%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SEU308+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 : 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 17:44:00 EDT 2023 % Result : Theorem 9.97s 2.24s % Output : Proof 15.03s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SEU308+1 : TPTP v8.1.2. Released v3.3.0. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.14/0.35 % Computer : n021.cluster.edu % 0.14/0.35 % Model : x86_64 x86_64 % 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.35 % Memory : 8042.1875MB % 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.35 % CPULimit : 300 % 0.14/0.35 % WCLimit : 300 % 0.14/0.35 % DateTime : Wed Aug 23 13:44:54 EDT 2023 % 0.14/0.35 % CPUTime : % 0.21/0.62 ________ _____ % 0.21/0.62 ___ __ \_________(_)________________________________ % 0.21/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.21/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.21/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.21/0.62 % 0.21/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.21/0.62 (2023-06-19) % 0.21/0.62 % 0.21/0.62 (c) Philipp Rümmer, 2009-2023 % 0.21/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.21/0.62 Amanda Stjerna. % 0.21/0.62 Free software under BSD-3-Clause. % 0.21/0.62 % 0.21/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.21/0.62 % 0.21/0.62 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.21/0.63 Running up to 7 provers in parallel. % 0.21/0.65 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.21/0.65 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.21/0.65 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.21/0.65 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.21/0.65 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.21/0.65 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.21/0.65 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 3.02/1.24 Prover 4: Preprocessing ... % 3.02/1.24 Prover 1: Preprocessing ... % 3.62/1.28 Prover 3: Preprocessing ... % 3.62/1.28 Prover 6: Preprocessing ... % 3.62/1.28 Prover 5: Preprocessing ... % 3.62/1.28 Prover 0: Preprocessing ... % 3.62/1.28 Prover 2: Preprocessing ... % 7.99/1.91 Prover 1: Warning: ignoring some quantifiers % 7.99/1.92 Prover 5: Proving ... % 8.19/1.95 Prover 1: Constructing countermodel ... % 8.19/1.97 Prover 6: Proving ... % 8.19/1.99 Prover 2: Proving ... % 8.19/1.99 Prover 3: Warning: ignoring some quantifiers % 8.19/2.01 Prover 3: Constructing countermodel ... % 9.97/2.21 Prover 4: Warning: ignoring some quantifiers % 9.97/2.24 Prover 5: proved (1583ms) % 9.97/2.24 % 9.97/2.24 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 9.97/2.24 % 9.97/2.24 Prover 3: stopped % 9.97/2.24 Prover 2: stopped % 9.97/2.26 Prover 6: stopped % 9.97/2.26 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 9.97/2.26 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 9.97/2.26 Prover 4: Constructing countermodel ... % 9.97/2.26 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 9.97/2.26 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 10.69/2.32 Prover 7: Preprocessing ... % 10.69/2.37 Prover 8: Preprocessing ... % 10.69/2.40 Prover 10: Preprocessing ... % 10.69/2.41 Prover 11: Preprocessing ... % 12.11/2.49 Prover 0: Proving ... % 12.11/2.50 Prover 0: stopped % 12.11/2.50 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 12.11/2.50 Prover 7: Warning: ignoring some quantifiers % 12.11/2.52 Prover 7: Constructing countermodel ... % 12.11/2.53 Prover 10: Warning: ignoring some quantifiers % 12.11/2.54 Prover 13: Preprocessing ... % 12.84/2.57 Prover 10: Constructing countermodel ... % 13.10/2.60 Prover 8: Warning: ignoring some quantifiers % 13.10/2.62 Prover 8: Constructing countermodel ... % 13.34/2.66 Prover 13: Warning: ignoring some quantifiers % 13.34/2.68 Prover 13: Constructing countermodel ... % 14.08/2.77 Prover 10: Found proof (size 62) % 14.08/2.77 Prover 10: proved (512ms) % 14.08/2.77 Prover 7: stopped % 14.08/2.77 Prover 4: stopped % 14.08/2.77 Prover 1: stopped % 14.08/2.77 Prover 13: stopped % 14.08/2.78 Prover 8: stopped % 14.08/2.79 Prover 11: Warning: ignoring some quantifiers % 14.54/2.80 Prover 11: Constructing countermodel ... % 14.54/2.82 Prover 11: stopped % 14.54/2.82 % 14.54/2.82 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 14.54/2.82 % 14.54/2.83 % SZS output start Proof for theBenchmark % 14.54/2.83 Assumptions after simplification: % 14.54/2.83 --------------------------------- % 14.54/2.83 % 14.54/2.83 (d3_pre_topc) % 14.54/2.86 ! [v0: $i] : ! [v1: $i] : ( ~ (cast_as_carrier_subset(v0) = v1) | ~ $i(v0) % 14.54/2.86 | ~ one_sorted_str(v0) | (the_carrier(v0) = v1 & $i(v1))) % 14.54/2.86 % 14.54/2.86 (d5_subset_1) % 14.54/2.86 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (subset_complement(v0, v1) = v2) % 14.54/2.86 | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : ((v4 = v2 & % 14.54/2.86 set_difference(v0, v1) = v2 & $i(v2)) | (powerset(v0) = v3 & $i(v3) & ~ % 14.54/2.86 element(v1, v3)))) % 14.54/2.86 % 14.54/2.86 (dt_k2_pre_topc) % 14.54/2.86 ! [v0: $i] : ! [v1: $i] : ( ~ (cast_as_carrier_subset(v0) = v1) | ~ $i(v0) % 14.54/2.86 | ~ one_sorted_str(v0) | ? [v2: $i] : ? [v3: $i] : (the_carrier(v0) = v2 % 14.54/2.86 & powerset(v2) = v3 & $i(v3) & $i(v2) & element(v1, v3))) % 14.54/2.86 % 14.54/2.86 (dt_k3_subset_1) % 14.54/2.86 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (subset_complement(v0, v1) = v2) % 14.54/2.86 | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : (powerset(v0) = v3 & $i(v3) & ( ~ % 14.86/2.86 element(v1, v3) | element(v2, v3)))) % 14.86/2.86 % 14.86/2.86 (dt_k6_subset_1) % 14.87/2.87 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 14.87/2.87 (subset_difference(v0, v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 14.87/2.87 ? [v4: $i] : (powerset(v0) = v4 & $i(v4) & ( ~ element(v2, v4) | ~ % 14.87/2.87 element(v1, v4) | element(v3, v4)))) % 14.87/2.87 % 14.87/2.87 (redefinition_k6_subset_1) % 14.87/2.87 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 14.87/2.87 (subset_difference(v0, v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 14.87/2.87 ? [v4: $i] : ? [v5: $i] : ((v5 = v3 & set_difference(v1, v2) = v3 & $i(v3)) % 14.87/2.87 | (powerset(v0) = v4 & $i(v4) & ( ~ element(v2, v4) | ~ element(v1, % 14.87/2.87 v4))))) % 14.87/2.87 % 14.87/2.87 (t17_pre_topc) % 14.87/2.87 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: % 14.87/2.87 $i] : ? [v6: $i] : ( ~ (v6 = v5) & cast_as_carrier_subset(v0) = v3 & % 14.87/2.87 the_carrier(v0) = v1 & subset_difference(v1, v3, v4) = v6 & % 14.87/2.87 subset_complement(v1, v4) = v5 & powerset(v1) = v2 & $i(v6) & $i(v5) & % 14.87/2.87 $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & one_sorted_str(v0) & % 14.87/2.87 element(v4, v2)) % 14.87/2.87 % 14.87/2.87 (function-axioms) % 14.87/2.87 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 % 14.87/2.87 | ~ (subset_difference(v4, v3, v2) = v1) | ~ (subset_difference(v4, v3, % 14.87/2.87 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 % 14.87/2.87 = v0 | ~ (subset_complement(v3, v2) = v1) | ~ (subset_complement(v3, v2) = % 14.87/2.87 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | % 14.87/2.87 ~ (set_difference(v3, v2) = v1) | ~ (set_difference(v3, v2) = v0)) & ! % 14.87/2.87 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 14.87/2.87 (cast_as_carrier_subset(v2) = v1) | ~ (cast_as_carrier_subset(v2) = v0)) & % 14.87/2.87 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (the_carrier(v2) = v1) % 14.87/2.87 | ~ (the_carrier(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 % 14.87/2.87 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0)) % 14.87/2.87 % 14.87/2.87 Further assumptions not needed in the proof: % 14.87/2.87 -------------------------------------------- % 14.87/2.88 antisymmetry_r2_hidden, cc10_membered, cc11_membered, cc12_membered, % 14.87/2.88 cc13_membered, cc14_membered, cc15_membered, cc16_membered, cc17_membered, % 14.87/2.88 cc18_membered, cc19_membered, cc1_membered, cc20_membered, cc2_membered, % 14.87/2.88 cc3_membered, cc4_membered, dt_k1_xboole_0, dt_k1_zfmisc_1, dt_k4_xboole_0, % 14.87/2.88 dt_l1_struct_0, dt_m1_subset_1, dt_u1_struct_0, existence_l1_struct_0, % 14.87/2.88 existence_m1_subset_1, fc1_subset_1, fc37_membered, fc38_membered, % 14.87/2.88 fc39_membered, fc40_membered, fc41_membered, fc6_membered, % 14.87/2.88 involutiveness_k3_subset_1, rc1_membered, rc1_subset_1, rc2_subset_1, % 14.87/2.88 reflexivity_r1_tarski, t1_subset, t2_subset, t3_boole, t3_subset, t4_boole, % 14.87/2.88 t4_subset, t5_subset, t6_boole, t7_boole, t8_boole % 14.87/2.88 % 14.87/2.88 Those formulas are unsatisfiable: % 14.87/2.88 --------------------------------- % 14.87/2.88 % 14.87/2.88 Begin of proof % 14.87/2.88 | % 14.87/2.88 | ALPHA: (function-axioms) implies: % 14.87/2.89 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (powerset(v2) = % 14.87/2.89 | v1) | ~ (powerset(v2) = v0)) % 14.87/2.89 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 14.87/2.89 | (the_carrier(v2) = v1) | ~ (the_carrier(v2) = v0)) % 14.87/2.89 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 14.87/2.89 | (set_difference(v3, v2) = v1) | ~ (set_difference(v3, v2) = v0)) % 14.87/2.89 | % 14.87/2.89 | DELTA: instantiating (t17_pre_topc) with fresh symbols all_51_0, all_51_1, % 14.87/2.89 | all_51_2, all_51_3, all_51_4, all_51_5, all_51_6 gives: % 14.87/2.89 | (4) ~ (all_51_0 = all_51_1) & cast_as_carrier_subset(all_51_6) = all_51_3 % 14.87/2.89 | & the_carrier(all_51_6) = all_51_5 & subset_difference(all_51_5, % 14.87/2.89 | all_51_3, all_51_2) = all_51_0 & subset_complement(all_51_5, % 14.87/2.89 | all_51_2) = all_51_1 & powerset(all_51_5) = all_51_4 & $i(all_51_0) & % 14.87/2.89 | $i(all_51_1) & $i(all_51_2) & $i(all_51_3) & $i(all_51_4) & % 14.87/2.89 | $i(all_51_5) & $i(all_51_6) & one_sorted_str(all_51_6) & % 14.87/2.89 | element(all_51_2, all_51_4) % 14.87/2.89 | % 14.87/2.89 | ALPHA: (4) implies: % 14.87/2.89 | (5) ~ (all_51_0 = all_51_1) % 14.87/2.89 | (6) element(all_51_2, all_51_4) % 14.87/2.89 | (7) one_sorted_str(all_51_6) % 14.87/2.89 | (8) $i(all_51_6) % 14.87/2.89 | (9) $i(all_51_5) % 14.87/2.89 | (10) $i(all_51_3) % 14.87/2.89 | (11) $i(all_51_2) % 14.87/2.89 | (12) powerset(all_51_5) = all_51_4 % 14.87/2.89 | (13) subset_complement(all_51_5, all_51_2) = all_51_1 % 14.87/2.89 | (14) subset_difference(all_51_5, all_51_3, all_51_2) = all_51_0 % 14.87/2.89 | (15) the_carrier(all_51_6) = all_51_5 % 14.87/2.89 | (16) cast_as_carrier_subset(all_51_6) = all_51_3 % 14.87/2.89 | % 14.87/2.89 | GROUND_INST: instantiating (d5_subset_1) with all_51_5, all_51_2, all_51_1, % 14.87/2.89 | simplifying with (9), (11), (13) gives: % 14.87/2.89 | (17) ? [v0: $i] : ? [v1: int] : ((v1 = all_51_1 & % 14.87/2.89 | set_difference(all_51_5, all_51_2) = all_51_1 & $i(all_51_1)) | % 14.87/2.89 | (powerset(all_51_5) = v0 & $i(v0) & ~ element(all_51_2, v0))) % 14.87/2.89 | % 14.87/2.89 | GROUND_INST: instantiating (dt_k3_subset_1) with all_51_5, all_51_2, all_51_1, % 14.87/2.89 | simplifying with (9), (11), (13) gives: % 14.87/2.89 | (18) ? [v0: $i] : (powerset(all_51_5) = v0 & $i(v0) & ( ~ % 14.87/2.89 | element(all_51_2, v0) | element(all_51_1, v0))) % 14.87/2.89 | % 14.87/2.89 | GROUND_INST: instantiating (redefinition_k6_subset_1) with all_51_5, all_51_3, % 14.87/2.89 | all_51_2, all_51_0, simplifying with (9), (10), (11), (14) gives: % 14.87/2.90 | (19) ? [v0: $i] : ? [v1: int] : ((v1 = all_51_0 & % 14.87/2.90 | set_difference(all_51_3, all_51_2) = all_51_0 & $i(all_51_0)) | % 14.87/2.90 | (powerset(all_51_5) = v0 & $i(v0) & ( ~ element(all_51_2, v0) | ~ % 14.87/2.90 | element(all_51_3, v0)))) % 14.87/2.90 | % 14.87/2.90 | GROUND_INST: instantiating (dt_k6_subset_1) with all_51_5, all_51_3, all_51_2, % 14.87/2.90 | all_51_0, simplifying with (9), (10), (11), (14) gives: % 15.03/2.90 | (20) ? [v0: $i] : (powerset(all_51_5) = v0 & $i(v0) & ( ~ % 15.03/2.90 | element(all_51_2, v0) | ~ element(all_51_3, v0) | % 15.03/2.90 | element(all_51_0, v0))) % 15.03/2.90 | % 15.03/2.90 | GROUND_INST: instantiating (dt_k2_pre_topc) with all_51_6, all_51_3, % 15.03/2.90 | simplifying with (7), (8), (16) gives: % 15.03/2.90 | (21) ? [v0: $i] : ? [v1: $i] : (the_carrier(all_51_6) = v0 & powerset(v0) % 15.03/2.90 | = v1 & $i(v1) & $i(v0) & element(all_51_3, v1)) % 15.03/2.90 | % 15.03/2.90 | GROUND_INST: instantiating (d3_pre_topc) with all_51_6, all_51_3, simplifying % 15.03/2.90 | with (7), (8), (16) gives: % 15.03/2.90 | (22) the_carrier(all_51_6) = all_51_3 & $i(all_51_3) % 15.03/2.90 | % 15.03/2.90 | ALPHA: (22) implies: % 15.03/2.90 | (23) the_carrier(all_51_6) = all_51_3 % 15.03/2.90 | % 15.03/2.90 | DELTA: instantiating (18) with fresh symbol all_61_0 gives: % 15.03/2.90 | (24) powerset(all_51_5) = all_61_0 & $i(all_61_0) & ( ~ element(all_51_2, % 15.03/2.90 | all_61_0) | element(all_51_1, all_61_0)) % 15.03/2.90 | % 15.03/2.90 | ALPHA: (24) implies: % 15.03/2.90 | (25) powerset(all_51_5) = all_61_0 % 15.03/2.90 | % 15.03/2.90 | DELTA: instantiating (21) with fresh symbols all_63_0, all_63_1 gives: % 15.03/2.90 | (26) the_carrier(all_51_6) = all_63_1 & powerset(all_63_1) = all_63_0 & % 15.03/2.90 | $i(all_63_0) & $i(all_63_1) & element(all_51_3, all_63_0) % 15.03/2.90 | % 15.03/2.90 | ALPHA: (26) implies: % 15.03/2.90 | (27) element(all_51_3, all_63_0) % 15.03/2.90 | (28) powerset(all_63_1) = all_63_0 % 15.03/2.90 | (29) the_carrier(all_51_6) = all_63_1 % 15.03/2.90 | % 15.03/2.90 | DELTA: instantiating (20) with fresh symbol all_65_0 gives: % 15.03/2.90 | (30) powerset(all_51_5) = all_65_0 & $i(all_65_0) & ( ~ element(all_51_2, % 15.03/2.90 | all_65_0) | ~ element(all_51_3, all_65_0) | element(all_51_0, % 15.03/2.90 | all_65_0)) % 15.03/2.90 | % 15.03/2.90 | ALPHA: (30) implies: % 15.03/2.90 | (31) powerset(all_51_5) = all_65_0 % 15.03/2.90 | % 15.03/2.90 | DELTA: instantiating (17) with fresh symbols all_67_0, all_67_1 gives: % 15.03/2.90 | (32) (all_67_0 = all_51_1 & set_difference(all_51_5, all_51_2) = all_51_1 & % 15.03/2.90 | $i(all_51_1)) | (powerset(all_51_5) = all_67_1 & $i(all_67_1) & ~ % 15.03/2.90 | element(all_51_2, all_67_1)) % 15.03/2.90 | % 15.03/2.90 | DELTA: instantiating (19) with fresh symbols all_68_0, all_68_1 gives: % 15.03/2.90 | (33) (all_68_0 = all_51_0 & set_difference(all_51_3, all_51_2) = all_51_0 & % 15.03/2.90 | $i(all_51_0)) | (powerset(all_51_5) = all_68_1 & $i(all_68_1) & ( ~ % 15.03/2.90 | element(all_51_2, all_68_1) | ~ element(all_51_3, all_68_1))) % 15.03/2.90 | % 15.03/2.90 | BETA: splitting (32) gives: % 15.03/2.90 | % 15.03/2.90 | Case 1: % 15.03/2.90 | | % 15.03/2.90 | | (34) all_67_0 = all_51_1 & set_difference(all_51_5, all_51_2) = all_51_1 % 15.03/2.90 | | & $i(all_51_1) % 15.03/2.90 | | % 15.03/2.90 | | ALPHA: (34) implies: % 15.03/2.90 | | (35) set_difference(all_51_5, all_51_2) = all_51_1 % 15.03/2.90 | | % 15.03/2.91 | | GROUND_INST: instantiating (1) with all_51_4, all_65_0, all_51_5, % 15.03/2.91 | | simplifying with (12), (31) gives: % 15.03/2.91 | | (36) all_65_0 = all_51_4 % 15.03/2.91 | | % 15.03/2.91 | | GROUND_INST: instantiating (1) with all_61_0, all_65_0, all_51_5, % 15.03/2.91 | | simplifying with (25), (31) gives: % 15.03/2.91 | | (37) all_65_0 = all_61_0 % 15.03/2.91 | | % 15.03/2.91 | | GROUND_INST: instantiating (2) with all_51_5, all_63_1, all_51_6, % 15.03/2.91 | | simplifying with (15), (29) gives: % 15.03/2.91 | | (38) all_63_1 = all_51_5 % 15.03/2.91 | | % 15.03/2.91 | | GROUND_INST: instantiating (2) with all_51_3, all_63_1, all_51_6, % 15.03/2.91 | | simplifying with (23), (29) gives: % 15.03/2.91 | | (39) all_63_1 = all_51_3 % 15.03/2.91 | | % 15.03/2.91 | | COMBINE_EQS: (36), (37) imply: % 15.03/2.91 | | (40) all_61_0 = all_51_4 % 15.03/2.91 | | % 15.03/2.91 | | COMBINE_EQS: (38), (39) imply: % 15.03/2.91 | | (41) all_51_3 = all_51_5 % 15.03/2.91 | | % 15.03/2.91 | | REDUCE: (28), (38) imply: % 15.03/2.91 | | (42) powerset(all_51_5) = all_63_0 % 15.03/2.91 | | % 15.03/2.91 | | REDUCE: (27), (41) imply: % 15.03/2.91 | | (43) element(all_51_5, all_63_0) % 15.03/2.91 | | % 15.03/2.91 | | BETA: splitting (33) gives: % 15.03/2.91 | | % 15.03/2.91 | | Case 1: % 15.03/2.91 | | | % 15.03/2.91 | | | (44) all_68_0 = all_51_0 & set_difference(all_51_3, all_51_2) = % 15.03/2.91 | | | all_51_0 & $i(all_51_0) % 15.03/2.91 | | | % 15.03/2.91 | | | ALPHA: (44) implies: % 15.03/2.91 | | | (45) set_difference(all_51_3, all_51_2) = all_51_0 % 15.03/2.91 | | | % 15.03/2.91 | | | REDUCE: (41), (45) imply: % 15.03/2.91 | | | (46) set_difference(all_51_5, all_51_2) = all_51_0 % 15.03/2.91 | | | % 15.03/2.91 | | | GROUND_INST: instantiating (3) with all_51_1, all_51_0, all_51_2, % 15.03/2.91 | | | all_51_5, simplifying with (35), (46) gives: % 15.03/2.91 | | | (47) all_51_0 = all_51_1 % 15.03/2.91 | | | % 15.03/2.91 | | | REDUCE: (5), (47) imply: % 15.03/2.91 | | | (48) $false % 15.03/2.91 | | | % 15.03/2.91 | | | CLOSE: (48) is inconsistent. % 15.03/2.91 | | | % 15.03/2.91 | | Case 2: % 15.03/2.91 | | | % 15.03/2.91 | | | (49) powerset(all_51_5) = all_68_1 & $i(all_68_1) & ( ~ % 15.03/2.91 | | | element(all_51_2, all_68_1) | ~ element(all_51_3, all_68_1)) % 15.03/2.91 | | | % 15.03/2.91 | | | ALPHA: (49) implies: % 15.03/2.91 | | | (50) powerset(all_51_5) = all_68_1 % 15.03/2.91 | | | (51) ~ element(all_51_2, all_68_1) | ~ element(all_51_3, all_68_1) % 15.03/2.91 | | | % 15.03/2.91 | | | GROUND_INST: instantiating (1) with all_51_4, all_68_1, all_51_5, % 15.03/2.91 | | | simplifying with (12), (50) gives: % 15.03/2.91 | | | (52) all_68_1 = all_51_4 % 15.03/2.91 | | | % 15.03/2.91 | | | GROUND_INST: instantiating (1) with all_63_0, all_68_1, all_51_5, % 15.03/2.91 | | | simplifying with (42), (50) gives: % 15.03/2.91 | | | (53) all_68_1 = all_63_0 % 15.03/2.91 | | | % 15.03/2.91 | | | COMBINE_EQS: (52), (53) imply: % 15.03/2.91 | | | (54) all_63_0 = all_51_4 % 15.03/2.91 | | | % 15.03/2.91 | | | REDUCE: (43), (54) imply: % 15.03/2.91 | | | (55) element(all_51_5, all_51_4) % 15.03/2.91 | | | % 15.03/2.91 | | | BETA: splitting (51) gives: % 15.03/2.91 | | | % 15.03/2.91 | | | Case 1: % 15.03/2.91 | | | | % 15.03/2.91 | | | | (56) ~ element(all_51_2, all_68_1) % 15.03/2.91 | | | | % 15.03/2.91 | | | | REDUCE: (52), (56) imply: % 15.03/2.91 | | | | (57) ~ element(all_51_2, all_51_4) % 15.03/2.91 | | | | % 15.03/2.91 | | | | PRED_UNIFY: (6), (57) imply: % 15.03/2.91 | | | | (58) $false % 15.03/2.91 | | | | % 15.03/2.91 | | | | CLOSE: (58) is inconsistent. % 15.03/2.91 | | | | % 15.03/2.91 | | | Case 2: % 15.03/2.91 | | | | % 15.03/2.91 | | | | (59) ~ element(all_51_3, all_68_1) % 15.03/2.91 | | | | % 15.03/2.91 | | | | REDUCE: (41), (52), (59) imply: % 15.03/2.91 | | | | (60) ~ element(all_51_5, all_51_4) % 15.03/2.91 | | | | % 15.03/2.91 | | | | PRED_UNIFY: (55), (60) imply: % 15.03/2.91 | | | | (61) $false % 15.03/2.91 | | | | % 15.03/2.91 | | | | CLOSE: (61) is inconsistent. % 15.03/2.91 | | | | % 15.03/2.92 | | | End of split % 15.03/2.92 | | | % 15.03/2.92 | | End of split % 15.03/2.92 | | % 15.03/2.92 | Case 2: % 15.03/2.92 | | % 15.03/2.92 | | (62) powerset(all_51_5) = all_67_1 & $i(all_67_1) & ~ element(all_51_2, % 15.03/2.92 | | all_67_1) % 15.03/2.92 | | % 15.03/2.92 | | ALPHA: (62) implies: % 15.03/2.92 | | (63) ~ element(all_51_2, all_67_1) % 15.03/2.92 | | (64) powerset(all_51_5) = all_67_1 % 15.03/2.92 | | % 15.03/2.92 | | GROUND_INST: instantiating (1) with all_51_4, all_65_0, all_51_5, % 15.03/2.92 | | simplifying with (12), (31) gives: % 15.03/2.92 | | (65) all_65_0 = all_51_4 % 15.03/2.92 | | % 15.03/2.92 | | GROUND_INST: instantiating (1) with all_65_0, all_67_1, all_51_5, % 15.03/2.92 | | simplifying with (31), (64) gives: % 15.03/2.92 | | (66) all_67_1 = all_65_0 % 15.03/2.92 | | % 15.03/2.92 | | GROUND_INST: instantiating (1) with all_61_0, all_67_1, all_51_5, % 15.03/2.92 | | simplifying with (25), (64) gives: % 15.03/2.92 | | (67) all_67_1 = all_61_0 % 15.03/2.92 | | % 15.03/2.92 | | COMBINE_EQS: (66), (67) imply: % 15.03/2.92 | | (68) all_65_0 = all_61_0 % 15.03/2.92 | | % 15.03/2.92 | | SIMP: (68) implies: % 15.03/2.92 | | (69) all_65_0 = all_61_0 % 15.03/2.92 | | % 15.03/2.92 | | COMBINE_EQS: (65), (69) imply: % 15.03/2.92 | | (70) all_61_0 = all_51_4 % 15.03/2.92 | | % 15.03/2.92 | | SIMP: (70) implies: % 15.03/2.92 | | (71) all_61_0 = all_51_4 % 15.03/2.92 | | % 15.03/2.92 | | COMBINE_EQS: (67), (71) imply: % 15.03/2.92 | | (72) all_67_1 = all_51_4 % 15.03/2.92 | | % 15.03/2.92 | | REDUCE: (63), (72) imply: % 15.03/2.92 | | (73) ~ element(all_51_2, all_51_4) % 15.03/2.92 | | % 15.03/2.92 | | PRED_UNIFY: (6), (73) imply: % 15.03/2.92 | | (74) $false % 15.03/2.92 | | % 15.03/2.92 | | CLOSE: (74) is inconsistent. % 15.03/2.92 | | % 15.03/2.92 | End of split % 15.03/2.92 | % 15.03/2.92 End of proof % 15.03/2.92 % SZS output end Proof for theBenchmark % 15.03/2.92 % 15.03/2.92 2298ms %------------------------------------------------------------------------------