%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SEU309+1 : TPTP v8.1.2. Released v3.3.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n012.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 300s % DateTime : Thu Aug 31 17:44:00 EDT 2023 % Result : Theorem 14.26s 2.68s % Output : Proof 33.94s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SEU309+1 : TPTP v8.1.2. Released v3.3.0. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.34 % Computer : n012.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 300 % 0.13/0.34 % DateTime : Thu Aug 24 01:36:57 EDT 2023 % 0.13/0.34 % CPUTime : % 0.19/0.60 ________ _____ % 0.19/0.60 ___ __ \_________(_)________________________________ % 0.19/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.19/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.19/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.19/0.60 % 0.19/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.19/0.60 (2023-06-19) % 0.19/0.60 % 0.19/0.60 (c) Philipp Rümmer, 2009-2023 % 0.19/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.19/0.60 Amanda Stjerna. % 0.19/0.60 Free software under BSD-3-Clause. % 0.19/0.60 % 0.19/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.19/0.60 % 0.19/0.60 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.19/0.61 Running up to 7 provers in parallel. % 0.19/0.62 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.19/0.62 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.19/0.62 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.19/0.62 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.19/0.62 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.19/0.62 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.19/0.62 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 3.08/1.18 Prover 4: Preprocessing ... % 3.08/1.18 Prover 1: Preprocessing ... % 3.88/1.21 Prover 6: Preprocessing ... % 3.88/1.21 Prover 5: Preprocessing ... % 3.88/1.21 Prover 0: Preprocessing ... % 3.88/1.21 Prover 2: Preprocessing ... % 3.88/1.21 Prover 3: Preprocessing ... % 8.55/1.90 Prover 1: Warning: ignoring some quantifiers % 9.00/1.95 Prover 5: Proving ... % 9.00/1.98 Prover 1: Constructing countermodel ... % 9.49/2.02 Prover 2: Proving ... % 9.49/2.04 Prover 3: Warning: ignoring some quantifiers % 9.49/2.04 Prover 6: Proving ... % 9.89/2.07 Prover 3: Constructing countermodel ... % 9.89/2.14 Prover 4: Warning: ignoring some quantifiers % 9.89/2.19 Prover 4: Constructing countermodel ... % 11.52/2.34 Prover 0: Proving ... % 14.26/2.67 Prover 5: proved (2049ms) % 14.26/2.67 % 14.26/2.68 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 14.26/2.68 % 14.26/2.68 Prover 2: stopped % 14.26/2.68 Prover 0: stopped % 14.26/2.68 Prover 6: stopped % 14.26/2.69 Prover 3: stopped % 14.26/2.69 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 14.26/2.69 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 14.26/2.69 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 14.26/2.69 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 14.26/2.69 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 14.96/2.76 Prover 8: Preprocessing ... % 15.36/2.80 Prover 10: Preprocessing ... % 15.36/2.80 Prover 13: Preprocessing ... % 15.36/2.81 Prover 7: Preprocessing ... % 15.36/2.81 Prover 11: Preprocessing ... % 15.36/3.00 Prover 8: Warning: ignoring some quantifiers % 15.36/3.01 Prover 10: Warning: ignoring some quantifiers % 15.36/3.01 Prover 7: Warning: ignoring some quantifiers % 15.89/3.02 Prover 8: Constructing countermodel ... % 15.89/3.03 Prover 10: Constructing countermodel ... % 15.89/3.03 Prover 13: Warning: ignoring some quantifiers % 15.89/3.04 Prover 7: Constructing countermodel ... % 15.89/3.05 Prover 13: Constructing countermodel ... % 18.57/3.25 Prover 11: Warning: ignoring some quantifiers % 18.57/3.26 Prover 11: Constructing countermodel ... % 20.18/3.50 Prover 10: gave up % 20.18/3.52 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 20.87/3.57 Prover 16: Preprocessing ... % 21.69/3.77 Prover 16: Warning: ignoring some quantifiers % 22.51/3.78 Prover 16: Constructing countermodel ... % 31.29/5.16 Prover 13: Found proof (size 423) % 31.29/5.16 Prover 13: proved (2469ms) % 31.29/5.16 Prover 16: stopped % 31.29/5.16 Prover 4: stopped % 31.91/5.16 Prover 7: stopped % 31.91/5.16 Prover 8: stopped % 31.91/5.17 Prover 1: stopped % 31.91/5.17 Prover 11: stopped % 31.91/5.17 % 31.91/5.17 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 31.91/5.17 % 31.91/5.23 % SZS output start Proof for theBenchmark % 33.30/5.23 Assumptions after simplification: % 33.30/5.23 --------------------------------- % 33.30/5.23 % 33.30/5.23 (commutativity_k3_xboole_0) % 33.31/5.26 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (set_intersection2(v0, v1) = v2) % 33.31/5.26 | ~ $i(v1) | ~ $i(v0) | (set_intersection2(v1, v0) = v2 & $i(v2))) % 33.31/5.26 % 33.31/5.26 (commutativity_k5_subset_1) % 33.31/5.26 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 33.31/5.26 (subset_intersection2(v0, v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) % 33.31/5.26 | ? [v4: $i] : ? [v5: $i] : (subset_intersection2(v0, v2, v1) = v5 & % 33.31/5.26 powerset(v0) = v4 & $i(v5) & $i(v4) & (v5 = v3 | ~ element(v2, v4) | ~ % 33.31/5.26 element(v1, v4)))) % 33.31/5.26 % 33.31/5.26 (d3_pre_topc) % 33.31/5.26 ! [v0: $i] : ! [v1: $i] : ( ~ (cast_as_carrier_subset(v0) = v1) | ~ $i(v0) % 33.31/5.26 | ~ one_sorted_str(v0) | (the_carrier(v0) = v1 & $i(v1))) & ! [v0: $i] : ( % 33.31/5.26 ~ $i(v0) | ~ one_sorted_str(v0) | ? [v1: $i] : (cast_as_carrier_subset(v0) % 33.31/5.26 = v1 & the_carrier(v0) = v1 & $i(v1))) % 33.31/5.26 % 33.31/5.26 (dt_k2_pre_topc) % 33.31/5.26 ! [v0: $i] : ! [v1: $i] : ( ~ (cast_as_carrier_subset(v0) = v1) | ~ $i(v0) % 33.31/5.26 | ~ one_sorted_str(v0) | ? [v2: $i] : ? [v3: $i] : (the_carrier(v0) = v2 % 33.31/5.26 & powerset(v2) = v3 & $i(v3) & $i(v2) & element(v1, v3))) & ! [v0: $i] : % 33.31/5.27 ( ~ $i(v0) | ~ one_sorted_str(v0) | ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : % 33.31/5.27 (cast_as_carrier_subset(v0) = v1 & the_carrier(v0) = v2 & powerset(v2) = v3 % 33.31/5.27 & $i(v3) & $i(v2) & $i(v1) & element(v1, v3))) % 33.31/5.27 % 33.31/5.27 (dt_k6_subset_1) % 33.31/5.27 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 33.31/5.27 (subset_difference(v0, v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 33.31/5.27 ? [v4: $i] : (powerset(v0) = v4 & $i(v4) & ( ~ element(v2, v4) | ~ % 33.31/5.27 element(v1, v4) | element(v3, v4)))) % 33.31/5.27 % 33.31/5.27 (existence_l1_struct_0) % 33.31/5.27 ? [v0: $i] : ($i(v0) & one_sorted_str(v0)) % 33.31/5.27 % 33.31/5.27 (rc1_subset_1) % 33.31/5.27 ! [v0: $i] : ! [v1: $i] : ( ~ (powerset(v0) = v1) | ~ $i(v0) | empty(v0) | % 33.31/5.27 ? [v2: $i] : ($i(v2) & element(v2, v1) & ~ empty(v2))) % 33.31/5.27 % 33.31/5.27 (rc2_subset_1) % 33.31/5.27 ! [v0: $i] : ! [v1: $i] : ( ~ (powerset(v0) = v1) | ~ $i(v0) | ? [v2: $i] % 33.31/5.27 : ($i(v2) & empty(v2) & element(v2, v1))) % 33.31/5.27 % 33.31/5.27 (redefinition_k5_subset_1) % 33.31/5.27 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 33.31/5.27 (subset_intersection2(v0, v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) % 33.31/5.27 | ? [v4: $i] : ? [v5: $i] : (set_intersection2(v1, v2) = v5 & powerset(v0) % 33.31/5.27 = v4 & $i(v5) & $i(v4) & (v5 = v3 | ~ element(v2, v4) | ~ element(v1, % 33.31/5.27 v4)))) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ( ~ $i(v2) | ~ % 33.31/5.27 $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : % 33.31/5.27 (subset_intersection2(v0, v1, v2) = v4 & set_intersection2(v1, v2) = v5 & % 33.31/5.27 powerset(v0) = v3 & $i(v5) & $i(v4) & $i(v3) & (v5 = v4 | ~ element(v2, % 33.31/5.27 v3) | ~ element(v1, v3)))) % 33.31/5.27 % 33.31/5.27 (redefinition_k6_subset_1) % 33.31/5.28 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 33.31/5.28 (subset_difference(v0, v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 33.31/5.28 ? [v4: $i] : ? [v5: $i] : (set_difference(v1, v2) = v5 & powerset(v0) = v4 % 33.31/5.28 & $i(v5) & $i(v4) & (v5 = v3 | ~ element(v2, v4) | ~ element(v1, v4)))) % 33.31/5.28 & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ $i(v0) % 33.31/5.28 | ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : (set_difference(v1, v2) = v5 & % 33.31/5.28 subset_difference(v0, v1, v2) = v4 & powerset(v0) = v3 & $i(v5) & $i(v4) & % 33.31/5.28 $i(v3) & (v5 = v4 | ~ element(v2, v3) | ~ element(v1, v3)))) % 33.31/5.28 % 33.31/5.28 (t15_pre_topc) % 33.31/5.28 ! [v0: $i] : ! [v1: $i] : ( ~ (cast_as_carrier_subset(v0) = v1) | ~ $i(v0) % 33.31/5.28 | ~ one_sorted_str(v0) | ? [v2: $i] : ? [v3: $i] : (the_carrier(v0) = v2 % 33.31/5.28 & powerset(v2) = v3 & $i(v3) & $i(v2) & ! [v4: $i] : ! [v5: $i] : (v5 = % 33.31/5.28 v4 | ~ (subset_intersection2(v2, v4, v1) = v5) | ~ $i(v4) | ~ % 33.31/5.28 element(v4, v3)))) & ! [v0: $i] : ( ~ $i(v0) | ~ one_sorted_str(v0) | % 33.31/5.28 ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : (cast_as_carrier_subset(v0) = v3 & % 33.31/5.28 the_carrier(v0) = v1 & powerset(v1) = v2 & $i(v3) & $i(v2) & $i(v1) & ! % 33.31/5.28 [v4: $i] : ( ~ $i(v4) | ~ element(v4, v2) | subset_intersection2(v1, v4, % 33.31/5.28 v3) = v4))) % 33.31/5.28 % 33.31/5.28 (t22_pre_topc) % 33.31/5.28 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: % 33.31/5.28 $i] : ? [v6: $i] : ( ~ (v6 = v4) & subset_difference(v1, v3, v5) = v6 & % 33.31/5.28 subset_difference(v1, v3, v4) = v5 & cast_as_carrier_subset(v0) = v3 & % 33.31/5.28 the_carrier(v0) = v1 & powerset(v1) = v2 & $i(v6) & $i(v5) & $i(v4) & $i(v3) % 33.31/5.28 & $i(v2) & $i(v1) & $i(v0) & one_sorted_str(v0) & element(v4, v2)) % 33.31/5.28 % 33.31/5.28 (t48_xboole_1) % 33.31/5.28 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 33.31/5.28 (set_difference(v0, v2) = v3) | ~ (set_difference(v0, v1) = v2) | ~ $i(v1) % 33.31/5.28 | ~ $i(v0) | (set_intersection2(v0, v1) = v3 & $i(v3))) % 33.31/5.28 % 33.31/5.28 (t4_boole) % 33.31/5.29 $i(empty_set) & ! [v0: $i] : ! [v1: $i] : (v1 = empty_set | ~ % 33.31/5.29 (set_difference(empty_set, v0) = v1) | ~ $i(v0)) % 33.31/5.29 % 33.31/5.29 (t6_boole) % 33.31/5.29 $i(empty_set) & ! [v0: $i] : (v0 = empty_set | ~ $i(v0) | ~ empty(v0)) % 33.31/5.29 % 33.31/5.29 (function-axioms) % 33.31/5.29 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 % 33.31/5.29 | ~ (subset_difference(v4, v3, v2) = v1) | ~ (subset_difference(v4, v3, % 33.31/5.29 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! % 33.31/5.29 [v4: $i] : (v1 = v0 | ~ (subset_intersection2(v4, v3, v2) = v1) | ~ % 33.31/5.29 (subset_intersection2(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 33.31/5.29 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (set_difference(v3, v2) = v1) | ~ % 33.31/5.29 (set_difference(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 33.31/5.29 ! [v3: $i] : (v1 = v0 | ~ (set_intersection2(v3, v2) = v1) | ~ % 33.31/5.29 (set_intersection2(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 33.31/5.29 : (v1 = v0 | ~ (cast_as_carrier_subset(v2) = v1) | ~ % 33.31/5.29 (cast_as_carrier_subset(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 33.31/5.29 : (v1 = v0 | ~ (the_carrier(v2) = v1) | ~ (the_carrier(v2) = v0)) & ! [v0: % 33.31/5.29 $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ % 33.31/5.29 (powerset(v2) = v0)) % 33.31/5.29 % 33.31/5.29 Further assumptions not needed in the proof: % 33.31/5.29 -------------------------------------------- % 33.31/5.29 antisymmetry_r2_hidden, cc10_membered, cc11_membered, cc12_membered, % 33.31/5.29 cc13_membered, cc14_membered, cc15_membered, cc16_membered, cc17_membered, % 33.31/5.29 cc18_membered, cc19_membered, cc1_membered, cc20_membered, cc2_membered, % 33.31/5.29 cc3_membered, cc4_membered, dt_k1_xboole_0, dt_k1_zfmisc_1, dt_k3_xboole_0, % 33.31/5.29 dt_k4_xboole_0, dt_k5_subset_1, dt_l1_struct_0, dt_m1_subset_1, dt_u1_struct_0, % 33.31/5.29 existence_m1_subset_1, fc1_subset_1, fc27_membered, fc28_membered, % 33.31/5.29 fc29_membered, fc30_membered, fc31_membered, fc32_membered, fc33_membered, % 33.31/5.29 fc34_membered, fc35_membered, fc36_membered, fc37_membered, fc38_membered, % 33.31/5.29 fc39_membered, fc40_membered, fc41_membered, fc6_membered, % 33.31/5.29 idempotence_k3_xboole_0, idempotence_k5_subset_1, rc1_membered, % 33.31/5.29 reflexivity_r1_tarski, t1_subset, t2_boole, t2_subset, t3_boole, t3_subset, % 33.31/5.29 t4_subset, t5_subset, t7_boole, t8_boole % 33.31/5.29 % 33.31/5.29 Those formulas are unsatisfiable: % 33.31/5.29 --------------------------------- % 33.31/5.29 % 33.31/5.29 Begin of proof % 33.31/5.29 | % 33.31/5.29 | ALPHA: (d3_pre_topc) implies: % 33.31/5.29 | (1) ! [v0: $i] : ( ~ $i(v0) | ~ one_sorted_str(v0) | ? [v1: $i] : % 33.31/5.29 | (cast_as_carrier_subset(v0) = v1 & the_carrier(v0) = v1 & $i(v1))) % 33.31/5.29 | (2) ! [v0: $i] : ! [v1: $i] : ( ~ (cast_as_carrier_subset(v0) = v1) | ~ % 33.31/5.29 | $i(v0) | ~ one_sorted_str(v0) | (the_carrier(v0) = v1 & $i(v1))) % 33.31/5.29 | % 33.31/5.29 | ALPHA: (dt_k2_pre_topc) implies: % 33.31/5.29 | (3) ! [v0: $i] : ( ~ $i(v0) | ~ one_sorted_str(v0) | ? [v1: $i] : ? % 33.31/5.29 | [v2: $i] : ? [v3: $i] : (cast_as_carrier_subset(v0) = v1 & % 33.31/5.29 | the_carrier(v0) = v2 & powerset(v2) = v3 & $i(v3) & $i(v2) & $i(v1) % 33.31/5.29 | & element(v1, v3))) % 33.31/5.30 | (4) ! [v0: $i] : ! [v1: $i] : ( ~ (cast_as_carrier_subset(v0) = v1) | ~ % 33.31/5.30 | $i(v0) | ~ one_sorted_str(v0) | ? [v2: $i] : ? [v3: $i] : % 33.31/5.30 | (the_carrier(v0) = v2 & powerset(v2) = v3 & $i(v3) & $i(v2) & % 33.31/5.30 | element(v1, v3))) % 33.31/5.30 | % 33.31/5.30 | ALPHA: (redefinition_k5_subset_1) implies: % 33.31/5.30 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 33.31/5.30 | (subset_intersection2(v0, v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ % 33.31/5.30 | $i(v0) | ? [v4: $i] : ? [v5: $i] : (set_intersection2(v1, v2) = v5 % 33.31/5.30 | & powerset(v0) = v4 & $i(v5) & $i(v4) & (v5 = v3 | ~ element(v2, % 33.31/5.30 | v4) | ~ element(v1, v4)))) % 33.31/5.30 | % 33.31/5.30 | ALPHA: (redefinition_k6_subset_1) implies: % 33.31/5.30 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 33.31/5.30 | (subset_difference(v0, v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ % 33.31/5.30 | $i(v0) | ? [v4: $i] : ? [v5: $i] : (set_difference(v1, v2) = v5 & % 33.31/5.30 | powerset(v0) = v4 & $i(v5) & $i(v4) & (v5 = v3 | ~ element(v2, v4) % 33.31/5.30 | | ~ element(v1, v4)))) % 33.31/5.30 | % 33.31/5.30 | ALPHA: (t15_pre_topc) implies: % 33.31/5.30 | (7) ! [v0: $i] : ( ~ $i(v0) | ~ one_sorted_str(v0) | ? [v1: $i] : ? % 33.31/5.30 | [v2: $i] : ? [v3: $i] : (cast_as_carrier_subset(v0) = v3 & % 33.31/5.30 | the_carrier(v0) = v1 & powerset(v1) = v2 & $i(v3) & $i(v2) & $i(v1) % 33.31/5.30 | & ! [v4: $i] : ( ~ $i(v4) | ~ element(v4, v2) | % 33.31/5.30 | subset_intersection2(v1, v4, v3) = v4))) % 33.31/5.30 | (8) ! [v0: $i] : ! [v1: $i] : ( ~ (cast_as_carrier_subset(v0) = v1) | ~ % 33.31/5.30 | $i(v0) | ~ one_sorted_str(v0) | ? [v2: $i] : ? [v3: $i] : % 33.31/5.30 | (the_carrier(v0) = v2 & powerset(v2) = v3 & $i(v3) & $i(v2) & ! [v4: % 33.31/5.30 | $i] : ! [v5: $i] : (v5 = v4 | ~ (subset_intersection2(v2, v4, % 33.31/5.30 | v1) = v5) | ~ $i(v4) | ~ element(v4, v3)))) % 33.31/5.30 | % 33.31/5.30 | ALPHA: (t4_boole) implies: % 33.63/5.30 | (9) ! [v0: $i] : ! [v1: $i] : (v1 = empty_set | ~ % 33.63/5.30 | (set_difference(empty_set, v0) = v1) | ~ $i(v0)) % 33.63/5.30 | % 33.63/5.30 | ALPHA: (t6_boole) implies: % 33.63/5.30 | (10) ! [v0: $i] : (v0 = empty_set | ~ $i(v0) | ~ empty(v0)) % 33.63/5.30 | % 33.63/5.30 | ALPHA: (function-axioms) implies: % 33.63/5.30 | (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (powerset(v2) % 33.63/5.30 | = v1) | ~ (powerset(v2) = v0)) % 33.63/5.30 | (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 33.63/5.30 | (the_carrier(v2) = v1) | ~ (the_carrier(v2) = v0)) % 33.63/5.30 | (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 33.63/5.30 | (cast_as_carrier_subset(v2) = v1) | ~ (cast_as_carrier_subset(v2) = % 33.63/5.30 | v0)) % 33.63/5.30 | (14) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 33.63/5.30 | (set_intersection2(v3, v2) = v1) | ~ (set_intersection2(v3, v2) = % 33.63/5.30 | v0)) % 33.63/5.30 | % 33.63/5.30 | DELTA: instantiating (existence_l1_struct_0) with fresh symbol all_61_0 gives: % 33.63/5.30 | (15) $i(all_61_0) & one_sorted_str(all_61_0) % 33.63/5.30 | % 33.63/5.30 | ALPHA: (15) implies: % 33.63/5.30 | (16) one_sorted_str(all_61_0) % 33.63/5.30 | (17) $i(all_61_0) % 33.63/5.30 | % 33.63/5.30 | DELTA: instantiating (t22_pre_topc) with fresh symbols all_70_0, all_70_1, % 33.63/5.30 | all_70_2, all_70_3, all_70_4, all_70_5, all_70_6 gives: % 33.63/5.30 | (18) ~ (all_70_0 = all_70_2) & subset_difference(all_70_5, all_70_3, % 33.63/5.30 | all_70_1) = all_70_0 & subset_difference(all_70_5, all_70_3, % 33.63/5.30 | all_70_2) = all_70_1 & cast_as_carrier_subset(all_70_6) = all_70_3 & % 33.63/5.30 | the_carrier(all_70_6) = all_70_5 & powerset(all_70_5) = all_70_4 & % 33.63/5.30 | $i(all_70_0) & $i(all_70_1) & $i(all_70_2) & $i(all_70_3) & % 33.63/5.30 | $i(all_70_4) & $i(all_70_5) & $i(all_70_6) & one_sorted_str(all_70_6) % 33.63/5.30 | & element(all_70_2, all_70_4) % 33.63/5.30 | % 33.63/5.30 | ALPHA: (18) implies: % 33.63/5.30 | (19) ~ (all_70_0 = all_70_2) % 33.63/5.30 | (20) element(all_70_2, all_70_4) % 33.63/5.30 | (21) one_sorted_str(all_70_6) % 33.63/5.30 | (22) $i(all_70_6) % 33.63/5.30 | (23) $i(all_70_5) % 33.63/5.30 | (24) $i(all_70_2) % 33.63/5.31 | (25) $i(all_70_1) % 33.63/5.31 | (26) powerset(all_70_5) = all_70_4 % 33.63/5.31 | (27) the_carrier(all_70_6) = all_70_5 % 33.63/5.31 | (28) cast_as_carrier_subset(all_70_6) = all_70_3 % 33.63/5.31 | (29) subset_difference(all_70_5, all_70_3, all_70_2) = all_70_1 % 33.63/5.31 | (30) subset_difference(all_70_5, all_70_3, all_70_1) = all_70_0 % 33.63/5.31 | % 33.63/5.31 | GROUND_INST: instantiating (7) with all_61_0, simplifying with (16), (17) % 33.63/5.31 | gives: % 33.63/5.31 | (31) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 33.63/5.31 | (cast_as_carrier_subset(all_61_0) = v2 & the_carrier(all_61_0) = v0 & % 33.63/5.31 | powerset(v0) = v1 & $i(v2) & $i(v1) & $i(v0) & ! [v3: $i] : ( ~ % 33.63/5.31 | $i(v3) | ~ element(v3, v1) | subset_intersection2(v0, v3, v2) = % 33.63/5.31 | v3)) % 33.63/5.31 | % 33.63/5.31 | GROUND_INST: instantiating (3) with all_61_0, simplifying with (16), (17) % 33.63/5.31 | gives: % 33.63/5.31 | (32) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 33.63/5.31 | (cast_as_carrier_subset(all_61_0) = v0 & the_carrier(all_61_0) = v1 & % 33.63/5.31 | powerset(v1) = v2 & $i(v2) & $i(v1) & $i(v0) & element(v0, v2)) % 33.63/5.31 | % 33.63/5.31 | GROUND_INST: instantiating (1) with all_61_0, simplifying with (16), (17) % 33.63/5.31 | gives: % 33.63/5.31 | (33) ? [v0: $i] : (cast_as_carrier_subset(all_61_0) = v0 & % 33.63/5.31 | the_carrier(all_61_0) = v0 & $i(v0)) % 33.63/5.31 | % 33.63/5.31 | GROUND_INST: instantiating (7) with all_70_6, simplifying with (21), (22) % 33.63/5.31 | gives: % 33.63/5.31 | (34) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 33.63/5.31 | (cast_as_carrier_subset(all_70_6) = v2 & the_carrier(all_70_6) = v0 & % 33.63/5.31 | powerset(v0) = v1 & $i(v2) & $i(v1) & $i(v0) & ! [v3: $i] : ( ~ % 33.63/5.31 | $i(v3) | ~ element(v3, v1) | subset_intersection2(v0, v3, v2) = % 33.63/5.31 | v3)) % 33.63/5.31 | % 33.63/5.31 | GROUND_INST: instantiating (3) with all_70_6, simplifying with (21), (22) % 33.63/5.31 | gives: % 33.63/5.31 | (35) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 33.63/5.31 | (cast_as_carrier_subset(all_70_6) = v0 & the_carrier(all_70_6) = v1 & % 33.63/5.31 | powerset(v1) = v2 & $i(v2) & $i(v1) & $i(v0) & element(v0, v2)) % 33.63/5.31 | % 33.63/5.31 | GROUND_INST: instantiating (1) with all_70_6, simplifying with (21), (22) % 33.63/5.31 | gives: % 33.63/5.31 | (36) ? [v0: $i] : (cast_as_carrier_subset(all_70_6) = v0 & % 33.63/5.31 | the_carrier(all_70_6) = v0 & $i(v0)) % 33.63/5.31 | % 33.63/5.31 | GROUND_INST: instantiating (rc1_subset_1) with all_70_5, all_70_4, simplifying % 33.63/5.31 | with (23), (26) gives: % 33.63/5.31 | (37) empty(all_70_5) | ? [v0: $i] : ($i(v0) & element(v0, all_70_4) & ~ % 33.63/5.31 | empty(v0)) % 33.63/5.31 | % 33.63/5.31 | GROUND_INST: instantiating (rc2_subset_1) with all_70_5, all_70_4, simplifying % 33.63/5.31 | with (23), (26) gives: % 33.63/5.31 | (38) ? [v0: $i] : ($i(v0) & empty(v0) & element(v0, all_70_4)) % 33.63/5.31 | % 33.63/5.31 | GROUND_INST: instantiating (4) with all_70_6, all_70_3, simplifying with (21), % 33.63/5.31 | (22), (28) gives: % 33.63/5.31 | (39) ? [v0: $i] : ? [v1: $i] : (the_carrier(all_70_6) = v0 & powerset(v0) % 33.63/5.31 | = v1 & $i(v1) & $i(v0) & element(all_70_3, v1)) % 33.63/5.31 | % 33.63/5.31 | GROUND_INST: instantiating (8) with all_70_6, all_70_3, simplifying with (21), % 33.63/5.31 | (22), (28) gives: % 33.63/5.31 | (40) ? [v0: $i] : ? [v1: $i] : (the_carrier(all_70_6) = v0 & powerset(v0) % 33.63/5.31 | = v1 & $i(v1) & $i(v0) & ! [v2: $i] : ! [v3: $i] : (v3 = v2 | ~ % 33.63/5.31 | (subset_intersection2(v0, v2, all_70_3) = v3) | ~ $i(v2) | ~ % 33.63/5.31 | element(v2, v1))) % 33.63/5.31 | % 33.63/5.31 | GROUND_INST: instantiating (2) with all_70_6, all_70_3, simplifying with (21), % 33.63/5.31 | (22), (28) gives: % 33.63/5.31 | (41) the_carrier(all_70_6) = all_70_3 & $i(all_70_3) % 33.63/5.31 | % 33.63/5.31 | ALPHA: (41) implies: % 33.63/5.31 | (42) $i(all_70_3) % 33.63/5.31 | (43) the_carrier(all_70_6) = all_70_3 % 33.63/5.31 | % 33.63/5.31 | GROUND_INST: instantiating (6) with all_70_5, all_70_3, all_70_2, all_70_1, % 33.63/5.31 | simplifying with (23), (24), (29), (42) gives: % 33.63/5.32 | (44) ? [v0: $i] : ? [v1: $i] : (set_difference(all_70_3, all_70_2) = v1 & % 33.63/5.32 | powerset(all_70_5) = v0 & $i(v1) & $i(v0) & (v1 = all_70_1 | ~ % 33.63/5.32 | element(all_70_2, v0) | ~ element(all_70_3, v0))) % 33.63/5.32 | % 33.63/5.32 | GROUND_INST: instantiating (dt_k6_subset_1) with all_70_5, all_70_3, all_70_2, % 33.63/5.32 | all_70_1, simplifying with (23), (24), (29), (42) gives: % 33.63/5.32 | (45) ? [v0: $i] : (powerset(all_70_5) = v0 & $i(v0) & ( ~ % 33.63/5.32 | element(all_70_2, v0) | ~ element(all_70_3, v0) | % 33.63/5.32 | element(all_70_1, v0))) % 33.63/5.32 | % 33.63/5.32 | GROUND_INST: instantiating (6) with all_70_5, all_70_3, all_70_1, all_70_0, % 33.63/5.32 | simplifying with (23), (25), (30), (42) gives: % 33.63/5.32 | (46) ? [v0: $i] : ? [v1: $i] : (set_difference(all_70_3, all_70_1) = v1 & % 33.63/5.32 | powerset(all_70_5) = v0 & $i(v1) & $i(v0) & (v1 = all_70_0 | ~ % 33.63/5.32 | element(all_70_1, v0) | ~ element(all_70_3, v0))) % 33.63/5.32 | % 33.63/5.32 | GROUND_INST: instantiating (dt_k6_subset_1) with all_70_5, all_70_3, all_70_1, % 33.63/5.32 | all_70_0, simplifying with (23), (25), (30), (42) gives: % 33.63/5.32 | (47) ? [v0: $i] : (powerset(all_70_5) = v0 & $i(v0) & ( ~ % 33.63/5.32 | element(all_70_1, v0) | ~ element(all_70_3, v0) | % 33.63/5.32 | element(all_70_0, v0))) % 33.63/5.32 | % 33.63/5.32 | DELTA: instantiating (33) with fresh symbol all_78_0 gives: % 33.63/5.32 | (48) cast_as_carrier_subset(all_61_0) = all_78_0 & the_carrier(all_61_0) = % 33.63/5.32 | all_78_0 & $i(all_78_0) % 33.63/5.32 | % 33.63/5.32 | ALPHA: (48) implies: % 33.63/5.32 | (49) the_carrier(all_61_0) = all_78_0 % 33.63/5.32 | (50) cast_as_carrier_subset(all_61_0) = all_78_0 % 33.63/5.32 | % 33.63/5.32 | DELTA: instantiating (38) with fresh symbol all_80_0 gives: % 33.63/5.32 | (51) $i(all_80_0) & empty(all_80_0) & element(all_80_0, all_70_4) % 33.63/5.32 | % 33.63/5.32 | ALPHA: (51) implies: % 33.63/5.32 | (52) element(all_80_0, all_70_4) % 33.63/5.32 | (53) empty(all_80_0) % 33.63/5.32 | (54) $i(all_80_0) % 33.63/5.32 | % 33.63/5.32 | DELTA: instantiating (36) with fresh symbol all_82_0 gives: % 33.63/5.32 | (55) cast_as_carrier_subset(all_70_6) = all_82_0 & the_carrier(all_70_6) = % 33.63/5.32 | all_82_0 & $i(all_82_0) % 33.63/5.32 | % 33.63/5.32 | ALPHA: (55) implies: % 33.63/5.32 | (56) the_carrier(all_70_6) = all_82_0 % 33.63/5.32 | (57) cast_as_carrier_subset(all_70_6) = all_82_0 % 33.63/5.32 | % 33.63/5.32 | DELTA: instantiating (45) with fresh symbol all_84_0 gives: % 33.63/5.32 | (58) powerset(all_70_5) = all_84_0 & $i(all_84_0) & ( ~ element(all_70_2, % 33.63/5.32 | all_84_0) | ~ element(all_70_3, all_84_0) | element(all_70_1, % 33.63/5.32 | all_84_0)) % 33.63/5.32 | % 33.63/5.32 | ALPHA: (58) implies: % 33.63/5.32 | (59) powerset(all_70_5) = all_84_0 % 33.63/5.32 | (60) ~ element(all_70_2, all_84_0) | ~ element(all_70_3, all_84_0) | % 33.63/5.32 | element(all_70_1, all_84_0) % 33.63/5.32 | % 33.63/5.32 | DELTA: instantiating (47) with fresh symbol all_86_0 gives: % 33.63/5.32 | (61) powerset(all_70_5) = all_86_0 & $i(all_86_0) & ( ~ element(all_70_1, % 33.63/5.32 | all_86_0) | ~ element(all_70_3, all_86_0) | element(all_70_0, % 33.63/5.32 | all_86_0)) % 33.63/5.32 | % 33.63/5.32 | ALPHA: (61) implies: % 33.63/5.32 | (62) powerset(all_70_5) = all_86_0 % 33.63/5.32 | (63) ~ element(all_70_1, all_86_0) | ~ element(all_70_3, all_86_0) | % 33.63/5.32 | element(all_70_0, all_86_0) % 33.63/5.32 | % 33.63/5.32 | DELTA: instantiating (39) with fresh symbols all_88_0, all_88_1 gives: % 33.63/5.32 | (64) the_carrier(all_70_6) = all_88_1 & powerset(all_88_1) = all_88_0 & % 33.63/5.32 | $i(all_88_0) & $i(all_88_1) & element(all_70_3, all_88_0) % 33.63/5.32 | % 33.63/5.32 | ALPHA: (64) implies: % 33.63/5.32 | (65) element(all_70_3, all_88_0) % 33.63/5.32 | (66) powerset(all_88_1) = all_88_0 % 33.63/5.32 | (67) the_carrier(all_70_6) = all_88_1 % 33.63/5.32 | % 33.63/5.32 | DELTA: instantiating (44) with fresh symbols all_90_0, all_90_1 gives: % 33.63/5.32 | (68) set_difference(all_70_3, all_70_2) = all_90_0 & powerset(all_70_5) = % 33.63/5.32 | all_90_1 & $i(all_90_0) & $i(all_90_1) & (all_90_0 = all_70_1 | ~ % 33.63/5.32 | element(all_70_2, all_90_1) | ~ element(all_70_3, all_90_1)) % 33.63/5.32 | % 33.63/5.32 | ALPHA: (68) implies: % 33.63/5.32 | (69) $i(all_90_0) % 33.63/5.32 | (70) powerset(all_70_5) = all_90_1 % 33.63/5.32 | (71) set_difference(all_70_3, all_70_2) = all_90_0 % 33.63/5.32 | (72) all_90_0 = all_70_1 | ~ element(all_70_2, all_90_1) | ~ % 33.63/5.32 | element(all_70_3, all_90_1) % 33.63/5.32 | % 33.63/5.32 | DELTA: instantiating (35) with fresh symbols all_92_0, all_92_1, all_92_2 % 33.63/5.32 | gives: % 33.63/5.32 | (73) cast_as_carrier_subset(all_70_6) = all_92_2 & the_carrier(all_70_6) = % 33.63/5.32 | all_92_1 & powerset(all_92_1) = all_92_0 & $i(all_92_0) & $i(all_92_1) % 33.63/5.32 | & $i(all_92_2) & element(all_92_2, all_92_0) % 33.63/5.32 | % 33.63/5.32 | ALPHA: (73) implies: % 33.63/5.33 | (74) powerset(all_92_1) = all_92_0 % 33.63/5.33 | (75) the_carrier(all_70_6) = all_92_1 % 33.63/5.33 | % 33.63/5.33 | DELTA: instantiating (46) with fresh symbols all_94_0, all_94_1 gives: % 33.63/5.33 | (76) set_difference(all_70_3, all_70_1) = all_94_0 & powerset(all_70_5) = % 33.63/5.33 | all_94_1 & $i(all_94_0) & $i(all_94_1) & (all_94_0 = all_70_0 | ~ % 33.63/5.33 | element(all_70_1, all_94_1) | ~ element(all_70_3, all_94_1)) % 33.63/5.33 | % 33.63/5.33 | ALPHA: (76) implies: % 33.63/5.33 | (77) powerset(all_70_5) = all_94_1 % 33.63/5.33 | (78) set_difference(all_70_3, all_70_1) = all_94_0 % 33.63/5.33 | (79) all_94_0 = all_70_0 | ~ element(all_70_1, all_94_1) | ~ % 33.63/5.33 | element(all_70_3, all_94_1) % 33.63/5.33 | % 33.63/5.33 | DELTA: instantiating (32) with fresh symbols all_96_0, all_96_1, all_96_2 % 33.63/5.33 | gives: % 33.63/5.33 | (80) cast_as_carrier_subset(all_61_0) = all_96_2 & the_carrier(all_61_0) = % 33.63/5.33 | all_96_1 & powerset(all_96_1) = all_96_0 & $i(all_96_0) & $i(all_96_1) % 33.63/5.33 | & $i(all_96_2) & element(all_96_2, all_96_0) % 33.63/5.33 | % 33.63/5.33 | ALPHA: (80) implies: % 33.63/5.33 | (81) element(all_96_2, all_96_0) % 33.63/5.33 | (82) $i(all_96_2) % 33.63/5.33 | (83) powerset(all_96_1) = all_96_0 % 33.63/5.33 | (84) the_carrier(all_61_0) = all_96_1 % 33.63/5.33 | (85) cast_as_carrier_subset(all_61_0) = all_96_2 % 33.63/5.33 | % 33.63/5.33 | DELTA: instantiating (40) with fresh symbols all_98_0, all_98_1 gives: % 33.63/5.33 | (86) the_carrier(all_70_6) = all_98_1 & powerset(all_98_1) = all_98_0 & % 33.63/5.33 | $i(all_98_0) & $i(all_98_1) & ! [v0: $i] : ! [v1: $i] : (v1 = v0 | % 33.63/5.33 | ~ (subset_intersection2(all_98_1, v0, all_70_3) = v1) | ~ $i(v0) | % 33.63/5.33 | ~ element(v0, all_98_0)) % 33.63/5.33 | % 33.63/5.33 | ALPHA: (86) implies: % 33.63/5.33 | (87) powerset(all_98_1) = all_98_0 % 33.63/5.33 | (88) the_carrier(all_70_6) = all_98_1 % 33.63/5.33 | % 33.63/5.33 | DELTA: instantiating (31) with fresh symbols all_101_0, all_101_1, all_101_2 % 33.63/5.33 | gives: % 33.63/5.33 | (89) cast_as_carrier_subset(all_61_0) = all_101_0 & the_carrier(all_61_0) = % 33.63/5.33 | all_101_2 & powerset(all_101_2) = all_101_1 & $i(all_101_0) & % 33.63/5.33 | $i(all_101_1) & $i(all_101_2) & ! [v0: $i] : ( ~ $i(v0) | ~ % 33.63/5.33 | element(v0, all_101_1) | subset_intersection2(all_101_2, v0, % 33.63/5.33 | all_101_0) = v0) % 33.63/5.33 | % 33.63/5.33 | ALPHA: (89) implies: % 33.63/5.33 | (90) powerset(all_101_2) = all_101_1 % 33.63/5.33 | (91) the_carrier(all_61_0) = all_101_2 % 33.63/5.33 | (92) cast_as_carrier_subset(all_61_0) = all_101_0 % 33.63/5.33 | (93) ! [v0: $i] : ( ~ $i(v0) | ~ element(v0, all_101_1) | % 33.63/5.33 | subset_intersection2(all_101_2, v0, all_101_0) = v0) % 33.63/5.33 | % 33.63/5.33 | DELTA: instantiating (34) with fresh symbols all_104_0, all_104_1, all_104_2 % 33.63/5.33 | gives: % 33.63/5.33 | (94) cast_as_carrier_subset(all_70_6) = all_104_0 & the_carrier(all_70_6) = % 33.63/5.33 | all_104_2 & powerset(all_104_2) = all_104_1 & $i(all_104_0) & % 33.63/5.33 | $i(all_104_1) & $i(all_104_2) & ! [v0: $i] : ( ~ $i(v0) | ~ % 33.63/5.33 | element(v0, all_104_1) | subset_intersection2(all_104_2, v0, % 33.63/5.33 | all_104_0) = v0) % 33.63/5.33 | % 33.63/5.33 | ALPHA: (94) implies: % 33.63/5.33 | (95) powerset(all_104_2) = all_104_1 % 33.63/5.33 | (96) the_carrier(all_70_6) = all_104_2 % 33.63/5.33 | (97) cast_as_carrier_subset(all_70_6) = all_104_0 % 33.63/5.33 | (98) ! [v0: $i] : ( ~ $i(v0) | ~ element(v0, all_104_1) | % 33.63/5.33 | subset_intersection2(all_104_2, v0, all_104_0) = v0) % 33.63/5.33 | % 33.63/5.33 | GROUND_INST: instantiating (11) with all_84_0, all_86_0, all_70_5, simplifying % 33.63/5.33 | with (59), (62) gives: % 33.63/5.33 | (99) all_86_0 = all_84_0 % 33.63/5.33 | % 33.63/5.33 | GROUND_INST: instantiating (11) with all_86_0, all_90_1, all_70_5, simplifying % 33.63/5.33 | with (62), (70) gives: % 33.63/5.33 | (100) all_90_1 = all_86_0 % 33.63/5.33 | % 33.63/5.33 | GROUND_INST: instantiating (11) with all_70_4, all_94_1, all_70_5, simplifying % 33.63/5.33 | with (26), (77) gives: % 33.63/5.33 | (101) all_94_1 = all_70_4 % 33.63/5.33 | % 33.63/5.33 | GROUND_INST: instantiating (11) with all_90_1, all_94_1, all_70_5, simplifying % 33.63/5.33 | with (70), (77) gives: % 33.63/5.33 | (102) all_94_1 = all_90_1 % 33.63/5.33 | % 33.63/5.33 | GROUND_INST: instantiating (12) with all_96_1, all_101_2, all_61_0, % 33.63/5.33 | simplifying with (84), (91) gives: % 33.63/5.33 | (103) all_101_2 = all_96_1 % 33.63/5.33 | % 33.63/5.33 | GROUND_INST: instantiating (12) with all_78_0, all_101_2, all_61_0, % 33.63/5.33 | simplifying with (49), (91) gives: % 33.63/5.33 | (104) all_101_2 = all_78_0 % 33.63/5.33 | % 33.63/5.33 | GROUND_INST: instantiating (12) with all_82_0, all_88_1, all_70_6, simplifying % 33.63/5.33 | with (56), (67) gives: % 33.63/5.33 | (105) all_88_1 = all_82_0 % 33.63/5.33 | % 33.63/5.33 | GROUND_INST: instantiating (12) with all_70_3, all_88_1, all_70_6, simplifying % 33.63/5.33 | with (43), (67) gives: % 33.63/5.34 | (106) all_88_1 = all_70_3 % 33.63/5.34 | % 33.63/5.34 | GROUND_INST: instantiating (12) with all_70_5, all_98_1, all_70_6, simplifying % 33.63/5.34 | with (27), (88) gives: % 33.63/5.34 | (107) all_98_1 = all_70_5 % 33.63/5.34 | % 33.63/5.34 | GROUND_INST: instantiating (12) with all_88_1, all_98_1, all_70_6, simplifying % 33.63/5.34 | with (67), (88) gives: % 33.63/5.34 | (108) all_98_1 = all_88_1 % 33.63/5.34 | % 33.63/5.34 | GROUND_INST: instantiating (12) with all_98_1, all_104_2, all_70_6, % 33.63/5.34 | simplifying with (88), (96) gives: % 33.63/5.34 | (109) all_104_2 = all_98_1 % 33.63/5.34 | % 33.63/5.34 | GROUND_INST: instantiating (12) with all_92_1, all_104_2, all_70_6, % 33.63/5.34 | simplifying with (75), (96) gives: % 33.63/5.34 | (110) all_104_2 = all_92_1 % 33.63/5.34 | % 33.63/5.34 | GROUND_INST: instantiating (13) with all_96_2, all_101_0, all_61_0, % 33.63/5.34 | simplifying with (85), (92) gives: % 33.63/5.34 | (111) all_101_0 = all_96_2 % 33.63/5.34 | % 33.63/5.34 | GROUND_INST: instantiating (13) with all_78_0, all_101_0, all_61_0, % 33.63/5.34 | simplifying with (50), (92) gives: % 33.63/5.34 | (112) all_101_0 = all_78_0 % 33.63/5.34 | % 33.63/5.34 | GROUND_INST: instantiating (13) with all_82_0, all_104_0, all_70_6, % 33.63/5.34 | simplifying with (57), (97) gives: % 33.63/5.34 | (113) all_104_0 = all_82_0 % 33.63/5.34 | % 33.63/5.34 | COMBINE_EQS: (109), (110) imply: % 33.63/5.34 | (114) all_98_1 = all_92_1 % 33.63/5.34 | % 33.63/5.34 | SIMP: (114) implies: % 33.63/5.34 | (115) all_98_1 = all_92_1 % 33.63/5.34 | % 33.63/5.34 | COMBINE_EQS: (111), (112) imply: % 33.63/5.34 | (116) all_96_2 = all_78_0 % 33.63/5.34 | % 33.63/5.34 | SIMP: (116) implies: % 33.63/5.34 | (117) all_96_2 = all_78_0 % 33.63/5.34 | % 33.63/5.34 | COMBINE_EQS: (103), (104) imply: % 33.63/5.34 | (118) all_96_1 = all_78_0 % 33.63/5.34 | % 33.63/5.34 | COMBINE_EQS: (108), (115) imply: % 33.63/5.34 | (119) all_92_1 = all_88_1 % 33.63/5.34 | % 33.63/5.34 | COMBINE_EQS: (107), (115) imply: % 33.63/5.34 | (120) all_92_1 = all_70_5 % 33.63/5.34 | % 33.63/5.34 | COMBINE_EQS: (101), (102) imply: % 33.63/5.34 | (121) all_90_1 = all_70_4 % 33.63/5.34 | % 33.63/5.34 | SIMP: (121) implies: % 33.63/5.34 | (122) all_90_1 = all_70_4 % 33.63/5.34 | % 33.63/5.34 | COMBINE_EQS: (119), (120) imply: % 33.63/5.34 | (123) all_88_1 = all_70_5 % 33.63/5.34 | % 33.63/5.34 | SIMP: (123) implies: % 33.63/5.34 | (124) all_88_1 = all_70_5 % 33.63/5.34 | % 33.63/5.34 | COMBINE_EQS: (100), (122) imply: % 33.63/5.34 | (125) all_86_0 = all_70_4 % 33.63/5.34 | % 33.63/5.34 | SIMP: (125) implies: % 33.63/5.34 | (126) all_86_0 = all_70_4 % 33.63/5.34 | % 33.63/5.34 | COMBINE_EQS: (105), (124) imply: % 33.63/5.34 | (127) all_82_0 = all_70_5 % 33.63/5.34 | % 33.63/5.34 | COMBINE_EQS: (105), (106) imply: % 33.63/5.34 | (128) all_82_0 = all_70_3 % 33.63/5.34 | % 33.63/5.34 | COMBINE_EQS: (99), (126) imply: % 33.63/5.34 | (129) all_84_0 = all_70_4 % 33.63/5.34 | % 33.63/5.34 | SIMP: (129) implies: % 33.63/5.34 | (130) all_84_0 = all_70_4 % 33.63/5.34 | % 33.63/5.34 | COMBINE_EQS: (127), (128) imply: % 33.63/5.34 | (131) all_70_3 = all_70_5 % 33.63/5.34 | % 33.63/5.34 | SIMP: (131) implies: % 33.63/5.34 | (132) all_70_3 = all_70_5 % 33.63/5.34 | % 33.63/5.34 | COMBINE_EQS: (110), (120) imply: % 33.63/5.34 | (133) all_104_2 = all_70_5 % 33.63/5.34 | % 33.63/5.34 | COMBINE_EQS: (113), (127) imply: % 33.63/5.34 | (134) all_104_0 = all_70_5 % 33.63/5.34 | % 33.63/5.34 | REDUCE: (78), (132) imply: % 33.63/5.34 | (135) set_difference(all_70_5, all_70_1) = all_94_0 % 33.63/5.34 | % 33.63/5.34 | REDUCE: (71), (132) imply: % 33.63/5.34 | (136) set_difference(all_70_5, all_70_2) = all_90_0 % 33.63/5.34 | % 33.63/5.34 | REDUCE: (28), (132) imply: % 33.63/5.34 | (137) cast_as_carrier_subset(all_70_6) = all_70_5 % 33.63/5.34 | % 33.63/5.34 | REDUCE: (95), (133) imply: % 33.63/5.34 | (138) powerset(all_70_5) = all_104_1 % 33.63/5.34 | % 33.63/5.34 | REDUCE: (90), (104) imply: % 33.63/5.34 | (139) powerset(all_78_0) = all_101_1 % 33.63/5.34 | % 33.63/5.34 | REDUCE: (87), (107) imply: % 33.63/5.34 | (140) powerset(all_70_5) = all_98_0 % 33.63/5.34 | % 33.63/5.34 | REDUCE: (83), (118) imply: % 33.63/5.34 | (141) powerset(all_78_0) = all_96_0 % 33.63/5.34 | % 33.63/5.34 | REDUCE: (74), (120) imply: % 33.63/5.34 | (142) powerset(all_70_5) = all_92_0 % 33.63/5.34 | % 33.63/5.34 | REDUCE: (66), (124) imply: % 33.63/5.34 | (143) powerset(all_70_5) = all_88_0 % 33.63/5.34 | % 33.63/5.34 | REDUCE: (82), (117) imply: % 33.63/5.34 | (144) $i(all_78_0) % 33.63/5.34 | % 33.63/5.34 | REDUCE: (81), (117) imply: % 33.63/5.34 | (145) element(all_78_0, all_96_0) % 33.63/5.34 | % 33.63/5.34 | REDUCE: (65), (132) imply: % 33.63/5.34 | (146) element(all_70_5, all_88_0) % 33.63/5.34 | % 33.63/5.34 | GROUND_INST: instantiating (11) with all_70_4, all_92_0, all_70_5, simplifying % 33.63/5.34 | with (26), (142) gives: % 33.63/5.34 | (147) all_92_0 = all_70_4 % 33.63/5.34 | % 33.63/5.34 | GROUND_INST: instantiating (11) with all_92_0, all_98_0, all_70_5, simplifying % 33.63/5.34 | with (140), (142) gives: % 33.63/5.34 | (148) all_98_0 = all_92_0 % 33.63/5.34 | % 33.63/5.34 | GROUND_INST: instantiating (11) with all_98_0, all_104_1, all_70_5, % 33.63/5.34 | simplifying with (138), (140) gives: % 33.63/5.34 | (149) all_104_1 = all_98_0 % 33.63/5.34 | % 33.63/5.34 | GROUND_INST: instantiating (11) with all_88_0, all_104_1, all_70_5, % 33.63/5.34 | simplifying with (138), (143) gives: % 33.63/5.34 | (150) all_104_1 = all_88_0 % 33.63/5.34 | % 33.63/5.34 | GROUND_INST: instantiating (11) with all_96_0, all_101_1, all_78_0, % 33.63/5.34 | simplifying with (139), (141) gives: % 33.63/5.34 | (151) all_101_1 = all_96_0 % 33.63/5.34 | % 33.63/5.34 | COMBINE_EQS: (149), (150) imply: % 33.63/5.34 | (152) all_98_0 = all_88_0 % 33.63/5.34 | % 33.63/5.34 | SIMP: (152) implies: % 33.63/5.34 | (153) all_98_0 = all_88_0 % 33.63/5.34 | % 33.63/5.34 | COMBINE_EQS: (148), (153) imply: % 33.63/5.34 | (154) all_92_0 = all_88_0 % 33.63/5.34 | % 33.63/5.34 | SIMP: (154) implies: % 33.63/5.34 | (155) all_92_0 = all_88_0 % 33.63/5.34 | % 33.63/5.34 | COMBINE_EQS: (147), (155) imply: % 33.63/5.34 | (156) all_88_0 = all_70_4 % 33.63/5.34 | % 33.63/5.34 | COMBINE_EQS: (150), (156) imply: % 33.63/5.34 | (157) all_104_1 = all_70_4 % 33.63/5.35 | % 33.63/5.35 | REDUCE: (146), (156) imply: % 33.63/5.35 | (158) element(all_70_5, all_70_4) % 33.63/5.35 | % 33.63/5.35 | BETA: splitting (60) gives: % 33.63/5.35 | % 33.63/5.35 | Case 1: % 33.63/5.35 | | % 33.63/5.35 | | (159) ~ element(all_70_2, all_84_0) % 33.63/5.35 | | % 33.63/5.35 | | REDUCE: (130), (159) imply: % 33.63/5.35 | | (160) ~ element(all_70_2, all_70_4) % 33.63/5.35 | | % 33.63/5.35 | | PRED_UNIFY: (20), (160) imply: % 33.63/5.35 | | (161) $false % 33.63/5.35 | | % 33.63/5.35 | | CLOSE: (161) is inconsistent. % 33.63/5.35 | | % 33.63/5.35 | Case 2: % 33.63/5.35 | | % 33.63/5.35 | | (162) element(all_70_2, all_84_0) % 33.63/5.35 | | (163) ~ element(all_70_3, all_84_0) | element(all_70_1, all_84_0) % 33.63/5.35 | | % 33.63/5.35 | | BETA: splitting (163) gives: % 33.63/5.35 | | % 33.63/5.35 | | Case 1: % 33.63/5.35 | | | % 33.63/5.35 | | | (164) ~ element(all_70_3, all_84_0) % 33.63/5.35 | | | % 33.63/5.35 | | | REDUCE: (130), (132), (164) imply: % 33.63/5.35 | | | (165) ~ element(all_70_5, all_70_4) % 33.63/5.35 | | | % 33.63/5.35 | | | PRED_UNIFY: (158), (165) imply: % 33.63/5.35 | | | (166) $false % 33.63/5.35 | | | % 33.63/5.35 | | | CLOSE: (166) is inconsistent. % 33.63/5.35 | | | % 33.63/5.35 | | Case 2: % 33.63/5.35 | | | % 33.63/5.35 | | | (167) element(all_70_3, all_84_0) % 33.63/5.35 | | | (168) element(all_70_1, all_84_0) % 33.63/5.35 | | | % 33.63/5.35 | | | REDUCE: (130), (168) imply: % 33.63/5.35 | | | (169) element(all_70_1, all_70_4) % 33.63/5.35 | | | % 33.63/5.35 | | | BETA: splitting (63) gives: % 33.63/5.35 | | | % 33.63/5.35 | | | Case 1: % 33.63/5.35 | | | | % 33.63/5.35 | | | | (170) ~ element(all_70_1, all_86_0) % 33.63/5.35 | | | | % 33.63/5.35 | | | | REDUCE: (126), (170) imply: % 33.63/5.35 | | | | (171) ~ element(all_70_1, all_70_4) % 33.63/5.35 | | | | % 33.63/5.35 | | | | PRED_UNIFY: (169), (171) imply: % 33.63/5.35 | | | | (172) $false % 33.63/5.35 | | | | % 33.63/5.35 | | | | CLOSE: (172) is inconsistent. % 33.63/5.35 | | | | % 33.63/5.35 | | | Case 2: % 33.63/5.35 | | | | % 33.63/5.35 | | | | (173) element(all_70_1, all_86_0) % 33.63/5.35 | | | | (174) ~ element(all_70_3, all_86_0) | element(all_70_0, all_86_0) % 33.63/5.35 | | | | % 33.63/5.35 | | | | BETA: splitting (174) gives: % 33.63/5.35 | | | | % 33.63/5.35 | | | | Case 1: % 33.63/5.35 | | | | | % 33.63/5.35 | | | | | (175) ~ element(all_70_3, all_86_0) % 33.63/5.35 | | | | | % 33.63/5.35 | | | | | REDUCE: (126), (132), (175) imply: % 33.63/5.35 | | | | | (176) ~ element(all_70_5, all_70_4) % 33.63/5.35 | | | | | % 33.63/5.35 | | | | | PRED_UNIFY: (158), (176) imply: % 33.63/5.35 | | | | | (177) $false % 33.63/5.35 | | | | | % 33.63/5.35 | | | | | CLOSE: (177) is inconsistent. % 33.63/5.35 | | | | | % 33.63/5.35 | | | | Case 2: % 33.63/5.35 | | | | | % 33.63/5.35 | | | | | (178) element(all_70_3, all_86_0) % 33.63/5.35 | | | | | (179) element(all_70_0, all_86_0) % 33.63/5.35 | | | | | % 33.63/5.35 | | | | | REDUCE: (126), (179) imply: % 33.63/5.35 | | | | | (180) element(all_70_0, all_70_4) % 33.63/5.35 | | | | | % 33.63/5.35 | | | | | BETA: splitting (72) gives: % 33.63/5.35 | | | | | % 33.63/5.35 | | | | | Case 1: % 33.63/5.35 | | | | | | % 33.63/5.35 | | | | | | (181) ~ element(all_70_2, all_90_1) % 33.63/5.35 | | | | | | % 33.63/5.35 | | | | | | REDUCE: (122), (181) imply: % 33.63/5.35 | | | | | | (182) ~ element(all_70_2, all_70_4) % 33.63/5.35 | | | | | | % 33.63/5.35 | | | | | | PRED_UNIFY: (20), (182) imply: % 33.63/5.35 | | | | | | (183) $false % 33.63/5.35 | | | | | | % 33.63/5.35 | | | | | | CLOSE: (183) is inconsistent. % 33.63/5.35 | | | | | | % 33.63/5.35 | | | | | Case 2: % 33.63/5.35 | | | | | | % 33.63/5.35 | | | | | | (184) element(all_70_2, all_90_1) % 33.63/5.35 | | | | | | (185) all_90_0 = all_70_1 | ~ element(all_70_3, all_90_1) % 33.63/5.35 | | | | | | % 33.63/5.35 | | | | | | BETA: splitting (185) gives: % 33.63/5.35 | | | | | | % 33.63/5.35 | | | | | | Case 1: % 33.63/5.35 | | | | | | | % 33.63/5.35 | | | | | | | (186) ~ element(all_70_3, all_90_1) % 33.63/5.35 | | | | | | | % 33.63/5.35 | | | | | | | REDUCE: (122), (132), (186) imply: % 33.63/5.35 | | | | | | | (187) ~ element(all_70_5, all_70_4) % 33.63/5.35 | | | | | | | % 33.63/5.35 | | | | | | | PRED_UNIFY: (158), (187) imply: % 33.63/5.35 | | | | | | | (188) $false % 33.63/5.35 | | | | | | | % 33.63/5.35 | | | | | | | CLOSE: (188) is inconsistent. % 33.63/5.35 | | | | | | | % 33.63/5.35 | | | | | | Case 2: % 33.63/5.35 | | | | | | | % 33.63/5.35 | | | | | | | (189) all_90_0 = all_70_1 % 33.63/5.35 | | | | | | | (190) element(all_70_3, all_90_1) % 33.63/5.35 | | | | | | | % 33.63/5.35 | | | | | | | REDUCE: (136), (189) imply: % 33.63/5.35 | | | | | | | (191) set_difference(all_70_5, all_70_2) = all_70_1 % 33.63/5.35 | | | | | | | % 33.63/5.35 | | | | | | | BETA: splitting (79) gives: % 33.63/5.35 | | | | | | | % 33.63/5.35 | | | | | | | Case 1: % 33.63/5.35 | | | | | | | | % 33.63/5.35 | | | | | | | | (192) ~ element(all_70_1, all_94_1) % 33.63/5.35 | | | | | | | | % 33.63/5.35 | | | | | | | | REDUCE: (101), (192) imply: % 33.63/5.35 | | | | | | | | (193) ~ element(all_70_1, all_70_4) % 33.63/5.35 | | | | | | | | % 33.63/5.35 | | | | | | | | PRED_UNIFY: (169), (193) imply: % 33.63/5.35 | | | | | | | | (194) $false % 33.63/5.35 | | | | | | | | % 33.63/5.35 | | | | | | | | CLOSE: (194) is inconsistent. % 33.63/5.35 | | | | | | | | % 33.63/5.35 | | | | | | | Case 2: % 33.63/5.35 | | | | | | | | % 33.63/5.35 | | | | | | | | (195) element(all_70_1, all_94_1) % 33.63/5.35 | | | | | | | | (196) all_94_0 = all_70_0 | ~ element(all_70_3, all_94_1) % 33.63/5.35 | | | | | | | | % 33.63/5.35 | | | | | | | | BETA: splitting (196) gives: % 33.63/5.35 | | | | | | | | % 33.63/5.35 | | | | | | | | Case 1: % 33.63/5.35 | | | | | | | | | % 33.63/5.35 | | | | | | | | | (197) ~ element(all_70_3, all_94_1) % 33.63/5.35 | | | | | | | | | % 33.63/5.35 | | | | | | | | | REDUCE: (101), (132), (197) imply: % 33.63/5.35 | | | | | | | | | (198) ~ element(all_70_5, all_70_4) % 33.63/5.35 | | | | | | | | | % 33.63/5.35 | | | | | | | | | PRED_UNIFY: (158), (198) imply: % 33.63/5.35 | | | | | | | | | (199) $false % 33.63/5.35 | | | | | | | | | % 33.63/5.35 | | | | | | | | | CLOSE: (199) is inconsistent. % 33.63/5.35 | | | | | | | | | % 33.63/5.35 | | | | | | | | Case 2: % 33.63/5.35 | | | | | | | | | % 33.63/5.35 | | | | | | | | | (200) all_94_0 = all_70_0 % 33.63/5.35 | | | | | | | | | (201) element(all_70_3, all_94_1) % 33.63/5.35 | | | | | | | | | % 33.63/5.35 | | | | | | | | | REDUCE: (135), (200) imply: % 33.63/5.35 | | | | | | | | | (202) set_difference(all_70_5, all_70_1) = all_70_0 % 33.63/5.35 | | | | | | | | | % 33.63/5.35 | | | | | | | | | GROUND_INST: instantiating (10) with all_80_0, simplifying with % 33.63/5.35 | | | | | | | | | (53), (54) gives: % 33.63/5.35 | | | | | | | | | (203) all_80_0 = empty_set % 33.63/5.35 | | | | | | | | | % 33.63/5.35 | | | | | | | | | GROUND_INST: instantiating (rc1_subset_1) with all_78_0, % 33.63/5.35 | | | | | | | | | all_96_0, simplifying with (141), (144) gives: % 33.63/5.35 | | | | | | | | | (204) empty(all_78_0) | ? [v0: $i] : ($i(v0) & element(v0, % 33.63/5.35 | | | | | | | | | all_96_0) & ~ empty(v0)) % 33.63/5.35 | | | | | | | | | % 33.63/5.35 | | | | | | | | | GROUND_INST: instantiating (rc2_subset_1) with all_78_0, % 33.63/5.35 | | | | | | | | | all_96_0, simplifying with (141), (144) gives: % 33.63/5.36 | | | | | | | | | (205) ? [v0: $i] : ($i(v0) & empty(v0) & element(v0, % 33.63/5.36 | | | | | | | | | all_96_0)) % 33.63/5.36 | | | | | | | | | % 33.63/5.36 | | | | | | | | | GROUND_INST: instantiating (8) with all_61_0, all_78_0, % 33.63/5.36 | | | | | | | | | simplifying with (16), (17), (50) gives: % 33.63/5.36 | | | | | | | | | (206) ? [v0: $i] : ? [v1: $i] : (the_carrier(all_61_0) = % 33.63/5.36 | | | | | | | | | v0 & powerset(v0) = v1 & $i(v1) & $i(v0) & ! [v2: % 33.63/5.36 | | | | | | | | | $i] : ! [v3: $i] : (v3 = v2 | ~ % 33.63/5.36 | | | | | | | | | (subset_intersection2(v0, v2, all_78_0) = v3) | % 33.63/5.36 | | | | | | | | | ~ $i(v2) | ~ element(v2, v1))) % 33.63/5.36 | | | | | | | | | % 33.63/5.36 | | | | | | | | | GROUND_INST: instantiating (t48_xboole_1) with all_70_5, % 33.63/5.36 | | | | | | | | | all_70_2, all_70_1, all_70_0, simplifying with % 33.63/5.36 | | | | | | | | | (23), (24), (191), (202) gives: % 33.63/5.36 | | | | | | | | | (207) set_intersection2(all_70_5, all_70_2) = all_70_0 & % 33.63/5.36 | | | | | | | | | $i(all_70_0) % 33.63/5.36 | | | | | | | | | % 33.63/5.36 | | | | | | | | | ALPHA: (207) implies: % 33.63/5.36 | | | | | | | | | (208) set_intersection2(all_70_5, all_70_2) = all_70_0 % 33.63/5.36 | | | | | | | | | % 33.63/5.36 | | | | | | | | | DELTA: instantiating (205) with fresh symbol all_153_0 gives: % 33.63/5.36 | | | | | | | | | (209) $i(all_153_0) & empty(all_153_0) & element(all_153_0, % 33.63/5.36 | | | | | | | | | all_96_0) % 33.63/5.36 | | | | | | | | | % 33.63/5.36 | | | | | | | | | ALPHA: (209) implies: % 33.63/5.36 | | | | | | | | | (210) empty(all_153_0) % 33.63/5.36 | | | | | | | | | (211) $i(all_153_0) % 33.63/5.36 | | | | | | | | | % 33.63/5.36 | | | | | | | | | DELTA: instantiating (206) with fresh symbols all_155_0, % 33.63/5.36 | | | | | | | | | all_155_1 gives: % 33.63/5.36 | | | | | | | | | (212) the_carrier(all_61_0) = all_155_1 & % 33.63/5.36 | | | | | | | | | powerset(all_155_1) = all_155_0 & $i(all_155_0) & % 33.63/5.36 | | | | | | | | | $i(all_155_1) & ! [v0: $i] : ! [v1: $i] : (v1 = v0 % 33.63/5.36 | | | | | | | | | | ~ (subset_intersection2(all_155_1, v0, all_78_0) % 33.63/5.36 | | | | | | | | | = v1) | ~ $i(v0) | ~ element(v0, all_155_0)) % 33.63/5.36 | | | | | | | | | % 33.63/5.36 | | | | | | | | | ALPHA: (212) implies: % 33.63/5.36 | | | | | | | | | (213) $i(all_155_1) % 33.63/5.36 | | | | | | | | | (214) powerset(all_155_1) = all_155_0 % 33.63/5.36 | | | | | | | | | (215) the_carrier(all_61_0) = all_155_1 % 33.63/5.36 | | | | | | | | | % 33.63/5.36 | | | | | | | | | REDUCE: (52), (203) imply: % 33.63/5.36 | | | | | | | | | (216) element(empty_set, all_70_4) % 33.63/5.36 | | | | | | | | | % 33.63/5.36 | | | | | | | | | GROUND_INST: instantiating (12) with all_78_0, all_155_1, % 33.63/5.36 | | | | | | | | | all_61_0, simplifying with (49), (215) gives: % 33.63/5.36 | | | | | | | | | (217) all_155_1 = all_78_0 % 33.63/5.36 | | | | | | | | | % 33.63/5.36 | | | | | | | | | REDUCE: (214), (217) imply: % 33.63/5.36 | | | | | | | | | (218) powerset(all_78_0) = all_155_0 % 33.63/5.36 | | | | | | | | | % 33.63/5.36 | | | | | | | | | GROUND_INST: instantiating (11) with all_96_0, all_155_0, % 33.63/5.36 | | | | | | | | | all_78_0, simplifying with (141), (218) gives: % 33.63/5.36 | | | | | | | | | (219) all_155_0 = all_96_0 % 33.63/5.36 | | | | | | | | | % 33.63/5.36 | | | | | | | | | GROUND_INST: instantiating (10) with all_153_0, simplifying % 33.63/5.36 | | | | | | | | | with (210), (211) gives: % 33.63/5.36 | | | | | | | | | (220) all_153_0 = empty_set % 33.63/5.36 | | | | | | | | | % 33.63/5.36 | | | | | | | | | GROUND_INST: instantiating (commutativity_k3_xboole_0) with % 33.63/5.36 | | | | | | | | | all_70_5, all_70_2, all_70_0, simplifying with % 33.63/5.36 | | | | | | | | | (23), (24), (208) gives: % 33.63/5.36 | | | | | | | | | (221) set_intersection2(all_70_2, all_70_5) = all_70_0 & % 33.63/5.36 | | | | | | | | | $i(all_70_0) % 33.63/5.36 | | | | | | | | | % 33.63/5.36 | | | | | | | | | ALPHA: (221) implies: % 33.63/5.36 | | | | | | | | | (222) $i(all_70_0) % 33.63/5.36 | | | | | | | | | (223) set_intersection2(all_70_2, all_70_5) = all_70_0 % 33.63/5.36 | | | | | | | | | % 33.63/5.36 | | | | | | | | | REDUCE: (211), (220) imply: % 33.63/5.36 | | | | | | | | | (224) $i(empty_set) % 33.63/5.36 | | | | | | | | | % 33.63/5.36 | | | | | | | | | BETA: splitting (37) gives: % 33.63/5.36 | | | | | | | | | % 33.63/5.36 | | | | | | | | | Case 1: % 33.63/5.36 | | | | | | | | | | % 33.63/5.36 | | | | | | | | | | (225) empty(all_70_5) % 33.63/5.36 | | | | | | | | | | % 33.63/5.36 | | | | | | | | | | GROUND_INST: instantiating (10) with all_70_5, simplifying with % 33.63/5.36 | | | | | | | | | | (23), (225) gives: % 33.63/5.36 | | | | | | | | | | (226) all_70_5 = empty_set % 33.63/5.36 | | | | | | | | | | % 33.63/5.36 | | | | | | | | | | COMBINE_EQS: (133), (226) imply: % 33.63/5.36 | | | | | | | | | | (227) all_104_2 = empty_set % 33.63/5.36 | | | | | | | | | | % 33.63/5.36 | | | | | | | | | | COMBINE_EQS: (134), (226) imply: % 33.63/5.36 | | | | | | | | | | (228) all_104_0 = empty_set % 33.63/5.36 | | | | | | | | | | % 33.63/5.36 | | | | | | | | | | REDUCE: (202), (226) imply: % 33.63/5.36 | | | | | | | | | | (229) set_difference(empty_set, all_70_1) = all_70_0 % 33.63/5.36 | | | | | | | | | | % 33.63/5.36 | | | | | | | | | | REDUCE: (137), (226) imply: % 33.63/5.36 | | | | | | | | | | (230) cast_as_carrier_subset(all_70_6) = empty_set % 33.63/5.36 | | | | | | | | | | % 33.63/5.36 | | | | | | | | | | REDUCE: (27), (226) imply: % 33.63/5.36 | | | | | | | | | | (231) the_carrier(all_70_6) = empty_set % 33.63/5.36 | | | | | | | | | | % 33.63/5.36 | | | | | | | | | | REDUCE: (223), (226) imply: % 33.63/5.36 | | | | | | | | | | (232) set_intersection2(all_70_2, empty_set) = all_70_0 % 33.63/5.36 | | | | | | | | | | % 33.63/5.36 | | | | | | | | | | REDUCE: (26), (226) imply: % 33.63/5.36 | | | | | | | | | | (233) powerset(empty_set) = all_70_4 % 33.63/5.36 | | | | | | | | | | % 33.63/5.36 | | | | | | | | | | GROUND_INST: instantiating (8) with all_70_6, empty_set, % 33.63/5.36 | | | | | | | | | | simplifying with (21), (22), (230) gives: % 33.63/5.36 | | | | | | | | | | (234) ? [v0: $i] : ? [v1: $i] : (the_carrier(all_70_6) % 33.63/5.36 | | | | | | | | | | = v0 & powerset(v0) = v1 & $i(v1) & $i(v0) & ! % 33.63/5.36 | | | | | | | | | | [v2: $i] : ! [v3: $i] : (v3 = v2 | ~ % 33.63/5.36 | | | | | | | | | | (subset_intersection2(v0, v2, empty_set) = v3) % 33.63/5.36 | | | | | | | | | | | ~ $i(v2) | ~ element(v2, v1))) % 33.63/5.36 | | | | | | | | | | % 33.63/5.36 | | | | | | | | | | GROUND_INST: instantiating (9) with all_70_1, all_70_0, % 33.63/5.36 | | | | | | | | | | simplifying with (25), (229) gives: % 33.63/5.36 | | | | | | | | | | (235) all_70_0 = empty_set % 33.63/5.36 | | | | | | | | | | % 33.63/5.36 | | | | | | | | | | DELTA: instantiating (38) with fresh symbol all_237_0 gives: % 33.94/5.36 | | | | | | | | | | (236) $i(all_237_0) & empty(all_237_0) & % 33.94/5.36 | | | | | | | | | | element(all_237_0, all_70_4) % 33.94/5.36 | | | | | | | | | | % 33.94/5.36 | | | | | | | | | | ALPHA: (236) implies: % 33.94/5.36 | | | | | | | | | | (237) element(all_237_0, all_70_4) % 33.94/5.36 | | | | | | | | | | (238) empty(all_237_0) % 33.94/5.36 | | | | | | | | | | (239) $i(all_237_0) % 33.94/5.36 | | | | | | | | | | % 33.94/5.36 | | | | | | | | | | DELTA: instantiating (234) with fresh symbols all_239_0, % 33.94/5.36 | | | | | | | | | | all_239_1 gives: % 33.94/5.36 | | | | | | | | | | (240) the_carrier(all_70_6) = all_239_1 & % 33.94/5.36 | | | | | | | | | | powerset(all_239_1) = all_239_0 & $i(all_239_0) & % 33.94/5.36 | | | | | | | | | | $i(all_239_1) & ! [v0: $i] : ! [v1: $i] : (v1 = % 33.94/5.36 | | | | | | | | | | v0 | ~ (subset_intersection2(all_239_1, v0, % 33.94/5.36 | | | | | | | | | | empty_set) = v1) | ~ $i(v0) | ~ element(v0, % 33.94/5.36 | | | | | | | | | | all_239_0)) % 33.94/5.36 | | | | | | | | | | % 33.94/5.36 | | | | | | | | | | ALPHA: (240) implies: % 33.94/5.36 | | | | | | | | | | (241) powerset(all_239_1) = all_239_0 % 33.94/5.36 | | | | | | | | | | (242) the_carrier(all_70_6) = all_239_1 % 33.94/5.36 | | | | | | | | | | % 33.94/5.36 | | | | | | | | | | REDUCE: (19), (235) imply: % 33.94/5.36 | | | | | | | | | | (243) ~ (all_70_2 = empty_set) % 33.94/5.36 | | | | | | | | | | % 33.94/5.36 | | | | | | | | | | SIMP: (243) implies: % 33.94/5.36 | | | | | | | | | | (244) ~ (all_70_2 = empty_set) % 33.94/5.36 | | | | | | | | | | % 33.94/5.36 | | | | | | | | | | REDUCE: (232), (235) imply: % 33.94/5.36 | | | | | | | | | | (245) set_intersection2(all_70_2, empty_set) = empty_set % 33.94/5.36 | | | | | | | | | | % 33.94/5.36 | | | | | | | | | | GROUND_INST: instantiating (12) with empty_set, all_239_1, % 33.94/5.36 | | | | | | | | | | all_70_6, simplifying with (231), (242) gives: % 33.94/5.36 | | | | | | | | | | (246) all_239_1 = empty_set % 33.94/5.36 | | | | | | | | | | % 33.94/5.36 | | | | | | | | | | REDUCE: (241), (246) imply: % 33.94/5.36 | | | | | | | | | | (247) powerset(empty_set) = all_239_0 % 33.94/5.36 | | | | | | | | | | % 33.94/5.36 | | | | | | | | | | GROUND_INST: instantiating (11) with all_70_4, all_239_0, % 33.94/5.36 | | | | | | | | | | empty_set, simplifying with (233), (247) gives: % 33.94/5.36 | | | | | | | | | | (248) all_239_0 = all_70_4 % 33.94/5.36 | | | | | | | | | | % 33.94/5.36 | | | | | | | | | | GROUND_INST: instantiating (10) with all_237_0, simplifying % 33.94/5.36 | | | | | | | | | | with (238), (239) gives: % 33.94/5.36 | | | | | | | | | | (249) all_237_0 = empty_set % 33.94/5.36 | | | | | | | | | | % 33.94/5.36 | | | | | | | | | | BETA: splitting (204) gives: % 33.94/5.36 | | | | | | | | | | % 33.94/5.36 | | | | | | | | | | Case 1: % 33.94/5.36 | | | | | | | | | | | % 33.94/5.36 | | | | | | | | | | | (250) empty(all_78_0) % 33.94/5.36 | | | | | | | | | | | % 33.94/5.36 | | | | | | | | | | | GROUND_INST: instantiating (10) with all_78_0, simplifying with % 33.94/5.36 | | | | | | | | | | | (144), (250) gives: % 33.94/5.36 | | | | | | | | | | | (251) all_78_0 = empty_set % 33.94/5.36 | | | | | | | | | | | % 33.94/5.36 | | | | | | | | | | | COMBINE_EQS: (104), (251) imply: % 33.94/5.36 | | | | | | | | | | | (252) all_101_2 = empty_set % 33.94/5.36 | | | | | | | | | | | % 33.94/5.36 | | | | | | | | | | | COMBINE_EQS: (112), (251) imply: % 33.94/5.36 | | | | | | | | | | | (253) all_101_0 = empty_set % 33.94/5.36 | | | | | | | | | | | % 33.94/5.36 | | | | | | | | | | | REDUCE: (141), (251) imply: % 33.94/5.36 | | | | | | | | | | | (254) powerset(empty_set) = all_96_0 % 33.94/5.36 | | | | | | | | | | | % 33.94/5.36 | | | | | | | | | | | REDUCE: (145), (251) imply: % 33.94/5.36 | | | | | | | | | | | (255) element(empty_set, all_96_0) % 33.94/5.36 | | | | | | | | | | | % 33.94/5.36 | | | | | | | | | | | GROUND_INST: instantiating (11) with all_70_4, all_96_0, % 33.94/5.36 | | | | | | | | | | | empty_set, simplifying with (233), (254) gives: % 33.94/5.36 | | | | | | | | | | | (256) all_96_0 = all_70_4 % 33.94/5.36 | | | | | | | | | | | % 33.94/5.36 | | | | | | | | | | | COMBINE_EQS: (151), (256) imply: % 33.94/5.37 | | | | | | | | | | | (257) all_101_1 = all_70_4 % 33.94/5.37 | | | | | | | | | | | % 33.94/5.37 | | | | | | | | | | | GROUND_INST: instantiating (93) with all_70_2, simplifying with % 33.94/5.37 | | | | | | | | | | | (24) gives: % 33.94/5.37 | | | | | | | | | | | (258) ~ element(all_70_2, all_101_1) | % 33.94/5.37 | | | | | | | | | | | subset_intersection2(all_101_2, all_70_2, % 33.94/5.37 | | | | | | | | | | | all_101_0) = all_70_2 % 33.94/5.37 | | | | | | | | | | | % 33.94/5.37 | | | | | | | | | | | BETA: splitting (258) gives: % 33.94/5.37 | | | | | | | | | | | % 33.94/5.37 | | | | | | | | | | | Case 1: % 33.94/5.37 | | | | | | | | | | | | % 33.94/5.37 | | | | | | | | | | | | (259) ~ element(all_70_2, all_101_1) % 33.94/5.37 | | | | | | | | | | | | % 33.94/5.37 | | | | | | | | | | | | REDUCE: (257), (259) imply: % 33.94/5.37 | | | | | | | | | | | | (260) ~ element(all_70_2, all_70_4) % 33.94/5.37 | | | | | | | | | | | | % 33.94/5.37 | | | | | | | | | | | | PRED_UNIFY: (20), (260) imply: % 33.94/5.37 | | | | | | | | | | | | (261) $false % 33.94/5.37 | | | | | | | | | | | | % 33.94/5.37 | | | | | | | | | | | | CLOSE: (261) is inconsistent. % 33.94/5.37 | | | | | | | | | | | | % 33.94/5.37 | | | | | | | | | | | Case 2: % 33.94/5.37 | | | | | | | | | | | | % 33.94/5.37 | | | | | | | | | | | | (262) element(all_70_2, all_101_1) % 33.94/5.37 | | | | | | | | | | | | (263) subset_intersection2(all_101_2, all_70_2, % 33.94/5.37 | | | | | | | | | | | | all_101_0) = all_70_2 % 33.94/5.37 | | | | | | | | | | | | % 33.94/5.37 | | | | | | | | | | | | REDUCE: (252), (253), (263) imply: % 33.94/5.37 | | | | | | | | | | | | (264) subset_intersection2(empty_set, all_70_2, % 33.94/5.37 | | | | | | | | | | | | empty_set) = all_70_2 % 33.94/5.37 | | | | | | | | | | | | % 33.94/5.37 | | | | | | | | | | | | GROUND_INST: instantiating (commutativity_k5_subset_1) with % 33.94/5.37 | | | | | | | | | | | | empty_set, all_70_2, empty_set, all_70_2, % 33.94/5.37 | | | | | | | | | | | | simplifying with (24), (224), (264) gives: % 33.94/5.37 | | | | | | | | | | | | (265) ? [v0: $i] : ? [v1: $i] : % 33.94/5.37 | | | | | | | | | | | | (subset_intersection2(empty_set, empty_set, % 33.94/5.37 | | | | | | | | | | | | all_70_2) = v1 & powerset(empty_set) = v0 & % 33.94/5.37 | | | | | | | | | | | | $i(v1) & $i(v0) & (v1 = all_70_2 | ~ % 33.94/5.37 | | | | | | | | | | | | element(all_70_2, v0) | ~ element(empty_set, % 33.94/5.37 | | | | | | | | | | | | v0))) % 33.94/5.37 | | | | | | | | | | | | % 33.94/5.37 | | | | | | | | | | | | GROUND_INST: instantiating (5) with empty_set, all_70_2, % 33.94/5.37 | | | | | | | | | | | | empty_set, all_70_2, simplifying with (24), (224), % 33.94/5.37 | | | | | | | | | | | | (264) gives: % 33.94/5.37 | | | | | | | | | | | | (266) ? [v0: $i] : ? [v1: $i] : % 33.94/5.37 | | | | | | | | | | | | (set_intersection2(all_70_2, empty_set) = v1 & % 33.94/5.37 | | | | | | | | | | | | powerset(empty_set) = v0 & $i(v1) & $i(v0) & (v1 % 33.94/5.37 | | | | | | | | | | | | = all_70_2 | ~ element(all_70_2, v0) | ~ % 33.94/5.37 | | | | | | | | | | | | element(empty_set, v0))) % 33.94/5.37 | | | | | | | | | | | | % 33.94/5.37 | | | | | | | | | | | | DELTA: instantiating (266) with fresh symbols all_420_0, % 33.94/5.37 | | | | | | | | | | | | all_420_1 gives: % 33.94/5.37 | | | | | | | | | | | | (267) set_intersection2(all_70_2, empty_set) = all_420_0 % 33.94/5.37 | | | | | | | | | | | | & powerset(empty_set) = all_420_1 & $i(all_420_0) % 33.94/5.37 | | | | | | | | | | | | & $i(all_420_1) & (all_420_0 = all_70_2 | ~ % 33.94/5.37 | | | | | | | | | | | | element(all_70_2, all_420_1) | ~ % 33.94/5.37 | | | | | | | | | | | | element(empty_set, all_420_1)) % 33.94/5.37 | | | | | | | | | | | | % 33.94/5.37 | | | | | | | | | | | | ALPHA: (267) implies: % 33.94/5.37 | | | | | | | | | | | | (268) powerset(empty_set) = all_420_1 % 33.94/5.37 | | | | | | | | | | | | (269) set_intersection2(all_70_2, empty_set) = all_420_0 % 33.94/5.37 | | | | | | | | | | | | (270) all_420_0 = all_70_2 | ~ element(all_70_2, % 33.94/5.37 | | | | | | | | | | | | all_420_1) | ~ element(empty_set, all_420_1) % 33.94/5.37 | | | | | | | | | | | | % 33.94/5.37 | | | | | | | | | | | | DELTA: instantiating (265) with fresh symbols all_422_0, % 33.94/5.37 | | | | | | | | | | | | all_422_1 gives: % 33.94/5.37 | | | | | | | | | | | | (271) subset_intersection2(empty_set, empty_set, % 33.94/5.37 | | | | | | | | | | | | all_70_2) = all_422_0 & powerset(empty_set) = % 33.94/5.37 | | | | | | | | | | | | all_422_1 & $i(all_422_0) & $i(all_422_1) & % 33.94/5.37 | | | | | | | | | | | | (all_422_0 = all_70_2 | ~ element(all_70_2, % 33.94/5.37 | | | | | | | | | | | | all_422_1) | ~ element(empty_set, all_422_1)) % 33.94/5.37 | | | | | | | | | | | | % 33.94/5.37 | | | | | | | | | | | | ALPHA: (271) implies: % 33.94/5.37 | | | | | | | | | | | | (272) powerset(empty_set) = all_422_1 % 33.94/5.37 | | | | | | | | | | | | % 33.94/5.37 | | | | | | | | | | | | GROUND_INST: instantiating (11) with all_70_4, all_422_1, % 33.94/5.37 | | | | | | | | | | | | empty_set, simplifying with (233), (272) gives: % 33.94/5.37 | | | | | | | | | | | | (273) all_422_1 = all_70_4 % 33.94/5.37 | | | | | | | | | | | | % 33.94/5.37 | | | | | | | | | | | | GROUND_INST: instantiating (11) with all_420_1, all_422_1, % 33.94/5.37 | | | | | | | | | | | | empty_set, simplifying with (268), (272) gives: % 33.94/5.37 | | | | | | | | | | | | (274) all_422_1 = all_420_1 % 33.94/5.37 | | | | | | | | | | | | % 33.94/5.37 | | | | | | | | | | | | GROUND_INST: instantiating (14) with empty_set, all_420_0, % 33.94/5.37 | | | | | | | | | | | | empty_set, all_70_2, simplifying with (245), (269) % 33.94/5.37 | | | | | | | | | | | | gives: % 33.94/5.37 | | | | | | | | | | | | (275) all_420_0 = empty_set % 33.94/5.37 | | | | | | | | | | | | % 33.94/5.37 | | | | | | | | | | | | COMBINE_EQS: (273), (274) imply: % 33.94/5.37 | | | | | | | | | | | | (276) all_420_1 = all_70_4 % 33.94/5.37 | | | | | | | | | | | | % 33.94/5.37 | | | | | | | | | | | | BETA: splitting (270) gives: % 33.94/5.37 | | | | | | | | | | | | % 33.94/5.37 | | | | | | | | | | | | Case 1: % 33.94/5.37 | | | | | | | | | | | | | % 33.94/5.37 | | | | | | | | | | | | | (277) ~ element(empty_set, all_420_1) % 33.94/5.37 | | | | | | | | | | | | | % 33.94/5.37 | | | | | | | | | | | | | REDUCE: (276), (277) imply: % 33.94/5.37 | | | | | | | | | | | | | (278) ~ element(empty_set, all_70_4) % 33.94/5.37 | | | | | | | | | | | | | % 33.94/5.37 | | | | | | | | | | | | | PRED_UNIFY: (216), (278) imply: % 33.94/5.37 | | | | | | | | | | | | | (279) $false % 33.94/5.37 | | | | | | | | | | | | | % 33.94/5.37 | | | | | | | | | | | | | CLOSE: (279) is inconsistent. % 33.94/5.37 | | | | | | | | | | | | | % 33.94/5.37 | | | | | | | | | | | | Case 2: % 33.94/5.37 | | | | | | | | | | | | | % 33.94/5.37 | | | | | | | | | | | | | (280) all_420_0 = all_70_2 | ~ element(all_70_2, % 33.94/5.37 | | | | | | | | | | | | | all_420_1) % 33.94/5.37 | | | | | | | | | | | | | % 33.94/5.37 | | | | | | | | | | | | | BETA: splitting (280) gives: % 33.94/5.37 | | | | | | | | | | | | | % 33.94/5.37 | | | | | | | | | | | | | Case 1: % 33.94/5.37 | | | | | | | | | | | | | | % 33.94/5.37 | | | | | | | | | | | | | | (281) ~ element(all_70_2, all_420_1) % 33.94/5.37 | | | | | | | | | | | | | | % 33.94/5.37 | | | | | | | | | | | | | | REDUCE: (276), (281) imply: % 33.94/5.37 | | | | | | | | | | | | | | (282) ~ element(all_70_2, all_70_4) % 33.94/5.37 | | | | | | | | | | | | | | % 33.94/5.37 | | | | | | | | | | | | | | PRED_UNIFY: (20), (282) imply: % 33.94/5.37 | | | | | | | | | | | | | | (283) $false % 33.94/5.37 | | | | | | | | | | | | | | % 33.94/5.37 | | | | | | | | | | | | | | CLOSE: (283) is inconsistent. % 33.94/5.37 | | | | | | | | | | | | | | % 33.94/5.37 | | | | | | | | | | | | | Case 2: % 33.94/5.37 | | | | | | | | | | | | | | % 33.94/5.37 | | | | | | | | | | | | | | (284) all_420_0 = all_70_2 % 33.94/5.37 | | | | | | | | | | | | | | % 33.94/5.37 | | | | | | | | | | | | | | COMBINE_EQS: (275), (284) imply: % 33.94/5.37 | | | | | | | | | | | | | | (285) all_70_2 = empty_set % 33.94/5.37 | | | | | | | | | | | | | | % 33.94/5.37 | | | | | | | | | | | | | | SIMP: (285) implies: % 33.94/5.37 | | | | | | | | | | | | | | (286) all_70_2 = empty_set % 33.94/5.37 | | | | | | | | | | | | | | % 33.94/5.37 | | | | | | | | | | | | | | REDUCE: (244), (286) imply: % 33.94/5.37 | | | | | | | | | | | | | | (287) $false % 33.94/5.37 | | | | | | | | | | | | | | % 33.94/5.37 | | | | | | | | | | | | | | CLOSE: (287) is inconsistent. % 33.94/5.37 | | | | | | | | | | | | | | % 33.94/5.37 | | | | | | | | | | | | | End of split % 33.94/5.37 | | | | | | | | | | | | | % 33.94/5.37 | | | | | | | | | | | | End of split % 33.94/5.37 | | | | | | | | | | | | % 33.94/5.37 | | | | | | | | | | | End of split % 33.94/5.37 | | | | | | | | | | | % 33.94/5.37 | | | | | | | | | | Case 2: % 33.94/5.37 | | | | | | | | | | | % 33.94/5.37 | | | | | | | | | | | (288) ? [v0: $i] : ($i(v0) & element(v0, all_96_0) & ~ % 33.94/5.37 | | | | | | | | | | | empty(v0)) % 33.94/5.37 | | | | | | | | | | | % 33.94/5.37 | | | | | | | | | | | DELTA: instantiating (288) with fresh symbol all_262_0 % 33.94/5.37 | | | | | | | | | | | gives: % 33.94/5.37 | | | | | | | | | | | (289) $i(all_262_0) & element(all_262_0, all_96_0) & ~ % 33.94/5.37 | | | | | | | | | | | empty(all_262_0) % 33.94/5.37 | | | | | | | | | | | % 33.94/5.37 | | | | | | | | | | | ALPHA: (289) implies: % 33.94/5.37 | | | | | | | | | | | (290) element(all_262_0, all_96_0) % 33.94/5.37 | | | | | | | | | | | (291) $i(all_262_0) % 33.94/5.37 | | | | | | | | | | | % 33.94/5.37 | | | | | | | | | | | GROUND_INST: instantiating (98) with all_70_2, simplifying with % 33.94/5.37 | | | | | | | | | | | (24) gives: % 33.94/5.37 | | | | | | | | | | | (292) ~ element(all_70_2, all_104_1) | % 33.94/5.37 | | | | | | | | | | | subset_intersection2(all_104_2, all_70_2, % 33.94/5.37 | | | | | | | | | | | all_104_0) = all_70_2 % 33.94/5.37 | | | | | | | | | | | % 33.94/5.37 | | | | | | | | | | | GROUND_INST: instantiating (93) with all_262_0, simplifying % 33.94/5.37 | | | | | | | | | | | with (291) gives: % 33.94/5.37 | | | | | | | | | | | (293) ~ element(all_262_0, all_101_1) | % 33.94/5.37 | | | | | | | | | | | subset_intersection2(all_101_2, all_262_0, % 33.94/5.37 | | | | | | | | | | | all_101_0) = all_262_0 % 33.94/5.37 | | | | | | | | | | | % 33.94/5.37 | | | | | | | | | | | BETA: splitting (292) gives: % 33.94/5.37 | | | | | | | | | | | % 33.94/5.37 | | | | | | | | | | | Case 1: % 33.94/5.37 | | | | | | | | | | | | % 33.94/5.37 | | | | | | | | | | | | (294) ~ element(all_70_2, all_104_1) % 33.94/5.37 | | | | | | | | | | | | % 33.94/5.37 | | | | | | | | | | | | REDUCE: (157), (294) imply: % 33.94/5.37 | | | | | | | | | | | | (295) ~ element(all_70_2, all_70_4) % 33.94/5.37 | | | | | | | | | | | | % 33.94/5.37 | | | | | | | | | | | | PRED_UNIFY: (20), (295) imply: % 33.94/5.37 | | | | | | | | | | | | (296) $false % 33.94/5.37 | | | | | | | | | | | | % 33.94/5.37 | | | | | | | | | | | | CLOSE: (296) is inconsistent. % 33.94/5.37 | | | | | | | | | | | | % 33.94/5.37 | | | | | | | | | | | Case 2: % 33.94/5.37 | | | | | | | | | | | | % 33.94/5.37 | | | | | | | | | | | | (297) element(all_70_2, all_104_1) % 33.94/5.37 | | | | | | | | | | | | (298) subset_intersection2(all_104_2, all_70_2, % 33.94/5.37 | | | | | | | | | | | | all_104_0) = all_70_2 % 33.94/5.37 | | | | | | | | | | | | % 33.94/5.37 | | | | | | | | | | | | REDUCE: (227), (228), (298) imply: % 33.94/5.37 | | | | | | | | | | | | (299) subset_intersection2(empty_set, all_70_2, % 33.94/5.37 | | | | | | | | | | | | empty_set) = all_70_2 % 33.94/5.37 | | | | | | | | | | | | % 33.94/5.37 | | | | | | | | | | | | BETA: splitting (293) gives: % 33.94/5.37 | | | | | | | | | | | | % 33.94/5.37 | | | | | | | | | | | | Case 1: % 33.94/5.37 | | | | | | | | | | | | | % 33.94/5.37 | | | | | | | | | | | | | (300) ~ element(all_262_0, all_101_1) % 33.94/5.37 | | | | | | | | | | | | | % 33.94/5.37 | | | | | | | | | | | | | REDUCE: (151), (300) imply: % 33.94/5.37 | | | | | | | | | | | | | (301) ~ element(all_262_0, all_96_0) % 33.94/5.37 | | | | | | | | | | | | | % 33.94/5.37 | | | | | | | | | | | | | PRED_UNIFY: (290), (301) imply: % 33.94/5.37 | | | | | | | | | | | | | (302) $false % 33.94/5.37 | | | | | | | | | | | | | % 33.94/5.37 | | | | | | | | | | | | | CLOSE: (302) is inconsistent. % 33.94/5.37 | | | | | | | | | | | | | % 33.94/5.37 | | | | | | | | | | | | Case 2: % 33.94/5.37 | | | | | | | | | | | | | % 33.94/5.37 | | | | | | | | | | | | | % 33.94/5.37 | | | | | | | | | | | | | GROUND_INST: instantiating (commutativity_k5_subset_1) with % 33.94/5.37 | | | | | | | | | | | | | empty_set, all_70_2, empty_set, all_70_2, % 33.94/5.37 | | | | | | | | | | | | | simplifying with (24), (224), (299) gives: % 33.94/5.37 | | | | | | | | | | | | | (303) ? [v0: $i] : ? [v1: $i] : % 33.94/5.37 | | | | | | | | | | | | | (subset_intersection2(empty_set, empty_set, % 33.94/5.37 | | | | | | | | | | | | | all_70_2) = v1 & powerset(empty_set) = v0 & % 33.94/5.37 | | | | | | | | | | | | | $i(v1) & $i(v0) & (v1 = all_70_2 | ~ % 33.94/5.37 | | | | | | | | | | | | | element(all_70_2, v0) | ~ element(empty_set, % 33.94/5.37 | | | | | | | | | | | | | v0))) % 33.94/5.37 | | | | | | | | | | | | | % 33.94/5.37 | | | | | | | | | | | | | GROUND_INST: instantiating (5) with empty_set, all_70_2, % 33.94/5.37 | | | | | | | | | | | | | empty_set, all_70_2, simplifying with (24), (224), % 33.94/5.37 | | | | | | | | | | | | | (299) gives: % 33.94/5.37 | | | | | | | | | | | | | (304) ? [v0: $i] : ? [v1: $i] : % 33.94/5.37 | | | | | | | | | | | | | (set_intersection2(all_70_2, empty_set) = v1 & % 33.94/5.37 | | | | | | | | | | | | | powerset(empty_set) = v0 & $i(v1) & $i(v0) & (v1 % 33.94/5.37 | | | | | | | | | | | | | = all_70_2 | ~ element(all_70_2, v0) | ~ % 33.94/5.37 | | | | | | | | | | | | | element(empty_set, v0))) % 33.94/5.37 | | | | | | | | | | | | | % 33.94/5.37 | | | | | | | | | | | | | DELTA: instantiating (304) with fresh symbols all_359_0, % 33.94/5.37 | | | | | | | | | | | | | all_359_1 gives: % 33.94/5.37 | | | | | | | | | | | | | (305) set_intersection2(all_70_2, empty_set) = all_359_0 % 33.94/5.37 | | | | | | | | | | | | | & powerset(empty_set) = all_359_1 & $i(all_359_0) % 33.94/5.37 | | | | | | | | | | | | | & $i(all_359_1) & (all_359_0 = all_70_2 | ~ % 33.94/5.37 | | | | | | | | | | | | | element(all_70_2, all_359_1) | ~ % 33.94/5.37 | | | | | | | | | | | | | element(empty_set, all_359_1)) % 33.94/5.37 | | | | | | | | | | | | | % 33.94/5.37 | | | | | | | | | | | | | ALPHA: (305) implies: % 33.94/5.38 | | | | | | | | | | | | | (306) powerset(empty_set) = all_359_1 % 33.94/5.38 | | | | | | | | | | | | | (307) set_intersection2(all_70_2, empty_set) = all_359_0 % 33.94/5.38 | | | | | | | | | | | | | (308) all_359_0 = all_70_2 | ~ element(all_70_2, % 33.94/5.38 | | | | | | | | | | | | | all_359_1) | ~ element(empty_set, all_359_1) % 33.94/5.38 | | | | | | | | | | | | | % 33.94/5.38 | | | | | | | | | | | | | DELTA: instantiating (303) with fresh symbols all_361_0, % 33.94/5.38 | | | | | | | | | | | | | all_361_1 gives: % 33.94/5.38 | | | | | | | | | | | | | (309) subset_intersection2(empty_set, empty_set, % 33.94/5.38 | | | | | | | | | | | | | all_70_2) = all_361_0 & powerset(empty_set) = % 33.94/5.38 | | | | | | | | | | | | | all_361_1 & $i(all_361_0) & $i(all_361_1) & % 33.94/5.38 | | | | | | | | | | | | | (all_361_0 = all_70_2 | ~ element(all_70_2, % 33.94/5.38 | | | | | | | | | | | | | all_361_1) | ~ element(empty_set, all_361_1)) % 33.94/5.38 | | | | | | | | | | | | | % 33.94/5.38 | | | | | | | | | | | | | ALPHA: (309) implies: % 33.94/5.38 | | | | | | | | | | | | | (310) powerset(empty_set) = all_361_1 % 33.94/5.38 | | | | | | | | | | | | | % 33.94/5.38 | | | | | | | | | | | | | GROUND_INST: instantiating (11) with all_70_4, all_361_1, % 33.94/5.38 | | | | | | | | | | | | | empty_set, simplifying with (233), (310) gives: % 33.94/5.38 | | | | | | | | | | | | | (311) all_361_1 = all_70_4 % 33.94/5.38 | | | | | | | | | | | | | % 33.94/5.38 | | | | | | | | | | | | | GROUND_INST: instantiating (11) with all_359_1, all_361_1, % 33.94/5.38 | | | | | | | | | | | | | empty_set, simplifying with (306), (310) gives: % 33.94/5.38 | | | | | | | | | | | | | (312) all_361_1 = all_359_1 % 33.94/5.38 | | | | | | | | | | | | | % 33.94/5.38 | | | | | | | | | | | | | GROUND_INST: instantiating (14) with empty_set, all_359_0, % 33.94/5.38 | | | | | | | | | | | | | empty_set, all_70_2, simplifying with (245), (307) % 33.94/5.38 | | | | | | | | | | | | | gives: % 33.94/5.38 | | | | | | | | | | | | | (313) all_359_0 = empty_set % 33.94/5.38 | | | | | | | | | | | | | % 33.94/5.38 | | | | | | | | | | | | | COMBINE_EQS: (311), (312) imply: % 33.94/5.38 | | | | | | | | | | | | | (314) all_359_1 = all_70_4 % 33.94/5.38 | | | | | | | | | | | | | % 33.94/5.38 | | | | | | | | | | | | | BETA: splitting (308) gives: % 33.94/5.38 | | | | | | | | | | | | | % 33.94/5.38 | | | | | | | | | | | | | Case 1: % 33.94/5.38 | | | | | | | | | | | | | | % 33.94/5.38 | | | | | | | | | | | | | | (315) ~ element(empty_set, all_359_1) % 33.94/5.38 | | | | | | | | | | | | | | % 33.94/5.38 | | | | | | | | | | | | | | REDUCE: (314), (315) imply: % 33.94/5.38 | | | | | | | | | | | | | | (316) ~ element(empty_set, all_70_4) % 33.94/5.38 | | | | | | | | | | | | | | % 33.94/5.38 | | | | | | | | | | | | | | PRED_UNIFY: (216), (316) imply: % 33.94/5.38 | | | | | | | | | | | | | | (317) $false % 33.94/5.38 | | | | | | | | | | | | | | % 33.94/5.38 | | | | | | | | | | | | | | CLOSE: (317) is inconsistent. % 33.94/5.38 | | | | | | | | | | | | | | % 33.94/5.38 | | | | | | | | | | | | | Case 2: % 33.94/5.38 | | | | | | | | | | | | | | % 33.94/5.38 | | | | | | | | | | | | | | (318) all_359_0 = all_70_2 | ~ element(all_70_2, % 33.94/5.38 | | | | | | | | | | | | | | all_359_1) % 33.94/5.38 | | | | | | | | | | | | | | % 33.94/5.38 | | | | | | | | | | | | | | BETA: splitting (318) gives: % 33.94/5.38 | | | | | | | | | | | | | | % 33.94/5.38 | | | | | | | | | | | | | | Case 1: % 33.94/5.38 | | | | | | | | | | | | | | | % 33.94/5.38 | | | | | | | | | | | | | | | (319) ~ element(all_70_2, all_359_1) % 33.94/5.38 | | | | | | | | | | | | | | | % 33.94/5.38 | | | | | | | | | | | | | | | REDUCE: (314), (319) imply: % 33.94/5.38 | | | | | | | | | | | | | | | (320) ~ element(all_70_2, all_70_4) % 33.94/5.38 | | | | | | | | | | | | | | | % 33.94/5.38 | | | | | | | | | | | | | | | PRED_UNIFY: (20), (320) imply: % 33.94/5.38 | | | | | | | | | | | | | | | (321) $false % 33.94/5.38 | | | | | | | | | | | | | | | % 33.94/5.38 | | | | | | | | | | | | | | | CLOSE: (321) is inconsistent. % 33.94/5.38 | | | | | | | | | | | | | | | % 33.94/5.38 | | | | | | | | | | | | | | Case 2: % 33.94/5.38 | | | | | | | | | | | | | | | % 33.94/5.38 | | | | | | | | | | | | | | | (322) all_359_0 = all_70_2 % 33.94/5.38 | | | | | | | | | | | | | | | % 33.94/5.38 | | | | | | | | | | | | | | | COMBINE_EQS: (313), (322) imply: % 33.94/5.38 | | | | | | | | | | | | | | | (323) all_70_2 = empty_set % 33.94/5.38 | | | | | | | | | | | | | | | % 33.94/5.38 | | | | | | | | | | | | | | | SIMP: (323) implies: % 33.94/5.38 | | | | | | | | | | | | | | | (324) all_70_2 = empty_set % 33.94/5.38 | | | | | | | | | | | | | | | % 33.94/5.38 | | | | | | | | | | | | | | | REDUCE: (244), (324) imply: % 33.94/5.38 | | | | | | | | | | | | | | | (325) $false % 33.94/5.38 | | | | | | | | | | | | | | | % 33.94/5.38 | | | | | | | | | | | | | | | CLOSE: (325) is inconsistent. % 33.94/5.38 | | | | | | | | | | | | | | | % 33.94/5.38 | | | | | | | | | | | | | | End of split % 33.94/5.38 | | | | | | | | | | | | | | % 33.94/5.38 | | | | | | | | | | | | | End of split % 33.94/5.38 | | | | | | | | | | | | | % 33.94/5.38 | | | | | | | | | | | | End of split % 33.94/5.38 | | | | | | | | | | | | % 33.94/5.38 | | | | | | | | | | | End of split % 33.94/5.38 | | | | | | | | | | | % 33.94/5.38 | | | | | | | | | | End of split % 33.94/5.38 | | | | | | | | | | % 33.94/5.38 | | | | | | | | | Case 2: % 33.94/5.38 | | | | | | | | | | % 33.94/5.38 | | | | | | | | | | (326) ? [v0: $i] : ($i(v0) & element(v0, all_70_4) & ~ % 33.94/5.38 | | | | | | | | | | empty(v0)) % 33.94/5.38 | | | | | | | | | | % 33.94/5.38 | | | | | | | | | | DELTA: instantiating (326) with fresh symbol all_203_0 % 33.94/5.38 | | | | | | | | | | gives: % 33.94/5.38 | | | | | | | | | | (327) $i(all_203_0) & element(all_203_0, all_70_4) & ~ % 33.94/5.38 | | | | | | | | | | empty(all_203_0) % 33.94/5.38 | | | | | | | | | | % 33.94/5.38 | | | | | | | | | | ALPHA: (327) implies: % 33.94/5.38 | | | | | | | | | | (328) element(all_203_0, all_70_4) % 33.94/5.38 | | | | | | | | | | (329) $i(all_203_0) % 33.94/5.38 | | | | | | | | | | % 33.94/5.38 | | | | | | | | | | GROUND_INST: instantiating (98) with empty_set, simplifying % 33.94/5.38 | | | | | | | | | | with (224) gives: % 33.94/5.38 | | | | | | | | | | (330) ~ element(empty_set, all_104_1) | % 33.94/5.38 | | | | | | | | | | subset_intersection2(all_104_2, empty_set, % 33.94/5.38 | | | | | | | | | | all_104_0) = empty_set % 33.94/5.38 | | | | | | | | | | % 33.94/5.38 | | | | | | | | | | GROUND_INST: instantiating (98) with all_70_5, simplifying with % 33.94/5.38 | | | | | | | | | | (23) gives: % 33.94/5.38 | | | | | | | | | | (331) ~ element(all_70_5, all_104_1) | % 33.94/5.38 | | | | | | | | | | subset_intersection2(all_104_2, all_70_5, % 33.94/5.38 | | | | | | | | | | all_104_0) = all_70_5 % 33.94/5.38 | | | | | | | | | | % 33.94/5.38 | | | | | | | | | | GROUND_INST: instantiating (98) with all_70_2, simplifying with % 33.94/5.38 | | | | | | | | | | (24) gives: % 33.94/5.38 | | | | | | | | | | (332) ~ element(all_70_2, all_104_1) | % 33.94/5.38 | | | | | | | | | | subset_intersection2(all_104_2, all_70_2, % 33.94/5.38 | | | | | | | | | | all_104_0) = all_70_2 % 33.94/5.38 | | | | | | | | | | % 33.94/5.38 | | | | | | | | | | GROUND_INST: instantiating (98) with all_70_1, simplifying with % 33.94/5.38 | | | | | | | | | | (25) gives: % 33.94/5.38 | | | | | | | | | | (333) ~ element(all_70_1, all_104_1) | % 33.94/5.38 | | | | | | | | | | subset_intersection2(all_104_2, all_70_1, % 33.94/5.38 | | | | | | | | | | all_104_0) = all_70_1 % 33.94/5.38 | | | | | | | | | | % 33.94/5.38 | | | | | | | | | | GROUND_INST: instantiating (98) with all_70_0, simplifying with % 33.94/5.38 | | | | | | | | | | (222) gives: % 33.94/5.38 | | | | | | | | | | (334) ~ element(all_70_0, all_104_1) | % 33.94/5.38 | | | | | | | | | | subset_intersection2(all_104_2, all_70_0, % 33.94/5.38 | | | | | | | | | | all_104_0) = all_70_0 % 33.94/5.38 | | | | | | | | | | % 33.94/5.38 | | | | | | | | | | GROUND_INST: instantiating (98) with all_203_0, simplifying % 33.94/5.38 | | | | | | | | | | with (329) gives: % 33.94/5.38 | | | | | | | | | | (335) ~ element(all_203_0, all_104_1) | % 33.94/5.38 | | | | | | | | | | subset_intersection2(all_104_2, all_203_0, % 33.94/5.38 | | | | | | | | | | all_104_0) = all_203_0 % 33.94/5.38 | | | | | | | | | | % 33.94/5.38 | | | | | | | | | | BETA: splitting (335) gives: % 33.94/5.38 | | | | | | | | | | % 33.94/5.38 | | | | | | | | | | Case 1: % 33.94/5.38 | | | | | | | | | | | % 33.94/5.38 | | | | | | | | | | | (336) ~ element(all_203_0, all_104_1) % 33.94/5.38 | | | | | | | | | | | % 33.94/5.38 | | | | | | | | | | | REDUCE: (157), (336) imply: % 33.94/5.38 | | | | | | | | | | | (337) ~ element(all_203_0, all_70_4) % 33.94/5.38 | | | | | | | | | | | % 33.94/5.38 | | | | | | | | | | | PRED_UNIFY: (328), (337) imply: % 33.94/5.38 | | | | | | | | | | | (338) $false % 33.94/5.38 | | | | | | | | | | | % 33.94/5.38 | | | | | | | | | | | CLOSE: (338) is inconsistent. % 33.94/5.38 | | | | | | | | | | | % 33.94/5.38 | | | | | | | | | | Case 2: % 33.94/5.38 | | | | | | | | | | | % 33.94/5.38 | | | | | | | | | | | (339) subset_intersection2(all_104_2, all_203_0, % 33.94/5.38 | | | | | | | | | | | all_104_0) = all_203_0 % 33.94/5.38 | | | | | | | | | | | % 33.94/5.38 | | | | | | | | | | | REDUCE: (133), (134), (339) imply: % 33.94/5.38 | | | | | | | | | | | (340) subset_intersection2(all_70_5, all_203_0, % 33.94/5.38 | | | | | | | | | | | all_70_5) = all_203_0 % 33.94/5.38 | | | | | | | | | | | % 33.94/5.38 | | | | | | | | | | | BETA: splitting (334) gives: % 33.94/5.38 | | | | | | | | | | | % 33.94/5.38 | | | | | | | | | | | Case 1: % 33.94/5.38 | | | | | | | | | | | | % 33.94/5.38 | | | | | | | | | | | | (341) ~ element(all_70_0, all_104_1) % 33.94/5.38 | | | | | | | | | | | | % 33.94/5.38 | | | | | | | | | | | | REDUCE: (157), (341) imply: % 33.94/5.38 | | | | | | | | | | | | (342) ~ element(all_70_0, all_70_4) % 33.94/5.38 | | | | | | | | | | | | % 33.94/5.38 | | | | | | | | | | | | PRED_UNIFY: (180), (342) imply: % 33.94/5.38 | | | | | | | | | | | | (343) $false % 33.94/5.38 | | | | | | | | | | | | % 33.94/5.38 | | | | | | | | | | | | CLOSE: (343) is inconsistent. % 33.94/5.38 | | | | | | | | | | | | % 33.94/5.38 | | | | | | | | | | | Case 2: % 33.94/5.38 | | | | | | | | | | | | % 33.94/5.38 | | | | | | | | | | | | (344) subset_intersection2(all_104_2, all_70_0, % 33.94/5.38 | | | | | | | | | | | | all_104_0) = all_70_0 % 33.94/5.38 | | | | | | | | | | | | % 33.94/5.38 | | | | | | | | | | | | REDUCE: (133), (134), (344) imply: % 33.94/5.38 | | | | | | | | | | | | (345) subset_intersection2(all_70_5, all_70_0, all_70_5) % 33.94/5.38 | | | | | | | | | | | | = all_70_0 % 33.94/5.38 | | | | | | | | | | | | % 33.94/5.38 | | | | | | | | | | | | BETA: splitting (333) gives: % 33.94/5.38 | | | | | | | | | | | | % 33.94/5.38 | | | | | | | | | | | | Case 1: % 33.94/5.38 | | | | | | | | | | | | | % 33.94/5.38 | | | | | | | | | | | | | (346) ~ element(all_70_1, all_104_1) % 33.94/5.38 | | | | | | | | | | | | | % 33.94/5.38 | | | | | | | | | | | | | REDUCE: (157), (346) imply: % 33.94/5.38 | | | | | | | | | | | | | (347) ~ element(all_70_1, all_70_4) % 33.94/5.38 | | | | | | | | | | | | | % 33.94/5.38 | | | | | | | | | | | | | PRED_UNIFY: (169), (347) imply: % 33.94/5.38 | | | | | | | | | | | | | (348) $false % 33.94/5.38 | | | | | | | | | | | | | % 33.94/5.38 | | | | | | | | | | | | | CLOSE: (348) is inconsistent. % 33.94/5.38 | | | | | | | | | | | | | % 33.94/5.38 | | | | | | | | | | | | Case 2: % 33.94/5.38 | | | | | | | | | | | | | % 33.94/5.38 | | | | | | | | | | | | | (349) subset_intersection2(all_104_2, all_70_1, % 33.94/5.38 | | | | | | | | | | | | | all_104_0) = all_70_1 % 33.94/5.38 | | | | | | | | | | | | | % 33.94/5.38 | | | | | | | | | | | | | REDUCE: (133), (134), (349) imply: % 33.94/5.38 | | | | | | | | | | | | | (350) subset_intersection2(all_70_5, all_70_1, all_70_5) % 33.94/5.38 | | | | | | | | | | | | | = all_70_1 % 33.94/5.38 | | | | | | | | | | | | | % 33.94/5.38 | | | | | | | | | | | | | BETA: splitting (330) gives: % 33.94/5.38 | | | | | | | | | | | | | % 33.94/5.38 | | | | | | | | | | | | | Case 1: % 33.94/5.38 | | | | | | | | | | | | | | % 33.94/5.38 | | | | | | | | | | | | | | (351) ~ element(empty_set, all_104_1) % 33.94/5.38 | | | | | | | | | | | | | | % 33.94/5.38 | | | | | | | | | | | | | | REDUCE: (157), (351) imply: % 33.94/5.38 | | | | | | | | | | | | | | (352) ~ element(empty_set, all_70_4) % 33.94/5.38 | | | | | | | | | | | | | | % 33.94/5.38 | | | | | | | | | | | | | | PRED_UNIFY: (216), (352) imply: % 33.94/5.38 | | | | | | | | | | | | | | (353) $false % 33.94/5.38 | | | | | | | | | | | | | | % 33.94/5.38 | | | | | | | | | | | | | | CLOSE: (353) is inconsistent. % 33.94/5.38 | | | | | | | | | | | | | | % 33.94/5.38 | | | | | | | | | | | | | Case 2: % 33.94/5.38 | | | | | | | | | | | | | | % 33.94/5.38 | | | | | | | | | | | | | | (354) subset_intersection2(all_104_2, empty_set, % 33.94/5.38 | | | | | | | | | | | | | | all_104_0) = empty_set % 33.94/5.38 | | | | | | | | | | | | | | % 33.94/5.38 | | | | | | | | | | | | | | REDUCE: (133), (134), (354) imply: % 33.94/5.38 | | | | | | | | | | | | | | (355) subset_intersection2(all_70_5, empty_set, % 33.94/5.38 | | | | | | | | | | | | | | all_70_5) = empty_set % 33.94/5.38 | | | | | | | | | | | | | | % 33.94/5.38 | | | | | | | | | | | | | | BETA: splitting (332) gives: % 33.94/5.38 | | | | | | | | | | | | | | % 33.94/5.38 | | | | | | | | | | | | | | Case 1: % 33.94/5.38 | | | | | | | | | | | | | | | % 33.94/5.38 | | | | | | | | | | | | | | | (356) ~ element(all_70_2, all_104_1) % 33.94/5.38 | | | | | | | | | | | | | | | % 33.94/5.38 | | | | | | | | | | | | | | | REDUCE: (157), (356) imply: % 33.94/5.38 | | | | | | | | | | | | | | | (357) ~ element(all_70_2, all_70_4) % 33.94/5.38 | | | | | | | | | | | | | | | % 33.94/5.38 | | | | | | | | | | | | | | | PRED_UNIFY: (20), (357) imply: % 33.94/5.38 | | | | | | | | | | | | | | | (358) $false % 33.94/5.38 | | | | | | | | | | | | | | | % 33.94/5.38 | | | | | | | | | | | | | | | CLOSE: (358) is inconsistent. % 33.94/5.38 | | | | | | | | | | | | | | | % 33.94/5.38 | | | | | | | | | | | | | | Case 2: % 33.94/5.38 | | | | | | | | | | | | | | | % 33.94/5.38 | | | | | | | | | | | | | | | (359) element(all_70_2, all_104_1) % 33.94/5.38 | | | | | | | | | | | | | | | (360) subset_intersection2(all_104_2, all_70_2, % 33.94/5.38 | | | | | | | | | | | | | | | all_104_0) = all_70_2 % 33.94/5.38 | | | | | | | | | | | | | | | % 33.94/5.38 | | | | | | | | | | | | | | | REDUCE: (133), (134), (360) imply: % 33.94/5.38 | | | | | | | | | | | | | | | (361) subset_intersection2(all_70_5, all_70_2, all_70_5) % 33.94/5.38 | | | | | | | | | | | | | | | = all_70_2 % 33.94/5.38 | | | | | | | | | | | | | | | % 33.94/5.38 | | | | | | | | | | | | | | | BETA: splitting (331) gives: % 33.94/5.38 | | | | | | | | | | | | | | | % 33.94/5.38 | | | | | | | | | | | | | | | Case 1: % 33.94/5.38 | | | | | | | | | | | | | | | | % 33.94/5.38 | | | | | | | | | | | | | | | | (362) ~ element(all_70_5, all_104_1) % 33.94/5.38 | | | | | | | | | | | | | | | | % 33.94/5.38 | | | | | | | | | | | | | | | | REDUCE: (157), (362) imply: % 33.94/5.38 | | | | | | | | | | | | | | | | (363) ~ element(all_70_5, all_70_4) % 33.94/5.38 | | | | | | | | | | | | | | | | % 33.94/5.38 | | | | | | | | | | | | | | | | PRED_UNIFY: (158), (363) imply: % 33.94/5.38 | | | | | | | | | | | | | | | | (364) $false % 33.94/5.38 | | | | | | | | | | | | | | | | % 33.94/5.38 | | | | | | | | | | | | | | | | CLOSE: (364) is inconsistent. % 33.94/5.38 | | | | | | | | | | | | | | | | % 33.94/5.38 | | | | | | | | | | | | | | | Case 2: % 33.94/5.38 | | | | | | | | | | | | | | | | % 33.94/5.38 | | | | | | | | | | | | | | | | (365) element(all_70_5, all_104_1) % 33.94/5.38 | | | | | | | | | | | | | | | | (366) subset_intersection2(all_104_2, all_70_5, % 33.94/5.38 | | | | | | | | | | | | | | | | all_104_0) = all_70_5 % 33.94/5.38 | | | | | | | | | | | | | | | | % 33.94/5.38 | | | | | | | | | | | | | | | | REDUCE: (133), (134), (366) imply: % 33.94/5.38 | | | | | | | | | | | | | | | | (367) subset_intersection2(all_70_5, all_70_5, all_70_5) % 33.94/5.38 | | | | | | | | | | | | | | | | = all_70_5 % 33.94/5.38 | | | | | | | | | | | | | | | | % 33.94/5.38 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (commutativity_k5_subset_1) with % 33.94/5.38 | | | | | | | | | | | | | | | | all_70_5, empty_set, all_70_5, empty_set, % 33.94/5.38 | | | | | | | | | | | | | | | | simplifying with (23), (224), (355) gives: % 33.94/5.39 | | | | | | | | | | | | | | | | (368) ? [v0: $i] : ? [v1: $i] : % 33.94/5.39 | | | | | | | | | | | | | | | | (subset_intersection2(all_70_5, all_70_5, % 33.94/5.39 | | | | | | | | | | | | | | | | empty_set) = v1 & powerset(all_70_5) = v0 & % 33.94/5.39 | | | | | | | | | | | | | | | | $i(v1) & $i(v0) & (v1 = empty_set | ~ % 33.94/5.39 | | | | | | | | | | | | | | | | element(all_70_5, v0) | ~ element(empty_set, % 33.94/5.39 | | | | | | | | | | | | | | | | v0))) % 33.94/5.39 | | | | | | | | | | | | | | | | % 33.94/5.39 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (5) with all_70_5, empty_set, % 33.94/5.39 | | | | | | | | | | | | | | | | all_70_5, empty_set, simplifying with (23), (224), % 33.94/5.39 | | | | | | | | | | | | | | | | (355) gives: % 33.94/5.39 | | | | | | | | | | | | | | | | (369) ? [v0: $i] : ? [v1: $i] : % 33.94/5.39 | | | | | | | | | | | | | | | | (set_intersection2(empty_set, all_70_5) = v1 & % 33.94/5.39 | | | | | | | | | | | | | | | | powerset(all_70_5) = v0 & $i(v1) & $i(v0) & (v1 % 33.94/5.39 | | | | | | | | | | | | | | | | = empty_set | ~ element(all_70_5, v0) | ~ % 33.94/5.39 | | | | | | | | | | | | | | | | element(empty_set, v0))) % 33.94/5.39 | | | | | | | | | | | | | | | | % 33.94/5.39 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (5) with all_70_5, all_70_5, % 33.94/5.39 | | | | | | | | | | | | | | | | all_70_5, all_70_5, simplifying with (23), (367) % 33.94/5.39 | | | | | | | | | | | | | | | | gives: % 33.94/5.39 | | | | | | | | | | | | | | | | (370) ? [v0: $i] : ? [v1: $i] : % 33.94/5.39 | | | | | | | | | | | | | | | | (set_intersection2(all_70_5, all_70_5) = v1 & % 33.94/5.39 | | | | | | | | | | | | | | | | powerset(all_70_5) = v0 & $i(v1) & $i(v0) & (v1 % 33.94/5.39 | | | | | | | | | | | | | | | | = all_70_5 | ~ element(all_70_5, v0))) % 33.94/5.39 | | | | | | | | | | | | | | | | % 33.94/5.39 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (commutativity_k5_subset_1) with % 33.94/5.39 | | | | | | | | | | | | | | | | all_70_5, all_70_2, all_70_5, all_70_2, % 33.94/5.39 | | | | | | | | | | | | | | | | simplifying with (23), (24), (361) gives: % 33.94/5.39 | | | | | | | | | | | | | | | | (371) ? [v0: $i] : ? [v1: $i] : % 33.94/5.39 | | | | | | | | | | | | | | | | (subset_intersection2(all_70_5, all_70_5, % 33.94/5.39 | | | | | | | | | | | | | | | | all_70_2) = v1 & powerset(all_70_5) = v0 & % 33.94/5.39 | | | | | | | | | | | | | | | | $i(v1) & $i(v0) & (v1 = all_70_2 | ~ % 33.94/5.39 | | | | | | | | | | | | | | | | element(all_70_2, v0) | ~ element(all_70_5, % 33.94/5.39 | | | | | | | | | | | | | | | | v0))) % 33.94/5.39 | | | | | | | | | | | | | | | | % 33.94/5.39 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (5) with all_70_5, all_70_2, % 33.94/5.39 | | | | | | | | | | | | | | | | all_70_5, all_70_2, simplifying with (23), (24), % 33.94/5.39 | | | | | | | | | | | | | | | | (361) gives: % 33.94/5.39 | | | | | | | | | | | | | | | | (372) ? [v0: $i] : ? [v1: $i] : % 33.94/5.39 | | | | | | | | | | | | | | | | (set_intersection2(all_70_2, all_70_5) = v1 & % 33.94/5.39 | | | | | | | | | | | | | | | | powerset(all_70_5) = v0 & $i(v1) & $i(v0) & (v1 % 33.94/5.39 | | | | | | | | | | | | | | | | = all_70_2 | ~ element(all_70_2, v0) | ~ % 33.94/5.39 | | | | | | | | | | | | | | | | element(all_70_5, v0))) % 33.94/5.39 | | | | | | | | | | | | | | | | % 33.94/5.39 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (commutativity_k5_subset_1) with % 33.94/5.39 | | | | | | | | | | | | | | | | all_70_5, all_70_1, all_70_5, all_70_1, % 33.94/5.39 | | | | | | | | | | | | | | | | simplifying with (23), (25), (350) gives: % 33.94/5.39 | | | | | | | | | | | | | | | | (373) ? [v0: $i] : ? [v1: $i] : % 33.94/5.39 | | | | | | | | | | | | | | | | (subset_intersection2(all_70_5, all_70_5, % 33.94/5.39 | | | | | | | | | | | | | | | | all_70_1) = v1 & powerset(all_70_5) = v0 & % 33.94/5.39 | | | | | | | | | | | | | | | | $i(v1) & $i(v0) & (v1 = all_70_1 | ~ % 33.94/5.39 | | | | | | | | | | | | | | | | element(all_70_1, v0) | ~ element(all_70_5, % 33.94/5.39 | | | | | | | | | | | | | | | | v0))) % 33.94/5.39 | | | | | | | | | | | | | | | | % 33.94/5.39 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (5) with all_70_5, all_70_1, % 33.94/5.39 | | | | | | | | | | | | | | | | all_70_5, all_70_1, simplifying with (23), (25), % 33.94/5.39 | | | | | | | | | | | | | | | | (350) gives: % 33.94/5.39 | | | | | | | | | | | | | | | | (374) ? [v0: $i] : ? [v1: $i] : % 33.94/5.39 | | | | | | | | | | | | | | | | (set_intersection2(all_70_1, all_70_5) = v1 & % 33.94/5.39 | | | | | | | | | | | | | | | | powerset(all_70_5) = v0 & $i(v1) & $i(v0) & (v1 % 33.94/5.39 | | | | | | | | | | | | | | | | = all_70_1 | ~ element(all_70_1, v0) | ~ % 33.94/5.39 | | | | | | | | | | | | | | | | element(all_70_5, v0))) % 33.94/5.39 | | | | | | | | | | | | | | | | % 33.94/5.39 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (commutativity_k5_subset_1) with % 33.94/5.39 | | | | | | | | | | | | | | | | all_70_5, all_70_0, all_70_5, all_70_0, % 33.94/5.39 | | | | | | | | | | | | | | | | simplifying with (23), (222), (345) gives: % 33.94/5.39 | | | | | | | | | | | | | | | | (375) ? [v0: $i] : ? [v1: $i] : % 33.94/5.39 | | | | | | | | | | | | | | | | (subset_intersection2(all_70_5, all_70_5, % 33.94/5.39 | | | | | | | | | | | | | | | | all_70_0) = v1 & powerset(all_70_5) = v0 & % 33.94/5.39 | | | | | | | | | | | | | | | | $i(v1) & $i(v0) & (v1 = all_70_0 | ~ % 33.94/5.39 | | | | | | | | | | | | | | | | element(all_70_0, v0) | ~ element(all_70_5, % 33.94/5.39 | | | | | | | | | | | | | | | | v0))) % 33.94/5.39 | | | | | | | | | | | | | | | | % 33.94/5.39 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (5) with all_70_5, all_70_0, % 33.94/5.39 | | | | | | | | | | | | | | | | all_70_5, all_70_0, simplifying with (23), (222), % 33.94/5.39 | | | | | | | | | | | | | | | | (345) gives: % 33.94/5.39 | | | | | | | | | | | | | | | | (376) ? [v0: $i] : ? [v1: $i] : % 33.94/5.39 | | | | | | | | | | | | | | | | (set_intersection2(all_70_0, all_70_5) = v1 & % 33.94/5.39 | | | | | | | | | | | | | | | | powerset(all_70_5) = v0 & $i(v1) & $i(v0) & (v1 % 33.94/5.39 | | | | | | | | | | | | | | | | = all_70_0 | ~ element(all_70_0, v0) | ~ % 33.94/5.39 | | | | | | | | | | | | | | | | element(all_70_5, v0))) % 33.94/5.39 | | | | | | | | | | | | | | | | % 33.94/5.39 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (commutativity_k5_subset_1) with % 33.94/5.39 | | | | | | | | | | | | | | | | all_70_5, all_203_0, all_70_5, all_203_0, % 33.94/5.39 | | | | | | | | | | | | | | | | simplifying with (23), (329), (340) gives: % 33.94/5.39 | | | | | | | | | | | | | | | | (377) ? [v0: $i] : ? [v1: $i] : % 33.94/5.39 | | | | | | | | | | | | | | | | (subset_intersection2(all_70_5, all_70_5, % 33.94/5.39 | | | | | | | | | | | | | | | | all_203_0) = v1 & powerset(all_70_5) = v0 & % 33.94/5.39 | | | | | | | | | | | | | | | | $i(v1) & $i(v0) & (v1 = all_203_0 | ~ % 33.94/5.39 | | | | | | | | | | | | | | | | element(all_203_0, v0) | ~ element(all_70_5, % 33.94/5.39 | | | | | | | | | | | | | | | | v0))) % 33.94/5.39 | | | | | | | | | | | | | | | | % 33.94/5.39 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (5) with all_70_5, all_203_0, % 33.94/5.39 | | | | | | | | | | | | | | | | all_70_5, all_203_0, simplifying with (23), (329), % 33.94/5.39 | | | | | | | | | | | | | | | | (340) gives: % 33.94/5.39 | | | | | | | | | | | | | | | | (378) ? [v0: $i] : ? [v1: $i] : % 33.94/5.39 | | | | | | | | | | | | | | | | (set_intersection2(all_203_0, all_70_5) = v1 & % 33.94/5.39 | | | | | | | | | | | | | | | | powerset(all_70_5) = v0 & $i(v1) & $i(v0) & (v1 % 33.94/5.39 | | | | | | | | | | | | | | | | = all_203_0 | ~ element(all_203_0, v0) | ~ % 33.94/5.39 | | | | | | | | | | | | | | | | element(all_70_5, v0))) % 33.94/5.39 | | | | | | | | | | | | | | | | % 33.94/5.39 | | | | | | | | | | | | | | | | DELTA: instantiating (370) with fresh symbols all_322_0, % 33.94/5.39 | | | | | | | | | | | | | | | | all_322_1 gives: % 33.94/5.39 | | | | | | | | | | | | | | | | (379) set_intersection2(all_70_5, all_70_5) = all_322_0 % 33.94/5.39 | | | | | | | | | | | | | | | | & powerset(all_70_5) = all_322_1 & $i(all_322_0) & % 33.94/5.39 | | | | | | | | | | | | | | | | $i(all_322_1) & (all_322_0 = all_70_5 | ~ % 33.94/5.39 | | | | | | | | | | | | | | | | element(all_70_5, all_322_1)) % 33.94/5.39 | | | | | | | | | | | | | | | | % 33.94/5.39 | | | | | | | | | | | | | | | | ALPHA: (379) implies: % 33.94/5.39 | | | | | | | | | | | | | | | | (380) powerset(all_70_5) = all_322_1 % 33.94/5.39 | | | | | | | | | | | | | | | | % 33.94/5.39 | | | | | | | | | | | | | | | | DELTA: instantiating (374) with fresh symbols all_326_0, % 33.94/5.39 | | | | | | | | | | | | | | | | all_326_1 gives: % 33.94/5.39 | | | | | | | | | | | | | | | | (381) set_intersection2(all_70_1, all_70_5) = all_326_0 % 33.94/5.39 | | | | | | | | | | | | | | | | & powerset(all_70_5) = all_326_1 & $i(all_326_0) & % 33.94/5.39 | | | | | | | | | | | | | | | | $i(all_326_1) & (all_326_0 = all_70_1 | ~ % 33.94/5.39 | | | | | | | | | | | | | | | | element(all_70_1, all_326_1) | ~ % 33.94/5.39 | | | | | | | | | | | | | | | | element(all_70_5, all_326_1)) % 33.94/5.39 | | | | | | | | | | | | | | | | % 33.94/5.39 | | | | | | | | | | | | | | | | ALPHA: (381) implies: % 33.94/5.39 | | | | | | | | | | | | | | | | (382) powerset(all_70_5) = all_326_1 % 33.94/5.39 | | | | | | | | | | | | | | | | % 33.94/5.39 | | | | | | | | | | | | | | | | DELTA: instantiating (373) with fresh symbols all_328_0, % 33.94/5.39 | | | | | | | | | | | | | | | | all_328_1 gives: % 33.94/5.39 | | | | | | | | | | | | | | | | (383) subset_intersection2(all_70_5, all_70_5, all_70_1) % 33.94/5.39 | | | | | | | | | | | | | | | | = all_328_0 & powerset(all_70_5) = all_328_1 & % 33.94/5.39 | | | | | | | | | | | | | | | | $i(all_328_0) & $i(all_328_1) & (all_328_0 = % 33.94/5.39 | | | | | | | | | | | | | | | | all_70_1 | ~ element(all_70_1, all_328_1) | ~ % 33.94/5.39 | | | | | | | | | | | | | | | | element(all_70_5, all_328_1)) % 33.94/5.39 | | | | | | | | | | | | | | | | % 33.94/5.39 | | | | | | | | | | | | | | | | ALPHA: (383) implies: % 33.94/5.39 | | | | | | | | | | | | | | | | (384) powerset(all_70_5) = all_328_1 % 33.94/5.39 | | | | | | | | | | | | | | | | % 33.94/5.39 | | | | | | | | | | | | | | | | DELTA: instantiating (369) with fresh symbols all_330_0, % 33.94/5.39 | | | | | | | | | | | | | | | | all_330_1 gives: % 33.94/5.39 | | | | | | | | | | | | | | | | (385) set_intersection2(empty_set, all_70_5) = all_330_0 % 33.94/5.39 | | | | | | | | | | | | | | | | & powerset(all_70_5) = all_330_1 & $i(all_330_0) & % 33.94/5.39 | | | | | | | | | | | | | | | | $i(all_330_1) & (all_330_0 = empty_set | ~ % 33.94/5.39 | | | | | | | | | | | | | | | | element(all_70_5, all_330_1) | ~ % 33.94/5.39 | | | | | | | | | | | | | | | | element(empty_set, all_330_1)) % 33.94/5.39 | | | | | | | | | | | | | | | | % 33.94/5.39 | | | | | | | | | | | | | | | | ALPHA: (385) implies: % 33.94/5.39 | | | | | | | | | | | | | | | | (386) powerset(all_70_5) = all_330_1 % 33.94/5.39 | | | | | | | | | | | | | | | | % 33.94/5.39 | | | | | | | | | | | | | | | | DELTA: instantiating (368) with fresh symbols all_332_0, % 33.94/5.39 | | | | | | | | | | | | | | | | all_332_1 gives: % 33.94/5.39 | | | | | | | | | | | | | | | | (387) subset_intersection2(all_70_5, all_70_5, % 33.94/5.39 | | | | | | | | | | | | | | | | empty_set) = all_332_0 & powerset(all_70_5) = % 33.94/5.39 | | | | | | | | | | | | | | | | all_332_1 & $i(all_332_0) & $i(all_332_1) & % 33.94/5.39 | | | | | | | | | | | | | | | | (all_332_0 = empty_set | ~ element(all_70_5, % 33.94/5.39 | | | | | | | | | | | | | | | | all_332_1) | ~ element(empty_set, all_332_1)) % 33.94/5.39 | | | | | | | | | | | | | | | | % 33.94/5.39 | | | | | | | | | | | | | | | | ALPHA: (387) implies: % 33.94/5.39 | | | | | | | | | | | | | | | | (388) powerset(all_70_5) = all_332_1 % 33.94/5.39 | | | | | | | | | | | | | | | | % 33.94/5.39 | | | | | | | | | | | | | | | | DELTA: instantiating (372) with fresh symbols all_334_0, % 33.94/5.39 | | | | | | | | | | | | | | | | all_334_1 gives: % 33.94/5.39 | | | | | | | | | | | | | | | | (389) set_intersection2(all_70_2, all_70_5) = all_334_0 % 33.94/5.39 | | | | | | | | | | | | | | | | & powerset(all_70_5) = all_334_1 & $i(all_334_0) & % 33.94/5.39 | | | | | | | | | | | | | | | | $i(all_334_1) & (all_334_0 = all_70_2 | ~ % 33.94/5.39 | | | | | | | | | | | | | | | | element(all_70_2, all_334_1) | ~ % 33.94/5.39 | | | | | | | | | | | | | | | | element(all_70_5, all_334_1)) % 33.94/5.39 | | | | | | | | | | | | | | | | % 33.94/5.39 | | | | | | | | | | | | | | | | ALPHA: (389) implies: % 33.94/5.39 | | | | | | | | | | | | | | | | (390) powerset(all_70_5) = all_334_1 % 33.94/5.39 | | | | | | | | | | | | | | | | (391) set_intersection2(all_70_2, all_70_5) = all_334_0 % 33.94/5.39 | | | | | | | | | | | | | | | | (392) all_334_0 = all_70_2 | ~ element(all_70_2, % 33.94/5.39 | | | | | | | | | | | | | | | | all_334_1) | ~ element(all_70_5, all_334_1) % 33.94/5.39 | | | | | | | | | | | | | | | | % 33.94/5.39 | | | | | | | | | | | | | | | | DELTA: instantiating (371) with fresh symbols all_336_0, % 33.94/5.39 | | | | | | | | | | | | | | | | all_336_1 gives: % 33.94/5.39 | | | | | | | | | | | | | | | | (393) subset_intersection2(all_70_5, all_70_5, all_70_2) % 33.94/5.39 | | | | | | | | | | | | | | | | = all_336_0 & powerset(all_70_5) = all_336_1 & % 33.94/5.39 | | | | | | | | | | | | | | | | $i(all_336_0) & $i(all_336_1) & (all_336_0 = % 33.94/5.39 | | | | | | | | | | | | | | | | all_70_2 | ~ element(all_70_2, all_336_1) | ~ % 33.94/5.39 | | | | | | | | | | | | | | | | element(all_70_5, all_336_1)) % 33.94/5.39 | | | | | | | | | | | | | | | | % 33.94/5.39 | | | | | | | | | | | | | | | | ALPHA: (393) implies: % 33.94/5.39 | | | | | | | | | | | | | | | | (394) powerset(all_70_5) = all_336_1 % 33.94/5.39 | | | | | | | | | | | | | | | | % 33.94/5.39 | | | | | | | | | | | | | | | | DELTA: instantiating (378) with fresh symbols all_338_0, % 33.94/5.39 | | | | | | | | | | | | | | | | all_338_1 gives: % 33.94/5.39 | | | | | | | | | | | | | | | | (395) set_intersection2(all_203_0, all_70_5) = all_338_0 % 33.94/5.39 | | | | | | | | | | | | | | | | & powerset(all_70_5) = all_338_1 & $i(all_338_0) & % 33.94/5.39 | | | | | | | | | | | | | | | | $i(all_338_1) & (all_338_0 = all_203_0 | ~ % 33.94/5.39 | | | | | | | | | | | | | | | | element(all_203_0, all_338_1) | ~ % 33.94/5.39 | | | | | | | | | | | | | | | | element(all_70_5, all_338_1)) % 33.94/5.39 | | | | | | | | | | | | | | | | % 33.94/5.39 | | | | | | | | | | | | | | | | ALPHA: (395) implies: % 33.94/5.39 | | | | | | | | | | | | | | | | (396) powerset(all_70_5) = all_338_1 % 33.94/5.39 | | | | | | | | | | | | | | | | % 33.94/5.39 | | | | | | | | | | | | | | | | DELTA: instantiating (377) with fresh symbols all_340_0, % 33.94/5.39 | | | | | | | | | | | | | | | | all_340_1 gives: % 33.94/5.39 | | | | | | | | | | | | | | | | (397) subset_intersection2(all_70_5, all_70_5, % 33.94/5.39 | | | | | | | | | | | | | | | | all_203_0) = all_340_0 & powerset(all_70_5) = % 33.94/5.39 | | | | | | | | | | | | | | | | all_340_1 & $i(all_340_0) & $i(all_340_1) & % 33.94/5.39 | | | | | | | | | | | | | | | | (all_340_0 = all_203_0 | ~ element(all_203_0, % 33.94/5.39 | | | | | | | | | | | | | | | | all_340_1) | ~ element(all_70_5, all_340_1)) % 33.94/5.39 | | | | | | | | | | | | | | | | % 33.94/5.39 | | | | | | | | | | | | | | | | ALPHA: (397) implies: % 33.94/5.39 | | | | | | | | | | | | | | | | (398) powerset(all_70_5) = all_340_1 % 33.94/5.39 | | | | | | | | | | | | | | | | % 33.94/5.39 | | | | | | | | | | | | | | | | DELTA: instantiating (376) with fresh symbols all_342_0, % 33.94/5.39 | | | | | | | | | | | | | | | | all_342_1 gives: % 33.94/5.39 | | | | | | | | | | | | | | | | (399) set_intersection2(all_70_0, all_70_5) = all_342_0 % 33.94/5.39 | | | | | | | | | | | | | | | | & powerset(all_70_5) = all_342_1 & $i(all_342_0) & % 33.94/5.39 | | | | | | | | | | | | | | | | $i(all_342_1) & (all_342_0 = all_70_0 | ~ % 33.94/5.39 | | | | | | | | | | | | | | | | element(all_70_0, all_342_1) | ~ % 33.94/5.39 | | | | | | | | | | | | | | | | element(all_70_5, all_342_1)) % 33.94/5.39 | | | | | | | | | | | | | | | | % 33.94/5.39 | | | | | | | | | | | | | | | | ALPHA: (399) implies: % 33.94/5.39 | | | | | | | | | | | | | | | | (400) powerset(all_70_5) = all_342_1 % 33.94/5.39 | | | | | | | | | | | | | | | | % 33.94/5.39 | | | | | | | | | | | | | | | | DELTA: instantiating (375) with fresh symbols all_344_0, % 33.94/5.39 | | | | | | | | | | | | | | | | all_344_1 gives: % 33.94/5.39 | | | | | | | | | | | | | | | | (401) subset_intersection2(all_70_5, all_70_5, all_70_0) % 33.94/5.39 | | | | | | | | | | | | | | | | = all_344_0 & powerset(all_70_5) = all_344_1 & % 33.94/5.39 | | | | | | | | | | | | | | | | $i(all_344_0) & $i(all_344_1) & (all_344_0 = % 33.94/5.39 | | | | | | | | | | | | | | | | all_70_0 | ~ element(all_70_0, all_344_1) | ~ % 33.94/5.39 | | | | | | | | | | | | | | | | element(all_70_5, all_344_1)) % 33.94/5.39 | | | | | | | | | | | | | | | | % 33.94/5.39 | | | | | | | | | | | | | | | | ALPHA: (401) implies: % 33.94/5.39 | | | | | | | | | | | | | | | | (402) powerset(all_70_5) = all_344_1 % 33.94/5.39 | | | | | | | | | | | | | | | | % 33.94/5.39 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (11) with all_328_1, all_330_1, % 33.94/5.39 | | | | | | | | | | | | | | | | all_70_5, simplifying with (384), (386) gives: % 33.94/5.39 | | | | | | | | | | | | | | | | (403) all_330_1 = all_328_1 % 33.94/5.39 | | | | | | | | | | | | | | | | % 33.94/5.39 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (11) with all_330_1, all_332_1, % 33.94/5.39 | | | | | | | | | | | | | | | | all_70_5, simplifying with (386), (388) gives: % 33.94/5.39 | | | | | | | | | | | | | | | | (404) all_332_1 = all_330_1 % 33.94/5.39 | | | | | | | | | | | | | | | | % 33.94/5.39 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (11) with all_332_1, all_334_1, % 33.94/5.39 | | | | | | | | | | | | | | | | all_70_5, simplifying with (388), (390) gives: % 33.94/5.39 | | | | | | | | | | | | | | | | (405) all_334_1 = all_332_1 % 33.94/5.39 | | | | | | | | | | | | | | | | % 33.94/5.39 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (11) with all_70_4, all_338_1, % 33.94/5.39 | | | | | | | | | | | | | | | | all_70_5, simplifying with (26), (396) gives: % 33.94/5.39 | | | | | | | | | | | | | | | | (406) all_338_1 = all_70_4 % 33.94/5.39 | | | | | | | | | | | | | | | | % 33.94/5.39 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (11) with all_336_1, all_338_1, % 33.94/5.39 | | | | | | | | | | | | | | | | all_70_5, simplifying with (394), (396) gives: % 33.94/5.39 | | | | | | | | | | | | | | | | (407) all_338_1 = all_336_1 % 33.94/5.39 | | | | | | | | | | | | | | | | % 33.94/5.39 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (11) with all_328_1, all_338_1, % 33.94/5.39 | | | | | | | | | | | | | | | | all_70_5, simplifying with (384), (396) gives: % 33.94/5.39 | | | | | | | | | | | | | | | | (408) all_338_1 = all_328_1 % 33.94/5.39 | | | | | | | | | | | | | | | | % 33.94/5.39 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (11) with all_326_1, all_338_1, % 33.94/5.39 | | | | | | | | | | | | | | | | all_70_5, simplifying with (382), (396) gives: % 33.94/5.39 | | | | | | | | | | | | | | | | (409) all_338_1 = all_326_1 % 33.94/5.39 | | | | | | | | | | | | | | | | % 33.94/5.39 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (11) with all_340_1, all_342_1, % 33.94/5.39 | | | | | | | | | | | | | | | | all_70_5, simplifying with (398), (400) gives: % 33.94/5.39 | | | | | | | | | | | | | | | | (410) all_342_1 = all_340_1 % 33.94/5.39 | | | | | | | | | | | | | | | | % 33.94/5.39 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (11) with all_334_1, all_342_1, % 33.94/5.39 | | | | | | | | | | | | | | | | all_70_5, simplifying with (390), (400) gives: % 33.94/5.39 | | | | | | | | | | | | | | | | (411) all_342_1 = all_334_1 % 33.94/5.39 | | | | | | | | | | | | | | | | % 33.94/5.39 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (11) with all_342_1, all_344_1, % 33.94/5.39 | | | | | | | | | | | | | | | | all_70_5, simplifying with (400), (402) gives: % 33.94/5.39 | | | | | | | | | | | | | | | | (412) all_344_1 = all_342_1 % 33.94/5.39 | | | | | | | | | | | | | | | | % 33.94/5.39 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (11) with all_322_1, all_344_1, % 33.94/5.39 | | | | | | | | | | | | | | | | all_70_5, simplifying with (380), (402) gives: % 33.94/5.39 | | | | | | | | | | | | | | | | (413) all_344_1 = all_322_1 % 33.94/5.39 | | | | | | | | | | | | | | | | % 33.94/5.39 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (14) with all_70_0, all_334_0, % 33.94/5.39 | | | | | | | | | | | | | | | | all_70_5, all_70_2, simplifying with (223), (391) % 33.94/5.39 | | | | | | | | | | | | | | | | gives: % 33.94/5.39 | | | | | | | | | | | | | | | | (414) all_334_0 = all_70_0 % 33.94/5.39 | | | | | | | | | | | | | | | | % 33.94/5.39 | | | | | | | | | | | | | | | | COMBINE_EQS: (412), (413) imply: % 33.94/5.39 | | | | | | | | | | | | | | | | (415) all_342_1 = all_322_1 % 33.94/5.39 | | | | | | | | | | | | | | | | % 33.94/5.39 | | | | | | | | | | | | | | | | SIMP: (415) implies: % 33.94/5.40 | | | | | | | | | | | | | | | | (416) all_342_1 = all_322_1 % 33.94/5.40 | | | | | | | | | | | | | | | | % 33.94/5.40 | | | | | | | | | | | | | | | | COMBINE_EQS: (410), (416) imply: % 33.94/5.40 | | | | | | | | | | | | | | | | (417) all_340_1 = all_322_1 % 33.94/5.40 | | | | | | | | | | | | | | | | % 33.94/5.40 | | | | | | | | | | | | | | | | COMBINE_EQS: (410), (411) imply: % 33.94/5.40 | | | | | | | | | | | | | | | | (418) all_340_1 = all_334_1 % 33.94/5.40 | | | | | | | | | | | | | | | | % 33.94/5.40 | | | | | | | | | | | | | | | | COMBINE_EQS: (417), (418) imply: % 33.94/5.40 | | | | | | | | | | | | | | | | (419) all_334_1 = all_322_1 % 33.94/5.40 | | | | | | | | | | | | | | | | % 33.94/5.40 | | | | | | | | | | | | | | | | SIMP: (419) implies: % 33.94/5.40 | | | | | | | | | | | | | | | | (420) all_334_1 = all_322_1 % 33.94/5.40 | | | | | | | | | | | | | | | | % 33.94/5.40 | | | | | | | | | | | | | | | | COMBINE_EQS: (406), (407) imply: % 33.94/5.40 | | | | | | | | | | | | | | | | (421) all_336_1 = all_70_4 % 33.94/5.40 | | | | | | | | | | | | | | | | % 33.94/5.40 | | | | | | | | | | | | | | | | COMBINE_EQS: (407), (408) imply: % 33.94/5.40 | | | | | | | | | | | | | | | | (422) all_336_1 = all_328_1 % 33.94/5.40 | | | | | | | | | | | | | | | | % 33.94/5.40 | | | | | | | | | | | | | | | | COMBINE_EQS: (407), (409) imply: % 33.94/5.40 | | | | | | | | | | | | | | | | (423) all_336_1 = all_326_1 % 33.94/5.40 | | | | | | | | | | | | | | | | % 33.94/5.40 | | | | | | | | | | | | | | | | COMBINE_EQS: (421), (423) imply: % 33.94/5.40 | | | | | | | | | | | | | | | | (424) all_326_1 = all_70_4 % 33.94/5.40 | | | | | | | | | | | | | | | | % 33.94/5.40 | | | | | | | | | | | | | | | | COMBINE_EQS: (422), (423) imply: % 33.94/5.40 | | | | | | | | | | | | | | | | (425) all_328_1 = all_326_1 % 33.94/5.40 | | | | | | | | | | | | | | | | % 33.94/5.40 | | | | | | | | | | | | | | | | SIMP: (425) implies: % 33.94/5.40 | | | | | | | | | | | | | | | | (426) all_328_1 = all_326_1 % 33.94/5.40 | | | | | | | | | | | | | | | | % 33.94/5.40 | | | | | | | | | | | | | | | | COMBINE_EQS: (405), (420) imply: % 33.94/5.40 | | | | | | | | | | | | | | | | (427) all_332_1 = all_322_1 % 33.94/5.40 | | | | | | | | | | | | | | | | % 33.94/5.40 | | | | | | | | | | | | | | | | SIMP: (427) implies: % 33.94/5.40 | | | | | | | | | | | | | | | | (428) all_332_1 = all_322_1 % 33.94/5.40 | | | | | | | | | | | | | | | | % 33.94/5.40 | | | | | | | | | | | | | | | | COMBINE_EQS: (404), (428) imply: % 33.94/5.40 | | | | | | | | | | | | | | | | (429) all_330_1 = all_322_1 % 33.94/5.40 | | | | | | | | | | | | | | | | % 33.94/5.40 | | | | | | | | | | | | | | | | SIMP: (429) implies: % 33.94/5.40 | | | | | | | | | | | | | | | | (430) all_330_1 = all_322_1 % 33.94/5.40 | | | | | | | | | | | | | | | | % 33.94/5.40 | | | | | | | | | | | | | | | | COMBINE_EQS: (403), (430) imply: % 33.94/5.40 | | | | | | | | | | | | | | | | (431) all_328_1 = all_322_1 % 33.94/5.40 | | | | | | | | | | | | | | | | % 33.94/5.40 | | | | | | | | | | | | | | | | SIMP: (431) implies: % 33.94/5.40 | | | | | | | | | | | | | | | | (432) all_328_1 = all_322_1 % 33.94/5.40 | | | | | | | | | | | | | | | | % 33.94/5.40 | | | | | | | | | | | | | | | | COMBINE_EQS: (426), (432) imply: % 33.94/5.40 | | | | | | | | | | | | | | | | (433) all_326_1 = all_322_1 % 33.94/5.40 | | | | | | | | | | | | | | | | % 33.94/5.40 | | | | | | | | | | | | | | | | SIMP: (433) implies: % 33.94/5.40 | | | | | | | | | | | | | | | | (434) all_326_1 = all_322_1 % 33.94/5.40 | | | | | | | | | | | | | | | | % 33.94/5.40 | | | | | | | | | | | | | | | | COMBINE_EQS: (424), (434) imply: % 33.94/5.40 | | | | | | | | | | | | | | | | (435) all_322_1 = all_70_4 % 33.94/5.40 | | | | | | | | | | | | | | | | % 33.94/5.40 | | | | | | | | | | | | | | | | COMBINE_EQS: (420), (435) imply: % 33.94/5.40 | | | | | | | | | | | | | | | | (436) all_334_1 = all_70_4 % 33.94/5.40 | | | | | | | | | | | | | | | | % 33.94/5.40 | | | | | | | | | | | | | | | | BETA: splitting (392) gives: % 33.94/5.40 | | | | | | | | | | | | | | | | % 33.94/5.40 | | | | | | | | | | | | | | | | Case 1: % 33.94/5.40 | | | | | | | | | | | | | | | | | % 33.94/5.40 | | | | | | | | | | | | | | | | | (437) ~ element(all_70_2, all_334_1) % 33.94/5.40 | | | | | | | | | | | | | | | | | % 33.94/5.40 | | | | | | | | | | | | | | | | | REDUCE: (436), (437) imply: % 33.94/5.40 | | | | | | | | | | | | | | | | | (438) ~ element(all_70_2, all_70_4) % 33.94/5.40 | | | | | | | | | | | | | | | | | % 33.94/5.40 | | | | | | | | | | | | | | | | | PRED_UNIFY: (20), (438) imply: % 33.94/5.40 | | | | | | | | | | | | | | | | | (439) $false % 33.94/5.40 | | | | | | | | | | | | | | | | | % 33.94/5.40 | | | | | | | | | | | | | | | | | CLOSE: (439) is inconsistent. % 33.94/5.40 | | | | | | | | | | | | | | | | | % 33.94/5.40 | | | | | | | | | | | | | | | | Case 2: % 33.94/5.40 | | | | | | | | | | | | | | | | | % 33.94/5.40 | | | | | | | | | | | | | | | | | (440) all_334_0 = all_70_2 | ~ element(all_70_5, % 33.94/5.40 | | | | | | | | | | | | | | | | | all_334_1) % 33.94/5.40 | | | | | | | | | | | | | | | | | % 33.94/5.40 | | | | | | | | | | | | | | | | | BETA: splitting (440) gives: % 33.94/5.40 | | | | | | | | | | | | | | | | | % 33.94/5.40 | | | | | | | | | | | | | | | | | Case 1: % 33.94/5.40 | | | | | | | | | | | | | | | | | | % 33.94/5.40 | | | | | | | | | | | | | | | | | | (441) ~ element(all_70_5, all_334_1) % 33.94/5.40 | | | | | | | | | | | | | | | | | | % 33.94/5.40 | | | | | | | | | | | | | | | | | | REDUCE: (436), (441) imply: % 33.94/5.40 | | | | | | | | | | | | | | | | | | (442) ~ element(all_70_5, all_70_4) % 33.94/5.40 | | | | | | | | | | | | | | | | | | % 33.94/5.40 | | | | | | | | | | | | | | | | | | PRED_UNIFY: (158), (442) imply: % 33.94/5.40 | | | | | | | | | | | | | | | | | | (443) $false % 33.94/5.40 | | | | | | | | | | | | | | | | | | % 33.94/5.40 | | | | | | | | | | | | | | | | | | CLOSE: (443) is inconsistent. % 33.94/5.40 | | | | | | | | | | | | | | | | | | % 33.94/5.40 | | | | | | | | | | | | | | | | | Case 2: % 33.94/5.40 | | | | | | | | | | | | | | | | | | % 33.94/5.40 | | | | | | | | | | | | | | | | | | (444) all_334_0 = all_70_2 % 33.94/5.40 | | | | | | | | | | | | | | | | | | % 33.94/5.40 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (414), (444) imply: % 33.94/5.40 | | | | | | | | | | | | | | | | | | (445) all_70_0 = all_70_2 % 33.94/5.40 | | | | | | | | | | | | | | | | | | % 33.94/5.40 | | | | | | | | | | | | | | | | | | REDUCE: (19), (445) imply: % 33.94/5.40 | | | | | | | | | | | | | | | | | | (446) $false % 33.94/5.40 | | | | | | | | | | | | | | | | | | % 33.94/5.40 | | | | | | | | | | | | | | | | | | CLOSE: (446) is inconsistent. % 33.94/5.40 | | | | | | | | | | | | | | | | | | % 33.94/5.40 | | | | | | | | | | | | | | | | | End of split % 33.94/5.40 | | | | | | | | | | | | | | | | | % 33.94/5.40 | | | | | | | | | | | | | | | | End of split % 33.94/5.40 | | | | | | | | | | | | | | | | % 33.94/5.40 | | | | | | | | | | | | | | | End of split % 33.94/5.40 | | | | | | | | | | | | | | | % 33.94/5.40 | | | | | | | | | | | | | | End of split % 33.94/5.40 | | | | | | | | | | | | | | % 33.94/5.40 | | | | | | | | | | | | | End of split % 33.94/5.40 | | | | | | | | | | | | | % 33.94/5.40 | | | | | | | | | | | | End of split % 33.94/5.40 | | | | | | | | | | | | % 33.94/5.40 | | | | | | | | | | | End of split % 33.94/5.40 | | | | | | | | | | | % 33.94/5.40 | | | | | | | | | | End of split % 33.94/5.40 | | | | | | | | | | % 33.94/5.40 | | | | | | | | | End of split % 33.94/5.40 | | | | | | | | | % 33.94/5.40 | | | | | | | | End of split % 33.94/5.40 | | | | | | | | % 33.94/5.40 | | | | | | | End of split % 33.94/5.40 | | | | | | | % 33.94/5.40 | | | | | | End of split % 33.94/5.40 | | | | | | % 33.94/5.40 | | | | | End of split % 33.94/5.40 | | | | | % 33.94/5.40 | | | | End of split % 33.94/5.40 | | | | % 33.94/5.40 | | | End of split % 33.94/5.40 | | | % 33.94/5.40 | | End of split % 33.94/5.40 | | % 33.94/5.40 | End of split % 33.94/5.40 | % 33.94/5.40 End of proof % 33.94/5.40 % SZS output end Proof for theBenchmark % 33.94/5.40 % 33.94/5.40 4801ms %------------------------------------------------------------------------------