%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SEU200+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 : n013.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 17:43:13 EDT 2023 % Result : Theorem 24.11s 4.10s % Output : Proof 36.33s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.14 % Problem : SEU200+2 : TPTP v8.1.2. Released v3.3.0. % 0.15/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.15/0.36 % Computer : n013.cluster.edu % 0.15/0.36 % Model : x86_64 x86_64 % 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.15/0.36 % Memory : 8042.1875MB % 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64 % 0.15/0.36 % CPULimit : 300 % 0.15/0.36 % WCLimit : 300 % 0.15/0.36 % DateTime : Thu Aug 24 01:28:47 EDT 2023 % 0.15/0.36 % CPUTime : % 0.22/0.63 ________ _____ % 0.22/0.63 ___ __ \_________(_)________________________________ % 0.22/0.63 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.22/0.63 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.22/0.63 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.22/0.63 % 0.22/0.63 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.22/0.63 (2023-06-19) % 0.22/0.63 % 0.22/0.63 (c) Philipp Rümmer, 2009-2023 % 0.22/0.63 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.22/0.63 Amanda Stjerna. % 0.22/0.63 Free software under BSD-3-Clause. % 0.22/0.63 % 0.22/0.63 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.22/0.63 % 0.22/0.63 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.22/0.64 Running up to 7 provers in parallel. % 0.22/0.66 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.22/0.66 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.22/0.66 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.22/0.66 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.22/0.66 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.22/0.66 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.22/0.66 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 4.49/1.53 Prover 1: Preprocessing ... % 4.49/1.53 Prover 4: Preprocessing ... % 4.49/1.59 Prover 2: Preprocessing ... % 4.49/1.59 Prover 5: Preprocessing ... % 4.49/1.59 Prover 3: Preprocessing ... % 4.49/1.59 Prover 6: Preprocessing ... % 4.49/1.60 Prover 0: Preprocessing ... % 16.18/3.05 Prover 1: Warning: ignoring some quantifiers % 17.24/3.19 Prover 3: Warning: ignoring some quantifiers % 17.24/3.20 Prover 1: Constructing countermodel ... % 17.24/3.22 Prover 5: Proving ... % 17.95/3.23 Prover 6: Proving ... % 17.95/3.24 Prover 3: Constructing countermodel ... % 19.27/3.55 Prover 4: Warning: ignoring some quantifiers % 21.02/3.66 Prover 4: Constructing countermodel ... % 21.02/3.66 Prover 2: Proving ... % 22.59/3.88 Prover 0: Proving ... % 24.11/4.10 Prover 3: proved (3448ms) % 24.11/4.10 % 24.11/4.10 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 24.11/4.10 % 24.11/4.10 Prover 6: stopped % 24.11/4.10 Prover 0: stopped % 24.11/4.11 Prover 5: stopped % 24.11/4.11 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 24.11/4.11 Prover 2: stopped % 24.11/4.11 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 24.11/4.12 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 24.11/4.12 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 24.11/4.12 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 26.61/4.41 Prover 13: Preprocessing ... % 26.69/4.42 Prover 11: Preprocessing ... % 26.69/4.45 Prover 8: Preprocessing ... % 26.69/4.47 Prover 10: Preprocessing ... % 26.69/4.50 Prover 7: Preprocessing ... % 29.74/5.03 Prover 8: Warning: ignoring some quantifiers % 30.75/5.07 Prover 8: Constructing countermodel ... % 30.75/5.12 Prover 10: Warning: ignoring some quantifiers % 32.14/5.15 Prover 10: Constructing countermodel ... % 32.85/5.25 Prover 7: Warning: ignoring some quantifiers % 32.85/5.25 Prover 13: Warning: ignoring some quantifiers % 33.36/5.30 Prover 7: Constructing countermodel ... % 33.36/5.30 Prover 13: Constructing countermodel ... % 35.17/5.55 Prover 11: Warning: ignoring some quantifiers % 35.69/5.64 Prover 1: Found proof (size 122) % 35.69/5.64 Prover 1: proved (4989ms) % 35.69/5.64 Prover 7: stopped % 35.69/5.64 Prover 8: stopped % 35.69/5.64 Prover 4: stopped % 35.69/5.64 Prover 13: stopped % 35.69/5.64 Prover 10: stopped % 35.69/5.66 Prover 11: Constructing countermodel ... % 36.14/5.70 Prover 11: stopped % 36.14/5.70 % 36.14/5.70 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 36.14/5.70 % 36.14/5.71 % SZS output start Proof for theBenchmark % 36.14/5.72 Assumptions after simplification: % 36.14/5.72 --------------------------------- % 36.14/5.72 % 36.14/5.72 (cc1_relat_1) % 36.14/5.74 ! [v0: $i] : ( ~ (empty(v0) = 0) | ~ $i(v0) | relation(v0) = 0) % 36.14/5.74 % 36.14/5.74 (d2_subset_1) % 36.14/5.75 ! [v0: $i] : ! [v1: $i] : ! [v2: any] : ( ~ (element(v1, v0) = v2) | ~ % 36.14/5.75 $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : (empty(v0) = v3 & in(v1, % 36.14/5.75 v0) = v4 & (v3 = 0 | (( ~ (v4 = 0) | v2 = 0) & ( ~ (v2 = 0) | v4 = % 36.14/5.75 0))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: any] : ( ~ (empty(v1) = % 36.14/5.75 v2) | ~ (empty(v0) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : % 36.14/5.75 (element(v1, v0) = v3 & ( ~ (v3 = 0) | v2 = 0) & ( ~ (v2 = 0) | v3 = 0))) % 36.14/5.75 % 36.14/5.75 (d3_tarski) % 36.14/5.75 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) = v2) % 36.14/5.75 | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & in(v3, % 36.14/5.75 v1) = v4 & in(v3, v0) = 0 & $i(v3))) & ! [v0: $i] : ! [v1: $i] : ( ~ % 36.14/5.75 (subset(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ! [v2: $i] : ( ~ (in(v2, v0) % 36.14/5.75 = 0) | ~ $i(v2) | in(v2, v1) = 0)) % 36.14/5.75 % 36.14/5.75 (d5_relat_1) % 36.14/5.75 ! [v0: $i] : ! [v1: $i] : ( ~ (relation_rng(v0) = v1) | ~ $i(v0) | ? [v2: % 36.14/5.75 int] : ( ~ (v2 = 0) & relation(v0) = v2) | ( ? [v2: $i] : (v2 = v1 | ~ % 36.14/5.75 $i(v2) | ? [v3: $i] : ? [v4: any] : (in(v3, v2) = v4 & $i(v3) & ( ~ % 36.14/5.75 (v4 = 0) | ! [v5: $i] : ! [v6: $i] : ( ~ (ordered_pair(v5, v3) = % 36.14/5.75 v6) | ~ (in(v6, v0) = 0) | ~ $i(v5))) & (v4 = 0 | ? [v5: $i] % 36.14/5.75 : ? [v6: $i] : (ordered_pair(v5, v3) = v6 & in(v6, v0) = 0 & $i(v6) % 36.14/5.75 & $i(v5))))) & ( ~ $i(v1) | ( ! [v2: $i] : ! [v3: int] : (v3 = 0 % 36.14/5.75 | ~ (in(v2, v1) = v3) | ~ $i(v2) | ! [v4: $i] : ! [v5: $i] : ( ~ % 36.14/5.75 (ordered_pair(v4, v2) = v5) | ~ (in(v5, v0) = 0) | ~ $i(v4))) & % 36.14/5.75 ! [v2: $i] : ( ~ (in(v2, v1) = 0) | ~ $i(v2) | ? [v3: $i] : ? [v4: % 36.14/5.75 $i] : (ordered_pair(v3, v2) = v4 & in(v4, v0) = 0 & $i(v4) & % 36.14/5.75 $i(v3))))))) % 36.14/5.75 % 36.14/5.75 (dt_k8_relat_1) % 36.14/5.75 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (relation_rng_restriction(v0, % 36.14/5.75 v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : % 36.14/5.75 (relation(v2) = v4 & relation(v1) = v3 & ( ~ (v3 = 0) | v4 = 0))) % 36.14/5.75 % 36.14/5.75 (fc6_relat_1) % 36.14/5.75 ! [v0: $i] : ! [v1: $i] : ( ~ (relation_rng(v0) = v1) | ~ $i(v0) | ? [v2: % 36.14/5.75 any] : ? [v3: any] : ? [v4: any] : (empty(v1) = v4 & empty(v0) = v2 & % 36.14/5.75 relation(v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | v2 = 0))) % 36.14/5.75 % 36.14/5.75 (rc1_relat_1) % 36.14/5.75 ? [v0: $i] : (empty(v0) = 0 & relation(v0) = 0 & $i(v0)) % 36.14/5.75 % 36.14/5.75 (rc1_subset_1) % 36.14/5.75 ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (empty(v0) = v1) | ~ $i(v0) | ? % 36.14/5.75 [v2: $i] : (powerset(v0) = v2 & $i(v2) & ? [v3: $i] : ? [v4: int] : ( ~ % 36.14/5.75 (v4 = 0) & element(v3, v2) = 0 & empty(v3) = v4 & $i(v3)))) % 36.14/5.75 % 36.14/5.75 (rc1_xboole_0) % 36.14/5.76 ? [v0: $i] : (empty(v0) = 0 & $i(v0)) % 36.14/5.76 % 36.14/5.76 (rc2_xboole_0) % 36.14/5.76 ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & empty(v0) = v1 & $i(v0)) % 36.14/5.76 % 36.14/5.76 (t115_relat_1) % 36.14/5.76 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 36.14/5.76 any] : ( ~ (relation_rng(v3) = v4) | ~ (relation_rng_restriction(v1, v2) = % 36.14/5.76 v3) | ~ (in(v0, v4) = v5) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: % 36.14/5.76 any] : ? [v7: any] : ? [v8: $i] : ? [v9: any] : (relation_rng(v2) = v8 % 36.14/5.76 & relation(v2) = v6 & in(v0, v8) = v9 & in(v0, v1) = v7 & $i(v8) & ( ~ (v6 % 36.14/5.76 = 0) | (( ~ (v9 = 0) | ~ (v7 = 0) | v5 = 0) & ( ~ (v5 = 0) | (v9 = 0 % 36.14/5.76 & v7 = 0)))))) % 36.14/5.76 % 36.14/5.76 (t118_relat_1) % 36.14/5.76 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: % 36.14/5.76 int] : ( ~ (v5 = 0) & relation_rng(v2) = v3 & relation_rng(v1) = v4 & % 36.14/5.76 relation_rng_restriction(v0, v1) = v2 & subset(v3, v4) = v5 & relation(v1) = % 36.14/5.76 0 & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 36.14/5.76 % 36.14/5.76 (t25_relat_1) % 36.14/5.76 ! [v0: $i] : ! [v1: $i] : ( ~ (relation_dom(v0) = v1) | ~ $i(v0) | ? [v2: % 36.14/5.76 any] : ? [v3: $i] : (relation_rng(v0) = v3 & relation(v0) = v2 & $i(v3) & % 36.14/5.76 ( ~ (v2 = 0) | ! [v4: $i] : ! [v5: $i] : ! [v6: any] : ( ~ % 36.14/5.76 (relation_dom(v4) = v5) | ~ (subset(v1, v5) = v6) | ~ $i(v4) | ? % 36.14/5.76 [v7: any] : ? [v8: any] : ? [v9: $i] : ? [v10: any] : % 36.14/5.76 (relation_rng(v4) = v9 & subset(v3, v9) = v10 & subset(v0, v4) = v8 & % 36.14/5.76 relation(v4) = v7 & $i(v9) & ( ~ (v8 = 0) | ~ (v7 = 0) | (v10 = 0 & % 36.14/5.76 v6 = 0))))))) % 36.14/5.76 % 36.14/5.76 (t46_relat_1) % 36.14/5.76 ! [v0: $i] : ! [v1: $i] : ( ~ (relation_dom(v0) = v1) | ~ $i(v0) | ? [v2: % 36.14/5.76 any] : ? [v3: $i] : (relation_rng(v0) = v3 & relation(v0) = v2 & $i(v3) & % 36.14/5.76 ( ~ (v2 = 0) | ! [v4: $i] : ! [v5: $i] : ( ~ (relation_dom(v4) = v5) | % 36.14/5.76 ~ (subset(v3, v5) = 0) | ~ $i(v4) | ? [v6: any] : ? [v7: $i] : ? % 36.14/5.76 [v8: $i] : (relation_composition(v0, v4) = v7 & relation_dom(v7) = v8 % 36.14/5.76 & relation(v4) = v6 & $i(v8) & $i(v7) & ( ~ (v6 = 0) | v8 = v1)))))) % 36.14/5.76 % 36.14/5.76 (t47_relat_1) % 36.14/5.76 ! [v0: $i] : ! [v1: $i] : ( ~ (relation_dom(v0) = v1) | ~ $i(v0) | ? [v2: % 36.14/5.76 any] : ? [v3: $i] : (relation_rng(v0) = v3 & relation(v0) = v2 & $i(v3) & % 36.14/5.76 ( ~ (v2 = 0) | ! [v4: $i] : ! [v5: $i] : ( ~ (relation_rng(v4) = v5) | % 36.14/5.76 ~ (subset(v1, v5) = 0) | ~ $i(v4) | ? [v6: any] : ? [v7: $i] : ? % 36.14/5.76 [v8: $i] : (relation_composition(v4, v0) = v7 & relation_rng(v7) = v8 % 36.14/5.76 & relation(v4) = v6 & $i(v8) & $i(v7) & ( ~ (v6 = 0) | v8 = v3)))))) % 36.14/5.76 % 36.14/5.76 (t60_relat_1) % 36.14/5.76 relation_rng(empty_set) = empty_set & relation_dom(empty_set) = empty_set & % 36.14/5.76 $i(empty_set) % 36.14/5.76 % 36.14/5.76 (t6_boole) % 36.14/5.76 $i(empty_set) & ! [v0: $i] : (v0 = empty_set | ~ (empty(v0) = 0) | ~ % 36.14/5.76 $i(v0)) % 36.14/5.76 % 36.14/5.76 (t8_boole) % 36.14/5.76 ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (empty(v1) = 0) | ~ (empty(v0) = 0) % 36.14/5.76 | ~ $i(v1) | ~ $i(v0)) % 36.14/5.76 % 36.14/5.76 (function-axioms) % 36.14/5.77 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 % 36.14/5.77 | ~ (subset_difference(v4, v3, v2) = v1) | ~ (subset_difference(v4, v3, % 36.14/5.77 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : % 36.14/5.77 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (are_equipotent(v3, v2) = v1) | ~ % 36.14/5.77 (are_equipotent(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 36.14/5.77 ! [v3: $i] : (v1 = v0 | ~ (meet_of_subsets(v3, v2) = v1) | ~ % 36.14/5.77 (meet_of_subsets(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 36.14/5.77 ! [v3: $i] : (v1 = v0 | ~ (union_of_subsets(v3, v2) = v1) | ~ % 36.14/5.77 (union_of_subsets(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 36.14/5.77 ! [v3: $i] : (v1 = v0 | ~ (complements_of_subsets(v3, v2) = v1) | ~ % 36.14/5.77 (complements_of_subsets(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 36.14/5.77 $i] : ! [v3: $i] : (v1 = v0 | ~ (relation_composition(v3, v2) = v1) | ~ % 36.14/5.77 (relation_composition(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 36.14/5.77 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (disjoint(v3, % 36.14/5.77 v2) = v1) | ~ (disjoint(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 36.14/5.77 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (subset_complement(v3, v2) = v1) | ~ % 36.14/5.77 (subset_complement(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 36.14/5.77 : ! [v3: $i] : (v1 = v0 | ~ (set_difference(v3, v2) = v1) | ~ % 36.14/5.77 (set_difference(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 36.14/5.77 ! [v3: $i] : (v1 = v0 | ~ (cartesian_product2(v3, v2) = v1) | ~ % 36.14/5.77 (cartesian_product2(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 36.14/5.77 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (element(v3, % 36.14/5.77 v2) = v1) | ~ (element(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 36.14/5.77 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (relation_rng_restriction(v3, v2) = v1) % 36.14/5.77 | ~ (relation_rng_restriction(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : % 36.14/5.77 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (relation_dom_restriction(v3, v2) = % 36.14/5.77 v1) | ~ (relation_dom_restriction(v3, v2) = v0)) & ! [v0: % 36.14/5.77 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 36.14/5.77 : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0: % 36.14/5.77 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 36.14/5.77 (ordered_pair(v3, v2) = v1) | ~ (ordered_pair(v3, v2) = v0)) & ! [v0: $i] % 36.14/5.77 : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 36.14/5.77 (set_intersection2(v3, v2) = v1) | ~ (set_intersection2(v3, v2) = v0)) & ! % 36.14/5.77 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 36.14/5.77 (set_union2(v3, v2) = v1) | ~ (set_union2(v3, v2) = v0)) & ! [v0: $i] : ! % 36.14/5.77 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (unordered_pair(v3, v2) = % 36.14/5.77 v1) | ~ (unordered_pair(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! % 36.14/5.77 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 36.14/5.77 (proper_subset(v3, v2) = v1) | ~ (proper_subset(v3, v2) = v0)) & ! [v0: % 36.14/5.77 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 36.14/5.77 : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) & ! [v0: $i] : ! % 36.14/5.77 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (relation_inverse(v2) = v1) | ~ % 36.14/5.77 (relation_inverse(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 % 36.14/5.77 = v0 | ~ (relation_field(v2) = v1) | ~ (relation_field(v2) = v0)) & ! % 36.14/5.77 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (relation_rng(v2) = v1) | % 36.14/5.77 ~ (relation_rng(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 % 36.14/5.77 = v0 | ~ (union(v2) = v1) | ~ (union(v2) = v0)) & ! [v0: $i] : ! [v1: % 36.14/5.77 $i] : ! [v2: $i] : (v1 = v0 | ~ (cast_to_subset(v2) = v1) | ~ % 36.14/5.77 (cast_to_subset(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = % 36.14/5.77 v0 | ~ (relation_dom(v2) = v1) | ~ (relation_dom(v2) = v0)) & ! [v0: $i] % 36.14/5.77 : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ % 36.14/5.77 (powerset(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | % 36.14/5.77 ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ! [v0: $i] : ! [v1: % 36.14/5.77 $i] : ! [v2: $i] : (v1 = v0 | ~ (set_meet(v2) = v1) | ~ (set_meet(v2) = % 36.14/5.77 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 36.14/5.77 (identity_relation(v2) = v1) | ~ (identity_relation(v2) = v0)) & ! [v0: % 36.14/5.77 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 36.14/5.77 ~ (empty(v2) = v1) | ~ (empty(v2) = v0)) & ! [v0: MultipleValueBool] : ! % 36.14/5.77 [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (relation(v2) = v1) | ~ % 36.14/5.77 (relation(v2) = v0)) % 36.14/5.77 % 36.14/5.77 Further assumptions not needed in the proof: % 36.14/5.77 -------------------------------------------- % 36.14/5.77 antisymmetry_r2_hidden, antisymmetry_r2_xboole_0, commutativity_k2_tarski, % 36.14/5.77 commutativity_k2_xboole_0, commutativity_k3_xboole_0, d10_relat_1, d10_xboole_0, % 36.14/5.77 d11_relat_1, d12_relat_1, d1_relat_1, d1_setfam_1, d1_tarski, d1_xboole_0, % 36.14/5.77 d1_zfmisc_1, d2_relat_1, d2_tarski, d2_xboole_0, d2_zfmisc_1, d3_relat_1, % 36.14/5.77 d3_xboole_0, d4_relat_1, d4_subset_1, d4_tarski, d4_xboole_0, d5_subset_1, % 36.14/5.77 d5_tarski, d6_relat_1, d7_relat_1, d7_xboole_0, d8_relat_1, d8_setfam_1, % 36.14/5.77 d8_xboole_0, dt_k1_relat_1, dt_k1_setfam_1, dt_k1_tarski, dt_k1_xboole_0, % 36.14/5.77 dt_k1_zfmisc_1, dt_k2_relat_1, dt_k2_subset_1, dt_k2_tarski, dt_k2_xboole_0, % 36.14/5.77 dt_k2_zfmisc_1, dt_k3_relat_1, dt_k3_subset_1, dt_k3_tarski, dt_k3_xboole_0, % 36.14/5.77 dt_k4_relat_1, dt_k4_tarski, dt_k4_xboole_0, dt_k5_relat_1, dt_k5_setfam_1, % 36.14/5.77 dt_k6_relat_1, dt_k6_setfam_1, dt_k6_subset_1, dt_k7_relat_1, dt_k7_setfam_1, % 36.14/5.77 dt_m1_subset_1, existence_m1_subset_1, fc10_relat_1, fc1_relat_1, fc1_subset_1, % 36.14/5.77 fc1_xboole_0, fc1_zfmisc_1, fc2_relat_1, fc2_subset_1, fc2_xboole_0, % 36.14/5.77 fc3_subset_1, fc3_xboole_0, fc4_relat_1, fc4_subset_1, fc5_relat_1, fc7_relat_1, % 36.14/5.77 fc8_relat_1, fc9_relat_1, idempotence_k2_xboole_0, idempotence_k3_xboole_0, % 36.14/5.78 involutiveness_k3_subset_1, involutiveness_k4_relat_1, % 36.14/5.78 involutiveness_k7_setfam_1, irreflexivity_r2_xboole_0, l1_zfmisc_1, % 36.14/5.78 l23_zfmisc_1, l25_zfmisc_1, l28_zfmisc_1, l2_zfmisc_1, l32_xboole_1, % 36.14/5.78 l3_subset_1, l3_zfmisc_1, l4_zfmisc_1, l50_zfmisc_1, l55_zfmisc_1, l71_subset_1, % 36.14/5.78 rc2_relat_1, rc2_subset_1, redefinition_k5_setfam_1, redefinition_k6_setfam_1, % 36.14/5.78 redefinition_k6_subset_1, reflexivity_r1_tarski, symmetry_r1_xboole_0, % 36.14/5.78 t106_zfmisc_1, t10_zfmisc_1, t116_relat_1, t117_relat_1, t118_zfmisc_1, % 36.14/5.78 t119_zfmisc_1, t12_xboole_1, t136_zfmisc_1, t17_xboole_1, t19_xboole_1, % 36.14/5.78 t1_boole, t1_subset, t1_xboole_1, t1_zfmisc_1, t20_relat_1, t21_relat_1, % 36.14/5.78 t26_xboole_1, t28_xboole_1, t2_boole, t2_subset, t2_tarski, t2_xboole_1, % 36.14/5.78 t30_relat_1, t33_xboole_1, t33_zfmisc_1, t36_xboole_1, t37_relat_1, % 36.14/5.78 t37_xboole_1, t37_zfmisc_1, t38_zfmisc_1, t39_xboole_1, t39_zfmisc_1, t3_boole, % 36.14/5.78 t3_subset, t3_xboole_0, t3_xboole_1, t40_xboole_1, t43_subset_1, t44_relat_1, % 36.14/5.78 t45_relat_1, t45_xboole_1, t46_setfam_1, t46_zfmisc_1, t47_setfam_1, % 36.14/5.78 t48_setfam_1, t48_xboole_1, t4_boole, t4_subset, t4_xboole_0, t50_subset_1, % 36.14/5.78 t54_subset_1, t56_relat_1, t5_subset, t60_xboole_1, t63_xboole_1, t64_relat_1, % 36.14/5.78 t65_relat_1, t65_zfmisc_1, t69_enumset1, t6_zfmisc_1, t71_relat_1, t74_relat_1, % 36.14/5.78 t7_boole, t7_xboole_1, t83_xboole_1, t86_relat_1, t88_relat_1, t8_xboole_1, % 36.14/5.78 t8_zfmisc_1, t90_relat_1, t92_zfmisc_1, t94_relat_1, t99_relat_1, t99_zfmisc_1, % 36.14/5.78 t9_tarski, t9_zfmisc_1 % 36.14/5.78 % 36.14/5.78 Those formulas are unsatisfiable: % 36.14/5.78 --------------------------------- % 36.14/5.78 % 36.14/5.78 Begin of proof % 36.14/5.78 | % 36.14/5.78 | ALPHA: (d2_subset_1) implies: % 36.14/5.78 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: any] : ( ~ (empty(v1) = v2) | ~ % 36.14/5.78 | (empty(v0) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : (element(v1, % 36.14/5.78 | v0) = v3 & ( ~ (v3 = 0) | v2 = 0) & ( ~ (v2 = 0) | v3 = 0))) % 36.14/5.78 | % 36.14/5.78 | ALPHA: (d3_tarski) implies: % 36.14/5.78 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) % 36.14/5.78 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ % 36.14/5.78 | (v4 = 0) & in(v3, v1) = v4 & in(v3, v0) = 0 & $i(v3))) % 36.14/5.78 | % 36.14/5.78 | ALPHA: (t60_relat_1) implies: % 36.14/5.78 | (3) relation_dom(empty_set) = empty_set % 36.14/5.78 | (4) relation_rng(empty_set) = empty_set % 36.14/5.78 | % 36.14/5.78 | ALPHA: (t6_boole) implies: % 36.14/5.78 | (5) $i(empty_set) % 36.14/5.78 | (6) ! [v0: $i] : (v0 = empty_set | ~ (empty(v0) = 0) | ~ $i(v0)) % 36.14/5.78 | % 36.14/5.78 | ALPHA: (function-axioms) implies: % 36.14/5.78 | (7) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 36.14/5.78 | (v1 = v0 | ~ (relation(v2) = v1) | ~ (relation(v2) = v0)) % 36.14/5.78 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 36.14/5.78 | (relation_rng(v2) = v1) | ~ (relation_rng(v2) = v0)) % 36.14/5.78 | (9) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 36.14/5.78 | ! [v3: $i] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) % 36.14/5.78 | % 36.14/5.78 | DELTA: instantiating (rc1_xboole_0) with fresh symbol all_164_0 gives: % 36.14/5.78 | (10) empty(all_164_0) = 0 & $i(all_164_0) % 36.14/5.78 | % 36.14/5.78 | ALPHA: (10) implies: % 36.14/5.78 | (11) $i(all_164_0) % 36.14/5.78 | (12) empty(all_164_0) = 0 % 36.14/5.78 | % 36.14/5.78 | DELTA: instantiating (rc1_relat_1) with fresh symbol all_166_0 gives: % 36.14/5.78 | (13) empty(all_166_0) = 0 & relation(all_166_0) = 0 & $i(all_166_0) % 36.14/5.78 | % 36.14/5.78 | ALPHA: (13) implies: % 36.14/5.79 | (14) $i(all_166_0) % 36.14/5.79 | (15) empty(all_166_0) = 0 % 36.14/5.79 | % 36.14/5.79 | DELTA: instantiating (rc2_xboole_0) with fresh symbols all_171_0, all_171_1 % 36.14/5.79 | gives: % 36.14/5.79 | (16) ~ (all_171_0 = 0) & empty(all_171_1) = all_171_0 & $i(all_171_1) % 36.14/5.79 | % 36.14/5.79 | ALPHA: (16) implies: % 36.14/5.79 | (17) ~ (all_171_0 = 0) % 36.14/5.79 | (18) $i(all_171_1) % 36.14/5.79 | (19) empty(all_171_1) = all_171_0 % 36.14/5.79 | % 36.14/5.79 | DELTA: instantiating (t118_relat_1) with fresh symbols all_189_0, all_189_1, % 36.14/5.79 | all_189_2, all_189_3, all_189_4, all_189_5 gives: % 36.14/5.79 | (20) ~ (all_189_0 = 0) & relation_rng(all_189_3) = all_189_2 & % 36.14/5.79 | relation_rng(all_189_4) = all_189_1 & % 36.14/5.79 | relation_rng_restriction(all_189_5, all_189_4) = all_189_3 & % 36.14/5.79 | subset(all_189_2, all_189_1) = all_189_0 & relation(all_189_4) = 0 & % 36.14/5.79 | $i(all_189_1) & $i(all_189_2) & $i(all_189_3) & $i(all_189_4) & % 36.14/5.79 | $i(all_189_5) % 36.14/5.79 | % 36.14/5.79 | ALPHA: (20) implies: % 36.14/5.79 | (21) ~ (all_189_0 = 0) % 36.14/5.79 | (22) $i(all_189_5) % 36.14/5.79 | (23) $i(all_189_4) % 36.14/5.79 | (24) $i(all_189_3) % 36.14/5.79 | (25) $i(all_189_2) % 36.14/5.79 | (26) $i(all_189_1) % 36.14/5.79 | (27) relation(all_189_4) = 0 % 36.14/5.79 | (28) subset(all_189_2, all_189_1) = all_189_0 % 36.14/5.79 | (29) relation_rng_restriction(all_189_5, all_189_4) = all_189_3 % 36.14/5.79 | (30) relation_rng(all_189_4) = all_189_1 % 36.14/5.79 | (31) relation_rng(all_189_3) = all_189_2 % 36.14/5.79 | % 36.14/5.79 | GROUND_INST: instantiating (cc1_relat_1) with all_164_0, simplifying with % 36.14/5.79 | (11), (12) gives: % 36.14/5.79 | (32) relation(all_164_0) = 0 % 36.14/5.79 | % 36.14/5.79 | GROUND_INST: instantiating (t8_boole) with all_164_0, all_166_0, simplifying % 36.14/5.79 | with (11), (12), (14), (15) gives: % 36.14/5.79 | (33) all_166_0 = all_164_0 % 36.14/5.79 | % 36.14/5.79 | GROUND_INST: instantiating (6) with all_166_0, simplifying with (14), (15) % 36.14/5.79 | gives: % 36.14/5.79 | (34) all_166_0 = empty_set % 36.14/5.79 | % 36.14/5.79 | GROUND_INST: instantiating (rc1_subset_1) with all_171_1, all_171_0, % 36.14/5.79 | simplifying with (18), (19) gives: % 36.14/5.79 | (35) all_171_0 = 0 | ? [v0: $i] : (powerset(all_171_1) = v0 & $i(v0) & ? % 36.14/5.79 | [v1: $i] : ? [v2: int] : ( ~ (v2 = 0) & element(v1, v0) = 0 & % 36.14/5.79 | empty(v1) = v2 & $i(v1))) % 36.14/5.79 | % 36.14/5.79 | GROUND_INST: instantiating (2) with all_189_2, all_189_1, all_189_0, % 36.14/5.79 | simplifying with (25), (26), (28) gives: % 36.14/5.79 | (36) all_189_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & in(v0, % 36.14/5.79 | all_189_1) = v1 & in(v0, all_189_2) = 0 & $i(v0)) % 36.14/5.79 | % 36.14/5.79 | GROUND_INST: instantiating (dt_k8_relat_1) with all_189_5, all_189_4, % 36.14/5.79 | all_189_3, simplifying with (22), (23), (29) gives: % 36.14/5.79 | (37) ? [v0: any] : ? [v1: any] : (relation(all_189_3) = v1 & % 36.14/5.79 | relation(all_189_4) = v0 & ( ~ (v0 = 0) | v1 = 0)) % 36.14/5.79 | % 36.14/5.79 | GROUND_INST: instantiating (t25_relat_1) with empty_set, empty_set, % 36.14/5.79 | simplifying with (3), (5) gives: % 36.14/5.79 | (38) ? [v0: any] : ? [v1: $i] : (relation_rng(empty_set) = v1 & % 36.14/5.80 | relation(empty_set) = v0 & $i(v1) & ( ~ (v0 = 0) | ! [v2: $i] : ! % 36.14/5.80 | [v3: $i] : ! [v4: any] : ( ~ (relation_dom(v2) = v3) | ~ % 36.14/5.80 | (subset(empty_set, v3) = v4) | ~ $i(v2) | ? [v5: any] : ? % 36.14/5.80 | [v6: any] : ? [v7: $i] : ? [v8: any] : (relation_rng(v2) = v7 % 36.14/5.80 | & subset(v1, v7) = v8 & subset(empty_set, v2) = v6 & % 36.14/5.80 | relation(v2) = v5 & $i(v7) & ( ~ (v6 = 0) | ~ (v5 = 0) | (v8 % 36.14/5.80 | = 0 & v4 = 0)))))) % 36.14/5.80 | % 36.14/5.80 | GROUND_INST: instantiating (t47_relat_1) with empty_set, empty_set, % 36.14/5.80 | simplifying with (3), (5) gives: % 36.14/5.80 | (39) ? [v0: any] : ? [v1: $i] : (relation_rng(empty_set) = v1 & % 36.14/5.80 | relation(empty_set) = v0 & $i(v1) & ( ~ (v0 = 0) | ! [v2: $i] : ! % 36.14/5.80 | [v3: $i] : ( ~ (relation_rng(v2) = v3) | ~ (subset(empty_set, v3) % 36.14/5.80 | = 0) | ~ $i(v2) | ? [v4: any] : ? [v5: $i] : ? [v6: $i] : % 36.14/5.80 | (relation_composition(v2, empty_set) = v5 & relation_rng(v5) = % 36.14/5.80 | v6 & relation(v2) = v4 & $i(v6) & $i(v5) & ( ~ (v4 = 0) | v6 = % 36.14/5.80 | v1))))) % 36.14/5.80 | % 36.14/5.80 | GROUND_INST: instantiating (t46_relat_1) with empty_set, empty_set, % 36.14/5.80 | simplifying with (3), (5) gives: % 36.14/5.80 | (40) ? [v0: any] : ? [v1: $i] : (relation_rng(empty_set) = v1 & % 36.14/5.80 | relation(empty_set) = v0 & $i(v1) & ( ~ (v0 = 0) | ! [v2: $i] : ! % 36.14/5.80 | [v3: $i] : ( ~ (relation_dom(v2) = v3) | ~ (subset(v1, v3) = 0) | % 36.14/5.80 | ~ $i(v2) | ? [v4: any] : ? [v5: $i] : ? [v6: $i] : % 36.14/5.80 | (relation_composition(empty_set, v2) = v5 & relation_dom(v5) = % 36.14/5.80 | v6 & relation(v2) = v4 & $i(v6) & $i(v5) & ( ~ (v4 = 0) | v6 = % 36.14/5.80 | empty_set))))) % 36.14/5.80 | % 36.14/5.80 | GROUND_INST: instantiating (fc6_relat_1) with all_189_4, all_189_1, % 36.14/5.80 | simplifying with (23), (30) gives: % 36.14/5.80 | (41) ? [v0: any] : ? [v1: any] : ? [v2: any] : (empty(all_189_1) = v2 & % 36.14/5.80 | empty(all_189_4) = v0 & relation(all_189_4) = v1 & ( ~ (v2 = 0) | ~ % 36.14/5.80 | (v1 = 0) | v0 = 0)) % 36.14/5.80 | % 36.14/5.80 | GROUND_INST: instantiating (fc6_relat_1) with all_189_3, all_189_2, % 36.14/5.80 | simplifying with (24), (31) gives: % 36.14/5.80 | (42) ? [v0: any] : ? [v1: any] : ? [v2: any] : (empty(all_189_2) = v2 & % 36.14/5.80 | empty(all_189_3) = v0 & relation(all_189_3) = v1 & ( ~ (v2 = 0) | ~ % 36.14/5.80 | (v1 = 0) | v0 = 0)) % 36.14/5.80 | % 36.14/5.80 | GROUND_INST: instantiating (d5_relat_1) with all_189_3, all_189_2, simplifying % 36.14/5.80 | with (24), (31) gives: % 36.33/5.80 | (43) ? [v0: int] : ( ~ (v0 = 0) & relation(all_189_3) = v0) | ( ? [v0: % 36.33/5.80 | any] : (v0 = all_189_2 | ~ $i(v0) | ? [v1: $i] : ? [v2: any] : % 36.33/5.80 | (in(v1, v0) = v2 & $i(v1) & ( ~ (v2 = 0) | ! [v3: $i] : ! [v4: % 36.33/5.80 | $i] : ( ~ (ordered_pair(v3, v1) = v4) | ~ (in(v4, % 36.33/5.80 | all_189_3) = 0) | ~ $i(v3))) & (v2 = 0 | ? [v3: $i] : % 36.33/5.80 | ? [v4: $i] : (ordered_pair(v3, v1) = v4 & in(v4, all_189_3) = % 36.33/5.80 | 0 & $i(v4) & $i(v3))))) & ( ~ $i(all_189_2) | ( ! [v0: $i] : % 36.33/5.80 | ! [v1: int] : (v1 = 0 | ~ (in(v0, all_189_2) = v1) | ~ $i(v0) % 36.33/5.80 | | ! [v2: $i] : ! [v3: $i] : ( ~ (ordered_pair(v2, v0) = v3) % 36.33/5.80 | | ~ (in(v3, all_189_3) = 0) | ~ $i(v2))) & ! [v0: $i] : ( % 36.33/5.80 | ~ (in(v0, all_189_2) = 0) | ~ $i(v0) | ? [v1: $i] : ? [v2: % 36.33/5.80 | $i] : (ordered_pair(v1, v0) = v2 & in(v2, all_189_3) = 0 & % 36.33/5.80 | $i(v2) & $i(v1)))))) % 36.33/5.80 | % 36.33/5.80 | COMBINE_EQS: (33), (34) imply: % 36.33/5.80 | (44) all_164_0 = empty_set % 36.33/5.80 | % 36.33/5.80 | SIMP: (44) implies: % 36.33/5.80 | (45) all_164_0 = empty_set % 36.33/5.80 | % 36.33/5.80 | DELTA: instantiating (37) with fresh symbols all_245_0, all_245_1 gives: % 36.33/5.80 | (46) relation(all_189_3) = all_245_0 & relation(all_189_4) = all_245_1 & ( % 36.33/5.80 | ~ (all_245_1 = 0) | all_245_0 = 0) % 36.33/5.80 | % 36.33/5.80 | ALPHA: (46) implies: % 36.33/5.80 | (47) relation(all_189_4) = all_245_1 % 36.33/5.80 | (48) relation(all_189_3) = all_245_0 % 36.33/5.80 | (49) ~ (all_245_1 = 0) | all_245_0 = 0 % 36.33/5.80 | % 36.33/5.80 | DELTA: instantiating (42) with fresh symbols all_261_0, all_261_1, all_261_2 % 36.33/5.80 | gives: % 36.33/5.81 | (50) empty(all_189_2) = all_261_0 & empty(all_189_3) = all_261_2 & % 36.33/5.81 | relation(all_189_3) = all_261_1 & ( ~ (all_261_0 = 0) | ~ (all_261_1 % 36.33/5.81 | = 0) | all_261_2 = 0) % 36.33/5.81 | % 36.33/5.81 | ALPHA: (50) implies: % 36.33/5.81 | (51) relation(all_189_3) = all_261_1 % 36.33/5.81 | % 36.33/5.81 | DELTA: instantiating (41) with fresh symbols all_265_0, all_265_1, all_265_2 % 36.33/5.81 | gives: % 36.33/5.81 | (52) empty(all_189_1) = all_265_0 & empty(all_189_4) = all_265_2 & % 36.33/5.81 | relation(all_189_4) = all_265_1 & ( ~ (all_265_0 = 0) | ~ (all_265_1 % 36.33/5.81 | = 0) | all_265_2 = 0) % 36.33/5.81 | % 36.33/5.81 | ALPHA: (52) implies: % 36.33/5.81 | (53) relation(all_189_4) = all_265_1 % 36.33/5.81 | % 36.33/5.81 | DELTA: instantiating (39) with fresh symbols all_267_0, all_267_1 gives: % 36.33/5.81 | (54) relation_rng(empty_set) = all_267_0 & relation(empty_set) = all_267_1 % 36.33/5.81 | & $i(all_267_0) & ( ~ (all_267_1 = 0) | ! [v0: $i] : ! [v1: $i] : ( % 36.33/5.81 | ~ (relation_rng(v0) = v1) | ~ (subset(empty_set, v1) = 0) | ~ % 36.33/5.81 | $i(v0) | ? [v2: any] : ? [v3: $i] : ? [v4: $i] : % 36.33/5.81 | (relation_composition(v0, empty_set) = v3 & relation_rng(v3) = v4 % 36.33/5.81 | & relation(v0) = v2 & $i(v4) & $i(v3) & ( ~ (v2 = 0) | v4 = % 36.33/5.81 | all_267_0)))) % 36.33/5.81 | % 36.33/5.81 | ALPHA: (54) implies: % 36.33/5.81 | (55) $i(all_267_0) % 36.33/5.81 | (56) relation(empty_set) = all_267_1 % 36.33/5.81 | (57) relation_rng(empty_set) = all_267_0 % 36.33/5.81 | % 36.33/5.81 | DELTA: instantiating (40) with fresh symbols all_269_0, all_269_1 gives: % 36.33/5.81 | (58) relation_rng(empty_set) = all_269_0 & relation(empty_set) = all_269_1 % 36.33/5.81 | & $i(all_269_0) & ( ~ (all_269_1 = 0) | ! [v0: $i] : ! [v1: $i] : ( % 36.33/5.81 | ~ (relation_dom(v0) = v1) | ~ (subset(all_269_0, v1) = 0) | ~ % 36.33/5.81 | $i(v0) | ? [v2: any] : ? [v3: $i] : ? [v4: $i] : % 36.33/5.81 | (relation_composition(empty_set, v0) = v3 & relation_dom(v3) = v4 % 36.33/5.81 | & relation(v0) = v2 & $i(v4) & $i(v3) & ( ~ (v2 = 0) | v4 = % 36.33/5.81 | empty_set)))) % 36.33/5.81 | % 36.33/5.81 | ALPHA: (58) implies: % 36.33/5.81 | (59) relation(empty_set) = all_269_1 % 36.33/5.81 | (60) relation_rng(empty_set) = all_269_0 % 36.33/5.81 | (61) ~ (all_269_1 = 0) | ! [v0: $i] : ! [v1: $i] : ( ~ (relation_dom(v0) % 36.33/5.81 | = v1) | ~ (subset(all_269_0, v1) = 0) | ~ $i(v0) | ? [v2: any] % 36.33/5.81 | : ? [v3: $i] : ? [v4: $i] : (relation_composition(empty_set, v0) = % 36.33/5.81 | v3 & relation_dom(v3) = v4 & relation(v0) = v2 & $i(v4) & $i(v3) & % 36.33/5.81 | ( ~ (v2 = 0) | v4 = empty_set))) % 36.33/5.81 | % 36.33/5.81 | DELTA: instantiating (38) with fresh symbols all_273_0, all_273_1 gives: % 36.33/5.81 | (62) relation_rng(empty_set) = all_273_0 & relation(empty_set) = all_273_1 % 36.33/5.81 | & $i(all_273_0) & ( ~ (all_273_1 = 0) | ! [v0: $i] : ! [v1: $i] : ! % 36.33/5.81 | [v2: any] : ( ~ (relation_dom(v0) = v1) | ~ (subset(empty_set, v1) % 36.33/5.81 | = v2) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ? [v5: $i] : % 36.33/5.81 | ? [v6: any] : (relation_rng(v0) = v5 & subset(all_273_0, v5) = v6 % 36.33/5.81 | & subset(empty_set, v0) = v4 & relation(v0) = v3 & $i(v5) & ( ~ % 36.33/5.81 | (v4 = 0) | ~ (v3 = 0) | (v6 = 0 & v2 = 0))))) % 36.33/5.81 | % 36.33/5.81 | ALPHA: (62) implies: % 36.33/5.81 | (63) relation(empty_set) = all_273_1 % 36.33/5.81 | (64) relation_rng(empty_set) = all_273_0 % 36.33/5.81 | % 36.33/5.81 | REDUCE: (12), (45) imply: % 36.33/5.81 | (65) empty(empty_set) = 0 % 36.33/5.81 | % 36.33/5.81 | REDUCE: (32), (45) imply: % 36.33/5.81 | (66) relation(empty_set) = 0 % 36.33/5.81 | % 36.33/5.81 | BETA: splitting (36) gives: % 36.33/5.81 | % 36.33/5.81 | Case 1: % 36.33/5.81 | | % 36.33/5.81 | | (67) all_189_0 = 0 % 36.33/5.81 | | % 36.33/5.81 | | REDUCE: (21), (67) imply: % 36.33/5.81 | | (68) $false % 36.33/5.81 | | % 36.33/5.81 | | CLOSE: (68) is inconsistent. % 36.33/5.81 | | % 36.33/5.81 | Case 2: % 36.33/5.81 | | % 36.33/5.81 | | (69) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & in(v0, all_189_1) = v1 & % 36.33/5.81 | | in(v0, all_189_2) = 0 & $i(v0)) % 36.33/5.81 | | % 36.33/5.81 | | DELTA: instantiating (69) with fresh symbols all_332_0, all_332_1 gives: % 36.33/5.81 | | (70) ~ (all_332_0 = 0) & in(all_332_1, all_189_1) = all_332_0 & % 36.33/5.81 | | in(all_332_1, all_189_2) = 0 & $i(all_332_1) % 36.33/5.81 | | % 36.33/5.81 | | ALPHA: (70) implies: % 36.33/5.81 | | (71) ~ (all_332_0 = 0) % 36.33/5.81 | | (72) $i(all_332_1) % 36.33/5.82 | | (73) in(all_332_1, all_189_2) = 0 % 36.33/5.82 | | (74) in(all_332_1, all_189_1) = all_332_0 % 36.33/5.82 | | % 36.33/5.82 | | BETA: splitting (35) gives: % 36.33/5.82 | | % 36.33/5.82 | | Case 1: % 36.33/5.82 | | | % 36.33/5.82 | | | (75) all_171_0 = 0 % 36.33/5.82 | | | % 36.33/5.82 | | | REDUCE: (17), (75) imply: % 36.33/5.82 | | | (76) $false % 36.33/5.82 | | | % 36.33/5.82 | | | CLOSE: (76) is inconsistent. % 36.33/5.82 | | | % 36.33/5.82 | | Case 2: % 36.33/5.82 | | | % 36.33/5.82 | | | (77) ? [v0: $i] : (powerset(all_171_1) = v0 & $i(v0) & ? [v1: $i] : % 36.33/5.82 | | | ? [v2: int] : ( ~ (v2 = 0) & element(v1, v0) = 0 & empty(v1) = % 36.33/5.82 | | | v2 & $i(v1))) % 36.33/5.82 | | | % 36.33/5.82 | | | DELTA: instantiating (77) with fresh symbol all_356_0 gives: % 36.33/5.82 | | | (78) powerset(all_171_1) = all_356_0 & $i(all_356_0) & ? [v0: $i] : ? % 36.33/5.82 | | | [v1: int] : ( ~ (v1 = 0) & element(v0, all_356_0) = 0 & empty(v0) % 36.33/5.82 | | | = v1 & $i(v0)) % 36.33/5.82 | | | % 36.33/5.82 | | | ALPHA: (78) implies: % 36.33/5.82 | | | (79) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & element(v0, all_356_0) % 36.33/5.82 | | | = 0 & empty(v0) = v1 & $i(v0)) % 36.33/5.82 | | | % 36.33/5.82 | | | DELTA: instantiating (79) with fresh symbols all_358_0, all_358_1 gives: % 36.33/5.82 | | | (80) ~ (all_358_0 = 0) & element(all_358_1, all_356_0) = 0 & % 36.33/5.82 | | | empty(all_358_1) = all_358_0 & $i(all_358_1) % 36.33/5.82 | | | % 36.33/5.82 | | | ALPHA: (80) implies: % 36.33/5.82 | | | (81) ~ (all_358_0 = 0) % 36.33/5.82 | | | (82) $i(all_358_1) % 36.33/5.82 | | | (83) empty(all_358_1) = all_358_0 % 36.33/5.82 | | | % 36.33/5.82 | | | GROUND_INST: instantiating (7) with 0, all_269_1, empty_set, simplifying % 36.33/5.82 | | | with (59), (66) gives: % 36.33/5.82 | | | (84) all_269_1 = 0 % 36.33/5.82 | | | % 36.33/5.82 | | | GROUND_INST: instantiating (7) with all_269_1, all_273_1, empty_set, % 36.33/5.82 | | | simplifying with (59), (63) gives: % 36.33/5.82 | | | (85) all_273_1 = all_269_1 % 36.33/5.82 | | | % 36.33/5.82 | | | GROUND_INST: instantiating (7) with all_267_1, all_273_1, empty_set, % 36.33/5.82 | | | simplifying with (56), (63) gives: % 36.33/5.82 | | | (86) all_273_1 = all_267_1 % 36.33/5.82 | | | % 36.33/5.82 | | | GROUND_INST: instantiating (7) with 0, all_265_1, all_189_4, simplifying % 36.33/5.82 | | | with (27), (53) gives: % 36.33/5.82 | | | (87) all_265_1 = 0 % 36.33/5.82 | | | % 36.33/5.82 | | | GROUND_INST: instantiating (7) with all_245_1, all_265_1, all_189_4, % 36.33/5.82 | | | simplifying with (47), (53) gives: % 36.33/5.82 | | | (88) all_265_1 = all_245_1 % 36.33/5.82 | | | % 36.33/5.82 | | | GROUND_INST: instantiating (7) with all_245_0, all_261_1, all_189_3, % 36.33/5.82 | | | simplifying with (48), (51) gives: % 36.33/5.82 | | | (89) all_261_1 = all_245_0 % 36.33/5.82 | | | % 36.33/5.82 | | | GROUND_INST: instantiating (8) with empty_set, all_269_0, empty_set, % 36.33/5.82 | | | simplifying with (4), (60) gives: % 36.33/5.82 | | | (90) all_269_0 = empty_set % 36.33/5.82 | | | % 36.33/5.82 | | | GROUND_INST: instantiating (8) with all_269_0, all_273_0, empty_set, % 36.33/5.82 | | | simplifying with (60), (64) gives: % 36.33/5.82 | | | (91) all_273_0 = all_269_0 % 36.33/5.82 | | | % 36.33/5.82 | | | GROUND_INST: instantiating (8) with all_267_0, all_273_0, empty_set, % 36.33/5.82 | | | simplifying with (57), (64) gives: % 36.33/5.82 | | | (92) all_273_0 = all_267_0 % 36.33/5.82 | | | % 36.33/5.82 | | | COMBINE_EQS: (91), (92) imply: % 36.33/5.82 | | | (93) all_269_0 = all_267_0 % 36.33/5.82 | | | % 36.33/5.82 | | | SIMP: (93) implies: % 36.33/5.82 | | | (94) all_269_0 = all_267_0 % 36.33/5.82 | | | % 36.33/5.82 | | | COMBINE_EQS: (85), (86) imply: % 36.33/5.82 | | | (95) all_269_1 = all_267_1 % 36.33/5.82 | | | % 36.33/5.82 | | | SIMP: (95) implies: % 36.33/5.82 | | | (96) all_269_1 = all_267_1 % 36.33/5.82 | | | % 36.33/5.82 | | | COMBINE_EQS: (90), (94) imply: % 36.33/5.82 | | | (97) all_267_0 = empty_set % 36.33/5.82 | | | % 36.33/5.82 | | | COMBINE_EQS: (84), (96) imply: % 36.33/5.82 | | | (98) all_267_1 = 0 % 36.33/5.82 | | | % 36.33/5.82 | | | COMBINE_EQS: (87), (88) imply: % 36.33/5.82 | | | (99) all_245_1 = 0 % 36.33/5.82 | | | % 36.33/5.82 | | | SIMP: (99) implies: % 36.33/5.82 | | | (100) all_245_1 = 0 % 36.33/5.82 | | | % 36.33/5.82 | | | BETA: splitting (49) gives: % 36.33/5.82 | | | % 36.33/5.82 | | | Case 1: % 36.33/5.82 | | | | % 36.33/5.82 | | | | (101) ~ (all_245_1 = 0) % 36.33/5.82 | | | | % 36.33/5.82 | | | | REDUCE: (100), (101) imply: % 36.33/5.82 | | | | (102) $false % 36.33/5.82 | | | | % 36.33/5.82 | | | | CLOSE: (102) is inconsistent. % 36.33/5.82 | | | | % 36.33/5.82 | | | Case 2: % 36.33/5.82 | | | | % 36.33/5.82 | | | | (103) all_245_0 = 0 % 36.33/5.82 | | | | % 36.33/5.82 | | | | REDUCE: (48), (103) imply: % 36.33/5.82 | | | | (104) relation(all_189_3) = 0 % 36.33/5.82 | | | | % 36.33/5.82 | | | | BETA: splitting (43) gives: % 36.33/5.82 | | | | % 36.33/5.82 | | | | Case 1: % 36.33/5.82 | | | | | % 36.33/5.82 | | | | | (105) ? [v0: int] : ( ~ (v0 = 0) & relation(all_189_3) = v0) % 36.33/5.82 | | | | | % 36.33/5.82 | | | | | BETA: splitting (61) gives: % 36.33/5.82 | | | | | % 36.33/5.82 | | | | | Case 1: % 36.33/5.82 | | | | | | % 36.33/5.82 | | | | | | (106) ~ (all_269_1 = 0) % 36.33/5.82 | | | | | | % 36.33/5.82 | | | | | | REDUCE: (84), (106) imply: % 36.33/5.82 | | | | | | (107) $false % 36.33/5.82 | | | | | | % 36.33/5.82 | | | | | | CLOSE: (107) is inconsistent. % 36.33/5.82 | | | | | | % 36.33/5.82 | | | | | Case 2: % 36.33/5.82 | | | | | | % 36.33/5.82 | | | | | | % 36.33/5.82 | | | | | | DELTA: instantiating (105) with fresh symbol all_403_0 gives: % 36.33/5.82 | | | | | | (108) ~ (all_403_0 = 0) & relation(all_189_3) = all_403_0 % 36.33/5.82 | | | | | | % 36.33/5.82 | | | | | | ALPHA: (108) implies: % 36.33/5.82 | | | | | | (109) ~ (all_403_0 = 0) % 36.33/5.82 | | | | | | (110) relation(all_189_3) = all_403_0 % 36.33/5.82 | | | | | | % 36.33/5.82 | | | | | | GROUND_INST: instantiating (7) with 0, all_403_0, all_189_3, % 36.33/5.82 | | | | | | simplifying with (104), (110) gives: % 36.33/5.82 | | | | | | (111) all_403_0 = 0 % 36.33/5.82 | | | | | | % 36.33/5.82 | | | | | | REDUCE: (109), (111) imply: % 36.33/5.82 | | | | | | (112) $false % 36.33/5.82 | | | | | | % 36.33/5.82 | | | | | | CLOSE: (112) is inconsistent. % 36.33/5.82 | | | | | | % 36.33/5.82 | | | | | End of split % 36.33/5.82 | | | | | % 36.33/5.82 | | | | Case 2: % 36.33/5.82 | | | | | % 36.33/5.83 | | | | | (113) ? [v0: any] : (v0 = all_189_2 | ~ $i(v0) | ? [v1: $i] : ? % 36.33/5.83 | | | | | [v2: any] : (in(v1, v0) = v2 & $i(v1) & ( ~ (v2 = 0) | ! % 36.33/5.83 | | | | | [v3: $i] : ! [v4: $i] : ( ~ (ordered_pair(v3, v1) = % 36.33/5.83 | | | | | v4) | ~ (in(v4, all_189_3) = 0) | ~ $i(v3))) & % 36.33/5.83 | | | | | (v2 = 0 | ? [v3: $i] : ? [v4: $i] : (ordered_pair(v3, % 36.33/5.83 | | | | | v1) = v4 & in(v4, all_189_3) = 0 & $i(v4) & % 36.33/5.83 | | | | | $i(v3))))) & ( ~ $i(all_189_2) | ( ! [v0: $i] : ! % 36.33/5.83 | | | | | [v1: int] : (v1 = 0 | ~ (in(v0, all_189_2) = v1) | ~ % 36.33/5.83 | | | | | $i(v0) | ! [v2: $i] : ! [v3: $i] : ( ~ % 36.33/5.83 | | | | | (ordered_pair(v2, v0) = v3) | ~ (in(v3, all_189_3) = % 36.33/5.83 | | | | | 0) | ~ $i(v2))) & ! [v0: $i] : ( ~ (in(v0, % 36.33/5.83 | | | | | all_189_2) = 0) | ~ $i(v0) | ? [v1: $i] : ? [v2: % 36.33/5.83 | | | | | $i] : (ordered_pair(v1, v0) = v2 & in(v2, all_189_3) % 36.33/5.83 | | | | | = 0 & $i(v2) & $i(v1))))) % 36.33/5.83 | | | | | % 36.33/5.83 | | | | | ALPHA: (113) implies: % 36.33/5.83 | | | | | (114) ~ $i(all_189_2) | ( ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ % 36.33/5.83 | | | | | (in(v0, all_189_2) = v1) | ~ $i(v0) | ! [v2: $i] : ! % 36.33/5.83 | | | | | [v3: $i] : ( ~ (ordered_pair(v2, v0) = v3) | ~ (in(v3, % 36.33/5.83 | | | | | all_189_3) = 0) | ~ $i(v2))) & ! [v0: $i] : ( ~ % 36.33/5.83 | | | | | (in(v0, all_189_2) = 0) | ~ $i(v0) | ? [v1: $i] : ? % 36.33/5.83 | | | | | [v2: $i] : (ordered_pair(v1, v0) = v2 & in(v2, all_189_3) % 36.33/5.83 | | | | | = 0 & $i(v2) & $i(v1)))) % 36.33/5.83 | | | | | % 36.33/5.83 | | | | | BETA: splitting (114) gives: % 36.33/5.83 | | | | | % 36.33/5.83 | | | | | Case 1: % 36.33/5.83 | | | | | | % 36.33/5.83 | | | | | | (115) ~ $i(all_189_2) % 36.33/5.83 | | | | | | % 36.33/5.83 | | | | | | PRED_UNIFY: (25), (115) imply: % 36.33/5.83 | | | | | | (116) $false % 36.33/5.83 | | | | | | % 36.33/5.83 | | | | | | CLOSE: (116) is inconsistent. % 36.33/5.83 | | | | | | % 36.33/5.83 | | | | | Case 2: % 36.33/5.83 | | | | | | % 36.33/5.83 | | | | | | % 36.33/5.83 | | | | | | GROUND_INST: instantiating (t115_relat_1) with all_332_1, all_189_5, % 36.33/5.83 | | | | | | all_189_4, all_189_3, all_189_2, 0, simplifying with % 36.33/5.83 | | | | | | (22), (23), (29), (31), (72), (73) gives: % 36.33/5.83 | | | | | | (117) ? [v0: any] : ? [v1: any] : ? [v2: $i] : ? [v3: any] : % 36.33/5.83 | | | | | | (relation_rng(all_189_4) = v2 & relation(all_189_4) = v0 & % 36.33/5.83 | | | | | | in(all_332_1, v2) = v3 & in(all_332_1, all_189_5) = v1 & % 36.33/5.83 | | | | | | $i(v2) & ( ~ (v0 = 0) | (v3 = 0 & v1 = 0))) % 36.33/5.83 | | | | | | % 36.33/5.83 | | | | | | GROUND_INST: instantiating (1) with empty_set, all_358_1, all_358_0, % 36.33/5.83 | | | | | | simplifying with (5), (65), (82), (83) gives: % 36.33/5.83 | | | | | | (118) ? [v0: any] : (element(all_358_1, empty_set) = v0 & ( ~ % 36.33/5.83 | | | | | | (v0 = 0) | all_358_0 = 0) & ( ~ (all_358_0 = 0) | v0 = % 36.33/5.83 | | | | | | 0)) % 36.33/5.83 | | | | | | % 36.33/5.83 | | | | | | DELTA: instantiating (118) with fresh symbol all_487_0 gives: % 36.33/5.83 | | | | | | (119) element(all_358_1, empty_set) = all_487_0 & ( ~ (all_487_0 % 36.33/5.83 | | | | | | = 0) | all_358_0 = 0) & ( ~ (all_358_0 = 0) | all_487_0 % 36.33/5.83 | | | | | | = 0) % 36.33/5.83 | | | | | | % 36.33/5.83 | | | | | | ALPHA: (119) implies: % 36.33/5.83 | | | | | | (120) ~ (all_487_0 = 0) | all_358_0 = 0 % 36.33/5.83 | | | | | | % 36.33/5.83 | | | | | | DELTA: instantiating (117) with fresh symbols all_511_0, all_511_1, % 36.33/5.83 | | | | | | all_511_2, all_511_3 gives: % 36.33/5.83 | | | | | | (121) relation_rng(all_189_4) = all_511_1 & relation(all_189_4) = % 36.33/5.83 | | | | | | all_511_3 & in(all_332_1, all_511_1) = all_511_0 & % 36.33/5.83 | | | | | | in(all_332_1, all_189_5) = all_511_2 & $i(all_511_1) & ( ~ % 36.33/5.83 | | | | | | (all_511_3 = 0) | (all_511_0 = 0 & all_511_2 = 0)) % 36.33/5.83 | | | | | | % 36.33/5.83 | | | | | | ALPHA: (121) implies: % 36.33/5.83 | | | | | | (122) in(all_332_1, all_511_1) = all_511_0 % 36.33/5.83 | | | | | | (123) relation(all_189_4) = all_511_3 % 36.33/5.83 | | | | | | (124) relation_rng(all_189_4) = all_511_1 % 36.33/5.83 | | | | | | (125) ~ (all_511_3 = 0) | (all_511_0 = 0 & all_511_2 = 0) % 36.33/5.83 | | | | | | % 36.33/5.83 | | | | | | BETA: splitting (120) gives: % 36.33/5.83 | | | | | | % 36.33/5.83 | | | | | | Case 1: % 36.33/5.83 | | | | | | | % 36.33/5.83 | | | | | | | % 36.33/5.83 | | | | | | | GROUND_INST: instantiating (7) with 0, all_511_3, all_189_4, % 36.33/5.83 | | | | | | | simplifying with (27), (123) gives: % 36.33/5.83 | | | | | | | (126) all_511_3 = 0 % 36.33/5.83 | | | | | | | % 36.33/5.83 | | | | | | | GROUND_INST: instantiating (8) with all_189_1, all_511_1, % 36.33/5.83 | | | | | | | all_189_4, simplifying with (30), (124) gives: % 36.33/5.83 | | | | | | | (127) all_511_1 = all_189_1 % 36.33/5.83 | | | | | | | % 36.33/5.83 | | | | | | | REDUCE: (122), (127) imply: % 36.33/5.83 | | | | | | | (128) in(all_332_1, all_189_1) = all_511_0 % 36.33/5.83 | | | | | | | % 36.33/5.83 | | | | | | | BETA: splitting (125) gives: % 36.33/5.83 | | | | | | | % 36.33/5.83 | | | | | | | Case 1: % 36.33/5.83 | | | | | | | | % 36.33/5.83 | | | | | | | | (129) ~ (all_511_3 = 0) % 36.33/5.83 | | | | | | | | % 36.33/5.83 | | | | | | | | REDUCE: (126), (129) imply: % 36.33/5.83 | | | | | | | | (130) $false % 36.33/5.83 | | | | | | | | % 36.33/5.83 | | | | | | | | CLOSE: (130) is inconsistent. % 36.33/5.83 | | | | | | | | % 36.33/5.83 | | | | | | | Case 2: % 36.33/5.83 | | | | | | | | % 36.33/5.83 | | | | | | | | (131) all_511_0 = 0 & all_511_2 = 0 % 36.33/5.83 | | | | | | | | % 36.33/5.83 | | | | | | | | ALPHA: (131) implies: % 36.33/5.83 | | | | | | | | (132) all_511_0 = 0 % 36.33/5.83 | | | | | | | | % 36.33/5.83 | | | | | | | | REDUCE: (128), (132) imply: % 36.33/5.83 | | | | | | | | (133) in(all_332_1, all_189_1) = 0 % 36.33/5.83 | | | | | | | | % 36.33/5.83 | | | | | | | | GROUND_INST: instantiating (9) with all_332_0, 0, all_189_1, % 36.33/5.83 | | | | | | | | all_332_1, simplifying with (74), (133) gives: % 36.33/5.83 | | | | | | | | (134) all_332_0 = 0 % 36.33/5.83 | | | | | | | | % 36.33/5.83 | | | | | | | | REDUCE: (71), (134) imply: % 36.33/5.83 | | | | | | | | (135) $false % 36.33/5.83 | | | | | | | | % 36.33/5.83 | | | | | | | | CLOSE: (135) is inconsistent. % 36.33/5.83 | | | | | | | | % 36.33/5.83 | | | | | | | End of split % 36.33/5.83 | | | | | | | % 36.33/5.83 | | | | | | Case 2: % 36.33/5.83 | | | | | | | % 36.33/5.83 | | | | | | | (136) all_358_0 = 0 % 36.33/5.83 | | | | | | | % 36.33/5.83 | | | | | | | REDUCE: (81), (136) imply: % 36.33/5.83 | | | | | | | (137) $false % 36.33/5.83 | | | | | | | % 36.33/5.83 | | | | | | | CLOSE: (137) is inconsistent. % 36.33/5.83 | | | | | | | % 36.33/5.83 | | | | | | End of split % 36.33/5.83 | | | | | | % 36.33/5.83 | | | | | End of split % 36.33/5.83 | | | | | % 36.33/5.83 | | | | End of split % 36.33/5.83 | | | | % 36.33/5.83 | | | End of split % 36.33/5.83 | | | % 36.33/5.83 | | End of split % 36.33/5.83 | | % 36.33/5.83 | End of split % 36.33/5.83 | % 36.33/5.83 End of proof % 36.33/5.83 % SZS output end Proof for theBenchmark % 36.33/5.83 % 36.33/5.83 5208ms %------------------------------------------------------------------------------