%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SEU226+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 : n025.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 17:43:27 EDT 2023 % Result : Theorem 61.10s 9.03s % Output : Proof 184.92s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SEU226+2 : TPTP v8.1.2. Released v3.3.0. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.34 % Computer : n025.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 300 % 0.13/0.34 % DateTime : Wed Aug 23 14:34:20 EDT 2023 % 0.13/0.34 % CPUTime : % 0.19/0.61 ________ _____ % 0.19/0.61 ___ __ \_________(_)________________________________ % 0.19/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.19/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.19/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.19/0.61 % 0.19/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.19/0.61 (2023-06-19) % 0.19/0.61 % 0.19/0.61 (c) Philipp Rümmer, 2009-2023 % 0.19/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.19/0.61 Amanda Stjerna. % 0.19/0.61 Free software under BSD-3-Clause. % 0.19/0.61 % 0.19/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.19/0.61 % 0.19/0.61 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.19/0.62 Running up to 7 provers in parallel. % 0.19/0.65 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.19/0.65 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.19/0.65 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.19/0.65 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.19/0.65 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.19/0.65 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.19/0.65 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 6.39/1.73 Prover 4: Preprocessing ... % 6.39/1.75 Prover 1: Preprocessing ... % 7.08/1.78 Prover 2: Preprocessing ... % 7.08/1.78 Prover 0: Preprocessing ... % 7.08/1.78 Prover 6: Preprocessing ... % 7.08/1.78 Prover 3: Preprocessing ... % 7.08/1.78 Prover 5: Preprocessing ... % 19.54/3.50 Prover 1: Warning: ignoring some quantifiers % 20.71/3.64 Prover 3: Warning: ignoring some quantifiers % 20.71/3.64 Prover 6: Proving ... % 20.71/3.65 Prover 1: Constructing countermodel ... % 21.14/3.66 Prover 3: Constructing countermodel ... % 21.14/3.70 Prover 5: Proving ... % 24.82/4.21 Prover 2: Proving ... % 28.68/4.70 Prover 4: Warning: ignoring some quantifiers % 30.09/4.86 Prover 4: Constructing countermodel ... % 31.57/5.12 Prover 0: Proving ... % 61.10/9.03 Prover 3: proved (8386ms) % 61.10/9.03 % 61.10/9.03 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 61.10/9.03 % 61.10/9.05 Prover 5: stopped % 61.10/9.06 Prover 6: stopped % 61.10/9.07 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 61.10/9.07 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 61.10/9.07 Prover 2: stopped % 61.10/9.09 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 61.10/9.09 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 61.99/9.12 Prover 0: stopped % 61.99/9.13 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 64.49/9.46 Prover 7: Preprocessing ... % 65.30/9.50 Prover 8: Preprocessing ... % 65.30/9.50 Prover 13: Preprocessing ... % 65.46/9.54 Prover 10: Preprocessing ... % 65.46/9.57 Prover 11: Preprocessing ... % 67.57/9.91 Prover 10: Warning: ignoring some quantifiers % 68.57/9.95 Prover 7: Warning: ignoring some quantifiers % 68.57/9.97 Prover 10: Constructing countermodel ... % 68.57/10.00 Prover 8: Warning: ignoring some quantifiers % 69.32/10.02 Prover 7: Constructing countermodel ... % 69.32/10.03 Prover 8: Constructing countermodel ... % 69.32/10.07 Prover 13: Warning: ignoring some quantifiers % 70.48/10.19 Prover 13: Constructing countermodel ... % 77.34/11.07 Prover 11: Warning: ignoring some quantifiers % 77.34/11.20 Prover 11: Constructing countermodel ... % 95.44/13.48 Prover 13: stopped % 95.67/13.49 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 97.08/13.70 Prover 16: Preprocessing ... % 99.93/14.05 Prover 16: Warning: ignoring some quantifiers % 100.09/14.11 Prover 16: Constructing countermodel ... % 113.44/15.98 Prover 1: stopped % 113.44/16.00 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085 % 115.58/16.16 Prover 19: Preprocessing ... % 118.68/16.71 Prover 19: Warning: ignoring some quantifiers % 120.14/16.77 Prover 19: Constructing countermodel ... % 134.60/18.67 Prover 16: stopped % 141.79/19.61 Prover 19: stopped % 183.51/26.93 Prover 8: Found proof (size 80) % 183.51/26.93 Prover 8: proved (17777ms) % 183.51/26.94 Prover 10: stopped % 183.51/26.94 Prover 4: stopped % 183.51/26.94 Prover 7: stopped % 184.13/26.97 Prover 11: stopped % 184.13/26.97 % 184.13/26.97 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 184.13/26.97 % 184.13/26.98 % SZS output start Proof for theBenchmark % 184.13/26.99 Assumptions after simplification: % 184.13/26.99 --------------------------------- % 184.13/26.99 % 184.13/26.99 (d12_funct_1) % 184.29/27.02 ! [v0: $i] : ( ~ (function(v0) = 0) | ~ $i(v0) | ? [v1: any] : ? [v2: $i] % 184.29/27.02 : (relation_dom(v0) = v2 & relation(v0) = v1 & $i(v2) & ( ~ (v1 = 0) | ( ? % 184.29/27.02 [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v5 = v3 | ~ % 184.29/27.02 (relation_image(v0, v4) = v5) | ~ $i(v4) | ~ $i(v3) | ? [v6: $i] % 184.29/27.02 : ? [v7: any] : (in(v6, v3) = v7 & $i(v6) & ( ~ (v7 = 0) | ! [v8: % 184.29/27.02 $i] : ( ~ (in(v8, v2) = 0) | ~ $i(v8) | ? [v9: any] : ? % 184.29/27.02 [v10: $i] : (apply(v0, v8) = v10 & in(v8, v4) = v9 & $i(v10) & % 184.29/27.02 ( ~ (v10 = v6) | ~ (v9 = 0))))) & (v7 = 0 | ? [v8: $i] : % 184.29/27.02 (apply(v0, v8) = v6 & in(v8, v4) = 0 & in(v8, v2) = 0 & % 184.29/27.02 $i(v8))))) & ! [v3: $i] : ! [v4: $i] : ( ~ % 184.29/27.02 (relation_image(v0, v3) = v4) | ~ $i(v4) | ~ $i(v3) | ( ! [v5: $i] % 184.29/27.02 : ! [v6: int] : (v6 = 0 | ~ (in(v5, v4) = v6) | ~ $i(v5) | ! % 184.29/27.02 [v7: $i] : ( ~ (in(v7, v2) = 0) | ~ $i(v7) | ? [v8: any] : ? % 184.29/27.02 [v9: $i] : (apply(v0, v7) = v9 & in(v7, v3) = v8 & $i(v9) & ( % 184.29/27.02 ~ (v9 = v5) | ~ (v8 = 0))))) & ! [v5: $i] : ( ~ (in(v5, % 184.29/27.02 v4) = 0) | ~ $i(v5) | ? [v6: $i] : (apply(v0, v6) = v5 & % 184.29/27.02 in(v6, v3) = 0 & in(v6, v2) = 0 & $i(v6))))))))) % 184.29/27.02 % 184.29/27.02 (d13_funct_1) % 184.29/27.03 ! [v0: $i] : ( ~ (function(v0) = 0) | ~ $i(v0) | ? [v1: any] : ? [v2: $i] % 184.29/27.03 : (relation_dom(v0) = v2 & relation(v0) = v1 & $i(v2) & ( ~ (v1 = 0) | ( ? % 184.29/27.03 [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v5 = v3 | ~ % 184.29/27.03 (relation_inverse_image(v0, v4) = v5) | ~ $i(v4) | ~ $i(v3) | ? % 184.29/27.03 [v6: $i] : ? [v7: any] : ? [v8: any] : ? [v9: $i] : ? [v10: any] % 184.29/27.03 : (apply(v0, v6) = v9 & in(v9, v4) = v10 & in(v6, v3) = v7 & in(v6, % 184.29/27.03 v2) = v8 & $i(v9) & $i(v6) & ( ~ (v10 = 0) | ~ (v8 = 0) | ~ % 184.29/27.03 (v7 = 0)) & (v7 = 0 | (v10 = 0 & v8 = 0)))) & ! [v3: $i] : ! % 184.29/27.03 [v4: $i] : ( ~ (relation_inverse_image(v0, v3) = v4) | ~ $i(v4) | ~ % 184.29/27.03 $i(v3) | ( ! [v5: $i] : ! [v6: $i] : ! [v7: any] : ( ~ (apply(v0, % 184.29/27.03 v5) = v6) | ~ (in(v6, v3) = v7) | ~ $i(v5) | ? [v8: any] % 184.29/27.03 : ? [v9: any] : (in(v5, v4) = v8 & in(v5, v2) = v9 & ( ~ (v8 = % 184.29/27.03 0) | (v9 = 0 & v7 = 0)))) & ! [v5: $i] : ! [v6: $i] : ( % 184.29/27.03 ~ (apply(v0, v5) = v6) | ~ (in(v6, v3) = 0) | ~ $i(v5) | ? % 184.29/27.03 [v7: any] : ? [v8: any] : (in(v5, v4) = v8 & in(v5, v2) = v7 & % 184.29/27.03 ( ~ (v7 = 0) | v8 = 0))))))))) % 184.29/27.03 % 184.29/27.03 (d3_tarski) % 184.29/27.03 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) = v2) % 184.29/27.03 | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & in(v3, % 184.29/27.03 v1) = v4 & in(v3, v0) = 0 & $i(v3))) & ! [v0: $i] : ! [v1: $i] : ( ~ % 184.29/27.03 (subset(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ! [v2: $i] : ( ~ (in(v2, v0) % 184.29/27.03 = 0) | ~ $i(v2) | in(v2, v1) = 0)) % 184.29/27.03 % 184.29/27.03 (d4_funct_1) % 184.45/27.03 $i(empty_set) & ! [v0: $i] : ( ~ (function(v0) = 0) | ~ $i(v0) | ? [v1: % 184.45/27.03 any] : ? [v2: $i] : (relation_dom(v0) = v2 & relation(v0) = v1 & $i(v2) & % 184.45/27.03 ( ~ (v1 = 0) | ( ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: any] : ( % 184.45/27.03 ~ (ordered_pair(v3, v4) = v5) | ~ (in(v5, v0) = v6) | ~ $i(v4) | % 184.45/27.03 ~ $i(v3) | ? [v7: any] : ? [v8: $i] : (apply(v0, v3) = v8 & in(v3, % 184.45/27.03 v2) = v7 & $i(v8) & ( ~ (v7 = 0) | (( ~ (v8 = v4) | v6 = 0) & ( % 184.45/27.03 ~ (v6 = 0) | v8 = v4))))) & ? [v3: $i] : ! [v4: $i] : ! % 184.45/27.03 [v5: int] : (v5 = 0 | ~ (in(v4, v2) = v5) | ~ $i(v4) | ~ $i(v3) | % 184.45/27.03 ? [v6: $i] : (apply(v0, v4) = v6 & $i(v6) & ( ~ (v6 = v3) | v3 = % 184.45/27.03 empty_set) & ( ~ (v3 = empty_set) | v6 = empty_set))))))) % 184.45/27.03 % 184.45/27.03 (d8_funct_1) % 184.45/27.04 ! [v0: $i] : ! [v1: any] : ( ~ (one_to_one(v0) = v1) | ~ $i(v0) | ? [v2: % 184.45/27.04 any] : ? [v3: any] : ? [v4: $i] : (relation_dom(v0) = v4 & relation(v0) % 184.45/27.04 = v2 & function(v0) = v3 & $i(v4) & ( ~ (v3 = 0) | ~ (v2 = 0) | (( ~ (v1 % 184.45/27.04 = 0) | ! [v5: $i] : ! [v6: $i] : (v6 = v5 | ~ (in(v6, v4) = 0) % 184.45/27.04 | ~ (in(v5, v4) = 0) | ~ $i(v6) | ~ $i(v5) | ? [v7: $i] : ? % 184.45/27.04 [v8: $i] : ( ~ (v8 = v7) & apply(v0, v6) = v8 & apply(v0, v5) = v7 % 184.45/27.04 & $i(v8) & $i(v7)))) & (v1 = 0 | ? [v5: $i] : ? [v6: $i] : ? % 184.45/27.04 [v7: $i] : ( ~ (v6 = v5) & apply(v0, v6) = v7 & apply(v0, v5) = v7 & % 184.45/27.04 in(v6, v4) = 0 & in(v5, v4) = 0 & $i(v7) & $i(v6) & $i(v5))))))) % 184.45/27.04 % 184.45/27.04 (rc1_subset_1) % 184.45/27.04 ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (empty(v0) = v1) | ~ $i(v0) | ? % 184.45/27.04 [v2: $i] : (powerset(v0) = v2 & $i(v2) & ? [v3: $i] : ? [v4: int] : ( ~ % 184.45/27.04 (v4 = 0) & element(v3, v2) = 0 & empty(v3) = v4 & $i(v3)))) % 184.45/27.04 % 184.45/27.04 (rc2_relat_1) % 184.45/27.04 ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & relation(v0) = 0 & empty(v0) = v1 % 184.45/27.04 & $i(v0)) % 184.45/27.04 % 184.45/27.04 (rc3_funct_1) % 184.45/27.04 ? [v0: $i] : (one_to_one(v0) = 0 & relation(v0) = 0 & function(v0) = 0 & % 184.45/27.04 $i(v0)) % 184.45/27.04 % 184.45/27.04 (t145_funct_1) % 184.45/27.04 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: int] : ( ~ (v4 % 184.45/27.04 = 0) & relation_inverse_image(v1, v0) = v2 & relation_image(v1, v2) = v3 & % 184.45/27.04 subset(v3, v0) = v4 & relation(v1) = 0 & function(v1) = 0 & $i(v3) & $i(v2) % 184.45/27.04 & $i(v1) & $i(v0)) % 184.45/27.04 % 184.45/27.04 (function-axioms) % 184.45/27.06 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 % 184.45/27.06 | ~ (subset_difference(v4, v3, v2) = v1) | ~ (subset_difference(v4, v3, % 184.45/27.06 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : % 184.45/27.06 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (are_equipotent(v3, v2) = v1) | ~ % 184.45/27.06 (are_equipotent(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 184.45/27.06 ! [v3: $i] : (v1 = v0 | ~ (meet_of_subsets(v3, v2) = v1) | ~ % 184.45/27.06 (meet_of_subsets(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 184.45/27.06 ! [v3: $i] : (v1 = v0 | ~ (union_of_subsets(v3, v2) = v1) | ~ % 184.45/27.06 (union_of_subsets(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 184.45/27.06 ! [v3: $i] : (v1 = v0 | ~ (complements_of_subsets(v3, v2) = v1) | ~ % 184.45/27.06 (complements_of_subsets(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 184.45/27.06 $i] : ! [v3: $i] : (v1 = v0 | ~ (relation_composition(v3, v2) = v1) | ~ % 184.45/27.06 (relation_composition(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 184.45/27.06 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (disjoint(v3, % 184.45/27.06 v2) = v1) | ~ (disjoint(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 184.45/27.06 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (subset_complement(v3, v2) = v1) | ~ % 184.45/27.06 (subset_complement(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 184.45/27.06 : ! [v3: $i] : (v1 = v0 | ~ (set_difference(v3, v2) = v1) | ~ % 184.45/27.06 (set_difference(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 184.45/27.06 ! [v3: $i] : (v1 = v0 | ~ (cartesian_product2(v3, v2) = v1) | ~ % 184.45/27.06 (cartesian_product2(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 184.45/27.06 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (element(v3, % 184.45/27.06 v2) = v1) | ~ (element(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 184.45/27.06 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (relation_inverse_image(v3, v2) = v1) | % 184.45/27.06 ~ (relation_inverse_image(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 184.45/27.06 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (relation_rng_restriction(v3, v2) = v1) % 184.45/27.06 | ~ (relation_rng_restriction(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : % 184.45/27.06 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (relation_image(v3, v2) = v1) | ~ % 184.45/27.06 (relation_image(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 184.45/27.06 ! [v3: $i] : (v1 = v0 | ~ (apply(v3, v2) = v1) | ~ (apply(v3, v2) = v0)) & % 184.45/27.06 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 184.45/27.06 (relation_dom_restriction(v3, v2) = v1) | ~ (relation_dom_restriction(v3, % 184.45/27.06 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : % 184.45/27.06 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ % 184.45/27.06 (subset(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 184.45/27.06 $i] : (v1 = v0 | ~ (ordered_pair(v3, v2) = v1) | ~ (ordered_pair(v3, v2) = % 184.45/27.06 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | % 184.45/27.06 ~ (set_intersection2(v3, v2) = v1) | ~ (set_intersection2(v3, v2) = v0)) & % 184.45/27.06 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 184.45/27.06 (set_union2(v3, v2) = v1) | ~ (set_union2(v3, v2) = v0)) & ! [v0: $i] : ! % 184.45/27.06 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (unordered_pair(v3, v2) = % 184.45/27.06 v1) | ~ (unordered_pair(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! % 184.45/27.06 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 184.45/27.06 (proper_subset(v3, v2) = v1) | ~ (proper_subset(v3, v2) = v0)) & ! [v0: % 184.45/27.06 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 184.45/27.06 : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) & ! [v0: % 184.45/27.06 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 184.45/27.06 ~ (relation_empty_yielding(v2) = v1) | ~ (relation_empty_yielding(v2) = % 184.45/27.06 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 184.45/27.06 (function_inverse(v2) = v1) | ~ (function_inverse(v2) = v0)) & ! [v0: $i] % 184.45/27.06 : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (relation_inverse(v2) = v1) | ~ % 184.45/27.06 (relation_inverse(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 % 184.45/27.06 = v0 | ~ (relation_field(v2) = v1) | ~ (relation_field(v2) = v0)) & ! % 184.45/27.06 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (relation_rng(v2) = v1) | % 184.45/27.06 ~ (relation_rng(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 % 184.45/27.06 = v0 | ~ (union(v2) = v1) | ~ (union(v2) = v0)) & ! [v0: $i] : ! [v1: % 184.45/27.06 $i] : ! [v2: $i] : (v1 = v0 | ~ (cast_to_subset(v2) = v1) | ~ % 184.45/27.06 (cast_to_subset(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = % 184.45/27.06 v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0)) & ! [v0: $i] : ! % 184.45/27.06 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ % 184.45/27.06 (singleton(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | % 184.45/27.06 ~ (set_meet(v2) = v1) | ~ (set_meet(v2) = v0)) & ! [v0: $i] : ! [v1: $i] % 184.45/27.06 : ! [v2: $i] : (v1 = v0 | ~ (relation_dom(v2) = v1) | ~ (relation_dom(v2) = % 184.45/27.06 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 184.45/27.06 (identity_relation(v2) = v1) | ~ (identity_relation(v2) = v0)) & ! [v0: % 184.45/27.06 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 184.45/27.06 ~ (one_to_one(v2) = v1) | ~ (one_to_one(v2) = v0)) & ! [v0: % 184.45/27.06 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 184.45/27.06 ~ (relation(v2) = v1) | ~ (relation(v2) = v0)) & ! [v0: MultipleValueBool] % 184.45/27.06 : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (function(v2) = v1) % 184.45/27.06 | ~ (function(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 184.45/27.06 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (empty(v2) = v1) | ~ % 184.45/27.06 (empty(v2) = v0)) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : % 184.45/27.06 (subset_difference(v2, v1, v0) = v3 & $i(v3)) & ? [v0: $i] : ? [v1: $i] : ? % 184.45/27.06 [v2: MultipleValueBool] : (are_equipotent(v1, v0) = v2) & ? [v0: $i] : ? % 184.45/27.06 [v1: $i] : ? [v2: MultipleValueBool] : (disjoint(v1, v0) = v2) & ? [v0: $i] % 184.45/27.06 : ? [v1: $i] : ? [v2: MultipleValueBool] : (element(v1, v0) = v2) & ? [v0: % 184.45/27.06 $i] : ? [v1: $i] : ? [v2: MultipleValueBool] : (subset(v1, v0) = v2) & ? % 184.45/27.06 [v0: $i] : ? [v1: $i] : ? [v2: MultipleValueBool] : (proper_subset(v1, v0) = % 184.45/27.06 v2) & ? [v0: $i] : ? [v1: $i] : ? [v2: MultipleValueBool] : (in(v1, v0) = % 184.45/27.06 v2) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (meet_of_subsets(v1, v0) = % 184.45/27.06 v2 & $i(v2)) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 184.45/27.06 (union_of_subsets(v1, v0) = v2 & $i(v2)) & ? [v0: $i] : ? [v1: $i] : ? [v2: % 184.45/27.06 $i] : (complements_of_subsets(v1, v0) = v2 & $i(v2)) & ? [v0: $i] : ? [v1: % 184.45/27.06 $i] : ? [v2: $i] : (relation_composition(v1, v0) = v2 & $i(v2)) & ? [v0: % 184.45/27.06 $i] : ? [v1: $i] : ? [v2: $i] : (subset_complement(v1, v0) = v2 & $i(v2)) % 184.45/27.06 & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (set_difference(v1, v0) = v2 & % 184.45/27.06 $i(v2)) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (cartesian_product2(v1, % 184.45/27.06 v0) = v2 & $i(v2)) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 184.45/27.06 (relation_inverse_image(v1, v0) = v2 & $i(v2)) & ? [v0: $i] : ? [v1: $i] : % 184.45/27.06 ? [v2: $i] : (relation_rng_restriction(v1, v0) = v2 & $i(v2)) & ? [v0: $i] : % 184.45/27.06 ? [v1: $i] : ? [v2: $i] : (relation_image(v1, v0) = v2 & $i(v2)) & ? [v0: % 184.45/27.06 $i] : ? [v1: $i] : ? [v2: $i] : (apply(v1, v0) = v2 & $i(v2)) & ? [v0: % 184.45/27.06 $i] : ? [v1: $i] : ? [v2: $i] : (relation_dom_restriction(v1, v0) = v2 & % 184.45/27.06 $i(v2)) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (ordered_pair(v1, v0) = % 184.45/27.06 v2 & $i(v2)) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 184.45/27.06 (set_intersection2(v1, v0) = v2 & $i(v2)) & ? [v0: $i] : ? [v1: $i] : ? % 184.45/27.06 [v2: $i] : (set_union2(v1, v0) = v2 & $i(v2)) & ? [v0: $i] : ? [v1: $i] : ? % 184.45/27.06 [v2: $i] : (unordered_pair(v1, v0) = v2 & $i(v2)) & ? [v0: $i] : ? [v1: % 184.45/27.06 MultipleValueBool] : (relation_empty_yielding(v0) = v1) & ? [v0: $i] : ? % 184.45/27.06 [v1: MultipleValueBool] : (one_to_one(v0) = v1) & ? [v0: $i] : ? [v1: % 184.45/27.06 MultipleValueBool] : (relation(v0) = v1) & ? [v0: $i] : ? [v1: % 184.45/27.06 MultipleValueBool] : (function(v0) = v1) & ? [v0: $i] : ? [v1: % 184.45/27.07 MultipleValueBool] : (empty(v0) = v1) & ? [v0: $i] : ? [v1: $i] : % 184.45/27.07 (function_inverse(v0) = v1 & $i(v1)) & ? [v0: $i] : ? [v1: $i] : % 184.45/27.07 (relation_inverse(v0) = v1 & $i(v1)) & ? [v0: $i] : ? [v1: $i] : % 184.45/27.07 (relation_field(v0) = v1 & $i(v1)) & ? [v0: $i] : ? [v1: $i] : % 184.45/27.07 (relation_rng(v0) = v1 & $i(v1)) & ? [v0: $i] : ? [v1: $i] : (union(v0) = v1 % 184.45/27.07 & $i(v1)) & ? [v0: $i] : ? [v1: $i] : (cast_to_subset(v0) = v1 & $i(v1)) & % 184.45/27.07 ? [v0: $i] : ? [v1: $i] : (powerset(v0) = v1 & $i(v1)) & ? [v0: $i] : ? % 184.45/27.07 [v1: $i] : (singleton(v0) = v1 & $i(v1)) & ? [v0: $i] : ? [v1: $i] : % 184.45/27.07 (set_meet(v0) = v1 & $i(v1)) & ? [v0: $i] : ? [v1: $i] : (relation_dom(v0) = % 184.45/27.07 v1 & $i(v1)) & ? [v0: $i] : ? [v1: $i] : (identity_relation(v0) = v1 & % 184.45/27.07 $i(v1)) % 184.45/27.07 % 184.45/27.07 Further assumptions not needed in the proof: % 184.45/27.07 -------------------------------------------- % 184.45/27.07 antisymmetry_r2_hidden, antisymmetry_r2_xboole_0, cc1_funct_1, cc1_relat_1, % 184.45/27.07 cc2_funct_1, commutativity_k2_tarski, commutativity_k2_xboole_0, % 184.45/27.07 commutativity_k3_xboole_0, d10_relat_1, d10_xboole_0, d11_relat_1, d12_relat_1, % 184.45/27.07 d13_relat_1, d14_relat_1, d1_relat_1, d1_setfam_1, d1_tarski, d1_xboole_0, % 184.45/27.07 d1_zfmisc_1, d2_relat_1, d2_subset_1, d2_tarski, d2_xboole_0, d2_zfmisc_1, % 184.45/27.07 d3_relat_1, d3_xboole_0, d4_relat_1, d4_subset_1, d4_tarski, d4_xboole_0, % 184.45/27.07 d5_relat_1, d5_subset_1, d5_tarski, d6_relat_1, d7_relat_1, d7_xboole_0, % 184.45/27.07 d8_relat_1, d8_setfam_1, d8_xboole_0, d9_funct_1, dt_k10_relat_1, dt_k1_funct_1, % 184.45/27.07 dt_k1_relat_1, dt_k1_setfam_1, dt_k1_tarski, dt_k1_xboole_0, dt_k1_zfmisc_1, % 184.45/27.07 dt_k2_funct_1, dt_k2_relat_1, dt_k2_subset_1, dt_k2_tarski, dt_k2_xboole_0, % 184.45/27.07 dt_k2_zfmisc_1, dt_k3_relat_1, dt_k3_subset_1, dt_k3_tarski, dt_k3_xboole_0, % 184.45/27.07 dt_k4_relat_1, dt_k4_tarski, dt_k4_xboole_0, dt_k5_relat_1, dt_k5_setfam_1, % 184.45/27.07 dt_k6_relat_1, dt_k6_setfam_1, dt_k6_subset_1, dt_k7_relat_1, dt_k7_setfam_1, % 184.45/27.07 dt_k8_relat_1, dt_k9_relat_1, dt_m1_subset_1, existence_m1_subset_1, % 184.45/27.07 fc10_relat_1, fc11_relat_1, fc12_relat_1, fc13_relat_1, fc1_funct_1, % 184.45/27.07 fc1_relat_1, fc1_subset_1, fc1_xboole_0, fc1_zfmisc_1, fc2_funct_1, fc2_relat_1, % 184.45/27.07 fc2_subset_1, fc2_xboole_0, fc3_funct_1, fc3_subset_1, fc3_xboole_0, % 184.45/27.07 fc4_funct_1, fc4_relat_1, fc4_subset_1, fc5_relat_1, fc6_relat_1, fc7_relat_1, % 184.45/27.07 fc8_relat_1, fc9_relat_1, idempotence_k2_xboole_0, idempotence_k3_xboole_0, % 184.45/27.07 involutiveness_k3_subset_1, involutiveness_k4_relat_1, % 184.45/27.07 involutiveness_k7_setfam_1, irreflexivity_r2_xboole_0, l1_zfmisc_1, % 184.45/27.07 l23_zfmisc_1, l25_zfmisc_1, l28_zfmisc_1, l2_zfmisc_1, l32_xboole_1, % 184.45/27.07 l3_subset_1, l3_zfmisc_1, l4_zfmisc_1, l50_zfmisc_1, l55_zfmisc_1, l71_subset_1, % 184.45/27.07 l82_funct_1, rc1_funct_1, rc1_relat_1, rc1_xboole_0, rc2_funct_1, rc2_subset_1, % 184.45/27.07 rc2_xboole_0, rc3_relat_1, redefinition_k5_setfam_1, redefinition_k6_setfam_1, % 184.45/27.07 redefinition_k6_subset_1, reflexivity_r1_tarski, symmetry_r1_xboole_0, % 184.45/27.07 t106_zfmisc_1, t10_zfmisc_1, t115_relat_1, t116_relat_1, t117_relat_1, % 184.45/27.07 t118_relat_1, t118_zfmisc_1, t119_relat_1, t119_zfmisc_1, t12_xboole_1, % 184.45/27.07 t136_zfmisc_1, t140_relat_1, t143_relat_1, t144_relat_1, t145_relat_1, % 184.45/27.07 t146_relat_1, t160_relat_1, t166_relat_1, t167_relat_1, t174_relat_1, % 184.45/27.07 t178_relat_1, t17_xboole_1, t19_xboole_1, t1_boole, t1_subset, t1_xboole_1, % 184.45/27.07 t1_zfmisc_1, t20_relat_1, t21_funct_1, t21_relat_1, t22_funct_1, t23_funct_1, % 184.45/27.07 t25_relat_1, t26_xboole_1, t28_xboole_1, t2_boole, t2_subset, t2_tarski, % 184.45/27.07 t2_xboole_1, t30_relat_1, t33_xboole_1, t33_zfmisc_1, t34_funct_1, t35_funct_1, % 184.45/27.07 t36_xboole_1, t37_relat_1, t37_xboole_1, t37_zfmisc_1, t38_zfmisc_1, % 184.45/27.07 t39_xboole_1, t39_zfmisc_1, t3_boole, t3_subset, t3_xboole_0, t3_xboole_1, % 184.45/27.07 t40_xboole_1, t43_subset_1, t44_relat_1, t45_relat_1, t45_xboole_1, t46_relat_1, % 184.45/27.07 t46_setfam_1, t46_zfmisc_1, t47_relat_1, t47_setfam_1, t48_setfam_1, % 184.45/27.07 t48_xboole_1, t4_boole, t4_subset, t4_xboole_0, t50_subset_1, t54_funct_1, % 184.45/27.07 t54_subset_1, t55_funct_1, t56_relat_1, t57_funct_1, t5_subset, t60_relat_1, % 184.45/27.07 t60_xboole_1, t62_funct_1, t63_xboole_1, t64_relat_1, t65_relat_1, t65_zfmisc_1, % 184.45/27.07 t68_funct_1, t69_enumset1, t6_boole, t6_zfmisc_1, t70_funct_1, t71_relat_1, % 184.45/27.07 t72_funct_1, t74_relat_1, t7_boole, t7_xboole_1, t83_xboole_1, t86_relat_1, % 184.45/27.07 t88_relat_1, t8_boole, t8_funct_1, t8_xboole_1, t8_zfmisc_1, t90_relat_1, % 184.45/27.07 t92_zfmisc_1, t94_relat_1, t99_relat_1, t99_zfmisc_1, t9_tarski, t9_zfmisc_1 % 184.45/27.07 % 184.45/27.07 Those formulas are unsatisfiable: % 184.45/27.07 --------------------------------- % 184.45/27.07 % 184.45/27.07 Begin of proof % 184.45/27.07 | % 184.45/27.07 | ALPHA: (d3_tarski) implies: % 184.45/27.07 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) % 184.45/27.07 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ % 184.45/27.07 | (v4 = 0) & in(v3, v1) = v4 & in(v3, v0) = 0 & $i(v3))) % 184.45/27.07 | % 184.45/27.07 | ALPHA: (d4_funct_1) implies: % 184.45/27.07 | (2) ! [v0: $i] : ( ~ (function(v0) = 0) | ~ $i(v0) | ? [v1: any] : ? % 184.45/27.07 | [v2: $i] : (relation_dom(v0) = v2 & relation(v0) = v1 & $i(v2) & ( ~ % 184.45/27.07 | (v1 = 0) | ( ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: % 184.45/27.07 | any] : ( ~ (ordered_pair(v3, v4) = v5) | ~ (in(v5, v0) = v6) % 184.45/27.07 | | ~ $i(v4) | ~ $i(v3) | ? [v7: any] : ? [v8: $i] : % 184.45/27.07 | (apply(v0, v3) = v8 & in(v3, v2) = v7 & $i(v8) & ( ~ (v7 = 0) % 184.45/27.07 | | (( ~ (v8 = v4) | v6 = 0) & ( ~ (v6 = 0) | v8 = v4))))) % 184.45/27.07 | & ? [v3: $i] : ! [v4: $i] : ! [v5: int] : (v5 = 0 | ~ % 184.45/27.07 | (in(v4, v2) = v5) | ~ $i(v4) | ~ $i(v3) | ? [v6: $i] : % 184.45/27.07 | (apply(v0, v4) = v6 & $i(v6) & ( ~ (v6 = v3) | v3 = % 184.45/27.07 | empty_set) & ( ~ (v3 = empty_set) | v6 = empty_set))))))) % 184.45/27.07 | % 184.45/27.07 | ALPHA: (function-axioms) implies: % 184.45/27.08 | (3) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 184.45/27.08 | (v1 = v0 | ~ (relation(v2) = v1) | ~ (relation(v2) = v0)) % 184.45/27.08 | (4) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 184.45/27.08 | ! [v3: $i] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) % 184.45/27.08 | % 184.45/27.08 | DELTA: instantiating (rc2_relat_1) with fresh symbols all_298_0, all_298_1 % 184.45/27.08 | gives: % 184.45/27.08 | (5) ~ (all_298_0 = 0) & relation(all_298_1) = 0 & empty(all_298_1) = % 184.45/27.08 | all_298_0 & $i(all_298_1) % 184.45/27.08 | % 184.45/27.08 | ALPHA: (5) implies: % 184.45/27.08 | (6) ~ (all_298_0 = 0) % 184.45/27.08 | (7) $i(all_298_1) % 184.45/27.08 | (8) empty(all_298_1) = all_298_0 % 184.45/27.08 | % 184.45/27.08 | DELTA: instantiating (rc3_funct_1) with fresh symbol all_303_0 gives: % 184.45/27.08 | (9) one_to_one(all_303_0) = 0 & relation(all_303_0) = 0 & % 184.45/27.08 | function(all_303_0) = 0 & $i(all_303_0) % 184.45/27.08 | % 184.45/27.08 | ALPHA: (9) implies: % 184.45/27.08 | (10) $i(all_303_0) % 184.45/27.08 | (11) function(all_303_0) = 0 % 184.45/27.08 | (12) relation(all_303_0) = 0 % 184.45/27.08 | (13) one_to_one(all_303_0) = 0 % 184.45/27.08 | % 184.45/27.08 | DELTA: instantiating (t145_funct_1) with fresh symbols all_313_0, all_313_1, % 184.45/27.08 | all_313_2, all_313_3, all_313_4 gives: % 184.45/27.08 | (14) ~ (all_313_0 = 0) & relation_inverse_image(all_313_3, all_313_4) = % 184.45/27.08 | all_313_2 & relation_image(all_313_3, all_313_2) = all_313_1 & % 184.45/27.08 | subset(all_313_1, all_313_4) = all_313_0 & relation(all_313_3) = 0 & % 184.45/27.08 | function(all_313_3) = 0 & $i(all_313_1) & $i(all_313_2) & % 184.45/27.08 | $i(all_313_3) & $i(all_313_4) % 184.45/27.08 | % 184.45/27.08 | ALPHA: (14) implies: % 184.45/27.08 | (15) ~ (all_313_0 = 0) % 184.45/27.08 | (16) $i(all_313_4) % 184.45/27.08 | (17) $i(all_313_3) % 184.45/27.08 | (18) $i(all_313_2) % 184.45/27.08 | (19) $i(all_313_1) % 184.45/27.08 | (20) function(all_313_3) = 0 % 184.45/27.08 | (21) relation(all_313_3) = 0 % 184.45/27.08 | (22) subset(all_313_1, all_313_4) = all_313_0 % 184.45/27.08 | (23) relation_image(all_313_3, all_313_2) = all_313_1 % 184.45/27.08 | (24) relation_inverse_image(all_313_3, all_313_4) = all_313_2 % 184.45/27.08 | % 184.45/27.08 | GROUND_INST: instantiating (rc1_subset_1) with all_298_1, all_298_0, % 184.45/27.08 | simplifying with (7), (8) gives: % 184.45/27.08 | (25) all_298_0 = 0 | ? [v0: $i] : (powerset(all_298_1) = v0 & $i(v0) & ? % 184.45/27.08 | [v1: $i] : ? [v2: int] : ( ~ (v2 = 0) & element(v1, v0) = 0 & % 184.45/27.08 | empty(v1) = v2 & $i(v1))) % 184.45/27.08 | % 184.45/27.08 | GROUND_INST: instantiating (2) with all_303_0, simplifying with (10), (11) % 184.45/27.08 | gives: % 184.45/27.09 | (26) ? [v0: any] : ? [v1: $i] : (relation_dom(all_303_0) = v1 & % 184.45/27.09 | relation(all_303_0) = v0 & $i(v1) & ( ~ (v0 = 0) | ( ! [v2: $i] : ! % 184.45/27.09 | [v3: $i] : ! [v4: $i] : ! [v5: any] : ( ~ (ordered_pair(v2, % 184.45/27.09 | v3) = v4) | ~ (in(v4, all_303_0) = v5) | ~ $i(v3) | ~ % 184.45/27.09 | $i(v2) | ? [v6: any] : ? [v7: $i] : (apply(all_303_0, v2) = % 184.45/27.09 | v7 & in(v2, v1) = v6 & $i(v7) & ( ~ (v6 = 0) | (( ~ (v7 = % 184.45/27.09 | v3) | v5 = 0) & ( ~ (v5 = 0) | v7 = v3))))) & ? % 184.45/27.09 | [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0 | ~ (in(v3, v1) % 184.45/27.09 | = v4) | ~ $i(v3) | ~ $i(v2) | ? [v5: $i] : % 184.45/27.09 | (apply(all_303_0, v3) = v5 & $i(v5) & ( ~ (v5 = v2) | v2 = % 184.45/27.09 | empty_set) & ( ~ (v2 = empty_set) | v5 = empty_set)))))) % 184.45/27.09 | % 184.45/27.09 | GROUND_INST: instantiating (d12_funct_1) with all_303_0, simplifying with % 184.45/27.09 | (10), (11) gives: % 184.45/27.09 | (27) ? [v0: any] : ? [v1: $i] : (relation_dom(all_303_0) = v1 & % 184.45/27.09 | relation(all_303_0) = v0 & $i(v1) & ( ~ (v0 = 0) | ( ? [v2: $i] : ! % 184.45/27.09 | [v3: $i] : ! [v4: $i] : (v4 = v2 | ~ % 184.45/27.09 | (relation_image(all_303_0, v3) = v4) | ~ $i(v3) | ~ $i(v2) | % 184.45/27.09 | ? [v5: $i] : ? [v6: any] : (in(v5, v2) = v6 & $i(v5) & ( ~ % 184.45/27.09 | (v6 = 0) | ! [v7: $i] : ( ~ (in(v7, v1) = 0) | ~ $i(v7) % 184.45/27.09 | | ? [v8: any] : ? [v9: $i] : (apply(all_303_0, v7) = % 184.45/27.09 | v9 & in(v7, v3) = v8 & $i(v9) & ( ~ (v9 = v5) | ~ (v8 % 184.45/27.09 | = 0))))) & (v6 = 0 | ? [v7: $i] : % 184.45/27.09 | (apply(all_303_0, v7) = v5 & in(v7, v3) = 0 & in(v7, v1) = % 184.45/27.09 | 0 & $i(v7))))) & ! [v2: $i] : ! [v3: $i] : ( ~ % 184.45/27.09 | (relation_image(all_303_0, v2) = v3) | ~ $i(v3) | ~ $i(v2) | % 184.45/27.09 | ( ! [v4: $i] : ! [v5: int] : (v5 = 0 | ~ (in(v4, v3) = v5) | % 184.45/27.09 | ~ $i(v4) | ! [v6: $i] : ( ~ (in(v6, v1) = 0) | ~ $i(v6) % 184.45/27.09 | | ? [v7: any] : ? [v8: $i] : (apply(all_303_0, v6) = % 184.45/27.09 | v8 & in(v6, v2) = v7 & $i(v8) & ( ~ (v8 = v4) | ~ (v7 % 184.45/27.09 | = 0))))) & ! [v4: $i] : ( ~ (in(v4, v3) = 0) | ~ % 184.45/27.09 | $i(v4) | ? [v5: $i] : (apply(all_303_0, v5) = v4 & in(v5, % 184.45/27.09 | v2) = 0 & in(v5, v1) = 0 & $i(v5)))))))) % 184.45/27.09 | % 184.45/27.09 | GROUND_INST: instantiating (d13_funct_1) with all_313_3, simplifying with % 184.45/27.09 | (17), (20) gives: % 184.45/27.10 | (28) ? [v0: any] : ? [v1: $i] : (relation_dom(all_313_3) = v1 & % 184.45/27.10 | relation(all_313_3) = v0 & $i(v1) & ( ~ (v0 = 0) | ( ? [v2: $i] : ! % 184.45/27.10 | [v3: $i] : ! [v4: $i] : (v4 = v2 | ~ % 184.45/27.10 | (relation_inverse_image(all_313_3, v3) = v4) | ~ $i(v3) | ~ % 184.45/27.10 | $i(v2) | ? [v5: $i] : ? [v6: any] : ? [v7: any] : ? [v8: % 184.45/27.10 | $i] : ? [v9: any] : (apply(all_313_3, v5) = v8 & in(v8, v3) % 184.45/27.10 | = v9 & in(v5, v2) = v6 & in(v5, v1) = v7 & $i(v8) & $i(v5) & % 184.45/27.10 | ( ~ (v9 = 0) | ~ (v7 = 0) | ~ (v6 = 0)) & (v6 = 0 | (v9 = % 184.45/27.10 | 0 & v7 = 0)))) & ! [v2: $i] : ! [v3: $i] : ( ~ % 184.45/27.10 | (relation_inverse_image(all_313_3, v2) = v3) | ~ $i(v3) | ~ % 184.45/27.10 | $i(v2) | ( ! [v4: $i] : ! [v5: $i] : ! [v6: any] : ( ~ % 184.45/27.10 | (apply(all_313_3, v4) = v5) | ~ (in(v5, v2) = v6) | ~ % 184.45/27.10 | $i(v4) | ? [v7: any] : ? [v8: any] : (in(v4, v3) = v7 & % 184.45/27.10 | in(v4, v1) = v8 & ( ~ (v7 = 0) | (v8 = 0 & v6 = 0)))) & % 184.45/27.10 | ! [v4: $i] : ! [v5: $i] : ( ~ (apply(all_313_3, v4) = v5) | % 184.45/27.10 | ~ (in(v5, v2) = 0) | ~ $i(v4) | ? [v6: any] : ? [v7: % 184.45/27.10 | any] : (in(v4, v3) = v7 & in(v4, v1) = v6 & ( ~ (v6 = 0) % 184.45/27.10 | | v7 = 0)))))))) % 184.45/27.10 | % 184.45/27.10 | GROUND_INST: instantiating (d12_funct_1) with all_313_3, simplifying with % 184.45/27.10 | (17), (20) gives: % 184.45/27.10 | (29) ? [v0: any] : ? [v1: $i] : (relation_dom(all_313_3) = v1 & % 184.45/27.10 | relation(all_313_3) = v0 & $i(v1) & ( ~ (v0 = 0) | ( ? [v2: $i] : ! % 184.45/27.10 | [v3: $i] : ! [v4: $i] : (v4 = v2 | ~ % 184.45/27.10 | (relation_image(all_313_3, v3) = v4) | ~ $i(v3) | ~ $i(v2) | % 184.45/27.10 | ? [v5: $i] : ? [v6: any] : (in(v5, v2) = v6 & $i(v5) & ( ~ % 184.45/27.10 | (v6 = 0) | ! [v7: $i] : ( ~ (in(v7, v1) = 0) | ~ $i(v7) % 184.45/27.10 | | ? [v8: any] : ? [v9: $i] : (apply(all_313_3, v7) = % 184.45/27.10 | v9 & in(v7, v3) = v8 & $i(v9) & ( ~ (v9 = v5) | ~ (v8 % 184.45/27.10 | = 0))))) & (v6 = 0 | ? [v7: $i] : % 184.45/27.10 | (apply(all_313_3, v7) = v5 & in(v7, v3) = 0 & in(v7, v1) = % 184.45/27.10 | 0 & $i(v7))))) & ! [v2: $i] : ! [v3: $i] : ( ~ % 184.45/27.10 | (relation_image(all_313_3, v2) = v3) | ~ $i(v3) | ~ $i(v2) | % 184.45/27.10 | ( ! [v4: $i] : ! [v5: int] : (v5 = 0 | ~ (in(v4, v3) = v5) | % 184.45/27.10 | ~ $i(v4) | ! [v6: $i] : ( ~ (in(v6, v1) = 0) | ~ $i(v6) % 184.45/27.10 | | ? [v7: any] : ? [v8: $i] : (apply(all_313_3, v6) = % 184.45/27.10 | v8 & in(v6, v2) = v7 & $i(v8) & ( ~ (v8 = v4) | ~ (v7 % 184.45/27.10 | = 0))))) & ! [v4: $i] : ( ~ (in(v4, v3) = 0) | ~ % 184.45/27.10 | $i(v4) | ? [v5: $i] : (apply(all_313_3, v5) = v4 & in(v5, % 184.45/27.10 | v2) = 0 & in(v5, v1) = 0 & $i(v5)))))))) % 184.45/27.10 | % 184.45/27.10 | GROUND_INST: instantiating (d8_funct_1) with all_303_0, 0, simplifying with % 184.45/27.10 | (10), (13) gives: % 184.45/27.10 | (30) ? [v0: any] : ? [v1: any] : ? [v2: $i] : (relation_dom(all_303_0) = % 184.45/27.10 | v2 & relation(all_303_0) = v0 & function(all_303_0) = v1 & $i(v2) & % 184.45/27.10 | ( ~ (v1 = 0) | ~ (v0 = 0) | ! [v3: $i] : ! [v4: $i] : (v4 = v3 | % 184.45/27.10 | ~ (in(v4, v2) = 0) | ~ (in(v3, v2) = 0) | ~ $i(v4) | ~ $i(v3) % 184.45/27.10 | | ? [v5: $i] : ? [v6: $i] : ( ~ (v6 = v5) & apply(all_303_0, % 184.45/27.10 | v4) = v6 & apply(all_303_0, v3) = v5 & $i(v6) & $i(v5))))) % 184.45/27.10 | % 184.45/27.10 | GROUND_INST: instantiating (1) with all_313_1, all_313_4, all_313_0, % 184.45/27.10 | simplifying with (16), (19), (22) gives: % 184.45/27.10 | (31) all_313_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & in(v0, % 184.45/27.10 | all_313_1) = 0 & in(v0, all_313_4) = v1 & $i(v0)) % 184.45/27.10 | % 184.45/27.10 | DELTA: instantiating (30) with fresh symbols all_438_0, all_438_1, all_438_2 % 184.45/27.10 | gives: % 184.45/27.11 | (32) relation_dom(all_303_0) = all_438_0 & relation(all_303_0) = all_438_2 % 184.45/27.11 | & function(all_303_0) = all_438_1 & $i(all_438_0) & ( ~ (all_438_1 = % 184.45/27.11 | 0) | ~ (all_438_2 = 0) | ! [v0: $i] : ! [v1: $i] : (v1 = v0 | % 184.45/27.11 | ~ (in(v1, all_438_0) = 0) | ~ (in(v0, all_438_0) = 0) | ~ $i(v1) % 184.45/27.11 | | ~ $i(v0) | ? [v2: $i] : ? [v3: $i] : ( ~ (v3 = v2) & % 184.45/27.11 | apply(all_303_0, v1) = v3 & apply(all_303_0, v0) = v2 & $i(v3) & % 184.45/27.11 | $i(v2)))) % 184.45/27.11 | % 184.45/27.11 | ALPHA: (32) implies: % 184.45/27.11 | (33) relation(all_303_0) = all_438_2 % 184.45/27.11 | % 184.45/27.11 | DELTA: instantiating (26) with fresh symbols all_476_0, all_476_1 gives: % 184.45/27.11 | (34) relation_dom(all_303_0) = all_476_0 & relation(all_303_0) = all_476_1 % 184.45/27.11 | & $i(all_476_0) & ( ~ (all_476_1 = 0) | ( ! [v0: $i] : ! [v1: $i] : % 184.45/27.11 | ! [v2: $i] : ! [v3: any] : ( ~ (ordered_pair(v0, v1) = v2) | ~ % 184.45/27.11 | (in(v2, all_303_0) = v3) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] % 184.45/27.11 | : ? [v5: $i] : (apply(all_303_0, v0) = v5 & in(v0, all_476_0) = % 184.45/27.11 | v4 & $i(v5) & ( ~ (v4 = 0) | (( ~ (v5 = v1) | v3 = 0) & ( ~ % 184.45/27.11 | (v3 = 0) | v5 = v1))))) & ? [v0: $i] : ! [v1: $i] : ! % 184.45/27.11 | [v2: int] : (v2 = 0 | ~ (in(v1, all_476_0) = v2) | ~ $i(v1) | ~ % 184.45/27.11 | $i(v0) | ? [v3: $i] : (apply(all_303_0, v1) = v3 & $i(v3) & ( ~ % 184.45/27.11 | (v3 = v0) | v0 = empty_set) & ( ~ (v0 = empty_set) | v3 = % 184.45/27.11 | empty_set))))) % 184.45/27.11 | % 184.45/27.11 | ALPHA: (34) implies: % 184.45/27.11 | (35) relation(all_303_0) = all_476_1 % 184.45/27.11 | % 184.45/27.11 | DELTA: instantiating (28) with fresh symbols all_482_0, all_482_1 gives: % 184.45/27.11 | (36) relation_dom(all_313_3) = all_482_0 & relation(all_313_3) = all_482_1 % 184.45/27.11 | & $i(all_482_0) & ( ~ (all_482_1 = 0) | ( ? [v0: $i] : ! [v1: $i] : % 184.45/27.11 | ! [v2: $i] : (v2 = v0 | ~ (relation_inverse_image(all_313_3, v1) % 184.45/27.11 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: any] : % 184.45/27.11 | ? [v5: any] : ? [v6: $i] : ? [v7: any] : (apply(all_313_3, v3) % 184.45/27.11 | = v6 & in(v6, v1) = v7 & in(v3, v0) = v4 & in(v3, all_482_0) = % 184.45/27.11 | v5 & $i(v6) & $i(v3) & ( ~ (v7 = 0) | ~ (v5 = 0) | ~ (v4 = % 184.45/27.11 | 0)) & (v4 = 0 | (v7 = 0 & v5 = 0)))) & ! [v0: $i] : ! % 184.45/27.11 | [v1: $i] : ( ~ (relation_inverse_image(all_313_3, v0) = v1) | ~ % 184.45/27.11 | $i(v1) | ~ $i(v0) | ( ! [v2: $i] : ! [v3: $i] : ! [v4: any] : % 184.45/27.11 | ( ~ (apply(all_313_3, v2) = v3) | ~ (in(v3, v0) = v4) | ~ % 184.45/27.11 | $i(v2) | ? [v5: any] : ? [v6: any] : (in(v2, v1) = v5 & % 184.45/27.11 | in(v2, all_482_0) = v6 & ( ~ (v5 = 0) | (v6 = 0 & v4 = % 184.45/27.11 | 0)))) & ! [v2: $i] : ! [v3: $i] : ( ~ % 184.45/27.11 | (apply(all_313_3, v2) = v3) | ~ (in(v3, v0) = 0) | ~ % 184.45/27.11 | $i(v2) | ? [v4: any] : ? [v5: any] : (in(v2, v1) = v5 & % 184.45/27.11 | in(v2, all_482_0) = v4 & ( ~ (v4 = 0) | v5 = 0))))))) % 184.45/27.12 | % 184.45/27.12 | ALPHA: (36) implies: % 184.45/27.12 | (37) relation(all_313_3) = all_482_1 % 184.45/27.12 | (38) ~ (all_482_1 = 0) | ( ? [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = % 184.45/27.12 | v0 | ~ (relation_inverse_image(all_313_3, v1) = v2) | ~ $i(v1) | % 184.45/27.12 | ~ $i(v0) | ? [v3: $i] : ? [v4: any] : ? [v5: any] : ? [v6: % 184.45/27.12 | $i] : ? [v7: any] : (apply(all_313_3, v3) = v6 & in(v6, v1) = % 184.45/27.12 | v7 & in(v3, v0) = v4 & in(v3, all_482_0) = v5 & $i(v6) & $i(v3) % 184.45/27.12 | & ( ~ (v7 = 0) | ~ (v5 = 0) | ~ (v4 = 0)) & (v4 = 0 | (v7 = 0 % 184.45/27.12 | & v5 = 0)))) & ! [v0: $i] : ! [v1: $i] : ( ~ % 184.45/27.12 | (relation_inverse_image(all_313_3, v0) = v1) | ~ $i(v1) | ~ % 184.45/27.12 | $i(v0) | ( ! [v2: $i] : ! [v3: $i] : ! [v4: any] : ( ~ % 184.45/27.12 | (apply(all_313_3, v2) = v3) | ~ (in(v3, v0) = v4) | ~ $i(v2) % 184.45/27.12 | | ? [v5: any] : ? [v6: any] : (in(v2, v1) = v5 & in(v2, % 184.45/27.12 | all_482_0) = v6 & ( ~ (v5 = 0) | (v6 = 0 & v4 = 0)))) & ! % 184.45/27.12 | [v2: $i] : ! [v3: $i] : ( ~ (apply(all_313_3, v2) = v3) | ~ % 184.45/27.12 | (in(v3, v0) = 0) | ~ $i(v2) | ? [v4: any] : ? [v5: any] : % 184.45/27.12 | (in(v2, v1) = v5 & in(v2, all_482_0) = v4 & ( ~ (v4 = 0) | v5 % 184.45/27.12 | = 0)))))) % 184.45/27.12 | % 184.45/27.12 | DELTA: instantiating (27) with fresh symbols all_490_0, all_490_1 gives: % 184.45/27.12 | (39) relation_dom(all_303_0) = all_490_0 & relation(all_303_0) = all_490_1 % 184.45/27.12 | & $i(all_490_0) & ( ~ (all_490_1 = 0) | ( ? [v0: $i] : ! [v1: $i] : % 184.45/27.12 | ! [v2: $i] : (v2 = v0 | ~ (relation_image(all_303_0, v1) = v2) | % 184.45/27.12 | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: any] : (in(v3, v0) % 184.45/27.12 | = v4 & $i(v3) & ( ~ (v4 = 0) | ! [v5: $i] : ( ~ (in(v5, % 184.45/27.12 | all_490_0) = 0) | ~ $i(v5) | ? [v6: any] : ? [v7: % 184.45/27.12 | $i] : (apply(all_303_0, v5) = v7 & in(v5, v1) = v6 & % 184.45/27.12 | $i(v7) & ( ~ (v7 = v3) | ~ (v6 = 0))))) & (v4 = 0 | ? % 184.45/27.12 | [v5: $i] : (apply(all_303_0, v5) = v3 & in(v5, v1) = 0 & % 184.45/27.12 | in(v5, all_490_0) = 0 & $i(v5))))) & ! [v0: $i] : ! [v1: % 184.45/27.12 | $i] : ( ~ (relation_image(all_303_0, v0) = v1) | ~ $i(v1) | ~ % 184.45/27.12 | $i(v0) | ( ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (in(v2, v1) % 184.45/27.12 | = v3) | ~ $i(v2) | ! [v4: $i] : ( ~ (in(v4, all_490_0) = % 184.45/27.12 | 0) | ~ $i(v4) | ? [v5: any] : ? [v6: $i] : % 184.45/27.12 | (apply(all_303_0, v4) = v6 & in(v4, v0) = v5 & $i(v6) & ( % 184.45/27.12 | ~ (v6 = v2) | ~ (v5 = 0))))) & ! [v2: $i] : ( ~ % 184.45/27.12 | (in(v2, v1) = 0) | ~ $i(v2) | ? [v3: $i] : % 184.45/27.12 | (apply(all_303_0, v3) = v2 & in(v3, v0) = 0 & in(v3, % 184.45/27.12 | all_490_0) = 0 & $i(v3))))))) % 184.45/27.12 | % 184.45/27.12 | ALPHA: (39) implies: % 184.45/27.12 | (40) relation(all_303_0) = all_490_1 % 184.45/27.13 | (41) ~ (all_490_1 = 0) | ( ? [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = % 184.45/27.13 | v0 | ~ (relation_image(all_303_0, v1) = v2) | ~ $i(v1) | ~ % 184.45/27.13 | $i(v0) | ? [v3: $i] : ? [v4: any] : (in(v3, v0) = v4 & $i(v3) & % 184.45/27.13 | ( ~ (v4 = 0) | ! [v5: $i] : ( ~ (in(v5, all_490_0) = 0) | ~ % 184.45/27.13 | $i(v5) | ? [v6: any] : ? [v7: $i] : (apply(all_303_0, v5) % 184.45/27.13 | = v7 & in(v5, v1) = v6 & $i(v7) & ( ~ (v7 = v3) | ~ (v6 = % 184.45/27.13 | 0))))) & (v4 = 0 | ? [v5: $i] : (apply(all_303_0, v5) % 184.45/27.13 | = v3 & in(v5, v1) = 0 & in(v5, all_490_0) = 0 & $i(v5))))) & % 184.45/27.13 | ! [v0: $i] : ! [v1: $i] : ( ~ (relation_image(all_303_0, v0) = v1) % 184.45/27.13 | | ~ $i(v1) | ~ $i(v0) | ( ! [v2: $i] : ! [v3: int] : (v3 = 0 | % 184.45/27.13 | ~ (in(v2, v1) = v3) | ~ $i(v2) | ! [v4: $i] : ( ~ (in(v4, % 184.45/27.13 | all_490_0) = 0) | ~ $i(v4) | ? [v5: any] : ? [v6: $i] % 184.45/27.13 | : (apply(all_303_0, v4) = v6 & in(v4, v0) = v5 & $i(v6) & ( % 184.45/27.13 | ~ (v6 = v2) | ~ (v5 = 0))))) & ! [v2: $i] : ( ~ % 184.45/27.13 | (in(v2, v1) = 0) | ~ $i(v2) | ? [v3: $i] : (apply(all_303_0, % 184.45/27.13 | v3) = v2 & in(v3, v0) = 0 & in(v3, all_490_0) = 0 & % 184.45/27.13 | $i(v3)))))) % 184.45/27.13 | % 184.45/27.13 | DELTA: instantiating (29) with fresh symbols all_494_0, all_494_1 gives: % 184.45/27.13 | (42) relation_dom(all_313_3) = all_494_0 & relation(all_313_3) = all_494_1 % 184.45/27.13 | & $i(all_494_0) & ( ~ (all_494_1 = 0) | ( ? [v0: $i] : ! [v1: $i] : % 184.45/27.13 | ! [v2: $i] : (v2 = v0 | ~ (relation_image(all_313_3, v1) = v2) | % 184.45/27.13 | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: any] : (in(v3, v0) % 184.45/27.13 | = v4 & $i(v3) & ( ~ (v4 = 0) | ! [v5: $i] : ( ~ (in(v5, % 184.45/27.13 | all_494_0) = 0) | ~ $i(v5) | ? [v6: any] : ? [v7: % 184.45/27.13 | $i] : (apply(all_313_3, v5) = v7 & in(v5, v1) = v6 & % 184.45/27.13 | $i(v7) & ( ~ (v7 = v3) | ~ (v6 = 0))))) & (v4 = 0 | ? % 184.45/27.13 | [v5: $i] : (apply(all_313_3, v5) = v3 & in(v5, v1) = 0 & % 184.45/27.13 | in(v5, all_494_0) = 0 & $i(v5))))) & ! [v0: $i] : ! [v1: % 184.45/27.13 | $i] : ( ~ (relation_image(all_313_3, v0) = v1) | ~ $i(v1) | ~ % 184.45/27.13 | $i(v0) | ( ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (in(v2, v1) % 184.45/27.13 | = v3) | ~ $i(v2) | ! [v4: $i] : ( ~ (in(v4, all_494_0) = % 184.45/27.13 | 0) | ~ $i(v4) | ? [v5: any] : ? [v6: $i] : % 184.45/27.13 | (apply(all_313_3, v4) = v6 & in(v4, v0) = v5 & $i(v6) & ( % 184.45/27.13 | ~ (v6 = v2) | ~ (v5 = 0))))) & ! [v2: $i] : ( ~ % 184.45/27.13 | (in(v2, v1) = 0) | ~ $i(v2) | ? [v3: $i] : % 184.45/27.13 | (apply(all_313_3, v3) = v2 & in(v3, v0) = 0 & in(v3, % 184.45/27.13 | all_494_0) = 0 & $i(v3))))))) % 184.45/27.13 | % 184.45/27.13 | ALPHA: (42) implies: % 184.45/27.13 | (43) relation(all_313_3) = all_494_1 % 184.92/27.13 | (44) ~ (all_494_1 = 0) | ( ? [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = % 184.92/27.13 | v0 | ~ (relation_image(all_313_3, v1) = v2) | ~ $i(v1) | ~ % 184.92/27.13 | $i(v0) | ? [v3: $i] : ? [v4: any] : (in(v3, v0) = v4 & $i(v3) & % 184.92/27.13 | ( ~ (v4 = 0) | ! [v5: $i] : ( ~ (in(v5, all_494_0) = 0) | ~ % 184.92/27.13 | $i(v5) | ? [v6: any] : ? [v7: $i] : (apply(all_313_3, v5) % 184.92/27.13 | = v7 & in(v5, v1) = v6 & $i(v7) & ( ~ (v7 = v3) | ~ (v6 = % 184.92/27.13 | 0))))) & (v4 = 0 | ? [v5: $i] : (apply(all_313_3, v5) % 184.92/27.13 | = v3 & in(v5, v1) = 0 & in(v5, all_494_0) = 0 & $i(v5))))) & % 184.92/27.13 | ! [v0: $i] : ! [v1: $i] : ( ~ (relation_image(all_313_3, v0) = v1) % 184.92/27.13 | | ~ $i(v1) | ~ $i(v0) | ( ! [v2: $i] : ! [v3: int] : (v3 = 0 | % 184.92/27.13 | ~ (in(v2, v1) = v3) | ~ $i(v2) | ! [v4: $i] : ( ~ (in(v4, % 184.92/27.13 | all_494_0) = 0) | ~ $i(v4) | ? [v5: any] : ? [v6: $i] % 184.92/27.13 | : (apply(all_313_3, v4) = v6 & in(v4, v0) = v5 & $i(v6) & ( % 184.92/27.13 | ~ (v6 = v2) | ~ (v5 = 0))))) & ! [v2: $i] : ( ~ % 184.92/27.13 | (in(v2, v1) = 0) | ~ $i(v2) | ? [v3: $i] : (apply(all_313_3, % 184.92/27.13 | v3) = v2 & in(v3, v0) = 0 & in(v3, all_494_0) = 0 & % 184.92/27.13 | $i(v3)))))) % 184.92/27.13 | % 184.92/27.13 | BETA: splitting (31) gives: % 184.92/27.13 | % 184.92/27.13 | Case 1: % 184.92/27.13 | | % 184.92/27.13 | | (45) all_313_0 = 0 % 184.92/27.13 | | % 184.92/27.13 | | REDUCE: (15), (45) imply: % 184.92/27.13 | | (46) $false % 184.92/27.14 | | % 184.92/27.14 | | CLOSE: (46) is inconsistent. % 184.92/27.14 | | % 184.92/27.14 | Case 2: % 184.92/27.14 | | % 184.92/27.14 | | (47) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & in(v0, all_313_1) = 0 & % 184.92/27.14 | | in(v0, all_313_4) = v1 & $i(v0)) % 184.92/27.14 | | % 184.92/27.14 | | DELTA: instantiating (47) with fresh symbols all_502_0, all_502_1 gives: % 184.92/27.14 | | (48) ~ (all_502_0 = 0) & in(all_502_1, all_313_1) = 0 & in(all_502_1, % 184.92/27.14 | | all_313_4) = all_502_0 & $i(all_502_1) % 184.92/27.14 | | % 184.92/27.14 | | ALPHA: (48) implies: % 184.92/27.14 | | (49) ~ (all_502_0 = 0) % 184.92/27.14 | | (50) $i(all_502_1) % 184.92/27.14 | | (51) in(all_502_1, all_313_4) = all_502_0 % 184.92/27.14 | | (52) in(all_502_1, all_313_1) = 0 % 184.92/27.14 | | % 184.92/27.14 | | BETA: splitting (25) gives: % 184.92/27.14 | | % 184.92/27.14 | | Case 1: % 184.92/27.14 | | | % 184.92/27.14 | | | (53) all_298_0 = 0 % 184.92/27.14 | | | % 184.92/27.14 | | | REDUCE: (6), (53) imply: % 184.92/27.14 | | | (54) $false % 184.92/27.14 | | | % 184.92/27.14 | | | CLOSE: (54) is inconsistent. % 184.92/27.14 | | | % 184.92/27.14 | | Case 2: % 184.92/27.14 | | | % 184.92/27.14 | | | % 184.92/27.14 | | | GROUND_INST: instantiating (3) with 0, all_490_1, all_303_0, simplifying % 184.92/27.14 | | | with (12), (40) gives: % 184.92/27.14 | | | (55) all_490_1 = 0 % 184.92/27.14 | | | % 184.92/27.14 | | | GROUND_INST: instantiating (3) with all_476_1, all_490_1, all_303_0, % 184.92/27.14 | | | simplifying with (35), (40) gives: % 184.92/27.14 | | | (56) all_490_1 = all_476_1 % 184.92/27.14 | | | % 184.92/27.14 | | | GROUND_INST: instantiating (3) with all_438_2, all_490_1, all_303_0, % 184.92/27.14 | | | simplifying with (33), (40) gives: % 184.92/27.14 | | | (57) all_490_1 = all_438_2 % 184.92/27.14 | | | % 184.92/27.14 | | | GROUND_INST: instantiating (3) with 0, all_494_1, all_313_3, simplifying % 184.92/27.14 | | | with (21), (43) gives: % 184.92/27.14 | | | (58) all_494_1 = 0 % 184.92/27.14 | | | % 184.92/27.14 | | | GROUND_INST: instantiating (3) with all_482_1, all_494_1, all_313_3, % 184.92/27.14 | | | simplifying with (37), (43) gives: % 184.92/27.14 | | | (59) all_494_1 = all_482_1 % 184.92/27.14 | | | % 184.92/27.14 | | | COMBINE_EQS: (58), (59) imply: % 184.92/27.14 | | | (60) all_482_1 = 0 % 184.92/27.14 | | | % 184.92/27.14 | | | COMBINE_EQS: (55), (56) imply: % 184.92/27.14 | | | (61) all_476_1 = 0 % 184.92/27.14 | | | % 184.92/27.14 | | | COMBINE_EQS: (56), (57) imply: % 184.92/27.14 | | | (62) all_476_1 = all_438_2 % 184.92/27.14 | | | % 184.92/27.14 | | | COMBINE_EQS: (61), (62) imply: % 184.92/27.14 | | | (63) all_438_2 = 0 % 184.92/27.14 | | | % 184.92/27.14 | | | BETA: splitting (44) gives: % 184.92/27.14 | | | % 184.92/27.14 | | | Case 1: % 184.92/27.14 | | | | % 184.92/27.14 | | | | (64) ~ (all_494_1 = 0) % 184.92/27.14 | | | | % 184.92/27.14 | | | | REDUCE: (58), (64) imply: % 184.92/27.14 | | | | (65) $false % 184.92/27.14 | | | | % 184.92/27.14 | | | | CLOSE: (65) is inconsistent. % 184.92/27.14 | | | | % 184.92/27.14 | | | Case 2: % 184.92/27.14 | | | | % 184.92/27.14 | | | | (66) ? [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v0 | ~ % 184.92/27.14 | | | | (relation_image(all_313_3, v1) = v2) | ~ $i(v1) | ~ $i(v0) | % 184.92/27.14 | | | | ? [v3: $i] : ? [v4: any] : (in(v3, v0) = v4 & $i(v3) & ( ~ % 184.92/27.14 | | | | (v4 = 0) | ! [v5: $i] : ( ~ (in(v5, all_494_0) = 0) | ~ % 184.92/27.14 | | | | $i(v5) | ? [v6: any] : ? [v7: $i] : (apply(all_313_3, % 184.92/27.14 | | | | v5) = v7 & in(v5, v1) = v6 & $i(v7) & ( ~ (v7 = v3) % 184.92/27.14 | | | | | ~ (v6 = 0))))) & (v4 = 0 | ? [v5: $i] : % 184.92/27.14 | | | | (apply(all_313_3, v5) = v3 & in(v5, v1) = 0 & in(v5, % 184.92/27.14 | | | | all_494_0) = 0 & $i(v5))))) & ! [v0: $i] : ! [v1: % 184.92/27.14 | | | | $i] : ( ~ (relation_image(all_313_3, v0) = v1) | ~ $i(v1) | % 184.92/27.14 | | | | ~ $i(v0) | ( ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (in(v2, % 184.92/27.14 | | | | v1) = v3) | ~ $i(v2) | ! [v4: $i] : ( ~ (in(v4, % 184.92/27.14 | | | | all_494_0) = 0) | ~ $i(v4) | ? [v5: any] : ? [v6: % 184.92/27.14 | | | | $i] : (apply(all_313_3, v4) = v6 & in(v4, v0) = v5 & % 184.92/27.14 | | | | $i(v6) & ( ~ (v6 = v2) | ~ (v5 = 0))))) & ! [v2: $i] % 184.92/27.14 | | | | : ( ~ (in(v2, v1) = 0) | ~ $i(v2) | ? [v3: $i] : % 184.92/27.14 | | | | (apply(all_313_3, v3) = v2 & in(v3, v0) = 0 & in(v3, % 184.92/27.14 | | | | all_494_0) = 0 & $i(v3))))) % 184.92/27.14 | | | | % 184.92/27.14 | | | | ALPHA: (66) implies: % 184.92/27.14 | | | | (67) ! [v0: $i] : ! [v1: $i] : ( ~ (relation_image(all_313_3, v0) = % 184.92/27.14 | | | | v1) | ~ $i(v1) | ~ $i(v0) | ( ! [v2: $i] : ! [v3: int] : % 184.92/27.14 | | | | (v3 = 0 | ~ (in(v2, v1) = v3) | ~ $i(v2) | ! [v4: $i] : ( % 184.92/27.14 | | | | ~ (in(v4, all_494_0) = 0) | ~ $i(v4) | ? [v5: any] : % 184.92/27.14 | | | | ? [v6: $i] : (apply(all_313_3, v4) = v6 & in(v4, v0) = % 184.92/27.14 | | | | v5 & $i(v6) & ( ~ (v6 = v2) | ~ (v5 = 0))))) & ! % 184.92/27.14 | | | | [v2: $i] : ( ~ (in(v2, v1) = 0) | ~ $i(v2) | ? [v3: $i] : % 184.92/27.14 | | | | (apply(all_313_3, v3) = v2 & in(v3, v0) = 0 & in(v3, % 184.92/27.14 | | | | all_494_0) = 0 & $i(v3))))) % 184.92/27.14 | | | | % 184.92/27.14 | | | | GROUND_INST: instantiating (67) with all_313_2, all_313_1, simplifying % 184.92/27.14 | | | | with (18), (19), (23) gives: % 184.92/27.15 | | | | (68) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (in(v0, all_313_1) = % 184.92/27.15 | | | | v1) | ~ $i(v0) | ! [v2: $i] : ( ~ (in(v2, all_494_0) = 0) % 184.92/27.15 | | | | | ~ $i(v2) | ? [v3: any] : ? [v4: $i] : (apply(all_313_3, % 184.92/27.15 | | | | v2) = v4 & in(v2, all_313_2) = v3 & $i(v4) & ( ~ (v4 = % 184.92/27.15 | | | | v0) | ~ (v3 = 0))))) & ! [v0: $i] : ( ~ (in(v0, % 184.92/27.15 | | | | all_313_1) = 0) | ~ $i(v0) | ? [v1: $i] : % 184.92/27.15 | | | | (apply(all_313_3, v1) = v0 & in(v1, all_494_0) = 0 & in(v1, % 184.92/27.15 | | | | all_313_2) = 0 & $i(v1))) % 184.92/27.15 | | | | % 184.92/27.15 | | | | ALPHA: (68) implies: % 184.92/27.15 | | | | (69) ! [v0: $i] : ( ~ (in(v0, all_313_1) = 0) | ~ $i(v0) | ? [v1: % 184.92/27.15 | | | | $i] : (apply(all_313_3, v1) = v0 & in(v1, all_494_0) = 0 & % 184.92/27.15 | | | | in(v1, all_313_2) = 0 & $i(v1))) % 184.92/27.15 | | | | % 184.92/27.15 | | | | BETA: splitting (38) gives: % 184.92/27.15 | | | | % 184.92/27.15 | | | | Case 1: % 184.92/27.15 | | | | | % 184.92/27.15 | | | | | (70) ~ (all_482_1 = 0) % 184.92/27.15 | | | | | % 184.92/27.15 | | | | | REDUCE: (60), (70) imply: % 184.92/27.15 | | | | | (71) $false % 184.92/27.15 | | | | | % 184.92/27.15 | | | | | CLOSE: (71) is inconsistent. % 184.92/27.15 | | | | | % 184.92/27.15 | | | | Case 2: % 184.92/27.15 | | | | | % 184.92/27.15 | | | | | (72) ? [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v0 | ~ % 184.92/27.15 | | | | | (relation_inverse_image(all_313_3, v1) = v2) | ~ $i(v1) | % 184.92/27.15 | | | | | ~ $i(v0) | ? [v3: $i] : ? [v4: any] : ? [v5: any] : ? % 184.92/27.15 | | | | | [v6: $i] : ? [v7: any] : (apply(all_313_3, v3) = v6 & % 184.92/27.15 | | | | | in(v6, v1) = v7 & in(v3, v0) = v4 & in(v3, all_482_0) = v5 % 184.92/27.15 | | | | | & $i(v6) & $i(v3) & ( ~ (v7 = 0) | ~ (v5 = 0) | ~ (v4 = % 184.92/27.15 | | | | | 0)) & (v4 = 0 | (v7 = 0 & v5 = 0)))) & ! [v0: $i] : % 184.92/27.15 | | | | | ! [v1: $i] : ( ~ (relation_inverse_image(all_313_3, v0) = v1) % 184.92/27.15 | | | | | | ~ $i(v1) | ~ $i(v0) | ( ! [v2: $i] : ! [v3: $i] : ! % 184.92/27.15 | | | | | [v4: any] : ( ~ (apply(all_313_3, v2) = v3) | ~ (in(v3, % 184.92/27.15 | | | | | v0) = v4) | ~ $i(v2) | ? [v5: any] : ? [v6: any] % 184.92/27.15 | | | | | : (in(v2, v1) = v5 & in(v2, all_482_0) = v6 & ( ~ (v5 = % 184.92/27.15 | | | | | 0) | (v6 = 0 & v4 = 0)))) & ! [v2: $i] : ! [v3: % 184.92/27.15 | | | | | $i] : ( ~ (apply(all_313_3, v2) = v3) | ~ (in(v3, v0) = % 184.92/27.15 | | | | | 0) | ~ $i(v2) | ? [v4: any] : ? [v5: any] : (in(v2, % 184.92/27.15 | | | | | v1) = v5 & in(v2, all_482_0) = v4 & ( ~ (v4 = 0) | % 184.92/27.15 | | | | | v5 = 0))))) % 184.92/27.15 | | | | | % 184.92/27.15 | | | | | ALPHA: (72) implies: % 184.92/27.15 | | | | | (73) ! [v0: $i] : ! [v1: $i] : ( ~ % 184.92/27.15 | | | | | (relation_inverse_image(all_313_3, v0) = v1) | ~ $i(v1) | % 184.92/27.15 | | | | | ~ $i(v0) | ( ! [v2: $i] : ! [v3: $i] : ! [v4: any] : ( ~ % 184.92/27.15 | | | | | (apply(all_313_3, v2) = v3) | ~ (in(v3, v0) = v4) | ~ % 184.92/27.15 | | | | | $i(v2) | ? [v5: any] : ? [v6: any] : (in(v2, v1) = v5 % 184.92/27.15 | | | | | & in(v2, all_482_0) = v6 & ( ~ (v5 = 0) | (v6 = 0 & v4 % 184.92/27.15 | | | | | = 0)))) & ! [v2: $i] : ! [v3: $i] : ( ~ % 184.92/27.15 | | | | | (apply(all_313_3, v2) = v3) | ~ (in(v3, v0) = 0) | ~ % 184.92/27.15 | | | | | $i(v2) | ? [v4: any] : ? [v5: any] : (in(v2, v1) = v5 % 184.92/27.15 | | | | | & in(v2, all_482_0) = v4 & ( ~ (v4 = 0) | v5 = 0))))) % 184.92/27.15 | | | | | % 184.92/27.15 | | | | | GROUND_INST: instantiating (73) with all_313_4, all_313_2, simplifying % 184.92/27.15 | | | | | with (16), (18), (24) gives: % 184.92/27.15 | | | | | (74) ! [v0: $i] : ! [v1: $i] : ! [v2: any] : ( ~ % 184.92/27.15 | | | | | (apply(all_313_3, v0) = v1) | ~ (in(v1, all_313_4) = v2) | % 184.92/27.15 | | | | | ~ $i(v0) | ? [v3: any] : ? [v4: any] : (in(v0, all_482_0) % 184.92/27.15 | | | | | = v4 & in(v0, all_313_2) = v3 & ( ~ (v3 = 0) | (v4 = 0 & % 184.92/27.15 | | | | | v2 = 0)))) & ! [v0: $i] : ! [v1: $i] : ( ~ % 184.92/27.15 | | | | | (apply(all_313_3, v0) = v1) | ~ (in(v1, all_313_4) = 0) | % 184.92/27.15 | | | | | ~ $i(v0) | ? [v2: any] : ? [v3: any] : (in(v0, all_482_0) % 184.92/27.15 | | | | | = v2 & in(v0, all_313_2) = v3 & ( ~ (v2 = 0) | v3 = 0))) % 184.92/27.15 | | | | | % 184.92/27.15 | | | | | ALPHA: (74) implies: % 184.92/27.15 | | | | | (75) ! [v0: $i] : ! [v1: $i] : ! [v2: any] : ( ~ % 184.92/27.15 | | | | | (apply(all_313_3, v0) = v1) | ~ (in(v1, all_313_4) = v2) | % 184.92/27.15 | | | | | ~ $i(v0) | ? [v3: any] : ? [v4: any] : (in(v0, all_482_0) % 184.92/27.15 | | | | | = v4 & in(v0, all_313_2) = v3 & ( ~ (v3 = 0) | (v4 = 0 & % 184.92/27.15 | | | | | v2 = 0)))) % 184.92/27.15 | | | | | % 184.92/27.15 | | | | | BETA: splitting (41) gives: % 184.92/27.15 | | | | | % 184.92/27.15 | | | | | Case 1: % 184.92/27.15 | | | | | | % 184.92/27.15 | | | | | | (76) ~ (all_490_1 = 0) % 184.92/27.15 | | | | | | % 184.92/27.15 | | | | | | REDUCE: (55), (76) imply: % 184.92/27.15 | | | | | | (77) $false % 184.92/27.15 | | | | | | % 184.92/27.15 | | | | | | CLOSE: (77) is inconsistent. % 184.92/27.15 | | | | | | % 184.92/27.15 | | | | | Case 2: % 184.92/27.15 | | | | | | % 184.92/27.15 | | | | | | % 184.92/27.15 | | | | | | GROUND_INST: instantiating (69) with all_502_1, simplifying with % 184.92/27.15 | | | | | | (50), (52) gives: % 184.92/27.15 | | | | | | (78) ? [v0: $i] : (apply(all_313_3, v0) = all_502_1 & in(v0, % 184.92/27.15 | | | | | | all_494_0) = 0 & in(v0, all_313_2) = 0 & $i(v0)) % 184.92/27.15 | | | | | | % 184.92/27.15 | | | | | | DELTA: instantiating (78) with fresh symbol all_711_0 gives: % 184.92/27.16 | | | | | | (79) apply(all_313_3, all_711_0) = all_502_1 & in(all_711_0, % 184.92/27.16 | | | | | | all_494_0) = 0 & in(all_711_0, all_313_2) = 0 & % 184.92/27.16 | | | | | | $i(all_711_0) % 184.92/27.16 | | | | | | % 184.92/27.16 | | | | | | ALPHA: (79) implies: % 184.92/27.16 | | | | | | (80) $i(all_711_0) % 184.92/27.16 | | | | | | (81) in(all_711_0, all_313_2) = 0 % 184.92/27.16 | | | | | | (82) apply(all_313_3, all_711_0) = all_502_1 % 184.92/27.16 | | | | | | % 184.92/27.16 | | | | | | GROUND_INST: instantiating (75) with all_711_0, all_502_1, % 184.92/27.16 | | | | | | all_502_0, simplifying with (51), (80), (82) gives: % 184.92/27.16 | | | | | | (83) ? [v0: any] : ? [v1: any] : (in(all_711_0, all_482_0) = v1 % 184.92/27.16 | | | | | | & in(all_711_0, all_313_2) = v0 & ( ~ (v0 = 0) | (v1 = 0 & % 184.92/27.16 | | | | | | all_502_0 = 0))) % 184.92/27.16 | | | | | | % 184.92/27.16 | | | | | | DELTA: instantiating (83) with fresh symbols all_1997_0, all_1997_1 % 184.92/27.16 | | | | | | gives: % 184.92/27.16 | | | | | | (84) in(all_711_0, all_482_0) = all_1997_0 & in(all_711_0, % 184.92/27.16 | | | | | | all_313_2) = all_1997_1 & ( ~ (all_1997_1 = 0) | % 184.92/27.16 | | | | | | (all_1997_0 = 0 & all_502_0 = 0)) % 184.92/27.16 | | | | | | % 184.92/27.16 | | | | | | ALPHA: (84) implies: % 184.92/27.16 | | | | | | (85) in(all_711_0, all_313_2) = all_1997_1 % 184.92/27.16 | | | | | | (86) ~ (all_1997_1 = 0) | (all_1997_0 = 0 & all_502_0 = 0) % 184.92/27.16 | | | | | | % 184.92/27.16 | | | | | | BETA: splitting (86) gives: % 184.92/27.16 | | | | | | % 184.92/27.16 | | | | | | Case 1: % 184.92/27.16 | | | | | | | % 184.92/27.16 | | | | | | | (87) ~ (all_1997_1 = 0) % 184.92/27.16 | | | | | | | % 184.92/27.16 | | | | | | | GROUND_INST: instantiating (4) with 0, all_1997_1, all_313_2, % 184.92/27.16 | | | | | | | all_711_0, simplifying with (81), (85) gives: % 184.92/27.16 | | | | | | | (88) all_1997_1 = 0 % 184.92/27.16 | | | | | | | % 184.92/27.16 | | | | | | | REDUCE: (87), (88) imply: % 184.92/27.16 | | | | | | | (89) $false % 184.92/27.16 | | | | | | | % 184.92/27.16 | | | | | | | CLOSE: (89) is inconsistent. % 184.92/27.16 | | | | | | | % 184.92/27.16 | | | | | | Case 2: % 184.92/27.16 | | | | | | | % 184.92/27.16 | | | | | | | (90) all_1997_0 = 0 & all_502_0 = 0 % 184.92/27.16 | | | | | | | % 184.92/27.16 | | | | | | | ALPHA: (90) implies: % 184.92/27.16 | | | | | | | (91) all_502_0 = 0 % 184.92/27.16 | | | | | | | % 184.92/27.16 | | | | | | | REDUCE: (49), (91) imply: % 184.92/27.16 | | | | | | | (92) $false % 184.92/27.16 | | | | | | | % 184.92/27.16 | | | | | | | CLOSE: (92) is inconsistent. % 184.92/27.16 | | | | | | | % 184.92/27.16 | | | | | | End of split % 184.92/27.16 | | | | | | % 184.92/27.16 | | | | | End of split % 184.92/27.16 | | | | | % 184.92/27.16 | | | | End of split % 184.92/27.16 | | | | % 184.92/27.16 | | | End of split % 184.92/27.16 | | | % 184.92/27.16 | | End of split % 184.92/27.16 | | % 184.92/27.16 | End of split % 184.92/27.16 | % 184.92/27.16 End of proof % 184.92/27.16 % SZS output end Proof for theBenchmark % 184.92/27.16 % 184.92/27.16 26545ms %------------------------------------------------------------------------------