%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SEU307+2 : TPTP v8.1.2. Released v3.3.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n024.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 17:43:59 EDT 2023 % Result : Theorem 161.29s 21.90s % Output : Proof 161.71s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : SEU307+2 : TPTP v8.1.2. Released v3.3.0. % 0.07/0.12 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.33 % Computer : n024.cluster.edu % 0.13/0.33 % Model : x86_64 x86_64 % 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.33 % Memory : 8042.1875MB % 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.33 % CPULimit : 300 % 0.13/0.33 % WCLimit : 300 % 0.13/0.33 % DateTime : Wed Aug 23 22:44:54 EDT 2023 % 0.13/0.33 % CPUTime : % 0.19/0.59 ________ _____ % 0.19/0.59 ___ __ \_________(_)________________________________ % 0.19/0.59 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.19/0.59 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.19/0.59 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.19/0.59 % 0.19/0.59 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.19/0.59 (2023-06-19) % 0.19/0.59 % 0.19/0.59 (c) Philipp Rümmer, 2009-2023 % 0.19/0.59 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.19/0.59 Amanda Stjerna. % 0.19/0.59 Free software under BSD-3-Clause. % 0.19/0.59 % 0.19/0.59 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.19/0.59 % 0.19/0.59 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.62/0.60 Running up to 7 provers in parallel. % 0.62/0.61 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.62/0.61 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.62/0.61 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.62/0.61 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.62/0.61 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.62/0.61 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 0.62/0.61 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 11.16/2.19 Prover 1: Preprocessing ... % 11.16/2.23 Prover 6: Preprocessing ... % 11.16/2.23 Prover 5: Preprocessing ... % 11.16/2.23 Prover 3: Preprocessing ... % 11.70/2.25 Prover 4: Preprocessing ... % 11.70/2.26 Prover 2: Preprocessing ... % 11.70/2.31 Prover 0: Preprocessing ... % 35.56/5.47 Prover 1: Warning: ignoring some quantifiers % 36.07/5.56 Prover 3: Warning: ignoring some quantifiers % 36.07/5.61 Prover 6: Proving ... % 37.11/5.63 Prover 3: Constructing countermodel ... % 37.28/5.65 Prover 1: Constructing countermodel ... % 37.28/5.65 Prover 5: Proving ... % 47.45/6.97 Prover 2: Proving ... % 63.49/9.09 Prover 4: Warning: ignoring some quantifiers % 64.58/9.35 Prover 4: Constructing countermodel ... % 73.51/10.41 Prover 0: Proving ... % 95.25/13.36 Prover 2: stopped % 95.25/13.38 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 99.26/13.79 Prover 7: Preprocessing ... % 99.94/13.94 Prover 5: stopped % 99.94/13.96 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 102.92/14.27 Prover 8: Preprocessing ... % 104.65/14.53 Prover 7: Warning: ignoring some quantifiers % 106.03/14.66 Prover 7: Constructing countermodel ... % 109.70/15.17 Prover 8: Warning: ignoring some quantifiers % 110.20/15.22 Prover 8: Constructing countermodel ... % 115.95/15.96 Prover 1: stopped % 115.95/15.96 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889 % 119.09/16.36 Prover 9: Preprocessing ... % 130.78/17.86 Prover 6: stopped % 130.78/17.88 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 134.49/18.33 Prover 10: Preprocessing ... % 138.80/18.98 Prover 10: Warning: ignoring some quantifiers % 139.73/19.06 Prover 10: Constructing countermodel ... % 142.73/19.40 Prover 9: Warning: ignoring some quantifiers % 142.82/19.48 Prover 9: Constructing countermodel ... % 161.29/21.87 Prover 10: Found proof (size 45) % 161.29/21.87 Prover 10: proved (3987ms) % 161.29/21.87 Prover 3: stopped % 161.29/21.87 Prover 9: stopped % 161.29/21.87 Prover 7: stopped % 161.29/21.88 Prover 8: stopped % 161.29/21.88 Prover 4: stopped % 161.29/21.90 Prover 0: stopped % 161.29/21.90 % 161.29/21.90 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 161.29/21.90 % 161.54/21.91 % SZS output start Proof for theBenchmark % 161.54/21.92 Assumptions after simplification: % 161.54/21.92 --------------------------------- % 161.54/21.92 % 161.54/21.92 (d3_pre_topc) % 161.71/21.95 ! [v0: $i] : ! [v1: $i] : ( ~ (cast_as_carrier_subset(v0) = v1) | ~ $i(v0) % 161.71/21.95 | ~ one_sorted_str(v0) | (the_carrier(v0) = v1 & $i(v1))) % 161.71/21.95 % 161.71/21.95 (dt_k2_pre_topc) % 161.71/21.95 ! [v0: $i] : ! [v1: $i] : ( ~ (cast_as_carrier_subset(v0) = v1) | ~ $i(v0) % 161.71/21.95 | ~ one_sorted_str(v0) | ? [v2: $i] : ? [v3: $i] : (the_carrier(v0) = v2 % 161.71/21.95 & powerset(v2) = v3 & $i(v3) & $i(v2) & element(v1, v3))) % 161.71/21.95 % 161.71/21.95 (dt_k5_subset_1) % 161.71/21.96 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 161.71/21.96 (subset_intersection2(v0, v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) % 161.71/21.96 | ? [v4: $i] : (powerset(v0) = v4 & $i(v4) & ( ~ element(v2, v4) | ~ % 161.71/21.96 element(v1, v4) | element(v3, v4)))) % 161.71/21.96 % 161.71/21.96 (redefinition_k5_subset_1) % 161.71/21.96 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 161.71/21.96 (subset_intersection2(v0, v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) % 161.71/21.96 | ? [v4: $i] : ? [v5: $i] : ((v5 = v3 & set_intersection2(v1, v2) = v3 & % 161.71/21.96 $i(v3)) | (powerset(v0) = v4 & $i(v4) & ( ~ element(v2, v4) | ~ % 161.71/21.96 element(v1, v4))))) % 161.71/21.96 % 161.71/21.96 (t12_pre_topc) % 161.71/21.96 ! [v0: $i] : ! [v1: $i] : ( ~ (cast_as_carrier_subset(v0) = v1) | ~ $i(v0) % 161.71/21.96 | ~ one_sorted_str(v0) | (the_carrier(v0) = v1 & $i(v1))) % 161.71/21.96 % 161.71/21.96 (t15_pre_topc) % 161.71/21.96 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: % 161.71/21.96 $i] : ( ~ (v5 = v4) & cast_as_carrier_subset(v0) = v3 & % 161.71/21.96 subset_intersection2(v1, v4, v3) = v5 & the_carrier(v0) = v1 & powerset(v1) % 161.71/21.96 = v2 & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & % 161.71/21.96 one_sorted_str(v0) & element(v4, v2)) % 161.71/21.96 % 161.71/21.96 (t28_xboole_1) % 161.71/21.96 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v0 | ~ (set_intersection2(v0, % 161.71/21.96 v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ subset(v0, v1)) % 161.71/21.96 % 161.71/21.96 (t3_subset) % 161.71/21.96 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (powerset(v1) = v2) | ~ $i(v1) % 161.71/21.96 | ~ $i(v0) | ~ subset(v0, v1) | element(v0, v2)) & ! [v0: $i] : ! [v1: % 161.71/21.96 $i] : ! [v2: $i] : ( ~ (powerset(v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ % 161.71/21.96 element(v0, v2) | subset(v0, v1)) % 161.71/21.96 % 161.71/21.96 (function-axioms) % 161.71/21.98 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 161.71/21.98 $i] : ! [v6: $i] : ! [v7: $i] : (v1 = v0 | ~ (apply_binary_as_element(v7, % 161.71/21.98 v6, v5, v4, v3, v2) = v1) | ~ (apply_binary_as_element(v7, v6, v5, v4, % 161.71/21.98 v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : % 161.71/21.98 ! [v4: $i] : (v1 = v0 | ~ (apply_binary(v4, v3, v2) = v1) | ~ % 161.71/21.98 (apply_binary(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 161.71/21.98 ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (subset_difference(v4, v3, v2) = v1) % 161.71/21.98 | ~ (subset_difference(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 161.71/21.98 [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ % 161.71/21.98 (relation_rng_as_subset(v4, v3, v2) = v1) | ~ (relation_rng_as_subset(v4, % 161.71/21.98 v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : % 161.71/21.98 ! [v4: $i] : (v1 = v0 | ~ (meet(v4, v3, v2) = v1) | ~ (meet(v4, v3, v2) = % 161.71/21.98 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] % 161.71/21.98 : (v1 = v0 | ~ (join(v4, v3, v2) = v1) | ~ (join(v4, v3, v2) = v0)) & ! % 161.71/21.98 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | % 161.71/21.98 ~ (relation_dom_as_subset(v4, v3, v2) = v1) | ~ (relation_dom_as_subset(v4, % 161.71/21.98 v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : % 161.71/21.98 ! [v4: $i] : (v1 = v0 | ~ (unordered_triple(v4, v3, v2) = v1) | ~ % 161.71/21.98 (unordered_triple(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 161.71/21.98 $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (subset_intersection2(v4, % 161.71/21.98 v3, v2) = v1) | ~ (subset_intersection2(v4, v3, v2) = v0)) & ! [v0: % 161.71/21.98 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ % 161.71/21.98 (meet_commut(v4, v3, v2) = v1) | ~ (meet_commut(v4, v3, v2) = v0)) & ! % 161.71/21.98 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | % 161.71/21.98 ~ (join_commut(v4, v3, v2) = v1) | ~ (join_commut(v4, v3, v2) = v0)) & ! % 161.71/21.98 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 161.71/21.98 (meet_of_subsets(v3, v2) = v1) | ~ (meet_of_subsets(v3, v2) = v0)) & ! % 161.71/21.98 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 161.71/21.98 (union_of_subsets(v3, v2) = v1) | ~ (union_of_subsets(v3, v2) = v0)) & ! % 161.71/21.98 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 161.71/21.98 (complements_of_subsets(v3, v2) = v1) | ~ (complements_of_subsets(v3, v2) = % 161.71/21.98 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | % 161.71/21.98 ~ (relation_composition(v3, v2) = v1) | ~ (relation_composition(v3, v2) = % 161.71/21.98 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | % 161.71/21.98 ~ (relation_restriction(v3, v2) = v1) | ~ (relation_restriction(v3, v2) = % 161.71/21.98 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | % 161.71/21.98 ~ (subset_complement(v3, v2) = v1) | ~ (subset_complement(v3, v2) = v0)) & % 161.71/21.98 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 161.71/21.98 (set_difference(v3, v2) = v1) | ~ (set_difference(v3, v2) = v0)) & ! [v0: % 161.71/21.98 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (fiber(v3, v2) % 161.71/21.98 = v1) | ~ (fiber(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 161.71/21.98 : ! [v3: $i] : (v1 = v0 | ~ (relation_inverse_image(v3, v2) = v1) | ~ % 161.71/21.98 (relation_inverse_image(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 161.71/21.98 $i] : ! [v3: $i] : (v1 = v0 | ~ (relation_rng_restriction(v3, v2) = v1) | % 161.71/21.98 ~ (relation_rng_restriction(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 161.71/21.98 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (relation_image(v3, v2) = v1) | ~ % 161.71/21.98 (relation_image(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 161.71/21.98 ! [v3: $i] : (v1 = v0 | ~ (apply(v3, v2) = v1) | ~ (apply(v3, v2) = v0)) & % 161.71/21.98 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 161.71/21.98 (relation_dom_restriction(v3, v2) = v1) | ~ (relation_dom_restriction(v3, % 161.71/21.98 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 % 161.71/21.98 = v0 | ~ (ordered_pair(v3, v2) = v1) | ~ (ordered_pair(v3, v2) = v0)) & ! % 161.71/21.98 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 161.71/21.98 (set_intersection2(v3, v2) = v1) | ~ (set_intersection2(v3, v2) = v0)) & ! % 161.71/21.98 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 161.71/21.98 (set_union2(v3, v2) = v1) | ~ (set_union2(v3, v2) = v0)) & ! [v0: $i] : ! % 161.71/21.98 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (unordered_pair(v3, v2) = % 161.71/21.98 v1) | ~ (unordered_pair(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 161.71/21.98 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (cartesian_product2(v3, v2) = v1) | ~ % 161.71/21.98 (cartesian_product2(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 161.71/21.98 : (v1 = v0 | ~ (function_inverse(v2) = v1) | ~ (function_inverse(v2) = v0)) % 161.71/21.98 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 161.71/21.98 (relation_inverse(v2) = v1) | ~ (relation_inverse(v2) = v0)) & ! [v0: $i] % 161.71/21.98 : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (union(v2) = v1) | ~ (union(v2) = % 161.71/21.98 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 161.71/21.98 (cast_to_subset(v2) = v1) | ~ (cast_to_subset(v2) = v0)) & ! [v0: $i] : ! % 161.71/21.98 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (cast_as_carrier_subset(v2) = v1) | ~ % 161.71/21.98 (cast_as_carrier_subset(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 161.71/21.98 : (v1 = v0 | ~ (pair_second(v2) = v1) | ~ (pair_second(v2) = v0)) & ! [v0: % 161.71/21.98 $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (the_L_meet(v2) = v1) | ~ % 161.71/21.98 (the_L_meet(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 % 161.71/21.98 | ~ (inclusion_relation(v2) = v1) | ~ (inclusion_relation(v2) = v0)) & ! % 161.71/21.98 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (set_meet(v2) = v1) | ~ % 161.71/21.98 (set_meet(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | % 161.71/21.98 ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ! [v0: $i] : ! [v1: % 161.71/21.98 $i] : ! [v2: $i] : (v1 = v0 | ~ (succ(v2) = v1) | ~ (succ(v2) = v0)) & ! % 161.71/21.98 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (pair_first(v2) = v1) | % 161.71/21.98 ~ (pair_first(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = % 161.71/21.98 v0 | ~ (the_L_join(v2) = v1) | ~ (the_L_join(v2) = v0)) & ! [v0: $i] : ! % 161.71/21.98 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (relation_rng(v2) = v1) | ~ % 161.71/21.98 (relation_rng(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = % 161.71/21.98 v0 | ~ (relation_field(v2) = v1) | ~ (relation_field(v2) = v0)) & ! [v0: % 161.71/21.98 $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (relation_dom(v2) = v1) | ~ % 161.71/21.98 (relation_dom(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = % 161.71/21.98 v0 | ~ (identity_relation(v2) = v1) | ~ (identity_relation(v2) = v0)) & ! % 161.71/21.98 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (the_carrier(v2) = v1) | % 161.71/21.98 ~ (the_carrier(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = % 161.71/21.98 v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0)) % 161.71/21.98 % 161.71/21.98 Further assumptions not needed in the proof: % 161.71/21.98 -------------------------------------------- % 161.71/21.98 antisymmetry_r2_hidden, antisymmetry_r2_xboole_0, cc10_membered, cc11_membered, % 161.71/21.98 cc12_membered, cc13_membered, cc14_membered, cc15_membered, cc16_membered, % 161.71/21.98 cc17_membered, cc18_membered, cc19_membered, cc1_arytm_3, cc1_finset_1, % 161.71/21.98 cc1_finsub_1, cc1_funct_1, cc1_membered, cc1_ordinal1, cc1_relat_1, % 161.71/21.98 cc1_relset_1, cc20_membered, cc2_arytm_3, cc2_finset_1, cc2_finsub_1, % 161.71/21.98 cc2_funct_1, cc2_membered, cc2_ordinal1, cc3_arytm_3, cc3_membered, % 161.71/21.98 cc3_ordinal1, cc4_membered, commutativity_k2_tarski, commutativity_k2_xboole_0, % 161.71/21.98 commutativity_k3_lattices, commutativity_k3_xboole_0, commutativity_k4_lattices, % 161.71/21.98 commutativity_k5_subset_1, connectedness_r1_ordinal1, d10_relat_1, d10_xboole_0, % 161.71/21.98 d11_relat_1, d12_funct_1, d12_relat_1, d12_relat_2, d13_funct_1, d13_relat_1, % 161.71/21.98 d14_relat_1, d14_relat_2, d16_relat_2, d1_enumset1, d1_finset_1, d1_funct_1, % 161.71/21.98 d1_funct_2, d1_lattices, d1_mcart_1, d1_ordinal1, d1_relat_1, d1_relat_2, % 161.71/21.98 d1_relset_1, d1_setfam_1, d1_tarski, d1_wellord1, d1_wellord2, d1_xboole_0, % 161.71/21.98 d1_zfmisc_1, d2_lattices, d2_mcart_1, d2_ordinal1, d2_relat_1, d2_subset_1, % 161.71/21.98 d2_tarski, d2_wellord1, d2_xboole_0, d2_zfmisc_1, d3_lattices, d3_ordinal1, % 161.71/21.98 d3_relat_1, d3_tarski, d3_wellord1, d3_xboole_0, d4_funct_1, d4_ordinal1, % 161.71/21.98 d4_relat_1, d4_relat_2, d4_subset_1, d4_tarski, d4_wellord1, d4_wellord2, % 161.71/21.98 d4_xboole_0, d5_funct_1, d5_ordinal2, d5_relat_1, d5_subset_1, d5_tarski, % 161.71/21.98 d5_wellord1, d6_ordinal1, d6_relat_1, d6_relat_2, d6_wellord1, d7_relat_1, % 161.71/21.98 d7_wellord1, d7_xboole_0, d8_funct_1, d8_lattices, d8_relat_1, d8_relat_2, % 161.71/21.98 d8_setfam_1, d8_xboole_0, d9_funct_1, d9_relat_2, dt_k10_relat_1, dt_k1_binop_1, % 161.71/21.98 dt_k1_enumset1, dt_k1_funct_1, dt_k1_lattices, dt_k1_mcart_1, dt_k1_ordinal1, % 161.71/21.98 dt_k1_relat_1, dt_k1_setfam_1, dt_k1_tarski, dt_k1_wellord1, dt_k1_wellord2, % 161.71/21.98 dt_k1_xboole_0, dt_k1_zfmisc_1, dt_k2_binop_1, dt_k2_funct_1, dt_k2_lattices, % 161.71/21.98 dt_k2_mcart_1, dt_k2_relat_1, dt_k2_subset_1, dt_k2_tarski, dt_k2_wellord1, % 161.71/21.98 dt_k2_xboole_0, dt_k2_zfmisc_1, dt_k3_lattices, dt_k3_relat_1, dt_k3_subset_1, % 161.71/21.98 dt_k3_tarski, dt_k3_xboole_0, dt_k4_lattices, dt_k4_relat_1, dt_k4_relset_1, % 161.71/21.98 dt_k4_tarski, dt_k4_xboole_0, dt_k5_ordinal2, dt_k5_relat_1, dt_k5_relset_1, % 161.71/21.98 dt_k5_setfam_1, dt_k6_relat_1, dt_k6_setfam_1, dt_k6_subset_1, dt_k7_relat_1, % 161.71/21.98 dt_k7_setfam_1, dt_k8_relat_1, dt_k9_relat_1, dt_l1_lattices, dt_l1_struct_0, % 161.71/21.98 dt_l2_lattices, dt_l3_lattices, dt_m1_relset_1, dt_m1_subset_1, dt_m2_relset_1, % 161.71/21.98 dt_u1_lattices, dt_u1_struct_0, dt_u2_lattices, existence_l1_lattices, % 161.71/21.98 existence_l1_struct_0, existence_l2_lattices, existence_l3_lattices, % 161.71/21.98 existence_m1_relset_1, existence_m1_subset_1, existence_m2_relset_1, % 161.71/21.98 fc10_finset_1, fc10_relat_1, fc11_finset_1, fc11_relat_1, fc12_finset_1, % 161.71/21.98 fc12_relat_1, fc13_finset_1, fc13_relat_1, fc1_finset_1, fc1_finsub_1, % 161.71/21.98 fc1_funct_1, fc1_ordinal1, fc1_ordinal2, fc1_relat_1, fc1_struct_0, % 161.71/21.98 fc1_subset_1, fc1_xboole_0, fc1_zfmisc_1, fc27_membered, fc28_membered, % 161.71/21.98 fc29_membered, fc2_arytm_3, fc2_funct_1, fc2_ordinal1, fc2_relat_1, % 161.71/21.98 fc2_subset_1, fc2_xboole_0, fc30_membered, fc31_membered, fc32_membered, % 161.71/21.98 fc33_membered, fc34_membered, fc35_membered, fc36_membered, fc3_funct_1, % 161.71/21.98 fc3_ordinal1, fc3_relat_1, fc3_subset_1, fc3_xboole_0, fc4_funct_1, % 161.71/21.98 fc4_ordinal1, fc4_relat_1, fc4_subset_1, fc5_funct_1, fc5_relat_1, fc6_membered, % 161.71/21.98 fc6_relat_1, fc7_relat_1, fc8_relat_1, fc9_finset_1, fc9_relat_1, % 161.71/21.98 idempotence_k2_xboole_0, idempotence_k3_xboole_0, idempotence_k5_subset_1, % 161.71/21.98 involutiveness_k3_subset_1, involutiveness_k4_relat_1, % 161.71/21.98 involutiveness_k7_setfam_1, irreflexivity_r2_xboole_0, l1_wellord1, l1_zfmisc_1, % 161.71/21.98 l23_zfmisc_1, l25_zfmisc_1, l28_zfmisc_1, l29_wellord1, l2_wellord1, % 161.71/21.98 l2_zfmisc_1, l30_wellord2, l32_xboole_1, l3_subset_1, l3_wellord1, l3_zfmisc_1, % 161.71/21.98 l4_wellord1, l4_zfmisc_1, l50_zfmisc_1, l55_zfmisc_1, l71_subset_1, l82_funct_1, % 161.71/21.98 rc1_arytm_3, rc1_finset_1, rc1_funct_1, rc1_funct_2, rc1_membered, rc1_ordinal1, % 161.71/21.98 rc1_ordinal2, rc1_partfun1, rc1_relat_1, rc1_subset_1, rc1_xboole_0, % 161.71/21.98 rc2_finset_1, rc2_funct_1, rc2_ordinal1, rc2_partfun1, rc2_relat_1, % 161.71/21.98 rc2_subset_1, rc2_xboole_0, rc3_finset_1, rc3_funct_1, rc3_ordinal1, % 161.71/21.98 rc3_relat_1, rc3_struct_0, rc4_funct_1, rc5_struct_0, redefinition_k2_binop_1, % 161.71/21.98 redefinition_k3_lattices, redefinition_k4_lattices, redefinition_k4_relset_1, % 161.71/21.98 redefinition_k5_relset_1, redefinition_k5_setfam_1, redefinition_k6_setfam_1, % 161.71/21.98 redefinition_k6_subset_1, redefinition_m2_relset_1, redefinition_r1_ordinal1, % 161.71/21.98 redefinition_r2_wellord2, reflexivity_r1_ordinal1, reflexivity_r1_tarski, % 161.71/21.98 reflexivity_r2_wellord2, s1_funct_1__e10_24__wellord2__1, % 161.71/21.98 s1_funct_1__e16_22__wellord2__1, s1_ordinal1__e8_6__wellord2, % 161.71/21.98 s1_ordinal2__e18_27__finset_1, s1_relat_1__e6_21__wellord2, % 161.71/21.98 s1_tarski__e10_24__wellord2__1, s1_tarski__e10_24__wellord2__2, % 161.71/21.98 s1_tarski__e16_22__wellord2__1, s1_tarski__e16_22__wellord2__2, % 161.71/21.98 s1_tarski__e18_27__finset_1__1, s1_tarski__e4_27_3_1__finset_1__1, % 161.71/21.98 s1_tarski__e6_21__wellord2__1, s1_tarski__e6_22__wellord2__1, % 161.71/21.98 s1_tarski__e6_27__finset_1__1, s1_tarski__e8_6__wellord2__1, % 161.71/21.99 s1_xboole_0__e10_24__wellord2__1, s1_xboole_0__e16_22__wellord2__1, % 161.71/21.99 s1_xboole_0__e18_27__finset_1__1, s1_xboole_0__e4_27_3_1__finset_1, % 161.71/21.99 s1_xboole_0__e6_21__wellord2__1, s1_xboole_0__e6_22__wellord2, % 161.71/21.99 s1_xboole_0__e6_27__finset_1, s1_xboole_0__e8_6__wellord2__1, % 161.71/21.99 s2_funct_1__e10_24__wellord2, s2_funct_1__e16_22__wellord2__1, % 161.71/21.99 s2_ordinal1__e18_27__finset_1__1, s3_funct_1__e16_22__wellord2, % 161.71/21.99 symmetry_r1_xboole_0, symmetry_r2_wellord2, t106_zfmisc_1, t10_ordinal1, % 161.71/21.99 t10_zfmisc_1, t115_relat_1, t116_relat_1, t117_relat_1, t118_relat_1, % 161.71/21.99 t118_zfmisc_1, t119_relat_1, t119_zfmisc_1, t12_relset_1, t12_xboole_1, % 161.71/21.99 t136_zfmisc_1, t13_finset_1, t140_relat_1, t143_relat_1, t144_relat_1, % 161.71/21.99 t145_funct_1, t145_relat_1, t146_funct_1, t146_relat_1, t147_funct_1, % 161.71/21.99 t14_relset_1, t15_finset_1, t160_relat_1, t166_relat_1, t167_relat_1, % 161.71/21.99 t16_relset_1, t16_wellord1, t174_relat_1, t178_relat_1, t17_finset_1, % 161.71/21.99 t17_wellord1, t17_xboole_1, t18_finset_1, t18_wellord1, t19_wellord1, % 161.71/21.99 t19_xboole_1, t1_boole, t1_subset, t1_xboole_1, t1_zfmisc_1, t20_relat_1, % 161.71/21.99 t20_wellord1, t21_funct_1, t21_funct_2, t21_ordinal1, t21_relat_1, t21_wellord1, % 161.71/21.99 t22_funct_1, t22_relset_1, t22_wellord1, t23_funct_1, t23_lattices, % 161.71/21.99 t23_ordinal1, t23_relset_1, t23_wellord1, t24_ordinal1, t24_wellord1, % 161.71/21.99 t25_relat_1, t25_wellord1, t25_wellord2, t26_finset_1, t26_lattices, % 161.71/21.99 t26_wellord2, t26_xboole_1, t28_wellord2, t2_boole, t2_subset, t2_tarski, % 161.71/21.99 t2_wellord2, t2_xboole_1, t30_relat_1, t31_ordinal1, t31_wellord1, t32_ordinal1, % 161.71/21.99 t32_wellord1, t33_ordinal1, t33_xboole_1, t33_zfmisc_1, t34_funct_1, % 161.71/21.99 t35_funct_1, t36_xboole_1, t37_relat_1, t37_xboole_1, t37_zfmisc_1, % 161.71/21.99 t38_zfmisc_1, t39_wellord1, t39_xboole_1, t39_zfmisc_1, t3_boole, t3_ordinal1, % 161.71/21.99 t3_wellord2, t3_xboole_0, t3_xboole_1, t40_xboole_1, t41_ordinal1, t42_ordinal1, % 161.71/21.99 t43_subset_1, t44_relat_1, t45_relat_1, t45_xboole_1, t46_funct_2, t46_relat_1, % 161.71/21.99 t46_setfam_1, t46_zfmisc_1, t47_relat_1, t47_setfam_1, t48_setfam_1, % 161.71/21.99 t48_xboole_1, t49_wellord1, t4_boole, t4_subset, t4_wellord2, t4_xboole_0, % 161.71/21.99 t50_subset_1, t53_wellord1, t54_funct_1, t54_subset_1, t54_wellord1, % 161.71/21.99 t55_funct_1, t56_relat_1, t57_funct_1, t5_subset, t5_wellord1, t5_wellord2, % 161.71/21.99 t60_relat_1, t60_xboole_1, t62_funct_1, t63_xboole_1, t64_relat_1, t65_relat_1, % 161.71/21.99 t65_zfmisc_1, t68_funct_1, t69_enumset1, t6_boole, t6_funct_2, t6_wellord2, % 161.71/21.99 t6_zfmisc_1, t70_funct_1, t71_relat_1, t72_funct_1, t74_relat_1, t7_boole, % 161.71/21.99 t7_mcart_1, t7_tarski, t7_wellord2, t7_xboole_1, t83_xboole_1, t86_relat_1, % 161.71/21.99 t88_relat_1, t8_boole, t8_funct_1, t8_wellord1, t8_xboole_1, t8_zfmisc_1, % 161.71/21.99 t90_relat_1, t92_zfmisc_1, t94_relat_1, t99_relat_1, t99_zfmisc_1, t9_funct_2, % 161.71/21.99 t9_tarski, t9_zfmisc_1 % 161.71/21.99 % 161.71/21.99 Those formulas are unsatisfiable: % 161.71/21.99 --------------------------------- % 161.71/21.99 % 161.71/21.99 Begin of proof % 161.71/21.99 | % 161.71/21.99 | ALPHA: (t3_subset) implies: % 161.71/21.99 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (powerset(v1) = v2) | ~ % 161.71/21.99 | $i(v1) | ~ $i(v0) | ~ element(v0, v2) | subset(v0, v1)) % 161.71/21.99 | % 161.71/21.99 | ALPHA: (function-axioms) implies: % 161.71/21.99 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (powerset(v2) = % 161.71/21.99 | v1) | ~ (powerset(v2) = v0)) % 161.71/21.99 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 161.71/21.99 | (the_carrier(v2) = v1) | ~ (the_carrier(v2) = v0)) % 161.71/21.99 | % 161.71/21.99 | DELTA: instantiating (t15_pre_topc) with fresh symbols all_492_0, all_492_1, % 161.71/21.99 | all_492_2, all_492_3, all_492_4, all_492_5 gives: % 161.71/21.99 | (4) ~ (all_492_0 = all_492_1) & cast_as_carrier_subset(all_492_5) = % 161.71/21.99 | all_492_2 & subset_intersection2(all_492_4, all_492_1, all_492_2) = % 161.71/21.99 | all_492_0 & the_carrier(all_492_5) = all_492_4 & powerset(all_492_4) = % 161.71/21.99 | all_492_3 & $i(all_492_0) & $i(all_492_1) & $i(all_492_2) & % 161.71/21.99 | $i(all_492_3) & $i(all_492_4) & $i(all_492_5) & % 161.71/21.99 | one_sorted_str(all_492_5) & element(all_492_1, all_492_3) % 161.71/21.99 | % 161.71/21.99 | ALPHA: (4) implies: % 161.71/21.99 | (5) ~ (all_492_0 = all_492_1) % 161.71/21.99 | (6) element(all_492_1, all_492_3) % 161.71/21.99 | (7) one_sorted_str(all_492_5) % 161.71/21.99 | (8) $i(all_492_5) % 161.71/21.99 | (9) $i(all_492_4) % 161.71/21.99 | (10) $i(all_492_2) % 161.71/21.99 | (11) $i(all_492_1) % 161.71/21.99 | (12) powerset(all_492_4) = all_492_3 % 161.71/21.99 | (13) the_carrier(all_492_5) = all_492_4 % 161.71/21.99 | (14) subset_intersection2(all_492_4, all_492_1, all_492_2) = all_492_0 % 161.71/21.99 | (15) cast_as_carrier_subset(all_492_5) = all_492_2 % 161.71/21.99 | % 161.71/21.99 | GROUND_INST: instantiating (1) with all_492_1, all_492_4, all_492_3, % 161.71/21.99 | simplifying with (6), (9), (11), (12) gives: % 161.71/22.00 | (16) subset(all_492_1, all_492_4) % 161.71/22.00 | % 161.71/22.00 | GROUND_INST: instantiating (redefinition_k5_subset_1) with all_492_4, % 161.71/22.00 | all_492_1, all_492_2, all_492_0, simplifying with (9), (10), % 161.71/22.00 | (11), (14) gives: % 161.71/22.00 | (17) ? [v0: $i] : ? [v1: int] : ((v1 = all_492_0 & % 161.71/22.00 | set_intersection2(all_492_1, all_492_2) = all_492_0 & % 161.71/22.00 | $i(all_492_0)) | (powerset(all_492_4) = v0 & $i(v0) & ( ~ % 161.71/22.00 | element(all_492_1, v0) | ~ element(all_492_2, v0)))) % 161.71/22.00 | % 161.71/22.00 | GROUND_INST: instantiating (dt_k5_subset_1) with all_492_4, all_492_1, % 161.71/22.00 | all_492_2, all_492_0, simplifying with (9), (10), (11), (14) % 161.71/22.00 | gives: % 161.71/22.00 | (18) ? [v0: $i] : (powerset(all_492_4) = v0 & $i(v0) & ( ~ % 161.71/22.00 | element(all_492_1, v0) | ~ element(all_492_2, v0) | % 161.71/22.00 | element(all_492_0, v0))) % 161.71/22.00 | % 161.71/22.00 | GROUND_INST: instantiating (dt_k2_pre_topc) with all_492_5, all_492_2, % 161.71/22.00 | simplifying with (7), (8), (15) gives: % 161.71/22.00 | (19) ? [v0: $i] : ? [v1: $i] : (the_carrier(all_492_5) = v0 & % 161.71/22.00 | powerset(v0) = v1 & $i(v1) & $i(v0) & element(all_492_2, v1)) % 161.71/22.00 | % 161.71/22.00 | GROUND_INST: instantiating (t12_pre_topc) with all_492_5, all_492_2, % 161.71/22.00 | simplifying with (7), (8), (15) gives: % 161.71/22.00 | (20) the_carrier(all_492_5) = all_492_2 & $i(all_492_2) % 161.71/22.00 | % 161.71/22.00 | ALPHA: (20) implies: % 161.71/22.00 | (21) the_carrier(all_492_5) = all_492_2 % 161.71/22.00 | % 161.71/22.00 | DELTA: instantiating (18) with fresh symbol all_579_0 gives: % 161.71/22.00 | (22) powerset(all_492_4) = all_579_0 & $i(all_579_0) & ( ~ % 161.71/22.00 | element(all_492_1, all_579_0) | ~ element(all_492_2, all_579_0) | % 161.71/22.00 | element(all_492_0, all_579_0)) % 161.71/22.00 | % 161.71/22.00 | ALPHA: (22) implies: % 161.71/22.00 | (23) powerset(all_492_4) = all_579_0 % 161.71/22.00 | % 161.71/22.00 | DELTA: instantiating (19) with fresh symbols all_581_0, all_581_1 gives: % 161.71/22.00 | (24) the_carrier(all_492_5) = all_581_1 & powerset(all_581_1) = all_581_0 & % 161.71/22.00 | $i(all_581_0) & $i(all_581_1) & element(all_492_2, all_581_0) % 161.71/22.00 | % 161.71/22.00 | ALPHA: (24) implies: % 161.71/22.00 | (25) element(all_492_2, all_581_0) % 161.71/22.00 | (26) powerset(all_581_1) = all_581_0 % 161.71/22.00 | (27) the_carrier(all_492_5) = all_581_1 % 161.71/22.00 | % 161.71/22.00 | DELTA: instantiating (17) with fresh symbols all_583_0, all_583_1 gives: % 161.71/22.00 | (28) (all_583_0 = all_492_0 & set_intersection2(all_492_1, all_492_2) = % 161.71/22.00 | all_492_0 & $i(all_492_0)) | (powerset(all_492_4) = all_583_1 & % 161.71/22.00 | $i(all_583_1) & ( ~ element(all_492_1, all_583_1) | ~ % 161.71/22.00 | element(all_492_2, all_583_1))) % 161.71/22.00 | % 161.71/22.00 | GROUND_INST: instantiating (2) with all_492_3, all_579_0, all_492_4, % 161.71/22.00 | simplifying with (12), (23) gives: % 161.71/22.00 | (29) all_579_0 = all_492_3 % 161.71/22.00 | % 161.71/22.00 | GROUND_INST: instantiating (3) with all_492_4, all_581_1, all_492_5, % 161.71/22.00 | simplifying with (13), (27) gives: % 161.71/22.00 | (30) all_581_1 = all_492_4 % 161.71/22.00 | % 161.71/22.00 | GROUND_INST: instantiating (3) with all_492_2, all_581_1, all_492_5, % 161.71/22.00 | simplifying with (21), (27) gives: % 161.71/22.00 | (31) all_581_1 = all_492_2 % 161.71/22.00 | % 161.71/22.00 | COMBINE_EQS: (30), (31) imply: % 161.71/22.00 | (32) all_492_2 = all_492_4 % 161.71/22.00 | % 161.71/22.00 | REDUCE: (26), (30) imply: % 161.71/22.00 | (33) powerset(all_492_4) = all_581_0 % 161.71/22.00 | % 161.71/22.00 | REDUCE: (25), (32) imply: % 161.71/22.00 | (34) element(all_492_4, all_581_0) % 161.71/22.00 | % 161.71/22.00 | GROUND_INST: instantiating (2) with all_492_3, all_581_0, all_492_4, % 161.71/22.00 | simplifying with (12), (33) gives: % 161.71/22.00 | (35) all_581_0 = all_492_3 % 161.71/22.00 | % 161.71/22.00 | REDUCE: (34), (35) imply: % 161.71/22.00 | (36) element(all_492_4, all_492_3) % 161.71/22.00 | % 161.71/22.00 | BETA: splitting (28) gives: % 161.71/22.00 | % 161.71/22.00 | Case 1: % 161.71/22.00 | | % 161.71/22.01 | | (37) all_583_0 = all_492_0 & set_intersection2(all_492_1, all_492_2) = % 161.71/22.01 | | all_492_0 & $i(all_492_0) % 161.71/22.01 | | % 161.71/22.01 | | ALPHA: (37) implies: % 161.71/22.01 | | (38) set_intersection2(all_492_1, all_492_2) = all_492_0 % 161.71/22.01 | | % 161.71/22.01 | | REDUCE: (32), (38) imply: % 161.71/22.01 | | (39) set_intersection2(all_492_1, all_492_4) = all_492_0 % 161.71/22.01 | | % 161.71/22.01 | | GROUND_INST: instantiating (t28_xboole_1) with all_492_1, all_492_4, % 161.71/22.01 | | all_492_0, simplifying with (9), (11), (16), (39) gives: % 161.71/22.01 | | (40) all_492_0 = all_492_1 % 161.71/22.01 | | % 161.71/22.01 | | REDUCE: (5), (40) imply: % 161.71/22.01 | | (41) $false % 161.71/22.01 | | % 161.71/22.01 | | CLOSE: (41) is inconsistent. % 161.71/22.01 | | % 161.71/22.01 | Case 2: % 161.71/22.01 | | % 161.71/22.01 | | (42) powerset(all_492_4) = all_583_1 & $i(all_583_1) & ( ~ % 161.71/22.01 | | element(all_492_1, all_583_1) | ~ element(all_492_2, all_583_1)) % 161.71/22.01 | | % 161.71/22.01 | | ALPHA: (42) implies: % 161.71/22.01 | | (43) powerset(all_492_4) = all_583_1 % 161.71/22.01 | | (44) ~ element(all_492_1, all_583_1) | ~ element(all_492_2, all_583_1) % 161.71/22.01 | | % 161.71/22.01 | | GROUND_INST: instantiating (2) with all_492_3, all_583_1, all_492_4, % 161.71/22.01 | | simplifying with (12), (43) gives: % 161.71/22.01 | | (45) all_583_1 = all_492_3 % 161.71/22.01 | | % 161.71/22.01 | | BETA: splitting (44) gives: % 161.71/22.01 | | % 161.71/22.01 | | Case 1: % 161.71/22.01 | | | % 161.71/22.01 | | | (46) ~ element(all_492_1, all_583_1) % 161.71/22.01 | | | % 161.71/22.01 | | | REDUCE: (45), (46) imply: % 161.71/22.01 | | | (47) ~ element(all_492_1, all_492_3) % 161.71/22.01 | | | % 161.71/22.01 | | | PRED_UNIFY: (6), (47) imply: % 161.71/22.01 | | | (48) $false % 161.71/22.01 | | | % 161.71/22.01 | | | CLOSE: (48) is inconsistent. % 161.71/22.01 | | | % 161.71/22.01 | | Case 2: % 161.71/22.01 | | | % 161.71/22.01 | | | (49) ~ element(all_492_2, all_583_1) % 161.71/22.01 | | | % 161.71/22.01 | | | REDUCE: (32), (45), (49) imply: % 161.71/22.01 | | | (50) ~ element(all_492_4, all_492_3) % 161.71/22.01 | | | % 161.71/22.01 | | | PRED_UNIFY: (36), (50) imply: % 161.71/22.01 | | | (51) $false % 161.71/22.01 | | | % 161.71/22.01 | | | CLOSE: (51) is inconsistent. % 161.71/22.01 | | | % 161.71/22.01 | | End of split % 161.71/22.01 | | % 161.71/22.01 | End of split % 161.71/22.01 | % 161.71/22.01 End of proof % 161.71/22.01 % SZS output end Proof for theBenchmark % 161.71/22.01 % 161.71/22.01 21421ms %------------------------------------------------------------------------------