifying with (447), (742) gives: % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | (757) all_828_4 = 0 % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (33) with all_818_5, all_828_4, % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | all_42_4, all_42_1, simplifying with (726), (742) % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | gives: % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | (758) all_828_4 = all_818_5 % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (35) with all_114_1, all_824_1, % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | all_42_1, all_42_3, simplifying with (225), (734) % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | gives: % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | (759) all_824_1 = all_114_1 % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (35) with all_820_1, all_824_1, % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | all_42_1, all_42_3, simplifying with (729), (734) % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | gives: % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | (760) all_824_1 = all_820_1 % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (35) with all_824_1, all_826_1, % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | all_42_1, all_42_3, simplifying with (734), (739) % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | gives: % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | (761) all_826_1 = all_824_1 % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (35) with all_814_1, all_826_1, % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | all_42_1, all_42_3, simplifying with (718), (739) % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | gives: % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | (762) all_826_1 = all_814_1 % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (757), (758) imply: % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | (763) all_818_5 = 0 % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | SIMP: (763) implies: % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | (764) all_818_5 = 0 % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (751), (752) imply: % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | (765) all_826_5 = all_814_3 % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | SIMP: (765) implies: % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | (766) all_826_5 = all_814_3 % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (761), (762) imply: % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | (767) all_824_1 = all_814_1 % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | SIMP: (767) implies: % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | (768) all_824_1 = all_814_1 % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (755), (756) imply: % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | (769) all_816_4 = all_814_2 % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | SIMP: (769) implies: % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | (770) all_816_4 = all_814_2 % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (749), (750) imply: % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | (771) all_824_4 = all_818_4 % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | SIMP: (771) implies: % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | (772) all_824_4 = all_818_4 % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (750), (766) imply: % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | (773) all_818_4 = all_814_3 % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (759), (760) imply: % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | (774) all_820_1 = all_114_1 % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (760), (768) imply: % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | (775) all_820_1 = all_814_1 % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (747), (748) imply: % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | (776) all_816_3 = 0 % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (748), (772) imply: % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | (777) all_818_4 = all_816_3 % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | SIMP: (777) implies: % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | (778) all_818_4 = all_816_3 % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (745), (746) imply: % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | (779) all_814_4 = 0 % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | SIMP: (779) implies: % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | (780) all_814_4 = 0 % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (774), (775) imply: % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | (781) all_814_1 = all_114_1 % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (773), (778) imply: % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | (782) all_816_3 = all_814_3 % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | SIMP: (782) implies: % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | (783) all_816_3 = all_814_3 % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (754), (764) imply: % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | (784) all_816_2 = 0 % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | SIMP: (784) implies: % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | (785) all_816_2 = 0 % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (753), (785) imply: % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | (786) all_816_4 = 0 % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | SIMP: (786) implies: % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | (787) all_816_4 = 0 % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (776), (783) imply: % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | (788) all_814_3 = 0 % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (770), (787) imply: % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | (789) all_814_2 = 0 % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | SIMP: (789) implies: % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | (790) all_814_2 = 0 % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (762), (781) imply: % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | (791) all_826_1 = all_114_1 % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | REDUCE: (738), (791) imply: % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | (792) in(all_114_1, all_56_1) = all_826_0 % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | REDUCE: (733), (759) imply: % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | (793) in(all_114_1, all_56_1) = all_824_0 % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | REDUCE: (728), (774) imply: % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | (794) in(all_114_1, all_56_1) = all_820_0 % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | REDUCE: (717), (781) imply: % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | (795) in(all_114_1, all_56_1) = all_814_0 % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | BETA: splitting (719) gives: % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | Case 1: % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | | % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | | (796) ~ (all_814_2 = 0) % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | | % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | | REDUCE: (790), (796) imply: % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | | (797) $false % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | | % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | | CLOSE: (797) is inconsistent. % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | | % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | Case 2: % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | | % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | | (798) ~ (all_814_3 = 0) | ~ (all_814_4 = 0) | % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | | all_814_0 = 0 % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | | % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (798) gives: % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | | % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | | Case 1: % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | | | % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | | | (799) ~ (all_814_3 = 0) % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | | | % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (788), (799) imply: % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | | | (800) $false % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | | | % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | | | CLOSE: (800) is inconsistent. % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | | | % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | | Case 2: % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | | | % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | | | (801) ~ (all_814_4 = 0) | all_814_0 = 0 % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | | | % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (801) gives: % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | | | % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | | | | % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | | | | (802) ~ (all_814_4 = 0) % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | | | | % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (780), (802) imply: % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | | | | (803) $false % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | | | | % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (803) is inconsistent. % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | | | | % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | | | | % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | | | | (804) all_814_0 = 0 % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | | | | % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (795), (804) imply: % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | | | | (805) in(all_114_1, all_56_1) = 0 % 81.04/16.08 | | | | | | | | | | | | | | | | | | | | | | | % 81.04/16.09 | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (33) with 0, all_824_0, all_56_1, % 81.04/16.09 | | | | | | | | | | | | | | | | | | | | | | | all_114_1, simplifying with (793), (805) gives: % 81.04/16.09 | | | | | | | | | | | | | | | | | | | | | | | (806) all_824_0 = 0 % 81.04/16.09 | | | | | | | | | | | | | | | | | | | | | | | % 81.04/16.09 | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (33) with all_114_0, all_826_0, % 81.04/16.09 | | | | | | | | | | | | | | | | | | | | | | | all_56_1, all_114_1, simplifying with (269), (792) % 81.04/16.09 | | | | | | | | | | | | | | | | | | | | | | | gives: % 81.04/16.09 | | | | | | | | | | | | | | | | | | | | | | | (807) all_826_0 = all_114_0 % 81.04/16.09 | | | | | | | | | | | | | | | | | | | | | | | % 81.04/16.09 | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (33) with all_824_0, all_826_0, % 81.04/16.09 | | | | | | | | | | | | | | | | | | | | | | | all_56_1, all_114_1, simplifying with (792), (793) % 81.04/16.09 | | | | | | | | | | | | | | | | | | | | | | | gives: % 81.04/16.09 | | | | | | | | | | | | | | | | | | | | | | | (808) all_826_0 = all_824_0 % 81.04/16.09 | | | | | | | | | | | | | | | | | | | | | | | % 81.04/16.09 | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (33) with all_820_0, all_826_0, % 81.04/16.09 | | | | | | | | | | | | | | | | | | | | | | | all_56_1, all_114_1, simplifying with (792), (794) % 81.04/16.09 | | | | | | | | | | | | | | | | | | | | | | | gives: % 81.04/16.09 | | | | | | | | | | | | | | | | | | | | | | | (809) all_826_0 = all_820_0 % 81.04/16.09 | | | | | | | | | | | | | | | | | | | | | | | % 81.04/16.09 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (808), (809) imply: % 81.04/16.09 | | | | | | | | | | | | | | | | | | | | | | | (810) all_824_0 = all_820_0 % 81.04/16.09 | | | | | | | | | | | | | | | | | | | | | | | % 81.04/16.09 | | | | | | | | | | | | | | | | | | | | | | | SIMP: (810) implies: % 81.04/16.09 | | | | | | | | | | | | | | | | | | | | | | | (811) all_824_0 = all_820_0 % 81.04/16.09 | | | | | | | | | | | | | | | | | | | | | | | % 81.04/16.09 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (807), (809) imply: % 81.04/16.09 | | | | | | | | | | | | | | | | | | | | | | | (812) all_820_0 = all_114_0 % 81.04/16.09 | | | | | | | | | | | | | | | | | | | | | | | % 81.04/16.09 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (806), (811) imply: % 81.04/16.09 | | | | | | | | | | | | | | | | | | | | | | | (813) all_820_0 = 0 % 81.04/16.09 | | | | | | | | | | | | | | | | | | | | | | | % 81.04/16.09 | | | | | | | | | | | | | | | | | | | | | | | SIMP: (813) implies: % 81.04/16.09 | | | | | | | | | | | | | | | | | | | | | | | (814) all_820_0 = 0 % 81.04/16.09 | | | | | | | | | | | | | | | | | | | | | | | % 81.04/16.09 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (812), (814) imply: % 81.04/16.09 | | | | | | | | | | | | | | | | | | | | | | | (815) all_114_0 = 0 % 81.04/16.09 | | | | | | | | | | | | | | | | | | | | | | | % 81.04/16.09 | | | | | | | | | | | | | | | | | | | | | | | SIMP: (815) implies: % 81.04/16.09 | | | | | | | | | | | | | | | | | | | | | | | (816) all_114_0 = 0 % 81.04/16.09 | | | | | | | | | | | | | | | | | | | | | | | % 81.04/16.09 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (301), (816) imply: % 81.04/16.09 | | | | | | | | | | | | | | | | | | | | | | | (817) $false % 81.04/16.09 | | | | | | | | | | | | | | | | | | | | | | | % 81.04/16.09 | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (817) is inconsistent. % 81.04/16.09 | | | | | | | | | | | | | | | | | | | | | | | % 81.04/16.09 | | | | | | | | | | | | | | | | | | | | | | End of split % 81.04/16.09 | | | | | | | | | | | | | | | | | | | | | | % 81.04/16.09 | | | | | | | | | | | | | | | | | | | | | End of split % 81.04/16.09 | | | | | | | | | | | | | | | | | | | | | % 81.04/16.09 | | | | | | | | | | | | | | | | | | | | End of split % 81.04/16.09 | | | | | | | | | | | | | | | | | | | | % 81.04/16.09 | | | | | | | | | | | | | | | | | | | End of split % 81.04/16.09 | | | | | | | | | | | | | | | | | | | % 81.04/16.09 | | | | | | | | | | | | | | | | | | Case 2: % 81.04/16.09 | | | | | | | | | | | | | | | | | | | % 81.04/16.09 | | | | | | | | | | | | | | | | | | | (818) all_126_2 = 0 % 81.04/16.09 | | | | | | | | | | | | | | | | | | | % 81.04/16.09 | | | | | | | | | | | | | | | | | | | REDUCE: (704), (818) imply: % 81.04/16.09 | | | | | | | | | | | | | | | | | | | (819) $false % 81.04/16.09 | | | | | | | | | | | | | | | | | | | % 81.04/16.09 | | | | | | | | | | | | | | | | | | | CLOSE: (819) is inconsistent. % 81.04/16.09 | | | | | | | | | | | | | | | | | | | % 81.04/16.09 | | | | | | | | | | | | | | | | | | End of split % 81.04/16.09 | | | | | | | | | | | | | | | | | | % 81.04/16.09 | | | | | | | | | | | | | | | | | Case 2: % 81.04/16.09 | | | | | | | | | | | | | | | | | | % 81.04/16.09 | | | | | | | | | | | | | | | | | | % 81.04/16.09 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (10) with all_56_1, all_42_4, % 81.04/16.09 | | | | | | | | | | | | | | | | | | all_42_3, all_42_2, all_42_1, all_110_1, % 81.04/16.09 | | | | | | | | | | | | | | | | | | all_108_1, simplifying with (50), (51), (52), % 81.04/16.09 | | | | | | | | | | | | | | | | | | (53), (194), (215), (219), (274), (294), (299), % 81.04/16.09 | | | | | | | | | | | | | | | | | | (454) gives: % 81.04/16.09 | | | | | | | | | | | | | | | | | | (820) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? % 81.04/16.09 | | | | | | | | | | | | | | | | | | [v3: $i] : ? [v4: any] : (ordered_pair(all_42_3, % 81.04/16.09 | | | | | | | | | | | | | | | | | | all_42_1) = v3 & in(v3, all_56_1) = v4 & % 81.04/16.09 | | | | | | | | | | | | | | | | | | in(all_42_1, all_42_4) = v2 & in(all_42_2, % 81.04/16.09 | | | | | | | | | | | | | | | | | | all_42_4) = v1 & in(all_42_3, all_42_4) = v0 & % 81.04/16.09 | | | | | | | | | | | | | | | | | | $i(v3) & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = % 81.04/16.09 | | | | | | | | | | | | | | | | | | 0) | v4 = 0)) % 81.04/16.09 | | | | | | | | | | | | | | | | | | % 81.04/16.09 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (9) with all_56_1, all_42_4, % 81.04/16.09 | | | | | | | | | | | | | | | | | | all_42_3, all_42_2, all_42_1, all_108_1, % 81.04/16.09 | | | | | | | | | | | | | | | | | | simplifying with (50), (51), (52), (53), (194), % 81.04/16.09 | | | | | | | | | | | | | | | | | | (215), (274), (299), (451), (454) gives: % 81.04/16.09 | | | | | | | | | | | | | | | | | | (821) ? [v0: any] : ? [v1: any] : ? [v2: $i] : ? % 81.04/16.09 | | | | | | | | | | | | | | | | | | [v3: any] : ? [v4: $i] : ? [v5: any] : % 81.04/16.09 | | | | | | | | | | | | | | | | | | (ordered_pair(all_42_3, all_42_1) = v4 & % 81.04/16.09 | | | | | | | | | | | | | | | | | | ordered_pair(all_42_3, all_42_2) = v2 & in(v4, % 81.04/16.09 | | | | | | | | | | | | | | | | | | all_56_1) = v5 & in(v2, all_56_1) = v3 & % 81.04/16.09 | | | | | | | | | | | | | | | | | | in(all_42_1, all_42_4) = v1 & in(all_42_2, % 81.04/16.09 | | | | | | | | | | | | | | | | | | all_42_4) = v0 & $i(v4) & $i(v2) & ( ~ (v3 = % 81.04/16.09 | | | | | | | | | | | | | | | | | | 0) | ~ (v1 = 0) | ~ (v0 = 0) | v5 = 0)) % 81.04/16.09 | | | | | | | | | | | | | | | | | | % 81.04/16.09 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (8) with all_56_1, all_42_4, % 81.04/16.09 | | | | | | | | | | | | | | | | | | all_42_3, all_42_2, all_42_1, all_110_1, % 81.04/16.09 | | | | | | | | | | | | | | | | | | simplifying with (50), (51), (52), (53), (194), % 81.04/16.09 | | | | | | | | | | | | | | | | | | (219), (274), (294), (447), (454) gives: % 81.04/16.09 | | | | | | | | | | | | | | | | | | (822) ? [v0: any] : ? [v1: any] : ? [v2: $i] : ? % 81.04/16.09 | | | | | | | | | | | | | | | | | | [v3: any] : ? [v4: $i] : ? [v5: any] : % 81.04/16.09 | | | | | | | | | | | | | | | | | | (ordered_pair(all_42_2, all_42_1) = v2 & % 81.04/16.09 | | | | | | | | | | | | | | | | | | ordered_pair(all_42_3, all_42_1) = v4 & in(v4, % 81.04/16.09 | | | | | | | | | | | | | | | | | | all_56_1) = v5 & in(v2, all_56_1) = v3 & % 81.04/16.09 | | | | | | | | | | | | | | | | | | in(all_42_2, all_42_4) = v1 & in(all_42_3, % 81.04/16.09 | | | | | | | | | | | | | | | | | | all_42_4) = v0 & $i(v4) & $i(v2) & ( ~ (v3 = % 81.04/16.09 | | | | | | | | | | | | | | | | | | 0) | ~ (v1 = 0) | ~ (v0 = 0) | v5 = 0)) % 81.04/16.09 | | | | | | | | | | | | | | | | | | % 81.04/16.09 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (7) with all_56_1, all_42_4, % 81.04/16.09 | | | | | | | | | | | | | | | | | | all_42_3, all_42_2, all_42_1, simplifying with % 81.04/16.09 | | | | | | | | | | | | | | | | | | (50), (51), (52), (53), (194), (274), (447), % 81.04/16.09 | | | | | | | | | | | | | | | | | | (449), (451), (454) gives: % 81.04/16.09 | | | | | | | | | | | | | | | | | | (823) ? [v0: $i] : ? [v1: any] : ? [v2: $i] : ? [v3: % 81.04/16.09 | | | | | | | | | | | | | | | | | | any] : ? [v4: $i] : ? [v5: any] : % 81.04/16.09 | | | | | | | | | | | | | | | | | | (ordered_pair(all_42_2, all_42_1) = v2 & % 81.04/16.09 | | | | | | | | | | | | | | | | | | ordered_pair(all_42_3, all_42_1) = v4 & % 81.04/16.09 | | | | | | | | | | | | | | | | | | ordered_pair(all_42_3, all_42_2) = v0 & in(v4, % 81.04/16.09 | | | | | | | | | | | | | | | | | | all_56_1) = v5 & in(v2, all_56_1) = v3 & % 81.04/16.09 | | | | | | | | | | | | | | | | | | in(v0, all_56_1) = v1 & $i(v4) & $i(v2) & $i(v0) % 81.04/16.09 | | | | | | | | | | | | | | | | | | & ( ~ (v3 = 0) | ~ (v1 = 0) | v5 = 0)) % 81.04/16.09 | | | | | | | | | | | | | | | | | | % 81.04/16.09 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (19) with all_82_2, all_190_1, % 81.04/16.09 | | | | | | | | | | | | | | | | | | all_420_0, simplifying with (138), (516), (517) % 81.04/16.09 | | | | | | | | | | | | | | | | | | gives: % 81.04/16.09 | | | | | | | | | | | | | | | | | | (824) all_420_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & % 81.04/16.09 | | | | | | | | | | | | | | | | | | in(all_82_2, all_190_1) = v0) % 81.04/16.09 | | | | | | | | | | | | | | | | | | % 81.04/16.09 | | | | | | | | | | | | | | | | | | DELTA: instantiating (820) with fresh symbols all_798_0, % 81.04/16.09 | | | | | | | | | | | | | | | | | | all_798_1, all_798_2, all_798_3, all_798_4 gives: % 81.04/16.09 | | | | | | | | | | | | | | | | | | (825) ordered_pair(all_42_3, all_42_1) = all_798_1 & % 81.04/16.09 | | | | | | | | | | | | | | | | | | in(all_798_1, all_56_1) = all_798_0 & in(all_42_1, % 81.04/16.09 | | | | | | | | | | | | | | | | | | all_42_4) = all_798_2 & in(all_42_2, all_42_4) = % 81.04/16.09 | | | | | | | | | | | | | | | | | | all_798_3 & in(all_42_3, all_42_4) = all_798_4 & % 81.04/16.09 | | | | | | | | | | | | | | | | | | $i(all_798_1) & ( ~ (all_798_2 = 0) | ~ % 81.04/16.09 | | | | | | | | | | | | | | | | | | (all_798_3 = 0) | ~ (all_798_4 = 0) | all_798_0 % 81.04/16.09 | | | | | | | | | | | | | | | | | | = 0) % 81.04/16.09 | | | | | | | | | | | | | | | | | | % 81.04/16.09 | | | | | | | | | | | | | | | | | | ALPHA: (825) implies: % 81.04/16.09 | | | | | | | | | | | | | | | | | | (826) in(all_42_3, all_42_4) = all_798_4 % 81.04/16.09 | | | | | | | | | | | | | | | | | | (827) in(all_42_2, all_42_4) = all_798_3 % 81.04/16.09 | | | | | | | | | | | | | | | | | | (828) in(all_42_1, all_42_4) = all_798_2 % 81.04/16.09 | | | | | | | | | | | | | | | | | | (829) in(all_798_1, all_56_1) = all_798_0 % 81.04/16.09 | | | | | | | | | | | | | | | | | | (830) ordered_pair(all_42_3, all_42_1) = all_798_1 % 81.04/16.09 | | | | | | | | | | | | | | | | | | (831) ~ (all_798_2 = 0) | ~ (all_798_3 = 0) | ~ % 81.04/16.09 | | | | | | | | | | | | | | | | | | (all_798_4 = 0) | all_798_0 = 0 % 81.04/16.09 | | | | | | | | | | | | | | | | | | % 81.04/16.09 | | | | | | | | | | | | | | | | | | DELTA: instantiating (821) with fresh symbols all_800_0, % 81.04/16.09 | | | | | | | | | | | | | | | | | | all_800_1, all_800_2, all_800_3, all_800_4, % 81.04/16.09 | | | | | | | | | | | | | | | | | | all_800_5 gives: % 81.04/16.09 | | | | | | | | | | | | | | | | | | (832) ordered_pair(all_42_3, all_42_1) = all_800_1 & % 81.04/16.09 | | | | | | | | | | | | | | | | | | ordered_pair(all_42_3, all_42_2) = all_800_3 & % 81.04/16.09 | | | | | | | | | | | | | | | | | | in(all_800_1, all_56_1) = all_800_0 & % 81.04/16.09 | | | | | | | | | | | | | | | | | | in(all_800_3, all_56_1) = all_800_2 & in(all_42_1, % 81.04/16.09 | | | | | | | | | | | | | | | | | | all_42_4) = all_800_4 & in(all_42_2, all_42_4) = % 81.04/16.09 | | | | | | | | | | | | | | | | | | all_800_5 & $i(all_800_1) & $i(all_800_3) & ( ~ % 81.04/16.09 | | | | | | | | | | | | | | | | | | (all_800_2 = 0) | ~ (all_800_4 = 0) | ~ % 81.04/16.09 | | | | | | | | | | | | | | | | | | (all_800_5 = 0) | all_800_0 = 0) % 81.04/16.09 | | | | | | | | | | | | | | | | | | % 81.04/16.09 | | | | | | | | | | | | | | | | | | ALPHA: (832) implies: % 81.04/16.09 | | | | | | | | | | | | | | | | | | (833) in(all_42_2, all_42_4) = all_800_5 % 81.04/16.09 | | | | | | | | | | | | | | | | | | (834) in(all_42_1, all_42_4) = all_800_4 % 81.04/16.09 | | | | | | | | | | | | | | | | | | (835) in(all_800_1, all_56_1) = all_800_0 % 81.04/16.09 | | | | | | | | | | | | | | | | | | (836) ordered_pair(all_42_3, all_42_1) = all_800_1 % 81.04/16.09 | | | | | | | | | | | | | | | | | | % 81.04/16.09 | | | | | | | | | | | | | | | | | | DELTA: instantiating (823) with fresh symbols all_802_0, % 81.04/16.09 | | | | | | | | | | | | | | | | | | all_802_1, all_802_2, all_802_3, all_802_4, % 81.04/16.09 | | | | | | | | | | | | | | | | | | all_802_5 gives: % 81.04/16.09 | | | | | | | | | | | | | | | | | | (837) ordered_pair(all_42_2, all_42_1) = all_802_3 & % 81.04/16.09 | | | | | | | | | | | | | | | | | | ordered_pair(all_42_3, all_42_1) = all_802_1 & % 81.04/16.09 | | | | | | | | | | | | | | | | | | ordered_pair(all_42_3, all_42_2) = all_802_5 & % 81.04/16.09 | | | | | | | | | | | | | | | | | | in(all_802_1, all_56_1) = all_802_0 & % 81.04/16.09 | | | | | | | | | | | | | | | | | | in(all_802_3, all_56_1) = all_802_2 & % 81.04/16.09 | | | | | | | | | | | | | | | | | | in(all_802_5, all_56_1) = all_802_4 & % 81.04/16.09 | | | | | | | | | | | | | | | | | | $i(all_802_1) & $i(all_802_3) & $i(all_802_5) & ( % 81.04/16.09 | | | | | | | | | | | | | | | | | | ~ (all_802_2 = 0) | ~ (all_802_4 = 0) | % 81.04/16.09 | | | | | | | | | | | | | | | | | | all_802_0 = 0) % 81.04/16.09 | | | | | | | | | | | | | | | | | | % 81.04/16.09 | | | | | | | | | | | | | | | | | | ALPHA: (837) implies: % 81.04/16.09 | | | | | | | | | | | | | | | | | | (838) in(all_802_1, all_56_1) = all_802_0 % 81.04/16.09 | | | | | | | | | | | | | | | | | | (839) ordered_pair(all_42_3, all_42_1) = all_802_1 % 81.04/16.09 | | | | | | | | | | | | | | | | | | % 81.04/16.09 | | | | | | | | | | | | | | | | | | DELTA: instantiating (822) with fresh symbols all_804_0, % 81.04/16.09 | | | | | | | | | | | | | | | | | | all_804_1, all_804_2, all_804_3, all_804_4, % 81.04/16.09 | | | | | | | | | | | | | | | | | | all_804_5 gives: % 81.04/16.09 | | | | | | | | | | | | | | | | | | (840) ordered_pair(all_42_2, all_42_1) = all_804_3 & % 81.04/16.09 | | | | | | | | | | | | | | | | | | ordered_pair(all_42_3, all_42_1) = all_804_1 & % 81.04/16.09 | | | | | | | | | | | | | | | | | | in(all_804_1, all_56_1) = all_804_0 & % 81.04/16.09 | | | | | | | | | | | | | | | | | | in(all_804_3, all_56_1) = all_804_2 & in(all_42_2, % 81.04/16.09 | | | | | | | | | | | | | | | | | | all_42_4) = all_804_4 & in(all_42_3, all_42_4) = % 81.04/16.09 | | | | | | | | | | | | | | | | | | all_804_5 & $i(all_804_1) & $i(all_804_3) & ( ~ % 81.04/16.09 | | | | | | | | | | | | | | | | | | (all_804_2 = 0) | ~ (all_804_4 = 0) | ~ % 81.04/16.09 | | | | | | | | | | | | | | | | | | (all_804_5 = 0) | all_804_0 = 0) % 81.04/16.09 | | | | | | | | | | | | | | | | | | % 81.04/16.09 | | | | | | | | | | | | | | | | | | ALPHA: (840) implies: % 81.04/16.09 | | | | | | | | | | | | | | | | | | (841) in(all_42_3, all_42_4) = all_804_5 % 81.04/16.09 | | | | | | | | | | | | | | | | | | (842) in(all_42_2, all_42_4) = all_804_4 % 81.04/16.09 | | | | | | | | | | | | | | | | | | (843) in(all_804_1, all_56_1) = all_804_0 % 81.04/16.09 | | | | | | | | | | | | | | | | | | (844) ordered_pair(all_42_3, all_42_1) = all_804_1 % 81.04/16.09 | | | | | | | | | | | | | | | | | | % 81.04/16.09 | | | | | | | | | | | | | | | | | | BETA: splitting (824) gives: % 81.04/16.09 | | | | | | | | | | | | | | | | | | % 81.04/16.09 | | | | | | | | | | | | | | | | | | Case 1: % 81.04/16.09 | | | | | | | | | | | | | | | | | | | % 81.04/16.09 | | | | | | | | | | | | | | | | | | | (845) all_420_0 = 0 % 81.04/16.09 | | | | | | | | | | | | | | | | | | | % 81.04/16.09 | | | | | | | | | | | | | | | | | | | REDUCE: (483), (845) imply: % 81.04/16.09 | | | | | | | | | | | | | | | | | | | (846) $false % 81.04/16.09 | | | | | | | | | | | | | | | | | | | % 81.04/16.09 | | | | | | | | | | | | | | | | | | | CLOSE: (846) is inconsistent. % 81.04/16.09 | | | | | | | | | | | | | | | | | | | % 81.04/16.09 | | | | | | | | | | | | | | | | | | Case 2: % 81.04/16.09 | | | | | | | | | | | | | | | | | | | % 81.04/16.09 | | | | | | | | | | | | | | | | | | | % 81.04/16.09 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (33) with 0, all_804_5, all_42_4, % 81.04/16.09 | | | | | | | | | | | | | | | | | | | all_42_3, simplifying with (451), (841) gives: % 81.04/16.09 | | | | | | | | | | | | | | | | | | | (847) all_804_5 = 0 % 81.04/16.09 | | | | | | | | | | | | | | | | | | | % 81.04/16.09 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (33) with all_798_4, all_804_5, % 81.04/16.09 | | | | | | | | | | | | | | | | | | | all_42_4, all_42_3, simplifying with (826), (841) % 81.04/16.09 | | | | | | | | | | | | | | | | | | | gives: % 81.04/16.09 | | | | | | | | | | | | | | | | | | | (848) all_804_5 = all_798_4 % 81.04/16.09 | | | | | | | | | | | | | | | | | | | % 81.04/16.09 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (33) with 0, all_804_4, all_42_4, % 81.04/16.09 | | | | | | | | | | | | | | | | | | | all_42_2, simplifying with (449), (842) gives: % 81.04/16.09 | | | | | | | | | | | | | | | | | | | (849) all_804_4 = 0 % 81.04/16.09 | | | | | | | | | | | | | | | | | | | % 81.04/16.09 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (33) with all_800_5, all_804_4, % 81.04/16.09 | | | | | | | | | | | | | | | | | | | all_42_4, all_42_2, simplifying with (833), (842) % 81.04/16.09 | | | | | | | | | | | | | | | | | | | gives: % 81.04/16.09 | | | | | | | | | | | | | | | | | | | (850) all_804_4 = all_800_5 % 81.04/16.09 | | | | | | | | | | | | | | | | | | | % 81.04/16.09 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (33) with all_798_3, all_804_4, % 81.04/16.09 | | | | | | | | | | | | | | | | | | | all_42_4, all_42_2, simplifying with (827), (842) % 81.04/16.09 | | | | | | | | | | | | | | | | | | | gives: % 81.04/16.09 | | | | | | | | | | | | | | | | | | | (851) all_804_4 = all_798_3 % 81.04/16.09 | | | | | | | | | | | | | | | | | | | % 81.04/16.09 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (33) with 0, all_800_4, all_42_4, % 81.04/16.09 | | | | | | | | | | | | | | | | | | | all_42_1, simplifying with (447), (834) gives: % 81.04/16.09 | | | | | | | | | | | | | | | | | | | (852) all_800_4 = 0 % 81.04/16.09 | | | | | | | | | | | | | | | | | | | % 81.04/16.09 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (33) with all_798_2, all_800_4, % 81.04/16.09 | | | | | | | | | | | | | | | | | | | all_42_4, all_42_1, simplifying with (828), (834) % 81.04/16.09 | | | | | | | | | | | | | | | | | | | gives: % 81.04/16.09 | | | | | | | | | | | | | | | | | | | (853) all_800_4 = all_798_2 % 81.04/16.09 | | | | | | | | | | | | | | | | | | | % 81.04/16.09 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (35) with all_114_1, all_800_1, % 81.04/16.09 | | | | | | | | | | | | | | | | | | | all_42_1, all_42_3, simplifying with (225), (836) % 81.04/16.09 | | | | | | | | | | | | | | | | | | | gives: % 81.04/16.09 | | | | | | | | | | | | | | | | | | | (854) all_800_1 = all_114_1 % 81.04/16.09 | | | | | | | | | | | | | | | | | | | % 81.04/16.09 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (35) with all_802_1, all_804_1, % 81.04/16.09 | | | | | | | | | | | | | | | | | | | all_42_1, all_42_3, simplifying with (839), (844) % 81.04/16.09 | | | | | | | | | | | | | | | | | | | gives: % 81.04/16.09 | | | | | | | | | | | | | | | | | | | (855) all_804_1 = all_802_1 % 81.04/16.09 | | | | | | | | | | | | | | | | | | | % 81.04/16.09 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (35) with all_800_1, all_804_1, % 81.04/16.09 | | | | | | | | | | | | | | | | | | | all_42_1, all_42_3, simplifying with (836), (844) % 81.04/16.09 | | | | | | | | | | | | | | | | | | | gives: % 81.04/16.09 | | | | | | | | | | | | | | | | | | | (856) all_804_1 = all_800_1 % 81.04/16.09 | | | | | | | | | | | | | | | | | | | % 81.04/16.09 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (35) with all_798_1, all_804_1, % 81.04/16.09 | | | | | | | | | | | | | | | | | | | all_42_1, all_42_3, simplifying with (830), (844) % 81.04/16.09 | | | | | | | | | | | | | | | | | | | gives: % 81.04/16.09 | | | | | | | | | | | | | | | | | | | (857) all_804_1 = all_798_1 % 81.04/16.09 | | | | | | | | | | | | | | | | | | | % 81.04/16.09 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (855), (856) imply: % 81.04/16.09 | | | | | | | | | | | | | | | | | | | (858) all_802_1 = all_800_1 % 81.04/16.09 | | | | | | | | | | | | | | | | | | | % 81.04/16.09 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (855), (857) imply: % 81.04/16.09 | | | | | | | | | | | | | | | | | | | (859) all_802_1 = all_798_1 % 81.04/16.09 | | | | | | | | | | | | | | | | | | | % 81.04/16.09 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (849), (850) imply: % 81.04/16.09 | | | | | | | | | | | | | | | | | | | (860) all_800_5 = 0 % 81.04/16.09 | | | | | | | | | | | | | | | | | | | % 81.04/16.09 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (850), (851) imply: % 81.04/16.09 | | | | | | | | | | | | | | | | | | | (861) all_800_5 = all_798_3 % 81.04/16.09 | | | | | | | | | | | | | | | | | | | % 81.04/16.09 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (847), (848) imply: % 81.04/16.09 | | | | | | | | | | | | | | | | | | | (862) all_798_4 = 0 % 81.04/16.09 | | | | | | | | | | | | | | | | | | | % 81.04/16.09 | | | | | | | | | | | | | | | | | | | SIMP: (862) implies: % 81.04/16.09 | | | | | | | | | | | | | | | | | | | (863) all_798_4 = 0 % 81.04/16.09 | | | | | | | | | | | | | | | | | | | % 81.04/16.09 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (858), (859) imply: % 81.04/16.09 | | | | | | | | | | | | | | | | | | | (864) all_800_1 = all_798_1 % 81.04/16.09 | | | | | | | | | | | | | | | | | | | % 81.04/16.09 | | | | | | | | | | | | | | | | | | | SIMP: (864) implies: % 81.04/16.09 | | | | | | | | | | | | | | | | | | | (865) all_800_1 = all_798_1 % 81.04/16.09 | | | | | | | | | | | | | | | | | | | % 81.04/16.09 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (854), (865) imply: % 81.04/16.09 | | | | | | | | | | | | | | | | | | | (866) all_798_1 = all_114_1 % 81.04/16.09 | | | | | | | | | | | | | | | | | | | % 81.04/16.09 | | | | | | | | | | | | | | | | | | | SIMP: (866) implies: % 81.04/16.10 | | | | | | | | | | | | | | | | | | | (867) all_798_1 = all_114_1 % 81.04/16.10 | | | | | | | | | | | | | | | | | | | % 81.04/16.10 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (852), (853) imply: % 81.04/16.10 | | | | | | | | | | | | | | | | | | | (868) all_798_2 = 0 % 81.04/16.10 | | | | | | | | | | | | | | | | | | | % 81.04/16.10 | | | | | | | | | | | | | | | | | | | SIMP: (868) implies: % 81.04/16.10 | | | | | | | | | | | | | | | | | | | (869) all_798_2 = 0 % 81.04/16.10 | | | | | | | | | | | | | | | | | | | % 81.04/16.10 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (860), (861) imply: % 81.04/16.10 | | | | | | | | | | | | | | | | | | | (870) all_798_3 = 0 % 81.04/16.10 | | | | | | | | | | | | | | | | | | | % 81.04/16.10 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (859), (867) imply: % 81.04/16.10 | | | | | | | | | | | | | | | | | | | (871) all_802_1 = all_114_1 % 81.04/16.10 | | | | | | | | | | | | | | | | | | | % 81.04/16.10 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (855), (871) imply: % 81.04/16.10 | | | | | | | | | | | | | | | | | | | (872) all_804_1 = all_114_1 % 81.04/16.10 | | | | | | | | | | | | | | | | | | | % 81.04/16.10 | | | | | | | | | | | | | | | | | | | REDUCE: (843), (872) imply: % 81.04/16.10 | | | | | | | | | | | | | | | | | | | (873) in(all_114_1, all_56_1) = all_804_0 % 81.04/16.10 | | | | | | | | | | | | | | | | | | | % 81.04/16.10 | | | | | | | | | | | | | | | | | | | REDUCE: (838), (871) imply: % 81.04/16.10 | | | | | | | | | | | | | | | | | | | (874) in(all_114_1, all_56_1) = all_802_0 % 81.04/16.10 | | | | | | | | | | | | | | | | | | | % 81.04/16.10 | | | | | | | | | | | | | | | | | | | REDUCE: (835), (854) imply: % 81.04/16.10 | | | | | | | | | | | | | | | | | | | (875) in(all_114_1, all_56_1) = all_800_0 % 81.04/16.10 | | | | | | | | | | | | | | | | | | | % 81.04/16.10 | | | | | | | | | | | | | | | | | | | REDUCE: (829), (867) imply: % 81.04/16.10 | | | | | | | | | | | | | | | | | | | (876) in(all_114_1, all_56_1) = all_798_0 % 81.04/16.10 | | | | | | | | | | | | | | | | | | | % 81.04/16.10 | | | | | | | | | | | | | | | | | | | BETA: splitting (831) gives: % 81.04/16.10 | | | | | | | | | | | | | | | | | | | % 81.04/16.10 | | | | | | | | | | | | | | | | | | | Case 1: % 81.04/16.10 | | | | | | | | | | | | | | | | | | | | % 81.04/16.10 | | | | | | | | | | | | | | | | | | | | (877) ~ (all_798_2 = 0) % 81.04/16.10 | | | | | | | | | | | | | | | | | | | | % 81.04/16.10 | | | | | | | | | | | | | | | | | | | | REDUCE: (869), (877) imply: % 81.04/16.10 | | | | | | | | | | | | | | | | | | | | (878) $false % 81.04/16.10 | | | | | | | | | | | | | | | | | | | | % 81.04/16.10 | | | | | | | | | | | | | | | | | | | | CLOSE: (878) is inconsistent. % 81.04/16.10 | | | | | | | | | | | | | | | | | | | | % 81.04/16.10 | | | | | | | | | | | | | | | | | | | Case 2: % 81.04/16.10 | | | | | | | | | | | | | | | | | | | | % 81.04/16.10 | | | | | | | | | | | | | | | | | | | | (879) ~ (all_798_3 = 0) | ~ (all_798_4 = 0) | % 81.04/16.10 | | | | | | | | | | | | | | | | | | | | all_798_0 = 0 % 81.04/16.10 | | | | | | | | | | | | | | | | | | | | % 81.04/16.10 | | | | | | | | | | | | | | | | | | | | BETA: splitting (879) gives: % 81.04/16.10 | | | | | | | | | | | | | | | | | | | | % 81.04/16.10 | | | | | | | | | | | | | | | | | | | | Case 1: % 81.04/16.10 | | | | | | | | | | | | | | | | | | | | | % 81.04/16.10 | | | | | | | | | | | | | | | | | | | | | (880) ~ (all_798_3 = 0) % 81.04/16.10 | | | | | | | | | | | | | | | | | | | | | % 81.04/16.10 | | | | | | | | | | | | | | | | | | | | | REDUCE: (870), (880) imply: % 81.04/16.10 | | | | | | | | | | | | | | | | | | | | | (881) $false % 81.04/16.10 | | | | | | | | | | | | | | | | | | | | | % 81.04/16.10 | | | | | | | | | | | | | | | | | | | | | CLOSE: (881) is inconsistent. % 81.04/16.10 | | | | | | | | | | | | | | | | | | | | | % 81.04/16.10 | | | | | | | | | | | | | | | | | | | | Case 2: % 81.04/16.10 | | | | | | | | | | | | | | | | | | | | | % 81.04/16.10 | | | | | | | | | | | | | | | | | | | | | (882) ~ (all_798_4 = 0) | all_798_0 = 0 % 81.04/16.10 | | | | | | | | | | | | | | | | | | | | | % 81.04/16.10 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (882) gives: % 81.04/16.10 | | | | | | | | | | | | | | | | | | | | | % 81.04/16.10 | | | | | | | | | | | | | | | | | | | | | Case 1: % 81.04/16.10 | | | | | | | | | | | | | | | | | | | | | | % 81.04/16.10 | | | | | | | | | | | | | | | | | | | | | | (883) ~ (all_798_4 = 0) % 81.04/16.10 | | | | | | | | | | | | | | | | | | | | | | % 81.04/16.10 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (863), (883) imply: % 81.04/16.10 | | | | | | | | | | | | | | | | | | | | | | (884) $false % 81.04/16.10 | | | | | | | | | | | | | | | | | | | | | | % 81.04/16.10 | | | | | | | | | | | | | | | | | | | | | | CLOSE: (884) is inconsistent. % 81.04/16.10 | | | | | | | | | | | | | | | | | | | | | | % 81.04/16.10 | | | | | | | | | | | | | | | | | | | | | Case 2: % 81.04/16.10 | | | | | | | | | | | | | | | | | | | | | | % 81.04/16.10 | | | | | | | | | | | | | | | | | | | | | | (885) all_798_0 = 0 % 81.04/16.10 | | | | | | | | | | | | | | | | | | | | | | % 81.04/16.10 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (876), (885) imply: % 81.04/16.10 | | | | | | | | | | | | | | | | | | | | | | (886) in(all_114_1, all_56_1) = 0 % 81.04/16.10 | | | | | | | | | | | | | | | | | | | | | | % 81.04/16.10 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (33) with all_114_0, all_802_0, % 81.04/16.10 | | | | | | | | | | | | | | | | | | | | | | all_56_1, all_114_1, simplifying with (269), (874) % 81.04/16.10 | | | | | | | | | | | | | | | | | | | | | | gives: % 81.04/16.10 | | | | | | | | | | | | | | | | | | | | | | (887) all_802_0 = all_114_0 % 81.04/16.10 | | | | | | | | | | | | | | | | | | | | | | % 81.04/16.10 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (33) with 0, all_802_0, all_56_1, % 81.04/16.10 | | | | | | | | | | | | | | | | | | | | | | all_114_1, simplifying with (874), (886) gives: % 81.04/16.10 | | | | | | | | | | | | | | | | | | | | | | (888) all_802_0 = 0 % 81.04/16.10 | | | | | | | | | | | | | | | | | | | | | | % 81.04/16.10 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (33) with all_802_0, all_804_0, % 81.04/16.10 | | | | | | | | | | | | | | | | | | | | | | all_56_1, all_114_1, simplifying with (873), (874) % 81.04/16.10 | | | | | | | | | | | | | | | | | | | | | | gives: % 81.04/16.10 | | | | | | | | | | | | | | | | | | | | | | (889) all_804_0 = all_802_0 % 81.04/16.10 | | | | | | | | | | | | | | | | | | | | | | % 81.04/16.10 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (33) with all_800_0, all_804_0, % 81.04/16.10 | | | | | | | | | | | | | | | | | | | | | | all_56_1, all_114_1, simplifying with (873), (875) % 81.04/16.10 | | | | | | | | | | | | | | | | | | | | | | gives: % 81.04/16.10 | | | | | | | | | | | | | | | | | | | | | | (890) all_804_0 = all_800_0 % 81.04/16.10 | | | | | | | | | | | | | | | | | | | | | | % 81.04/16.10 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (889), (890) imply: % 81.04/16.10 | | | | | | | | | | | | | | | | | | | | | | (891) all_802_0 = all_800_0 % 81.04/16.10 | | | | | | | | | | | | | | | | | | | | | | % 81.04/16.10 | | | | | | | | | | | | | | | | | | | | | | SIMP: (891) implies: % 81.04/16.10 | | | | | | | | | | | | | | | | | | | | | | (892) all_802_0 = all_800_0 % 81.04/16.10 | | | | | | | | | | | | | | | | | | | | | | % 81.04/16.10 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (887), (892) imply: % 81.04/16.10 | | | | | | | | | | | | | | | | | | | | | | (893) all_800_0 = all_114_0 % 81.04/16.10 | | | | | | | | | | | | | | | | | | | | | | % 81.04/16.10 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (888), (892) imply: % 81.04/16.10 | | | | | | | | | | | | | | | | | | | | | | (894) all_800_0 = 0 % 81.04/16.10 | | | | | | | | | | | | | | | | | | | | | | % 81.04/16.10 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (893), (894) imply: % 81.04/16.10 | | | | | | | | | | | | | | | | | | | | | | (895) all_114_0 = 0 % 81.04/16.10 | | | | | | | | | | | | | | | | | | | | | | % 81.04/16.10 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (301), (895) imply: % 81.04/16.10 | | | | | | | | | | | | | | | | | | | | | | (896) $false % 81.04/16.10 | | | | | | | | | | | | | | | | | | | | | | % 81.04/16.10 | | | | | | | | | | | | | | | | | | | | | | CLOSE: (896) is inconsistent. % 81.04/16.10 | | | | | | | | | | | | | | | | | | | | | | % 81.04/16.10 | | | | | | | | | | | | | | | | | | | | | End of split % 81.04/16.10 | | | | | | | | | | | | | | | | | | | | | % 81.04/16.10 | | | | | | | | | | | | | | | | | | | | End of split % 81.04/16.10 | | | | | | | | | | | | | | | | | | | | % 81.04/16.10 | | | | | | | | | | | | | | | | | | | End of split % 81.04/16.10 | | | | | | | | | | | | | | | | | | | % 81.04/16.10 | | | | | | | | | | | | | | | | | | End of split % 81.04/16.10 | | | | | | | | | | | | | | | | | | % 81.04/16.10 | | | | | | | | | | | | | | | | | End of split % 81.04/16.10 | | | | | | | | | | | | | | | | | % 81.04/16.10 | | | | | | | | | | | | | | | | End of split % 81.04/16.10 | | | | | | | | | | | | | | | | % 81.04/16.10 | | | | | | | | | | | | | | | End of split % 81.04/16.10 | | | | | | | | | | | | | | | % 81.04/16.10 | | | | | | | | | | | | | | End of split % 81.04/16.10 | | | | | | | | | | | | | | % 81.04/16.10 | | | | | | | | | | | | | Case 2: % 81.04/16.10 | | | | | | | | | | | | | | % 81.04/16.10 | | | | | | | | | | | | | | (897) all_54_1 = 0 % 81.04/16.10 | | | | | | | | | | | | | | % 81.04/16.10 | | | | | | | | | | | | | | COMBINE_EQS: (162), (897) imply: % 81.04/16.10 | | | | | | | | | | | | | | (898) all_50_1 = 0 % 81.04/16.10 | | | | | | | | | | | | | | % 81.04/16.10 | | | | | | | | | | | | | | REDUCE: (80), (898) imply: % 81.04/16.10 | | | | | | | | | | | | | | (899) empty(all_42_4) = 0 % 81.04/16.10 | | | | | | | | | | | | | | % 81.04/16.10 | | | | | | | | | | | | | | GROUND_INST: instantiating (t7_boole) with all_42_1, all_42_4, % 81.04/16.10 | | | | | | | | | | | | | | simplifying with (50), (53), (447) gives: % 81.04/16.10 | | | | | | | | | | | | | | (900) ? [v0: int] : ( ~ (v0 = 0) & empty(all_42_4) = % 81.04/16.10 | | | | | | | | | | | | | | v0) % 81.04/16.10 | | | | | | | | | | | | | | % 81.04/16.10 | | | | | | | | | | | | | | GROUND_INST: instantiating (fc4_subset_1) with all_42_4, % 81.04/16.10 | | | | | | | | | | | | | | all_42_4, all_194_1, simplifying with (50), (352) % 81.04/16.10 | | | | | | | | | | | | | | gives: % 81.04/16.10 | | | | | | | | | | | | | | (901) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 81.04/16.10 | | | | | | | | | | | | | | (empty(all_194_1) = v2 & empty(all_42_4) = v1 & % 81.04/16.10 | | | | | | | | | | | | | | empty(all_42_4) = v0 & ( ~ (v2 = 0) | v1 = 0 | % 81.04/16.10 | | | | | | | | | | | | | | v0 = 0)) % 81.04/16.10 | | | | | | | | | | | | | | % 81.04/16.10 | | | | | | | | | | | | | | GROUND_INST: instantiating (t8_boole) with all_42_4, all_186_0, % 81.04/16.10 | | | | | | | | | | | | | | simplifying with (50), (336), (337), (899) gives: % 81.04/16.10 | | | | | | | | | | | | | | (902) all_186_0 = all_42_4 % 81.04/16.10 | | | | | | | | | | | | | | % 81.04/16.10 | | | | | | | | | | | | | | GROUND_INST: instantiating (26) with all_186_0, simplifying % 81.04/16.10 | | | | | | | | | | | | | | with (336), (337) gives: % 81.04/16.10 | | | | | | | | | | | | | | (903) all_186_0 = empty_set % 81.04/16.10 | | | | | | | | | | | | | | % 81.04/16.10 | | | | | | | | | | | | | | COMBINE_EQS: (902), (903) imply: % 81.04/16.10 | | | | | | | | | | | | | | (904) all_42_4 = empty_set % 81.04/16.10 | | | | | | | | | | | | | | % 81.04/16.10 | | | | | | | | | | | | | | DELTA: instantiating (900) with fresh symbol all_354_0 % 81.04/16.10 | | | | | | | | | | | | | | gives: % 81.04/16.10 | | | | | | | | | | | | | | (905) ~ (all_354_0 = 0) & empty(all_42_4) = all_354_0 % 81.04/16.10 | | | | | | | | | | | | | | % 81.04/16.10 | | | | | | | | | | | | | | ALPHA: (905) implies: % 81.04/16.10 | | | | | | | | | | | | | | (906) ~ (all_354_0 = 0) % 81.04/16.10 | | | | | | | | | | | | | | (907) empty(all_42_4) = all_354_0 % 81.04/16.10 | | | | | | | | | | | | | | % 81.04/16.10 | | | | | | | | | | | | | | DELTA: instantiating (901) with fresh symbols all_460_0, % 81.04/16.10 | | | | | | | | | | | | | | all_460_1, all_460_2 gives: % 81.04/16.10 | | | | | | | | | | | | | | (908) empty(all_194_1) = all_460_0 & empty(all_42_4) = % 81.04/16.10 | | | | | | | | | | | | | | all_460_1 & empty(all_42_4) = all_460_2 & ( ~ % 81.04/16.10 | | | | | | | | | | | | | | (all_460_0 = 0) | all_460_1 = 0 | all_460_2 = 0) % 81.04/16.10 | | | | | | | | | | | | | | % 81.04/16.10 | | | | | | | | | | | | | | ALPHA: (908) implies: % 81.04/16.10 | | | | | | | | | | | | | | (909) empty(all_42_4) = all_460_2 % 81.04/16.10 | | | | | | | | | | | | | | (910) empty(all_42_4) = all_460_1 % 81.04/16.10 | | | | | | | | | | | | | | % 81.04/16.10 | | | | | | | | | | | | | | REDUCE: (904), (910) imply: % 81.04/16.10 | | | | | | | | | | | | | | (911) empty(empty_set) = all_460_1 % 81.04/16.10 | | | | | | | | | | | | | | % 81.04/16.10 | | | | | | | | | | | | | | REDUCE: (904), (909) imply: % 81.04/16.10 | | | | | | | | | | | | | | (912) empty(empty_set) = all_460_2 % 81.04/16.10 | | | | | | | | | | | | | | % 81.04/16.10 | | | | | | | | | | | | | | REDUCE: (904), (907) imply: % 81.04/16.10 | | | | | | | | | | | | | | (913) empty(empty_set) = all_354_0 % 81.04/16.10 | | | | | | | | | | | | | | % 81.04/16.10 | | | | | | | | | | | | | | GROUND_INST: instantiating (32) with 0, all_460_2, empty_set, % 81.04/16.10 | | | | | | | | | | | | | | simplifying with (131), (912) gives: % 81.04/16.10 | | | | | | | | | | | | | | (914) all_460_2 = 0 % 81.04/16.10 | | | | | | | | | | | | | | % 81.04/16.10 | | | | | | | | | | | | | | GROUND_INST: instantiating (32) with all_460_2, all_460_1, % 81.04/16.10 | | | | | | | | | | | | | | empty_set, simplifying with (911), (912) gives: % 81.04/16.10 | | | | | | | | | | | | | | (915) all_460_1 = all_460_2 % 81.04/16.10 | | | | | | | | | | | | | | % 81.04/16.10 | | | | | | | | | | | | | | GROUND_INST: instantiating (32) with all_354_0, all_460_1, % 81.04/16.10 | | | | | | | | | | | | | | empty_set, simplifying with (911), (913) gives: % 81.04/16.10 | | | | | | | | | | | | | | (916) all_460_1 = all_354_0 % 81.04/16.10 | | | | | | | | | | | | | | % 81.04/16.10 | | | | | | | | | | | | | | COMBINE_EQS: (915), (916) imply: % 81.04/16.10 | | | | | | | | | | | | | | (917) all_460_2 = all_354_0 % 81.04/16.10 | | | | | | | | | | | | | | % 81.04/16.10 | | | | | | | | | | | | | | SIMP: (917) implies: % 81.04/16.10 | | | | | | | | | | | | | | (918) all_460_2 = all_354_0 % 81.04/16.10 | | | | | | | | | | | | | | % 81.04/16.10 | | | | | | | | | | | | | | COMBINE_EQS: (914), (918) imply: % 81.04/16.10 | | | | | | | | | | | | | | (919) all_354_0 = 0 % 81.04/16.10 | | | | | | | | | | | | | | % 81.04/16.10 | | | | | | | | | | | | | | REDUCE: (906), (919) imply: % 81.04/16.10 | | | | | | | | | | | | | | (920) $false % 81.04/16.10 | | | | | | | | | | | | | | % 81.04/16.10 | | | | | | | | | | | | | | CLOSE: (920) is inconsistent. % 81.04/16.10 | | | | | | | | | | | | | | % 81.04/16.10 | | | | | | | | | | | | | End of split % 81.04/16.10 | | | | | | | | | | | | | % 81.04/16.10 | | | | | | | | | | | | Case 2: % 81.04/16.10 | | | | | | | | | | | | | % 81.04/16.10 | | | | | | | | | | | | | (921) all_52_1 = 0 % 81.04/16.10 | | | | | | | | | | | | | % 81.04/16.10 | | | | | | | | | | | | | COMBINE_EQS: (187), (921) imply: % 81.04/16.10 | | | | | | | | | | | | | (922) all_50_1 = 0 % 81.04/16.10 | | | | | | | | | | | | | % 81.04/16.10 | | | | | | | | | | | | | SIMP: (922) implies: % 81.04/16.10 | | | | | | | | | | | | | (923) all_50_1 = 0 % 81.04/16.10 | | | | | | | | | | | | | % 81.04/16.10 | | | | | | | | | | | | | REDUCE: (80), (923) imply: % 81.04/16.10 | | | | | | | | | | | | | (924) empty(all_42_4) = 0 % 81.04/16.10 | | | | | | | | | | | | | % 81.04/16.10 | | | | | | | | | | | | | GROUND_INST: instantiating (t7_boole) with all_42_1, all_42_4, % 81.04/16.10 | | | | | | | | | | | | | simplifying with (50), (53), (447) gives: % 81.04/16.10 | | | | | | | | | | | | | (925) ? [v0: int] : ( ~ (v0 = 0) & empty(all_42_4) = % 81.04/16.10 | | | | | | | | | | | | | v0) % 81.04/16.10 | | | | | | | | | | | | | % 81.04/16.10 | | | | | | | | | | | | | GROUND_INST: instantiating (fc4_subset_1) with all_42_4, % 81.04/16.10 | | | | | | | | | | | | | all_42_4, all_194_1, simplifying with (50), (352) % 81.04/16.10 | | | | | | | | | | | | | gives: % 81.04/16.10 | | | | | | | | | | | | | (926) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 81.04/16.10 | | | | | | | | | | | | | (empty(all_194_1) = v2 & empty(all_42_4) = v1 & % 81.04/16.10 | | | | | | | | | | | | | empty(all_42_4) = v0 & ( ~ (v2 = 0) | v1 = 0 | % 81.04/16.10 | | | | | | | | | | | | | v0 = 0)) % 81.04/16.10 | | | | | | | | | | | | | % 81.04/16.10 | | | | | | | | | | | | | GROUND_INST: instantiating (t8_boole) with all_42_4, all_186_0, % 81.04/16.10 | | | | | | | | | | | | | simplifying with (50), (336), (337), (924) gives: % 81.04/16.10 | | | | | | | | | | | | | (927) all_186_0 = all_42_4 % 81.04/16.10 | | | | | | | | | | | | | % 81.04/16.10 | | | | | | | | | | | | | GROUND_INST: instantiating (26) with all_186_0, simplifying % 81.04/16.10 | | | | | | | | | | | | | with (336), (337) gives: % 81.04/16.10 | | | | | | | | | | | | | (928) all_186_0 = empty_set % 81.04/16.10 | | | | | | | | | | | | | % 81.04/16.10 | | | | | | | | | | | | | COMBINE_EQS: (927), (928) imply: % 81.04/16.10 | | | | | | | | | | | | | (929) all_42_4 = empty_set % 81.04/16.10 | | | | | | | | | | | | | % 81.04/16.10 | | | | | | | | | | | | | DELTA: instantiating (925) with fresh symbol all_394_0 % 81.04/16.10 | | | | | | | | | | | | | gives: % 81.04/16.10 | | | | | | | | | | | | | (930) ~ (all_394_0 = 0) & empty(all_42_4) = all_394_0 % 81.04/16.10 | | | | | | | | | | | | | % 81.04/16.10 | | | | | | | | | | | | | ALPHA: (930) implies: % 81.04/16.10 | | | | | | | | | | | | | (931) ~ (all_394_0 = 0) % 81.04/16.10 | | | | | | | | | | | | | (932) empty(all_42_4) = all_394_0 % 81.04/16.10 | | | | | | | | | | | | | % 81.04/16.10 | | | | | | | | | | | | | DELTA: instantiating (926) with fresh symbols all_452_0, % 81.04/16.10 | | | | | | | | | | | | | all_452_1, all_452_2 gives: % 81.04/16.10 | | | | | | | | | | | | | (933) empty(all_194_1) = all_452_0 & empty(all_42_4) = % 81.04/16.10 | | | | | | | | | | | | | all_452_1 & empty(all_42_4) = all_452_2 & ( ~ % 81.04/16.10 | | | | | | | | | | | | | (all_452_0 = 0) | all_452_1 = 0 | all_452_2 = 0) % 81.04/16.10 | | | | | | | | | | | | | % 81.04/16.10 | | | | | | | | | | | | | ALPHA: (933) implies: % 81.04/16.10 | | | | | | | | | | | | | (934) empty(all_42_4) = all_452_2 % 81.04/16.10 | | | | | | | | | | | | | (935) empty(all_42_4) = all_452_1 % 81.04/16.10 | | | | | | | | | | | | | % 81.04/16.10 | | | | | | | | | | | | | REDUCE: (929), (935) imply: % 81.04/16.10 | | | | | | | | | | | | | (936) empty(empty_set) = all_452_1 % 81.04/16.10 | | | | | | | | | | | | | % 81.04/16.10 | | | | | | | | | | | | | REDUCE: (929), (934) imply: % 81.04/16.10 | | | | | | | | | | | | | (937) empty(empty_set) = all_452_2 % 81.04/16.10 | | | | | | | | | | | | | % 81.04/16.10 | | | | | | | | | | | | | REDUCE: (929), (932) imply: % 81.04/16.10 | | | | | | | | | | | | | (938) empty(empty_set) = all_394_0 % 81.04/16.10 | | | | | | | | | | | | | % 81.04/16.10 | | | | | | | | | | | | | GROUND_INST: instantiating (32) with 0, all_452_2, empty_set, % 81.04/16.10 | | | | | | | | | | | | | simplifying with (131), (937) gives: % 81.04/16.10 | | | | | | | | | | | | | (939) all_452_2 = 0 % 81.04/16.10 | | | | | | | | | | | | | % 81.04/16.10 | | | | | | | | | | | | | GROUND_INST: instantiating (32) with all_452_2, all_452_1, % 81.04/16.10 | | | | | | | | | | | | | empty_set, simplifying with (936), (937) gives: % 81.04/16.10 | | | | | | | | | | | | | (940) all_452_1 = all_452_2 % 81.04/16.10 | | | | | | | | | | | | | % 81.04/16.10 | | | | | | | | | | | | | GROUND_INST: instantiating (32) with all_394_0, all_452_1, % 81.04/16.10 | | | | | | | | | | | | | empty_set, simplifying with (936), (938) gives: % 81.04/16.10 | | | | | | | | | | | | | (941) all_452_1 = all_394_0 % 81.04/16.10 | | | | | | | | | | | | | % 81.04/16.10 | | | | | | | | | | | | | COMBINE_EQS: (940), (941) imply: % 81.04/16.10 | | | | | | | | | | | | | (942) all_452_2 = all_394_0 % 81.04/16.10 | | | | | | | | | | | | | % 81.04/16.10 | | | | | | | | | | | | | SIMP: (942) implies: % 81.04/16.10 | | | | | | | | | | | | | (943) all_452_2 = all_394_0 % 81.04/16.10 | | | | | | | | | | | | | % 81.04/16.10 | | | | | | | | | | | | | COMBINE_EQS: (939), (943) imply: % 81.04/16.10 | | | | | | | | | | | | | (944) all_394_0 = 0 % 81.04/16.10 | | | | | | | | | | | | | % 81.04/16.10 | | | | | | | | | | | | | REDUCE: (931), (944) imply: % 81.04/16.10 | | | | | | | | | | | | | (945) $false % 81.04/16.10 | | | | | | | | | | | | | % 81.04/16.10 | | | | | | | | | | | | | CLOSE: (945) is inconsistent. % 81.04/16.10 | | | | | | | | | | | | | % 81.04/16.10 | | | | | | | | | | | | End of split % 81.04/16.10 | | | | | | | | | | | | % 81.04/16.10 | | | | | | | | | | | Case 2: % 81.04/16.10 | | | | | | | | | | | | % 81.04/16.10 | | | | | | | | | | | | (946) all_50_1 = 0 % 81.04/16.10 | | | | | | | | | | | | (947) ~ (all_50_0 = 0) % 81.04/16.10 | | | | | | | | | | | | % 81.04/16.10 | | | | | | | | | | | | REDUCE: (80), (946) imply: % 81.04/16.10 | | | | | | | | | | | | (948) empty(all_42_4) = 0 % 81.04/16.10 | | | | | | | | | | | | % 81.04/16.10 | | | | | | | | | | | | GROUND_INST: instantiating (rc2_subset_1) with empty_set, % 81.04/16.10 | | | | | | | | | | | | all_190_1, simplifying with (132), (343) gives: % 81.04/16.10 | | | | | | | | | | | | (949) ? [v0: $i] : (empty(v0) = 0 & element(v0, % 81.04/16.10 | | | | | | | | | | | | all_190_1) = 0 & $i(v0)) % 81.04/16.10 | | | | | | | | | | | | % 81.04/16.10 | | | | | | | | | | | | GROUND_INST: instantiating (rc2_subset_1) with all_82_1, % 81.04/16.10 | | | | | | | | | | | | all_259_2, simplifying with (139), (408) gives: % 81.04/16.10 | | | | | | | | | | | | (950) ? [v0: $i] : (empty(v0) = 0 & element(v0, % 81.04/16.10 | | | | | | | | | | | | all_259_2) = 0 & $i(v0)) % 81.04/16.10 | | | | | | | | | | | | % 81.04/16.10 | | | | | | | | | | | | GROUND_INST: instantiating (rc2_subset_1) with all_192_1, % 81.04/16.10 | | | | | | | | | | | | all_192_0, simplifying with (345), (346) gives: % 81.04/16.10 | | | | | | | | | | | | (951) ? [v0: $i] : (empty(v0) = 0 & element(v0, % 81.04/16.10 | | | | | | | | | | | | all_192_0) = 0 & $i(v0)) % 81.04/16.10 | | | | | | | | | | | | % 81.04/16.11 | | | | | | | | | | | | GROUND_INST: instantiating (22) with all_110_1, all_56_1, % 81.04/16.11 | | | | | | | | | | | | all_194_1, all_194_0, simplifying with (194), % 81.04/16.11 | | | | | | | | | | | | (286), (294), (349), (350), (351) gives: % 81.04/16.11 | | | | | | | | | | | | (952) element(all_110_1, all_194_1) = 0 % 81.04/16.11 | | | | | | | | | | | | % 81.04/16.11 | | | | | | | | | | | | GROUND_INST: instantiating (22) with all_108_1, all_56_1, % 81.04/16.11 | | | | | | | | | | | | all_194_1, all_194_0, simplifying with (194), % 81.04/16.11 | | | | | | | | | | | | (299), (349), (350), (351), (369) gives: % 81.04/16.11 | | | | | | | | | | | | (953) element(all_108_1, all_194_1) = 0 % 81.04/16.11 | | | | | | | | | | | | % 81.04/16.11 | | | | | | | | | | | | GROUND_INST: instantiating (25) with all_108_1, all_56_1, % 81.04/16.11 | | | | | | | | | | | | all_194_1, all_194_0, simplifying with (194), % 81.04/16.11 | | | | | | | | | | | | (299), (349), (350), (351), (369) gives: % 81.04/16.11 | | | | | | | | | | | | (954) ? [v0: int] : ( ~ (v0 = 0) & empty(all_194_1) = % 81.04/16.11 | | | | | | | | | | | | v0) % 81.04/16.11 | | | | | | | | | | | | % 81.04/16.11 | | | | | | | | | | | | GROUND_INST: instantiating (rc2_subset_1) with all_194_1, % 81.04/16.11 | | | | | | | | | | | | all_194_0, simplifying with (349), (351) gives: % 81.04/16.11 | | | | | | | | | | | | (955) ? [v0: $i] : (empty(v0) = 0 & element(v0, % 81.04/16.11 | | | | | | | | | | | | all_194_0) = 0 & $i(v0)) % 81.04/16.11 | | | | | | | | | | | | % 81.04/16.11 | | | | | | | | | | | | GROUND_INST: instantiating (cc1_relset_1) with all_42_4, % 81.04/16.11 | | | | | | | | | | | | all_42_4, all_56_1, all_194_1, all_194_0, % 81.04/16.11 | | | | | | | | | | | | simplifying with (50), (194), (350), (351), (352) % 81.04/16.11 | | | | | | | | | | | | gives: % 81.04/16.11 | | | | | | | | | | | | (956) relation(all_56_1) = 0 % 81.04/16.11 | | | | | | | | | | | | % 81.04/16.11 | | | | | | | | | | | | GROUND_INST: instantiating (fc4_subset_1) with all_58_0, % 81.04/16.11 | | | | | | | | | | | | all_58_0, all_192_1, simplifying with (192), (347) % 81.04/16.11 | | | | | | | | | | | | gives: % 81.04/16.11 | | | | | | | | | | | | (957) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 81.04/16.11 | | | | | | | | | | | | (empty(all_192_1) = v2 & empty(all_58_0) = v1 & % 81.04/16.11 | | | | | | | | | | | | empty(all_58_0) = v0 & ( ~ (v2 = 0) | v1 = 0 | % 81.04/16.11 | | | | | | | | | | | | v0 = 0)) % 81.04/16.11 | | | | | | | | | | | | % 81.04/16.11 | | | | | | | | | | | | GROUND_INST: instantiating (1) with all_42_2, all_42_3, % 81.04/16.11 | | | | | | | | | | | | all_210_1, simplifying with (51), (52), (382) % 81.04/16.11 | | | | | | | | | | | | gives: % 81.04/16.11 | | | | | | | | | | | | (958) unordered_pair(all_42_2, all_42_3) = all_210_1 & % 81.04/16.11 | | | | | | | | | | | | $i(all_210_1) % 81.04/16.11 | | | | | | | | | | | | % 81.04/16.11 | | | | | | | | | | | | ALPHA: (958) implies: % 81.04/16.11 | | | | | | | | | | | | (959) $i(all_210_1) % 81.04/16.11 | | | | | | | | | | | | % 81.04/16.11 | | | | | | | | | | | | GROUND_INST: instantiating (1) with all_42_1, all_42_3, % 81.04/16.11 | | | | | | | | | | | | all_196_1, simplifying with (51), (53), (354) % 81.04/16.11 | | | | | | | | | | | | gives: % 81.04/16.11 | | | | | | | | | | | | (960) unordered_pair(all_42_1, all_42_3) = all_196_1 & % 81.04/16.11 | | | | | | | | | | | | $i(all_196_1) % 81.04/16.11 | | | | | | | | | | | | % 81.04/16.11 | | | | | | | | | | | | ALPHA: (960) implies: % 81.04/16.11 | | | | | | | | | | | | (961) $i(all_196_1) % 81.04/16.11 | | | | | | | | | | | | % 81.04/16.11 | | | | | | | | | | | | GROUND_INST: instantiating (1) with all_42_1, all_42_2, % 81.04/16.11 | | | | | | | | | | | | all_204_1, simplifying with (52), (53), (370) % 81.04/16.11 | | | | | | | | | | | | gives: % 81.04/16.11 | | | | | | | | | | | | (962) unordered_pair(all_42_1, all_42_2) = all_204_1 & % 81.04/16.11 | | | | | | | | | | | | $i(all_204_1) % 81.04/16.11 | | | | | | | | | | | | % 81.04/16.11 | | | | | | | | | | | | ALPHA: (962) implies: % 81.04/16.11 | | | | | | | | | | | | (963) $i(all_204_1) % 81.04/16.11 | | | | | | | | | | | | % 81.04/16.11 | | | | | | | | | | | | GROUND_INST: instantiating (1) with all_196_0, all_196_1, % 81.04/16.11 | | | | | | | | | | | | all_114_1, simplifying with (355), (441), (961) % 81.04/16.11 | | | | | | | | | | | | gives: % 81.04/16.11 | | | | | | | | | | | | (964) unordered_pair(all_196_0, all_196_1) = all_114_1 & % 81.04/16.11 | | | | | | | | | | | | $i(all_114_1) % 81.04/16.11 | | | | | | | | | | | | % 81.04/16.11 | | | | | | | | | | | | GROUND_INST: instantiating (fc3_subset_1) with all_196_1, % 81.04/16.11 | | | | | | | | | | | | all_196_0, all_114_1, simplifying with (355), % 81.04/16.11 | | | | | | | | | | | | (441), (961) gives: % 81.04/16.11 | | | | | | | | | | | | (965) ? [v0: int] : ( ~ (v0 = 0) & empty(all_114_1) = % 81.04/16.11 | | | | | | | | | | | | v0) % 81.04/16.11 | | | | | | | | | | | | % 81.04/16.11 | | | | | | | | | | | | GROUND_INST: instantiating (1) with all_204_0, all_204_1, % 81.04/16.11 | | | | | | | | | | | | all_108_1, simplifying with (371), (442), (963) % 81.04/16.11 | | | | | | | | | | | | gives: % 81.04/16.11 | | | | | | | | | | | | (966) unordered_pair(all_204_0, all_204_1) = all_108_1 & % 81.04/16.11 | | | | | | | | | | | | $i(all_108_1) % 81.04/16.11 | | | | | | | | | | | | % 81.04/16.11 | | | | | | | | | | | | GROUND_INST: instantiating (1) with all_196_0, all_210_1, % 81.04/16.11 | | | | | | | | | | | | all_110_1, simplifying with (438), (441), (959) % 81.04/16.11 | | | | | | | | | | | | gives: % 81.04/16.11 | | | | | | | | | | | | (967) unordered_pair(all_196_0, all_210_1) = all_110_1 & % 81.04/16.11 | | | | | | | | | | | | $i(all_110_1) % 81.04/16.11 | | | | | | | | | | | | % 81.04/16.11 | | | | | | | | | | | | GROUND_INST: instantiating (17) with all_82_2, all_178_0, % 81.04/16.11 | | | | | | | | | | | | simplifying with (138), (331) gives: % 81.04/16.11 | | | | | | | | | | | | (968) all_178_0 = 0 | ? [v0: $i] : ? [v1: $i] : ? % 81.04/16.11 | | | | | | | | | | | | [v2: int] : ( ~ (v2 = 0) & empty(v1) = v2 & % 81.04/16.11 | | | | | | | | | | | | powerset(all_82_2) = v0 & element(v1, v0) = 0 & % 81.04/16.11 | | | | | | | | | | | | $i(v1) & $i(v0)) % 81.04/16.11 | | | | | | | | | | | | % 81.04/16.11 | | | | | | | | | | | | GROUND_INST: instantiating (t8_boole) with all_42_4, all_186_0, % 81.04/16.11 | | | | | | | | | | | | simplifying with (50), (336), (337), (948) gives: % 81.04/16.11 | | | | | | | | | | | | (969) all_186_0 = all_42_4 % 81.04/16.11 | | | | | | | | | | | | % 81.04/16.11 | | | | | | | | | | | | GROUND_INST: instantiating (26) with all_186_0, simplifying % 81.04/16.11 | | | | | | | | | | | | with (336), (337) gives: % 81.04/16.11 | | | | | | | | | | | | (970) all_186_0 = empty_set % 81.04/16.11 | | | | | | | | | | | | % 81.04/16.11 | | | | | | | | | | | | COMBINE_EQS: (969), (970) imply: % 81.04/16.11 | | | | | | | | | | | | (971) all_42_4 = empty_set % 81.04/16.11 | | | | | | | | | | | | % 81.04/16.11 | | | | | | | | | | | | DELTA: instantiating (965) with fresh symbol all_350_0 % 81.04/16.11 | | | | | | | | | | | | gives: % 81.04/16.11 | | | | | | | | | | | | (972) ~ (all_350_0 = 0) & empty(all_114_1) = all_350_0 % 81.04/16.11 | | | | | | | | | | | | % 81.04/16.11 | | | | | | | | | | | | ALPHA: (972) implies: % 81.04/16.11 | | | | | | | | | | | | (973) ~ (all_350_0 = 0) % 81.04/16.11 | | | | | | | | | | | | (974) empty(all_114_1) = all_350_0 % 81.04/16.11 | | | | | | | | | | | | % 81.04/16.11 | | | | | | | | | | | | DELTA: instantiating (954) with fresh symbol all_366_0 % 81.04/16.11 | | | | | | | | | | | | gives: % 81.04/16.11 | | | | | | | | | | | | (975) ~ (all_366_0 = 0) & empty(all_194_1) = all_366_0 % 81.04/16.11 | | | | | | | | | | | | % 81.04/16.11 | | | | | | | | | | | | ALPHA: (975) implies: % 81.04/16.11 | | | | | | | | | | | | (976) ~ (all_366_0 = 0) % 81.04/16.11 | | | | | | | | | | | | (977) empty(all_194_1) = all_366_0 % 81.04/16.11 | | | | | | | | | | | | % 81.04/16.11 | | | | | | | | | | | | DELTA: instantiating (950) with fresh symbol all_388_0 % 81.04/16.11 | | | | | | | | | | | | gives: % 81.04/16.11 | | | | | | | | | | | | (978) empty(all_388_0) = 0 & element(all_388_0, % 81.04/16.11 | | | | | | | | | | | | all_259_2) = 0 & $i(all_388_0) % 81.04/16.11 | | | | | | | | | | | | % 81.04/16.11 | | | | | | | | | | | | ALPHA: (978) implies: % 81.04/16.11 | | | | | | | | | | | | (979) $i(all_388_0) % 81.04/16.11 | | | | | | | | | | | | (980) empty(all_388_0) = 0 % 81.04/16.11 | | | | | | | | | | | | % 81.04/16.11 | | | | | | | | | | | | DELTA: instantiating (949) with fresh symbol all_390_0 % 81.04/16.11 | | | | | | | | | | | | gives: % 81.04/16.11 | | | | | | | | | | | | (981) empty(all_390_0) = 0 & element(all_390_0, % 81.04/16.11 | | | | | | | | | | | | all_190_1) = 0 & $i(all_390_0) % 81.04/16.11 | | | | | | | | | | | | % 81.04/16.11 | | | | | | | | | | | | ALPHA: (981) implies: % 81.04/16.11 | | | | | | | | | | | | (982) $i(all_390_0) % 81.04/16.11 | | | | | | | | | | | | (983) empty(all_390_0) = 0 % 81.04/16.11 | | | | | | | | | | | | % 81.04/16.11 | | | | | | | | | | | | DELTA: instantiating (951) with fresh symbol all_392_0 % 81.04/16.11 | | | | | | | | | | | | gives: % 81.04/16.11 | | | | | | | | | | | | (984) empty(all_392_0) = 0 & element(all_392_0, % 81.04/16.11 | | | | | | | | | | | | all_192_0) = 0 & $i(all_392_0) % 81.04/16.11 | | | | | | | | | | | | % 81.04/16.11 | | | | | | | | | | | | ALPHA: (984) implies: % 81.04/16.11 | | | | | | | | | | | | (985) $i(all_392_0) % 81.04/16.11 | | | | | | | | | | | | (986) empty(all_392_0) = 0 % 81.04/16.11 | | | | | | | | | | | | % 81.04/16.11 | | | | | | | | | | | | DELTA: instantiating (955) with fresh symbol all_394_0 % 81.04/16.11 | | | | | | | | | | | | gives: % 81.04/16.11 | | | | | | | | | | | | (987) empty(all_394_0) = 0 & element(all_394_0, % 81.04/16.11 | | | | | | | | | | | | all_194_0) = 0 & $i(all_394_0) % 81.04/16.11 | | | | | | | | | | | | % 81.04/16.11 | | | | | | | | | | | | ALPHA: (987) implies: % 81.04/16.11 | | | | | | | | | | | | (988) $i(all_394_0) % 81.04/16.11 | | | | | | | | | | | | (989) empty(all_394_0) = 0 % 81.04/16.11 | | | | | | | | | | | | % 81.04/16.11 | | | | | | | | | | | | DELTA: instantiating (957) with fresh symbols all_436_0, % 81.04/16.11 | | | | | | | | | | | | all_436_1, all_436_2 gives: % 81.04/16.11 | | | | | | | | | | | | (990) empty(all_192_1) = all_436_0 & empty(all_58_0) = % 81.04/16.11 | | | | | | | | | | | | all_436_1 & empty(all_58_0) = all_436_2 & ( ~ % 81.04/16.11 | | | | | | | | | | | | (all_436_0 = 0) | all_436_1 = 0 | all_436_2 = 0) % 81.04/16.11 | | | | | | | | | | | | % 81.04/16.11 | | | | | | | | | | | | ALPHA: (990) implies: % 81.04/16.11 | | | | | | | | | | | | (991) empty(all_192_1) = all_436_0 % 81.04/16.11 | | | | | | | | | | | | (992) ~ (all_436_0 = 0) | all_436_1 = 0 | all_436_2 = 0 % 81.04/16.11 | | | | | | | | | | | | % 81.04/16.11 | | | | | | | | | | | | REDUCE: (274), (971) imply: % 81.04/16.11 | | | | | | | | | | | | (993) is_transitive_in(all_56_1, empty_set) = 0 % 81.04/16.11 | | | | | | | | | | | | % 81.04/16.11 | | | | | | | | | | | | REDUCE: (352), (971) imply: % 81.04/16.11 | | | | | | | | | | | | (994) cartesian_product2(empty_set, empty_set) = % 81.04/16.11 | | | | | | | | | | | | all_194_1 % 81.04/16.11 | | | | | | | | | | | | % 81.04/16.11 | | | | | | | | | | | | REDUCE: (79), (971) imply: % 81.04/16.11 | | | | | | | | | | | | (995) in(all_42_1, empty_set) = all_50_0 % 81.04/16.11 | | | | | | | | | | | | % 81.04/16.11 | | | | | | | | | | | | BETA: splitting (968) gives: % 81.04/16.11 | | | | | | | | | | | | % 81.04/16.11 | | | | | | | | | | | | Case 1: % 81.04/16.11 | | | | | | | | | | | | | % 81.04/16.11 | | | | | | | | | | | | | (996) all_178_0 = 0 % 81.04/16.11 | | | | | | | | | | | | | % 81.04/16.11 | | | | | | | | | | | | | REDUCE: (330), (996) imply: % 81.04/16.11 | | | | | | | | | | | | | (997) $false % 81.04/16.11 | | | | | | | | | | | | | % 81.04/16.11 | | | | | | | | | | | | | CLOSE: (997) is inconsistent. % 81.04/16.11 | | | | | | | | | | | | | % 81.04/16.11 | | | | | | | | | | | | Case 2: % 81.04/16.11 | | | | | | | | | | | | | % 81.04/16.11 | | | | | | | | | | | | | (998) ? [v0: $i] : ? [v1: $i] : ? [v2: int] : ( ~ (v2 % 81.04/16.11 | | | | | | | | | | | | | = 0) & empty(v1) = v2 & powerset(all_82_2) = % 81.04/16.11 | | | | | | | | | | | | | v0 & element(v1, v0) = 0 & $i(v1) & $i(v0)) % 81.04/16.11 | | | | | | | | | | | | | % 81.04/16.11 | | | | | | | | | | | | | DELTA: instantiating (998) with fresh symbols all_460_0, % 81.04/16.11 | | | | | | | | | | | | | all_460_1, all_460_2 gives: % 81.04/16.11 | | | | | | | | | | | | | (999) ~ (all_460_0 = 0) & empty(all_460_1) = all_460_0 % 81.04/16.11 | | | | | | | | | | | | | & powerset(all_82_2) = all_460_2 & % 81.04/16.11 | | | | | | | | | | | | | element(all_460_1, all_460_2) = 0 & $i(all_460_1) % 81.04/16.11 | | | | | | | | | | | | | & $i(all_460_2) % 81.04/16.11 | | | | | | | | | | | | | % 81.04/16.11 | | | | | | | | | | | | | ALPHA: (999) implies: % 81.04/16.11 | | | | | | | | | | | | | (1000) ~ (all_460_0 = 0) % 81.04/16.11 | | | | | | | | | | | | | (1001) $i(all_460_1) % 81.04/16.11 | | | | | | | | | | | | | (1002) empty(all_460_1) = all_460_0 % 81.04/16.11 | | | | | | | | | | | | | % 81.04/16.11 | | | | | | | | | | | | | BETA: splitting (257) gives: % 81.04/16.11 | | | | | | | | | | | | | % 81.04/16.11 | | | | | | | | | | | | | Case 1: % 81.04/16.11 | | | | | | | | | | | | | | % 81.04/16.11 | | | | | | | | | | | | | | (1003) ~ (all_128_0 = 0) % 81.04/16.11 | | | | | | | | | | | | | | % 81.04/16.11 | | | | | | | | | | | | | | BETA: splitting (307) gives: % 81.04/16.11 | | | | | | | | | | | | | | % 81.04/16.11 | | | | | | | | | | | | | | Case 1: % 81.04/16.11 | | | | | | | | | | | | | | | % 81.04/16.11 | | | | | | | | | | | | | | | (1004) all_128_0 = 0 % 81.04/16.11 | | | | | | | | | | | | | | | % 81.04/16.11 | | | | | | | | | | | | | | | REDUCE: (1003), (1004) imply: % 81.04/16.11 | | | | | | | | | | | | | | | (1005) $false % 81.04/16.11 | | | | | | | | | | | | | | | % 81.04/16.11 | | | | | | | | | | | | | | | CLOSE: (1005) is inconsistent. % 81.04/16.11 | | | | | | | | | | | | | | | % 81.04/16.11 | | | | | | | | | | | | | | Case 2: % 81.04/16.11 | | | | | | | | | | | | | | | % 81.04/16.11 | | | | | | | | | | | | | | | (1006) ? [v0: any] : ? [v1: any] : (empty(all_56_1) = % 81.04/16.11 | | | | | | | | | | | | | | | v1 & element(all_128_1, all_56_1) = v0 & ( ~ (v0 % 81.04/16.11 | | | | | | | | | | | | | | | = 0) | v1 = 0)) % 81.04/16.11 | | | | | | | | | | | | | | | % 81.04/16.11 | | | | | | | | | | | | | | | DELTA: instantiating (1006) with fresh symbols all_666_0, % 81.04/16.11 | | | | | | | | | | | | | | | all_666_1 gives: % 81.04/16.11 | | | | | | | | | | | | | | | (1007) empty(all_56_1) = all_666_0 & element(all_128_1, % 81.04/16.11 | | | | | | | | | | | | | | | all_56_1) = all_666_1 & ( ~ (all_666_1 = 0) | % 81.04/16.11 | | | | | | | | | | | | | | | all_666_0 = 0) % 81.04/16.11 | | | | | | | | | | | | | | | % 81.04/16.11 | | | | | | | | | | | | | | | ALPHA: (1007) implies: % 81.04/16.11 | | | | | | | | | | | | | | | (1008) empty(all_56_1) = all_666_0 % 81.04/16.11 | | | | | | | | | | | | | | | (1009) ~ (all_666_1 = 0) | all_666_0 = 0 % 81.04/16.11 | | | | | | | | | | | | | | | % 81.04/16.11 | | | | | | | | | | | | | | | GROUND_INST: instantiating (32) with all_182_0, all_666_0, % 81.04/16.11 | | | | | | | | | | | | | | | all_56_1, simplifying with (334), (1008) gives: % 81.04/16.11 | | | | | | | | | | | | | | | (1010) all_666_0 = all_182_0 % 81.04/16.11 | | | | | | | | | | | | | | | % 81.04/16.11 | | | | | | | | | | | | | | | BETA: splitting (1009) gives: % 81.04/16.11 | | | | | | | | | | | | | | | % 81.04/16.11 | | | | | | | | | | | | | | | Case 1: % 81.04/16.11 | | | | | | | | | | | | | | | | % 81.04/16.11 | | | | | | | | | | | | | | | | % 81.04/16.11 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (20) with all_108_1, all_194_1, % 81.04/16.11 | | | | | | | | | | | | | | | | simplifying with (349), (369), (953) gives: % 81.04/16.11 | | | | | | | | | | | | | | | | (1011) ? [v0: any] : ? [v1: any] : (empty(all_194_1) = % 81.04/16.11 | | | | | | | | | | | | | | | | v0 & in(all_108_1, all_194_1) = v1 & (v1 = 0 | % 81.04/16.11 | | | | | | | | | | | | | | | | v0 = 0)) % 81.04/16.11 | | | | | | | | | | | | | | | | % 81.04/16.11 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (20) with all_110_1, all_194_1, % 81.04/16.11 | | | | | | | | | | | | | | | | simplifying with (286), (349), (952) gives: % 81.04/16.11 | | | | | | | | | | | | | | | | (1012) ? [v0: any] : ? [v1: any] : (empty(all_194_1) = % 81.04/16.11 | | | | | | | | | | | | | | | | v0 & in(all_110_1, all_194_1) = v1 & (v1 = 0 | % 81.04/16.11 | | | | | | | | | | | | | | | | v0 = 0)) % 81.04/16.11 | | | | | | | | | | | | | | | | % 81.04/16.11 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (10) with all_56_1, empty_set, % 81.04/16.11 | | | | | | | | | | | | | | | | all_42_3, all_42_2, all_42_1, all_110_1, % 81.04/16.11 | | | | | | | | | | | | | | | | all_108_1, simplifying with (51), (52), (53), % 81.04/16.11 | | | | | | | | | | | | | | | | (132), (194), (215), (219), (294), (299), (956), % 81.04/16.11 | | | | | | | | | | | | | | | | (993) gives: % 81.04/16.11 | | | | | | | | | | | | | | | | (1013) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? % 81.04/16.11 | | | | | | | | | | | | | | | | [v3: $i] : ? [v4: any] : (ordered_pair(all_42_3, % 81.04/16.11 | | | | | | | | | | | | | | | | all_42_1) = v3 & in(v3, all_56_1) = v4 & % 81.04/16.11 | | | | | | | | | | | | | | | | in(all_42_1, empty_set) = v2 & in(all_42_2, % 81.04/16.11 | | | | | | | | | | | | | | | | empty_set) = v1 & in(all_42_3, empty_set) = v0 % 81.04/16.11 | | | | | | | | | | | | | | | | & $i(v3) & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = % 81.04/16.11 | | | | | | | | | | | | | | | | 0) | v4 = 0)) % 81.04/16.11 | | | | | | | | | | | | | | | | % 81.04/16.11 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with all_114_1, all_350_0, % 81.04/16.11 | | | | | | | | | | | | | | | | simplifying with (285), (974) gives: % 81.04/16.11 | | | | | | | | | | | | | | | | (1014) all_350_0 = 0 | ? [v0: $i] : ? [v1: $i] : ? % 81.04/16.11 | | | | | | | | | | | | | | | | [v2: int] : ( ~ (v2 = 0) & empty(v1) = v2 & % 81.04/16.11 | | | | | | | | | | | | | | | | powerset(all_114_1) = v0 & element(v1, v0) = 0 & % 81.04/16.11 | | | | | | | | | | | | | | | | $i(v1) & $i(v0)) % 81.04/16.11 | | | | | | | | | | | | | | | | % 81.04/16.11 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with all_192_1, all_436_0, % 81.04/16.11 | | | | | | | | | | | | | | | | simplifying with (345), (991) gives: % 81.04/16.11 | | | | | | | | | | | | | | | | (1015) all_436_0 = 0 | ? [v0: $i] : ? [v1: $i] : ? % 81.04/16.11 | | | | | | | | | | | | | | | | [v2: int] : ( ~ (v2 = 0) & empty(v1) = v2 & % 81.04/16.11 | | | | | | | | | | | | | | | | powerset(all_192_1) = v0 & element(v1, v0) = 0 & % 81.04/16.11 | | | | | | | | | | | | | | | | $i(v1) & $i(v0)) % 81.04/16.11 | | | | | | | | | | | | | | | | % 81.04/16.11 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (t8_boole) with all_390_0, % 81.04/16.11 | | | | | | | | | | | | | | | | all_392_0, simplifying with (982), (983), (985), % 81.04/16.11 | | | | | | | | | | | | | | | | (986) gives: % 81.04/16.11 | | | | | | | | | | | | | | | | (1016) all_392_0 = all_390_0 % 81.04/16.11 | | | | | | | | | | | | | | | | % 81.04/16.11 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (26) with all_392_0, simplifying % 81.04/16.11 | | | | | | | | | | | | | | | | with (985), (986) gives: % 81.04/16.11 | | | | | | | | | | | | | | | | (1017) all_392_0 = empty_set % 81.04/16.11 | | | | | | | | | | | | | | | | % 81.04/16.11 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (t8_boole) with all_390_0, % 81.04/16.11 | | | | | | | | | | | | | | | | all_394_0, simplifying with (982), (983), (988), % 81.04/16.11 | | | | | | | | | | | | | | | | (989) gives: % 81.04/16.11 | | | | | | | | | | | | | | | | (1018) all_394_0 = all_390_0 % 81.04/16.11 | | | | | | | | | | | | | | | | % 81.04/16.11 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (t8_boole) with all_388_0, % 81.04/16.11 | | | | | | | | | | | | | | | | all_394_0, simplifying with (979), (980), (988), % 81.04/16.11 | | | | | | | | | | | | | | | | (989) gives: % 81.04/16.11 | | | | | | | | | | | | | | | | (1019) all_394_0 = all_388_0 % 81.04/16.11 | | | | | | | | | | | | | | | | % 81.04/16.11 | | | | | | | | | | | | | | | | COMBINE_EQS: (1018), (1019) imply: % 81.04/16.11 | | | | | | | | | | | | | | | | (1020) all_390_0 = all_388_0 % 81.04/16.11 | | | | | | | | | | | | | | | | % 81.04/16.11 | | | | | | | | | | | | | | | | SIMP: (1020) implies: % 81.04/16.11 | | | | | | | | | | | | | | | | (1021) all_390_0 = all_388_0 % 81.04/16.11 | | | | | | | | | | | | | | | | % 81.04/16.11 | | | | | | | | | | | | | | | | COMBINE_EQS: (1016), (1017) imply: % 81.04/16.11 | | | | | | | | | | | | | | | | (1022) all_390_0 = empty_set % 81.04/16.11 | | | | | | | | | | | | | | | | % 81.04/16.11 | | | | | | | | | | | | | | | | SIMP: (1022) implies: % 81.04/16.11 | | | | | | | | | | | | | | | | (1023) all_390_0 = empty_set % 81.04/16.11 | | | | | | | | | | | | | | | | % 81.04/16.11 | | | | | | | | | | | | | | | | COMBINE_EQS: (1021), (1023) imply: % 81.04/16.11 | | | | | | | | | | | | | | | | (1024) all_388_0 = empty_set % 81.04/16.11 | | | | | | | | | | | | | | | | % 81.04/16.11 | | | | | | | | | | | | | | | | DELTA: instantiating (1012) with fresh symbols all_788_0, % 81.04/16.11 | | | | | | | | | | | | | | | | all_788_1 gives: % 81.04/16.11 | | | | | | | | | | | | | | | | (1025) empty(all_194_1) = all_788_1 & in(all_110_1, % 81.04/16.11 | | | | | | | | | | | | | | | | all_194_1) = all_788_0 & (all_788_0 = 0 | % 81.04/16.11 | | | | | | | | | | | | | | | | all_788_1 = 0) % 81.04/16.11 | | | | | | | | | | | | | | | | % 81.04/16.11 | | | | | | | | | | | | | | | | ALPHA: (1025) implies: % 81.04/16.11 | | | | | | | | | | | | | | | | (1026) empty(all_194_1) = all_788_1 % 81.04/16.11 | | | | | | | | | | | | | | | | % 81.04/16.11 | | | | | | | | | | | | | | | | DELTA: instantiating (1011) with fresh symbols all_802_0, % 81.04/16.11 | | | | | | | | | | | | | | | | all_802_1 gives: % 81.04/16.11 | | | | | | | | | | | | | | | | (1027) empty(all_194_1) = all_802_1 & in(all_108_1, % 81.04/16.11 | | | | | | | | | | | | | | | | all_194_1) = all_802_0 & (all_802_0 = 0 | % 81.04/16.11 | | | | | | | | | | | | | | | | all_802_1 = 0) % 81.04/16.11 | | | | | | | | | | | | | | | | % 81.04/16.11 | | | | | | | | | | | | | | | | ALPHA: (1027) implies: % 81.04/16.11 | | | | | | | | | | | | | | | | (1028) in(all_108_1, all_194_1) = all_802_0 % 81.04/16.11 | | | | | | | | | | | | | | | | (1029) empty(all_194_1) = all_802_1 % 81.04/16.11 | | | | | | | | | | | | | | | | (1030) all_802_0 = 0 | all_802_1 = 0 % 81.04/16.11 | | | | | | | | | | | | | | | | % 81.04/16.11 | | | | | | | | | | | | | | | | DELTA: instantiating (1013) with fresh symbols all_852_0, % 81.04/16.11 | | | | | | | | | | | | | | | | all_852_1, all_852_2, all_852_3, all_852_4 gives: % 81.04/16.11 | | | | | | | | | | | | | | | | (1031) ordered_pair(all_42_3, all_42_1) = all_852_1 & % 81.04/16.11 | | | | | | | | | | | | | | | | in(all_852_1, all_56_1) = all_852_0 & in(all_42_1, % 81.04/16.11 | | | | | | | | | | | | | | | | empty_set) = all_852_2 & in(all_42_2, empty_set) % 81.04/16.11 | | | | | | | | | | | | | | | | = all_852_3 & in(all_42_3, empty_set) = all_852_4 % 81.04/16.11 | | | | | | | | | | | | | | | | & $i(all_852_1) & ( ~ (all_852_2 = 0) | ~ % 81.04/16.11 | | | | | | | | | | | | | | | | (all_852_3 = 0) | ~ (all_852_4 = 0) | all_852_0 % 81.04/16.11 | | | | | | | | | | | | | | | | = 0) % 81.04/16.11 | | | | | | | | | | | | | | | | % 81.04/16.11 | | | | | | | | | | | | | | | | ALPHA: (1031) implies: % 81.04/16.11 | | | | | | | | | | | | | | | | (1032) in(all_42_1, empty_set) = all_852_2 % 81.04/16.11 | | | | | | | | | | | | | | | | % 81.04/16.11 | | | | | | | | | | | | | | | | BETA: splitting (1014) gives: % 81.04/16.11 | | | | | | | | | | | | | | | | % 81.04/16.11 | | | | | | | | | | | | | | | | Case 1: % 81.04/16.11 | | | | | | | | | | | | | | | | | % 81.04/16.11 | | | | | | | | | | | | | | | | | (1033) all_350_0 = 0 % 81.04/16.11 | | | | | | | | | | | | | | | | | % 81.04/16.11 | | | | | | | | | | | | | | | | | REDUCE: (973), (1033) imply: % 81.04/16.11 | | | | | | | | | | | | | | | | | (1034) $false % 81.04/16.11 | | | | | | | | | | | | | | | | | % 81.04/16.11 | | | | | | | | | | | | | | | | | CLOSE: (1034) is inconsistent. % 81.04/16.11 | | | | | | | | | | | | | | | | | % 81.04/16.11 | | | | | | | | | | | | | | | | Case 2: % 81.04/16.11 | | | | | | | | | | | | | | | | | % 81.04/16.11 | | | | | | | | | | | | | | | | | % 81.04/16.11 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (33) with all_50_0, all_852_2, % 81.04/16.11 | | | | | | | | | | | | | | | | | empty_set, all_42_1, simplifying with (995), % 81.04/16.11 | | | | | | | | | | | | | | | | | (1032) gives: % 81.04/16.11 | | | | | | | | | | | | | | | | | (1035) all_852_2 = all_50_0 % 81.04/16.11 | | | | | | | | | | | | | | | | | % 81.04/16.11 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (32) with all_366_0, all_802_1, % 81.04/16.11 | | | | | | | | | | | | | | | | | all_194_1, simplifying with (977), (1029) gives: % 81.04/16.11 | | | | | | | | | | | | | | | | | (1036) all_802_1 = all_366_0 % 81.04/16.11 | | | | | | | | | | | | | | | | | % 81.04/16.11 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (32) with all_788_1, all_802_1, % 81.04/16.11 | | | | | | | | | | | | | | | | | all_194_1, simplifying with (1026), (1029) gives: % 81.04/16.11 | | | | | | | | | | | | | | | | | (1037) all_802_1 = all_788_1 % 81.04/16.11 | | | | | | | | | | | | | | | | | % 81.04/16.11 | | | | | | | | | | | | | | | | | COMBINE_EQS: (1036), (1037) imply: % 81.04/16.11 | | | | | | | | | | | | | | | | | (1038) all_788_1 = all_366_0 % 81.04/16.11 | | | | | | | | | | | | | | | | | % 81.04/16.11 | | | | | | | | | | | | | | | | | BETA: splitting (1030) gives: % 81.04/16.11 | | | | | | | | | | | | | | | | | % 81.04/16.11 | | | | | | | | | | | | | | | | | Case 1: % 81.04/16.11 | | | | | | | | | | | | | | | | | | % 81.04/16.11 | | | | | | | | | | | | | | | | | | (1039) all_802_0 = 0 % 81.04/16.11 | | | | | | | | | | | | | | | | | | % 81.04/16.11 | | | | | | | | | | | | | | | | | | REDUCE: (1028), (1039) imply: % 81.04/16.11 | | | | | | | | | | | | | | | | | | (1040) in(all_108_1, all_194_1) = 0 % 81.04/16.11 | | | | | | | | | | | | | | | | | | % 81.04/16.11 | | | | | | | | | | | | | | | | | | REF_CLOSE: (18), (33), (52), (53), (132), (215), (947), % 81.04/16.11 | | | | | | | | | | | | | | | | | | (992), (994), (995), (1015), (1040) are % 81.04/16.11 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1. % 81.04/16.11 | | | | | | | | | | | | | | | | | | % 81.04/16.11 | | | | | | | | | | | | | | | | | Case 2: % 81.04/16.11 | | | | | | | | | | | | | | | | | | % 81.04/16.11 | | | | | | | | | | | | | | | | | | (1041) all_802_1 = 0 % 81.04/16.11 | | | | | | | | | | | | | | | | | | % 81.04/16.11 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1036), (1041) imply: % 81.04/16.11 | | | | | | | | | | | | | | | | | | (1042) all_366_0 = 0 % 81.04/16.11 | | | | | | | | | | | | | | | | | | % 81.04/16.11 | | | | | | | | | | | | | | | | | | SIMP: (1042) implies: % 81.04/16.11 | | | | | | | | | | | | | | | | | | (1043) all_366_0 = 0 % 81.04/16.11 | | | | | | | | | | | | | | | | | | % 81.04/16.11 | | | | | | | | | | | | | | | | | | REDUCE: (976), (1043) imply: % 81.04/16.11 | | | | | | | | | | | | | | | | | | (1044) $false % 81.04/16.11 | | | | | | | | | | | | | | | | | | % 81.04/16.11 | | | | | | | | | | | | | | | | | | CLOSE: (1044) is inconsistent. % 81.04/16.11 | | | | | | | | | | | | | | | | | | % 81.04/16.11 | | | | | | | | | | | | | | | | | End of split % 81.04/16.11 | | | | | | | | | | | | | | | | | % 81.04/16.11 | | | | | | | | | | | | | | | | End of split % 81.04/16.11 | | | | | | | | | | | | | | | | % 81.04/16.11 | | | | | | | | | | | | | | | Case 2: % 81.04/16.11 | | | | | | | | | | | | | | | | % 81.04/16.12 | | | | | | | | | | | | | | | | (1045) all_666_0 = 0 % 81.04/16.12 | | | | | | | | | | | | | | | | % 81.04/16.12 | | | | | | | | | | | | | | | | COMBINE_EQS: (1010), (1045) imply: % 81.04/16.12 | | | | | | | | | | | | | | | | (1046) all_182_0 = 0 % 81.04/16.12 | | | | | | | | | | | | | | | | % 81.04/16.12 | | | | | | | | | | | | | | | | REDUCE: (333), (1046) imply: % 81.04/16.12 | | | | | | | | | | | | | | | | (1047) $false % 81.04/16.12 | | | | | | | | | | | | | | | | % 81.04/16.12 | | | | | | | | | | | | | | | | CLOSE: (1047) is inconsistent. % 81.04/16.12 | | | | | | | | | | | | | | | | % 81.04/16.12 | | | | | | | | | | | | | | | End of split % 81.04/16.12 | | | | | | | | | | | | | | | % 81.04/16.12 | | | | | | | | | | | | | | End of split % 81.04/16.12 | | | | | | | | | | | | | | % 81.04/16.12 | | | | | | | | | | | | | Case 2: % 81.04/16.12 | | | | | | | | | | | | | | % 81.04/16.12 | | | | | | | | | | | | | | % 81.04/16.12 | | | | | | | | | | | | | | GROUND_INST: instantiating (20) with all_108_1, all_194_1, % 81.04/16.12 | | | | | | | | | | | | | | simplifying with (349), (369), (953) gives: % 81.04/16.12 | | | | | | | | | | | | | | (1048) ? [v0: any] : ? [v1: any] : (empty(all_194_1) = % 81.04/16.12 | | | | | | | | | | | | | | v0 & in(all_108_1, all_194_1) = v1 & (v1 = 0 | % 81.04/16.12 | | | | | | | | | | | | | | v0 = 0)) % 81.04/16.12 | | | | | | | | | | | | | | % 81.04/16.12 | | | | | | | | | | | | | | GROUND_INST: instantiating (10) with all_56_1, empty_set, % 81.04/16.12 | | | | | | | | | | | | | | all_42_3, all_42_2, all_42_1, all_110_1, % 81.04/16.12 | | | | | | | | | | | | | | all_108_1, simplifying with (51), (52), (53), % 81.04/16.12 | | | | | | | | | | | | | | (132), (194), (215), (219), (294), (299), (956), % 81.04/16.12 | | | | | | | | | | | | | | (993) gives: % 81.04/16.12 | | | | | | | | | | | | | | (1049) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? % 81.04/16.12 | | | | | | | | | | | | | | [v3: $i] : ? [v4: any] : (ordered_pair(all_42_3, % 81.04/16.12 | | | | | | | | | | | | | | all_42_1) = v3 & in(v3, all_56_1) = v4 & % 81.04/16.12 | | | | | | | | | | | | | | in(all_42_1, empty_set) = v2 & in(all_42_2, % 81.04/16.12 | | | | | | | | | | | | | | empty_set) = v1 & in(all_42_3, empty_set) = v0 % 81.04/16.12 | | | | | | | | | | | | | | & $i(v3) & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = % 81.04/16.12 | | | | | | | | | | | | | | 0) | v4 = 0)) % 81.04/16.12 | | | | | | | | | | | | | | % 81.04/16.12 | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with all_192_1, all_436_0, % 81.04/16.12 | | | | | | | | | | | | | | simplifying with (345), (991) gives: % 81.04/16.12 | | | | | | | | | | | | | | (1050) all_436_0 = 0 | ? [v0: $i] : ? [v1: $i] : ? % 81.04/16.12 | | | | | | | | | | | | | | [v2: int] : ( ~ (v2 = 0) & empty(v1) = v2 & % 81.04/16.12 | | | | | | | | | | | | | | powerset(all_192_1) = v0 & element(v1, v0) = 0 & % 81.04/16.12 | | | | | | | | | | | | | | $i(v1) & $i(v0)) % 81.04/16.12 | | | | | | | | | | | | | | % 81.04/16.12 | | | | | | | | | | | | | | GROUND_INST: instantiating (26) with all_390_0, simplifying % 81.04/16.12 | | | | | | | | | | | | | | with (982), (983) gives: % 81.04/16.12 | | | | | | | | | | | | | | (1051) all_390_0 = empty_set % 81.04/16.12 | | | | | | | | | | | | | | % 81.04/16.12 | | | | | | | | | | | | | | GROUND_INST: instantiating (t8_boole) with all_390_0, % 81.04/16.12 | | | | | | | | | | | | | | all_392_0, simplifying with (982), (983), (985), % 81.04/16.12 | | | | | | | | | | | | | | (986) gives: % 81.04/16.12 | | | | | | | | | | | | | | (1052) all_392_0 = all_390_0 % 81.04/16.12 | | | | | | | | | | | | | | % 81.04/16.12 | | | | | | | | | | | | | | GROUND_INST: instantiating (t8_boole) with all_392_0, % 81.04/16.12 | | | | | | | | | | | | | | all_394_0, simplifying with (985), (986), (988), % 81.04/16.12 | | | | | | | | | | | | | | (989) gives: % 81.04/16.12 | | | | | | | | | | | | | | (1053) all_394_0 = all_392_0 % 81.04/16.12 | | | | | | | | | | | | | | % 81.04/16.12 | | | | | | | | | | | | | | GROUND_INST: instantiating (t8_boole) with all_388_0, % 81.04/16.12 | | | | | | | | | | | | | | all_394_0, simplifying with (979), (980), (988), % 81.04/16.12 | | | | | | | | | | | | | | (989) gives: % 81.04/16.12 | | | | | | | | | | | | | | (1054) all_394_0 = all_388_0 % 81.04/16.12 | | | | | | | | | | | | | | % 81.04/16.12 | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with all_460_1, all_460_0, % 81.04/16.12 | | | | | | | | | | | | | | simplifying with (1001), (1002) gives: % 81.04/16.12 | | | | | | | | | | | | | | (1055) all_460_0 = 0 | ? [v0: $i] : ? [v1: $i] : ? % 81.04/16.12 | | | | | | | | | | | | | | [v2: int] : ( ~ (v2 = 0) & empty(v1) = v2 & % 81.04/16.12 | | | | | | | | | | | | | | powerset(all_460_1) = v0 & element(v1, v0) = 0 & % 81.04/16.12 | | | | | | | | | | | | | | $i(v1) & $i(v0)) % 81.04/16.12 | | | | | | | | | | | | | | % 81.04/16.12 | | | | | | | | | | | | | | COMBINE_EQS: (1053), (1054) imply: % 81.04/16.12 | | | | | | | | | | | | | | (1056) all_392_0 = all_388_0 % 81.04/16.12 | | | | | | | | | | | | | | % 81.04/16.12 | | | | | | | | | | | | | | SIMP: (1056) implies: % 81.04/16.12 | | | | | | | | | | | | | | (1057) all_392_0 = all_388_0 % 81.04/16.12 | | | | | | | | | | | | | | % 81.04/16.12 | | | | | | | | | | | | | | COMBINE_EQS: (1052), (1057) imply: % 81.04/16.12 | | | | | | | | | | | | | | (1058) all_390_0 = all_388_0 % 81.04/16.12 | | | | | | | | | | | | | | % 81.04/16.12 | | | | | | | | | | | | | | SIMP: (1058) implies: % 81.04/16.12 | | | | | | | | | | | | | | (1059) all_390_0 = all_388_0 % 81.04/16.12 | | | | | | | | | | | | | | % 81.04/16.12 | | | | | | | | | | | | | | COMBINE_EQS: (1051), (1059) imply: % 81.04/16.12 | | | | | | | | | | | | | | (1060) all_388_0 = empty_set % 81.04/16.12 | | | | | | | | | | | | | | % 81.04/16.12 | | | | | | | | | | | | | | DELTA: instantiating (1048) with fresh symbols all_732_0, % 81.04/16.12 | | | | | | | | | | | | | | all_732_1 gives: % 81.04/16.12 | | | | | | | | | | | | | | (1061) empty(all_194_1) = all_732_1 & in(all_108_1, % 81.04/16.12 | | | | | | | | | | | | | | all_194_1) = all_732_0 & (all_732_0 = 0 | % 81.04/16.12 | | | | | | | | | | | | | | all_732_1 = 0) % 81.04/16.12 | | | | | | | | | | | | | | % 81.04/16.12 | | | | | | | | | | | | | | ALPHA: (1061) implies: % 81.04/16.12 | | | | | | | | | | | | | | (1062) in(all_108_1, all_194_1) = all_732_0 % 81.04/16.12 | | | | | | | | | | | | | | (1063) empty(all_194_1) = all_732_1 % 81.04/16.12 | | | | | | | | | | | | | | (1064) all_732_0 = 0 | all_732_1 = 0 % 81.04/16.12 | | | | | | | | | | | | | | % 81.04/16.12 | | | | | | | | | | | | | | DELTA: instantiating (1049) with fresh symbols all_840_0, % 81.04/16.12 | | | | | | | | | | | | | | all_840_1, all_840_2, all_840_3, all_840_4 gives: % 81.04/16.12 | | | | | | | | | | | | | | (1065) ordered_pair(all_42_3, all_42_1) = all_840_1 & % 81.04/16.12 | | | | | | | | | | | | | | in(all_840_1, all_56_1) = all_840_0 & in(all_42_1, % 81.04/16.12 | | | | | | | | | | | | | | empty_set) = all_840_2 & in(all_42_2, empty_set) % 81.04/16.12 | | | | | | | | | | | | | | = all_840_3 & in(all_42_3, empty_set) = all_840_4 % 81.04/16.12 | | | | | | | | | | | | | | & $i(all_840_1) & ( ~ (all_840_2 = 0) | ~ % 81.04/16.12 | | | | | | | | | | | | | | (all_840_3 = 0) | ~ (all_840_4 = 0) | all_840_0 % 81.04/16.12 | | | | | | | | | | | | | | = 0) % 81.04/16.12 | | | | | | | | | | | | | | % 81.04/16.12 | | | | | | | | | | | | | | ALPHA: (1065) implies: % 81.04/16.12 | | | | | | | | | | | | | | (1066) in(all_42_1, empty_set) = all_840_2 % 81.04/16.12 | | | | | | | | | | | | | | % 81.04/16.12 | | | | | | | | | | | | | | BETA: splitting (1055) gives: % 81.04/16.12 | | | | | | | | | | | | | | % 81.04/16.12 | | | | | | | | | | | | | | Case 1: % 81.04/16.12 | | | | | | | | | | | | | | | % 81.04/16.12 | | | | | | | | | | | | | | | (1067) all_460_0 = 0 % 81.04/16.12 | | | | | | | | | | | | | | | % 81.04/16.12 | | | | | | | | | | | | | | | REDUCE: (1000), (1067) imply: % 81.04/16.12 | | | | | | | | | | | | | | | (1068) $false % 81.04/16.12 | | | | | | | | | | | | | | | % 81.04/16.12 | | | | | | | | | | | | | | | CLOSE: (1068) is inconsistent. % 81.04/16.12 | | | | | | | | | | | | | | | % 81.04/16.12 | | | | | | | | | | | | | | Case 2: % 81.04/16.12 | | | | | | | | | | | | | | | % 81.04/16.12 | | | | | | | | | | | | | | | % 81.04/16.12 | | | | | | | | | | | | | | | GROUND_INST: instantiating (33) with all_50_0, all_840_2, % 81.04/16.12 | | | | | | | | | | | | | | | empty_set, all_42_1, simplifying with (995), % 81.04/16.12 | | | | | | | | | | | | | | | (1066) gives: % 81.04/16.12 | | | | | | | | | | | | | | | (1069) all_840_2 = all_50_0 % 81.04/16.12 | | | | | | | | | | | | | | | % 81.04/16.12 | | | | | | | | | | | | | | | GROUND_INST: instantiating (32) with all_366_0, all_732_1, % 81.04/16.12 | | | | | | | | | | | | | | | all_194_1, simplifying with (977), (1063) gives: % 81.04/16.12 | | | | | | | | | | | | | | | (1070) all_732_1 = all_366_0 % 81.04/16.12 | | | | | | | | | | | | | | | % 81.04/16.12 | | | | | | | | | | | | | | | BETA: splitting (1064) gives: % 81.04/16.12 | | | | | | | | | | | | | | | % 81.04/16.12 | | | | | | | | | | | | | | | Case 1: % 81.04/16.12 | | | | | | | | | | | | | | | | % 81.04/16.12 | | | | | | | | | | | | | | | | (1071) all_732_0 = 0 % 81.04/16.12 | | | | | | | | | | | | | | | | % 81.04/16.12 | | | | | | | | | | | | | | | | REDUCE: (1062), (1071) imply: % 81.04/16.12 | | | | | | | | | | | | | | | | (1072) in(all_108_1, all_194_1) = 0 % 81.04/16.12 | | | | | | | | | | | | | | | | % 81.04/16.12 | | | | | | | | | | | | | | | | REF_CLOSE: (18), (33), (52), (53), (132), (215), (947), % 81.04/16.12 | | | | | | | | | | | | | | | | (992), (994), (995), (1050), (1072) are % 81.04/16.12 | | | | | | | | | | | | | | | | inconsistent by sub-proof #1. % 81.04/16.12 | | | | | | | | | | | | | | | | % 81.04/16.12 | | | | | | | | | | | | | | | Case 2: % 81.04/16.12 | | | | | | | | | | | | | | | | % 81.04/16.12 | | | | | | | | | | | | | | | | (1073) all_732_1 = 0 % 81.04/16.12 | | | | | | | | | | | | | | | | % 81.04/16.12 | | | | | | | | | | | | | | | | COMBINE_EQS: (1070), (1073) imply: % 81.38/16.12 | | | | | | | | | | | | | | | | (1074) all_366_0 = 0 % 81.38/16.12 | | | | | | | | | | | | | | | | % 81.38/16.12 | | | | | | | | | | | | | | | | SIMP: (1074) implies: % 81.38/16.12 | | | | | | | | | | | | | | | | (1075) all_366_0 = 0 % 81.38/16.12 | | | | | | | | | | | | | | | | % 81.38/16.12 | | | | | | | | | | | | | | | | REDUCE: (976), (1075) imply: % 81.38/16.12 | | | | | | | | | | | | | | | | (1076) $false % 81.38/16.12 | | | | | | | | | | | | | | | | % 81.38/16.12 | | | | | | | | | | | | | | | | CLOSE: (1076) is inconsistent. % 81.38/16.12 | | | | | | | | | | | | | | | | % 81.38/16.12 | | | | | | | | | | | | | | | End of split % 81.38/16.12 | | | | | | | | | | | | | | | % 81.38/16.12 | | | | | | | | | | | | | | End of split % 81.38/16.12 | | | | | | | | | | | | | | % 81.38/16.12 | | | | | | | | | | | | | End of split % 81.38/16.12 | | | | | | | | | | | | | % 81.38/16.12 | | | | | | | | | | | | End of split % 81.38/16.12 | | | | | | | | | | | | % 81.38/16.12 | | | | | | | | | | | End of split % 81.38/16.12 | | | | | | | | | | | % 81.38/16.12 | | | | | | | | | | Case 2: % 81.38/16.12 | | | | | | | | | | | % 81.38/16.12 | | | | | | | | | | | (1077) all_188_1 = 0 % 81.38/16.12 | | | | | | | | | | | % 81.38/16.12 | | | | | | | | | | | COMBINE_EQS: (428), (1077) imply: % 81.38/16.12 | | | | | | | | | | | (1078) all_178_0 = 0 % 81.38/16.12 | | | | | | | | | | | % 81.38/16.12 | | | | | | | | | | | SIMP: (1078) implies: % 81.38/16.12 | | | | | | | | | | | (1079) all_178_0 = 0 % 81.38/16.12 | | | | | | | | | | | % 81.38/16.12 | | | | | | | | | | | REDUCE: (330), (1079) imply: % 81.38/16.12 | | | | | | | | | | | (1080) $false % 81.38/16.12 | | | | | | | | | | | % 81.38/16.12 | | | | | | | | | | | CLOSE: (1080) is inconsistent. % 81.38/16.12 | | | | | | | | | | | % 81.38/16.12 | | | | | | | | | | End of split % 81.38/16.12 | | | | | | | | | | % 81.38/16.12 | | | | | | | | | End of split % 81.38/16.12 | | | | | | | | | % 81.38/16.12 | | | | | | | | End of split % 81.38/16.12 | | | | | | | | % 81.38/16.12 | | | | | | | End of split % 81.38/16.12 | | | | | | | % 81.38/16.12 | | | | | | Case 2: % 81.38/16.12 | | | | | | | % 81.38/16.12 | | | | | | | (1081) all_42_0 = 0 % 81.38/16.12 | | | | | | | % 81.38/16.12 | | | | | | | REDUCE: (48), (1081) imply: % 81.38/16.12 | | | | | | | (1082) $false % 81.38/16.12 | | | | | | | % 81.38/16.12 | | | | | | | CLOSE: (1082) is inconsistent. % 81.38/16.12 | | | | | | | % 81.38/16.12 | | | | | | End of split % 81.38/16.12 | | | | | | % 81.38/16.12 | | | | | End of split % 81.38/16.12 | | | | | % 81.38/16.12 | | | | End of split % 81.38/16.12 | | | | % 81.38/16.12 | | | End of split % 81.38/16.12 | | | % 81.38/16.12 | | End of split % 81.38/16.12 | | % 81.38/16.12 | End of split % 81.38/16.12 | % 81.38/16.12 End of proof % 81.38/16.12 % 81.38/16.12 Sub-proof #1 shows that the following formulas are inconsistent: % 81.38/16.12 ---------------------------------------------------------------- % 81.38/16.12 (1) ordered_pair(all_42_2, all_42_1) = all_108_1 % 81.38/16.12 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! % 81.38/16.12 [v5: $i] : ( ~ (ordered_pair(v0, v1) = v4) | ~ (cartesian_product2(v2, % 81.38/16.12 v3) = v5) | ~ (in(v4, v5) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) % 81.38/16.12 | ~ $i(v0) | (in(v1, v3) = 0 & in(v0, v2) = 0)) % 81.38/16.12 (3) $i(empty_set) % 81.38/16.12 (4) cartesian_product2(empty_set, empty_set) = all_194_1 % 81.38/16.12 (5) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 81.38/16.12 ! [v3: $i] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) % 81.38/16.12 (6) $i(all_42_1) % 81.38/16.12 (7) all_436_0 = 0 | ? [v0: $i] : ? [v1: $i] : ? [v2: int] : ( ~ (v2 = 0) & % 81.38/16.12 empty(v1) = v2 & powerset(all_192_1) = v0 & element(v1, v0) = 0 & % 81.38/16.12 $i(v1) & $i(v0)) % 81.38/16.12 (8) $i(all_42_2) % 81.38/16.12 (9) in(all_42_1, empty_set) = all_50_0 % 81.38/16.12 (10) in(all_108_1, all_194_1) = 0 % 81.38/16.12 (11) ~ (all_50_0 = 0) % 81.38/16.12 (12) ~ (all_436_0 = 0) | all_436_1 = 0 | all_436_2 = 0 % 81.38/16.12 % 81.38/16.12 Begin of proof % 81.38/16.12 | % 81.38/16.12 | BETA: splitting (12) gives: % 81.38/16.12 | % 81.38/16.12 | Case 1: % 81.38/16.12 | | % 81.38/16.12 | | (13) ~ (all_436_0 = 0) % 81.38/16.12 | | % 81.38/16.12 | | BETA: splitting (7) gives: % 81.38/16.12 | | % 81.38/16.12 | | Case 1: % 81.38/16.12 | | | % 81.38/16.12 | | | (14) all_436_0 = 0 % 81.38/16.12 | | | % 81.38/16.12 | | | REDUCE: (13), (14) imply: % 81.38/16.12 | | | (15) $false % 81.38/16.12 | | | % 81.38/16.12 | | | CLOSE: (15) is inconsistent. % 81.38/16.12 | | | % 81.38/16.12 | | Case 2: % 81.38/16.12 | | | % 81.38/16.12 | | | % 81.38/16.12 | | | GROUND_INST: instantiating (2) with all_42_2, all_42_1, empty_set, % 81.38/16.12 | | | empty_set, all_108_1, all_194_1, simplifying with (1), (3), % 81.38/16.12 | | | (4), (6), (8), (10) gives: % 81.38/16.12 | | | (16) in(all_42_1, empty_set) = 0 & in(all_42_2, empty_set) = 0 % 81.38/16.12 | | | % 81.38/16.12 | | | REF_CLOSE: (5), (9), (11), (16) are inconsistent by sub-proof #2. % 81.38/16.12 | | | % 81.38/16.12 | | End of split % 81.38/16.12 | | % 81.38/16.12 | Case 2: % 81.38/16.12 | | % 81.38/16.12 | | % 81.38/16.12 | | GROUND_INST: instantiating (2) with all_42_2, all_42_1, empty_set, % 81.38/16.12 | | empty_set, all_108_1, all_194_1, simplifying with (1), (3), % 81.38/16.12 | | (4), (6), (8), (10) gives: % 81.38/16.12 | | (17) in(all_42_1, empty_set) = 0 & in(all_42_2, empty_set) = 0 % 81.38/16.12 | | % 81.38/16.12 | | REF_CLOSE: (5), (9), (11), (17) are inconsistent by sub-proof #2. % 81.38/16.12 | | % 81.38/16.12 | End of split % 81.38/16.12 | % 81.38/16.12 End of proof % 81.38/16.12 % 81.38/16.12 Sub-proof #2 shows that the following formulas are inconsistent: % 81.38/16.12 ---------------------------------------------------------------- % 81.38/16.12 (1) in(all_42_1, empty_set) = 0 & in(all_42_2, empty_set) = 0 % 81.38/16.12 (2) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 81.38/16.12 ! [v3: $i] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) % 81.38/16.12 (3) in(all_42_1, empty_set) = all_50_0 % 81.38/16.12 (4) ~ (all_50_0 = 0) % 81.38/16.12 % 81.38/16.12 Begin of proof % 81.38/16.12 | % 81.38/16.12 | ALPHA: (1) implies: % 81.38/16.12 | (5) in(all_42_1, empty_set) = 0 % 81.38/16.12 | % 81.38/16.12 | GROUND_INST: instantiating (2) with all_50_0, 0, empty_set, all_42_1, % 81.38/16.12 | simplifying with (3), (5) gives: % 81.38/16.12 | (6) all_50_0 = 0 % 81.38/16.12 | % 81.38/16.12 | REDUCE: (4), (6) imply: % 81.38/16.12 | (7) $false % 81.38/16.12 | % 81.38/16.12 | CLOSE: (7) is inconsistent. % 81.38/16.12 | % 81.38/16.12 End of proof % 81.38/16.12 % SZS output end Proof for theBenchmark % 81.38/16.12 % 81.38/16.12 15558ms %------------------------------------------------------------------------------