%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SEU224+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 : n019.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 17:43:26 EDT 2023 % Result : Theorem 44.35s 6.92s % Output : Proof 74.52s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.13 % Problem : SEU224+2 : TPTP v8.1.2. Released v3.3.0. % 0.00/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.12/0.34 % Computer : n019.cluster.edu % 0.12/0.34 % Model : x86_64 x86_64 % 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.34 % Memory : 8042.1875MB % 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.34 % CPULimit : 300 % 0.12/0.34 % WCLimit : 300 % 0.12/0.34 % DateTime : Wed Aug 23 16:32:29 EDT 2023 % 0.12/0.35 % CPUTime : % 0.19/0.64 ________ _____ % 0.19/0.64 ___ __ \_________(_)________________________________ % 0.19/0.64 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.19/0.64 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.19/0.64 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.19/0.64 % 0.19/0.64 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.19/0.64 (2023-06-19) % 0.19/0.64 % 0.19/0.64 (c) Philipp Rümmer, 2009-2023 % 0.19/0.64 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.19/0.64 Amanda Stjerna. % 0.19/0.64 Free software under BSD-3-Clause. % 0.19/0.64 % 0.19/0.64 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.19/0.65 % 0.19/0.65 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.19/0.66 Running up to 7 provers in parallel. % 0.19/0.68 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.19/0.68 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.19/0.68 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.19/0.68 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.19/0.68 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.19/0.68 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.19/0.68 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 8.10/1.93 Prover 4: Preprocessing ... % 8.33/1.98 Prover 1: Preprocessing ... % 8.33/2.00 Prover 6: Preprocessing ... % 8.33/2.00 Prover 5: Preprocessing ... % 8.33/2.00 Prover 2: Preprocessing ... % 8.33/2.00 Prover 0: Preprocessing ... % 8.33/2.00 Prover 3: Preprocessing ... % 24.99/4.27 Prover 1: Warning: ignoring some quantifiers % 26.61/4.45 Prover 3: Warning: ignoring some quantifiers % 26.61/4.49 Prover 1: Constructing countermodel ... % 26.61/4.52 Prover 3: Constructing countermodel ... % 26.61/4.60 Prover 6: Proving ... % 28.88/4.82 Prover 5: Proving ... % 33.16/5.55 Prover 2: Proving ... % 38.72/6.16 Prover 4: Warning: ignoring some quantifiers % 39.31/6.43 Prover 4: Constructing countermodel ... % 44.35/6.92 Prover 3: proved (6230ms) % 44.35/6.92 % 44.35/6.92 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 44.35/6.92 % 44.35/6.92 Prover 6: stopped % 44.35/6.92 Prover 5: stopped % 44.79/6.92 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 44.96/6.96 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 44.96/6.98 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 44.96/7.08 Prover 2: stopped % 44.96/7.09 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 48.73/7.48 Prover 7: Preprocessing ... % 48.73/7.53 Prover 8: Preprocessing ... % 49.67/7.59 Prover 0: Proving ... % 49.67/7.59 Prover 0: stopped % 49.67/7.60 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 50.03/7.69 Prover 11: Preprocessing ... % 50.61/7.71 Prover 10: Preprocessing ... % 51.71/7.98 Prover 13: Preprocessing ... % 54.59/8.29 Prover 8: Warning: ignoring some quantifiers % 54.59/8.30 Prover 7: Warning: ignoring some quantifiers % 54.59/8.33 Prover 10: Warning: ignoring some quantifiers % 55.20/8.36 Prover 8: Constructing countermodel ... % 55.52/8.44 Prover 10: Constructing countermodel ... % 56.02/8.48 Prover 7: Constructing countermodel ... % 56.71/8.79 Prover 13: Warning: ignoring some quantifiers % 59.08/8.88 Prover 13: Constructing countermodel ... % 69.56/10.53 Prover 1: Found proof (size 125) % 69.56/10.53 Prover 1: proved (9863ms) % 69.56/10.53 Prover 4: stopped % 69.56/10.54 Prover 7: stopped % 69.56/10.54 Prover 13: stopped % 69.56/10.54 Prover 10: stopped % 69.56/10.54 Prover 8: stopped % 72.19/10.68 Prover 11: Warning: ignoring some quantifiers % 72.94/10.82 Prover 11: Constructing countermodel ... % 73.24/10.94 Prover 11: stopped % 73.24/10.94 % 73.24/10.94 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 73.24/10.94 % 73.71/10.97 % SZS output start Proof for theBenchmark % 73.84/11.00 Assumptions after simplification: % 73.84/11.00 --------------------------------- % 73.84/11.00 % 73.84/11.00 (d4_funct_1) % 74.00/11.09 $i(empty_set) & ! [v0: $i] : ( ~ (function(v0) = 0) | ~ $i(v0) | ? [v1: % 74.00/11.09 any] : ? [v2: $i] : (relation_dom(v0) = v2 & relation(v0) = v1 & $i(v2) & % 74.00/11.09 ( ~ (v1 = 0) | ( ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: any] : ( % 74.00/11.09 ~ (ordered_pair(v3, v4) = v5) | ~ (in(v5, v0) = v6) | ~ $i(v4) | % 74.00/11.09 ~ $i(v3) | ? [v7: any] : ? [v8: $i] : (apply(v0, v3) = v8 & in(v3, % 74.00/11.09 v2) = v7 & $i(v8) & ( ~ (v7 = 0) | (( ~ (v8 = v4) | v6 = 0) & ( % 74.00/11.09 ~ (v6 = 0) | v8 = v4))))) & ? [v3: $i] : ! [v4: $i] : ! % 74.00/11.09 [v5: int] : (v5 = 0 | ~ (in(v4, v2) = v5) | ~ $i(v4) | ~ $i(v3) | % 74.00/11.09 ? [v6: $i] : (apply(v0, v4) = v6 & $i(v6) & ( ~ (v6 = v3) | v3 = % 74.00/11.09 empty_set) & ( ~ (v3 = empty_set) | v6 = empty_set))))))) % 74.00/11.09 % 74.00/11.09 (dt_k7_relat_1) % 74.00/11.09 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (relation_dom_restriction(v0, % 74.00/11.09 v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : % 74.00/11.09 (relation(v2) = v4 & relation(v0) = v3 & ( ~ (v3 = 0) | v4 = 0))) % 74.00/11.09 % 74.00/11.09 (fc13_relat_1) % 74.00/11.10 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (relation_dom_restriction(v0, % 74.00/11.10 v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ? % 74.00/11.10 [v5: any] : ? [v6: any] : (relation_empty_yielding(v2) = v6 & % 74.00/11.10 relation_empty_yielding(v0) = v4 & relation(v2) = v5 & relation(v0) = v3 & % 74.00/11.10 ( ~ (v4 = 0) | ~ (v3 = 0) | (v6 = 0 & v5 = 0)))) % 74.00/11.10 % 74.00/11.10 (fc4_funct_1) % 74.25/11.10 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (relation_dom_restriction(v0, % 74.25/11.10 v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ? % 74.25/11.10 [v5: any] : ? [v6: any] : (relation(v2) = v5 & relation(v0) = v3 & % 74.25/11.10 function(v2) = v6 & function(v0) = v4 & ( ~ (v4 = 0) | ~ (v3 = 0) | (v6 = % 74.25/11.10 0 & v5 = 0)))) % 74.25/11.10 % 74.25/11.10 (fc5_relat_1) % 74.25/11.10 ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (empty(v0) = v1) | ~ $i(v0) | ? % 74.25/11.10 [v2: any] : ? [v3: $i] : ? [v4: any] : (relation_dom(v0) = v3 & % 74.25/11.10 relation(v0) = v2 & empty(v3) = v4 & $i(v3) & ( ~ (v4 = 0) | ~ (v2 = % 74.25/11.10 0)))) % 74.25/11.10 % 74.25/11.10 (l82_funct_1) % 74.25/11.11 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: % 74.25/11.11 any] : ? [v6: $i] : ? [v7: any] : ? [v8: any] : (relation_dom(v3) = v4 & % 74.25/11.11 relation_dom(v2) = v6 & relation_dom_restriction(v2, v0) = v3 & relation(v2) % 74.25/11.11 = 0 & function(v2) = 0 & in(v1, v6) = v7 & in(v1, v4) = v5 & in(v1, v0) = v8 % 74.25/11.11 & $i(v6) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & ((v8 = 0 & v7 = 0 & % 74.25/11.11 ~ (v5 = 0)) | (v5 = 0 & ( ~ (v8 = 0) | ~ (v7 = 0))))) % 74.25/11.11 % 74.25/11.11 (rc2_relat_1) % 74.25/11.11 ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & relation(v0) = 0 & empty(v0) = v1 % 74.25/11.11 & $i(v0)) % 74.25/11.11 % 74.25/11.11 (t23_funct_1) % 74.25/11.11 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ( ~ (relation_dom(v1) % 74.25/11.11 = v2) | ~ (in(v0, v2) = v3) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? % 74.25/11.11 [v5: any] : ? [v6: $i] : (apply(v1, v0) = v6 & relation(v1) = v4 & % 74.25/11.11 function(v1) = v5 & $i(v6) & ( ~ (v5 = 0) | ~ (v4 = 0) | ! [v7: $i] : ! % 74.25/11.11 [v8: $i] : ! [v9: $i] : ( ~ (v3 = 0) | ~ (relation_composition(v1, v7) % 74.25/11.11 = v8) | ~ (apply(v8, v0) = v9) | ~ $i(v7) | ? [v10: any] : ? % 74.25/11.11 [v11: any] : ? [v12: $i] : (apply(v7, v6) = v12 & relation(v7) = v10 % 74.25/11.12 & function(v7) = v11 & $i(v12) & ( ~ (v11 = 0) | ~ (v10 = 0) | v12 % 74.25/11.12 = v9)))))) % 74.25/11.12 % 74.25/11.12 (t86_relat_1) % 74.25/11.12 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 74.25/11.12 any] : ( ~ (relation_dom(v3) = v4) | ~ (relation_dom_restriction(v2, v1) = % 74.25/11.12 v3) | ~ (in(v0, v4) = v5) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: % 74.25/11.12 any] : ? [v7: any] : ? [v8: $i] : ? [v9: any] : (relation_dom(v2) = v8 % 74.25/11.12 & relation(v2) = v6 & in(v0, v8) = v9 & in(v0, v1) = v7 & $i(v8) & ( ~ (v6 % 74.25/11.12 = 0) | (( ~ (v9 = 0) | ~ (v7 = 0) | v5 = 0) & ( ~ (v5 = 0) | (v9 = 0 % 74.25/11.12 & v7 = 0)))))) % 74.25/11.12 % 74.25/11.12 (function-axioms) % 74.25/11.14 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 % 74.25/11.14 | ~ (subset_difference(v4, v3, v2) = v1) | ~ (subset_difference(v4, v3, % 74.25/11.14 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : % 74.25/11.14 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (are_equipotent(v3, v2) = v1) | ~ % 74.25/11.14 (are_equipotent(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 74.25/11.14 ! [v3: $i] : (v1 = v0 | ~ (meet_of_subsets(v3, v2) = v1) | ~ % 74.25/11.14 (meet_of_subsets(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 74.25/11.14 ! [v3: $i] : (v1 = v0 | ~ (union_of_subsets(v3, v2) = v1) | ~ % 74.25/11.14 (union_of_subsets(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 74.25/11.14 ! [v3: $i] : (v1 = v0 | ~ (complements_of_subsets(v3, v2) = v1) | ~ % 74.25/11.14 (complements_of_subsets(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 74.25/11.14 $i] : ! [v3: $i] : (v1 = v0 | ~ (relation_composition(v3, v2) = v1) | ~ % 74.25/11.14 (relation_composition(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 74.25/11.14 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (disjoint(v3, % 74.25/11.14 v2) = v1) | ~ (disjoint(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 74.25/11.14 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (subset_complement(v3, v2) = v1) | ~ % 74.25/11.14 (subset_complement(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 74.25/11.14 : ! [v3: $i] : (v1 = v0 | ~ (set_difference(v3, v2) = v1) | ~ % 74.25/11.14 (set_difference(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 74.25/11.14 ! [v3: $i] : (v1 = v0 | ~ (apply(v3, v2) = v1) | ~ (apply(v3, v2) = v0)) & % 74.25/11.14 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 74.25/11.14 (cartesian_product2(v3, v2) = v1) | ~ (cartesian_product2(v3, v2) = v0)) & % 74.25/11.15 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 74.25/11.15 $i] : (v1 = v0 | ~ (element(v3, v2) = v1) | ~ (element(v3, v2) = v0)) & ! % 74.25/11.15 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 74.25/11.15 (relation_inverse_image(v3, v2) = v1) | ~ (relation_inverse_image(v3, v2) = % 74.25/11.15 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | % 74.25/11.15 ~ (relation_image(v3, v2) = v1) | ~ (relation_image(v3, v2) = v0)) & ! % 74.25/11.15 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 74.25/11.15 (relation_rng_restriction(v3, v2) = v1) | ~ (relation_rng_restriction(v3, % 74.25/11.15 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 % 74.25/11.15 = v0 | ~ (relation_dom_restriction(v3, v2) = v1) | ~ % 74.25/11.15 (relation_dom_restriction(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! % 74.25/11.15 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 74.25/11.15 (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0: $i] : ! [v1: % 74.25/11.15 $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (ordered_pair(v3, v2) = v1) % 74.25/11.15 | ~ (ordered_pair(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 74.25/11.15 : ! [v3: $i] : (v1 = v0 | ~ (set_intersection2(v3, v2) = v1) | ~ % 74.25/11.15 (set_intersection2(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 74.25/11.15 : ! [v3: $i] : (v1 = v0 | ~ (set_union2(v3, v2) = v1) | ~ (set_union2(v3, % 74.25/11.15 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 % 74.25/11.15 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) % 74.25/11.15 & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 74.25/11.15 [v3: $i] : (v1 = v0 | ~ (proper_subset(v3, v2) = v1) | ~ (proper_subset(v3, % 74.25/11.15 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : % 74.25/11.15 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = % 74.25/11.15 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 74.25/11.15 $i] : (v1 = v0 | ~ (relation_empty_yielding(v2) = v1) | ~ % 74.25/11.15 (relation_empty_yielding(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 74.25/11.15 $i] : (v1 = v0 | ~ (function_inverse(v2) = v1) | ~ (function_inverse(v2) = % 74.25/11.15 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 74.25/11.15 (relation_inverse(v2) = v1) | ~ (relation_inverse(v2) = v0)) & ! [v0: $i] % 74.25/11.15 : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (relation_field(v2) = v1) | ~ % 74.25/11.15 (relation_field(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = % 74.25/11.15 v0 | ~ (relation_rng(v2) = v1) | ~ (relation_rng(v2) = v0)) & ! [v0: $i] % 74.25/11.15 : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (union(v2) = v1) | ~ (union(v2) = % 74.25/11.15 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 74.25/11.15 (cast_to_subset(v2) = v1) | ~ (cast_to_subset(v2) = v0)) & ! [v0: $i] : ! % 74.25/11.15 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (relation_dom(v2) = v1) | ~ % 74.25/11.15 (relation_dom(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = % 74.25/11.15 v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0)) & ! [v0: $i] : ! % 74.25/11.15 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ % 74.25/11.15 (singleton(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | % 74.25/11.15 ~ (set_meet(v2) = v1) | ~ (set_meet(v2) = v0)) & ! [v0: $i] : ! [v1: $i] % 74.25/11.15 : ! [v2: $i] : (v1 = v0 | ~ (identity_relation(v2) = v1) | ~ % 74.25/11.15 (identity_relation(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 74.25/11.15 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (one_to_one(v2) = v1) | ~ % 74.25/11.15 (one_to_one(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 74.25/11.15 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (relation(v2) = v1) | ~ % 74.25/11.15 (relation(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 74.25/11.15 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (function(v2) = v1) | ~ % 74.25/11.15 (function(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 74.25/11.15 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (empty(v2) = v1) | ~ % 74.25/11.15 (empty(v2) = v0)) % 74.25/11.15 % 74.25/11.15 Further assumptions not needed in the proof: % 74.25/11.15 -------------------------------------------- % 74.25/11.15 antisymmetry_r2_hidden, antisymmetry_r2_xboole_0, cc1_funct_1, cc1_relat_1, % 74.25/11.15 cc2_funct_1, commutativity_k2_tarski, commutativity_k2_xboole_0, % 74.25/11.15 commutativity_k3_xboole_0, d10_relat_1, d10_xboole_0, d11_relat_1, d12_relat_1, % 74.25/11.15 d13_relat_1, d14_relat_1, d1_relat_1, d1_setfam_1, d1_tarski, d1_xboole_0, % 74.25/11.15 d1_zfmisc_1, d2_relat_1, d2_subset_1, d2_tarski, d2_xboole_0, d2_zfmisc_1, % 74.25/11.15 d3_relat_1, d3_tarski, d3_xboole_0, d4_relat_1, d4_subset_1, d4_tarski, % 74.25/11.15 d4_xboole_0, d5_relat_1, d5_subset_1, d5_tarski, d6_relat_1, d7_relat_1, % 74.25/11.15 d7_xboole_0, d8_funct_1, d8_relat_1, d8_setfam_1, d8_xboole_0, d9_funct_1, % 74.25/11.15 dt_k10_relat_1, dt_k1_funct_1, dt_k1_relat_1, dt_k1_setfam_1, dt_k1_tarski, % 74.25/11.15 dt_k1_xboole_0, dt_k1_zfmisc_1, dt_k2_funct_1, dt_k2_relat_1, dt_k2_subset_1, % 74.25/11.15 dt_k2_tarski, dt_k2_xboole_0, dt_k2_zfmisc_1, dt_k3_relat_1, dt_k3_subset_1, % 74.25/11.15 dt_k3_tarski, dt_k3_xboole_0, dt_k4_relat_1, dt_k4_tarski, dt_k4_xboole_0, % 74.25/11.15 dt_k5_relat_1, dt_k5_setfam_1, dt_k6_relat_1, dt_k6_setfam_1, dt_k6_subset_1, % 74.25/11.15 dt_k7_setfam_1, dt_k8_relat_1, dt_k9_relat_1, dt_m1_subset_1, % 74.25/11.15 existence_m1_subset_1, fc10_relat_1, fc11_relat_1, fc12_relat_1, fc1_funct_1, % 74.25/11.15 fc1_relat_1, fc1_subset_1, fc1_xboole_0, fc1_zfmisc_1, fc2_funct_1, fc2_relat_1, % 74.25/11.15 fc2_subset_1, fc2_xboole_0, fc3_funct_1, fc3_subset_1, fc3_xboole_0, % 74.25/11.15 fc4_relat_1, fc4_subset_1, fc6_relat_1, fc7_relat_1, fc8_relat_1, fc9_relat_1, % 74.25/11.15 idempotence_k2_xboole_0, idempotence_k3_xboole_0, involutiveness_k3_subset_1, % 74.25/11.15 involutiveness_k4_relat_1, involutiveness_k7_setfam_1, % 74.25/11.15 irreflexivity_r2_xboole_0, l1_zfmisc_1, l23_zfmisc_1, l25_zfmisc_1, % 74.25/11.15 l28_zfmisc_1, l2_zfmisc_1, l32_xboole_1, l3_subset_1, l3_zfmisc_1, l4_zfmisc_1, % 74.25/11.15 l50_zfmisc_1, l55_zfmisc_1, l71_subset_1, rc1_funct_1, rc1_relat_1, % 74.25/11.15 rc1_subset_1, rc1_xboole_0, rc2_funct_1, rc2_subset_1, rc2_xboole_0, % 74.25/11.15 rc3_funct_1, rc3_relat_1, redefinition_k5_setfam_1, redefinition_k6_setfam_1, % 74.25/11.15 redefinition_k6_subset_1, reflexivity_r1_tarski, symmetry_r1_xboole_0, % 74.25/11.15 t106_zfmisc_1, t10_zfmisc_1, t115_relat_1, t116_relat_1, t117_relat_1, % 74.25/11.15 t118_relat_1, t118_zfmisc_1, t119_relat_1, t119_zfmisc_1, t12_xboole_1, % 74.25/11.15 t136_zfmisc_1, t140_relat_1, t143_relat_1, t144_relat_1, t145_relat_1, % 74.25/11.15 t146_relat_1, t160_relat_1, t166_relat_1, t167_relat_1, t174_relat_1, % 74.25/11.15 t178_relat_1, t17_xboole_1, t19_xboole_1, t1_boole, t1_subset, t1_xboole_1, % 74.25/11.15 t1_zfmisc_1, t20_relat_1, t21_funct_1, t21_relat_1, t22_funct_1, t25_relat_1, % 74.25/11.15 t26_xboole_1, t28_xboole_1, t2_boole, t2_subset, t2_tarski, t2_xboole_1, % 74.25/11.15 t30_relat_1, t33_xboole_1, t33_zfmisc_1, t34_funct_1, t35_funct_1, t36_xboole_1, % 74.25/11.15 t37_relat_1, t37_xboole_1, t37_zfmisc_1, t38_zfmisc_1, t39_xboole_1, % 74.25/11.15 t39_zfmisc_1, t3_boole, t3_subset, t3_xboole_0, t3_xboole_1, t40_xboole_1, % 74.25/11.15 t43_subset_1, t44_relat_1, t45_relat_1, t45_xboole_1, t46_relat_1, t46_setfam_1, % 74.25/11.15 t46_zfmisc_1, t47_relat_1, t47_setfam_1, t48_setfam_1, t48_xboole_1, t4_boole, % 74.25/11.15 t4_subset, t4_xboole_0, t50_subset_1, t54_funct_1, t54_subset_1, t55_funct_1, % 74.25/11.15 t56_relat_1, t57_funct_1, t5_subset, t60_relat_1, t60_xboole_1, t62_funct_1, % 74.25/11.15 t63_xboole_1, t64_relat_1, t65_relat_1, t65_zfmisc_1, t68_funct_1, t69_enumset1, % 74.25/11.15 t6_boole, t6_zfmisc_1, t70_funct_1, t71_relat_1, t74_relat_1, t7_boole, % 74.25/11.15 t7_xboole_1, t83_xboole_1, t88_relat_1, t8_boole, t8_funct_1, t8_xboole_1, % 74.25/11.15 t8_zfmisc_1, t90_relat_1, t92_zfmisc_1, t94_relat_1, t99_relat_1, t99_zfmisc_1, % 74.25/11.15 t9_tarski, t9_zfmisc_1 % 74.25/11.15 % 74.25/11.15 Those formulas are unsatisfiable: % 74.25/11.15 --------------------------------- % 74.25/11.15 % 74.25/11.15 Begin of proof % 74.25/11.15 | % 74.25/11.16 | ALPHA: (d4_funct_1) implies: % 74.25/11.16 | (1) ! [v0: $i] : ( ~ (function(v0) = 0) | ~ $i(v0) | ? [v1: any] : ? % 74.25/11.16 | [v2: $i] : (relation_dom(v0) = v2 & relation(v0) = v1 & $i(v2) & ( ~ % 74.25/11.16 | (v1 = 0) | ( ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: % 74.25/11.16 | any] : ( ~ (ordered_pair(v3, v4) = v5) | ~ (in(v5, v0) = v6) % 74.25/11.16 | | ~ $i(v4) | ~ $i(v3) | ? [v7: any] : ? [v8: $i] : % 74.25/11.16 | (apply(v0, v3) = v8 & in(v3, v2) = v7 & $i(v8) & ( ~ (v7 = 0) % 74.25/11.16 | | (( ~ (v8 = v4) | v6 = 0) & ( ~ (v6 = 0) | v8 = v4))))) % 74.25/11.16 | & ? [v3: $i] : ! [v4: $i] : ! [v5: int] : (v5 = 0 | ~ % 74.25/11.16 | (in(v4, v2) = v5) | ~ $i(v4) | ~ $i(v3) | ? [v6: $i] : % 74.25/11.16 | (apply(v0, v4) = v6 & $i(v6) & ( ~ (v6 = v3) | v3 = % 74.52/11.16 | empty_set) & ( ~ (v3 = empty_set) | v6 = empty_set))))))) % 74.52/11.16 | % 74.52/11.16 | ALPHA: (function-axioms) implies: % 74.52/11.16 | (2) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 74.52/11.16 | (v1 = v0 | ~ (function(v2) = v1) | ~ (function(v2) = v0)) % 74.52/11.17 | (3) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 74.52/11.17 | (v1 = v0 | ~ (relation(v2) = v1) | ~ (relation(v2) = v0)) % 74.52/11.17 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 74.52/11.17 | (relation_dom(v2) = v1) | ~ (relation_dom(v2) = v0)) % 74.52/11.17 | (5) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 74.52/11.17 | ! [v3: $i] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) % 74.52/11.17 | % 74.52/11.17 | DELTA: instantiating (rc2_relat_1) with fresh symbols all_223_0, all_223_1 % 74.52/11.17 | gives: % 74.52/11.17 | (6) ~ (all_223_0 = 0) & relation(all_223_1) = 0 & empty(all_223_1) = % 74.52/11.17 | all_223_0 & $i(all_223_1) % 74.52/11.17 | % 74.52/11.17 | ALPHA: (6) implies: % 74.52/11.17 | (7) ~ (all_223_0 = 0) % 74.52/11.17 | (8) $i(all_223_1) % 74.52/11.17 | (9) empty(all_223_1) = all_223_0 % 74.52/11.17 | % 74.52/11.17 | DELTA: instantiating (l82_funct_1) with fresh symbols all_244_0, all_244_1, % 74.52/11.17 | all_244_2, all_244_3, all_244_4, all_244_5, all_244_6, all_244_7, % 74.52/11.17 | all_244_8 gives: % 74.52/11.17 | (10) relation_dom(all_244_5) = all_244_4 & relation_dom(all_244_6) = % 74.52/11.17 | all_244_2 & relation_dom_restriction(all_244_6, all_244_8) = all_244_5 % 74.52/11.17 | & relation(all_244_6) = 0 & function(all_244_6) = 0 & in(all_244_7, % 74.52/11.17 | all_244_2) = all_244_1 & in(all_244_7, all_244_4) = all_244_3 & % 74.52/11.17 | in(all_244_7, all_244_8) = all_244_0 & $i(all_244_2) & $i(all_244_4) & % 74.52/11.17 | $i(all_244_5) & $i(all_244_6) & $i(all_244_7) & $i(all_244_8) & % 74.52/11.17 | ((all_244_0 = 0 & all_244_1 = 0 & ~ (all_244_3 = 0)) | (all_244_3 = 0 % 74.52/11.17 | & ( ~ (all_244_0 = 0) | ~ (all_244_1 = 0)))) % 74.52/11.17 | % 74.52/11.17 | ALPHA: (10) implies: % 74.52/11.18 | (11) $i(all_244_8) % 74.52/11.18 | (12) $i(all_244_7) % 74.52/11.18 | (13) $i(all_244_6) % 74.52/11.18 | (14) $i(all_244_5) % 74.52/11.18 | (15) in(all_244_7, all_244_8) = all_244_0 % 74.52/11.18 | (16) in(all_244_7, all_244_4) = all_244_3 % 74.52/11.18 | (17) in(all_244_7, all_244_2) = all_244_1 % 74.52/11.18 | (18) function(all_244_6) = 0 % 74.52/11.18 | (19) relation(all_244_6) = 0 % 74.52/11.18 | (20) relation_dom_restriction(all_244_6, all_244_8) = all_244_5 % 74.52/11.18 | (21) relation_dom(all_244_6) = all_244_2 % 74.52/11.18 | (22) relation_dom(all_244_5) = all_244_4 % 74.52/11.18 | (23) (all_244_0 = 0 & all_244_1 = 0 & ~ (all_244_3 = 0)) | (all_244_3 = 0 % 74.52/11.18 | & ( ~ (all_244_0 = 0) | ~ (all_244_1 = 0))) % 74.52/11.18 | % 74.52/11.18 | GROUND_INST: instantiating (fc5_relat_1) with all_223_1, all_223_0, % 74.52/11.18 | simplifying with (8), (9) gives: % 74.52/11.18 | (24) all_223_0 = 0 | ? [v0: any] : ? [v1: $i] : ? [v2: any] : % 74.52/11.18 | (relation_dom(all_223_1) = v1 & relation(all_223_1) = v0 & empty(v1) = % 74.52/11.18 | v2 & $i(v1) & ( ~ (v2 = 0) | ~ (v0 = 0))) % 74.52/11.18 | % 74.52/11.18 | GROUND_INST: instantiating (1) with all_244_6, simplifying with (13), (18) % 74.52/11.18 | gives: % 74.52/11.19 | (25) ? [v0: any] : ? [v1: $i] : (relation_dom(all_244_6) = v1 & % 74.52/11.19 | relation(all_244_6) = v0 & $i(v1) & ( ~ (v0 = 0) | ( ! [v2: $i] : ! % 74.52/11.19 | [v3: $i] : ! [v4: $i] : ! [v5: any] : ( ~ (ordered_pair(v2, % 74.52/11.19 | v3) = v4) | ~ (in(v4, all_244_6) = v5) | ~ $i(v3) | ~ % 74.52/11.19 | $i(v2) | ? [v6: any] : ? [v7: $i] : (apply(all_244_6, v2) = % 74.52/11.19 | v7 & in(v2, v1) = v6 & $i(v7) & ( ~ (v6 = 0) | (( ~ (v7 = % 74.52/11.19 | v3) | v5 = 0) & ( ~ (v5 = 0) | v7 = v3))))) & ? % 74.52/11.19 | [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0 | ~ (in(v3, v1) % 74.52/11.19 | = v4) | ~ $i(v3) | ~ $i(v2) | ? [v5: $i] : % 74.52/11.19 | (apply(all_244_6, v3) = v5 & $i(v5) & ( ~ (v5 = v2) | v2 = % 74.52/11.19 | empty_set) & ( ~ (v2 = empty_set) | v5 = empty_set)))))) % 74.52/11.19 | % 74.52/11.19 | GROUND_INST: instantiating (fc13_relat_1) with all_244_6, all_244_8, % 74.52/11.19 | all_244_5, simplifying with (11), (13), (20) gives: % 74.52/11.19 | (26) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] : % 74.52/11.19 | (relation_empty_yielding(all_244_5) = v3 & % 74.52/11.19 | relation_empty_yielding(all_244_6) = v1 & relation(all_244_5) = v2 & % 74.52/11.19 | relation(all_244_6) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | (v3 = 0 & v2 % 74.52/11.19 | = 0))) % 74.52/11.19 | % 74.52/11.19 | GROUND_INST: instantiating (fc4_funct_1) with all_244_6, all_244_8, all_244_5, % 74.52/11.19 | simplifying with (11), (13), (20) gives: % 74.52/11.19 | (27) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] : % 74.52/11.19 | (relation(all_244_5) = v2 & relation(all_244_6) = v0 & % 74.52/11.19 | function(all_244_5) = v3 & function(all_244_6) = v1 & ( ~ (v1 = 0) | % 74.52/11.19 | ~ (v0 = 0) | (v3 = 0 & v2 = 0))) % 74.52/11.19 | % 74.52/11.19 | GROUND_INST: instantiating (dt_k7_relat_1) with all_244_6, all_244_8, % 74.52/11.19 | all_244_5, simplifying with (11), (13), (20) gives: % 74.52/11.19 | (28) ? [v0: any] : ? [v1: any] : (relation(all_244_5) = v1 & % 74.52/11.19 | relation(all_244_6) = v0 & ( ~ (v0 = 0) | v1 = 0)) % 74.52/11.20 | % 74.52/11.20 | GROUND_INST: instantiating (t23_funct_1) with all_244_7, all_244_6, all_244_2, % 74.52/11.20 | all_244_1, simplifying with (12), (13), (17), (21) gives: % 74.52/11.20 | (29) ? [v0: any] : ? [v1: any] : ? [v2: $i] : (apply(all_244_6, % 74.52/11.20 | all_244_7) = v2 & relation(all_244_6) = v0 & function(all_244_6) = % 74.52/11.20 | v1 & $i(v2) & ( ~ (v1 = 0) | ~ (v0 = 0) | ! [v3: $i] : ! [v4: $i] % 74.52/11.20 | : ! [v5: $i] : ( ~ (all_244_1 = 0) | ~ % 74.52/11.20 | (relation_composition(all_244_6, v3) = v4) | ~ (apply(v4, % 74.52/11.20 | all_244_7) = v5) | ~ $i(v3) | ? [v6: any] : ? [v7: any] : % 74.52/11.20 | ? [v8: $i] : (apply(v3, v2) = v8 & relation(v3) = v6 & % 74.52/11.20 | function(v3) = v7 & $i(v8) & ( ~ (v7 = 0) | ~ (v6 = 0) | v8 = % 74.52/11.20 | v5))))) % 74.52/11.20 | % 74.52/11.20 | GROUND_INST: instantiating (t86_relat_1) with all_244_7, all_244_8, all_244_6, % 74.52/11.20 | all_244_5, all_244_4, all_244_3, simplifying with (11), (12), % 74.52/11.20 | (13), (16), (20), (22) gives: % 74.52/11.20 | (30) ? [v0: any] : ? [v1: any] : ? [v2: $i] : ? [v3: any] : % 74.52/11.20 | (relation_dom(all_244_6) = v2 & relation(all_244_6) = v0 & % 74.52/11.20 | in(all_244_7, v2) = v3 & in(all_244_7, all_244_8) = v1 & $i(v2) & ( % 74.52/11.20 | ~ (v0 = 0) | (( ~ (v3 = 0) | ~ (v1 = 0) | all_244_3 = 0) & ( ~ % 74.52/11.20 | (all_244_3 = 0) | (v3 = 0 & v1 = 0))))) % 74.52/11.20 | % 74.52/11.20 | GROUND_INST: instantiating (t23_funct_1) with all_244_7, all_244_5, all_244_4, % 74.52/11.20 | all_244_3, simplifying with (12), (14), (16), (22) gives: % 74.52/11.21 | (31) ? [v0: any] : ? [v1: any] : ? [v2: $i] : (apply(all_244_5, % 74.52/11.21 | all_244_7) = v2 & relation(all_244_5) = v0 & function(all_244_5) = % 74.52/11.21 | v1 & $i(v2) & ( ~ (v1 = 0) | ~ (v0 = 0) | ! [v3: $i] : ! [v4: $i] % 74.52/11.21 | : ! [v5: $i] : ( ~ (all_244_3 = 0) | ~ % 74.52/11.21 | (relation_composition(all_244_5, v3) = v4) | ~ (apply(v4, % 74.52/11.21 | all_244_7) = v5) | ~ $i(v3) | ? [v6: any] : ? [v7: any] : % 74.52/11.21 | ? [v8: $i] : (apply(v3, v2) = v8 & relation(v3) = v6 & % 74.52/11.21 | function(v3) = v7 & $i(v8) & ( ~ (v7 = 0) | ~ (v6 = 0) | v8 = % 74.52/11.21 | v5))))) % 74.52/11.21 | % 74.52/11.21 | DELTA: instantiating (28) with fresh symbols all_336_0, all_336_1 gives: % 74.52/11.21 | (32) relation(all_244_5) = all_336_0 & relation(all_244_6) = all_336_1 & ( % 74.52/11.21 | ~ (all_336_1 = 0) | all_336_0 = 0) % 74.52/11.21 | % 74.52/11.21 | ALPHA: (32) implies: % 74.52/11.21 | (33) relation(all_244_6) = all_336_1 % 74.52/11.21 | (34) relation(all_244_5) = all_336_0 % 74.52/11.21 | (35) ~ (all_336_1 = 0) | all_336_0 = 0 % 74.52/11.21 | % 74.52/11.21 | DELTA: instantiating (26) with fresh symbols all_350_0, all_350_1, all_350_2, % 74.52/11.21 | all_350_3 gives: % 74.52/11.21 | (36) relation_empty_yielding(all_244_5) = all_350_0 & % 74.52/11.21 | relation_empty_yielding(all_244_6) = all_350_2 & relation(all_244_5) = % 74.52/11.21 | all_350_1 & relation(all_244_6) = all_350_3 & ( ~ (all_350_2 = 0) | ~ % 74.52/11.22 | (all_350_3 = 0) | (all_350_0 = 0 & all_350_1 = 0)) % 74.52/11.22 | % 74.52/11.22 | ALPHA: (36) implies: % 74.52/11.22 | (37) relation(all_244_6) = all_350_3 % 74.52/11.22 | (38) relation(all_244_5) = all_350_1 % 74.52/11.22 | % 74.52/11.22 | DELTA: instantiating (27) with fresh symbols all_352_0, all_352_1, all_352_2, % 74.52/11.22 | all_352_3 gives: % 74.52/11.22 | (39) relation(all_244_5) = all_352_1 & relation(all_244_6) = all_352_3 & % 74.52/11.22 | function(all_244_5) = all_352_0 & function(all_244_6) = all_352_2 & ( % 74.52/11.22 | ~ (all_352_2 = 0) | ~ (all_352_3 = 0) | (all_352_0 = 0 & all_352_1 % 74.52/11.22 | = 0)) % 74.52/11.22 | % 74.52/11.22 | ALPHA: (39) implies: % 74.52/11.22 | (40) function(all_244_6) = all_352_2 % 74.52/11.22 | (41) function(all_244_5) = all_352_0 % 74.52/11.22 | (42) relation(all_244_6) = all_352_3 % 74.52/11.22 | (43) relation(all_244_5) = all_352_1 % 74.52/11.22 | (44) ~ (all_352_2 = 0) | ~ (all_352_3 = 0) | (all_352_0 = 0 & all_352_1 = % 74.52/11.22 | 0) % 74.52/11.22 | % 74.52/11.22 | DELTA: instantiating (30) with fresh symbols all_356_0, all_356_1, all_356_2, % 74.52/11.22 | all_356_3 gives: % 74.52/11.22 | (45) relation_dom(all_244_6) = all_356_1 & relation(all_244_6) = all_356_3 % 74.52/11.22 | & in(all_244_7, all_356_1) = all_356_0 & in(all_244_7, all_244_8) = % 74.52/11.22 | all_356_2 & $i(all_356_1) & ( ~ (all_356_3 = 0) | (( ~ (all_356_0 = 0) % 74.52/11.22 | | ~ (all_356_2 = 0) | all_244_3 = 0) & ( ~ (all_244_3 = 0) | % 74.52/11.22 | (all_356_0 = 0 & all_356_2 = 0)))) % 74.52/11.22 | % 74.52/11.22 | ALPHA: (45) implies: % 74.52/11.22 | (46) in(all_244_7, all_244_8) = all_356_2 % 74.52/11.22 | (47) in(all_244_7, all_356_1) = all_356_0 % 74.52/11.22 | (48) relation(all_244_6) = all_356_3 % 74.52/11.22 | (49) relation_dom(all_244_6) = all_356_1 % 74.52/11.22 | (50) ~ (all_356_3 = 0) | (( ~ (all_356_0 = 0) | ~ (all_356_2 = 0) | % 74.52/11.22 | all_244_3 = 0) & ( ~ (all_244_3 = 0) | (all_356_0 = 0 & all_356_2 % 74.52/11.22 | = 0))) % 74.52/11.22 | % 74.52/11.22 | DELTA: instantiating (31) with fresh symbols all_366_0, all_366_1, all_366_2 % 74.52/11.22 | gives: % 74.52/11.23 | (51) apply(all_244_5, all_244_7) = all_366_0 & relation(all_244_5) = % 74.52/11.23 | all_366_2 & function(all_244_5) = all_366_1 & $i(all_366_0) & ( ~ % 74.52/11.23 | (all_366_1 = 0) | ~ (all_366_2 = 0) | ! [v0: $i] : ! [v1: $i] : % 74.52/11.23 | ! [v2: $i] : ( ~ (all_244_3 = 0) | ~ % 74.52/11.23 | (relation_composition(all_244_5, v0) = v1) | ~ (apply(v1, % 74.52/11.23 | all_244_7) = v2) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : % 74.52/11.23 | ? [v5: $i] : (apply(v0, all_366_0) = v5 & relation(v0) = v3 & % 74.52/11.23 | function(v0) = v4 & $i(v5) & ( ~ (v4 = 0) | ~ (v3 = 0) | v5 = % 74.52/11.23 | v2)))) % 74.52/11.23 | % 74.52/11.23 | ALPHA: (51) implies: % 74.52/11.23 | (52) function(all_244_5) = all_366_1 % 74.52/11.23 | (53) relation(all_244_5) = all_366_2 % 74.52/11.23 | (54) ~ (all_366_1 = 0) | ~ (all_366_2 = 0) | ! [v0: $i] : ! [v1: $i] : % 74.52/11.23 | ! [v2: $i] : ( ~ (all_244_3 = 0) | ~ (relation_composition(all_244_5, % 74.52/11.23 | v0) = v1) | ~ (apply(v1, all_244_7) = v2) | ~ $i(v0) | ? [v3: % 74.52/11.23 | any] : ? [v4: any] : ? [v5: $i] : (apply(v0, all_366_0) = v5 & % 74.52/11.23 | relation(v0) = v3 & function(v0) = v4 & $i(v5) & ( ~ (v4 = 0) | ~ % 74.52/11.23 | (v3 = 0) | v5 = v2))) % 74.52/11.23 | % 74.52/11.23 | DELTA: instantiating (29) with fresh symbols all_368_0, all_368_1, all_368_2 % 74.52/11.23 | gives: % 74.52/11.24 | (55) apply(all_244_6, all_244_7) = all_368_0 & relation(all_244_6) = % 74.52/11.24 | all_368_2 & function(all_244_6) = all_368_1 & $i(all_368_0) & ( ~ % 74.52/11.24 | (all_368_1 = 0) | ~ (all_368_2 = 0) | ! [v0: $i] : ! [v1: $i] : % 74.52/11.24 | ! [v2: $i] : ( ~ (all_244_1 = 0) | ~ % 74.52/11.24 | (relation_composition(all_244_6, v0) = v1) | ~ (apply(v1, % 74.52/11.24 | all_244_7) = v2) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : % 74.52/11.24 | ? [v5: $i] : (apply(v0, all_368_0) = v5 & relation(v0) = v3 & % 74.52/11.24 | function(v0) = v4 & $i(v5) & ( ~ (v4 = 0) | ~ (v3 = 0) | v5 = % 74.52/11.24 | v2)))) % 74.52/11.24 | % 74.52/11.24 | ALPHA: (55) implies: % 74.52/11.24 | (56) function(all_244_6) = all_368_1 % 74.52/11.24 | (57) relation(all_244_6) = all_368_2 % 74.52/11.24 | % 74.52/11.24 | DELTA: instantiating (25) with fresh symbols all_404_0, all_404_1 gives: % 74.52/11.24 | (58) relation_dom(all_244_6) = all_404_0 & relation(all_244_6) = all_404_1 % 74.52/11.24 | & $i(all_404_0) & ( ~ (all_404_1 = 0) | ( ! [v0: $i] : ! [v1: $i] : % 74.52/11.24 | ! [v2: $i] : ! [v3: any] : ( ~ (ordered_pair(v0, v1) = v2) | ~ % 74.52/11.24 | (in(v2, all_244_6) = v3) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] % 74.52/11.24 | : ? [v5: $i] : (apply(all_244_6, v0) = v5 & in(v0, all_404_0) = % 74.52/11.24 | v4 & $i(v5) & ( ~ (v4 = 0) | (( ~ (v5 = v1) | v3 = 0) & ( ~ % 74.52/11.24 | (v3 = 0) | v5 = v1))))) & ? [v0: $i] : ! [v1: $i] : ! % 74.52/11.24 | [v2: int] : (v2 = 0 | ~ (in(v1, all_404_0) = v2) | ~ $i(v1) | ~ % 74.52/11.24 | $i(v0) | ? [v3: $i] : (apply(all_244_6, v1) = v3 & $i(v3) & ( ~ % 74.52/11.24 | (v3 = v0) | v0 = empty_set) & ( ~ (v0 = empty_set) | v3 = % 74.52/11.24 | empty_set))))) % 74.52/11.24 | % 74.52/11.24 | ALPHA: (58) implies: % 74.52/11.24 | (59) relation(all_244_6) = all_404_1 % 74.52/11.24 | (60) relation_dom(all_244_6) = all_404_0 % 74.52/11.24 | % 74.52/11.24 | BETA: splitting (24) gives: % 74.52/11.24 | % 74.52/11.25 | Case 1: % 74.52/11.25 | | % 74.52/11.25 | | (61) all_223_0 = 0 % 74.52/11.25 | | % 74.52/11.25 | | REDUCE: (7), (61) imply: % 74.52/11.25 | | (62) $false % 74.52/11.25 | | % 74.52/11.25 | | CLOSE: (62) is inconsistent. % 74.52/11.25 | | % 74.52/11.25 | Case 2: % 74.52/11.25 | | % 74.52/11.25 | | % 74.52/11.25 | | GROUND_INST: instantiating (5) with all_244_0, all_356_2, all_244_8, % 74.52/11.25 | | all_244_7, simplifying with (15), (46) gives: % 74.52/11.25 | | (63) all_356_2 = all_244_0 % 74.52/11.25 | | % 74.52/11.25 | | GROUND_INST: instantiating (2) with 0, all_368_1, all_244_6, simplifying % 74.52/11.25 | | with (18), (56) gives: % 74.52/11.25 | | (64) all_368_1 = 0 % 74.52/11.25 | | % 74.52/11.25 | | GROUND_INST: instantiating (2) with all_352_2, all_368_1, all_244_6, % 74.52/11.25 | | simplifying with (40), (56) gives: % 74.52/11.25 | | (65) all_368_1 = all_352_2 % 74.52/11.25 | | % 74.52/11.25 | | GROUND_INST: instantiating (2) with all_352_0, all_366_1, all_244_5, % 74.52/11.25 | | simplifying with (41), (52) gives: % 74.52/11.25 | | (66) all_366_1 = all_352_0 % 74.52/11.25 | | % 74.52/11.25 | | GROUND_INST: instantiating (3) with all_350_3, all_352_3, all_244_6, % 74.52/11.25 | | simplifying with (37), (42) gives: % 74.52/11.25 | | (67) all_352_3 = all_350_3 % 74.52/11.25 | | % 74.52/11.25 | | GROUND_INST: instantiating (3) with 0, all_356_3, all_244_6, simplifying % 74.52/11.25 | | with (19), (48) gives: % 74.52/11.25 | | (68) all_356_3 = 0 % 74.52/11.25 | | % 74.52/11.25 | | GROUND_INST: instantiating (3) with all_352_3, all_356_3, all_244_6, % 74.52/11.25 | | simplifying with (42), (48) gives: % 74.52/11.25 | | (69) all_356_3 = all_352_3 % 74.52/11.25 | | % 74.52/11.26 | | GROUND_INST: instantiating (3) with all_352_3, all_368_2, all_244_6, % 74.52/11.26 | | simplifying with (42), (57) gives: % 74.52/11.26 | | (70) all_368_2 = all_352_3 % 74.52/11.26 | | % 74.52/11.26 | | GROUND_INST: instantiating (3) with all_368_2, all_404_1, all_244_6, % 74.52/11.26 | | simplifying with (57), (59) gives: % 74.52/11.26 | | (71) all_404_1 = all_368_2 % 74.52/11.26 | | % 74.52/11.26 | | GROUND_INST: instantiating (3) with all_336_1, all_404_1, all_244_6, % 74.52/11.26 | | simplifying with (33), (59) gives: % 74.52/11.26 | | (72) all_404_1 = all_336_1 % 74.52/11.26 | | % 74.52/11.26 | | GROUND_INST: instantiating (3) with all_352_1, all_366_2, all_244_5, % 74.52/11.26 | | simplifying with (43), (53) gives: % 74.52/11.26 | | (73) all_366_2 = all_352_1 % 74.52/11.26 | | % 74.52/11.26 | | GROUND_INST: instantiating (3) with all_350_1, all_366_2, all_244_5, % 74.52/11.26 | | simplifying with (38), (53) gives: % 74.52/11.26 | | (74) all_366_2 = all_350_1 % 74.52/11.26 | | % 74.52/11.26 | | GROUND_INST: instantiating (3) with all_336_0, all_366_2, all_244_5, % 74.52/11.26 | | simplifying with (34), (53) gives: % 74.52/11.26 | | (75) all_366_2 = all_336_0 % 74.52/11.26 | | % 74.52/11.26 | | GROUND_INST: instantiating (4) with all_244_2, all_404_0, all_244_6, % 74.52/11.26 | | simplifying with (21), (60) gives: % 74.52/11.26 | | (76) all_404_0 = all_244_2 % 74.52/11.26 | | % 74.52/11.26 | | GROUND_INST: instantiating (4) with all_356_1, all_404_0, all_244_6, % 74.52/11.26 | | simplifying with (49), (60) gives: % 74.52/11.26 | | (77) all_404_0 = all_356_1 % 74.52/11.26 | | % 74.52/11.26 | | COMBINE_EQS: (76), (77) imply: % 74.52/11.26 | | (78) all_356_1 = all_244_2 % 74.52/11.26 | | % 74.52/11.26 | | COMBINE_EQS: (71), (72) imply: % 74.52/11.26 | | (79) all_368_2 = all_336_1 % 74.52/11.26 | | % 74.52/11.26 | | SIMP: (79) implies: % 74.52/11.26 | | (80) all_368_2 = all_336_1 % 74.52/11.26 | | % 74.52/11.26 | | COMBINE_EQS: (64), (65) imply: % 74.52/11.26 | | (81) all_352_2 = 0 % 74.52/11.26 | | % 74.52/11.26 | | COMBINE_EQS: (70), (80) imply: % 74.52/11.26 | | (82) all_352_3 = all_336_1 % 74.52/11.26 | | % 74.52/11.26 | | SIMP: (82) implies: % 74.52/11.26 | | (83) all_352_3 = all_336_1 % 74.52/11.26 | | % 74.52/11.26 | | COMBINE_EQS: (73), (75) imply: % 74.52/11.26 | | (84) all_352_1 = all_336_0 % 74.52/11.26 | | % 74.52/11.26 | | COMBINE_EQS: (73), (74) imply: % 74.52/11.26 | | (85) all_352_1 = all_350_1 % 74.52/11.26 | | % 74.52/11.26 | | COMBINE_EQS: (68), (69) imply: % 74.52/11.28 | | (86) all_352_3 = 0 % 74.52/11.28 | | % 74.52/11.28 | | SIMP: (86) implies: % 74.52/11.28 | | (87) all_352_3 = 0 % 74.52/11.28 | | % 74.52/11.28 | | COMBINE_EQS: (84), (85) imply: % 74.52/11.28 | | (88) all_350_1 = all_336_0 % 74.52/11.28 | | % 74.52/11.28 | | COMBINE_EQS: (67), (83) imply: % 74.52/11.28 | | (89) all_350_3 = all_336_1 % 74.52/11.28 | | % 74.52/11.28 | | COMBINE_EQS: (67), (87) imply: % 74.52/11.28 | | (90) all_350_3 = 0 % 74.52/11.28 | | % 74.52/11.28 | | COMBINE_EQS: (89), (90) imply: % 74.52/11.28 | | (91) all_336_1 = 0 % 74.52/11.28 | | % 74.52/11.28 | | SIMP: (91) implies: % 74.52/11.28 | | (92) all_336_1 = 0 % 74.52/11.28 | | % 74.52/11.28 | | REDUCE: (47), (78) imply: % 74.52/11.28 | | (93) in(all_244_7, all_244_2) = all_356_0 % 74.52/11.28 | | % 74.52/11.28 | | BETA: splitting (44) gives: % 74.52/11.28 | | % 74.52/11.28 | | Case 1: % 74.52/11.28 | | | % 74.52/11.28 | | | (94) ~ (all_352_2 = 0) % 74.52/11.28 | | | % 74.52/11.28 | | | REDUCE: (81), (94) imply: % 74.52/11.28 | | | (95) $false % 74.52/11.28 | | | % 74.52/11.28 | | | CLOSE: (95) is inconsistent. % 74.52/11.28 | | | % 74.52/11.28 | | Case 2: % 74.52/11.28 | | | % 74.52/11.29 | | | (96) ~ (all_352_3 = 0) | (all_352_0 = 0 & all_352_1 = 0) % 74.52/11.29 | | | % 74.52/11.29 | | | BETA: splitting (35) gives: % 74.52/11.29 | | | % 74.52/11.29 | | | Case 1: % 74.52/11.29 | | | | % 74.52/11.29 | | | | (97) ~ (all_336_1 = 0) % 74.52/11.29 | | | | % 74.52/11.29 | | | | REDUCE: (92), (97) imply: % 74.52/11.29 | | | | (98) $false % 74.52/11.29 | | | | % 74.52/11.29 | | | | CLOSE: (98) is inconsistent. % 74.52/11.29 | | | | % 74.52/11.29 | | | Case 2: % 74.52/11.29 | | | | % 74.52/11.29 | | | | (99) all_336_0 = 0 % 74.52/11.29 | | | | % 74.52/11.29 | | | | COMBINE_EQS: (75), (99) imply: % 74.52/11.29 | | | | (100) all_366_2 = 0 % 74.52/11.29 | | | | % 74.52/11.29 | | | | BETA: splitting (96) gives: % 74.52/11.29 | | | | % 74.52/11.29 | | | | Case 1: % 74.52/11.29 | | | | | % 74.52/11.29 | | | | | (101) ~ (all_352_3 = 0) % 74.52/11.29 | | | | | % 74.52/11.29 | | | | | REDUCE: (87), (101) imply: % 74.52/11.29 | | | | | (102) $false % 74.52/11.29 | | | | | % 74.52/11.29 | | | | | CLOSE: (102) is inconsistent. % 74.52/11.29 | | | | | % 74.52/11.29 | | | | Case 2: % 74.52/11.29 | | | | | % 74.52/11.29 | | | | | (103) all_352_0 = 0 & all_352_1 = 0 % 74.52/11.29 | | | | | % 74.52/11.29 | | | | | ALPHA: (103) implies: % 74.52/11.29 | | | | | (104) all_352_0 = 0 % 74.52/11.29 | | | | | % 74.52/11.29 | | | | | COMBINE_EQS: (66), (104) imply: % 74.52/11.29 | | | | | (105) all_366_1 = 0 % 74.52/11.29 | | | | | % 74.52/11.29 | | | | | BETA: splitting (54) gives: % 74.52/11.29 | | | | | % 74.52/11.29 | | | | | Case 1: % 74.52/11.29 | | | | | | % 74.52/11.29 | | | | | | (106) ~ (all_366_1 = 0) % 74.52/11.29 | | | | | | % 74.52/11.29 | | | | | | REDUCE: (105), (106) imply: % 74.52/11.29 | | | | | | (107) $false % 74.52/11.29 | | | | | | % 74.52/11.29 | | | | | | CLOSE: (107) is inconsistent. % 74.52/11.29 | | | | | | % 74.52/11.29 | | | | | Case 2: % 74.52/11.29 | | | | | | % 74.52/11.30 | | | | | | (108) ~ (all_366_2 = 0) | ! [v0: $i] : ! [v1: $i] : ! [v2: % 74.52/11.30 | | | | | | $i] : ( ~ (all_244_3 = 0) | ~ % 74.52/11.30 | | | | | | (relation_composition(all_244_5, v0) = v1) | ~ % 74.52/11.30 | | | | | | (apply(v1, all_244_7) = v2) | ~ $i(v0) | ? [v3: any] : % 74.52/11.30 | | | | | | ? [v4: any] : ? [v5: $i] : (apply(v0, all_366_0) = v5 & % 74.52/11.30 | | | | | | relation(v0) = v3 & function(v0) = v4 & $i(v5) & ( ~ % 74.52/11.30 | | | | | | (v4 = 0) | ~ (v3 = 0) | v5 = v2))) % 74.52/11.30 | | | | | | % 74.52/11.30 | | | | | | BETA: splitting (108) gives: % 74.52/11.30 | | | | | | % 74.52/11.30 | | | | | | Case 1: % 74.52/11.30 | | | | | | | % 74.52/11.30 | | | | | | | (109) ~ (all_366_2 = 0) % 74.52/11.30 | | | | | | | % 74.52/11.30 | | | | | | | REDUCE: (100), (109) imply: % 74.52/11.30 | | | | | | | (110) $false % 74.52/11.30 | | | | | | | % 74.52/11.30 | | | | | | | CLOSE: (110) is inconsistent. % 74.52/11.30 | | | | | | | % 74.52/11.30 | | | | | | Case 2: % 74.52/11.30 | | | | | | | % 74.52/11.30 | | | | | | | % 74.52/11.30 | | | | | | | GROUND_INST: instantiating (5) with all_244_1, all_356_0, % 74.52/11.30 | | | | | | | all_244_2, all_244_7, simplifying with (17), (93) % 74.52/11.30 | | | | | | | gives: % 74.52/11.30 | | | | | | | (111) all_356_0 = all_244_1 % 74.52/11.30 | | | | | | | % 74.52/11.30 | | | | | | | BETA: splitting (23) gives: % 74.52/11.30 | | | | | | | % 74.52/11.30 | | | | | | | Case 1: % 74.52/11.30 | | | | | | | | % 74.52/11.30 | | | | | | | | (112) all_244_0 = 0 & all_244_1 = 0 & ~ (all_244_3 = 0) % 74.52/11.30 | | | | | | | | % 74.52/11.30 | | | | | | | | ALPHA: (112) implies: % 74.52/11.30 | | | | | | | | (113) all_244_1 = 0 % 74.52/11.30 | | | | | | | | (114) all_244_0 = 0 % 74.52/11.30 | | | | | | | | (115) ~ (all_244_3 = 0) % 74.52/11.30 | | | | | | | | % 74.52/11.30 | | | | | | | | COMBINE_EQS: (63), (114) imply: % 74.52/11.30 | | | | | | | | (116) all_356_2 = 0 % 74.52/11.30 | | | | | | | | % 74.52/11.30 | | | | | | | | COMBINE_EQS: (111), (113) imply: % 74.52/11.30 | | | | | | | | (117) all_356_0 = 0 % 74.52/11.30 | | | | | | | | % 74.52/11.30 | | | | | | | | BETA: splitting (50) gives: % 74.52/11.30 | | | | | | | | % 74.52/11.30 | | | | | | | | Case 1: % 74.52/11.30 | | | | | | | | | % 74.52/11.30 | | | | | | | | | (118) ~ (all_356_3 = 0) % 74.52/11.30 | | | | | | | | | % 74.52/11.30 | | | | | | | | | REDUCE: (68), (118) imply: % 74.52/11.30 | | | | | | | | | (119) $false % 74.52/11.30 | | | | | | | | | % 74.52/11.30 | | | | | | | | | CLOSE: (119) is inconsistent. % 74.52/11.30 | | | | | | | | | % 74.52/11.30 | | | | | | | | Case 2: % 74.52/11.30 | | | | | | | | | % 74.52/11.30 | | | | | | | | | (120) ( ~ (all_356_0 = 0) | ~ (all_356_2 = 0) | all_244_3 % 74.52/11.30 | | | | | | | | | = 0) & ( ~ (all_244_3 = 0) | (all_356_0 = 0 & % 74.52/11.30 | | | | | | | | | all_356_2 = 0)) % 74.52/11.30 | | | | | | | | | % 74.52/11.30 | | | | | | | | | ALPHA: (120) implies: % 74.52/11.30 | | | | | | | | | (121) ~ (all_356_0 = 0) | ~ (all_356_2 = 0) | all_244_3 = % 74.52/11.30 | | | | | | | | | 0 % 74.52/11.30 | | | | | | | | | % 74.52/11.30 | | | | | | | | | BETA: splitting (121) gives: % 74.52/11.30 | | | | | | | | | % 74.52/11.30 | | | | | | | | | Case 1: % 74.52/11.30 | | | | | | | | | | % 74.52/11.30 | | | | | | | | | | (122) ~ (all_356_0 = 0) % 74.52/11.30 | | | | | | | | | | % 74.52/11.30 | | | | | | | | | | REDUCE: (117), (122) imply: % 74.52/11.30 | | | | | | | | | | (123) $false % 74.52/11.30 | | | | | | | | | | % 74.52/11.30 | | | | | | | | | | CLOSE: (123) is inconsistent. % 74.52/11.30 | | | | | | | | | | % 74.52/11.30 | | | | | | | | | Case 2: % 74.52/11.30 | | | | | | | | | | % 74.52/11.30 | | | | | | | | | | (124) ~ (all_356_2 = 0) | all_244_3 = 0 % 74.52/11.30 | | | | | | | | | | % 74.52/11.30 | | | | | | | | | | BETA: splitting (124) gives: % 74.52/11.30 | | | | | | | | | | % 74.52/11.30 | | | | | | | | | | Case 1: % 74.52/11.30 | | | | | | | | | | | % 74.52/11.30 | | | | | | | | | | | (125) ~ (all_356_2 = 0) % 74.52/11.30 | | | | | | | | | | | % 74.52/11.31 | | | | | | | | | | | REDUCE: (116), (125) imply: % 74.52/11.31 | | | | | | | | | | | (126) $false % 74.52/11.31 | | | | | | | | | | | % 74.52/11.31 | | | | | | | | | | | CLOSE: (126) is inconsistent. % 74.52/11.31 | | | | | | | | | | | % 74.52/11.31 | | | | | | | | | | Case 2: % 74.52/11.31 | | | | | | | | | | | % 74.52/11.31 | | | | | | | | | | | (127) all_244_3 = 0 % 74.52/11.31 | | | | | | | | | | | % 74.52/11.31 | | | | | | | | | | | REDUCE: (115), (127) imply: % 74.52/11.31 | | | | | | | | | | | (128) $false % 74.52/11.31 | | | | | | | | | | | % 74.52/11.31 | | | | | | | | | | | CLOSE: (128) is inconsistent. % 74.52/11.31 | | | | | | | | | | | % 74.52/11.31 | | | | | | | | | | End of split % 74.52/11.31 | | | | | | | | | | % 74.52/11.31 | | | | | | | | | End of split % 74.52/11.31 | | | | | | | | | % 74.52/11.31 | | | | | | | | End of split % 74.52/11.31 | | | | | | | | % 74.52/11.31 | | | | | | | Case 2: % 74.52/11.31 | | | | | | | | % 74.52/11.31 | | | | | | | | (129) all_244_3 = 0 & ( ~ (all_244_0 = 0) | ~ (all_244_1 = % 74.52/11.31 | | | | | | | | 0)) % 74.52/11.31 | | | | | | | | % 74.52/11.31 | | | | | | | | ALPHA: (129) implies: % 74.52/11.31 | | | | | | | | (130) all_244_3 = 0 % 74.52/11.31 | | | | | | | | (131) ~ (all_244_0 = 0) | ~ (all_244_1 = 0) % 74.52/11.31 | | | | | | | | % 74.52/11.31 | | | | | | | | BETA: splitting (50) gives: % 74.52/11.31 | | | | | | | | % 74.52/11.31 | | | | | | | | Case 1: % 74.52/11.31 | | | | | | | | | % 74.52/11.31 | | | | | | | | | (132) ~ (all_356_3 = 0) % 74.52/11.31 | | | | | | | | | % 74.52/11.31 | | | | | | | | | REDUCE: (68), (132) imply: % 74.52/11.31 | | | | | | | | | (133) $false % 74.52/11.31 | | | | | | | | | % 74.52/11.31 | | | | | | | | | CLOSE: (133) is inconsistent. % 74.52/11.31 | | | | | | | | | % 74.52/11.31 | | | | | | | | Case 2: % 74.52/11.31 | | | | | | | | | % 74.52/11.31 | | | | | | | | | (134) ( ~ (all_356_0 = 0) | ~ (all_356_2 = 0) | all_244_3 % 74.52/11.31 | | | | | | | | | = 0) & ( ~ (all_244_3 = 0) | (all_356_0 = 0 & % 74.52/11.31 | | | | | | | | | all_356_2 = 0)) % 74.52/11.31 | | | | | | | | | % 74.52/11.31 | | | | | | | | | ALPHA: (134) implies: % 74.52/11.31 | | | | | | | | | (135) ~ (all_244_3 = 0) | (all_356_0 = 0 & all_356_2 = 0) % 74.52/11.31 | | | | | | | | | % 74.52/11.31 | | | | | | | | | BETA: splitting (135) gives: % 74.52/11.31 | | | | | | | | | % 74.52/11.31 | | | | | | | | | Case 1: % 74.52/11.31 | | | | | | | | | | % 74.52/11.31 | | | | | | | | | | (136) ~ (all_244_3 = 0) % 74.52/11.31 | | | | | | | | | | % 74.52/11.31 | | | | | | | | | | REDUCE: (130), (136) imply: % 74.52/11.31 | | | | | | | | | | (137) $false % 74.52/11.31 | | | | | | | | | | % 74.52/11.31 | | | | | | | | | | CLOSE: (137) is inconsistent. % 74.52/11.31 | | | | | | | | | | % 74.52/11.31 | | | | | | | | | Case 2: % 74.52/11.31 | | | | | | | | | | % 74.52/11.31 | | | | | | | | | | (138) all_356_0 = 0 & all_356_2 = 0 % 74.52/11.31 | | | | | | | | | | % 74.52/11.31 | | | | | | | | | | ALPHA: (138) implies: % 74.52/11.31 | | | | | | | | | | (139) all_356_2 = 0 % 74.52/11.31 | | | | | | | | | | (140) all_356_0 = 0 % 74.52/11.31 | | | | | | | | | | % 74.52/11.31 | | | | | | | | | | COMBINE_EQS: (111), (140) imply: % 74.52/11.31 | | | | | | | | | | (141) all_244_1 = 0 % 74.52/11.31 | | | | | | | | | | % 74.52/11.31 | | | | | | | | | | SIMP: (141) implies: % 74.52/11.31 | | | | | | | | | | (142) all_244_1 = 0 % 74.52/11.31 | | | | | | | | | | % 74.52/11.31 | | | | | | | | | | COMBINE_EQS: (63), (139) imply: % 74.52/11.31 | | | | | | | | | | (143) all_244_0 = 0 % 74.52/11.31 | | | | | | | | | | % 74.52/11.31 | | | | | | | | | | SIMP: (143) implies: % 74.52/11.31 | | | | | | | | | | (144) all_244_0 = 0 % 74.52/11.31 | | | | | | | | | | % 74.52/11.31 | | | | | | | | | | BETA: splitting (131) gives: % 74.52/11.31 | | | | | | | | | | % 74.52/11.31 | | | | | | | | | | Case 1: % 74.52/11.31 | | | | | | | | | | | % 74.52/11.31 | | | | | | | | | | | (145) ~ (all_244_0 = 0) % 74.52/11.31 | | | | | | | | | | | % 74.52/11.31 | | | | | | | | | | | REDUCE: (144), (145) imply: % 74.52/11.32 | | | | | | | | | | | (146) $false % 74.52/11.32 | | | | | | | | | | | % 74.52/11.32 | | | | | | | | | | | CLOSE: (146) is inconsistent. % 74.52/11.32 | | | | | | | | | | | % 74.52/11.32 | | | | | | | | | | Case 2: % 74.52/11.32 | | | | | | | | | | | % 74.52/11.32 | | | | | | | | | | | (147) ~ (all_244_1 = 0) % 74.52/11.32 | | | | | | | | | | | % 74.52/11.32 | | | | | | | | | | | REDUCE: (142), (147) imply: % 74.52/11.32 | | | | | | | | | | | (148) $false % 74.52/11.32 | | | | | | | | | | | % 74.52/11.32 | | | | | | | | | | | CLOSE: (148) is inconsistent. % 74.52/11.32 | | | | | | | | | | | % 74.52/11.32 | | | | | | | | | | End of split % 74.52/11.32 | | | | | | | | | | % 74.52/11.32 | | | | | | | | | End of split % 74.52/11.32 | | | | | | | | | % 74.52/11.32 | | | | | | | | End of split % 74.52/11.32 | | | | | | | | % 74.52/11.32 | | | | | | | End of split % 74.52/11.32 | | | | | | | % 74.52/11.32 | | | | | | End of split % 74.52/11.32 | | | | | | % 74.52/11.32 | | | | | End of split % 74.52/11.32 | | | | | % 74.52/11.32 | | | | End of split % 74.52/11.32 | | | | % 74.52/11.32 | | | End of split % 74.52/11.32 | | | % 74.52/11.32 | | End of split % 74.52/11.32 | | % 74.52/11.32 | End of split % 74.52/11.32 | % 74.52/11.32 End of proof % 74.52/11.32 % SZS output end Proof for theBenchmark % 74.52/11.32 % 74.52/11.32 10672ms %------------------------------------------------------------------------------