%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SEU223+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 : n011.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 128.00s 17.83s % Output : Proof 129.62s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SEU223+2 : TPTP v8.1.2. Released v3.3.0. % 0.00/0.12 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.16/0.33 % Computer : n011.cluster.edu % 0.16/0.33 % Model : x86_64 x86_64 % 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.16/0.33 % Memory : 8042.1875MB % 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.16/0.34 % CPULimit : 300 % 0.16/0.34 % WCLimit : 300 % 0.16/0.34 % DateTime : Wed Aug 23 15:20:21 EDT 2023 % 0.16/0.34 % CPUTime : % 0.19/0.60 ________ _____ % 0.19/0.60 ___ __ \_________(_)________________________________ % 0.19/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.19/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.19/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.19/0.60 % 0.19/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.19/0.60 (2023-06-19) % 0.19/0.60 % 0.19/0.60 (c) Philipp Rümmer, 2009-2023 % 0.19/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.19/0.60 Amanda Stjerna. % 0.19/0.60 Free software under BSD-3-Clause. % 0.19/0.60 % 0.19/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.19/0.60 % 0.19/0.60 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.19/0.62 Running up to 7 provers in parallel. % 0.19/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.19/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.19/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.19/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.19/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.19/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.19/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 6.22/1.62 Prover 1: Preprocessing ... % 6.53/1.64 Prover 4: Preprocessing ... % 6.60/1.65 Prover 0: Preprocessing ... % 6.60/1.65 Prover 2: Preprocessing ... % 6.60/1.65 Prover 6: Preprocessing ... % 6.60/1.65 Prover 3: Preprocessing ... % 6.60/1.65 Prover 5: Preprocessing ... % 20.47/3.53 Prover 1: Warning: ignoring some quantifiers % 20.98/3.61 Prover 3: Warning: ignoring some quantifiers % 20.98/3.65 Prover 5: Proving ... % 20.98/3.66 Prover 3: Constructing countermodel ... % 20.98/3.66 Prover 6: Proving ... % 20.98/3.68 Prover 1: Constructing countermodel ... % 24.54/4.10 Prover 2: Proving ... % 26.03/4.29 Prover 4: Warning: ignoring some quantifiers % 26.03/4.40 Prover 4: Constructing countermodel ... % 32.01/5.11 Prover 0: Proving ... % 73.87/10.60 Prover 2: stopped % 73.87/10.62 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 75.70/10.85 Prover 7: Preprocessing ... % 78.98/11.34 Prover 7: Warning: ignoring some quantifiers % 78.98/11.40 Prover 7: Constructing countermodel ... % 100.06/13.97 Prover 5: stopped % 100.06/13.98 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 101.37/14.16 Prover 8: Preprocessing ... % 105.21/14.66 Prover 8: Warning: ignoring some quantifiers % 105.63/14.70 Prover 8: Constructing countermodel ... % 115.41/15.98 Prover 1: stopped % 115.41/16.00 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889 % 116.54/16.13 Prover 9: Preprocessing ... % 122.94/17.10 Prover 9: Warning: ignoring some quantifiers % 122.94/17.17 Prover 9: Constructing countermodel ... % 128.00/17.80 Prover 7: Found proof (size 75) % 128.00/17.81 Prover 7: proved (7128ms) % 128.00/17.81 Prover 6: stopped % 128.00/17.81 Prover 9: stopped % 128.00/17.82 Prover 3: stopped % 128.00/17.82 Prover 0: stopped % 128.00/17.82 Prover 8: stopped % 128.00/17.83 Prover 4: stopped % 128.00/17.83 % 128.00/17.83 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 128.00/17.83 % 128.00/17.84 % SZS output start Proof for theBenchmark % 129.13/17.85 Assumptions after simplification: % 129.13/17.85 --------------------------------- % 129.13/17.85 % 129.13/17.85 (cc1_funct_1) % 129.13/17.85 ! [v0: $i] : ( ~ $i(v0) | ~ empty(v0) | function(v0)) % 129.13/17.85 % 129.13/17.85 (dt_k7_relat_1) % 129.29/17.87 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (relation_dom_restriction(v0, % 129.29/17.87 v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ relation(v0) | relation(v2)) % 129.29/17.87 % 129.29/17.87 (fc4_funct_1) % 129.29/17.87 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (relation_dom_restriction(v0, % 129.29/17.87 v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ relation(v0) | ~ function(v0) | % 129.29/17.88 relation(v2)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 129.29/17.88 (relation_dom_restriction(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ % 129.29/17.88 relation(v0) | ~ function(v0) | function(v2)) % 129.29/17.88 % 129.29/17.88 (fc4_relat_1) % 129.29/17.88 $i(empty_set) & relation(empty_set) & empty(empty_set) % 129.29/17.88 % 129.29/17.88 (rc1_relat_1) % 129.29/17.88 ? [v0: $i] : ($i(v0) & relation(v0) & empty(v0)) % 129.29/17.88 % 129.29/17.88 (rc1_xboole_0) % 129.29/17.88 ? [v0: $i] : ($i(v0) & empty(v0)) % 129.29/17.88 % 129.29/17.88 (rc2_funct_1) % 129.29/17.88 ? [v0: $i] : ($i(v0) & relation(v0) & function(v0) & empty(v0)) % 129.29/17.88 % 129.29/17.88 (t22_funct_1) % 129.29/17.88 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (apply(v2, v0) = % 129.29/17.88 v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ relation(v2) | ~ % 129.29/17.88 relation(v1) | ~ function(v2) | ~ function(v1) | ? [v4: $i] : ? [v5: $i] % 129.29/17.88 : ? [v6: $i] : ? [v7: $i] : (relation_composition(v2, v1) = v4 & $i(v4) & % 129.29/17.88 ((v7 = v6 & apply(v4, v0) = v6 & apply(v1, v3) = v6 & $i(v6)) | % 129.29/17.88 (relation_dom(v4) = v5 & $i(v5) & ~ in(v0, v5))))) & ? [v0: $i] : ! % 129.29/17.88 [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (relation_composition(v2, v1) = v3) % 129.29/17.88 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ relation(v2) | ~ relation(v1) | ~ % 129.29/17.88 function(v2) | ~ function(v1) | ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : % 129.29/17.88 ? [v7: $i] : ((v7 = v5 & apply(v3, v0) = v5 & apply(v2, v0) = v6 & apply(v1, % 129.29/17.88 v6) = v5 & $i(v6) & $i(v5)) | (relation_dom(v3) = v4 & $i(v4) & ~ % 129.29/17.88 in(v0, v4)))) % 129.29/17.88 % 129.29/17.88 (t45_relat_1) % 129.29/17.89 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (relation_composition(v0, v1) = % 129.29/17.89 v2) | ~ $i(v1) | ~ $i(v0) | ~ relation(v1) | ~ relation(v0) | ? [v3: % 129.29/17.89 $i] : ? [v4: $i] : (relation_rng(v2) = v3 & relation_rng(v1) = v4 & % 129.29/17.89 $i(v4) & $i(v3) & subset(v3, v4))) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 129.29/17.89 $i] : ( ~ (relation_rng(v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ relation(v1) % 129.29/17.89 | ~ relation(v0) | ? [v3: $i] : ? [v4: $i] : (relation_composition(v0, % 129.29/17.89 v1) = v3 & relation_rng(v3) = v4 & $i(v4) & $i(v3) & subset(v4, v2))) % 129.29/17.89 % 129.29/17.89 (t60_relat_1) % 129.29/17.89 relation_rng(empty_set) = empty_set & relation_dom(empty_set) = empty_set & % 129.29/17.89 $i(empty_set) % 129.29/17.89 % 129.29/17.89 (t68_funct_1) % 129.29/17.89 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 129.29/17.89 (relation_dom(v1) = v2) | ~ (relation_dom_restriction(v3, v0) = v4) | ~ % 129.29/17.89 $i(v3) | ~ $i(v1) | ~ $i(v0) | ~ relation(v3) | ~ relation(v1) | ~ % 129.29/17.89 function(v3) | ~ function(v1) | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : % 129.29/17.89 ? [v8: $i] : ? [v9: $i] : ($i(v7) & ( ~ (v4 = v1) | (v6 = v2 & % 129.29/17.89 relation_dom(v3) = v5 & set_intersection2(v5, v0) = v2 & $i(v5) & % 129.29/17.89 $i(v2) & ! [v10: $i] : ! [v11: $i] : ( ~ (apply(v3, v10) = v11) | ~ % 129.29/17.89 $i(v10) | ~ in(v10, v2) | (apply(v1, v10) = v11 & $i(v11))) & ! % 129.29/17.89 [v10: $i] : ! [v11: $i] : ( ~ (apply(v1, v10) = v11) | ~ $i(v10) | % 129.29/17.89 ~ in(v10, v2) | (apply(v3, v10) = v11 & $i(v11))))) & (v4 = v1 | ( ~ % 129.29/17.89 (v9 = v8) & apply(v3, v7) = v9 & apply(v1, v7) = v8 & $i(v9) & $i(v8) % 129.29/17.89 & in(v7, v2)) | ( ~ (v6 = v2) & relation_dom(v3) = v5 & % 129.29/17.89 set_intersection2(v5, v0) = v6 & $i(v6) & $i(v5))))) & ? [v0: $i] : % 129.29/17.89 ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (relation_dom(v3) = % 129.29/17.89 v4) | ~ (relation_dom(v1) = v2) | ~ $i(v3) | ~ $i(v1) | ~ $i(v0) | ~ % 129.29/17.89 relation(v3) | ~ relation(v1) | ~ function(v3) | ~ function(v1) | ? [v5: % 129.29/17.89 $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ($i(v7) & % 129.29/17.89 ((v6 = v2 & set_intersection2(v4, v0) = v2 & $i(v2) & ! [v10: $i] : ! % 129.29/17.89 [v11: $i] : ( ~ (apply(v3, v10) = v11) | ~ $i(v10) | ~ in(v10, v2) | % 129.29/17.90 (apply(v1, v10) = v11 & $i(v11))) & ! [v10: $i] : ! [v11: $i] : ( % 129.29/17.90 ~ (apply(v1, v10) = v11) | ~ $i(v10) | ~ in(v10, v2) | (apply(v3, % 129.29/17.90 v10) = v11 & $i(v11)))) | ( ~ (v5 = v1) & % 129.29/17.90 relation_dom_restriction(v3, v0) = v5 & $i(v5))) & ((v5 = v1 & % 129.29/17.90 relation_dom_restriction(v3, v0) = v1) | ( ~ (v9 = v8) & apply(v3, v7) % 129.29/17.90 = v9 & apply(v1, v7) = v8 & $i(v9) & $i(v8) & in(v7, v2)) | ( ~ (v6 = % 129.29/17.90 v2) & set_intersection2(v4, v0) = v6 & $i(v6))))) % 129.29/17.90 % 129.29/17.90 (t6_boole) % 129.29/17.90 $i(empty_set) & ! [v0: $i] : (v0 = empty_set | ~ $i(v0) | ~ empty(v0)) % 129.29/17.90 % 129.29/17.90 (t70_funct_1) % 129.29/17.90 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: % 129.29/17.90 $i] : ? [v6: $i] : ( ~ (v6 = v5) & relation_dom(v3) = v4 & apply(v3, v1) = % 129.29/17.90 v5 & apply(v2, v1) = v6 & relation_dom_restriction(v2, v0) = v3 & $i(v6) & % 129.29/17.90 $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & relation(v2) & % 129.29/17.90 function(v2) & in(v1, v4)) % 129.29/17.90 % 129.29/17.90 (t8_boole) % 129.29/17.90 ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ $i(v1) | ~ $i(v0) | ~ empty(v1) | % 129.29/17.90 ~ empty(v0)) % 129.29/17.90 % 129.29/17.90 (t90_relat_1) % 129.29/17.90 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (relation_dom(v1) % 129.29/17.90 = v2) | ~ (set_intersection2(v2, v0) = v3) | ~ $i(v1) | ~ $i(v0) | ~ % 129.29/17.90 relation(v1) | ? [v4: $i] : (relation_dom(v4) = v3 & % 129.29/17.90 relation_dom_restriction(v1, v0) = v4 & $i(v4) & $i(v3))) & ! [v0: $i] : % 129.29/17.90 ! [v1: $i] : ! [v2: $i] : ( ~ (relation_dom_restriction(v1, v0) = v2) | ~ % 129.29/17.90 $i(v1) | ~ $i(v0) | ~ relation(v1) | ? [v3: $i] : ? [v4: $i] : % 129.29/17.90 (relation_dom(v2) = v3 & relation_dom(v1) = v4 & set_intersection2(v4, v0) = % 129.29/17.90 v3 & $i(v4) & $i(v3))) % 129.29/17.90 % 129.29/17.90 (t94_relat_1) % 129.29/17.90 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 129.29/17.90 (relation_composition(v2, v1) = v3) | ~ (identity_relation(v0) = v2) | ~ % 129.29/17.90 $i(v1) | ~ $i(v0) | ~ relation(v1) | (relation_dom_restriction(v1, v0) = % 129.29/17.90 v3 & $i(v3))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 129.29/17.90 (relation_dom_restriction(v1, v0) = v2) | ~ $i(v1) | ~ $i(v0) | ~ % 129.29/17.90 relation(v1) | ? [v3: $i] : (relation_composition(v3, v1) = v2 & % 129.29/17.90 identity_relation(v0) = v3 & $i(v3) & $i(v2))) % 129.29/17.90 % 129.29/17.90 (function-axioms) % 129.29/17.91 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 % 129.29/17.91 | ~ (subset_difference(v4, v3, v2) = v1) | ~ (subset_difference(v4, v3, % 129.29/17.91 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 % 129.29/17.91 = v0 | ~ (meet_of_subsets(v3, v2) = v1) | ~ (meet_of_subsets(v3, v2) = % 129.29/17.91 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | % 129.29/17.91 ~ (union_of_subsets(v3, v2) = v1) | ~ (union_of_subsets(v3, v2) = v0)) & ! % 129.29/17.91 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 129.29/17.91 (complements_of_subsets(v3, v2) = v1) | ~ (complements_of_subsets(v3, v2) = % 129.29/17.91 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | % 129.29/17.91 ~ (relation_composition(v3, v2) = v1) | ~ (relation_composition(v3, v2) = % 129.29/17.91 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | % 129.29/17.91 ~ (subset_complement(v3, v2) = v1) | ~ (subset_complement(v3, v2) = v0)) & % 129.29/17.91 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 129.29/17.91 (set_difference(v3, v2) = v1) | ~ (set_difference(v3, v2) = v0)) & ! [v0: % 129.29/17.91 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (apply(v3, v2) % 129.29/17.91 = v1) | ~ (apply(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 129.29/17.91 : ! [v3: $i] : (v1 = v0 | ~ (cartesian_product2(v3, v2) = v1) | ~ % 129.29/17.91 (cartesian_product2(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 129.29/17.91 : ! [v3: $i] : (v1 = v0 | ~ (relation_inverse_image(v3, v2) = v1) | ~ % 129.29/17.91 (relation_inverse_image(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 129.29/17.91 $i] : ! [v3: $i] : (v1 = v0 | ~ (relation_image(v3, v2) = v1) | ~ % 129.29/17.91 (relation_image(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 129.29/17.91 ! [v3: $i] : (v1 = v0 | ~ (relation_rng_restriction(v3, v2) = v1) | ~ % 129.29/17.91 (relation_rng_restriction(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 129.29/17.91 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (relation_dom_restriction(v3, v2) = v1) % 129.29/17.91 | ~ (relation_dom_restriction(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : % 129.29/17.91 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (ordered_pair(v3, v2) = v1) | ~ % 129.29/17.91 (ordered_pair(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 129.29/17.91 [v3: $i] : (v1 = v0 | ~ (set_intersection2(v3, v2) = v1) | ~ % 129.29/17.91 (set_intersection2(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 129.29/17.91 : ! [v3: $i] : (v1 = v0 | ~ (set_union2(v3, v2) = v1) | ~ (set_union2(v3, % 129.29/17.91 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 % 129.29/17.91 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) % 129.29/17.91 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 129.29/17.91 (function_inverse(v2) = v1) | ~ (function_inverse(v2) = v0)) & ! [v0: $i] % 129.29/17.91 : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (relation_inverse(v2) = v1) | ~ % 129.29/17.91 (relation_inverse(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 % 129.29/17.91 = v0 | ~ (relation_field(v2) = v1) | ~ (relation_field(v2) = v0)) & ! % 129.29/17.91 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (relation_rng(v2) = v1) | % 129.29/17.91 ~ (relation_rng(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 % 129.29/17.91 = v0 | ~ (union(v2) = v1) | ~ (union(v2) = v0)) & ! [v0: $i] : ! [v1: % 129.29/17.91 $i] : ! [v2: $i] : (v1 = v0 | ~ (cast_to_subset(v2) = v1) | ~ % 129.29/17.91 (cast_to_subset(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = % 129.29/17.91 v0 | ~ (relation_dom(v2) = v1) | ~ (relation_dom(v2) = v0)) & ! [v0: $i] % 129.29/17.91 : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ % 129.29/17.91 (powerset(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | % 129.29/17.91 ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ! [v0: $i] : ! [v1: % 129.29/17.91 $i] : ! [v2: $i] : (v1 = v0 | ~ (set_meet(v2) = v1) | ~ (set_meet(v2) = % 129.29/17.91 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 129.29/17.91 (identity_relation(v2) = v1) | ~ (identity_relation(v2) = v0)) % 129.29/17.91 % 129.29/17.91 Further assumptions not needed in the proof: % 129.29/17.91 -------------------------------------------- % 129.29/17.91 antisymmetry_r2_hidden, antisymmetry_r2_xboole_0, cc1_relat_1, cc2_funct_1, % 129.29/17.91 commutativity_k2_tarski, commutativity_k2_xboole_0, commutativity_k3_xboole_0, % 129.29/17.91 d10_relat_1, d10_xboole_0, d11_relat_1, d12_relat_1, d13_relat_1, d14_relat_1, % 129.29/17.91 d1_relat_1, d1_setfam_1, d1_tarski, d1_xboole_0, d1_zfmisc_1, d2_relat_1, % 129.29/17.91 d2_subset_1, d2_tarski, d2_xboole_0, d2_zfmisc_1, d3_relat_1, d3_tarski, % 129.29/17.91 d3_xboole_0, d4_funct_1, d4_relat_1, d4_subset_1, d4_tarski, d4_xboole_0, % 129.29/17.91 d5_relat_1, d5_subset_1, d5_tarski, d6_relat_1, d7_relat_1, d7_xboole_0, % 129.29/17.91 d8_funct_1, d8_relat_1, d8_setfam_1, d8_xboole_0, d9_funct_1, dt_k10_relat_1, % 129.29/17.91 dt_k1_funct_1, dt_k1_relat_1, dt_k1_setfam_1, dt_k1_tarski, dt_k1_xboole_0, % 129.29/17.91 dt_k1_zfmisc_1, dt_k2_funct_1, dt_k2_relat_1, dt_k2_subset_1, dt_k2_tarski, % 129.29/17.91 dt_k2_xboole_0, dt_k2_zfmisc_1, dt_k3_relat_1, dt_k3_subset_1, dt_k3_tarski, % 129.29/17.91 dt_k3_xboole_0, dt_k4_relat_1, dt_k4_tarski, dt_k4_xboole_0, dt_k5_relat_1, % 129.29/17.91 dt_k5_setfam_1, dt_k6_relat_1, dt_k6_setfam_1, dt_k6_subset_1, dt_k7_setfam_1, % 129.29/17.91 dt_k8_relat_1, dt_k9_relat_1, dt_m1_subset_1, existence_m1_subset_1, % 129.29/17.91 fc10_relat_1, fc11_relat_1, fc12_relat_1, fc13_relat_1, fc1_funct_1, % 129.29/17.91 fc1_relat_1, fc1_subset_1, fc1_xboole_0, fc1_zfmisc_1, fc2_funct_1, fc2_relat_1, % 129.29/17.91 fc2_subset_1, fc2_xboole_0, fc3_funct_1, fc3_subset_1, fc3_xboole_0, % 129.29/17.91 fc4_subset_1, fc5_relat_1, fc6_relat_1, fc7_relat_1, fc8_relat_1, fc9_relat_1, % 129.29/17.91 idempotence_k2_xboole_0, idempotence_k3_xboole_0, involutiveness_k3_subset_1, % 129.29/17.91 involutiveness_k4_relat_1, involutiveness_k7_setfam_1, % 129.29/17.91 irreflexivity_r2_xboole_0, l1_zfmisc_1, l23_zfmisc_1, l25_zfmisc_1, % 129.29/17.91 l28_zfmisc_1, l2_zfmisc_1, l32_xboole_1, l3_subset_1, l3_zfmisc_1, l4_zfmisc_1, % 129.29/17.91 l50_zfmisc_1, l55_zfmisc_1, l71_subset_1, rc1_funct_1, rc1_subset_1, % 129.29/17.91 rc2_relat_1, rc2_subset_1, rc2_xboole_0, rc3_funct_1, rc3_relat_1, % 129.29/17.91 redefinition_k5_setfam_1, redefinition_k6_setfam_1, redefinition_k6_subset_1, % 129.29/17.91 reflexivity_r1_tarski, symmetry_r1_xboole_0, t106_zfmisc_1, t10_zfmisc_1, % 129.29/17.91 t115_relat_1, t116_relat_1, t117_relat_1, t118_relat_1, t118_zfmisc_1, % 129.29/17.91 t119_relat_1, t119_zfmisc_1, t12_xboole_1, t136_zfmisc_1, t140_relat_1, % 129.29/17.91 t143_relat_1, t144_relat_1, t145_relat_1, t146_relat_1, t160_relat_1, % 129.29/17.91 t166_relat_1, t167_relat_1, t174_relat_1, t178_relat_1, t17_xboole_1, % 129.29/17.91 t19_xboole_1, t1_boole, t1_subset, t1_xboole_1, t1_zfmisc_1, t20_relat_1, % 129.29/17.91 t21_funct_1, t21_relat_1, t23_funct_1, t25_relat_1, t26_xboole_1, t28_xboole_1, % 129.29/17.91 t2_boole, t2_subset, t2_tarski, t2_xboole_1, t30_relat_1, t33_xboole_1, % 129.29/17.91 t33_zfmisc_1, t34_funct_1, t35_funct_1, t36_xboole_1, t37_relat_1, t37_xboole_1, % 129.29/17.91 t37_zfmisc_1, t38_zfmisc_1, t39_xboole_1, t39_zfmisc_1, t3_boole, t3_subset, % 129.29/17.91 t3_xboole_0, t3_xboole_1, t40_xboole_1, t43_subset_1, t44_relat_1, t45_xboole_1, % 129.29/17.91 t46_relat_1, t46_setfam_1, t46_zfmisc_1, t47_relat_1, t47_setfam_1, % 129.29/17.91 t48_setfam_1, t48_xboole_1, t4_boole, t4_subset, t4_xboole_0, t50_subset_1, % 129.29/17.91 t54_funct_1, t54_subset_1, t55_funct_1, t56_relat_1, t57_funct_1, t5_subset, % 129.29/17.91 t60_xboole_1, t62_funct_1, t63_xboole_1, t64_relat_1, t65_relat_1, t65_zfmisc_1, % 129.29/17.91 t69_enumset1, t6_zfmisc_1, t71_relat_1, t74_relat_1, t7_boole, t7_xboole_1, % 129.29/17.91 t83_xboole_1, t86_relat_1, t88_relat_1, t8_funct_1, t8_xboole_1, t8_zfmisc_1, % 129.29/17.91 t92_zfmisc_1, t99_relat_1, t99_zfmisc_1, t9_tarski, t9_zfmisc_1 % 129.29/17.91 % 129.29/17.91 Those formulas are unsatisfiable: % 129.29/17.91 --------------------------------- % 129.29/17.91 % 129.29/17.91 Begin of proof % 129.29/17.91 | % 129.29/17.91 | ALPHA: (fc4_funct_1) implies: % 129.29/17.92 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 129.29/17.92 | (relation_dom_restriction(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ % 129.29/17.92 | relation(v0) | ~ function(v0) | function(v2)) % 129.29/17.92 | % 129.29/17.92 | ALPHA: (fc4_relat_1) implies: % 129.29/17.92 | (2) relation(empty_set) % 129.29/17.92 | % 129.29/17.92 | ALPHA: (t22_funct_1) implies: % 129.29/17.92 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (apply(v2, % 129.29/17.92 | v0) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ relation(v2) | % 129.29/17.92 | ~ relation(v1) | ~ function(v2) | ~ function(v1) | ? [v4: $i] : % 129.29/17.92 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : (relation_composition(v2, % 129.29/17.92 | v1) = v4 & $i(v4) & ((v7 = v6 & apply(v4, v0) = v6 & apply(v1, % 129.29/17.92 | v3) = v6 & $i(v6)) | (relation_dom(v4) = v5 & $i(v5) & ~ % 129.29/17.92 | in(v0, v5))))) % 129.29/17.92 | % 129.29/17.92 | ALPHA: (t45_relat_1) implies: % 129.29/17.92 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (relation_rng(v1) = v2) | % 129.29/17.92 | ~ $i(v1) | ~ $i(v0) | ~ relation(v1) | ~ relation(v0) | ? [v3: % 129.29/17.92 | $i] : ? [v4: $i] : (relation_composition(v0, v1) = v3 & % 129.29/17.92 | relation_rng(v3) = v4 & $i(v4) & $i(v3) & subset(v4, v2))) % 129.29/17.92 | % 129.29/17.92 | ALPHA: (t60_relat_1) implies: % 129.29/17.92 | (5) relation_rng(empty_set) = empty_set % 129.29/17.92 | % 129.29/17.92 | ALPHA: (t68_funct_1) implies: % 129.29/17.92 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( % 129.29/17.92 | ~ (relation_dom(v1) = v2) | ~ (relation_dom_restriction(v3, v0) = % 129.29/17.92 | v4) | ~ $i(v3) | ~ $i(v1) | ~ $i(v0) | ~ relation(v3) | ~ % 129.29/17.92 | relation(v1) | ~ function(v3) | ~ function(v1) | ? [v5: $i] : ? % 129.29/17.92 | [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ($i(v7) & ( ~ % 129.29/17.92 | (v4 = v1) | (v6 = v2 & relation_dom(v3) = v5 & % 129.29/17.92 | set_intersection2(v5, v0) = v2 & $i(v5) & $i(v2) & ! [v10: $i] % 129.29/17.92 | : ! [v11: $i] : ( ~ (apply(v3, v10) = v11) | ~ $i(v10) | ~ % 129.29/17.92 | in(v10, v2) | (apply(v1, v10) = v11 & $i(v11))) & ! [v10: % 129.29/17.92 | $i] : ! [v11: $i] : ( ~ (apply(v1, v10) = v11) | ~ $i(v10) % 129.29/17.92 | | ~ in(v10, v2) | (apply(v3, v10) = v11 & $i(v11))))) & (v4 % 129.29/17.92 | = v1 | ( ~ (v9 = v8) & apply(v3, v7) = v9 & apply(v1, v7) = v8 & % 129.29/17.92 | $i(v9) & $i(v8) & in(v7, v2)) | ( ~ (v6 = v2) & % 129.29/17.92 | relation_dom(v3) = v5 & set_intersection2(v5, v0) = v6 & $i(v6) % 129.29/17.92 | & $i(v5))))) % 129.29/17.92 | % 129.29/17.92 | ALPHA: (t6_boole) implies: % 129.29/17.92 | (7) $i(empty_set) % 129.29/17.92 | (8) ! [v0: $i] : (v0 = empty_set | ~ $i(v0) | ~ empty(v0)) % 129.29/17.92 | % 129.29/17.92 | ALPHA: (t90_relat_1) implies: % 129.29/17.92 | (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 129.29/17.92 | (relation_dom_restriction(v1, v0) = v2) | ~ $i(v1) | ~ $i(v0) | ~ % 129.29/17.92 | relation(v1) | ? [v3: $i] : ? [v4: $i] : (relation_dom(v2) = v3 & % 129.29/17.92 | relation_dom(v1) = v4 & set_intersection2(v4, v0) = v3 & $i(v4) & % 129.29/17.92 | $i(v3))) % 129.29/17.92 | % 129.29/17.92 | ALPHA: (t94_relat_1) implies: % 129.29/17.93 | (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 129.29/17.93 | (relation_dom_restriction(v1, v0) = v2) | ~ $i(v1) | ~ $i(v0) | ~ % 129.29/17.93 | relation(v1) | ? [v3: $i] : (relation_composition(v3, v1) = v2 & % 129.29/17.93 | identity_relation(v0) = v3 & $i(v3) & $i(v2))) % 129.29/17.93 | % 129.29/17.93 | ALPHA: (function-axioms) implies: % 129.29/17.93 | (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 129.29/17.93 | (relation_dom(v2) = v1) | ~ (relation_dom(v2) = v0)) % 129.29/17.93 | (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 129.29/17.93 | (relation_rng(v2) = v1) | ~ (relation_rng(v2) = v0)) % 129.29/17.93 | (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 129.29/17.93 | (apply(v3, v2) = v1) | ~ (apply(v3, v2) = v0)) % 129.29/17.93 | (14) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 129.29/17.93 | (relation_composition(v3, v2) = v1) | ~ (relation_composition(v3, % 129.29/17.93 | v2) = v0)) % 129.29/17.93 | % 129.29/17.93 | DELTA: instantiating (rc1_xboole_0) with fresh symbol all_200_0 gives: % 129.29/17.93 | (15) $i(all_200_0) & empty(all_200_0) % 129.29/17.93 | % 129.29/17.93 | ALPHA: (15) implies: % 129.29/17.93 | (16) empty(all_200_0) % 129.29/17.93 | (17) $i(all_200_0) % 129.29/17.93 | % 129.29/17.93 | DELTA: instantiating (rc1_relat_1) with fresh symbol all_207_0 gives: % 129.29/17.93 | (18) $i(all_207_0) & relation(all_207_0) & empty(all_207_0) % 129.29/17.93 | % 129.29/17.93 | ALPHA: (18) implies: % 129.29/17.93 | (19) empty(all_207_0) % 129.29/17.93 | (20) relation(all_207_0) % 129.29/17.93 | (21) $i(all_207_0) % 129.29/17.93 | % 129.29/17.93 | DELTA: instantiating (rc2_funct_1) with fresh symbol all_218_0 gives: % 129.29/17.93 | (22) $i(all_218_0) & relation(all_218_0) & function(all_218_0) & % 129.29/17.93 | empty(all_218_0) % 129.29/17.93 | % 129.29/17.93 | ALPHA: (22) implies: % 129.29/17.93 | (23) empty(all_218_0) % 129.29/17.93 | (24) relation(all_218_0) % 129.29/17.93 | (25) $i(all_218_0) % 129.29/17.93 | % 129.29/17.93 | DELTA: instantiating (t70_funct_1) with fresh symbols all_247_0, all_247_1, % 129.29/17.93 | all_247_2, all_247_3, all_247_4, all_247_5, all_247_6 gives: % 129.29/17.93 | (26) ~ (all_247_0 = all_247_1) & relation_dom(all_247_3) = all_247_2 & % 129.29/17.93 | apply(all_247_3, all_247_5) = all_247_1 & apply(all_247_4, all_247_5) % 129.29/17.93 | = all_247_0 & relation_dom_restriction(all_247_4, all_247_6) = % 129.29/17.93 | all_247_3 & $i(all_247_0) & $i(all_247_1) & $i(all_247_2) & % 129.29/17.93 | $i(all_247_3) & $i(all_247_4) & $i(all_247_5) & $i(all_247_6) & % 129.29/17.93 | relation(all_247_4) & function(all_247_4) & in(all_247_5, all_247_2) % 129.29/17.93 | % 129.29/17.93 | ALPHA: (26) implies: % 129.29/17.93 | (27) ~ (all_247_0 = all_247_1) % 129.29/17.93 | (28) in(all_247_5, all_247_2) % 129.29/17.93 | (29) function(all_247_4) % 129.29/17.93 | (30) relation(all_247_4) % 129.29/17.93 | (31) $i(all_247_6) % 129.29/17.93 | (32) $i(all_247_5) % 129.29/17.93 | (33) $i(all_247_4) % 129.29/17.93 | (34) relation_dom_restriction(all_247_4, all_247_6) = all_247_3 % 129.29/17.93 | (35) apply(all_247_4, all_247_5) = all_247_0 % 129.29/17.93 | (36) apply(all_247_3, all_247_5) = all_247_1 % 129.29/17.93 | (37) relation_dom(all_247_3) = all_247_2 % 129.29/17.93 | % 129.29/17.93 | GROUND_INST: instantiating (13) with all_247_0, all_247_1, all_247_5, % 129.29/17.93 | all_247_4, simplifying with (35) gives: % 129.29/17.93 | (38) all_247_0 = all_247_1 | ~ (apply(all_247_4, all_247_5) = all_247_1) % 129.29/17.93 | % 129.62/17.93 | GROUND_INST: instantiating (cc1_funct_1) with all_200_0, simplifying with % 129.62/17.93 | (16), (17) gives: % 129.62/17.93 | (39) function(all_200_0) % 129.62/17.93 | % 129.62/17.94 | GROUND_INST: instantiating (t8_boole) with all_200_0, all_207_0, simplifying % 129.62/17.94 | with (16), (17), (19), (21) gives: % 129.62/17.94 | (40) all_207_0 = all_200_0 % 129.62/17.94 | % 129.62/17.94 | GROUND_INST: instantiating (t8_boole) with all_207_0, all_218_0, simplifying % 129.62/17.94 | with (19), (21), (23), (25) gives: % 129.62/17.94 | (41) all_218_0 = all_207_0 % 129.62/17.94 | % 129.62/17.94 | GROUND_INST: instantiating (8) with all_218_0, simplifying with (23), (25) % 129.62/17.94 | gives: % 129.62/17.94 | (42) all_218_0 = empty_set % 129.62/17.94 | % 129.62/17.94 | GROUND_INST: instantiating (1) with all_247_4, all_247_6, all_247_3, % 129.62/17.94 | simplifying with (29), (30), (31), (33), (34) gives: % 129.62/17.94 | (43) function(all_247_3) % 129.62/17.94 | % 129.62/17.94 | GROUND_INST: instantiating (9) with all_247_6, all_247_4, all_247_3, % 129.62/17.94 | simplifying with (30), (31), (33), (34) gives: % 129.62/17.94 | (44) ? [v0: $i] : ? [v1: $i] : (relation_dom(all_247_3) = v0 & % 129.62/17.94 | relation_dom(all_247_4) = v1 & set_intersection2(v1, all_247_6) = v0 % 129.62/17.94 | & $i(v1) & $i(v0)) % 129.62/17.94 | % 129.62/17.94 | GROUND_INST: instantiating (10) with all_247_6, all_247_4, all_247_3, % 129.62/17.94 | simplifying with (30), (31), (33), (34) gives: % 129.62/17.94 | (45) ? [v0: $i] : (relation_composition(v0, all_247_4) = all_247_3 & % 129.62/17.94 | identity_relation(all_247_6) = v0 & $i(v0) & $i(all_247_3)) % 129.62/17.94 | % 129.62/17.94 | GROUND_INST: instantiating (dt_k7_relat_1) with all_247_4, all_247_6, % 129.62/17.94 | all_247_3, simplifying with (30), (31), (33), (34) gives: % 129.62/17.94 | (46) relation(all_247_3) % 129.62/17.94 | % 129.62/17.94 | GROUND_INST: instantiating (3) with all_247_5, all_207_0, all_247_4, % 129.62/17.94 | all_247_0, simplifying with (20), (21), (29), (30), (32), (33), % 129.62/17.94 | (35) gives: % 129.62/17.94 | (47) ~ function(all_207_0) | ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? % 129.62/17.94 | [v3: $i] : (relation_composition(all_247_4, all_207_0) = v0 & $i(v0) & % 129.62/17.94 | ((v3 = v2 & apply(v0, all_247_5) = v2 & apply(all_207_0, all_247_0) % 129.62/17.94 | = v2 & $i(v2)) | (relation_dom(v0) = v1 & $i(v1) & ~ % 129.62/17.94 | in(all_247_5, v1)))) % 129.62/17.94 | % 129.62/17.94 | GROUND_INST: instantiating (4) with all_218_0, empty_set, empty_set, % 129.62/17.94 | simplifying with (2), (5), (7), (24), (25) gives: % 129.62/17.94 | (48) ? [v0: $i] : ? [v1: $i] : (relation_composition(all_218_0, % 129.62/17.94 | empty_set) = v0 & relation_rng(v0) = v1 & $i(v1) & $i(v0) & % 129.62/17.94 | subset(v1, empty_set)) % 129.62/17.94 | % 129.62/17.94 | GROUND_INST: instantiating (4) with all_207_0, empty_set, empty_set, % 129.62/17.94 | simplifying with (2), (5), (7), (20), (21) gives: % 129.62/17.94 | (49) ? [v0: $i] : ? [v1: $i] : (relation_composition(all_207_0, % 129.62/17.94 | empty_set) = v0 & relation_rng(v0) = v1 & $i(v1) & $i(v0) & % 129.62/17.94 | subset(v1, empty_set)) % 129.62/17.94 | % 129.62/17.94 | GROUND_INST: instantiating (4) with empty_set, empty_set, empty_set, % 129.62/17.94 | simplifying with (2), (5), (7) gives: % 129.62/17.94 | (50) ? [v0: $i] : ? [v1: $i] : (relation_composition(empty_set, % 129.62/17.94 | empty_set) = v0 & relation_rng(v0) = v1 & $i(v1) & $i(v0) & % 129.62/17.94 | subset(v1, empty_set)) % 129.62/17.94 | % 129.62/17.94 | COMBINE_EQS: (41), (42) imply: % 129.62/17.94 | (51) all_207_0 = empty_set % 129.62/17.94 | % 129.62/17.95 | SIMP: (51) implies: % 129.62/17.95 | (52) all_207_0 = empty_set % 129.62/17.95 | % 129.62/17.95 | COMBINE_EQS: (40), (52) imply: % 129.62/17.95 | (53) all_200_0 = empty_set % 129.62/17.95 | % 129.62/17.95 | DELTA: instantiating (45) with fresh symbol all_295_0 gives: % 129.62/17.95 | (54) relation_composition(all_295_0, all_247_4) = all_247_3 & % 129.62/17.95 | identity_relation(all_247_6) = all_295_0 & $i(all_295_0) & % 129.62/17.95 | $i(all_247_3) % 129.62/17.95 | % 129.62/17.95 | ALPHA: (54) implies: % 129.62/17.95 | (55) $i(all_247_3) % 129.62/17.95 | % 129.62/17.95 | DELTA: instantiating (48) with fresh symbols all_305_0, all_305_1 gives: % 129.62/17.95 | (56) relation_composition(all_218_0, empty_set) = all_305_1 & % 129.62/17.95 | relation_rng(all_305_1) = all_305_0 & $i(all_305_0) & $i(all_305_1) & % 129.62/17.95 | subset(all_305_0, empty_set) % 129.62/17.95 | % 129.62/17.95 | ALPHA: (56) implies: % 129.62/17.95 | (57) relation_rng(all_305_1) = all_305_0 % 129.62/17.95 | (58) relation_composition(all_218_0, empty_set) = all_305_1 % 129.62/17.95 | % 129.62/17.95 | DELTA: instantiating (50) with fresh symbols all_309_0, all_309_1 gives: % 129.62/17.95 | (59) relation_composition(empty_set, empty_set) = all_309_1 & % 129.62/17.95 | relation_rng(all_309_1) = all_309_0 & $i(all_309_0) & $i(all_309_1) & % 129.62/17.95 | subset(all_309_0, empty_set) % 129.62/17.95 | % 129.62/17.95 | ALPHA: (59) implies: % 129.62/17.95 | (60) relation_rng(all_309_1) = all_309_0 % 129.62/17.95 | (61) relation_composition(empty_set, empty_set) = all_309_1 % 129.62/17.95 | % 129.62/17.95 | DELTA: instantiating (49) with fresh symbols all_311_0, all_311_1 gives: % 129.62/17.95 | (62) relation_composition(all_207_0, empty_set) = all_311_1 & % 129.62/17.95 | relation_rng(all_311_1) = all_311_0 & $i(all_311_0) & $i(all_311_1) & % 129.62/17.95 | subset(all_311_0, empty_set) % 129.62/17.95 | % 129.62/17.95 | ALPHA: (62) implies: % 129.62/17.95 | (63) relation_composition(all_207_0, empty_set) = all_311_1 % 129.62/17.95 | % 129.62/17.95 | DELTA: instantiating (44) with fresh symbols all_315_0, all_315_1 gives: % 129.62/17.95 | (64) relation_dom(all_247_3) = all_315_1 & relation_dom(all_247_4) = % 129.62/17.95 | all_315_0 & set_intersection2(all_315_0, all_247_6) = all_315_1 & % 129.62/17.95 | $i(all_315_0) & $i(all_315_1) % 129.62/17.95 | % 129.62/17.95 | ALPHA: (64) implies: % 129.62/17.95 | (65) relation_dom(all_247_3) = all_315_1 % 129.62/17.95 | % 129.62/17.95 | REDUCE: (42), (58) imply: % 129.62/17.95 | (66) relation_composition(empty_set, empty_set) = all_305_1 % 129.62/17.95 | % 129.62/17.95 | REDUCE: (52), (63) imply: % 129.62/17.95 | (67) relation_composition(empty_set, empty_set) = all_311_1 % 129.62/17.95 | % 129.62/17.95 | REDUCE: (39), (53) imply: % 129.62/17.95 | (68) function(empty_set) % 129.62/17.95 | % 129.62/17.95 | BETA: splitting (47) gives: % 129.62/17.95 | % 129.62/17.95 | Case 1: % 129.62/17.95 | | % 129.62/17.95 | | (69) ~ function(all_207_0) % 129.62/17.95 | | % 129.62/17.95 | | REDUCE: (52), (69) imply: % 129.62/17.95 | | (70) ~ function(empty_set) % 129.62/17.95 | | % 129.62/17.95 | | PRED_UNIFY: (68), (70) imply: % 129.62/17.95 | | (71) $false % 129.62/17.95 | | % 129.62/17.95 | | CLOSE: (71) is inconsistent. % 129.62/17.95 | | % 129.62/17.95 | Case 2: % 129.62/17.95 | | % 129.62/17.95 | | % 129.62/17.95 | | GROUND_INST: instantiating (11) with all_247_2, all_315_1, all_247_3, % 129.62/17.95 | | simplifying with (37), (65) gives: % 129.62/17.95 | | (72) all_315_1 = all_247_2 % 129.62/17.95 | | % 129.62/17.95 | | GROUND_INST: instantiating (12) with all_305_0, all_309_0, all_305_1, % 129.62/17.95 | | simplifying with (57) gives: % 129.62/17.95 | | (73) all_309_0 = all_305_0 | ~ (relation_rng(all_305_1) = all_309_0) % 129.62/17.95 | | % 129.62/17.95 | | GROUND_INST: instantiating (14) with all_309_1, all_311_1, empty_set, % 129.62/17.95 | | empty_set, simplifying with (61), (67) gives: % 129.62/17.95 | | (74) all_311_1 = all_309_1 % 129.62/17.95 | | % 129.62/17.95 | | GROUND_INST: instantiating (14) with all_305_1, all_311_1, empty_set, % 129.62/17.95 | | empty_set, simplifying with (66), (67) gives: % 129.62/17.95 | | (75) all_311_1 = all_305_1 % 129.62/17.95 | | % 129.62/17.95 | | COMBINE_EQS: (74), (75) imply: % 129.62/17.95 | | (76) all_309_1 = all_305_1 % 129.62/17.95 | | % 129.62/17.95 | | REDUCE: (60), (76) imply: % 129.62/17.95 | | (77) relation_rng(all_305_1) = all_309_0 % 129.62/17.95 | | % 129.62/17.95 | | BETA: splitting (73) gives: % 129.62/17.95 | | % 129.62/17.95 | | Case 1: % 129.62/17.95 | | | % 129.62/17.95 | | | (78) ~ (relation_rng(all_305_1) = all_309_0) % 129.62/17.95 | | | % 129.62/17.95 | | | PRED_UNIFY: (77), (78) imply: % 129.62/17.95 | | | (79) $false % 129.62/17.95 | | | % 129.62/17.95 | | | CLOSE: (79) is inconsistent. % 129.62/17.95 | | | % 129.62/17.95 | | Case 2: % 129.62/17.95 | | | % 129.62/17.95 | | | % 129.62/17.96 | | | GROUND_INST: instantiating (6) with all_247_6, all_247_3, all_247_2, % 129.62/17.96 | | | all_247_4, all_247_3, simplifying with (29), (30), (31), % 129.62/17.96 | | | (33), (34), (37), (43), (46), (55) gives: % 129.62/17.96 | | | (80) ? [v0: $i] : ? [v1: $i] : (relation_dom(all_247_4) = v0 & % 129.62/17.96 | | | set_intersection2(v0, all_247_6) = all_247_2 & $i(v1) & $i(v0) & % 129.62/17.96 | | | $i(all_247_2) & ! [v2: $i] : ! [v3: $i] : ( ~ % 129.62/17.96 | | | (apply(all_247_3, v2) = v3) | ~ $i(v2) | ~ in(v2, all_247_2) % 129.62/17.96 | | | | (apply(all_247_4, v2) = v3 & $i(v3))) & ! [v2: $i] : ! % 129.62/17.96 | | | [v3: $i] : ( ~ (apply(all_247_4, v2) = v3) | ~ $i(v2) | ~ % 129.62/17.96 | | | in(v2, all_247_2) | (apply(all_247_3, v2) = v3 & $i(v3)))) % 129.62/17.96 | | | % 129.62/17.96 | | | DELTA: instantiating (80) with fresh symbols all_583_0, all_583_1 gives: % 129.62/17.96 | | | (81) relation_dom(all_247_4) = all_583_1 & set_intersection2(all_583_1, % 129.62/17.96 | | | all_247_6) = all_247_2 & $i(all_583_0) & $i(all_583_1) & % 129.62/17.96 | | | $i(all_247_2) & ! [v0: $i] : ! [v1: $i] : ( ~ (apply(all_247_3, % 129.62/17.96 | | | v0) = v1) | ~ $i(v0) | ~ in(v0, all_247_2) | % 129.62/17.96 | | | (apply(all_247_4, v0) = v1 & $i(v1))) & ! [v0: $i] : ! [v1: % 129.62/17.96 | | | $i] : ( ~ (apply(all_247_4, v0) = v1) | ~ $i(v0) | ~ in(v0, % 129.62/17.96 | | | all_247_2) | (apply(all_247_3, v0) = v1 & $i(v1))) % 129.62/17.96 | | | % 129.62/17.96 | | | ALPHA: (81) implies: % 129.62/17.96 | | | (82) ! [v0: $i] : ! [v1: $i] : ( ~ (apply(all_247_3, v0) = v1) | ~ % 129.62/17.96 | | | $i(v0) | ~ in(v0, all_247_2) | (apply(all_247_4, v0) = v1 & % 129.62/17.96 | | | $i(v1))) % 129.62/17.96 | | | % 129.62/17.96 | | | GROUND_INST: instantiating (82) with all_247_5, all_247_1, simplifying % 129.62/17.96 | | | with (28), (32), (36) gives: % 129.62/17.96 | | | (83) apply(all_247_4, all_247_5) = all_247_1 & $i(all_247_1) % 129.62/17.96 | | | % 129.62/17.96 | | | ALPHA: (83) implies: % 129.62/17.96 | | | (84) apply(all_247_4, all_247_5) = all_247_1 % 129.62/17.96 | | | % 129.62/17.96 | | | BETA: splitting (38) gives: % 129.62/17.96 | | | % 129.62/17.96 | | | Case 1: % 129.62/17.96 | | | | % 129.62/17.96 | | | | (85) ~ (apply(all_247_4, all_247_5) = all_247_1) % 129.62/17.96 | | | | % 129.62/17.96 | | | | PRED_UNIFY: (84), (85) imply: % 129.62/17.96 | | | | (86) $false % 129.62/17.96 | | | | % 129.62/17.96 | | | | CLOSE: (86) is inconsistent. % 129.62/17.96 | | | | % 129.62/17.96 | | | Case 2: % 129.62/17.96 | | | | % 129.62/17.96 | | | | (87) all_247_0 = all_247_1 % 129.62/17.96 | | | | % 129.62/17.96 | | | | REDUCE: (27), (87) imply: % 129.62/17.96 | | | | (88) $false % 129.62/17.96 | | | | % 129.62/17.96 | | | | CLOSE: (88) is inconsistent. % 129.62/17.96 | | | | % 129.62/17.96 | | | End of split % 129.62/17.96 | | | % 129.62/17.96 | | End of split % 129.62/17.96 | | % 129.62/17.96 | End of split % 129.62/17.96 | % 129.62/17.96 End of proof % 129.62/17.96 % SZS output end Proof for theBenchmark % 129.62/17.96 % 129.62/17.96 17355ms %------------------------------------------------------------------------------