TSTP Solution File: SCT123+1 by Princess---230619
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SCT123+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 : n007.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 14:20:43 EDT 2023
% Result : Theorem 83.34s 11.59s
% Output : Proof 100.47s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SCT123+1 : TPTP v8.1.2. Released v5.2.0.
% 0.07/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.34 % Computer : n007.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Thu Aug 24 16:13:40 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.60 ________ _____
% 0.19/0.60 ___ __ \_________(_)________________________________
% 0.19/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.19/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.19/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.19/0.60
% 0.19/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.19/0.60 (2023-06-19)
% 0.19/0.60
% 0.19/0.60 (c) Philipp Rümmer, 2009-2023
% 0.19/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.19/0.60 Amanda Stjerna.
% 0.19/0.60 Free software under BSD-3-Clause.
% 0.19/0.60
% 0.19/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.19/0.60
% 0.19/0.60 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.19/0.61 Running up to 7 provers in parallel.
% 0.19/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.19/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.19/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.19/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.19/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.19/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.19/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 16.30/2.95 Prover 4: Preprocessing ...
% 17.00/2.95 Prover 1: Preprocessing ...
% 17.31/3.00 Prover 0: Preprocessing ...
% 17.31/3.00 Prover 5: Preprocessing ...
% 17.31/3.00 Prover 6: Preprocessing ...
% 17.71/3.04 Prover 3: Preprocessing ...
% 17.71/3.09 Prover 2: Preprocessing ...
% 49.82/7.23 Prover 1: Warning: ignoring some quantifiers
% 50.50/7.32 Prover 3: Warning: ignoring some quantifiers
% 51.16/7.44 Prover 6: Proving ...
% 51.16/7.45 Prover 3: Constructing countermodel ...
% 51.84/7.52 Prover 1: Constructing countermodel ...
% 57.79/8.28 Prover 4: Warning: ignoring some quantifiers
% 60.25/8.58 Prover 4: Constructing countermodel ...
% 60.68/8.64 Prover 5: Proving ...
% 63.30/9.02 Prover 0: Proving ...
% 77.01/10.80 Prover 2: Proving ...
% 83.34/11.58 Prover 3: proved (10959ms)
% 83.34/11.58
% 83.34/11.59 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 83.34/11.59
% 83.34/11.59 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 83.34/11.59 Prover 2: stopped
% 83.34/11.59 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 83.34/11.63 Prover 6: stopped
% 83.34/11.63 Prover 5: stopped
% 83.34/11.64 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 83.34/11.64 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 83.34/11.64 Prover 0: stopped
% 83.34/11.64 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 89.94/12.47 Prover 8: Preprocessing ...
% 89.94/12.52 Prover 13: Preprocessing ...
% 90.71/12.62 Prover 10: Preprocessing ...
% 90.71/12.62 Prover 7: Preprocessing ...
% 90.71/12.62 Prover 11: Preprocessing ...
% 93.02/12.90 Prover 1: Found proof (size 482)
% 93.02/12.90 Prover 1: proved (12279ms)
% 93.76/12.96 Prover 10: stopped
% 93.76/12.98 Prover 4: stopped
% 94.15/13.05 Prover 7: stopped
% 95.08/13.15 Prover 11: stopped
% 95.08/13.28 Prover 13: stopped
% 96.33/13.44 Prover 8: Warning: ignoring some quantifiers
% 97.16/13.60 Prover 8: Constructing countermodel ...
% 97.16/13.63 Prover 8: stopped
% 97.16/13.63
% 97.16/13.64 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 97.16/13.64
% 98.73/14.03 % SZS output start Proof for theBenchmark
% 99.07/14.06 Assumptions after simplification:
% 99.07/14.06 ---------------------------------
% 99.07/14.06
% 99.07/14.06 (arity_HOL__Obool__Complete__Lattice_Ocomplete__lattice)
% 99.07/14.09 class_Complete__Lattice_Ocomplete__lattice(tc_HOL_Obool) = 0 &
% 99.07/14.09 $i(tc_HOL_Obool)
% 99.07/14.09
% 99.07/14.09 (arity_fun__Complete__Lattice_Ocomplete__lattice)
% 99.07/14.09 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (tc_fun(v0, v1) = v2) | ~
% 99.07/14.09 $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] :
% 99.07/14.09 (class_Complete__Lattice_Ocomplete__lattice(v2) = v4 &
% 99.07/14.09 class_Complete__Lattice_Ocomplete__lattice(v1) = v3 & ( ~ (v3 = 0) | v4 =
% 99.07/14.09 0)))
% 99.07/14.09
% 99.07/14.09 (conj_0)
% 99.07/14.09 $i(v_L) & $i(c_Arrow__Order__Mirabelle_OLin) & $i(tc_HOL_Obool) &
% 99.07/14.09 $i(tc_Arrow__Order__Mirabelle_Oalt) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i]
% 99.07/14.09 : ? [v3: $i] : ? [v4: $i] : (tc_prod(tc_Arrow__Order__Mirabelle_Oalt,
% 99.07/14.09 tc_Arrow__Order__Mirabelle_Oalt) = v0 & tc_fun(v0, tc_HOL_Obool) = v1 &
% 99.07/14.09 c_member(v1) = v2 & hBOOL(v4) = 0 & hAPP(v3, c_Arrow__Order__Mirabelle_OLin)
% 99.07/14.09 = v4 & hAPP(v2, v_L) = v3 & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 99.07/14.09
% 99.07/14.09 (conj_1)
% 99.07/14.10 $i(v_L) & $i(c_Arrow__Order__Mirabelle_OProf) &
% 99.07/14.10 $i(tc_Arrow__Order__Mirabelle_Oindi) & $i(tc_HOL_Obool) &
% 99.07/14.10 $i(tc_Arrow__Order__Mirabelle_Oalt) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i]
% 99.07/14.10 : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: int] : ( ~
% 99.07/14.10 (v7 = 0) & c_COMBK(v1, tc_Arrow__Order__Mirabelle_Oindi, v_L) = v4 &
% 99.07/14.10 tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt) =
% 99.07/14.10 v0 & tc_fun(v0, tc_HOL_Obool) = v1 &
% 99.07/14.10 tc_fun(tc_Arrow__Order__Mirabelle_Oindi, v1) = v2 & c_member(v2) = v3 &
% 99.07/14.10 hBOOL(v6) = v7 & hAPP(v5, c_Arrow__Order__Mirabelle_OProf) = v6 & hAPP(v3,
% 99.07/14.10 v4) = v5 & $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 99.07/14.10
% 99.07/14.10 (fact_IIA__def)
% 99.34/14.11 $i(c_Arrow__Order__Mirabelle_OProf) & $i(tc_Arrow__Order__Mirabelle_Oindi) &
% 99.34/14.11 $i(tc_HOL_Obool) & $i(tc_Arrow__Order__Mirabelle_Oalt) & ? [v0: $i] : ? [v1:
% 99.34/14.11 $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] :
% 99.34/14.11 (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 99.34/14.11 tc_Arrow__Order__Mirabelle_Oalt) = v5 &
% 99.34/14.11 tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt) =
% 99.34/14.11 v0 & tc_fun(v0, tc_HOL_Obool) = v1 &
% 99.34/14.11 tc_fun(tc_Arrow__Order__Mirabelle_Oindi, v1) = v2 & c_member(v2) = v3 &
% 99.34/14.11 c_member(v0) = v4 & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & !
% 99.34/14.11 [v6: $i] : ! [v7: int] : (v7 = 0 | ~ (c_Arrow__Order__Mirabelle_OIIA(v6) =
% 99.34/14.11 v7) | ~ $i(v6) | ? [v8: $i] : ? [v9: $i] : ? [v10: $i] : ? [v11:
% 99.34/14.11 $i] : (hBOOL(v10) = 0 & hAPP(v9, c_Arrow__Order__Mirabelle_OProf) = v10
% 99.34/14.11 & hAPP(v6, v8) = v11 & hAPP(v3, v8) = v9 & $i(v11) & $i(v10) & $i(v9) &
% 99.34/14.11 $i(v8) & ? [v12: $i] : ? [v13: $i] : ? [v14: $i] : ? [v15: $i] :
% 99.34/14.11 (hBOOL(v14) = 0 & hAPP(v13, c_Arrow__Order__Mirabelle_OProf) = v14 &
% 99.34/14.11 hAPP(v6, v12) = v15 & hAPP(v3, v12) = v13 & $i(v15) & $i(v14) &
% 99.34/14.11 $i(v13) & $i(v12) & ? [v16: $i] : ? [v17: $i] : ? [v18: $i] : ?
% 99.34/14.11 [v19: $i] : ? [v20: $i] : ? [v21: $i] : ? [v22: any] : ? [v23: $i]
% 99.34/14.11 : ? [v24: any] : (hBOOL(v23) = v24 & hBOOL(v21) = v22 & hAPP(v20,
% 99.34/14.11 v15) = v23 & hAPP(v20, v11) = v21 & hAPP(v18, v17) = v19 &
% 99.34/14.11 hAPP(v5, v16) = v18 & hAPP(v4, v19) = v20 & $i(v23) & $i(v21) &
% 99.34/14.11 $i(v20) & $i(v19) & $i(v18) & $i(v17) & $i(v16) & ! [v25: $i] : !
% 99.34/14.11 [v26: $i] : ! [v27: $i] : ( ~ (hAPP(v20, v26) = v27) | ~ (hAPP(v8,
% 99.34/14.11 v25) = v26) | ~ $i(v25) | ? [v28: any] : ? [v29: $i] : ?
% 99.34/14.11 [v30: $i] : ? [v31: any] : (hBOOL(v30) = v31 & hBOOL(v27) = v28 &
% 99.34/14.11 hAPP(v20, v29) = v30 & hAPP(v12, v25) = v29 & $i(v30) & $i(v29)
% 99.34/14.11 & ( ~ (v28 = 0) | v31 = 0))) & ! [v25: $i] : ! [v26: $i] : !
% 99.34/14.11 [v27: $i] : ( ~ (hAPP(v20, v26) = v27) | ~ (hAPP(v8, v25) = v26) |
% 99.34/14.11 ~ $i(v25) | ? [v28: $i] : ? [v29: $i] : ? [v30: any] : ? [v31:
% 99.34/14.11 any] : (hBOOL(v29) = v30 & hBOOL(v27) = v31 & hAPP(v20, v28) =
% 99.34/14.11 v29 & hAPP(v12, v25) = v28 & $i(v29) & $i(v28) & ( ~ (v30 = 0) |
% 99.34/14.11 v31 = 0))) & ( ~ (v24 = 0) | ~ (v22 = 0)) & (v24 = 0 | v22 =
% 99.34/14.11 0))))) & ! [v6: $i] : ( ~ (c_Arrow__Order__Mirabelle_OIIA(v6) =
% 99.34/14.11 0) | ~ $i(v6) | ! [v7: $i] : ! [v8: $i] : ( ~ (hAPP(v3, v7) = v8) |
% 99.34/14.11 ~ $i(v7) | ? [v9: $i] : ? [v10: any] : ? [v11: $i] : (hBOOL(v9) = v10
% 99.34/14.11 & hAPP(v8, c_Arrow__Order__Mirabelle_OProf) = v9 & hAPP(v6, v7) = v11
% 99.34/14.11 & $i(v11) & $i(v9) & ( ~ (v10 = 0) | ! [v12: $i] : ! [v13: $i] : ( ~
% 99.34/14.11 (hAPP(v3, v12) = v13) | ~ $i(v12) | ? [v14: $i] : ? [v15: any]
% 99.34/14.11 : ? [v16: $i] : (hBOOL(v14) = v15 & hAPP(v13,
% 99.34/14.11 c_Arrow__Order__Mirabelle_OProf) = v14 & hAPP(v6, v12) = v16 &
% 99.34/14.11 $i(v16) & $i(v14) & ( ~ (v15 = 0) | ! [v17: $i] : ! [v18: $i]
% 99.34/14.11 : ! [v19: $i] : ! [v20: $i] : ! [v21: $i] : ! [v22: $i] :
% 99.34/14.11 ( ~ (hAPP(v21, v11) = v22) | ~ (hAPP(v19, v18) = v20) | ~
% 99.34/14.11 (hAPP(v5, v17) = v19) | ~ (hAPP(v4, v20) = v21) | ~
% 99.34/14.11 $i(v18) | ~ $i(v17) | ? [v23: $i] : ? [v24: $i] : ?
% 99.34/14.11 [v25: $i] : ? [v26: any] : ? [v27: $i] : ? [v28: $i] : ?
% 99.34/14.11 [v29: any] : (hBOOL(v28) = v29 & hBOOL(v25) = v26 &
% 99.34/14.11 hAPP(v21, v27) = v28 & hAPP(v21, v24) = v25 & hAPP(v12,
% 99.34/14.11 v23) = v27 & hAPP(v7, v23) = v24 & $i(v28) & $i(v27) &
% 99.34/14.11 $i(v25) & $i(v24) & $i(v23) & ( ~ (v29 = 0) | ~ (v26 =
% 99.34/14.11 0)) & (v29 = 0 | v26 = 0)) | ? [v23: any] : ? [v24:
% 99.34/14.11 $i] : ? [v25: any] : (hBOOL(v24) = v25 & hBOOL(v22) = v23
% 99.34/14.11 & hAPP(v21, v16) = v24 & $i(v24) & ( ~ (v25 = 0) | v23 =
% 99.34/14.11 0) & ( ~ (v23 = 0) | v25 = 0)))))))))))
% 99.34/14.11
% 99.34/14.11 (fact_Id__compose)
% 99.34/14.12 $i(tc_HOL_Obool) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : !
% 99.34/14.12 [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i]
% 99.34/14.12 : ! [v10: $i] : ! [v11: $i] : ( ~ (c_COMBK(v8, v4, v0) = v9) | ~
% 99.34/14.12 (c_FuncSet_OPi(v4, v3, v1, v9) = v10) | ~ (tc_fun(v4, v3) = v5) | ~
% 99.34/14.12 (tc_fun(v3, tc_HOL_Obool) = v8) | ~ (c_member(v5) = v6) | ~ (hAPP(v7, v10)
% 99.34/14.12 = v11) | ~ (hAPP(v6, v2) = v7) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~
% 99.34/14.12 $i(v1) | ~ $i(v0) | ? [v12: any] : ? [v13: $i] : ? [v14: $i] : ? [v15:
% 99.34/14.12 any] : ? [v16: $i] : ? [v17: $i] : ? [v18: $i] :
% 99.34/14.12 (c_FuncSet_Orestrict(v3, v3, v16, v0) = v17 & c_FuncSet_Oextensional(v4, v3,
% 99.34/14.12 v1) = v13 & c_FuncSet_Ocompose(v4, v3, v3, v1, v17, v2) = v18 &
% 99.34/14.12 c_COMBI(v3) = v16 & hBOOL(v14) = v15 & hBOOL(v11) = v12 & hAPP(v7, v13) =
% 99.34/14.12 v14 & $i(v18) & $i(v17) & $i(v16) & $i(v14) & $i(v13) & ( ~ (v15 = 0) | ~
% 99.34/14.12 (v12 = 0) | v18 = v2)))
% 99.34/14.12
% 99.34/14.12 (fact_Lin__irrefl)
% 99.34/14.12 $i(c_Arrow__Order__Mirabelle_OLin) & $i(tc_HOL_Obool) &
% 99.34/14.12 $i(tc_Arrow__Order__Mirabelle_Oalt) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i]
% 99.34/14.12 : ? [v3: $i] : ? [v4: $i] :
% 99.34/14.12 (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 99.34/14.12 tc_Arrow__Order__Mirabelle_Oalt) = v4 &
% 99.34/14.12 tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt) =
% 99.34/14.12 v0 & tc_fun(v0, tc_HOL_Obool) = v1 & c_member(v1) = v2 & c_member(v0) = v3 &
% 99.34/14.12 $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & ! [v5: $i] : ! [v6: $i] : !
% 99.34/14.12 [v7: $i] : ! [v8: $i] : ! [v9: $i] : ! [v10: $i] : ! [v11: $i] : ( ~
% 99.34/14.12 (hAPP(v10, v7) = v11) | ~ (hAPP(v8, v6) = v9) | ~ (hAPP(v4, v5) = v8) |
% 99.34/14.12 ~ (hAPP(v3, v9) = v10) | ~ $i(v7) | ~ $i(v6) | ~ $i(v5) | ? [v12: $i]
% 99.34/14.12 : ? [v13: $i] : ? [v14: any] : ? [v15: $i] : ? [v16: $i] : ? [v17:
% 99.34/14.12 $i] : ? [v18: $i] : ? [v19: any] : ? [v20: any] : (hBOOL(v18) = v19 &
% 99.34/14.12 hBOOL(v13) = v14 & hBOOL(v11) = v20 & hAPP(v17, v7) = v18 & hAPP(v15,
% 99.34/14.12 v5) = v16 & hAPP(v12, c_Arrow__Order__Mirabelle_OLin) = v13 & hAPP(v4,
% 99.34/14.12 v6) = v15 & hAPP(v3, v16) = v17 & hAPP(v2, v7) = v12 & $i(v18) &
% 99.34/14.12 $i(v17) & $i(v16) & $i(v15) & $i(v13) & $i(v12) & ( ~ (v20 = 0) | ~
% 99.34/14.12 (v19 = 0) | ~ (v14 = 0)))))
% 99.34/14.12
% 99.34/14.12 (fact_Pi__I)
% 99.34/14.12 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 99.34/14.12 $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : ( ~
% 99.34/14.12 (c_FuncSet_OPi(v4, v2, v3, v0) = v8) | ~ (tc_fun(v4, v2) = v5) | ~
% 99.34/14.12 (c_member(v5) = v6) | ~ (hAPP(v7, v8) = v9) | ~ (hAPP(v6, v1) = v7) | ~
% 99.34/14.12 $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v10: $i] : ?
% 99.34/14.12 [v11: $i] : ? [v12: any] : (c_member(v4) = v10 & c_member(v2) = v11 &
% 99.34/14.12 hBOOL(v9) = v12 & $i(v11) & $i(v10) & (v12 = 0 | ? [v13: $i] : ? [v14:
% 99.34/14.12 $i] : ? [v15: $i] : ? [v16: $i] : ? [v17: $i] : ? [v18: $i] : ?
% 99.34/14.12 [v19: $i] : ? [v20: int] : ( ~ (v20 = 0) & hBOOL(v19) = v20 &
% 99.34/14.12 hBOOL(v15) = 0 & hAPP(v17, v18) = v19 & hAPP(v14, v3) = v15 &
% 99.34/14.12 hAPP(v11, v16) = v17 & hAPP(v10, v13) = v14 & hAPP(v1, v13) = v16 &
% 99.34/14.12 hAPP(v0, v13) = v18 & $i(v19) & $i(v18) & $i(v17) & $i(v16) & $i(v15)
% 99.34/14.12 & $i(v14) & $i(v13)))))
% 99.34/14.12
% 99.34/14.12 (fact_Pi__I_H)
% 99.34/14.13 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 99.34/14.13 $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : ( ~
% 99.34/14.13 (c_FuncSet_OPi(v4, v2, v3, v0) = v8) | ~ (tc_fun(v4, v2) = v5) | ~
% 99.34/14.13 (c_member(v5) = v6) | ~ (hAPP(v7, v8) = v9) | ~ (hAPP(v6, v1) = v7) | ~
% 99.34/14.13 $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v10: $i] : ?
% 99.34/14.13 [v11: $i] : ? [v12: any] : (c_member(v4) = v10 & c_member(v2) = v11 &
% 99.34/14.13 hBOOL(v9) = v12 & $i(v11) & $i(v10) & (v12 = 0 | ? [v13: $i] : ? [v14:
% 99.34/14.13 $i] : ? [v15: $i] : ? [v16: $i] : ? [v17: $i] : ? [v18: $i] : ?
% 99.34/14.13 [v19: $i] : ? [v20: int] : ( ~ (v20 = 0) & hBOOL(v19) = v20 &
% 99.34/14.13 hBOOL(v15) = 0 & hAPP(v17, v18) = v19 & hAPP(v14, v3) = v15 &
% 99.34/14.13 hAPP(v11, v16) = v17 & hAPP(v10, v13) = v14 & hAPP(v1, v13) = v16 &
% 99.34/14.13 hAPP(v0, v13) = v18 & $i(v19) & $i(v18) & $i(v17) & $i(v16) & $i(v15)
% 99.34/14.13 & $i(v14) & $i(v13)))))
% 99.34/14.13
% 99.34/14.13 (fact_Pi__cong)
% 99.34/14.13 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 99.34/14.13 $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : ! [v10: $i] :
% 99.34/14.13 ! [v11: $i] : ! [v12: $i] : ( ~ (c_FuncSet_OPi(v5, v1, v4, v0) = v9) | ~
% 99.34/14.13 (tc_fun(v5, v1) = v6) | ~ (c_member(v6) = v7) | ~ (hAPP(v11, v9) = v12) |
% 99.34/14.13 ~ (hAPP(v8, v9) = v10) | ~ (hAPP(v7, v3) = v8) | ~ (hAPP(v7, v2) = v11) |
% 99.34/14.13 ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ?
% 99.34/14.13 [v13: $i] : ? [v14: any] : ? [v15: any] : (c_member(v5) = v13 & hBOOL(v12)
% 99.34/14.13 = v15 & hBOOL(v10) = v14 & $i(v13) & ( ? [v16: $i] : ? [v17: $i] : ?
% 99.34/14.13 [v18: $i] : ? [v19: $i] : ? [v20: $i] : ( ~ (v20 = v19) & hBOOL(v18) =
% 99.34/14.13 0 & hAPP(v17, v4) = v18 & hAPP(v13, v16) = v17 & hAPP(v3, v16) = v19 &
% 99.34/14.13 hAPP(v2, v16) = v20 & $i(v20) & $i(v19) & $i(v18) & $i(v17) & $i(v16))
% 99.34/14.13 | (( ~ (v15 = 0) | v14 = 0) & ( ~ (v14 = 0) | v15 = 0)))))
% 99.34/14.13
% 99.34/14.13 (fact_Pi__eq__empty)
% 99.34/14.13 $i(tc_HOL_Obool) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : !
% 99.34/14.13 [v4: $i] : ( ~ (c_FuncSet_OPi(v3, v2, v1, v0) = v4) | ~ $i(v3) | ~ $i(v2) |
% 99.34/14.13 ~ $i(v1) | ~ $i(v0) | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i]
% 99.34/14.14 : ? [v9: $i] : ? [v10: $i] : (c_Orderings_Obot__class_Obot(v9) = v10 &
% 99.34/14.14 c_Orderings_Obot__class_Obot(v6) = v7 & tc_fun(v8, tc_HOL_Obool) = v9 &
% 99.34/14.14 tc_fun(v3, v2) = v8 & tc_fun(v2, tc_HOL_Obool) = v6 & c_member(v3) = v5 &
% 99.34/14.14 $i(v10) & $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5) & (v10 = v4 | !
% 99.34/14.14 [v11: $i] : ! [v12: $i] : ! [v13: $i] : ( ~ (hAPP(v12, v1) = v13) | ~
% 99.34/14.14 (hAPP(v5, v11) = v12) | ~ $i(v11) | ? [v14: any] : ? [v15: $i] :
% 99.34/14.14 (hBOOL(v13) = v14 & hAPP(v0, v11) = v15 & $i(v15) & ( ~ (v15 = v7) |
% 99.34/14.14 ~ (v14 = 0))))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 99.34/14.14 [v3: $i] : ! [v4: $i] : ( ~ (c_FuncSet_OPi(v3, v2, v1, v0) = v4) | ~ $i(v3)
% 99.34/14.14 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: $i] : ? [v6: $i] : ? [v7:
% 99.34/14.14 $i] : ? [v8: $i] : ? [v9: $i] : ? [v10: $i] :
% 99.34/14.14 (c_Orderings_Obot__class_Obot(v9) = v10 & c_Orderings_Obot__class_Obot(v6) =
% 99.34/14.14 v7 & tc_fun(v5, tc_HOL_Obool) = v6 & tc_fun(v3, v2) = v5 & tc_fun(v2,
% 99.34/14.14 tc_HOL_Obool) = v9 & c_member(v3) = v8 & $i(v10) & $i(v9) & $i(v8) &
% 99.34/14.14 $i(v7) & $i(v6) & $i(v5) & ( ~ (v7 = v4) | ? [v11: $i] : ? [v12: $i] :
% 99.34/14.14 ? [v13: $i] : (hBOOL(v13) = 0 & hAPP(v12, v1) = v13 & hAPP(v8, v11) =
% 99.34/14.14 v12 & hAPP(v0, v11) = v10 & $i(v13) & $i(v12) & $i(v11)))))
% 99.34/14.14
% 99.34/14.14 (fact_Prof__def)
% 99.34/14.14 $i(c_Arrow__Order__Mirabelle_OProf) & $i(tc_Arrow__Order__Mirabelle_Oindi) &
% 99.34/14.14 $i(c_Arrow__Order__Mirabelle_OLin) & $i(tc_HOL_Obool) &
% 99.34/14.14 $i(tc_Arrow__Order__Mirabelle_Oalt) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i]
% 99.34/14.14 : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : (c_COMBK(v4,
% 99.34/14.14 tc_Arrow__Order__Mirabelle_Oindi, c_Arrow__Order__Mirabelle_OLin) = v5 &
% 99.34/14.14 c_FuncSet_OPi(tc_Arrow__Order__Mirabelle_Oindi, v1, v3, v5) =
% 99.34/14.14 c_Arrow__Order__Mirabelle_OProf & c_Orderings_Otop__class_Otop(v2) = v3 &
% 99.34/14.14 tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt) =
% 99.34/14.14 v0 & tc_fun(v1, tc_HOL_Obool) = v4 & tc_fun(v0, tc_HOL_Obool) = v1 &
% 99.34/14.14 tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_HOL_Obool) = v2 & $i(v5) &
% 99.34/14.14 $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 99.34/14.14
% 99.34/14.14 (fact_above__Lin)
% 99.34/14.14 $i(c_Arrow__Order__Mirabelle_OLin) & $i(tc_HOL_Obool) &
% 99.34/14.14 $i(tc_Arrow__Order__Mirabelle_Oalt) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i]
% 99.34/14.14 : (tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt) =
% 99.34/14.14 v0 & tc_fun(v0, tc_HOL_Obool) = v1 & c_member(v1) = v2 & $i(v2) & $i(v1) &
% 99.34/14.14 $i(v0) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v5 = v4 |
% 99.34/14.14 ~ (c_Arrow__Order__Mirabelle_Oabove(v3, v5, v4) = v6) | ~ $i(v5) | ~
% 99.34/14.14 $i(v4) | ~ $i(v3) | ? [v7: $i] : ? [v8: $i] : ? [v9: any] : ? [v10:
% 99.34/14.14 $i] : ? [v11: $i] : ? [v12: any] : (hBOOL(v11) = v12 & hBOOL(v8) = v9
% 99.34/14.14 & hAPP(v10, c_Arrow__Order__Mirabelle_OLin) = v11 & hAPP(v7,
% 99.34/14.14 c_Arrow__Order__Mirabelle_OLin) = v8 & hAPP(v2, v6) = v10 & hAPP(v2,
% 99.34/14.14 v3) = v7 & $i(v11) & $i(v10) & $i(v8) & $i(v7) & ( ~ (v9 = 0) | v12 =
% 99.34/14.14 0))))
% 99.34/14.14
% 99.34/14.14 (fact_below__Lin)
% 99.34/14.14 $i(c_Arrow__Order__Mirabelle_OLin) & $i(tc_HOL_Obool) &
% 99.34/14.14 $i(tc_Arrow__Order__Mirabelle_Oalt) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i]
% 99.34/14.14 : (tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt) =
% 99.34/14.14 v0 & tc_fun(v0, tc_HOL_Obool) = v1 & c_member(v1) = v2 & $i(v2) & $i(v1) &
% 99.34/14.14 $i(v0) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v5 = v4 |
% 99.34/14.14 ~ (c_Arrow__Order__Mirabelle_Obelow(v3, v5, v4) = v6) | ~ $i(v5) | ~
% 99.34/14.14 $i(v4) | ~ $i(v3) | ? [v7: $i] : ? [v8: $i] : ? [v9: any] : ? [v10:
% 99.34/14.14 $i] : ? [v11: $i] : ? [v12: any] : (hBOOL(v11) = v12 & hBOOL(v8) = v9
% 99.34/14.14 & hAPP(v10, c_Arrow__Order__Mirabelle_OLin) = v11 & hAPP(v7,
% 99.34/14.14 c_Arrow__Order__Mirabelle_OLin) = v8 & hAPP(v2, v6) = v10 & hAPP(v2,
% 99.34/14.14 v3) = v7 & $i(v11) & $i(v10) & $i(v8) & $i(v7) & ( ~ (v9 = 0) | v12 =
% 99.34/14.14 0))))
% 99.34/14.14
% 99.34/14.14 (fact_compose__Id)
% 99.34/14.14 $i(tc_HOL_Obool) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : !
% 99.34/14.14 [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i]
% 99.34/14.14 : ! [v10: $i] : ! [v11: $i] : ( ~ (c_COMBK(v8, v4, v0) = v9) | ~
% 99.34/14.14 (c_FuncSet_OPi(v4, v3, v1, v9) = v10) | ~ (tc_fun(v4, v3) = v5) | ~
% 99.34/14.14 (tc_fun(v3, tc_HOL_Obool) = v8) | ~ (c_member(v5) = v6) | ~ (hAPP(v7, v10)
% 99.34/14.14 = v11) | ~ (hAPP(v6, v2) = v7) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~
% 99.34/14.14 $i(v1) | ~ $i(v0) | ? [v12: any] : ? [v13: $i] : ? [v14: $i] : ? [v15:
% 99.34/14.14 any] : ? [v16: $i] : ? [v17: $i] : ? [v18: $i] :
% 99.34/14.14 (c_FuncSet_Orestrict(v4, v4, v16, v1) = v17 & c_FuncSet_Oextensional(v4, v3,
% 99.34/14.14 v1) = v13 & c_FuncSet_Ocompose(v4, v4, v3, v1, v2, v17) = v18 &
% 99.34/14.14 c_COMBI(v4) = v16 & hBOOL(v14) = v15 & hBOOL(v11) = v12 & hAPP(v7, v13) =
% 99.34/14.14 v14 & $i(v18) & $i(v17) & $i(v16) & $i(v14) & $i(v13) & ( ~ (v15 = 0) | ~
% 99.34/14.14 (v12 = 0) | v18 = v2)))
% 99.34/14.14
% 99.34/14.14 (fact_converse__in__Lin)
% 99.34/14.15 $i(c_Arrow__Order__Mirabelle_OLin) & $i(tc_HOL_Obool) &
% 99.34/14.15 $i(tc_Arrow__Order__Mirabelle_Oalt) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i]
% 99.34/14.15 : ? [v3: $i] : (c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt,
% 99.34/14.15 tc_Arrow__Order__Mirabelle_Oalt) = v3 &
% 99.34/14.15 tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt) =
% 99.34/14.15 v0 & tc_fun(v0, tc_HOL_Obool) = v1 & c_member(v1) = v2 & $i(v3) & $i(v2) &
% 99.34/14.15 $i(v1) & $i(v0) & ! [v4: $i] : ! [v5: $i] : ( ~ (hAPP(v2, v4) = v5) | ~
% 99.34/14.15 $i(v4) | ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: any] : ? [v10:
% 99.34/14.15 $i] : ? [v11: any] : (hBOOL(v10) = v11 & hBOOL(v8) = v9 & hAPP(v7,
% 99.34/14.15 c_Arrow__Order__Mirabelle_OLin) = v8 & hAPP(v5,
% 99.34/14.15 c_Arrow__Order__Mirabelle_OLin) = v10 & hAPP(v3, v4) = v6 & hAPP(v2,
% 99.34/14.15 v6) = v7 & $i(v10) & $i(v8) & $i(v7) & $i(v6) & ( ~ (v9 = 0) | v11 =
% 99.34/14.15 0))) & ! [v4: $i] : ! [v5: $i] : ( ~ (hAPP(v2, v4) = v5) | ~ $i(v4)
% 99.34/14.15 | ? [v6: $i] : ? [v7: any] : ? [v8: $i] : ? [v9: $i] : ? [v10: $i] :
% 99.34/14.15 ? [v11: any] : (hBOOL(v10) = v11 & hBOOL(v6) = v7 & hAPP(v9,
% 99.34/14.15 c_Arrow__Order__Mirabelle_OLin) = v10 & hAPP(v5,
% 99.34/14.15 c_Arrow__Order__Mirabelle_OLin) = v6 & hAPP(v3, v4) = v8 & hAPP(v2,
% 99.34/14.15 v8) = v9 & $i(v10) & $i(v9) & $i(v8) & $i(v6) & ( ~ (v7 = 0) | v11 =
% 99.34/14.15 0))))
% 99.34/14.15
% 99.34/14.15 (fact_dictatorI)
% 99.34/14.15 $i(c_Arrow__Order__Mirabelle_OProf) & $i(tc_Arrow__Order__Mirabelle_Oindi) &
% 99.34/14.15 $i(c_Arrow__Order__Mirabelle_OLin) & $i(tc_HOL_Obool) &
% 99.34/14.15 $i(tc_Arrow__Order__Mirabelle_Oalt) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i]
% 99.34/14.15 : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ?
% 99.34/14.15 [v8: $i] : ? [v9: $i] : ? [v10: $i] : (c_COMBK(v5, v2,
% 99.34/14.15 c_Arrow__Order__Mirabelle_OLin) = v6 & c_FuncSet_OPi(v2, v1,
% 99.34/14.15 c_Arrow__Order__Mirabelle_OProf, v6) = v7 &
% 99.34/14.15 c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 99.34/14.15 tc_Arrow__Order__Mirabelle_Oalt) = v10 &
% 99.34/14.15 tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt) =
% 99.34/14.15 v0 & tc_fun(v2, v1) = v3 & tc_fun(v1, tc_HOL_Obool) = v5 & tc_fun(v0,
% 99.34/14.15 tc_HOL_Obool) = v1 & tc_fun(tc_Arrow__Order__Mirabelle_Oindi, v1) = v2 &
% 99.34/14.15 c_member(v3) = v4 & c_member(v2) = v8 & c_member(v0) = v9 & $i(v10) & $i(v9)
% 99.34/14.15 & $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) &
% 99.34/14.15 $i(v0) & ! [v11: $i] : ! [v12: $i] : ! [v13: int] : (v13 = 0 | ~
% 99.34/14.15 (c_Arrow__Order__Mirabelle_Odictator(v12, v11) = v13) | ~ $i(v12) | ~
% 99.34/14.15 $i(v11) | ? [v14: $i] : ? [v15: $i] : ? [v16: $i] : ? [v17: $i] : ?
% 99.34/14.15 [v18: $i] : (hBOOL(v16) = 0 & hAPP(v15, c_Arrow__Order__Mirabelle_OProf) =
% 99.34/14.15 v16 & hAPP(v14, v11) = v17 & hAPP(v12, v14) = v18 & hAPP(v8, v14) = v15
% 99.34/14.15 & $i(v18) & $i(v17) & $i(v16) & $i(v15) & $i(v14) & ? [v19: $i] : ?
% 99.34/14.15 [v20: $i] : ? [v21: $i] : ? [v22: $i] : ? [v23: $i] : ? [v24: $i] :
% 99.34/14.15 ? [v25: $i] : ? [v26: int] : ( ~ (v26 = 0) & ~ (v20 = v19) &
% 99.34/14.15 hBOOL(v25) = v26 & hBOOL(v24) = 0 & hAPP(v23, v18) = v25 & hAPP(v23,
% 99.34/14.15 v17) = v24 & hAPP(v21, v20) = v22 & hAPP(v10, v19) = v21 & hAPP(v9,
% 99.34/14.15 v22) = v23 & $i(v25) & $i(v24) & $i(v23) & $i(v22) & $i(v21) &
% 99.34/14.15 $i(v20) & $i(v19))) | ? [v14: $i] : ? [v15: $i] : ? [v16: int] : (
% 99.34/14.15 ~ (v16 = 0) & hBOOL(v15) = v16 & hAPP(v14, v7) = v15 & hAPP(v4, v12) =
% 99.34/14.15 v14 & $i(v15) & $i(v14))))
% 99.34/14.15
% 99.34/14.15 (fact_dictator__def)
% 99.57/14.16 $i(c_Arrow__Order__Mirabelle_OProf) & $i(tc_Arrow__Order__Mirabelle_Oindi) &
% 99.57/14.16 $i(tc_HOL_Obool) & $i(tc_Arrow__Order__Mirabelle_Oalt) & ? [v0: $i] : ? [v1:
% 99.57/14.16 $i] : ? [v2: $i] : ? [v3: $i] : (tc_prod(tc_Arrow__Order__Mirabelle_Oalt,
% 99.57/14.16 tc_Arrow__Order__Mirabelle_Oalt) = v0 & tc_fun(v0, tc_HOL_Obool) = v1 &
% 99.57/14.16 tc_fun(tc_Arrow__Order__Mirabelle_Oindi, v1) = v2 & c_member(v2) = v3 &
% 99.57/14.16 $i(v3) & $i(v2) & $i(v1) & $i(v0) & ! [v4: $i] : ! [v5: $i] : ! [v6: int]
% 99.57/14.16 : (v6 = 0 | ~ (c_Arrow__Order__Mirabelle_Odictator(v5, v4) = v6) | ~
% 99.57/14.16 $i(v5) | ~ $i(v4) | ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ? [v10:
% 99.57/14.16 $i] : ? [v11: $i] : ( ~ (v11 = v10) & hBOOL(v9) = 0 & hAPP(v8,
% 99.57/14.16 c_Arrow__Order__Mirabelle_OProf) = v9 & hAPP(v7, v4) = v11 & hAPP(v5,
% 99.57/14.16 v7) = v10 & hAPP(v3, v7) = v8 & $i(v11) & $i(v10) & $i(v9) & $i(v8) &
% 99.57/14.16 $i(v7))) & ! [v4: $i] : ! [v5: $i] : ( ~
% 99.57/14.16 (c_Arrow__Order__Mirabelle_Odictator(v5, v4) = 0) | ~ $i(v5) | ~ $i(v4)
% 99.57/14.16 | ! [v6: $i] : ! [v7: $i] : ( ~ (hAPP(v3, v6) = v7) | ~ $i(v6) | ?
% 99.57/14.16 [v8: $i] : ? [v9: any] : ? [v10: $i] : ? [v11: $i] : (hBOOL(v8) = v9
% 99.57/14.16 & hAPP(v7, c_Arrow__Order__Mirabelle_OProf) = v8 & hAPP(v6, v4) = v11
% 99.57/14.16 & hAPP(v5, v6) = v10 & $i(v11) & $i(v10) & $i(v8) & ( ~ (v9 = 0) | v11
% 99.57/14.16 = v10)))))
% 99.57/14.16
% 99.57/14.16 (fact_equals0D)
% 99.57/14.16 $i(tc_HOL_Obool) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : !
% 99.57/14.16 [v4: $i] : ! [v5: $i] : ( ~ (c_member(v1) = v3) | ~ (hAPP(v4, v2) = v5) | ~
% 99.57/14.16 (hAPP(v3, v0) = v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: $i] : ?
% 99.57/14.16 [v7: $i] : ? [v8: any] : (c_Orderings_Obot__class_Obot(v6) = v7 &
% 99.57/14.16 tc_fun(v1, tc_HOL_Obool) = v6 & hBOOL(v5) = v8 & $i(v7) & $i(v6) & ( ~ (v8
% 99.57/14.16 = 0) | ~ (v7 = v2))))
% 99.57/14.16
% 99.57/14.16 (fact_funcsetI)
% 99.57/14.16 $i(tc_HOL_Obool) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : !
% 99.57/14.16 [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i]
% 99.57/14.16 : ! [v10: $i] : ! [v11: $i] : ( ~ (c_COMBK(v8, v4, v0) = v9) | ~
% 99.57/14.16 (c_FuncSet_OPi(v4, v2, v3, v9) = v10) | ~ (tc_fun(v4, v2) = v5) | ~
% 99.57/14.16 (tc_fun(v2, tc_HOL_Obool) = v8) | ~ (c_member(v5) = v6) | ~ (hAPP(v7, v10)
% 99.57/14.16 = v11) | ~ (hAPP(v6, v1) = v7) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~
% 99.57/14.16 $i(v1) | ~ $i(v0) | ? [v12: $i] : ? [v13: $i] : ? [v14: any] :
% 99.57/14.16 (c_member(v4) = v12 & c_member(v2) = v13 & hBOOL(v11) = v14 & $i(v13) &
% 99.57/14.16 $i(v12) & (v14 = 0 | ? [v15: $i] : ? [v16: $i] : ? [v17: $i] : ? [v18:
% 99.57/14.16 $i] : ? [v19: $i] : ? [v20: $i] : ? [v21: int] : ( ~ (v21 = 0) &
% 99.57/14.16 hBOOL(v20) = v21 & hBOOL(v17) = 0 & hAPP(v19, v0) = v20 & hAPP(v16,
% 99.57/14.16 v3) = v17 & hAPP(v13, v18) = v19 & hAPP(v12, v15) = v16 & hAPP(v1,
% 99.57/14.16 v15) = v18 & $i(v20) & $i(v19) & $i(v18) & $i(v17) & $i(v16) &
% 99.57/14.16 $i(v15)))))
% 99.57/14.16
% 99.57/14.16 (fact_in__above)
% 99.57/14.17 $i(c_Arrow__Order__Mirabelle_OLin) & $i(tc_HOL_Obool) &
% 99.57/14.17 $i(tc_Arrow__Order__Mirabelle_Oalt) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i]
% 99.57/14.17 : ? [v3: $i] : ? [v4: $i] :
% 99.57/14.17 (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 99.57/14.17 tc_Arrow__Order__Mirabelle_Oalt) = v4 &
% 99.57/14.17 tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt) =
% 99.57/14.17 v0 & tc_fun(v0, tc_HOL_Obool) = v1 & c_member(v1) = v2 & c_member(v0) = v3 &
% 99.57/14.17 $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & ! [v5: $i] : ! [v6: $i] : !
% 99.57/14.17 [v7: $i] : ! [v8: $i] : ! [v9: $i] : ! [v10: $i] : ! [v11: $i] : !
% 99.57/14.17 [v12: $i] : ! [v13: $i] : ! [v14: $i] : (v9 = v8 | ~
% 99.57/14.17 (c_Arrow__Order__Mirabelle_Oabove(v7, v9, v8) = v13) | ~ (hAPP(v12, v13)
% 99.57/14.17 = v14) | ~ (hAPP(v10, v5) = v11) | ~ (hAPP(v4, v6) = v10) | ~
% 99.57/14.17 (hAPP(v3, v11) = v12) | ~ $i(v9) | ~ $i(v8) | ~ $i(v7) | ~ $i(v6) | ~
% 99.57/14.17 $i(v5) | ? [v15: $i] : ? [v16: $i] : ? [v17: any] : ? [v18: any] : ?
% 99.57/14.17 [v19: $i] : ? [v20: $i] : ? [v21: $i] : ? [v22: $i] : ? [v23: any] :
% 99.57/14.17 ? [v24: $i] : ? [v25: $i] : ? [v26: $i] : ? [v27: any] : ? [v28: $i] :
% 99.57/14.17 ? [v29: any] : (hBOOL(v28) = v29 & hBOOL(v26) = v27 & hBOOL(v22) = v23 &
% 99.57/14.17 hBOOL(v16) = v17 & hBOOL(v14) = v18 & hAPP(v25, v7) = v26 & hAPP(v21,
% 99.57/14.17 v7) = v22 & hAPP(v19, v5) = v20 & hAPP(v15,
% 99.57/14.17 c_Arrow__Order__Mirabelle_OLin) = v16 & hAPP(v12, v7) = v28 &
% 99.57/14.17 hAPP(v10, v9) = v24 & hAPP(v4, v9) = v19 & hAPP(v3, v24) = v25 &
% 99.57/14.17 hAPP(v3, v20) = v21 & hAPP(v2, v7) = v15 & $i(v28) & $i(v26) & $i(v25) &
% 99.57/14.17 $i(v24) & $i(v22) & $i(v21) & $i(v20) & $i(v19) & $i(v16) & $i(v15) & (
% 99.57/14.17 ~ (v17 = 0) | (( ~ (v18 = 0) | ( ~ (v6 = v5) & ( ~ (v8 = v6) | v23 =
% 99.57/14.17 0) & (v8 = v6 | (( ~ (v8 = v5) | v27 = 0 | v9 = v6) & (v29 = 0
% 99.57/14.17 | v8 = v5))))) & (v18 = 0 | v6 = v5 | (v8 = v6 & ~ (v23 =
% 99.57/14.17 0)) | ( ~ (v8 = v6) & ((v8 = v5 & ~ (v27 = 0) & ~ (v9 = v6))
% 99.57/14.17 | ( ~ (v29 = 0) & ~ (v8 = v5))))))))))
% 99.57/14.17
% 99.57/14.17 (fact_in__below)
% 99.57/14.17 $i(c_Arrow__Order__Mirabelle_OLin) & $i(tc_HOL_Obool) &
% 99.57/14.17 $i(tc_Arrow__Order__Mirabelle_Oalt) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i]
% 99.57/14.17 : ? [v3: $i] : ? [v4: $i] :
% 99.57/14.17 (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 99.57/14.17 tc_Arrow__Order__Mirabelle_Oalt) = v4 &
% 99.57/14.17 tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt) =
% 99.57/14.17 v0 & tc_fun(v0, tc_HOL_Obool) = v1 & c_member(v1) = v2 & c_member(v0) = v3 &
% 99.57/14.17 $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & ! [v5: $i] : ! [v6: $i] : !
% 99.57/14.17 [v7: $i] : ! [v8: $i] : ! [v9: $i] : ! [v10: $i] : ! [v11: $i] : !
% 99.57/14.17 [v12: $i] : ! [v13: $i] : ! [v14: $i] : (v9 = v8 | ~
% 99.57/14.17 (c_Arrow__Order__Mirabelle_Obelow(v7, v9, v8) = v13) | ~ (hAPP(v12, v13)
% 99.57/14.17 = v14) | ~ (hAPP(v10, v5) = v11) | ~ (hAPP(v4, v6) = v10) | ~
% 99.57/14.17 (hAPP(v3, v11) = v12) | ~ $i(v9) | ~ $i(v8) | ~ $i(v7) | ~ $i(v6) | ~
% 99.57/14.17 $i(v5) | ? [v15: $i] : ? [v16: $i] : ? [v17: any] : ? [v18: any] : ?
% 99.57/14.17 [v19: $i] : ? [v20: $i] : ? [v21: $i] : ? [v22: any] : ? [v23: $i] :
% 99.57/14.17 ? [v24: $i] : ? [v25: $i] : ? [v26: $i] : ? [v27: any] : ? [v28: $i] :
% 99.57/14.17 ? [v29: any] : (hBOOL(v28) = v29 & hBOOL(v26) = v27 & hBOOL(v21) = v22 &
% 99.57/14.17 hBOOL(v16) = v17 & hBOOL(v14) = v18 & hAPP(v25, v7) = v26 & hAPP(v23,
% 99.57/14.17 v5) = v24 & hAPP(v20, v7) = v21 & hAPP(v15,
% 99.57/14.17 c_Arrow__Order__Mirabelle_OLin) = v16 & hAPP(v12, v7) = v28 &
% 99.57/14.17 hAPP(v10, v8) = v19 & hAPP(v4, v8) = v23 & hAPP(v3, v24) = v25 &
% 99.57/14.17 hAPP(v3, v19) = v20 & hAPP(v2, v7) = v15 & $i(v28) & $i(v26) & $i(v25) &
% 99.57/14.17 $i(v24) & $i(v23) & $i(v21) & $i(v20) & $i(v19) & $i(v16) & $i(v15) & (
% 99.57/14.17 ~ (v17 = 0) | (( ~ (v18 = 0) | ( ~ (v6 = v5) & ( ~ (v9 = v5) | v22 =
% 99.57/14.17 0) & (v9 = v5 | (( ~ (v9 = v6) | v27 = 0 | v8 = v5) & (v29 = 0
% 99.57/14.17 | v9 = v6))))) & (v18 = 0 | v6 = v5 | (v9 = v5 & ~ (v22 =
% 99.57/14.17 0)) | ( ~ (v9 = v5) & ((v9 = v6 & ~ (v27 = 0) & ~ (v8 = v5))
% 99.57/14.17 | ( ~ (v29 = 0) & ~ (v9 = v6))))))))))
% 99.57/14.17
% 99.57/14.17 (fact_in__mkbot)
% 99.57/14.18 $i(tc_Arrow__Order__Mirabelle_Oalt) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i]
% 99.57/14.18 : (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 99.57/14.18 tc_Arrow__Order__Mirabelle_Oalt) = v2 &
% 99.57/14.18 tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt) =
% 99.57/14.18 v0 & c_member(v0) = v1 & $i(v2) & $i(v1) & $i(v0) & ! [v3: $i] : ! [v4:
% 99.57/14.18 $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i]
% 99.57/14.18 : ! [v10: $i] : ! [v11: $i] : (v5 = v3 | ~
% 99.57/14.18 (c_Arrow__Order__Mirabelle_Omkbot(v4, v3) = v10) | ~ (hAPP(v9, v10) =
% 99.57/14.18 v11) | ~ (hAPP(v7, v5) = v8) | ~ (hAPP(v2, v6) = v7) | ~ (hAPP(v1,
% 99.57/14.18 v8) = v9) | ~ $i(v6) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ? [v12:
% 99.57/14.18 $i] : ? [v13: any] : ? [v14: any] : (hBOOL(v12) = v13 & hBOOL(v11) =
% 99.57/14.18 v14 & hAPP(v9, v4) = v12 & $i(v12) & (v14 = 0 | ( ~ (v13 = 0) & ~ (v6 =
% 99.57/14.18 v3))))) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] :
% 99.57/14.18 ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : ! [v10: $i] : ! [v11: $i] : ( ~
% 99.57/14.18 (c_Arrow__Order__Mirabelle_Omkbot(v4, v3) = v10) | ~ (hAPP(v9, v10) =
% 99.57/14.18 v11) | ~ (hAPP(v7, v5) = v8) | ~ (hAPP(v2, v6) = v7) | ~ (hAPP(v1,
% 99.57/14.18 v8) = v9) | ~ $i(v6) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ? [v12:
% 99.57/14.18 any] : ? [v13: $i] : ? [v14: any] : (hBOOL(v13) = v14 & hBOOL(v11) =
% 99.57/14.18 v12 & hAPP(v9, v4) = v13 & $i(v13) & ( ~ (v12 = 0) | ( ~ (v5 = v3) &
% 99.57/14.18 (v14 = 0 | v6 = v3))))))
% 99.57/14.18
% 99.57/14.18 (fact_in__mktop)
% 99.57/14.18 $i(tc_Arrow__Order__Mirabelle_Oalt) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i]
% 99.57/14.18 : (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 99.57/14.18 tc_Arrow__Order__Mirabelle_Oalt) = v2 &
% 99.57/14.18 tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt) =
% 99.57/14.18 v0 & c_member(v0) = v1 & $i(v2) & $i(v1) & $i(v0) & ! [v3: $i] : ! [v4:
% 99.57/14.18 $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i]
% 99.57/14.18 : ! [v10: $i] : ! [v11: $i] : (v6 = v3 | ~
% 99.57/14.18 (c_Arrow__Order__Mirabelle_Omktop(v4, v3) = v10) | ~ (hAPP(v9, v10) =
% 99.57/14.18 v11) | ~ (hAPP(v7, v5) = v8) | ~ (hAPP(v2, v6) = v7) | ~ (hAPP(v1,
% 99.57/14.18 v8) = v9) | ~ $i(v6) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ? [v12:
% 99.57/14.18 $i] : ? [v13: any] : ? [v14: any] : (hBOOL(v12) = v13 & hBOOL(v11) =
% 99.57/14.18 v14 & hAPP(v9, v4) = v12 & $i(v12) & (v14 = 0 | ( ~ (v13 = 0) & ~ (v5 =
% 99.57/14.18 v3))))) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] :
% 99.57/14.18 ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : ! [v10: $i] : ! [v11: $i] : ( ~
% 99.57/14.18 (c_Arrow__Order__Mirabelle_Omktop(v4, v3) = v10) | ~ (hAPP(v9, v10) =
% 99.57/14.18 v11) | ~ (hAPP(v7, v5) = v8) | ~ (hAPP(v2, v6) = v7) | ~ (hAPP(v1,
% 99.57/14.18 v8) = v9) | ~ $i(v6) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ? [v12:
% 99.57/14.18 any] : ? [v13: $i] : ? [v14: any] : (hBOOL(v13) = v14 & hBOOL(v11) =
% 99.57/14.18 v12 & hAPP(v9, v4) = v13 & $i(v13) & ( ~ (v12 = 0) | ( ~ (v6 = v3) &
% 99.57/14.18 (v14 = 0 | v5 = v3))))))
% 99.57/14.18
% 99.57/14.18 (fact_linear__alt)
% 99.57/14.18 $i(c_Arrow__Order__Mirabelle_OLin) & $i(tc_HOL_Obool) &
% 99.57/14.18 $i(tc_Arrow__Order__Mirabelle_Oalt) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i]
% 99.57/14.18 : (tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt) =
% 99.57/14.18 v0 & tc_fun(v0, tc_HOL_Obool) = v1 & c_member(v1) = v2 & $i(v2) & $i(v1) &
% 99.57/14.18 $i(v0) & ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : (hBOOL(v5) = 0 & hAPP(v4,
% 99.57/14.18 c_Arrow__Order__Mirabelle_OLin) = v5 & hAPP(v2, v3) = v4 & $i(v5) &
% 99.57/14.18 $i(v4) & $i(v3)))
% 99.57/14.18
% 99.57/14.18 (fact_mem__def)
% 99.57/14.18 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 99.57/14.18 $i] : ( ~ (c_member(v2) = v3) | ~ (hAPP(v4, v0) = v5) | ~ (hAPP(v3, v1) =
% 99.57/14.18 v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: $i] : ?
% 99.57/14.18 [v8: any] : (hBOOL(v7) = v8 & hBOOL(v5) = v6 & hAPP(v0, v1) = v7 & $i(v7) &
% 99.57/14.18 ( ~ (v6 = 0) | v8 = 0))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 99.57/14.18 [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (c_member(v2) = v3) | ~ (hAPP(v4,
% 99.57/14.18 v0) = v5) | ~ (hAPP(v3, v1) = v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 99.57/14.18 ? [v6: $i] : ? [v7: any] : ? [v8: any] : (hBOOL(v6) = v7 & hBOOL(v5) = v8
% 99.57/14.18 & hAPP(v0, v1) = v6 & $i(v6) & ( ~ (v7 = 0) | v8 = 0)))
% 99.57/14.18
% 99.57/14.19 (fact_mkbot__Lin)
% 99.57/14.19 $i(c_Arrow__Order__Mirabelle_OLin) & $i(tc_HOL_Obool) &
% 99.57/14.19 $i(tc_Arrow__Order__Mirabelle_Oalt) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i]
% 99.57/14.19 : (tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt) =
% 99.57/14.19 v0 & tc_fun(v0, tc_HOL_Obool) = v1 & c_member(v1) = v2 & $i(v2) & $i(v1) &
% 99.57/14.19 $i(v0) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~
% 99.57/14.19 (c_Arrow__Order__Mirabelle_Omkbot(v4, v3) = v5) | ~ $i(v4) | ~ $i(v3) |
% 99.57/14.19 ? [v6: $i] : ? [v7: $i] : ? [v8: any] : ? [v9: $i] : ? [v10: $i] : ?
% 99.57/14.19 [v11: any] : (hBOOL(v10) = v11 & hBOOL(v7) = v8 & hAPP(v9,
% 99.57/14.19 c_Arrow__Order__Mirabelle_OLin) = v10 & hAPP(v6,
% 99.57/14.19 c_Arrow__Order__Mirabelle_OLin) = v7 & hAPP(v2, v5) = v9 & hAPP(v2,
% 99.57/14.19 v4) = v6 & $i(v10) & $i(v9) & $i(v7) & $i(v6) & ( ~ (v8 = 0) | v11 =
% 99.57/14.19 0))))
% 99.57/14.19
% 99.57/14.19 (fact_mktop__Lin)
% 99.57/14.19 $i(c_Arrow__Order__Mirabelle_OLin) & $i(tc_HOL_Obool) &
% 99.57/14.19 $i(tc_Arrow__Order__Mirabelle_Oalt) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i]
% 99.57/14.19 : (tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt) =
% 99.57/14.19 v0 & tc_fun(v0, tc_HOL_Obool) = v1 & c_member(v1) = v2 & $i(v2) & $i(v1) &
% 99.57/14.19 $i(v0) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~
% 99.57/14.19 (c_Arrow__Order__Mirabelle_Omktop(v4, v3) = v5) | ~ $i(v4) | ~ $i(v3) |
% 99.57/14.19 ? [v6: $i] : ? [v7: $i] : ? [v8: any] : ? [v9: $i] : ? [v10: $i] : ?
% 99.57/14.19 [v11: any] : (hBOOL(v10) = v11 & hBOOL(v7) = v8 & hAPP(v9,
% 99.57/14.19 c_Arrow__Order__Mirabelle_OLin) = v10 & hAPP(v6,
% 99.57/14.19 c_Arrow__Order__Mirabelle_OLin) = v7 & hAPP(v2, v5) = v9 & hAPP(v2,
% 99.57/14.19 v4) = v6 & $i(v10) & $i(v9) & $i(v7) & $i(v6) & ( ~ (v8 = 0) | v11 =
% 99.57/14.19 0))))
% 99.57/14.19
% 99.57/14.19 (fact_notin__Lin__iff)
% 99.57/14.19 $i(c_Arrow__Order__Mirabelle_OLin) & $i(tc_HOL_Obool) &
% 99.57/14.19 $i(tc_Arrow__Order__Mirabelle_Oalt) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i]
% 99.57/14.19 : ? [v3: $i] : ? [v4: $i] :
% 99.57/14.19 (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 99.57/14.19 tc_Arrow__Order__Mirabelle_Oalt) = v4 &
% 99.57/14.19 tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt) =
% 99.57/14.19 v0 & tc_fun(v0, tc_HOL_Obool) = v1 & c_member(v1) = v2 & c_member(v0) = v3 &
% 99.57/14.19 $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & ! [v5: $i] : ! [v6: $i] : !
% 99.57/14.19 [v7: $i] : ! [v8: $i] : ! [v9: $i] : ! [v10: $i] : ! [v11: $i] : (v6 =
% 99.57/14.19 v5 | ~ (hAPP(v10, v7) = v11) | ~ (hAPP(v8, v6) = v9) | ~ (hAPP(v4, v5)
% 99.57/14.19 = v8) | ~ (hAPP(v3, v9) = v10) | ~ $i(v7) | ~ $i(v6) | ~ $i(v5) | ?
% 99.57/14.19 [v12: $i] : ? [v13: $i] : ? [v14: any] : ? [v15: $i] : ? [v16: $i] :
% 99.57/14.19 ? [v17: $i] : ? [v18: $i] : ? [v19: any] : ? [v20: any] : (hBOOL(v18) =
% 99.57/14.19 v19 & hBOOL(v13) = v14 & hBOOL(v11) = v20 & hAPP(v17, v7) = v18 &
% 99.57/14.19 hAPP(v15, v5) = v16 & hAPP(v12, c_Arrow__Order__Mirabelle_OLin) = v13 &
% 99.57/14.19 hAPP(v4, v6) = v15 & hAPP(v3, v16) = v17 & hAPP(v2, v7) = v12 & $i(v18)
% 99.57/14.19 & $i(v17) & $i(v16) & $i(v15) & $i(v13) & $i(v12) & ( ~ (v14 = 0) | (( ~
% 99.57/14.19 (v20 = 0) | ~ (v19 = 0)) & (v20 = 0 | v19 = 0))))))
% 99.57/14.19
% 99.57/14.19 (fact_unanimity__def)
% 99.57/14.20 $i(c_Arrow__Order__Mirabelle_OProf) & $i(tc_Arrow__Order__Mirabelle_Oindi) &
% 99.57/14.20 $i(tc_HOL_Obool) & $i(tc_Arrow__Order__Mirabelle_Oalt) & ? [v0: $i] : ? [v1:
% 99.57/14.20 $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] :
% 99.57/14.20 (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 99.57/14.20 tc_Arrow__Order__Mirabelle_Oalt) = v5 &
% 99.57/14.20 tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt) =
% 99.57/14.20 v0 & tc_fun(v0, tc_HOL_Obool) = v1 &
% 99.57/14.20 tc_fun(tc_Arrow__Order__Mirabelle_Oindi, v1) = v2 & c_member(v2) = v3 &
% 99.57/14.20 c_member(v0) = v4 & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & !
% 99.57/14.20 [v6: $i] : ! [v7: int] : (v7 = 0 | ~
% 99.57/14.20 (c_Arrow__Order__Mirabelle_Ounanimity(v6) = v7) | ~ $i(v6) | ? [v8: $i]
% 99.57/14.20 : ? [v9: $i] : ? [v10: $i] : ? [v11: $i] : (hBOOL(v10) = 0 & hAPP(v9,
% 99.57/14.20 c_Arrow__Order__Mirabelle_OProf) = v10 & hAPP(v6, v8) = v11 & hAPP(v3,
% 99.57/14.20 v8) = v9 & $i(v11) & $i(v10) & $i(v9) & $i(v8) & ? [v12: $i] : ?
% 99.57/14.20 [v13: $i] : ? [v14: $i] : ? [v15: $i] : ? [v16: $i] : ? [v17: $i] :
% 99.57/14.20 ? [v18: int] : ( ~ (v18 = 0) & hBOOL(v17) = v18 & hAPP(v16, v11) = v17 &
% 99.57/14.20 hAPP(v14, v13) = v15 & hAPP(v5, v12) = v14 & hAPP(v4, v15) = v16 &
% 99.57/14.20 $i(v17) & $i(v16) & $i(v15) & $i(v14) & $i(v13) & $i(v12) & ! [v19:
% 99.57/14.20 $i] : ! [v20: $i] : ! [v21: $i] : ( ~ (hAPP(v16, v20) = v21) | ~
% 99.57/14.20 (hAPP(v8, v19) = v20) | ~ $i(v19) | hBOOL(v21) = 0)))) & ! [v6:
% 99.57/14.20 $i] : ( ~ (c_Arrow__Order__Mirabelle_Ounanimity(v6) = 0) | ~ $i(v6) | !
% 99.57/14.20 [v7: $i] : ! [v8: $i] : ( ~ (hAPP(v3, v7) = v8) | ~ $i(v7) | ? [v9: $i]
% 99.57/14.20 : ? [v10: any] : ? [v11: $i] : (hBOOL(v9) = v10 & hAPP(v8,
% 99.57/14.20 c_Arrow__Order__Mirabelle_OProf) = v9 & hAPP(v6, v7) = v11 & $i(v11)
% 99.57/14.20 & $i(v9) & ( ~ (v10 = 0) | ! [v12: $i] : ! [v13: $i] : ! [v14: $i]
% 99.57/14.20 : ! [v15: $i] : ! [v16: $i] : ! [v17: $i] : ( ~ (hAPP(v16, v11) =
% 99.57/14.20 v17) | ~ (hAPP(v14, v13) = v15) | ~ (hAPP(v5, v12) = v14) | ~
% 99.57/14.20 (hAPP(v4, v15) = v16) | ~ $i(v13) | ~ $i(v12) | hBOOL(v17) = 0 |
% 99.57/14.20 ? [v18: $i] : ? [v19: $i] : ? [v20: $i] : ? [v21: int] : ( ~
% 99.57/14.20 (v21 = 0) & hBOOL(v20) = v21 & hAPP(v16, v19) = v20 & hAPP(v7,
% 99.57/14.20 v18) = v19 & $i(v20) & $i(v19) & $i(v18))))))))
% 99.57/14.20
% 99.57/14.20 (help_c__COMBK__1)
% 99.57/14.20 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 99.57/14.20 $i] : (v5 = v1 | ~ (c_COMBK(v3, v2, v1) = v4) | ~ (hAPP(v4, v0) = v5) | ~
% 99.57/14.20 $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0))
% 99.57/14.20
% 99.57/14.20 (function-axioms)
% 99.57/14.22 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 99.57/14.22 [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : (v1 = v0 |
% 99.57/14.22 ~ (c_Equiv__Relations_Ocongruent2(v7, v6, v5, v4, v3, v2) = v1) | ~
% 99.57/14.22 (c_Equiv__Relations_Ocongruent2(v7, v6, v5, v4, v3, v2) = v0)) & ! [v0:
% 99.57/14.22 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 99.57/14.22 : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : (v1 = v0 | ~
% 99.57/14.22 (c_Nitpick_Ofold__graph_H(v7, v6, v5, v4, v3, v2) = v1) | ~
% 99.57/14.22 (c_Nitpick_Ofold__graph_H(v7, v6, v5, v4, v3, v2) = v0)) & ! [v0: $i] : !
% 99.57/14.22 [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i]
% 99.57/14.22 : ! [v7: $i] : (v1 = v0 | ~ (c_FuncSet_Ocompose(v7, v6, v5, v4, v3, v2) =
% 99.57/14.22 v1) | ~ (c_FuncSet_Ocompose(v7, v6, v5, v4, v3, v2) = v0)) & ! [v0:
% 99.57/14.22 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 99.57/14.22 : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : (v1 = v0 | ~
% 99.57/14.22 (c_Predicate_Oinv__imagep(v7, v6, v5, v4, v3, v2) = v1) | ~
% 99.57/14.22 (c_Predicate_Oinv__imagep(v7, v6, v5, v4, v3, v2) = v0)) & ! [v0: $i] : !
% 99.57/14.22 [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i]
% 99.57/14.22 : (v1 = v0 | ~ (c_Fun_Ofun__upd(v6, v5, v4, v3, v2) = v1) | ~
% 99.57/14.22 (c_Fun_Ofun__upd(v6, v5, v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] :
% 99.57/14.22 ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 99.57/14.22 $i] : ! [v6: $i] : (v1 = v0 | ~ (c_FunDef_Oin__rel(v6, v5, v4, v3, v2) =
% 99.57/14.22 v1) | ~ (c_FunDef_Oin__rel(v6, v5, v4, v3, v2) = v0)) & ! [v0:
% 99.57/14.22 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 99.57/14.22 : ! [v4: $i] : ! [v5: $i] : (v1 = v0 | ~ (c_Equiv__Relations_Ocongruent(v5,
% 99.57/14.22 v4, v3, v2) = v1) | ~ (c_Equiv__Relations_Ocongruent(v5, v4, v3, v2) =
% 99.57/14.22 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 99.57/14.22 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v1 = v0 | ~
% 99.57/14.22 (c_Recdef_Oadm__wf(v5, v4, v3, v2) = v1) | ~ (c_Recdef_Oadm__wf(v5, v4, v3,
% 99.57/14.22 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : !
% 99.57/14.22 [v4: $i] : ! [v5: $i] : (v1 = v0 | ~ (c_FuncSet_Oextensional__funcset(v5,
% 99.57/14.22 v4, v3, v2) = v1) | ~ (c_FuncSet_Oextensional__funcset(v5, v4, v3, v2)
% 99.57/14.22 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4:
% 99.57/14.22 $i] : ! [v5: $i] : (v1 = v0 | ~ (c_FuncSet_Orestrict(v5, v4, v3, v2) = v1)
% 99.57/14.22 | ~ (c_FuncSet_Orestrict(v5, v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i]
% 99.57/14.22 : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v1 = v0 | ~
% 99.57/14.22 (c_Relation_Oinv__image(v5, v4, v3, v2) = v1) | ~
% 99.57/14.22 (c_Relation_Oinv__image(v5, v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] :
% 99.57/14.22 ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v1 = v0 | ~
% 99.57/14.22 (c_FuncSet_OPi(v5, v4, v3, v2) = v1) | ~ (c_FuncSet_OPi(v5, v4, v3, v2) =
% 99.57/14.22 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 99.57/14.22 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v1 = v0 | ~
% 99.57/14.22 (c_Predicate_ODomainP(v5, v4, v3, v2) = v1) | ~ (c_Predicate_ODomainP(v5,
% 99.57/14.22 v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 99.57/14.22 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] :
% 99.57/14.22 (v1 = v0 | ~ (c_Predicate_ORangeP(v5, v4, v3, v2) = v1) | ~
% 99.57/14.22 (c_Predicate_ORangeP(v5, v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 99.57/14.22 [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v1 = v0 | ~
% 99.57/14.22 (c_Wellfounded_Olex__prod(v5, v4, v3, v2) = v1) | ~
% 99.57/14.22 (c_Wellfounded_Olex__prod(v5, v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i]
% 99.57/14.22 : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v1 = v0 | ~
% 99.57/14.22 (c_Recdef_Osame__fst(v5, v4, v3, v2) = v1) | ~ (c_Recdef_Osame__fst(v5, v4,
% 99.57/14.22 v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool]
% 99.57/14.22 : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~
% 99.57/14.22 (c_Orderings_Oord__class_Oless__eq(v4, v3, v2) = v1) | ~
% 99.57/14.22 (c_Orderings_Oord__class_Oless__eq(v4, v3, v2) = v0)) & ! [v0: $i] : !
% 99.57/14.22 [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~
% 99.57/14.22 (c_Equiv__Relations_Oquotient(v4, v3, v2) = v1) | ~
% 99.57/14.22 (c_Equiv__Relations_Oquotient(v4, v3, v2) = v0)) & ! [v0:
% 99.57/14.22 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 99.57/14.22 : ! [v4: $i] : (v1 = v0 | ~ (c_Equiv__Relations_Oequiv(v4, v3, v2) = v1) |
% 99.57/14.22 ~ (c_Equiv__Relations_Oequiv(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i]
% 99.57/14.22 : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~
% 99.57/14.22 (c_Relation_OImage(v4, v3, v2) = v1) | ~ (c_Relation_OImage(v4, v3, v2) =
% 99.57/14.22 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 99.57/14.22 $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (c_Relation_Orefl__on(v4,
% 99.57/14.22 v3, v2) = v1) | ~ (c_Relation_Orefl__on(v4, v3, v2) = v0)) & ! [v0:
% 99.57/14.22 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 99.57/14.22 : ! [v4: $i] : (v1 = v0 | ~ (c_Relation_Osingle__valued(v4, v3, v2) = v1) |
% 99.57/14.22 ~ (c_Relation_Osingle__valued(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i]
% 99.57/14.22 : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (c_COMBS(v4, v3, v2)
% 99.57/14.22 = v1) | ~ (c_COMBS(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : !
% 99.57/14.22 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 |
% 99.57/14.22 ~ (c_Wellfounded_Oaccp(v4, v3, v2) = v1) | ~ (c_Wellfounded_Oaccp(v4, v3,
% 99.57/14.22 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] :
% 99.57/14.22 ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~
% 99.57/14.22 (c_Relation_Ototal__on(v4, v3, v2) = v1) | ~ (c_Relation_Ototal__on(v4, v3,
% 99.57/14.22 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : !
% 99.57/14.22 [v4: $i] : (v1 = v0 | ~ (c_FuncSet_Oextensional(v4, v3, v2) = v1) | ~
% 99.57/14.22 (c_FuncSet_Oextensional(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 99.57/14.22 [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (c_COMBK(v4, v3, v2) =
% 99.57/14.22 v1) | ~ (c_COMBK(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 99.57/14.22 $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (c_Predicate_Oconversep(v4,
% 99.57/14.22 v3, v2) = v1) | ~ (c_Predicate_Oconversep(v4, v3, v2) = v0)) & ! [v0:
% 99.57/14.22 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~
% 99.57/14.22 (c_Relation_ODomain(v4, v3, v2) = v1) | ~ (c_Relation_ODomain(v4, v3, v2) =
% 99.57/14.22 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i]
% 99.57/14.22 : (v1 = v0 | ~ (c_Relation_ORange(v4, v3, v2) = v1) | ~
% 99.57/14.22 (c_Relation_ORange(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 99.57/14.22 $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (c_COMBB(v4, v3, v2) = v1) |
% 99.57/14.22 ~ (c_COMBB(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 99.57/14.22 ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (c_COMBC(v4, v3, v2) = v1) | ~
% 99.57/14.22 (c_COMBC(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 99.57/14.22 [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (c_Arrow__Order__Mirabelle_Obelow(v4,
% 99.57/14.22 v3, v2) = v1) | ~ (c_Arrow__Order__Mirabelle_Obelow(v4, v3, v2) = v0))
% 99.57/14.22 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 =
% 99.57/14.22 v0 | ~ (c_Arrow__Order__Mirabelle_Oabove(v4, v3, v2) = v1) | ~
% 99.57/14.22 (c_Arrow__Order__Mirabelle_Oabove(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1:
% 99.57/14.22 $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (c_Set_Othe__elem(v3, v2) =
% 99.57/14.22 v1) | ~ (c_Set_Othe__elem(v3, v2) = v0)) & ! [v0: MultipleValueBool] :
% 99.57/14.22 ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 99.57/14.22 (c_Wellfounded_Oacyclic(v3, v2) = v1) | ~ (c_Wellfounded_Oacyclic(v3, v2) =
% 99.57/14.22 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 |
% 99.57/14.22 ~ (c_Transitive__Closure_Otrancl(v3, v2) = v1) | ~
% 99.57/14.22 (c_Transitive__Closure_Otrancl(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] :
% 99.57/14.22 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (c_Transitive__Closure_Ortrancl(v3,
% 99.57/14.22 v2) = v1) | ~ (c_Transitive__Closure_Ortrancl(v3, v2) = v0)) & ! [v0:
% 99.57/14.22 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 99.57/14.22 (c_Recdef_Ocut(v3, v2) = v1) | ~ (c_Recdef_Ocut(v3, v2) = v0)) & ! [v0:
% 99.57/14.22 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 99.57/14.22 (c_Wellfounded_Oacc(v3, v2) = v1) | ~ (c_Wellfounded_Oacc(v3, v2) = v0)) &
% 99.57/14.22 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 99.57/14.22 $i] : (v1 = v0 | ~ (c_Nitpick_Orefl_H(v3, v2) = v1) | ~
% 99.57/14.22 (c_Nitpick_Orefl_H(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 99.57/14.22 : ! [v3: $i] : (v1 = v0 | ~ (c_Relation_OId__on(v3, v2) = v1) | ~
% 99.57/14.22 (c_Relation_OId__on(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 99.57/14.22 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 99.57/14.22 (c_Relation_Oirrefl(v3, v2) = v1) | ~ (c_Relation_Oirrefl(v3, v2) = v0)) &
% 99.57/14.22 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 99.57/14.22 (c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v3, v2) = v1) | ~
% 99.57/14.22 (c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v3, v2) = v0)) & !
% 99.57/14.22 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 99.57/14.22 (c_Complete__Lattice_Ocomplete__lattice__class_OINFI(v3, v2) = v1) | ~
% 99.57/14.22 (c_Complete__Lattice_Ocomplete__lattice__class_OINFI(v3, v2) = v0)) & !
% 99.57/14.22 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 99.57/14.22 (c_Relation_Oconverse(v3, v2) = v1) | ~ (c_Relation_Oconverse(v3, v2) =
% 99.57/14.22 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 |
% 99.57/14.22 ~ (c_Product__Type_OPair(v3, v2) = v1) | ~ (c_Product__Type_OPair(v3, v2) =
% 99.57/14.22 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 99.57/14.22 $i] : ! [v3: $i] : (v1 = v0 | ~ (c_Arrow__Order__Mirabelle_Odictator(v3,
% 99.57/14.22 v2) = v1) | ~ (c_Arrow__Order__Mirabelle_Odictator(v3, v2) = v0)) & !
% 99.57/14.22 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 99.57/14.22 (c_Arrow__Order__Mirabelle_Omktop(v3, v2) = v1) | ~
% 99.57/14.22 (c_Arrow__Order__Mirabelle_Omktop(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i]
% 99.57/14.22 : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 99.57/14.22 (c_Arrow__Order__Mirabelle_Omkbot(v3, v2) = v1) | ~
% 99.57/14.22 (c_Arrow__Order__Mirabelle_Omkbot(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i]
% 99.57/14.22 : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (tc_prod(v3, v2) = v1) | ~
% 99.57/14.22 (tc_prod(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 99.57/14.22 $i] : (v1 = v0 | ~ (tc_fun(v3, v2) = v1) | ~ (tc_fun(v3, v2) = v0)) & !
% 99.57/14.22 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP(v3,
% 99.57/14.22 v2) = v1) | ~ (hAPP(v3, v2) = v0)) & ! [v0: MultipleValueBool] : !
% 99.57/14.22 [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~
% 99.57/14.22 (class_Lattices_Obounded__lattice(v2) = v1) | ~
% 99.57/14.22 (class_Lattices_Obounded__lattice(v2) = v0)) & ! [v0: MultipleValueBool] :
% 99.57/14.22 ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~
% 99.57/14.22 (class_Orderings_Oorder(v2) = v1) | ~ (class_Orderings_Oorder(v2) = v0)) &
% 99.57/14.22 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 =
% 99.57/14.22 v0 | ~ (class_Orderings_Oord(v2) = v1) | ~ (class_Orderings_Oord(v2) =
% 99.57/14.22 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 99.57/14.22 $i] : (v1 = v0 | ~ (class_Orderings_Olinorder(v2) = v1) | ~
% 99.57/14.22 (class_Orderings_Olinorder(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 99.57/14.22 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~
% 99.57/14.22 (class_Orderings_Opreorder(v2) = v1) | ~ (class_Orderings_Opreorder(v2) =
% 99.57/14.22 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 99.57/14.22 (c_Set_Oinsert(v2) = v1) | ~ (c_Set_Oinsert(v2) = v0)) & ! [v0:
% 99.57/14.22 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 |
% 99.57/14.22 ~ (class_Groups_Ominus(v2) = v1) | ~ (class_Groups_Ominus(v2) = v0)) & !
% 99.57/14.22 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 99.57/14.22 (c_Groups_Ominus__class_Ominus(v2) = v1) | ~
% 99.57/14.22 (c_Groups_Ominus__class_Ominus(v2) = v0)) & ! [v0: MultipleValueBool] : !
% 99.57/14.22 [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~
% 99.57/14.22 (class_Lattices_Obounded__lattice__bot(v2) = v1) | ~
% 99.57/14.22 (class_Lattices_Obounded__lattice__bot(v2) = v0)) & ! [v0:
% 99.57/14.22 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 |
% 99.57/14.22 ~ (class_Orderings_Obot(v2) = v1) | ~ (class_Orderings_Obot(v2) = v0)) & !
% 99.57/14.22 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 99.57/14.22 (c_Orderings_Obot__class_Obot(v2) = v1) | ~
% 99.57/14.22 (c_Orderings_Obot__class_Obot(v2) = v0)) & ! [v0: MultipleValueBool] : !
% 99.57/14.22 [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~
% 99.57/14.22 (class_Lattices_Osemilattice__inf(v2) = v1) | ~
% 99.57/14.22 (class_Lattices_Osemilattice__inf(v2) = v0)) & ! [v0: MultipleValueBool] :
% 99.57/14.22 ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~
% 99.57/14.22 (class_Lattices_Obounded__lattice__top(v2) = v1) | ~
% 99.57/14.22 (class_Lattices_Obounded__lattice__top(v2) = v0)) & ! [v0:
% 99.57/14.22 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 |
% 99.57/14.22 ~ (class_Lattices_Olattice(v2) = v1) | ~ (class_Lattices_Olattice(v2) =
% 99.57/14.22 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 99.57/14.22 (c_Lattices_Osemilattice__inf__class_Oinf(v2) = v1) | ~
% 99.57/14.22 (c_Lattices_Osemilattice__inf__class_Oinf(v2) = v0)) & ! [v0: $i] : ! [v1:
% 99.57/14.22 $i] : ! [v2: $i] : (v1 = v0 | ~ (c_HOL_Oundefined(v2) = v1) | ~
% 99.57/14.22 (c_HOL_Oundefined(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 99.57/14.22 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~
% 99.57/14.22 (c_Arrow__Order__Mirabelle_OIIA(v2) = v1) | ~
% 99.57/14.22 (c_Arrow__Order__Mirabelle_OIIA(v2) = v0)) & ! [v0: MultipleValueBool] : !
% 99.57/14.22 [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~
% 99.57/14.22 (class_Orderings_Otop(v2) = v1) | ~ (class_Orderings_Otop(v2) = v0)) & !
% 99.57/14.22 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (c_COMBI(v2) = v1) | ~
% 99.57/14.22 (c_COMBI(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 99.57/14.22 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~
% 99.57/14.22 (c_Arrow__Order__Mirabelle_Ounanimity(v2) = v1) | ~
% 99.57/14.22 (c_Arrow__Order__Mirabelle_Ounanimity(v2) = v0)) & ! [v0: $i] : ! [v1: $i]
% 99.57/14.22 : ! [v2: $i] : (v1 = v0 | ~ (c_Orderings_Otop__class_Otop(v2) = v1) | ~
% 99.57/14.22 (c_Orderings_Otop__class_Otop(v2) = v0)) & ! [v0: MultipleValueBool] : !
% 99.57/14.22 [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~
% 99.57/14.22 (class_Complete__Lattice_Ocomplete__lattice(v2) = v1) | ~
% 99.57/14.22 (class_Complete__Lattice_Ocomplete__lattice(v2) = v0)) & ! [v0: $i] : !
% 99.57/14.22 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (c_member(v2) = v1) | ~ (c_member(v2)
% 99.57/14.22 = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 99.57/14.22 $i] : (v1 = v0 | ~ (hBOOL(v2) = v1) | ~ (hBOOL(v2) = v0))
% 99.57/14.22
% 99.57/14.22 Further assumptions not needed in the proof:
% 99.57/14.22 --------------------------------------------
% 99.57/14.22 arity_HOL__Obool__Groups_Ominus, arity_HOL__Obool__Lattices_Obounded__lattice,
% 99.57/14.22 arity_HOL__Obool__Lattices_Obounded__lattice__bot,
% 99.57/14.22 arity_HOL__Obool__Lattices_Obounded__lattice__top,
% 99.57/14.22 arity_HOL__Obool__Lattices_Olattice,
% 99.57/14.22 arity_HOL__Obool__Lattices_Osemilattice__inf, arity_HOL__Obool__Orderings_Obot,
% 99.57/14.22 arity_HOL__Obool__Orderings_Oord, arity_HOL__Obool__Orderings_Oorder,
% 99.57/14.22 arity_HOL__Obool__Orderings_Opreorder, arity_HOL__Obool__Orderings_Otop,
% 99.57/14.22 arity_fun__Groups_Ominus, arity_fun__Lattices_Obounded__lattice,
% 99.57/14.22 arity_fun__Lattices_Obounded__lattice__bot,
% 99.57/14.22 arity_fun__Lattices_Obounded__lattice__top, arity_fun__Lattices_Olattice,
% 99.57/14.22 arity_fun__Lattices_Osemilattice__inf, arity_fun__Orderings_Obot,
% 99.57/14.22 arity_fun__Orderings_Oord, arity_fun__Orderings_Oorder,
% 99.57/14.22 arity_fun__Orderings_Opreorder, arity_fun__Orderings_Otop, fact_DiffD1,
% 99.57/14.22 fact_DiffD2, fact_DiffE, fact_DiffI, fact_Diff__Int2, fact_Diff__Int__distrib,
% 99.57/14.22 fact_Diff__Int__distrib2, fact_Diff__UNIV, fact_Diff__cancel,
% 99.57/14.22 fact_Diff__disjoint, fact_Diff__empty, fact_Diff__idemp, fact_Diff__iff,
% 99.57/14.22 fact_Diff__insert, fact_Diff__insert2, fact_Diff__insert__absorb,
% 99.57/14.22 fact_Diff__mono, fact_Diff__subset, fact_Diff__triv, fact_DomainE, fact_DomainI,
% 99.57/14.22 fact_DomainP_Ointros, fact_DomainP__Domain__eq, fact_Domain__Id__on,
% 99.57/14.22 fact_Domain__converse, fact_Domain__empty, fact_Domain__empty__iff,
% 99.57/14.22 fact_Domain__iff, fact_Domain__insert, fact_Domain__mono, fact_Domain__rtrancl,
% 99.57/14.22 fact_INF1__D, fact_INF1__E, fact_INF1__I, fact_INF1__iff, fact_INF2__D,
% 99.57/14.22 fact_INF2__E, fact_INF2__I, fact_INF2__iff, fact_INFI__apply, fact_INF__INT__eq,
% 99.57/14.22 fact_INF__INT__eq2, fact_INF__commute, fact_INF__const, fact_INF__leI,
% 99.57/14.22 fact_INF__subset, fact_INTER__UNIV__conv_I1_J, fact_INTER__UNIV__conv_I2_J,
% 99.57/14.22 fact_INT__D, fact_INT__E, fact_INT__I, fact_INT__Int__distrib, fact_INT__absorb,
% 99.57/14.22 fact_INT__constant, fact_INT__empty, fact_INT__extend__simps_I1_J,
% 99.57/14.22 fact_INT__extend__simps_I2_J, fact_INT__extend__simps_I3_J,
% 99.57/14.22 fact_INT__extend__simps_I4_J, fact_INT__extend__simps_I5_J,
% 99.57/14.22 fact_INT__extend__simps_I9_J, fact_INT__iff, fact_INT__insert,
% 99.57/14.22 fact_INT__insert__distrib, fact_INT__simps_I1_J, fact_INT__simps_I2_J,
% 99.57/14.22 fact_INT__simps_I3_J, fact_INT__simps_I4_J, fact_INT__simps_I5_J,
% 99.57/14.22 fact_INT__simps_I9_J, fact_INT__subset__iff, fact_Id__onE, fact_Id__on__def,
% 99.57/14.22 fact_Id__on__empty, fact_Id__on__eqI, fact_Id__on__iff, fact_ImageE,
% 99.57/14.22 fact_Image__INT__eq, fact_Image__INT__subset, fact_Image__Id__on,
% 99.57/14.22 fact_Image__Int__eq, fact_Image__UN, fact_Image__empty, fact_Image__eq__UN,
% 99.57/14.22 fact_Image__iff, fact_Image__mono, fact_Image__singleton__iff, fact_IntD1,
% 99.57/14.22 fact_IntD2, fact_IntE, fact_IntI, fact_Int__Diff, fact_Int__UNIV__left,
% 99.57/14.22 fact_Int__UNIV__right, fact_Int__UN__distrib, fact_Int__UN__distrib2,
% 99.57/14.22 fact_Int__absorb, fact_Int__absorb1, fact_Int__absorb2, fact_Int__assoc,
% 99.57/14.22 fact_Int__commute, fact_Int__empty__left, fact_Int__empty__right,
% 99.57/14.22 fact_Int__greatest, fact_Int__iff, fact_Int__insert__left,
% 99.57/14.22 fact_Int__insert__left__if0, fact_Int__insert__left__if1,
% 99.57/14.22 fact_Int__insert__right, fact_Int__insert__right__if0,
% 99.57/14.22 fact_Int__insert__right__if1, fact_Int__left__absorb, fact_Int__left__commute,
% 99.57/14.22 fact_Int__lower1, fact_Int__lower2, fact_Int__mono, fact_Nitpick_Orefl_H__def,
% 99.57/14.22 fact_Not__Domain__rtrancl, fact_PiE, fact_Pi__UNIV, fact_Pi__anti__mono,
% 99.57/14.22 fact_Pi__empty, fact_Pi__mem, fact_RangeE, fact_RangeI, fact_RangeP_Oequations,
% 99.57/14.22 fact_RangeP_Ointros, fact_RangeP__Range__eq, fact_Range__Id__on,
% 99.57/14.22 fact_Range__converse, fact_Range__def, fact_Range__empty,
% 99.57/14.22 fact_Range__empty__iff, fact_Range__iff, fact_Range__insert,
% 99.57/14.22 fact_Range__rtrancl, fact_SUP1__E, fact_SUP1__I, fact_SUP1__iff, fact_SUP2__E,
% 99.57/14.23 fact_SUP2__I, fact_SUP2__iff, fact_SUPR__apply, fact_SUP__UN__eq,
% 99.57/14.23 fact_SUP__UN__eq2, fact_SUP__commute, fact_SUP__const, fact_SUP__le__iff,
% 99.57/14.23 fact_SUP__subset, fact_Transitive__Closure_Otrancl__into__trancl,
% 99.57/14.23 fact_UNION__empty__conv_I1_J, fact_UNION__empty__conv_I2_J, fact_UNIV__I,
% 99.57/14.23 fact_UNIV__not__empty, fact_UN__E, fact_UN__I, fact_UN__UN__flatten,
% 99.57/14.23 fact_UN__constant, fact_UN__empty2, fact_UN__equiv__class,
% 99.57/14.23 fact_UN__equiv__class2, fact_UN__extend__simps_I1_J,
% 99.57/14.23 fact_UN__extend__simps_I4_J, fact_UN__extend__simps_I5_J,
% 99.57/14.23 fact_UN__extend__simps_I6_J, fact_UN__extend__simps_I7_J,
% 99.57/14.23 fact_UN__extend__simps_I9_J, fact_UN__iff, fact_UN__insert__distrib,
% 99.57/14.23 fact_UN__simps_I1_J, fact_UN__simps_I4_J, fact_UN__simps_I5_J,
% 99.57/14.23 fact_UN__simps_I6_J, fact_UN__simps_I7_J, fact_UN__simps_I9_J,
% 99.57/14.23 fact_UN__singleton, fact_UN__subset__iff, fact_UN__upper, fact_acc_OaccI,
% 99.57/14.23 fact_acc_Osimps, fact_acc__downward, fact_acc__downwards,
% 99.57/14.23 fact_acc__downwards__aux, fact_acc__subset, fact_accp_Oequations,
% 99.57/14.23 fact_accp_Osimps, fact_accp__acc__eq, fact_accp__downward,
% 99.57/14.23 fact_acyclic__converse, fact_acyclic__def, fact_acyclic__insert,
% 99.57/14.23 fact_acyclic__subset, fact_adm__lemma, fact_adm__wf__def,
% 99.57/14.23 fact_all__not__in__conv, fact_ball__UN, fact_bot2E, fact_bot__apply,
% 99.57/14.23 fact_bot__empty__eq, fact_bot__empty__eq2, fact_bot__fun__def, fact_bot__least,
% 99.57/14.23 fact_compose__assoc, fact_compose__def, fact_compose__eq,
% 99.57/14.23 fact_compose__extensional, fact_congruent2D,
% 99.57/14.23 fact_congruent2__implies__congruent, fact_congruent2__implies__congruent__UN,
% 99.57/14.23 fact_congruentD, fact_converseD, fact_converseE, fact_converseI,
% 99.57/14.23 fact_converse__INTER, fact_converse__Id__on, fact_converse__Int,
% 99.57/14.23 fact_converse__UNION, fact_converse__converse, fact_converse__iff,
% 99.57/14.23 fact_converse__inv__image, fact_converse__meet, fact_converse__rtranclE,
% 99.57/14.23 fact_converse__rtranclE2, fact_converse__rtrancl__induct,
% 99.57/14.23 fact_converse__rtrancl__induct2, fact_converse__rtrancl__into__rtrancl,
% 99.57/14.23 fact_conversepD, fact_conversep_Oequations, fact_conversep_Ointros,
% 99.57/14.23 fact_conversep__converse__eq, fact_conversep__conversep, fact_conversep__eq,
% 99.57/14.23 fact_conversep__iff, fact_conversep__noteq, fact_cut__apply, fact_cut__def,
% 99.57/14.23 fact_cuts__eq, fact_disjoint__iff__not__equal, fact_double__diff,
% 99.57/14.23 fact_doubleton__eq__iff, fact_emptyE, fact_empty__Diff, fact_empty__iff,
% 99.57/14.23 fact_empty__not__insert, fact_empty__subsetI, fact_eq__equiv__class,
% 99.57/14.23 fact_eq__equiv__class__iff, fact_eq__equiv__class__iff2, fact_eq__mem,
% 99.57/14.23 fact_eq__mem__trans, fact_eqelem__imp__iff, fact_eqset__imp__iff,
% 99.57/14.23 fact_equalityCE, fact_equalityD1, fact_equalityD2, fact_equalityE,
% 99.57/14.23 fact_equalityI, fact_equiv__class__eq, fact_equiv__class__eq__iff,
% 99.57/14.23 fact_equiv__class__nondisjoint, fact_equiv__class__self, fact_ex__in__conv,
% 99.57/14.23 fact_ext, fact_extensional__arb, fact_extensional__empty,
% 99.57/14.23 fact_extensional__funcset__arb, fact_extensional__funcset__def,
% 99.57/14.23 fact_extensional__funcset__empty__domain,
% 99.57/14.23 fact_extensional__funcset__empty__range,
% 99.57/14.23 fact_extensional__funcset__extend__domainI,
% 99.57/14.23 fact_extensional__funcset__fun__upd__extends__rangeI,
% 99.57/14.23 fact_extensional__funcset__fun__upd__restricts__rangeI,
% 99.57/14.23 fact_extensional__funcset__mem, fact_extensional__funcset__restrict__domain,
% 99.57/14.23 fact_extensional__restrict, fact_extensional__subset, fact_extensionalityI,
% 99.57/14.23 fact_fold__graph_H_Oequations_I1_J, fact_fold__graph_H_Oequations_I2_J,
% 99.57/14.23 fact_fold__graph_H_Ointros_I1_J, fact_fold__graph_H_Ointros_I2_J,
% 99.57/14.23 fact_fun__diff__def, fact_fun__upd__apply, fact_fun__upd__def,
% 99.57/14.23 fact_fun__upd__idem, fact_fun__upd__idem__iff, fact_fun__upd__other,
% 99.57/14.23 fact_fun__upd__same, fact_fun__upd__triv, fact_fun__upd__twist,
% 99.57/14.23 fact_fun__upd__upd, fact_funcset__compose, fact_funcset__id, fact_funcset__mem,
% 99.57/14.23 fact_in__inv__image, fact_in__inv__imagep, fact_in__lex__prod, fact_in__mono,
% 99.57/14.23 fact_in__rel__def, fact_inf1D1, fact_inf1D2, fact_inf1E, fact_inf1I,
% 99.57/14.23 fact_inf2D1, fact_inf2D2, fact_inf2E, fact_inf2I, fact_inf_Oassoc,
% 99.57/14.23 fact_inf_Ocommute, fact_inf_Oidem, fact_inf_Oleft__commute,
% 99.57/14.23 fact_inf_Oleft__idem, fact_inf__Int__eq, fact_inf__Int__eq2, fact_inf__absorb1,
% 99.57/14.23 fact_inf__absorb2, fact_inf__apply, fact_inf__assoc, fact_inf__bot__left,
% 99.57/14.23 fact_inf__bot__right, fact_inf__commute, fact_inf__eq__top__iff,
% 99.57/14.23 fact_inf__fun__def, fact_inf__greatest, fact_inf__idem, fact_inf__le1,
% 99.57/14.23 fact_inf__le2, fact_inf__left__commute, fact_inf__left__idem, fact_inf__mono,
% 99.57/14.23 fact_inf__sup__aci_I1_J, fact_inf__sup__aci_I2_J, fact_inf__sup__aci_I3_J,
% 99.57/14.23 fact_inf__sup__aci_I4_J, fact_inf__sup__ord_I1_J, fact_inf__sup__ord_I2_J,
% 99.57/14.23 fact_inf__top__left, fact_inf__top__right, fact_insertCI, fact_insertE,
% 99.57/14.23 fact_insertI1, fact_insertI2, fact_insert__Diff, fact_insert__Diff1,
% 99.57/14.23 fact_insert__Diff__if, fact_insert__Diff__single, fact_insert__absorb,
% 99.57/14.23 fact_insert__absorb2, fact_insert__code, fact_insert__commute,
% 99.57/14.23 fact_insert__ident, fact_insert__iff, fact_insert__inter__insert,
% 99.57/14.23 fact_insert__not__empty, fact_inv__imagep__def, fact_irrefl__def,
% 99.57/14.23 fact_irrefl__tranclI, fact_iso__tuple__UNIV__I, fact_le__INF__iff,
% 99.57/14.23 fact_le__funD, fact_le__funE, fact_le__fun__def, fact_le__iff__inf,
% 99.57/14.23 fact_le__infE, fact_le__infI, fact_le__infI1, fact_le__infI2, fact_le__inf__iff,
% 99.57/14.23 fact_less__by__empty, fact_linorder__le__cases, fact_linorder__linear,
% 99.57/14.23 fact_minus__apply, fact_not__acc__down, fact_ord__eq__le__trans,
% 99.57/14.23 fact_ord__le__eq__trans, fact_order__antisym, fact_order__antisym__conv,
% 99.57/14.23 fact_order__eq__iff, fact_order__eq__refl, fact_order__refl, fact_order__trans,
% 99.57/14.23 fact_pred__equals__eq, fact_pred__equals__eq2, fact_pred__subset__eq,
% 99.57/14.23 fact_predicate1D, fact_r__into__rtrancl, fact_r__into__trancl_H,
% 99.57/14.23 fact_r__r__into__trancl, fact_refl__onD, fact_refl__onD1, fact_refl__onD2,
% 99.57/14.23 fact_refl__on__INTER, fact_refl__on__Id__on, fact_refl__on__Int,
% 99.57/14.23 fact_refl__on__converse, fact_refl__on__empty, fact_refl__rtrancl,
% 99.57/14.23 fact_restrictI, fact_restrict__apply, fact_restrict__def,
% 99.57/14.23 fact_restrict__extensional, fact_restrict__in__funcset, fact_rev__ImageI,
% 99.57/14.23 fact_rev__predicate1D, fact_rtranclD, fact_rtranclE,
% 99.57/14.23 fact_rtrancl_Ortrancl__into__rtrancl, fact_rtrancl_Ortrancl__refl,
% 99.57/14.23 fact_rtrancl__converse, fact_rtrancl__converseD, fact_rtrancl__converseI,
% 99.57/14.23 fact_rtrancl__eq__or__trancl, fact_rtrancl__idemp, fact_rtrancl__induct,
% 99.57/14.23 fact_rtrancl__induct2, fact_rtrancl__into__trancl1, fact_rtrancl__into__trancl2,
% 99.57/14.23 fact_rtrancl__mono, fact_rtrancl__subset, fact_rtrancl__subset__rtrancl,
% 99.57/14.23 fact_rtrancl__trancl__absorb, fact_rtrancl__trancl__trancl, fact_rtrancl__trans,
% 99.57/14.23 fact_same__fstI, fact_set__eq__subset, fact_set__mp, fact_set__rev__mp,
% 99.57/14.23 fact_single__valuedD, fact_single__valuedI, fact_single__valued__Id__on,
% 99.57/14.23 fact_single__valued__confluent, fact_single__valued__def,
% 99.57/14.23 fact_single__valued__subset, fact_singletonE, fact_singleton__iff,
% 99.57/14.23 fact_singleton__inject, fact_subsetD, fact_subset__UNIV, fact_subset__empty,
% 99.57/14.23 fact_subset__equiv__class, fact_subset__refl, fact_subset__trans,
% 99.57/14.23 fact_tfl__cut__apply, fact_the__elem__eq, fact_top1I, fact_top__apply,
% 99.57/14.23 fact_top__greatest, fact_total__on__converse, fact_total__on__def,
% 99.57/14.23 fact_total__on__empty, fact_tranclD, fact_tranclD2,
% 99.57/14.23 fact_trancl_Or__into__trancl, fact_trancl__converse, fact_trancl__converseD,
% 99.57/14.23 fact_trancl__converseI, fact_trancl__domain, fact_trancl__empty,
% 99.57/14.23 fact_trancl__into__rtrancl, fact_trancl__into__trancl2, fact_trancl__range,
% 99.57/14.23 fact_trancl__rtrancl__absorb, fact_trancl__rtrancl__trancl, fact_trancl__trans,
% 99.57/14.23 fact_xt1_I3_J, fact_xt1_I4_J, fact_xt1_I5_J, fact_xt1_I6_J, help_c__COMBB__1,
% 99.57/14.23 help_c__COMBC__1, help_c__COMBI__1, help_c__COMBS__1, help_c__fNot__1,
% 99.57/14.23 help_c__fNot__2, help_c__fequal__1, help_c__fequal__2
% 99.57/14.23
% 99.57/14.23 Those formulas are unsatisfiable:
% 99.57/14.23 ---------------------------------
% 99.57/14.23
% 99.57/14.23 Begin of proof
% 99.57/14.23 |
% 99.57/14.23 | ALPHA: (fact_above__Lin) implies:
% 99.57/14.23 | (1) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 99.57/14.23 | (tc_prod(tc_Arrow__Order__Mirabelle_Oalt,
% 99.57/14.23 | tc_Arrow__Order__Mirabelle_Oalt) = v0 & tc_fun(v0, tc_HOL_Obool) =
% 99.57/14.23 | v1 & c_member(v1) = v2 & $i(v2) & $i(v1) & $i(v0) & ! [v3: $i] : !
% 99.57/14.23 | [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v5 = v4 | ~
% 99.57/14.23 | (c_Arrow__Order__Mirabelle_Oabove(v3, v5, v4) = v6) | ~ $i(v5) |
% 99.57/14.23 | ~ $i(v4) | ~ $i(v3) | ? [v7: $i] : ? [v8: $i] : ? [v9: any] :
% 99.57/14.23 | ? [v10: $i] : ? [v11: $i] : ? [v12: any] : (hBOOL(v11) = v12 &
% 99.57/14.23 | hBOOL(v8) = v9 & hAPP(v10, c_Arrow__Order__Mirabelle_OLin) = v11
% 99.57/14.23 | & hAPP(v7, c_Arrow__Order__Mirabelle_OLin) = v8 & hAPP(v2, v6) =
% 99.57/14.23 | v10 & hAPP(v2, v3) = v7 & $i(v11) & $i(v10) & $i(v8) & $i(v7) & (
% 99.57/14.23 | ~ (v9 = 0) | v12 = 0))))
% 99.57/14.23 |
% 99.57/14.23 | ALPHA: (fact_below__Lin) implies:
% 99.57/14.23 | (2) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 99.57/14.23 | (tc_prod(tc_Arrow__Order__Mirabelle_Oalt,
% 99.57/14.23 | tc_Arrow__Order__Mirabelle_Oalt) = v0 & tc_fun(v0, tc_HOL_Obool) =
% 99.57/14.23 | v1 & c_member(v1) = v2 & $i(v2) & $i(v1) & $i(v0) & ! [v3: $i] : !
% 99.57/14.23 | [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v5 = v4 | ~
% 99.57/14.23 | (c_Arrow__Order__Mirabelle_Obelow(v3, v5, v4) = v6) | ~ $i(v5) |
% 99.57/14.23 | ~ $i(v4) | ~ $i(v3) | ? [v7: $i] : ? [v8: $i] : ? [v9: any] :
% 99.57/14.23 | ? [v10: $i] : ? [v11: $i] : ? [v12: any] : (hBOOL(v11) = v12 &
% 99.57/14.23 | hBOOL(v8) = v9 & hAPP(v10, c_Arrow__Order__Mirabelle_OLin) = v11
% 99.57/14.23 | & hAPP(v7, c_Arrow__Order__Mirabelle_OLin) = v8 & hAPP(v2, v6) =
% 99.57/14.23 | v10 & hAPP(v2, v3) = v7 & $i(v11) & $i(v10) & $i(v8) & $i(v7) & (
% 99.57/14.23 | ~ (v9 = 0) | v12 = 0))))
% 99.57/14.23 |
% 99.57/14.23 | ALPHA: (fact_mkbot__Lin) implies:
% 99.57/14.23 | (3) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 99.57/14.23 | (tc_prod(tc_Arrow__Order__Mirabelle_Oalt,
% 99.57/14.23 | tc_Arrow__Order__Mirabelle_Oalt) = v0 & tc_fun(v0, tc_HOL_Obool) =
% 99.57/14.23 | v1 & c_member(v1) = v2 & $i(v2) & $i(v1) & $i(v0) & ! [v3: $i] : !
% 99.57/14.23 | [v4: $i] : ! [v5: $i] : ( ~ (c_Arrow__Order__Mirabelle_Omkbot(v4,
% 99.57/14.23 | v3) = v5) | ~ $i(v4) | ~ $i(v3) | ? [v6: $i] : ? [v7: $i] :
% 99.57/14.23 | ? [v8: any] : ? [v9: $i] : ? [v10: $i] : ? [v11: any] :
% 99.57/14.23 | (hBOOL(v10) = v11 & hBOOL(v7) = v8 & hAPP(v9,
% 99.57/14.23 | c_Arrow__Order__Mirabelle_OLin) = v10 & hAPP(v6,
% 99.57/14.23 | c_Arrow__Order__Mirabelle_OLin) = v7 & hAPP(v2, v5) = v9 &
% 99.57/14.23 | hAPP(v2, v4) = v6 & $i(v10) & $i(v9) & $i(v7) & $i(v6) & ( ~ (v8
% 99.57/14.23 | = 0) | v11 = 0))))
% 99.57/14.23 |
% 99.57/14.23 | ALPHA: (fact_mktop__Lin) implies:
% 99.57/14.24 | (4) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 99.57/14.24 | (tc_prod(tc_Arrow__Order__Mirabelle_Oalt,
% 99.57/14.24 | tc_Arrow__Order__Mirabelle_Oalt) = v0 & tc_fun(v0, tc_HOL_Obool) =
% 99.57/14.24 | v1 & c_member(v1) = v2 & $i(v2) & $i(v1) & $i(v0) & ! [v3: $i] : !
% 99.57/14.24 | [v4: $i] : ! [v5: $i] : ( ~ (c_Arrow__Order__Mirabelle_Omktop(v4,
% 99.57/14.24 | v3) = v5) | ~ $i(v4) | ~ $i(v3) | ? [v6: $i] : ? [v7: $i] :
% 99.57/14.24 | ? [v8: any] : ? [v9: $i] : ? [v10: $i] : ? [v11: any] :
% 99.57/14.24 | (hBOOL(v10) = v11 & hBOOL(v7) = v8 & hAPP(v9,
% 99.57/14.24 | c_Arrow__Order__Mirabelle_OLin) = v10 & hAPP(v6,
% 99.57/14.24 | c_Arrow__Order__Mirabelle_OLin) = v7 & hAPP(v2, v5) = v9 &
% 99.57/14.24 | hAPP(v2, v4) = v6 & $i(v10) & $i(v9) & $i(v7) & $i(v6) & ( ~ (v8
% 99.57/14.24 | = 0) | v11 = 0))))
% 99.57/14.24 |
% 99.57/14.24 | ALPHA: (fact_dictator__def) implies:
% 99.57/14.24 | (5) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] :
% 99.57/14.24 | (tc_prod(tc_Arrow__Order__Mirabelle_Oalt,
% 99.57/14.24 | tc_Arrow__Order__Mirabelle_Oalt) = v0 & tc_fun(v0, tc_HOL_Obool) =
% 99.57/14.24 | v1 & tc_fun(tc_Arrow__Order__Mirabelle_Oindi, v1) = v2 & c_member(v2)
% 99.57/14.24 | = v3 & $i(v3) & $i(v2) & $i(v1) & $i(v0) & ! [v4: $i] : ! [v5: $i]
% 99.57/14.24 | : ! [v6: int] : (v6 = 0 | ~
% 99.57/14.24 | (c_Arrow__Order__Mirabelle_Odictator(v5, v4) = v6) | ~ $i(v5) | ~
% 99.57/14.24 | $i(v4) | ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ? [v10: $i] :
% 99.57/14.24 | ? [v11: $i] : ( ~ (v11 = v10) & hBOOL(v9) = 0 & hAPP(v8,
% 99.57/14.24 | c_Arrow__Order__Mirabelle_OProf) = v9 & hAPP(v7, v4) = v11 &
% 99.57/14.24 | hAPP(v5, v7) = v10 & hAPP(v3, v7) = v8 & $i(v11) & $i(v10) &
% 99.57/14.24 | $i(v9) & $i(v8) & $i(v7))) & ! [v4: $i] : ! [v5: $i] : ( ~
% 99.57/14.24 | (c_Arrow__Order__Mirabelle_Odictator(v5, v4) = 0) | ~ $i(v5) | ~
% 99.57/14.24 | $i(v4) | ! [v6: $i] : ! [v7: $i] : ( ~ (hAPP(v3, v6) = v7) | ~
% 99.57/14.24 | $i(v6) | ? [v8: $i] : ? [v9: any] : ? [v10: $i] : ? [v11: $i]
% 99.57/14.24 | : (hBOOL(v8) = v9 & hAPP(v7, c_Arrow__Order__Mirabelle_OProf) =
% 99.57/14.24 | v8 & hAPP(v6, v4) = v11 & hAPP(v5, v6) = v10 & $i(v11) &
% 99.57/14.24 | $i(v10) & $i(v8) & ( ~ (v9 = 0) | v11 = v10)))))
% 99.57/14.24 |
% 99.57/14.24 | ALPHA: (fact_linear__alt) implies:
% 99.57/14.24 | (6) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 99.57/14.24 | (tc_prod(tc_Arrow__Order__Mirabelle_Oalt,
% 99.57/14.24 | tc_Arrow__Order__Mirabelle_Oalt) = v0 & tc_fun(v0, tc_HOL_Obool) =
% 99.57/14.24 | v1 & c_member(v1) = v2 & $i(v2) & $i(v1) & $i(v0) & ? [v3: $i] : ?
% 99.57/14.24 | [v4: $i] : ? [v5: $i] : (hBOOL(v5) = 0 & hAPP(v4,
% 99.57/14.24 | c_Arrow__Order__Mirabelle_OLin) = v5 & hAPP(v2, v3) = v4 & $i(v5)
% 99.57/14.24 | & $i(v4) & $i(v3)))
% 99.57/14.24 |
% 99.57/14.24 | ALPHA: (fact_mem__def) implies:
% 99.57/14.24 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 99.57/14.24 | ! [v5: $i] : ( ~ (c_member(v2) = v3) | ~ (hAPP(v4, v0) = v5) | ~
% 99.57/14.24 | (hAPP(v3, v1) = v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: $i]
% 99.57/14.24 | : ? [v7: any] : ? [v8: any] : (hBOOL(v6) = v7 & hBOOL(v5) = v8 &
% 99.57/14.24 | hAPP(v0, v1) = v6 & $i(v6) & ( ~ (v7 = 0) | v8 = 0)))
% 99.57/14.24 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 99.57/14.24 | ! [v5: $i] : ( ~ (c_member(v2) = v3) | ~ (hAPP(v4, v0) = v5) | ~
% 99.57/14.24 | (hAPP(v3, v1) = v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6:
% 99.57/14.24 | any] : ? [v7: $i] : ? [v8: any] : (hBOOL(v7) = v8 & hBOOL(v5) =
% 99.57/14.24 | v6 & hAPP(v0, v1) = v7 & $i(v7) & ( ~ (v6 = 0) | v8 = 0)))
% 99.57/14.24 |
% 99.57/14.24 | ALPHA: (fact_in__below) implies:
% 99.99/14.24 | (9) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 99.99/14.24 | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 99.99/14.24 | tc_Arrow__Order__Mirabelle_Oalt) = v4 &
% 99.99/14.24 | tc_prod(tc_Arrow__Order__Mirabelle_Oalt,
% 99.99/14.24 | tc_Arrow__Order__Mirabelle_Oalt) = v0 & tc_fun(v0, tc_HOL_Obool) =
% 99.99/14.24 | v1 & c_member(v1) = v2 & c_member(v0) = v3 & $i(v4) & $i(v3) & $i(v2)
% 99.99/14.24 | & $i(v1) & $i(v0) & ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8:
% 99.99/14.24 | $i] : ! [v9: $i] : ! [v10: $i] : ! [v11: $i] : ! [v12: $i] : !
% 99.99/14.24 | [v13: $i] : ! [v14: $i] : (v9 = v8 | ~
% 99.99/14.24 | (c_Arrow__Order__Mirabelle_Obelow(v7, v9, v8) = v13) | ~
% 99.99/14.24 | (hAPP(v12, v13) = v14) | ~ (hAPP(v10, v5) = v11) | ~ (hAPP(v4,
% 99.99/14.24 | v6) = v10) | ~ (hAPP(v3, v11) = v12) | ~ $i(v9) | ~ $i(v8) |
% 99.99/14.24 | ~ $i(v7) | ~ $i(v6) | ~ $i(v5) | ? [v15: $i] : ? [v16: $i] :
% 99.99/14.24 | ? [v17: any] : ? [v18: any] : ? [v19: $i] : ? [v20: $i] : ?
% 99.99/14.24 | [v21: $i] : ? [v22: any] : ? [v23: $i] : ? [v24: $i] : ? [v25:
% 99.99/14.24 | $i] : ? [v26: $i] : ? [v27: any] : ? [v28: $i] : ? [v29: any]
% 99.99/14.25 | : (hBOOL(v28) = v29 & hBOOL(v26) = v27 & hBOOL(v21) = v22 &
% 99.99/14.25 | hBOOL(v16) = v17 & hBOOL(v14) = v18 & hAPP(v25, v7) = v26 &
% 99.99/14.25 | hAPP(v23, v5) = v24 & hAPP(v20, v7) = v21 & hAPP(v15,
% 99.99/14.25 | c_Arrow__Order__Mirabelle_OLin) = v16 & hAPP(v12, v7) = v28 &
% 99.99/14.25 | hAPP(v10, v8) = v19 & hAPP(v4, v8) = v23 & hAPP(v3, v24) = v25 &
% 99.99/14.25 | hAPP(v3, v19) = v20 & hAPP(v2, v7) = v15 & $i(v28) & $i(v26) &
% 99.99/14.25 | $i(v25) & $i(v24) & $i(v23) & $i(v21) & $i(v20) & $i(v19) &
% 99.99/14.25 | $i(v16) & $i(v15) & ( ~ (v17 = 0) | (( ~ (v18 = 0) | ( ~ (v6 =
% 99.99/14.25 | v5) & ( ~ (v9 = v5) | v22 = 0) & (v9 = v5 | (( ~ (v9 =
% 99.99/14.25 | v6) | v27 = 0 | v8 = v5) & (v29 = 0 | v9 =
% 99.99/14.25 | v6))))) & (v18 = 0 | v6 = v5 | (v9 = v5 & ~ (v22 =
% 99.99/14.25 | 0)) | ( ~ (v9 = v5) & ((v9 = v6 & ~ (v27 = 0) & ~ (v8
% 99.99/14.25 | = v5)) | ( ~ (v29 = 0) & ~ (v9 = v6))))))))))
% 99.99/14.25 |
% 99.99/14.25 | ALPHA: (fact_in__above) implies:
% 99.99/14.25 | (10) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 99.99/14.25 | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 99.99/14.25 | tc_Arrow__Order__Mirabelle_Oalt) = v4 &
% 99.99/14.25 | tc_prod(tc_Arrow__Order__Mirabelle_Oalt,
% 99.99/14.25 | tc_Arrow__Order__Mirabelle_Oalt) = v0 & tc_fun(v0, tc_HOL_Obool) =
% 99.99/14.25 | v1 & c_member(v1) = v2 & c_member(v0) = v3 & $i(v4) & $i(v3) &
% 99.99/14.25 | $i(v2) & $i(v1) & $i(v0) & ! [v5: $i] : ! [v6: $i] : ! [v7: $i] :
% 99.99/14.25 | ! [v8: $i] : ! [v9: $i] : ! [v10: $i] : ! [v11: $i] : ! [v12:
% 99.99/14.25 | $i] : ! [v13: $i] : ! [v14: $i] : (v9 = v8 | ~
% 99.99/14.25 | (c_Arrow__Order__Mirabelle_Oabove(v7, v9, v8) = v13) | ~
% 99.99/14.25 | (hAPP(v12, v13) = v14) | ~ (hAPP(v10, v5) = v11) | ~ (hAPP(v4,
% 99.99/14.25 | v6) = v10) | ~ (hAPP(v3, v11) = v12) | ~ $i(v9) | ~ $i(v8)
% 99.99/14.25 | | ~ $i(v7) | ~ $i(v6) | ~ $i(v5) | ? [v15: $i] : ? [v16: $i]
% 99.99/14.25 | : ? [v17: any] : ? [v18: any] : ? [v19: $i] : ? [v20: $i] : ?
% 99.99/14.25 | [v21: $i] : ? [v22: $i] : ? [v23: any] : ? [v24: $i] : ? [v25:
% 99.99/14.25 | $i] : ? [v26: $i] : ? [v27: any] : ? [v28: $i] : ? [v29:
% 99.99/14.25 | any] : (hBOOL(v28) = v29 & hBOOL(v26) = v27 & hBOOL(v22) = v23 &
% 99.99/14.25 | hBOOL(v16) = v17 & hBOOL(v14) = v18 & hAPP(v25, v7) = v26 &
% 99.99/14.25 | hAPP(v21, v7) = v22 & hAPP(v19, v5) = v20 & hAPP(v15,
% 99.99/14.25 | c_Arrow__Order__Mirabelle_OLin) = v16 & hAPP(v12, v7) = v28 &
% 99.99/14.25 | hAPP(v10, v9) = v24 & hAPP(v4, v9) = v19 & hAPP(v3, v24) = v25 &
% 99.99/14.25 | hAPP(v3, v20) = v21 & hAPP(v2, v7) = v15 & $i(v28) & $i(v26) &
% 99.99/14.25 | $i(v25) & $i(v24) & $i(v22) & $i(v21) & $i(v20) & $i(v19) &
% 99.99/14.25 | $i(v16) & $i(v15) & ( ~ (v17 = 0) | (( ~ (v18 = 0) | ( ~ (v6 =
% 99.99/14.25 | v5) & ( ~ (v8 = v6) | v23 = 0) & (v8 = v6 | (( ~ (v8 =
% 99.99/14.25 | v5) | v27 = 0 | v9 = v6) & (v29 = 0 | v8 =
% 99.99/14.25 | v5))))) & (v18 = 0 | v6 = v5 | (v8 = v6 & ~ (v23
% 99.99/14.25 | = 0)) | ( ~ (v8 = v6) & ((v8 = v5 & ~ (v27 = 0) & ~
% 99.99/14.25 | (v9 = v6)) | ( ~ (v29 = 0) & ~ (v8 = v5))))))))))
% 99.99/14.25 |
% 99.99/14.25 | ALPHA: (fact_converse__in__Lin) implies:
% 99.99/14.25 | (11) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] :
% 99.99/14.25 | (c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt,
% 99.99/14.25 | tc_Arrow__Order__Mirabelle_Oalt) = v3 &
% 99.99/14.25 | tc_prod(tc_Arrow__Order__Mirabelle_Oalt,
% 99.99/14.25 | tc_Arrow__Order__Mirabelle_Oalt) = v0 & tc_fun(v0, tc_HOL_Obool) =
% 99.99/14.25 | v1 & c_member(v1) = v2 & $i(v3) & $i(v2) & $i(v1) & $i(v0) & ! [v4:
% 99.99/14.25 | $i] : ! [v5: $i] : ( ~ (hAPP(v2, v4) = v5) | ~ $i(v4) | ? [v6:
% 99.99/14.25 | $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: any] : ? [v10: $i] :
% 99.99/14.25 | ? [v11: any] : (hBOOL(v10) = v11 & hBOOL(v8) = v9 & hAPP(v7,
% 99.99/14.25 | c_Arrow__Order__Mirabelle_OLin) = v8 & hAPP(v5,
% 99.99/14.25 | c_Arrow__Order__Mirabelle_OLin) = v10 & hAPP(v3, v4) = v6 &
% 99.99/14.25 | hAPP(v2, v6) = v7 & $i(v10) & $i(v8) & $i(v7) & $i(v6) & ( ~ (v9
% 99.99/14.25 | = 0) | v11 = 0))) & ! [v4: $i] : ! [v5: $i] : ( ~
% 99.99/14.25 | (hAPP(v2, v4) = v5) | ~ $i(v4) | ? [v6: $i] : ? [v7: any] : ?
% 99.99/14.25 | [v8: $i] : ? [v9: $i] : ? [v10: $i] : ? [v11: any] :
% 99.99/14.25 | (hBOOL(v10) = v11 & hBOOL(v6) = v7 & hAPP(v9,
% 99.99/14.25 | c_Arrow__Order__Mirabelle_OLin) = v10 & hAPP(v5,
% 99.99/14.25 | c_Arrow__Order__Mirabelle_OLin) = v6 & hAPP(v3, v4) = v8 &
% 99.99/14.25 | hAPP(v2, v8) = v9 & $i(v10) & $i(v9) & $i(v8) & $i(v6) & ( ~ (v7
% 99.99/14.25 | = 0) | v11 = 0))))
% 99.99/14.25 |
% 99.99/14.25 | ALPHA: (fact_Lin__irrefl) implies:
% 99.99/14.25 | (12) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 99.99/14.25 | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 99.99/14.25 | tc_Arrow__Order__Mirabelle_Oalt) = v4 &
% 99.99/14.25 | tc_prod(tc_Arrow__Order__Mirabelle_Oalt,
% 99.99/14.25 | tc_Arrow__Order__Mirabelle_Oalt) = v0 & tc_fun(v0, tc_HOL_Obool) =
% 99.99/14.25 | v1 & c_member(v1) = v2 & c_member(v0) = v3 & $i(v4) & $i(v3) &
% 99.99/14.25 | $i(v2) & $i(v1) & $i(v0) & ! [v5: $i] : ! [v6: $i] : ! [v7: $i] :
% 99.99/14.25 | ! [v8: $i] : ! [v9: $i] : ! [v10: $i] : ! [v11: $i] : ( ~
% 99.99/14.25 | (hAPP(v10, v7) = v11) | ~ (hAPP(v8, v6) = v9) | ~ (hAPP(v4, v5)
% 99.99/14.25 | = v8) | ~ (hAPP(v3, v9) = v10) | ~ $i(v7) | ~ $i(v6) | ~
% 99.99/14.25 | $i(v5) | ? [v12: $i] : ? [v13: $i] : ? [v14: any] : ? [v15:
% 99.99/14.25 | $i] : ? [v16: $i] : ? [v17: $i] : ? [v18: $i] : ? [v19: any]
% 99.99/14.25 | : ? [v20: any] : (hBOOL(v18) = v19 & hBOOL(v13) = v14 &
% 99.99/14.25 | hBOOL(v11) = v20 & hAPP(v17, v7) = v18 & hAPP(v15, v5) = v16 &
% 99.99/14.25 | hAPP(v12, c_Arrow__Order__Mirabelle_OLin) = v13 & hAPP(v4, v6) =
% 99.99/14.25 | v15 & hAPP(v3, v16) = v17 & hAPP(v2, v7) = v12 & $i(v18) &
% 99.99/14.25 | $i(v17) & $i(v16) & $i(v15) & $i(v13) & $i(v12) & ( ~ (v20 = 0)
% 99.99/14.25 | | ~ (v19 = 0) | ~ (v14 = 0)))))
% 99.99/14.25 |
% 99.99/14.25 | ALPHA: (fact_notin__Lin__iff) implies:
% 99.99/14.25 | (13) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 99.99/14.26 | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 99.99/14.26 | tc_Arrow__Order__Mirabelle_Oalt) = v4 &
% 99.99/14.26 | tc_prod(tc_Arrow__Order__Mirabelle_Oalt,
% 99.99/14.26 | tc_Arrow__Order__Mirabelle_Oalt) = v0 & tc_fun(v0, tc_HOL_Obool) =
% 99.99/14.26 | v1 & c_member(v1) = v2 & c_member(v0) = v3 & $i(v4) & $i(v3) &
% 99.99/14.26 | $i(v2) & $i(v1) & $i(v0) & ! [v5: $i] : ! [v6: $i] : ! [v7: $i] :
% 99.99/14.26 | ! [v8: $i] : ! [v9: $i] : ! [v10: $i] : ! [v11: $i] : (v6 = v5 |
% 99.99/14.26 | ~ (hAPP(v10, v7) = v11) | ~ (hAPP(v8, v6) = v9) | ~ (hAPP(v4,
% 99.99/14.26 | v5) = v8) | ~ (hAPP(v3, v9) = v10) | ~ $i(v7) | ~ $i(v6) |
% 99.99/14.26 | ~ $i(v5) | ? [v12: $i] : ? [v13: $i] : ? [v14: any] : ? [v15:
% 99.99/14.26 | $i] : ? [v16: $i] : ? [v17: $i] : ? [v18: $i] : ? [v19: any]
% 99.99/14.26 | : ? [v20: any] : (hBOOL(v18) = v19 & hBOOL(v13) = v14 &
% 99.99/14.26 | hBOOL(v11) = v20 & hAPP(v17, v7) = v18 & hAPP(v15, v5) = v16 &
% 99.99/14.26 | hAPP(v12, c_Arrow__Order__Mirabelle_OLin) = v13 & hAPP(v4, v6) =
% 99.99/14.26 | v15 & hAPP(v3, v16) = v17 & hAPP(v2, v7) = v12 & $i(v18) &
% 99.99/14.26 | $i(v17) & $i(v16) & $i(v15) & $i(v13) & $i(v12) & ( ~ (v14 = 0)
% 99.99/14.26 | | (( ~ (v20 = 0) | ~ (v19 = 0)) & (v20 = 0 | v19 = 0))))))
% 99.99/14.26 |
% 99.99/14.26 | ALPHA: (fact_in__mkbot) implies:
% 99.99/14.26 | (14) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 99.99/14.26 | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 99.99/14.26 | tc_Arrow__Order__Mirabelle_Oalt) = v2 &
% 99.99/14.26 | tc_prod(tc_Arrow__Order__Mirabelle_Oalt,
% 99.99/14.26 | tc_Arrow__Order__Mirabelle_Oalt) = v0 & c_member(v0) = v1 & $i(v2)
% 99.99/14.26 | & $i(v1) & $i(v0) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : !
% 99.99/14.26 | [v6: $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : ! [v10: $i] :
% 99.99/14.26 | ! [v11: $i] : (v5 = v3 | ~ (c_Arrow__Order__Mirabelle_Omkbot(v4,
% 99.99/14.26 | v3) = v10) | ~ (hAPP(v9, v10) = v11) | ~ (hAPP(v7, v5) = v8)
% 99.99/14.26 | | ~ (hAPP(v2, v6) = v7) | ~ (hAPP(v1, v8) = v9) | ~ $i(v6) | ~
% 99.99/14.26 | $i(v5) | ~ $i(v4) | ~ $i(v3) | ? [v12: $i] : ? [v13: any] : ?
% 99.99/14.26 | [v14: any] : (hBOOL(v12) = v13 & hBOOL(v11) = v14 & hAPP(v9, v4) =
% 99.99/14.26 | v12 & $i(v12) & (v14 = 0 | ( ~ (v13 = 0) & ~ (v6 = v3))))) & !
% 99.99/14.26 | [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] :
% 99.99/14.26 | ! [v8: $i] : ! [v9: $i] : ! [v10: $i] : ! [v11: $i] : ( ~
% 99.99/14.26 | (c_Arrow__Order__Mirabelle_Omkbot(v4, v3) = v10) | ~ (hAPP(v9,
% 99.99/14.26 | v10) = v11) | ~ (hAPP(v7, v5) = v8) | ~ (hAPP(v2, v6) = v7)
% 99.99/14.26 | | ~ (hAPP(v1, v8) = v9) | ~ $i(v6) | ~ $i(v5) | ~ $i(v4) | ~
% 99.99/14.26 | $i(v3) | ? [v12: any] : ? [v13: $i] : ? [v14: any] :
% 99.99/14.26 | (hBOOL(v13) = v14 & hBOOL(v11) = v12 & hAPP(v9, v4) = v13 &
% 99.99/14.26 | $i(v13) & ( ~ (v12 = 0) | ( ~ (v5 = v3) & (v14 = 0 | v6 =
% 99.99/14.26 | v3))))))
% 99.99/14.26 |
% 99.99/14.26 | ALPHA: (fact_in__mktop) implies:
% 99.99/14.26 | (15) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 99.99/14.26 | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 99.99/14.26 | tc_Arrow__Order__Mirabelle_Oalt) = v2 &
% 99.99/14.26 | tc_prod(tc_Arrow__Order__Mirabelle_Oalt,
% 99.99/14.26 | tc_Arrow__Order__Mirabelle_Oalt) = v0 & c_member(v0) = v1 & $i(v2)
% 99.99/14.26 | & $i(v1) & $i(v0) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : !
% 99.99/14.26 | [v6: $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : ! [v10: $i] :
% 99.99/14.26 | ! [v11: $i] : (v6 = v3 | ~ (c_Arrow__Order__Mirabelle_Omktop(v4,
% 99.99/14.26 | v3) = v10) | ~ (hAPP(v9, v10) = v11) | ~ (hAPP(v7, v5) = v8)
% 99.99/14.26 | | ~ (hAPP(v2, v6) = v7) | ~ (hAPP(v1, v8) = v9) | ~ $i(v6) | ~
% 99.99/14.26 | $i(v5) | ~ $i(v4) | ~ $i(v3) | ? [v12: $i] : ? [v13: any] : ?
% 99.99/14.26 | [v14: any] : (hBOOL(v12) = v13 & hBOOL(v11) = v14 & hAPP(v9, v4) =
% 99.99/14.26 | v12 & $i(v12) & (v14 = 0 | ( ~ (v13 = 0) & ~ (v5 = v3))))) & !
% 99.99/14.26 | [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] :
% 99.99/14.26 | ! [v8: $i] : ! [v9: $i] : ! [v10: $i] : ! [v11: $i] : ( ~
% 99.99/14.26 | (c_Arrow__Order__Mirabelle_Omktop(v4, v3) = v10) | ~ (hAPP(v9,
% 99.99/14.26 | v10) = v11) | ~ (hAPP(v7, v5) = v8) | ~ (hAPP(v2, v6) = v7)
% 99.99/14.26 | | ~ (hAPP(v1, v8) = v9) | ~ $i(v6) | ~ $i(v5) | ~ $i(v4) | ~
% 99.99/14.26 | $i(v3) | ? [v12: any] : ? [v13: $i] : ? [v14: any] :
% 99.99/14.26 | (hBOOL(v13) = v14 & hBOOL(v11) = v12 & hAPP(v9, v4) = v13 &
% 99.99/14.26 | $i(v13) & ( ~ (v12 = 0) | ( ~ (v6 = v3) & (v14 = 0 | v5 =
% 99.99/14.26 | v3))))))
% 99.99/14.26 |
% 99.99/14.26 | ALPHA: (fact_dictatorI) implies:
% 99.99/14.26 | (16) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 99.99/14.26 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] :
% 99.99/14.26 | ? [v10: $i] : (c_COMBK(v5, v2, c_Arrow__Order__Mirabelle_OLin) = v6 &
% 99.99/14.26 | c_FuncSet_OPi(v2, v1, c_Arrow__Order__Mirabelle_OProf, v6) = v7 &
% 99.99/14.26 | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 99.99/14.26 | tc_Arrow__Order__Mirabelle_Oalt) = v10 &
% 99.99/14.26 | tc_prod(tc_Arrow__Order__Mirabelle_Oalt,
% 99.99/14.26 | tc_Arrow__Order__Mirabelle_Oalt) = v0 & tc_fun(v2, v1) = v3 &
% 99.99/14.26 | tc_fun(v1, tc_HOL_Obool) = v5 & tc_fun(v0, tc_HOL_Obool) = v1 &
% 99.99/14.26 | tc_fun(tc_Arrow__Order__Mirabelle_Oindi, v1) = v2 & c_member(v3) =
% 99.99/14.26 | v4 & c_member(v2) = v8 & c_member(v0) = v9 & $i(v10) & $i(v9) &
% 99.99/14.26 | $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) &
% 99.99/14.26 | $i(v1) & $i(v0) & ! [v11: $i] : ! [v12: $i] : ! [v13: int] : (v13
% 99.99/14.26 | = 0 | ~ (c_Arrow__Order__Mirabelle_Odictator(v12, v11) = v13) |
% 99.99/14.26 | ~ $i(v12) | ~ $i(v11) | ? [v14: $i] : ? [v15: $i] : ? [v16:
% 99.99/14.26 | $i] : ? [v17: $i] : ? [v18: $i] : (hBOOL(v16) = 0 & hAPP(v15,
% 99.99/14.26 | c_Arrow__Order__Mirabelle_OProf) = v16 & hAPP(v14, v11) = v17
% 99.99/14.26 | & hAPP(v12, v14) = v18 & hAPP(v8, v14) = v15 & $i(v18) & $i(v17)
% 99.99/14.26 | & $i(v16) & $i(v15) & $i(v14) & ? [v19: $i] : ? [v20: $i] : ?
% 99.99/14.26 | [v21: $i] : ? [v22: $i] : ? [v23: $i] : ? [v24: $i] : ?
% 99.99/14.26 | [v25: $i] : ? [v26: int] : ( ~ (v26 = 0) & ~ (v20 = v19) &
% 99.99/14.26 | hBOOL(v25) = v26 & hBOOL(v24) = 0 & hAPP(v23, v18) = v25 &
% 99.99/14.26 | hAPP(v23, v17) = v24 & hAPP(v21, v20) = v22 & hAPP(v10, v19) =
% 99.99/14.26 | v21 & hAPP(v9, v22) = v23 & $i(v25) & $i(v24) & $i(v23) &
% 99.99/14.26 | $i(v22) & $i(v21) & $i(v20) & $i(v19))) | ? [v14: $i] : ?
% 99.99/14.26 | [v15: $i] : ? [v16: int] : ( ~ (v16 = 0) & hBOOL(v15) = v16 &
% 99.99/14.26 | hAPP(v14, v7) = v15 & hAPP(v4, v12) = v14 & $i(v15) & $i(v14))))
% 99.99/14.26 |
% 99.99/14.26 | ALPHA: (fact_unanimity__def) implies:
% 99.99/14.27 | (17) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 99.99/14.27 | ? [v5: $i] : (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 99.99/14.27 | tc_Arrow__Order__Mirabelle_Oalt) = v5 &
% 99.99/14.27 | tc_prod(tc_Arrow__Order__Mirabelle_Oalt,
% 99.99/14.27 | tc_Arrow__Order__Mirabelle_Oalt) = v0 & tc_fun(v0, tc_HOL_Obool) =
% 99.99/14.27 | v1 & tc_fun(tc_Arrow__Order__Mirabelle_Oindi, v1) = v2 &
% 99.99/14.27 | c_member(v2) = v3 & c_member(v0) = v4 & $i(v5) & $i(v4) & $i(v3) &
% 99.99/14.27 | $i(v2) & $i(v1) & $i(v0) & ! [v6: $i] : ! [v7: int] : (v7 = 0 | ~
% 99.99/14.27 | (c_Arrow__Order__Mirabelle_Ounanimity(v6) = v7) | ~ $i(v6) | ?
% 99.99/14.27 | [v8: $i] : ? [v9: $i] : ? [v10: $i] : ? [v11: $i] : (hBOOL(v10)
% 99.99/14.27 | = 0 & hAPP(v9, c_Arrow__Order__Mirabelle_OProf) = v10 & hAPP(v6,
% 99.99/14.27 | v8) = v11 & hAPP(v3, v8) = v9 & $i(v11) & $i(v10) & $i(v9) &
% 99.99/14.27 | $i(v8) & ? [v12: $i] : ? [v13: $i] : ? [v14: $i] : ? [v15:
% 99.99/14.27 | $i] : ? [v16: $i] : ? [v17: $i] : ? [v18: int] : ( ~ (v18 =
% 99.99/14.27 | 0) & hBOOL(v17) = v18 & hAPP(v16, v11) = v17 & hAPP(v14,
% 99.99/14.27 | v13) = v15 & hAPP(v5, v12) = v14 & hAPP(v4, v15) = v16 &
% 99.99/14.27 | $i(v17) & $i(v16) & $i(v15) & $i(v14) & $i(v13) & $i(v12) & !
% 99.99/14.27 | [v19: $i] : ! [v20: $i] : ! [v21: $i] : ( ~ (hAPP(v16, v20)
% 99.99/14.27 | = v21) | ~ (hAPP(v8, v19) = v20) | ~ $i(v19) |
% 99.99/14.27 | hBOOL(v21) = 0)))) & ! [v6: $i] : ( ~
% 99.99/14.27 | (c_Arrow__Order__Mirabelle_Ounanimity(v6) = 0) | ~ $i(v6) | !
% 99.99/14.27 | [v7: $i] : ! [v8: $i] : ( ~ (hAPP(v3, v7) = v8) | ~ $i(v7) | ?
% 99.99/14.27 | [v9: $i] : ? [v10: any] : ? [v11: $i] : (hBOOL(v9) = v10 &
% 99.99/14.27 | hAPP(v8, c_Arrow__Order__Mirabelle_OProf) = v9 & hAPP(v6, v7)
% 99.99/14.27 | = v11 & $i(v11) & $i(v9) & ( ~ (v10 = 0) | ! [v12: $i] : !
% 99.99/14.27 | [v13: $i] : ! [v14: $i] : ! [v15: $i] : ! [v16: $i] : !
% 99.99/14.27 | [v17: $i] : ( ~ (hAPP(v16, v11) = v17) | ~ (hAPP(v14, v13)
% 99.99/14.27 | = v15) | ~ (hAPP(v5, v12) = v14) | ~ (hAPP(v4, v15) =
% 99.99/14.27 | v16) | ~ $i(v13) | ~ $i(v12) | hBOOL(v17) = 0 | ?
% 99.99/14.27 | [v18: $i] : ? [v19: $i] : ? [v20: $i] : ? [v21: int] :
% 99.99/14.27 | ( ~ (v21 = 0) & hBOOL(v20) = v21 & hAPP(v16, v19) = v20 &
% 99.99/14.27 | hAPP(v7, v18) = v19 & $i(v20) & $i(v19) & $i(v18))))))))
% 99.99/14.27 |
% 99.99/14.27 | ALPHA: (fact_IIA__def) implies:
% 99.99/14.27 | (18) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 99.99/14.27 | ? [v5: $i] : (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 99.99/14.27 | tc_Arrow__Order__Mirabelle_Oalt) = v5 &
% 99.99/14.27 | tc_prod(tc_Arrow__Order__Mirabelle_Oalt,
% 99.99/14.27 | tc_Arrow__Order__Mirabelle_Oalt) = v0 & tc_fun(v0, tc_HOL_Obool) =
% 99.99/14.27 | v1 & tc_fun(tc_Arrow__Order__Mirabelle_Oindi, v1) = v2 &
% 99.99/14.27 | c_member(v2) = v3 & c_member(v0) = v4 & $i(v5) & $i(v4) & $i(v3) &
% 99.99/14.27 | $i(v2) & $i(v1) & $i(v0) & ! [v6: $i] : ! [v7: int] : (v7 = 0 | ~
% 99.99/14.27 | (c_Arrow__Order__Mirabelle_OIIA(v6) = v7) | ~ $i(v6) | ? [v8:
% 99.99/14.27 | $i] : ? [v9: $i] : ? [v10: $i] : ? [v11: $i] : (hBOOL(v10) =
% 99.99/14.27 | 0 & hAPP(v9, c_Arrow__Order__Mirabelle_OProf) = v10 & hAPP(v6,
% 99.99/14.27 | v8) = v11 & hAPP(v3, v8) = v9 & $i(v11) & $i(v10) & $i(v9) &
% 99.99/14.27 | $i(v8) & ? [v12: $i] : ? [v13: $i] : ? [v14: $i] : ? [v15:
% 99.99/14.27 | $i] : (hBOOL(v14) = 0 & hAPP(v13,
% 99.99/14.27 | c_Arrow__Order__Mirabelle_OProf) = v14 & hAPP(v6, v12) = v15
% 99.99/14.27 | & hAPP(v3, v12) = v13 & $i(v15) & $i(v14) & $i(v13) & $i(v12)
% 99.99/14.27 | & ? [v16: $i] : ? [v17: $i] : ? [v18: $i] : ? [v19: $i] :
% 99.99/14.27 | ? [v20: $i] : ? [v21: $i] : ? [v22: any] : ? [v23: $i] : ?
% 99.99/14.27 | [v24: any] : (hBOOL(v23) = v24 & hBOOL(v21) = v22 & hAPP(v20,
% 99.99/14.27 | v15) = v23 & hAPP(v20, v11) = v21 & hAPP(v18, v17) = v19 &
% 99.99/14.27 | hAPP(v5, v16) = v18 & hAPP(v4, v19) = v20 & $i(v23) &
% 99.99/14.27 | $i(v21) & $i(v20) & $i(v19) & $i(v18) & $i(v17) & $i(v16) &
% 99.99/14.27 | ! [v25: $i] : ! [v26: $i] : ! [v27: $i] : ( ~ (hAPP(v20,
% 99.99/14.27 | v26) = v27) | ~ (hAPP(v8, v25) = v26) | ~ $i(v25) |
% 99.99/14.27 | ? [v28: any] : ? [v29: $i] : ? [v30: $i] : ? [v31: any]
% 99.99/14.27 | : (hBOOL(v30) = v31 & hBOOL(v27) = v28 & hAPP(v20, v29) =
% 99.99/14.27 | v30 & hAPP(v12, v25) = v29 & $i(v30) & $i(v29) & ( ~
% 99.99/14.27 | (v28 = 0) | v31 = 0))) & ! [v25: $i] : ! [v26: $i] :
% 99.99/14.27 | ! [v27: $i] : ( ~ (hAPP(v20, v26) = v27) | ~ (hAPP(v8,
% 99.99/14.27 | v25) = v26) | ~ $i(v25) | ? [v28: $i] : ? [v29: $i]
% 99.99/14.27 | : ? [v30: any] : ? [v31: any] : (hBOOL(v29) = v30 &
% 99.99/14.27 | hBOOL(v27) = v31 & hAPP(v20, v28) = v29 & hAPP(v12, v25)
% 99.99/14.27 | = v28 & $i(v29) & $i(v28) & ( ~ (v30 = 0) | v31 = 0))) &
% 99.99/14.27 | ( ~ (v24 = 0) | ~ (v22 = 0)) & (v24 = 0 | v22 = 0))))) & !
% 99.99/14.27 | [v6: $i] : ( ~ (c_Arrow__Order__Mirabelle_OIIA(v6) = 0) | ~ $i(v6)
% 99.99/14.27 | | ! [v7: $i] : ! [v8: $i] : ( ~ (hAPP(v3, v7) = v8) | ~ $i(v7)
% 99.99/14.27 | | ? [v9: $i] : ? [v10: any] : ? [v11: $i] : (hBOOL(v9) = v10
% 99.99/14.27 | & hAPP(v8, c_Arrow__Order__Mirabelle_OProf) = v9 & hAPP(v6,
% 99.99/14.27 | v7) = v11 & $i(v11) & $i(v9) & ( ~ (v10 = 0) | ! [v12: $i]
% 99.99/14.27 | : ! [v13: $i] : ( ~ (hAPP(v3, v12) = v13) | ~ $i(v12) | ?
% 99.99/14.27 | [v14: $i] : ? [v15: any] : ? [v16: $i] : (hBOOL(v14) =
% 99.99/14.27 | v15 & hAPP(v13, c_Arrow__Order__Mirabelle_OProf) = v14 &
% 99.99/14.27 | hAPP(v6, v12) = v16 & $i(v16) & $i(v14) & ( ~ (v15 = 0)
% 99.99/14.27 | | ! [v17: $i] : ! [v18: $i] : ! [v19: $i] : !
% 99.99/14.27 | [v20: $i] : ! [v21: $i] : ! [v22: $i] : ( ~
% 99.99/14.27 | (hAPP(v21, v11) = v22) | ~ (hAPP(v19, v18) = v20) |
% 99.99/14.27 | ~ (hAPP(v5, v17) = v19) | ~ (hAPP(v4, v20) = v21)
% 99.99/14.27 | | ~ $i(v18) | ~ $i(v17) | ? [v23: $i] : ? [v24:
% 99.99/14.27 | $i] : ? [v25: $i] : ? [v26: any] : ? [v27: $i]
% 99.99/14.27 | : ? [v28: $i] : ? [v29: any] : (hBOOL(v28) = v29 &
% 99.99/14.27 | hBOOL(v25) = v26 & hAPP(v21, v27) = v28 &
% 99.99/14.27 | hAPP(v21, v24) = v25 & hAPP(v12, v23) = v27 &
% 99.99/14.27 | hAPP(v7, v23) = v24 & $i(v28) & $i(v27) & $i(v25)
% 99.99/14.27 | & $i(v24) & $i(v23) & ( ~ (v29 = 0) | ~ (v26 =
% 99.99/14.27 | 0)) & (v29 = 0 | v26 = 0)) | ? [v23: any] :
% 99.99/14.27 | ? [v24: $i] : ? [v25: any] : (hBOOL(v24) = v25 &
% 99.99/14.27 | hBOOL(v22) = v23 & hAPP(v21, v16) = v24 & $i(v24)
% 99.99/14.27 | & ( ~ (v25 = 0) | v23 = 0) & ( ~ (v23 = 0) | v25 =
% 99.99/14.27 | 0)))))))))))
% 99.99/14.27 |
% 99.99/14.27 | ALPHA: (fact_Prof__def) implies:
% 99.99/14.27 | (19) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 99.99/14.27 | ? [v5: $i] : (c_COMBK(v4, tc_Arrow__Order__Mirabelle_Oindi,
% 99.99/14.27 | c_Arrow__Order__Mirabelle_OLin) = v5 &
% 99.99/14.27 | c_FuncSet_OPi(tc_Arrow__Order__Mirabelle_Oindi, v1, v3, v5) =
% 99.99/14.27 | c_Arrow__Order__Mirabelle_OProf & c_Orderings_Otop__class_Otop(v2) =
% 99.99/14.27 | v3 & tc_prod(tc_Arrow__Order__Mirabelle_Oalt,
% 99.99/14.27 | tc_Arrow__Order__Mirabelle_Oalt) = v0 & tc_fun(v1, tc_HOL_Obool) =
% 99.99/14.27 | v4 & tc_fun(v0, tc_HOL_Obool) = v1 &
% 99.99/14.27 | tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_HOL_Obool) = v2 & $i(v5)
% 99.99/14.27 | & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 99.99/14.27 |
% 99.99/14.27 | ALPHA: (fact_funcsetI) implies:
% 99.99/14.28 | (20) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 99.99/14.28 | ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] :
% 99.99/14.28 | ! [v10: $i] : ! [v11: $i] : ( ~ (c_COMBK(v8, v4, v0) = v9) | ~
% 99.99/14.28 | (c_FuncSet_OPi(v4, v2, v3, v9) = v10) | ~ (tc_fun(v4, v2) = v5) |
% 99.99/14.28 | ~ (tc_fun(v2, tc_HOL_Obool) = v8) | ~ (c_member(v5) = v6) | ~
% 99.99/14.28 | (hAPP(v7, v10) = v11) | ~ (hAPP(v6, v1) = v7) | ~ $i(v4) | ~
% 99.99/14.28 | $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v12: $i] : ? [v13:
% 99.99/14.28 | $i] : ? [v14: any] : (c_member(v4) = v12 & c_member(v2) = v13 &
% 99.99/14.28 | hBOOL(v11) = v14 & $i(v13) & $i(v12) & (v14 = 0 | ? [v15: $i] :
% 99.99/14.28 | ? [v16: $i] : ? [v17: $i] : ? [v18: $i] : ? [v19: $i] : ?
% 99.99/14.28 | [v20: $i] : ? [v21: int] : ( ~ (v21 = 0) & hBOOL(v20) = v21 &
% 99.99/14.28 | hBOOL(v17) = 0 & hAPP(v19, v0) = v20 & hAPP(v16, v3) = v17 &
% 99.99/14.28 | hAPP(v13, v18) = v19 & hAPP(v12, v15) = v16 & hAPP(v1, v15) =
% 99.99/14.28 | v18 & $i(v20) & $i(v19) & $i(v18) & $i(v17) & $i(v16) &
% 99.99/14.28 | $i(v15)))))
% 99.99/14.28 |
% 99.99/14.28 | ALPHA: (fact_compose__Id) implies:
% 99.99/14.28 | (21) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 99.99/14.28 | ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] :
% 99.99/14.28 | ! [v10: $i] : ! [v11: $i] : ( ~ (c_COMBK(v8, v4, v0) = v9) | ~
% 99.99/14.28 | (c_FuncSet_OPi(v4, v3, v1, v9) = v10) | ~ (tc_fun(v4, v3) = v5) |
% 99.99/14.28 | ~ (tc_fun(v3, tc_HOL_Obool) = v8) | ~ (c_member(v5) = v6) | ~
% 99.99/14.28 | (hAPP(v7, v10) = v11) | ~ (hAPP(v6, v2) = v7) | ~ $i(v4) | ~
% 99.99/14.28 | $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v12: any] : ?
% 99.99/14.28 | [v13: $i] : ? [v14: $i] : ? [v15: any] : ? [v16: $i] : ? [v17:
% 99.99/14.28 | $i] : ? [v18: $i] : (c_FuncSet_Orestrict(v4, v4, v16, v1) = v17 &
% 99.99/14.28 | c_FuncSet_Oextensional(v4, v3, v1) = v13 & c_FuncSet_Ocompose(v4,
% 99.99/14.28 | v4, v3, v1, v2, v17) = v18 & c_COMBI(v4) = v16 & hBOOL(v14) =
% 99.99/14.28 | v15 & hBOOL(v11) = v12 & hAPP(v7, v13) = v14 & $i(v18) & $i(v17) &
% 99.99/14.28 | $i(v16) & $i(v14) & $i(v13) & ( ~ (v15 = 0) | ~ (v12 = 0) | v18 =
% 99.99/14.28 | v2)))
% 99.99/14.28 |
% 99.99/14.28 | ALPHA: (fact_Id__compose) implies:
% 99.99/14.28 | (22) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 99.99/14.28 | ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] :
% 99.99/14.28 | ! [v10: $i] : ! [v11: $i] : ( ~ (c_COMBK(v8, v4, v0) = v9) | ~
% 99.99/14.28 | (c_FuncSet_OPi(v4, v3, v1, v9) = v10) | ~ (tc_fun(v4, v3) = v5) |
% 99.99/14.28 | ~ (tc_fun(v3, tc_HOL_Obool) = v8) | ~ (c_member(v5) = v6) | ~
% 99.99/14.28 | (hAPP(v7, v10) = v11) | ~ (hAPP(v6, v2) = v7) | ~ $i(v4) | ~
% 99.99/14.28 | $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v12: any] : ?
% 99.99/14.28 | [v13: $i] : ? [v14: $i] : ? [v15: any] : ? [v16: $i] : ? [v17:
% 99.99/14.28 | $i] : ? [v18: $i] : (c_FuncSet_Orestrict(v3, v3, v16, v0) = v17 &
% 99.99/14.28 | c_FuncSet_Oextensional(v4, v3, v1) = v13 & c_FuncSet_Ocompose(v4,
% 99.99/14.28 | v3, v3, v1, v17, v2) = v18 & c_COMBI(v3) = v16 & hBOOL(v14) =
% 99.99/14.28 | v15 & hBOOL(v11) = v12 & hAPP(v7, v13) = v14 & $i(v18) & $i(v17) &
% 99.99/14.28 | $i(v16) & $i(v14) & $i(v13) & ( ~ (v15 = 0) | ~ (v12 = 0) | v18 =
% 99.99/14.28 | v2)))
% 99.99/14.28 |
% 99.99/14.28 | ALPHA: (fact_Pi__eq__empty) implies:
% 99.99/14.28 | (23) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 99.99/14.28 | ( ~ (c_FuncSet_OPi(v3, v2, v1, v0) = v4) | ~ $i(v3) | ~ $i(v2) | ~
% 99.99/14.28 | $i(v1) | ~ $i(v0) | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ?
% 99.99/14.28 | [v8: $i] : ? [v9: $i] : ? [v10: $i] :
% 99.99/14.28 | (c_Orderings_Obot__class_Obot(v9) = v10 &
% 99.99/14.28 | c_Orderings_Obot__class_Obot(v6) = v7 & tc_fun(v5, tc_HOL_Obool) =
% 99.99/14.28 | v6 & tc_fun(v3, v2) = v5 & tc_fun(v2, tc_HOL_Obool) = v9 &
% 99.99/14.28 | c_member(v3) = v8 & $i(v10) & $i(v9) & $i(v8) & $i(v7) & $i(v6) &
% 99.99/14.28 | $i(v5) & ( ~ (v7 = v4) | ? [v11: $i] : ? [v12: $i] : ? [v13:
% 99.99/14.28 | $i] : (hBOOL(v13) = 0 & hAPP(v12, v1) = v13 & hAPP(v8, v11) =
% 99.99/14.28 | v12 & hAPP(v0, v11) = v10 & $i(v13) & $i(v12) & $i(v11)))))
% 99.99/14.28 | (24) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 99.99/14.28 | ( ~ (c_FuncSet_OPi(v3, v2, v1, v0) = v4) | ~ $i(v3) | ~ $i(v2) | ~
% 99.99/14.28 | $i(v1) | ~ $i(v0) | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ?
% 99.99/14.28 | [v8: $i] : ? [v9: $i] : ? [v10: $i] :
% 99.99/14.28 | (c_Orderings_Obot__class_Obot(v9) = v10 &
% 99.99/14.28 | c_Orderings_Obot__class_Obot(v6) = v7 & tc_fun(v8, tc_HOL_Obool) =
% 99.99/14.28 | v9 & tc_fun(v3, v2) = v8 & tc_fun(v2, tc_HOL_Obool) = v6 &
% 99.99/14.28 | c_member(v3) = v5 & $i(v10) & $i(v9) & $i(v8) & $i(v7) & $i(v6) &
% 99.99/14.28 | $i(v5) & (v10 = v4 | ! [v11: $i] : ! [v12: $i] : ! [v13: $i] :
% 99.99/14.28 | ( ~ (hAPP(v12, v1) = v13) | ~ (hAPP(v5, v11) = v12) | ~
% 99.99/14.28 | $i(v11) | ? [v14: any] : ? [v15: $i] : (hBOOL(v13) = v14 &
% 99.99/14.28 | hAPP(v0, v11) = v15 & $i(v15) & ( ~ (v15 = v7) | ~ (v14 =
% 99.99/14.28 | 0)))))))
% 99.99/14.28 |
% 99.99/14.28 | ALPHA: (fact_equals0D) implies:
% 99.99/14.28 | (25) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 99.99/14.28 | ! [v5: $i] : ( ~ (c_member(v1) = v3) | ~ (hAPP(v4, v2) = v5) | ~
% 99.99/14.28 | (hAPP(v3, v0) = v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6:
% 99.99/14.28 | $i] : ? [v7: $i] : ? [v8: any] :
% 99.99/14.28 | (c_Orderings_Obot__class_Obot(v6) = v7 & tc_fun(v1, tc_HOL_Obool) =
% 99.99/14.28 | v6 & hBOOL(v5) = v8 & $i(v7) & $i(v6) & ( ~ (v8 = 0) | ~ (v7 =
% 99.99/14.28 | v2))))
% 99.99/14.28 |
% 99.99/14.28 | ALPHA: (arity_HOL__Obool__Complete__Lattice_Ocomplete__lattice) implies:
% 99.99/14.28 | (26) class_Complete__Lattice_Ocomplete__lattice(tc_HOL_Obool) = 0
% 99.99/14.28 |
% 99.99/14.28 | ALPHA: (conj_0) implies:
% 99.99/14.28 | (27) $i(c_Arrow__Order__Mirabelle_OLin)
% 99.99/14.28 | (28) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 99.99/14.28 | (tc_prod(tc_Arrow__Order__Mirabelle_Oalt,
% 99.99/14.28 | tc_Arrow__Order__Mirabelle_Oalt) = v0 & tc_fun(v0, tc_HOL_Obool) =
% 99.99/14.28 | v1 & c_member(v1) = v2 & hBOOL(v4) = 0 & hAPP(v3,
% 99.99/14.28 | c_Arrow__Order__Mirabelle_OLin) = v4 & hAPP(v2, v_L) = v3 & $i(v4)
% 99.99/14.28 | & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 99.99/14.28 |
% 99.99/14.28 | ALPHA: (conj_1) implies:
% 100.17/14.28 | (29) $i(tc_HOL_Obool)
% 100.17/14.28 | (30) $i(tc_Arrow__Order__Mirabelle_Oindi)
% 100.17/14.28 | (31) $i(c_Arrow__Order__Mirabelle_OProf)
% 100.17/14.28 | (32) $i(v_L)
% 100.17/14.29 | (33) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 100.17/14.29 | ? [v5: $i] : ? [v6: $i] : ? [v7: int] : ( ~ (v7 = 0) & c_COMBK(v1,
% 100.17/14.29 | tc_Arrow__Order__Mirabelle_Oindi, v_L) = v4 &
% 100.17/14.29 | tc_prod(tc_Arrow__Order__Mirabelle_Oalt,
% 100.17/14.29 | tc_Arrow__Order__Mirabelle_Oalt) = v0 & tc_fun(v0, tc_HOL_Obool) =
% 100.17/14.29 | v1 & tc_fun(tc_Arrow__Order__Mirabelle_Oindi, v1) = v2 &
% 100.17/14.29 | c_member(v2) = v3 & hBOOL(v6) = v7 & hAPP(v5,
% 100.17/14.29 | c_Arrow__Order__Mirabelle_OProf) = v6 & hAPP(v3, v4) = v5 & $i(v6)
% 100.17/14.29 | & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 100.17/14.29 |
% 100.17/14.29 | ALPHA: (function-axioms) implies:
% 100.17/14.29 | (34) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 100.17/14.29 | : (v1 = v0 | ~ (hBOOL(v2) = v1) | ~ (hBOOL(v2) = v0))
% 100.17/14.29 | (35) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (c_member(v2)
% 100.17/14.29 | = v1) | ~ (c_member(v2) = v0))
% 100.17/14.29 | (36) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 100.17/14.29 | : (v1 = v0 | ~ (class_Complete__Lattice_Ocomplete__lattice(v2) = v1)
% 100.17/14.29 | | ~ (class_Complete__Lattice_Ocomplete__lattice(v2) = v0))
% 100.17/14.29 | (37) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 100.17/14.29 | (hAPP(v3, v2) = v1) | ~ (hAPP(v3, v2) = v0))
% 100.17/14.29 | (38) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 100.17/14.29 | (tc_fun(v3, v2) = v1) | ~ (tc_fun(v3, v2) = v0))
% 100.17/14.29 | (39) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 100.17/14.29 | (tc_prod(v3, v2) = v1) | ~ (tc_prod(v3, v2) = v0))
% 100.17/14.29 |
% 100.17/14.29 | DELTA: instantiating (28) with fresh symbols all_495_0, all_495_1, all_495_2,
% 100.17/14.29 | all_495_3, all_495_4 gives:
% 100.17/14.29 | (40) tc_prod(tc_Arrow__Order__Mirabelle_Oalt,
% 100.17/14.29 | tc_Arrow__Order__Mirabelle_Oalt) = all_495_4 & tc_fun(all_495_4,
% 100.17/14.29 | tc_HOL_Obool) = all_495_3 & c_member(all_495_3) = all_495_2 &
% 100.17/14.29 | hBOOL(all_495_0) = 0 & hAPP(all_495_1, c_Arrow__Order__Mirabelle_OLin)
% 100.17/14.29 | = all_495_0 & hAPP(all_495_2, v_L) = all_495_1 & $i(all_495_0) &
% 100.17/14.29 | $i(all_495_1) & $i(all_495_2) & $i(all_495_3) & $i(all_495_4)
% 100.17/14.29 |
% 100.17/14.29 | ALPHA: (40) implies:
% 100.17/14.29 | (41) hAPP(all_495_2, v_L) = all_495_1
% 100.17/14.29 | (42) hAPP(all_495_1, c_Arrow__Order__Mirabelle_OLin) = all_495_0
% 100.17/14.29 | (43) hBOOL(all_495_0) = 0
% 100.17/14.29 | (44) c_member(all_495_3) = all_495_2
% 100.17/14.29 | (45) tc_fun(all_495_4, tc_HOL_Obool) = all_495_3
% 100.17/14.29 | (46) tc_prod(tc_Arrow__Order__Mirabelle_Oalt,
% 100.17/14.29 | tc_Arrow__Order__Mirabelle_Oalt) = all_495_4
% 100.17/14.29 |
% 100.17/14.29 | DELTA: instantiating (6) with fresh symbols all_497_0, all_497_1, all_497_2
% 100.17/14.29 | gives:
% 100.17/14.29 | (47) tc_prod(tc_Arrow__Order__Mirabelle_Oalt,
% 100.17/14.29 | tc_Arrow__Order__Mirabelle_Oalt) = all_497_2 & tc_fun(all_497_2,
% 100.17/14.29 | tc_HOL_Obool) = all_497_1 & c_member(all_497_1) = all_497_0 &
% 100.17/14.29 | $i(all_497_0) & $i(all_497_1) & $i(all_497_2) & ? [v0: $i] : ? [v1:
% 100.17/14.29 | $i] : ? [v2: $i] : (hBOOL(v2) = 0 & hAPP(v1,
% 100.17/14.29 | c_Arrow__Order__Mirabelle_OLin) = v2 & hAPP(all_497_0, v0) = v1 &
% 100.17/14.29 | $i(v2) & $i(v1) & $i(v0))
% 100.17/14.29 |
% 100.17/14.29 | ALPHA: (47) implies:
% 100.17/14.29 | (48) $i(all_497_1)
% 100.17/14.29 | (49) c_member(all_497_1) = all_497_0
% 100.17/14.29 | (50) tc_fun(all_497_2, tc_HOL_Obool) = all_497_1
% 100.17/14.29 | (51) tc_prod(tc_Arrow__Order__Mirabelle_Oalt,
% 100.17/14.29 | tc_Arrow__Order__Mirabelle_Oalt) = all_497_2
% 100.17/14.29 | (52) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (hBOOL(v2) = 0 & hAPP(v1,
% 100.17/14.29 | c_Arrow__Order__Mirabelle_OLin) = v2 & hAPP(all_497_0, v0) = v1 &
% 100.17/14.29 | $i(v2) & $i(v1) & $i(v0))
% 100.17/14.29 |
% 100.17/14.29 | DELTA: instantiating (19) with fresh symbols all_503_0, all_503_1, all_503_2,
% 100.17/14.29 | all_503_3, all_503_4, all_503_5 gives:
% 100.17/14.29 | (53) c_COMBK(all_503_1, tc_Arrow__Order__Mirabelle_Oindi,
% 100.17/14.29 | c_Arrow__Order__Mirabelle_OLin) = all_503_0 &
% 100.17/14.29 | c_FuncSet_OPi(tc_Arrow__Order__Mirabelle_Oindi, all_503_4, all_503_2,
% 100.17/14.29 | all_503_0) = c_Arrow__Order__Mirabelle_OProf &
% 100.17/14.29 | c_Orderings_Otop__class_Otop(all_503_3) = all_503_2 &
% 100.17/14.29 | tc_prod(tc_Arrow__Order__Mirabelle_Oalt,
% 100.17/14.29 | tc_Arrow__Order__Mirabelle_Oalt) = all_503_5 & tc_fun(all_503_4,
% 100.17/14.29 | tc_HOL_Obool) = all_503_1 & tc_fun(all_503_5, tc_HOL_Obool) =
% 100.17/14.29 | all_503_4 & tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_HOL_Obool) =
% 100.17/14.29 | all_503_3 & $i(all_503_0) & $i(all_503_1) & $i(all_503_2) &
% 100.17/14.29 | $i(all_503_3) & $i(all_503_4) & $i(all_503_5)
% 100.17/14.29 |
% 100.17/14.29 | ALPHA: (53) implies:
% 100.17/14.29 | (54) $i(all_503_2)
% 100.17/14.29 | (55) $i(all_503_0)
% 100.17/14.29 | (56) tc_fun(all_503_5, tc_HOL_Obool) = all_503_4
% 100.17/14.29 | (57) tc_fun(all_503_4, tc_HOL_Obool) = all_503_1
% 100.17/14.29 | (58) tc_prod(tc_Arrow__Order__Mirabelle_Oalt,
% 100.17/14.29 | tc_Arrow__Order__Mirabelle_Oalt) = all_503_5
% 100.17/14.29 | (59) c_FuncSet_OPi(tc_Arrow__Order__Mirabelle_Oindi, all_503_4, all_503_2,
% 100.17/14.29 | all_503_0) = c_Arrow__Order__Mirabelle_OProf
% 100.17/14.29 | (60) c_COMBK(all_503_1, tc_Arrow__Order__Mirabelle_Oindi,
% 100.17/14.29 | c_Arrow__Order__Mirabelle_OLin) = all_503_0
% 100.17/14.29 |
% 100.17/14.29 | DELTA: instantiating (33) with fresh symbols all_509_0, all_509_1, all_509_2,
% 100.17/14.29 | all_509_3, all_509_4, all_509_5, all_509_6, all_509_7 gives:
% 100.17/14.29 | (61) ~ (all_509_0 = 0) & c_COMBK(all_509_6,
% 100.17/14.29 | tc_Arrow__Order__Mirabelle_Oindi, v_L) = all_509_3 &
% 100.17/14.29 | tc_prod(tc_Arrow__Order__Mirabelle_Oalt,
% 100.17/14.29 | tc_Arrow__Order__Mirabelle_Oalt) = all_509_7 & tc_fun(all_509_7,
% 100.17/14.29 | tc_HOL_Obool) = all_509_6 & tc_fun(tc_Arrow__Order__Mirabelle_Oindi,
% 100.17/14.29 | all_509_6) = all_509_5 & c_member(all_509_5) = all_509_4 &
% 100.17/14.29 | hBOOL(all_509_1) = all_509_0 & hAPP(all_509_2,
% 100.17/14.29 | c_Arrow__Order__Mirabelle_OProf) = all_509_1 & hAPP(all_509_4,
% 100.17/14.29 | all_509_3) = all_509_2 & $i(all_509_1) & $i(all_509_2) &
% 100.17/14.29 | $i(all_509_3) & $i(all_509_4) & $i(all_509_5) & $i(all_509_6) &
% 100.17/14.29 | $i(all_509_7)
% 100.17/14.29 |
% 100.17/14.29 | ALPHA: (61) implies:
% 100.17/14.29 | (62) ~ (all_509_0 = 0)
% 100.17/14.29 | (63) $i(all_509_3)
% 100.17/14.29 | (64) hAPP(all_509_4, all_509_3) = all_509_2
% 100.17/14.29 | (65) hAPP(all_509_2, c_Arrow__Order__Mirabelle_OProf) = all_509_1
% 100.17/14.29 | (66) hBOOL(all_509_1) = all_509_0
% 100.17/14.29 | (67) c_member(all_509_5) = all_509_4
% 100.17/14.29 | (68) tc_fun(tc_Arrow__Order__Mirabelle_Oindi, all_509_6) = all_509_5
% 100.17/14.30 | (69) tc_fun(all_509_7, tc_HOL_Obool) = all_509_6
% 100.17/14.30 | (70) tc_prod(tc_Arrow__Order__Mirabelle_Oalt,
% 100.17/14.30 | tc_Arrow__Order__Mirabelle_Oalt) = all_509_7
% 100.17/14.30 | (71) c_COMBK(all_509_6, tc_Arrow__Order__Mirabelle_Oindi, v_L) = all_509_3
% 100.17/14.30 |
% 100.17/14.30 | DELTA: instantiating (3) with fresh symbols all_511_0, all_511_1, all_511_2
% 100.17/14.30 | gives:
% 100.17/14.30 | (72) tc_prod(tc_Arrow__Order__Mirabelle_Oalt,
% 100.17/14.30 | tc_Arrow__Order__Mirabelle_Oalt) = all_511_2 & tc_fun(all_511_2,
% 100.17/14.30 | tc_HOL_Obool) = all_511_1 & c_member(all_511_1) = all_511_0 &
% 100.17/14.30 | $i(all_511_0) & $i(all_511_1) & $i(all_511_2) & ! [v0: $i] : ! [v1:
% 100.17/14.30 | $i] : ! [v2: $i] : ( ~ (c_Arrow__Order__Mirabelle_Omkbot(v1, v0) =
% 100.17/14.30 | v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : ? [v5:
% 100.17/14.30 | any] : ? [v6: $i] : ? [v7: $i] : ? [v8: any] : (hBOOL(v7) = v8
% 100.17/14.30 | & hBOOL(v4) = v5 & hAPP(v6, c_Arrow__Order__Mirabelle_OLin) = v7 &
% 100.17/14.30 | hAPP(v3, c_Arrow__Order__Mirabelle_OLin) = v4 & hAPP(all_511_0,
% 100.17/14.30 | v2) = v6 & hAPP(all_511_0, v1) = v3 & $i(v7) & $i(v6) & $i(v4) &
% 100.17/14.30 | $i(v3) & ( ~ (v5 = 0) | v8 = 0)))
% 100.17/14.30 |
% 100.17/14.30 | ALPHA: (72) implies:
% 100.17/14.30 | (73) c_member(all_511_1) = all_511_0
% 100.17/14.30 | (74) tc_fun(all_511_2, tc_HOL_Obool) = all_511_1
% 100.17/14.30 | (75) tc_prod(tc_Arrow__Order__Mirabelle_Oalt,
% 100.17/14.30 | tc_Arrow__Order__Mirabelle_Oalt) = all_511_2
% 100.17/14.30 |
% 100.17/14.30 | DELTA: instantiating (4) with fresh symbols all_514_0, all_514_1, all_514_2
% 100.17/14.30 | gives:
% 100.17/14.30 | (76) tc_prod(tc_Arrow__Order__Mirabelle_Oalt,
% 100.17/14.30 | tc_Arrow__Order__Mirabelle_Oalt) = all_514_2 & tc_fun(all_514_2,
% 100.17/14.30 | tc_HOL_Obool) = all_514_1 & c_member(all_514_1) = all_514_0 &
% 100.17/14.30 | $i(all_514_0) & $i(all_514_1) & $i(all_514_2) & ! [v0: $i] : ! [v1:
% 100.17/14.30 | $i] : ! [v2: $i] : ( ~ (c_Arrow__Order__Mirabelle_Omktop(v1, v0) =
% 100.17/14.30 | v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : ? [v5:
% 100.17/14.30 | any] : ? [v6: $i] : ? [v7: $i] : ? [v8: any] : (hBOOL(v7) = v8
% 100.17/14.30 | & hBOOL(v4) = v5 & hAPP(v6, c_Arrow__Order__Mirabelle_OLin) = v7 &
% 100.17/14.30 | hAPP(v3, c_Arrow__Order__Mirabelle_OLin) = v4 & hAPP(all_514_0,
% 100.17/14.30 | v2) = v6 & hAPP(all_514_0, v1) = v3 & $i(v7) & $i(v6) & $i(v4) &
% 100.17/14.30 | $i(v3) & ( ~ (v5 = 0) | v8 = 0)))
% 100.17/14.30 |
% 100.17/14.30 | ALPHA: (76) implies:
% 100.17/14.30 | (77) c_member(all_514_1) = all_514_0
% 100.17/14.30 | (78) tc_fun(all_514_2, tc_HOL_Obool) = all_514_1
% 100.17/14.30 | (79) tc_prod(tc_Arrow__Order__Mirabelle_Oalt,
% 100.17/14.30 | tc_Arrow__Order__Mirabelle_Oalt) = all_514_2
% 100.17/14.30 |
% 100.17/14.30 | DELTA: instantiating (1) with fresh symbols all_517_0, all_517_1, all_517_2
% 100.17/14.30 | gives:
% 100.17/14.30 | (80) tc_prod(tc_Arrow__Order__Mirabelle_Oalt,
% 100.17/14.30 | tc_Arrow__Order__Mirabelle_Oalt) = all_517_2 & tc_fun(all_517_2,
% 100.17/14.30 | tc_HOL_Obool) = all_517_1 & c_member(all_517_1) = all_517_0 &
% 100.17/14.30 | $i(all_517_0) & $i(all_517_1) & $i(all_517_2) & ! [v0: $i] : ! [v1:
% 100.17/14.30 | $i] : ! [v2: $i] : ! [v3: $i] : (v2 = v1 | ~
% 100.17/14.30 | (c_Arrow__Order__Mirabelle_Oabove(v0, v2, v1) = v3) | ~ $i(v2) | ~
% 100.17/14.30 | $i(v1) | ~ $i(v0) | ? [v4: $i] : ? [v5: $i] : ? [v6: any] : ?
% 100.17/14.30 | [v7: $i] : ? [v8: $i] : ? [v9: any] : (hBOOL(v8) = v9 & hBOOL(v5)
% 100.17/14.30 | = v6 & hAPP(v7, c_Arrow__Order__Mirabelle_OLin) = v8 & hAPP(v4,
% 100.17/14.30 | c_Arrow__Order__Mirabelle_OLin) = v5 & hAPP(all_517_0, v3) = v7
% 100.17/14.30 | & hAPP(all_517_0, v0) = v4 & $i(v8) & $i(v7) & $i(v5) & $i(v4) & (
% 100.17/14.30 | ~ (v6 = 0) | v9 = 0)))
% 100.17/14.30 |
% 100.17/14.30 | ALPHA: (80) implies:
% 100.17/14.30 | (81) c_member(all_517_1) = all_517_0
% 100.17/14.30 | (82) tc_fun(all_517_2, tc_HOL_Obool) = all_517_1
% 100.17/14.30 | (83) tc_prod(tc_Arrow__Order__Mirabelle_Oalt,
% 100.17/14.30 | tc_Arrow__Order__Mirabelle_Oalt) = all_517_2
% 100.17/14.30 |
% 100.17/14.30 | DELTA: instantiating (2) with fresh symbols all_520_0, all_520_1, all_520_2
% 100.17/14.30 | gives:
% 100.17/14.30 | (84) tc_prod(tc_Arrow__Order__Mirabelle_Oalt,
% 100.17/14.30 | tc_Arrow__Order__Mirabelle_Oalt) = all_520_2 & tc_fun(all_520_2,
% 100.17/14.30 | tc_HOL_Obool) = all_520_1 & c_member(all_520_1) = all_520_0 &
% 100.17/14.30 | $i(all_520_0) & $i(all_520_1) & $i(all_520_2) & ! [v0: $i] : ! [v1:
% 100.17/14.30 | $i] : ! [v2: $i] : ! [v3: $i] : (v2 = v1 | ~
% 100.17/14.30 | (c_Arrow__Order__Mirabelle_Obelow(v0, v2, v1) = v3) | ~ $i(v2) | ~
% 100.17/14.30 | $i(v1) | ~ $i(v0) | ? [v4: $i] : ? [v5: $i] : ? [v6: any] : ?
% 100.17/14.30 | [v7: $i] : ? [v8: $i] : ? [v9: any] : (hBOOL(v8) = v9 & hBOOL(v5)
% 100.17/14.30 | = v6 & hAPP(v7, c_Arrow__Order__Mirabelle_OLin) = v8 & hAPP(v4,
% 100.17/14.30 | c_Arrow__Order__Mirabelle_OLin) = v5 & hAPP(all_520_0, v3) = v7
% 100.17/14.30 | & hAPP(all_520_0, v0) = v4 & $i(v8) & $i(v7) & $i(v5) & $i(v4) & (
% 100.17/14.30 | ~ (v6 = 0) | v9 = 0)))
% 100.17/14.30 |
% 100.17/14.30 | ALPHA: (84) implies:
% 100.17/14.30 | (85) c_member(all_520_1) = all_520_0
% 100.17/14.30 | (86) tc_fun(all_520_2, tc_HOL_Obool) = all_520_1
% 100.17/14.30 | (87) tc_prod(tc_Arrow__Order__Mirabelle_Oalt,
% 100.17/14.30 | tc_Arrow__Order__Mirabelle_Oalt) = all_520_2
% 100.17/14.30 |
% 100.17/14.30 | DELTA: instantiating (12) with fresh symbols all_523_0, all_523_1, all_523_2,
% 100.17/14.30 | all_523_3, all_523_4 gives:
% 100.17/14.30 | (88) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 100.17/14.30 | tc_Arrow__Order__Mirabelle_Oalt) = all_523_0 &
% 100.17/14.30 | tc_prod(tc_Arrow__Order__Mirabelle_Oalt,
% 100.17/14.30 | tc_Arrow__Order__Mirabelle_Oalt) = all_523_4 & tc_fun(all_523_4,
% 100.17/14.30 | tc_HOL_Obool) = all_523_3 & c_member(all_523_3) = all_523_2 &
% 100.17/14.30 | c_member(all_523_4) = all_523_1 & $i(all_523_0) & $i(all_523_1) &
% 100.17/14.30 | $i(all_523_2) & $i(all_523_3) & $i(all_523_4) & ! [v0: $i] : ! [v1:
% 100.17/14.30 | $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : !
% 100.17/14.30 | [v6: $i] : ( ~ (hAPP(v5, v2) = v6) | ~ (hAPP(v3, v1) = v4) | ~
% 100.17/14.30 | (hAPP(all_523_0, v0) = v3) | ~ (hAPP(all_523_1, v4) = v5) | ~
% 100.17/14.30 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v7: $i] : ? [v8: $i] : ? [v9:
% 100.17/14.30 | any] : ? [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13: $i] :
% 100.17/14.30 | ? [v14: any] : ? [v15: any] : (hBOOL(v13) = v14 & hBOOL(v8) = v9 &
% 100.17/14.30 | hBOOL(v6) = v15 & hAPP(v12, v2) = v13 & hAPP(v10, v0) = v11 &
% 100.17/14.30 | hAPP(v7, c_Arrow__Order__Mirabelle_OLin) = v8 & hAPP(all_523_0,
% 100.17/14.30 | v1) = v10 & hAPP(all_523_1, v11) = v12 & hAPP(all_523_2, v2) =
% 100.17/14.30 | v7 & $i(v13) & $i(v12) & $i(v11) & $i(v10) & $i(v8) & $i(v7) & ( ~
% 100.17/14.30 | (v15 = 0) | ~ (v14 = 0) | ~ (v9 = 0))))
% 100.17/14.30 |
% 100.17/14.30 | ALPHA: (88) implies:
% 100.17/14.30 | (89) c_member(all_523_3) = all_523_2
% 100.17/14.30 | (90) tc_fun(all_523_4, tc_HOL_Obool) = all_523_3
% 100.17/14.30 | (91) tc_prod(tc_Arrow__Order__Mirabelle_Oalt,
% 100.17/14.30 | tc_Arrow__Order__Mirabelle_Oalt) = all_523_4
% 100.17/14.30 |
% 100.17/14.30 | DELTA: instantiating (11) with fresh symbols all_526_0, all_526_1, all_526_2,
% 100.17/14.30 | all_526_3 gives:
% 100.17/14.31 | (92) c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt,
% 100.17/14.31 | tc_Arrow__Order__Mirabelle_Oalt) = all_526_0 &
% 100.17/14.31 | tc_prod(tc_Arrow__Order__Mirabelle_Oalt,
% 100.17/14.31 | tc_Arrow__Order__Mirabelle_Oalt) = all_526_3 & tc_fun(all_526_3,
% 100.17/14.31 | tc_HOL_Obool) = all_526_2 & c_member(all_526_2) = all_526_1 &
% 100.17/14.31 | $i(all_526_0) & $i(all_526_1) & $i(all_526_2) & $i(all_526_3) & !
% 100.17/14.31 | [v0: $i] : ! [v1: $i] : ( ~ (hAPP(all_526_1, v0) = v1) | ~ $i(v0) |
% 100.17/14.31 | ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: any] : ? [v6: $i]
% 100.17/14.31 | : ? [v7: any] : (hBOOL(v6) = v7 & hBOOL(v4) = v5 & hAPP(v3,
% 100.17/14.31 | c_Arrow__Order__Mirabelle_OLin) = v4 & hAPP(v1,
% 100.17/14.31 | c_Arrow__Order__Mirabelle_OLin) = v6 & hAPP(all_526_0, v0) = v2
% 100.17/14.31 | & hAPP(all_526_1, v2) = v3 & $i(v6) & $i(v4) & $i(v3) & $i(v2) & (
% 100.17/14.31 | ~ (v5 = 0) | v7 = 0))) & ! [v0: $i] : ! [v1: $i] : ( ~
% 100.17/14.31 | (hAPP(all_526_1, v0) = v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: any]
% 100.17/14.31 | : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: any] :
% 100.17/14.31 | (hBOOL(v6) = v7 & hBOOL(v2) = v3 & hAPP(v5,
% 100.17/14.31 | c_Arrow__Order__Mirabelle_OLin) = v6 & hAPP(v1,
% 100.17/14.31 | c_Arrow__Order__Mirabelle_OLin) = v2 & hAPP(all_526_0, v0) = v4
% 100.17/14.31 | & hAPP(all_526_1, v4) = v5 & $i(v6) & $i(v5) & $i(v4) & $i(v2) & (
% 100.17/14.31 | ~ (v3 = 0) | v7 = 0)))
% 100.17/14.31 |
% 100.17/14.31 | ALPHA: (92) implies:
% 100.17/14.31 | (93) c_member(all_526_2) = all_526_1
% 100.17/14.31 | (94) tc_fun(all_526_3, tc_HOL_Obool) = all_526_2
% 100.17/14.31 | (95) tc_prod(tc_Arrow__Order__Mirabelle_Oalt,
% 100.17/14.31 | tc_Arrow__Order__Mirabelle_Oalt) = all_526_3
% 100.17/14.31 |
% 100.17/14.31 | DELTA: instantiating (5) with fresh symbols all_529_0, all_529_1, all_529_2,
% 100.17/14.31 | all_529_3 gives:
% 100.17/14.31 | (96) tc_prod(tc_Arrow__Order__Mirabelle_Oalt,
% 100.17/14.31 | tc_Arrow__Order__Mirabelle_Oalt) = all_529_3 & tc_fun(all_529_3,
% 100.17/14.31 | tc_HOL_Obool) = all_529_2 & tc_fun(tc_Arrow__Order__Mirabelle_Oindi,
% 100.17/14.31 | all_529_2) = all_529_1 & c_member(all_529_1) = all_529_0 &
% 100.17/14.31 | $i(all_529_0) & $i(all_529_1) & $i(all_529_2) & $i(all_529_3) & !
% 100.17/14.31 | [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~
% 100.17/14.31 | (c_Arrow__Order__Mirabelle_Odictator(v1, v0) = v2) | ~ $i(v1) | ~
% 100.17/14.31 | $i(v0) | ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ?
% 100.17/14.31 | [v7: $i] : ( ~ (v7 = v6) & hBOOL(v5) = 0 & hAPP(v4,
% 100.17/14.31 | c_Arrow__Order__Mirabelle_OProf) = v5 & hAPP(v3, v0) = v7 &
% 100.17/14.31 | hAPP(v1, v3) = v6 & hAPP(all_529_0, v3) = v4 & $i(v7) & $i(v6) &
% 100.17/14.31 | $i(v5) & $i(v4) & $i(v3))) & ! [v0: $i] : ! [v1: $i] : ( ~
% 100.17/14.31 | (c_Arrow__Order__Mirabelle_Odictator(v1, v0) = 0) | ~ $i(v1) | ~
% 100.17/14.31 | $i(v0) | ! [v2: $i] : ! [v3: $i] : ( ~ (hAPP(all_529_0, v2) = v3)
% 100.17/14.31 | | ~ $i(v2) | ? [v4: $i] : ? [v5: any] : ? [v6: $i] : ? [v7:
% 100.17/14.31 | $i] : (hBOOL(v4) = v5 & hAPP(v3,
% 100.17/14.31 | c_Arrow__Order__Mirabelle_OProf) = v4 & hAPP(v2, v0) = v7 &
% 100.17/14.31 | hAPP(v1, v2) = v6 & $i(v7) & $i(v6) & $i(v4) & ( ~ (v5 = 0) | v7
% 100.17/14.31 | = v6))))
% 100.17/14.31 |
% 100.17/14.31 | ALPHA: (96) implies:
% 100.17/14.31 | (97) $i(all_529_1)
% 100.17/14.31 | (98) c_member(all_529_1) = all_529_0
% 100.17/14.31 | (99) tc_fun(tc_Arrow__Order__Mirabelle_Oindi, all_529_2) = all_529_1
% 100.17/14.31 | (100) tc_fun(all_529_3, tc_HOL_Obool) = all_529_2
% 100.17/14.31 | (101) tc_prod(tc_Arrow__Order__Mirabelle_Oalt,
% 100.17/14.31 | tc_Arrow__Order__Mirabelle_Oalt) = all_529_3
% 100.17/14.31 |
% 100.17/14.31 | DELTA: instantiating (13) with fresh symbols all_532_0, all_532_1, all_532_2,
% 100.17/14.31 | all_532_3, all_532_4 gives:
% 100.17/14.31 | (102) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 100.17/14.31 | tc_Arrow__Order__Mirabelle_Oalt) = all_532_0 &
% 100.17/14.31 | tc_prod(tc_Arrow__Order__Mirabelle_Oalt,
% 100.17/14.31 | tc_Arrow__Order__Mirabelle_Oalt) = all_532_4 & tc_fun(all_532_4,
% 100.17/14.31 | tc_HOL_Obool) = all_532_3 & c_member(all_532_3) = all_532_2 &
% 100.17/14.31 | c_member(all_532_4) = all_532_1 & $i(all_532_0) & $i(all_532_1) &
% 100.17/14.31 | $i(all_532_2) & $i(all_532_3) & $i(all_532_4) & ! [v0: $i] : ! [v1:
% 100.17/14.31 | $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : !
% 100.17/14.31 | [v6: $i] : (v1 = v0 | ~ (hAPP(v5, v2) = v6) | ~ (hAPP(v3, v1) = v4)
% 100.17/14.31 | | ~ (hAPP(all_532_0, v0) = v3) | ~ (hAPP(all_532_1, v4) = v5) |
% 100.17/14.31 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v7: $i] : ? [v8: $i] : ?
% 100.17/14.31 | [v9: any] : ? [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13:
% 100.17/14.31 | $i] : ? [v14: any] : ? [v15: any] : (hBOOL(v13) = v14 &
% 100.17/14.31 | hBOOL(v8) = v9 & hBOOL(v6) = v15 & hAPP(v12, v2) = v13 &
% 100.17/14.31 | hAPP(v10, v0) = v11 & hAPP(v7, c_Arrow__Order__Mirabelle_OLin) =
% 100.17/14.31 | v8 & hAPP(all_532_0, v1) = v10 & hAPP(all_532_1, v11) = v12 &
% 100.17/14.31 | hAPP(all_532_2, v2) = v7 & $i(v13) & $i(v12) & $i(v11) & $i(v10)
% 100.17/14.31 | & $i(v8) & $i(v7) & ( ~ (v9 = 0) | (( ~ (v15 = 0) | ~ (v14 = 0))
% 100.17/14.31 | & (v15 = 0 | v14 = 0)))))
% 100.17/14.31 |
% 100.17/14.31 | ALPHA: (102) implies:
% 100.17/14.31 | (103) c_member(all_532_3) = all_532_2
% 100.17/14.31 | (104) tc_fun(all_532_4, tc_HOL_Obool) = all_532_3
% 100.17/14.31 | (105) tc_prod(tc_Arrow__Order__Mirabelle_Oalt,
% 100.17/14.31 | tc_Arrow__Order__Mirabelle_Oalt) = all_532_4
% 100.17/14.31 |
% 100.17/14.31 | DELTA: instantiating (14) with fresh symbols all_537_0, all_537_1, all_537_2
% 100.17/14.31 | gives:
% 100.17/14.31 | (106) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 100.17/14.31 | tc_Arrow__Order__Mirabelle_Oalt) = all_537_0 &
% 100.17/14.31 | tc_prod(tc_Arrow__Order__Mirabelle_Oalt,
% 100.17/14.31 | tc_Arrow__Order__Mirabelle_Oalt) = all_537_2 & c_member(all_537_2)
% 100.17/14.31 | = all_537_1 & $i(all_537_0) & $i(all_537_1) & $i(all_537_2) & ! [v0:
% 100.17/14.31 | $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : !
% 100.17/14.31 | [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : (v2 = v0 | ~
% 100.17/14.31 | (c_Arrow__Order__Mirabelle_Omkbot(v1, v0) = v7) | ~ (hAPP(v6, v7)
% 100.17/14.31 | = v8) | ~ (hAPP(v4, v2) = v5) | ~ (hAPP(all_537_0, v3) = v4) |
% 100.17/14.31 | ~ (hAPP(all_537_1, v5) = v6) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) |
% 100.17/14.31 | ~ $i(v0) | ? [v9: $i] : ? [v10: any] : ? [v11: any] : (hBOOL(v9)
% 100.17/14.31 | = v10 & hBOOL(v8) = v11 & hAPP(v6, v1) = v9 & $i(v9) & (v11 = 0 |
% 100.17/14.31 | ( ~ (v10 = 0) & ~ (v3 = v0))))) & ! [v0: $i] : ! [v1: $i] :
% 100.17/14.31 | ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] :
% 100.17/14.32 | ! [v7: $i] : ! [v8: $i] : ( ~ (c_Arrow__Order__Mirabelle_Omkbot(v1,
% 100.17/14.32 | v0) = v7) | ~ (hAPP(v6, v7) = v8) | ~ (hAPP(v4, v2) = v5) |
% 100.17/14.32 | ~ (hAPP(all_537_0, v3) = v4) | ~ (hAPP(all_537_1, v5) = v6) | ~
% 100.17/14.32 | $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v9: any] : ?
% 100.17/14.32 | [v10: $i] : ? [v11: any] : (hBOOL(v10) = v11 & hBOOL(v8) = v9 &
% 100.17/14.32 | hAPP(v6, v1) = v10 & $i(v10) & ( ~ (v9 = 0) | ( ~ (v2 = v0) &
% 100.17/14.32 | (v11 = 0 | v3 = v0)))))
% 100.17/14.32 |
% 100.17/14.32 | ALPHA: (106) implies:
% 100.17/14.32 | (107) tc_prod(tc_Arrow__Order__Mirabelle_Oalt,
% 100.17/14.32 | tc_Arrow__Order__Mirabelle_Oalt) = all_537_2
% 100.17/14.32 |
% 100.17/14.32 | DELTA: instantiating (15) with fresh symbols all_542_0, all_542_1, all_542_2
% 100.17/14.32 | gives:
% 100.17/14.32 | (108) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 100.17/14.32 | tc_Arrow__Order__Mirabelle_Oalt) = all_542_0 &
% 100.17/14.32 | tc_prod(tc_Arrow__Order__Mirabelle_Oalt,
% 100.17/14.32 | tc_Arrow__Order__Mirabelle_Oalt) = all_542_2 & c_member(all_542_2)
% 100.17/14.32 | = all_542_1 & $i(all_542_0) & $i(all_542_1) & $i(all_542_2) & ! [v0:
% 100.17/14.32 | $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : !
% 100.17/14.32 | [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : (v3 = v0 | ~
% 100.17/14.32 | (c_Arrow__Order__Mirabelle_Omktop(v1, v0) = v7) | ~ (hAPP(v6, v7)
% 100.17/14.32 | = v8) | ~ (hAPP(v4, v2) = v5) | ~ (hAPP(all_542_0, v3) = v4) |
% 100.17/14.32 | ~ (hAPP(all_542_1, v5) = v6) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) |
% 100.17/14.32 | ~ $i(v0) | ? [v9: $i] : ? [v10: any] : ? [v11: any] : (hBOOL(v9)
% 100.17/14.32 | = v10 & hBOOL(v8) = v11 & hAPP(v6, v1) = v9 & $i(v9) & (v11 = 0 |
% 100.17/14.32 | ( ~ (v10 = 0) & ~ (v2 = v0))))) & ! [v0: $i] : ! [v1: $i] :
% 100.17/14.32 | ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] :
% 100.17/14.32 | ! [v7: $i] : ! [v8: $i] : ( ~ (c_Arrow__Order__Mirabelle_Omktop(v1,
% 100.17/14.32 | v0) = v7) | ~ (hAPP(v6, v7) = v8) | ~ (hAPP(v4, v2) = v5) |
% 100.17/14.32 | ~ (hAPP(all_542_0, v3) = v4) | ~ (hAPP(all_542_1, v5) = v6) | ~
% 100.17/14.32 | $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v9: any] : ?
% 100.17/14.32 | [v10: $i] : ? [v11: any] : (hBOOL(v10) = v11 & hBOOL(v8) = v9 &
% 100.17/14.32 | hAPP(v6, v1) = v10 & $i(v10) & ( ~ (v9 = 0) | ( ~ (v3 = v0) &
% 100.17/14.32 | (v11 = 0 | v2 = v0)))))
% 100.17/14.32 |
% 100.17/14.32 | ALPHA: (108) implies:
% 100.17/14.32 | (109) tc_prod(tc_Arrow__Order__Mirabelle_Oalt,
% 100.17/14.32 | tc_Arrow__Order__Mirabelle_Oalt) = all_542_2
% 100.17/14.32 |
% 100.17/14.32 | DELTA: instantiating (16) with fresh symbols all_545_0, all_545_1, all_545_2,
% 100.17/14.32 | all_545_3, all_545_4, all_545_5, all_545_6, all_545_7, all_545_8,
% 100.17/14.32 | all_545_9, all_545_10 gives:
% 100.17/14.32 | (110) c_COMBK(all_545_5, all_545_8, c_Arrow__Order__Mirabelle_OLin) =
% 100.17/14.32 | all_545_4 & c_FuncSet_OPi(all_545_8, all_545_9,
% 100.17/14.32 | c_Arrow__Order__Mirabelle_OProf, all_545_4) = all_545_3 &
% 100.17/14.32 | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 100.17/14.32 | tc_Arrow__Order__Mirabelle_Oalt) = all_545_0 &
% 100.17/14.32 | tc_prod(tc_Arrow__Order__Mirabelle_Oalt,
% 100.17/14.32 | tc_Arrow__Order__Mirabelle_Oalt) = all_545_10 & tc_fun(all_545_8,
% 100.17/14.32 | all_545_9) = all_545_7 & tc_fun(all_545_9, tc_HOL_Obool) =
% 100.17/14.32 | all_545_5 & tc_fun(all_545_10, tc_HOL_Obool) = all_545_9 &
% 100.17/14.32 | tc_fun(tc_Arrow__Order__Mirabelle_Oindi, all_545_9) = all_545_8 &
% 100.17/14.32 | c_member(all_545_7) = all_545_6 & c_member(all_545_8) = all_545_2 &
% 100.17/14.32 | c_member(all_545_10) = all_545_1 & $i(all_545_0) & $i(all_545_1) &
% 100.17/14.32 | $i(all_545_2) & $i(all_545_3) & $i(all_545_4) & $i(all_545_5) &
% 100.17/14.32 | $i(all_545_6) & $i(all_545_7) & $i(all_545_8) & $i(all_545_9) &
% 100.17/14.32 | $i(all_545_10) & ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 |
% 100.17/14.32 | ~ (c_Arrow__Order__Mirabelle_Odictator(v1, v0) = v2) | ~ $i(v1) |
% 100.17/14.32 | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] :
% 100.17/14.32 | ? [v7: $i] : (hBOOL(v5) = 0 & hAPP(v4,
% 100.17/14.32 | c_Arrow__Order__Mirabelle_OProf) = v5 & hAPP(v3, v0) = v6 &
% 100.17/14.32 | hAPP(v1, v3) = v7 & hAPP(all_545_2, v3) = v4 & $i(v7) & $i(v6) &
% 100.17/14.32 | $i(v5) & $i(v4) & $i(v3) & ? [v8: $i] : ? [v9: $i] : ? [v10:
% 100.17/14.32 | $i] : ? [v11: $i] : ? [v12: $i] : ? [v13: $i] : ? [v14: $i]
% 100.17/14.32 | : ? [v15: int] : ( ~ (v15 = 0) & ~ (v9 = v8) & hBOOL(v14) = v15
% 100.17/14.32 | & hBOOL(v13) = 0 & hAPP(v12, v7) = v14 & hAPP(v12, v6) = v13 &
% 100.17/14.32 | hAPP(v10, v9) = v11 & hAPP(all_545_0, v8) = v10 &
% 100.17/14.32 | hAPP(all_545_1, v11) = v12 & $i(v14) & $i(v13) & $i(v12) &
% 100.17/14.32 | $i(v11) & $i(v10) & $i(v9) & $i(v8))) | ? [v3: $i] : ? [v4:
% 100.17/14.32 | $i] : ? [v5: int] : ( ~ (v5 = 0) & hBOOL(v4) = v5 & hAPP(v3,
% 100.17/14.32 | all_545_3) = v4 & hAPP(all_545_6, v1) = v3 & $i(v4) & $i(v3)))
% 100.17/14.32 |
% 100.17/14.32 | ALPHA: (110) implies:
% 100.17/14.32 | (111) $i(all_545_4)
% 100.17/14.32 | (112) c_member(all_545_8) = all_545_2
% 100.17/14.32 | (113) tc_fun(tc_Arrow__Order__Mirabelle_Oindi, all_545_9) = all_545_8
% 100.17/14.32 | (114) tc_fun(all_545_10, tc_HOL_Obool) = all_545_9
% 100.17/14.32 | (115) tc_fun(all_545_9, tc_HOL_Obool) = all_545_5
% 100.17/14.32 | (116) tc_prod(tc_Arrow__Order__Mirabelle_Oalt,
% 100.17/14.32 | tc_Arrow__Order__Mirabelle_Oalt) = all_545_10
% 100.17/14.32 | (117) c_FuncSet_OPi(all_545_8, all_545_9, c_Arrow__Order__Mirabelle_OProf,
% 100.17/14.32 | all_545_4) = all_545_3
% 100.17/14.32 |
% 100.17/14.32 | DELTA: instantiating (17) with fresh symbols all_548_0, all_548_1, all_548_2,
% 100.17/14.32 | all_548_3, all_548_4, all_548_5 gives:
% 100.17/14.32 | (118) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 100.17/14.32 | tc_Arrow__Order__Mirabelle_Oalt) = all_548_0 &
% 100.17/14.32 | tc_prod(tc_Arrow__Order__Mirabelle_Oalt,
% 100.17/14.32 | tc_Arrow__Order__Mirabelle_Oalt) = all_548_5 & tc_fun(all_548_5,
% 100.17/14.32 | tc_HOL_Obool) = all_548_4 &
% 100.17/14.32 | tc_fun(tc_Arrow__Order__Mirabelle_Oindi, all_548_4) = all_548_3 &
% 100.17/14.32 | c_member(all_548_3) = all_548_2 & c_member(all_548_5) = all_548_1 &
% 100.17/14.32 | $i(all_548_0) & $i(all_548_1) & $i(all_548_2) & $i(all_548_3) &
% 100.17/14.32 | $i(all_548_4) & $i(all_548_5) & ! [v0: $i] : ! [v1: int] : (v1 = 0
% 100.17/14.32 | | ~ (c_Arrow__Order__Mirabelle_Ounanimity(v0) = v1) | ~ $i(v0) |
% 100.17/14.32 | ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : (hBOOL(v4) =
% 100.17/14.32 | 0 & hAPP(v3, c_Arrow__Order__Mirabelle_OProf) = v4 & hAPP(v0, v2)
% 100.17/14.32 | = v5 & hAPP(all_548_2, v2) = v3 & $i(v5) & $i(v4) & $i(v3) &
% 100.17/14.32 | $i(v2) & ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] :
% 100.17/14.32 | ? [v10: $i] : ? [v11: $i] : ? [v12: int] : ( ~ (v12 = 0) &
% 100.17/14.32 | hBOOL(v11) = v12 & hAPP(v10, v5) = v11 & hAPP(v8, v7) = v9 &
% 100.17/14.32 | hAPP(all_548_0, v6) = v8 & hAPP(all_548_1, v9) = v10 & $i(v11)
% 100.17/14.32 | & $i(v10) & $i(v9) & $i(v8) & $i(v7) & $i(v6) & ! [v13: $i] :
% 100.17/14.32 | ! [v14: $i] : ! [v15: $i] : ( ~ (hAPP(v10, v14) = v15) | ~
% 100.17/14.32 | (hAPP(v2, v13) = v14) | ~ $i(v13) | hBOOL(v15) = 0)))) & !
% 100.17/14.32 | [v0: $i] : ( ~ (c_Arrow__Order__Mirabelle_Ounanimity(v0) = 0) | ~
% 100.17/14.32 | $i(v0) | ! [v1: $i] : ! [v2: $i] : ( ~ (hAPP(all_548_2, v1) = v2)
% 100.17/14.32 | | ~ $i(v1) | ? [v3: $i] : ? [v4: any] : ? [v5: $i] :
% 100.17/14.32 | (hBOOL(v3) = v4 & hAPP(v2, c_Arrow__Order__Mirabelle_OProf) = v3
% 100.17/14.32 | & hAPP(v0, v1) = v5 & $i(v5) & $i(v3) & ( ~ (v4 = 0) | ! [v6:
% 100.17/14.32 | $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : ! [v10:
% 100.17/14.32 | $i] : ! [v11: $i] : ( ~ (hAPP(v10, v5) = v11) | ~
% 100.17/14.32 | (hAPP(v8, v7) = v9) | ~ (hAPP(all_548_0, v6) = v8) | ~
% 100.17/14.32 | (hAPP(all_548_1, v9) = v10) | ~ $i(v7) | ~ $i(v6) |
% 100.17/14.32 | hBOOL(v11) = 0 | ? [v12: $i] : ? [v13: $i] : ? [v14: $i]
% 100.17/14.32 | : ? [v15: int] : ( ~ (v15 = 0) & hBOOL(v14) = v15 &
% 100.17/14.32 | hAPP(v10, v13) = v14 & hAPP(v1, v12) = v13 & $i(v14) &
% 100.17/14.32 | $i(v13) & $i(v12)))))))
% 100.17/14.32 |
% 100.17/14.32 | ALPHA: (118) implies:
% 100.17/14.32 | (119) c_member(all_548_3) = all_548_2
% 100.17/14.32 | (120) tc_fun(tc_Arrow__Order__Mirabelle_Oindi, all_548_4) = all_548_3
% 100.17/14.33 | (121) tc_fun(all_548_5, tc_HOL_Obool) = all_548_4
% 100.17/14.33 | (122) tc_prod(tc_Arrow__Order__Mirabelle_Oalt,
% 100.17/14.33 | tc_Arrow__Order__Mirabelle_Oalt) = all_548_5
% 100.17/14.33 |
% 100.17/14.33 | DELTA: instantiating (9) with fresh symbols all_551_0, all_551_1, all_551_2,
% 100.17/14.33 | all_551_3, all_551_4 gives:
% 100.17/14.33 | (123) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 100.17/14.33 | tc_Arrow__Order__Mirabelle_Oalt) = all_551_0 &
% 100.17/14.33 | tc_prod(tc_Arrow__Order__Mirabelle_Oalt,
% 100.17/14.33 | tc_Arrow__Order__Mirabelle_Oalt) = all_551_4 & tc_fun(all_551_4,
% 100.17/14.33 | tc_HOL_Obool) = all_551_3 & c_member(all_551_3) = all_551_2 &
% 100.17/14.33 | c_member(all_551_4) = all_551_1 & $i(all_551_0) & $i(all_551_1) &
% 100.17/14.33 | $i(all_551_2) & $i(all_551_3) & $i(all_551_4) & ! [v0: $i] : ! [v1:
% 100.17/14.33 | $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : !
% 100.17/14.33 | [v6: $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : (v4 = v3 | ~
% 100.17/14.33 | (c_Arrow__Order__Mirabelle_Obelow(v2, v4, v3) = v8) | ~ (hAPP(v7,
% 100.17/14.33 | v8) = v9) | ~ (hAPP(v5, v0) = v6) | ~ (hAPP(all_551_0, v1) =
% 100.17/14.33 | v5) | ~ (hAPP(all_551_1, v6) = v7) | ~ $i(v4) | ~ $i(v3) | ~
% 100.17/14.33 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v10: $i] : ? [v11: $i] : ?
% 100.17/14.33 | [v12: any] : ? [v13: any] : ? [v14: $i] : ? [v15: $i] : ? [v16:
% 100.17/14.33 | $i] : ? [v17: any] : ? [v18: $i] : ? [v19: $i] : ? [v20: $i]
% 100.17/14.33 | : ? [v21: $i] : ? [v22: any] : ? [v23: $i] : ? [v24: any] :
% 100.17/14.33 | (hBOOL(v23) = v24 & hBOOL(v21) = v22 & hBOOL(v16) = v17 &
% 100.17/14.33 | hBOOL(v11) = v12 & hBOOL(v9) = v13 & hAPP(v20, v2) = v21 &
% 100.17/14.33 | hAPP(v18, v0) = v19 & hAPP(v15, v2) = v16 & hAPP(v10,
% 100.17/14.33 | c_Arrow__Order__Mirabelle_OLin) = v11 & hAPP(v7, v2) = v23 &
% 100.17/14.33 | hAPP(v5, v3) = v14 & hAPP(all_551_0, v3) = v18 & hAPP(all_551_1,
% 100.17/14.33 | v19) = v20 & hAPP(all_551_1, v14) = v15 & hAPP(all_551_2, v2) =
% 100.17/14.33 | v10 & $i(v23) & $i(v21) & $i(v20) & $i(v19) & $i(v18) & $i(v16) &
% 100.17/14.33 | $i(v15) & $i(v14) & $i(v11) & $i(v10) & ( ~ (v12 = 0) | (( ~ (v13
% 100.17/14.33 | = 0) | ( ~ (v1 = v0) & ( ~ (v4 = v0) | v17 = 0) & (v4 =
% 100.17/14.33 | v0 | (( ~ (v4 = v1) | v22 = 0 | v3 = v0) & (v24 = 0 |
% 100.17/14.33 | v4 = v1))))) & (v13 = 0 | v1 = v0 | (v4 = v0 & ~
% 100.17/14.33 | (v17 = 0)) | ( ~ (v4 = v0) & ((v4 = v1 & ~ (v22 = 0) &
% 100.17/14.33 | ~ (v3 = v0)) | ( ~ (v24 = 0) & ~ (v4 = v1)))))))))
% 100.17/14.33 |
% 100.17/14.33 | ALPHA: (123) implies:
% 100.17/14.33 | (124) c_member(all_551_3) = all_551_2
% 100.17/14.33 | (125) tc_fun(all_551_4, tc_HOL_Obool) = all_551_3
% 100.17/14.33 | (126) tc_prod(tc_Arrow__Order__Mirabelle_Oalt,
% 100.17/14.33 | tc_Arrow__Order__Mirabelle_Oalt) = all_551_4
% 100.17/14.33 |
% 100.17/14.33 | DELTA: instantiating (10) with fresh symbols all_554_0, all_554_1, all_554_2,
% 100.17/14.33 | all_554_3, all_554_4 gives:
% 100.17/14.33 | (127) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 100.17/14.33 | tc_Arrow__Order__Mirabelle_Oalt) = all_554_0 &
% 100.17/14.33 | tc_prod(tc_Arrow__Order__Mirabelle_Oalt,
% 100.17/14.33 | tc_Arrow__Order__Mirabelle_Oalt) = all_554_4 & tc_fun(all_554_4,
% 100.17/14.33 | tc_HOL_Obool) = all_554_3 & c_member(all_554_3) = all_554_2 &
% 100.17/14.33 | c_member(all_554_4) = all_554_1 & $i(all_554_0) & $i(all_554_1) &
% 100.17/14.33 | $i(all_554_2) & $i(all_554_3) & $i(all_554_4) & ! [v0: $i] : ! [v1:
% 100.17/14.33 | $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : !
% 100.17/14.33 | [v6: $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : (v4 = v3 | ~
% 100.17/14.33 | (c_Arrow__Order__Mirabelle_Oabove(v2, v4, v3) = v8) | ~ (hAPP(v7,
% 100.17/14.33 | v8) = v9) | ~ (hAPP(v5, v0) = v6) | ~ (hAPP(all_554_0, v1) =
% 100.17/14.33 | v5) | ~ (hAPP(all_554_1, v6) = v7) | ~ $i(v4) | ~ $i(v3) | ~
% 100.17/14.33 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v10: $i] : ? [v11: $i] : ?
% 100.17/14.33 | [v12: any] : ? [v13: any] : ? [v14: $i] : ? [v15: $i] : ? [v16:
% 100.17/14.33 | $i] : ? [v17: $i] : ? [v18: any] : ? [v19: $i] : ? [v20: $i]
% 100.17/14.33 | : ? [v21: $i] : ? [v22: any] : ? [v23: $i] : ? [v24: any] :
% 100.17/14.33 | (hBOOL(v23) = v24 & hBOOL(v21) = v22 & hBOOL(v17) = v18 &
% 100.17/14.33 | hBOOL(v11) = v12 & hBOOL(v9) = v13 & hAPP(v20, v2) = v21 &
% 100.17/14.33 | hAPP(v16, v2) = v17 & hAPP(v14, v0) = v15 & hAPP(v10,
% 100.17/14.33 | c_Arrow__Order__Mirabelle_OLin) = v11 & hAPP(v7, v2) = v23 &
% 100.17/14.33 | hAPP(v5, v4) = v19 & hAPP(all_554_0, v4) = v14 & hAPP(all_554_1,
% 100.17/14.33 | v19) = v20 & hAPP(all_554_1, v15) = v16 & hAPP(all_554_2, v2) =
% 100.17/14.33 | v10 & $i(v23) & $i(v21) & $i(v20) & $i(v19) & $i(v17) & $i(v16) &
% 100.17/14.33 | $i(v15) & $i(v14) & $i(v11) & $i(v10) & ( ~ (v12 = 0) | (( ~ (v13
% 100.17/14.33 | = 0) | ( ~ (v1 = v0) & ( ~ (v3 = v1) | v18 = 0) & (v3 =
% 100.17/14.33 | v1 | (( ~ (v3 = v0) | v22 = 0 | v4 = v1) & (v24 = 0 |
% 100.17/14.33 | v3 = v0))))) & (v13 = 0 | v1 = v0 | (v3 = v1 & ~
% 100.17/14.33 | (v18 = 0)) | ( ~ (v3 = v1) & ((v3 = v0 & ~ (v22 = 0) &
% 100.17/14.33 | ~ (v4 = v1)) | ( ~ (v24 = 0) & ~ (v3 = v0)))))))))
% 100.17/14.33 |
% 100.17/14.33 | ALPHA: (127) implies:
% 100.17/14.33 | (128) c_member(all_554_3) = all_554_2
% 100.17/14.33 | (129) tc_fun(all_554_4, tc_HOL_Obool) = all_554_3
% 100.17/14.33 | (130) tc_prod(tc_Arrow__Order__Mirabelle_Oalt,
% 100.17/14.33 | tc_Arrow__Order__Mirabelle_Oalt) = all_554_4
% 100.17/14.33 |
% 100.17/14.33 | DELTA: instantiating (18) with fresh symbols all_557_0, all_557_1, all_557_2,
% 100.17/14.33 | all_557_3, all_557_4, all_557_5 gives:
% 100.17/14.33 | (131) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 100.17/14.33 | tc_Arrow__Order__Mirabelle_Oalt) = all_557_0 &
% 100.17/14.33 | tc_prod(tc_Arrow__Order__Mirabelle_Oalt,
% 100.17/14.33 | tc_Arrow__Order__Mirabelle_Oalt) = all_557_5 & tc_fun(all_557_5,
% 100.17/14.33 | tc_HOL_Obool) = all_557_4 &
% 100.17/14.33 | tc_fun(tc_Arrow__Order__Mirabelle_Oindi, all_557_4) = all_557_3 &
% 100.17/14.33 | c_member(all_557_3) = all_557_2 & c_member(all_557_5) = all_557_1 &
% 100.17/14.33 | $i(all_557_0) & $i(all_557_1) & $i(all_557_2) & $i(all_557_3) &
% 100.17/14.33 | $i(all_557_4) & $i(all_557_5) & ! [v0: $i] : ! [v1: int] : (v1 = 0
% 100.17/14.33 | | ~ (c_Arrow__Order__Mirabelle_OIIA(v0) = v1) | ~ $i(v0) | ?
% 100.17/14.33 | [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : (hBOOL(v4) = 0
% 100.17/14.33 | & hAPP(v3, c_Arrow__Order__Mirabelle_OProf) = v4 & hAPP(v0, v2) =
% 100.17/14.33 | v5 & hAPP(all_557_2, v2) = v3 & $i(v5) & $i(v4) & $i(v3) & $i(v2)
% 100.17/14.33 | & ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] :
% 100.17/14.33 | (hBOOL(v8) = 0 & hAPP(v7, c_Arrow__Order__Mirabelle_OProf) = v8 &
% 100.17/14.33 | hAPP(v0, v6) = v9 & hAPP(all_557_2, v6) = v7 & $i(v9) & $i(v8)
% 100.17/14.33 | & $i(v7) & $i(v6) & ? [v10: $i] : ? [v11: $i] : ? [v12: $i]
% 100.17/14.33 | : ? [v13: $i] : ? [v14: $i] : ? [v15: $i] : ? [v16: any] :
% 100.17/14.33 | ? [v17: $i] : ? [v18: any] : (hBOOL(v17) = v18 & hBOOL(v15) =
% 100.17/14.33 | v16 & hAPP(v14, v9) = v17 & hAPP(v14, v5) = v15 & hAPP(v12,
% 100.17/14.33 | v11) = v13 & hAPP(all_557_0, v10) = v12 & hAPP(all_557_1,
% 100.17/14.33 | v13) = v14 & $i(v17) & $i(v15) & $i(v14) & $i(v13) &
% 100.17/14.33 | $i(v12) & $i(v11) & $i(v10) & ! [v19: $i] : ! [v20: $i] :
% 100.17/14.33 | ! [v21: $i] : ( ~ (hAPP(v14, v20) = v21) | ~ (hAPP(v2, v19)
% 100.17/14.33 | = v20) | ~ $i(v19) | ? [v22: any] : ? [v23: $i] : ?
% 100.17/14.33 | [v24: $i] : ? [v25: any] : (hBOOL(v24) = v25 & hBOOL(v21)
% 100.17/14.33 | = v22 & hAPP(v14, v23) = v24 & hAPP(v6, v19) = v23 &
% 100.17/14.33 | $i(v24) & $i(v23) & ( ~ (v22 = 0) | v25 = 0))) & ! [v19:
% 100.17/14.33 | $i] : ! [v20: $i] : ! [v21: $i] : ( ~ (hAPP(v14, v20) =
% 100.17/14.33 | v21) | ~ (hAPP(v2, v19) = v20) | ~ $i(v19) | ? [v22:
% 100.17/14.33 | $i] : ? [v23: $i] : ? [v24: any] : ? [v25: any] :
% 100.17/14.33 | (hBOOL(v23) = v24 & hBOOL(v21) = v25 & hAPP(v14, v22) = v23
% 100.17/14.33 | & hAPP(v6, v19) = v22 & $i(v23) & $i(v22) & ( ~ (v24 = 0)
% 100.17/14.33 | | v25 = 0))) & ( ~ (v18 = 0) | ~ (v16 = 0)) & (v18 = 0
% 100.17/14.33 | | v16 = 0))))) & ! [v0: $i] : ( ~
% 100.17/14.33 | (c_Arrow__Order__Mirabelle_OIIA(v0) = 0) | ~ $i(v0) | ! [v1: $i]
% 100.17/14.33 | : ! [v2: $i] : ( ~ (hAPP(all_557_2, v1) = v2) | ~ $i(v1) | ?
% 100.17/14.33 | [v3: $i] : ? [v4: any] : ? [v5: $i] : (hBOOL(v3) = v4 &
% 100.17/14.33 | hAPP(v2, c_Arrow__Order__Mirabelle_OProf) = v3 & hAPP(v0, v1) =
% 100.17/14.33 | v5 & $i(v5) & $i(v3) & ( ~ (v4 = 0) | ! [v6: $i] : ! [v7: $i]
% 100.17/14.33 | : ( ~ (hAPP(all_557_2, v6) = v7) | ~ $i(v6) | ? [v8: $i] :
% 100.17/14.33 | ? [v9: any] : ? [v10: $i] : (hBOOL(v8) = v9 & hAPP(v7,
% 100.17/14.33 | c_Arrow__Order__Mirabelle_OProf) = v8 & hAPP(v0, v6) =
% 100.17/14.33 | v10 & $i(v10) & $i(v8) & ( ~ (v9 = 0) | ! [v11: $i] : !
% 100.17/14.33 | [v12: $i] : ! [v13: $i] : ! [v14: $i] : ! [v15: $i]
% 100.17/14.33 | : ! [v16: $i] : ( ~ (hAPP(v15, v5) = v16) | ~
% 100.17/14.33 | (hAPP(v13, v12) = v14) | ~ (hAPP(all_557_0, v11) =
% 100.17/14.33 | v13) | ~ (hAPP(all_557_1, v14) = v15) | ~ $i(v12)
% 100.17/14.33 | | ~ $i(v11) | ? [v17: $i] : ? [v18: $i] : ? [v19:
% 100.17/14.33 | $i] : ? [v20: any] : ? [v21: $i] : ? [v22: $i] :
% 100.17/14.33 | ? [v23: any] : (hBOOL(v22) = v23 & hBOOL(v19) = v20
% 100.17/14.33 | & hAPP(v15, v21) = v22 & hAPP(v15, v18) = v19 &
% 100.17/14.33 | hAPP(v6, v17) = v21 & hAPP(v1, v17) = v18 & $i(v22)
% 100.17/14.33 | & $i(v21) & $i(v19) & $i(v18) & $i(v17) & ( ~ (v23
% 100.17/14.33 | = 0) | ~ (v20 = 0)) & (v23 = 0 | v20 = 0)) |
% 100.17/14.33 | ? [v17: any] : ? [v18: $i] : ? [v19: any] :
% 100.17/14.33 | (hBOOL(v18) = v19 & hBOOL(v16) = v17 & hAPP(v15, v10)
% 100.17/14.33 | = v18 & $i(v18) & ( ~ (v19 = 0) | v17 = 0) & ( ~
% 100.17/14.33 | (v17 = 0) | v19 = 0))))))))))
% 100.17/14.33 |
% 100.17/14.33 | ALPHA: (131) implies:
% 100.17/14.33 | (132) c_member(all_557_3) = all_557_2
% 100.17/14.33 | (133) tc_fun(tc_Arrow__Order__Mirabelle_Oindi, all_557_4) = all_557_3
% 100.17/14.33 | (134) tc_fun(all_557_5, tc_HOL_Obool) = all_557_4
% 100.17/14.33 | (135) tc_prod(tc_Arrow__Order__Mirabelle_Oalt,
% 100.17/14.33 | tc_Arrow__Order__Mirabelle_Oalt) = all_557_5
% 100.17/14.33 |
% 100.17/14.33 | DELTA: instantiating (52) with fresh symbols all_560_0, all_560_1, all_560_2
% 100.17/14.33 | gives:
% 100.17/14.33 | (136) hBOOL(all_560_0) = 0 & hAPP(all_560_1,
% 100.17/14.33 | c_Arrow__Order__Mirabelle_OLin) = all_560_0 & hAPP(all_497_0,
% 100.17/14.33 | all_560_2) = all_560_1 & $i(all_560_0) & $i(all_560_1) &
% 100.17/14.33 | $i(all_560_2)
% 100.17/14.33 |
% 100.17/14.33 | ALPHA: (136) implies:
% 100.17/14.33 | (137) $i(all_560_2)
% 100.17/14.33 | (138) hAPP(all_497_0, all_560_2) = all_560_1
% 100.17/14.33 | (139) hAPP(all_560_1, c_Arrow__Order__Mirabelle_OLin) = all_560_0
% 100.17/14.33 |
% 100.17/14.33 | GROUND_INST: instantiating (39) with all_497_2, all_509_7,
% 100.17/14.33 | tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt,
% 100.17/14.33 | simplifying with (51), (70) gives:
% 100.17/14.33 | (140) all_509_7 = all_497_2
% 100.17/14.33 |
% 100.17/14.33 | GROUND_INST: instantiating (39) with all_509_7, all_511_2,
% 100.17/14.33 | tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt,
% 100.17/14.33 | simplifying with (70), (75) gives:
% 100.17/14.33 | (141) all_511_2 = all_509_7
% 100.17/14.33 |
% 100.17/14.33 | GROUND_INST: instantiating (39) with all_511_2, all_514_2,
% 100.17/14.33 | tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt,
% 100.17/14.33 | simplifying with (75), (79) gives:
% 100.17/14.33 | (142) all_514_2 = all_511_2
% 100.17/14.33 |
% 100.17/14.33 | GROUND_INST: instantiating (39) with all_514_2, all_517_2,
% 100.17/14.33 | tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt,
% 100.17/14.33 | simplifying with (79), (83) gives:
% 100.17/14.33 | (143) all_517_2 = all_514_2
% 100.17/14.33 |
% 100.17/14.33 | GROUND_INST: instantiating (39) with all_517_2, all_520_2,
% 100.17/14.33 | tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt,
% 100.17/14.33 | simplifying with (83), (87) gives:
% 100.17/14.33 | (144) all_520_2 = all_517_2
% 100.17/14.33 |
% 100.17/14.33 | GROUND_INST: instantiating (39) with all_520_2, all_526_3,
% 100.17/14.33 | tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt,
% 100.17/14.33 | simplifying with (87), (95) gives:
% 100.17/14.33 | (145) all_526_3 = all_520_2
% 100.17/14.33 |
% 100.17/14.33 | GROUND_INST: instantiating (39) with all_526_3, all_532_4,
% 100.17/14.33 | tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt,
% 100.17/14.33 | simplifying with (95), (105) gives:
% 100.17/14.33 | (146) all_532_4 = all_526_3
% 100.17/14.33 |
% 100.17/14.33 | GROUND_INST: instantiating (39) with all_532_4, all_545_10,
% 100.17/14.33 | tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt,
% 100.17/14.33 | simplifying with (105), (116) gives:
% 100.17/14.34 | (147) all_545_10 = all_532_4
% 100.17/14.34 |
% 100.17/14.34 | GROUND_INST: instantiating (39) with all_495_4, all_545_10,
% 100.17/14.34 | tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt,
% 100.17/14.34 | simplifying with (46), (116) gives:
% 100.17/14.34 | (148) all_545_10 = all_495_4
% 100.17/14.34 |
% 100.17/14.34 | GROUND_INST: instantiating (39) with all_537_2, all_551_4,
% 100.17/14.34 | tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt,
% 100.17/14.34 | simplifying with (107), (126) gives:
% 100.17/14.34 | (149) all_551_4 = all_537_2
% 100.17/14.34 |
% 100.17/14.34 | GROUND_INST: instantiating (39) with all_551_4, all_554_4,
% 100.17/14.34 | tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt,
% 100.17/14.34 | simplifying with (126), (130) gives:
% 100.17/14.34 | (150) all_554_4 = all_551_4
% 100.17/14.34 |
% 100.17/14.34 | GROUND_INST: instantiating (39) with all_548_5, all_554_4,
% 100.17/14.34 | tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt,
% 100.17/14.34 | simplifying with (122), (130) gives:
% 100.17/14.34 | (151) all_554_4 = all_548_5
% 100.17/14.34 |
% 100.17/14.34 | GROUND_INST: instantiating (39) with all_542_2, all_554_4,
% 100.17/14.34 | tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt,
% 100.17/14.34 | simplifying with (109), (130) gives:
% 100.17/14.34 | (152) all_554_4 = all_542_2
% 100.17/14.34 |
% 100.17/14.34 | GROUND_INST: instantiating (39) with all_529_3, all_554_4,
% 100.17/14.34 | tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt,
% 100.17/14.34 | simplifying with (101), (130) gives:
% 100.17/14.34 | (153) all_554_4 = all_529_3
% 100.17/14.34 |
% 100.17/14.34 | GROUND_INST: instantiating (39) with all_509_7, all_554_4,
% 100.17/14.34 | tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt,
% 100.17/14.34 | simplifying with (70), (130) gives:
% 100.17/14.34 | (154) all_554_4 = all_509_7
% 100.17/14.34 |
% 100.17/14.34 | GROUND_INST: instantiating (39) with all_503_5, all_554_4,
% 100.17/14.34 | tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt,
% 100.17/14.34 | simplifying with (58), (130) gives:
% 100.17/14.34 | (155) all_554_4 = all_503_5
% 100.17/14.34 |
% 100.17/14.34 | GROUND_INST: instantiating (39) with all_548_5, all_557_5,
% 100.17/14.34 | tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt,
% 100.17/14.34 | simplifying with (122), (135) gives:
% 100.17/14.34 | (156) all_557_5 = all_548_5
% 100.17/14.34 |
% 100.17/14.34 | GROUND_INST: instantiating (39) with all_523_4, all_557_5,
% 100.17/14.34 | tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt,
% 100.17/14.34 | simplifying with (91), (135) gives:
% 100.17/14.34 | (157) all_557_5 = all_523_4
% 100.17/14.34 |
% 100.17/14.34 | COMBINE_EQS: (156), (157) imply:
% 100.17/14.34 | (158) all_548_5 = all_523_4
% 100.17/14.34 |
% 100.17/14.34 | SIMP: (158) implies:
% 100.17/14.34 | (159) all_548_5 = all_523_4
% 100.17/14.34 |
% 100.17/14.34 | COMBINE_EQS: (151), (152) imply:
% 100.17/14.34 | (160) all_548_5 = all_542_2
% 100.17/14.34 |
% 100.17/14.34 | SIMP: (160) implies:
% 100.17/14.34 | (161) all_548_5 = all_542_2
% 100.17/14.34 |
% 100.17/14.34 | COMBINE_EQS: (150), (152) imply:
% 100.17/14.34 | (162) all_551_4 = all_542_2
% 100.17/14.34 |
% 100.17/14.34 | SIMP: (162) implies:
% 100.17/14.34 | (163) all_551_4 = all_542_2
% 100.17/14.34 |
% 100.17/14.34 | COMBINE_EQS: (152), (154) imply:
% 100.17/14.34 | (164) all_542_2 = all_509_7
% 100.17/14.34 |
% 100.17/14.34 | COMBINE_EQS: (152), (153) imply:
% 100.17/14.34 | (165) all_542_2 = all_529_3
% 100.17/14.34 |
% 100.17/14.34 | COMBINE_EQS: (152), (155) imply:
% 100.17/14.34 | (166) all_542_2 = all_503_5
% 100.17/14.34 |
% 100.17/14.34 | COMBINE_EQS: (149), (163) imply:
% 100.17/14.34 | (167) all_542_2 = all_537_2
% 100.17/14.34 |
% 100.17/14.34 | SIMP: (167) implies:
% 100.17/14.34 | (168) all_542_2 = all_537_2
% 100.17/14.34 |
% 100.17/14.34 | COMBINE_EQS: (159), (161) imply:
% 100.17/14.34 | (169) all_542_2 = all_523_4
% 100.17/14.34 |
% 100.17/14.34 | SIMP: (169) implies:
% 100.17/14.34 | (170) all_542_2 = all_523_4
% 100.17/14.34 |
% 100.41/14.34 | COMBINE_EQS: (147), (148) imply:
% 100.41/14.34 | (171) all_532_4 = all_495_4
% 100.41/14.34 |
% 100.41/14.34 | SIMP: (171) implies:
% 100.41/14.34 | (172) all_532_4 = all_495_4
% 100.41/14.34 |
% 100.41/14.34 | COMBINE_EQS: (164), (168) imply:
% 100.41/14.34 | (173) all_537_2 = all_509_7
% 100.41/14.34 |
% 100.41/14.34 | COMBINE_EQS: (165), (168) imply:
% 100.41/14.34 | (174) all_537_2 = all_529_3
% 100.41/14.34 |
% 100.41/14.34 | COMBINE_EQS: (166), (168) imply:
% 100.41/14.34 | (175) all_537_2 = all_503_5
% 100.41/14.34 |
% 100.41/14.34 | COMBINE_EQS: (168), (170) imply:
% 100.41/14.34 | (176) all_537_2 = all_523_4
% 100.41/14.34 |
% 100.41/14.34 | COMBINE_EQS: (174), (176) imply:
% 100.41/14.34 | (177) all_529_3 = all_523_4
% 100.41/14.34 |
% 100.41/14.34 | COMBINE_EQS: (174), (175) imply:
% 100.41/14.34 | (178) all_529_3 = all_503_5
% 100.41/14.34 |
% 100.41/14.34 | COMBINE_EQS: (173), (174) imply:
% 100.41/14.34 | (179) all_529_3 = all_509_7
% 100.41/14.34 |
% 100.41/14.34 | COMBINE_EQS: (146), (172) imply:
% 100.41/14.34 | (180) all_526_3 = all_495_4
% 100.41/14.34 |
% 100.41/14.34 | SIMP: (180) implies:
% 100.41/14.34 | (181) all_526_3 = all_495_4
% 100.41/14.34 |
% 100.41/14.34 | COMBINE_EQS: (177), (179) imply:
% 100.41/14.34 | (182) all_523_4 = all_509_7
% 100.41/14.34 |
% 100.41/14.34 | COMBINE_EQS: (177), (178) imply:
% 100.41/14.34 | (183) all_523_4 = all_503_5
% 100.41/14.34 |
% 100.41/14.34 | COMBINE_EQS: (145), (181) imply:
% 100.41/14.34 | (184) all_520_2 = all_495_4
% 100.41/14.34 |
% 100.41/14.34 | SIMP: (184) implies:
% 100.41/14.34 | (185) all_520_2 = all_495_4
% 100.41/14.34 |
% 100.41/14.34 | COMBINE_EQS: (182), (183) imply:
% 100.41/14.34 | (186) all_509_7 = all_503_5
% 100.41/14.34 |
% 100.41/14.34 | SIMP: (186) implies:
% 100.41/14.34 | (187) all_509_7 = all_503_5
% 100.41/14.34 |
% 100.41/14.34 | COMBINE_EQS: (144), (185) imply:
% 100.41/14.34 | (188) all_517_2 = all_495_4
% 100.41/14.34 |
% 100.41/14.34 | SIMP: (188) implies:
% 100.41/14.34 | (189) all_517_2 = all_495_4
% 100.41/14.34 |
% 100.41/14.34 | COMBINE_EQS: (143), (189) imply:
% 100.41/14.34 | (190) all_514_2 = all_495_4
% 100.41/14.34 |
% 100.41/14.34 | SIMP: (190) implies:
% 100.41/14.34 | (191) all_514_2 = all_495_4
% 100.41/14.34 |
% 100.41/14.34 | COMBINE_EQS: (142), (191) imply:
% 100.41/14.34 | (192) all_511_2 = all_495_4
% 100.41/14.34 |
% 100.41/14.34 | SIMP: (192) implies:
% 100.41/14.34 | (193) all_511_2 = all_495_4
% 100.41/14.34 |
% 100.41/14.34 | COMBINE_EQS: (141), (193) imply:
% 100.41/14.34 | (194) all_509_7 = all_495_4
% 100.41/14.34 |
% 100.41/14.34 | SIMP: (194) implies:
% 100.41/14.34 | (195) all_509_7 = all_495_4
% 100.41/14.34 |
% 100.41/14.34 | COMBINE_EQS: (140), (187) imply:
% 100.41/14.34 | (196) all_503_5 = all_497_2
% 100.41/14.34 |
% 100.41/14.34 | COMBINE_EQS: (187), (195) imply:
% 100.41/14.34 | (197) all_503_5 = all_495_4
% 100.41/14.34 |
% 100.41/14.34 | COMBINE_EQS: (196), (197) imply:
% 100.41/14.34 | (198) all_497_2 = all_495_4
% 100.41/14.34 |
% 100.41/14.34 | SIMP: (198) implies:
% 100.41/14.34 | (199) all_497_2 = all_495_4
% 100.41/14.34 |
% 100.41/14.34 | COMBINE_EQS: (183), (197) imply:
% 100.41/14.34 | (200) all_523_4 = all_495_4
% 100.41/14.34 |
% 100.41/14.34 | COMBINE_EQS: (177), (200) imply:
% 100.41/14.34 | (201) all_529_3 = all_495_4
% 100.41/14.34 |
% 100.41/14.34 | COMBINE_EQS: (174), (201) imply:
% 100.41/14.34 | (202) all_537_2 = all_495_4
% 100.41/14.34 |
% 100.41/14.34 | COMBINE_EQS: (168), (202) imply:
% 100.41/14.34 | (203) all_542_2 = all_495_4
% 100.41/14.34 |
% 100.41/14.34 | COMBINE_EQS: (159), (200) imply:
% 100.41/14.34 | (204) all_548_5 = all_495_4
% 100.41/14.34 |
% 100.41/14.34 | COMBINE_EQS: (149), (202) imply:
% 100.41/14.34 | (205) all_551_4 = all_495_4
% 100.41/14.34 |
% 100.41/14.34 | COMBINE_EQS: (152), (203) imply:
% 100.41/14.34 | (206) all_554_4 = all_495_4
% 100.41/14.34 |
% 100.41/14.34 | COMBINE_EQS: (157), (200) imply:
% 100.41/14.34 | (207) all_557_5 = all_495_4
% 100.41/14.34 |
% 100.41/14.34 | REDUCE: (134), (207) imply:
% 100.41/14.34 | (208) tc_fun(all_495_4, tc_HOL_Obool) = all_557_4
% 100.41/14.34 |
% 100.41/14.34 | REDUCE: (129), (206) imply:
% 100.41/14.34 | (209) tc_fun(all_495_4, tc_HOL_Obool) = all_554_3
% 100.41/14.34 |
% 100.41/14.34 | REDUCE: (125), (205) imply:
% 100.41/14.34 | (210) tc_fun(all_495_4, tc_HOL_Obool) = all_551_3
% 100.41/14.34 |
% 100.41/14.34 | REDUCE: (121), (204) imply:
% 100.41/14.34 | (211) tc_fun(all_495_4, tc_HOL_Obool) = all_548_4
% 100.41/14.34 |
% 100.41/14.34 | REDUCE: (114), (148) imply:
% 100.41/14.34 | (212) tc_fun(all_495_4, tc_HOL_Obool) = all_545_9
% 100.41/14.34 |
% 100.41/14.34 | REDUCE: (104), (172) imply:
% 100.41/14.34 | (213) tc_fun(all_495_4, tc_HOL_Obool) = all_532_3
% 100.41/14.34 |
% 100.41/14.34 | REDUCE: (100), (201) imply:
% 100.41/14.34 | (214) tc_fun(all_495_4, tc_HOL_Obool) = all_529_2
% 100.41/14.34 |
% 100.41/14.34 | REDUCE: (94), (181) imply:
% 100.41/14.34 | (215) tc_fun(all_495_4, tc_HOL_Obool) = all_526_2
% 100.41/14.34 |
% 100.41/14.34 | REDUCE: (90), (200) imply:
% 100.41/14.34 | (216) tc_fun(all_495_4, tc_HOL_Obool) = all_523_3
% 100.41/14.34 |
% 100.41/14.34 | REDUCE: (86), (185) imply:
% 100.41/14.34 | (217) tc_fun(all_495_4, tc_HOL_Obool) = all_520_1
% 100.41/14.34 |
% 100.41/14.34 | REDUCE: (82), (189) imply:
% 100.41/14.34 | (218) tc_fun(all_495_4, tc_HOL_Obool) = all_517_1
% 100.41/14.34 |
% 100.41/14.34 | REDUCE: (78), (191) imply:
% 100.41/14.35 | (219) tc_fun(all_495_4, tc_HOL_Obool) = all_514_1
% 100.41/14.35 |
% 100.41/14.35 | REDUCE: (74), (193) imply:
% 100.41/14.35 | (220) tc_fun(all_495_4, tc_HOL_Obool) = all_511_1
% 100.41/14.35 |
% 100.41/14.35 | REDUCE: (69), (195) imply:
% 100.41/14.35 | (221) tc_fun(all_495_4, tc_HOL_Obool) = all_509_6
% 100.41/14.35 |
% 100.41/14.35 | REDUCE: (56), (197) imply:
% 100.41/14.35 | (222) tc_fun(all_495_4, tc_HOL_Obool) = all_503_4
% 100.41/14.35 |
% 100.41/14.35 | REDUCE: (50), (199) imply:
% 100.41/14.35 | (223) tc_fun(all_495_4, tc_HOL_Obool) = all_497_1
% 100.41/14.35 |
% 100.41/14.35 | GROUND_INST: instantiating (38) with all_503_4, all_509_6, tc_HOL_Obool,
% 100.41/14.35 | all_495_4, simplifying with (221), (222) gives:
% 100.41/14.35 | (224) all_509_6 = all_503_4
% 100.41/14.35 |
% 100.41/14.35 | GROUND_INST: instantiating (38) with all_509_6, all_511_1, tc_HOL_Obool,
% 100.41/14.35 | all_495_4, simplifying with (220), (221) gives:
% 100.41/14.35 | (225) all_511_1 = all_509_6
% 100.41/14.35 |
% 100.41/14.35 | GROUND_INST: instantiating (38) with all_511_1, all_514_1, tc_HOL_Obool,
% 100.41/14.35 | all_495_4, simplifying with (219), (220) gives:
% 100.41/14.35 | (226) all_514_1 = all_511_1
% 100.41/14.35 |
% 100.41/14.35 | GROUND_INST: instantiating (38) with all_517_1, all_529_2, tc_HOL_Obool,
% 100.41/14.35 | all_495_4, simplifying with (214), (218) gives:
% 100.41/14.35 | (227) all_529_2 = all_517_1
% 100.41/14.35 |
% 100.41/14.35 | GROUND_INST: instantiating (38) with all_529_2, all_532_3, tc_HOL_Obool,
% 100.41/14.35 | all_495_4, simplifying with (213), (214) gives:
% 100.41/14.35 | (228) all_532_3 = all_529_2
% 100.41/14.35 |
% 100.41/14.35 | GROUND_INST: instantiating (38) with all_523_3, all_532_3, tc_HOL_Obool,
% 100.41/14.35 | all_495_4, simplifying with (213), (216) gives:
% 100.41/14.35 | (229) all_532_3 = all_523_3
% 100.41/14.35 |
% 100.41/14.35 | GROUND_INST: instantiating (38) with all_514_1, all_532_3, tc_HOL_Obool,
% 100.41/14.35 | all_495_4, simplifying with (213), (219) gives:
% 100.41/14.35 | (230) all_532_3 = all_514_1
% 100.41/14.35 |
% 100.41/14.35 | GROUND_INST: instantiating (38) with all_545_9, all_548_4, tc_HOL_Obool,
% 100.41/14.35 | all_495_4, simplifying with (211), (212) gives:
% 100.41/14.35 | (231) all_548_4 = all_545_9
% 100.41/14.35 |
% 100.41/14.35 | GROUND_INST: instantiating (38) with all_526_2, all_548_4, tc_HOL_Obool,
% 100.41/14.35 | all_495_4, simplifying with (211), (215) gives:
% 100.41/14.35 | (232) all_548_4 = all_526_2
% 100.41/14.35 |
% 100.41/14.35 | GROUND_INST: instantiating (38) with all_548_4, all_551_3, tc_HOL_Obool,
% 100.41/14.35 | all_495_4, simplifying with (210), (211) gives:
% 100.41/14.35 | (233) all_551_3 = all_548_4
% 100.41/14.35 |
% 100.41/14.35 | GROUND_INST: instantiating (38) with all_497_1, all_551_3, tc_HOL_Obool,
% 100.41/14.35 | all_495_4, simplifying with (210), (223) gives:
% 100.41/14.35 | (234) all_551_3 = all_497_1
% 100.41/14.35 |
% 100.41/14.35 | GROUND_INST: instantiating (38) with all_495_3, all_554_3, tc_HOL_Obool,
% 100.41/14.35 | all_495_4, simplifying with (45), (209) gives:
% 100.41/14.35 | (235) all_554_3 = all_495_3
% 100.41/14.35 |
% 100.41/14.35 | GROUND_INST: instantiating (38) with all_503_4, all_554_3, tc_HOL_Obool,
% 100.41/14.35 | all_495_4, simplifying with (209), (222) gives:
% 100.41/14.35 | (236) all_554_3 = all_503_4
% 100.41/14.35 |
% 100.41/14.35 | GROUND_INST: instantiating (38) with all_532_3, all_557_4, tc_HOL_Obool,
% 100.41/14.35 | all_495_4, simplifying with (208), (213) gives:
% 100.41/14.35 | (237) all_557_4 = all_532_3
% 100.41/14.35 |
% 100.41/14.35 | GROUND_INST: instantiating (38) with all_526_2, all_557_4, tc_HOL_Obool,
% 100.41/14.35 | all_495_4, simplifying with (208), (215) gives:
% 100.41/14.35 | (238) all_557_4 = all_526_2
% 100.41/14.35 |
% 100.41/14.35 | GROUND_INST: instantiating (38) with all_520_1, all_557_4, tc_HOL_Obool,
% 100.41/14.35 | all_495_4, simplifying with (208), (217) gives:
% 100.41/14.35 | (239) all_557_4 = all_520_1
% 100.41/14.35 |
% 100.41/14.35 | COMBINE_EQS: (237), (239) imply:
% 100.41/14.35 | (240) all_532_3 = all_520_1
% 100.41/14.35 |
% 100.41/14.35 | SIMP: (240) implies:
% 100.41/14.35 | (241) all_532_3 = all_520_1
% 100.41/14.35 |
% 100.41/14.35 | COMBINE_EQS: (238), (239) imply:
% 100.41/14.35 | (242) all_526_2 = all_520_1
% 100.41/14.35 |
% 100.41/14.35 | SIMP: (242) implies:
% 100.41/14.35 | (243) all_526_2 = all_520_1
% 100.41/14.35 |
% 100.41/14.35 | COMBINE_EQS: (235), (236) imply:
% 100.41/14.35 | (244) all_503_4 = all_495_3
% 100.41/14.35 |
% 100.41/14.35 | SIMP: (244) implies:
% 100.41/14.35 | (245) all_503_4 = all_495_3
% 100.41/14.35 |
% 100.41/14.35 | COMBINE_EQS: (233), (234) imply:
% 100.41/14.35 | (246) all_548_4 = all_497_1
% 100.41/14.35 |
% 100.41/14.35 | SIMP: (246) implies:
% 100.41/14.35 | (247) all_548_4 = all_497_1
% 100.41/14.35 |
% 100.41/14.35 | COMBINE_EQS: (231), (232) imply:
% 100.41/14.35 | (248) all_545_9 = all_526_2
% 100.41/14.35 |
% 100.41/14.35 | COMBINE_EQS: (231), (247) imply:
% 100.41/14.35 | (249) all_545_9 = all_497_1
% 100.41/14.35 |
% 100.41/14.35 | COMBINE_EQS: (248), (249) imply:
% 100.41/14.35 | (250) all_526_2 = all_497_1
% 100.41/14.35 |
% 100.41/14.35 | SIMP: (250) implies:
% 100.41/14.35 | (251) all_526_2 = all_497_1
% 100.41/14.35 |
% 100.41/14.35 | COMBINE_EQS: (228), (229) imply:
% 100.41/14.35 | (252) all_529_2 = all_523_3
% 100.41/14.35 |
% 100.41/14.35 | SIMP: (252) implies:
% 100.41/14.35 | (253) all_529_2 = all_523_3
% 100.41/14.35 |
% 100.41/14.35 | COMBINE_EQS: (229), (230) imply:
% 100.41/14.35 | (254) all_523_3 = all_514_1
% 100.41/14.35 |
% 100.41/14.35 | COMBINE_EQS: (229), (241) imply:
% 100.41/14.35 | (255) all_523_3 = all_520_1
% 100.41/14.35 |
% 100.41/14.35 | COMBINE_EQS: (227), (253) imply:
% 100.41/14.35 | (256) all_523_3 = all_517_1
% 100.41/14.35 |
% 100.41/14.35 | SIMP: (256) implies:
% 100.41/14.35 | (257) all_523_3 = all_517_1
% 100.41/14.35 |
% 100.41/14.35 | COMBINE_EQS: (243), (251) imply:
% 100.41/14.35 | (258) all_520_1 = all_497_1
% 100.41/14.35 |
% 100.41/14.35 | SIMP: (258) implies:
% 100.41/14.35 | (259) all_520_1 = all_497_1
% 100.41/14.35 |
% 100.41/14.35 | COMBINE_EQS: (254), (257) imply:
% 100.41/14.35 | (260) all_517_1 = all_514_1
% 100.41/14.35 |
% 100.47/14.35 | COMBINE_EQS: (255), (257) imply:
% 100.47/14.35 | (261) all_520_1 = all_517_1
% 100.47/14.35 |
% 100.47/14.35 | SIMP: (261) implies:
% 100.47/14.35 | (262) all_520_1 = all_517_1
% 100.47/14.35 |
% 100.47/14.35 | COMBINE_EQS: (259), (262) imply:
% 100.47/14.35 | (263) all_517_1 = all_497_1
% 100.47/14.35 |
% 100.47/14.35 | SIMP: (263) implies:
% 100.47/14.35 | (264) all_517_1 = all_497_1
% 100.47/14.35 |
% 100.47/14.35 | COMBINE_EQS: (260), (264) imply:
% 100.47/14.35 | (265) all_514_1 = all_497_1
% 100.47/14.35 |
% 100.47/14.35 | SIMP: (265) implies:
% 100.47/14.35 | (266) all_514_1 = all_497_1
% 100.47/14.35 |
% 100.47/14.35 | COMBINE_EQS: (226), (266) imply:
% 100.47/14.35 | (267) all_511_1 = all_497_1
% 100.47/14.35 |
% 100.47/14.35 | SIMP: (267) implies:
% 100.47/14.35 | (268) all_511_1 = all_497_1
% 100.47/14.35 |
% 100.47/14.35 | COMBINE_EQS: (225), (268) imply:
% 100.47/14.35 | (269) all_509_6 = all_497_1
% 100.47/14.35 |
% 100.47/14.35 | SIMP: (269) implies:
% 100.47/14.35 | (270) all_509_6 = all_497_1
% 100.47/14.35 |
% 100.47/14.35 | COMBINE_EQS: (224), (270) imply:
% 100.47/14.35 | (271) all_503_4 = all_497_1
% 100.47/14.35 |
% 100.47/14.35 | SIMP: (271) implies:
% 100.47/14.35 | (272) all_503_4 = all_497_1
% 100.47/14.35 |
% 100.47/14.35 | COMBINE_EQS: (245), (272) imply:
% 100.47/14.35 | (273) all_497_1 = all_495_3
% 100.47/14.35 |
% 100.47/14.35 | COMBINE_EQS: (270), (273) imply:
% 100.47/14.35 | (274) all_509_6 = all_495_3
% 100.47/14.35 |
% 100.47/14.35 | COMBINE_EQS: (268), (273) imply:
% 100.47/14.35 | (275) all_511_1 = all_495_3
% 100.47/14.35 |
% 100.47/14.35 | COMBINE_EQS: (266), (273) imply:
% 100.47/14.35 | (276) all_514_1 = all_495_3
% 100.47/14.35 |
% 100.47/14.35 | COMBINE_EQS: (264), (273) imply:
% 100.47/14.35 | (277) all_517_1 = all_495_3
% 100.47/14.35 |
% 100.47/14.35 | COMBINE_EQS: (259), (273) imply:
% 100.47/14.35 | (278) all_520_1 = all_495_3
% 100.47/14.35 |
% 100.47/14.35 | COMBINE_EQS: (257), (277) imply:
% 100.47/14.35 | (279) all_523_3 = all_495_3
% 100.47/14.35 |
% 100.47/14.35 | COMBINE_EQS: (251), (273) imply:
% 100.47/14.35 | (280) all_526_2 = all_495_3
% 100.47/14.35 |
% 100.47/14.35 | COMBINE_EQS: (227), (277) imply:
% 100.47/14.35 | (281) all_529_2 = all_495_3
% 100.47/14.35 |
% 100.47/14.35 | COMBINE_EQS: (229), (279) imply:
% 100.47/14.35 | (282) all_532_3 = all_495_3
% 100.47/14.35 |
% 100.47/14.35 | COMBINE_EQS: (249), (273) imply:
% 100.47/14.35 | (283) all_545_9 = all_495_3
% 100.47/14.35 |
% 100.47/14.35 | COMBINE_EQS: (231), (283) imply:
% 100.47/14.35 | (284) all_548_4 = all_495_3
% 100.47/14.35 |
% 100.47/14.35 | COMBINE_EQS: (234), (273) imply:
% 100.47/14.35 | (285) all_551_3 = all_495_3
% 100.47/14.35 |
% 100.47/14.35 | COMBINE_EQS: (239), (278) imply:
% 100.47/14.35 | (286) all_557_4 = all_495_3
% 100.47/14.35 |
% 100.47/14.35 | REDUCE: (71), (274) imply:
% 100.47/14.35 | (287) c_COMBK(all_495_3, tc_Arrow__Order__Mirabelle_Oindi, v_L) = all_509_3
% 100.47/14.35 |
% 100.47/14.35 | REDUCE: (117), (283) imply:
% 100.47/14.35 | (288) c_FuncSet_OPi(all_545_8, all_495_3, c_Arrow__Order__Mirabelle_OProf,
% 100.47/14.35 | all_545_4) = all_545_3
% 100.47/14.35 |
% 100.47/14.35 | REDUCE: (59), (245) imply:
% 100.47/14.35 | (289) c_FuncSet_OPi(tc_Arrow__Order__Mirabelle_Oindi, all_495_3, all_503_2,
% 100.47/14.35 | all_503_0) = c_Arrow__Order__Mirabelle_OProf
% 100.47/14.35 |
% 100.47/14.35 | REDUCE: (115), (283) imply:
% 100.47/14.35 | (290) tc_fun(all_495_3, tc_HOL_Obool) = all_545_5
% 100.47/14.35 |
% 100.47/14.35 | REDUCE: (57), (245) imply:
% 100.47/14.35 | (291) tc_fun(all_495_3, tc_HOL_Obool) = all_503_1
% 100.47/14.35 |
% 100.47/14.35 | REDUCE: (133), (286) imply:
% 100.47/14.35 | (292) tc_fun(tc_Arrow__Order__Mirabelle_Oindi, all_495_3) = all_557_3
% 100.47/14.36 |
% 100.47/14.36 | REDUCE: (120), (284) imply:
% 100.47/14.36 | (293) tc_fun(tc_Arrow__Order__Mirabelle_Oindi, all_495_3) = all_548_3
% 100.47/14.36 |
% 100.47/14.36 | REDUCE: (113), (283) imply:
% 100.47/14.36 | (294) tc_fun(tc_Arrow__Order__Mirabelle_Oindi, all_495_3) = all_545_8
% 100.47/14.36 |
% 100.47/14.36 | REDUCE: (99), (281) imply:
% 100.47/14.36 | (295) tc_fun(tc_Arrow__Order__Mirabelle_Oindi, all_495_3) = all_529_1
% 100.47/14.36 |
% 100.47/14.36 | REDUCE: (68), (274) imply:
% 100.47/14.36 | (296) tc_fun(tc_Arrow__Order__Mirabelle_Oindi, all_495_3) = all_509_5
% 100.47/14.36 |
% 100.47/14.36 | REDUCE: (128), (235) imply:
% 100.47/14.36 | (297) c_member(all_495_3) = all_554_2
% 100.47/14.36 |
% 100.47/14.36 | REDUCE: (124), (285) imply:
% 100.47/14.36 | (298) c_member(all_495_3) = all_551_2
% 100.47/14.36 |
% 100.47/14.36 | REDUCE: (103), (282) imply:
% 100.47/14.36 | (299) c_member(all_495_3) = all_532_2
% 100.47/14.36 |
% 100.47/14.36 | REDUCE: (93), (280) imply:
% 100.47/14.36 | (300) c_member(all_495_3) = all_526_1
% 100.47/14.36 |
% 100.47/14.36 | REDUCE: (89), (279) imply:
% 100.47/14.36 | (301) c_member(all_495_3) = all_523_2
% 100.47/14.36 |
% 100.47/14.36 | REDUCE: (85), (278) imply:
% 100.47/14.36 | (302) c_member(all_495_3) = all_520_0
% 100.47/14.36 |
% 100.47/14.36 | REDUCE: (81), (277) imply:
% 100.47/14.36 | (303) c_member(all_495_3) = all_517_0
% 100.47/14.36 |
% 100.47/14.36 | REDUCE: (77), (276) imply:
% 100.47/14.36 | (304) c_member(all_495_3) = all_514_0
% 100.47/14.36 |
% 100.47/14.36 | REDUCE: (73), (275) imply:
% 100.47/14.36 | (305) c_member(all_495_3) = all_511_0
% 100.47/14.36 |
% 100.47/14.36 | REDUCE: (49), (273) imply:
% 100.47/14.36 | (306) c_member(all_495_3) = all_497_0
% 100.47/14.36 |
% 100.47/14.36 | REDUCE: (48), (273) imply:
% 100.47/14.36 | (307) $i(all_495_3)
% 100.47/14.36 |
% 100.47/14.36 | GROUND_INST: instantiating (35) with all_514_0, all_517_0, all_495_3,
% 100.47/14.36 | simplifying with (303), (304) gives:
% 100.47/14.36 | (308) all_517_0 = all_514_0
% 100.47/14.36 |
% 100.47/14.36 | GROUND_INST: instantiating (35) with all_517_0, all_520_0, all_495_3,
% 100.47/14.36 | simplifying with (302), (303) gives:
% 100.47/14.36 | (309) all_520_0 = all_517_0
% 100.47/14.36 |
% 100.47/14.36 | GROUND_INST: instantiating (35) with all_495_2, all_526_1, all_495_3,
% 100.47/14.36 | simplifying with (44), (300) gives:
% 100.47/14.36 | (310) all_526_1 = all_495_2
% 100.47/14.36 |
% 100.47/14.36 | GROUND_INST: instantiating (35) with all_523_2, all_526_1, all_495_3,
% 100.47/14.36 | simplifying with (300), (301) gives:
% 100.47/14.36 | (311) all_526_1 = all_523_2
% 100.47/14.36 |
% 100.47/14.36 | GROUND_INST: instantiating (35) with all_517_0, all_526_1, all_495_3,
% 100.47/14.36 | simplifying with (300), (303) gives:
% 100.47/14.36 | (312) all_526_1 = all_517_0
% 100.47/14.36 |
% 100.47/14.36 | GROUND_INST: instantiating (35) with all_517_0, all_532_2, all_495_3,
% 100.47/14.36 | simplifying with (299), (303) gives:
% 100.47/14.36 | (313) all_532_2 = all_517_0
% 100.47/14.36 |
% 100.47/14.36 | GROUND_INST: instantiating (35) with all_497_0, all_532_2, all_495_3,
% 100.47/14.36 | simplifying with (299), (306) gives:
% 100.47/14.36 | (314) all_532_2 = all_497_0
% 100.47/14.36 |
% 100.47/14.36 | GROUND_INST: instantiating (35) with all_551_2, all_554_2, all_495_3,
% 100.47/14.36 | simplifying with (297), (298) gives:
% 100.47/14.36 | (315) all_554_2 = all_551_2
% 100.47/14.36 |
% 100.47/14.36 | GROUND_INST: instantiating (35) with all_520_0, all_554_2, all_495_3,
% 100.47/14.36 | simplifying with (297), (302) gives:
% 100.47/14.36 | (316) all_554_2 = all_520_0
% 100.47/14.36 |
% 100.47/14.36 | GROUND_INST: instantiating (35) with all_511_0, all_554_2, all_495_3,
% 100.47/14.36 | simplifying with (297), (305) gives:
% 100.47/14.36 | (317) all_554_2 = all_511_0
% 100.47/14.36 |
% 100.47/14.36 | GROUND_INST: instantiating (38) with all_545_8, all_548_3, all_495_3,
% 100.47/14.36 | tc_Arrow__Order__Mirabelle_Oindi, simplifying with (293), (294)
% 100.47/14.36 | gives:
% 100.47/14.36 | (318) all_548_3 = all_545_8
% 100.47/14.36 |
% 100.47/14.36 | GROUND_INST: instantiating (38) with all_509_5, all_548_3, all_495_3,
% 100.47/14.36 | tc_Arrow__Order__Mirabelle_Oindi, simplifying with (293), (296)
% 100.47/14.36 | gives:
% 100.47/14.36 | (319) all_548_3 = all_509_5
% 100.47/14.36 |
% 100.47/14.36 | GROUND_INST: instantiating (38) with all_545_8, all_557_3, all_495_3,
% 100.47/14.36 | tc_Arrow__Order__Mirabelle_Oindi, simplifying with (292), (294)
% 100.47/14.36 | gives:
% 100.47/14.36 | (320) all_557_3 = all_545_8
% 100.47/14.36 |
% 100.47/14.36 | GROUND_INST: instantiating (38) with all_529_1, all_557_3, all_495_3,
% 100.47/14.36 | tc_Arrow__Order__Mirabelle_Oindi, simplifying with (292), (295)
% 100.47/14.36 | gives:
% 100.47/14.36 | (321) all_557_3 = all_529_1
% 100.47/14.36 |
% 100.47/14.36 | GROUND_INST: instantiating (38) with all_503_1, all_545_5, tc_HOL_Obool,
% 100.47/14.36 | all_495_3, simplifying with (290), (291) gives:
% 100.47/14.36 | (322) all_545_5 = all_503_1
% 100.47/14.36 |
% 100.47/14.36 | COMBINE_EQS: (320), (321) imply:
% 100.47/14.36 | (323) all_545_8 = all_529_1
% 100.47/14.36 |
% 100.47/14.36 | SIMP: (323) implies:
% 100.47/14.36 | (324) all_545_8 = all_529_1
% 100.47/14.36 |
% 100.47/14.36 | COMBINE_EQS: (315), (316) imply:
% 100.47/14.36 | (325) all_551_2 = all_520_0
% 100.47/14.36 |
% 100.47/14.36 | COMBINE_EQS: (315), (317) imply:
% 100.47/14.36 | (326) all_551_2 = all_511_0
% 100.47/14.36 |
% 100.47/14.36 | COMBINE_EQS: (325), (326) imply:
% 100.47/14.36 | (327) all_520_0 = all_511_0
% 100.47/14.36 |
% 100.47/14.36 | SIMP: (327) implies:
% 100.47/14.36 | (328) all_520_0 = all_511_0
% 100.47/14.36 |
% 100.47/14.36 | COMBINE_EQS: (318), (319) imply:
% 100.47/14.36 | (329) all_545_8 = all_509_5
% 100.47/14.36 |
% 100.47/14.36 | SIMP: (329) implies:
% 100.47/14.36 | (330) all_545_8 = all_509_5
% 100.47/14.36 |
% 100.47/14.36 | COMBINE_EQS: (324), (330) imply:
% 100.47/14.36 | (331) all_529_1 = all_509_5
% 100.47/14.36 |
% 100.47/14.36 | SIMP: (331) implies:
% 100.47/14.36 | (332) all_529_1 = all_509_5
% 100.47/14.36 |
% 100.47/14.36 | COMBINE_EQS: (313), (314) imply:
% 100.47/14.36 | (333) all_517_0 = all_497_0
% 100.47/14.36 |
% 100.47/14.36 | SIMP: (333) implies:
% 100.47/14.36 | (334) all_517_0 = all_497_0
% 100.47/14.36 |
% 100.47/14.36 | COMBINE_EQS: (311), (312) imply:
% 100.47/14.36 | (335) all_523_2 = all_517_0
% 100.47/14.36 |
% 100.47/14.36 | COMBINE_EQS: (310), (311) imply:
% 100.47/14.36 | (336) all_523_2 = all_495_2
% 100.47/14.36 |
% 100.47/14.36 | COMBINE_EQS: (335), (336) imply:
% 100.47/14.36 | (337) all_517_0 = all_495_2
% 100.47/14.36 |
% 100.47/14.36 | SIMP: (337) implies:
% 100.47/14.36 | (338) all_517_0 = all_495_2
% 100.47/14.36 |
% 100.47/14.36 | COMBINE_EQS: (309), (328) imply:
% 100.47/14.36 | (339) all_517_0 = all_511_0
% 100.47/14.36 |
% 100.47/14.36 | SIMP: (339) implies:
% 100.47/14.36 | (340) all_517_0 = all_511_0
% 100.47/14.36 |
% 100.47/14.36 | COMBINE_EQS: (308), (334) imply:
% 100.47/14.36 | (341) all_514_0 = all_497_0
% 100.47/14.36 |
% 100.47/14.36 | COMBINE_EQS: (308), (340) imply:
% 100.47/14.36 | (342) all_514_0 = all_511_0
% 100.47/14.36 |
% 100.47/14.36 | COMBINE_EQS: (308), (338) imply:
% 100.47/14.36 | (343) all_514_0 = all_495_2
% 100.47/14.36 |
% 100.47/14.36 | COMBINE_EQS: (341), (342) imply:
% 100.47/14.36 | (344) all_511_0 = all_497_0
% 100.47/14.36 |
% 100.47/14.36 | COMBINE_EQS: (342), (343) imply:
% 100.47/14.36 | (345) all_511_0 = all_495_2
% 100.47/14.36 |
% 100.47/14.36 | COMBINE_EQS: (344), (345) imply:
% 100.47/14.36 | (346) all_497_0 = all_495_2
% 100.47/14.36 |
% 100.47/14.36 | SIMP: (346) implies:
% 100.47/14.36 | (347) all_497_0 = all_495_2
% 100.47/14.36 |
% 100.47/14.36 | COMBINE_EQS: (321), (332) imply:
% 100.47/14.36 | (348) all_557_3 = all_509_5
% 100.47/14.36 |
% 100.47/14.36 | REDUCE: (288), (330) imply:
% 100.47/14.36 | (349) c_FuncSet_OPi(all_509_5, all_495_3, c_Arrow__Order__Mirabelle_OProf,
% 100.47/14.36 | all_545_4) = all_545_3
% 100.47/14.36 |
% 100.47/14.36 | REDUCE: (132), (348) imply:
% 100.47/14.36 | (350) c_member(all_509_5) = all_557_2
% 100.47/14.36 |
% 100.47/14.36 | REDUCE: (119), (319) imply:
% 100.47/14.36 | (351) c_member(all_509_5) = all_548_2
% 100.47/14.36 |
% 100.47/14.36 | REDUCE: (112), (330) imply:
% 100.47/14.36 | (352) c_member(all_509_5) = all_545_2
% 100.47/14.36 |
% 100.47/14.36 | REDUCE: (98), (332) imply:
% 100.47/14.36 | (353) c_member(all_509_5) = all_529_0
% 100.47/14.36 |
% 100.47/14.36 | REDUCE: (138), (347) imply:
% 100.47/14.36 | (354) hAPP(all_495_2, all_560_2) = all_560_1
% 100.47/14.36 |
% 100.47/14.36 | REDUCE: (97), (332) imply:
% 100.47/14.36 | (355) $i(all_509_5)
% 100.47/14.36 |
% 100.47/14.36 | GROUND_INST: instantiating (35) with all_509_4, all_545_2, all_509_5,
% 100.47/14.36 | simplifying with (67), (352) gives:
% 100.47/14.36 | (356) all_545_2 = all_509_4
% 100.47/14.36 |
% 100.47/14.36 | GROUND_INST: instantiating (35) with all_545_2, all_548_2, all_509_5,
% 100.47/14.36 | simplifying with (351), (352) gives:
% 100.47/14.36 | (357) all_548_2 = all_545_2
% 100.47/14.36 |
% 100.47/14.36 | GROUND_INST: instantiating (35) with all_548_2, all_557_2, all_509_5,
% 100.47/14.36 | simplifying with (350), (351) gives:
% 100.47/14.36 | (358) all_557_2 = all_548_2
% 100.47/14.36 |
% 100.47/14.36 | GROUND_INST: instantiating (35) with all_529_0, all_557_2, all_509_5,
% 100.47/14.36 | simplifying with (350), (353) gives:
% 100.47/14.36 | (359) all_557_2 = all_529_0
% 100.47/14.36 |
% 100.47/14.36 | COMBINE_EQS: (358), (359) imply:
% 100.47/14.36 | (360) all_548_2 = all_529_0
% 100.47/14.36 |
% 100.47/14.36 | SIMP: (360) implies:
% 100.47/14.36 | (361) all_548_2 = all_529_0
% 100.47/14.36 |
% 100.47/14.36 | COMBINE_EQS: (357), (361) imply:
% 100.47/14.36 | (362) all_545_2 = all_529_0
% 100.47/14.36 |
% 100.47/14.36 | SIMP: (362) implies:
% 100.47/14.36 | (363) all_545_2 = all_529_0
% 100.47/14.36 |
% 100.47/14.36 | COMBINE_EQS: (356), (363) imply:
% 100.47/14.36 | (364) all_529_0 = all_509_4
% 100.47/14.36 |
% 100.47/14.36 | GROUND_INST: instantiating (25) with all_560_2, all_495_3,
% 100.47/14.36 | c_Arrow__Order__Mirabelle_OLin, all_495_2, all_560_1, all_560_0,
% 100.47/14.36 | simplifying with (27), (44), (137), (139), (307), (354) gives:
% 100.47/14.37 | (365) ? [v0: $i] : ? [v1: $i] : ? [v2: any] :
% 100.47/14.37 | (c_Orderings_Obot__class_Obot(v0) = v1 & tc_fun(all_495_3,
% 100.47/14.37 | tc_HOL_Obool) = v0 & hBOOL(all_560_0) = v2 & $i(v1) & $i(v0) & (
% 100.47/14.37 | ~ (v2 = 0) | ~ (v1 = c_Arrow__Order__Mirabelle_OLin)))
% 100.47/14.37 |
% 100.47/14.37 | GROUND_INST: instantiating (8) with c_Arrow__Order__Mirabelle_OLin, v_L,
% 100.47/14.37 | all_495_3, all_495_2, all_495_1, all_495_0, simplifying with
% 100.47/14.37 | (27), (32), (41), (42), (44), (307) gives:
% 100.47/14.37 | (366) ? [v0: any] : ? [v1: $i] : ? [v2: any] : (hBOOL(v1) = v2 &
% 100.47/14.37 | hBOOL(all_495_0) = v0 & hAPP(c_Arrow__Order__Mirabelle_OLin, v_L) =
% 100.47/14.37 | v1 & $i(v1) & ( ~ (v0 = 0) | v2 = 0))
% 100.47/14.37 |
% 100.47/14.37 | GROUND_INST: instantiating (7) with c_Arrow__Order__Mirabelle_OLin, v_L,
% 100.47/14.37 | all_495_3, all_495_2, all_495_1, all_495_0, simplifying with
% 100.47/14.37 | (27), (32), (41), (42), (44), (307) gives:
% 100.47/14.37 | (367) ? [v0: $i] : ? [v1: any] : ? [v2: any] : (hBOOL(v0) = v1 &
% 100.47/14.37 | hBOOL(all_495_0) = v2 & hAPP(c_Arrow__Order__Mirabelle_OLin, v_L) =
% 100.47/14.37 | v0 & $i(v0) & ( ~ (v1 = 0) | v2 = 0))
% 100.47/14.37 |
% 100.47/14.37 | GROUND_INST: instantiating (25) with v_L, all_495_3,
% 100.47/14.37 | c_Arrow__Order__Mirabelle_OLin, all_495_2, all_495_1, all_495_0,
% 100.47/14.37 | simplifying with (27), (32), (41), (42), (44), (307) gives:
% 100.47/14.37 | (368) ? [v0: $i] : ? [v1: $i] : ? [v2: any] :
% 100.47/14.37 | (c_Orderings_Obot__class_Obot(v0) = v1 & tc_fun(all_495_3,
% 100.47/14.37 | tc_HOL_Obool) = v0 & hBOOL(all_495_0) = v2 & $i(v1) & $i(v0) & (
% 100.47/14.37 | ~ (v2 = 0) | ~ (v1 = c_Arrow__Order__Mirabelle_OLin)))
% 100.47/14.37 |
% 100.47/14.37 | GROUND_INST: instantiating (8) with c_Arrow__Order__Mirabelle_OProf,
% 100.47/14.37 | all_509_3, all_509_5, all_509_4, all_509_2, all_509_1,
% 100.47/14.37 | simplifying with (31), (63), (64), (65), (67), (355) gives:
% 100.47/14.37 | (369) ? [v0: any] : ? [v1: $i] : ? [v2: any] : (hBOOL(v1) = v2 &
% 100.47/14.37 | hBOOL(all_509_1) = v0 & hAPP(c_Arrow__Order__Mirabelle_OProf,
% 100.47/14.37 | all_509_3) = v1 & $i(v1) & ( ~ (v0 = 0) | v2 = 0))
% 100.47/14.37 |
% 100.47/14.37 | GROUND_INST: instantiating (7) with c_Arrow__Order__Mirabelle_OProf,
% 100.47/14.37 | all_509_3, all_509_5, all_509_4, all_509_2, all_509_1,
% 100.47/14.37 | simplifying with (31), (63), (64), (65), (67), (355) gives:
% 100.47/14.37 | (370) ? [v0: $i] : ? [v1: any] : ? [v2: any] : (hBOOL(v0) = v1 &
% 100.47/14.37 | hBOOL(all_509_1) = v2 & hAPP(c_Arrow__Order__Mirabelle_OProf,
% 100.47/14.37 | all_509_3) = v0 & $i(v0) & ( ~ (v1 = 0) | v2 = 0))
% 100.47/14.37 |
% 100.47/14.37 | GROUND_INST: instantiating (25) with all_509_3, all_509_5,
% 100.47/14.37 | c_Arrow__Order__Mirabelle_OProf, all_509_4, all_509_2, all_509_1,
% 100.47/14.37 | simplifying with (31), (63), (64), (65), (67), (355) gives:
% 100.47/14.37 | (371) ? [v0: $i] : ? [v1: $i] : ? [v2: any] :
% 100.47/14.37 | (c_Orderings_Obot__class_Obot(v0) = v1 & tc_fun(all_509_5,
% 100.47/14.37 | tc_HOL_Obool) = v0 & hBOOL(all_509_1) = v2 & $i(v1) & $i(v0) & (
% 100.47/14.37 | ~ (v2 = 0) | ~ (v1 = c_Arrow__Order__Mirabelle_OProf)))
% 100.47/14.37 |
% 100.47/14.37 | GROUND_INST: instantiating (arity_fun__Complete__Lattice_Ocomplete__lattice)
% 100.47/14.37 | with all_495_3, tc_HOL_Obool, all_503_1, simplifying with (29),
% 100.47/14.37 | (291), (307) gives:
% 100.47/14.37 | (372) ? [v0: any] : ? [v1: any] :
% 100.47/14.37 | (class_Complete__Lattice_Ocomplete__lattice(all_503_1) = v1 &
% 100.47/14.37 | class_Complete__Lattice_Ocomplete__lattice(tc_HOL_Obool) = v0 & ( ~
% 100.47/14.37 | (v0 = 0) | v1 = 0))
% 100.47/14.37 |
% 100.47/14.37 | GROUND_INST: instantiating (fact_Pi__cong) with all_503_0, all_495_3,
% 100.47/14.37 | all_509_3, all_509_3, all_503_2,
% 100.47/14.37 | tc_Arrow__Order__Mirabelle_Oindi, all_509_5, all_509_4,
% 100.47/14.37 | all_509_2, c_Arrow__Order__Mirabelle_OProf, all_509_1, all_509_2,
% 100.47/14.37 | all_509_1, simplifying with (30), (54), (55), (63), (64), (65),
% 100.47/14.37 | (67), (289), (296), (307) gives:
% 100.47/14.37 | (373) ? [v0: $i] : ? [v1: any] : ? [v2: any] :
% 100.47/14.37 | (c_member(tc_Arrow__Order__Mirabelle_Oindi) = v0 & hBOOL(all_509_1) =
% 100.47/14.37 | v2 & hBOOL(all_509_1) = v1 & $i(v0) & ( ? [v3: $i] : ? [v4: $i] :
% 100.47/14.37 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ( ~ (v7 = v6) &
% 100.47/14.37 | hBOOL(v5) = 0 & hAPP(v4, all_503_2) = v5 & hAPP(v0, v3) = v4 &
% 100.47/14.37 | hAPP(all_509_3, v3) = v7 & hAPP(all_509_3, v3) = v6 & $i(v7) &
% 100.47/14.37 | $i(v6) & $i(v5) & $i(v4) & $i(v3)) | (( ~ (v2 = 0) | v1 = 0) &
% 100.47/14.37 | ( ~ (v1 = 0) | v2 = 0))))
% 100.47/14.37 |
% 100.47/14.37 | GROUND_INST: instantiating (fact_Pi__I_H) with all_503_0, all_509_3,
% 100.47/14.37 | all_495_3, all_503_2, tc_Arrow__Order__Mirabelle_Oindi,
% 100.47/14.37 | all_509_5, all_509_4, all_509_2, c_Arrow__Order__Mirabelle_OProf,
% 100.47/14.37 | all_509_1, simplifying with (30), (54), (55), (63), (64), (65),
% 100.47/14.37 | (67), (289), (296), (307) gives:
% 100.47/14.37 | (374) ? [v0: $i] : ? [v1: $i] : ? [v2: any] : (c_member(all_495_3) = v1
% 100.47/14.37 | & c_member(tc_Arrow__Order__Mirabelle_Oindi) = v0 &
% 100.47/14.37 | hBOOL(all_509_1) = v2 & $i(v1) & $i(v0) & (v2 = 0 | ? [v3: $i] :
% 100.47/14.37 | ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8:
% 100.47/14.37 | $i] : ? [v9: $i] : ? [v10: int] : ( ~ (v10 = 0) & hBOOL(v9) =
% 100.47/14.37 | v10 & hBOOL(v5) = 0 & hAPP(v7, v8) = v9 & hAPP(v4, all_503_2) =
% 100.47/14.37 | v5 & hAPP(v1, v6) = v7 & hAPP(v0, v3) = v4 & hAPP(all_509_3,
% 100.47/14.37 | v3) = v6 & hAPP(all_503_0, v3) = v8 & $i(v9) & $i(v8) &
% 100.47/14.37 | $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3))))
% 100.47/14.37 |
% 100.47/14.37 | GROUND_INST: instantiating (24) with all_503_0, all_503_2, all_495_3,
% 100.47/14.37 | tc_Arrow__Order__Mirabelle_Oindi,
% 100.47/14.37 | c_Arrow__Order__Mirabelle_OProf, simplifying with (30), (54),
% 100.47/14.37 | (55), (289), (307) gives:
% 100.47/14.37 | (375) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 100.47/14.37 | ? [v5: $i] : (c_Orderings_Obot__class_Obot(v4) = v5 &
% 100.47/14.37 | c_Orderings_Obot__class_Obot(v1) = v2 & tc_fun(v3, tc_HOL_Obool) =
% 100.47/14.37 | v4 & tc_fun(all_495_3, tc_HOL_Obool) = v1 &
% 100.47/14.37 | tc_fun(tc_Arrow__Order__Mirabelle_Oindi, all_495_3) = v3 &
% 100.47/14.37 | c_member(tc_Arrow__Order__Mirabelle_Oindi) = v0 & $i(v5) & $i(v4) &
% 100.47/14.37 | $i(v3) & $i(v2) & $i(v1) & $i(v0) & (v5 =
% 100.47/14.37 | c_Arrow__Order__Mirabelle_OProf | ! [v6: $i] : ! [v7: $i] : !
% 100.47/14.37 | [v8: $i] : ( ~ (hAPP(v7, all_503_2) = v8) | ~ (hAPP(v0, v6) =
% 100.47/14.37 | v7) | ~ $i(v6) | ? [v9: any] : ? [v10: $i] : (hBOOL(v8) =
% 100.47/14.37 | v9 & hAPP(all_503_0, v6) = v10 & $i(v10) & ( ~ (v10 = v2) |
% 100.47/14.37 | ~ (v9 = 0))))))
% 100.47/14.37 |
% 100.47/14.37 | GROUND_INST: instantiating (23) with all_503_0, all_503_2, all_495_3,
% 100.47/14.37 | tc_Arrow__Order__Mirabelle_Oindi,
% 100.47/14.37 | c_Arrow__Order__Mirabelle_OProf, simplifying with (30), (54),
% 100.47/14.37 | (55), (289), (307) gives:
% 100.47/14.37 | (376) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 100.47/14.37 | ? [v5: $i] : (c_Orderings_Obot__class_Obot(v4) = v5 &
% 100.47/14.37 | c_Orderings_Obot__class_Obot(v1) = v2 & tc_fun(v0, tc_HOL_Obool) =
% 100.47/14.37 | v1 & tc_fun(all_495_3, tc_HOL_Obool) = v4 &
% 100.47/14.37 | tc_fun(tc_Arrow__Order__Mirabelle_Oindi, all_495_3) = v0 &
% 100.47/14.37 | c_member(tc_Arrow__Order__Mirabelle_Oindi) = v3 & $i(v5) & $i(v4) &
% 100.47/14.37 | $i(v3) & $i(v2) & $i(v1) & $i(v0) & ( ~ (v2 =
% 100.47/14.37 | c_Arrow__Order__Mirabelle_OProf) | ? [v6: $i] : ? [v7: $i] :
% 100.47/14.37 | ? [v8: $i] : (hBOOL(v8) = 0 & hAPP(v7, all_503_2) = v8 & hAPP(v3,
% 100.47/14.37 | v6) = v7 & hAPP(all_503_0, v6) = v5 & $i(v8) & $i(v7) &
% 100.47/14.37 | $i(v6))))
% 100.47/14.37 |
% 100.47/14.37 | GROUND_INST: instantiating (24) with all_545_4,
% 100.47/14.37 | c_Arrow__Order__Mirabelle_OProf, all_495_3, all_509_5, all_545_3,
% 100.47/14.37 | simplifying with (31), (111), (307), (349), (355) gives:
% 100.47/14.37 | (377) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 100.47/14.37 | ? [v5: $i] : (c_Orderings_Obot__class_Obot(v4) = v5 &
% 100.47/14.37 | c_Orderings_Obot__class_Obot(v1) = v2 & tc_fun(v3, tc_HOL_Obool) =
% 100.47/14.37 | v4 & tc_fun(all_509_5, all_495_3) = v3 & tc_fun(all_495_3,
% 100.47/14.37 | tc_HOL_Obool) = v1 & c_member(all_509_5) = v0 & $i(v5) & $i(v4) &
% 100.47/14.37 | $i(v3) & $i(v2) & $i(v1) & $i(v0) & (v5 = all_545_3 | ! [v6: $i] :
% 100.47/14.37 | ! [v7: $i] : ! [v8: $i] : ( ~ (hAPP(v7,
% 100.47/14.37 | c_Arrow__Order__Mirabelle_OProf) = v8) | ~ (hAPP(v0, v6) =
% 100.47/14.37 | v7) | ~ $i(v6) | ? [v9: any] : ? [v10: $i] : (hBOOL(v8) =
% 100.47/14.37 | v9 & hAPP(all_545_4, v6) = v10 & $i(v10) & ( ~ (v10 = v2) |
% 100.47/14.37 | ~ (v9 = 0))))))
% 100.47/14.37 |
% 100.47/14.37 | GROUND_INST: instantiating (23) with all_545_4,
% 100.47/14.37 | c_Arrow__Order__Mirabelle_OProf, all_495_3, all_509_5, all_545_3,
% 100.47/14.37 | simplifying with (31), (111), (307), (349), (355) gives:
% 100.47/14.37 | (378) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 100.47/14.37 | ? [v5: $i] : (c_Orderings_Obot__class_Obot(v4) = v5 &
% 100.47/14.37 | c_Orderings_Obot__class_Obot(v1) = v2 & tc_fun(v0, tc_HOL_Obool) =
% 100.47/14.37 | v1 & tc_fun(all_509_5, all_495_3) = v0 & tc_fun(all_495_3,
% 100.47/14.37 | tc_HOL_Obool) = v4 & c_member(all_509_5) = v3 & $i(v5) & $i(v4) &
% 100.47/14.37 | $i(v3) & $i(v2) & $i(v1) & $i(v0) & ( ~ (v2 = all_545_3) | ? [v6:
% 100.47/14.37 | $i] : ? [v7: $i] : ? [v8: $i] : (hBOOL(v8) = 0 & hAPP(v7,
% 100.47/14.37 | c_Arrow__Order__Mirabelle_OProf) = v8 & hAPP(v3, v6) = v7 &
% 100.47/14.37 | hAPP(all_545_4, v6) = v5 & $i(v8) & $i(v7) & $i(v6))))
% 100.47/14.37 |
% 100.47/14.37 | GROUND_INST: instantiating (21) with c_Arrow__Order__Mirabelle_OLin,
% 100.47/14.37 | all_503_2, all_509_3, all_495_3,
% 100.47/14.37 | tc_Arrow__Order__Mirabelle_Oindi, all_509_5, all_509_4,
% 100.47/14.37 | all_509_2, all_503_1, all_503_0, c_Arrow__Order__Mirabelle_OProf,
% 100.47/14.37 | all_509_1, simplifying with (27), (30), (54), (60), (63), (64),
% 100.47/14.37 | (65), (67), (289), (291), (296), (307) gives:
% 100.47/14.37 | (379) ? [v0: any] : ? [v1: $i] : ? [v2: $i] : ? [v3: any] : ? [v4: $i]
% 100.47/14.37 | : ? [v5: $i] : ? [v6: $i] :
% 100.47/14.37 | (c_FuncSet_Orestrict(tc_Arrow__Order__Mirabelle_Oindi,
% 100.47/14.37 | tc_Arrow__Order__Mirabelle_Oindi, v4, all_503_2) = v5 &
% 100.47/14.37 | c_FuncSet_Oextensional(tc_Arrow__Order__Mirabelle_Oindi, all_495_3,
% 100.47/14.37 | all_503_2) = v1 &
% 100.47/14.37 | c_FuncSet_Ocompose(tc_Arrow__Order__Mirabelle_Oindi,
% 100.47/14.37 | tc_Arrow__Order__Mirabelle_Oindi, all_495_3, all_503_2,
% 100.47/14.37 | all_509_3, v5) = v6 & c_COMBI(tc_Arrow__Order__Mirabelle_Oindi) =
% 100.47/14.37 | v4 & hBOOL(v2) = v3 & hBOOL(all_509_1) = v0 & hAPP(all_509_2, v1) =
% 100.47/14.37 | v2 & $i(v6) & $i(v5) & $i(v4) & $i(v2) & $i(v1) & ( ~ (v3 = 0) | ~
% 100.47/14.37 | (v0 = 0) | v6 = all_509_3))
% 100.47/14.37 |
% 100.47/14.37 | GROUND_INST: instantiating (22) with c_Arrow__Order__Mirabelle_OLin,
% 100.47/14.37 | all_503_2, all_509_3, all_495_3,
% 100.47/14.37 | tc_Arrow__Order__Mirabelle_Oindi, all_509_5, all_509_4,
% 100.47/14.37 | all_509_2, all_503_1, all_503_0, c_Arrow__Order__Mirabelle_OProf,
% 100.47/14.37 | all_509_1, simplifying with (27), (30), (54), (60), (63), (64),
% 100.47/14.37 | (65), (67), (289), (291), (296), (307) gives:
% 100.47/14.37 | (380) ? [v0: any] : ? [v1: $i] : ? [v2: $i] : ? [v3: any] : ? [v4: $i]
% 100.47/14.37 | : ? [v5: $i] : ? [v6: $i] : (c_FuncSet_Orestrict(all_495_3,
% 100.47/14.37 | all_495_3, v4, c_Arrow__Order__Mirabelle_OLin) = v5 &
% 100.47/14.37 | c_FuncSet_Oextensional(tc_Arrow__Order__Mirabelle_Oindi, all_495_3,
% 100.47/14.37 | all_503_2) = v1 &
% 100.47/14.37 | c_FuncSet_Ocompose(tc_Arrow__Order__Mirabelle_Oindi, all_495_3,
% 100.47/14.37 | all_495_3, all_503_2, v5, all_509_3) = v6 & c_COMBI(all_495_3) =
% 100.47/14.37 | v4 & hBOOL(v2) = v3 & hBOOL(all_509_1) = v0 & hAPP(all_509_2, v1) =
% 100.47/14.37 | v2 & $i(v6) & $i(v5) & $i(v4) & $i(v2) & $i(v1) & ( ~ (v3 = 0) | ~
% 100.47/14.37 | (v0 = 0) | v6 = all_509_3))
% 100.47/14.37 |
% 100.47/14.37 | GROUND_INST: instantiating (20) with c_Arrow__Order__Mirabelle_OLin,
% 100.47/14.37 | all_509_3, all_495_3, all_503_2,
% 100.47/14.37 | tc_Arrow__Order__Mirabelle_Oindi, all_509_5, all_509_4,
% 100.47/14.37 | all_509_2, all_503_1, all_503_0, c_Arrow__Order__Mirabelle_OProf,
% 100.47/14.37 | all_509_1, simplifying with (27), (30), (54), (60), (63), (64),
% 100.47/14.37 | (65), (67), (289), (291), (296), (307) gives:
% 100.47/14.37 | (381) ? [v0: $i] : ? [v1: $i] : ? [v2: any] : (c_member(all_495_3) = v1
% 100.47/14.37 | & c_member(tc_Arrow__Order__Mirabelle_Oindi) = v0 &
% 100.47/14.37 | hBOOL(all_509_1) = v2 & $i(v1) & $i(v0) & (v2 = 0 | ? [v3: $i] :
% 100.47/14.37 | ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8:
% 100.47/14.37 | $i] : ? [v9: int] : ( ~ (v9 = 0) & hBOOL(v8) = v9 & hBOOL(v5)
% 100.47/14.37 | = 0 & hAPP(v7, c_Arrow__Order__Mirabelle_OLin) = v8 & hAPP(v4,
% 100.47/14.37 | all_503_2) = v5 & hAPP(v1, v6) = v7 & hAPP(v0, v3) = v4 &
% 100.47/14.37 | hAPP(all_509_3, v3) = v6 & $i(v8) & $i(v7) & $i(v6) & $i(v5) &
% 100.47/14.37 | $i(v4) & $i(v3))))
% 100.47/14.37 |
% 100.47/14.37 | DELTA: instantiating (372) with fresh symbols all_697_0, all_697_1 gives:
% 100.47/14.38 | (382) class_Complete__Lattice_Ocomplete__lattice(all_503_1) = all_697_0 &
% 100.47/14.38 | class_Complete__Lattice_Ocomplete__lattice(tc_HOL_Obool) = all_697_1
% 100.47/14.38 | & ( ~ (all_697_1 = 0) | all_697_0 = 0)
% 100.47/14.38 |
% 100.47/14.38 | ALPHA: (382) implies:
% 100.47/14.38 | (383) class_Complete__Lattice_Ocomplete__lattice(tc_HOL_Obool) = all_697_1
% 100.47/14.38 | (384) ~ (all_697_1 = 0) | all_697_0 = 0
% 100.47/14.38 |
% 100.47/14.38 | DELTA: instantiating (370) with fresh symbols all_709_0, all_709_1, all_709_2
% 100.47/14.38 | gives:
% 100.47/14.38 | (385) hBOOL(all_709_2) = all_709_1 & hBOOL(all_509_1) = all_709_0 &
% 100.47/14.38 | hAPP(c_Arrow__Order__Mirabelle_OProf, all_509_3) = all_709_2 &
% 100.47/14.38 | $i(all_709_2) & ( ~ (all_709_1 = 0) | all_709_0 = 0)
% 100.47/14.38 |
% 100.47/14.38 | ALPHA: (385) implies:
% 100.47/14.38 | (386) hBOOL(all_509_1) = all_709_0
% 100.47/14.38 |
% 100.47/14.38 | DELTA: instantiating (369) with fresh symbols all_711_0, all_711_1, all_711_2
% 100.47/14.38 | gives:
% 100.47/14.38 | (387) hBOOL(all_711_1) = all_711_0 & hBOOL(all_509_1) = all_711_2 &
% 100.47/14.38 | hAPP(c_Arrow__Order__Mirabelle_OProf, all_509_3) = all_711_1 &
% 100.47/14.38 | $i(all_711_1) & ( ~ (all_711_2 = 0) | all_711_0 = 0)
% 100.47/14.38 |
% 100.47/14.38 | ALPHA: (387) implies:
% 100.47/14.38 | (388) hBOOL(all_509_1) = all_711_2
% 100.47/14.38 |
% 100.47/14.38 | DELTA: instantiating (367) with fresh symbols all_713_0, all_713_1, all_713_2
% 100.47/14.38 | gives:
% 100.47/14.38 | (389) hBOOL(all_713_2) = all_713_1 & hBOOL(all_495_0) = all_713_0 &
% 100.47/14.38 | hAPP(c_Arrow__Order__Mirabelle_OLin, v_L) = all_713_2 & $i(all_713_2)
% 100.47/14.38 | & ( ~ (all_713_1 = 0) | all_713_0 = 0)
% 100.47/14.38 |
% 100.47/14.38 | ALPHA: (389) implies:
% 100.47/14.38 | (390) hAPP(c_Arrow__Order__Mirabelle_OLin, v_L) = all_713_2
% 100.47/14.38 | (391) hBOOL(all_495_0) = all_713_0
% 100.47/14.38 | (392) hBOOL(all_713_2) = all_713_1
% 100.47/14.38 |
% 100.47/14.38 | DELTA: instantiating (366) with fresh symbols all_715_0, all_715_1, all_715_2
% 100.47/14.38 | gives:
% 100.47/14.38 | (393) hBOOL(all_715_1) = all_715_0 & hBOOL(all_495_0) = all_715_2 &
% 100.47/14.38 | hAPP(c_Arrow__Order__Mirabelle_OLin, v_L) = all_715_1 & $i(all_715_1)
% 100.47/14.38 | & ( ~ (all_715_2 = 0) | all_715_0 = 0)
% 100.47/14.38 |
% 100.47/14.38 | ALPHA: (393) implies:
% 100.47/14.38 | (394) hAPP(c_Arrow__Order__Mirabelle_OLin, v_L) = all_715_1
% 100.47/14.38 | (395) hBOOL(all_495_0) = all_715_2
% 100.47/14.38 | (396) hBOOL(all_715_1) = all_715_0
% 100.47/14.38 | (397) ~ (all_715_2 = 0) | all_715_0 = 0
% 100.47/14.38 |
% 100.47/14.38 | DELTA: instantiating (371) with fresh symbols all_721_0, all_721_1, all_721_2
% 100.47/14.38 | gives:
% 100.47/14.38 | (398) c_Orderings_Obot__class_Obot(all_721_2) = all_721_1 &
% 100.47/14.38 | tc_fun(all_509_5, tc_HOL_Obool) = all_721_2 & hBOOL(all_509_1) =
% 100.47/14.38 | all_721_0 & $i(all_721_1) & $i(all_721_2) & ( ~ (all_721_0 = 0) | ~
% 100.47/14.38 | (all_721_1 = c_Arrow__Order__Mirabelle_OProf))
% 100.47/14.38 |
% 100.47/14.38 | ALPHA: (398) implies:
% 100.47/14.38 | (399) hBOOL(all_509_1) = all_721_0
% 100.47/14.38 |
% 100.47/14.38 | DELTA: instantiating (368) with fresh symbols all_723_0, all_723_1, all_723_2
% 100.47/14.38 | gives:
% 100.47/14.38 | (400) c_Orderings_Obot__class_Obot(all_723_2) = all_723_1 &
% 100.47/14.38 | tc_fun(all_495_3, tc_HOL_Obool) = all_723_2 & hBOOL(all_495_0) =
% 100.47/14.38 | all_723_0 & $i(all_723_1) & $i(all_723_2) & ( ~ (all_723_0 = 0) | ~
% 100.47/14.38 | (all_723_1 = c_Arrow__Order__Mirabelle_OLin))
% 100.47/14.38 |
% 100.47/14.38 | ALPHA: (400) implies:
% 100.47/14.38 | (401) $i(all_723_2)
% 100.47/14.38 | (402) hBOOL(all_495_0) = all_723_0
% 100.47/14.38 | (403) tc_fun(all_495_3, tc_HOL_Obool) = all_723_2
% 100.47/14.38 |
% 100.47/14.38 | DELTA: instantiating (365) with fresh symbols all_725_0, all_725_1, all_725_2
% 100.47/14.38 | gives:
% 100.47/14.38 | (404) c_Orderings_Obot__class_Obot(all_725_2) = all_725_1 &
% 100.47/14.38 | tc_fun(all_495_3, tc_HOL_Obool) = all_725_2 & hBOOL(all_560_0) =
% 100.47/14.38 | all_725_0 & $i(all_725_1) & $i(all_725_2) & ( ~ (all_725_0 = 0) | ~
% 100.47/14.38 | (all_725_1 = c_Arrow__Order__Mirabelle_OLin))
% 100.47/14.38 |
% 100.47/14.38 | ALPHA: (404) implies:
% 100.47/14.38 | (405) tc_fun(all_495_3, tc_HOL_Obool) = all_725_2
% 100.47/14.38 |
% 100.47/14.38 | DELTA: instantiating (380) with fresh symbols all_727_0, all_727_1, all_727_2,
% 100.47/14.38 | all_727_3, all_727_4, all_727_5, all_727_6 gives:
% 100.47/14.38 | (406) c_FuncSet_Orestrict(all_495_3, all_495_3, all_727_2,
% 100.47/14.38 | c_Arrow__Order__Mirabelle_OLin) = all_727_1 &
% 100.47/14.38 | c_FuncSet_Oextensional(tc_Arrow__Order__Mirabelle_Oindi, all_495_3,
% 100.47/14.38 | all_503_2) = all_727_5 &
% 100.47/14.38 | c_FuncSet_Ocompose(tc_Arrow__Order__Mirabelle_Oindi, all_495_3,
% 100.47/14.38 | all_495_3, all_503_2, all_727_1, all_509_3) = all_727_0 &
% 100.47/14.38 | c_COMBI(all_495_3) = all_727_2 & hBOOL(all_727_4) = all_727_3 &
% 100.47/14.38 | hBOOL(all_509_1) = all_727_6 & hAPP(all_509_2, all_727_5) = all_727_4
% 100.47/14.38 | & $i(all_727_0) & $i(all_727_1) & $i(all_727_2) & $i(all_727_4) &
% 100.47/14.38 | $i(all_727_5) & ( ~ (all_727_3 = 0) | ~ (all_727_6 = 0) | all_727_0
% 100.47/14.38 | = all_509_3)
% 100.47/14.38 |
% 100.47/14.38 | ALPHA: (406) implies:
% 100.47/14.38 | (407) hBOOL(all_509_1) = all_727_6
% 100.47/14.38 |
% 100.47/14.38 | DELTA: instantiating (379) with fresh symbols all_729_0, all_729_1, all_729_2,
% 100.47/14.38 | all_729_3, all_729_4, all_729_5, all_729_6 gives:
% 100.47/14.38 | (408) c_FuncSet_Orestrict(tc_Arrow__Order__Mirabelle_Oindi,
% 100.47/14.38 | tc_Arrow__Order__Mirabelle_Oindi, all_729_2, all_503_2) = all_729_1
% 100.47/14.38 | & c_FuncSet_Oextensional(tc_Arrow__Order__Mirabelle_Oindi, all_495_3,
% 100.47/14.38 | all_503_2) = all_729_5 &
% 100.47/14.38 | c_FuncSet_Ocompose(tc_Arrow__Order__Mirabelle_Oindi,
% 100.47/14.38 | tc_Arrow__Order__Mirabelle_Oindi, all_495_3, all_503_2, all_509_3,
% 100.47/14.38 | all_729_1) = all_729_0 & c_COMBI(tc_Arrow__Order__Mirabelle_Oindi)
% 100.47/14.38 | = all_729_2 & hBOOL(all_729_4) = all_729_3 & hBOOL(all_509_1) =
% 100.47/14.38 | all_729_6 & hAPP(all_509_2, all_729_5) = all_729_4 & $i(all_729_0) &
% 100.47/14.38 | $i(all_729_1) & $i(all_729_2) & $i(all_729_4) & $i(all_729_5) & ( ~
% 100.47/14.38 | (all_729_3 = 0) | ~ (all_729_6 = 0) | all_729_0 = all_509_3)
% 100.47/14.38 |
% 100.47/14.38 | ALPHA: (408) implies:
% 100.47/14.38 | (409) hBOOL(all_509_1) = all_729_6
% 100.47/14.38 |
% 100.47/14.38 | DELTA: instantiating (373) with fresh symbols all_731_0, all_731_1, all_731_2
% 100.47/14.38 | gives:
% 100.47/14.38 | (410) c_member(tc_Arrow__Order__Mirabelle_Oindi) = all_731_2 &
% 100.47/14.38 | hBOOL(all_509_1) = all_731_0 & hBOOL(all_509_1) = all_731_1 &
% 100.47/14.38 | $i(all_731_2) & ( ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3:
% 100.47/14.38 | $i] : ? [v4: $i] : ( ~ (v4 = v3) & hBOOL(v2) = 0 & hAPP(v1,
% 100.47/14.38 | all_503_2) = v2 & hAPP(all_731_2, v0) = v1 & hAPP(all_509_3,
% 100.47/14.38 | v0) = v4 & hAPP(all_509_3, v0) = v3 & $i(v4) & $i(v3) & $i(v2)
% 100.47/14.38 | & $i(v1) & $i(v0)) | (( ~ (all_731_0 = 0) | all_731_1 = 0) & ( ~
% 100.47/14.38 | (all_731_1 = 0) | all_731_0 = 0)))
% 100.47/14.38 |
% 100.47/14.38 | ALPHA: (410) implies:
% 100.47/14.38 | (411) hBOOL(all_509_1) = all_731_1
% 100.47/14.38 | (412) hBOOL(all_509_1) = all_731_0
% 100.47/14.38 |
% 100.47/14.38 | DELTA: instantiating (376) with fresh symbols all_733_0, all_733_1, all_733_2,
% 100.47/14.38 | all_733_3, all_733_4, all_733_5 gives:
% 100.47/14.38 | (413) c_Orderings_Obot__class_Obot(all_733_1) = all_733_0 &
% 100.47/14.38 | c_Orderings_Obot__class_Obot(all_733_4) = all_733_3 &
% 100.47/14.38 | tc_fun(all_733_5, tc_HOL_Obool) = all_733_4 & tc_fun(all_495_3,
% 100.47/14.38 | tc_HOL_Obool) = all_733_1 &
% 100.47/14.38 | tc_fun(tc_Arrow__Order__Mirabelle_Oindi, all_495_3) = all_733_5 &
% 100.47/14.38 | c_member(tc_Arrow__Order__Mirabelle_Oindi) = all_733_2 &
% 100.47/14.38 | $i(all_733_0) & $i(all_733_1) & $i(all_733_2) & $i(all_733_3) &
% 100.47/14.38 | $i(all_733_4) & $i(all_733_5) & ( ~ (all_733_3 =
% 100.47/14.38 | c_Arrow__Order__Mirabelle_OProf) | ? [v0: $i] : ? [v1: $i] : ?
% 100.47/14.38 | [v2: $i] : (hBOOL(v2) = 0 & hAPP(v1, all_503_2) = v2 &
% 100.47/14.38 | hAPP(all_733_2, v0) = v1 & hAPP(all_503_0, v0) = all_733_0 &
% 100.47/14.38 | $i(v2) & $i(v1) & $i(v0)))
% 100.47/14.38 |
% 100.47/14.38 | ALPHA: (413) implies:
% 100.47/14.38 | (414) tc_fun(all_495_3, tc_HOL_Obool) = all_733_1
% 100.47/14.38 |
% 100.47/14.38 | DELTA: instantiating (381) with fresh symbols all_735_0, all_735_1, all_735_2
% 100.47/14.38 | gives:
% 100.47/14.38 | (415) c_member(all_495_3) = all_735_1 &
% 100.47/14.38 | c_member(tc_Arrow__Order__Mirabelle_Oindi) = all_735_2 &
% 100.47/14.38 | hBOOL(all_509_1) = all_735_0 & $i(all_735_1) & $i(all_735_2) &
% 100.47/14.38 | (all_735_0 = 0 | ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3:
% 100.47/14.38 | $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: int] : ( ~ (v6 = 0) &
% 100.47/14.38 | hBOOL(v5) = v6 & hBOOL(v2) = 0 & hAPP(v4,
% 100.47/14.38 | c_Arrow__Order__Mirabelle_OLin) = v5 & hAPP(v1, all_503_2) = v2
% 100.47/14.38 | & hAPP(all_735_1, v3) = v4 & hAPP(all_735_2, v0) = v1 &
% 100.47/14.38 | hAPP(all_509_3, v0) = v3 & $i(v5) & $i(v4) & $i(v3) & $i(v2) &
% 100.47/14.38 | $i(v1) & $i(v0)))
% 100.47/14.38 |
% 100.47/14.38 | ALPHA: (415) implies:
% 100.47/14.38 | (416) hBOOL(all_509_1) = all_735_0
% 100.47/14.38 | (417) c_member(all_495_3) = all_735_1
% 100.47/14.38 | (418) all_735_0 = 0 | ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i]
% 100.47/14.38 | : ? [v4: $i] : ? [v5: $i] : ? [v6: int] : ( ~ (v6 = 0) & hBOOL(v5)
% 100.47/14.38 | = v6 & hBOOL(v2) = 0 & hAPP(v4, c_Arrow__Order__Mirabelle_OLin) =
% 100.47/14.38 | v5 & hAPP(v1, all_503_2) = v2 & hAPP(all_735_1, v3) = v4 &
% 100.47/14.38 | hAPP(all_735_2, v0) = v1 & hAPP(all_509_3, v0) = v3 & $i(v5) &
% 100.47/14.38 | $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 100.47/14.38 |
% 100.47/14.38 | DELTA: instantiating (378) with fresh symbols all_737_0, all_737_1, all_737_2,
% 100.47/14.38 | all_737_3, all_737_4, all_737_5 gives:
% 100.47/14.38 | (419) c_Orderings_Obot__class_Obot(all_737_1) = all_737_0 &
% 100.47/14.38 | c_Orderings_Obot__class_Obot(all_737_4) = all_737_3 &
% 100.47/14.38 | tc_fun(all_737_5, tc_HOL_Obool) = all_737_4 & tc_fun(all_509_5,
% 100.47/14.38 | all_495_3) = all_737_5 & tc_fun(all_495_3, tc_HOL_Obool) =
% 100.47/14.38 | all_737_1 & c_member(all_509_5) = all_737_2 & $i(all_737_0) &
% 100.47/14.38 | $i(all_737_1) & $i(all_737_2) & $i(all_737_3) & $i(all_737_4) &
% 100.47/14.38 | $i(all_737_5) & ( ~ (all_737_3 = all_545_3) | ? [v0: $i] : ? [v1:
% 100.47/14.38 | $i] : ? [v2: $i] : (hBOOL(v2) = 0 & hAPP(v1,
% 100.47/14.38 | c_Arrow__Order__Mirabelle_OProf) = v2 & hAPP(all_737_2, v0) =
% 100.47/14.38 | v1 & hAPP(all_545_4, v0) = all_737_0 & $i(v2) & $i(v1) & $i(v0)))
% 100.47/14.38 |
% 100.47/14.38 | ALPHA: (419) implies:
% 100.47/14.38 | (420) tc_fun(all_495_3, tc_HOL_Obool) = all_737_1
% 100.47/14.38 |
% 100.47/14.38 | DELTA: instantiating (377) with fresh symbols all_739_0, all_739_1, all_739_2,
% 100.47/14.38 | all_739_3, all_739_4, all_739_5 gives:
% 100.47/14.38 | (421) c_Orderings_Obot__class_Obot(all_739_1) = all_739_0 &
% 100.47/14.38 | c_Orderings_Obot__class_Obot(all_739_4) = all_739_3 &
% 100.47/14.38 | tc_fun(all_739_2, tc_HOL_Obool) = all_739_1 & tc_fun(all_509_5,
% 100.47/14.38 | all_495_3) = all_739_2 & tc_fun(all_495_3, tc_HOL_Obool) =
% 100.47/14.38 | all_739_4 & c_member(all_509_5) = all_739_5 & $i(all_739_0) &
% 100.47/14.38 | $i(all_739_1) & $i(all_739_2) & $i(all_739_3) & $i(all_739_4) &
% 100.47/14.38 | $i(all_739_5) & (all_739_0 = all_545_3 | ! [v0: $i] : ! [v1: $i] :
% 100.47/14.38 | ! [v2: $i] : ( ~ (hAPP(v1, c_Arrow__Order__Mirabelle_OProf) = v2) |
% 100.47/14.38 | ~ (hAPP(all_739_5, v0) = v1) | ~ $i(v0) | ? [v3: any] : ?
% 100.47/14.38 | [v4: $i] : (hBOOL(v2) = v3 & hAPP(all_545_4, v0) = v4 & $i(v4) &
% 100.47/14.38 | ( ~ (v4 = all_739_3) | ~ (v3 = 0)))))
% 100.47/14.38 |
% 100.47/14.38 | ALPHA: (421) implies:
% 100.47/14.38 | (422) tc_fun(all_495_3, tc_HOL_Obool) = all_739_4
% 100.47/14.38 |
% 100.47/14.38 | DELTA: instantiating (375) with fresh symbols all_741_0, all_741_1, all_741_2,
% 100.47/14.38 | all_741_3, all_741_4, all_741_5 gives:
% 100.47/14.38 | (423) c_Orderings_Obot__class_Obot(all_741_1) = all_741_0 &
% 100.47/14.38 | c_Orderings_Obot__class_Obot(all_741_4) = all_741_3 &
% 100.47/14.38 | tc_fun(all_741_2, tc_HOL_Obool) = all_741_1 & tc_fun(all_495_3,
% 100.47/14.38 | tc_HOL_Obool) = all_741_4 &
% 100.47/14.38 | tc_fun(tc_Arrow__Order__Mirabelle_Oindi, all_495_3) = all_741_2 &
% 100.47/14.38 | c_member(tc_Arrow__Order__Mirabelle_Oindi) = all_741_5 &
% 100.47/14.38 | $i(all_741_0) & $i(all_741_1) & $i(all_741_2) & $i(all_741_3) &
% 100.47/14.38 | $i(all_741_4) & $i(all_741_5) & (all_741_0 =
% 100.47/14.38 | c_Arrow__Order__Mirabelle_OProf | ! [v0: $i] : ! [v1: $i] : !
% 100.47/14.38 | [v2: $i] : ( ~ (hAPP(v1, all_503_2) = v2) | ~ (hAPP(all_741_5, v0)
% 100.47/14.38 | = v1) | ~ $i(v0) | ? [v3: any] : ? [v4: $i] : (hBOOL(v2) =
% 100.47/14.38 | v3 & hAPP(all_503_0, v0) = v4 & $i(v4) & ( ~ (v4 = all_741_3) |
% 100.47/14.38 | ~ (v3 = 0)))))
% 100.47/14.38 |
% 100.47/14.38 | ALPHA: (423) implies:
% 100.47/14.38 | (424) tc_fun(all_495_3, tc_HOL_Obool) = all_741_4
% 100.47/14.38 |
% 100.47/14.38 | DELTA: instantiating (374) with fresh symbols all_743_0, all_743_1, all_743_2
% 100.47/14.38 | gives:
% 100.47/14.38 | (425) c_member(all_495_3) = all_743_1 &
% 100.47/14.38 | c_member(tc_Arrow__Order__Mirabelle_Oindi) = all_743_2 &
% 100.47/14.38 | hBOOL(all_509_1) = all_743_0 & $i(all_743_1) & $i(all_743_2) &
% 100.47/14.38 | (all_743_0 = 0 | ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3:
% 100.47/14.38 | $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: int] : (
% 100.47/14.38 | ~ (v7 = 0) & hBOOL(v6) = v7 & hBOOL(v2) = 0 & hAPP(v4, v5) = v6 &
% 100.47/14.38 | hAPP(v1, all_503_2) = v2 & hAPP(all_743_1, v3) = v4 &
% 100.47/14.38 | hAPP(all_743_2, v0) = v1 & hAPP(all_509_3, v0) = v3 &
% 100.47/14.38 | hAPP(all_503_0, v0) = v5 & $i(v6) & $i(v5) & $i(v4) & $i(v3) &
% 100.47/14.38 | $i(v2) & $i(v1) & $i(v0)))
% 100.47/14.38 |
% 100.47/14.38 | ALPHA: (425) implies:
% 100.47/14.38 | (426) hBOOL(all_509_1) = all_743_0
% 100.47/14.38 | (427) c_member(all_495_3) = all_743_1
% 100.47/14.38 | (428) all_743_0 = 0 | ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i]
% 100.47/14.38 | : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: int] : ( ~ (v7 =
% 100.47/14.38 | 0) & hBOOL(v6) = v7 & hBOOL(v2) = 0 & hAPP(v4, v5) = v6 &
% 100.47/14.38 | hAPP(v1, all_503_2) = v2 & hAPP(all_743_1, v3) = v4 &
% 100.47/14.38 | hAPP(all_743_2, v0) = v1 & hAPP(all_509_3, v0) = v3 &
% 100.47/14.38 | hAPP(all_503_0, v0) = v5 & $i(v6) & $i(v5) & $i(v4) & $i(v3) &
% 100.47/14.38 | $i(v2) & $i(v1) & $i(v0))
% 100.47/14.38 |
% 100.47/14.38 | GROUND_INST: instantiating (37) with all_713_2, all_715_1, v_L,
% 100.47/14.38 | c_Arrow__Order__Mirabelle_OLin, simplifying with (390), (394)
% 100.47/14.38 | gives:
% 100.47/14.38 | (429) all_715_1 = all_713_2
% 100.47/14.38 |
% 100.47/14.38 | GROUND_INST: instantiating (34) with 0, all_723_0, all_495_0, simplifying with
% 100.47/14.38 | (43), (402) gives:
% 100.47/14.38 | (430) all_723_0 = 0
% 100.47/14.38 |
% 100.47/14.38 | GROUND_INST: instantiating (34) with all_715_2, all_723_0, all_495_0,
% 100.47/14.38 | simplifying with (395), (402) gives:
% 100.47/14.38 | (431) all_723_0 = all_715_2
% 100.47/14.38 |
% 100.47/14.38 | GROUND_INST: instantiating (34) with all_713_0, all_723_0, all_495_0,
% 100.47/14.38 | simplifying with (391), (402) gives:
% 100.47/14.38 | (432) all_723_0 = all_713_0
% 100.47/14.38 |
% 100.47/14.38 | GROUND_INST: instantiating (34) with all_509_0, all_721_0, all_509_1,
% 100.47/14.38 | simplifying with (66), (399) gives:
% 100.47/14.38 | (433) all_721_0 = all_509_0
% 100.47/14.38 |
% 100.47/14.38 | GROUND_INST: instantiating (34) with all_721_0, all_727_6, all_509_1,
% 100.47/14.38 | simplifying with (399), (407) gives:
% 100.47/14.38 | (434) all_727_6 = all_721_0
% 100.47/14.38 |
% 100.47/14.38 | GROUND_INST: instantiating (34) with all_727_6, all_729_6, all_509_1,
% 100.47/14.38 | simplifying with (407), (409) gives:
% 100.47/14.38 | (435) all_729_6 = all_727_6
% 100.47/14.38 |
% 100.47/14.39 | GROUND_INST: instantiating (34) with all_729_6, all_731_1, all_509_1,
% 100.47/14.39 | simplifying with (409), (411) gives:
% 100.47/14.39 | (436) all_731_1 = all_729_6
% 100.47/14.39 |
% 100.47/14.39 | GROUND_INST: instantiating (34) with all_731_1, all_731_0, all_509_1,
% 100.47/14.39 | simplifying with (411), (412) gives:
% 100.47/14.39 | (437) all_731_0 = all_731_1
% 100.47/14.39 |
% 100.47/14.39 | GROUND_INST: instantiating (34) with all_731_0, all_735_0, all_509_1,
% 100.47/14.39 | simplifying with (412), (416) gives:
% 100.47/14.39 | (438) all_735_0 = all_731_0
% 100.47/14.39 |
% 100.47/14.39 | GROUND_INST: instantiating (34) with all_711_2, all_735_0, all_509_1,
% 100.47/14.39 | simplifying with (388), (416) gives:
% 100.47/14.39 | (439) all_735_0 = all_711_2
% 100.47/14.39 |
% 100.47/14.39 | GROUND_INST: instantiating (34) with all_721_0, all_743_0, all_509_1,
% 100.47/14.39 | simplifying with (399), (426) gives:
% 100.47/14.39 | (440) all_743_0 = all_721_0
% 100.47/14.39 |
% 100.47/14.39 | GROUND_INST: instantiating (34) with all_709_0, all_743_0, all_509_1,
% 100.47/14.39 | simplifying with (386), (426) gives:
% 100.47/14.39 | (441) all_743_0 = all_709_0
% 100.47/14.39 |
% 100.47/14.39 | GROUND_INST: instantiating (35) with all_495_2, all_743_1, all_495_3,
% 100.47/14.39 | simplifying with (44), (427) gives:
% 100.47/14.39 | (442) all_743_1 = all_495_2
% 100.47/14.39 |
% 100.47/14.39 | GROUND_INST: instantiating (35) with all_735_1, all_743_1, all_495_3,
% 100.47/14.39 | simplifying with (417), (427) gives:
% 100.47/14.39 | (443) all_743_1 = all_735_1
% 100.47/14.39 |
% 100.47/14.39 | GROUND_INST: instantiating (38) with all_503_1, all_737_1, tc_HOL_Obool,
% 100.47/14.39 | all_495_3, simplifying with (291), (420) gives:
% 100.47/14.39 | (444) all_737_1 = all_503_1
% 100.47/14.39 |
% 100.47/14.39 | GROUND_INST: instantiating (38) with all_733_1, all_737_1, tc_HOL_Obool,
% 100.47/14.39 | all_495_3, simplifying with (414), (420) gives:
% 100.47/14.39 | (445) all_737_1 = all_733_1
% 100.47/14.39 |
% 100.47/14.39 | GROUND_INST: instantiating (38) with all_725_2, all_737_1, tc_HOL_Obool,
% 100.47/14.39 | all_495_3, simplifying with (405), (420) gives:
% 100.47/14.39 | (446) all_737_1 = all_725_2
% 100.47/14.39 |
% 100.47/14.39 | GROUND_INST: instantiating (38) with all_739_4, all_741_4, tc_HOL_Obool,
% 100.47/14.39 | all_495_3, simplifying with (422), (424) gives:
% 100.47/14.39 | (447) all_741_4 = all_739_4
% 100.47/14.39 |
% 100.47/14.39 | GROUND_INST: instantiating (38) with all_737_1, all_741_4, tc_HOL_Obool,
% 100.47/14.39 | all_495_3, simplifying with (420), (424) gives:
% 100.47/14.39 | (448) all_741_4 = all_737_1
% 100.47/14.39 |
% 100.47/14.39 | GROUND_INST: instantiating (38) with all_723_2, all_741_4, tc_HOL_Obool,
% 100.47/14.39 | all_495_3, simplifying with (403), (424) gives:
% 100.47/14.39 | (449) all_741_4 = all_723_2
% 100.47/14.39 |
% 100.47/14.39 | GROUND_INST: instantiating (36) with 0, all_697_1, tc_HOL_Obool, simplifying
% 100.47/14.39 | with (26), (383) gives:
% 100.47/14.39 | (450) all_697_1 = 0
% 100.47/14.39 |
% 100.47/14.39 | COMBINE_EQS: (440), (441) imply:
% 100.47/14.39 | (451) all_721_0 = all_709_0
% 100.47/14.39 |
% 100.47/14.39 | SIMP: (451) implies:
% 100.47/14.39 | (452) all_721_0 = all_709_0
% 100.47/14.39 |
% 100.47/14.39 | COMBINE_EQS: (442), (443) imply:
% 100.47/14.39 | (453) all_735_1 = all_495_2
% 100.47/14.39 |
% 100.47/14.39 | SIMP: (453) implies:
% 100.47/14.39 | (454) all_735_1 = all_495_2
% 100.47/14.39 |
% 100.47/14.39 | COMBINE_EQS: (447), (449) imply:
% 100.47/14.39 | (455) all_739_4 = all_723_2
% 100.47/14.39 |
% 100.47/14.39 | COMBINE_EQS: (447), (448) imply:
% 100.47/14.39 | (456) all_739_4 = all_737_1
% 100.47/14.39 |
% 100.47/14.39 | COMBINE_EQS: (455), (456) imply:
% 100.47/14.39 | (457) all_737_1 = all_723_2
% 100.47/14.39 |
% 100.47/14.39 | SIMP: (457) implies:
% 100.47/14.39 | (458) all_737_1 = all_723_2
% 100.47/14.39 |
% 100.47/14.39 | COMBINE_EQS: (445), (446) imply:
% 100.47/14.39 | (459) all_733_1 = all_725_2
% 100.47/14.39 |
% 100.47/14.39 | COMBINE_EQS: (444), (445) imply:
% 100.47/14.39 | (460) all_733_1 = all_503_1
% 100.47/14.39 |
% 100.47/14.39 | COMBINE_EQS: (445), (458) imply:
% 100.47/14.39 | (461) all_733_1 = all_723_2
% 100.47/14.39 |
% 100.47/14.39 | COMBINE_EQS: (438), (439) imply:
% 100.47/14.39 | (462) all_731_0 = all_711_2
% 100.47/14.39 |
% 100.47/14.39 | SIMP: (462) implies:
% 100.47/14.39 | (463) all_731_0 = all_711_2
% 100.47/14.39 |
% 100.47/14.39 | COMBINE_EQS: (459), (460) imply:
% 100.47/14.39 | (464) all_725_2 = all_503_1
% 100.47/14.39 |
% 100.47/14.39 | COMBINE_EQS: (459), (461) imply:
% 100.47/14.39 | (465) all_725_2 = all_723_2
% 100.47/14.39 |
% 100.47/14.39 | COMBINE_EQS: (437), (463) imply:
% 100.47/14.39 | (466) all_731_1 = all_711_2
% 100.47/14.39 |
% 100.47/14.39 | SIMP: (466) implies:
% 100.47/14.39 | (467) all_731_1 = all_711_2
% 100.47/14.39 |
% 100.47/14.39 | COMBINE_EQS: (436), (467) imply:
% 100.47/14.39 | (468) all_729_6 = all_711_2
% 100.47/14.39 |
% 100.47/14.39 | SIMP: (468) implies:
% 100.47/14.39 | (469) all_729_6 = all_711_2
% 100.47/14.39 |
% 100.47/14.39 | COMBINE_EQS: (435), (469) imply:
% 100.47/14.39 | (470) all_727_6 = all_711_2
% 100.47/14.39 |
% 100.47/14.39 | SIMP: (470) implies:
% 100.47/14.39 | (471) all_727_6 = all_711_2
% 100.47/14.39 |
% 100.47/14.39 | COMBINE_EQS: (434), (471) imply:
% 100.47/14.39 | (472) all_721_0 = all_711_2
% 100.47/14.39 |
% 100.47/14.39 | SIMP: (472) implies:
% 100.47/14.39 | (473) all_721_0 = all_711_2
% 100.47/14.39 |
% 100.47/14.39 | COMBINE_EQS: (464), (465) imply:
% 100.47/14.39 | (474) all_723_2 = all_503_1
% 100.47/14.39 |
% 100.47/14.39 | COMBINE_EQS: (430), (431) imply:
% 100.47/14.39 | (475) all_715_2 = 0
% 100.47/14.39 |
% 100.47/14.39 | COMBINE_EQS: (431), (432) imply:
% 100.47/14.39 | (476) all_715_2 = all_713_0
% 100.47/14.39 |
% 100.47/14.39 | COMBINE_EQS: (433), (473) imply:
% 100.47/14.39 | (477) all_711_2 = all_509_0
% 100.47/14.39 |
% 100.47/14.39 | COMBINE_EQS: (452), (473) imply:
% 100.47/14.39 | (478) all_711_2 = all_709_0
% 100.47/14.39 |
% 100.47/14.39 | COMBINE_EQS: (475), (476) imply:
% 100.47/14.39 | (479) all_713_0 = 0
% 100.47/14.39 |
% 100.47/14.39 | COMBINE_EQS: (477), (478) imply:
% 100.47/14.39 | (480) all_709_0 = all_509_0
% 100.47/14.39 |
% 100.47/14.39 | COMBINE_EQS: (439), (477) imply:
% 100.47/14.39 | (481) all_735_0 = all_509_0
% 100.47/14.39 |
% 100.47/14.39 | COMBINE_EQS: (441), (480) imply:
% 100.47/14.39 | (482) all_743_0 = all_509_0
% 100.47/14.39 |
% 100.47/14.39 | REDUCE: (396), (429) imply:
% 100.47/14.39 | (483) hBOOL(all_713_2) = all_715_0
% 100.47/14.39 |
% 100.47/14.39 | REDUCE: (401), (474) imply:
% 100.47/14.39 | (484) $i(all_503_1)
% 100.47/14.39 |
% 100.47/14.39 | BETA: splitting (428) gives:
% 100.47/14.39 |
% 100.47/14.39 | Case 1:
% 100.47/14.39 | |
% 100.47/14.39 | | (485) all_743_0 = 0
% 100.47/14.39 | |
% 100.47/14.39 | | COMBINE_EQS: (482), (485) imply:
% 100.47/14.39 | | (486) all_509_0 = 0
% 100.47/14.39 | |
% 100.47/14.39 | | REDUCE: (62), (486) imply:
% 100.47/14.39 | | (487) $false
% 100.47/14.39 | |
% 100.47/14.39 | | CLOSE: (487) is inconsistent.
% 100.47/14.39 | |
% 100.47/14.39 | Case 2:
% 100.47/14.39 | |
% 100.47/14.39 | | (488) ~ (all_743_0 = 0)
% 100.47/14.39 | | (489) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i]
% 100.47/14.39 | | : ? [v5: $i] : ? [v6: $i] : ? [v7: int] : ( ~ (v7 = 0) &
% 100.47/14.39 | | hBOOL(v6) = v7 & hBOOL(v2) = 0 & hAPP(v4, v5) = v6 & hAPP(v1,
% 100.47/14.39 | | all_503_2) = v2 & hAPP(all_743_1, v3) = v4 & hAPP(all_743_2,
% 100.47/14.39 | | v0) = v1 & hAPP(all_509_3, v0) = v3 & hAPP(all_503_0, v0) = v5
% 100.47/14.39 | | & $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 100.47/14.39 | |
% 100.47/14.39 | | DELTA: instantiating (489) with fresh symbols all_944_0, all_944_1,
% 100.47/14.39 | | all_944_2, all_944_3, all_944_4, all_944_5, all_944_6, all_944_7
% 100.47/14.39 | | gives:
% 100.47/14.39 | | (490) ~ (all_944_0 = 0) & hBOOL(all_944_1) = all_944_0 &
% 100.47/14.39 | | hBOOL(all_944_5) = 0 & hAPP(all_944_3, all_944_2) = all_944_1 &
% 100.47/14.39 | | hAPP(all_944_6, all_503_2) = all_944_5 & hAPP(all_743_1, all_944_4)
% 100.47/14.39 | | = all_944_3 & hAPP(all_743_2, all_944_7) = all_944_6 &
% 100.47/14.39 | | hAPP(all_509_3, all_944_7) = all_944_4 & hAPP(all_503_0, all_944_7)
% 100.47/14.39 | | = all_944_2 & $i(all_944_1) & $i(all_944_2) & $i(all_944_3) &
% 100.47/14.39 | | $i(all_944_4) & $i(all_944_5) & $i(all_944_6) & $i(all_944_7)
% 100.47/14.39 | |
% 100.47/14.39 | | ALPHA: (490) implies:
% 100.47/14.39 | | (491) ~ (all_944_0 = 0)
% 100.47/14.39 | | (492) $i(all_944_7)
% 100.47/14.39 | | (493) $i(all_944_4)
% 100.47/14.39 | | (494) $i(all_944_2)
% 100.47/14.39 | | (495) hAPP(all_503_0, all_944_7) = all_944_2
% 100.47/14.39 | | (496) hAPP(all_509_3, all_944_7) = all_944_4
% 100.47/14.39 | | (497) hAPP(all_743_1, all_944_4) = all_944_3
% 100.47/14.39 | | (498) hAPP(all_944_3, all_944_2) = all_944_1
% 100.47/14.39 | | (499) hBOOL(all_944_1) = all_944_0
% 100.47/14.39 | |
% 100.47/14.39 | | REDUCE: (442), (497) imply:
% 100.47/14.39 | | (500) hAPP(all_495_2, all_944_4) = all_944_3
% 100.47/14.39 | |
% 100.47/14.39 | | BETA: splitting (418) gives:
% 100.47/14.39 | |
% 100.47/14.39 | | Case 1:
% 100.47/14.39 | | |
% 100.47/14.39 | | | (501) all_735_0 = 0
% 100.47/14.39 | | |
% 100.47/14.39 | | | COMBINE_EQS: (481), (501) imply:
% 100.47/14.39 | | | (502) all_509_0 = 0
% 100.47/14.39 | | |
% 100.47/14.39 | | | SIMP: (502) implies:
% 100.47/14.39 | | | (503) all_509_0 = 0
% 100.47/14.39 | | |
% 100.47/14.39 | | | REDUCE: (62), (503) imply:
% 100.47/14.39 | | | (504) $false
% 100.47/14.39 | | |
% 100.47/14.39 | | | CLOSE: (504) is inconsistent.
% 100.47/14.39 | | |
% 100.47/14.39 | | Case 2:
% 100.47/14.39 | | |
% 100.47/14.39 | | | (505) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4:
% 100.47/14.39 | | | $i] : ? [v5: $i] : ? [v6: int] : ( ~ (v6 = 0) & hBOOL(v5) =
% 100.47/14.39 | | | v6 & hBOOL(v2) = 0 & hAPP(v4, c_Arrow__Order__Mirabelle_OLin) =
% 100.47/14.39 | | | v5 & hAPP(v1, all_503_2) = v2 & hAPP(all_735_1, v3) = v4 &
% 100.47/14.39 | | | hAPP(all_735_2, v0) = v1 & hAPP(all_509_3, v0) = v3 & $i(v5) &
% 100.47/14.39 | | | $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 100.47/14.39 | | |
% 100.47/14.39 | | | DELTA: instantiating (505) with fresh symbols all_989_0, all_989_1,
% 100.47/14.39 | | | all_989_2, all_989_3, all_989_4, all_989_5, all_989_6 gives:
% 100.47/14.39 | | | (506) ~ (all_989_0 = 0) & hBOOL(all_989_1) = all_989_0 &
% 100.47/14.39 | | | hBOOL(all_989_4) = 0 & hAPP(all_989_2,
% 100.47/14.39 | | | c_Arrow__Order__Mirabelle_OLin) = all_989_1 & hAPP(all_989_5,
% 100.47/14.39 | | | all_503_2) = all_989_4 & hAPP(all_735_1, all_989_3) = all_989_2
% 100.47/14.39 | | | & hAPP(all_735_2, all_989_6) = all_989_5 & hAPP(all_509_3,
% 100.47/14.39 | | | all_989_6) = all_989_3 & $i(all_989_1) & $i(all_989_2) &
% 100.47/14.39 | | | $i(all_989_3) & $i(all_989_4) & $i(all_989_5) & $i(all_989_6)
% 100.47/14.39 | | |
% 100.47/14.39 | | | ALPHA: (506) implies:
% 100.47/14.39 | | | (507) $i(all_989_6)
% 100.47/14.39 | | | (508) $i(all_989_3)
% 100.47/14.39 | | | (509) hAPP(all_509_3, all_989_6) = all_989_3
% 100.47/14.39 | | | (510) hAPP(all_735_1, all_989_3) = all_989_2
% 100.47/14.39 | | | (511) hAPP(all_989_2, c_Arrow__Order__Mirabelle_OLin) = all_989_1
% 100.47/14.39 | | |
% 100.47/14.39 | | | REDUCE: (454), (510) imply:
% 100.47/14.39 | | | (512) hAPP(all_495_2, all_989_3) = all_989_2
% 100.47/14.39 | | |
% 100.47/14.39 | | | BETA: splitting (397) gives:
% 100.47/14.39 | | |
% 100.47/14.39 | | | Case 1:
% 100.47/14.39 | | | |
% 100.47/14.39 | | | | (513) ~ (all_715_2 = 0)
% 100.47/14.39 | | | |
% 100.47/14.39 | | | | REDUCE: (475), (513) imply:
% 100.47/14.39 | | | | (514) $false
% 100.47/14.39 | | | |
% 100.47/14.39 | | | | CLOSE: (514) is inconsistent.
% 100.47/14.39 | | | |
% 100.47/14.39 | | | Case 2:
% 100.47/14.39 | | | |
% 100.47/14.39 | | | | (515) all_715_0 = 0
% 100.47/14.39 | | | |
% 100.47/14.39 | | | | REDUCE: (483), (515) imply:
% 100.47/14.39 | | | | (516) hBOOL(all_713_2) = 0
% 100.47/14.39 | | | |
% 100.47/14.40 | | | | BETA: splitting (384) gives:
% 100.47/14.40 | | | |
% 100.47/14.40 | | | | Case 1:
% 100.47/14.40 | | | | |
% 100.47/14.40 | | | | | (517) ~ (all_697_1 = 0)
% 100.47/14.40 | | | | |
% 100.47/14.40 | | | | | REDUCE: (450), (517) imply:
% 100.47/14.40 | | | | | (518) $false
% 100.47/14.40 | | | | |
% 100.47/14.40 | | | | | CLOSE: (518) is inconsistent.
% 100.47/14.40 | | | | |
% 100.47/14.40 | | | | Case 2:
% 100.47/14.40 | | | | |
% 100.47/14.40 | | | | |
% 100.47/14.40 | | | | | GROUND_INST: instantiating (34) with all_713_1, 0, all_713_2,
% 100.47/14.40 | | | | | simplifying with (392), (516) gives:
% 100.47/14.40 | | | | | (519) all_713_1 = 0
% 100.47/14.40 | | | | |
% 100.47/14.40 | | | | | GROUND_INST: instantiating (help_c__COMBK__1) with all_944_7,
% 100.47/14.40 | | | | | c_Arrow__Order__Mirabelle_OLin,
% 100.47/14.40 | | | | | tc_Arrow__Order__Mirabelle_Oindi, all_503_1, all_503_0,
% 100.47/14.40 | | | | | all_944_2, simplifying with (27), (30), (60), (484),
% 100.47/14.40 | | | | | (492), (495) gives:
% 100.47/14.40 | | | | | (520) all_944_2 = c_Arrow__Order__Mirabelle_OLin
% 100.47/14.40 | | | | |
% 100.47/14.40 | | | | | GROUND_INST: instantiating (help_c__COMBK__1) with all_944_7, v_L,
% 100.47/14.40 | | | | | tc_Arrow__Order__Mirabelle_Oindi, all_495_3, all_509_3,
% 100.47/14.40 | | | | | all_944_4, simplifying with (30), (32), (287), (307),
% 100.47/14.40 | | | | | (492), (496) gives:
% 100.47/14.40 | | | | | (521) all_944_4 = v_L
% 100.47/14.40 | | | | |
% 100.47/14.40 | | | | | GROUND_INST: instantiating (help_c__COMBK__1) with all_989_6, v_L,
% 100.47/14.40 | | | | | tc_Arrow__Order__Mirabelle_Oindi, all_495_3, all_509_3,
% 100.47/14.40 | | | | | all_989_3, simplifying with (30), (32), (287), (307),
% 100.47/14.40 | | | | | (507), (509) gives:
% 100.47/14.40 | | | | | (522) all_989_3 = v_L
% 100.47/14.40 | | | | |
% 100.47/14.40 | | | | | GROUND_INST: instantiating (8) with all_944_2, all_944_4, all_495_3,
% 100.47/14.40 | | | | | all_495_2, all_944_3, all_944_1, simplifying with (44),
% 100.47/14.40 | | | | | (307), (493), (494), (498), (500) gives:
% 100.47/14.40 | | | | | (523) ? [v0: any] : ? [v1: $i] : ? [v2: any] : (hBOOL(v1) = v2 &
% 100.47/14.40 | | | | | hBOOL(all_944_1) = v0 & hAPP(all_944_2, all_944_4) = v1 &
% 100.47/14.40 | | | | | $i(v1) & ( ~ (v0 = 0) | v2 = 0))
% 100.47/14.40 | | | | |
% 100.47/14.40 | | | | | GROUND_INST: instantiating (7) with all_944_2, all_944_4, all_495_3,
% 100.47/14.40 | | | | | all_495_2, all_944_3, all_944_1, simplifying with (44),
% 100.47/14.40 | | | | | (307), (493), (494), (498), (500) gives:
% 100.47/14.40 | | | | | (524) ? [v0: $i] : ? [v1: any] : ? [v2: any] : (hBOOL(v0) = v1 &
% 100.47/14.40 | | | | | hBOOL(all_944_1) = v2 & hAPP(all_944_2, all_944_4) = v0 &
% 100.47/14.40 | | | | | $i(v0) & ( ~ (v1 = 0) | v2 = 0))
% 100.47/14.40 | | | | |
% 100.47/14.40 | | | | | GROUND_INST: instantiating (7) with c_Arrow__Order__Mirabelle_OLin,
% 100.47/14.40 | | | | | all_989_3, all_495_3, all_495_2, all_989_2, all_989_1,
% 100.47/14.40 | | | | | simplifying with (27), (44), (307), (508), (511), (512)
% 100.47/14.40 | | | | | gives:
% 100.47/14.40 | | | | | (525) ? [v0: $i] : ? [v1: any] : ? [v2: any] : (hBOOL(v0) = v1 &
% 100.47/14.40 | | | | | hBOOL(all_989_1) = v2 &
% 100.47/14.40 | | | | | hAPP(c_Arrow__Order__Mirabelle_OLin, all_989_3) = v0 &
% 100.47/14.40 | | | | | $i(v0) & ( ~ (v1 = 0) | v2 = 0))
% 100.47/14.40 | | | | |
% 100.47/14.40 | | | | | DELTA: instantiating (524) with fresh symbols all_1099_0, all_1099_1,
% 100.47/14.40 | | | | | all_1099_2 gives:
% 100.47/14.40 | | | | | (526) hBOOL(all_1099_2) = all_1099_1 & hBOOL(all_944_1) =
% 100.47/14.40 | | | | | all_1099_0 & hAPP(all_944_2, all_944_4) = all_1099_2 &
% 100.47/14.40 | | | | | $i(all_1099_2) & ( ~ (all_1099_1 = 0) | all_1099_0 = 0)
% 100.47/14.40 | | | | |
% 100.47/14.40 | | | | | ALPHA: (526) implies:
% 100.47/14.40 | | | | | (527) hAPP(all_944_2, all_944_4) = all_1099_2
% 100.47/14.40 | | | | | (528) hBOOL(all_944_1) = all_1099_0
% 100.47/14.40 | | | | | (529) hBOOL(all_1099_2) = all_1099_1
% 100.47/14.40 | | | | | (530) ~ (all_1099_1 = 0) | all_1099_0 = 0
% 100.47/14.40 | | | | |
% 100.47/14.40 | | | | | DELTA: instantiating (525) with fresh symbols all_1107_0, all_1107_1,
% 100.47/14.40 | | | | | all_1107_2 gives:
% 100.47/14.40 | | | | | (531) hBOOL(all_1107_2) = all_1107_1 & hBOOL(all_989_1) =
% 100.47/14.40 | | | | | all_1107_0 & hAPP(c_Arrow__Order__Mirabelle_OLin, all_989_3)
% 100.47/14.40 | | | | | = all_1107_2 & $i(all_1107_2) & ( ~ (all_1107_1 = 0) |
% 100.47/14.40 | | | | | all_1107_0 = 0)
% 100.47/14.40 | | | | |
% 100.47/14.40 | | | | | ALPHA: (531) implies:
% 100.47/14.40 | | | | | (532) hAPP(c_Arrow__Order__Mirabelle_OLin, all_989_3) = all_1107_2
% 100.47/14.40 | | | | | (533) hBOOL(all_1107_2) = all_1107_1
% 100.47/14.40 | | | | |
% 100.47/14.40 | | | | | DELTA: instantiating (523) with fresh symbols all_1111_0, all_1111_1,
% 100.47/14.40 | | | | | all_1111_2 gives:
% 100.47/14.40 | | | | | (534) hBOOL(all_1111_1) = all_1111_0 & hBOOL(all_944_1) =
% 100.47/14.40 | | | | | all_1111_2 & hAPP(all_944_2, all_944_4) = all_1111_1 &
% 100.47/14.40 | | | | | $i(all_1111_1) & ( ~ (all_1111_2 = 0) | all_1111_0 = 0)
% 100.47/14.40 | | | | |
% 100.47/14.40 | | | | | ALPHA: (534) implies:
% 100.47/14.40 | | | | | (535) hAPP(all_944_2, all_944_4) = all_1111_1
% 100.47/14.40 | | | | | (536) hBOOL(all_944_1) = all_1111_2
% 100.47/14.40 | | | | | (537) hBOOL(all_1111_1) = all_1111_0
% 100.47/14.40 | | | | |
% 100.47/14.40 | | | | | REDUCE: (520), (521), (535) imply:
% 100.47/14.40 | | | | | (538) hAPP(c_Arrow__Order__Mirabelle_OLin, v_L) = all_1111_1
% 100.47/14.40 | | | | |
% 100.47/14.40 | | | | | REDUCE: (520), (521), (527) imply:
% 100.47/14.40 | | | | | (539) hAPP(c_Arrow__Order__Mirabelle_OLin, v_L) = all_1099_2
% 100.47/14.40 | | | | |
% 100.47/14.40 | | | | | REDUCE: (522), (532) imply:
% 100.47/14.40 | | | | | (540) hAPP(c_Arrow__Order__Mirabelle_OLin, v_L) = all_1107_2
% 100.47/14.40 | | | | |
% 100.47/14.40 | | | | | GROUND_INST: instantiating (37) with all_713_2, all_1111_1, v_L,
% 100.47/14.40 | | | | | c_Arrow__Order__Mirabelle_OLin, simplifying with (390),
% 100.47/14.40 | | | | | (538) gives:
% 100.47/14.40 | | | | | (541) all_1111_1 = all_713_2
% 100.47/14.40 | | | | |
% 100.47/14.40 | | | | | GROUND_INST: instantiating (37) with all_1107_2, all_1111_1, v_L,
% 100.47/14.40 | | | | | c_Arrow__Order__Mirabelle_OLin, simplifying with (538),
% 100.47/14.40 | | | | | (540) gives:
% 100.47/14.40 | | | | | (542) all_1111_1 = all_1107_2
% 100.47/14.40 | | | | |
% 100.47/14.40 | | | | | GROUND_INST: instantiating (37) with all_1099_2, all_1111_1, v_L,
% 100.47/14.40 | | | | | c_Arrow__Order__Mirabelle_OLin, simplifying with (538),
% 100.47/14.40 | | | | | (539) gives:
% 100.47/14.40 | | | | | (543) all_1111_1 = all_1099_2
% 100.47/14.40 | | | | |
% 100.47/14.40 | | | | | GROUND_INST: instantiating (34) with all_944_0, all_1111_2, all_944_1,
% 100.47/14.40 | | | | | simplifying with (499), (536) gives:
% 100.47/14.40 | | | | | (544) all_1111_2 = all_944_0
% 100.47/14.40 | | | | |
% 100.47/14.40 | | | | | GROUND_INST: instantiating (34) with all_1099_0, all_1111_2,
% 100.47/14.40 | | | | | all_944_1, simplifying with (528), (536) gives:
% 100.47/14.40 | | | | | (545) all_1111_2 = all_1099_0
% 100.47/14.40 | | | | |
% 100.47/14.40 | | | | | COMBINE_EQS: (542), (543) imply:
% 100.47/14.40 | | | | | (546) all_1107_2 = all_1099_2
% 100.47/14.40 | | | | |
% 100.47/14.40 | | | | | COMBINE_EQS: (541), (542) imply:
% 100.47/14.40 | | | | | (547) all_1107_2 = all_713_2
% 100.47/14.40 | | | | |
% 100.47/14.40 | | | | | COMBINE_EQS: (544), (545) imply:
% 100.47/14.40 | | | | | (548) all_1099_0 = all_944_0
% 100.47/14.40 | | | | |
% 100.47/14.40 | | | | | SIMP: (548) implies:
% 100.47/14.40 | | | | | (549) all_1099_0 = all_944_0
% 100.47/14.40 | | | | |
% 100.47/14.40 | | | | | COMBINE_EQS: (546), (547) imply:
% 100.47/14.40 | | | | | (550) all_1099_2 = all_713_2
% 100.47/14.40 | | | | |
% 100.47/14.40 | | | | | REDUCE: (537), (541) imply:
% 100.47/14.40 | | | | | (551) hBOOL(all_713_2) = all_1111_0
% 100.47/14.40 | | | | |
% 100.47/14.40 | | | | | REDUCE: (533), (547) imply:
% 100.47/14.40 | | | | | (552) hBOOL(all_713_2) = all_1107_1
% 100.47/14.40 | | | | |
% 100.47/14.40 | | | | | REDUCE: (529), (550) imply:
% 100.47/14.40 | | | | | (553) hBOOL(all_713_2) = all_1099_1
% 100.47/14.40 | | | | |
% 100.47/14.40 | | | | | BETA: splitting (530) gives:
% 100.47/14.40 | | | | |
% 100.47/14.40 | | | | | Case 1:
% 100.47/14.40 | | | | | |
% 100.47/14.40 | | | | | | (554) ~ (all_1099_1 = 0)
% 100.47/14.40 | | | | | |
% 100.47/14.40 | | | | | | GROUND_INST: instantiating (34) with 0, all_1107_1, all_713_2,
% 100.47/14.40 | | | | | | simplifying with (516), (552) gives:
% 100.47/14.40 | | | | | | (555) all_1107_1 = 0
% 100.47/14.40 | | | | | |
% 100.47/14.40 | | | | | | GROUND_INST: instantiating (34) with all_1107_1, all_1111_0,
% 100.47/14.40 | | | | | | all_713_2, simplifying with (551), (552) gives:
% 100.47/14.40 | | | | | | (556) all_1111_0 = all_1107_1
% 100.47/14.40 | | | | | |
% 100.47/14.40 | | | | | | GROUND_INST: instantiating (34) with all_1099_1, all_1111_0,
% 100.47/14.40 | | | | | | all_713_2, simplifying with (551), (553) gives:
% 100.47/14.40 | | | | | | (557) all_1111_0 = all_1099_1
% 100.47/14.40 | | | | | |
% 100.47/14.40 | | | | | | COMBINE_EQS: (556), (557) imply:
% 100.47/14.40 | | | | | | (558) all_1107_1 = all_1099_1
% 100.47/14.40 | | | | | |
% 100.47/14.40 | | | | | | SIMP: (558) implies:
% 100.47/14.40 | | | | | | (559) all_1107_1 = all_1099_1
% 100.47/14.40 | | | | | |
% 100.47/14.40 | | | | | | COMBINE_EQS: (555), (559) imply:
% 100.47/14.40 | | | | | | (560) all_1099_1 = 0
% 100.47/14.40 | | | | | |
% 100.47/14.40 | | | | | | REDUCE: (554), (560) imply:
% 100.47/14.40 | | | | | | (561) $false
% 100.47/14.40 | | | | | |
% 100.47/14.40 | | | | | | CLOSE: (561) is inconsistent.
% 100.47/14.40 | | | | | |
% 100.47/14.40 | | | | | Case 2:
% 100.47/14.40 | | | | | |
% 100.47/14.40 | | | | | | (562) all_1099_0 = 0
% 100.47/14.40 | | | | | |
% 100.47/14.40 | | | | | | COMBINE_EQS: (549), (562) imply:
% 100.47/14.40 | | | | | | (563) all_944_0 = 0
% 100.47/14.40 | | | | | |
% 100.47/14.40 | | | | | | REDUCE: (491), (563) imply:
% 100.47/14.40 | | | | | | (564) $false
% 100.47/14.40 | | | | | |
% 100.47/14.40 | | | | | | CLOSE: (564) is inconsistent.
% 100.47/14.40 | | | | | |
% 100.47/14.40 | | | | | End of split
% 100.47/14.40 | | | | |
% 100.47/14.40 | | | | End of split
% 100.47/14.40 | | | |
% 100.47/14.40 | | | End of split
% 100.47/14.40 | | |
% 100.47/14.40 | | End of split
% 100.47/14.40 | |
% 100.47/14.40 | End of split
% 100.47/14.40 |
% 100.47/14.40 End of proof
% 100.47/14.40 % SZS output end Proof for theBenchmark
% 100.47/14.40
% 100.47/14.40 13800ms
%------------------------------------------------------------------------------