%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SEU308+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 : n026.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 146.93s 20.57s % Output : Proof 153.61s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.11 % Problem : SEU308+2 : TPTP v8.1.2. Released v3.3.0. % 0.00/0.12 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.12/0.33 % Computer : n026.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 18:14:16 EDT 2023 % 0.19/0.33 % CPUTime : % 0.19/0.56 ________ _____ % 0.19/0.56 ___ __ \_________(_)________________________________ % 0.19/0.56 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.19/0.56 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.19/0.56 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.19/0.56 % 0.19/0.56 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.19/0.56 (2023-06-19) % 0.19/0.56 % 0.19/0.56 (c) Philipp Rümmer, 2009-2023 % 0.19/0.56 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.19/0.56 Amanda Stjerna. % 0.19/0.56 Free software under BSD-3-Clause. % 0.19/0.56 % 0.19/0.56 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.19/0.56 % 0.19/0.56 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.19/0.58 Running up to 7 provers in parallel. % 0.19/0.58 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.19/0.58 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.19/0.58 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.19/0.58 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.19/0.58 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.19/0.58 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.19/0.59 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 11.15/2.31 Prover 4: Preprocessing ... % 11.15/2.32 Prover 1: Preprocessing ... % 11.15/2.34 Prover 2: Preprocessing ... % 11.15/2.34 Prover 3: Preprocessing ... % 11.15/2.34 Prover 0: Preprocessing ... % 11.80/2.35 Prover 6: Preprocessing ... % 11.80/2.37 Prover 5: Preprocessing ... % 36.65/5.82 Prover 1: Warning: ignoring some quantifiers % 39.40/6.06 Prover 1: Constructing countermodel ... % 40.44/6.23 Prover 6: Proving ... % 41.45/6.43 Prover 3: Warning: ignoring some quantifiers % 41.45/6.51 Prover 5: Proving ... % 41.45/6.53 Prover 3: Constructing countermodel ... % 54.55/8.14 Prover 2: Proving ... % 67.04/9.84 Prover 4: Warning: ignoring some quantifiers % 68.94/10.21 Prover 4: Constructing countermodel ... % 86.14/12.41 Prover 0: Proving ... % 97.30/13.93 Prover 5: stopped % 97.30/13.94 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 100.05/14.46 Prover 7: Preprocessing ... % 107.66/15.35 Prover 7: Warning: ignoring some quantifiers % 108.47/15.49 Prover 7: Constructing countermodel ... % 110.74/15.72 Prover 2: stopped % 110.74/15.72 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 111.49/15.93 Prover 1: stopped % 111.49/15.93 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889 % 114.76/16.29 Prover 8: Preprocessing ... % 116.00/16.45 Prover 9: Preprocessing ... % 122.24/17.22 Prover 8: Warning: ignoring some quantifiers % 122.51/17.30 Prover 8: Constructing countermodel ... % 126.64/17.83 Prover 6: stopped % 126.64/17.85 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 132.50/18.60 Prover 10: Preprocessing ... % 136.27/19.15 Prover 10: Warning: ignoring some quantifiers % 136.68/19.24 Prover 10: Constructing countermodel ... % 143.36/20.11 Prover 9: Warning: ignoring some quantifiers % 144.36/20.25 Prover 9: Constructing countermodel ... % 146.93/20.57 Prover 9: proved (4638ms) % 146.93/20.57 % 146.93/20.57 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 146.93/20.57 % 147.15/20.59 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 147.62/20.66 Prover 3: stopped % 147.62/20.66 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 147.62/20.69 Prover 0: stopped % 147.62/20.71 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 149.97/21.08 Prover 11: Preprocessing ... % 149.97/21.15 Prover 10: Found proof (size 73) % 149.97/21.15 Prover 10: proved (3304ms) % 150.72/21.19 Prover 4: stopped % 150.72/21.19 Prover 8: stopped % 150.72/21.20 Prover 7: stopped % 150.72/21.20 Prover 13: Preprocessing ... % 150.72/21.21 Prover 16: Preprocessing ... % 152.88/21.41 Prover 13: stopped % 152.88/21.46 Prover 16: stopped % 152.88/21.47 Prover 11: stopped % 152.88/21.47 % 152.88/21.47 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 152.88/21.47 % 153.37/21.48 % SZS output start Proof for theBenchmark % 153.45/21.50 Assumptions after simplification: % 153.45/21.50 --------------------------------- % 153.45/21.50 % 153.45/21.50 (d3_pre_topc) % 153.57/21.52 ! [v0: $i] : ! [v1: $i] : ( ~ (cast_as_carrier_subset(v0) = v1) | ~ $i(v0) % 153.61/21.52 | ~ one_sorted_str(v0) | (the_carrier(v0) = v1 & $i(v1))) % 153.61/21.52 % 153.61/21.52 (d5_subset_1) % 153.61/21.52 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (subset_complement(v0, v1) = v2) % 153.61/21.53 | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : ((v4 = v2 & % 153.61/21.53 set_difference(v0, v1) = v2 & $i(v2)) | (powerset(v0) = v3 & $i(v3) & ~ % 153.61/21.53 element(v1, v3)))) % 153.61/21.53 % 153.61/21.53 (dt_k2_pre_topc) % 153.61/21.53 ! [v0: $i] : ! [v1: $i] : ( ~ (cast_as_carrier_subset(v0) = v1) | ~ $i(v0) % 153.61/21.53 | ~ one_sorted_str(v0) | ? [v2: $i] : ? [v3: $i] : (the_carrier(v0) = v2 % 153.61/21.53 & powerset(v2) = v3 & $i(v3) & $i(v2) & element(v1, v3))) % 153.61/21.53 % 153.61/21.53 (dt_k3_subset_1) % 153.61/21.53 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (subset_complement(v0, v1) = v2) % 153.61/21.53 | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : (powerset(v0) = v3 & $i(v3) & ( ~ % 153.61/21.53 element(v1, v3) | element(v2, v3)))) % 153.61/21.53 % 153.61/21.53 (dt_k6_subset_1) % 153.61/21.53 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 153.61/21.53 (subset_difference(v0, v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 153.61/21.53 ? [v4: $i] : (powerset(v0) = v4 & $i(v4) & ( ~ element(v2, v4) | ~ % 153.61/21.53 element(v1, v4) | element(v3, v4)))) % 153.61/21.53 % 153.61/21.53 (redefinition_k6_subset_1) % 153.61/21.53 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 153.61/21.53 (subset_difference(v0, v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 153.61/21.53 ? [v4: $i] : ? [v5: $i] : ((v5 = v3 & set_difference(v1, v2) = v3 & $i(v3)) % 153.61/21.53 | (powerset(v0) = v4 & $i(v4) & ( ~ element(v2, v4) | ~ element(v1, % 153.61/21.53 v4))))) % 153.61/21.53 % 153.61/21.53 (t12_pre_topc) % 153.61/21.53 ! [v0: $i] : ! [v1: $i] : ( ~ (cast_as_carrier_subset(v0) = v1) | ~ $i(v0) % 153.61/21.53 | ~ one_sorted_str(v0) | (the_carrier(v0) = v1 & $i(v1))) % 153.61/21.53 % 153.61/21.53 (t15_pre_topc) % 153.61/21.54 ! [v0: $i] : ! [v1: $i] : ( ~ (cast_as_carrier_subset(v0) = v1) | ~ $i(v0) % 153.61/21.54 | ~ one_sorted_str(v0) | ? [v2: $i] : ? [v3: $i] : (the_carrier(v0) = v2 % 153.61/21.54 & powerset(v2) = v3 & $i(v3) & $i(v2) & ! [v4: $i] : ! [v5: $i] : (v5 = % 153.61/21.54 v4 | ~ (subset_intersection2(v2, v4, v1) = v5) | ~ $i(v4) | ~ % 153.61/21.54 element(v4, v3)))) % 153.61/21.54 % 153.61/21.54 (t17_pre_topc) % 153.61/21.54 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: % 153.61/21.54 $i] : ? [v6: $i] : ( ~ (v6 = v5) & subset_difference(v1, v3, v4) = v6 & % 153.61/21.54 subset_complement(v1, v4) = v5 & cast_as_carrier_subset(v0) = v3 & % 153.61/21.54 the_carrier(v0) = v1 & powerset(v1) = v2 & $i(v6) & $i(v5) & $i(v4) & $i(v3) % 153.61/21.54 & $i(v2) & $i(v1) & $i(v0) & one_sorted_str(v0) & element(v4, v2)) % 153.61/21.54 % 153.61/21.54 (function-axioms) % 153.61/21.56 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 153.61/21.56 $i] : ! [v6: $i] : ! [v7: $i] : (v1 = v0 | ~ (apply_binary_as_element(v7, % 153.61/21.56 v6, v5, v4, v3, v2) = v1) | ~ (apply_binary_as_element(v7, v6, v5, v4, % 153.61/21.56 v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : % 153.61/21.56 ! [v4: $i] : (v1 = v0 | ~ (apply_binary(v4, v3, v2) = v1) | ~ % 153.61/21.56 (apply_binary(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 153.61/21.56 ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (subset_difference(v4, v3, v2) = v1) % 153.61/21.56 | ~ (subset_difference(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 153.61/21.56 [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ % 153.61/21.56 (relation_rng_as_subset(v4, v3, v2) = v1) | ~ (relation_rng_as_subset(v4, % 153.61/21.56 v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : % 153.61/21.56 ! [v4: $i] : (v1 = v0 | ~ (meet(v4, v3, v2) = v1) | ~ (meet(v4, v3, v2) = % 153.61/21.56 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] % 153.61/21.56 : (v1 = v0 | ~ (join(v4, v3, v2) = v1) | ~ (join(v4, v3, v2) = v0)) & ! % 153.61/21.56 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | % 153.61/21.56 ~ (relation_dom_as_subset(v4, v3, v2) = v1) | ~ (relation_dom_as_subset(v4, % 153.61/21.56 v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : % 153.61/21.56 ! [v4: $i] : (v1 = v0 | ~ (unordered_triple(v4, v3, v2) = v1) | ~ % 153.61/21.56 (unordered_triple(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 153.61/21.56 $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (subset_intersection2(v4, % 153.61/21.56 v3, v2) = v1) | ~ (subset_intersection2(v4, v3, v2) = v0)) & ! [v0: % 153.61/21.56 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ % 153.61/21.56 (meet_commut(v4, v3, v2) = v1) | ~ (meet_commut(v4, v3, v2) = v0)) & ! % 153.61/21.56 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | % 153.61/21.56 ~ (join_commut(v4, v3, v2) = v1) | ~ (join_commut(v4, v3, v2) = v0)) & ! % 153.61/21.56 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 153.61/21.56 (meet_of_subsets(v3, v2) = v1) | ~ (meet_of_subsets(v3, v2) = v0)) & ! % 153.61/21.56 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 153.61/21.56 (union_of_subsets(v3, v2) = v1) | ~ (union_of_subsets(v3, v2) = v0)) & ! % 153.61/21.56 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 153.61/21.56 (complements_of_subsets(v3, v2) = v1) | ~ (complements_of_subsets(v3, v2) = % 153.61/21.56 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | % 153.61/21.56 ~ (relation_composition(v3, v2) = v1) | ~ (relation_composition(v3, v2) = % 153.61/21.56 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | % 153.61/21.56 ~ (relation_restriction(v3, v2) = v1) | ~ (relation_restriction(v3, v2) = % 153.61/21.56 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | % 153.61/21.56 ~ (subset_complement(v3, v2) = v1) | ~ (subset_complement(v3, v2) = v0)) & % 153.61/21.56 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 153.61/21.56 (set_difference(v3, v2) = v1) | ~ (set_difference(v3, v2) = v0)) & ! [v0: % 153.61/21.56 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (fiber(v3, v2) % 153.61/21.56 = v1) | ~ (fiber(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 153.61/21.56 : ! [v3: $i] : (v1 = v0 | ~ (relation_inverse_image(v3, v2) = v1) | ~ % 153.61/21.56 (relation_inverse_image(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 153.61/21.56 $i] : ! [v3: $i] : (v1 = v0 | ~ (relation_rng_restriction(v3, v2) = v1) | % 153.61/21.56 ~ (relation_rng_restriction(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 153.61/21.56 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (relation_image(v3, v2) = v1) | ~ % 153.61/21.56 (relation_image(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 153.61/21.56 ! [v3: $i] : (v1 = v0 | ~ (apply(v3, v2) = v1) | ~ (apply(v3, v2) = v0)) & % 153.61/21.56 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 153.61/21.56 (relation_dom_restriction(v3, v2) = v1) | ~ (relation_dom_restriction(v3, % 153.61/21.56 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 % 153.61/21.56 = v0 | ~ (ordered_pair(v3, v2) = v1) | ~ (ordered_pair(v3, v2) = v0)) & ! % 153.61/21.56 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 153.61/21.56 (set_intersection2(v3, v2) = v1) | ~ (set_intersection2(v3, v2) = v0)) & ! % 153.61/21.56 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 153.61/21.56 (set_union2(v3, v2) = v1) | ~ (set_union2(v3, v2) = v0)) & ! [v0: $i] : ! % 153.61/21.56 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (unordered_pair(v3, v2) = % 153.61/21.56 v1) | ~ (unordered_pair(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 153.61/21.56 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (cartesian_product2(v3, v2) = v1) | ~ % 153.61/21.56 (cartesian_product2(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 153.61/21.56 : (v1 = v0 | ~ (function_inverse(v2) = v1) | ~ (function_inverse(v2) = v0)) % 153.61/21.56 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 153.61/21.56 (relation_inverse(v2) = v1) | ~ (relation_inverse(v2) = v0)) & ! [v0: $i] % 153.61/21.56 : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (union(v2) = v1) | ~ (union(v2) = % 153.61/21.56 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 153.61/21.56 (cast_to_subset(v2) = v1) | ~ (cast_to_subset(v2) = v0)) & ! [v0: $i] : ! % 153.61/21.56 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (cast_as_carrier_subset(v2) = v1) | ~ % 153.61/21.56 (cast_as_carrier_subset(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 153.61/21.56 : (v1 = v0 | ~ (pair_second(v2) = v1) | ~ (pair_second(v2) = v0)) & ! [v0: % 153.61/21.56 $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (the_L_meet(v2) = v1) | ~ % 153.61/21.56 (the_L_meet(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 % 153.61/21.56 | ~ (inclusion_relation(v2) = v1) | ~ (inclusion_relation(v2) = v0)) & ! % 153.61/21.56 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (set_meet(v2) = v1) | ~ % 153.61/21.56 (set_meet(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | % 153.61/21.56 ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ! [v0: $i] : ! [v1: % 153.61/21.56 $i] : ! [v2: $i] : (v1 = v0 | ~ (succ(v2) = v1) | ~ (succ(v2) = v0)) & ! % 153.61/21.56 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (pair_first(v2) = v1) | % 153.61/21.56 ~ (pair_first(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = % 153.61/21.56 v0 | ~ (the_L_join(v2) = v1) | ~ (the_L_join(v2) = v0)) & ! [v0: $i] : ! % 153.61/21.56 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (relation_rng(v2) = v1) | ~ % 153.61/21.56 (relation_rng(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = % 153.61/21.56 v0 | ~ (relation_field(v2) = v1) | ~ (relation_field(v2) = v0)) & ! [v0: % 153.61/21.56 $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (relation_dom(v2) = v1) | ~ % 153.61/21.56 (relation_dom(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = % 153.61/21.56 v0 | ~ (identity_relation(v2) = v1) | ~ (identity_relation(v2) = v0)) & ! % 153.61/21.56 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (the_carrier(v2) = v1) | % 153.61/21.56 ~ (the_carrier(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = % 153.61/21.56 v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0)) % 153.61/21.56 % 153.61/21.56 Further assumptions not needed in the proof: % 153.61/21.56 -------------------------------------------- % 153.61/21.56 antisymmetry_r2_hidden, antisymmetry_r2_xboole_0, cc10_membered, cc11_membered, % 153.61/21.56 cc12_membered, cc13_membered, cc14_membered, cc15_membered, cc16_membered, % 153.61/21.56 cc17_membered, cc18_membered, cc19_membered, cc1_arytm_3, cc1_finset_1, % 153.61/21.56 cc1_finsub_1, cc1_funct_1, cc1_membered, cc1_ordinal1, cc1_relat_1, % 153.61/21.56 cc1_relset_1, cc20_membered, cc2_arytm_3, cc2_finset_1, cc2_finsub_1, % 153.61/21.56 cc2_funct_1, cc2_membered, cc2_ordinal1, cc3_arytm_3, cc3_membered, % 153.61/21.56 cc3_ordinal1, cc4_membered, commutativity_k2_tarski, commutativity_k2_xboole_0, % 153.61/21.56 commutativity_k3_lattices, commutativity_k3_xboole_0, commutativity_k4_lattices, % 153.61/21.56 commutativity_k5_subset_1, connectedness_r1_ordinal1, d10_relat_1, d10_xboole_0, % 153.61/21.56 d11_relat_1, d12_funct_1, d12_relat_1, d12_relat_2, d13_funct_1, d13_relat_1, % 153.61/21.56 d14_relat_1, d14_relat_2, d16_relat_2, d1_enumset1, d1_finset_1, d1_funct_1, % 153.61/21.56 d1_funct_2, d1_lattices, d1_mcart_1, d1_ordinal1, d1_relat_1, d1_relat_2, % 153.61/21.56 d1_relset_1, d1_setfam_1, d1_tarski, d1_wellord1, d1_wellord2, d1_xboole_0, % 153.61/21.56 d1_zfmisc_1, d2_lattices, d2_mcart_1, d2_ordinal1, d2_relat_1, d2_subset_1, % 153.61/21.56 d2_tarski, d2_wellord1, d2_xboole_0, d2_zfmisc_1, d3_lattices, d3_ordinal1, % 153.61/21.56 d3_relat_1, d3_tarski, d3_wellord1, d3_xboole_0, d4_funct_1, d4_ordinal1, % 153.61/21.56 d4_relat_1, d4_relat_2, d4_subset_1, d4_tarski, d4_wellord1, d4_wellord2, % 153.61/21.56 d4_xboole_0, d5_funct_1, d5_ordinal2, d5_relat_1, d5_tarski, d5_wellord1, % 153.61/21.57 d6_ordinal1, d6_relat_1, d6_relat_2, d6_wellord1, d7_relat_1, d7_wellord1, % 153.61/21.57 d7_xboole_0, d8_funct_1, d8_lattices, d8_relat_1, d8_relat_2, d8_setfam_1, % 153.61/21.57 d8_xboole_0, d9_funct_1, d9_relat_2, dt_k10_relat_1, dt_k1_binop_1, % 153.61/21.57 dt_k1_enumset1, dt_k1_funct_1, dt_k1_lattices, dt_k1_mcart_1, dt_k1_ordinal1, % 153.61/21.57 dt_k1_relat_1, dt_k1_setfam_1, dt_k1_tarski, dt_k1_wellord1, dt_k1_wellord2, % 153.61/21.57 dt_k1_xboole_0, dt_k1_zfmisc_1, dt_k2_binop_1, dt_k2_funct_1, dt_k2_lattices, % 153.61/21.57 dt_k2_mcart_1, dt_k2_relat_1, dt_k2_subset_1, dt_k2_tarski, dt_k2_wellord1, % 153.61/21.57 dt_k2_xboole_0, dt_k2_zfmisc_1, dt_k3_lattices, dt_k3_relat_1, dt_k3_tarski, % 153.61/21.57 dt_k3_xboole_0, dt_k4_lattices, dt_k4_relat_1, dt_k4_relset_1, dt_k4_tarski, % 153.61/21.57 dt_k4_xboole_0, dt_k5_ordinal2, dt_k5_relat_1, dt_k5_relset_1, dt_k5_setfam_1, % 153.61/21.57 dt_k5_subset_1, dt_k6_relat_1, dt_k6_setfam_1, dt_k7_relat_1, dt_k7_setfam_1, % 153.61/21.57 dt_k8_relat_1, dt_k9_relat_1, dt_l1_lattices, dt_l1_struct_0, dt_l2_lattices, % 153.61/21.57 dt_l3_lattices, dt_m1_relset_1, dt_m1_subset_1, dt_m2_relset_1, dt_u1_lattices, % 153.61/21.57 dt_u1_struct_0, dt_u2_lattices, existence_l1_lattices, existence_l1_struct_0, % 153.61/21.57 existence_l2_lattices, existence_l3_lattices, existence_m1_relset_1, % 153.61/21.57 existence_m1_subset_1, existence_m2_relset_1, fc10_finset_1, fc10_relat_1, % 153.61/21.57 fc11_finset_1, fc11_relat_1, fc12_finset_1, fc12_relat_1, fc13_finset_1, % 153.61/21.57 fc13_relat_1, fc1_finset_1, fc1_finsub_1, fc1_funct_1, fc1_ordinal1, % 153.61/21.57 fc1_ordinal2, fc1_relat_1, fc1_struct_0, fc1_subset_1, fc1_xboole_0, % 153.61/21.57 fc1_zfmisc_1, fc27_membered, fc28_membered, fc29_membered, fc2_arytm_3, % 153.61/21.57 fc2_funct_1, fc2_ordinal1, fc2_relat_1, fc2_subset_1, fc2_xboole_0, % 153.61/21.57 fc30_membered, fc31_membered, fc32_membered, fc33_membered, fc34_membered, % 153.61/21.57 fc35_membered, fc36_membered, fc37_membered, fc38_membered, fc39_membered, % 153.61/21.57 fc3_funct_1, fc3_ordinal1, fc3_relat_1, fc3_subset_1, fc3_xboole_0, % 153.61/21.57 fc40_membered, fc41_membered, fc4_funct_1, fc4_ordinal1, fc4_relat_1, % 153.61/21.57 fc4_subset_1, fc5_funct_1, fc5_relat_1, fc6_membered, fc6_relat_1, fc7_relat_1, % 153.61/21.57 fc8_relat_1, fc9_finset_1, fc9_relat_1, idempotence_k2_xboole_0, % 153.61/21.57 idempotence_k3_xboole_0, idempotence_k5_subset_1, involutiveness_k3_subset_1, % 153.61/21.57 involutiveness_k4_relat_1, involutiveness_k7_setfam_1, % 153.61/21.57 irreflexivity_r2_xboole_0, l1_wellord1, l1_zfmisc_1, l23_zfmisc_1, l25_zfmisc_1, % 153.61/21.57 l28_zfmisc_1, l29_wellord1, l2_wellord1, l2_zfmisc_1, l30_wellord2, % 153.61/21.57 l32_xboole_1, l3_subset_1, l3_wellord1, l3_zfmisc_1, l4_wellord1, l4_zfmisc_1, % 153.61/21.57 l50_zfmisc_1, l55_zfmisc_1, l71_subset_1, l82_funct_1, rc1_arytm_3, % 153.61/21.57 rc1_finset_1, rc1_funct_1, rc1_funct_2, rc1_membered, rc1_ordinal1, % 153.61/21.57 rc1_ordinal2, rc1_partfun1, rc1_relat_1, rc1_subset_1, rc1_xboole_0, % 153.61/21.57 rc2_finset_1, rc2_funct_1, rc2_ordinal1, rc2_partfun1, rc2_relat_1, % 153.61/21.57 rc2_subset_1, rc2_xboole_0, rc3_finset_1, rc3_funct_1, rc3_ordinal1, % 153.61/21.57 rc3_relat_1, rc3_struct_0, rc4_funct_1, rc5_struct_0, redefinition_k2_binop_1, % 153.61/21.57 redefinition_k3_lattices, redefinition_k4_lattices, redefinition_k4_relset_1, % 153.61/21.57 redefinition_k5_relset_1, redefinition_k5_setfam_1, redefinition_k5_subset_1, % 153.61/21.57 redefinition_k6_setfam_1, redefinition_m2_relset_1, redefinition_r1_ordinal1, % 153.61/21.57 redefinition_r2_wellord2, reflexivity_r1_ordinal1, reflexivity_r1_tarski, % 153.61/21.57 reflexivity_r2_wellord2, s1_funct_1__e10_24__wellord2__1, % 153.61/21.57 s1_funct_1__e16_22__wellord2__1, s1_ordinal1__e8_6__wellord2, % 153.61/21.57 s1_ordinal2__e18_27__finset_1, s1_relat_1__e6_21__wellord2, % 153.61/21.57 s1_tarski__e10_24__wellord2__1, s1_tarski__e10_24__wellord2__2, % 153.61/21.57 s1_tarski__e16_22__wellord2__1, s1_tarski__e16_22__wellord2__2, % 153.61/21.57 s1_tarski__e18_27__finset_1__1, s1_tarski__e4_27_3_1__finset_1__1, % 153.61/21.57 s1_tarski__e6_21__wellord2__1, s1_tarski__e6_22__wellord2__1, % 153.61/21.57 s1_tarski__e6_27__finset_1__1, s1_tarski__e8_6__wellord2__1, % 153.61/21.57 s1_xboole_0__e10_24__wellord2__1, s1_xboole_0__e16_22__wellord2__1, % 153.61/21.57 s1_xboole_0__e18_27__finset_1__1, s1_xboole_0__e4_27_3_1__finset_1, % 153.61/21.57 s1_xboole_0__e6_21__wellord2__1, s1_xboole_0__e6_22__wellord2, % 153.61/21.57 s1_xboole_0__e6_27__finset_1, s1_xboole_0__e8_6__wellord2__1, % 153.61/21.57 s2_funct_1__e10_24__wellord2, s2_funct_1__e16_22__wellord2__1, % 153.61/21.57 s2_ordinal1__e18_27__finset_1__1, s3_funct_1__e16_22__wellord2, % 153.61/21.57 symmetry_r1_xboole_0, symmetry_r2_wellord2, t106_zfmisc_1, t10_ordinal1, % 153.61/21.57 t10_zfmisc_1, t115_relat_1, t116_relat_1, t117_relat_1, t118_relat_1, % 153.61/21.57 t118_zfmisc_1, t119_relat_1, t119_zfmisc_1, t12_relset_1, t12_xboole_1, % 153.61/21.57 t136_zfmisc_1, t13_finset_1, t140_relat_1, t143_relat_1, t144_relat_1, % 153.61/21.57 t145_funct_1, t145_relat_1, t146_funct_1, t146_relat_1, t147_funct_1, % 153.61/21.57 t14_relset_1, t15_finset_1, t160_relat_1, t166_relat_1, t167_relat_1, % 153.61/21.57 t16_relset_1, t16_wellord1, t174_relat_1, t178_relat_1, t17_finset_1, % 153.61/21.57 t17_wellord1, t17_xboole_1, t18_finset_1, t18_wellord1, t19_wellord1, % 153.61/21.57 t19_xboole_1, t1_boole, t1_subset, t1_xboole_1, t1_zfmisc_1, t20_relat_1, % 153.61/21.57 t20_wellord1, t21_funct_1, t21_funct_2, t21_ordinal1, t21_relat_1, t21_wellord1, % 153.61/21.57 t22_funct_1, t22_relset_1, t22_wellord1, t23_funct_1, t23_lattices, % 153.61/21.57 t23_ordinal1, t23_relset_1, t23_wellord1, t24_ordinal1, t24_wellord1, % 153.61/21.57 t25_relat_1, t25_wellord1, t25_wellord2, t26_finset_1, t26_lattices, % 153.61/21.57 t26_wellord2, t26_xboole_1, t28_wellord2, t28_xboole_1, t2_boole, t2_subset, % 153.61/21.57 t2_tarski, t2_wellord2, t2_xboole_1, t30_relat_1, t31_ordinal1, t31_wellord1, % 153.61/21.57 t32_ordinal1, t32_wellord1, t33_ordinal1, t33_xboole_1, t33_zfmisc_1, % 153.61/21.57 t34_funct_1, t35_funct_1, t36_xboole_1, t37_relat_1, t37_xboole_1, t37_zfmisc_1, % 153.61/21.57 t38_zfmisc_1, t39_wellord1, t39_xboole_1, t39_zfmisc_1, t3_boole, t3_ordinal1, % 153.61/21.57 t3_subset, t3_wellord2, t3_xboole_0, t3_xboole_1, t40_xboole_1, t41_ordinal1, % 153.61/21.57 t42_ordinal1, t43_subset_1, t44_relat_1, t45_relat_1, t45_xboole_1, t46_funct_2, % 153.61/21.57 t46_relat_1, t46_setfam_1, t46_zfmisc_1, t47_relat_1, t47_setfam_1, % 153.61/21.57 t48_setfam_1, t48_xboole_1, t49_wellord1, t4_boole, t4_subset, t4_wellord2, % 153.61/21.57 t4_xboole_0, t50_subset_1, t53_wellord1, t54_funct_1, t54_subset_1, % 153.61/21.57 t54_wellord1, t55_funct_1, t56_relat_1, t57_funct_1, t5_subset, t5_wellord1, % 153.61/21.57 t5_wellord2, t60_relat_1, t60_xboole_1, t62_funct_1, t63_xboole_1, t64_relat_1, % 153.61/21.57 t65_relat_1, t65_zfmisc_1, t68_funct_1, t69_enumset1, t6_boole, t6_funct_2, % 153.61/21.57 t6_wellord2, t6_zfmisc_1, t70_funct_1, t71_relat_1, t72_funct_1, t74_relat_1, % 153.61/21.57 t7_boole, t7_mcart_1, t7_tarski, t7_wellord2, t7_xboole_1, t83_xboole_1, % 153.61/21.57 t86_relat_1, t88_relat_1, t8_boole, t8_funct_1, t8_wellord1, t8_xboole_1, % 153.61/21.57 t8_zfmisc_1, t90_relat_1, t92_zfmisc_1, t94_relat_1, t99_relat_1, t99_zfmisc_1, % 153.61/21.57 t9_funct_2, t9_tarski, t9_zfmisc_1 % 153.61/21.57 % 153.61/21.57 Those formulas are unsatisfiable: % 153.61/21.57 --------------------------------- % 153.61/21.57 % 153.61/21.57 Begin of proof % 153.61/21.57 | % 153.61/21.57 | ALPHA: (function-axioms) implies: % 153.61/21.57 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (powerset(v2) = % 153.61/21.57 | v1) | ~ (powerset(v2) = v0)) % 153.61/21.57 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 153.61/21.57 | (the_carrier(v2) = v1) | ~ (the_carrier(v2) = v0)) % 153.61/21.57 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 153.61/21.57 | (set_difference(v3, v2) = v1) | ~ (set_difference(v3, v2) = v0)) % 153.61/21.57 | % 153.61/21.57 | DELTA: instantiating (t17_pre_topc) with fresh symbols all_510_0, all_510_1, % 153.61/21.57 | all_510_2, all_510_3, all_510_4, all_510_5, all_510_6 gives: % 153.61/21.57 | (4) ~ (all_510_0 = all_510_1) & subset_difference(all_510_5, all_510_3, % 153.61/21.57 | all_510_2) = all_510_0 & subset_complement(all_510_5, all_510_2) = % 153.61/21.57 | all_510_1 & cast_as_carrier_subset(all_510_6) = all_510_3 & % 153.61/21.57 | the_carrier(all_510_6) = all_510_5 & powerset(all_510_5) = all_510_4 & % 153.61/21.57 | $i(all_510_0) & $i(all_510_1) & $i(all_510_2) & $i(all_510_3) & % 153.61/21.57 | $i(all_510_4) & $i(all_510_5) & $i(all_510_6) & % 153.61/21.57 | one_sorted_str(all_510_6) & element(all_510_2, all_510_4) % 153.61/21.57 | % 153.61/21.57 | ALPHA: (4) implies: % 153.61/21.57 | (5) ~ (all_510_0 = all_510_1) % 153.61/21.57 | (6) element(all_510_2, all_510_4) % 153.61/21.57 | (7) one_sorted_str(all_510_6) % 153.61/21.57 | (8) $i(all_510_6) % 153.61/21.57 | (9) $i(all_510_5) % 153.61/21.57 | (10) $i(all_510_2) % 153.61/21.57 | (11) powerset(all_510_5) = all_510_4 % 153.61/21.57 | (12) the_carrier(all_510_6) = all_510_5 % 153.61/21.57 | (13) cast_as_carrier_subset(all_510_6) = all_510_3 % 153.61/21.57 | (14) subset_complement(all_510_5, all_510_2) = all_510_1 % 153.61/21.57 | (15) subset_difference(all_510_5, all_510_3, all_510_2) = all_510_0 % 153.61/21.57 | % 153.61/21.58 | GROUND_INST: instantiating (dt_k2_pre_topc) with all_510_6, all_510_3, % 153.61/21.58 | simplifying with (7), (8), (13) gives: % 153.61/21.58 | (16) ? [v0: $i] : ? [v1: $i] : (the_carrier(all_510_6) = v0 & % 153.61/21.58 | powerset(v0) = v1 & $i(v1) & $i(v0) & element(all_510_3, v1)) % 153.61/21.58 | % 153.61/21.58 | GROUND_INST: instantiating (t15_pre_topc) with all_510_6, all_510_3, % 153.61/21.58 | simplifying with (7), (8), (13) gives: % 153.61/21.58 | (17) ? [v0: $i] : ? [v1: $i] : (the_carrier(all_510_6) = v0 & % 153.61/21.58 | powerset(v0) = v1 & $i(v1) & $i(v0) & ! [v2: $i] : ! [v3: $i] : % 153.61/21.58 | (v3 = v2 | ~ (subset_intersection2(v0, v2, all_510_3) = v3) | ~ % 153.61/21.58 | $i(v2) | ~ element(v2, v1))) % 153.61/21.58 | % 153.61/21.58 | GROUND_INST: instantiating (t12_pre_topc) with all_510_6, all_510_3, % 153.61/21.58 | simplifying with (7), (8), (13) gives: % 153.61/21.58 | (18) the_carrier(all_510_6) = all_510_3 & $i(all_510_3) % 153.61/21.58 | % 153.61/21.58 | ALPHA: (18) implies: % 153.61/21.58 | (19) $i(all_510_3) % 153.61/21.58 | (20) the_carrier(all_510_6) = all_510_3 % 153.61/21.58 | % 153.61/21.58 | GROUND_INST: instantiating (d5_subset_1) with all_510_5, all_510_2, all_510_1, % 153.61/21.58 | simplifying with (9), (10), (14) gives: % 153.61/21.58 | (21) ? [v0: $i] : ? [v1: int] : ((v1 = all_510_1 & % 153.61/21.58 | set_difference(all_510_5, all_510_2) = all_510_1 & $i(all_510_1)) % 153.61/21.58 | | (powerset(all_510_5) = v0 & $i(v0) & ~ element(all_510_2, v0))) % 153.61/21.58 | % 153.61/21.58 | GROUND_INST: instantiating (dt_k3_subset_1) with all_510_5, all_510_2, % 153.61/21.58 | all_510_1, simplifying with (9), (10), (14) gives: % 153.61/21.58 | (22) ? [v0: $i] : (powerset(all_510_5) = v0 & $i(v0) & ( ~ % 153.61/21.58 | element(all_510_2, v0) | element(all_510_1, v0))) % 153.61/21.58 | % 153.61/21.58 | GROUND_INST: instantiating (redefinition_k6_subset_1) with all_510_5, % 153.61/21.58 | all_510_3, all_510_2, all_510_0, simplifying with (9), (10), % 153.61/21.58 | (15), (19) gives: % 153.61/21.58 | (23) ? [v0: $i] : ? [v1: int] : ((v1 = all_510_0 & % 153.61/21.58 | set_difference(all_510_3, all_510_2) = all_510_0 & $i(all_510_0)) % 153.61/21.58 | | (powerset(all_510_5) = v0 & $i(v0) & ( ~ element(all_510_2, v0) | % 153.61/21.58 | ~ element(all_510_3, v0)))) % 153.61/21.58 | % 153.61/21.58 | GROUND_INST: instantiating (dt_k6_subset_1) with all_510_5, all_510_3, % 153.61/21.58 | all_510_2, all_510_0, simplifying with (9), (10), (15), (19) % 153.61/21.58 | gives: % 153.61/21.58 | (24) ? [v0: $i] : (powerset(all_510_5) = v0 & $i(v0) & ( ~ % 153.61/21.58 | element(all_510_2, v0) | ~ element(all_510_3, v0) | % 153.61/21.58 | element(all_510_0, v0))) % 153.61/21.58 | % 153.61/21.58 | DELTA: instantiating (22) with fresh symbol all_582_0 gives: % 153.61/21.58 | (25) powerset(all_510_5) = all_582_0 & $i(all_582_0) & ( ~ % 153.61/21.58 | element(all_510_2, all_582_0) | element(all_510_1, all_582_0)) % 153.61/21.58 | % 153.61/21.58 | ALPHA: (25) implies: % 153.61/21.58 | (26) powerset(all_510_5) = all_582_0 % 153.61/21.58 | % 153.61/21.58 | DELTA: instantiating (24) with fresh symbol all_587_0 gives: % 153.61/21.58 | (27) powerset(all_510_5) = all_587_0 & $i(all_587_0) & ( ~ % 153.61/21.58 | element(all_510_2, all_587_0) | ~ element(all_510_3, all_587_0) | % 153.61/21.58 | element(all_510_0, all_587_0)) % 153.61/21.58 | % 153.61/21.58 | ALPHA: (27) implies: % 153.61/21.58 | (28) powerset(all_510_5) = all_587_0 % 153.61/21.58 | % 153.61/21.58 | DELTA: instantiating (16) with fresh symbols all_589_0, all_589_1 gives: % 153.61/21.59 | (29) the_carrier(all_510_6) = all_589_1 & powerset(all_589_1) = all_589_0 & % 153.61/21.59 | $i(all_589_0) & $i(all_589_1) & element(all_510_3, all_589_0) % 153.61/21.59 | % 153.61/21.59 | ALPHA: (29) implies: % 153.61/21.59 | (30) element(all_510_3, all_589_0) % 153.61/21.59 | (31) powerset(all_589_1) = all_589_0 % 153.61/21.59 | (32) the_carrier(all_510_6) = all_589_1 % 153.61/21.59 | % 153.61/21.59 | DELTA: instantiating (21) with fresh symbols all_591_0, all_591_1 gives: % 153.61/21.59 | (33) (all_591_0 = all_510_1 & set_difference(all_510_5, all_510_2) = % 153.61/21.59 | all_510_1 & $i(all_510_1)) | (powerset(all_510_5) = all_591_1 & % 153.61/21.59 | $i(all_591_1) & ~ element(all_510_2, all_591_1)) % 153.61/21.59 | % 153.61/21.59 | DELTA: instantiating (23) with fresh symbols all_592_0, all_592_1 gives: % 153.61/21.59 | (34) (all_592_0 = all_510_0 & set_difference(all_510_3, all_510_2) = % 153.61/21.59 | all_510_0 & $i(all_510_0)) | (powerset(all_510_5) = all_592_1 & % 153.61/21.59 | $i(all_592_1) & ( ~ element(all_510_2, all_592_1) | ~ % 153.61/21.59 | element(all_510_3, all_592_1))) % 153.61/21.59 | % 153.61/21.59 | DELTA: instantiating (17) with fresh symbols all_599_0, all_599_1 gives: % 153.61/21.59 | (35) the_carrier(all_510_6) = all_599_1 & powerset(all_599_1) = all_599_0 & % 153.61/21.59 | $i(all_599_0) & $i(all_599_1) & ! [v0: $i] : ! [v1: $i] : (v1 = v0 | % 153.61/21.59 | ~ (subset_intersection2(all_599_1, v0, all_510_3) = v1) | ~ $i(v0) % 153.61/21.59 | | ~ element(v0, all_599_0)) % 153.61/21.59 | % 153.61/21.59 | ALPHA: (35) implies: % 153.61/21.59 | (36) powerset(all_599_1) = all_599_0 % 153.61/21.59 | (37) the_carrier(all_510_6) = all_599_1 % 153.61/21.59 | % 153.61/21.59 | GROUND_INST: instantiating (1) with all_510_4, all_587_0, all_510_5, % 153.61/21.59 | simplifying with (11), (28) gives: % 153.61/21.59 | (38) all_587_0 = all_510_4 % 153.61/21.59 | % 153.61/21.59 | GROUND_INST: instantiating (1) with all_582_0, all_587_0, all_510_5, % 153.61/21.59 | simplifying with (26), (28) gives: % 153.61/21.59 | (39) all_587_0 = all_582_0 % 153.61/21.59 | % 153.61/21.59 | GROUND_INST: instantiating (2) with all_510_5, all_589_1, all_510_6, % 153.61/21.59 | simplifying with (12), (32) gives: % 153.61/21.59 | (40) all_589_1 = all_510_5 % 153.61/21.59 | % 153.61/21.59 | GROUND_INST: instantiating (2) with all_589_1, all_599_1, all_510_6, % 153.61/21.59 | simplifying with (32), (37) gives: % 153.61/21.59 | (41) all_599_1 = all_589_1 % 153.61/21.59 | % 153.61/21.59 | GROUND_INST: instantiating (2) with all_510_3, all_599_1, all_510_6, % 153.61/21.59 | simplifying with (20), (37) gives: % 153.61/21.59 | (42) all_599_1 = all_510_3 % 153.61/21.59 | % 153.61/21.59 | COMBINE_EQS: (41), (42) imply: % 153.61/21.59 | (43) all_589_1 = all_510_3 % 153.61/21.59 | % 153.61/21.59 | SIMP: (43) implies: % 153.61/21.59 | (44) all_589_1 = all_510_3 % 153.61/21.59 | % 153.61/21.59 | COMBINE_EQS: (40), (44) imply: % 153.61/21.59 | (45) all_510_3 = all_510_5 % 153.61/21.59 | % 153.61/21.59 | COMBINE_EQS: (38), (39) imply: % 153.61/21.59 | (46) all_582_0 = all_510_4 % 153.61/21.59 | % 153.61/21.59 | SIMP: (46) implies: % 153.61/21.59 | (47) all_582_0 = all_510_4 % 153.61/21.59 | % 153.61/21.59 | COMBINE_EQS: (42), (45) imply: % 153.61/21.59 | (48) all_599_1 = all_510_5 % 153.61/21.59 | % 153.61/21.59 | REDUCE: (36), (48) imply: % 153.61/21.59 | (49) powerset(all_510_5) = all_599_0 % 153.61/21.59 | % 153.61/21.59 | REDUCE: (31), (40) imply: % 153.61/21.59 | (50) powerset(all_510_5) = all_589_0 % 153.61/21.59 | % 153.61/21.59 | REDUCE: (30), (45) imply: % 153.61/21.59 | (51) element(all_510_5, all_589_0) % 153.61/21.59 | % 153.61/21.59 | BETA: splitting (33) gives: % 153.61/21.59 | % 153.61/21.59 | Case 1: % 153.61/21.59 | | % 153.61/21.59 | | (52) all_591_0 = all_510_1 & set_difference(all_510_5, all_510_2) = % 153.61/21.59 | | all_510_1 & $i(all_510_1) % 153.61/21.59 | | % 153.61/21.59 | | ALPHA: (52) implies: % 153.61/21.59 | | (53) set_difference(all_510_5, all_510_2) = all_510_1 % 153.61/21.59 | | % 153.61/21.59 | | BETA: splitting (34) gives: % 153.61/21.59 | | % 153.61/21.59 | | Case 1: % 153.61/21.59 | | | % 153.61/21.59 | | | (54) all_592_0 = all_510_0 & set_difference(all_510_3, all_510_2) = % 153.61/21.59 | | | all_510_0 & $i(all_510_0) % 153.61/21.59 | | | % 153.61/21.59 | | | ALPHA: (54) implies: % 153.61/21.59 | | | (55) set_difference(all_510_3, all_510_2) = all_510_0 % 153.61/21.59 | | | % 153.61/21.59 | | | REDUCE: (45), (55) imply: % 153.61/21.59 | | | (56) set_difference(all_510_5, all_510_2) = all_510_0 % 153.61/21.59 | | | % 153.61/21.59 | | | GROUND_INST: instantiating (3) with all_510_1, all_510_0, all_510_2, % 153.61/21.59 | | | all_510_5, simplifying with (53), (56) gives: % 153.61/21.60 | | | (57) all_510_0 = all_510_1 % 153.61/21.60 | | | % 153.61/21.60 | | | REDUCE: (5), (57) imply: % 153.61/21.60 | | | (58) $false % 153.61/21.60 | | | % 153.61/21.60 | | | CLOSE: (58) is inconsistent. % 153.61/21.60 | | | % 153.61/21.60 | | Case 2: % 153.61/21.60 | | | % 153.61/21.60 | | | (59) powerset(all_510_5) = all_592_1 & $i(all_592_1) & ( ~ % 153.61/21.60 | | | element(all_510_2, all_592_1) | ~ element(all_510_3, % 153.61/21.60 | | | all_592_1)) % 153.61/21.60 | | | % 153.61/21.60 | | | ALPHA: (59) implies: % 153.61/21.60 | | | (60) powerset(all_510_5) = all_592_1 % 153.61/21.60 | | | (61) ~ element(all_510_2, all_592_1) | ~ element(all_510_3, % 153.61/21.60 | | | all_592_1) % 153.61/21.60 | | | % 153.61/21.60 | | | GROUND_INST: instantiating (1) with all_510_4, all_592_1, all_510_5, % 153.61/21.60 | | | simplifying with (11), (60) gives: % 153.61/21.60 | | | (62) all_592_1 = all_510_4 % 153.61/21.60 | | | % 153.61/21.60 | | | GROUND_INST: instantiating (1) with all_592_1, all_599_0, all_510_5, % 153.61/21.60 | | | simplifying with (49), (60) gives: % 153.61/21.60 | | | (63) all_599_0 = all_592_1 % 153.61/21.60 | | | % 153.61/21.60 | | | GROUND_INST: instantiating (1) with all_589_0, all_599_0, all_510_5, % 153.61/21.60 | | | simplifying with (49), (50) gives: % 153.61/21.60 | | | (64) all_599_0 = all_589_0 % 153.61/21.60 | | | % 153.61/21.60 | | | COMBINE_EQS: (63), (64) imply: % 153.61/21.60 | | | (65) all_592_1 = all_589_0 % 153.61/21.60 | | | % 153.61/21.60 | | | SIMP: (65) implies: % 153.61/21.60 | | | (66) all_592_1 = all_589_0 % 153.61/21.60 | | | % 153.61/21.60 | | | COMBINE_EQS: (62), (66) imply: % 153.61/21.60 | | | (67) all_589_0 = all_510_4 % 153.61/21.60 | | | % 153.61/21.60 | | | SIMP: (67) implies: % 153.61/21.60 | | | (68) all_589_0 = all_510_4 % 153.61/21.60 | | | % 153.61/21.60 | | | REDUCE: (51), (68) imply: % 153.61/21.60 | | | (69) element(all_510_5, all_510_4) % 153.61/21.60 | | | % 153.61/21.60 | | | BETA: splitting (61) gives: % 153.61/21.60 | | | % 153.61/21.60 | | | Case 1: % 153.61/21.60 | | | | % 153.61/21.60 | | | | (70) ~ element(all_510_2, all_592_1) % 153.61/21.60 | | | | % 153.61/21.60 | | | | REDUCE: (62), (70) imply: % 153.61/21.60 | | | | (71) ~ element(all_510_2, all_510_4) % 153.61/21.60 | | | | % 153.61/21.60 | | | | PRED_UNIFY: (6), (71) imply: % 153.61/21.60 | | | | (72) $false % 153.61/21.60 | | | | % 153.61/21.60 | | | | CLOSE: (72) is inconsistent. % 153.61/21.60 | | | | % 153.61/21.60 | | | Case 2: % 153.61/21.60 | | | | % 153.61/21.60 | | | | (73) ~ element(all_510_3, all_592_1) % 153.61/21.60 | | | | % 153.61/21.60 | | | | REDUCE: (45), (62), (73) imply: % 153.61/21.60 | | | | (74) ~ element(all_510_5, all_510_4) % 153.61/21.60 | | | | % 153.61/21.60 | | | | PRED_UNIFY: (69), (74) imply: % 153.61/21.60 | | | | (75) $false % 153.61/21.60 | | | | % 153.61/21.60 | | | | CLOSE: (75) is inconsistent. % 153.61/21.60 | | | | % 153.61/21.60 | | | End of split % 153.61/21.60 | | | % 153.61/21.60 | | End of split % 153.61/21.60 | | % 153.61/21.60 | Case 2: % 153.61/21.60 | | % 153.61/21.60 | | (76) powerset(all_510_5) = all_591_1 & $i(all_591_1) & ~ % 153.61/21.60 | | element(all_510_2, all_591_1) % 153.61/21.60 | | % 153.61/21.60 | | ALPHA: (76) implies: % 153.61/21.60 | | (77) ~ element(all_510_2, all_591_1) % 153.61/21.60 | | (78) powerset(all_510_5) = all_591_1 % 153.61/21.60 | | % 153.61/21.60 | | GROUND_INST: instantiating (1) with all_589_0, all_591_1, all_510_5, % 153.61/21.60 | | simplifying with (50), (78) gives: % 153.61/21.60 | | (79) all_591_1 = all_589_0 % 153.61/21.60 | | % 153.61/21.60 | | GROUND_INST: instantiating (1) with all_510_4, all_599_0, all_510_5, % 153.61/21.60 | | simplifying with (11), (49) gives: % 153.61/21.60 | | (80) all_599_0 = all_510_4 % 153.61/21.60 | | % 153.61/21.60 | | GROUND_INST: instantiating (1) with all_591_1, all_599_0, all_510_5, % 153.61/21.60 | | simplifying with (49), (78) gives: % 153.61/21.60 | | (81) all_599_0 = all_591_1 % 153.61/21.60 | | % 153.61/21.60 | | COMBINE_EQS: (80), (81) imply: % 153.61/21.60 | | (82) all_591_1 = all_510_4 % 153.61/21.60 | | % 153.61/21.60 | | SIMP: (82) implies: % 153.61/21.60 | | (83) all_591_1 = all_510_4 % 153.61/21.60 | | % 153.61/21.60 | | COMBINE_EQS: (79), (83) imply: % 153.61/21.60 | | (84) all_589_0 = all_510_4 % 153.61/21.60 | | % 153.61/21.60 | | REDUCE: (77), (83) imply: % 153.61/21.60 | | (85) ~ element(all_510_2, all_510_4) % 153.61/21.60 | | % 153.61/21.60 | | PRED_UNIFY: (6), (85) imply: % 153.61/21.60 | | (86) $false % 153.61/21.60 | | % 153.61/21.60 | | CLOSE: (86) is inconsistent. % 153.61/21.60 | | % 153.61/21.60 | End of split % 153.61/21.60 | % 153.61/21.60 End of proof % 153.61/21.60 % SZS output end Proof for theBenchmark % 154.02/21.61 % 154.02/21.61 21041ms %------------------------------------------------------------------------------