%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SEU320+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 : n017.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 17:44:04 EDT 2023 % Result : Theorem 4.84s 1.56s % Output : Proof 8.50s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SEU320+1 : TPTP v8.1.2. Released v3.3.0. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.34 % Computer : n017.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 300 % 0.13/0.34 % DateTime : Thu Aug 24 00:12:38 EDT 2023 % 0.13/0.34 % CPUTime : % 0.19/0.61 ________ _____ % 0.19/0.61 ___ __ \_________(_)________________________________ % 0.19/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.19/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.19/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.19/0.61 % 0.19/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.19/0.61 (2023-06-19) % 0.19/0.61 % 0.19/0.61 (c) Philipp Rümmer, 2009-2023 % 0.19/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.19/0.61 Amanda Stjerna. % 0.19/0.61 Free software under BSD-3-Clause. % 0.19/0.61 % 0.19/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.19/0.61 % 0.19/0.61 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.19/0.62 Running up to 7 provers in parallel. % 0.19/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.19/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.19/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.19/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.19/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.19/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.19/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 1.78/1.01 Prover 1: Preprocessing ... % 1.78/1.01 Prover 4: Preprocessing ... % 2.29/1.05 Prover 0: Preprocessing ... % 2.29/1.05 Prover 2: Preprocessing ... % 2.29/1.05 Prover 5: Preprocessing ... % 2.29/1.05 Prover 6: Preprocessing ... % 2.29/1.05 Prover 3: Preprocessing ... % 3.87/1.29 Prover 1: Warning: ignoring some quantifiers % 3.87/1.29 Prover 3: Warning: ignoring some quantifiers % 3.87/1.30 Prover 2: Proving ... % 3.87/1.30 Prover 1: Constructing countermodel ... % 3.87/1.31 Prover 3: Constructing countermodel ... % 3.87/1.31 Prover 4: Warning: ignoring some quantifiers % 3.87/1.31 Prover 6: Proving ... % 3.87/1.31 Prover 5: Proving ... % 4.32/1.32 Prover 4: Constructing countermodel ... % 4.32/1.36 Prover 0: Proving ... % 4.32/1.48 Prover 3: gave up % 4.32/1.49 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 4.32/1.52 Prover 7: Preprocessing ... % 4.84/1.55 Prover 7: Warning: ignoring some quantifiers % 4.84/1.55 Prover 1: gave up % 4.84/1.56 Prover 2: proved (929ms) % 4.84/1.56 % 4.84/1.56 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 4.84/1.56 % 4.84/1.56 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 4.84/1.56 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 4.84/1.56 Prover 7: Constructing countermodel ... % 4.84/1.56 Prover 6: stopped % 4.84/1.56 Prover 5: stopped % 4.84/1.56 Prover 0: stopped % 4.84/1.59 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 4.84/1.59 Prover 10: Preprocessing ... % 4.84/1.59 Prover 11: Preprocessing ... % 4.84/1.59 Prover 8: Preprocessing ... % 4.84/1.59 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 4.84/1.59 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 6.33/1.61 Prover 13: Preprocessing ... % 6.33/1.61 Prover 16: Preprocessing ... % 6.33/1.63 Prover 10: Warning: ignoring some quantifiers % 6.33/1.63 Prover 10: Constructing countermodel ... % 6.56/1.64 Prover 8: Warning: ignoring some quantifiers % 6.56/1.64 Prover 8: Constructing countermodel ... % 6.56/1.65 Prover 13: Warning: ignoring some quantifiers % 6.56/1.66 Prover 13: Constructing countermodel ... % 6.56/1.66 Prover 16: Warning: ignoring some quantifiers % 6.56/1.66 Prover 16: Constructing countermodel ... % 6.56/1.67 Prover 11: Warning: ignoring some quantifiers % 6.56/1.68 Prover 11: Constructing countermodel ... % 7.28/1.74 Prover 10: gave up % 7.28/1.75 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085 % 7.28/1.75 Prover 8: gave up % 7.28/1.76 Prover 19: Preprocessing ... % 7.76/1.80 Prover 7: Found proof (size 41) % 7.76/1.80 Prover 7: proved (310ms) % 7.76/1.80 Prover 11: stopped % 7.76/1.80 Prover 13: stopped % 7.76/1.80 Prover 16: stopped % 7.76/1.81 Prover 4: stopped % 7.76/1.83 Prover 19: Warning: ignoring some quantifiers % 7.76/1.84 Prover 19: Constructing countermodel ... % 7.76/1.85 Prover 19: stopped % 7.76/1.85 % 7.76/1.85 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 7.76/1.85 % 7.76/1.85 % SZS output start Proof for theBenchmark % 7.76/1.86 Assumptions after simplification: % 7.76/1.86 --------------------------------- % 7.76/1.86 % 7.76/1.86 (dt_k3_subset_1) % 8.19/1.88 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (subset_complement(v0, v1) = v2) % 8.19/1.88 | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : (powerset(v0) = v3 & $i(v3) & ( ~ % 8.19/1.88 element(v1, v3) | element(v2, v3)))) % 8.19/1.88 % 8.19/1.88 (involutiveness_k3_subset_1) % 8.19/1.89 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (subset_complement(v0, v1) = v2) % 8.19/1.89 | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : ((v4 = v1 & % 8.19/1.89 subset_complement(v0, v2) = v1) | (powerset(v0) = v3 & $i(v3) & ~ % 8.19/1.89 element(v1, v3)))) % 8.19/1.89 % 8.19/1.89 (t29_tops_1) % 8.19/1.89 ! [v0: $i] : ! [v1: $i] : ( ~ (the_carrier(v0) = v1) | ~ $i(v0) | ~ % 8.19/1.89 top_str(v0) | ? [v2: $i] : (powerset(v1) = v2 & $i(v2) & ! [v3: $i] : ! % 8.19/1.89 [v4: $i] : ( ~ (subset_complement(v1, v3) = v4) | ~ $i(v3) | ~ % 8.19/1.89 open_subset(v4, v0) | ~ element(v3, v2) | closed_subset(v3, v0)) & ! % 8.19/1.89 [v3: $i] : ! [v4: $i] : ( ~ (subset_complement(v1, v3) = v4) | ~ $i(v3) % 8.19/1.89 | ~ closed_subset(v3, v0) | ~ element(v3, v2) | open_subset(v4, v0)))) % 8.19/1.89 % 8.19/1.89 (t30_tops_1) % 8.19/1.89 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 8.19/1.89 (the_carrier(v0) = v1 & subset_complement(v1, v3) = v4 & powerset(v1) = v2 & % 8.19/1.89 $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & top_str(v0) & element(v3, v2) & % 8.19/1.89 ((open_subset(v3, v0) & ~ closed_subset(v4, v0)) | (closed_subset(v4, v0) & % 8.19/1.89 ~ open_subset(v3, v0)))) % 8.19/1.89 % 8.19/1.89 (function-axioms) % 8.19/1.90 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 8.19/1.90 (subset_complement(v3, v2) = v1) | ~ (subset_complement(v3, v2) = v0)) & ! % 8.19/1.90 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (the_carrier(v2) = v1) | % 8.19/1.90 ~ (the_carrier(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = % 8.19/1.90 v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0)) % 8.19/1.90 % 8.19/1.90 Further assumptions not needed in the proof: % 8.19/1.90 -------------------------------------------- % 8.19/1.90 dt_k1_zfmisc_1, dt_l1_pre_topc, dt_l1_struct_0, dt_m1_subset_1, dt_u1_struct_0, % 8.19/1.90 existence_l1_pre_topc, existence_l1_struct_0, existence_m1_subset_1, % 8.19/1.90 reflexivity_r1_tarski, t3_subset % 8.19/1.90 % 8.19/1.90 Those formulas are unsatisfiable: % 8.19/1.90 --------------------------------- % 8.19/1.90 % 8.19/1.90 Begin of proof % 8.19/1.90 | % 8.19/1.90 | ALPHA: (function-axioms) implies: % 8.19/1.90 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (powerset(v2) = % 8.19/1.90 | v1) | ~ (powerset(v2) = v0)) % 8.19/1.90 | % 8.19/1.90 | DELTA: instantiating (t30_tops_1) with fresh symbols all_14_0, all_14_1, % 8.19/1.90 | all_14_2, all_14_3, all_14_4 gives: % 8.36/1.90 | (2) the_carrier(all_14_4) = all_14_3 & subset_complement(all_14_3, % 8.36/1.90 | all_14_1) = all_14_0 & powerset(all_14_3) = all_14_2 & $i(all_14_0) & % 8.36/1.90 | $i(all_14_1) & $i(all_14_2) & $i(all_14_3) & $i(all_14_4) & % 8.36/1.90 | top_str(all_14_4) & element(all_14_1, all_14_2) & % 8.36/1.90 | ((open_subset(all_14_1, all_14_4) & ~ closed_subset(all_14_0, % 8.36/1.90 | all_14_4)) | (closed_subset(all_14_0, all_14_4) & ~ % 8.36/1.90 | open_subset(all_14_1, all_14_4))) % 8.36/1.90 | % 8.36/1.90 | ALPHA: (2) implies: % 8.36/1.91 | (3) element(all_14_1, all_14_2) % 8.36/1.91 | (4) top_str(all_14_4) % 8.36/1.91 | (5) $i(all_14_4) % 8.36/1.91 | (6) $i(all_14_3) % 8.36/1.91 | (7) $i(all_14_1) % 8.36/1.91 | (8) $i(all_14_0) % 8.36/1.91 | (9) powerset(all_14_3) = all_14_2 % 8.36/1.91 | (10) subset_complement(all_14_3, all_14_1) = all_14_0 % 8.36/1.91 | (11) the_carrier(all_14_4) = all_14_3 % 8.36/1.91 | (12) (open_subset(all_14_1, all_14_4) & ~ closed_subset(all_14_0, % 8.36/1.91 | all_14_4)) | (closed_subset(all_14_0, all_14_4) & ~ % 8.36/1.91 | open_subset(all_14_1, all_14_4)) % 8.36/1.91 | % 8.36/1.91 | GROUND_INST: instantiating (involutiveness_k3_subset_1) with all_14_3, % 8.36/1.91 | all_14_1, all_14_0, simplifying with (6), (7), (10) gives: % 8.36/1.91 | (13) ? [v0: $i] : ? [v1: int] : ((v1 = all_14_1 & % 8.36/1.91 | subset_complement(all_14_3, all_14_0) = all_14_1) | % 8.36/1.91 | (powerset(all_14_3) = v0 & $i(v0) & ~ element(all_14_1, v0))) % 8.36/1.91 | % 8.36/1.91 | GROUND_INST: instantiating (dt_k3_subset_1) with all_14_3, all_14_1, all_14_0, % 8.36/1.91 | simplifying with (6), (7), (10) gives: % 8.36/1.91 | (14) ? [v0: $i] : (powerset(all_14_3) = v0 & $i(v0) & ( ~ % 8.36/1.91 | element(all_14_1, v0) | element(all_14_0, v0))) % 8.36/1.91 | % 8.36/1.91 | GROUND_INST: instantiating (t29_tops_1) with all_14_4, all_14_3, simplifying % 8.36/1.91 | with (4), (5), (11) gives: % 8.36/1.92 | (15) ? [v0: $i] : (powerset(all_14_3) = v0 & $i(v0) & ! [v1: $i] : ! % 8.36/1.92 | [v2: $i] : ( ~ (subset_complement(all_14_3, v1) = v2) | ~ $i(v1) | % 8.36/1.92 | ~ open_subset(v2, all_14_4) | ~ element(v1, v0) | % 8.36/1.92 | closed_subset(v1, all_14_4)) & ! [v1: $i] : ! [v2: $i] : ( ~ % 8.36/1.92 | (subset_complement(all_14_3, v1) = v2) | ~ $i(v1) | ~ % 8.36/1.92 | closed_subset(v1, all_14_4) | ~ element(v1, v0) | open_subset(v2, % 8.36/1.92 | all_14_4))) % 8.36/1.92 | % 8.36/1.92 | DELTA: instantiating (14) with fresh symbol all_22_0 gives: % 8.36/1.92 | (16) powerset(all_14_3) = all_22_0 & $i(all_22_0) & ( ~ element(all_14_1, % 8.36/1.92 | all_22_0) | element(all_14_0, all_22_0)) % 8.36/1.92 | % 8.36/1.92 | ALPHA: (16) implies: % 8.36/1.92 | (17) powerset(all_14_3) = all_22_0 % 8.36/1.92 | (18) ~ element(all_14_1, all_22_0) | element(all_14_0, all_22_0) % 8.36/1.92 | % 8.36/1.92 | DELTA: instantiating (13) with fresh symbols all_24_0, all_24_1 gives: % 8.36/1.92 | (19) (all_24_0 = all_14_1 & subset_complement(all_14_3, all_14_0) = % 8.36/1.92 | all_14_1) | (powerset(all_14_3) = all_24_1 & $i(all_24_1) & ~ % 8.36/1.92 | element(all_14_1, all_24_1)) % 8.36/1.92 | % 8.36/1.92 | DELTA: instantiating (15) with fresh symbol all_25_0 gives: % 8.36/1.92 | (20) powerset(all_14_3) = all_25_0 & $i(all_25_0) & ! [v0: $i] : ! [v1: % 8.36/1.92 | $i] : ( ~ (subset_complement(all_14_3, v0) = v1) | ~ $i(v0) | ~ % 8.36/1.92 | open_subset(v1, all_14_4) | ~ element(v0, all_25_0) | % 8.36/1.92 | closed_subset(v0, all_14_4)) & ! [v0: $i] : ! [v1: $i] : ( ~ % 8.36/1.92 | (subset_complement(all_14_3, v0) = v1) | ~ $i(v0) | ~ % 8.36/1.92 | closed_subset(v0, all_14_4) | ~ element(v0, all_25_0) | % 8.36/1.92 | open_subset(v1, all_14_4)) % 8.36/1.92 | % 8.36/1.92 | ALPHA: (20) implies: % 8.36/1.92 | (21) powerset(all_14_3) = all_25_0 % 8.36/1.92 | (22) ! [v0: $i] : ! [v1: $i] : ( ~ (subset_complement(all_14_3, v0) = v1) % 8.36/1.92 | | ~ $i(v0) | ~ closed_subset(v0, all_14_4) | ~ element(v0, % 8.36/1.92 | all_25_0) | open_subset(v1, all_14_4)) % 8.36/1.92 | (23) ! [v0: $i] : ! [v1: $i] : ( ~ (subset_complement(all_14_3, v0) = v1) % 8.36/1.92 | | ~ $i(v0) | ~ open_subset(v1, all_14_4) | ~ element(v0, % 8.36/1.92 | all_25_0) | closed_subset(v0, all_14_4)) % 8.36/1.92 | % 8.36/1.92 | GROUND_INST: instantiating (1) with all_14_2, all_25_0, all_14_3, simplifying % 8.36/1.92 | with (9), (21) gives: % 8.36/1.92 | (24) all_25_0 = all_14_2 % 8.36/1.92 | % 8.36/1.92 | GROUND_INST: instantiating (1) with all_22_0, all_25_0, all_14_3, simplifying % 8.36/1.92 | with (17), (21) gives: % 8.36/1.92 | (25) all_25_0 = all_22_0 % 8.36/1.92 | % 8.36/1.92 | COMBINE_EQS: (24), (25) imply: % 8.36/1.92 | (26) all_22_0 = all_14_2 % 8.36/1.92 | % 8.36/1.92 | BETA: splitting (18) gives: % 8.36/1.92 | % 8.36/1.92 | Case 1: % 8.36/1.92 | | % 8.36/1.92 | | (27) ~ element(all_14_1, all_22_0) % 8.36/1.92 | | % 8.36/1.92 | | REDUCE: (26), (27) imply: % 8.36/1.92 | | (28) ~ element(all_14_1, all_14_2) % 8.36/1.92 | | % 8.36/1.92 | | PRED_UNIFY: (3), (28) imply: % 8.36/1.92 | | (29) $false % 8.36/1.93 | | % 8.36/1.93 | | CLOSE: (29) is inconsistent. % 8.36/1.93 | | % 8.36/1.93 | Case 2: % 8.36/1.93 | | % 8.36/1.93 | | (30) element(all_14_1, all_22_0) % 8.36/1.93 | | (31) element(all_14_0, all_22_0) % 8.36/1.93 | | % 8.36/1.93 | | REDUCE: (26), (31) imply: % 8.36/1.93 | | (32) element(all_14_0, all_14_2) % 8.36/1.93 | | % 8.36/1.93 | | BETA: splitting (19) gives: % 8.36/1.93 | | % 8.36/1.93 | | Case 1: % 8.36/1.93 | | | % 8.36/1.93 | | | (33) all_24_0 = all_14_1 & subset_complement(all_14_3, all_14_0) = % 8.36/1.93 | | | all_14_1 % 8.36/1.93 | | | % 8.36/1.93 | | | ALPHA: (33) implies: % 8.36/1.93 | | | (34) subset_complement(all_14_3, all_14_0) = all_14_1 % 8.36/1.93 | | | % 8.36/1.93 | | | BETA: splitting (12) gives: % 8.36/1.93 | | | % 8.36/1.93 | | | Case 1: % 8.36/1.93 | | | | % 8.36/1.93 | | | | (35) open_subset(all_14_1, all_14_4) & ~ closed_subset(all_14_0, % 8.36/1.93 | | | | all_14_4) % 8.36/1.93 | | | | % 8.36/1.93 | | | | ALPHA: (35) implies: % 8.36/1.93 | | | | (36) ~ closed_subset(all_14_0, all_14_4) % 8.36/1.93 | | | | (37) open_subset(all_14_1, all_14_4) % 8.36/1.93 | | | | % 8.36/1.93 | | | | GROUND_INST: instantiating (23) with all_14_0, all_14_1, simplifying % 8.36/1.93 | | | | with (8), (34), (36), (37) gives: % 8.36/1.93 | | | | (38) ~ element(all_14_0, all_25_0) % 8.36/1.93 | | | | % 8.36/1.93 | | | | REDUCE: (24), (38) imply: % 8.50/1.93 | | | | (39) ~ element(all_14_0, all_14_2) % 8.50/1.93 | | | | % 8.50/1.93 | | | | PRED_UNIFY: (32), (39) imply: % 8.50/1.93 | | | | (40) $false % 8.50/1.93 | | | | % 8.50/1.93 | | | | CLOSE: (40) is inconsistent. % 8.50/1.93 | | | | % 8.50/1.93 | | | Case 2: % 8.50/1.93 | | | | % 8.50/1.93 | | | | (41) closed_subset(all_14_0, all_14_4) & ~ open_subset(all_14_1, % 8.50/1.93 | | | | all_14_4) % 8.50/1.93 | | | | % 8.50/1.93 | | | | ALPHA: (41) implies: % 8.50/1.93 | | | | (42) ~ open_subset(all_14_1, all_14_4) % 8.50/1.93 | | | | (43) closed_subset(all_14_0, all_14_4) % 8.50/1.93 | | | | % 8.50/1.93 | | | | GROUND_INST: instantiating (22) with all_14_0, all_14_1, simplifying % 8.50/1.93 | | | | with (8), (34), (42), (43) gives: % 8.50/1.93 | | | | (44) ~ element(all_14_0, all_25_0) % 8.50/1.93 | | | | % 8.50/1.93 | | | | REDUCE: (24), (44) imply: % 8.50/1.93 | | | | (45) ~ element(all_14_0, all_14_2) % 8.50/1.93 | | | | % 8.50/1.93 | | | | PRED_UNIFY: (32), (45) imply: % 8.50/1.93 | | | | (46) $false % 8.50/1.93 | | | | % 8.50/1.93 | | | | CLOSE: (46) is inconsistent. % 8.50/1.93 | | | | % 8.50/1.93 | | | End of split % 8.50/1.93 | | | % 8.50/1.93 | | Case 2: % 8.50/1.93 | | | % 8.50/1.93 | | | (47) powerset(all_14_3) = all_24_1 & $i(all_24_1) & ~ % 8.50/1.93 | | | element(all_14_1, all_24_1) % 8.50/1.93 | | | % 8.50/1.93 | | | ALPHA: (47) implies: % 8.50/1.93 | | | (48) ~ element(all_14_1, all_24_1) % 8.50/1.93 | | | (49) powerset(all_14_3) = all_24_1 % 8.50/1.93 | | | % 8.50/1.93 | | | GROUND_INST: instantiating (1) with all_14_2, all_24_1, all_14_3, % 8.50/1.93 | | | simplifying with (9), (49) gives: % 8.50/1.93 | | | (50) all_24_1 = all_14_2 % 8.50/1.93 | | | % 8.50/1.93 | | | PRED_UNIFY: (3), (48) imply: % 8.50/1.93 | | | (51) ~ (all_24_1 = all_14_2) % 8.50/1.93 | | | % 8.50/1.93 | | | REDUCE: (50), (51) imply: % 8.50/1.93 | | | (52) $false % 8.50/1.94 | | | % 8.50/1.94 | | | CLOSE: (52) is inconsistent. % 8.50/1.94 | | | % 8.50/1.94 | | End of split % 8.50/1.94 | | % 8.50/1.94 | End of split % 8.50/1.94 | % 8.50/1.94 End of proof % 8.50/1.94 % SZS output end Proof for theBenchmark % 8.50/1.94 % 8.50/1.94 1326ms %------------------------------------------------------------------------------