%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SEU268+1 : 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 17:43:45 EDT 2023 % Result : Theorem 13.90s 2.65s % Output : Proof 24.11s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SEU268+1 : 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 14:43:20 EDT 2023 % 0.13/0.34 % CPUTime : % 0.20/0.60 ________ _____ % 0.20/0.60 ___ __ \_________(_)________________________________ % 0.20/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.20/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.20/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.20/0.60 % 0.20/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.20/0.60 (2023-06-19) % 0.20/0.60 % 0.20/0.60 (c) Philipp Rümmer, 2009-2023 % 0.20/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.20/0.60 Amanda Stjerna. % 0.20/0.60 Free software under BSD-3-Clause. % 0.20/0.60 % 0.20/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.20/0.60 % 0.20/0.60 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.20/0.61 Running up to 7 provers in parallel. % 0.20/0.62 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.20/0.62 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.20/0.62 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.20/0.62 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.20/0.62 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.20/0.62 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.20/0.62 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.65/1.09 Prover 1: Preprocessing ... % 2.65/1.09 Prover 4: Preprocessing ... % 2.94/1.13 Prover 3: Preprocessing ... % 2.94/1.13 Prover 6: Preprocessing ... % 2.94/1.13 Prover 0: Preprocessing ... % 2.94/1.13 Prover 2: Preprocessing ... % 2.94/1.13 Prover 5: Preprocessing ... % 5.89/1.58 Prover 1: Warning: ignoring some quantifiers % 5.89/1.59 Prover 5: Proving ... % 5.89/1.61 Prover 1: Constructing countermodel ... % 6.57/1.67 Prover 3: Warning: ignoring some quantifiers % 6.57/1.69 Prover 6: Proving ... % 6.57/1.69 Prover 2: Proving ... % 6.57/1.70 Prover 3: Constructing countermodel ... % 7.65/1.77 Prover 4: Warning: ignoring some quantifiers % 8.03/1.84 Prover 4: Constructing countermodel ... % 8.41/1.93 Prover 0: Proving ... % 9.48/2.05 Prover 3: gave up % 9.98/2.06 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 10.31/2.12 Prover 7: Preprocessing ... % 10.58/2.15 Prover 1: gave up % 10.58/2.16 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 10.58/2.20 Prover 8: Preprocessing ... % 11.30/2.24 Prover 7: Warning: ignoring some quantifiers % 11.30/2.27 Prover 7: Constructing countermodel ... % 11.30/2.40 Prover 8: Warning: ignoring some quantifiers % 11.30/2.41 Prover 8: Constructing countermodel ... % 13.90/2.65 Prover 0: proved (2037ms) % 13.90/2.65 % 13.90/2.65 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 13.90/2.65 % 13.90/2.66 Prover 2: stopped % 13.90/2.66 Prover 5: stopped % 13.90/2.66 Prover 6: stopped % 13.90/2.66 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 13.90/2.66 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 13.90/2.66 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 13.90/2.66 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 14.58/2.70 Prover 11: Preprocessing ... % 14.58/2.71 Prover 13: Preprocessing ... % 14.58/2.71 Prover 16: Preprocessing ... % 14.58/2.71 Prover 10: Preprocessing ... % 15.46/2.81 Prover 13: Warning: ignoring some quantifiers % 15.46/2.83 Prover 10: Warning: ignoring some quantifiers % 15.46/2.83 Prover 13: Constructing countermodel ... % 15.46/2.83 Prover 10: Constructing countermodel ... % 15.46/2.83 Prover 16: Warning: ignoring some quantifiers % 15.46/2.84 Prover 16: Constructing countermodel ... % 15.46/2.85 Prover 8: gave up % 15.46/2.85 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085 % 15.46/2.87 Prover 19: Preprocessing ... % 16.20/2.93 Prover 11: Warning: ignoring some quantifiers % 16.20/2.93 Prover 11: Constructing countermodel ... % 16.20/2.94 Prover 10: gave up % 16.20/3.05 Prover 19: Warning: ignoring some quantifiers % 16.20/3.08 Prover 19: Constructing countermodel ... % 22.00/3.72 Prover 19: gave up % 23.53/3.91 Prover 4: Found proof (size 107) % 23.53/3.91 Prover 4: proved (3285ms) % 23.53/3.91 Prover 7: stopped % 23.53/3.91 Prover 13: stopped % 23.53/3.91 Prover 16: stopped % 23.53/3.91 Prover 11: stopped % 23.53/3.91 % 23.53/3.91 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 23.53/3.91 % 23.73/3.92 % SZS output start Proof for theBenchmark % 23.74/3.93 Assumptions after simplification: % 23.74/3.93 --------------------------------- % 23.74/3.93 % 23.74/3.93 (cc2_funct_1) % 23.74/3.95 ! [v0: $i] : ! [v1: any] : ( ~ (one_to_one(v0) = v1) | ~ $i(v0) | ? [v2: % 23.74/3.95 any] : ? [v3: any] : ? [v4: any] : (relation(v0) = v2 & function(v0) = % 23.74/3.95 v4 & empty(v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | ~ (v2 = 0) | v1 = 0))) % 23.74/3.95 & ! [v0: $i] : ( ~ (relation(v0) = 0) | ~ $i(v0) | ? [v1: any] : ? [v2: % 23.74/3.95 any] : ? [v3: any] : (one_to_one(v0) = v3 & function(v0) = v2 & empty(v0) % 23.74/3.95 = v1 & ( ~ (v2 = 0) | ~ (v1 = 0) | v3 = 0))) & ! [v0: $i] : ( ~ % 23.74/3.95 (function(v0) = 0) | ~ $i(v0) | ? [v1: any] : ? [v2: any] : ? [v3: any] % 23.74/3.95 : (one_to_one(v0) = v3 & relation(v0) = v1 & empty(v0) = v2 & ( ~ (v2 = 0) | % 23.74/3.95 ~ (v1 = 0) | v3 = 0))) & ! [v0: $i] : ( ~ (empty(v0) = 0) | ~ $i(v0) % 23.74/3.95 | ? [v1: any] : ? [v2: any] : ? [v3: any] : (one_to_one(v0) = v3 & % 23.74/3.95 relation(v0) = v1 & function(v0) = v2 & ( ~ (v2 = 0) | ~ (v1 = 0) | v3 = % 23.74/3.95 0))) % 23.74/3.95 % 23.74/3.96 (commutativity_k2_xboole_0) % 23.74/3.96 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (set_union2(v1, v0) = v2) | ~ % 23.74/3.96 $i(v1) | ~ $i(v0) | (set_union2(v0, v1) = v2 & $i(v2))) & ! [v0: $i] : ! % 23.74/3.96 [v1: $i] : ! [v2: $i] : ( ~ (set_union2(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) % 23.74/3.96 | (set_union2(v1, v0) = v2 & $i(v2))) % 23.74/3.96 % 23.74/3.96 (d1_relat_2) % 23.74/3.96 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 23.74/3.96 (is_reflexive_in(v0, v1) = 0) | ~ (ordered_pair(v2, v2) = v3) | ~ % 23.74/3.96 (relation(v0) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? % 23.74/3.96 [v5: any] : (in(v3, v0) = v5 & in(v2, v1) = v4 & ( ~ (v4 = 0) | v5 = 0))) & % 23.74/3.96 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (is_reflexive_in(v0, % 23.74/3.96 v1) = v2) | ~ (relation(v0) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] % 23.74/3.96 : ? [v4: $i] : ? [v5: int] : ( ~ (v5 = 0) & ordered_pair(v3, v3) = v4 & % 23.74/3.96 in(v4, v0) = v5 & in(v3, v1) = 0 & $i(v4) & $i(v3))) & ! [v0: $i] : ! % 23.74/3.96 [v1: $i] : ! [v2: $i] : ( ~ (is_reflexive_in(v0, v1) = 0) | ~ (relation(v0) % 23.74/3.96 = 0) | ~ (in(v2, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: % 23.74/3.96 $i] : (ordered_pair(v2, v2) = v3 & in(v3, v0) = 0 & $i(v3))) % 23.74/3.96 % 23.74/3.96 (d1_wellord2) % 23.74/3.97 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 23.74/3.97 any] : ( ~ (inclusion_relation(v0) = v1) | ~ (relation_field(v1) = v2) | ~ % 23.74/3.97 (subset(v3, v4) = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v1) | ~ $i(v0) | ? % 23.74/3.97 [v6: int] : ? [v7: any] : ? [v8: $i] : ? [v9: any] : (( ~ (v6 = 0) & % 23.74/3.97 relation(v1) = v6) | (ordered_pair(v3, v4) = v8 & in(v8, v1) = v9 & % 23.74/3.97 in(v4, v0) = v7 & in(v3, v0) = v6 & $i(v8) & ( ~ (v7 = 0) | ~ (v6 = 0) % 23.74/3.97 | (( ~ (v9 = 0) | v5 = 0) & ( ~ (v5 = 0) | v9 = 0)))))) & ! [v0: $i] % 23.74/3.97 : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ % 23.74/3.97 (inclusion_relation(v0) = v1) | ~ (relation_field(v1) = v2) | ~ % 23.74/3.97 (ordered_pair(v3, v4) = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v1) | ~ $i(v0) % 23.74/3.97 | ? [v6: int] : ? [v7: any] : ? [v8: any] : ? [v9: any] : (( ~ (v6 = 0) % 23.74/3.97 & relation(v1) = v6) | (subset(v3, v4) = v9 & in(v5, v1) = v8 & in(v4, % 23.74/3.97 v0) = v7 & in(v3, v0) = v6 & ( ~ (v7 = 0) | ~ (v6 = 0) | (( ~ (v9 = % 23.74/3.97 0) | v8 = 0) & ( ~ (v8 = 0) | v9 = 0)))))) & ! [v0: $i] : ! % 23.74/3.97 [v1: $i] : ! [v2: $i] : (v2 = v1 | ~ (inclusion_relation(v0) = v2) | ~ % 23.74/3.97 (relation_field(v1) = v0) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ? [v4: % 23.74/3.97 $i] : ? [v5: $i] : ? [v6: int] : ? [v7: int] : ? [v8: $i] : ? [v9: % 23.74/3.97 any] : ? [v10: any] : ($i(v5) & $i(v4) & ((v7 = 0 & v6 = 0 & subset(v4, % 23.74/3.97 v5) = v10 & ordered_pair(v4, v5) = v8 & in(v8, v1) = v9 & in(v5, v0) % 23.74/3.97 = 0 & in(v4, v0) = 0 & $i(v8) & ( ~ (v10 = 0) | ~ (v9 = 0)) & (v10 = % 23.74/3.97 0 | v9 = 0)) | ( ~ (v3 = 0) & relation(v1) = v3)))) & ! [v0: $i] : % 23.74/3.97 ! [v1: $i] : ! [v2: $i] : (v2 = v0 | ~ (inclusion_relation(v0) = v1) | ~ % 23.74/3.97 (relation_field(v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ( ~ (v3 = % 23.74/3.97 0) & relation(v1) = v3)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 23.74/3.97 (inclusion_relation(v0) = v2) | ~ (relation(v1) = 0) | ~ $i(v1) | ~ % 23.74/3.97 $i(v0) | ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: int] : ? [v7: % 23.74/3.97 int] : ? [v8: $i] : ? [v9: any] : ? [v10: any] : (relation_field(v1) = % 23.74/3.97 v3 & $i(v5) & $i(v4) & $i(v3) & ( ~ (v3 = v0) | v2 = v1 | (v7 = 0 & v6 = 0 % 23.74/3.97 & subset(v4, v5) = v10 & ordered_pair(v4, v5) = v8 & in(v8, v1) = v9 & % 23.74/3.97 in(v5, v0) = 0 & in(v4, v0) = 0 & $i(v8) & ( ~ (v10 = 0) | ~ (v9 = % 23.74/3.97 0)) & (v10 = 0 | v9 = 0))) & ( ~ (v2 = v1) | (v3 = v0 & ! [v11: % 23.74/3.97 $i] : ! [v12: $i] : ! [v13: any] : ( ~ (subset(v11, v12) = v13) | % 23.74/3.97 ~ $i(v12) | ~ $i(v11) | ? [v14: any] : ? [v15: any] : ? [v16: % 23.74/3.97 $i] : ? [v17: any] : (ordered_pair(v11, v12) = v16 & in(v16, v1) % 23.74/3.97 = v17 & in(v12, v0) = v15 & in(v11, v0) = v14 & $i(v16) & ( ~ (v15 % 23.74/3.97 = 0) | ~ (v14 = 0) | (( ~ (v17 = 0) | v13 = 0) & ( ~ (v13 = % 23.74/3.97 0) | v17 = 0))))) & ! [v11: $i] : ! [v12: $i] : ! [v13: % 23.74/3.97 $i] : ( ~ (ordered_pair(v11, v12) = v13) | ~ $i(v12) | ~ $i(v11) | % 23.74/3.97 ? [v14: any] : ? [v15: any] : ? [v16: any] : ? [v17: any] : % 23.74/3.97 (subset(v11, v12) = v17 & in(v13, v1) = v16 & in(v12, v0) = v15 & % 23.74/3.97 in(v11, v0) = v14 & ( ~ (v15 = 0) | ~ (v14 = 0) | (( ~ (v17 = 0) % 23.74/3.97 | v16 = 0) & ( ~ (v16 = 0) | v17 = 0))))))))) % 23.74/3.97 % 23.74/3.97 (d6_relat_1) % 23.74/3.98 ! [v0: $i] : ! [v1: $i] : ( ~ (relation_dom(v0) = v1) | ~ $i(v0) | ? [v2: % 23.74/3.98 any] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : (relation_rng(v0) = v4 & % 23.74/3.98 relation_field(v0) = v3 & set_union2(v1, v4) = v5 & relation(v0) = v2 & % 23.74/3.98 $i(v5) & $i(v4) & $i(v3) & ( ~ (v2 = 0) | v5 = v3))) & ! [v0: $i] : ! % 23.74/3.98 [v1: $i] : ( ~ (relation_rng(v0) = v1) | ~ $i(v0) | ? [v2: any] : ? [v3: % 23.74/3.98 $i] : ? [v4: $i] : ? [v5: $i] : (relation_dom(v0) = v4 & % 23.74/3.98 relation_field(v0) = v3 & set_union2(v4, v1) = v5 & relation(v0) = v2 & % 23.74/3.98 $i(v5) & $i(v4) & $i(v3) & ( ~ (v2 = 0) | v5 = v3))) & ! [v0: $i] : ! % 23.74/3.98 [v1: $i] : ( ~ (relation_field(v0) = v1) | ~ $i(v0) | ? [v2: any] : ? [v3: % 23.74/3.98 $i] : ? [v4: $i] : ? [v5: $i] : (relation_dom(v0) = v3 & % 23.74/3.98 relation_rng(v0) = v4 & set_union2(v3, v4) = v5 & relation(v0) = v2 & % 23.74/3.98 $i(v5) & $i(v4) & $i(v3) & ( ~ (v2 = 0) | v5 = v1))) & ! [v0: $i] : ( ~ % 23.74/3.98 (relation(v0) = 0) | ~ $i(v0) | ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : % 23.74/3.98 (relation_dom(v0) = v2 & relation_rng(v0) = v3 & relation_field(v0) = v1 & % 23.74/3.98 set_union2(v2, v3) = v1 & $i(v3) & $i(v2) & $i(v1))) % 23.74/3.98 % 23.74/3.98 (d9_relat_2) % 23.74/3.98 ! [v0: $i] : ! [v1: any] : ( ~ (reflexive(v0) = v1) | ~ $i(v0) | ? [v2: % 23.74/3.98 any] : ? [v3: $i] : ? [v4: any] : (relation_field(v0) = v3 & % 23.74/3.98 is_reflexive_in(v0, v3) = v4 & relation(v0) = v2 & $i(v3) & ( ~ (v2 = 0) | % 23.74/3.98 (( ~ (v4 = 0) | v1 = 0) & ( ~ (v1 = 0) | v4 = 0))))) & ! [v0: $i] : ! % 23.74/3.98 [v1: $i] : ( ~ (relation_field(v0) = v1) | ~ $i(v0) | ? [v2: any] : ? [v3: % 23.74/3.98 any] : ? [v4: any] : (reflexive(v0) = v3 & is_reflexive_in(v0, v1) = v4 & % 23.74/3.98 relation(v0) = v2 & ( ~ (v2 = 0) | (( ~ (v4 = 0) | v3 = 0) & ( ~ (v3 = 0) % 23.74/3.98 | v4 = 0))))) & ! [v0: $i] : ( ~ (relation(v0) = 0) | ~ $i(v0) | % 23.74/3.98 ? [v1: any] : ? [v2: $i] : ? [v3: any] : (reflexive(v0) = v1 & % 23.74/3.98 relation_field(v0) = v2 & is_reflexive_in(v0, v2) = v3 & $i(v2) & ( ~ (v3 % 23.74/3.98 = 0) | v1 = 0) & ( ~ (v1 = 0) | v3 = 0))) % 23.74/3.98 % 23.74/3.98 (dt_k1_wellord2) % 23.74/3.98 ! [v0: $i] : ! [v1: $i] : ( ~ (inclusion_relation(v0) = v1) | ~ $i(v0) | % 23.74/3.98 relation(v1) = 0) % 23.74/3.98 % 23.74/3.98 (reflexivity_r1_tarski) % 23.74/3.98 ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (subset(v0, v0) = v1) | ~ $i(v0)) % 23.74/3.98 % 23.74/3.98 (t2_wellord2) % 23.74/3.98 ? [v0: $i] : ? [v1: $i] : ? [v2: int] : ( ~ (v2 = 0) & reflexive(v1) = v2 & % 23.74/3.98 inclusion_relation(v0) = v1 & $i(v1) & $i(v0)) % 23.74/3.98 % 23.74/3.98 (function-axioms) % 23.74/3.98 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 23.74/3.98 [v3: $i] : (v1 = v0 | ~ (element(v3, v2) = v1) | ~ (element(v3, v2) = v0)) & % 23.74/3.98 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 23.74/3.98 [v3: $i] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) & % 23.74/3.98 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 23.74/3.98 $i] : (v1 = v0 | ~ (is_reflexive_in(v3, v2) = v1) | ~ (is_reflexive_in(v3, % 23.74/3.98 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 % 23.74/3.98 = v0 | ~ (ordered_pair(v3, v2) = v1) | ~ (ordered_pair(v3, v2) = v0)) & ! % 23.74/3.98 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 23.74/3.98 (set_union2(v3, v2) = v1) | ~ (set_union2(v3, v2) = v0)) & ! [v0: $i] : ! % 23.74/3.98 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (unordered_pair(v3, v2) = % 23.74/3.98 v1) | ~ (unordered_pair(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! % 23.74/3.98 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (in(v3, % 23.74/3.98 v2) = v1) | ~ (in(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 23.74/3.98 $i] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0)) & ! [v0: % 23.74/3.98 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 23.74/3.98 ~ (relation_empty_yielding(v2) = v1) | ~ (relation_empty_yielding(v2) = % 23.74/3.98 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 23.74/3.98 $i] : (v1 = v0 | ~ (reflexive(v2) = v1) | ~ (reflexive(v2) = v0)) & ! % 23.74/3.98 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (relation_dom(v2) = v1) | % 23.74/3.98 ~ (relation_dom(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 % 23.74/3.98 = v0 | ~ (relation_rng(v2) = v1) | ~ (relation_rng(v2) = v0)) & ! [v0: % 23.74/3.98 $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ % 23.74/3.98 (singleton(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | % 23.74/3.98 ~ (inclusion_relation(v2) = v1) | ~ (inclusion_relation(v2) = v0)) & ! % 23.74/3.98 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (relation_field(v2) = v1) % 23.74/3.99 | ~ (relation_field(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 23.74/3.99 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (one_to_one(v2) = v1) | ~ % 23.74/3.99 (one_to_one(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 23.74/3.99 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (relation(v2) = v1) | ~ % 23.74/3.99 (relation(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 23.74/3.99 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (epsilon_transitive(v2) = % 23.74/3.99 v1) | ~ (epsilon_transitive(v2) = v0)) & ! [v0: MultipleValueBool] : ! % 23.74/3.99 [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (ordinal(v2) = v1) | ~ % 23.74/3.99 (ordinal(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 23.74/3.99 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (epsilon_connected(v2) = % 23.74/3.99 v1) | ~ (epsilon_connected(v2) = v0)) & ! [v0: MultipleValueBool] : ! % 23.74/3.99 [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (function(v2) = v1) | ~ % 23.74/3.99 (function(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 23.74/3.99 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (empty(v2) = v1) | ~ % 23.74/3.99 (empty(v2) = v0)) % 23.74/3.99 % 23.74/3.99 Further assumptions not needed in the proof: % 23.74/3.99 -------------------------------------------- % 23.74/3.99 antisymmetry_r2_hidden, cc1_funct_1, cc1_ordinal1, cc2_ordinal1, cc3_ordinal1, % 23.74/3.99 commutativity_k2_tarski, d5_tarski, dt_k1_relat_1, dt_k1_tarski, dt_k1_xboole_0, % 23.74/3.99 dt_k1_zfmisc_1, dt_k2_relat_1, dt_k2_tarski, dt_k2_xboole_0, dt_k3_relat_1, % 23.74/3.99 dt_k4_tarski, dt_m1_subset_1, existence_m1_subset_1, fc1_xboole_0, fc1_zfmisc_1, % 23.74/3.99 fc2_ordinal1, fc2_xboole_0, fc3_xboole_0, idempotence_k2_xboole_0, rc1_funct_1, % 23.74/3.99 rc1_ordinal1, rc1_xboole_0, rc2_funct_1, rc2_ordinal1, rc2_xboole_0, % 23.74/3.99 rc3_funct_1, rc3_ordinal1, rc4_funct_1, t1_boole, t1_subset, t2_subset, % 23.74/3.99 t3_subset, t4_subset, t5_subset, t6_boole, t7_boole, t8_boole % 23.74/3.99 % 23.74/3.99 Those formulas are unsatisfiable: % 23.74/3.99 --------------------------------- % 23.74/3.99 % 23.74/3.99 Begin of proof % 23.74/3.99 | % 23.74/3.99 | ALPHA: (cc2_funct_1) implies: % 23.74/3.99 | (1) ! [v0: $i] : ( ~ (relation(v0) = 0) | ~ $i(v0) | ? [v1: any] : ? % 23.74/3.99 | [v2: any] : ? [v3: any] : (one_to_one(v0) = v3 & function(v0) = v2 & % 23.74/3.99 | empty(v0) = v1 & ( ~ (v2 = 0) | ~ (v1 = 0) | v3 = 0))) % 23.74/3.99 | (2) ! [v0: $i] : ! [v1: any] : ( ~ (one_to_one(v0) = v1) | ~ $i(v0) | ? % 23.74/3.99 | [v2: any] : ? [v3: any] : ? [v4: any] : (relation(v0) = v2 & % 23.74/3.99 | function(v0) = v4 & empty(v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | % 23.74/3.99 | ~ (v2 = 0) | v1 = 0))) % 23.74/3.99 | % 23.74/3.99 | ALPHA: (commutativity_k2_xboole_0) implies: % 23.74/3.99 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (set_union2(v1, v0) = v2) % 23.74/3.99 | | ~ $i(v1) | ~ $i(v0) | (set_union2(v0, v1) = v2 & $i(v2))) % 23.74/3.99 | % 23.74/3.99 | ALPHA: (d1_relat_2) implies: % 23.74/3.99 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ % 23.74/3.99 | (is_reflexive_in(v0, v1) = v2) | ~ (relation(v0) = 0) | ~ $i(v1) | % 23.74/3.99 | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : ? [v5: int] : ( ~ (v5 = 0) & % 23.74/3.99 | ordered_pair(v3, v3) = v4 & in(v4, v0) = v5 & in(v3, v1) = 0 & % 23.74/3.99 | $i(v4) & $i(v3))) % 23.74/3.99 | % 23.74/3.99 | ALPHA: (d1_wellord2) implies: % 23.74/3.99 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (inclusion_relation(v0) = % 23.74/3.99 | v2) | ~ (relation(v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : % 23.74/3.99 | ? [v4: $i] : ? [v5: $i] : ? [v6: int] : ? [v7: int] : ? [v8: $i] % 23.74/3.99 | : ? [v9: any] : ? [v10: any] : (relation_field(v1) = v3 & $i(v5) & % 23.74/3.99 | $i(v4) & $i(v3) & ( ~ (v3 = v0) | v2 = v1 | (v7 = 0 & v6 = 0 & % 23.74/3.99 | subset(v4, v5) = v10 & ordered_pair(v4, v5) = v8 & in(v8, v1) = % 23.74/3.99 | v9 & in(v5, v0) = 0 & in(v4, v0) = 0 & $i(v8) & ( ~ (v10 = 0) | % 23.74/3.99 | ~ (v9 = 0)) & (v10 = 0 | v9 = 0))) & ( ~ (v2 = v1) | (v3 = % 23.74/3.99 | v0 & ! [v11: $i] : ! [v12: $i] : ! [v13: any] : ( ~ % 23.74/3.99 | (subset(v11, v12) = v13) | ~ $i(v12) | ~ $i(v11) | ? [v14: % 23.74/3.99 | any] : ? [v15: any] : ? [v16: $i] : ? [v17: any] : % 23.74/3.99 | (ordered_pair(v11, v12) = v16 & in(v16, v1) = v17 & in(v12, % 23.74/3.99 | v0) = v15 & in(v11, v0) = v14 & $i(v16) & ( ~ (v15 = 0) | % 23.74/3.99 | ~ (v14 = 0) | (( ~ (v17 = 0) | v13 = 0) & ( ~ (v13 = 0) % 23.74/4.00 | | v17 = 0))))) & ! [v11: $i] : ! [v12: $i] : ! % 23.74/4.00 | [v13: $i] : ( ~ (ordered_pair(v11, v12) = v13) | ~ $i(v12) | % 23.74/4.00 | ~ $i(v11) | ? [v14: any] : ? [v15: any] : ? [v16: any] : % 23.74/4.00 | ? [v17: any] : (subset(v11, v12) = v17 & in(v13, v1) = v16 & % 23.74/4.00 | in(v12, v0) = v15 & in(v11, v0) = v14 & ( ~ (v15 = 0) | ~ % 23.74/4.00 | (v14 = 0) | (( ~ (v17 = 0) | v16 = 0) & ( ~ (v16 = 0) | % 23.74/4.00 | v17 = 0))))))))) % 23.74/4.00 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 23.74/4.00 | ! [v5: $i] : ( ~ (inclusion_relation(v0) = v1) | ~ (relation_field(v1) % 23.74/4.00 | = v2) | ~ (ordered_pair(v3, v4) = v5) | ~ $i(v4) | ~ $i(v3) | ~ % 23.74/4.00 | $i(v1) | ~ $i(v0) | ? [v6: int] : ? [v7: any] : ? [v8: any] : ? % 23.74/4.00 | [v9: any] : (( ~ (v6 = 0) & relation(v1) = v6) | (subset(v3, v4) = v9 % 23.74/4.00 | & in(v5, v1) = v8 & in(v4, v0) = v7 & in(v3, v0) = v6 & ( ~ (v7 = % 23.74/4.00 | 0) | ~ (v6 = 0) | (( ~ (v9 = 0) | v8 = 0) & ( ~ (v8 = 0) | % 23.74/4.00 | v9 = 0)))))) % 23.74/4.00 | % 23.74/4.00 | ALPHA: (d6_relat_1) implies: % 23.74/4.00 | (7) ! [v0: $i] : ( ~ (relation(v0) = 0) | ~ $i(v0) | ? [v1: $i] : ? % 23.74/4.00 | [v2: $i] : ? [v3: $i] : (relation_dom(v0) = v2 & relation_rng(v0) = % 23.74/4.00 | v3 & relation_field(v0) = v1 & set_union2(v2, v3) = v1 & $i(v3) & % 23.74/4.00 | $i(v2) & $i(v1))) % 23.74/4.00 | (8) ! [v0: $i] : ! [v1: $i] : ( ~ (relation_field(v0) = v1) | ~ $i(v0) | % 23.74/4.00 | ? [v2: any] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : % 23.74/4.00 | (relation_dom(v0) = v3 & relation_rng(v0) = v4 & set_union2(v3, v4) = % 23.74/4.00 | v5 & relation(v0) = v2 & $i(v5) & $i(v4) & $i(v3) & ( ~ (v2 = 0) | % 23.74/4.00 | v5 = v1))) % 23.74/4.00 | % 23.74/4.00 | ALPHA: (d9_relat_2) implies: % 23.74/4.00 | (9) ! [v0: $i] : ! [v1: any] : ( ~ (reflexive(v0) = v1) | ~ $i(v0) | ? % 23.74/4.00 | [v2: any] : ? [v3: $i] : ? [v4: any] : (relation_field(v0) = v3 & % 23.74/4.00 | is_reflexive_in(v0, v3) = v4 & relation(v0) = v2 & $i(v3) & ( ~ (v2 % 23.74/4.00 | = 0) | (( ~ (v4 = 0) | v1 = 0) & ( ~ (v1 = 0) | v4 = 0))))) % 23.74/4.00 | % 23.74/4.00 | ALPHA: (function-axioms) implies: % 23.74/4.00 | (10) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 23.74/4.00 | : (v1 = v0 | ~ (relation(v2) = v1) | ~ (relation(v2) = v0)) % 24.11/4.00 | (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 24.11/4.00 | (relation_field(v2) = v1) | ~ (relation_field(v2) = v0)) % 24.11/4.00 | (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 24.11/4.00 | (relation_rng(v2) = v1) | ~ (relation_rng(v2) = v0)) % 24.11/4.00 | (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 24.11/4.00 | (relation_dom(v2) = v1) | ~ (relation_dom(v2) = v0)) % 24.11/4.00 | (14) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 24.11/4.00 | : ! [v3: $i] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = % 24.11/4.00 | v0)) % 24.11/4.00 | (15) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 24.11/4.00 | : ! [v3: $i] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, % 24.11/4.00 | v2) = v0)) % 24.11/4.00 | % 24.11/4.00 | DELTA: instantiating (t2_wellord2) with fresh symbols all_47_0, all_47_1, % 24.11/4.00 | all_47_2 gives: % 24.11/4.00 | (16) ~ (all_47_0 = 0) & reflexive(all_47_1) = all_47_0 & % 24.11/4.00 | inclusion_relation(all_47_2) = all_47_1 & $i(all_47_1) & $i(all_47_2) % 24.11/4.00 | % 24.11/4.00 | ALPHA: (16) implies: % 24.11/4.00 | (17) ~ (all_47_0 = 0) % 24.11/4.00 | (18) $i(all_47_2) % 24.11/4.00 | (19) $i(all_47_1) % 24.11/4.00 | (20) inclusion_relation(all_47_2) = all_47_1 % 24.11/4.00 | (21) reflexive(all_47_1) = all_47_0 % 24.11/4.00 | % 24.11/4.00 | GROUND_INST: instantiating (dt_k1_wellord2) with all_47_2, all_47_1, % 24.11/4.00 | simplifying with (18), (20) gives: % 24.11/4.01 | (22) relation(all_47_1) = 0 % 24.11/4.01 | % 24.11/4.01 | GROUND_INST: instantiating (9) with all_47_1, all_47_0, simplifying with (19), % 24.11/4.01 | (21) gives: % 24.11/4.01 | (23) ? [v0: any] : ? [v1: $i] : ? [v2: any] : (relation_field(all_47_1) % 24.11/4.01 | = v1 & is_reflexive_in(all_47_1, v1) = v2 & relation(all_47_1) = v0 % 24.11/4.01 | & $i(v1) & ( ~ (v0 = 0) | (( ~ (v2 = 0) | all_47_0 = 0) & ( ~ % 24.11/4.01 | (all_47_0 = 0) | v2 = 0)))) % 24.11/4.01 | % 24.11/4.01 | DELTA: instantiating (23) with fresh symbols all_111_0, all_111_1, all_111_2 % 24.11/4.01 | gives: % 24.11/4.01 | (24) relation_field(all_47_1) = all_111_1 & is_reflexive_in(all_47_1, % 24.11/4.01 | all_111_1) = all_111_0 & relation(all_47_1) = all_111_2 & % 24.11/4.01 | $i(all_111_1) & ( ~ (all_111_2 = 0) | (( ~ (all_111_0 = 0) | all_47_0 % 24.11/4.01 | = 0) & ( ~ (all_47_0 = 0) | all_111_0 = 0))) % 24.11/4.01 | % 24.11/4.01 | ALPHA: (24) implies: % 24.11/4.01 | (25) $i(all_111_1) % 24.11/4.01 | (26) relation(all_47_1) = all_111_2 % 24.11/4.01 | (27) is_reflexive_in(all_47_1, all_111_1) = all_111_0 % 24.11/4.01 | (28) relation_field(all_47_1) = all_111_1 % 24.11/4.01 | (29) ~ (all_111_2 = 0) | (( ~ (all_111_0 = 0) | all_47_0 = 0) & ( ~ % 24.11/4.01 | (all_47_0 = 0) | all_111_0 = 0)) % 24.11/4.01 | % 24.11/4.01 | GROUND_INST: instantiating (10) with 0, all_111_2, all_47_1, simplifying with % 24.11/4.01 | (22), (26) gives: % 24.11/4.01 | (30) all_111_2 = 0 % 24.11/4.01 | % 24.11/4.01 | BETA: splitting (29) gives: % 24.11/4.01 | % 24.11/4.01 | Case 1: % 24.11/4.01 | | % 24.11/4.01 | | (31) ~ (all_111_2 = 0) % 24.11/4.01 | | % 24.11/4.01 | | REDUCE: (30), (31) imply: % 24.11/4.01 | | (32) $false % 24.11/4.01 | | % 24.11/4.01 | | CLOSE: (32) is inconsistent. % 24.11/4.01 | | % 24.11/4.01 | Case 2: % 24.11/4.01 | | % 24.11/4.01 | | (33) ( ~ (all_111_0 = 0) | all_47_0 = 0) & ( ~ (all_47_0 = 0) | all_111_0 % 24.11/4.01 | | = 0) % 24.11/4.01 | | % 24.11/4.01 | | ALPHA: (33) implies: % 24.11/4.01 | | (34) ~ (all_111_0 = 0) | all_47_0 = 0 % 24.11/4.01 | | % 24.11/4.01 | | BETA: splitting (34) gives: % 24.11/4.01 | | % 24.11/4.01 | | Case 1: % 24.11/4.01 | | | % 24.11/4.01 | | | (35) ~ (all_111_0 = 0) % 24.11/4.01 | | | % 24.11/4.01 | | | GROUND_INST: instantiating (5) with all_47_2, all_47_1, all_47_1, % 24.11/4.01 | | | simplifying with (18), (19), (20), (22) gives: % 24.11/4.01 | | | (36) ? [v0: $i] : ? [v1: $i] : (relation_field(all_47_1) = all_47_2 & % 24.11/4.01 | | | $i(v1) & $i(v0) & ! [v2: $i] : ! [v3: $i] : ! [v4: any] : ( ~ % 24.11/4.01 | | | (subset(v2, v3) = v4) | ~ $i(v3) | ~ $i(v2) | ? [v5: any] : % 24.11/4.01 | | | ? [v6: any] : ? [v7: $i] : ? [v8: any] : (ordered_pair(v2, % 24.11/4.01 | | | v3) = v7 & in(v7, all_47_1) = v8 & in(v3, all_47_2) = v6 & % 24.11/4.01 | | | in(v2, all_47_2) = v5 & $i(v7) & ( ~ (v6 = 0) | ~ (v5 = 0) % 24.11/4.01 | | | | (( ~ (v8 = 0) | v4 = 0) & ( ~ (v4 = 0) | v8 = 0))))) & % 24.11/4.01 | | | ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (ordered_pair(v2, % 24.11/4.01 | | | v3) = v4) | ~ $i(v3) | ~ $i(v2) | ? [v5: any] : ? [v6: % 24.11/4.01 | | | any] : ? [v7: any] : ? [v8: any] : (subset(v2, v3) = v8 & % 24.11/4.01 | | | in(v4, all_47_1) = v7 & in(v3, all_47_2) = v6 & in(v2, % 24.11/4.01 | | | all_47_2) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0) | (( ~ (v8 = % 24.11/4.01 | | | 0) | v7 = 0) & ( ~ (v7 = 0) | v8 = 0)))))) % 24.11/4.01 | | | % 24.11/4.01 | | | GROUND_INST: instantiating (7) with all_47_1, simplifying with (19), (22) % 24.11/4.01 | | | gives: % 24.11/4.01 | | | (37) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (relation_dom(all_47_1) % 24.11/4.01 | | | = v1 & relation_rng(all_47_1) = v2 & relation_field(all_47_1) = % 24.11/4.01 | | | v0 & set_union2(v1, v2) = v0 & $i(v2) & $i(v1) & $i(v0)) % 24.11/4.01 | | | % 24.11/4.01 | | | GROUND_INST: instantiating (1) with all_47_1, simplifying with (19), (22) % 24.11/4.01 | | | gives: % 24.11/4.02 | | | (38) ? [v0: any] : ? [v1: any] : ? [v2: any] : (one_to_one(all_47_1) % 24.11/4.02 | | | = v2 & function(all_47_1) = v1 & empty(all_47_1) = v0 & ( ~ (v1 % 24.11/4.02 | | | = 0) | ~ (v0 = 0) | v2 = 0)) % 24.11/4.02 | | | % 24.11/4.02 | | | GROUND_INST: instantiating (4) with all_47_1, all_111_1, all_111_0, % 24.11/4.02 | | | simplifying with (19), (22), (25), (27) gives: % 24.11/4.02 | | | (39) all_111_0 = 0 | ? [v0: $i] : ? [v1: $i] : ? [v2: int] : ( ~ (v2 % 24.11/4.02 | | | = 0) & ordered_pair(v0, v0) = v1 & in(v1, all_47_1) = v2 & % 24.11/4.02 | | | in(v0, all_111_1) = 0 & $i(v1) & $i(v0)) % 24.11/4.02 | | | % 24.11/4.02 | | | GROUND_INST: instantiating (8) with all_47_1, all_111_1, simplifying with % 24.11/4.02 | | | (19), (28) gives: % 24.11/4.02 | | | (40) ? [v0: any] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : % 24.11/4.02 | | | (relation_dom(all_47_1) = v1 & relation_rng(all_47_1) = v2 & % 24.11/4.02 | | | set_union2(v1, v2) = v3 & relation(all_47_1) = v0 & $i(v3) & % 24.11/4.02 | | | $i(v2) & $i(v1) & ( ~ (v0 = 0) | v3 = all_111_1)) % 24.11/4.02 | | | % 24.11/4.02 | | | DELTA: instantiating (38) with fresh symbols all_163_0, all_163_1, % 24.11/4.02 | | | all_163_2 gives: % 24.11/4.02 | | | (41) one_to_one(all_47_1) = all_163_0 & function(all_47_1) = all_163_1 % 24.11/4.02 | | | & empty(all_47_1) = all_163_2 & ( ~ (all_163_1 = 0) | ~ % 24.11/4.02 | | | (all_163_2 = 0) | all_163_0 = 0) % 24.11/4.02 | | | % 24.11/4.02 | | | ALPHA: (41) implies: % 24.11/4.02 | | | (42) one_to_one(all_47_1) = all_163_0 % 24.11/4.02 | | | % 24.11/4.02 | | | DELTA: instantiating (37) with fresh symbols all_165_0, all_165_1, % 24.11/4.02 | | | all_165_2 gives: % 24.11/4.02 | | | (43) relation_dom(all_47_1) = all_165_1 & relation_rng(all_47_1) = % 24.11/4.02 | | | all_165_0 & relation_field(all_47_1) = all_165_2 & % 24.11/4.02 | | | set_union2(all_165_1, all_165_0) = all_165_2 & $i(all_165_0) & % 24.11/4.02 | | | $i(all_165_1) & $i(all_165_2) % 24.11/4.02 | | | % 24.11/4.02 | | | ALPHA: (43) implies: % 24.11/4.02 | | | (44) set_union2(all_165_1, all_165_0) = all_165_2 % 24.11/4.02 | | | (45) relation_field(all_47_1) = all_165_2 % 24.11/4.02 | | | (46) relation_rng(all_47_1) = all_165_0 % 24.11/4.02 | | | (47) relation_dom(all_47_1) = all_165_1 % 24.11/4.02 | | | % 24.11/4.02 | | | DELTA: instantiating (40) with fresh symbols all_179_0, all_179_1, % 24.11/4.02 | | | all_179_2, all_179_3 gives: % 24.11/4.02 | | | (48) relation_dom(all_47_1) = all_179_2 & relation_rng(all_47_1) = % 24.11/4.02 | | | all_179_1 & set_union2(all_179_2, all_179_1) = all_179_0 & % 24.11/4.02 | | | relation(all_47_1) = all_179_3 & $i(all_179_0) & $i(all_179_1) & % 24.11/4.02 | | | $i(all_179_2) & ( ~ (all_179_3 = 0) | all_179_0 = all_111_1) % 24.11/4.02 | | | % 24.11/4.02 | | | ALPHA: (48) implies: % 24.11/4.02 | | | (49) $i(all_179_2) % 24.11/4.02 | | | (50) $i(all_179_1) % 24.11/4.02 | | | (51) relation(all_47_1) = all_179_3 % 24.11/4.02 | | | (52) relation_rng(all_47_1) = all_179_1 % 24.11/4.02 | | | (53) relation_dom(all_47_1) = all_179_2 % 24.11/4.02 | | | % 24.11/4.02 | | | DELTA: instantiating (36) with fresh symbols all_189_0, all_189_1 gives: % 24.11/4.02 | | | (54) relation_field(all_47_1) = all_47_2 & $i(all_189_0) & % 24.11/4.02 | | | $i(all_189_1) & ! [v0: $i] : ! [v1: $i] : ! [v2: any] : ( ~ % 24.11/4.02 | | | (subset(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : % 24.11/4.02 | | | ? [v4: any] : ? [v5: $i] : ? [v6: any] : (ordered_pair(v0, v1) % 24.11/4.02 | | | = v5 & in(v5, all_47_1) = v6 & in(v1, all_47_2) = v4 & in(v0, % 24.11/4.02 | | | all_47_2) = v3 & $i(v5) & ( ~ (v4 = 0) | ~ (v3 = 0) | (( ~ % 24.11/4.02 | | | (v6 = 0) | v2 = 0) & ( ~ (v2 = 0) | v6 = 0))))) & ! % 24.11/4.02 | | | [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (ordered_pair(v0, v1) = % 24.11/4.02 | | | v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ? % 24.11/4.02 | | | [v5: any] : ? [v6: any] : (subset(v0, v1) = v6 & in(v2, % 24.11/4.02 | | | all_47_1) = v5 & in(v1, all_47_2) = v4 & in(v0, all_47_2) = % 24.11/4.02 | | | v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | (( ~ (v6 = 0) | v5 = 0) & ( % 24.11/4.02 | | | ~ (v5 = 0) | v6 = 0))))) % 24.11/4.02 | | | % 24.11/4.02 | | | ALPHA: (54) implies: % 24.11/4.02 | | | (55) relation_field(all_47_1) = all_47_2 % 24.11/4.02 | | | (56) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (ordered_pair(v0, % 24.11/4.02 | | | v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: % 24.11/4.02 | | | any] : ? [v5: any] : ? [v6: any] : (subset(v0, v1) = v6 & % 24.11/4.02 | | | in(v2, all_47_1) = v5 & in(v1, all_47_2) = v4 & in(v0, % 24.11/4.02 | | | all_47_2) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | (( ~ (v6 = 0) % 24.11/4.02 | | | | v5 = 0) & ( ~ (v5 = 0) | v6 = 0))))) % 24.11/4.02 | | | % 24.11/4.02 | | | BETA: splitting (39) gives: % 24.11/4.02 | | | % 24.11/4.02 | | | Case 1: % 24.11/4.02 | | | | % 24.11/4.02 | | | | (57) all_111_0 = 0 % 24.11/4.02 | | | | % 24.11/4.02 | | | | REDUCE: (35), (57) imply: % 24.11/4.02 | | | | (58) $false % 24.11/4.02 | | | | % 24.11/4.02 | | | | CLOSE: (58) is inconsistent. % 24.11/4.02 | | | | % 24.11/4.02 | | | Case 2: % 24.11/4.02 | | | | % 24.11/4.02 | | | | (59) ? [v0: $i] : ? [v1: $i] : ? [v2: int] : ( ~ (v2 = 0) & % 24.11/4.02 | | | | ordered_pair(v0, v0) = v1 & in(v1, all_47_1) = v2 & in(v0, % 24.11/4.02 | | | | all_111_1) = 0 & $i(v1) & $i(v0)) % 24.11/4.02 | | | | % 24.11/4.02 | | | | DELTA: instantiating (59) with fresh symbols all_196_0, all_196_1, % 24.11/4.02 | | | | all_196_2 gives: % 24.11/4.03 | | | | (60) ~ (all_196_0 = 0) & ordered_pair(all_196_2, all_196_2) = % 24.11/4.03 | | | | all_196_1 & in(all_196_1, all_47_1) = all_196_0 & in(all_196_2, % 24.11/4.03 | | | | all_111_1) = 0 & $i(all_196_1) & $i(all_196_2) % 24.11/4.03 | | | | % 24.11/4.03 | | | | ALPHA: (60) implies: % 24.11/4.03 | | | | (61) ~ (all_196_0 = 0) % 24.11/4.03 | | | | (62) $i(all_196_2) % 24.11/4.03 | | | | (63) in(all_196_2, all_111_1) = 0 % 24.11/4.03 | | | | (64) in(all_196_1, all_47_1) = all_196_0 % 24.11/4.03 | | | | (65) ordered_pair(all_196_2, all_196_2) = all_196_1 % 24.11/4.03 | | | | % 24.11/4.03 | | | | GROUND_INST: instantiating (10) with 0, all_179_3, all_47_1, simplifying % 24.11/4.03 | | | | with (22), (51) gives: % 24.11/4.03 | | | | (66) all_179_3 = 0 % 24.11/4.03 | | | | % 24.11/4.03 | | | | GROUND_INST: instantiating (11) with all_111_1, all_165_2, all_47_1, % 24.11/4.03 | | | | simplifying with (28), (45) gives: % 24.11/4.03 | | | | (67) all_165_2 = all_111_1 % 24.11/4.03 | | | | % 24.11/4.03 | | | | GROUND_INST: instantiating (11) with all_47_2, all_165_2, all_47_1, % 24.11/4.03 | | | | simplifying with (45), (55) gives: % 24.11/4.03 | | | | (68) all_165_2 = all_47_2 % 24.11/4.03 | | | | % 24.11/4.03 | | | | GROUND_INST: instantiating (12) with all_165_0, all_179_1, all_47_1, % 24.11/4.03 | | | | simplifying with (46), (52) gives: % 24.11/4.03 | | | | (69) all_179_1 = all_165_0 % 24.11/4.03 | | | | % 24.11/4.03 | | | | GROUND_INST: instantiating (13) with all_165_1, all_179_2, all_47_1, % 24.11/4.03 | | | | simplifying with (47), (53) gives: % 24.11/4.03 | | | | (70) all_179_2 = all_165_1 % 24.11/4.03 | | | | % 24.11/4.03 | | | | COMBINE_EQS: (67), (68) imply: % 24.11/4.03 | | | | (71) all_111_1 = all_47_2 % 24.11/4.03 | | | | % 24.11/4.03 | | | | SIMP: (71) implies: % 24.11/4.03 | | | | (72) all_111_1 = all_47_2 % 24.11/4.03 | | | | % 24.11/4.03 | | | | REDUCE: (44), (68) imply: % 24.11/4.03 | | | | (73) set_union2(all_165_1, all_165_0) = all_47_2 % 24.11/4.03 | | | | % 24.11/4.03 | | | | REDUCE: (63), (72) imply: % 24.11/4.03 | | | | (74) in(all_196_2, all_47_2) = 0 % 24.11/4.03 | | | | % 24.11/4.03 | | | | REDUCE: (50), (69) imply: % 24.11/4.03 | | | | (75) $i(all_165_0) % 24.11/4.03 | | | | % 24.11/4.03 | | | | REDUCE: (49), (70) imply: % 24.11/4.03 | | | | (76) $i(all_165_1) % 24.11/4.03 | | | | % 24.11/4.03 | | | | GROUND_INST: instantiating (2) with all_47_1, all_163_0, simplifying % 24.11/4.03 | | | | with (19), (42) gives: % 24.11/4.03 | | | | (77) ? [v0: any] : ? [v1: any] : ? [v2: any] : (relation(all_47_1) % 24.11/4.03 | | | | = v0 & function(all_47_1) = v2 & empty(all_47_1) = v1 & ( ~ % 24.11/4.03 | | | | (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | all_163_0 = 0)) % 24.11/4.03 | | | | % 24.11/4.03 | | | | GROUND_INST: instantiating (3) with all_165_0, all_165_1, all_47_2, % 24.11/4.03 | | | | simplifying with (73), (75), (76) gives: % 24.11/4.03 | | | | (78) set_union2(all_165_0, all_165_1) = all_47_2 & $i(all_47_2) % 24.11/4.03 | | | | % 24.11/4.03 | | | | GROUND_INST: instantiating (56) with all_196_2, all_196_2, all_196_1, % 24.11/4.03 | | | | simplifying with (62), (65) gives: % 24.11/4.03 | | | | (79) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] : % 24.11/4.03 | | | | (subset(all_196_2, all_196_2) = v3 & in(all_196_1, all_47_1) = % 24.11/4.03 | | | | v2 & in(all_196_2, all_47_2) = v1 & in(all_196_2, all_47_2) = % 24.11/4.03 | | | | v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | (( ~ (v3 = 0) | v2 = 0) & ( % 24.11/4.03 | | | | ~ (v2 = 0) | v3 = 0)))) % 24.11/4.03 | | | | % 24.11/4.03 | | | | GROUND_INST: instantiating (6) with all_47_2, all_47_1, all_47_2, % 24.11/4.03 | | | | all_196_2, all_196_2, all_196_1, simplifying with (18), % 24.11/4.03 | | | | (19), (20), (55), (62), (65) gives: % 24.11/4.03 | | | | (80) ? [v0: int] : ? [v1: any] : ? [v2: any] : ? [v3: any] : (( ~ % 24.11/4.03 | | | | (v0 = 0) & relation(all_47_1) = v0) | (subset(all_196_2, % 24.11/4.03 | | | | all_196_2) = v3 & in(all_196_1, all_47_1) = v2 & % 24.11/4.03 | | | | in(all_196_2, all_47_2) = v1 & in(all_196_2, all_47_2) = v0 % 24.11/4.03 | | | | & ( ~ (v1 = 0) | ~ (v0 = 0) | (( ~ (v3 = 0) | v2 = 0) & ( ~ % 24.11/4.03 | | | | (v2 = 0) | v3 = 0))))) % 24.11/4.03 | | | | % 24.11/4.03 | | | | DELTA: instantiating (77) with fresh symbols all_256_0, all_256_1, % 24.11/4.03 | | | | all_256_2 gives: % 24.11/4.03 | | | | (81) relation(all_47_1) = all_256_2 & function(all_47_1) = all_256_0 % 24.11/4.03 | | | | & empty(all_47_1) = all_256_1 & ( ~ (all_256_0 = 0) | ~ % 24.11/4.03 | | | | (all_256_1 = 0) | ~ (all_256_2 = 0) | all_163_0 = 0) % 24.11/4.03 | | | | % 24.11/4.03 | | | | ALPHA: (81) implies: % 24.11/4.03 | | | | (82) relation(all_47_1) = all_256_2 % 24.11/4.03 | | | | % 24.11/4.03 | | | | DELTA: instantiating (79) with fresh symbols all_258_0, all_258_1, % 24.11/4.03 | | | | all_258_2, all_258_3 gives: % 24.11/4.03 | | | | (83) subset(all_196_2, all_196_2) = all_258_0 & in(all_196_1, % 24.11/4.03 | | | | all_47_1) = all_258_1 & in(all_196_2, all_47_2) = all_258_2 & % 24.11/4.03 | | | | in(all_196_2, all_47_2) = all_258_3 & ( ~ (all_258_2 = 0) | ~ % 24.11/4.03 | | | | (all_258_3 = 0) | (( ~ (all_258_0 = 0) | all_258_1 = 0) & ( ~ % 24.11/4.03 | | | | (all_258_1 = 0) | all_258_0 = 0))) % 24.11/4.03 | | | | % 24.11/4.03 | | | | ALPHA: (83) implies: % 24.11/4.03 | | | | (84) in(all_196_2, all_47_2) = all_258_3 % 24.11/4.03 | | | | (85) in(all_196_2, all_47_2) = all_258_2 % 24.11/4.03 | | | | (86) in(all_196_1, all_47_1) = all_258_1 % 24.11/4.03 | | | | (87) subset(all_196_2, all_196_2) = all_258_0 % 24.11/4.03 | | | | (88) ~ (all_258_2 = 0) | ~ (all_258_3 = 0) | (( ~ (all_258_0 = 0) | % 24.11/4.03 | | | | all_258_1 = 0) & ( ~ (all_258_1 = 0) | all_258_0 = 0)) % 24.11/4.03 | | | | % 24.11/4.03 | | | | DELTA: instantiating (80) with fresh symbols all_260_0, all_260_1, % 24.11/4.03 | | | | all_260_2, all_260_3 gives: % 24.11/4.04 | | | | (89) ( ~ (all_260_3 = 0) & relation(all_47_1) = all_260_3) | % 24.11/4.04 | | | | (subset(all_196_2, all_196_2) = all_260_0 & in(all_196_1, % 24.11/4.04 | | | | all_47_1) = all_260_1 & in(all_196_2, all_47_2) = all_260_2 % 24.11/4.04 | | | | & in(all_196_2, all_47_2) = all_260_3 & ( ~ (all_260_2 = 0) | % 24.11/4.04 | | | | ~ (all_260_3 = 0) | (( ~ (all_260_0 = 0) | all_260_1 = 0) & % 24.11/4.04 | | | | ( ~ (all_260_1 = 0) | all_260_0 = 0)))) % 24.11/4.04 | | | | % 24.11/4.04 | | | | BETA: splitting (89) gives: % 24.11/4.04 | | | | % 24.11/4.04 | | | | Case 1: % 24.11/4.04 | | | | | % 24.11/4.04 | | | | | (90) ~ (all_260_3 = 0) & relation(all_47_1) = all_260_3 % 24.11/4.04 | | | | | % 24.11/4.04 | | | | | ALPHA: (90) implies: % 24.11/4.04 | | | | | (91) ~ (all_260_3 = 0) % 24.11/4.04 | | | | | (92) relation(all_47_1) = all_260_3 % 24.11/4.04 | | | | | % 24.11/4.04 | | | | | GROUND_INST: instantiating (10) with 0, all_260_3, all_47_1, % 24.11/4.04 | | | | | simplifying with (22), (92) gives: % 24.11/4.04 | | | | | (93) all_260_3 = 0 % 24.11/4.04 | | | | | % 24.11/4.04 | | | | | GROUND_INST: instantiating (10) with all_256_2, all_260_3, all_47_1, % 24.11/4.04 | | | | | simplifying with (82), (92) gives: % 24.11/4.04 | | | | | (94) all_260_3 = all_256_2 % 24.11/4.04 | | | | | % 24.11/4.04 | | | | | COMBINE_EQS: (93), (94) imply: % 24.11/4.04 | | | | | (95) all_256_2 = 0 % 24.11/4.04 | | | | | % 24.11/4.04 | | | | | REDUCE: (91), (93) imply: % 24.11/4.04 | | | | | (96) $false % 24.11/4.04 | | | | | % 24.11/4.04 | | | | | CLOSE: (96) is inconsistent. % 24.11/4.04 | | | | | % 24.11/4.04 | | | | Case 2: % 24.11/4.04 | | | | | % 24.11/4.04 | | | | | (97) subset(all_196_2, all_196_2) = all_260_0 & in(all_196_1, % 24.11/4.04 | | | | | all_47_1) = all_260_1 & in(all_196_2, all_47_2) = all_260_2 % 24.11/4.04 | | | | | & in(all_196_2, all_47_2) = all_260_3 & ( ~ (all_260_2 = 0) | % 24.11/4.04 | | | | | ~ (all_260_3 = 0) | (( ~ (all_260_0 = 0) | all_260_1 = 0) & % 24.11/4.04 | | | | | ( ~ (all_260_1 = 0) | all_260_0 = 0))) % 24.11/4.04 | | | | | % 24.11/4.04 | | | | | ALPHA: (97) implies: % 24.11/4.04 | | | | | (98) in(all_196_2, all_47_2) = all_260_3 % 24.11/4.04 | | | | | (99) in(all_196_2, all_47_2) = all_260_2 % 24.11/4.04 | | | | | (100) in(all_196_1, all_47_1) = all_260_1 % 24.11/4.04 | | | | | (101) subset(all_196_2, all_196_2) = all_260_0 % 24.11/4.04 | | | | | % 24.11/4.04 | | | | | GROUND_INST: instantiating (14) with 0, all_258_2, all_47_2, % 24.11/4.04 | | | | | all_196_2, simplifying with (74), (85) gives: % 24.11/4.04 | | | | | (102) all_258_2 = 0 % 24.11/4.04 | | | | | % 24.11/4.04 | | | | | GROUND_INST: instantiating (14) with all_258_2, all_260_3, all_47_2, % 24.11/4.04 | | | | | all_196_2, simplifying with (85), (98) gives: % 24.11/4.04 | | | | | (103) all_260_3 = all_258_2 % 24.11/4.04 | | | | | % 24.11/4.04 | | | | | GROUND_INST: instantiating (14) with all_260_3, all_260_2, all_47_2, % 24.11/4.04 | | | | | all_196_2, simplifying with (98), (99) gives: % 24.11/4.04 | | | | | (104) all_260_2 = all_260_3 % 24.11/4.04 | | | | | % 24.11/4.04 | | | | | GROUND_INST: instantiating (14) with all_258_3, all_260_2, all_47_2, % 24.11/4.04 | | | | | all_196_2, simplifying with (84), (99) gives: % 24.11/4.04 | | | | | (105) all_260_2 = all_258_3 % 24.11/4.04 | | | | | % 24.11/4.04 | | | | | GROUND_INST: instantiating (14) with all_196_0, all_260_1, all_47_1, % 24.11/4.04 | | | | | all_196_1, simplifying with (64), (100) gives: % 24.11/4.04 | | | | | (106) all_260_1 = all_196_0 % 24.11/4.04 | | | | | % 24.11/4.04 | | | | | GROUND_INST: instantiating (14) with all_258_1, all_260_1, all_47_1, % 24.11/4.04 | | | | | all_196_1, simplifying with (86), (100) gives: % 24.11/4.04 | | | | | (107) all_260_1 = all_258_1 % 24.11/4.04 | | | | | % 24.11/4.04 | | | | | GROUND_INST: instantiating (15) with all_258_0, all_260_0, all_196_2, % 24.11/4.04 | | | | | all_196_2, simplifying with (87), (101) gives: % 24.11/4.04 | | | | | (108) all_260_0 = all_258_0 % 24.11/4.04 | | | | | % 24.11/4.04 | | | | | COMBINE_EQS: (106), (107) imply: % 24.11/4.04 | | | | | (109) all_258_1 = all_196_0 % 24.11/4.04 | | | | | % 24.11/4.04 | | | | | SIMP: (109) implies: % 24.11/4.04 | | | | | (110) all_258_1 = all_196_0 % 24.11/4.04 | | | | | % 24.11/4.04 | | | | | COMBINE_EQS: (104), (105) imply: % 24.11/4.04 | | | | | (111) all_260_3 = all_258_3 % 24.11/4.04 | | | | | % 24.11/4.04 | | | | | SIMP: (111) implies: % 24.11/4.04 | | | | | (112) all_260_3 = all_258_3 % 24.11/4.04 | | | | | % 24.11/4.04 | | | | | COMBINE_EQS: (103), (112) imply: % 24.11/4.04 | | | | | (113) all_258_2 = all_258_3 % 24.11/4.04 | | | | | % 24.11/4.04 | | | | | SIMP: (113) implies: % 24.11/4.04 | | | | | (114) all_258_2 = all_258_3 % 24.11/4.04 | | | | | % 24.11/4.04 | | | | | COMBINE_EQS: (102), (114) imply: % 24.11/4.04 | | | | | (115) all_258_3 = 0 % 24.11/4.04 | | | | | % 24.11/4.04 | | | | | SIMP: (115) implies: % 24.11/4.04 | | | | | (116) all_258_3 = 0 % 24.11/4.04 | | | | | % 24.11/4.04 | | | | | BETA: splitting (88) gives: % 24.11/4.04 | | | | | % 24.11/4.04 | | | | | Case 1: % 24.11/4.04 | | | | | | % 24.11/4.04 | | | | | | (117) ~ (all_258_2 = 0) % 24.11/4.04 | | | | | | % 24.11/4.04 | | | | | | REDUCE: (102), (117) imply: % 24.11/4.04 | | | | | | (118) $false % 24.11/4.04 | | | | | | % 24.11/4.04 | | | | | | CLOSE: (118) is inconsistent. % 24.11/4.04 | | | | | | % 24.11/4.04 | | | | | Case 2: % 24.11/4.04 | | | | | | % 24.11/4.04 | | | | | | (119) ~ (all_258_3 = 0) | (( ~ (all_258_0 = 0) | all_258_1 = 0) % 24.11/4.04 | | | | | | & ( ~ (all_258_1 = 0) | all_258_0 = 0)) % 24.11/4.04 | | | | | | % 24.11/4.04 | | | | | | BETA: splitting (119) gives: % 24.11/4.04 | | | | | | % 24.11/4.04 | | | | | | Case 1: % 24.11/4.04 | | | | | | | % 24.11/4.04 | | | | | | | (120) ~ (all_258_3 = 0) % 24.11/4.04 | | | | | | | % 24.11/4.04 | | | | | | | REDUCE: (116), (120) imply: % 24.11/4.04 | | | | | | | (121) $false % 24.11/4.04 | | | | | | | % 24.11/4.04 | | | | | | | CLOSE: (121) is inconsistent. % 24.11/4.04 | | | | | | | % 24.11/4.04 | | | | | | Case 2: % 24.11/4.04 | | | | | | | % 24.11/4.04 | | | | | | | (122) ( ~ (all_258_0 = 0) | all_258_1 = 0) & ( ~ (all_258_1 = % 24.11/4.04 | | | | | | | 0) | all_258_0 = 0) % 24.11/4.04 | | | | | | | % 24.11/4.04 | | | | | | | ALPHA: (122) implies: % 24.11/4.04 | | | | | | | (123) ~ (all_258_0 = 0) | all_258_1 = 0 % 24.11/4.04 | | | | | | | % 24.11/4.04 | | | | | | | BETA: splitting (123) gives: % 24.11/4.04 | | | | | | | % 24.11/4.04 | | | | | | | Case 1: % 24.11/4.04 | | | | | | | | % 24.11/4.04 | | | | | | | | (124) ~ (all_258_0 = 0) % 24.11/4.04 | | | | | | | | % 24.11/4.04 | | | | | | | | GROUND_INST: instantiating (reflexivity_r1_tarski) with % 24.11/4.04 | | | | | | | | all_196_2, all_258_0, simplifying with (62), (87) % 24.11/4.04 | | | | | | | | gives: % 24.11/4.04 | | | | | | | | (125) all_258_0 = 0 % 24.11/4.04 | | | | | | | | % 24.11/4.04 | | | | | | | | REDUCE: (124), (125) imply: % 24.11/4.04 | | | | | | | | (126) $false % 24.11/4.04 | | | | | | | | % 24.11/4.04 | | | | | | | | CLOSE: (126) is inconsistent. % 24.11/4.04 | | | | | | | | % 24.11/4.04 | | | | | | | Case 2: % 24.11/4.04 | | | | | | | | % 24.11/4.04 | | | | | | | | (127) all_258_1 = 0 % 24.11/4.04 | | | | | | | | % 24.11/4.04 | | | | | | | | COMBINE_EQS: (110), (127) imply: % 24.11/4.04 | | | | | | | | (128) all_196_0 = 0 % 24.11/4.04 | | | | | | | | % 24.11/4.04 | | | | | | | | SIMP: (128) implies: % 24.11/4.04 | | | | | | | | (129) all_196_0 = 0 % 24.11/4.04 | | | | | | | | % 24.11/4.04 | | | | | | | | REDUCE: (61), (129) imply: % 24.11/4.04 | | | | | | | | (130) $false % 24.11/4.04 | | | | | | | | % 24.11/4.04 | | | | | | | | CLOSE: (130) is inconsistent. % 24.11/4.04 | | | | | | | | % 24.11/4.04 | | | | | | | End of split % 24.11/4.04 | | | | | | | % 24.11/4.04 | | | | | | End of split % 24.11/4.04 | | | | | | % 24.11/4.04 | | | | | End of split % 24.11/4.04 | | | | | % 24.11/4.04 | | | | End of split % 24.11/4.04 | | | | % 24.11/4.04 | | | End of split % 24.11/4.04 | | | % 24.11/4.04 | | Case 2: % 24.11/4.04 | | | % 24.11/4.04 | | | (131) all_47_0 = 0 % 24.11/4.04 | | | % 24.11/4.04 | | | REDUCE: (17), (131) imply: % 24.11/4.04 | | | (132) $false % 24.11/4.04 | | | % 24.11/4.04 | | | CLOSE: (132) is inconsistent. % 24.11/4.04 | | | % 24.11/4.04 | | End of split % 24.11/4.04 | | % 24.11/4.04 | End of split % 24.11/4.04 | % 24.11/4.04 End of proof % 24.11/4.05 % SZS output end Proof for theBenchmark % 24.11/4.05 % 24.11/4.05 3446ms %------------------------------------------------------------------------------