%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SCT126+1 : TPTP v8.1.2. Released v5.2.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n020.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 300s % DateTime : Thu Aug 31 14:20:44 EDT 2023 % Result : Theorem 67.61s 9.59s % Output : Proof 98.54s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SCT126+1 : TPTP v8.1.2. Released v5.2.0. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.12/0.34 % Computer : n020.cluster.edu % 0.12/0.34 % Model : x86_64 x86_64 % 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.34 % Memory : 8042.1875MB % 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.34 % CPULimit : 300 % 0.12/0.34 % WCLimit : 300 % 0.12/0.34 % DateTime : Thu Aug 24 15:17:30 EDT 2023 % 0.12/0.34 % CPUTime : % 0.20/0.57 ________ _____ % 0.20/0.57 ___ __ \_________(_)________________________________ % 0.20/0.57 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.20/0.57 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.20/0.57 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.20/0.57 % 0.20/0.57 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.20/0.57 (2023-06-19) % 0.20/0.57 % 0.20/0.57 (c) Philipp Rümmer, 2009-2023 % 0.20/0.57 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.20/0.57 Amanda Stjerna. % 0.20/0.57 Free software under BSD-3-Clause. % 0.20/0.57 % 0.20/0.57 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.20/0.57 % 0.20/0.57 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.20/0.58 Running up to 7 provers in parallel. % 0.20/0.60 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.20/0.60 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.20/0.60 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.20/0.60 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.20/0.60 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.20/0.60 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.20/0.60 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 14.13/2.57 Prover 1: Preprocessing ... % 14.39/2.65 Prover 4: Preprocessing ... % 14.39/2.66 Prover 6: Preprocessing ... % 14.39/2.66 Prover 5: Preprocessing ... % 14.39/2.74 Prover 0: Preprocessing ... % 15.55/2.76 Prover 2: Preprocessing ... % 15.55/2.78 Prover 3: Preprocessing ... % 45.91/6.74 Prover 1: Warning: ignoring some quantifiers % 45.91/6.76 Prover 3: Warning: ignoring some quantifiers % 47.18/6.92 Prover 6: Proving ... % 47.18/6.94 Prover 3: Constructing countermodel ... % 47.97/7.00 Prover 1: Constructing countermodel ... % 53.86/7.81 Prover 4: Warning: ignoring some quantifiers % 54.43/7.89 Prover 5: Proving ... % 56.60/8.16 Prover 4: Constructing countermodel ... % 58.91/8.61 Prover 0: Proving ... % 67.61/9.59 Prover 3: proved (8995ms) % 67.61/9.59 % 67.61/9.59 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 67.61/9.59 % 67.61/9.59 Prover 5: stopped % 67.61/9.59 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 67.61/9.60 Prover 6: stopped % 67.61/9.61 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 67.61/9.61 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 68.27/9.67 Prover 0: stopped % 68.27/9.67 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 70.61/10.04 Prover 2: Proving ... % 70.61/10.04 Prover 2: stopped % 71.24/10.05 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 76.45/10.77 Prover 10: Preprocessing ... % 76.45/10.78 Prover 7: Preprocessing ... % 76.45/10.81 Prover 11: Preprocessing ... % 77.16/10.83 Prover 8: Preprocessing ... % 78.69/11.02 Prover 13: Preprocessing ... % 87.73/12.23 Prover 8: Warning: ignoring some quantifiers % 88.45/12.29 Prover 10: Warning: ignoring some quantifiers % 88.92/12.38 Prover 1: Found proof (size 561) % 88.92/12.38 Prover 1: proved (11790ms) % 89.61/12.45 Prover 8: Constructing countermodel ... % 90.10/12.49 Prover 8: stopped % 90.10/12.50 Prover 10: Constructing countermodel ... % 90.10/12.52 Prover 4: stopped % 90.66/12.57 Prover 10: stopped % 90.75/12.75 Prover 7: Warning: ignoring some quantifiers % 91.98/12.86 Prover 13: Warning: ignoring some quantifiers % 92.93/13.00 Prover 7: Constructing countermodel ... % 93.46/13.05 Prover 13: Constructing countermodel ... % 93.92/13.10 Prover 7: stopped % 93.92/13.13 Prover 13: stopped % 94.43/13.17 Prover 11: Warning: ignoring some quantifiers % 95.02/13.37 Prover 11: Constructing countermodel ... % 95.44/13.42 Prover 11: stopped % 95.44/13.42 % 95.44/13.42 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 95.44/13.42 % 96.75/13.84 % SZS output start Proof for theBenchmark % 96.75/13.86 Assumptions after simplification: % 96.75/13.86 --------------------------------- % 96.75/13.86 % 96.75/13.86 (arity_HOL__Obool__Orderings_Obot) % 96.98/13.88 class_Orderings_Obot(tc_HOL_Obool) = 0 & $i(tc_HOL_Obool) % 96.98/13.88 % 96.98/13.88 (arity_fun__Orderings_Obot) % 96.98/13.88 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (tc_fun(v0, v1) = v2) | ~ % 96.98/13.88 $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : (class_Orderings_Obot(v2) % 96.98/13.88 = v4 & class_Orderings_Obot(v1) = v3 & ( ~ (v3 = 0) | v4 = 0))) % 96.98/13.88 % 96.98/13.88 (conj_0) % 96.98/13.89 $i(c_Arrow__Order__Mirabelle_OLin) & $i(v_Q____) & $i(tc_HOL_Obool) & % 96.98/13.89 $i(tc_Arrow__Order__Mirabelle_Oalt) & $i(v_F) & ? [v0: $i] : ? [v1: $i] : ? % 96.98/13.89 [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: int] : ( ~ (v6 = % 96.98/13.89 0) & tc_prod(tc_Arrow__Order__Mirabelle_Oalt, % 96.98/13.89 tc_Arrow__Order__Mirabelle_Oalt) = v0 & tc_fun(v0, tc_HOL_Obool) = v1 & % 96.98/13.89 c_member(v1) = v2 & hBOOL(v5) = v6 & hAPP(v4, % 96.98/13.89 c_Arrow__Order__Mirabelle_OLin) = v5 & hAPP(v2, v3) = v4 & hAPP(v_F, % 96.98/13.89 v_Q____) = v3 & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 96.98/13.89 % 96.98/13.89 (fact_IIA__def) % 97.11/13.90 $i(c_Arrow__Order__Mirabelle_OProf) & $i(tc_HOL_Obool) & % 97.11/13.90 $i(tc_Arrow__Order__Mirabelle_Oalt) & $i(tc_Arrow__Order__Mirabelle_Oindi) & % 97.11/13.90 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: % 97.11/13.90 $i] : (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 97.11/13.90 tc_Arrow__Order__Mirabelle_Oalt) = v5 & % 97.11/13.90 tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt) = % 97.11/13.90 v0 & tc_fun(v0, tc_HOL_Obool) = v1 & % 97.11/13.90 tc_fun(tc_Arrow__Order__Mirabelle_Oindi, v1) = v2 & c_member(v2) = v3 & % 97.11/13.90 c_member(v0) = v4 & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & ! % 97.11/13.90 [v6: $i] : ! [v7: int] : (v7 = 0 | ~ (c_Arrow__Order__Mirabelle_OIIA(v6) = % 97.11/13.90 v7) | ~ $i(v6) | ? [v8: $i] : ? [v9: $i] : ? [v10: $i] : ? [v11: % 97.11/13.90 $i] : (hBOOL(v10) = 0 & hAPP(v9, c_Arrow__Order__Mirabelle_OProf) = v10 % 97.11/13.90 & hAPP(v6, v8) = v11 & hAPP(v3, v8) = v9 & $i(v11) & $i(v10) & $i(v9) & % 97.11/13.90 $i(v8) & ? [v12: $i] : ? [v13: $i] : ? [v14: $i] : ? [v15: $i] : % 97.11/13.90 (hBOOL(v14) = 0 & hAPP(v13, c_Arrow__Order__Mirabelle_OProf) = v14 & % 97.11/13.90 hAPP(v6, v12) = v15 & hAPP(v3, v12) = v13 & $i(v15) & $i(v14) & % 97.11/13.90 $i(v13) & $i(v12) & ? [v16: $i] : ? [v17: $i] : ? [v18: $i] : ? % 97.11/13.90 [v19: $i] : ? [v20: $i] : ? [v21: $i] : ? [v22: any] : ? [v23: $i] % 97.11/13.90 : ? [v24: any] : (hBOOL(v23) = v24 & hBOOL(v21) = v22 & hAPP(v20, % 97.11/13.90 v15) = v23 & hAPP(v20, v11) = v21 & hAPP(v18, v17) = v19 & % 97.11/13.90 hAPP(v5, v16) = v18 & hAPP(v4, v19) = v20 & $i(v23) & $i(v21) & % 97.11/13.90 $i(v20) & $i(v19) & $i(v18) & $i(v17) & $i(v16) & ! [v25: $i] : ! % 97.11/13.90 [v26: $i] : ! [v27: $i] : ( ~ (hAPP(v20, v26) = v27) | ~ (hAPP(v8, % 97.11/13.90 v25) = v26) | ~ $i(v25) | ? [v28: any] : ? [v29: $i] : ? % 97.11/13.90 [v30: $i] : ? [v31: any] : (hBOOL(v30) = v31 & hBOOL(v27) = v28 & % 97.11/13.90 hAPP(v20, v29) = v30 & hAPP(v12, v25) = v29 & $i(v30) & $i(v29) % 97.11/13.90 & ( ~ (v28 = 0) | v31 = 0))) & ! [v25: $i] : ! [v26: $i] : ! % 97.11/13.90 [v27: $i] : ( ~ (hAPP(v20, v26) = v27) | ~ (hAPP(v8, v25) = v26) | % 97.11/13.90 ~ $i(v25) | ? [v28: $i] : ? [v29: $i] : ? [v30: any] : ? [v31: % 97.11/13.90 any] : (hBOOL(v29) = v30 & hBOOL(v27) = v31 & hAPP(v20, v28) = % 97.11/13.90 v29 & hAPP(v12, v25) = v28 & $i(v29) & $i(v28) & ( ~ (v30 = 0) | % 97.11/13.90 v31 = 0))) & ( ~ (v24 = 0) | ~ (v22 = 0)) & (v24 = 0 | v22 = % 97.11/13.90 0))))) & ! [v6: $i] : ( ~ (c_Arrow__Order__Mirabelle_OIIA(v6) = % 97.11/13.90 0) | ~ $i(v6) | ! [v7: $i] : ! [v8: $i] : ( ~ (hAPP(v3, v7) = v8) | % 97.11/13.90 ~ $i(v7) | ? [v9: $i] : ? [v10: any] : ? [v11: $i] : (hBOOL(v9) = v10 % 97.11/13.90 & hAPP(v8, c_Arrow__Order__Mirabelle_OProf) = v9 & hAPP(v6, v7) = v11 % 97.11/13.90 & $i(v11) & $i(v9) & ( ~ (v10 = 0) | ! [v12: $i] : ! [v13: $i] : ( ~ % 97.11/13.90 (hAPP(v3, v12) = v13) | ~ $i(v12) | ? [v14: $i] : ? [v15: any] % 97.11/13.90 : ? [v16: $i] : (hBOOL(v14) = v15 & hAPP(v13, % 97.11/13.90 c_Arrow__Order__Mirabelle_OProf) = v14 & hAPP(v6, v12) = v16 & % 97.11/13.90 $i(v16) & $i(v14) & ( ~ (v15 = 0) | ! [v17: $i] : ! [v18: $i] % 97.11/13.90 : ! [v19: $i] : ! [v20: $i] : ! [v21: $i] : ! [v22: $i] : % 97.11/13.90 ( ~ (hAPP(v21, v11) = v22) | ~ (hAPP(v19, v18) = v20) | ~ % 97.11/13.90 (hAPP(v5, v17) = v19) | ~ (hAPP(v4, v20) = v21) | ~ % 97.11/13.90 $i(v18) | ~ $i(v17) | ? [v23: $i] : ? [v24: $i] : ? % 97.11/13.90 [v25: $i] : ? [v26: any] : ? [v27: $i] : ? [v28: $i] : ? % 97.11/13.90 [v29: any] : (hBOOL(v28) = v29 & hBOOL(v25) = v26 & % 97.11/13.90 hAPP(v21, v27) = v28 & hAPP(v21, v24) = v25 & hAPP(v12, % 97.11/13.90 v23) = v27 & hAPP(v7, v23) = v24 & $i(v28) & $i(v27) & % 97.11/13.90 $i(v25) & $i(v24) & $i(v23) & ( ~ (v29 = 0) | ~ (v26 = % 97.11/13.90 0)) & (v29 = 0 | v26 = 0)) | ? [v23: any] : ? [v24: % 97.11/13.90 $i] : ? [v25: any] : (hBOOL(v24) = v25 & hBOOL(v22) = v23 % 97.11/13.90 & hAPP(v21, v16) = v24 & $i(v24) & ( ~ (v25 = 0) | v23 = % 97.11/13.90 0) & ( ~ (v23 = 0) | v25 = 0))))))))))) % 97.11/13.90 % 97.11/13.90 (fact_Id__compose) % 97.11/13.91 $i(tc_HOL_Obool) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! % 97.11/13.91 [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] % 97.11/13.91 : ! [v10: $i] : ! [v11: $i] : ( ~ (c_COMBK(v8, v4, v0) = v9) | ~ % 97.11/13.91 (c_FuncSet_OPi(v4, v3, v1, v9) = v10) | ~ (tc_fun(v4, v3) = v5) | ~ % 97.11/13.91 (tc_fun(v3, tc_HOL_Obool) = v8) | ~ (c_member(v5) = v6) | ~ (hAPP(v7, v10) % 97.11/13.91 = v11) | ~ (hAPP(v6, v2) = v7) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ % 97.11/13.91 $i(v1) | ~ $i(v0) | ? [v12: any] : ? [v13: $i] : ? [v14: $i] : ? [v15: % 97.11/13.91 any] : ? [v16: $i] : ? [v17: $i] : ? [v18: $i] : % 97.11/13.91 (c_FuncSet_Orestrict(v3, v3, v16, v0) = v17 & c_FuncSet_Oextensional(v4, v3, % 97.11/13.91 v1) = v13 & c_FuncSet_Ocompose(v4, v3, v3, v1, v17, v2) = v18 & % 97.11/13.91 c_COMBI(v3) = v16 & hBOOL(v14) = v15 & hBOOL(v11) = v12 & hAPP(v7, v13) = % 97.11/13.91 v14 & $i(v18) & $i(v17) & $i(v16) & $i(v14) & $i(v13) & ( ~ (v15 = 0) | ~ % 97.11/13.91 (v12 = 0) | v18 = v2))) % 97.11/13.91 % 97.11/13.91 (fact_Lin__irrefl) % 97.11/13.91 $i(c_Arrow__Order__Mirabelle_OLin) & $i(tc_HOL_Obool) & % 97.11/13.91 $i(tc_Arrow__Order__Mirabelle_Oalt) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] % 97.11/13.91 : ? [v3: $i] : ? [v4: $i] : % 97.11/13.91 (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 97.11/13.91 tc_Arrow__Order__Mirabelle_Oalt) = v4 & % 97.11/13.91 tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt) = % 97.11/13.91 v0 & tc_fun(v0, tc_HOL_Obool) = v1 & c_member(v1) = v2 & c_member(v0) = v3 & % 97.11/13.91 $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & ! [v5: $i] : ! [v6: $i] : ! % 97.11/13.91 [v7: $i] : ! [v8: $i] : ! [v9: $i] : ! [v10: $i] : ! [v11: $i] : ( ~ % 97.11/13.91 (hAPP(v10, v7) = v11) | ~ (hAPP(v8, v6) = v9) | ~ (hAPP(v4, v5) = v8) | % 97.11/13.91 ~ (hAPP(v3, v9) = v10) | ~ $i(v7) | ~ $i(v6) | ~ $i(v5) | ? [v12: $i] % 97.11/13.91 : ? [v13: $i] : ? [v14: any] : ? [v15: $i] : ? [v16: $i] : ? [v17: % 97.11/13.91 $i] : ? [v18: $i] : ? [v19: any] : ? [v20: any] : (hBOOL(v18) = v19 & % 97.11/13.91 hBOOL(v13) = v14 & hBOOL(v11) = v20 & hAPP(v17, v7) = v18 & hAPP(v15, % 97.11/13.91 v5) = v16 & hAPP(v12, c_Arrow__Order__Mirabelle_OLin) = v13 & hAPP(v4, % 97.11/13.91 v6) = v15 & hAPP(v3, v16) = v17 & hAPP(v2, v7) = v12 & $i(v18) & % 97.11/13.91 $i(v17) & $i(v16) & $i(v15) & $i(v13) & $i(v12) & ( ~ (v20 = 0) | ~ % 97.11/13.91 (v19 = 0) | ~ (v14 = 0))))) % 97.11/13.91 % 97.11/13.91 (fact_Pi__eq__empty) % 97.11/13.92 $i(tc_HOL_Obool) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! % 97.11/13.92 [v4: $i] : ( ~ (c_FuncSet_OPi(v3, v2, v1, v0) = v4) | ~ $i(v3) | ~ $i(v2) | % 97.11/13.92 ~ $i(v1) | ~ $i(v0) | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] % 97.11/13.92 : ? [v9: $i] : ? [v10: $i] : (c_Orderings_Obot__class_Obot(v9) = v10 & % 97.11/13.92 c_Orderings_Obot__class_Obot(v6) = v7 & tc_fun(v8, tc_HOL_Obool) = v9 & % 97.11/13.92 tc_fun(v3, v2) = v8 & tc_fun(v2, tc_HOL_Obool) = v6 & c_member(v3) = v5 & % 97.11/13.92 $i(v10) & $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5) & (v10 = v4 | ! % 97.11/13.92 [v11: $i] : ! [v12: $i] : ! [v13: $i] : ( ~ (hAPP(v12, v1) = v13) | ~ % 97.11/13.92 (hAPP(v5, v11) = v12) | ~ $i(v11) | ? [v14: any] : ? [v15: $i] : % 97.11/13.92 (hBOOL(v13) = v14 & hAPP(v0, v11) = v15 & $i(v15) & ( ~ (v15 = v7) | % 97.11/13.92 ~ (v14 = 0))))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 97.11/13.92 [v3: $i] : ! [v4: $i] : ( ~ (c_FuncSet_OPi(v3, v2, v1, v0) = v4) | ~ $i(v3) % 97.11/13.92 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: $i] : ? [v6: $i] : ? [v7: % 97.11/13.92 $i] : ? [v8: $i] : ? [v9: $i] : ? [v10: $i] : % 97.11/13.92 (c_Orderings_Obot__class_Obot(v9) = v10 & c_Orderings_Obot__class_Obot(v6) = % 97.11/13.92 v7 & tc_fun(v5, tc_HOL_Obool) = v6 & tc_fun(v3, v2) = v5 & tc_fun(v2, % 97.11/13.92 tc_HOL_Obool) = v9 & c_member(v3) = v8 & $i(v10) & $i(v9) & $i(v8) & % 97.11/13.92 $i(v7) & $i(v6) & $i(v5) & ( ~ (v7 = v4) | ? [v11: $i] : ? [v12: $i] : % 97.11/13.92 ? [v13: $i] : (hBOOL(v13) = 0 & hAPP(v12, v1) = v13 & hAPP(v8, v11) = % 97.11/13.92 v12 & hAPP(v0, v11) = v10 & $i(v13) & $i(v12) & $i(v11))))) % 97.11/13.92 % 97.11/13.92 (fact_Q__def) % 97.11/13.92 $i(c_fequal) & $i(v_P____) & $i(v_a____) & $i(v_b____) & $i(v_a_H____) & % 97.11/13.92 $i(v_b_H____) & $i(c_Arrow__Order__Mirabelle_Oabove) & $i(v_Q____) & % 97.11/13.92 $i(tc_HOL_Obool) & $i(tc_Arrow__Order__Mirabelle_Oalt) & ? [v0: $i] : ? [v1: % 97.11/13.92 $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : % 97.11/13.92 ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ? [v10: $i] : ? [v11: $i] : ? % 97.11/13.92 [v12: $i] : ? [v13: $i] : ? [v14: $i] : ? [v15: $i] : ? [v16: $i] : ? % 97.11/13.92 [v17: $i] : (c_COMBS(v1, v1, v1) = v5 & c_If(v1, v7) = v8 & c_If(v1, v3) = v4 % 97.11/13.92 & c_COMBC(v1, tc_Arrow__Order__Mirabelle_Oalt, v11) = v12 & c_COMBC(v1, % 97.11/13.92 tc_Arrow__Order__Mirabelle_Oalt, v1) = v10 & % 97.11/13.92 tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt) = % 97.11/13.92 v0 & tc_fun(v0, tc_HOL_Obool) = v1 & tc_fun(tc_Arrow__Order__Mirabelle_Oalt, % 97.11/13.92 v1) = v11 & hAPP(v15, v_b_H____) = v16 & hAPP(v13, v_b____) = v14 & % 97.11/13.92 hAPP(v12, c_Arrow__Order__Mirabelle_Oabove) = v13 & hAPP(v10, v14) = v15 & % 97.11/13.92 hAPP(v9, v16) = v17 & hAPP(v6, v_b_H____) = v7 & hAPP(v5, v8) = v9 & % 97.11/13.92 hAPP(v2, v_a_H____) = v3 & hAPP(c_fequal, v_a____) = v2 & hAPP(c_fequal, % 97.11/13.92 v_b____) = v6 & $i(v17) & $i(v16) & $i(v15) & $i(v14) & $i(v13) & $i(v12) % 97.11/13.92 & $i(v11) & $i(v10) & $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) & % 97.11/13.92 $i(v3) & $i(v2) & $i(v1) & $i(v0) & ! [v18: $i] : ! [v19: $i] : ! [v20: % 97.11/13.92 $i] : ! [v21: $i] : ! [v22: $i] : ( ~ % 97.11/13.92 (c_Arrow__Order__Mirabelle_Obelow(v19, v_a_H____, v_a____) = v21) | ~ % 97.11/13.92 (hAPP(v20, v21) = v22) | ~ (hAPP(v4, v19) = v20) | ~ (hAPP(v_P____, v18) % 97.11/13.92 = v19) | ~ $i(v18) | ? [v23: $i] : (c_HOL_OLet(v1, v1, v22, v17) = v23 % 97.11/13.92 & hAPP(v_Q____, v18) = v23 & $i(v23)))) % 97.11/13.92 % 97.11/13.92 (fact__096P_A_058_AProf_096) % 97.11/13.92 $i(v_P____) & $i(c_Arrow__Order__Mirabelle_OProf) & $i(tc_HOL_Obool) & % 97.11/13.92 $i(tc_Arrow__Order__Mirabelle_Oalt) & $i(tc_Arrow__Order__Mirabelle_Oindi) & % 97.11/13.92 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: % 97.11/13.92 $i] : (tc_prod(tc_Arrow__Order__Mirabelle_Oalt, % 97.11/13.92 tc_Arrow__Order__Mirabelle_Oalt) = v0 & tc_fun(v0, tc_HOL_Obool) = v1 & % 97.11/13.92 tc_fun(tc_Arrow__Order__Mirabelle_Oindi, v1) = v2 & c_member(v2) = v3 & % 97.11/13.92 hBOOL(v5) = 0 & hAPP(v4, c_Arrow__Order__Mirabelle_OProf) = v5 & hAPP(v3, % 97.11/13.92 v_P____) = v4 & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 97.11/13.92 % 97.11/13.92 (fact__096P_H_A_058_AProf_096) % 97.11/13.93 $i(v_P_H____) & $i(c_Arrow__Order__Mirabelle_OProf) & $i(tc_HOL_Obool) & % 97.11/13.93 $i(tc_Arrow__Order__Mirabelle_Oalt) & $i(tc_Arrow__Order__Mirabelle_Oindi) & % 97.11/13.93 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: % 97.11/13.93 $i] : (tc_prod(tc_Arrow__Order__Mirabelle_Oalt, % 97.11/13.93 tc_Arrow__Order__Mirabelle_Oalt) = v0 & tc_fun(v0, tc_HOL_Obool) = v1 & % 97.11/13.93 tc_fun(tc_Arrow__Order__Mirabelle_Oindi, v1) = v2 & c_member(v2) = v3 & % 97.11/13.93 hBOOL(v5) = 0 & hAPP(v4, c_Arrow__Order__Mirabelle_OProf) = v5 & hAPP(v3, % 97.11/13.93 v_P_H____) = v4 & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 97.11/13.93 % 97.11/13.93 (fact__096Q_A_058_AProf_096) % 97.11/13.93 $i(c_Arrow__Order__Mirabelle_OProf) & $i(v_Q____) & $i(tc_HOL_Obool) & % 97.11/13.93 $i(tc_Arrow__Order__Mirabelle_Oalt) & $i(tc_Arrow__Order__Mirabelle_Oindi) & % 97.11/13.93 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: % 97.11/13.93 $i] : (tc_prod(tc_Arrow__Order__Mirabelle_Oalt, % 97.11/13.93 tc_Arrow__Order__Mirabelle_Oalt) = v0 & tc_fun(v0, tc_HOL_Obool) = v1 & % 97.11/13.93 tc_fun(tc_Arrow__Order__Mirabelle_Oindi, v1) = v2 & c_member(v2) = v3 & % 97.11/13.93 hBOOL(v5) = 0 & hAPP(v4, c_Arrow__Order__Mirabelle_OProf) = v5 & hAPP(v3, % 97.11/13.93 v_Q____) = v4 & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 97.11/13.93 % 97.11/13.93 (fact__096a_A_060_092_060_094bsub_062F_AP_092_060_094esub_062_Ab_096) % 97.11/13.93 $i(v_P____) & $i(v_a____) & $i(v_b____) & $i(tc_Arrow__Order__Mirabelle_Oalt) % 97.11/13.93 & $i(v_F) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: % 97.11/13.93 $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : % 97.11/13.93 (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 97.11/13.93 tc_Arrow__Order__Mirabelle_Oalt) = v2 & % 97.11/13.93 tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt) = % 97.11/13.93 v0 & c_member(v0) = v1 & hBOOL(v7) = 0 & hAPP(v5, v6) = v7 & hAPP(v3, % 97.11/13.93 v_b____) = v4 & hAPP(v2, v_a____) = v3 & hAPP(v1, v4) = v5 & hAPP(v_F, % 97.11/13.93 v_P____) = v6 & $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & % 97.11/13.93 $i(v1) & $i(v0)) % 97.11/13.93 % 97.11/13.93 (fact__C1_C) % 97.11/13.93 $i(v_P____) & $i(v_a____) & $i(v_b____) & $i(v_P_H____) & $i(v_a_H____) & % 97.11/13.93 $i(v_b_H____) & $i(tc_Arrow__Order__Mirabelle_Oalt) & ? [v0: $i] : ? [v1: % 97.11/13.93 $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : % 97.11/13.93 ? [v7: $i] : ? [v8: $i] : % 97.11/13.93 (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 97.11/13.93 tc_Arrow__Order__Mirabelle_Oalt) = v2 & % 97.11/13.94 tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt) = % 97.11/13.94 v0 & c_member(v0) = v1 & hAPP(v6, v_b_H____) = v7 & hAPP(v3, v_b____) = v4 & % 97.11/13.94 hAPP(v2, v_a____) = v3 & hAPP(v2, v_a_H____) = v6 & hAPP(v1, v7) = v8 & % 97.11/13.94 hAPP(v1, v4) = v5 & $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) & % 97.11/13.94 $i(v2) & $i(v1) & $i(v0) & ! [v9: $i] : ! [v10: $i] : ( ~ (hAPP(v_P_H____, % 97.11/13.94 v9) = v10) | ~ $i(v9) | ? [v11: $i] : ? [v12: $i] : ? [v13: any] : % 97.11/13.94 ? [v14: $i] : ? [v15: any] : (hBOOL(v14) = v15 & hBOOL(v12) = v13 & % 97.11/13.94 hAPP(v8, v10) = v14 & hAPP(v5, v11) = v12 & hAPP(v_P____, v9) = v11 & % 97.11/13.94 $i(v14) & $i(v12) & $i(v11) & ( ~ (v13 = 0) | v15 = 0))) & ! [v9: $i] : % 97.11/13.94 ! [v10: $i] : ( ~ (hAPP(v_P_H____, v9) = v10) | ~ $i(v9) | ? [v11: $i] : % 97.11/13.94 ? [v12: any] : ? [v13: $i] : ? [v14: $i] : ? [v15: any] : (hBOOL(v14) = % 97.11/13.94 v15 & hBOOL(v11) = v12 & hAPP(v8, v10) = v11 & hAPP(v5, v13) = v14 & % 97.11/13.94 hAPP(v_P____, v9) = v13 & $i(v14) & $i(v13) & $i(v11) & ( ~ (v12 = 0) | % 97.11/13.94 v15 = 0)))) % 97.11/13.94 % 97.11/13.94 (fact_above__Lin) % 97.11/13.94 $i(c_Arrow__Order__Mirabelle_Oabove) & $i(c_Arrow__Order__Mirabelle_OLin) & % 97.11/13.94 $i(tc_HOL_Obool) & $i(tc_Arrow__Order__Mirabelle_Oalt) & ? [v0: $i] : ? [v1: % 97.11/13.94 $i] : ? [v2: $i] : (tc_prod(tc_Arrow__Order__Mirabelle_Oalt, % 97.11/13.94 tc_Arrow__Order__Mirabelle_Oalt) = v0 & tc_fun(v0, tc_HOL_Obool) = v1 & % 97.11/13.94 c_member(v1) = v2 & $i(v2) & $i(v1) & $i(v0) & ! [v3: $i] : ! [v4: $i] : % 97.11/13.94 ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : (v5 = v4 | ~ % 97.11/13.94 (hAPP(v7, v4) = v8) | ~ (hAPP(v6, v5) = v7) | ~ % 97.11/13.94 (hAPP(c_Arrow__Order__Mirabelle_Oabove, v3) = v6) | ~ $i(v5) | ~ $i(v4) % 97.11/13.94 | ~ $i(v3) | ? [v9: $i] : ? [v10: $i] : ? [v11: any] : ? [v12: $i] : % 97.11/13.94 ? [v13: $i] : ? [v14: any] : (hBOOL(v13) = v14 & hBOOL(v10) = v11 & % 97.11/13.94 hAPP(v12, c_Arrow__Order__Mirabelle_OLin) = v13 & hAPP(v9, % 97.11/13.94 c_Arrow__Order__Mirabelle_OLin) = v10 & hAPP(v2, v8) = v12 & hAPP(v2, % 97.11/13.94 v3) = v9 & $i(v13) & $i(v12) & $i(v10) & $i(v9) & ( ~ (v11 = 0) | v14 % 97.11/13.94 = 0)))) % 97.11/13.94 % 97.11/13.94 (fact_assms_I1_J) % 97.11/13.94 $i(c_Arrow__Order__Mirabelle_OLin) & $i(c_Arrow__Order__Mirabelle_OProf) & % 97.11/13.94 $i(tc_HOL_Obool) & $i(tc_Arrow__Order__Mirabelle_Oalt) & % 97.11/13.94 $i(tc_Arrow__Order__Mirabelle_Oindi) & $i(v_F) & ? [v0: $i] : ? [v1: $i] : % 97.11/13.94 ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: % 97.11/13.94 $i] : ? [v8: $i] : ? [v9: $i] : (c_COMBK(v6, v2, % 97.11/13.94 c_Arrow__Order__Mirabelle_OLin) = v7 & c_FuncSet_OPi(v2, v1, % 97.11/13.94 c_Arrow__Order__Mirabelle_OProf, v7) = v8 & % 97.11/13.94 tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt) = % 97.11/13.94 v0 & tc_fun(v2, v1) = v3 & tc_fun(v1, tc_HOL_Obool) = v6 & tc_fun(v0, % 97.11/13.94 tc_HOL_Obool) = v1 & tc_fun(tc_Arrow__Order__Mirabelle_Oindi, v1) = v2 & % 97.11/13.94 c_member(v3) = v4 & hBOOL(v9) = 0 & hAPP(v5, v8) = v9 & hAPP(v4, v_F) = v5 & % 97.11/13.94 $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & % 97.11/13.94 $i(v1) & $i(v0)) % 97.11/13.94 % 97.11/13.94 (fact_below__Lin) % 97.11/13.94 $i(c_Arrow__Order__Mirabelle_OLin) & $i(tc_HOL_Obool) & % 97.11/13.94 $i(tc_Arrow__Order__Mirabelle_Oalt) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] % 97.11/13.94 : (tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt) = % 97.11/13.94 v0 & tc_fun(v0, tc_HOL_Obool) = v1 & c_member(v1) = v2 & $i(v2) & $i(v1) & % 97.11/13.94 $i(v0) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v5 = v4 | % 97.11/13.94 ~ (c_Arrow__Order__Mirabelle_Obelow(v3, v5, v4) = v6) | ~ $i(v5) | ~ % 97.11/13.94 $i(v4) | ~ $i(v3) | ? [v7: $i] : ? [v8: $i] : ? [v9: any] : ? [v10: % 97.11/13.94 $i] : ? [v11: $i] : ? [v12: any] : (hBOOL(v11) = v12 & hBOOL(v8) = v9 % 97.11/13.94 & hAPP(v10, c_Arrow__Order__Mirabelle_OLin) = v11 & hAPP(v7, % 97.11/13.94 c_Arrow__Order__Mirabelle_OLin) = v8 & hAPP(v2, v6) = v10 & hAPP(v2, % 97.11/13.94 v3) = v7 & $i(v11) & $i(v10) & $i(v8) & $i(v7) & ( ~ (v9 = 0) | v12 = % 97.11/13.94 0)))) % 97.11/13.94 % 97.11/13.94 (fact_complete__Lin) % 97.11/13.95 $i(c_Arrow__Order__Mirabelle_OLin) & $i(tc_HOL_Obool) & % 97.11/13.95 $i(tc_Arrow__Order__Mirabelle_Oalt) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] % 97.11/13.95 : ? [v3: $i] : ? [v4: $i] : % 97.11/13.95 (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 97.11/13.95 tc_Arrow__Order__Mirabelle_Oalt) = v4 & % 97.11/13.95 tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt) = % 97.11/13.95 v0 & tc_fun(v0, tc_HOL_Obool) = v1 & c_member(v1) = v2 & c_member(v0) = v3 & % 97.11/13.95 $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & ! [v5: $i] : ! [v6: $i] : ! % 97.11/13.95 [v7: $i] : ! [v8: $i] : (v6 = v5 | ~ (hAPP(v7, v5) = v8) | ~ (hAPP(v4, % 97.11/13.95 v6) = v7) | ~ $i(v6) | ~ $i(v5) | ? [v9: $i] : (hAPP(v3, v8) = v9 & % 97.11/13.95 $i(v9) & ? [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13: $i] : % 97.11/13.95 (hBOOL(v13) = 0 & hBOOL(v12) = 0 & hAPP(v11, % 97.11/13.95 c_Arrow__Order__Mirabelle_OLin) = v12 & hAPP(v9, v10) = v13 & % 97.11/13.95 hAPP(v2, v10) = v11 & $i(v13) & $i(v12) & $i(v11) & $i(v10))))) % 97.11/13.95 % 97.11/13.95 (fact_compose__Id) % 97.11/13.95 $i(tc_HOL_Obool) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! % 97.11/13.95 [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] % 97.11/13.95 : ! [v10: $i] : ! [v11: $i] : ( ~ (c_COMBK(v8, v4, v0) = v9) | ~ % 97.11/13.95 (c_FuncSet_OPi(v4, v3, v1, v9) = v10) | ~ (tc_fun(v4, v3) = v5) | ~ % 97.11/13.95 (tc_fun(v3, tc_HOL_Obool) = v8) | ~ (c_member(v5) = v6) | ~ (hAPP(v7, v10) % 97.11/13.95 = v11) | ~ (hAPP(v6, v2) = v7) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ % 97.11/13.95 $i(v1) | ~ $i(v0) | ? [v12: any] : ? [v13: $i] : ? [v14: $i] : ? [v15: % 97.11/13.95 any] : ? [v16: $i] : ? [v17: $i] : ? [v18: $i] : % 97.11/13.95 (c_FuncSet_Orestrict(v4, v4, v16, v1) = v17 & c_FuncSet_Oextensional(v4, v3, % 97.11/13.95 v1) = v13 & c_FuncSet_Ocompose(v4, v4, v3, v1, v2, v17) = v18 & % 97.11/13.95 c_COMBI(v4) = v16 & hBOOL(v14) = v15 & hBOOL(v11) = v12 & hAPP(v7, v13) = % 97.11/13.95 v14 & $i(v18) & $i(v17) & $i(v16) & $i(v14) & $i(v13) & ( ~ (v15 = 0) | ~ % 97.11/13.95 (v12 = 0) | v18 = v2))) % 97.11/13.95 % 97.11/13.95 (fact_const__Lin__Prof) % 97.11/13.95 $i(c_Arrow__Order__Mirabelle_OLin) & $i(c_Arrow__Order__Mirabelle_OProf) & % 97.11/13.95 $i(tc_HOL_Obool) & $i(tc_Arrow__Order__Mirabelle_Oalt) & % 97.11/13.95 $i(tc_Arrow__Order__Mirabelle_Oindi) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] % 97.11/13.95 : ? [v3: $i] : ? [v4: $i] : (tc_prod(tc_Arrow__Order__Mirabelle_Oalt, % 97.11/13.95 tc_Arrow__Order__Mirabelle_Oalt) = v0 & tc_fun(v0, tc_HOL_Obool) = v1 & % 97.11/13.95 tc_fun(tc_Arrow__Order__Mirabelle_Oindi, v1) = v3 & c_member(v3) = v4 & % 97.11/13.95 c_member(v1) = v2 & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & ! [v5: $i] % 97.11/13.95 : ! [v6: $i] : ( ~ (c_COMBK(v1, tc_Arrow__Order__Mirabelle_Oindi, v5) = v6) % 97.11/13.95 | ~ $i(v5) | ? [v7: $i] : ? [v8: $i] : ? [v9: any] : ? [v10: $i] : ? % 97.11/13.95 [v11: $i] : ? [v12: any] : (hBOOL(v11) = v12 & hBOOL(v8) = v9 & hAPP(v10, % 97.11/13.95 c_Arrow__Order__Mirabelle_OProf) = v11 & hAPP(v7, % 97.11/13.95 c_Arrow__Order__Mirabelle_OLin) = v8 & hAPP(v4, v6) = v10 & hAPP(v2, % 97.11/13.95 v5) = v7 & $i(v11) & $i(v10) & $i(v8) & $i(v7) & ( ~ (v9 = 0) | v12 = % 97.11/13.95 0)))) % 97.11/13.95 % 97.11/13.95 (fact_converse__in__Lin) % 97.11/13.95 $i(c_Arrow__Order__Mirabelle_OLin) & $i(tc_HOL_Obool) & % 97.11/13.95 $i(tc_Arrow__Order__Mirabelle_Oalt) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] % 97.11/13.95 : (tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt) = % 97.11/13.95 v0 & tc_fun(v0, tc_HOL_Obool) = v1 & c_member(v1) = v2 & $i(v2) & $i(v1) & % 97.11/13.95 $i(v0) & ! [v3: $i] : ! [v4: $i] : ( ~ (hAPP(v2, v3) = v4) | ~ $i(v3) | % 97.11/13.95 ? [v5: $i] : ? [v6: any] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ? % 97.11/13.95 [v10: any] : (c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt, % 97.11/13.95 tc_Arrow__Order__Mirabelle_Oalt, v3) = v7 & hBOOL(v9) = v10 & % 97.11/13.95 hBOOL(v5) = v6 & hAPP(v8, c_Arrow__Order__Mirabelle_OLin) = v9 & % 97.11/13.95 hAPP(v4, c_Arrow__Order__Mirabelle_OLin) = v5 & hAPP(v2, v7) = v8 & % 97.11/13.95 $i(v9) & $i(v8) & $i(v7) & $i(v5) & ( ~ (v6 = 0) | v10 = 0))) & ! [v3: % 97.11/13.95 $i] : ! [v4: $i] : ( ~ (hAPP(v2, v3) = v4) | ~ $i(v3) | ? [v5: $i] : ? % 97.11/13.95 [v6: $i] : ? [v7: $i] : ? [v8: any] : ? [v9: $i] : ? [v10: any] : % 97.11/13.95 (c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt, % 97.11/13.96 tc_Arrow__Order__Mirabelle_Oalt, v3) = v5 & hBOOL(v9) = v10 & % 97.11/13.96 hBOOL(v7) = v8 & hAPP(v6, c_Arrow__Order__Mirabelle_OLin) = v7 & % 97.11/13.96 hAPP(v4, c_Arrow__Order__Mirabelle_OLin) = v9 & hAPP(v2, v5) = v6 & % 97.11/13.96 $i(v9) & $i(v7) & $i(v6) & $i(v5) & ( ~ (v8 = 0) | v10 = 0)))) % 97.11/13.96 % 97.11/13.96 (fact_dictatorI) % 97.11/13.96 $i(c_Arrow__Order__Mirabelle_OLin) & $i(c_Arrow__Order__Mirabelle_OProf) & % 97.11/13.96 $i(tc_HOL_Obool) & $i(tc_Arrow__Order__Mirabelle_Oalt) & % 97.11/13.96 $i(tc_Arrow__Order__Mirabelle_Oindi) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] % 97.11/13.96 : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? % 97.11/13.96 [v8: $i] : ? [v9: $i] : ? [v10: $i] : (c_COMBK(v5, v2, % 97.11/13.96 c_Arrow__Order__Mirabelle_OLin) = v6 & c_FuncSet_OPi(v2, v1, % 97.11/13.96 c_Arrow__Order__Mirabelle_OProf, v6) = v7 & % 97.11/13.96 c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 97.11/13.96 tc_Arrow__Order__Mirabelle_Oalt) = v10 & % 97.11/13.96 tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt) = % 97.11/13.96 v0 & tc_fun(v2, v1) = v3 & tc_fun(v1, tc_HOL_Obool) = v5 & tc_fun(v0, % 97.11/13.96 tc_HOL_Obool) = v1 & tc_fun(tc_Arrow__Order__Mirabelle_Oindi, v1) = v2 & % 97.11/13.96 c_member(v3) = v4 & c_member(v2) = v8 & c_member(v0) = v9 & $i(v10) & $i(v9) % 97.11/13.96 & $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & % 97.11/13.96 $i(v0) & ! [v11: $i] : ! [v12: $i] : ! [v13: int] : (v13 = 0 | ~ % 97.11/13.96 (c_Arrow__Order__Mirabelle_Odictator(v12, v11) = v13) | ~ $i(v12) | ~ % 97.11/13.96 $i(v11) | ? [v14: $i] : ? [v15: $i] : ? [v16: $i] : ? [v17: $i] : ? % 97.11/13.96 [v18: $i] : (hBOOL(v16) = 0 & hAPP(v15, c_Arrow__Order__Mirabelle_OProf) = % 97.11/13.96 v16 & hAPP(v14, v11) = v17 & hAPP(v12, v14) = v18 & hAPP(v8, v14) = v15 % 97.11/13.96 & $i(v18) & $i(v17) & $i(v16) & $i(v15) & $i(v14) & ? [v19: $i] : ? % 97.11/13.96 [v20: $i] : ? [v21: $i] : ? [v22: $i] : ? [v23: $i] : ? [v24: $i] : % 97.11/13.96 ? [v25: $i] : ? [v26: int] : ( ~ (v26 = 0) & ~ (v20 = v19) & % 97.11/13.96 hBOOL(v25) = v26 & hBOOL(v24) = 0 & hAPP(v23, v18) = v25 & hAPP(v23, % 97.11/13.96 v17) = v24 & hAPP(v21, v20) = v22 & hAPP(v10, v19) = v21 & hAPP(v9, % 97.11/13.96 v22) = v23 & $i(v25) & $i(v24) & $i(v23) & $i(v22) & $i(v21) & % 97.11/13.96 $i(v20) & $i(v19))) | ? [v14: $i] : ? [v15: $i] : ? [v16: int] : ( % 97.11/13.96 ~ (v16 = 0) & hBOOL(v15) = v16 & hAPP(v14, v7) = v15 & hAPP(v4, v12) = % 97.11/13.96 v14 & $i(v15) & $i(v14)))) % 97.11/13.96 % 97.11/13.96 (fact_dictator__def) % 97.11/13.96 $i(c_Arrow__Order__Mirabelle_OProf) & $i(tc_HOL_Obool) & % 97.11/13.96 $i(tc_Arrow__Order__Mirabelle_Oalt) & $i(tc_Arrow__Order__Mirabelle_Oindi) & % 97.11/13.96 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : % 97.11/13.96 (tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt) = % 97.11/13.96 v0 & tc_fun(v0, tc_HOL_Obool) = v1 & % 97.11/13.96 tc_fun(tc_Arrow__Order__Mirabelle_Oindi, v1) = v2 & c_member(v2) = v3 & % 97.11/13.96 $i(v3) & $i(v2) & $i(v1) & $i(v0) & ! [v4: $i] : ! [v5: $i] : ! [v6: int] % 97.11/13.96 : (v6 = 0 | ~ (c_Arrow__Order__Mirabelle_Odictator(v5, v4) = v6) | ~ % 97.11/13.96 $i(v5) | ~ $i(v4) | ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ? [v10: % 97.11/13.96 $i] : ? [v11: $i] : ( ~ (v11 = v10) & hBOOL(v9) = 0 & hAPP(v8, % 97.11/13.96 c_Arrow__Order__Mirabelle_OProf) = v9 & hAPP(v7, v4) = v11 & hAPP(v5, % 97.11/13.96 v7) = v10 & hAPP(v3, v7) = v8 & $i(v11) & $i(v10) & $i(v9) & $i(v8) & % 97.11/13.96 $i(v7))) & ! [v4: $i] : ! [v5: $i] : ( ~ % 97.11/13.96 (c_Arrow__Order__Mirabelle_Odictator(v5, v4) = 0) | ~ $i(v5) | ~ $i(v4) % 97.11/13.96 | ! [v6: $i] : ! [v7: $i] : ( ~ (hAPP(v3, v6) = v7) | ~ $i(v6) | ? % 97.11/13.96 [v8: $i] : ? [v9: any] : ? [v10: $i] : ? [v11: $i] : (hBOOL(v8) = v9 % 97.11/13.96 & hAPP(v7, c_Arrow__Order__Mirabelle_OProf) = v8 & hAPP(v6, v4) = v11 % 97.11/13.96 & hAPP(v5, v6) = v10 & $i(v11) & $i(v10) & $i(v8) & ( ~ (v9 = 0) | v11 % 97.11/13.96 = v10))))) % 97.11/13.96 % 97.11/13.96 (fact_equals0D) % 97.11/13.97 $i(tc_HOL_Obool) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! % 97.11/13.97 [v4: $i] : ! [v5: $i] : ( ~ (c_member(v1) = v3) | ~ (hAPP(v4, v2) = v5) | ~ % 97.11/13.97 (hAPP(v3, v0) = v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: $i] : ? % 97.11/13.97 [v7: $i] : ? [v8: any] : (c_Orderings_Obot__class_Obot(v6) = v7 & % 97.11/13.97 tc_fun(v1, tc_HOL_Obool) = v6 & hBOOL(v5) = v8 & $i(v7) & $i(v6) & ( ~ (v8 % 97.11/13.97 = 0) | ~ (v7 = v2)))) % 97.11/13.97 % 97.11/13.97 (fact_funcset__image) % 97.11/13.97 $i(tc_HOL_Obool) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! % 97.11/13.97 [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] % 97.11/13.97 : ! [v10: $i] : ! [v11: $i] : ( ~ (c_COMBK(v8, v4, v0) = v9) | ~ % 97.11/13.97 (c_FuncSet_OPi(v4, v3, v1, v9) = v10) | ~ (tc_fun(v4, v3) = v5) | ~ % 97.11/13.97 (tc_fun(v3, tc_HOL_Obool) = v8) | ~ (c_member(v5) = v6) | ~ (hAPP(v7, v10) % 97.11/13.97 = v11) | ~ (hAPP(v6, v2) = v7) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ % 97.11/13.97 $i(v1) | ~ $i(v0) | ? [v12: any] : ? [v13: $i] : ? [v14: any] : % 97.11/13.97 (c_Orderings_Oord__class_Oless__eq(v8, v13, v0) = v14 & c_Set_Oimage(v4, v3, % 97.11/13.97 v2, v1) = v13 & hBOOL(v11) = v12 & $i(v13) & ( ~ (v12 = 0) | v14 = 0))) % 97.11/13.97 % 97.11/13.97 (fact_funcset__mem) % 97.11/13.97 $i(tc_HOL_Obool) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! % 97.11/13.97 [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] % 97.11/13.97 : ! [v10: $i] : ! [v11: $i] : ! [v12: $i] : ! [v13: $i] : ! [v14: $i] : % 97.11/13.97 ! [v15: $i] : ! [v16: $i] : ( ~ (c_COMBK(v9, v5, v1) = v10) | ~ % 97.11/13.97 (c_FuncSet_OPi(v5, v4, v2, v10) = v11) | ~ (tc_fun(v5, v4) = v6) | ~ % 97.11/13.97 (tc_fun(v4, tc_HOL_Obool) = v9) | ~ (c_member(v6) = v7) | ~ (c_member(v4) % 97.11/13.97 = v13) | ~ (hAPP(v15, v1) = v16) | ~ (hAPP(v13, v14) = v15) | ~ % 97.11/13.97 (hAPP(v8, v11) = v12) | ~ (hAPP(v7, v3) = v8) | ~ (hAPP(v3, v0) = v14) | % 97.11/13.97 ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 97.11/13.97 [v17: any] : ? [v18: $i] : ? [v19: $i] : ? [v20: $i] : ? [v21: any] : ? % 97.11/13.97 [v22: any] : (c_member(v5) = v18 & hBOOL(v20) = v21 & hBOOL(v16) = v22 & % 97.11/13.97 hBOOL(v12) = v17 & hAPP(v19, v2) = v20 & hAPP(v18, v0) = v19 & $i(v20) & % 97.11/13.97 $i(v19) & $i(v18) & ( ~ (v21 = 0) | ~ (v17 = 0) | v22 = 0))) % 97.11/13.97 % 97.11/13.97 (fact_in__above) % 97.11/13.98 $i(c_Arrow__Order__Mirabelle_Oabove) & $i(c_Arrow__Order__Mirabelle_OLin) & % 97.11/13.98 $i(tc_HOL_Obool) & $i(tc_Arrow__Order__Mirabelle_Oalt) & ? [v0: $i] : ? [v1: % 97.11/13.98 $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 97.11/13.98 (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 97.11/13.98 tc_Arrow__Order__Mirabelle_Oalt) = v4 & % 97.11/13.98 tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt) = % 97.11/13.98 v0 & tc_fun(v0, tc_HOL_Obool) = v1 & c_member(v1) = v2 & c_member(v0) = v3 & % 97.11/13.98 $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & ! [v5: $i] : ! [v6: $i] : ! % 97.11/13.98 [v7: $i] : ! [v8: $i] : ! [v9: $i] : ! [v10: $i] : ! [v11: $i] : ! % 97.11/13.98 [v12: $i] : ! [v13: $i] : ! [v14: $i] : ! [v15: $i] : ! [v16: $i] : (v9 % 97.11/13.98 = v8 | ~ (hAPP(v14, v8) = v15) | ~ (hAPP(v13, v9) = v14) | ~ (hAPP(v12, % 97.11/13.98 v15) = v16) | ~ (hAPP(v10, v5) = v11) | ~ (hAPP(v4, v6) = v10) | ~ % 97.11/13.98 (hAPP(v3, v11) = v12) | ~ (hAPP(c_Arrow__Order__Mirabelle_Oabove, v7) = % 97.11/13.98 v13) | ~ $i(v9) | ~ $i(v8) | ~ $i(v7) | ~ $i(v6) | ~ $i(v5) | ? % 97.11/13.98 [v17: $i] : ? [v18: $i] : ? [v19: any] : ? [v20: any] : ? [v21: $i] : % 97.11/13.98 ? [v22: $i] : ? [v23: $i] : ? [v24: $i] : ? [v25: any] : ? [v26: $i] : % 97.11/13.98 ? [v27: $i] : ? [v28: $i] : ? [v29: any] : ? [v30: $i] : ? [v31: any] % 97.11/13.98 : (hBOOL(v30) = v31 & hBOOL(v28) = v29 & hBOOL(v24) = v25 & hBOOL(v18) = % 97.11/13.98 v19 & hBOOL(v16) = v20 & hAPP(v27, v7) = v28 & hAPP(v23, v7) = v24 & % 97.11/13.98 hAPP(v21, v5) = v22 & hAPP(v17, c_Arrow__Order__Mirabelle_OLin) = v18 & % 97.11/13.98 hAPP(v12, v7) = v30 & hAPP(v10, v9) = v26 & hAPP(v4, v9) = v21 & % 97.11/13.98 hAPP(v3, v26) = v27 & hAPP(v3, v22) = v23 & hAPP(v2, v7) = v17 & $i(v30) % 97.11/13.98 & $i(v28) & $i(v27) & $i(v26) & $i(v24) & $i(v23) & $i(v22) & $i(v21) & % 97.11/13.98 $i(v18) & $i(v17) & ( ~ (v19 = 0) | (( ~ (v20 = 0) | ( ~ (v6 = v5) & ( ~ % 97.11/13.98 (v8 = v6) | v25 = 0) & (v8 = v6 | (( ~ (v8 = v5) | v29 = 0 | % 97.11/13.98 v9 = v6) & (v31 = 0 | v8 = v5))))) & (v20 = 0 | v6 = v5 | % 97.11/13.98 (v8 = v6 & ~ (v25 = 0)) | ( ~ (v8 = v6) & ((v8 = v5 & ~ (v29 = % 97.11/13.98 0) & ~ (v9 = v6)) | ( ~ (v31 = 0) & ~ (v8 = v5)))))))))) % 97.11/13.98 % 97.11/13.98 (fact_in__below) % 97.11/13.98 $i(c_Arrow__Order__Mirabelle_OLin) & $i(tc_HOL_Obool) & % 97.11/13.98 $i(tc_Arrow__Order__Mirabelle_Oalt) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] % 97.11/13.98 : ? [v3: $i] : ? [v4: $i] : % 97.11/13.98 (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 97.11/13.98 tc_Arrow__Order__Mirabelle_Oalt) = v4 & % 97.11/13.98 tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt) = % 97.11/13.98 v0 & tc_fun(v0, tc_HOL_Obool) = v1 & c_member(v1) = v2 & c_member(v0) = v3 & % 97.11/13.98 $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & ! [v5: $i] : ! [v6: $i] : ! % 97.11/13.98 [v7: $i] : ! [v8: $i] : ! [v9: $i] : ! [v10: $i] : ! [v11: $i] : ! % 97.11/13.98 [v12: $i] : ! [v13: $i] : ! [v14: $i] : (v9 = v8 | ~ % 97.11/13.98 (c_Arrow__Order__Mirabelle_Obelow(v7, v9, v8) = v13) | ~ (hAPP(v12, v13) % 97.11/13.98 = v14) | ~ (hAPP(v10, v5) = v11) | ~ (hAPP(v4, v6) = v10) | ~ % 97.11/13.98 (hAPP(v3, v11) = v12) | ~ $i(v9) | ~ $i(v8) | ~ $i(v7) | ~ $i(v6) | ~ % 97.11/13.98 $i(v5) | ? [v15: $i] : ? [v16: $i] : ? [v17: any] : ? [v18: any] : ? % 97.11/13.98 [v19: $i] : ? [v20: $i] : ? [v21: $i] : ? [v22: any] : ? [v23: $i] : % 97.11/13.98 ? [v24: $i] : ? [v25: $i] : ? [v26: $i] : ? [v27: any] : ? [v28: $i] : % 97.11/13.98 ? [v29: any] : (hBOOL(v28) = v29 & hBOOL(v26) = v27 & hBOOL(v21) = v22 & % 97.11/13.98 hBOOL(v16) = v17 & hBOOL(v14) = v18 & hAPP(v25, v7) = v26 & hAPP(v23, % 97.11/13.98 v5) = v24 & hAPP(v20, v7) = v21 & hAPP(v15, % 97.11/13.98 c_Arrow__Order__Mirabelle_OLin) = v16 & hAPP(v12, v7) = v28 & % 97.11/13.98 hAPP(v10, v8) = v19 & hAPP(v4, v8) = v23 & hAPP(v3, v24) = v25 & % 97.11/13.98 hAPP(v3, v19) = v20 & hAPP(v2, v7) = v15 & $i(v28) & $i(v26) & $i(v25) & % 97.11/13.98 $i(v24) & $i(v23) & $i(v21) & $i(v20) & $i(v19) & $i(v16) & $i(v15) & ( % 97.11/13.98 ~ (v17 = 0) | (( ~ (v18 = 0) | ( ~ (v6 = v5) & ( ~ (v9 = v5) | v22 = % 97.11/13.98 0) & (v9 = v5 | (( ~ (v9 = v6) | v27 = 0 | v8 = v5) & (v29 = 0 % 97.11/13.98 | v9 = v6))))) & (v18 = 0 | v6 = v5 | (v9 = v5 & ~ (v22 = % 97.11/13.98 0)) | ( ~ (v9 = v5) & ((v9 = v6 & ~ (v27 = 0) & ~ (v8 = v5)) % 97.11/13.98 | ( ~ (v29 = 0) & ~ (v9 = v6)))))))))) % 97.11/13.98 % 97.11/13.98 (fact_in__mkbot) % 97.11/13.99 $i(tc_Arrow__Order__Mirabelle_Oalt) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] % 97.11/13.99 : (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 97.11/13.99 tc_Arrow__Order__Mirabelle_Oalt) = v2 & % 97.11/13.99 tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt) = % 97.11/13.99 v0 & c_member(v0) = v1 & $i(v2) & $i(v1) & $i(v0) & ! [v3: $i] : ! [v4: % 97.11/13.99 $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] % 97.11/13.99 : ! [v10: $i] : ! [v11: $i] : (v5 = v3 | ~ % 97.11/13.99 (c_Arrow__Order__Mirabelle_Omkbot(v4, v3) = v10) | ~ (hAPP(v9, v10) = % 97.11/13.99 v11) | ~ (hAPP(v7, v5) = v8) | ~ (hAPP(v2, v6) = v7) | ~ (hAPP(v1, % 97.11/13.99 v8) = v9) | ~ $i(v6) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ? [v12: % 97.11/13.99 $i] : ? [v13: any] : ? [v14: any] : (hBOOL(v12) = v13 & hBOOL(v11) = % 97.11/13.99 v14 & hAPP(v9, v4) = v12 & $i(v12) & (v14 = 0 | ( ~ (v13 = 0) & ~ (v6 = % 97.11/13.99 v3))))) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : % 97.11/13.99 ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : ! [v10: $i] : ! [v11: $i] : ( ~ % 97.11/13.99 (c_Arrow__Order__Mirabelle_Omkbot(v4, v3) = v10) | ~ (hAPP(v9, v10) = % 97.11/13.99 v11) | ~ (hAPP(v7, v5) = v8) | ~ (hAPP(v2, v6) = v7) | ~ (hAPP(v1, % 97.11/13.99 v8) = v9) | ~ $i(v6) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ? [v12: % 97.11/13.99 any] : ? [v13: $i] : ? [v14: any] : (hBOOL(v13) = v14 & hBOOL(v11) = % 97.11/13.99 v12 & hAPP(v9, v4) = v13 & $i(v13) & ( ~ (v12 = 0) | ( ~ (v5 = v3) & % 97.11/13.99 (v14 = 0 | v6 = v3)))))) % 97.11/13.99 % 97.11/13.99 (fact_in__mktop) % 97.11/13.99 $i(tc_Arrow__Order__Mirabelle_Oalt) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] % 97.11/13.99 : (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 97.11/13.99 tc_Arrow__Order__Mirabelle_Oalt) = v2 & % 97.11/13.99 tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt) = % 97.11/13.99 v0 & c_member(v0) = v1 & $i(v2) & $i(v1) & $i(v0) & ! [v3: $i] : ! [v4: % 97.11/13.99 $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] % 97.11/13.99 : ! [v10: $i] : ! [v11: $i] : (v6 = v3 | ~ % 97.11/13.99 (c_Arrow__Order__Mirabelle_Omktop(v4, v3) = v10) | ~ (hAPP(v9, v10) = % 97.11/13.99 v11) | ~ (hAPP(v7, v5) = v8) | ~ (hAPP(v2, v6) = v7) | ~ (hAPP(v1, % 97.11/13.99 v8) = v9) | ~ $i(v6) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ? [v12: % 97.11/13.99 $i] : ? [v13: any] : ? [v14: any] : (hBOOL(v12) = v13 & hBOOL(v11) = % 97.11/13.99 v14 & hAPP(v9, v4) = v12 & $i(v12) & (v14 = 0 | ( ~ (v13 = 0) & ~ (v5 = % 97.11/13.99 v3))))) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : % 97.11/13.99 ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : ! [v10: $i] : ! [v11: $i] : ( ~ % 97.11/13.99 (c_Arrow__Order__Mirabelle_Omktop(v4, v3) = v10) | ~ (hAPP(v9, v10) = % 97.11/13.99 v11) | ~ (hAPP(v7, v5) = v8) | ~ (hAPP(v2, v6) = v7) | ~ (hAPP(v1, % 97.11/13.99 v8) = v9) | ~ $i(v6) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ? [v12: % 97.11/13.99 any] : ? [v13: $i] : ? [v14: any] : (hBOOL(v13) = v14 & hBOOL(v11) = % 97.11/13.99 v12 & hAPP(v9, v4) = v13 & $i(v13) & ( ~ (v12 = 0) | ( ~ (v6 = v3) & % 97.11/13.99 (v14 = 0 | v5 = v3)))))) % 97.11/13.99 % 97.11/13.99 (fact_linear__alt) % 97.11/13.99 $i(c_Arrow__Order__Mirabelle_OLin) & $i(tc_HOL_Obool) & % 97.11/13.99 $i(tc_Arrow__Order__Mirabelle_Oalt) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] % 97.11/13.99 : (tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt) = % 97.11/13.99 v0 & tc_fun(v0, tc_HOL_Obool) = v1 & c_member(v1) = v2 & $i(v2) & $i(v1) & % 97.11/13.99 $i(v0) & ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : (hBOOL(v5) = 0 & hAPP(v4, % 97.11/13.99 c_Arrow__Order__Mirabelle_OLin) = v5 & hAPP(v2, v3) = v4 & $i(v5) & % 97.11/13.99 $i(v4) & $i(v3))) % 97.11/13.99 % 97.11/13.99 (fact_mem__def) % 97.11/13.99 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 97.11/13.99 $i] : ( ~ (c_member(v2) = v3) | ~ (hAPP(v4, v0) = v5) | ~ (hAPP(v3, v1) = % 97.11/13.99 v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: $i] : ? % 97.11/13.99 [v8: any] : (hBOOL(v7) = v8 & hBOOL(v5) = v6 & hAPP(v0, v1) = v7 & $i(v7) & % 97.11/13.99 ( ~ (v6 = 0) | v8 = 0))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 97.11/13.99 [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (c_member(v2) = v3) | ~ (hAPP(v4, % 97.11/13.99 v0) = v5) | ~ (hAPP(v3, v1) = v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 97.11/13.99 ? [v6: $i] : ? [v7: any] : ? [v8: any] : (hBOOL(v6) = v7 & hBOOL(v5) = v8 % 97.11/13.99 & hAPP(v0, v1) = v6 & $i(v6) & ( ~ (v7 = 0) | v8 = 0))) % 97.11/13.99 % 97.11/13.99 (fact_mkbot__Lin) % 97.11/14.00 $i(c_Arrow__Order__Mirabelle_OLin) & $i(tc_HOL_Obool) & % 97.11/14.00 $i(tc_Arrow__Order__Mirabelle_Oalt) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] % 97.11/14.00 : (tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt) = % 97.11/14.00 v0 & tc_fun(v0, tc_HOL_Obool) = v1 & c_member(v1) = v2 & $i(v2) & $i(v1) & % 97.11/14.00 $i(v0) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ % 97.11/14.00 (c_Arrow__Order__Mirabelle_Omkbot(v4, v3) = v5) | ~ $i(v4) | ~ $i(v3) | % 97.11/14.00 ? [v6: $i] : ? [v7: $i] : ? [v8: any] : ? [v9: $i] : ? [v10: $i] : ? % 97.11/14.00 [v11: any] : (hBOOL(v10) = v11 & hBOOL(v7) = v8 & hAPP(v9, % 97.11/14.00 c_Arrow__Order__Mirabelle_OLin) = v10 & hAPP(v6, % 97.11/14.00 c_Arrow__Order__Mirabelle_OLin) = v7 & hAPP(v2, v5) = v9 & hAPP(v2, % 97.11/14.00 v4) = v6 & $i(v10) & $i(v9) & $i(v7) & $i(v6) & ( ~ (v8 = 0) | v11 = % 97.11/14.00 0)))) % 97.11/14.00 % 97.11/14.00 (fact_mktop__Lin) % 97.11/14.00 $i(c_Arrow__Order__Mirabelle_OLin) & $i(tc_HOL_Obool) & % 97.11/14.00 $i(tc_Arrow__Order__Mirabelle_Oalt) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] % 97.11/14.00 : (tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt) = % 97.11/14.00 v0 & tc_fun(v0, tc_HOL_Obool) = v1 & c_member(v1) = v2 & $i(v2) & $i(v1) & % 97.11/14.00 $i(v0) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ % 97.11/14.00 (c_Arrow__Order__Mirabelle_Omktop(v4, v3) = v5) | ~ $i(v4) | ~ $i(v3) | % 97.11/14.00 ? [v6: $i] : ? [v7: $i] : ? [v8: any] : ? [v9: $i] : ? [v10: $i] : ? % 97.11/14.00 [v11: any] : (hBOOL(v10) = v11 & hBOOL(v7) = v8 & hAPP(v9, % 97.11/14.00 c_Arrow__Order__Mirabelle_OLin) = v10 & hAPP(v6, % 97.11/14.00 c_Arrow__Order__Mirabelle_OLin) = v7 & hAPP(v2, v5) = v9 & hAPP(v2, % 97.11/14.00 v4) = v6 & $i(v10) & $i(v9) & $i(v7) & $i(v6) & ( ~ (v8 = 0) | v11 = % 97.11/14.00 0)))) % 97.11/14.00 % 97.11/14.00 (fact_notin__Lin__iff) % 97.11/14.00 $i(c_Arrow__Order__Mirabelle_OLin) & $i(tc_HOL_Obool) & % 97.11/14.00 $i(tc_Arrow__Order__Mirabelle_Oalt) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] % 97.11/14.00 : ? [v3: $i] : ? [v4: $i] : % 97.11/14.00 (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 97.11/14.00 tc_Arrow__Order__Mirabelle_Oalt) = v4 & % 97.11/14.00 tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt) = % 97.11/14.00 v0 & tc_fun(v0, tc_HOL_Obool) = v1 & c_member(v1) = v2 & c_member(v0) = v3 & % 97.11/14.00 $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & ! [v5: $i] : ! [v6: $i] : ! % 97.11/14.00 [v7: $i] : ! [v8: $i] : ! [v9: $i] : ! [v10: $i] : ! [v11: $i] : (v6 = % 97.11/14.00 v5 | ~ (hAPP(v10, v7) = v11) | ~ (hAPP(v8, v6) = v9) | ~ (hAPP(v4, v5) % 97.11/14.00 = v8) | ~ (hAPP(v3, v9) = v10) | ~ $i(v7) | ~ $i(v6) | ~ $i(v5) | ? % 97.11/14.00 [v12: $i] : ? [v13: $i] : ? [v14: any] : ? [v15: $i] : ? [v16: $i] : % 97.11/14.00 ? [v17: $i] : ? [v18: $i] : ? [v19: any] : ? [v20: any] : (hBOOL(v18) = % 97.11/14.00 v19 & hBOOL(v13) = v14 & hBOOL(v11) = v20 & hAPP(v17, v7) = v18 & % 97.11/14.00 hAPP(v15, v5) = v16 & hAPP(v12, c_Arrow__Order__Mirabelle_OLin) = v13 & % 97.11/14.00 hAPP(v4, v6) = v15 & hAPP(v3, v16) = v17 & hAPP(v2, v7) = v12 & $i(v18) % 97.11/14.00 & $i(v17) & $i(v16) & $i(v15) & $i(v13) & $i(v12) & ( ~ (v14 = 0) | (( ~ % 97.11/14.00 (v20 = 0) | ~ (v19 = 0)) & (v20 = 0 | v19 = 0)))))) % 97.11/14.00 % 97.11/14.00 (fact_the__inv__into__def) % 97.11/14.01 $i(c_fconj) & $i(c_fequal) & $i(tc_HOL_Obool) & ? [v0: $i] : % 97.11/14.01 (tc_fun(tc_HOL_Obool, tc_HOL_Obool) = v0 & $i(v0) & ! [v1: $i] : ! [v2: $i] % 97.11/14.01 : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! % 97.11/14.01 [v8: $i] : ! [v9: $i] : ! [v10: $i] : ! [v11: $i] : ! [v12: $i] : ! % 97.11/14.01 [v13: $i] : ! [v14: $i] : ! [v15: $i] : ! [v16: $i] : ! [v17: $i] : ! % 97.11/14.01 [v18: $i] : ! [v19: $i] : ! [v20: $i] : ! [v21: $i] : ! [v22: $i] : ( ~ % 97.11/14.01 (c_HOL_OThe(v5, v21) = v22) | ~ (c_COMBB(v4, v16, v5, c_fequal) = v17) | % 97.11/14.01 ~ (c_COMBB(tc_HOL_Obool, v0, v5, c_fconj) = v7) | ~ (c_COMBS(v5, % 97.11/14.01 tc_HOL_Obool, tc_HOL_Obool) = v6) | ~ (c_COMBC(v5, v8, tc_HOL_Obool) % 97.11/14.01 = v9) | ~ (c_COMBC(v5, v4, tc_HOL_Obool) = v15) | ~ (tc_fun(v5, % 97.11/14.01 tc_HOL_Obool) = v8) | ~ (tc_fun(v4, tc_HOL_Obool) = v16) | ~ % 97.11/14.01 (c_member(v5) = v10) | ~ (hAPP(v19, v1) = v20) | ~ (hAPP(v17, v2) = v18) % 97.11/14.01 | ~ (hAPP(v15, v18) = v19) | ~ (hAPP(v14, v20) = v21) | ~ (hAPP(v11, % 97.11/14.01 v3) = v12) | ~ (hAPP(v9, v10) = v11) | ~ (hAPP(v7, v12) = v13) | ~ % 97.11/14.01 (hAPP(v6, v13) = v14) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ % 97.11/14.01 $i(v1) | ? [v23: $i] : (c_Fun_Othe__inv__into(v5, v4, v3, v2) = v23 & % 97.11/14.01 hAPP(v23, v1) = v22 & $i(v23) & $i(v22)))) % 97.11/14.01 % 97.11/14.01 (fact_unanimity__def) % 97.11/14.01 $i(c_Arrow__Order__Mirabelle_OProf) & $i(tc_HOL_Obool) & % 97.11/14.01 $i(tc_Arrow__Order__Mirabelle_Oalt) & $i(tc_Arrow__Order__Mirabelle_Oindi) & % 97.11/14.01 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: % 97.11/14.01 $i] : (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 97.11/14.01 tc_Arrow__Order__Mirabelle_Oalt) = v5 & % 97.11/14.01 tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt) = % 97.11/14.01 v0 & tc_fun(v0, tc_HOL_Obool) = v1 & % 97.11/14.01 tc_fun(tc_Arrow__Order__Mirabelle_Oindi, v1) = v2 & c_member(v2) = v3 & % 97.11/14.01 c_member(v0) = v4 & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & ! % 97.11/14.01 [v6: $i] : ! [v7: int] : (v7 = 0 | ~ % 97.11/14.01 (c_Arrow__Order__Mirabelle_Ounanimity(v6) = v7) | ~ $i(v6) | ? [v8: $i] % 97.11/14.01 : ? [v9: $i] : ? [v10: $i] : ? [v11: $i] : (hBOOL(v10) = 0 & hAPP(v9, % 97.11/14.01 c_Arrow__Order__Mirabelle_OProf) = v10 & hAPP(v6, v8) = v11 & hAPP(v3, % 97.11/14.01 v8) = v9 & $i(v11) & $i(v10) & $i(v9) & $i(v8) & ? [v12: $i] : ? % 97.11/14.01 [v13: $i] : ? [v14: $i] : ? [v15: $i] : ? [v16: $i] : ? [v17: $i] : % 97.11/14.01 ? [v18: int] : ( ~ (v18 = 0) & hBOOL(v17) = v18 & hAPP(v16, v11) = v17 & % 97.11/14.01 hAPP(v14, v13) = v15 & hAPP(v5, v12) = v14 & hAPP(v4, v15) = v16 & % 97.11/14.01 $i(v17) & $i(v16) & $i(v15) & $i(v14) & $i(v13) & $i(v12) & ! [v19: % 97.11/14.01 $i] : ! [v20: $i] : ! [v21: $i] : ( ~ (hAPP(v16, v20) = v21) | ~ % 97.11/14.01 (hAPP(v8, v19) = v20) | ~ $i(v19) | hBOOL(v21) = 0)))) & ! [v6: % 97.11/14.01 $i] : ( ~ (c_Arrow__Order__Mirabelle_Ounanimity(v6) = 0) | ~ $i(v6) | ! % 97.11/14.01 [v7: $i] : ! [v8: $i] : ( ~ (hAPP(v3, v7) = v8) | ~ $i(v7) | ? [v9: $i] % 97.11/14.01 : ? [v10: any] : ? [v11: $i] : (hBOOL(v9) = v10 & hAPP(v8, % 97.11/14.01 c_Arrow__Order__Mirabelle_OProf) = v9 & hAPP(v6, v7) = v11 & $i(v11) % 97.11/14.01 & $i(v9) & ( ~ (v10 = 0) | ! [v12: $i] : ! [v13: $i] : ! [v14: $i] % 97.11/14.01 : ! [v15: $i] : ! [v16: $i] : ! [v17: $i] : ( ~ (hAPP(v16, v11) = % 97.11/14.01 v17) | ~ (hAPP(v14, v13) = v15) | ~ (hAPP(v5, v12) = v14) | ~ % 97.11/14.01 (hAPP(v4, v15) = v16) | ~ $i(v13) | ~ $i(v12) | hBOOL(v17) = 0 | % 97.11/14.01 ? [v18: $i] : ? [v19: $i] : ? [v20: $i] : ? [v21: int] : ( ~ % 97.11/14.01 (v21 = 0) & hBOOL(v20) = v21 & hAPP(v16, v19) = v20 & hAPP(v7, % 97.11/14.01 v18) = v19 & $i(v20) & $i(v19) & $i(v18)))))))) % 97.11/14.01 % 97.11/14.01 (function-axioms) % 97.11/14.03 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 97.11/14.03 [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : (v1 = v0 | % 97.11/14.03 ~ (c_Nitpick_Ofold__graph_H(v7, v6, v5, v4, v3, v2) = v1) | ~ % 97.11/14.03 (c_Nitpick_Ofold__graph_H(v7, v6, v5, v4, v3, v2) = v0)) & ! [v0: $i] : ! % 97.11/14.03 [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] % 97.11/14.03 : ! [v7: $i] : (v1 = v0 | ~ (c_FuncSet_Ocompose(v7, v6, v5, v4, v3, v2) = % 97.11/14.03 v1) | ~ (c_FuncSet_Ocompose(v7, v6, v5, v4, v3, v2) = v0)) & ! [v0: $i] % 97.11/14.03 : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! % 97.11/14.03 [v6: $i] : (v1 = v0 | ~ (c_Fun_Ofun__upd(v6, v5, v4, v3, v2) = v1) | ~ % 97.11/14.03 (c_Fun_Ofun__upd(v6, v5, v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : % 97.11/14.03 ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 97.11/14.03 $i] : ! [v6: $i] : (v1 = v0 | ~ (c_FunDef_Oin__rel(v6, v5, v4, v3, v2) = % 97.11/14.03 v1) | ~ (c_FunDef_Oin__rel(v6, v5, v4, v3, v2) = v0)) & ! [v0: % 97.11/14.03 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 97.11/14.03 : ! [v4: $i] : ! [v5: $i] : (v1 = v0 | ~ (c_Equiv__Relations_Ocongruent(v5, % 97.11/14.03 v4, v3, v2) = v1) | ~ (c_Equiv__Relations_Ocongruent(v5, v4, v3, v2) = % 97.11/14.03 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] % 97.11/14.03 : ! [v5: $i] : (v1 = v0 | ~ % 97.11/14.03 (c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v5, v4, v3, v2) = v1) | % 97.11/14.03 ~ (c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v5, v4, v3, v2) = % 97.11/14.03 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] % 97.11/14.03 : ! [v5: $i] : (v1 = v0 | ~ (c_Fun_Othe__inv__into(v5, v4, v3, v2) = v1) | % 97.11/14.03 ~ (c_Fun_Othe__inv__into(v5, v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] % 97.11/14.03 : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v1 = v0 | ~ % 97.11/14.03 (c_Hilbert__Choice_Oinv__into(v5, v4, v3, v2) = v1) | ~ % 97.11/14.03 (c_Hilbert__Choice_Oinv__into(v5, v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: % 97.11/14.03 $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v1 = v0 | ~ % 97.11/14.03 (c_Set_Oimage(v5, v4, v3, v2) = v1) | ~ (c_Set_Oimage(v5, v4, v3, v2) = % 97.11/14.03 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 97.11/14.03 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v1 = v0 | ~ % 97.11/14.03 (c_Fun_Oinj__on(v5, v4, v3, v2) = v1) | ~ (c_Fun_Oinj__on(v5, v4, v3, v2) = % 97.11/14.03 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 97.11/14.03 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v1 = v0 | ~ % 97.11/14.03 (c_Recdef_Oadm__wf(v5, v4, v3, v2) = v1) | ~ (c_Recdef_Oadm__wf(v5, v4, v3, % 97.11/14.03 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! % 97.11/14.03 [v4: $i] : ! [v5: $i] : (v1 = v0 | ~ (c_FuncSet_Oextensional__funcset(v5, % 97.11/14.03 v4, v3, v2) = v1) | ~ (c_FuncSet_Oextensional__funcset(v5, v4, v3, v2) % 97.11/14.03 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: % 97.11/14.03 $i] : ! [v5: $i] : (v1 = v0 | ~ (c_FuncSet_Orestrict(v5, v4, v3, v2) = v1) % 97.11/14.03 | ~ (c_FuncSet_Orestrict(v5, v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] % 97.11/14.03 : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v1 = v0 | ~ % 97.11/14.03 (c_Relation_Oinv__image(v5, v4, v3, v2) = v1) | ~ % 97.11/14.03 (c_Relation_Oinv__image(v5, v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] % 97.11/14.03 : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! % 97.11/14.03 [v5: $i] : (v1 = v0 | ~ (c_Predicate_ODomainP(v5, v4, v3, v2) = v1) | ~ % 97.11/14.03 (c_Predicate_ODomainP(v5, v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : % 97.11/14.03 ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v1 = v0 | ~ % 97.11/14.03 (c_Wellfounded_Olex__prod(v5, v4, v3, v2) = v1) | ~ % 97.11/14.03 (c_Wellfounded_Olex__prod(v5, v4, v3, v2) = v0)) & ! [v0: % 97.11/14.03 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 97.11/14.03 : ! [v4: $i] : ! [v5: $i] : (v1 = v0 | ~ (c_Predicate_ORangeP(v5, v4, v3, % 97.11/14.03 v2) = v1) | ~ (c_Predicate_ORangeP(v5, v4, v3, v2) = v0)) & ! [v0: $i] % 97.11/14.03 : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v1 = % 97.11/14.03 v0 | ~ (c_Recdef_Osame__fst(v5, v4, v3, v2) = v1) | ~ % 97.11/14.03 (c_Recdef_Osame__fst(v5, v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 97.11/14.03 [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v1 = v0 | ~ % 97.11/14.03 (c_COMBB(v5, v4, v3, v2) = v1) | ~ (c_COMBB(v5, v4, v3, v2) = v0)) & ! % 97.11/14.03 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] % 97.11/14.03 : (v1 = v0 | ~ (c_FuncSet_OPi(v5, v4, v3, v2) = v1) | ~ (c_FuncSet_OPi(v5, % 97.11/14.03 v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 97.11/14.03 $i] : ! [v4: $i] : ! [v5: $i] : (v1 = v0 | ~ (c_HOL_OLet(v5, v4, v3, v2) % 97.11/14.03 = v1) | ~ (c_HOL_OLet(v5, v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] % 97.11/14.03 : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ % 97.11/14.03 (c_Partial__Function_Oflat__lub(v4, v3, v2) = v1) | ~ % 97.11/14.03 (c_Partial__Function_Oflat__lub(v4, v3, v2) = v0)) & ! [v0: % 97.11/14.03 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 97.11/14.03 : ! [v4: $i] : (v1 = v0 | ~ (c_Orderings_Oord__class_Oless__eq(v4, v3, v2) = % 97.11/14.03 v1) | ~ (c_Orderings_Oord__class_Oless__eq(v4, v3, v2) = v0)) & ! [v0: % 97.11/14.03 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 97.11/14.03 : ! [v4: $i] : (v1 = v0 | ~ (c_Equiv__Relations_Oequiv(v4, v3, v2) = v1) | % 97.11/14.03 ~ (c_Equiv__Relations_Oequiv(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] % 97.11/14.03 : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ % 97.11/14.03 (c_Relation_OImage(v4, v3, v2) = v1) | ~ (c_Relation_OImage(v4, v3, v2) = % 97.11/14.03 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] % 97.11/14.03 : (v1 = v0 | ~ (c_Groups_Ominus__class_Ominus(v4, v3, v2) = v1) | ~ % 97.11/14.03 (c_Groups_Ominus__class_Ominus(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: % 97.11/14.03 $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ % 97.11/14.03 (c_Lattices_Osemilattice__inf__class_Oinf(v4, v3, v2) = v1) | ~ % 97.11/14.03 (c_Lattices_Osemilattice__inf__class_Oinf(v4, v3, v2) = v0)) & ! [v0: % 97.11/14.03 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 97.11/14.03 : ! [v4: $i] : (v1 = v0 | ~ (c_Relation_Osingle__valued(v4, v3, v2) = v1) | % 97.11/14.03 ~ (c_Relation_Osingle__valued(v4, v3, v2) = v0)) & ! [v0: % 97.11/14.03 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 97.11/14.03 : ! [v4: $i] : (v1 = v0 | ~ (c_Relation_Orefl__on(v4, v3, v2) = v1) | ~ % 97.11/14.03 (c_Relation_Orefl__on(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 97.11/14.03 [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ % 97.11/14.03 (c_FuncSet_Oextensional(v4, v3, v2) = v1) | ~ (c_FuncSet_Oextensional(v4, % 97.11/14.03 v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] % 97.11/14.03 : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ % 97.11/14.03 (c_Relation_Ototal__on(v4, v3, v2) = v1) | ~ (c_Relation_Ototal__on(v4, v3, % 97.11/14.03 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! % 97.11/14.03 [v4: $i] : (v1 = v0 | ~ (c_Predicate_Oconversep(v4, v3, v2) = v1) | ~ % 97.11/14.03 (c_Predicate_Oconversep(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 97.11/14.03 [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (c_Relation_ODomain(v4, % 97.11/14.03 v3, v2) = v1) | ~ (c_Relation_ODomain(v4, v3, v2) = v0)) & ! [v0: $i] % 97.11/14.03 : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ % 97.11/14.03 (c_Relation_ORange(v4, v3, v2) = v1) | ~ (c_Relation_ORange(v4, v3, v2) = % 97.11/14.03 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] % 97.11/14.03 : (v1 = v0 | ~ (c_Relation_Oconverse(v4, v3, v2) = v1) | ~ % 97.11/14.03 (c_Relation_Oconverse(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 97.11/14.03 [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (c_COMBK(v4, v3, v2) = % 97.11/14.03 v1) | ~ (c_COMBK(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 97.11/14.03 $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (c_COMBS(v4, v3, v2) = v1) | % 97.11/14.03 ~ (c_COMBS(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 97.11/14.03 ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (c_COMBC(v4, v3, v2) = v1) | ~ % 97.11/14.03 (c_COMBC(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 97.11/14.03 [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (c_Arrow__Order__Mirabelle_Obelow(v4, % 97.11/14.03 v3, v2) = v1) | ~ (c_Arrow__Order__Mirabelle_Obelow(v4, v3, v2) = v0)) % 97.11/14.03 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 97.11/14.03 (c_HOL_OThe(v3, v2) = v1) | ~ (c_HOL_OThe(v3, v2) = v0)) & ! [v0: $i] : ! % 97.11/14.03 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (c_Set_Othe__elem(v3, v2) % 97.11/14.03 = v1) | ~ (c_Set_Othe__elem(v3, v2) = v0)) & ! [v0: MultipleValueBool] : % 97.11/14.03 ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 97.11/14.03 (c_Wellfounded_Oacyclic(v3, v2) = v1) | ~ (c_Wellfounded_Oacyclic(v3, v2) = % 97.11/14.03 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | % 97.11/14.03 ~ (c_Transitive__Closure_Otrancl(v3, v2) = v1) | ~ % 97.11/14.03 (c_Transitive__Closure_Otrancl(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : % 97.11/14.03 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (c_Recdef_Ocut(v3, v2) = v1) | ~ % 97.11/14.03 (c_Recdef_Ocut(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 97.11/14.03 [v3: $i] : (v1 = v0 | ~ (c_Transitive__Closure_Ortrancl(v3, v2) = v1) | ~ % 97.11/14.03 (c_Transitive__Closure_Ortrancl(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : % 97.11/14.03 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (c_Wellfounded_Oaccp(v3, v2) = v1) | % 97.11/14.03 ~ (c_Wellfounded_Oaccp(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 97.11/14.03 $i] : ! [v3: $i] : (v1 = v0 | ~ (c_Wellfounded_Oacc(v3, v2) = v1) | ~ % 97.11/14.03 (c_Wellfounded_Oacc(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 97.11/14.03 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 97.11/14.03 (c_Nitpick_Orefl_H(v3, v2) = v1) | ~ (c_Nitpick_Orefl_H(v3, v2) = v0)) & ! % 97.11/14.03 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 97.11/14.03 (c_Relation_OId__on(v3, v2) = v1) | ~ (c_Relation_OId__on(v3, v2) = v0)) & % 97.11/14.03 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 97.11/14.03 $i] : (v1 = v0 | ~ (c_Relation_Oirrefl(v3, v2) = v1) | ~ % 97.11/14.03 (c_Relation_Oirrefl(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 97.11/14.03 : ! [v3: $i] : (v1 = v0 | ~ (c_If(v3, v2) = v1) | ~ (c_If(v3, v2) = v0)) & % 97.11/14.03 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 97.11/14.03 (c_Product__Type_OPair(v3, v2) = v1) | ~ (c_Product__Type_OPair(v3, v2) = % 97.11/14.03 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 97.11/14.03 $i] : ! [v3: $i] : (v1 = v0 | ~ (c_Arrow__Order__Mirabelle_Odictator(v3, % 97.11/14.03 v2) = v1) | ~ (c_Arrow__Order__Mirabelle_Odictator(v3, v2) = v0)) & ! % 97.11/14.03 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 97.11/14.03 (c_Arrow__Order__Mirabelle_Omktop(v3, v2) = v1) | ~ % 97.11/14.03 (c_Arrow__Order__Mirabelle_Omktop(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] % 97.11/14.03 : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 97.11/14.03 (c_Arrow__Order__Mirabelle_Omkbot(v3, v2) = v1) | ~ % 97.11/14.03 (c_Arrow__Order__Mirabelle_Omkbot(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] % 97.11/14.03 : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (tc_prod(v3, v2) = v1) | ~ % 97.11/14.03 (tc_prod(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 97.11/14.03 $i] : (v1 = v0 | ~ (tc_fun(v3, v2) = v1) | ~ (tc_fun(v3, v2) = v0)) & ! % 97.11/14.03 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP(v3, % 97.11/14.03 v2) = v1) | ~ (hAPP(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! % 97.11/14.03 [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ % 97.11/14.03 (class_Lattices_Obounded__lattice(v2) = v1) | ~ % 97.11/14.03 (class_Lattices_Obounded__lattice(v2) = v0)) & ! [v0: MultipleValueBool] : % 97.11/14.03 ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ % 97.11/14.03 (class_Groups_Oab__group__add(v2) = v1) | ~ % 97.11/14.03 (class_Groups_Oab__group__add(v2) = v0)) & ! [v0: MultipleValueBool] : ! % 97.11/14.03 [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ % 97.11/14.04 (class_Groups_Oordered__ab__group__add(v2) = v1) | ~ % 97.11/14.04 (class_Groups_Oordered__ab__group__add(v2) = v0)) & ! [v0: % 97.11/14.04 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 97.11/14.04 ~ (class_Orderings_Oorder(v2) = v1) | ~ (class_Orderings_Oorder(v2) = v0)) % 97.11/14.04 & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 % 97.11/14.04 = v0 | ~ (class_Orderings_Oord(v2) = v1) | ~ (class_Orderings_Oord(v2) = % 97.11/14.04 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 97.11/14.04 $i] : (v1 = v0 | ~ (class_Orderings_Olinorder(v2) = v1) | ~ % 97.11/14.04 (class_Orderings_Olinorder(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 97.11/14.04 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ % 97.11/14.04 (class_Orderings_Opreorder(v2) = v1) | ~ (class_Orderings_Opreorder(v2) = % 97.11/14.04 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 97.11/14.04 (c_Equiv__Relations_Oquotient(v2) = v1) | ~ % 97.11/14.04 (c_Equiv__Relations_Oquotient(v2) = v0)) & ! [v0: MultipleValueBool] : ! % 97.11/14.04 [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (class_Groups_Ominus(v2) % 97.11/14.04 = v1) | ~ (class_Groups_Ominus(v2) = v0)) & ! [v0: MultipleValueBool] : % 97.11/14.04 ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ % 97.11/14.04 (class_Orderings_Obot(v2) = v1) | ~ (class_Orderings_Obot(v2) = v0)) & ! % 97.11/14.04 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 % 97.11/14.04 | ~ (class_Lattices_Obounded__lattice__bot(v2) = v1) | ~ % 97.11/14.04 (class_Lattices_Obounded__lattice__bot(v2) = v0)) & ! [v0: $i] : ! [v1: % 97.11/14.04 $i] : ! [v2: $i] : (v1 = v0 | ~ (c_Set_Oinsert(v2) = v1) | ~ % 97.11/14.04 (c_Set_Oinsert(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = % 97.11/14.04 v0 | ~ (c_Orderings_Obot__class_Obot(v2) = v1) | ~ % 97.11/14.04 (c_Orderings_Obot__class_Obot(v2) = v0)) & ! [v0: MultipleValueBool] : ! % 97.11/14.04 [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ % 97.11/14.04 (class_Lattices_Osemilattice__inf(v2) = v1) | ~ % 97.11/14.04 (class_Lattices_Osemilattice__inf(v2) = v0)) & ! [v0: MultipleValueBool] : % 97.11/14.04 ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ % 97.11/14.04 (class_Lattices_Olattice(v2) = v1) | ~ (class_Lattices_Olattice(v2) = v0)) % 97.11/14.04 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 97.11/14.04 (c_HOL_Oundefined(v2) = v1) | ~ (c_HOL_Oundefined(v2) = v0)) & ! [v0: $i] % 97.11/14.04 : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (c_COMBI(v2) = v1) | ~ % 97.11/14.04 (c_COMBI(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | % 97.11/14.04 ~ (c_member(v2) = v1) | ~ (c_member(v2) = v0)) & ! [v0: MultipleValueBool] % 97.11/14.04 : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (hBOOL(v2) = v1) | % 97.11/14.04 ~ (hBOOL(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 97.11/14.04 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ % 97.11/14.04 (c_Arrow__Order__Mirabelle_Ounanimity(v2) = v1) | ~ % 97.11/14.04 (c_Arrow__Order__Mirabelle_Ounanimity(v2) = v0)) & ! [v0: % 97.11/14.04 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 97.11/14.04 ~ (c_Arrow__Order__Mirabelle_OIIA(v2) = v1) | ~ % 97.11/14.04 (c_Arrow__Order__Mirabelle_OIIA(v2) = v0)) % 97.11/14.04 % 97.11/14.04 Further assumptions not needed in the proof: % 97.11/14.04 -------------------------------------------- % 97.11/14.04 arity_HOL__Obool__Groups_Ominus, arity_HOL__Obool__Lattices_Obounded__lattice, % 97.11/14.04 arity_HOL__Obool__Lattices_Obounded__lattice__bot, % 97.11/14.04 arity_HOL__Obool__Lattices_Olattice, % 97.11/14.04 arity_HOL__Obool__Lattices_Osemilattice__inf, arity_HOL__Obool__Orderings_Oord, % 97.11/14.04 arity_HOL__Obool__Orderings_Oorder, arity_HOL__Obool__Orderings_Opreorder, % 97.11/14.04 arity_fun__Groups_Ominus, arity_fun__Lattices_Obounded__lattice, % 97.11/14.04 arity_fun__Lattices_Obounded__lattice__bot, arity_fun__Lattices_Olattice, % 97.11/14.04 arity_fun__Lattices_Osemilattice__inf, arity_fun__Orderings_Oord, % 97.11/14.04 arity_fun__Orderings_Oorder, arity_fun__Orderings_Opreorder, fact_DiffD1, % 97.11/14.04 fact_DiffD2, fact_DiffE, fact_DiffI, fact_Diff__Int2, fact_Diff__Int__distrib, % 97.11/14.04 fact_Diff__Int__distrib2, fact_Diff__cancel, fact_Diff__disjoint, % 97.11/14.04 fact_Diff__empty, fact_Diff__idemp, fact_Diff__iff, fact_Diff__insert, % 97.11/14.04 fact_Diff__insert2, fact_Diff__insert__absorb, fact_Diff__mono, % 97.11/14.04 fact_Diff__subset, fact_Diff__triv, fact_DomainE, fact_DomainI, % 97.11/14.04 fact_DomainP_Ointros, fact_DomainP__Domain__eq, fact_Domain__Diff__subset, % 97.11/14.04 fact_Domain__Id__on, fact_Domain__Int__subset, fact_Domain__converse, % 97.11/14.04 fact_Domain__empty, fact_Domain__empty__iff, fact_Domain__iff, % 97.11/14.04 fact_Domain__insert, fact_Domain__mono, fact_Id__onE, fact_Id__on__empty, % 97.11/14.04 fact_Id__on__eqI, fact_Id__on__iff, fact_ImageE, fact_Image__Id__on, % 97.11/14.04 fact_Image__Int__eq, fact_Image__Int__subset, fact_Image__UN, % 97.11/14.04 fact_Image__closed__trancl, fact_Image__empty, fact_Image__eq__UN, % 97.11/14.04 fact_Image__iff, fact_Image__mono, fact_Image__singleton__iff, fact_IntD1, % 97.11/14.04 fact_IntD2, fact_IntE, fact_IntI, fact_Int__Diff, fact_Int__absorb, % 97.11/14.04 fact_Int__absorb1, fact_Int__absorb2, fact_Int__assoc, fact_Int__commute, % 97.11/14.04 fact_Int__empty__left, fact_Int__empty__right, fact_Int__greatest, % 97.11/14.04 fact_Int__iff, fact_Int__insert__left, fact_Int__insert__left__if0, % 97.11/14.04 fact_Int__insert__left__if1, fact_Int__insert__right, % 97.11/14.04 fact_Int__insert__right__if0, fact_Int__insert__right__if1, % 97.11/14.04 fact_Int__left__absorb, fact_Int__left__commute, fact_Int__lower1, % 97.11/14.04 fact_Int__lower2, fact_Int__mono, fact_Nitpick_Orefl_H__def, % 97.11/14.04 fact_Not__Domain__rtrancl, fact_PiE, fact_Pi__I, fact_Pi__I_H, % 97.11/14.04 fact_Pi__anti__mono, fact_Pi__cong, fact_Pi__mem, fact_RangeE, fact_RangeI, % 97.11/14.04 fact_RangeP_Oequations, fact_RangeP_Ointros, fact_RangeP__Range__eq, % 97.11/14.04 fact_Range__Diff__subset, fact_Range__Id__on, fact_Range__Int__subset, % 97.11/14.04 fact_Range__converse, fact_Range__def, fact_Range__empty, % 97.11/14.04 fact_Range__empty__iff, fact_Range__iff, fact_Range__insert, fact_SUP1__I, % 97.11/14.04 fact_SUP1__iff, fact_Transitive__Closure_Otrancl__into__trancl, fact_UN__I, % 97.11/14.04 fact_UN__equiv__class, fact_acc_OaccI, fact_acc_Osimps, fact_acc__downward, % 97.11/14.04 fact_acc__downwards, fact_acc__downwards__aux, fact_acc__subset, % 97.11/14.04 fact_accp_Oequations, fact_accp_Osimps, fact_accp__acc__eq, fact_accp__downward, % 97.11/14.04 fact_accp__subset, fact_acyclicI, fact_acyclic__converse, fact_acyclic__def, % 97.11/14.04 fact_acyclic__insert, fact_acyclic__subset, fact_adm__lemma, fact_adm__wf__def, % 97.11/14.04 fact_all__not__in__conv, fact_assms_I3_J, fact_bot2E, fact_bot__apply, % 97.11/14.04 fact_bot__empty__eq, fact_bot__empty__eq2, fact_bot__fun__def, fact_bot__least, % 97.11/14.04 fact_compose__assoc, fact_compose__def, fact_compose__eq, % 97.11/14.04 fact_compose__extensional, fact_compose__id__inv__into, fact_congruentD, % 97.11/14.04 fact_converseD, fact_converseE, fact_converseI, fact_converse__Id__on, % 97.11/14.04 fact_converse__Int, fact_converse__converse, fact_converse__iff, % 97.11/14.04 fact_converse__inv__image, fact_converse__meet, fact_converse__rtranclE, % 97.11/14.04 fact_converse__rtranclE2, fact_converse__rtrancl__induct, % 97.11/14.04 fact_converse__rtrancl__induct2, fact_converse__rtrancl__into__rtrancl, % 97.11/14.04 fact_converse__tranclE, fact_conversepD, fact_conversep_Oequations, % 97.11/14.04 fact_conversep_Ointros, fact_conversep__converse__eq, fact_conversep__conversep, % 97.11/14.04 fact_conversep__eq, fact_conversep__iff, fact_conversep__noteq, fact_cut__apply, % 97.11/14.04 fact_cut__def, fact_cuts__eq, fact_d1_I1_J, fact_d1_I2_J, fact_d2_I1_J, % 97.11/14.04 fact_d2_I2_J, fact_diff__eq__diff__eq, fact_diff__eq__diff__less__eq, % 97.11/14.04 fact_diff__single__insert, fact_disjoint__iff__not__equal, fact_double__diff, % 97.11/14.04 fact_doubleton__eq__iff, fact_emptyE, fact_empty__Diff, fact_empty__iff, % 97.11/14.04 fact_empty__is__image, fact_empty__not__insert, fact_empty__subsetI, % 97.11/14.04 fact_eq__equiv__class, fact_eq__equiv__class__iff, fact_eq__equiv__class__iff2, % 97.11/14.04 fact_eq__mem, fact_eq__mem__trans, fact_eqelem__imp__iff, fact_eqset__imp__iff, % 97.11/14.04 fact_equalityCE, fact_equalityD1, fact_equalityD2, fact_equalityE, % 97.11/14.04 fact_equalityI, fact_equiv__class__eq, fact_equiv__class__eq__iff, % 97.11/14.04 fact_equiv__class__nondisjoint, fact_equiv__class__self, % 97.11/14.04 fact_equiv__class__subset, fact_ex__in__conv, fact_ext, fact_extensional__arb, % 97.11/14.04 fact_extensional__empty, fact_extensional__funcset__arb, % 97.11/14.04 fact_extensional__funcset__def, fact_extensional__funcset__empty__domain, % 97.11/14.04 fact_extensional__funcset__empty__range, % 97.11/14.04 fact_extensional__funcset__extend__domainI, % 97.11/14.04 fact_extensional__funcset__fun__upd__extends__rangeI, % 97.11/14.04 fact_extensional__funcset__fun__upd__inj__onI, % 97.11/14.04 fact_extensional__funcset__fun__upd__restricts__rangeI, % 97.11/14.04 fact_extensional__funcset__mem, fact_extensional__funcset__restrict__domain, % 97.11/14.04 fact_extensional__restrict, fact_extensional__subset, fact_extensionalityI, % 97.11/14.04 fact_f__inv__into__f, fact_f__the__inv__into__f, fact_flat__lub__def, % 97.11/14.04 fact_fold__graph_H_Oequations_I1_J, fact_fold__graph_H_Oequations_I2_J, % 97.11/14.04 fact_fold__graph_H_Ointros_I1_J, fact_fold__graph_H_Ointros_I2_J, % 97.11/14.04 fact_fun__diff__def, fact_fun__upd__apply, fact_fun__upd__def, % 97.11/14.04 fact_fun__upd__idem, fact_fun__upd__idem__iff, fact_fun__upd__image, % 97.11/14.04 fact_fun__upd__other, fact_fun__upd__same, fact_fun__upd__triv, % 97.11/14.04 fact_fun__upd__twist, fact_fun__upd__upd, fact_funcsetI, fact_funcset__compose, % 97.11/14.04 fact_funcset__id, fact_imageI, fact_image__Int__subset, fact_image__constant, % 97.11/14.04 fact_image__constant__conv, fact_image__diff__subset, fact_image__empty, % 97.11/14.04 fact_image__eqI, fact_image__ident, fact_image__iff, fact_image__image, % 97.11/14.04 fact_image__insert, fact_image__inv__into__cancel, fact_image__is__empty, % 97.11/14.04 fact_image__mono, fact_image__restrict__eq, fact_in__inv__image, % 97.11/14.04 fact_in__lex__prod, fact_in__mono, fact_in__rel__def, fact_inf1D1, fact_inf1D2, % 97.11/14.04 fact_inf1E, fact_inf1I, fact_inf2D1, fact_inf2D2, fact_inf2E, fact_inf2I, % 97.11/14.04 fact_inf_Oassoc, fact_inf_Ocommute, fact_inf_Oidem, fact_inf_Oleft__commute, % 97.11/14.04 fact_inf_Oleft__idem, fact_inf__Int__eq, fact_inf__Int__eq2, fact_inf__absorb1, % 97.11/14.04 fact_inf__absorb2, fact_inf__apply, fact_inf__assoc, fact_inf__bot__left, % 97.11/14.04 fact_inf__bot__right, fact_inf__commute, fact_inf__fun__def, fact_inf__greatest, % 97.11/14.04 fact_inf__idem, fact_inf__le1, fact_inf__le2, fact_inf__left__commute, % 97.11/14.04 fact_inf__left__idem, fact_inf__mono, fact_inf__sup__aci_I1_J, % 97.11/14.04 fact_inf__sup__aci_I2_J, fact_inf__sup__aci_I3_J, fact_inf__sup__aci_I4_J, % 97.11/14.04 fact_inf__sup__ord_I1_J, fact_inf__sup__ord_I2_J, fact_inj__onD, % 97.11/14.04 fact_inj__on__Int, fact_inj__on__contraD, fact_inj__on__def, fact_inj__on__diff, % 97.11/14.04 fact_inj__on__empty, fact_inj__on__fun__updI, fact_inj__on__id2, % 97.11/14.04 fact_inj__on__iff, fact_inj__on__iff__surj, fact_inj__on__image__Int, % 97.11/14.04 fact_inj__on__image__set__diff, fact_inj__on__insert, fact_inj__on__inv__into, % 97.11/14.04 fact_inj__on__restrict__eq, fact_inj__on__the__inv__into, fact_insertCI, % 97.11/14.04 fact_insertE, fact_insertI1, fact_insertI2, fact_insert__Diff, % 97.11/14.04 fact_insert__Diff1, fact_insert__Diff__if, fact_insert__Diff__single, % 97.11/14.04 fact_insert__absorb, fact_insert__absorb2, fact_insert__code, % 97.11/14.04 fact_insert__commute, fact_insert__ident, fact_insert__iff, fact_insert__image, % 97.11/14.04 fact_insert__inter__insert, fact_insert__mono, fact_insert__not__empty, % 97.11/14.04 fact_insert__subset, fact_inv__into__f__eq, fact_inv__into__f__f, % 97.11/14.04 fact_inv__into__funcset, fact_inv__into__image__cancel, % 97.11/14.04 fact_inv__into__injective, fact_inv__into__into, fact_irrefl__def, % 97.11/14.04 fact_irrefl__tranclI, fact_le__funD, fact_le__funE, fact_le__fun__def, % 97.11/14.04 fact_le__iff__inf, fact_le__infE, fact_le__infI, fact_le__infI1, fact_le__infI2, % 97.11/14.04 fact_le__inf__iff, fact_less__by__empty, fact_linorder__le__cases, % 97.11/14.04 fact_linorder__linear, fact_minus__apply, fact_not__acc__down, % 97.11/14.04 fact_ord__eq__le__trans, fact_ord__le__eq__trans, fact_order__antisym, % 97.11/14.04 fact_order__antisym__conv, fact_order__eq__iff, fact_order__eq__refl, % 97.11/14.04 fact_order__refl, fact_order__trans, fact_pred__equals__eq, % 97.11/14.04 fact_pred__equals__eq2, fact_pred__subset__eq, fact_pred__subset__eq2, % 97.11/14.04 fact_predicate1D, fact_predicate2D, fact_quotientE, fact_quotientI, % 97.11/14.04 fact_quotient__def, fact_quotient__diff1, fact_quotient__disj, % 97.11/14.04 fact_quotient__empty, fact_quotient__eqI, fact_quotient__eq__iff, % 97.11/14.04 fact_quotient__is__empty, fact_quotient__is__empty2, fact_r__into__rtrancl, % 97.11/14.04 fact_r__into__trancl_H, fact_r__r__into__trancl, fact_refl__onD, % 97.11/14.04 fact_refl__onD1, fact_refl__onD2, fact_refl__on__Id__on, fact_refl__on__Int, % 97.11/14.04 fact_refl__on__converse, fact_refl__on__empty, fact_restrictI, % 97.11/14.04 fact_restrict__apply, fact_restrict__def, fact_restrict__extensional, % 97.11/14.04 fact_restrict__in__funcset, fact_rev__ImageI, fact_rev__image__eqI, % 97.11/14.04 fact_rev__predicate1D, fact_rev__predicate2D, fact_rtranclD, fact_rtranclE, % 97.11/14.04 fact_rtrancl_Ortrancl__into__rtrancl, fact_rtrancl_Ortrancl__refl, % 97.11/14.04 fact_rtrancl__converse, fact_rtrancl__converseD, fact_rtrancl__converseI, % 97.11/14.04 fact_rtrancl__eq__or__trancl, fact_rtrancl__idemp, fact_rtrancl__induct, % 97.11/14.04 fact_rtrancl__induct2, fact_rtrancl__into__trancl1, fact_rtrancl__into__trancl2, % 97.11/14.04 fact_rtrancl__mono, fact_rtrancl__subset, fact_rtrancl__subset__rtrancl, % 97.11/14.04 fact_rtrancl__trancl__absorb, fact_rtrancl__trancl__trancl, fact_rtrancl__trans, % 97.11/14.04 fact_same__fstI, fact_set__eq__subset, fact_set__mp, fact_set__rev__mp, % 97.11/14.04 fact_single__valuedD, fact_single__valuedI, fact_single__valued__Id__on, % 97.11/14.04 fact_single__valued__confluent, fact_single__valued__def, % 97.11/14.04 fact_single__valued__subset, fact_singletonE, fact_singleton__iff, % 97.11/14.04 fact_singleton__inject, fact_singleton__quotient, fact_subsetD, % 97.11/14.04 fact_subset__empty, fact_subset__equiv__class, fact_subset__image__iff, % 97.11/14.04 fact_subset__inj__on, fact_subset__insert, fact_subset__insertI, % 97.11/14.04 fact_subset__insertI2, fact_subset__insert__iff, fact_subset__refl, % 97.11/14.04 fact_subset__singletonD, fact_subset__trans, fact_surj__compose, % 97.11/14.04 fact_tfl__cut__apply, fact_the__elem__def, fact_the__elem__eq, % 97.11/14.04 fact_the__eq__trivial, fact_the__inv__into__f__eq, fact_the__inv__into__f__f, % 97.11/14.04 fact_the__inv__into__into, fact_the__inv__into__onto, % 97.11/14.04 fact_the__sym__eq__trivial, fact_total__on__converse, fact_total__on__def, % 97.11/14.04 fact_total__on__empty, fact_tranclD, fact_tranclD2, fact_tranclE, % 97.11/14.04 fact_trancl_Or__into__trancl, fact_trancl__converse, fact_trancl__converseD, % 97.11/14.04 fact_trancl__converseI, fact_trancl__domain, fact_trancl__empty, % 97.11/14.04 fact_trancl__into__rtrancl, fact_trancl__into__trancl2, fact_trancl__mono, % 97.11/14.04 fact_trancl__range, fact_trancl__rtrancl__absorb, fact_trancl__rtrancl__trancl, % 97.11/14.04 fact_trancl__trans, fact_u, fact_xt1_I3_J, fact_xt1_I4_J, fact_xt1_I5_J, % 97.11/14.04 fact_xt1_I6_J, help_c__COMBB__1, help_c__COMBC__1, help_c__COMBI__1, % 97.11/14.04 help_c__COMBK__1, help_c__COMBS__1, help_c__fNot__1, help_c__fNot__2, % 97.11/14.04 help_c__fconj__1, help_c__fconj__2, help_c__fconj__3, help_c__fequal__1, % 97.11/14.04 help_c__fequal__2 % 97.11/14.04 % 97.11/14.04 Those formulas are unsatisfiable: % 97.11/14.04 --------------------------------- % 97.11/14.04 % 97.11/14.04 Begin of proof % 97.11/14.04 | % 97.11/14.04 | ALPHA: (fact__096Q_A_058_AProf_096) implies: % 97.11/14.04 | (1) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 97.11/14.04 | ? [v5: $i] : (tc_prod(tc_Arrow__Order__Mirabelle_Oalt, % 97.11/14.04 | tc_Arrow__Order__Mirabelle_Oalt) = v0 & tc_fun(v0, tc_HOL_Obool) = % 97.11/14.04 | v1 & tc_fun(tc_Arrow__Order__Mirabelle_Oindi, v1) = v2 & c_member(v2) % 97.11/14.04 | = v3 & hBOOL(v5) = 0 & hAPP(v4, c_Arrow__Order__Mirabelle_OProf) = v5 % 97.11/14.04 | & hAPP(v3, v_Q____) = v4 & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) % 97.11/14.04 | & $i(v0)) % 97.11/14.04 | % 97.11/14.04 | ALPHA: (fact_mkbot__Lin) implies: % 97.11/14.05 | (2) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 97.11/14.05 | (tc_prod(tc_Arrow__Order__Mirabelle_Oalt, % 97.11/14.05 | tc_Arrow__Order__Mirabelle_Oalt) = v0 & tc_fun(v0, tc_HOL_Obool) = % 97.11/14.05 | v1 & c_member(v1) = v2 & $i(v2) & $i(v1) & $i(v0) & ! [v3: $i] : ! % 97.11/14.05 | [v4: $i] : ! [v5: $i] : ( ~ (c_Arrow__Order__Mirabelle_Omkbot(v4, % 97.11/14.05 | v3) = v5) | ~ $i(v4) | ~ $i(v3) | ? [v6: $i] : ? [v7: $i] : % 97.11/14.05 | ? [v8: any] : ? [v9: $i] : ? [v10: $i] : ? [v11: any] : % 97.11/14.05 | (hBOOL(v10) = v11 & hBOOL(v7) = v8 & hAPP(v9, % 97.11/14.05 | c_Arrow__Order__Mirabelle_OLin) = v10 & hAPP(v6, % 97.11/14.05 | c_Arrow__Order__Mirabelle_OLin) = v7 & hAPP(v2, v5) = v9 & % 97.11/14.05 | hAPP(v2, v4) = v6 & $i(v10) & $i(v9) & $i(v7) & $i(v6) & ( ~ (v8 % 97.11/14.05 | = 0) | v11 = 0)))) % 97.11/14.05 | % 97.11/14.05 | ALPHA: (fact_mktop__Lin) implies: % 97.11/14.05 | (3) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 97.11/14.05 | (tc_prod(tc_Arrow__Order__Mirabelle_Oalt, % 97.11/14.05 | tc_Arrow__Order__Mirabelle_Oalt) = v0 & tc_fun(v0, tc_HOL_Obool) = % 97.11/14.05 | v1 & c_member(v1) = v2 & $i(v2) & $i(v1) & $i(v0) & ! [v3: $i] : ! % 97.11/14.05 | [v4: $i] : ! [v5: $i] : ( ~ (c_Arrow__Order__Mirabelle_Omktop(v4, % 97.11/14.05 | v3) = v5) | ~ $i(v4) | ~ $i(v3) | ? [v6: $i] : ? [v7: $i] : % 97.11/14.05 | ? [v8: any] : ? [v9: $i] : ? [v10: $i] : ? [v11: any] : % 97.11/14.05 | (hBOOL(v10) = v11 & hBOOL(v7) = v8 & hAPP(v9, % 97.11/14.05 | c_Arrow__Order__Mirabelle_OLin) = v10 & hAPP(v6, % 97.11/14.05 | c_Arrow__Order__Mirabelle_OLin) = v7 & hAPP(v2, v5) = v9 & % 97.11/14.05 | hAPP(v2, v4) = v6 & $i(v10) & $i(v9) & $i(v7) & $i(v6) & ( ~ (v8 % 97.11/14.05 | = 0) | v11 = 0)))) % 97.11/14.05 | % 97.11/14.05 | ALPHA: (fact_above__Lin) implies: % 97.11/14.05 | (4) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 97.11/14.05 | (tc_prod(tc_Arrow__Order__Mirabelle_Oalt, % 97.11/14.05 | tc_Arrow__Order__Mirabelle_Oalt) = v0 & tc_fun(v0, tc_HOL_Obool) = % 97.11/14.05 | v1 & c_member(v1) = v2 & $i(v2) & $i(v1) & $i(v0) & ! [v3: $i] : ! % 97.11/14.05 | [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : % 97.11/14.05 | (v5 = v4 | ~ (hAPP(v7, v4) = v8) | ~ (hAPP(v6, v5) = v7) | ~ % 97.11/14.05 | (hAPP(c_Arrow__Order__Mirabelle_Oabove, v3) = v6) | ~ $i(v5) | ~ % 97.11/14.05 | $i(v4) | ~ $i(v3) | ? [v9: $i] : ? [v10: $i] : ? [v11: any] : % 97.11/14.05 | ? [v12: $i] : ? [v13: $i] : ? [v14: any] : (hBOOL(v13) = v14 & % 97.11/14.05 | hBOOL(v10) = v11 & hAPP(v12, c_Arrow__Order__Mirabelle_OLin) = % 97.11/14.05 | v13 & hAPP(v9, c_Arrow__Order__Mirabelle_OLin) = v10 & hAPP(v2, % 97.11/14.05 | v8) = v12 & hAPP(v2, v3) = v9 & $i(v13) & $i(v12) & $i(v10) & % 97.11/14.05 | $i(v9) & ( ~ (v11 = 0) | v14 = 0)))) % 97.11/14.05 | % 97.11/14.05 | ALPHA: (fact_below__Lin) implies: % 97.11/14.05 | (5) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 97.11/14.05 | (tc_prod(tc_Arrow__Order__Mirabelle_Oalt, % 97.11/14.05 | tc_Arrow__Order__Mirabelle_Oalt) = v0 & tc_fun(v0, tc_HOL_Obool) = % 97.11/14.05 | v1 & c_member(v1) = v2 & $i(v2) & $i(v1) & $i(v0) & ! [v3: $i] : ! % 97.11/14.05 | [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v5 = v4 | ~ % 97.11/14.05 | (c_Arrow__Order__Mirabelle_Obelow(v3, v5, v4) = v6) | ~ $i(v5) | % 97.11/14.05 | ~ $i(v4) | ~ $i(v3) | ? [v7: $i] : ? [v8: $i] : ? [v9: any] : % 97.11/14.05 | ? [v10: $i] : ? [v11: $i] : ? [v12: any] : (hBOOL(v11) = v12 & % 97.11/14.05 | hBOOL(v8) = v9 & hAPP(v10, c_Arrow__Order__Mirabelle_OLin) = v11 % 97.11/14.05 | & hAPP(v7, c_Arrow__Order__Mirabelle_OLin) = v8 & hAPP(v2, v6) = % 97.11/14.05 | v10 & hAPP(v2, v3) = v7 & $i(v11) & $i(v10) & $i(v8) & $i(v7) & ( % 97.11/14.05 | ~ (v9 = 0) | v12 = 0)))) % 97.11/14.05 | % 97.11/14.05 | ALPHA: (fact_linear__alt) implies: % 97.11/14.05 | (6) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 97.11/14.05 | (tc_prod(tc_Arrow__Order__Mirabelle_Oalt, % 97.11/14.05 | tc_Arrow__Order__Mirabelle_Oalt) = v0 & tc_fun(v0, tc_HOL_Obool) = % 97.11/14.05 | v1 & c_member(v1) = v2 & $i(v2) & $i(v1) & $i(v0) & ? [v3: $i] : ? % 97.11/14.05 | [v4: $i] : ? [v5: $i] : (hBOOL(v5) = 0 & hAPP(v4, % 97.11/14.05 | c_Arrow__Order__Mirabelle_OLin) = v5 & hAPP(v2, v3) = v4 & $i(v5) % 97.11/14.05 | & $i(v4) & $i(v3))) % 97.11/14.05 | % 97.11/14.05 | ALPHA: (fact_mem__def) implies: % 97.11/14.05 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 97.11/14.05 | ! [v5: $i] : ( ~ (c_member(v2) = v3) | ~ (hAPP(v4, v0) = v5) | ~ % 97.11/14.05 | (hAPP(v3, v1) = v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: $i] % 97.11/14.05 | : ? [v7: any] : ? [v8: any] : (hBOOL(v6) = v7 & hBOOL(v5) = v8 & % 97.11/14.05 | hAPP(v0, v1) = v6 & $i(v6) & ( ~ (v7 = 0) | v8 = 0))) % 97.11/14.05 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 97.11/14.05 | ! [v5: $i] : ( ~ (c_member(v2) = v3) | ~ (hAPP(v4, v0) = v5) | ~ % 97.11/14.05 | (hAPP(v3, v1) = v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: % 97.11/14.05 | any] : ? [v7: $i] : ? [v8: any] : (hBOOL(v7) = v8 & hBOOL(v5) = % 97.11/14.05 | v6 & hAPP(v0, v1) = v7 & $i(v7) & ( ~ (v6 = 0) | v8 = 0))) % 97.11/14.05 | % 97.11/14.05 | ALPHA: (fact__096P_H_A_058_AProf_096) implies: % 97.11/14.06 | (9) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 97.11/14.06 | ? [v5: $i] : (tc_prod(tc_Arrow__Order__Mirabelle_Oalt, % 97.11/14.06 | tc_Arrow__Order__Mirabelle_Oalt) = v0 & tc_fun(v0, tc_HOL_Obool) = % 97.11/14.06 | v1 & tc_fun(tc_Arrow__Order__Mirabelle_Oindi, v1) = v2 & c_member(v2) % 97.11/14.06 | = v3 & hBOOL(v5) = 0 & hAPP(v4, c_Arrow__Order__Mirabelle_OProf) = v5 % 97.11/14.06 | & hAPP(v3, v_P_H____) = v4 & $i(v5) & $i(v4) & $i(v3) & $i(v2) & % 97.11/14.06 | $i(v1) & $i(v0)) % 97.11/14.06 | % 97.11/14.06 | ALPHA: (fact__096P_A_058_AProf_096) implies: % 97.11/14.06 | (10) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 97.11/14.06 | ? [v5: $i] : (tc_prod(tc_Arrow__Order__Mirabelle_Oalt, % 97.11/14.06 | tc_Arrow__Order__Mirabelle_Oalt) = v0 & tc_fun(v0, tc_HOL_Obool) = % 97.11/14.06 | v1 & tc_fun(tc_Arrow__Order__Mirabelle_Oindi, v1) = v2 & % 97.11/14.06 | c_member(v2) = v3 & hBOOL(v5) = 0 & hAPP(v4, % 97.11/14.06 | c_Arrow__Order__Mirabelle_OProf) = v5 & hAPP(v3, v_P____) = v4 & % 97.11/14.06 | $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 97.11/14.06 | % 97.11/14.06 | ALPHA: (fact_dictator__def) implies: % 97.11/14.06 | (11) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : % 97.11/14.06 | (tc_prod(tc_Arrow__Order__Mirabelle_Oalt, % 97.11/14.06 | tc_Arrow__Order__Mirabelle_Oalt) = v0 & tc_fun(v0, tc_HOL_Obool) = % 97.11/14.06 | v1 & tc_fun(tc_Arrow__Order__Mirabelle_Oindi, v1) = v2 & % 97.11/14.06 | c_member(v2) = v3 & $i(v3) & $i(v2) & $i(v1) & $i(v0) & ! [v4: $i] % 97.11/14.06 | : ! [v5: $i] : ! [v6: int] : (v6 = 0 | ~ % 97.11/14.06 | (c_Arrow__Order__Mirabelle_Odictator(v5, v4) = v6) | ~ $i(v5) | % 97.11/14.06 | ~ $i(v4) | ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ? [v10: $i] % 97.11/14.06 | : ? [v11: $i] : ( ~ (v11 = v10) & hBOOL(v9) = 0 & hAPP(v8, % 97.11/14.06 | c_Arrow__Order__Mirabelle_OProf) = v9 & hAPP(v7, v4) = v11 & % 97.11/14.06 | hAPP(v5, v7) = v10 & hAPP(v3, v7) = v8 & $i(v11) & $i(v10) & % 97.11/14.06 | $i(v9) & $i(v8) & $i(v7))) & ! [v4: $i] : ! [v5: $i] : ( ~ % 97.11/14.06 | (c_Arrow__Order__Mirabelle_Odictator(v5, v4) = 0) | ~ $i(v5) | ~ % 97.11/14.06 | $i(v4) | ! [v6: $i] : ! [v7: $i] : ( ~ (hAPP(v3, v6) = v7) | ~ % 97.11/14.06 | $i(v6) | ? [v8: $i] : ? [v9: any] : ? [v10: $i] : ? [v11: % 97.11/14.06 | $i] : (hBOOL(v8) = v9 & hAPP(v7, % 97.11/14.06 | c_Arrow__Order__Mirabelle_OProf) = v8 & hAPP(v6, v4) = v11 & % 97.11/14.06 | hAPP(v5, v6) = v10 & $i(v11) & $i(v10) & $i(v8) & ( ~ (v9 = 0) % 97.11/14.06 | | v11 = v10))))) % 97.11/14.06 | % 97.11/14.06 | ALPHA: (fact_in__below) implies: % 97.11/14.06 | (12) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 97.11/14.06 | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 97.11/14.06 | tc_Arrow__Order__Mirabelle_Oalt) = v4 & % 97.11/14.06 | tc_prod(tc_Arrow__Order__Mirabelle_Oalt, % 97.11/14.06 | tc_Arrow__Order__Mirabelle_Oalt) = v0 & tc_fun(v0, tc_HOL_Obool) = % 97.11/14.06 | v1 & c_member(v1) = v2 & c_member(v0) = v3 & $i(v4) & $i(v3) & % 97.11/14.06 | $i(v2) & $i(v1) & $i(v0) & ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : % 97.11/14.06 | ! [v8: $i] : ! [v9: $i] : ! [v10: $i] : ! [v11: $i] : ! [v12: % 97.11/14.06 | $i] : ! [v13: $i] : ! [v14: $i] : (v9 = v8 | ~ % 97.11/14.06 | (c_Arrow__Order__Mirabelle_Obelow(v7, v9, v8) = v13) | ~ % 97.11/14.06 | (hAPP(v12, v13) = v14) | ~ (hAPP(v10, v5) = v11) | ~ (hAPP(v4, % 97.11/14.06 | v6) = v10) | ~ (hAPP(v3, v11) = v12) | ~ $i(v9) | ~ $i(v8) % 97.11/14.06 | | ~ $i(v7) | ~ $i(v6) | ~ $i(v5) | ? [v15: $i] : ? [v16: $i] % 97.11/14.06 | : ? [v17: any] : ? [v18: any] : ? [v19: $i] : ? [v20: $i] : ? % 97.11/14.06 | [v21: $i] : ? [v22: any] : ? [v23: $i] : ? [v24: $i] : ? [v25: % 97.11/14.06 | $i] : ? [v26: $i] : ? [v27: any] : ? [v28: $i] : ? [v29: % 97.11/14.06 | any] : (hBOOL(v28) = v29 & hBOOL(v26) = v27 & hBOOL(v21) = v22 & % 97.11/14.06 | hBOOL(v16) = v17 & hBOOL(v14) = v18 & hAPP(v25, v7) = v26 & % 97.11/14.06 | hAPP(v23, v5) = v24 & hAPP(v20, v7) = v21 & hAPP(v15, % 97.11/14.06 | c_Arrow__Order__Mirabelle_OLin) = v16 & hAPP(v12, v7) = v28 & % 97.11/14.06 | hAPP(v10, v8) = v19 & hAPP(v4, v8) = v23 & hAPP(v3, v24) = v25 & % 97.11/14.06 | hAPP(v3, v19) = v20 & hAPP(v2, v7) = v15 & $i(v28) & $i(v26) & % 97.11/14.06 | $i(v25) & $i(v24) & $i(v23) & $i(v21) & $i(v20) & $i(v19) & % 97.11/14.06 | $i(v16) & $i(v15) & ( ~ (v17 = 0) | (( ~ (v18 = 0) | ( ~ (v6 = % 97.11/14.06 | v5) & ( ~ (v9 = v5) | v22 = 0) & (v9 = v5 | (( ~ (v9 = % 97.11/14.06 | v6) | v27 = 0 | v8 = v5) & (v29 = 0 | v9 = % 97.11/14.06 | v6))))) & (v18 = 0 | v6 = v5 | (v9 = v5 & ~ (v22 % 97.11/14.06 | = 0)) | ( ~ (v9 = v5) & ((v9 = v6 & ~ (v27 = 0) & ~ % 97.11/14.06 | (v8 = v5)) | ( ~ (v29 = 0) & ~ (v9 = v6)))))))))) % 97.11/14.06 | % 97.11/14.06 | ALPHA: (fact_in__above) implies: % 97.11/14.07 | (13) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 97.11/14.07 | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 97.11/14.07 | tc_Arrow__Order__Mirabelle_Oalt) = v4 & % 97.11/14.07 | tc_prod(tc_Arrow__Order__Mirabelle_Oalt, % 97.11/14.07 | tc_Arrow__Order__Mirabelle_Oalt) = v0 & tc_fun(v0, tc_HOL_Obool) = % 97.11/14.07 | v1 & c_member(v1) = v2 & c_member(v0) = v3 & $i(v4) & $i(v3) & % 97.11/14.07 | $i(v2) & $i(v1) & $i(v0) & ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : % 97.11/14.07 | ! [v8: $i] : ! [v9: $i] : ! [v10: $i] : ! [v11: $i] : ! [v12: % 97.11/14.07 | $i] : ! [v13: $i] : ! [v14: $i] : ! [v15: $i] : ! [v16: $i] : % 97.11/14.07 | (v9 = v8 | ~ (hAPP(v14, v8) = v15) | ~ (hAPP(v13, v9) = v14) | ~ % 97.11/14.07 | (hAPP(v12, v15) = v16) | ~ (hAPP(v10, v5) = v11) | ~ (hAPP(v4, % 97.11/14.07 | v6) = v10) | ~ (hAPP(v3, v11) = v12) | ~ % 97.11/14.07 | (hAPP(c_Arrow__Order__Mirabelle_Oabove, v7) = v13) | ~ $i(v9) | % 97.11/14.07 | ~ $i(v8) | ~ $i(v7) | ~ $i(v6) | ~ $i(v5) | ? [v17: $i] : ? % 97.11/14.07 | [v18: $i] : ? [v19: any] : ? [v20: any] : ? [v21: $i] : ? % 97.11/14.07 | [v22: $i] : ? [v23: $i] : ? [v24: $i] : ? [v25: any] : ? [v26: % 97.11/14.07 | $i] : ? [v27: $i] : ? [v28: $i] : ? [v29: any] : ? [v30: $i] % 97.11/14.07 | : ? [v31: any] : (hBOOL(v30) = v31 & hBOOL(v28) = v29 & % 97.11/14.07 | hBOOL(v24) = v25 & hBOOL(v18) = v19 & hBOOL(v16) = v20 & % 97.11/14.07 | hAPP(v27, v7) = v28 & hAPP(v23, v7) = v24 & hAPP(v21, v5) = v22 % 97.11/14.07 | & hAPP(v17, c_Arrow__Order__Mirabelle_OLin) = v18 & hAPP(v12, % 97.11/14.07 | v7) = v30 & hAPP(v10, v9) = v26 & hAPP(v4, v9) = v21 & % 97.11/14.07 | hAPP(v3, v26) = v27 & hAPP(v3, v22) = v23 & hAPP(v2, v7) = v17 & % 97.11/14.07 | $i(v30) & $i(v28) & $i(v27) & $i(v26) & $i(v24) & $i(v23) & % 97.11/14.07 | $i(v22) & $i(v21) & $i(v18) & $i(v17) & ( ~ (v19 = 0) | (( ~ % 97.11/14.07 | (v20 = 0) | ( ~ (v6 = v5) & ( ~ (v8 = v6) | v25 = 0) & (v8 % 97.11/14.07 | = v6 | (( ~ (v8 = v5) | v29 = 0 | v9 = v6) & (v31 = 0 % 97.11/14.07 | | v8 = v5))))) & (v20 = 0 | v6 = v5 | (v8 = v6 & % 97.11/14.07 | ~ (v25 = 0)) | ( ~ (v8 = v6) & ((v8 = v5 & ~ (v29 = 0) % 97.11/14.07 | & ~ (v9 = v6)) | ( ~ (v31 = 0) & ~ (v8 = % 97.11/14.07 | v5)))))))))) % 97.11/14.07 | % 97.11/14.07 | ALPHA: (fact_Q__def) implies: % 97.11/14.07 | (14) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 97.11/14.07 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : % 97.11/14.07 | ? [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13: $i] : ? [v14: % 97.11/14.07 | $i] : ? [v15: $i] : ? [v16: $i] : ? [v17: $i] : (c_COMBS(v1, v1, % 97.11/14.07 | v1) = v5 & c_If(v1, v7) = v8 & c_If(v1, v3) = v4 & c_COMBC(v1, % 97.11/14.07 | tc_Arrow__Order__Mirabelle_Oalt, v11) = v12 & c_COMBC(v1, % 97.11/14.07 | tc_Arrow__Order__Mirabelle_Oalt, v1) = v10 & % 97.11/14.07 | tc_prod(tc_Arrow__Order__Mirabelle_Oalt, % 97.11/14.07 | tc_Arrow__Order__Mirabelle_Oalt) = v0 & tc_fun(v0, tc_HOL_Obool) = % 97.11/14.07 | v1 & tc_fun(tc_Arrow__Order__Mirabelle_Oalt, v1) = v11 & hAPP(v15, % 97.11/14.07 | v_b_H____) = v16 & hAPP(v13, v_b____) = v14 & hAPP(v12, % 97.11/14.07 | c_Arrow__Order__Mirabelle_Oabove) = v13 & hAPP(v10, v14) = v15 & % 97.11/14.07 | hAPP(v9, v16) = v17 & hAPP(v6, v_b_H____) = v7 & hAPP(v5, v8) = v9 & % 97.11/14.07 | hAPP(v2, v_a_H____) = v3 & hAPP(c_fequal, v_a____) = v2 & % 97.11/14.07 | hAPP(c_fequal, v_b____) = v6 & $i(v17) & $i(v16) & $i(v15) & $i(v14) % 97.11/14.07 | & $i(v13) & $i(v12) & $i(v11) & $i(v10) & $i(v9) & $i(v8) & $i(v7) & % 97.11/14.07 | $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & ! % 97.11/14.07 | [v18: $i] : ! [v19: $i] : ! [v20: $i] : ! [v21: $i] : ! [v22: % 97.11/14.07 | $i] : ( ~ (c_Arrow__Order__Mirabelle_Obelow(v19, v_a_H____, % 97.11/14.07 | v_a____) = v21) | ~ (hAPP(v20, v21) = v22) | ~ (hAPP(v4, % 97.11/14.07 | v19) = v20) | ~ (hAPP(v_P____, v18) = v19) | ~ $i(v18) | ? % 97.11/14.07 | [v23: $i] : (c_HOL_OLet(v1, v1, v22, v17) = v23 & hAPP(v_Q____, % 97.11/14.07 | v18) = v23 & $i(v23)))) % 97.11/14.07 | % 97.11/14.07 | ALPHA: (fact_assms_I1_J) implies: % 97.11/14.07 | (15) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 97.11/14.07 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : % 97.11/14.07 | (c_COMBK(v6, v2, c_Arrow__Order__Mirabelle_OLin) = v7 & % 97.11/14.07 | c_FuncSet_OPi(v2, v1, c_Arrow__Order__Mirabelle_OProf, v7) = v8 & % 97.11/14.07 | tc_prod(tc_Arrow__Order__Mirabelle_Oalt, % 97.11/14.07 | tc_Arrow__Order__Mirabelle_Oalt) = v0 & tc_fun(v2, v1) = v3 & % 97.11/14.07 | tc_fun(v1, tc_HOL_Obool) = v6 & tc_fun(v0, tc_HOL_Obool) = v1 & % 97.11/14.07 | tc_fun(tc_Arrow__Order__Mirabelle_Oindi, v1) = v2 & c_member(v3) = % 97.11/14.07 | v4 & hBOOL(v9) = 0 & hAPP(v5, v8) = v9 & hAPP(v4, v_F) = v5 & $i(v9) % 97.11/14.07 | & $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & % 97.11/14.07 | $i(v1) & $i(v0)) % 97.11/14.07 | % 97.11/14.07 | ALPHA: (fact_converse__in__Lin) implies: % 97.11/14.07 | (16) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 97.11/14.07 | (tc_prod(tc_Arrow__Order__Mirabelle_Oalt, % 97.11/14.07 | tc_Arrow__Order__Mirabelle_Oalt) = v0 & tc_fun(v0, tc_HOL_Obool) = % 97.11/14.07 | v1 & c_member(v1) = v2 & $i(v2) & $i(v1) & $i(v0) & ! [v3: $i] : ! % 97.11/14.07 | [v4: $i] : ( ~ (hAPP(v2, v3) = v4) | ~ $i(v3) | ? [v5: $i] : ? % 97.11/14.07 | [v6: any] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ? [v10: % 97.11/14.07 | any] : (c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt, % 97.11/14.07 | tc_Arrow__Order__Mirabelle_Oalt, v3) = v7 & hBOOL(v9) = v10 & % 97.11/14.07 | hBOOL(v5) = v6 & hAPP(v8, c_Arrow__Order__Mirabelle_OLin) = v9 & % 97.11/14.07 | hAPP(v4, c_Arrow__Order__Mirabelle_OLin) = v5 & hAPP(v2, v7) = % 97.11/14.07 | v8 & $i(v9) & $i(v8) & $i(v7) & $i(v5) & ( ~ (v6 = 0) | v10 = % 97.11/14.07 | 0))) & ! [v3: $i] : ! [v4: $i] : ( ~ (hAPP(v2, v3) = v4) | % 97.11/14.07 | ~ $i(v3) | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: any] % 97.11/14.07 | : ? [v9: $i] : ? [v10: any] : % 97.11/14.07 | (c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt, % 97.11/14.07 | tc_Arrow__Order__Mirabelle_Oalt, v3) = v5 & hBOOL(v9) = v10 & % 97.11/14.07 | hBOOL(v7) = v8 & hAPP(v6, c_Arrow__Order__Mirabelle_OLin) = v7 & % 97.11/14.07 | hAPP(v4, c_Arrow__Order__Mirabelle_OLin) = v9 & hAPP(v2, v5) = % 97.11/14.07 | v6 & $i(v9) & $i(v7) & $i(v6) & $i(v5) & ( ~ (v8 = 0) | v10 = % 97.11/14.07 | 0)))) % 97.11/14.07 | % 97.11/14.07 | ALPHA: (fact_Lin__irrefl) implies: % 97.11/14.07 | (17) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 97.11/14.07 | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 97.11/14.07 | tc_Arrow__Order__Mirabelle_Oalt) = v4 & % 97.11/14.07 | tc_prod(tc_Arrow__Order__Mirabelle_Oalt, % 97.11/14.07 | tc_Arrow__Order__Mirabelle_Oalt) = v0 & tc_fun(v0, tc_HOL_Obool) = % 97.11/14.07 | v1 & c_member(v1) = v2 & c_member(v0) = v3 & $i(v4) & $i(v3) & % 97.11/14.07 | $i(v2) & $i(v1) & $i(v0) & ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : % 97.11/14.07 | ! [v8: $i] : ! [v9: $i] : ! [v10: $i] : ! [v11: $i] : ( ~ % 97.11/14.07 | (hAPP(v10, v7) = v11) | ~ (hAPP(v8, v6) = v9) | ~ (hAPP(v4, v5) % 97.11/14.07 | = v8) | ~ (hAPP(v3, v9) = v10) | ~ $i(v7) | ~ $i(v6) | ~ % 97.11/14.07 | $i(v5) | ? [v12: $i] : ? [v13: $i] : ? [v14: any] : ? [v15: % 97.11/14.07 | $i] : ? [v16: $i] : ? [v17: $i] : ? [v18: $i] : ? [v19: any] % 97.11/14.07 | : ? [v20: any] : (hBOOL(v18) = v19 & hBOOL(v13) = v14 & % 97.11/14.07 | hBOOL(v11) = v20 & hAPP(v17, v7) = v18 & hAPP(v15, v5) = v16 & % 97.11/14.07 | hAPP(v12, c_Arrow__Order__Mirabelle_OLin) = v13 & hAPP(v4, v6) = % 97.11/14.07 | v15 & hAPP(v3, v16) = v17 & hAPP(v2, v7) = v12 & $i(v18) & % 97.11/14.07 | $i(v17) & $i(v16) & $i(v15) & $i(v13) & $i(v12) & ( ~ (v20 = 0) % 97.11/14.07 | | ~ (v19 = 0) | ~ (v14 = 0))))) % 97.11/14.07 | % 97.11/14.07 | ALPHA: (fact_notin__Lin__iff) implies: % 97.11/14.07 | (18) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 97.11/14.07 | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 97.11/14.07 | tc_Arrow__Order__Mirabelle_Oalt) = v4 & % 97.11/14.07 | tc_prod(tc_Arrow__Order__Mirabelle_Oalt, % 97.11/14.07 | tc_Arrow__Order__Mirabelle_Oalt) = v0 & tc_fun(v0, tc_HOL_Obool) = % 97.11/14.07 | v1 & c_member(v1) = v2 & c_member(v0) = v3 & $i(v4) & $i(v3) & % 97.11/14.07 | $i(v2) & $i(v1) & $i(v0) & ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : % 97.11/14.07 | ! [v8: $i] : ! [v9: $i] : ! [v10: $i] : ! [v11: $i] : (v6 = v5 | % 97.11/14.07 | ~ (hAPP(v10, v7) = v11) | ~ (hAPP(v8, v6) = v9) | ~ (hAPP(v4, % 97.11/14.07 | v5) = v8) | ~ (hAPP(v3, v9) = v10) | ~ $i(v7) | ~ $i(v6) | % 97.11/14.07 | ~ $i(v5) | ? [v12: $i] : ? [v13: $i] : ? [v14: any] : ? [v15: % 97.11/14.07 | $i] : ? [v16: $i] : ? [v17: $i] : ? [v18: $i] : ? [v19: any] % 97.11/14.07 | : ? [v20: any] : (hBOOL(v18) = v19 & hBOOL(v13) = v14 & % 97.11/14.07 | hBOOL(v11) = v20 & hAPP(v17, v7) = v18 & hAPP(v15, v5) = v16 & % 97.11/14.07 | hAPP(v12, c_Arrow__Order__Mirabelle_OLin) = v13 & hAPP(v4, v6) = % 97.11/14.07 | v15 & hAPP(v3, v16) = v17 & hAPP(v2, v7) = v12 & $i(v18) & % 97.11/14.07 | $i(v17) & $i(v16) & $i(v15) & $i(v13) & $i(v12) & ( ~ (v14 = 0) % 97.11/14.07 | | (( ~ (v20 = 0) | ~ (v19 = 0)) & (v20 = 0 | v19 = 0)))))) % 97.11/14.07 | % 97.11/14.07 | ALPHA: (fact_const__Lin__Prof) implies: % 97.11/14.08 | (19) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 97.11/14.08 | (tc_prod(tc_Arrow__Order__Mirabelle_Oalt, % 97.11/14.08 | tc_Arrow__Order__Mirabelle_Oalt) = v0 & tc_fun(v0, tc_HOL_Obool) = % 97.11/14.08 | v1 & tc_fun(tc_Arrow__Order__Mirabelle_Oindi, v1) = v3 & % 97.11/14.08 | c_member(v3) = v4 & c_member(v1) = v2 & $i(v4) & $i(v3) & $i(v2) & % 97.11/14.08 | $i(v1) & $i(v0) & ! [v5: $i] : ! [v6: $i] : ( ~ (c_COMBK(v1, % 97.11/14.08 | tc_Arrow__Order__Mirabelle_Oindi, v5) = v6) | ~ $i(v5) | ? % 97.11/14.08 | [v7: $i] : ? [v8: $i] : ? [v9: any] : ? [v10: $i] : ? [v11: % 97.11/14.08 | $i] : ? [v12: any] : (hBOOL(v11) = v12 & hBOOL(v8) = v9 & % 97.11/14.08 | hAPP(v10, c_Arrow__Order__Mirabelle_OProf) = v11 & hAPP(v7, % 97.11/14.08 | c_Arrow__Order__Mirabelle_OLin) = v8 & hAPP(v4, v6) = v10 & % 97.11/14.08 | hAPP(v2, v5) = v7 & $i(v11) & $i(v10) & $i(v8) & $i(v7) & ( ~ % 97.11/14.08 | (v9 = 0) | v12 = 0)))) % 97.11/14.08 | % 97.11/14.08 | ALPHA: (fact__C1_C) implies: % 97.11/14.08 | (20) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 97.11/14.08 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : % 97.11/14.08 | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 97.11/14.08 | tc_Arrow__Order__Mirabelle_Oalt) = v2 & % 97.11/14.08 | tc_prod(tc_Arrow__Order__Mirabelle_Oalt, % 97.11/14.08 | tc_Arrow__Order__Mirabelle_Oalt) = v0 & c_member(v0) = v1 & % 97.11/14.08 | hAPP(v6, v_b_H____) = v7 & hAPP(v3, v_b____) = v4 & hAPP(v2, % 97.11/14.08 | v_a____) = v3 & hAPP(v2, v_a_H____) = v6 & hAPP(v1, v7) = v8 & % 97.11/14.08 | hAPP(v1, v4) = v5 & $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) & % 97.11/14.08 | $i(v3) & $i(v2) & $i(v1) & $i(v0) & ! [v9: $i] : ! [v10: $i] : ( ~ % 97.11/14.08 | (hAPP(v_P_H____, v9) = v10) | ~ $i(v9) | ? [v11: $i] : ? [v12: % 97.11/14.08 | $i] : ? [v13: any] : ? [v14: $i] : ? [v15: any] : (hBOOL(v14) % 97.11/14.08 | = v15 & hBOOL(v12) = v13 & hAPP(v8, v10) = v14 & hAPP(v5, v11) = % 97.11/14.08 | v12 & hAPP(v_P____, v9) = v11 & $i(v14) & $i(v12) & $i(v11) & ( % 97.11/14.08 | ~ (v13 = 0) | v15 = 0))) & ! [v9: $i] : ! [v10: $i] : ( ~ % 97.11/14.08 | (hAPP(v_P_H____, v9) = v10) | ~ $i(v9) | ? [v11: $i] : ? [v12: % 97.11/14.08 | any] : ? [v13: $i] : ? [v14: $i] : ? [v15: any] : (hBOOL(v14) % 97.11/14.08 | = v15 & hBOOL(v11) = v12 & hAPP(v8, v10) = v11 & hAPP(v5, v13) = % 97.11/14.08 | v14 & hAPP(v_P____, v9) = v13 & $i(v14) & $i(v13) & $i(v11) & ( % 97.11/14.08 | ~ (v12 = 0) | v15 = 0)))) % 97.11/14.08 | % 97.11/14.08 | ALPHA: (fact__096a_A_060_092_060_094bsub_062F_AP_092_060_094esub_062_Ab_096) % 97.11/14.08 | implies: % 97.11/14.08 | (21) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 97.11/14.08 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : % 97.11/14.08 | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 97.11/14.08 | tc_Arrow__Order__Mirabelle_Oalt) = v2 & % 97.11/14.08 | tc_prod(tc_Arrow__Order__Mirabelle_Oalt, % 97.11/14.08 | tc_Arrow__Order__Mirabelle_Oalt) = v0 & c_member(v0) = v1 & % 97.11/14.08 | hBOOL(v7) = 0 & hAPP(v5, v6) = v7 & hAPP(v3, v_b____) = v4 & % 97.11/14.08 | hAPP(v2, v_a____) = v3 & hAPP(v1, v4) = v5 & hAPP(v_F, v_P____) = v6 % 97.11/14.08 | & $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & % 97.11/14.08 | $i(v0)) % 97.11/14.08 | % 97.11/14.08 | ALPHA: (fact_in__mktop) implies: % 97.11/14.08 | (22) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 97.11/14.08 | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 97.11/14.08 | tc_Arrow__Order__Mirabelle_Oalt) = v2 & % 97.11/14.08 | tc_prod(tc_Arrow__Order__Mirabelle_Oalt, % 97.11/14.08 | tc_Arrow__Order__Mirabelle_Oalt) = v0 & c_member(v0) = v1 & $i(v2) % 97.11/14.08 | & $i(v1) & $i(v0) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! % 97.11/14.08 | [v6: $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : ! [v10: $i] : % 97.11/14.08 | ! [v11: $i] : (v6 = v3 | ~ (c_Arrow__Order__Mirabelle_Omktop(v4, % 97.11/14.08 | v3) = v10) | ~ (hAPP(v9, v10) = v11) | ~ (hAPP(v7, v5) = v8) % 97.11/14.08 | | ~ (hAPP(v2, v6) = v7) | ~ (hAPP(v1, v8) = v9) | ~ $i(v6) | ~ % 97.11/14.08 | $i(v5) | ~ $i(v4) | ~ $i(v3) | ? [v12: $i] : ? [v13: any] : ? % 97.11/14.08 | [v14: any] : (hBOOL(v12) = v13 & hBOOL(v11) = v14 & hAPP(v9, v4) = % 97.11/14.08 | v12 & $i(v12) & (v14 = 0 | ( ~ (v13 = 0) & ~ (v5 = v3))))) & ! % 97.11/14.08 | [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : % 97.11/14.08 | ! [v8: $i] : ! [v9: $i] : ! [v10: $i] : ! [v11: $i] : ( ~ % 97.11/14.08 | (c_Arrow__Order__Mirabelle_Omktop(v4, v3) = v10) | ~ (hAPP(v9, % 97.11/14.08 | v10) = v11) | ~ (hAPP(v7, v5) = v8) | ~ (hAPP(v2, v6) = v7) % 97.11/14.08 | | ~ (hAPP(v1, v8) = v9) | ~ $i(v6) | ~ $i(v5) | ~ $i(v4) | ~ % 97.11/14.08 | $i(v3) | ? [v12: any] : ? [v13: $i] : ? [v14: any] : % 97.11/14.08 | (hBOOL(v13) = v14 & hBOOL(v11) = v12 & hAPP(v9, v4) = v13 & % 97.11/14.08 | $i(v13) & ( ~ (v12 = 0) | ( ~ (v6 = v3) & (v14 = 0 | v5 = % 97.11/14.08 | v3)))))) % 97.11/14.08 | % 97.11/14.08 | ALPHA: (fact_in__mkbot) implies: % 97.11/14.08 | (23) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 97.11/14.08 | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 97.11/14.08 | tc_Arrow__Order__Mirabelle_Oalt) = v2 & % 97.11/14.08 | tc_prod(tc_Arrow__Order__Mirabelle_Oalt, % 97.11/14.08 | tc_Arrow__Order__Mirabelle_Oalt) = v0 & c_member(v0) = v1 & $i(v2) % 97.11/14.08 | & $i(v1) & $i(v0) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! % 97.11/14.08 | [v6: $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : ! [v10: $i] : % 97.11/14.08 | ! [v11: $i] : (v5 = v3 | ~ (c_Arrow__Order__Mirabelle_Omkbot(v4, % 97.11/14.08 | v3) = v10) | ~ (hAPP(v9, v10) = v11) | ~ (hAPP(v7, v5) = v8) % 97.11/14.08 | | ~ (hAPP(v2, v6) = v7) | ~ (hAPP(v1, v8) = v9) | ~ $i(v6) | ~ % 97.11/14.08 | $i(v5) | ~ $i(v4) | ~ $i(v3) | ? [v12: $i] : ? [v13: any] : ? % 97.11/14.08 | [v14: any] : (hBOOL(v12) = v13 & hBOOL(v11) = v14 & hAPP(v9, v4) = % 97.11/14.08 | v12 & $i(v12) & (v14 = 0 | ( ~ (v13 = 0) & ~ (v6 = v3))))) & ! % 97.11/14.08 | [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : % 97.11/14.08 | ! [v8: $i] : ! [v9: $i] : ! [v10: $i] : ! [v11: $i] : ( ~ % 97.11/14.08 | (c_Arrow__Order__Mirabelle_Omkbot(v4, v3) = v10) | ~ (hAPP(v9, % 97.11/14.08 | v10) = v11) | ~ (hAPP(v7, v5) = v8) | ~ (hAPP(v2, v6) = v7) % 97.11/14.08 | | ~ (hAPP(v1, v8) = v9) | ~ $i(v6) | ~ $i(v5) | ~ $i(v4) | ~ % 97.11/14.08 | $i(v3) | ? [v12: any] : ? [v13: $i] : ? [v14: any] : % 97.11/14.08 | (hBOOL(v13) = v14 & hBOOL(v11) = v12 & hAPP(v9, v4) = v13 & % 97.11/14.08 | $i(v13) & ( ~ (v12 = 0) | ( ~ (v5 = v3) & (v14 = 0 | v6 = % 97.11/14.08 | v3)))))) % 97.11/14.08 | % 97.11/14.08 | ALPHA: (fact_dictatorI) implies: % 97.11/14.09 | (24) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 97.11/14.09 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : % 97.11/14.09 | ? [v10: $i] : (c_COMBK(v5, v2, c_Arrow__Order__Mirabelle_OLin) = v6 & % 97.11/14.09 | c_FuncSet_OPi(v2, v1, c_Arrow__Order__Mirabelle_OProf, v6) = v7 & % 97.11/14.09 | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 97.11/14.09 | tc_Arrow__Order__Mirabelle_Oalt) = v10 & % 97.11/14.09 | tc_prod(tc_Arrow__Order__Mirabelle_Oalt, % 97.11/14.09 | tc_Arrow__Order__Mirabelle_Oalt) = v0 & tc_fun(v2, v1) = v3 & % 97.11/14.09 | tc_fun(v1, tc_HOL_Obool) = v5 & tc_fun(v0, tc_HOL_Obool) = v1 & % 97.11/14.09 | tc_fun(tc_Arrow__Order__Mirabelle_Oindi, v1) = v2 & c_member(v3) = % 97.11/14.09 | v4 & c_member(v2) = v8 & c_member(v0) = v9 & $i(v10) & $i(v9) & % 97.11/14.09 | $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & % 97.11/14.09 | $i(v1) & $i(v0) & ! [v11: $i] : ! [v12: $i] : ! [v13: int] : (v13 % 97.11/14.09 | = 0 | ~ (c_Arrow__Order__Mirabelle_Odictator(v12, v11) = v13) | % 97.11/14.09 | ~ $i(v12) | ~ $i(v11) | ? [v14: $i] : ? [v15: $i] : ? [v16: % 97.11/14.09 | $i] : ? [v17: $i] : ? [v18: $i] : (hBOOL(v16) = 0 & hAPP(v15, % 97.11/14.09 | c_Arrow__Order__Mirabelle_OProf) = v16 & hAPP(v14, v11) = v17 % 97.11/14.09 | & hAPP(v12, v14) = v18 & hAPP(v8, v14) = v15 & $i(v18) & $i(v17) % 97.11/14.09 | & $i(v16) & $i(v15) & $i(v14) & ? [v19: $i] : ? [v20: $i] : ? % 97.11/14.09 | [v21: $i] : ? [v22: $i] : ? [v23: $i] : ? [v24: $i] : ? % 97.11/14.09 | [v25: $i] : ? [v26: int] : ( ~ (v26 = 0) & ~ (v20 = v19) & % 97.11/14.09 | hBOOL(v25) = v26 & hBOOL(v24) = 0 & hAPP(v23, v18) = v25 & % 97.11/14.09 | hAPP(v23, v17) = v24 & hAPP(v21, v20) = v22 & hAPP(v10, v19) = % 97.11/14.09 | v21 & hAPP(v9, v22) = v23 & $i(v25) & $i(v24) & $i(v23) & % 97.11/14.09 | $i(v22) & $i(v21) & $i(v20) & $i(v19))) | ? [v14: $i] : ? % 97.11/14.09 | [v15: $i] : ? [v16: int] : ( ~ (v16 = 0) & hBOOL(v15) = v16 & % 97.11/14.09 | hAPP(v14, v7) = v15 & hAPP(v4, v12) = v14 & $i(v15) & $i(v14)))) % 97.11/14.09 | % 97.11/14.09 | ALPHA: (fact_funcset__mem) implies: % 97.11/14.09 | (25) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 97.11/14.09 | ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : % 97.11/14.09 | ! [v10: $i] : ! [v11: $i] : ! [v12: $i] : ! [v13: $i] : ! [v14: % 97.11/14.09 | $i] : ! [v15: $i] : ! [v16: $i] : ( ~ (c_COMBK(v9, v5, v1) = v10) % 97.11/14.09 | | ~ (c_FuncSet_OPi(v5, v4, v2, v10) = v11) | ~ (tc_fun(v5, v4) = % 97.11/14.09 | v6) | ~ (tc_fun(v4, tc_HOL_Obool) = v9) | ~ (c_member(v6) = v7) % 97.11/14.09 | | ~ (c_member(v4) = v13) | ~ (hAPP(v15, v1) = v16) | ~ (hAPP(v13, % 97.11/14.09 | v14) = v15) | ~ (hAPP(v8, v11) = v12) | ~ (hAPP(v7, v3) = v8) % 97.11/14.09 | | ~ (hAPP(v3, v0) = v14) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ % 97.11/14.09 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v17: any] : ? [v18: $i] : ? % 97.11/14.09 | [v19: $i] : ? [v20: $i] : ? [v21: any] : ? [v22: any] : % 97.11/14.09 | (c_member(v5) = v18 & hBOOL(v20) = v21 & hBOOL(v16) = v22 & % 97.11/14.09 | hBOOL(v12) = v17 & hAPP(v19, v2) = v20 & hAPP(v18, v0) = v19 & % 97.11/14.09 | $i(v20) & $i(v19) & $i(v18) & ( ~ (v21 = 0) | ~ (v17 = 0) | v22 = % 97.11/14.09 | 0))) % 97.11/14.09 | % 97.11/14.09 | ALPHA: (fact_IIA__def) implies: % 97.11/14.09 | (26) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 97.11/14.09 | ? [v5: $i] : (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 97.11/14.09 | tc_Arrow__Order__Mirabelle_Oalt) = v5 & % 97.11/14.09 | tc_prod(tc_Arrow__Order__Mirabelle_Oalt, % 97.11/14.09 | tc_Arrow__Order__Mirabelle_Oalt) = v0 & tc_fun(v0, tc_HOL_Obool) = % 97.11/14.09 | v1 & tc_fun(tc_Arrow__Order__Mirabelle_Oindi, v1) = v2 & % 97.11/14.09 | c_member(v2) = v3 & c_member(v0) = v4 & $i(v5) & $i(v4) & $i(v3) & % 97.11/14.09 | $i(v2) & $i(v1) & $i(v0) & ! [v6: $i] : ! [v7: int] : (v7 = 0 | ~ % 97.11/14.09 | (c_Arrow__Order__Mirabelle_OIIA(v6) = v7) | ~ $i(v6) | ? [v8: % 97.11/14.09 | $i] : ? [v9: $i] : ? [v10: $i] : ? [v11: $i] : (hBOOL(v10) = % 97.11/14.09 | 0 & hAPP(v9, c_Arrow__Order__Mirabelle_OProf) = v10 & hAPP(v6, % 97.11/14.09 | v8) = v11 & hAPP(v3, v8) = v9 & $i(v11) & $i(v10) & $i(v9) & % 97.11/14.09 | $i(v8) & ? [v12: $i] : ? [v13: $i] : ? [v14: $i] : ? [v15: % 97.11/14.09 | $i] : (hBOOL(v14) = 0 & hAPP(v13, % 97.11/14.09 | c_Arrow__Order__Mirabelle_OProf) = v14 & hAPP(v6, v12) = v15 % 97.11/14.09 | & hAPP(v3, v12) = v13 & $i(v15) & $i(v14) & $i(v13) & $i(v12) % 97.11/14.09 | & ? [v16: $i] : ? [v17: $i] : ? [v18: $i] : ? [v19: $i] : % 97.11/14.09 | ? [v20: $i] : ? [v21: $i] : ? [v22: any] : ? [v23: $i] : ? % 97.11/14.09 | [v24: any] : (hBOOL(v23) = v24 & hBOOL(v21) = v22 & hAPP(v20, % 97.11/14.09 | v15) = v23 & hAPP(v20, v11) = v21 & hAPP(v18, v17) = v19 & % 97.11/14.09 | hAPP(v5, v16) = v18 & hAPP(v4, v19) = v20 & $i(v23) & % 97.11/14.09 | $i(v21) & $i(v20) & $i(v19) & $i(v18) & $i(v17) & $i(v16) & % 97.11/14.09 | ! [v25: $i] : ! [v26: $i] : ! [v27: $i] : ( ~ (hAPP(v20, % 97.11/14.09 | v26) = v27) | ~ (hAPP(v8, v25) = v26) | ~ $i(v25) | % 97.11/14.09 | ? [v28: any] : ? [v29: $i] : ? [v30: $i] : ? [v31: any] % 97.11/14.09 | : (hBOOL(v30) = v31 & hBOOL(v27) = v28 & hAPP(v20, v29) = % 97.11/14.09 | v30 & hAPP(v12, v25) = v29 & $i(v30) & $i(v29) & ( ~ % 97.11/14.09 | (v28 = 0) | v31 = 0))) & ! [v25: $i] : ! [v26: $i] : % 97.11/14.09 | ! [v27: $i] : ( ~ (hAPP(v20, v26) = v27) | ~ (hAPP(v8, % 97.11/14.09 | v25) = v26) | ~ $i(v25) | ? [v28: $i] : ? [v29: $i] % 97.11/14.09 | : ? [v30: any] : ? [v31: any] : (hBOOL(v29) = v30 & % 97.11/14.09 | hBOOL(v27) = v31 & hAPP(v20, v28) = v29 & hAPP(v12, v25) % 97.11/14.09 | = v28 & $i(v29) & $i(v28) & ( ~ (v30 = 0) | v31 = 0))) & % 97.11/14.09 | ( ~ (v24 = 0) | ~ (v22 = 0)) & (v24 = 0 | v22 = 0))))) & ! % 97.11/14.09 | [v6: $i] : ( ~ (c_Arrow__Order__Mirabelle_OIIA(v6) = 0) | ~ $i(v6) % 97.11/14.09 | | ! [v7: $i] : ! [v8: $i] : ( ~ (hAPP(v3, v7) = v8) | ~ $i(v7) % 97.11/14.09 | | ? [v9: $i] : ? [v10: any] : ? [v11: $i] : (hBOOL(v9) = v10 % 97.11/14.09 | & hAPP(v8, c_Arrow__Order__Mirabelle_OProf) = v9 & hAPP(v6, % 97.11/14.09 | v7) = v11 & $i(v11) & $i(v9) & ( ~ (v10 = 0) | ! [v12: $i] % 97.11/14.09 | : ! [v13: $i] : ( ~ (hAPP(v3, v12) = v13) | ~ $i(v12) | ? % 97.11/14.09 | [v14: $i] : ? [v15: any] : ? [v16: $i] : (hBOOL(v14) = % 97.11/14.09 | v15 & hAPP(v13, c_Arrow__Order__Mirabelle_OProf) = v14 & % 97.11/14.09 | hAPP(v6, v12) = v16 & $i(v16) & $i(v14) & ( ~ (v15 = 0) % 97.11/14.09 | | ! [v17: $i] : ! [v18: $i] : ! [v19: $i] : ! % 97.11/14.09 | [v20: $i] : ! [v21: $i] : ! [v22: $i] : ( ~ % 97.11/14.09 | (hAPP(v21, v11) = v22) | ~ (hAPP(v19, v18) = v20) | % 97.11/14.09 | ~ (hAPP(v5, v17) = v19) | ~ (hAPP(v4, v20) = v21) % 97.11/14.09 | | ~ $i(v18) | ~ $i(v17) | ? [v23: $i] : ? [v24: % 97.11/14.09 | $i] : ? [v25: $i] : ? [v26: any] : ? [v27: $i] % 97.11/14.09 | : ? [v28: $i] : ? [v29: any] : (hBOOL(v28) = v29 & % 97.11/14.09 | hBOOL(v25) = v26 & hAPP(v21, v27) = v28 & % 97.11/14.09 | hAPP(v21, v24) = v25 & hAPP(v12, v23) = v27 & % 97.11/14.09 | hAPP(v7, v23) = v24 & $i(v28) & $i(v27) & $i(v25) % 97.11/14.09 | & $i(v24) & $i(v23) & ( ~ (v29 = 0) | ~ (v26 = % 97.11/14.09 | 0)) & (v29 = 0 | v26 = 0)) | ? [v23: any] : % 97.11/14.09 | ? [v24: $i] : ? [v25: any] : (hBOOL(v24) = v25 & % 97.11/14.09 | hBOOL(v22) = v23 & hAPP(v21, v16) = v24 & $i(v24) % 97.11/14.09 | & ( ~ (v25 = 0) | v23 = 0) & ( ~ (v23 = 0) | v25 = % 97.11/14.09 | 0))))))))))) % 97.11/14.09 | % 97.11/14.09 | ALPHA: (fact_unanimity__def) implies: % 97.11/14.10 | (27) $i(tc_Arrow__Order__Mirabelle_Oindi) % 97.11/14.10 | (28) $i(c_Arrow__Order__Mirabelle_OProf) % 97.11/14.10 | (29) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 97.11/14.10 | ? [v5: $i] : (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 97.11/14.10 | tc_Arrow__Order__Mirabelle_Oalt) = v5 & % 97.11/14.10 | tc_prod(tc_Arrow__Order__Mirabelle_Oalt, % 97.11/14.10 | tc_Arrow__Order__Mirabelle_Oalt) = v0 & tc_fun(v0, tc_HOL_Obool) = % 97.11/14.10 | v1 & tc_fun(tc_Arrow__Order__Mirabelle_Oindi, v1) = v2 & % 97.11/14.10 | c_member(v2) = v3 & c_member(v0) = v4 & $i(v5) & $i(v4) & $i(v3) & % 97.11/14.10 | $i(v2) & $i(v1) & $i(v0) & ! [v6: $i] : ! [v7: int] : (v7 = 0 | ~ % 97.11/14.10 | (c_Arrow__Order__Mirabelle_Ounanimity(v6) = v7) | ~ $i(v6) | ? % 97.11/14.10 | [v8: $i] : ? [v9: $i] : ? [v10: $i] : ? [v11: $i] : (hBOOL(v10) % 97.11/14.10 | = 0 & hAPP(v9, c_Arrow__Order__Mirabelle_OProf) = v10 & hAPP(v6, % 97.11/14.10 | v8) = v11 & hAPP(v3, v8) = v9 & $i(v11) & $i(v10) & $i(v9) & % 97.11/14.10 | $i(v8) & ? [v12: $i] : ? [v13: $i] : ? [v14: $i] : ? [v15: % 97.11/14.10 | $i] : ? [v16: $i] : ? [v17: $i] : ? [v18: int] : ( ~ (v18 = % 97.11/14.10 | 0) & hBOOL(v17) = v18 & hAPP(v16, v11) = v17 & hAPP(v14, % 97.11/14.10 | v13) = v15 & hAPP(v5, v12) = v14 & hAPP(v4, v15) = v16 & % 97.11/14.10 | $i(v17) & $i(v16) & $i(v15) & $i(v14) & $i(v13) & $i(v12) & ! % 97.11/14.10 | [v19: $i] : ! [v20: $i] : ! [v21: $i] : ( ~ (hAPP(v16, v20) % 97.11/14.10 | = v21) | ~ (hAPP(v8, v19) = v20) | ~ $i(v19) | % 97.11/14.10 | hBOOL(v21) = 0)))) & ! [v6: $i] : ( ~ % 97.11/14.10 | (c_Arrow__Order__Mirabelle_Ounanimity(v6) = 0) | ~ $i(v6) | ! % 97.11/14.10 | [v7: $i] : ! [v8: $i] : ( ~ (hAPP(v3, v7) = v8) | ~ $i(v7) | ? % 97.11/14.10 | [v9: $i] : ? [v10: any] : ? [v11: $i] : (hBOOL(v9) = v10 & % 97.11/14.10 | hAPP(v8, c_Arrow__Order__Mirabelle_OProf) = v9 & hAPP(v6, v7) % 97.11/14.10 | = v11 & $i(v11) & $i(v9) & ( ~ (v10 = 0) | ! [v12: $i] : ! % 97.11/14.10 | [v13: $i] : ! [v14: $i] : ! [v15: $i] : ! [v16: $i] : ! % 97.11/14.10 | [v17: $i] : ( ~ (hAPP(v16, v11) = v17) | ~ (hAPP(v14, v13) % 97.11/14.10 | = v15) | ~ (hAPP(v5, v12) = v14) | ~ (hAPP(v4, v15) = % 97.11/14.10 | v16) | ~ $i(v13) | ~ $i(v12) | hBOOL(v17) = 0 | ? % 97.11/14.10 | [v18: $i] : ? [v19: $i] : ? [v20: $i] : ? [v21: int] : % 97.11/14.10 | ( ~ (v21 = 0) & hBOOL(v20) = v21 & hAPP(v16, v19) = v20 & % 97.11/14.10 | hAPP(v7, v18) = v19 & $i(v20) & $i(v19) & $i(v18)))))))) % 97.11/14.10 | % 97.11/14.10 | ALPHA: (fact_complete__Lin) implies: % 97.11/14.10 | (30) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 97.11/14.10 | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 97.11/14.10 | tc_Arrow__Order__Mirabelle_Oalt) = v4 & % 97.11/14.10 | tc_prod(tc_Arrow__Order__Mirabelle_Oalt, % 97.11/14.10 | tc_Arrow__Order__Mirabelle_Oalt) = v0 & tc_fun(v0, tc_HOL_Obool) = % 97.11/14.10 | v1 & c_member(v1) = v2 & c_member(v0) = v3 & $i(v4) & $i(v3) & % 97.11/14.10 | $i(v2) & $i(v1) & $i(v0) & ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : % 97.11/14.10 | ! [v8: $i] : (v6 = v5 | ~ (hAPP(v7, v5) = v8) | ~ (hAPP(v4, v6) = % 97.11/14.10 | v7) | ~ $i(v6) | ~ $i(v5) | ? [v9: $i] : (hAPP(v3, v8) = v9 & % 97.11/14.10 | $i(v9) & ? [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13: % 97.11/14.10 | $i] : (hBOOL(v13) = 0 & hBOOL(v12) = 0 & hAPP(v11, % 97.11/14.10 | c_Arrow__Order__Mirabelle_OLin) = v12 & hAPP(v9, v10) = v13 % 97.11/14.10 | & hAPP(v2, v10) = v11 & $i(v13) & $i(v12) & $i(v11) & % 97.11/14.10 | $i(v10))))) % 97.11/14.10 | % 97.11/14.10 | ALPHA: (fact_compose__Id) implies: % 97.11/14.10 | (31) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 97.11/14.10 | ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : % 97.11/14.10 | ! [v10: $i] : ! [v11: $i] : ( ~ (c_COMBK(v8, v4, v0) = v9) | ~ % 97.11/14.10 | (c_FuncSet_OPi(v4, v3, v1, v9) = v10) | ~ (tc_fun(v4, v3) = v5) | % 97.11/14.10 | ~ (tc_fun(v3, tc_HOL_Obool) = v8) | ~ (c_member(v5) = v6) | ~ % 97.11/14.10 | (hAPP(v7, v10) = v11) | ~ (hAPP(v6, v2) = v7) | ~ $i(v4) | ~ % 97.11/14.10 | $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v12: any] : ? % 97.11/14.10 | [v13: $i] : ? [v14: $i] : ? [v15: any] : ? [v16: $i] : ? [v17: % 97.11/14.10 | $i] : ? [v18: $i] : (c_FuncSet_Orestrict(v4, v4, v16, v1) = v17 & % 97.11/14.10 | c_FuncSet_Oextensional(v4, v3, v1) = v13 & c_FuncSet_Ocompose(v4, % 97.11/14.10 | v4, v3, v1, v2, v17) = v18 & c_COMBI(v4) = v16 & hBOOL(v14) = % 97.11/14.10 | v15 & hBOOL(v11) = v12 & hAPP(v7, v13) = v14 & $i(v18) & $i(v17) & % 97.11/14.10 | $i(v16) & $i(v14) & $i(v13) & ( ~ (v15 = 0) | ~ (v12 = 0) | v18 = % 97.11/14.10 | v2))) % 97.11/14.10 | % 97.11/14.10 | ALPHA: (fact_Id__compose) implies: % 97.11/14.10 | (32) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 97.11/14.10 | ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : % 97.11/14.10 | ! [v10: $i] : ! [v11: $i] : ( ~ (c_COMBK(v8, v4, v0) = v9) | ~ % 97.11/14.10 | (c_FuncSet_OPi(v4, v3, v1, v9) = v10) | ~ (tc_fun(v4, v3) = v5) | % 97.11/14.10 | ~ (tc_fun(v3, tc_HOL_Obool) = v8) | ~ (c_member(v5) = v6) | ~ % 97.11/14.10 | (hAPP(v7, v10) = v11) | ~ (hAPP(v6, v2) = v7) | ~ $i(v4) | ~ % 97.11/14.10 | $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v12: any] : ? % 97.11/14.10 | [v13: $i] : ? [v14: $i] : ? [v15: any] : ? [v16: $i] : ? [v17: % 97.11/14.10 | $i] : ? [v18: $i] : (c_FuncSet_Orestrict(v3, v3, v16, v0) = v17 & % 97.11/14.10 | c_FuncSet_Oextensional(v4, v3, v1) = v13 & c_FuncSet_Ocompose(v4, % 97.11/14.10 | v3, v3, v1, v17, v2) = v18 & c_COMBI(v3) = v16 & hBOOL(v14) = % 97.11/14.10 | v15 & hBOOL(v11) = v12 & hAPP(v7, v13) = v14 & $i(v18) & $i(v17) & % 97.11/14.10 | $i(v16) & $i(v14) & $i(v13) & ( ~ (v15 = 0) | ~ (v12 = 0) | v18 = % 97.11/14.10 | v2))) % 97.11/14.10 | % 97.11/14.10 | ALPHA: (fact_equals0D) implies: % 97.11/14.10 | (33) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 97.11/14.10 | ! [v5: $i] : ( ~ (c_member(v1) = v3) | ~ (hAPP(v4, v2) = v5) | ~ % 97.11/14.10 | (hAPP(v3, v0) = v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: % 97.11/14.10 | $i] : ? [v7: $i] : ? [v8: any] : % 97.11/14.10 | (c_Orderings_Obot__class_Obot(v6) = v7 & tc_fun(v1, tc_HOL_Obool) = % 97.11/14.10 | v6 & hBOOL(v5) = v8 & $i(v7) & $i(v6) & ( ~ (v8 = 0) | ~ (v7 = % 97.11/14.10 | v2)))) % 97.11/14.10 | % 97.11/14.10 | ALPHA: (fact_Pi__eq__empty) implies: % 97.11/14.10 | (34) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 97.11/14.10 | ( ~ (c_FuncSet_OPi(v3, v2, v1, v0) = v4) | ~ $i(v3) | ~ $i(v2) | ~ % 97.11/14.10 | $i(v1) | ~ $i(v0) | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? % 97.11/14.10 | [v8: $i] : ? [v9: $i] : ? [v10: $i] : % 97.11/14.10 | (c_Orderings_Obot__class_Obot(v9) = v10 & % 97.11/14.10 | c_Orderings_Obot__class_Obot(v6) = v7 & tc_fun(v5, tc_HOL_Obool) = % 97.11/14.10 | v6 & tc_fun(v3, v2) = v5 & tc_fun(v2, tc_HOL_Obool) = v9 & % 97.11/14.10 | c_member(v3) = v8 & $i(v10) & $i(v9) & $i(v8) & $i(v7) & $i(v6) & % 97.11/14.10 | $i(v5) & ( ~ (v7 = v4) | ? [v11: $i] : ? [v12: $i] : ? [v13: % 97.11/14.10 | $i] : (hBOOL(v13) = 0 & hAPP(v12, v1) = v13 & hAPP(v8, v11) = % 97.11/14.10 | v12 & hAPP(v0, v11) = v10 & $i(v13) & $i(v12) & $i(v11))))) % 97.11/14.10 | (35) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 97.11/14.10 | ( ~ (c_FuncSet_OPi(v3, v2, v1, v0) = v4) | ~ $i(v3) | ~ $i(v2) | ~ % 97.11/14.10 | $i(v1) | ~ $i(v0) | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? % 97.11/14.10 | [v8: $i] : ? [v9: $i] : ? [v10: $i] : % 97.11/14.10 | (c_Orderings_Obot__class_Obot(v9) = v10 & % 97.11/14.10 | c_Orderings_Obot__class_Obot(v6) = v7 & tc_fun(v8, tc_HOL_Obool) = % 97.11/14.10 | v9 & tc_fun(v3, v2) = v8 & tc_fun(v2, tc_HOL_Obool) = v6 & % 97.11/14.10 | c_member(v3) = v5 & $i(v10) & $i(v9) & $i(v8) & $i(v7) & $i(v6) & % 97.11/14.10 | $i(v5) & (v10 = v4 | ! [v11: $i] : ! [v12: $i] : ! [v13: $i] : % 97.11/14.10 | ( ~ (hAPP(v12, v1) = v13) | ~ (hAPP(v5, v11) = v12) | ~ % 97.11/14.10 | $i(v11) | ? [v14: any] : ? [v15: $i] : (hBOOL(v13) = v14 & % 97.11/14.10 | hAPP(v0, v11) = v15 & $i(v15) & ( ~ (v15 = v7) | ~ (v14 = % 97.11/14.10 | 0))))))) % 97.11/14.10 | % 97.11/14.10 | ALPHA: (fact_funcset__image) implies: % 97.11/14.10 | (36) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 97.11/14.10 | ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : % 97.11/14.10 | ! [v10: $i] : ! [v11: $i] : ( ~ (c_COMBK(v8, v4, v0) = v9) | ~ % 97.11/14.10 | (c_FuncSet_OPi(v4, v3, v1, v9) = v10) | ~ (tc_fun(v4, v3) = v5) | % 97.11/14.10 | ~ (tc_fun(v3, tc_HOL_Obool) = v8) | ~ (c_member(v5) = v6) | ~ % 97.11/14.10 | (hAPP(v7, v10) = v11) | ~ (hAPP(v6, v2) = v7) | ~ $i(v4) | ~ % 97.11/14.10 | $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v12: any] : ? % 97.11/14.10 | [v13: $i] : ? [v14: any] : (c_Orderings_Oord__class_Oless__eq(v8, % 97.11/14.10 | v13, v0) = v14 & c_Set_Oimage(v4, v3, v2, v1) = v13 & hBOOL(v11) % 97.11/14.10 | = v12 & $i(v13) & ( ~ (v12 = 0) | v14 = 0))) % 97.11/14.10 | % 97.11/14.10 | ALPHA: (fact_the__inv__into__def) implies: % 97.11/14.10 | (37) ? [v0: $i] : (tc_fun(tc_HOL_Obool, tc_HOL_Obool) = v0 & $i(v0) & ! % 97.11/14.10 | [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : % 97.11/14.10 | ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : ! [v10: $i] % 97.11/14.10 | : ! [v11: $i] : ! [v12: $i] : ! [v13: $i] : ! [v14: $i] : ! % 97.11/14.10 | [v15: $i] : ! [v16: $i] : ! [v17: $i] : ! [v18: $i] : ! [v19: % 97.11/14.10 | $i] : ! [v20: $i] : ! [v21: $i] : ! [v22: $i] : ( ~ % 97.11/14.10 | (c_HOL_OThe(v5, v21) = v22) | ~ (c_COMBB(v4, v16, v5, c_fequal) = % 97.11/14.10 | v17) | ~ (c_COMBB(tc_HOL_Obool, v0, v5, c_fconj) = v7) | ~ % 97.11/14.10 | (c_COMBS(v5, tc_HOL_Obool, tc_HOL_Obool) = v6) | ~ (c_COMBC(v5, % 97.11/14.10 | v8, tc_HOL_Obool) = v9) | ~ (c_COMBC(v5, v4, tc_HOL_Obool) = % 97.11/14.10 | v15) | ~ (tc_fun(v5, tc_HOL_Obool) = v8) | ~ (tc_fun(v4, % 97.11/14.10 | tc_HOL_Obool) = v16) | ~ (c_member(v5) = v10) | ~ (hAPP(v19, % 97.11/14.10 | v1) = v20) | ~ (hAPP(v17, v2) = v18) | ~ (hAPP(v15, v18) = % 97.11/14.10 | v19) | ~ (hAPP(v14, v20) = v21) | ~ (hAPP(v11, v3) = v12) | ~ % 97.11/14.10 | (hAPP(v9, v10) = v11) | ~ (hAPP(v7, v12) = v13) | ~ (hAPP(v6, % 97.11/14.10 | v13) = v14) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | % 97.11/14.10 | ~ $i(v1) | ? [v23: $i] : (c_Fun_Othe__inv__into(v5, v4, v3, v2) = % 97.11/14.10 | v23 & hAPP(v23, v1) = v22 & $i(v23) & $i(v22)))) % 97.11/14.10 | % 97.11/14.10 | ALPHA: (arity_HOL__Obool__Orderings_Obot) implies: % 97.11/14.10 | (38) class_Orderings_Obot(tc_HOL_Obool) = 0 % 97.11/14.10 | % 97.11/14.10 | ALPHA: (conj_0) implies: % 97.11/14.10 | (39) $i(v_F) % 97.11/14.10 | (40) $i(tc_Arrow__Order__Mirabelle_Oalt) % 97.11/14.10 | (41) $i(tc_HOL_Obool) % 97.11/14.10 | (42) $i(v_Q____) % 97.11/14.10 | (43) $i(c_Arrow__Order__Mirabelle_OLin) % 97.11/14.11 | (44) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 97.11/14.11 | ? [v5: $i] : ? [v6: int] : ( ~ (v6 = 0) & % 97.11/14.11 | tc_prod(tc_Arrow__Order__Mirabelle_Oalt, % 97.11/14.11 | tc_Arrow__Order__Mirabelle_Oalt) = v0 & tc_fun(v0, tc_HOL_Obool) = % 97.11/14.11 | v1 & c_member(v1) = v2 & hBOOL(v5) = v6 & hAPP(v4, % 97.11/14.11 | c_Arrow__Order__Mirabelle_OLin) = v5 & hAPP(v2, v3) = v4 & % 97.11/14.11 | hAPP(v_F, v_Q____) = v3 & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) % 97.11/14.11 | & $i(v0)) % 97.11/14.11 | % 97.11/14.11 | ALPHA: (function-axioms) implies: % 97.11/14.11 | (45) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 97.11/14.11 | : (v1 = v0 | ~ (hBOOL(v2) = v1) | ~ (hBOOL(v2) = v0)) % 97.11/14.11 | (46) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (c_member(v2) % 97.11/14.11 | = v1) | ~ (c_member(v2) = v0)) % 97.11/14.11 | (47) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 97.11/14.11 | : (v1 = v0 | ~ (class_Orderings_Obot(v2) = v1) | ~ % 97.11/14.11 | (class_Orderings_Obot(v2) = v0)) % 97.11/14.11 | (48) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 97.11/14.11 | (hAPP(v3, v2) = v1) | ~ (hAPP(v3, v2) = v0)) % 97.11/14.11 | (49) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 97.11/14.11 | (tc_fun(v3, v2) = v1) | ~ (tc_fun(v3, v2) = v0)) % 97.11/14.11 | (50) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 97.11/14.11 | (tc_prod(v3, v2) = v1) | ~ (tc_prod(v3, v2) = v0)) % 97.11/14.11 | (51) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 97.11/14.11 | (v1 = v0 | ~ (c_COMBK(v4, v3, v2) = v1) | ~ (c_COMBK(v4, v3, v2) = % 97.11/14.11 | v0)) % 97.11/14.11 | (52) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 97.11/14.11 | ! [v5: $i] : (v1 = v0 | ~ (c_FuncSet_OPi(v5, v4, v3, v2) = v1) | ~ % 97.11/14.11 | (c_FuncSet_OPi(v5, v4, v3, v2) = v0)) % 97.11/14.11 | % 97.11/14.11 | DELTA: instantiating (6) with fresh symbols all_480_0, all_480_1, all_480_2 % 97.11/14.11 | gives: % 97.11/14.11 | (53) tc_prod(tc_Arrow__Order__Mirabelle_Oalt, % 97.11/14.11 | tc_Arrow__Order__Mirabelle_Oalt) = all_480_2 & tc_fun(all_480_2, % 97.11/14.11 | tc_HOL_Obool) = all_480_1 & c_member(all_480_1) = all_480_0 & % 97.11/14.11 | $i(all_480_0) & $i(all_480_1) & $i(all_480_2) & ? [v0: $i] : ? [v1: % 97.11/14.11 | $i] : ? [v2: $i] : (hBOOL(v2) = 0 & hAPP(v1, % 97.11/14.11 | c_Arrow__Order__Mirabelle_OLin) = v2 & hAPP(all_480_0, v0) = v1 & % 97.11/14.11 | $i(v2) & $i(v1) & $i(v0)) % 97.11/14.11 | % 97.11/14.11 | ALPHA: (53) implies: % 97.11/14.11 | (54) c_member(all_480_1) = all_480_0 % 97.11/14.11 | (55) tc_fun(all_480_2, tc_HOL_Obool) = all_480_1 % 97.11/14.11 | (56) tc_prod(tc_Arrow__Order__Mirabelle_Oalt, % 97.11/14.11 | tc_Arrow__Order__Mirabelle_Oalt) = all_480_2 % 97.11/14.11 | % 97.11/14.11 | DELTA: instantiating (10) with fresh symbols all_482_0, all_482_1, all_482_2, % 97.11/14.11 | all_482_3, all_482_4, all_482_5 gives: % 97.11/14.11 | (57) tc_prod(tc_Arrow__Order__Mirabelle_Oalt, % 97.11/14.11 | tc_Arrow__Order__Mirabelle_Oalt) = all_482_5 & tc_fun(all_482_5, % 97.11/14.11 | tc_HOL_Obool) = all_482_4 & tc_fun(tc_Arrow__Order__Mirabelle_Oindi, % 97.11/14.11 | all_482_4) = all_482_3 & c_member(all_482_3) = all_482_2 & % 97.11/14.11 | hBOOL(all_482_0) = 0 & hAPP(all_482_1, % 97.11/14.11 | c_Arrow__Order__Mirabelle_OProf) = all_482_0 & hAPP(all_482_2, % 97.11/14.11 | v_P____) = all_482_1 & $i(all_482_0) & $i(all_482_1) & $i(all_482_2) % 97.11/14.11 | & $i(all_482_3) & $i(all_482_4) & $i(all_482_5) % 97.11/14.11 | % 97.11/14.11 | ALPHA: (57) implies: % 97.11/14.11 | (58) $i(all_482_5) % 97.11/14.11 | (59) $i(all_482_4) % 97.11/14.11 | (60) c_member(all_482_3) = all_482_2 % 97.11/14.11 | (61) tc_fun(tc_Arrow__Order__Mirabelle_Oindi, all_482_4) = all_482_3 % 97.11/14.11 | (62) tc_fun(all_482_5, tc_HOL_Obool) = all_482_4 % 97.11/14.11 | (63) tc_prod(tc_Arrow__Order__Mirabelle_Oalt, % 97.11/14.11 | tc_Arrow__Order__Mirabelle_Oalt) = all_482_5 % 97.11/14.11 | % 97.11/14.11 | DELTA: instantiating (9) with fresh symbols all_484_0, all_484_1, all_484_2, % 97.11/14.11 | all_484_3, all_484_4, all_484_5 gives: % 97.11/14.11 | (64) tc_prod(tc_Arrow__Order__Mirabelle_Oalt, % 97.11/14.11 | tc_Arrow__Order__Mirabelle_Oalt) = all_484_5 & tc_fun(all_484_5, % 97.11/14.11 | tc_HOL_Obool) = all_484_4 & tc_fun(tc_Arrow__Order__Mirabelle_Oindi, % 97.11/14.11 | all_484_4) = all_484_3 & c_member(all_484_3) = all_484_2 & % 97.11/14.11 | hBOOL(all_484_0) = 0 & hAPP(all_484_1, % 97.11/14.11 | c_Arrow__Order__Mirabelle_OProf) = all_484_0 & hAPP(all_484_2, % 97.11/14.11 | v_P_H____) = all_484_1 & $i(all_484_0) & $i(all_484_1) & % 97.11/14.11 | $i(all_484_2) & $i(all_484_3) & $i(all_484_4) & $i(all_484_5) % 97.11/14.11 | % 97.11/14.11 | ALPHA: (64) implies: % 97.11/14.11 | (65) $i(all_484_3) % 97.11/14.11 | (66) c_member(all_484_3) = all_484_2 % 97.11/14.11 | (67) tc_fun(tc_Arrow__Order__Mirabelle_Oindi, all_484_4) = all_484_3 % 97.11/14.11 | (68) tc_fun(all_484_5, tc_HOL_Obool) = all_484_4 % 97.11/14.11 | (69) tc_prod(tc_Arrow__Order__Mirabelle_Oalt, % 97.11/14.11 | tc_Arrow__Order__Mirabelle_Oalt) = all_484_5 % 97.11/14.11 | % 97.11/14.11 | DELTA: instantiating (1) with fresh symbols all_486_0, all_486_1, all_486_2, % 97.11/14.11 | all_486_3, all_486_4, all_486_5 gives: % 97.11/14.11 | (70) tc_prod(tc_Arrow__Order__Mirabelle_Oalt, % 97.11/14.11 | tc_Arrow__Order__Mirabelle_Oalt) = all_486_5 & tc_fun(all_486_5, % 97.11/14.11 | tc_HOL_Obool) = all_486_4 & tc_fun(tc_Arrow__Order__Mirabelle_Oindi, % 97.11/14.11 | all_486_4) = all_486_3 & c_member(all_486_3) = all_486_2 & % 97.11/14.11 | hBOOL(all_486_0) = 0 & hAPP(all_486_1, % 97.11/14.11 | c_Arrow__Order__Mirabelle_OProf) = all_486_0 & hAPP(all_486_2, % 97.11/14.11 | v_Q____) = all_486_1 & $i(all_486_0) & $i(all_486_1) & $i(all_486_2) % 97.11/14.11 | & $i(all_486_3) & $i(all_486_4) & $i(all_486_5) % 97.11/14.11 | % 97.11/14.11 | ALPHA: (70) implies: % 97.11/14.11 | (71) hAPP(all_486_2, v_Q____) = all_486_1 % 97.11/14.11 | (72) hAPP(all_486_1, c_Arrow__Order__Mirabelle_OProf) = all_486_0 % 97.11/14.11 | (73) hBOOL(all_486_0) = 0 % 97.11/14.11 | (74) c_member(all_486_3) = all_486_2 % 97.11/14.11 | (75) tc_fun(tc_Arrow__Order__Mirabelle_Oindi, all_486_4) = all_486_3 % 97.11/14.11 | (76) tc_fun(all_486_5, tc_HOL_Obool) = all_486_4 % 97.11/14.11 | (77) tc_prod(tc_Arrow__Order__Mirabelle_Oalt, % 97.11/14.11 | tc_Arrow__Order__Mirabelle_Oalt) = all_486_5 % 97.11/14.11 | % 97.11/14.11 | DELTA: instantiating (44) with fresh symbols all_492_0, all_492_1, all_492_2, % 97.11/14.11 | all_492_3, all_492_4, all_492_5, all_492_6 gives: % 97.11/14.11 | (78) ~ (all_492_0 = 0) & tc_prod(tc_Arrow__Order__Mirabelle_Oalt, % 97.11/14.11 | tc_Arrow__Order__Mirabelle_Oalt) = all_492_6 & tc_fun(all_492_6, % 97.11/14.11 | tc_HOL_Obool) = all_492_5 & c_member(all_492_5) = all_492_4 & % 97.11/14.11 | hBOOL(all_492_1) = all_492_0 & hAPP(all_492_2, % 97.11/14.11 | c_Arrow__Order__Mirabelle_OLin) = all_492_1 & hAPP(all_492_4, % 97.11/14.11 | all_492_3) = all_492_2 & hAPP(v_F, v_Q____) = all_492_3 & % 97.11/14.11 | $i(all_492_1) & $i(all_492_2) & $i(all_492_3) & $i(all_492_4) & % 97.11/14.11 | $i(all_492_5) & $i(all_492_6) % 97.11/14.11 | % 97.11/14.11 | ALPHA: (78) implies: % 97.11/14.11 | (79) ~ (all_492_0 = 0) % 97.11/14.11 | (80) hAPP(v_F, v_Q____) = all_492_3 % 97.11/14.11 | (81) hAPP(all_492_4, all_492_3) = all_492_2 % 97.11/14.11 | (82) hAPP(all_492_2, c_Arrow__Order__Mirabelle_OLin) = all_492_1 % 97.11/14.11 | (83) hBOOL(all_492_1) = all_492_0 % 97.11/14.11 | (84) c_member(all_492_5) = all_492_4 % 97.11/14.11 | (85) tc_fun(all_492_6, tc_HOL_Obool) = all_492_5 % 97.11/14.11 | (86) tc_prod(tc_Arrow__Order__Mirabelle_Oalt, % 97.11/14.11 | tc_Arrow__Order__Mirabelle_Oalt) = all_492_6 % 97.11/14.11 | % 97.11/14.11 | DELTA: instantiating (21) with fresh symbols all_498_0, all_498_1, all_498_2, % 97.11/14.11 | all_498_3, all_498_4, all_498_5, all_498_6, all_498_7 gives: % 97.11/14.11 | (87) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 97.11/14.11 | tc_Arrow__Order__Mirabelle_Oalt) = all_498_5 & % 97.11/14.11 | tc_prod(tc_Arrow__Order__Mirabelle_Oalt, % 97.11/14.11 | tc_Arrow__Order__Mirabelle_Oalt) = all_498_7 & c_member(all_498_7) = % 97.11/14.11 | all_498_6 & hBOOL(all_498_0) = 0 & hAPP(all_498_2, all_498_1) = % 97.11/14.11 | all_498_0 & hAPP(all_498_4, v_b____) = all_498_3 & hAPP(all_498_5, % 97.11/14.11 | v_a____) = all_498_4 & hAPP(all_498_6, all_498_3) = all_498_2 & % 97.11/14.11 | hAPP(v_F, v_P____) = all_498_1 & $i(all_498_0) & $i(all_498_1) & % 97.11/14.11 | $i(all_498_2) & $i(all_498_3) & $i(all_498_4) & $i(all_498_5) & % 97.11/14.11 | $i(all_498_6) & $i(all_498_7) % 97.11/14.11 | % 97.11/14.11 | ALPHA: (87) implies: % 97.11/14.11 | (88) tc_prod(tc_Arrow__Order__Mirabelle_Oalt, % 97.11/14.11 | tc_Arrow__Order__Mirabelle_Oalt) = all_498_7 % 97.11/14.11 | % 97.11/14.11 | DELTA: instantiating (3) with fresh symbols all_500_0, all_500_1, all_500_2 % 97.11/14.11 | gives: % 97.11/14.11 | (89) tc_prod(tc_Arrow__Order__Mirabelle_Oalt, % 97.11/14.11 | tc_Arrow__Order__Mirabelle_Oalt) = all_500_2 & tc_fun(all_500_2, % 97.11/14.11 | tc_HOL_Obool) = all_500_1 & c_member(all_500_1) = all_500_0 & % 97.11/14.11 | $i(all_500_0) & $i(all_500_1) & $i(all_500_2) & ! [v0: $i] : ! [v1: % 97.11/14.11 | $i] : ! [v2: $i] : ( ~ (c_Arrow__Order__Mirabelle_Omktop(v1, v0) = % 97.11/14.11 | v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : ? [v5: % 97.11/14.11 | any] : ? [v6: $i] : ? [v7: $i] : ? [v8: any] : (hBOOL(v7) = v8 % 97.11/14.11 | & hBOOL(v4) = v5 & hAPP(v6, c_Arrow__Order__Mirabelle_OLin) = v7 & % 97.11/14.11 | hAPP(v3, c_Arrow__Order__Mirabelle_OLin) = v4 & hAPP(all_500_0, % 97.11/14.11 | v2) = v6 & hAPP(all_500_0, v1) = v3 & $i(v7) & $i(v6) & $i(v4) & % 97.11/14.11 | $i(v3) & ( ~ (v5 = 0) | v8 = 0))) % 97.11/14.11 | % 97.11/14.11 | ALPHA: (89) implies: % 97.11/14.11 | (90) c_member(all_500_1) = all_500_0 % 97.11/14.11 | (91) tc_fun(all_500_2, tc_HOL_Obool) = all_500_1 % 97.11/14.11 | (92) tc_prod(tc_Arrow__Order__Mirabelle_Oalt, % 97.11/14.11 | tc_Arrow__Order__Mirabelle_Oalt) = all_500_2 % 97.11/14.11 | % 97.11/14.11 | DELTA: instantiating (2) with fresh symbols all_505_0, all_505_1, all_505_2 % 97.11/14.11 | gives: % 97.11/14.12 | (93) tc_prod(tc_Arrow__Order__Mirabelle_Oalt, % 97.11/14.12 | tc_Arrow__Order__Mirabelle_Oalt) = all_505_2 & tc_fun(all_505_2, % 97.11/14.12 | tc_HOL_Obool) = all_505_1 & c_member(all_505_1) = all_505_0 & % 97.11/14.12 | $i(all_505_0) & $i(all_505_1) & $i(all_505_2) & ! [v0: $i] : ! [v1: % 97.11/14.12 | $i] : ! [v2: $i] : ( ~ (c_Arrow__Order__Mirabelle_Omkbot(v1, v0) = % 97.11/14.12 | v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : ? [v5: % 97.11/14.12 | any] : ? [v6: $i] : ? [v7: $i] : ? [v8: any] : (hBOOL(v7) = v8 % 97.11/14.12 | & hBOOL(v4) = v5 & hAPP(v6, c_Arrow__Order__Mirabelle_OLin) = v7 & % 97.11/14.12 | hAPP(v3, c_Arrow__Order__Mirabelle_OLin) = v4 & hAPP(all_505_0, % 97.11/14.12 | v2) = v6 & hAPP(all_505_0, v1) = v3 & $i(v7) & $i(v6) & $i(v4) & % 97.11/14.12 | $i(v3) & ( ~ (v5 = 0) | v8 = 0))) % 97.11/14.12 | % 97.11/14.12 | ALPHA: (93) implies: % 97.11/14.12 | (94) c_member(all_505_1) = all_505_0 % 97.11/14.12 | (95) tc_fun(all_505_2, tc_HOL_Obool) = all_505_1 % 97.11/14.12 | (96) tc_prod(tc_Arrow__Order__Mirabelle_Oalt, % 97.11/14.12 | tc_Arrow__Order__Mirabelle_Oalt) = all_505_2 % 97.11/14.12 | % 97.11/14.12 | DELTA: instantiating (15) with fresh symbols all_508_0, all_508_1, all_508_2, % 97.11/14.12 | all_508_3, all_508_4, all_508_5, all_508_6, all_508_7, all_508_8, % 97.11/14.12 | all_508_9 gives: % 97.11/14.12 | (97) c_COMBK(all_508_3, all_508_7, c_Arrow__Order__Mirabelle_OLin) = % 97.11/14.12 | all_508_2 & c_FuncSet_OPi(all_508_7, all_508_8, % 97.11/14.12 | c_Arrow__Order__Mirabelle_OProf, all_508_2) = all_508_1 & % 97.11/14.12 | tc_prod(tc_Arrow__Order__Mirabelle_Oalt, % 97.11/14.12 | tc_Arrow__Order__Mirabelle_Oalt) = all_508_9 & tc_fun(all_508_7, % 97.11/14.12 | all_508_8) = all_508_6 & tc_fun(all_508_8, tc_HOL_Obool) = all_508_3 % 97.11/14.12 | & tc_fun(all_508_9, tc_HOL_Obool) = all_508_8 & % 97.11/14.12 | tc_fun(tc_Arrow__Order__Mirabelle_Oindi, all_508_8) = all_508_7 & % 97.11/14.12 | c_member(all_508_6) = all_508_5 & hBOOL(all_508_0) = 0 & % 97.11/14.12 | hAPP(all_508_4, all_508_1) = all_508_0 & hAPP(all_508_5, v_F) = % 97.11/14.12 | all_508_4 & $i(all_508_0) & $i(all_508_1) & $i(all_508_2) & % 97.11/14.12 | $i(all_508_3) & $i(all_508_4) & $i(all_508_5) & $i(all_508_6) & % 97.11/14.12 | $i(all_508_7) & $i(all_508_8) & $i(all_508_9) % 97.11/14.12 | % 97.11/14.12 | ALPHA: (97) implies: % 97.11/14.12 | (98) hAPP(all_508_5, v_F) = all_508_4 % 97.11/14.12 | (99) hAPP(all_508_4, all_508_1) = all_508_0 % 97.11/14.12 | (100) hBOOL(all_508_0) = 0 % 97.11/14.12 | (101) c_member(all_508_6) = all_508_5 % 97.11/14.12 | (102) tc_fun(tc_Arrow__Order__Mirabelle_Oindi, all_508_8) = all_508_7 % 97.11/14.12 | (103) tc_fun(all_508_9, tc_HOL_Obool) = all_508_8 % 97.11/14.12 | (104) tc_fun(all_508_8, tc_HOL_Obool) = all_508_3 % 97.11/14.12 | (105) tc_fun(all_508_7, all_508_8) = all_508_6 % 97.11/14.12 | (106) tc_prod(tc_Arrow__Order__Mirabelle_Oalt, % 97.11/14.12 | tc_Arrow__Order__Mirabelle_Oalt) = all_508_9 % 97.11/14.12 | (107) c_FuncSet_OPi(all_508_7, all_508_8, c_Arrow__Order__Mirabelle_OProf, % 97.11/14.12 | all_508_2) = all_508_1 % 97.11/14.12 | (108) c_COMBK(all_508_3, all_508_7, c_Arrow__Order__Mirabelle_OLin) = % 97.11/14.12 | all_508_2 % 97.11/14.12 | % 97.11/14.12 | DELTA: instantiating (5) with fresh symbols all_510_0, all_510_1, all_510_2 % 97.11/14.12 | gives: % 97.11/14.12 | (109) tc_prod(tc_Arrow__Order__Mirabelle_Oalt, % 97.11/14.12 | tc_Arrow__Order__Mirabelle_Oalt) = all_510_2 & tc_fun(all_510_2, % 97.11/14.12 | tc_HOL_Obool) = all_510_1 & c_member(all_510_1) = all_510_0 & % 97.11/14.12 | $i(all_510_0) & $i(all_510_1) & $i(all_510_2) & ! [v0: $i] : ! [v1: % 97.11/14.12 | $i] : ! [v2: $i] : ! [v3: $i] : (v2 = v1 | ~ % 97.11/14.12 | (c_Arrow__Order__Mirabelle_Obelow(v0, v2, v1) = v3) | ~ $i(v2) | % 97.11/14.12 | ~ $i(v1) | ~ $i(v0) | ? [v4: $i] : ? [v5: $i] : ? [v6: any] : % 97.11/14.12 | ? [v7: $i] : ? [v8: $i] : ? [v9: any] : (hBOOL(v8) = v9 & % 97.11/14.12 | hBOOL(v5) = v6 & hAPP(v7, c_Arrow__Order__Mirabelle_OLin) = v8 & % 97.11/14.12 | hAPP(v4, c_Arrow__Order__Mirabelle_OLin) = v5 & hAPP(all_510_0, % 97.11/14.12 | v3) = v7 & hAPP(all_510_0, v0) = v4 & $i(v8) & $i(v7) & $i(v5) % 97.11/14.12 | & $i(v4) & ( ~ (v6 = 0) | v9 = 0))) % 97.11/14.12 | % 97.11/14.12 | ALPHA: (109) implies: % 97.11/14.12 | (110) c_member(all_510_1) = all_510_0 % 97.11/14.12 | (111) tc_fun(all_510_2, tc_HOL_Obool) = all_510_1 % 97.11/14.12 | (112) tc_prod(tc_Arrow__Order__Mirabelle_Oalt, % 97.11/14.12 | tc_Arrow__Order__Mirabelle_Oalt) = all_510_2 % 97.11/14.12 | % 97.11/14.12 | DELTA: instantiating (19) with fresh symbols all_513_0, all_513_1, all_513_2, % 97.11/14.12 | all_513_3, all_513_4 gives: % 97.11/14.12 | (113) tc_prod(tc_Arrow__Order__Mirabelle_Oalt, % 97.11/14.12 | tc_Arrow__Order__Mirabelle_Oalt) = all_513_4 & tc_fun(all_513_4, % 97.11/14.12 | tc_HOL_Obool) = all_513_3 & % 97.11/14.12 | tc_fun(tc_Arrow__Order__Mirabelle_Oindi, all_513_3) = all_513_1 & % 97.11/14.12 | c_member(all_513_1) = all_513_0 & c_member(all_513_3) = all_513_2 & % 97.11/14.12 | $i(all_513_0) & $i(all_513_1) & $i(all_513_2) & $i(all_513_3) & % 97.11/14.12 | $i(all_513_4) & ! [v0: $i] : ! [v1: $i] : ( ~ (c_COMBK(all_513_3, % 97.11/14.12 | tc_Arrow__Order__Mirabelle_Oindi, v0) = v1) | ~ $i(v0) | ? % 97.11/14.12 | [v2: $i] : ? [v3: $i] : ? [v4: any] : ? [v5: $i] : ? [v6: $i] : % 97.11/14.12 | ? [v7: any] : (hBOOL(v6) = v7 & hBOOL(v3) = v4 & hAPP(v5, % 97.11/14.12 | c_Arrow__Order__Mirabelle_OProf) = v6 & hAPP(v2, % 97.11/14.12 | c_Arrow__Order__Mirabelle_OLin) = v3 & hAPP(all_513_0, v1) = v5 % 97.11/14.12 | & hAPP(all_513_2, v0) = v2 & $i(v6) & $i(v5) & $i(v3) & $i(v2) & % 97.11/14.12 | ( ~ (v4 = 0) | v7 = 0))) % 97.11/14.12 | % 97.11/14.12 | ALPHA: (113) implies: % 97.11/14.12 | (114) c_member(all_513_3) = all_513_2 % 97.11/14.12 | (115) c_member(all_513_1) = all_513_0 % 97.11/14.12 | (116) tc_fun(tc_Arrow__Order__Mirabelle_Oindi, all_513_3) = all_513_1 % 97.11/14.12 | (117) tc_fun(all_513_4, tc_HOL_Obool) = all_513_3 % 97.11/14.12 | (118) tc_prod(tc_Arrow__Order__Mirabelle_Oalt, % 97.11/14.12 | tc_Arrow__Order__Mirabelle_Oalt) = all_513_4 % 97.11/14.12 | % 97.11/14.12 | DELTA: instantiating (4) with fresh symbols all_516_0, all_516_1, all_516_2 % 97.11/14.12 | gives: % 97.11/14.12 | (119) tc_prod(tc_Arrow__Order__Mirabelle_Oalt, % 97.11/14.12 | tc_Arrow__Order__Mirabelle_Oalt) = all_516_2 & tc_fun(all_516_2, % 97.11/14.12 | tc_HOL_Obool) = all_516_1 & c_member(all_516_1) = all_516_0 & % 97.11/14.12 | $i(all_516_0) & $i(all_516_1) & $i(all_516_2) & ! [v0: $i] : ! [v1: % 97.11/14.12 | $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v2 = % 97.11/14.12 | v1 | ~ (hAPP(v4, v1) = v5) | ~ (hAPP(v3, v2) = v4) | ~ % 97.11/14.12 | (hAPP(c_Arrow__Order__Mirabelle_Oabove, v0) = v3) | ~ $i(v2) | ~ % 97.11/14.12 | $i(v1) | ~ $i(v0) | ? [v6: $i] : ? [v7: $i] : ? [v8: any] : ? % 97.11/14.12 | [v9: $i] : ? [v10: $i] : ? [v11: any] : (hBOOL(v10) = v11 & % 97.11/14.12 | hBOOL(v7) = v8 & hAPP(v9, c_Arrow__Order__Mirabelle_OLin) = v10 & % 97.11/14.12 | hAPP(v6, c_Arrow__Order__Mirabelle_OLin) = v7 & hAPP(all_516_0, % 97.11/14.12 | v5) = v9 & hAPP(all_516_0, v0) = v6 & $i(v10) & $i(v9) & $i(v7) % 97.11/14.12 | & $i(v6) & ( ~ (v8 = 0) | v11 = 0))) % 97.11/14.12 | % 97.11/14.12 | ALPHA: (119) implies: % 97.11/14.12 | (120) c_member(all_516_1) = all_516_0 % 97.11/14.12 | (121) tc_fun(all_516_2, tc_HOL_Obool) = all_516_1 % 97.11/14.12 | (122) tc_prod(tc_Arrow__Order__Mirabelle_Oalt, % 97.11/14.12 | tc_Arrow__Order__Mirabelle_Oalt) = all_516_2 % 97.11/14.12 | % 97.11/14.12 | DELTA: instantiating (30) with fresh symbols all_519_0, all_519_1, all_519_2, % 97.11/14.12 | all_519_3, all_519_4 gives: % 97.11/14.12 | (123) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 97.11/14.12 | tc_Arrow__Order__Mirabelle_Oalt) = all_519_0 & % 97.11/14.12 | tc_prod(tc_Arrow__Order__Mirabelle_Oalt, % 97.11/14.12 | tc_Arrow__Order__Mirabelle_Oalt) = all_519_4 & tc_fun(all_519_4, % 97.11/14.12 | tc_HOL_Obool) = all_519_3 & c_member(all_519_3) = all_519_2 & % 97.11/14.12 | c_member(all_519_4) = all_519_1 & $i(all_519_0) & $i(all_519_1) & % 97.11/14.12 | $i(all_519_2) & $i(all_519_3) & $i(all_519_4) & ! [v0: $i] : ! [v1: % 97.11/14.12 | $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP(v2, v0) = v3) % 97.11/14.12 | | ~ (hAPP(all_519_0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: % 97.11/14.12 | $i] : (hAPP(all_519_1, v3) = v4 & $i(v4) & ? [v5: $i] : ? [v6: % 97.11/14.12 | $i] : ? [v7: $i] : ? [v8: $i] : (hBOOL(v8) = 0 & hBOOL(v7) = % 97.11/14.12 | 0 & hAPP(v6, c_Arrow__Order__Mirabelle_OLin) = v7 & hAPP(v4, % 97.11/14.12 | v5) = v8 & hAPP(all_519_2, v5) = v6 & $i(v8) & $i(v7) & % 97.11/14.12 | $i(v6) & $i(v5)))) % 97.11/14.12 | % 97.11/14.12 | ALPHA: (123) implies: % 97.11/14.12 | (124) c_member(all_519_3) = all_519_2 % 97.11/14.12 | (125) tc_fun(all_519_4, tc_HOL_Obool) = all_519_3 % 97.11/14.12 | (126) tc_prod(tc_Arrow__Order__Mirabelle_Oalt, % 97.11/14.12 | tc_Arrow__Order__Mirabelle_Oalt) = all_519_4 % 97.11/14.12 | % 97.11/14.12 | DELTA: instantiating (37) with fresh symbol all_522_0 gives: % 97.11/14.12 | (127) tc_fun(tc_HOL_Obool, tc_HOL_Obool) = all_522_0 & $i(all_522_0) & ! % 97.11/14.12 | [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! % 97.11/14.12 | [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : ! % 97.11/14.12 | [v10: $i] : ! [v11: $i] : ! [v12: $i] : ! [v13: $i] : ! [v14: $i] % 97.11/14.12 | : ! [v15: $i] : ! [v16: $i] : ! [v17: $i] : ! [v18: $i] : ! % 97.11/14.12 | [v19: $i] : ! [v20: $i] : ! [v21: $i] : ( ~ (c_HOL_OThe(v4, v20) = % 97.11/14.12 | v21) | ~ (c_COMBB(v3, v15, v4, c_fequal) = v16) | ~ % 97.11/14.12 | (c_COMBB(tc_HOL_Obool, all_522_0, v4, c_fconj) = v6) | ~ % 97.11/14.12 | (c_COMBS(v4, tc_HOL_Obool, tc_HOL_Obool) = v5) | ~ (c_COMBC(v4, % 97.11/14.12 | v7, tc_HOL_Obool) = v8) | ~ (c_COMBC(v4, v3, tc_HOL_Obool) = % 97.11/14.12 | v14) | ~ (tc_fun(v4, tc_HOL_Obool) = v7) | ~ (tc_fun(v3, % 97.11/14.12 | tc_HOL_Obool) = v15) | ~ (c_member(v4) = v9) | ~ (hAPP(v18, % 97.11/14.12 | v0) = v19) | ~ (hAPP(v16, v1) = v17) | ~ (hAPP(v14, v17) = % 97.11/14.12 | v18) | ~ (hAPP(v13, v19) = v20) | ~ (hAPP(v10, v2) = v11) | ~ % 97.11/14.12 | (hAPP(v8, v9) = v10) | ~ (hAPP(v6, v11) = v12) | ~ (hAPP(v5, v12) % 97.11/14.12 | = v13) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 97.11/14.12 | $i(v0) | ? [v22: $i] : (c_Fun_Othe__inv__into(v4, v3, v2, v1) = % 97.11/14.12 | v22 & hAPP(v22, v0) = v21 & $i(v22) & $i(v21))) % 97.11/14.12 | % 97.11/14.12 | ALPHA: (127) implies: % 97.11/14.12 | (128) tc_fun(tc_HOL_Obool, tc_HOL_Obool) = all_522_0 % 97.11/14.12 | % 97.11/14.12 | DELTA: instantiating (16) with fresh symbols all_525_0, all_525_1, all_525_2 % 97.11/14.12 | gives: % 97.11/14.12 | (129) tc_prod(tc_Arrow__Order__Mirabelle_Oalt, % 97.11/14.12 | tc_Arrow__Order__Mirabelle_Oalt) = all_525_2 & tc_fun(all_525_2, % 97.11/14.12 | tc_HOL_Obool) = all_525_1 & c_member(all_525_1) = all_525_0 & % 97.11/14.12 | $i(all_525_0) & $i(all_525_1) & $i(all_525_2) & ! [v0: $i] : ! [v1: % 97.11/14.12 | $i] : ( ~ (hAPP(all_525_0, v0) = v1) | ~ $i(v0) | ? [v2: $i] : ? % 97.11/14.12 | [v3: any] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: any] % 97.11/14.12 | : (c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt, % 97.11/14.12 | tc_Arrow__Order__Mirabelle_Oalt, v0) = v4 & hBOOL(v6) = v7 & % 97.11/14.12 | hBOOL(v2) = v3 & hAPP(v5, c_Arrow__Order__Mirabelle_OLin) = v6 & % 97.11/14.12 | hAPP(v1, c_Arrow__Order__Mirabelle_OLin) = v2 & hAPP(all_525_0, % 97.11/14.12 | v4) = v5 & $i(v6) & $i(v5) & $i(v4) & $i(v2) & ( ~ (v3 = 0) | % 97.11/14.12 | v7 = 0))) & ! [v0: $i] : ! [v1: $i] : ( ~ (hAPP(all_525_0, % 97.11/14.12 | v0) = v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: $i] : ? [v4: $i] % 97.11/14.12 | : ? [v5: any] : ? [v6: $i] : ? [v7: any] : % 97.11/14.12 | (c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt, % 97.11/14.12 | tc_Arrow__Order__Mirabelle_Oalt, v0) = v2 & hBOOL(v6) = v7 & % 97.11/14.12 | hBOOL(v4) = v5 & hAPP(v3, c_Arrow__Order__Mirabelle_OLin) = v4 & % 97.11/14.12 | hAPP(v1, c_Arrow__Order__Mirabelle_OLin) = v6 & hAPP(all_525_0, % 97.11/14.12 | v2) = v3 & $i(v6) & $i(v4) & $i(v3) & $i(v2) & ( ~ (v5 = 0) | % 97.11/14.12 | v7 = 0))) % 97.11/14.12 | % 97.11/14.12 | ALPHA: (129) implies: % 97.11/14.12 | (130) c_member(all_525_1) = all_525_0 % 97.11/14.12 | (131) tc_fun(all_525_2, tc_HOL_Obool) = all_525_1 % 97.11/14.12 | (132) tc_prod(tc_Arrow__Order__Mirabelle_Oalt, % 97.11/14.12 | tc_Arrow__Order__Mirabelle_Oalt) = all_525_2 % 97.11/14.12 | % 97.11/14.12 | DELTA: instantiating (17) with fresh symbols all_528_0, all_528_1, all_528_2, % 97.11/14.12 | all_528_3, all_528_4 gives: % 97.11/14.12 | (133) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 97.11/14.12 | tc_Arrow__Order__Mirabelle_Oalt) = all_528_0 & % 97.11/14.12 | tc_prod(tc_Arrow__Order__Mirabelle_Oalt, % 97.11/14.12 | tc_Arrow__Order__Mirabelle_Oalt) = all_528_4 & tc_fun(all_528_4, % 97.11/14.12 | tc_HOL_Obool) = all_528_3 & c_member(all_528_3) = all_528_2 & % 97.11/14.12 | c_member(all_528_4) = all_528_1 & $i(all_528_0) & $i(all_528_1) & % 97.11/14.12 | $i(all_528_2) & $i(all_528_3) & $i(all_528_4) & ! [v0: $i] : ! [v1: % 97.11/14.12 | $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! % 97.11/14.12 | [v6: $i] : ( ~ (hAPP(v5, v2) = v6) | ~ (hAPP(v3, v1) = v4) | ~ % 97.11/14.12 | (hAPP(all_528_0, v0) = v3) | ~ (hAPP(all_528_1, v4) = v5) | ~ % 97.11/14.12 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v7: $i] : ? [v8: $i] : ? % 97.11/14.12 | [v9: any] : ? [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13: % 97.11/14.12 | $i] : ? [v14: any] : ? [v15: any] : (hBOOL(v13) = v14 & % 97.11/14.12 | hBOOL(v8) = v9 & hBOOL(v6) = v15 & hAPP(v12, v2) = v13 & % 97.11/14.12 | hAPP(v10, v0) = v11 & hAPP(v7, c_Arrow__Order__Mirabelle_OLin) = % 97.11/14.12 | v8 & hAPP(all_528_0, v1) = v10 & hAPP(all_528_1, v11) = v12 & % 97.11/14.12 | hAPP(all_528_2, v2) = v7 & $i(v13) & $i(v12) & $i(v11) & $i(v10) % 97.11/14.12 | & $i(v8) & $i(v7) & ( ~ (v15 = 0) | ~ (v14 = 0) | ~ (v9 = 0)))) % 97.11/14.12 | % 97.11/14.12 | ALPHA: (133) implies: % 97.11/14.12 | (134) c_member(all_528_3) = all_528_2 % 97.11/14.12 | (135) tc_fun(all_528_4, tc_HOL_Obool) = all_528_3 % 97.11/14.13 | (136) tc_prod(tc_Arrow__Order__Mirabelle_Oalt, % 97.11/14.13 | tc_Arrow__Order__Mirabelle_Oalt) = all_528_4 % 97.11/14.13 | % 97.11/14.13 | DELTA: instantiating (11) with fresh symbols all_531_0, all_531_1, all_531_2, % 97.11/14.13 | all_531_3 gives: % 98.05/14.13 | (137) tc_prod(tc_Arrow__Order__Mirabelle_Oalt, % 98.05/14.13 | tc_Arrow__Order__Mirabelle_Oalt) = all_531_3 & tc_fun(all_531_3, % 98.05/14.13 | tc_HOL_Obool) = all_531_2 & % 98.05/14.13 | tc_fun(tc_Arrow__Order__Mirabelle_Oindi, all_531_2) = all_531_1 & % 98.05/14.13 | c_member(all_531_1) = all_531_0 & $i(all_531_0) & $i(all_531_1) & % 98.05/14.13 | $i(all_531_2) & $i(all_531_3) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 98.05/14.13 | int] : (v2 = 0 | ~ (c_Arrow__Order__Mirabelle_Odictator(v1, v0) = % 98.05/14.13 | v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : ? [v5: % 98.05/14.13 | $i] : ? [v6: $i] : ? [v7: $i] : ( ~ (v7 = v6) & hBOOL(v5) = 0 & % 98.05/14.13 | hAPP(v4, c_Arrow__Order__Mirabelle_OProf) = v5 & hAPP(v3, v0) = % 98.05/14.13 | v7 & hAPP(v1, v3) = v6 & hAPP(all_531_0, v3) = v4 & $i(v7) & % 98.05/14.13 | $i(v6) & $i(v5) & $i(v4) & $i(v3))) & ! [v0: $i] : ! [v1: $i] : % 98.05/14.13 | ( ~ (c_Arrow__Order__Mirabelle_Odictator(v1, v0) = 0) | ~ $i(v1) | % 98.05/14.13 | ~ $i(v0) | ! [v2: $i] : ! [v3: $i] : ( ~ (hAPP(all_531_0, v2) = % 98.05/14.13 | v3) | ~ $i(v2) | ? [v4: $i] : ? [v5: any] : ? [v6: $i] : ? % 98.05/14.13 | [v7: $i] : (hBOOL(v4) = v5 & hAPP(v3, % 98.05/14.13 | c_Arrow__Order__Mirabelle_OProf) = v4 & hAPP(v2, v0) = v7 & % 98.05/14.13 | hAPP(v1, v2) = v6 & $i(v7) & $i(v6) & $i(v4) & ( ~ (v5 = 0) | % 98.05/14.13 | v7 = v6)))) % 98.05/14.13 | % 98.05/14.13 | ALPHA: (137) implies: % 98.05/14.13 | (138) c_member(all_531_1) = all_531_0 % 98.05/14.13 | (139) tc_fun(tc_Arrow__Order__Mirabelle_Oindi, all_531_2) = all_531_1 % 98.05/14.13 | (140) tc_fun(all_531_3, tc_HOL_Obool) = all_531_2 % 98.05/14.13 | (141) tc_prod(tc_Arrow__Order__Mirabelle_Oalt, % 98.05/14.13 | tc_Arrow__Order__Mirabelle_Oalt) = all_531_3 % 98.05/14.13 | % 98.05/14.13 | DELTA: instantiating (18) with fresh symbols all_534_0, all_534_1, all_534_2, % 98.05/14.13 | all_534_3, all_534_4 gives: % 98.05/14.13 | (142) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 98.05/14.13 | tc_Arrow__Order__Mirabelle_Oalt) = all_534_0 & % 98.05/14.13 | tc_prod(tc_Arrow__Order__Mirabelle_Oalt, % 98.05/14.13 | tc_Arrow__Order__Mirabelle_Oalt) = all_534_4 & tc_fun(all_534_4, % 98.05/14.13 | tc_HOL_Obool) = all_534_3 & c_member(all_534_3) = all_534_2 & % 98.05/14.13 | c_member(all_534_4) = all_534_1 & $i(all_534_0) & $i(all_534_1) & % 98.05/14.13 | $i(all_534_2) & $i(all_534_3) & $i(all_534_4) & ! [v0: $i] : ! [v1: % 98.05/14.13 | $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! % 98.05/14.13 | [v6: $i] : (v1 = v0 | ~ (hAPP(v5, v2) = v6) | ~ (hAPP(v3, v1) = v4) % 98.05/14.13 | | ~ (hAPP(all_534_0, v0) = v3) | ~ (hAPP(all_534_1, v4) = v5) | % 98.05/14.13 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v7: $i] : ? [v8: $i] : ? % 98.05/14.13 | [v9: any] : ? [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13: % 98.05/14.13 | $i] : ? [v14: any] : ? [v15: any] : (hBOOL(v13) = v14 & % 98.05/14.13 | hBOOL(v8) = v9 & hBOOL(v6) = v15 & hAPP(v12, v2) = v13 & % 98.05/14.13 | hAPP(v10, v0) = v11 & hAPP(v7, c_Arrow__Order__Mirabelle_OLin) = % 98.05/14.13 | v8 & hAPP(all_534_0, v1) = v10 & hAPP(all_534_1, v11) = v12 & % 98.05/14.13 | hAPP(all_534_2, v2) = v7 & $i(v13) & $i(v12) & $i(v11) & $i(v10) % 98.05/14.13 | & $i(v8) & $i(v7) & ( ~ (v9 = 0) | (( ~ (v15 = 0) | ~ (v14 = 0)) % 98.05/14.13 | & (v15 = 0 | v14 = 0))))) % 98.05/14.13 | % 98.05/14.13 | ALPHA: (142) implies: % 98.05/14.13 | (143) c_member(all_534_3) = all_534_2 % 98.05/14.13 | (144) tc_fun(all_534_4, tc_HOL_Obool) = all_534_3 % 98.05/14.13 | (145) tc_prod(tc_Arrow__Order__Mirabelle_Oalt, % 98.05/14.13 | tc_Arrow__Order__Mirabelle_Oalt) = all_534_4 % 98.05/14.13 | % 98.05/14.13 | DELTA: instantiating (22) with fresh symbols all_537_0, all_537_1, all_537_2 % 98.05/14.13 | gives: % 98.21/14.13 | (146) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 98.21/14.13 | tc_Arrow__Order__Mirabelle_Oalt) = all_537_0 & % 98.21/14.13 | tc_prod(tc_Arrow__Order__Mirabelle_Oalt, % 98.21/14.13 | tc_Arrow__Order__Mirabelle_Oalt) = all_537_2 & c_member(all_537_2) % 98.21/14.13 | = all_537_1 & $i(all_537_0) & $i(all_537_1) & $i(all_537_2) & ! [v0: % 98.21/14.13 | $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! % 98.21/14.13 | [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : (v3 = v0 | ~ % 98.21/14.13 | (c_Arrow__Order__Mirabelle_Omktop(v1, v0) = v7) | ~ (hAPP(v6, v7) % 98.21/14.13 | = v8) | ~ (hAPP(v4, v2) = v5) | ~ (hAPP(all_537_0, v3) = v4) | % 98.21/14.13 | ~ (hAPP(all_537_1, v5) = v6) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | % 98.21/14.13 | ~ $i(v0) | ? [v9: $i] : ? [v10: any] : ? [v11: any] : (hBOOL(v9) % 98.21/14.13 | = v10 & hBOOL(v8) = v11 & hAPP(v6, v1) = v9 & $i(v9) & (v11 = 0 | % 98.21/14.13 | ( ~ (v10 = 0) & ~ (v2 = v0))))) & ! [v0: $i] : ! [v1: $i] : % 98.21/14.13 | ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : % 98.21/14.13 | ! [v7: $i] : ! [v8: $i] : ( ~ (c_Arrow__Order__Mirabelle_Omktop(v1, % 98.21/14.13 | v0) = v7) | ~ (hAPP(v6, v7) = v8) | ~ (hAPP(v4, v2) = v5) | % 98.21/14.13 | ~ (hAPP(all_537_0, v3) = v4) | ~ (hAPP(all_537_1, v5) = v6) | ~ % 98.21/14.13 | $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v9: any] : ? % 98.21/14.13 | [v10: $i] : ? [v11: any] : (hBOOL(v10) = v11 & hBOOL(v8) = v9 & % 98.21/14.13 | hAPP(v6, v1) = v10 & $i(v10) & ( ~ (v9 = 0) | ( ~ (v3 = v0) & % 98.21/14.13 | (v11 = 0 | v2 = v0))))) % 98.21/14.13 | % 98.21/14.13 | ALPHA: (146) implies: % 98.21/14.13 | (147) tc_prod(tc_Arrow__Order__Mirabelle_Oalt, % 98.21/14.13 | tc_Arrow__Order__Mirabelle_Oalt) = all_537_2 % 98.21/14.13 | % 98.21/14.13 | DELTA: instantiating (23) with fresh symbols all_540_0, all_540_1, all_540_2 % 98.21/14.13 | gives: % 98.21/14.13 | (148) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 98.21/14.13 | tc_Arrow__Order__Mirabelle_Oalt) = all_540_0 & % 98.21/14.13 | tc_prod(tc_Arrow__Order__Mirabelle_Oalt, % 98.21/14.13 | tc_Arrow__Order__Mirabelle_Oalt) = all_540_2 & c_member(all_540_2) % 98.21/14.13 | = all_540_1 & $i(all_540_0) & $i(all_540_1) & $i(all_540_2) & ! [v0: % 98.21/14.13 | $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! % 98.21/14.13 | [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : (v2 = v0 | ~ % 98.21/14.13 | (c_Arrow__Order__Mirabelle_Omkbot(v1, v0) = v7) | ~ (hAPP(v6, v7) % 98.21/14.13 | = v8) | ~ (hAPP(v4, v2) = v5) | ~ (hAPP(all_540_0, v3) = v4) | % 98.21/14.13 | ~ (hAPP(all_540_1, v5) = v6) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | % 98.21/14.13 | ~ $i(v0) | ? [v9: $i] : ? [v10: any] : ? [v11: any] : (hBOOL(v9) % 98.21/14.13 | = v10 & hBOOL(v8) = v11 & hAPP(v6, v1) = v9 & $i(v9) & (v11 = 0 | % 98.21/14.13 | ( ~ (v10 = 0) & ~ (v3 = v0))))) & ! [v0: $i] : ! [v1: $i] : % 98.21/14.13 | ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : % 98.21/14.13 | ! [v7: $i] : ! [v8: $i] : ( ~ (c_Arrow__Order__Mirabelle_Omkbot(v1, % 98.21/14.13 | v0) = v7) | ~ (hAPP(v6, v7) = v8) | ~ (hAPP(v4, v2) = v5) | % 98.21/14.13 | ~ (hAPP(all_540_0, v3) = v4) | ~ (hAPP(all_540_1, v5) = v6) | ~ % 98.21/14.13 | $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v9: any] : ? % 98.21/14.13 | [v10: $i] : ? [v11: any] : (hBOOL(v10) = v11 & hBOOL(v8) = v9 & % 98.21/14.13 | hAPP(v6, v1) = v10 & $i(v10) & ( ~ (v9 = 0) | ( ~ (v2 = v0) & % 98.21/14.13 | (v11 = 0 | v3 = v0))))) % 98.21/14.13 | % 98.21/14.13 | ALPHA: (148) implies: % 98.21/14.13 | (149) tc_prod(tc_Arrow__Order__Mirabelle_Oalt, % 98.21/14.13 | tc_Arrow__Order__Mirabelle_Oalt) = all_540_2 % 98.21/14.13 | % 98.21/14.13 | DELTA: instantiating (20) with fresh symbols all_543_0, all_543_1, all_543_2, % 98.21/14.13 | all_543_3, all_543_4, all_543_5, all_543_6, all_543_7, all_543_8 gives: % 98.21/14.13 | (150) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 98.21/14.13 | tc_Arrow__Order__Mirabelle_Oalt) = all_543_6 & % 98.21/14.13 | tc_prod(tc_Arrow__Order__Mirabelle_Oalt, % 98.21/14.13 | tc_Arrow__Order__Mirabelle_Oalt) = all_543_8 & c_member(all_543_8) % 98.21/14.13 | = all_543_7 & hAPP(all_543_2, v_b_H____) = all_543_1 & % 98.21/14.13 | hAPP(all_543_5, v_b____) = all_543_4 & hAPP(all_543_6, v_a____) = % 98.21/14.13 | all_543_5 & hAPP(all_543_6, v_a_H____) = all_543_2 & hAPP(all_543_7, % 98.21/14.13 | all_543_1) = all_543_0 & hAPP(all_543_7, all_543_4) = all_543_3 & % 98.21/14.13 | $i(all_543_0) & $i(all_543_1) & $i(all_543_2) & $i(all_543_3) & % 98.21/14.13 | $i(all_543_4) & $i(all_543_5) & $i(all_543_6) & $i(all_543_7) & % 98.21/14.13 | $i(all_543_8) & ! [v0: $i] : ! [v1: $i] : ( ~ (hAPP(v_P_H____, v0) % 98.21/14.13 | = v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: $i] : ? [v4: any] : ? % 98.21/14.13 | [v5: $i] : ? [v6: any] : (hBOOL(v5) = v6 & hBOOL(v3) = v4 & % 98.21/14.13 | hAPP(all_543_0, v1) = v5 & hAPP(all_543_3, v2) = v3 & % 98.21/14.13 | hAPP(v_P____, v0) = v2 & $i(v5) & $i(v3) & $i(v2) & ( ~ (v4 = 0) % 98.21/14.13 | | v6 = 0))) & ! [v0: $i] : ! [v1: $i] : ( ~ (hAPP(v_P_H____, % 98.21/14.13 | v0) = v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: any] : ? [v4: % 98.21/14.13 | $i] : ? [v5: $i] : ? [v6: any] : (hBOOL(v5) = v6 & hBOOL(v2) = % 98.21/14.13 | v3 & hAPP(all_543_0, v1) = v2 & hAPP(all_543_3, v4) = v5 & % 98.21/14.13 | hAPP(v_P____, v0) = v4 & $i(v5) & $i(v4) & $i(v2) & ( ~ (v3 = 0) % 98.21/14.13 | | v6 = 0))) % 98.21/14.13 | % 98.21/14.13 | ALPHA: (150) implies: % 98.21/14.13 | (151) tc_prod(tc_Arrow__Order__Mirabelle_Oalt, % 98.21/14.13 | tc_Arrow__Order__Mirabelle_Oalt) = all_543_8 % 98.21/14.13 | % 98.21/14.13 | DELTA: instantiating (14) with fresh symbols all_546_0, all_546_1, all_546_2, % 98.21/14.13 | all_546_3, all_546_4, all_546_5, all_546_6, all_546_7, all_546_8, % 98.21/14.13 | all_546_9, all_546_10, all_546_11, all_546_12, all_546_13, all_546_14, % 98.21/14.13 | all_546_15, all_546_16, all_546_17 gives: % 98.21/14.13 | (152) c_COMBS(all_546_16, all_546_16, all_546_16) = all_546_12 & % 98.21/14.13 | c_If(all_546_16, all_546_10) = all_546_9 & c_If(all_546_16, % 98.21/14.13 | all_546_14) = all_546_13 & c_COMBC(all_546_16, % 98.21/14.13 | tc_Arrow__Order__Mirabelle_Oalt, all_546_6) = all_546_5 & % 98.21/14.13 | c_COMBC(all_546_16, tc_Arrow__Order__Mirabelle_Oalt, all_546_16) = % 98.21/14.13 | all_546_7 & tc_prod(tc_Arrow__Order__Mirabelle_Oalt, % 98.21/14.13 | tc_Arrow__Order__Mirabelle_Oalt) = all_546_17 & tc_fun(all_546_17, % 98.21/14.13 | tc_HOL_Obool) = all_546_16 & % 98.21/14.13 | tc_fun(tc_Arrow__Order__Mirabelle_Oalt, all_546_16) = all_546_6 & % 98.21/14.13 | hAPP(all_546_2, v_b_H____) = all_546_1 & hAPP(all_546_4, v_b____) = % 98.21/14.13 | all_546_3 & hAPP(all_546_5, c_Arrow__Order__Mirabelle_Oabove) = % 98.21/14.13 | all_546_4 & hAPP(all_546_7, all_546_3) = all_546_2 & hAPP(all_546_8, % 98.21/14.13 | all_546_1) = all_546_0 & hAPP(all_546_11, v_b_H____) = all_546_10 & % 98.21/14.13 | hAPP(all_546_12, all_546_9) = all_546_8 & hAPP(all_546_15, v_a_H____) % 98.21/14.13 | = all_546_14 & hAPP(c_fequal, v_a____) = all_546_15 & hAPP(c_fequal, % 98.21/14.13 | v_b____) = all_546_11 & $i(all_546_0) & $i(all_546_1) & % 98.21/14.13 | $i(all_546_2) & $i(all_546_3) & $i(all_546_4) & $i(all_546_5) & % 98.21/14.13 | $i(all_546_6) & $i(all_546_7) & $i(all_546_8) & $i(all_546_9) & % 98.21/14.13 | $i(all_546_10) & $i(all_546_11) & $i(all_546_12) & $i(all_546_13) & % 98.21/14.13 | $i(all_546_14) & $i(all_546_15) & $i(all_546_16) & $i(all_546_17) & % 98.21/14.13 | ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 98.21/14.13 | ( ~ (c_Arrow__Order__Mirabelle_Obelow(v1, v_a_H____, v_a____) = v3) | % 98.21/14.13 | ~ (hAPP(v2, v3) = v4) | ~ (hAPP(all_546_13, v1) = v2) | ~ % 98.21/14.13 | (hAPP(v_P____, v0) = v1) | ~ $i(v0) | ? [v5: $i] : % 98.21/14.13 | (c_HOL_OLet(all_546_16, all_546_16, v4, all_546_0) = v5 & % 98.21/14.13 | hAPP(v_Q____, v0) = v5 & $i(v5))) % 98.21/14.13 | % 98.21/14.13 | ALPHA: (152) implies: % 98.21/14.13 | (153) tc_fun(tc_Arrow__Order__Mirabelle_Oalt, all_546_16) = all_546_6 % 98.21/14.13 | (154) tc_fun(all_546_17, tc_HOL_Obool) = all_546_16 % 98.21/14.13 | (155) tc_prod(tc_Arrow__Order__Mirabelle_Oalt, % 98.21/14.13 | tc_Arrow__Order__Mirabelle_Oalt) = all_546_17 % 98.21/14.13 | % 98.21/14.13 | DELTA: instantiating (24) with fresh symbols all_549_0, all_549_1, all_549_2, % 98.21/14.13 | all_549_3, all_549_4, all_549_5, all_549_6, all_549_7, all_549_8, % 98.21/14.13 | all_549_9, all_549_10 gives: % 98.21/14.13 | (156) c_COMBK(all_549_5, all_549_8, c_Arrow__Order__Mirabelle_OLin) = % 98.21/14.13 | all_549_4 & c_FuncSet_OPi(all_549_8, all_549_9, % 98.21/14.13 | c_Arrow__Order__Mirabelle_OProf, all_549_4) = all_549_3 & % 98.21/14.13 | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 98.21/14.13 | tc_Arrow__Order__Mirabelle_Oalt) = all_549_0 & % 98.21/14.13 | tc_prod(tc_Arrow__Order__Mirabelle_Oalt, % 98.21/14.13 | tc_Arrow__Order__Mirabelle_Oalt) = all_549_10 & tc_fun(all_549_8, % 98.21/14.13 | all_549_9) = all_549_7 & tc_fun(all_549_9, tc_HOL_Obool) = % 98.21/14.13 | all_549_5 & tc_fun(all_549_10, tc_HOL_Obool) = all_549_9 & % 98.21/14.13 | tc_fun(tc_Arrow__Order__Mirabelle_Oindi, all_549_9) = all_549_8 & % 98.21/14.13 | c_member(all_549_7) = all_549_6 & c_member(all_549_8) = all_549_2 & % 98.21/14.13 | c_member(all_549_10) = all_549_1 & $i(all_549_0) & $i(all_549_1) & % 98.21/14.13 | $i(all_549_2) & $i(all_549_3) & $i(all_549_4) & $i(all_549_5) & % 98.21/14.13 | $i(all_549_6) & $i(all_549_7) & $i(all_549_8) & $i(all_549_9) & % 98.21/14.13 | $i(all_549_10) & ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | % 98.21/14.13 | ~ (c_Arrow__Order__Mirabelle_Odictator(v1, v0) = v2) | ~ $i(v1) | % 98.21/14.13 | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : % 98.21/14.13 | ? [v7: $i] : (hBOOL(v5) = 0 & hAPP(v4, % 98.21/14.13 | c_Arrow__Order__Mirabelle_OProf) = v5 & hAPP(v3, v0) = v6 & % 98.21/14.13 | hAPP(v1, v3) = v7 & hAPP(all_549_2, v3) = v4 & $i(v7) & $i(v6) & % 98.21/14.13 | $i(v5) & $i(v4) & $i(v3) & ? [v8: $i] : ? [v9: $i] : ? [v10: % 98.21/14.13 | $i] : ? [v11: $i] : ? [v12: $i] : ? [v13: $i] : ? [v14: $i] % 98.21/14.13 | : ? [v15: int] : ( ~ (v15 = 0) & ~ (v9 = v8) & hBOOL(v14) = v15 % 98.21/14.13 | & hBOOL(v13) = 0 & hAPP(v12, v7) = v14 & hAPP(v12, v6) = v13 & % 98.21/14.13 | hAPP(v10, v9) = v11 & hAPP(all_549_0, v8) = v10 & % 98.21/14.13 | hAPP(all_549_1, v11) = v12 & $i(v14) & $i(v13) & $i(v12) & % 98.21/14.13 | $i(v11) & $i(v10) & $i(v9) & $i(v8))) | ? [v3: $i] : ? [v4: % 98.21/14.13 | $i] : ? [v5: int] : ( ~ (v5 = 0) & hBOOL(v4) = v5 & hAPP(v3, % 98.21/14.13 | all_549_3) = v4 & hAPP(all_549_6, v1) = v3 & $i(v4) & $i(v3))) % 98.21/14.13 | % 98.21/14.13 | ALPHA: (156) implies: % 98.21/14.13 | (157) $i(all_549_7) % 98.21/14.13 | (158) $i(all_549_4) % 98.21/14.13 | (159) $i(all_549_3) % 98.21/14.13 | (160) c_member(all_549_8) = all_549_2 % 98.21/14.13 | (161) c_member(all_549_7) = all_549_6 % 98.21/14.13 | (162) tc_fun(tc_Arrow__Order__Mirabelle_Oindi, all_549_9) = all_549_8 % 98.21/14.13 | (163) tc_fun(all_549_10, tc_HOL_Obool) = all_549_9 % 98.21/14.13 | (164) tc_fun(all_549_9, tc_HOL_Obool) = all_549_5 % 98.21/14.13 | (165) tc_fun(all_549_8, all_549_9) = all_549_7 % 98.21/14.13 | (166) tc_prod(tc_Arrow__Order__Mirabelle_Oalt, % 98.21/14.13 | tc_Arrow__Order__Mirabelle_Oalt) = all_549_10 % 98.21/14.14 | (167) c_FuncSet_OPi(all_549_8, all_549_9, c_Arrow__Order__Mirabelle_OProf, % 98.21/14.14 | all_549_4) = all_549_3 % 98.21/14.14 | (168) c_COMBK(all_549_5, all_549_8, c_Arrow__Order__Mirabelle_OLin) = % 98.21/14.14 | all_549_4 % 98.21/14.14 | % 98.21/14.14 | DELTA: instantiating (29) with fresh symbols all_552_0, all_552_1, all_552_2, % 98.21/14.14 | all_552_3, all_552_4, all_552_5 gives: % 98.21/14.14 | (169) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 98.21/14.14 | tc_Arrow__Order__Mirabelle_Oalt) = all_552_0 & % 98.21/14.14 | tc_prod(tc_Arrow__Order__Mirabelle_Oalt, % 98.21/14.14 | tc_Arrow__Order__Mirabelle_Oalt) = all_552_5 & tc_fun(all_552_5, % 98.21/14.14 | tc_HOL_Obool) = all_552_4 & % 98.21/14.14 | tc_fun(tc_Arrow__Order__Mirabelle_Oindi, all_552_4) = all_552_3 & % 98.21/14.14 | c_member(all_552_3) = all_552_2 & c_member(all_552_5) = all_552_1 & % 98.21/14.14 | $i(all_552_0) & $i(all_552_1) & $i(all_552_2) & $i(all_552_3) & % 98.21/14.14 | $i(all_552_4) & $i(all_552_5) & ! [v0: $i] : ! [v1: int] : (v1 = 0 % 98.21/14.14 | | ~ (c_Arrow__Order__Mirabelle_Ounanimity(v0) = v1) | ~ $i(v0) | % 98.21/14.14 | ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : (hBOOL(v4) = % 98.21/14.14 | 0 & hAPP(v3, c_Arrow__Order__Mirabelle_OProf) = v4 & hAPP(v0, v2) % 98.21/14.14 | = v5 & hAPP(all_552_2, v2) = v3 & $i(v5) & $i(v4) & $i(v3) & % 98.21/14.14 | $i(v2) & ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : % 98.21/14.14 | ? [v10: $i] : ? [v11: $i] : ? [v12: int] : ( ~ (v12 = 0) & % 98.21/14.14 | hBOOL(v11) = v12 & hAPP(v10, v5) = v11 & hAPP(v8, v7) = v9 & % 98.21/14.14 | hAPP(all_552_0, v6) = v8 & hAPP(all_552_1, v9) = v10 & $i(v11) % 98.21/14.14 | & $i(v10) & $i(v9) & $i(v8) & $i(v7) & $i(v6) & ! [v13: $i] : % 98.21/14.14 | ! [v14: $i] : ! [v15: $i] : ( ~ (hAPP(v10, v14) = v15) | ~ % 98.21/14.14 | (hAPP(v2, v13) = v14) | ~ $i(v13) | hBOOL(v15) = 0)))) & ! % 98.21/14.14 | [v0: $i] : ( ~ (c_Arrow__Order__Mirabelle_Ounanimity(v0) = 0) | ~ % 98.21/14.14 | $i(v0) | ! [v1: $i] : ! [v2: $i] : ( ~ (hAPP(all_552_2, v1) = v2) % 98.21/14.14 | | ~ $i(v1) | ? [v3: $i] : ? [v4: any] : ? [v5: $i] : % 98.21/14.14 | (hBOOL(v3) = v4 & hAPP(v2, c_Arrow__Order__Mirabelle_OProf) = v3 % 98.21/14.14 | & hAPP(v0, v1) = v5 & $i(v5) & $i(v3) & ( ~ (v4 = 0) | ! [v6: % 98.21/14.14 | $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : ! [v10: % 98.21/14.14 | $i] : ! [v11: $i] : ( ~ (hAPP(v10, v5) = v11) | ~ % 98.21/14.14 | (hAPP(v8, v7) = v9) | ~ (hAPP(all_552_0, v6) = v8) | ~ % 98.21/14.14 | (hAPP(all_552_1, v9) = v10) | ~ $i(v7) | ~ $i(v6) | % 98.21/14.14 | hBOOL(v11) = 0 | ? [v12: $i] : ? [v13: $i] : ? [v14: $i] % 98.21/14.14 | : ? [v15: int] : ( ~ (v15 = 0) & hBOOL(v14) = v15 & % 98.21/14.14 | hAPP(v10, v13) = v14 & hAPP(v1, v12) = v13 & $i(v14) & % 98.21/14.14 | $i(v13) & $i(v12))))))) % 98.21/14.14 | % 98.21/14.14 | ALPHA: (169) implies: % 98.21/14.14 | (170) c_member(all_552_3) = all_552_2 % 98.21/14.14 | (171) tc_fun(tc_Arrow__Order__Mirabelle_Oindi, all_552_4) = all_552_3 % 98.21/14.14 | (172) tc_fun(all_552_5, tc_HOL_Obool) = all_552_4 % 98.21/14.14 | (173) tc_prod(tc_Arrow__Order__Mirabelle_Oalt, % 98.21/14.14 | tc_Arrow__Order__Mirabelle_Oalt) = all_552_5 % 98.21/14.14 | % 98.21/14.14 | DELTA: instantiating (12) with fresh symbols all_555_0, all_555_1, all_555_2, % 98.21/14.14 | all_555_3, all_555_4 gives: % 98.21/14.14 | (174) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 98.21/14.14 | tc_Arrow__Order__Mirabelle_Oalt) = all_555_0 & % 98.21/14.14 | tc_prod(tc_Arrow__Order__Mirabelle_Oalt, % 98.21/14.14 | tc_Arrow__Order__Mirabelle_Oalt) = all_555_4 & tc_fun(all_555_4, % 98.21/14.14 | tc_HOL_Obool) = all_555_3 & c_member(all_555_3) = all_555_2 & % 98.21/14.14 | c_member(all_555_4) = all_555_1 & $i(all_555_0) & $i(all_555_1) & % 98.21/14.14 | $i(all_555_2) & $i(all_555_3) & $i(all_555_4) & ! [v0: $i] : ! [v1: % 98.21/14.14 | $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! % 98.21/14.14 | [v6: $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : (v4 = v3 | ~ % 98.21/14.14 | (c_Arrow__Order__Mirabelle_Obelow(v2, v4, v3) = v8) | ~ (hAPP(v7, % 98.21/14.14 | v8) = v9) | ~ (hAPP(v5, v0) = v6) | ~ (hAPP(all_555_0, v1) = % 98.21/14.14 | v5) | ~ (hAPP(all_555_1, v6) = v7) | ~ $i(v4) | ~ $i(v3) | ~ % 98.21/14.14 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v10: $i] : ? [v11: $i] : ? % 98.21/14.14 | [v12: any] : ? [v13: any] : ? [v14: $i] : ? [v15: $i] : ? [v16: % 98.21/14.14 | $i] : ? [v17: any] : ? [v18: $i] : ? [v19: $i] : ? [v20: $i] % 98.21/14.14 | : ? [v21: $i] : ? [v22: any] : ? [v23: $i] : ? [v24: any] : % 98.21/14.14 | (hBOOL(v23) = v24 & hBOOL(v21) = v22 & hBOOL(v16) = v17 & % 98.21/14.14 | hBOOL(v11) = v12 & hBOOL(v9) = v13 & hAPP(v20, v2) = v21 & % 98.21/14.14 | hAPP(v18, v0) = v19 & hAPP(v15, v2) = v16 & hAPP(v10, % 98.21/14.14 | c_Arrow__Order__Mirabelle_OLin) = v11 & hAPP(v7, v2) = v23 & % 98.21/14.14 | hAPP(v5, v3) = v14 & hAPP(all_555_0, v3) = v18 & hAPP(all_555_1, % 98.21/14.14 | v19) = v20 & hAPP(all_555_1, v14) = v15 & hAPP(all_555_2, v2) = % 98.21/14.14 | v10 & $i(v23) & $i(v21) & $i(v20) & $i(v19) & $i(v18) & $i(v16) & % 98.21/14.14 | $i(v15) & $i(v14) & $i(v11) & $i(v10) & ( ~ (v12 = 0) | (( ~ (v13 % 98.21/14.14 | = 0) | ( ~ (v1 = v0) & ( ~ (v4 = v0) | v17 = 0) & (v4 = % 98.21/14.14 | v0 | (( ~ (v4 = v1) | v22 = 0 | v3 = v0) & (v24 = 0 | % 98.21/14.14 | v4 = v1))))) & (v13 = 0 | v1 = v0 | (v4 = v0 & ~ % 98.21/14.14 | (v17 = 0)) | ( ~ (v4 = v0) & ((v4 = v1 & ~ (v22 = 0) & % 98.21/14.14 | ~ (v3 = v0)) | ( ~ (v24 = 0) & ~ (v4 = v1))))))))) % 98.21/14.14 | % 98.21/14.14 | ALPHA: (174) implies: % 98.21/14.14 | (175) c_member(all_555_3) = all_555_2 % 98.21/14.14 | (176) tc_fun(all_555_4, tc_HOL_Obool) = all_555_3 % 98.21/14.14 | (177) tc_prod(tc_Arrow__Order__Mirabelle_Oalt, % 98.21/14.14 | tc_Arrow__Order__Mirabelle_Oalt) = all_555_4 % 98.21/14.14 | % 98.21/14.14 | DELTA: instantiating (13) with fresh symbols all_558_0, all_558_1, all_558_2, % 98.21/14.14 | all_558_3, all_558_4 gives: % 98.21/14.14 | (178) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 98.21/14.14 | tc_Arrow__Order__Mirabelle_Oalt) = all_558_0 & % 98.21/14.14 | tc_prod(tc_Arrow__Order__Mirabelle_Oalt, % 98.21/14.14 | tc_Arrow__Order__Mirabelle_Oalt) = all_558_4 & tc_fun(all_558_4, % 98.21/14.14 | tc_HOL_Obool) = all_558_3 & c_member(all_558_3) = all_558_2 & % 98.21/14.14 | c_member(all_558_4) = all_558_1 & $i(all_558_0) & $i(all_558_1) & % 98.21/14.14 | $i(all_558_2) & $i(all_558_3) & $i(all_558_4) & ! [v0: $i] : ! [v1: % 98.21/14.14 | $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! % 98.21/14.14 | [v6: $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : ! [v10: $i] : % 98.21/14.14 | ! [v11: $i] : (v4 = v3 | ~ (hAPP(v9, v3) = v10) | ~ (hAPP(v8, v4) = % 98.21/14.14 | v9) | ~ (hAPP(v7, v10) = v11) | ~ (hAPP(v5, v0) = v6) | ~ % 98.21/14.14 | (hAPP(all_558_0, v1) = v5) | ~ (hAPP(all_558_1, v6) = v7) | ~ % 98.21/14.14 | (hAPP(c_Arrow__Order__Mirabelle_Oabove, v2) = v8) | ~ $i(v4) | ~ % 98.21/14.14 | $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v12: $i] : ? % 98.21/14.14 | [v13: $i] : ? [v14: any] : ? [v15: any] : ? [v16: $i] : ? [v17: % 98.21/14.14 | $i] : ? [v18: $i] : ? [v19: $i] : ? [v20: any] : ? [v21: $i] % 98.21/14.14 | : ? [v22: $i] : ? [v23: $i] : ? [v24: any] : ? [v25: $i] : ? % 98.21/14.14 | [v26: any] : (hBOOL(v25) = v26 & hBOOL(v23) = v24 & hBOOL(v19) = % 98.21/14.14 | v20 & hBOOL(v13) = v14 & hBOOL(v11) = v15 & hAPP(v22, v2) = v23 & % 98.21/14.14 | hAPP(v18, v2) = v19 & hAPP(v16, v0) = v17 & hAPP(v12, % 98.21/14.14 | c_Arrow__Order__Mirabelle_OLin) = v13 & hAPP(v7, v2) = v25 & % 98.21/14.14 | hAPP(v5, v4) = v21 & hAPP(all_558_0, v4) = v16 & hAPP(all_558_1, % 98.21/14.14 | v21) = v22 & hAPP(all_558_1, v17) = v18 & hAPP(all_558_2, v2) = % 98.21/14.14 | v12 & $i(v25) & $i(v23) & $i(v22) & $i(v21) & $i(v19) & $i(v18) & % 98.21/14.14 | $i(v17) & $i(v16) & $i(v13) & $i(v12) & ( ~ (v14 = 0) | (( ~ (v15 % 98.21/14.14 | = 0) | ( ~ (v1 = v0) & ( ~ (v3 = v1) | v20 = 0) & (v3 = % 98.21/14.14 | v1 | (( ~ (v3 = v0) | v24 = 0 | v4 = v1) & (v26 = 0 | % 98.21/14.14 | v3 = v0))))) & (v15 = 0 | v1 = v0 | (v3 = v1 & ~ % 98.21/14.14 | (v20 = 0)) | ( ~ (v3 = v1) & ((v3 = v0 & ~ (v24 = 0) & % 98.21/14.14 | ~ (v4 = v1)) | ( ~ (v26 = 0) & ~ (v3 = v0))))))))) % 98.21/14.14 | % 98.21/14.14 | ALPHA: (178) implies: % 98.21/14.14 | (179) c_member(all_558_3) = all_558_2 % 98.21/14.14 | (180) tc_fun(all_558_4, tc_HOL_Obool) = all_558_3 % 98.21/14.14 | (181) tc_prod(tc_Arrow__Order__Mirabelle_Oalt, % 98.21/14.14 | tc_Arrow__Order__Mirabelle_Oalt) = all_558_4 % 98.21/14.14 | % 98.21/14.14 | DELTA: instantiating (26) with fresh symbols all_561_0, all_561_1, all_561_2, % 98.21/14.14 | all_561_3, all_561_4, all_561_5 gives: % 98.21/14.14 | (182) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 98.21/14.14 | tc_Arrow__Order__Mirabelle_Oalt) = all_561_0 & % 98.21/14.14 | tc_prod(tc_Arrow__Order__Mirabelle_Oalt, % 98.21/14.14 | tc_Arrow__Order__Mirabelle_Oalt) = all_561_5 & tc_fun(all_561_5, % 98.21/14.14 | tc_HOL_Obool) = all_561_4 & % 98.21/14.14 | tc_fun(tc_Arrow__Order__Mirabelle_Oindi, all_561_4) = all_561_3 & % 98.21/14.14 | c_member(all_561_3) = all_561_2 & c_member(all_561_5) = all_561_1 & % 98.21/14.14 | $i(all_561_0) & $i(all_561_1) & $i(all_561_2) & $i(all_561_3) & % 98.21/14.14 | $i(all_561_4) & $i(all_561_5) & ! [v0: $i] : ! [v1: int] : (v1 = 0 % 98.21/14.14 | | ~ (c_Arrow__Order__Mirabelle_OIIA(v0) = v1) | ~ $i(v0) | ? % 98.21/14.14 | [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : (hBOOL(v4) = 0 % 98.21/14.14 | & hAPP(v3, c_Arrow__Order__Mirabelle_OProf) = v4 & hAPP(v0, v2) = % 98.21/14.14 | v5 & hAPP(all_561_2, v2) = v3 & $i(v5) & $i(v4) & $i(v3) & $i(v2) % 98.21/14.14 | & ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : % 98.21/14.14 | (hBOOL(v8) = 0 & hAPP(v7, c_Arrow__Order__Mirabelle_OProf) = v8 & % 98.21/14.14 | hAPP(v0, v6) = v9 & hAPP(all_561_2, v6) = v7 & $i(v9) & $i(v8) % 98.21/14.14 | & $i(v7) & $i(v6) & ? [v10: $i] : ? [v11: $i] : ? [v12: $i] % 98.21/14.14 | : ? [v13: $i] : ? [v14: $i] : ? [v15: $i] : ? [v16: any] : % 98.21/14.14 | ? [v17: $i] : ? [v18: any] : (hBOOL(v17) = v18 & hBOOL(v15) = % 98.21/14.14 | v16 & hAPP(v14, v9) = v17 & hAPP(v14, v5) = v15 & hAPP(v12, % 98.21/14.14 | v11) = v13 & hAPP(all_561_0, v10) = v12 & hAPP(all_561_1, % 98.21/14.14 | v13) = v14 & $i(v17) & $i(v15) & $i(v14) & $i(v13) & % 98.21/14.14 | $i(v12) & $i(v11) & $i(v10) & ! [v19: $i] : ! [v20: $i] : % 98.21/14.14 | ! [v21: $i] : ( ~ (hAPP(v14, v20) = v21) | ~ (hAPP(v2, v19) % 98.21/14.14 | = v20) | ~ $i(v19) | ? [v22: any] : ? [v23: $i] : ? % 98.21/14.14 | [v24: $i] : ? [v25: any] : (hBOOL(v24) = v25 & hBOOL(v21) % 98.21/14.14 | = v22 & hAPP(v14, v23) = v24 & hAPP(v6, v19) = v23 & % 98.21/14.14 | $i(v24) & $i(v23) & ( ~ (v22 = 0) | v25 = 0))) & ! [v19: % 98.21/14.14 | $i] : ! [v20: $i] : ! [v21: $i] : ( ~ (hAPP(v14, v20) = % 98.21/14.14 | v21) | ~ (hAPP(v2, v19) = v20) | ~ $i(v19) | ? [v22: % 98.21/14.14 | $i] : ? [v23: $i] : ? [v24: any] : ? [v25: any] : % 98.21/14.14 | (hBOOL(v23) = v24 & hBOOL(v21) = v25 & hAPP(v14, v22) = v23 % 98.21/14.14 | & hAPP(v6, v19) = v22 & $i(v23) & $i(v22) & ( ~ (v24 = 0) % 98.21/14.14 | | v25 = 0))) & ( ~ (v18 = 0) | ~ (v16 = 0)) & (v18 = 0 % 98.21/14.14 | | v16 = 0))))) & ! [v0: $i] : ( ~ % 98.21/14.14 | (c_Arrow__Order__Mirabelle_OIIA(v0) = 0) | ~ $i(v0) | ! [v1: $i] % 98.21/14.14 | : ! [v2: $i] : ( ~ (hAPP(all_561_2, v1) = v2) | ~ $i(v1) | ? % 98.21/14.14 | [v3: $i] : ? [v4: any] : ? [v5: $i] : (hBOOL(v3) = v4 & % 98.21/14.14 | hAPP(v2, c_Arrow__Order__Mirabelle_OProf) = v3 & hAPP(v0, v1) = % 98.21/14.14 | v5 & $i(v5) & $i(v3) & ( ~ (v4 = 0) | ! [v6: $i] : ! [v7: $i] % 98.21/14.14 | : ( ~ (hAPP(all_561_2, v6) = v7) | ~ $i(v6) | ? [v8: $i] : % 98.21/14.14 | ? [v9: any] : ? [v10: $i] : (hBOOL(v8) = v9 & hAPP(v7, % 98.21/14.14 | c_Arrow__Order__Mirabelle_OProf) = v8 & hAPP(v0, v6) = % 98.21/14.14 | v10 & $i(v10) & $i(v8) & ( ~ (v9 = 0) | ! [v11: $i] : ! % 98.21/14.14 | [v12: $i] : ! [v13: $i] : ! [v14: $i] : ! [v15: $i] % 98.21/14.14 | : ! [v16: $i] : ( ~ (hAPP(v15, v5) = v16) | ~ % 98.21/14.14 | (hAPP(v13, v12) = v14) | ~ (hAPP(all_561_0, v11) = % 98.21/14.14 | v13) | ~ (hAPP(all_561_1, v14) = v15) | ~ $i(v12) % 98.21/14.14 | | ~ $i(v11) | ? [v17: $i] : ? [v18: $i] : ? [v19: % 98.21/14.14 | $i] : ? [v20: any] : ? [v21: $i] : ? [v22: $i] : % 98.21/14.14 | ? [v23: any] : (hBOOL(v22) = v23 & hBOOL(v19) = v20 % 98.21/14.14 | & hAPP(v15, v21) = v22 & hAPP(v15, v18) = v19 & % 98.21/14.14 | hAPP(v6, v17) = v21 & hAPP(v1, v17) = v18 & $i(v22) % 98.21/14.14 | & $i(v21) & $i(v19) & $i(v18) & $i(v17) & ( ~ (v23 % 98.21/14.14 | = 0) | ~ (v20 = 0)) & (v23 = 0 | v20 = 0)) | % 98.21/14.14 | ? [v17: any] : ? [v18: $i] : ? [v19: any] : % 98.21/14.14 | (hBOOL(v18) = v19 & hBOOL(v16) = v17 & hAPP(v15, v10) % 98.21/14.14 | = v18 & $i(v18) & ( ~ (v19 = 0) | v17 = 0) & ( ~ % 98.21/14.14 | (v17 = 0) | v19 = 0)))))))))) % 98.21/14.14 | % 98.21/14.14 | ALPHA: (182) implies: % 98.21/14.14 | (183) c_member(all_561_3) = all_561_2 % 98.21/14.14 | (184) tc_fun(tc_Arrow__Order__Mirabelle_Oindi, all_561_4) = all_561_3 % 98.21/14.14 | (185) tc_fun(all_561_5, tc_HOL_Obool) = all_561_4 % 98.21/14.14 | (186) tc_prod(tc_Arrow__Order__Mirabelle_Oalt, % 98.21/14.14 | tc_Arrow__Order__Mirabelle_Oalt) = all_561_5 % 98.21/14.14 | % 98.21/14.14 | GROUND_INST: instantiating (50) with all_486_5, all_492_6, % 98.21/14.14 | tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt, % 98.21/14.14 | simplifying with (77), (86) gives: % 98.21/14.14 | (187) all_492_6 = all_486_5 % 98.21/14.14 | % 98.21/14.14 | GROUND_INST: instantiating (50) with all_505_2, all_508_9, % 98.21/14.14 | tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt, % 98.21/14.14 | simplifying with (96), (106) gives: % 98.21/14.14 | (188) all_508_9 = all_505_2 % 98.21/14.15 | % 98.21/14.15 | GROUND_INST: instantiating (50) with all_508_9, all_510_2, % 98.21/14.15 | tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt, % 98.21/14.15 | simplifying with (106), (112) gives: % 98.21/14.15 | (189) all_510_2 = all_508_9 % 98.21/14.15 | % 98.21/14.15 | GROUND_INST: instantiating (50) with all_492_6, all_513_4, % 98.21/14.15 | tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt, % 98.21/14.15 | simplifying with (86), (118) gives: % 98.21/14.15 | (190) all_513_4 = all_492_6 % 98.21/14.15 | % 98.21/14.15 | GROUND_INST: instantiating (50) with all_510_2, all_516_2, % 98.21/14.15 | tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt, % 98.21/14.15 | simplifying with (112), (122) gives: % 98.21/14.15 | (191) all_516_2 = all_510_2 % 98.21/14.15 | % 98.21/14.15 | GROUND_INST: instantiating (50) with all_516_2, all_525_2, % 98.21/14.15 | tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt, % 98.21/14.15 | simplifying with (122), (132) gives: % 98.21/14.15 | (192) all_525_2 = all_516_2 % 98.21/14.15 | % 98.21/14.15 | GROUND_INST: instantiating (50) with all_505_2, all_528_4, % 98.21/14.15 | tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt, % 98.21/14.15 | simplifying with (96), (136) gives: % 98.21/14.15 | (193) all_528_4 = all_505_2 % 98.21/14.15 | % 98.21/14.15 | GROUND_INST: instantiating (50) with all_498_7, all_528_4, % 98.21/14.15 | tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt, % 98.21/14.15 | simplifying with (88), (136) gives: % 98.21/14.15 | (194) all_528_4 = all_498_7 % 98.21/14.15 | % 98.21/14.15 | GROUND_INST: instantiating (50) with all_492_6, all_528_4, % 98.21/14.15 | tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt, % 98.21/14.15 | simplifying with (86), (136) gives: % 98.21/14.15 | (195) all_528_4 = all_492_6 % 98.21/14.15 | % 98.21/14.15 | GROUND_INST: instantiating (50) with all_505_2, all_531_3, % 98.21/14.15 | tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt, % 98.21/14.15 | simplifying with (96), (141) gives: % 98.21/14.15 | (196) all_531_3 = all_505_2 % 98.21/14.15 | % 98.21/14.15 | GROUND_INST: instantiating (50) with all_531_3, all_534_4, % 98.21/14.15 | tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt, % 98.21/14.15 | simplifying with (141), (145) gives: % 98.21/14.15 | (197) all_534_4 = all_531_3 % 98.21/14.15 | % 98.21/14.15 | GROUND_INST: instantiating (50) with all_540_2, all_543_8, % 98.21/14.15 | tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt, % 98.21/14.15 | simplifying with (149), (151) gives: % 98.21/14.15 | (198) all_543_8 = all_540_2 % 98.21/14.15 | % 98.21/14.15 | GROUND_INST: instantiating (50) with all_513_4, all_543_8, % 98.21/14.15 | tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt, % 98.21/14.15 | simplifying with (118), (151) gives: % 98.21/14.15 | (199) all_543_8 = all_513_4 % 98.21/14.15 | % 98.21/14.15 | GROUND_INST: instantiating (50) with all_537_2, all_546_17, % 98.21/14.15 | tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt, % 98.21/14.15 | simplifying with (147), (155) gives: % 98.21/14.15 | (200) all_546_17 = all_537_2 % 98.21/14.15 | % 98.21/14.15 | GROUND_INST: instantiating (50) with all_519_4, all_546_17, % 98.21/14.15 | tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt, % 98.21/14.15 | simplifying with (126), (155) gives: % 98.21/14.15 | (201) all_546_17 = all_519_4 % 98.21/14.15 | % 98.21/14.15 | GROUND_INST: instantiating (50) with all_486_5, all_546_17, % 98.21/14.15 | tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt, % 98.21/14.15 | simplifying with (77), (155) gives: % 98.21/14.15 | (202) all_546_17 = all_486_5 % 98.21/14.15 | % 98.21/14.15 | GROUND_INST: instantiating (50) with all_480_2, all_546_17, % 98.21/14.15 | tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt, % 98.21/14.15 | simplifying with (56), (155) gives: % 98.21/14.15 | (203) all_546_17 = all_480_2 % 98.21/14.15 | % 98.21/14.15 | GROUND_INST: instantiating (50) with all_534_4, all_549_10, % 98.21/14.15 | tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt, % 98.21/14.15 | simplifying with (145), (166) gives: % 98.21/14.15 | (204) all_549_10 = all_534_4 % 98.21/14.15 | % 98.21/14.15 | GROUND_INST: instantiating (50) with all_525_2, all_555_4, % 98.21/14.15 | tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt, % 98.21/14.15 | simplifying with (132), (177) gives: % 98.21/14.15 | (205) all_555_4 = all_525_2 % 98.21/14.15 | % 98.21/14.15 | GROUND_INST: instantiating (50) with all_500_2, all_555_4, % 98.21/14.15 | tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt, % 98.21/14.15 | simplifying with (92), (177) gives: % 98.21/14.15 | (206) all_555_4 = all_500_2 % 98.21/14.15 | % 98.21/14.15 | GROUND_INST: instantiating (50) with all_549_10, all_558_4, % 98.21/14.15 | tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt, % 98.21/14.15 | simplifying with (166), (181) gives: % 98.21/14.15 | (207) all_558_4 = all_549_10 % 98.21/14.15 | % 98.21/14.15 | GROUND_INST: instantiating (50) with all_482_5, all_558_4, % 98.21/14.15 | tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt, % 98.21/14.15 | simplifying with (63), (181) gives: % 98.21/14.15 | (208) all_558_4 = all_482_5 % 98.21/14.15 | % 98.21/14.15 | GROUND_INST: instantiating (50) with all_552_5, all_561_5, % 98.21/14.15 | tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt, % 98.21/14.15 | simplifying with (173), (186) gives: % 98.21/14.15 | (209) all_561_5 = all_552_5 % 98.21/14.15 | % 98.21/14.15 | GROUND_INST: instantiating (50) with all_543_8, all_561_5, % 98.21/14.15 | tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt, % 98.21/14.15 | simplifying with (151), (186) gives: % 98.21/14.15 | (210) all_561_5 = all_543_8 % 98.21/14.15 | % 98.21/14.15 | GROUND_INST: instantiating (50) with all_484_5, all_561_5, % 98.21/14.15 | tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt, % 98.21/14.15 | simplifying with (69), (186) gives: % 98.21/14.15 | (211) all_561_5 = all_484_5 % 98.21/14.15 | % 98.21/14.15 | COMBINE_EQS: (209), (211) imply: % 98.21/14.15 | (212) all_552_5 = all_484_5 % 98.21/14.15 | % 98.21/14.15 | COMBINE_EQS: (209), (210) imply: % 98.21/14.15 | (213) all_552_5 = all_543_8 % 98.21/14.15 | % 98.21/14.15 | COMBINE_EQS: (207), (208) imply: % 98.21/14.15 | (214) all_549_10 = all_482_5 % 98.21/14.15 | % 98.21/14.15 | SIMP: (214) implies: % 98.21/14.15 | (215) all_549_10 = all_482_5 % 98.21/14.15 | % 98.21/14.15 | COMBINE_EQS: (205), (206) imply: % 98.21/14.15 | (216) all_525_2 = all_500_2 % 98.21/14.15 | % 98.21/14.15 | SIMP: (216) implies: % 98.21/14.15 | (217) all_525_2 = all_500_2 % 98.21/14.15 | % 98.21/14.15 | COMBINE_EQS: (212), (213) imply: % 98.21/14.15 | (218) all_543_8 = all_484_5 % 98.21/14.15 | % 98.21/14.15 | SIMP: (218) implies: % 98.21/14.15 | (219) all_543_8 = all_484_5 % 98.21/14.15 | % 98.21/14.15 | COMBINE_EQS: (204), (215) imply: % 98.21/14.15 | (220) all_534_4 = all_482_5 % 98.21/14.15 | % 98.21/14.15 | SIMP: (220) implies: % 98.21/14.15 | (221) all_534_4 = all_482_5 % 98.21/14.15 | % 98.21/14.15 | COMBINE_EQS: (200), (203) imply: % 98.21/14.15 | (222) all_537_2 = all_480_2 % 98.21/14.15 | % 98.21/14.15 | COMBINE_EQS: (200), (202) imply: % 98.21/14.15 | (223) all_537_2 = all_486_5 % 98.21/14.15 | % 98.21/14.15 | COMBINE_EQS: (200), (201) imply: % 98.21/14.15 | (224) all_537_2 = all_519_4 % 98.21/14.15 | % 98.21/14.15 | COMBINE_EQS: (198), (219) imply: % 98.21/14.15 | (225) all_540_2 = all_484_5 % 98.21/14.15 | % 98.21/14.15 | COMBINE_EQS: (198), (199) imply: % 98.21/14.15 | (226) all_540_2 = all_513_4 % 98.21/14.15 | % 98.21/14.15 | COMBINE_EQS: (225), (226) imply: % 98.21/14.15 | (227) all_513_4 = all_484_5 % 98.21/14.15 | % 98.21/14.15 | SIMP: (227) implies: % 98.21/14.15 | (228) all_513_4 = all_484_5 % 98.21/14.15 | % 98.21/14.15 | COMBINE_EQS: (223), (224) imply: % 98.21/14.15 | (229) all_519_4 = all_486_5 % 98.21/14.15 | % 98.21/14.15 | COMBINE_EQS: (222), (224) imply: % 98.21/14.15 | (230) all_519_4 = all_480_2 % 98.21/14.15 | % 98.21/14.15 | COMBINE_EQS: (197), (221) imply: % 98.21/14.15 | (231) all_531_3 = all_482_5 % 98.21/14.15 | % 98.21/14.15 | SIMP: (231) implies: % 98.21/14.15 | (232) all_531_3 = all_482_5 % 98.21/14.15 | % 98.21/14.15 | COMBINE_EQS: (196), (232) imply: % 98.21/14.15 | (233) all_505_2 = all_482_5 % 98.21/14.15 | % 98.21/14.15 | SIMP: (233) implies: % 98.21/14.15 | (234) all_505_2 = all_482_5 % 98.21/14.15 | % 98.21/14.15 | COMBINE_EQS: (194), (195) imply: % 98.21/14.15 | (235) all_498_7 = all_492_6 % 98.21/14.15 | % 98.21/14.15 | COMBINE_EQS: (193), (194) imply: % 98.21/14.15 | (236) all_505_2 = all_498_7 % 98.21/14.15 | % 98.21/14.15 | SIMP: (236) implies: % 98.21/14.15 | (237) all_505_2 = all_498_7 % 98.21/14.15 | % 98.21/14.15 | COMBINE_EQS: (192), (217) imply: % 98.21/14.15 | (238) all_516_2 = all_500_2 % 98.21/14.15 | % 98.21/14.15 | SIMP: (238) implies: % 98.21/14.15 | (239) all_516_2 = all_500_2 % 98.21/14.15 | % 98.21/14.15 | COMBINE_EQS: (229), (230) imply: % 98.21/14.15 | (240) all_486_5 = all_480_2 % 98.21/14.15 | % 98.21/14.15 | SIMP: (240) implies: % 98.21/14.15 | (241) all_486_5 = all_480_2 % 98.21/14.15 | % 98.21/14.15 | COMBINE_EQS: (191), (239) imply: % 98.21/14.15 | (242) all_510_2 = all_500_2 % 98.21/14.15 | % 98.21/14.15 | SIMP: (242) implies: % 98.21/14.15 | (243) all_510_2 = all_500_2 % 98.21/14.15 | % 98.21/14.15 | COMBINE_EQS: (190), (228) imply: % 98.21/14.15 | (244) all_492_6 = all_484_5 % 98.21/14.15 | % 98.21/14.15 | SIMP: (244) implies: % 98.21/14.15 | (245) all_492_6 = all_484_5 % 98.21/14.15 | % 98.21/14.15 | COMBINE_EQS: (189), (243) imply: % 98.21/14.15 | (246) all_508_9 = all_500_2 % 98.21/14.15 | % 98.21/14.15 | SIMP: (246) implies: % 98.21/14.15 | (247) all_508_9 = all_500_2 % 98.21/14.15 | % 98.21/14.15 | COMBINE_EQS: (188), (247) imply: % 98.21/14.15 | (248) all_505_2 = all_500_2 % 98.21/14.15 | % 98.21/14.15 | SIMP: (248) implies: % 98.21/14.15 | (249) all_505_2 = all_500_2 % 98.21/14.15 | % 98.21/14.15 | COMBINE_EQS: (237), (249) imply: % 98.21/14.15 | (250) all_500_2 = all_498_7 % 98.21/14.15 | % 98.21/14.15 | COMBINE_EQS: (234), (249) imply: % 98.21/14.15 | (251) all_500_2 = all_482_5 % 98.21/14.15 | % 98.21/14.15 | COMBINE_EQS: (250), (251) imply: % 98.21/14.15 | (252) all_498_7 = all_482_5 % 98.21/14.15 | % 98.21/14.15 | SIMP: (252) implies: % 98.21/14.15 | (253) all_498_7 = all_482_5 % 98.21/14.15 | % 98.21/14.15 | COMBINE_EQS: (235), (253) imply: % 98.21/14.15 | (254) all_492_6 = all_482_5 % 98.21/14.15 | % 98.21/14.15 | SIMP: (254) implies: % 98.21/14.15 | (255) all_492_6 = all_482_5 % 98.21/14.15 | % 98.21/14.15 | COMBINE_EQS: (245), (255) imply: % 98.21/14.15 | (256) all_484_5 = all_482_5 % 98.21/14.15 | % 98.21/14.15 | COMBINE_EQS: (187), (245) imply: % 98.21/14.15 | (257) all_486_5 = all_484_5 % 98.21/14.15 | % 98.21/14.15 | SIMP: (257) implies: % 98.21/14.15 | (258) all_486_5 = all_484_5 % 98.21/14.15 | % 98.21/14.15 | COMBINE_EQS: (241), (258) imply: % 98.21/14.15 | (259) all_484_5 = all_480_2 % 98.21/14.15 | % 98.21/14.15 | SIMP: (259) implies: % 98.21/14.16 | (260) all_484_5 = all_480_2 % 98.21/14.16 | % 98.21/14.16 | COMBINE_EQS: (256), (260) imply: % 98.21/14.16 | (261) all_482_5 = all_480_2 % 98.21/14.16 | % 98.21/14.16 | COMBINE_EQS: (245), (260) imply: % 98.21/14.16 | (262) all_492_6 = all_480_2 % 98.21/14.16 | % 98.21/14.16 | COMBINE_EQS: (253), (261) imply: % 98.21/14.16 | (263) all_498_7 = all_480_2 % 98.21/14.16 | % 98.21/14.16 | COMBINE_EQS: (251), (261) imply: % 98.21/14.16 | (264) all_500_2 = all_480_2 % 98.21/14.16 | % 98.21/14.16 | COMBINE_EQS: (249), (264) imply: % 98.21/14.16 | (265) all_505_2 = all_480_2 % 98.21/14.16 | % 98.21/14.16 | COMBINE_EQS: (247), (264) imply: % 98.21/14.16 | (266) all_508_9 = all_480_2 % 98.21/14.16 | % 98.21/14.16 | COMBINE_EQS: (243), (264) imply: % 98.21/14.16 | (267) all_510_2 = all_480_2 % 98.21/14.16 | % 98.21/14.16 | COMBINE_EQS: (228), (260) imply: % 98.21/14.16 | (268) all_513_4 = all_480_2 % 98.21/14.16 | % 98.21/14.16 | COMBINE_EQS: (239), (264) imply: % 98.21/14.16 | (269) all_516_2 = all_480_2 % 98.21/14.16 | % 98.21/14.16 | COMBINE_EQS: (217), (264) imply: % 98.21/14.16 | (270) all_525_2 = all_480_2 % 98.21/14.16 | % 98.21/14.16 | COMBINE_EQS: (194), (263) imply: % 98.21/14.16 | (271) all_528_4 = all_480_2 % 98.21/14.16 | % 98.21/14.16 | COMBINE_EQS: (232), (261) imply: % 98.21/14.16 | (272) all_531_3 = all_480_2 % 98.21/14.16 | % 98.21/14.16 | COMBINE_EQS: (221), (261) imply: % 98.21/14.16 | (273) all_534_4 = all_480_2 % 98.21/14.16 | % 98.21/14.16 | COMBINE_EQS: (215), (261) imply: % 98.21/14.16 | (274) all_549_10 = all_480_2 % 98.21/14.16 | % 98.21/14.16 | COMBINE_EQS: (212), (260) imply: % 98.21/14.16 | (275) all_552_5 = all_480_2 % 98.21/14.16 | % 98.21/14.16 | COMBINE_EQS: (206), (264) imply: % 98.21/14.16 | (276) all_555_4 = all_480_2 % 98.21/14.16 | % 98.21/14.16 | COMBINE_EQS: (208), (261) imply: % 98.21/14.16 | (277) all_558_4 = all_480_2 % 98.21/14.16 | % 98.21/14.16 | COMBINE_EQS: (209), (275) imply: % 98.21/14.16 | (278) all_561_5 = all_480_2 % 98.21/14.16 | % 98.21/14.16 | REDUCE: (185), (278) imply: % 98.21/14.16 | (279) tc_fun(all_480_2, tc_HOL_Obool) = all_561_4 % 98.21/14.16 | % 98.21/14.16 | REDUCE: (180), (277) imply: % 98.21/14.16 | (280) tc_fun(all_480_2, tc_HOL_Obool) = all_558_3 % 98.21/14.16 | % 98.21/14.16 | REDUCE: (176), (276) imply: % 98.21/14.16 | (281) tc_fun(all_480_2, tc_HOL_Obool) = all_555_3 % 98.21/14.16 | % 98.21/14.16 | REDUCE: (172), (275) imply: % 98.21/14.16 | (282) tc_fun(all_480_2, tc_HOL_Obool) = all_552_4 % 98.21/14.16 | % 98.21/14.16 | REDUCE: (163), (274) imply: % 98.21/14.16 | (283) tc_fun(all_480_2, tc_HOL_Obool) = all_549_9 % 98.21/14.16 | % 98.21/14.16 | REDUCE: (154), (203) imply: % 98.21/14.16 | (284) tc_fun(all_480_2, tc_HOL_Obool) = all_546_16 % 98.21/14.16 | % 98.21/14.16 | REDUCE: (144), (273) imply: % 98.21/14.16 | (285) tc_fun(all_480_2, tc_HOL_Obool) = all_534_3 % 98.21/14.16 | % 98.21/14.16 | REDUCE: (140), (272) imply: % 98.21/14.16 | (286) tc_fun(all_480_2, tc_HOL_Obool) = all_531_2 % 98.21/14.16 | % 98.21/14.16 | REDUCE: (135), (271) imply: % 98.21/14.16 | (287) tc_fun(all_480_2, tc_HOL_Obool) = all_528_3 % 98.21/14.16 | % 98.21/14.16 | REDUCE: (131), (270) imply: % 98.21/14.16 | (288) tc_fun(all_480_2, tc_HOL_Obool) = all_525_1 % 98.21/14.16 | % 98.21/14.16 | REDUCE: (125), (230) imply: % 98.21/14.16 | (289) tc_fun(all_480_2, tc_HOL_Obool) = all_519_3 % 98.21/14.16 | % 98.21/14.16 | REDUCE: (121), (269) imply: % 98.21/14.16 | (290) tc_fun(all_480_2, tc_HOL_Obool) = all_516_1 % 98.21/14.16 | % 98.21/14.16 | REDUCE: (117), (268) imply: % 98.21/14.16 | (291) tc_fun(all_480_2, tc_HOL_Obool) = all_513_3 % 98.21/14.16 | % 98.21/14.16 | REDUCE: (111), (267) imply: % 98.21/14.16 | (292) tc_fun(all_480_2, tc_HOL_Obool) = all_510_1 % 98.21/14.16 | % 98.21/14.16 | REDUCE: (103), (266) imply: % 98.21/14.16 | (293) tc_fun(all_480_2, tc_HOL_Obool) = all_508_8 % 98.21/14.16 | % 98.21/14.16 | REDUCE: (95), (265) imply: % 98.21/14.16 | (294) tc_fun(all_480_2, tc_HOL_Obool) = all_505_1 % 98.21/14.16 | % 98.21/14.16 | REDUCE: (91), (264) imply: % 98.21/14.16 | (295) tc_fun(all_480_2, tc_HOL_Obool) = all_500_1 % 98.21/14.16 | % 98.21/14.16 | REDUCE: (85), (262) imply: % 98.21/14.16 | (296) tc_fun(all_480_2, tc_HOL_Obool) = all_492_5 % 98.21/14.16 | % 98.21/14.16 | REDUCE: (76), (241) imply: % 98.21/14.16 | (297) tc_fun(all_480_2, tc_HOL_Obool) = all_486_4 % 98.21/14.16 | % 98.21/14.16 | REDUCE: (68), (260) imply: % 98.21/14.16 | (298) tc_fun(all_480_2, tc_HOL_Obool) = all_484_4 % 98.21/14.16 | % 98.21/14.16 | REDUCE: (62), (261) imply: % 98.21/14.16 | (299) tc_fun(all_480_2, tc_HOL_Obool) = all_482_4 % 98.21/14.16 | % 98.21/14.16 | REDUCE: (58), (261) imply: % 98.21/14.16 | (300) $i(all_480_2) % 98.21/14.16 | % 98.21/14.16 | GROUND_INST: instantiating (49) with all_500_1, all_505_1, tc_HOL_Obool, % 98.21/14.16 | all_480_2, simplifying with (294), (295) gives: % 98.21/14.16 | (301) all_505_1 = all_500_1 % 98.21/14.16 | % 98.21/14.16 | GROUND_INST: instantiating (49) with all_480_1, all_508_8, tc_HOL_Obool, % 98.21/14.16 | all_480_2, simplifying with (55), (293) gives: % 98.21/14.16 | (302) all_508_8 = all_480_1 % 98.21/14.16 | % 98.21/14.16 | GROUND_INST: instantiating (49) with all_500_1, all_508_8, tc_HOL_Obool, % 98.21/14.16 | all_480_2, simplifying with (293), (295) gives: % 98.21/14.16 | (303) all_508_8 = all_500_1 % 98.21/14.16 | % 98.21/14.16 | GROUND_INST: instantiating (49) with all_516_1, all_519_3, tc_HOL_Obool, % 98.21/14.16 | all_480_2, simplifying with (289), (290) gives: % 98.21/14.16 | (304) all_519_3 = all_516_1 % 98.21/14.16 | % 98.21/14.16 | GROUND_INST: instantiating (49) with all_513_3, all_519_3, tc_HOL_Obool, % 98.21/14.16 | all_480_2, simplifying with (289), (291) gives: % 98.21/14.16 | (305) all_519_3 = all_513_3 % 98.21/14.16 | % 98.21/14.16 | GROUND_INST: instantiating (49) with all_500_1, all_519_3, tc_HOL_Obool, % 98.21/14.16 | all_480_2, simplifying with (289), (295) gives: % 98.21/14.16 | (306) all_519_3 = all_500_1 % 98.21/14.16 | % 98.21/14.16 | GROUND_INST: instantiating (49) with all_516_1, all_525_1, tc_HOL_Obool, % 98.21/14.16 | all_480_2, simplifying with (288), (290) gives: % 98.21/14.16 | (307) all_525_1 = all_516_1 % 98.21/14.16 | % 98.21/14.16 | GROUND_INST: instantiating (49) with all_492_5, all_525_1, tc_HOL_Obool, % 98.21/14.16 | all_480_2, simplifying with (288), (296) gives: % 98.21/14.16 | (308) all_525_1 = all_492_5 % 98.21/14.16 | % 98.21/14.16 | GROUND_INST: instantiating (49) with all_528_3, all_531_2, tc_HOL_Obool, % 98.21/14.16 | all_480_2, simplifying with (286), (287) gives: % 98.21/14.16 | (309) all_531_2 = all_528_3 % 98.21/14.16 | % 98.21/14.16 | GROUND_INST: instantiating (49) with all_519_3, all_531_2, tc_HOL_Obool, % 98.21/14.16 | all_480_2, simplifying with (286), (289) gives: % 98.21/14.16 | (310) all_531_2 = all_519_3 % 98.21/14.16 | % 98.21/14.16 | GROUND_INST: instantiating (49) with all_534_3, all_546_16, tc_HOL_Obool, % 98.21/14.16 | all_480_2, simplifying with (284), (285) gives: % 98.21/14.16 | (311) all_546_16 = all_534_3 % 98.21/14.16 | % 98.21/14.16 | GROUND_INST: instantiating (49) with all_531_2, all_546_16, tc_HOL_Obool, % 98.21/14.16 | all_480_2, simplifying with (284), (286) gives: % 98.21/14.16 | (312) all_546_16 = all_531_2 % 98.21/14.16 | % 98.21/14.16 | GROUND_INST: instantiating (49) with all_510_1, all_546_16, tc_HOL_Obool, % 98.21/14.16 | all_480_2, simplifying with (284), (292) gives: % 98.21/14.16 | (313) all_546_16 = all_510_1 % 98.21/14.16 | % 98.21/14.16 | GROUND_INST: instantiating (49) with all_505_1, all_549_9, tc_HOL_Obool, % 98.21/14.16 | all_480_2, simplifying with (283), (294) gives: % 98.21/14.16 | (314) all_549_9 = all_505_1 % 98.21/14.16 | % 98.21/14.16 | GROUND_INST: instantiating (49) with all_508_8, all_552_4, tc_HOL_Obool, % 98.21/14.16 | all_480_2, simplifying with (282), (293) gives: % 98.21/14.16 | (315) all_552_4 = all_508_8 % 98.21/14.16 | % 98.21/14.16 | GROUND_INST: instantiating (49) with all_486_4, all_552_4, tc_HOL_Obool, % 98.21/14.16 | all_480_2, simplifying with (282), (297) gives: % 98.21/14.16 | (316) all_552_4 = all_486_4 % 98.21/14.16 | % 98.21/14.16 | GROUND_INST: instantiating (49) with all_549_9, all_555_3, tc_HOL_Obool, % 98.21/14.16 | all_480_2, simplifying with (281), (283) gives: % 98.21/14.16 | (317) all_555_3 = all_549_9 % 98.21/14.16 | % 98.21/14.16 | GROUND_INST: instantiating (49) with all_555_3, all_558_3, tc_HOL_Obool, % 98.21/14.16 | all_480_2, simplifying with (280), (281) gives: % 98.21/14.16 | (318) all_558_3 = all_555_3 % 98.21/14.16 | % 98.21/14.16 | GROUND_INST: instantiating (49) with all_482_4, all_558_3, tc_HOL_Obool, % 98.21/14.16 | all_480_2, simplifying with (280), (299) gives: % 98.21/14.16 | (319) all_558_3 = all_482_4 % 98.21/14.16 | % 98.21/14.16 | GROUND_INST: instantiating (49) with all_500_1, all_561_4, tc_HOL_Obool, % 98.21/14.16 | all_480_2, simplifying with (279), (295) gives: % 98.21/14.16 | (320) all_561_4 = all_500_1 % 98.21/14.16 | % 98.21/14.16 | GROUND_INST: instantiating (49) with all_484_4, all_561_4, tc_HOL_Obool, % 98.21/14.16 | all_480_2, simplifying with (279), (298) gives: % 98.21/14.16 | (321) all_561_4 = all_484_4 % 98.21/14.16 | % 98.21/14.16 | COMBINE_EQS: (320), (321) imply: % 98.21/14.16 | (322) all_500_1 = all_484_4 % 98.21/14.16 | % 98.21/14.16 | SIMP: (322) implies: % 98.21/14.16 | (323) all_500_1 = all_484_4 % 98.21/14.16 | % 98.21/14.16 | COMBINE_EQS: (318), (319) imply: % 98.21/14.16 | (324) all_555_3 = all_482_4 % 98.21/14.16 | % 98.21/14.16 | SIMP: (324) implies: % 98.21/14.16 | (325) all_555_3 = all_482_4 % 98.21/14.16 | % 98.21/14.16 | COMBINE_EQS: (317), (325) imply: % 98.21/14.16 | (326) all_549_9 = all_482_4 % 98.21/14.16 | % 98.21/14.16 | SIMP: (326) implies: % 98.21/14.16 | (327) all_549_9 = all_482_4 % 98.21/14.16 | % 98.21/14.16 | COMBINE_EQS: (315), (316) imply: % 98.21/14.16 | (328) all_508_8 = all_486_4 % 98.21/14.16 | % 98.21/14.16 | SIMP: (328) implies: % 98.21/14.16 | (329) all_508_8 = all_486_4 % 98.21/14.16 | % 98.21/14.16 | COMBINE_EQS: (314), (327) imply: % 98.21/14.16 | (330) all_505_1 = all_482_4 % 98.21/14.16 | % 98.21/14.16 | SIMP: (330) implies: % 98.21/14.16 | (331) all_505_1 = all_482_4 % 98.21/14.16 | % 98.21/14.16 | COMBINE_EQS: (311), (313) imply: % 98.21/14.16 | (332) all_534_3 = all_510_1 % 98.21/14.16 | % 98.21/14.16 | COMBINE_EQS: (311), (312) imply: % 98.21/14.16 | (333) all_534_3 = all_531_2 % 98.21/14.16 | % 98.21/14.16 | COMBINE_EQS: (332), (333) imply: % 98.21/14.16 | (334) all_531_2 = all_510_1 % 98.21/14.16 | % 98.21/14.16 | SIMP: (334) implies: % 98.21/14.16 | (335) all_531_2 = all_510_1 % 98.21/14.16 | % 98.21/14.16 | COMBINE_EQS: (309), (310) imply: % 98.21/14.16 | (336) all_528_3 = all_519_3 % 98.21/14.16 | % 98.21/14.16 | COMBINE_EQS: (309), (335) imply: % 98.21/14.16 | (337) all_528_3 = all_510_1 % 98.21/14.16 | % 98.21/14.16 | COMBINE_EQS: (336), (337) imply: % 98.21/14.16 | (338) all_519_3 = all_510_1 % 98.21/14.16 | % 98.21/14.16 | SIMP: (338) implies: % 98.21/14.16 | (339) all_519_3 = all_510_1 % 98.21/14.16 | % 98.21/14.16 | COMBINE_EQS: (307), (308) imply: % 98.21/14.16 | (340) all_516_1 = all_492_5 % 98.21/14.16 | % 98.21/14.16 | SIMP: (340) implies: % 98.21/14.16 | (341) all_516_1 = all_492_5 % 98.21/14.16 | % 98.21/14.16 | COMBINE_EQS: (304), (305) imply: % 98.21/14.16 | (342) all_516_1 = all_513_3 % 98.21/14.16 | % 98.21/14.16 | SIMP: (342) implies: % 98.21/14.16 | (343) all_516_1 = all_513_3 % 98.21/14.16 | % 98.21/14.16 | COMBINE_EQS: (305), (339) imply: % 98.21/14.16 | (344) all_513_3 = all_510_1 % 98.21/14.16 | % 98.21/14.16 | COMBINE_EQS: (305), (306) imply: % 98.21/14.16 | (345) all_513_3 = all_500_1 % 98.21/14.16 | % 98.21/14.16 | COMBINE_EQS: (341), (343) imply: % 98.21/14.16 | (346) all_513_3 = all_492_5 % 98.21/14.16 | % 98.21/14.16 | SIMP: (346) implies: % 98.21/14.16 | (347) all_513_3 = all_492_5 % 98.21/14.17 | % 98.21/14.17 | COMBINE_EQS: (344), (347) imply: % 98.21/14.17 | (348) all_510_1 = all_492_5 % 98.21/14.17 | % 98.21/14.17 | COMBINE_EQS: (344), (345) imply: % 98.21/14.17 | (349) all_510_1 = all_500_1 % 98.21/14.17 | % 98.21/14.17 | COMBINE_EQS: (348), (349) imply: % 98.21/14.17 | (350) all_500_1 = all_492_5 % 98.21/14.17 | % 98.21/14.17 | SIMP: (350) implies: % 98.21/14.17 | (351) all_500_1 = all_492_5 % 98.21/14.17 | % 98.21/14.17 | COMBINE_EQS: (303), (329) imply: % 98.21/14.17 | (352) all_500_1 = all_486_4 % 98.21/14.17 | % 98.21/14.17 | SIMP: (352) implies: % 98.21/14.17 | (353) all_500_1 = all_486_4 % 98.21/14.17 | % 98.21/14.17 | COMBINE_EQS: (302), (329) imply: % 98.21/14.17 | (354) all_486_4 = all_480_1 % 98.21/14.17 | % 98.21/14.17 | COMBINE_EQS: (301), (331) imply: % 98.21/14.17 | (355) all_500_1 = all_482_4 % 98.21/14.17 | % 98.21/14.17 | SIMP: (355) implies: % 98.21/14.17 | (356) all_500_1 = all_482_4 % 98.21/14.17 | % 98.21/14.17 | COMBINE_EQS: (351), (356) imply: % 98.21/14.17 | (357) all_492_5 = all_482_4 % 98.21/14.17 | % 98.21/14.17 | COMBINE_EQS: (351), (353) imply: % 98.21/14.17 | (358) all_492_5 = all_486_4 % 98.21/14.17 | % 98.21/14.17 | COMBINE_EQS: (323), (351) imply: % 98.21/14.17 | (359) all_492_5 = all_484_4 % 98.21/14.17 | % 98.21/14.17 | COMBINE_EQS: (358), (359) imply: % 98.21/14.17 | (360) all_486_4 = all_484_4 % 98.21/14.17 | % 98.21/14.17 | SIMP: (360) implies: % 98.21/14.17 | (361) all_486_4 = all_484_4 % 98.21/14.17 | % 98.21/14.17 | COMBINE_EQS: (357), (359) imply: % 98.21/14.17 | (362) all_484_4 = all_482_4 % 98.21/14.17 | % 98.21/14.17 | COMBINE_EQS: (354), (361) imply: % 98.21/14.17 | (363) all_484_4 = all_480_1 % 98.21/14.17 | % 98.21/14.17 | SIMP: (363) implies: % 98.21/14.17 | (364) all_484_4 = all_480_1 % 98.21/14.17 | % 98.21/14.17 | COMBINE_EQS: (362), (364) imply: % 98.21/14.17 | (365) all_482_4 = all_480_1 % 98.21/14.17 | % 98.21/14.17 | SIMP: (365) implies: % 98.21/14.17 | (366) all_482_4 = all_480_1 % 98.21/14.17 | % 98.21/14.17 | COMBINE_EQS: (359), (364) imply: % 98.21/14.17 | (367) all_492_5 = all_480_1 % 98.21/14.17 | % 98.21/14.17 | COMBINE_EQS: (351), (367) imply: % 98.21/14.17 | (368) all_500_1 = all_480_1 % 98.21/14.17 | % 98.21/14.17 | COMBINE_EQS: (331), (366) imply: % 98.21/14.17 | (369) all_505_1 = all_480_1 % 98.21/14.17 | % 98.21/14.17 | COMBINE_EQS: (348), (367) imply: % 98.21/14.17 | (370) all_510_1 = all_480_1 % 98.21/14.17 | % 98.21/14.17 | COMBINE_EQS: (344), (370) imply: % 98.21/14.17 | (371) all_513_3 = all_480_1 % 98.21/14.17 | % 98.21/14.17 | COMBINE_EQS: (341), (367) imply: % 98.21/14.17 | (372) all_516_1 = all_480_1 % 98.21/14.17 | % 98.21/14.17 | COMBINE_EQS: (305), (371) imply: % 98.21/14.17 | (373) all_519_3 = all_480_1 % 98.21/14.17 | % 98.21/14.17 | COMBINE_EQS: (308), (367) imply: % 98.21/14.17 | (374) all_525_1 = all_480_1 % 98.21/14.17 | % 98.21/14.17 | COMBINE_EQS: (337), (370) imply: % 98.21/14.17 | (375) all_528_3 = all_480_1 % 98.21/14.17 | % 98.21/14.17 | COMBINE_EQS: (309), (375) imply: % 98.21/14.17 | (376) all_531_2 = all_480_1 % 98.21/14.17 | % 98.21/14.17 | COMBINE_EQS: (332), (370) imply: % 98.21/14.17 | (377) all_534_3 = all_480_1 % 98.21/14.17 | % 98.21/14.17 | COMBINE_EQS: (311), (377) imply: % 98.21/14.17 | (378) all_546_16 = all_480_1 % 98.21/14.17 | % 98.21/14.17 | COMBINE_EQS: (327), (366) imply: % 98.21/14.17 | (379) all_549_9 = all_480_1 % 98.21/14.17 | % 98.21/14.17 | COMBINE_EQS: (316), (354) imply: % 98.21/14.17 | (380) all_552_4 = all_480_1 % 98.21/14.17 | % 98.21/14.17 | COMBINE_EQS: (325), (366) imply: % 98.21/14.17 | (381) all_555_3 = all_480_1 % 98.21/14.17 | % 98.21/14.17 | COMBINE_EQS: (319), (366) imply: % 98.21/14.17 | (382) all_558_3 = all_480_1 % 98.21/14.17 | % 98.21/14.17 | COMBINE_EQS: (321), (364) imply: % 98.21/14.17 | (383) all_561_4 = all_480_1 % 98.21/14.17 | % 98.21/14.17 | REDUCE: (167), (379) imply: % 98.21/14.17 | (384) c_FuncSet_OPi(all_549_8, all_480_1, c_Arrow__Order__Mirabelle_OProf, % 98.21/14.17 | all_549_4) = all_549_3 % 98.21/14.17 | % 98.21/14.17 | REDUCE: (107), (302) imply: % 98.21/14.17 | (385) c_FuncSet_OPi(all_508_7, all_480_1, c_Arrow__Order__Mirabelle_OProf, % 98.21/14.17 | all_508_2) = all_508_1 % 98.21/14.17 | % 98.21/14.17 | REDUCE: (165), (379) imply: % 98.21/14.17 | (386) tc_fun(all_549_8, all_480_1) = all_549_7 % 98.21/14.17 | % 98.21/14.17 | REDUCE: (164), (379) imply: % 98.21/14.17 | (387) tc_fun(all_480_1, tc_HOL_Obool) = all_549_5 % 98.21/14.17 | % 98.21/14.17 | REDUCE: (105), (302) imply: % 98.21/14.17 | (388) tc_fun(all_508_7, all_480_1) = all_508_6 % 98.21/14.17 | % 98.21/14.17 | REDUCE: (104), (302) imply: % 98.21/14.17 | (389) tc_fun(all_480_1, tc_HOL_Obool) = all_508_3 % 98.21/14.17 | % 98.21/14.17 | REDUCE: (153), (378) imply: % 98.21/14.17 | (390) tc_fun(tc_Arrow__Order__Mirabelle_Oalt, all_480_1) = all_546_6 % 98.21/14.17 | % 98.21/14.17 | REDUCE: (184), (383) imply: % 98.21/14.17 | (391) tc_fun(tc_Arrow__Order__Mirabelle_Oindi, all_480_1) = all_561_3 % 98.21/14.17 | % 98.21/14.17 | REDUCE: (171), (380) imply: % 98.21/14.17 | (392) tc_fun(tc_Arrow__Order__Mirabelle_Oindi, all_480_1) = all_552_3 % 98.21/14.17 | % 98.21/14.17 | REDUCE: (162), (379) imply: % 98.21/14.17 | (393) tc_fun(tc_Arrow__Order__Mirabelle_Oindi, all_480_1) = all_549_8 % 98.21/14.17 | % 98.21/14.17 | REDUCE: (139), (376) imply: % 98.21/14.17 | (394) tc_fun(tc_Arrow__Order__Mirabelle_Oindi, all_480_1) = all_531_1 % 98.21/14.17 | % 98.21/14.17 | REDUCE: (116), (371) imply: % 98.21/14.17 | (395) tc_fun(tc_Arrow__Order__Mirabelle_Oindi, all_480_1) = all_513_1 % 98.21/14.17 | % 98.21/14.17 | REDUCE: (102), (302) imply: % 98.21/14.17 | (396) tc_fun(tc_Arrow__Order__Mirabelle_Oindi, all_480_1) = all_508_7 % 98.21/14.17 | % 98.21/14.17 | REDUCE: (75), (354) imply: % 98.21/14.17 | (397) tc_fun(tc_Arrow__Order__Mirabelle_Oindi, all_480_1) = all_486_3 % 98.21/14.17 | % 98.21/14.17 | REDUCE: (67), (364) imply: % 98.21/14.17 | (398) tc_fun(tc_Arrow__Order__Mirabelle_Oindi, all_480_1) = all_484_3 % 98.21/14.17 | % 98.21/14.17 | REDUCE: (61), (366) imply: % 98.21/14.17 | (399) tc_fun(tc_Arrow__Order__Mirabelle_Oindi, all_480_1) = all_482_3 % 98.21/14.17 | % 98.21/14.17 | REDUCE: (179), (382) imply: % 98.21/14.17 | (400) c_member(all_480_1) = all_558_2 % 98.21/14.17 | % 98.21/14.17 | REDUCE: (175), (381) imply: % 98.21/14.17 | (401) c_member(all_480_1) = all_555_2 % 98.21/14.17 | % 98.21/14.17 | REDUCE: (143), (377) imply: % 98.21/14.17 | (402) c_member(all_480_1) = all_534_2 % 98.21/14.17 | % 98.21/14.17 | REDUCE: (134), (375) imply: % 98.21/14.17 | (403) c_member(all_480_1) = all_528_2 % 98.21/14.17 | % 98.21/14.17 | REDUCE: (130), (374) imply: % 98.21/14.17 | (404) c_member(all_480_1) = all_525_0 % 98.21/14.17 | % 98.21/14.17 | REDUCE: (124), (373) imply: % 98.21/14.17 | (405) c_member(all_480_1) = all_519_2 % 98.21/14.17 | % 98.21/14.17 | REDUCE: (120), (372) imply: % 98.21/14.17 | (406) c_member(all_480_1) = all_516_0 % 98.21/14.17 | % 98.21/14.17 | REDUCE: (114), (371) imply: % 98.21/14.17 | (407) c_member(all_480_1) = all_513_2 % 98.21/14.17 | % 98.21/14.17 | REDUCE: (110), (370) imply: % 98.21/14.17 | (408) c_member(all_480_1) = all_510_0 % 98.21/14.17 | % 98.21/14.17 | REDUCE: (94), (369) imply: % 98.21/14.17 | (409) c_member(all_480_1) = all_505_0 % 98.21/14.17 | % 98.21/14.17 | REDUCE: (90), (368) imply: % 98.21/14.17 | (410) c_member(all_480_1) = all_500_0 % 98.21/14.17 | % 98.21/14.17 | REDUCE: (84), (367) imply: % 98.21/14.17 | (411) c_member(all_480_1) = all_492_4 % 98.21/14.17 | % 98.21/14.17 | REDUCE: (59), (366) imply: % 98.21/14.17 | (412) $i(all_480_1) % 98.21/14.17 | % 98.21/14.17 | GROUND_INST: instantiating (46) with all_505_0, all_510_0, all_480_1, % 98.21/14.17 | simplifying with (408), (409) gives: % 98.21/14.17 | (413) all_510_0 = all_505_0 % 98.21/14.17 | % 98.21/14.17 | GROUND_INST: instantiating (46) with all_500_0, all_510_0, all_480_1, % 98.21/14.17 | simplifying with (408), (410) gives: % 98.21/14.17 | (414) all_510_0 = all_500_0 % 98.21/14.17 | % 98.21/14.17 | GROUND_INST: instantiating (46) with all_480_0, all_516_0, all_480_1, % 98.21/14.17 | simplifying with (54), (406) gives: % 98.21/14.17 | (415) all_516_0 = all_480_0 % 98.21/14.17 | % 98.21/14.17 | GROUND_INST: instantiating (46) with all_510_0, all_516_0, all_480_1, % 98.21/14.17 | simplifying with (406), (408) gives: % 98.21/14.17 | (416) all_516_0 = all_510_0 % 98.21/14.17 | % 98.21/14.17 | GROUND_INST: instantiating (46) with all_516_0, all_528_2, all_480_1, % 98.21/14.17 | simplifying with (403), (406) gives: % 98.21/14.17 | (417) all_528_2 = all_516_0 % 98.21/14.17 | % 98.21/14.17 | GROUND_INST: instantiating (46) with all_528_2, all_534_2, all_480_1, % 98.21/14.17 | simplifying with (402), (403) gives: % 98.21/14.17 | (418) all_534_2 = all_528_2 % 98.21/14.17 | % 98.21/14.17 | GROUND_INST: instantiating (46) with all_525_0, all_534_2, all_480_1, % 98.21/14.17 | simplifying with (402), (404) gives: % 98.21/14.17 | (419) all_534_2 = all_525_0 % 98.21/14.17 | % 98.21/14.17 | GROUND_INST: instantiating (46) with all_513_2, all_534_2, all_480_1, % 98.21/14.17 | simplifying with (402), (407) gives: % 98.21/14.17 | (420) all_534_2 = all_513_2 % 98.21/14.17 | % 98.21/14.17 | GROUND_INST: instantiating (46) with all_528_2, all_555_2, all_480_1, % 98.21/14.17 | simplifying with (401), (403) gives: % 98.21/14.17 | (421) all_555_2 = all_528_2 % 98.21/14.17 | % 98.21/14.17 | GROUND_INST: instantiating (46) with all_519_2, all_555_2, all_480_1, % 98.21/14.17 | simplifying with (401), (405) gives: % 98.21/14.17 | (422) all_555_2 = all_519_2 % 98.21/14.17 | % 98.21/14.17 | GROUND_INST: instantiating (46) with all_500_0, all_558_2, all_480_1, % 98.21/14.17 | simplifying with (400), (410) gives: % 98.21/14.17 | (423) all_558_2 = all_500_0 % 98.21/14.17 | % 98.21/14.17 | GROUND_INST: instantiating (46) with all_492_4, all_558_2, all_480_1, % 98.21/14.17 | simplifying with (400), (411) gives: % 98.21/14.17 | (424) all_558_2 = all_492_4 % 98.21/14.17 | % 98.21/14.17 | GROUND_INST: instantiating (49) with all_486_3, all_508_7, all_480_1, % 98.21/14.17 | tc_Arrow__Order__Mirabelle_Oindi, simplifying with (396), (397) % 98.21/14.17 | gives: % 98.21/14.17 | (425) all_508_7 = all_486_3 % 98.21/14.17 | % 98.21/14.17 | GROUND_INST: instantiating (49) with all_486_3, all_513_1, all_480_1, % 98.21/14.17 | tc_Arrow__Order__Mirabelle_Oindi, simplifying with (395), (397) % 98.21/14.17 | gives: % 98.21/14.17 | (426) all_513_1 = all_486_3 % 98.21/14.17 | % 98.21/14.17 | GROUND_INST: instantiating (49) with all_513_1, all_531_1, all_480_1, % 98.21/14.17 | tc_Arrow__Order__Mirabelle_Oindi, simplifying with (394), (395) % 98.21/14.17 | gives: % 98.21/14.17 | (427) all_531_1 = all_513_1 % 98.21/14.17 | % 98.21/14.17 | GROUND_INST: instantiating (49) with all_531_1, all_549_8, all_480_1, % 98.21/14.17 | tc_Arrow__Order__Mirabelle_Oindi, simplifying with (393), (394) % 98.21/14.17 | gives: % 98.21/14.17 | (428) all_549_8 = all_531_1 % 98.21/14.17 | % 98.21/14.17 | GROUND_INST: instantiating (49) with all_508_7, all_552_3, all_480_1, % 98.21/14.17 | tc_Arrow__Order__Mirabelle_Oindi, simplifying with (392), (396) % 98.21/14.17 | gives: % 98.21/14.17 | (429) all_552_3 = all_508_7 % 98.21/14.17 | % 98.21/14.17 | GROUND_INST: instantiating (49) with all_484_3, all_552_3, all_480_1, % 98.21/14.17 | tc_Arrow__Order__Mirabelle_Oindi, simplifying with (392), (398) % 98.21/14.17 | gives: % 98.21/14.17 | (430) all_552_3 = all_484_3 % 98.21/14.17 | % 98.21/14.17 | GROUND_INST: instantiating (49) with all_549_8, all_561_3, all_480_1, % 98.21/14.17 | tc_Arrow__Order__Mirabelle_Oindi, simplifying with (391), (393) % 98.21/14.17 | gives: % 98.21/14.17 | (431) all_561_3 = all_549_8 % 98.21/14.17 | % 98.21/14.17 | GROUND_INST: instantiating (49) with all_482_3, all_561_3, all_480_1, % 98.21/14.17 | tc_Arrow__Order__Mirabelle_Oindi, simplifying with (391), (399) % 98.21/14.17 | gives: % 98.21/14.17 | (432) all_561_3 = all_482_3 % 98.21/14.17 | % 98.21/14.17 | GROUND_INST: instantiating (49) with all_508_3, all_549_5, tc_HOL_Obool, % 98.21/14.17 | all_480_1, simplifying with (387), (389) gives: % 98.21/14.17 | (433) all_549_5 = all_508_3 % 98.21/14.17 | % 98.21/14.17 | COMBINE_EQS: (431), (432) imply: % 98.21/14.17 | (434) all_549_8 = all_482_3 % 98.21/14.17 | % 98.21/14.17 | SIMP: (434) implies: % 98.21/14.17 | (435) all_549_8 = all_482_3 % 98.21/14.17 | % 98.21/14.17 | COMBINE_EQS: (423), (424) imply: % 98.21/14.17 | (436) all_500_0 = all_492_4 % 98.21/14.17 | % 98.21/14.17 | SIMP: (436) implies: % 98.21/14.17 | (437) all_500_0 = all_492_4 % 98.21/14.17 | % 98.21/14.17 | COMBINE_EQS: (421), (422) imply: % 98.21/14.17 | (438) all_528_2 = all_519_2 % 98.21/14.17 | % 98.21/14.17 | SIMP: (438) implies: % 98.21/14.17 | (439) all_528_2 = all_519_2 % 98.21/14.17 | % 98.21/14.17 | COMBINE_EQS: (429), (430) imply: % 98.21/14.17 | (440) all_508_7 = all_484_3 % 98.21/14.17 | % 98.21/14.17 | SIMP: (440) implies: % 98.21/14.17 | (441) all_508_7 = all_484_3 % 98.21/14.17 | % 98.21/14.17 | COMBINE_EQS: (428), (435) imply: % 98.21/14.17 | (442) all_531_1 = all_482_3 % 98.21/14.17 | % 98.21/14.17 | SIMP: (442) implies: % 98.21/14.17 | (443) all_531_1 = all_482_3 % 98.21/14.17 | % 98.21/14.17 | COMBINE_EQS: (419), (420) imply: % 98.21/14.17 | (444) all_525_0 = all_513_2 % 98.21/14.17 | % 98.21/14.17 | COMBINE_EQS: (418), (419) imply: % 98.21/14.17 | (445) all_528_2 = all_525_0 % 98.21/14.17 | % 98.21/14.17 | SIMP: (445) implies: % 98.21/14.17 | (446) all_528_2 = all_525_0 % 98.21/14.17 | % 98.21/14.17 | COMBINE_EQS: (427), (443) imply: % 98.21/14.17 | (447) all_513_1 = all_482_3 % 98.21/14.17 | % 98.21/14.17 | SIMP: (447) implies: % 98.21/14.17 | (448) all_513_1 = all_482_3 % 98.21/14.17 | % 98.21/14.17 | COMBINE_EQS: (439), (446) imply: % 98.21/14.17 | (449) all_525_0 = all_519_2 % 98.21/14.17 | % 98.21/14.17 | SIMP: (449) implies: % 98.21/14.17 | (450) all_525_0 = all_519_2 % 98.21/14.17 | % 98.21/14.17 | COMBINE_EQS: (417), (439) imply: % 98.21/14.17 | (451) all_519_2 = all_516_0 % 98.21/14.17 | % 98.21/14.17 | COMBINE_EQS: (444), (450) imply: % 98.21/14.18 | (452) all_519_2 = all_513_2 % 98.21/14.18 | % 98.21/14.18 | SIMP: (452) implies: % 98.21/14.18 | (453) all_519_2 = all_513_2 % 98.21/14.18 | % 98.21/14.18 | COMBINE_EQS: (451), (453) imply: % 98.21/14.18 | (454) all_516_0 = all_513_2 % 98.21/14.18 | % 98.21/14.18 | SIMP: (454) implies: % 98.21/14.18 | (455) all_516_0 = all_513_2 % 98.21/14.18 | % 98.21/14.18 | COMBINE_EQS: (415), (455) imply: % 98.21/14.18 | (456) all_513_2 = all_480_0 % 98.21/14.18 | % 98.21/14.18 | COMBINE_EQS: (416), (455) imply: % 98.21/14.18 | (457) all_513_2 = all_510_0 % 98.21/14.18 | % 98.21/14.18 | COMBINE_EQS: (426), (448) imply: % 98.21/14.18 | (458) all_486_3 = all_482_3 % 98.21/14.18 | % 98.21/14.18 | SIMP: (458) implies: % 98.21/14.18 | (459) all_486_3 = all_482_3 % 98.21/14.18 | % 98.21/14.18 | COMBINE_EQS: (456), (457) imply: % 98.21/14.18 | (460) all_510_0 = all_480_0 % 98.21/14.18 | % 98.21/14.18 | SIMP: (460) implies: % 98.21/14.18 | (461) all_510_0 = all_480_0 % 98.21/14.18 | % 98.21/14.18 | COMBINE_EQS: (413), (414) imply: % 98.21/14.18 | (462) all_505_0 = all_500_0 % 98.21/14.18 | % 98.21/14.18 | COMBINE_EQS: (413), (461) imply: % 98.21/14.18 | (463) all_505_0 = all_480_0 % 98.21/14.18 | % 98.21/14.18 | COMBINE_EQS: (425), (441) imply: % 98.21/14.18 | (464) all_486_3 = all_484_3 % 98.21/14.18 | % 98.21/14.18 | SIMP: (464) implies: % 98.21/14.18 | (465) all_486_3 = all_484_3 % 98.21/14.18 | % 98.21/14.18 | COMBINE_EQS: (462), (463) imply: % 98.21/14.18 | (466) all_500_0 = all_480_0 % 98.21/14.18 | % 98.21/14.18 | SIMP: (466) implies: % 98.21/14.18 | (467) all_500_0 = all_480_0 % 98.21/14.18 | % 98.21/14.18 | COMBINE_EQS: (437), (467) imply: % 98.21/14.18 | (468) all_492_4 = all_480_0 % 98.21/14.18 | % 98.21/14.18 | SIMP: (468) implies: % 98.21/14.18 | (469) all_492_4 = all_480_0 % 98.21/14.18 | % 98.21/14.18 | COMBINE_EQS: (459), (465) imply: % 98.21/14.18 | (470) all_484_3 = all_482_3 % 98.21/14.18 | % 98.21/14.18 | SIMP: (470) implies: % 98.21/14.18 | (471) all_484_3 = all_482_3 % 98.21/14.18 | % 98.21/14.18 | COMBINE_EQS: (441), (471) imply: % 98.21/14.18 | (472) all_508_7 = all_482_3 % 98.21/14.18 | % 98.21/14.18 | COMBINE_EQS: (430), (471) imply: % 98.21/14.18 | (473) all_552_3 = all_482_3 % 98.21/14.18 | % 98.21/14.18 | REDUCE: (168), (433), (435) imply: % 98.21/14.18 | (474) c_COMBK(all_508_3, all_482_3, c_Arrow__Order__Mirabelle_OLin) = % 98.21/14.18 | all_549_4 % 98.21/14.18 | % 98.21/14.18 | REDUCE: (108), (472) imply: % 98.21/14.18 | (475) c_COMBK(all_508_3, all_482_3, c_Arrow__Order__Mirabelle_OLin) = % 98.21/14.18 | all_508_2 % 98.21/14.18 | % 98.21/14.18 | REDUCE: (384), (435) imply: % 98.21/14.18 | (476) c_FuncSet_OPi(all_482_3, all_480_1, c_Arrow__Order__Mirabelle_OProf, % 98.21/14.18 | all_549_4) = all_549_3 % 98.21/14.18 | % 98.21/14.18 | REDUCE: (385), (472) imply: % 98.21/14.18 | (477) c_FuncSet_OPi(all_482_3, all_480_1, c_Arrow__Order__Mirabelle_OProf, % 98.21/14.18 | all_508_2) = all_508_1 % 98.21/14.18 | % 98.21/14.18 | REDUCE: (386), (435) imply: % 98.21/14.18 | (478) tc_fun(all_482_3, all_480_1) = all_549_7 % 98.21/14.18 | % 98.21/14.18 | REDUCE: (388), (472) imply: % 98.21/14.18 | (479) tc_fun(all_482_3, all_480_1) = all_508_6 % 98.21/14.18 | % 98.21/14.18 | REDUCE: (183), (432) imply: % 98.21/14.18 | (480) c_member(all_482_3) = all_561_2 % 98.21/14.18 | % 98.21/14.18 | REDUCE: (170), (473) imply: % 98.21/14.18 | (481) c_member(all_482_3) = all_552_2 % 98.21/14.18 | % 98.21/14.18 | REDUCE: (160), (435) imply: % 98.21/14.18 | (482) c_member(all_482_3) = all_549_2 % 98.21/14.18 | % 98.21/14.18 | REDUCE: (138), (443) imply: % 98.21/14.18 | (483) c_member(all_482_3) = all_531_0 % 98.21/14.18 | % 98.21/14.18 | REDUCE: (115), (448) imply: % 98.21/14.18 | (484) c_member(all_482_3) = all_513_0 % 98.21/14.18 | % 98.21/14.18 | REDUCE: (74), (459) imply: % 98.21/14.18 | (485) c_member(all_482_3) = all_486_2 % 98.21/14.18 | % 98.21/14.18 | REDUCE: (66), (471) imply: % 98.21/14.18 | (486) c_member(all_482_3) = all_484_2 % 98.21/14.18 | % 98.21/14.18 | REDUCE: (81), (469) imply: % 98.21/14.18 | (487) hAPP(all_480_0, all_492_3) = all_492_2 % 98.21/14.18 | % 98.21/14.18 | REDUCE: (65), (471) imply: % 98.21/14.18 | (488) $i(all_482_3) % 98.21/14.18 | % 98.21/14.18 | GROUND_INST: instantiating (46) with all_482_2, all_513_0, all_482_3, % 98.21/14.18 | simplifying with (60), (484) gives: % 98.21/14.18 | (489) all_513_0 = all_482_2 % 98.21/14.18 | % 98.21/14.18 | GROUND_INST: instantiating (46) with all_531_0, all_549_2, all_482_3, % 98.21/14.18 | simplifying with (482), (483) gives: % 98.21/14.18 | (490) all_549_2 = all_531_0 % 98.21/14.18 | % 98.21/14.18 | GROUND_INST: instantiating (46) with all_513_0, all_549_2, all_482_3, % 98.21/14.18 | simplifying with (482), (484) gives: % 98.21/14.18 | (491) all_549_2 = all_513_0 % 98.21/14.18 | % 98.21/14.18 | GROUND_INST: instantiating (46) with all_486_2, all_549_2, all_482_3, % 98.21/14.18 | simplifying with (482), (485) gives: % 98.21/14.18 | (492) all_549_2 = all_486_2 % 98.21/14.18 | % 98.21/14.18 | GROUND_INST: instantiating (46) with all_531_0, all_552_2, all_482_3, % 98.21/14.18 | simplifying with (481), (483) gives: % 98.21/14.18 | (493) all_552_2 = all_531_0 % 98.21/14.18 | % 98.21/14.18 | GROUND_INST: instantiating (46) with all_552_2, all_561_2, all_482_3, % 98.21/14.18 | simplifying with (480), (481) gives: % 98.21/14.18 | (494) all_561_2 = all_552_2 % 98.21/14.18 | % 98.21/14.18 | GROUND_INST: instantiating (46) with all_484_2, all_561_2, all_482_3, % 98.21/14.18 | simplifying with (480), (486) gives: % 98.21/14.18 | (495) all_561_2 = all_484_2 % 98.21/14.18 | % 98.21/14.18 | GROUND_INST: instantiating (49) with all_508_6, all_549_7, all_480_1, % 98.21/14.18 | all_482_3, simplifying with (478), (479) gives: % 98.21/14.18 | (496) all_549_7 = all_508_6 % 98.21/14.18 | % 98.21/14.18 | GROUND_INST: instantiating (51) with all_508_2, all_549_4, % 98.21/14.18 | c_Arrow__Order__Mirabelle_OLin, all_482_3, all_508_3, simplifying % 98.21/14.18 | with (474), (475) gives: % 98.21/14.18 | (497) all_549_4 = all_508_2 % 98.21/14.18 | % 98.21/14.18 | COMBINE_EQS: (494), (495) imply: % 98.21/14.18 | (498) all_552_2 = all_484_2 % 98.21/14.18 | % 98.21/14.18 | SIMP: (498) implies: % 98.21/14.18 | (499) all_552_2 = all_484_2 % 98.21/14.18 | % 98.21/14.18 | COMBINE_EQS: (493), (499) imply: % 98.21/14.18 | (500) all_531_0 = all_484_2 % 98.21/14.18 | % 98.21/14.18 | SIMP: (500) implies: % 98.21/14.18 | (501) all_531_0 = all_484_2 % 98.21/14.18 | % 98.21/14.18 | COMBINE_EQS: (491), (492) imply: % 98.21/14.18 | (502) all_513_0 = all_486_2 % 98.21/14.18 | % 98.21/14.18 | SIMP: (502) implies: % 98.21/14.18 | (503) all_513_0 = all_486_2 % 98.21/14.18 | % 98.21/14.18 | COMBINE_EQS: (490), (492) imply: % 98.21/14.18 | (504) all_531_0 = all_486_2 % 98.21/14.18 | % 98.21/14.18 | SIMP: (504) implies: % 98.21/14.18 | (505) all_531_0 = all_486_2 % 98.21/14.18 | % 98.21/14.18 | COMBINE_EQS: (501), (505) imply: % 98.21/14.18 | (506) all_486_2 = all_484_2 % 98.21/14.18 | % 98.21/14.18 | SIMP: (506) implies: % 98.21/14.18 | (507) all_486_2 = all_484_2 % 98.21/14.18 | % 98.21/14.18 | COMBINE_EQS: (489), (503) imply: % 98.21/14.18 | (508) all_486_2 = all_482_2 % 98.21/14.18 | % 98.21/14.18 | SIMP: (508) implies: % 98.21/14.18 | (509) all_486_2 = all_482_2 % 98.21/14.18 | % 98.21/14.18 | COMBINE_EQS: (507), (509) imply: % 98.21/14.18 | (510) all_484_2 = all_482_2 % 98.21/14.18 | % 98.21/14.18 | REDUCE: (476), (497) imply: % 98.21/14.18 | (511) c_FuncSet_OPi(all_482_3, all_480_1, c_Arrow__Order__Mirabelle_OProf, % 98.21/14.18 | all_508_2) = all_549_3 % 98.21/14.18 | % 98.21/14.18 | REDUCE: (161), (496) imply: % 98.21/14.18 | (512) c_member(all_508_6) = all_549_6 % 98.21/14.18 | % 98.21/14.18 | REDUCE: (71), (509) imply: % 98.21/14.18 | (513) hAPP(all_482_2, v_Q____) = all_486_1 % 98.21/14.18 | % 98.21/14.18 | REDUCE: (158), (497) imply: % 98.21/14.18 | (514) $i(all_508_2) % 98.21/14.18 | % 98.21/14.18 | REDUCE: (157), (496) imply: % 98.21/14.18 | (515) $i(all_508_6) % 98.21/14.18 | % 98.21/14.18 | GROUND_INST: instantiating (46) with all_508_5, all_549_6, all_508_6, % 98.21/14.18 | simplifying with (101), (512) gives: % 98.21/14.18 | (516) all_549_6 = all_508_5 % 98.21/14.18 | % 98.21/14.18 | GROUND_INST: instantiating (52) with all_508_1, all_549_3, all_508_2, % 98.21/14.18 | c_Arrow__Order__Mirabelle_OProf, all_480_1, all_482_3, % 98.21/14.18 | simplifying with (477), (511) gives: % 98.21/14.18 | (517) all_549_3 = all_508_1 % 98.21/14.18 | % 98.21/14.18 | REDUCE: (159), (517) imply: % 98.21/14.18 | (518) $i(all_508_1) % 98.21/14.18 | % 98.21/14.18 | GROUND_INST: instantiating (8) with c_Arrow__Order__Mirabelle_OProf, v_Q____, % 98.21/14.18 | all_482_3, all_482_2, all_486_1, all_486_0, simplifying with % 98.21/14.18 | (28), (42), (60), (72), (488), (513) gives: % 98.21/14.18 | (519) ? [v0: any] : ? [v1: $i] : ? [v2: any] : (hBOOL(v1) = v2 & % 98.21/14.18 | hBOOL(all_486_0) = v0 & hAPP(c_Arrow__Order__Mirabelle_OProf, % 98.21/14.18 | v_Q____) = v1 & $i(v1) & ( ~ (v0 = 0) | v2 = 0)) % 98.21/14.18 | % 98.21/14.18 | GROUND_INST: instantiating (7) with c_Arrow__Order__Mirabelle_OProf, v_Q____, % 98.21/14.18 | all_482_3, all_482_2, all_486_1, all_486_0, simplifying with % 98.21/14.18 | (28), (42), (60), (72), (488), (513) gives: % 98.21/14.18 | (520) ? [v0: $i] : ? [v1: any] : ? [v2: any] : (hBOOL(v0) = v1 & % 98.21/14.18 | hBOOL(all_486_0) = v2 & hAPP(c_Arrow__Order__Mirabelle_OProf, % 98.21/14.18 | v_Q____) = v0 & $i(v0) & ( ~ (v1 = 0) | v2 = 0)) % 98.21/14.18 | % 98.21/14.18 | GROUND_INST: instantiating (33) with v_Q____, all_482_3, % 98.21/14.18 | c_Arrow__Order__Mirabelle_OProf, all_482_2, all_486_1, all_486_0, % 98.21/14.18 | simplifying with (28), (42), (60), (72), (488), (513) gives: % 98.21/14.18 | (521) ? [v0: $i] : ? [v1: $i] : ? [v2: any] : % 98.21/14.18 | (c_Orderings_Obot__class_Obot(v0) = v1 & tc_fun(all_482_3, % 98.21/14.18 | tc_HOL_Obool) = v0 & hBOOL(all_486_0) = v2 & $i(v1) & $i(v0) & ( % 98.21/14.18 | ~ (v2 = 0) | ~ (v1 = c_Arrow__Order__Mirabelle_OProf))) % 98.21/14.18 | % 98.21/14.18 | GROUND_INST: instantiating (8) with all_508_1, v_F, all_508_6, all_508_5, % 98.21/14.18 | all_508_4, all_508_0, simplifying with (39), (98), (99), (101), % 98.21/14.18 | (515), (518) gives: % 98.21/14.18 | (522) ? [v0: any] : ? [v1: $i] : ? [v2: any] : (hBOOL(v1) = v2 & % 98.21/14.18 | hBOOL(all_508_0) = v0 & hAPP(all_508_1, v_F) = v1 & $i(v1) & ( ~ % 98.21/14.18 | (v0 = 0) | v2 = 0)) % 98.21/14.18 | % 98.21/14.18 | GROUND_INST: instantiating (7) with all_508_1, v_F, all_508_6, all_508_5, % 98.21/14.18 | all_508_4, all_508_0, simplifying with (39), (98), (99), (101), % 98.21/14.18 | (515), (518) gives: % 98.21/14.18 | (523) ? [v0: $i] : ? [v1: any] : ? [v2: any] : (hBOOL(v0) = v1 & % 98.21/14.18 | hBOOL(all_508_0) = v2 & hAPP(all_508_1, v_F) = v0 & $i(v0) & ( ~ % 98.21/14.18 | (v1 = 0) | v2 = 0)) % 98.21/14.18 | % 98.21/14.18 | GROUND_INST: instantiating (33) with v_F, all_508_6, all_508_1, all_508_5, % 98.21/14.18 | all_508_4, all_508_0, simplifying with (39), (98), (99), (101), % 98.21/14.18 | (515), (518) gives: % 98.21/14.18 | (524) ? [v0: $i] : ? [v1: $i] : ? [v2: any] : % 98.21/14.18 | (c_Orderings_Obot__class_Obot(v0) = v1 & tc_fun(all_508_6, % 98.21/14.18 | tc_HOL_Obool) = v0 & hBOOL(all_508_0) = v2 & $i(v1) & $i(v0) & ( % 98.21/14.18 | ~ (v2 = 0) | ~ (v1 = all_508_1))) % 98.21/14.18 | % 98.21/14.18 | GROUND_INST: instantiating (arity_fun__Orderings_Obot) with % 98.21/14.18 | tc_Arrow__Order__Mirabelle_Oindi, all_480_1, all_482_3, % 98.21/14.18 | simplifying with (27), (399), (412) gives: % 98.21/14.18 | (525) ? [v0: any] : ? [v1: any] : (class_Orderings_Obot(all_482_3) = v1 & % 98.21/14.18 | class_Orderings_Obot(all_480_1) = v0 & ( ~ (v0 = 0) | v1 = 0)) % 98.21/14.18 | % 98.21/14.18 | GROUND_INST: instantiating (arity_fun__Orderings_Obot) with % 98.21/14.18 | tc_Arrow__Order__Mirabelle_Oalt, all_480_1, all_546_6, % 98.21/14.18 | simplifying with (40), (390), (412) gives: % 98.21/14.18 | (526) ? [v0: any] : ? [v1: any] : (class_Orderings_Obot(all_546_6) = v1 & % 98.21/14.18 | class_Orderings_Obot(all_480_1) = v0 & ( ~ (v0 = 0) | v1 = 0)) % 98.21/14.18 | % 98.21/14.18 | GROUND_INST: instantiating (arity_fun__Orderings_Obot) with tc_HOL_Obool, % 98.21/14.18 | tc_HOL_Obool, all_522_0, simplifying with (41), (128) gives: % 98.21/14.18 | (527) ? [v0: any] : ? [v1: any] : (class_Orderings_Obot(all_522_0) = v1 & % 98.21/14.18 | class_Orderings_Obot(tc_HOL_Obool) = v0 & ( ~ (v0 = 0) | v1 = 0)) % 98.21/14.18 | % 98.21/14.18 | GROUND_INST: instantiating (arity_fun__Orderings_Obot) with all_480_2, % 98.21/14.18 | tc_HOL_Obool, all_480_1, simplifying with (41), (55), (300) % 98.21/14.18 | gives: % 98.21/14.18 | (528) ? [v0: any] : ? [v1: any] : (class_Orderings_Obot(all_480_1) = v1 & % 98.21/14.18 | class_Orderings_Obot(tc_HOL_Obool) = v0 & ( ~ (v0 = 0) | v1 = 0)) % 98.21/14.18 | % 98.21/14.18 | GROUND_INST: instantiating (arity_fun__Orderings_Obot) with all_480_1, % 98.21/14.18 | tc_HOL_Obool, all_508_3, simplifying with (41), (389), (412) % 98.21/14.18 | gives: % 98.21/14.18 | (529) ? [v0: any] : ? [v1: any] : (class_Orderings_Obot(all_508_3) = v1 & % 98.21/14.18 | class_Orderings_Obot(tc_HOL_Obool) = v0 & ( ~ (v0 = 0) | v1 = 0)) % 98.21/14.18 | % 98.21/14.18 | GROUND_INST: instantiating (35) with all_508_2, % 98.21/14.18 | c_Arrow__Order__Mirabelle_OProf, all_480_1, all_482_3, all_508_1, % 98.21/14.18 | simplifying with (28), (412), (477), (488), (514) gives: % 98.21/14.18 | (530) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 98.21/14.18 | ? [v5: $i] : (c_Orderings_Obot__class_Obot(v4) = v5 & % 98.21/14.18 | c_Orderings_Obot__class_Obot(v1) = v2 & tc_fun(v3, tc_HOL_Obool) = % 98.21/14.18 | v4 & tc_fun(all_482_3, all_480_1) = v3 & tc_fun(all_480_1, % 98.21/14.18 | tc_HOL_Obool) = v1 & c_member(all_482_3) = v0 & $i(v5) & $i(v4) & % 98.21/14.18 | $i(v3) & $i(v2) & $i(v1) & $i(v0) & (v5 = all_508_1 | ! [v6: $i] : % 98.21/14.18 | ! [v7: $i] : ! [v8: $i] : ( ~ (hAPP(v7, % 98.21/14.18 | c_Arrow__Order__Mirabelle_OProf) = v8) | ~ (hAPP(v0, v6) = % 98.21/14.18 | v7) | ~ $i(v6) | ? [v9: any] : ? [v10: $i] : (hBOOL(v8) = % 98.21/14.18 | v9 & hAPP(all_508_2, v6) = v10 & $i(v10) & ( ~ (v10 = v2) | % 98.21/14.19 | ~ (v9 = 0)))))) % 98.21/14.19 | % 98.21/14.19 | GROUND_INST: instantiating (34) with all_508_2, % 98.21/14.19 | c_Arrow__Order__Mirabelle_OProf, all_480_1, all_482_3, all_508_1, % 98.21/14.19 | simplifying with (28), (412), (477), (488), (514) gives: % 98.21/14.19 | (531) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 98.21/14.19 | ? [v5: $i] : (c_Orderings_Obot__class_Obot(v4) = v5 & % 98.21/14.19 | c_Orderings_Obot__class_Obot(v1) = v2 & tc_fun(v0, tc_HOL_Obool) = % 98.21/14.19 | v1 & tc_fun(all_482_3, all_480_1) = v0 & tc_fun(all_480_1, % 98.21/14.19 | tc_HOL_Obool) = v4 & c_member(all_482_3) = v3 & $i(v5) & $i(v4) & % 98.21/14.19 | $i(v3) & $i(v2) & $i(v1) & $i(v0) & ( ~ (v2 = all_508_1) | ? [v6: % 98.21/14.19 | $i] : ? [v7: $i] : ? [v8: $i] : (hBOOL(v8) = 0 & hAPP(v7, % 98.21/14.19 | c_Arrow__Order__Mirabelle_OProf) = v8 & hAPP(v3, v6) = v7 & % 98.21/14.19 | hAPP(all_508_2, v6) = v5 & $i(v8) & $i(v7) & $i(v6)))) % 98.21/14.19 | % 98.21/14.19 | GROUND_INST: instantiating (25) with v_Q____, c_Arrow__Order__Mirabelle_OLin, % 98.21/14.19 | c_Arrow__Order__Mirabelle_OProf, v_F, all_480_1, all_482_3, % 98.21/14.19 | all_508_6, all_508_5, all_508_4, all_508_3, all_508_2, all_508_1, % 98.21/14.19 | all_508_0, all_480_0, all_492_3, all_492_2, all_492_1, % 98.21/14.19 | simplifying with (28), (39), (42), (43), (54), (80), (82), (98), % 98.21/14.19 | (99), (101), (389), (412), (475), (477), (479), (487), (488) % 98.21/14.19 | gives: % 98.21/14.19 | (532) ? [v0: any] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: any] % 98.21/14.19 | : ? [v5: any] : (c_member(all_482_3) = v1 & hBOOL(v3) = v4 & % 98.21/14.19 | hBOOL(all_508_0) = v0 & hBOOL(all_492_1) = v5 & hAPP(v2, % 98.21/14.19 | c_Arrow__Order__Mirabelle_OProf) = v3 & hAPP(v1, v_Q____) = v2 & % 98.21/14.19 | $i(v3) & $i(v2) & $i(v1) & ( ~ (v4 = 0) | ~ (v0 = 0) | v5 = 0)) % 98.21/14.19 | % 98.21/14.19 | GROUND_INST: instantiating (31) with c_Arrow__Order__Mirabelle_OLin, % 98.21/14.19 | c_Arrow__Order__Mirabelle_OProf, v_F, all_480_1, all_482_3, % 98.21/14.19 | all_508_6, all_508_5, all_508_4, all_508_3, all_508_2, all_508_1, % 98.21/14.19 | all_508_0, simplifying with (28), (39), (43), (98), (99), (101), % 98.21/14.19 | (389), (412), (475), (477), (479), (488) gives: % 98.21/14.19 | (533) ? [v0: any] : ? [v1: $i] : ? [v2: $i] : ? [v3: any] : ? [v4: $i] % 98.21/14.19 | : ? [v5: $i] : ? [v6: $i] : (c_FuncSet_Orestrict(all_482_3, % 98.21/14.19 | all_482_3, v4, c_Arrow__Order__Mirabelle_OProf) = v5 & % 98.21/14.19 | c_FuncSet_Oextensional(all_482_3, all_480_1, % 98.21/14.19 | c_Arrow__Order__Mirabelle_OProf) = v1 & % 98.21/14.19 | c_FuncSet_Ocompose(all_482_3, all_482_3, all_480_1, % 98.21/14.19 | c_Arrow__Order__Mirabelle_OProf, v_F, v5) = v6 & % 98.21/14.19 | c_COMBI(all_482_3) = v4 & hBOOL(v2) = v3 & hBOOL(all_508_0) = v0 & % 98.21/14.19 | hAPP(all_508_4, v1) = v2 & $i(v6) & $i(v5) & $i(v4) & $i(v2) & % 98.21/14.19 | $i(v1) & ( ~ (v3 = 0) | ~ (v0 = 0) | v6 = v_F)) % 98.21/14.19 | % 98.21/14.19 | GROUND_INST: instantiating (32) with c_Arrow__Order__Mirabelle_OLin, % 98.21/14.19 | c_Arrow__Order__Mirabelle_OProf, v_F, all_480_1, all_482_3, % 98.21/14.19 | all_508_6, all_508_5, all_508_4, all_508_3, all_508_2, all_508_1, % 98.21/14.19 | all_508_0, simplifying with (28), (39), (43), (98), (99), (101), % 98.21/14.19 | (389), (412), (475), (477), (479), (488) gives: % 98.21/14.19 | (534) ? [v0: any] : ? [v1: $i] : ? [v2: $i] : ? [v3: any] : ? [v4: $i] % 98.21/14.19 | : ? [v5: $i] : ? [v6: $i] : (c_FuncSet_Orestrict(all_480_1, % 98.21/14.19 | all_480_1, v4, c_Arrow__Order__Mirabelle_OLin) = v5 & % 98.21/14.19 | c_FuncSet_Oextensional(all_482_3, all_480_1, % 98.21/14.19 | c_Arrow__Order__Mirabelle_OProf) = v1 & % 98.21/14.19 | c_FuncSet_Ocompose(all_482_3, all_480_1, all_480_1, % 98.21/14.19 | c_Arrow__Order__Mirabelle_OProf, v5, v_F) = v6 & % 98.21/14.19 | c_COMBI(all_480_1) = v4 & hBOOL(v2) = v3 & hBOOL(all_508_0) = v0 & % 98.21/14.19 | hAPP(all_508_4, v1) = v2 & $i(v6) & $i(v5) & $i(v4) & $i(v2) & % 98.21/14.19 | $i(v1) & ( ~ (v3 = 0) | ~ (v0 = 0) | v6 = v_F)) % 98.21/14.19 | % 98.21/14.19 | GROUND_INST: instantiating (36) with c_Arrow__Order__Mirabelle_OLin, % 98.21/14.19 | c_Arrow__Order__Mirabelle_OProf, v_F, all_480_1, all_482_3, % 98.21/14.19 | all_508_6, all_508_5, all_508_4, all_508_3, all_508_2, all_508_1, % 98.21/14.19 | all_508_0, simplifying with (28), (39), (43), (98), (99), (101), % 98.21/14.19 | (389), (412), (475), (477), (479), (488) gives: % 98.21/14.19 | (535) ? [v0: any] : ? [v1: $i] : ? [v2: any] : % 98.21/14.19 | (c_Orderings_Oord__class_Oless__eq(all_508_3, v1, % 98.21/14.19 | c_Arrow__Order__Mirabelle_OLin) = v2 & c_Set_Oimage(all_482_3, % 98.21/14.19 | all_480_1, v_F, c_Arrow__Order__Mirabelle_OProf) = v1 & % 98.21/14.19 | hBOOL(all_508_0) = v0 & $i(v1) & ( ~ (v0 = 0) | v2 = 0)) % 98.21/14.19 | % 98.21/14.19 | DELTA: instantiating (528) with fresh symbols all_621_0, all_621_1 gives: % 98.21/14.19 | (536) class_Orderings_Obot(all_480_1) = all_621_0 & % 98.21/14.19 | class_Orderings_Obot(tc_HOL_Obool) = all_621_1 & ( ~ (all_621_1 = 0) % 98.21/14.19 | | all_621_0 = 0) % 98.21/14.19 | % 98.21/14.19 | ALPHA: (536) implies: % 98.21/14.19 | (537) class_Orderings_Obot(tc_HOL_Obool) = all_621_1 % 98.21/14.19 | (538) class_Orderings_Obot(all_480_1) = all_621_0 % 98.21/14.19 | (539) ~ (all_621_1 = 0) | all_621_0 = 0 % 98.21/14.19 | % 98.21/14.19 | DELTA: instantiating (529) with fresh symbols all_653_0, all_653_1 gives: % 98.21/14.19 | (540) class_Orderings_Obot(all_508_3) = all_653_0 & % 98.21/14.19 | class_Orderings_Obot(tc_HOL_Obool) = all_653_1 & ( ~ (all_653_1 = 0) % 98.21/14.19 | | all_653_0 = 0) % 98.21/14.19 | % 98.21/14.19 | ALPHA: (540) implies: % 98.21/14.19 | (541) class_Orderings_Obot(tc_HOL_Obool) = all_653_1 % 98.21/14.19 | % 98.21/14.19 | DELTA: instantiating (527) with fresh symbols all_665_0, all_665_1 gives: % 98.21/14.19 | (542) class_Orderings_Obot(all_522_0) = all_665_0 & % 98.21/14.19 | class_Orderings_Obot(tc_HOL_Obool) = all_665_1 & ( ~ (all_665_1 = 0) % 98.21/14.19 | | all_665_0 = 0) % 98.21/14.19 | % 98.21/14.19 | ALPHA: (542) implies: % 98.21/14.19 | (543) class_Orderings_Obot(tc_HOL_Obool) = all_665_1 % 98.21/14.19 | % 98.21/14.19 | DELTA: instantiating (526) with fresh symbols all_683_0, all_683_1 gives: % 98.21/14.19 | (544) class_Orderings_Obot(all_546_6) = all_683_0 & % 98.21/14.19 | class_Orderings_Obot(all_480_1) = all_683_1 & ( ~ (all_683_1 = 0) | % 98.21/14.19 | all_683_0 = 0) % 98.21/14.19 | % 98.21/14.19 | ALPHA: (544) implies: % 98.21/14.19 | (545) class_Orderings_Obot(all_480_1) = all_683_1 % 98.21/14.19 | % 98.21/14.19 | DELTA: instantiating (525) with fresh symbols all_703_0, all_703_1 gives: % 98.21/14.19 | (546) class_Orderings_Obot(all_482_3) = all_703_0 & % 98.21/14.19 | class_Orderings_Obot(all_480_1) = all_703_1 & ( ~ (all_703_1 = 0) | % 98.21/14.19 | all_703_0 = 0) % 98.21/14.19 | % 98.21/14.19 | ALPHA: (546) implies: % 98.21/14.19 | (547) class_Orderings_Obot(all_480_1) = all_703_1 % 98.21/14.19 | (548) ~ (all_703_1 = 0) | all_703_0 = 0 % 98.21/14.19 | % 98.21/14.19 | DELTA: instantiating (520) with fresh symbols all_705_0, all_705_1, all_705_2 % 98.21/14.19 | gives: % 98.21/14.19 | (549) hBOOL(all_705_2) = all_705_1 & hBOOL(all_486_0) = all_705_0 & % 98.21/14.19 | hAPP(c_Arrow__Order__Mirabelle_OProf, v_Q____) = all_705_2 & % 98.21/14.19 | $i(all_705_2) & ( ~ (all_705_1 = 0) | all_705_0 = 0) % 98.21/14.19 | % 98.21/14.19 | ALPHA: (549) implies: % 98.21/14.19 | (550) hBOOL(all_486_0) = all_705_0 % 98.21/14.19 | % 98.21/14.19 | DELTA: instantiating (519) with fresh symbols all_707_0, all_707_1, all_707_2 % 98.21/14.19 | gives: % 98.21/14.19 | (551) hBOOL(all_707_1) = all_707_0 & hBOOL(all_486_0) = all_707_2 & % 98.21/14.19 | hAPP(c_Arrow__Order__Mirabelle_OProf, v_Q____) = all_707_1 & % 98.21/14.19 | $i(all_707_1) & ( ~ (all_707_2 = 0) | all_707_0 = 0) % 98.21/14.19 | % 98.21/14.19 | ALPHA: (551) implies: % 98.21/14.19 | (552) hBOOL(all_486_0) = all_707_2 % 98.21/14.19 | % 98.21/14.19 | DELTA: instantiating (522) with fresh symbols all_717_0, all_717_1, all_717_2 % 98.21/14.19 | gives: % 98.21/14.19 | (553) hBOOL(all_717_1) = all_717_0 & hBOOL(all_508_0) = all_717_2 & % 98.21/14.19 | hAPP(all_508_1, v_F) = all_717_1 & $i(all_717_1) & ( ~ (all_717_2 = % 98.21/14.19 | 0) | all_717_0 = 0) % 98.21/14.19 | % 98.21/14.19 | ALPHA: (553) implies: % 98.21/14.19 | (554) hBOOL(all_508_0) = all_717_2 % 98.21/14.19 | % 98.21/14.19 | DELTA: instantiating (535) with fresh symbols all_729_0, all_729_1, all_729_2 % 98.21/14.19 | gives: % 98.21/14.19 | (555) c_Orderings_Oord__class_Oless__eq(all_508_3, all_729_1, % 98.21/14.19 | c_Arrow__Order__Mirabelle_OLin) = all_729_0 & % 98.21/14.19 | c_Set_Oimage(all_482_3, all_480_1, v_F, % 98.21/14.19 | c_Arrow__Order__Mirabelle_OProf) = all_729_1 & hBOOL(all_508_0) = % 98.21/14.19 | all_729_2 & $i(all_729_1) & ( ~ (all_729_2 = 0) | all_729_0 = 0) % 98.21/14.19 | % 98.21/14.19 | ALPHA: (555) implies: % 98.21/14.19 | (556) hBOOL(all_508_0) = all_729_2 % 98.21/14.19 | % 98.21/14.19 | DELTA: instantiating (523) with fresh symbols all_733_0, all_733_1, all_733_2 % 98.21/14.19 | gives: % 98.21/14.19 | (557) hBOOL(all_733_2) = all_733_1 & hBOOL(all_508_0) = all_733_0 & % 98.21/14.19 | hAPP(all_508_1, v_F) = all_733_2 & $i(all_733_2) & ( ~ (all_733_1 = % 98.21/14.19 | 0) | all_733_0 = 0) % 98.21/14.19 | % 98.21/14.19 | ALPHA: (557) implies: % 98.21/14.19 | (558) hBOOL(all_508_0) = all_733_0 % 98.21/14.19 | % 98.21/14.19 | DELTA: instantiating (524) with fresh symbols all_737_0, all_737_1, all_737_2 % 98.21/14.19 | gives: % 98.21/14.19 | (559) c_Orderings_Obot__class_Obot(all_737_2) = all_737_1 & % 98.21/14.19 | tc_fun(all_508_6, tc_HOL_Obool) = all_737_2 & hBOOL(all_508_0) = % 98.21/14.19 | all_737_0 & $i(all_737_1) & $i(all_737_2) & ( ~ (all_737_0 = 0) | ~ % 98.21/14.19 | (all_737_1 = all_508_1)) % 98.21/14.19 | % 98.21/14.19 | ALPHA: (559) implies: % 98.21/14.19 | (560) hBOOL(all_508_0) = all_737_0 % 98.21/14.19 | % 98.21/14.19 | DELTA: instantiating (521) with fresh symbols all_739_0, all_739_1, all_739_2 % 98.21/14.19 | gives: % 98.21/14.19 | (561) c_Orderings_Obot__class_Obot(all_739_2) = all_739_1 & % 98.21/14.19 | tc_fun(all_482_3, tc_HOL_Obool) = all_739_2 & hBOOL(all_486_0) = % 98.21/14.19 | all_739_0 & $i(all_739_1) & $i(all_739_2) & ( ~ (all_739_0 = 0) | ~ % 98.21/14.19 | (all_739_1 = c_Arrow__Order__Mirabelle_OProf)) % 98.21/14.19 | % 98.21/14.19 | ALPHA: (561) implies: % 98.21/14.19 | (562) hBOOL(all_486_0) = all_739_0 % 98.21/14.19 | % 98.21/14.19 | DELTA: instantiating (532) with fresh symbols all_753_0, all_753_1, all_753_2, % 98.21/14.19 | all_753_3, all_753_4, all_753_5 gives: % 98.21/14.19 | (563) c_member(all_482_3) = all_753_4 & hBOOL(all_753_2) = all_753_1 & % 98.21/14.19 | hBOOL(all_508_0) = all_753_5 & hBOOL(all_492_1) = all_753_0 & % 98.21/14.19 | hAPP(all_753_3, c_Arrow__Order__Mirabelle_OProf) = all_753_2 & % 98.21/14.19 | hAPP(all_753_4, v_Q____) = all_753_3 & $i(all_753_2) & $i(all_753_3) % 98.21/14.19 | & $i(all_753_4) & ( ~ (all_753_1 = 0) | ~ (all_753_5 = 0) | % 98.21/14.19 | all_753_0 = 0) % 98.21/14.19 | % 98.21/14.19 | ALPHA: (563) implies: % 98.21/14.19 | (564) hAPP(all_753_4, v_Q____) = all_753_3 % 98.21/14.19 | (565) hAPP(all_753_3, c_Arrow__Order__Mirabelle_OProf) = all_753_2 % 98.21/14.19 | (566) hBOOL(all_492_1) = all_753_0 % 98.21/14.19 | (567) hBOOL(all_508_0) = all_753_5 % 98.21/14.19 | (568) hBOOL(all_753_2) = all_753_1 % 98.21/14.19 | (569) c_member(all_482_3) = all_753_4 % 98.21/14.19 | (570) ~ (all_753_1 = 0) | ~ (all_753_5 = 0) | all_753_0 = 0 % 98.21/14.19 | % 98.21/14.19 | DELTA: instantiating (533) with fresh symbols all_755_0, all_755_1, all_755_2, % 98.21/14.19 | all_755_3, all_755_4, all_755_5, all_755_6 gives: % 98.21/14.19 | (571) c_FuncSet_Orestrict(all_482_3, all_482_3, all_755_2, % 98.21/14.19 | c_Arrow__Order__Mirabelle_OProf) = all_755_1 & % 98.21/14.19 | c_FuncSet_Oextensional(all_482_3, all_480_1, % 98.21/14.19 | c_Arrow__Order__Mirabelle_OProf) = all_755_5 & % 98.21/14.19 | c_FuncSet_Ocompose(all_482_3, all_482_3, all_480_1, % 98.21/14.19 | c_Arrow__Order__Mirabelle_OProf, v_F, all_755_1) = all_755_0 & % 98.21/14.19 | c_COMBI(all_482_3) = all_755_2 & hBOOL(all_755_4) = all_755_3 & % 98.21/14.19 | hBOOL(all_508_0) = all_755_6 & hAPP(all_508_4, all_755_5) = all_755_4 % 98.21/14.19 | & $i(all_755_0) & $i(all_755_1) & $i(all_755_2) & $i(all_755_4) & % 98.21/14.19 | $i(all_755_5) & ( ~ (all_755_3 = 0) | ~ (all_755_6 = 0) | all_755_0 % 98.21/14.19 | = v_F) % 98.21/14.19 | % 98.21/14.19 | ALPHA: (571) implies: % 98.21/14.19 | (572) hBOOL(all_508_0) = all_755_6 % 98.21/14.19 | % 98.21/14.19 | DELTA: instantiating (534) with fresh symbols all_757_0, all_757_1, all_757_2, % 98.21/14.19 | all_757_3, all_757_4, all_757_5, all_757_6 gives: % 98.21/14.19 | (573) c_FuncSet_Orestrict(all_480_1, all_480_1, all_757_2, % 98.21/14.19 | c_Arrow__Order__Mirabelle_OLin) = all_757_1 & % 98.21/14.19 | c_FuncSet_Oextensional(all_482_3, all_480_1, % 98.21/14.19 | c_Arrow__Order__Mirabelle_OProf) = all_757_5 & % 98.21/14.19 | c_FuncSet_Ocompose(all_482_3, all_480_1, all_480_1, % 98.21/14.19 | c_Arrow__Order__Mirabelle_OProf, all_757_1, v_F) = all_757_0 & % 98.21/14.19 | c_COMBI(all_480_1) = all_757_2 & hBOOL(all_757_4) = all_757_3 & % 98.21/14.19 | hBOOL(all_508_0) = all_757_6 & hAPP(all_508_4, all_757_5) = all_757_4 % 98.21/14.19 | & $i(all_757_0) & $i(all_757_1) & $i(all_757_2) & $i(all_757_4) & % 98.21/14.19 | $i(all_757_5) & ( ~ (all_757_3 = 0) | ~ (all_757_6 = 0) | all_757_0 % 98.21/14.19 | = v_F) % 98.21/14.19 | % 98.21/14.19 | ALPHA: (573) implies: % 98.21/14.19 | (574) hBOOL(all_508_0) = all_757_6 % 98.21/14.19 | % 98.21/14.19 | DELTA: instantiating (531) with fresh symbols all_761_0, all_761_1, all_761_2, % 98.21/14.19 | all_761_3, all_761_4, all_761_5 gives: % 98.21/14.19 | (575) c_Orderings_Obot__class_Obot(all_761_1) = all_761_0 & % 98.21/14.19 | c_Orderings_Obot__class_Obot(all_761_4) = all_761_3 & % 98.21/14.19 | tc_fun(all_761_5, tc_HOL_Obool) = all_761_4 & tc_fun(all_482_3, % 98.21/14.19 | all_480_1) = all_761_5 & tc_fun(all_480_1, tc_HOL_Obool) = % 98.21/14.19 | all_761_1 & c_member(all_482_3) = all_761_2 & $i(all_761_0) & % 98.21/14.19 | $i(all_761_1) & $i(all_761_2) & $i(all_761_3) & $i(all_761_4) & % 98.21/14.19 | $i(all_761_5) & ( ~ (all_761_3 = all_508_1) | ? [v0: $i] : ? [v1: % 98.21/14.19 | $i] : ? [v2: $i] : (hBOOL(v2) = 0 & hAPP(v1, % 98.21/14.19 | c_Arrow__Order__Mirabelle_OProf) = v2 & hAPP(all_761_2, v0) = % 98.21/14.19 | v1 & hAPP(all_508_2, v0) = all_761_0 & $i(v2) & $i(v1) & $i(v0))) % 98.21/14.19 | % 98.21/14.19 | ALPHA: (575) implies: % 98.21/14.19 | (576) c_member(all_482_3) = all_761_2 % 98.21/14.19 | % 98.21/14.19 | DELTA: instantiating (530) with fresh symbols all_763_0, all_763_1, all_763_2, % 98.21/14.19 | all_763_3, all_763_4, all_763_5 gives: % 98.21/14.19 | (577) c_Orderings_Obot__class_Obot(all_763_1) = all_763_0 & % 98.21/14.19 | c_Orderings_Obot__class_Obot(all_763_4) = all_763_3 & % 98.21/14.19 | tc_fun(all_763_2, tc_HOL_Obool) = all_763_1 & tc_fun(all_482_3, % 98.21/14.19 | all_480_1) = all_763_2 & tc_fun(all_480_1, tc_HOL_Obool) = % 98.21/14.19 | all_763_4 & c_member(all_482_3) = all_763_5 & $i(all_763_0) & % 98.21/14.19 | $i(all_763_1) & $i(all_763_2) & $i(all_763_3) & $i(all_763_4) & % 98.21/14.19 | $i(all_763_5) & (all_763_0 = all_508_1 | ! [v0: $i] : ! [v1: $i] : % 98.21/14.19 | ! [v2: $i] : ( ~ (hAPP(v1, c_Arrow__Order__Mirabelle_OProf) = v2) | % 98.21/14.19 | ~ (hAPP(all_763_5, v0) = v1) | ~ $i(v0) | ? [v3: any] : ? % 98.21/14.19 | [v4: $i] : (hBOOL(v2) = v3 & hAPP(all_508_2, v0) = v4 & $i(v4) & % 98.21/14.19 | ( ~ (v4 = all_763_3) | ~ (v3 = 0))))) % 98.21/14.19 | % 98.21/14.19 | ALPHA: (577) implies: % 98.21/14.19 | (578) c_member(all_482_3) = all_763_5 % 98.21/14.19 | % 98.21/14.19 | GROUND_INST: instantiating (45) with 0, all_707_2, all_486_0, simplifying with % 98.21/14.19 | (73), (552) gives: % 98.21/14.19 | (579) all_707_2 = 0 % 98.21/14.19 | % 98.21/14.19 | GROUND_INST: instantiating (45) with all_707_2, all_739_0, all_486_0, % 98.21/14.19 | simplifying with (552), (562) gives: % 98.21/14.19 | (580) all_739_0 = all_707_2 % 98.21/14.19 | % 98.21/14.20 | GROUND_INST: instantiating (45) with all_705_0, all_739_0, all_486_0, % 98.21/14.20 | simplifying with (550), (562) gives: % 98.21/14.20 | (581) all_739_0 = all_705_0 % 98.21/14.20 | % 98.21/14.20 | GROUND_INST: instantiating (45) with all_492_0, all_753_0, all_492_1, % 98.21/14.20 | simplifying with (83), (566) gives: % 98.21/14.20 | (582) all_753_0 = all_492_0 % 98.21/14.20 | % 98.21/14.20 | GROUND_INST: instantiating (45) with all_717_2, all_737_0, all_508_0, % 98.21/14.20 | simplifying with (554), (560) gives: % 98.21/14.20 | (583) all_737_0 = all_717_2 % 98.21/14.20 | % 98.21/14.20 | GROUND_INST: instantiating (45) with all_737_0, all_753_5, all_508_0, % 98.21/14.20 | simplifying with (560), (567) gives: % 98.21/14.20 | (584) all_753_5 = all_737_0 % 98.21/14.20 | % 98.21/14.20 | GROUND_INST: instantiating (45) with 0, all_755_6, all_508_0, simplifying with % 98.21/14.20 | (100), (572) gives: % 98.21/14.20 | (585) all_755_6 = 0 % 98.21/14.20 | % 98.21/14.20 | GROUND_INST: instantiating (45) with all_737_0, all_755_6, all_508_0, % 98.21/14.20 | simplifying with (560), (572) gives: % 98.21/14.20 | (586) all_755_6 = all_737_0 % 98.21/14.20 | % 98.21/14.20 | GROUND_INST: instantiating (45) with all_733_0, all_755_6, all_508_0, % 98.21/14.20 | simplifying with (558), (572) gives: % 98.21/14.20 | (587) all_755_6 = all_733_0 % 98.21/14.20 | % 98.21/14.20 | GROUND_INST: instantiating (45) with all_753_5, all_757_6, all_508_0, % 98.21/14.20 | simplifying with (567), (574) gives: % 98.21/14.20 | (588) all_757_6 = all_753_5 % 98.21/14.20 | % 98.21/14.20 | GROUND_INST: instantiating (45) with all_729_2, all_757_6, all_508_0, % 98.21/14.20 | simplifying with (556), (574) gives: % 98.21/14.20 | (589) all_757_6 = all_729_2 % 98.21/14.20 | % 98.21/14.20 | GROUND_INST: instantiating (46) with all_753_4, all_761_2, all_482_3, % 98.21/14.20 | simplifying with (569), (576) gives: % 98.21/14.20 | (590) all_761_2 = all_753_4 % 98.21/14.20 | % 98.21/14.20 | GROUND_INST: instantiating (46) with all_482_2, all_763_5, all_482_3, % 98.21/14.20 | simplifying with (60), (578) gives: % 98.21/14.20 | (591) all_763_5 = all_482_2 % 98.21/14.20 | % 98.21/14.20 | GROUND_INST: instantiating (46) with all_761_2, all_763_5, all_482_3, % 98.21/14.20 | simplifying with (576), (578) gives: % 98.21/14.20 | (592) all_763_5 = all_761_2 % 98.21/14.20 | % 98.21/14.20 | GROUND_INST: instantiating (47) with 0, all_665_1, tc_HOL_Obool, simplifying % 98.21/14.20 | with (38), (543) gives: % 98.21/14.20 | (593) all_665_1 = 0 % 98.21/14.20 | % 98.21/14.20 | GROUND_INST: instantiating (47) with all_653_1, all_665_1, tc_HOL_Obool, % 98.21/14.20 | simplifying with (541), (543) gives: % 98.21/14.20 | (594) all_665_1 = all_653_1 % 98.21/14.20 | % 98.21/14.20 | GROUND_INST: instantiating (47) with all_621_1, all_665_1, tc_HOL_Obool, % 98.21/14.20 | simplifying with (537), (543) gives: % 98.21/14.20 | (595) all_665_1 = all_621_1 % 98.21/14.20 | % 98.21/14.20 | GROUND_INST: instantiating (47) with all_683_1, all_703_1, all_480_1, % 98.21/14.20 | simplifying with (545), (547) gives: % 98.21/14.20 | (596) all_703_1 = all_683_1 % 98.21/14.20 | % 98.21/14.20 | GROUND_INST: instantiating (47) with all_621_0, all_703_1, all_480_1, % 98.21/14.20 | simplifying with (538), (547) gives: % 98.21/14.20 | (597) all_703_1 = all_621_0 % 98.21/14.20 | % 98.21/14.20 | COMBINE_EQS: (591), (592) imply: % 98.21/14.20 | (598) all_761_2 = all_482_2 % 98.21/14.20 | % 98.21/14.20 | SIMP: (598) implies: % 98.21/14.20 | (599) all_761_2 = all_482_2 % 98.21/14.20 | % 98.21/14.20 | COMBINE_EQS: (590), (599) imply: % 98.21/14.20 | (600) all_753_4 = all_482_2 % 98.21/14.20 | % 98.21/14.20 | COMBINE_EQS: (588), (589) imply: % 98.21/14.20 | (601) all_753_5 = all_729_2 % 98.21/14.20 | % 98.21/14.20 | SIMP: (601) implies: % 98.21/14.20 | (602) all_753_5 = all_729_2 % 98.21/14.20 | % 98.21/14.20 | COMBINE_EQS: (586), (587) imply: % 98.21/14.20 | (603) all_737_0 = all_733_0 % 98.21/14.20 | % 98.21/14.20 | SIMP: (603) implies: % 98.21/14.20 | (604) all_737_0 = all_733_0 % 98.21/14.20 | % 98.21/14.20 | COMBINE_EQS: (585), (587) imply: % 98.21/14.20 | (605) all_733_0 = 0 % 98.21/14.20 | % 98.21/14.20 | COMBINE_EQS: (584), (602) imply: % 98.21/14.20 | (606) all_737_0 = all_729_2 % 98.21/14.20 | % 98.21/14.20 | SIMP: (606) implies: % 98.21/14.20 | (607) all_737_0 = all_729_2 % 98.21/14.20 | % 98.21/14.20 | COMBINE_EQS: (580), (581) imply: % 98.21/14.20 | (608) all_707_2 = all_705_0 % 98.21/14.20 | % 98.21/14.20 | SIMP: (608) implies: % 98.21/14.20 | (609) all_707_2 = all_705_0 % 98.21/14.20 | % 98.21/14.20 | COMBINE_EQS: (604), (607) imply: % 98.21/14.20 | (610) all_733_0 = all_729_2 % 98.21/14.20 | % 98.21/14.20 | SIMP: (610) implies: % 98.21/14.20 | (611) all_733_0 = all_729_2 % 98.21/14.20 | % 98.21/14.20 | COMBINE_EQS: (583), (607) imply: % 98.21/14.20 | (612) all_729_2 = all_717_2 % 98.21/14.20 | % 98.21/14.20 | COMBINE_EQS: (605), (611) imply: % 98.21/14.20 | (613) all_729_2 = 0 % 98.21/14.20 | % 98.21/14.20 | SIMP: (613) implies: % 98.21/14.20 | (614) all_729_2 = 0 % 98.21/14.20 | % 98.21/14.20 | COMBINE_EQS: (612), (614) imply: % 98.21/14.20 | (615) all_717_2 = 0 % 98.21/14.20 | % 98.21/14.20 | COMBINE_EQS: (579), (609) imply: % 98.21/14.20 | (616) all_705_0 = 0 % 98.21/14.20 | % 98.21/14.20 | COMBINE_EQS: (596), (597) imply: % 98.21/14.20 | (617) all_683_1 = all_621_0 % 98.21/14.20 | % 98.21/14.20 | COMBINE_EQS: (593), (594) imply: % 98.21/14.20 | (618) all_653_1 = 0 % 98.21/14.20 | % 98.21/14.20 | COMBINE_EQS: (594), (595) imply: % 98.21/14.20 | (619) all_653_1 = all_621_1 % 98.21/14.20 | % 98.21/14.20 | COMBINE_EQS: (618), (619) imply: % 98.21/14.20 | (620) all_621_1 = 0 % 98.21/14.20 | % 98.21/14.20 | SIMP: (620) implies: % 98.21/14.20 | (621) all_621_1 = 0 % 98.21/14.20 | % 98.21/14.20 | COMBINE_EQS: (602), (614) imply: % 98.21/14.20 | (622) all_753_5 = 0 % 98.21/14.20 | % 98.21/14.20 | REDUCE: (564), (600) imply: % 98.21/14.20 | (623) hAPP(all_482_2, v_Q____) = all_753_3 % 98.21/14.20 | % 98.21/14.20 | BETA: splitting (570) gives: % 98.21/14.20 | % 98.21/14.20 | Case 1: % 98.21/14.20 | | % 98.21/14.20 | | (624) ~ (all_753_1 = 0) % 98.21/14.20 | | % 98.21/14.20 | | BETA: splitting (539) gives: % 98.21/14.20 | | % 98.21/14.20 | | Case 1: % 98.21/14.20 | | | % 98.21/14.20 | | | (625) ~ (all_621_1 = 0) % 98.21/14.20 | | | % 98.21/14.20 | | | REDUCE: (621), (625) imply: % 98.21/14.20 | | | (626) $false % 98.21/14.20 | | | % 98.21/14.20 | | | CLOSE: (626) is inconsistent. % 98.21/14.20 | | | % 98.21/14.20 | | Case 2: % 98.21/14.20 | | | % 98.21/14.20 | | | (627) all_621_0 = 0 % 98.21/14.20 | | | % 98.21/14.20 | | | COMBINE_EQS: (597), (627) imply: % 98.21/14.20 | | | (628) all_703_1 = 0 % 98.21/14.20 | | | % 98.21/14.20 | | | BETA: splitting (548) gives: % 98.21/14.20 | | | % 98.21/14.20 | | | Case 1: % 98.21/14.20 | | | | % 98.21/14.20 | | | | (629) ~ (all_703_1 = 0) % 98.21/14.20 | | | | % 98.21/14.20 | | | | REDUCE: (628), (629) imply: % 98.21/14.20 | | | | (630) $false % 98.21/14.20 | | | | % 98.21/14.20 | | | | CLOSE: (630) is inconsistent. % 98.21/14.20 | | | | % 98.54/14.20 | | | Case 2: % 98.54/14.20 | | | | % 98.54/14.20 | | | | % 98.54/14.20 | | | | GROUND_INST: instantiating (48) with all_486_1, all_753_3, v_Q____, % 98.54/14.20 | | | | all_482_2, simplifying with (513), (623) gives: % 98.54/14.20 | | | | (631) all_753_3 = all_486_1 % 98.54/14.20 | | | | % 98.54/14.20 | | | | REDUCE: (565), (631) imply: % 98.54/14.20 | | | | (632) hAPP(all_486_1, c_Arrow__Order__Mirabelle_OProf) = all_753_2 % 98.54/14.20 | | | | % 98.54/14.20 | | | | GROUND_INST: instantiating (48) with all_486_0, all_753_2, % 98.54/14.20 | | | | c_Arrow__Order__Mirabelle_OProf, all_486_1, simplifying % 98.54/14.20 | | | | with (72), (632) gives: % 98.54/14.20 | | | | (633) all_753_2 = all_486_0 % 98.54/14.20 | | | | % 98.54/14.20 | | | | REDUCE: (568), (633) imply: % 98.54/14.20 | | | | (634) hBOOL(all_486_0) = all_753_1 % 98.54/14.20 | | | | % 98.54/14.20 | | | | GROUND_INST: instantiating (45) with 0, all_753_1, all_486_0, % 98.54/14.20 | | | | simplifying with (73), (634) gives: % 98.54/14.20 | | | | (635) all_753_1 = 0 % 98.54/14.20 | | | | % 98.54/14.20 | | | | REDUCE: (624), (635) imply: % 98.54/14.20 | | | | (636) $false % 98.54/14.20 | | | | % 98.54/14.20 | | | | CLOSE: (636) is inconsistent. % 98.54/14.20 | | | | % 98.54/14.20 | | | End of split % 98.54/14.20 | | | % 98.54/14.20 | | End of split % 98.54/14.20 | | % 98.54/14.20 | Case 2: % 98.54/14.20 | | % 98.54/14.20 | | (637) ~ (all_753_5 = 0) | all_753_0 = 0 % 98.54/14.20 | | % 98.54/14.20 | | BETA: splitting (637) gives: % 98.54/14.20 | | % 98.54/14.20 | | Case 1: % 98.54/14.20 | | | % 98.54/14.20 | | | (638) ~ (all_753_5 = 0) % 98.54/14.20 | | | % 98.54/14.20 | | | REDUCE: (622), (638) imply: % 98.54/14.20 | | | (639) $false % 98.54/14.20 | | | % 98.54/14.20 | | | CLOSE: (639) is inconsistent. % 98.54/14.20 | | | % 98.54/14.20 | | Case 2: % 98.54/14.20 | | | % 98.54/14.20 | | | (640) all_753_0 = 0 % 98.54/14.20 | | | % 98.54/14.20 | | | COMBINE_EQS: (582), (640) imply: % 98.54/14.20 | | | (641) all_492_0 = 0 % 98.54/14.20 | | | % 98.54/14.20 | | | REDUCE: (79), (641) imply: % 98.54/14.20 | | | (642) $false % 98.54/14.20 | | | % 98.54/14.20 | | | CLOSE: (642) is inconsistent. % 98.54/14.20 | | | % 98.54/14.20 | | End of split % 98.54/14.20 | | % 98.54/14.20 | End of split % 98.54/14.20 | % 98.54/14.20 End of proof % 98.54/14.20 % SZS output end Proof for theBenchmark % 98.54/14.20 % 98.54/14.20 13632ms %------------------------------------------------------------------------------