%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SEU188+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 : n027.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 17:43:08 EDT 2023 % Result : Theorem 27.46s 4.43s % Output : Proof 32.44s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SEU188+2 : TPTP v8.1.2. Released v3.3.0. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.34 % Computer : n027.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 300 % 0.13/0.34 % DateTime : Wed Aug 23 19:37:31 EDT 2023 % 0.13/0.34 % 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/sandbox/benchmark/theBenchmark.p ... % 0.19/0.63 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 % 5.24/1.39 Prover 1: Preprocessing ... % 5.24/1.39 Prover 4: Preprocessing ... % 5.24/1.43 Prover 6: Preprocessing ... % 5.24/1.43 Prover 2: Preprocessing ... % 5.24/1.43 Prover 5: Preprocessing ... % 5.24/1.43 Prover 3: Preprocessing ... % 5.24/1.43 Prover 0: Preprocessing ... % 15.15/2.80 Prover 1: Warning: ignoring some quantifiers % 15.15/2.91 Prover 3: Warning: ignoring some quantifiers % 15.15/2.95 Prover 6: Proving ... % 16.03/2.97 Prover 1: Constructing countermodel ... % 16.03/2.99 Prover 3: Constructing countermodel ... % 16.03/2.99 Prover 5: Proving ... % 18.31/3.26 Prover 4: Warning: ignoring some quantifiers % 19.31/3.34 Prover 2: Proving ... % 19.31/3.37 Prover 4: Constructing countermodel ... % 22.44/3.76 Prover 0: Proving ... % 27.46/4.43 Prover 3: proved (3793ms) % 27.46/4.43 % 27.46/4.43 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 27.46/4.43 % 27.46/4.43 Prover 5: stopped % 27.46/4.43 Prover 0: stopped % 27.46/4.43 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 27.46/4.43 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 27.46/4.44 Prover 2: stopped % 27.46/4.44 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 27.46/4.44 Prover 6: stopped % 27.46/4.44 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 27.46/4.44 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 27.79/4.48 Prover 1: Found proof (size 225) % 27.79/4.48 Prover 1: proved (3847ms) % 27.79/4.51 Prover 4: stopped % 29.09/4.64 Prover 10: Preprocessing ... % 29.20/4.67 Prover 8: Preprocessing ... % 29.20/4.67 Prover 13: Preprocessing ... % 29.20/4.68 Prover 7: Preprocessing ... % 29.61/4.72 Prover 11: Preprocessing ... % 29.91/4.83 Prover 7: stopped % 30.54/4.85 Prover 10: stopped % 30.86/4.89 Prover 13: stopped % 30.86/4.97 Prover 11: stopped % 30.86/5.03 Prover 8: Warning: ignoring some quantifiers % 30.86/5.06 Prover 8: Constructing countermodel ... % 31.44/5.06 Prover 8: stopped % 31.44/5.07 % 31.44/5.07 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 31.44/5.07 % 31.77/5.10 % SZS output start Proof for theBenchmark % 31.77/5.11 Assumptions after simplification: % 31.77/5.11 --------------------------------- % 31.77/5.11 % 31.77/5.11 (cc1_relat_1) % 31.77/5.13 ! [v0: $i] : ( ~ (empty(v0) = 0) | ~ $i(v0) | relation(v0) = 0) % 31.77/5.13 % 31.77/5.13 (d2_subset_1) % 32.01/5.13 ! [v0: $i] : ! [v1: $i] : ! [v2: any] : ( ~ (element(v1, v0) = v2) | ~ % 32.01/5.13 $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : (empty(v0) = v3 & in(v1, % 32.01/5.13 v0) = v4 & (v3 = 0 | (( ~ (v4 = 0) | v2 = 0) & ( ~ (v2 = 0) | v4 = % 32.01/5.13 0))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: any] : ( ~ (empty(v1) = % 32.01/5.13 v2) | ~ (empty(v0) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : % 32.01/5.13 (element(v1, v0) = v3 & ( ~ (v3 = 0) | v2 = 0) & ( ~ (v2 = 0) | v3 = 0))) % 32.01/5.13 % 32.01/5.13 (d4_relat_1) % 32.01/5.14 ! [v0: $i] : ! [v1: $i] : ( ~ (relation_dom(v0) = v1) | ~ $i(v0) | ? [v2: % 32.01/5.14 int] : ( ~ (v2 = 0) & relation(v0) = v2) | ( ? [v2: $i] : (v2 = v1 | ~ % 32.01/5.14 $i(v2) | ? [v3: $i] : ? [v4: any] : (in(v3, v2) = v4 & $i(v3) & ( ~ % 32.01/5.14 (v4 = 0) | ! [v5: $i] : ! [v6: $i] : ( ~ (ordered_pair(v3, v5) = % 32.01/5.14 v6) | ~ (in(v6, v0) = 0) | ~ $i(v5))) & (v4 = 0 | ? [v5: $i] % 32.01/5.14 : ? [v6: $i] : (ordered_pair(v3, v5) = v6 & in(v6, v0) = 0 & $i(v6) % 32.01/5.14 & $i(v5))))) & ( ~ $i(v1) | ( ! [v2: $i] : ! [v3: int] : (v3 = 0 % 32.01/5.14 | ~ (in(v2, v1) = v3) | ~ $i(v2) | ! [v4: $i] : ! [v5: $i] : ( ~ % 32.01/5.14 (ordered_pair(v2, v4) = v5) | ~ (in(v5, v0) = 0) | ~ $i(v4))) & % 32.01/5.14 ! [v2: $i] : ( ~ (in(v2, v1) = 0) | ~ $i(v2) | ? [v3: $i] : ? [v4: % 32.01/5.14 $i] : (ordered_pair(v2, v3) = v4 & in(v4, v0) = 0 & $i(v4) & % 32.01/5.14 $i(v3))))))) % 32.01/5.14 % 32.01/5.14 (fc4_relat_1) % 32.01/5.14 empty(empty_set) = 0 & relation(empty_set) = 0 & $i(empty_set) % 32.01/5.14 % 32.01/5.14 (fc5_relat_1) % 32.01/5.14 ! [v0: $i] : ! [v1: $i] : ( ~ (relation_dom(v0) = v1) | ~ $i(v0) | ? [v2: % 32.01/5.14 any] : ? [v3: any] : ? [v4: any] : (empty(v1) = v4 & empty(v0) = v2 & % 32.01/5.14 relation(v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | v2 = 0))) % 32.01/5.14 % 32.01/5.14 (fc6_relat_1) % 32.01/5.14 ! [v0: $i] : ! [v1: $i] : ( ~ (relation_rng(v0) = v1) | ~ $i(v0) | ? [v2: % 32.01/5.14 any] : ? [v3: any] : ? [v4: any] : (empty(v1) = v4 & empty(v0) = v2 & % 32.01/5.14 relation(v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | v2 = 0))) % 32.01/5.14 % 32.01/5.14 (fc7_relat_1) % 32.01/5.14 ! [v0: $i] : ! [v1: $i] : ( ~ (relation_dom(v0) = v1) | ~ $i(v0) | ? [v2: % 32.01/5.14 any] : ? [v3: any] : ? [v4: any] : (empty(v1) = v3 & empty(v0) = v2 & % 32.01/5.14 relation(v1) = v4 & ( ~ (v2 = 0) | (v4 = 0 & v3 = 0)))) % 32.01/5.14 % 32.01/5.14 (fc8_relat_1) % 32.01/5.14 ! [v0: $i] : ! [v1: $i] : ( ~ (relation_rng(v0) = v1) | ~ $i(v0) | ? [v2: % 32.01/5.14 any] : ? [v3: any] : ? [v4: any] : (empty(v1) = v3 & empty(v0) = v2 & % 32.01/5.14 relation(v1) = v4 & ( ~ (v2 = 0) | (v4 = 0 & v3 = 0)))) % 32.01/5.14 % 32.01/5.14 (rc1_relat_1) % 32.01/5.14 ? [v0: $i] : (empty(v0) = 0 & relation(v0) = 0 & $i(v0)) % 32.01/5.14 % 32.01/5.14 (rc1_xboole_0) % 32.01/5.14 ? [v0: $i] : (empty(v0) = 0 & $i(v0)) % 32.01/5.14 % 32.01/5.14 (rc2_relat_1) % 32.01/5.14 ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & empty(v0) = v1 & relation(v0) = 0 % 32.01/5.14 & $i(v0)) % 32.01/5.14 % 32.01/5.14 (rc2_subset_1) % 32.01/5.15 ! [v0: $i] : ! [v1: $i] : ( ~ (powerset(v0) = v1) | ~ $i(v0) | ? [v2: $i] % 32.01/5.15 : (element(v2, v1) = 0 & empty(v2) = 0 & $i(v2))) % 32.01/5.15 % 32.01/5.15 (rc2_xboole_0) % 32.01/5.15 ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & empty(v0) = v1 & $i(v0)) % 32.01/5.15 % 32.01/5.15 (t1_zfmisc_1) % 32.01/5.15 $i(empty_set) & ? [v0: $i] : (powerset(empty_set) = v0 & singleton(empty_set) % 32.01/5.15 = v0 & $i(v0)) % 32.01/5.15 % 32.01/5.15 (t25_relat_1) % 32.01/5.15 ! [v0: $i] : ! [v1: $i] : ( ~ (relation_rng(v0) = v1) | ~ $i(v0) | ? [v2: % 32.01/5.15 any] : ? [v3: $i] : (relation_dom(v0) = v3 & relation(v0) = v2 & $i(v3) & % 32.01/5.15 ( ~ (v2 = 0) | ! [v4: $i] : ! [v5: $i] : ! [v6: any] : ( ~ % 32.01/5.15 (relation_rng(v4) = v5) | ~ (subset(v1, v5) = v6) | ~ $i(v4) | ? % 32.01/5.15 [v7: any] : ? [v8: any] : ? [v9: $i] : ? [v10: any] : % 32.01/5.15 (relation_dom(v4) = v9 & subset(v3, v9) = v10 & subset(v0, v4) = v8 & % 32.01/5.15 relation(v4) = v7 & $i(v9) & ( ~ (v8 = 0) | ~ (v7 = 0) | (v10 = 0 & % 32.01/5.15 v6 = 0))))))) % 32.01/5.15 % 32.01/5.15 (t2_subset) % 32.01/5.15 ! [v0: $i] : ! [v1: $i] : ( ~ (element(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) % 32.01/5.15 | ? [v2: any] : ? [v3: any] : (empty(v1) = v2 & in(v0, v1) = v3 & (v3 = 0 % 32.01/5.15 | v2 = 0))) % 32.01/5.15 % 32.01/5.15 (t46_relat_1) % 32.01/5.15 ! [v0: $i] : ! [v1: $i] : ( ~ (relation_rng(v0) = v1) | ~ $i(v0) | ? [v2: % 32.01/5.15 any] : ? [v3: $i] : (relation_dom(v0) = v3 & relation(v0) = v2 & $i(v3) & % 32.01/5.15 ( ~ (v2 = 0) | ! [v4: $i] : ! [v5: $i] : ( ~ (relation_dom(v4) = v5) | % 32.01/5.15 ~ (subset(v1, v5) = 0) | ~ $i(v4) | ? [v6: any] : ? [v7: $i] : ? % 32.01/5.15 [v8: $i] : (relation_composition(v0, v4) = v7 & relation_dom(v7) = v8 % 32.01/5.15 & relation(v4) = v6 & $i(v8) & $i(v7) & ( ~ (v6 = 0) | v8 = v3)))))) % 32.01/5.15 % 32.01/5.15 (t47_relat_1) % 32.01/5.15 ! [v0: $i] : ! [v1: $i] : ( ~ (relation_rng(v0) = v1) | ~ $i(v0) | ? [v2: % 32.01/5.15 any] : ? [v3: $i] : (relation_dom(v0) = v3 & relation(v0) = v2 & $i(v3) & % 32.01/5.15 ( ~ (v2 = 0) | ! [v4: $i] : ! [v5: $i] : ( ~ (relation_rng(v4) = v5) | % 32.01/5.15 ~ (subset(v3, v5) = 0) | ~ $i(v4) | ? [v6: any] : ? [v7: $i] : ? % 32.01/5.15 [v8: $i] : (relation_composition(v4, v0) = v7 & relation_rng(v7) = v8 % 32.01/5.15 & relation(v4) = v6 & $i(v8) & $i(v7) & ( ~ (v6 = 0) | v8 = v1)))))) % 32.01/5.15 % 32.01/5.15 (t56_relat_1) % 32.01/5.15 $i(empty_set) & ! [v0: $i] : (v0 = empty_set | ~ (relation(v0) = 0) | ~ % 32.01/5.15 $i(v0) | ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : (ordered_pair(v1, v2) = % 32.01/5.15 v3 & in(v3, v0) = 0 & $i(v3) & $i(v2) & $i(v1))) % 32.01/5.15 % 32.01/5.15 (t60_relat_1) % 32.11/5.15 relation_rng(empty_set) = empty_set & relation_dom(empty_set) = empty_set & % 32.11/5.15 $i(empty_set) % 32.11/5.15 % 32.11/5.15 (t64_relat_1) % 32.11/5.15 $i(empty_set) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ( ~ (v0 = empty_set) % 32.11/5.15 & relation_rng(v0) = v2 & relation_dom(v0) = v1 & relation(v0) = 0 & $i(v2) % 32.11/5.15 & $i(v1) & $i(v0) & (v2 = empty_set | v1 = empty_set)) % 32.11/5.15 % 32.11/5.15 (t6_boole) % 32.11/5.15 $i(empty_set) & ! [v0: $i] : (v0 = empty_set | ~ (empty(v0) = 0) | ~ % 32.11/5.15 $i(v0)) % 32.11/5.15 % 32.11/5.15 (t7_boole) % 32.11/5.15 ! [v0: $i] : ! [v1: $i] : ( ~ (in(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? % 32.11/5.15 [v2: int] : ( ~ (v2 = 0) & empty(v1) = v2)) % 32.11/5.15 % 32.11/5.15 (t8_boole) % 32.11/5.16 ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (empty(v1) = 0) | ~ (empty(v0) = 0) % 32.11/5.16 | ~ $i(v1) | ~ $i(v0)) % 32.11/5.16 % 32.11/5.16 (function-axioms) % 32.11/5.16 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 % 32.11/5.16 | ~ (subset_difference(v4, v3, v2) = v1) | ~ (subset_difference(v4, v3, % 32.11/5.16 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : % 32.11/5.16 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (are_equipotent(v3, v2) = v1) | ~ % 32.11/5.16 (are_equipotent(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 32.11/5.16 ! [v3: $i] : (v1 = v0 | ~ (meet_of_subsets(v3, v2) = v1) | ~ % 32.11/5.16 (meet_of_subsets(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 32.11/5.16 ! [v3: $i] : (v1 = v0 | ~ (union_of_subsets(v3, v2) = v1) | ~ % 32.11/5.16 (union_of_subsets(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 32.11/5.16 ! [v3: $i] : (v1 = v0 | ~ (complements_of_subsets(v3, v2) = v1) | ~ % 32.11/5.16 (complements_of_subsets(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 32.11/5.16 $i] : ! [v3: $i] : (v1 = v0 | ~ (relation_composition(v3, v2) = v1) | ~ % 32.11/5.16 (relation_composition(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 32.11/5.16 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (disjoint(v3, % 32.11/5.16 v2) = v1) | ~ (disjoint(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 32.11/5.16 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (subset_complement(v3, v2) = v1) | ~ % 32.11/5.16 (subset_complement(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 32.11/5.16 : ! [v3: $i] : (v1 = v0 | ~ (set_difference(v3, v2) = v1) | ~ % 32.11/5.16 (set_difference(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 32.11/5.16 ! [v3: $i] : (v1 = v0 | ~ (cartesian_product2(v3, v2) = v1) | ~ % 32.11/5.16 (cartesian_product2(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 32.11/5.16 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (element(v3, % 32.11/5.16 v2) = v1) | ~ (element(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 32.11/5.16 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (ordered_pair(v3, v2) = v1) | ~ % 32.11/5.16 (ordered_pair(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 32.11/5.16 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (subset(v3, % 32.11/5.16 v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 32.11/5.16 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (set_intersection2(v3, v2) = v1) | ~ % 32.11/5.16 (set_intersection2(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 32.11/5.16 : ! [v3: $i] : (v1 = v0 | ~ (set_union2(v3, v2) = v1) | ~ (set_union2(v3, % 32.11/5.16 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 % 32.11/5.16 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) % 32.11/5.16 & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 32.11/5.16 [v3: $i] : (v1 = v0 | ~ (proper_subset(v3, v2) = v1) | ~ (proper_subset(v3, % 32.11/5.16 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : % 32.11/5.16 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = % 32.11/5.16 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 32.11/5.16 (relation_inverse(v2) = v1) | ~ (relation_inverse(v2) = v0)) & ! [v0: $i] % 32.11/5.16 : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (relation_field(v2) = v1) | ~ % 32.11/5.16 (relation_field(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = % 32.11/5.16 v0 | ~ (relation_rng(v2) = v1) | ~ (relation_rng(v2) = v0)) & ! [v0: $i] % 32.11/5.16 : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (union(v2) = v1) | ~ (union(v2) = % 32.11/5.16 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 32.11/5.16 (cast_to_subset(v2) = v1) | ~ (cast_to_subset(v2) = v0)) & ! [v0: $i] : ! % 32.11/5.16 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (relation_dom(v2) = v1) | ~ % 32.11/5.16 (relation_dom(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = % 32.11/5.16 v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0)) & ! [v0: $i] : ! % 32.11/5.16 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ % 32.11/5.16 (singleton(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | % 32.11/5.16 ~ (set_meet(v2) = v1) | ~ (set_meet(v2) = v0)) & ! [v0: % 32.11/5.16 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 32.11/5.16 ~ (empty(v2) = v1) | ~ (empty(v2) = v0)) & ! [v0: MultipleValueBool] : ! % 32.11/5.16 [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (relation(v2) = v1) | ~ % 32.11/5.16 (relation(v2) = v0)) % 32.11/5.16 % 32.11/5.16 Further assumptions not needed in the proof: % 32.11/5.16 -------------------------------------------- % 32.11/5.16 antisymmetry_r2_hidden, antisymmetry_r2_xboole_0, commutativity_k2_tarski, % 32.11/5.16 commutativity_k2_xboole_0, commutativity_k3_xboole_0, d10_xboole_0, d1_relat_1, % 32.11/5.16 d1_setfam_1, d1_tarski, d1_xboole_0, d1_zfmisc_1, d2_tarski, d2_xboole_0, % 32.11/5.16 d2_zfmisc_1, d3_tarski, d3_xboole_0, d4_subset_1, d4_tarski, d4_xboole_0, % 32.11/5.16 d5_relat_1, d5_subset_1, d5_tarski, d6_relat_1, d7_relat_1, d7_xboole_0, % 32.11/5.16 d8_relat_1, d8_setfam_1, d8_xboole_0, dt_k1_relat_1, dt_k1_setfam_1, % 32.11/5.16 dt_k1_tarski, dt_k1_xboole_0, dt_k1_zfmisc_1, dt_k2_relat_1, dt_k2_subset_1, % 32.11/5.16 dt_k2_tarski, dt_k2_xboole_0, dt_k2_zfmisc_1, dt_k3_relat_1, dt_k3_subset_1, % 32.11/5.16 dt_k3_tarski, dt_k3_xboole_0, dt_k4_relat_1, dt_k4_tarski, dt_k4_xboole_0, % 32.11/5.16 dt_k5_relat_1, dt_k5_setfam_1, dt_k6_setfam_1, dt_k6_subset_1, dt_k7_setfam_1, % 32.11/5.16 dt_m1_subset_1, existence_m1_subset_1, fc1_subset_1, fc1_xboole_0, fc1_zfmisc_1, % 32.11/5.16 fc2_relat_1, fc2_subset_1, fc2_xboole_0, fc3_subset_1, fc3_xboole_0, % 32.11/5.16 fc4_subset_1, idempotence_k2_xboole_0, idempotence_k3_xboole_0, % 32.11/5.16 involutiveness_k3_subset_1, involutiveness_k4_relat_1, % 32.11/5.16 involutiveness_k7_setfam_1, irreflexivity_r2_xboole_0, l1_zfmisc_1, % 32.11/5.16 l23_zfmisc_1, l25_zfmisc_1, l28_zfmisc_1, l2_zfmisc_1, l32_xboole_1, % 32.11/5.16 l3_subset_1, l3_zfmisc_1, l4_zfmisc_1, l50_zfmisc_1, l55_zfmisc_1, l71_subset_1, % 32.11/5.16 rc1_subset_1, redefinition_k5_setfam_1, redefinition_k6_setfam_1, % 32.11/5.16 redefinition_k6_subset_1, reflexivity_r1_tarski, symmetry_r1_xboole_0, % 32.11/5.16 t106_zfmisc_1, t10_zfmisc_1, t118_zfmisc_1, t119_zfmisc_1, t12_xboole_1, % 32.11/5.16 t136_zfmisc_1, t17_xboole_1, t19_xboole_1, t1_boole, t1_subset, t1_xboole_1, % 32.11/5.16 t20_relat_1, t21_relat_1, t26_xboole_1, t28_xboole_1, t2_boole, t2_tarski, % 32.11/5.16 t2_xboole_1, t30_relat_1, t33_xboole_1, t33_zfmisc_1, t36_xboole_1, t37_relat_1, % 32.11/5.16 t37_xboole_1, t37_zfmisc_1, t38_zfmisc_1, t39_xboole_1, t39_zfmisc_1, t3_boole, % 32.11/5.16 t3_subset, t3_xboole_0, t3_xboole_1, t40_xboole_1, t43_subset_1, t44_relat_1, % 32.11/5.16 t45_relat_1, t45_xboole_1, t46_setfam_1, t46_zfmisc_1, t47_setfam_1, % 32.11/5.16 t48_setfam_1, t48_xboole_1, t4_boole, t4_subset, t4_xboole_0, t50_subset_1, % 32.11/5.16 t54_subset_1, t5_subset, t60_xboole_1, t63_xboole_1, t65_zfmisc_1, t69_enumset1, % 32.11/5.16 t6_zfmisc_1, t7_xboole_1, t83_xboole_1, t8_xboole_1, t8_zfmisc_1, t92_zfmisc_1, % 32.11/5.16 t99_zfmisc_1, t9_tarski, t9_zfmisc_1 % 32.11/5.16 % 32.11/5.16 Those formulas are unsatisfiable: % 32.11/5.16 --------------------------------- % 32.11/5.16 % 32.11/5.16 Begin of proof % 32.11/5.17 | % 32.11/5.17 | ALPHA: (d2_subset_1) implies: % 32.11/5.17 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: any] : ( ~ (empty(v1) = v2) | ~ % 32.11/5.17 | (empty(v0) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : (element(v1, % 32.11/5.17 | v0) = v3 & ( ~ (v3 = 0) | v2 = 0) & ( ~ (v2 = 0) | v3 = 0))) % 32.11/5.17 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: any] : ( ~ (element(v1, v0) = v2) | % 32.11/5.17 | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : (empty(v0) = v3 % 32.11/5.17 | & in(v1, v0) = v4 & (v3 = 0 | (( ~ (v4 = 0) | v2 = 0) & ( ~ (v2 = % 32.11/5.17 | 0) | v4 = 0))))) % 32.11/5.17 | % 32.11/5.17 | ALPHA: (fc4_relat_1) implies: % 32.11/5.17 | (3) empty(empty_set) = 0 % 32.11/5.17 | % 32.11/5.17 | ALPHA: (t1_zfmisc_1) implies: % 32.11/5.17 | (4) ? [v0: $i] : (powerset(empty_set) = v0 & singleton(empty_set) = v0 & % 32.11/5.17 | $i(v0)) % 32.11/5.17 | % 32.11/5.17 | ALPHA: (t56_relat_1) implies: % 32.11/5.17 | (5) ! [v0: $i] : (v0 = empty_set | ~ (relation(v0) = 0) | ~ $i(v0) | ? % 32.11/5.17 | [v1: $i] : ? [v2: $i] : ? [v3: $i] : (ordered_pair(v1, v2) = v3 & % 32.11/5.17 | in(v3, v0) = 0 & $i(v3) & $i(v2) & $i(v1))) % 32.11/5.17 | % 32.11/5.17 | ALPHA: (t60_relat_1) implies: % 32.11/5.17 | (6) relation_dom(empty_set) = empty_set % 32.11/5.17 | (7) relation_rng(empty_set) = empty_set % 32.11/5.17 | % 32.11/5.17 | ALPHA: (t6_boole) implies: % 32.11/5.17 | (8) ! [v0: $i] : (v0 = empty_set | ~ (empty(v0) = 0) | ~ $i(v0)) % 32.11/5.17 | % 32.11/5.17 | ALPHA: (t64_relat_1) implies: % 32.11/5.17 | (9) $i(empty_set) % 32.11/5.17 | (10) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ( ~ (v0 = empty_set) & % 32.11/5.17 | relation_rng(v0) = v2 & relation_dom(v0) = v1 & relation(v0) = 0 & % 32.11/5.17 | $i(v2) & $i(v1) & $i(v0) & (v2 = empty_set | v1 = empty_set)) % 32.11/5.17 | % 32.11/5.17 | ALPHA: (function-axioms) implies: % 32.11/5.17 | (11) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 32.11/5.17 | : (v1 = v0 | ~ (relation(v2) = v1) | ~ (relation(v2) = v0)) % 32.11/5.17 | (12) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 32.11/5.17 | : (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0)) % 32.11/5.17 | (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 32.11/5.17 | (relation_dom(v2) = v1) | ~ (relation_dom(v2) = v0)) % 32.11/5.17 | (14) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 32.11/5.17 | : ! [v3: $i] : (v1 = v0 | ~ (element(v3, v2) = v1) | ~ (element(v3, % 32.11/5.17 | v2) = v0)) % 32.11/5.17 | % 32.11/5.17 | DELTA: instantiating (rc1_xboole_0) with fresh symbol all_141_0 gives: % 32.11/5.17 | (15) empty(all_141_0) = 0 & $i(all_141_0) % 32.11/5.17 | % 32.11/5.17 | ALPHA: (15) implies: % 32.11/5.18 | (16) $i(all_141_0) % 32.11/5.18 | (17) empty(all_141_0) = 0 % 32.11/5.18 | % 32.11/5.18 | DELTA: instantiating (rc1_relat_1) with fresh symbol all_143_0 gives: % 32.11/5.18 | (18) empty(all_143_0) = 0 & relation(all_143_0) = 0 & $i(all_143_0) % 32.11/5.18 | % 32.11/5.18 | ALPHA: (18) implies: % 32.11/5.18 | (19) $i(all_143_0) % 32.11/5.18 | (20) empty(all_143_0) = 0 % 32.11/5.18 | % 32.11/5.18 | DELTA: instantiating (rc2_xboole_0) with fresh symbols all_145_0, all_145_1 % 32.11/5.18 | gives: % 32.11/5.18 | (21) ~ (all_145_0 = 0) & empty(all_145_1) = all_145_0 & $i(all_145_1) % 32.11/5.18 | % 32.11/5.18 | ALPHA: (21) implies: % 32.11/5.18 | (22) $i(all_145_1) % 32.11/5.18 | (23) empty(all_145_1) = all_145_0 % 32.11/5.18 | % 32.11/5.18 | DELTA: instantiating (4) with fresh symbol all_150_0 gives: % 32.11/5.18 | (24) powerset(empty_set) = all_150_0 & singleton(empty_set) = all_150_0 & % 32.11/5.18 | $i(all_150_0) % 32.11/5.18 | % 32.11/5.18 | ALPHA: (24) implies: % 32.11/5.18 | (25) powerset(empty_set) = all_150_0 % 32.11/5.18 | % 32.11/5.18 | DELTA: instantiating (rc2_relat_1) with fresh symbols all_153_0, all_153_1 % 32.11/5.18 | gives: % 32.11/5.18 | (26) ~ (all_153_0 = 0) & empty(all_153_1) = all_153_0 & % 32.11/5.18 | relation(all_153_1) = 0 & $i(all_153_1) % 32.11/5.18 | % 32.11/5.18 | ALPHA: (26) implies: % 32.11/5.18 | (27) ~ (all_153_0 = 0) % 32.11/5.18 | (28) $i(all_153_1) % 32.11/5.18 | (29) empty(all_153_1) = all_153_0 % 32.11/5.18 | % 32.11/5.18 | DELTA: instantiating (10) with fresh symbols all_163_0, all_163_1, all_163_2 % 32.11/5.18 | gives: % 32.11/5.18 | (30) ~ (all_163_2 = empty_set) & relation_rng(all_163_2) = all_163_0 & % 32.11/5.18 | relation_dom(all_163_2) = all_163_1 & relation(all_163_2) = 0 & % 32.11/5.18 | $i(all_163_0) & $i(all_163_1) & $i(all_163_2) & (all_163_0 = empty_set % 32.11/5.18 | | all_163_1 = empty_set) % 32.11/5.18 | % 32.11/5.18 | ALPHA: (30) implies: % 32.11/5.18 | (31) ~ (all_163_2 = empty_set) % 32.11/5.18 | (32) $i(all_163_2) % 32.11/5.18 | (33) relation(all_163_2) = 0 % 32.11/5.18 | (34) relation_dom(all_163_2) = all_163_1 % 32.11/5.18 | (35) relation_rng(all_163_2) = all_163_0 % 32.11/5.18 | (36) all_163_0 = empty_set | all_163_1 = empty_set % 32.11/5.18 | % 32.11/5.18 | GROUND_INST: instantiating (5) with all_163_2, simplifying with (32), (33) % 32.11/5.18 | gives: % 32.11/5.18 | (37) all_163_2 = empty_set | ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 32.11/5.18 | (ordered_pair(v0, v1) = v2 & in(v2, all_163_2) = 0 & $i(v2) & $i(v1) & % 32.11/5.18 | $i(v0)) % 32.11/5.18 | % 32.11/5.18 | GROUND_INST: instantiating (1) with all_141_0, empty_set, 0, simplifying with % 32.11/5.18 | (3), (9), (16), (17) gives: % 32.11/5.18 | (38) element(empty_set, all_141_0) = 0 % 32.11/5.18 | % 32.11/5.18 | GROUND_INST: instantiating (cc1_relat_1) with all_141_0, simplifying with % 32.11/5.18 | (16), (17) gives: % 32.11/5.18 | (39) relation(all_141_0) = 0 % 32.11/5.18 | % 32.11/5.18 | GROUND_INST: instantiating (t8_boole) with all_141_0, all_143_0, simplifying % 32.11/5.18 | with (16), (17), (19), (20) gives: % 32.11/5.18 | (40) all_143_0 = all_141_0 % 32.11/5.18 | % 32.11/5.18 | GROUND_INST: instantiating (8) with all_143_0, simplifying with (19), (20) % 32.11/5.18 | gives: % 32.11/5.18 | (41) all_143_0 = empty_set % 32.11/5.18 | % 32.11/5.18 | GROUND_INST: instantiating (1) with all_143_0, all_145_1, all_145_0, % 32.11/5.18 | simplifying with (19), (20), (22), (23) gives: % 32.11/5.19 | (42) ? [v0: any] : (element(all_145_1, all_143_0) = v0 & ( ~ (v0 = 0) | % 32.11/5.19 | all_145_0 = 0) & ( ~ (all_145_0 = 0) | v0 = 0)) % 32.11/5.19 | % 32.11/5.19 | GROUND_INST: instantiating (1) with all_141_0, all_145_1, all_145_0, % 32.11/5.19 | simplifying with (16), (17), (22), (23) gives: % 32.11/5.19 | (43) ? [v0: any] : (element(all_145_1, all_141_0) = v0 & ( ~ (v0 = 0) | % 32.11/5.19 | all_145_0 = 0) & ( ~ (all_145_0 = 0) | v0 = 0)) % 32.11/5.19 | % 32.11/5.19 | GROUND_INST: instantiating (1) with empty_set, all_145_1, all_145_0, % 32.11/5.19 | simplifying with (3), (9), (22), (23) gives: % 32.11/5.19 | (44) ? [v0: any] : (element(all_145_1, empty_set) = v0 & ( ~ (v0 = 0) | % 32.11/5.19 | all_145_0 = 0) & ( ~ (all_145_0 = 0) | v0 = 0)) % 32.11/5.19 | % 32.11/5.19 | GROUND_INST: instantiating (1) with all_143_0, all_153_1, all_153_0, % 32.11/5.19 | simplifying with (19), (20), (28), (29) gives: % 32.11/5.19 | (45) ? [v0: any] : (element(all_153_1, all_143_0) = v0 & ( ~ (v0 = 0) | % 32.11/5.19 | all_153_0 = 0) & ( ~ (all_153_0 = 0) | v0 = 0)) % 32.11/5.19 | % 32.11/5.19 | GROUND_INST: instantiating (1) with all_141_0, all_153_1, all_153_0, % 32.11/5.19 | simplifying with (16), (17), (28), (29) gives: % 32.11/5.19 | (46) ? [v0: any] : (element(all_153_1, all_141_0) = v0 & ( ~ (v0 = 0) | % 32.11/5.19 | all_153_0 = 0) & ( ~ (all_153_0 = 0) | v0 = 0)) % 32.11/5.19 | % 32.11/5.19 | GROUND_INST: instantiating (1) with empty_set, all_153_1, all_153_0, % 32.11/5.19 | simplifying with (3), (9), (28), (29) gives: % 32.11/5.19 | (47) ? [v0: any] : (element(all_153_1, empty_set) = v0 & ( ~ (v0 = 0) | % 32.11/5.19 | all_153_0 = 0) & ( ~ (all_153_0 = 0) | v0 = 0)) % 32.11/5.19 | % 32.11/5.19 | GROUND_INST: instantiating (rc2_subset_1) with empty_set, all_150_0, % 32.11/5.19 | simplifying with (9), (25) gives: % 32.11/5.19 | (48) ? [v0: $i] : (element(v0, all_150_0) = 0 & empty(v0) = 0 & $i(v0)) % 32.11/5.19 | % 32.11/5.19 | GROUND_INST: instantiating (fc5_relat_1) with all_163_2, all_163_1, % 32.11/5.19 | simplifying with (32), (34) gives: % 32.11/5.19 | (49) ? [v0: any] : ? [v1: any] : ? [v2: any] : (empty(all_163_1) = v2 & % 32.11/5.19 | empty(all_163_2) = v0 & relation(all_163_2) = v1 & ( ~ (v2 = 0) | ~ % 32.11/5.19 | (v1 = 0) | v0 = 0)) % 32.11/5.19 | % 32.11/5.19 | GROUND_INST: instantiating (fc7_relat_1) with all_163_2, all_163_1, % 32.11/5.19 | simplifying with (32), (34) gives: % 32.11/5.19 | (50) ? [v0: any] : ? [v1: any] : ? [v2: any] : (empty(all_163_1) = v1 & % 32.11/5.19 | empty(all_163_2) = v0 & relation(all_163_1) = v2 & ( ~ (v0 = 0) | % 32.11/5.19 | (v2 = 0 & v1 = 0))) % 32.11/5.19 | % 32.11/5.19 | GROUND_INST: instantiating (d4_relat_1) with all_163_2, all_163_1, simplifying % 32.11/5.19 | with (32), (34) gives: % 32.11/5.19 | (51) ? [v0: int] : ( ~ (v0 = 0) & relation(all_163_2) = v0) | ( ? [v0: % 32.11/5.19 | any] : (v0 = all_163_1 | ~ $i(v0) | ? [v1: $i] : ? [v2: any] : % 32.11/5.19 | (in(v1, v0) = v2 & $i(v1) & ( ~ (v2 = 0) | ! [v3: $i] : ! [v4: % 32.11/5.19 | $i] : ( ~ (ordered_pair(v1, v3) = v4) | ~ (in(v4, % 32.11/5.19 | all_163_2) = 0) | ~ $i(v3))) & (v2 = 0 | ? [v3: $i] : % 32.11/5.19 | ? [v4: $i] : (ordered_pair(v1, v3) = v4 & in(v4, all_163_2) = % 32.11/5.19 | 0 & $i(v4) & $i(v3))))) & ( ~ $i(all_163_1) | ( ! [v0: $i] : % 32.11/5.19 | ! [v1: int] : (v1 = 0 | ~ (in(v0, all_163_1) = v1) | ~ $i(v0) % 32.11/5.19 | | ! [v2: $i] : ! [v3: $i] : ( ~ (ordered_pair(v0, v2) = v3) % 32.11/5.19 | | ~ (in(v3, all_163_2) = 0) | ~ $i(v2))) & ! [v0: $i] : ( % 32.11/5.19 | ~ (in(v0, all_163_1) = 0) | ~ $i(v0) | ? [v1: $i] : ? [v2: % 32.11/5.19 | $i] : (ordered_pair(v0, v1) = v2 & in(v2, all_163_2) = 0 & % 32.11/5.19 | $i(v2) & $i(v1)))))) % 32.11/5.19 | % 32.11/5.19 | GROUND_INST: instantiating (t25_relat_1) with empty_set, empty_set, % 32.11/5.19 | simplifying with (7), (9) gives: % 32.11/5.20 | (52) ? [v0: any] : ? [v1: $i] : (relation_dom(empty_set) = v1 & % 32.11/5.20 | relation(empty_set) = v0 & $i(v1) & ( ~ (v0 = 0) | ! [v2: $i] : ! % 32.11/5.20 | [v3: $i] : ! [v4: any] : ( ~ (relation_rng(v2) = v3) | ~ % 32.11/5.20 | (subset(empty_set, v3) = v4) | ~ $i(v2) | ? [v5: any] : ? % 32.11/5.20 | [v6: any] : ? [v7: $i] : ? [v8: any] : (relation_dom(v2) = v7 % 32.11/5.20 | & subset(v1, v7) = v8 & subset(empty_set, v2) = v6 & % 32.11/5.20 | relation(v2) = v5 & $i(v7) & ( ~ (v6 = 0) | ~ (v5 = 0) | (v8 % 32.11/5.20 | = 0 & v4 = 0)))))) % 32.11/5.20 | % 32.11/5.20 | GROUND_INST: instantiating (t47_relat_1) with empty_set, empty_set, % 32.11/5.20 | simplifying with (7), (9) gives: % 32.11/5.20 | (53) ? [v0: any] : ? [v1: $i] : (relation_dom(empty_set) = v1 & % 32.11/5.20 | relation(empty_set) = v0 & $i(v1) & ( ~ (v0 = 0) | ! [v2: $i] : ! % 32.11/5.20 | [v3: $i] : ( ~ (relation_rng(v2) = v3) | ~ (subset(v1, v3) = 0) | % 32.11/5.20 | ~ $i(v2) | ? [v4: any] : ? [v5: $i] : ? [v6: $i] : % 32.11/5.20 | (relation_composition(v2, empty_set) = v5 & relation_rng(v5) = % 32.11/5.20 | v6 & relation(v2) = v4 & $i(v6) & $i(v5) & ( ~ (v4 = 0) | v6 = % 32.11/5.20 | empty_set))))) % 32.11/5.20 | % 32.11/5.20 | GROUND_INST: instantiating (t46_relat_1) with empty_set, empty_set, % 32.11/5.20 | simplifying with (7), (9) gives: % 32.11/5.20 | (54) ? [v0: any] : ? [v1: $i] : (relation_dom(empty_set) = v1 & % 32.11/5.20 | relation(empty_set) = v0 & $i(v1) & ( ~ (v0 = 0) | ! [v2: $i] : ! % 32.11/5.20 | [v3: $i] : ( ~ (relation_dom(v2) = v3) | ~ (subset(empty_set, v3) % 32.11/5.20 | = 0) | ~ $i(v2) | ? [v4: any] : ? [v5: $i] : ? [v6: $i] : % 32.11/5.20 | (relation_composition(empty_set, v2) = v5 & relation_dom(v5) = % 32.11/5.20 | v6 & relation(v2) = v4 & $i(v6) & $i(v5) & ( ~ (v4 = 0) | v6 = % 32.11/5.20 | v1))))) % 32.11/5.20 | % 32.11/5.20 | GROUND_INST: instantiating (fc6_relat_1) with all_163_2, all_163_0, % 32.11/5.20 | simplifying with (32), (35) gives: % 32.11/5.20 | (55) ? [v0: any] : ? [v1: any] : ? [v2: any] : (empty(all_163_0) = v2 & % 32.11/5.20 | empty(all_163_2) = v0 & relation(all_163_2) = v1 & ( ~ (v2 = 0) | ~ % 32.11/5.20 | (v1 = 0) | v0 = 0)) % 32.11/5.20 | % 32.11/5.20 | GROUND_INST: instantiating (fc8_relat_1) with all_163_2, all_163_0, % 32.11/5.20 | simplifying with (32), (35) gives: % 32.11/5.20 | (56) ? [v0: any] : ? [v1: any] : ? [v2: any] : (empty(all_163_0) = v1 & % 32.11/5.20 | empty(all_163_2) = v0 & relation(all_163_0) = v2 & ( ~ (v0 = 0) | % 32.11/5.20 | (v2 = 0 & v1 = 0))) % 32.11/5.20 | % 32.11/5.20 | GROUND_INST: instantiating (t25_relat_1) with all_163_2, all_163_0, % 32.11/5.20 | simplifying with (32), (35) gives: % 32.11/5.21 | (57) ? [v0: any] : ? [v1: $i] : (relation_dom(all_163_2) = v1 & % 32.11/5.21 | relation(all_163_2) = v0 & $i(v1) & ( ~ (v0 = 0) | ! [v2: $i] : ! % 32.11/5.21 | [v3: $i] : ! [v4: any] : ( ~ (relation_rng(v2) = v3) | ~ % 32.11/5.21 | (subset(all_163_0, v3) = v4) | ~ $i(v2) | ? [v5: any] : ? % 32.11/5.21 | [v6: any] : ? [v7: $i] : ? [v8: any] : (relation_dom(v2) = v7 % 32.11/5.21 | & subset(v1, v7) = v8 & subset(all_163_2, v2) = v6 & % 32.11/5.21 | relation(v2) = v5 & $i(v7) & ( ~ (v6 = 0) | ~ (v5 = 0) | (v8 % 32.11/5.21 | = 0 & v4 = 0)))))) % 32.11/5.21 | % 32.11/5.21 | GROUND_INST: instantiating (t47_relat_1) with all_163_2, all_163_0, % 32.11/5.21 | simplifying with (32), (35) gives: % 32.11/5.21 | (58) ? [v0: any] : ? [v1: $i] : (relation_dom(all_163_2) = v1 & % 32.11/5.21 | relation(all_163_2) = v0 & $i(v1) & ( ~ (v0 = 0) | ! [v2: $i] : ! % 32.11/5.21 | [v3: $i] : ( ~ (relation_rng(v2) = v3) | ~ (subset(v1, v3) = 0) | % 32.11/5.21 | ~ $i(v2) | ? [v4: any] : ? [v5: $i] : ? [v6: $i] : % 32.11/5.21 | (relation_composition(v2, all_163_2) = v5 & relation_rng(v5) = % 32.11/5.21 | v6 & relation(v2) = v4 & $i(v6) & $i(v5) & ( ~ (v4 = 0) | v6 = % 32.11/5.21 | all_163_0))))) % 32.11/5.21 | % 32.11/5.21 | GROUND_INST: instantiating (t46_relat_1) with all_163_2, all_163_0, % 32.11/5.21 | simplifying with (32), (35) gives: % 32.11/5.21 | (59) ? [v0: any] : ? [v1: $i] : (relation_dom(all_163_2) = v1 & % 32.11/5.21 | relation(all_163_2) = v0 & $i(v1) & ( ~ (v0 = 0) | ! [v2: $i] : ! % 32.11/5.21 | [v3: $i] : ( ~ (relation_dom(v2) = v3) | ~ (subset(all_163_0, v3) % 32.11/5.21 | = 0) | ~ $i(v2) | ? [v4: any] : ? [v5: $i] : ? [v6: $i] : % 32.11/5.21 | (relation_composition(all_163_2, v2) = v5 & relation_dom(v5) = % 32.11/5.21 | v6 & relation(v2) = v4 & $i(v6) & $i(v5) & ( ~ (v4 = 0) | v6 = % 32.11/5.21 | v1))))) % 32.11/5.21 | % 32.11/5.21 | COMBINE_EQS: (40), (41) imply: % 32.11/5.21 | (60) all_141_0 = empty_set % 32.11/5.21 | % 32.11/5.21 | SIMP: (60) implies: % 32.11/5.21 | (61) all_141_0 = empty_set % 32.11/5.21 | % 32.11/5.21 | DELTA: instantiating (48) with fresh symbol all_208_0 gives: % 32.11/5.21 | (62) element(all_208_0, all_150_0) = 0 & empty(all_208_0) = 0 & % 32.11/5.21 | $i(all_208_0) % 32.11/5.21 | % 32.11/5.21 | ALPHA: (62) implies: % 32.11/5.21 | (63) $i(all_208_0) % 32.11/5.21 | (64) empty(all_208_0) = 0 % 32.11/5.21 | % 32.11/5.21 | DELTA: instantiating (47) with fresh symbol all_210_0 gives: % 32.11/5.21 | (65) element(all_153_1, empty_set) = all_210_0 & ( ~ (all_210_0 = 0) | % 32.11/5.21 | all_153_0 = 0) & ( ~ (all_153_0 = 0) | all_210_0 = 0) % 32.11/5.21 | % 32.11/5.21 | ALPHA: (65) implies: % 32.11/5.21 | (66) element(all_153_1, empty_set) = all_210_0 % 32.11/5.21 | (67) ~ (all_210_0 = 0) | all_153_0 = 0 % 32.11/5.21 | % 32.11/5.21 | DELTA: instantiating (46) with fresh symbol all_212_0 gives: % 32.11/5.21 | (68) element(all_153_1, all_141_0) = all_212_0 & ( ~ (all_212_0 = 0) | % 32.11/5.21 | all_153_0 = 0) & ( ~ (all_153_0 = 0) | all_212_0 = 0) % 32.11/5.21 | % 32.11/5.21 | ALPHA: (68) implies: % 32.11/5.21 | (69) element(all_153_1, all_141_0) = all_212_0 % 32.11/5.21 | % 32.11/5.21 | DELTA: instantiating (45) with fresh symbol all_214_0 gives: % 32.11/5.21 | (70) element(all_153_1, all_143_0) = all_214_0 & ( ~ (all_214_0 = 0) | % 32.11/5.21 | all_153_0 = 0) & ( ~ (all_153_0 = 0) | all_214_0 = 0) % 32.11/5.21 | % 32.11/5.21 | ALPHA: (70) implies: % 32.11/5.21 | (71) element(all_153_1, all_143_0) = all_214_0 % 32.11/5.21 | % 32.11/5.21 | DELTA: instantiating (44) with fresh symbol all_216_0 gives: % 32.11/5.22 | (72) element(all_145_1, empty_set) = all_216_0 & ( ~ (all_216_0 = 0) | % 32.11/5.22 | all_145_0 = 0) & ( ~ (all_145_0 = 0) | all_216_0 = 0) % 32.11/5.22 | % 32.11/5.22 | ALPHA: (72) implies: % 32.11/5.22 | (73) element(all_145_1, empty_set) = all_216_0 % 32.11/5.22 | % 32.11/5.22 | DELTA: instantiating (43) with fresh symbol all_218_0 gives: % 32.11/5.22 | (74) element(all_145_1, all_141_0) = all_218_0 & ( ~ (all_218_0 = 0) | % 32.11/5.22 | all_145_0 = 0) & ( ~ (all_145_0 = 0) | all_218_0 = 0) % 32.11/5.22 | % 32.11/5.22 | ALPHA: (74) implies: % 32.11/5.22 | (75) element(all_145_1, all_141_0) = all_218_0 % 32.11/5.22 | % 32.11/5.22 | DELTA: instantiating (42) with fresh symbol all_220_0 gives: % 32.11/5.22 | (76) element(all_145_1, all_143_0) = all_220_0 & ( ~ (all_220_0 = 0) | % 32.11/5.22 | all_145_0 = 0) & ( ~ (all_145_0 = 0) | all_220_0 = 0) % 32.11/5.22 | % 32.11/5.22 | ALPHA: (76) implies: % 32.11/5.22 | (77) element(all_145_1, all_143_0) = all_220_0 % 32.11/5.22 | % 32.11/5.22 | DELTA: instantiating (56) with fresh symbols all_222_0, all_222_1, all_222_2 % 32.11/5.22 | gives: % 32.11/5.22 | (78) empty(all_163_0) = all_222_1 & empty(all_163_2) = all_222_2 & % 32.11/5.22 | relation(all_163_0) = all_222_0 & ( ~ (all_222_2 = 0) | (all_222_0 = 0 % 32.11/5.22 | & all_222_1 = 0)) % 32.11/5.22 | % 32.11/5.22 | ALPHA: (78) implies: % 32.44/5.22 | (79) empty(all_163_2) = all_222_2 % 32.44/5.22 | (80) empty(all_163_0) = all_222_1 % 32.44/5.22 | % 32.44/5.22 | DELTA: instantiating (55) with fresh symbols all_224_0, all_224_1, all_224_2 % 32.44/5.22 | gives: % 32.44/5.22 | (81) empty(all_163_0) = all_224_0 & empty(all_163_2) = all_224_2 & % 32.44/5.22 | relation(all_163_2) = all_224_1 & ( ~ (all_224_0 = 0) | ~ (all_224_1 % 32.44/5.22 | = 0) | all_224_2 = 0) % 32.44/5.22 | % 32.44/5.22 | ALPHA: (81) implies: % 32.44/5.22 | (82) relation(all_163_2) = all_224_1 % 32.44/5.22 | (83) empty(all_163_2) = all_224_2 % 32.44/5.22 | (84) empty(all_163_0) = all_224_0 % 32.44/5.22 | (85) ~ (all_224_0 = 0) | ~ (all_224_1 = 0) | all_224_2 = 0 % 32.44/5.22 | % 32.44/5.22 | DELTA: instantiating (50) with fresh symbols all_226_0, all_226_1, all_226_2 % 32.44/5.22 | gives: % 32.44/5.22 | (86) empty(all_163_1) = all_226_1 & empty(all_163_2) = all_226_2 & % 32.44/5.22 | relation(all_163_1) = all_226_0 & ( ~ (all_226_2 = 0) | (all_226_0 = 0 % 32.44/5.22 | & all_226_1 = 0)) % 32.44/5.22 | % 32.44/5.22 | ALPHA: (86) implies: % 32.44/5.22 | (87) empty(all_163_2) = all_226_2 % 32.44/5.22 | (88) empty(all_163_1) = all_226_1 % 32.44/5.22 | % 32.44/5.22 | DELTA: instantiating (49) with fresh symbols all_228_0, all_228_1, all_228_2 % 32.44/5.22 | gives: % 32.44/5.22 | (89) empty(all_163_1) = all_228_0 & empty(all_163_2) = all_228_2 & % 32.44/5.22 | relation(all_163_2) = all_228_1 & ( ~ (all_228_0 = 0) | ~ (all_228_1 % 32.44/5.22 | = 0) | all_228_2 = 0) % 32.44/5.22 | % 32.44/5.22 | ALPHA: (89) implies: % 32.44/5.22 | (90) relation(all_163_2) = all_228_1 % 32.44/5.22 | (91) empty(all_163_2) = all_228_2 % 32.44/5.22 | (92) empty(all_163_1) = all_228_0 % 32.44/5.22 | (93) ~ (all_228_0 = 0) | ~ (all_228_1 = 0) | all_228_2 = 0 % 32.44/5.22 | % 32.44/5.22 | DELTA: instantiating (59) with fresh symbols all_230_0, all_230_1 gives: % 32.44/5.22 | (94) relation_dom(all_163_2) = all_230_0 & relation(all_163_2) = all_230_1 % 32.44/5.22 | & $i(all_230_0) & ( ~ (all_230_1 = 0) | ! [v0: $i] : ! [v1: $i] : ( % 32.44/5.22 | ~ (relation_dom(v0) = v1) | ~ (subset(all_163_0, v1) = 0) | ~ % 32.44/5.22 | $i(v0) | ? [v2: any] : ? [v3: $i] : ? [v4: $i] : % 32.44/5.22 | (relation_composition(all_163_2, v0) = v3 & relation_dom(v3) = v4 % 32.44/5.22 | & relation(v0) = v2 & $i(v4) & $i(v3) & ( ~ (v2 = 0) | v4 = % 32.44/5.22 | all_230_0)))) % 32.44/5.22 | % 32.44/5.22 | ALPHA: (94) implies: % 32.44/5.22 | (95) $i(all_230_0) % 32.44/5.22 | (96) relation(all_163_2) = all_230_1 % 32.44/5.22 | (97) relation_dom(all_163_2) = all_230_0 % 32.44/5.22 | % 32.44/5.22 | DELTA: instantiating (58) with fresh symbols all_232_0, all_232_1 gives: % 32.44/5.22 | (98) relation_dom(all_163_2) = all_232_0 & relation(all_163_2) = all_232_1 % 32.44/5.22 | & $i(all_232_0) & ( ~ (all_232_1 = 0) | ! [v0: $i] : ! [v1: $i] : ( % 32.44/5.22 | ~ (relation_rng(v0) = v1) | ~ (subset(all_232_0, v1) = 0) | ~ % 32.44/5.22 | $i(v0) | ? [v2: any] : ? [v3: $i] : ? [v4: $i] : % 32.44/5.22 | (relation_composition(v0, all_163_2) = v3 & relation_rng(v3) = v4 % 32.44/5.22 | & relation(v0) = v2 & $i(v4) & $i(v3) & ( ~ (v2 = 0) | v4 = % 32.44/5.22 | all_163_0)))) % 32.44/5.22 | % 32.44/5.22 | ALPHA: (98) implies: % 32.44/5.22 | (99) relation(all_163_2) = all_232_1 % 32.44/5.22 | (100) relation_dom(all_163_2) = all_232_0 % 32.44/5.22 | % 32.44/5.22 | DELTA: instantiating (54) with fresh symbols all_234_0, all_234_1 gives: % 32.44/5.22 | (101) relation_dom(empty_set) = all_234_0 & relation(empty_set) = all_234_1 % 32.44/5.22 | & $i(all_234_0) & ( ~ (all_234_1 = 0) | ! [v0: $i] : ! [v1: $i] : ( % 32.44/5.22 | ~ (relation_dom(v0) = v1) | ~ (subset(empty_set, v1) = 0) | ~ % 32.44/5.22 | $i(v0) | ? [v2: any] : ? [v3: $i] : ? [v4: $i] : % 32.44/5.22 | (relation_composition(empty_set, v0) = v3 & relation_dom(v3) = v4 % 32.44/5.22 | & relation(v0) = v2 & $i(v4) & $i(v3) & ( ~ (v2 = 0) | v4 = % 32.44/5.22 | all_234_0)))) % 32.44/5.22 | % 32.44/5.22 | ALPHA: (101) implies: % 32.44/5.22 | (102) $i(all_234_0) % 32.44/5.22 | (103) relation(empty_set) = all_234_1 % 32.44/5.22 | (104) relation_dom(empty_set) = all_234_0 % 32.44/5.22 | % 32.44/5.22 | DELTA: instantiating (53) with fresh symbols all_236_0, all_236_1 gives: % 32.44/5.22 | (105) relation_dom(empty_set) = all_236_0 & relation(empty_set) = all_236_1 % 32.44/5.22 | & $i(all_236_0) & ( ~ (all_236_1 = 0) | ! [v0: $i] : ! [v1: $i] : ( % 32.44/5.22 | ~ (relation_rng(v0) = v1) | ~ (subset(all_236_0, v1) = 0) | ~ % 32.44/5.22 | $i(v0) | ? [v2: any] : ? [v3: $i] : ? [v4: $i] : % 32.44/5.22 | (relation_composition(v0, empty_set) = v3 & relation_rng(v3) = v4 % 32.44/5.22 | & relation(v0) = v2 & $i(v4) & $i(v3) & ( ~ (v2 = 0) | v4 = % 32.44/5.22 | empty_set)))) % 32.44/5.22 | % 32.44/5.22 | ALPHA: (105) implies: % 32.44/5.22 | (106) relation(empty_set) = all_236_1 % 32.44/5.22 | (107) relation_dom(empty_set) = all_236_0 % 32.44/5.22 | (108) ~ (all_236_1 = 0) | ! [v0: $i] : ! [v1: $i] : ( ~ % 32.44/5.22 | (relation_rng(v0) = v1) | ~ (subset(all_236_0, v1) = 0) | ~ % 32.44/5.22 | $i(v0) | ? [v2: any] : ? [v3: $i] : ? [v4: $i] : % 32.44/5.22 | (relation_composition(v0, empty_set) = v3 & relation_rng(v3) = v4 & % 32.44/5.22 | relation(v0) = v2 & $i(v4) & $i(v3) & ( ~ (v2 = 0) | v4 = % 32.44/5.22 | empty_set))) % 32.44/5.22 | % 32.44/5.22 | DELTA: instantiating (52) with fresh symbols all_238_0, all_238_1 gives: % 32.44/5.22 | (109) relation_dom(empty_set) = all_238_0 & relation(empty_set) = all_238_1 % 32.44/5.22 | & $i(all_238_0) & ( ~ (all_238_1 = 0) | ! [v0: $i] : ! [v1: $i] : % 32.44/5.22 | ! [v2: any] : ( ~ (relation_rng(v0) = v1) | ~ (subset(empty_set, % 32.44/5.22 | v1) = v2) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ? [v5: % 32.44/5.22 | $i] : ? [v6: any] : (relation_dom(v0) = v5 & subset(all_238_0, % 32.44/5.22 | v5) = v6 & subset(empty_set, v0) = v4 & relation(v0) = v3 & % 32.44/5.22 | $i(v5) & ( ~ (v4 = 0) | ~ (v3 = 0) | (v6 = 0 & v2 = 0))))) % 32.44/5.22 | % 32.44/5.22 | ALPHA: (109) implies: % 32.44/5.23 | (110) relation(empty_set) = all_238_1 % 32.44/5.23 | (111) relation_dom(empty_set) = all_238_0 % 32.44/5.23 | % 32.44/5.23 | DELTA: instantiating (57) with fresh symbols all_240_0, all_240_1 gives: % 32.44/5.23 | (112) relation_dom(all_163_2) = all_240_0 & relation(all_163_2) = all_240_1 % 32.44/5.23 | & $i(all_240_0) & ( ~ (all_240_1 = 0) | ! [v0: $i] : ! [v1: $i] : % 32.44/5.23 | ! [v2: any] : ( ~ (relation_rng(v0) = v1) | ~ (subset(all_163_0, % 32.44/5.23 | v1) = v2) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ? [v5: % 32.44/5.23 | $i] : ? [v6: any] : (relation_dom(v0) = v5 & subset(all_240_0, % 32.44/5.23 | v5) = v6 & subset(all_163_2, v0) = v4 & relation(v0) = v3 & % 32.44/5.23 | $i(v5) & ( ~ (v4 = 0) | ~ (v3 = 0) | (v6 = 0 & v2 = 0))))) % 32.44/5.23 | % 32.44/5.23 | ALPHA: (112) implies: % 32.44/5.23 | (113) relation(all_163_2) = all_240_1 % 32.44/5.23 | (114) relation_dom(all_163_2) = all_240_0 % 32.44/5.23 | % 32.44/5.23 | REDUCE: (41), (71) imply: % 32.44/5.23 | (115) element(all_153_1, empty_set) = all_214_0 % 32.44/5.23 | % 32.44/5.23 | REDUCE: (61), (69) imply: % 32.44/5.23 | (116) element(all_153_1, empty_set) = all_212_0 % 32.44/5.23 | % 32.44/5.23 | REDUCE: (41), (77) imply: % 32.44/5.23 | (117) element(all_145_1, empty_set) = all_220_0 % 32.44/5.23 | % 32.44/5.23 | REDUCE: (61), (75) imply: % 32.44/5.23 | (118) element(all_145_1, empty_set) = all_218_0 % 32.44/5.23 | % 32.44/5.23 | REDUCE: (38), (61) imply: % 32.44/5.23 | (119) element(empty_set, empty_set) = 0 % 32.44/5.23 | % 32.44/5.23 | REDUCE: (39), (61) imply: % 32.44/5.23 | (120) relation(empty_set) = 0 % 32.44/5.23 | % 32.44/5.23 | BETA: splitting (37) gives: % 32.44/5.23 | % 32.44/5.23 | Case 1: % 32.44/5.23 | | % 32.44/5.23 | | (121) all_163_2 = empty_set % 32.44/5.23 | | % 32.44/5.23 | | REDUCE: (31), (121) imply: % 32.44/5.23 | | (122) $false % 32.44/5.23 | | % 32.44/5.23 | | CLOSE: (122) is inconsistent. % 32.44/5.23 | | % 32.44/5.23 | Case 2: % 32.44/5.23 | | % 32.44/5.23 | | (123) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (ordered_pair(v0, v1) = % 32.44/5.23 | | v2 & in(v2, all_163_2) = 0 & $i(v2) & $i(v1) & $i(v0)) % 32.44/5.23 | | % 32.44/5.23 | | DELTA: instantiating (123) with fresh symbols all_264_0, all_264_1, % 32.44/5.23 | | all_264_2 gives: % 32.44/5.23 | | (124) ordered_pair(all_264_2, all_264_1) = all_264_0 & in(all_264_0, % 32.44/5.23 | | all_163_2) = 0 & $i(all_264_0) & $i(all_264_1) & $i(all_264_2) % 32.44/5.23 | | % 32.44/5.23 | | ALPHA: (124) implies: % 32.44/5.23 | | (125) $i(all_264_0) % 32.44/5.23 | | (126) in(all_264_0, all_163_2) = 0 % 32.44/5.23 | | % 32.44/5.23 | | BETA: splitting (67) gives: % 32.44/5.23 | | % 32.44/5.23 | | Case 1: % 32.44/5.23 | | | % 32.44/5.23 | | | % 32.44/5.23 | | | GROUND_INST: instantiating (11) with 0, all_236_1, empty_set, simplifying % 32.44/5.23 | | | with (106), (120) gives: % 32.44/5.23 | | | (127) all_236_1 = 0 % 32.44/5.23 | | | % 32.44/5.23 | | | GROUND_INST: instantiating (11) with all_236_1, all_238_1, empty_set, % 32.44/5.23 | | | simplifying with (106), (110) gives: % 32.44/5.23 | | | (128) all_238_1 = all_236_1 % 32.44/5.23 | | | % 32.44/5.23 | | | GROUND_INST: instantiating (11) with all_234_1, all_238_1, empty_set, % 32.44/5.23 | | | simplifying with (103), (110) gives: % 32.44/5.23 | | | (129) all_238_1 = all_234_1 % 32.44/5.23 | | | % 32.44/5.23 | | | GROUND_INST: instantiating (11) with all_224_1, all_228_1, all_163_2, % 32.44/5.23 | | | simplifying with (82), (90) gives: % 32.44/5.23 | | | (130) all_228_1 = all_224_1 % 32.44/5.23 | | | % 32.44/5.23 | | | GROUND_INST: instantiating (11) with all_230_1, all_232_1, all_163_2, % 32.44/5.23 | | | simplifying with (96), (99) gives: % 32.44/5.23 | | | (131) all_232_1 = all_230_1 % 32.44/5.23 | | | % 32.44/5.23 | | | GROUND_INST: instantiating (11) with all_228_1, all_232_1, all_163_2, % 32.44/5.23 | | | simplifying with (90), (99) gives: % 32.44/5.23 | | | (132) all_232_1 = all_228_1 % 32.44/5.23 | | | % 32.44/5.23 | | | GROUND_INST: instantiating (11) with 0, all_240_1, all_163_2, simplifying % 32.44/5.23 | | | with (33), (113) gives: % 32.44/5.23 | | | (133) all_240_1 = 0 % 32.44/5.23 | | | % 32.44/5.23 | | | GROUND_INST: instantiating (11) with all_232_1, all_240_1, all_163_2, % 32.44/5.23 | | | simplifying with (99), (113) gives: % 32.44/5.23 | | | (134) all_240_1 = all_232_1 % 32.44/5.23 | | | % 32.44/5.23 | | | GROUND_INST: instantiating (12) with all_226_2, all_228_2, all_163_2, % 32.44/5.23 | | | simplifying with (87), (91) gives: % 32.44/5.23 | | | (135) all_228_2 = all_226_2 % 32.44/5.23 | | | % 32.44/5.23 | | | GROUND_INST: instantiating (12) with all_224_2, all_228_2, all_163_2, % 32.44/5.23 | | | simplifying with (83), (91) gives: % 32.44/5.23 | | | (136) all_228_2 = all_224_2 % 32.44/5.23 | | | % 32.44/5.23 | | | GROUND_INST: instantiating (12) with all_222_2, all_228_2, all_163_2, % 32.44/5.23 | | | simplifying with (79), (91) gives: % 32.44/5.23 | | | (137) all_228_2 = all_222_2 % 32.44/5.23 | | | % 32.44/5.23 | | | GROUND_INST: instantiating (12) with all_226_1, all_228_0, all_163_1, % 32.44/5.23 | | | simplifying with (88), (92) gives: % 32.44/5.23 | | | (138) all_228_0 = all_226_1 % 32.44/5.23 | | | % 32.44/5.23 | | | GROUND_INST: instantiating (12) with all_222_1, all_224_0, all_163_0, % 32.44/5.23 | | | simplifying with (80), (84) gives: % 32.44/5.23 | | | (139) all_224_0 = all_222_1 % 32.44/5.23 | | | % 32.44/5.23 | | | GROUND_INST: instantiating (14) with all_218_0, all_220_0, empty_set, % 32.44/5.23 | | | all_145_1, simplifying with (117), (118) gives: % 32.44/5.23 | | | (140) all_220_0 = all_218_0 % 32.44/5.23 | | | % 32.44/5.23 | | | GROUND_INST: instantiating (14) with all_216_0, all_220_0, empty_set, % 32.44/5.23 | | | all_145_1, simplifying with (73), (117) gives: % 32.44/5.23 | | | (141) all_220_0 = all_216_0 % 32.44/5.23 | | | % 32.44/5.23 | | | GROUND_INST: instantiating (14) with all_212_0, all_214_0, empty_set, % 32.44/5.23 | | | all_153_1, simplifying with (115), (116) gives: % 32.44/5.23 | | | (142) all_214_0 = all_212_0 % 32.44/5.23 | | | % 32.44/5.23 | | | GROUND_INST: instantiating (14) with all_210_0, all_214_0, empty_set, % 32.44/5.23 | | | all_153_1, simplifying with (66), (115) gives: % 32.44/5.23 | | | (143) all_214_0 = all_210_0 % 32.44/5.23 | | | % 32.44/5.23 | | | GROUND_INST: instantiating (13) with all_234_0, all_236_0, empty_set, % 32.44/5.23 | | | simplifying with (104), (107) gives: % 32.44/5.23 | | | (144) all_236_0 = all_234_0 % 32.44/5.23 | | | % 32.44/5.23 | | | GROUND_INST: instantiating (13) with empty_set, all_238_0, empty_set, % 32.44/5.23 | | | simplifying with (6), (111) gives: % 32.44/5.23 | | | (145) all_238_0 = empty_set % 32.44/5.23 | | | % 32.44/5.23 | | | GROUND_INST: instantiating (13) with all_236_0, all_238_0, empty_set, % 32.44/5.23 | | | simplifying with (107), (111) gives: % 32.44/5.23 | | | (146) all_238_0 = all_236_0 % 32.44/5.23 | | | % 32.44/5.23 | | | GROUND_INST: instantiating (13) with all_163_1, all_232_0, all_163_2, % 32.44/5.23 | | | simplifying with (34), (100) gives: % 32.44/5.24 | | | (147) all_232_0 = all_163_1 % 32.44/5.24 | | | % 32.44/5.24 | | | GROUND_INST: instantiating (13) with all_232_0, all_240_0, all_163_2, % 32.44/5.24 | | | simplifying with (100), (114) gives: % 32.44/5.24 | | | (148) all_240_0 = all_232_0 % 32.44/5.24 | | | % 32.44/5.24 | | | GROUND_INST: instantiating (13) with all_230_0, all_240_0, all_163_2, % 32.44/5.24 | | | simplifying with (97), (114) gives: % 32.44/5.24 | | | (149) all_240_0 = all_230_0 % 32.44/5.24 | | | % 32.44/5.24 | | | COMBINE_EQS: (148), (149) imply: % 32.44/5.24 | | | (150) all_232_0 = all_230_0 % 32.44/5.24 | | | % 32.44/5.24 | | | SIMP: (150) implies: % 32.44/5.24 | | | (151) all_232_0 = all_230_0 % 32.44/5.24 | | | % 32.44/5.24 | | | COMBINE_EQS: (133), (134) imply: % 32.44/5.24 | | | (152) all_232_1 = 0 % 32.44/5.24 | | | % 32.44/5.24 | | | SIMP: (152) implies: % 32.44/5.24 | | | (153) all_232_1 = 0 % 32.44/5.24 | | | % 32.44/5.24 | | | COMBINE_EQS: (145), (146) imply: % 32.44/5.24 | | | (154) all_236_0 = empty_set % 32.44/5.24 | | | % 32.44/5.24 | | | SIMP: (154) implies: % 32.44/5.24 | | | (155) all_236_0 = empty_set % 32.44/5.24 | | | % 32.44/5.24 | | | COMBINE_EQS: (128), (129) imply: % 32.44/5.24 | | | (156) all_236_1 = all_234_1 % 32.44/5.24 | | | % 32.44/5.24 | | | SIMP: (156) implies: % 32.44/5.24 | | | (157) all_236_1 = all_234_1 % 32.44/5.24 | | | % 32.44/5.24 | | | COMBINE_EQS: (144), (155) imply: % 32.44/5.24 | | | (158) all_234_0 = empty_set % 32.44/5.24 | | | % 32.44/5.24 | | | SIMP: (158) implies: % 32.44/5.24 | | | (159) all_234_0 = empty_set % 32.44/5.24 | | | % 32.44/5.24 | | | COMBINE_EQS: (127), (157) imply: % 32.44/5.24 | | | (160) all_234_1 = 0 % 32.44/5.24 | | | % 32.44/5.24 | | | COMBINE_EQS: (147), (151) imply: % 32.44/5.24 | | | (161) all_230_0 = all_163_1 % 32.44/5.24 | | | % 32.44/5.24 | | | COMBINE_EQS: (131), (153) imply: % 32.44/5.24 | | | (162) all_230_1 = 0 % 32.44/5.24 | | | % 32.44/5.24 | | | COMBINE_EQS: (131), (132) imply: % 32.44/5.24 | | | (163) all_230_1 = all_228_1 % 32.44/5.24 | | | % 32.44/5.24 | | | COMBINE_EQS: (162), (163) imply: % 32.44/5.24 | | | (164) all_228_1 = 0 % 32.44/5.24 | | | % 32.44/5.24 | | | SIMP: (164) implies: % 32.44/5.24 | | | (165) all_228_1 = 0 % 32.44/5.24 | | | % 32.44/5.24 | | | COMBINE_EQS: (130), (165) imply: % 32.44/5.24 | | | (166) all_224_1 = 0 % 32.44/5.24 | | | % 32.44/5.24 | | | COMBINE_EQS: (135), (136) imply: % 32.44/5.24 | | | (167) all_226_2 = all_224_2 % 32.44/5.24 | | | % 32.44/5.24 | | | COMBINE_EQS: (135), (137) imply: % 32.44/5.24 | | | (168) all_226_2 = all_222_2 % 32.44/5.24 | | | % 32.44/5.24 | | | COMBINE_EQS: (167), (168) imply: % 32.44/5.24 | | | (169) all_224_2 = all_222_2 % 32.44/5.24 | | | % 32.44/5.24 | | | COMBINE_EQS: (140), (141) imply: % 32.44/5.24 | | | (170) all_218_0 = all_216_0 % 32.44/5.24 | | | % 32.44/5.24 | | | SIMP: (170) implies: % 32.44/5.24 | | | (171) all_218_0 = all_216_0 % 32.44/5.24 | | | % 32.44/5.24 | | | COMBINE_EQS: (142), (143) imply: % 32.44/5.24 | | | (172) all_212_0 = all_210_0 % 32.44/5.24 | | | % 32.44/5.24 | | | SIMP: (172) implies: % 32.44/5.24 | | | (173) all_212_0 = all_210_0 % 32.44/5.24 | | | % 32.44/5.24 | | | REDUCE: (95), (161) imply: % 32.44/5.24 | | | (174) $i(all_163_1) % 32.44/5.24 | | | % 32.44/5.24 | | | BETA: splitting (51) gives: % 32.44/5.24 | | | % 32.44/5.24 | | | Case 1: % 32.44/5.24 | | | | % 32.44/5.24 | | | | (175) ? [v0: int] : ( ~ (v0 = 0) & relation(all_163_2) = v0) % 32.44/5.24 | | | | % 32.44/5.24 | | | | BETA: splitting (108) gives: % 32.44/5.24 | | | | % 32.44/5.24 | | | | Case 1: % 32.44/5.24 | | | | | % 32.44/5.24 | | | | | (176) ~ (all_236_1 = 0) % 32.44/5.24 | | | | | % 32.44/5.24 | | | | | REDUCE: (127), (176) imply: % 32.44/5.24 | | | | | (177) $false % 32.44/5.24 | | | | | % 32.44/5.24 | | | | | CLOSE: (177) is inconsistent. % 32.44/5.24 | | | | | % 32.44/5.24 | | | | Case 2: % 32.44/5.24 | | | | | % 32.44/5.24 | | | | | % 32.44/5.24 | | | | | DELTA: instantiating (175) with fresh symbol all_322_0 gives: % 32.44/5.24 | | | | | (178) ~ (all_322_0 = 0) & relation(all_163_2) = all_322_0 % 32.44/5.24 | | | | | % 32.44/5.24 | | | | | ALPHA: (178) implies: % 32.44/5.24 | | | | | (179) ~ (all_322_0 = 0) % 32.44/5.24 | | | | | (180) relation(all_163_2) = all_322_0 % 32.44/5.24 | | | | | % 32.44/5.24 | | | | | GROUND_INST: instantiating (11) with 0, all_322_0, all_163_2, % 32.44/5.24 | | | | | simplifying with (33), (180) gives: % 32.44/5.24 | | | | | (181) all_322_0 = 0 % 32.44/5.24 | | | | | % 32.44/5.24 | | | | | REDUCE: (179), (181) imply: % 32.44/5.24 | | | | | (182) $false % 32.44/5.24 | | | | | % 32.44/5.24 | | | | | CLOSE: (182) is inconsistent. % 32.44/5.24 | | | | | % 32.44/5.24 | | | | End of split % 32.44/5.24 | | | | % 32.44/5.24 | | | Case 2: % 32.44/5.24 | | | | % 32.44/5.24 | | | | (183) ? [v0: any] : (v0 = all_163_1 | ~ $i(v0) | ? [v1: $i] : ? % 32.44/5.24 | | | | [v2: any] : (in(v1, v0) = v2 & $i(v1) & ( ~ (v2 = 0) | ! % 32.44/5.24 | | | | [v3: $i] : ! [v4: $i] : ( ~ (ordered_pair(v1, v3) = v4) % 32.44/5.24 | | | | | ~ (in(v4, all_163_2) = 0) | ~ $i(v3))) & (v2 = 0 | % 32.44/5.24 | | | | ? [v3: $i] : ? [v4: $i] : (ordered_pair(v1, v3) = v4 & % 32.44/5.24 | | | | in(v4, all_163_2) = 0 & $i(v4) & $i(v3))))) & ( ~ % 32.44/5.24 | | | | $i(all_163_1) | ( ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ % 32.44/5.24 | | | | (in(v0, all_163_1) = v1) | ~ $i(v0) | ! [v2: $i] : ! % 32.44/5.24 | | | | [v3: $i] : ( ~ (ordered_pair(v0, v2) = v3) | ~ (in(v3, % 32.44/5.24 | | | | all_163_2) = 0) | ~ $i(v2))) & ! [v0: $i] : ( ~ % 32.44/5.24 | | | | (in(v0, all_163_1) = 0) | ~ $i(v0) | ? [v1: $i] : ? % 32.44/5.24 | | | | [v2: $i] : (ordered_pair(v0, v1) = v2 & in(v2, all_163_2) % 32.44/5.24 | | | | = 0 & $i(v2) & $i(v1))))) % 32.44/5.24 | | | | % 32.44/5.24 | | | | ALPHA: (183) implies: % 32.44/5.24 | | | | (184) ~ $i(all_163_1) | ( ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ % 32.44/5.24 | | | | (in(v0, all_163_1) = v1) | ~ $i(v0) | ! [v2: $i] : ! % 32.44/5.24 | | | | [v3: $i] : ( ~ (ordered_pair(v0, v2) = v3) | ~ (in(v3, % 32.44/5.24 | | | | all_163_2) = 0) | ~ $i(v2))) & ! [v0: $i] : ( ~ % 32.44/5.24 | | | | (in(v0, all_163_1) = 0) | ~ $i(v0) | ? [v1: $i] : ? [v2: % 32.44/5.24 | | | | $i] : (ordered_pair(v0, v1) = v2 & in(v2, all_163_2) = 0 % 32.44/5.24 | | | | & $i(v2) & $i(v1)))) % 32.44/5.24 | | | | % 32.44/5.24 | | | | BETA: splitting (184) gives: % 32.44/5.24 | | | | % 32.44/5.24 | | | | Case 1: % 32.44/5.24 | | | | | % 32.44/5.24 | | | | | (185) ~ $i(all_163_1) % 32.44/5.24 | | | | | % 32.44/5.24 | | | | | PRED_UNIFY: (174), (185) imply: % 32.44/5.24 | | | | | (186) $false % 32.44/5.24 | | | | | % 32.44/5.24 | | | | | CLOSE: (186) is inconsistent. % 32.44/5.24 | | | | | % 32.44/5.24 | | | | Case 2: % 32.44/5.24 | | | | | % 32.44/5.24 | | | | | % 32.44/5.24 | | | | | GROUND_INST: instantiating (t7_boole) with all_264_0, all_163_2, % 32.44/5.24 | | | | | simplifying with (32), (125), (126) gives: % 32.44/5.24 | | | | | (187) ? [v0: int] : ( ~ (v0 = 0) & empty(all_163_2) = v0) % 32.44/5.24 | | | | | % 32.44/5.24 | | | | | GROUND_INST: instantiating (8) with all_208_0, simplifying with (63), % 32.44/5.24 | | | | | (64) gives: % 32.44/5.24 | | | | | (188) all_208_0 = empty_set % 32.44/5.24 | | | | | % 32.44/5.24 | | | | | GROUND_INST: instantiating (t2_subset) with empty_set, empty_set, % 32.44/5.24 | | | | | simplifying with (9), (119) gives: % 32.44/5.24 | | | | | (189) ? [v0: any] : ? [v1: any] : (empty(empty_set) = v0 & % 32.44/5.24 | | | | | in(empty_set, empty_set) = v1 & (v1 = 0 | v0 = 0)) % 32.44/5.24 | | | | | % 32.44/5.24 | | | | | GROUND_INST: instantiating (2) with empty_set, all_145_1, all_216_0, % 32.44/5.24 | | | | | simplifying with (9), (22), (73) gives: % 32.44/5.24 | | | | | (190) ? [v0: any] : ? [v1: any] : (empty(empty_set) = v0 & % 32.44/5.24 | | | | | in(all_145_1, empty_set) = v1 & (v0 = 0 | (( ~ (v1 = 0) | % 32.44/5.24 | | | | | all_216_0 = 0) & ( ~ (all_216_0 = 0) | v1 = 0)))) % 32.44/5.24 | | | | | % 32.44/5.24 | | | | | GROUND_INST: instantiating (2) with empty_set, all_153_1, all_210_0, % 32.44/5.24 | | | | | simplifying with (9), (28), (66) gives: % 32.44/5.24 | | | | | (191) ? [v0: any] : ? [v1: any] : (empty(empty_set) = v0 & % 32.44/5.24 | | | | | in(all_153_1, empty_set) = v1 & (v0 = 0 | (( ~ (v1 = 0) | % 32.44/5.24 | | | | | all_210_0 = 0) & ( ~ (all_210_0 = 0) | v1 = 0)))) % 32.44/5.24 | | | | | % 32.44/5.24 | | | | | DELTA: instantiating (187) with fresh symbol all_360_0 gives: % 32.44/5.24 | | | | | (192) ~ (all_360_0 = 0) & empty(all_163_2) = all_360_0 % 32.44/5.24 | | | | | % 32.44/5.24 | | | | | ALPHA: (192) implies: % 32.44/5.24 | | | | | (193) ~ (all_360_0 = 0) % 32.44/5.24 | | | | | (194) empty(all_163_2) = all_360_0 % 32.44/5.24 | | | | | % 32.44/5.24 | | | | | DELTA: instantiating (189) with fresh symbols all_386_0, all_386_1 % 32.44/5.24 | | | | | gives: % 32.44/5.25 | | | | | (195) empty(empty_set) = all_386_1 & in(empty_set, empty_set) = % 32.44/5.25 | | | | | all_386_0 & (all_386_0 = 0 | all_386_1 = 0) % 32.44/5.25 | | | | | % 32.44/5.25 | | | | | ALPHA: (195) implies: % 32.44/5.25 | | | | | (196) empty(empty_set) = all_386_1 % 32.44/5.25 | | | | | % 32.44/5.25 | | | | | DELTA: instantiating (191) with fresh symbols all_416_0, all_416_1 % 32.44/5.25 | | | | | gives: % 32.44/5.25 | | | | | (197) empty(empty_set) = all_416_1 & in(all_153_1, empty_set) = % 32.44/5.25 | | | | | all_416_0 & (all_416_1 = 0 | (( ~ (all_416_0 = 0) | all_210_0 % 32.44/5.25 | | | | | = 0) & ( ~ (all_210_0 = 0) | all_416_0 = 0))) % 32.44/5.25 | | | | | % 32.44/5.25 | | | | | ALPHA: (197) implies: % 32.44/5.25 | | | | | (198) empty(empty_set) = all_416_1 % 32.44/5.25 | | | | | % 32.44/5.25 | | | | | DELTA: instantiating (190) with fresh symbols all_418_0, all_418_1 % 32.44/5.25 | | | | | gives: % 32.44/5.25 | | | | | (199) empty(empty_set) = all_418_1 & in(all_145_1, empty_set) = % 32.44/5.25 | | | | | all_418_0 & (all_418_1 = 0 | (( ~ (all_418_0 = 0) | all_216_0 % 32.44/5.25 | | | | | = 0) & ( ~ (all_216_0 = 0) | all_418_0 = 0))) % 32.44/5.25 | | | | | % 32.44/5.25 | | | | | ALPHA: (199) implies: % 32.44/5.25 | | | | | (200) empty(empty_set) = all_418_1 % 32.44/5.25 | | | | | % 32.44/5.25 | | | | | GROUND_INST: instantiating (12) with 0, all_416_1, empty_set, % 32.44/5.25 | | | | | simplifying with (3), (198) gives: % 32.44/5.25 | | | | | (201) all_416_1 = 0 % 32.44/5.25 | | | | | % 32.44/5.25 | | | | | GROUND_INST: instantiating (12) with all_416_1, all_418_1, empty_set, % 32.44/5.25 | | | | | simplifying with (198), (200) gives: % 32.44/5.25 | | | | | (202) all_418_1 = all_416_1 % 32.44/5.25 | | | | | % 32.44/5.25 | | | | | GROUND_INST: instantiating (12) with all_386_1, all_418_1, empty_set, % 32.44/5.25 | | | | | simplifying with (196), (200) gives: % 32.44/5.25 | | | | | (203) all_418_1 = all_386_1 % 32.44/5.25 | | | | | % 32.44/5.25 | | | | | GROUND_INST: instantiating (12) with all_222_2, all_360_0, all_163_2, % 32.44/5.25 | | | | | simplifying with (79), (194) gives: % 32.44/5.25 | | | | | (204) all_360_0 = all_222_2 % 32.44/5.25 | | | | | % 32.44/5.25 | | | | | COMBINE_EQS: (202), (203) imply: % 32.44/5.25 | | | | | (205) all_416_1 = all_386_1 % 32.44/5.25 | | | | | % 32.44/5.25 | | | | | SIMP: (205) implies: % 32.44/5.25 | | | | | (206) all_416_1 = all_386_1 % 32.44/5.25 | | | | | % 32.44/5.25 | | | | | COMBINE_EQS: (201), (206) imply: % 32.44/5.25 | | | | | (207) all_386_1 = 0 % 32.44/5.25 | | | | | % 32.44/5.25 | | | | | REDUCE: (193), (204) imply: % 32.44/5.25 | | | | | (208) ~ (all_222_2 = 0) % 32.44/5.25 | | | | | % 32.44/5.25 | | | | | BETA: splitting (93) gives: % 32.44/5.25 | | | | | % 32.44/5.25 | | | | | Case 1: % 32.44/5.25 | | | | | | % 32.44/5.25 | | | | | | (209) ~ (all_228_0 = 0) % 32.44/5.25 | | | | | | % 32.44/5.25 | | | | | | REDUCE: (138), (209) imply: % 32.44/5.25 | | | | | | (210) ~ (all_226_1 = 0) % 32.44/5.25 | | | | | | % 32.44/5.25 | | | | | | BETA: splitting (85) gives: % 32.44/5.25 | | | | | | % 32.44/5.25 | | | | | | Case 1: % 32.44/5.25 | | | | | | | % 32.44/5.25 | | | | | | | (211) ~ (all_224_0 = 0) % 32.44/5.25 | | | | | | | % 32.44/5.25 | | | | | | | REDUCE: (139), (211) imply: % 32.44/5.25 | | | | | | | (212) ~ (all_222_1 = 0) % 32.44/5.25 | | | | | | | % 32.44/5.25 | | | | | | | BETA: splitting (36) gives: % 32.44/5.25 | | | | | | | % 32.44/5.25 | | | | | | | Case 1: % 32.44/5.25 | | | | | | | | % 32.44/5.25 | | | | | | | | (213) all_163_0 = empty_set % 32.44/5.25 | | | | | | | | % 32.44/5.25 | | | | | | | | REDUCE: (80), (213) imply: % 32.44/5.25 | | | | | | | | (214) empty(empty_set) = all_222_1 % 32.44/5.25 | | | | | | | | % 32.44/5.25 | | | | | | | | GROUND_INST: instantiating (12) with 0, all_222_1, empty_set, % 32.44/5.25 | | | | | | | | simplifying with (3), (214) gives: % 32.44/5.25 | | | | | | | | (215) all_222_1 = 0 % 32.44/5.25 | | | | | | | | % 32.44/5.25 | | | | | | | | REDUCE: (212), (215) imply: % 32.44/5.25 | | | | | | | | (216) $false % 32.44/5.25 | | | | | | | | % 32.44/5.25 | | | | | | | | CLOSE: (216) is inconsistent. % 32.44/5.25 | | | | | | | | % 32.44/5.25 | | | | | | | Case 2: % 32.44/5.25 | | | | | | | | % 32.44/5.25 | | | | | | | | (217) all_163_1 = empty_set % 32.44/5.25 | | | | | | | | % 32.44/5.25 | | | | | | | | REDUCE: (88), (217) imply: % 32.44/5.25 | | | | | | | | (218) empty(empty_set) = all_226_1 % 32.44/5.25 | | | | | | | | % 32.44/5.25 | | | | | | | | GROUND_INST: instantiating (12) with 0, all_226_1, empty_set, % 32.44/5.25 | | | | | | | | simplifying with (3), (218) gives: % 32.44/5.25 | | | | | | | | (219) all_226_1 = 0 % 32.44/5.25 | | | | | | | | % 32.44/5.25 | | | | | | | | REDUCE: (210), (219) imply: % 32.44/5.25 | | | | | | | | (220) $false % 32.44/5.25 | | | | | | | | % 32.44/5.25 | | | | | | | | CLOSE: (220) is inconsistent. % 32.44/5.25 | | | | | | | | % 32.44/5.25 | | | | | | | End of split % 32.44/5.25 | | | | | | | % 32.44/5.25 | | | | | | Case 2: % 32.44/5.25 | | | | | | | % 32.44/5.25 | | | | | | | (221) ~ (all_224_1 = 0) | all_224_2 = 0 % 32.44/5.25 | | | | | | | % 32.44/5.25 | | | | | | | BETA: splitting (221) gives: % 32.44/5.25 | | | | | | | % 32.44/5.25 | | | | | | | Case 1: % 32.44/5.25 | | | | | | | | % 32.44/5.25 | | | | | | | | (222) ~ (all_224_1 = 0) % 32.44/5.25 | | | | | | | | % 32.44/5.25 | | | | | | | | REDUCE: (166), (222) imply: % 32.44/5.25 | | | | | | | | (223) $false % 32.44/5.25 | | | | | | | | % 32.44/5.25 | | | | | | | | CLOSE: (223) is inconsistent. % 32.44/5.25 | | | | | | | | % 32.44/5.25 | | | | | | | Case 2: % 32.44/5.25 | | | | | | | | % 32.44/5.25 | | | | | | | | (224) all_224_2 = 0 % 32.44/5.25 | | | | | | | | % 32.44/5.25 | | | | | | | | COMBINE_EQS: (169), (224) imply: % 32.44/5.25 | | | | | | | | (225) all_222_2 = 0 % 32.44/5.25 | | | | | | | | % 32.44/5.25 | | | | | | | | SIMP: (225) implies: % 32.44/5.25 | | | | | | | | (226) all_222_2 = 0 % 32.44/5.25 | | | | | | | | % 32.44/5.25 | | | | | | | | REDUCE: (208), (226) imply: % 32.44/5.25 | | | | | | | | (227) $false % 32.44/5.25 | | | | | | | | % 32.44/5.25 | | | | | | | | CLOSE: (227) is inconsistent. % 32.44/5.25 | | | | | | | | % 32.44/5.25 | | | | | | | End of split % 32.44/5.25 | | | | | | | % 32.44/5.25 | | | | | | End of split % 32.44/5.25 | | | | | | % 32.44/5.25 | | | | | Case 2: % 32.44/5.25 | | | | | | % 32.44/5.25 | | | | | | (228) ~ (all_228_1 = 0) | all_228_2 = 0 % 32.44/5.25 | | | | | | % 32.44/5.25 | | | | | | BETA: splitting (228) gives: % 32.44/5.25 | | | | | | % 32.44/5.25 | | | | | | Case 1: % 32.44/5.25 | | | | | | | % 32.44/5.25 | | | | | | | (229) ~ (all_228_1 = 0) % 32.44/5.25 | | | | | | | % 32.44/5.25 | | | | | | | REDUCE: (165), (229) imply: % 32.44/5.25 | | | | | | | (230) $false % 32.44/5.25 | | | | | | | % 32.44/5.25 | | | | | | | CLOSE: (230) is inconsistent. % 32.44/5.25 | | | | | | | % 32.44/5.25 | | | | | | Case 2: % 32.44/5.25 | | | | | | | % 32.44/5.25 | | | | | | | (231) all_228_2 = 0 % 32.44/5.25 | | | | | | | % 32.44/5.25 | | | | | | | COMBINE_EQS: (137), (231) imply: % 32.44/5.25 | | | | | | | (232) all_222_2 = 0 % 32.44/5.25 | | | | | | | % 32.44/5.25 | | | | | | | REDUCE: (208), (232) imply: % 32.44/5.25 | | | | | | | (233) $false % 32.44/5.25 | | | | | | | % 32.44/5.25 | | | | | | | CLOSE: (233) is inconsistent. % 32.44/5.25 | | | | | | | % 32.44/5.25 | | | | | | End of split % 32.44/5.25 | | | | | | % 32.44/5.25 | | | | | End of split % 32.44/5.25 | | | | | % 32.44/5.25 | | | | End of split % 32.44/5.25 | | | | % 32.44/5.25 | | | End of split % 32.44/5.25 | | | % 32.44/5.25 | | Case 2: % 32.44/5.25 | | | % 32.44/5.25 | | | (234) all_153_0 = 0 % 32.44/5.25 | | | % 32.44/5.25 | | | REDUCE: (27), (234) imply: % 32.44/5.25 | | | (235) $false % 32.44/5.25 | | | % 32.44/5.25 | | | CLOSE: (235) is inconsistent. % 32.44/5.25 | | | % 32.44/5.25 | | End of split % 32.44/5.25 | | % 32.44/5.25 | End of split % 32.44/5.25 | % 32.44/5.25 End of proof % 32.44/5.25 % SZS output end Proof for theBenchmark % 32.44/5.25 % 32.44/5.25 4637ms %------------------------------------------------------------------------------