%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SEU197+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 : n014.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 17:43:12 EDT 2023 % Result : Theorem 259.72s 36.15s % Output : Proof 261.21s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.11 % Problem : SEU197+2 : TPTP v8.1.2. Released v3.3.0. % 0.00/0.12 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.12/0.33 % Computer : n014.cluster.edu % 0.12/0.33 % Model : x86_64 x86_64 % 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.33 % Memory : 8042.1875MB % 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.33 % CPULimit : 300 % 0.12/0.33 % WCLimit : 300 % 0.12/0.33 % DateTime : Wed Aug 23 19:13:19 EDT 2023 % 0.19/0.34 % CPUTime : % 0.19/0.61 ________ _____ % 0.19/0.61 ___ __ \_________(_)________________________________ % 0.19/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.19/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.19/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.19/0.61 % 0.19/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.19/0.61 (2023-06-19) % 0.19/0.61 % 0.19/0.61 (c) Philipp Rümmer, 2009-2023 % 0.19/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.19/0.61 Amanda Stjerna. % 0.19/0.61 Free software under BSD-3-Clause. % 0.19/0.61 % 0.19/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.19/0.61 % 0.19/0.61 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.19/0.62 Running up to 7 provers in parallel. % 0.19/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.19/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.19/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.19/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.19/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.19/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.19/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 4.66/1.52 Prover 4: Preprocessing ... % 4.66/1.52 Prover 1: Preprocessing ... % 4.66/1.56 Prover 3: Preprocessing ... % 4.66/1.56 Prover 0: Preprocessing ... % 4.66/1.56 Prover 5: Preprocessing ... % 4.66/1.56 Prover 2: Preprocessing ... % 4.66/1.58 Prover 6: Preprocessing ... % 16.98/3.12 Prover 1: Warning: ignoring some quantifiers % 17.59/3.19 Prover 3: Warning: ignoring some quantifiers % 18.15/3.25 Prover 1: Constructing countermodel ... % 18.15/3.25 Prover 3: Constructing countermodel ... % 18.15/3.27 Prover 5: Proving ... % 18.50/3.28 Prover 6: Proving ... % 19.79/3.47 Prover 4: Warning: ignoring some quantifiers % 19.79/3.58 Prover 0: Proving ... % 19.79/3.62 Prover 4: Constructing countermodel ... % 20.36/3.72 Prover 2: Proving ... % 71.93/10.35 Prover 2: stopped % 72.10/10.36 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 72.56/10.52 Prover 7: Preprocessing ... % 75.67/10.86 Prover 7: Warning: ignoring some quantifiers % 76.09/10.90 Prover 7: Constructing countermodel ... % 98.92/13.97 Prover 5: stopped % 98.92/13.97 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 99.30/14.17 Prover 8: Preprocessing ... % 103.02/14.48 Prover 8: Warning: ignoring some quantifiers % 103.41/14.52 Prover 8: Constructing countermodel ... % 114.45/15.98 Prover 1: stopped % 114.45/15.98 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889 % 115.15/16.05 Prover 9: Preprocessing ... % 119.99/16.68 Prover 9: Warning: ignoring some quantifiers % 119.99/16.71 Prover 9: Constructing countermodel ... % 128.66/17.90 Prover 6: stopped % 128.66/17.92 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 130.14/18.06 Prover 10: Preprocessing ... % 130.96/18.29 Prover 10: Warning: ignoring some quantifiers % 130.96/18.32 Prover 10: Constructing countermodel ... % 200.95/27.98 Prover 4: stopped % 200.95/27.99 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 201.38/28.10 Prover 11: Preprocessing ... % 205.56/28.63 Prover 11: Warning: ignoring some quantifiers % 206.36/28.68 Prover 11: Constructing countermodel ... % 217.83/30.32 Prover 7: stopped % 217.83/30.32 Prover 12: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=2024365391 % 218.83/30.41 Prover 12: Preprocessing ... % 221.73/30.85 Prover 12: Proving ... % 226.44/31.46 Prover 12: stopped % 226.44/31.46 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 226.77/31.54 Prover 13: Preprocessing ... % 229.09/31.80 Prover 13: Warning: ignoring some quantifiers % 229.09/31.84 Prover 13: Constructing countermodel ... % 258.94/36.01 Prover 10: Found proof (size 873) % 258.94/36.01 Prover 10: proved (18093ms) % 258.94/36.02 Prover 13: stopped % 259.48/36.02 Prover 0: stopped % 259.48/36.03 Prover 11: stopped % 259.48/36.03 Prover 3: stopped % 259.48/36.04 Prover 9: stopped % 259.72/36.15 Prover 8: stopped % 259.72/36.15 % 259.72/36.15 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 259.72/36.15 % 259.72/36.18 % SZS output start Proof for theBenchmark % 259.72/36.19 Assumptions after simplification: % 259.72/36.19 --------------------------------- % 259.72/36.19 % 259.72/36.19 (cc1_relat_1) % 259.72/36.20 ! [v0: $i] : ( ~ $i(v0) | ~ empty(v0) | relation(v0)) % 259.72/36.20 % 259.72/36.20 (d10_xboole_0) % 259.72/36.20 ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ $i(v1) | ~ $i(v0) | ~ subset(v1, % 259.72/36.20 v0) | ~ subset(v0, v1)) & ? [v0: $i] : ( ~ $i(v0) | subset(v0, v0)) % 259.72/36.20 % 259.72/36.20 (d12_relat_1) % 259.72/36.23 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 259.72/36.23 $i] : ( ~ (relation_rng_restriction(v0, v1) = v2) | ~ (ordered_pair(v3, v4) % 259.72/36.23 = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 259.72/36.23 relation(v2) | ~ relation(v1) | ~ in(v5, v2) | in(v5, v1)) & ! [v0: $i] : % 259.72/36.23 ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ % 259.72/36.23 (relation_rng_restriction(v0, v1) = v2) | ~ (ordered_pair(v3, v4) = v5) | % 259.72/36.23 ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ relation(v2) | % 259.72/36.23 ~ relation(v1) | ~ in(v5, v2) | in(v4, v0)) & ! [v0: $i] : ! [v1: $i] : % 259.72/36.23 ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ % 259.72/36.23 (relation_rng_restriction(v0, v1) = v2) | ~ (ordered_pair(v3, v4) = v5) | % 259.72/36.23 ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ relation(v2) | % 259.72/36.23 ~ relation(v1) | ~ in(v5, v1) | ~ in(v4, v0) | in(v5, v2)) & ! [v0: $i] % 259.72/36.23 : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v2 | ~ % 259.72/36.23 (relation_rng_restriction(v0, v1) = v2) | ~ $i(v3) | ~ $i(v1) | ~ $i(v0) % 259.72/36.23 | ~ relation(v3) | ~ relation(v1) | ? [v4: $i] : ? [v5: $i] : ? [v6: % 259.72/36.23 $i] : (ordered_pair(v4, v5) = v6 & $i(v6) & $i(v5) & $i(v4) & ( ~ in(v6, % 259.72/36.23 v3) | ~ in(v6, v1) | ~ in(v5, v0)) & (in(v6, v3) | (in(v6, v1) & % 259.72/36.23 in(v5, v0))))) % 259.72/36.23 % 259.72/36.23 (d1_xboole_0) % 259.72/36.23 $i(empty_set) & ! [v0: $i] : ( ~ $i(v0) | ~ in(v0, empty_set)) & ? [v0: $i] % 259.72/36.23 : (v0 = empty_set | ~ $i(v0) | ? [v1: $i] : ($i(v1) & in(v1, v0))) % 259.72/36.23 % 259.72/36.23 (d2_relat_1) % 259.72/36.23 ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ $i(v1) | ~ $i(v0) | ~ relation(v1) % 259.72/36.23 | ~ relation(v0) | ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 259.72/36.23 (ordered_pair(v2, v3) = v4 & $i(v4) & $i(v3) & $i(v2) & ( ~ in(v4, v1) | ~ % 259.72/36.23 in(v4, v0)) & (in(v4, v1) | in(v4, v0)))) % 259.72/36.23 % 259.72/36.23 (d3_relat_1) % 259.72/36.23 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 259.72/36.23 (ordered_pair(v2, v3) = v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) % 259.72/36.23 | ~ subset(v0, v1) | ~ relation(v1) | ~ relation(v0) | ~ in(v4, v0) | % 259.72/36.23 in(v4, v1)) & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ % 259.72/36.23 relation(v1) | ~ relation(v0) | subset(v0, v1) | ? [v2: $i] : ? [v3: $i] % 259.72/36.23 : ? [v4: $i] : (ordered_pair(v2, v3) = v4 & $i(v4) & $i(v3) & $i(v2) & % 259.72/36.23 in(v4, v0) & ~ in(v4, v1))) % 259.72/36.23 % 259.72/36.23 (d3_tarski) % 259.72/36.24 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 259.72/36.24 ~ subset(v0, v1) | ~ in(v2, v0) | in(v2, v1)) & ? [v0: $i] : ? [v1: $i] % 259.72/36.24 : ( ~ $i(v1) | ~ $i(v0) | subset(v0, v1) | ? [v2: $i] : ($i(v2) & in(v2, v0) % 259.72/36.24 & ~ in(v2, v1))) % 259.72/36.24 % 259.72/36.24 (d5_relat_1) % 259.72/36.24 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 259.72/36.24 (relation_rng(v0) = v1) | ~ (ordered_pair(v3, v2) = v4) | ~ $i(v3) | ~ % 259.72/36.24 $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ relation(v0) | ~ in(v4, v0) | in(v2, % 259.72/36.24 v1)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (relation_rng(v0) = % 259.72/36.24 v1) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ relation(v0) | ~ in(v2, v1) % 259.72/36.24 | ? [v3: $i] : ? [v4: $i] : (ordered_pair(v3, v2) = v4 & $i(v4) & $i(v3) & % 259.72/36.24 in(v4, v0))) & ? [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v0 | ~ % 259.72/36.24 (relation_rng(v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ relation(v1) | ? [v3: % 259.72/36.24 $i] : ? [v4: $i] : ? [v5: $i] : ($i(v4) & $i(v3) & ( ~ in(v3, v0) | ! % 259.72/36.24 [v6: $i] : ! [v7: $i] : ( ~ (ordered_pair(v6, v3) = v7) | ~ $i(v6) | % 259.72/36.24 ~ in(v7, v1))) & (in(v3, v0) | (ordered_pair(v4, v3) = v5 & $i(v5) & % 259.72/36.24 in(v5, v1))))) % 259.72/36.24 % 259.72/36.24 (dt_k8_relat_1) % 259.72/36.24 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (relation_rng_restriction(v0, % 259.72/36.24 v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ relation(v1) | relation(v2)) % 259.72/36.24 % 259.72/36.24 (fc4_relat_1) % 259.72/36.24 $i(empty_set) & relation(empty_set) & empty(empty_set) % 259.72/36.24 % 259.72/36.24 (rc1_relat_1) % 259.72/36.24 ? [v0: $i] : ($i(v0) & relation(v0) & empty(v0)) % 259.72/36.24 % 259.72/36.24 (rc1_xboole_0) % 259.72/36.24 ? [v0: $i] : ($i(v0) & empty(v0)) % 259.72/36.24 % 259.72/36.24 (rc2_relat_1) % 259.72/36.24 ? [v0: $i] : ($i(v0) & relation(v0) & ~ empty(v0)) % 259.72/36.24 % 259.72/36.24 (rc2_subset_1) % 259.72/36.24 ! [v0: $i] : ! [v1: $i] : ( ~ (powerset(v0) = v1) | ~ $i(v0) | ? [v2: $i] % 259.72/36.24 : ($i(v2) & element(v2, v1) & empty(v2))) % 259.72/36.24 % 259.72/36.24 (t115_relat_1) % 259.72/36.25 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: % 259.72/36.25 $i] : (relation_rng(v3) = v4 & relation_rng_restriction(v1, v2) = v3 & % 259.72/36.25 $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & relation(v2) & % 259.72/36.25 ((relation_rng(v2) = v5 & $i(v5) & in(v0, v5) & in(v0, v1) & ~ in(v0, v4)) % 259.72/36.25 | (in(v0, v4) & ( ~ in(v0, v1) | (relation_rng(v2) = v5 & $i(v5) & ~ % 259.72/36.25 in(v0, v5)))))) % 259.72/36.25 % 259.72/36.25 (t1_zfmisc_1) % 259.72/36.25 $i(empty_set) & ? [v0: $i] : (powerset(empty_set) = v0 & singleton(empty_set) % 259.72/36.25 = v0 & $i(v0)) % 259.72/36.25 % 259.72/36.25 (t25_relat_1) % 259.72/36.25 ! [v0: $i] : ! [v1: $i] : ( ~ (relation_rng(v0) = v1) | ~ $i(v0) | ~ % 259.72/36.25 relation(v0) | ? [v2: $i] : (relation_dom(v0) = v2 & $i(v2) & ! [v3: $i] : % 259.72/36.25 ! [v4: $i] : ( ~ (relation_rng(v3) = v4) | ~ $i(v3) | ~ subset(v0, v3) % 259.72/36.25 | ~ relation(v3) | subset(v1, v4)) & ! [v3: $i] : ! [v4: $i] : ( ~ % 259.72/36.25 (relation_rng(v3) = v4) | ~ $i(v3) | ~ subset(v0, v3) | ~ % 259.72/36.25 relation(v3) | ? [v5: $i] : (relation_dom(v3) = v5 & $i(v5) & % 259.72/36.25 subset(v2, v5))))) % 259.72/36.25 % 259.72/36.25 (t3_xboole_1) % 259.72/36.25 $i(empty_set) & ! [v0: $i] : (v0 = empty_set | ~ $i(v0) | ~ subset(v0, % 259.72/36.25 empty_set)) % 259.72/36.25 % 259.72/36.25 (t46_relat_1) % 259.72/36.25 ! [v0: $i] : ! [v1: $i] : ( ~ (relation_rng(v0) = v1) | ~ $i(v0) | ~ % 259.72/36.25 relation(v0) | ? [v2: $i] : (relation_dom(v0) = v2 & $i(v2) & ! [v3: $i] : % 259.72/36.25 ! [v4: $i] : ( ~ (relation_composition(v0, v3) = v4) | ~ $i(v3) | ~ % 259.72/36.25 relation(v3) | ? [v5: $i] : ? [v6: $i] : ((v6 = v2 & relation_dom(v4) % 259.72/36.25 = v2) | (relation_dom(v3) = v5 & $i(v5) & ~ subset(v1, v5)))))) % 259.72/36.25 % 259.72/36.25 (t47_relat_1) % 260.03/36.25 ! [v0: $i] : ! [v1: $i] : ( ~ (relation_rng(v0) = v1) | ~ $i(v0) | ~ % 260.03/36.25 relation(v0) | ? [v2: $i] : (relation_dom(v0) = v2 & $i(v2) & ! [v3: $i] : % 260.03/36.25 ! [v4: $i] : ( ~ (relation_composition(v3, v0) = v4) | ~ $i(v3) | ~ % 260.03/36.25 relation(v3) | ? [v5: $i] : ? [v6: $i] : ((v6 = v1 & relation_rng(v4) % 260.03/36.25 = v1 & $i(v1)) | (relation_rng(v3) = v5 & $i(v5) & ~ subset(v2, % 260.03/36.25 v5)))))) % 260.03/36.25 % 260.03/36.25 (t56_relat_1) % 260.03/36.25 $i(empty_set) & ! [v0: $i] : (v0 = empty_set | ~ $i(v0) | ~ relation(v0) | % 260.03/36.25 ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : (ordered_pair(v1, v2) = v3 & $i(v3) % 260.03/36.25 & $i(v2) & $i(v1) & in(v3, v0))) % 260.03/36.25 % 260.03/36.25 (t60_relat_1) % 260.03/36.25 relation_rng(empty_set) = empty_set & relation_dom(empty_set) = empty_set & % 260.03/36.25 $i(empty_set) % 260.03/36.25 % 260.03/36.25 (t64_relat_1) % 260.03/36.26 $i(empty_set) & ! [v0: $i] : ! [v1: $i] : (v0 = empty_set | ~ % 260.03/36.26 (relation_rng(v0) = v1) | ~ $i(v0) | ~ relation(v0) | ? [v2: $i] : ( ~ % 260.03/36.26 (v2 = empty_set) & relation_dom(v0) = v2 & $i(v2))) & ! [v0: $i] : (v0 = % 260.03/36.26 empty_set | ~ (relation_rng(v0) = empty_set) | ~ $i(v0) | ~ relation(v0)) % 260.03/36.26 % 260.03/36.26 (t65_relat_1) % 260.03/36.26 $i(empty_set) & ! [v0: $i] : ! [v1: $i] : ( ~ (relation_rng(v0) = v1) | ~ % 260.03/36.26 $i(v0) | ~ relation(v0) | ? [v2: $i] : (( ~ (v1 = empty_set) | (v2 = % 260.03/36.26 empty_set & relation_dom(v0) = empty_set)) & (v1 = empty_set | ( ~ (v2 % 260.03/36.26 = empty_set) & relation_dom(v0) = v2 & $i(v2))))) % 260.03/36.26 % 260.03/36.26 (t6_boole) % 260.03/36.26 $i(empty_set) & ! [v0: $i] : (v0 = empty_set | ~ $i(v0) | ~ empty(v0)) % 260.03/36.26 % 260.03/36.26 (t8_boole) % 260.03/36.26 ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ $i(v1) | ~ $i(v0) | ~ empty(v1) | % 260.03/36.26 ~ empty(v0)) % 260.03/36.26 % 260.03/36.26 (function-axioms) % 260.03/36.27 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 % 260.03/36.27 | ~ (subset_difference(v4, v3, v2) = v1) | ~ (subset_difference(v4, v3, % 260.03/36.27 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 % 260.03/36.27 = v0 | ~ (meet_of_subsets(v3, v2) = v1) | ~ (meet_of_subsets(v3, v2) = % 260.03/36.27 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | % 260.03/36.27 ~ (union_of_subsets(v3, v2) = v1) | ~ (union_of_subsets(v3, v2) = v0)) & ! % 260.03/36.27 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 260.03/36.27 (complements_of_subsets(v3, v2) = v1) | ~ (complements_of_subsets(v3, v2) = % 260.03/36.27 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | % 260.03/36.27 ~ (relation_composition(v3, v2) = v1) | ~ (relation_composition(v3, v2) = % 260.03/36.27 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | % 260.03/36.27 ~ (subset_complement(v3, v2) = v1) | ~ (subset_complement(v3, v2) = v0)) & % 260.03/36.27 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 260.03/36.27 (set_difference(v3, v2) = v1) | ~ (set_difference(v3, v2) = v0)) & ! [v0: % 260.03/36.27 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 260.03/36.27 (cartesian_product2(v3, v2) = v1) | ~ (cartesian_product2(v3, v2) = v0)) & % 260.03/36.27 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 260.03/36.27 (relation_rng_restriction(v3, v2) = v1) | ~ (relation_rng_restriction(v3, % 260.03/36.27 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 % 260.03/36.27 = v0 | ~ (relation_dom_restriction(v3, v2) = v1) | ~ % 260.03/36.27 (relation_dom_restriction(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 260.03/36.27 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (ordered_pair(v3, v2) = v1) | ~ % 260.03/36.27 (ordered_pair(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 260.03/36.27 [v3: $i] : (v1 = v0 | ~ (set_intersection2(v3, v2) = v1) | ~ % 260.03/36.27 (set_intersection2(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 260.03/36.27 : ! [v3: $i] : (v1 = v0 | ~ (set_union2(v3, v2) = v1) | ~ (set_union2(v3, % 260.03/36.27 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 % 260.03/36.27 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) % 260.03/36.27 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 260.03/36.27 (relation_inverse(v2) = v1) | ~ (relation_inverse(v2) = v0)) & ! [v0: $i] % 260.03/36.27 : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (relation_field(v2) = v1) | ~ % 260.03/36.27 (relation_field(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = % 260.03/36.27 v0 | ~ (relation_rng(v2) = v1) | ~ (relation_rng(v2) = v0)) & ! [v0: $i] % 260.03/36.27 : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (union(v2) = v1) | ~ (union(v2) = % 260.03/36.27 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 260.03/36.27 (cast_to_subset(v2) = v1) | ~ (cast_to_subset(v2) = v0)) & ! [v0: $i] : ! % 260.03/36.27 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (relation_dom(v2) = v1) | ~ % 260.03/36.27 (relation_dom(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = % 260.03/36.27 v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0)) & ! [v0: $i] : ! % 260.03/36.27 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ % 260.03/36.27 (singleton(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | % 260.03/36.27 ~ (set_meet(v2) = v1) | ~ (set_meet(v2) = v0)) & ! [v0: $i] : ! [v1: $i] % 260.03/36.27 : ! [v2: $i] : (v1 = v0 | ~ (identity_relation(v2) = v1) | ~ % 260.03/36.27 (identity_relation(v2) = v0)) % 260.03/36.27 % 260.03/36.27 Further assumptions not needed in the proof: % 260.03/36.27 -------------------------------------------- % 260.03/36.27 antisymmetry_r2_hidden, antisymmetry_r2_xboole_0, commutativity_k2_tarski, % 260.03/36.27 commutativity_k2_xboole_0, commutativity_k3_xboole_0, d10_relat_1, d11_relat_1, % 260.03/36.27 d1_relat_1, d1_setfam_1, d1_tarski, d1_zfmisc_1, d2_subset_1, d2_tarski, % 260.03/36.27 d2_xboole_0, d2_zfmisc_1, d3_xboole_0, d4_relat_1, d4_subset_1, d4_tarski, % 260.03/36.27 d4_xboole_0, d5_subset_1, d5_tarski, d6_relat_1, d7_relat_1, d7_xboole_0, % 260.03/36.27 d8_relat_1, d8_setfam_1, d8_xboole_0, dt_k1_relat_1, dt_k1_setfam_1, % 260.03/36.27 dt_k1_tarski, dt_k1_xboole_0, dt_k1_zfmisc_1, dt_k2_relat_1, dt_k2_subset_1, % 260.03/36.27 dt_k2_tarski, dt_k2_xboole_0, dt_k2_zfmisc_1, dt_k3_relat_1, dt_k3_subset_1, % 260.03/36.27 dt_k3_tarski, dt_k3_xboole_0, dt_k4_relat_1, dt_k4_tarski, dt_k4_xboole_0, % 260.03/36.27 dt_k5_relat_1, dt_k5_setfam_1, dt_k6_relat_1, dt_k6_setfam_1, dt_k6_subset_1, % 260.03/36.27 dt_k7_relat_1, dt_k7_setfam_1, dt_m1_subset_1, existence_m1_subset_1, % 260.03/36.27 fc10_relat_1, fc1_relat_1, fc1_subset_1, fc1_xboole_0, fc1_zfmisc_1, % 260.03/36.27 fc2_relat_1, fc2_subset_1, fc2_xboole_0, fc3_subset_1, fc3_xboole_0, % 260.03/36.27 fc4_subset_1, fc5_relat_1, fc6_relat_1, fc7_relat_1, fc8_relat_1, fc9_relat_1, % 260.03/36.27 idempotence_k2_xboole_0, idempotence_k3_xboole_0, involutiveness_k3_subset_1, % 260.03/36.27 involutiveness_k4_relat_1, involutiveness_k7_setfam_1, % 260.03/36.27 irreflexivity_r2_xboole_0, l1_zfmisc_1, l23_zfmisc_1, l25_zfmisc_1, % 260.03/36.27 l28_zfmisc_1, l2_zfmisc_1, l32_xboole_1, l3_subset_1, l3_zfmisc_1, l4_zfmisc_1, % 260.03/36.27 l50_zfmisc_1, l55_zfmisc_1, l71_subset_1, rc1_subset_1, rc2_xboole_0, % 260.03/36.27 redefinition_k5_setfam_1, redefinition_k6_setfam_1, redefinition_k6_subset_1, % 260.03/36.27 reflexivity_r1_tarski, symmetry_r1_xboole_0, t106_zfmisc_1, t10_zfmisc_1, % 260.03/36.27 t118_zfmisc_1, t119_zfmisc_1, t12_xboole_1, t136_zfmisc_1, t17_xboole_1, % 260.03/36.27 t19_xboole_1, t1_boole, t1_subset, t1_xboole_1, t20_relat_1, t21_relat_1, % 260.03/36.27 t26_xboole_1, t28_xboole_1, t2_boole, t2_subset, t2_tarski, t2_xboole_1, % 260.03/36.27 t30_relat_1, t33_xboole_1, t33_zfmisc_1, t36_xboole_1, t37_relat_1, % 260.03/36.27 t37_xboole_1, t37_zfmisc_1, t38_zfmisc_1, t39_xboole_1, t39_zfmisc_1, t3_boole, % 260.03/36.27 t3_subset, t3_xboole_0, t40_xboole_1, t43_subset_1, t44_relat_1, t45_relat_1, % 260.03/36.27 t45_xboole_1, t46_setfam_1, t46_zfmisc_1, t47_setfam_1, t48_setfam_1, % 260.03/36.27 t48_xboole_1, t4_boole, t4_subset, t4_xboole_0, t50_subset_1, t54_subset_1, % 260.03/36.27 t5_subset, t60_xboole_1, t63_xboole_1, t65_zfmisc_1, t69_enumset1, t6_zfmisc_1, % 260.03/36.27 t71_relat_1, t74_relat_1, t7_boole, t7_xboole_1, t83_xboole_1, t86_relat_1, % 260.03/36.27 t88_relat_1, t8_xboole_1, t8_zfmisc_1, t90_relat_1, t92_zfmisc_1, t94_relat_1, % 260.03/36.27 t99_relat_1, t99_zfmisc_1, t9_tarski, t9_zfmisc_1 % 260.03/36.27 % 260.03/36.27 Those formulas are unsatisfiable: % 260.03/36.27 --------------------------------- % 260.03/36.27 % 260.03/36.27 Begin of proof % 260.03/36.27 | % 260.03/36.27 | ALPHA: (d10_xboole_0) implies: % 260.03/36.27 | (1) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ $i(v1) | ~ $i(v0) | ~ % 260.03/36.27 | subset(v1, v0) | ~ subset(v0, v1)) % 260.03/36.27 | % 260.03/36.27 | ALPHA: (d12_relat_1) implies: % 260.03/36.27 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v2 | ~ % 260.03/36.27 | (relation_rng_restriction(v0, v1) = v2) | ~ $i(v3) | ~ $i(v1) | ~ % 260.03/36.27 | $i(v0) | ~ relation(v3) | ~ relation(v1) | ? [v4: $i] : ? [v5: % 260.03/36.27 | $i] : ? [v6: $i] : (ordered_pair(v4, v5) = v6 & $i(v6) & $i(v5) & % 260.03/36.27 | $i(v4) & ( ~ in(v6, v3) | ~ in(v6, v1) | ~ in(v5, v0)) & (in(v6, % 260.03/36.27 | v3) | (in(v6, v1) & in(v5, v0))))) % 260.03/36.28 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 260.03/36.28 | ! [v5: $i] : ( ~ (relation_rng_restriction(v0, v1) = v2) | ~ % 260.03/36.28 | (ordered_pair(v3, v4) = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ % 260.03/36.28 | $i(v1) | ~ $i(v0) | ~ relation(v2) | ~ relation(v1) | ~ in(v5, % 260.03/36.28 | v1) | ~ in(v4, v0) | in(v5, v2)) % 260.03/36.28 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 260.03/36.28 | ! [v5: $i] : ( ~ (relation_rng_restriction(v0, v1) = v2) | ~ % 260.03/36.28 | (ordered_pair(v3, v4) = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ % 260.03/36.28 | $i(v1) | ~ $i(v0) | ~ relation(v2) | ~ relation(v1) | ~ in(v5, % 260.03/36.28 | v2) | in(v4, v0)) % 260.03/36.28 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 260.03/36.28 | ! [v5: $i] : ( ~ (relation_rng_restriction(v0, v1) = v2) | ~ % 260.03/36.28 | (ordered_pair(v3, v4) = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ % 260.03/36.28 | $i(v1) | ~ $i(v0) | ~ relation(v2) | ~ relation(v1) | ~ in(v5, % 260.03/36.28 | v2) | in(v5, v1)) % 260.03/36.28 | % 260.03/36.28 | ALPHA: (d1_xboole_0) implies: % 260.03/36.28 | (6) ! [v0: $i] : ( ~ $i(v0) | ~ in(v0, empty_set)) % 260.03/36.28 | % 260.03/36.28 | ALPHA: (d3_relat_1) implies: % 260.03/36.28 | (7) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ relation(v1) | % 260.03/36.28 | ~ relation(v0) | subset(v0, v1) | ? [v2: $i] : ? [v3: $i] : ? [v4: % 260.03/36.28 | $i] : (ordered_pair(v2, v3) = v4 & $i(v4) & $i(v3) & $i(v2) & % 260.03/36.28 | in(v4, v0) & ~ in(v4, v1))) % 260.55/36.28 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( % 260.55/36.28 | ~ (ordered_pair(v2, v3) = v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | % 260.55/36.28 | ~ $i(v0) | ~ subset(v0, v1) | ~ relation(v1) | ~ relation(v0) | ~ % 260.55/36.28 | in(v4, v0) | in(v4, v1)) % 260.55/36.28 | % 260.55/36.28 | ALPHA: (d3_tarski) implies: % 260.55/36.28 | (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ % 260.55/36.28 | $i(v0) | ~ subset(v0, v1) | ~ in(v2, v0) | in(v2, v1)) % 260.55/36.28 | % 260.55/36.28 | ALPHA: (d5_relat_1) implies: % 260.55/36.28 | (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (relation_rng(v0) = v1) % 260.55/36.28 | | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ relation(v0) | ~ in(v2, % 260.55/36.28 | v1) | ? [v3: $i] : ? [v4: $i] : (ordered_pair(v3, v2) = v4 & % 260.55/36.28 | $i(v4) & $i(v3) & in(v4, v0))) % 260.55/36.28 | (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 260.55/36.28 | ( ~ (relation_rng(v0) = v1) | ~ (ordered_pair(v3, v2) = v4) | ~ % 260.55/36.28 | $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ relation(v0) | ~ % 260.55/36.28 | in(v4, v0) | in(v2, v1)) % 260.55/36.28 | % 260.55/36.28 | ALPHA: (fc4_relat_1) implies: % 260.55/36.28 | (12) relation(empty_set) % 260.55/36.28 | % 260.55/36.28 | ALPHA: (t1_zfmisc_1) implies: % 260.55/36.28 | (13) ? [v0: $i] : (powerset(empty_set) = v0 & singleton(empty_set) = v0 & % 260.55/36.28 | $i(v0)) % 260.55/36.28 | % 260.55/36.28 | ALPHA: (t3_xboole_1) implies: % 260.55/36.28 | (14) ! [v0: $i] : (v0 = empty_set | ~ $i(v0) | ~ subset(v0, empty_set)) % 260.55/36.28 | % 260.55/36.28 | ALPHA: (t56_relat_1) implies: % 260.55/36.29 | (15) ! [v0: $i] : (v0 = empty_set | ~ $i(v0) | ~ relation(v0) | ? [v1: % 260.55/36.29 | $i] : ? [v2: $i] : ? [v3: $i] : (ordered_pair(v1, v2) = v3 & % 260.55/36.29 | $i(v3) & $i(v2) & $i(v1) & in(v3, v0))) % 260.55/36.29 | % 260.55/36.29 | ALPHA: (t60_relat_1) implies: % 260.55/36.29 | (16) relation_dom(empty_set) = empty_set % 260.55/36.29 | (17) relation_rng(empty_set) = empty_set % 260.55/36.29 | % 260.55/36.29 | ALPHA: (t64_relat_1) implies: % 260.55/36.29 | (18) ! [v0: $i] : ! [v1: $i] : (v0 = empty_set | ~ (relation_rng(v0) = % 260.55/36.29 | v1) | ~ $i(v0) | ~ relation(v0) | ? [v2: $i] : ( ~ (v2 = % 260.55/36.29 | empty_set) & relation_dom(v0) = v2 & $i(v2))) % 260.55/36.29 | % 260.55/36.29 | ALPHA: (t65_relat_1) implies: % 260.55/36.29 | (19) ! [v0: $i] : ! [v1: $i] : ( ~ (relation_rng(v0) = v1) | ~ $i(v0) | % 260.55/36.29 | ~ relation(v0) | ? [v2: $i] : (( ~ (v1 = empty_set) | (v2 = % 260.55/36.29 | empty_set & relation_dom(v0) = empty_set)) & (v1 = empty_set | % 260.55/36.29 | ( ~ (v2 = empty_set) & relation_dom(v0) = v2 & $i(v2))))) % 260.55/36.29 | % 260.55/36.29 | ALPHA: (t6_boole) implies: % 260.55/36.29 | (20) $i(empty_set) % 260.55/36.29 | (21) ! [v0: $i] : (v0 = empty_set | ~ $i(v0) | ~ empty(v0)) % 260.55/36.29 | % 260.55/36.29 | ALPHA: (function-axioms) implies: % 260.55/36.29 | (22) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 260.55/36.29 | (relation_dom(v2) = v1) | ~ (relation_dom(v2) = v0)) % 260.55/36.29 | (23) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 260.55/36.29 | (relation_rng(v2) = v1) | ~ (relation_rng(v2) = v0)) % 260.55/36.29 | % 260.55/36.29 | DELTA: instantiating (rc1_xboole_0) with fresh symbol all_165_0 gives: % 260.55/36.29 | (24) $i(all_165_0) & empty(all_165_0) % 260.55/36.29 | % 260.55/36.29 | ALPHA: (24) implies: % 260.55/36.29 | (25) empty(all_165_0) % 260.55/36.29 | (26) $i(all_165_0) % 260.55/36.29 | % 260.55/36.29 | DELTA: instantiating (13) with fresh symbol all_168_0 gives: % 260.55/36.29 | (27) powerset(empty_set) = all_168_0 & singleton(empty_set) = all_168_0 & % 260.55/36.29 | $i(all_168_0) % 260.55/36.29 | % 260.55/36.29 | ALPHA: (27) implies: % 260.55/36.29 | (28) powerset(empty_set) = all_168_0 % 260.55/36.29 | % 260.55/36.29 | DELTA: instantiating (rc1_relat_1) with fresh symbol all_170_0 gives: % 260.55/36.29 | (29) $i(all_170_0) & relation(all_170_0) & empty(all_170_0) % 260.55/36.29 | % 260.55/36.29 | ALPHA: (29) implies: % 260.55/36.29 | (30) empty(all_170_0) % 260.55/36.29 | (31) relation(all_170_0) % 260.55/36.29 | (32) $i(all_170_0) % 260.55/36.29 | % 260.55/36.29 | DELTA: instantiating (rc2_relat_1) with fresh symbol all_172_0 gives: % 260.55/36.29 | (33) $i(all_172_0) & relation(all_172_0) & ~ empty(all_172_0) % 260.55/36.29 | % 260.55/36.29 | ALPHA: (33) implies: % 260.55/36.29 | (34) ~ empty(all_172_0) % 260.55/36.29 | (35) relation(all_172_0) % 260.55/36.29 | (36) $i(all_172_0) % 260.55/36.29 | % 260.55/36.29 | DELTA: instantiating (t115_relat_1) with fresh symbols all_207_0, all_207_1, % 260.55/36.29 | all_207_2, all_207_3, all_207_4, all_207_5 gives: % 260.55/36.29 | (37) relation_rng(all_207_2) = all_207_1 & % 260.55/36.29 | relation_rng_restriction(all_207_4, all_207_3) = all_207_2 & % 260.55/36.29 | $i(all_207_1) & $i(all_207_2) & $i(all_207_3) & $i(all_207_4) & % 260.55/36.29 | $i(all_207_5) & relation(all_207_3) & ((relation_rng(all_207_3) = % 260.55/36.29 | all_207_0 & $i(all_207_0) & in(all_207_5, all_207_0) & % 260.55/36.29 | in(all_207_5, all_207_4) & ~ in(all_207_5, all_207_1)) | % 260.55/36.29 | (in(all_207_5, all_207_1) & ( ~ in(all_207_5, all_207_4) | % 260.55/36.29 | (relation_rng(all_207_3) = all_207_0 & $i(all_207_0) & ~ % 260.55/36.29 | in(all_207_5, all_207_0))))) % 260.55/36.29 | % 260.55/36.29 | ALPHA: (37) implies: % 260.55/36.30 | (38) relation(all_207_3) % 260.55/36.30 | (39) $i(all_207_5) % 260.55/36.30 | (40) $i(all_207_4) % 260.55/36.30 | (41) $i(all_207_3) % 260.55/36.30 | (42) $i(all_207_2) % 260.55/36.30 | (43) $i(all_207_1) % 260.55/36.30 | (44) relation_rng_restriction(all_207_4, all_207_3) = all_207_2 % 260.55/36.30 | (45) relation_rng(all_207_2) = all_207_1 % 260.55/36.30 | (46) (relation_rng(all_207_3) = all_207_0 & $i(all_207_0) & in(all_207_5, % 260.55/36.30 | all_207_0) & in(all_207_5, all_207_4) & ~ in(all_207_5, % 260.55/36.30 | all_207_1)) | (in(all_207_5, all_207_1) & ( ~ in(all_207_5, % 260.55/36.30 | all_207_4) | (relation_rng(all_207_3) = all_207_0 & % 260.55/36.30 | $i(all_207_0) & ~ in(all_207_5, all_207_0)))) % 260.55/36.30 | % 260.55/36.30 | GROUND_INST: instantiating (cc1_relat_1) with all_165_0, simplifying with % 260.55/36.30 | (25), (26) gives: % 260.55/36.30 | (47) relation(all_165_0) % 260.55/36.30 | % 260.55/36.30 | GROUND_INST: instantiating (t8_boole) with all_165_0, all_170_0, simplifying % 260.55/36.30 | with (25), (26), (30), (32) gives: % 260.55/36.30 | (48) all_170_0 = all_165_0 % 260.55/36.30 | % 260.55/36.30 | GROUND_INST: instantiating (21) with all_170_0, simplifying with (30), (32) % 260.55/36.30 | gives: % 260.55/36.30 | (49) all_170_0 = empty_set % 260.55/36.30 | % 260.55/36.30 | GROUND_INST: instantiating (d2_relat_1) with all_170_0, all_172_0, simplifying % 260.55/36.30 | with (31), (32), (35), (36) gives: % 260.55/36.30 | (50) all_172_0 = all_170_0 | ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 260.55/36.30 | (ordered_pair(v0, v1) = v2 & $i(v2) & $i(v1) & $i(v0) & ( ~ in(v2, % 260.55/36.30 | all_172_0) | ~ in(v2, all_170_0)) & (in(v2, all_172_0) | in(v2, % 260.55/36.30 | all_170_0))) % 260.55/36.30 | % 260.55/36.30 | GROUND_INST: instantiating (7) with all_170_0, all_172_0, simplifying with % 260.55/36.30 | (31), (32), (35), (36) gives: % 260.55/36.30 | (51) subset(all_170_0, all_172_0) | ? [v0: $i] : ? [v1: $i] : ? [v2: $i] % 260.55/36.30 | : (ordered_pair(v0, v1) = v2 & $i(v2) & $i(v1) & $i(v0) & in(v2, % 260.55/36.30 | all_170_0) & ~ in(v2, all_172_0)) % 260.55/36.30 | % 260.55/36.30 | GROUND_INST: instantiating (7) with empty_set, all_172_0, simplifying with % 260.55/36.30 | (12), (20), (35), (36) gives: % 260.55/36.30 | (52) subset(empty_set, all_172_0) | ? [v0: $i] : ? [v1: $i] : ? [v2: $i] % 260.55/36.30 | : (ordered_pair(v0, v1) = v2 & $i(v2) & $i(v1) & $i(v0) & in(v2, % 260.55/36.30 | empty_set) & ~ in(v2, all_172_0)) % 260.55/36.30 | % 260.55/36.30 | GROUND_INST: instantiating (7) with all_172_0, empty_set, simplifying with % 260.55/36.30 | (12), (20), (35), (36) gives: % 260.55/36.30 | (53) subset(all_172_0, empty_set) | ? [v0: $i] : ? [v1: $i] : ? [v2: $i] % 260.55/36.30 | : (ordered_pair(v0, v1) = v2 & $i(v2) & $i(v1) & $i(v0) & in(v2, % 260.55/36.30 | all_172_0) & ~ in(v2, empty_set)) % 260.55/36.30 | % 260.55/36.30 | GROUND_INST: instantiating (15) with all_172_0, simplifying with (35), (36) % 260.55/36.30 | gives: % 260.55/36.31 | (54) all_172_0 = empty_set | ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 260.55/36.31 | (ordered_pair(v0, v1) = v2 & $i(v2) & $i(v1) & $i(v0) & in(v2, % 260.55/36.31 | all_172_0)) % 260.55/36.31 | % 260.55/36.31 | GROUND_INST: instantiating (7) with all_207_3, all_207_3, simplifying with % 260.55/36.31 | (38), (41) gives: % 260.55/36.31 | (55) subset(all_207_3, all_207_3) % 260.55/36.31 | % 260.55/36.31 | GROUND_INST: instantiating (d2_relat_1) with all_172_0, all_207_3, simplifying % 260.55/36.31 | with (35), (36), (38), (41) gives: % 260.55/36.31 | (56) all_207_3 = all_172_0 | ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 260.55/36.31 | (ordered_pair(v0, v1) = v2 & $i(v2) & $i(v1) & $i(v0) & ( ~ in(v2, % 260.55/36.31 | all_207_3) | ~ in(v2, all_172_0)) & (in(v2, all_207_3) | in(v2, % 260.55/36.31 | all_172_0))) % 260.55/36.31 | % 260.55/36.31 | GROUND_INST: instantiating (7) with all_172_0, all_207_3, simplifying with % 260.55/36.31 | (35), (36), (38), (41) gives: % 260.55/36.31 | (57) subset(all_172_0, all_207_3) | ? [v0: $i] : ? [v1: $i] : ? [v2: $i] % 260.55/36.31 | : (ordered_pair(v0, v1) = v2 & $i(v2) & $i(v1) & $i(v0) & in(v2, % 260.55/36.31 | all_172_0) & ~ in(v2, all_207_3)) % 260.55/36.31 | % 260.55/36.31 | GROUND_INST: instantiating (7) with all_207_3, all_172_0, simplifying with % 260.55/36.31 | (35), (36), (38), (41) gives: % 260.55/36.31 | (58) subset(all_207_3, all_172_0) | ? [v0: $i] : ? [v1: $i] : ? [v2: $i] % 260.55/36.31 | : (ordered_pair(v0, v1) = v2 & $i(v2) & $i(v1) & $i(v0) & in(v2, % 260.55/36.31 | all_207_3) & ~ in(v2, all_172_0)) % 260.55/36.31 | % 260.55/36.31 | GROUND_INST: instantiating (d2_relat_1) with all_170_0, all_207_3, simplifying % 260.55/36.31 | with (31), (32), (38), (41) gives: % 260.55/36.31 | (59) all_207_3 = all_170_0 | ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 260.55/36.31 | (ordered_pair(v0, v1) = v2 & $i(v2) & $i(v1) & $i(v0) & ( ~ in(v2, % 260.55/36.31 | all_207_3) | ~ in(v2, all_170_0)) & (in(v2, all_207_3) | in(v2, % 260.55/36.31 | all_170_0))) % 260.55/36.31 | % 260.55/36.31 | GROUND_INST: instantiating (7) with all_207_3, all_170_0, simplifying with % 260.55/36.31 | (31), (32), (38), (41) gives: % 260.55/36.31 | (60) subset(all_207_3, all_170_0) | ? [v0: $i] : ? [v1: $i] : ? [v2: $i] % 260.55/36.31 | : (ordered_pair(v0, v1) = v2 & $i(v2) & $i(v1) & $i(v0) & in(v2, % 260.55/36.31 | all_207_3) & ~ in(v2, all_170_0)) % 260.55/36.31 | % 260.55/36.31 | GROUND_INST: instantiating (d2_relat_1) with empty_set, all_207_3, simplifying % 260.55/36.31 | with (12), (20), (38), (41) gives: % 260.55/36.32 | (61) all_207_3 = empty_set | ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 260.55/36.32 | (ordered_pair(v0, v1) = v2 & $i(v2) & $i(v1) & $i(v0) & ( ~ in(v2, % 260.55/36.32 | all_207_3) | ~ in(v2, empty_set)) & (in(v2, all_207_3) | in(v2, % 260.55/36.32 | empty_set))) % 260.55/36.32 | % 260.55/36.32 | GROUND_INST: instantiating (7) with empty_set, all_207_3, simplifying with % 260.55/36.32 | (12), (20), (38), (41) gives: % 260.55/36.32 | (62) subset(empty_set, all_207_3) | ? [v0: $i] : ? [v1: $i] : ? [v2: $i] % 260.55/36.32 | : (ordered_pair(v0, v1) = v2 & $i(v2) & $i(v1) & $i(v0) & in(v2, % 260.55/36.32 | empty_set) & ~ in(v2, all_207_3)) % 260.55/36.32 | % 260.55/36.32 | GROUND_INST: instantiating (15) with all_207_3, simplifying with (38), (41) % 260.55/36.32 | gives: % 260.55/36.32 | (63) all_207_3 = empty_set | ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 260.55/36.32 | (ordered_pair(v0, v1) = v2 & $i(v2) & $i(v1) & $i(v0) & in(v2, % 260.55/36.32 | all_207_3)) % 260.55/36.32 | % 260.55/36.32 | GROUND_INST: instantiating (2) with all_207_4, all_207_3, all_207_2, % 260.55/36.32 | all_207_3, simplifying with (38), (40), (41), (44) gives: % 260.55/36.32 | (64) all_207_2 = all_207_3 | ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 260.55/36.32 | (ordered_pair(v0, v1) = v2 & $i(v2) & $i(v1) & $i(v0) & in(v2, % 260.55/36.32 | all_207_3) & ~ in(v1, all_207_4)) % 260.55/36.32 | % 260.55/36.32 | GROUND_INST: instantiating (dt_k8_relat_1) with all_207_4, all_207_3, % 260.55/36.32 | all_207_2, simplifying with (38), (40), (41), (44) gives: % 260.55/36.32 | (65) relation(all_207_2) % 260.55/36.32 | % 260.55/36.32 | GROUND_INST: instantiating (2) with all_207_4, all_207_3, all_207_2, % 260.55/36.32 | all_172_0, simplifying with (35), (36), (38), (40), (41), (44) % 260.55/36.32 | gives: % 260.55/36.32 | (66) all_207_2 = all_172_0 | ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 260.55/36.32 | (ordered_pair(v0, v1) = v2 & $i(v2) & $i(v1) & $i(v0) & ( ~ in(v2, % 260.55/36.32 | all_207_3) | ~ in(v2, all_172_0) | ~ in(v1, all_207_4)) & % 260.55/36.32 | (in(v2, all_172_0) | (in(v2, all_207_3) & in(v1, all_207_4)))) % 260.55/36.32 | % 260.55/36.32 | GROUND_INST: instantiating (2) with all_207_4, all_207_3, all_207_2, % 260.55/36.32 | all_170_0, simplifying with (31), (32), (38), (40), (41), (44) % 260.55/36.32 | gives: % 260.55/36.32 | (67) all_207_2 = all_170_0 | ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 260.55/36.32 | (ordered_pair(v0, v1) = v2 & $i(v2) & $i(v1) & $i(v0) & ( ~ in(v2, % 260.55/36.32 | all_207_3) | ~ in(v2, all_170_0) | ~ in(v1, all_207_4)) & % 260.55/36.32 | (in(v2, all_170_0) | (in(v2, all_207_3) & in(v1, all_207_4)))) % 260.55/36.32 | % 260.55/36.32 | GROUND_INST: instantiating (2) with all_207_4, all_207_3, all_207_2, % 260.55/36.32 | empty_set, simplifying with (12), (20), (38), (40), (41), (44) % 260.55/36.32 | gives: % 260.55/36.32 | (68) all_207_2 = empty_set | ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 260.55/36.32 | (ordered_pair(v0, v1) = v2 & $i(v2) & $i(v1) & $i(v0) & ( ~ in(v2, % 260.55/36.32 | all_207_3) | ~ in(v2, empty_set) | ~ in(v1, all_207_4)) & % 260.55/36.32 | (in(v2, empty_set) | (in(v2, all_207_3) & in(v1, all_207_4)))) % 260.55/36.32 | % 260.55/36.32 | GROUND_INST: instantiating (rc2_subset_1) with empty_set, all_168_0, % 260.55/36.33 | simplifying with (20), (28) gives: % 260.55/36.33 | (69) ? [v0: $i] : ($i(v0) & element(v0, all_168_0) & empty(v0)) % 260.55/36.33 | % 260.55/36.33 | GROUND_INST: instantiating (t47_relat_1) with empty_set, empty_set, % 260.55/36.33 | simplifying with (12), (17), (20) gives: % 260.55/36.33 | (70) ? [v0: $i] : (relation_dom(empty_set) = v0 & $i(v0) & ! [v1: $i] : % 260.55/36.33 | ! [v2: $i] : ( ~ (relation_composition(v1, empty_set) = v2) | ~ % 260.55/36.33 | $i(v1) | ~ relation(v1) | ? [v3: $i] : ? [v4: $i] : ((v4 = % 260.55/36.33 | empty_set & relation_rng(v2) = empty_set) | (relation_rng(v1) % 260.55/36.33 | = v3 & $i(v3) & ~ subset(v0, v3))))) % 260.55/36.33 | % 260.80/36.33 | GROUND_INST: instantiating (t46_relat_1) with empty_set, empty_set, % 260.80/36.33 | simplifying with (12), (17), (20) gives: % 260.80/36.33 | (71) ? [v0: $i] : (relation_dom(empty_set) = v0 & $i(v0) & ! [v1: $i] : % 260.80/36.33 | ! [v2: $i] : ( ~ (relation_composition(empty_set, v1) = v2) | ~ % 260.80/36.33 | $i(v1) | ~ relation(v1) | ? [v3: $i] : ? [v4: $i] : ((v4 = v0 & % 260.80/36.33 | relation_dom(v2) = v0) | (relation_dom(v1) = v3 & $i(v3) & ~ % 260.80/36.33 | subset(empty_set, v3))))) % 260.80/36.33 | % 260.80/36.33 | GROUND_INST: instantiating (t25_relat_1) with empty_set, empty_set, % 260.80/36.33 | simplifying with (12), (17), (20) gives: % 260.80/36.33 | (72) ? [v0: $i] : (relation_dom(empty_set) = v0 & $i(v0) & ! [v1: $i] : % 260.80/36.33 | ! [v2: $i] : ( ~ (relation_rng(v1) = v2) | ~ $i(v1) | ~ % 260.80/36.33 | subset(empty_set, v1) | ~ relation(v1) | subset(empty_set, v2)) & % 260.80/36.33 | ! [v1: $i] : ! [v2: $i] : ( ~ (relation_rng(v1) = v2) | ~ $i(v1) % 260.80/36.33 | | ~ subset(empty_set, v1) | ~ relation(v1) | ? [v3: $i] : % 260.80/36.33 | (relation_dom(v1) = v3 & $i(v3) & subset(v0, v3)))) % 260.80/36.33 | % 260.80/36.33 | COMBINE_EQS: (48), (49) imply: % 260.80/36.33 | (73) all_165_0 = empty_set % 260.80/36.33 | % 260.80/36.33 | DELTA: instantiating (69) with fresh symbol all_220_0 gives: % 260.80/36.33 | (74) $i(all_220_0) & element(all_220_0, all_168_0) & empty(all_220_0) % 260.80/36.33 | % 260.80/36.33 | ALPHA: (74) implies: % 260.80/36.33 | (75) empty(all_220_0) % 260.80/36.33 | (76) $i(all_220_0) % 260.80/36.33 | % 260.80/36.33 | DELTA: instantiating (71) with fresh symbol all_222_0 gives: % 260.80/36.33 | (77) relation_dom(empty_set) = all_222_0 & $i(all_222_0) & ! [v0: $i] : ! % 260.80/36.33 | [v1: $i] : ( ~ (relation_composition(empty_set, v0) = v1) | ~ $i(v0) % 260.80/36.33 | | ~ relation(v0) | ? [v2: $i] : ? [v3: int] : ((v3 = all_222_0 & % 260.80/36.33 | relation_dom(v1) = all_222_0) | (relation_dom(v0) = v2 & $i(v2) % 260.80/36.33 | & ~ subset(empty_set, v2)))) % 260.80/36.33 | % 260.80/36.33 | ALPHA: (77) implies: % 260.80/36.33 | (78) $i(all_222_0) % 260.80/36.33 | (79) relation_dom(empty_set) = all_222_0 % 260.80/36.33 | % 260.80/36.33 | DELTA: instantiating (70) with fresh symbol all_225_0 gives: % 260.80/36.33 | (80) relation_dom(empty_set) = all_225_0 & $i(all_225_0) & ! [v0: $i] : ! % 260.80/36.33 | [v1: $i] : ( ~ (relation_composition(v0, empty_set) = v1) | ~ $i(v0) % 260.80/36.33 | | ~ relation(v0) | ? [v2: $i] : ? [v3: $i] : ((v3 = empty_set & % 260.80/36.33 | relation_rng(v1) = empty_set) | (relation_rng(v0) = v2 & $i(v2) % 260.80/36.33 | & ~ subset(all_225_0, v2)))) % 260.80/36.33 | % 260.80/36.33 | ALPHA: (80) implies: % 260.80/36.33 | (81) relation_dom(empty_set) = all_225_0 % 260.80/36.33 | % 260.80/36.33 | DELTA: instantiating (72) with fresh symbol all_228_0 gives: % 260.80/36.34 | (82) relation_dom(empty_set) = all_228_0 & $i(all_228_0) & ! [v0: $i] : ! % 260.80/36.34 | [v1: $i] : ( ~ (relation_rng(v0) = v1) | ~ $i(v0) | ~ % 260.80/36.34 | subset(empty_set, v0) | ~ relation(v0) | subset(empty_set, v1)) & % 260.80/36.34 | ! [v0: $i] : ! [v1: $i] : ( ~ (relation_rng(v0) = v1) | ~ $i(v0) | % 260.80/36.34 | ~ subset(empty_set, v0) | ~ relation(v0) | ? [v2: $i] : % 260.80/36.34 | (relation_dom(v0) = v2 & $i(v2) & subset(all_228_0, v2))) % 260.80/36.34 | % 260.80/36.34 | ALPHA: (82) implies: % 260.80/36.34 | (83) relation_dom(empty_set) = all_228_0 % 260.80/36.34 | % 260.80/36.34 | GROUND_INST: instantiating (22) with empty_set, all_225_0, empty_set, % 260.80/36.34 | simplifying with (16), (81) gives: % 260.80/36.34 | (84) all_225_0 = empty_set % 260.80/36.34 | % 260.80/36.34 | GROUND_INST: instantiating (22) with all_225_0, all_228_0, empty_set, % 260.80/36.34 | simplifying with (81), (83) gives: % 260.80/36.34 | (85) all_228_0 = all_225_0 % 260.80/36.34 | % 260.80/36.34 | GROUND_INST: instantiating (22) with all_222_0, all_228_0, empty_set, % 260.80/36.34 | simplifying with (79), (83) gives: % 260.80/36.34 | (86) all_228_0 = all_222_0 % 260.80/36.34 | % 260.80/36.34 | COMBINE_EQS: (85), (86) imply: % 260.80/36.34 | (87) all_225_0 = all_222_0 % 260.80/36.34 | % 260.80/36.34 | SIMP: (87) implies: % 260.80/36.34 | (88) all_225_0 = all_222_0 % 260.80/36.34 | % 260.80/36.34 | COMBINE_EQS: (84), (88) imply: % 260.80/36.34 | (89) all_222_0 = empty_set % 260.80/36.34 | % 260.80/36.34 | GROUND_INST: instantiating (21) with all_220_0, simplifying with (75), (76) % 260.80/36.34 | gives: % 260.80/36.34 | (90) all_220_0 = empty_set % 260.80/36.34 | % 260.80/36.34 | GROUND_INST: instantiating (18) with all_207_2, all_207_1, simplifying with % 260.80/36.34 | (42), (45), (65) gives: % 260.80/36.34 | (91) all_207_2 = empty_set | ? [v0: $i] : ( ~ (v0 = empty_set) & % 260.80/36.34 | relation_dom(all_207_2) = v0 & $i(v0)) % 260.80/36.34 | % 260.80/36.34 | GROUND_INST: instantiating (t47_relat_1) with all_207_2, all_207_1, % 260.80/36.34 | simplifying with (42), (45), (65) gives: % 260.80/36.34 | (92) ? [v0: $i] : (relation_dom(all_207_2) = v0 & $i(v0) & ! [v1: $i] : % 260.80/36.34 | ! [v2: $i] : ( ~ (relation_composition(v1, all_207_2) = v2) | ~ % 260.80/36.34 | $i(v1) | ~ relation(v1) | ? [v3: $i] : ? [v4: int] : ((v4 = % 260.80/36.34 | all_207_1 & relation_rng(v2) = all_207_1 & $i(all_207_1)) | % 260.80/36.34 | (relation_rng(v1) = v3 & $i(v3) & ~ subset(v0, v3))))) % 260.80/36.34 | % 260.80/36.34 | GROUND_INST: instantiating (t46_relat_1) with all_207_2, all_207_1, % 260.80/36.34 | simplifying with (42), (45), (65) gives: % 260.80/36.34 | (93) ? [v0: $i] : (relation_dom(all_207_2) = v0 & $i(v0) & ! [v1: $i] : % 260.80/36.34 | ! [v2: $i] : ( ~ (relation_composition(all_207_2, v1) = v2) | ~ % 260.80/36.34 | $i(v1) | ~ relation(v1) | ? [v3: $i] : ? [v4: $i] : ((v4 = v0 & % 260.80/36.34 | relation_dom(v2) = v0) | (relation_dom(v1) = v3 & $i(v3) & ~ % 260.80/36.34 | subset(all_207_1, v3))))) % 260.80/36.34 | % 260.80/36.34 | GROUND_INST: instantiating (t25_relat_1) with all_207_2, all_207_1, % 260.80/36.34 | simplifying with (42), (45), (65) gives: % 260.80/36.34 | (94) ? [v0: $i] : (relation_dom(all_207_2) = v0 & $i(v0) & ! [v1: $i] : % 260.80/36.34 | ! [v2: $i] : ( ~ (relation_rng(v1) = v2) | ~ $i(v1) | ~ % 260.80/36.34 | subset(all_207_2, v1) | ~ relation(v1) | subset(all_207_1, v2)) & % 260.80/36.34 | ! [v1: $i] : ! [v2: $i] : ( ~ (relation_rng(v1) = v2) | ~ $i(v1) % 260.80/36.34 | | ~ subset(all_207_2, v1) | ~ relation(v1) | ? [v3: $i] : % 260.80/36.34 | (relation_dom(v1) = v3 & $i(v3) & subset(v0, v3)))) % 260.80/36.34 | % 260.80/36.34 | GROUND_INST: instantiating (19) with all_207_2, all_207_1, simplifying with % 260.80/36.34 | (42), (45), (65) gives: % 260.80/36.34 | (95) ? [v0: $i] : (( ~ (all_207_1 = empty_set) | (v0 = empty_set & % 260.80/36.34 | relation_dom(all_207_2) = empty_set)) & (all_207_1 = empty_set | % 260.80/36.34 | ( ~ (v0 = empty_set) & relation_dom(all_207_2) = v0 & $i(v0)))) % 260.80/36.34 | % 260.80/36.34 | GROUND_INST: instantiating (d2_relat_1) with all_207_3, all_207_2, simplifying % 260.80/36.34 | with (38), (41), (42), (65) gives: % 260.80/36.34 | (96) all_207_2 = all_207_3 | ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 260.80/36.34 | (ordered_pair(v0, v1) = v2 & $i(v2) & $i(v1) & $i(v0) & ( ~ in(v2, % 260.80/36.34 | all_207_2) | ~ in(v2, all_207_3)) & (in(v2, all_207_2) | in(v2, % 260.80/36.34 | all_207_3))) % 260.80/36.34 | % 260.80/36.34 | GROUND_INST: instantiating (7) with all_207_3, all_207_2, simplifying with % 260.80/36.34 | (38), (41), (42), (65) gives: % 260.80/36.34 | (97) subset(all_207_3, all_207_2) | ? [v0: $i] : ? [v1: $i] : ? [v2: $i] % 260.80/36.34 | : (ordered_pair(v0, v1) = v2 & $i(v2) & $i(v1) & $i(v0) & in(v2, % 260.80/36.34 | all_207_3) & ~ in(v2, all_207_2)) % 260.80/36.34 | % 260.80/36.34 | GROUND_INST: instantiating (7) with all_207_2, all_207_3, simplifying with % 260.80/36.34 | (38), (41), (42), (65) gives: % 260.80/36.35 | (98) subset(all_207_2, all_207_3) | ? [v0: $i] : ? [v1: $i] : ? [v2: $i] % 260.80/36.35 | : (ordered_pair(v0, v1) = v2 & $i(v2) & $i(v1) & $i(v0) & in(v2, % 260.80/36.35 | all_207_2) & ~ in(v2, all_207_3)) % 260.80/36.35 | % 260.80/36.35 | GROUND_INST: instantiating (d2_relat_1) with all_172_0, all_207_2, simplifying % 260.80/36.35 | with (35), (36), (42), (65) gives: % 260.89/36.35 | (99) all_207_2 = all_172_0 | ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 260.89/36.35 | (ordered_pair(v0, v1) = v2 & $i(v2) & $i(v1) & $i(v0) & ( ~ in(v2, % 260.89/36.35 | all_207_2) | ~ in(v2, all_172_0)) & (in(v2, all_207_2) | in(v2, % 260.89/36.35 | all_172_0))) % 260.89/36.35 | % 260.89/36.35 | GROUND_INST: instantiating (7) with all_207_2, empty_set, simplifying with % 260.89/36.35 | (12), (20), (42), (65) gives: % 260.89/36.35 | (100) subset(all_207_2, empty_set) | ? [v0: $i] : ? [v1: $i] : ? [v2: % 260.89/36.35 | $i] : (ordered_pair(v0, v1) = v2 & $i(v2) & $i(v1) & $i(v0) & % 260.89/36.35 | in(v2, all_207_2) & ~ in(v2, empty_set)) % 260.89/36.35 | % 260.89/36.35 | GROUND_INST: instantiating (7) with all_207_2, all_207_2, simplifying with % 260.89/36.35 | (42), (65) gives: % 260.89/36.35 | (101) subset(all_207_2, all_207_2) % 260.89/36.35 | % 260.89/36.35 | DELTA: instantiating (95) with fresh symbol all_241_0 gives: % 260.89/36.35 | (102) ( ~ (all_207_1 = empty_set) | (all_241_0 = empty_set & % 260.89/36.35 | relation_dom(all_207_2) = empty_set)) & (all_207_1 = empty_set | % 260.89/36.35 | ( ~ (all_241_0 = empty_set) & relation_dom(all_207_2) = all_241_0 & % 260.89/36.35 | $i(all_241_0))) % 260.89/36.35 | % 260.89/36.35 | ALPHA: (102) implies: % 260.89/36.35 | (103) all_207_1 = empty_set | ( ~ (all_241_0 = empty_set) & % 260.89/36.35 | relation_dom(all_207_2) = all_241_0 & $i(all_241_0)) % 260.89/36.35 | (104) ~ (all_207_1 = empty_set) | (all_241_0 = empty_set & % 260.89/36.35 | relation_dom(all_207_2) = empty_set) % 260.89/36.35 | % 260.89/36.35 | DELTA: instantiating (93) with fresh symbol all_242_0 gives: % 260.89/36.35 | (105) relation_dom(all_207_2) = all_242_0 & $i(all_242_0) & ! [v0: $i] : % 260.89/36.35 | ! [v1: $i] : ( ~ (relation_composition(all_207_2, v0) = v1) | ~ % 260.89/36.35 | $i(v0) | ~ relation(v0) | ? [v2: $i] : ? [v3: int] : ((v3 = % 260.89/36.35 | all_242_0 & relation_dom(v1) = all_242_0) | (relation_dom(v0) = % 260.89/36.35 | v2 & $i(v2) & ~ subset(all_207_1, v2)))) % 260.89/36.35 | % 260.89/36.35 | ALPHA: (105) implies: % 260.89/36.35 | (106) relation_dom(all_207_2) = all_242_0 % 260.89/36.35 | % 260.89/36.35 | DELTA: instantiating (92) with fresh symbol all_245_0 gives: % 260.89/36.35 | (107) relation_dom(all_207_2) = all_245_0 & $i(all_245_0) & ! [v0: $i] : % 260.89/36.35 | ! [v1: $i] : ( ~ (relation_composition(v0, all_207_2) = v1) | ~ % 260.89/36.35 | $i(v0) | ~ relation(v0) | ? [v2: $i] : ? [v3: int] : ((v3 = % 260.89/36.35 | all_207_1 & relation_rng(v1) = all_207_1 & $i(all_207_1)) | % 260.89/36.35 | (relation_rng(v0) = v2 & $i(v2) & ~ subset(all_245_0, v2)))) % 260.89/36.35 | % 260.89/36.35 | ALPHA: (107) implies: % 260.89/36.35 | (108) relation_dom(all_207_2) = all_245_0 % 260.89/36.35 | % 260.89/36.35 | DELTA: instantiating (94) with fresh symbol all_248_0 gives: % 260.89/36.35 | (109) relation_dom(all_207_2) = all_248_0 & $i(all_248_0) & ! [v0: $i] : % 260.89/36.35 | ! [v1: $i] : ( ~ (relation_rng(v0) = v1) | ~ $i(v0) | ~ % 260.89/36.35 | subset(all_207_2, v0) | ~ relation(v0) | subset(all_207_1, v1)) & % 260.89/36.35 | ! [v0: $i] : ! [v1: $i] : ( ~ (relation_rng(v0) = v1) | ~ $i(v0) | % 260.89/36.35 | ~ subset(all_207_2, v0) | ~ relation(v0) | ? [v2: $i] : % 260.89/36.35 | (relation_dom(v0) = v2 & $i(v2) & subset(all_248_0, v2))) % 260.89/36.35 | % 260.89/36.35 | ALPHA: (109) implies: % 260.89/36.35 | (110) relation_dom(all_207_2) = all_248_0 % 260.89/36.35 | (111) ! [v0: $i] : ! [v1: $i] : ( ~ (relation_rng(v0) = v1) | ~ $i(v0) | % 260.89/36.35 | ~ subset(all_207_2, v0) | ~ relation(v0) | ? [v2: $i] : % 260.89/36.35 | (relation_dom(v0) = v2 & $i(v2) & subset(all_248_0, v2))) % 260.89/36.35 | (112) ! [v0: $i] : ! [v1: $i] : ( ~ (relation_rng(v0) = v1) | ~ $i(v0) | % 260.89/36.35 | ~ subset(all_207_2, v0) | ~ relation(v0) | subset(all_207_1, v1)) % 260.89/36.35 | % 260.89/36.35 | REDUCE: (75), (90) imply: % 260.89/36.35 | (113) empty(empty_set) % 260.89/36.35 | % 260.89/36.35 | GROUND_INST: instantiating (22) with all_245_0, all_248_0, all_207_2, % 260.89/36.35 | simplifying with (108), (110) gives: % 260.89/36.35 | (114) all_248_0 = all_245_0 % 260.89/36.35 | % 260.89/36.35 | GROUND_INST: instantiating (22) with all_242_0, all_248_0, all_207_2, % 260.89/36.35 | simplifying with (106), (110) gives: % 260.89/36.35 | (115) all_248_0 = all_242_0 % 260.89/36.35 | % 260.89/36.35 | COMBINE_EQS: (114), (115) imply: % 260.89/36.35 | (116) all_245_0 = all_242_0 % 260.89/36.35 | % 260.89/36.35 | SIMP: (116) implies: % 260.89/36.35 | (117) all_245_0 = all_242_0 % 260.89/36.35 | % 260.89/36.35 | GROUND_INST: instantiating (111) with all_207_2, all_207_1, simplifying with % 260.89/36.35 | (42), (45), (65), (101) gives: % 260.89/36.35 | (118) ? [v0: $i] : (relation_dom(all_207_2) = v0 & $i(v0) & % 260.89/36.35 | subset(all_248_0, v0)) % 260.89/36.35 | % 260.89/36.35 | DELTA: instantiating (118) with fresh symbol all_261_0 gives: % 260.89/36.35 | (119) relation_dom(all_207_2) = all_261_0 & $i(all_261_0) & % 260.89/36.35 | subset(all_248_0, all_261_0) % 260.89/36.35 | % 260.89/36.35 | ALPHA: (119) implies: % 260.89/36.35 | (120) relation_dom(all_207_2) = all_261_0 % 260.89/36.35 | % 260.89/36.35 | GROUND_INST: instantiating (22) with all_242_0, all_261_0, all_207_2, % 260.89/36.35 | simplifying with (106), (120) gives: % 260.89/36.36 | (121) all_261_0 = all_242_0 % 260.89/36.36 | % 260.89/36.36 | BETA: splitting (46) gives: % 260.89/36.36 | % 260.89/36.36 | Case 1: % 260.89/36.36 | | % 260.89/36.36 | | (122) relation_rng(all_207_3) = all_207_0 & $i(all_207_0) & in(all_207_5, % 260.89/36.36 | | all_207_0) & in(all_207_5, all_207_4) & ~ in(all_207_5, % 260.89/36.36 | | all_207_1) % 260.89/36.36 | | % 260.89/36.36 | | ALPHA: (122) implies: % 260.89/36.36 | | (123) ~ in(all_207_5, all_207_1) % 260.89/36.36 | | (124) in(all_207_5, all_207_4) % 260.89/36.36 | | (125) in(all_207_5, all_207_0) % 260.89/36.36 | | (126) $i(all_207_0) % 260.89/36.36 | | (127) relation_rng(all_207_3) = all_207_0 % 260.89/36.36 | | % 260.89/36.36 | | BETA: splitting (62) gives: % 260.89/36.36 | | % 260.89/36.36 | | Case 1: % 260.89/36.36 | | | % 260.89/36.36 | | | (128) subset(empty_set, all_207_3) % 260.89/36.36 | | | % 260.89/36.36 | | | BETA: splitting (60) gives: % 260.89/36.36 | | | % 260.89/36.36 | | | Case 1: % 260.89/36.36 | | | | % 260.89/36.36 | | | | (129) subset(all_207_3, all_170_0) % 260.89/36.36 | | | | % 260.89/36.36 | | | | REDUCE: (49), (129) imply: % 260.89/36.36 | | | | (130) subset(all_207_3, empty_set) % 260.89/36.36 | | | | % 260.89/36.36 | | | | BETA: splitting (64) gives: % 260.89/36.36 | | | | % 260.89/36.36 | | | | Case 1: % 260.89/36.36 | | | | | % 260.89/36.36 | | | | | (131) all_207_2 = all_207_3 % 260.89/36.36 | | | | | % 260.89/36.36 | | | | | REDUCE: (45), (131) imply: % 260.89/36.36 | | | | | (132) relation_rng(all_207_3) = all_207_1 % 260.89/36.36 | | | | | % 260.89/36.36 | | | | | REF_CLOSE: (23), (123), (125), (127), (132) are inconsistent by % 260.89/36.36 | | | | | sub-proof #8. % 260.89/36.36 | | | | | % 260.89/36.36 | | | | Case 2: % 260.89/36.36 | | | | | % 260.89/36.36 | | | | | (133) ~ (all_207_2 = all_207_3) % 260.89/36.36 | | | | | % 260.89/36.36 | | | | | REF_CLOSE: (6), (14), (41), (49), (61), (67), (130), (133) are % 260.89/36.36 | | | | | inconsistent by sub-proof #6. % 260.89/36.36 | | | | | % 260.89/36.36 | | | | End of split % 260.89/36.36 | | | | % 260.89/36.36 | | | Case 2: % 260.89/36.36 | | | | % 260.89/36.36 | | | | (134) ~ subset(all_207_3, all_170_0) % 260.89/36.36 | | | | % 260.89/36.36 | | | | REDUCE: (49), (134) imply: % 260.89/36.36 | | | | (135) ~ subset(all_207_3, empty_set) % 260.89/36.36 | | | | % 260.89/36.36 | | | | BETA: splitting (57) gives: % 260.89/36.36 | | | | % 260.89/36.36 | | | | Case 1: % 260.89/36.36 | | | | | % 260.89/36.36 | | | | | (136) subset(all_172_0, all_207_3) % 260.89/36.36 | | | | | % 260.89/36.36 | | | | | BETA: splitting (52) gives: % 260.89/36.36 | | | | | % 260.89/36.36 | | | | | Case 1: % 260.89/36.36 | | | | | | % 260.89/36.36 | | | | | | (137) subset(empty_set, all_172_0) % 260.89/36.36 | | | | | | % 260.89/36.36 | | | | | | BETA: splitting (58) gives: % 260.89/36.36 | | | | | | % 260.89/36.36 | | | | | | Case 1: % 260.89/36.36 | | | | | | | % 260.89/36.36 | | | | | | | (138) subset(all_207_3, all_172_0) % 260.89/36.36 | | | | | | | % 260.89/36.36 | | | | | | | BETA: splitting (64) gives: % 260.89/36.36 | | | | | | | % 260.89/36.36 | | | | | | | Case 1: % 260.89/36.36 | | | | | | | | % 260.89/36.36 | | | | | | | | (139) all_207_2 = all_207_3 % 260.89/36.36 | | | | | | | | % 260.89/36.36 | | | | | | | | REDUCE: (45), (139) imply: % 260.89/36.36 | | | | | | | | (140) relation_rng(all_207_3) = all_207_1 % 260.89/36.36 | | | | | | | | % 260.89/36.36 | | | | | | | | REF_CLOSE: (23), (123), (125), (127), (140) are inconsistent by % 260.89/36.36 | | | | | | | | sub-proof #8. % 260.89/36.36 | | | | | | | | % 260.89/36.36 | | | | | | | Case 2: % 260.89/36.36 | | | | | | | | % 260.89/36.36 | | | | | | | | (141) ~ (all_207_2 = all_207_3) % 260.89/36.36 | | | | | | | | % 260.89/36.36 | | | | | | | | BETA: splitting (96) gives: % 260.89/36.36 | | | | | | | | % 260.89/36.36 | | | | | | | | Case 1: % 260.89/36.36 | | | | | | | | | % 260.89/36.36 | | | | | | | | | (142) all_207_2 = all_207_3 % 260.89/36.36 | | | | | | | | | % 260.89/36.36 | | | | | | | | | REDUCE: (141), (142) imply: % 260.89/36.36 | | | | | | | | | (143) $false % 260.89/36.36 | | | | | | | | | % 260.89/36.36 | | | | | | | | | CLOSE: (143) is inconsistent. % 260.89/36.36 | | | | | | | | | % 260.89/36.36 | | | | | | | | Case 2: % 260.89/36.36 | | | | | | | | | % 260.89/36.36 | | | | | | | | | (144) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 260.89/36.36 | | | | | | | | | (ordered_pair(v0, v1) = v2 & $i(v2) & $i(v1) & $i(v0) % 260.89/36.36 | | | | | | | | | & ( ~ in(v2, all_207_2) | ~ in(v2, all_207_3)) & % 260.89/36.36 | | | | | | | | | (in(v2, all_207_2) | in(v2, all_207_3))) % 260.89/36.36 | | | | | | | | | % 260.89/36.36 | | | | | | | | | DELTA: instantiating (144) with fresh symbols all_442_0, % 260.89/36.36 | | | | | | | | | all_442_1, all_442_2 gives: % 260.89/36.36 | | | | | | | | | (145) ordered_pair(all_442_2, all_442_1) = all_442_0 & % 260.89/36.36 | | | | | | | | | $i(all_442_0) & $i(all_442_1) & $i(all_442_2) & ( ~ % 260.89/36.36 | | | | | | | | | in(all_442_0, all_207_2) | ~ in(all_442_0, % 260.89/36.36 | | | | | | | | | all_207_3)) & (in(all_442_0, all_207_2) | % 260.89/36.36 | | | | | | | | | in(all_442_0, all_207_3)) % 260.89/36.36 | | | | | | | | | % 260.89/36.36 | | | | | | | | | ALPHA: (145) implies: % 260.89/36.36 | | | | | | | | | (146) $i(all_442_0) % 260.89/36.36 | | | | | | | | | (147) in(all_442_0, all_207_2) | in(all_442_0, all_207_3) % 260.89/36.36 | | | | | | | | | % 260.89/36.36 | | | | | | | | | BETA: splitting (68) gives: % 260.89/36.36 | | | | | | | | | % 260.89/36.36 | | | | | | | | | Case 1: % 260.89/36.36 | | | | | | | | | | % 260.89/36.36 | | | | | | | | | | (148) all_207_2 = empty_set % 260.89/36.36 | | | | | | | | | | % 260.89/36.36 | | | | | | | | | | REDUCE: (44), (148) imply: % 260.89/36.36 | | | | | | | | | | (149) relation_rng_restriction(all_207_4, all_207_3) = % 260.89/36.36 | | | | | | | | | | empty_set % 260.89/36.36 | | | | | | | | | | % 260.89/36.36 | | | | | | | | | | BETA: splitting (54) gives: % 260.89/36.36 | | | | | | | | | | % 260.89/36.36 | | | | | | | | | | Case 1: % 260.89/36.36 | | | | | | | | | | | % 260.89/36.36 | | | | | | | | | | | (150) all_172_0 = empty_set % 260.89/36.36 | | | | | | | | | | | % 260.89/36.36 | | | | | | | | | | | REDUCE: (138), (150) imply: % 260.89/36.36 | | | | | | | | | | | (151) subset(all_207_3, empty_set) % 260.89/36.36 | | | | | | | | | | | % 260.89/36.36 | | | | | | | | | | | PRED_UNIFY: (135), (151) imply: % 260.89/36.36 | | | | | | | | | | | (152) $false % 260.89/36.36 | | | | | | | | | | | % 260.89/36.36 | | | | | | | | | | | CLOSE: (152) is inconsistent. % 260.89/36.36 | | | | | | | | | | | % 260.89/36.36 | | | | | | | | | | Case 2: % 260.89/36.36 | | | | | | | | | | | % 260.89/36.36 | | | | | | | | | | | (153) ~ (all_172_0 = empty_set) % 260.89/36.36 | | | | | | | | | | | % 260.89/36.36 | | | | | | | | | | | BETA: splitting (66) gives: % 260.89/36.36 | | | | | | | | | | | % 260.89/36.36 | | | | | | | | | | | Case 1: % 260.89/36.36 | | | | | | | | | | | | % 260.89/36.36 | | | | | | | | | | | | (154) all_207_2 = all_172_0 % 260.89/36.36 | | | | | | | | | | | | % 260.89/36.36 | | | | | | | | | | | | COMBINE_EQS: (148), (154) imply: % 260.89/36.36 | | | | | | | | | | | | (155) all_172_0 = empty_set % 260.89/36.36 | | | | | | | | | | | | % 260.89/36.36 | | | | | | | | | | | | REDUCE: (153), (155) imply: % 260.89/36.36 | | | | | | | | | | | | (156) $false % 260.89/36.36 | | | | | | | | | | | | % 260.89/36.36 | | | | | | | | | | | | CLOSE: (156) is inconsistent. % 260.89/36.36 | | | | | | | | | | | | % 260.89/36.36 | | | | | | | | | | | Case 2: % 260.89/36.36 | | | | | | | | | | | | % 260.89/36.37 | | | | | | | | | | | | (157) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 260.89/36.37 | | | | | | | | | | | | (ordered_pair(v0, v1) = v2 & $i(v2) & $i(v1) & % 260.89/36.37 | | | | | | | | | | | | $i(v0) & ( ~ in(v2, all_207_3) | ~ in(v2, % 260.89/36.37 | | | | | | | | | | | | all_172_0) | ~ in(v1, all_207_4)) & (in(v2, % 260.89/36.37 | | | | | | | | | | | | all_172_0) | (in(v2, all_207_3) & in(v1, % 260.89/36.37 | | | | | | | | | | | | all_207_4)))) % 260.89/36.37 | | | | | | | | | | | | % 260.89/36.37 | | | | | | | | | | | | DELTA: instantiating (157) with fresh symbols all_491_0, % 260.89/36.37 | | | | | | | | | | | | all_491_1, all_491_2 gives: % 260.89/36.37 | | | | | | | | | | | | (158) ordered_pair(all_491_2, all_491_1) = all_491_0 & % 260.89/36.37 | | | | | | | | | | | | $i(all_491_0) & $i(all_491_1) & $i(all_491_2) & ( % 260.89/36.37 | | | | | | | | | | | | ~ in(all_491_0, all_207_3) | ~ in(all_491_0, % 260.89/36.37 | | | | | | | | | | | | all_172_0) | ~ in(all_491_1, all_207_4)) & % 260.89/36.37 | | | | | | | | | | | | (in(all_491_0, all_172_0) | (in(all_491_0, % 260.89/36.37 | | | | | | | | | | | | all_207_3) & in(all_491_1, all_207_4))) % 260.89/36.37 | | | | | | | | | | | | % 260.89/36.37 | | | | | | | | | | | | ALPHA: (158) implies: % 260.89/36.37 | | | | | | | | | | | | (159) in(all_491_0, all_172_0) | (in(all_491_0, % 260.89/36.37 | | | | | | | | | | | | all_207_3) & in(all_491_1, all_207_4)) % 260.89/36.37 | | | | | | | | | | | | % 260.89/36.37 | | | | | | | | | | | | BETA: splitting (56) gives: % 260.89/36.37 | | | | | | | | | | | | % 260.89/36.37 | | | | | | | | | | | | Case 1: % 260.89/36.37 | | | | | | | | | | | | | % 260.89/36.37 | | | | | | | | | | | | | (160) all_207_3 = all_172_0 % 260.89/36.37 | | | | | | | | | | | | | % 260.89/36.37 | | | | | | | | | | | | | REDUCE: (127), (160) imply: % 260.89/36.37 | | | | | | | | | | | | | (161) relation_rng(all_172_0) = all_207_0 % 260.89/36.37 | | | | | | | | | | | | | % 260.89/36.37 | | | | | | | | | | | | | REDUCE: (149), (160) imply: % 260.89/36.37 | | | | | | | | | | | | | (162) relation_rng_restriction(all_207_4, all_172_0) = % 260.89/36.37 | | | | | | | | | | | | | empty_set % 260.89/36.37 | | | | | | | | | | | | | % 260.89/36.37 | | | | | | | | | | | | | BETA: splitting (159) gives: % 260.89/36.37 | | | | | | | | | | | | | % 260.89/36.37 | | | | | | | | | | | | | Case 1: % 260.89/36.37 | | | | | | | | | | | | | | % 260.89/36.37 | | | | | | | | | | | | | | % 260.89/36.37 | | | | | | | | | | | | | | GROUND_INST: instantiating (10) with all_172_0, all_207_0, % 260.89/36.37 | | | | | | | | | | | | | | all_207_5, simplifying with (35), (36), (39), % 260.89/36.37 | | | | | | | | | | | | | | (125), (126), (161) gives: % 260.89/36.37 | | | | | | | | | | | | | | (163) ? [v0: $i] : ? [v1: $i] : (ordered_pair(v0, % 260.89/36.37 | | | | | | | | | | | | | | all_207_5) = v1 & $i(v1) & $i(v0) & in(v1, % 260.89/36.37 | | | | | | | | | | | | | | all_172_0)) % 260.89/36.37 | | | | | | | | | | | | | | % 260.89/36.37 | | | | | | | | | | | | | | DELTA: instantiating (163) with fresh symbols all_588_0, % 260.89/36.37 | | | | | | | | | | | | | | all_588_1 gives: % 260.89/36.37 | | | | | | | | | | | | | | (164) ordered_pair(all_588_1, all_207_5) = all_588_0 & % 260.89/36.37 | | | | | | | | | | | | | | $i(all_588_0) & $i(all_588_1) & in(all_588_0, % 260.89/36.37 | | | | | | | | | | | | | | all_172_0) % 260.89/36.37 | | | | | | | | | | | | | | % 260.89/36.37 | | | | | | | | | | | | | | ALPHA: (164) implies: % 260.89/36.37 | | | | | | | | | | | | | | (165) in(all_588_0, all_172_0) % 260.89/36.37 | | | | | | | | | | | | | | (166) $i(all_588_1) % 260.89/36.37 | | | | | | | | | | | | | | (167) $i(all_588_0) % 260.89/36.37 | | | | | | | | | | | | | | (168) ordered_pair(all_588_1, all_207_5) = all_588_0 % 260.89/36.37 | | | | | | | | | | | | | | % 260.89/36.37 | | | | | | | | | | | | | | BETA: splitting (147) gives: % 260.89/36.37 | | | | | | | | | | | | | | % 260.89/36.37 | | | | | | | | | | | | | | Case 1: % 260.89/36.37 | | | | | | | | | | | | | | | % 260.89/36.37 | | | | | | | | | | | | | | | (169) in(all_442_0, all_207_2) % 260.89/36.37 | | | | | | | | | | | | | | | % 260.89/36.37 | | | | | | | | | | | | | | | REDUCE: (148), (169) imply: % 260.89/36.37 | | | | | | | | | | | | | | | (170) in(all_442_0, empty_set) % 260.89/36.37 | | | | | | | | | | | | | | | % 260.89/36.37 | | | | | | | | | | | | | | | GROUND_INST: instantiating (6) with all_442_0, simplifying with % 260.89/36.37 | | | | | | | | | | | | | | | (146), (170) gives: % 260.89/36.37 | | | | | | | | | | | | | | | (171) $false % 260.89/36.37 | | | | | | | | | | | | | | | % 260.89/36.37 | | | | | | | | | | | | | | | CLOSE: (171) is inconsistent. % 260.89/36.37 | | | | | | | | | | | | | | | % 260.89/36.37 | | | | | | | | | | | | | | Case 2: % 260.89/36.37 | | | | | | | | | | | | | | | % 260.89/36.37 | | | | | | | | | | | | | | | % 260.89/36.37 | | | | | | | | | | | | | | | GROUND_INST: instantiating (3) with all_207_4, all_172_0, % 260.89/36.37 | | | | | | | | | | | | | | | empty_set, all_588_1, all_207_5, all_588_0, % 260.89/36.37 | | | | | | | | | | | | | | | simplifying with (12), (20), (35), (36), (39), % 260.89/36.37 | | | | | | | | | | | | | | | (40), (124), (162), (165), (166), (168) gives: % 260.89/36.37 | | | | | | | | | | | | | | | (172) in(all_588_0, empty_set) % 260.89/36.37 | | | | | | | | | | | | | | | % 260.89/36.37 | | | | | | | | | | | | | | | GROUND_INST: instantiating (6) with all_588_0, simplifying with % 260.89/36.37 | | | | | | | | | | | | | | | (167), (172) gives: % 260.89/36.37 | | | | | | | | | | | | | | | (173) $false % 260.89/36.37 | | | | | | | | | | | | | | | % 260.89/36.37 | | | | | | | | | | | | | | | CLOSE: (173) is inconsistent. % 260.89/36.37 | | | | | | | | | | | | | | | % 260.89/36.37 | | | | | | | | | | | | | | End of split % 260.89/36.37 | | | | | | | | | | | | | | % 260.89/36.37 | | | | | | | | | | | | | Case 2: % 260.89/36.37 | | | | | | | | | | | | | | % 260.89/36.37 | | | | | | | | | | | | | | (174) ~ in(all_491_0, all_172_0) % 260.89/36.37 | | | | | | | | | | | | | | (175) in(all_491_0, all_207_3) & in(all_491_1, % 260.89/36.37 | | | | | | | | | | | | | | all_207_4) % 260.89/36.37 | | | | | | | | | | | | | | % 260.89/36.37 | | | | | | | | | | | | | | ALPHA: (175) implies: % 260.89/36.37 | | | | | | | | | | | | | | (176) in(all_491_0, all_207_3) % 260.89/36.37 | | | | | | | | | | | | | | % 260.89/36.37 | | | | | | | | | | | | | | REDUCE: (160), (176) imply: % 260.89/36.37 | | | | | | | | | | | | | | (177) in(all_491_0, all_172_0) % 260.89/36.37 | | | | | | | | | | | | | | % 260.89/36.37 | | | | | | | | | | | | | | PRED_UNIFY: (174), (177) imply: % 260.89/36.37 | | | | | | | | | | | | | | (178) $false % 260.89/36.37 | | | | | | | | | | | | | | % 260.89/36.37 | | | | | | | | | | | | | | CLOSE: (178) is inconsistent. % 260.89/36.37 | | | | | | | | | | | | | | % 260.89/36.37 | | | | | | | | | | | | | End of split % 260.89/36.37 | | | | | | | | | | | | | % 260.89/36.37 | | | | | | | | | | | | Case 2: % 260.89/36.37 | | | | | | | | | | | | | % 260.89/36.37 | | | | | | | | | | | | | (179) ~ (all_207_3 = all_172_0) % 260.89/36.37 | | | | | | | | | | | | | % 260.89/36.37 | | | | | | | | | | | | | REF_CLOSE: (1), (36), (41), (136), (138), (179) are % 260.89/36.37 | | | | | | | | | | | | | inconsistent by sub-proof #5. % 260.89/36.37 | | | | | | | | | | | | | % 260.89/36.37 | | | | | | | | | | | | End of split % 260.89/36.37 | | | | | | | | | | | | % 260.89/36.37 | | | | | | | | | | | End of split % 260.89/36.37 | | | | | | | | | | | % 260.89/36.37 | | | | | | | | | | End of split % 260.89/36.37 | | | | | | | | | | % 260.89/36.37 | | | | | | | | | Case 2: % 260.89/36.37 | | | | | | | | | | % 260.89/36.37 | | | | | | | | | | (180) ~ (all_207_2 = empty_set) % 260.89/36.37 | | | | | | | | | | % 260.89/36.37 | | | | | | | | | | BETA: splitting (67) gives: % 260.89/36.37 | | | | | | | | | | % 260.89/36.37 | | | | | | | | | | Case 1: % 260.89/36.37 | | | | | | | | | | | % 260.89/36.37 | | | | | | | | | | | (181) all_207_2 = all_170_0 % 260.89/36.37 | | | | | | | | | | | % 260.89/36.37 | | | | | | | | | | | COMBINE_EQS: (49), (181) imply: % 260.89/36.37 | | | | | | | | | | | (182) all_207_2 = empty_set % 260.89/36.37 | | | | | | | | | | | % 260.89/36.37 | | | | | | | | | | | REDUCE: (180), (182) imply: % 260.89/36.37 | | | | | | | | | | | (183) $false % 260.89/36.37 | | | | | | | | | | | % 260.89/36.37 | | | | | | | | | | | CLOSE: (183) is inconsistent. % 260.89/36.37 | | | | | | | | | | | % 260.89/36.37 | | | | | | | | | | Case 2: % 260.89/36.37 | | | | | | | | | | | % 260.89/36.37 | | | | | | | | | | | (184) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 260.89/36.37 | | | | | | | | | | | (ordered_pair(v0, v1) = v2 & $i(v2) & $i(v1) & % 260.89/36.37 | | | | | | | | | | | $i(v0) & ( ~ in(v2, all_207_3) | ~ in(v2, % 260.89/36.37 | | | | | | | | | | | all_170_0) | ~ in(v1, all_207_4)) & (in(v2, % 260.89/36.37 | | | | | | | | | | | all_170_0) | (in(v2, all_207_3) & in(v1, % 260.89/36.37 | | | | | | | | | | | all_207_4)))) % 260.89/36.37 | | | | | | | | | | | % 260.89/36.37 | | | | | | | | | | | DELTA: instantiating (184) with fresh symbols all_462_0, % 260.89/36.37 | | | | | | | | | | | all_462_1, all_462_2 gives: % 260.89/36.37 | | | | | | | | | | | (185) ordered_pair(all_462_2, all_462_1) = all_462_0 & % 260.89/36.37 | | | | | | | | | | | $i(all_462_0) & $i(all_462_1) & $i(all_462_2) & ( % 260.89/36.37 | | | | | | | | | | | ~ in(all_462_0, all_207_3) | ~ in(all_462_0, % 260.89/36.37 | | | | | | | | | | | all_170_0) | ~ in(all_462_1, all_207_4)) & % 260.89/36.37 | | | | | | | | | | | (in(all_462_0, all_170_0) | (in(all_462_0, % 260.89/36.37 | | | | | | | | | | | all_207_3) & in(all_462_1, all_207_4))) % 260.89/36.37 | | | | | | | | | | | % 260.89/36.37 | | | | | | | | | | | ALPHA: (185) implies: % 260.89/36.37 | | | | | | | | | | | (186) $i(all_462_0) % 260.89/36.37 | | | | | | | | | | | (187) in(all_462_0, all_170_0) | (in(all_462_0, % 260.89/36.37 | | | | | | | | | | | all_207_3) & in(all_462_1, all_207_4)) % 260.89/36.37 | | | | | | | | | | | (188) ~ in(all_462_0, all_207_3) | ~ in(all_462_0, % 260.89/36.37 | | | | | | | | | | | all_170_0) | ~ in(all_462_1, all_207_4) % 260.89/36.37 | | | | | | | | | | | % 260.89/36.37 | | | | | | | | | | | BETA: splitting (66) gives: % 260.89/36.37 | | | | | | | | | | | % 260.89/36.37 | | | | | | | | | | | Case 1: % 260.89/36.37 | | | | | | | | | | | | % 260.89/36.37 | | | | | | | | | | | | (189) all_207_2 = all_172_0 % 260.89/36.37 | | | | | | | | | | | | % 260.89/36.37 | | | | | | | | | | | | REDUCE: (141), (189) imply: % 260.89/36.37 | | | | | | | | | | | | (190) ~ (all_207_3 = all_172_0) % 260.89/36.37 | | | | | | | | | | | | % 260.89/36.37 | | | | | | | | | | | | SIMP: (190) implies: % 260.89/36.37 | | | | | | | | | | | | (191) ~ (all_207_3 = all_172_0) % 260.89/36.37 | | | | | | | | | | | | % 260.89/36.37 | | | | | | | | | | | | GROUND_INST: instantiating (1) with all_172_0, all_207_3, % 260.89/36.37 | | | | | | | | | | | | simplifying with (36), (41), (136), (138) gives: % 260.89/36.37 | | | | | | | | | | | | (192) all_207_3 = all_172_0 % 260.89/36.37 | | | | | | | | | | | | % 260.89/36.37 | | | | | | | | | | | | REDUCE: (191), (192) imply: % 260.89/36.37 | | | | | | | | | | | | (193) $false % 260.89/36.37 | | | | | | | | | | | | % 260.89/36.37 | | | | | | | | | | | | CLOSE: (193) is inconsistent. % 260.89/36.37 | | | | | | | | | | | | % 260.89/36.37 | | | | | | | | | | | Case 2: % 260.89/36.37 | | | | | | | | | | | | % 260.89/36.38 | | | | | | | | | | | | (194) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 260.89/36.38 | | | | | | | | | | | | (ordered_pair(v0, v1) = v2 & $i(v2) & $i(v1) & % 260.89/36.38 | | | | | | | | | | | | $i(v0) & ( ~ in(v2, all_207_3) | ~ in(v2, % 260.89/36.38 | | | | | | | | | | | | all_172_0) | ~ in(v1, all_207_4)) & (in(v2, % 260.89/36.38 | | | | | | | | | | | | all_172_0) | (in(v2, all_207_3) & in(v1, % 260.89/36.38 | | | | | | | | | | | | all_207_4)))) % 260.89/36.38 | | | | | | | | | | | | % 260.89/36.38 | | | | | | | | | | | | DELTA: instantiating (194) with fresh symbols all_515_0, % 260.89/36.38 | | | | | | | | | | | | all_515_1, all_515_2 gives: % 260.89/36.38 | | | | | | | | | | | | (195) ordered_pair(all_515_2, all_515_1) = all_515_0 & % 260.89/36.38 | | | | | | | | | | | | $i(all_515_0) & $i(all_515_1) & $i(all_515_2) & ( % 260.89/36.38 | | | | | | | | | | | | ~ in(all_515_0, all_207_3) | ~ in(all_515_0, % 260.89/36.38 | | | | | | | | | | | | all_172_0) | ~ in(all_515_1, all_207_4)) & % 260.89/36.38 | | | | | | | | | | | | (in(all_515_0, all_172_0) | (in(all_515_0, % 260.89/36.38 | | | | | | | | | | | | all_207_3) & in(all_515_1, all_207_4))) % 260.89/36.38 | | | | | | | | | | | | % 260.89/36.38 | | | | | | | | | | | | ALPHA: (195) implies: % 260.89/36.38 | | | | | | | | | | | | (196) in(all_515_0, all_172_0) | (in(all_515_0, % 260.89/36.38 | | | | | | | | | | | | all_207_3) & in(all_515_1, all_207_4)) % 260.89/36.38 | | | | | | | | | | | | (197) ~ in(all_515_0, all_207_3) | ~ in(all_515_0, % 260.89/36.38 | | | | | | | | | | | | all_172_0) | ~ in(all_515_1, all_207_4) % 260.89/36.38 | | | | | | | | | | | | % 260.89/36.38 | | | | | | | | | | | | BETA: splitting (56) gives: % 260.89/36.38 | | | | | | | | | | | | % 260.89/36.38 | | | | | | | | | | | | Case 1: % 260.89/36.38 | | | | | | | | | | | | | % 260.89/36.38 | | | | | | | | | | | | | (198) all_207_3 = all_172_0 % 260.89/36.38 | | | | | | | | | | | | | % 260.89/36.38 | | | | | | | | | | | | | REDUCE: (127), (198) imply: % 260.89/36.38 | | | | | | | | | | | | | (199) relation_rng(all_172_0) = all_207_0 % 260.89/36.38 | | | | | | | | | | | | | % 260.89/36.38 | | | | | | | | | | | | | REDUCE: (44), (198) imply: % 260.89/36.38 | | | | | | | | | | | | | (200) relation_rng_restriction(all_207_4, all_172_0) = % 260.89/36.38 | | | | | | | | | | | | | all_207_2 % 260.89/36.38 | | | | | | | | | | | | | % 260.89/36.38 | | | | | | | | | | | | | BETA: splitting (196) gives: % 260.89/36.38 | | | | | | | | | | | | | % 260.89/36.38 | | | | | | | | | | | | | Case 1: % 260.89/36.38 | | | | | | | | | | | | | | % 260.89/36.38 | | | | | | | | | | | | | | (201) in(all_515_0, all_172_0) % 260.89/36.38 | | | | | | | | | | | | | | % 260.89/36.38 | | | | | | | | | | | | | | BETA: splitting (197) gives: % 260.89/36.38 | | | | | | | | | | | | | | % 260.89/36.38 | | | | | | | | | | | | | | Case 1: % 260.89/36.38 | | | | | | | | | | | | | | | % 260.89/36.38 | | | | | | | | | | | | | | | (202) ~ in(all_515_0, all_207_3) % 260.89/36.38 | | | | | | | | | | | | | | | % 260.89/36.38 | | | | | | | | | | | | | | | REDUCE: (198), (202) imply: % 260.89/36.38 | | | | | | | | | | | | | | | (203) ~ in(all_515_0, all_172_0) % 260.89/36.38 | | | | | | | | | | | | | | | % 260.89/36.38 | | | | | | | | | | | | | | | PRED_UNIFY: (201), (203) imply: % 260.89/36.38 | | | | | | | | | | | | | | | (204) $false % 260.89/36.38 | | | | | | | | | | | | | | | % 260.89/36.38 | | | | | | | | | | | | | | | CLOSE: (204) is inconsistent. % 260.89/36.38 | | | | | | | | | | | | | | | % 260.89/36.38 | | | | | | | | | | | | | | Case 2: % 260.89/36.38 | | | | | | | | | | | | | | | % 260.89/36.38 | | | | | | | | | | | | | | | (205) in(all_515_0, all_207_3) % 260.89/36.38 | | | | | | | | | | | | | | | (206) ~ in(all_515_0, all_172_0) | ~ in(all_515_1, % 260.89/36.38 | | | | | | | | | | | | | | | all_207_4) % 260.89/36.38 | | | | | | | | | | | | | | | % 260.89/36.38 | | | | | | | | | | | | | | | BETA: splitting (206) gives: % 260.89/36.38 | | | | | | | | | | | | | | | % 260.89/36.38 | | | | | | | | | | | | | | | Case 1: % 260.89/36.38 | | | | | | | | | | | | | | | | % 260.89/36.38 | | | | | | | | | | | | | | | | (207) ~ in(all_515_0, all_172_0) % 260.89/36.38 | | | | | | | | | | | | | | | | % 260.89/36.38 | | | | | | | | | | | | | | | | PRED_UNIFY: (201), (207) imply: % 260.89/36.38 | | | | | | | | | | | | | | | | (208) $false % 260.89/36.38 | | | | | | | | | | | | | | | | % 260.89/36.38 | | | | | | | | | | | | | | | | CLOSE: (208) is inconsistent. % 260.89/36.38 | | | | | | | | | | | | | | | | % 260.89/36.38 | | | | | | | | | | | | | | | Case 2: % 260.89/36.38 | | | | | | | | | | | | | | | | % 260.89/36.38 | | | | | | | | | | | | | | | | % 260.89/36.38 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (10) with all_172_0, all_207_0, % 260.89/36.38 | | | | | | | | | | | | | | | | all_207_5, simplifying with (35), (36), (39), % 260.89/36.38 | | | | | | | | | | | | | | | | (125), (126), (199) gives: % 260.89/36.38 | | | | | | | | | | | | | | | | (209) ? [v0: $i] : ? [v1: $i] : (ordered_pair(v0, % 260.89/36.38 | | | | | | | | | | | | | | | | all_207_5) = v1 & $i(v1) & $i(v0) & in(v1, % 260.89/36.38 | | | | | | | | | | | | | | | | all_172_0)) % 260.89/36.38 | | | | | | | | | | | | | | | | % 260.89/36.38 | | | | | | | | | | | | | | | | DELTA: instantiating (209) with fresh symbols all_609_0, % 260.89/36.38 | | | | | | | | | | | | | | | | all_609_1 gives: % 260.89/36.38 | | | | | | | | | | | | | | | | (210) ordered_pair(all_609_1, all_207_5) = all_609_0 & % 260.89/36.38 | | | | | | | | | | | | | | | | $i(all_609_0) & $i(all_609_1) & in(all_609_0, % 260.89/36.38 | | | | | | | | | | | | | | | | all_172_0) % 260.89/36.38 | | | | | | | | | | | | | | | | % 260.89/36.38 | | | | | | | | | | | | | | | | ALPHA: (210) implies: % 260.89/36.38 | | | | | | | | | | | | | | | | (211) in(all_609_0, all_172_0) % 260.89/36.38 | | | | | | | | | | | | | | | | (212) $i(all_609_1) % 260.89/36.38 | | | | | | | | | | | | | | | | (213) ordered_pair(all_609_1, all_207_5) = all_609_0 % 260.89/36.38 | | | | | | | | | | | | | | | | % 260.89/36.38 | | | | | | | | | | | | | | | | BETA: splitting (188) gives: % 260.89/36.38 | | | | | | | | | | | | | | | | % 260.89/36.38 | | | | | | | | | | | | | | | | Case 1: % 260.89/36.38 | | | | | | | | | | | | | | | | | % 260.89/36.38 | | | | | | | | | | | | | | | | | (214) ~ in(all_462_0, all_207_3) % 260.89/36.38 | | | | | | | | | | | | | | | | | % 260.89/36.38 | | | | | | | | | | | | | | | | | REDUCE: (198), (214) imply: % 260.89/36.38 | | | | | | | | | | | | | | | | | (215) ~ in(all_462_0, all_172_0) % 260.89/36.38 | | | | | | | | | | | | | | | | | % 260.89/36.38 | | | | | | | | | | | | | | | | | BETA: splitting (187) gives: % 260.89/36.38 | | | | | | | | | | | | | | | | | % 260.89/36.38 | | | | | | | | | | | | | | | | | Case 1: % 260.89/36.38 | | | | | | | | | | | | | | | | | | % 260.89/36.38 | | | | | | | | | | | | | | | | | | (216) in(all_462_0, all_170_0) % 260.89/36.38 | | | | | | | | | | | | | | | | | | % 260.89/36.38 | | | | | | | | | | | | | | | | | | REDUCE: (49), (216) imply: % 260.89/36.38 | | | | | | | | | | | | | | | | | | (217) in(all_462_0, empty_set) % 260.89/36.38 | | | | | | | | | | | | | | | | | | % 260.89/36.38 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (6) with all_462_0, simplifying with % 260.89/36.38 | | | | | | | | | | | | | | | | | | (186), (217) gives: % 260.89/36.38 | | | | | | | | | | | | | | | | | | (218) $false % 260.89/36.38 | | | | | | | | | | | | | | | | | | % 260.89/36.38 | | | | | | | | | | | | | | | | | | CLOSE: (218) is inconsistent. % 260.89/36.38 | | | | | | | | | | | | | | | | | | % 260.89/36.38 | | | | | | | | | | | | | | | | | Case 2: % 260.89/36.38 | | | | | | | | | | | | | | | | | | % 260.89/36.38 | | | | | | | | | | | | | | | | | | (219) in(all_462_0, all_207_3) & in(all_462_1, % 260.89/36.38 | | | | | | | | | | | | | | | | | | all_207_4) % 260.89/36.38 | | | | | | | | | | | | | | | | | | % 260.89/36.38 | | | | | | | | | | | | | | | | | | ALPHA: (219) implies: % 260.89/36.38 | | | | | | | | | | | | | | | | | | (220) in(all_462_0, all_207_3) % 260.89/36.38 | | | | | | | | | | | | | | | | | | % 260.89/36.38 | | | | | | | | | | | | | | | | | | REDUCE: (198), (220) imply: % 260.89/36.38 | | | | | | | | | | | | | | | | | | (221) in(all_462_0, all_172_0) % 260.89/36.38 | | | | | | | | | | | | | | | | | | % 260.89/36.38 | | | | | | | | | | | | | | | | | | PRED_UNIFY: (215), (221) imply: % 260.89/36.38 | | | | | | | | | | | | | | | | | | (222) $false % 260.89/36.38 | | | | | | | | | | | | | | | | | | % 260.89/36.38 | | | | | | | | | | | | | | | | | | CLOSE: (222) is inconsistent. % 260.89/36.38 | | | | | | | | | | | | | | | | | | % 260.89/36.38 | | | | | | | | | | | | | | | | | End of split % 260.89/36.38 | | | | | | | | | | | | | | | | | % 260.89/36.38 | | | | | | | | | | | | | | | | Case 2: % 260.89/36.38 | | | | | | | | | | | | | | | | | % 260.89/36.38 | | | | | | | | | | | | | | | | | % 260.89/36.38 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (3) with all_207_4, all_172_0, % 260.89/36.38 | | | | | | | | | | | | | | | | | all_207_2, all_609_1, all_207_5, all_609_0, % 260.89/36.38 | | | | | | | | | | | | | | | | | simplifying with (35), (36), (39), (40), (42), % 260.89/36.38 | | | | | | | | | | | | | | | | | (65), (124), (200), (211), (212), (213) gives: % 260.89/36.38 | | | | | | | | | | | | | | | | | (223) in(all_609_0, all_207_2) % 260.89/36.38 | | | | | | | | | | | | | | | | | % 260.89/36.38 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (11) with all_207_2, all_207_1, % 260.89/36.38 | | | | | | | | | | | | | | | | | all_207_5, all_609_1, all_609_0, simplifying with % 260.89/36.38 | | | | | | | | | | | | | | | | | (39), (42), (43), (45), (65), (123), (212), (213), % 260.89/36.38 | | | | | | | | | | | | | | | | | (223) gives: % 260.89/36.38 | | | | | | | | | | | | | | | | | (224) $false % 260.89/36.38 | | | | | | | | | | | | | | | | | % 260.89/36.38 | | | | | | | | | | | | | | | | | CLOSE: (224) is inconsistent. % 260.89/36.38 | | | | | | | | | | | | | | | | | % 260.89/36.38 | | | | | | | | | | | | | | | | End of split % 260.89/36.38 | | | | | | | | | | | | | | | | % 260.89/36.38 | | | | | | | | | | | | | | | End of split % 260.89/36.38 | | | | | | | | | | | | | | | % 260.89/36.38 | | | | | | | | | | | | | | End of split % 260.89/36.38 | | | | | | | | | | | | | | % 260.89/36.38 | | | | | | | | | | | | | Case 2: % 260.89/36.38 | | | | | | | | | | | | | | % 260.89/36.38 | | | | | | | | | | | | | | (225) ~ in(all_515_0, all_172_0) % 260.89/36.38 | | | | | | | | | | | | | | (226) in(all_515_0, all_207_3) & in(all_515_1, % 260.89/36.38 | | | | | | | | | | | | | | all_207_4) % 260.89/36.38 | | | | | | | | | | | | | | % 260.89/36.38 | | | | | | | | | | | | | | ALPHA: (226) implies: % 260.89/36.38 | | | | | | | | | | | | | | (227) in(all_515_0, all_207_3) % 260.89/36.38 | | | | | | | | | | | | | | % 260.89/36.38 | | | | | | | | | | | | | | REDUCE: (198), (227) imply: % 260.89/36.38 | | | | | | | | | | | | | | (228) in(all_515_0, all_172_0) % 260.89/36.38 | | | | | | | | | | | | | | % 260.89/36.38 | | | | | | | | | | | | | | PRED_UNIFY: (225), (228) imply: % 260.89/36.38 | | | | | | | | | | | | | | (229) $false % 260.89/36.38 | | | | | | | | | | | | | | % 260.89/36.38 | | | | | | | | | | | | | | CLOSE: (229) is inconsistent. % 260.89/36.38 | | | | | | | | | | | | | | % 260.89/36.38 | | | | | | | | | | | | | End of split % 260.89/36.38 | | | | | | | | | | | | | % 260.89/36.38 | | | | | | | | | | | | Case 2: % 260.89/36.38 | | | | | | | | | | | | | % 260.89/36.38 | | | | | | | | | | | | | (230) ~ (all_207_3 = all_172_0) % 260.89/36.38 | | | | | | | | | | | | | % 260.89/36.38 | | | | | | | | | | | | | REF_CLOSE: (1), (36), (41), (136), (138), (230) are % 260.89/36.38 | | | | | | | | | | | | | inconsistent by sub-proof #5. % 260.89/36.38 | | | | | | | | | | | | | % 260.89/36.38 | | | | | | | | | | | | End of split % 260.89/36.38 | | | | | | | | | | | | % 260.89/36.38 | | | | | | | | | | | End of split % 260.89/36.38 | | | | | | | | | | | % 260.89/36.38 | | | | | | | | | | End of split % 260.89/36.38 | | | | | | | | | | % 260.89/36.38 | | | | | | | | | End of split % 260.89/36.38 | | | | | | | | | % 260.89/36.38 | | | | | | | | End of split % 260.89/36.38 | | | | | | | | % 260.89/36.38 | | | | | | | End of split % 260.89/36.38 | | | | | | | % 260.89/36.38 | | | | | | Case 2: % 260.89/36.38 | | | | | | | % 260.89/36.38 | | | | | | | (231) ~ subset(all_207_3, all_172_0) % 260.89/36.38 | | | | | | | % 260.89/36.38 | | | | | | | BETA: splitting (53) gives: % 260.89/36.38 | | | | | | | % 260.89/36.38 | | | | | | | Case 1: % 260.89/36.38 | | | | | | | | % 260.89/36.38 | | | | | | | | (232) subset(all_172_0, empty_set) % 260.89/36.38 | | | | | | | | % 260.89/36.38 | | | | | | | | REF_CLOSE: (14), (34), (36), (54), (113), (232) are inconsistent % 260.89/36.38 | | | | | | | | by sub-proof #4. % 260.89/36.38 | | | | | | | | % 260.89/36.38 | | | | | | | Case 2: % 260.89/36.38 | | | | | | | | % 260.89/36.38 | | | | | | | | (233) ~ subset(all_172_0, empty_set) % 260.89/36.38 | | | | | | | | % 260.89/36.38 | | | | | | | | BETA: splitting (59) gives: % 260.89/36.38 | | | | | | | | % 260.89/36.38 | | | | | | | | Case 1: % 260.89/36.38 | | | | | | | | | % 260.89/36.38 | | | | | | | | | (234) all_207_3 = all_170_0 % 260.89/36.38 | | | | | | | | | % 260.89/36.38 | | | | | | | | | COMBINE_EQS: (49), (234) imply: % 260.89/36.38 | | | | | | | | | (235) all_207_3 = empty_set % 260.89/36.38 | | | | | | | | | % 260.89/36.38 | | | | | | | | | REDUCE: (231), (235) imply: % 260.89/36.38 | | | | | | | | | (236) ~ subset(empty_set, all_172_0) % 260.89/36.38 | | | | | | | | | % 260.89/36.38 | | | | | | | | | PRED_UNIFY: (137), (236) imply: % 260.89/36.38 | | | | | | | | | (237) $false % 260.89/36.38 | | | | | | | | | % 260.89/36.38 | | | | | | | | | CLOSE: (237) is inconsistent. % 260.89/36.38 | | | | | | | | | % 260.89/36.38 | | | | | | | | Case 2: % 260.89/36.38 | | | | | | | | | % 260.89/36.38 | | | | | | | | | (238) ~ (all_207_3 = all_170_0) % 260.89/36.38 | | | | | | | | | % 260.89/36.38 | | | | | | | | | REDUCE: (49), (238) imply: % 260.89/36.38 | | | | | | | | | (239) ~ (all_207_3 = empty_set) % 260.89/36.38 | | | | | | | | | % 260.89/36.39 | | | | | | | | | REF_CLOSE: (3), (6), (10), (11), (38), (39), (40), (41), (42), % 260.89/36.39 | | | | | | | | | (43), (44), (45), (49), (54), (61), (65), (66), % 260.89/36.39 | | | | | | | | | (67), (68), (99), (123), (124), (125), (126), % 260.89/36.39 | | | | | | | | | (127), (137), (233), (239) are inconsistent by % 260.89/36.39 | | | | | | | | | sub-proof #3. % 260.89/36.39 | | | | | | | | | % 260.89/36.39 | | | | | | | | End of split % 260.89/36.39 | | | | | | | | % 260.89/36.39 | | | | | | | End of split % 260.89/36.39 | | | | | | | % 260.89/36.39 | | | | | | End of split % 260.89/36.39 | | | | | | % 260.89/36.39 | | | | | Case 2: % 260.89/36.39 | | | | | | % 260.89/36.39 | | | | | | (240) ~ subset(empty_set, all_172_0) % 260.89/36.39 | | | | | | % 260.89/36.39 | | | | | | REF_CLOSE: (6), (49), (51), (240) are inconsistent by sub-proof #2. % 260.89/36.39 | | | | | | % 260.89/36.39 | | | | | End of split % 260.89/36.39 | | | | | % 260.89/36.39 | | | | Case 2: % 260.89/36.39 | | | | | % 260.89/36.39 | | | | | (241) ~ subset(all_172_0, all_207_3) % 260.89/36.39 | | | | | % 260.89/36.39 | | | | | BETA: splitting (52) gives: % 260.89/36.39 | | | | | % 260.89/36.39 | | | | | Case 1: % 260.89/36.39 | | | | | | % 260.89/36.39 | | | | | | (242) subset(empty_set, all_172_0) % 260.89/36.39 | | | | | | % 260.89/36.39 | | | | | | BETA: splitting (58) gives: % 260.89/36.39 | | | | | | % 260.89/36.39 | | | | | | Case 1: % 260.89/36.39 | | | | | | | % 260.89/36.39 | | | | | | | (243) subset(all_207_3, all_172_0) % 260.89/36.39 | | | | | | | % 260.89/36.39 | | | | | | | BETA: splitting (59) gives: % 260.89/36.39 | | | | | | | % 260.89/36.39 | | | | | | | Case 1: % 260.89/36.39 | | | | | | | | % 260.89/36.39 | | | | | | | | (244) all_207_3 = all_170_0 % 260.89/36.39 | | | | | | | | % 260.89/36.39 | | | | | | | | COMBINE_EQS: (49), (244) imply: % 260.89/36.39 | | | | | | | | (245) all_207_3 = empty_set % 260.89/36.39 | | | | | | | | % 260.89/36.39 | | | | | | | | REDUCE: (128), (245) imply: % 260.89/36.39 | | | | | | | | (246) subset(empty_set, empty_set) % 260.89/36.39 | | | | | | | | % 260.89/36.39 | | | | | | | | REDUCE: (135), (245) imply: % 260.89/36.39 | | | | | | | | (247) ~ subset(empty_set, empty_set) % 260.89/36.39 | | | | | | | | % 260.89/36.39 | | | | | | | | PRED_UNIFY: (246), (247) imply: % 260.89/36.39 | | | | | | | | (248) $false % 260.89/36.39 | | | | | | | | % 260.89/36.39 | | | | | | | | CLOSE: (248) is inconsistent. % 260.89/36.39 | | | | | | | | % 260.89/36.39 | | | | | | | Case 2: % 260.89/36.39 | | | | | | | | % 260.89/36.39 | | | | | | | | (249) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 260.89/36.39 | | | | | | | | (ordered_pair(v0, v1) = v2 & $i(v2) & $i(v1) & $i(v0) & % 260.89/36.39 | | | | | | | | ( ~ in(v2, all_207_3) | ~ in(v2, all_170_0)) & % 260.89/36.39 | | | | | | | | (in(v2, all_207_3) | in(v2, all_170_0))) % 260.89/36.39 | | | | | | | | % 260.89/36.39 | | | | | | | | DELTA: instantiating (249) with fresh symbols all_419_0, % 260.89/36.39 | | | | | | | | all_419_1, all_419_2 gives: % 260.89/36.39 | | | | | | | | (250) ordered_pair(all_419_2, all_419_1) = all_419_0 & % 260.89/36.39 | | | | | | | | $i(all_419_0) & $i(all_419_1) & $i(all_419_2) & ( ~ % 260.89/36.39 | | | | | | | | in(all_419_0, all_207_3) | ~ in(all_419_0, % 260.89/36.39 | | | | | | | | all_170_0)) & (in(all_419_0, all_207_3) | % 260.89/36.39 | | | | | | | | in(all_419_0, all_170_0)) % 260.89/36.39 | | | | | | | | % 260.89/36.39 | | | | | | | | ALPHA: (250) implies: % 260.89/36.39 | | | | | | | | (251) $i(all_419_0) % 260.89/36.39 | | | | | | | | (252) in(all_419_0, all_207_3) | in(all_419_0, all_170_0) % 260.89/36.39 | | | | | | | | (253) ~ in(all_419_0, all_207_3) | ~ in(all_419_0, % 260.89/36.39 | | | | | | | | all_170_0) % 260.89/36.39 | | | | | | | | % 260.89/36.39 | | | | | | | | BETA: splitting (54) gives: % 260.89/36.39 | | | | | | | | % 260.89/36.39 | | | | | | | | Case 1: % 260.89/36.39 | | | | | | | | | % 260.89/36.39 | | | | | | | | | (254) all_172_0 = empty_set % 260.89/36.39 | | | | | | | | | % 260.89/36.39 | | | | | | | | | REDUCE: (243), (254) imply: % 260.89/36.39 | | | | | | | | | (255) subset(all_207_3, empty_set) % 260.89/36.39 | | | | | | | | | % 260.89/36.39 | | | | | | | | | PRED_UNIFY: (135), (255) imply: % 260.89/36.39 | | | | | | | | | (256) $false % 260.89/36.39 | | | | | | | | | % 260.89/36.39 | | | | | | | | | CLOSE: (256) is inconsistent. % 260.89/36.39 | | | | | | | | | % 260.89/36.39 | | | | | | | | Case 2: % 260.89/36.39 | | | | | | | | | % 260.89/36.39 | | | | | | | | | (257) ~ (all_172_0 = empty_set) % 260.89/36.39 | | | | | | | | | % 260.89/36.39 | | | | | | | | | BETA: splitting (50) gives: % 260.89/36.39 | | | | | | | | | % 260.89/36.39 | | | | | | | | | Case 1: % 260.89/36.39 | | | | | | | | | | % 260.89/36.39 | | | | | | | | | | (258) all_172_0 = all_170_0 % 260.89/36.39 | | | | | | | | | | % 260.89/36.39 | | | | | | | | | | COMBINE_EQS: (49), (258) imply: % 260.89/36.39 | | | | | | | | | | (259) all_172_0 = empty_set % 260.89/36.39 | | | | | | | | | | % 260.89/36.39 | | | | | | | | | | REDUCE: (257), (259) imply: % 260.89/36.39 | | | | | | | | | | (260) $false % 260.89/36.39 | | | | | | | | | | % 260.89/36.39 | | | | | | | | | | CLOSE: (260) is inconsistent. % 260.89/36.39 | | | | | | | | | | % 260.89/36.39 | | | | | | | | | Case 2: % 260.89/36.39 | | | | | | | | | | % 260.89/36.39 | | | | | | | | | | (261) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 260.89/36.39 | | | | | | | | | | (ordered_pair(v0, v1) = v2 & $i(v2) & $i(v1) & % 260.89/36.39 | | | | | | | | | | $i(v0) & ( ~ in(v2, all_172_0) | ~ in(v2, % 260.89/36.39 | | | | | | | | | | all_170_0)) & (in(v2, all_172_0) | in(v2, % 260.89/36.39 | | | | | | | | | | all_170_0))) % 260.89/36.39 | | | | | | | | | | % 260.89/36.39 | | | | | | | | | | DELTA: instantiating (261) with fresh symbols all_463_0, % 260.89/36.39 | | | | | | | | | | all_463_1, all_463_2 gives: % 260.89/36.39 | | | | | | | | | | (262) ordered_pair(all_463_2, all_463_1) = all_463_0 & % 260.89/36.39 | | | | | | | | | | $i(all_463_0) & $i(all_463_1) & $i(all_463_2) & ( ~ % 260.89/36.39 | | | | | | | | | | in(all_463_0, all_172_0) | ~ in(all_463_0, % 260.89/36.39 | | | | | | | | | | all_170_0)) & (in(all_463_0, all_172_0) | % 260.89/36.39 | | | | | | | | | | in(all_463_0, all_170_0)) % 260.89/36.39 | | | | | | | | | | % 260.89/36.39 | | | | | | | | | | ALPHA: (262) implies: % 260.89/36.39 | | | | | | | | | | (263) $i(all_463_0) % 260.89/36.39 | | | | | | | | | | (264) in(all_463_0, all_172_0) | in(all_463_0, all_170_0) % 260.89/36.39 | | | | | | | | | | (265) ~ in(all_463_0, all_172_0) | ~ in(all_463_0, % 260.89/36.39 | | | | | | | | | | all_170_0) % 260.89/36.39 | | | | | | | | | | % 260.89/36.39 | | | | | | | | | | BETA: splitting (68) gives: % 260.89/36.39 | | | | | | | | | | % 260.89/36.39 | | | | | | | | | | Case 1: % 260.89/36.39 | | | | | | | | | | | % 260.89/36.39 | | | | | | | | | | | (266) all_207_2 = empty_set % 260.89/36.39 | | | | | | | | | | | % 260.89/36.39 | | | | | | | | | | | REDUCE: (44), (266) imply: % 260.89/36.39 | | | | | | | | | | | (267) relation_rng_restriction(all_207_4, all_207_3) = % 260.89/36.39 | | | | | | | | | | | empty_set % 260.89/36.39 | | | | | | | | | | | % 260.89/36.39 | | | | | | | | | | | BETA: splitting (56) gives: % 260.89/36.39 | | | | | | | | | | | % 260.89/36.39 | | | | | | | | | | | Case 1: % 260.89/36.39 | | | | | | | | | | | | % 260.89/36.39 | | | | | | | | | | | | (268) all_207_3 = all_172_0 % 260.89/36.39 | | | | | | | | | | | | % 260.89/36.39 | | | | | | | | | | | | REDUCE: (243), (268) imply: % 260.89/36.39 | | | | | | | | | | | | (269) subset(all_172_0, all_172_0) % 260.89/36.39 | | | | | | | | | | | | % 260.89/36.39 | | | | | | | | | | | | REDUCE: (241), (268) imply: % 260.89/36.39 | | | | | | | | | | | | (270) ~ subset(all_172_0, all_172_0) % 260.89/36.39 | | | | | | | | | | | | % 260.89/36.39 | | | | | | | | | | | | PRED_UNIFY: (269), (270) imply: % 260.89/36.39 | | | | | | | | | | | | (271) $false % 260.89/36.39 | | | | | | | | | | | | % 260.89/36.39 | | | | | | | | | | | | CLOSE: (271) is inconsistent. % 260.89/36.39 | | | | | | | | | | | | % 260.89/36.39 | | | | | | | | | | | Case 2: % 260.89/36.39 | | | | | | | | | | | | % 260.89/36.39 | | | | | | | | | | | | % 260.89/36.39 | | | | | | | | | | | | GROUND_INST: instantiating (10) with all_207_3, all_207_0, % 260.89/36.39 | | | | | | | | | | | | all_207_5, simplifying with (38), (39), (41), % 260.89/36.39 | | | | | | | | | | | | (125), (126), (127) gives: % 260.89/36.39 | | | | | | | | | | | | (272) ? [v0: $i] : ? [v1: $i] : (ordered_pair(v0, % 260.89/36.39 | | | | | | | | | | | | all_207_5) = v1 & $i(v1) & $i(v0) & in(v1, % 260.89/36.39 | | | | | | | | | | | | all_207_3)) % 260.89/36.39 | | | | | | | | | | | | % 260.89/36.39 | | | | | | | | | | | | DELTA: instantiating (272) with fresh symbols all_570_0, % 260.89/36.39 | | | | | | | | | | | | all_570_1 gives: % 260.89/36.39 | | | | | | | | | | | | (273) ordered_pair(all_570_1, all_207_5) = all_570_0 & % 260.89/36.39 | | | | | | | | | | | | $i(all_570_0) & $i(all_570_1) & in(all_570_0, % 260.89/36.39 | | | | | | | | | | | | all_207_3) % 260.89/36.39 | | | | | | | | | | | | % 260.89/36.39 | | | | | | | | | | | | ALPHA: (273) implies: % 260.89/36.39 | | | | | | | | | | | | (274) in(all_570_0, all_207_3) % 260.89/36.39 | | | | | | | | | | | | (275) $i(all_570_1) % 260.89/36.39 | | | | | | | | | | | | (276) $i(all_570_0) % 260.89/36.39 | | | | | | | | | | | | (277) ordered_pair(all_570_1, all_207_5) = all_570_0 % 260.89/36.39 | | | | | | | | | | | | % 260.89/36.39 | | | | | | | | | | | | BETA: splitting (253) gives: % 260.89/36.39 | | | | | | | | | | | | % 260.89/36.39 | | | | | | | | | | | | Case 1: % 260.89/36.39 | | | | | | | | | | | | | % 260.89/36.39 | | | | | | | | | | | | | (278) ~ in(all_419_0, all_207_3) % 260.89/36.39 | | | | | | | | | | | | | % 260.89/36.39 | | | | | | | | | | | | | BETA: splitting (252) gives: % 260.89/36.39 | | | | | | | | | | | | | % 260.89/36.39 | | | | | | | | | | | | | Case 1: % 260.89/36.39 | | | | | | | | | | | | | | % 260.89/36.39 | | | | | | | | | | | | | | (279) in(all_419_0, all_207_3) % 260.89/36.39 | | | | | | | | | | | | | | % 260.89/36.39 | | | | | | | | | | | | | | PRED_UNIFY: (278), (279) imply: % 260.89/36.39 | | | | | | | | | | | | | | (280) $false % 260.89/36.39 | | | | | | | | | | | | | | % 260.89/36.39 | | | | | | | | | | | | | | CLOSE: (280) is inconsistent. % 260.89/36.39 | | | | | | | | | | | | | | % 260.89/36.39 | | | | | | | | | | | | | Case 2: % 260.89/36.39 | | | | | | | | | | | | | | % 260.89/36.39 | | | | | | | | | | | | | | (281) in(all_419_0, all_170_0) % 260.89/36.39 | | | | | | | | | | | | | | % 260.89/36.39 | | | | | | | | | | | | | | REDUCE: (49), (281) imply: % 260.89/36.39 | | | | | | | | | | | | | | (282) in(all_419_0, empty_set) % 260.89/36.39 | | | | | | | | | | | | | | % 260.89/36.39 | | | | | | | | | | | | | | GROUND_INST: instantiating (6) with all_419_0, simplifying with % 260.89/36.39 | | | | | | | | | | | | | | (251), (282) gives: % 260.89/36.39 | | | | | | | | | | | | | | (283) $false % 260.89/36.39 | | | | | | | | | | | | | | % 260.89/36.39 | | | | | | | | | | | | | | CLOSE: (283) is inconsistent. % 260.89/36.39 | | | | | | | | | | | | | | % 260.89/36.39 | | | | | | | | | | | | | End of split % 260.89/36.39 | | | | | | | | | | | | | % 260.89/36.39 | | | | | | | | | | | | Case 2: % 260.89/36.39 | | | | | | | | | | | | | % 260.89/36.39 | | | | | | | | | | | | | % 260.89/36.39 | | | | | | | | | | | | | GROUND_INST: instantiating (3) with all_207_4, all_207_3, % 260.89/36.39 | | | | | | | | | | | | | empty_set, all_570_1, all_207_5, all_570_0, % 260.89/36.39 | | | | | | | | | | | | | simplifying with (12), (20), (38), (39), (40), % 260.89/36.39 | | | | | | | | | | | | | (41), (124), (267), (274), (275), (277) gives: % 260.89/36.39 | | | | | | | | | | | | | (284) in(all_570_0, empty_set) % 260.89/36.39 | | | | | | | | | | | | | % 260.89/36.39 | | | | | | | | | | | | | GROUND_INST: instantiating (6) with all_570_0, simplifying with % 260.89/36.39 | | | | | | | | | | | | | (276), (284) gives: % 260.89/36.39 | | | | | | | | | | | | | (285) $false % 260.89/36.39 | | | | | | | | | | | | | % 260.89/36.39 | | | | | | | | | | | | | CLOSE: (285) is inconsistent. % 260.89/36.39 | | | | | | | | | | | | | % 260.89/36.39 | | | | | | | | | | | | End of split % 260.89/36.39 | | | | | | | | | | | | % 260.89/36.39 | | | | | | | | | | | End of split % 260.89/36.39 | | | | | | | | | | | % 260.89/36.39 | | | | | | | | | | Case 2: % 260.89/36.39 | | | | | | | | | | | % 260.89/36.39 | | | | | | | | | | | (286) ~ (all_207_2 = empty_set) % 260.89/36.39 | | | | | | | | | | | % 260.89/36.39 | | | | | | | | | | | BETA: splitting (91) gives: % 260.89/36.39 | | | | | | | | | | | % 260.89/36.39 | | | | | | | | | | | Case 1: % 260.89/36.39 | | | | | | | | | | | | % 260.89/36.39 | | | | | | | | | | | | (287) all_207_2 = empty_set % 260.89/36.39 | | | | | | | | | | | | % 260.89/36.39 | | | | | | | | | | | | REDUCE: (286), (287) imply: % 260.89/36.39 | | | | | | | | | | | | (288) $false % 260.89/36.39 | | | | | | | | | | | | % 260.89/36.39 | | | | | | | | | | | | CLOSE: (288) is inconsistent. % 260.89/36.39 | | | | | | | | | | | | % 260.89/36.39 | | | | | | | | | | | Case 2: % 260.89/36.39 | | | | | | | | | | | | % 260.89/36.39 | | | | | | | | | | | | (289) ? [v0: $i] : ( ~ (v0 = empty_set) & % 260.89/36.39 | | | | | | | | | | | | relation_dom(all_207_2) = v0 & $i(v0)) % 260.89/36.39 | | | | | | | | | | | | % 260.89/36.39 | | | | | | | | | | | | DELTA: instantiating (289) with fresh symbol all_477_0 % 260.89/36.39 | | | | | | | | | | | | gives: % 260.89/36.40 | | | | | | | | | | | | (290) ~ (all_477_0 = empty_set) & % 260.89/36.40 | | | | | | | | | | | | relation_dom(all_207_2) = all_477_0 & % 260.89/36.40 | | | | | | | | | | | | $i(all_477_0) % 260.89/36.40 | | | | | | | | | | | | % 260.89/36.40 | | | | | | | | | | | | ALPHA: (290) implies: % 260.89/36.40 | | | | | | | | | | | | (291) ~ (all_477_0 = empty_set) % 260.89/36.40 | | | | | | | | | | | | (292) relation_dom(all_207_2) = all_477_0 % 260.89/36.40 | | | | | | | | | | | | % 260.89/36.40 | | | | | | | | | | | | GROUND_INST: instantiating (22) with all_242_0, all_477_0, % 260.89/36.40 | | | | | | | | | | | | all_207_2, simplifying with (106), (292) gives: % 260.89/36.40 | | | | | | | | | | | | (293) all_477_0 = all_242_0 % 260.89/36.40 | | | | | | | | | | | | % 260.89/36.40 | | | | | | | | | | | | REDUCE: (291), (293) imply: % 260.89/36.40 | | | | | | | | | | | | (294) ~ (all_242_0 = empty_set) % 260.89/36.40 | | | | | | | | | | | | % 260.89/36.40 | | | | | | | | | | | | BETA: splitting (104) gives: % 260.89/36.40 | | | | | | | | | | | | % 260.89/36.40 | | | | | | | | | | | | Case 1: % 260.89/36.40 | | | | | | | | | | | | | % 260.89/36.40 | | | | | | | | | | | | | % 260.89/36.40 | | | | | | | | | | | | | GROUND_INST: instantiating (10) with all_207_3, all_207_0, % 260.89/36.40 | | | | | | | | | | | | | all_207_5, simplifying with (38), (39), (41), % 260.89/36.40 | | | | | | | | | | | | | (125), (126), (127) gives: % 260.89/36.40 | | | | | | | | | | | | | (295) ? [v0: $i] : ? [v1: $i] : (ordered_pair(v0, % 260.89/36.40 | | | | | | | | | | | | | all_207_5) = v1 & $i(v1) & $i(v0) & in(v1, % 260.89/36.40 | | | | | | | | | | | | | all_207_3)) % 260.89/36.40 | | | | | | | | | | | | | % 260.89/36.40 | | | | | | | | | | | | | DELTA: instantiating (295) with fresh symbols all_593_0, % 260.89/36.40 | | | | | | | | | | | | | all_593_1 gives: % 260.89/36.40 | | | | | | | | | | | | | (296) ordered_pair(all_593_1, all_207_5) = all_593_0 & % 260.89/36.40 | | | | | | | | | | | | | $i(all_593_0) & $i(all_593_1) & in(all_593_0, % 260.89/36.40 | | | | | | | | | | | | | all_207_3) % 260.89/36.40 | | | | | | | | | | | | | % 260.89/36.40 | | | | | | | | | | | | | ALPHA: (296) implies: % 260.89/36.40 | | | | | | | | | | | | | (297) in(all_593_0, all_207_3) % 260.89/36.40 | | | | | | | | | | | | | (298) $i(all_593_1) % 260.89/36.40 | | | | | | | | | | | | | (299) ordered_pair(all_593_1, all_207_5) = all_593_0 % 260.89/36.40 | | | | | | | | | | | | | % 260.89/36.40 | | | | | | | | | | | | | BETA: splitting (264) gives: % 260.89/36.40 | | | | | | | | | | | | | % 260.89/36.40 | | | | | | | | | | | | | Case 1: % 260.89/36.40 | | | | | | | | | | | | | | % 260.89/36.40 | | | | | | | | | | | | | | (300) in(all_463_0, all_172_0) % 260.89/36.40 | | | | | | | | | | | | | | % 260.89/36.40 | | | | | | | | | | | | | | BETA: splitting (265) gives: % 260.89/36.40 | | | | | | | | | | | | | | % 260.89/36.40 | | | | | | | | | | | | | | Case 1: % 260.89/36.40 | | | | | | | | | | | | | | | % 260.89/36.40 | | | | | | | | | | | | | | | (301) ~ in(all_463_0, all_172_0) % 260.89/36.40 | | | | | | | | | | | | | | | % 260.89/36.40 | | | | | | | | | | | | | | | PRED_UNIFY: (300), (301) imply: % 260.89/36.40 | | | | | | | | | | | | | | | (302) $false % 260.89/36.40 | | | | | | | | | | | | | | | % 260.89/36.40 | | | | | | | | | | | | | | | CLOSE: (302) is inconsistent. % 260.89/36.40 | | | | | | | | | | | | | | | % 260.89/36.40 | | | | | | | | | | | | | | Case 2: % 260.89/36.40 | | | | | | | | | | | | | | | % 260.89/36.40 | | | | | | | | | | | | | | | % 260.89/36.40 | | | | | | | | | | | | | | | GROUND_INST: instantiating (3) with all_207_4, all_207_3, % 260.89/36.40 | | | | | | | | | | | | | | | all_207_2, all_593_1, all_207_5, all_593_0, % 260.89/36.40 | | | | | | | | | | | | | | | simplifying with (38), (39), (40), (41), (42), % 260.89/36.40 | | | | | | | | | | | | | | | (44), (65), (124), (297), (298), (299) gives: % 260.89/36.40 | | | | | | | | | | | | | | | (303) in(all_593_0, all_207_2) % 260.89/36.40 | | | | | | | | | | | | | | | % 260.89/36.40 | | | | | | | | | | | | | | | GROUND_INST: instantiating (11) with all_207_2, all_207_1, % 260.89/36.40 | | | | | | | | | | | | | | | all_207_5, all_593_1, all_593_0, simplifying with % 260.89/36.40 | | | | | | | | | | | | | | | (39), (42), (43), (45), (65), (123), (298), (299), % 260.89/36.40 | | | | | | | | | | | | | | | (303) gives: % 260.89/36.40 | | | | | | | | | | | | | | | (304) $false % 260.89/36.40 | | | | | | | | | | | | | | | % 260.89/36.40 | | | | | | | | | | | | | | | CLOSE: (304) is inconsistent. % 260.89/36.40 | | | | | | | | | | | | | | | % 260.89/36.40 | | | | | | | | | | | | | | End of split % 260.89/36.40 | | | | | | | | | | | | | | % 260.89/36.40 | | | | | | | | | | | | | Case 2: % 260.89/36.40 | | | | | | | | | | | | | | % 260.89/36.40 | | | | | | | | | | | | | | (305) in(all_463_0, all_170_0) % 260.89/36.40 | | | | | | | | | | | | | | % 260.89/36.40 | | | | | | | | | | | | | | REDUCE: (49), (305) imply: % 260.89/36.40 | | | | | | | | | | | | | | (306) in(all_463_0, empty_set) % 260.89/36.40 | | | | | | | | | | | | | | % 260.89/36.40 | | | | | | | | | | | | | | GROUND_INST: instantiating (6) with all_463_0, simplifying with % 260.89/36.40 | | | | | | | | | | | | | | (263), (306) gives: % 260.89/36.40 | | | | | | | | | | | | | | (307) $false % 260.89/36.40 | | | | | | | | | | | | | | % 260.89/36.40 | | | | | | | | | | | | | | CLOSE: (307) is inconsistent. % 260.89/36.40 | | | | | | | | | | | | | | % 260.89/36.40 | | | | | | | | | | | | | End of split % 260.89/36.40 | | | | | | | | | | | | | % 260.89/36.40 | | | | | | | | | | | | Case 2: % 260.89/36.40 | | | | | | | | | | | | | % 260.89/36.40 | | | | | | | | | | | | | (308) all_241_0 = empty_set & relation_dom(all_207_2) = % 260.89/36.40 | | | | | | | | | | | | | empty_set % 260.89/36.40 | | | | | | | | | | | | | % 260.89/36.40 | | | | | | | | | | | | | ALPHA: (308) implies: % 260.89/36.40 | | | | | | | | | | | | | (309) relation_dom(all_207_2) = empty_set % 260.89/36.40 | | | | | | | | | | | | | % 260.89/36.40 | | | | | | | | | | | | | REF_CLOSE: (22), (106), (294), (309) are inconsistent by % 260.89/36.40 | | | | | | | | | | | | | sub-proof #1. % 260.89/36.40 | | | | | | | | | | | | | % 260.89/36.40 | | | | | | | | | | | | End of split % 260.89/36.40 | | | | | | | | | | | | % 260.89/36.40 | | | | | | | | | | | End of split % 260.89/36.40 | | | | | | | | | | | % 260.89/36.40 | | | | | | | | | | End of split % 260.89/36.40 | | | | | | | | | | % 260.89/36.40 | | | | | | | | | End of split % 260.89/36.40 | | | | | | | | | % 260.89/36.40 | | | | | | | | End of split % 260.89/36.40 | | | | | | | | % 260.89/36.40 | | | | | | | End of split % 260.89/36.40 | | | | | | | % 260.89/36.40 | | | | | | Case 2: % 260.89/36.40 | | | | | | | % 260.89/36.40 | | | | | | | (310) ~ subset(all_207_3, all_172_0) % 260.89/36.40 | | | | | | | % 260.89/36.40 | | | | | | | BETA: splitting (59) gives: % 260.89/36.40 | | | | | | | % 260.89/36.40 | | | | | | | Case 1: % 260.89/36.40 | | | | | | | | % 260.89/36.40 | | | | | | | | (311) all_207_3 = all_170_0 % 260.89/36.40 | | | | | | | | % 260.89/36.40 | | | | | | | | COMBINE_EQS: (49), (311) imply: % 260.89/36.40 | | | | | | | | (312) all_207_3 = empty_set % 260.89/36.40 | | | | | | | | % 260.89/36.40 | | | | | | | | REDUCE: (310), (312) imply: % 260.89/36.40 | | | | | | | | (313) ~ subset(empty_set, all_172_0) % 260.89/36.40 | | | | | | | | % 260.89/36.40 | | | | | | | | PRED_UNIFY: (242), (313) imply: % 260.89/36.40 | | | | | | | | (314) $false % 260.89/36.40 | | | | | | | | % 260.89/36.40 | | | | | | | | CLOSE: (314) is inconsistent. % 260.89/36.40 | | | | | | | | % 260.89/36.40 | | | | | | | Case 2: % 260.89/36.40 | | | | | | | | % 260.89/36.40 | | | | | | | | (315) ~ (all_207_3 = all_170_0) % 260.89/36.40 | | | | | | | | % 260.89/36.40 | | | | | | | | REDUCE: (49), (315) imply: % 260.89/36.40 | | | | | | | | (316) ~ (all_207_3 = empty_set) % 260.89/36.40 | | | | | | | | % 260.89/36.40 | | | | | | | | BETA: splitting (61) gives: % 260.89/36.40 | | | | | | | | % 260.89/36.40 | | | | | | | | Case 1: % 260.89/36.40 | | | | | | | | | % 260.89/36.40 | | | | | | | | | (317) all_207_3 = empty_set % 260.89/36.40 | | | | | | | | | % 260.89/36.40 | | | | | | | | | REDUCE: (316), (317) imply: % 260.89/36.40 | | | | | | | | | (318) $false % 260.89/36.40 | | | | | | | | | % 260.89/36.40 | | | | | | | | | CLOSE: (318) is inconsistent. % 260.89/36.40 | | | | | | | | | % 260.89/36.40 | | | | | | | | Case 2: % 260.89/36.40 | | | | | | | | | % 260.89/36.40 | | | | | | | | | (319) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 260.89/36.40 | | | | | | | | | (ordered_pair(v0, v1) = v2 & $i(v2) & $i(v1) & $i(v0) % 260.89/36.40 | | | | | | | | | & ( ~ in(v2, all_207_3) | ~ in(v2, empty_set)) & % 260.89/36.40 | | | | | | | | | (in(v2, all_207_3) | in(v2, empty_set))) % 260.89/36.40 | | | | | | | | | % 260.89/36.40 | | | | | | | | | DELTA: instantiating (319) with fresh symbols all_432_0, % 260.89/36.40 | | | | | | | | | all_432_1, all_432_2 gives: % 260.89/36.40 | | | | | | | | | (320) ordered_pair(all_432_2, all_432_1) = all_432_0 & % 260.89/36.40 | | | | | | | | | $i(all_432_0) & $i(all_432_1) & $i(all_432_2) & ( ~ % 260.89/36.40 | | | | | | | | | in(all_432_0, all_207_3) | ~ in(all_432_0, % 260.89/36.40 | | | | | | | | | empty_set)) & (in(all_432_0, all_207_3) | % 260.89/36.40 | | | | | | | | | in(all_432_0, empty_set)) % 260.89/36.40 | | | | | | | | | % 260.89/36.40 | | | | | | | | | ALPHA: (320) implies: % 260.89/36.40 | | | | | | | | | (321) $i(all_432_0) % 260.89/36.40 | | | | | | | | | (322) in(all_432_0, all_207_3) | in(all_432_0, empty_set) % 260.89/36.40 | | | | | | | | | % 260.89/36.40 | | | | | | | | | BETA: splitting (54) gives: % 260.89/36.40 | | | | | | | | | % 260.89/36.40 | | | | | | | | | Case 1: % 260.89/36.40 | | | | | | | | | | % 260.89/36.40 | | | | | | | | | | (323) all_172_0 = empty_set % 260.89/36.40 | | | | | | | | | | % 260.89/36.40 | | | | | | | | | | REDUCE: (241), (323) imply: % 260.89/36.40 | | | | | | | | | | (324) ~ subset(empty_set, all_207_3) % 260.89/36.40 | | | | | | | | | | % 260.89/36.40 | | | | | | | | | | PRED_UNIFY: (128), (324) imply: % 260.89/36.40 | | | | | | | | | | (325) $false % 260.89/36.40 | | | | | | | | | | % 260.89/36.40 | | | | | | | | | | CLOSE: (325) is inconsistent. % 260.89/36.40 | | | | | | | | | | % 260.89/36.40 | | | | | | | | | Case 2: % 260.89/36.40 | | | | | | | | | | % 260.89/36.40 | | | | | | | | | | (326) ~ (all_172_0 = empty_set) % 260.89/36.40 | | | | | | | | | | % 260.89/36.40 | | | | | | | | | | BETA: splitting (50) gives: % 260.89/36.40 | | | | | | | | | | % 260.89/36.40 | | | | | | | | | | Case 1: % 260.89/36.40 | | | | | | | | | | | % 260.89/36.40 | | | | | | | | | | | (327) all_172_0 = all_170_0 % 260.89/36.40 | | | | | | | | | | | % 260.89/36.40 | | | | | | | | | | | COMBINE_EQS: (49), (327) imply: % 260.89/36.40 | | | | | | | | | | | (328) all_172_0 = empty_set % 260.89/36.40 | | | | | | | | | | | % 260.89/36.40 | | | | | | | | | | | REDUCE: (326), (328) imply: % 260.89/36.40 | | | | | | | | | | | (329) $false % 260.89/36.40 | | | | | | | | | | | % 260.89/36.40 | | | | | | | | | | | CLOSE: (329) is inconsistent. % 260.89/36.40 | | | | | | | | | | | % 260.89/36.40 | | | | | | | | | | Case 2: % 260.89/36.40 | | | | | | | | | | | % 260.89/36.40 | | | | | | | | | | | (330) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 260.89/36.40 | | | | | | | | | | | (ordered_pair(v0, v1) = v2 & $i(v2) & $i(v1) & % 260.89/36.40 | | | | | | | | | | | $i(v0) & ( ~ in(v2, all_172_0) | ~ in(v2, % 260.89/36.40 | | | | | | | | | | | all_170_0)) & (in(v2, all_172_0) | in(v2, % 260.89/36.40 | | | | | | | | | | | all_170_0))) % 260.89/36.40 | | | | | | | | | | | % 260.89/36.40 | | | | | | | | | | | DELTA: instantiating (330) with fresh symbols all_465_0, % 260.89/36.40 | | | | | | | | | | | all_465_1, all_465_2 gives: % 260.89/36.40 | | | | | | | | | | | (331) ordered_pair(all_465_2, all_465_1) = all_465_0 & % 260.89/36.40 | | | | | | | | | | | $i(all_465_0) & $i(all_465_1) & $i(all_465_2) & ( % 260.89/36.40 | | | | | | | | | | | ~ in(all_465_0, all_172_0) | ~ in(all_465_0, % 260.89/36.40 | | | | | | | | | | | all_170_0)) & (in(all_465_0, all_172_0) | % 260.89/36.40 | | | | | | | | | | | in(all_465_0, all_170_0)) % 260.89/36.40 | | | | | | | | | | | % 260.89/36.40 | | | | | | | | | | | ALPHA: (331) implies: % 260.89/36.40 | | | | | | | | | | | (332) $i(all_465_0) % 260.89/36.40 | | | | | | | | | | | (333) in(all_465_0, all_172_0) | in(all_465_0, % 260.89/36.40 | | | | | | | | | | | all_170_0) % 260.89/36.40 | | | | | | | | | | | (334) ~ in(all_465_0, all_172_0) | ~ in(all_465_0, % 260.89/36.40 | | | | | | | | | | | all_170_0) % 260.89/36.40 | | | | | | | | | | | % 260.89/36.40 | | | | | | | | | | | BETA: splitting (68) gives: % 260.89/36.40 | | | | | | | | | | | % 260.89/36.40 | | | | | | | | | | | Case 1: % 260.89/36.40 | | | | | | | | | | | | % 260.89/36.40 | | | | | | | | | | | | (335) all_207_2 = empty_set % 260.89/36.40 | | | | | | | | | | | | % 260.89/36.40 | | | | | | | | | | | | REDUCE: (44), (335) imply: % 260.89/36.40 | | | | | | | | | | | | (336) relation_rng_restriction(all_207_4, all_207_3) = % 260.89/36.40 | | | | | | | | | | | | empty_set % 260.89/36.40 | | | | | | | | | | | | % 260.89/36.40 | | | | | | | | | | | | BETA: splitting (56) gives: % 260.89/36.40 | | | | | | | | | | | | % 260.89/36.40 | | | | | | | | | | | | Case 1: % 260.89/36.40 | | | | | | | | | | | | | % 260.89/36.40 | | | | | | | | | | | | | (337) all_207_3 = all_172_0 % 260.89/36.40 | | | | | | | | | | | | | % 260.89/36.40 | | | | | | | | | | | | | REDUCE: (55), (337) imply: % 260.89/36.40 | | | | | | | | | | | | | (338) subset(all_172_0, all_172_0) % 260.89/36.40 | | | | | | | | | | | | | % 260.89/36.40 | | | | | | | | | | | | | REDUCE: (241), (337) imply: % 260.89/36.40 | | | | | | | | | | | | | (339) ~ subset(all_172_0, all_172_0) % 260.89/36.40 | | | | | | | | | | | | | % 260.89/36.40 | | | | | | | | | | | | | PRED_UNIFY: (338), (339) imply: % 260.89/36.40 | | | | | | | | | | | | | (340) $false % 260.89/36.40 | | | | | | | | | | | | | % 260.89/36.40 | | | | | | | | | | | | | CLOSE: (340) is inconsistent. % 260.89/36.40 | | | | | | | | | | | | | % 260.89/36.40 | | | | | | | | | | | | Case 2: % 260.89/36.40 | | | | | | | | | | | | | % 260.89/36.40 | | | | | | | | | | | | | % 260.89/36.41 | | | | | | | | | | | | | GROUND_INST: instantiating (10) with all_207_3, all_207_0, % 260.89/36.41 | | | | | | | | | | | | | all_207_5, simplifying with (38), (39), (41), % 260.89/36.41 | | | | | | | | | | | | | (125), (126), (127) gives: % 260.89/36.41 | | | | | | | | | | | | | (341) ? [v0: $i] : ? [v1: $i] : (ordered_pair(v0, % 260.89/36.41 | | | | | | | | | | | | | all_207_5) = v1 & $i(v1) & $i(v0) & in(v1, % 260.89/36.41 | | | | | | | | | | | | | all_207_3)) % 260.89/36.41 | | | | | | | | | | | | | % 260.89/36.41 | | | | | | | | | | | | | DELTA: instantiating (341) with fresh symbols all_576_0, % 260.89/36.41 | | | | | | | | | | | | | all_576_1 gives: % 260.89/36.41 | | | | | | | | | | | | | (342) ordered_pair(all_576_1, all_207_5) = all_576_0 & % 260.89/36.41 | | | | | | | | | | | | | $i(all_576_0) & $i(all_576_1) & in(all_576_0, % 260.89/36.41 | | | | | | | | | | | | | all_207_3) % 260.89/36.41 | | | | | | | | | | | | | % 260.89/36.41 | | | | | | | | | | | | | ALPHA: (342) implies: % 260.89/36.41 | | | | | | | | | | | | | (343) in(all_576_0, all_207_3) % 260.89/36.41 | | | | | | | | | | | | | (344) $i(all_576_1) % 260.89/36.41 | | | | | | | | | | | | | (345) $i(all_576_0) % 260.89/36.41 | | | | | | | | | | | | | (346) ordered_pair(all_576_1, all_207_5) = all_576_0 % 260.89/36.41 | | | | | | | | | | | | | % 260.89/36.41 | | | | | | | | | | | | | BETA: splitting (322) gives: % 260.89/36.41 | | | | | | | | | | | | | % 260.89/36.41 | | | | | | | | | | | | | Case 1: % 260.89/36.41 | | | | | | | | | | | | | | % 260.89/36.41 | | | | | | | | | | | | | | (347) in(all_432_0, empty_set) % 260.89/36.41 | | | | | | | | | | | | | | % 260.89/36.41 | | | | | | | | | | | | | | GROUND_INST: instantiating (6) with all_432_0, simplifying with % 260.89/36.41 | | | | | | | | | | | | | | (321), (347) gives: % 260.89/36.41 | | | | | | | | | | | | | | (348) $false % 260.89/36.41 | | | | | | | | | | | | | | % 260.89/36.41 | | | | | | | | | | | | | | CLOSE: (348) is inconsistent. % 260.89/36.41 | | | | | | | | | | | | | | % 260.89/36.41 | | | | | | | | | | | | | Case 2: % 260.89/36.41 | | | | | | | | | | | | | | % 260.89/36.41 | | | | | | | | | | | | | | % 260.89/36.41 | | | | | | | | | | | | | | GROUND_INST: instantiating (3) with all_207_4, all_207_3, % 260.89/36.41 | | | | | | | | | | | | | | empty_set, all_576_1, all_207_5, all_576_0, % 260.89/36.41 | | | | | | | | | | | | | | simplifying with (12), (20), (38), (39), (40), % 260.89/36.41 | | | | | | | | | | | | | | (41), (124), (336), (343), (344), (346) gives: % 260.89/36.41 | | | | | | | | | | | | | | (349) in(all_576_0, empty_set) % 260.89/36.41 | | | | | | | | | | | | | | % 260.89/36.41 | | | | | | | | | | | | | | GROUND_INST: instantiating (6) with all_576_0, simplifying with % 260.89/36.41 | | | | | | | | | | | | | | (345), (349) gives: % 260.89/36.41 | | | | | | | | | | | | | | (350) $false % 260.89/36.41 | | | | | | | | | | | | | | % 260.89/36.41 | | | | | | | | | | | | | | CLOSE: (350) is inconsistent. % 260.89/36.41 | | | | | | | | | | | | | | % 260.89/36.41 | | | | | | | | | | | | | End of split % 260.89/36.41 | | | | | | | | | | | | | % 260.89/36.41 | | | | | | | | | | | | End of split % 260.89/36.41 | | | | | | | | | | | | % 260.89/36.41 | | | | | | | | | | | Case 2: % 260.89/36.41 | | | | | | | | | | | | % 260.89/36.41 | | | | | | | | | | | | (351) ~ (all_207_2 = empty_set) % 260.89/36.41 | | | | | | | | | | | | % 260.89/36.41 | | | | | | | | | | | | BETA: splitting (91) gives: % 260.89/36.41 | | | | | | | | | | | | % 260.89/36.41 | | | | | | | | | | | | Case 1: % 260.89/36.41 | | | | | | | | | | | | | % 260.89/36.41 | | | | | | | | | | | | | (352) all_207_2 = empty_set % 260.89/36.41 | | | | | | | | | | | | | % 260.89/36.41 | | | | | | | | | | | | | REDUCE: (351), (352) imply: % 260.89/36.41 | | | | | | | | | | | | | (353) $false % 260.89/36.41 | | | | | | | | | | | | | % 260.89/36.41 | | | | | | | | | | | | | CLOSE: (353) is inconsistent. % 260.89/36.41 | | | | | | | | | | | | | % 260.89/36.41 | | | | | | | | | | | | Case 2: % 260.89/36.41 | | | | | | | | | | | | | % 260.89/36.41 | | | | | | | | | | | | | (354) ? [v0: $i] : ( ~ (v0 = empty_set) & % 260.89/36.41 | | | | | | | | | | | | | relation_dom(all_207_2) = v0 & $i(v0)) % 260.89/36.41 | | | | | | | | | | | | | % 260.89/36.41 | | | | | | | | | | | | | DELTA: instantiating (354) with fresh symbol all_479_0 % 260.89/36.41 | | | | | | | | | | | | | gives: % 260.89/36.41 | | | | | | | | | | | | | (355) ~ (all_479_0 = empty_set) & % 260.89/36.41 | | | | | | | | | | | | | relation_dom(all_207_2) = all_479_0 & % 260.89/36.41 | | | | | | | | | | | | | $i(all_479_0) % 260.89/36.41 | | | | | | | | | | | | | % 260.89/36.41 | | | | | | | | | | | | | ALPHA: (355) implies: % 260.89/36.41 | | | | | | | | | | | | | (356) ~ (all_479_0 = empty_set) % 260.89/36.41 | | | | | | | | | | | | | (357) relation_dom(all_207_2) = all_479_0 % 260.89/36.41 | | | | | | | | | | | | | % 260.89/36.41 | | | | | | | | | | | | | GROUND_INST: instantiating (22) with all_242_0, all_479_0, % 260.89/36.41 | | | | | | | | | | | | | all_207_2, simplifying with (106), (357) gives: % 260.89/36.41 | | | | | | | | | | | | | (358) all_479_0 = all_242_0 % 260.89/36.41 | | | | | | | | | | | | | % 260.89/36.41 | | | | | | | | | | | | | REDUCE: (356), (358) imply: % 260.89/36.41 | | | | | | | | | | | | | (359) ~ (all_242_0 = empty_set) % 260.89/36.41 | | | | | | | | | | | | | % 260.89/36.41 | | | | | | | | | | | | | BETA: splitting (104) gives: % 260.89/36.41 | | | | | | | | | | | | | % 260.89/36.41 | | | | | | | | | | | | | Case 1: % 260.89/36.41 | | | | | | | | | | | | | | % 260.89/36.41 | | | | | | | | | | | | | | (360) ~ (all_207_1 = empty_set) % 260.89/36.41 | | | | | | | | | | | | | | % 260.89/36.41 | | | | | | | | | | | | | | BETA: splitting (103) gives: % 260.89/36.41 | | | | | | | | | | | | | | % 260.89/36.41 | | | | | | | | | | | | | | Case 1: % 260.89/36.41 | | | | | | | | | | | | | | | % 260.89/36.41 | | | | | | | | | | | | | | | (361) all_207_1 = empty_set % 260.89/36.41 | | | | | | | | | | | | | | | % 260.89/36.41 | | | | | | | | | | | | | | | REDUCE: (360), (361) imply: % 260.89/36.41 | | | | | | | | | | | | | | | (362) $false % 260.89/36.41 | | | | | | | | | | | | | | | % 260.89/36.41 | | | | | | | | | | | | | | | CLOSE: (362) is inconsistent. % 260.89/36.41 | | | | | | | | | | | | | | | % 260.89/36.41 | | | | | | | | | | | | | | Case 2: % 260.89/36.41 | | | | | | | | | | | | | | | % 260.89/36.41 | | | | | | | | | | | | | | | % 260.89/36.41 | | | | | | | | | | | | | | | GROUND_INST: instantiating (10) with all_207_3, all_207_0, % 260.89/36.41 | | | | | | | | | | | | | | | all_207_5, simplifying with (38), (39), (41), % 260.89/36.41 | | | | | | | | | | | | | | | (125), (126), (127) gives: % 260.89/36.41 | | | | | | | | | | | | | | | (363) ? [v0: $i] : ? [v1: $i] : (ordered_pair(v0, % 260.89/36.41 | | | | | | | | | | | | | | | all_207_5) = v1 & $i(v1) & $i(v0) & in(v1, % 260.89/36.41 | | | | | | | | | | | | | | | all_207_3)) % 260.89/36.41 | | | | | | | | | | | | | | | % 260.89/36.41 | | | | | | | | | | | | | | | DELTA: instantiating (363) with fresh symbols all_599_0, % 260.89/36.41 | | | | | | | | | | | | | | | all_599_1 gives: % 260.89/36.41 | | | | | | | | | | | | | | | (364) ordered_pair(all_599_1, all_207_5) = all_599_0 & % 260.89/36.41 | | | | | | | | | | | | | | | $i(all_599_0) & $i(all_599_1) & in(all_599_0, % 260.89/36.41 | | | | | | | | | | | | | | | all_207_3) % 260.89/36.41 | | | | | | | | | | | | | | | % 260.89/36.41 | | | | | | | | | | | | | | | ALPHA: (364) implies: % 260.89/36.41 | | | | | | | | | | | | | | | (365) in(all_599_0, all_207_3) % 260.89/36.41 | | | | | | | | | | | | | | | (366) $i(all_599_1) % 260.89/36.41 | | | | | | | | | | | | | | | (367) ordered_pair(all_599_1, all_207_5) = all_599_0 % 260.89/36.41 | | | | | | | | | | | | | | | % 260.89/36.41 | | | | | | | | | | | | | | | BETA: splitting (333) gives: % 260.89/36.41 | | | | | | | | | | | | | | | % 260.89/36.41 | | | | | | | | | | | | | | | Case 1: % 260.89/36.41 | | | | | | | | | | | | | | | | % 260.89/36.41 | | | | | | | | | | | | | | | | (368) in(all_465_0, all_172_0) % 260.89/36.41 | | | | | | | | | | | | | | | | % 260.89/36.41 | | | | | | | | | | | | | | | | BETA: splitting (334) gives: % 260.89/36.41 | | | | | | | | | | | | | | | | % 260.89/36.41 | | | | | | | | | | | | | | | | Case 1: % 260.89/36.41 | | | | | | | | | | | | | | | | | % 260.89/36.41 | | | | | | | | | | | | | | | | | (369) ~ in(all_465_0, all_172_0) % 260.89/36.41 | | | | | | | | | | | | | | | | | % 260.89/36.41 | | | | | | | | | | | | | | | | | PRED_UNIFY: (368), (369) imply: % 260.89/36.41 | | | | | | | | | | | | | | | | | (370) $false % 260.89/36.41 | | | | | | | | | | | | | | | | | % 260.89/36.41 | | | | | | | | | | | | | | | | | CLOSE: (370) is inconsistent. % 260.89/36.41 | | | | | | | | | | | | | | | | | % 260.89/36.41 | | | | | | | | | | | | | | | | Case 2: % 260.89/36.41 | | | | | | | | | | | | | | | | | % 260.89/36.41 | | | | | | | | | | | | | | | | | % 260.89/36.41 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (3) with all_207_4, all_207_3, % 260.89/36.41 | | | | | | | | | | | | | | | | | all_207_2, all_599_1, all_207_5, all_599_0, % 260.89/36.41 | | | | | | | | | | | | | | | | | simplifying with (38), (39), (40), (41), (42), % 260.89/36.41 | | | | | | | | | | | | | | | | | (44), (65), (124), (365), (366), (367) gives: % 260.89/36.41 | | | | | | | | | | | | | | | | | (371) in(all_599_0, all_207_2) % 260.89/36.41 | | | | | | | | | | | | | | | | | % 260.89/36.41 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (11) with all_207_2, all_207_1, % 260.89/36.41 | | | | | | | | | | | | | | | | | all_207_5, all_599_1, all_599_0, simplifying with % 260.89/36.41 | | | | | | | | | | | | | | | | | (39), (42), (43), (45), (65), (123), (366), (367), % 260.89/36.41 | | | | | | | | | | | | | | | | | (371) gives: % 260.89/36.41 | | | | | | | | | | | | | | | | | (372) $false % 260.89/36.41 | | | | | | | | | | | | | | | | | % 260.89/36.41 | | | | | | | | | | | | | | | | | CLOSE: (372) is inconsistent. % 260.89/36.41 | | | | | | | | | | | | | | | | | % 260.89/36.41 | | | | | | | | | | | | | | | | End of split % 260.89/36.41 | | | | | | | | | | | | | | | | % 260.89/36.41 | | | | | | | | | | | | | | | Case 2: % 260.89/36.41 | | | | | | | | | | | | | | | | % 260.89/36.41 | | | | | | | | | | | | | | | | (373) in(all_465_0, all_170_0) % 260.89/36.41 | | | | | | | | | | | | | | | | % 260.89/36.41 | | | | | | | | | | | | | | | | REDUCE: (49), (373) imply: % 260.89/36.41 | | | | | | | | | | | | | | | | (374) in(all_465_0, empty_set) % 260.89/36.41 | | | | | | | | | | | | | | | | % 260.89/36.41 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (6) with all_465_0, simplifying with % 260.89/36.41 | | | | | | | | | | | | | | | | (332), (374) gives: % 260.89/36.41 | | | | | | | | | | | | | | | | (375) $false % 260.89/36.41 | | | | | | | | | | | | | | | | % 260.89/36.41 | | | | | | | | | | | | | | | | CLOSE: (375) is inconsistent. % 260.89/36.41 | | | | | | | | | | | | | | | | % 260.89/36.41 | | | | | | | | | | | | | | | End of split % 260.89/36.41 | | | | | | | | | | | | | | | % 260.89/36.41 | | | | | | | | | | | | | | End of split % 260.89/36.41 | | | | | | | | | | | | | | % 260.89/36.41 | | | | | | | | | | | | | Case 2: % 260.89/36.41 | | | | | | | | | | | | | | % 260.89/36.41 | | | | | | | | | | | | | | (376) all_241_0 = empty_set & relation_dom(all_207_2) = % 260.89/36.41 | | | | | | | | | | | | | | empty_set % 260.89/36.41 | | | | | | | | | | | | | | % 260.89/36.41 | | | | | | | | | | | | | | ALPHA: (376) implies: % 260.89/36.41 | | | | | | | | | | | | | | (377) relation_dom(all_207_2) = empty_set % 260.89/36.41 | | | | | | | | | | | | | | % 260.89/36.41 | | | | | | | | | | | | | | REF_CLOSE: (22), (106), (359), (377) are inconsistent by % 260.89/36.41 | | | | | | | | | | | | | | sub-proof #1. % 260.89/36.41 | | | | | | | | | | | | | | % 260.89/36.41 | | | | | | | | | | | | | End of split % 260.89/36.41 | | | | | | | | | | | | | % 260.89/36.41 | | | | | | | | | | | | End of split % 260.89/36.41 | | | | | | | | | | | | % 260.89/36.41 | | | | | | | | | | | End of split % 260.89/36.41 | | | | | | | | | | | % 260.89/36.41 | | | | | | | | | | End of split % 260.89/36.41 | | | | | | | | | | % 260.89/36.41 | | | | | | | | | End of split % 260.89/36.41 | | | | | | | | | % 260.89/36.41 | | | | | | | | End of split % 260.89/36.41 | | | | | | | | % 260.89/36.41 | | | | | | | End of split % 260.89/36.41 | | | | | | | % 260.89/36.41 | | | | | | End of split % 260.89/36.41 | | | | | | % 260.89/36.41 | | | | | Case 2: % 260.89/36.41 | | | | | | % 260.89/36.41 | | | | | | (378) ~ subset(empty_set, all_172_0) % 260.89/36.41 | | | | | | % 260.89/36.41 | | | | | | REF_CLOSE: (6), (49), (51), (378) are inconsistent by sub-proof #2. % 260.89/36.41 | | | | | | % 260.89/36.41 | | | | | End of split % 260.89/36.41 | | | | | % 260.89/36.41 | | | | End of split % 260.89/36.41 | | | | % 260.89/36.41 | | | End of split % 260.89/36.41 | | | % 260.89/36.41 | | Case 2: % 260.89/36.41 | | | % 260.89/36.41 | | | (379) ~ subset(empty_set, all_207_3) % 260.89/36.41 | | | % 260.89/36.41 | | | BETA: splitting (53) gives: % 260.89/36.41 | | | % 260.89/36.41 | | | Case 1: % 260.89/36.41 | | | | % 260.89/36.41 | | | | (380) subset(all_172_0, empty_set) % 260.89/36.41 | | | | % 260.89/36.41 | | | | REF_CLOSE: (14), (34), (36), (54), (113), (380) are inconsistent by % 260.89/36.41 | | | | sub-proof #4. % 260.89/36.41 | | | | % 260.89/36.41 | | | Case 2: % 260.89/36.41 | | | | % 260.89/36.41 | | | | (381) ~ subset(all_172_0, empty_set) % 260.89/36.41 | | | | % 260.89/36.41 | | | | BETA: splitting (51) gives: % 260.89/36.41 | | | | % 260.89/36.41 | | | | Case 1: % 260.89/36.41 | | | | | % 260.89/36.41 | | | | | (382) subset(all_170_0, all_172_0) % 260.89/36.41 | | | | | % 260.89/36.41 | | | | | REDUCE: (49), (382) imply: % 260.89/36.41 | | | | | (383) subset(empty_set, all_172_0) % 260.89/36.41 | | | | | % 260.89/36.41 | | | | | BETA: splitting (59) gives: % 260.89/36.41 | | | | | % 260.89/36.41 | | | | | Case 1: % 260.89/36.41 | | | | | | % 260.89/36.41 | | | | | | (384) all_207_3 = all_170_0 % 260.89/36.41 | | | | | | % 260.89/36.41 | | | | | | COMBINE_EQS: (49), (384) imply: % 260.89/36.41 | | | | | | (385) all_207_3 = empty_set % 260.89/36.41 | | | | | | % 260.89/36.41 | | | | | | REDUCE: (55), (385) imply: % 260.89/36.41 | | | | | | (386) subset(empty_set, empty_set) % 260.89/36.41 | | | | | | % 260.89/36.41 | | | | | | REDUCE: (379), (385) imply: % 260.89/36.41 | | | | | | (387) ~ subset(empty_set, empty_set) % 260.89/36.41 | | | | | | % 260.89/36.41 | | | | | | PRED_UNIFY: (386), (387) imply: % 260.89/36.41 | | | | | | (388) $false % 260.89/36.41 | | | | | | % 260.89/36.41 | | | | | | CLOSE: (388) is inconsistent. % 260.89/36.41 | | | | | | % 260.89/36.41 | | | | | Case 2: % 260.89/36.41 | | | | | | % 260.89/36.41 | | | | | | (389) ~ (all_207_3 = all_170_0) % 260.89/36.41 | | | | | | % 260.89/36.41 | | | | | | REDUCE: (49), (389) imply: % 260.89/36.41 | | | | | | (390) ~ (all_207_3 = empty_set) % 260.89/36.41 | | | | | | % 260.89/36.41 | | | | | | REF_CLOSE: (3), (6), (10), (11), (38), (39), (40), (41), (42), (43), % 260.89/36.41 | | | | | | (44), (45), (49), (54), (61), (65), (66), (67), (68), % 260.89/36.41 | | | | | | (99), (123), (124), (125), (126), (127), (381), (383), % 260.89/36.41 | | | | | | (390) are inconsistent by sub-proof #3. % 260.89/36.41 | | | | | | % 260.89/36.41 | | | | | End of split % 260.89/36.41 | | | | | % 260.89/36.41 | | | | Case 2: % 260.89/36.41 | | | | | % 260.89/36.41 | | | | | (391) ~ subset(all_170_0, all_172_0) % 260.89/36.41 | | | | | % 260.89/36.41 | | | | | REDUCE: (49), (391) imply: % 260.89/36.41 | | | | | (392) ~ subset(empty_set, all_172_0) % 260.89/36.41 | | | | | % 260.89/36.41 | | | | | REF_CLOSE: (6), (49), (51), (392) are inconsistent by sub-proof #2. % 260.89/36.41 | | | | | % 260.89/36.41 | | | | End of split % 260.89/36.41 | | | | % 260.89/36.41 | | | End of split % 260.89/36.41 | | | % 260.89/36.41 | | End of split % 260.89/36.41 | | % 260.89/36.41 | Case 2: % 260.89/36.41 | | % 260.89/36.41 | | (393) in(all_207_5, all_207_1) & ( ~ in(all_207_5, all_207_4) | % 260.89/36.41 | | (relation_rng(all_207_3) = all_207_0 & $i(all_207_0) & ~ % 260.89/36.41 | | in(all_207_5, all_207_0))) % 260.89/36.41 | | % 260.89/36.41 | | ALPHA: (393) implies: % 260.89/36.42 | | (394) in(all_207_5, all_207_1) % 260.89/36.42 | | (395) ~ in(all_207_5, all_207_4) | (relation_rng(all_207_3) = all_207_0 % 260.89/36.42 | | & $i(all_207_0) & ~ in(all_207_5, all_207_0)) % 260.89/36.42 | | % 260.89/36.42 | | BETA: splitting (60) gives: % 260.89/36.42 | | % 260.89/36.42 | | Case 1: % 260.89/36.42 | | | % 260.89/36.42 | | | (396) subset(all_207_3, all_170_0) % 260.89/36.42 | | | % 260.89/36.42 | | | REDUCE: (49), (396) imply: % 260.89/36.42 | | | (397) subset(all_207_3, empty_set) % 260.89/36.42 | | | % 261.21/36.42 | | | BETA: splitting (64) gives: % 261.21/36.42 | | | % 261.21/36.42 | | | Case 1: % 261.21/36.42 | | | | % 261.21/36.42 | | | | (398) all_207_2 = all_207_3 % 261.21/36.42 | | | | % 261.21/36.42 | | | | REDUCE: (45), (398) imply: % 261.21/36.42 | | | | (399) relation_rng(all_207_3) = all_207_1 % 261.21/36.42 | | | | % 261.21/36.42 | | | | BETA: splitting (63) gives: % 261.21/36.42 | | | | % 261.21/36.42 | | | | Case 1: % 261.21/36.42 | | | | | % 261.21/36.42 | | | | | (400) all_207_3 = empty_set % 261.21/36.42 | | | | | % 261.21/36.42 | | | | | REDUCE: (399), (400) imply: % 261.21/36.42 | | | | | (401) relation_rng(empty_set) = all_207_1 % 261.21/36.42 | | | | | % 261.21/36.42 | | | | | GROUND_INST: instantiating (23) with empty_set, all_207_1, empty_set, % 261.21/36.42 | | | | | simplifying with (17), (401) gives: % 261.21/36.42 | | | | | (402) all_207_1 = empty_set % 261.21/36.42 | | | | | % 261.21/36.42 | | | | | REDUCE: (394), (402) imply: % 261.21/36.42 | | | | | (403) in(all_207_5, empty_set) % 261.21/36.42 | | | | | % 261.21/36.42 | | | | | GROUND_INST: instantiating (6) with all_207_5, simplifying with (39), % 261.21/36.42 | | | | | (403) gives: % 261.21/36.42 | | | | | (404) $false % 261.21/36.42 | | | | | % 261.21/36.42 | | | | | CLOSE: (404) is inconsistent. % 261.21/36.42 | | | | | % 261.21/36.42 | | | | Case 2: % 261.21/36.42 | | | | | % 261.21/36.42 | | | | | (405) ~ (all_207_3 = empty_set) % 261.21/36.42 | | | | | % 261.21/36.42 | | | | | REF_CLOSE: (14), (41), (397), (405) are inconsistent by sub-proof #7. % 261.21/36.42 | | | | | % 261.21/36.42 | | | | End of split % 261.21/36.42 | | | | % 261.21/36.42 | | | Case 2: % 261.21/36.42 | | | | % 261.21/36.42 | | | | (406) ~ (all_207_2 = all_207_3) % 261.21/36.42 | | | | % 261.21/36.42 | | | | REF_CLOSE: (6), (14), (41), (49), (61), (67), (397), (406) are % 261.21/36.42 | | | | inconsistent by sub-proof #6. % 261.21/36.42 | | | | % 261.21/36.42 | | | End of split % 261.21/36.42 | | | % 261.21/36.42 | | Case 2: % 261.21/36.42 | | | % 261.21/36.42 | | | (407) ~ subset(all_207_3, all_170_0) % 261.21/36.42 | | | % 261.21/36.42 | | | REDUCE: (49), (407) imply: % 261.21/36.42 | | | (408) ~ subset(all_207_3, empty_set) % 261.21/36.42 | | | % 261.21/36.42 | | | BETA: splitting (57) gives: % 261.21/36.42 | | | % 261.21/36.42 | | | Case 1: % 261.21/36.42 | | | | % 261.21/36.42 | | | | (409) subset(all_172_0, all_207_3) % 261.21/36.42 | | | | % 261.21/36.42 | | | | BETA: splitting (52) gives: % 261.21/36.42 | | | | % 261.21/36.42 | | | | Case 1: % 261.21/36.42 | | | | | % 261.21/36.42 | | | | | (410) subset(empty_set, all_172_0) % 261.21/36.42 | | | | | % 261.21/36.42 | | | | | BETA: splitting (53) gives: % 261.21/36.42 | | | | | % 261.21/36.42 | | | | | Case 1: % 261.21/36.42 | | | | | | % 261.21/36.42 | | | | | | (411) subset(all_172_0, empty_set) % 261.21/36.42 | | | | | | % 261.21/36.42 | | | | | | REF_CLOSE: (14), (34), (36), (54), (113), (411) are inconsistent by % 261.21/36.42 | | | | | | sub-proof #4. % 261.21/36.42 | | | | | | % 261.21/36.42 | | | | | Case 2: % 261.21/36.42 | | | | | | % 261.21/36.42 | | | | | | (412) ~ subset(all_172_0, empty_set) % 261.21/36.42 | | | | | | % 261.21/36.42 | | | | | | BETA: splitting (54) gives: % 261.21/36.42 | | | | | | % 261.21/36.42 | | | | | | Case 1: % 261.21/36.42 | | | | | | | % 261.21/36.42 | | | | | | | (413) all_172_0 = empty_set % 261.21/36.42 | | | | | | | % 261.21/36.42 | | | | | | | REDUCE: (410), (413) imply: % 261.21/36.42 | | | | | | | (414) subset(empty_set, empty_set) % 261.21/36.42 | | | | | | | % 261.21/36.42 | | | | | | | REDUCE: (412), (413) imply: % 261.21/36.42 | | | | | | | (415) ~ subset(empty_set, empty_set) % 261.21/36.42 | | | | | | | % 261.21/36.42 | | | | | | | PRED_UNIFY: (414), (415) imply: % 261.21/36.42 | | | | | | | (416) $false % 261.21/36.42 | | | | | | | % 261.21/36.42 | | | | | | | CLOSE: (416) is inconsistent. % 261.21/36.42 | | | | | | | % 261.21/36.42 | | | | | | Case 2: % 261.21/36.42 | | | | | | | % 261.21/36.42 | | | | | | | (417) ~ (all_172_0 = empty_set) % 261.21/36.42 | | | | | | | % 261.21/36.42 | | | | | | | BETA: splitting (50) gives: % 261.21/36.42 | | | | | | | % 261.21/36.42 | | | | | | | Case 1: % 261.21/36.42 | | | | | | | | % 261.21/36.42 | | | | | | | | (418) all_172_0 = all_170_0 % 261.21/36.42 | | | | | | | | % 261.21/36.42 | | | | | | | | COMBINE_EQS: (49), (418) imply: % 261.21/36.42 | | | | | | | | (419) all_172_0 = empty_set % 261.21/36.42 | | | | | | | | % 261.21/36.42 | | | | | | | | REDUCE: (417), (419) imply: % 261.21/36.42 | | | | | | | | (420) $false % 261.21/36.42 | | | | | | | | % 261.21/36.42 | | | | | | | | CLOSE: (420) is inconsistent. % 261.21/36.42 | | | | | | | | % 261.21/36.42 | | | | | | | Case 2: % 261.21/36.42 | | | | | | | | % 261.21/36.42 | | | | | | | | (421) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 261.21/36.42 | | | | | | | | (ordered_pair(v0, v1) = v2 & $i(v2) & $i(v1) & $i(v0) & % 261.21/36.42 | | | | | | | | ( ~ in(v2, all_172_0) | ~ in(v2, all_170_0)) & % 261.21/36.42 | | | | | | | | (in(v2, all_172_0) | in(v2, all_170_0))) % 261.21/36.42 | | | | | | | | % 261.21/36.42 | | | | | | | | DELTA: instantiating (421) with fresh symbols all_463_0, % 261.21/36.42 | | | | | | | | all_463_1, all_463_2 gives: % 261.21/36.42 | | | | | | | | (422) ordered_pair(all_463_2, all_463_1) = all_463_0 & % 261.21/36.42 | | | | | | | | $i(all_463_0) & $i(all_463_1) & $i(all_463_2) & ( ~ % 261.21/36.42 | | | | | | | | in(all_463_0, all_172_0) | ~ in(all_463_0, % 261.21/36.42 | | | | | | | | all_170_0)) & (in(all_463_0, all_172_0) | % 261.21/36.42 | | | | | | | | in(all_463_0, all_170_0)) % 261.21/36.42 | | | | | | | | % 261.21/36.42 | | | | | | | | ALPHA: (422) implies: % 261.21/36.42 | | | | | | | | (423) $i(all_463_0) % 261.21/36.42 | | | | | | | | (424) in(all_463_0, all_172_0) | in(all_463_0, all_170_0) % 261.21/36.42 | | | | | | | | (425) ~ in(all_463_0, all_172_0) | ~ in(all_463_0, % 261.21/36.42 | | | | | | | | all_170_0) % 261.21/36.42 | | | | | | | | % 261.21/36.42 | | | | | | | | BETA: splitting (66) gives: % 261.21/36.42 | | | | | | | | % 261.21/36.42 | | | | | | | | Case 1: % 261.21/36.42 | | | | | | | | | % 261.21/36.42 | | | | | | | | | (426) all_207_2 = all_172_0 % 261.21/36.42 | | | | | | | | | % 261.21/36.42 | | | | | | | | | REDUCE: (45), (426) imply: % 261.21/36.42 | | | | | | | | | (427) relation_rng(all_172_0) = all_207_1 % 261.21/36.42 | | | | | | | | | % 261.21/36.42 | | | | | | | | | REDUCE: (44), (426) imply: % 261.21/36.42 | | | | | | | | | (428) relation_rng_restriction(all_207_4, all_207_3) = % 261.21/36.42 | | | | | | | | | all_172_0 % 261.21/36.42 | | | | | | | | | % 261.21/36.42 | | | | | | | | | BETA: splitting (100) gives: % 261.21/36.42 | | | | | | | | | % 261.21/36.42 | | | | | | | | | Case 1: % 261.21/36.42 | | | | | | | | | | % 261.21/36.42 | | | | | | | | | | (429) subset(all_207_2, empty_set) % 261.21/36.42 | | | | | | | | | | % 261.21/36.42 | | | | | | | | | | REDUCE: (426), (429) imply: % 261.21/36.42 | | | | | | | | | | (430) subset(all_172_0, empty_set) % 261.21/36.42 | | | | | | | | | | % 261.21/36.42 | | | | | | | | | | PRED_UNIFY: (412), (430) imply: % 261.21/36.42 | | | | | | | | | | (431) $false % 261.21/36.42 | | | | | | | | | | % 261.21/36.42 | | | | | | | | | | CLOSE: (431) is inconsistent. % 261.21/36.42 | | | | | | | | | | % 261.21/36.42 | | | | | | | | | Case 2: % 261.21/36.42 | | | | | | | | | | % 261.21/36.42 | | | | | | | | | | % 261.21/36.42 | | | | | | | | | | GROUND_INST: instantiating (10) with all_172_0, all_207_1, % 261.21/36.42 | | | | | | | | | | all_207_5, simplifying with (35), (36), (39), % 261.21/36.42 | | | | | | | | | | (43), (394), (427) gives: % 261.21/36.42 | | | | | | | | | | (432) ? [v0: $i] : ? [v1: $i] : (ordered_pair(v0, % 261.21/36.42 | | | | | | | | | | all_207_5) = v1 & $i(v1) & $i(v0) & in(v1, % 261.21/36.42 | | | | | | | | | | all_172_0)) % 261.21/36.42 | | | | | | | | | | % 261.21/36.42 | | | | | | | | | | DELTA: instantiating (432) with fresh symbols all_599_0, % 261.21/36.42 | | | | | | | | | | all_599_1 gives: % 261.21/36.42 | | | | | | | | | | (433) ordered_pair(all_599_1, all_207_5) = all_599_0 & % 261.21/36.42 | | | | | | | | | | $i(all_599_0) & $i(all_599_1) & in(all_599_0, % 261.21/36.42 | | | | | | | | | | all_172_0) % 261.21/36.42 | | | | | | | | | | % 261.21/36.42 | | | | | | | | | | ALPHA: (433) implies: % 261.21/36.42 | | | | | | | | | | (434) in(all_599_0, all_172_0) % 261.21/36.42 | | | | | | | | | | (435) $i(all_599_1) % 261.21/36.42 | | | | | | | | | | (436) ordered_pair(all_599_1, all_207_5) = all_599_0 % 261.21/36.42 | | | | | | | | | | % 261.21/36.42 | | | | | | | | | | BETA: splitting (395) gives: % 261.21/36.42 | | | | | | | | | | % 261.21/36.42 | | | | | | | | | | Case 1: % 261.21/36.42 | | | | | | | | | | | % 261.21/36.42 | | | | | | | | | | | (437) ~ in(all_207_5, all_207_4) % 261.21/36.42 | | | | | | | | | | | % 261.21/36.42 | | | | | | | | | | | GROUND_INST: instantiating (4) with all_207_4, all_207_3, % 261.21/36.42 | | | | | | | | | | | all_172_0, all_599_1, all_207_5, all_599_0, % 261.21/36.42 | | | | | | | | | | | simplifying with (35), (36), (38), (39), (40), % 261.21/36.42 | | | | | | | | | | | (41), (428), (434), (435), (436), (437) gives: % 261.21/36.42 | | | | | | | | | | | (438) $false % 261.21/36.42 | | | | | | | | | | | % 261.21/36.42 | | | | | | | | | | | CLOSE: (438) is inconsistent. % 261.21/36.42 | | | | | | | | | | | % 261.21/36.42 | | | | | | | | | | Case 2: % 261.21/36.42 | | | | | | | | | | | % 261.21/36.42 | | | | | | | | | | | (439) relation_rng(all_207_3) = all_207_0 & % 261.21/36.42 | | | | | | | | | | | $i(all_207_0) & ~ in(all_207_5, all_207_0) % 261.21/36.42 | | | | | | | | | | | % 261.21/36.42 | | | | | | | | | | | ALPHA: (439) implies: % 261.21/36.42 | | | | | | | | | | | (440) ~ in(all_207_5, all_207_0) % 261.21/36.42 | | | | | | | | | | | (441) $i(all_207_0) % 261.21/36.42 | | | | | | | | | | | (442) relation_rng(all_207_3) = all_207_0 % 261.21/36.42 | | | | | | | | | | | % 261.21/36.42 | | | | | | | | | | | BETA: splitting (424) gives: % 261.21/36.42 | | | | | | | | | | | % 261.21/36.42 | | | | | | | | | | | Case 1: % 261.21/36.42 | | | | | | | | | | | | % 261.21/36.42 | | | | | | | | | | | | (443) in(all_463_0, all_172_0) % 261.21/36.42 | | | | | | | | | | | | % 261.21/36.42 | | | | | | | | | | | | BETA: splitting (425) gives: % 261.21/36.42 | | | | | | | | | | | | % 261.21/36.42 | | | | | | | | | | | | Case 1: % 261.21/36.42 | | | | | | | | | | | | | % 261.21/36.42 | | | | | | | | | | | | | (444) ~ in(all_463_0, all_172_0) % 261.21/36.42 | | | | | | | | | | | | | % 261.21/36.42 | | | | | | | | | | | | | PRED_UNIFY: (443), (444) imply: % 261.21/36.42 | | | | | | | | | | | | | (445) $false % 261.21/36.42 | | | | | | | | | | | | | % 261.21/36.42 | | | | | | | | | | | | | CLOSE: (445) is inconsistent. % 261.21/36.42 | | | | | | | | | | | | | % 261.21/36.42 | | | | | | | | | | | | Case 2: % 261.21/36.42 | | | | | | | | | | | | | % 261.21/36.42 | | | | | | | | | | | | | % 261.21/36.42 | | | | | | | | | | | | | GROUND_INST: instantiating (8) with all_172_0, all_207_3, % 261.21/36.42 | | | | | | | | | | | | | all_599_1, all_207_5, all_599_0, simplifying with % 261.21/36.42 | | | | | | | | | | | | | (35), (36), (38), (39), (41), (409), (434), (435), % 261.21/36.42 | | | | | | | | | | | | | (436) gives: % 261.21/36.42 | | | | | | | | | | | | | (446) in(all_599_0, all_207_3) % 261.21/36.42 | | | | | | | | | | | | | % 261.21/36.42 | | | | | | | | | | | | | GROUND_INST: instantiating (11) with all_207_3, all_207_0, % 261.21/36.42 | | | | | | | | | | | | | all_207_5, all_599_1, all_599_0, simplifying with % 261.21/36.42 | | | | | | | | | | | | | (38), (39), (41), (435), (436), (440), (441), % 261.21/36.42 | | | | | | | | | | | | | (442), (446) gives: % 261.21/36.42 | | | | | | | | | | | | | (447) $false % 261.21/36.42 | | | | | | | | | | | | | % 261.21/36.42 | | | | | | | | | | | | | CLOSE: (447) is inconsistent. % 261.21/36.42 | | | | | | | | | | | | | % 261.21/36.42 | | | | | | | | | | | | End of split % 261.21/36.42 | | | | | | | | | | | | % 261.21/36.42 | | | | | | | | | | | Case 2: % 261.21/36.42 | | | | | | | | | | | | % 261.21/36.42 | | | | | | | | | | | | (448) in(all_463_0, all_170_0) % 261.21/36.42 | | | | | | | | | | | | % 261.21/36.42 | | | | | | | | | | | | REDUCE: (49), (448) imply: % 261.21/36.42 | | | | | | | | | | | | (449) in(all_463_0, empty_set) % 261.21/36.42 | | | | | | | | | | | | % 261.21/36.42 | | | | | | | | | | | | GROUND_INST: instantiating (6) with all_463_0, simplifying with % 261.21/36.42 | | | | | | | | | | | | (423), (449) gives: % 261.21/36.42 | | | | | | | | | | | | (450) $false % 261.21/36.42 | | | | | | | | | | | | % 261.21/36.42 | | | | | | | | | | | | CLOSE: (450) is inconsistent. % 261.21/36.42 | | | | | | | | | | | | % 261.21/36.42 | | | | | | | | | | | End of split % 261.21/36.42 | | | | | | | | | | | % 261.21/36.42 | | | | | | | | | | End of split % 261.21/36.42 | | | | | | | | | | % 261.21/36.42 | | | | | | | | | End of split % 261.21/36.42 | | | | | | | | | % 261.21/36.42 | | | | | | | | Case 2: % 261.21/36.42 | | | | | | | | | % 261.21/36.42 | | | | | | | | | (451) ~ (all_207_2 = all_172_0) % 261.21/36.42 | | | | | | | | | % 261.21/36.42 | | | | | | | | | BETA: splitting (99) gives: % 261.21/36.42 | | | | | | | | | % 261.21/36.42 | | | | | | | | | Case 1: % 261.21/36.42 | | | | | | | | | | % 261.21/36.42 | | | | | | | | | | (452) all_207_2 = all_172_0 % 261.21/36.42 | | | | | | | | | | % 261.21/36.43 | | | | | | | | | | REDUCE: (451), (452) imply: % 261.21/36.43 | | | | | | | | | | (453) $false % 261.21/36.43 | | | | | | | | | | % 261.21/36.43 | | | | | | | | | | CLOSE: (453) is inconsistent. % 261.21/36.43 | | | | | | | | | | % 261.21/36.43 | | | | | | | | | Case 2: % 261.21/36.43 | | | | | | | | | | % 261.21/36.43 | | | | | | | | | | % 261.21/36.43 | | | | | | | | | | GROUND_INST: instantiating (10) with all_207_2, all_207_1, % 261.21/36.43 | | | | | | | | | | all_207_5, simplifying with (39), (42), (43), % 261.21/36.43 | | | | | | | | | | (45), (65), (394) gives: % 261.21/36.43 | | | | | | | | | | (454) ? [v0: $i] : ? [v1: $i] : (ordered_pair(v0, % 261.21/36.43 | | | | | | | | | | all_207_5) = v1 & $i(v1) & $i(v0) & in(v1, % 261.21/36.43 | | | | | | | | | | all_207_2)) % 261.21/36.43 | | | | | | | | | | % 261.21/36.43 | | | | | | | | | | DELTA: instantiating (454) with fresh symbols all_582_0, % 261.21/36.43 | | | | | | | | | | all_582_1 gives: % 261.21/36.43 | | | | | | | | | | (455) ordered_pair(all_582_1, all_207_5) = all_582_0 & % 261.21/36.43 | | | | | | | | | | $i(all_582_0) & $i(all_582_1) & in(all_582_0, % 261.21/36.43 | | | | | | | | | | all_207_2) % 261.21/36.43 | | | | | | | | | | % 261.21/36.43 | | | | | | | | | | ALPHA: (455) implies: % 261.21/36.43 | | | | | | | | | | (456) in(all_582_0, all_207_2) % 261.21/36.43 | | | | | | | | | | (457) $i(all_582_1) % 261.21/36.43 | | | | | | | | | | (458) ordered_pair(all_582_1, all_207_5) = all_582_0 % 261.21/36.43 | | | | | | | | | | % 261.21/36.43 | | | | | | | | | | BETA: splitting (98) gives: % 261.21/36.43 | | | | | | | | | | % 261.21/36.43 | | | | | | | | | | Case 1: % 261.21/36.43 | | | | | | | | | | | % 261.21/36.43 | | | | | | | | | | | (459) subset(all_207_2, all_207_3) % 261.21/36.43 | | | | | | | | | | | % 261.21/36.43 | | | | | | | | | | | BETA: splitting (395) gives: % 261.21/36.43 | | | | | | | | | | | % 261.21/36.43 | | | | | | | | | | | Case 1: % 261.21/36.43 | | | | | | | | | | | | % 261.21/36.43 | | | | | | | | | | | | (460) ~ in(all_207_5, all_207_4) % 261.21/36.43 | | | | | | | | | | | | % 261.21/36.43 | | | | | | | | | | | | GROUND_INST: instantiating (4) with all_207_4, all_207_3, % 261.21/36.43 | | | | | | | | | | | | all_207_2, all_582_1, all_207_5, all_582_0, % 261.21/36.43 | | | | | | | | | | | | simplifying with (38), (39), (40), (41), (42), % 261.21/36.43 | | | | | | | | | | | | (44), (65), (456), (457), (458), (460) gives: % 261.21/36.43 | | | | | | | | | | | | (461) $false % 261.21/36.43 | | | | | | | | | | | | % 261.21/36.43 | | | | | | | | | | | | CLOSE: (461) is inconsistent. % 261.21/36.43 | | | | | | | | | | | | % 261.21/36.43 | | | | | | | | | | | Case 2: % 261.21/36.43 | | | | | | | | | | | | % 261.21/36.43 | | | | | | | | | | | | (462) relation_rng(all_207_3) = all_207_0 & % 261.21/36.43 | | | | | | | | | | | | $i(all_207_0) & ~ in(all_207_5, all_207_0) % 261.21/36.43 | | | | | | | | | | | | % 261.21/36.43 | | | | | | | | | | | | ALPHA: (462) implies: % 261.21/36.43 | | | | | | | | | | | | (463) ~ in(all_207_5, all_207_0) % 261.21/36.43 | | | | | | | | | | | | (464) $i(all_207_0) % 261.21/36.43 | | | | | | | | | | | | (465) relation_rng(all_207_3) = all_207_0 % 261.21/36.43 | | | | | | | | | | | | % 261.21/36.43 | | | | | | | | | | | | BETA: splitting (424) gives: % 261.21/36.43 | | | | | | | | | | | | % 261.21/36.43 | | | | | | | | | | | | Case 1: % 261.21/36.43 | | | | | | | | | | | | | % 261.21/36.43 | | | | | | | | | | | | | (466) in(all_463_0, all_172_0) % 261.21/36.43 | | | | | | | | | | | | | % 261.21/36.43 | | | | | | | | | | | | | BETA: splitting (425) gives: % 261.21/36.43 | | | | | | | | | | | | | % 261.21/36.43 | | | | | | | | | | | | | Case 1: % 261.21/36.43 | | | | | | | | | | | | | | % 261.21/36.43 | | | | | | | | | | | | | | (467) ~ in(all_463_0, all_172_0) % 261.21/36.43 | | | | | | | | | | | | | | % 261.21/36.43 | | | | | | | | | | | | | | PRED_UNIFY: (466), (467) imply: % 261.21/36.43 | | | | | | | | | | | | | | (468) $false % 261.21/36.43 | | | | | | | | | | | | | | % 261.21/36.43 | | | | | | | | | | | | | | CLOSE: (468) is inconsistent. % 261.21/36.43 | | | | | | | | | | | | | | % 261.21/36.43 | | | | | | | | | | | | | Case 2: % 261.21/36.43 | | | | | | | | | | | | | | % 261.21/36.43 | | | | | | | | | | | | | | % 261.21/36.43 | | | | | | | | | | | | | | GROUND_INST: instantiating (112) with all_207_3, all_207_0, % 261.21/36.43 | | | | | | | | | | | | | | simplifying with (38), (41), (459), (465) gives: % 261.21/36.43 | | | | | | | | | | | | | | (469) subset(all_207_1, all_207_0) % 261.21/36.43 | | | | | | | | | | | | | | % 261.21/36.43 | | | | | | | | | | | | | | GROUND_INST: instantiating (9) with all_207_1, all_207_0, % 261.21/36.43 | | | | | | | | | | | | | | all_207_5, simplifying with (39), (43), (394), % 261.21/36.43 | | | | | | | | | | | | | | (463), (464), (469) gives: % 261.21/36.43 | | | | | | | | | | | | | | (470) $false % 261.21/36.43 | | | | | | | | | | | | | | % 261.21/36.43 | | | | | | | | | | | | | | CLOSE: (470) is inconsistent. % 261.21/36.43 | | | | | | | | | | | | | | % 261.21/36.43 | | | | | | | | | | | | | End of split % 261.21/36.43 | | | | | | | | | | | | | % 261.21/36.43 | | | | | | | | | | | | Case 2: % 261.21/36.43 | | | | | | | | | | | | | % 261.21/36.43 | | | | | | | | | | | | | (471) in(all_463_0, all_170_0) % 261.21/36.43 | | | | | | | | | | | | | % 261.21/36.43 | | | | | | | | | | | | | REDUCE: (49), (471) imply: % 261.21/36.43 | | | | | | | | | | | | | (472) in(all_463_0, empty_set) % 261.21/36.43 | | | | | | | | | | | | | % 261.21/36.43 | | | | | | | | | | | | | GROUND_INST: instantiating (6) with all_463_0, simplifying with % 261.21/36.43 | | | | | | | | | | | | | (423), (472) gives: % 261.21/36.43 | | | | | | | | | | | | | (473) $false % 261.21/36.43 | | | | | | | | | | | | | % 261.21/36.43 | | | | | | | | | | | | | CLOSE: (473) is inconsistent. % 261.21/36.43 | | | | | | | | | | | | | % 261.21/36.43 | | | | | | | | | | | | End of split % 261.21/36.43 | | | | | | | | | | | | % 261.21/36.43 | | | | | | | | | | | End of split % 261.21/36.43 | | | | | | | | | | | % 261.21/36.43 | | | | | | | | | | Case 2: % 261.21/36.43 | | | | | | | | | | | % 261.21/36.43 | | | | | | | | | | | (474) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 261.21/36.43 | | | | | | | | | | | (ordered_pair(v0, v1) = v2 & $i(v2) & $i(v1) & % 261.21/36.43 | | | | | | | | | | | $i(v0) & in(v2, all_207_2) & ~ in(v2, % 261.21/36.43 | | | | | | | | | | | all_207_3)) % 261.21/36.43 | | | | | | | | | | | % 261.21/36.43 | | | | | | | | | | | DELTA: instantiating (474) with fresh symbols all_637_0, % 261.21/36.43 | | | | | | | | | | | all_637_1, all_637_2 gives: % 261.21/36.43 | | | | | | | | | | | (475) ordered_pair(all_637_2, all_637_1) = all_637_0 & % 261.21/36.43 | | | | | | | | | | | $i(all_637_0) & $i(all_637_1) & $i(all_637_2) & % 261.21/36.43 | | | | | | | | | | | in(all_637_0, all_207_2) & ~ in(all_637_0, % 261.21/36.43 | | | | | | | | | | | all_207_3) % 261.21/36.43 | | | | | | | | | | | % 261.21/36.43 | | | | | | | | | | | ALPHA: (475) implies: % 261.21/36.43 | | | | | | | | | | | (476) ~ in(all_637_0, all_207_3) % 261.21/36.43 | | | | | | | | | | | (477) in(all_637_0, all_207_2) % 261.21/36.43 | | | | | | | | | | | (478) $i(all_637_2) % 261.21/36.43 | | | | | | | | | | | (479) $i(all_637_1) % 261.21/36.43 | | | | | | | | | | | (480) ordered_pair(all_637_2, all_637_1) = all_637_0 % 261.21/36.43 | | | | | | | | | | | % 261.21/36.43 | | | | | | | | | | | GROUND_INST: instantiating (5) with all_207_4, all_207_3, % 261.21/36.43 | | | | | | | | | | | all_207_2, all_637_2, all_637_1, all_637_0, % 261.21/36.43 | | | | | | | | | | | simplifying with (38), (40), (41), (42), (44), % 261.21/36.43 | | | | | | | | | | | (65), (476), (477), (478), (479), (480) gives: % 261.21/36.43 | | | | | | | | | | | (481) $false % 261.21/36.43 | | | | | | | | | | | % 261.21/36.43 | | | | | | | | | | | CLOSE: (481) is inconsistent. % 261.21/36.43 | | | | | | | | | | | % 261.21/36.43 | | | | | | | | | | End of split % 261.21/36.43 | | | | | | | | | | % 261.21/36.43 | | | | | | | | | End of split % 261.21/36.43 | | | | | | | | | % 261.21/36.43 | | | | | | | | End of split % 261.21/36.43 | | | | | | | | % 261.21/36.43 | | | | | | | End of split % 261.21/36.43 | | | | | | | % 261.21/36.43 | | | | | | End of split % 261.21/36.43 | | | | | | % 261.21/36.43 | | | | | End of split % 261.21/36.43 | | | | | % 261.21/36.43 | | | | Case 2: % 261.21/36.43 | | | | | % 261.21/36.43 | | | | | (482) ~ subset(empty_set, all_172_0) % 261.21/36.43 | | | | | % 261.21/36.43 | | | | | REF_CLOSE: (6), (49), (51), (482) are inconsistent by sub-proof #2. % 261.21/36.43 | | | | | % 261.21/36.43 | | | | End of split % 261.21/36.43 | | | | % 261.21/36.43 | | | Case 2: % 261.21/36.43 | | | | % 261.21/36.43 | | | | (483) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (ordered_pair(v0, v1) % 261.21/36.43 | | | | = v2 & $i(v2) & $i(v1) & $i(v0) & in(v2, all_172_0) & ~ % 261.21/36.43 | | | | in(v2, all_207_3)) % 261.21/36.43 | | | | % 261.21/36.43 | | | | DELTA: instantiating (483) with fresh symbols all_379_0, all_379_1, % 261.21/36.43 | | | | all_379_2 gives: % 261.21/36.43 | | | | (484) ordered_pair(all_379_2, all_379_1) = all_379_0 & $i(all_379_0) % 261.21/36.43 | | | | & $i(all_379_1) & $i(all_379_2) & in(all_379_0, all_172_0) & ~ % 261.21/36.43 | | | | in(all_379_0, all_207_3) % 261.21/36.43 | | | | % 261.21/36.43 | | | | ALPHA: (484) implies: % 261.21/36.43 | | | | (485) ~ in(all_379_0, all_207_3) % 261.21/36.43 | | | | (486) in(all_379_0, all_172_0) % 261.21/36.43 | | | | (487) $i(all_379_2) % 261.21/36.43 | | | | (488) $i(all_379_1) % 261.21/36.43 | | | | (489) ordered_pair(all_379_2, all_379_1) = all_379_0 % 261.21/36.43 | | | | % 261.21/36.43 | | | | BETA: splitting (68) gives: % 261.21/36.43 | | | | % 261.21/36.43 | | | | Case 1: % 261.21/36.43 | | | | | % 261.21/36.43 | | | | | (490) all_207_2 = empty_set % 261.21/36.43 | | | | | % 261.21/36.43 | | | | | REDUCE: (45), (490) imply: % 261.21/36.43 | | | | | (491) relation_rng(empty_set) = all_207_1 % 261.21/36.43 | | | | | % 261.21/36.43 | | | | | BETA: splitting (97) gives: % 261.21/36.43 | | | | | % 261.21/36.43 | | | | | Case 1: % 261.21/36.43 | | | | | | % 261.21/36.43 | | | | | | (492) subset(all_207_3, all_207_2) % 261.21/36.43 | | | | | | % 261.21/36.43 | | | | | | REDUCE: (490), (492) imply: % 261.21/36.43 | | | | | | (493) subset(all_207_3, empty_set) % 261.21/36.43 | | | | | | % 261.21/36.43 | | | | | | PRED_UNIFY: (408), (493) imply: % 261.21/36.43 | | | | | | (494) $false % 261.21/36.43 | | | | | | % 261.21/36.43 | | | | | | CLOSE: (494) is inconsistent. % 261.21/36.43 | | | | | | % 261.21/36.43 | | | | | Case 2: % 261.21/36.43 | | | | | | % 261.21/36.43 | | | | | | % 261.21/36.43 | | | | | | GROUND_INST: instantiating (23) with empty_set, all_207_1, % 261.21/36.43 | | | | | | empty_set, simplifying with (17), (491) gives: % 261.21/36.43 | | | | | | (495) all_207_1 = empty_set % 261.21/36.43 | | | | | | % 261.21/36.43 | | | | | | REDUCE: (394), (495) imply: % 261.21/36.43 | | | | | | (496) in(all_207_5, empty_set) % 261.21/36.43 | | | | | | % 261.21/36.43 | | | | | | GROUND_INST: instantiating (6) with all_207_5, simplifying with % 261.21/36.43 | | | | | | (39), (496) gives: % 261.21/36.43 | | | | | | (497) $false % 261.21/36.43 | | | | | | % 261.21/36.43 | | | | | | CLOSE: (497) is inconsistent. % 261.21/36.43 | | | | | | % 261.21/36.43 | | | | | End of split % 261.21/36.43 | | | | | % 261.21/36.43 | | | | Case 2: % 261.21/36.43 | | | | | % 261.21/36.43 | | | | | (498) ~ (all_207_2 = empty_set) % 261.21/36.43 | | | | | % 261.21/36.43 | | | | | BETA: splitting (67) gives: % 261.21/36.43 | | | | | % 261.21/36.43 | | | | | Case 1: % 261.21/36.43 | | | | | | % 261.21/36.43 | | | | | | (499) all_207_2 = all_170_0 % 261.21/36.43 | | | | | | % 261.21/36.43 | | | | | | COMBINE_EQS: (49), (499) imply: % 261.21/36.43 | | | | | | (500) all_207_2 = empty_set % 261.21/36.43 | | | | | | % 261.21/36.43 | | | | | | REDUCE: (498), (500) imply: % 261.21/36.43 | | | | | | (501) $false % 261.21/36.43 | | | | | | % 261.21/36.43 | | | | | | CLOSE: (501) is inconsistent. % 261.21/36.43 | | | | | | % 261.21/36.43 | | | | | Case 2: % 261.21/36.43 | | | | | | % 261.21/36.43 | | | | | | (502) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (ordered_pair(v0, % 261.21/36.43 | | | | | | v1) = v2 & $i(v2) & $i(v1) & $i(v0) & ( ~ in(v2, % 261.21/36.43 | | | | | | all_207_3) | ~ in(v2, all_170_0) | ~ in(v1, % 261.21/36.43 | | | | | | all_207_4)) & (in(v2, all_170_0) | (in(v2, all_207_3) % 261.21/36.43 | | | | | | & in(v1, all_207_4)))) % 261.21/36.43 | | | | | | % 261.21/36.43 | | | | | | DELTA: instantiating (502) with fresh symbols all_466_0, all_466_1, % 261.21/36.43 | | | | | | all_466_2 gives: % 261.21/36.43 | | | | | | (503) ordered_pair(all_466_2, all_466_1) = all_466_0 & % 261.21/36.43 | | | | | | $i(all_466_0) & $i(all_466_1) & $i(all_466_2) & ( ~ % 261.21/36.43 | | | | | | in(all_466_0, all_207_3) | ~ in(all_466_0, all_170_0) | % 261.21/36.43 | | | | | | ~ in(all_466_1, all_207_4)) & (in(all_466_0, all_170_0) | % 261.21/36.43 | | | | | | (in(all_466_0, all_207_3) & in(all_466_1, all_207_4))) % 261.21/36.43 | | | | | | % 261.21/36.43 | | | | | | ALPHA: (503) implies: % 261.21/36.43 | | | | | | (504) $i(all_466_0) % 261.21/36.43 | | | | | | (505) in(all_466_0, all_170_0) | (in(all_466_0, all_207_3) & % 261.21/36.43 | | | | | | in(all_466_1, all_207_4)) % 261.21/36.43 | | | | | | (506) ~ in(all_466_0, all_207_3) | ~ in(all_466_0, all_170_0) | % 261.21/36.43 | | | | | | ~ in(all_466_1, all_207_4) % 261.21/36.43 | | | | | | % 261.21/36.43 | | | | | | BETA: splitting (66) gives: % 261.21/36.43 | | | | | | % 261.21/36.43 | | | | | | Case 1: % 261.21/36.43 | | | | | | | % 261.21/36.43 | | | | | | | (507) all_207_2 = all_172_0 % 261.21/36.43 | | | | | | | % 261.21/36.43 | | | | | | | REDUCE: (44), (507) imply: % 261.21/36.43 | | | | | | | (508) relation_rng_restriction(all_207_4, all_207_3) = % 261.21/36.43 | | | | | | | all_172_0 % 261.21/36.43 | | | | | | | % 261.21/36.43 | | | | | | | GROUND_INST: instantiating (5) with all_207_4, all_207_3, % 261.21/36.43 | | | | | | | all_172_0, all_379_2, all_379_1, all_379_0, % 261.21/36.43 | | | | | | | simplifying with (35), (36), (38), (40), (41), (485), % 261.21/36.43 | | | | | | | (486), (487), (488), (489), (508) gives: % 261.21/36.43 | | | | | | | (509) $false % 261.21/36.43 | | | | | | | % 261.21/36.43 | | | | | | | CLOSE: (509) is inconsistent. % 261.21/36.43 | | | | | | | % 261.21/36.43 | | | | | | Case 2: % 261.21/36.43 | | | | | | | % 261.21/36.43 | | | | | | | (510) ~ (all_207_2 = all_172_0) % 261.21/36.43 | | | | | | | % 261.21/36.43 | | | | | | | BETA: splitting (99) gives: % 261.21/36.43 | | | | | | | % 261.21/36.43 | | | | | | | Case 1: % 261.21/36.43 | | | | | | | | % 261.21/36.43 | | | | | | | | (511) all_207_2 = all_172_0 % 261.21/36.43 | | | | | | | | % 261.21/36.43 | | | | | | | | REDUCE: (510), (511) imply: % 261.21/36.43 | | | | | | | | (512) $false % 261.21/36.43 | | | | | | | | % 261.21/36.43 | | | | | | | | CLOSE: (512) is inconsistent. % 261.21/36.43 | | | | | | | | % 261.21/36.43 | | | | | | | Case 2: % 261.21/36.43 | | | | | | | | % 261.21/36.43 | | | | | | | | % 261.21/36.43 | | | | | | | | GROUND_INST: instantiating (10) with all_207_2, all_207_1, % 261.21/36.43 | | | | | | | | all_207_5, simplifying with (39), (42), (43), (45), % 261.21/36.43 | | | | | | | | (65), (394) gives: % 261.21/36.43 | | | | | | | | (513) ? [v0: $i] : ? [v1: $i] : (ordered_pair(v0, % 261.21/36.43 | | | | | | | | all_207_5) = v1 & $i(v1) & $i(v0) & in(v1, % 261.21/36.43 | | | | | | | | all_207_2)) % 261.21/36.43 | | | | | | | | % 261.21/36.43 | | | | | | | | DELTA: instantiating (513) with fresh symbols all_587_0, % 261.21/36.43 | | | | | | | | all_587_1 gives: % 261.21/36.43 | | | | | | | | (514) ordered_pair(all_587_1, all_207_5) = all_587_0 & % 261.21/36.43 | | | | | | | | $i(all_587_0) & $i(all_587_1) & in(all_587_0, % 261.21/36.43 | | | | | | | | all_207_2) % 261.21/36.43 | | | | | | | | % 261.21/36.43 | | | | | | | | ALPHA: (514) implies: % 261.21/36.43 | | | | | | | | (515) in(all_587_0, all_207_2) % 261.21/36.43 | | | | | | | | (516) $i(all_587_1) % 261.21/36.43 | | | | | | | | (517) ordered_pair(all_587_1, all_207_5) = all_587_0 % 261.21/36.43 | | | | | | | | % 261.21/36.43 | | | | | | | | BETA: splitting (98) gives: % 261.21/36.43 | | | | | | | | % 261.21/36.43 | | | | | | | | Case 1: % 261.21/36.43 | | | | | | | | | % 261.21/36.43 | | | | | | | | | (518) subset(all_207_2, all_207_3) % 261.21/36.43 | | | | | | | | | % 261.21/36.43 | | | | | | | | | BETA: splitting (395) gives: % 261.21/36.43 | | | | | | | | | % 261.21/36.43 | | | | | | | | | Case 1: % 261.21/36.43 | | | | | | | | | | % 261.21/36.44 | | | | | | | | | | (519) ~ in(all_207_5, all_207_4) % 261.21/36.44 | | | | | | | | | | % 261.21/36.44 | | | | | | | | | | GROUND_INST: instantiating (4) with all_207_4, all_207_3, % 261.21/36.44 | | | | | | | | | | all_207_2, all_587_1, all_207_5, all_587_0, % 261.21/36.44 | | | | | | | | | | simplifying with (38), (39), (40), (41), (42), % 261.21/36.44 | | | | | | | | | | (44), (65), (515), (516), (517), (519) gives: % 261.21/36.44 | | | | | | | | | | (520) $false % 261.21/36.44 | | | | | | | | | | % 261.21/36.44 | | | | | | | | | | CLOSE: (520) is inconsistent. % 261.21/36.44 | | | | | | | | | | % 261.21/36.44 | | | | | | | | | Case 2: % 261.21/36.44 | | | | | | | | | | % 261.21/36.44 | | | | | | | | | | (521) relation_rng(all_207_3) = all_207_0 & $i(all_207_0) % 261.21/36.44 | | | | | | | | | | & ~ in(all_207_5, all_207_0) % 261.21/36.44 | | | | | | | | | | % 261.21/36.44 | | | | | | | | | | ALPHA: (521) implies: % 261.21/36.44 | | | | | | | | | | (522) ~ in(all_207_5, all_207_0) % 261.21/36.44 | | | | | | | | | | (523) $i(all_207_0) % 261.21/36.44 | | | | | | | | | | (524) relation_rng(all_207_3) = all_207_0 % 261.21/36.44 | | | | | | | | | | % 261.21/36.44 | | | | | | | | | | BETA: splitting (506) gives: % 261.21/36.44 | | | | | | | | | | % 261.21/36.44 | | | | | | | | | | Case 1: % 261.21/36.44 | | | | | | | | | | | % 261.21/36.44 | | | | | | | | | | | (525) ~ in(all_466_0, all_207_3) % 261.21/36.44 | | | | | | | | | | | % 261.21/36.44 | | | | | | | | | | | BETA: splitting (505) gives: % 261.21/36.44 | | | | | | | | | | | % 261.21/36.44 | | | | | | | | | | | Case 1: % 261.21/36.44 | | | | | | | | | | | | % 261.21/36.44 | | | | | | | | | | | | (526) in(all_466_0, all_170_0) % 261.21/36.44 | | | | | | | | | | | | % 261.21/36.44 | | | | | | | | | | | | REDUCE: (49), (526) imply: % 261.21/36.44 | | | | | | | | | | | | (527) in(all_466_0, empty_set) % 261.21/36.44 | | | | | | | | | | | | % 261.21/36.44 | | | | | | | | | | | | GROUND_INST: instantiating (6) with all_466_0, simplifying with % 261.21/36.44 | | | | | | | | | | | | (504), (527) gives: % 261.21/36.44 | | | | | | | | | | | | (528) $false % 261.21/36.44 | | | | | | | | | | | | % 261.21/36.44 | | | | | | | | | | | | CLOSE: (528) is inconsistent. % 261.21/36.44 | | | | | | | | | | | | % 261.21/36.44 | | | | | | | | | | | Case 2: % 261.21/36.44 | | | | | | | | | | | | % 261.21/36.44 | | | | | | | | | | | | (529) in(all_466_0, all_207_3) & in(all_466_1, % 261.21/36.44 | | | | | | | | | | | | all_207_4) % 261.21/36.44 | | | | | | | | | | | | % 261.21/36.44 | | | | | | | | | | | | ALPHA: (529) implies: % 261.21/36.44 | | | | | | | | | | | | (530) in(all_466_0, all_207_3) % 261.21/36.44 | | | | | | | | | | | | % 261.21/36.44 | | | | | | | | | | | | PRED_UNIFY: (525), (530) imply: % 261.21/36.44 | | | | | | | | | | | | (531) $false % 261.21/36.44 | | | | | | | | | | | | % 261.21/36.44 | | | | | | | | | | | | CLOSE: (531) is inconsistent. % 261.21/36.44 | | | | | | | | | | | | % 261.21/36.44 | | | | | | | | | | | End of split % 261.21/36.44 | | | | | | | | | | | % 261.21/36.44 | | | | | | | | | | Case 2: % 261.21/36.44 | | | | | | | | | | | % 261.21/36.44 | | | | | | | | | | | % 261.21/36.44 | | | | | | | | | | | GROUND_INST: instantiating (112) with all_207_3, all_207_0, % 261.21/36.44 | | | | | | | | | | | simplifying with (38), (41), (518), (524) gives: % 261.21/36.44 | | | | | | | | | | | (532) subset(all_207_1, all_207_0) % 261.21/36.44 | | | | | | | | | | | % 261.21/36.44 | | | | | | | | | | | GROUND_INST: instantiating (9) with all_207_1, all_207_0, % 261.21/36.44 | | | | | | | | | | | all_207_5, simplifying with (39), (43), (394), % 261.21/36.44 | | | | | | | | | | | (522), (523), (532) gives: % 261.21/36.44 | | | | | | | | | | | (533) $false % 261.21/36.44 | | | | | | | | | | | % 261.21/36.44 | | | | | | | | | | | CLOSE: (533) is inconsistent. % 261.21/36.44 | | | | | | | | | | | % 261.21/36.44 | | | | | | | | | | End of split % 261.21/36.44 | | | | | | | | | | % 261.21/36.44 | | | | | | | | | End of split % 261.21/36.44 | | | | | | | | | % 261.21/36.44 | | | | | | | | Case 2: % 261.21/36.44 | | | | | | | | | % 261.21/36.44 | | | | | | | | | (534) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 261.21/36.44 | | | | | | | | | (ordered_pair(v0, v1) = v2 & $i(v2) & $i(v1) & $i(v0) % 261.21/36.44 | | | | | | | | | & in(v2, all_207_2) & ~ in(v2, all_207_3)) % 261.21/36.44 | | | | | | | | | % 261.21/36.44 | | | | | | | | | DELTA: instantiating (534) with fresh symbols all_626_0, % 261.21/36.44 | | | | | | | | | all_626_1, all_626_2 gives: % 261.21/36.44 | | | | | | | | | (535) ordered_pair(all_626_2, all_626_1) = all_626_0 & % 261.21/36.44 | | | | | | | | | $i(all_626_0) & $i(all_626_1) & $i(all_626_2) & % 261.21/36.44 | | | | | | | | | in(all_626_0, all_207_2) & ~ in(all_626_0, % 261.21/36.44 | | | | | | | | | all_207_3) % 261.21/36.44 | | | | | | | | | % 261.21/36.44 | | | | | | | | | ALPHA: (535) implies: % 261.21/36.44 | | | | | | | | | (536) ~ in(all_626_0, all_207_3) % 261.21/36.44 | | | | | | | | | (537) in(all_626_0, all_207_2) % 261.21/36.44 | | | | | | | | | (538) $i(all_626_2) % 261.21/36.44 | | | | | | | | | (539) $i(all_626_1) % 261.21/36.44 | | | | | | | | | (540) ordered_pair(all_626_2, all_626_1) = all_626_0 % 261.21/36.44 | | | | | | | | | % 261.21/36.44 | | | | | | | | | GROUND_INST: instantiating (5) with all_207_4, all_207_3, % 261.21/36.44 | | | | | | | | | all_207_2, all_626_2, all_626_1, all_626_0, % 261.21/36.44 | | | | | | | | | simplifying with (38), (40), (41), (42), (44), % 261.21/36.44 | | | | | | | | | (65), (536), (537), (538), (539), (540) gives: % 261.21/36.44 | | | | | | | | | (541) $false % 261.21/36.44 | | | | | | | | | % 261.21/36.44 | | | | | | | | | CLOSE: (541) is inconsistent. % 261.21/36.44 | | | | | | | | | % 261.21/36.44 | | | | | | | | End of split % 261.21/36.44 | | | | | | | | % 261.21/36.44 | | | | | | | End of split % 261.21/36.44 | | | | | | | % 261.21/36.44 | | | | | | End of split % 261.21/36.44 | | | | | | % 261.21/36.44 | | | | | End of split % 261.21/36.44 | | | | | % 261.21/36.44 | | | | End of split % 261.21/36.44 | | | | % 261.21/36.44 | | | End of split % 261.21/36.44 | | | % 261.21/36.44 | | End of split % 261.21/36.44 | | % 261.21/36.44 | End of split % 261.21/36.44 | % 261.21/36.44 End of proof % 261.21/36.44 % 261.21/36.44 Sub-proof #1 shows that the following formulas are inconsistent: % 261.21/36.44 ---------------------------------------------------------------- % 261.21/36.44 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (relation_dom(v2) % 261.21/36.44 = v1) | ~ (relation_dom(v2) = v0)) % 261.21/36.44 (2) relation_dom(all_207_2) = all_242_0 % 261.21/36.44 (3) relation_dom(all_207_2) = empty_set % 261.21/36.44 (4) ~ (all_242_0 = empty_set) % 261.21/36.44 % 261.21/36.44 Begin of proof % 261.21/36.44 | % 261.21/36.44 | GROUND_INST: instantiating (1) with all_242_0, empty_set, all_207_2, % 261.21/36.44 | simplifying with (2), (3) gives: % 261.21/36.44 | (5) all_242_0 = empty_set % 261.21/36.44 | % 261.21/36.44 | REDUCE: (4), (5) imply: % 261.21/36.44 | (6) $false % 261.21/36.44 | % 261.21/36.44 | CLOSE: (6) is inconsistent. % 261.21/36.44 | % 261.21/36.44 End of proof % 261.21/36.44 % 261.21/36.44 Sub-proof #2 shows that the following formulas are inconsistent: % 261.21/36.44 ---------------------------------------------------------------- % 261.21/36.44 (1) subset(all_170_0, all_172_0) | ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 261.21/36.44 (ordered_pair(v0, v1) = v2 & $i(v2) & $i(v1) & $i(v0) & in(v2, all_170_0) % 261.21/36.44 & ~ in(v2, all_172_0)) % 261.21/36.44 (2) all_170_0 = empty_set % 261.21/36.44 (3) ~ subset(empty_set, all_172_0) % 261.21/36.44 (4) ! [v0: $i] : ( ~ $i(v0) | ~ in(v0, empty_set)) % 261.21/36.44 % 261.21/36.44 Begin of proof % 261.21/36.44 | % 261.21/36.44 | BETA: splitting (1) gives: % 261.21/36.44 | % 261.21/36.44 | Case 1: % 261.21/36.44 | | % 261.21/36.44 | | (5) subset(all_170_0, all_172_0) % 261.21/36.44 | | % 261.21/36.44 | | REDUCE: (2), (5) imply: % 261.21/36.44 | | (6) subset(empty_set, all_172_0) % 261.21/36.44 | | % 261.21/36.44 | | PRED_UNIFY: (3), (6) imply: % 261.21/36.44 | | (7) $false % 261.21/36.44 | | % 261.21/36.44 | | CLOSE: (7) is inconsistent. % 261.21/36.44 | | % 261.21/36.44 | Case 2: % 261.21/36.44 | | % 261.21/36.44 | | (8) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (ordered_pair(v0, v1) = v2 % 261.21/36.44 | | & $i(v2) & $i(v1) & $i(v0) & in(v2, all_170_0) & ~ in(v2, % 261.21/36.44 | | all_172_0)) % 261.21/36.44 | | % 261.21/36.44 | | DELTA: instantiating (8) with fresh symbols all_393_0, all_393_1, all_393_2 % 261.21/36.44 | | gives: % 261.21/36.44 | | (9) ordered_pair(all_393_2, all_393_1) = all_393_0 & $i(all_393_0) & % 261.21/36.44 | | $i(all_393_1) & $i(all_393_2) & in(all_393_0, all_170_0) & ~ % 261.21/36.44 | | in(all_393_0, all_172_0) % 261.21/36.44 | | % 261.21/36.44 | | ALPHA: (9) implies: % 261.21/36.44 | | (10) in(all_393_0, all_170_0) % 261.21/36.44 | | (11) $i(all_393_0) % 261.21/36.44 | | % 261.21/36.44 | | REDUCE: (2), (10) imply: % 261.21/36.44 | | (12) in(all_393_0, empty_set) % 261.21/36.44 | | % 261.21/36.44 | | GROUND_INST: instantiating (4) with all_393_0, simplifying with (11), (12) % 261.21/36.44 | | gives: % 261.21/36.44 | | (13) $false % 261.21/36.44 | | % 261.21/36.44 | | CLOSE: (13) is inconsistent. % 261.21/36.44 | | % 261.21/36.44 | End of split % 261.21/36.44 | % 261.21/36.44 End of proof % 261.21/36.44 % 261.21/36.44 Sub-proof #3 shows that the following formulas are inconsistent: % 261.21/36.44 ---------------------------------------------------------------- % 261.21/36.44 (1) all_172_0 = empty_set | ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 261.21/36.44 (ordered_pair(v0, v1) = v2 & $i(v2) & $i(v1) & $i(v0) & in(v2, % 261.21/36.44 all_172_0)) % 261.21/36.44 (2) $i(all_207_3) % 261.21/36.44 (3) $i(all_207_0) % 261.21/36.44 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! % 261.21/36.44 [v5: $i] : ( ~ (relation_rng_restriction(v0, v1) = v2) | ~ % 261.21/36.44 (ordered_pair(v3, v4) = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ % 261.21/36.44 $i(v1) | ~ $i(v0) | ~ relation(v2) | ~ relation(v1) | ~ in(v5, v1) % 261.21/36.44 | ~ in(v4, v0) | in(v5, v2)) % 261.21/36.44 (5) all_207_2 = all_172_0 | ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 261.21/36.44 (ordered_pair(v0, v1) = v2 & $i(v2) & $i(v1) & $i(v0) & ( ~ in(v2, % 261.21/36.44 all_207_3) | ~ in(v2, all_172_0) | ~ in(v1, all_207_4)) & (in(v2, % 261.21/36.44 all_172_0) | (in(v2, all_207_3) & in(v1, all_207_4)))) % 261.21/36.44 (6) $i(all_207_5) % 261.21/36.44 (7) relation_rng(all_207_3) = all_207_0 % 261.21/36.44 (8) all_207_2 = all_170_0 | ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 261.21/36.44 (ordered_pair(v0, v1) = v2 & $i(v2) & $i(v1) & $i(v0) & ( ~ in(v2, % 261.21/36.44 all_207_3) | ~ in(v2, all_170_0) | ~ in(v1, all_207_4)) & (in(v2, % 261.21/36.44 all_170_0) | (in(v2, all_207_3) & in(v1, all_207_4)))) % 261.21/36.44 (9) $i(all_207_4) % 261.21/36.44 (10) $i(all_207_2) % 261.21/36.44 (11) ! [v0: $i] : ( ~ $i(v0) | ~ in(v0, empty_set)) % 261.21/36.44 (12) in(all_207_5, all_207_0) % 261.21/36.44 (13) all_207_3 = empty_set | ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 261.21/36.44 (ordered_pair(v0, v1) = v2 & $i(v2) & $i(v1) & $i(v0) & ( ~ in(v2, % 261.21/36.44 all_207_3) | ~ in(v2, empty_set)) & (in(v2, all_207_3) | in(v2, % 261.21/36.44 empty_set))) % 261.21/36.44 (14) all_207_2 = empty_set | ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 261.21/36.44 (ordered_pair(v0, v1) = v2 & $i(v2) & $i(v1) & $i(v0) & ( ~ in(v2, % 261.21/36.44 all_207_3) | ~ in(v2, empty_set) | ~ in(v1, all_207_4)) & % 261.21/36.44 (in(v2, empty_set) | (in(v2, all_207_3) & in(v1, all_207_4)))) % 261.21/36.44 (15) relation(all_207_2) % 261.21/36.44 (16) ~ (all_207_3 = empty_set) % 261.21/36.44 (17) subset(empty_set, all_172_0) % 261.21/36.44 (18) relation_rng_restriction(all_207_4, all_207_3) = all_207_2 % 261.21/36.44 (19) ~ in(all_207_5, all_207_1) % 261.21/36.44 (20) all_207_2 = all_172_0 | ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 261.21/36.44 (ordered_pair(v0, v1) = v2 & $i(v2) & $i(v1) & $i(v0) & ( ~ in(v2, % 261.21/36.44 all_207_2) | ~ in(v2, all_172_0)) & (in(v2, all_207_2) | in(v2, % 261.21/36.44 all_172_0))) % 261.21/36.44 (21) relation_rng(all_207_2) = all_207_1 % 261.21/36.44 (22) relation(all_207_3) % 261.21/36.44 (23) $i(all_207_1) % 261.21/36.44 (24) in(all_207_5, all_207_4) % 261.21/36.44 (25) all_170_0 = empty_set % 261.21/36.44 (26) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( % 261.21/36.44 ~ (relation_rng(v0) = v1) | ~ (ordered_pair(v3, v2) = v4) | ~ $i(v3) % 261.21/36.44 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ relation(v0) | ~ in(v4, v0) % 261.21/36.44 | in(v2, v1)) % 261.21/36.45 (27) ~ subset(all_172_0, empty_set) % 261.21/36.45 (28) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (relation_rng(v0) = v1) | % 261.21/36.45 ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ relation(v0) | ~ in(v2, v1) | % 261.21/36.45 ? [v3: $i] : ? [v4: $i] : (ordered_pair(v3, v2) = v4 & $i(v4) & % 261.21/36.45 $i(v3) & in(v4, v0))) % 261.21/36.45 % 261.21/36.45 Begin of proof % 261.21/36.45 | % 261.21/36.45 | BETA: splitting (13) gives: % 261.21/36.45 | % 261.21/36.45 | Case 1: % 261.21/36.45 | | % 261.21/36.45 | | (29) all_207_3 = empty_set % 261.21/36.45 | | % 261.21/36.45 | | REDUCE: (16), (29) imply: % 261.21/36.45 | | (30) $false % 261.21/36.45 | | % 261.21/36.45 | | CLOSE: (30) is inconsistent. % 261.21/36.45 | | % 261.21/36.45 | Case 2: % 261.21/36.45 | | % 261.21/36.45 | | (31) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (ordered_pair(v0, v1) = v2 % 261.21/36.45 | | & $i(v2) & $i(v1) & $i(v0) & ( ~ in(v2, all_207_3) | ~ in(v2, % 261.21/36.45 | | empty_set)) & (in(v2, all_207_3) | in(v2, empty_set))) % 261.21/36.45 | | % 261.21/36.45 | | DELTA: instantiating (31) with fresh symbols all_430_0, all_430_1, all_430_2 % 261.21/36.45 | | gives: % 261.21/36.45 | | (32) ordered_pair(all_430_2, all_430_1) = all_430_0 & $i(all_430_0) & % 261.21/36.45 | | $i(all_430_1) & $i(all_430_2) & ( ~ in(all_430_0, all_207_3) | ~ % 261.21/36.45 | | in(all_430_0, empty_set)) & (in(all_430_0, all_207_3) | % 261.21/36.45 | | in(all_430_0, empty_set)) % 261.21/36.45 | | % 261.21/36.45 | | ALPHA: (32) implies: % 261.21/36.45 | | (33) $i(all_430_0) % 261.21/36.45 | | (34) in(all_430_0, all_207_3) | in(all_430_0, empty_set) % 261.21/36.45 | | % 261.21/36.45 | | BETA: splitting (14) gives: % 261.21/36.45 | | % 261.21/36.45 | | Case 1: % 261.21/36.45 | | | % 261.21/36.45 | | | (35) all_207_2 = empty_set % 261.21/36.45 | | | % 261.21/36.45 | | | REDUCE: (18), (35) imply: % 261.21/36.45 | | | (36) relation_rng_restriction(all_207_4, all_207_3) = empty_set % 261.21/36.45 | | | % 261.21/36.45 | | | REDUCE: (10), (35) imply: % 261.21/36.45 | | | (37) $i(empty_set) % 261.21/36.45 | | | % 261.21/36.45 | | | REDUCE: (15), (35) imply: % 261.21/36.45 | | | (38) relation(empty_set) % 261.21/36.45 | | | % 261.21/36.45 | | | BETA: splitting (1) gives: % 261.21/36.45 | | | % 261.21/36.45 | | | Case 1: % 261.21/36.45 | | | | % 261.21/36.45 | | | | (39) all_172_0 = empty_set % 261.21/36.45 | | | | % 261.21/36.45 | | | | REDUCE: (17), (39) imply: % 261.21/36.45 | | | | (40) subset(empty_set, empty_set) % 261.21/36.45 | | | | % 261.21/36.45 | | | | REDUCE: (27), (39) imply: % 261.21/36.45 | | | | (41) ~ subset(empty_set, empty_set) % 261.21/36.45 | | | | % 261.21/36.45 | | | | PRED_UNIFY: (40), (41) imply: % 261.21/36.45 | | | | (42) $false % 261.21/36.45 | | | | % 261.21/36.45 | | | | CLOSE: (42) is inconsistent. % 261.21/36.45 | | | | % 261.21/36.45 | | | Case 2: % 261.21/36.45 | | | | % 261.21/36.45 | | | | (43) ~ (all_172_0 = empty_set) % 261.21/36.45 | | | | % 261.21/36.45 | | | | BETA: splitting (5) gives: % 261.21/36.45 | | | | % 261.21/36.45 | | | | Case 1: % 261.21/36.45 | | | | | % 261.21/36.45 | | | | | (44) all_207_2 = all_172_0 % 261.21/36.45 | | | | | % 261.21/36.45 | | | | | COMBINE_EQS: (35), (44) imply: % 261.21/36.45 | | | | | (45) all_172_0 = empty_set % 261.21/36.45 | | | | | % 261.21/36.45 | | | | | REDUCE: (43), (45) imply: % 261.21/36.45 | | | | | (46) $false % 261.21/36.45 | | | | | % 261.21/36.45 | | | | | CLOSE: (46) is inconsistent. % 261.21/36.45 | | | | | % 261.21/36.45 | | | | Case 2: % 261.21/36.45 | | | | | % 261.21/36.45 | | | | | % 261.21/36.45 | | | | | GROUND_INST: instantiating (28) with all_207_3, all_207_0, all_207_5, % 261.21/36.45 | | | | | simplifying with (2), (3), (6), (7), (12), (22) gives: % 261.21/36.45 | | | | | (47) ? [v0: $i] : ? [v1: $i] : (ordered_pair(v0, all_207_5) = v1 % 261.21/36.45 | | | | | & $i(v1) & $i(v0) & in(v1, all_207_3)) % 261.21/36.45 | | | | | % 261.21/36.45 | | | | | DELTA: instantiating (47) with fresh symbols all_572_0, all_572_1 % 261.21/36.45 | | | | | gives: % 261.21/36.45 | | | | | (48) ordered_pair(all_572_1, all_207_5) = all_572_0 & $i(all_572_0) % 261.21/36.45 | | | | | & $i(all_572_1) & in(all_572_0, all_207_3) % 261.21/36.45 | | | | | % 261.21/36.45 | | | | | ALPHA: (48) implies: % 261.21/36.45 | | | | | (49) in(all_572_0, all_207_3) % 261.21/36.45 | | | | | (50) $i(all_572_1) % 261.21/36.45 | | | | | (51) $i(all_572_0) % 261.21/36.45 | | | | | (52) ordered_pair(all_572_1, all_207_5) = all_572_0 % 261.21/36.45 | | | | | % 261.21/36.45 | | | | | BETA: splitting (34) gives: % 261.21/36.45 | | | | | % 261.21/36.45 | | | | | Case 1: % 261.21/36.45 | | | | | | % 261.21/36.45 | | | | | | (53) in(all_430_0, empty_set) % 261.21/36.45 | | | | | | % 261.21/36.45 | | | | | | GROUND_INST: instantiating (11) with all_430_0, simplifying with % 261.21/36.45 | | | | | | (33), (53) gives: % 261.21/36.45 | | | | | | (54) $false % 261.21/36.45 | | | | | | % 261.21/36.45 | | | | | | CLOSE: (54) is inconsistent. % 261.21/36.45 | | | | | | % 261.21/36.45 | | | | | Case 2: % 261.21/36.45 | | | | | | % 261.21/36.45 | | | | | | % 261.21/36.45 | | | | | | GROUND_INST: instantiating (4) with all_207_4, all_207_3, empty_set, % 261.21/36.45 | | | | | | all_572_1, all_207_5, all_572_0, simplifying with (2), % 261.21/36.45 | | | | | | (6), (9), (22), (24), (36), (37), (38), (49), (50), % 261.21/36.45 | | | | | | (52) gives: % 261.21/36.45 | | | | | | (55) in(all_572_0, empty_set) % 261.21/36.45 | | | | | | % 261.21/36.45 | | | | | | GROUND_INST: instantiating (11) with all_572_0, simplifying with % 261.21/36.45 | | | | | | (51), (55) gives: % 261.21/36.45 | | | | | | (56) $false % 261.21/36.45 | | | | | | % 261.21/36.45 | | | | | | CLOSE: (56) is inconsistent. % 261.21/36.45 | | | | | | % 261.21/36.45 | | | | | End of split % 261.21/36.45 | | | | | % 261.21/36.45 | | | | End of split % 261.21/36.45 | | | | % 261.21/36.45 | | | End of split % 261.21/36.45 | | | % 261.21/36.45 | | Case 2: % 261.21/36.45 | | | % 261.21/36.45 | | | (57) ~ (all_207_2 = empty_set) % 261.21/36.45 | | | % 261.21/36.45 | | | BETA: splitting (8) gives: % 261.21/36.45 | | | % 261.21/36.45 | | | Case 1: % 261.21/36.45 | | | | % 261.21/36.45 | | | | (58) all_207_2 = all_170_0 % 261.21/36.45 | | | | % 261.21/36.45 | | | | COMBINE_EQS: (25), (58) imply: % 261.21/36.45 | | | | (59) all_207_2 = empty_set % 261.21/36.45 | | | | % 261.21/36.45 | | | | REDUCE: (57), (59) imply: % 261.21/36.45 | | | | (60) $false % 261.21/36.45 | | | | % 261.21/36.45 | | | | CLOSE: (60) is inconsistent. % 261.21/36.45 | | | | % 261.21/36.45 | | | Case 2: % 261.21/36.45 | | | | % 261.21/36.45 | | | | (61) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (ordered_pair(v0, v1) % 261.21/36.45 | | | | = v2 & $i(v2) & $i(v1) & $i(v0) & ( ~ in(v2, all_207_3) | ~ % 261.21/36.45 | | | | in(v2, all_170_0) | ~ in(v1, all_207_4)) & (in(v2, % 261.21/36.45 | | | | all_170_0) | (in(v2, all_207_3) & in(v1, all_207_4)))) % 261.21/36.45 | | | | % 261.21/36.45 | | | | DELTA: instantiating (61) with fresh symbols all_464_0, all_464_1, % 261.21/36.45 | | | | all_464_2 gives: % 261.21/36.45 | | | | (62) ordered_pair(all_464_2, all_464_1) = all_464_0 & $i(all_464_0) & % 261.21/36.45 | | | | $i(all_464_1) & $i(all_464_2) & ( ~ in(all_464_0, all_207_3) | % 261.21/36.45 | | | | ~ in(all_464_0, all_170_0) | ~ in(all_464_1, all_207_4)) & % 261.21/36.45 | | | | (in(all_464_0, all_170_0) | (in(all_464_0, all_207_3) & % 261.21/36.45 | | | | in(all_464_1, all_207_4))) % 261.21/36.45 | | | | % 261.21/36.45 | | | | ALPHA: (62) implies: % 261.21/36.45 | | | | (63) $i(all_464_0) % 261.21/36.45 | | | | (64) in(all_464_0, all_170_0) | (in(all_464_0, all_207_3) & % 261.21/36.45 | | | | in(all_464_1, all_207_4)) % 261.21/36.45 | | | | (65) ~ in(all_464_0, all_207_3) | ~ in(all_464_0, all_170_0) | ~ % 261.21/36.45 | | | | in(all_464_1, all_207_4) % 261.21/36.45 | | | | % 261.21/36.45 | | | | BETA: splitting (5) gives: % 261.21/36.45 | | | | % 261.21/36.45 | | | | Case 1: % 261.21/36.45 | | | | | % 261.21/36.45 | | | | | (66) all_207_2 = all_172_0 % 261.21/36.45 | | | | | % 261.21/36.45 | | | | | REDUCE: (21), (66) imply: % 261.21/36.45 | | | | | (67) relation_rng(all_172_0) = all_207_1 % 261.21/36.45 | | | | | % 261.21/36.45 | | | | | REDUCE: (18), (66) imply: % 261.21/36.45 | | | | | (68) relation_rng_restriction(all_207_4, all_207_3) = all_172_0 % 261.21/36.45 | | | | | % 261.21/36.45 | | | | | REDUCE: (10), (66) imply: % 261.21/36.45 | | | | | (69) $i(all_172_0) % 261.21/36.45 | | | | | % 261.21/36.45 | | | | | REDUCE: (15), (66) imply: % 261.21/36.45 | | | | | (70) relation(all_172_0) % 261.21/36.45 | | | | | % 261.21/36.45 | | | | | GROUND_INST: instantiating (28) with all_207_3, all_207_0, all_207_5, % 261.21/36.45 | | | | | simplifying with (2), (3), (6), (7), (12), (22) gives: % 261.21/36.45 | | | | | (71) ? [v0: $i] : ? [v1: $i] : (ordered_pair(v0, all_207_5) = v1 % 261.21/36.45 | | | | | & $i(v1) & $i(v0) & in(v1, all_207_3)) % 261.21/36.45 | | | | | % 261.21/36.45 | | | | | DELTA: instantiating (71) with fresh symbols all_611_0, all_611_1 % 261.21/36.45 | | | | | gives: % 261.21/36.45 | | | | | (72) ordered_pair(all_611_1, all_207_5) = all_611_0 & $i(all_611_0) % 261.21/36.45 | | | | | & $i(all_611_1) & in(all_611_0, all_207_3) % 261.21/36.45 | | | | | % 261.21/36.45 | | | | | ALPHA: (72) implies: % 261.21/36.45 | | | | | (73) in(all_611_0, all_207_3) % 261.21/36.45 | | | | | (74) $i(all_611_1) % 261.21/36.45 | | | | | (75) ordered_pair(all_611_1, all_207_5) = all_611_0 % 261.21/36.45 | | | | | % 261.21/36.45 | | | | | BETA: splitting (64) gives: % 261.21/36.45 | | | | | % 261.21/36.45 | | | | | Case 1: % 261.21/36.45 | | | | | | % 261.21/36.45 | | | | | | (76) in(all_464_0, all_170_0) % 261.21/36.45 | | | | | | % 261.21/36.45 | | | | | | REDUCE: (25), (76) imply: % 261.21/36.45 | | | | | | (77) in(all_464_0, empty_set) % 261.21/36.45 | | | | | | % 261.21/36.45 | | | | | | GROUND_INST: instantiating (11) with all_464_0, simplifying with % 261.21/36.45 | | | | | | (63), (77) gives: % 261.21/36.45 | | | | | | (78) $false % 261.21/36.45 | | | | | | % 261.21/36.45 | | | | | | CLOSE: (78) is inconsistent. % 261.21/36.45 | | | | | | % 261.21/36.45 | | | | | Case 2: % 261.21/36.45 | | | | | | % 261.21/36.45 | | | | | | % 261.21/36.45 | | | | | | GROUND_INST: instantiating (4) with all_207_4, all_207_3, all_172_0, % 261.21/36.45 | | | | | | all_611_1, all_207_5, all_611_0, simplifying with (2), % 261.21/36.45 | | | | | | (6), (9), (22), (24), (68), (69), (70), (73), (74), % 261.21/36.45 | | | | | | (75) gives: % 261.21/36.45 | | | | | | (79) in(all_611_0, all_172_0) % 261.21/36.45 | | | | | | % 261.21/36.45 | | | | | | GROUND_INST: instantiating (26) with all_172_0, all_207_1, % 261.21/36.45 | | | | | | all_207_5, all_611_1, all_611_0, simplifying with (6), % 261.21/36.45 | | | | | | (19), (23), (67), (69), (70), (74), (75), (79) gives: % 261.21/36.45 | | | | | | (80) $false % 261.21/36.45 | | | | | | % 261.21/36.45 | | | | | | CLOSE: (80) is inconsistent. % 261.21/36.45 | | | | | | % 261.21/36.45 | | | | | End of split % 261.21/36.45 | | | | | % 261.21/36.45 | | | | Case 2: % 261.21/36.45 | | | | | % 261.21/36.45 | | | | | (81) ~ (all_207_2 = all_172_0) % 261.21/36.45 | | | | | % 261.21/36.45 | | | | | BETA: splitting (20) gives: % 261.21/36.45 | | | | | % 261.21/36.45 | | | | | Case 1: % 261.21/36.45 | | | | | | % 261.21/36.45 | | | | | | (82) all_207_2 = all_172_0 % 261.21/36.45 | | | | | | % 261.21/36.45 | | | | | | REDUCE: (81), (82) imply: % 261.21/36.45 | | | | | | (83) $false % 261.21/36.45 | | | | | | % 261.21/36.45 | | | | | | CLOSE: (83) is inconsistent. % 261.21/36.45 | | | | | | % 261.21/36.45 | | | | | Case 2: % 261.21/36.45 | | | | | | % 261.21/36.45 | | | | | | % 261.21/36.45 | | | | | | GROUND_INST: instantiating (28) with all_207_3, all_207_0, % 261.21/36.45 | | | | | | all_207_5, simplifying with (2), (3), (6), (7), (12), % 261.21/36.45 | | | | | | (22) gives: % 261.21/36.45 | | | | | | (84) ? [v0: $i] : ? [v1: $i] : (ordered_pair(v0, all_207_5) = % 261.21/36.45 | | | | | | v1 & $i(v1) & $i(v0) & in(v1, all_207_3)) % 261.21/36.45 | | | | | | % 261.21/36.45 | | | | | | DELTA: instantiating (84) with fresh symbols all_595_0, all_595_1 % 261.21/36.45 | | | | | | gives: % 261.21/36.45 | | | | | | (85) ordered_pair(all_595_1, all_207_5) = all_595_0 & % 261.21/36.45 | | | | | | $i(all_595_0) & $i(all_595_1) & in(all_595_0, all_207_3) % 261.21/36.45 | | | | | | % 261.21/36.45 | | | | | | ALPHA: (85) implies: % 261.21/36.45 | | | | | | (86) in(all_595_0, all_207_3) % 261.21/36.45 | | | | | | (87) $i(all_595_1) % 261.21/36.45 | | | | | | (88) ordered_pair(all_595_1, all_207_5) = all_595_0 % 261.21/36.45 | | | | | | % 261.21/36.45 | | | | | | BETA: splitting (65) gives: % 261.21/36.45 | | | | | | % 261.21/36.45 | | | | | | Case 1: % 261.21/36.45 | | | | | | | % 261.21/36.45 | | | | | | | (89) ~ in(all_464_0, all_207_3) % 261.21/36.45 | | | | | | | % 261.21/36.45 | | | | | | | BETA: splitting (64) gives: % 261.21/36.45 | | | | | | | % 261.21/36.45 | | | | | | | Case 1: % 261.21/36.45 | | | | | | | | % 261.21/36.45 | | | | | | | | (90) in(all_464_0, all_170_0) % 261.21/36.45 | | | | | | | | % 261.21/36.45 | | | | | | | | REDUCE: (25), (90) imply: % 261.21/36.45 | | | | | | | | (91) in(all_464_0, empty_set) % 261.21/36.45 | | | | | | | | % 261.21/36.45 | | | | | | | | GROUND_INST: instantiating (11) with all_464_0, simplifying with % 261.21/36.45 | | | | | | | | (63), (91) gives: % 261.21/36.45 | | | | | | | | (92) $false % 261.21/36.45 | | | | | | | | % 261.21/36.45 | | | | | | | | CLOSE: (92) is inconsistent. % 261.21/36.45 | | | | | | | | % 261.21/36.45 | | | | | | | Case 2: % 261.21/36.45 | | | | | | | | % 261.21/36.45 | | | | | | | | (93) in(all_464_0, all_207_3) & in(all_464_1, all_207_4) % 261.21/36.45 | | | | | | | | % 261.21/36.45 | | | | | | | | ALPHA: (93) implies: % 261.21/36.45 | | | | | | | | (94) in(all_464_0, all_207_3) % 261.21/36.45 | | | | | | | | % 261.21/36.45 | | | | | | | | PRED_UNIFY: (89), (94) imply: % 261.21/36.45 | | | | | | | | (95) $false % 261.21/36.45 | | | | | | | | % 261.21/36.45 | | | | | | | | CLOSE: (95) is inconsistent. % 261.21/36.45 | | | | | | | | % 261.21/36.45 | | | | | | | End of split % 261.21/36.45 | | | | | | | % 261.21/36.45 | | | | | | Case 2: % 261.21/36.45 | | | | | | | % 261.21/36.45 | | | | | | | % 261.21/36.45 | | | | | | | GROUND_INST: instantiating (4) with all_207_4, all_207_3, % 261.21/36.45 | | | | | | | all_207_2, all_595_1, all_207_5, all_595_0, % 261.21/36.45 | | | | | | | simplifying with (2), (6), (9), (10), (15), (18), % 261.21/36.45 | | | | | | | (22), (24), (86), (87), (88) gives: % 261.21/36.45 | | | | | | | (96) in(all_595_0, all_207_2) % 261.21/36.45 | | | | | | | % 261.21/36.45 | | | | | | | GROUND_INST: instantiating (26) with all_207_2, all_207_1, % 261.21/36.45 | | | | | | | all_207_5, all_595_1, all_595_0, simplifying with % 261.21/36.45 | | | | | | | (6), (10), (15), (19), (21), (23), (87), (88), (96) % 261.21/36.45 | | | | | | | gives: % 261.21/36.45 | | | | | | | (97) $false % 261.21/36.45 | | | | | | | % 261.21/36.45 | | | | | | | CLOSE: (97) is inconsistent. % 261.21/36.45 | | | | | | | % 261.21/36.45 | | | | | | End of split % 261.21/36.45 | | | | | | % 261.21/36.45 | | | | | End of split % 261.21/36.45 | | | | | % 261.21/36.45 | | | | End of split % 261.21/36.45 | | | | % 261.21/36.45 | | | End of split % 261.21/36.45 | | | % 261.21/36.45 | | End of split % 261.21/36.45 | | % 261.21/36.45 | End of split % 261.21/36.45 | % 261.21/36.45 End of proof % 261.21/36.45 % 261.21/36.45 Sub-proof #4 shows that the following formulas are inconsistent: % 261.21/36.45 ---------------------------------------------------------------- % 261.21/36.45 (1) all_172_0 = empty_set | ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 261.21/36.45 (ordered_pair(v0, v1) = v2 & $i(v2) & $i(v1) & $i(v0) & in(v2, % 261.21/36.45 all_172_0)) % 261.21/36.45 (2) ! [v0: $i] : (v0 = empty_set | ~ $i(v0) | ~ subset(v0, empty_set)) % 261.21/36.45 (3) $i(all_172_0) % 261.21/36.46 (4) subset(all_172_0, empty_set) % 261.21/36.46 (5) empty(empty_set) % 261.21/36.46 (6) ~ empty(all_172_0) % 261.21/36.46 % 261.21/36.46 Begin of proof % 261.21/36.46 | % 261.21/36.46 | BETA: splitting (1) gives: % 261.21/36.46 | % 261.21/36.46 | Case 1: % 261.21/36.46 | | % 261.21/36.46 | | (7) all_172_0 = empty_set % 261.21/36.46 | | % 261.21/36.46 | | REDUCE: (6), (7) imply: % 261.21/36.46 | | (8) ~ empty(empty_set) % 261.21/36.46 | | % 261.21/36.46 | | PRED_UNIFY: (5), (8) imply: % 261.21/36.46 | | (9) $false % 261.21/36.46 | | % 261.21/36.46 | | CLOSE: (9) is inconsistent. % 261.21/36.46 | | % 261.21/36.46 | Case 2: % 261.21/36.46 | | % 261.21/36.46 | | (10) ~ (all_172_0 = empty_set) % 261.21/36.46 | | % 261.21/36.46 | | GROUND_INST: instantiating (2) with all_172_0, simplifying with (3), (4) % 261.21/36.46 | | gives: % 261.21/36.46 | | (11) all_172_0 = empty_set % 261.21/36.46 | | % 261.21/36.46 | | REDUCE: (10), (11) imply: % 261.21/36.46 | | (12) $false % 261.21/36.46 | | % 261.21/36.46 | | CLOSE: (12) is inconsistent. % 261.21/36.46 | | % 261.21/36.46 | End of split % 261.21/36.46 | % 261.21/36.46 End of proof % 261.21/36.46 % 261.21/36.46 Sub-proof #5 shows that the following formulas are inconsistent: % 261.21/36.46 ---------------------------------------------------------------- % 261.21/36.46 (1) $i(all_207_3) % 261.21/36.46 (2) subset(all_207_3, all_172_0) % 261.21/36.46 (3) subset(all_172_0, all_207_3) % 261.21/36.46 (4) $i(all_172_0) % 261.21/36.46 (5) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ $i(v1) | ~ $i(v0) | ~ % 261.21/36.46 subset(v1, v0) | ~ subset(v0, v1)) % 261.21/36.46 (6) ~ (all_207_3 = all_172_0) % 261.21/36.46 % 261.21/36.46 Begin of proof % 261.21/36.46 | % 261.21/36.46 | GROUND_INST: instantiating (5) with all_172_0, all_207_3, simplifying with % 261.21/36.46 | (1), (2), (3), (4) gives: % 261.21/36.46 | (7) all_207_3 = all_172_0 % 261.21/36.46 | % 261.21/36.46 | REDUCE: (6), (7) imply: % 261.21/36.46 | (8) $false % 261.21/36.46 | % 261.21/36.46 | CLOSE: (8) is inconsistent. % 261.21/36.46 | % 261.21/36.46 End of proof % 261.21/36.46 % 261.21/36.46 Sub-proof #6 shows that the following formulas are inconsistent: % 261.21/36.46 ---------------------------------------------------------------- % 261.21/36.46 (1) $i(all_207_3) % 261.21/36.46 (2) ! [v0: $i] : (v0 = empty_set | ~ $i(v0) | ~ subset(v0, empty_set)) % 261.21/36.46 (3) all_207_2 = all_170_0 | ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 261.21/36.46 (ordered_pair(v0, v1) = v2 & $i(v2) & $i(v1) & $i(v0) & ( ~ in(v2, % 261.21/36.46 all_207_3) | ~ in(v2, all_170_0) | ~ in(v1, all_207_4)) & (in(v2, % 261.21/36.46 all_170_0) | (in(v2, all_207_3) & in(v1, all_207_4)))) % 261.21/36.46 (4) ! [v0: $i] : ( ~ $i(v0) | ~ in(v0, empty_set)) % 261.21/36.46 (5) all_207_3 = empty_set | ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 261.21/36.46 (ordered_pair(v0, v1) = v2 & $i(v2) & $i(v1) & $i(v0) & ( ~ in(v2, % 261.21/36.46 all_207_3) | ~ in(v2, empty_set)) & (in(v2, all_207_3) | in(v2, % 261.21/36.46 empty_set))) % 261.21/36.46 (6) ~ (all_207_2 = all_207_3) % 261.21/36.46 (7) subset(all_207_3, empty_set) % 261.21/36.46 (8) all_170_0 = empty_set % 261.21/36.46 % 261.21/36.46 Begin of proof % 261.21/36.46 | % 261.21/36.46 | BETA: splitting (5) gives: % 261.21/36.46 | % 261.21/36.46 | Case 1: % 261.21/36.46 | | % 261.21/36.46 | | (9) all_207_3 = empty_set % 261.21/36.46 | | % 261.21/36.46 | | REDUCE: (6), (9) imply: % 261.21/36.46 | | (10) ~ (all_207_2 = empty_set) % 261.21/36.46 | | % 261.21/36.46 | | BETA: splitting (3) gives: % 261.21/36.46 | | % 261.21/36.46 | | Case 1: % 261.21/36.46 | | | % 261.21/36.46 | | | (11) all_207_2 = all_170_0 % 261.21/36.46 | | | % 261.21/36.46 | | | COMBINE_EQS: (8), (11) imply: % 261.21/36.46 | | | (12) all_207_2 = empty_set % 261.21/36.46 | | | % 261.21/36.46 | | | REDUCE: (10), (12) imply: % 261.21/36.46 | | | (13) $false % 261.21/36.46 | | | % 261.21/36.46 | | | CLOSE: (13) is inconsistent. % 261.21/36.46 | | | % 261.21/36.46 | | Case 2: % 261.21/36.46 | | | % 261.21/36.46 | | | (14) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (ordered_pair(v0, v1) = % 261.21/36.46 | | | v2 & $i(v2) & $i(v1) & $i(v0) & ( ~ in(v2, all_207_3) | ~ % 261.21/36.46 | | | in(v2, all_170_0) | ~ in(v1, all_207_4)) & (in(v2, all_170_0) % 261.21/36.46 | | | | (in(v2, all_207_3) & in(v1, all_207_4)))) % 261.21/36.46 | | | % 261.21/36.46 | | | DELTA: instantiating (14) with fresh symbols all_440_0, all_440_1, % 261.21/36.46 | | | all_440_2 gives: % 261.21/36.46 | | | (15) ordered_pair(all_440_2, all_440_1) = all_440_0 & $i(all_440_0) & % 261.21/36.46 | | | $i(all_440_1) & $i(all_440_2) & ( ~ in(all_440_0, all_207_3) | ~ % 261.21/36.46 | | | in(all_440_0, all_170_0) | ~ in(all_440_1, all_207_4)) & % 261.21/36.46 | | | (in(all_440_0, all_170_0) | (in(all_440_0, all_207_3) & % 261.21/36.46 | | | in(all_440_1, all_207_4))) % 261.21/36.46 | | | % 261.21/36.46 | | | ALPHA: (15) implies: % 261.21/36.46 | | | (16) $i(all_440_0) % 261.21/36.46 | | | (17) in(all_440_0, all_170_0) | (in(all_440_0, all_207_3) & % 261.21/36.46 | | | in(all_440_1, all_207_4)) % 261.21/36.46 | | | % 261.21/36.46 | | | BETA: splitting (17) gives: % 261.21/36.46 | | | % 261.21/36.46 | | | Case 1: % 261.21/36.46 | | | | % 261.21/36.46 | | | | (18) in(all_440_0, all_170_0) % 261.21/36.46 | | | | % 261.21/36.46 | | | | REDUCE: (8), (18) imply: % 261.21/36.46 | | | | (19) in(all_440_0, empty_set) % 261.21/36.46 | | | | % 261.21/36.46 | | | | GROUND_INST: instantiating (4) with all_440_0, simplifying with (16), % 261.21/36.46 | | | | (19) gives: % 261.21/36.46 | | | | (20) $false % 261.21/36.46 | | | | % 261.21/36.46 | | | | CLOSE: (20) is inconsistent. % 261.21/36.46 | | | | % 261.21/36.46 | | | Case 2: % 261.21/36.46 | | | | % 261.21/36.46 | | | | (21) ~ in(all_440_0, all_170_0) % 261.21/36.46 | | | | (22) in(all_440_0, all_207_3) & in(all_440_1, all_207_4) % 261.21/36.46 | | | | % 261.21/36.46 | | | | ALPHA: (22) implies: % 261.21/36.46 | | | | (23) in(all_440_0, all_207_3) % 261.21/36.46 | | | | % 261.21/36.46 | | | | REDUCE: (9), (23) imply: % 261.21/36.46 | | | | (24) in(all_440_0, empty_set) % 261.21/36.46 | | | | % 261.21/36.46 | | | | REDUCE: (8), (21) imply: % 261.21/36.46 | | | | (25) ~ in(all_440_0, empty_set) % 261.21/36.46 | | | | % 261.21/36.46 | | | | PRED_UNIFY: (24), (25) imply: % 261.21/36.46 | | | | (26) $false % 261.21/36.46 | | | | % 261.21/36.46 | | | | CLOSE: (26) is inconsistent. % 261.21/36.46 | | | | % 261.21/36.46 | | | End of split % 261.21/36.46 | | | % 261.21/36.46 | | End of split % 261.21/36.46 | | % 261.21/36.46 | Case 2: % 261.21/36.46 | | % 261.21/36.46 | | (27) ~ (all_207_3 = empty_set) % 261.21/36.46 | | % 261.21/36.46 | | REF_CLOSE: (1), (2), (7), (27) are inconsistent by sub-proof #7. % 261.21/36.46 | | % 261.21/36.46 | End of split % 261.21/36.46 | % 261.21/36.46 End of proof % 261.21/36.46 % 261.21/36.46 Sub-proof #7 shows that the following formulas are inconsistent: % 261.21/36.46 ---------------------------------------------------------------- % 261.21/36.46 (1) ! [v0: $i] : (v0 = empty_set | ~ $i(v0) | ~ subset(v0, empty_set)) % 261.21/36.46 (2) $i(all_207_3) % 261.21/36.46 (3) subset(all_207_3, empty_set) % 261.21/36.46 (4) ~ (all_207_3 = empty_set) % 261.21/36.46 % 261.21/36.46 Begin of proof % 261.21/36.46 | % 261.21/36.46 | GROUND_INST: instantiating (1) with all_207_3, simplifying with (2), (3) % 261.21/36.46 | gives: % 261.21/36.46 | (5) all_207_3 = empty_set % 261.21/36.46 | % 261.21/36.46 | REDUCE: (4), (5) imply: % 261.21/36.46 | (6) $false % 261.21/36.46 | % 261.21/36.46 | CLOSE: (6) is inconsistent. % 261.21/36.46 | % 261.21/36.46 End of proof % 261.21/36.46 % 261.21/36.46 Sub-proof #8 shows that the following formulas are inconsistent: % 261.21/36.46 ---------------------------------------------------------------- % 261.21/36.46 (1) relation_rng(all_207_3) = all_207_1 % 261.21/36.46 (2) relation_rng(all_207_3) = all_207_0 % 261.21/36.46 (3) in(all_207_5, all_207_0) % 261.21/36.46 (4) ~ in(all_207_5, all_207_1) % 261.21/36.46 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (relation_rng(v2) % 261.21/36.46 = v1) | ~ (relation_rng(v2) = v0)) % 261.21/36.46 % 261.21/36.46 Begin of proof % 261.21/36.46 | % 261.21/36.46 | GROUND_INST: instantiating (5) with all_207_0, all_207_1, all_207_3, % 261.21/36.46 | simplifying with (1), (2) gives: % 261.21/36.46 | (6) all_207_0 = all_207_1 % 261.21/36.46 | % 261.21/36.46 | REDUCE: (3), (6) imply: % 261.21/36.46 | (7) in(all_207_5, all_207_1) % 261.21/36.46 | % 261.21/36.46 | PRED_UNIFY: (4), (7) imply: % 261.21/36.46 | (8) $false % 261.21/36.46 | % 261.21/36.46 | CLOSE: (8) is inconsistent. % 261.21/36.46 | % 261.21/36.46 End of proof % 261.21/36.46 % SZS output end Proof for theBenchmark % 261.21/36.46 % 261.21/36.46 35852ms %------------------------------------------------------------------------------