%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SEU191+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 : n006.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 17:43:10 EDT 2023 % Result : Theorem 178.54s 24.48s % Output : Proof 179.92s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.10 % Problem : SEU191+2 : TPTP v8.1.2. Released v3.3.0. % 0.00/0.11 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.10/0.31 % Computer : n006.cluster.edu % 0.10/0.31 % Model : x86_64 x86_64 % 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.10/0.31 % Memory : 8042.1875MB % 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64 % 0.10/0.31 % CPULimit : 300 % 0.10/0.31 % WCLimit : 300 % 0.10/0.31 % DateTime : Wed Aug 23 16:09:38 EDT 2023 % 0.10/0.32 % CPUTime : % 0.16/0.60 ________ _____ % 0.16/0.60 ___ __ \_________(_)________________________________ % 0.16/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.16/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.16/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.16/0.60 % 0.16/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.16/0.60 (2023-06-19) % 0.16/0.60 % 0.16/0.60 (c) Philipp Rümmer, 2009-2023 % 0.16/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.16/0.60 Amanda Stjerna. % 0.16/0.60 Free software under BSD-3-Clause. % 0.16/0.60 % 0.16/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.16/0.60 % 0.16/0.60 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.16/0.62 Running up to 7 provers in parallel. % 0.16/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.16/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.16/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.16/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.16/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.16/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 0.16/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 5.81/1.59 Prover 4: Preprocessing ... % 5.81/1.61 Prover 1: Preprocessing ... % 5.81/1.61 Prover 3: Preprocessing ... % 5.81/1.61 Prover 5: Preprocessing ... % 5.81/1.61 Prover 6: Preprocessing ... % 5.81/1.62 Prover 0: Preprocessing ... % 5.81/1.62 Prover 2: Preprocessing ... % 21.11/3.71 Prover 1: Warning: ignoring some quantifiers % 22.46/3.86 Prover 6: Proving ... % 22.46/3.87 Prover 3: Warning: ignoring some quantifiers % 22.46/3.90 Prover 1: Constructing countermodel ... % 22.46/3.90 Prover 3: Constructing countermodel ... % 23.35/3.97 Prover 5: Proving ... % 23.35/4.00 Prover 4: Warning: ignoring some quantifiers % 24.22/4.20 Prover 2: Proving ... % 24.22/4.21 Prover 4: Constructing countermodel ... % 24.22/4.21 Prover 0: Proving ... % 71.00/10.31 Prover 2: stopped % 71.00/10.31 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 73.33/10.61 Prover 7: Preprocessing ... % 76.98/11.08 Prover 7: Warning: ignoring some quantifiers % 76.98/11.12 Prover 7: Constructing countermodel ... % 98.79/13.96 Prover 5: stopped % 98.79/13.98 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 101.29/14.29 Prover 8: Preprocessing ... % 105.73/14.90 Prover 8: Warning: ignoring some quantifiers % 106.51/14.98 Prover 8: Constructing countermodel ... % 112.58/15.97 Prover 1: stopped % 112.58/15.99 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889 % 116.34/16.31 Prover 9: Preprocessing ... % 121.71/17.01 Prover 9: Warning: ignoring some quantifiers % 121.71/17.03 Prover 9: Constructing countermodel ... % 128.31/17.89 Prover 6: stopped % 128.31/17.90 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 129.36/18.25 Prover 10: Preprocessing ... % 133.15/18.51 Prover 10: Warning: ignoring some quantifiers % 133.50/18.54 Prover 10: Constructing countermodel ... % 177.97/24.43 Prover 10: Found proof (size 372) % 177.97/24.43 Prover 10: proved (6530ms) % 177.97/24.44 Prover 3: stopped % 177.97/24.44 Prover 4: stopped % 177.97/24.45 Prover 7: stopped % 177.97/24.45 Prover 9: stopped % 177.97/24.45 Prover 8: stopped % 178.54/24.47 Prover 0: stopped % 178.54/24.47 % 178.54/24.48 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 178.54/24.48 % 178.82/24.54 % SZS output start Proof for theBenchmark % 178.82/24.56 Assumptions after simplification: % 178.82/24.56 --------------------------------- % 178.82/24.56 % 178.82/24.56 (d10_relat_1) % 178.82/24.61 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v3 = v2 % 178.82/24.61 | ~ (identity_relation(v0) = v1) | ~ (ordered_pair(v2, v3) = v4) | ~ % 178.82/24.61 $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ relation(v1) | ~ in(v4, % 178.82/24.61 v1)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] % 178.82/24.61 : ( ~ (identity_relation(v0) = v1) | ~ (ordered_pair(v2, v3) = v4) | ~ % 178.82/24.61 $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ relation(v1) | ~ in(v4, v1) % 178.82/24.61 | in(v2, v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 178.82/24.61 (identity_relation(v0) = v1) | ~ (ordered_pair(v2, v2) = v3) | ~ $i(v2) | % 178.82/24.61 ~ $i(v1) | ~ $i(v0) | ~ relation(v1) | ~ in(v2, v0) | in(v3, v1)) & ! % 178.82/24.61 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v1 | ~ (identity_relation(v0) = % 178.82/24.61 v2) | ~ $i(v1) | ~ $i(v0) | ~ relation(v1) | ? [v3: $i] : ? [v4: $i] % 178.82/24.61 : ? [v5: $i] : ($i(v4) & $i(v3) & ( ~ (v4 = v3) | ~ in(v3, v0) | % 178.82/24.61 (ordered_pair(v3, v3) = v5 & $i(v5) & ~ in(v5, v1))) & ((v4 = v3 & % 178.82/24.61 in(v3, v0)) | (ordered_pair(v3, v4) = v5 & $i(v5) & in(v5, v1))))) % 178.82/24.61 % 178.82/24.61 (d1_relat_1) % 178.82/24.61 ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ relation(v0) | ~ % 178.82/24.61 in(v1, v0) | ? [v2: $i] : ? [v3: $i] : (ordered_pair(v2, v3) = v1 & $i(v3) % 178.82/24.61 & $i(v2))) & ? [v0: $i] : ( ~ $i(v0) | relation(v0) | ? [v1: $i] : % 178.82/24.61 ($i(v1) & in(v1, v0) & ! [v2: $i] : ! [v3: $i] : ( ~ (ordered_pair(v2, v3) % 178.82/24.61 = v1) | ~ $i(v3) | ~ $i(v2)))) % 178.82/24.61 % 178.82/24.61 (d1_xboole_0) % 178.82/24.61 $i(empty_set) & ! [v0: $i] : ( ~ $i(v0) | ~ in(v0, empty_set)) & ? [v0: $i] % 178.82/24.61 : (v0 = empty_set | ~ $i(v0) | ? [v1: $i] : ($i(v1) & in(v1, v0))) % 178.82/24.61 % 178.82/24.61 (d4_relat_1) % 178.82/24.62 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 178.82/24.62 (relation_dom(v0) = v1) | ~ (ordered_pair(v2, v3) = v4) | ~ $i(v3) | ~ % 178.82/24.62 $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ relation(v0) | ~ in(v4, v0) | in(v2, % 178.82/24.62 v1)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (relation_dom(v0) = % 178.82/24.62 v1) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ relation(v0) | ~ in(v2, v1) % 178.82/24.62 | ? [v3: $i] : ? [v4: $i] : (ordered_pair(v2, v3) = v4 & $i(v4) & $i(v3) & % 178.82/24.62 in(v4, v0))) & ? [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v0 | ~ % 178.82/24.62 (relation_dom(v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ relation(v1) | ? [v3: % 178.82/24.62 $i] : ? [v4: $i] : ? [v5: $i] : ($i(v4) & $i(v3) & ( ~ in(v3, v0) | ! % 178.82/24.62 [v6: $i] : ! [v7: $i] : ( ~ (ordered_pair(v3, v6) = v7) | ~ $i(v6) | % 178.82/24.62 ~ in(v7, v1))) & (in(v3, v0) | (ordered_pair(v3, v4) = v5 & $i(v5) & % 178.82/24.62 in(v5, v1))))) % 178.82/24.62 % 178.82/24.62 (d8_relat_1) % 178.82/24.63 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 178.82/24.63 $i] : ! [v6: $i] : ! [v7: $i] : ( ~ (relation_composition(v0, v1) = v2) | % 178.82/24.63 ~ (ordered_pair(v3, v6) = v7) | ~ (ordered_pair(v3, v4) = v5) | ~ $i(v6) | % 178.82/24.63 ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ relation(v2) % 178.82/24.63 | ~ relation(v1) | ~ relation(v0) | ~ in(v7, v0) | in(v5, v2) | ? [v8: % 178.82/24.63 $i] : (ordered_pair(v6, v4) = v8 & $i(v8) & ~ in(v8, v1))) & ! [v0: $i] % 178.82/24.63 : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ % 178.82/24.63 (relation_composition(v0, v1) = v2) | ~ (ordered_pair(v3, v4) = v5) | ~ % 178.82/24.63 $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ relation(v2) | % 178.82/24.63 ~ relation(v1) | ~ relation(v0) | ~ in(v5, v2) | ? [v6: $i] : ? [v7: $i] % 178.82/24.63 : ? [v8: $i] : (ordered_pair(v6, v4) = v8 & ordered_pair(v3, v6) = v7 & % 178.82/24.63 $i(v8) & $i(v7) & $i(v6) & in(v8, v1) & in(v7, v0))) & ! [v0: $i] : ! % 178.82/24.63 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v2 | ~ (relation_composition(v0, % 178.82/24.63 v1) = v2) | ~ $i(v3) | ~ $i(v1) | ~ $i(v0) | ~ relation(v3) | ~ % 178.82/24.63 relation(v1) | ~ relation(v0) | ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : % 178.82/24.63 ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ($i(v7) & $i(v5) & $i(v4) & ( ! % 178.82/24.63 [v10: $i] : ! [v11: $i] : ( ~ (ordered_pair(v4, v10) = v11) | ~ % 178.82/24.63 $i(v10) | ~ in(v11, v0) | ? [v12: $i] : (ordered_pair(v10, v5) = v12 % 178.82/24.63 & $i(v12) & ~ in(v12, v1))) | (ordered_pair(v4, v5) = v6 & $i(v6) & % 178.82/24.63 ~ in(v6, v3))) & ((ordered_pair(v7, v5) = v9 & ordered_pair(v4, v7) = % 178.82/24.63 v8 & $i(v9) & $i(v8) & in(v9, v1) & in(v8, v0)) | (ordered_pair(v4, % 178.82/24.63 v5) = v6 & $i(v6) & in(v6, v3))))) % 178.82/24.63 % 178.82/24.63 (dt_k5_relat_1) % 178.82/24.63 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (relation_composition(v0, v1) = % 178.82/24.63 v2) | ~ $i(v1) | ~ $i(v0) | ~ relation(v1) | ~ relation(v0) | % 178.82/24.63 relation(v2)) % 179.27/24.63 % 179.27/24.63 (dt_k6_relat_1) % 179.27/24.63 ! [v0: $i] : ! [v1: $i] : ( ~ (identity_relation(v0) = v1) | ~ $i(v0) | % 179.27/24.63 relation(v1)) % 179.27/24.63 % 179.27/24.63 (fc4_relat_1) % 179.27/24.63 $i(empty_set) & relation(empty_set) & empty(empty_set) % 179.27/24.63 % 179.27/24.63 (rc2_subset_1) % 179.27/24.63 ! [v0: $i] : ! [v1: $i] : ( ~ (powerset(v0) = v1) | ~ $i(v0) | ? [v2: $i] % 179.27/24.63 : ($i(v2) & element(v2, v1) & empty(v2))) % 179.27/24.63 % 179.27/24.63 (t1_zfmisc_1) % 179.27/24.63 $i(empty_set) & ? [v0: $i] : (powerset(empty_set) = v0 & singleton(empty_set) % 179.27/24.63 = v0 & $i(v0)) % 179.27/24.63 % 179.27/24.63 (t20_relat_1) % 179.27/24.64 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 179.27/24.64 (relation_rng(v2) = v4) | ~ (ordered_pair(v0, v1) = v3) | ~ $i(v2) | ~ % 179.27/24.64 $i(v1) | ~ $i(v0) | ~ relation(v2) | ~ in(v3, v2) | in(v1, v4)) & ! [v0: % 179.27/24.64 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 179.27/24.64 (relation_rng(v2) = v4) | ~ (ordered_pair(v0, v1) = v3) | ~ $i(v2) | ~ % 179.27/24.64 $i(v1) | ~ $i(v0) | ~ relation(v2) | ~ in(v3, v2) | ? [v5: $i] : % 179.27/24.64 (relation_dom(v2) = v5 & $i(v5) & in(v0, v5))) % 179.27/24.64 % 179.27/24.64 (t25_relat_1) % 179.27/24.64 ! [v0: $i] : ! [v1: $i] : ( ~ (relation_rng(v0) = v1) | ~ $i(v0) | ~ % 179.27/24.64 relation(v0) | ? [v2: $i] : (relation_dom(v0) = v2 & $i(v2) & ! [v3: $i] : % 179.27/24.64 ! [v4: $i] : ( ~ (relation_rng(v3) = v4) | ~ $i(v3) | ~ subset(v0, v3) % 179.27/24.64 | ~ relation(v3) | subset(v1, v4)) & ! [v3: $i] : ! [v4: $i] : ( ~ % 179.27/24.64 (relation_rng(v3) = v4) | ~ $i(v3) | ~ subset(v0, v3) | ~ % 179.27/24.64 relation(v3) | ? [v5: $i] : (relation_dom(v3) = v5 & $i(v5) & % 179.27/24.64 subset(v2, v5))))) % 179.27/24.64 % 179.27/24.64 (t33_zfmisc_1) % 179.27/24.64 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v3 = v1 % 179.27/24.64 | ~ (ordered_pair(v2, v3) = v4) | ~ (ordered_pair(v0, v1) = v4) | ~ % 179.27/24.64 $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0)) & ! [v0: $i] : ! [v1: $i] : ! % 179.27/24.64 [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v2 = v0 | ~ (ordered_pair(v2, v3) = % 179.27/24.64 v4) | ~ (ordered_pair(v0, v1) = v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | % 179.27/24.64 ~ $i(v0)) % 179.27/24.64 % 179.27/24.64 (t3_subset) % 179.27/24.64 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (powerset(v1) = v2) | ~ $i(v1) % 179.27/24.64 | ~ $i(v0) | ~ element(v0, v2) | subset(v0, v1)) & ! [v0: $i] : ! [v1: % 179.27/24.64 $i] : ! [v2: $i] : ( ~ (powerset(v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ % 179.27/24.64 subset(v0, v1) | element(v0, v2)) % 179.27/24.64 % 179.27/24.64 (t3_xboole_1) % 179.27/24.64 $i(empty_set) & ! [v0: $i] : (v0 = empty_set | ~ $i(v0) | ~ subset(v0, % 179.27/24.64 empty_set)) % 179.27/24.64 % 179.27/24.64 (t44_relat_1) % 179.27/24.65 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 179.27/24.65 (relation_composition(v0, v2) = v3) | ~ (relation_dom(v0) = v1) | ~ $i(v2) % 179.27/24.65 | ~ $i(v0) | ~ relation(v2) | ~ relation(v0) | ? [v4: $i] : % 179.27/24.65 (relation_dom(v3) = v4 & $i(v4) & subset(v4, v1))) % 179.27/24.65 % 179.27/24.65 (t45_relat_1) % 179.27/24.65 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (relation_composition(v0, v1) = % 179.27/24.65 v2) | ~ $i(v1) | ~ $i(v0) | ~ relation(v1) | ~ relation(v0) | ? [v3: % 179.27/24.65 $i] : ? [v4: $i] : (relation_rng(v2) = v3 & relation_rng(v1) = v4 & % 179.27/24.65 $i(v4) & $i(v3) & subset(v3, v4))) % 179.27/24.65 % 179.27/24.65 (t46_relat_1) % 179.27/24.65 ! [v0: $i] : ! [v1: $i] : ( ~ (relation_rng(v0) = v1) | ~ $i(v0) | ~ % 179.27/24.65 relation(v0) | ? [v2: $i] : (relation_dom(v0) = v2 & $i(v2) & ! [v3: $i] : % 179.27/24.65 ! [v4: $i] : ( ~ (relation_composition(v0, v3) = v4) | ~ $i(v3) | ~ % 179.27/24.65 relation(v3) | ? [v5: $i] : ? [v6: $i] : ((v6 = v2 & relation_dom(v4) % 179.27/24.65 = v2) | (relation_dom(v3) = v5 & $i(v5) & ~ subset(v1, v5)))))) % 179.27/24.65 % 179.27/24.65 (t47_relat_1) % 179.27/24.65 ! [v0: $i] : ! [v1: $i] : ( ~ (relation_rng(v0) = v1) | ~ $i(v0) | ~ % 179.27/24.65 relation(v0) | ? [v2: $i] : (relation_dom(v0) = v2 & $i(v2) & ! [v3: $i] : % 179.27/24.65 ! [v4: $i] : ( ~ (relation_composition(v3, v0) = v4) | ~ $i(v3) | ~ % 179.27/24.65 relation(v3) | ? [v5: $i] : ? [v6: $i] : ((v6 = v1 & relation_rng(v4) % 179.27/24.65 = v1 & $i(v1)) | (relation_rng(v3) = v5 & $i(v5) & ~ subset(v2, % 179.27/24.65 v5)))))) % 179.27/24.65 % 179.27/24.65 (t56_relat_1) % 179.27/24.65 $i(empty_set) & ! [v0: $i] : (v0 = empty_set | ~ $i(v0) | ~ relation(v0) | % 179.27/24.65 ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : (ordered_pair(v1, v2) = v3 & $i(v3) % 179.27/24.65 & $i(v2) & $i(v1) & in(v3, v0))) % 179.27/24.65 % 179.27/24.65 (t60_relat_1) % 179.27/24.65 relation_rng(empty_set) = empty_set & relation_dom(empty_set) = empty_set & % 179.27/24.65 $i(empty_set) % 179.27/24.65 % 179.27/24.65 (t64_relat_1) % 179.27/24.65 $i(empty_set) & ! [v0: $i] : ! [v1: $i] : (v0 = empty_set | ~ % 179.27/24.65 (relation_rng(v0) = v1) | ~ $i(v0) | ~ relation(v0) | ? [v2: $i] : ( ~ % 179.27/24.65 (v2 = empty_set) & relation_dom(v0) = v2 & $i(v2))) & ! [v0: $i] : (v0 = % 179.27/24.65 empty_set | ~ (relation_rng(v0) = empty_set) | ~ $i(v0) | ~ relation(v0)) % 179.27/24.65 % 179.27/24.65 (t65_relat_1) % 179.27/24.66 $i(empty_set) & ! [v0: $i] : ! [v1: $i] : ( ~ (relation_rng(v0) = v1) | ~ % 179.27/24.66 $i(v0) | ~ relation(v0) | ? [v2: $i] : (( ~ (v1 = empty_set) | (v2 = % 179.27/24.66 empty_set & relation_dom(v0) = empty_set)) & (v1 = empty_set | ( ~ (v2 % 179.27/24.66 = empty_set) & relation_dom(v0) = v2 & $i(v2))))) % 179.27/24.66 % 179.27/24.66 (t6_boole) % 179.27/24.66 $i(empty_set) & ! [v0: $i] : (v0 = empty_set | ~ $i(v0) | ~ empty(v0)) % 179.27/24.66 % 179.27/24.66 (t71_relat_1) % 179.27/24.66 ! [v0: $i] : ! [v1: $i] : ( ~ (identity_relation(v0) = v1) | ~ $i(v0) | % 179.27/24.66 relation_rng(v1) = v0) & ! [v0: $i] : ! [v1: $i] : ( ~ % 179.27/24.66 (identity_relation(v0) = v1) | ~ $i(v0) | relation_dom(v1) = v0) % 179.27/24.66 % 179.27/24.66 (t74_relat_1) % 179.27/24.66 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: % 179.27/24.66 $i] : ? [v6: $i] : (relation_composition(v5, v3) = v6 & % 179.27/24.66 identity_relation(v2) = v5 & ordered_pair(v0, v1) = v4 & $i(v6) & $i(v5) & % 179.27/24.66 $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & relation(v3) & ((in(v4, v6) & ( % 179.27/24.66 ~ in(v4, v3) | ~ in(v0, v2))) | (in(v4, v3) & in(v0, v2) & ~ in(v4, % 179.27/24.66 v6)))) % 179.27/24.66 % 179.27/24.66 (function-axioms) % 179.27/24.67 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 % 179.27/24.67 | ~ (subset_difference(v4, v3, v2) = v1) | ~ (subset_difference(v4, v3, % 179.27/24.67 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 % 179.27/24.67 = v0 | ~ (meet_of_subsets(v3, v2) = v1) | ~ (meet_of_subsets(v3, v2) = % 179.27/24.67 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | % 179.27/24.67 ~ (union_of_subsets(v3, v2) = v1) | ~ (union_of_subsets(v3, v2) = v0)) & ! % 179.27/24.67 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 179.27/24.67 (complements_of_subsets(v3, v2) = v1) | ~ (complements_of_subsets(v3, v2) = % 179.27/24.67 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | % 179.27/24.67 ~ (relation_composition(v3, v2) = v1) | ~ (relation_composition(v3, v2) = % 179.27/24.67 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | % 179.27/24.67 ~ (subset_complement(v3, v2) = v1) | ~ (subset_complement(v3, v2) = v0)) & % 179.27/24.67 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 179.27/24.67 (set_difference(v3, v2) = v1) | ~ (set_difference(v3, v2) = v0)) & ! [v0: % 179.27/24.67 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 179.27/24.67 (cartesian_product2(v3, v2) = v1) | ~ (cartesian_product2(v3, v2) = v0)) & % 179.27/24.67 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 179.27/24.67 (ordered_pair(v3, v2) = v1) | ~ (ordered_pair(v3, v2) = v0)) & ! [v0: $i] % 179.27/24.67 : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 179.27/24.67 (set_intersection2(v3, v2) = v1) | ~ (set_intersection2(v3, v2) = v0)) & ! % 179.27/24.67 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 179.27/24.67 (set_union2(v3, v2) = v1) | ~ (set_union2(v3, v2) = v0)) & ! [v0: $i] : ! % 179.27/24.67 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (unordered_pair(v3, v2) = % 179.27/24.67 v1) | ~ (unordered_pair(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 179.27/24.67 [v2: $i] : (v1 = v0 | ~ (relation_inverse(v2) = v1) | ~ % 179.27/24.67 (relation_inverse(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 % 179.27/24.67 = v0 | ~ (relation_field(v2) = v1) | ~ (relation_field(v2) = v0)) & ! % 179.27/24.67 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (relation_rng(v2) = v1) | % 179.27/24.67 ~ (relation_rng(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 % 179.27/24.67 = v0 | ~ (union(v2) = v1) | ~ (union(v2) = v0)) & ! [v0: $i] : ! [v1: % 179.27/24.67 $i] : ! [v2: $i] : (v1 = v0 | ~ (cast_to_subset(v2) = v1) | ~ % 179.27/24.67 (cast_to_subset(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = % 179.27/24.67 v0 | ~ (relation_dom(v2) = v1) | ~ (relation_dom(v2) = v0)) & ! [v0: $i] % 179.27/24.67 : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ % 179.27/24.67 (powerset(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | % 179.27/24.67 ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ! [v0: $i] : ! [v1: % 179.27/24.67 $i] : ! [v2: $i] : (v1 = v0 | ~ (set_meet(v2) = v1) | ~ (set_meet(v2) = % 179.27/24.67 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 179.27/24.67 (identity_relation(v2) = v1) | ~ (identity_relation(v2) = v0)) % 179.27/24.67 % 179.27/24.67 Further assumptions not needed in the proof: % 179.27/24.67 -------------------------------------------- % 179.27/24.68 antisymmetry_r2_hidden, antisymmetry_r2_xboole_0, cc1_relat_1, % 179.27/24.68 commutativity_k2_tarski, commutativity_k2_xboole_0, commutativity_k3_xboole_0, % 179.27/24.68 d10_xboole_0, d1_setfam_1, d1_tarski, d1_zfmisc_1, d2_subset_1, d2_tarski, % 179.27/24.68 d2_xboole_0, d2_zfmisc_1, d3_tarski, d3_xboole_0, d4_subset_1, d4_tarski, % 179.27/24.68 d4_xboole_0, d5_relat_1, d5_subset_1, d5_tarski, d6_relat_1, d7_relat_1, % 179.27/24.68 d7_xboole_0, d8_setfam_1, d8_xboole_0, dt_k1_relat_1, dt_k1_setfam_1, % 179.27/24.68 dt_k1_tarski, dt_k1_xboole_0, dt_k1_zfmisc_1, dt_k2_relat_1, dt_k2_subset_1, % 179.27/24.68 dt_k2_tarski, dt_k2_xboole_0, dt_k2_zfmisc_1, dt_k3_relat_1, dt_k3_subset_1, % 179.27/24.68 dt_k3_tarski, dt_k3_xboole_0, dt_k4_relat_1, dt_k4_tarski, dt_k4_xboole_0, % 179.27/24.68 dt_k5_setfam_1, dt_k6_setfam_1, dt_k6_subset_1, dt_k7_setfam_1, dt_m1_subset_1, % 179.27/24.68 existence_m1_subset_1, fc10_relat_1, fc1_subset_1, fc1_xboole_0, fc1_zfmisc_1, % 179.27/24.68 fc2_relat_1, fc2_subset_1, fc2_xboole_0, fc3_subset_1, fc3_xboole_0, % 179.27/24.68 fc4_subset_1, fc5_relat_1, fc6_relat_1, fc7_relat_1, fc8_relat_1, fc9_relat_1, % 179.27/24.68 idempotence_k2_xboole_0, idempotence_k3_xboole_0, involutiveness_k3_subset_1, % 179.27/24.68 involutiveness_k4_relat_1, involutiveness_k7_setfam_1, % 179.27/24.68 irreflexivity_r2_xboole_0, l1_zfmisc_1, l23_zfmisc_1, l25_zfmisc_1, % 179.27/24.68 l28_zfmisc_1, l2_zfmisc_1, l32_xboole_1, l3_subset_1, l3_zfmisc_1, l4_zfmisc_1, % 179.27/24.68 l50_zfmisc_1, l55_zfmisc_1, l71_subset_1, rc1_relat_1, rc1_subset_1, % 179.27/24.68 rc1_xboole_0, rc2_relat_1, rc2_xboole_0, redefinition_k5_setfam_1, % 179.27/24.68 redefinition_k6_setfam_1, redefinition_k6_subset_1, reflexivity_r1_tarski, % 179.27/24.68 symmetry_r1_xboole_0, t106_zfmisc_1, t10_zfmisc_1, t118_zfmisc_1, t119_zfmisc_1, % 179.27/24.68 t12_xboole_1, t136_zfmisc_1, t17_xboole_1, t19_xboole_1, t1_boole, t1_subset, % 179.27/24.68 t1_xboole_1, t21_relat_1, t26_xboole_1, t28_xboole_1, t2_boole, t2_subset, % 179.27/24.68 t2_tarski, t2_xboole_1, t30_relat_1, t33_xboole_1, t36_xboole_1, t37_relat_1, % 179.27/24.68 t37_xboole_1, t37_zfmisc_1, t38_zfmisc_1, t39_xboole_1, t39_zfmisc_1, t3_boole, % 179.27/24.68 t3_xboole_0, t40_xboole_1, t43_subset_1, t45_xboole_1, t46_setfam_1, % 179.27/24.68 t46_zfmisc_1, t47_setfam_1, t48_setfam_1, t48_xboole_1, t4_boole, t4_subset, % 179.27/24.68 t4_xboole_0, t50_subset_1, t54_subset_1, t5_subset, t60_xboole_1, t63_xboole_1, % 179.27/24.68 t65_zfmisc_1, t69_enumset1, t6_zfmisc_1, t7_boole, t7_xboole_1, t83_xboole_1, % 179.27/24.68 t8_boole, t8_xboole_1, t8_zfmisc_1, t92_zfmisc_1, t99_zfmisc_1, t9_tarski, % 179.27/24.68 t9_zfmisc_1 % 179.27/24.68 % 179.27/24.68 Those formulas are unsatisfiable: % 179.27/24.68 --------------------------------- % 179.27/24.68 % 179.27/24.68 Begin of proof % 179.27/24.68 | % 179.27/24.68 | ALPHA: (d10_relat_1) implies: % 179.27/24.68 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v1 | ~ % 179.27/24.68 | (identity_relation(v0) = v2) | ~ $i(v1) | ~ $i(v0) | ~ % 179.27/24.68 | relation(v1) | ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ($i(v4) & % 179.27/24.68 | $i(v3) & ( ~ (v4 = v3) | ~ in(v3, v0) | (ordered_pair(v3, v3) = v5 % 179.27/24.68 | & $i(v5) & ~ in(v5, v1))) & ((v4 = v3 & in(v3, v0)) | % 179.27/24.68 | (ordered_pair(v3, v4) = v5 & $i(v5) & in(v5, v1))))) % 179.27/24.69 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( % 179.27/24.69 | ~ (identity_relation(v0) = v1) | ~ (ordered_pair(v2, v3) = v4) | ~ % 179.27/24.69 | $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ relation(v1) | ~ % 179.27/24.69 | in(v4, v1) | in(v2, v0)) % 179.27/24.69 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 179.27/24.69 | (v3 = v2 | ~ (identity_relation(v0) = v1) | ~ (ordered_pair(v2, v3) = % 179.27/24.69 | v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 179.27/24.69 | relation(v1) | ~ in(v4, v1)) % 179.27/24.69 | % 179.27/24.69 | ALPHA: (d1_relat_1) implies: % 179.27/24.69 | (4) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ relation(v0) | % 179.27/24.69 | ~ in(v1, v0) | ? [v2: $i] : ? [v3: $i] : (ordered_pair(v2, v3) = v1 % 179.27/24.69 | & $i(v3) & $i(v2))) % 179.27/24.69 | % 179.27/24.69 | ALPHA: (d1_xboole_0) implies: % 179.27/24.69 | (5) ! [v0: $i] : ( ~ $i(v0) | ~ in(v0, empty_set)) % 179.27/24.69 | % 179.27/24.69 | ALPHA: (d4_relat_1) implies: % 179.27/24.69 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (relation_dom(v0) = v1) | % 179.27/24.69 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ relation(v0) | ~ in(v2, v1) | % 179.27/24.69 | ? [v3: $i] : ? [v4: $i] : (ordered_pair(v2, v3) = v4 & $i(v4) & % 179.27/24.69 | $i(v3) & in(v4, v0))) % 179.27/24.69 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( % 179.27/24.69 | ~ (relation_dom(v0) = v1) | ~ (ordered_pair(v2, v3) = v4) | ~ % 179.27/24.69 | $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ relation(v0) | ~ % 179.27/24.69 | in(v4, v0) | in(v2, v1)) % 179.27/24.69 | % 179.27/24.69 | ALPHA: (d8_relat_1) implies: % 179.27/24.69 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 179.27/24.69 | ! [v5: $i] : ( ~ (relation_composition(v0, v1) = v2) | ~ % 179.27/24.69 | (ordered_pair(v3, v4) = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ % 179.27/24.69 | $i(v1) | ~ $i(v0) | ~ relation(v2) | ~ relation(v1) | ~ % 179.27/24.69 | relation(v0) | ~ in(v5, v2) | ? [v6: $i] : ? [v7: $i] : ? [v8: % 179.27/24.69 | $i] : (ordered_pair(v6, v4) = v8 & ordered_pair(v3, v6) = v7 & % 179.27/24.69 | $i(v8) & $i(v7) & $i(v6) & in(v8, v1) & in(v7, v0))) % 179.27/24.70 | (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 179.27/24.70 | ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ( ~ (relation_composition(v0, % 179.27/24.70 | v1) = v2) | ~ (ordered_pair(v3, v6) = v7) | ~ (ordered_pair(v3, % 179.27/24.70 | v4) = v5) | ~ $i(v6) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ % 179.27/24.70 | $i(v1) | ~ $i(v0) | ~ relation(v2) | ~ relation(v1) | ~ % 179.27/24.70 | relation(v0) | ~ in(v7, v0) | in(v5, v2) | ? [v8: $i] : % 179.59/24.70 | (ordered_pair(v6, v4) = v8 & $i(v8) & ~ in(v8, v1))) % 179.59/24.70 | % 179.59/24.70 | ALPHA: (fc4_relat_1) implies: % 179.59/24.70 | (10) relation(empty_set) % 179.59/24.70 | % 179.59/24.70 | ALPHA: (t1_zfmisc_1) implies: % 179.59/24.70 | (11) ? [v0: $i] : (powerset(empty_set) = v0 & singleton(empty_set) = v0 & % 179.59/24.70 | $i(v0)) % 179.59/24.70 | % 179.59/24.70 | ALPHA: (t20_relat_1) implies: % 179.59/24.70 | (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 179.59/24.70 | ( ~ (relation_rng(v2) = v4) | ~ (ordered_pair(v0, v1) = v3) | ~ % 179.59/24.70 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ relation(v2) | ~ in(v3, v2) | % 179.59/24.70 | ? [v5: $i] : (relation_dom(v2) = v5 & $i(v5) & in(v0, v5))) % 179.59/24.70 | % 179.59/24.70 | ALPHA: (t33_zfmisc_1) implies: % 179.59/24.70 | (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 179.59/24.70 | (v2 = v0 | ~ (ordered_pair(v2, v3) = v4) | ~ (ordered_pair(v0, v1) = % 179.59/24.70 | v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0)) % 179.59/24.70 | (14) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 179.59/24.70 | (v3 = v1 | ~ (ordered_pair(v2, v3) = v4) | ~ (ordered_pair(v0, v1) = % 179.59/24.70 | v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0)) % 179.59/24.70 | % 179.59/24.70 | ALPHA: (t3_subset) implies: % 179.59/24.70 | (15) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (powerset(v1) = v2) | ~ % 179.59/24.70 | $i(v1) | ~ $i(v0) | ~ element(v0, v2) | subset(v0, v1)) % 179.59/24.70 | % 179.59/24.70 | ALPHA: (t3_xboole_1) implies: % 179.59/24.70 | (16) ! [v0: $i] : (v0 = empty_set | ~ $i(v0) | ~ subset(v0, empty_set)) % 179.59/24.70 | % 179.59/24.70 | ALPHA: (t56_relat_1) implies: % 179.59/24.70 | (17) ! [v0: $i] : (v0 = empty_set | ~ $i(v0) | ~ relation(v0) | ? [v1: % 179.59/24.70 | $i] : ? [v2: $i] : ? [v3: $i] : (ordered_pair(v1, v2) = v3 & % 179.59/24.70 | $i(v3) & $i(v2) & $i(v1) & in(v3, v0))) % 179.59/24.70 | % 179.59/24.70 | ALPHA: (t60_relat_1) implies: % 179.59/24.71 | (18) relation_dom(empty_set) = empty_set % 179.59/24.71 | (19) relation_rng(empty_set) = empty_set % 179.59/24.71 | % 179.59/24.71 | ALPHA: (t64_relat_1) implies: % 179.59/24.71 | (20) ! [v0: $i] : ! [v1: $i] : (v0 = empty_set | ~ (relation_rng(v0) = % 179.59/24.71 | v1) | ~ $i(v0) | ~ relation(v0) | ? [v2: $i] : ( ~ (v2 = % 179.59/24.71 | empty_set) & relation_dom(v0) = v2 & $i(v2))) % 179.59/24.71 | % 179.59/24.71 | ALPHA: (t65_relat_1) implies: % 179.59/24.71 | (21) ! [v0: $i] : ! [v1: $i] : ( ~ (relation_rng(v0) = v1) | ~ $i(v0) | % 179.59/24.71 | ~ relation(v0) | ? [v2: $i] : (( ~ (v1 = empty_set) | (v2 = % 179.59/24.71 | empty_set & relation_dom(v0) = empty_set)) & (v1 = empty_set | % 179.59/24.71 | ( ~ (v2 = empty_set) & relation_dom(v0) = v2 & $i(v2))))) % 179.59/24.71 | % 179.59/24.71 | ALPHA: (t6_boole) implies: % 179.59/24.71 | (22) $i(empty_set) % 179.59/24.71 | (23) ! [v0: $i] : (v0 = empty_set | ~ $i(v0) | ~ empty(v0)) % 179.59/24.71 | % 179.59/24.71 | ALPHA: (t71_relat_1) implies: % 179.59/24.71 | (24) ! [v0: $i] : ! [v1: $i] : ( ~ (identity_relation(v0) = v1) | ~ % 179.59/24.71 | $i(v0) | relation_dom(v1) = v0) % 179.59/24.71 | (25) ! [v0: $i] : ! [v1: $i] : ( ~ (identity_relation(v0) = v1) | ~ % 179.59/24.71 | $i(v0) | relation_rng(v1) = v0) % 179.59/24.71 | % 179.59/24.71 | ALPHA: (function-axioms) implies: % 179.59/24.72 | (26) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 179.59/24.72 | (relation_dom(v2) = v1) | ~ (relation_dom(v2) = v0)) % 179.59/24.72 | (27) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 179.59/24.72 | (relation_rng(v2) = v1) | ~ (relation_rng(v2) = v0)) % 179.59/24.72 | (28) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 179.59/24.72 | (ordered_pair(v3, v2) = v1) | ~ (ordered_pair(v3, v2) = v0)) % 179.59/24.72 | % 179.59/24.72 | DELTA: instantiating (11) with fresh symbol all_159_0 gives: % 179.59/24.72 | (29) powerset(empty_set) = all_159_0 & singleton(empty_set) = all_159_0 & % 179.59/24.72 | $i(all_159_0) % 179.59/24.72 | % 179.59/24.72 | ALPHA: (29) implies: % 179.59/24.72 | (30) powerset(empty_set) = all_159_0 % 179.59/24.72 | % 179.59/24.72 | DELTA: instantiating (t74_relat_1) with fresh symbols all_195_0, all_195_1, % 179.59/24.72 | all_195_2, all_195_3, all_195_4, all_195_5, all_195_6 gives: % 179.59/24.72 | (31) relation_composition(all_195_1, all_195_3) = all_195_0 & % 179.59/24.72 | identity_relation(all_195_4) = all_195_1 & ordered_pair(all_195_6, % 179.59/24.72 | all_195_5) = all_195_2 & $i(all_195_0) & $i(all_195_1) & % 179.59/24.72 | $i(all_195_2) & $i(all_195_3) & $i(all_195_4) & $i(all_195_5) & % 179.59/24.72 | $i(all_195_6) & relation(all_195_3) & ((in(all_195_2, all_195_0) & ( ~ % 179.59/24.72 | in(all_195_2, all_195_3) | ~ in(all_195_6, all_195_4))) | % 179.59/24.72 | (in(all_195_2, all_195_3) & in(all_195_6, all_195_4) & ~ % 179.59/24.72 | in(all_195_2, all_195_0))) % 179.59/24.72 | % 179.59/24.72 | ALPHA: (31) implies: % 179.59/24.72 | (32) relation(all_195_3) % 179.59/24.72 | (33) $i(all_195_6) % 179.59/24.72 | (34) $i(all_195_5) % 179.59/24.72 | (35) $i(all_195_4) % 179.59/24.72 | (36) $i(all_195_3) % 179.59/24.72 | (37) $i(all_195_2) % 179.59/24.72 | (38) $i(all_195_1) % 179.59/24.72 | (39) $i(all_195_0) % 179.59/24.72 | (40) ordered_pair(all_195_6, all_195_5) = all_195_2 % 179.59/24.72 | (41) identity_relation(all_195_4) = all_195_1 % 179.59/24.72 | (42) relation_composition(all_195_1, all_195_3) = all_195_0 % 179.59/24.72 | (43) (in(all_195_2, all_195_0) & ( ~ in(all_195_2, all_195_3) | ~ % 179.59/24.72 | in(all_195_6, all_195_4))) | (in(all_195_2, all_195_3) & % 179.59/24.72 | in(all_195_6, all_195_4) & ~ in(all_195_2, all_195_0)) % 179.59/24.72 | % 179.59/24.72 | GROUND_INST: instantiating (17) with all_195_3, simplifying with (32), (36) % 179.59/24.72 | gives: % 179.59/24.72 | (44) all_195_3 = empty_set | ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 179.59/24.72 | (ordered_pair(v0, v1) = v2 & $i(v2) & $i(v1) & $i(v0) & in(v2, % 179.59/24.72 | all_195_3)) % 179.59/24.72 | % 179.59/24.72 | GROUND_INST: instantiating (1) with all_195_4, all_195_3, all_195_1, % 179.59/24.72 | simplifying with (32), (35), (36), (41) gives: % 179.59/24.73 | (45) all_195_1 = all_195_3 | ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 179.59/24.73 | ($i(v1) & $i(v0) & ( ~ (v1 = v0) | ~ in(v0, all_195_4) | % 179.59/24.73 | (ordered_pair(v0, v0) = v2 & $i(v2) & ~ in(v2, all_195_3))) & % 179.59/24.73 | ((v1 = v0 & in(v0, all_195_4)) | (ordered_pair(v0, v1) = v2 & $i(v2) % 179.59/24.73 | & in(v2, all_195_3)))) % 179.59/24.73 | % 179.59/24.73 | GROUND_INST: instantiating (1) with all_195_4, empty_set, all_195_1, % 179.59/24.73 | simplifying with (10), (22), (35), (41) gives: % 179.59/24.73 | (46) all_195_1 = empty_set | ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 179.59/24.73 | ($i(v1) & $i(v0) & ( ~ (v1 = v0) | ~ in(v0, all_195_4) | % 179.59/24.73 | (ordered_pair(v0, v0) = v2 & $i(v2) & ~ in(v2, empty_set))) & % 179.59/24.73 | ((v1 = v0 & in(v0, all_195_4)) | (ordered_pair(v0, v1) = v2 & $i(v2) % 179.59/24.73 | & in(v2, empty_set)))) % 179.59/24.73 | % 179.59/24.73 | GROUND_INST: instantiating (25) with all_195_4, all_195_1, simplifying with % 179.59/24.73 | (35), (41) gives: % 179.59/24.73 | (47) relation_rng(all_195_1) = all_195_4 % 179.59/24.73 | % 179.59/24.73 | GROUND_INST: instantiating (24) with all_195_4, all_195_1, simplifying with % 179.59/24.73 | (35), (41) gives: % 179.59/24.73 | (48) relation_dom(all_195_1) = all_195_4 % 179.59/24.73 | % 179.59/24.73 | GROUND_INST: instantiating (dt_k6_relat_1) with all_195_4, all_195_1, % 179.59/24.73 | simplifying with (35), (41) gives: % 179.59/24.73 | (49) relation(all_195_1) % 179.59/24.73 | % 179.59/24.73 | GROUND_INST: instantiating (rc2_subset_1) with empty_set, all_159_0, % 179.59/24.73 | simplifying with (22), (30) gives: % 179.59/24.73 | (50) ? [v0: $i] : ($i(v0) & element(v0, all_159_0) & empty(v0)) % 179.59/24.73 | % 179.59/24.73 | GROUND_INST: instantiating (t47_relat_1) with empty_set, empty_set, % 179.59/24.73 | simplifying with (10), (19), (22) gives: % 179.59/24.73 | (51) ? [v0: $i] : (relation_dom(empty_set) = v0 & $i(v0) & ! [v1: $i] : % 179.59/24.73 | ! [v2: $i] : ( ~ (relation_composition(v1, empty_set) = v2) | ~ % 179.59/24.73 | $i(v1) | ~ relation(v1) | ? [v3: $i] : ? [v4: $i] : ((v4 = % 179.59/24.73 | empty_set & relation_rng(v2) = empty_set) | (relation_rng(v1) % 179.59/24.73 | = v3 & $i(v3) & ~ subset(v0, v3))))) % 179.59/24.73 | % 179.59/24.73 | GROUND_INST: instantiating (t46_relat_1) with empty_set, empty_set, % 179.59/24.73 | simplifying with (10), (19), (22) gives: % 179.59/24.73 | (52) ? [v0: $i] : (relation_dom(empty_set) = v0 & $i(v0) & ! [v1: $i] : % 179.59/24.73 | ! [v2: $i] : ( ~ (relation_composition(empty_set, v1) = v2) | ~ % 179.59/24.73 | $i(v1) | ~ relation(v1) | ? [v3: $i] : ? [v4: $i] : ((v4 = v0 & % 179.59/24.73 | relation_dom(v2) = v0) | (relation_dom(v1) = v3 & $i(v3) & ~ % 179.59/24.73 | subset(empty_set, v3))))) % 179.59/24.73 | % 179.59/24.73 | GROUND_INST: instantiating (t25_relat_1) with empty_set, empty_set, % 179.59/24.73 | simplifying with (10), (19), (22) gives: % 179.59/24.73 | (53) ? [v0: $i] : (relation_dom(empty_set) = v0 & $i(v0) & ! [v1: $i] : % 179.59/24.73 | ! [v2: $i] : ( ~ (relation_rng(v1) = v2) | ~ $i(v1) | ~ % 179.59/24.73 | subset(empty_set, v1) | ~ relation(v1) | subset(empty_set, v2)) & % 179.59/24.73 | ! [v1: $i] : ! [v2: $i] : ( ~ (relation_rng(v1) = v2) | ~ $i(v1) % 179.59/24.73 | | ~ subset(empty_set, v1) | ~ relation(v1) | ? [v3: $i] : % 179.59/24.73 | (relation_dom(v1) = v3 & $i(v3) & subset(v0, v3)))) % 179.59/24.73 | % 179.59/24.73 | DELTA: instantiating (50) with fresh symbol all_206_0 gives: % 179.59/24.73 | (54) $i(all_206_0) & element(all_206_0, all_159_0) & empty(all_206_0) % 179.59/24.73 | % 179.59/24.73 | ALPHA: (54) implies: % 179.59/24.73 | (55) empty(all_206_0) % 179.59/24.73 | (56) element(all_206_0, all_159_0) % 179.59/24.74 | (57) $i(all_206_0) % 179.59/24.74 | % 179.59/24.74 | DELTA: instantiating (52) with fresh symbol all_208_0 gives: % 179.59/24.74 | (58) relation_dom(empty_set) = all_208_0 & $i(all_208_0) & ! [v0: $i] : ! % 179.59/24.74 | [v1: $i] : ( ~ (relation_composition(empty_set, v0) = v1) | ~ $i(v0) % 179.59/24.74 | | ~ relation(v0) | ? [v2: $i] : ? [v3: int] : ((v3 = all_208_0 & % 179.59/24.74 | relation_dom(v1) = all_208_0) | (relation_dom(v0) = v2 & $i(v2) % 179.59/24.74 | & ~ subset(empty_set, v2)))) % 179.59/24.74 | % 179.59/24.74 | ALPHA: (58) implies: % 179.59/24.74 | (59) $i(all_208_0) % 179.59/24.74 | (60) relation_dom(empty_set) = all_208_0 % 179.59/24.74 | % 179.59/24.74 | DELTA: instantiating (51) with fresh symbol all_211_0 gives: % 179.59/24.74 | (61) relation_dom(empty_set) = all_211_0 & $i(all_211_0) & ! [v0: $i] : ! % 179.59/24.74 | [v1: $i] : ( ~ (relation_composition(v0, empty_set) = v1) | ~ $i(v0) % 179.59/24.74 | | ~ relation(v0) | ? [v2: $i] : ? [v3: $i] : ((v3 = empty_set & % 179.59/24.74 | relation_rng(v1) = empty_set) | (relation_rng(v0) = v2 & $i(v2) % 179.59/24.74 | & ~ subset(all_211_0, v2)))) % 179.59/24.74 | % 179.59/24.74 | ALPHA: (61) implies: % 179.59/24.74 | (62) relation_dom(empty_set) = all_211_0 % 179.59/24.74 | % 179.59/24.74 | DELTA: instantiating (53) with fresh symbol all_214_0 gives: % 179.59/24.74 | (63) relation_dom(empty_set) = all_214_0 & $i(all_214_0) & ! [v0: $i] : ! % 179.59/24.74 | [v1: $i] : ( ~ (relation_rng(v0) = v1) | ~ $i(v0) | ~ % 179.59/24.74 | subset(empty_set, v0) | ~ relation(v0) | subset(empty_set, v1)) & % 179.59/24.74 | ! [v0: $i] : ! [v1: $i] : ( ~ (relation_rng(v0) = v1) | ~ $i(v0) | % 179.59/24.74 | ~ subset(empty_set, v0) | ~ relation(v0) | ? [v2: $i] : % 179.59/24.74 | (relation_dom(v0) = v2 & $i(v2) & subset(all_214_0, v2))) % 179.59/24.74 | % 179.59/24.74 | ALPHA: (63) implies: % 179.59/24.74 | (64) relation_dom(empty_set) = all_214_0 % 179.59/24.74 | % 179.59/24.74 | GROUND_INST: instantiating (26) with empty_set, all_211_0, empty_set, % 179.59/24.74 | simplifying with (18), (62) gives: % 179.59/24.74 | (65) all_211_0 = empty_set % 179.59/24.74 | % 179.59/24.74 | GROUND_INST: instantiating (26) with all_211_0, all_214_0, empty_set, % 179.59/24.74 | simplifying with (62), (64) gives: % 179.59/24.74 | (66) all_214_0 = all_211_0 % 179.59/24.74 | % 179.59/24.74 | GROUND_INST: instantiating (26) with all_208_0, all_214_0, empty_set, % 179.59/24.74 | simplifying with (60), (64) gives: % 179.59/24.74 | (67) all_214_0 = all_208_0 % 179.59/24.74 | % 179.59/24.74 | COMBINE_EQS: (66), (67) imply: % 179.59/24.74 | (68) all_211_0 = all_208_0 % 179.59/24.74 | % 179.59/24.74 | SIMP: (68) implies: % 179.59/24.74 | (69) all_211_0 = all_208_0 % 179.59/24.74 | % 179.59/24.74 | COMBINE_EQS: (65), (69) imply: % 179.59/24.74 | (70) all_208_0 = empty_set % 179.59/24.74 | % 179.59/24.74 | GROUND_INST: instantiating (23) with all_206_0, simplifying with (55), (57) % 179.59/24.74 | gives: % 179.59/24.74 | (71) all_206_0 = empty_set % 179.59/24.74 | % 179.59/24.74 | GROUND_INST: instantiating (dt_k5_relat_1) with all_195_1, all_195_3, % 179.59/24.74 | all_195_0, simplifying with (32), (36), (38), (42), (49) gives: % 179.59/24.74 | (72) relation(all_195_0) % 179.59/24.74 | % 179.59/24.74 | GROUND_INST: instantiating (t45_relat_1) with all_195_1, all_195_3, all_195_0, % 179.59/24.74 | simplifying with (32), (36), (38), (42), (49) gives: % 179.59/24.74 | (73) ? [v0: $i] : ? [v1: $i] : (relation_rng(all_195_0) = v0 & % 179.59/24.74 | relation_rng(all_195_3) = v1 & $i(v1) & $i(v0) & subset(v0, v1)) % 179.59/24.74 | % 179.59/24.74 | GROUND_INST: instantiating (17) with all_195_1, simplifying with (38), (49) % 179.59/24.74 | gives: % 179.59/24.74 | (74) all_195_1 = empty_set | ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 179.59/24.74 | (ordered_pair(v0, v1) = v2 & $i(v2) & $i(v1) & $i(v0) & in(v2, % 179.59/24.74 | all_195_1)) % 179.59/24.74 | % 179.59/24.74 | GROUND_INST: instantiating (15) with all_206_0, empty_set, all_159_0, % 179.59/24.74 | simplifying with (22), (30), (56), (57) gives: % 179.59/24.74 | (75) subset(all_206_0, empty_set) % 179.59/24.74 | % 179.59/24.75 | GROUND_INST: instantiating (t44_relat_1) with all_195_1, all_195_4, all_195_3, % 179.59/24.75 | all_195_0, simplifying with (32), (36), (38), (42), (48), (49) % 179.59/24.75 | gives: % 179.59/24.75 | (76) ? [v0: $i] : (relation_dom(all_195_0) = v0 & $i(v0) & subset(v0, % 179.59/24.75 | all_195_4)) % 179.59/24.75 | % 179.59/24.75 | GROUND_INST: instantiating (20) with all_195_1, all_195_4, simplifying with % 179.59/24.75 | (38), (47), (49) gives: % 179.59/24.75 | (77) all_195_1 = empty_set | ? [v0: $i] : ( ~ (v0 = empty_set) & % 179.59/24.75 | relation_dom(all_195_1) = v0 & $i(v0)) % 179.59/24.75 | % 179.59/24.75 | GROUND_INST: instantiating (t47_relat_1) with all_195_1, all_195_4, % 179.59/24.75 | simplifying with (38), (47), (49) gives: % 179.59/24.75 | (78) ? [v0: $i] : (relation_dom(all_195_1) = v0 & $i(v0) & ! [v1: $i] : % 179.59/24.75 | ! [v2: $i] : ( ~ (relation_composition(v1, all_195_1) = v2) | ~ % 179.59/24.75 | $i(v1) | ~ relation(v1) | ? [v3: $i] : ? [v4: int] : ((v4 = % 179.59/24.75 | all_195_4 & relation_rng(v2) = all_195_4 & $i(all_195_4)) | % 179.59/24.75 | (relation_rng(v1) = v3 & $i(v3) & ~ subset(v0, v3))))) % 179.59/24.75 | % 179.59/24.75 | GROUND_INST: instantiating (t46_relat_1) with all_195_1, all_195_4, % 179.59/24.75 | simplifying with (38), (47), (49) gives: % 179.59/24.75 | (79) ? [v0: $i] : (relation_dom(all_195_1) = v0 & $i(v0) & ! [v1: $i] : % 179.59/24.75 | ! [v2: $i] : ( ~ (relation_composition(all_195_1, v1) = v2) | ~ % 179.59/24.75 | $i(v1) | ~ relation(v1) | ? [v3: $i] : ? [v4: $i] : ((v4 = v0 & % 179.59/24.75 | relation_dom(v2) = v0) | (relation_dom(v1) = v3 & $i(v3) & ~ % 179.59/24.75 | subset(all_195_4, v3))))) % 179.59/24.75 | % 179.59/24.75 | GROUND_INST: instantiating (t25_relat_1) with all_195_1, all_195_4, % 179.59/24.75 | simplifying with (38), (47), (49) gives: % 179.59/24.75 | (80) ? [v0: $i] : (relation_dom(all_195_1) = v0 & $i(v0) & ! [v1: $i] : % 179.59/24.75 | ! [v2: $i] : ( ~ (relation_rng(v1) = v2) | ~ $i(v1) | ~ % 179.59/24.75 | subset(all_195_1, v1) | ~ relation(v1) | subset(all_195_4, v2)) & % 179.59/24.75 | ! [v1: $i] : ! [v2: $i] : ( ~ (relation_rng(v1) = v2) | ~ $i(v1) % 179.59/24.75 | | ~ subset(all_195_1, v1) | ~ relation(v1) | ? [v3: $i] : % 179.59/24.75 | (relation_dom(v1) = v3 & $i(v3) & subset(v0, v3)))) % 179.59/24.75 | % 179.59/24.75 | DELTA: instantiating (76) with fresh symbol all_227_0 gives: % 179.59/24.75 | (81) relation_dom(all_195_0) = all_227_0 & $i(all_227_0) & % 179.59/24.75 | subset(all_227_0, all_195_4) % 179.59/24.75 | % 179.59/24.75 | ALPHA: (81) implies: % 179.59/24.75 | (82) relation_dom(all_195_0) = all_227_0 % 179.59/24.75 | % 179.59/24.75 | DELTA: instantiating (73) with fresh symbols all_229_0, all_229_1 gives: % 179.59/24.75 | (83) relation_rng(all_195_0) = all_229_1 & relation_rng(all_195_3) = % 179.59/24.75 | all_229_0 & $i(all_229_0) & $i(all_229_1) & subset(all_229_1, % 179.59/24.75 | all_229_0) % 179.59/24.75 | % 179.59/24.75 | ALPHA: (83) implies: % 179.59/24.75 | (84) subset(all_229_1, all_229_0) % 179.59/24.75 | (85) $i(all_229_1) % 179.59/24.75 | (86) $i(all_229_0) % 179.59/24.75 | (87) relation_rng(all_195_3) = all_229_0 % 179.59/24.75 | (88) relation_rng(all_195_0) = all_229_1 % 179.59/24.75 | % 179.59/24.75 | DELTA: instantiating (79) with fresh symbol all_232_0 gives: % 179.59/24.75 | (89) relation_dom(all_195_1) = all_232_0 & $i(all_232_0) & ! [v0: $i] : ! % 179.59/24.75 | [v1: $i] : ( ~ (relation_composition(all_195_1, v0) = v1) | ~ $i(v0) % 179.59/24.75 | | ~ relation(v0) | ? [v2: $i] : ? [v3: int] : ((v3 = all_232_0 & % 179.59/24.75 | relation_dom(v1) = all_232_0) | (relation_dom(v0) = v2 & $i(v2) % 179.59/24.75 | & ~ subset(all_195_4, v2)))) % 179.59/24.75 | % 179.59/24.75 | ALPHA: (89) implies: % 179.59/24.75 | (90) $i(all_232_0) % 179.59/24.75 | (91) relation_dom(all_195_1) = all_232_0 % 179.59/24.75 | (92) ! [v0: $i] : ! [v1: $i] : ( ~ (relation_composition(all_195_1, v0) = % 179.59/24.75 | v1) | ~ $i(v0) | ~ relation(v0) | ? [v2: $i] : ? [v3: int] : % 179.59/24.75 | ((v3 = all_232_0 & relation_dom(v1) = all_232_0) | (relation_dom(v0) % 179.59/24.75 | = v2 & $i(v2) & ~ subset(all_195_4, v2)))) % 179.59/24.75 | % 179.59/24.75 | GROUND_INST: instantiating (92) with all_195_3, all_195_0, simplifying with % 179.59/24.75 | (32), (36), (42) gives: % 179.59/24.75 | (93) ? [v0: $i] : ? [v1: int] : ((v1 = all_232_0 & % 179.59/24.75 | relation_dom(all_195_0) = all_232_0) | (relation_dom(all_195_3) = % 179.59/24.75 | v0 & $i(v0) & ~ subset(all_195_4, v0))) % 179.59/24.75 | % 179.59/24.75 | DELTA: instantiating (78) with fresh symbol all_235_0 gives: % 179.59/24.76 | (94) relation_dom(all_195_1) = all_235_0 & $i(all_235_0) & ! [v0: $i] : ! % 179.59/24.76 | [v1: $i] : ( ~ (relation_composition(v0, all_195_1) = v1) | ~ $i(v0) % 179.59/24.76 | | ~ relation(v0) | ? [v2: $i] : ? [v3: int] : ((v3 = all_195_4 & % 179.59/24.76 | relation_rng(v1) = all_195_4 & $i(all_195_4)) | % 179.59/24.76 | (relation_rng(v0) = v2 & $i(v2) & ~ subset(all_235_0, v2)))) % 179.59/24.76 | % 179.59/24.76 | ALPHA: (94) implies: % 179.59/24.76 | (95) relation_dom(all_195_1) = all_235_0 % 179.59/24.76 | % 179.59/24.76 | DELTA: instantiating (80) with fresh symbol all_238_0 gives: % 179.59/24.76 | (96) relation_dom(all_195_1) = all_238_0 & $i(all_238_0) & ! [v0: $i] : ! % 179.59/24.76 | [v1: $i] : ( ~ (relation_rng(v0) = v1) | ~ $i(v0) | ~ % 179.59/24.76 | subset(all_195_1, v0) | ~ relation(v0) | subset(all_195_4, v1)) & % 179.59/24.76 | ! [v0: $i] : ! [v1: $i] : ( ~ (relation_rng(v0) = v1) | ~ $i(v0) | % 179.59/24.76 | ~ subset(all_195_1, v0) | ~ relation(v0) | ? [v2: $i] : % 179.59/24.76 | (relation_dom(v0) = v2 & $i(v2) & subset(all_238_0, v2))) % 179.59/24.76 | % 179.59/24.76 | ALPHA: (96) implies: % 179.59/24.76 | (97) relation_dom(all_195_1) = all_238_0 % 179.59/24.76 | % 179.59/24.76 | DELTA: instantiating (93) with fresh symbols all_241_0, all_241_1 gives: % 179.59/24.76 | (98) (all_241_0 = all_232_0 & relation_dom(all_195_0) = all_232_0) | % 179.59/24.76 | (relation_dom(all_195_3) = all_241_1 & $i(all_241_1) & ~ % 179.59/24.76 | subset(all_195_4, all_241_1)) % 179.59/24.76 | % 179.59/24.76 | REDUCE: (71), (75) imply: % 179.59/24.76 | (99) subset(empty_set, empty_set) % 179.59/24.76 | % 179.59/24.76 | GROUND_INST: instantiating (26) with all_195_4, all_235_0, all_195_1, % 179.59/24.76 | simplifying with (48), (95) gives: % 179.59/24.76 | (100) all_235_0 = all_195_4 % 179.59/24.76 | % 179.59/24.76 | GROUND_INST: instantiating (26) with all_235_0, all_238_0, all_195_1, % 179.59/24.76 | simplifying with (95), (97) gives: % 179.59/24.76 | (101) all_238_0 = all_235_0 % 179.59/24.76 | % 179.59/24.76 | GROUND_INST: instantiating (26) with all_232_0, all_238_0, all_195_1, % 179.59/24.76 | simplifying with (91), (97) gives: % 179.59/24.76 | (102) all_238_0 = all_232_0 % 179.59/24.76 | % 179.59/24.76 | COMBINE_EQS: (101), (102) imply: % 179.59/24.76 | (103) all_235_0 = all_232_0 % 179.59/24.76 | % 179.59/24.76 | SIMP: (103) implies: % 179.59/24.76 | (104) all_235_0 = all_232_0 % 179.59/24.76 | % 179.59/24.76 | COMBINE_EQS: (100), (104) imply: % 179.59/24.76 | (105) all_232_0 = all_195_4 % 179.59/24.76 | % 179.59/24.76 | SIMP: (105) implies: % 179.59/24.76 | (106) all_232_0 = all_195_4 % 179.59/24.76 | % 179.59/24.76 | GROUND_INST: instantiating (20) with all_195_3, all_229_0, simplifying with % 179.59/24.76 | (32), (36), (87) gives: % 179.59/24.76 | (107) all_195_3 = empty_set | ? [v0: $i] : ( ~ (v0 = empty_set) & % 179.59/24.76 | relation_dom(all_195_3) = v0 & $i(v0)) % 179.59/24.76 | % 179.59/24.76 | GROUND_INST: instantiating (t47_relat_1) with all_195_3, all_229_0, % 179.59/24.76 | simplifying with (32), (36), (87) gives: % 179.59/24.76 | (108) ? [v0: $i] : (relation_dom(all_195_3) = v0 & $i(v0) & ! [v1: $i] : % 179.59/24.76 | ! [v2: $i] : ( ~ (relation_composition(v1, all_195_3) = v2) | ~ % 179.59/24.76 | $i(v1) | ~ relation(v1) | ? [v3: $i] : ? [v4: int] : ((v4 = % 179.59/24.76 | all_229_0 & relation_rng(v2) = all_229_0 & $i(all_229_0)) | % 179.59/24.76 | (relation_rng(v1) = v3 & $i(v3) & ~ subset(v0, v3))))) % 179.59/24.76 | % 179.59/24.76 | GROUND_INST: instantiating (t46_relat_1) with all_195_3, all_229_0, % 179.59/24.76 | simplifying with (32), (36), (87) gives: % 179.92/24.76 | (109) ? [v0: $i] : (relation_dom(all_195_3) = v0 & $i(v0) & ! [v1: $i] : % 179.92/24.76 | ! [v2: $i] : ( ~ (relation_composition(all_195_3, v1) = v2) | ~ % 179.92/24.76 | $i(v1) | ~ relation(v1) | ? [v3: $i] : ? [v4: $i] : ((v4 = v0 % 179.92/24.76 | & relation_dom(v2) = v0) | (relation_dom(v1) = v3 & $i(v3) & % 179.92/24.76 | ~ subset(all_229_0, v3))))) % 179.92/24.76 | % 179.92/24.76 | GROUND_INST: instantiating (t25_relat_1) with all_195_3, all_229_0, % 179.92/24.76 | simplifying with (32), (36), (87) gives: % 179.92/24.76 | (110) ? [v0: $i] : (relation_dom(all_195_3) = v0 & $i(v0) & ! [v1: $i] : % 179.92/24.76 | ! [v2: $i] : ( ~ (relation_rng(v1) = v2) | ~ $i(v1) | ~ % 179.92/24.76 | subset(all_195_3, v1) | ~ relation(v1) | subset(all_229_0, v2)) % 179.92/24.76 | & ! [v1: $i] : ! [v2: $i] : ( ~ (relation_rng(v1) = v2) | ~ % 179.92/24.76 | $i(v1) | ~ subset(all_195_3, v1) | ~ relation(v1) | ? [v3: $i] % 179.92/24.76 | : (relation_dom(v1) = v3 & $i(v3) & subset(v0, v3)))) % 179.92/24.76 | % 179.92/24.76 | GROUND_INST: instantiating (21) with all_195_3, all_229_0, simplifying with % 179.92/24.76 | (32), (36), (87) gives: % 179.92/24.76 | (111) ? [v0: $i] : (( ~ (all_229_0 = empty_set) | (v0 = empty_set & % 179.92/24.76 | relation_dom(all_195_3) = empty_set)) & (all_229_0 = empty_set % 179.92/24.76 | | ( ~ (v0 = empty_set) & relation_dom(all_195_3) = v0 & $i(v0)))) % 179.92/24.76 | % 179.92/24.76 | GROUND_INST: instantiating (20) with all_195_0, all_229_1, simplifying with % 179.92/24.76 | (39), (72), (88) gives: % 179.92/24.76 | (112) all_195_0 = empty_set | ? [v0: $i] : ( ~ (v0 = empty_set) & % 179.92/24.76 | relation_dom(all_195_0) = v0 & $i(v0)) % 179.92/24.76 | % 179.92/24.77 | GROUND_INST: instantiating (t47_relat_1) with all_195_0, all_229_1, % 179.92/24.77 | simplifying with (39), (72), (88) gives: % 179.92/24.77 | (113) ? [v0: $i] : (relation_dom(all_195_0) = v0 & $i(v0) & ! [v1: $i] : % 179.92/24.77 | ! [v2: $i] : ( ~ (relation_composition(v1, all_195_0) = v2) | ~ % 179.92/24.77 | $i(v1) | ~ relation(v1) | ? [v3: $i] : ? [v4: int] : ((v4 = % 179.92/24.77 | all_229_1 & relation_rng(v2) = all_229_1 & $i(all_229_1)) | % 179.92/24.77 | (relation_rng(v1) = v3 & $i(v3) & ~ subset(v0, v3))))) % 179.92/24.77 | % 179.92/24.77 | GROUND_INST: instantiating (t46_relat_1) with all_195_0, all_229_1, % 179.92/24.77 | simplifying with (39), (72), (88) gives: % 179.92/24.77 | (114) ? [v0: $i] : (relation_dom(all_195_0) = v0 & $i(v0) & ! [v1: $i] : % 179.92/24.77 | ! [v2: $i] : ( ~ (relation_composition(all_195_0, v1) = v2) | ~ % 179.92/24.77 | $i(v1) | ~ relation(v1) | ? [v3: $i] : ? [v4: $i] : ((v4 = v0 % 179.92/24.77 | & relation_dom(v2) = v0) | (relation_dom(v1) = v3 & $i(v3) & % 179.92/24.77 | ~ subset(all_229_1, v3))))) % 179.92/24.77 | % 179.92/24.77 | GROUND_INST: instantiating (t25_relat_1) with all_195_0, all_229_1, % 179.92/24.77 | simplifying with (39), (72), (88) gives: % 179.92/24.77 | (115) ? [v0: $i] : (relation_dom(all_195_0) = v0 & $i(v0) & ! [v1: $i] : % 179.92/24.77 | ! [v2: $i] : ( ~ (relation_rng(v1) = v2) | ~ $i(v1) | ~ % 179.92/24.77 | subset(all_195_0, v1) | ~ relation(v1) | subset(all_229_1, v2)) % 179.92/24.77 | & ! [v1: $i] : ! [v2: $i] : ( ~ (relation_rng(v1) = v2) | ~ % 179.92/24.77 | $i(v1) | ~ subset(all_195_0, v1) | ~ relation(v1) | ? [v3: $i] % 179.92/24.77 | : (relation_dom(v1) = v3 & $i(v3) & subset(v0, v3)))) % 179.92/24.77 | % 179.92/24.77 | GROUND_INST: instantiating (21) with all_195_0, all_229_1, simplifying with % 179.92/24.77 | (39), (72), (88) gives: % 179.92/24.77 | (116) ? [v0: $i] : (( ~ (all_229_1 = empty_set) | (v0 = empty_set & % 179.92/24.77 | relation_dom(all_195_0) = empty_set)) & (all_229_1 = empty_set % 179.92/24.77 | | ( ~ (v0 = empty_set) & relation_dom(all_195_0) = v0 & $i(v0)))) % 179.92/24.77 | % 179.92/24.77 | DELTA: instantiating (116) with fresh symbol all_251_0 gives: % 179.92/24.77 | (117) ( ~ (all_229_1 = empty_set) | (all_251_0 = empty_set & % 179.92/24.77 | relation_dom(all_195_0) = empty_set)) & (all_229_1 = empty_set | % 179.92/24.77 | ( ~ (all_251_0 = empty_set) & relation_dom(all_195_0) = all_251_0 & % 179.92/24.77 | $i(all_251_0))) % 179.92/24.77 | % 179.92/24.77 | ALPHA: (117) implies: % 179.92/24.77 | (118) ~ (all_229_1 = empty_set) | (all_251_0 = empty_set & % 179.92/24.77 | relation_dom(all_195_0) = empty_set) % 179.92/24.77 | % 179.92/24.77 | DELTA: instantiating (111) with fresh symbol all_252_0 gives: % 179.92/24.77 | (119) ( ~ (all_229_0 = empty_set) | (all_252_0 = empty_set & % 179.92/24.77 | relation_dom(all_195_3) = empty_set)) & (all_229_0 = empty_set | % 179.92/24.77 | ( ~ (all_252_0 = empty_set) & relation_dom(all_195_3) = all_252_0 & % 179.92/24.77 | $i(all_252_0))) % 179.92/24.77 | % 179.92/24.77 | ALPHA: (119) implies: % 179.92/24.77 | (120) all_229_0 = empty_set | ( ~ (all_252_0 = empty_set) & % 179.92/24.77 | relation_dom(all_195_3) = all_252_0 & $i(all_252_0)) % 179.92/24.77 | (121) ~ (all_229_0 = empty_set) | (all_252_0 = empty_set & % 179.92/24.77 | relation_dom(all_195_3) = empty_set) % 179.92/24.77 | % 179.92/24.77 | DELTA: instantiating (109) with fresh symbol all_253_0 gives: % 179.92/24.77 | (122) relation_dom(all_195_3) = all_253_0 & $i(all_253_0) & ! [v0: $i] : % 179.92/24.77 | ! [v1: $i] : ( ~ (relation_composition(all_195_3, v0) = v1) | ~ % 179.92/24.77 | $i(v0) | ~ relation(v0) | ? [v2: $i] : ? [v3: int] : ((v3 = % 179.92/24.77 | all_253_0 & relation_dom(v1) = all_253_0) | (relation_dom(v0) = % 179.92/24.77 | v2 & $i(v2) & ~ subset(all_229_0, v2)))) % 179.92/24.77 | % 179.92/24.77 | ALPHA: (122) implies: % 179.92/24.77 | (123) relation_dom(all_195_3) = all_253_0 % 179.92/24.77 | % 179.92/24.77 | DELTA: instantiating (114) with fresh symbol all_256_0 gives: % 179.92/24.77 | (124) relation_dom(all_195_0) = all_256_0 & $i(all_256_0) & ! [v0: $i] : % 179.92/24.77 | ! [v1: $i] : ( ~ (relation_composition(all_195_0, v0) = v1) | ~ % 179.92/24.77 | $i(v0) | ~ relation(v0) | ? [v2: $i] : ? [v3: int] : ((v3 = % 179.92/24.77 | all_256_0 & relation_dom(v1) = all_256_0) | (relation_dom(v0) = % 179.92/24.77 | v2 & $i(v2) & ~ subset(all_229_1, v2)))) % 179.92/24.77 | % 179.92/24.77 | ALPHA: (124) implies: % 179.92/24.77 | (125) relation_dom(all_195_0) = all_256_0 % 179.92/24.77 | % 179.92/24.77 | DELTA: instantiating (113) with fresh symbol all_259_0 gives: % 179.92/24.77 | (126) relation_dom(all_195_0) = all_259_0 & $i(all_259_0) & ! [v0: $i] : % 179.92/24.77 | ! [v1: $i] : ( ~ (relation_composition(v0, all_195_0) = v1) | ~ % 179.92/24.77 | $i(v0) | ~ relation(v0) | ? [v2: $i] : ? [v3: int] : ((v3 = % 179.92/24.77 | all_229_1 & relation_rng(v1) = all_229_1 & $i(all_229_1)) | % 179.92/24.77 | (relation_rng(v0) = v2 & $i(v2) & ~ subset(all_259_0, v2)))) % 179.92/24.77 | % 179.92/24.77 | ALPHA: (126) implies: % 179.92/24.77 | (127) relation_dom(all_195_0) = all_259_0 % 179.92/24.77 | % 179.92/24.77 | DELTA: instantiating (108) with fresh symbol all_262_0 gives: % 179.92/24.77 | (128) relation_dom(all_195_3) = all_262_0 & $i(all_262_0) & ! [v0: $i] : % 179.92/24.77 | ! [v1: $i] : ( ~ (relation_composition(v0, all_195_3) = v1) | ~ % 179.92/24.77 | $i(v0) | ~ relation(v0) | ? [v2: $i] : ? [v3: int] : ((v3 = % 179.92/24.77 | all_229_0 & relation_rng(v1) = all_229_0 & $i(all_229_0)) | % 179.92/24.77 | (relation_rng(v0) = v2 & $i(v2) & ~ subset(all_262_0, v2)))) % 179.92/24.77 | % 179.92/24.77 | ALPHA: (128) implies: % 179.92/24.77 | (129) relation_dom(all_195_3) = all_262_0 % 179.92/24.77 | % 179.92/24.77 | DELTA: instantiating (110) with fresh symbol all_265_0 gives: % 179.92/24.78 | (130) relation_dom(all_195_3) = all_265_0 & $i(all_265_0) & ! [v0: $i] : % 179.92/24.78 | ! [v1: $i] : ( ~ (relation_rng(v0) = v1) | ~ $i(v0) | ~ % 179.92/24.78 | subset(all_195_3, v0) | ~ relation(v0) | subset(all_229_0, v1)) & % 179.92/24.78 | ! [v0: $i] : ! [v1: $i] : ( ~ (relation_rng(v0) = v1) | ~ $i(v0) | % 179.92/24.78 | ~ subset(all_195_3, v0) | ~ relation(v0) | ? [v2: $i] : % 179.92/24.78 | (relation_dom(v0) = v2 & $i(v2) & subset(all_265_0, v2))) % 179.92/24.78 | % 179.92/24.78 | ALPHA: (130) implies: % 179.92/24.78 | (131) relation_dom(all_195_3) = all_265_0 % 179.92/24.78 | % 179.92/24.78 | DELTA: instantiating (115) with fresh symbol all_268_0 gives: % 179.92/24.78 | (132) relation_dom(all_195_0) = all_268_0 & $i(all_268_0) & ! [v0: $i] : % 179.92/24.78 | ! [v1: $i] : ( ~ (relation_rng(v0) = v1) | ~ $i(v0) | ~ % 179.92/24.78 | subset(all_195_0, v0) | ~ relation(v0) | subset(all_229_1, v1)) & % 179.92/24.78 | ! [v0: $i] : ! [v1: $i] : ( ~ (relation_rng(v0) = v1) | ~ $i(v0) | % 179.92/24.78 | ~ subset(all_195_0, v0) | ~ relation(v0) | ? [v2: $i] : % 179.92/24.78 | (relation_dom(v0) = v2 & $i(v2) & subset(all_268_0, v2))) % 179.92/24.78 | % 179.92/24.78 | ALPHA: (132) implies: % 179.92/24.78 | (133) relation_dom(all_195_0) = all_268_0 % 179.92/24.78 | % 179.92/24.78 | GROUND_INST: instantiating (26) with all_262_0, all_265_0, all_195_3, % 179.92/24.78 | simplifying with (129), (131) gives: % 179.92/24.78 | (134) all_265_0 = all_262_0 % 179.92/24.78 | % 179.92/24.78 | GROUND_INST: instantiating (26) with all_253_0, all_265_0, all_195_3, % 179.92/24.78 | simplifying with (123), (131) gives: % 179.92/24.78 | (135) all_265_0 = all_253_0 % 179.92/24.78 | % 179.92/24.78 | GROUND_INST: instantiating (26) with all_227_0, all_259_0, all_195_0, % 179.92/24.78 | simplifying with (82), (127) gives: % 179.92/24.78 | (136) all_259_0 = all_227_0 % 179.92/24.78 | % 179.92/24.78 | GROUND_INST: instantiating (26) with all_259_0, all_268_0, all_195_0, % 179.92/24.78 | simplifying with (127), (133) gives: % 179.92/24.78 | (137) all_268_0 = all_259_0 % 179.92/24.78 | % 179.92/24.78 | GROUND_INST: instantiating (26) with all_256_0, all_268_0, all_195_0, % 179.92/24.78 | simplifying with (125), (133) gives: % 179.92/24.78 | (138) all_268_0 = all_256_0 % 179.92/24.78 | % 179.92/24.78 | COMBINE_EQS: (137), (138) imply: % 179.92/24.78 | (139) all_259_0 = all_256_0 % 179.92/24.78 | % 179.92/24.78 | SIMP: (139) implies: % 179.92/24.78 | (140) all_259_0 = all_256_0 % 179.92/24.78 | % 179.92/24.78 | COMBINE_EQS: (134), (135) imply: % 179.92/24.78 | (141) all_262_0 = all_253_0 % 179.92/24.78 | % 179.92/24.78 | COMBINE_EQS: (136), (140) imply: % 179.92/24.78 | (142) all_256_0 = all_227_0 % 179.92/24.78 | % 179.92/24.78 | BETA: splitting (43) gives: % 179.92/24.78 | % 179.92/24.78 | Case 1: % 179.92/24.78 | | % 179.92/24.78 | | (143) in(all_195_2, all_195_0) & ( ~ in(all_195_2, all_195_3) | ~ % 179.92/24.78 | | in(all_195_6, all_195_4)) % 179.92/24.78 | | % 179.92/24.78 | | ALPHA: (143) implies: % 179.92/24.78 | | (144) in(all_195_2, all_195_0) % 179.92/24.78 | | (145) ~ in(all_195_2, all_195_3) | ~ in(all_195_6, all_195_4) % 179.92/24.78 | | % 179.92/24.78 | | BETA: splitting (46) gives: % 179.92/24.78 | | % 179.92/24.78 | | Case 1: % 179.92/24.78 | | | % 179.92/24.78 | | | (146) all_195_1 = empty_set % 179.92/24.78 | | | % 179.92/24.78 | | | REDUCE: (42), (146) imply: % 179.92/24.78 | | | (147) relation_composition(empty_set, all_195_3) = all_195_0 % 179.92/24.78 | | | % 179.92/24.78 | | | REDUCE: (47), (146) imply: % 179.92/24.78 | | | (148) relation_rng(empty_set) = all_195_4 % 179.92/24.78 | | | % 179.92/24.78 | | | REDUCE: (48), (146) imply: % 179.92/24.78 | | | (149) relation_dom(empty_set) = all_195_4 % 179.92/24.78 | | | % 179.92/24.78 | | | REDUCE: (41), (146) imply: % 179.92/24.78 | | | (150) identity_relation(all_195_4) = empty_set % 179.92/24.78 | | | % 179.92/24.78 | | | GROUND_INST: instantiating (27) with empty_set, all_195_4, empty_set, % 179.92/24.78 | | | simplifying with (19), (148) gives: % 179.92/24.78 | | | (151) all_195_4 = empty_set % 179.92/24.78 | | | % 179.92/24.78 | | | COMBINE_EQS: (106), (151) imply: % 179.92/24.78 | | | (152) all_232_0 = empty_set % 179.92/24.78 | | | % 179.92/24.78 | | | REDUCE: (150), (151) imply: % 179.92/24.78 | | | (153) identity_relation(empty_set) = empty_set % 179.92/24.78 | | | % 179.92/24.78 | | | BETA: splitting (45) gives: % 179.92/24.78 | | | % 179.92/24.78 | | | Case 1: % 179.92/24.78 | | | | % 179.92/24.78 | | | | (154) all_195_1 = all_195_3 % 179.92/24.78 | | | | % 179.92/24.78 | | | | COMBINE_EQS: (146), (154) imply: % 179.92/24.78 | | | | (155) all_195_3 = empty_set % 179.92/24.78 | | | | % 179.92/24.78 | | | | REDUCE: (123), (155) imply: % 179.92/24.78 | | | | (156) relation_dom(empty_set) = all_253_0 % 179.92/24.78 | | | | % 179.92/24.78 | | | | GROUND_INST: instantiating (26) with empty_set, all_253_0, empty_set, % 179.92/24.78 | | | | simplifying with (18), (156) gives: % 179.92/24.78 | | | | (157) all_253_0 = empty_set % 179.92/24.78 | | | | % 179.92/24.78 | | | | BETA: splitting (98) gives: % 179.92/24.78 | | | | % 179.92/24.78 | | | | Case 1: % 179.92/24.78 | | | | | % 179.92/24.78 | | | | | (158) all_241_0 = all_232_0 & relation_dom(all_195_0) = all_232_0 % 179.92/24.78 | | | | | % 179.92/24.78 | | | | | ALPHA: (158) implies: % 179.92/24.78 | | | | | (159) relation_dom(all_195_0) = all_232_0 % 179.92/24.78 | | | | | % 179.92/24.78 | | | | | REDUCE: (152), (159) imply: % 179.92/24.78 | | | | | (160) relation_dom(all_195_0) = empty_set % 179.92/24.78 | | | | | % 179.92/24.78 | | | | | GROUND_INST: instantiating (26) with all_227_0, empty_set, all_195_0, % 179.92/24.78 | | | | | simplifying with (82), (160) gives: % 179.92/24.78 | | | | | (161) all_227_0 = empty_set % 179.92/24.78 | | | | | % 179.92/24.78 | | | | | BETA: splitting (112) gives: % 179.92/24.78 | | | | | % 179.92/24.78 | | | | | Case 1: % 179.92/24.78 | | | | | | % 179.92/24.78 | | | | | | (162) all_195_0 = empty_set % 179.92/24.78 | | | | | | % 179.92/24.78 | | | | | | REDUCE: (144), (162) imply: % 179.92/24.78 | | | | | | (163) in(all_195_2, empty_set) % 179.92/24.78 | | | | | | % 179.92/24.78 | | | | | | BETA: splitting (145) gives: % 179.92/24.78 | | | | | | % 179.92/24.78 | | | | | | Case 1: % 179.92/24.78 | | | | | | | % 179.92/24.78 | | | | | | | (164) ~ in(all_195_2, all_195_3) % 179.92/24.78 | | | | | | | % 179.92/24.78 | | | | | | | REDUCE: (155), (164) imply: % 179.92/24.78 | | | | | | | (165) ~ in(all_195_2, empty_set) % 179.92/24.78 | | | | | | | % 179.92/24.78 | | | | | | | PRED_UNIFY: (163), (165) imply: % 179.92/24.78 | | | | | | | (166) $false % 179.92/24.79 | | | | | | | % 179.92/24.79 | | | | | | | CLOSE: (166) is inconsistent. % 179.92/24.79 | | | | | | | % 179.92/24.79 | | | | | | Case 2: % 179.92/24.79 | | | | | | | % 179.92/24.79 | | | | | | | (167) ~ in(all_195_6, all_195_4) % 179.92/24.79 | | | | | | | (168) in(all_195_2, all_195_3) % 179.92/24.79 | | | | | | | % 179.92/24.79 | | | | | | | REDUCE: (151), (167) imply: % 179.92/24.79 | | | | | | | (169) ~ in(all_195_6, empty_set) % 179.92/24.79 | | | | | | | % 179.92/24.79 | | | | | | | GROUND_INST: instantiating (2) with empty_set, empty_set, % 179.92/24.79 | | | | | | | all_195_6, all_195_5, all_195_2, simplifying with % 179.92/24.79 | | | | | | | (10), (22), (33), (34), (40), (153), (163), (169) % 179.92/24.79 | | | | | | | gives: % 179.92/24.79 | | | | | | | (170) $false % 179.92/24.79 | | | | | | | % 179.92/24.79 | | | | | | | CLOSE: (170) is inconsistent. % 179.92/24.79 | | | | | | | % 179.92/24.79 | | | | | | End of split % 179.92/24.79 | | | | | | % 179.92/24.79 | | | | | Case 2: % 179.92/24.79 | | | | | | % 179.92/24.79 | | | | | | (171) ? [v0: $i] : ( ~ (v0 = empty_set) & % 179.92/24.79 | | | | | | relation_dom(all_195_0) = v0 & $i(v0)) % 179.92/24.79 | | | | | | % 179.92/24.79 | | | | | | DELTA: instantiating (171) with fresh symbol all_422_0 gives: % 179.92/24.79 | | | | | | (172) ~ (all_422_0 = empty_set) & relation_dom(all_195_0) = % 179.92/24.79 | | | | | | all_422_0 & $i(all_422_0) % 179.92/24.79 | | | | | | % 179.92/24.79 | | | | | | ALPHA: (172) implies: % 179.92/24.79 | | | | | | (173) ~ (all_422_0 = empty_set) % 179.92/24.79 | | | | | | (174) relation_dom(all_195_0) = all_422_0 % 179.92/24.79 | | | | | | % 179.92/24.79 | | | | | | GROUND_INST: instantiating (26) with empty_set, all_422_0, % 179.92/24.79 | | | | | | all_195_0, simplifying with (160), (174) gives: % 179.92/24.79 | | | | | | (175) all_422_0 = empty_set % 179.92/24.79 | | | | | | % 179.92/24.79 | | | | | | REDUCE: (173), (175) imply: % 179.92/24.79 | | | | | | (176) $false % 179.92/24.79 | | | | | | % 179.92/24.79 | | | | | | CLOSE: (176) is inconsistent. % 179.92/24.79 | | | | | | % 179.92/24.79 | | | | | End of split % 179.92/24.79 | | | | | % 179.92/24.79 | | | | Case 2: % 179.92/24.79 | | | | | % 179.92/24.79 | | | | | (177) relation_dom(all_195_3) = all_241_1 & $i(all_241_1) & ~ % 179.92/24.79 | | | | | subset(all_195_4, all_241_1) % 179.92/24.79 | | | | | % 179.92/24.79 | | | | | ALPHA: (177) implies: % 179.92/24.79 | | | | | (178) ~ subset(all_195_4, all_241_1) % 179.92/24.79 | | | | | (179) relation_dom(all_195_3) = all_241_1 % 179.92/24.79 | | | | | % 179.92/24.79 | | | | | REDUCE: (155), (179) imply: % 179.92/24.79 | | | | | (180) relation_dom(empty_set) = all_241_1 % 179.92/24.79 | | | | | % 179.92/24.79 | | | | | REDUCE: (151), (178) imply: % 179.92/24.79 | | | | | (181) ~ subset(empty_set, all_241_1) % 179.92/24.79 | | | | | % 179.92/24.79 | | | | | GROUND_INST: instantiating (26) with empty_set, all_241_1, empty_set, % 179.92/24.79 | | | | | simplifying with (18), (180) gives: % 179.92/24.79 | | | | | (182) all_241_1 = empty_set % 179.92/24.79 | | | | | % 179.92/24.79 | | | | | REDUCE: (181), (182) imply: % 179.92/24.79 | | | | | (183) ~ subset(empty_set, empty_set) % 179.92/24.79 | | | | | % 179.92/24.79 | | | | | PRED_UNIFY: (99), (183) imply: % 179.92/24.79 | | | | | (184) $false % 179.92/24.79 | | | | | % 179.92/24.79 | | | | | CLOSE: (184) is inconsistent. % 179.92/24.79 | | | | | % 179.92/24.79 | | | | End of split % 179.92/24.79 | | | | % 179.92/24.79 | | | Case 2: % 179.92/24.79 | | | | % 179.92/24.79 | | | | (185) ~ (all_195_1 = all_195_3) % 179.92/24.79 | | | | % 179.92/24.79 | | | | REDUCE: (146), (185) imply: % 179.92/24.79 | | | | (186) ~ (all_195_3 = empty_set) % 179.92/24.79 | | | | % 179.92/24.79 | | | | SIMP: (186) implies: % 179.92/24.79 | | | | (187) ~ (all_195_3 = empty_set) % 179.92/24.79 | | | | % 179.92/24.79 | | | | BETA: splitting (107) gives: % 179.92/24.79 | | | | % 179.92/24.79 | | | | Case 1: % 179.92/24.79 | | | | | % 179.92/24.79 | | | | | (188) all_195_3 = empty_set % 179.92/24.79 | | | | | % 179.92/24.79 | | | | | REDUCE: (187), (188) imply: % 179.92/24.79 | | | | | (189) $false % 179.92/24.79 | | | | | % 179.92/24.79 | | | | | CLOSE: (189) is inconsistent. % 179.92/24.79 | | | | | % 179.92/24.79 | | | | Case 2: % 179.92/24.79 | | | | | % 179.92/24.79 | | | | | (190) ? [v0: $i] : ( ~ (v0 = empty_set) & relation_dom(all_195_3) % 179.92/24.79 | | | | | = v0 & $i(v0)) % 179.92/24.79 | | | | | % 179.92/24.79 | | | | | DELTA: instantiating (190) with fresh symbol all_404_0 gives: % 179.92/24.79 | | | | | (191) ~ (all_404_0 = empty_set) & relation_dom(all_195_3) = % 179.92/24.79 | | | | | all_404_0 & $i(all_404_0) % 179.92/24.79 | | | | | % 179.92/24.79 | | | | | ALPHA: (191) implies: % 179.92/24.79 | | | | | (192) ~ (all_404_0 = empty_set) % 179.92/24.79 | | | | | (193) relation_dom(all_195_3) = all_404_0 % 179.92/24.79 | | | | | % 179.92/24.79 | | | | | GROUND_INST: instantiating (26) with all_253_0, all_404_0, all_195_3, % 179.92/24.79 | | | | | simplifying with (123), (193) gives: % 179.92/24.79 | | | | | (194) all_404_0 = all_253_0 % 179.92/24.79 | | | | | % 179.92/24.79 | | | | | REDUCE: (192), (194) imply: % 179.92/24.79 | | | | | (195) ~ (all_253_0 = empty_set) % 179.92/24.79 | | | | | % 179.92/24.79 | | | | | BETA: splitting (121) gives: % 179.92/24.79 | | | | | % 179.92/24.79 | | | | | Case 1: % 179.92/24.79 | | | | | | % 179.92/24.79 | | | | | | (196) ~ (all_229_0 = empty_set) % 179.92/24.79 | | | | | | % 179.92/24.79 | | | | | | BETA: splitting (120) gives: % 179.92/24.79 | | | | | | % 179.92/24.79 | | | | | | Case 1: % 179.92/24.79 | | | | | | | % 179.92/24.79 | | | | | | | (197) all_229_0 = empty_set % 179.92/24.79 | | | | | | | % 179.92/24.79 | | | | | | | REDUCE: (196), (197) imply: % 179.92/24.79 | | | | | | | (198) $false % 179.92/24.79 | | | | | | | % 179.92/24.79 | | | | | | | CLOSE: (198) is inconsistent. % 179.92/24.79 | | | | | | | % 179.92/24.79 | | | | | | Case 2: % 179.92/24.79 | | | | | | | % 179.92/24.79 | | | | | | | % 179.92/24.79 | | | | | | | GROUND_INST: instantiating (8) with empty_set, all_195_3, % 179.92/24.79 | | | | | | | all_195_0, all_195_6, all_195_5, all_195_2, % 179.92/24.79 | | | | | | | simplifying with (10), (22), (32), (33), (34), (36), % 179.92/24.79 | | | | | | | (39), (40), (72), (144), (147) gives: % 179.92/24.79 | | | | | | | (199) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 179.92/24.79 | | | | | | | (ordered_pair(v0, all_195_5) = v2 & % 179.92/24.79 | | | | | | | ordered_pair(all_195_6, v0) = v1 & $i(v2) & $i(v1) & % 179.92/24.79 | | | | | | | $i(v0) & in(v2, all_195_3) & in(v1, empty_set)) % 179.92/24.79 | | | | | | | % 179.92/24.79 | | | | | | | DELTA: instantiating (199) with fresh symbols all_469_0, % 179.92/24.79 | | | | | | | all_469_1, all_469_2 gives: % 179.92/24.79 | | | | | | | (200) ordered_pair(all_469_2, all_195_5) = all_469_0 & % 179.92/24.79 | | | | | | | ordered_pair(all_195_6, all_469_2) = all_469_1 & % 179.92/24.79 | | | | | | | $i(all_469_0) & $i(all_469_1) & $i(all_469_2) & % 179.92/24.79 | | | | | | | in(all_469_0, all_195_3) & in(all_469_1, empty_set) % 179.92/24.79 | | | | | | | % 179.92/24.79 | | | | | | | ALPHA: (200) implies: % 179.92/24.79 | | | | | | | (201) in(all_469_1, empty_set) % 179.92/24.79 | | | | | | | (202) $i(all_469_1) % 179.92/24.79 | | | | | | | % 179.92/24.79 | | | | | | | GROUND_INST: instantiating (5) with all_469_1, simplifying with % 179.92/24.79 | | | | | | | (201), (202) gives: % 179.92/24.79 | | | | | | | (203) $false % 179.92/24.79 | | | | | | | % 179.92/24.79 | | | | | | | CLOSE: (203) is inconsistent. % 179.92/24.79 | | | | | | | % 179.92/24.79 | | | | | | End of split % 179.92/24.79 | | | | | | % 179.92/24.79 | | | | | Case 2: % 179.92/24.79 | | | | | | % 179.92/24.80 | | | | | | (204) all_252_0 = empty_set & relation_dom(all_195_3) = empty_set % 179.92/24.80 | | | | | | % 179.92/24.80 | | | | | | ALPHA: (204) implies: % 179.92/24.80 | | | | | | (205) relation_dom(all_195_3) = empty_set % 179.92/24.80 | | | | | | % 179.92/24.80 | | | | | | GROUND_INST: instantiating (26) with all_253_0, empty_set, % 179.92/24.80 | | | | | | all_195_3, simplifying with (123), (205) gives: % 179.92/24.80 | | | | | | (206) all_253_0 = empty_set % 179.92/24.80 | | | | | | % 179.92/24.80 | | | | | | REDUCE: (195), (206) imply: % 179.92/24.80 | | | | | | (207) $false % 179.92/24.80 | | | | | | % 179.92/24.80 | | | | | | CLOSE: (207) is inconsistent. % 179.92/24.80 | | | | | | % 179.92/24.80 | | | | | End of split % 179.92/24.80 | | | | | % 179.92/24.80 | | | | End of split % 179.92/24.80 | | | | % 179.92/24.80 | | | End of split % 179.92/24.80 | | | % 179.92/24.80 | | Case 2: % 179.92/24.80 | | | % 179.92/24.80 | | | (208) ~ (all_195_1 = empty_set) % 179.92/24.80 | | | % 179.92/24.80 | | | BETA: splitting (77) gives: % 179.92/24.80 | | | % 179.92/24.80 | | | Case 1: % 179.92/24.80 | | | | % 179.92/24.80 | | | | (209) all_195_1 = empty_set % 179.92/24.80 | | | | % 179.92/24.80 | | | | REDUCE: (208), (209) imply: % 179.92/24.80 | | | | (210) $false % 179.92/24.80 | | | | % 179.92/24.80 | | | | CLOSE: (210) is inconsistent. % 179.92/24.80 | | | | % 179.92/24.80 | | | Case 2: % 179.92/24.80 | | | | % 179.92/24.80 | | | | (211) ? [v0: $i] : ( ~ (v0 = empty_set) & relation_dom(all_195_1) = % 179.92/24.80 | | | | v0 & $i(v0)) % 179.92/24.80 | | | | % 179.92/24.80 | | | | DELTA: instantiating (211) with fresh symbol all_376_0 gives: % 179.92/24.80 | | | | (212) ~ (all_376_0 = empty_set) & relation_dom(all_195_1) = % 179.92/24.80 | | | | all_376_0 & $i(all_376_0) % 179.92/24.80 | | | | % 179.92/24.80 | | | | ALPHA: (212) implies: % 179.92/24.80 | | | | (213) relation_dom(all_195_1) = all_376_0 % 179.92/24.80 | | | | % 179.92/24.80 | | | | BETA: splitting (74) gives: % 179.92/24.80 | | | | % 179.92/24.80 | | | | Case 1: % 179.92/24.80 | | | | | % 179.92/24.80 | | | | | (214) all_195_1 = empty_set % 179.92/24.80 | | | | | % 179.92/24.80 | | | | | REDUCE: (208), (214) imply: % 179.92/24.80 | | | | | (215) $false % 179.92/24.80 | | | | | % 179.92/24.80 | | | | | CLOSE: (215) is inconsistent. % 179.92/24.80 | | | | | % 179.92/24.80 | | | | Case 2: % 179.92/24.80 | | | | | % 179.92/24.80 | | | | | (216) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (ordered_pair(v0, % 179.92/24.80 | | | | | v1) = v2 & $i(v2) & $i(v1) & $i(v0) & in(v2, all_195_1)) % 179.92/24.80 | | | | | % 179.92/24.80 | | | | | DELTA: instantiating (216) with fresh symbols all_386_0, all_386_1, % 179.92/24.80 | | | | | all_386_2 gives: % 179.92/24.80 | | | | | (217) ordered_pair(all_386_2, all_386_1) = all_386_0 & % 179.92/24.80 | | | | | $i(all_386_0) & $i(all_386_1) & $i(all_386_2) & in(all_386_0, % 179.92/24.80 | | | | | all_195_1) % 179.92/24.80 | | | | | % 179.92/24.80 | | | | | ALPHA: (217) implies: % 179.92/24.80 | | | | | (218) in(all_386_0, all_195_1) % 179.92/24.80 | | | | | (219) $i(all_386_2) % 179.92/24.80 | | | | | (220) $i(all_386_1) % 179.92/24.80 | | | | | (221) ordered_pair(all_386_2, all_386_1) = all_386_0 % 179.92/24.80 | | | | | % 179.92/24.80 | | | | | GROUND_INST: instantiating (26) with all_195_4, all_376_0, all_195_1, % 179.92/24.80 | | | | | simplifying with (48), (213) gives: % 179.92/24.80 | | | | | (222) all_376_0 = all_195_4 % 179.92/24.80 | | | | | % 179.92/24.80 | | | | | BETA: splitting (44) gives: % 179.92/24.80 | | | | | % 179.92/24.80 | | | | | Case 1: % 179.92/24.80 | | | | | | % 179.92/24.80 | | | | | | (223) all_195_3 = empty_set % 179.92/24.80 | | | | | | % 179.92/24.80 | | | | | | REDUCE: (42), (223) imply: % 179.92/24.80 | | | | | | (224) relation_composition(all_195_1, empty_set) = all_195_0 % 179.92/24.80 | | | | | | % 179.92/24.80 | | | | | | REDUCE: (87), (223) imply: % 179.92/24.80 | | | | | | (225) relation_rng(empty_set) = all_229_0 % 179.92/24.80 | | | | | | % 179.92/24.80 | | | | | | GROUND_INST: instantiating (27) with empty_set, all_229_0, % 179.92/24.80 | | | | | | empty_set, simplifying with (19), (225) gives: % 179.92/24.80 | | | | | | (226) all_229_0 = empty_set % 179.92/24.80 | | | | | | % 179.92/24.80 | | | | | | REDUCE: (84), (226) imply: % 179.92/24.80 | | | | | | (227) subset(all_229_1, empty_set) % 179.92/24.80 | | | | | | % 179.92/24.80 | | | | | | GROUND_INST: instantiating (12) with all_195_6, all_195_5, % 179.92/24.80 | | | | | | all_195_0, all_195_2, all_229_1, simplifying with (33), % 179.92/24.80 | | | | | | (34), (39), (40), (72), (88), (144) gives: % 179.92/24.80 | | | | | | (228) ? [v0: $i] : (relation_dom(all_195_0) = v0 & $i(v0) & % 179.92/24.80 | | | | | | in(all_195_6, v0)) % 179.92/24.80 | | | | | | % 179.92/24.80 | | | | | | GROUND_INST: instantiating (16) with all_229_1, simplifying with % 179.92/24.80 | | | | | | (85), (227) gives: % 179.92/24.80 | | | | | | (229) all_229_1 = empty_set % 179.92/24.80 | | | | | | % 179.92/24.80 | | | | | | GROUND_INST: instantiating (12) with all_386_2, all_386_1, % 179.92/24.80 | | | | | | all_195_1, all_386_0, all_195_4, simplifying with (38), % 179.92/24.80 | | | | | | (47), (49), (218), (219), (220), (221) gives: % 179.92/24.80 | | | | | | (230) ? [v0: $i] : (relation_dom(all_195_1) = v0 & $i(v0) & % 179.92/24.80 | | | | | | in(all_386_2, v0)) % 179.92/24.80 | | | | | | % 179.92/24.80 | | | | | | GROUND_INST: instantiating (8) with all_195_1, empty_set, all_195_0, % 179.92/24.80 | | | | | | all_195_6, all_195_5, all_195_2, simplifying with (10), % 179.92/24.80 | | | | | | (22), (33), (34), (38), (39), (40), (49), (72), (144), % 179.92/24.80 | | | | | | (224) gives: % 179.92/24.80 | | | | | | (231) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (ordered_pair(v0, % 179.92/24.80 | | | | | | all_195_5) = v2 & ordered_pair(all_195_6, v0) = v1 & % 179.92/24.80 | | | | | | $i(v2) & $i(v1) & $i(v0) & in(v2, empty_set) & in(v1, % 179.92/24.80 | | | | | | all_195_1)) % 179.92/24.80 | | | | | | % 179.92/24.80 | | | | | | DELTA: instantiating (228) with fresh symbol all_470_0 gives: % 179.92/24.80 | | | | | | (232) relation_dom(all_195_0) = all_470_0 & $i(all_470_0) & % 179.92/24.80 | | | | | | in(all_195_6, all_470_0) % 179.92/24.80 | | | | | | % 179.92/24.80 | | | | | | ALPHA: (232) implies: % 179.92/24.80 | | | | | | (233) relation_dom(all_195_0) = all_470_0 % 179.92/24.80 | | | | | | % 179.92/24.80 | | | | | | DELTA: instantiating (230) with fresh symbol all_474_0 gives: % 179.92/24.80 | | | | | | (234) relation_dom(all_195_1) = all_474_0 & $i(all_474_0) & % 179.92/24.80 | | | | | | in(all_386_2, all_474_0) % 179.92/24.80 | | | | | | % 179.92/24.80 | | | | | | ALPHA: (234) implies: % 179.92/24.80 | | | | | | (235) $i(all_474_0) % 179.92/24.80 | | | | | | (236) relation_dom(all_195_1) = all_474_0 % 179.92/24.80 | | | | | | % 179.92/24.80 | | | | | | DELTA: instantiating (231) with fresh symbols all_480_0, all_480_1, % 179.92/24.80 | | | | | | all_480_2 gives: % 179.92/24.80 | | | | | | (237) ordered_pair(all_480_2, all_195_5) = all_480_0 & % 179.92/24.80 | | | | | | ordered_pair(all_195_6, all_480_2) = all_480_1 & % 179.92/24.80 | | | | | | $i(all_480_0) & $i(all_480_1) & $i(all_480_2) & % 179.92/24.80 | | | | | | in(all_480_0, empty_set) & in(all_480_1, all_195_1) % 179.92/24.80 | | | | | | % 179.92/24.80 | | | | | | ALPHA: (237) implies: % 179.92/24.80 | | | | | | (238) in(all_480_1, all_195_1) % 179.92/24.80 | | | | | | (239) $i(all_480_2) % 179.92/24.80 | | | | | | (240) ordered_pair(all_195_6, all_480_2) = all_480_1 % 179.92/24.80 | | | | | | % 179.92/24.80 | | | | | | BETA: splitting (118) gives: % 179.92/24.80 | | | | | | % 179.92/24.80 | | | | | | Case 1: % 179.92/24.80 | | | | | | | % 179.92/24.80 | | | | | | | (241) ~ (all_229_1 = empty_set) % 179.92/24.80 | | | | | | | % 179.92/24.80 | | | | | | | REDUCE: (229), (241) imply: % 179.92/24.80 | | | | | | | (242) $false % 179.92/24.80 | | | | | | | % 179.92/24.80 | | | | | | | CLOSE: (242) is inconsistent. % 179.92/24.80 | | | | | | | % 179.92/24.80 | | | | | | Case 2: % 179.92/24.80 | | | | | | | % 179.92/24.80 | | | | | | | (243) all_251_0 = empty_set & relation_dom(all_195_0) = % 179.92/24.80 | | | | | | | empty_set % 179.92/24.80 | | | | | | | % 179.92/24.80 | | | | | | | ALPHA: (243) implies: % 179.92/24.80 | | | | | | | (244) relation_dom(all_195_0) = empty_set % 179.92/24.80 | | | | | | | % 179.92/24.80 | | | | | | | GROUND_INST: instantiating (26) with all_195_4, all_474_0, % 179.92/24.80 | | | | | | | all_195_1, simplifying with (48), (236) gives: % 179.92/24.80 | | | | | | | (245) all_474_0 = all_195_4 % 179.92/24.80 | | | | | | | % 179.92/24.80 | | | | | | | GROUND_INST: instantiating (26) with all_227_0, all_470_0, % 179.92/24.80 | | | | | | | all_195_0, simplifying with (82), (233) gives: % 179.92/24.80 | | | | | | | (246) all_470_0 = all_227_0 % 179.92/24.80 | | | | | | | % 179.92/24.80 | | | | | | | GROUND_INST: instantiating (26) with empty_set, all_470_0, % 179.92/24.80 | | | | | | | all_195_0, simplifying with (233), (244) gives: % 179.92/24.80 | | | | | | | (247) all_470_0 = empty_set % 179.92/24.81 | | | | | | | % 179.92/24.81 | | | | | | | COMBINE_EQS: (246), (247) imply: % 179.92/24.81 | | | | | | | (248) all_227_0 = empty_set % 179.92/24.81 | | | | | | | % 179.92/24.81 | | | | | | | SIMP: (248) implies: % 179.92/24.81 | | | | | | | (249) all_227_0 = empty_set % 179.92/24.81 | | | | | | | % 179.92/24.81 | | | | | | | BETA: splitting (112) gives: % 179.92/24.81 | | | | | | | % 179.92/24.81 | | | | | | | Case 1: % 179.92/24.81 | | | | | | | | % 179.92/24.81 | | | | | | | | (250) all_195_0 = empty_set % 179.92/24.81 | | | | | | | | % 179.92/24.81 | | | | | | | | REDUCE: (144), (250) imply: % 179.92/24.81 | | | | | | | | (251) in(all_195_2, empty_set) % 179.92/24.81 | | | | | | | | % 179.92/24.81 | | | | | | | | BETA: splitting (145) gives: % 179.92/24.81 | | | | | | | | % 179.92/24.81 | | | | | | | | Case 1: % 179.92/24.81 | | | | | | | | | % 179.92/24.81 | | | | | | | | | (252) ~ in(all_195_2, all_195_3) % 179.92/24.81 | | | | | | | | | % 179.92/24.81 | | | | | | | | | REDUCE: (223), (252) imply: % 179.92/24.81 | | | | | | | | | (253) ~ in(all_195_2, empty_set) % 179.92/24.81 | | | | | | | | | % 179.92/24.81 | | | | | | | | | PRED_UNIFY: (251), (253) imply: % 179.92/24.81 | | | | | | | | | (254) $false % 179.92/24.81 | | | | | | | | | % 179.92/24.81 | | | | | | | | | CLOSE: (254) is inconsistent. % 179.92/24.81 | | | | | | | | | % 179.92/24.81 | | | | | | | | Case 2: % 179.92/24.81 | | | | | | | | | % 179.92/24.81 | | | | | | | | | (255) ~ in(all_195_6, all_195_4) % 179.92/24.81 | | | | | | | | | % 179.92/24.81 | | | | | | | | | GROUND_INST: instantiating (7) with all_195_1, all_195_4, % 179.92/24.81 | | | | | | | | | all_195_6, all_480_2, all_480_1, simplifying with % 179.92/24.81 | | | | | | | | | (33), (35), (38), (48), (49), (238), (239), (240), % 179.92/24.81 | | | | | | | | | (255) gives: % 179.92/24.81 | | | | | | | | | (256) $false % 179.92/24.81 | | | | | | | | | % 179.92/24.81 | | | | | | | | | CLOSE: (256) is inconsistent. % 179.92/24.81 | | | | | | | | | % 179.92/24.81 | | | | | | | | End of split % 179.92/24.81 | | | | | | | | % 179.92/24.81 | | | | | | | Case 2: % 179.92/24.81 | | | | | | | | % 179.92/24.81 | | | | | | | | (257) ? [v0: $i] : ( ~ (v0 = empty_set) & % 179.92/24.81 | | | | | | | | relation_dom(all_195_0) = v0 & $i(v0)) % 179.92/24.81 | | | | | | | | % 179.92/24.81 | | | | | | | | DELTA: instantiating (257) with fresh symbol all_494_0 gives: % 179.92/24.81 | | | | | | | | (258) ~ (all_494_0 = empty_set) & relation_dom(all_195_0) = % 179.92/24.81 | | | | | | | | all_494_0 & $i(all_494_0) % 179.92/24.81 | | | | | | | | % 179.92/24.81 | | | | | | | | ALPHA: (258) implies: % 179.92/24.81 | | | | | | | | (259) ~ (all_494_0 = empty_set) % 179.92/24.81 | | | | | | | | (260) relation_dom(all_195_0) = all_494_0 % 179.92/24.81 | | | | | | | | % 179.92/24.81 | | | | | | | | GROUND_INST: instantiating (26) with empty_set, all_494_0, % 179.92/24.81 | | | | | | | | all_195_0, simplifying with (244), (260) gives: % 179.92/24.81 | | | | | | | | (261) all_494_0 = empty_set % 179.92/24.81 | | | | | | | | % 179.92/24.81 | | | | | | | | REDUCE: (259), (261) imply: % 179.92/24.81 | | | | | | | | (262) $false % 179.92/24.81 | | | | | | | | % 179.92/24.81 | | | | | | | | CLOSE: (262) is inconsistent. % 179.92/24.81 | | | | | | | | % 179.92/24.81 | | | | | | | End of split % 179.92/24.81 | | | | | | | % 179.92/24.81 | | | | | | End of split % 179.92/24.81 | | | | | | % 179.92/24.81 | | | | | Case 2: % 179.92/24.81 | | | | | | % 179.92/24.81 | | | | | | (263) ~ (all_195_3 = empty_set) % 179.92/24.81 | | | | | | % 179.92/24.81 | | | | | | BETA: splitting (107) gives: % 179.92/24.81 | | | | | | % 179.92/24.81 | | | | | | Case 1: % 179.92/24.81 | | | | | | | % 179.92/24.81 | | | | | | | (264) all_195_3 = empty_set % 179.92/24.81 | | | | | | | % 179.92/24.81 | | | | | | | REDUCE: (263), (264) imply: % 179.92/24.81 | | | | | | | (265) $false % 179.92/24.81 | | | | | | | % 179.92/24.81 | | | | | | | CLOSE: (265) is inconsistent. % 179.92/24.81 | | | | | | | % 179.92/24.81 | | | | | | Case 2: % 179.92/24.81 | | | | | | | % 179.92/24.81 | | | | | | | (266) ? [v0: $i] : ( ~ (v0 = empty_set) & % 179.92/24.81 | | | | | | | relation_dom(all_195_3) = v0 & $i(v0)) % 179.92/24.81 | | | | | | | % 179.92/24.81 | | | | | | | DELTA: instantiating (266) with fresh symbol all_428_0 gives: % 179.92/24.81 | | | | | | | (267) ~ (all_428_0 = empty_set) & relation_dom(all_195_3) = % 179.92/24.81 | | | | | | | all_428_0 & $i(all_428_0) % 179.92/24.81 | | | | | | | % 179.92/24.81 | | | | | | | ALPHA: (267) implies: % 179.92/24.81 | | | | | | | (268) ~ (all_428_0 = empty_set) % 179.92/24.81 | | | | | | | (269) relation_dom(all_195_3) = all_428_0 % 179.92/24.81 | | | | | | | % 179.92/24.81 | | | | | | | GROUND_INST: instantiating (26) with all_253_0, all_428_0, % 179.92/24.81 | | | | | | | all_195_3, simplifying with (123), (269) gives: % 179.92/24.81 | | | | | | | (270) all_428_0 = all_253_0 % 179.92/24.81 | | | | | | | % 179.92/24.81 | | | | | | | REDUCE: (268), (270) imply: % 179.92/24.81 | | | | | | | (271) ~ (all_253_0 = empty_set) % 179.92/24.81 | | | | | | | % 179.92/24.81 | | | | | | | BETA: splitting (121) gives: % 179.92/24.81 | | | | | | | % 179.92/24.81 | | | | | | | Case 1: % 179.92/24.81 | | | | | | | | % 179.92/24.81 | | | | | | | | % 179.92/24.81 | | | | | | | | GROUND_INST: instantiating (8) with all_195_1, all_195_3, % 179.92/24.81 | | | | | | | | all_195_0, all_195_6, all_195_5, all_195_2, % 179.92/24.81 | | | | | | | | simplifying with (32), (33), (34), (36), (38), % 179.92/24.81 | | | | | | | | (39), (40), (42), (49), (72), (144) gives: % 179.92/24.81 | | | | | | | | (272) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 179.92/24.81 | | | | | | | | (ordered_pair(v0, all_195_5) = v2 & % 179.92/24.81 | | | | | | | | ordered_pair(all_195_6, v0) = v1 & $i(v2) & $i(v1) & % 179.92/24.81 | | | | | | | | $i(v0) & in(v2, all_195_3) & in(v1, all_195_1)) % 179.92/24.81 | | | | | | | | % 179.92/24.81 | | | | | | | | GROUND_INST: instantiating (4) with all_195_0, all_195_2, % 179.92/24.81 | | | | | | | | simplifying with (37), (39), (72), (144) gives: % 179.92/24.81 | | | | | | | | (273) ? [v0: $i] : ? [v1: $i] : (ordered_pair(v0, v1) = % 179.92/24.81 | | | | | | | | all_195_2 & $i(v1) & $i(v0)) % 179.92/24.81 | | | | | | | | % 179.92/24.81 | | | | | | | | GROUND_INST: instantiating (12) with all_386_2, all_386_1, % 179.92/24.81 | | | | | | | | all_195_1, all_386_0, all_195_4, simplifying with % 179.92/24.81 | | | | | | | | (38), (47), (49), (218), (219), (220), (221) gives: % 179.92/24.81 | | | | | | | | (274) ? [v0: $i] : (relation_dom(all_195_1) = v0 & $i(v0) & % 179.92/24.81 | | | | | | | | in(all_386_2, v0)) % 179.92/24.81 | | | | | | | | % 179.92/24.81 | | | | | | | | DELTA: instantiating (273) with fresh symbols all_490_0, % 179.92/24.81 | | | | | | | | all_490_1 gives: % 179.92/24.81 | | | | | | | | (275) ordered_pair(all_490_1, all_490_0) = all_195_2 & % 179.92/24.81 | | | | | | | | $i(all_490_0) & $i(all_490_1) % 179.92/24.81 | | | | | | | | % 179.92/24.81 | | | | | | | | ALPHA: (275) implies: % 179.92/24.81 | | | | | | | | (276) $i(all_490_1) % 179.92/24.81 | | | | | | | | (277) $i(all_490_0) % 179.92/24.81 | | | | | | | | (278) ordered_pair(all_490_1, all_490_0) = all_195_2 % 179.92/24.81 | | | | | | | | % 179.92/24.81 | | | | | | | | DELTA: instantiating (274) with fresh symbol all_496_0 gives: % 179.92/24.81 | | | | | | | | (279) relation_dom(all_195_1) = all_496_0 & $i(all_496_0) & % 179.92/24.81 | | | | | | | | in(all_386_2, all_496_0) % 179.92/24.81 | | | | | | | | % 179.92/24.81 | | | | | | | | ALPHA: (279) implies: % 179.92/24.81 | | | | | | | | (280) $i(all_496_0) % 179.92/24.81 | | | | | | | | (281) relation_dom(all_195_1) = all_496_0 % 179.92/24.81 | | | | | | | | % 179.92/24.81 | | | | | | | | DELTA: instantiating (272) with fresh symbols all_498_0, % 179.92/24.81 | | | | | | | | all_498_1, all_498_2 gives: % 179.92/24.81 | | | | | | | | (282) ordered_pair(all_498_2, all_195_5) = all_498_0 & % 179.92/24.81 | | | | | | | | ordered_pair(all_195_6, all_498_2) = all_498_1 & % 179.92/24.81 | | | | | | | | $i(all_498_0) & $i(all_498_1) & $i(all_498_2) & % 179.92/24.81 | | | | | | | | in(all_498_0, all_195_3) & in(all_498_1, all_195_1) % 179.92/24.81 | | | | | | | | % 179.92/24.81 | | | | | | | | ALPHA: (282) implies: % 179.92/24.81 | | | | | | | | (283) in(all_498_1, all_195_1) % 179.92/24.81 | | | | | | | | (284) in(all_498_0, all_195_3) % 179.92/24.81 | | | | | | | | (285) $i(all_498_2) % 179.92/24.81 | | | | | | | | (286) ordered_pair(all_195_6, all_498_2) = all_498_1 % 179.92/24.81 | | | | | | | | (287) ordered_pair(all_498_2, all_195_5) = all_498_0 % 179.92/24.81 | | | | | | | | % 179.92/24.81 | | | | | | | | GROUND_INST: instantiating (26) with all_195_4, all_496_0, % 179.92/24.81 | | | | | | | | all_195_1, simplifying with (48), (281) gives: % 179.92/24.81 | | | | | | | | (288) all_496_0 = all_195_4 % 179.92/24.81 | | | | | | | | % 179.92/24.81 | | | | | | | | BETA: splitting (145) gives: % 179.92/24.81 | | | | | | | | % 179.92/24.81 | | | | | | | | Case 1: % 179.92/24.81 | | | | | | | | | % 179.92/24.81 | | | | | | | | | (289) ~ in(all_195_2, all_195_3) % 179.92/24.81 | | | | | | | | | % 179.92/24.81 | | | | | | | | | GROUND_INST: instantiating (3) with all_195_4, all_195_1, % 179.92/24.81 | | | | | | | | | all_195_6, all_498_2, all_498_1, simplifying with % 179.92/24.81 | | | | | | | | | (33), (35), (38), (41), (49), (283), (285), (286) % 179.92/24.81 | | | | | | | | | gives: % 179.92/24.81 | | | | | | | | | (290) all_498_2 = all_195_6 % 179.92/24.81 | | | | | | | | | % 179.92/24.81 | | | | | | | | | GROUND_INST: instantiating (14) with all_195_6, all_195_5, % 179.92/24.81 | | | | | | | | | all_490_1, all_490_0, all_195_2, simplifying with % 179.92/24.81 | | | | | | | | | (33), (34), (40), (276), (277), (278) gives: % 179.92/24.81 | | | | | | | | | (291) all_490_0 = all_195_5 % 179.92/24.81 | | | | | | | | | % 179.92/24.81 | | | | | | | | | GROUND_INST: instantiating (13) with all_195_6, all_195_5, % 179.92/24.81 | | | | | | | | | all_490_1, all_490_0, all_195_2, simplifying with % 179.92/24.81 | | | | | | | | | (33), (34), (40), (276), (277), (278) gives: % 179.92/24.81 | | | | | | | | | (292) all_490_1 = all_195_6 % 179.92/24.81 | | | | | | | | | % 179.92/24.81 | | | | | | | | | REDUCE: (287), (290) imply: % 179.92/24.81 | | | | | | | | | (293) ordered_pair(all_195_6, all_195_5) = all_498_0 % 179.92/24.81 | | | | | | | | | % 179.92/24.81 | | | | | | | | | GROUND_INST: instantiating (28) with all_195_2, all_498_0, % 179.92/24.81 | | | | | | | | | all_195_5, all_195_6, simplifying with (40), (293) % 179.92/24.81 | | | | | | | | | gives: % 179.92/24.81 | | | | | | | | | (294) all_498_0 = all_195_2 % 179.92/24.81 | | | | | | | | | % 179.92/24.81 | | | | | | | | | REDUCE: (284), (294) imply: % 179.92/24.81 | | | | | | | | | (295) in(all_195_2, all_195_3) % 179.92/24.81 | | | | | | | | | % 179.92/24.82 | | | | | | | | | PRED_UNIFY: (289), (295) imply: % 179.92/24.82 | | | | | | | | | (296) $false % 179.92/24.82 | | | | | | | | | % 179.92/24.82 | | | | | | | | | CLOSE: (296) is inconsistent. % 179.92/24.82 | | | | | | | | | % 179.92/24.82 | | | | | | | | Case 2: % 179.92/24.82 | | | | | | | | | % 179.92/24.82 | | | | | | | | | (297) ~ in(all_195_6, all_195_4) % 179.92/24.82 | | | | | | | | | % 179.92/24.82 | | | | | | | | | GROUND_INST: instantiating (7) with all_195_1, all_195_4, % 179.92/24.82 | | | | | | | | | all_195_6, all_498_2, all_498_1, simplifying with % 179.92/24.82 | | | | | | | | | (33), (35), (38), (48), (49), (283), (285), (286), % 179.92/24.82 | | | | | | | | | (297) gives: % 179.92/24.82 | | | | | | | | | (298) $false % 179.92/24.82 | | | | | | | | | % 179.92/24.82 | | | | | | | | | CLOSE: (298) is inconsistent. % 179.92/24.82 | | | | | | | | | % 179.92/24.82 | | | | | | | | End of split % 179.92/24.82 | | | | | | | | % 179.92/24.82 | | | | | | | Case 2: % 179.92/24.82 | | | | | | | | % 179.92/24.82 | | | | | | | | (299) all_252_0 = empty_set & relation_dom(all_195_3) = % 179.92/24.82 | | | | | | | | empty_set % 179.92/24.82 | | | | | | | | % 179.92/24.82 | | | | | | | | ALPHA: (299) implies: % 179.92/24.82 | | | | | | | | (300) relation_dom(all_195_3) = empty_set % 179.92/24.82 | | | | | | | | % 179.92/24.82 | | | | | | | | REF_CLOSE: (26), (123), (271), (300) are inconsistent by % 179.92/24.82 | | | | | | | | sub-proof #1. % 179.92/24.82 | | | | | | | | % 179.92/24.82 | | | | | | | End of split % 179.92/24.82 | | | | | | | % 179.92/24.82 | | | | | | End of split % 179.92/24.82 | | | | | | % 179.92/24.82 | | | | | End of split % 179.92/24.82 | | | | | % 179.92/24.82 | | | | End of split % 179.92/24.82 | | | | % 179.92/24.82 | | | End of split % 179.92/24.82 | | | % 179.92/24.82 | | End of split % 179.92/24.82 | | % 179.92/24.82 | Case 2: % 179.92/24.82 | | % 179.92/24.82 | | (301) in(all_195_2, all_195_3) & in(all_195_6, all_195_4) & ~ % 179.92/24.82 | | in(all_195_2, all_195_0) % 179.92/24.82 | | % 179.92/24.82 | | ALPHA: (301) implies: % 179.92/24.82 | | (302) ~ in(all_195_2, all_195_0) % 179.92/24.82 | | (303) in(all_195_6, all_195_4) % 179.92/24.82 | | (304) in(all_195_2, all_195_3) % 179.92/24.82 | | % 179.92/24.82 | | BETA: splitting (46) gives: % 179.92/24.82 | | % 179.92/24.82 | | Case 1: % 179.92/24.82 | | | % 179.92/24.82 | | | (305) all_195_1 = empty_set % 179.92/24.82 | | | % 179.92/24.82 | | | REDUCE: (47), (305) imply: % 179.92/24.82 | | | (306) relation_rng(empty_set) = all_195_4 % 179.92/24.82 | | | % 179.92/24.82 | | | GROUND_INST: instantiating (27) with empty_set, all_195_4, empty_set, % 179.92/24.82 | | | simplifying with (19), (306) gives: % 179.92/24.82 | | | (307) all_195_4 = empty_set % 179.92/24.82 | | | % 179.92/24.82 | | | REDUCE: (303), (307) imply: % 179.92/24.82 | | | (308) in(all_195_6, empty_set) % 179.92/24.82 | | | % 179.92/24.82 | | | GROUND_INST: instantiating (5) with all_195_6, simplifying with (33), % 179.92/24.82 | | | (308) gives: % 179.92/24.82 | | | (309) $false % 179.92/24.82 | | | % 179.92/24.82 | | | CLOSE: (309) is inconsistent. % 179.92/24.82 | | | % 179.92/24.82 | | Case 2: % 179.92/24.82 | | | % 179.92/24.82 | | | (310) ~ (all_195_1 = empty_set) % 179.92/24.82 | | | % 179.92/24.82 | | | BETA: splitting (74) gives: % 179.92/24.82 | | | % 179.92/24.82 | | | Case 1: % 179.92/24.82 | | | | % 179.92/24.82 | | | | (311) all_195_1 = empty_set % 179.92/24.82 | | | | % 179.92/24.82 | | | | REDUCE: (310), (311) imply: % 179.92/24.82 | | | | (312) $false % 179.92/24.82 | | | | % 179.92/24.82 | | | | CLOSE: (312) is inconsistent. % 179.92/24.82 | | | | % 179.92/24.82 | | | Case 2: % 179.92/24.82 | | | | % 179.92/24.82 | | | | (313) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (ordered_pair(v0, v1) % 179.92/24.82 | | | | = v2 & $i(v2) & $i(v1) & $i(v0) & in(v2, all_195_1)) % 179.92/24.82 | | | | % 179.92/24.82 | | | | DELTA: instantiating (313) with fresh symbols all_381_0, all_381_1, % 179.92/24.82 | | | | all_381_2 gives: % 179.92/24.82 | | | | (314) ordered_pair(all_381_2, all_381_1) = all_381_0 & $i(all_381_0) % 179.92/24.82 | | | | & $i(all_381_1) & $i(all_381_2) & in(all_381_0, all_195_1) % 179.92/24.82 | | | | % 179.92/24.82 | | | | ALPHA: (314) implies: % 179.92/24.82 | | | | (315) in(all_381_0, all_195_1) % 179.92/24.82 | | | | (316) $i(all_381_2) % 179.92/24.82 | | | | (317) $i(all_381_1) % 179.92/24.82 | | | | (318) ordered_pair(all_381_2, all_381_1) = all_381_0 % 179.92/24.82 | | | | % 179.92/24.82 | | | | BETA: splitting (44) gives: % 179.92/24.82 | | | | % 179.92/24.82 | | | | Case 1: % 179.92/24.82 | | | | | % 179.92/24.82 | | | | | (319) all_195_3 = empty_set % 179.92/24.82 | | | | | % 179.92/24.82 | | | | | REDUCE: (87), (319) imply: % 179.92/24.82 | | | | | (320) relation_rng(empty_set) = all_229_0 % 179.92/24.82 | | | | | % 179.92/24.82 | | | | | REDUCE: (304), (319) imply: % 179.92/24.82 | | | | | (321) in(all_195_2, empty_set) % 179.92/24.82 | | | | | % 179.92/24.82 | | | | | GROUND_INST: instantiating (27) with empty_set, all_229_0, empty_set, % 179.92/24.82 | | | | | simplifying with (19), (320) gives: % 179.92/24.82 | | | | | (322) all_229_0 = empty_set % 179.92/24.82 | | | | | % 179.92/24.82 | | | | | BETA: splitting (121) gives: % 179.92/24.82 | | | | | % 179.92/24.82 | | | | | Case 1: % 179.92/24.82 | | | | | | % 179.92/24.82 | | | | | | (323) ~ (all_229_0 = empty_set) % 179.92/24.82 | | | | | | % 179.92/24.82 | | | | | | REDUCE: (322), (323) imply: % 179.92/24.82 | | | | | | (324) $false % 179.92/24.82 | | | | | | % 179.92/24.82 | | | | | | CLOSE: (324) is inconsistent. % 179.92/24.82 | | | | | | % 179.92/24.82 | | | | | Case 2: % 179.92/24.82 | | | | | | % 179.92/24.82 | | | | | | (325) all_252_0 = empty_set & relation_dom(all_195_3) = empty_set % 179.92/24.82 | | | | | | % 179.92/24.82 | | | | | | ALPHA: (325) implies: % 179.92/24.82 | | | | | | (326) relation_dom(all_195_3) = empty_set % 179.92/24.82 | | | | | | % 179.92/24.82 | | | | | | GROUND_INST: instantiating (7) with empty_set, empty_set, all_195_6, % 179.92/24.82 | | | | | | all_195_5, all_195_2, simplifying with (10), (18), % 179.92/24.82 | | | | | | (22), (33), (34), (40), (321) gives: % 179.92/24.82 | | | | | | (327) in(all_195_6, empty_set) % 179.92/24.82 | | | | | | % 179.92/24.82 | | | | | | GROUND_INST: instantiating (5) with all_195_6, simplifying with % 179.92/24.82 | | | | | | (33), (327) gives: % 179.92/24.82 | | | | | | (328) $false % 179.92/24.82 | | | | | | % 179.92/24.82 | | | | | | CLOSE: (328) is inconsistent. % 179.92/24.82 | | | | | | % 179.92/24.82 | | | | | End of split % 179.92/24.82 | | | | | % 179.92/24.82 | | | | Case 2: % 179.92/24.82 | | | | | % 179.92/24.82 | | | | | (329) ~ (all_195_3 = empty_set) % 179.92/24.82 | | | | | % 179.92/24.82 | | | | | BETA: splitting (107) gives: % 179.92/24.82 | | | | | % 179.92/24.82 | | | | | Case 1: % 179.92/24.82 | | | | | | % 179.92/24.82 | | | | | | (330) all_195_3 = empty_set % 179.92/24.82 | | | | | | % 179.92/24.82 | | | | | | REDUCE: (329), (330) imply: % 179.92/24.82 | | | | | | (331) $false % 179.92/24.82 | | | | | | % 179.92/24.82 | | | | | | CLOSE: (331) is inconsistent. % 179.92/24.82 | | | | | | % 179.92/24.82 | | | | | Case 2: % 179.92/24.82 | | | | | | % 179.92/24.82 | | | | | | (332) ? [v0: $i] : ( ~ (v0 = empty_set) & % 179.92/24.82 | | | | | | relation_dom(all_195_3) = v0 & $i(v0)) % 179.92/24.82 | | | | | | % 179.92/24.82 | | | | | | DELTA: instantiating (332) with fresh symbol all_437_0 gives: % 179.92/24.82 | | | | | | (333) ~ (all_437_0 = empty_set) & relation_dom(all_195_3) = % 179.92/24.82 | | | | | | all_437_0 & $i(all_437_0) % 179.92/24.82 | | | | | | % 179.92/24.82 | | | | | | ALPHA: (333) implies: % 179.92/24.82 | | | | | | (334) ~ (all_437_0 = empty_set) % 179.92/24.82 | | | | | | (335) relation_dom(all_195_3) = all_437_0 % 179.92/24.82 | | | | | | % 179.92/24.82 | | | | | | GROUND_INST: instantiating (26) with all_253_0, all_437_0, % 179.92/24.82 | | | | | | all_195_3, simplifying with (123), (335) gives: % 179.92/24.82 | | | | | | (336) all_437_0 = all_253_0 % 179.92/24.82 | | | | | | % 179.92/24.82 | | | | | | REDUCE: (334), (336) imply: % 179.92/24.82 | | | | | | (337) ~ (all_253_0 = empty_set) % 179.92/24.82 | | | | | | % 179.92/24.82 | | | | | | BETA: splitting (121) gives: % 179.92/24.82 | | | | | | % 179.92/24.82 | | | | | | Case 1: % 179.92/24.82 | | | | | | | % 179.92/24.82 | | | | | | | (338) ~ (all_229_0 = empty_set) % 179.92/24.82 | | | | | | | % 179.92/24.82 | | | | | | | BETA: splitting (120) gives: % 179.92/24.82 | | | | | | | % 179.92/24.82 | | | | | | | Case 1: % 179.92/24.82 | | | | | | | | % 179.92/24.82 | | | | | | | | (339) all_229_0 = empty_set % 179.92/24.82 | | | | | | | | % 179.92/24.82 | | | | | | | | REDUCE: (338), (339) imply: % 179.92/24.82 | | | | | | | | (340) $false % 179.92/24.82 | | | | | | | | % 179.92/24.82 | | | | | | | | CLOSE: (340) is inconsistent. % 179.92/24.82 | | | | | | | | % 179.92/24.82 | | | | | | | Case 2: % 179.92/24.82 | | | | | | | | % 179.92/24.82 | | | | | | | | % 179.92/24.82 | | | | | | | | GROUND_INST: instantiating (6) with all_195_1, all_195_4, % 179.92/24.82 | | | | | | | | all_195_6, simplifying with (33), (35), (38), (48), % 179.92/24.82 | | | | | | | | (49), (303) gives: % 179.92/24.82 | | | | | | | | (341) ? [v0: $i] : ? [v1: $i] : (ordered_pair(all_195_6, % 179.92/24.82 | | | | | | | | v0) = v1 & $i(v1) & $i(v0) & in(v1, all_195_1)) % 179.92/24.82 | | | | | | | | % 179.92/24.82 | | | | | | | | GROUND_INST: instantiating (4) with all_195_3, all_195_2, % 179.92/24.82 | | | | | | | | simplifying with (32), (36), (37), (304) gives: % 179.92/24.82 | | | | | | | | (342) ? [v0: $i] : ? [v1: $i] : (ordered_pair(v0, v1) = % 179.92/24.82 | | | | | | | | all_195_2 & $i(v1) & $i(v0)) % 179.92/24.82 | | | | | | | | % 179.92/24.82 | | | | | | | | GROUND_INST: instantiating (12) with all_381_2, all_381_1, % 179.92/24.82 | | | | | | | | all_195_1, all_381_0, all_195_4, simplifying with % 179.92/24.82 | | | | | | | | (38), (47), (49), (315), (316), (317), (318) gives: % 179.92/24.82 | | | | | | | | (343) ? [v0: $i] : (relation_dom(all_195_1) = v0 & $i(v0) & % 179.92/24.82 | | | | | | | | in(all_381_2, v0)) % 179.92/24.82 | | | | | | | | % 179.92/24.82 | | | | | | | | DELTA: instantiating (342) with fresh symbols all_485_0, % 179.92/24.82 | | | | | | | | all_485_1 gives: % 179.92/24.82 | | | | | | | | (344) ordered_pair(all_485_1, all_485_0) = all_195_2 & % 179.92/24.82 | | | | | | | | $i(all_485_0) & $i(all_485_1) % 179.92/24.82 | | | | | | | | % 179.92/24.82 | | | | | | | | ALPHA: (344) implies: % 179.92/24.82 | | | | | | | | (345) $i(all_485_1) % 179.92/24.82 | | | | | | | | (346) $i(all_485_0) % 179.92/24.83 | | | | | | | | (347) ordered_pair(all_485_1, all_485_0) = all_195_2 % 179.92/24.83 | | | | | | | | % 179.92/24.83 | | | | | | | | DELTA: instantiating (343) with fresh symbol all_489_0 gives: % 179.92/24.83 | | | | | | | | (348) relation_dom(all_195_1) = all_489_0 & $i(all_489_0) & % 179.92/24.83 | | | | | | | | in(all_381_2, all_489_0) % 179.92/24.83 | | | | | | | | % 179.92/24.83 | | | | | | | | ALPHA: (348) implies: % 179.92/24.83 | | | | | | | | (349) $i(all_489_0) % 179.92/24.83 | | | | | | | | (350) relation_dom(all_195_1) = all_489_0 % 179.92/24.83 | | | | | | | | % 179.92/24.83 | | | | | | | | DELTA: instantiating (341) with fresh symbols all_499_0, % 179.92/24.83 | | | | | | | | all_499_1 gives: % 179.92/24.83 | | | | | | | | (351) ordered_pair(all_195_6, all_499_1) = all_499_0 & % 179.92/24.83 | | | | | | | | $i(all_499_0) & $i(all_499_1) & in(all_499_0, % 179.92/24.83 | | | | | | | | all_195_1) % 179.92/24.83 | | | | | | | | % 179.92/24.83 | | | | | | | | ALPHA: (351) implies: % 179.92/24.83 | | | | | | | | (352) in(all_499_0, all_195_1) % 179.92/24.83 | | | | | | | | (353) $i(all_499_1) % 179.92/24.83 | | | | | | | | (354) ordered_pair(all_195_6, all_499_1) = all_499_0 % 179.92/24.83 | | | | | | | | % 179.92/24.83 | | | | | | | | GROUND_INST: instantiating (26) with all_195_4, all_489_0, % 179.92/24.83 | | | | | | | | all_195_1, simplifying with (48), (350) gives: % 179.92/24.83 | | | | | | | | (355) all_489_0 = all_195_4 % 179.92/24.83 | | | | | | | | % 179.92/24.83 | | | | | | | | GROUND_INST: instantiating (9) with all_195_1, all_195_3, % 179.92/24.83 | | | | | | | | all_195_0, all_195_6, all_195_5, all_195_2, % 179.92/24.83 | | | | | | | | all_499_1, all_499_0, simplifying with (32), (33), % 179.92/24.83 | | | | | | | | (34), (36), (38), (39), (40), (42), (49), (72), % 179.92/24.83 | | | | | | | | (302), (352), (353), (354) gives: % 179.92/24.83 | | | | | | | | (356) ? [v0: $i] : (ordered_pair(all_499_1, all_195_5) = v0 % 179.92/24.83 | | | | | | | | & $i(v0) & ~ in(v0, all_195_3)) % 179.92/24.83 | | | | | | | | % 179.92/24.83 | | | | | | | | GROUND_INST: instantiating (3) with all_195_4, all_195_1, % 179.92/24.83 | | | | | | | | all_195_6, all_499_1, all_499_0, simplifying with % 179.92/24.83 | | | | | | | | (33), (35), (38), (41), (49), (352), (353), (354) % 179.92/24.83 | | | | | | | | gives: % 179.92/24.83 | | | | | | | | (357) all_499_1 = all_195_6 % 179.92/24.83 | | | | | | | | % 179.92/24.83 | | | | | | | | GROUND_INST: instantiating (14) with all_195_6, all_195_5, % 179.92/24.83 | | | | | | | | all_485_1, all_485_0, all_195_2, simplifying with % 179.92/24.83 | | | | | | | | (33), (34), (40), (345), (346), (347) gives: % 179.92/24.83 | | | | | | | | (358) all_485_0 = all_195_5 % 179.92/24.83 | | | | | | | | % 179.92/24.83 | | | | | | | | GROUND_INST: instantiating (13) with all_195_6, all_195_5, % 179.92/24.83 | | | | | | | | all_485_1, all_485_0, all_195_2, simplifying with % 179.92/24.83 | | | | | | | | (33), (34), (40), (345), (346), (347) gives: % 179.92/24.83 | | | | | | | | (359) all_485_1 = all_195_6 % 179.92/24.83 | | | | | | | | % 179.92/24.83 | | | | | | | | DELTA: instantiating (356) with fresh symbol all_671_0 gives: % 179.92/24.83 | | | | | | | | (360) ordered_pair(all_499_1, all_195_5) = all_671_0 & % 179.92/24.83 | | | | | | | | $i(all_671_0) & ~ in(all_671_0, all_195_3) % 179.92/24.83 | | | | | | | | % 179.92/24.83 | | | | | | | | ALPHA: (360) implies: % 179.92/24.83 | | | | | | | | (361) ~ in(all_671_0, all_195_3) % 179.92/24.83 | | | | | | | | (362) ordered_pair(all_499_1, all_195_5) = all_671_0 % 179.92/24.83 | | | | | | | | % 179.92/24.83 | | | | | | | | REDUCE: (357), (362) imply: % 179.92/24.83 | | | | | | | | (363) ordered_pair(all_195_6, all_195_5) = all_671_0 % 179.92/24.83 | | | | | | | | % 179.92/24.83 | | | | | | | | GROUND_INST: instantiating (28) with all_195_2, all_671_0, % 179.92/24.83 | | | | | | | | all_195_5, all_195_6, simplifying with (40), (363) % 179.92/24.83 | | | | | | | | gives: % 179.92/24.83 | | | | | | | | (364) all_671_0 = all_195_2 % 179.92/24.83 | | | | | | | | % 179.92/24.83 | | | | | | | | REDUCE: (361), (364) imply: % 179.92/24.83 | | | | | | | | (365) ~ in(all_195_2, all_195_3) % 179.92/24.83 | | | | | | | | % 179.92/24.83 | | | | | | | | PRED_UNIFY: (304), (365) imply: % 179.92/24.83 | | | | | | | | (366) $false % 179.92/24.83 | | | | | | | | % 179.92/24.83 | | | | | | | | CLOSE: (366) is inconsistent. % 179.92/24.83 | | | | | | | | % 179.92/24.83 | | | | | | | End of split % 179.92/24.83 | | | | | | | % 179.92/24.83 | | | | | | Case 2: % 179.92/24.83 | | | | | | | % 179.92/24.83 | | | | | | | (367) all_252_0 = empty_set & relation_dom(all_195_3) = % 179.92/24.83 | | | | | | | empty_set % 179.92/24.83 | | | | | | | % 179.92/24.83 | | | | | | | ALPHA: (367) implies: % 179.92/24.83 | | | | | | | (368) relation_dom(all_195_3) = empty_set % 179.92/24.83 | | | | | | | % 179.92/24.83 | | | | | | | REF_CLOSE: (26), (123), (337), (368) are inconsistent by sub-proof % 179.92/24.83 | | | | | | | #1. % 179.92/24.83 | | | | | | | % 179.92/24.83 | | | | | | End of split % 179.92/24.83 | | | | | | % 179.92/24.83 | | | | | End of split % 179.92/24.83 | | | | | % 179.92/24.83 | | | | End of split % 179.92/24.83 | | | | % 179.92/24.83 | | | End of split % 179.92/24.83 | | | % 179.92/24.83 | | End of split % 179.92/24.83 | | % 179.92/24.83 | End of split % 179.92/24.83 | % 179.92/24.83 End of proof % 179.92/24.83 % 179.92/24.83 Sub-proof #1 shows that the following formulas are inconsistent: % 179.92/24.83 ---------------------------------------------------------------- % 179.92/24.83 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (relation_dom(v2) % 179.92/24.83 = v1) | ~ (relation_dom(v2) = v0)) % 179.92/24.83 (2) relation_dom(all_195_3) = all_253_0 % 179.92/24.83 (3) relation_dom(all_195_3) = empty_set % 179.92/24.83 (4) ~ (all_253_0 = empty_set) % 179.92/24.83 % 179.92/24.83 Begin of proof % 179.92/24.83 | % 179.92/24.83 | GROUND_INST: instantiating (1) with all_253_0, empty_set, all_195_3, % 179.92/24.83 | simplifying with (2), (3) gives: % 179.92/24.83 | (5) all_253_0 = empty_set % 179.92/24.83 | % 179.92/24.83 | REDUCE: (4), (5) imply: % 179.92/24.83 | (6) $false % 179.92/24.83 | % 179.92/24.83 | CLOSE: (6) is inconsistent. % 179.92/24.83 | % 179.92/24.83 End of proof % 179.92/24.83 % SZS output end Proof for theBenchmark % 179.92/24.83 % 179.92/24.83 24230ms %------------------------------------------------------------------------------