%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SEU198+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 : n020.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 300s % DateTime : Thu Aug 31 17:43:12 EDT 2023 % Result : Theorem 22.32s 4.05s % Output : Proof 33.98s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SEU198+2 : TPTP v8.1.2. Released v3.3.0. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.14/0.34 % Computer : n020.cluster.edu % 0.14/0.34 % Model : x86_64 x86_64 % 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.34 % Memory : 8042.1875MB % 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.34 % CPULimit : 300 % 0.14/0.34 % WCLimit : 300 % 0.14/0.34 % DateTime : Wed Aug 23 13:50:15 EDT 2023 % 0.14/0.34 % CPUTime : % 0.20/0.61 ________ _____ % 0.20/0.61 ___ __ \_________(_)________________________________ % 0.20/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.20/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.20/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.20/0.61 % 0.20/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.20/0.61 (2023-06-19) % 0.20/0.61 % 0.20/0.61 (c) Philipp Rümmer, 2009-2023 % 0.20/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.20/0.61 Amanda Stjerna. % 0.20/0.61 Free software under BSD-3-Clause. % 0.20/0.61 % 0.20/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.20/0.61 % 0.20/0.61 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.20/0.62 Running up to 7 provers in parallel. % 0.20/0.65 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.20/0.65 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.20/0.65 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.20/0.65 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.20/0.65 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.20/0.65 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.20/0.65 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 5.54/1.56 Prover 4: Preprocessing ... % 5.54/1.56 Prover 1: Preprocessing ... % 5.54/1.61 Prover 0: Preprocessing ... % 5.54/1.61 Prover 5: Preprocessing ... % 5.54/1.61 Prover 3: Preprocessing ... % 5.54/1.61 Prover 2: Preprocessing ... % 5.99/1.62 Prover 6: Preprocessing ... % 15.59/3.10 Prover 1: Warning: ignoring some quantifiers % 16.30/3.18 Prover 6: Proving ... % 16.68/3.20 Prover 3: Warning: ignoring some quantifiers % 16.68/3.23 Prover 3: Constructing countermodel ... % 16.68/3.24 Prover 1: Constructing countermodel ... % 16.68/3.25 Prover 5: Proving ... % 18.32/3.49 Prover 4: Warning: ignoring some quantifiers % 18.32/3.51 Prover 2: Proving ... % 19.06/3.60 Prover 4: Constructing countermodel ... % 20.14/3.73 Prover 0: Proving ... % 22.32/4.04 Prover 3: proved (3383ms) % 22.32/4.04 % 22.32/4.05 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 22.32/4.05 % 22.32/4.05 Prover 5: stopped % 22.32/4.05 Prover 0: stopped % 22.32/4.07 Prover 6: stopped % 22.32/4.08 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 22.32/4.08 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 22.32/4.08 Prover 2: stopped % 22.88/4.10 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 22.88/4.10 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 22.88/4.10 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 24.42/4.45 Prover 10: Preprocessing ... % 24.42/4.45 Prover 7: Preprocessing ... % 24.42/4.49 Prover 8: Preprocessing ... % 24.42/4.50 Prover 11: Preprocessing ... % 24.42/4.51 Prover 13: Preprocessing ... % 29.18/5.00 Prover 10: Warning: ignoring some quantifiers % 29.18/5.05 Prover 8: Warning: ignoring some quantifiers % 29.18/5.06 Prover 7: Warning: ignoring some quantifiers % 29.75/5.08 Prover 8: Constructing countermodel ... % 29.75/5.08 Prover 10: Constructing countermodel ... % 29.75/5.14 Prover 7: Constructing countermodel ... % 30.47/5.26 Prover 13: Warning: ignoring some quantifiers % 31.20/5.32 Prover 13: Constructing countermodel ... % 32.47/5.56 Prover 1: Found proof (size 120) % 32.47/5.56 Prover 1: proved (4921ms) % 32.47/5.56 Prover 13: stopped % 32.47/5.56 Prover 8: stopped % 32.47/5.56 Prover 4: stopped % 33.15/5.56 Prover 7: stopped % 33.15/5.56 Prover 10: stopped % 33.47/5.67 Prover 11: Warning: ignoring some quantifiers % 33.73/5.71 Prover 11: Constructing countermodel ... % 33.73/5.74 Prover 11: stopped % 33.73/5.74 % 33.73/5.74 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 33.73/5.74 % 33.73/5.75 % SZS output start Proof for theBenchmark % 33.73/5.76 Assumptions after simplification: % 33.73/5.76 --------------------------------- % 33.73/5.76 % 33.73/5.76 (cc1_relat_1) % 33.98/5.78 ! [v0: $i] : ( ~ (empty(v0) = 0) | ~ $i(v0) | relation(v0) = 0) % 33.98/5.78 % 33.98/5.78 (d2_subset_1) % 33.98/5.79 ! [v0: $i] : ! [v1: $i] : ! [v2: any] : ( ~ (element(v1, v0) = v2) | ~ % 33.98/5.79 $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : (empty(v0) = v3 & in(v1, % 33.98/5.79 v0) = v4 & (v3 = 0 | (( ~ (v4 = 0) | v2 = 0) & ( ~ (v2 = 0) | v4 = % 33.98/5.79 0))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: any] : ( ~ (empty(v1) = % 33.98/5.79 v2) | ~ (empty(v0) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : % 33.98/5.79 (element(v1, v0) = v3 & ( ~ (v3 = 0) | v2 = 0) & ( ~ (v2 = 0) | v3 = 0))) % 33.98/5.79 % 33.98/5.79 (d3_relat_1) % 33.98/5.79 ! [v0: $i] : ( ~ (relation(v0) = 0) | ~ $i(v0) | ! [v1: $i] : ( ~ % 33.98/5.79 (relation(v1) = 0) | ~ $i(v1) | ? [v2: any] : (subset(v0, v1) = v2 & ( ~ % 33.98/5.79 (v2 = 0) | ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ % 33.98/5.79 (ordered_pair(v3, v4) = v5) | ~ (in(v5, v0) = 0) | ~ $i(v4) | ~ % 33.98/5.79 $i(v3) | in(v5, v1) = 0)) & (v2 = 0 | ? [v3: $i] : ? [v4: $i] : ? % 33.98/5.79 [v5: $i] : ? [v6: int] : ( ~ (v6 = 0) & ordered_pair(v3, v4) = v5 & % 33.98/5.79 in(v5, v1) = v6 & in(v5, v0) = 0 & $i(v5) & $i(v4) & $i(v3)))))) % 33.98/5.79 % 33.98/5.79 (d3_tarski) % 33.98/5.79 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) = v2) % 33.98/5.79 | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & in(v3, % 33.98/5.79 v1) = v4 & in(v3, v0) = 0 & $i(v3))) & ! [v0: $i] : ! [v1: $i] : ( ~ % 33.98/5.79 (subset(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ! [v2: $i] : ( ~ (in(v2, v0) % 33.98/5.79 = 0) | ~ $i(v2) | in(v2, v1) = 0)) % 33.98/5.79 % 33.98/5.79 (dt_k8_relat_1) % 33.98/5.79 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (relation_rng_restriction(v0, % 33.98/5.79 v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : % 33.98/5.79 (relation(v2) = v4 & relation(v1) = v3 & ( ~ (v3 = 0) | v4 = 0))) % 33.98/5.79 % 33.98/5.79 (fc4_relat_1) % 33.98/5.79 empty(empty_set) = 0 & relation(empty_set) = 0 & $i(empty_set) % 33.98/5.79 % 33.98/5.79 (rc1_relat_1) % 33.98/5.79 ? [v0: $i] : (empty(v0) = 0 & relation(v0) = 0 & $i(v0)) % 33.98/5.79 % 33.98/5.79 (rc1_subset_1) % 33.98/5.80 ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (empty(v0) = v1) | ~ $i(v0) | ? % 33.98/5.80 [v2: $i] : (powerset(v0) = v2 & $i(v2) & ? [v3: $i] : ? [v4: int] : ( ~ % 33.98/5.80 (v4 = 0) & element(v3, v2) = 0 & empty(v3) = v4 & $i(v3)))) % 33.98/5.80 % 33.98/5.80 (rc1_xboole_0) % 33.98/5.80 ? [v0: $i] : (empty(v0) = 0 & $i(v0)) % 33.98/5.80 % 33.98/5.80 (rc2_relat_1) % 33.98/5.80 ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & empty(v0) = v1 & relation(v0) = 0 % 33.98/5.80 & $i(v0)) % 33.98/5.80 % 33.98/5.80 (t115_relat_1) % 33.98/5.80 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 33.98/5.80 any] : ( ~ (relation_rng(v3) = v4) | ~ (relation_rng_restriction(v1, v2) = % 33.98/5.80 v3) | ~ (in(v0, v4) = v5) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: % 33.98/5.80 any] : ? [v7: any] : ? [v8: $i] : ? [v9: any] : (relation_rng(v2) = v8 % 33.98/5.80 & relation(v2) = v6 & in(v0, v8) = v9 & in(v0, v1) = v7 & $i(v8) & ( ~ (v6 % 33.98/5.80 = 0) | (( ~ (v9 = 0) | ~ (v7 = 0) | v5 = 0) & ( ~ (v5 = 0) | (v9 = 0 % 33.98/5.80 & v7 = 0)))))) % 33.98/5.80 % 33.98/5.80 (t116_relat_1) % 33.98/5.80 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: int] : ( ~ (v4 % 33.98/5.80 = 0) & relation_rng(v2) = v3 & relation_rng_restriction(v0, v1) = v2 & % 33.98/5.80 subset(v3, v0) = v4 & relation(v1) = 0 & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 33.98/5.80 % 33.98/5.80 (t25_relat_1) % 33.98/5.80 ! [v0: $i] : ! [v1: $i] : ( ~ (relation_dom(v0) = v1) | ~ $i(v0) | ? [v2: % 33.98/5.80 any] : ? [v3: $i] : (relation_rng(v0) = v3 & relation(v0) = v2 & $i(v3) & % 33.98/5.80 ( ~ (v2 = 0) | ! [v4: $i] : ! [v5: $i] : ! [v6: any] : ( ~ % 33.98/5.80 (relation_dom(v4) = v5) | ~ (subset(v1, v5) = v6) | ~ $i(v4) | ? % 33.98/5.80 [v7: any] : ? [v8: any] : ? [v9: $i] : ? [v10: any] : % 33.98/5.80 (relation_rng(v4) = v9 & subset(v3, v9) = v10 & subset(v0, v4) = v8 & % 33.98/5.80 relation(v4) = v7 & $i(v9) & ( ~ (v8 = 0) | ~ (v7 = 0) | (v10 = 0 & % 33.98/5.80 v6 = 0))))))) % 33.98/5.80 % 33.98/5.80 (t46_relat_1) % 33.98/5.80 ! [v0: $i] : ! [v1: $i] : ( ~ (relation_dom(v0) = v1) | ~ $i(v0) | ? [v2: % 33.98/5.80 any] : ? [v3: $i] : (relation_rng(v0) = v3 & relation(v0) = v2 & $i(v3) & % 33.98/5.80 ( ~ (v2 = 0) | ! [v4: $i] : ! [v5: $i] : ( ~ (relation_dom(v4) = v5) | % 33.98/5.80 ~ (subset(v3, v5) = 0) | ~ $i(v4) | ? [v6: any] : ? [v7: $i] : ? % 33.98/5.80 [v8: $i] : (relation_composition(v0, v4) = v7 & relation_dom(v7) = v8 % 33.98/5.80 & relation(v4) = v6 & $i(v8) & $i(v7) & ( ~ (v6 = 0) | v8 = v1)))))) % 33.98/5.80 % 33.98/5.80 (t47_relat_1) % 33.98/5.80 ! [v0: $i] : ! [v1: $i] : ( ~ (relation_dom(v0) = v1) | ~ $i(v0) | ? [v2: % 33.98/5.80 any] : ? [v3: $i] : (relation_rng(v0) = v3 & relation(v0) = v2 & $i(v3) & % 33.98/5.80 ( ~ (v2 = 0) | ! [v4: $i] : ! [v5: $i] : ( ~ (relation_rng(v4) = v5) | % 33.98/5.80 ~ (subset(v1, v5) = 0) | ~ $i(v4) | ? [v6: any] : ? [v7: $i] : ? % 33.98/5.80 [v8: $i] : (relation_composition(v4, v0) = v7 & relation_rng(v7) = v8 % 33.98/5.80 & relation(v4) = v6 & $i(v8) & $i(v7) & ( ~ (v6 = 0) | v8 = v3)))))) % 33.98/5.80 % 33.98/5.80 (t60_relat_1) % 33.98/5.80 relation_rng(empty_set) = empty_set & relation_dom(empty_set) = empty_set & % 33.98/5.80 $i(empty_set) % 33.98/5.80 % 33.98/5.80 (t6_boole) % 33.98/5.81 $i(empty_set) & ! [v0: $i] : (v0 = empty_set | ~ (empty(v0) = 0) | ~ % 33.98/5.81 $i(v0)) % 33.98/5.81 % 33.98/5.81 (t8_boole) % 33.98/5.81 ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (empty(v1) = 0) | ~ (empty(v0) = 0) % 33.98/5.81 | ~ $i(v1) | ~ $i(v0)) % 33.98/5.81 % 33.98/5.81 (function-axioms) % 33.98/5.82 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 % 33.98/5.82 | ~ (subset_difference(v4, v3, v2) = v1) | ~ (subset_difference(v4, v3, % 33.98/5.82 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : % 33.98/5.82 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (are_equipotent(v3, v2) = v1) | ~ % 33.98/5.82 (are_equipotent(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 33.98/5.82 ! [v3: $i] : (v1 = v0 | ~ (meet_of_subsets(v3, v2) = v1) | ~ % 33.98/5.82 (meet_of_subsets(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 33.98/5.82 ! [v3: $i] : (v1 = v0 | ~ (union_of_subsets(v3, v2) = v1) | ~ % 33.98/5.82 (union_of_subsets(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 33.98/5.82 ! [v3: $i] : (v1 = v0 | ~ (complements_of_subsets(v3, v2) = v1) | ~ % 33.98/5.82 (complements_of_subsets(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 33.98/5.82 $i] : ! [v3: $i] : (v1 = v0 | ~ (relation_composition(v3, v2) = v1) | ~ % 33.98/5.82 (relation_composition(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 33.98/5.82 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (disjoint(v3, % 33.98/5.82 v2) = v1) | ~ (disjoint(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 33.98/5.82 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (subset_complement(v3, v2) = v1) | ~ % 33.98/5.82 (subset_complement(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 33.98/5.82 : ! [v3: $i] : (v1 = v0 | ~ (set_difference(v3, v2) = v1) | ~ % 33.98/5.82 (set_difference(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 33.98/5.82 ! [v3: $i] : (v1 = v0 | ~ (cartesian_product2(v3, v2) = v1) | ~ % 33.98/5.82 (cartesian_product2(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 33.98/5.82 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (element(v3, % 33.98/5.82 v2) = v1) | ~ (element(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 33.98/5.82 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (relation_rng_restriction(v3, v2) = v1) % 33.98/5.82 | ~ (relation_rng_restriction(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : % 33.98/5.82 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (relation_dom_restriction(v3, v2) = % 33.98/5.82 v1) | ~ (relation_dom_restriction(v3, v2) = v0)) & ! [v0: % 33.98/5.82 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 33.98/5.82 : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0: % 33.98/5.82 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 33.98/5.82 (ordered_pair(v3, v2) = v1) | ~ (ordered_pair(v3, v2) = v0)) & ! [v0: $i] % 33.98/5.82 : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 33.98/5.82 (set_intersection2(v3, v2) = v1) | ~ (set_intersection2(v3, v2) = v0)) & ! % 33.98/5.82 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 33.98/5.82 (set_union2(v3, v2) = v1) | ~ (set_union2(v3, v2) = v0)) & ! [v0: $i] : ! % 33.98/5.82 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (unordered_pair(v3, v2) = % 33.98/5.82 v1) | ~ (unordered_pair(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! % 33.98/5.82 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 33.98/5.82 (proper_subset(v3, v2) = v1) | ~ (proper_subset(v3, v2) = v0)) & ! [v0: % 33.98/5.82 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 33.98/5.82 : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) & ! [v0: $i] : ! % 33.98/5.82 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (relation_inverse(v2) = v1) | ~ % 33.98/5.82 (relation_inverse(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 % 33.98/5.82 = v0 | ~ (relation_field(v2) = v1) | ~ (relation_field(v2) = v0)) & ! % 33.98/5.82 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (relation_rng(v2) = v1) | % 33.98/5.82 ~ (relation_rng(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 % 33.98/5.82 = v0 | ~ (union(v2) = v1) | ~ (union(v2) = v0)) & ! [v0: $i] : ! [v1: % 33.98/5.82 $i] : ! [v2: $i] : (v1 = v0 | ~ (cast_to_subset(v2) = v1) | ~ % 33.98/5.82 (cast_to_subset(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = % 33.98/5.82 v0 | ~ (relation_dom(v2) = v1) | ~ (relation_dom(v2) = v0)) & ! [v0: $i] % 33.98/5.82 : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ % 33.98/5.82 (powerset(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | % 33.98/5.82 ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ! [v0: $i] : ! [v1: % 33.98/5.82 $i] : ! [v2: $i] : (v1 = v0 | ~ (set_meet(v2) = v1) | ~ (set_meet(v2) = % 33.98/5.82 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 33.98/5.82 (identity_relation(v2) = v1) | ~ (identity_relation(v2) = v0)) & ! [v0: % 33.98/5.82 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 33.98/5.82 ~ (empty(v2) = v1) | ~ (empty(v2) = v0)) & ! [v0: MultipleValueBool] : ! % 33.98/5.82 [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (relation(v2) = v1) | ~ % 33.98/5.82 (relation(v2) = v0)) % 33.98/5.82 % 33.98/5.82 Further assumptions not needed in the proof: % 33.98/5.82 -------------------------------------------- % 33.98/5.82 antisymmetry_r2_hidden, antisymmetry_r2_xboole_0, commutativity_k2_tarski, % 33.98/5.82 commutativity_k2_xboole_0, commutativity_k3_xboole_0, d10_relat_1, d10_xboole_0, % 33.98/5.82 d11_relat_1, d12_relat_1, d1_relat_1, d1_setfam_1, d1_tarski, d1_xboole_0, % 33.98/5.82 d1_zfmisc_1, d2_relat_1, d2_tarski, d2_xboole_0, d2_zfmisc_1, d3_xboole_0, % 33.98/5.82 d4_relat_1, d4_subset_1, d4_tarski, d4_xboole_0, d5_relat_1, d5_subset_1, % 33.98/5.82 d5_tarski, d6_relat_1, d7_relat_1, d7_xboole_0, d8_relat_1, d8_setfam_1, % 33.98/5.82 d8_xboole_0, dt_k1_relat_1, dt_k1_setfam_1, dt_k1_tarski, dt_k1_xboole_0, % 33.98/5.82 dt_k1_zfmisc_1, dt_k2_relat_1, dt_k2_subset_1, dt_k2_tarski, dt_k2_xboole_0, % 33.98/5.82 dt_k2_zfmisc_1, dt_k3_relat_1, dt_k3_subset_1, dt_k3_tarski, dt_k3_xboole_0, % 33.98/5.82 dt_k4_relat_1, dt_k4_tarski, dt_k4_xboole_0, dt_k5_relat_1, dt_k5_setfam_1, % 33.98/5.82 dt_k6_relat_1, dt_k6_setfam_1, dt_k6_subset_1, dt_k7_relat_1, dt_k7_setfam_1, % 33.98/5.82 dt_m1_subset_1, existence_m1_subset_1, fc10_relat_1, fc1_relat_1, fc1_subset_1, % 33.98/5.82 fc1_xboole_0, fc1_zfmisc_1, fc2_relat_1, fc2_subset_1, fc2_xboole_0, % 33.98/5.82 fc3_subset_1, fc3_xboole_0, fc4_subset_1, fc5_relat_1, fc6_relat_1, fc7_relat_1, % 33.98/5.82 fc8_relat_1, fc9_relat_1, idempotence_k2_xboole_0, idempotence_k3_xboole_0, % 33.98/5.82 involutiveness_k3_subset_1, involutiveness_k4_relat_1, % 33.98/5.82 involutiveness_k7_setfam_1, irreflexivity_r2_xboole_0, l1_zfmisc_1, % 33.98/5.82 l23_zfmisc_1, l25_zfmisc_1, l28_zfmisc_1, l2_zfmisc_1, l32_xboole_1, % 33.98/5.82 l3_subset_1, l3_zfmisc_1, l4_zfmisc_1, l50_zfmisc_1, l55_zfmisc_1, l71_subset_1, % 33.98/5.82 rc2_subset_1, rc2_xboole_0, redefinition_k5_setfam_1, redefinition_k6_setfam_1, % 33.98/5.82 redefinition_k6_subset_1, reflexivity_r1_tarski, symmetry_r1_xboole_0, % 33.98/5.82 t106_zfmisc_1, t10_zfmisc_1, t118_zfmisc_1, t119_zfmisc_1, t12_xboole_1, % 33.98/5.82 t136_zfmisc_1, t17_xboole_1, t19_xboole_1, t1_boole, t1_subset, t1_xboole_1, % 33.98/5.82 t1_zfmisc_1, t20_relat_1, t21_relat_1, t26_xboole_1, t28_xboole_1, t2_boole, % 33.98/5.82 t2_subset, t2_tarski, t2_xboole_1, t30_relat_1, t33_xboole_1, t33_zfmisc_1, % 33.98/5.82 t36_xboole_1, t37_relat_1, t37_xboole_1, t37_zfmisc_1, t38_zfmisc_1, % 33.98/5.82 t39_xboole_1, t39_zfmisc_1, t3_boole, t3_subset, t3_xboole_0, t3_xboole_1, % 33.98/5.82 t40_xboole_1, t43_subset_1, t44_relat_1, t45_relat_1, t45_xboole_1, % 33.98/5.82 t46_setfam_1, t46_zfmisc_1, t47_setfam_1, t48_setfam_1, t48_xboole_1, t4_boole, % 33.98/5.82 t4_subset, t4_xboole_0, t50_subset_1, t54_subset_1, t56_relat_1, t5_subset, % 33.98/5.82 t60_xboole_1, t63_xboole_1, t64_relat_1, t65_relat_1, t65_zfmisc_1, % 33.98/5.82 t69_enumset1, t6_zfmisc_1, t71_relat_1, t74_relat_1, t7_boole, t7_xboole_1, % 33.98/5.82 t83_xboole_1, t86_relat_1, t88_relat_1, t8_xboole_1, t8_zfmisc_1, t90_relat_1, % 33.98/5.82 t92_zfmisc_1, t94_relat_1, t99_relat_1, t99_zfmisc_1, t9_tarski, t9_zfmisc_1 % 33.98/5.82 % 33.98/5.82 Those formulas are unsatisfiable: % 33.98/5.82 --------------------------------- % 33.98/5.82 % 33.98/5.82 Begin of proof % 33.98/5.82 | % 33.98/5.82 | ALPHA: (d2_subset_1) implies: % 33.98/5.82 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: any] : ( ~ (empty(v1) = v2) | ~ % 33.98/5.82 | (empty(v0) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : (element(v1, % 33.98/5.82 | v0) = v3 & ( ~ (v3 = 0) | v2 = 0) & ( ~ (v2 = 0) | v3 = 0))) % 33.98/5.82 | % 33.98/5.82 | ALPHA: (d3_tarski) implies: % 33.98/5.82 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) % 33.98/5.82 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ % 33.98/5.82 | (v4 = 0) & in(v3, v1) = v4 & in(v3, v0) = 0 & $i(v3))) % 33.98/5.82 | % 33.98/5.82 | ALPHA: (fc4_relat_1) implies: % 33.98/5.82 | (3) relation(empty_set) = 0 % 33.98/5.82 | % 33.98/5.82 | ALPHA: (t60_relat_1) implies: % 33.98/5.82 | (4) relation_dom(empty_set) = empty_set % 33.98/5.82 | (5) relation_rng(empty_set) = empty_set % 33.98/5.82 | % 33.98/5.82 | ALPHA: (t6_boole) implies: % 33.98/5.82 | (6) $i(empty_set) % 33.98/5.82 | (7) ! [v0: $i] : (v0 = empty_set | ~ (empty(v0) = 0) | ~ $i(v0)) % 33.98/5.82 | % 33.98/5.82 | ALPHA: (function-axioms) implies: % 33.98/5.83 | (8) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 33.98/5.83 | (v1 = v0 | ~ (relation(v2) = v1) | ~ (relation(v2) = v0)) % 33.98/5.83 | (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 33.98/5.83 | (relation_rng(v2) = v1) | ~ (relation_rng(v2) = v0)) % 33.98/5.83 | (10) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 33.98/5.83 | : ! [v3: $i] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = % 33.98/5.83 | v0)) % 33.98/5.83 | (11) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 33.98/5.83 | : ! [v3: $i] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, % 33.98/5.83 | v2) = v0)) % 33.98/5.83 | % 33.98/5.83 | DELTA: instantiating (rc1_xboole_0) with fresh symbol all_162_0 gives: % 33.98/5.83 | (12) empty(all_162_0) = 0 & $i(all_162_0) % 33.98/5.83 | % 33.98/5.83 | ALPHA: (12) implies: % 33.98/5.83 | (13) $i(all_162_0) % 33.98/5.83 | (14) empty(all_162_0) = 0 % 33.98/5.83 | % 33.98/5.83 | DELTA: instantiating (rc1_relat_1) with fresh symbol all_167_0 gives: % 33.98/5.83 | (15) empty(all_167_0) = 0 & relation(all_167_0) = 0 & $i(all_167_0) % 33.98/5.83 | % 33.98/5.83 | ALPHA: (15) implies: % 33.98/5.83 | (16) $i(all_167_0) % 33.98/5.83 | (17) relation(all_167_0) = 0 % 33.98/5.83 | (18) empty(all_167_0) = 0 % 33.98/5.83 | % 33.98/5.83 | DELTA: instantiating (rc2_relat_1) with fresh symbols all_180_0, all_180_1 % 33.98/5.83 | gives: % 33.98/5.83 | (19) ~ (all_180_0 = 0) & empty(all_180_1) = all_180_0 & % 33.98/5.83 | relation(all_180_1) = 0 & $i(all_180_1) % 33.98/5.83 | % 33.98/5.83 | ALPHA: (19) implies: % 33.98/5.83 | (20) ~ (all_180_0 = 0) % 33.98/5.83 | (21) $i(all_180_1) % 33.98/5.83 | (22) empty(all_180_1) = all_180_0 % 33.98/5.83 | % 33.98/5.83 | DELTA: instantiating (t116_relat_1) with fresh symbols all_184_0, all_184_1, % 33.98/5.83 | all_184_2, all_184_3, all_184_4 gives: % 33.98/5.83 | (23) ~ (all_184_0 = 0) & relation_rng(all_184_2) = all_184_1 & % 33.98/5.83 | relation_rng_restriction(all_184_4, all_184_3) = all_184_2 & % 33.98/5.83 | subset(all_184_1, all_184_4) = all_184_0 & relation(all_184_3) = 0 & % 33.98/5.83 | $i(all_184_1) & $i(all_184_2) & $i(all_184_3) & $i(all_184_4) % 33.98/5.83 | % 33.98/5.83 | ALPHA: (23) implies: % 33.98/5.83 | (24) ~ (all_184_0 = 0) % 33.98/5.83 | (25) $i(all_184_4) % 33.98/5.83 | (26) $i(all_184_3) % 33.98/5.83 | (27) $i(all_184_1) % 33.98/5.83 | (28) relation(all_184_3) = 0 % 33.98/5.83 | (29) subset(all_184_1, all_184_4) = all_184_0 % 33.98/5.83 | (30) relation_rng_restriction(all_184_4, all_184_3) = all_184_2 % 33.98/5.83 | (31) relation_rng(all_184_2) = all_184_1 % 33.98/5.83 | % 33.98/5.83 | GROUND_INST: instantiating (d3_relat_1) with empty_set, simplifying with (3), % 33.98/5.83 | (6) gives: % 33.98/5.84 | (32) ! [v0: $i] : ( ~ (relation(v0) = 0) | ~ $i(v0) | ? [v1: any] : % 33.98/5.84 | (subset(empty_set, v0) = v1 & ( ~ (v1 = 0) | ! [v2: $i] : ! [v3: % 33.98/5.84 | $i] : ! [v4: $i] : ( ~ (ordered_pair(v2, v3) = v4) | ~ % 33.98/5.84 | (in(v4, empty_set) = 0) | ~ $i(v3) | ~ $i(v2) | in(v4, v0) = % 33.98/5.84 | 0)) & (v1 = 0 | ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? % 33.98/5.84 | [v5: int] : ( ~ (v5 = 0) & ordered_pair(v2, v3) = v4 & in(v4, % 33.98/5.84 | v0) = v5 & in(v4, empty_set) = 0 & $i(v4) & $i(v3) & % 33.98/5.84 | $i(v2))))) % 33.98/5.84 | % 33.98/5.84 | GROUND_INST: instantiating (d3_relat_1) with all_167_0, simplifying with (16), % 33.98/5.84 | (17) gives: % 33.98/5.84 | (33) ! [v0: $i] : ( ~ (relation(v0) = 0) | ~ $i(v0) | ? [v1: any] : % 33.98/5.84 | (subset(all_167_0, v0) = v1 & ( ~ (v1 = 0) | ! [v2: $i] : ! [v3: % 33.98/5.84 | $i] : ! [v4: $i] : ( ~ (ordered_pair(v2, v3) = v4) | ~ % 33.98/5.84 | (in(v4, all_167_0) = 0) | ~ $i(v3) | ~ $i(v2) | in(v4, v0) = % 33.98/5.84 | 0)) & (v1 = 0 | ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? % 33.98/5.84 | [v5: int] : ( ~ (v5 = 0) & ordered_pair(v2, v3) = v4 & in(v4, % 33.98/5.84 | v0) = v5 & in(v4, all_167_0) = 0 & $i(v4) & $i(v3) & % 33.98/5.84 | $i(v2))))) % 33.98/5.84 | % 33.98/5.84 | GROUND_INST: instantiating (cc1_relat_1) with all_162_0, simplifying with % 33.98/5.84 | (13), (14) gives: % 33.98/5.84 | (34) relation(all_162_0) = 0 % 33.98/5.84 | % 33.98/5.84 | GROUND_INST: instantiating (t8_boole) with all_162_0, all_167_0, simplifying % 33.98/5.84 | with (13), (14), (16), (18) gives: % 33.98/5.84 | (35) all_167_0 = all_162_0 % 33.98/5.84 | % 33.98/5.84 | GROUND_INST: instantiating (7) with all_167_0, simplifying with (16), (18) % 33.98/5.84 | gives: % 33.98/5.84 | (36) all_167_0 = empty_set % 33.98/5.84 | % 33.98/5.84 | GROUND_INST: instantiating (rc1_subset_1) with all_180_1, all_180_0, % 33.98/5.84 | simplifying with (21), (22) gives: % 33.98/5.84 | (37) all_180_0 = 0 | ? [v0: $i] : (powerset(all_180_1) = v0 & $i(v0) & ? % 33.98/5.84 | [v1: $i] : ? [v2: int] : ( ~ (v2 = 0) & element(v1, v0) = 0 & % 33.98/5.84 | empty(v1) = v2 & $i(v1))) % 33.98/5.84 | % 33.98/5.84 | GROUND_INST: instantiating (2) with all_184_1, all_184_4, all_184_0, % 33.98/5.84 | simplifying with (25), (27), (29) gives: % 33.98/5.84 | (38) all_184_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & in(v0, % 33.98/5.84 | all_184_1) = 0 & in(v0, all_184_4) = v1 & $i(v0)) % 33.98/5.84 | % 33.98/5.84 | GROUND_INST: instantiating (dt_k8_relat_1) with all_184_4, all_184_3, % 33.98/5.84 | all_184_2, simplifying with (25), (26), (30) gives: % 33.98/5.84 | (39) ? [v0: any] : ? [v1: any] : (relation(all_184_2) = v1 & % 33.98/5.84 | relation(all_184_3) = v0 & ( ~ (v0 = 0) | v1 = 0)) % 33.98/5.84 | % 33.98/5.84 | GROUND_INST: instantiating (t25_relat_1) with empty_set, empty_set, % 33.98/5.84 | simplifying with (4), (6) gives: % 33.98/5.84 | (40) ? [v0: any] : ? [v1: $i] : (relation_rng(empty_set) = v1 & % 33.98/5.84 | relation(empty_set) = v0 & $i(v1) & ( ~ (v0 = 0) | ! [v2: $i] : ! % 33.98/5.84 | [v3: $i] : ! [v4: any] : ( ~ (relation_dom(v2) = v3) | ~ % 33.98/5.84 | (subset(empty_set, v3) = v4) | ~ $i(v2) | ? [v5: any] : ? % 33.98/5.84 | [v6: any] : ? [v7: $i] : ? [v8: any] : (relation_rng(v2) = v7 % 33.98/5.84 | & subset(v1, v7) = v8 & subset(empty_set, v2) = v6 & % 33.98/5.84 | relation(v2) = v5 & $i(v7) & ( ~ (v6 = 0) | ~ (v5 = 0) | (v8 % 33.98/5.84 | = 0 & v4 = 0)))))) % 33.98/5.84 | % 33.98/5.84 | GROUND_INST: instantiating (t47_relat_1) with empty_set, empty_set, % 33.98/5.84 | simplifying with (4), (6) gives: % 33.98/5.84 | (41) ? [v0: any] : ? [v1: $i] : (relation_rng(empty_set) = v1 & % 33.98/5.84 | relation(empty_set) = v0 & $i(v1) & ( ~ (v0 = 0) | ! [v2: $i] : ! % 33.98/5.84 | [v3: $i] : ( ~ (relation_rng(v2) = v3) | ~ (subset(empty_set, v3) % 33.98/5.84 | = 0) | ~ $i(v2) | ? [v4: any] : ? [v5: $i] : ? [v6: $i] : % 33.98/5.84 | (relation_composition(v2, empty_set) = v5 & relation_rng(v5) = % 33.98/5.84 | v6 & relation(v2) = v4 & $i(v6) & $i(v5) & ( ~ (v4 = 0) | v6 = % 33.98/5.84 | v1))))) % 33.98/5.84 | % 33.98/5.84 | GROUND_INST: instantiating (t46_relat_1) with empty_set, empty_set, % 33.98/5.84 | simplifying with (4), (6) gives: % 33.98/5.85 | (42) ? [v0: any] : ? [v1: $i] : (relation_rng(empty_set) = v1 & % 33.98/5.85 | relation(empty_set) = v0 & $i(v1) & ( ~ (v0 = 0) | ! [v2: $i] : ! % 33.98/5.85 | [v3: $i] : ( ~ (relation_dom(v2) = v3) | ~ (subset(v1, v3) = 0) | % 33.98/5.85 | ~ $i(v2) | ? [v4: any] : ? [v5: $i] : ? [v6: $i] : % 33.98/5.85 | (relation_composition(empty_set, v2) = v5 & relation_dom(v5) = % 33.98/5.85 | v6 & relation(v2) = v4 & $i(v6) & $i(v5) & ( ~ (v4 = 0) | v6 = % 33.98/5.85 | empty_set))))) % 33.98/5.85 | % 33.98/5.85 | COMBINE_EQS: (35), (36) imply: % 33.98/5.85 | (43) all_162_0 = empty_set % 33.98/5.85 | % 33.98/5.85 | SIMP: (43) implies: % 33.98/5.85 | (44) all_162_0 = empty_set % 33.98/5.85 | % 33.98/5.85 | GROUND_INST: instantiating (32) with empty_set, simplifying with (3), (6) % 33.98/5.85 | gives: % 33.98/5.85 | (45) ? [v0: any] : (subset(empty_set, empty_set) = v0 & (v0 = 0 | ? [v1: % 33.98/5.85 | $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & % 33.98/5.85 | ordered_pair(v1, v2) = v3 & in(v3, empty_set) = v4 & in(v3, % 33.98/5.85 | empty_set) = 0 & $i(v3) & $i(v2) & $i(v1)))) % 33.98/5.85 | % 33.98/5.85 | GROUND_INST: instantiating (32) with all_167_0, simplifying with (16), (17) % 33.98/5.85 | gives: % 33.98/5.85 | (46) ? [v0: any] : (subset(empty_set, all_167_0) = v0 & ( ~ (v0 = 0) | ! % 33.98/5.85 | [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (ordered_pair(v1, v2) = % 33.98/5.85 | v3) | ~ (in(v3, empty_set) = 0) | ~ $i(v2) | ~ $i(v1) | % 33.98/5.85 | in(v3, all_167_0) = 0)) & (v0 = 0 | ? [v1: $i] : ? [v2: $i] : % 33.98/5.85 | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & ordered_pair(v1, v2) = % 33.98/5.85 | v3 & in(v3, all_167_0) = v4 & in(v3, empty_set) = 0 & $i(v3) & % 33.98/5.85 | $i(v2) & $i(v1)))) % 33.98/5.85 | % 33.98/5.85 | GROUND_INST: instantiating (33) with empty_set, simplifying with (3), (6) % 33.98/5.85 | gives: % 33.98/5.85 | (47) ? [v0: any] : (subset(all_167_0, empty_set) = v0 & ( ~ (v0 = 0) | ! % 33.98/5.85 | [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (ordered_pair(v1, v2) = % 33.98/5.85 | v3) | ~ (in(v3, all_167_0) = 0) | ~ $i(v2) | ~ $i(v1) | % 33.98/5.85 | in(v3, empty_set) = 0)) & (v0 = 0 | ? [v1: $i] : ? [v2: $i] : % 33.98/5.85 | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & ordered_pair(v1, v2) = % 33.98/5.85 | v3 & in(v3, all_167_0) = 0 & in(v3, empty_set) = v4 & $i(v3) & % 33.98/5.85 | $i(v2) & $i(v1)))) % 33.98/5.85 | % 33.98/5.85 | DELTA: instantiating (39) with fresh symbols all_243_0, all_243_1 gives: % 33.98/5.85 | (48) relation(all_184_2) = all_243_0 & relation(all_184_3) = all_243_1 & ( % 33.98/5.85 | ~ (all_243_1 = 0) | all_243_0 = 0) % 33.98/5.85 | % 33.98/5.85 | ALPHA: (48) implies: % 33.98/5.85 | (49) relation(all_184_3) = all_243_1 % 33.98/5.85 | % 33.98/5.85 | DELTA: instantiating (41) with fresh symbols all_261_0, all_261_1 gives: % 33.98/5.85 | (50) relation_rng(empty_set) = all_261_0 & relation(empty_set) = all_261_1 % 33.98/5.85 | & $i(all_261_0) & ( ~ (all_261_1 = 0) | ! [v0: $i] : ! [v1: $i] : ( % 33.98/5.85 | ~ (relation_rng(v0) = v1) | ~ (subset(empty_set, v1) = 0) | ~ % 33.98/5.85 | $i(v0) | ? [v2: any] : ? [v3: $i] : ? [v4: $i] : % 33.98/5.85 | (relation_composition(v0, empty_set) = v3 & relation_rng(v3) = v4 % 33.98/5.85 | & relation(v0) = v2 & $i(v4) & $i(v3) & ( ~ (v2 = 0) | v4 = % 33.98/5.85 | all_261_0)))) % 33.98/5.85 | % 33.98/5.85 | ALPHA: (50) implies: % 33.98/5.85 | (51) $i(all_261_0) % 33.98/5.85 | (52) relation(empty_set) = all_261_1 % 33.98/5.85 | (53) relation_rng(empty_set) = all_261_0 % 33.98/5.85 | (54) ~ (all_261_1 = 0) | ! [v0: $i] : ! [v1: $i] : ( ~ (relation_rng(v0) % 33.98/5.85 | = v1) | ~ (subset(empty_set, v1) = 0) | ~ $i(v0) | ? [v2: any] % 33.98/5.85 | : ? [v3: $i] : ? [v4: $i] : (relation_composition(v0, empty_set) = % 33.98/5.85 | v3 & relation_rng(v3) = v4 & relation(v0) = v2 & $i(v4) & $i(v3) & % 33.98/5.85 | ( ~ (v2 = 0) | v4 = all_261_0))) % 33.98/5.85 | % 33.98/5.85 | DELTA: instantiating (42) with fresh symbols all_263_0, all_263_1 gives: % 33.98/5.85 | (55) relation_rng(empty_set) = all_263_0 & relation(empty_set) = all_263_1 % 33.98/5.85 | & $i(all_263_0) & ( ~ (all_263_1 = 0) | ! [v0: $i] : ! [v1: $i] : ( % 33.98/5.85 | ~ (relation_dom(v0) = v1) | ~ (subset(all_263_0, v1) = 0) | ~ % 33.98/5.85 | $i(v0) | ? [v2: any] : ? [v3: $i] : ? [v4: $i] : % 33.98/5.85 | (relation_composition(empty_set, v0) = v3 & relation_dom(v3) = v4 % 33.98/5.85 | & relation(v0) = v2 & $i(v4) & $i(v3) & ( ~ (v2 = 0) | v4 = % 33.98/5.85 | empty_set)))) % 33.98/5.85 | % 33.98/5.85 | ALPHA: (55) implies: % 33.98/5.85 | (56) relation(empty_set) = all_263_1 % 33.98/5.85 | (57) relation_rng(empty_set) = all_263_0 % 33.98/5.85 | % 33.98/5.85 | DELTA: instantiating (40) with fresh symbols all_265_0, all_265_1 gives: % 33.98/5.86 | (58) relation_rng(empty_set) = all_265_0 & relation(empty_set) = all_265_1 % 33.98/5.86 | & $i(all_265_0) & ( ~ (all_265_1 = 0) | ! [v0: $i] : ! [v1: $i] : ! % 33.98/5.86 | [v2: any] : ( ~ (relation_dom(v0) = v1) | ~ (subset(empty_set, v1) % 33.98/5.86 | = v2) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ? [v5: $i] : % 33.98/5.86 | ? [v6: any] : (relation_rng(v0) = v5 & subset(all_265_0, v5) = v6 % 33.98/5.86 | & subset(empty_set, v0) = v4 & relation(v0) = v3 & $i(v5) & ( ~ % 33.98/5.86 | (v4 = 0) | ~ (v3 = 0) | (v6 = 0 & v2 = 0))))) % 33.98/5.86 | % 33.98/5.86 | ALPHA: (58) implies: % 33.98/5.86 | (59) relation(empty_set) = all_265_1 % 33.98/5.86 | (60) relation_rng(empty_set) = all_265_0 % 33.98/5.86 | % 33.98/5.86 | DELTA: instantiating (45) with fresh symbol all_273_0 gives: % 33.98/5.86 | (61) subset(empty_set, empty_set) = all_273_0 & (all_273_0 = 0 | ? [v0: % 33.98/5.86 | $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) & % 33.98/5.86 | ordered_pair(v0, v1) = v2 & in(v2, empty_set) = v3 & in(v2, % 33.98/5.86 | empty_set) = 0 & $i(v2) & $i(v1) & $i(v0))) % 33.98/5.86 | % 33.98/5.86 | ALPHA: (61) implies: % 33.98/5.86 | (62) subset(empty_set, empty_set) = all_273_0 % 33.98/5.86 | (63) all_273_0 = 0 | ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: int] % 33.98/5.86 | : ( ~ (v3 = 0) & ordered_pair(v0, v1) = v2 & in(v2, empty_set) = v3 & % 33.98/5.86 | in(v2, empty_set) = 0 & $i(v2) & $i(v1) & $i(v0)) % 33.98/5.86 | % 33.98/5.86 | DELTA: instantiating (46) with fresh symbol all_279_0 gives: % 33.98/5.86 | (64) subset(empty_set, all_167_0) = all_279_0 & ( ~ (all_279_0 = 0) | ! % 33.98/5.86 | [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (ordered_pair(v0, v1) = % 33.98/5.86 | v2) | ~ (in(v2, empty_set) = 0) | ~ $i(v1) | ~ $i(v0) | % 33.98/5.86 | in(v2, all_167_0) = 0)) & (all_279_0 = 0 | ? [v0: $i] : ? [v1: % 33.98/5.86 | $i] : ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) & ordered_pair(v0, % 33.98/5.86 | v1) = v2 & in(v2, all_167_0) = v3 & in(v2, empty_set) = 0 & % 33.98/5.86 | $i(v2) & $i(v1) & $i(v0))) % 33.98/5.86 | % 33.98/5.86 | ALPHA: (64) implies: % 33.98/5.86 | (65) subset(empty_set, all_167_0) = all_279_0 % 33.98/5.86 | % 33.98/5.86 | DELTA: instantiating (47) with fresh symbol all_285_0 gives: % 33.98/5.86 | (66) subset(all_167_0, empty_set) = all_285_0 & ( ~ (all_285_0 = 0) | ! % 33.98/5.86 | [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (ordered_pair(v0, v1) = % 33.98/5.86 | v2) | ~ (in(v2, all_167_0) = 0) | ~ $i(v1) | ~ $i(v0) | % 33.98/5.86 | in(v2, empty_set) = 0)) & (all_285_0 = 0 | ? [v0: $i] : ? [v1: % 33.98/5.86 | $i] : ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) & ordered_pair(v0, % 33.98/5.86 | v1) = v2 & in(v2, all_167_0) = 0 & in(v2, empty_set) = v3 & % 33.98/5.86 | $i(v2) & $i(v1) & $i(v0))) % 33.98/5.86 | % 33.98/5.86 | ALPHA: (66) implies: % 33.98/5.86 | (67) subset(all_167_0, empty_set) = all_285_0 % 33.98/5.86 | (68) all_285_0 = 0 | ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: int] % 33.98/5.86 | : ( ~ (v3 = 0) & ordered_pair(v0, v1) = v2 & in(v2, all_167_0) = 0 & % 33.98/5.86 | in(v2, empty_set) = v3 & $i(v2) & $i(v1) & $i(v0)) % 33.98/5.86 | % 33.98/5.86 | REDUCE: (36), (67) imply: % 33.98/5.86 | (69) subset(empty_set, empty_set) = all_285_0 % 33.98/5.86 | % 33.98/5.86 | REDUCE: (36), (65) imply: % 33.98/5.86 | (70) subset(empty_set, empty_set) = all_279_0 % 33.98/5.86 | % 33.98/5.86 | REDUCE: (14), (44) imply: % 33.98/5.86 | (71) empty(empty_set) = 0 % 33.98/5.86 | % 33.98/5.86 | BETA: splitting (68) gives: % 33.98/5.86 | % 33.98/5.86 | Case 1: % 33.98/5.86 | | % 33.98/5.86 | | (72) all_285_0 = 0 % 33.98/5.86 | | % 33.98/5.86 | | REDUCE: (69), (72) imply: % 33.98/5.86 | | (73) subset(empty_set, empty_set) = 0 % 33.98/5.86 | | % 33.98/5.86 | | BETA: splitting (38) gives: % 33.98/5.86 | | % 33.98/5.86 | | Case 1: % 33.98/5.86 | | | % 33.98/5.86 | | | (74) all_184_0 = 0 % 33.98/5.86 | | | % 33.98/5.86 | | | REDUCE: (24), (74) imply: % 33.98/5.86 | | | (75) $false % 33.98/5.86 | | | % 33.98/5.86 | | | CLOSE: (75) is inconsistent. % 33.98/5.86 | | | % 33.98/5.86 | | Case 2: % 33.98/5.86 | | | % 33.98/5.86 | | | (76) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & in(v0, all_184_1) = 0 % 33.98/5.86 | | | & in(v0, all_184_4) = v1 & $i(v0)) % 33.98/5.86 | | | % 33.98/5.86 | | | DELTA: instantiating (76) with fresh symbols all_314_0, all_314_1 gives: % 33.98/5.87 | | | (77) ~ (all_314_0 = 0) & in(all_314_1, all_184_1) = 0 & in(all_314_1, % 33.98/5.87 | | | all_184_4) = all_314_0 & $i(all_314_1) % 33.98/5.87 | | | % 33.98/5.87 | | | ALPHA: (77) implies: % 33.98/5.87 | | | (78) ~ (all_314_0 = 0) % 33.98/5.87 | | | (79) $i(all_314_1) % 33.98/5.87 | | | (80) in(all_314_1, all_184_4) = all_314_0 % 33.98/5.87 | | | (81) in(all_314_1, all_184_1) = 0 % 33.98/5.87 | | | % 33.98/5.87 | | | BETA: splitting (37) gives: % 33.98/5.87 | | | % 33.98/5.87 | | | Case 1: % 33.98/5.87 | | | | % 33.98/5.87 | | | | (82) all_180_0 = 0 % 33.98/5.87 | | | | % 33.98/5.87 | | | | REDUCE: (20), (82) imply: % 33.98/5.87 | | | | (83) $false % 33.98/5.87 | | | | % 33.98/5.87 | | | | CLOSE: (83) is inconsistent. % 33.98/5.87 | | | | % 33.98/5.87 | | | Case 2: % 33.98/5.87 | | | | % 33.98/5.87 | | | | (84) ? [v0: $i] : (powerset(all_180_1) = v0 & $i(v0) & ? [v1: $i] : % 33.98/5.87 | | | | ? [v2: int] : ( ~ (v2 = 0) & element(v1, v0) = 0 & empty(v1) % 33.98/5.87 | | | | = v2 & $i(v1))) % 33.98/5.87 | | | | % 33.98/5.87 | | | | DELTA: instantiating (84) with fresh symbol all_327_0 gives: % 33.98/5.87 | | | | (85) powerset(all_180_1) = all_327_0 & $i(all_327_0) & ? [v0: $i] : % 33.98/5.87 | | | | ? [v1: int] : ( ~ (v1 = 0) & element(v0, all_327_0) = 0 & % 33.98/5.87 | | | | empty(v0) = v1 & $i(v0)) % 33.98/5.87 | | | | % 33.98/5.87 | | | | ALPHA: (85) implies: % 33.98/5.87 | | | | (86) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & element(v0, % 33.98/5.87 | | | | all_327_0) = 0 & empty(v0) = v1 & $i(v0)) % 33.98/5.87 | | | | % 33.98/5.87 | | | | DELTA: instantiating (86) with fresh symbols all_329_0, all_329_1 gives: % 33.98/5.87 | | | | (87) ~ (all_329_0 = 0) & element(all_329_1, all_327_0) = 0 & % 33.98/5.87 | | | | empty(all_329_1) = all_329_0 & $i(all_329_1) % 33.98/5.87 | | | | % 33.98/5.87 | | | | ALPHA: (87) implies: % 33.98/5.87 | | | | (88) ~ (all_329_0 = 0) % 33.98/5.87 | | | | (89) $i(all_329_1) % 33.98/5.87 | | | | (90) empty(all_329_1) = all_329_0 % 33.98/5.87 | | | | % 33.98/5.87 | | | | BETA: splitting (63) gives: % 33.98/5.87 | | | | % 33.98/5.87 | | | | Case 1: % 33.98/5.87 | | | | | % 33.98/5.87 | | | | | % 33.98/5.87 | | | | | GROUND_INST: instantiating (8) with 0, all_265_1, empty_set, % 33.98/5.87 | | | | | simplifying with (3), (59) gives: % 33.98/5.87 | | | | | (91) all_265_1 = 0 % 33.98/5.87 | | | | | % 33.98/5.87 | | | | | GROUND_INST: instantiating (8) with all_263_1, all_265_1, empty_set, % 33.98/5.87 | | | | | simplifying with (56), (59) gives: % 33.98/5.87 | | | | | (92) all_265_1 = all_263_1 % 33.98/5.87 | | | | | % 33.98/5.87 | | | | | GROUND_INST: instantiating (8) with all_261_1, all_265_1, empty_set, % 33.98/5.87 | | | | | simplifying with (52), (59) gives: % 33.98/5.87 | | | | | (93) all_265_1 = all_261_1 % 33.98/5.87 | | | | | % 33.98/5.87 | | | | | GROUND_INST: instantiating (8) with 0, all_243_1, all_184_3, % 33.98/5.87 | | | | | simplifying with (28), (49) gives: % 33.98/5.87 | | | | | (94) all_243_1 = 0 % 33.98/5.87 | | | | | % 33.98/5.87 | | | | | GROUND_INST: instantiating (9) with empty_set, all_263_0, empty_set, % 33.98/5.87 | | | | | simplifying with (5), (57) gives: % 33.98/5.87 | | | | | (95) all_263_0 = empty_set % 33.98/5.87 | | | | | % 33.98/5.87 | | | | | GROUND_INST: instantiating (9) with all_263_0, all_265_0, empty_set, % 33.98/5.87 | | | | | simplifying with (57), (60) gives: % 33.98/5.87 | | | | | (96) all_265_0 = all_263_0 % 33.98/5.87 | | | | | % 33.98/5.87 | | | | | GROUND_INST: instantiating (9) with all_261_0, all_265_0, empty_set, % 33.98/5.87 | | | | | simplifying with (53), (60) gives: % 33.98/5.87 | | | | | (97) all_265_0 = all_261_0 % 33.98/5.87 | | | | | % 33.98/5.87 | | | | | COMBINE_EQS: (96), (97) imply: % 33.98/5.87 | | | | | (98) all_263_0 = all_261_0 % 33.98/5.87 | | | | | % 33.98/5.87 | | | | | SIMP: (98) implies: % 33.98/5.87 | | | | | (99) all_263_0 = all_261_0 % 33.98/5.87 | | | | | % 33.98/5.87 | | | | | COMBINE_EQS: (92), (93) imply: % 33.98/5.87 | | | | | (100) all_263_1 = all_261_1 % 33.98/5.87 | | | | | % 33.98/5.87 | | | | | COMBINE_EQS: (91), (92) imply: % 33.98/5.87 | | | | | (101) all_263_1 = 0 % 33.98/5.87 | | | | | % 33.98/5.87 | | | | | COMBINE_EQS: (95), (99) imply: % 33.98/5.87 | | | | | (102) all_261_0 = empty_set % 33.98/5.87 | | | | | % 33.98/5.87 | | | | | SIMP: (102) implies: % 33.98/5.87 | | | | | (103) all_261_0 = empty_set % 33.98/5.87 | | | | | % 33.98/5.87 | | | | | COMBINE_EQS: (100), (101) imply: % 33.98/5.87 | | | | | (104) all_261_1 = 0 % 33.98/5.87 | | | | | % 33.98/5.87 | | | | | BETA: splitting (54) gives: % 33.98/5.87 | | | | | % 33.98/5.87 | | | | | Case 1: % 33.98/5.87 | | | | | | % 33.98/5.87 | | | | | | (105) ~ (all_261_1 = 0) % 33.98/5.87 | | | | | | % 33.98/5.87 | | | | | | REDUCE: (104), (105) imply: % 33.98/5.87 | | | | | | (106) $false % 33.98/5.87 | | | | | | % 33.98/5.87 | | | | | | CLOSE: (106) is inconsistent. % 33.98/5.87 | | | | | | % 33.98/5.87 | | | | | Case 2: % 33.98/5.87 | | | | | | % 33.98/5.87 | | | | | | % 33.98/5.87 | | | | | | GROUND_INST: instantiating (t115_relat_1) with all_314_1, all_184_4, % 33.98/5.87 | | | | | | all_184_3, all_184_2, all_184_1, 0, simplifying with % 33.98/5.87 | | | | | | (25), (26), (30), (31), (79), (81) gives: % 33.98/5.87 | | | | | | (107) ? [v0: any] : ? [v1: any] : ? [v2: $i] : ? [v3: any] : % 33.98/5.87 | | | | | | (relation_rng(all_184_3) = v2 & relation(all_184_3) = v0 & % 33.98/5.87 | | | | | | in(all_314_1, v2) = v3 & in(all_314_1, all_184_4) = v1 & % 33.98/5.87 | | | | | | $i(v2) & ( ~ (v0 = 0) | (v3 = 0 & v1 = 0))) % 33.98/5.87 | | | | | | % 33.98/5.87 | | | | | | GROUND_INST: instantiating (1) with empty_set, all_329_1, all_329_0, % 33.98/5.87 | | | | | | simplifying with (6), (71), (89), (90) gives: % 33.98/5.87 | | | | | | (108) ? [v0: any] : (element(all_329_1, empty_set) = v0 & ( ~ % 33.98/5.87 | | | | | | (v0 = 0) | all_329_0 = 0) & ( ~ (all_329_0 = 0) | v0 = % 33.98/5.87 | | | | | | 0)) % 33.98/5.87 | | | | | | % 33.98/5.87 | | | | | | DELTA: instantiating (108) with fresh symbol all_481_0 gives: % 33.98/5.87 | | | | | | (109) element(all_329_1, empty_set) = all_481_0 & ( ~ (all_481_0 % 33.98/5.87 | | | | | | = 0) | all_329_0 = 0) & ( ~ (all_329_0 = 0) | all_481_0 % 33.98/5.87 | | | | | | = 0) % 33.98/5.87 | | | | | | % 33.98/5.87 | | | | | | ALPHA: (109) implies: % 33.98/5.87 | | | | | | (110) ~ (all_481_0 = 0) | all_329_0 = 0 % 33.98/5.87 | | | | | | % 33.98/5.87 | | | | | | DELTA: instantiating (107) with fresh symbols all_491_0, all_491_1, % 33.98/5.87 | | | | | | all_491_2, all_491_3 gives: % 33.98/5.87 | | | | | | (111) relation_rng(all_184_3) = all_491_1 & relation(all_184_3) = % 33.98/5.87 | | | | | | all_491_3 & in(all_314_1, all_491_1) = all_491_0 & % 33.98/5.87 | | | | | | in(all_314_1, all_184_4) = all_491_2 & $i(all_491_1) & ( ~ % 33.98/5.87 | | | | | | (all_491_3 = 0) | (all_491_0 = 0 & all_491_2 = 0)) % 33.98/5.87 | | | | | | % 33.98/5.87 | | | | | | ALPHA: (111) implies: % 33.98/5.87 | | | | | | (112) in(all_314_1, all_184_4) = all_491_2 % 33.98/5.87 | | | | | | (113) relation(all_184_3) = all_491_3 % 33.98/5.88 | | | | | | (114) ~ (all_491_3 = 0) | (all_491_0 = 0 & all_491_2 = 0) % 33.98/5.88 | | | | | | % 33.98/5.88 | | | | | | BETA: splitting (110) gives: % 33.98/5.88 | | | | | | % 33.98/5.88 | | | | | | Case 1: % 33.98/5.88 | | | | | | | % 33.98/5.88 | | | | | | | % 33.98/5.88 | | | | | | | GROUND_INST: instantiating (10) with all_314_0, all_491_2, % 33.98/5.88 | | | | | | | all_184_4, all_314_1, simplifying with (80), (112) % 33.98/5.88 | | | | | | | gives: % 33.98/5.88 | | | | | | | (115) all_491_2 = all_314_0 % 33.98/5.88 | | | | | | | % 33.98/5.88 | | | | | | | GROUND_INST: instantiating (8) with 0, all_491_3, all_184_3, % 33.98/5.88 | | | | | | | simplifying with (28), (113) gives: % 33.98/5.88 | | | | | | | (116) all_491_3 = 0 % 33.98/5.88 | | | | | | | % 33.98/5.88 | | | | | | | BETA: splitting (114) gives: % 33.98/5.88 | | | | | | | % 33.98/5.88 | | | | | | | Case 1: % 33.98/5.88 | | | | | | | | % 33.98/5.88 | | | | | | | | (117) ~ (all_491_3 = 0) % 33.98/5.88 | | | | | | | | % 33.98/5.88 | | | | | | | | REDUCE: (116), (117) imply: % 33.98/5.88 | | | | | | | | (118) $false % 33.98/5.88 | | | | | | | | % 33.98/5.88 | | | | | | | | CLOSE: (118) is inconsistent. % 33.98/5.88 | | | | | | | | % 33.98/5.88 | | | | | | | Case 2: % 33.98/5.88 | | | | | | | | % 33.98/5.88 | | | | | | | | (119) all_491_0 = 0 & all_491_2 = 0 % 33.98/5.88 | | | | | | | | % 33.98/5.88 | | | | | | | | ALPHA: (119) implies: % 33.98/5.88 | | | | | | | | (120) all_491_2 = 0 % 33.98/5.88 | | | | | | | | % 33.98/5.88 | | | | | | | | COMBINE_EQS: (115), (120) imply: % 33.98/5.88 | | | | | | | | (121) all_314_0 = 0 % 33.98/5.88 | | | | | | | | % 33.98/5.88 | | | | | | | | REDUCE: (78), (121) imply: % 33.98/5.88 | | | | | | | | (122) $false % 33.98/5.88 | | | | | | | | % 33.98/5.88 | | | | | | | | CLOSE: (122) is inconsistent. % 33.98/5.88 | | | | | | | | % 33.98/5.88 | | | | | | | End of split % 33.98/5.88 | | | | | | | % 33.98/5.88 | | | | | | Case 2: % 33.98/5.88 | | | | | | | % 33.98/5.88 | | | | | | | (123) all_329_0 = 0 % 33.98/5.88 | | | | | | | % 33.98/5.88 | | | | | | | REDUCE: (88), (123) imply: % 33.98/5.88 | | | | | | | (124) $false % 33.98/5.88 | | | | | | | % 33.98/5.88 | | | | | | | CLOSE: (124) is inconsistent. % 33.98/5.88 | | | | | | | % 33.98/5.88 | | | | | | End of split % 33.98/5.88 | | | | | | % 33.98/5.88 | | | | | End of split % 33.98/5.88 | | | | | % 33.98/5.88 | | | | Case 2: % 33.98/5.88 | | | | | % 33.98/5.88 | | | | | (125) ~ (all_273_0 = 0) % 33.98/5.88 | | | | | % 33.98/5.88 | | | | | GROUND_INST: instantiating (11) with all_273_0, all_279_0, empty_set, % 33.98/5.88 | | | | | empty_set, simplifying with (62), (70) gives: % 33.98/5.88 | | | | | (126) all_279_0 = all_273_0 % 33.98/5.88 | | | | | % 33.98/5.88 | | | | | GROUND_INST: instantiating (11) with 0, all_279_0, empty_set, % 33.98/5.88 | | | | | empty_set, simplifying with (70), (73) gives: % 33.98/5.88 | | | | | (127) all_279_0 = 0 % 33.98/5.88 | | | | | % 33.98/5.88 | | | | | COMBINE_EQS: (126), (127) imply: % 33.98/5.88 | | | | | (128) all_273_0 = 0 % 33.98/5.88 | | | | | % 33.98/5.88 | | | | | SIMP: (128) implies: % 33.98/5.88 | | | | | (129) all_273_0 = 0 % 33.98/5.88 | | | | | % 33.98/5.88 | | | | | REDUCE: (125), (129) imply: % 33.98/5.88 | | | | | (130) $false % 33.98/5.88 | | | | | % 33.98/5.88 | | | | | CLOSE: (130) is inconsistent. % 33.98/5.88 | | | | | % 33.98/5.88 | | | | End of split % 33.98/5.88 | | | | % 33.98/5.88 | | | End of split % 33.98/5.88 | | | % 33.98/5.88 | | End of split % 33.98/5.88 | | % 33.98/5.88 | Case 2: % 33.98/5.88 | | % 33.98/5.88 | | (131) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: int] : ( ~ (v3 = % 33.98/5.88 | | 0) & ordered_pair(v0, v1) = v2 & in(v2, all_167_0) = 0 & in(v2, % 33.98/5.88 | | empty_set) = v3 & $i(v2) & $i(v1) & $i(v0)) % 33.98/5.88 | | % 33.98/5.88 | | DELTA: instantiating (131) with fresh symbols all_303_0, all_303_1, % 33.98/5.88 | | all_303_2, all_303_3 gives: % 33.98/5.88 | | (132) ~ (all_303_0 = 0) & ordered_pair(all_303_3, all_303_2) = all_303_1 % 33.98/5.88 | | & in(all_303_1, all_167_0) = 0 & in(all_303_1, empty_set) = % 33.98/5.88 | | all_303_0 & $i(all_303_1) & $i(all_303_2) & $i(all_303_3) % 33.98/5.88 | | % 33.98/5.88 | | ALPHA: (132) implies: % 33.98/5.88 | | (133) ~ (all_303_0 = 0) % 33.98/5.88 | | (134) in(all_303_1, empty_set) = all_303_0 % 33.98/5.88 | | (135) in(all_303_1, all_167_0) = 0 % 33.98/5.88 | | % 33.98/5.88 | | REDUCE: (36), (135) imply: % 33.98/5.88 | | (136) in(all_303_1, empty_set) = 0 % 33.98/5.88 | | % 33.98/5.88 | | GROUND_INST: instantiating (10) with 0, all_303_0, empty_set, all_303_1, % 33.98/5.88 | | simplifying with (134), (136) gives: % 33.98/5.88 | | (137) all_303_0 = 0 % 33.98/5.88 | | % 33.98/5.88 | | REDUCE: (133), (137) imply: % 33.98/5.88 | | (138) $false % 33.98/5.88 | | % 33.98/5.88 | | CLOSE: (138) is inconsistent. % 33.98/5.88 | | % 33.98/5.88 | End of split % 33.98/5.88 | % 33.98/5.88 End of proof % 33.98/5.88 % SZS output end Proof for theBenchmark % 33.98/5.88 % 33.98/5.88 5268ms %------------------------------------------------------------------------------