%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SEU323+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 : n015.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 17:44:05 EDT 2023 % Result : Theorem 9.75s 2.91s % Output : Proof 12.84s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.13 % Problem : SEU323+1 : TPTP v8.1.2. Released v3.3.0. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.12/0.34 % Computer : n015.cluster.edu % 0.12/0.34 % Model : x86_64 x86_64 % 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.34 % Memory : 8042.1875MB % 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.34 % CPULimit : 300 % 0.12/0.34 % WCLimit : 300 % 0.12/0.34 % DateTime : Thu Aug 24 01:34:20 EDT 2023 % 0.12/0.34 % CPUTime : % 0.17/0.58 ________ _____ % 0.17/0.58 ___ __ \_________(_)________________________________ % 0.17/0.58 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.17/0.58 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.17/0.58 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.17/0.58 % 0.17/0.58 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.17/0.58 (2023-06-19) % 0.17/0.58 % 0.17/0.58 (c) Philipp Rümmer, 2009-2023 % 0.17/0.58 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.17/0.58 Amanda Stjerna. % 0.17/0.58 Free software under BSD-3-Clause. % 0.17/0.58 % 0.17/0.58 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.17/0.58 % 0.17/0.58 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.17/0.59 Running up to 7 provers in parallel. % 0.17/0.65 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.17/0.65 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.17/0.65 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.17/0.65 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.17/0.65 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.17/0.65 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.17/0.65 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.05/1.07 Prover 4: Preprocessing ... % 2.05/1.08 Prover 1: Preprocessing ... % 2.41/1.17 Prover 3: Preprocessing ... % 2.41/1.17 Prover 6: Preprocessing ... % 2.41/1.17 Prover 2: Preprocessing ... % 2.41/1.17 Prover 0: Preprocessing ... % 2.41/1.17 Prover 5: Preprocessing ... % 3.53/1.74 Prover 1: Warning: ignoring some quantifiers % 4.66/1.81 Prover 3: Warning: ignoring some quantifiers % 4.66/1.81 Prover 6: Proving ... % 4.82/1.84 Prover 1: Constructing countermodel ... % 4.82/1.84 Prover 3: Constructing countermodel ... % 4.92/1.85 Prover 2: Proving ... % 4.92/1.89 Prover 5: Proving ... % 5.23/1.95 Prover 4: Warning: ignoring some quantifiers % 5.40/2.03 Prover 4: Constructing countermodel ... % 6.33/2.15 Prover 0: Proving ... % 6.33/2.24 Prover 3: gave up % 6.33/2.29 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 6.33/2.33 Prover 7: Preprocessing ... % 7.55/2.46 Prover 7: Warning: ignoring some quantifiers % 8.02/2.48 Prover 7: Constructing countermodel ... % 8.33/2.58 Prover 1: gave up % 8.33/2.60 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 8.79/2.64 Prover 8: Preprocessing ... % 9.15/2.76 Prover 8: Warning: ignoring some quantifiers % 9.64/2.78 Prover 8: Constructing countermodel ... % 9.75/2.91 Prover 0: proved (2307ms) % 9.75/2.91 % 9.75/2.91 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 9.75/2.91 % 9.75/2.92 Prover 6: stopped % 9.75/2.93 Prover 5: stopped % 9.75/2.95 Prover 2: stopped % 9.75/2.96 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 9.75/2.96 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 9.75/2.96 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 9.75/2.96 Prover 10: Preprocessing ... % 9.75/2.96 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 9.75/2.96 Prover 11: Preprocessing ... % 9.98/3.01 Prover 13: Preprocessing ... % 9.98/3.02 Prover 16: Preprocessing ... % 9.98/3.04 Prover 10: Warning: ignoring some quantifiers % 9.98/3.07 Prover 10: Constructing countermodel ... % 11.19/3.10 Prover 16: Warning: ignoring some quantifiers % 11.19/3.11 Prover 16: Constructing countermodel ... % 11.19/3.13 Prover 13: Warning: ignoring some quantifiers % 11.19/3.16 Prover 13: Constructing countermodel ... % 11.62/3.18 Prover 8: gave up % 11.62/3.20 Prover 10: gave up % 11.62/3.20 Prover 11: Warning: ignoring some quantifiers % 11.62/3.20 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085 % 11.62/3.21 Prover 11: Constructing countermodel ... % 11.62/3.22 Prover 19: Preprocessing ... % 11.62/3.25 Prover 7: Found proof (size 86) % 11.62/3.25 Prover 7: proved (959ms) % 11.62/3.25 Prover 11: stopped % 11.62/3.25 Prover 16: stopped % 11.62/3.25 Prover 4: stopped % 11.62/3.25 Prover 13: stopped % 12.34/3.31 Prover 19: Warning: ignoring some quantifiers % 12.34/3.32 Prover 19: Constructing countermodel ... % 12.34/3.32 Prover 19: stopped % 12.34/3.32 % 12.34/3.32 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 12.34/3.32 % 12.50/3.34 % SZS output start Proof for theBenchmark % 12.50/3.34 Assumptions after simplification: % 12.50/3.34 --------------------------------- % 12.50/3.34 % 12.50/3.34 (d1_tops_1) % 12.50/3.37 ! [v0: $i] : ! [v1: $i] : ( ~ (the_carrier(v0) = v1) | ~ $i(v0) | ~ % 12.50/3.37 top_str(v0) | ? [v2: $i] : (powerset(v1) = v2 & $i(v2) & ! [v3: $i] : ! % 12.50/3.37 [v4: $i] : ( ~ (interior(v0, v3) = v4) | ~ $i(v3) | ~ element(v3, v2) | % 12.50/3.37 ? [v5: $i] : ? [v6: $i] : (topstr_closure(v0, v5) = v6 & % 12.50/3.37 subset_complement(v1, v6) = v4 & subset_complement(v1, v3) = v5 & % 12.50/3.37 $i(v6) & $i(v5) & $i(v4))) & ! [v3: $i] : ! [v4: $i] : ( ~ % 12.50/3.37 (subset_complement(v1, v3) = v4) | ~ $i(v3) | ~ element(v3, v2) | ? % 12.50/3.37 [v5: $i] : ? [v6: $i] : (interior(v0, v3) = v5 & topstr_closure(v0, v4) % 12.50/3.37 = v6 & subset_complement(v1, v6) = v5 & $i(v6) & $i(v5))))) % 12.50/3.37 % 12.50/3.37 (dt_k1_tops_1) % 12.50/3.38 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (interior(v0, v1) = v2) | ~ % 12.50/3.38 $i(v1) | ~ $i(v0) | ~ top_str(v0) | ? [v3: $i] : ? [v4: $i] : % 12.50/3.38 (the_carrier(v0) = v3 & powerset(v3) = v4 & $i(v4) & $i(v3) & ( ~ % 12.50/3.38 element(v1, v4) | element(v2, v4)))) % 12.50/3.38 % 12.50/3.38 (dt_k3_subset_1) % 12.50/3.38 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (subset_complement(v0, v1) = v2) % 12.50/3.38 | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : (powerset(v0) = v3 & $i(v3) & ( ~ % 12.50/3.38 element(v1, v3) | element(v2, v3)))) % 12.50/3.38 % 12.50/3.38 (dt_k6_pre_topc) % 12.50/3.38 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (topstr_closure(v0, v1) = v2) | % 12.50/3.38 ~ $i(v1) | ~ $i(v0) | ~ top_str(v0) | ? [v3: $i] : ? [v4: $i] : % 12.50/3.38 (the_carrier(v0) = v3 & powerset(v3) = v4 & $i(v4) & $i(v3) & ( ~ % 12.50/3.38 element(v1, v4) | element(v2, v4)))) % 12.50/3.38 % 12.50/3.38 (fc2_tops_1) % 12.50/3.38 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (topstr_closure(v0, v1) = v2) | % 12.50/3.39 ~ $i(v1) | ~ $i(v0) | ~ top_str(v0) | ~ topological_space(v0) | % 12.50/3.39 closed_subset(v2, v0) | ? [v3: $i] : ? [v4: $i] : (the_carrier(v0) = v3 & % 12.50/3.39 powerset(v3) = v4 & $i(v4) & $i(v3) & ~ element(v1, v4))) % 12.50/3.39 % 12.50/3.39 (fc3_tops_1) % 12.50/3.39 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (the_carrier(v0) = % 12.50/3.39 v2) | ~ (subset_complement(v2, v1) = v3) | ~ $i(v1) | ~ $i(v0) | ~ % 12.50/3.39 closed_subset(v1, v0) | ~ top_str(v0) | ~ topological_space(v0) | % 12.50/3.39 open_subset(v3, v0) | ? [v4: $i] : (powerset(v2) = v4 & $i(v4) & ~ % 12.50/3.39 element(v1, v4))) % 12.50/3.39 % 12.50/3.39 (rc1_tops_1) % 12.50/3.39 ! [v0: $i] : ! [v1: $i] : ( ~ (the_carrier(v0) = v1) | ~ $i(v0) | ~ % 12.50/3.39 top_str(v0) | ~ topological_space(v0) | ? [v2: $i] : ? [v3: $i] : % 12.50/3.39 (powerset(v1) = v2 & $i(v3) & $i(v2) & open_subset(v3, v0) & element(v3, % 12.50/3.39 v2))) % 12.50/3.39 % 12.50/3.39 (rc6_pre_topc) % 12.50/3.39 ! [v0: $i] : ! [v1: $i] : ( ~ (the_carrier(v0) = v1) | ~ $i(v0) | ~ % 12.50/3.39 top_str(v0) | ~ topological_space(v0) | ? [v2: $i] : ? [v3: $i] : % 12.50/3.39 (powerset(v1) = v2 & $i(v3) & $i(v2) & element(v3, v2) & closed_subset(v3, % 12.50/3.39 v0))) % 12.50/3.39 % 12.50/3.39 (t51_tops_1) % 12.50/3.39 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 12.50/3.39 (interior(v0, v3) = v4 & the_carrier(v0) = v1 & powerset(v1) = v2 & $i(v4) & % 12.50/3.39 $i(v3) & $i(v2) & $i(v1) & $i(v0) & element(v3, v2) & top_str(v0) & % 12.50/3.39 topological_space(v0) & ~ open_subset(v4, v0)) % 12.50/3.39 % 12.50/3.39 (function-axioms) % 12.50/3.40 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 12.50/3.40 (interior(v3, v2) = v1) | ~ (interior(v3, v2) = v0)) & ! [v0: $i] : ! % 12.50/3.40 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (topstr_closure(v3, v2) = % 12.84/3.40 v1) | ~ (topstr_closure(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 12.84/3.40 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (subset_complement(v3, v2) = v1) | ~ % 12.84/3.40 (subset_complement(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 12.84/3.40 : (v1 = v0 | ~ (the_carrier(v2) = v1) | ~ (the_carrier(v2) = v0)) & ! [v0: % 12.84/3.40 $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ % 12.84/3.40 (powerset(v2) = v0)) % 12.84/3.40 % 12.84/3.40 Further assumptions not needed in the proof: % 12.84/3.40 -------------------------------------------- % 12.84/3.40 dt_k1_zfmisc_1, dt_l1_pre_topc, dt_l1_struct_0, dt_m1_subset_1, dt_u1_struct_0, % 12.84/3.40 existence_l1_pre_topc, existence_l1_struct_0, existence_m1_subset_1, fc4_tops_1, % 12.84/3.40 involutiveness_k3_subset_1, reflexivity_r1_tarski, t3_subset % 12.84/3.40 % 12.84/3.40 Those formulas are unsatisfiable: % 12.84/3.40 --------------------------------- % 12.84/3.40 % 12.84/3.40 Begin of proof % 12.84/3.40 | % 12.84/3.40 | ALPHA: (function-axioms) implies: % 12.84/3.40 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (powerset(v2) = % 12.84/3.40 | v1) | ~ (powerset(v2) = v0)) % 12.84/3.40 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 12.84/3.40 | (the_carrier(v2) = v1) | ~ (the_carrier(v2) = v0)) % 12.84/3.40 | % 12.84/3.40 | DELTA: instantiating (t51_tops_1) with fresh symbols all_21_0, all_21_1, % 12.84/3.40 | all_21_2, all_21_3, all_21_4 gives: % 12.84/3.40 | (3) interior(all_21_4, all_21_1) = all_21_0 & the_carrier(all_21_4) = % 12.84/3.40 | all_21_3 & powerset(all_21_3) = all_21_2 & $i(all_21_0) & $i(all_21_1) % 12.84/3.40 | & $i(all_21_2) & $i(all_21_3) & $i(all_21_4) & element(all_21_1, % 12.84/3.40 | all_21_2) & top_str(all_21_4) & topological_space(all_21_4) & ~ % 12.84/3.40 | open_subset(all_21_0, all_21_4) % 12.84/3.41 | % 12.84/3.41 | ALPHA: (3) implies: % 12.84/3.41 | (4) ~ open_subset(all_21_0, all_21_4) % 12.84/3.41 | (5) topological_space(all_21_4) % 12.84/3.41 | (6) top_str(all_21_4) % 12.84/3.41 | (7) element(all_21_1, all_21_2) % 12.84/3.41 | (8) $i(all_21_4) % 12.84/3.41 | (9) $i(all_21_1) % 12.84/3.41 | (10) powerset(all_21_3) = all_21_2 % 12.84/3.41 | (11) the_carrier(all_21_4) = all_21_3 % 12.84/3.41 | (12) interior(all_21_4, all_21_1) = all_21_0 % 12.84/3.41 | % 12.84/3.41 | GROUND_INST: instantiating (rc1_tops_1) with all_21_4, all_21_3, simplifying % 12.84/3.41 | with (5), (6), (8), (11) gives: % 12.84/3.41 | (13) ? [v0: $i] : ? [v1: $i] : (powerset(all_21_3) = v0 & $i(v1) & $i(v0) % 12.84/3.41 | & open_subset(v1, all_21_4) & element(v1, v0)) % 12.84/3.41 | % 12.84/3.41 | GROUND_INST: instantiating (rc6_pre_topc) with all_21_4, all_21_3, simplifying % 12.84/3.41 | with (5), (6), (8), (11) gives: % 12.84/3.41 | (14) ? [v0: $i] : ? [v1: $i] : (powerset(all_21_3) = v0 & $i(v1) & $i(v0) % 12.84/3.41 | & element(v1, v0) & closed_subset(v1, all_21_4)) % 12.84/3.41 | % 12.84/3.41 | GROUND_INST: instantiating (d1_tops_1) with all_21_4, all_21_3, simplifying % 12.84/3.41 | with (6), (8), (11) gives: % 12.84/3.41 | (15) ? [v0: $i] : (powerset(all_21_3) = v0 & $i(v0) & ! [v1: $i] : ! % 12.84/3.41 | [v2: $i] : ( ~ (interior(all_21_4, v1) = v2) | ~ $i(v1) | ~ % 12.84/3.41 | element(v1, v0) | ? [v3: $i] : ? [v4: $i] : % 12.84/3.41 | (topstr_closure(all_21_4, v3) = v4 & subset_complement(all_21_3, % 12.84/3.41 | v4) = v2 & subset_complement(all_21_3, v1) = v3 & $i(v4) & % 12.84/3.41 | $i(v3) & $i(v2))) & ! [v1: $i] : ! [v2: $i] : ( ~ % 12.84/3.41 | (subset_complement(all_21_3, v1) = v2) | ~ $i(v1) | ~ % 12.84/3.41 | element(v1, v0) | ? [v3: $i] : ? [v4: $i] : (interior(all_21_4, % 12.84/3.41 | v1) = v3 & topstr_closure(all_21_4, v2) = v4 & % 12.84/3.41 | subset_complement(all_21_3, v4) = v3 & $i(v4) & $i(v3)))) % 12.84/3.41 | % 12.84/3.42 | GROUND_INST: instantiating (dt_k1_tops_1) with all_21_4, all_21_1, all_21_0, % 12.84/3.42 | simplifying with (6), (8), (9), (12) gives: % 12.84/3.42 | (16) ? [v0: $i] : ? [v1: $i] : (the_carrier(all_21_4) = v0 & powerset(v0) % 12.84/3.42 | = v1 & $i(v1) & $i(v0) & ( ~ element(all_21_1, v1) | % 12.84/3.42 | element(all_21_0, v1))) % 12.84/3.42 | % 12.84/3.42 | DELTA: instantiating (14) with fresh symbols all_29_0, all_29_1 gives: % 12.84/3.42 | (17) powerset(all_21_3) = all_29_1 & $i(all_29_0) & $i(all_29_1) & % 12.84/3.42 | element(all_29_0, all_29_1) & closed_subset(all_29_0, all_21_4) % 12.84/3.42 | % 12.84/3.42 | ALPHA: (17) implies: % 12.84/3.42 | (18) powerset(all_21_3) = all_29_1 % 12.84/3.42 | % 12.84/3.42 | DELTA: instantiating (13) with fresh symbols all_31_0, all_31_1 gives: % 12.84/3.42 | (19) powerset(all_21_3) = all_31_1 & $i(all_31_0) & $i(all_31_1) & % 12.84/3.42 | open_subset(all_31_0, all_21_4) & element(all_31_0, all_31_1) % 12.84/3.42 | % 12.84/3.42 | ALPHA: (19) implies: % 12.84/3.42 | (20) powerset(all_21_3) = all_31_1 % 12.84/3.42 | % 12.84/3.42 | DELTA: instantiating (16) with fresh symbols all_33_0, all_33_1 gives: % 12.84/3.42 | (21) the_carrier(all_21_4) = all_33_1 & powerset(all_33_1) = all_33_0 & % 12.84/3.42 | $i(all_33_0) & $i(all_33_1) & ( ~ element(all_21_1, all_33_0) | % 12.84/3.42 | element(all_21_0, all_33_0)) % 12.84/3.42 | % 12.84/3.42 | ALPHA: (21) implies: % 12.84/3.42 | (22) $i(all_33_1) % 12.84/3.42 | (23) the_carrier(all_21_4) = all_33_1 % 12.84/3.42 | % 12.84/3.42 | DELTA: instantiating (15) with fresh symbol all_35_0 gives: % 12.84/3.42 | (24) powerset(all_21_3) = all_35_0 & $i(all_35_0) & ! [v0: $i] : ! [v1: % 12.84/3.42 | $i] : ( ~ (interior(all_21_4, v0) = v1) | ~ $i(v0) | ~ element(v0, % 12.84/3.42 | all_35_0) | ? [v2: $i] : ? [v3: $i] : (topstr_closure(all_21_4, % 12.84/3.42 | v2) = v3 & subset_complement(all_21_3, v3) = v1 & % 12.84/3.42 | subset_complement(all_21_3, v0) = v2 & $i(v3) & $i(v2) & $i(v1))) % 12.84/3.42 | & ! [v0: $i] : ! [v1: $i] : ( ~ (subset_complement(all_21_3, v0) = % 12.84/3.42 | v1) | ~ $i(v0) | ~ element(v0, all_35_0) | ? [v2: $i] : ? [v3: % 12.84/3.42 | $i] : (interior(all_21_4, v0) = v2 & topstr_closure(all_21_4, v1) % 12.84/3.42 | = v3 & subset_complement(all_21_3, v3) = v2 & $i(v3) & $i(v2))) % 12.84/3.42 | % 12.84/3.42 | ALPHA: (24) implies: % 12.84/3.42 | (25) powerset(all_21_3) = all_35_0 % 12.84/3.42 | (26) ! [v0: $i] : ! [v1: $i] : ( ~ (interior(all_21_4, v0) = v1) | ~ % 12.84/3.42 | $i(v0) | ~ element(v0, all_35_0) | ? [v2: $i] : ? [v3: $i] : % 12.84/3.42 | (topstr_closure(all_21_4, v2) = v3 & subset_complement(all_21_3, v3) % 12.84/3.42 | = v1 & subset_complement(all_21_3, v0) = v2 & $i(v3) & $i(v2) & % 12.84/3.42 | $i(v1))) % 12.84/3.42 | % 12.84/3.42 | GROUND_INST: instantiating (26) with all_21_1, all_21_0, simplifying with (9), % 12.84/3.42 | (12) gives: % 12.84/3.42 | (27) ~ element(all_21_1, all_35_0) | ? [v0: $i] : ? [v1: $i] : % 12.84/3.43 | (topstr_closure(all_21_4, v0) = v1 & subset_complement(all_21_3, v1) = % 12.84/3.43 | all_21_0 & subset_complement(all_21_3, all_21_1) = v0 & $i(v1) & % 12.84/3.43 | $i(v0) & $i(all_21_0)) % 12.84/3.43 | % 12.84/3.43 | GROUND_INST: instantiating (1) with all_21_2, all_31_1, all_21_3, simplifying % 12.84/3.43 | with (10), (20) gives: % 12.84/3.43 | (28) all_31_1 = all_21_2 % 12.84/3.43 | % 12.84/3.43 | GROUND_INST: instantiating (1) with all_31_1, all_35_0, all_21_3, simplifying % 12.84/3.43 | with (20), (25) gives: % 12.84/3.43 | (29) all_35_0 = all_31_1 % 12.84/3.43 | % 12.84/3.43 | GROUND_INST: instantiating (1) with all_29_1, all_35_0, all_21_3, simplifying % 12.84/3.43 | with (18), (25) gives: % 12.84/3.43 | (30) all_35_0 = all_29_1 % 12.84/3.43 | % 12.84/3.43 | GROUND_INST: instantiating (2) with all_21_3, all_33_1, all_21_4, simplifying % 12.84/3.43 | with (11), (23) gives: % 12.84/3.43 | (31) all_33_1 = all_21_3 % 12.84/3.43 | % 12.84/3.43 | COMBINE_EQS: (29), (30) imply: % 12.84/3.43 | (32) all_31_1 = all_29_1 % 12.84/3.43 | % 12.84/3.43 | SIMP: (32) implies: % 12.84/3.43 | (33) all_31_1 = all_29_1 % 12.84/3.43 | % 12.84/3.43 | COMBINE_EQS: (28), (33) imply: % 12.84/3.43 | (34) all_29_1 = all_21_2 % 12.84/3.43 | % 12.84/3.43 | COMBINE_EQS: (30), (34) imply: % 12.84/3.43 | (35) all_35_0 = all_21_2 % 12.84/3.43 | % 12.84/3.43 | REDUCE: (22), (31) imply: % 12.84/3.43 | (36) $i(all_21_3) % 12.84/3.43 | % 12.84/3.43 | BETA: splitting (27) gives: % 12.84/3.43 | % 12.84/3.43 | Case 1: % 12.84/3.43 | | % 12.84/3.43 | | (37) ~ element(all_21_1, all_35_0) % 12.84/3.43 | | % 12.84/3.43 | | REDUCE: (35), (37) imply: % 12.84/3.43 | | (38) ~ element(all_21_1, all_21_2) % 12.84/3.43 | | % 12.84/3.43 | | PRED_UNIFY: (7), (38) imply: % 12.84/3.43 | | (39) $false % 12.84/3.43 | | % 12.84/3.43 | | CLOSE: (39) is inconsistent. % 12.84/3.43 | | % 12.84/3.43 | Case 2: % 12.84/3.43 | | % 12.84/3.43 | | (40) element(all_21_1, all_35_0) % 12.84/3.43 | | (41) ? [v0: $i] : ? [v1: $i] : (topstr_closure(all_21_4, v0) = v1 & % 12.84/3.43 | | subset_complement(all_21_3, v1) = all_21_0 & % 12.84/3.43 | | subset_complement(all_21_3, all_21_1) = v0 & $i(v1) & $i(v0) & % 12.84/3.43 | | $i(all_21_0)) % 12.84/3.43 | | % 12.84/3.43 | | DELTA: instantiating (41) with fresh symbols all_53_0, all_53_1 gives: % 12.84/3.43 | | (42) topstr_closure(all_21_4, all_53_1) = all_53_0 & % 12.84/3.43 | | subset_complement(all_21_3, all_53_0) = all_21_0 & % 12.84/3.43 | | subset_complement(all_21_3, all_21_1) = all_53_1 & $i(all_53_0) & % 12.84/3.43 | | $i(all_53_1) & $i(all_21_0) % 12.84/3.43 | | % 12.84/3.43 | | ALPHA: (42) implies: % 12.84/3.43 | | (43) $i(all_53_1) % 12.84/3.43 | | (44) $i(all_53_0) % 12.84/3.44 | | (45) subset_complement(all_21_3, all_21_1) = all_53_1 % 12.84/3.44 | | (46) subset_complement(all_21_3, all_53_0) = all_21_0 % 12.84/3.44 | | (47) topstr_closure(all_21_4, all_53_1) = all_53_0 % 12.84/3.44 | | % 12.84/3.44 | | GROUND_INST: instantiating (dt_k3_subset_1) with all_21_3, all_21_1, % 12.84/3.44 | | all_53_1, simplifying with (9), (36), (45) gives: % 12.84/3.44 | | (48) ? [v0: $i] : (powerset(all_21_3) = v0 & $i(v0) & ( ~ % 12.84/3.44 | | element(all_21_1, v0) | element(all_53_1, v0))) % 12.84/3.44 | | % 12.84/3.44 | | GROUND_INST: instantiating (fc2_tops_1) with all_21_4, all_53_1, all_53_0, % 12.84/3.44 | | simplifying with (5), (6), (8), (43), (47) gives: % 12.84/3.44 | | (49) closed_subset(all_53_0, all_21_4) | ? [v0: $i] : ? [v1: $i] : % 12.84/3.44 | | (the_carrier(all_21_4) = v0 & powerset(v0) = v1 & $i(v1) & $i(v0) & % 12.84/3.44 | | ~ element(all_53_1, v1)) % 12.84/3.44 | | % 12.84/3.44 | | GROUND_INST: instantiating (dt_k6_pre_topc) with all_21_4, all_53_1, % 12.84/3.44 | | all_53_0, simplifying with (6), (8), (43), (47) gives: % 12.84/3.44 | | (50) ? [v0: $i] : ? [v1: $i] : (the_carrier(all_21_4) = v0 & % 12.84/3.44 | | powerset(v0) = v1 & $i(v1) & $i(v0) & ( ~ element(all_53_1, v1) | % 12.84/3.44 | | element(all_53_0, v1))) % 12.84/3.44 | | % 12.84/3.44 | | DELTA: instantiating (48) with fresh symbol all_61_0 gives: % 12.84/3.44 | | (51) powerset(all_21_3) = all_61_0 & $i(all_61_0) & ( ~ element(all_21_1, % 12.84/3.44 | | all_61_0) | element(all_53_1, all_61_0)) % 12.84/3.44 | | % 12.84/3.44 | | ALPHA: (51) implies: % 12.84/3.44 | | (52) powerset(all_21_3) = all_61_0 % 12.84/3.44 | | (53) ~ element(all_21_1, all_61_0) | element(all_53_1, all_61_0) % 12.84/3.44 | | % 12.84/3.44 | | DELTA: instantiating (50) with fresh symbols all_65_0, all_65_1 gives: % 12.84/3.44 | | (54) the_carrier(all_21_4) = all_65_1 & powerset(all_65_1) = all_65_0 & % 12.84/3.44 | | $i(all_65_0) & $i(all_65_1) & ( ~ element(all_53_1, all_65_0) | % 12.84/3.44 | | element(all_53_0, all_65_0)) % 12.84/3.44 | | % 12.84/3.44 | | ALPHA: (54) implies: % 12.84/3.44 | | (55) powerset(all_65_1) = all_65_0 % 12.84/3.44 | | (56) the_carrier(all_21_4) = all_65_1 % 12.84/3.44 | | (57) ~ element(all_53_1, all_65_0) | element(all_53_0, all_65_0) % 12.84/3.44 | | % 12.84/3.44 | | GROUND_INST: instantiating (1) with all_21_2, all_61_0, all_21_3, % 12.84/3.44 | | simplifying with (10), (52) gives: % 12.84/3.44 | | (58) all_61_0 = all_21_2 % 12.84/3.44 | | % 12.84/3.44 | | GROUND_INST: instantiating (1) with all_61_0, all_65_0, all_21_3, % 12.84/3.44 | | simplifying with (52) gives: % 12.84/3.44 | | (59) all_65_0 = all_61_0 | ~ (powerset(all_21_3) = all_65_0) % 12.84/3.44 | | % 12.84/3.44 | | GROUND_INST: instantiating (2) with all_21_3, all_65_1, all_21_4, % 12.84/3.44 | | simplifying with (11), (56) gives: % 12.84/3.44 | | (60) all_65_1 = all_21_3 % 12.84/3.44 | | % 12.84/3.44 | | REDUCE: (55), (60) imply: % 12.84/3.44 | | (61) powerset(all_21_3) = all_65_0 % 12.84/3.44 | | % 12.84/3.44 | | BETA: splitting (53) gives: % 12.84/3.44 | | % 12.84/3.44 | | Case 1: % 12.84/3.44 | | | % 12.84/3.44 | | | (62) ~ element(all_21_1, all_61_0) % 12.84/3.44 | | | % 12.84/3.44 | | | REDUCE: (58), (62) imply: % 12.84/3.44 | | | (63) ~ element(all_21_1, all_21_2) % 12.84/3.44 | | | % 12.84/3.44 | | | PRED_UNIFY: (7), (63) imply: % 12.84/3.44 | | | (64) $false % 12.84/3.44 | | | % 12.84/3.44 | | | CLOSE: (64) is inconsistent. % 12.84/3.44 | | | % 12.84/3.44 | | Case 2: % 12.84/3.44 | | | % 12.84/3.45 | | | (65) element(all_53_1, all_61_0) % 12.84/3.45 | | | % 12.84/3.45 | | | REDUCE: (58), (65) imply: % 12.84/3.45 | | | (66) element(all_53_1, all_21_2) % 12.84/3.45 | | | % 12.84/3.45 | | | BETA: splitting (59) gives: % 12.84/3.45 | | | % 12.84/3.45 | | | Case 1: % 12.84/3.45 | | | | % 12.84/3.45 | | | | (67) ~ (powerset(all_21_3) = all_65_0) % 12.84/3.45 | | | | % 12.84/3.45 | | | | PRED_UNIFY: (61), (67) imply: % 12.84/3.45 | | | | (68) $false % 12.84/3.45 | | | | % 12.84/3.45 | | | | CLOSE: (68) is inconsistent. % 12.84/3.45 | | | | % 12.84/3.45 | | | Case 2: % 12.84/3.45 | | | | % 12.84/3.45 | | | | (69) all_65_0 = all_61_0 % 12.84/3.45 | | | | % 12.84/3.45 | | | | COMBINE_EQS: (58), (69) imply: % 12.84/3.45 | | | | (70) all_65_0 = all_21_2 % 12.84/3.45 | | | | % 12.84/3.45 | | | | BETA: splitting (57) gives: % 12.84/3.45 | | | | % 12.84/3.45 | | | | Case 1: % 12.84/3.45 | | | | | % 12.84/3.45 | | | | | (71) ~ element(all_53_1, all_65_0) % 12.84/3.45 | | | | | % 12.84/3.45 | | | | | REDUCE: (70), (71) imply: % 12.84/3.45 | | | | | (72) ~ element(all_53_1, all_21_2) % 12.84/3.45 | | | | | % 12.84/3.45 | | | | | PRED_UNIFY: (66), (72) imply: % 12.84/3.45 | | | | | (73) $false % 12.84/3.45 | | | | | % 12.84/3.45 | | | | | CLOSE: (73) is inconsistent. % 12.84/3.45 | | | | | % 12.84/3.45 | | | | Case 2: % 12.84/3.45 | | | | | % 12.84/3.45 | | | | | (74) element(all_53_1, all_65_0) % 12.84/3.45 | | | | | (75) element(all_53_0, all_65_0) % 12.84/3.45 | | | | | % 12.84/3.45 | | | | | REDUCE: (70), (75) imply: % 12.84/3.45 | | | | | (76) element(all_53_0, all_21_2) % 12.84/3.45 | | | | | % 12.84/3.45 | | | | | BETA: splitting (49) gives: % 12.84/3.45 | | | | | % 12.84/3.45 | | | | | Case 1: % 12.84/3.45 | | | | | | % 12.84/3.45 | | | | | | (77) closed_subset(all_53_0, all_21_4) % 12.84/3.45 | | | | | | % 12.84/3.45 | | | | | | GROUND_INST: instantiating (fc3_tops_1) with all_21_4, all_53_0, % 12.84/3.45 | | | | | | all_21_3, all_21_0, simplifying with (4), (5), (6), % 12.84/3.45 | | | | | | (8), (11), (44), (46), (77) gives: % 12.84/3.45 | | | | | | (78) ? [v0: $i] : (powerset(all_21_3) = v0 & $i(v0) & ~ % 12.84/3.45 | | | | | | element(all_53_0, v0)) % 12.84/3.45 | | | | | | % 12.84/3.45 | | | | | | DELTA: instantiating (78) with fresh symbol all_109_0 gives: % 12.84/3.45 | | | | | | (79) powerset(all_21_3) = all_109_0 & $i(all_109_0) & ~ % 12.84/3.45 | | | | | | element(all_53_0, all_109_0) % 12.84/3.45 | | | | | | % 12.84/3.45 | | | | | | ALPHA: (79) implies: % 12.84/3.45 | | | | | | (80) ~ element(all_53_0, all_109_0) % 12.84/3.45 | | | | | | (81) powerset(all_21_3) = all_109_0 % 12.84/3.45 | | | | | | % 12.84/3.45 | | | | | | GROUND_INST: instantiating (1) with all_21_2, all_109_0, all_21_3, % 12.84/3.45 | | | | | | simplifying with (10), (81) gives: % 12.84/3.45 | | | | | | (82) all_109_0 = all_21_2 % 12.84/3.45 | | | | | | % 12.84/3.45 | | | | | | PRED_UNIFY: (76), (80) imply: % 12.84/3.45 | | | | | | (83) ~ (all_109_0 = all_21_2) % 12.84/3.45 | | | | | | % 12.84/3.45 | | | | | | REDUCE: (82), (83) imply: % 12.84/3.45 | | | | | | (84) $false % 12.84/3.45 | | | | | | % 12.84/3.45 | | | | | | CLOSE: (84) is inconsistent. % 12.84/3.45 | | | | | | % 12.84/3.45 | | | | | Case 2: % 12.84/3.45 | | | | | | % 12.84/3.45 | | | | | | (85) ? [v0: $i] : ? [v1: $i] : (the_carrier(all_21_4) = v0 & % 12.84/3.45 | | | | | | powerset(v0) = v1 & $i(v1) & $i(v0) & ~ element(all_53_1, % 12.84/3.45 | | | | | | v1)) % 12.84/3.45 | | | | | | % 12.84/3.45 | | | | | | DELTA: instantiating (85) with fresh symbols all_95_0, all_95_1 % 12.84/3.45 | | | | | | gives: % 12.84/3.45 | | | | | | (86) the_carrier(all_21_4) = all_95_1 & powerset(all_95_1) = % 12.84/3.45 | | | | | | all_95_0 & $i(all_95_0) & $i(all_95_1) & ~ % 12.84/3.45 | | | | | | element(all_53_1, all_95_0) % 12.84/3.45 | | | | | | % 12.84/3.45 | | | | | | ALPHA: (86) implies: % 12.84/3.45 | | | | | | (87) ~ element(all_53_1, all_95_0) % 12.84/3.45 | | | | | | (88) powerset(all_95_1) = all_95_0 % 12.84/3.45 | | | | | | (89) the_carrier(all_21_4) = all_95_1 % 12.84/3.46 | | | | | | % 12.84/3.46 | | | | | | GROUND_INST: instantiating (1) with all_21_2, all_95_0, all_21_3, % 12.84/3.46 | | | | | | simplifying with (10) gives: % 12.84/3.46 | | | | | | (90) all_95_0 = all_21_2 | ~ (powerset(all_21_3) = all_95_0) % 12.84/3.46 | | | | | | % 12.84/3.46 | | | | | | GROUND_INST: instantiating (2) with all_21_3, all_95_1, all_21_4, % 12.84/3.46 | | | | | | simplifying with (11), (89) gives: % 12.84/3.46 | | | | | | (91) all_95_1 = all_21_3 % 12.84/3.46 | | | | | | % 12.84/3.46 | | | | | | PRED_UNIFY: (66), (87) imply: % 12.84/3.46 | | | | | | (92) ~ (all_95_0 = all_21_2) % 12.84/3.46 | | | | | | % 12.84/3.46 | | | | | | REDUCE: (88), (91) imply: % 12.84/3.46 | | | | | | (93) powerset(all_21_3) = all_95_0 % 12.84/3.46 | | | | | | % 12.84/3.46 | | | | | | BETA: splitting (90) gives: % 12.84/3.46 | | | | | | % 12.84/3.46 | | | | | | Case 1: % 12.84/3.46 | | | | | | | % 12.84/3.46 | | | | | | | (94) ~ (powerset(all_21_3) = all_95_0) % 12.84/3.46 | | | | | | | % 12.84/3.46 | | | | | | | PRED_UNIFY: (93), (94) imply: % 12.84/3.46 | | | | | | | (95) $false % 12.84/3.46 | | | | | | | % 12.84/3.46 | | | | | | | CLOSE: (95) is inconsistent. % 12.84/3.46 | | | | | | | % 12.84/3.46 | | | | | | Case 2: % 12.84/3.46 | | | | | | | % 12.84/3.46 | | | | | | | (96) all_95_0 = all_21_2 % 12.84/3.46 | | | | | | | % 12.84/3.46 | | | | | | | REDUCE: (92), (96) imply: % 12.84/3.46 | | | | | | | (97) $false % 12.84/3.46 | | | | | | | % 12.84/3.46 | | | | | | | CLOSE: (97) is inconsistent. % 12.84/3.46 | | | | | | | % 12.84/3.46 | | | | | | End of split % 12.84/3.46 | | | | | | % 12.84/3.46 | | | | | End of split % 12.84/3.46 | | | | | % 12.84/3.46 | | | | End of split % 12.84/3.46 | | | | % 12.84/3.46 | | | End of split % 12.84/3.46 | | | % 12.84/3.46 | | End of split % 12.84/3.46 | | % 12.84/3.46 | End of split % 12.84/3.46 | % 12.84/3.46 End of proof % 12.84/3.46 % SZS output end Proof for theBenchmark % 12.84/3.46 % 12.84/3.46 2881ms %------------------------------------------------------------------------------