%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SEU114+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 : n021.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 13.01s 2.50s % Output : Proof 17.15s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SEU114+1 : TPTP v8.1.2. Released v3.2.0. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.12/0.33 % Computer : n021.cluster.edu % 0.12/0.33 % Model : x86_64 x86_64 % 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.33 % Memory : 8042.1875MB % 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.33 % CPULimit : 300 % 0.12/0.33 % WCLimit : 300 % 0.12/0.33 % DateTime : Wed Aug 23 22:05:39 EDT 2023 % 0.12/0.33 % CPUTime : % 0.18/0.61 ________ _____ % 0.18/0.61 ___ __ \_________(_)________________________________ % 0.18/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.18/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.18/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.18/0.61 % 0.18/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.18/0.61 (2023-06-19) % 0.18/0.61 % 0.18/0.61 (c) Philipp Rümmer, 2009-2023 % 0.18/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.18/0.61 Amanda Stjerna. % 0.18/0.61 Free software under BSD-3-Clause. % 0.18/0.61 % 0.18/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.18/0.61 % 0.18/0.61 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.18/0.62 Running up to 7 provers in parallel. % 0.18/0.65 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.18/0.65 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.18/0.65 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.18/0.65 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.18/0.65 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.18/0.65 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.18/0.65 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.68/1.06 Prover 1: Preprocessing ... % 2.68/1.07 Prover 4: Preprocessing ... % 2.68/1.10 Prover 3: Preprocessing ... % 2.68/1.10 Prover 0: Preprocessing ... % 2.68/1.10 Prover 6: Preprocessing ... % 2.68/1.10 Prover 2: Preprocessing ... % 2.68/1.11 Prover 5: Preprocessing ... % 5.70/1.53 Prover 5: Proving ... % 6.44/1.57 Prover 2: Proving ... % 6.44/1.59 Prover 1: Warning: ignoring some quantifiers % 6.77/1.60 Prover 3: Warning: ignoring some quantifiers % 6.77/1.63 Prover 3: Constructing countermodel ... % 6.77/1.63 Prover 1: Constructing countermodel ... % 7.09/1.65 Prover 6: Proving ... % 7.09/1.65 Prover 4: Warning: ignoring some quantifiers % 7.09/1.69 Prover 4: Constructing countermodel ... % 7.09/1.69 Prover 0: Proving ... % 13.01/2.50 Prover 5: proved (1853ms) % 13.01/2.50 % 13.01/2.50 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 13.01/2.50 % 13.01/2.50 Prover 3: stopped % 13.01/2.50 Prover 6: stopped % 13.01/2.50 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 13.01/2.50 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 13.01/2.50 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 13.01/2.51 Prover 0: stopped % 13.01/2.51 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 13.01/2.51 Prover 2: stopped % 13.01/2.52 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 13.71/2.56 Prover 10: Preprocessing ... % 13.71/2.58 Prover 8: Preprocessing ... % 13.71/2.59 Prover 7: Preprocessing ... % 14.02/2.60 Prover 11: Preprocessing ... % 14.02/2.60 Prover 13: Preprocessing ... % 14.02/2.64 Prover 10: Warning: ignoring some quantifiers % 14.02/2.66 Prover 7: Warning: ignoring some quantifiers % 14.02/2.67 Prover 10: Constructing countermodel ... % 14.02/2.70 Prover 13: Warning: ignoring some quantifiers % 14.02/2.71 Prover 7: Constructing countermodel ... % 14.02/2.71 Prover 13: Constructing countermodel ... % 14.02/2.74 Prover 8: Warning: ignoring some quantifiers % 14.02/2.76 Prover 8: Constructing countermodel ... % 15.39/2.83 Prover 11: Warning: ignoring some quantifiers % 15.39/2.85 Prover 11: Constructing countermodel ... % 16.53/2.99 Prover 10: Found proof (size 59) % 16.53/2.99 Prover 10: proved (484ms) % 16.53/2.99 Prover 11: stopped % 16.53/2.99 Prover 7: stopped % 16.53/2.99 Prover 1: stopped % 16.53/2.99 Prover 4: stopped % 16.53/2.99 Prover 13: stopped % 16.53/2.99 Prover 8: stopped % 16.53/2.99 % 16.53/2.99 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 16.53/2.99 % 16.53/3.00 % SZS output start Proof for theBenchmark % 16.53/3.01 Assumptions after simplification: % 16.53/3.01 --------------------------------- % 16.53/3.01 % 16.53/3.01 (cc2_finset_1) % 16.53/3.03 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (powerset(v0) = v1) | ~ $i(v2) % 16.53/3.03 | ~ $i(v0) | ~ element(v2, v1) | ~ finite(v0) | finite(v2)) % 16.53/3.03 % 16.53/3.03 (d3_tarski) % 16.53/3.03 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 16.53/3.03 ~ subset(v0, v1) | ~ in(v2, v0) | in(v2, v1)) & ? [v0: $i] : ? [v1: $i] % 16.53/3.03 : ( ~ $i(v1) | ~ $i(v0) | subset(v0, v1) | ? [v2: $i] : ($i(v2) & in(v2, v0) % 16.53/3.03 & ~ in(v2, v1))) % 16.53/3.03 % 16.53/3.03 (d5_finsub_1) % 17.15/3.04 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v1 | ~ (finite_subsets(v0) = % 17.15/3.04 v2) | ~ $i(v1) | ~ $i(v0) | ~ preboolean(v1) | ? [v3: $i] : ($i(v3) & % 17.15/3.04 ( ~ subset(v3, v0) | ~ finite(v3) | ~ in(v3, v1)) & (in(v3, v1) | % 17.15/3.04 (subset(v3, v0) & finite(v3))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 17.15/3.04 $i] : ( ~ (finite_subsets(v0) = v1) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 17.15/3.04 subset(v2, v0) | ~ preboolean(v1) | ~ finite(v2) | in(v2, v1)) & ! [v0: % 17.15/3.04 $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (finite_subsets(v0) = v1) | ~ $i(v2) % 17.15/3.04 | ~ $i(v1) | ~ $i(v0) | ~ preboolean(v1) | ~ in(v2, v1) | subset(v2, % 17.15/3.04 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (finite_subsets(v0) = % 17.15/3.04 v1) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ preboolean(v1) | ~ in(v2, % 17.15/3.04 v1) | finite(v2)) % 17.15/3.04 % 17.15/3.04 (fc1_finsub_1) % 17.15/3.04 ! [v0: $i] : ! [v1: $i] : ( ~ (powerset(v0) = v1) | ~ $i(v0) | ~ % 17.15/3.04 empty(v1)) & ! [v0: $i] : ! [v1: $i] : ( ~ (powerset(v0) = v1) | ~ $i(v0) % 17.15/3.04 | diff_closed(v1)) & ! [v0: $i] : ! [v1: $i] : ( ~ (powerset(v0) = v1) | % 17.15/3.04 ~ $i(v0) | cup_closed(v1)) & ! [v0: $i] : ! [v1: $i] : ( ~ (powerset(v0) = % 17.15/3.04 v1) | ~ $i(v0) | preboolean(v1)) % 17.15/3.04 % 17.15/3.04 (fc2_finsub_1) % 17.15/3.04 ! [v0: $i] : ! [v1: $i] : ( ~ (finite_subsets(v0) = v1) | ~ $i(v0) | ~ % 17.15/3.04 empty(v1)) & ! [v0: $i] : ! [v1: $i] : ( ~ (finite_subsets(v0) = v1) | ~ % 17.15/3.04 $i(v0) | diff_closed(v1)) & ! [v0: $i] : ! [v1: $i] : ( ~ % 17.15/3.04 (finite_subsets(v0) = v1) | ~ $i(v0) | cup_closed(v1)) & ! [v0: $i] : ! % 17.15/3.04 [v1: $i] : ( ~ (finite_subsets(v0) = v1) | ~ $i(v0) | preboolean(v1)) % 17.15/3.04 % 17.15/3.04 (rc2_finset_1) % 17.15/3.05 ! [v0: $i] : ! [v1: $i] : ( ~ (powerset(v0) = v1) | ~ $i(v0) | ? [v2: $i] % 17.15/3.05 : ($i(v2) & natural(v2) & ordinal(v2) & epsilon_connected(v2) & % 17.15/3.05 epsilon_transitive(v2) & one_to_one(v2) & function(v2) & relation(v2) & % 17.15/3.05 element(v2, v1) & finite(v2) & empty(v2))) % 17.15/3.05 % 17.15/3.05 (rc2_subset_1) % 17.15/3.05 ! [v0: $i] : ! [v1: $i] : ( ~ (powerset(v0) = v1) | ~ $i(v0) | ? [v2: $i] % 17.15/3.05 : ($i(v2) & element(v2, v1) & empty(v2))) % 17.15/3.05 % 17.15/3.05 (t13_finset_1) % 17.15/3.05 ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ subset(v0, v1) | ~ % 17.15/3.05 finite(v1) | finite(v0)) % 17.15/3.05 % 17.15/3.05 (t1_subset) % 17.15/3.05 ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ in(v0, v1) | % 17.15/3.05 element(v0, v1)) % 17.15/3.05 % 17.15/3.05 (t26_finsub_1) % 17.15/3.05 ! [v0: $i] : ! [v1: $i] : ( ~ (finite_subsets(v0) = v1) | ~ $i(v0) | ? % 17.15/3.05 [v2: $i] : (powerset(v0) = v2 & $i(v2) & subset(v1, v2))) % 17.15/3.05 % 17.15/3.05 (t27_finsub_1) % 17.15/3.05 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ( ~ (v2 = v1) & finite_subsets(v0) = % 17.15/3.05 v1 & powerset(v0) = v2 & $i(v2) & $i(v1) & $i(v0) & finite(v0)) % 17.15/3.05 % 17.15/3.05 (t2_subset) % 17.15/3.05 ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ element(v0, v1) | % 17.15/3.05 empty(v1) | in(v0, v1)) % 17.15/3.05 % 17.15/3.05 (t3_subset) % 17.15/3.05 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (powerset(v1) = v2) | ~ $i(v1) % 17.15/3.05 | ~ $i(v0) | ~ subset(v0, v1) | element(v0, v2)) & ! [v0: $i] : ! [v1: % 17.15/3.05 $i] : ! [v2: $i] : ( ~ (powerset(v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ % 17.15/3.05 element(v0, v2) | subset(v0, v1)) % 17.15/3.05 % 17.15/3.05 (t6_boole) % 17.15/3.05 $i(empty_set) & ! [v0: $i] : (v0 = empty_set | ~ $i(v0) | ~ empty(v0)) % 17.15/3.05 % 17.15/3.05 (t7_boole) % 17.15/3.05 ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ empty(v1) | ~ in(v0, % 17.15/3.05 v1)) % 17.15/3.05 % 17.15/3.05 (t8_boole) % 17.15/3.05 ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ $i(v1) | ~ $i(v0) | ~ empty(v1) | % 17.15/3.05 ~ empty(v0)) % 17.15/3.05 % 17.15/3.05 (function-axioms) % 17.15/3.06 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (finite_subsets(v2) = % 17.15/3.06 v1) | ~ (finite_subsets(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 17.15/3.06 $i] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0)) % 17.15/3.06 % 17.15/3.06 Further assumptions not needed in the proof: % 17.15/3.06 -------------------------------------------- % 17.15/3.06 antisymmetry_r2_hidden, cc1_finset_1, cc1_finsub_1, cc2_finsub_1, cc3_finsub_1, % 17.15/3.06 d10_xboole_0, dt_k5_finsub_1, existence_m1_subset_1, fc1_subset_1, fc1_xboole_0, % 17.15/3.06 rc1_finset_1, rc1_finsub_1, rc1_subset_1, rc1_xboole_0, rc2_xboole_0, % 17.15/3.06 rc3_finset_1, rc4_finset_1, reflexivity_r1_tarski, t4_subset, t5_subset % 17.15/3.06 % 17.15/3.06 Those formulas are unsatisfiable: % 17.15/3.06 --------------------------------- % 17.15/3.06 % 17.15/3.06 Begin of proof % 17.15/3.06 | % 17.15/3.06 | ALPHA: (d3_tarski) implies: % 17.15/3.06 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ % 17.15/3.06 | $i(v0) | ~ subset(v0, v1) | ~ in(v2, v0) | in(v2, v1)) % 17.15/3.06 | % 17.15/3.06 | ALPHA: (d5_finsub_1) implies: % 17.15/3.06 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (finite_subsets(v0) = v1) % 17.15/3.06 | | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ subset(v2, v0) | ~ % 17.15/3.06 | preboolean(v1) | ~ finite(v2) | in(v2, v1)) % 17.15/3.06 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v1 | ~ % 17.15/3.06 | (finite_subsets(v0) = v2) | ~ $i(v1) | ~ $i(v0) | ~ preboolean(v1) % 17.15/3.06 | | ? [v3: $i] : ($i(v3) & ( ~ subset(v3, v0) | ~ finite(v3) | ~ % 17.15/3.06 | in(v3, v1)) & (in(v3, v1) | (subset(v3, v0) & finite(v3))))) % 17.15/3.06 | % 17.15/3.06 | ALPHA: (fc1_finsub_1) implies: % 17.15/3.06 | (4) ! [v0: $i] : ! [v1: $i] : ( ~ (powerset(v0) = v1) | ~ $i(v0) | % 17.15/3.06 | preboolean(v1)) % 17.15/3.06 | % 17.15/3.06 | ALPHA: (fc2_finsub_1) implies: % 17.15/3.06 | (5) ! [v0: $i] : ! [v1: $i] : ( ~ (finite_subsets(v0) = v1) | ~ $i(v0) | % 17.15/3.06 | preboolean(v1)) % 17.15/3.06 | % 17.15/3.06 | ALPHA: (t3_subset) implies: % 17.15/3.06 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (powerset(v1) = v2) | ~ % 17.15/3.06 | $i(v1) | ~ $i(v0) | ~ element(v0, v2) | subset(v0, v1)) % 17.15/3.06 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (powerset(v1) = v2) | ~ % 17.15/3.06 | $i(v1) | ~ $i(v0) | ~ subset(v0, v1) | element(v0, v2)) % 17.15/3.06 | % 17.15/3.06 | ALPHA: (t6_boole) implies: % 17.15/3.06 | (8) ! [v0: $i] : (v0 = empty_set | ~ $i(v0) | ~ empty(v0)) % 17.15/3.06 | % 17.15/3.06 | ALPHA: (function-axioms) implies: % 17.15/3.06 | (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (powerset(v2) = % 17.15/3.06 | v1) | ~ (powerset(v2) = v0)) % 17.15/3.06 | % 17.15/3.06 | DELTA: instantiating (t27_finsub_1) with fresh symbols all_44_0, all_44_1, % 17.15/3.06 | all_44_2 gives: % 17.15/3.06 | (10) ~ (all_44_0 = all_44_1) & finite_subsets(all_44_2) = all_44_1 & % 17.15/3.06 | powerset(all_44_2) = all_44_0 & $i(all_44_0) & $i(all_44_1) & % 17.15/3.06 | $i(all_44_2) & finite(all_44_2) % 17.15/3.06 | % 17.15/3.06 | ALPHA: (10) implies: % 17.15/3.06 | (11) ~ (all_44_0 = all_44_1) % 17.15/3.06 | (12) finite(all_44_2) % 17.15/3.07 | (13) $i(all_44_2) % 17.15/3.07 | (14) $i(all_44_1) % 17.15/3.07 | (15) powerset(all_44_2) = all_44_0 % 17.15/3.07 | (16) finite_subsets(all_44_2) = all_44_1 % 17.15/3.07 | % 17.15/3.07 | GROUND_INST: instantiating (4) with all_44_2, all_44_0, simplifying with (13), % 17.15/3.07 | (15) gives: % 17.15/3.07 | (17) preboolean(all_44_0) % 17.15/3.07 | % 17.15/3.07 | GROUND_INST: instantiating (rc2_finset_1) with all_44_2, all_44_0, simplifying % 17.15/3.07 | with (13), (15) gives: % 17.15/3.07 | (18) ? [v0: $i] : ($i(v0) & natural(v0) & ordinal(v0) & % 17.15/3.07 | epsilon_connected(v0) & epsilon_transitive(v0) & one_to_one(v0) & % 17.15/3.07 | function(v0) & relation(v0) & element(v0, all_44_0) & finite(v0) & % 17.15/3.07 | empty(v0)) % 17.15/3.07 | % 17.15/3.07 | GROUND_INST: instantiating (rc2_subset_1) with all_44_2, all_44_0, simplifying % 17.15/3.07 | with (13), (15) gives: % 17.15/3.07 | (19) ? [v0: $i] : ($i(v0) & element(v0, all_44_0) & empty(v0)) % 17.15/3.07 | % 17.15/3.07 | GROUND_INST: instantiating (5) with all_44_2, all_44_1, simplifying with (13), % 17.15/3.07 | (16) gives: % 17.15/3.07 | (20) preboolean(all_44_1) % 17.15/3.07 | % 17.15/3.07 | GROUND_INST: instantiating (t26_finsub_1) with all_44_2, all_44_1, simplifying % 17.15/3.07 | with (13), (16) gives: % 17.15/3.07 | (21) ? [v0: $i] : (powerset(all_44_2) = v0 & $i(v0) & subset(all_44_1, % 17.15/3.07 | v0)) % 17.15/3.07 | % 17.15/3.07 | DELTA: instantiating (19) with fresh symbol all_52_0 gives: % 17.15/3.07 | (22) $i(all_52_0) & element(all_52_0, all_44_0) & empty(all_52_0) % 17.15/3.07 | % 17.15/3.07 | ALPHA: (22) implies: % 17.15/3.07 | (23) empty(all_52_0) % 17.15/3.07 | (24) element(all_52_0, all_44_0) % 17.15/3.07 | (25) $i(all_52_0) % 17.15/3.07 | % 17.15/3.07 | DELTA: instantiating (21) with fresh symbol all_54_0 gives: % 17.15/3.07 | (26) powerset(all_44_2) = all_54_0 & $i(all_54_0) & subset(all_44_1, % 17.15/3.07 | all_54_0) % 17.15/3.07 | % 17.15/3.07 | ALPHA: (26) implies: % 17.15/3.07 | (27) subset(all_44_1, all_54_0) % 17.15/3.07 | (28) $i(all_54_0) % 17.15/3.07 | (29) powerset(all_44_2) = all_54_0 % 17.15/3.07 | % 17.15/3.07 | DELTA: instantiating (18) with fresh symbol all_56_0 gives: % 17.15/3.07 | (30) $i(all_56_0) & natural(all_56_0) & ordinal(all_56_0) & % 17.15/3.07 | epsilon_connected(all_56_0) & epsilon_transitive(all_56_0) & % 17.15/3.07 | one_to_one(all_56_0) & function(all_56_0) & relation(all_56_0) & % 17.15/3.07 | element(all_56_0, all_44_0) & finite(all_56_0) & empty(all_56_0) % 17.15/3.07 | % 17.15/3.07 | ALPHA: (30) implies: % 17.15/3.07 | (31) empty(all_56_0) % 17.15/3.07 | (32) $i(all_56_0) % 17.15/3.07 | % 17.15/3.07 | GROUND_INST: instantiating (9) with all_44_0, all_54_0, all_44_2, simplifying % 17.15/3.07 | with (15), (29) gives: % 17.15/3.07 | (33) all_54_0 = all_44_0 % 17.15/3.07 | % 17.15/3.07 | REDUCE: (28), (33) imply: % 17.15/3.07 | (34) $i(all_44_0) % 17.15/3.07 | % 17.15/3.07 | REDUCE: (27), (33) imply: % 17.15/3.07 | (35) subset(all_44_1, all_44_0) % 17.15/3.07 | % 17.15/3.07 | GROUND_INST: instantiating (t8_boole) with all_52_0, all_56_0, simplifying % 17.15/3.07 | with (23), (25), (31), (32) gives: % 17.15/3.07 | (36) all_56_0 = all_52_0 % 17.15/3.07 | % 17.15/3.07 | GROUND_INST: instantiating (8) with all_56_0, simplifying with (31), (32) % 17.15/3.07 | gives: % 17.15/3.07 | (37) all_56_0 = empty_set % 17.15/3.07 | % 17.15/3.07 | GROUND_INST: instantiating (3) with all_44_2, all_44_0, all_44_1, simplifying % 17.15/3.07 | with (13), (16), (17), (34) gives: % 17.15/3.07 | (38) all_44_0 = all_44_1 | ? [v0: $i] : ($i(v0) & ( ~ subset(v0, all_44_2) % 17.15/3.07 | | ~ finite(v0) | ~ in(v0, all_44_0)) & (in(v0, all_44_0) | % 17.15/3.07 | (subset(v0, all_44_2) & finite(v0)))) % 17.15/3.07 | % 17.15/3.07 | GROUND_INST: instantiating (cc2_finset_1) with all_44_2, all_44_0, all_52_0, % 17.15/3.07 | simplifying with (12), (13), (15), (24), (25) gives: % 17.15/3.07 | (39) finite(all_52_0) % 17.15/3.07 | % 17.15/3.08 | GROUND_INST: instantiating (6) with all_52_0, all_44_2, all_44_0, simplifying % 17.15/3.08 | with (13), (15), (24), (25) gives: % 17.15/3.08 | (40) subset(all_52_0, all_44_2) % 17.15/3.08 | % 17.15/3.08 | COMBINE_EQS: (36), (37) imply: % 17.15/3.08 | (41) all_52_0 = empty_set % 17.15/3.08 | % 17.15/3.08 | REDUCE: (25), (41) imply: % 17.15/3.08 | (42) $i(empty_set) % 17.15/3.08 | % 17.15/3.08 | REDUCE: (40), (41) imply: % 17.15/3.08 | (43) subset(empty_set, all_44_2) % 17.15/3.08 | % 17.15/3.08 | REDUCE: (39), (41) imply: % 17.15/3.08 | (44) finite(empty_set) % 17.15/3.08 | % 17.15/3.08 | BETA: splitting (38) gives: % 17.15/3.08 | % 17.15/3.08 | Case 1: % 17.15/3.08 | | % 17.15/3.08 | | (45) all_44_0 = all_44_1 % 17.15/3.08 | | % 17.15/3.08 | | REDUCE: (11), (45) imply: % 17.15/3.08 | | (46) $false % 17.15/3.08 | | % 17.15/3.08 | | CLOSE: (46) is inconsistent. % 17.15/3.08 | | % 17.15/3.08 | Case 2: % 17.15/3.08 | | % 17.15/3.08 | | (47) ? [v0: $i] : ($i(v0) & ( ~ subset(v0, all_44_2) | ~ finite(v0) | % 17.15/3.08 | | ~ in(v0, all_44_0)) & (in(v0, all_44_0) | (subset(v0, all_44_2) % 17.15/3.08 | | & finite(v0)))) % 17.15/3.08 | | % 17.15/3.08 | | DELTA: instantiating (47) with fresh symbol all_72_0 gives: % 17.15/3.08 | | (48) $i(all_72_0) & ( ~ subset(all_72_0, all_44_2) | ~ finite(all_72_0) % 17.15/3.08 | | | ~ in(all_72_0, all_44_0)) & (in(all_72_0, all_44_0) | % 17.15/3.08 | | (subset(all_72_0, all_44_2) & finite(all_72_0))) % 17.15/3.08 | | % 17.15/3.08 | | ALPHA: (48) implies: % 17.15/3.08 | | (49) $i(all_72_0) % 17.15/3.08 | | (50) in(all_72_0, all_44_0) | (subset(all_72_0, all_44_2) & % 17.15/3.08 | | finite(all_72_0)) % 17.15/3.08 | | (51) ~ subset(all_72_0, all_44_2) | ~ finite(all_72_0) | ~ % 17.15/3.08 | | in(all_72_0, all_44_0) % 17.15/3.08 | | % 17.15/3.08 | | GROUND_INST: instantiating (2) with all_44_2, all_44_1, empty_set, % 17.15/3.08 | | simplifying with (13), (14), (16), (20), (42), (43), (44) % 17.15/3.08 | | gives: % 17.15/3.08 | | (52) in(empty_set, all_44_1) % 17.15/3.08 | | % 17.15/3.08 | | GROUND_INST: instantiating (1) with all_44_1, all_44_0, empty_set, % 17.15/3.08 | | simplifying with (14), (34), (35), (42), (52) gives: % 17.15/3.08 | | (53) in(empty_set, all_44_0) % 17.15/3.08 | | % 17.15/3.08 | | BETA: splitting (51) gives: % 17.15/3.08 | | % 17.15/3.08 | | Case 1: % 17.15/3.08 | | | % 17.15/3.08 | | | (54) ~ subset(all_72_0, all_44_2) % 17.15/3.08 | | | % 17.15/3.08 | | | BETA: splitting (50) gives: % 17.15/3.08 | | | % 17.15/3.08 | | | Case 1: % 17.15/3.08 | | | | % 17.15/3.08 | | | | (55) in(all_72_0, all_44_0) % 17.15/3.08 | | | | % 17.15/3.08 | | | | GROUND_INST: instantiating (t1_subset) with all_72_0, all_44_0, % 17.15/3.08 | | | | simplifying with (34), (49), (55) gives: % 17.15/3.08 | | | | (56) element(all_72_0, all_44_0) % 17.15/3.08 | | | | % 17.15/3.08 | | | | GROUND_INST: instantiating (6) with all_72_0, all_44_2, all_44_0, % 17.15/3.08 | | | | simplifying with (13), (15), (49), (54), (56) gives: % 17.15/3.08 | | | | (57) $false % 17.15/3.08 | | | | % 17.15/3.08 | | | | CLOSE: (57) is inconsistent. % 17.15/3.08 | | | | % 17.15/3.08 | | | Case 2: % 17.15/3.08 | | | | % 17.15/3.08 | | | | (58) subset(all_72_0, all_44_2) & finite(all_72_0) % 17.15/3.08 | | | | % 17.15/3.08 | | | | ALPHA: (58) implies: % 17.15/3.08 | | | | (59) subset(all_72_0, all_44_2) % 17.15/3.08 | | | | % 17.15/3.08 | | | | PRED_UNIFY: (54), (59) imply: % 17.15/3.08 | | | | (60) $false % 17.15/3.08 | | | | % 17.15/3.08 | | | | CLOSE: (60) is inconsistent. % 17.15/3.08 | | | | % 17.15/3.08 | | | End of split % 17.15/3.08 | | | % 17.15/3.08 | | Case 2: % 17.15/3.08 | | | % 17.15/3.08 | | | (61) subset(all_72_0, all_44_2) % 17.15/3.08 | | | (62) ~ finite(all_72_0) | ~ in(all_72_0, all_44_0) % 17.15/3.08 | | | % 17.15/3.08 | | | GROUND_INST: instantiating (7) with all_72_0, all_44_2, all_44_0, % 17.15/3.09 | | | simplifying with (13), (15), (49), (61) gives: % 17.15/3.09 | | | (63) element(all_72_0, all_44_0) % 17.15/3.09 | | | % 17.15/3.09 | | | GROUND_INST: instantiating (t13_finset_1) with all_72_0, all_44_2, % 17.15/3.09 | | | simplifying with (12), (13), (49), (61) gives: % 17.15/3.09 | | | (64) finite(all_72_0) % 17.15/3.09 | | | % 17.15/3.09 | | | BETA: splitting (62) gives: % 17.15/3.09 | | | % 17.15/3.09 | | | Case 1: % 17.15/3.09 | | | | % 17.15/3.09 | | | | (65) ~ finite(all_72_0) % 17.15/3.09 | | | | % 17.15/3.09 | | | | PRED_UNIFY: (64), (65) imply: % 17.15/3.09 | | | | (66) $false % 17.15/3.09 | | | | % 17.15/3.09 | | | | CLOSE: (66) is inconsistent. % 17.15/3.09 | | | | % 17.15/3.09 | | | Case 2: % 17.15/3.09 | | | | % 17.15/3.09 | | | | (67) ~ in(all_72_0, all_44_0) % 17.15/3.09 | | | | % 17.15/3.09 | | | | GROUND_INST: instantiating (t2_subset) with all_72_0, all_44_0, % 17.15/3.09 | | | | simplifying with (34), (49), (63), (67) gives: % 17.15/3.09 | | | | (68) empty(all_44_0) % 17.15/3.09 | | | | % 17.15/3.09 | | | | GROUND_INST: instantiating (t7_boole) with empty_set, all_44_0, % 17.15/3.09 | | | | simplifying with (34), (42), (53), (68) gives: % 17.15/3.09 | | | | (69) $false % 17.15/3.09 | | | | % 17.15/3.09 | | | | CLOSE: (69) is inconsistent. % 17.15/3.09 | | | | % 17.15/3.09 | | | End of split % 17.15/3.09 | | | % 17.15/3.09 | | End of split % 17.15/3.09 | | % 17.15/3.09 | End of split % 17.15/3.09 | % 17.15/3.09 End of proof % 17.15/3.09 % SZS output end Proof for theBenchmark % 17.15/3.09 % 17.15/3.09 2475ms %------------------------------------------------------------------------------