%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SEU326+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 : n023.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 17:44:06 EDT 2023 % Result : Theorem 39.60s 5.95s % Output : Proof 43.92s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : SEU326+1 : TPTP v8.1.2. Released v3.3.0. % 0.07/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.14/0.34 % Computer : n023.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 18:24:58 EDT 2023 % 0.14/0.35 % CPUTime : % 0.21/0.61 ________ _____ % 0.21/0.61 ___ __ \_________(_)________________________________ % 0.21/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.21/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.21/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.21/0.61 % 0.21/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.21/0.61 (2023-06-19) % 0.21/0.61 % 0.21/0.61 (c) Philipp Rümmer, 2009-2023 % 0.21/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.21/0.61 Amanda Stjerna. % 0.21/0.61 Free software under BSD-3-Clause. % 0.21/0.61 % 0.21/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.21/0.61 % 0.21/0.62 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.21/0.63 Running up to 7 provers in parallel. % 0.21/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.21/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.21/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.21/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.21/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.21/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.21/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.53/1.10 Prover 4: Preprocessing ... % 2.53/1.10 Prover 1: Preprocessing ... % 3.08/1.14 Prover 3: Preprocessing ... % 3.08/1.14 Prover 5: Preprocessing ... % 3.08/1.14 Prover 0: Preprocessing ... % 3.08/1.14 Prover 6: Preprocessing ... % 3.08/1.14 Prover 2: Preprocessing ... % 6.52/1.60 Prover 5: Proving ... % 6.52/1.65 Prover 2: Proving ... % 6.52/1.66 Prover 1: Warning: ignoring some quantifiers % 6.52/1.67 Prover 6: Proving ... % 6.52/1.68 Prover 3: Warning: ignoring some quantifiers % 7.25/1.69 Prover 1: Constructing countermodel ... % 7.32/1.70 Prover 3: Constructing countermodel ... % 8.71/1.90 Prover 4: Warning: ignoring some quantifiers % 8.71/1.97 Prover 4: Constructing countermodel ... % 9.92/2.06 Prover 0: Proving ... % 39.60/5.94 Prover 2: proved (5258ms) % 39.60/5.94 % 39.60/5.95 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 39.60/5.95 % 39.97/5.96 Prover 3: stopped % 39.97/5.96 Prover 6: stopped % 39.97/5.97 Prover 5: stopped % 39.97/5.97 Prover 0: stopped % 39.97/5.97 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 39.97/5.97 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 39.97/5.97 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 39.97/5.97 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 39.97/5.97 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 39.97/6.00 Prover 7: Preprocessing ... % 40.67/6.07 Prover 10: Preprocessing ... % 40.67/6.07 Prover 13: Preprocessing ... % 40.67/6.07 Prover 8: Preprocessing ... % 40.67/6.08 Prover 11: Preprocessing ... % 41.06/6.10 Prover 10: Warning: ignoring some quantifiers % 41.06/6.11 Prover 7: Warning: ignoring some quantifiers % 41.06/6.11 Prover 10: Constructing countermodel ... % 41.06/6.11 Prover 7: Constructing countermodel ... % 41.06/6.12 Prover 13: Warning: ignoring some quantifiers % 41.06/6.12 Prover 13: Constructing countermodel ... % 41.46/6.18 Prover 8: Warning: ignoring some quantifiers % 41.46/6.19 Prover 8: Constructing countermodel ... % 41.85/6.23 Prover 13: gave up % 41.85/6.24 Prover 10: gave up % 41.85/6.25 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 41.85/6.25 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085 % 42.21/6.28 Prover 16: Preprocessing ... % 42.21/6.31 Prover 16: Warning: ignoring some quantifiers % 42.21/6.31 Prover 16: Constructing countermodel ... % 42.21/6.32 Prover 19: Preprocessing ... % 42.21/6.33 Prover 11: Warning: ignoring some quantifiers % 42.99/6.35 Prover 11: Constructing countermodel ... % 43.38/6.40 Prover 7: Found proof (size 82) % 43.38/6.40 Prover 7: proved (440ms) % 43.38/6.40 Prover 11: stopped % 43.38/6.40 Prover 16: stopped % 43.38/6.40 Prover 8: stopped % 43.38/6.40 Prover 4: stopped % 43.38/6.41 Prover 1: stopped % 43.38/6.42 Prover 19: Warning: ignoring some quantifiers % 43.38/6.43 Prover 19: Constructing countermodel ... % 43.38/6.43 Prover 19: stopped % 43.38/6.43 % 43.38/6.43 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 43.38/6.43 % 43.38/6.44 % SZS output start Proof for theBenchmark % 43.38/6.44 Assumptions after simplification: % 43.38/6.44 --------------------------------- % 43.38/6.44 % 43.38/6.44 (dt_k7_setfam_1) % 43.38/6.47 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (complements_of_subsets(v0, v1) % 43.38/6.47 = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : (powerset(v3) % 43.38/6.47 = v4 & powerset(v0) = v3 & $i(v4) & $i(v3) & ( ~ element(v1, v4) | % 43.38/6.47 element(v2, v4)))) % 43.38/6.47 % 43.38/6.47 (involutiveness_k7_setfam_1) % 43.38/6.47 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (complements_of_subsets(v0, v1) % 43.38/6.47 = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : % 43.38/6.47 ((v5 = v1 & complements_of_subsets(v0, v2) = v1) | (powerset(v3) = v4 & % 43.38/6.47 powerset(v0) = v3 & $i(v4) & $i(v3) & ~ element(v1, v4)))) % 43.38/6.47 % 43.38/6.47 (t10_tops_2) % 43.38/6.47 $i(empty_set) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? % 43.38/6.47 [v4: $i] : (complements_of_subsets(v0, v1) = v4 & powerset(v2) = v3 & % 43.38/6.47 powerset(v0) = v2 & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & element(v1, % 43.38/6.47 v3) & ((v4 = empty_set & ~ (v1 = empty_set)) | (v1 = empty_set & ~ (v4 = % 43.38/6.47 empty_set)))) % 43.38/6.47 % 43.38/6.47 (t46_setfam_1) % 43.38/6.47 $i(empty_set) & ! [v0: $i] : ! [v1: $i] : (v1 = empty_set | ~ % 43.38/6.47 (complements_of_subsets(v0, v1) = empty_set) | ~ $i(v1) | ~ $i(v0) | ? % 43.38/6.47 [v2: $i] : ? [v3: $i] : (powerset(v2) = v3 & powerset(v0) = v2 & $i(v3) & % 43.38/6.47 $i(v2) & ~ element(v1, v3))) % 43.38/6.47 % 43.38/6.47 (function-axioms) % 43.38/6.47 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 43.38/6.47 (complements_of_subsets(v3, v2) = v1) | ~ (complements_of_subsets(v3, v2) = % 43.38/6.47 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 43.38/6.47 (powerset(v2) = v1) | ~ (powerset(v2) = v0)) % 43.38/6.47 % 43.38/6.47 Further assumptions not needed in the proof: % 43.38/6.47 -------------------------------------------- % 43.38/6.47 antisymmetry_r2_hidden, cc10_membered, cc11_membered, cc12_membered, % 43.38/6.47 cc13_membered, cc14_membered, cc15_membered, cc16_membered, cc17_membered, % 43.38/6.47 cc18_membered, cc19_membered, cc1_membered, cc20_membered, cc2_membered, % 43.38/6.47 cc3_membered, cc4_membered, dt_k1_xboole_0, dt_k1_zfmisc_1, dt_m1_subset_1, % 43.38/6.47 existence_m1_subset_1, fc1_subset_1, fc6_membered, rc1_membered, rc1_subset_1, % 43.38/6.47 rc2_subset_1, reflexivity_r1_tarski, t1_subset, t2_subset, t3_subset, t4_subset, % 43.38/6.47 t5_subset, t6_boole, t7_boole, t8_boole % 43.38/6.47 % 43.38/6.47 Those formulas are unsatisfiable: % 43.38/6.47 --------------------------------- % 43.38/6.47 % 43.38/6.47 Begin of proof % 43.38/6.48 | % 43.38/6.48 | ALPHA: (t46_setfam_1) implies: % 43.38/6.48 | (1) ! [v0: $i] : ! [v1: $i] : (v1 = empty_set | ~ % 43.38/6.48 | (complements_of_subsets(v0, v1) = empty_set) | ~ $i(v1) | ~ $i(v0) % 43.38/6.48 | | ? [v2: $i] : ? [v3: $i] : (powerset(v2) = v3 & powerset(v0) = v2 % 43.38/6.48 | & $i(v3) & $i(v2) & ~ element(v1, v3))) % 43.38/6.48 | % 43.38/6.48 | ALPHA: (t10_tops_2) implies: % 43.38/6.48 | (2) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 43.38/6.48 | (complements_of_subsets(v0, v1) = v4 & powerset(v2) = v3 & powerset(v0) % 43.38/6.48 | = v2 & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & element(v1, v3) & % 43.38/6.48 | ((v4 = empty_set & ~ (v1 = empty_set)) | (v1 = empty_set & ~ (v4 = % 43.38/6.48 | empty_set)))) % 43.38/6.48 | % 43.38/6.48 | ALPHA: (function-axioms) implies: % 43.38/6.48 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (powerset(v2) = % 43.38/6.48 | v1) | ~ (powerset(v2) = v0)) % 43.38/6.48 | % 43.38/6.48 | DELTA: instantiating (2) with fresh symbols all_38_0, all_38_1, all_38_2, % 43.38/6.48 | all_38_3, all_38_4 gives: % 43.38/6.48 | (4) complements_of_subsets(all_38_4, all_38_3) = all_38_0 & % 43.38/6.48 | powerset(all_38_2) = all_38_1 & powerset(all_38_4) = all_38_2 & % 43.38/6.48 | $i(all_38_0) & $i(all_38_1) & $i(all_38_2) & $i(all_38_3) & % 43.38/6.48 | $i(all_38_4) & element(all_38_3, all_38_1) & ((all_38_0 = empty_set & % 43.38/6.48 | ~ (all_38_3 = empty_set)) | (all_38_3 = empty_set & ~ (all_38_0 = % 43.38/6.48 | empty_set))) % 43.38/6.48 | % 43.38/6.48 | ALPHA: (4) implies: % 43.38/6.48 | (5) element(all_38_3, all_38_1) % 43.38/6.48 | (6) $i(all_38_4) % 43.38/6.48 | (7) $i(all_38_3) % 43.38/6.48 | (8) $i(all_38_0) % 43.38/6.48 | (9) powerset(all_38_4) = all_38_2 % 43.38/6.48 | (10) powerset(all_38_2) = all_38_1 % 43.38/6.48 | (11) complements_of_subsets(all_38_4, all_38_3) = all_38_0 % 43.38/6.48 | (12) (all_38_0 = empty_set & ~ (all_38_3 = empty_set)) | (all_38_3 = % 43.38/6.48 | empty_set & ~ (all_38_0 = empty_set)) % 43.38/6.48 | % 43.38/6.48 | GROUND_INST: instantiating (1) with all_38_4, all_38_3, simplifying with (6), % 43.38/6.48 | (7) gives: % 43.38/6.48 | (13) all_38_3 = empty_set | ~ (complements_of_subsets(all_38_4, all_38_3) % 43.38/6.48 | = empty_set) | ? [v0: $i] : ? [v1: $i] : (powerset(v0) = v1 & % 43.38/6.48 | powerset(all_38_4) = v0 & $i(v1) & $i(v0) & ~ element(all_38_3, % 43.38/6.48 | v1)) % 43.38/6.48 | % 43.38/6.49 | GROUND_INST: instantiating (involutiveness_k7_setfam_1) with all_38_4, % 43.38/6.49 | all_38_3, all_38_0, simplifying with (6), (7), (11) gives: % 43.38/6.49 | (14) ? [v0: $i] : ? [v1: $i] : ? [v2: int] : ((v2 = all_38_3 & % 43.38/6.49 | complements_of_subsets(all_38_4, all_38_0) = all_38_3) | % 43.38/6.49 | (powerset(v0) = v1 & powerset(all_38_4) = v0 & $i(v1) & $i(v0) & ~ % 43.38/6.49 | element(all_38_3, v1))) % 43.38/6.49 | % 43.38/6.49 | GROUND_INST: instantiating (dt_k7_setfam_1) with all_38_4, all_38_3, all_38_0, % 43.38/6.49 | simplifying with (6), (7), (11) gives: % 43.38/6.49 | (15) ? [v0: $i] : ? [v1: $i] : (powerset(v0) = v1 & powerset(all_38_4) = % 43.38/6.49 | v0 & $i(v1) & $i(v0) & ( ~ element(all_38_3, v1) | element(all_38_0, % 43.38/6.49 | v1))) % 43.38/6.49 | % 43.38/6.49 | DELTA: instantiating (15) with fresh symbols all_54_0, all_54_1 gives: % 43.38/6.49 | (16) powerset(all_54_1) = all_54_0 & powerset(all_38_4) = all_54_1 & % 43.38/6.49 | $i(all_54_0) & $i(all_54_1) & ( ~ element(all_38_3, all_54_0) | % 43.38/6.49 | element(all_38_0, all_54_0)) % 43.38/6.49 | % 43.38/6.49 | ALPHA: (16) implies: % 43.38/6.49 | (17) powerset(all_38_4) = all_54_1 % 43.38/6.49 | (18) powerset(all_54_1) = all_54_0 % 43.38/6.49 | (19) ~ element(all_38_3, all_54_0) | element(all_38_0, all_54_0) % 43.38/6.49 | % 43.38/6.49 | DELTA: instantiating (14) with fresh symbols all_56_0, all_56_1, all_56_2 % 43.38/6.49 | gives: % 43.38/6.49 | (20) (all_56_0 = all_38_3 & complements_of_subsets(all_38_4, all_38_0) = % 43.38/6.49 | all_38_3) | (powerset(all_56_2) = all_56_1 & powerset(all_38_4) = % 43.38/6.49 | all_56_2 & $i(all_56_1) & $i(all_56_2) & ~ element(all_38_3, % 43.38/6.49 | all_56_1)) % 43.38/6.49 | % 43.38/6.49 | BETA: splitting (20) gives: % 43.38/6.49 | % 43.38/6.49 | Case 1: % 43.38/6.49 | | % 43.38/6.49 | | (21) all_56_0 = all_38_3 & complements_of_subsets(all_38_4, all_38_0) = % 43.38/6.49 | | all_38_3 % 43.38/6.49 | | % 43.38/6.49 | | ALPHA: (21) implies: % 43.38/6.49 | | (22) complements_of_subsets(all_38_4, all_38_0) = all_38_3 % 43.38/6.49 | | % 43.38/6.49 | | GROUND_INST: instantiating (3) with all_38_2, all_54_1, all_38_4, % 43.38/6.49 | | simplifying with (9), (17) gives: % 43.38/6.49 | | (23) all_54_1 = all_38_2 % 43.38/6.49 | | % 43.38/6.49 | | GROUND_INST: instantiating (3) with all_38_1, all_54_0, all_38_2, % 43.38/6.49 | | simplifying with (10) gives: % 43.38/6.49 | | (24) all_54_0 = all_38_1 | ~ (powerset(all_38_2) = all_54_0) % 43.38/6.49 | | % 43.38/6.49 | | REDUCE: (18), (23) imply: % 43.38/6.49 | | (25) powerset(all_38_2) = all_54_0 % 43.38/6.49 | | % 43.38/6.49 | | BETA: splitting (24) gives: % 43.38/6.49 | | % 43.38/6.49 | | Case 1: % 43.38/6.49 | | | % 43.38/6.49 | | | (26) ~ (powerset(all_38_2) = all_54_0) % 43.38/6.49 | | | % 43.38/6.49 | | | PRED_UNIFY: (25), (26) imply: % 43.38/6.49 | | | (27) $false % 43.38/6.49 | | | % 43.38/6.49 | | | CLOSE: (27) is inconsistent. % 43.38/6.49 | | | % 43.38/6.49 | | Case 2: % 43.38/6.49 | | | % 43.38/6.49 | | | (28) all_54_0 = all_38_1 % 43.38/6.49 | | | % 43.38/6.49 | | | BETA: splitting (19) gives: % 43.38/6.49 | | | % 43.38/6.49 | | | Case 1: % 43.38/6.49 | | | | % 43.38/6.49 | | | | (29) ~ element(all_38_3, all_54_0) % 43.38/6.49 | | | | % 43.38/6.49 | | | | REDUCE: (28), (29) imply: % 43.38/6.49 | | | | (30) ~ element(all_38_3, all_38_1) % 43.38/6.49 | | | | % 43.38/6.49 | | | | PRED_UNIFY: (5), (30) imply: % 43.38/6.49 | | | | (31) $false % 43.38/6.49 | | | | % 43.38/6.49 | | | | CLOSE: (31) is inconsistent. % 43.38/6.49 | | | | % 43.38/6.49 | | | Case 2: % 43.38/6.49 | | | | % 43.38/6.49 | | | | (32) element(all_38_3, all_54_0) % 43.38/6.49 | | | | (33) element(all_38_0, all_54_0) % 43.38/6.49 | | | | % 43.38/6.49 | | | | REDUCE: (28), (33) imply: % 43.38/6.49 | | | | (34) element(all_38_0, all_38_1) % 43.38/6.49 | | | | % 43.38/6.49 | | | | GROUND_INST: instantiating (1) with all_38_4, all_38_0, simplifying with % 43.38/6.49 | | | | (6), (8) gives: % 43.38/6.49 | | | | (35) all_38_0 = empty_set | ~ (complements_of_subsets(all_38_4, % 43.38/6.49 | | | | all_38_0) = empty_set) | ? [v0: $i] : ? [v1: $i] : % 43.38/6.49 | | | | (powerset(v0) = v1 & powerset(all_38_4) = v0 & $i(v1) & $i(v0) & % 43.38/6.49 | | | | ~ element(all_38_0, v1)) % 43.38/6.49 | | | | % 43.38/6.49 | | | | BETA: splitting (12) gives: % 43.38/6.49 | | | | % 43.38/6.49 | | | | Case 1: % 43.38/6.49 | | | | | % 43.38/6.49 | | | | | (36) all_38_0 = empty_set & ~ (all_38_3 = empty_set) % 43.38/6.49 | | | | | % 43.38/6.49 | | | | | ALPHA: (36) implies: % 43.38/6.50 | | | | | (37) all_38_0 = empty_set % 43.38/6.50 | | | | | (38) ~ (all_38_3 = empty_set) % 43.38/6.50 | | | | | % 43.38/6.50 | | | | | REDUCE: (11), (37) imply: % 43.38/6.50 | | | | | (39) complements_of_subsets(all_38_4, all_38_3) = empty_set % 43.38/6.50 | | | | | % 43.38/6.50 | | | | | BETA: splitting (13) gives: % 43.38/6.50 | | | | | % 43.38/6.50 | | | | | Case 1: % 43.38/6.50 | | | | | | % 43.38/6.50 | | | | | | (40) ~ (complements_of_subsets(all_38_4, all_38_3) = empty_set) % 43.38/6.50 | | | | | | % 43.38/6.50 | | | | | | PRED_UNIFY: (39), (40) imply: % 43.38/6.50 | | | | | | (41) $false % 43.38/6.50 | | | | | | % 43.38/6.50 | | | | | | CLOSE: (41) is inconsistent. % 43.38/6.50 | | | | | | % 43.38/6.50 | | | | | Case 2: % 43.38/6.50 | | | | | | % 43.38/6.50 | | | | | | (42) all_38_3 = empty_set | ? [v0: $i] : ? [v1: $i] : % 43.38/6.50 | | | | | | (powerset(v0) = v1 & powerset(all_38_4) = v0 & $i(v1) & % 43.38/6.50 | | | | | | $i(v0) & ~ element(all_38_3, v1)) % 43.38/6.50 | | | | | | % 43.38/6.50 | | | | | | BETA: splitting (42) gives: % 43.38/6.50 | | | | | | % 43.38/6.50 | | | | | | Case 1: % 43.38/6.50 | | | | | | | % 43.38/6.50 | | | | | | | (43) all_38_3 = empty_set % 43.38/6.50 | | | | | | | % 43.38/6.50 | | | | | | | REDUCE: (38), (43) imply: % 43.38/6.50 | | | | | | | (44) $false % 43.38/6.50 | | | | | | | % 43.38/6.50 | | | | | | | CLOSE: (44) is inconsistent. % 43.38/6.50 | | | | | | | % 43.38/6.50 | | | | | | Case 2: % 43.38/6.50 | | | | | | | % 43.38/6.50 | | | | | | | (45) ? [v0: $i] : ? [v1: $i] : (powerset(v0) = v1 & % 43.38/6.50 | | | | | | | powerset(all_38_4) = v0 & $i(v1) & $i(v0) & ~ % 43.38/6.50 | | | | | | | element(all_38_3, v1)) % 43.38/6.50 | | | | | | | % 43.38/6.50 | | | | | | | DELTA: instantiating (45) with fresh symbols all_147_0, all_147_1 % 43.38/6.50 | | | | | | | gives: % 43.38/6.50 | | | | | | | (46) powerset(all_147_1) = all_147_0 & powerset(all_38_4) = % 43.38/6.50 | | | | | | | all_147_1 & $i(all_147_0) & $i(all_147_1) & ~ % 43.38/6.50 | | | | | | | element(all_38_3, all_147_0) % 43.38/6.50 | | | | | | | % 43.38/6.50 | | | | | | | ALPHA: (46) implies: % 43.38/6.50 | | | | | | | (47) ~ element(all_38_3, all_147_0) % 43.38/6.50 | | | | | | | (48) powerset(all_38_4) = all_147_1 % 43.38/6.50 | | | | | | | (49) powerset(all_147_1) = all_147_0 % 43.38/6.50 | | | | | | | % 43.38/6.50 | | | | | | | GROUND_INST: instantiating (3) with all_38_2, all_147_1, all_38_4, % 43.38/6.50 | | | | | | | simplifying with (9), (48) gives: % 43.38/6.50 | | | | | | | (50) all_147_1 = all_38_2 % 43.38/6.50 | | | | | | | % 43.38/6.50 | | | | | | | GROUND_INST: instantiating (3) with all_38_1, all_147_0, all_38_2, % 43.38/6.50 | | | | | | | simplifying with (10) gives: % 43.38/6.50 | | | | | | | (51) all_147_0 = all_38_1 | ~ (powerset(all_38_2) = all_147_0) % 43.38/6.50 | | | | | | | % 43.38/6.50 | | | | | | | PRED_UNIFY: (5), (47) imply: % 43.38/6.50 | | | | | | | (52) ~ (all_147_0 = all_38_1) % 43.38/6.50 | | | | | | | % 43.38/6.50 | | | | | | | REDUCE: (49), (50) imply: % 43.38/6.50 | | | | | | | (53) powerset(all_38_2) = all_147_0 % 43.38/6.50 | | | | | | | % 43.38/6.50 | | | | | | | BETA: splitting (51) gives: % 43.38/6.50 | | | | | | | % 43.38/6.50 | | | | | | | Case 1: % 43.38/6.50 | | | | | | | | % 43.38/6.50 | | | | | | | | (54) ~ (powerset(all_38_2) = all_147_0) % 43.38/6.50 | | | | | | | | % 43.38/6.50 | | | | | | | | PRED_UNIFY: (53), (54) imply: % 43.38/6.50 | | | | | | | | (55) $false % 43.38/6.50 | | | | | | | | % 43.38/6.50 | | | | | | | | CLOSE: (55) is inconsistent. % 43.38/6.50 | | | | | | | | % 43.38/6.50 | | | | | | | Case 2: % 43.38/6.50 | | | | | | | | % 43.38/6.50 | | | | | | | | (56) all_147_0 = all_38_1 % 43.38/6.50 | | | | | | | | % 43.38/6.50 | | | | | | | | REDUCE: (52), (56) imply: % 43.38/6.50 | | | | | | | | (57) $false % 43.38/6.50 | | | | | | | | % 43.38/6.50 | | | | | | | | CLOSE: (57) is inconsistent. % 43.38/6.50 | | | | | | | | % 43.38/6.50 | | | | | | | End of split % 43.38/6.50 | | | | | | | % 43.38/6.50 | | | | | | End of split % 43.38/6.50 | | | | | | % 43.38/6.50 | | | | | End of split % 43.38/6.50 | | | | | % 43.38/6.50 | | | | Case 2: % 43.38/6.50 | | | | | % 43.38/6.50 | | | | | (58) all_38_3 = empty_set & ~ (all_38_0 = empty_set) % 43.38/6.50 | | | | | % 43.38/6.50 | | | | | ALPHA: (58) implies: % 43.38/6.50 | | | | | (59) all_38_3 = empty_set % 43.38/6.50 | | | | | (60) ~ (all_38_0 = empty_set) % 43.38/6.50 | | | | | % 43.38/6.50 | | | | | REDUCE: (22), (59) imply: % 43.38/6.50 | | | | | (61) complements_of_subsets(all_38_4, all_38_0) = empty_set % 43.38/6.50 | | | | | % 43.38/6.50 | | | | | BETA: splitting (35) gives: % 43.38/6.50 | | | | | % 43.38/6.50 | | | | | Case 1: % 43.38/6.50 | | | | | | % 43.38/6.50 | | | | | | (62) ~ (complements_of_subsets(all_38_4, all_38_0) = empty_set) % 43.38/6.50 | | | | | | % 43.38/6.50 | | | | | | PRED_UNIFY: (61), (62) imply: % 43.38/6.50 | | | | | | (63) $false % 43.38/6.50 | | | | | | % 43.38/6.50 | | | | | | CLOSE: (63) is inconsistent. % 43.38/6.50 | | | | | | % 43.38/6.50 | | | | | Case 2: % 43.38/6.50 | | | | | | % 43.38/6.50 | | | | | | (64) all_38_0 = empty_set | ? [v0: $i] : ? [v1: $i] : % 43.38/6.50 | | | | | | (powerset(v0) = v1 & powerset(all_38_4) = v0 & $i(v1) & % 43.38/6.50 | | | | | | $i(v0) & ~ element(all_38_0, v1)) % 43.38/6.50 | | | | | | % 43.38/6.50 | | | | | | BETA: splitting (64) gives: % 43.38/6.50 | | | | | | % 43.38/6.50 | | | | | | Case 1: % 43.38/6.50 | | | | | | | % 43.38/6.50 | | | | | | | (65) all_38_0 = empty_set % 43.38/6.50 | | | | | | | % 43.38/6.50 | | | | | | | REDUCE: (60), (65) imply: % 43.38/6.50 | | | | | | | (66) $false % 43.38/6.50 | | | | | | | % 43.38/6.50 | | | | | | | CLOSE: (66) is inconsistent. % 43.38/6.50 | | | | | | | % 43.38/6.50 | | | | | | Case 2: % 43.38/6.50 | | | | | | | % 43.38/6.50 | | | | | | | (67) ? [v0: $i] : ? [v1: $i] : (powerset(v0) = v1 & % 43.38/6.50 | | | | | | | powerset(all_38_4) = v0 & $i(v1) & $i(v0) & ~ % 43.38/6.50 | | | | | | | element(all_38_0, v1)) % 43.38/6.50 | | | | | | | % 43.38/6.50 | | | | | | | DELTA: instantiating (67) with fresh symbols all_147_0, all_147_1 % 43.38/6.50 | | | | | | | gives: % 43.38/6.50 | | | | | | | (68) powerset(all_147_1) = all_147_0 & powerset(all_38_4) = % 43.38/6.50 | | | | | | | all_147_1 & $i(all_147_0) & $i(all_147_1) & ~ % 43.38/6.50 | | | | | | | element(all_38_0, all_147_0) % 43.38/6.50 | | | | | | | % 43.38/6.50 | | | | | | | ALPHA: (68) implies: % 43.38/6.50 | | | | | | | (69) ~ element(all_38_0, all_147_0) % 43.38/6.50 | | | | | | | (70) powerset(all_38_4) = all_147_1 % 43.38/6.50 | | | | | | | (71) powerset(all_147_1) = all_147_0 % 43.38/6.50 | | | | | | | % 43.38/6.50 | | | | | | | GROUND_INST: instantiating (3) with all_38_2, all_147_1, all_38_4, % 43.38/6.50 | | | | | | | simplifying with (9), (70) gives: % 43.38/6.50 | | | | | | | (72) all_147_1 = all_38_2 % 43.38/6.50 | | | | | | | % 43.38/6.50 | | | | | | | GROUND_INST: instantiating (3) with all_38_1, all_147_0, all_38_2, % 43.38/6.50 | | | | | | | simplifying with (10) gives: % 43.38/6.51 | | | | | | | (73) all_147_0 = all_38_1 | ~ (powerset(all_38_2) = all_147_0) % 43.38/6.51 | | | | | | | % 43.38/6.51 | | | | | | | PRED_UNIFY: (34), (69) imply: % 43.38/6.51 | | | | | | | (74) ~ (all_147_0 = all_38_1) % 43.38/6.51 | | | | | | | % 43.38/6.51 | | | | | | | REDUCE: (71), (72) imply: % 43.38/6.51 | | | | | | | (75) powerset(all_38_2) = all_147_0 % 43.38/6.51 | | | | | | | % 43.38/6.51 | | | | | | | BETA: splitting (73) gives: % 43.38/6.51 | | | | | | | % 43.38/6.51 | | | | | | | Case 1: % 43.38/6.51 | | | | | | | | % 43.38/6.51 | | | | | | | | (76) ~ (powerset(all_38_2) = all_147_0) % 43.38/6.51 | | | | | | | | % 43.38/6.51 | | | | | | | | PRED_UNIFY: (75), (76) imply: % 43.38/6.51 | | | | | | | | (77) $false % 43.38/6.51 | | | | | | | | % 43.38/6.51 | | | | | | | | CLOSE: (77) is inconsistent. % 43.38/6.51 | | | | | | | | % 43.38/6.51 | | | | | | | Case 2: % 43.38/6.51 | | | | | | | | % 43.38/6.51 | | | | | | | | (78) all_147_0 = all_38_1 % 43.38/6.51 | | | | | | | | % 43.38/6.51 | | | | | | | | REDUCE: (74), (78) imply: % 43.38/6.51 | | | | | | | | (79) $false % 43.38/6.51 | | | | | | | | % 43.38/6.51 | | | | | | | | CLOSE: (79) is inconsistent. % 43.38/6.51 | | | | | | | | % 43.38/6.51 | | | | | | | End of split % 43.38/6.51 | | | | | | | % 43.38/6.51 | | | | | | End of split % 43.38/6.51 | | | | | | % 43.38/6.51 | | | | | End of split % 43.38/6.51 | | | | | % 43.38/6.51 | | | | End of split % 43.38/6.51 | | | | % 43.38/6.51 | | | End of split % 43.38/6.51 | | | % 43.38/6.51 | | End of split % 43.38/6.51 | | % 43.38/6.51 | Case 2: % 43.38/6.51 | | % 43.38/6.51 | | (80) powerset(all_56_2) = all_56_1 & powerset(all_38_4) = all_56_2 & % 43.38/6.51 | | $i(all_56_1) & $i(all_56_2) & ~ element(all_38_3, all_56_1) % 43.38/6.51 | | % 43.38/6.51 | | ALPHA: (80) implies: % 43.70/6.51 | | (81) ~ element(all_38_3, all_56_1) % 43.70/6.51 | | (82) powerset(all_38_4) = all_56_2 % 43.70/6.51 | | (83) powerset(all_56_2) = all_56_1 % 43.70/6.51 | | % 43.70/6.51 | | GROUND_INST: instantiating (3) with all_38_2, all_56_2, all_38_4, % 43.70/6.51 | | simplifying with (9), (82) gives: % 43.70/6.51 | | (84) all_56_2 = all_38_2 % 43.70/6.51 | | % 43.92/6.51 | | GROUND_INST: instantiating (3) with all_54_1, all_56_2, all_38_4, % 43.92/6.51 | | simplifying with (17), (82) gives: % 43.92/6.51 | | (85) all_56_2 = all_54_1 % 43.92/6.51 | | % 43.92/6.51 | | GROUND_INST: instantiating (3) with all_38_1, all_56_1, all_38_2, % 43.92/6.51 | | simplifying with (10) gives: % 43.92/6.51 | | (86) all_56_1 = all_38_1 | ~ (powerset(all_38_2) = all_56_1) % 43.92/6.51 | | % 43.92/6.51 | | PRED_UNIFY: (5), (81) imply: % 43.92/6.51 | | (87) ~ (all_56_1 = all_38_1) % 43.92/6.51 | | % 43.92/6.51 | | COMBINE_EQS: (84), (85) imply: % 43.92/6.51 | | (88) all_54_1 = all_38_2 % 43.92/6.51 | | % 43.92/6.51 | | REDUCE: (83), (84) imply: % 43.92/6.51 | | (89) powerset(all_38_2) = all_56_1 % 43.92/6.51 | | % 43.92/6.51 | | BETA: splitting (86) gives: % 43.92/6.51 | | % 43.92/6.51 | | Case 1: % 43.92/6.51 | | | % 43.92/6.51 | | | (90) ~ (powerset(all_38_2) = all_56_1) % 43.92/6.51 | | | % 43.92/6.51 | | | PRED_UNIFY: (89), (90) imply: % 43.92/6.51 | | | (91) $false % 43.92/6.51 | | | % 43.92/6.51 | | | CLOSE: (91) is inconsistent. % 43.92/6.51 | | | % 43.92/6.51 | | Case 2: % 43.92/6.51 | | | % 43.92/6.51 | | | (92) all_56_1 = all_38_1 % 43.92/6.51 | | | % 43.92/6.51 | | | REDUCE: (87), (92) imply: % 43.92/6.51 | | | (93) $false % 43.92/6.51 | | | % 43.92/6.51 | | | CLOSE: (93) is inconsistent. % 43.92/6.51 | | | % 43.92/6.51 | | End of split % 43.92/6.51 | | % 43.92/6.51 | End of split % 43.92/6.51 | % 43.92/6.51 End of proof % 43.92/6.51 % SZS output end Proof for theBenchmark % 43.92/6.51 % 43.92/6.51 5895ms %------------------------------------------------------------------------------