%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SEU115+1 : TPTP v8.1.2. Released v3.2.0. % 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 17:42:34 EDT 2023 % Result : Theorem 7.64s 1.81s % Output : Proof 9.78s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SEU115+1 : TPTP v8.1.2. Released v3.2.0. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.14/0.34 % Computer : n017.cluster.edu % 0.14/0.34 % Model : x86_64 x86_64 % 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.34 % Memory : 8042.1875MB % 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.34 % CPULimit : 300 % 0.14/0.34 % WCLimit : 300 % 0.14/0.34 % DateTime : Wed Aug 23 15:06:08 EDT 2023 % 0.14/0.34 % CPUTime : % 0.21/0.58 ________ _____ % 0.21/0.58 ___ __ \_________(_)________________________________ % 0.21/0.58 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.21/0.58 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.21/0.58 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.21/0.58 % 0.21/0.58 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.21/0.58 (2023-06-19) % 0.21/0.58 % 0.21/0.58 (c) Philipp Rümmer, 2009-2023 % 0.21/0.58 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.21/0.58 Amanda Stjerna. % 0.21/0.58 Free software under BSD-3-Clause. % 0.21/0.58 % 0.21/0.59 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.21/0.59 % 0.21/0.59 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.21/0.61 Running up to 7 provers in parallel. % 0.21/0.62 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.21/0.62 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.21/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.21/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.21/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.21/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.21/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.43/1.07 Prover 1: Preprocessing ... % 2.43/1.07 Prover 4: Preprocessing ... % 3.04/1.11 Prover 2: Preprocessing ... % 3.04/1.11 Prover 5: Preprocessing ... % 3.04/1.12 Prover 6: Preprocessing ... % 3.04/1.12 Prover 0: Preprocessing ... % 3.04/1.12 Prover 3: Preprocessing ... % 5.05/1.55 Prover 1: Warning: ignoring some quantifiers % 5.05/1.58 Prover 5: Proving ... % 5.05/1.60 Prover 1: Constructing countermodel ... % 5.05/1.63 Prover 2: Proving ... % 6.75/1.64 Prover 6: Proving ... % 6.80/1.64 Prover 3: Warning: ignoring some quantifiers % 6.80/1.66 Prover 4: Warning: ignoring some quantifiers % 6.80/1.68 Prover 3: Constructing countermodel ... % 6.80/1.69 Prover 4: Constructing countermodel ... % 7.24/1.72 Prover 0: Proving ... % 7.64/1.81 Prover 3: proved (1185ms) % 7.64/1.81 % 7.64/1.81 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 7.64/1.81 % 7.64/1.81 Prover 0: stopped % 7.64/1.81 Prover 2: stopped % 7.64/1.81 Prover 5: stopped % 7.64/1.81 Prover 6: stopped % 7.64/1.81 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 7.64/1.81 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 7.64/1.81 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 7.64/1.81 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 7.64/1.82 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 8.37/1.87 Prover 8: Preprocessing ... % 8.37/1.88 Prover 11: Preprocessing ... % 8.37/1.88 Prover 13: Preprocessing ... % 8.37/1.88 Prover 7: Preprocessing ... % 8.37/1.89 Prover 10: Preprocessing ... % 9.00/1.99 Prover 13: Warning: ignoring some quantifiers % 9.00/1.99 Prover 7: Warning: ignoring some quantifiers % 9.00/2.00 Prover 13: Constructing countermodel ... % 9.00/2.00 Prover 10: Warning: ignoring some quantifiers % 9.42/2.00 Prover 7: Constructing countermodel ... % 9.42/2.01 Prover 10: Constructing countermodel ... % 9.42/2.02 Prover 1: Found proof (size 35) % 9.42/2.02 Prover 1: proved (1400ms) % 9.42/2.02 Prover 4: stopped % 9.42/2.02 Prover 10: stopped % 9.42/2.02 Prover 13: stopped % 9.42/2.03 Prover 7: stopped % 9.42/2.04 Prover 8: Warning: ignoring some quantifiers % 9.42/2.05 Prover 8: Constructing countermodel ... % 9.78/2.06 Prover 8: stopped % 9.78/2.08 Prover 11: Warning: ignoring some quantifiers % 9.78/2.09 Prover 11: Constructing countermodel ... % 9.78/2.10 Prover 11: stopped % 9.78/2.10 % 9.78/2.10 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 9.78/2.10 % 9.78/2.10 % SZS output start Proof for theBenchmark % 9.78/2.11 Assumptions after simplification: % 9.78/2.11 --------------------------------- % 9.78/2.11 % 9.78/2.11 (rc2_finset_1) % 9.78/2.13 ! [v0: $i] : ! [v1: $i] : ( ~ (powerset(v0) = v1) | ~ $i(v0) | ? [v2: $i] % 9.78/2.13 : (relation(v2) = 0 & function(v2) = 0 & one_to_one(v2) = 0 & % 9.78/2.13 epsilon_transitive(v2) = 0 & epsilon_connected(v2) = 0 & ordinal(v2) = 0 & % 9.78/2.13 natural(v2) = 0 & finite(v2) = 0 & empty(v2) = 0 & element(v2, v1) = 0 & % 9.78/2.13 $i(v2))) % 9.78/2.13 % 9.78/2.13 (rc2_subset_1) % 9.78/2.13 ! [v0: $i] : ! [v1: $i] : ( ~ (powerset(v0) = v1) | ~ $i(v0) | ? [v2: $i] % 9.78/2.13 : (empty(v2) = 0 & element(v2, v1) = 0 & $i(v2))) % 9.78/2.13 % 9.78/2.13 (t1_zfmisc_1) % 9.78/2.14 $i(empty_set) & ? [v0: $i] : (singleton(empty_set) = v0 & powerset(empty_set) % 9.78/2.14 = v0 & $i(v0)) % 9.78/2.14 % 9.78/2.14 (t27_finsub_1) % 9.78/2.14 ! [v0: $i] : ! [v1: $i] : ( ~ (finite_subsets(v0) = v1) | ~ $i(v0) | ? % 9.78/2.14 [v2: any] : ? [v3: $i] : (finite(v0) = v2 & powerset(v0) = v3 & $i(v3) & ( % 9.78/2.14 ~ (v2 = 0) | v3 = v1))) % 9.78/2.14 % 9.78/2.14 (t28_finsub_1) % 9.78/2.14 $i(empty_set) & ? [v0: $i] : ? [v1: $i] : ( ~ (v1 = v0) & % 9.78/2.14 singleton(empty_set) = v1 & finite_subsets(empty_set) = v0 & $i(v1) & % 9.78/2.14 $i(v0)) % 9.78/2.14 % 9.78/2.14 (t6_boole) % 9.78/2.14 $i(empty_set) & ! [v0: $i] : (v0 = empty_set | ~ (empty(v0) = 0) | ~ % 9.78/2.14 $i(v0)) % 9.78/2.14 % 9.78/2.14 (t8_boole) % 9.78/2.14 ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (empty(v1) = 0) | ~ (empty(v0) = 0) % 9.78/2.14 | ~ $i(v1) | ~ $i(v0)) % 9.78/2.14 % 9.78/2.14 (function-axioms) % 9.78/2.15 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 9.78/2.15 [v3: $i] : (v1 = v0 | ~ (element(v3, v2) = v1) | ~ (element(v3, v2) = v0)) & % 9.78/2.15 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 9.78/2.15 [v3: $i] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) & ! [v0: % 9.78/2.15 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 9.78/2.15 : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0: % 9.78/2.15 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 9.78/2.15 ~ (relation(v2) = v1) | ~ (relation(v2) = v0)) & ! [v0: MultipleValueBool] % 9.78/2.15 : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (function(v2) = v1) % 9.78/2.15 | ~ (function(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 9.78/2.15 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (one_to_one(v2) = v1) | ~ % 9.78/2.15 (one_to_one(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 9.78/2.15 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (epsilon_transitive(v2) = % 9.78/2.15 v1) | ~ (epsilon_transitive(v2) = v0)) & ! [v0: MultipleValueBool] : ! % 9.78/2.15 [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (epsilon_connected(v2) = % 9.78/2.15 v1) | ~ (epsilon_connected(v2) = v0)) & ! [v0: MultipleValueBool] : ! % 9.78/2.15 [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (ordinal(v2) = v1) | ~ % 9.78/2.15 (ordinal(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 9.78/2.15 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (natural(v2) = v1) | ~ % 9.78/2.15 (natural(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | % 9.78/2.15 ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ! [v0: % 9.78/2.15 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 9.78/2.15 ~ (cap_closed(v2) = v1) | ~ (cap_closed(v2) = v0)) & ! [v0: $i] : ! [v1: % 9.78/2.15 $i] : ! [v2: $i] : (v1 = v0 | ~ (finite_subsets(v2) = v1) | ~ % 9.78/2.15 (finite_subsets(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 9.78/2.15 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (finite(v2) = v1) | ~ % 9.78/2.15 (finite(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] % 9.78/2.15 : ! [v2: $i] : (v1 = v0 | ~ (diff_closed(v2) = v1) | ~ (diff_closed(v2) = % 9.78/2.15 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 9.78/2.15 $i] : (v1 = v0 | ~ (preboolean(v2) = v1) | ~ (preboolean(v2) = v0)) & ! % 9.78/2.15 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 % 9.78/2.15 | ~ (cup_closed(v2) = v1) | ~ (cup_closed(v2) = v0)) & ! [v0: % 9.78/2.15 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 9.78/2.15 ~ (empty(v2) = v1) | ~ (empty(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 9.78/2.15 [v2: $i] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0)) % 9.78/2.15 % 9.78/2.15 Further assumptions not needed in the proof: % 9.78/2.15 -------------------------------------------- % 9.78/2.15 antisymmetry_r2_hidden, cc1_finset_1, cc1_finsub_1, cc2_finset_1, cc2_finsub_1, % 9.78/2.15 cc3_finsub_1, dt_k5_finsub_1, existence_m1_subset_1, fc1_finset_1, fc1_finsub_1, % 9.78/2.15 fc1_subset_1, fc1_xboole_0, fc2_finsub_1, fc2_subset_1, rc1_finset_1, % 9.78/2.15 rc1_finsub_1, rc1_subset_1, rc1_xboole_0, rc2_xboole_0, rc3_finset_1, % 9.78/2.15 rc4_finset_1, reflexivity_r1_tarski, t1_subset, t2_subset, t3_subset, t4_subset, % 9.78/2.15 t5_subset, t7_boole % 9.78/2.15 % 9.78/2.15 Those formulas are unsatisfiable: % 9.78/2.15 --------------------------------- % 9.78/2.15 % 9.78/2.15 Begin of proof % 9.78/2.15 | % 9.78/2.15 | ALPHA: (t6_boole) implies: % 9.78/2.16 | (1) ! [v0: $i] : (v0 = empty_set | ~ (empty(v0) = 0) | ~ $i(v0)) % 9.78/2.16 | % 9.78/2.16 | ALPHA: (t1_zfmisc_1) implies: % 9.78/2.16 | (2) ? [v0: $i] : (singleton(empty_set) = v0 & powerset(empty_set) = v0 & % 9.78/2.16 | $i(v0)) % 9.78/2.16 | % 9.78/2.16 | ALPHA: (t28_finsub_1) implies: % 9.78/2.16 | (3) $i(empty_set) % 9.78/2.16 | (4) ? [v0: $i] : ? [v1: $i] : ( ~ (v1 = v0) & singleton(empty_set) = v1 & % 9.78/2.16 | finite_subsets(empty_set) = v0 & $i(v1) & $i(v0)) % 9.78/2.16 | % 9.78/2.16 | ALPHA: (function-axioms) implies: % 9.78/2.16 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (powerset(v2) = % 9.78/2.16 | v1) | ~ (powerset(v2) = v0)) % 9.78/2.16 | (6) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 9.78/2.16 | (v1 = v0 | ~ (finite(v2) = v1) | ~ (finite(v2) = v0)) % 9.78/2.16 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (singleton(v2) % 9.78/2.16 | = v1) | ~ (singleton(v2) = v0)) % 9.78/2.16 | % 9.78/2.16 | DELTA: instantiating (2) with fresh symbol all_32_0 gives: % 9.78/2.16 | (8) singleton(empty_set) = all_32_0 & powerset(empty_set) = all_32_0 & % 9.78/2.16 | $i(all_32_0) % 9.78/2.16 | % 9.78/2.16 | ALPHA: (8) implies: % 9.78/2.16 | (9) powerset(empty_set) = all_32_0 % 9.78/2.16 | (10) singleton(empty_set) = all_32_0 % 9.78/2.16 | % 9.78/2.16 | DELTA: instantiating (4) with fresh symbols all_41_0, all_41_1 gives: % 9.78/2.16 | (11) ~ (all_41_0 = all_41_1) & singleton(empty_set) = all_41_0 & % 9.78/2.16 | finite_subsets(empty_set) = all_41_1 & $i(all_41_0) & $i(all_41_1) % 9.78/2.16 | % 9.78/2.16 | ALPHA: (11) implies: % 9.78/2.16 | (12) ~ (all_41_0 = all_41_1) % 9.78/2.16 | (13) finite_subsets(empty_set) = all_41_1 % 9.78/2.16 | (14) singleton(empty_set) = all_41_0 % 9.78/2.16 | % 9.78/2.16 | GROUND_INST: instantiating (7) with all_32_0, all_41_0, empty_set, simplifying % 9.78/2.16 | with (10), (14) gives: % 9.78/2.16 | (15) all_41_0 = all_32_0 % 9.78/2.16 | % 9.78/2.16 | REDUCE: (12), (15) imply: % 9.78/2.16 | (16) ~ (all_41_1 = all_32_0) % 9.78/2.16 | % 9.78/2.16 | SIMP: (16) implies: % 9.78/2.16 | (17) ~ (all_41_1 = all_32_0) % 9.78/2.16 | % 9.78/2.17 | GROUND_INST: instantiating (rc2_finset_1) with empty_set, all_32_0, % 9.78/2.17 | simplifying with (3), (9) gives: % 9.78/2.17 | (18) ? [v0: $i] : (relation(v0) = 0 & function(v0) = 0 & one_to_one(v0) = % 9.78/2.17 | 0 & epsilon_transitive(v0) = 0 & epsilon_connected(v0) = 0 & % 9.78/2.17 | ordinal(v0) = 0 & natural(v0) = 0 & finite(v0) = 0 & empty(v0) = 0 & % 9.78/2.17 | element(v0, all_32_0) = 0 & $i(v0)) % 9.78/2.17 | % 9.78/2.17 | GROUND_INST: instantiating (rc2_subset_1) with empty_set, all_32_0, % 9.78/2.17 | simplifying with (3), (9) gives: % 9.78/2.17 | (19) ? [v0: $i] : (empty(v0) = 0 & element(v0, all_32_0) = 0 & $i(v0)) % 9.78/2.17 | % 9.78/2.17 | GROUND_INST: instantiating (t27_finsub_1) with empty_set, all_41_1, % 9.78/2.17 | simplifying with (3), (13) gives: % 9.78/2.17 | (20) ? [v0: any] : ? [v1: $i] : (finite(empty_set) = v0 & % 9.78/2.17 | powerset(empty_set) = v1 & $i(v1) & ( ~ (v0 = 0) | v1 = all_41_1)) % 9.78/2.17 | % 9.78/2.17 | DELTA: instantiating (19) with fresh symbol all_59_0 gives: % 9.78/2.17 | (21) empty(all_59_0) = 0 & element(all_59_0, all_32_0) = 0 & $i(all_59_0) % 9.78/2.17 | % 9.78/2.17 | ALPHA: (21) implies: % 9.78/2.17 | (22) $i(all_59_0) % 9.78/2.17 | (23) empty(all_59_0) = 0 % 9.78/2.17 | % 9.78/2.17 | DELTA: instantiating (20) with fresh symbols all_64_0, all_64_1 gives: % 9.78/2.17 | (24) finite(empty_set) = all_64_1 & powerset(empty_set) = all_64_0 & % 9.78/2.17 | $i(all_64_0) & ( ~ (all_64_1 = 0) | all_64_0 = all_41_1) % 9.78/2.17 | % 9.78/2.17 | ALPHA: (24) implies: % 9.78/2.17 | (25) powerset(empty_set) = all_64_0 % 9.78/2.17 | (26) finite(empty_set) = all_64_1 % 9.78/2.17 | (27) ~ (all_64_1 = 0) | all_64_0 = all_41_1 % 9.78/2.17 | % 9.78/2.17 | DELTA: instantiating (18) with fresh symbol all_66_0 gives: % 9.78/2.17 | (28) relation(all_66_0) = 0 & function(all_66_0) = 0 & one_to_one(all_66_0) % 9.78/2.17 | = 0 & epsilon_transitive(all_66_0) = 0 & epsilon_connected(all_66_0) = % 9.78/2.17 | 0 & ordinal(all_66_0) = 0 & natural(all_66_0) = 0 & finite(all_66_0) = % 9.78/2.17 | 0 & empty(all_66_0) = 0 & element(all_66_0, all_32_0) = 0 & % 9.78/2.17 | $i(all_66_0) % 9.78/2.17 | % 9.78/2.17 | ALPHA: (28) implies: % 9.78/2.17 | (29) $i(all_66_0) % 9.78/2.17 | (30) empty(all_66_0) = 0 % 9.78/2.17 | (31) finite(all_66_0) = 0 % 9.78/2.17 | % 9.78/2.17 | GROUND_INST: instantiating (5) with all_32_0, all_64_0, empty_set, simplifying % 9.78/2.17 | with (9), (25) gives: % 9.78/2.17 | (32) all_64_0 = all_32_0 % 9.78/2.17 | % 9.78/2.17 | BETA: splitting (27) gives: % 9.78/2.17 | % 9.78/2.17 | Case 1: % 9.78/2.17 | | % 9.78/2.17 | | (33) ~ (all_64_1 = 0) % 9.78/2.17 | | % 9.78/2.17 | | GROUND_INST: instantiating (t8_boole) with all_59_0, all_66_0, simplifying % 9.78/2.17 | | with (22), (23), (29), (30) gives: % 9.78/2.17 | | (34) all_66_0 = all_59_0 % 9.78/2.17 | | % 9.78/2.17 | | GROUND_INST: instantiating (1) with all_66_0, simplifying with (29), (30) % 9.78/2.17 | | gives: % 9.78/2.17 | | (35) all_66_0 = empty_set % 9.78/2.17 | | % 9.78/2.17 | | COMBINE_EQS: (34), (35) imply: % 9.78/2.17 | | (36) all_59_0 = empty_set % 9.78/2.17 | | % 9.78/2.17 | | REDUCE: (31), (35) imply: % 9.78/2.17 | | (37) finite(empty_set) = 0 % 9.78/2.17 | | % 9.78/2.17 | | GROUND_INST: instantiating (6) with all_64_1, 0, empty_set, simplifying with % 9.78/2.17 | | (26), (37) gives: % 9.78/2.18 | | (38) all_64_1 = 0 % 9.78/2.18 | | % 9.78/2.18 | | REDUCE: (33), (38) imply: % 9.78/2.18 | | (39) $false % 9.78/2.18 | | % 9.78/2.18 | | CLOSE: (39) is inconsistent. % 9.78/2.18 | | % 9.78/2.18 | Case 2: % 9.78/2.18 | | % 9.78/2.18 | | (40) all_64_0 = all_41_1 % 9.78/2.18 | | % 9.78/2.18 | | COMBINE_EQS: (32), (40) imply: % 9.78/2.18 | | (41) all_41_1 = all_32_0 % 9.78/2.18 | | % 9.78/2.18 | | SIMP: (41) implies: % 9.78/2.18 | | (42) all_41_1 = all_32_0 % 9.78/2.18 | | % 9.78/2.18 | | REDUCE: (17), (42) imply: % 9.78/2.18 | | (43) $false % 9.78/2.18 | | % 9.78/2.18 | | CLOSE: (43) is inconsistent. % 9.78/2.18 | | % 9.78/2.18 | End of split % 9.78/2.18 | % 9.78/2.18 End of proof % 9.78/2.18 % SZS output end Proof for theBenchmark % 9.78/2.18 % 9.78/2.18 1591ms %------------------------------------------------------------------------------