%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SEU341+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 : n007.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 300s % DateTime : Thu Aug 31 17:44:11 EDT 2023 % Result : Theorem 10.70s 2.20s % Output : Proof 27.04s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SEU341+1 : TPTP v8.1.2. Released v3.3.0. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.12/0.35 % Computer : n007.cluster.edu % 0.12/0.35 % Model : x86_64 x86_64 % 0.12/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.35 % Memory : 8042.1875MB % 0.12/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.35 % CPULimit : 300 % 0.12/0.35 % WCLimit : 300 % 0.12/0.35 % DateTime : Wed Aug 23 15:53:24 EDT 2023 % 0.12/0.35 % CPUTime : % 0.21/0.62 ________ _____ % 0.21/0.62 ___ __ \_________(_)________________________________ % 0.21/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.21/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.21/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.21/0.62 % 0.21/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.21/0.62 (2023-06-19) % 0.21/0.62 % 0.21/0.62 (c) Philipp Rümmer, 2009-2023 % 0.21/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.21/0.62 Amanda Stjerna. % 0.21/0.62 Free software under BSD-3-Clause. % 0.21/0.62 % 0.21/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.21/0.62 % 0.21/0.62 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.21/0.63 Running up to 7 provers in parallel. % 0.21/0.65 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.21/0.65 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.21/0.65 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.21/0.65 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.21/0.65 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.21/0.65 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.21/0.66 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 3.19/1.12 Prover 1: Preprocessing ... % 3.19/1.12 Prover 4: Preprocessing ... % 3.33/1.15 Prover 3: Preprocessing ... % 3.33/1.15 Prover 5: Preprocessing ... % 3.33/1.15 Prover 0: Preprocessing ... % 3.33/1.15 Prover 6: Preprocessing ... % 3.33/1.15 Prover 2: Preprocessing ... % 6.94/1.71 Prover 5: Proving ... % 7.58/1.76 Prover 1: Warning: ignoring some quantifiers % 7.99/1.81 Prover 1: Constructing countermodel ... % 7.99/1.82 Prover 3: Warning: ignoring some quantifiers % 7.99/1.84 Prover 6: Proving ... % 7.99/1.84 Prover 3: Constructing countermodel ... % 7.99/1.84 Prover 2: Proving ... % 10.70/2.20 Prover 5: proved (1541ms) % 10.70/2.20 % 10.70/2.20 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 10.70/2.20 % 10.70/2.20 Prover 2: stopped % 10.70/2.20 Prover 6: stopped % 10.70/2.20 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 10.70/2.20 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 10.70/2.20 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 10.70/2.20 Prover 3: stopped % 10.70/2.21 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 11.14/2.27 Prover 7: Preprocessing ... % 11.14/2.29 Prover 4: Warning: ignoring some quantifiers % 11.14/2.30 Prover 10: Preprocessing ... % 11.72/2.32 Prover 8: Preprocessing ... % 11.72/2.32 Prover 11: Preprocessing ... % 11.72/2.33 Prover 4: Constructing countermodel ... % 11.72/2.34 Prover 7: Warning: ignoring some quantifiers % 11.72/2.35 Prover 7: Constructing countermodel ... % 11.72/2.35 Prover 10: Warning: ignoring some quantifiers % 11.72/2.36 Prover 10: Constructing countermodel ... % 12.21/2.41 Prover 0: Proving ... % 12.21/2.43 Prover 0: stopped % 12.21/2.44 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 13.05/2.51 Prover 13: Preprocessing ... % 13.31/2.52 Prover 8: Warning: ignoring some quantifiers % 13.41/2.53 Prover 8: Constructing countermodel ... % 14.00/2.62 Prover 13: Warning: ignoring some quantifiers % 14.00/2.63 Prover 13: Constructing countermodel ... % 14.00/2.67 Prover 10: gave up % 14.00/2.67 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 14.50/2.70 Prover 16: Preprocessing ... % 14.50/2.76 Prover 16: Warning: ignoring some quantifiers % 15.19/2.77 Prover 16: Constructing countermodel ... % 15.19/2.85 Prover 11: Warning: ignoring some quantifiers % 15.19/2.87 Prover 11: Constructing countermodel ... % 22.52/3.79 Prover 7: gave up % 22.52/3.79 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085 % 22.52/3.84 Prover 19: Preprocessing ... % 24.33/4.05 Prover 19: Warning: ignoring some quantifiers % 24.33/4.06 Prover 19: Constructing countermodel ... % 25.48/4.31 Prover 13: Found proof (size 156) % 25.48/4.31 Prover 13: proved (1870ms) % 25.48/4.31 Prover 19: stopped % 25.48/4.31 Prover 4: stopped % 25.48/4.31 Prover 11: stopped % 25.48/4.32 Prover 16: stopped % 25.48/4.32 Prover 1: stopped % 25.48/4.32 Prover 8: stopped % 25.48/4.32 % 25.48/4.32 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 25.48/4.32 % 26.62/4.34 % SZS output start Proof for theBenchmark % 26.62/4.34 Assumptions after simplification: % 26.62/4.34 --------------------------------- % 26.62/4.34 % 26.62/4.34 (d1_connsp_2) % 26.62/4.37 ! [v0: $i] : ! [v1: $i] : ( ~ (the_carrier(v0) = v1) | ~ $i(v0) | ~ % 26.62/4.37 top_str(v0) | ~ topological_space(v0) | empty_carrier(v0) | ? [v2: $i] : % 26.62/4.37 (powerset(v1) = v2 & $i(v2) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ % 26.62/4.37 (interior(v0, v4) = v5) | ~ $i(v4) | ~ $i(v3) | ~ % 26.62/4.37 point_neighbourhood(v4, v0, v3) | ~ element(v4, v2) | ~ element(v3, % 26.62/4.37 v1) | in(v3, v5)) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ % 26.62/4.37 (interior(v0, v4) = v5) | ~ $i(v4) | ~ $i(v3) | ~ element(v4, v2) | % 26.62/4.37 ~ element(v3, v1) | ~ in(v3, v5) | point_neighbourhood(v4, v0, v3)))) & % 26.62/4.37 ! [v0: $i] : ( ~ $i(v0) | ~ top_str(v0) | ~ topological_space(v0) | % 26.62/4.37 empty_carrier(v0) | ? [v1: $i] : ? [v2: $i] : (the_carrier(v0) = v1 & % 26.62/4.37 powerset(v1) = v2 & $i(v2) & $i(v1) & ! [v3: $i] : ! [v4: $i] : ( ~ % 26.62/4.37 $i(v4) | ~ $i(v3) | ~ element(v4, v2) | ~ element(v3, v1) | ? [v5: % 26.62/4.37 $i] : (interior(v0, v4) = v5 & $i(v5) & ( ~ point_neighbourhood(v4, % 26.62/4.37 v0, v3) | in(v3, v5)) & ( ~ in(v3, v5) | point_neighbourhood(v4, % 26.79/4.37 v0, v3)))))) % 26.79/4.37 % 26.79/4.37 (dt_m1_connsp_2) % 26.79/4.37 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (the_carrier(v0) = v2) | ~ % 26.79/4.37 $i(v1) | ~ $i(v0) | ~ top_str(v0) | ~ topological_space(v0) | ~ % 26.79/4.37 element(v1, v2) | empty_carrier(v0) | ? [v3: $i] : (powerset(v2) = v3 & % 26.79/4.37 $i(v3) & ! [v4: $i] : ( ~ $i(v4) | ~ point_neighbourhood(v4, v0, v1) | % 26.79/4.37 element(v4, v3)))) & ? [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) % 26.79/4.37 | ~ top_str(v1) | ~ topological_space(v1) | empty_carrier(v1) | ? [v2: % 26.79/4.37 $i] : ? [v3: $i] : (the_carrier(v1) = v2 & powerset(v2) = v3 & $i(v3) & % 26.79/4.37 $i(v2) & ( ~ element(v0, v2) | ! [v4: $i] : ( ~ $i(v4) | ~ % 26.79/4.37 point_neighbourhood(v4, v1, v0) | element(v4, v3))))) % 26.79/4.37 % 26.79/4.37 (existence_l1_pre_topc) % 26.79/4.38 ? [v0: $i] : ($i(v0) & top_str(v0)) % 26.79/4.38 % 26.79/4.38 (fc1_subset_1) % 26.79/4.38 ! [v0: $i] : ! [v1: $i] : ( ~ (powerset(v0) = v1) | ~ $i(v0) | ~ % 26.79/4.38 empty(v1)) % 26.79/4.38 % 26.79/4.38 (rc2_subset_1) % 26.79/4.38 ! [v0: $i] : ! [v1: $i] : ( ~ (powerset(v0) = v1) | ~ $i(v0) | ? [v2: $i] % 26.79/4.38 : ($i(v2) & empty(v2) & element(v2, v1))) & ? [v0: $i] : ( ~ $i(v0) | ? % 26.79/4.38 [v1: $i] : ? [v2: $i] : (powerset(v0) = v1 & $i(v2) & $i(v1) & empty(v2) & % 26.79/4.38 element(v2, v1))) % 26.79/4.38 % 26.79/4.38 (t2_subset) % 26.79/4.38 ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ element(v0, v1) | % 26.79/4.38 empty(v1) | in(v0, v1)) % 26.79/4.38 % 26.79/4.38 (t55_tops_1) % 26.79/4.38 ! [v0: $i] : ! [v1: $i] : ( ~ (the_carrier(v0) = v1) | ~ $i(v0) | ~ % 26.79/4.38 top_str(v0) | ~ topological_space(v0) | ? [v2: $i] : (powerset(v1) = v2 & % 26.79/4.38 $i(v2) & ! [v3: $i] : ! [v4: $i] : ( ~ (the_carrier(v3) = v4) | ~ % 26.79/4.38 $i(v3) | ~ top_str(v3) | ? [v5: $i] : (powerset(v4) = v5 & $i(v5) & ! % 26.79/4.38 [v6: $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : (v9 = v8 | ~ % 26.79/4.38 (interior(v3, v8) = v9) | ~ (interior(v0, v6) = v7) | ~ $i(v8) | % 26.79/4.38 ~ $i(v6) | ~ open_subset(v8, v3) | ~ element(v8, v5) | ~ % 26.79/4.38 element(v6, v2)) & ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ( ~ % 26.79/4.38 (interior(v3, v7) = v8) | ~ (interior(v0, v6) = v6) | ~ $i(v7) | % 26.79/4.38 ~ $i(v6) | ~ element(v7, v5) | ~ element(v6, v2) | open_subset(v6, % 26.79/4.38 v0)))))) & ! [v0: $i] : ( ~ $i(v0) | ~ top_str(v0) | ~ % 26.79/4.38 topological_space(v0) | ? [v1: $i] : ? [v2: $i] : (the_carrier(v0) = v1 & % 26.79/4.38 powerset(v1) = v2 & $i(v2) & $i(v1) & ! [v3: $i] : ( ~ $i(v3) | ~ % 26.79/4.38 top_str(v3) | ? [v4: $i] : ? [v5: $i] : (the_carrier(v3) = v4 & % 26.79/4.38 powerset(v4) = v5 & $i(v5) & $i(v4) & ! [v6: $i] : ( ~ $i(v6) | ~ % 26.79/4.38 element(v6, v2) | ? [v7: $i] : (interior(v0, v6) = v7 & $i(v7) & ! % 26.79/4.38 [v8: $i] : ( ~ (v7 = v6) | ~ $i(v8) | ~ element(v8, v5) | % 26.79/4.38 open_subset(v6, v0)) & ! [v8: $i] : ( ~ $i(v8) | ~ % 26.79/4.38 open_subset(v8, v3) | ~ element(v8, v5) | interior(v3, v8) = % 26.79/4.38 v8))))))) % 26.79/4.38 % 26.79/4.38 (t5_connsp_2) % 26.79/4.38 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 26.79/4.38 (the_carrier(v0) = v1 & powerset(v1) = v2 & $i(v4) & $i(v3) & $i(v2) & $i(v1) % 26.79/4.38 & $i(v0) & open_subset(v3, v0) & top_str(v0) & topological_space(v0) & % 26.79/4.38 element(v4, v1) & element(v3, v2) & in(v4, v3) & ~ point_neighbourhood(v3, % 26.79/4.38 v0, v4) & ~ empty_carrier(v0)) % 26.79/4.38 % 26.79/4.38 (function-axioms) % 26.79/4.39 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 26.79/4.39 (interior(v3, v2) = v1) | ~ (interior(v3, v2) = v0)) & ! [v0: $i] : ! % 26.79/4.39 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (the_carrier(v2) = v1) | ~ % 26.79/4.39 (the_carrier(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 % 26.79/4.39 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0)) % 26.79/4.39 % 26.79/4.39 Further assumptions not needed in the proof: % 26.79/4.39 -------------------------------------------- % 26.79/4.39 antisymmetry_r2_hidden, cc10_membered, cc11_membered, cc12_membered, % 26.79/4.39 cc13_membered, cc14_membered, cc15_membered, cc16_membered, cc17_membered, % 26.79/4.39 cc18_membered, cc19_membered, cc1_membered, cc20_membered, cc2_membered, % 26.79/4.39 cc3_membered, cc4_membered, dt_k1_tops_1, dt_k1_xboole_0, dt_k1_zfmisc_1, % 26.79/4.39 dt_l1_pre_topc, dt_l1_struct_0, dt_m1_subset_1, dt_u1_struct_0, % 26.79/4.39 existence_l1_struct_0, existence_m1_connsp_2, existence_m1_subset_1, % 26.79/4.39 fc6_membered, rc1_membered, rc1_subset_1, reflexivity_r1_tarski, t1_subset, % 26.79/4.39 t3_subset, t4_subset, t5_subset, t6_boole, t7_boole, t8_boole % 26.79/4.39 % 26.79/4.39 Those formulas are unsatisfiable: % 26.79/4.39 --------------------------------- % 26.79/4.39 % 26.79/4.39 Begin of proof % 26.79/4.39 | % 26.79/4.39 | ALPHA: (d1_connsp_2) implies: % 26.88/4.39 | (1) ! [v0: $i] : ( ~ $i(v0) | ~ top_str(v0) | ~ topological_space(v0) | % 26.88/4.39 | empty_carrier(v0) | ? [v1: $i] : ? [v2: $i] : (the_carrier(v0) = v1 % 26.88/4.39 | & powerset(v1) = v2 & $i(v2) & $i(v1) & ! [v3: $i] : ! [v4: $i] : % 26.88/4.39 | ( ~ $i(v4) | ~ $i(v3) | ~ element(v4, v2) | ~ element(v3, v1) | % 26.88/4.39 | ? [v5: $i] : (interior(v0, v4) = v5 & $i(v5) & ( ~ % 26.88/4.39 | point_neighbourhood(v4, v0, v3) | in(v3, v5)) & ( ~ in(v3, % 26.88/4.39 | v5) | point_neighbourhood(v4, v0, v3)))))) % 26.88/4.39 | (2) ! [v0: $i] : ! [v1: $i] : ( ~ (the_carrier(v0) = v1) | ~ $i(v0) | ~ % 26.88/4.39 | top_str(v0) | ~ topological_space(v0) | empty_carrier(v0) | ? [v2: % 26.88/4.39 | $i] : (powerset(v1) = v2 & $i(v2) & ! [v3: $i] : ! [v4: $i] : ! % 26.88/4.39 | [v5: $i] : ( ~ (interior(v0, v4) = v5) | ~ $i(v4) | ~ $i(v3) | ~ % 26.88/4.39 | point_neighbourhood(v4, v0, v3) | ~ element(v4, v2) | ~ % 26.88/4.39 | element(v3, v1) | in(v3, v5)) & ! [v3: $i] : ! [v4: $i] : ! % 26.88/4.39 | [v5: $i] : ( ~ (interior(v0, v4) = v5) | ~ $i(v4) | ~ $i(v3) | ~ % 26.88/4.39 | element(v4, v2) | ~ element(v3, v1) | ~ in(v3, v5) | % 26.88/4.39 | point_neighbourhood(v4, v0, v3)))) % 26.88/4.39 | % 26.88/4.39 | ALPHA: (dt_m1_connsp_2) implies: % 26.88/4.39 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (the_carrier(v0) = v2) | % 26.88/4.39 | ~ $i(v1) | ~ $i(v0) | ~ top_str(v0) | ~ topological_space(v0) | ~ % 26.88/4.39 | element(v1, v2) | empty_carrier(v0) | ? [v3: $i] : (powerset(v2) = % 26.88/4.39 | v3 & $i(v3) & ! [v4: $i] : ( ~ $i(v4) | ~ point_neighbourhood(v4, % 26.88/4.39 | v0, v1) | element(v4, v3)))) % 26.88/4.39 | % 26.88/4.39 | ALPHA: (rc2_subset_1) implies: % 26.88/4.40 | (4) ! [v0: $i] : ! [v1: $i] : ( ~ (powerset(v0) = v1) | ~ $i(v0) | ? % 26.88/4.40 | [v2: $i] : ($i(v2) & empty(v2) & element(v2, v1))) % 26.88/4.40 | % 26.88/4.40 | ALPHA: (t55_tops_1) implies: % 26.88/4.40 | (5) ! [v0: $i] : ( ~ $i(v0) | ~ top_str(v0) | ~ topological_space(v0) | % 26.88/4.40 | ? [v1: $i] : ? [v2: $i] : (the_carrier(v0) = v1 & powerset(v1) = v2 % 26.88/4.40 | & $i(v2) & $i(v1) & ! [v3: $i] : ( ~ $i(v3) | ~ top_str(v3) | ? % 26.88/4.40 | [v4: $i] : ? [v5: $i] : (the_carrier(v3) = v4 & powerset(v4) = % 26.88/4.40 | v5 & $i(v5) & $i(v4) & ! [v6: $i] : ( ~ $i(v6) | ~ % 26.88/4.40 | element(v6, v2) | ? [v7: $i] : (interior(v0, v6) = v7 & % 26.88/4.40 | $i(v7) & ! [v8: $i] : ( ~ (v7 = v6) | ~ $i(v8) | ~ % 26.88/4.40 | element(v8, v5) | open_subset(v6, v0)) & ! [v8: $i] : ( % 26.88/4.40 | ~ $i(v8) | ~ open_subset(v8, v3) | ~ element(v8, v5) | % 26.88/4.40 | interior(v3, v8) = v8))))))) % 26.88/4.40 | (6) ! [v0: $i] : ! [v1: $i] : ( ~ (the_carrier(v0) = v1) | ~ $i(v0) | ~ % 26.88/4.40 | top_str(v0) | ~ topological_space(v0) | ? [v2: $i] : (powerset(v1) % 26.88/4.40 | = v2 & $i(v2) & ! [v3: $i] : ! [v4: $i] : ( ~ (the_carrier(v3) = % 26.88/4.40 | v4) | ~ $i(v3) | ~ top_str(v3) | ? [v5: $i] : (powerset(v4) % 26.88/4.40 | = v5 & $i(v5) & ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ! % 26.88/4.40 | [v9: $i] : (v9 = v8 | ~ (interior(v3, v8) = v9) | ~ % 26.88/4.40 | (interior(v0, v6) = v7) | ~ $i(v8) | ~ $i(v6) | ~ % 26.88/4.40 | open_subset(v8, v3) | ~ element(v8, v5) | ~ element(v6, % 26.88/4.40 | v2)) & ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ( ~ % 26.88/4.40 | (interior(v3, v7) = v8) | ~ (interior(v0, v6) = v6) | ~ % 26.88/4.40 | $i(v7) | ~ $i(v6) | ~ element(v7, v5) | ~ element(v6, v2) % 26.88/4.40 | | open_subset(v6, v0)))))) % 26.88/4.40 | % 26.88/4.40 | ALPHA: (function-axioms) implies: % 26.88/4.40 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (powerset(v2) = % 26.88/4.40 | v1) | ~ (powerset(v2) = v0)) % 26.88/4.40 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 26.88/4.40 | (the_carrier(v2) = v1) | ~ (the_carrier(v2) = v0)) % 26.88/4.40 | (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 26.88/4.40 | (interior(v3, v2) = v1) | ~ (interior(v3, v2) = v0)) % 26.88/4.40 | % 26.88/4.40 | DELTA: instantiating (existence_l1_pre_topc) with fresh symbol all_40_0 gives: % 26.88/4.40 | (10) $i(all_40_0) & top_str(all_40_0) % 26.88/4.40 | % 26.88/4.40 | ALPHA: (10) implies: % 26.88/4.40 | (11) top_str(all_40_0) % 26.88/4.40 | (12) $i(all_40_0) % 26.88/4.40 | % 26.88/4.40 | DELTA: instantiating (t5_connsp_2) with fresh symbols all_52_0, all_52_1, % 26.88/4.40 | all_52_2, all_52_3, all_52_4 gives: % 26.88/4.40 | (13) the_carrier(all_52_4) = all_52_3 & powerset(all_52_3) = all_52_2 & % 26.88/4.40 | $i(all_52_0) & $i(all_52_1) & $i(all_52_2) & $i(all_52_3) & % 26.88/4.40 | $i(all_52_4) & open_subset(all_52_1, all_52_4) & top_str(all_52_4) & % 26.88/4.40 | topological_space(all_52_4) & element(all_52_0, all_52_3) & % 26.88/4.40 | element(all_52_1, all_52_2) & in(all_52_0, all_52_1) & ~ % 26.88/4.40 | point_neighbourhood(all_52_1, all_52_4, all_52_0) & ~ % 26.88/4.40 | empty_carrier(all_52_4) % 26.88/4.40 | % 26.88/4.40 | ALPHA: (13) implies: % 26.88/4.41 | (14) ~ empty_carrier(all_52_4) % 26.88/4.41 | (15) ~ point_neighbourhood(all_52_1, all_52_4, all_52_0) % 26.88/4.41 | (16) in(all_52_0, all_52_1) % 26.88/4.41 | (17) element(all_52_1, all_52_2) % 26.88/4.41 | (18) element(all_52_0, all_52_3) % 26.88/4.41 | (19) topological_space(all_52_4) % 26.88/4.41 | (20) top_str(all_52_4) % 26.88/4.41 | (21) open_subset(all_52_1, all_52_4) % 26.88/4.41 | (22) $i(all_52_4) % 26.88/4.41 | (23) $i(all_52_1) % 26.88/4.41 | (24) $i(all_52_0) % 26.88/4.41 | (25) powerset(all_52_3) = all_52_2 % 26.88/4.41 | (26) the_carrier(all_52_4) = all_52_3 % 26.88/4.41 | % 26.88/4.41 | GROUND_INST: instantiating (1) with all_52_4, simplifying with (14), (19), % 26.88/4.41 | (20), (22) gives: % 26.88/4.41 | (27) ? [v0: $i] : ? [v1: $i] : (the_carrier(all_52_4) = v0 & powerset(v0) % 26.88/4.41 | = v1 & $i(v1) & $i(v0) & ! [v2: $i] : ! [v3: $i] : ( ~ $i(v3) | ~ % 26.88/4.41 | $i(v2) | ~ element(v3, v1) | ~ element(v2, v0) | ? [v4: $i] : % 26.88/4.41 | (interior(all_52_4, v3) = v4 & $i(v4) & ( ~ % 26.88/4.41 | point_neighbourhood(v3, all_52_4, v2) | in(v2, v4)) & ( ~ % 26.88/4.41 | in(v2, v4) | point_neighbourhood(v3, all_52_4, v2))))) % 26.88/4.41 | % 26.88/4.41 | GROUND_INST: instantiating (5) with all_52_4, simplifying with (19), (20), % 26.88/4.41 | (22) gives: % 26.88/4.41 | (28) ? [v0: $i] : ? [v1: $i] : (the_carrier(all_52_4) = v0 & powerset(v0) % 26.88/4.41 | = v1 & $i(v1) & $i(v0) & ! [v2: $i] : ( ~ $i(v2) | ~ top_str(v2) | % 26.88/4.41 | ? [v3: $i] : ? [v4: $i] : (the_carrier(v2) = v3 & powerset(v3) = % 26.88/4.41 | v4 & $i(v4) & $i(v3) & ! [v5: $i] : ( ~ $i(v5) | ~ element(v5, % 26.88/4.41 | v1) | ? [v6: $i] : (interior(all_52_4, v5) = v6 & $i(v6) & % 26.88/4.41 | ! [v7: $i] : ( ~ (v6 = v5) | ~ $i(v7) | ~ element(v7, v4) % 26.88/4.41 | | open_subset(v5, all_52_4)) & ! [v7: $i] : ( ~ $i(v7) | % 26.88/4.41 | ~ open_subset(v7, v2) | ~ element(v7, v4) | interior(v2, % 26.88/4.41 | v7) = v7)))))) % 26.88/4.41 | % 26.88/4.41 | GROUND_INST: instantiating (3) with all_52_4, all_52_0, all_52_3, simplifying % 26.88/4.41 | with (14), (18), (19), (20), (22), (24), (26) gives: % 26.88/4.41 | (29) ? [v0: $i] : (powerset(all_52_3) = v0 & $i(v0) & ! [v1: $i] : ( ~ % 26.88/4.41 | $i(v1) | ~ point_neighbourhood(v1, all_52_4, all_52_0) | % 26.88/4.41 | element(v1, v0))) % 26.88/4.41 | % 26.88/4.41 | GROUND_INST: instantiating (2) with all_52_4, all_52_3, simplifying with (14), % 26.88/4.41 | (19), (20), (22), (26) gives: % 26.88/4.41 | (30) ? [v0: $i] : (powerset(all_52_3) = v0 & $i(v0) & ! [v1: $i] : ! % 26.88/4.41 | [v2: $i] : ! [v3: $i] : ( ~ (interior(all_52_4, v2) = v3) | ~ % 26.88/4.41 | $i(v2) | ~ $i(v1) | ~ point_neighbourhood(v2, all_52_4, v1) | ~ % 26.88/4.41 | element(v2, v0) | ~ element(v1, all_52_3) | in(v1, v3)) & ! [v1: % 26.88/4.41 | $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (interior(all_52_4, v2) = % 26.88/4.41 | v3) | ~ $i(v2) | ~ $i(v1) | ~ element(v2, v0) | ~ % 26.88/4.41 | element(v1, all_52_3) | ~ in(v1, v3) | point_neighbourhood(v2, % 26.88/4.41 | all_52_4, v1))) % 26.88/4.41 | % 27.01/4.41 | GROUND_INST: instantiating (6) with all_52_4, all_52_3, simplifying with (19), % 27.01/4.41 | (20), (22), (26) gives: % 27.01/4.42 | (31) ? [v0: $i] : (powerset(all_52_3) = v0 & $i(v0) & ! [v1: $i] : ! % 27.01/4.42 | [v2: $i] : ( ~ (the_carrier(v1) = v2) | ~ $i(v1) | ~ top_str(v1) | % 27.01/4.42 | ? [v3: $i] : (powerset(v2) = v3 & $i(v3) & ! [v4: $i] : ! [v5: % 27.01/4.42 | $i] : ! [v6: $i] : ! [v7: $i] : (v7 = v6 | ~ (interior(v1, % 27.01/4.42 | v6) = v7) | ~ (interior(all_52_4, v4) = v5) | ~ $i(v6) | % 27.01/4.42 | ~ $i(v4) | ~ open_subset(v6, v1) | ~ element(v6, v3) | ~ % 27.01/4.42 | element(v4, v0)) & ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( % 27.01/4.42 | ~ (interior(v1, v5) = v6) | ~ (interior(all_52_4, v4) = v4) | % 27.01/4.42 | ~ $i(v5) | ~ $i(v4) | ~ element(v5, v3) | ~ element(v4, % 27.01/4.42 | v0) | open_subset(v4, all_52_4))))) % 27.01/4.42 | % 27.01/4.42 | DELTA: instantiating (29) with fresh symbol all_64_0 gives: % 27.01/4.42 | (32) powerset(all_52_3) = all_64_0 & $i(all_64_0) & ! [v0: $i] : ( ~ % 27.01/4.42 | $i(v0) | ~ point_neighbourhood(v0, all_52_4, all_52_0) | % 27.01/4.42 | element(v0, all_64_0)) % 27.01/4.42 | % 27.01/4.42 | ALPHA: (32) implies: % 27.01/4.42 | (33) powerset(all_52_3) = all_64_0 % 27.01/4.42 | % 27.01/4.42 | DELTA: instantiating (27) with fresh symbols all_67_0, all_67_1 gives: % 27.01/4.42 | (34) the_carrier(all_52_4) = all_67_1 & powerset(all_67_1) = all_67_0 & % 27.01/4.42 | $i(all_67_0) & $i(all_67_1) & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | % 27.01/4.42 | ~ $i(v0) | ~ element(v1, all_67_0) | ~ element(v0, all_67_1) | ? % 27.01/4.42 | [v2: $i] : (interior(all_52_4, v1) = v2 & $i(v2) & ( ~ % 27.01/4.42 | point_neighbourhood(v1, all_52_4, v0) | in(v0, v2)) & ( ~ in(v0, % 27.01/4.42 | v2) | point_neighbourhood(v1, all_52_4, v0)))) % 27.01/4.42 | % 27.01/4.42 | ALPHA: (34) implies: % 27.01/4.42 | (35) powerset(all_67_1) = all_67_0 % 27.01/4.42 | (36) the_carrier(all_52_4) = all_67_1 % 27.01/4.42 | (37) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ element(v1, % 27.01/4.42 | all_67_0) | ~ element(v0, all_67_1) | ? [v2: $i] : % 27.01/4.42 | (interior(all_52_4, v1) = v2 & $i(v2) & ( ~ point_neighbourhood(v1, % 27.01/4.42 | all_52_4, v0) | in(v0, v2)) & ( ~ in(v0, v2) | % 27.01/4.42 | point_neighbourhood(v1, all_52_4, v0)))) % 27.01/4.42 | % 27.01/4.42 | DELTA: instantiating (30) with fresh symbol all_70_0 gives: % 27.01/4.42 | (38) powerset(all_52_3) = all_70_0 & $i(all_70_0) & ! [v0: $i] : ! [v1: % 27.01/4.42 | $i] : ! [v2: $i] : ( ~ (interior(all_52_4, v1) = v2) | ~ $i(v1) | % 27.01/4.42 | ~ $i(v0) | ~ point_neighbourhood(v1, all_52_4, v0) | ~ element(v1, % 27.01/4.42 | all_70_0) | ~ element(v0, all_52_3) | in(v0, v2)) & ! [v0: $i] : % 27.01/4.42 | ! [v1: $i] : ! [v2: $i] : ( ~ (interior(all_52_4, v1) = v2) | ~ % 27.04/4.42 | $i(v1) | ~ $i(v0) | ~ element(v1, all_70_0) | ~ element(v0, % 27.04/4.42 | all_52_3) | ~ in(v0, v2) | point_neighbourhood(v1, all_52_4, v0)) % 27.04/4.42 | % 27.04/4.42 | ALPHA: (38) implies: % 27.04/4.42 | (39) powerset(all_52_3) = all_70_0 % 27.04/4.42 | % 27.04/4.42 | DELTA: instantiating (31) with fresh symbol all_73_0 gives: % 27.04/4.43 | (40) powerset(all_52_3) = all_73_0 & $i(all_73_0) & ! [v0: $i] : ! [v1: % 27.04/4.43 | $i] : ( ~ (the_carrier(v0) = v1) | ~ $i(v0) | ~ top_str(v0) | ? % 27.04/4.43 | [v2: $i] : (powerset(v1) = v2 & $i(v2) & ! [v3: $i] : ! [v4: $i] : % 27.04/4.43 | ! [v5: $i] : ! [v6: $i] : (v6 = v5 | ~ (interior(v0, v5) = v6) % 27.04/4.43 | | ~ (interior(all_52_4, v3) = v4) | ~ $i(v5) | ~ $i(v3) | ~ % 27.04/4.43 | open_subset(v5, v0) | ~ element(v5, v2) | ~ element(v3, % 27.04/4.43 | all_73_0)) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ % 27.04/4.43 | (interior(v0, v4) = v5) | ~ (interior(all_52_4, v3) = v3) | ~ % 27.04/4.43 | $i(v4) | ~ $i(v3) | ~ element(v4, v2) | ~ element(v3, % 27.04/4.43 | all_73_0) | open_subset(v3, all_52_4)))) % 27.04/4.43 | % 27.04/4.43 | ALPHA: (40) implies: % 27.04/4.43 | (41) powerset(all_52_3) = all_73_0 % 27.04/4.43 | (42) ! [v0: $i] : ! [v1: $i] : ( ~ (the_carrier(v0) = v1) | ~ $i(v0) | % 27.04/4.43 | ~ top_str(v0) | ? [v2: $i] : (powerset(v1) = v2 & $i(v2) & ! [v3: % 27.04/4.43 | $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v6 = v5 | ~ % 27.04/4.43 | (interior(v0, v5) = v6) | ~ (interior(all_52_4, v3) = v4) | ~ % 27.04/4.43 | $i(v5) | ~ $i(v3) | ~ open_subset(v5, v0) | ~ element(v5, v2) % 27.04/4.43 | | ~ element(v3, all_73_0)) & ! [v3: $i] : ! [v4: $i] : ! % 27.04/4.43 | [v5: $i] : ( ~ (interior(v0, v4) = v5) | ~ (interior(all_52_4, % 27.04/4.43 | v3) = v3) | ~ $i(v4) | ~ $i(v3) | ~ element(v4, v2) | ~ % 27.04/4.43 | element(v3, all_73_0) | open_subset(v3, all_52_4)))) % 27.04/4.43 | % 27.04/4.43 | GROUND_INST: instantiating (42) with all_52_4, all_52_3, simplifying with % 27.04/4.43 | (20), (22), (26) gives: % 27.04/4.43 | (43) ? [v0: $i] : (powerset(all_52_3) = v0 & $i(v0) & ! [v1: $i] : ! % 27.04/4.43 | [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v4 = v3 | ~ % 27.04/4.43 | (interior(all_52_4, v3) = v4) | ~ (interior(all_52_4, v1) = v2) | % 27.04/4.43 | ~ $i(v3) | ~ $i(v1) | ~ open_subset(v3, all_52_4) | ~ % 27.04/4.43 | element(v3, v0) | ~ element(v1, all_73_0)) & ! [v1: $i] : ! % 27.04/4.43 | [v2: $i] : ! [v3: $i] : ( ~ (interior(all_52_4, v2) = v3) | ~ % 27.04/4.43 | (interior(all_52_4, v1) = v1) | ~ $i(v2) | ~ $i(v1) | ~ % 27.04/4.43 | element(v2, v0) | ~ element(v1, all_73_0) | open_subset(v1, % 27.04/4.43 | all_52_4))) % 27.04/4.43 | % 27.04/4.43 | DELTA: instantiating (28) with fresh symbols all_76_0, all_76_1 gives: % 27.04/4.43 | (44) the_carrier(all_52_4) = all_76_1 & powerset(all_76_1) = all_76_0 & % 27.04/4.43 | $i(all_76_0) & $i(all_76_1) & ! [v0: $i] : ( ~ $i(v0) | ~ % 27.04/4.43 | top_str(v0) | ? [v1: $i] : ? [v2: $i] : (the_carrier(v0) = v1 & % 27.04/4.43 | powerset(v1) = v2 & $i(v2) & $i(v1) & ! [v3: $i] : ( ~ $i(v3) | % 27.04/4.43 | ~ element(v3, all_76_0) | ? [v4: $i] : (interior(all_52_4, v3) % 27.04/4.43 | = v4 & $i(v4) & ! [v5: $i] : ( ~ (v4 = v3) | ~ $i(v5) | ~ % 27.04/4.43 | element(v5, v2) | open_subset(v3, all_52_4)) & ! [v5: $i] : % 27.04/4.43 | ( ~ $i(v5) | ~ open_subset(v5, v0) | ~ element(v5, v2) | % 27.04/4.43 | interior(v0, v5) = v5))))) % 27.04/4.43 | % 27.04/4.43 | ALPHA: (44) implies: % 27.04/4.43 | (45) powerset(all_76_1) = all_76_0 % 27.04/4.43 | (46) the_carrier(all_52_4) = all_76_1 % 27.04/4.43 | (47) ! [v0: $i] : ( ~ $i(v0) | ~ top_str(v0) | ? [v1: $i] : ? [v2: $i] % 27.04/4.43 | : (the_carrier(v0) = v1 & powerset(v1) = v2 & $i(v2) & $i(v1) & ! % 27.04/4.43 | [v3: $i] : ( ~ $i(v3) | ~ element(v3, all_76_0) | ? [v4: $i] : % 27.04/4.43 | (interior(all_52_4, v3) = v4 & $i(v4) & ! [v5: $i] : ( ~ (v4 = % 27.04/4.43 | v3) | ~ $i(v5) | ~ element(v5, v2) | open_subset(v3, % 27.04/4.43 | all_52_4)) & ! [v5: $i] : ( ~ $i(v5) | ~ open_subset(v5, % 27.04/4.43 | v0) | ~ element(v5, v2) | interior(v0, v5) = v5))))) % 27.04/4.43 | % 27.04/4.43 | GROUND_INST: instantiating (47) with all_40_0, simplifying with (11), (12) % 27.04/4.43 | gives: % 27.04/4.43 | (48) ? [v0: $i] : ? [v1: $i] : (the_carrier(all_40_0) = v0 & powerset(v0) % 27.04/4.43 | = v1 & $i(v1) & $i(v0) & ! [v2: $i] : ( ~ $i(v2) | ~ element(v2, % 27.04/4.43 | all_76_0) | ? [v3: $i] : (interior(all_52_4, v2) = v3 & $i(v3) % 27.04/4.43 | & ! [v4: $i] : ( ~ (v3 = v2) | ~ $i(v4) | ~ element(v4, v1) | % 27.04/4.43 | open_subset(v2, all_52_4)) & ! [v4: $i] : ( ~ $i(v4) | ~ % 27.04/4.43 | open_subset(v4, all_40_0) | ~ element(v4, v1) | % 27.04/4.43 | interior(all_40_0, v4) = v4)))) % 27.04/4.43 | % 27.04/4.43 | GROUND_INST: instantiating (47) with all_52_4, simplifying with (20), (22) % 27.04/4.43 | gives: % 27.04/4.44 | (49) ? [v0: $i] : ? [v1: $i] : (the_carrier(all_52_4) = v0 & powerset(v0) % 27.04/4.44 | = v1 & $i(v1) & $i(v0) & ! [v2: $i] : ( ~ $i(v2) | ~ element(v2, % 27.04/4.44 | all_76_0) | ? [v3: $i] : (interior(all_52_4, v2) = v3 & $i(v3) % 27.04/4.44 | & ! [v4: $i] : ( ~ (v3 = v2) | ~ $i(v4) | ~ element(v4, v1) | % 27.04/4.44 | open_subset(v2, all_52_4)) & ! [v4: $i] : ( ~ $i(v4) | ~ % 27.04/4.44 | open_subset(v4, all_52_4) | ~ element(v4, v1) | % 27.04/4.44 | interior(all_52_4, v4) = v4)))) % 27.04/4.44 | % 27.04/4.44 | DELTA: instantiating (43) with fresh symbol all_79_0 gives: % 27.04/4.44 | (50) powerset(all_52_3) = all_79_0 & $i(all_79_0) & ! [v0: $i] : ! [v1: % 27.04/4.44 | $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v2 | ~ (interior(all_52_4, % 27.04/4.44 | v2) = v3) | ~ (interior(all_52_4, v0) = v1) | ~ $i(v2) | ~ % 27.04/4.44 | $i(v0) | ~ open_subset(v2, all_52_4) | ~ element(v2, all_79_0) | % 27.04/4.44 | ~ element(v0, all_73_0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 27.04/4.44 | ( ~ (interior(all_52_4, v1) = v2) | ~ (interior(all_52_4, v0) = v0) | % 27.04/4.44 | ~ $i(v1) | ~ $i(v0) | ~ element(v1, all_79_0) | ~ element(v0, % 27.04/4.44 | all_73_0) | open_subset(v0, all_52_4)) % 27.04/4.44 | % 27.04/4.44 | ALPHA: (50) implies: % 27.04/4.44 | (51) powerset(all_52_3) = all_79_0 % 27.04/4.44 | % 27.04/4.44 | DELTA: instantiating (49) with fresh symbols all_82_0, all_82_1 gives: % 27.04/4.44 | (52) the_carrier(all_52_4) = all_82_1 & powerset(all_82_1) = all_82_0 & % 27.04/4.44 | $i(all_82_0) & $i(all_82_1) & ! [v0: $i] : ( ~ $i(v0) | ~ % 27.04/4.44 | element(v0, all_76_0) | ? [v1: $i] : (interior(all_52_4, v0) = v1 & % 27.04/4.44 | $i(v1) & ! [v2: $i] : ( ~ (v1 = v0) | ~ $i(v2) | ~ element(v2, % 27.04/4.44 | all_82_0) | open_subset(v0, all_52_4)) & ! [v2: $i] : ( ~ % 27.04/4.44 | $i(v2) | ~ open_subset(v2, all_52_4) | ~ element(v2, all_82_0) % 27.04/4.44 | | interior(all_52_4, v2) = v2))) % 27.04/4.44 | % 27.04/4.44 | ALPHA: (52) implies: % 27.04/4.44 | (53) powerset(all_82_1) = all_82_0 % 27.04/4.44 | (54) the_carrier(all_52_4) = all_82_1 % 27.04/4.44 | (55) ! [v0: $i] : ( ~ $i(v0) | ~ element(v0, all_76_0) | ? [v1: $i] : % 27.04/4.44 | (interior(all_52_4, v0) = v1 & $i(v1) & ! [v2: $i] : ( ~ (v1 = v0) % 27.04/4.44 | | ~ $i(v2) | ~ element(v2, all_82_0) | open_subset(v0, % 27.04/4.44 | all_52_4)) & ! [v2: $i] : ( ~ $i(v2) | ~ open_subset(v2, % 27.04/4.44 | all_52_4) | ~ element(v2, all_82_0) | interior(all_52_4, v2) % 27.04/4.44 | = v2))) % 27.04/4.44 | % 27.04/4.44 | DELTA: instantiating (48) with fresh symbols all_85_0, all_85_1 gives: % 27.04/4.44 | (56) the_carrier(all_40_0) = all_85_1 & powerset(all_85_1) = all_85_0 & % 27.04/4.44 | $i(all_85_0) & $i(all_85_1) & ! [v0: $i] : ( ~ $i(v0) | ~ % 27.04/4.44 | element(v0, all_76_0) | ? [v1: $i] : (interior(all_52_4, v0) = v1 & % 27.04/4.44 | $i(v1) & ! [v2: $i] : ( ~ (v1 = v0) | ~ $i(v2) | ~ element(v2, % 27.04/4.44 | all_85_0) | open_subset(v0, all_52_4)) & ! [v2: $i] : ( ~ % 27.04/4.44 | $i(v2) | ~ open_subset(v2, all_40_0) | ~ element(v2, all_85_0) % 27.04/4.44 | | interior(all_40_0, v2) = v2))) % 27.04/4.44 | % 27.04/4.44 | ALPHA: (56) implies: % 27.04/4.44 | (57) $i(all_85_1) % 27.04/4.44 | (58) powerset(all_85_1) = all_85_0 % 27.04/4.44 | (59) the_carrier(all_40_0) = all_85_1 % 27.04/4.44 | (60) ! [v0: $i] : ( ~ $i(v0) | ~ element(v0, all_76_0) | ? [v1: $i] : % 27.04/4.44 | (interior(all_52_4, v0) = v1 & $i(v1) & ! [v2: $i] : ( ~ (v1 = v0) % 27.04/4.44 | | ~ $i(v2) | ~ element(v2, all_85_0) | open_subset(v0, % 27.04/4.44 | all_52_4)) & ! [v2: $i] : ( ~ $i(v2) | ~ open_subset(v2, % 27.04/4.44 | all_40_0) | ~ element(v2, all_85_0) | interior(all_40_0, v2) % 27.04/4.44 | = v2))) % 27.04/4.44 | % 27.04/4.44 | GROUND_INST: instantiating (7) with all_52_2, all_70_0, all_52_3, simplifying % 27.04/4.44 | with (25), (39) gives: % 27.04/4.44 | (61) all_70_0 = all_52_2 % 27.04/4.44 | % 27.04/4.44 | GROUND_INST: instantiating (7) with all_73_0, all_79_0, all_52_3, simplifying % 27.04/4.44 | with (41), (51) gives: % 27.04/4.44 | (62) all_79_0 = all_73_0 % 27.04/4.44 | % 27.04/4.44 | GROUND_INST: instantiating (7) with all_70_0, all_79_0, all_52_3, simplifying % 27.04/4.44 | with (39), (51) gives: % 27.04/4.44 | (63) all_79_0 = all_70_0 % 27.04/4.44 | % 27.04/4.44 | GROUND_INST: instantiating (7) with all_64_0, all_79_0, all_52_3, simplifying % 27.04/4.44 | with (33), (51) gives: % 27.04/4.44 | (64) all_79_0 = all_64_0 % 27.04/4.44 | % 27.04/4.44 | GROUND_INST: instantiating (8) with all_52_3, all_76_1, all_52_4, simplifying % 27.04/4.44 | with (26), (46) gives: % 27.04/4.44 | (65) all_76_1 = all_52_3 % 27.04/4.44 | % 27.04/4.44 | GROUND_INST: instantiating (8) with all_76_1, all_82_1, all_52_4, simplifying % 27.04/4.44 | with (46), (54) gives: % 27.04/4.44 | (66) all_82_1 = all_76_1 % 27.04/4.44 | % 27.04/4.44 | GROUND_INST: instantiating (8) with all_67_1, all_82_1, all_52_4, simplifying % 27.04/4.44 | with (36), (54) gives: % 27.04/4.44 | (67) all_82_1 = all_67_1 % 27.04/4.44 | % 27.04/4.44 | COMBINE_EQS: (66), (67) imply: % 27.04/4.44 | (68) all_76_1 = all_67_1 % 27.04/4.44 | % 27.04/4.44 | SIMP: (68) implies: % 27.04/4.44 | (69) all_76_1 = all_67_1 % 27.04/4.44 | % 27.04/4.44 | COMBINE_EQS: (62), (64) imply: % 27.04/4.45 | (70) all_73_0 = all_64_0 % 27.04/4.45 | % 27.04/4.45 | COMBINE_EQS: (62), (63) imply: % 27.04/4.45 | (71) all_73_0 = all_70_0 % 27.04/4.45 | % 27.04/4.45 | COMBINE_EQS: (65), (69) imply: % 27.04/4.45 | (72) all_67_1 = all_52_3 % 27.04/4.45 | % 27.04/4.45 | COMBINE_EQS: (70), (71) imply: % 27.04/4.45 | (73) all_70_0 = all_64_0 % 27.04/4.45 | % 27.04/4.45 | SIMP: (73) implies: % 27.04/4.45 | (74) all_70_0 = all_64_0 % 27.04/4.45 | % 27.04/4.45 | COMBINE_EQS: (61), (74) imply: % 27.04/4.45 | (75) all_64_0 = all_52_2 % 27.04/4.45 | % 27.04/4.45 | SIMP: (75) implies: % 27.04/4.45 | (76) all_64_0 = all_52_2 % 27.04/4.45 | % 27.04/4.45 | COMBINE_EQS: (67), (72) imply: % 27.04/4.45 | (77) all_82_1 = all_52_3 % 27.04/4.45 | % 27.04/4.45 | REDUCE: (53), (77) imply: % 27.04/4.45 | (78) powerset(all_52_3) = all_82_0 % 27.04/4.45 | % 27.04/4.45 | REDUCE: (45), (65) imply: % 27.04/4.45 | (79) powerset(all_52_3) = all_76_0 % 27.04/4.45 | % 27.04/4.45 | REDUCE: (35), (72) imply: % 27.04/4.45 | (80) powerset(all_52_3) = all_67_0 % 27.04/4.45 | % 27.04/4.45 | GROUND_INST: instantiating (7) with all_52_2, all_76_0, all_52_3, simplifying % 27.04/4.45 | with (25), (79) gives: % 27.04/4.45 | (81) all_76_0 = all_52_2 % 27.04/4.45 | % 27.04/4.45 | GROUND_INST: instantiating (7) with all_76_0, all_82_0, all_52_3, simplifying % 27.04/4.45 | with (78), (79) gives: % 27.04/4.45 | (82) all_82_0 = all_76_0 % 27.04/4.45 | % 27.04/4.45 | GROUND_INST: instantiating (7) with all_67_0, all_82_0, all_52_3, simplifying % 27.04/4.45 | with (78), (80) gives: % 27.04/4.45 | (83) all_82_0 = all_67_0 % 27.04/4.45 | % 27.04/4.45 | COMBINE_EQS: (82), (83) imply: % 27.04/4.45 | (84) all_76_0 = all_67_0 % 27.04/4.45 | % 27.04/4.45 | SIMP: (84) implies: % 27.04/4.45 | (85) all_76_0 = all_67_0 % 27.04/4.45 | % 27.04/4.45 | COMBINE_EQS: (81), (85) imply: % 27.04/4.45 | (86) all_67_0 = all_52_2 % 27.04/4.45 | % 27.04/4.45 | SIMP: (86) implies: % 27.04/4.45 | (87) all_67_0 = all_52_2 % 27.04/4.45 | % 27.04/4.45 | COMBINE_EQS: (83), (87) imply: % 27.04/4.45 | (88) all_82_0 = all_52_2 % 27.04/4.45 | % 27.04/4.45 | GROUND_INST: instantiating (4) with all_85_1, all_85_0, simplifying with (57), % 27.04/4.45 | (58) gives: % 27.04/4.45 | (89) ? [v0: $i] : ($i(v0) & empty(v0) & element(v0, all_85_0)) % 27.04/4.45 | % 27.04/4.45 | GROUND_INST: instantiating (42) with all_40_0, all_85_1, simplifying with % 27.04/4.45 | (11), (12), (59) gives: % 27.04/4.45 | (90) ? [v0: $i] : (powerset(all_85_1) = v0 & $i(v0) & ! [v1: $i] : ! % 27.04/4.45 | [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v4 = v3 | ~ % 27.04/4.45 | (interior(all_52_4, v1) = v2) | ~ (interior(all_40_0, v3) = v4) | % 27.04/4.45 | ~ $i(v3) | ~ $i(v1) | ~ open_subset(v3, all_40_0) | ~ % 27.04/4.45 | element(v3, v0) | ~ element(v1, all_73_0)) & ! [v1: $i] : ! % 27.04/4.45 | [v2: $i] : ! [v3: $i] : ( ~ (interior(all_52_4, v1) = v1) | ~ % 27.04/4.45 | (interior(all_40_0, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ % 27.04/4.45 | element(v2, v0) | ~ element(v1, all_73_0) | open_subset(v1, % 27.04/4.45 | all_52_4))) % 27.04/4.45 | % 27.04/4.45 | DELTA: instantiating (89) with fresh symbol all_102_0 gives: % 27.04/4.45 | (91) $i(all_102_0) & empty(all_102_0) & element(all_102_0, all_85_0) % 27.04/4.45 | % 27.04/4.45 | ALPHA: (91) implies: % 27.04/4.45 | (92) element(all_102_0, all_85_0) % 27.04/4.45 | (93) $i(all_102_0) % 27.04/4.45 | % 27.04/4.45 | DELTA: instantiating (90) with fresh symbol all_104_0 gives: % 27.04/4.45 | (94) powerset(all_85_1) = all_104_0 & $i(all_104_0) & ! [v0: $i] : ! [v1: % 27.04/4.45 | $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v2 | ~ (interior(all_52_4, % 27.04/4.45 | v0) = v1) | ~ (interior(all_40_0, v2) = v3) | ~ $i(v2) | ~ % 27.04/4.45 | $i(v0) | ~ open_subset(v2, all_40_0) | ~ element(v2, all_104_0) | % 27.04/4.45 | ~ element(v0, all_73_0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 27.04/4.45 | ( ~ (interior(all_52_4, v0) = v0) | ~ (interior(all_40_0, v1) = v2) | % 27.04/4.45 | ~ $i(v1) | ~ $i(v0) | ~ element(v1, all_104_0) | ~ element(v0, % 27.04/4.45 | all_73_0) | open_subset(v0, all_52_4)) % 27.04/4.45 | % 27.04/4.45 | ALPHA: (94) implies: % 27.04/4.45 | (95) $i(all_104_0) % 27.04/4.45 | (96) powerset(all_85_1) = all_104_0 % 27.04/4.45 | % 27.04/4.45 | GROUND_INST: instantiating (7) with all_85_0, all_104_0, all_85_1, simplifying % 27.04/4.45 | with (58), (96) gives: % 27.04/4.45 | (97) all_104_0 = all_85_0 % 27.04/4.45 | % 27.04/4.45 | REDUCE: (95), (97) imply: % 27.04/4.45 | (98) $i(all_85_0) % 27.04/4.45 | % 27.04/4.45 | GROUND_INST: instantiating (t2_subset) with all_102_0, all_85_0, simplifying % 27.04/4.45 | with (92), (93), (98) gives: % 27.04/4.45 | (99) empty(all_85_0) | in(all_102_0, all_85_0) % 27.04/4.45 | % 27.04/4.45 | BETA: splitting (99) gives: % 27.04/4.45 | % 27.04/4.45 | Case 1: % 27.04/4.45 | | % 27.04/4.45 | | (100) empty(all_85_0) % 27.04/4.45 | | % 27.04/4.45 | | GROUND_INST: instantiating (fc1_subset_1) with all_85_1, all_85_0, % 27.04/4.45 | | simplifying with (57), (58), (100) gives: % 27.04/4.45 | | (101) $false % 27.04/4.45 | | % 27.04/4.45 | | CLOSE: (101) is inconsistent. % 27.04/4.45 | | % 27.04/4.45 | Case 2: % 27.04/4.45 | | % 27.04/4.45 | | % 27.04/4.45 | | DELTA: instantiating (49) with fresh symbols all_372_0, all_372_1 gives: % 27.04/4.46 | | (102) the_carrier(all_52_4) = all_372_1 & powerset(all_372_1) = all_372_0 % 27.04/4.46 | | & $i(all_372_0) & $i(all_372_1) & ! [v0: $i] : ( ~ $i(v0) | ~ % 27.04/4.46 | | element(v0, all_76_0) | ? [v1: $i] : (interior(all_52_4, v0) = % 27.04/4.46 | | v1 & $i(v1) & ! [v2: $i] : ( ~ (v1 = v0) | ~ $i(v2) | ~ % 27.04/4.46 | | element(v2, all_372_0) | open_subset(v0, all_52_4)) & ! [v2: % 27.04/4.46 | | $i] : ( ~ $i(v2) | ~ open_subset(v2, all_52_4) | ~ % 27.04/4.46 | | element(v2, all_372_0) | interior(all_52_4, v2) = v2))) % 27.04/4.46 | | % 27.04/4.46 | | ALPHA: (102) implies: % 27.04/4.46 | | (103) ! [v0: $i] : ( ~ $i(v0) | ~ element(v0, all_76_0) | ? [v1: $i] : % 27.04/4.46 | | (interior(all_52_4, v0) = v1 & $i(v1) & ! [v2: $i] : ( ~ (v1 = % 27.04/4.46 | | v0) | ~ $i(v2) | ~ element(v2, all_372_0) | % 27.04/4.46 | | open_subset(v0, all_52_4)) & ! [v2: $i] : ( ~ $i(v2) | ~ % 27.04/4.46 | | open_subset(v2, all_52_4) | ~ element(v2, all_372_0) | % 27.04/4.46 | | interior(all_52_4, v2) = v2))) % 27.04/4.46 | | % 27.04/4.46 | | DELTA: instantiating (48) with fresh symbols all_375_0, all_375_1 gives: % 27.04/4.46 | | (104) the_carrier(all_40_0) = all_375_1 & powerset(all_375_1) = all_375_0 % 27.04/4.46 | | & $i(all_375_0) & $i(all_375_1) & ! [v0: $i] : ( ~ $i(v0) | ~ % 27.04/4.46 | | element(v0, all_76_0) | ? [v1: $i] : (interior(all_52_4, v0) = % 27.04/4.46 | | v1 & $i(v1) & ! [v2: $i] : ( ~ (v1 = v0) | ~ $i(v2) | ~ % 27.04/4.46 | | element(v2, all_375_0) | open_subset(v0, all_52_4)) & ! [v2: % 27.04/4.46 | | $i] : ( ~ $i(v2) | ~ open_subset(v2, all_40_0) | ~ % 27.04/4.46 | | element(v2, all_375_0) | interior(all_40_0, v2) = v2))) % 27.04/4.46 | | % 27.04/4.46 | | ALPHA: (104) implies: % 27.04/4.46 | | (105) ! [v0: $i] : ( ~ $i(v0) | ~ element(v0, all_76_0) | ? [v1: $i] : % 27.04/4.46 | | (interior(all_52_4, v0) = v1 & $i(v1) & ! [v2: $i] : ( ~ (v1 = % 27.04/4.46 | | v0) | ~ $i(v2) | ~ element(v2, all_375_0) | % 27.04/4.46 | | open_subset(v0, all_52_4)) & ! [v2: $i] : ( ~ $i(v2) | ~ % 27.04/4.46 | | open_subset(v2, all_40_0) | ~ element(v2, all_375_0) | % 27.04/4.46 | | interior(all_40_0, v2) = v2))) % 27.04/4.46 | | % 27.04/4.46 | | GROUND_INST: instantiating (105) with all_52_1, simplifying with (23) gives: % 27.04/4.46 | | (106) ~ element(all_52_1, all_76_0) | ? [v0: $i] : (interior(all_52_4, % 27.04/4.46 | | all_52_1) = v0 & $i(v0) & ! [v1: $i] : ( ~ (v0 = all_52_1) | % 27.04/4.46 | | ~ $i(v1) | ~ element(v1, all_375_0) | open_subset(all_52_1, % 27.04/4.46 | | all_52_4)) & ! [v1: $i] : ( ~ $i(v1) | ~ open_subset(v1, % 27.04/4.46 | | all_40_0) | ~ element(v1, all_375_0) | interior(all_40_0, % 27.04/4.46 | | v1) = v1)) % 27.04/4.46 | | % 27.04/4.46 | | GROUND_INST: instantiating (103) with all_52_1, simplifying with (23) gives: % 27.04/4.46 | | (107) ~ element(all_52_1, all_76_0) | ? [v0: $i] : (interior(all_52_4, % 27.04/4.46 | | all_52_1) = v0 & $i(v0) & ! [v1: $i] : ( ~ (v0 = all_52_1) | % 27.04/4.46 | | ~ $i(v1) | ~ element(v1, all_372_0) | open_subset(all_52_1, % 27.04/4.46 | | all_52_4)) & ! [v1: $i] : ( ~ $i(v1) | ~ open_subset(v1, % 27.04/4.46 | | all_52_4) | ~ element(v1, all_372_0) | interior(all_52_4, % 27.04/4.46 | | v1) = v1)) % 27.04/4.46 | | % 27.04/4.46 | | GROUND_INST: instantiating (60) with all_52_1, simplifying with (23) gives: % 27.04/4.46 | | (108) ~ element(all_52_1, all_76_0) | ? [v0: $i] : (interior(all_52_4, % 27.04/4.46 | | all_52_1) = v0 & $i(v0) & ! [v1: $i] : ( ~ (v0 = all_52_1) | % 27.04/4.46 | | ~ $i(v1) | ~ element(v1, all_85_0) | open_subset(all_52_1, % 27.04/4.46 | | all_52_4)) & ! [v1: $i] : ( ~ $i(v1) | ~ open_subset(v1, % 27.04/4.46 | | all_40_0) | ~ element(v1, all_85_0) | interior(all_40_0, v1) % 27.04/4.46 | | = v1)) % 27.04/4.46 | | % 27.04/4.46 | | GROUND_INST: instantiating (55) with all_52_1, simplifying with (23) gives: % 27.04/4.46 | | (109) ~ element(all_52_1, all_76_0) | ? [v0: $i] : (interior(all_52_4, % 27.04/4.46 | | all_52_1) = v0 & $i(v0) & ! [v1: $i] : ( ~ (v0 = all_52_1) | % 27.04/4.46 | | ~ $i(v1) | ~ element(v1, all_82_0) | open_subset(all_52_1, % 27.04/4.46 | | all_52_4)) & ! [v1: $i] : ( ~ $i(v1) | ~ open_subset(v1, % 27.04/4.46 | | all_52_4) | ~ element(v1, all_82_0) | interior(all_52_4, v1) % 27.04/4.46 | | = v1)) % 27.04/4.46 | | % 27.04/4.46 | | GROUND_INST: instantiating (37) with all_52_0, all_52_1, simplifying with % 27.04/4.46 | | (23), (24) gives: % 27.04/4.46 | | (110) ~ element(all_52_0, all_67_1) | ~ element(all_52_1, all_67_0) | % 27.04/4.46 | | ? [v0: $i] : (interior(all_52_4, all_52_1) = v0 & $i(v0) & ( ~ % 27.04/4.46 | | point_neighbourhood(all_52_1, all_52_4, all_52_0) | % 27.04/4.46 | | in(all_52_0, v0)) & ( ~ in(all_52_0, v0) | % 27.04/4.46 | | point_neighbourhood(all_52_1, all_52_4, all_52_0))) % 27.04/4.46 | | % 27.04/4.46 | | BETA: splitting (110) gives: % 27.04/4.46 | | % 27.04/4.46 | | Case 1: % 27.04/4.46 | | | % 27.04/4.46 | | | (111) ~ element(all_52_0, all_67_1) % 27.04/4.46 | | | % 27.04/4.46 | | | REDUCE: (72), (111) imply: % 27.04/4.46 | | | (112) ~ element(all_52_0, all_52_3) % 27.04/4.46 | | | % 27.04/4.46 | | | PRED_UNIFY: (18), (112) imply: % 27.04/4.46 | | | (113) $false % 27.04/4.46 | | | % 27.04/4.46 | | | CLOSE: (113) is inconsistent. % 27.04/4.46 | | | % 27.04/4.46 | | Case 2: % 27.04/4.46 | | | % 27.04/4.46 | | | (114) ~ element(all_52_1, all_67_0) | ? [v0: $i] : % 27.04/4.46 | | | (interior(all_52_4, all_52_1) = v0 & $i(v0) & ( ~ % 27.04/4.46 | | | point_neighbourhood(all_52_1, all_52_4, all_52_0) | % 27.04/4.46 | | | in(all_52_0, v0)) & ( ~ in(all_52_0, v0) | % 27.04/4.46 | | | point_neighbourhood(all_52_1, all_52_4, all_52_0))) % 27.04/4.46 | | | % 27.04/4.46 | | | BETA: splitting (109) gives: % 27.04/4.46 | | | % 27.04/4.46 | | | Case 1: % 27.04/4.46 | | | | % 27.04/4.46 | | | | (115) ~ element(all_52_1, all_76_0) % 27.04/4.46 | | | | % 27.04/4.46 | | | | REDUCE: (81), (115) imply: % 27.04/4.46 | | | | (116) ~ element(all_52_1, all_52_2) % 27.04/4.46 | | | | % 27.04/4.46 | | | | PRED_UNIFY: (17), (116) imply: % 27.04/4.46 | | | | (117) $false % 27.04/4.46 | | | | % 27.04/4.46 | | | | CLOSE: (117) is inconsistent. % 27.04/4.46 | | | | % 27.04/4.46 | | | Case 2: % 27.04/4.46 | | | | % 27.04/4.46 | | | | (118) element(all_52_1, all_76_0) % 27.04/4.46 | | | | (119) ? [v0: $i] : (interior(all_52_4, all_52_1) = v0 & $i(v0) & ! % 27.04/4.46 | | | | [v1: $i] : ( ~ (v0 = all_52_1) | ~ $i(v1) | ~ element(v1, % 27.04/4.46 | | | | all_82_0) | open_subset(all_52_1, all_52_4)) & ! [v1: % 27.04/4.46 | | | | $i] : ( ~ $i(v1) | ~ open_subset(v1, all_52_4) | ~ % 27.04/4.46 | | | | element(v1, all_82_0) | interior(all_52_4, v1) = v1)) % 27.04/4.46 | | | | % 27.04/4.46 | | | | DELTA: instantiating (119) with fresh symbol all_435_0 gives: % 27.04/4.47 | | | | (120) interior(all_52_4, all_52_1) = all_435_0 & $i(all_435_0) & ! % 27.04/4.47 | | | | [v0: $i] : ( ~ (all_435_0 = all_52_1) | ~ $i(v0) | ~ % 27.04/4.47 | | | | element(v0, all_82_0) | open_subset(all_52_1, all_52_4)) & ! % 27.04/4.47 | | | | [v0: $i] : ( ~ $i(v0) | ~ open_subset(v0, all_52_4) | ~ % 27.04/4.47 | | | | element(v0, all_82_0) | interior(all_52_4, v0) = v0) % 27.04/4.47 | | | | % 27.04/4.47 | | | | ALPHA: (120) implies: % 27.04/4.47 | | | | (121) interior(all_52_4, all_52_1) = all_435_0 % 27.04/4.47 | | | | (122) ! [v0: $i] : ( ~ $i(v0) | ~ open_subset(v0, all_52_4) | ~ % 27.04/4.47 | | | | element(v0, all_82_0) | interior(all_52_4, v0) = v0) % 27.04/4.47 | | | | % 27.04/4.47 | | | | GROUND_INST: instantiating (122) with all_52_1, simplifying with (21), % 27.04/4.47 | | | | (23) gives: % 27.04/4.47 | | | | (123) ~ element(all_52_1, all_82_0) | interior(all_52_4, all_52_1) = % 27.04/4.47 | | | | all_52_1 % 27.04/4.47 | | | | % 27.04/4.47 | | | | BETA: splitting (108) gives: % 27.04/4.47 | | | | % 27.04/4.47 | | | | Case 1: % 27.04/4.47 | | | | | % 27.04/4.47 | | | | | (124) ~ element(all_52_1, all_76_0) % 27.04/4.47 | | | | | % 27.04/4.47 | | | | | REDUCE: (81), (124) imply: % 27.04/4.47 | | | | | (125) ~ element(all_52_1, all_52_2) % 27.04/4.47 | | | | | % 27.04/4.47 | | | | | PRED_UNIFY: (17), (125) imply: % 27.04/4.47 | | | | | (126) $false % 27.04/4.47 | | | | | % 27.04/4.47 | | | | | CLOSE: (126) is inconsistent. % 27.04/4.47 | | | | | % 27.04/4.47 | | | | Case 2: % 27.04/4.47 | | | | | % 27.04/4.47 | | | | | (127) ? [v0: $i] : (interior(all_52_4, all_52_1) = v0 & $i(v0) & % 27.04/4.47 | | | | | ! [v1: $i] : ( ~ (v0 = all_52_1) | ~ $i(v1) | ~ % 27.04/4.47 | | | | | element(v1, all_85_0) | open_subset(all_52_1, all_52_4)) % 27.04/4.47 | | | | | & ! [v1: $i] : ( ~ $i(v1) | ~ open_subset(v1, all_40_0) | % 27.04/4.47 | | | | | ~ element(v1, all_85_0) | interior(all_40_0, v1) = v1)) % 27.04/4.47 | | | | | % 27.04/4.47 | | | | | DELTA: instantiating (127) with fresh symbol all_441_0 gives: % 27.04/4.47 | | | | | (128) interior(all_52_4, all_52_1) = all_441_0 & $i(all_441_0) & ! % 27.04/4.47 | | | | | [v0: $i] : ( ~ (all_441_0 = all_52_1) | ~ $i(v0) | ~ % 27.04/4.47 | | | | | element(v0, all_85_0) | open_subset(all_52_1, all_52_4)) & % 27.04/4.47 | | | | | ! [v0: $i] : ( ~ $i(v0) | ~ open_subset(v0, all_40_0) | ~ % 27.04/4.47 | | | | | element(v0, all_85_0) | interior(all_40_0, v0) = v0) % 27.04/4.47 | | | | | % 27.04/4.47 | | | | | ALPHA: (128) implies: % 27.04/4.47 | | | | | (129) interior(all_52_4, all_52_1) = all_441_0 % 27.04/4.47 | | | | | % 27.04/4.47 | | | | | BETA: splitting (106) gives: % 27.04/4.47 | | | | | % 27.04/4.47 | | | | | Case 1: % 27.04/4.47 | | | | | | % 27.04/4.47 | | | | | | (130) ~ element(all_52_1, all_76_0) % 27.04/4.47 | | | | | | % 27.04/4.47 | | | | | | REDUCE: (81), (130) imply: % 27.04/4.47 | | | | | | (131) ~ element(all_52_1, all_52_2) % 27.04/4.47 | | | | | | % 27.04/4.47 | | | | | | PRED_UNIFY: (17), (131) imply: % 27.04/4.47 | | | | | | (132) $false % 27.04/4.47 | | | | | | % 27.04/4.47 | | | | | | CLOSE: (132) is inconsistent. % 27.04/4.47 | | | | | | % 27.04/4.47 | | | | | Case 2: % 27.04/4.47 | | | | | | % 27.04/4.47 | | | | | | (133) ? [v0: $i] : (interior(all_52_4, all_52_1) = v0 & $i(v0) & % 27.04/4.47 | | | | | | ! [v1: $i] : ( ~ (v0 = all_52_1) | ~ $i(v1) | ~ % 27.04/4.47 | | | | | | element(v1, all_375_0) | open_subset(all_52_1, % 27.04/4.47 | | | | | | all_52_4)) & ! [v1: $i] : ( ~ $i(v1) | ~ % 27.04/4.47 | | | | | | open_subset(v1, all_40_0) | ~ element(v1, all_375_0) | % 27.04/4.47 | | | | | | interior(all_40_0, v1) = v1)) % 27.04/4.47 | | | | | | % 27.04/4.47 | | | | | | DELTA: instantiating (133) with fresh symbol all_447_0 gives: % 27.04/4.47 | | | | | | (134) interior(all_52_4, all_52_1) = all_447_0 & $i(all_447_0) & % 27.04/4.47 | | | | | | ! [v0: $i] : ( ~ (all_447_0 = all_52_1) | ~ $i(v0) | ~ % 27.04/4.47 | | | | | | element(v0, all_375_0) | open_subset(all_52_1, all_52_4)) % 27.04/4.47 | | | | | | & ! [v0: $i] : ( ~ $i(v0) | ~ open_subset(v0, all_40_0) | % 27.04/4.47 | | | | | | ~ element(v0, all_375_0) | interior(all_40_0, v0) = v0) % 27.04/4.47 | | | | | | % 27.04/4.47 | | | | | | ALPHA: (134) implies: % 27.04/4.47 | | | | | | (135) interior(all_52_4, all_52_1) = all_447_0 % 27.04/4.47 | | | | | | % 27.04/4.47 | | | | | | BETA: splitting (107) gives: % 27.04/4.47 | | | | | | % 27.04/4.47 | | | | | | Case 1: % 27.04/4.47 | | | | | | | % 27.04/4.47 | | | | | | | (136) ~ element(all_52_1, all_76_0) % 27.04/4.47 | | | | | | | % 27.04/4.47 | | | | | | | REDUCE: (81), (136) imply: % 27.04/4.47 | | | | | | | (137) ~ element(all_52_1, all_52_2) % 27.04/4.47 | | | | | | | % 27.04/4.47 | | | | | | | PRED_UNIFY: (17), (137) imply: % 27.04/4.47 | | | | | | | (138) $false % 27.04/4.47 | | | | | | | % 27.04/4.47 | | | | | | | CLOSE: (138) is inconsistent. % 27.04/4.47 | | | | | | | % 27.04/4.47 | | | | | | Case 2: % 27.04/4.47 | | | | | | | % 27.04/4.47 | | | | | | | (139) ? [v0: $i] : (interior(all_52_4, all_52_1) = v0 & $i(v0) % 27.04/4.47 | | | | | | | & ! [v1: $i] : ( ~ (v0 = all_52_1) | ~ $i(v1) | ~ % 27.04/4.47 | | | | | | | element(v1, all_372_0) | open_subset(all_52_1, % 27.04/4.47 | | | | | | | all_52_4)) & ! [v1: $i] : ( ~ $i(v1) | ~ % 27.04/4.47 | | | | | | | open_subset(v1, all_52_4) | ~ element(v1, all_372_0) % 27.04/4.47 | | | | | | | | interior(all_52_4, v1) = v1)) % 27.04/4.47 | | | | | | | % 27.04/4.47 | | | | | | | DELTA: instantiating (139) with fresh symbol all_453_0 gives: % 27.04/4.47 | | | | | | | (140) interior(all_52_4, all_52_1) = all_453_0 & $i(all_453_0) % 27.04/4.47 | | | | | | | & ! [v0: $i] : ( ~ (all_453_0 = all_52_1) | ~ $i(v0) | % 27.04/4.47 | | | | | | | ~ element(v0, all_372_0) | open_subset(all_52_1, % 27.04/4.47 | | | | | | | all_52_4)) & ! [v0: $i] : ( ~ $i(v0) | ~ % 27.04/4.47 | | | | | | | open_subset(v0, all_52_4) | ~ element(v0, all_372_0) | % 27.04/4.47 | | | | | | | interior(all_52_4, v0) = v0) % 27.04/4.47 | | | | | | | % 27.04/4.47 | | | | | | | ALPHA: (140) implies: % 27.04/4.47 | | | | | | | (141) interior(all_52_4, all_52_1) = all_453_0 % 27.04/4.47 | | | | | | | % 27.04/4.47 | | | | | | | BETA: splitting (123) gives: % 27.04/4.47 | | | | | | | % 27.04/4.47 | | | | | | | Case 1: % 27.04/4.47 | | | | | | | | % 27.04/4.47 | | | | | | | | (142) ~ element(all_52_1, all_82_0) % 27.04/4.47 | | | | | | | | % 27.04/4.47 | | | | | | | | REDUCE: (88), (142) imply: % 27.04/4.47 | | | | | | | | (143) ~ element(all_52_1, all_52_2) % 27.04/4.47 | | | | | | | | % 27.04/4.47 | | | | | | | | PRED_UNIFY: (17), (143) imply: % 27.04/4.47 | | | | | | | | (144) $false % 27.04/4.47 | | | | | | | | % 27.04/4.47 | | | | | | | | CLOSE: (144) is inconsistent. % 27.04/4.47 | | | | | | | | % 27.04/4.47 | | | | | | | Case 2: % 27.04/4.47 | | | | | | | | % 27.04/4.47 | | | | | | | | (145) element(all_52_1, all_82_0) % 27.04/4.47 | | | | | | | | (146) interior(all_52_4, all_52_1) = all_52_1 % 27.04/4.47 | | | | | | | | % 27.04/4.47 | | | | | | | | BETA: splitting (114) gives: % 27.04/4.47 | | | | | | | | % 27.04/4.47 | | | | | | | | Case 1: % 27.04/4.47 | | | | | | | | | % 27.04/4.47 | | | | | | | | | (147) ~ element(all_52_1, all_67_0) % 27.04/4.47 | | | | | | | | | % 27.04/4.47 | | | | | | | | | REDUCE: (87), (147) imply: % 27.04/4.47 | | | | | | | | | (148) ~ element(all_52_1, all_52_2) % 27.04/4.47 | | | | | | | | | % 27.04/4.47 | | | | | | | | | PRED_UNIFY: (17), (148) imply: % 27.04/4.47 | | | | | | | | | (149) $false % 27.04/4.47 | | | | | | | | | % 27.04/4.47 | | | | | | | | | CLOSE: (149) is inconsistent. % 27.04/4.47 | | | | | | | | | % 27.04/4.47 | | | | | | | | Case 2: % 27.04/4.47 | | | | | | | | | % 27.04/4.47 | | | | | | | | | (150) ? [v0: $i] : (interior(all_52_4, all_52_1) = v0 & % 27.04/4.47 | | | | | | | | | $i(v0) & ( ~ point_neighbourhood(all_52_1, % 27.04/4.47 | | | | | | | | | all_52_4, all_52_0) | in(all_52_0, v0)) & ( ~ % 27.04/4.47 | | | | | | | | | in(all_52_0, v0) | point_neighbourhood(all_52_1, % 27.04/4.47 | | | | | | | | | all_52_4, all_52_0))) % 27.04/4.47 | | | | | | | | | % 27.04/4.47 | | | | | | | | | DELTA: instantiating (150) with fresh symbol all_611_0 gives: % 27.04/4.47 | | | | | | | | | (151) interior(all_52_4, all_52_1) = all_611_0 & % 27.04/4.47 | | | | | | | | | $i(all_611_0) & ( ~ point_neighbourhood(all_52_1, % 27.04/4.47 | | | | | | | | | all_52_4, all_52_0) | in(all_52_0, all_611_0)) & % 27.04/4.47 | | | | | | | | | ( ~ in(all_52_0, all_611_0) | % 27.04/4.47 | | | | | | | | | point_neighbourhood(all_52_1, all_52_4, all_52_0)) % 27.04/4.47 | | | | | | | | | % 27.04/4.47 | | | | | | | | | ALPHA: (151) implies: % 27.04/4.47 | | | | | | | | | (152) interior(all_52_4, all_52_1) = all_611_0 % 27.04/4.47 | | | | | | | | | (153) ~ in(all_52_0, all_611_0) | % 27.04/4.47 | | | | | | | | | point_neighbourhood(all_52_1, all_52_4, all_52_0) % 27.04/4.47 | | | | | | | | | % 27.04/4.47 | | | | | | | | | BETA: splitting (153) gives: % 27.04/4.47 | | | | | | | | | % 27.04/4.47 | | | | | | | | | Case 1: % 27.04/4.47 | | | | | | | | | | % 27.04/4.47 | | | | | | | | | | (154) ~ in(all_52_0, all_611_0) % 27.04/4.47 | | | | | | | | | | % 27.04/4.48 | | | | | | | | | | GROUND_INST: instantiating (9) with all_52_1, all_441_0, % 27.04/4.48 | | | | | | | | | | all_52_1, all_52_4, simplifying with (129), (146) % 27.04/4.48 | | | | | | | | | | gives: % 27.04/4.48 | | | | | | | | | | (155) all_441_0 = all_52_1 % 27.04/4.48 | | | | | | | | | | % 27.04/4.48 | | | | | | | | | | GROUND_INST: instantiating (9) with all_441_0, all_453_0, % 27.04/4.48 | | | | | | | | | | all_52_1, all_52_4, simplifying with (129), (141) % 27.04/4.48 | | | | | | | | | | gives: % 27.04/4.48 | | | | | | | | | | (156) all_453_0 = all_441_0 % 27.04/4.48 | | | | | | | | | | % 27.04/4.48 | | | | | | | | | | GROUND_INST: instantiating (9) with all_435_0, all_453_0, % 27.04/4.48 | | | | | | | | | | all_52_1, all_52_4, simplifying with (121), (141) % 27.04/4.48 | | | | | | | | | | gives: % 27.04/4.48 | | | | | | | | | | (157) all_453_0 = all_435_0 % 27.04/4.48 | | | | | | | | | | % 27.04/4.48 | | | | | | | | | | GROUND_INST: instantiating (9) with all_453_0, all_611_0, % 27.04/4.48 | | | | | | | | | | all_52_1, all_52_4, simplifying with (141), (152) % 27.04/4.48 | | | | | | | | | | gives: % 27.04/4.48 | | | | | | | | | | (158) all_611_0 = all_453_0 % 27.04/4.48 | | | | | | | | | | % 27.04/4.48 | | | | | | | | | | GROUND_INST: instantiating (9) with all_447_0, all_611_0, % 27.04/4.48 | | | | | | | | | | all_52_1, all_52_4, simplifying with (135), (152) % 27.04/4.48 | | | | | | | | | | gives: % 27.04/4.48 | | | | | | | | | | (159) all_611_0 = all_447_0 % 27.04/4.48 | | | | | | | | | | % 27.04/4.48 | | | | | | | | | | COMBINE_EQS: (158), (159) imply: % 27.04/4.48 | | | | | | | | | | (160) all_453_0 = all_447_0 % 27.04/4.48 | | | | | | | | | | % 27.04/4.48 | | | | | | | | | | SIMP: (160) implies: % 27.04/4.48 | | | | | | | | | | (161) all_453_0 = all_447_0 % 27.04/4.48 | | | | | | | | | | % 27.04/4.48 | | | | | | | | | | COMBINE_EQS: (157), (161) imply: % 27.04/4.48 | | | | | | | | | | (162) all_447_0 = all_435_0 % 27.04/4.48 | | | | | | | | | | % 27.04/4.48 | | | | | | | | | | COMBINE_EQS: (156), (161) imply: % 27.04/4.48 | | | | | | | | | | (163) all_447_0 = all_441_0 % 27.04/4.48 | | | | | | | | | | % 27.04/4.48 | | | | | | | | | | COMBINE_EQS: (162), (163) imply: % 27.04/4.48 | | | | | | | | | | (164) all_441_0 = all_435_0 % 27.04/4.48 | | | | | | | | | | % 27.04/4.48 | | | | | | | | | | SIMP: (164) implies: % 27.04/4.48 | | | | | | | | | | (165) all_441_0 = all_435_0 % 27.04/4.48 | | | | | | | | | | % 27.04/4.48 | | | | | | | | | | COMBINE_EQS: (155), (165) imply: % 27.04/4.48 | | | | | | | | | | (166) all_435_0 = all_52_1 % 27.04/4.48 | | | | | | | | | | % 27.04/4.48 | | | | | | | | | | COMBINE_EQS: (162), (166) imply: % 27.04/4.48 | | | | | | | | | | (167) all_447_0 = all_52_1 % 27.04/4.48 | | | | | | | | | | % 27.04/4.48 | | | | | | | | | | COMBINE_EQS: (159), (167) imply: % 27.04/4.48 | | | | | | | | | | (168) all_611_0 = all_52_1 % 27.04/4.48 | | | | | | | | | | % 27.04/4.48 | | | | | | | | | | REDUCE: (154), (168) imply: % 27.04/4.48 | | | | | | | | | | (169) ~ in(all_52_0, all_52_1) % 27.04/4.48 | | | | | | | | | | % 27.04/4.48 | | | | | | | | | | PRED_UNIFY: (16), (169) imply: % 27.04/4.48 | | | | | | | | | | (170) $false % 27.04/4.48 | | | | | | | | | | % 27.04/4.48 | | | | | | | | | | CLOSE: (170) is inconsistent. % 27.04/4.48 | | | | | | | | | | % 27.04/4.48 | | | | | | | | | Case 2: % 27.04/4.48 | | | | | | | | | | % 27.04/4.48 | | | | | | | | | | (171) point_neighbourhood(all_52_1, all_52_4, all_52_0) % 27.04/4.48 | | | | | | | | | | % 27.04/4.48 | | | | | | | | | | PRED_UNIFY: (15), (171) imply: % 27.04/4.48 | | | | | | | | | | (172) $false % 27.04/4.48 | | | | | | | | | | % 27.04/4.48 | | | | | | | | | | CLOSE: (172) is inconsistent. % 27.04/4.48 | | | | | | | | | | % 27.04/4.48 | | | | | | | | | End of split % 27.04/4.48 | | | | | | | | | % 27.04/4.48 | | | | | | | | End of split % 27.04/4.48 | | | | | | | | % 27.04/4.48 | | | | | | | End of split % 27.04/4.48 | | | | | | | % 27.04/4.48 | | | | | | End of split % 27.04/4.48 | | | | | | % 27.04/4.48 | | | | | End of split % 27.04/4.48 | | | | | % 27.04/4.48 | | | | End of split % 27.04/4.48 | | | | % 27.04/4.48 | | | End of split % 27.04/4.48 | | | % 27.04/4.48 | | End of split % 27.04/4.48 | | % 27.04/4.48 | End of split % 27.04/4.48 | % 27.04/4.48 End of proof % 27.04/4.48 % SZS output end Proof for theBenchmark % 27.04/4.48 % 27.04/4.48 3856ms %------------------------------------------------------------------------------