TSTP Solution File: SWW473+3 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SWW473+3 : TPTP v8.1.2. Released v5.3.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n013.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 : Fri Sep 1 00:50:19 EDT 2023
% Result : Theorem 97.87s 13.81s
% Output : Proof 288.29s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SWW473+3 : TPTP v8.1.2. Released v5.3.0.
% 0.00/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.15/0.35 % Computer : n013.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Sun Aug 27 17:55:32 EDT 2023
% 0.15/0.35 % CPUTime :
% 0.22/0.61 ________ _____
% 0.22/0.61 ___ __ \_________(_)________________________________
% 0.22/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.22/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.22/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.22/0.61
% 0.22/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.22/0.61 (2023-06-19)
% 0.22/0.61
% 0.22/0.61 (c) Philipp Rümmer, 2009-2023
% 0.22/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.22/0.61 Amanda Stjerna.
% 0.22/0.61 Free software under BSD-3-Clause.
% 0.22/0.61
% 0.22/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.22/0.61
% 0.22/0.62 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.22/0.63 Running up to 7 provers in parallel.
% 0.22/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.22/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.22/0.65 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.22/0.65 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.22/0.65 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.22/0.65 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.22/0.65 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 20.15/3.68 Prover 1: Preprocessing ...
% 20.15/3.70 Prover 4: Preprocessing ...
% 20.15/3.70 Prover 5: Preprocessing ...
% 20.15/3.70 Prover 2: Preprocessing ...
% 21.31/3.74 Prover 6: Preprocessing ...
% 21.31/3.74 Prover 3: Preprocessing ...
% 22.22/3.77 Prover 0: Preprocessing ...
% 63.73/9.27 Prover 1: Warning: ignoring some quantifiers
% 65.63/9.52 Prover 3: Warning: ignoring some quantifiers
% 65.89/9.68 Prover 1: Constructing countermodel ...
% 65.89/9.75 Prover 3: Constructing countermodel ...
% 71.03/10.24 Prover 6: Proving ...
% 72.22/10.37 Prover 4: Warning: ignoring some quantifiers
% 75.49/10.83 Prover 4: Constructing countermodel ...
% 81.65/11.78 Prover 0: Proving ...
% 95.81/13.47 Prover 5: Proving ...
% 97.87/13.80 Prover 3: proved (13165ms)
% 97.87/13.80
% 97.87/13.81 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 97.87/13.81
% 97.87/13.82 Prover 6: stopped
% 97.87/13.82 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 97.87/13.82 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 97.87/13.83 Prover 5: stopped
% 97.87/13.83 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 98.63/13.89 Prover 0: stopped
% 98.63/13.90 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 112.54/15.83 Prover 10: Preprocessing ...
% 114.54/15.98 Prover 1: stopped
% 114.54/15.98 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 114.54/16.02 Prover 7: Preprocessing ...
% 116.88/16.31 Prover 11: Preprocessing ...
% 117.33/16.47 Prover 8: Preprocessing ...
% 120.35/16.74 Prover 2: Proving ...
% 120.35/16.74 Prover 2: stopped
% 120.35/16.76 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 122.71/17.14 Prover 13: Preprocessing ...
% 130.27/18.07 Prover 16: Preprocessing ...
% 133.14/18.46 Prover 10: Warning: ignoring some quantifiers
% 133.66/18.54 Prover 8: Warning: ignoring some quantifiers
% 133.66/18.65 Prover 10: Constructing countermodel ...
% 135.78/18.79 Prover 8: Constructing countermodel ...
% 138.12/19.07 Prover 7: Warning: ignoring some quantifiers
% 141.07/19.49 Prover 7: Constructing countermodel ...
% 143.87/19.97 Prover 11: Warning: ignoring some quantifiers
% 146.83/20.22 Prover 13: Warning: ignoring some quantifiers
% 147.24/20.29 Prover 11: Constructing countermodel ...
% 148.72/20.46 Prover 16: Warning: ignoring some quantifiers
% 149.19/20.51 Prover 13: Constructing countermodel ...
% 154.65/21.28 Prover 16: Constructing countermodel ...
% 157.02/21.63 Prover 16: stopped
% 157.02/21.64 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085
% 162.91/22.43 Prover 19: Preprocessing ...
% 183.35/25.08 Prover 13: stopped
% 186.44/25.43 Prover 19: Warning: ignoring some quantifiers
% 187.49/25.69 Prover 19: Constructing countermodel ...
% 219.57/29.77 Prover 19: stopped
% 241.86/33.19 Prover 7: stopped
% 284.85/40.31 Prover 10: Found proof (size 633)
% 284.85/40.31 Prover 10: proved (26485ms)
% 284.85/40.32 Prover 8: stopped
% 284.85/40.32 Prover 11: stopped
% 284.85/40.32 Prover 4: stopped
% 284.85/40.32
% 284.85/40.32 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 284.85/40.32
% 285.88/40.57 % SZS output start Proof for theBenchmark
% 285.88/40.60 Assumptions after simplification:
% 285.88/40.60 ---------------------------------
% 285.88/40.60
% 285.88/40.60 (conj_1)
% 286.09/40.62 $i(mgt_call) & $i(ord_le1311769555a_bool) & $i(u) & $i(g) & ? [v0: $i] : ?
% 286.09/40.62 [v1: $i] : ? [v2: $i] : (hAPP_f1631501043l_bool(ord_le1311769555a_bool, g) =
% 286.09/40.62 v0 & hAPP_fun_a_bool_bool(v0, v1) = v2 & image_pname_a(mgt_call, u) = v1 &
% 286.09/40.62 $i(v2) & $i(v1) & $i(v0) & hBOOL(v2))
% 286.09/40.62
% 286.09/40.62 (conj_2)
% 286.09/40.63 $i(na) & $i(mgt_call) & $i(suc) & $i(finite_card_a) & $i(ord_less_eq_nat) &
% 286.09/40.63 $i(u) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 286.09/40.63 (hAPP_nat_nat(suc, na) = v0 & hAPP_fun_a_bool_nat(finite_card_a, v2) = v3 &
% 286.09/40.63 hAPP_n1699378549t_bool(ord_less_eq_nat, v0) = v1 & hAPP_nat_bool(v1, v3) =
% 286.09/40.63 v4 & image_pname_a(mgt_call, u) = v2 & $i(v4) & $i(v3) & $i(v2) & $i(v1) &
% 286.09/40.63 $i(v0) & hBOOL(v4))
% 286.09/40.63
% 286.09/40.63 (conj_3)
% 286.09/40.63 $i(na) & $i(mgt_call) & $i(minus_minus_nat) & $i(suc) & $i(finite_card_a) &
% 286.09/40.63 $i(u) & $i(g) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ?
% 286.09/40.63 [v4: $i] : (hAPP_nat_fun_nat_nat(minus_minus_nat, v2) = v3 & hAPP_nat_nat(v3,
% 286.09/40.63 v4) = v0 & hAPP_nat_nat(suc, na) = v4 & hAPP_fun_a_bool_nat(finite_card_a,
% 286.09/40.63 v1) = v2 & hAPP_fun_a_bool_nat(finite_card_a, g) = v0 &
% 286.09/40.63 image_pname_a(mgt_call, u) = v1 & $i(v4) & $i(v3) & $i(v2) & $i(v1) &
% 286.09/40.63 $i(v0))
% 286.09/40.63
% 286.09/40.63 (conj_4)
% 286.09/40.63 $i(member_pname) & $i(pn) & $i(u) & ? [v0: $i] : ? [v1: $i] :
% 286.09/40.63 (hAPP_f1664156314l_bool(v0, u) = v1 & hAPP_p338031245l_bool(member_pname, pn)
% 286.09/40.63 = v0 & $i(v1) & $i(v0) & hBOOL(v1))
% 286.09/40.63
% 286.09/40.63 (conj_5)
% 286.09/40.63 $i(mgt_call) & $i(member_a) & $i(pn) & $i(g) & ? [v0: $i] : ? [v1: $i] : ?
% 286.09/40.63 [v2: $i] : (hAPP_fun_a_bool_bool(v1, g) = v2 & hAPP_pname_a(mgt_call, pn) = v0
% 286.09/40.63 & hAPP_a85458249l_bool(member_a, v0) = v1 & $i(v2) & $i(v1) & $i(v0) & ~
% 286.09/40.63 hBOOL(v2))
% 286.09/40.63
% 286.09/40.63 (conj_6)
% 286.09/40.63 $i(mgt_call) & $i(insert_a) & $i(ord_le1311769555a_bool) & $i(pn) & $i(u) &
% 286.09/40.64 $i(g) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 286.09/40.64 ? [v5: $i] : (hAPP_a1206381875a_bool(insert_a, v0) = v1 &
% 286.09/40.64 hAPP_f1631501043l_bool(ord_le1311769555a_bool, v2) = v3 &
% 286.09/40.64 hAPP_f2050579477a_bool(v1, g) = v2 & hAPP_fun_a_bool_bool(v3, v4) = v5 &
% 286.09/40.64 hAPP_pname_a(mgt_call, pn) = v0 & image_pname_a(mgt_call, u) = v4 & $i(v5) &
% 286.09/40.64 $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & ~ hBOOL(v5))
% 286.09/40.64
% 286.09/40.64 (fact_1008_n__less__m__mult__n)
% 286.09/40.64 $i(times_times_nat) & $i(zero_zero_nat) & $i(ord_less_nat) & $i(suc) & ? [v0:
% 286.09/40.64 $i] : ? [v1: $i] : (hAPP_nat_nat(suc, zero_zero_nat) = v0 &
% 286.09/40.64 hAPP_n1699378549t_bool(ord_less_nat, v0) = v1 & $i(v1) & $i(v0) & ! [v2:
% 286.09/40.64 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (hAPP_nat_bool(v1, v3)
% 286.09/40.64 = v4) | ~ (hAPP_nat_bool(v1, v2) = v5) | ~ $i(v3) | ~ $i(v2) | ~
% 286.09/40.64 hBOOL(v5) | ~ hBOOL(v4) | ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ?
% 286.09/40.64 [v9: $i] : (hAPP_nat_fun_nat_nat(times_times_nat, v2) = v7 &
% 286.09/40.64 hAPP_nat_nat(v7, v3) = v8 & hAPP_n1699378549t_bool(ord_less_nat, v3) =
% 286.09/40.64 v6 & hAPP_nat_bool(v6, v8) = v9 & $i(v9) & $i(v8) & $i(v7) & $i(v6) &
% 286.09/40.64 hBOOL(v9))))
% 286.09/40.64
% 286.09/40.64 (fact_1009_n__less__n__mult__m)
% 286.09/40.64 $i(times_times_nat) & $i(zero_zero_nat) & $i(ord_less_nat) & $i(suc) & ? [v0:
% 286.09/40.64 $i] : ? [v1: $i] : (hAPP_nat_nat(suc, zero_zero_nat) = v0 &
% 286.09/40.64 hAPP_n1699378549t_bool(ord_less_nat, v0) = v1 & $i(v1) & $i(v0) & ! [v2:
% 286.09/40.64 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (hAPP_nat_bool(v1, v3)
% 286.09/40.64 = v4) | ~ (hAPP_nat_bool(v1, v2) = v5) | ~ $i(v3) | ~ $i(v2) | ~
% 286.09/40.64 hBOOL(v5) | ~ hBOOL(v4) | ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ?
% 286.09/40.64 [v9: $i] : (hAPP_nat_fun_nat_nat(times_times_nat, v3) = v7 &
% 286.09/40.64 hAPP_nat_nat(v7, v2) = v8 & hAPP_n1699378549t_bool(ord_less_nat, v3) =
% 286.09/40.64 v6 & hAPP_nat_bool(v6, v8) = v9 & $i(v9) & $i(v8) & $i(v7) & $i(v6) &
% 286.09/40.64 hBOOL(v9))))
% 286.09/40.64
% 286.09/40.64 (fact_1010_one__less__mult)
% 286.09/40.65 $i(times_times_nat) & $i(zero_zero_nat) & $i(ord_less_nat) & $i(suc) & ? [v0:
% 286.09/40.65 $i] : ? [v1: $i] : (hAPP_nat_nat(suc, zero_zero_nat) = v0 &
% 286.09/40.65 hAPP_n1699378549t_bool(ord_less_nat, v0) = v1 & $i(v1) & $i(v0) & ! [v2:
% 286.09/40.65 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (hAPP_nat_bool(v1, v3)
% 286.09/40.65 = v4) | ~ (hAPP_nat_bool(v1, v2) = v5) | ~ $i(v3) | ~ $i(v2) | ~
% 286.09/40.65 hBOOL(v5) | ~ hBOOL(v4) | ? [v6: $i] : ? [v7: $i] : ? [v8: $i] :
% 286.09/40.65 (hAPP_nat_fun_nat_nat(times_times_nat, v2) = v6 & hAPP_nat_nat(v6, v3) =
% 286.09/40.65 v7 & hAPP_nat_bool(v1, v7) = v8 & $i(v8) & $i(v7) & $i(v6) &
% 286.09/40.65 hBOOL(v8))))
% 286.09/40.65
% 286.09/40.65 (fact_1011_one__le__mult__iff)
% 286.09/40.65 $i(times_times_nat) & $i(zero_zero_nat) & $i(suc) & $i(ord_less_eq_nat) & ?
% 286.09/40.65 [v0: $i] : ? [v1: $i] : (hAPP_nat_nat(suc, zero_zero_nat) = v0 &
% 286.09/40.65 hAPP_n1699378549t_bool(ord_less_eq_nat, v0) = v1 & $i(v1) & $i(v0) & ! [v2:
% 286.09/40.65 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (hAPP_nat_bool(v1, v3)
% 286.09/40.65 = v5) | ~ (hAPP_nat_bool(v1, v2) = v4) | ~ $i(v3) | ~ $i(v2) | ~
% 286.09/40.65 hBOOL(v5) | ~ hBOOL(v4) | ? [v6: $i] : ? [v7: $i] : ? [v8: $i] :
% 286.09/40.65 (hAPP_nat_fun_nat_nat(times_times_nat, v2) = v6 & hAPP_nat_nat(v6, v3) =
% 286.09/40.65 v7 & hAPP_nat_bool(v1, v7) = v8 & $i(v8) & $i(v7) & $i(v6) & hBOOL(v8)))
% 286.09/40.65 & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~
% 286.09/40.65 (hAPP_nat_bool(v1, v3) = v5) | ~ (hAPP_nat_bool(v1, v2) = v4) | ~ $i(v3)
% 286.09/40.65 | ~ $i(v2) | hBOOL(v5) | ? [v6: $i] : ? [v7: $i] : ? [v8: $i] :
% 286.09/40.65 (hAPP_nat_fun_nat_nat(times_times_nat, v2) = v6 & hAPP_nat_nat(v6, v3) =
% 286.09/40.65 v7 & hAPP_nat_bool(v1, v7) = v8 & $i(v8) & $i(v7) & $i(v6) & ~
% 286.09/40.65 hBOOL(v8))) & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (
% 286.09/40.65 ~ (hAPP_nat_bool(v1, v3) = v5) | ~ (hAPP_nat_bool(v1, v2) = v4) | ~
% 286.09/40.65 $i(v3) | ~ $i(v2) | hBOOL(v4) | ? [v6: $i] : ? [v7: $i] : ? [v8: $i] :
% 286.09/40.65 (hAPP_nat_fun_nat_nat(times_times_nat, v2) = v6 & hAPP_nat_nat(v6, v3) =
% 286.09/40.65 v7 & hAPP_nat_bool(v1, v7) = v8 & $i(v8) & $i(v7) & $i(v6) & ~
% 286.09/40.65 hBOOL(v8))))
% 286.09/40.65
% 286.09/40.65 (fact_1030_zmult__zless__mono2)
% 286.09/40.66 $i(zero_zero_int) & $i(times_times_int) & $i(ord_less_int) & ? [v0: $i] :
% 286.09/40.66 (hAPP_i1948725293t_bool(ord_less_int, zero_zero_int) = v0 & $i(v0) & ! [v1:
% 286.09/40.66 $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i]
% 286.09/40.66 : ! [v7: $i] : ! [v8: $i] : ( ~ (hAPP_int_fun_int_int(times_times_int, v1)
% 286.09/40.66 = v4) | ~ (hAPP_int_int(v4, v3) = v7) | ~ (hAPP_int_int(v4, v2) = v5)
% 286.09/40.66 | ~ (hAPP_i1948725293t_bool(ord_less_int, v5) = v6) | ~
% 286.09/40.66 (hAPP_int_bool(v6, v7) = v8) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) |
% 286.09/40.66 hBOOL(v8) | ? [v9: $i] : ? [v10: $i] : ? [v11: $i] :
% 286.09/40.66 ((hAPP_i1948725293t_bool(ord_less_int, v2) = v9 & hAPP_int_bool(v9, v3) =
% 286.09/40.66 v10 & $i(v10) & $i(v9) & ~ hBOOL(v10)) | (hAPP_int_bool(v0, v1) = v11
% 286.09/40.66 & $i(v11) & ~ hBOOL(v11)))))
% 286.09/40.66
% 286.09/40.66 (fact_1031_pos__zmult__eq__1__iff)
% 286.09/40.66 $i(zero_zero_int) & $i(times_times_int) & $i(ord_less_int) & $i(one_one_int) &
% 286.09/40.66 ? [v0: $i] : (hAPP_i1948725293t_bool(ord_less_int, zero_zero_int) = v0 &
% 286.09/40.66 $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v2 = one_one_int | ~
% 286.09/40.66 (hAPP_int_fun_int_int(times_times_int, v2) = v3) | ~ (hAPP_int_int(v3,
% 286.09/40.66 v1) = one_one_int) | ~ $i(v2) | ~ $i(v1) | ? [v4: $i] :
% 286.09/40.66 (hAPP_int_bool(v0, v2) = v4 & $i(v4) & ~ hBOOL(v4))) & ! [v1: $i] : !
% 286.09/40.66 [v2: $i] : ! [v3: $i] : (v1 = one_one_int | ~
% 286.09/40.66 (hAPP_int_fun_int_int(times_times_int, v2) = v3) | ~ (hAPP_int_int(v3,
% 286.09/40.66 v1) = one_one_int) | ~ $i(v2) | ~ $i(v1) | ? [v4: $i] :
% 286.09/40.66 (hAPP_int_bool(v0, v2) = v4 & $i(v4) & ~ hBOOL(v4))) & ! [v1: $i] : !
% 286.09/40.66 [v2: $i] : (v2 = one_one_int | ~ (hAPP_int_fun_int_int(times_times_int,
% 286.09/40.66 one_one_int) = v1) | ~ (hAPP_int_int(v1, one_one_int) = v2) | ? [v3:
% 286.09/40.66 $i] : (hAPP_int_bool(v0, one_one_int) = v3 & $i(v3) & ~ hBOOL(v3))))
% 286.09/40.66
% 286.09/40.66 (fact_1035_int__0__less__1)
% 286.09/40.66 $i(zero_zero_int) & $i(ord_less_int) & $i(one_one_int) & ? [v0: $i] : ? [v1:
% 286.09/40.66 $i] : (hAPP_i1948725293t_bool(ord_less_int, zero_zero_int) = v0 &
% 286.09/40.66 hAPP_int_bool(v0, one_one_int) = v1 & $i(v1) & $i(v0) & hBOOL(v1))
% 286.09/40.66
% 286.09/40.66 (fact_1036_int__one__le__iff__zero__less)
% 286.09/40.67 $i(zero_zero_int) & $i(ord_less_int) & $i(one_one_int) & $i(ord_less_eq_int) &
% 286.09/40.67 ? [v0: $i] : ? [v1: $i] : (hAPP_i1948725293t_bool(ord_less_int,
% 286.09/40.67 zero_zero_int) = v1 & hAPP_i1948725293t_bool(ord_less_eq_int, one_one_int)
% 286.09/40.67 = v0 & $i(v1) & $i(v0) & ! [v2: $i] : ! [v3: $i] : ( ~ (hAPP_int_bool(v1,
% 286.09/40.67 v2) = v3) | ~ $i(v2) | ~ hBOOL(v3) | ? [v4: $i] :
% 286.09/40.67 (hAPP_int_bool(v0, v2) = v4 & $i(v4) & hBOOL(v4))) & ! [v2: $i] : ! [v3:
% 286.09/40.67 $i] : ( ~ (hAPP_int_bool(v1, v2) = v3) | ~ $i(v2) | hBOOL(v3) | ? [v4:
% 286.09/40.67 $i] : (hAPP_int_bool(v0, v2) = v4 & $i(v4) & ~ hBOOL(v4))))
% 286.09/40.67
% 286.09/40.67 (fact_1038_le__imp__0__less)
% 286.09/40.67 $i(zero_zero_int) & $i(ord_less_int) & $i(plus_plus_int) & $i(one_one_int) &
% 286.09/40.67 $i(ord_less_eq_int) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 286.09/40.67 (hAPP_int_fun_int_int(plus_plus_int, one_one_int) = v2 &
% 286.09/40.67 hAPP_i1948725293t_bool(ord_less_int, zero_zero_int) = v1 &
% 286.09/40.67 hAPP_i1948725293t_bool(ord_less_eq_int, zero_zero_int) = v0 & $i(v2) &
% 286.09/40.67 $i(v1) & $i(v0) & ! [v3: $i] : ! [v4: $i] : ( ~ (hAPP_int_int(v2, v3) =
% 286.09/40.67 v4) | ~ $i(v3) | ? [v5: $i] : ? [v6: $i] : ((hAPP_int_bool(v1, v4) =
% 286.09/40.67 v6 & $i(v6) & hBOOL(v6)) | (hAPP_int_bool(v0, v3) = v5 & $i(v5) & ~
% 286.09/40.67 hBOOL(v5)))))
% 286.09/40.67
% 286.09/40.67 (fact_1047_zle__antisym)
% 286.09/40.67 $i(ord_less_eq_int) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] :
% 286.09/40.67 (v1 = v0 | ~ (hAPP_i1948725293t_bool(ord_less_eq_int, v0) = v2) | ~
% 286.09/40.67 (hAPP_int_bool(v2, v1) = v3) | ~ $i(v1) | ~ $i(v0) | ~ hBOOL(v3) | ?
% 286.09/40.67 [v4: $i] : ? [v5: $i] : (hAPP_i1948725293t_bool(ord_less_eq_int, v1) = v4 &
% 286.09/40.67 hAPP_int_bool(v4, v0) = v5 & $i(v5) & $i(v4) & ~ hBOOL(v5)))
% 286.09/40.67
% 286.09/40.67 (fact_1069_zdiv__mono2__neg__lemma)
% 286.09/40.68 $i(zero_zero_int) & $i(times_times_int) & $i(ord_less_int) & $i(plus_plus_int)
% 286.09/40.68 & $i(ord_less_eq_int) & ? [v0: $i] : ? [v1: $i] :
% 286.09/40.68 (hAPP_i1948725293t_bool(ord_less_int, zero_zero_int) = v1 &
% 286.09/40.68 hAPP_i1948725293t_bool(ord_less_eq_int, zero_zero_int) = v0 & $i(v1) &
% 286.09/40.68 $i(v0) & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i]
% 286.09/40.68 : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : ! [v10: $i] : ! [v11: $i] : !
% 286.09/40.68 [v12: $i] : ! [v13: $i] : ! [v14: $i] : ( ~
% 286.09/40.68 (hAPP_int_fun_int_int(times_times_int, v5) = v12) | ~
% 286.09/40.68 (hAPP_int_fun_int_int(times_times_int, v2) = v8) | ~
% 286.09/40.68 (hAPP_int_fun_int_int(plus_plus_int, v13) = v14) | ~
% 286.09/40.68 (hAPP_int_fun_int_int(plus_plus_int, v9) = v10) | ~ (hAPP_int_int(v14,
% 286.09/40.68 v7) = v11) | ~ (hAPP_int_int(v12, v6) = v13) | ~ (hAPP_int_int(v10,
% 286.09/40.68 v4) = v11) | ~ (hAPP_int_int(v8, v3) = v9) | ~ $i(v7) | ~ $i(v6) |
% 286.09/40.68 ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ? [v15: $i] : ? [v16: $i]
% 286.09/40.68 : ? [v17: $i] : ? [v18: $i] : ? [v19: $i] : ? [v20: $i] : ? [v21: $i]
% 286.09/40.68 : ? [v22: $i] : ? [v23: $i] : ? [v24: $i] :
% 286.09/40.68 ((hAPP_i1948725293t_bool(ord_less_int, v11) = v15 & hAPP_int_bool(v15,
% 286.09/40.68 zero_zero_int) = v16 & $i(v16) & $i(v15) & ~ hBOOL(v16)) |
% 286.09/40.68 (hAPP_i1948725293t_bool(ord_less_int, v4) = v17 & hAPP_int_bool(v17, v2)
% 286.09/40.68 = v18 & $i(v18) & $i(v17) & ~ hBOOL(v18)) |
% 286.09/40.68 (hAPP_i1948725293t_bool(ord_less_eq_int, v6) = v23 & hAPP_int_bool(v23,
% 286.09/40.68 v3) = v24 & $i(v24) & $i(v23) & hBOOL(v24)) |
% 286.09/40.68 (hAPP_i1948725293t_bool(ord_less_eq_int, v5) = v21 & hAPP_int_bool(v21,
% 286.09/40.68 v2) = v22 & $i(v22) & $i(v21) & ~ hBOOL(v22)) | (hAPP_int_bool(v1,
% 286.09/40.68 v5) = v20 & $i(v20) & ~ hBOOL(v20)) | (hAPP_int_bool(v0, v7) = v19
% 286.09/40.68 & $i(v19) & ~ hBOOL(v19)))))
% 286.09/40.68
% 286.09/40.68 (fact_1071_number__of__is__id)
% 286.09/40.68 ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (number_number_of_int(v0) = v1) | ~
% 286.09/40.68 $i(v0))
% 286.09/40.68
% 286.09/40.68 (fact_1072_int__0__neq__1)
% 286.09/40.68 ~ (zero_zero_int = one_one_int) & $i(zero_zero_int) & $i(one_one_int)
% 286.09/40.68
% 286.09/40.68 (fact_1073_self__quotient__aux1)
% 286.09/40.68 $i(zero_zero_int) & $i(times_times_int) & $i(ord_less_int) & $i(plus_plus_int)
% 286.09/40.68 & $i(one_one_int) & $i(ord_less_eq_int) & ? [v0: $i] : ? [v1: $i] :
% 286.09/40.68 (hAPP_i1948725293t_bool(ord_less_int, zero_zero_int) = v0 &
% 286.09/40.68 hAPP_i1948725293t_bool(ord_less_eq_int, one_one_int) = v1 & $i(v1) & $i(v0)
% 286.09/40.68 & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : !
% 286.09/40.68 [v7: $i] : ( ~ (hAPP_int_fun_int_int(times_times_int, v4) = v6) | ~
% 286.09/40.68 (hAPP_int_fun_int_int(plus_plus_int, v2) = v5) | ~ (hAPP_int_int(v6, v3)
% 286.09/40.68 = v7) | ~ (hAPP_int_int(v5, v7) = v4) | ~ $i(v4) | ~ $i(v3) | ~
% 286.09/40.68 $i(v2) | ? [v8: $i] : ? [v9: $i] : ? [v10: $i] : ? [v11: $i] :
% 286.09/40.68 ((hAPP_i1948725293t_bool(ord_less_int, v2) = v9 & hAPP_int_bool(v9, v4) =
% 286.09/40.68 v10 & $i(v10) & $i(v9) & ~ hBOOL(v10)) | (hAPP_int_bool(v1, v3) = v11
% 286.09/40.68 & $i(v11) & hBOOL(v11)) | (hAPP_int_bool(v0, v4) = v8 & $i(v8) & ~
% 286.09/40.68 hBOOL(v8)))))
% 286.09/40.68
% 286.09/40.68 (fact_1074_self__quotient__aux2)
% 286.09/40.68 $i(zero_zero_int) & $i(times_times_int) & $i(ord_less_int) & $i(plus_plus_int)
% 286.09/40.68 & $i(one_one_int) & $i(ord_less_eq_int) & ? [v0: $i] : ? [v1: $i] :
% 286.09/40.68 (hAPP_i1948725293t_bool(ord_less_int, zero_zero_int) = v0 &
% 286.09/40.68 hAPP_i1948725293t_bool(ord_less_eq_int, zero_zero_int) = v1 & $i(v1) &
% 286.09/40.68 $i(v0) & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i]
% 286.09/40.68 : ! [v7: $i] : ( ~ (hAPP_int_fun_int_int(times_times_int, v4) = v6) | ~
% 286.09/40.68 (hAPP_int_fun_int_int(plus_plus_int, v2) = v5) | ~ (hAPP_int_int(v6, v3)
% 286.09/40.68 = v7) | ~ (hAPP_int_int(v5, v7) = v4) | ~ $i(v4) | ~ $i(v3) | ~
% 286.09/40.68 $i(v2) | ? [v8: $i] : ? [v9: $i] : ? [v10: $i] : ? [v11: $i] :
% 286.09/40.68 ((hAPP_i1948725293t_bool(ord_less_eq_int, v3) = v10 & hAPP_int_bool(v10,
% 286.09/40.68 one_one_int) = v11 & $i(v11) & $i(v10) & hBOOL(v11)) |
% 286.09/40.68 (hAPP_int_bool(v1, v2) = v9 & $i(v9) & ~ hBOOL(v9)) |
% 286.09/40.68 (hAPP_int_bool(v0, v4) = v8 & $i(v8) & ~ hBOOL(v8)))))
% 286.09/40.68
% 286.09/40.68 (fact_1075_q__pos__lemma)
% 286.09/40.69 $i(zero_zero_int) & $i(times_times_int) & $i(ord_less_int) & $i(plus_plus_int)
% 286.09/40.69 & $i(ord_less_eq_int) & ? [v0: $i] : ? [v1: $i] :
% 286.09/40.69 (hAPP_i1948725293t_bool(ord_less_int, zero_zero_int) = v1 &
% 286.09/40.69 hAPP_i1948725293t_bool(ord_less_eq_int, zero_zero_int) = v0 & $i(v1) &
% 286.09/40.69 $i(v0) & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i]
% 286.09/40.69 : ! [v7: $i] : ! [v8: $i] : ( ~ (hAPP_int_fun_int_int(times_times_int, v2)
% 286.09/40.69 = v5) | ~ (hAPP_int_fun_int_int(plus_plus_int, v6) = v7) | ~
% 286.09/40.69 (hAPP_int_int(v7, v4) = v8) | ~ (hAPP_int_int(v5, v3) = v6) | ~ $i(v4) |
% 286.09/40.69 ~ $i(v3) | ~ $i(v2) | ? [v9: $i] : ? [v10: $i] : ? [v11: $i] : ?
% 286.09/40.69 [v12: $i] : ? [v13: $i] : ((hAPP_i1948725293t_bool(ord_less_int, v4) =
% 286.09/40.69 v10 & hAPP_int_bool(v10, v2) = v11 & $i(v11) & $i(v10) & ~
% 286.09/40.69 hBOOL(v11)) | (hAPP_int_bool(v1, v2) = v12 & $i(v12) & ~ hBOOL(v12))
% 286.09/40.69 | (hAPP_int_bool(v0, v8) = v9 & $i(v9) & ~ hBOOL(v9)) |
% 286.09/40.69 (hAPP_int_bool(v0, v3) = v13 & $i(v13) & hBOOL(v13)))))
% 286.09/40.69
% 286.09/40.69 (fact_1076_q__neg__lemma)
% 286.52/40.69 $i(zero_zero_int) & $i(times_times_int) & $i(ord_less_int) & $i(plus_plus_int)
% 286.52/40.69 & $i(ord_less_eq_int) & ? [v0: $i] : ? [v1: $i] :
% 286.52/40.69 (hAPP_i1948725293t_bool(ord_less_int, zero_zero_int) = v1 &
% 286.52/40.69 hAPP_i1948725293t_bool(ord_less_eq_int, zero_zero_int) = v0 & $i(v1) &
% 286.52/40.69 $i(v0) & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i]
% 286.52/40.69 : ! [v7: $i] : ! [v8: $i] : ( ~ (hAPP_int_fun_int_int(times_times_int, v2)
% 286.52/40.69 = v5) | ~ (hAPP_int_fun_int_int(plus_plus_int, v6) = v7) | ~
% 286.52/40.69 (hAPP_int_int(v7, v4) = v8) | ~ (hAPP_int_int(v5, v3) = v6) | ~ $i(v4) |
% 286.52/40.69 ~ $i(v3) | ~ $i(v2) | ? [v9: $i] : ? [v10: $i] : ? [v11: $i] : ?
% 286.52/40.69 [v12: $i] : ? [v13: $i] : ? [v14: $i] :
% 286.52/40.69 ((hAPP_i1948725293t_bool(ord_less_int, v8) = v9 & hAPP_int_bool(v9,
% 286.52/40.69 zero_zero_int) = v10 & $i(v10) & $i(v9) & ~ hBOOL(v10)) |
% 286.52/40.69 (hAPP_i1948725293t_bool(ord_less_eq_int, v3) = v13 & hAPP_int_bool(v13,
% 286.52/40.69 zero_zero_int) = v14 & $i(v14) & $i(v13) & hBOOL(v14)) |
% 286.52/40.69 (hAPP_int_bool(v1, v2) = v12 & $i(v12) & ~ hBOOL(v12)) |
% 286.52/40.69 (hAPP_int_bool(v0, v4) = v11 & $i(v11) & ~ hBOOL(v11)))))
% 286.52/40.69
% 286.52/40.69 (fact_1077_unique__quotient__lemma)
% 286.52/40.69 $i(zero_zero_int) & $i(times_times_int) & $i(ord_less_int) & $i(plus_plus_int)
% 286.52/40.69 & $i(ord_less_eq_int) & ? [v0: $i] : (hAPP_i1948725293t_bool(ord_less_eq_int,
% 286.52/40.69 zero_zero_int) = v0 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] :
% 286.52/40.69 ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ! [v9:
% 286.52/40.69 $i] : ! [v10: $i] : ! [v11: $i] : ! [v12: $i] : ! [v13: $i] : ! [v14:
% 286.52/40.69 $i] : ( ~ (hAPP_int_fun_int_int(times_times_int, v1) = v6) | ~
% 286.52/40.69 (hAPP_int_fun_int_int(plus_plus_int, v11) = v12) | ~
% 286.52/40.69 (hAPP_int_fun_int_int(plus_plus_int, v7) = v8) | ~ (hAPP_int_int(v12, v5)
% 286.52/40.69 = v13) | ~ (hAPP_int_int(v8, v3) = v9) | ~ (hAPP_int_int(v6, v4) =
% 286.52/40.69 v11) | ~ (hAPP_int_int(v6, v2) = v7) | ~
% 286.52/40.69 (hAPP_i1948725293t_bool(ord_less_eq_int, v9) = v10) | ~
% 286.52/40.69 (hAPP_int_bool(v10, v13) = v14) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~
% 286.52/40.69 $i(v2) | ~ $i(v1) | ~ hBOOL(v14) | ? [v15: $i] : ? [v16: $i] : ?
% 286.52/40.69 [v17: $i] : ? [v18: $i] : ? [v19: $i] : ? [v20: $i] : ? [v21: $i] :
% 286.52/40.69 ((hAPP_i1948725293t_bool(ord_less_int, v5) = v18 & hAPP_int_bool(v18, v1)
% 286.52/40.69 = v19 & $i(v19) & $i(v18) & ~ hBOOL(v19)) |
% 286.52/40.69 (hAPP_i1948725293t_bool(ord_less_int, v3) = v16 & hAPP_int_bool(v16, v1)
% 286.52/40.69 = v17 & $i(v17) & $i(v16) & ~ hBOOL(v17)) |
% 286.52/40.69 (hAPP_i1948725293t_bool(ord_less_eq_int, v2) = v20 & hAPP_int_bool(v20,
% 286.52/40.69 v4) = v21 & $i(v21) & $i(v20) & hBOOL(v21)) | (hAPP_int_bool(v0, v3)
% 286.52/40.69 = v15 & $i(v15) & ~ hBOOL(v15)))))
% 286.52/40.69
% 286.52/40.69 (fact_1078_zdiv__mono2__lemma)
% 286.52/40.70 $i(zero_zero_int) & $i(times_times_int) & $i(ord_less_int) & $i(plus_plus_int)
% 286.52/40.70 & $i(ord_less_eq_int) & ? [v0: $i] : ? [v1: $i] :
% 286.52/40.70 (hAPP_i1948725293t_bool(ord_less_int, zero_zero_int) = v1 &
% 286.52/40.70 hAPP_i1948725293t_bool(ord_less_eq_int, zero_zero_int) = v0 & $i(v1) &
% 286.52/40.70 $i(v0) & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i]
% 286.52/40.70 : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : ! [v10: $i] : ! [v11: $i] : !
% 286.52/40.70 [v12: $i] : ! [v13: $i] : ! [v14: $i] : ( ~
% 286.52/40.70 (hAPP_int_fun_int_int(times_times_int, v5) = v12) | ~
% 286.52/40.70 (hAPP_int_fun_int_int(times_times_int, v2) = v8) | ~
% 286.52/40.70 (hAPP_int_fun_int_int(plus_plus_int, v13) = v14) | ~
% 286.52/40.70 (hAPP_int_fun_int_int(plus_plus_int, v9) = v10) | ~ (hAPP_int_int(v14,
% 286.52/40.70 v7) = v11) | ~ (hAPP_int_int(v12, v6) = v13) | ~ (hAPP_int_int(v10,
% 286.52/40.70 v4) = v11) | ~ (hAPP_int_int(v8, v3) = v9) | ~ $i(v7) | ~ $i(v6) |
% 286.52/40.70 ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ? [v15: $i] : ? [v16: $i]
% 286.52/40.70 : ? [v17: $i] : ? [v18: $i] : ? [v19: $i] : ? [v20: $i] : ? [v21: $i]
% 286.52/40.70 : ? [v22: $i] : ? [v23: $i] : ((hAPP_i1948725293t_bool(ord_less_int, v7)
% 286.52/40.70 = v16 & hAPP_int_bool(v16, v5) = v17 & $i(v17) & $i(v16) & ~
% 286.52/40.70 hBOOL(v17)) | (hAPP_i1948725293t_bool(ord_less_eq_int, v5) = v20 &
% 286.52/40.70 hAPP_int_bool(v20, v2) = v21 & $i(v21) & $i(v20) & ~ hBOOL(v21)) |
% 286.52/40.70 (hAPP_i1948725293t_bool(ord_less_eq_int, v3) = v22 & hAPP_int_bool(v22,
% 286.52/40.70 v6) = v23 & $i(v23) & $i(v22) & hBOOL(v23)) | (hAPP_int_bool(v1, v5)
% 286.52/40.70 = v19 & $i(v19) & ~ hBOOL(v19)) | (hAPP_int_bool(v0, v11) = v15 &
% 286.52/40.70 $i(v15) & ~ hBOOL(v15)) | (hAPP_int_bool(v0, v4) = v18 & $i(v18) & ~
% 286.52/40.70 hBOOL(v18)))))
% 286.52/40.70
% 286.52/40.70 (fact_1083_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J)
% 286.52/40.70 $i(zero_zero_int) & $i(times_times_int) & $i(ord_less_eq_int) & ? [v0: $i] :
% 286.52/40.70 (hAPP_i1948725293t_bool(ord_less_eq_int, zero_zero_int) = v0 & $i(v0) & !
% 286.52/40.70 [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (hAPP_int_bool(v0,
% 286.52/40.70 v2) = v3) | ~ (hAPP_int_bool(v0, v1) = v4) | ~ $i(v2) | ~ $i(v1) |
% 286.52/40.70 ~ hBOOL(v4) | ~ hBOOL(v3) | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] :
% 286.52/40.70 (hAPP_int_fun_int_int(times_times_int, v2) = v5 & hAPP_int_int(v5, v1) =
% 286.52/40.70 v6 & hAPP_int_bool(v0, v6) = v7 & $i(v7) & $i(v6) & $i(v5) &
% 286.52/40.70 hBOOL(v7))))
% 286.52/40.70
% 286.52/40.70 (fact_1084_Nat__Transfer_Otransfer__nat__int__function__closures_I5_J)
% 286.52/40.70 $i(zero_zero_int) & $i(ord_less_eq_int) & ? [v0: $i] : ? [v1: $i] :
% 286.52/40.70 (hAPP_i1948725293t_bool(ord_less_eq_int, zero_zero_int) = v0 &
% 286.52/40.70 hAPP_int_bool(v0, zero_zero_int) = v1 & $i(v1) & $i(v0) & hBOOL(v1))
% 286.52/40.70
% 286.52/40.70 (fact_1085_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J)
% 286.52/40.70 $i(zero_zero_int) & $i(plus_plus_int) & $i(ord_less_eq_int) & ? [v0: $i] :
% 286.52/40.70 (hAPP_i1948725293t_bool(ord_less_eq_int, zero_zero_int) = v0 & $i(v0) & !
% 286.52/40.70 [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (hAPP_int_bool(v0,
% 286.52/40.70 v2) = v3) | ~ (hAPP_int_bool(v0, v1) = v4) | ~ $i(v2) | ~ $i(v1) |
% 286.52/40.70 ~ hBOOL(v4) | ~ hBOOL(v3) | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] :
% 286.52/40.70 (hAPP_int_fun_int_int(plus_plus_int, v2) = v5 & hAPP_int_int(v5, v1) = v6
% 286.52/40.70 & hAPP_int_bool(v0, v6) = v7 & $i(v7) & $i(v6) & $i(v5) & hBOOL(v7))))
% 286.52/40.70
% 286.52/40.70 (fact_1086_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J)
% 286.52/40.71 $i(zero_zero_int) & $i(one_one_int) & $i(ord_less_eq_int) & ? [v0: $i] : ?
% 286.52/40.71 [v1: $i] : (hAPP_i1948725293t_bool(ord_less_eq_int, zero_zero_int) = v0 &
% 286.52/40.71 hAPP_int_bool(v0, one_one_int) = v1 & $i(v1) & $i(v0) & hBOOL(v1))
% 286.52/40.71
% 286.52/40.71 (fact_1087_transfer__nat__int__set__cong)
% 286.52/40.71 $i(zero_zero_int) & $i(ord_less_eq_int) & $i(fconj) & ? [v0: $i] : ? [v1:
% 286.52/40.71 $i] : (hAPP_i1948725293t_bool(ord_less_eq_int, zero_zero_int) = v0 &
% 286.52/40.71 cOMBB_1652995168ol_int(fconj, v0) = v1 & $i(v1) & $i(v0) & ! [v2: $i] : !
% 286.52/40.71 [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (cOMBS_int_bool_bool(v1, v3) =
% 286.52/40.71 v4) | ~ (cOMBS_int_bool_bool(v1, v2) = v5) | ~ $i(v3) | ~ $i(v2) | ?
% 286.52/40.71 [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ? [v10: $i] : ?
% 286.52/40.71 [v11: $i] : ($i(v8) & ((v7 = v6 & collect_int(v5) = v6 & collect_int(v4) =
% 286.52/40.71 v6 & $i(v6)) | (hAPP_int_bool(v0, v8) = v9 & $i(v9) & hBOOL(v9) &
% 286.52/40.71 ((hAPP_int_bool(v3, v8) = v10 & $i(v10) & hBOOL(v10)) |
% 286.52/40.71 (hAPP_int_bool(v2, v8) = v11 & $i(v11) & hBOOL(v11))) &
% 286.52/40.71 ((hAPP_int_bool(v3, v8) = v10 & $i(v10) & ~ hBOOL(v10)) |
% 286.52/40.71 (hAPP_int_bool(v2, v8) = v11 & $i(v11) & ~ hBOOL(v11))))))))
% 286.52/40.71
% 286.52/40.71 (fact_1088_decr__mult__lemma)
% 286.52/40.71 $i(zero_zero_int) & $i(times_times_int) & $i(ord_less_int) &
% 286.52/40.71 $i(minus_minus_int) & $i(ord_less_eq_int) & ? [v0: $i] : ? [v1: $i] :
% 286.52/40.71 (hAPP_i1948725293t_bool(ord_less_int, zero_zero_int) = v0 &
% 286.52/40.71 hAPP_i1948725293t_bool(ord_less_eq_int, zero_zero_int) = v1 & $i(v1) &
% 286.52/40.71 $i(v0) & ? [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i]
% 286.52/40.71 : ( ~ (hAPP_int_bool(v1, v3) = v6) | ~ (hAPP_int_bool(v0, v4) = v5) | ~
% 286.52/40.71 $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ hBOOL(v6) | ~ hBOOL(v5) | ? [v7: $i]
% 286.52/40.71 : ? [v8: $i] : ? [v9: $i] : ? [v10: $i] : ? [v11: $i] : ? [v12: $i] :
% 286.52/40.71 ? [v13: $i] : ($i(v9) & ((hAPP_int_fun_int_int(times_times_int, v3) = v7
% 286.52/40.71 & hAPP_int_int(v7, v4) = v8 & $i(v8) & $i(v7) & ! [v14: $i] : !
% 286.52/40.71 [v15: $i] : ! [v16: $i] : ! [v17: $i] : ( ~
% 286.52/40.71 (hAPP_int_fun_int_int(minus_minus_int, v14) = v15) | ~
% 286.52/40.71 (hAPP_int_int(v15, v8) = v16) | ~ (hAPP_int_bool(v2, v16) = v17)
% 286.52/40.71 | ~ $i(v14) | hBOOL(v17) | ? [v18: $i] : (hAPP_int_bool(v2, v14)
% 286.52/40.71 = v18 & $i(v18) & ~ hBOOL(v18)))) |
% 286.52/40.71 (hAPP_int_fun_int_int(minus_minus_int, v9) = v11 & hAPP_int_int(v11,
% 286.52/40.71 v4) = v12 & hAPP_int_bool(v2, v12) = v13 & hAPP_int_bool(v2, v9) =
% 286.52/40.71 v10 & $i(v13) & $i(v12) & $i(v11) & $i(v10) & hBOOL(v10) & ~
% 286.52/40.71 hBOOL(v13))))))
% 286.52/40.71
% 286.52/40.71 (fact_1089_conj__le__cong)
% 286.52/40.71 $i(zero_zero_int) & $i(ord_less_eq_int) & ? [v0: $i] :
% 286.52/40.71 (hAPP_i1948725293t_bool(ord_less_eq_int, zero_zero_int) = v0 & $i(v0))
% 286.52/40.71
% 286.52/40.71 (fact_1090_imp__le__cong)
% 286.52/40.71 $i(zero_zero_int) & $i(ord_less_eq_int) & ? [v0: $i] :
% 286.52/40.71 (hAPP_i1948725293t_bool(ord_less_eq_int, zero_zero_int) = v0 & $i(v0))
% 286.52/40.71
% 286.52/40.71 (fact_1091_incr__mult__lemma)
% 286.52/40.72 $i(zero_zero_int) & $i(times_times_int) & $i(ord_less_int) & $i(plus_plus_int)
% 286.52/40.72 & $i(ord_less_eq_int) & ? [v0: $i] : ? [v1: $i] :
% 286.52/40.72 (hAPP_i1948725293t_bool(ord_less_int, zero_zero_int) = v0 &
% 286.52/40.72 hAPP_i1948725293t_bool(ord_less_eq_int, zero_zero_int) = v1 & $i(v1) &
% 286.52/40.72 $i(v0) & ? [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i]
% 286.52/40.72 : ( ~ (hAPP_int_bool(v1, v3) = v6) | ~ (hAPP_int_bool(v0, v4) = v5) | ~
% 286.52/40.72 $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ hBOOL(v6) | ~ hBOOL(v5) | ? [v7: $i]
% 286.52/40.72 : ? [v8: $i] : ? [v9: $i] : ? [v10: $i] : ? [v11: $i] : ? [v12: $i] :
% 286.52/40.72 ? [v13: $i] : ($i(v9) & ((hAPP_int_fun_int_int(times_times_int, v3) = v7
% 286.52/40.72 & hAPP_int_int(v7, v4) = v8 & $i(v8) & $i(v7) & ! [v14: $i] : !
% 286.52/40.72 [v15: $i] : ! [v16: $i] : ! [v17: $i] : ( ~
% 286.52/40.72 (hAPP_int_fun_int_int(plus_plus_int, v14) = v15) | ~
% 286.52/40.72 (hAPP_int_int(v15, v8) = v16) | ~ (hAPP_int_bool(v2, v16) = v17)
% 286.52/40.72 | ~ $i(v14) | hBOOL(v17) | ? [v18: $i] : (hAPP_int_bool(v2, v14)
% 286.52/40.72 = v18 & $i(v18) & ~ hBOOL(v18)))) |
% 286.52/40.72 (hAPP_int_fun_int_int(plus_plus_int, v9) = v11 & hAPP_int_int(v11, v4)
% 286.52/40.72 = v12 & hAPP_int_bool(v2, v12) = v13 & hAPP_int_bool(v2, v9) = v10 &
% 286.52/40.72 $i(v13) & $i(v12) & $i(v11) & $i(v10) & hBOOL(v10) & ~
% 286.52/40.72 hBOOL(v13))))))
% 286.52/40.72
% 286.52/40.72 (fact_1093_minusinfinity)
% 286.52/40.72 $i(zero_zero_int) & $i(times_times_int) & $i(ord_less_int) &
% 286.52/40.72 $i(minus_minus_int) & ? [v0: $i] : (hAPP_i1948725293t_bool(ord_less_int,
% 286.52/40.72 zero_zero_int) = v0 & $i(v0) & ? [v1: $i] : ? [v2: $i] : ! [v3: $i] :
% 286.52/40.72 ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ( ~
% 286.52/40.72 (hAPP_int_bool(v3, v6) = v7) | ~ (hAPP_int_bool(v0, v4) = v5) | ~ $i(v6)
% 286.52/40.72 | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ hBOOL(v7) | ~
% 286.52/40.72 hBOOL(v5) | ? [v8: $i] : ? [v9: $i] : ? [v10: $i] : ? [v11: $i] : ?
% 286.52/40.72 [v12: $i] : ? [v13: $i] : ? [v14: $i] : ? [v15: $i] : ? [v16: $i] : ?
% 286.52/40.72 [v17: $i] : ? [v18: $i] : ? [v19: $i] : ? [v20: $i] : ? [v21: $i] : ?
% 286.52/40.72 [v22: $i] : ($i(v16) & $i(v15) & $i(v10) & $i(v8) &
% 286.52/40.72 ((hAPP_i1948725293t_bool(ord_less_int, v10) = v11 & hAPP_int_bool(v11,
% 286.52/40.72 v2) = v12 & $i(v12) & $i(v11) & hBOOL(v12) & ((hAPP_int_bool(v3,
% 286.52/40.72 v10) = v14 & $i(v14) & hBOOL(v14)) | (hAPP_int_bool(v1, v10) =
% 286.52/40.72 v13 & $i(v13) & hBOOL(v13))) & ((hAPP_int_bool(v3, v10) = v14 &
% 286.52/40.72 $i(v14) & ~ hBOOL(v14)) | (hAPP_int_bool(v1, v10) = v13 &
% 286.52/40.72 $i(v13) & ~ hBOOL(v13)))) | (hAPP_int_bool(v1, v8) = v9 &
% 286.52/40.72 $i(v9) & hBOOL(v9)) | (((hAPP_int_fun_int_int(times_times_int, v16)
% 286.52/40.72 = v19 & hAPP_int_fun_int_int(minus_minus_int, v15) = v18 &
% 286.52/40.72 hAPP_int_int(v19, v4) = v20 & hAPP_int_int(v18, v20) = v21 &
% 286.52/40.72 hAPP_int_bool(v3, v21) = v22 & $i(v22) & $i(v21) & $i(v20) &
% 286.52/40.72 $i(v19) & $i(v18) & hBOOL(v22)) | (hAPP_int_bool(v3, v15) = v17
% 286.52/40.72 & $i(v17) & hBOOL(v17))) &
% 286.52/40.72 ((hAPP_int_fun_int_int(times_times_int, v16) = v19 &
% 286.52/40.72 hAPP_int_fun_int_int(minus_minus_int, v15) = v18 &
% 286.52/40.72 hAPP_int_int(v19, v4) = v20 & hAPP_int_int(v18, v20) = v21 &
% 286.52/40.72 hAPP_int_bool(v3, v21) = v22 & $i(v22) & $i(v21) & $i(v20) &
% 286.52/40.72 $i(v19) & $i(v18) & ~ hBOOL(v22)) | (hAPP_int_bool(v3, v15) =
% 286.52/40.72 v17 & $i(v17) & ~ hBOOL(v17))))))))
% 286.52/40.72
% 286.52/40.72 (fact_1094_plusinfinity)
% 286.52/40.73 $i(zero_zero_int) & $i(times_times_int) & $i(ord_less_int) &
% 286.52/40.73 $i(minus_minus_int) & ? [v0: $i] : (hAPP_i1948725293t_bool(ord_less_int,
% 286.52/40.73 zero_zero_int) = v0 & $i(v0) & ? [v1: $i] : ! [v2: $i] : ! [v3: $i] :
% 286.52/40.73 ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ( ~
% 286.52/40.73 (hAPP_i1948725293t_bool(ord_less_int, v7) = v8) | ~ (hAPP_int_bool(v2,
% 286.52/40.73 v5) = v6) | ~ (hAPP_int_bool(v0, v3) = v4) | ~ $i(v7) | ~ $i(v5) |
% 286.52/40.73 ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ hBOOL(v6) | ~ hBOOL(v4) | ? [v9:
% 286.52/40.73 $i] : ? [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13: $i] : ?
% 286.52/40.73 [v14: $i] : ? [v15: $i] : ? [v16: $i] : ? [v17: $i] : ? [v18: $i] : ?
% 286.52/40.73 [v19: $i] : ? [v20: $i] : ? [v21: $i] : ? [v22: $i] : ($i(v16) &
% 286.52/40.73 $i(v15) & $i(v11) & $i(v9) & ((hAPP_int_bool(v8, v11) = v12 & $i(v12) &
% 286.52/40.73 hBOOL(v12) & ((hAPP_int_bool(v2, v11) = v14 & $i(v14) & hBOOL(v14))
% 286.52/40.73 | (hAPP_int_bool(v1, v11) = v13 & $i(v13) & hBOOL(v13))) &
% 286.52/40.73 ((hAPP_int_bool(v2, v11) = v14 & $i(v14) & ~ hBOOL(v14)) |
% 286.52/40.73 (hAPP_int_bool(v1, v11) = v13 & $i(v13) & ~ hBOOL(v13)))) |
% 286.52/40.73 (hAPP_int_bool(v1, v9) = v10 & $i(v10) & hBOOL(v10)) |
% 286.52/40.73 (((hAPP_int_fun_int_int(times_times_int, v16) = v19 &
% 286.52/40.73 hAPP_int_fun_int_int(minus_minus_int, v15) = v18 &
% 286.52/40.73 hAPP_int_int(v19, v3) = v20 & hAPP_int_int(v18, v20) = v21 &
% 286.52/40.73 hAPP_int_bool(v2, v21) = v22 & $i(v22) & $i(v21) & $i(v20) &
% 286.52/40.73 $i(v19) & $i(v18) & hBOOL(v22)) | (hAPP_int_bool(v2, v15) = v17
% 286.52/40.73 & $i(v17) & hBOOL(v17))) &
% 286.52/40.73 ((hAPP_int_fun_int_int(times_times_int, v16) = v19 &
% 286.52/40.73 hAPP_int_fun_int_int(minus_minus_int, v15) = v18 &
% 286.52/40.73 hAPP_int_int(v19, v3) = v20 & hAPP_int_int(v18, v20) = v21 &
% 286.52/40.73 hAPP_int_bool(v2, v21) = v22 & $i(v22) & $i(v21) & $i(v20) &
% 286.52/40.73 $i(v19) & $i(v18) & ~ hBOOL(v22)) | (hAPP_int_bool(v2, v15) =
% 286.52/40.73 v17 & $i(v17) & ~ hBOOL(v17))))))))
% 286.52/40.73
% 286.52/40.73 (fact_1096_zero__zle__int)
% 286.52/40.73 $i(semiri1621563631at_int) & $i(zero_zero_int) & $i(ord_less_eq_int) & ? [v0:
% 286.52/40.73 $i] : (hAPP_i1948725293t_bool(ord_less_eq_int, zero_zero_int) = v0 & $i(v0)
% 286.52/40.73 & ! [v1: $i] : ! [v2: $i] : ( ~ (hAPP_nat_int(semiri1621563631at_int, v1)
% 286.52/40.73 = v2) | ~ $i(v1) | ? [v3: $i] : (hAPP_int_bool(v0, v2) = v3 & $i(v3) &
% 286.52/40.73 hBOOL(v3))))
% 286.52/40.73
% 286.52/40.73 (fact_1099_int__0)
% 286.52/40.73 hAPP_nat_int(semiri1621563631at_int, zero_zero_nat) = zero_zero_int &
% 286.52/40.73 $i(semiri1621563631at_int) & $i(zero_zero_int) & $i(zero_zero_nat)
% 286.52/40.73
% 286.52/40.73 (fact_1116_transfer__int__nat__numerals_I1_J)
% 286.52/40.73 hAPP_nat_int(semiri1621563631at_int, zero_zero_nat) = zero_zero_int &
% 286.52/40.73 $i(semiri1621563631at_int) & $i(zero_zero_int) & $i(zero_zero_nat)
% 286.52/40.73
% 286.52/40.73 (fact_1117_Nat__Transfer_Otransfer__int__nat__set__functions_I5_J)
% 286.52/40.74 $i(semiri1621563631at_int) & $i(zero_zero_int) & $i(ord_less_eq_int) &
% 286.52/40.74 $i(fconj) & ? [v0: $i] : ? [v1: $i] :
% 286.52/40.74 (hAPP_i1948725293t_bool(ord_less_eq_int, zero_zero_int) = v0 &
% 286.52/40.74 cOMBB_1652995168ol_int(fconj, v0) = v1 & $i(v1) & $i(v0) & ! [v2: $i] : !
% 286.52/40.74 [v3: $i] : ( ~ (cOMBS_int_bool_bool(v1, v2) = v3) | ~ $i(v2) | ? [v4: $i]
% 286.52/40.74 : ? [v5: $i] : ? [v6: $i] : (cOMBB_int_bool_nat(v2,
% 286.52/40.74 semiri1621563631at_int) = v5 & collect_int(v3) = v4 & collect_nat(v5)
% 286.52/40.74 = v6 & image_nat_int(semiri1621563631at_int, v6) = v4 & $i(v6) & $i(v5)
% 286.52/40.74 & $i(v4))))
% 286.52/40.74
% 286.52/40.74 (fact_1118_Nat__Transfer_Otransfer__nat__int__function__closures_I9_J)
% 286.52/40.74 $i(semiri1621563631at_int) & $i(zero_zero_int) & $i(ord_less_eq_int) & ? [v0:
% 286.52/40.74 $i] : (hAPP_i1948725293t_bool(ord_less_eq_int, zero_zero_int) = v0 & $i(v0)
% 286.52/40.74 & ! [v1: $i] : ! [v2: $i] : ( ~ (hAPP_nat_int(semiri1621563631at_int, v1)
% 286.52/40.74 = v2) | ~ $i(v1) | ? [v3: $i] : (hAPP_int_bool(v0, v2) = v3 & $i(v3) &
% 286.52/40.74 hBOOL(v3))))
% 286.52/40.74
% 286.52/40.74 (fact_1119_transfer__int__nat__quantifiers_I2_J)
% 286.52/40.74 $i(semiri1621563631at_int) & $i(zero_zero_int) & $i(ord_less_eq_int) & ? [v0:
% 286.52/40.74 $i] : (hAPP_i1948725293t_bool(ord_less_eq_int, zero_zero_int) = v0 & $i(v0)
% 286.52/40.74 & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 286.52/40.74 (hAPP_nat_int(semiri1621563631at_int, v2) = v3) | ~ (hAPP_int_bool(v1,
% 286.52/40.74 v3) = v4) | ~ $i(v2) | ~ $i(v1) | ~ hBOOL(v4) | ? [v5: $i] : ?
% 286.52/40.74 [v6: $i] : ? [v7: $i] : (hAPP_int_bool(v1, v5) = v7 & hAPP_int_bool(v0,
% 286.52/40.74 v5) = v6 & $i(v7) & $i(v6) & $i(v5) & hBOOL(v7) & hBOOL(v6))) & ?
% 286.52/40.74 [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (hAPP_int_bool(v0, v2) = v3) | ~
% 286.52/40.74 $i(v2) | ~ $i(v1) | ~ hBOOL(v3) | ? [v4: $i] : ? [v5: $i] : ? [v6:
% 286.52/40.74 $i] : ? [v7: $i] : ($i(v4) & ((hAPP_nat_int(semiri1621563631at_int, v4)
% 286.52/40.74 = v5 & hAPP_int_bool(v1, v5) = v6 & $i(v6) & $i(v5) & hBOOL(v6)) |
% 286.52/40.74 (hAPP_int_bool(v1, v2) = v7 & $i(v7) & ~ hBOOL(v7))))))
% 286.52/40.74
% 286.52/40.74 (fact_1120_transfer__int__nat__quantifiers_I1_J)
% 286.52/40.74 $i(semiri1621563631at_int) & $i(zero_zero_int) & $i(ord_less_eq_int) & ? [v0:
% 286.52/40.74 $i] : (hAPP_i1948725293t_bool(ord_less_eq_int, zero_zero_int) = v0 & $i(v0)
% 286.52/40.74 & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 286.52/40.74 (hAPP_nat_int(semiri1621563631at_int, v2) = v3) | ~ (hAPP_int_bool(v1,
% 286.52/40.74 v3) = v4) | ~ $i(v2) | ~ $i(v1) | hBOOL(v4) | ? [v5: $i] : ? [v6:
% 286.52/40.74 $i] : ? [v7: $i] : (hAPP_int_bool(v1, v5) = v7 & hAPP_int_bool(v0, v5)
% 286.52/40.74 = v6 & $i(v7) & $i(v6) & $i(v5) & hBOOL(v6) & ~ hBOOL(v7))) & ? [v1:
% 286.52/40.74 $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (hAPP_int_bool(v0, v2) = v3) | ~
% 286.52/40.74 $i(v2) | ~ $i(v1) | ~ hBOOL(v3) | ? [v4: $i] : ? [v5: $i] : ? [v6:
% 286.52/40.74 $i] : ? [v7: $i] : ($i(v5) & ((hAPP_nat_int(semiri1621563631at_int, v5)
% 286.52/40.74 = v6 & hAPP_int_bool(v1, v6) = v7 & $i(v7) & $i(v6) & ~ hBOOL(v7))
% 286.52/40.74 | (hAPP_int_bool(v1, v2) = v4 & $i(v4) & hBOOL(v4))))))
% 286.52/40.74
% 286.52/40.74 (fact_1122_int__Suc0__eq__1)
% 286.52/40.74 $i(semiri1621563631at_int) & $i(zero_zero_nat) & $i(one_one_int) & $i(suc) &
% 286.52/40.74 ? [v0: $i] : (hAPP_nat_int(semiri1621563631at_int, v0) = one_one_int &
% 286.52/40.74 hAPP_nat_nat(suc, zero_zero_nat) = v0 & $i(v0))
% 286.52/40.74
% 286.52/40.74 (fact_1126_zero__less__int__conv)
% 286.52/40.74 $i(semiri1621563631at_int) & $i(zero_zero_int) & $i(ord_less_int) &
% 286.52/40.74 $i(zero_zero_nat) & $i(ord_less_nat) & ? [v0: $i] : ? [v1: $i] :
% 286.52/40.74 (hAPP_i1948725293t_bool(ord_less_int, zero_zero_int) = v0 &
% 286.52/40.74 hAPP_n1699378549t_bool(ord_less_nat, zero_zero_nat) = v1 & $i(v1) & $i(v0) &
% 286.52/40.74 ! [v2: $i] : ! [v3: $i] : ( ~ (hAPP_nat_bool(v1, v2) = v3) | ~ $i(v2) |
% 286.52/40.74 ~ hBOOL(v3) | ? [v4: $i] : ? [v5: $i] :
% 286.52/40.74 (hAPP_nat_int(semiri1621563631at_int, v2) = v4 & hAPP_int_bool(v0, v4) =
% 286.52/40.74 v5 & $i(v5) & $i(v4) & hBOOL(v5))) & ! [v2: $i] : ! [v3: $i] : ( ~
% 286.52/40.74 (hAPP_nat_bool(v1, v2) = v3) | ~ $i(v2) | hBOOL(v3) | ? [v4: $i] : ?
% 286.52/40.74 [v5: $i] : (hAPP_nat_int(semiri1621563631at_int, v2) = v4 &
% 286.52/40.74 hAPP_int_bool(v0, v4) = v5 & $i(v5) & $i(v4) & ~ hBOOL(v5))))
% 286.52/40.74
% 286.52/40.74 (fact_1128_Nat__Transfer_Otransfer__nat__int__function__closures_I3_J)
% 286.52/40.75 $i(nat_tsub) & $i(zero_zero_int) & $i(ord_less_eq_int) & ? [v0: $i] :
% 286.52/40.75 (hAPP_i1948725293t_bool(ord_less_eq_int, zero_zero_int) = v0 & $i(v0) & !
% 286.52/40.75 [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (hAPP_int_bool(v0,
% 286.52/40.75 v2) = v3) | ~ (hAPP_int_bool(v0, v1) = v4) | ~ $i(v2) | ~ $i(v1) |
% 286.52/40.75 ~ hBOOL(v4) | ~ hBOOL(v3) | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] :
% 286.52/40.75 (hAPP_int_fun_int_int(nat_tsub, v2) = v5 & hAPP_int_int(v5, v1) = v6 &
% 286.52/40.75 hAPP_int_bool(v0, v6) = v7 & $i(v7) & $i(v6) & $i(v5) & hBOOL(v7))))
% 286.52/40.75
% 286.52/40.75 (fact_1131_zero__less__imp__eq__int)
% 286.52/40.75 $i(semiri1621563631at_int) & $i(zero_zero_int) & $i(ord_less_int) &
% 286.52/40.75 $i(zero_zero_nat) & $i(ord_less_nat) & ? [v0: $i] : ? [v1: $i] :
% 286.52/40.75 (hAPP_i1948725293t_bool(ord_less_int, zero_zero_int) = v0 &
% 286.52/40.75 hAPP_n1699378549t_bool(ord_less_nat, zero_zero_nat) = v1 & $i(v1) & $i(v0) &
% 286.52/40.75 ! [v2: $i] : ! [v3: $i] : ( ~ (hAPP_int_bool(v0, v2) = v3) | ~ $i(v2) |
% 286.52/40.75 ~ hBOOL(v3) | ? [v4: $i] : ? [v5: $i] :
% 286.52/40.75 (hAPP_nat_int(semiri1621563631at_int, v4) = v2 & hAPP_nat_bool(v1, v4) =
% 286.52/40.75 v5 & $i(v5) & $i(v4) & hBOOL(v5))))
% 286.52/40.75
% 286.52/40.75 (fact_1140_nonneg__int__cases)
% 286.52/40.75 $i(semiri1621563631at_int) & $i(zero_zero_int) & $i(ord_less_eq_int) & ? [v0:
% 286.52/40.75 $i] : (hAPP_i1948725293t_bool(ord_less_eq_int, zero_zero_int) = v0 & $i(v0)
% 286.52/40.75 & ! [v1: $i] : ! [v2: $i] : ( ~ (hAPP_int_bool(v0, v1) = v2) | ~ $i(v1) |
% 286.52/40.75 ~ hBOOL(v2) | ? [v3: $i] : (hAPP_nat_int(semiri1621563631at_int, v3) =
% 286.52/40.75 v1 & $i(v3))))
% 286.52/40.75
% 286.52/40.75 (fact_1141_nonneg__eq__int)
% 286.52/40.75 $i(semiri1621563631at_int) & $i(zero_zero_int) & $i(ord_less_eq_int) & ? [v0:
% 286.52/40.75 $i] : (hAPP_i1948725293t_bool(ord_less_eq_int, zero_zero_int) = v0 & $i(v0)
% 286.52/40.75 & ! [v1: $i] : ! [v2: $i] : ( ~ (hAPP_int_bool(v0, v1) = v2) | ~ $i(v1) |
% 286.52/40.75 ~ hBOOL(v2) | ? [v3: $i] : (hAPP_nat_int(semiri1621563631at_int, v3) =
% 286.52/40.75 v1 & $i(v3))))
% 286.52/40.75
% 286.52/40.75 (fact_1142_zero__le__imp__eq__int)
% 286.52/40.75 $i(semiri1621563631at_int) & $i(zero_zero_int) & $i(ord_less_eq_int) & ? [v0:
% 286.52/40.75 $i] : (hAPP_i1948725293t_bool(ord_less_eq_int, zero_zero_int) = v0 & $i(v0)
% 286.52/40.75 & ! [v1: $i] : ! [v2: $i] : ( ~ (hAPP_int_bool(v0, v1) = v2) | ~ $i(v1) |
% 286.52/40.75 ~ hBOOL(v2) | ? [v3: $i] : (hAPP_nat_int(semiri1621563631at_int, v3) =
% 286.52/40.75 v1 & $i(v3))))
% 286.52/40.75
% 286.52/40.75 (fact_1144_decr__lemma)
% 286.52/40.75 $i(zero_zero_int) & $i(times_times_int) & $i(ord_less_int) & $i(plus_plus_int)
% 286.52/40.75 & $i(one_one_int) & $i(minus_minus_int) & ? [v0: $i] :
% 286.52/40.75 (hAPP_i1948725293t_bool(ord_less_int, zero_zero_int) = v0 & $i(v0) & ! [v1:
% 286.52/40.75 $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i]
% 286.52/40.75 : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : ! [v10: $i] : ! [v11: $i] : !
% 286.52/40.75 [v12: $i] : ! [v13: $i] : ( ~ (abs_abs_int(v5) = v6) | ~
% 286.52/40.75 (hAPP_int_fun_int_int(times_times_int, v8) = v9) | ~
% 286.52/40.75 (hAPP_int_fun_int_int(plus_plus_int, v6) = v7) | ~
% 286.52/40.75 (hAPP_int_fun_int_int(minus_minus_int, v1) = v4) | ~ (hAPP_int_int(v9,
% 286.52/40.75 v3) = v10) | ~ (hAPP_int_int(v7, one_one_int) = v8) | ~
% 286.52/40.75 (hAPP_int_int(v4, v10) = v11) | ~ (hAPP_int_int(v4, v2) = v5) | ~
% 286.52/40.75 (hAPP_i1948725293t_bool(ord_less_int, v11) = v12) | ~ (hAPP_int_bool(v12,
% 286.52/40.75 v2) = v13) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | hBOOL(v13) | ? [v14:
% 286.52/40.75 $i] : (hAPP_int_bool(v0, v3) = v14 & $i(v14) & ~ hBOOL(v14))))
% 286.52/40.75
% 286.52/40.75 (fact_1147_not__neg__eq__ge__0)
% 286.52/40.75 $i(nat_neg) & $i(zero_zero_int) & $i(ord_less_eq_int) & ? [v0: $i] :
% 286.52/40.75 (hAPP_i1948725293t_bool(ord_less_eq_int, zero_zero_int) = v0 & $i(v0) & !
% 286.52/40.75 [v1: $i] : ! [v2: $i] : ( ~ (hAPP_int_bool(v0, v1) = v2) | ~ $i(v1) | ~
% 286.52/40.75 hBOOL(v2) | ? [v3: $i] : (hAPP_int_bool(nat_neg, v1) = v3 & $i(v3) & ~
% 286.52/40.75 hBOOL(v3))) & ! [v1: $i] : ! [v2: $i] : ( ~ (hAPP_int_bool(v0, v1) =
% 286.52/40.75 v2) | ~ $i(v1) | hBOOL(v2) | ? [v3: $i] : (hAPP_int_bool(nat_neg, v1)
% 286.52/40.75 = v3 & $i(v3) & hBOOL(v3))))
% 286.52/40.75
% 286.52/40.75 (fact_1148_not__neg__1)
% 286.52/40.75 $i(nat_neg) & $i(one_one_int) & ? [v0: $i] : (hAPP_int_bool(nat_neg,
% 286.52/40.75 one_one_int) = v0 & $i(v0) & ~ hBOOL(v0))
% 286.52/40.75
% 286.52/40.75 (fact_1152_abs__int__eq)
% 286.52/40.75 $i(semiri1621563631at_int) & ! [v0: $i] : ! [v1: $i] : ( ~
% 286.52/40.75 (hAPP_nat_int(semiri1621563631at_int, v0) = v1) | ~ $i(v0) |
% 286.52/40.75 (abs_abs_int(v1) = v1 & $i(v1)))
% 286.52/40.75
% 286.52/40.75 (fact_1154_eq__nat__number__of)
% 286.52/40.76 $i(nat_neg) & $i(zero_zero_int) & $i(ord_less_eq_int) & ! [v0: $i] : ! [v1:
% 286.52/40.76 $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v2 | ~ (number_number_of_nat(v1) =
% 286.52/40.76 v3) | ~ (number_number_of_nat(v0) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v4:
% 286.52/40.76 $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i]
% 286.52/40.76 : (number_number_of_int(v1) = v6 & number_number_of_int(v0) = v4 &
% 286.52/40.76 hAPP_int_bool(nat_neg, v4) = v5 & $i(v6) & $i(v5) & $i(v4) &
% 286.52/40.76 ((hAPP_i1948725293t_bool(ord_less_eq_int, v6) = v7 & hAPP_int_bool(v7,
% 286.52/40.76 zero_zero_int) = v8 & $i(v8) & $i(v7) & hBOOL(v5) & ~ hBOOL(v8)) |
% 286.52/40.76 (hAPP_int_bool(nat_neg, v6) = v9 & $i(v9) & ~ hBOOL(v5) & (( ~ (v4 =
% 286.52/40.76 zero_zero_int) & hBOOL(v9)) | ( ~ (v1 = v0) & ~ hBOOL(v9)))))))
% 286.52/40.76 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (number_number_of_nat(v1) =
% 286.52/40.76 v2) | ~ (number_number_of_nat(v0) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3:
% 286.52/40.76 $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i]
% 286.52/40.76 : (((number_number_of_int(v1) = v5 & hAPP_i1948725293t_bool(ord_less_eq_int,
% 286.52/40.76 v5) = v6 & hAPP_int_bool(v6, zero_zero_int) = v7 & $i(v7) & $i(v6) &
% 286.52/40.76 $i(v5) & hBOOL(v7)) | (number_number_of_int(v0) = v3 &
% 286.52/40.76 hAPP_int_bool(nat_neg, v3) = v4 & $i(v4) & $i(v3) & ~ hBOOL(v4))) &
% 286.52/40.76 ((number_number_of_int(v0) = v3 & hAPP_int_bool(nat_neg, v3) = v4 & $i(v4)
% 286.52/40.76 & $i(v3) & hBOOL(v4)) | ((v1 = v0 | (number_number_of_int(v1) = v5 &
% 286.52/40.76 hAPP_int_bool(nat_neg, v5) = v8 & $i(v8) & $i(v5) & hBOOL(v8))) &
% 286.52/40.76 ((v3 = zero_zero_int & number_number_of_int(v0) = zero_zero_int) |
% 286.52/40.76 (number_number_of_int(v1) = v5 & hAPP_int_bool(nat_neg, v5) = v8 &
% 286.52/40.76 $i(v8) & $i(v5) & ~ hBOOL(v8)))))))
% 286.52/40.76
% 286.52/40.76 (fact_1157_incr__lemma)
% 286.52/40.76 $i(zero_zero_int) & $i(times_times_int) & $i(ord_less_int) & $i(plus_plus_int)
% 286.52/40.76 & $i(one_one_int) & $i(minus_minus_int) & ? [v0: $i] :
% 286.52/40.76 (hAPP_i1948725293t_bool(ord_less_int, zero_zero_int) = v0 & $i(v0) & ! [v1:
% 286.52/40.76 $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i]
% 286.52/40.76 : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : ! [v10: $i] : ! [v11: $i] : !
% 286.52/40.76 [v12: $i] : ! [v13: $i] : ! [v14: $i] : ( ~ (abs_abs_int(v7) = v8) | ~
% 286.52/40.76 (hAPP_int_fun_int_int(times_times_int, v10) = v11) | ~
% 286.52/40.76 (hAPP_int_fun_int_int(plus_plus_int, v8) = v9) | ~
% 286.52/40.76 (hAPP_int_fun_int_int(plus_plus_int, v2) = v5) | ~
% 286.52/40.76 (hAPP_int_fun_int_int(minus_minus_int, v2) = v6) | ~ (hAPP_int_int(v11,
% 286.52/40.76 v3) = v12) | ~ (hAPP_int_int(v9, one_one_int) = v10) | ~
% 286.52/40.76 (hAPP_int_int(v6, v1) = v7) | ~ (hAPP_int_int(v5, v12) = v13) | ~
% 286.52/40.76 (hAPP_i1948725293t_bool(ord_less_int, v1) = v4) | ~ (hAPP_int_bool(v4,
% 286.52/40.76 v13) = v14) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | hBOOL(v14) | ?
% 286.52/40.76 [v15: $i] : (hAPP_int_bool(v0, v3) = v15 & $i(v15) & ~ hBOOL(v15))))
% 286.52/40.76
% 286.52/40.76 (fact_1166_succ__Pls)
% 286.52/40.76 $i(pls) & ? [v0: $i] : (bit1(pls) = v0 & succ(pls) = v0 & $i(v0))
% 286.52/40.76
% 286.52/40.76 (fact_1167_neg__number__of__Bit1)
% 286.52/40.76 $i(nat_neg) & ! [v0: $i] : ! [v1: $i] : ( ~ (number_number_of_int(v0) = v1)
% 286.52/40.76 | ~ $i(v0) | ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] :
% 286.52/40.76 ((bit1(v0) = v3 & number_number_of_int(v3) = v4 & hAPP_int_bool(nat_neg, v4)
% 286.52/40.76 = v5 & $i(v5) & $i(v4) & $i(v3) & hBOOL(v5)) | (hAPP_int_bool(nat_neg,
% 286.52/40.76 v1) = v2 & $i(v2) & ~ hBOOL(v2)))) & ! [v0: $i] : ! [v1: $i] : ( ~
% 286.52/40.76 (number_number_of_int(v0) = v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: $i] : ?
% 286.52/40.76 [v4: $i] : ? [v5: $i] : ((bit1(v0) = v2 & number_number_of_int(v2) = v3 &
% 286.52/40.76 hAPP_int_bool(nat_neg, v3) = v4 & $i(v4) & $i(v3) & $i(v2) & ~
% 286.52/40.76 hBOOL(v4)) | (hAPP_int_bool(nat_neg, v1) = v5 & $i(v5) & hBOOL(v5))))
% 286.52/40.76
% 286.52/40.76 (fact_1169_transfer__int__nat__numerals_I4_J)
% 286.52/40.76 $i(pls) & $i(semiri1621563631at_int) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i]
% 286.52/40.76 : ? [v3: $i] : (bit1(v0) = v1 & bit1(pls) = v0 & number_number_of_int(v1) =
% 286.52/40.76 v2 & number_number_of_nat(v1) = v3 & hAPP_nat_int(semiri1621563631at_int,
% 286.52/40.76 v3) = v2 & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 286.52/40.76
% 286.52/40.76 (fact_1170_numeral__1__eq__Suc__0)
% 286.52/40.76 $i(pls) & $i(zero_zero_nat) & $i(suc) & ? [v0: $i] : ? [v1: $i] : (bit1(pls)
% 286.52/40.76 = v0 & number_number_of_nat(v0) = v1 & hAPP_nat_nat(suc, zero_zero_nat) = v1
% 286.52/40.76 & $i(v1) & $i(v0))
% 286.52/40.76
% 286.52/40.76 (fact_1171_numeral__3__eq__3)
% 286.52/40.76 $i(pls) & $i(zero_zero_nat) & $i(suc) & ? [v0: $i] : ? [v1: $i] : ? [v2:
% 286.52/40.76 $i] : ? [v3: $i] : ? [v4: $i] : (bit1(v0) = v1 & bit1(pls) = v0 &
% 286.52/40.76 number_number_of_nat(v1) = v2 & hAPP_nat_nat(suc, v4) = v2 &
% 286.52/40.76 hAPP_nat_nat(suc, v3) = v4 & hAPP_nat_nat(suc, zero_zero_nat) = v3 & $i(v4)
% 286.52/40.76 & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 286.52/40.76
% 286.52/40.76 (fact_1172_Suc3__eq__add__3)
% 286.52/40.77 $i(pls) & $i(plus_plus_nat) & $i(suc) & ? [v0: $i] : ? [v1: $i] : ? [v2:
% 286.52/40.77 $i] : ? [v3: $i] : (bit1(v0) = v1 & bit1(pls) = v0 &
% 286.52/40.77 number_number_of_nat(v1) = v2 & hAPP_nat_fun_nat_nat(plus_plus_nat, v2) = v3
% 286.52/40.77 & $i(v3) & $i(v2) & $i(v1) & $i(v0) & ! [v4: $i] : ! [v5: $i] : ( ~
% 286.52/40.77 (hAPP_nat_nat(v3, v4) = v5) | ~ $i(v4) | ? [v6: $i] : ? [v7: $i] :
% 286.52/40.77 (hAPP_nat_nat(suc, v7) = v5 & hAPP_nat_nat(suc, v6) = v7 &
% 286.52/40.77 hAPP_nat_nat(suc, v4) = v6 & $i(v7) & $i(v6) & $i(v5))))
% 286.52/40.77
% 286.52/40.77 (fact_1173_Numeral1__eq1__nat)
% 286.52/40.77 $i(pls) & $i(one_one_nat) & ? [v0: $i] : (bit1(pls) = v0 &
% 286.52/40.77 number_number_of_nat(v0) = one_one_nat & $i(v0))
% 286.52/40.77
% 286.52/40.77 (fact_1174_nat__numeral__1__eq__1)
% 286.52/40.77 $i(pls) & $i(one_one_nat) & ? [v0: $i] : (bit1(pls) = v0 &
% 286.52/40.77 number_number_of_nat(v0) = one_one_nat & $i(v0))
% 286.52/40.77
% 286.52/40.77 (fact_1175_one__is__num__one)
% 286.52/40.77 $i(pls) & $i(one_one_int) & ? [v0: $i] : (bit1(pls) = v0 &
% 286.52/40.77 number_number_of_int(v0) = one_one_int & $i(v0))
% 286.52/40.77
% 286.52/40.77 (fact_1178_nat__number__of__Pls)
% 286.52/40.77 number_number_of_nat(pls) = zero_zero_nat & $i(pls) & $i(zero_zero_nat)
% 286.52/40.77
% 286.52/40.77 (fact_1179_semiring__norm_I113_J)
% 286.52/40.77 number_number_of_nat(pls) = zero_zero_nat & $i(pls) & $i(zero_zero_nat)
% 286.52/40.77
% 286.52/40.77 (fact_1180_Pls__def)
% 286.52/40.77 pls = zero_zero_int & $i(zero_zero_int)
% 286.52/40.77
% 286.52/40.77 (fact_1188_Nat__Transfer_Otransfer__nat__int__function__closures_I8_J)
% 286.52/40.77 $i(pls) & $i(zero_zero_int) & $i(ord_less_eq_int) & ? [v0: $i] : ? [v1: $i]
% 286.52/40.77 : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : (bit1(v1) = v2 & bit1(pls) = v1 &
% 286.52/40.77 number_number_of_int(v2) = v3 & hAPP_i1948725293t_bool(ord_less_eq_int,
% 286.52/40.77 zero_zero_int) = v0 & hAPP_int_bool(v0, v3) = v4 & $i(v4) & $i(v3) &
% 286.52/40.77 $i(v2) & $i(v1) & $i(v0) & hBOOL(v4))
% 286.52/40.77
% 286.52/40.77 (fact_1189_rel__simps_I19_J)
% 286.52/40.77 $i(pls) & $i(ord_less_eq_int) & ? [v0: $i] : ? [v1: $i] :
% 286.52/40.77 (hAPP_i1948725293t_bool(ord_less_eq_int, pls) = v0 & hAPP_int_bool(v0, pls) =
% 286.52/40.77 v1 & $i(v1) & $i(v0) & hBOOL(v1))
% 286.52/40.77
% 286.52/40.77 (fact_1190_rel__simps_I22_J)
% 286.52/40.77 $i(pls) & $i(ord_less_eq_int) & ? [v0: $i] :
% 286.52/40.77 (hAPP_i1948725293t_bool(ord_less_eq_int, pls) = v0 & $i(v0) & ! [v1: $i] : !
% 286.52/40.77 [v2: $i] : ( ~ (hAPP_int_bool(v0, v1) = v2) | ~ $i(v1) | ~ hBOOL(v2) | ?
% 286.52/40.77 [v3: $i] : ? [v4: $i] : (bit1(v1) = v3 & hAPP_int_bool(v0, v3) = v4 &
% 286.52/40.77 $i(v4) & $i(v3) & hBOOL(v4))) & ! [v1: $i] : ! [v2: $i] : ( ~
% 286.52/40.77 (hAPP_int_bool(v0, v1) = v2) | ~ $i(v1) | hBOOL(v2) | ? [v3: $i] : ?
% 286.52/40.77 [v4: $i] : (bit1(v1) = v3 & hAPP_int_bool(v0, v3) = v4 & $i(v4) & $i(v3) &
% 286.52/40.77 ~ hBOOL(v4))))
% 286.52/40.77
% 286.52/40.77 (fact_1193_rel__simps_I2_J)
% 286.52/40.77 $i(pls) & $i(ord_less_int) & ? [v0: $i] : ? [v1: $i] :
% 286.52/40.77 (hAPP_i1948725293t_bool(ord_less_int, pls) = v0 & hAPP_int_bool(v0, pls) = v1
% 286.52/40.77 & $i(v1) & $i(v0) & ~ hBOOL(v1))
% 286.52/40.77
% 286.52/40.77 (fact_1194_rel__simps_I12_J)
% 286.52/40.77 $i(pls) & $i(ord_less_int) & ! [v0: $i] : ! [v1: $i] : ( ~
% 286.52/40.77 (hAPP_i1948725293t_bool(ord_less_int, v0) = v1) | ~ $i(v0) | ? [v2: $i] :
% 286.52/40.77 ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ((bit1(v0) = v3 &
% 286.52/40.77 hAPP_i1948725293t_bool(ord_less_int, v3) = v4 & hAPP_int_bool(v4, pls) =
% 286.52/40.77 v5 & $i(v5) & $i(v4) & $i(v3) & hBOOL(v5)) | (hAPP_int_bool(v1, pls) =
% 286.52/40.77 v2 & $i(v2) & ~ hBOOL(v2)))) & ! [v0: $i] : ! [v1: $i] : ( ~
% 286.52/40.77 (hAPP_i1948725293t_bool(ord_less_int, v0) = v1) | ~ $i(v0) | ? [v2: $i] :
% 286.52/40.77 ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ((bit1(v0) = v2 &
% 286.52/40.77 hAPP_i1948725293t_bool(ord_less_int, v2) = v3 & hAPP_int_bool(v3, pls) =
% 286.52/40.77 v4 & $i(v4) & $i(v3) & $i(v2) & ~ hBOOL(v4)) | (hAPP_int_bool(v1, pls)
% 286.52/40.77 = v5 & $i(v5) & hBOOL(v5))))
% 286.52/40.77
% 286.52/40.77 (fact_1197_rel__simps_I29_J)
% 286.52/40.77 $i(pls) & $i(ord_less_int) & $i(ord_less_eq_int) & ! [v0: $i] : ! [v1: $i] :
% 286.52/40.77 ( ~ (hAPP_i1948725293t_bool(ord_less_int, v0) = v1) | ~ $i(v0) | ? [v2: $i]
% 286.52/40.77 : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ((bit1(v0) = v3 &
% 286.52/40.77 hAPP_i1948725293t_bool(ord_less_eq_int, v3) = v4 & hAPP_int_bool(v4,
% 286.52/40.77 pls) = v5 & $i(v5) & $i(v4) & $i(v3) & hBOOL(v5)) | (hAPP_int_bool(v1,
% 286.52/40.77 pls) = v2 & $i(v2) & ~ hBOOL(v2)))) & ! [v0: $i] : ! [v1: $i] : ( ~
% 286.52/40.77 (hAPP_i1948725293t_bool(ord_less_int, v0) = v1) | ~ $i(v0) | ? [v2: $i] :
% 286.52/40.77 ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ((bit1(v0) = v2 &
% 286.52/40.77 hAPP_i1948725293t_bool(ord_less_eq_int, v2) = v3 & hAPP_int_bool(v3,
% 286.52/40.77 pls) = v4 & $i(v4) & $i(v3) & $i(v2) & ~ hBOOL(v4)) |
% 286.52/40.77 (hAPP_int_bool(v1, pls) = v5 & $i(v5) & hBOOL(v5))))
% 286.52/40.77
% 286.52/40.77 (fact_1198_rel__simps_I5_J)
% 286.52/40.77 $i(pls) & $i(ord_less_int) & $i(ord_less_eq_int) & ? [v0: $i] : ? [v1: $i] :
% 286.52/40.77 (hAPP_i1948725293t_bool(ord_less_int, pls) = v0 &
% 286.52/40.77 hAPP_i1948725293t_bool(ord_less_eq_int, pls) = v1 & $i(v1) & $i(v0) & !
% 286.52/40.77 [v2: $i] : ! [v3: $i] : ( ~ (hAPP_int_bool(v1, v2) = v3) | ~ $i(v2) | ~
% 286.52/40.78 hBOOL(v3) | ? [v4: $i] : ? [v5: $i] : (bit1(v2) = v4 & hAPP_int_bool(v0,
% 286.52/40.78 v4) = v5 & $i(v5) & $i(v4) & hBOOL(v5))) & ! [v2: $i] : ! [v3: $i] :
% 286.52/40.78 ( ~ (hAPP_int_bool(v1, v2) = v3) | ~ $i(v2) | hBOOL(v3) | ? [v4: $i] : ?
% 286.52/40.78 [v5: $i] : (bit1(v2) = v4 & hAPP_int_bool(v0, v4) = v5 & $i(v5) & $i(v4) &
% 286.52/40.78 ~ hBOOL(v5))))
% 286.52/40.78
% 286.52/40.78 (fact_320_order__antisym__conv)
% 286.52/40.78 $i(ord_less_eq_int) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] :
% 286.52/40.78 ( ~ (hAPP_i1948725293t_bool(ord_less_eq_int, v0) = v2) | ~ (hAPP_int_bool(v2,
% 286.52/40.78 v1) = v3) | ~ $i(v1) | ~ $i(v0) | ~ hBOOL(v3) | ? [v4: $i] : ? [v5:
% 286.52/40.78 $i] : (( ~ (v1 = v0) | (v4 = v2 & hAPP_int_bool(v2, v0) = v5 & $i(v5) &
% 286.52/40.78 hBOOL(v5))) & (v1 = v0 | (hAPP_i1948725293t_bool(ord_less_eq_int, v1)
% 286.52/40.78 = v4 & hAPP_int_bool(v4, v0) = v5 & $i(v5) & $i(v4) & ~ hBOOL(v5)))))
% 286.52/40.78
% 286.52/40.78 (fact_345_order__antisym)
% 286.52/40.78 $i(ord_less_eq_int) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] :
% 286.52/40.78 (v1 = v0 | ~ (hAPP_i1948725293t_bool(ord_less_eq_int, v0) = v2) | ~
% 286.52/40.78 (hAPP_int_bool(v2, v1) = v3) | ~ $i(v1) | ~ $i(v0) | ~ hBOOL(v3) | ?
% 286.52/40.78 [v4: $i] : ? [v5: $i] : (hAPP_i1948725293t_bool(ord_less_eq_int, v1) = v4 &
% 286.52/40.78 hAPP_int_bool(v4, v0) = v5 & $i(v5) & $i(v4) & ~ hBOOL(v5)))
% 286.52/40.78
% 286.52/40.78 (fact_355_xt1_I5_J)
% 286.52/40.78 $i(ord_less_eq_int) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] :
% 286.52/40.78 (v1 = v0 | ~ (hAPP_i1948725293t_bool(ord_less_eq_int, v0) = v2) | ~
% 286.52/40.78 (hAPP_int_bool(v2, v1) = v3) | ~ $i(v1) | ~ $i(v0) | ~ hBOOL(v3) | ?
% 286.52/40.78 [v4: $i] : ? [v5: $i] : (hAPP_i1948725293t_bool(ord_less_eq_int, v1) = v4 &
% 286.52/40.78 hAPP_int_bool(v4, v0) = v5 & $i(v5) & $i(v4) & ~ hBOOL(v5)))
% 286.52/40.78
% 286.52/40.78 (fact_436_rev__image__eqI)
% 286.52/40.78 $i(member_a) & $i(member_pname) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 286.52/40.78 [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i]
% 286.52/40.78 : ( ~ (hAPP_f1664156314l_bool(v4, v3) = v5) | ~ (hAPP_fun_a_bool_bool(v6, v7)
% 286.52/40.78 = v8) | ~ (hAPP_p338031245l_bool(member_pname, v2) = v4) | ~
% 286.52/40.78 (hAPP_a85458249l_bool(member_a, v0) = v6) | ~ (image_pname_a(v1, v3) = v7)
% 286.52/40.78 | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ hBOOL(v5) | hBOOL(v8) |
% 286.52/40.78 ? [v9: $i] : ( ~ (v9 = v0) & hAPP_pname_a(v1, v2) = v9 & $i(v9)))
% 286.52/40.78
% 286.52/40.78 (fact_453_insert__subset)
% 286.52/40.78 $i(member_a) & $i(insert_a) & $i(ord_le1311769555a_bool) & ! [v0: $i] : !
% 286.52/40.78 [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i]
% 286.52/40.78 : ( ~ (hAPP_a1206381875a_bool(insert_a, v0) = v3) | ~
% 286.52/40.78 (hAPP_f1631501043l_bool(ord_le1311769555a_bool, v4) = v5) | ~
% 286.52/40.78 (hAPP_f2050579477a_bool(v3, v1) = v4) | ~ (hAPP_fun_a_bool_bool(v5, v2) =
% 286.52/40.78 v6) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ hBOOL(v6) | ? [v7: $i] : ?
% 286.52/40.78 [v8: $i] : ? [v9: $i] : ? [v10: $i] :
% 286.52/40.78 (hAPP_f1631501043l_bool(ord_le1311769555a_bool, v1) = v9 &
% 286.52/40.78 hAPP_fun_a_bool_bool(v9, v2) = v10 & hAPP_fun_a_bool_bool(v7, v2) = v8 &
% 286.52/40.78 hAPP_a85458249l_bool(member_a, v0) = v7 & $i(v10) & $i(v9) & $i(v8) &
% 286.52/40.78 $i(v7) & hBOOL(v10) & hBOOL(v8))) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 286.52/40.78 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~
% 286.52/40.78 (hAPP_a1206381875a_bool(insert_a, v0) = v3) | ~
% 286.52/40.78 (hAPP_f1631501043l_bool(ord_le1311769555a_bool, v4) = v5) | ~
% 286.52/40.78 (hAPP_f2050579477a_bool(v3, v1) = v4) | ~ (hAPP_fun_a_bool_bool(v5, v2) =
% 286.52/40.78 v6) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | hBOOL(v6) | ? [v7: $i] : ?
% 286.52/40.78 [v8: $i] : ? [v9: $i] : ? [v10: $i] :
% 286.52/40.78 ((hAPP_f1631501043l_bool(ord_le1311769555a_bool, v1) = v9 &
% 286.52/40.78 hAPP_fun_a_bool_bool(v9, v2) = v10 & $i(v10) & $i(v9) & ~ hBOOL(v10)) |
% 286.52/40.78 (hAPP_fun_a_bool_bool(v7, v2) = v8 & hAPP_a85458249l_bool(member_a, v0) =
% 286.52/40.78 v7 & $i(v8) & $i(v7) & ~ hBOOL(v8))))
% 286.52/40.78
% 286.52/40.78 (fact_479_subsetI)
% 286.52/40.78 $i(member_a) & $i(ord_le1311769555a_bool) & ! [v0: $i] : ! [v1: $i] : !
% 286.52/40.78 [v2: $i] : ! [v3: $i] : ( ~ (hAPP_f1631501043l_bool(ord_le1311769555a_bool,
% 286.52/40.78 v1) = v2) | ~ (hAPP_fun_a_bool_bool(v2, v0) = v3) | ~ $i(v1) | ~
% 286.52/40.78 $i(v0) | hBOOL(v3) | ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] :
% 286.52/40.78 (hAPP_fun_a_bool_bool(v5, v1) = v6 & hAPP_fun_a_bool_bool(v5, v0) = v7 &
% 286.52/40.78 hAPP_a85458249l_bool(member_a, v4) = v5 & $i(v7) & $i(v6) & $i(v5) &
% 286.52/40.78 $i(v4) & hBOOL(v6) & is_a(v4) & ~ hBOOL(v7)))
% 286.52/40.78
% 286.52/40.78 (fact_930_bot__nat__def)
% 286.52/40.78 zero_zero_nat = bot_bot_nat & $i(bot_bot_nat)
% 286.52/40.78
% 286.52/40.78 (fact_947_less__Suc0)
% 286.52/40.78 $i(zero_zero_nat) & $i(ord_less_nat) & $i(suc) & ? [v0: $i] :
% 286.52/40.78 (hAPP_nat_nat(suc, zero_zero_nat) = v0 & $i(v0) & ! [v1: $i] : ! [v2: $i] :
% 286.52/40.78 (v1 = zero_zero_nat | ~ (hAPP_n1699378549t_bool(ord_less_nat, v1) = v2) |
% 286.52/40.78 ~ $i(v1) | ? [v3: $i] : (hAPP_nat_bool(v2, v0) = v3 & $i(v3) & ~
% 286.52/40.78 hBOOL(v3))) & ! [v1: $i] : ( ~ (hAPP_n1699378549t_bool(ord_less_nat,
% 286.52/40.78 zero_zero_nat) = v1) | ? [v2: $i] : (hAPP_nat_bool(v1, v0) = v2 &
% 286.52/40.78 $i(v2) & hBOOL(v2))))
% 286.52/40.78
% 286.52/40.78 (fact_949_one__is__add)
% 286.52/40.79 $i(zero_zero_nat) & $i(plus_plus_nat) & $i(suc) & ? [v0: $i] :
% 286.52/40.79 (hAPP_nat_nat(suc, zero_zero_nat) = v0 & $i(v0) & ! [v1: $i] : ! [v2: $i] :
% 286.52/40.79 ! [v3: $i] : (v2 = v0 | v2 = zero_zero_nat | ~
% 286.52/40.79 (hAPP_nat_fun_nat_nat(plus_plus_nat, v1) = v3) | ~ (hAPP_nat_nat(v3, v2)
% 286.52/40.79 = v0) | ~ $i(v2) | ~ $i(v1)) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i]
% 286.52/40.79 : (v2 = v0 | v1 = v0 | ~ (hAPP_nat_fun_nat_nat(plus_plus_nat, v1) = v3) |
% 286.52/40.79 ~ (hAPP_nat_nat(v3, v2) = v0) | ~ $i(v2) | ~ $i(v1)) & ! [v1: $i] : !
% 286.52/40.79 [v2: $i] : ! [v3: $i] : (v2 = zero_zero_nat | v1 = zero_zero_nat | ~
% 286.52/40.79 (hAPP_nat_fun_nat_nat(plus_plus_nat, v1) = v3) | ~ (hAPP_nat_nat(v3, v2)
% 286.52/40.79 = v0) | ~ $i(v2) | ~ $i(v1)) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i]
% 286.52/40.79 : (v1 = v0 | v1 = zero_zero_nat | ~ (hAPP_nat_fun_nat_nat(plus_plus_nat,
% 286.52/40.79 v1) = v3) | ~ (hAPP_nat_nat(v3, v2) = v0) | ~ $i(v2) | ~ $i(v1)) &
% 286.52/40.79 ! [v1: $i] : ! [v2: $i] : (v2 = v0 | ~
% 286.52/40.79 (hAPP_nat_fun_nat_nat(plus_plus_nat, v0) = v1) | ~ (hAPP_nat_nat(v1,
% 286.52/40.79 zero_zero_nat) = v2)) & ! [v1: $i] : ! [v2: $i] : (v2 = v0 | ~
% 286.52/40.79 (hAPP_nat_fun_nat_nat(plus_plus_nat, zero_zero_nat) = v1) | ~
% 286.52/40.79 (hAPP_nat_nat(v1, v0) = v2)))
% 286.52/40.79
% 286.52/40.79 (fact_950_add__is__1)
% 286.52/40.79 $i(zero_zero_nat) & $i(plus_plus_nat) & $i(suc) & ? [v0: $i] :
% 286.52/40.79 (hAPP_nat_nat(suc, zero_zero_nat) = v0 & $i(v0) & ! [v1: $i] : ! [v2: $i] :
% 286.52/40.79 ! [v3: $i] : (v2 = v0 | v2 = zero_zero_nat | ~
% 286.52/40.79 (hAPP_nat_fun_nat_nat(plus_plus_nat, v1) = v3) | ~ (hAPP_nat_nat(v3, v2)
% 286.52/40.79 = v0) | ~ $i(v2) | ~ $i(v1)) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i]
% 286.52/40.79 : (v2 = v0 | v1 = v0 | ~ (hAPP_nat_fun_nat_nat(plus_plus_nat, v1) = v3) |
% 286.52/40.79 ~ (hAPP_nat_nat(v3, v2) = v0) | ~ $i(v2) | ~ $i(v1)) & ! [v1: $i] : !
% 286.52/40.79 [v2: $i] : ! [v3: $i] : (v2 = zero_zero_nat | v1 = zero_zero_nat | ~
% 286.52/40.79 (hAPP_nat_fun_nat_nat(plus_plus_nat, v1) = v3) | ~ (hAPP_nat_nat(v3, v2)
% 286.52/40.79 = v0) | ~ $i(v2) | ~ $i(v1)) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i]
% 286.52/40.79 : (v1 = v0 | v1 = zero_zero_nat | ~ (hAPP_nat_fun_nat_nat(plus_plus_nat,
% 286.52/40.79 v1) = v3) | ~ (hAPP_nat_nat(v3, v2) = v0) | ~ $i(v2) | ~ $i(v1)) &
% 286.52/40.79 ! [v1: $i] : ! [v2: $i] : (v2 = v0 | ~
% 286.52/40.79 (hAPP_nat_fun_nat_nat(plus_plus_nat, v0) = v1) | ~ (hAPP_nat_nat(v1,
% 286.52/40.79 zero_zero_nat) = v2)) & ! [v1: $i] : ! [v2: $i] : (v2 = v0 | ~
% 286.52/40.79 (hAPP_nat_fun_nat_nat(plus_plus_nat, zero_zero_nat) = v1) | ~
% 286.52/40.79 (hAPP_nat_nat(v1, v0) = v2)))
% 286.52/40.79
% 286.52/40.79 (fact_957_One__nat__def)
% 286.52/40.79 hAPP_nat_nat(suc, zero_zero_nat) = one_one_nat & $i(zero_zero_nat) &
% 286.52/40.79 $i(one_one_nat) & $i(suc)
% 286.52/40.79
% 287.00/40.79 (fact_959_Suc__pred)
% 287.00/40.79 $i(zero_zero_nat) & $i(ord_less_nat) & $i(minus_minus_nat) & $i(suc) & ? [v0:
% 287.00/40.79 $i] : ? [v1: $i] : (hAPP_nat_nat(suc, zero_zero_nat) = v1 &
% 287.00/40.79 hAPP_n1699378549t_bool(ord_less_nat, zero_zero_nat) = v0 & $i(v1) & $i(v0) &
% 287.00/40.79 ! [v2: $i] : ! [v3: $i] : ( ~ (hAPP_nat_bool(v0, v2) = v3) | ~ $i(v2) |
% 287.00/40.79 ~ hBOOL(v3) | ? [v4: $i] : ? [v5: $i] :
% 287.00/40.79 (hAPP_nat_fun_nat_nat(minus_minus_nat, v2) = v4 & hAPP_nat_nat(v4, v1) =
% 287.00/40.79 v5 & hAPP_nat_nat(suc, v5) = v2 & $i(v5) & $i(v4))))
% 287.00/40.79
% 287.00/40.79 (fact_997_mult__eq__1__iff)
% 287.00/40.79 $i(times_times_nat) & $i(zero_zero_nat) & $i(suc) & ? [v0: $i] :
% 287.00/40.79 (hAPP_nat_nat(suc, zero_zero_nat) = v0 & $i(v0) & ! [v1: $i] : ! [v2: $i] :
% 287.00/40.79 ! [v3: $i] : (v2 = v0 | ~ (hAPP_nat_fun_nat_nat(times_times_nat, v1) = v3)
% 287.00/40.79 | ~ (hAPP_nat_nat(v3, v2) = v0) | ~ $i(v2) | ~ $i(v1)) & ! [v1: $i] :
% 287.00/40.79 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 287.00/40.79 (hAPP_nat_fun_nat_nat(times_times_nat, v1) = v3) | ~ (hAPP_nat_nat(v3,
% 287.00/40.79 v2) = v0) | ~ $i(v2) | ~ $i(v1)) & ! [v1: $i] : ! [v2: $i] : (v2 =
% 287.00/40.79 v0 | ~ (hAPP_nat_fun_nat_nat(times_times_nat, v0) = v1) | ~
% 287.00/40.79 (hAPP_nat_nat(v1, v0) = v2)))
% 287.00/40.79
% 287.00/40.79 (function-axioms)
% 287.08/40.84 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 287.08/40.84 (hAPP_f1476298914l_bool(v3, v2) = v1) | ~ (hAPP_f1476298914l_bool(v3, v2) =
% 287.08/40.84 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 |
% 287.08/40.84 ~ (hAPP_f1748468828l_bool(v3, v2) = v1) | ~ (hAPP_f1748468828l_bool(v3, v2)
% 287.08/40.84 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0
% 287.08/40.84 | ~ (hAPP_f1721100032l_bool(v3, v2) = v1) | ~ (hAPP_f1721100032l_bool(v3,
% 287.08/40.84 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1
% 287.08/40.84 = v0 | ~ (hAPP_n609083369l_bool(v3, v2) = v1) | ~
% 287.08/40.84 (hAPP_n609083369l_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 287.08/40.84 $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_i1718399025l_bool(v3, v2) = v1) | ~
% 287.08/40.84 (hAPP_i1718399025l_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 287.08/40.84 $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_f198738859l_bool(v3, v2) = v1) | ~
% 287.08/40.84 (hAPP_f198738859l_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 287.08/40.84 $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_p393069232l_bool(v3, v2) = v1) | ~
% 287.08/40.84 (hAPP_p393069232l_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 287.08/40.84 $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_n1006566506l_bool(v3, v2) = v1) | ~
% 287.08/40.84 (hAPP_n1006566506l_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 287.08/40.84 $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_i68813070l_bool(v3, v2) = v1) | ~
% 287.08/40.84 (hAPP_i68813070l_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 287.08/40.84 $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_a_fun_bool_bool(v3, v2) = v1) | ~
% 287.08/40.84 (hAPP_a_fun_bool_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 287.08/40.84 $i] : ! [v3: $i] : (v1 = v0 | ~ (cOMBB_int_bool_nat(v3, v2) = v1) | ~
% 287.08/40.84 (cOMBB_int_bool_nat(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 287.08/40.84 : ! [v3: $i] : (v1 = v0 | ~ (cOMBB_1146692694ol_nat(v3, v2) = v1) | ~
% 287.08/40.84 (cOMBB_1146692694ol_nat(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 287.08/40.84 $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_f1048215610t_bool(v3, v2) = v1) | ~
% 287.08/40.84 (hAPP_f1048215610t_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 287.08/40.84 $i] : ! [v3: $i] : (v1 = v0 | ~ (cOMBB_1418110531ol_int(v3, v2) = v1) | ~
% 287.08/40.84 (cOMBB_1418110531ol_int(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 287.08/40.84 $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_f1570313510t_bool(v3, v2) = v1) | ~
% 287.08/40.84 (hAPP_f1570313510t_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 287.08/40.84 $i] : ! [v3: $i] : (v1 = v0 | ~ (cOMBB_955900739ol_nat(v3, v2) = v1) | ~
% 287.08/40.84 (cOMBB_955900739ol_nat(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 287.08/40.84 $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_f1038053735a_bool(v3, v2) = v1) | ~
% 287.08/40.84 (hAPP_f1038053735a_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 287.08/40.84 $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_p1170154830_pname(v3, v2) = v1) | ~
% 287.08/40.84 (hAPP_p1170154830_pname(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 287.08/40.84 $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_a_fun_a_a(v3, v2) = v1) | ~
% 287.08/40.84 (hAPP_a_fun_a_a(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 287.08/40.84 ! [v3: $i] : (v1 = v0 | ~ (hAPP_f1594865479ol_int(v3, v2) = v1) | ~
% 287.08/40.84 (hAPP_f1594865479ol_int(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 287.08/40.84 $i] : ! [v3: $i] : (v1 = v0 | ~ (cOMBB_800536526ol_nat(v3, v2) = v1) | ~
% 287.08/40.84 (cOMBB_800536526ol_nat(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 287.08/40.84 $i] : ! [v3: $i] : (v1 = v0 | ~ (nat_case_nat(v3, v2) = v1) | ~
% 287.08/40.84 (nat_case_nat(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 287.08/40.84 [v3: $i] : (v1 = v0 | ~ (hAPP_f1791771145a_bool(v3, v2) = v1) | ~
% 287.08/40.84 (hAPP_f1791771145a_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 287.08/40.84 $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_f1388330588e_bool(v3, v2) = v1) | ~
% 287.08/40.84 (hAPP_f1388330588e_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 287.08/40.84 $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_f1730770594t_bool(v3, v2) = v1) | ~
% 287.08/40.84 (hAPP_f1730770594t_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 287.08/40.84 $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_f1223193598t_bool(v3, v2) = v1) | ~
% 287.08/40.84 (hAPP_f1223193598t_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 287.08/40.84 $i] : ! [v3: $i] : (v1 = v0 | ~ (nat_case_bool(v3, v2) = v1) | ~
% 287.08/40.84 (nat_case_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 287.08/40.84 [v3: $i] : (v1 = v0 | ~ (hAPP_int_fun_int_int(v3, v2) = v1) | ~
% 287.08/40.84 (hAPP_int_fun_int_int(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 287.08/40.84 $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_int_int(v3, v2) = v1) | ~
% 287.08/40.84 (hAPP_int_int(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 287.08/40.84 [v3: $i] : (v1 = v0 | ~ (cOMBB_bool_bool_nat(v3, v2) = v1) | ~
% 287.08/40.84 (cOMBB_bool_bool_nat(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 287.08/40.84 $i] : ! [v3: $i] : (v1 = v0 | ~ (cOMBB_bool_bool_int(v3, v2) = v1) | ~
% 287.08/40.84 (cOMBB_bool_bool_int(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 287.08/40.84 $i] : ! [v3: $i] : (v1 = v0 | ~ (cOMBB_1628441366ol_nat(v3, v2) = v1) | ~
% 287.08/40.84 (cOMBB_1628441366ol_nat(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 287.08/40.84 $i] : ! [v3: $i] : (v1 = v0 | ~ (cOMBB_1897541054_pname(v3, v2) = v1) | ~
% 287.08/40.84 (cOMBB_1897541054_pname(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 287.08/40.84 $i] : ! [v3: $i] : (v1 = v0 | ~ (cOMBB_313729068ol_int(v3, v2) = v1) | ~
% 287.08/40.84 (cOMBB_313729068ol_int(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 287.08/40.84 $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_f1812805200t_bool(v3, v2) = v1) | ~
% 287.08/40.84 (hAPP_f1812805200t_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 287.08/40.84 $i] : ! [v3: $i] : (v1 = v0 | ~ (cOMBB_607112096ol_int(v3, v2) = v1) | ~
% 287.08/40.84 (cOMBB_607112096ol_int(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 287.08/40.84 $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_f449020825t_bool(v3, v2) = v1) | ~
% 287.08/40.84 (hAPP_f449020825t_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 287.08/40.84 $i] : ! [v3: $i] : (v1 = v0 | ~ (cOMBB_516767136ol_int(v3, v2) = v1) | ~
% 287.08/40.84 (cOMBB_516767136ol_int(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 287.08/40.84 $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_i418383825t_bool(v3, v2) = v1) | ~
% 287.08/40.84 (hAPP_i418383825t_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 287.08/40.84 $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_f183368031t_bool(v3, v2) = v1) | ~
% 287.08/40.84 (hAPP_f183368031t_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 287.08/40.84 $i] : ! [v3: $i] : (v1 = v0 | ~ (cOMBB_1761098400ol_int(v3, v2) = v1) | ~
% 287.08/40.84 (cOMBB_1761098400ol_int(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 287.08/40.84 $i] : ! [v3: $i] : (v1 = v0 | ~ (cOMBB_375279840ol_int(v3, v2) = v1) | ~
% 287.08/40.84 (cOMBB_375279840ol_int(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 287.08/40.84 $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_a_fun_int_bool(v3, v2) = v1) | ~
% 287.08/40.84 (hAPP_a_fun_int_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 287.08/40.84 $i] : ! [v3: $i] : (v1 = v0 | ~ (cOMBB_1823939024ol_nat(v3, v2) = v1) | ~
% 287.08/40.84 (cOMBB_1823939024ol_nat(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 287.08/40.84 $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_f282463732t_bool(v3, v2) = v1) | ~
% 287.08/40.84 (hAPP_f282463732t_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 287.08/40.84 $i] : ! [v3: $i] : (v1 = v0 | ~ (cOMBB_2117322052ol_nat(v3, v2) = v1) | ~
% 287.08/40.84 (cOMBB_2117322052ol_nat(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 287.08/40.84 $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_f1066163005t_bool(v3, v2) = v1) | ~
% 287.08/40.84 (hAPP_f1066163005t_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 287.08/40.84 $i] : ! [v3: $i] : (v1 = v0 | ~ (cOMBB_2026977092ol_nat(v3, v2) = v1) | ~
% 287.08/40.84 (cOMBB_2026977092ol_nat(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 287.08/40.84 $i] : ! [v3: $i] : (v1 = v0 | ~ (cOMBB_1123824708ol_nat(v3, v2) = v1) | ~
% 287.08/40.84 (cOMBB_1123824708ol_nat(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 287.08/40.84 $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_f274826591t_bool(v3, v2) = v1) | ~
% 287.08/40.84 (hAPP_f274826591t_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 287.08/40.84 $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_n1082236369t_bool(v3, v2) = v1) | ~
% 287.08/40.84 (hAPP_n1082236369t_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 287.08/40.84 $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_i1948725293t_bool(v3, v2) = v1) | ~
% 287.08/40.84 (hAPP_i1948725293t_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 287.08/40.84 $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_nat_int(v3, v2) = v1) | ~
% 287.08/40.84 (hAPP_nat_int(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 287.08/40.84 [v3: $i] : (v1 = v0 | ~ (hAPP_b589554111l_bool(v3, v2) = v1) | ~
% 287.08/40.84 (hAPP_b589554111l_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 287.08/40.84 $i] : ! [v3: $i] : (v1 = v0 | ~ (image_a_fun_nat_bool(v3, v2) = v1) | ~
% 287.08/40.84 (image_a_fun_nat_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 287.08/40.84 $i] : ! [v3: $i] : (v1 = v0 | ~ (image_a_fun_int_bool(v3, v2) = v1) | ~
% 287.08/40.84 (image_a_fun_int_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 287.08/40.84 $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_nat_fun_nat_nat(v3, v2) = v1) | ~
% 287.08/40.84 (hAPP_nat_fun_nat_nat(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 287.08/40.84 $i] : ! [v3: $i] : (v1 = v0 | ~ (cOMBB_1652995168ol_int(v3, v2) = v1) | ~
% 287.08/40.84 (cOMBB_1652995168ol_int(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 287.08/40.84 $i] : ! [v3: $i] : (v1 = v0 | ~ (cOMBS_int_bool_bool(v3, v2) = v1) | ~
% 287.08/40.84 (cOMBS_int_bool_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 287.08/40.84 $i] : ! [v3: $i] : (v1 = v0 | ~ (cOMBB_1015721476ol_nat(v3, v2) = v1) | ~
% 287.08/40.84 (cOMBB_1015721476ol_nat(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 287.08/40.84 $i] : ! [v3: $i] : (v1 = v0 | ~ (cOMBS_nat_bool_bool(v3, v2) = v1) | ~
% 287.08/40.84 (cOMBS_nat_bool_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 287.08/40.84 $i] : ! [v3: $i] : (v1 = v0 | ~ (cOMBB_675860798_pname(v3, v2) = v1) | ~
% 287.08/40.84 (cOMBB_675860798_pname(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 287.08/40.84 $i] : ! [v3: $i] : (v1 = v0 | ~ (cOMBB_338059395a_bool(v3, v2) = v1) | ~
% 287.08/40.84 (cOMBB_338059395a_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 287.08/40.84 $i] : ! [v3: $i] : (v1 = v0 | ~ (cOMBB_2095475776e_bool(v3, v2) = v1) | ~
% 287.08/40.84 (cOMBB_2095475776e_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 287.08/40.84 $i] : ! [v3: $i] : (v1 = v0 | ~ (cOMBB_444170502t_bool(v3, v2) = v1) | ~
% 287.08/40.84 (cOMBB_444170502t_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 287.08/40.84 $i] : ! [v3: $i] : (v1 = v0 | ~ (cOMBS_1187019125l_bool(v3, v2) = v1) | ~
% 287.08/40.84 (cOMBS_1187019125l_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 287.08/40.84 $i] : ! [v3: $i] : (v1 = v0 | ~ (cOMBB_1974511970t_bool(v3, v2) = v1) | ~
% 287.08/40.84 (cOMBB_1974511970t_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 287.08/40.84 $i] : ! [v3: $i] : (v1 = v0 | ~ (cOMBS_1912792529l_bool(v3, v2) = v1) | ~
% 287.08/40.84 (cOMBS_1912792529l_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 287.08/40.84 $i] : ! [v3: $i] : (v1 = v0 | ~ (cOMBB_1972296269bool_a(v3, v2) = v1) | ~
% 287.08/40.84 (cOMBB_1972296269bool_a(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 287.08/40.84 $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_i2112223885l_bool(v3, v2) = v1) | ~
% 287.08/40.84 (hAPP_i2112223885l_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 287.08/40.84 $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_n215258509l_bool(v3, v2) = v1) | ~
% 287.08/40.84 (hAPP_n215258509l_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 287.08/40.84 $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_f285962445l_bool(v3, v2) = v1) | ~
% 287.08/40.84 (hAPP_f285962445l_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 287.08/40.84 $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_f556039215l_bool(v3, v2) = v1) | ~
% 287.08/40.84 (hAPP_f556039215l_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 287.08/40.84 $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_f1951378235l_bool(v3, v2) = v1) | ~
% 287.08/40.84 (hAPP_f1951378235l_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 287.08/40.84 $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_f628503027l_bool(v3, v2) = v1) | ~
% 287.08/40.84 (hAPP_f628503027l_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 287.08/40.84 $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_nat_nat(v3, v2) = v1) | ~
% 287.08/40.84 (hAPP_nat_nat(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 287.08/40.84 [v3: $i] : (v1 = v0 | ~ (image_pname_int(v3, v2) = v1) | ~
% 287.08/40.84 (image_pname_int(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 287.08/40.84 ! [v3: $i] : (v1 = v0 | ~ (hAPP_f957591787ol_nat(v3, v2) = v1) | ~
% 287.08/40.84 (hAPP_f957591787ol_nat(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 287.08/40.84 $i] : ! [v3: $i] : (v1 = v0 | ~ (image_pname_nat(v3, v2) = v1) | ~
% 287.08/40.84 (image_pname_nat(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 287.08/40.84 ! [v3: $i] : (v1 = v0 | ~ (hAPP_f22106695ol_nat(v3, v2) = v1) | ~
% 287.08/40.84 (hAPP_f22106695ol_nat(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 287.08/40.84 $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_f2009550088ol_nat(v3, v2) = v1) | ~
% 287.08/40.84 (hAPP_f2009550088ol_nat(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 287.08/40.84 $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_f55526627ol_nat(v3, v2) = v1) | ~
% 287.08/40.84 (hAPP_f55526627ol_nat(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 287.08/40.84 $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_f696928925ol_nat(v3, v2) = v1) | ~
% 287.08/40.84 (hAPP_f696928925ol_nat(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 287.08/40.84 $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_f521865025ol_nat(v3, v2) = v1) | ~
% 287.08/40.84 (hAPP_f521865025ol_nat(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 287.08/40.84 $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_fun_a_bool_nat(v3, v2) = v1) | ~
% 287.08/40.84 (hAPP_fun_a_bool_nat(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 287.08/40.84 $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_n1699378549t_bool(v3, v2) = v1) | ~
% 287.08/40.84 (hAPP_n1699378549t_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 287.08/40.84 $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_f921600141ol_nat(v3, v2) = v1) | ~
% 287.08/40.84 (hAPP_f921600141ol_nat(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 287.08/40.84 $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_a1206381875a_bool(v3, v2) = v1) | ~
% 287.08/40.84 (hAPP_a1206381875a_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 287.08/40.84 $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_i1529485324t_bool(v3, v2) = v1) | ~
% 287.08/40.84 (hAPP_i1529485324t_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 287.08/40.84 $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_f1805168059t_bool(v3, v2) = v1) | ~
% 287.08/40.84 (hAPP_f1805168059t_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 287.08/40.84 $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_n1512601776t_bool(v3, v2) = v1) | ~
% 287.08/40.84 (hAPP_n1512601776t_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 287.08/40.84 $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_f800510211t_bool(v3, v2) = v1) | ~
% 287.08/40.84 (hAPP_f800510211t_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 287.08/40.84 $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_p905327722e_bool(v3, v2) = v1) | ~
% 287.08/40.84 (hAPP_p905327722e_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 287.08/40.84 $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_f1531278575l_bool(v3, v2) = v1) | ~
% 287.08/40.84 (hAPP_f1531278575l_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 287.08/40.84 $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_f1320879424l_bool(v3, v2) = v1) | ~
% 287.08/40.84 (hAPP_f1320879424l_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 287.08/40.84 $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_f633452666l_bool(v3, v2) = v1) | ~
% 287.08/40.84 (hAPP_f633452666l_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 287.08/40.84 $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_f1246832597l_bool(v3, v2) = v1) | ~
% 287.08/40.84 (hAPP_f1246832597l_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 287.08/40.84 $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_f587666462l_bool(v3, v2) = v1) | ~
% 287.08/40.84 (hAPP_f587666462l_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 287.08/40.84 $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_f1948010709l_bool(v3, v2) = v1) | ~
% 287.08/40.84 (hAPP_f1948010709l_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 287.08/40.84 $i] : ! [v3: $i] : (v1 = v0 | ~ (image_nat_int(v3, v2) = v1) | ~
% 287.08/40.84 (image_nat_int(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 287.08/40.84 [v3: $i] : (v1 = v0 | ~ (image_fun_a_bool_int(v3, v2) = v1) | ~
% 287.08/40.84 (image_fun_a_bool_int(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 287.08/40.84 $i] : ! [v3: $i] : (v1 = v0 | ~ (image_41399353ol_int(v3, v2) = v1) | ~
% 287.08/40.84 (image_41399353ol_int(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 287.08/40.84 $i] : ! [v3: $i] : (v1 = v0 | ~ (image_1133522419ol_int(v3, v2) = v1) | ~
% 287.08/40.84 (image_1133522419ol_int(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 287.08/40.84 $i] : ! [v3: $i] : (v1 = v0 | ~ (image_2069007511ol_int(v3, v2) = v1) | ~
% 287.08/40.84 (image_2069007511ol_int(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 287.08/40.84 $i] : ! [v3: $i] : (v1 = v0 | ~ (image_a_int(v3, v2) = v1) | ~
% 287.08/40.84 (image_a_int(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 287.08/40.84 [v3: $i] : (v1 = v0 | ~ (image_fun_a_bool_nat(v3, v2) = v1) | ~
% 287.08/40.84 (image_fun_a_bool_nat(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 287.08/40.84 $i] : ! [v3: $i] : (v1 = v0 | ~ (image_1551609309ol_nat(v3, v2) = v1) | ~
% 287.08/40.84 (image_1551609309ol_nat(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 287.08/40.84 $i] : ! [v3: $i] : (v1 = v0 | ~ (image_496248727ol_nat(v3, v2) = v1) | ~
% 287.08/40.84 (image_496248727ol_nat(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 287.08/40.84 $i] : ! [v3: $i] : (v1 = v0 | ~ (image_1431733819ol_nat(v3, v2) = v1) | ~
% 287.08/40.84 (image_1431733819ol_nat(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 287.08/40.84 $i] : ! [v3: $i] : (v1 = v0 | ~ (image_a_nat(v3, v2) = v1) | ~
% 287.08/40.84 (image_a_nat(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 287.08/40.84 [v3: $i] : (v1 = v0 | ~ (image_892525857t_bool(v3, v2) = v1) | ~
% 287.08/40.84 (image_892525857t_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 287.08/40.84 $i] : ! [v3: $i] : (v1 = v0 | ~ (image_275383677t_bool(v3, v2) = v1) | ~
% 287.08/40.84 (image_275383677t_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 287.08/40.84 $i] : ! [v3: $i] : (v1 = v0 | ~ (image_26036933t_bool(v3, v2) = v1) | ~
% 287.08/40.84 (image_26036933t_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 287.08/40.84 $i] : ! [v3: $i] : (v1 = v0 | ~ (image_1556378401t_bool(v3, v2) = v1) | ~
% 287.08/40.84 (image_1556378401t_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 287.08/40.84 $i] : ! [v3: $i] : (v1 = v0 | ~ (image_2129980159t_bool(v3, v2) = v1) | ~
% 287.08/40.84 (image_2129980159t_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 287.08/40.84 $i] : ! [v3: $i] : (v1 = v0 | ~ (image_1512837979t_bool(v3, v2) = v1) | ~
% 287.08/40.84 (image_1512837979t_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 287.08/40.84 $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_f284875647l_bool(v3, v2) = v1) | ~
% 287.08/40.84 (hAPP_f284875647l_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 287.08/40.84 $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_f103356543l_bool(v3, v2) = v1) | ~
% 287.08/40.84 (hAPP_f103356543l_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 287.08/40.84 $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_f1434722111l_bool(v3, v2) = v1) | ~
% 287.08/40.84 (hAPP_f1434722111l_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 287.08/40.84 $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_f510955609l_bool(v3, v2) = v1) | ~
% 287.08/40.84 (hAPP_f510955609l_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 287.08/40.84 $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_f1772781669l_bool(v3, v2) = v1) | ~
% 287.08/40.84 (hAPP_f1772781669l_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 287.08/40.84 $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_f317860125l_bool(v3, v2) = v1) | ~
% 287.08/40.84 (hAPP_f317860125l_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 287.08/40.84 $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_f937997336l_bool(v3, v2) = v1) | ~
% 287.08/40.84 (hAPP_f937997336l_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 287.08/40.84 $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_f1593524852l_bool(v3, v2) = v1) | ~
% 287.08/40.84 (hAPP_f1593524852l_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 287.08/40.84 $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_f389811538l_bool(v3, v2) = v1) | ~
% 287.08/40.84 (hAPP_f389811538l_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 287.08/40.84 $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_f292226953l_bool(v3, v2) = v1) | ~
% 287.08/40.84 (hAPP_f292226953l_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 287.08/40.84 $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_f1637334154l_bool(v3, v2) = v1) | ~
% 287.08/40.84 (hAPP_f1637334154l_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 287.08/40.84 $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_f215623910l_bool(v3, v2) = v1) | ~
% 287.08/40.84 (hAPP_f215623910l_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 287.08/40.84 $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_f559147733l_bool(v3, v2) = v1) | ~
% 287.08/40.84 (hAPP_f559147733l_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 287.08/40.84 $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_f1935102916l_bool(v3, v2) = v1) | ~
% 287.08/40.84 (hAPP_f1935102916l_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 287.08/40.84 $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_f2117159681l_bool(v3, v2) = v1) | ~
% 287.08/40.84 (hAPP_f2117159681l_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 287.08/40.84 $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_f621171935l_bool(v3, v2) = v1) | ~
% 287.08/40.84 (hAPP_f621171935l_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 287.08/40.84 $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_f54304608l_bool(v3, v2) = v1) | ~
% 287.08/40.84 (hAPP_f54304608l_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 287.08/40.84 $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_f448129468l_bool(v3, v2) = v1) | ~
% 287.08/40.84 (hAPP_f448129468l_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 287.08/40.84 $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_f434788991l_bool(v3, v2) = v1) | ~
% 287.08/40.84 (hAPP_f434788991l_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 287.08/40.84 $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_f759274231e_bool(v3, v2) = v1) | ~
% 287.08/40.84 (hAPP_f759274231e_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 287.08/40.84 $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_f1664156314l_bool(v3, v2) = v1) | ~
% 287.08/40.84 (hAPP_f1664156314l_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 287.08/40.84 $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_f1297739591_pname(v3, v2) = v1) | ~
% 287.08/40.84 (hAPP_f1297739591_pname(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 287.08/40.84 $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_f1631501043l_bool(v3, v2) = v1) | ~
% 287.08/40.84 (hAPP_f1631501043l_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 287.08/40.84 $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_f2050579477a_bool(v3, v2) = v1) | ~
% 287.08/40.84 (hAPP_f2050579477a_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 287.08/40.84 $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_fun_a_bool_bool(v3, v2) = v1) | ~
% 287.08/40.84 (hAPP_fun_a_bool_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 287.08/40.84 $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_fun_a_bool_a(v3, v2) = v1) | ~
% 287.08/40.84 (hAPP_fun_a_bool_a(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 287.08/40.84 : ! [v3: $i] : (v1 = v0 | ~ (hAPP_n850744903l_bool(v3, v2) = v1) | ~
% 287.08/40.84 (hAPP_n850744903l_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 287.08/40.84 $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_n1414589940l_bool(v3, v2) = v1) | ~
% 287.08/40.84 (hAPP_n1414589940l_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 287.08/40.84 $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_n1025906991e_bool(v3, v2) = v1) | ~
% 287.08/40.84 (hAPP_n1025906991e_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 287.08/40.84 $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_nat_fun_a_bool(v3, v2) = v1) | ~
% 287.08/40.84 (hAPP_nat_fun_a_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 287.08/40.84 $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_nat_bool(v3, v2) = v1) | ~
% 287.08/40.84 (hAPP_nat_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 287.08/40.84 [v3: $i] : (v1 = v0 | ~ (hAPP_i1587699435l_bool(v3, v2) = v1) | ~
% 287.08/40.84 (hAPP_i1587699435l_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 287.08/40.84 $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_i888906320l_bool(v3, v2) = v1) | ~
% 287.08/40.84 (hAPP_i888906320l_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 287.08/40.85 $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_i7355787e_bool(v3, v2) = v1) | ~
% 287.08/40.85 (hAPP_i7355787e_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 287.08/40.85 $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_int_fun_a_bool(v3, v2) = v1) | ~
% 287.08/40.85 (hAPP_int_fun_a_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 287.08/40.85 $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_int_bool(v3, v2) = v1) | ~
% 287.08/40.85 (hAPP_int_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 287.08/40.85 [v3: $i] : (v1 = v0 | ~ (hAPP_int_a(v3, v2) = v1) | ~ (hAPP_int_a(v3, v2) =
% 287.08/40.85 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 |
% 287.08/40.85 ~ (hAPP_bool_bool(v3, v2) = v1) | ~ (hAPP_bool_bool(v3, v2) = v0)) & !
% 287.08/40.85 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 287.08/40.85 (hAPP_p338031245l_bool(v3, v2) = v1) | ~ (hAPP_p338031245l_bool(v3, v2) =
% 287.08/40.85 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 |
% 287.08/40.85 ~ (hAPP_p61793385e_bool(v3, v2) = v1) | ~ (hAPP_p61793385e_bool(v3, v2) =
% 287.08/40.85 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 |
% 287.08/40.85 ~ (hAPP_p1534023578a_bool(v3, v2) = v1) | ~ (hAPP_p1534023578a_bool(v3, v2)
% 287.08/40.85 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0
% 287.08/40.85 | ~ (hAPP_pname_bool(v3, v2) = v1) | ~ (hAPP_pname_bool(v3, v2) = v0)) &
% 287.08/40.85 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 287.08/40.85 (hAPP_pname_pname(v3, v2) = v1) | ~ (hAPP_pname_pname(v3, v2) = v0)) & !
% 287.08/40.85 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 287.08/40.85 (hAPP_pname_a(v3, v2) = v1) | ~ (hAPP_pname_a(v3, v2) = v0)) & ! [v0: $i]
% 287.08/40.85 : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 287.08/40.85 (hAPP_a85458249l_bool(v3, v2) = v1) | ~ (hAPP_a85458249l_bool(v3, v2) =
% 287.08/40.85 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 |
% 287.08/40.85 ~ (hAPP_a93125764e_bool(v3, v2) = v1) | ~ (hAPP_a93125764e_bool(v3, v2) =
% 287.08/40.85 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 |
% 287.08/40.85 ~ (hAPP_a_fun_a_bool(v3, v2) = v1) | ~ (hAPP_a_fun_a_bool(v3, v2) = v0)) &
% 287.08/40.85 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 287.08/40.85 (hAPP_a_bool(v3, v2) = v1) | ~ (hAPP_a_bool(v3, v2) = v0)) & ! [v0: $i] :
% 287.08/40.85 ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_a_a(v3, v2) = v1)
% 287.08/40.85 | ~ (hAPP_a_a(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 287.08/40.85 [v3: $i] : (v1 = v0 | ~ (image_1921560913_pname(v3, v2) = v1) | ~
% 287.08/40.85 (image_1921560913_pname(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 287.08/40.85 $i] : ! [v3: $i] : (v1 = v0 | ~ (image_fun_nat_bool_a(v3, v2) = v1) | ~
% 287.08/40.85 (image_fun_nat_bool_a(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 287.08/40.85 $i] : ! [v3: $i] : (v1 = v0 | ~ (image_62782965_pname(v3, v2) = v1) | ~
% 287.08/40.85 (image_62782965_pname(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 287.08/40.85 $i] : ! [v3: $i] : (v1 = v0 | ~ (image_fun_int_bool_a(v3, v2) = v1) | ~
% 287.08/40.85 (image_fun_int_bool_a(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 287.08/40.85 $i] : ! [v3: $i] : (v1 = v0 | ~ (image_1283814551_pname(v3, v2) = v1) | ~
% 287.08/40.85 (image_1283814551_pname(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 287.08/40.85 $i] : ! [v3: $i] : (v1 = v0 | ~ (image_876012084bool_a(v3, v2) = v1) | ~
% 287.08/40.85 (image_876012084bool_a(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 287.08/40.85 $i] : ! [v3: $i] : (v1 = v0 | ~ (image_1854862208_pname(v3, v2) = v1) | ~
% 287.08/40.85 (image_1854862208_pname(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 287.08/40.85 $i] : ! [v3: $i] : (v1 = v0 | ~ (image_fun_a_bool_a(v3, v2) = v1) | ~
% 287.08/40.85 (image_fun_a_bool_a(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 287.08/40.85 : ! [v3: $i] : (v1 = v0 | ~ (image_1655916159e_bool(v3, v2) = v1) | ~
% 287.08/40.85 (image_1655916159e_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 287.08/40.85 $i] : ! [v3: $i] : (v1 = v0 | ~ (image_nat_fun_a_bool(v3, v2) = v1) | ~
% 287.08/40.85 (image_nat_fun_a_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 287.08/40.85 $i] : ! [v3: $i] : (v1 = v0 | ~ (image_nat_pname(v3, v2) = v1) | ~
% 287.08/40.85 (image_nat_pname(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 287.08/40.85 ! [v3: $i] : (v1 = v0 | ~ (image_nat_a(v3, v2) = v1) | ~ (image_nat_a(v3,
% 287.08/40.85 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1
% 287.08/40.85 = v0 | ~ (image_637364955e_bool(v3, v2) = v1) | ~
% 287.08/40.85 (image_637364955e_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 287.08/40.85 $i] : ! [v3: $i] : (v1 = v0 | ~ (image_int_fun_a_bool(v3, v2) = v1) | ~
% 287.08/40.85 (image_int_fun_a_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 287.08/40.85 $i] : ! [v3: $i] : (v1 = v0 | ~ (image_int_pname(v3, v2) = v1) | ~
% 287.08/40.85 (image_int_pname(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 287.08/40.85 ! [v3: $i] : (v1 = v0 | ~ (image_int_a(v3, v2) = v1) | ~ (image_int_a(v3,
% 287.08/40.85 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1
% 287.08/40.85 = v0 | ~ (image_47868345e_bool(v3, v2) = v1) | ~ (image_47868345e_bool(v3,
% 287.08/40.85 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1
% 287.08/40.85 = v0 | ~ (image_112932426a_bool(v3, v2) = v1) | ~
% 287.08/40.85 (image_112932426a_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 287.08/40.85 $i] : ! [v3: $i] : (v1 = v0 | ~ (image_pname_pname(v3, v2) = v1) | ~
% 287.08/40.85 (image_pname_pname(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 287.08/40.85 : ! [v3: $i] : (v1 = v0 | ~ (image_pname_a(v3, v2) = v1) | ~
% 287.08/40.85 (image_pname_a(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 287.08/40.85 [v3: $i] : (v1 = v0 | ~ (image_819518260e_bool(v3, v2) = v1) | ~
% 287.08/40.85 (image_819518260e_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 287.08/40.85 $i] : ! [v3: $i] : (v1 = v0 | ~ (image_a_fun_a_bool(v3, v2) = v1) | ~
% 287.08/40.85 (image_a_fun_a_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 287.08/40.85 : ! [v3: $i] : (v1 = v0 | ~ (image_a_pname(v3, v2) = v1) | ~
% 287.08/40.85 (image_a_pname(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 287.08/40.85 [v3: $i] : (v1 = v0 | ~ (image_a_a(v3, v2) = v1) | ~ (image_a_a(v3, v2) =
% 287.08/40.85 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 |
% 287.08/40.85 ~ (fun(v3, v2) = v1) | ~ (fun(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] :
% 287.08/40.85 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (finite795500164em_nat(v3, v2) = v1)
% 287.08/40.85 | ~ (finite795500164em_nat(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 287.08/40.85 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (finite1432773856em_int(v3, v2) = v1) |
% 287.08/40.85 ~ (finite1432773856em_int(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 287.08/40.85 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (finite89670078_pname(v3, v2) = v1) |
% 287.08/40.85 ~ (finite89670078_pname(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 287.08/40.85 $i] : ! [v3: $i] : (v1 = v0 | ~ (finite1819937229idem_a(v3, v2) = v1) | ~
% 287.08/40.85 (finite1819937229idem_a(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 287.08/40.85 $i] : ! [v3: $i] : (v1 = v0 | ~ (finite988810631ne_nat(v3, v2) = v1) | ~
% 287.08/40.85 (finite988810631ne_nat(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 287.08/40.85 $i] : ! [v3: $i] : (v1 = v0 | ~ (finite1626084323ne_int(v3, v2) = v1) | ~
% 287.08/40.85 (finite1626084323ne_int(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 287.08/40.85 $i] : ! [v3: $i] : (v1 = v0 | ~ (finite1282449217_pname(v3, v2) = v1) | ~
% 287.08/40.85 (finite1282449217_pname(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 287.08/40.85 $i] : ! [v3: $i] : (v1 = v0 | ~ (finite_folding_one_a(v3, v2) = v1) | ~
% 287.08/40.85 (finite_folding_one_a(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 287.08/40.85 $i] : ! [v3: $i] : (v1 = v0 | ~ (cOMBS_350070575l_bool(v3, v2) = v1) | ~
% 287.08/40.85 (cOMBS_350070575l_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 287.08/40.85 $i] : ! [v3: $i] : (v1 = v0 | ~ (cOMBS_1035972772l_bool(v3, v2) = v1) | ~
% 287.08/40.85 (cOMBS_1035972772l_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 287.08/40.85 $i] : ! [v3: $i] : (v1 = v0 | ~ (cOMBS_568398431l_bool(v3, v2) = v1) | ~
% 287.08/40.85 (cOMBS_568398431l_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 287.08/40.85 $i] : ! [v3: $i] : (v1 = v0 | ~ (cOMBS_a_bool_bool(v3, v2) = v1) | ~
% 287.08/40.85 (cOMBS_a_bool_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 287.08/40.85 : ! [v3: $i] : (v1 = v0 | ~ (cOMBB_1273333599bool_a(v3, v2) = v1) | ~
% 287.08/40.85 (cOMBB_1273333599bool_a(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 287.08/40.85 $i] : ! [v3: $i] : (v1 = v0 | ~ (cOMBB_647938656_pname(v3, v2) = v1) | ~
% 287.08/40.85 (cOMBB_647938656_pname(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 287.08/40.85 $i] : ! [v3: $i] : (v1 = v0 | ~ (cOMBB_bool_bool_a(v3, v2) = v1) | ~
% 287.08/40.85 (cOMBB_bool_bool_a(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 287.08/40.85 : (v1 = v0 | ~ (bit1(v2) = v1) | ~ (bit1(v2) = v0)) & ! [v0: $i] : ! [v1:
% 287.08/40.85 $i] : ! [v2: $i] : (v1 = v0 | ~ (succ(v2) = v1) | ~ (succ(v2) = v0)) & !
% 287.08/40.85 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (abs_abs_int(v2) = v1) |
% 287.08/40.85 ~ (abs_abs_int(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 =
% 287.08/40.85 v0 | ~ (if_nat(v2) = v1) | ~ (if_nat(v2) = v0)) & ! [v0: $i] : ! [v1:
% 287.08/40.85 $i] : ! [v2: $i] : (v1 = v0 | ~ (number_number_of_int(v2) = v1) | ~
% 287.08/40.85 (number_number_of_int(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 287.08/40.85 (v1 = v0 | ~ (number_number_of_nat(v2) = v1) | ~ (number_number_of_nat(v2) =
% 287.08/40.85 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 287.08/40.85 (cOMBC_1683390479t_bool(v2) = v1) | ~ (cOMBC_1683390479t_bool(v2) = v0)) &
% 287.08/40.85 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 287.08/40.85 (cOMBC_178881787t_bool(v2) = v1) | ~ (cOMBC_178881787t_bool(v2) = v0)) & !
% 287.08/40.85 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 287.08/40.85 (cOMBC_394484100a_bool(v2) = v1) | ~ (cOMBC_394484100a_bool(v2) = v0)) & !
% 287.08/40.85 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (body(v2) = v1) | ~
% 287.08/40.85 (body(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 287.08/40.85 (the_com(v2) = v1) | ~ (the_com(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 287.08/40.85 [v2: $i] : (v1 = v0 | ~ (cOMBK_a_pname(v2) = v1) | ~ (cOMBK_a_pname(v2) =
% 287.08/40.85 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 287.08/40.85 (cOMBK_int_nat(v2) = v1) | ~ (cOMBK_int_nat(v2) = v0)) & ! [v0: $i] : !
% 287.08/40.85 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (cOMBK_bool_nat(v2) = v1) | ~
% 287.08/40.85 (cOMBK_bool_nat(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 =
% 287.08/40.85 v0 | ~ (cOMBK_bool_int(v2) = v1) | ~ (cOMBK_bool_int(v2) = v0)) & ! [v0:
% 287.08/40.85 $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (cOMBC_1149511130e_bool(v2)
% 287.08/40.85 = v1) | ~ (cOMBC_1149511130e_bool(v2) = v0)) & ! [v0: $i] : ! [v1: $i]
% 287.08/40.85 : ! [v2: $i] : (v1 = v0 | ~ (cOMBC_int_int_bool(v2) = v1) | ~
% 287.08/40.85 (cOMBC_int_int_bool(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 287.08/40.85 (v1 = v0 | ~ (cOMBC_a_a_bool(v2) = v1) | ~ (cOMBC_a_a_bool(v2) = v0)) & !
% 287.08/40.85 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 287.08/40.85 (cOMBC_1355376034l_bool(v2) = v1) | ~ (cOMBC_1355376034l_bool(v2) = v0)) &
% 287.08/40.85 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (cOMBC_nat_int_bool(v2)
% 287.08/40.85 = v1) | ~ (cOMBC_nat_int_bool(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 287.08/40.85 [v2: $i] : (v1 = v0 | ~ (cOMBC_1058051404l_bool(v2) = v1) | ~
% 287.08/40.85 (cOMBC_1058051404l_bool(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 287.08/40.85 : (v1 = v0 | ~ (cOMBC_pname_a_bool(v2) = v1) | ~ (cOMBC_pname_a_bool(v2) =
% 287.08/40.85 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 287.08/40.85 (cOMBC_1753430397l_bool(v2) = v1) | ~ (cOMBC_1753430397l_bool(v2) = v0)) &
% 287.08/40.85 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 287.08/40.85 (cOMBC_316919022l_bool(v2) = v1) | ~ (cOMBC_316919022l_bool(v2) = v0)) & !
% 287.08/40.85 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 287.08/40.85 (cOMBC_1848398772l_bool(v2) = v1) | ~ (cOMBC_1848398772l_bool(v2) = v0)) &
% 287.08/40.85 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 287.08/40.85 (cOMBC_94739984l_bool(v2) = v1) | ~ (cOMBC_94739984l_bool(v2) = v0)) & !
% 287.08/40.85 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (cOMBC_int_a_bool(v2) =
% 287.08/40.85 v1) | ~ (cOMBC_int_a_bool(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 287.08/40.85 [v2: $i] : (v1 = v0 | ~ (cOMBC_1928494297l_bool(v2) = v1) | ~
% 287.08/40.85 (cOMBC_1928494297l_bool(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 287.08/40.85 : (v1 = v0 | ~ (cOMBC_386238098l_bool(v2) = v1) | ~
% 287.08/40.85 (cOMBC_386238098l_bool(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 287.08/40.85 : (v1 = v0 | ~ (cOMBC_226598744l_bool(v2) = v1) | ~
% 287.08/40.85 (cOMBC_226598744l_bool(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 287.08/40.85 : (v1 = v0 | ~ (cOMBC_620423604l_bool(v2) = v1) | ~
% 287.08/40.85 (cOMBC_620423604l_bool(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 287.08/40.85 : (v1 = v0 | ~ (cOMBC_nat_nat_bool(v2) = v1) | ~ (cOMBC_nat_nat_bool(v2) =
% 287.08/40.85 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 287.08/40.85 (collect_int(v2) = v1) | ~ (collect_int(v2) = v0)) & ! [v0: $i] : ! [v1:
% 287.08/40.85 $i] : ! [v2: $i] : (v1 = v0 | ~ (collect_nat(v2) = v1) | ~
% 287.08/40.85 (collect_nat(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0
% 287.08/40.85 | ~ (cOMBC_605892544l_bool(v2) = v1) | ~ (cOMBC_605892544l_bool(v2) = v0))
% 287.08/40.85 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 287.08/40.85 (collect_fun_int_bool(v2) = v1) | ~ (collect_fun_int_bool(v2) = v0)) & !
% 287.08/40.85 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 287.08/40.85 (cOMBC_1693257480l_bool(v2) = v1) | ~ (cOMBC_1693257480l_bool(v2) = v0)) &
% 287.08/40.85 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 287.08/40.85 (collect_fun_nat_bool(v2) = v1) | ~ (collect_fun_nat_bool(v2) = v0)) & !
% 287.08/40.85 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 287.08/40.85 (cOMBC_1284144636l_bool(v2) = v1) | ~ (cOMBC_1284144636l_bool(v2) = v0)) &
% 287.08/40.85 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 287.08/40.85 (cOMBC_1732670874l_bool(v2) = v1) | ~ (cOMBC_1732670874l_bool(v2) = v0)) &
% 287.08/40.85 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 287.08/40.85 (cOMBC_331553030l_bool(v2) = v1) | ~ (cOMBC_331553030l_bool(v2) = v0)) & !
% 287.08/40.85 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 287.08/40.85 (collec707592106l_bool(v2) = v1) | ~ (collec707592106l_bool(v2) = v0)) & !
% 287.08/40.85 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (cOMBC_7971162l_bool(v2)
% 287.08/40.85 = v1) | ~ (cOMBC_7971162l_bool(v2) = v0)) & ! [v0: $i] : ! [v1: $i] :
% 287.08/40.85 ! [v2: $i] : (v1 = v0 | ~ (collec1613912337l_bool(v2) = v1) | ~
% 287.08/40.85 (collec1613912337l_bool(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 287.08/40.85 : (v1 = v0 | ~ (cOMBC_595898202l_bool(v2) = v1) | ~
% 287.08/40.85 (cOMBC_595898202l_bool(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 287.08/40.85 : (v1 = v0 | ~ (collec1015864663l_bool(v2) = v1) | ~
% 287.08/40.85 (collec1015864663l_bool(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 287.08/40.85 : (v1 = v0 | ~ (cOMBC_348868698l_bool(v2) = v1) | ~
% 287.08/40.85 (cOMBC_348868698l_bool(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 287.08/40.85 : (v1 = v0 | ~ (collec1409689523l_bool(v2) = v1) | ~
% 287.08/40.85 (collec1409689523l_bool(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 287.08/40.85 : (v1 = v0 | ~ (wt(v2) = v1) | ~ (wt(v2) = v0)) & ! [v0: $i] : ! [v1: $i]
% 287.08/40.85 : ! [v2: $i] : (v1 = v0 | ~ (mgt(v2) = v1) | ~ (mgt(v2) = v0)) & ! [v0:
% 287.08/40.85 $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (p(v2) = v1) | ~ (p(v2) =
% 287.08/40.85 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 287.08/40.85 (collec1974731493e_bool(v2) = v1) | ~ (collec1974731493e_bool(v2) = v0)) &
% 287.08/40.85 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (collect_fun_a_bool(v2)
% 287.08/40.85 = v1) | ~ (collect_fun_a_bool(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 287.08/40.85 [v2: $i] : (v1 = v0 | ~ (collect_pname(v2) = v1) | ~ (collect_pname(v2) =
% 287.08/40.85 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 287.08/40.85 (collect_a(v2) = v1) | ~ (collect_a(v2) = v0)) & ! [v0: $i] : ! [v1: $i]
% 287.08/40.85 : ! [v2: $i] : (v1 = v0 | ~ (undefi64961550l_bool(v2) = v1) | ~
% 287.08/40.85 (undefi64961550l_bool(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 287.08/40.85 (v1 = v0 | ~ (undefi1699038445l_bool(v2) = v1) | ~
% 287.08/40.85 (undefi1699038445l_bool(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 287.08/40.85 : (v1 = v0 | ~ (undefi17486888e_bool(v2) = v1) | ~ (undefi17486888e_bool(v2)
% 287.08/40.85 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 287.08/40.85 (undefined_fun_a_bool(v2) = v1) | ~ (undefined_fun_a_bool(v2) = v0)) & !
% 287.08/40.85 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (undefined_pname(v2) =
% 287.08/40.85 v1) | ~ (undefined_pname(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 287.08/40.85 $i] : (v1 = v0 | ~ (undefined_a(v2) = v1) | ~ (undefined_a(v2) = v0)) & !
% 287.08/40.85 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (cOMBK_bool_a(v2) = v1) |
% 287.08/40.85 ~ (cOMBK_bool_a(v2) = v0))
% 287.08/40.85
% 287.08/40.85 Further assumptions not needed in the proof:
% 287.08/40.85 --------------------------------------------
% 287.08/40.85 conj_0, fact_0_assms_I1_J, fact_1000_mult__less__cancel2,
% 287.08/40.85 fact_1001_mult__less__cancel1, fact_1002_nat__0__less__mult__iff,
% 287.08/40.85 fact_1003_Suc__mult__less__cancel1, fact_1004_mult__Suc__right,
% 287.08/40.85 fact_1005_mult__Suc, fact_1006_Suc__mult__le__cancel1,
% 287.08/40.85 fact_1007_mult__eq__self__implies__10, fact_100_card__insert__if,
% 287.08/40.85 fact_1012_mult__le__cancel1, fact_1013_mult__le__cancel2,
% 287.08/40.85 fact_1014_mult__eq__if, fact_1015_nat__less__add__iff2,
% 287.08/40.85 fact_1016_nat__mult__commute, fact_1017_nat__mult__assoc,
% 287.08/40.85 fact_1018_less__number__of__int__code, fact_1019_zmult__1,
% 287.08/40.85 fact_101_card__insert__if, fact_1020_zmult__1__right, fact_1021_zmult__commute,
% 287.08/40.85 fact_1022_times__numeral__code_I5_J, fact_1023_zmult__assoc,
% 287.08/40.85 fact_1024_less__eq__number__of__int__code, fact_1025_zdiff__zmult__distrib,
% 287.08/40.85 fact_1026_zdiff__zmult__distrib2, fact_1027_zadd__zmult__distrib2,
% 287.08/40.85 fact_1028_plus__numeral__code_I9_J, fact_1029_zadd__zmult__distrib,
% 287.08/40.85 fact_102_card__insert__if, fact_1032_odd__nonzero, fact_1033_zadd__0__right,
% 287.08/40.85 fact_1034_zadd__0, fact_1037_less__bin__lemma, fact_1039_odd__less__0,
% 287.08/40.85 fact_103_card__insert__disjoint, fact_1040_zadd__left__mono,
% 287.08/40.85 fact_1041_zadd__assoc, fact_1042_zadd__left__commute, fact_1043_zadd__commute,
% 287.08/40.85 fact_1044_zle__refl, fact_1045_zle__linear, fact_1046_zle__trans,
% 287.08/40.85 fact_1048_zle__diff1__eq, fact_1049_zless__linear,
% 287.08/40.85 fact_104_card__insert__disjoint, fact_1050_zless__le,
% 287.08/40.85 fact_1051_zadd__strict__right__mono, fact_1052_zadd__zless__mono,
% 287.08/40.85 fact_1053_zle__add1__eq__le, fact_1054_add1__zle__eq,
% 287.08/40.85 fact_1055_zless__imp__add1__zle, fact_1056_zless__add1__eq,
% 287.08/40.85 fact_1057_nat__mult__eq__cancel__disj, fact_1058_left__add__mult__distrib,
% 287.08/40.85 fact_1059_nat__mult__eq__cancel1, fact_105_card__insert__disjoint,
% 287.08/40.85 fact_1060_nat__mult__less__cancel1, fact_1061_nat__mult__le__cancel1,
% 287.08/40.85 fact_1062_nat__le__add__iff1, fact_1063_nat__diff__add__eq1,
% 287.08/40.85 fact_1064_nat__eq__add__iff1, fact_1065_nat__le__add__iff2,
% 287.08/40.85 fact_1066_nat__diff__add__eq2, fact_1067_nat__eq__add__iff2,
% 287.08/40.85 fact_1068_nat__less__add__iff1, fact_106_card__insert__disjoint,
% 287.08/40.85 fact_1070_unique__quotient__lemma__neg, fact_1079_int__less__induct,
% 287.08/40.85 fact_107_card__insert__disjoint, fact_1080_int__le__induct,
% 287.08/40.85 fact_1081_int__gr__induct, fact_1082_int__ge__induct,
% 287.08/40.85 fact_108_card__insert__disjoint, fact_1092_int__induct, fact_1095_tsub__def,
% 287.08/40.85 fact_1097_int__less__0__conv, fact_1098_int__1, fact_109_card__insert__disjoint,
% 287.08/40.85 fact_10_finite__imageI, fact_1100_int__eq__0__conv, fact_1101_zless__int,
% 287.08/40.85 fact_1102_zle__int, fact_1103_zadd__int, fact_1104_zadd__int__left,
% 287.08/40.85 fact_1105_zle__iff__zadd, fact_1106_zmult__int, fact_1107_int__mult,
% 287.08/40.85 fact_1108_Nat__Transfer_Otransfer__int__nat__functions_I2_J,
% 287.08/40.85 fact_1109_transfer__int__nat__relations_I2_J, fact_110_card__insert__disjoint,
% 287.08/40.85 fact_1110_transfer__int__nat__relations_I3_J,
% 287.08/40.85 fact_1111_Nat__Transfer_Otransfer__int__nat__functions_I3_J,
% 287.08/40.85 fact_1112_Nat__Transfer_Otransfer__int__nat__functions_I1_J,
% 287.08/40.85 fact_1113_Nat__Transfer_Otransfer__nat__int__set__functions_I1_J,
% 287.08/40.85 fact_1114_transfer__nat__int__set__relations_I1_J,
% 287.08/40.85 fact_1115_transfer__int__nat__numerals_I2_J, fact_111_finite__Collect__conjI,
% 287.08/40.85 fact_1121_int__le__0__conv, fact_1123_zless__iff__Suc__zadd, fact_1124_int__Suc,
% 287.08/40.85 fact_1125_zdiff__int, fact_1127_zmult__zless__mono2__lemma,
% 287.08/40.85 fact_1129_zdiff__int__split, fact_112_finite__Collect__conjI,
% 287.08/40.85 fact_1130_tsub__eq, fact_1132_int__int__eq,
% 287.08/40.85 fact_1133_transfer__nat__int__set__relations_I4_J,
% 287.08/40.85 fact_1134_transfer__nat__int__set__relations_I5_J,
% 287.08/40.85 fact_1135_Nat__Transfer_Otransfer__int__nat__set__functions_I2_J,
% 287.08/40.85 fact_1136_transfer__nat__int__set__relations_I3_J,
% 287.08/40.85 fact_1137_transfer__nat__int__set__relations_I2_J, fact_1138_int__if__cong,
% 287.08/40.85 fact_1139_transfer__int__nat__relations_I1_J, fact_113_finite__Collect__conjI,
% 287.08/40.85 fact_1143_int__diff__cases, fact_1145_zabs__less__one__iff, fact_1146_neg__def,
% 287.08/40.85 fact_1149_not__neg__0, fact_114_finite__Collect__conjI,
% 287.08/40.85 fact_1150_abs__zmult__eq__1, fact_1151_not__neg__int,
% 287.08/40.85 fact_1153_neg__imp__number__of__eq__0, fact_1155_nat__number__of__add__left,
% 287.08/40.85 fact_1156_int__nat__number__of, fact_1158_int__val__lemma,
% 287.08/40.85 fact_1159_nat0__intermed__int__val, fact_115_finite__Collect__conjI,
% 287.08/40.85 fact_1160_nat__intermed__int__val, fact_1161_Suc__nat__number__of__add,
% 287.08/40.85 fact_1162_succ__def, fact_1163_Suc__nat__number__of,
% 287.08/40.85 fact_1164_nat__number__of__Bit1, fact_1165_nat__1__add__number__of,
% 287.08/40.85 fact_1168_not__neg__number__of__Pls, fact_116_finite__Collect__conjI,
% 287.08/40.85 fact_1176_zero__is__num__zero, fact_1177_Bit1__def,
% 287.08/40.85 fact_117_finite__Collect__conjI, fact_1181_rel__simps_I51_J,
% 287.08/40.85 fact_1182_rel__simps_I46_J, fact_1183_rel__simps_I39_J,
% 287.08/40.85 fact_1184_diff__bin__simps_I1_J, fact_1185_add__Pls, fact_1186_add__Pls__right,
% 287.08/40.85 fact_1187_mult__Pls, fact_118_finite__Collect__conjI,
% 287.08/40.85 fact_1191_rel__simps_I34_J, fact_1192_less__eq__int__code_I16_J,
% 287.08/40.85 fact_1195_rel__simps_I17_J, fact_1196_less__int__code_I16_J,
% 287.08/40.85 fact_119_Suc__diff__le, fact_11_finite__imageI,
% 287.08/40.85 fact_120_finite__Collect__le__nat, fact_121_card__Collect__le__nat,
% 287.08/40.85 fact_122_Suc__inject, fact_123_nat_Oinject, fact_124_Suc__n__not__n,
% 287.08/40.85 fact_125_n__not__Suc__n, fact_126_le__antisym, fact_127_le__trans,
% 287.08/40.85 fact_128_eq__imp__le, fact_129_nat__le__linear, fact_12_finite__imageI,
% 287.08/40.85 fact_130_le__refl, fact_131_diff__commute, fact_132_finite__Collect__disjI,
% 287.08/40.85 fact_133_finite__Collect__disjI, fact_134_finite__Collect__disjI,
% 287.08/40.85 fact_135_finite__Collect__disjI, fact_136_finite__Collect__disjI,
% 287.08/40.85 fact_137_finite__Collect__disjI, fact_138_finite__Collect__disjI,
% 287.08/40.85 fact_139_finite__Collect__disjI, fact_13_finite__imageI,
% 287.08/40.85 fact_140_finite__insert, fact_141_finite__insert, fact_142_finite__insert,
% 287.08/40.85 fact_143_finite__insert, fact_144_finite__insert, fact_145_finite__insert,
% 287.08/40.85 fact_146_finite__insert, fact_147_finite__insert, fact_148_finite__subset,
% 287.08/40.85 fact_149_finite__subset, fact_14_finite__imageI, fact_150_finite__subset,
% 287.08/40.85 fact_151_finite__subset, fact_152_finite__subset, fact_153_finite__subset,
% 287.08/40.85 fact_154_finite__subset, fact_155_finite__subset, fact_156_rev__finite__subset,
% 287.08/40.85 fact_157_rev__finite__subset, fact_158_rev__finite__subset,
% 287.08/40.85 fact_159_rev__finite__subset, fact_15_finite__imageI,
% 287.08/40.85 fact_160_rev__finite__subset, fact_161_rev__finite__subset,
% 287.08/40.85 fact_162_rev__finite__subset, fact_163_rev__finite__subset, fact_164_Suc__leD,
% 287.08/40.85 fact_165_le__SucE, fact_166_le__SucI, fact_167_Suc__le__mono,
% 287.08/40.85 fact_168_le__Suc__eq, fact_169_not__less__eq__eq, fact_16_finite__imageI,
% 287.08/40.85 fact_170_Suc__n__not__le__n, fact_171_Suc__diff__diff, fact_172_diff__Suc__Suc,
% 287.08/40.85 fact_173_le__diff__iff, fact_174_Nat_Odiff__diff__eq, fact_175_eq__diff__iff,
% 287.08/40.85 fact_176_diff__diff__cancel, fact_177_diff__le__mono, fact_178_diff__le__mono2,
% 287.08/40.85 fact_179_diff__le__self, fact_17_finite__imageI, fact_180_finite__surj,
% 287.08/40.85 fact_181_finite__surj, fact_182_finite__surj, fact_183_finite__surj,
% 287.08/40.85 fact_184_finite__surj, fact_185_finite__surj, fact_186_finite__surj,
% 287.08/40.85 fact_187_finite__surj, fact_188_finite__surj, fact_189_finite__surj,
% 287.08/40.85 fact_18_finite__imageI, fact_190_finite__surj, fact_191_finite__surj,
% 287.08/40.85 fact_192_finite__surj, fact_193_finite__surj, fact_194_finite__surj,
% 287.08/40.85 fact_195_finite__surj, fact_196_finite__surj, fact_197_finite__surj,
% 287.08/40.85 fact_198_finite__surj, fact_199_finite__surj, fact_19_finite__imageI,
% 287.08/40.85 fact_1_finite__Collect__subsets, fact_200_finite__surj, fact_201_finite__surj,
% 287.08/40.85 fact_202_finite__surj, fact_203_finite__surj, fact_204_finite__surj,
% 287.08/40.85 fact_205_finite__surj, fact_206_finite__surj, fact_207_finite__surj,
% 287.08/40.85 fact_208_finite__surj, fact_209_finite__surj, fact_20_finite__imageI,
% 287.08/40.85 fact_210_finite__surj, fact_211_finite__surj, fact_212_finite__surj,
% 287.08/40.85 fact_213_finite__surj, fact_214_finite__surj, fact_215_finite__surj,
% 287.08/40.85 fact_216_finite__surj, fact_217_finite__surj, fact_218_finite__surj,
% 287.08/40.85 fact_219_finite__subset__image, fact_21_finite__imageI,
% 287.08/40.85 fact_220_finite__subset__image, fact_221_finite__subset__image,
% 287.08/40.85 fact_222_finite__subset__image, fact_223_finite__subset__image,
% 287.08/40.85 fact_224_finite__subset__image, fact_225_finite__subset__image,
% 287.08/40.85 fact_226_finite__subset__image, fact_227_finite__subset__image,
% 287.08/40.85 fact_228_finite__subset__image, fact_229_finite__subset__image,
% 287.08/40.85 fact_22_finite__imageI, fact_230_finite__subset__image,
% 287.08/40.85 fact_231_finite__subset__image, fact_232_finite__subset__image,
% 287.08/40.85 fact_233_finite__subset__image, fact_234_finite__subset__image,
% 287.08/40.85 fact_235_finite__subset__image, fact_236_finite__subset__image,
% 287.08/40.85 fact_237_finite__subset__image, fact_238_finite__subset__image,
% 287.08/40.85 fact_239_finite__subset__image, fact_23_finite__imageI,
% 287.08/40.85 fact_240_finite__subset__image, fact_241_finite__subset__image,
% 287.08/40.85 fact_242_finite__subset__image, fact_243_finite__subset__image,
% 287.08/40.85 fact_244_finite__subset__image, fact_245_finite__subset__image,
% 287.08/40.85 fact_246_finite__subset__image, fact_247_finite__subset__image,
% 287.08/40.85 fact_248_finite__subset__image, fact_249_finite__subset__image,
% 287.08/40.85 fact_24_finite__imageI, fact_250_finite__subset__image,
% 287.08/40.85 fact_251_finite__subset__image, fact_252_finite__subset__image,
% 287.08/40.85 fact_253_finite__subset__image, fact_254_finite__subset__image,
% 287.08/40.85 fact_255_finite__subset__image, fact_256_finite__subset__image,
% 287.08/40.85 fact_257_finite__subset__image, fact_258_finite__subset__image,
% 287.08/40.85 fact_259_finite__subset__image, fact_25_finite__imageI,
% 287.08/40.85 fact_260_finite__subset__image, fact_261_finite__subset__image,
% 287.08/40.85 fact_262_finite__subset__image, fact_263_finite__subset__image,
% 287.08/40.85 fact_264_lift__Suc__mono__le, fact_265_lift__Suc__mono__le,
% 287.08/40.85 fact_266_lift__Suc__mono__le, fact_267_lift__Suc__mono__le,
% 287.08/40.85 fact_268_lift__Suc__mono__le, fact_269_lift__Suc__mono__le,
% 287.08/40.85 fact_26_finite__imageI, fact_270_lift__Suc__mono__le,
% 287.08/40.85 fact_271_pigeonhole__infinite, fact_272_pigeonhole__infinite,
% 287.08/40.85 fact_273_pigeonhole__infinite, fact_274_pigeonhole__infinite,
% 287.08/40.85 fact_275_pigeonhole__infinite, fact_276_pigeonhole__infinite,
% 287.08/40.85 fact_277_pigeonhole__infinite, fact_278_pigeonhole__infinite,
% 287.08/40.85 fact_279_pigeonhole__infinite, fact_27_finite__imageI,
% 287.08/40.85 fact_280_pigeonhole__infinite, fact_281_pigeonhole__infinite,
% 287.08/40.85 fact_282_image__eqI, fact_283_image__eqI, fact_284_equalityI,
% 287.08/40.85 fact_285_equalityI, fact_286_equalityI, fact_287_subsetD, fact_288_subsetD,
% 287.08/40.85 fact_289_subsetD, fact_28_finite__imageI, fact_290_subsetD, fact_291_insertCI,
% 287.08/40.85 fact_292_insertCI, fact_293_insertCI, fact_294_insertCI, fact_295_insertE,
% 287.08/40.85 fact_296_insertE, fact_297_insertE, fact_298_insertE,
% 287.08/40.85 fact_299_zero__induct__lemma, fact_29_finite__imageI,
% 287.08/40.85 fact_2_finite__Collect__subsets, fact_300_Suc__le__D, fact_301_order__refl,
% 287.08/40.85 fact_302_order__refl, fact_303_order__refl, fact_304_order__refl,
% 287.08/40.85 fact_305_order__refl, fact_306_linorder__linear, fact_307_linorder__linear,
% 287.08/40.85 fact_308_order__eq__iff, fact_309_order__eq__iff, fact_30_finite__imageI,
% 287.08/40.85 fact_310_order__eq__iff, fact_311_order__eq__iff, fact_312_order__eq__iff,
% 287.08/40.85 fact_313_order__eq__refl, fact_314_order__eq__refl, fact_315_order__eq__refl,
% 287.08/40.85 fact_316_order__eq__refl, fact_317_order__eq__refl,
% 287.08/40.85 fact_318_order__antisym__conv, fact_319_order__antisym__conv,
% 287.08/40.85 fact_31_finite__imageI, fact_321_order__antisym__conv,
% 287.08/40.85 fact_322_order__antisym__conv, fact_323_ord__eq__le__trans,
% 287.08/40.85 fact_324_ord__eq__le__trans, fact_325_ord__eq__le__trans,
% 287.08/40.85 fact_326_ord__eq__le__trans, fact_327_ord__eq__le__trans, fact_328_xt1_I3_J,
% 287.08/40.85 fact_329_xt1_I3_J, fact_32_finite__imageI, fact_330_xt1_I3_J, fact_331_xt1_I3_J,
% 287.08/40.85 fact_332_xt1_I3_J, fact_333_ord__le__eq__trans, fact_334_ord__le__eq__trans,
% 287.08/40.85 fact_335_ord__le__eq__trans, fact_336_ord__le__eq__trans,
% 287.08/40.85 fact_337_ord__le__eq__trans, fact_338_xt1_I4_J, fact_339_xt1_I4_J,
% 287.08/40.85 fact_33_finite__imageI, fact_340_xt1_I4_J, fact_341_xt1_I4_J, fact_342_xt1_I4_J,
% 287.08/40.85 fact_343_order__antisym, fact_344_order__antisym, fact_346_order__antisym,
% 287.08/40.85 fact_347_order__antisym, fact_348_order__trans, fact_349_order__trans,
% 287.08/40.85 fact_34_finite__imageI, fact_350_order__trans, fact_351_order__trans,
% 287.08/40.85 fact_352_order__trans, fact_353_xt1_I5_J, fact_354_xt1_I5_J, fact_356_xt1_I5_J,
% 287.08/40.85 fact_357_xt1_I5_J, fact_358_xt1_I6_J, fact_359_xt1_I6_J, fact_35_finite__imageI,
% 287.08/40.85 fact_360_xt1_I6_J, fact_361_xt1_I6_J, fact_362_xt1_I6_J,
% 287.08/40.85 fact_363_linorder__le__cases, fact_364_linorder__le__cases, fact_365_insertI1,
% 287.08/40.85 fact_366_insertI1, fact_367_insertI1, fact_368_insertI1, fact_369_insert__compr,
% 287.08/40.85 fact_36_finite__imageI, fact_370_insert__compr, fact_371_insert__compr,
% 287.08/40.85 fact_372_insert__compr, fact_373_insert__Collect, fact_374_insert__Collect,
% 287.08/40.85 fact_375_insert__Collect, fact_376_mem__def, fact_377_mem__def,
% 287.08/40.85 fact_378_mem__def, fact_379_mem__def, fact_37_finite__imageI,
% 287.08/40.85 fact_380_Collect__def, fact_381_Collect__def, fact_382_insert__absorb2,
% 287.08/40.85 fact_383_insert__commute, fact_384_insert__iff, fact_385_insert__iff,
% 287.08/40.85 fact_386_insert__iff, fact_387_insert__iff, fact_388_insert__code,
% 287.08/40.85 fact_389_insert__ident, fact_38_finite__imageI, fact_390_insert__ident,
% 287.08/40.85 fact_391_insert__ident, fact_392_insert__ident, fact_393_insertI2,
% 287.08/40.85 fact_394_insertI2, fact_395_insertI2, fact_396_insertI2,
% 287.08/40.85 fact_397_insert__absorb, fact_398_insert__absorb, fact_399_insert__absorb,
% 287.08/40.85 fact_39_finite__imageI, fact_3_finite__Collect__subsets,
% 287.08/40.85 fact_400_insert__absorb, fact_401_subset__refl, fact_402_subset__refl,
% 287.08/40.85 fact_403_subset__refl, fact_404_set__eq__subset, fact_405_set__eq__subset,
% 287.08/40.85 fact_406_set__eq__subset, fact_407_equalityD1, fact_408_equalityD1,
% 287.08/40.85 fact_409_equalityD1, fact_40_finite_OinsertI, fact_410_equalityD2,
% 287.08/40.85 fact_411_equalityD2, fact_412_equalityD2, fact_413_in__mono, fact_414_in__mono,
% 287.08/40.85 fact_415_in__mono, fact_416_in__mono, fact_417_set__rev__mp,
% 287.08/40.85 fact_418_set__rev__mp, fact_419_set__rev__mp, fact_41_finite_OinsertI,
% 287.08/40.85 fact_420_set__rev__mp, fact_421_set__mp, fact_422_set__mp, fact_423_set__mp,
% 287.08/40.85 fact_424_set__mp, fact_425_subset__trans, fact_426_subset__trans,
% 287.08/40.85 fact_427_subset__trans, fact_428_equalityE, fact_429_equalityE,
% 287.08/40.85 fact_42_finite_OinsertI, fact_430_equalityE, fact_431_image__iff,
% 287.08/40.85 fact_432_image__iff, fact_433_imageI, fact_434_imageI, fact_435_rev__image__eqI,
% 287.08/40.85 fact_437_insert__compr__raw, fact_438_insert__compr__raw,
% 287.08/40.85 fact_439_insert__compr__raw, fact_43_finite_OinsertI,
% 287.08/40.85 fact_440_insert__compr__raw, fact_441_le__fun__def, fact_442_le__fun__def,
% 287.08/40.85 fact_443_le__fun__def, fact_444_le__funD, fact_445_le__funD, fact_446_le__funD,
% 287.08/40.85 fact_447_le__funE, fact_448_le__funE, fact_449_le__funE,
% 287.08/40.85 fact_44_finite_OinsertI, fact_450_subset__insertI, fact_451_subset__insertI,
% 287.08/40.85 fact_452_subset__insertI, fact_454_insert__subset, fact_455_insert__subset,
% 287.08/40.85 fact_456_insert__subset, fact_457_subset__insert, fact_458_subset__insert,
% 287.08/40.85 fact_459_subset__insert, fact_45_finite_OinsertI, fact_460_subset__insert,
% 287.08/40.85 fact_461_subset__insertI2, fact_462_subset__insertI2, fact_463_subset__insertI2,
% 287.08/40.85 fact_464_insert__mono, fact_465_insert__mono, fact_466_insert__mono,
% 287.08/40.85 fact_467_image__insert, fact_468_image__insert, fact_469_insert__image,
% 287.08/40.85 fact_46_finite_OinsertI, fact_470_insert__image, fact_471_subset__image__iff,
% 287.08/40.85 fact_472_subset__image__iff, fact_473_image__mono, fact_474_image__mono,
% 287.08/40.85 fact_475_imageE, fact_476_imageE, fact_477_subsetI, fact_478_subsetI,
% 287.08/40.85 fact_47_finite_OinsertI, fact_480_subsetI, fact_481_image__subsetI,
% 287.08/40.85 fact_482_image__subsetI, fact_483_le__funI, fact_484_le__funI,
% 287.08/40.85 fact_485_le__funI, fact_486_finite__nat__set__iff__bounded__le,
% 287.08/40.85 fact_487_assms_I3_J, fact_488_diff__eq__diff__less__eq,
% 287.08/40.85 fact_489_less__eq__nat_Osimps_I2_J, fact_48_card__image__le, fact_490_emptyE,
% 287.08/40.85 fact_491_emptyE, fact_492_emptyE, fact_493_emptyE, fact_494_finite__Diff,
% 287.08/40.85 fact_495_finite__Diff, fact_496_finite__Diff, fact_497_finite_OemptyI,
% 287.08/40.85 fact_498_finite_OemptyI, fact_499_finite_OemptyI, fact_49_card__image__le,
% 287.08/40.85 fact_4_finite__Collect__subsets, fact_500_finite_OemptyI,
% 287.08/40.85 fact_501_empty__subsetI, fact_502_empty__subsetI, fact_503_empty__subsetI,
% 287.08/40.85 fact_504_equals0D, fact_505_equals0D, fact_506_equals0D, fact_507_equals0D,
% 287.08/40.85 fact_508_Collect__empty__eq, fact_509_Collect__empty__eq,
% 287.08/40.85 fact_50_card__image__le, fact_510_Collect__empty__eq, fact_511_Diff__cancel,
% 287.08/40.85 fact_512_Diff__cancel, fact_513_Diff__cancel, fact_514_Diff__empty,
% 287.08/40.85 fact_515_Diff__empty, fact_516_Diff__empty, fact_517_empty__iff,
% 287.08/40.85 fact_518_empty__iff, fact_519_empty__iff, fact_51_card__image__le,
% 287.08/40.85 fact_520_empty__iff, fact_521_empty__Collect__eq, fact_522_empty__Collect__eq,
% 287.08/40.85 fact_523_empty__Collect__eq, fact_524_empty__Diff, fact_525_empty__Diff,
% 287.08/40.85 fact_526_empty__Diff, fact_527_ex__in__conv, fact_528_ex__in__conv,
% 287.08/40.85 fact_529_ex__in__conv, fact_52_card__image__le, fact_530_ex__in__conv,
% 287.08/40.85 fact_531_all__not__in__conv, fact_532_all__not__in__conv,
% 287.08/40.85 fact_533_all__not__in__conv, fact_534_all__not__in__conv, fact_535_bot__apply,
% 287.08/40.85 fact_536_bot__apply, fact_537_bot__apply, fact_538_empty__def,
% 287.08/40.85 fact_539_empty__def, fact_53_card__image__le, fact_540_empty__def,
% 287.08/40.85 fact_541_bot__fun__def, fact_542_bot__fun__def, fact_543_bot__fun__def,
% 287.08/40.85 fact_544_insert__Diff, fact_545_insert__Diff, fact_546_insert__Diff,
% 287.08/40.85 fact_547_insert__Diff, fact_548_Diff__insert__absorb,
% 287.08/40.85 fact_549_Diff__insert__absorb, fact_54_card__image__le,
% 287.08/40.85 fact_550_Diff__insert__absorb, fact_551_Diff__insert__absorb,
% 287.08/40.85 fact_552_insert__Diff__single, fact_553_insert__Diff__single,
% 287.08/40.85 fact_554_insert__Diff__single, fact_555_Diff__insert2, fact_556_Diff__insert2,
% 287.08/40.85 fact_557_Diff__insert2, fact_558_Diff__insert, fact_559_Diff__insert,
% 287.08/40.85 fact_55_card__image__le, fact_560_Diff__insert, fact_561_diff__single__insert,
% 287.08/40.85 fact_562_diff__single__insert, fact_563_diff__single__insert,
% 287.08/40.85 fact_564_diff__single__insert, fact_565_subset__insert__iff,
% 287.08/40.85 fact_566_subset__insert__iff, fact_567_subset__insert__iff,
% 287.08/40.85 fact_568_subset__insert__iff, fact_569_finite__Diff2, fact_56_card__image__le,
% 287.08/40.85 fact_570_finite__Diff2, fact_571_finite__Diff2, fact_572_insert__Diff1,
% 287.08/40.85 fact_573_insert__Diff1, fact_574_insert__Diff1, fact_575_insert__Diff1,
% 287.08/40.85 fact_576_insert__Diff__if, fact_577_insert__Diff__if, fact_578_insert__Diff__if,
% 287.08/40.85 fact_579_insert__Diff__if, fact_57_card__image__le, fact_580_double__diff,
% 287.08/40.85 fact_581_double__diff, fact_582_double__diff, fact_583_Diff__mono,
% 287.08/40.85 fact_584_Diff__mono, fact_585_Diff__mono, fact_586_Diff__subset,
% 287.08/40.85 fact_587_Diff__subset, fact_588_Diff__subset, fact_589_singleton__inject,
% 287.08/40.85 fact_58_card__image__le, fact_590_singleton__inject, fact_591_singleton__inject,
% 287.08/40.85 fact_592_singletonE, fact_593_singletonE, fact_594_singletonE,
% 287.08/40.85 fact_595_singletonE, fact_596_doubleton__eq__iff, fact_597_doubleton__eq__iff,
% 287.08/40.85 fact_598_doubleton__eq__iff, fact_599_singleton__iff, fact_59_card__image__le,
% 287.08/40.85 fact_5_finite__Collect__subsets, fact_600_singleton__iff,
% 287.08/40.85 fact_601_singleton__iff, fact_602_singleton__iff, fact_603_insert__not__empty,
% 287.08/40.85 fact_604_insert__not__empty, fact_605_insert__not__empty,
% 287.08/40.85 fact_606_empty__not__insert, fact_607_empty__not__insert,
% 287.08/40.85 fact_608_empty__not__insert, fact_609_subset__empty, fact_60_card__image__le,
% 287.08/40.85 fact_610_subset__empty, fact_611_subset__empty, fact_612_image__is__empty,
% 287.08/40.85 fact_613_image__is__empty, fact_614_image__empty, fact_615_image__empty,
% 287.08/40.85 fact_616_empty__is__image, fact_617_empty__is__image, fact_618_le__bot,
% 287.08/40.85 fact_619_le__bot, fact_61_card__image__le, fact_620_le__bot, fact_621_le__bot,
% 287.08/40.85 fact_622_bot__unique, fact_623_bot__unique, fact_624_bot__unique,
% 287.08/40.85 fact_625_bot__unique, fact_626_bot__least, fact_627_bot__least,
% 287.08/40.85 fact_628_bot__least, fact_629_bot__least, fact_62_card__image__le,
% 287.08/40.85 fact_630_Collect__conv__if, fact_631_Collect__conv__if,
% 287.08/40.85 fact_632_Collect__conv__if, fact_633_Collect__conv__if2,
% 287.08/40.85 fact_634_Collect__conv__if2, fact_635_Collect__conv__if2,
% 287.08/40.85 fact_636_singleton__conv, fact_637_singleton__conv, fact_638_singleton__conv,
% 287.08/40.85 fact_639_singleton__conv2, fact_63_card__image__le, fact_640_singleton__conv2,
% 287.08/40.85 fact_641_singleton__conv2, fact_642_card__Suc__Diff1, fact_643_card__Suc__Diff1,
% 287.08/40.85 fact_644_card__Suc__Diff1, fact_645_card__Suc__Diff1, fact_646_card__insert,
% 287.08/40.85 fact_647_card__insert, fact_648_card__insert, fact_649_card__insert,
% 287.08/40.85 fact_64_card__image__le, fact_650_card__Diff1__le, fact_651_card__Diff1__le,
% 287.08/40.85 fact_652_card__Diff1__le, fact_653_card__Diff1__le,
% 287.08/40.85 fact_654_finite__Diff__insert, fact_655_finite__Diff__insert,
% 287.08/40.85 fact_656_finite__Diff__insert, fact_657_finite__Diff__insert,
% 287.08/40.85 fact_658_image__diff__subset, fact_659_image__diff__subset,
% 287.08/40.85 fact_65_card__image__le, fact_660_subset__singletonD,
% 287.08/40.85 fact_661_subset__singletonD, fact_662_subset__singletonD,
% 287.08/40.85 fact_663_nat__case__Suc, fact_664_nat__case__Suc, fact_665_image__constant,
% 287.08/40.85 fact_666_image__constant, fact_667_image__constant__conv,
% 287.08/40.85 fact_668_image__constant__conv, fact_669_diff__eq__diff__eq,
% 287.08/40.85 fact_66_card__image__le, fact_670_card__Diff__subset,
% 287.08/40.85 fact_671_card__Diff__subset, fact_672_card__Diff__subset,
% 287.08/40.85 fact_673_card__Diff__subset, fact_674_diff__card__le__card__Diff,
% 287.08/40.85 fact_675_diff__card__le__card__Diff, fact_676_diff__card__le__card__Diff,
% 287.08/40.85 fact_677_diff__card__le__card__Diff, fact_678_finite__subset__induct,
% 287.08/40.85 fact_679_finite__subset__induct, fact_67_card__image__le,
% 287.08/40.85 fact_680_finite__subset__induct, fact_681_finite__subset__induct,
% 287.08/40.85 fact_682_assms_I2_J, fact_683_finite__empty__induct,
% 287.08/40.85 fact_684_finite__empty__induct, fact_685_finite__empty__induct,
% 287.08/40.85 fact_686_finite__empty__induct, fact_687_finite__induct,
% 287.08/40.85 fact_688_finite__induct, fact_689_finite__induct, fact_68_card__image__le,
% 287.08/40.85 fact_690_finite__induct, fact_691_finite_Osimps, fact_692_finite_Osimps,
% 287.08/40.85 fact_693_finite_Osimps, fact_694_finite_Osimps, fact_695_finite__less__ub,
% 287.08/40.85 fact_696_the__elem__eq, fact_697_the__elem__eq, fact_698_the__elem__eq,
% 287.08/40.85 fact_699_nonempty__iff, fact_69_card__image__le,
% 287.08/40.85 fact_6_finite__Collect__subsets, fact_700_nonempty__iff, fact_701_nonempty__iff,
% 287.08/40.85 fact_702_nonempty__iff, fact_703_assms_I4_J, fact_704_DiffE, fact_705_DiffE,
% 287.08/40.85 fact_706_DiffE, fact_707_DiffE, fact_708_DiffI, fact_709_DiffI,
% 287.08/40.85 fact_70_card__image__le, fact_710_DiffI, fact_711_DiffI, fact_712_DiffD2,
% 287.08/40.85 fact_713_DiffD2, fact_714_DiffD2, fact_715_DiffD2, fact_716_DiffD1,
% 287.08/40.85 fact_717_DiffD1, fact_718_DiffD1, fact_719_DiffD1, fact_71_card__mono,
% 287.08/40.85 fact_720_Diff__iff, fact_721_Diff__iff, fact_722_Diff__iff, fact_723_Diff__iff,
% 287.08/40.85 fact_724_set__diff__eq, fact_725_set__diff__eq, fact_726_set__diff__eq,
% 287.08/40.85 fact_727_set__diff__eq, fact_728_folding__one_Oinsert__remove,
% 287.08/40.85 fact_729_folding__one_Oinsert__remove, fact_72_card__mono,
% 287.08/40.85 fact_730_folding__one_Oinsert__remove, fact_731_folding__one_Oinsert__remove,
% 287.08/40.85 fact_732_folding__one_Oremove, fact_733_folding__one_Oremove,
% 287.08/40.85 fact_734_folding__one_Oremove, fact_735_folding__one_Oremove,
% 287.08/40.85 fact_736_card__Diff__singleton__if, fact_737_card__Diff__singleton__if,
% 287.08/40.85 fact_738_card__Diff__singleton__if, fact_739_card__Diff__singleton__if,
% 287.08/40.85 fact_73_card__mono, fact_740_card__Diff__singleton,
% 287.08/40.85 fact_741_card__Diff__singleton, fact_742_card__Diff__singleton,
% 287.08/40.85 fact_743_card__Diff__singleton, fact_744_one__reorient, fact_745_one__reorient,
% 287.08/40.85 fact_746_diff__Suc__1, fact_747_diff__Suc__eq__diff__pred,
% 287.08/40.85 fact_748_folding__one_Osingleton, fact_749_folding__one_Osingleton,
% 287.08/40.85 fact_74_card__mono, fact_750_folding__one_Osingleton,
% 287.08/40.85 fact_751_card__Diff__insert, fact_752_card__Diff__insert,
% 287.08/40.85 fact_753_card__Diff__insert, fact_754_card__Diff__insert,
% 287.08/40.85 fact_755_folding__one_Oinsert, fact_756_folding__one_Oinsert,
% 287.08/40.85 fact_757_folding__one_Oinsert, fact_758_folding__one_Oinsert,
% 287.08/40.85 fact_759_folding__one_Oclosed, fact_75_card__mono,
% 287.08/40.85 fact_760_folding__one_Oclosed, fact_761_folding__one_Oclosed,
% 287.08/40.85 fact_762_folding__one_Oclosed, fact_763_card_Oremove, fact_764_card_Oremove,
% 287.08/40.85 fact_765_card_Oremove, fact_766_card_Oremove, fact_767_card_Oinsert__remove,
% 287.08/40.85 fact_768_card_Oinsert__remove, fact_769_card_Oinsert__remove,
% 287.08/40.85 fact_76_card__mono, fact_770_card_Oinsert__remove,
% 287.08/40.85 fact_771_folding__one__idem_Osubset__idem,
% 287.08/40.85 fact_772_folding__one__idem_Osubset__idem,
% 287.08/40.85 fact_773_folding__one__idem_Osubset__idem,
% 287.08/40.85 fact_774_folding__one__idem_Osubset__idem,
% 287.08/40.85 fact_775_folding__one__idem_Oinsert__idem,
% 287.08/40.85 fact_776_folding__one__idem_Oinsert__idem,
% 287.08/40.85 fact_777_folding__one__idem_Oinsert__idem,
% 287.08/40.85 fact_778_folding__one__idem_Oinsert__idem, fact_779_finite__ne__induct,
% 287.08/40.85 fact_77_card__mono, fact_780_finite__ne__induct, fact_781_finite__ne__induct,
% 287.08/40.85 fact_782_finite__ne__induct, fact_783_the__elem__def, fact_784_the__elem__def,
% 287.08/40.85 fact_785_the__elem__def, fact_786_ab__semigroup__add__class_Oadd__ac_I1_J,
% 287.08/40.85 fact_787_ab__semigroup__add__class_Oadd__ac_I1_J, fact_788_add__left__cancel,
% 287.08/40.85 fact_789_add__left__cancel, fact_78_card__mono, fact_790_add__right__cancel,
% 287.08/40.85 fact_791_add__right__cancel, fact_792_add__left__imp__eq,
% 287.08/40.85 fact_793_add__left__imp__eq, fact_794_add__imp__eq, fact_795_add__imp__eq,
% 287.08/40.85 fact_796_add__right__imp__eq, fact_797_add__right__imp__eq,
% 287.08/40.85 fact_798_nat__add__commute, fact_799_nat__add__left__commute,
% 287.08/40.85 fact_79_card__seteq, fact_7_finite__Collect__subsets, fact_800_nat__add__assoc,
% 287.08/40.85 fact_801_nat__add__left__cancel, fact_802_nat__add__right__cancel,
% 287.08/40.85 fact_803_add__le__cancel__right, fact_804_add__le__cancel__right,
% 287.08/40.85 fact_805_add__le__cancel__left, fact_806_add__le__cancel__left,
% 287.08/40.85 fact_807_add__right__mono, fact_808_add__right__mono, fact_809_add__left__mono,
% 287.08/40.85 fact_80_card__seteq, fact_810_add__left__mono, fact_811_add__mono,
% 287.08/40.85 fact_812_add__mono, fact_813_add__le__imp__le__right,
% 287.08/40.85 fact_814_add__le__imp__le__right, fact_815_add__le__imp__le__left,
% 287.08/40.85 fact_816_add__le__imp__le__left, fact_817_diff__add__cancel,
% 287.08/40.85 fact_818_add__diff__cancel, fact_819_add__Suc__right, fact_81_card__seteq,
% 287.08/40.85 fact_820_add__Suc, fact_821_add__Suc__shift, fact_822_le__add2,
% 287.08/40.85 fact_823_le__add1, fact_824_le__iff__add, fact_825_nat__add__left__cancel__le,
% 287.08/40.85 fact_826_trans__le__add1, fact_827_trans__le__add2, fact_828_add__le__mono1,
% 287.08/40.85 fact_829_add__le__mono, fact_82_card__seteq, fact_830_add__leD2,
% 287.08/40.85 fact_831_add__leD1, fact_832_add__leE, fact_833_diff__add__inverse2,
% 287.08/40.85 fact_834_diff__add__inverse, fact_835_diff__diff__left, fact_836_diff__cancel,
% 287.08/40.85 fact_837_diff__cancel2, fact_838_diff__diff__right, fact_839_le__diff__conv,
% 287.08/40.85 fact_83_card__seteq, fact_840_le__add__diff, fact_841_le__add__diff__inverse,
% 287.08/40.85 fact_842_add__diff__assoc, fact_843_le__diff__conv2,
% 287.08/40.85 fact_844_le__add__diff__inverse2, fact_845_le__imp__diff__is__add,
% 287.08/40.85 fact_846_diff__add__assoc, fact_847_add__diff__assoc2,
% 287.08/40.85 fact_848_diff__add__assoc2, fact_849_Suc__eq__plus1__left, fact_84_card__seteq,
% 287.08/40.85 fact_850_Suc__eq__plus1, fact_851_diff__Suc__diff__eq1,
% 287.08/40.85 fact_852_diff__Suc__diff__eq2, fact_853_termination__basic__simps_I4_J,
% 287.08/40.85 fact_854_termination__basic__simps_I3_J, fact_855_lessI, fact_856_Suc__mono,
% 287.08/40.85 fact_857_finite__Collect__less__nat, fact_858_less__not__refl,
% 287.08/40.85 fact_859_nat__neq__iff, fact_85_card__seteq, fact_860_linorder__neqE__nat,
% 287.08/40.85 fact_861_less__irrefl__nat, fact_862_less__not__refl2,
% 287.08/40.85 fact_863_less__not__refl3, fact_864_nat__less__cases, fact_865_not__less__eq,
% 287.08/40.85 fact_866_less__Suc__eq, fact_867_Suc__less__eq,
% 287.08/40.85 fact_868_not__less__less__Suc__eq, fact_869_less__antisym, fact_86_card__seteq,
% 287.08/40.85 fact_870_less__SucI, fact_871_Suc__lessI, fact_872_less__trans__Suc,
% 287.08/40.85 fact_873_less__SucE, fact_874_Suc__lessD, fact_875_Suc__less__SucD,
% 287.08/40.85 fact_876_not__add__less1, fact_877_not__add__less2,
% 287.08/40.85 fact_878_nat__add__left__cancel__less, fact_879_trans__less__add1,
% 287.08/40.85 fact_87_card__insert__le, fact_880_trans__less__add2, fact_881_add__less__mono1,
% 287.08/40.85 fact_882_add__less__mono, fact_883_less__add__eq__less, fact_884_add__lessD1,
% 287.08/40.85 fact_885_termination__basic__simps_I1_J,
% 287.08/40.85 fact_886_termination__basic__simps_I2_J, fact_887_nat__less__le,
% 287.08/40.85 fact_888_le__eq__less__or__eq, fact_889_less__imp__le__nat,
% 287.08/40.85 fact_88_card__insert__le, fact_890_le__neq__implies__less,
% 287.08/40.85 fact_891_less__or__eq__imp__le, fact_892_termination__basic__simps_I5_J,
% 287.08/40.85 fact_893_less__imp__diff__less, fact_894_diff__less__mono2,
% 287.08/40.85 fact_895_finite__nat__set__iff__bounded, fact_896_card__Collect__less__nat,
% 287.08/40.85 fact_897_finite__M__bounded__by__nat, fact_898_less__add__Suc1,
% 287.08/40.85 fact_899_less__add__Suc2, fact_89_card__insert__le,
% 287.08/40.85 fact_8_finite__Collect__subsets, fact_900_less__iff__Suc__add,
% 287.08/40.85 fact_901_less__eq__Suc__le, fact_902_less__Suc__eq__le, fact_903_Suc__le__eq,
% 287.08/40.85 fact_904_le__imp__less__Suc, fact_905_Suc__leI, fact_906_le__less__Suc__eq,
% 287.08/40.85 fact_907_Suc__le__lessD, fact_908_diff__less__Suc, fact_909_less__diff__conv,
% 287.08/40.85 fact_90_card__insert__le, fact_910_add__diff__inverse,
% 287.08/40.85 fact_911_diff__less__mono, fact_912_less__diff__iff,
% 287.08/40.85 fact_913_less__eq__Suc__le__raw, fact_914_mono__nat__linear__lb,
% 287.08/40.85 fact_915_inc__induct, fact_916_less__imp__Suc__add,
% 287.08/40.85 fact_917_bounded__nat__set__is__finite, fact_918_less__mono__imp__le__mono,
% 287.08/40.85 fact_919_lessE, fact_91_card__insert__le, fact_920_Suc__lessE,
% 287.08/40.85 fact_921_less__zeroE, fact_922_le0, fact_923_zero__less__Suc,
% 287.08/40.85 fact_924_le__0__eq, fact_925_less__eq__nat_Osimps_I1_J,
% 287.08/40.85 fact_926_diffs0__imp__equal, fact_927_diff__self__eq__0,
% 287.08/40.85 fact_928_minus__nat_Odiff__0, fact_929_diff__0__eq__0, fact_92_card__insert__le,
% 287.08/40.85 fact_931_add__eq__self__zero, fact_932_add__is__0, fact_933_Nat_Oadd__0__right,
% 287.08/40.85 fact_934_plus__nat_Oadd__0, fact_935_gr0I, fact_936_gr__implies__not0,
% 287.08/40.85 fact_937_less__nat__zero__code, fact_938_neq0__conv, fact_939_not__less0,
% 287.08/40.85 fact_93_card__insert__le, fact_940_Suc__neq__Zero, fact_941_Zero__neq__Suc,
% 287.08/40.85 fact_942_nat_Osimps_I3_J, fact_943_Suc__not__Zero, fact_944_nat_Osimps_I2_J,
% 287.08/40.85 fact_945_Zero__not__Suc, fact_946_gr0__conv__Suc,
% 287.08/40.85 fact_948_less__Suc__eq__0__disj, fact_94_card__insert__le, fact_951_add__gr__0,
% 287.08/40.85 fact_952_zero__less__diff, fact_953_diff__less, fact_954_diff__add__0,
% 287.08/40.85 fact_955_diff__is__0__eq, fact_956_diff__is__0__eq_H, fact_958_diff__Suc,
% 287.08/40.85 fact_95_card__insert__if, fact_960_diff__Suc__less, fact_961_nat__diff__split,
% 287.08/40.85 fact_962_nat__diff__split__asm, fact_963_card__less__Suc, fact_964_card__less,
% 287.08/40.85 fact_965_card__less__Suc2, fact_966_Suc__diff__1, fact_967_Suc__pred_H,
% 287.08/40.85 fact_968_add__eq__if, fact_969_ex__least__nat__less, fact_96_card__insert__if,
% 287.08/40.85 fact_970_ex__least__nat__le, fact_971_less__imp__add__positive,
% 287.08/40.85 fact_972_gr0__implies__Suc, fact_973_nat_Oexhaust, fact_974_zero__induct,
% 287.08/40.85 fact_975_not0__implies__Suc, fact_976_nat__induct, fact_977_expand__Suc,
% 287.08/40.85 fact_978_mult__0, fact_979_mult__0__right, fact_97_card__insert__if,
% 287.08/40.85 fact_980_mult__is__0, fact_981_mult__cancel1, fact_982_mult__cancel2,
% 287.08/40.85 fact_983_Suc__mult__cancel1, fact_984_add__mult__distrib,
% 287.08/40.85 fact_985_add__mult__distrib2, fact_986_mult__le__mono, fact_987_mult__le__mono2,
% 287.08/40.85 fact_988_mult__le__mono1, fact_989_le__cube, fact_98_card__insert__if,
% 287.08/40.85 fact_990_le__square, fact_991_diff__mult__distrib,
% 287.08/40.85 fact_992_diff__mult__distrib2, fact_993_nat__mult__eq__1__iff,
% 287.08/40.85 fact_994_nat__mult__1__right, fact_995_nat__1__eq__mult__iff,
% 287.08/40.85 fact_996_nat__mult__1, fact_998_mult__less__mono2, fact_999_mult__less__mono1,
% 287.08/40.85 fact_99_card__insert__if, fact_9_finite__imageI,
% 287.08/40.85 gsy_c_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000t__a,
% 287.08/40.85 gsy_c_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__Com__Opname,
% 287.08/40.85 gsy_c_COMBB_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__HOL__Obool_000t__a,
% 287.08/40.85 gsy_c_COMBK_000tc__HOL__Obool_000t__a,
% 287.08/40.85 gsy_c_COMBS_000t__a_000tc__HOL__Obool_000tc__HOL__Obool,
% 287.08/40.85 gsy_c_COMBS_000tc__Com__Opname_000tc__HOL__Obool_000tc__HOL__Obool,
% 287.08/40.85 gsy_c_COMBS_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__HOL__Obool_000tc__HOL__Obo,
% 287.08/40.85 gsy_c_COMBS_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__HOL__Obool_000t,
% 287.08/40.85 gsy_c_Finite__Set_Ofinite_000t__a, gsy_c_Finite__Set_Ofinite_000tc__Com__Opname,
% 287.08/40.85 gsy_c_Finite__Set_Ofolding__one_000t__a,
% 287.08/40.85 gsy_c_Finite__Set_Ofolding__one_000tc__Com__Opname,
% 287.08/40.85 gsy_c_Finite__Set_Ofolding__one_000tc__Int__Oint,
% 287.08/40.85 gsy_c_Finite__Set_Ofolding__one_000tc__Nat__Onat,
% 287.08/40.85 gsy_c_Finite__Set_Ofolding__one__idem_000t__a,
% 287.08/40.85 gsy_c_Finite__Set_Ofolding__one__idem_000tc__Com__Opname,
% 287.08/40.85 gsy_c_Finite__Set_Ofolding__one__idem_000tc__Int__Oint,
% 287.08/40.85 gsy_c_Finite__Set_Ofolding__one__idem_000tc__Nat__Onat,
% 287.08/40.85 gsy_c_HOL_Oundefined_000t__a, gsy_c_HOL_Oundefined_000tc__Com__Opname,
% 287.08/40.85 gsy_c_HOL_Oundefined_000tc__fun_It__a_Mtc__HOL__Obool_J,
% 287.08/40.85 gsy_c_HOL_Oundefined_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J,
% 287.08/40.85 gsy_c_HOL_Oundefined_000tc__fun_Itc__fun_It__a_Mtc__HOL__Obool_J_Mtc__HOL__Obool,
% 287.08/40.85 gsy_c_HOL_Oundefined_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_Mtc_,
% 287.08/40.85 gsy_c_Orderings_Obot__class_Obot_000tc__HOL__Obool,
% 287.08/40.85 gsy_c_Orderings_Obot__class_Obot_000tc__fun_It__a_Mtc__HOL__Obool_J,
% 287.08/40.85 gsy_c_Orderings_Obot__class_Obot_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J,
% 287.08/40.85 gsy_c_Set_OCollect_000t__a, gsy_c_Set_OCollect_000tc__Com__Opname,
% 287.08/40.85 gsy_c_Set_OCollect_000tc__fun_It__a_Mtc__HOL__Obool_J,
% 287.08/40.85 gsy_c_Set_OCollect_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J,
% 287.08/40.85 gsy_c_Set_Oimage_000t__a_000t__a, gsy_c_Set_Oimage_000t__a_000tc__Com__Opname,
% 287.08/40.85 gsy_c_Set_Oimage_000t__a_000tc__fun_It__a_Mtc__HOL__Obool_J,
% 287.08/40.85 gsy_c_Set_Oimage_000t__a_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J,
% 287.08/40.85 gsy_c_Set_Oimage_000tc__Com__Opname_000t__a,
% 287.08/40.85 gsy_c_Set_Oimage_000tc__Com__Opname_000tc__Com__Opname,
% 287.08/40.85 gsy_c_Set_Oimage_000tc__Com__Opname_000tc__fun_It__a_Mtc__HOL__Obool_J,
% 287.08/40.85 gsy_c_Set_Oimage_000tc__Com__Opname_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_,
% 287.08/40.85 gsy_c_Set_Oimage_000tc__Int__Oint_000t__a,
% 287.08/40.85 gsy_c_Set_Oimage_000tc__Int__Oint_000tc__Com__Opname,
% 287.08/40.85 gsy_c_Set_Oimage_000tc__Int__Oint_000tc__fun_It__a_Mtc__HOL__Obool_J,
% 287.08/40.85 gsy_c_Set_Oimage_000tc__Int__Oint_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J,
% 287.08/40.85 gsy_c_Set_Oimage_000tc__Nat__Onat_000t__a,
% 287.08/40.85 gsy_c_Set_Oimage_000tc__Nat__Onat_000tc__Com__Opname,
% 287.08/40.85 gsy_c_Set_Oimage_000tc__Nat__Onat_000tc__fun_It__a_Mtc__HOL__Obool_J,
% 287.08/40.85 gsy_c_Set_Oimage_000tc__Nat__Onat_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J,
% 287.08/40.85 gsy_c_Set_Oimage_000tc__fun_It__a_Mtc__HOL__Obool_J_000t__a,
% 287.08/40.85 gsy_c_Set_Oimage_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__Com__Opname,
% 287.08/40.85 gsy_c_Set_Oimage_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000t__a,
% 287.08/40.85 gsy_c_Set_Oimage_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__Com__Opnam,
% 287.08/40.85 gsy_c_Set_Oimage_000tc__fun_Itc__Int__Oint_Mtc__HOL__Obool_J_000t__a,
% 287.08/40.85 gsy_c_Set_Oimage_000tc__fun_Itc__Int__Oint_Mtc__HOL__Obool_J_000tc__Com__Opname,
% 287.08/40.85 gsy_c_Set_Oimage_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000t__a,
% 287.08/40.85 gsy_c_Set_Oimage_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__Com__Opname,
% 287.08/40.85 gsy_c_fFalse, gsy_c_fTrue, gsy_c_hAPP_000t__a_000t__a,
% 287.08/40.85 gsy_c_hAPP_000t__a_000tc__HOL__Obool,
% 287.08/40.85 gsy_c_hAPP_000t__a_000tc__fun_It__a_Mtc__HOL__Obool_J,
% 287.08/40.85 gsy_c_hAPP_000t__a_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J,
% 287.08/40.85 gsy_c_hAPP_000t__a_000tc__fun_Itc__fun_It__a_Mtc__HOL__Obool_J_Mtc__HOL__Obool_J,
% 287.08/40.85 gsy_c_hAPP_000tc__Com__Opname_000t__a,
% 287.08/40.85 gsy_c_hAPP_000tc__Com__Opname_000tc__Com__Opname,
% 287.08/40.85 gsy_c_hAPP_000tc__Com__Opname_000tc__HOL__Obool,
% 287.08/40.85 gsy_c_hAPP_000tc__Com__Opname_000tc__fun_It__a_Mtc__HOL__Obool_J,
% 287.08/40.85 gsy_c_hAPP_000tc__Com__Opname_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J,
% 287.08/40.85 gsy_c_hAPP_000tc__Com__Opname_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obo,
% 287.08/40.85 gsy_c_hAPP_000tc__HOL__Obool_000tc__HOL__Obool,
% 287.08/40.85 gsy_c_hAPP_000tc__Int__Oint_000t__a,
% 287.08/40.85 gsy_c_hAPP_000tc__Int__Oint_000tc__HOL__Obool,
% 287.08/40.85 gsy_c_hAPP_000tc__Int__Oint_000tc__fun_It__a_Mtc__HOL__Obool_J,
% 287.08/40.85 gsy_c_hAPP_000tc__Int__Oint_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J,
% 287.08/40.85 gsy_c_hAPP_000tc__Int__Oint_000tc__fun_Itc__fun_It__a_Mtc__HOL__Obool_J_Mtc__HOL,
% 287.08/40.85 gsy_c_hAPP_000tc__Int__Oint_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool,
% 287.08/40.85 gsy_c_hAPP_000tc__Nat__Onat_000tc__HOL__Obool,
% 287.08/40.85 gsy_c_hAPP_000tc__Nat__Onat_000tc__fun_It__a_Mtc__HOL__Obool_J,
% 287.08/40.85 gsy_c_hAPP_000tc__Nat__Onat_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J,
% 287.08/40.85 gsy_c_hAPP_000tc__Nat__Onat_000tc__fun_Itc__fun_It__a_Mtc__HOL__Obool_J_Mtc__HOL,
% 287.08/40.85 gsy_c_hAPP_000tc__Nat__Onat_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool,
% 287.08/40.85 gsy_c_hAPP_000tc__fun_It__a_Mtc__HOL__Obool_J_000t__a,
% 287.08/40.85 gsy_c_hAPP_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__HOL__Obool,
% 287.08/40.85 gsy_c_hAPP_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__fun_It__a_Mtc__HOL__Obool_J,
% 287.08/40.85 gsy_c_hAPP_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__fun_Itc__fun_It__a_Mtc__HOL,
% 287.08/40.85 gsy_c_hAPP_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__Com__Opname,
% 287.08/40.85 gsy_c_hAPP_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__HOL__Obool,
% 287.08/40.85 gsy_c_hAPP_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__fun_Itc__Com__Op,
% 287.08/40.85 gsy_c_hAPP_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__fun_Itc__fun_Itc,
% 287.08/40.85 gsy_c_hAPP_000tc__fun_Itc__Int__Oint_Mtc__HOL__Obool_J_000tc__HOL__Obool,
% 287.08/40.85 gsy_c_hAPP_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__HOL__Obool,
% 287.08/40.85 gsy_c_hAPP_000tc__fun_Itc__fun_It__a_Mtc__HOL__Obool_J_Mtc__HOL__Obool_J_000tc__,
% 287.08/40.85 gsy_c_hAPP_000tc__fun_Itc__fun_It__a_Mtc__HOL__Obool_J_Mtc__HOL__Obool_J_000tc___001,
% 287.08/40.85 gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_Mtc__HOL__Oboo,
% 287.08/40.85 gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_Mtc__HOL__Oboo_002,
% 287.08/40.85 gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Int__Oint_Mtc__HOL__Obool_J_Mtc__HOL__Obool_,
% 287.08/40.85 gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_Mtc__HOL__Obool_,
% 287.08/40.85 gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_It__a_Mtc__HOL__Obool_J_Mtc__HOL__Obool_,
% 287.08/40.85 gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_Mtc__,
% 287.08/40.85 gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__Int__Oint_Mtc__HOL__Obool_J_Mtc__HO,
% 287.08/40.85 gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_Mtc__HO,
% 287.08/40.85 gsy_v_G, gsy_v_P, gsy_v_U, gsy_v_mgt, gsy_v_pn, gsy_v_wt,
% 287.08/40.85 help_COMBB_1_1_COMBB_000t__a_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__Com__Opna,
% 287.08/40.85 help_COMBB_1_1_COMBB_000t__a_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__Int__Oint,
% 287.08/40.85 help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000t__a_U,
% 287.08/40.85 help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__Com__Opname_U,
% 287.08/40.85 help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__Int__Oint_U,
% 287.08/40.85 help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__Nat__Onat_U,
% 287.08/40.85 help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo,
% 287.08/40.85 help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_003,
% 287.08/40.85 help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_004,
% 287.08/40.85 help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_005,
% 287.08/40.85 help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_006,
% 287.08/40.85 help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_009,
% 287.08/40.85 help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_010,
% 287.08/40.85 help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_011,
% 287.08/40.85 help_COMBB_1_1_COMBB_000tc__Int__Oint_000tc__HOL__Obool_000tc__Nat__Onat_U,
% 287.08/40.85 help_COMBB_1_1_COMBB_000tc__Int__Oint_000tc__fun_Itc__Int__Oint_Mtc__HOL__Obool_,
% 287.08/40.85 help_COMBB_1_1_COMBB_000tc__Nat__Onat_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_,
% 287.08/40.85 help_COMBB_1_1_COMBB_000tc__Nat__Onat_000tc__fun_Itc__fun_Itc__Nat__Onat_Mtc__HO,
% 287.08/40.85 help_COMBB_1_1_COMBB_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__HOL__Obool_000t__,
% 287.08/40.85 help_COMBB_1_1_COMBB_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__fun_Itc__fun_It__,
% 287.08/40.85 help_COMBB_1_1_COMBB_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__fun_Itc__fun_It___012,
% 287.08/40.85 help_COMBB_1_1_COMBB_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__fun_It,
% 287.08/40.85 help_COMBB_1_1_COMBB_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__fun_It_015,
% 287.08/40.85 help_COMBB_1_1_COMBB_000tc__fun_Itc__Int__Oint_Mtc__HOL__Obool_J_000tc__HOL__Obo,
% 287.08/40.85 help_COMBB_1_1_COMBB_000tc__fun_Itc__Int__Oint_Mtc__HOL__Obool_J_000tc__fun_Itc_,
% 287.08/40.85 help_COMBB_1_1_COMBB_000tc__fun_Itc__Int__Oint_Mtc__HOL__Obool_J_000tc__fun_Itc__013,
% 287.08/40.85 help_COMBB_1_1_COMBB_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__HOL__Obo,
% 287.08/40.85 help_COMBB_1_1_COMBB_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__fun_Itc_,
% 287.08/40.85 help_COMBB_1_1_COMBB_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__fun_Itc__014,
% 287.08/40.85 help_COMBC_1_1_COMBC_000t__a_000t__a_000tc__HOL__Obool_U,
% 287.08/40.85 help_COMBC_1_1_COMBC_000t__a_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__HOL__Oboo,
% 287.08/40.85 help_COMBC_1_1_COMBC_000t__a_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__fun_It__a,
% 287.08/40.85 help_COMBC_1_1_COMBC_000tc__Com__Opname_000t__a_000tc__HOL__Obool_U,
% 287.08/40.85 help_COMBC_1_1_COMBC_000tc__Com__Opname_000tc__Com__Opname_000tc__HOL__Obool_U,
% 287.08/40.85 help_COMBC_1_1_COMBC_000tc__Com__Opname_000tc__fun_Itc__Com__Opname_Mtc__HOL__Ob,
% 287.08/40.85 help_COMBC_1_1_COMBC_000tc__Int__Oint_000t__a_000tc__HOL__Obool_U,
% 287.08/40.85 help_COMBC_1_1_COMBC_000tc__Int__Oint_000tc__Int__Oint_000tc__HOL__Obool_U,
% 287.08/40.85 help_COMBC_1_1_COMBC_000tc__Int__Oint_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__,
% 287.08/40.85 help_COMBC_1_1_COMBC_000tc__Int__Oint_000tc__fun_Itc__Com__Opname_Mtc__HOL__Oboo,
% 287.08/40.85 help_COMBC_1_1_COMBC_000tc__Int__Oint_000tc__fun_Itc__Int__Oint_Mtc__HOL__Obool_,
% 287.08/40.85 help_COMBC_1_1_COMBC_000tc__Int__Oint_000tc__fun_Itc__Int__Oint_Mtc__HOL__Obool__007,
% 287.08/40.85 help_COMBC_1_1_COMBC_000tc__Int__Oint_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_,
% 287.08/40.85 help_COMBC_1_1_COMBC_000tc__Nat__Onat_000tc__Int__Oint_000tc__HOL__Obool_U,
% 287.08/40.85 help_COMBC_1_1_COMBC_000tc__Nat__Onat_000tc__Nat__Onat_000tc__HOL__Obool_U,
% 287.08/40.85 help_COMBC_1_1_COMBC_000tc__Nat__Onat_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__,
% 287.08/40.85 help_COMBC_1_1_COMBC_000tc__Nat__Onat_000tc__fun_Itc__Com__Opname_Mtc__HOL__Oboo,
% 287.08/40.85 help_COMBC_1_1_COMBC_000tc__Nat__Onat_000tc__fun_Itc__Int__Oint_Mtc__HOL__Obool_,
% 287.08/40.85 help_COMBC_1_1_COMBC_000tc__Nat__Onat_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_,
% 287.08/40.85 help_COMBC_1_1_COMBC_000tc__Nat__Onat_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool__008,
% 287.08/40.85 help_COMBC_1_1_COMBC_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__fun_It__a_Mtc__HO,
% 287.08/40.85 help_COMBC_1_1_COMBC_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__fun_It,
% 287.08/40.85 help_COMBC_1_1_COMBC_000tc__fun_Itc__Int__Oint_Mtc__HOL__Obool_J_000tc__fun_Itc_,
% 287.08/40.85 help_COMBC_1_1_COMBC_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__fun_Itc_,
% 287.08/40.85 help_COMBC_1_1_COMBC_000tc__fun_Itc__fun_It__a_Mtc__HOL__Obool_J_Mtc__HOL__Obool,
% 287.08/40.85 help_COMBC_1_1_COMBC_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_Mtc_,
% 287.08/40.85 help_COMBC_1_1_COMBC_000tc__fun_Itc__fun_Itc__Int__Oint_Mtc__HOL__Obool_J_Mtc__H,
% 287.08/40.85 help_COMBC_1_1_COMBC_000tc__fun_Itc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_Mtc__H,
% 287.08/40.85 help_COMBI_1_1_COMBI_000tc__Nat__Onat_U,
% 287.08/40.85 help_COMBK_1_1_COMBK_000t__a_000tc__Com__Opname_U,
% 287.08/40.85 help_COMBK_1_1_COMBK_000tc__HOL__Obool_000t__a_U,
% 287.08/40.85 help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__Int__Oint_U,
% 287.08/40.85 help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__Nat__Onat_U,
% 287.08/40.85 help_COMBK_1_1_COMBK_000tc__Int__Oint_000tc__Nat__Onat_U,
% 287.08/40.85 help_COMBS_1_1_COMBS_000t__a_000tc__HOL__Obool_000tc__HOL__Obool_U,
% 287.08/40.85 help_COMBS_1_1_COMBS_000tc__Com__Opname_000tc__HOL__Obool_000tc__HOL__Obool_U,
% 287.08/40.85 help_COMBS_1_1_COMBS_000tc__Int__Oint_000tc__HOL__Obool_000tc__HOL__Obool_U,
% 287.08/40.85 help_COMBS_1_1_COMBS_000tc__Nat__Onat_000tc__HOL__Obool_000tc__HOL__Obool_U,
% 287.08/40.85 help_COMBS_1_1_COMBS_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__HOL__Obool_000tc_,
% 287.08/40.85 help_COMBS_1_1_COMBS_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__HOL__O,
% 287.08/40.85 help_COMBS_1_1_COMBS_000tc__fun_Itc__Int__Oint_Mtc__HOL__Obool_J_000tc__HOL__Obo,
% 287.08/40.85 help_COMBS_1_1_COMBS_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__HOL__Obo,
% 287.08/40.85 help_If_1_1_If_000tc__Nat__Onat_T, help_If_2_1_If_000tc__Nat__Onat_T,
% 287.08/40.85 help_If_3_1_If_000tc__Nat__Onat_T, help_fFalse_1_1_T, help_fFalse_1_1_U,
% 287.08/40.85 help_fNot_1_1_U, help_fNot_2_1_U, help_fconj_1_1_U, help_fconj_2_1_U,
% 287.08/40.85 help_fconj_3_1_U, help_fdisj_1_1_U, help_fdisj_2_1_U, help_fdisj_3_1_U,
% 287.08/40.85 help_fequal_1_1_fequal_000t__a_T, help_fequal_1_1_fequal_000tc__Com__Opname_T,
% 287.08/40.85 help_fequal_1_1_fequal_000tc__Int__Oint_T,
% 287.08/40.85 help_fequal_1_1_fequal_000tc__Nat__Onat_T,
% 287.08/40.85 help_fequal_1_1_fequal_000tc__fun_It__a_Mtc__HOL__Obool_J_T,
% 287.08/40.85 help_fequal_1_1_fequal_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_T,
% 287.08/40.85 help_fequal_1_1_fequal_000tc__fun_Itc__Int__Oint_Mtc__HOL__Obool_J_T,
% 287.08/40.85 help_fequal_1_1_fequal_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_T,
% 287.08/40.85 help_fequal_2_1_fequal_000t__a_T, help_fequal_2_1_fequal_000tc__Com__Opname_T,
% 287.08/40.85 help_fequal_2_1_fequal_000tc__Int__Oint_T,
% 287.08/40.85 help_fequal_2_1_fequal_000tc__Nat__Onat_T,
% 287.08/40.85 help_fequal_2_1_fequal_000tc__fun_It__a_Mtc__HOL__Obool_J_T,
% 287.08/40.85 help_fequal_2_1_fequal_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_T,
% 287.08/40.85 help_fequal_2_1_fequal_000tc__fun_Itc__Int__Oint_Mtc__HOL__Obool_J_T,
% 287.08/40.85 help_fequal_2_1_fequal_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_T,
% 287.08/40.85 help_fimplies_1_1_U, help_fimplies_2_1_U, help_fimplies_3_1_U
% 287.08/40.85
% 287.08/40.85 Those formulas are unsatisfiable:
% 287.08/40.85 ---------------------------------
% 287.08/40.85
% 287.08/40.85 Begin of proof
% 287.08/40.86 |
% 287.08/40.86 | ALPHA: (fact_320_order__antisym__conv) implies:
% 287.08/40.86 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 287.08/40.86 | (hAPP_i1948725293t_bool(ord_less_eq_int, v0) = v2) | ~
% 287.08/40.86 | (hAPP_int_bool(v2, v1) = v3) | ~ $i(v1) | ~ $i(v0) | ~ hBOOL(v3) |
% 287.08/40.86 | ? [v4: $i] : ? [v5: $i] : (( ~ (v1 = v0) | (v4 = v2 &
% 287.08/40.86 | hAPP_int_bool(v2, v0) = v5 & $i(v5) & hBOOL(v5))) & (v1 = v0 |
% 287.08/40.86 | (hAPP_i1948725293t_bool(ord_less_eq_int, v1) = v4 &
% 287.08/40.86 | hAPP_int_bool(v4, v0) = v5 & $i(v5) & $i(v4) & ~ hBOOL(v5)))))
% 287.08/40.86 |
% 287.08/40.86 | ALPHA: (fact_436_rev__image__eqI) implies:
% 287.08/40.86 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 287.08/40.86 | ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ( ~
% 287.08/40.86 | (hAPP_f1664156314l_bool(v4, v3) = v5) | ~ (hAPP_fun_a_bool_bool(v6,
% 287.08/40.86 | v7) = v8) | ~ (hAPP_p338031245l_bool(member_pname, v2) = v4) |
% 287.08/40.86 | ~ (hAPP_a85458249l_bool(member_a, v0) = v6) | ~ (image_pname_a(v1,
% 287.08/40.86 | v3) = v7) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 287.08/40.86 | hBOOL(v5) | hBOOL(v8) | ? [v9: $i] : ( ~ (v9 = v0) &
% 287.08/40.86 | hAPP_pname_a(v1, v2) = v9 & $i(v9)))
% 287.08/40.86 |
% 287.08/40.86 | ALPHA: (fact_453_insert__subset) implies:
% 287.08/40.86 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 287.08/40.86 | ! [v5: $i] : ! [v6: $i] : ( ~ (hAPP_a1206381875a_bool(insert_a, v0) =
% 287.08/40.86 | v3) | ~ (hAPP_f1631501043l_bool(ord_le1311769555a_bool, v4) = v5)
% 287.08/40.86 | | ~ (hAPP_f2050579477a_bool(v3, v1) = v4) | ~
% 287.08/40.86 | (hAPP_fun_a_bool_bool(v5, v2) = v6) | ~ $i(v2) | ~ $i(v1) | ~
% 287.08/40.86 | $i(v0) | hBOOL(v6) | ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ?
% 287.08/40.86 | [v10: $i] : ((hAPP_f1631501043l_bool(ord_le1311769555a_bool, v1) = v9
% 287.08/40.86 | & hAPP_fun_a_bool_bool(v9, v2) = v10 & $i(v10) & $i(v9) & ~
% 287.08/40.86 | hBOOL(v10)) | (hAPP_fun_a_bool_bool(v7, v2) = v8 &
% 287.08/40.86 | hAPP_a85458249l_bool(member_a, v0) = v7 & $i(v8) & $i(v7) & ~
% 287.08/40.86 | hBOOL(v8))))
% 287.08/40.86 |
% 287.08/40.86 | ALPHA: (fact_479_subsetI) implies:
% 287.08/40.86 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 287.08/40.86 | (hAPP_f1631501043l_bool(ord_le1311769555a_bool, v1) = v2) | ~
% 287.08/40.86 | (hAPP_fun_a_bool_bool(v2, v0) = v3) | ~ $i(v1) | ~ $i(v0) |
% 287.08/40.86 | hBOOL(v3) | ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] :
% 287.08/40.86 | (hAPP_fun_a_bool_bool(v5, v1) = v6 & hAPP_fun_a_bool_bool(v5, v0) =
% 287.08/40.86 | v7 & hAPP_a85458249l_bool(member_a, v4) = v5 & $i(v7) & $i(v6) &
% 287.08/40.86 | $i(v5) & $i(v4) & hBOOL(v6) & is_a(v4) & ~ hBOOL(v7)))
% 287.08/40.86 |
% 287.08/40.86 | ALPHA: (fact_930_bot__nat__def) implies:
% 287.08/40.86 | (5) zero_zero_nat = bot_bot_nat
% 287.08/40.86 |
% 287.08/40.86 | ALPHA: (fact_947_less__Suc0) implies:
% 287.08/40.86 | (6) ? [v0: $i] : (hAPP_nat_nat(suc, zero_zero_nat) = v0 & $i(v0) & ! [v1:
% 287.08/40.86 | $i] : ! [v2: $i] : (v1 = zero_zero_nat | ~
% 287.08/40.86 | (hAPP_n1699378549t_bool(ord_less_nat, v1) = v2) | ~ $i(v1) | ?
% 287.08/40.86 | [v3: $i] : (hAPP_nat_bool(v2, v0) = v3 & $i(v3) & ~ hBOOL(v3))) &
% 287.08/40.86 | ! [v1: $i] : ( ~ (hAPP_n1699378549t_bool(ord_less_nat, zero_zero_nat)
% 287.08/40.86 | = v1) | ? [v2: $i] : (hAPP_nat_bool(v1, v0) = v2 & $i(v2) &
% 287.08/40.86 | hBOOL(v2))))
% 287.08/40.86 |
% 287.08/40.86 | ALPHA: (fact_950_add__is__1) implies:
% 287.08/40.86 | (7) ? [v0: $i] : (hAPP_nat_nat(suc, zero_zero_nat) = v0 & $i(v0) & ! [v1:
% 287.08/40.86 | $i] : ! [v2: $i] : ! [v3: $i] : (v2 = v0 | v2 = zero_zero_nat |
% 287.08/40.86 | ~ (hAPP_nat_fun_nat_nat(plus_plus_nat, v1) = v3) | ~
% 287.08/40.86 | (hAPP_nat_nat(v3, v2) = v0) | ~ $i(v2) | ~ $i(v1)) & ! [v1: $i]
% 287.08/40.86 | : ! [v2: $i] : ! [v3: $i] : (v2 = v0 | v1 = v0 | ~
% 287.08/40.86 | (hAPP_nat_fun_nat_nat(plus_plus_nat, v1) = v3) | ~
% 287.08/40.86 | (hAPP_nat_nat(v3, v2) = v0) | ~ $i(v2) | ~ $i(v1)) & ! [v1: $i]
% 287.08/40.86 | : ! [v2: $i] : ! [v3: $i] : (v2 = zero_zero_nat | v1 =
% 287.08/40.86 | zero_zero_nat | ~ (hAPP_nat_fun_nat_nat(plus_plus_nat, v1) = v3) |
% 287.08/40.86 | ~ (hAPP_nat_nat(v3, v2) = v0) | ~ $i(v2) | ~ $i(v1)) & ! [v1:
% 287.08/40.86 | $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | v1 = zero_zero_nat |
% 287.08/40.86 | ~ (hAPP_nat_fun_nat_nat(plus_plus_nat, v1) = v3) | ~
% 287.08/40.86 | (hAPP_nat_nat(v3, v2) = v0) | ~ $i(v2) | ~ $i(v1)) & ! [v1: $i]
% 287.08/40.86 | : ! [v2: $i] : (v2 = v0 | ~ (hAPP_nat_fun_nat_nat(plus_plus_nat,
% 287.08/40.86 | v0) = v1) | ~ (hAPP_nat_nat(v1, zero_zero_nat) = v2)) & !
% 287.08/40.86 | [v1: $i] : ! [v2: $i] : (v2 = v0 | ~
% 287.08/40.86 | (hAPP_nat_fun_nat_nat(plus_plus_nat, zero_zero_nat) = v1) | ~
% 287.08/40.86 | (hAPP_nat_nat(v1, v0) = v2)))
% 287.08/40.86 |
% 287.08/40.87 | ALPHA: (fact_957_One__nat__def) implies:
% 287.08/40.87 | (8) hAPP_nat_nat(suc, zero_zero_nat) = one_one_nat
% 287.08/40.87 |
% 287.08/40.87 | ALPHA: (fact_959_Suc__pred) implies:
% 287.08/40.87 | (9) ? [v0: $i] : ? [v1: $i] : (hAPP_nat_nat(suc, zero_zero_nat) = v1 &
% 287.08/40.87 | hAPP_n1699378549t_bool(ord_less_nat, zero_zero_nat) = v0 & $i(v1) &
% 287.08/40.87 | $i(v0) & ! [v2: $i] : ! [v3: $i] : ( ~ (hAPP_nat_bool(v0, v2) = v3)
% 287.08/40.87 | | ~ $i(v2) | ~ hBOOL(v3) | ? [v4: $i] : ? [v5: $i] :
% 287.08/40.87 | (hAPP_nat_fun_nat_nat(minus_minus_nat, v2) = v4 & hAPP_nat_nat(v4,
% 287.08/40.87 | v1) = v5 & hAPP_nat_nat(suc, v5) = v2 & $i(v5) & $i(v4))))
% 287.08/40.87 |
% 287.08/40.87 | ALPHA: (fact_997_mult__eq__1__iff) implies:
% 287.08/40.87 | (10) ? [v0: $i] : (hAPP_nat_nat(suc, zero_zero_nat) = v0 & $i(v0) & !
% 287.08/40.87 | [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v2 = v0 | ~
% 287.08/40.87 | (hAPP_nat_fun_nat_nat(times_times_nat, v1) = v3) | ~
% 287.08/40.87 | (hAPP_nat_nat(v3, v2) = v0) | ~ $i(v2) | ~ $i(v1)) & ! [v1: $i]
% 287.08/40.87 | : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 287.08/40.87 | (hAPP_nat_fun_nat_nat(times_times_nat, v1) = v3) | ~
% 287.08/40.87 | (hAPP_nat_nat(v3, v2) = v0) | ~ $i(v2) | ~ $i(v1)) & ! [v1: $i]
% 287.08/40.87 | : ! [v2: $i] : (v2 = v0 | ~ (hAPP_nat_fun_nat_nat(times_times_nat,
% 287.08/40.87 | v0) = v1) | ~ (hAPP_nat_nat(v1, v0) = v2)))
% 287.08/40.87 |
% 287.08/40.87 | ALPHA: (fact_1008_n__less__m__mult__n) implies:
% 287.08/40.87 | (11) ? [v0: $i] : ? [v1: $i] : (hAPP_nat_nat(suc, zero_zero_nat) = v0 &
% 287.08/40.87 | hAPP_n1699378549t_bool(ord_less_nat, v0) = v1 & $i(v1) & $i(v0) & !
% 287.08/40.87 | [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~
% 287.08/40.87 | (hAPP_nat_bool(v1, v3) = v4) | ~ (hAPP_nat_bool(v1, v2) = v5) |
% 287.08/40.87 | ~ $i(v3) | ~ $i(v2) | ~ hBOOL(v5) | ~ hBOOL(v4) | ? [v6: $i] :
% 287.08/40.87 | ? [v7: $i] : ? [v8: $i] : ? [v9: $i] :
% 287.08/40.87 | (hAPP_nat_fun_nat_nat(times_times_nat, v2) = v7 & hAPP_nat_nat(v7,
% 287.08/40.87 | v3) = v8 & hAPP_n1699378549t_bool(ord_less_nat, v3) = v6 &
% 287.08/40.87 | hAPP_nat_bool(v6, v8) = v9 & $i(v9) & $i(v8) & $i(v7) & $i(v6) &
% 287.08/40.87 | hBOOL(v9))))
% 287.08/40.87 |
% 287.08/40.87 | ALPHA: (fact_1009_n__less__n__mult__m) implies:
% 287.08/40.87 | (12) ? [v0: $i] : ? [v1: $i] : (hAPP_nat_nat(suc, zero_zero_nat) = v0 &
% 287.08/40.87 | hAPP_n1699378549t_bool(ord_less_nat, v0) = v1 & $i(v1) & $i(v0) & !
% 287.08/40.87 | [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~
% 287.08/40.87 | (hAPP_nat_bool(v1, v3) = v4) | ~ (hAPP_nat_bool(v1, v2) = v5) |
% 287.08/40.87 | ~ $i(v3) | ~ $i(v2) | ~ hBOOL(v5) | ~ hBOOL(v4) | ? [v6: $i] :
% 287.08/40.87 | ? [v7: $i] : ? [v8: $i] : ? [v9: $i] :
% 287.08/40.87 | (hAPP_nat_fun_nat_nat(times_times_nat, v3) = v7 & hAPP_nat_nat(v7,
% 287.08/40.87 | v2) = v8 & hAPP_n1699378549t_bool(ord_less_nat, v3) = v6 &
% 287.08/40.87 | hAPP_nat_bool(v6, v8) = v9 & $i(v9) & $i(v8) & $i(v7) & $i(v6) &
% 287.08/40.87 | hBOOL(v9))))
% 287.08/40.87 |
% 287.08/40.87 | ALPHA: (fact_1010_one__less__mult) implies:
% 287.08/40.87 | (13) ? [v0: $i] : ? [v1: $i] : (hAPP_nat_nat(suc, zero_zero_nat) = v0 &
% 287.08/40.87 | hAPP_n1699378549t_bool(ord_less_nat, v0) = v1 & $i(v1) & $i(v0) & !
% 287.08/40.87 | [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~
% 287.08/40.87 | (hAPP_nat_bool(v1, v3) = v4) | ~ (hAPP_nat_bool(v1, v2) = v5) |
% 287.08/40.87 | ~ $i(v3) | ~ $i(v2) | ~ hBOOL(v5) | ~ hBOOL(v4) | ? [v6: $i] :
% 287.08/40.87 | ? [v7: $i] : ? [v8: $i] : (hAPP_nat_fun_nat_nat(times_times_nat,
% 287.08/40.87 | v2) = v6 & hAPP_nat_nat(v6, v3) = v7 & hAPP_nat_bool(v1, v7) =
% 287.08/40.87 | v8 & $i(v8) & $i(v7) & $i(v6) & hBOOL(v8))))
% 287.08/40.87 |
% 287.08/40.87 | ALPHA: (fact_1011_one__le__mult__iff) implies:
% 287.08/40.87 | (14) ? [v0: $i] : ? [v1: $i] : (hAPP_nat_nat(suc, zero_zero_nat) = v0 &
% 287.08/40.87 | hAPP_n1699378549t_bool(ord_less_eq_nat, v0) = v1 & $i(v1) & $i(v0) &
% 287.08/40.87 | ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~
% 287.08/40.87 | (hAPP_nat_bool(v1, v3) = v5) | ~ (hAPP_nat_bool(v1, v2) = v4) |
% 287.08/40.87 | ~ $i(v3) | ~ $i(v2) | ~ hBOOL(v5) | ~ hBOOL(v4) | ? [v6: $i] :
% 287.08/40.87 | ? [v7: $i] : ? [v8: $i] : (hAPP_nat_fun_nat_nat(times_times_nat,
% 287.08/40.87 | v2) = v6 & hAPP_nat_nat(v6, v3) = v7 & hAPP_nat_bool(v1, v7) =
% 287.08/40.87 | v8 & $i(v8) & $i(v7) & $i(v6) & hBOOL(v8))) & ! [v2: $i] : !
% 287.08/40.87 | [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (hAPP_nat_bool(v1, v3) =
% 287.08/40.87 | v5) | ~ (hAPP_nat_bool(v1, v2) = v4) | ~ $i(v3) | ~ $i(v2) |
% 287.08/40.87 | hBOOL(v5) | ? [v6: $i] : ? [v7: $i] : ? [v8: $i] :
% 287.08/40.87 | (hAPP_nat_fun_nat_nat(times_times_nat, v2) = v6 & hAPP_nat_nat(v6,
% 287.08/40.87 | v3) = v7 & hAPP_nat_bool(v1, v7) = v8 & $i(v8) & $i(v7) &
% 287.08/40.87 | $i(v6) & ~ hBOOL(v8))) & ! [v2: $i] : ! [v3: $i] : ! [v4:
% 287.08/40.87 | $i] : ! [v5: $i] : ( ~ (hAPP_nat_bool(v1, v3) = v5) | ~
% 287.08/40.87 | (hAPP_nat_bool(v1, v2) = v4) | ~ $i(v3) | ~ $i(v2) | hBOOL(v4) |
% 287.08/40.87 | ? [v6: $i] : ? [v7: $i] : ? [v8: $i] :
% 287.08/40.87 | (hAPP_nat_fun_nat_nat(times_times_nat, v2) = v6 & hAPP_nat_nat(v6,
% 287.08/40.87 | v3) = v7 & hAPP_nat_bool(v1, v7) = v8 & $i(v8) & $i(v7) &
% 287.08/40.87 | $i(v6) & ~ hBOOL(v8))))
% 287.08/40.87 |
% 287.08/40.87 | ALPHA: (fact_1030_zmult__zless__mono2) implies:
% 287.08/40.87 | (15) ? [v0: $i] : (hAPP_i1948725293t_bool(ord_less_int, zero_zero_int) =
% 287.08/40.87 | v0 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i]
% 287.08/40.87 | : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ( ~
% 287.08/40.87 | (hAPP_int_fun_int_int(times_times_int, v1) = v4) | ~
% 287.08/40.87 | (hAPP_int_int(v4, v3) = v7) | ~ (hAPP_int_int(v4, v2) = v5) | ~
% 287.08/40.87 | (hAPP_i1948725293t_bool(ord_less_int, v5) = v6) | ~
% 287.08/40.87 | (hAPP_int_bool(v6, v7) = v8) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) |
% 287.08/40.87 | hBOOL(v8) | ? [v9: $i] : ? [v10: $i] : ? [v11: $i] :
% 287.08/40.87 | ((hAPP_i1948725293t_bool(ord_less_int, v2) = v9 &
% 287.08/40.87 | hAPP_int_bool(v9, v3) = v10 & $i(v10) & $i(v9) & ~
% 287.08/40.87 | hBOOL(v10)) | (hAPP_int_bool(v0, v1) = v11 & $i(v11) & ~
% 287.08/40.87 | hBOOL(v11)))))
% 287.08/40.87 |
% 287.08/40.87 | ALPHA: (fact_1031_pos__zmult__eq__1__iff) implies:
% 287.08/40.87 | (16) ? [v0: $i] : (hAPP_i1948725293t_bool(ord_less_int, zero_zero_int) =
% 287.08/40.87 | v0 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v2 =
% 287.08/40.87 | one_one_int | ~ (hAPP_int_fun_int_int(times_times_int, v2) = v3)
% 287.08/40.87 | | ~ (hAPP_int_int(v3, v1) = one_one_int) | ~ $i(v2) | ~ $i(v1)
% 287.08/40.87 | | ? [v4: $i] : (hAPP_int_bool(v0, v2) = v4 & $i(v4) & ~
% 287.08/40.87 | hBOOL(v4))) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 =
% 287.08/40.87 | one_one_int | ~ (hAPP_int_fun_int_int(times_times_int, v2) = v3)
% 287.08/40.87 | | ~ (hAPP_int_int(v3, v1) = one_one_int) | ~ $i(v2) | ~ $i(v1)
% 287.08/40.87 | | ? [v4: $i] : (hAPP_int_bool(v0, v2) = v4 & $i(v4) & ~
% 287.08/40.87 | hBOOL(v4))) & ! [v1: $i] : ! [v2: $i] : (v2 = one_one_int | ~
% 287.08/40.87 | (hAPP_int_fun_int_int(times_times_int, one_one_int) = v1) | ~
% 287.08/40.87 | (hAPP_int_int(v1, one_one_int) = v2) | ? [v3: $i] :
% 287.08/40.87 | (hAPP_int_bool(v0, one_one_int) = v3 & $i(v3) & ~ hBOOL(v3))))
% 287.08/40.87 |
% 287.08/40.87 | ALPHA: (fact_1035_int__0__less__1) implies:
% 287.08/40.88 | (17) ? [v0: $i] : ? [v1: $i] : (hAPP_i1948725293t_bool(ord_less_int,
% 287.08/40.88 | zero_zero_int) = v0 & hAPP_int_bool(v0, one_one_int) = v1 & $i(v1)
% 287.08/40.88 | & $i(v0) & hBOOL(v1))
% 287.08/40.88 |
% 287.08/40.88 | ALPHA: (fact_1036_int__one__le__iff__zero__less) implies:
% 287.08/40.88 | (18) ? [v0: $i] : ? [v1: $i] : (hAPP_i1948725293t_bool(ord_less_int,
% 287.08/40.88 | zero_zero_int) = v1 & hAPP_i1948725293t_bool(ord_less_eq_int,
% 287.08/40.88 | one_one_int) = v0 & $i(v1) & $i(v0) & ! [v2: $i] : ! [v3: $i] :
% 287.08/40.88 | ( ~ (hAPP_int_bool(v1, v2) = v3) | ~ $i(v2) | ~ hBOOL(v3) | ?
% 287.08/40.88 | [v4: $i] : (hAPP_int_bool(v0, v2) = v4 & $i(v4) & hBOOL(v4))) & !
% 287.08/40.88 | [v2: $i] : ! [v3: $i] : ( ~ (hAPP_int_bool(v1, v2) = v3) | ~
% 287.08/40.88 | $i(v2) | hBOOL(v3) | ? [v4: $i] : (hAPP_int_bool(v0, v2) = v4 &
% 287.08/40.88 | $i(v4) & ~ hBOOL(v4))))
% 287.08/40.88 |
% 287.08/40.88 | ALPHA: (fact_1038_le__imp__0__less) implies:
% 287.08/40.88 | (19) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 287.08/40.88 | (hAPP_int_fun_int_int(plus_plus_int, one_one_int) = v2 &
% 287.08/40.88 | hAPP_i1948725293t_bool(ord_less_int, zero_zero_int) = v1 &
% 287.08/40.88 | hAPP_i1948725293t_bool(ord_less_eq_int, zero_zero_int) = v0 & $i(v2)
% 287.08/40.88 | & $i(v1) & $i(v0) & ! [v3: $i] : ! [v4: $i] : ( ~
% 287.08/40.88 | (hAPP_int_int(v2, v3) = v4) | ~ $i(v3) | ? [v5: $i] : ? [v6:
% 287.08/40.88 | $i] : ((hAPP_int_bool(v1, v4) = v6 & $i(v6) & hBOOL(v6)) |
% 287.08/40.88 | (hAPP_int_bool(v0, v3) = v5 & $i(v5) & ~ hBOOL(v5)))))
% 287.08/40.88 |
% 287.08/40.88 | ALPHA: (fact_355_xt1_I5_J) implies:
% 287.08/40.88 | (20) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 287.08/40.88 | (hAPP_i1948725293t_bool(ord_less_eq_int, v0) = v2) | ~
% 287.08/40.88 | (hAPP_int_bool(v2, v1) = v3) | ~ $i(v1) | ~ $i(v0) | ~ hBOOL(v3)
% 287.08/40.88 | | ? [v4: $i] : ? [v5: $i] :
% 287.08/40.88 | (hAPP_i1948725293t_bool(ord_less_eq_int, v1) = v4 &
% 287.08/40.88 | hAPP_int_bool(v4, v0) = v5 & $i(v5) & $i(v4) & ~ hBOOL(v5)))
% 287.08/40.88 |
% 287.08/40.88 | ALPHA: (fact_1069_zdiv__mono2__neg__lemma) implies:
% 287.08/40.88 | (21) ? [v0: $i] : ? [v1: $i] : (hAPP_i1948725293t_bool(ord_less_int,
% 287.08/40.88 | zero_zero_int) = v1 & hAPP_i1948725293t_bool(ord_less_eq_int,
% 287.08/40.88 | zero_zero_int) = v0 & $i(v1) & $i(v0) & ! [v2: $i] : ! [v3: $i]
% 287.08/40.88 | : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8:
% 287.08/40.88 | $i] : ! [v9: $i] : ! [v10: $i] : ! [v11: $i] : ! [v12: $i] :
% 287.08/40.88 | ! [v13: $i] : ! [v14: $i] : ( ~
% 287.08/40.88 | (hAPP_int_fun_int_int(times_times_int, v5) = v12) | ~
% 287.08/40.88 | (hAPP_int_fun_int_int(times_times_int, v2) = v8) | ~
% 287.08/40.88 | (hAPP_int_fun_int_int(plus_plus_int, v13) = v14) | ~
% 287.08/40.88 | (hAPP_int_fun_int_int(plus_plus_int, v9) = v10) | ~
% 287.08/40.88 | (hAPP_int_int(v14, v7) = v11) | ~ (hAPP_int_int(v12, v6) = v13) |
% 287.08/40.88 | ~ (hAPP_int_int(v10, v4) = v11) | ~ (hAPP_int_int(v8, v3) = v9)
% 287.08/40.88 | | ~ $i(v7) | ~ $i(v6) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~
% 287.08/40.88 | $i(v2) | ? [v15: $i] : ? [v16: $i] : ? [v17: $i] : ? [v18: $i]
% 287.08/40.88 | : ? [v19: $i] : ? [v20: $i] : ? [v21: $i] : ? [v22: $i] : ?
% 287.08/40.88 | [v23: $i] : ? [v24: $i] : ((hAPP_i1948725293t_bool(ord_less_int,
% 287.08/40.88 | v11) = v15 & hAPP_int_bool(v15, zero_zero_int) = v16 &
% 287.08/40.88 | $i(v16) & $i(v15) & ~ hBOOL(v16)) |
% 287.08/40.88 | (hAPP_i1948725293t_bool(ord_less_int, v4) = v17 &
% 287.08/40.88 | hAPP_int_bool(v17, v2) = v18 & $i(v18) & $i(v17) & ~
% 287.08/40.88 | hBOOL(v18)) | (hAPP_i1948725293t_bool(ord_less_eq_int, v6) =
% 287.08/40.88 | v23 & hAPP_int_bool(v23, v3) = v24 & $i(v24) & $i(v23) &
% 287.08/40.88 | hBOOL(v24)) | (hAPP_i1948725293t_bool(ord_less_eq_int, v5) =
% 287.08/40.88 | v21 & hAPP_int_bool(v21, v2) = v22 & $i(v22) & $i(v21) & ~
% 287.08/40.88 | hBOOL(v22)) | (hAPP_int_bool(v1, v5) = v20 & $i(v20) & ~
% 287.08/40.88 | hBOOL(v20)) | (hAPP_int_bool(v0, v7) = v19 & $i(v19) & ~
% 287.08/40.88 | hBOOL(v19)))))
% 287.08/40.88 |
% 287.08/40.88 | ALPHA: (fact_1072_int__0__neq__1) implies:
% 287.08/40.88 | (22) ~ (zero_zero_int = one_one_int)
% 287.08/40.88 |
% 287.08/40.88 | ALPHA: (fact_1073_self__quotient__aux1) implies:
% 287.08/40.88 | (23) ? [v0: $i] : ? [v1: $i] : (hAPP_i1948725293t_bool(ord_less_int,
% 287.08/40.88 | zero_zero_int) = v0 & hAPP_i1948725293t_bool(ord_less_eq_int,
% 287.08/40.88 | one_one_int) = v1 & $i(v1) & $i(v0) & ! [v2: $i] : ! [v3: $i] :
% 287.08/40.88 | ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ( ~
% 287.08/40.88 | (hAPP_int_fun_int_int(times_times_int, v4) = v6) | ~
% 287.08/40.88 | (hAPP_int_fun_int_int(plus_plus_int, v2) = v5) | ~
% 287.08/40.88 | (hAPP_int_int(v6, v3) = v7) | ~ (hAPP_int_int(v5, v7) = v4) | ~
% 287.08/40.88 | $i(v4) | ~ $i(v3) | ~ $i(v2) | ? [v8: $i] : ? [v9: $i] : ?
% 287.08/40.88 | [v10: $i] : ? [v11: $i] : ((hAPP_i1948725293t_bool(ord_less_int,
% 287.08/40.88 | v2) = v9 & hAPP_int_bool(v9, v4) = v10 & $i(v10) & $i(v9) &
% 287.08/40.88 | ~ hBOOL(v10)) | (hAPP_int_bool(v1, v3) = v11 & $i(v11) &
% 287.08/40.88 | hBOOL(v11)) | (hAPP_int_bool(v0, v4) = v8 & $i(v8) & ~
% 287.08/40.88 | hBOOL(v8)))))
% 287.08/40.88 |
% 287.08/40.88 | ALPHA: (fact_1074_self__quotient__aux2) implies:
% 287.08/40.88 | (24) ? [v0: $i] : ? [v1: $i] : (hAPP_i1948725293t_bool(ord_less_int,
% 287.08/40.88 | zero_zero_int) = v0 & hAPP_i1948725293t_bool(ord_less_eq_int,
% 287.08/40.88 | zero_zero_int) = v1 & $i(v1) & $i(v0) & ! [v2: $i] : ! [v3: $i]
% 287.08/40.88 | : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ( ~
% 287.08/40.88 | (hAPP_int_fun_int_int(times_times_int, v4) = v6) | ~
% 287.08/40.88 | (hAPP_int_fun_int_int(plus_plus_int, v2) = v5) | ~
% 287.08/40.88 | (hAPP_int_int(v6, v3) = v7) | ~ (hAPP_int_int(v5, v7) = v4) | ~
% 287.08/40.88 | $i(v4) | ~ $i(v3) | ~ $i(v2) | ? [v8: $i] : ? [v9: $i] : ?
% 287.08/40.88 | [v10: $i] : ? [v11: $i] :
% 287.08/40.88 | ((hAPP_i1948725293t_bool(ord_less_eq_int, v3) = v10 &
% 287.08/40.88 | hAPP_int_bool(v10, one_one_int) = v11 & $i(v11) & $i(v10) &
% 287.08/40.88 | hBOOL(v11)) | (hAPP_int_bool(v1, v2) = v9 & $i(v9) & ~
% 287.08/40.88 | hBOOL(v9)) | (hAPP_int_bool(v0, v4) = v8 & $i(v8) & ~
% 287.08/40.88 | hBOOL(v8)))))
% 287.08/40.88 |
% 287.08/40.88 | ALPHA: (fact_1075_q__pos__lemma) implies:
% 287.08/40.88 | (25) ? [v0: $i] : ? [v1: $i] : (hAPP_i1948725293t_bool(ord_less_int,
% 287.08/40.88 | zero_zero_int) = v1 & hAPP_i1948725293t_bool(ord_less_eq_int,
% 287.08/40.88 | zero_zero_int) = v0 & $i(v1) & $i(v0) & ! [v2: $i] : ! [v3: $i]
% 287.08/40.88 | : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8:
% 287.08/40.88 | $i] : ( ~ (hAPP_int_fun_int_int(times_times_int, v2) = v5) | ~
% 287.08/40.88 | (hAPP_int_fun_int_int(plus_plus_int, v6) = v7) | ~
% 287.08/40.88 | (hAPP_int_int(v7, v4) = v8) | ~ (hAPP_int_int(v5, v3) = v6) | ~
% 287.08/40.88 | $i(v4) | ~ $i(v3) | ~ $i(v2) | ? [v9: $i] : ? [v10: $i] : ?
% 287.08/40.88 | [v11: $i] : ? [v12: $i] : ? [v13: $i] :
% 287.08/40.88 | ((hAPP_i1948725293t_bool(ord_less_int, v4) = v10 &
% 287.08/40.88 | hAPP_int_bool(v10, v2) = v11 & $i(v11) & $i(v10) & ~
% 287.08/40.88 | hBOOL(v11)) | (hAPP_int_bool(v1, v2) = v12 & $i(v12) & ~
% 287.08/40.88 | hBOOL(v12)) | (hAPP_int_bool(v0, v8) = v9 & $i(v9) & ~
% 287.08/40.88 | hBOOL(v9)) | (hAPP_int_bool(v0, v3) = v13 & $i(v13) &
% 287.08/40.88 | hBOOL(v13)))))
% 287.08/40.88 |
% 287.08/40.88 | ALPHA: (fact_1076_q__neg__lemma) implies:
% 287.08/40.89 | (26) ? [v0: $i] : ? [v1: $i] : (hAPP_i1948725293t_bool(ord_less_int,
% 287.08/40.89 | zero_zero_int) = v1 & hAPP_i1948725293t_bool(ord_less_eq_int,
% 287.08/40.89 | zero_zero_int) = v0 & $i(v1) & $i(v0) & ! [v2: $i] : ! [v3: $i]
% 287.08/40.89 | : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8:
% 287.08/40.89 | $i] : ( ~ (hAPP_int_fun_int_int(times_times_int, v2) = v5) | ~
% 287.08/40.89 | (hAPP_int_fun_int_int(plus_plus_int, v6) = v7) | ~
% 287.08/40.89 | (hAPP_int_int(v7, v4) = v8) | ~ (hAPP_int_int(v5, v3) = v6) | ~
% 287.08/40.89 | $i(v4) | ~ $i(v3) | ~ $i(v2) | ? [v9: $i] : ? [v10: $i] : ?
% 287.08/40.89 | [v11: $i] : ? [v12: $i] : ? [v13: $i] : ? [v14: $i] :
% 287.08/40.89 | ((hAPP_i1948725293t_bool(ord_less_int, v8) = v9 &
% 287.08/40.89 | hAPP_int_bool(v9, zero_zero_int) = v10 & $i(v10) & $i(v9) & ~
% 287.08/40.89 | hBOOL(v10)) | (hAPP_i1948725293t_bool(ord_less_eq_int, v3) =
% 287.08/40.89 | v13 & hAPP_int_bool(v13, zero_zero_int) = v14 & $i(v14) &
% 287.08/40.89 | $i(v13) & hBOOL(v14)) | (hAPP_int_bool(v1, v2) = v12 & $i(v12)
% 287.08/40.89 | & ~ hBOOL(v12)) | (hAPP_int_bool(v0, v4) = v11 & $i(v11) & ~
% 287.08/40.89 | hBOOL(v11)))))
% 287.08/40.89 |
% 287.08/40.89 | ALPHA: (fact_1077_unique__quotient__lemma) implies:
% 287.08/40.89 | (27) ? [v0: $i] : (hAPP_i1948725293t_bool(ord_less_eq_int, zero_zero_int)
% 287.08/40.89 | = v0 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4:
% 287.08/40.89 | $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : !
% 287.08/40.89 | [v9: $i] : ! [v10: $i] : ! [v11: $i] : ! [v12: $i] : ! [v13: $i]
% 287.08/40.89 | : ! [v14: $i] : ( ~ (hAPP_int_fun_int_int(times_times_int, v1) =
% 287.08/40.89 | v6) | ~ (hAPP_int_fun_int_int(plus_plus_int, v11) = v12) | ~
% 287.08/40.89 | (hAPP_int_fun_int_int(plus_plus_int, v7) = v8) | ~
% 287.08/40.89 | (hAPP_int_int(v12, v5) = v13) | ~ (hAPP_int_int(v8, v3) = v9) |
% 287.08/40.89 | ~ (hAPP_int_int(v6, v4) = v11) | ~ (hAPP_int_int(v6, v2) = v7) |
% 287.08/40.89 | ~ (hAPP_i1948725293t_bool(ord_less_eq_int, v9) = v10) | ~
% 287.08/40.89 | (hAPP_int_bool(v10, v13) = v14) | ~ $i(v5) | ~ $i(v4) | ~
% 287.08/40.89 | $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ hBOOL(v14) | ? [v15: $i] : ?
% 287.08/40.89 | [v16: $i] : ? [v17: $i] : ? [v18: $i] : ? [v19: $i] : ? [v20:
% 287.08/40.89 | $i] : ? [v21: $i] : ((hAPP_i1948725293t_bool(ord_less_int, v5)
% 287.08/40.89 | = v18 & hAPP_int_bool(v18, v1) = v19 & $i(v19) & $i(v18) & ~
% 287.08/40.89 | hBOOL(v19)) | (hAPP_i1948725293t_bool(ord_less_int, v3) = v16
% 287.08/40.89 | & hAPP_int_bool(v16, v1) = v17 & $i(v17) & $i(v16) & ~
% 287.08/40.89 | hBOOL(v17)) | (hAPP_i1948725293t_bool(ord_less_eq_int, v2) =
% 287.08/40.89 | v20 & hAPP_int_bool(v20, v4) = v21 & $i(v21) & $i(v20) &
% 287.08/40.89 | hBOOL(v21)) | (hAPP_int_bool(v0, v3) = v15 & $i(v15) & ~
% 287.08/40.89 | hBOOL(v15)))))
% 287.08/40.89 |
% 287.08/40.89 | ALPHA: (fact_1078_zdiv__mono2__lemma) implies:
% 287.08/40.89 | (28) ? [v0: $i] : ? [v1: $i] : (hAPP_i1948725293t_bool(ord_less_int,
% 287.08/40.89 | zero_zero_int) = v1 & hAPP_i1948725293t_bool(ord_less_eq_int,
% 287.08/40.89 | zero_zero_int) = v0 & $i(v1) & $i(v0) & ! [v2: $i] : ! [v3: $i]
% 287.08/40.89 | : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8:
% 287.08/40.89 | $i] : ! [v9: $i] : ! [v10: $i] : ! [v11: $i] : ! [v12: $i] :
% 287.08/40.89 | ! [v13: $i] : ! [v14: $i] : ( ~
% 287.08/40.89 | (hAPP_int_fun_int_int(times_times_int, v5) = v12) | ~
% 287.08/40.89 | (hAPP_int_fun_int_int(times_times_int, v2) = v8) | ~
% 287.08/40.89 | (hAPP_int_fun_int_int(plus_plus_int, v13) = v14) | ~
% 287.08/40.89 | (hAPP_int_fun_int_int(plus_plus_int, v9) = v10) | ~
% 287.08/40.89 | (hAPP_int_int(v14, v7) = v11) | ~ (hAPP_int_int(v12, v6) = v13) |
% 287.08/40.89 | ~ (hAPP_int_int(v10, v4) = v11) | ~ (hAPP_int_int(v8, v3) = v9)
% 287.08/40.89 | | ~ $i(v7) | ~ $i(v6) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~
% 287.08/40.89 | $i(v2) | ? [v15: $i] : ? [v16: $i] : ? [v17: $i] : ? [v18: $i]
% 287.08/40.89 | : ? [v19: $i] : ? [v20: $i] : ? [v21: $i] : ? [v22: $i] : ?
% 287.08/40.89 | [v23: $i] : ((hAPP_i1948725293t_bool(ord_less_int, v7) = v16 &
% 287.08/40.89 | hAPP_int_bool(v16, v5) = v17 & $i(v17) & $i(v16) & ~
% 287.08/40.89 | hBOOL(v17)) | (hAPP_i1948725293t_bool(ord_less_eq_int, v5) =
% 287.08/40.89 | v20 & hAPP_int_bool(v20, v2) = v21 & $i(v21) & $i(v20) & ~
% 287.08/40.89 | hBOOL(v21)) | (hAPP_i1948725293t_bool(ord_less_eq_int, v3) =
% 287.08/40.89 | v22 & hAPP_int_bool(v22, v6) = v23 & $i(v23) & $i(v22) &
% 287.08/40.89 | hBOOL(v23)) | (hAPP_int_bool(v1, v5) = v19 & $i(v19) & ~
% 287.08/40.89 | hBOOL(v19)) | (hAPP_int_bool(v0, v11) = v15 & $i(v15) & ~
% 287.08/40.89 | hBOOL(v15)) | (hAPP_int_bool(v0, v4) = v18 & $i(v18) & ~
% 287.08/40.89 | hBOOL(v18)))))
% 287.08/40.89 |
% 287.08/40.89 | ALPHA: (fact_1083_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J)
% 287.08/40.89 | implies:
% 287.08/40.89 | (29) ? [v0: $i] : (hAPP_i1948725293t_bool(ord_less_eq_int, zero_zero_int)
% 287.08/40.89 | = v0 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4:
% 287.08/40.89 | $i] : ( ~ (hAPP_int_bool(v0, v2) = v3) | ~ (hAPP_int_bool(v0, v1)
% 287.08/40.89 | = v4) | ~ $i(v2) | ~ $i(v1) | ~ hBOOL(v4) | ~ hBOOL(v3) | ?
% 287.08/40.89 | [v5: $i] : ? [v6: $i] : ? [v7: $i] :
% 287.08/40.89 | (hAPP_int_fun_int_int(times_times_int, v2) = v5 & hAPP_int_int(v5,
% 287.08/40.89 | v1) = v6 & hAPP_int_bool(v0, v6) = v7 & $i(v7) & $i(v6) &
% 287.08/40.89 | $i(v5) & hBOOL(v7))))
% 287.08/40.89 |
% 287.08/40.89 | ALPHA: (fact_1084_Nat__Transfer_Otransfer__nat__int__function__closures_I5_J)
% 287.08/40.89 | implies:
% 287.08/40.89 | (30) ? [v0: $i] : ? [v1: $i] : (hAPP_i1948725293t_bool(ord_less_eq_int,
% 287.08/40.89 | zero_zero_int) = v0 & hAPP_int_bool(v0, zero_zero_int) = v1 &
% 287.08/40.89 | $i(v1) & $i(v0) & hBOOL(v1))
% 287.08/40.89 |
% 287.08/40.89 | ALPHA: (fact_1085_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J)
% 287.08/40.89 | implies:
% 287.08/40.89 | (31) ? [v0: $i] : (hAPP_i1948725293t_bool(ord_less_eq_int, zero_zero_int)
% 287.08/40.89 | = v0 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4:
% 287.08/40.89 | $i] : ( ~ (hAPP_int_bool(v0, v2) = v3) | ~ (hAPP_int_bool(v0, v1)
% 287.08/40.89 | = v4) | ~ $i(v2) | ~ $i(v1) | ~ hBOOL(v4) | ~ hBOOL(v3) | ?
% 287.08/40.89 | [v5: $i] : ? [v6: $i] : ? [v7: $i] :
% 287.08/40.89 | (hAPP_int_fun_int_int(plus_plus_int, v2) = v5 & hAPP_int_int(v5,
% 287.08/40.89 | v1) = v6 & hAPP_int_bool(v0, v6) = v7 & $i(v7) & $i(v6) &
% 287.08/40.89 | $i(v5) & hBOOL(v7))))
% 287.08/40.89 |
% 287.08/40.89 | ALPHA: (fact_1086_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J)
% 287.08/40.89 | implies:
% 287.08/40.89 | (32) ? [v0: $i] : ? [v1: $i] : (hAPP_i1948725293t_bool(ord_less_eq_int,
% 287.08/40.89 | zero_zero_int) = v0 & hAPP_int_bool(v0, one_one_int) = v1 & $i(v1)
% 287.08/40.89 | & $i(v0) & hBOOL(v1))
% 287.08/40.89 |
% 287.08/40.89 | ALPHA: (fact_1087_transfer__nat__int__set__cong) implies:
% 287.08/40.89 | (33) ? [v0: $i] : ? [v1: $i] : (hAPP_i1948725293t_bool(ord_less_eq_int,
% 287.08/40.89 | zero_zero_int) = v0 & cOMBB_1652995168ol_int(fconj, v0) = v1 &
% 287.08/40.89 | $i(v1) & $i(v0) & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 287.08/40.89 | $i] : ( ~ (cOMBS_int_bool_bool(v1, v3) = v4) | ~
% 287.08/40.89 | (cOMBS_int_bool_bool(v1, v2) = v5) | ~ $i(v3) | ~ $i(v2) | ?
% 287.08/40.89 | [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ? [v10: $i]
% 287.08/40.89 | : ? [v11: $i] : ($i(v8) & ((v7 = v6 & collect_int(v5) = v6 &
% 287.08/40.89 | collect_int(v4) = v6 & $i(v6)) | (hAPP_int_bool(v0, v8) = v9
% 287.08/40.89 | & $i(v9) & hBOOL(v9) & ((hAPP_int_bool(v3, v8) = v10 &
% 287.08/40.89 | $i(v10) & hBOOL(v10)) | (hAPP_int_bool(v2, v8) = v11 &
% 287.08/40.89 | $i(v11) & hBOOL(v11))) & ((hAPP_int_bool(v3, v8) = v10 &
% 287.08/40.89 | $i(v10) & ~ hBOOL(v10)) | (hAPP_int_bool(v2, v8) = v11
% 287.08/40.89 | & $i(v11) & ~ hBOOL(v11))))))))
% 287.08/40.89 |
% 287.08/40.89 | ALPHA: (fact_1088_decr__mult__lemma) implies:
% 287.08/40.90 | (34) ? [v0: $i] : ? [v1: $i] : (hAPP_i1948725293t_bool(ord_less_int,
% 287.08/40.90 | zero_zero_int) = v0 & hAPP_i1948725293t_bool(ord_less_eq_int,
% 287.08/40.90 | zero_zero_int) = v1 & $i(v1) & $i(v0) & ? [v2: $i] : ! [v3: $i]
% 287.08/40.90 | : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~ (hAPP_int_bool(v1,
% 287.08/40.90 | v3) = v6) | ~ (hAPP_int_bool(v0, v4) = v5) | ~ $i(v4) | ~
% 287.08/40.90 | $i(v3) | ~ $i(v2) | ~ hBOOL(v6) | ~ hBOOL(v5) | ? [v7: $i] :
% 287.08/40.90 | ? [v8: $i] : ? [v9: $i] : ? [v10: $i] : ? [v11: $i] : ? [v12:
% 287.08/40.90 | $i] : ? [v13: $i] : ($i(v9) &
% 287.08/40.90 | ((hAPP_int_fun_int_int(times_times_int, v3) = v7 &
% 287.08/40.90 | hAPP_int_int(v7, v4) = v8 & $i(v8) & $i(v7) & ! [v14: $i] :
% 287.08/40.90 | ! [v15: $i] : ! [v16: $i] : ! [v17: $i] : ( ~
% 287.08/40.90 | (hAPP_int_fun_int_int(minus_minus_int, v14) = v15) | ~
% 287.08/40.90 | (hAPP_int_int(v15, v8) = v16) | ~ (hAPP_int_bool(v2, v16)
% 287.08/40.90 | = v17) | ~ $i(v14) | hBOOL(v17) | ? [v18: $i] :
% 287.08/40.90 | (hAPP_int_bool(v2, v14) = v18 & $i(v18) & ~ hBOOL(v18))))
% 287.08/40.90 | | (hAPP_int_fun_int_int(minus_minus_int, v9) = v11 &
% 287.08/40.90 | hAPP_int_int(v11, v4) = v12 & hAPP_int_bool(v2, v12) = v13 &
% 287.08/40.90 | hAPP_int_bool(v2, v9) = v10 & $i(v13) & $i(v12) & $i(v11) &
% 287.08/40.90 | $i(v10) & hBOOL(v10) & ~ hBOOL(v13))))))
% 287.08/40.90 |
% 287.08/40.90 | ALPHA: (fact_1090_imp__le__cong) implies:
% 287.08/40.90 | (35) ? [v0: $i] : (hAPP_i1948725293t_bool(ord_less_eq_int, zero_zero_int)
% 287.08/40.90 | = v0 & $i(v0))
% 287.08/40.90 |
% 287.08/40.90 | ALPHA: (fact_1091_incr__mult__lemma) implies:
% 287.45/40.90 | (36) ? [v0: $i] : ? [v1: $i] : (hAPP_i1948725293t_bool(ord_less_int,
% 287.45/40.90 | zero_zero_int) = v0 & hAPP_i1948725293t_bool(ord_less_eq_int,
% 287.45/40.90 | zero_zero_int) = v1 & $i(v1) & $i(v0) & ? [v2: $i] : ! [v3: $i]
% 287.45/40.90 | : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~ (hAPP_int_bool(v1,
% 287.45/40.90 | v3) = v6) | ~ (hAPP_int_bool(v0, v4) = v5) | ~ $i(v4) | ~
% 287.45/40.90 | $i(v3) | ~ $i(v2) | ~ hBOOL(v6) | ~ hBOOL(v5) | ? [v7: $i] :
% 287.45/40.90 | ? [v8: $i] : ? [v9: $i] : ? [v10: $i] : ? [v11: $i] : ? [v12:
% 287.45/40.90 | $i] : ? [v13: $i] : ($i(v9) &
% 287.45/40.90 | ((hAPP_int_fun_int_int(times_times_int, v3) = v7 &
% 287.45/40.90 | hAPP_int_int(v7, v4) = v8 & $i(v8) & $i(v7) & ! [v14: $i] :
% 287.45/40.90 | ! [v15: $i] : ! [v16: $i] : ! [v17: $i] : ( ~
% 287.45/40.90 | (hAPP_int_fun_int_int(plus_plus_int, v14) = v15) | ~
% 287.45/40.90 | (hAPP_int_int(v15, v8) = v16) | ~ (hAPP_int_bool(v2, v16)
% 287.45/40.90 | = v17) | ~ $i(v14) | hBOOL(v17) | ? [v18: $i] :
% 287.45/40.90 | (hAPP_int_bool(v2, v14) = v18 & $i(v18) & ~ hBOOL(v18))))
% 287.45/40.90 | | (hAPP_int_fun_int_int(plus_plus_int, v9) = v11 &
% 287.45/40.90 | hAPP_int_int(v11, v4) = v12 & hAPP_int_bool(v2, v12) = v13 &
% 287.45/40.90 | hAPP_int_bool(v2, v9) = v10 & $i(v13) & $i(v12) & $i(v11) &
% 287.45/40.90 | $i(v10) & hBOOL(v10) & ~ hBOOL(v13))))))
% 287.45/40.90 |
% 287.45/40.90 | ALPHA: (fact_1093_minusinfinity) implies:
% 287.45/40.90 | (37) ? [v0: $i] : (hAPP_i1948725293t_bool(ord_less_int, zero_zero_int) =
% 287.45/40.90 | v0 & $i(v0) & ? [v1: $i] : ? [v2: $i] : ! [v3: $i] : ! [v4: $i]
% 287.45/40.90 | : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ( ~ (hAPP_int_bool(v3,
% 287.45/40.90 | v6) = v7) | ~ (hAPP_int_bool(v0, v4) = v5) | ~ $i(v6) | ~
% 287.45/40.90 | $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ hBOOL(v7) | ~
% 287.45/40.90 | hBOOL(v5) | ? [v8: $i] : ? [v9: $i] : ? [v10: $i] : ? [v11:
% 287.45/40.90 | $i] : ? [v12: $i] : ? [v13: $i] : ? [v14: $i] : ? [v15: $i]
% 287.45/40.90 | : ? [v16: $i] : ? [v17: $i] : ? [v18: $i] : ? [v19: $i] : ?
% 287.45/40.90 | [v20: $i] : ? [v21: $i] : ? [v22: $i] : ($i(v16) & $i(v15) &
% 287.45/40.90 | $i(v10) & $i(v8) & ((hAPP_i1948725293t_bool(ord_less_int, v10) =
% 287.45/40.90 | v11 & hAPP_int_bool(v11, v2) = v12 & $i(v12) & $i(v11) &
% 287.45/40.90 | hBOOL(v12) & ((hAPP_int_bool(v3, v10) = v14 & $i(v14) &
% 287.45/40.90 | hBOOL(v14)) | (hAPP_int_bool(v1, v10) = v13 & $i(v13) &
% 287.45/40.90 | hBOOL(v13))) & ((hAPP_int_bool(v3, v10) = v14 & $i(v14)
% 287.45/40.90 | & ~ hBOOL(v14)) | (hAPP_int_bool(v1, v10) = v13 &
% 287.45/40.90 | $i(v13) & ~ hBOOL(v13)))) | (hAPP_int_bool(v1, v8) = v9
% 287.45/40.90 | & $i(v9) & hBOOL(v9)) |
% 287.45/40.90 | (((hAPP_int_fun_int_int(times_times_int, v16) = v19 &
% 287.45/40.90 | hAPP_int_fun_int_int(minus_minus_int, v15) = v18 &
% 287.45/40.90 | hAPP_int_int(v19, v4) = v20 & hAPP_int_int(v18, v20) =
% 287.45/40.90 | v21 & hAPP_int_bool(v3, v21) = v22 & $i(v22) & $i(v21) &
% 287.45/40.90 | $i(v20) & $i(v19) & $i(v18) & hBOOL(v22)) |
% 287.45/40.90 | (hAPP_int_bool(v3, v15) = v17 & $i(v17) & hBOOL(v17))) &
% 287.45/40.90 | ((hAPP_int_fun_int_int(times_times_int, v16) = v19 &
% 287.45/40.90 | hAPP_int_fun_int_int(minus_minus_int, v15) = v18 &
% 287.45/40.90 | hAPP_int_int(v19, v4) = v20 & hAPP_int_int(v18, v20) =
% 287.45/40.90 | v21 & hAPP_int_bool(v3, v21) = v22 & $i(v22) & $i(v21) &
% 287.45/40.90 | $i(v20) & $i(v19) & $i(v18) & ~ hBOOL(v22)) |
% 287.45/40.90 | (hAPP_int_bool(v3, v15) = v17 & $i(v17) & ~
% 287.45/40.90 | hBOOL(v17))))))))
% 287.45/40.90 |
% 287.45/40.90 | ALPHA: (fact_1094_plusinfinity) implies:
% 287.45/40.90 | (38) ? [v0: $i] : (hAPP_i1948725293t_bool(ord_less_int, zero_zero_int) =
% 287.45/40.90 | v0 & $i(v0) & ? [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i]
% 287.45/40.90 | : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ( ~
% 287.45/40.90 | (hAPP_i1948725293t_bool(ord_less_int, v7) = v8) | ~
% 287.45/40.90 | (hAPP_int_bool(v2, v5) = v6) | ~ (hAPP_int_bool(v0, v3) = v4) |
% 287.45/40.90 | ~ $i(v7) | ~ $i(v5) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~
% 287.45/40.90 | hBOOL(v6) | ~ hBOOL(v4) | ? [v9: $i] : ? [v10: $i] : ? [v11:
% 287.45/40.90 | $i] : ? [v12: $i] : ? [v13: $i] : ? [v14: $i] : ? [v15: $i]
% 287.45/40.90 | : ? [v16: $i] : ? [v17: $i] : ? [v18: $i] : ? [v19: $i] : ?
% 287.45/40.90 | [v20: $i] : ? [v21: $i] : ? [v22: $i] : ($i(v16) & $i(v15) &
% 287.45/40.90 | $i(v11) & $i(v9) & ((hAPP_int_bool(v8, v11) = v12 & $i(v12) &
% 287.45/40.90 | hBOOL(v12) & ((hAPP_int_bool(v2, v11) = v14 & $i(v14) &
% 287.45/40.90 | hBOOL(v14)) | (hAPP_int_bool(v1, v11) = v13 & $i(v13) &
% 287.45/40.90 | hBOOL(v13))) & ((hAPP_int_bool(v2, v11) = v14 & $i(v14)
% 287.45/40.90 | & ~ hBOOL(v14)) | (hAPP_int_bool(v1, v11) = v13 &
% 287.45/40.90 | $i(v13) & ~ hBOOL(v13)))) | (hAPP_int_bool(v1, v9) =
% 287.45/40.90 | v10 & $i(v10) & hBOOL(v10)) |
% 287.45/40.90 | (((hAPP_int_fun_int_int(times_times_int, v16) = v19 &
% 287.45/40.90 | hAPP_int_fun_int_int(minus_minus_int, v15) = v18 &
% 287.45/40.90 | hAPP_int_int(v19, v3) = v20 & hAPP_int_int(v18, v20) =
% 287.45/40.90 | v21 & hAPP_int_bool(v2, v21) = v22 & $i(v22) & $i(v21) &
% 287.45/40.90 | $i(v20) & $i(v19) & $i(v18) & hBOOL(v22)) |
% 287.45/40.90 | (hAPP_int_bool(v2, v15) = v17 & $i(v17) & hBOOL(v17))) &
% 287.45/40.90 | ((hAPP_int_fun_int_int(times_times_int, v16) = v19 &
% 287.45/40.90 | hAPP_int_fun_int_int(minus_minus_int, v15) = v18 &
% 287.45/40.90 | hAPP_int_int(v19, v3) = v20 & hAPP_int_int(v18, v20) =
% 287.45/40.90 | v21 & hAPP_int_bool(v2, v21) = v22 & $i(v22) & $i(v21) &
% 287.45/40.90 | $i(v20) & $i(v19) & $i(v18) & ~ hBOOL(v22)) |
% 287.45/40.90 | (hAPP_int_bool(v2, v15) = v17 & $i(v17) & ~
% 287.45/40.90 | hBOOL(v17))))))))
% 287.45/40.90 |
% 287.45/40.90 | ALPHA: (fact_1116_transfer__int__nat__numerals_I1_J) implies:
% 287.45/40.90 | (39) hAPP_nat_int(semiri1621563631at_int, zero_zero_nat) = zero_zero_int
% 287.45/40.90 |
% 287.45/40.90 | ALPHA: (fact_1117_Nat__Transfer_Otransfer__int__nat__set__functions_I5_J)
% 287.45/40.90 | implies:
% 287.45/40.91 | (40) ? [v0: $i] : ? [v1: $i] : (hAPP_i1948725293t_bool(ord_less_eq_int,
% 287.45/40.91 | zero_zero_int) = v0 & cOMBB_1652995168ol_int(fconj, v0) = v1 &
% 287.45/40.91 | $i(v1) & $i(v0) & ! [v2: $i] : ! [v3: $i] : ( ~
% 287.45/40.91 | (cOMBS_int_bool_bool(v1, v2) = v3) | ~ $i(v2) | ? [v4: $i] : ?
% 287.45/40.91 | [v5: $i] : ? [v6: $i] : (cOMBB_int_bool_nat(v2,
% 287.45/40.91 | semiri1621563631at_int) = v5 & collect_int(v3) = v4 &
% 287.45/40.91 | collect_nat(v5) = v6 & image_nat_int(semiri1621563631at_int, v6)
% 287.45/40.91 | = v4 & $i(v6) & $i(v5) & $i(v4))))
% 287.45/40.91 |
% 287.45/40.91 | ALPHA: (fact_1118_Nat__Transfer_Otransfer__nat__int__function__closures_I9_J)
% 287.45/40.91 | implies:
% 287.45/40.91 | (41) ? [v0: $i] : (hAPP_i1948725293t_bool(ord_less_eq_int, zero_zero_int)
% 287.45/40.91 | = v0 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ( ~
% 287.45/40.91 | (hAPP_nat_int(semiri1621563631at_int, v1) = v2) | ~ $i(v1) | ?
% 287.45/40.91 | [v3: $i] : (hAPP_int_bool(v0, v2) = v3 & $i(v3) & hBOOL(v3))))
% 287.45/40.91 |
% 287.45/40.91 | ALPHA: (fact_1119_transfer__int__nat__quantifiers_I2_J) implies:
% 287.45/40.91 | (42) ? [v0: $i] : (hAPP_i1948725293t_bool(ord_less_eq_int, zero_zero_int)
% 287.45/40.91 | = v0 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4:
% 287.45/40.91 | $i] : ( ~ (hAPP_nat_int(semiri1621563631at_int, v2) = v3) | ~
% 287.45/40.91 | (hAPP_int_bool(v1, v3) = v4) | ~ $i(v2) | ~ $i(v1) | ~
% 287.45/40.91 | hBOOL(v4) | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] :
% 287.45/40.91 | (hAPP_int_bool(v1, v5) = v7 & hAPP_int_bool(v0, v5) = v6 & $i(v7)
% 287.45/40.91 | & $i(v6) & $i(v5) & hBOOL(v7) & hBOOL(v6))) & ? [v1: $i] : !
% 287.45/40.91 | [v2: $i] : ! [v3: $i] : ( ~ (hAPP_int_bool(v0, v2) = v3) | ~
% 287.45/40.91 | $i(v2) | ~ $i(v1) | ~ hBOOL(v3) | ? [v4: $i] : ? [v5: $i] : ?
% 287.45/40.91 | [v6: $i] : ? [v7: $i] : ($i(v4) &
% 287.45/40.91 | ((hAPP_nat_int(semiri1621563631at_int, v4) = v5 &
% 287.45/40.91 | hAPP_int_bool(v1, v5) = v6 & $i(v6) & $i(v5) & hBOOL(v6)) |
% 287.45/40.91 | (hAPP_int_bool(v1, v2) = v7 & $i(v7) & ~ hBOOL(v7))))))
% 287.45/40.91 |
% 287.45/40.91 | ALPHA: (fact_1120_transfer__int__nat__quantifiers_I1_J) implies:
% 287.45/40.91 | (43) ? [v0: $i] : (hAPP_i1948725293t_bool(ord_less_eq_int, zero_zero_int)
% 287.45/40.91 | = v0 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4:
% 287.45/40.91 | $i] : ( ~ (hAPP_nat_int(semiri1621563631at_int, v2) = v3) | ~
% 287.45/40.91 | (hAPP_int_bool(v1, v3) = v4) | ~ $i(v2) | ~ $i(v1) | hBOOL(v4) |
% 287.45/40.91 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : (hAPP_int_bool(v1, v5) =
% 287.45/40.91 | v7 & hAPP_int_bool(v0, v5) = v6 & $i(v7) & $i(v6) & $i(v5) &
% 287.45/40.91 | hBOOL(v6) & ~ hBOOL(v7))) & ? [v1: $i] : ! [v2: $i] : ! [v3:
% 287.45/40.91 | $i] : ( ~ (hAPP_int_bool(v0, v2) = v3) | ~ $i(v2) | ~ $i(v1) |
% 287.45/40.91 | ~ hBOOL(v3) | ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7:
% 287.45/40.91 | $i] : ($i(v5) & ((hAPP_nat_int(semiri1621563631at_int, v5) = v6
% 287.45/40.91 | & hAPP_int_bool(v1, v6) = v7 & $i(v7) & $i(v6) & ~
% 287.45/40.91 | hBOOL(v7)) | (hAPP_int_bool(v1, v2) = v4 & $i(v4) &
% 287.45/40.91 | hBOOL(v4))))))
% 287.45/40.91 |
% 287.45/40.91 | ALPHA: (fact_1122_int__Suc0__eq__1) implies:
% 287.45/40.91 | (44) ? [v0: $i] : (hAPP_nat_int(semiri1621563631at_int, v0) = one_one_int
% 287.45/40.91 | & hAPP_nat_nat(suc, zero_zero_nat) = v0 & $i(v0))
% 287.45/40.91 |
% 287.45/40.91 | ALPHA: (fact_1126_zero__less__int__conv) implies:
% 287.45/40.91 | (45) ? [v0: $i] : ? [v1: $i] : (hAPP_i1948725293t_bool(ord_less_int,
% 287.45/40.91 | zero_zero_int) = v0 & hAPP_n1699378549t_bool(ord_less_nat,
% 287.45/40.91 | zero_zero_nat) = v1 & $i(v1) & $i(v0) & ! [v2: $i] : ! [v3: $i]
% 287.45/40.91 | : ( ~ (hAPP_nat_bool(v1, v2) = v3) | ~ $i(v2) | ~ hBOOL(v3) | ?
% 287.45/40.91 | [v4: $i] : ? [v5: $i] : (hAPP_nat_int(semiri1621563631at_int, v2)
% 287.45/40.91 | = v4 & hAPP_int_bool(v0, v4) = v5 & $i(v5) & $i(v4) &
% 287.45/40.91 | hBOOL(v5))) & ! [v2: $i] : ! [v3: $i] : ( ~ (hAPP_nat_bool(v1,
% 287.45/40.91 | v2) = v3) | ~ $i(v2) | hBOOL(v3) | ? [v4: $i] : ? [v5: $i]
% 287.45/40.91 | : (hAPP_nat_int(semiri1621563631at_int, v2) = v4 &
% 287.45/40.91 | hAPP_int_bool(v0, v4) = v5 & $i(v5) & $i(v4) & ~ hBOOL(v5))))
% 287.45/40.91 |
% 287.45/40.91 | ALPHA: (fact_1128_Nat__Transfer_Otransfer__nat__int__function__closures_I3_J)
% 287.45/40.91 | implies:
% 287.45/40.91 | (46) ? [v0: $i] : (hAPP_i1948725293t_bool(ord_less_eq_int, zero_zero_int)
% 287.45/40.91 | = v0 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4:
% 287.45/40.91 | $i] : ( ~ (hAPP_int_bool(v0, v2) = v3) | ~ (hAPP_int_bool(v0, v1)
% 287.45/40.91 | = v4) | ~ $i(v2) | ~ $i(v1) | ~ hBOOL(v4) | ~ hBOOL(v3) | ?
% 287.45/40.91 | [v5: $i] : ? [v6: $i] : ? [v7: $i] :
% 287.45/40.91 | (hAPP_int_fun_int_int(nat_tsub, v2) = v5 & hAPP_int_int(v5, v1) =
% 287.45/40.91 | v6 & hAPP_int_bool(v0, v6) = v7 & $i(v7) & $i(v6) & $i(v5) &
% 287.45/40.91 | hBOOL(v7))))
% 287.45/40.91 |
% 287.45/40.91 | ALPHA: (fact_1131_zero__less__imp__eq__int) implies:
% 287.45/40.91 | (47) ? [v0: $i] : ? [v1: $i] : (hAPP_i1948725293t_bool(ord_less_int,
% 287.45/40.91 | zero_zero_int) = v0 & hAPP_n1699378549t_bool(ord_less_nat,
% 287.45/40.91 | zero_zero_nat) = v1 & $i(v1) & $i(v0) & ! [v2: $i] : ! [v3: $i]
% 287.45/40.91 | : ( ~ (hAPP_int_bool(v0, v2) = v3) | ~ $i(v2) | ~ hBOOL(v3) | ?
% 287.45/40.91 | [v4: $i] : ? [v5: $i] : (hAPP_nat_int(semiri1621563631at_int, v4)
% 287.45/40.91 | = v2 & hAPP_nat_bool(v1, v4) = v5 & $i(v5) & $i(v4) &
% 287.45/40.91 | hBOOL(v5))))
% 287.45/40.91 |
% 287.45/40.91 | ALPHA: (fact_1142_zero__le__imp__eq__int) implies:
% 287.45/40.91 | (48) ? [v0: $i] : (hAPP_i1948725293t_bool(ord_less_eq_int, zero_zero_int)
% 287.45/40.91 | = v0 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ( ~ (hAPP_int_bool(v0,
% 287.45/40.91 | v1) = v2) | ~ $i(v1) | ~ hBOOL(v2) | ? [v3: $i] :
% 287.45/40.91 | (hAPP_nat_int(semiri1621563631at_int, v3) = v1 & $i(v3))))
% 287.45/40.91 |
% 287.45/40.91 | ALPHA: (fact_1144_decr__lemma) implies:
% 287.45/40.91 | (49) ? [v0: $i] : (hAPP_i1948725293t_bool(ord_less_int, zero_zero_int) =
% 287.45/40.91 | v0 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i]
% 287.45/40.91 | : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ! [v9:
% 287.45/40.91 | $i] : ! [v10: $i] : ! [v11: $i] : ! [v12: $i] : ! [v13: $i] :
% 287.45/40.91 | ( ~ (abs_abs_int(v5) = v6) | ~
% 287.45/40.91 | (hAPP_int_fun_int_int(times_times_int, v8) = v9) | ~
% 287.45/40.91 | (hAPP_int_fun_int_int(plus_plus_int, v6) = v7) | ~
% 287.45/40.91 | (hAPP_int_fun_int_int(minus_minus_int, v1) = v4) | ~
% 287.45/40.91 | (hAPP_int_int(v9, v3) = v10) | ~ (hAPP_int_int(v7, one_one_int) =
% 287.45/40.91 | v8) | ~ (hAPP_int_int(v4, v10) = v11) | ~ (hAPP_int_int(v4,
% 287.45/40.91 | v2) = v5) | ~ (hAPP_i1948725293t_bool(ord_less_int, v11) =
% 287.45/40.91 | v12) | ~ (hAPP_int_bool(v12, v2) = v13) | ~ $i(v3) | ~ $i(v2)
% 287.45/40.91 | | ~ $i(v1) | hBOOL(v13) | ? [v14: $i] : (hAPP_int_bool(v0, v3) =
% 287.45/40.91 | v14 & $i(v14) & ~ hBOOL(v14))))
% 287.45/40.91 |
% 287.45/40.91 | ALPHA: (fact_1147_not__neg__eq__ge__0) implies:
% 287.45/40.91 | (50) ? [v0: $i] : (hAPP_i1948725293t_bool(ord_less_eq_int, zero_zero_int)
% 287.45/40.91 | = v0 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ( ~ (hAPP_int_bool(v0,
% 287.45/40.91 | v1) = v2) | ~ $i(v1) | ~ hBOOL(v2) | ? [v3: $i] :
% 287.45/40.91 | (hAPP_int_bool(nat_neg, v1) = v3 & $i(v3) & ~ hBOOL(v3))) & !
% 287.45/40.91 | [v1: $i] : ! [v2: $i] : ( ~ (hAPP_int_bool(v0, v1) = v2) | ~
% 287.45/40.91 | $i(v1) | hBOOL(v2) | ? [v3: $i] : (hAPP_int_bool(nat_neg, v1) =
% 287.45/40.91 | v3 & $i(v3) & hBOOL(v3))))
% 287.45/40.91 |
% 287.45/40.91 | ALPHA: (fact_1148_not__neg__1) implies:
% 287.45/40.92 | (51) ? [v0: $i] : (hAPP_int_bool(nat_neg, one_one_int) = v0 & $i(v0) & ~
% 287.45/40.92 | hBOOL(v0))
% 287.45/40.92 |
% 287.45/40.92 | ALPHA: (fact_1152_abs__int__eq) implies:
% 287.45/40.92 | (52) ! [v0: $i] : ! [v1: $i] : ( ~ (hAPP_nat_int(semiri1621563631at_int,
% 287.45/40.92 | v0) = v1) | ~ $i(v0) | (abs_abs_int(v1) = v1 & $i(v1)))
% 287.45/40.92 |
% 287.45/40.92 | ALPHA: (fact_1154_eq__nat__number__of) implies:
% 287.45/40.92 | (53) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 287.45/40.92 | (number_number_of_nat(v1) = v2) | ~ (number_number_of_nat(v0) = v2)
% 287.45/40.92 | | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : ? [v5: $i] :
% 287.45/40.92 | ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : (((number_number_of_int(v1)
% 287.45/40.92 | = v5 & hAPP_i1948725293t_bool(ord_less_eq_int, v5) = v6 &
% 287.45/40.92 | hAPP_int_bool(v6, zero_zero_int) = v7 & $i(v7) & $i(v6) &
% 287.45/40.92 | $i(v5) & hBOOL(v7)) | (number_number_of_int(v0) = v3 &
% 287.45/40.92 | hAPP_int_bool(nat_neg, v3) = v4 & $i(v4) & $i(v3) & ~
% 287.45/40.92 | hBOOL(v4))) & ((number_number_of_int(v0) = v3 &
% 287.45/40.92 | hAPP_int_bool(nat_neg, v3) = v4 & $i(v4) & $i(v3) & hBOOL(v4))
% 287.45/40.92 | | ((v1 = v0 | (number_number_of_int(v1) = v5 &
% 287.45/40.92 | hAPP_int_bool(nat_neg, v5) = v8 & $i(v8) & $i(v5) &
% 287.45/40.92 | hBOOL(v8))) & ((v3 = zero_zero_int &
% 287.45/40.92 | number_number_of_int(v0) = zero_zero_int) |
% 287.45/40.92 | (number_number_of_int(v1) = v5 & hAPP_int_bool(nat_neg, v5)
% 287.45/40.92 | = v8 & $i(v8) & $i(v5) & ~ hBOOL(v8)))))))
% 287.45/40.92 | (54) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v2 | ~
% 287.45/40.92 | (number_number_of_nat(v1) = v3) | ~ (number_number_of_nat(v0) = v2)
% 287.45/40.92 | | ~ $i(v1) | ~ $i(v0) | ? [v4: $i] : ? [v5: $i] : ? [v6: $i] :
% 287.45/40.92 | ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : (number_number_of_int(v1) =
% 287.45/40.92 | v6 & number_number_of_int(v0) = v4 & hAPP_int_bool(nat_neg, v4) =
% 287.45/40.92 | v5 & $i(v6) & $i(v5) & $i(v4) &
% 287.45/40.92 | ((hAPP_i1948725293t_bool(ord_less_eq_int, v6) = v7 &
% 287.45/40.92 | hAPP_int_bool(v7, zero_zero_int) = v8 & $i(v8) & $i(v7) &
% 287.45/40.92 | hBOOL(v5) & ~ hBOOL(v8)) | (hAPP_int_bool(nat_neg, v6) = v9 &
% 287.45/40.92 | $i(v9) & ~ hBOOL(v5) & (( ~ (v4 = zero_zero_int) & hBOOL(v9))
% 287.45/40.92 | | ( ~ (v1 = v0) & ~ hBOOL(v9)))))))
% 287.45/40.92 |
% 287.45/40.92 | ALPHA: (fact_1157_incr__lemma) implies:
% 287.45/40.92 | (55) ? [v0: $i] : (hAPP_i1948725293t_bool(ord_less_int, zero_zero_int) =
% 287.45/40.92 | v0 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i]
% 287.45/40.92 | : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ! [v9:
% 287.45/40.92 | $i] : ! [v10: $i] : ! [v11: $i] : ! [v12: $i] : ! [v13: $i] :
% 287.45/40.92 | ! [v14: $i] : ( ~ (abs_abs_int(v7) = v8) | ~
% 287.45/40.92 | (hAPP_int_fun_int_int(times_times_int, v10) = v11) | ~
% 287.45/40.92 | (hAPP_int_fun_int_int(plus_plus_int, v8) = v9) | ~
% 287.45/40.92 | (hAPP_int_fun_int_int(plus_plus_int, v2) = v5) | ~
% 287.45/40.92 | (hAPP_int_fun_int_int(minus_minus_int, v2) = v6) | ~
% 287.45/40.92 | (hAPP_int_int(v11, v3) = v12) | ~ (hAPP_int_int(v9, one_one_int)
% 287.45/40.92 | = v10) | ~ (hAPP_int_int(v6, v1) = v7) | ~ (hAPP_int_int(v5,
% 287.45/40.92 | v12) = v13) | ~ (hAPP_i1948725293t_bool(ord_less_int, v1) =
% 287.45/40.92 | v4) | ~ (hAPP_int_bool(v4, v13) = v14) | ~ $i(v3) | ~ $i(v2)
% 287.45/40.92 | | ~ $i(v1) | hBOOL(v14) | ? [v15: $i] : (hAPP_int_bool(v0, v3) =
% 287.45/40.92 | v15 & $i(v15) & ~ hBOOL(v15))))
% 287.45/40.92 |
% 287.45/40.92 | ALPHA: (fact_1166_succ__Pls) implies:
% 287.45/40.92 | (56) ? [v0: $i] : (bit1(pls) = v0 & succ(pls) = v0 & $i(v0))
% 287.45/40.92 |
% 287.45/40.92 | ALPHA: (fact_1167_neg__number__of__Bit1) implies:
% 287.45/40.92 | (57) ! [v0: $i] : ! [v1: $i] : ( ~ (number_number_of_int(v0) = v1) | ~
% 287.45/40.92 | $i(v0) | ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] :
% 287.45/40.92 | ((bit1(v0) = v2 & number_number_of_int(v2) = v3 &
% 287.45/40.92 | hAPP_int_bool(nat_neg, v3) = v4 & $i(v4) & $i(v3) & $i(v2) & ~
% 287.45/40.92 | hBOOL(v4)) | (hAPP_int_bool(nat_neg, v1) = v5 & $i(v5) &
% 287.45/40.92 | hBOOL(v5))))
% 287.45/40.92 |
% 287.45/40.92 | ALPHA: (fact_1169_transfer__int__nat__numerals_I4_J) implies:
% 287.45/40.92 | (58) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : (bit1(v0) = v1
% 287.45/40.92 | & bit1(pls) = v0 & number_number_of_int(v1) = v2 &
% 287.45/40.92 | number_number_of_nat(v1) = v3 & hAPP_nat_int(semiri1621563631at_int,
% 287.45/40.92 | v3) = v2 & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 287.45/40.92 |
% 287.45/40.92 | ALPHA: (fact_1170_numeral__1__eq__Suc__0) implies:
% 287.45/40.92 | (59) ? [v0: $i] : ? [v1: $i] : (bit1(pls) = v0 & number_number_of_nat(v0)
% 287.45/40.92 | = v1 & hAPP_nat_nat(suc, zero_zero_nat) = v1 & $i(v1) & $i(v0))
% 287.45/40.92 |
% 287.45/40.92 | ALPHA: (fact_1171_numeral__3__eq__3) implies:
% 287.45/40.92 | (60) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 287.45/40.92 | (bit1(v0) = v1 & bit1(pls) = v0 & number_number_of_nat(v1) = v2 &
% 287.45/40.92 | hAPP_nat_nat(suc, v4) = v2 & hAPP_nat_nat(suc, v3) = v4 &
% 287.45/40.92 | hAPP_nat_nat(suc, zero_zero_nat) = v3 & $i(v4) & $i(v3) & $i(v2) &
% 287.45/40.92 | $i(v1) & $i(v0))
% 287.45/40.92 |
% 287.45/40.92 | ALPHA: (fact_1172_Suc3__eq__add__3) implies:
% 287.45/40.92 | (61) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : (bit1(v0) = v1
% 287.45/40.92 | & bit1(pls) = v0 & number_number_of_nat(v1) = v2 &
% 287.45/40.92 | hAPP_nat_fun_nat_nat(plus_plus_nat, v2) = v3 & $i(v3) & $i(v2) &
% 287.45/40.92 | $i(v1) & $i(v0) & ! [v4: $i] : ! [v5: $i] : ( ~ (hAPP_nat_nat(v3,
% 287.45/40.92 | v4) = v5) | ~ $i(v4) | ? [v6: $i] : ? [v7: $i] :
% 287.45/40.92 | (hAPP_nat_nat(suc, v7) = v5 & hAPP_nat_nat(suc, v6) = v7 &
% 287.45/40.92 | hAPP_nat_nat(suc, v4) = v6 & $i(v7) & $i(v6) & $i(v5))))
% 287.45/40.92 |
% 287.45/40.92 | ALPHA: (fact_1174_nat__numeral__1__eq__1) implies:
% 287.45/40.92 | (62) ? [v0: $i] : (bit1(pls) = v0 & number_number_of_nat(v0) = one_one_nat
% 287.45/40.92 | & $i(v0))
% 287.45/40.92 |
% 287.45/40.92 | ALPHA: (fact_1175_one__is__num__one) implies:
% 287.45/40.92 | (63) ? [v0: $i] : (bit1(pls) = v0 & number_number_of_int(v0) = one_one_int
% 287.45/40.92 | & $i(v0))
% 287.45/40.92 |
% 287.45/40.92 | ALPHA: (fact_1179_semiring__norm_I113_J) implies:
% 287.45/40.92 | (64) $i(zero_zero_nat)
% 287.45/40.92 | (65) number_number_of_nat(pls) = zero_zero_nat
% 287.45/40.92 |
% 287.45/40.92 | ALPHA: (fact_1180_Pls__def) implies:
% 287.45/40.92 | (66) pls = zero_zero_int
% 287.45/40.93 |
% 287.45/40.93 | ALPHA: (fact_1188_Nat__Transfer_Otransfer__nat__int__function__closures_I8_J)
% 287.45/40.93 | implies:
% 287.45/40.93 | (67) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 287.45/40.93 | (bit1(v1) = v2 & bit1(pls) = v1 & number_number_of_int(v2) = v3 &
% 287.45/40.93 | hAPP_i1948725293t_bool(ord_less_eq_int, zero_zero_int) = v0 &
% 287.45/40.93 | hAPP_int_bool(v0, v3) = v4 & $i(v4) & $i(v3) & $i(v2) & $i(v1) &
% 287.45/40.93 | $i(v0) & hBOOL(v4))
% 287.45/40.93 |
% 287.45/40.93 | ALPHA: (fact_1189_rel__simps_I19_J) implies:
% 287.45/40.93 | (68) ? [v0: $i] : ? [v1: $i] : (hAPP_i1948725293t_bool(ord_less_eq_int,
% 287.45/40.93 | pls) = v0 & hAPP_int_bool(v0, pls) = v1 & $i(v1) & $i(v0) &
% 287.45/40.93 | hBOOL(v1))
% 287.45/40.93 |
% 287.45/40.93 | ALPHA: (fact_1190_rel__simps_I22_J) implies:
% 287.45/40.93 | (69) ? [v0: $i] : (hAPP_i1948725293t_bool(ord_less_eq_int, pls) = v0 &
% 287.45/40.93 | $i(v0) & ! [v1: $i] : ! [v2: $i] : ( ~ (hAPP_int_bool(v0, v1) =
% 287.45/40.93 | v2) | ~ $i(v1) | ~ hBOOL(v2) | ? [v3: $i] : ? [v4: $i] :
% 287.45/40.93 | (bit1(v1) = v3 & hAPP_int_bool(v0, v3) = v4 & $i(v4) & $i(v3) &
% 287.45/40.93 | hBOOL(v4))) & ! [v1: $i] : ! [v2: $i] : ( ~ (hAPP_int_bool(v0,
% 287.45/40.93 | v1) = v2) | ~ $i(v1) | hBOOL(v2) | ? [v3: $i] : ? [v4: $i]
% 287.45/40.93 | : (bit1(v1) = v3 & hAPP_int_bool(v0, v3) = v4 & $i(v4) & $i(v3) &
% 287.45/40.93 | ~ hBOOL(v4))))
% 287.45/40.93 |
% 287.45/40.93 | ALPHA: (fact_1193_rel__simps_I2_J) implies:
% 287.45/40.93 | (70) ? [v0: $i] : ? [v1: $i] : (hAPP_i1948725293t_bool(ord_less_int, pls)
% 287.45/40.93 | = v0 & hAPP_int_bool(v0, pls) = v1 & $i(v1) & $i(v0) & ~ hBOOL(v1))
% 287.45/40.93 |
% 287.45/40.93 | ALPHA: (fact_1194_rel__simps_I12_J) implies:
% 287.45/40.93 | (71) ! [v0: $i] : ! [v1: $i] : ( ~ (hAPP_i1948725293t_bool(ord_less_int,
% 287.45/40.93 | v0) = v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: $i] : ? [v4: $i]
% 287.45/40.93 | : ? [v5: $i] : ((bit1(v0) = v2 &
% 287.45/40.93 | hAPP_i1948725293t_bool(ord_less_int, v2) = v3 &
% 287.45/40.93 | hAPP_int_bool(v3, pls) = v4 & $i(v4) & $i(v3) & $i(v2) & ~
% 287.45/40.93 | hBOOL(v4)) | (hAPP_int_bool(v1, pls) = v5 & $i(v5) &
% 287.45/40.93 | hBOOL(v5))))
% 287.45/40.93 |
% 287.45/40.93 | ALPHA: (fact_1197_rel__simps_I29_J) implies:
% 287.45/40.93 | (72) ! [v0: $i] : ! [v1: $i] : ( ~ (hAPP_i1948725293t_bool(ord_less_int,
% 287.45/40.93 | v0) = v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: $i] : ? [v4: $i]
% 287.45/40.93 | : ? [v5: $i] : ((bit1(v0) = v2 &
% 287.45/40.93 | hAPP_i1948725293t_bool(ord_less_eq_int, v2) = v3 &
% 287.45/40.93 | hAPP_int_bool(v3, pls) = v4 & $i(v4) & $i(v3) & $i(v2) & ~
% 287.45/40.93 | hBOOL(v4)) | (hAPP_int_bool(v1, pls) = v5 & $i(v5) &
% 287.45/40.93 | hBOOL(v5))))
% 287.45/40.93 |
% 287.45/40.93 | ALPHA: (fact_1198_rel__simps_I5_J) implies:
% 287.45/40.93 | (73) ? [v0: $i] : ? [v1: $i] : (hAPP_i1948725293t_bool(ord_less_int, pls)
% 287.45/40.93 | = v0 & hAPP_i1948725293t_bool(ord_less_eq_int, pls) = v1 & $i(v1) &
% 287.45/40.93 | $i(v0) & ! [v2: $i] : ! [v3: $i] : ( ~ (hAPP_int_bool(v1, v2) =
% 287.45/40.93 | v3) | ~ $i(v2) | ~ hBOOL(v3) | ? [v4: $i] : ? [v5: $i] :
% 287.45/40.93 | (bit1(v2) = v4 & hAPP_int_bool(v0, v4) = v5 & $i(v5) & $i(v4) &
% 287.45/40.93 | hBOOL(v5))) & ! [v2: $i] : ! [v3: $i] : ( ~ (hAPP_int_bool(v1,
% 287.45/40.93 | v2) = v3) | ~ $i(v2) | hBOOL(v3) | ? [v4: $i] : ? [v5: $i]
% 287.45/40.93 | : (bit1(v2) = v4 & hAPP_int_bool(v0, v4) = v5 & $i(v5) & $i(v4) &
% 287.45/40.93 | ~ hBOOL(v5))))
% 287.45/40.93 |
% 287.45/40.93 | ALPHA: (conj_1) implies:
% 287.45/40.93 | (74) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 287.45/40.93 | (hAPP_f1631501043l_bool(ord_le1311769555a_bool, g) = v0 &
% 287.45/40.93 | hAPP_fun_a_bool_bool(v0, v1) = v2 & image_pname_a(mgt_call, u) = v1
% 287.45/40.93 | & $i(v2) & $i(v1) & $i(v0) & hBOOL(v2))
% 287.45/40.93 |
% 287.45/40.93 | ALPHA: (conj_2) implies:
% 287.45/40.93 | (75) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 287.45/40.93 | (hAPP_nat_nat(suc, na) = v0 & hAPP_fun_a_bool_nat(finite_card_a, v2) =
% 287.45/40.93 | v3 & hAPP_n1699378549t_bool(ord_less_eq_nat, v0) = v1 &
% 287.45/40.93 | hAPP_nat_bool(v1, v3) = v4 & image_pname_a(mgt_call, u) = v2 &
% 287.45/40.93 | $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & hBOOL(v4))
% 287.45/40.93 |
% 287.45/40.93 | ALPHA: (conj_3) implies:
% 287.45/40.93 | (76) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 287.45/40.93 | (hAPP_nat_fun_nat_nat(minus_minus_nat, v2) = v3 & hAPP_nat_nat(v3, v4)
% 287.45/40.93 | = v0 & hAPP_nat_nat(suc, na) = v4 &
% 287.45/40.93 | hAPP_fun_a_bool_nat(finite_card_a, v1) = v2 &
% 287.45/40.93 | hAPP_fun_a_bool_nat(finite_card_a, g) = v0 & image_pname_a(mgt_call,
% 287.45/40.93 | u) = v1 & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 287.45/40.93 |
% 287.45/40.93 | ALPHA: (conj_4) implies:
% 287.45/40.93 | (77) ? [v0: $i] : ? [v1: $i] : (hAPP_f1664156314l_bool(v0, u) = v1 &
% 287.45/40.93 | hAPP_p338031245l_bool(member_pname, pn) = v0 & $i(v1) & $i(v0) &
% 287.45/40.93 | hBOOL(v1))
% 287.45/40.93 |
% 287.45/40.93 | ALPHA: (conj_5) implies:
% 287.45/40.93 | (78) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (hAPP_fun_a_bool_bool(v1, g)
% 287.45/40.93 | = v2 & hAPP_pname_a(mgt_call, pn) = v0 &
% 287.45/40.93 | hAPP_a85458249l_bool(member_a, v0) = v1 & $i(v2) & $i(v1) & $i(v0) &
% 287.45/40.93 | ~ hBOOL(v2))
% 287.45/40.93 |
% 287.45/40.93 | ALPHA: (conj_6) implies:
% 287.45/40.93 | (79) $i(g)
% 287.45/40.93 | (80) $i(u)
% 287.45/40.93 | (81) $i(pn)
% 287.45/40.93 | (82) $i(mgt_call)
% 287.45/40.93 | (83) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 287.45/40.93 | ? [v5: $i] : (hAPP_a1206381875a_bool(insert_a, v0) = v1 &
% 287.45/40.93 | hAPP_f1631501043l_bool(ord_le1311769555a_bool, v2) = v3 &
% 287.45/40.93 | hAPP_f2050579477a_bool(v1, g) = v2 & hAPP_fun_a_bool_bool(v3, v4) =
% 287.45/40.93 | v5 & hAPP_pname_a(mgt_call, pn) = v0 & image_pname_a(mgt_call, u) =
% 287.45/40.93 | v4 & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & ~
% 287.45/40.93 | hBOOL(v5))
% 287.45/40.93 |
% 287.45/40.93 | ALPHA: (function-axioms) implies:
% 287.45/40.93 | (84) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 287.45/40.93 | (number_number_of_int(v2) = v1) | ~ (number_number_of_int(v2) =
% 287.45/40.93 | v0))
% 287.45/40.93 | (85) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (bit1(v2) =
% 287.45/40.93 | v1) | ~ (bit1(v2) = v0))
% 287.45/40.94 | (86) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 287.45/40.94 | (image_pname_a(v3, v2) = v1) | ~ (image_pname_a(v3, v2) = v0))
% 287.45/40.94 | (87) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 287.45/40.94 | (hAPP_a85458249l_bool(v3, v2) = v1) | ~ (hAPP_a85458249l_bool(v3,
% 287.45/40.94 | v2) = v0))
% 287.45/40.94 | (88) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 287.45/40.94 | (hAPP_pname_a(v3, v2) = v1) | ~ (hAPP_pname_a(v3, v2) = v0))
% 287.45/40.94 | (89) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 287.45/40.94 | (hAPP_int_bool(v3, v2) = v1) | ~ (hAPP_int_bool(v3, v2) = v0))
% 287.45/40.94 | (90) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 287.45/40.94 | (hAPP_fun_a_bool_bool(v3, v2) = v1) | ~ (hAPP_fun_a_bool_bool(v3,
% 287.45/40.94 | v2) = v0))
% 287.45/40.94 | (91) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 287.45/40.94 | (hAPP_f1631501043l_bool(v3, v2) = v1) | ~
% 287.45/40.94 | (hAPP_f1631501043l_bool(v3, v2) = v0))
% 287.45/40.94 | (92) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 287.45/40.94 | (hAPP_nat_nat(v3, v2) = v1) | ~ (hAPP_nat_nat(v3, v2) = v0))
% 287.45/40.94 | (93) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 287.45/40.94 | (hAPP_nat_int(v3, v2) = v1) | ~ (hAPP_nat_int(v3, v2) = v0))
% 287.45/40.94 | (94) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 287.45/40.94 | (hAPP_i1948725293t_bool(v3, v2) = v1) | ~
% 287.45/40.94 | (hAPP_i1948725293t_bool(v3, v2) = v0))
% 287.45/40.94 |
% 287.45/40.94 | DELTA: instantiating (35) with fresh symbol all_1174_0 gives:
% 287.45/40.94 | (95) hAPP_i1948725293t_bool(ord_less_eq_int, zero_zero_int) = all_1174_0 &
% 287.45/40.94 | $i(all_1174_0)
% 287.45/40.94 |
% 287.45/40.94 | ALPHA: (95) implies:
% 287.45/40.94 | (96) hAPP_i1948725293t_bool(ord_less_eq_int, zero_zero_int) = all_1174_0
% 287.45/40.94 |
% 287.45/40.94 | DELTA: instantiating (35) with fresh symbol all_1176_0 gives:
% 287.45/40.94 | (97) hAPP_i1948725293t_bool(ord_less_eq_int, zero_zero_int) = all_1176_0 &
% 287.45/40.94 | $i(all_1176_0)
% 287.45/40.94 |
% 287.45/40.94 | ALPHA: (97) implies:
% 287.45/40.94 | (98) hAPP_i1948725293t_bool(ord_less_eq_int, zero_zero_int) = all_1176_0
% 287.45/40.94 |
% 287.45/40.94 | DELTA: instantiating (62) with fresh symbol all_1182_0 gives:
% 287.45/40.94 | (99) bit1(pls) = all_1182_0 & number_number_of_nat(all_1182_0) =
% 287.45/40.94 | one_one_nat & $i(all_1182_0)
% 287.45/40.94 |
% 287.45/40.94 | ALPHA: (99) implies:
% 287.45/40.94 | (100) bit1(pls) = all_1182_0
% 287.45/40.94 |
% 287.45/40.94 | DELTA: instantiating (62) with fresh symbol all_1184_0 gives:
% 287.45/40.94 | (101) bit1(pls) = all_1184_0 & number_number_of_nat(all_1184_0) =
% 287.45/40.94 | one_one_nat & $i(all_1184_0)
% 287.45/40.94 |
% 287.45/40.94 | ALPHA: (101) implies:
% 287.45/40.94 | (102) $i(all_1184_0)
% 287.45/40.94 | (103) number_number_of_nat(all_1184_0) = one_one_nat
% 287.45/40.94 | (104) bit1(pls) = all_1184_0
% 287.45/40.94 |
% 287.45/40.94 | DELTA: instantiating (63) with fresh symbol all_1186_0 gives:
% 287.45/40.94 | (105) bit1(pls) = all_1186_0 & number_number_of_int(all_1186_0) =
% 287.45/40.94 | one_one_int & $i(all_1186_0)
% 287.45/40.94 |
% 287.45/40.94 | ALPHA: (105) implies:
% 287.45/40.94 | (106) number_number_of_int(all_1186_0) = one_one_int
% 287.45/40.94 | (107) bit1(pls) = all_1186_0
% 287.45/40.94 |
% 287.45/40.94 | DELTA: instantiating (44) with fresh symbol all_1196_0 gives:
% 287.45/40.94 | (108) hAPP_nat_int(semiri1621563631at_int, all_1196_0) = one_one_int &
% 287.45/40.94 | hAPP_nat_nat(suc, zero_zero_nat) = all_1196_0 & $i(all_1196_0)
% 287.45/40.94 |
% 287.45/40.94 | ALPHA: (108) implies:
% 287.45/40.94 | (109) $i(all_1196_0)
% 287.45/40.94 | (110) hAPP_nat_nat(suc, zero_zero_nat) = all_1196_0
% 287.45/40.94 | (111) hAPP_nat_int(semiri1621563631at_int, all_1196_0) = one_one_int
% 287.45/40.94 |
% 287.45/40.94 | DELTA: instantiating (51) with fresh symbol all_1200_0 gives:
% 287.45/40.94 | (112) hAPP_int_bool(nat_neg, one_one_int) = all_1200_0 & $i(all_1200_0) &
% 287.45/40.94 | ~ hBOOL(all_1200_0)
% 287.45/40.94 |
% 287.45/40.94 | ALPHA: (112) implies:
% 287.45/40.94 | (113) ~ hBOOL(all_1200_0)
% 287.45/40.94 | (114) hAPP_int_bool(nat_neg, one_one_int) = all_1200_0
% 287.45/40.94 |
% 287.45/40.94 | DELTA: instantiating (56) with fresh symbol all_1208_0 gives:
% 287.45/40.94 | (115) bit1(pls) = all_1208_0 & succ(pls) = all_1208_0 & $i(all_1208_0)
% 287.45/40.94 |
% 287.45/40.94 | ALPHA: (115) implies:
% 287.45/40.94 | (116) bit1(pls) = all_1208_0
% 287.45/40.94 |
% 287.45/40.94 | DELTA: instantiating (32) with fresh symbols all_1223_0, all_1223_1 gives:
% 287.45/40.94 | (117) hAPP_i1948725293t_bool(ord_less_eq_int, zero_zero_int) = all_1223_1 &
% 287.45/40.94 | hAPP_int_bool(all_1223_1, one_one_int) = all_1223_0 & $i(all_1223_0)
% 287.45/40.94 | & $i(all_1223_1) & hBOOL(all_1223_0)
% 287.45/40.94 |
% 287.45/40.94 | ALPHA: (117) implies:
% 287.45/40.94 | (118) hBOOL(all_1223_0)
% 287.45/40.94 | (119) hAPP_int_bool(all_1223_1, one_one_int) = all_1223_0
% 287.45/40.94 | (120) hAPP_i1948725293t_bool(ord_less_eq_int, zero_zero_int) = all_1223_1
% 287.45/40.94 |
% 287.45/40.94 | DELTA: instantiating (30) with fresh symbols all_1225_0, all_1225_1 gives:
% 287.45/40.94 | (121) hAPP_i1948725293t_bool(ord_less_eq_int, zero_zero_int) = all_1225_1 &
% 287.45/40.94 | hAPP_int_bool(all_1225_1, zero_zero_int) = all_1225_0 &
% 287.45/40.94 | $i(all_1225_0) & $i(all_1225_1) & hBOOL(all_1225_0)
% 287.45/40.94 |
% 287.45/40.94 | ALPHA: (121) implies:
% 287.45/40.94 | (122) hAPP_i1948725293t_bool(ord_less_eq_int, zero_zero_int) = all_1225_1
% 287.45/40.94 |
% 287.45/40.94 | DELTA: instantiating (77) with fresh symbols all_1235_0, all_1235_1 gives:
% 287.45/40.94 | (123) hAPP_f1664156314l_bool(all_1235_1, u) = all_1235_0 &
% 287.45/40.94 | hAPP_p338031245l_bool(member_pname, pn) = all_1235_1 & $i(all_1235_0)
% 287.45/40.94 | & $i(all_1235_1) & hBOOL(all_1235_0)
% 287.45/40.94 |
% 287.45/40.94 | ALPHA: (123) implies:
% 287.45/40.94 | (124) hBOOL(all_1235_0)
% 287.45/40.94 | (125) hAPP_p338031245l_bool(member_pname, pn) = all_1235_1
% 287.45/40.94 | (126) hAPP_f1664156314l_bool(all_1235_1, u) = all_1235_0
% 287.45/40.94 |
% 287.45/40.94 | DELTA: instantiating (70) with fresh symbols all_1245_0, all_1245_1 gives:
% 287.45/40.94 | (127) hAPP_i1948725293t_bool(ord_less_int, pls) = all_1245_1 &
% 287.45/40.94 | hAPP_int_bool(all_1245_1, pls) = all_1245_0 & $i(all_1245_0) &
% 287.45/40.94 | $i(all_1245_1) & ~ hBOOL(all_1245_0)
% 287.45/40.94 |
% 287.45/40.94 | ALPHA: (127) implies:
% 287.45/40.94 | (128) ~ hBOOL(all_1245_0)
% 287.45/40.94 | (129) hAPP_int_bool(all_1245_1, pls) = all_1245_0
% 287.45/40.94 | (130) hAPP_i1948725293t_bool(ord_less_int, pls) = all_1245_1
% 287.45/40.94 |
% 287.45/40.94 | DELTA: instantiating (17) with fresh symbols all_1256_0, all_1256_1 gives:
% 287.45/40.94 | (131) hAPP_i1948725293t_bool(ord_less_int, zero_zero_int) = all_1256_1 &
% 287.45/40.94 | hAPP_int_bool(all_1256_1, one_one_int) = all_1256_0 & $i(all_1256_0)
% 287.45/40.94 | & $i(all_1256_1) & hBOOL(all_1256_0)
% 287.45/40.94 |
% 287.45/40.94 | ALPHA: (131) implies:
% 287.45/40.94 | (132) hAPP_i1948725293t_bool(ord_less_int, zero_zero_int) = all_1256_1
% 287.45/40.94 |
% 287.45/40.94 | DELTA: instantiating (68) with fresh symbols all_1264_0, all_1264_1 gives:
% 287.45/40.94 | (133) hAPP_i1948725293t_bool(ord_less_eq_int, pls) = all_1264_1 &
% 287.45/40.94 | hAPP_int_bool(all_1264_1, pls) = all_1264_0 & $i(all_1264_0) &
% 287.45/40.94 | $i(all_1264_1) & hBOOL(all_1264_0)
% 287.45/40.94 |
% 287.45/40.94 | ALPHA: (133) implies:
% 287.45/40.94 | (134) hAPP_i1948725293t_bool(ord_less_eq_int, pls) = all_1264_1
% 287.45/40.94 |
% 287.45/40.94 | DELTA: instantiating (59) with fresh symbols all_1290_0, all_1290_1 gives:
% 287.45/40.95 | (135) bit1(pls) = all_1290_1 & number_number_of_nat(all_1290_1) =
% 287.45/40.95 | all_1290_0 & hAPP_nat_nat(suc, zero_zero_nat) = all_1290_0 &
% 287.45/40.95 | $i(all_1290_0) & $i(all_1290_1)
% 287.45/40.95 |
% 287.45/40.95 | ALPHA: (135) implies:
% 287.45/40.95 | (136) hAPP_nat_nat(suc, zero_zero_nat) = all_1290_0
% 287.45/40.95 | (137) bit1(pls) = all_1290_1
% 287.45/40.95 |
% 287.45/40.95 | DELTA: instantiating (48) with fresh symbol all_1314_0 gives:
% 287.45/40.95 | (138) hAPP_i1948725293t_bool(ord_less_eq_int, zero_zero_int) = all_1314_0 &
% 287.45/40.95 | $i(all_1314_0) & ! [v0: $i] : ! [v1: $i] : ( ~
% 287.45/40.95 | (hAPP_int_bool(all_1314_0, v0) = v1) | ~ $i(v0) | ~ hBOOL(v1) |
% 287.45/40.95 | ? [v2: $i] : (hAPP_nat_int(semiri1621563631at_int, v2) = v0 &
% 287.45/40.95 | $i(v2)))
% 287.45/40.95 |
% 287.45/40.95 | ALPHA: (138) implies:
% 287.45/40.95 | (139) hAPP_i1948725293t_bool(ord_less_eq_int, zero_zero_int) = all_1314_0
% 287.45/40.95 |
% 287.45/40.95 | DELTA: instantiating (48) with fresh symbol all_1317_0 gives:
% 287.45/40.95 | (140) hAPP_i1948725293t_bool(ord_less_eq_int, zero_zero_int) = all_1317_0 &
% 287.45/40.95 | $i(all_1317_0) & ! [v0: $i] : ! [v1: $i] : ( ~
% 287.45/40.95 | (hAPP_int_bool(all_1317_0, v0) = v1) | ~ $i(v0) | ~ hBOOL(v1) |
% 287.45/40.95 | ? [v2: $i] : (hAPP_nat_int(semiri1621563631at_int, v2) = v0 &
% 287.45/40.95 | $i(v2)))
% 287.45/40.95 |
% 287.45/40.95 | ALPHA: (140) implies:
% 287.45/40.95 | (141) hAPP_i1948725293t_bool(ord_less_eq_int, zero_zero_int) = all_1317_0
% 287.45/40.95 |
% 287.45/40.95 | DELTA: instantiating (48) with fresh symbol all_1322_0 gives:
% 287.45/40.95 | (142) hAPP_i1948725293t_bool(ord_less_eq_int, zero_zero_int) = all_1322_0 &
% 287.45/40.95 | $i(all_1322_0) & ! [v0: $i] : ! [v1: $i] : ( ~
% 287.45/40.95 | (hAPP_int_bool(all_1322_0, v0) = v1) | ~ $i(v0) | ~ hBOOL(v1) |
% 287.45/40.95 | ? [v2: $i] : (hAPP_nat_int(semiri1621563631at_int, v2) = v0 &
% 287.45/40.95 | $i(v2)))
% 287.45/40.95 |
% 287.45/40.95 | ALPHA: (142) implies:
% 287.45/40.95 | (143) hAPP_i1948725293t_bool(ord_less_eq_int, zero_zero_int) = all_1322_0
% 287.45/40.95 |
% 287.45/40.95 | DELTA: instantiating (41) with fresh symbol all_1325_0 gives:
% 287.45/40.95 | (144) hAPP_i1948725293t_bool(ord_less_eq_int, zero_zero_int) = all_1325_0 &
% 287.45/40.95 | $i(all_1325_0) & ! [v0: $i] : ! [v1: $i] : ( ~
% 287.45/40.95 | (hAPP_nat_int(semiri1621563631at_int, v0) = v1) | ~ $i(v0) | ?
% 287.45/40.95 | [v2: $i] : (hAPP_int_bool(all_1325_0, v1) = v2 & $i(v2) &
% 287.45/40.95 | hBOOL(v2)))
% 287.45/40.95 |
% 287.45/40.95 | ALPHA: (144) implies:
% 287.45/40.95 | (145) hAPP_i1948725293t_bool(ord_less_eq_int, zero_zero_int) = all_1325_0
% 287.45/40.95 |
% 287.45/40.95 | DELTA: instantiating (78) with fresh symbols all_1328_0, all_1328_1,
% 287.45/40.95 | all_1328_2 gives:
% 287.45/40.95 | (146) hAPP_fun_a_bool_bool(all_1328_1, g) = all_1328_0 &
% 287.45/40.95 | hAPP_pname_a(mgt_call, pn) = all_1328_2 &
% 287.45/40.95 | hAPP_a85458249l_bool(member_a, all_1328_2) = all_1328_1 &
% 287.45/40.95 | $i(all_1328_0) & $i(all_1328_1) & $i(all_1328_2) & ~
% 287.45/40.95 | hBOOL(all_1328_0)
% 287.45/40.95 |
% 287.45/40.95 | ALPHA: (146) implies:
% 287.45/40.95 | (147) hAPP_a85458249l_bool(member_a, all_1328_2) = all_1328_1
% 287.45/40.95 | (148) hAPP_pname_a(mgt_call, pn) = all_1328_2
% 287.45/40.95 |
% 287.45/40.95 | DELTA: instantiating (74) with fresh symbols all_1330_0, all_1330_1,
% 287.45/40.95 | all_1330_2 gives:
% 287.45/40.95 | (149) hAPP_f1631501043l_bool(ord_le1311769555a_bool, g) = all_1330_2 &
% 287.45/40.95 | hAPP_fun_a_bool_bool(all_1330_2, all_1330_1) = all_1330_0 &
% 287.45/40.95 | image_pname_a(mgt_call, u) = all_1330_1 & $i(all_1330_0) &
% 287.45/40.95 | $i(all_1330_1) & $i(all_1330_2) & hBOOL(all_1330_0)
% 287.45/40.95 |
% 287.45/40.95 | ALPHA: (149) implies:
% 287.45/40.95 | (150) hBOOL(all_1330_0)
% 287.45/40.95 | (151) image_pname_a(mgt_call, u) = all_1330_1
% 287.45/40.95 | (152) hAPP_fun_a_bool_bool(all_1330_2, all_1330_1) = all_1330_0
% 287.45/40.95 | (153) hAPP_f1631501043l_bool(ord_le1311769555a_bool, g) = all_1330_2
% 287.45/40.95 |
% 287.45/40.95 | DELTA: instantiating (41) with fresh symbol all_1335_0 gives:
% 287.45/40.95 | (154) hAPP_i1948725293t_bool(ord_less_eq_int, zero_zero_int) = all_1335_0 &
% 287.45/40.95 | $i(all_1335_0) & ! [v0: $i] : ! [v1: $i] : ( ~
% 287.45/40.95 | (hAPP_nat_int(semiri1621563631at_int, v0) = v1) | ~ $i(v0) | ?
% 287.45/40.95 | [v2: $i] : (hAPP_int_bool(all_1335_0, v1) = v2 & $i(v2) &
% 287.45/40.95 | hBOOL(v2)))
% 287.45/40.95 |
% 287.45/40.95 | ALPHA: (154) implies:
% 287.45/40.95 | (155) hAPP_i1948725293t_bool(ord_less_eq_int, zero_zero_int) = all_1335_0
% 287.45/40.95 |
% 287.45/40.95 | DELTA: instantiating (58) with fresh symbols all_1351_0, all_1351_1,
% 287.45/40.95 | all_1351_2, all_1351_3 gives:
% 287.45/40.95 | (156) bit1(all_1351_3) = all_1351_2 & bit1(pls) = all_1351_3 &
% 287.45/40.95 | number_number_of_int(all_1351_2) = all_1351_1 &
% 287.45/40.95 | number_number_of_nat(all_1351_2) = all_1351_0 &
% 287.45/40.95 | hAPP_nat_int(semiri1621563631at_int, all_1351_0) = all_1351_1 &
% 287.45/40.95 | $i(all_1351_0) & $i(all_1351_1) & $i(all_1351_2) & $i(all_1351_3)
% 287.45/40.95 |
% 287.45/40.95 | ALPHA: (156) implies:
% 287.45/40.95 | (157) bit1(pls) = all_1351_3
% 287.45/40.95 |
% 287.45/40.95 | DELTA: instantiating (75) with fresh symbols all_1381_0, all_1381_1,
% 287.45/40.95 | all_1381_2, all_1381_3, all_1381_4 gives:
% 287.45/40.95 | (158) hAPP_nat_nat(suc, na) = all_1381_4 &
% 287.45/40.95 | hAPP_fun_a_bool_nat(finite_card_a, all_1381_2) = all_1381_1 &
% 287.45/40.95 | hAPP_n1699378549t_bool(ord_less_eq_nat, all_1381_4) = all_1381_3 &
% 287.45/40.95 | hAPP_nat_bool(all_1381_3, all_1381_1) = all_1381_0 &
% 287.45/40.95 | image_pname_a(mgt_call, u) = all_1381_2 & $i(all_1381_0) &
% 287.45/40.95 | $i(all_1381_1) & $i(all_1381_2) & $i(all_1381_3) & $i(all_1381_4) &
% 287.45/40.95 | hBOOL(all_1381_0)
% 287.45/40.95 |
% 287.45/40.95 | ALPHA: (158) implies:
% 287.45/40.95 | (159) $i(all_1381_2)
% 287.45/40.95 | (160) image_pname_a(mgt_call, u) = all_1381_2
% 287.45/40.95 |
% 287.45/40.95 | DELTA: instantiating (67) with fresh symbols all_1383_0, all_1383_1,
% 287.45/40.95 | all_1383_2, all_1383_3, all_1383_4 gives:
% 287.45/40.95 | (161) bit1(all_1383_3) = all_1383_2 & bit1(pls) = all_1383_3 &
% 287.45/40.95 | number_number_of_int(all_1383_2) = all_1383_1 &
% 287.45/40.95 | hAPP_i1948725293t_bool(ord_less_eq_int, zero_zero_int) = all_1383_4 &
% 287.45/40.95 | hAPP_int_bool(all_1383_4, all_1383_1) = all_1383_0 & $i(all_1383_0) &
% 287.45/40.95 | $i(all_1383_1) & $i(all_1383_2) & $i(all_1383_3) & $i(all_1383_4) &
% 287.45/40.95 | hBOOL(all_1383_0)
% 287.45/40.95 |
% 287.45/40.95 | ALPHA: (161) implies:
% 287.45/40.95 | (162) hAPP_i1948725293t_bool(ord_less_eq_int, zero_zero_int) = all_1383_4
% 287.45/40.95 | (163) bit1(pls) = all_1383_3
% 287.45/40.95 |
% 287.45/40.95 | DELTA: instantiating (60) with fresh symbols all_1385_0, all_1385_1,
% 287.45/40.95 | all_1385_2, all_1385_3, all_1385_4 gives:
% 287.45/40.95 | (164) bit1(all_1385_4) = all_1385_3 & bit1(pls) = all_1385_4 &
% 287.45/40.95 | number_number_of_nat(all_1385_3) = all_1385_2 & hAPP_nat_nat(suc,
% 287.45/40.95 | all_1385_0) = all_1385_2 & hAPP_nat_nat(suc, all_1385_1) =
% 287.45/40.95 | all_1385_0 & hAPP_nat_nat(suc, zero_zero_nat) = all_1385_1 &
% 287.45/40.95 | $i(all_1385_0) & $i(all_1385_1) & $i(all_1385_2) & $i(all_1385_3) &
% 287.45/40.95 | $i(all_1385_4)
% 287.45/40.95 |
% 287.45/40.95 | ALPHA: (164) implies:
% 287.45/40.95 | (165) hAPP_nat_nat(suc, zero_zero_nat) = all_1385_1
% 287.45/40.95 | (166) bit1(pls) = all_1385_4
% 287.45/40.95 |
% 287.45/40.95 | DELTA: instantiating (76) with fresh symbols all_1387_0, all_1387_1,
% 287.45/40.95 | all_1387_2, all_1387_3, all_1387_4 gives:
% 287.45/40.95 | (167) hAPP_nat_fun_nat_nat(minus_minus_nat, all_1387_2) = all_1387_1 &
% 287.45/40.95 | hAPP_nat_nat(all_1387_1, all_1387_0) = all_1387_4 & hAPP_nat_nat(suc,
% 287.45/40.95 | na) = all_1387_0 & hAPP_fun_a_bool_nat(finite_card_a, all_1387_3) =
% 287.45/40.95 | all_1387_2 & hAPP_fun_a_bool_nat(finite_card_a, g) = all_1387_4 &
% 287.45/40.95 | image_pname_a(mgt_call, u) = all_1387_3 & $i(all_1387_0) &
% 287.45/40.95 | $i(all_1387_1) & $i(all_1387_2) & $i(all_1387_3) & $i(all_1387_4)
% 287.45/40.95 |
% 287.45/40.95 | ALPHA: (167) implies:
% 287.45/40.95 | (168) image_pname_a(mgt_call, u) = all_1387_3
% 287.45/40.95 |
% 287.45/40.95 | DELTA: instantiating (47) with fresh symbols all_1411_0, all_1411_1 gives:
% 287.45/40.95 | (169) hAPP_i1948725293t_bool(ord_less_int, zero_zero_int) = all_1411_1 &
% 287.45/40.95 | hAPP_n1699378549t_bool(ord_less_nat, zero_zero_nat) = all_1411_0 &
% 287.45/40.95 | $i(all_1411_0) & $i(all_1411_1) & ! [v0: $i] : ! [v1: $i] : ( ~
% 287.45/40.95 | (hAPP_int_bool(all_1411_1, v0) = v1) | ~ $i(v0) | ~ hBOOL(v1) |
% 287.45/40.95 | ? [v2: $i] : ? [v3: $i] : (hAPP_nat_int(semiri1621563631at_int,
% 287.45/40.95 | v2) = v0 & hAPP_nat_bool(all_1411_0, v2) = v3 & $i(v3) & $i(v2)
% 287.45/40.95 | & hBOOL(v3)))
% 287.45/40.95 |
% 287.45/40.95 | ALPHA: (169) implies:
% 287.45/40.95 | (170) hAPP_i1948725293t_bool(ord_less_int, zero_zero_int) = all_1411_1
% 287.45/40.95 |
% 287.45/40.95 | DELTA: instantiating (6) with fresh symbol all_1426_0 gives:
% 287.45/40.96 | (171) hAPP_nat_nat(suc, zero_zero_nat) = all_1426_0 & $i(all_1426_0) & !
% 287.45/40.96 | [v0: $i] : ! [v1: $i] : (v0 = zero_zero_nat | ~
% 287.45/40.96 | (hAPP_n1699378549t_bool(ord_less_nat, v0) = v1) | ~ $i(v0) | ?
% 287.45/40.96 | [v2: $i] : (hAPP_nat_bool(v1, all_1426_0) = v2 & $i(v2) & ~
% 287.45/40.96 | hBOOL(v2))) & ! [v0: $i] : ( ~
% 287.45/40.96 | (hAPP_n1699378549t_bool(ord_less_nat, zero_zero_nat) = v0) | ?
% 287.45/40.96 | [v1: $i] : (hAPP_nat_bool(v0, all_1426_0) = v1 & $i(v1) &
% 287.45/40.96 | hBOOL(v1)))
% 287.45/40.96 |
% 287.45/40.96 | ALPHA: (171) implies:
% 287.45/40.96 | (172) hAPP_nat_nat(suc, zero_zero_nat) = all_1426_0
% 287.45/40.96 |
% 287.45/40.96 | DELTA: instantiating (9) with fresh symbols all_1435_0, all_1435_1 gives:
% 287.45/40.96 | (173) hAPP_nat_nat(suc, zero_zero_nat) = all_1435_0 &
% 287.45/40.96 | hAPP_n1699378549t_bool(ord_less_nat, zero_zero_nat) = all_1435_1 &
% 287.45/40.96 | $i(all_1435_0) & $i(all_1435_1) & ! [v0: $i] : ! [v1: $i] : ( ~
% 287.45/40.96 | (hAPP_nat_bool(all_1435_1, v0) = v1) | ~ $i(v0) | ~ hBOOL(v1) |
% 287.45/40.96 | ? [v2: $i] : ? [v3: $i] : (hAPP_nat_fun_nat_nat(minus_minus_nat,
% 287.45/40.96 | v0) = v2 & hAPP_nat_nat(v2, all_1435_0) = v3 &
% 287.45/40.96 | hAPP_nat_nat(suc, v3) = v0 & $i(v3) & $i(v2)))
% 287.45/40.96 |
% 287.45/40.96 | ALPHA: (173) implies:
% 287.45/40.96 | (174) hAPP_nat_nat(suc, zero_zero_nat) = all_1435_0
% 287.45/40.96 |
% 287.45/40.96 | DELTA: instantiating (83) with fresh symbols all_1445_0, all_1445_1,
% 287.45/40.96 | all_1445_2, all_1445_3, all_1445_4, all_1445_5 gives:
% 287.45/40.96 | (175) hAPP_a1206381875a_bool(insert_a, all_1445_5) = all_1445_4 &
% 287.45/40.96 | hAPP_f1631501043l_bool(ord_le1311769555a_bool, all_1445_3) =
% 287.45/40.96 | all_1445_2 & hAPP_f2050579477a_bool(all_1445_4, g) = all_1445_3 &
% 287.45/40.96 | hAPP_fun_a_bool_bool(all_1445_2, all_1445_1) = all_1445_0 &
% 287.45/40.96 | hAPP_pname_a(mgt_call, pn) = all_1445_5 & image_pname_a(mgt_call, u)
% 287.45/40.96 | = all_1445_1 & $i(all_1445_0) & $i(all_1445_1) & $i(all_1445_2) &
% 287.45/40.96 | $i(all_1445_3) & $i(all_1445_4) & $i(all_1445_5) & ~
% 287.45/40.96 | hBOOL(all_1445_0)
% 287.45/40.96 |
% 287.45/40.96 | ALPHA: (175) implies:
% 287.45/40.96 | (176) ~ hBOOL(all_1445_0)
% 287.45/40.96 | (177) $i(all_1445_5)
% 287.45/40.96 | (178) $i(all_1445_3)
% 287.45/40.96 | (179) image_pname_a(mgt_call, u) = all_1445_1
% 287.45/40.96 | (180) hAPP_pname_a(mgt_call, pn) = all_1445_5
% 287.45/40.96 | (181) hAPP_fun_a_bool_bool(all_1445_2, all_1445_1) = all_1445_0
% 287.45/40.96 | (182) hAPP_f2050579477a_bool(all_1445_4, g) = all_1445_3
% 287.45/40.96 | (183) hAPP_f1631501043l_bool(ord_le1311769555a_bool, all_1445_3) =
% 287.45/40.96 | all_1445_2
% 287.45/40.96 | (184) hAPP_a1206381875a_bool(insert_a, all_1445_5) = all_1445_4
% 287.45/40.96 |
% 287.45/40.96 | DELTA: instantiating (40) with fresh symbols all_1447_0, all_1447_1 gives:
% 287.45/40.96 | (185) hAPP_i1948725293t_bool(ord_less_eq_int, zero_zero_int) = all_1447_1 &
% 287.45/40.96 | cOMBB_1652995168ol_int(fconj, all_1447_1) = all_1447_0 &
% 287.45/40.96 | $i(all_1447_0) & $i(all_1447_1) & ! [v0: $i] : ! [v1: $i] : ( ~
% 287.45/40.96 | (cOMBS_int_bool_bool(all_1447_0, v0) = v1) | ~ $i(v0) | ? [v2:
% 287.45/40.96 | $i] : ? [v3: $i] : ? [v4: $i] : (cOMBB_int_bool_nat(v0,
% 287.45/40.96 | semiri1621563631at_int) = v3 & collect_int(v1) = v2 &
% 287.45/40.96 | collect_nat(v3) = v4 & image_nat_int(semiri1621563631at_int, v4)
% 287.45/40.96 | = v2 & $i(v4) & $i(v3) & $i(v2)))
% 287.45/40.96 |
% 287.45/40.96 | ALPHA: (185) implies:
% 287.45/40.96 | (186) hAPP_i1948725293t_bool(ord_less_eq_int, zero_zero_int) = all_1447_1
% 287.45/40.96 |
% 287.45/40.96 | DELTA: instantiating (19) with fresh symbols all_1462_0, all_1462_1,
% 287.45/40.96 | all_1462_2 gives:
% 287.45/40.96 | (187) hAPP_int_fun_int_int(plus_plus_int, one_one_int) = all_1462_0 &
% 287.45/40.96 | hAPP_i1948725293t_bool(ord_less_int, zero_zero_int) = all_1462_1 &
% 287.45/40.96 | hAPP_i1948725293t_bool(ord_less_eq_int, zero_zero_int) = all_1462_2 &
% 287.45/40.96 | $i(all_1462_0) & $i(all_1462_1) & $i(all_1462_2) & ! [v0: $i] : !
% 287.45/40.96 | [v1: $i] : ( ~ (hAPP_int_int(all_1462_0, v0) = v1) | ~ $i(v0) | ?
% 287.45/40.96 | [v2: $i] : ? [v3: $i] : ((hAPP_int_bool(all_1462_1, v1) = v3 &
% 287.45/40.96 | $i(v3) & hBOOL(v3)) | (hAPP_int_bool(all_1462_2, v0) = v2 &
% 287.45/40.96 | $i(v2) & ~ hBOOL(v2))))
% 287.45/40.96 |
% 287.45/40.96 | ALPHA: (187) implies:
% 287.45/40.96 | (188) hAPP_i1948725293t_bool(ord_less_eq_int, zero_zero_int) = all_1462_2
% 287.45/40.96 | (189) hAPP_i1948725293t_bool(ord_less_int, zero_zero_int) = all_1462_1
% 287.45/40.96 |
% 287.45/40.96 | DELTA: instantiating (50) with fresh symbol all_1465_0 gives:
% 287.45/40.96 | (190) hAPP_i1948725293t_bool(ord_less_eq_int, zero_zero_int) = all_1465_0 &
% 287.45/40.96 | $i(all_1465_0) & ! [v0: $i] : ! [v1: $i] : ( ~
% 287.45/40.96 | (hAPP_int_bool(all_1465_0, v0) = v1) | ~ $i(v0) | ~ hBOOL(v1) |
% 287.45/40.96 | ? [v2: $i] : (hAPP_int_bool(nat_neg, v0) = v2 & $i(v2) & ~
% 287.45/40.96 | hBOOL(v2))) & ! [v0: $i] : ! [v1: $i] : ( ~
% 287.45/40.96 | (hAPP_int_bool(all_1465_0, v0) = v1) | ~ $i(v0) | hBOOL(v1) | ?
% 287.45/40.96 | [v2: $i] : (hAPP_int_bool(nat_neg, v0) = v2 & $i(v2) & hBOOL(v2)))
% 287.45/40.96 |
% 287.45/40.96 | ALPHA: (190) implies:
% 287.45/40.96 | (191) hAPP_i1948725293t_bool(ord_less_eq_int, zero_zero_int) = all_1465_0
% 287.45/40.96 |
% 287.45/40.96 | DELTA: instantiating (29) with fresh symbol all_1496_0 gives:
% 287.45/40.96 | (192) hAPP_i1948725293t_bool(ord_less_eq_int, zero_zero_int) = all_1496_0 &
% 287.45/40.96 | $i(all_1496_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 287.45/40.96 | $i] : ( ~ (hAPP_int_bool(all_1496_0, v1) = v2) | ~
% 287.45/40.96 | (hAPP_int_bool(all_1496_0, v0) = v3) | ~ $i(v1) | ~ $i(v0) | ~
% 287.45/40.96 | hBOOL(v3) | ~ hBOOL(v2) | ? [v4: $i] : ? [v5: $i] : ? [v6: $i]
% 287.45/40.96 | : (hAPP_int_fun_int_int(times_times_int, v1) = v4 &
% 287.45/40.96 | hAPP_int_int(v4, v0) = v5 & hAPP_int_bool(all_1496_0, v5) = v6 &
% 287.45/40.96 | $i(v6) & $i(v5) & $i(v4) & hBOOL(v6)))
% 287.45/40.96 |
% 287.45/40.96 | ALPHA: (192) implies:
% 287.45/40.96 | (193) hAPP_i1948725293t_bool(ord_less_eq_int, zero_zero_int) = all_1496_0
% 287.45/40.96 |
% 287.45/40.96 | DELTA: instantiating (10) with fresh symbol all_1505_0 gives:
% 287.45/40.96 | (194) hAPP_nat_nat(suc, zero_zero_nat) = all_1505_0 & $i(all_1505_0) & !
% 287.45/40.96 | [v0: $i] : ! [v1: any] : ! [v2: $i] : (v1 = all_1505_0 | ~
% 287.45/40.96 | (hAPP_nat_fun_nat_nat(times_times_nat, v0) = v2) | ~
% 287.45/40.96 | (hAPP_nat_nat(v2, v1) = all_1505_0) | ~ $i(v1) | ~ $i(v0)) & !
% 287.45/40.96 | [v0: any] : ! [v1: $i] : ! [v2: $i] : (v0 = all_1505_0 | ~
% 287.45/40.96 | (hAPP_nat_fun_nat_nat(times_times_nat, v0) = v2) | ~
% 287.45/40.96 | (hAPP_nat_nat(v2, v1) = all_1505_0) | ~ $i(v1) | ~ $i(v0)) & !
% 287.45/40.96 | [v0: $i] : ! [v1: int] : (v1 = all_1505_0 | ~
% 287.45/40.96 | (hAPP_nat_fun_nat_nat(times_times_nat, all_1505_0) = v0) | ~
% 287.45/40.96 | (hAPP_nat_nat(v0, all_1505_0) = v1))
% 287.45/40.96 |
% 287.45/40.96 | ALPHA: (194) implies:
% 287.45/40.96 | (195) hAPP_nat_nat(suc, zero_zero_nat) = all_1505_0
% 287.45/40.96 |
% 287.45/40.96 | DELTA: instantiating (46) with fresh symbol all_1508_0 gives:
% 287.45/40.96 | (196) hAPP_i1948725293t_bool(ord_less_eq_int, zero_zero_int) = all_1508_0 &
% 287.45/40.96 | $i(all_1508_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 287.45/40.96 | $i] : ( ~ (hAPP_int_bool(all_1508_0, v1) = v2) | ~
% 287.45/40.96 | (hAPP_int_bool(all_1508_0, v0) = v3) | ~ $i(v1) | ~ $i(v0) | ~
% 287.45/40.96 | hBOOL(v3) | ~ hBOOL(v2) | ? [v4: $i] : ? [v5: $i] : ? [v6: $i]
% 287.45/40.96 | : (hAPP_int_fun_int_int(nat_tsub, v1) = v4 & hAPP_int_int(v4, v0) =
% 287.45/40.96 | v5 & hAPP_int_bool(all_1508_0, v5) = v6 & $i(v6) & $i(v5) &
% 287.45/40.96 | $i(v4) & hBOOL(v6)))
% 287.45/40.96 |
% 287.45/40.96 | ALPHA: (196) implies:
% 287.45/40.96 | (197) hAPP_i1948725293t_bool(ord_less_eq_int, zero_zero_int) = all_1508_0
% 287.45/40.96 |
% 287.45/40.96 | DELTA: instantiating (31) with fresh symbol all_1517_0 gives:
% 287.45/40.97 | (198) hAPP_i1948725293t_bool(ord_less_eq_int, zero_zero_int) = all_1517_0 &
% 287.45/40.97 | $i(all_1517_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 287.45/40.97 | $i] : ( ~ (hAPP_int_bool(all_1517_0, v1) = v2) | ~
% 287.45/40.97 | (hAPP_int_bool(all_1517_0, v0) = v3) | ~ $i(v1) | ~ $i(v0) | ~
% 287.45/40.97 | hBOOL(v3) | ~ hBOOL(v2) | ? [v4: $i] : ? [v5: $i] : ? [v6: $i]
% 287.45/40.97 | : (hAPP_int_fun_int_int(plus_plus_int, v1) = v4 & hAPP_int_int(v4,
% 287.45/40.97 | v0) = v5 & hAPP_int_bool(all_1517_0, v5) = v6 & $i(v6) & $i(v5)
% 287.45/40.97 | & $i(v4) & hBOOL(v6)))
% 287.45/40.97 |
% 287.45/40.97 | ALPHA: (198) implies:
% 287.45/40.97 | (199) hAPP_i1948725293t_bool(ord_less_eq_int, zero_zero_int) = all_1517_0
% 287.45/40.97 |
% 287.45/40.97 | DELTA: instantiating (61) with fresh symbols all_1531_0, all_1531_1,
% 287.45/40.97 | all_1531_2, all_1531_3 gives:
% 287.45/40.97 | (200) bit1(all_1531_3) = all_1531_2 & bit1(pls) = all_1531_3 &
% 287.45/40.97 | number_number_of_nat(all_1531_2) = all_1531_1 &
% 287.45/40.97 | hAPP_nat_fun_nat_nat(plus_plus_nat, all_1531_1) = all_1531_0 &
% 287.45/40.97 | $i(all_1531_0) & $i(all_1531_1) & $i(all_1531_2) & $i(all_1531_3) &
% 287.45/40.97 | ! [v0: $i] : ! [v1: $i] : ( ~ (hAPP_nat_nat(all_1531_0, v0) = v1) |
% 287.45/40.97 | ~ $i(v0) | ? [v2: $i] : ? [v3: $i] : (hAPP_nat_nat(suc, v3) = v1
% 287.45/40.97 | & hAPP_nat_nat(suc, v2) = v3 & hAPP_nat_nat(suc, v0) = v2 &
% 287.45/40.97 | $i(v3) & $i(v2) & $i(v1)))
% 287.45/40.97 |
% 287.45/40.97 | ALPHA: (200) implies:
% 287.45/40.97 | (201) bit1(pls) = all_1531_3
% 287.45/40.97 |
% 287.45/40.97 | DELTA: instantiating (18) with fresh symbols all_1534_0, all_1534_1 gives:
% 287.45/40.97 | (202) hAPP_i1948725293t_bool(ord_less_int, zero_zero_int) = all_1534_0 &
% 287.45/40.97 | hAPP_i1948725293t_bool(ord_less_eq_int, one_one_int) = all_1534_1 &
% 287.45/40.97 | $i(all_1534_0) & $i(all_1534_1) & ! [v0: $i] : ! [v1: $i] : ( ~
% 287.45/40.97 | (hAPP_int_bool(all_1534_0, v0) = v1) | ~ $i(v0) | ~ hBOOL(v1) |
% 287.45/40.97 | ? [v2: $i] : (hAPP_int_bool(all_1534_1, v0) = v2 & $i(v2) &
% 287.45/40.97 | hBOOL(v2))) & ! [v0: $i] : ! [v1: $i] : ( ~
% 287.45/40.97 | (hAPP_int_bool(all_1534_0, v0) = v1) | ~ $i(v0) | hBOOL(v1) | ?
% 287.45/40.97 | [v2: $i] : (hAPP_int_bool(all_1534_1, v0) = v2 & $i(v2) & ~
% 287.45/40.97 | hBOOL(v2)))
% 287.45/40.97 |
% 287.45/40.97 | ALPHA: (202) implies:
% 287.45/40.97 | (203) hAPP_i1948725293t_bool(ord_less_eq_int, one_one_int) = all_1534_1
% 287.45/40.97 | (204) hAPP_i1948725293t_bool(ord_less_int, zero_zero_int) = all_1534_0
% 287.45/40.97 |
% 287.45/40.97 | DELTA: instantiating (13) with fresh symbols all_1537_0, all_1537_1 gives:
% 287.45/40.97 | (205) hAPP_nat_nat(suc, zero_zero_nat) = all_1537_1 &
% 287.45/40.97 | hAPP_n1699378549t_bool(ord_less_nat, all_1537_1) = all_1537_0 &
% 287.45/40.97 | $i(all_1537_0) & $i(all_1537_1) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 287.45/40.97 | $i] : ! [v3: $i] : ( ~ (hAPP_nat_bool(all_1537_0, v1) = v2) | ~
% 287.45/40.97 | (hAPP_nat_bool(all_1537_0, v0) = v3) | ~ $i(v1) | ~ $i(v0) | ~
% 287.45/40.97 | hBOOL(v3) | ~ hBOOL(v2) | ? [v4: $i] : ? [v5: $i] : ? [v6: $i]
% 287.45/40.97 | : (hAPP_nat_fun_nat_nat(times_times_nat, v0) = v4 &
% 287.45/40.97 | hAPP_nat_nat(v4, v1) = v5 & hAPP_nat_bool(all_1537_0, v5) = v6 &
% 287.45/40.97 | $i(v6) & $i(v5) & $i(v4) & hBOOL(v6)))
% 287.45/40.97 |
% 287.45/40.97 | ALPHA: (205) implies:
% 287.45/40.97 | (206) hAPP_nat_nat(suc, zero_zero_nat) = all_1537_1
% 287.45/40.97 |
% 287.45/40.97 | DELTA: instantiating (69) with fresh symbol all_1540_0 gives:
% 287.45/40.97 | (207) hAPP_i1948725293t_bool(ord_less_eq_int, pls) = all_1540_0 &
% 287.45/40.97 | $i(all_1540_0) & ! [v0: $i] : ! [v1: $i] : ( ~
% 287.45/40.97 | (hAPP_int_bool(all_1540_0, v0) = v1) | ~ $i(v0) | ~ hBOOL(v1) |
% 287.45/40.97 | ? [v2: $i] : ? [v3: $i] : (bit1(v0) = v2 &
% 287.45/40.97 | hAPP_int_bool(all_1540_0, v2) = v3 & $i(v3) & $i(v2) &
% 287.45/40.97 | hBOOL(v3))) & ! [v0: $i] : ! [v1: $i] : ( ~
% 287.45/40.97 | (hAPP_int_bool(all_1540_0, v0) = v1) | ~ $i(v0) | hBOOL(v1) | ?
% 287.45/40.97 | [v2: $i] : ? [v3: $i] : (bit1(v0) = v2 & hAPP_int_bool(all_1540_0,
% 287.45/40.97 | v2) = v3 & $i(v3) & $i(v2) & ~ hBOOL(v3)))
% 287.45/40.97 |
% 287.45/40.97 | ALPHA: (207) implies:
% 287.45/40.97 | (208) hAPP_i1948725293t_bool(ord_less_eq_int, pls) = all_1540_0
% 287.45/40.97 |
% 287.45/40.97 | DELTA: instantiating (11) with fresh symbols all_1546_0, all_1546_1 gives:
% 287.45/40.97 | (209) hAPP_nat_nat(suc, zero_zero_nat) = all_1546_1 &
% 287.45/40.97 | hAPP_n1699378549t_bool(ord_less_nat, all_1546_1) = all_1546_0 &
% 287.45/40.97 | $i(all_1546_0) & $i(all_1546_1) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 287.45/40.97 | $i] : ! [v3: $i] : ( ~ (hAPP_nat_bool(all_1546_0, v1) = v2) | ~
% 287.45/40.97 | (hAPP_nat_bool(all_1546_0, v0) = v3) | ~ $i(v1) | ~ $i(v0) | ~
% 287.45/40.97 | hBOOL(v3) | ~ hBOOL(v2) | ? [v4: $i] : ? [v5: $i] : ? [v6: $i]
% 287.45/40.97 | : ? [v7: $i] : (hAPP_nat_fun_nat_nat(times_times_nat, v0) = v5 &
% 287.45/40.97 | hAPP_nat_nat(v5, v1) = v6 & hAPP_n1699378549t_bool(ord_less_nat,
% 287.45/40.97 | v1) = v4 & hAPP_nat_bool(v4, v6) = v7 & $i(v7) & $i(v6) &
% 287.45/40.97 | $i(v5) & $i(v4) & hBOOL(v7)))
% 287.45/40.97 |
% 287.45/40.97 | ALPHA: (209) implies:
% 287.45/40.97 | (210) hAPP_nat_nat(suc, zero_zero_nat) = all_1546_1
% 287.45/40.97 |
% 287.45/40.97 | DELTA: instantiating (15) with fresh symbol all_1549_0 gives:
% 287.45/40.97 | (211) hAPP_i1948725293t_bool(ord_less_int, zero_zero_int) = all_1549_0 &
% 287.45/40.97 | $i(all_1549_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 287.45/40.97 | $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ( ~
% 287.45/40.97 | (hAPP_int_fun_int_int(times_times_int, v0) = v3) | ~
% 287.45/40.97 | (hAPP_int_int(v3, v2) = v6) | ~ (hAPP_int_int(v3, v1) = v4) | ~
% 287.45/40.97 | (hAPP_i1948725293t_bool(ord_less_int, v4) = v5) | ~
% 287.45/40.97 | (hAPP_int_bool(v5, v6) = v7) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 287.45/40.97 | hBOOL(v7) | ? [v8: $i] : ? [v9: $i] : ? [v10: $i] :
% 287.45/40.97 | ((hAPP_i1948725293t_bool(ord_less_int, v1) = v8 & hAPP_int_bool(v8,
% 287.45/40.97 | v2) = v9 & $i(v9) & $i(v8) & ~ hBOOL(v9)) |
% 287.45/40.97 | (hAPP_int_bool(all_1549_0, v0) = v10 & $i(v10) & ~ hBOOL(v10))))
% 287.45/40.97 |
% 287.45/40.97 | ALPHA: (211) implies:
% 287.45/40.97 | (212) hAPP_i1948725293t_bool(ord_less_int, zero_zero_int) = all_1549_0
% 287.45/40.97 |
% 287.45/40.97 | DELTA: instantiating (12) with fresh symbols all_1552_0, all_1552_1 gives:
% 287.45/40.97 | (213) hAPP_nat_nat(suc, zero_zero_nat) = all_1552_1 &
% 287.45/40.97 | hAPP_n1699378549t_bool(ord_less_nat, all_1552_1) = all_1552_0 &
% 287.45/40.97 | $i(all_1552_0) & $i(all_1552_1) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 287.45/40.97 | $i] : ! [v3: $i] : ( ~ (hAPP_nat_bool(all_1552_0, v1) = v2) | ~
% 287.45/40.97 | (hAPP_nat_bool(all_1552_0, v0) = v3) | ~ $i(v1) | ~ $i(v0) | ~
% 287.45/40.97 | hBOOL(v3) | ~ hBOOL(v2) | ? [v4: $i] : ? [v5: $i] : ? [v6: $i]
% 287.45/40.97 | : ? [v7: $i] : (hAPP_nat_fun_nat_nat(times_times_nat, v1) = v5 &
% 287.45/40.97 | hAPP_nat_nat(v5, v0) = v6 & hAPP_n1699378549t_bool(ord_less_nat,
% 287.45/40.97 | v1) = v4 & hAPP_nat_bool(v4, v6) = v7 & $i(v7) & $i(v6) &
% 287.45/40.97 | $i(v5) & $i(v4) & hBOOL(v7)))
% 287.45/40.97 |
% 287.45/40.97 | ALPHA: (213) implies:
% 287.45/40.97 | (214) hAPP_nat_nat(suc, zero_zero_nat) = all_1552_1
% 287.45/40.97 |
% 287.45/40.97 | DELTA: instantiating (49) with fresh symbol all_1564_0 gives:
% 287.45/40.98 | (215) hAPP_i1948725293t_bool(ord_less_int, zero_zero_int) = all_1564_0 &
% 287.45/40.98 | $i(all_1564_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 287.45/40.98 | $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : !
% 287.45/40.98 | [v8: $i] : ! [v9: $i] : ! [v10: $i] : ! [v11: $i] : ! [v12: $i] :
% 287.45/40.98 | ( ~ (abs_abs_int(v4) = v5) | ~
% 287.45/40.98 | (hAPP_int_fun_int_int(times_times_int, v7) = v8) | ~
% 287.45/40.98 | (hAPP_int_fun_int_int(plus_plus_int, v5) = v6) | ~
% 287.45/40.98 | (hAPP_int_fun_int_int(minus_minus_int, v0) = v3) | ~
% 287.45/40.98 | (hAPP_int_int(v8, v2) = v9) | ~ (hAPP_int_int(v6, one_one_int) =
% 287.45/40.98 | v7) | ~ (hAPP_int_int(v3, v9) = v10) | ~ (hAPP_int_int(v3, v1)
% 287.45/40.98 | = v4) | ~ (hAPP_i1948725293t_bool(ord_less_int, v10) = v11) | ~
% 287.45/40.98 | (hAPP_int_bool(v11, v1) = v12) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0)
% 287.45/40.98 | | hBOOL(v12) | ? [v13: $i] : (hAPP_int_bool(all_1564_0, v2) = v13
% 287.45/40.98 | & $i(v13) & ~ hBOOL(v13)))
% 287.45/40.98 |
% 287.45/40.98 | ALPHA: (215) implies:
% 287.45/40.98 | (216) hAPP_i1948725293t_bool(ord_less_int, zero_zero_int) = all_1564_0
% 287.45/40.98 |
% 287.45/40.98 | DELTA: instantiating (73) with fresh symbols all_1573_0, all_1573_1 gives:
% 287.45/40.98 | (217) hAPP_i1948725293t_bool(ord_less_int, pls) = all_1573_1 &
% 287.45/40.98 | hAPP_i1948725293t_bool(ord_less_eq_int, pls) = all_1573_0 &
% 287.45/40.98 | $i(all_1573_0) & $i(all_1573_1) & ! [v0: $i] : ! [v1: $i] : ( ~
% 287.45/40.98 | (hAPP_int_bool(all_1573_0, v0) = v1) | ~ $i(v0) | ~ hBOOL(v1) |
% 287.45/40.98 | ? [v2: $i] : ? [v3: $i] : (bit1(v0) = v2 &
% 287.45/40.98 | hAPP_int_bool(all_1573_1, v2) = v3 & $i(v3) & $i(v2) &
% 287.45/40.98 | hBOOL(v3))) & ! [v0: $i] : ! [v1: $i] : ( ~
% 287.45/40.98 | (hAPP_int_bool(all_1573_0, v0) = v1) | ~ $i(v0) | hBOOL(v1) | ?
% 287.45/40.98 | [v2: $i] : ? [v3: $i] : (bit1(v0) = v2 & hAPP_int_bool(all_1573_1,
% 287.45/40.98 | v2) = v3 & $i(v3) & $i(v2) & ~ hBOOL(v3)))
% 287.45/40.98 |
% 287.45/40.98 | ALPHA: (217) implies:
% 287.45/40.98 | (218) hAPP_i1948725293t_bool(ord_less_eq_int, pls) = all_1573_0
% 287.45/40.98 | (219) hAPP_i1948725293t_bool(ord_less_int, pls) = all_1573_1
% 287.45/40.98 |
% 287.45/40.98 | DELTA: instantiating (55) with fresh symbol all_1576_0 gives:
% 287.45/40.98 | (220) hAPP_i1948725293t_bool(ord_less_int, zero_zero_int) = all_1576_0 &
% 287.45/40.98 | $i(all_1576_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 287.45/40.98 | $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : !
% 287.45/40.98 | [v8: $i] : ! [v9: $i] : ! [v10: $i] : ! [v11: $i] : ! [v12: $i] :
% 287.45/40.98 | ! [v13: $i] : ( ~ (abs_abs_int(v6) = v7) | ~
% 287.45/40.98 | (hAPP_int_fun_int_int(times_times_int, v9) = v10) | ~
% 287.45/40.98 | (hAPP_int_fun_int_int(plus_plus_int, v7) = v8) | ~
% 287.45/40.98 | (hAPP_int_fun_int_int(plus_plus_int, v1) = v4) | ~
% 287.45/40.98 | (hAPP_int_fun_int_int(minus_minus_int, v1) = v5) | ~
% 287.45/40.98 | (hAPP_int_int(v10, v2) = v11) | ~ (hAPP_int_int(v8, one_one_int) =
% 287.45/40.98 | v9) | ~ (hAPP_int_int(v5, v0) = v6) | ~ (hAPP_int_int(v4, v11)
% 287.45/40.98 | = v12) | ~ (hAPP_i1948725293t_bool(ord_less_int, v0) = v3) | ~
% 287.45/40.98 | (hAPP_int_bool(v3, v12) = v13) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0)
% 287.45/40.98 | | hBOOL(v13) | ? [v14: $i] : (hAPP_int_bool(all_1576_0, v2) = v14
% 287.45/40.98 | & $i(v14) & ~ hBOOL(v14)))
% 287.45/40.98 |
% 287.45/40.98 | ALPHA: (220) implies:
% 287.45/40.98 | (221) hAPP_i1948725293t_bool(ord_less_int, zero_zero_int) = all_1576_0
% 287.45/40.98 |
% 287.45/40.98 | DELTA: instantiating (45) with fresh symbols all_1582_0, all_1582_1 gives:
% 287.45/40.98 | (222) hAPP_i1948725293t_bool(ord_less_int, zero_zero_int) = all_1582_1 &
% 287.45/40.98 | hAPP_n1699378549t_bool(ord_less_nat, zero_zero_nat) = all_1582_0 &
% 287.45/40.98 | $i(all_1582_0) & $i(all_1582_1) & ! [v0: $i] : ! [v1: $i] : ( ~
% 287.45/40.98 | (hAPP_nat_bool(all_1582_0, v0) = v1) | ~ $i(v0) | ~ hBOOL(v1) |
% 287.45/40.98 | ? [v2: $i] : ? [v3: $i] : (hAPP_nat_int(semiri1621563631at_int,
% 287.45/40.98 | v0) = v2 & hAPP_int_bool(all_1582_1, v2) = v3 & $i(v3) & $i(v2)
% 287.45/40.98 | & hBOOL(v3))) & ! [v0: $i] : ! [v1: $i] : ( ~
% 287.45/40.98 | (hAPP_nat_bool(all_1582_0, v0) = v1) | ~ $i(v0) | hBOOL(v1) | ?
% 287.45/40.98 | [v2: $i] : ? [v3: $i] : (hAPP_nat_int(semiri1621563631at_int, v0)
% 287.45/40.98 | = v2 & hAPP_int_bool(all_1582_1, v2) = v3 & $i(v3) & $i(v2) & ~
% 287.45/40.98 | hBOOL(v3)))
% 287.45/40.98 |
% 287.45/40.98 | ALPHA: (222) implies:
% 287.45/40.98 | (223) hAPP_i1948725293t_bool(ord_less_int, zero_zero_int) = all_1582_1
% 287.45/40.98 |
% 287.45/40.98 | DELTA: instantiating (23) with fresh symbols all_1591_0, all_1591_1 gives:
% 287.45/40.98 | (224) hAPP_i1948725293t_bool(ord_less_int, zero_zero_int) = all_1591_1 &
% 287.45/40.98 | hAPP_i1948725293t_bool(ord_less_eq_int, one_one_int) = all_1591_0 &
% 287.45/40.98 | $i(all_1591_0) & $i(all_1591_1) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 287.45/40.98 | $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~
% 287.45/40.98 | (hAPP_int_fun_int_int(times_times_int, v2) = v4) | ~
% 287.45/40.98 | (hAPP_int_fun_int_int(plus_plus_int, v0) = v3) | ~
% 287.45/40.98 | (hAPP_int_int(v4, v1) = v5) | ~ (hAPP_int_int(v3, v5) = v2) | ~
% 287.45/40.98 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: $i] : ? [v7: $i] : ?
% 287.45/40.98 | [v8: $i] : ? [v9: $i] : ((hAPP_i1948725293t_bool(ord_less_int, v0)
% 287.45/40.98 | = v7 & hAPP_int_bool(v7, v2) = v8 & $i(v8) & $i(v7) & ~
% 287.45/40.98 | hBOOL(v8)) | (hAPP_int_bool(all_1591_0, v1) = v9 & $i(v9) &
% 287.45/40.98 | hBOOL(v9)) | (hAPP_int_bool(all_1591_1, v2) = v6 & $i(v6) & ~
% 287.45/40.98 | hBOOL(v6))))
% 287.45/40.98 |
% 287.45/40.98 | ALPHA: (224) implies:
% 287.45/40.98 | (225) hAPP_i1948725293t_bool(ord_less_eq_int, one_one_int) = all_1591_0
% 287.45/40.98 | (226) hAPP_i1948725293t_bool(ord_less_int, zero_zero_int) = all_1591_1
% 287.45/40.98 |
% 287.45/40.98 | DELTA: instantiating (24) with fresh symbols all_1594_0, all_1594_1 gives:
% 287.45/40.98 | (227) hAPP_i1948725293t_bool(ord_less_int, zero_zero_int) = all_1594_1 &
% 287.45/40.98 | hAPP_i1948725293t_bool(ord_less_eq_int, zero_zero_int) = all_1594_0 &
% 287.45/40.98 | $i(all_1594_0) & $i(all_1594_1) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 287.45/40.98 | $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~
% 287.45/40.98 | (hAPP_int_fun_int_int(times_times_int, v2) = v4) | ~
% 287.45/40.98 | (hAPP_int_fun_int_int(plus_plus_int, v0) = v3) | ~
% 287.45/40.98 | (hAPP_int_int(v4, v1) = v5) | ~ (hAPP_int_int(v3, v5) = v2) | ~
% 287.45/40.98 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: $i] : ? [v7: $i] : ?
% 287.45/40.98 | [v8: $i] : ? [v9: $i] : ((hAPP_i1948725293t_bool(ord_less_eq_int,
% 287.45/40.98 | v1) = v8 & hAPP_int_bool(v8, one_one_int) = v9 & $i(v9) &
% 287.45/40.98 | $i(v8) & hBOOL(v9)) | (hAPP_int_bool(all_1594_0, v0) = v7 &
% 287.45/40.98 | $i(v7) & ~ hBOOL(v7)) | (hAPP_int_bool(all_1594_1, v2) = v6 &
% 287.45/40.98 | $i(v6) & ~ hBOOL(v6))))
% 287.45/40.98 |
% 287.45/40.98 | ALPHA: (227) implies:
% 287.45/40.98 | (228) hAPP_i1948725293t_bool(ord_less_eq_int, zero_zero_int) = all_1594_0
% 287.45/40.98 | (229) hAPP_i1948725293t_bool(ord_less_int, zero_zero_int) = all_1594_1
% 287.45/40.98 |
% 287.45/40.98 | DELTA: instantiating (16) with fresh symbol all_1606_0 gives:
% 287.45/40.98 | (230) hAPP_i1948725293t_bool(ord_less_int, zero_zero_int) = all_1606_0 &
% 287.45/40.98 | $i(all_1606_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 =
% 287.45/40.98 | one_one_int | ~ (hAPP_int_fun_int_int(times_times_int, v1) = v2) |
% 287.45/40.98 | ~ (hAPP_int_int(v2, v0) = one_one_int) | ~ $i(v1) | ~ $i(v0) |
% 287.45/40.98 | ? [v3: $i] : (hAPP_int_bool(all_1606_0, v1) = v3 & $i(v3) & ~
% 287.45/40.98 | hBOOL(v3))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v0 =
% 287.45/40.98 | one_one_int | ~ (hAPP_int_fun_int_int(times_times_int, v1) = v2) |
% 287.45/40.98 | ~ (hAPP_int_int(v2, v0) = one_one_int) | ~ $i(v1) | ~ $i(v0) |
% 287.45/40.98 | ? [v3: $i] : (hAPP_int_bool(all_1606_0, v1) = v3 & $i(v3) & ~
% 287.45/40.98 | hBOOL(v3))) & ! [v0: $i] : ! [v1: $i] : (v1 = one_one_int | ~
% 287.45/40.98 | (hAPP_int_fun_int_int(times_times_int, one_one_int) = v0) | ~
% 287.45/40.98 | (hAPP_int_int(v0, one_one_int) = v1) | ? [v2: $i] :
% 287.45/40.98 | (hAPP_int_bool(all_1606_0, one_one_int) = v2 & $i(v2) & ~
% 287.45/40.98 | hBOOL(v2)))
% 287.45/40.98 |
% 287.45/40.98 | ALPHA: (230) implies:
% 287.45/40.98 | (231) hAPP_i1948725293t_bool(ord_less_int, zero_zero_int) = all_1606_0
% 287.45/40.98 |
% 287.45/40.98 | DELTA: instantiating (25) with fresh symbols all_1612_0, all_1612_1 gives:
% 287.45/40.99 | (232) hAPP_i1948725293t_bool(ord_less_int, zero_zero_int) = all_1612_0 &
% 287.45/40.99 | hAPP_i1948725293t_bool(ord_less_eq_int, zero_zero_int) = all_1612_1 &
% 287.45/40.99 | $i(all_1612_0) & $i(all_1612_1) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 287.45/40.99 | $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~
% 287.45/40.99 | (hAPP_int_fun_int_int(times_times_int, v0) = v3) | ~
% 287.45/40.99 | (hAPP_int_fun_int_int(plus_plus_int, v4) = v5) | ~
% 287.45/40.99 | (hAPP_int_int(v5, v2) = v6) | ~ (hAPP_int_int(v3, v1) = v4) | ~
% 287.45/40.99 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v7: $i] : ? [v8: $i] : ?
% 287.45/40.99 | [v9: $i] : ? [v10: $i] : ? [v11: $i] :
% 287.45/40.99 | ((hAPP_i1948725293t_bool(ord_less_int, v2) = v8 & hAPP_int_bool(v8,
% 287.45/40.99 | v0) = v9 & $i(v9) & $i(v8) & ~ hBOOL(v9)) |
% 287.45/40.99 | (hAPP_int_bool(all_1612_0, v0) = v10 & $i(v10) & ~ hBOOL(v10)) |
% 287.45/40.99 | (hAPP_int_bool(all_1612_1, v6) = v7 & $i(v7) & ~ hBOOL(v7)) |
% 287.45/40.99 | (hAPP_int_bool(all_1612_1, v1) = v11 & $i(v11) & hBOOL(v11))))
% 287.45/40.99 |
% 287.45/40.99 | ALPHA: (232) implies:
% 287.45/40.99 | (233) hAPP_i1948725293t_bool(ord_less_eq_int, zero_zero_int) = all_1612_1
% 287.45/40.99 | (234) hAPP_i1948725293t_bool(ord_less_int, zero_zero_int) = all_1612_0
% 287.45/40.99 |
% 287.45/40.99 | DELTA: instantiating (42) with fresh symbol all_1633_0 gives:
% 287.84/40.99 | (235) hAPP_i1948725293t_bool(ord_less_eq_int, zero_zero_int) = all_1633_0 &
% 287.84/40.99 | $i(all_1633_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 287.84/40.99 | $i] : ( ~ (hAPP_nat_int(semiri1621563631at_int, v1) = v2) | ~
% 287.84/40.99 | (hAPP_int_bool(v0, v2) = v3) | ~ $i(v1) | ~ $i(v0) | ~ hBOOL(v3)
% 287.84/40.99 | | ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : (hAPP_int_bool(v0, v4)
% 287.84/40.99 | = v6 & hAPP_int_bool(all_1633_0, v4) = v5 & $i(v6) & $i(v5) &
% 287.84/40.99 | $i(v4) & hBOOL(v6) & hBOOL(v5))) & ? [v0: $i] : ! [v1: $i] : !
% 287.84/40.99 | [v2: $i] : ( ~ (hAPP_int_bool(all_1633_0, v1) = v2) | ~ $i(v1) | ~
% 287.84/40.99 | $i(v0) | ~ hBOOL(v2) | ? [v3: $i] : ? [v4: $i] : ? [v5: $i] :
% 287.84/40.99 | ? [v6: $i] : ($i(v3) & ((hAPP_nat_int(semiri1621563631at_int, v3) =
% 287.84/40.99 | v4 & hAPP_int_bool(v0, v4) = v5 & $i(v5) & $i(v4) &
% 287.84/40.99 | hBOOL(v5)) | (hAPP_int_bool(v0, v1) = v6 & $i(v6) & ~
% 287.84/40.99 | hBOOL(v6)))))
% 287.84/40.99 |
% 287.84/40.99 | ALPHA: (235) implies:
% 287.84/40.99 | (236) hAPP_i1948725293t_bool(ord_less_eq_int, zero_zero_int) = all_1633_0
% 287.84/40.99 |
% 287.84/40.99 | DELTA: instantiating (26) with fresh symbols all_1636_0, all_1636_1 gives:
% 287.84/40.99 | (237) hAPP_i1948725293t_bool(ord_less_int, zero_zero_int) = all_1636_0 &
% 287.84/40.99 | hAPP_i1948725293t_bool(ord_less_eq_int, zero_zero_int) = all_1636_1 &
% 287.84/40.99 | $i(all_1636_0) & $i(all_1636_1) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 287.84/40.99 | $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~
% 287.84/40.99 | (hAPP_int_fun_int_int(times_times_int, v0) = v3) | ~
% 287.84/40.99 | (hAPP_int_fun_int_int(plus_plus_int, v4) = v5) | ~
% 287.84/40.99 | (hAPP_int_int(v5, v2) = v6) | ~ (hAPP_int_int(v3, v1) = v4) | ~
% 287.84/40.99 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v7: $i] : ? [v8: $i] : ?
% 287.84/40.99 | [v9: $i] : ? [v10: $i] : ? [v11: $i] : ? [v12: $i] :
% 287.84/40.99 | ((hAPP_i1948725293t_bool(ord_less_int, v6) = v7 & hAPP_int_bool(v7,
% 287.84/40.99 | zero_zero_int) = v8 & $i(v8) & $i(v7) & ~ hBOOL(v8)) |
% 287.84/40.99 | (hAPP_i1948725293t_bool(ord_less_eq_int, v1) = v11 &
% 287.84/40.99 | hAPP_int_bool(v11, zero_zero_int) = v12 & $i(v12) & $i(v11) &
% 287.84/40.99 | hBOOL(v12)) | (hAPP_int_bool(all_1636_0, v0) = v10 & $i(v10) &
% 287.84/40.99 | ~ hBOOL(v10)) | (hAPP_int_bool(all_1636_1, v2) = v9 & $i(v9) &
% 287.84/40.99 | ~ hBOOL(v9))))
% 287.84/40.99 |
% 287.84/40.99 | ALPHA: (237) implies:
% 287.84/40.99 | (238) hAPP_i1948725293t_bool(ord_less_eq_int, zero_zero_int) = all_1636_1
% 287.84/40.99 | (239) hAPP_i1948725293t_bool(ord_less_int, zero_zero_int) = all_1636_0
% 287.84/40.99 |
% 287.84/40.99 | DELTA: instantiating (43) with fresh symbol all_1639_0 gives:
% 287.84/40.99 | (240) hAPP_i1948725293t_bool(ord_less_eq_int, zero_zero_int) = all_1639_0 &
% 287.84/40.99 | $i(all_1639_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 287.84/40.99 | $i] : ( ~ (hAPP_nat_int(semiri1621563631at_int, v1) = v2) | ~
% 287.84/40.99 | (hAPP_int_bool(v0, v2) = v3) | ~ $i(v1) | ~ $i(v0) | hBOOL(v3) |
% 287.84/40.99 | ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : (hAPP_int_bool(v0, v4) =
% 287.84/40.99 | v6 & hAPP_int_bool(all_1639_0, v4) = v5 & $i(v6) & $i(v5) &
% 287.84/40.99 | $i(v4) & hBOOL(v5) & ~ hBOOL(v6))) & ? [v0: $i] : ! [v1: $i] :
% 287.84/40.99 | ! [v2: $i] : ( ~ (hAPP_int_bool(all_1639_0, v1) = v2) | ~ $i(v1) |
% 287.84/40.99 | ~ $i(v0) | ~ hBOOL(v2) | ? [v3: $i] : ? [v4: $i] : ? [v5: $i] :
% 287.84/40.99 | ? [v6: $i] : ($i(v4) & ((hAPP_nat_int(semiri1621563631at_int, v4)
% 287.84/40.99 | = v5 & hAPP_int_bool(v0, v5) = v6 & $i(v6) & $i(v5) & ~
% 287.84/40.99 | hBOOL(v6)) | (hAPP_int_bool(v0, v1) = v3 & $i(v3) &
% 287.84/40.99 | hBOOL(v3)))))
% 287.84/40.99 |
% 287.84/40.99 | ALPHA: (240) implies:
% 287.84/40.99 | (241) hAPP_i1948725293t_bool(ord_less_eq_int, zero_zero_int) = all_1639_0
% 287.84/40.99 |
% 287.84/40.99 | DELTA: instantiating (33) with fresh symbols all_1642_0, all_1642_1 gives:
% 287.84/40.99 | (242) hAPP_i1948725293t_bool(ord_less_eq_int, zero_zero_int) = all_1642_1 &
% 287.84/40.99 | cOMBB_1652995168ol_int(fconj, all_1642_1) = all_1642_0 &
% 287.84/40.99 | $i(all_1642_0) & $i(all_1642_1) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 287.84/40.99 | $i] : ! [v3: $i] : ( ~ (cOMBS_int_bool_bool(all_1642_0, v1) = v2)
% 287.84/40.99 | | ~ (cOMBS_int_bool_bool(all_1642_0, v0) = v3) | ~ $i(v1) | ~
% 287.84/40.99 | $i(v0) | ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ?
% 287.84/40.99 | [v8: $i] : ? [v9: $i] : ($i(v6) & ((v5 = v4 & collect_int(v3) = v4
% 287.84/40.99 | & collect_int(v2) = v4 & $i(v4)) | (hAPP_int_bool(all_1642_1,
% 287.84/40.99 | v6) = v7 & $i(v7) & hBOOL(v7) & ((hAPP_int_bool(v1, v6) =
% 287.84/40.99 | v8 & $i(v8) & hBOOL(v8)) | (hAPP_int_bool(v0, v6) = v9 &
% 287.84/40.99 | $i(v9) & hBOOL(v9))) & ((hAPP_int_bool(v1, v6) = v8 &
% 287.84/40.99 | $i(v8) & ~ hBOOL(v8)) | (hAPP_int_bool(v0, v6) = v9 &
% 287.84/40.99 | $i(v9) & ~ hBOOL(v9)))))))
% 287.84/40.99 |
% 287.84/40.99 | ALPHA: (242) implies:
% 287.84/40.99 | (243) hAPP_i1948725293t_bool(ord_less_eq_int, zero_zero_int) = all_1642_1
% 287.84/40.99 |
% 287.84/40.99 | DELTA: instantiating (7) with fresh symbol all_1648_0 gives:
% 287.84/41.00 | (244) hAPP_nat_nat(suc, zero_zero_nat) = all_1648_0 & $i(all_1648_0) & !
% 287.84/41.00 | [v0: $i] : ! [v1: any] : ! [v2: $i] : (v1 = all_1648_0 | v1 =
% 287.84/41.00 | zero_zero_nat | ~ (hAPP_nat_fun_nat_nat(plus_plus_nat, v0) = v2) |
% 287.84/41.00 | ~ (hAPP_nat_nat(v2, v1) = all_1648_0) | ~ $i(v1) | ~ $i(v0)) &
% 287.84/41.00 | ! [v0: any] : ! [v1: any] : ! [v2: $i] : (v1 = all_1648_0 | v0 =
% 287.84/41.00 | all_1648_0 | ~ (hAPP_nat_fun_nat_nat(plus_plus_nat, v0) = v2) | ~
% 287.84/41.00 | (hAPP_nat_nat(v2, v1) = all_1648_0) | ~ $i(v1) | ~ $i(v0)) & !
% 287.84/41.00 | [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = zero_zero_nat | v0 =
% 287.84/41.00 | zero_zero_nat | ~ (hAPP_nat_fun_nat_nat(plus_plus_nat, v0) = v2) |
% 287.84/41.00 | ~ (hAPP_nat_nat(v2, v1) = all_1648_0) | ~ $i(v1) | ~ $i(v0)) &
% 287.84/41.00 | ! [v0: any] : ! [v1: $i] : ! [v2: $i] : (v0 = all_1648_0 | v0 =
% 287.84/41.00 | zero_zero_nat | ~ (hAPP_nat_fun_nat_nat(plus_plus_nat, v0) = v2) |
% 287.84/41.00 | ~ (hAPP_nat_nat(v2, v1) = all_1648_0) | ~ $i(v1) | ~ $i(v0)) &
% 287.84/41.00 | ! [v0: $i] : ! [v1: int] : (v1 = all_1648_0 | ~
% 287.84/41.00 | (hAPP_nat_fun_nat_nat(plus_plus_nat, all_1648_0) = v0) | ~
% 287.84/41.00 | (hAPP_nat_nat(v0, zero_zero_nat) = v1)) & ! [v0: $i] : ! [v1:
% 287.84/41.00 | int] : (v1 = all_1648_0 | ~ (hAPP_nat_fun_nat_nat(plus_plus_nat,
% 287.84/41.00 | zero_zero_nat) = v0) | ~ (hAPP_nat_nat(v0, all_1648_0) = v1))
% 287.84/41.00 |
% 287.84/41.00 | ALPHA: (244) implies:
% 287.84/41.00 | (245) hAPP_nat_nat(suc, zero_zero_nat) = all_1648_0
% 287.84/41.00 |
% 287.84/41.00 | DELTA: instantiating (7) with fresh symbol all_1651_0 gives:
% 287.84/41.00 | (246) hAPP_nat_nat(suc, zero_zero_nat) = all_1651_0 & $i(all_1651_0) & !
% 287.84/41.00 | [v0: $i] : ! [v1: any] : ! [v2: $i] : (v1 = all_1651_0 | v1 =
% 287.84/41.00 | zero_zero_nat | ~ (hAPP_nat_fun_nat_nat(plus_plus_nat, v0) = v2) |
% 287.84/41.00 | ~ (hAPP_nat_nat(v2, v1) = all_1651_0) | ~ $i(v1) | ~ $i(v0)) &
% 287.84/41.00 | ! [v0: any] : ! [v1: any] : ! [v2: $i] : (v1 = all_1651_0 | v0 =
% 287.84/41.00 | all_1651_0 | ~ (hAPP_nat_fun_nat_nat(plus_plus_nat, v0) = v2) | ~
% 287.84/41.00 | (hAPP_nat_nat(v2, v1) = all_1651_0) | ~ $i(v1) | ~ $i(v0)) & !
% 287.84/41.00 | [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = zero_zero_nat | v0 =
% 287.84/41.00 | zero_zero_nat | ~ (hAPP_nat_fun_nat_nat(plus_plus_nat, v0) = v2) |
% 287.84/41.00 | ~ (hAPP_nat_nat(v2, v1) = all_1651_0) | ~ $i(v1) | ~ $i(v0)) &
% 287.84/41.00 | ! [v0: any] : ! [v1: $i] : ! [v2: $i] : (v0 = all_1651_0 | v0 =
% 287.84/41.00 | zero_zero_nat | ~ (hAPP_nat_fun_nat_nat(plus_plus_nat, v0) = v2) |
% 287.84/41.00 | ~ (hAPP_nat_nat(v2, v1) = all_1651_0) | ~ $i(v1) | ~ $i(v0)) &
% 287.84/41.00 | ! [v0: $i] : ! [v1: int] : (v1 = all_1651_0 | ~
% 287.84/41.00 | (hAPP_nat_fun_nat_nat(plus_plus_nat, all_1651_0) = v0) | ~
% 287.84/41.00 | (hAPP_nat_nat(v0, zero_zero_nat) = v1)) & ! [v0: $i] : ! [v1:
% 287.84/41.00 | int] : (v1 = all_1651_0 | ~ (hAPP_nat_fun_nat_nat(plus_plus_nat,
% 287.84/41.00 | zero_zero_nat) = v0) | ~ (hAPP_nat_nat(v0, all_1651_0) = v1))
% 287.84/41.00 |
% 287.84/41.00 | ALPHA: (246) implies:
% 287.84/41.00 | (247) hAPP_nat_nat(suc, zero_zero_nat) = all_1651_0
% 287.84/41.00 |
% 287.84/41.00 | DELTA: instantiating (34) with fresh symbols all_1654_0, all_1654_1 gives:
% 287.84/41.00 | (248) hAPP_i1948725293t_bool(ord_less_int, zero_zero_int) = all_1654_1 &
% 287.84/41.00 | hAPP_i1948725293t_bool(ord_less_eq_int, zero_zero_int) = all_1654_0 &
% 287.84/41.00 | $i(all_1654_0) & $i(all_1654_1) & ? [v0: $i] : ! [v1: $i] : ! [v2:
% 287.84/41.00 | $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (hAPP_int_bool(all_1654_0,
% 287.84/41.00 | v1) = v4) | ~ (hAPP_int_bool(all_1654_1, v2) = v3) | ~ $i(v2)
% 287.84/41.00 | | ~ $i(v1) | ~ $i(v0) | ~ hBOOL(v4) | ~ hBOOL(v3) | ? [v5: $i]
% 287.84/41.00 | : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ? [v10:
% 287.84/41.00 | $i] : ? [v11: $i] : ($i(v7) &
% 287.84/41.00 | ((hAPP_int_fun_int_int(times_times_int, v1) = v5 &
% 287.84/41.00 | hAPP_int_int(v5, v2) = v6 & $i(v6) & $i(v5) & ! [v12: $i] :
% 287.84/41.00 | ! [v13: $i] : ! [v14: $i] : ! [v15: $i] : ( ~
% 287.84/41.00 | (hAPP_int_fun_int_int(minus_minus_int, v12) = v13) | ~
% 287.84/41.00 | (hAPP_int_int(v13, v6) = v14) | ~ (hAPP_int_bool(v0, v14)
% 287.84/41.00 | = v15) | ~ $i(v12) | hBOOL(v15) | ? [v16: $i] :
% 287.84/41.00 | (hAPP_int_bool(v0, v12) = v16 & $i(v16) & ~ hBOOL(v16))))
% 287.84/41.00 | | (hAPP_int_fun_int_int(minus_minus_int, v7) = v9 &
% 287.84/41.00 | hAPP_int_int(v9, v2) = v10 & hAPP_int_bool(v0, v10) = v11 &
% 287.84/41.00 | hAPP_int_bool(v0, v7) = v8 & $i(v11) & $i(v10) & $i(v9) &
% 287.84/41.00 | $i(v8) & hBOOL(v8) & ~ hBOOL(v11)))))
% 287.84/41.00 |
% 287.84/41.00 | ALPHA: (248) implies:
% 287.84/41.00 | (249) hAPP_i1948725293t_bool(ord_less_eq_int, zero_zero_int) = all_1654_0
% 287.84/41.00 | (250) hAPP_i1948725293t_bool(ord_less_int, zero_zero_int) = all_1654_1
% 287.84/41.00 |
% 287.84/41.00 | DELTA: instantiating (36) with fresh symbols all_1656_0, all_1656_1 gives:
% 287.84/41.00 | (251) hAPP_i1948725293t_bool(ord_less_int, zero_zero_int) = all_1656_1 &
% 287.84/41.00 | hAPP_i1948725293t_bool(ord_less_eq_int, zero_zero_int) = all_1656_0 &
% 287.84/41.00 | $i(all_1656_0) & $i(all_1656_1) & ? [v0: $i] : ! [v1: $i] : ! [v2:
% 287.84/41.00 | $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (hAPP_int_bool(all_1656_0,
% 287.84/41.00 | v1) = v4) | ~ (hAPP_int_bool(all_1656_1, v2) = v3) | ~ $i(v2)
% 287.84/41.00 | | ~ $i(v1) | ~ $i(v0) | ~ hBOOL(v4) | ~ hBOOL(v3) | ? [v5: $i]
% 287.84/41.00 | : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ? [v10:
% 287.84/41.00 | $i] : ? [v11: $i] : ($i(v7) &
% 287.84/41.00 | ((hAPP_int_fun_int_int(times_times_int, v1) = v5 &
% 287.84/41.00 | hAPP_int_int(v5, v2) = v6 & $i(v6) & $i(v5) & ! [v12: $i] :
% 287.84/41.00 | ! [v13: $i] : ! [v14: $i] : ! [v15: $i] : ( ~
% 287.84/41.00 | (hAPP_int_fun_int_int(plus_plus_int, v12) = v13) | ~
% 287.84/41.00 | (hAPP_int_int(v13, v6) = v14) | ~ (hAPP_int_bool(v0, v14)
% 287.84/41.00 | = v15) | ~ $i(v12) | hBOOL(v15) | ? [v16: $i] :
% 287.84/41.00 | (hAPP_int_bool(v0, v12) = v16 & $i(v16) & ~ hBOOL(v16))))
% 287.84/41.00 | | (hAPP_int_fun_int_int(plus_plus_int, v7) = v9 &
% 287.84/41.00 | hAPP_int_int(v9, v2) = v10 & hAPP_int_bool(v0, v10) = v11 &
% 287.84/41.00 | hAPP_int_bool(v0, v7) = v8 & $i(v11) & $i(v10) & $i(v9) &
% 287.84/41.00 | $i(v8) & hBOOL(v8) & ~ hBOOL(v11)))))
% 287.84/41.00 |
% 287.84/41.00 | ALPHA: (251) implies:
% 287.84/41.00 | (252) hAPP_i1948725293t_bool(ord_less_eq_int, zero_zero_int) = all_1656_0
% 287.84/41.00 | (253) hAPP_i1948725293t_bool(ord_less_int, zero_zero_int) = all_1656_1
% 287.84/41.00 |
% 287.84/41.00 | DELTA: instantiating (27) with fresh symbol all_1670_0 gives:
% 287.84/41.00 | (254) hAPP_i1948725293t_bool(ord_less_eq_int, zero_zero_int) = all_1670_0 &
% 287.84/41.00 | $i(all_1670_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 287.84/41.00 | $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : !
% 287.84/41.00 | [v8: $i] : ! [v9: $i] : ! [v10: $i] : ! [v11: $i] : ! [v12: $i] :
% 287.84/41.00 | ! [v13: $i] : ( ~ (hAPP_int_fun_int_int(times_times_int, v0) = v5) |
% 287.84/41.00 | ~ (hAPP_int_fun_int_int(plus_plus_int, v10) = v11) | ~
% 287.84/41.00 | (hAPP_int_fun_int_int(plus_plus_int, v6) = v7) | ~
% 287.84/41.00 | (hAPP_int_int(v11, v4) = v12) | ~ (hAPP_int_int(v7, v2) = v8) | ~
% 287.84/41.00 | (hAPP_int_int(v5, v3) = v10) | ~ (hAPP_int_int(v5, v1) = v6) | ~
% 287.84/41.00 | (hAPP_i1948725293t_bool(ord_less_eq_int, v8) = v9) | ~
% 287.84/41.00 | (hAPP_int_bool(v9, v12) = v13) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2)
% 287.84/41.00 | | ~ $i(v1) | ~ $i(v0) | ~ hBOOL(v13) | ? [v14: $i] : ? [v15:
% 287.84/41.00 | $i] : ? [v16: $i] : ? [v17: $i] : ? [v18: $i] : ? [v19: $i] :
% 287.84/41.00 | ? [v20: $i] : ((hAPP_i1948725293t_bool(ord_less_int, v4) = v17 &
% 287.84/41.00 | hAPP_int_bool(v17, v0) = v18 & $i(v18) & $i(v17) & ~
% 287.84/41.00 | hBOOL(v18)) | (hAPP_i1948725293t_bool(ord_less_int, v2) = v15 &
% 287.84/41.00 | hAPP_int_bool(v15, v0) = v16 & $i(v16) & $i(v15) & ~
% 287.84/41.00 | hBOOL(v16)) | (hAPP_i1948725293t_bool(ord_less_eq_int, v1) =
% 287.84/41.00 | v19 & hAPP_int_bool(v19, v3) = v20 & $i(v20) & $i(v19) &
% 287.84/41.00 | hBOOL(v20)) | (hAPP_int_bool(all_1670_0, v2) = v14 & $i(v14) &
% 287.84/41.00 | ~ hBOOL(v14))))
% 287.84/41.00 |
% 287.84/41.00 | ALPHA: (254) implies:
% 287.84/41.00 | (255) hAPP_i1948725293t_bool(ord_less_eq_int, zero_zero_int) = all_1670_0
% 287.84/41.00 |
% 287.84/41.00 | DELTA: instantiating (14) with fresh symbols all_1721_0, all_1721_1 gives:
% 287.84/41.01 | (256) hAPP_nat_nat(suc, zero_zero_nat) = all_1721_1 &
% 287.84/41.01 | hAPP_n1699378549t_bool(ord_less_eq_nat, all_1721_1) = all_1721_0 &
% 287.84/41.01 | $i(all_1721_0) & $i(all_1721_1) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 287.84/41.01 | $i] : ! [v3: $i] : ( ~ (hAPP_nat_bool(all_1721_0, v1) = v3) | ~
% 287.84/41.01 | (hAPP_nat_bool(all_1721_0, v0) = v2) | ~ $i(v1) | ~ $i(v0) | ~
% 287.84/41.01 | hBOOL(v3) | ~ hBOOL(v2) | ? [v4: $i] : ? [v5: $i] : ? [v6: $i]
% 287.84/41.01 | : (hAPP_nat_fun_nat_nat(times_times_nat, v0) = v4 &
% 287.84/41.01 | hAPP_nat_nat(v4, v1) = v5 & hAPP_nat_bool(all_1721_0, v5) = v6 &
% 287.84/41.01 | $i(v6) & $i(v5) & $i(v4) & hBOOL(v6))) & ! [v0: $i] : ! [v1:
% 287.84/41.01 | $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (hAPP_nat_bool(all_1721_0,
% 287.84/41.01 | v1) = v3) | ~ (hAPP_nat_bool(all_1721_0, v0) = v2) | ~ $i(v1)
% 287.84/41.01 | | ~ $i(v0) | hBOOL(v3) | ? [v4: $i] : ? [v5: $i] : ? [v6: $i] :
% 287.84/41.01 | (hAPP_nat_fun_nat_nat(times_times_nat, v0) = v4 & hAPP_nat_nat(v4,
% 287.84/41.01 | v1) = v5 & hAPP_nat_bool(all_1721_0, v5) = v6 & $i(v6) & $i(v5)
% 287.84/41.01 | & $i(v4) & ~ hBOOL(v6))) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 287.84/41.01 | $i] : ! [v3: $i] : ( ~ (hAPP_nat_bool(all_1721_0, v1) = v3) | ~
% 287.84/41.01 | (hAPP_nat_bool(all_1721_0, v0) = v2) | ~ $i(v1) | ~ $i(v0) |
% 287.84/41.01 | hBOOL(v2) | ? [v4: $i] : ? [v5: $i] : ? [v6: $i] :
% 287.84/41.01 | (hAPP_nat_fun_nat_nat(times_times_nat, v0) = v4 & hAPP_nat_nat(v4,
% 287.84/41.01 | v1) = v5 & hAPP_nat_bool(all_1721_0, v5) = v6 & $i(v6) & $i(v5)
% 287.84/41.01 | & $i(v4) & ~ hBOOL(v6)))
% 287.84/41.01 |
% 287.84/41.01 | ALPHA: (256) implies:
% 287.84/41.01 | (257) hAPP_nat_nat(suc, zero_zero_nat) = all_1721_1
% 287.84/41.01 |
% 287.84/41.01 | DELTA: instantiating (28) with fresh symbols all_1724_0, all_1724_1 gives:
% 287.84/41.01 | (258) hAPP_i1948725293t_bool(ord_less_int, zero_zero_int) = all_1724_0 &
% 287.84/41.01 | hAPP_i1948725293t_bool(ord_less_eq_int, zero_zero_int) = all_1724_1 &
% 287.84/41.01 | $i(all_1724_0) & $i(all_1724_1) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 287.84/41.01 | $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : !
% 287.84/41.01 | [v7: $i] : ! [v8: $i] : ! [v9: $i] : ! [v10: $i] : ! [v11: $i] :
% 287.84/41.01 | ! [v12: $i] : ( ~ (hAPP_int_fun_int_int(times_times_int, v3) = v10) |
% 287.84/41.01 | ~ (hAPP_int_fun_int_int(times_times_int, v0) = v6) | ~
% 287.84/41.01 | (hAPP_int_fun_int_int(plus_plus_int, v11) = v12) | ~
% 287.84/41.01 | (hAPP_int_fun_int_int(plus_plus_int, v7) = v8) | ~
% 287.84/41.01 | (hAPP_int_int(v12, v5) = v9) | ~ (hAPP_int_int(v10, v4) = v11) |
% 287.84/41.01 | ~ (hAPP_int_int(v8, v2) = v9) | ~ (hAPP_int_int(v6, v1) = v7) | ~
% 287.84/41.01 | $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0)
% 287.84/41.01 | | ? [v13: $i] : ? [v14: $i] : ? [v15: $i] : ? [v16: $i] : ?
% 287.84/41.01 | [v17: $i] : ? [v18: $i] : ? [v19: $i] : ? [v20: $i] : ? [v21:
% 287.84/41.01 | $i] : ((hAPP_i1948725293t_bool(ord_less_int, v5) = v14 &
% 287.84/41.01 | hAPP_int_bool(v14, v3) = v15 & $i(v15) & $i(v14) & ~
% 287.84/41.01 | hBOOL(v15)) | (hAPP_i1948725293t_bool(ord_less_eq_int, v3) =
% 287.84/41.01 | v18 & hAPP_int_bool(v18, v0) = v19 & $i(v19) & $i(v18) & ~
% 287.84/41.01 | hBOOL(v19)) | (hAPP_i1948725293t_bool(ord_less_eq_int, v1) =
% 287.84/41.01 | v20 & hAPP_int_bool(v20, v4) = v21 & $i(v21) & $i(v20) &
% 287.84/41.01 | hBOOL(v21)) | (hAPP_int_bool(all_1724_0, v3) = v17 & $i(v17) &
% 287.84/41.01 | ~ hBOOL(v17)) | (hAPP_int_bool(all_1724_1, v9) = v13 & $i(v13)
% 287.84/41.01 | & ~ hBOOL(v13)) | (hAPP_int_bool(all_1724_1, v2) = v16 &
% 287.84/41.01 | $i(v16) & ~ hBOOL(v16))))
% 287.84/41.01 |
% 287.84/41.01 | ALPHA: (258) implies:
% 287.84/41.01 | (259) hAPP_i1948725293t_bool(ord_less_eq_int, zero_zero_int) = all_1724_1
% 287.84/41.01 | (260) hAPP_i1948725293t_bool(ord_less_int, zero_zero_int) = all_1724_0
% 287.84/41.01 |
% 287.84/41.01 | DELTA: instantiating (21) with fresh symbols all_1727_0, all_1727_1 gives:
% 287.84/41.01 | (261) hAPP_i1948725293t_bool(ord_less_int, zero_zero_int) = all_1727_0 &
% 287.84/41.01 | hAPP_i1948725293t_bool(ord_less_eq_int, zero_zero_int) = all_1727_1 &
% 287.84/41.01 | $i(all_1727_0) & $i(all_1727_1) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 287.84/41.01 | $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : !
% 287.84/41.01 | [v7: $i] : ! [v8: $i] : ! [v9: $i] : ! [v10: $i] : ! [v11: $i] :
% 287.84/41.01 | ! [v12: $i] : ( ~ (hAPP_int_fun_int_int(times_times_int, v3) = v10) |
% 287.84/41.01 | ~ (hAPP_int_fun_int_int(times_times_int, v0) = v6) | ~
% 287.84/41.01 | (hAPP_int_fun_int_int(plus_plus_int, v11) = v12) | ~
% 287.84/41.01 | (hAPP_int_fun_int_int(plus_plus_int, v7) = v8) | ~
% 287.84/41.01 | (hAPP_int_int(v12, v5) = v9) | ~ (hAPP_int_int(v10, v4) = v11) |
% 287.84/41.01 | ~ (hAPP_int_int(v8, v2) = v9) | ~ (hAPP_int_int(v6, v1) = v7) | ~
% 287.84/41.01 | $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0)
% 287.84/41.01 | | ? [v13: $i] : ? [v14: $i] : ? [v15: $i] : ? [v16: $i] : ?
% 287.84/41.01 | [v17: $i] : ? [v18: $i] : ? [v19: $i] : ? [v20: $i] : ? [v21:
% 287.84/41.01 | $i] : ? [v22: $i] : ((hAPP_i1948725293t_bool(ord_less_int, v9) =
% 287.84/41.01 | v13 & hAPP_int_bool(v13, zero_zero_int) = v14 & $i(v14) &
% 287.84/41.01 | $i(v13) & ~ hBOOL(v14)) |
% 287.84/41.01 | (hAPP_i1948725293t_bool(ord_less_int, v2) = v15 &
% 287.84/41.01 | hAPP_int_bool(v15, v0) = v16 & $i(v16) & $i(v15) & ~
% 287.84/41.01 | hBOOL(v16)) | (hAPP_i1948725293t_bool(ord_less_eq_int, v4) =
% 287.84/41.01 | v21 & hAPP_int_bool(v21, v1) = v22 & $i(v22) & $i(v21) &
% 287.84/41.01 | hBOOL(v22)) | (hAPP_i1948725293t_bool(ord_less_eq_int, v3) =
% 287.84/41.01 | v19 & hAPP_int_bool(v19, v0) = v20 & $i(v20) & $i(v19) & ~
% 287.84/41.01 | hBOOL(v20)) | (hAPP_int_bool(all_1727_0, v3) = v18 & $i(v18) &
% 287.84/41.01 | ~ hBOOL(v18)) | (hAPP_int_bool(all_1727_1, v5) = v17 & $i(v17)
% 287.84/41.01 | & ~ hBOOL(v17))))
% 287.84/41.01 |
% 287.84/41.01 | ALPHA: (261) implies:
% 287.84/41.01 | (262) hAPP_i1948725293t_bool(ord_less_eq_int, zero_zero_int) = all_1727_1
% 287.84/41.01 | (263) hAPP_i1948725293t_bool(ord_less_int, zero_zero_int) = all_1727_0
% 287.84/41.01 |
% 287.84/41.01 | DELTA: instantiating (38) with fresh symbol all_1730_0 gives:
% 287.84/41.02 | (264) hAPP_i1948725293t_bool(ord_less_int, zero_zero_int) = all_1730_0 &
% 287.84/41.02 | $i(all_1730_0) & ? [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 287.84/41.02 | $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ( ~
% 287.84/41.02 | (hAPP_i1948725293t_bool(ord_less_int, v6) = v7) | ~
% 287.84/41.02 | (hAPP_int_bool(v1, v4) = v5) | ~ (hAPP_int_bool(all_1730_0, v2) =
% 287.84/41.02 | v3) | ~ $i(v6) | ~ $i(v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 287.84/41.02 | ~ hBOOL(v5) | ~ hBOOL(v3) | ? [v8: $i] : ? [v9: $i] : ? [v10:
% 287.84/41.02 | $i] : ? [v11: $i] : ? [v12: $i] : ? [v13: $i] : ? [v14: $i] :
% 287.84/41.02 | ? [v15: $i] : ? [v16: $i] : ? [v17: $i] : ? [v18: $i] : ?
% 287.84/41.02 | [v19: $i] : ? [v20: $i] : ? [v21: $i] : ($i(v15) & $i(v14) &
% 287.84/41.02 | $i(v10) & $i(v8) & ((hAPP_int_bool(v7, v10) = v11 & $i(v11) &
% 287.84/41.02 | hBOOL(v11) & ((hAPP_int_bool(v1, v10) = v13 & $i(v13) &
% 287.84/41.02 | hBOOL(v13)) | (hAPP_int_bool(v0, v10) = v12 & $i(v12) &
% 287.84/41.02 | hBOOL(v12))) & ((hAPP_int_bool(v1, v10) = v13 & $i(v13) &
% 287.84/41.02 | ~ hBOOL(v13)) | (hAPP_int_bool(v0, v10) = v12 & $i(v12)
% 287.84/41.02 | & ~ hBOOL(v12)))) | (hAPP_int_bool(v0, v8) = v9 & $i(v9)
% 287.84/41.02 | & hBOOL(v9)) | (((hAPP_int_fun_int_int(times_times_int, v15)
% 287.84/41.02 | = v18 & hAPP_int_fun_int_int(minus_minus_int, v14) = v17
% 287.84/41.02 | & hAPP_int_int(v18, v2) = v19 & hAPP_int_int(v17, v19) =
% 287.84/41.02 | v20 & hAPP_int_bool(v1, v20) = v21 & $i(v21) & $i(v20) &
% 287.84/41.02 | $i(v19) & $i(v18) & $i(v17) & hBOOL(v21)) |
% 287.84/41.02 | (hAPP_int_bool(v1, v14) = v16 & $i(v16) & hBOOL(v16))) &
% 287.84/41.02 | ((hAPP_int_fun_int_int(times_times_int, v15) = v18 &
% 287.84/41.02 | hAPP_int_fun_int_int(minus_minus_int, v14) = v17 &
% 287.84/41.02 | hAPP_int_int(v18, v2) = v19 & hAPP_int_int(v17, v19) =
% 287.84/41.02 | v20 & hAPP_int_bool(v1, v20) = v21 & $i(v21) & $i(v20) &
% 287.84/41.02 | $i(v19) & $i(v18) & $i(v17) & ~ hBOOL(v21)) |
% 287.84/41.02 | (hAPP_int_bool(v1, v14) = v16 & $i(v16) & ~
% 287.84/41.02 | hBOOL(v16)))))))
% 287.84/41.02 |
% 287.84/41.02 | ALPHA: (264) implies:
% 287.84/41.02 | (265) hAPP_i1948725293t_bool(ord_less_int, zero_zero_int) = all_1730_0
% 287.84/41.02 |
% 287.84/41.02 | DELTA: instantiating (37) with fresh symbol all_1732_0 gives:
% 287.84/41.02 | (266) hAPP_i1948725293t_bool(ord_less_int, zero_zero_int) = all_1732_0 &
% 287.84/41.02 | $i(all_1732_0) & ? [v0: $i] : ? [v1: $i] : ! [v2: $i] : ! [v3:
% 287.84/41.02 | $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~
% 287.84/41.02 | (hAPP_int_bool(v2, v5) = v6) | ~ (hAPP_int_bool(all_1732_0, v3) =
% 287.84/41.02 | v4) | ~ $i(v5) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 287.84/41.02 | ~ hBOOL(v6) | ~ hBOOL(v4) | ? [v7: $i] : ? [v8: $i] : ? [v9:
% 287.84/41.02 | $i] : ? [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13: $i] :
% 287.84/41.02 | ? [v14: $i] : ? [v15: $i] : ? [v16: $i] : ? [v17: $i] : ?
% 287.84/41.02 | [v18: $i] : ? [v19: $i] : ? [v20: $i] : ? [v21: $i] : ($i(v15) &
% 287.84/41.02 | $i(v14) & $i(v9) & $i(v7) &
% 287.84/41.02 | ((hAPP_i1948725293t_bool(ord_less_int, v9) = v10 &
% 287.84/41.02 | hAPP_int_bool(v10, v1) = v11 & $i(v11) & $i(v10) & hBOOL(v11)
% 287.84/41.02 | & ((hAPP_int_bool(v2, v9) = v13 & $i(v13) & hBOOL(v13)) |
% 287.84/41.02 | (hAPP_int_bool(v0, v9) = v12 & $i(v12) & hBOOL(v12))) &
% 287.84/41.02 | ((hAPP_int_bool(v2, v9) = v13 & $i(v13) & ~ hBOOL(v13)) |
% 287.84/41.02 | (hAPP_int_bool(v0, v9) = v12 & $i(v12) & ~ hBOOL(v12)))) |
% 287.84/41.02 | (hAPP_int_bool(v0, v7) = v8 & $i(v8) & hBOOL(v8)) |
% 287.84/41.02 | (((hAPP_int_fun_int_int(times_times_int, v15) = v18 &
% 287.84/41.02 | hAPP_int_fun_int_int(minus_minus_int, v14) = v17 &
% 287.84/41.02 | hAPP_int_int(v18, v3) = v19 & hAPP_int_int(v17, v19) =
% 287.84/41.02 | v20 & hAPP_int_bool(v2, v20) = v21 & $i(v21) & $i(v20) &
% 287.84/41.02 | $i(v19) & $i(v18) & $i(v17) & hBOOL(v21)) |
% 287.84/41.02 | (hAPP_int_bool(v2, v14) = v16 & $i(v16) & hBOOL(v16))) &
% 287.84/41.02 | ((hAPP_int_fun_int_int(times_times_int, v15) = v18 &
% 287.84/41.02 | hAPP_int_fun_int_int(minus_minus_int, v14) = v17 &
% 287.84/41.02 | hAPP_int_int(v18, v3) = v19 & hAPP_int_int(v17, v19) =
% 287.84/41.02 | v20 & hAPP_int_bool(v2, v20) = v21 & $i(v21) & $i(v20) &
% 287.84/41.02 | $i(v19) & $i(v18) & $i(v17) & ~ hBOOL(v21)) |
% 287.84/41.02 | (hAPP_int_bool(v2, v14) = v16 & $i(v16) & ~
% 287.84/41.02 | hBOOL(v16)))))))
% 287.84/41.02 |
% 287.84/41.02 | ALPHA: (266) implies:
% 287.84/41.02 | (267) hAPP_i1948725293t_bool(ord_less_int, zero_zero_int) = all_1732_0
% 287.84/41.02 |
% 287.84/41.02 | REDUCE: (66), (201) imply:
% 287.84/41.02 | (268) bit1(zero_zero_int) = all_1531_3
% 287.84/41.02 |
% 287.84/41.02 | REDUCE: (66), (166) imply:
% 287.84/41.02 | (269) bit1(zero_zero_int) = all_1385_4
% 287.84/41.02 |
% 287.84/41.02 | REDUCE: (66), (163) imply:
% 287.84/41.02 | (270) bit1(zero_zero_int) = all_1383_3
% 287.84/41.02 |
% 287.84/41.02 | REDUCE: (66), (157) imply:
% 287.84/41.02 | (271) bit1(zero_zero_int) = all_1351_3
% 287.84/41.02 |
% 287.84/41.02 | REDUCE: (66), (137) imply:
% 287.84/41.02 | (272) bit1(zero_zero_int) = all_1290_1
% 287.84/41.02 |
% 287.84/41.02 | REDUCE: (66), (116) imply:
% 287.84/41.02 | (273) bit1(zero_zero_int) = all_1208_0
% 287.84/41.02 |
% 287.84/41.02 | REDUCE: (66), (107) imply:
% 287.84/41.02 | (274) bit1(zero_zero_int) = all_1186_0
% 287.84/41.02 |
% 287.84/41.02 | REDUCE: (66), (104) imply:
% 287.84/41.02 | (275) bit1(zero_zero_int) = all_1184_0
% 287.84/41.02 |
% 287.84/41.02 | REDUCE: (66), (100) imply:
% 287.84/41.02 | (276) bit1(zero_zero_int) = all_1182_0
% 287.84/41.02 |
% 287.84/41.02 | REDUCE: (5), (65), (66) imply:
% 287.84/41.02 | (277) number_number_of_nat(zero_zero_int) = bot_bot_nat
% 287.84/41.02 |
% 287.84/41.02 | REDUCE: (66), (219) imply:
% 287.84/41.02 | (278) hAPP_i1948725293t_bool(ord_less_int, zero_zero_int) = all_1573_1
% 287.84/41.02 |
% 287.84/41.02 | REDUCE: (66), (130) imply:
% 287.84/41.02 | (279) hAPP_i1948725293t_bool(ord_less_int, zero_zero_int) = all_1245_1
% 287.84/41.02 |
% 287.84/41.02 | REDUCE: (66), (218) imply:
% 287.84/41.02 | (280) hAPP_i1948725293t_bool(ord_less_eq_int, zero_zero_int) = all_1573_0
% 287.84/41.02 |
% 287.84/41.02 | REDUCE: (66), (208) imply:
% 287.84/41.02 | (281) hAPP_i1948725293t_bool(ord_less_eq_int, zero_zero_int) = all_1540_0
% 287.84/41.02 |
% 287.84/41.02 | REDUCE: (66), (134) imply:
% 287.84/41.02 | (282) hAPP_i1948725293t_bool(ord_less_eq_int, zero_zero_int) = all_1264_1
% 287.84/41.02 |
% 287.84/41.02 | REDUCE: (5), (39) imply:
% 287.84/41.02 | (283) hAPP_nat_int(semiri1621563631at_int, bot_bot_nat) = zero_zero_int
% 287.84/41.02 |
% 287.84/41.02 | REDUCE: (5), (257) imply:
% 287.84/41.02 | (284) hAPP_nat_nat(suc, bot_bot_nat) = all_1721_1
% 287.84/41.02 |
% 287.84/41.02 | REDUCE: (5), (247) imply:
% 287.84/41.02 | (285) hAPP_nat_nat(suc, bot_bot_nat) = all_1651_0
% 287.84/41.02 |
% 287.84/41.02 | REDUCE: (5), (245) imply:
% 287.84/41.02 | (286) hAPP_nat_nat(suc, bot_bot_nat) = all_1648_0
% 287.84/41.02 |
% 287.84/41.02 | REDUCE: (5), (214) imply:
% 287.84/41.02 | (287) hAPP_nat_nat(suc, bot_bot_nat) = all_1552_1
% 287.84/41.02 |
% 287.84/41.02 | REDUCE: (5), (210) imply:
% 287.84/41.02 | (288) hAPP_nat_nat(suc, bot_bot_nat) = all_1546_1
% 287.84/41.02 |
% 287.84/41.02 | REDUCE: (5), (206) imply:
% 287.84/41.02 | (289) hAPP_nat_nat(suc, bot_bot_nat) = all_1537_1
% 287.84/41.02 |
% 287.84/41.02 | REDUCE: (5), (195) imply:
% 287.84/41.02 | (290) hAPP_nat_nat(suc, bot_bot_nat) = all_1505_0
% 287.84/41.02 |
% 287.84/41.02 | REDUCE: (5), (174) imply:
% 287.84/41.02 | (291) hAPP_nat_nat(suc, bot_bot_nat) = all_1435_0
% 287.84/41.02 |
% 287.84/41.02 | REDUCE: (5), (172) imply:
% 287.84/41.02 | (292) hAPP_nat_nat(suc, bot_bot_nat) = all_1426_0
% 287.84/41.02 |
% 287.84/41.02 | REDUCE: (5), (165) imply:
% 287.84/41.02 | (293) hAPP_nat_nat(suc, bot_bot_nat) = all_1385_1
% 287.84/41.02 |
% 287.84/41.02 | REDUCE: (5), (136) imply:
% 287.84/41.02 | (294) hAPP_nat_nat(suc, bot_bot_nat) = all_1290_0
% 287.84/41.02 |
% 287.84/41.02 | REDUCE: (5), (110) imply:
% 287.84/41.02 | (295) hAPP_nat_nat(suc, bot_bot_nat) = all_1196_0
% 287.84/41.02 |
% 287.84/41.02 | REDUCE: (5), (8) imply:
% 287.84/41.02 | (296) hAPP_nat_nat(suc, bot_bot_nat) = one_one_nat
% 287.84/41.02 |
% 287.84/41.02 | REDUCE: (66), (129) imply:
% 287.84/41.02 | (297) hAPP_int_bool(all_1245_1, zero_zero_int) = all_1245_0
% 287.84/41.02 |
% 287.84/41.02 | REDUCE: (5), (64) imply:
% 287.84/41.02 | (298) $i(bot_bot_nat)
% 287.84/41.02 |
% 287.84/41.02 | GROUND_INST: instantiating (86) with all_1387_3, all_1445_1, u, mgt_call,
% 287.84/41.02 | simplifying with (168), (179) gives:
% 287.84/41.02 | (299) all_1445_1 = all_1387_3
% 287.84/41.02 |
% 287.84/41.02 | GROUND_INST: instantiating (86) with all_1381_2, all_1445_1, u, mgt_call,
% 287.84/41.02 | simplifying with (160), (179) gives:
% 287.84/41.03 | (300) all_1445_1 = all_1381_2
% 287.84/41.03 |
% 287.84/41.03 | GROUND_INST: instantiating (86) with all_1330_1, all_1445_1, u, mgt_call,
% 287.84/41.03 | simplifying with (151), (179) gives:
% 287.84/41.03 | (301) all_1445_1 = all_1330_1
% 287.84/41.03 |
% 287.84/41.03 | GROUND_INST: instantiating (88) with all_1328_2, all_1445_5, pn, mgt_call,
% 287.84/41.03 | simplifying with (148), (180) gives:
% 287.84/41.03 | (302) all_1445_5 = all_1328_2
% 287.84/41.03 |
% 287.84/41.03 | GROUND_INST: instantiating (92) with all_1196_0, all_1290_0, bot_bot_nat, suc,
% 287.84/41.03 | simplifying with (294), (295) gives:
% 287.84/41.03 | (303) all_1290_0 = all_1196_0
% 287.84/41.03 |
% 287.84/41.03 | GROUND_INST: instantiating (92) with all_1290_0, all_1385_1, bot_bot_nat, suc,
% 287.84/41.03 | simplifying with (293), (294) gives:
% 287.84/41.03 | (304) all_1385_1 = all_1290_0
% 287.84/41.03 |
% 287.84/41.03 | GROUND_INST: instantiating (92) with all_1435_0, all_1505_0, bot_bot_nat, suc,
% 287.84/41.03 | simplifying with (290), (291) gives:
% 287.84/41.03 | (305) all_1505_0 = all_1435_0
% 287.84/41.03 |
% 287.84/41.03 | GROUND_INST: instantiating (92) with all_1505_0, all_1537_1, bot_bot_nat, suc,
% 287.84/41.03 | simplifying with (289), (290) gives:
% 287.84/41.03 | (306) all_1537_1 = all_1505_0
% 287.84/41.03 |
% 287.84/41.03 | GROUND_INST: instantiating (92) with all_1537_1, all_1546_1, bot_bot_nat, suc,
% 287.84/41.03 | simplifying with (288), (289) gives:
% 287.84/41.03 | (307) all_1546_1 = all_1537_1
% 287.84/41.03 |
% 287.84/41.03 | GROUND_INST: instantiating (92) with all_1435_0, all_1552_1, bot_bot_nat, suc,
% 287.84/41.03 | simplifying with (287), (291) gives:
% 287.84/41.03 | (308) all_1552_1 = all_1435_0
% 287.84/41.03 |
% 287.84/41.03 | GROUND_INST: instantiating (92) with all_1426_0, all_1552_1, bot_bot_nat, suc,
% 287.84/41.03 | simplifying with (287), (292) gives:
% 287.84/41.03 | (309) all_1552_1 = all_1426_0
% 287.84/41.03 |
% 287.84/41.03 | GROUND_INST: instantiating (92) with all_1385_1, all_1552_1, bot_bot_nat, suc,
% 287.84/41.03 | simplifying with (287), (293) gives:
% 287.84/41.03 | (310) all_1552_1 = all_1385_1
% 287.84/41.03 |
% 287.84/41.03 | GROUND_INST: instantiating (92) with all_1546_1, all_1648_0, bot_bot_nat, suc,
% 287.84/41.03 | simplifying with (286), (288) gives:
% 287.84/41.03 | (311) all_1648_0 = all_1546_1
% 287.84/41.03 |
% 287.84/41.03 | GROUND_INST: instantiating (92) with all_1648_0, all_1651_0, bot_bot_nat, suc,
% 287.84/41.03 | simplifying with (285), (286) gives:
% 287.84/41.03 | (312) all_1651_0 = all_1648_0
% 287.84/41.03 |
% 287.84/41.03 | GROUND_INST: instantiating (92) with all_1651_0, all_1721_1, bot_bot_nat, suc,
% 287.84/41.03 | simplifying with (284), (285) gives:
% 287.84/41.03 | (313) all_1721_1 = all_1651_0
% 287.84/41.03 |
% 287.84/41.03 | GROUND_INST: instantiating (92) with one_one_nat, all_1721_1, bot_bot_nat,
% 287.84/41.03 | suc, simplifying with (284), (296) gives:
% 287.84/41.03 | (314) all_1721_1 = one_one_nat
% 287.84/41.03 |
% 287.84/41.03 | GROUND_INST: instantiating (94) with all_1534_1, all_1591_0, one_one_int,
% 287.84/41.03 | ord_less_eq_int, simplifying with (203), (225) gives:
% 287.84/41.03 | (315) all_1591_0 = all_1534_1
% 287.84/41.03 |
% 287.84/41.03 | GROUND_INST: instantiating (94) with all_1174_0, all_1225_1, zero_zero_int,
% 287.84/41.03 | ord_less_eq_int, simplifying with (96), (122) gives:
% 287.84/41.03 | (316) all_1225_1 = all_1174_0
% 287.84/41.03 |
% 287.84/41.03 | GROUND_INST: instantiating (94) with all_1225_1, all_1264_1, zero_zero_int,
% 287.84/41.03 | ord_less_eq_int, simplifying with (122), (282) gives:
% 287.84/41.03 | (317) all_1264_1 = all_1225_1
% 287.84/41.03 |
% 287.84/41.03 | GROUND_INST: instantiating (94) with all_1317_0, all_1322_0, zero_zero_int,
% 287.84/41.03 | ord_less_eq_int, simplifying with (141), (143) gives:
% 287.84/41.03 | (318) all_1322_0 = all_1317_0
% 287.84/41.03 |
% 287.84/41.03 | GROUND_INST: instantiating (94) with all_1264_1, all_1322_0, zero_zero_int,
% 287.84/41.03 | ord_less_eq_int, simplifying with (143), (282) gives:
% 287.84/41.03 | (319) all_1322_0 = all_1264_1
% 287.84/41.03 |
% 287.84/41.03 | GROUND_INST: instantiating (94) with all_1225_1, all_1335_0, zero_zero_int,
% 287.84/41.03 | ord_less_eq_int, simplifying with (122), (155) gives:
% 287.84/41.03 | (320) all_1335_0 = all_1225_1
% 287.84/41.03 |
% 287.84/41.03 | GROUND_INST: instantiating (94) with all_1176_0, all_1335_0, zero_zero_int,
% 287.84/41.03 | ord_less_eq_int, simplifying with (98), (155) gives:
% 287.84/41.03 | (321) all_1335_0 = all_1176_0
% 287.84/41.03 |
% 287.84/41.03 | GROUND_INST: instantiating (94) with all_1317_0, all_1465_0, zero_zero_int,
% 287.84/41.03 | ord_less_eq_int, simplifying with (141), (191) gives:
% 287.84/41.03 | (322) all_1465_0 = all_1317_0
% 287.84/41.03 |
% 287.84/41.03 | GROUND_INST: instantiating (94) with all_1223_1, all_1465_0, zero_zero_int,
% 287.84/41.03 | ord_less_eq_int, simplifying with (120), (191) gives:
% 287.84/41.03 | (323) all_1465_0 = all_1223_1
% 287.84/41.03 |
% 287.84/41.03 | GROUND_INST: instantiating (94) with all_1462_2, all_1496_0, zero_zero_int,
% 287.84/41.03 | ord_less_eq_int, simplifying with (188), (193) gives:
% 287.84/41.03 | (324) all_1496_0 = all_1462_2
% 287.84/41.03 |
% 287.84/41.03 | GROUND_INST: instantiating (94) with all_1496_0, all_1508_0, zero_zero_int,
% 287.84/41.03 | ord_less_eq_int, simplifying with (193), (197) gives:
% 287.84/41.03 | (325) all_1508_0 = all_1496_0
% 287.84/41.03 |
% 287.84/41.03 | GROUND_INST: instantiating (94) with all_1465_0, all_1540_0, zero_zero_int,
% 287.84/41.03 | ord_less_eq_int, simplifying with (191), (281) gives:
% 287.84/41.03 | (326) all_1540_0 = all_1465_0
% 287.84/41.03 |
% 287.84/41.03 | GROUND_INST: instantiating (94) with all_1322_0, all_1594_0, zero_zero_int,
% 287.84/41.03 | ord_less_eq_int, simplifying with (143), (228) gives:
% 287.84/41.03 | (327) all_1594_0 = all_1322_0
% 287.84/41.03 |
% 287.84/41.03 | GROUND_INST: instantiating (94) with all_1612_1, all_1633_0, zero_zero_int,
% 287.84/41.03 | ord_less_eq_int, simplifying with (233), (236) gives:
% 287.84/41.03 | (328) all_1633_0 = all_1612_1
% 287.84/41.03 |
% 287.84/41.03 | GROUND_INST: instantiating (94) with all_1594_0, all_1636_1, zero_zero_int,
% 287.84/41.03 | ord_less_eq_int, simplifying with (228), (238) gives:
% 287.84/41.03 | (329) all_1636_1 = all_1594_0
% 287.84/41.03 |
% 287.84/41.03 | GROUND_INST: instantiating (94) with all_1594_0, all_1639_0, zero_zero_int,
% 287.84/41.03 | ord_less_eq_int, simplifying with (228), (241) gives:
% 287.84/41.03 | (330) all_1639_0 = all_1594_0
% 287.84/41.03 |
% 287.84/41.03 | GROUND_INST: instantiating (94) with all_1462_2, all_1639_0, zero_zero_int,
% 287.84/41.03 | ord_less_eq_int, simplifying with (188), (241) gives:
% 287.84/41.03 | (331) all_1639_0 = all_1462_2
% 287.84/41.03 |
% 287.84/41.03 | GROUND_INST: instantiating (94) with all_1383_4, all_1639_0, zero_zero_int,
% 287.84/41.03 | ord_less_eq_int, simplifying with (162), (241) gives:
% 287.84/41.03 | (332) all_1639_0 = all_1383_4
% 287.84/41.03 |
% 287.84/41.03 | GROUND_INST: instantiating (94) with all_1612_1, all_1642_1, zero_zero_int,
% 287.84/41.03 | ord_less_eq_int, simplifying with (233), (243) gives:
% 287.84/41.03 | (333) all_1642_1 = all_1612_1
% 287.84/41.03 |
% 287.84/41.03 | GROUND_INST: instantiating (94) with all_1573_0, all_1642_1, zero_zero_int,
% 287.84/41.03 | ord_less_eq_int, simplifying with (243), (280) gives:
% 287.84/41.03 | (334) all_1642_1 = all_1573_0
% 287.84/41.03 |
% 287.84/41.03 | GROUND_INST: instantiating (94) with all_1508_0, all_1642_1, zero_zero_int,
% 287.84/41.03 | ord_less_eq_int, simplifying with (197), (243) gives:
% 287.84/41.03 | (335) all_1642_1 = all_1508_0
% 287.84/41.03 |
% 287.84/41.03 | GROUND_INST: instantiating (94) with all_1314_0, all_1642_1, zero_zero_int,
% 287.84/41.03 | ord_less_eq_int, simplifying with (139), (243) gives:
% 287.84/41.03 | (336) all_1642_1 = all_1314_0
% 287.84/41.03 |
% 287.84/41.03 | GROUND_INST: instantiating (94) with all_1633_0, all_1656_0, zero_zero_int,
% 287.84/41.03 | ord_less_eq_int, simplifying with (236), (252) gives:
% 287.84/41.03 | (337) all_1656_0 = all_1633_0
% 287.84/41.03 |
% 287.84/41.03 | GROUND_INST: instantiating (94) with all_1517_0, all_1656_0, zero_zero_int,
% 287.84/41.03 | ord_less_eq_int, simplifying with (199), (252) gives:
% 287.84/41.03 | (338) all_1656_0 = all_1517_0
% 287.84/41.03 |
% 287.84/41.03 | GROUND_INST: instantiating (94) with all_1636_1, all_1670_0, zero_zero_int,
% 287.84/41.03 | ord_less_eq_int, simplifying with (238), (255) gives:
% 287.84/41.03 | (339) all_1670_0 = all_1636_1
% 287.84/41.03 |
% 287.84/41.03 | GROUND_INST: instantiating (94) with all_1670_0, all_1724_1, zero_zero_int,
% 287.84/41.03 | ord_less_eq_int, simplifying with (255), (259) gives:
% 287.84/41.03 | (340) all_1724_1 = all_1670_0
% 287.84/41.03 |
% 287.84/41.03 | GROUND_INST: instantiating (94) with all_1325_0, all_1724_1, zero_zero_int,
% 287.84/41.03 | ord_less_eq_int, simplifying with (145), (259) gives:
% 287.84/41.03 | (341) all_1724_1 = all_1325_0
% 287.84/41.03 |
% 287.84/41.03 | GROUND_INST: instantiating (94) with all_1654_0, all_1727_1, zero_zero_int,
% 287.84/41.03 | ord_less_eq_int, simplifying with (249), (262) gives:
% 287.84/41.03 | (342) all_1727_1 = all_1654_0
% 287.84/41.03 |
% 287.84/41.03 | GROUND_INST: instantiating (94) with all_1540_0, all_1727_1, zero_zero_int,
% 287.84/41.03 | ord_less_eq_int, simplifying with (262), (281) gives:
% 287.84/41.03 | (343) all_1727_1 = all_1540_0
% 287.84/41.03 |
% 287.84/41.03 | GROUND_INST: instantiating (94) with all_1447_1, all_1727_1, zero_zero_int,
% 287.84/41.03 | ord_less_eq_int, simplifying with (186), (262) gives:
% 287.84/41.03 | (344) all_1727_1 = all_1447_1
% 287.84/41.03 |
% 287.84/41.03 | GROUND_INST: instantiating (94) with all_1245_1, all_1549_0, zero_zero_int,
% 287.84/41.03 | ord_less_int, simplifying with (212), (279) gives:
% 287.84/41.03 | (345) all_1549_0 = all_1245_1
% 287.84/41.03 |
% 287.84/41.03 | GROUND_INST: instantiating (94) with all_1549_0, all_1576_0, zero_zero_int,
% 287.84/41.03 | ord_less_int, simplifying with (212), (221) gives:
% 287.84/41.03 | (346) all_1576_0 = all_1549_0
% 287.84/41.03 |
% 287.84/41.03 | GROUND_INST: instantiating (94) with all_1462_1, all_1576_0, zero_zero_int,
% 287.84/41.03 | ord_less_int, simplifying with (189), (221) gives:
% 287.84/41.03 | (347) all_1576_0 = all_1462_1
% 287.84/41.03 |
% 287.84/41.03 | GROUND_INST: instantiating (94) with all_1256_1, all_1576_0, zero_zero_int,
% 287.84/41.03 | ord_less_int, simplifying with (132), (221) gives:
% 287.84/41.03 | (348) all_1576_0 = all_1256_1
% 287.84/41.03 |
% 287.84/41.03 | GROUND_INST: instantiating (94) with all_1411_1, all_1582_1, zero_zero_int,
% 287.84/41.03 | ord_less_int, simplifying with (170), (223) gives:
% 287.84/41.03 | (349) all_1582_1 = all_1411_1
% 287.84/41.03 |
% 287.84/41.03 | GROUND_INST: instantiating (94) with all_1576_0, all_1591_1, zero_zero_int,
% 287.84/41.03 | ord_less_int, simplifying with (221), (226) gives:
% 287.84/41.03 | (350) all_1591_1 = all_1576_0
% 287.84/41.03 |
% 287.84/41.03 | GROUND_INST: instantiating (94) with all_1582_1, all_1594_1, zero_zero_int,
% 287.84/41.03 | ord_less_int, simplifying with (223), (229) gives:
% 287.84/41.03 | (351) all_1594_1 = all_1582_1
% 287.84/41.04 |
% 287.84/41.04 | GROUND_INST: instantiating (94) with all_1591_1, all_1606_0, zero_zero_int,
% 287.84/41.04 | ord_less_int, simplifying with (226), (231) gives:
% 287.84/41.04 | (352) all_1606_0 = all_1591_1
% 287.84/41.04 |
% 287.84/41.04 | GROUND_INST: instantiating (94) with all_1606_0, all_1612_0, zero_zero_int,
% 287.84/41.04 | ord_less_int, simplifying with (231), (234) gives:
% 287.84/41.04 | (353) all_1612_0 = all_1606_0
% 287.84/41.04 |
% 287.84/41.04 | GROUND_INST: instantiating (94) with all_1594_1, all_1636_0, zero_zero_int,
% 287.84/41.04 | ord_less_int, simplifying with (229), (239) gives:
% 287.84/41.04 | (354) all_1636_0 = all_1594_1
% 287.84/41.04 |
% 287.84/41.04 | GROUND_INST: instantiating (94) with all_1576_0, all_1636_0, zero_zero_int,
% 287.84/41.04 | ord_less_int, simplifying with (221), (239) gives:
% 287.84/41.04 | (355) all_1636_0 = all_1576_0
% 287.84/41.04 |
% 287.84/41.04 | GROUND_INST: instantiating (94) with all_1594_1, all_1654_1, zero_zero_int,
% 287.84/41.04 | ord_less_int, simplifying with (229), (250) gives:
% 287.84/41.04 | (356) all_1654_1 = all_1594_1
% 287.84/41.04 |
% 287.84/41.04 | GROUND_INST: instantiating (94) with all_1612_0, all_1656_1, zero_zero_int,
% 287.84/41.04 | ord_less_int, simplifying with (234), (253) gives:
% 287.84/41.04 | (357) all_1656_1 = all_1612_0
% 287.84/41.04 |
% 287.84/41.04 | GROUND_INST: instantiating (94) with all_1654_1, all_1724_0, zero_zero_int,
% 287.84/41.04 | ord_less_int, simplifying with (250), (260) gives:
% 287.84/41.04 | (358) all_1724_0 = all_1654_1
% 287.84/41.04 |
% 287.84/41.04 | GROUND_INST: instantiating (94) with all_1564_0, all_1724_0, zero_zero_int,
% 287.84/41.04 | ord_less_int, simplifying with (216), (260) gives:
% 287.84/41.04 | (359) all_1724_0 = all_1564_0
% 287.84/41.04 |
% 287.84/41.04 | GROUND_INST: instantiating (94) with all_1656_1, all_1727_0, zero_zero_int,
% 287.84/41.04 | ord_less_int, simplifying with (253), (263) gives:
% 287.84/41.04 | (360) all_1727_0 = all_1656_1
% 287.84/41.04 |
% 287.84/41.04 | GROUND_INST: instantiating (94) with all_1636_0, all_1730_0, zero_zero_int,
% 287.84/41.04 | ord_less_int, simplifying with (239), (265) gives:
% 287.84/41.04 | (361) all_1730_0 = all_1636_0
% 287.84/41.04 |
% 287.84/41.04 | GROUND_INST: instantiating (94) with all_1534_0, all_1730_0, zero_zero_int,
% 287.84/41.04 | ord_less_int, simplifying with (204), (265) gives:
% 287.84/41.04 | (362) all_1730_0 = all_1534_0
% 287.84/41.04 |
% 287.84/41.04 | GROUND_INST: instantiating (94) with all_1727_0, all_1732_0, zero_zero_int,
% 287.84/41.04 | ord_less_int, simplifying with (263), (267) gives:
% 287.84/41.04 | (363) all_1732_0 = all_1727_0
% 287.84/41.04 |
% 287.84/41.04 | GROUND_INST: instantiating (94) with all_1573_1, all_1732_0, zero_zero_int,
% 287.84/41.04 | ord_less_int, simplifying with (267), (278) gives:
% 287.84/41.04 | (364) all_1732_0 = all_1573_1
% 287.84/41.04 |
% 287.84/41.04 | GROUND_INST: instantiating (85) with all_1184_0, all_1208_0, zero_zero_int,
% 287.84/41.04 | simplifying with (273), (275) gives:
% 287.84/41.04 | (365) all_1208_0 = all_1184_0
% 287.84/41.04 |
% 287.84/41.04 | GROUND_INST: instantiating (85) with all_1208_0, all_1383_3, zero_zero_int,
% 287.84/41.04 | simplifying with (270), (273) gives:
% 287.84/41.04 | (366) all_1383_3 = all_1208_0
% 287.84/41.04 |
% 287.84/41.04 | GROUND_INST: instantiating (85) with all_1182_0, all_1383_3, zero_zero_int,
% 287.84/41.04 | simplifying with (270), (276) gives:
% 287.84/41.04 | (367) all_1383_3 = all_1182_0
% 287.84/41.04 |
% 287.84/41.04 | GROUND_INST: instantiating (85) with all_1290_1, all_1385_4, zero_zero_int,
% 287.84/41.04 | simplifying with (269), (272) gives:
% 287.84/41.04 | (368) all_1385_4 = all_1290_1
% 287.84/41.04 |
% 287.84/41.04 | GROUND_INST: instantiating (85) with all_1208_0, all_1385_4, zero_zero_int,
% 287.84/41.04 | simplifying with (269), (273) gives:
% 287.84/41.04 | (369) all_1385_4 = all_1208_0
% 287.84/41.04 |
% 287.84/41.04 | GROUND_INST: instantiating (85) with all_1186_0, all_1385_4, zero_zero_int,
% 287.84/41.04 | simplifying with (269), (274) gives:
% 287.84/41.04 | (370) all_1385_4 = all_1186_0
% 287.84/41.04 |
% 287.84/41.04 | GROUND_INST: instantiating (85) with all_1385_4, all_1531_3, zero_zero_int,
% 287.84/41.04 | simplifying with (268), (269) gives:
% 287.84/41.04 | (371) all_1531_3 = all_1385_4
% 287.84/41.04 |
% 287.84/41.04 | GROUND_INST: instantiating (85) with all_1351_3, all_1531_3, zero_zero_int,
% 287.84/41.04 | simplifying with (268), (271) gives:
% 287.84/41.04 | (372) all_1531_3 = all_1351_3
% 287.84/41.04 |
% 287.84/41.04 | COMBINE_EQS: (363), (364) imply:
% 287.84/41.04 | (373) all_1727_0 = all_1573_1
% 287.84/41.04 |
% 287.84/41.04 | SIMP: (373) implies:
% 287.84/41.04 | (374) all_1727_0 = all_1573_1
% 287.84/41.04 |
% 287.84/41.04 | COMBINE_EQS: (361), (362) imply:
% 287.84/41.04 | (375) all_1636_0 = all_1534_0
% 287.84/41.04 |
% 287.84/41.04 | SIMP: (375) implies:
% 287.84/41.04 | (376) all_1636_0 = all_1534_0
% 287.84/41.04 |
% 287.84/41.04 | COMBINE_EQS: (360), (374) imply:
% 287.84/41.04 | (377) all_1656_1 = all_1573_1
% 287.84/41.04 |
% 287.84/41.04 | SIMP: (377) implies:
% 287.84/41.04 | (378) all_1656_1 = all_1573_1
% 287.84/41.04 |
% 287.84/41.04 | COMBINE_EQS: (342), (344) imply:
% 287.84/41.04 | (379) all_1654_0 = all_1447_1
% 287.84/41.04 |
% 287.84/41.04 | COMBINE_EQS: (342), (343) imply:
% 287.84/41.04 | (380) all_1654_0 = all_1540_0
% 287.84/41.04 |
% 287.84/41.04 | COMBINE_EQS: (358), (359) imply:
% 287.84/41.04 | (381) all_1654_1 = all_1564_0
% 287.84/41.04 |
% 287.84/41.04 | SIMP: (381) implies:
% 287.84/41.04 | (382) all_1654_1 = all_1564_0
% 287.84/41.04 |
% 287.84/41.04 | COMBINE_EQS: (340), (341) imply:
% 287.84/41.04 | (383) all_1670_0 = all_1325_0
% 287.84/41.04 |
% 287.84/41.04 | SIMP: (383) implies:
% 287.84/41.04 | (384) all_1670_0 = all_1325_0
% 287.84/41.04 |
% 287.84/41.04 | COMBINE_EQS: (313), (314) imply:
% 287.84/41.04 | (385) all_1651_0 = one_one_nat
% 287.84/41.04 |
% 287.84/41.04 | SIMP: (385) implies:
% 287.84/41.04 | (386) all_1651_0 = one_one_nat
% 287.84/41.04 |
% 287.84/41.04 | COMBINE_EQS: (339), (384) imply:
% 287.84/41.04 | (387) all_1636_1 = all_1325_0
% 287.84/41.04 |
% 287.84/41.04 | SIMP: (387) implies:
% 287.84/41.04 | (388) all_1636_1 = all_1325_0
% 287.84/41.04 |
% 287.84/41.04 | COMBINE_EQS: (337), (338) imply:
% 287.84/41.04 | (389) all_1633_0 = all_1517_0
% 287.84/41.04 |
% 287.84/41.04 | SIMP: (389) implies:
% 287.84/41.04 | (390) all_1633_0 = all_1517_0
% 287.84/41.04 |
% 287.84/41.04 | COMBINE_EQS: (357), (378) imply:
% 287.84/41.04 | (391) all_1612_0 = all_1573_1
% 287.84/41.04 |
% 287.84/41.04 | SIMP: (391) implies:
% 287.84/41.04 | (392) all_1612_0 = all_1573_1
% 287.84/41.04 |
% 287.84/41.04 | COMBINE_EQS: (379), (380) imply:
% 287.84/41.04 | (393) all_1540_0 = all_1447_1
% 287.84/41.04 |
% 287.84/41.04 | SIMP: (393) implies:
% 287.84/41.04 | (394) all_1540_0 = all_1447_1
% 287.84/41.04 |
% 287.84/41.04 | COMBINE_EQS: (356), (382) imply:
% 287.84/41.04 | (395) all_1594_1 = all_1564_0
% 287.84/41.04 |
% 287.84/41.04 | SIMP: (395) implies:
% 287.84/41.04 | (396) all_1594_1 = all_1564_0
% 287.84/41.04 |
% 287.84/41.04 | COMBINE_EQS: (312), (386) imply:
% 287.84/41.04 | (397) all_1648_0 = one_one_nat
% 287.84/41.04 |
% 287.84/41.04 | SIMP: (397) implies:
% 287.84/41.04 | (398) all_1648_0 = one_one_nat
% 287.84/41.04 |
% 287.84/41.04 | COMBINE_EQS: (311), (398) imply:
% 287.84/41.04 | (399) all_1546_1 = one_one_nat
% 287.84/41.04 |
% 287.84/41.04 | SIMP: (399) implies:
% 287.84/41.04 | (400) all_1546_1 = one_one_nat
% 287.84/41.04 |
% 287.84/41.04 | COMBINE_EQS: (334), (336) imply:
% 287.84/41.04 | (401) all_1573_0 = all_1314_0
% 287.84/41.04 |
% 287.84/41.04 | COMBINE_EQS: (334), (335) imply:
% 287.84/41.04 | (402) all_1573_0 = all_1508_0
% 287.84/41.04 |
% 287.84/41.04 | COMBINE_EQS: (333), (334) imply:
% 287.84/41.04 | (403) all_1612_1 = all_1573_0
% 287.84/41.04 |
% 287.84/41.04 | SIMP: (403) implies:
% 287.84/41.04 | (404) all_1612_1 = all_1573_0
% 287.84/41.04 |
% 287.84/41.04 | COMBINE_EQS: (331), (332) imply:
% 287.84/41.04 | (405) all_1462_2 = all_1383_4
% 287.84/41.04 |
% 287.84/41.04 | SIMP: (405) implies:
% 287.84/41.04 | (406) all_1462_2 = all_1383_4
% 287.84/41.04 |
% 287.84/41.04 | COMBINE_EQS: (330), (332) imply:
% 287.84/41.04 | (407) all_1594_0 = all_1383_4
% 287.84/41.04 |
% 287.84/41.04 | SIMP: (407) implies:
% 287.84/41.04 | (408) all_1594_0 = all_1383_4
% 287.84/41.04 |
% 287.84/41.04 | COMBINE_EQS: (355), (376) imply:
% 287.84/41.04 | (409) all_1576_0 = all_1534_0
% 287.84/41.04 |
% 287.84/41.04 | SIMP: (409) implies:
% 287.84/41.04 | (410) all_1576_0 = all_1534_0
% 287.84/41.04 |
% 287.84/41.04 | COMBINE_EQS: (354), (376) imply:
% 287.84/41.04 | (411) all_1594_1 = all_1534_0
% 287.84/41.04 |
% 287.84/41.04 | SIMP: (411) implies:
% 287.84/41.04 | (412) all_1594_1 = all_1534_0
% 287.84/41.04 |
% 287.84/41.04 | COMBINE_EQS: (329), (388) imply:
% 287.84/41.04 | (413) all_1594_0 = all_1325_0
% 287.84/41.04 |
% 287.84/41.04 | SIMP: (413) implies:
% 287.84/41.04 | (414) all_1594_0 = all_1325_0
% 287.84/41.04 |
% 287.84/41.04 | COMBINE_EQS: (328), (390) imply:
% 287.84/41.04 | (415) all_1612_1 = all_1517_0
% 287.84/41.04 |
% 287.84/41.04 | SIMP: (415) implies:
% 287.84/41.04 | (416) all_1612_1 = all_1517_0
% 287.84/41.04 |
% 287.84/41.04 | COMBINE_EQS: (353), (392) imply:
% 287.84/41.04 | (417) all_1606_0 = all_1573_1
% 287.84/41.04 |
% 287.84/41.04 | SIMP: (417) implies:
% 287.84/41.04 | (418) all_1606_0 = all_1573_1
% 287.84/41.04 |
% 287.84/41.04 | COMBINE_EQS: (404), (416) imply:
% 287.84/41.04 | (419) all_1573_0 = all_1517_0
% 287.84/41.04 |
% 287.84/41.04 | SIMP: (419) implies:
% 287.84/41.04 | (420) all_1573_0 = all_1517_0
% 287.84/41.04 |
% 287.84/41.04 | COMBINE_EQS: (352), (418) imply:
% 287.84/41.04 | (421) all_1591_1 = all_1573_1
% 287.84/41.04 |
% 287.84/41.04 | SIMP: (421) implies:
% 287.84/41.04 | (422) all_1591_1 = all_1573_1
% 287.84/41.04 |
% 287.84/41.04 | COMBINE_EQS: (408), (414) imply:
% 287.84/41.04 | (423) all_1383_4 = all_1325_0
% 287.84/41.04 |
% 287.84/41.04 | SIMP: (423) implies:
% 287.84/41.04 | (424) all_1383_4 = all_1325_0
% 287.84/41.04 |
% 287.84/41.04 | COMBINE_EQS: (327), (414) imply:
% 287.84/41.04 | (425) all_1325_0 = all_1322_0
% 287.84/41.04 |
% 287.84/41.04 | COMBINE_EQS: (396), (412) imply:
% 287.84/41.04 | (426) all_1564_0 = all_1534_0
% 287.84/41.04 |
% 287.84/41.04 | COMBINE_EQS: (351), (396) imply:
% 287.84/41.04 | (427) all_1582_1 = all_1564_0
% 287.84/41.04 |
% 287.84/41.04 | SIMP: (427) implies:
% 287.84/41.04 | (428) all_1582_1 = all_1564_0
% 287.84/41.04 |
% 287.84/41.04 | COMBINE_EQS: (350), (422) imply:
% 287.84/41.04 | (429) all_1576_0 = all_1573_1
% 287.84/41.04 |
% 287.84/41.04 | SIMP: (429) implies:
% 287.84/41.04 | (430) all_1576_0 = all_1573_1
% 287.84/41.04 |
% 287.84/41.04 | COMBINE_EQS: (349), (428) imply:
% 287.84/41.04 | (431) all_1564_0 = all_1411_1
% 287.84/41.04 |
% 287.84/41.04 | SIMP: (431) implies:
% 287.84/41.04 | (432) all_1564_0 = all_1411_1
% 287.84/41.04 |
% 287.84/41.04 | COMBINE_EQS: (346), (430) imply:
% 287.84/41.04 | (433) all_1573_1 = all_1549_0
% 287.84/41.04 |
% 287.84/41.04 | COMBINE_EQS: (348), (430) imply:
% 287.84/41.04 | (434) all_1573_1 = all_1256_1
% 287.84/41.04 |
% 287.84/41.04 | COMBINE_EQS: (347), (430) imply:
% 287.84/41.04 | (435) all_1573_1 = all_1462_1
% 287.84/41.04 |
% 287.84/41.04 | COMBINE_EQS: (410), (430) imply:
% 287.84/41.04 | (436) all_1573_1 = all_1534_0
% 287.84/41.04 |
% 287.84/41.04 | COMBINE_EQS: (402), (420) imply:
% 287.84/41.04 | (437) all_1517_0 = all_1508_0
% 287.84/41.04 |
% 287.84/41.04 | COMBINE_EQS: (401), (420) imply:
% 287.84/41.04 | (438) all_1517_0 = all_1314_0
% 287.84/41.04 |
% 287.84/41.04 | COMBINE_EQS: (435), (436) imply:
% 287.84/41.04 | (439) all_1534_0 = all_1462_1
% 287.84/41.04 |
% 287.84/41.04 | SIMP: (439) implies:
% 287.84/41.05 | (440) all_1534_0 = all_1462_1
% 287.84/41.05 |
% 287.84/41.05 | COMBINE_EQS: (433), (435) imply:
% 287.84/41.05 | (441) all_1549_0 = all_1462_1
% 287.84/41.05 |
% 287.84/41.05 | SIMP: (441) implies:
% 287.84/41.05 | (442) all_1549_0 = all_1462_1
% 287.84/41.05 |
% 287.84/41.05 | COMBINE_EQS: (434), (435) imply:
% 287.84/41.05 | (443) all_1462_1 = all_1256_1
% 287.84/41.05 |
% 287.84/41.05 | COMBINE_EQS: (426), (432) imply:
% 287.84/41.05 | (444) all_1534_0 = all_1411_1
% 287.84/41.05 |
% 287.84/41.05 | SIMP: (444) implies:
% 287.84/41.05 | (445) all_1534_0 = all_1411_1
% 287.84/41.05 |
% 287.84/41.05 | COMBINE_EQS: (308), (309) imply:
% 287.84/41.05 | (446) all_1435_0 = all_1426_0
% 287.84/41.05 |
% 287.84/41.05 | SIMP: (446) implies:
% 287.84/41.05 | (447) all_1435_0 = all_1426_0
% 287.84/41.05 |
% 287.84/41.05 | COMBINE_EQS: (309), (310) imply:
% 287.84/41.05 | (448) all_1426_0 = all_1385_1
% 287.84/41.05 |
% 287.84/41.05 | COMBINE_EQS: (345), (442) imply:
% 287.84/41.05 | (449) all_1462_1 = all_1245_1
% 287.84/41.05 |
% 287.84/41.05 | SIMP: (449) implies:
% 287.84/41.05 | (450) all_1462_1 = all_1245_1
% 287.84/41.05 |
% 287.84/41.05 | COMBINE_EQS: (307), (400) imply:
% 287.84/41.05 | (451) all_1537_1 = one_one_nat
% 287.84/41.05 |
% 287.84/41.05 | SIMP: (451) implies:
% 287.84/41.05 | (452) all_1537_1 = one_one_nat
% 287.84/41.05 |
% 287.84/41.05 | COMBINE_EQS: (326), (394) imply:
% 287.84/41.05 | (453) all_1465_0 = all_1447_1
% 287.84/41.05 |
% 287.84/41.05 | SIMP: (453) implies:
% 287.84/41.05 | (454) all_1465_0 = all_1447_1
% 287.84/41.05 |
% 287.84/41.05 | COMBINE_EQS: (306), (452) imply:
% 287.84/41.05 | (455) all_1505_0 = one_one_nat
% 287.84/41.05 |
% 287.84/41.05 | SIMP: (455) implies:
% 287.84/41.05 | (456) all_1505_0 = one_one_nat
% 287.84/41.05 |
% 287.84/41.05 | COMBINE_EQS: (440), (445) imply:
% 287.84/41.05 | (457) all_1462_1 = all_1411_1
% 287.84/41.05 |
% 287.84/41.05 | SIMP: (457) implies:
% 287.84/41.05 | (458) all_1462_1 = all_1411_1
% 287.84/41.05 |
% 287.84/41.05 | COMBINE_EQS: (371), (372) imply:
% 287.84/41.05 | (459) all_1385_4 = all_1351_3
% 287.84/41.05 |
% 287.84/41.05 | SIMP: (459) implies:
% 287.84/41.05 | (460) all_1385_4 = all_1351_3
% 287.84/41.05 |
% 287.84/41.05 | COMBINE_EQS: (437), (438) imply:
% 287.84/41.05 | (461) all_1508_0 = all_1314_0
% 287.84/41.05 |
% 287.84/41.05 | SIMP: (461) implies:
% 287.84/41.05 | (462) all_1508_0 = all_1314_0
% 287.84/41.05 |
% 287.84/41.05 | COMBINE_EQS: (325), (462) imply:
% 287.84/41.05 | (463) all_1496_0 = all_1314_0
% 287.84/41.05 |
% 287.84/41.05 | SIMP: (463) implies:
% 287.84/41.05 | (464) all_1496_0 = all_1314_0
% 287.84/41.05 |
% 287.84/41.05 | COMBINE_EQS: (305), (456) imply:
% 287.84/41.05 | (465) all_1435_0 = one_one_nat
% 287.84/41.05 |
% 287.84/41.05 | SIMP: (465) implies:
% 287.84/41.05 | (466) all_1435_0 = one_one_nat
% 287.84/41.05 |
% 287.84/41.05 | COMBINE_EQS: (324), (464) imply:
% 287.84/41.05 | (467) all_1462_2 = all_1314_0
% 287.84/41.05 |
% 287.84/41.05 | SIMP: (467) implies:
% 287.84/41.05 | (468) all_1462_2 = all_1314_0
% 287.84/41.05 |
% 287.84/41.05 | COMBINE_EQS: (322), (454) imply:
% 287.84/41.05 | (469) all_1447_1 = all_1317_0
% 287.84/41.05 |
% 287.84/41.05 | COMBINE_EQS: (323), (454) imply:
% 287.84/41.05 | (470) all_1447_1 = all_1223_1
% 287.84/41.05 |
% 287.84/41.05 | COMBINE_EQS: (450), (458) imply:
% 287.84/41.05 | (471) all_1411_1 = all_1245_1
% 287.84/41.05 |
% 287.84/41.05 | COMBINE_EQS: (443), (458) imply:
% 287.84/41.05 | (472) all_1411_1 = all_1256_1
% 287.84/41.05 |
% 287.84/41.05 | COMBINE_EQS: (406), (468) imply:
% 287.84/41.05 | (473) all_1383_4 = all_1314_0
% 287.84/41.05 |
% 287.84/41.05 | SIMP: (473) implies:
% 287.84/41.05 | (474) all_1383_4 = all_1314_0
% 287.84/41.05 |
% 287.84/41.05 | COMBINE_EQS: (469), (470) imply:
% 287.84/41.05 | (475) all_1317_0 = all_1223_1
% 287.84/41.05 |
% 287.84/41.05 | SIMP: (475) implies:
% 287.84/41.05 | (476) all_1317_0 = all_1223_1
% 287.84/41.05 |
% 287.84/41.05 | COMBINE_EQS: (299), (300) imply:
% 287.84/41.05 | (477) all_1387_3 = all_1381_2
% 287.84/41.05 |
% 287.84/41.05 | COMBINE_EQS: (299), (301) imply:
% 287.84/41.05 | (478) all_1387_3 = all_1330_1
% 287.84/41.05 |
% 287.84/41.05 | COMBINE_EQS: (447), (466) imply:
% 287.84/41.05 | (479) all_1426_0 = one_one_nat
% 287.84/41.05 |
% 287.84/41.05 | SIMP: (479) implies:
% 287.84/41.05 | (480) all_1426_0 = one_one_nat
% 287.84/41.05 |
% 287.84/41.05 | COMBINE_EQS: (448), (480) imply:
% 287.84/41.05 | (481) all_1385_1 = one_one_nat
% 287.84/41.05 |
% 287.84/41.05 | SIMP: (481) implies:
% 287.84/41.05 | (482) all_1385_1 = one_one_nat
% 287.84/41.05 |
% 287.84/41.05 | COMBINE_EQS: (471), (472) imply:
% 287.84/41.05 | (483) all_1256_1 = all_1245_1
% 287.84/41.05 |
% 287.84/41.05 | COMBINE_EQS: (477), (478) imply:
% 287.84/41.05 | (484) all_1381_2 = all_1330_1
% 287.84/41.05 |
% 287.84/41.05 | COMBINE_EQS: (304), (482) imply:
% 287.84/41.05 | (485) all_1290_0 = one_one_nat
% 287.84/41.05 |
% 287.84/41.05 | SIMP: (485) implies:
% 287.84/41.05 | (486) all_1290_0 = one_one_nat
% 287.84/41.05 |
% 287.84/41.05 | COMBINE_EQS: (370), (460) imply:
% 287.84/41.05 | (487) all_1351_3 = all_1186_0
% 287.84/41.05 |
% 287.84/41.05 | COMBINE_EQS: (368), (460) imply:
% 287.84/41.05 | (488) all_1351_3 = all_1290_1
% 287.84/41.05 |
% 287.84/41.05 | COMBINE_EQS: (369), (460) imply:
% 287.84/41.05 | (489) all_1351_3 = all_1208_0
% 287.84/41.05 |
% 287.84/41.05 | COMBINE_EQS: (366), (367) imply:
% 287.84/41.05 | (490) all_1208_0 = all_1182_0
% 287.84/41.05 |
% 287.84/41.05 | SIMP: (490) implies:
% 287.84/41.05 | (491) all_1208_0 = all_1182_0
% 287.84/41.05 |
% 287.84/41.05 | COMBINE_EQS: (424), (474) imply:
% 287.84/41.05 | (492) all_1325_0 = all_1314_0
% 287.84/41.05 |
% 287.84/41.05 | SIMP: (492) implies:
% 287.84/41.05 | (493) all_1325_0 = all_1314_0
% 287.84/41.05 |
% 287.84/41.05 | COMBINE_EQS: (488), (489) imply:
% 287.84/41.05 | (494) all_1290_1 = all_1208_0
% 287.84/41.05 |
% 287.84/41.05 | COMBINE_EQS: (487), (488) imply:
% 287.84/41.05 | (495) all_1290_1 = all_1186_0
% 287.84/41.05 |
% 287.84/41.05 | COMBINE_EQS: (320), (321) imply:
% 287.84/41.05 | (496) all_1225_1 = all_1176_0
% 287.84/41.05 |
% 287.84/41.05 | SIMP: (496) implies:
% 287.84/41.05 | (497) all_1225_1 = all_1176_0
% 287.84/41.05 |
% 287.84/41.05 | COMBINE_EQS: (425), (493) imply:
% 287.84/41.05 | (498) all_1322_0 = all_1314_0
% 287.84/41.05 |
% 287.84/41.05 | SIMP: (498) implies:
% 287.84/41.05 | (499) all_1322_0 = all_1314_0
% 287.84/41.05 |
% 287.84/41.05 | COMBINE_EQS: (319), (499) imply:
% 287.84/41.05 | (500) all_1314_0 = all_1264_1
% 287.84/41.05 |
% 287.84/41.05 | COMBINE_EQS: (318), (499) imply:
% 287.84/41.05 | (501) all_1317_0 = all_1314_0
% 287.84/41.05 |
% 287.84/41.05 | SIMP: (501) implies:
% 287.84/41.05 | (502) all_1317_0 = all_1314_0
% 287.84/41.05 |
% 287.84/41.05 | COMBINE_EQS: (476), (502) imply:
% 287.84/41.05 | (503) all_1314_0 = all_1223_1
% 287.84/41.05 |
% 287.84/41.05 | SIMP: (503) implies:
% 287.84/41.05 | (504) all_1314_0 = all_1223_1
% 287.84/41.05 |
% 287.84/41.05 | COMBINE_EQS: (500), (504) imply:
% 287.84/41.05 | (505) all_1264_1 = all_1223_1
% 287.84/41.05 |
% 287.84/41.05 | SIMP: (505) implies:
% 287.84/41.05 | (506) all_1264_1 = all_1223_1
% 287.84/41.05 |
% 287.84/41.05 | COMBINE_EQS: (303), (486) imply:
% 287.84/41.05 | (507) all_1196_0 = one_one_nat
% 287.84/41.05 |
% 287.84/41.05 | SIMP: (507) implies:
% 287.84/41.05 | (508) all_1196_0 = one_one_nat
% 287.84/41.05 |
% 287.84/41.05 | COMBINE_EQS: (494), (495) imply:
% 287.84/41.05 | (509) all_1208_0 = all_1186_0
% 287.84/41.05 |
% 287.84/41.05 | SIMP: (509) implies:
% 287.84/41.05 | (510) all_1208_0 = all_1186_0
% 287.84/41.05 |
% 287.84/41.05 | COMBINE_EQS: (317), (506) imply:
% 287.84/41.05 | (511) all_1225_1 = all_1223_1
% 287.84/41.05 |
% 287.84/41.05 | SIMP: (511) implies:
% 287.84/41.05 | (512) all_1225_1 = all_1223_1
% 287.84/41.05 |
% 287.84/41.05 | COMBINE_EQS: (316), (512) imply:
% 287.84/41.05 | (513) all_1223_1 = all_1174_0
% 287.84/41.05 |
% 287.84/41.05 | COMBINE_EQS: (497), (512) imply:
% 287.84/41.05 | (514) all_1223_1 = all_1176_0
% 287.84/41.05 |
% 287.84/41.05 | COMBINE_EQS: (513), (514) imply:
% 287.84/41.05 | (515) all_1176_0 = all_1174_0
% 287.84/41.05 |
% 287.84/41.05 | SIMP: (515) implies:
% 287.84/41.05 | (516) all_1176_0 = all_1174_0
% 287.84/41.05 |
% 287.84/41.05 | COMBINE_EQS: (491), (510) imply:
% 287.84/41.05 | (517) all_1186_0 = all_1182_0
% 287.84/41.05 |
% 287.84/41.05 | COMBINE_EQS: (365), (510) imply:
% 287.84/41.05 | (518) all_1186_0 = all_1184_0
% 287.84/41.05 |
% 287.84/41.05 | COMBINE_EQS: (517), (518) imply:
% 287.84/41.05 | (519) all_1184_0 = all_1182_0
% 287.84/41.05 |
% 287.84/41.05 | SIMP: (519) implies:
% 287.84/41.05 | (520) all_1184_0 = all_1182_0
% 287.84/41.05 |
% 287.84/41.05 | REDUCE: (106), (517) imply:
% 287.84/41.05 | (521) number_number_of_int(all_1182_0) = one_one_int
% 287.84/41.05 |
% 287.84/41.05 | REDUCE: (103), (520) imply:
% 287.84/41.05 | (522) number_number_of_nat(all_1182_0) = one_one_nat
% 287.84/41.05 |
% 287.84/41.05 | REDUCE: (111), (508) imply:
% 287.84/41.05 | (523) hAPP_nat_int(semiri1621563631at_int, one_one_nat) = one_one_int
% 287.84/41.05 |
% 287.84/41.05 | REDUCE: (184), (302) imply:
% 287.84/41.05 | (524) hAPP_a1206381875a_bool(insert_a, all_1328_2) = all_1445_4
% 287.84/41.05 |
% 287.84/41.05 | REDUCE: (181), (301) imply:
% 287.84/41.05 | (525) hAPP_fun_a_bool_bool(all_1445_2, all_1330_1) = all_1445_0
% 287.84/41.05 |
% 287.84/41.05 | REDUCE: (119), (513) imply:
% 287.84/41.05 | (526) hAPP_int_bool(all_1174_0, one_one_int) = all_1223_0
% 287.84/41.05 |
% 287.84/41.05 | REDUCE: (177), (302) imply:
% 287.84/41.05 | (527) $i(all_1328_2)
% 287.84/41.05 |
% 287.84/41.05 | REDUCE: (159), (484) imply:
% 287.84/41.05 | (528) $i(all_1330_1)
% 287.84/41.05 |
% 287.84/41.05 | REDUCE: (109), (508) imply:
% 287.84/41.05 | (529) $i(one_one_nat)
% 287.84/41.05 |
% 287.84/41.05 | REDUCE: (102), (520) imply:
% 287.84/41.05 | (530) $i(all_1182_0)
% 287.84/41.05 |
% 287.84/41.05 | GROUND_INST: instantiating (4) with all_1330_1, all_1445_3, all_1445_2,
% 287.84/41.05 | all_1445_0, simplifying with (176), (178), (183), (525), (528)
% 287.84/41.05 | gives:
% 287.84/41.05 | (531) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] :
% 287.84/41.05 | (hAPP_fun_a_bool_bool(v1, all_1445_3) = v2 & hAPP_fun_a_bool_bool(v1,
% 287.84/41.05 | all_1330_1) = v3 & hAPP_a85458249l_bool(member_a, v0) = v1 &
% 287.84/41.05 | $i(v3) & $i(v2) & $i(v1) & $i(v0) & hBOOL(v2) & is_a(v0) & ~
% 287.84/41.05 | hBOOL(v3))
% 287.84/41.05 |
% 287.84/41.05 | GROUND_INST: instantiating (3) with all_1328_2, g, all_1330_1, all_1445_4,
% 287.84/41.05 | all_1445_3, all_1445_2, all_1445_0, simplifying with (79), (176),
% 287.84/41.05 | (182), (183), (524), (525), (527), (528) gives:
% 287.84/41.06 | (532) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] :
% 287.84/41.06 | ((hAPP_f1631501043l_bool(ord_le1311769555a_bool, g) = v2 &
% 287.84/41.06 | hAPP_fun_a_bool_bool(v2, all_1330_1) = v3 & $i(v3) & $i(v2) & ~
% 287.84/41.06 | hBOOL(v3)) | (hAPP_fun_a_bool_bool(v0, all_1330_1) = v1 &
% 287.84/41.06 | hAPP_a85458249l_bool(member_a, all_1328_2) = v0 & $i(v1) & $i(v0)
% 287.84/41.06 | & ~ hBOOL(v1)))
% 287.84/41.06 |
% 287.84/41.06 | GROUND_INST: instantiating (52) with bot_bot_nat, zero_zero_int, simplifying
% 287.84/41.06 | with (283), (298) gives:
% 287.84/41.06 | (533) abs_abs_int(zero_zero_int) = zero_zero_int & $i(zero_zero_int)
% 287.84/41.06 |
% 287.84/41.06 | ALPHA: (533) implies:
% 287.84/41.06 | (534) $i(zero_zero_int)
% 287.84/41.06 |
% 287.84/41.06 | GROUND_INST: instantiating (52) with one_one_nat, one_one_int, simplifying
% 287.84/41.06 | with (523), (529) gives:
% 287.84/41.06 | (535) abs_abs_int(one_one_int) = one_one_int & $i(one_one_int)
% 287.84/41.06 |
% 287.84/41.06 | ALPHA: (535) implies:
% 287.84/41.06 | (536) $i(one_one_int)
% 287.84/41.06 |
% 287.84/41.06 | GROUND_INST: instantiating (20) with zero_zero_int, one_one_int, all_1174_0,
% 287.84/41.06 | all_1223_0, simplifying with (96), (118), (526), (534), (536)
% 287.84/41.06 | gives:
% 287.84/41.06 | (537) zero_zero_int = one_one_int | ? [v0: $i] : ? [v1: $i] :
% 287.84/41.06 | (hAPP_i1948725293t_bool(ord_less_eq_int, one_one_int) = v0 &
% 287.84/41.06 | hAPP_int_bool(v0, zero_zero_int) = v1 & $i(v1) & $i(v0) & ~
% 287.84/41.06 | hBOOL(v1))
% 287.84/41.06 |
% 287.84/41.06 | GROUND_INST: instantiating (1) with zero_zero_int, one_one_int, all_1174_0,
% 287.84/41.06 | all_1223_0, simplifying with (96), (118), (526), (534), (536)
% 287.84/41.06 | gives:
% 287.84/41.06 | (538) ? [v0: any] : ? [v1: $i] : (( ~ (zero_zero_int = one_one_int) | (v0
% 287.84/41.06 | = all_1174_0 & hAPP_int_bool(all_1174_0, one_one_int) = v1 &
% 287.84/41.06 | $i(v1) & hBOOL(v1))) & (zero_zero_int = one_one_int |
% 287.84/41.06 | (hAPP_i1948725293t_bool(ord_less_eq_int, one_one_int) = v0 &
% 287.84/41.06 | hAPP_int_bool(v0, zero_zero_int) = v1 & $i(v1) & $i(v0) & ~
% 287.84/41.06 | hBOOL(v1))))
% 287.84/41.06 |
% 287.84/41.06 | GROUND_INST: instantiating (71) with zero_zero_int, all_1245_1, simplifying
% 287.84/41.06 | with (279), (534) gives:
% 287.84/41.06 | (539) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] :
% 287.84/41.06 | ((bit1(zero_zero_int) = v0 & hAPP_i1948725293t_bool(ord_less_int, v0)
% 287.84/41.06 | = v1 & hAPP_int_bool(v1, pls) = v2 & $i(v2) & $i(v1) & $i(v0) &
% 287.84/41.06 | ~ hBOOL(v2)) | (hAPP_int_bool(all_1245_1, pls) = v3 & $i(v3) &
% 287.84/41.06 | hBOOL(v3)))
% 287.84/41.06 |
% 287.84/41.06 | GROUND_INST: instantiating (72) with zero_zero_int, all_1245_1, simplifying
% 287.84/41.06 | with (279), (534) gives:
% 287.84/41.06 | (540) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] :
% 287.84/41.06 | ((bit1(zero_zero_int) = v0 & hAPP_i1948725293t_bool(ord_less_eq_int,
% 287.84/41.06 | v0) = v1 & hAPP_int_bool(v1, pls) = v2 & $i(v2) & $i(v1) &
% 287.84/41.06 | $i(v0) & ~ hBOOL(v2)) | (hAPP_int_bool(all_1245_1, pls) = v3 &
% 287.84/41.06 | $i(v3) & hBOOL(v3)))
% 287.84/41.06 |
% 287.84/41.06 | GROUND_INST: instantiating (53) with all_1182_0, all_1182_0, one_one_nat,
% 287.84/41.06 | simplifying with (522), (530) gives:
% 287.84/41.06 | (541) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 287.84/41.06 | ? [v5: $i] : (((v0 = zero_zero_int &
% 287.84/41.06 | number_number_of_int(all_1182_0) = zero_zero_int) |
% 287.84/41.06 | (number_number_of_int(all_1182_0) = v2 & hAPP_int_bool(nat_neg,
% 287.84/41.06 | v2) = v5 & $i(v5) & $i(v2) & ~ hBOOL(v5)) |
% 287.84/41.06 | (number_number_of_int(all_1182_0) = v0 & hAPP_int_bool(nat_neg,
% 287.84/41.06 | v0) = v1 & $i(v1) & $i(v0) & hBOOL(v1))) &
% 287.84/41.06 | ((number_number_of_int(all_1182_0) = v2 &
% 287.84/41.06 | hAPP_i1948725293t_bool(ord_less_eq_int, v2) = v3 &
% 287.84/41.06 | hAPP_int_bool(v3, zero_zero_int) = v4 & $i(v4) & $i(v3) &
% 287.84/41.06 | $i(v2) & hBOOL(v4)) | (number_number_of_int(all_1182_0) = v0 &
% 287.84/41.06 | hAPP_int_bool(nat_neg, v0) = v1 & $i(v1) & $i(v0) & ~
% 287.84/41.06 | hBOOL(v1))))
% 287.84/41.06 |
% 287.84/41.06 | GROUND_INST: instantiating (54) with zero_zero_int, all_1182_0, bot_bot_nat,
% 287.84/41.06 | one_one_nat, simplifying with (277), (522), (530), (534) gives:
% 287.84/41.06 | (542) one_one_nat = bot_bot_nat | ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 287.84/41.06 | ? [v3: $i] : ? [v4: $i] : ? [v5: $i] :
% 287.84/41.06 | (number_number_of_int(all_1182_0) = v2 &
% 287.84/41.06 | number_number_of_int(zero_zero_int) = v0 & hAPP_int_bool(nat_neg,
% 287.84/41.06 | v0) = v1 & $i(v2) & $i(v1) & $i(v0) &
% 287.84/41.06 | ((hAPP_i1948725293t_bool(ord_less_eq_int, v2) = v3 &
% 287.84/41.06 | hAPP_int_bool(v3, zero_zero_int) = v4 & $i(v4) & $i(v3) &
% 287.84/41.06 | hBOOL(v1) & ~ hBOOL(v4)) | (hAPP_int_bool(nat_neg, v2) = v5 &
% 287.84/41.06 | $i(v5) & ~ hBOOL(v1) & (( ~ (v0 = zero_zero_int) & hBOOL(v5))
% 287.84/41.06 | | ( ~ (all_1182_0 = zero_zero_int) & ~ hBOOL(v5))))))
% 287.84/41.06 |
% 287.84/41.06 | GROUND_INST: instantiating (fact_1071_number__of__is__id) with all_1182_0,
% 287.84/41.06 | one_one_int, simplifying with (521), (530) gives:
% 287.84/41.06 | (543) all_1182_0 = one_one_int
% 287.84/41.06 |
% 287.84/41.06 | GROUND_INST: instantiating (57) with all_1182_0, one_one_int, simplifying with
% 287.84/41.06 | (521), (530) gives:
% 287.84/41.06 | (544) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] :
% 287.84/41.06 | ((bit1(all_1182_0) = v0 & number_number_of_int(v0) = v1 &
% 287.84/41.06 | hAPP_int_bool(nat_neg, v1) = v2 & $i(v2) & $i(v1) & $i(v0) & ~
% 287.84/41.06 | hBOOL(v2)) | (hAPP_int_bool(nat_neg, one_one_int) = v3 & $i(v3) &
% 287.84/41.06 | hBOOL(v3)))
% 287.84/41.06 |
% 287.84/41.06 | DELTA: instantiating (531) with fresh symbols all_1910_0, all_1910_1,
% 287.84/41.06 | all_1910_2, all_1910_3 gives:
% 287.84/41.06 | (545) hAPP_fun_a_bool_bool(all_1910_2, all_1445_3) = all_1910_1 &
% 287.84/41.06 | hAPP_fun_a_bool_bool(all_1910_2, all_1330_1) = all_1910_0 &
% 287.84/41.06 | hAPP_a85458249l_bool(member_a, all_1910_3) = all_1910_2 &
% 287.84/41.06 | $i(all_1910_0) & $i(all_1910_1) & $i(all_1910_2) & $i(all_1910_3) &
% 287.84/41.06 | hBOOL(all_1910_1) & is_a(all_1910_3) & ~ hBOOL(all_1910_0)
% 287.84/41.06 |
% 287.84/41.06 | ALPHA: (545) implies:
% 287.84/41.06 | (546) ~ hBOOL(all_1910_0)
% 287.84/41.06 | (547) $i(all_1910_3)
% 287.84/41.06 | (548) hAPP_a85458249l_bool(member_a, all_1910_3) = all_1910_2
% 287.84/41.06 | (549) hAPP_fun_a_bool_bool(all_1910_2, all_1330_1) = all_1910_0
% 287.84/41.06 |
% 287.84/41.06 | DELTA: instantiating (540) with fresh symbols all_1917_0, all_1917_1,
% 287.84/41.06 | all_1917_2, all_1917_3 gives:
% 287.84/41.06 | (550) (bit1(zero_zero_int) = all_1917_3 &
% 287.84/41.06 | hAPP_i1948725293t_bool(ord_less_eq_int, all_1917_3) = all_1917_2 &
% 287.84/41.06 | hAPP_int_bool(all_1917_2, pls) = all_1917_1 & $i(all_1917_1) &
% 287.84/41.06 | $i(all_1917_2) & $i(all_1917_3) & ~ hBOOL(all_1917_1)) |
% 287.84/41.06 | (hAPP_int_bool(all_1245_1, pls) = all_1917_0 & $i(all_1917_0) &
% 287.84/41.06 | hBOOL(all_1917_0))
% 287.84/41.06 |
% 287.84/41.06 | DELTA: instantiating (544) with fresh symbols all_1919_0, all_1919_1,
% 287.84/41.06 | all_1919_2, all_1919_3 gives:
% 287.84/41.06 | (551) (bit1(all_1182_0) = all_1919_3 & number_number_of_int(all_1919_3) =
% 287.84/41.06 | all_1919_2 & hAPP_int_bool(nat_neg, all_1919_2) = all_1919_1 &
% 287.84/41.06 | $i(all_1919_1) & $i(all_1919_2) & $i(all_1919_3) & ~
% 287.84/41.06 | hBOOL(all_1919_1)) | (hAPP_int_bool(nat_neg, one_one_int) =
% 287.84/41.06 | all_1919_0 & $i(all_1919_0) & hBOOL(all_1919_0))
% 287.84/41.06 |
% 287.84/41.06 | DELTA: instantiating (539) with fresh symbols all_1926_0, all_1926_1,
% 287.84/41.06 | all_1926_2, all_1926_3 gives:
% 287.84/41.06 | (552) (bit1(zero_zero_int) = all_1926_3 &
% 287.84/41.06 | hAPP_i1948725293t_bool(ord_less_int, all_1926_3) = all_1926_2 &
% 287.84/41.06 | hAPP_int_bool(all_1926_2, pls) = all_1926_1 & $i(all_1926_1) &
% 287.84/41.06 | $i(all_1926_2) & $i(all_1926_3) & ~ hBOOL(all_1926_1)) |
% 287.84/41.06 | (hAPP_int_bool(all_1245_1, pls) = all_1926_0 & $i(all_1926_0) &
% 287.84/41.06 | hBOOL(all_1926_0))
% 287.84/41.06 |
% 287.84/41.06 | DELTA: instantiating (532) with fresh symbols all_1928_0, all_1928_1,
% 287.84/41.06 | all_1928_2, all_1928_3 gives:
% 287.84/41.06 | (553) (hAPP_f1631501043l_bool(ord_le1311769555a_bool, g) = all_1928_1 &
% 287.84/41.06 | hAPP_fun_a_bool_bool(all_1928_1, all_1330_1) = all_1928_0 &
% 287.84/41.06 | $i(all_1928_0) & $i(all_1928_1) & ~ hBOOL(all_1928_0)) |
% 287.84/41.06 | (hAPP_fun_a_bool_bool(all_1928_3, all_1330_1) = all_1928_2 &
% 287.84/41.06 | hAPP_a85458249l_bool(member_a, all_1328_2) = all_1928_3 &
% 287.84/41.06 | $i(all_1928_2) & $i(all_1928_3) & ~ hBOOL(all_1928_2))
% 287.84/41.06 |
% 287.84/41.06 | DELTA: instantiating (538) with fresh symbols all_1934_0, all_1934_1 gives:
% 287.84/41.07 | (554) ( ~ (zero_zero_int = one_one_int) | (all_1934_1 = all_1174_0 &
% 287.84/41.07 | hAPP_int_bool(all_1174_0, one_one_int) = all_1934_0 &
% 287.84/41.07 | $i(all_1934_0) & hBOOL(all_1934_0))) & (zero_zero_int =
% 287.84/41.07 | one_one_int | (hAPP_i1948725293t_bool(ord_less_eq_int, one_one_int)
% 287.84/41.07 | = all_1934_1 & hAPP_int_bool(all_1934_1, zero_zero_int) =
% 287.84/41.07 | all_1934_0 & $i(all_1934_0) & $i(all_1934_1) & ~
% 287.84/41.07 | hBOOL(all_1934_0)))
% 287.84/41.07 |
% 287.84/41.07 | ALPHA: (554) implies:
% 287.84/41.07 | (555) zero_zero_int = one_one_int |
% 287.84/41.07 | (hAPP_i1948725293t_bool(ord_less_eq_int, one_one_int) = all_1934_1 &
% 287.84/41.07 | hAPP_int_bool(all_1934_1, zero_zero_int) = all_1934_0 &
% 287.84/41.07 | $i(all_1934_0) & $i(all_1934_1) & ~ hBOOL(all_1934_0))
% 287.84/41.07 |
% 287.84/41.07 | DELTA: instantiating (541) with fresh symbols all_1970_0, all_1970_1,
% 287.84/41.07 | all_1970_2, all_1970_3, all_1970_4, all_1970_5 gives:
% 287.84/41.07 | (556) ((all_1970_5 = zero_zero_int & number_number_of_int(all_1182_0) =
% 287.84/41.07 | zero_zero_int) | (number_number_of_int(all_1182_0) = all_1970_3 &
% 287.84/41.07 | hAPP_int_bool(nat_neg, all_1970_3) = all_1970_0 & $i(all_1970_0)
% 287.84/41.07 | & $i(all_1970_3) & ~ hBOOL(all_1970_0)) |
% 287.84/41.07 | (number_number_of_int(all_1182_0) = all_1970_5 &
% 287.84/41.07 | hAPP_int_bool(nat_neg, all_1970_5) = all_1970_4 & $i(all_1970_4)
% 287.84/41.07 | & $i(all_1970_5) & hBOOL(all_1970_4))) &
% 287.84/41.07 | ((number_number_of_int(all_1182_0) = all_1970_3 &
% 287.84/41.07 | hAPP_i1948725293t_bool(ord_less_eq_int, all_1970_3) = all_1970_2
% 287.84/41.07 | & hAPP_int_bool(all_1970_2, zero_zero_int) = all_1970_1 &
% 287.84/41.07 | $i(all_1970_1) & $i(all_1970_2) & $i(all_1970_3) &
% 287.84/41.07 | hBOOL(all_1970_1)) | (number_number_of_int(all_1182_0) =
% 287.84/41.07 | all_1970_5 & hAPP_int_bool(nat_neg, all_1970_5) = all_1970_4 &
% 287.84/41.07 | $i(all_1970_4) & $i(all_1970_5) & ~ hBOOL(all_1970_4)))
% 287.84/41.07 |
% 287.84/41.07 | ALPHA: (556) implies:
% 287.84/41.07 | (557) (number_number_of_int(all_1182_0) = all_1970_3 &
% 287.84/41.07 | hAPP_i1948725293t_bool(ord_less_eq_int, all_1970_3) = all_1970_2 &
% 287.84/41.07 | hAPP_int_bool(all_1970_2, zero_zero_int) = all_1970_1 &
% 287.84/41.07 | $i(all_1970_1) & $i(all_1970_2) & $i(all_1970_3) &
% 287.84/41.07 | hBOOL(all_1970_1)) | (number_number_of_int(all_1182_0) = all_1970_5
% 287.84/41.07 | & hAPP_int_bool(nat_neg, all_1970_5) = all_1970_4 & $i(all_1970_4)
% 287.84/41.07 | & $i(all_1970_5) & ~ hBOOL(all_1970_4))
% 287.84/41.07 | (558) (all_1970_5 = zero_zero_int & number_number_of_int(all_1182_0) =
% 287.84/41.07 | zero_zero_int) | (number_number_of_int(all_1182_0) = all_1970_3 &
% 287.84/41.07 | hAPP_int_bool(nat_neg, all_1970_3) = all_1970_0 & $i(all_1970_0) &
% 287.84/41.07 | $i(all_1970_3) & ~ hBOOL(all_1970_0)) |
% 287.84/41.07 | (number_number_of_int(all_1182_0) = all_1970_5 &
% 287.84/41.07 | hAPP_int_bool(nat_neg, all_1970_5) = all_1970_4 & $i(all_1970_4) &
% 287.84/41.07 | $i(all_1970_5) & hBOOL(all_1970_4))
% 287.84/41.07 |
% 287.84/41.07 | REDUCE: (276), (543) imply:
% 287.84/41.07 | (559) bit1(zero_zero_int) = one_one_int
% 287.84/41.07 |
% 287.84/41.07 | REDUCE: (521), (543) imply:
% 287.84/41.07 | (560) number_number_of_int(one_one_int) = one_one_int
% 287.84/41.07 |
% 287.84/41.07 | BETA: splitting (537) gives:
% 287.84/41.07 |
% 287.84/41.07 | Case 1:
% 287.84/41.07 | |
% 287.84/41.07 | | (561) zero_zero_int = one_one_int
% 287.84/41.07 | |
% 287.84/41.07 | | REDUCE: (22), (561) imply:
% 287.84/41.07 | | (562) $false
% 287.84/41.07 | |
% 287.84/41.07 | | CLOSE: (562) is inconsistent.
% 287.84/41.07 | |
% 287.84/41.07 | Case 2:
% 287.84/41.07 | |
% 287.84/41.07 | | (563) ? [v0: $i] : ? [v1: $i] :
% 287.84/41.07 | | (hAPP_i1948725293t_bool(ord_less_eq_int, one_one_int) = v0 &
% 287.84/41.07 | | hAPP_int_bool(v0, zero_zero_int) = v1 & $i(v1) & $i(v0) & ~
% 287.84/41.07 | | hBOOL(v1))
% 287.84/41.07 | |
% 287.84/41.07 | | DELTA: instantiating (563) with fresh symbols all_2007_0, all_2007_1 gives:
% 287.84/41.07 | | (564) hAPP_i1948725293t_bool(ord_less_eq_int, one_one_int) = all_2007_1 &
% 287.84/41.07 | | hAPP_int_bool(all_2007_1, zero_zero_int) = all_2007_0 &
% 287.84/41.07 | | $i(all_2007_0) & $i(all_2007_1) & ~ hBOOL(all_2007_0)
% 287.84/41.07 | |
% 287.84/41.07 | | ALPHA: (564) implies:
% 287.84/41.07 | | (565) ~ hBOOL(all_2007_0)
% 287.84/41.07 | | (566) hAPP_int_bool(all_2007_1, zero_zero_int) = all_2007_0
% 287.84/41.07 | | (567) hAPP_i1948725293t_bool(ord_less_eq_int, one_one_int) = all_2007_1
% 287.84/41.07 | |
% 287.84/41.07 | | BETA: splitting (550) gives:
% 287.84/41.07 | |
% 287.84/41.07 | | Case 1:
% 287.84/41.07 | | |
% 287.84/41.07 | | | (568) bit1(zero_zero_int) = all_1917_3 &
% 287.84/41.07 | | | hAPP_i1948725293t_bool(ord_less_eq_int, all_1917_3) = all_1917_2
% 287.84/41.07 | | | & hAPP_int_bool(all_1917_2, pls) = all_1917_1 & $i(all_1917_1) &
% 287.84/41.07 | | | $i(all_1917_2) & $i(all_1917_3) & ~ hBOOL(all_1917_1)
% 287.84/41.07 | | |
% 287.84/41.07 | | | ALPHA: (568) implies:
% 287.84/41.07 | | | (569) hAPP_int_bool(all_1917_2, pls) = all_1917_1
% 287.84/41.07 | | | (570) hAPP_i1948725293t_bool(ord_less_eq_int, all_1917_3) = all_1917_2
% 287.84/41.07 | | | (571) bit1(zero_zero_int) = all_1917_3
% 287.84/41.07 | | |
% 287.84/41.07 | | | REDUCE: (66), (569) imply:
% 287.84/41.07 | | | (572) hAPP_int_bool(all_1917_2, zero_zero_int) = all_1917_1
% 287.84/41.07 | | |
% 287.84/41.07 | | | BETA: splitting (558) gives:
% 287.84/41.07 | | |
% 287.84/41.07 | | | Case 1:
% 287.84/41.07 | | | |
% 287.84/41.07 | | | | (573) all_1970_5 = zero_zero_int & number_number_of_int(all_1182_0) =
% 287.84/41.07 | | | | zero_zero_int
% 287.84/41.07 | | | |
% 287.84/41.07 | | | | ALPHA: (573) implies:
% 287.84/41.07 | | | | (574) number_number_of_int(all_1182_0) = zero_zero_int
% 287.84/41.07 | | | |
% 287.84/41.07 | | | | REDUCE: (543), (574) imply:
% 287.84/41.07 | | | | (575) number_number_of_int(one_one_int) = zero_zero_int
% 287.84/41.07 | | | |
% 287.84/41.07 | | | | GROUND_INST: instantiating (84) with one_one_int, zero_zero_int,
% 287.84/41.07 | | | | one_one_int, simplifying with (560), (575) gives:
% 287.84/41.07 | | | | (576) zero_zero_int = one_one_int
% 287.84/41.07 | | | |
% 287.84/41.07 | | | | REDUCE: (22), (576) imply:
% 287.84/41.07 | | | | (577) $false
% 287.84/41.07 | | | |
% 287.84/41.07 | | | | CLOSE: (577) is inconsistent.
% 287.84/41.07 | | | |
% 287.84/41.07 | | | Case 2:
% 287.84/41.07 | | | |
% 287.84/41.07 | | | | (578) (number_number_of_int(all_1182_0) = all_1970_3 &
% 287.84/41.07 | | | | hAPP_int_bool(nat_neg, all_1970_3) = all_1970_0 &
% 287.84/41.07 | | | | $i(all_1970_0) & $i(all_1970_3) & ~ hBOOL(all_1970_0)) |
% 287.84/41.07 | | | | (number_number_of_int(all_1182_0) = all_1970_5 &
% 287.84/41.07 | | | | hAPP_int_bool(nat_neg, all_1970_5) = all_1970_4 &
% 287.84/41.07 | | | | $i(all_1970_4) & $i(all_1970_5) & hBOOL(all_1970_4))
% 287.84/41.07 | | | |
% 287.84/41.07 | | | | BETA: splitting (578) gives:
% 287.84/41.07 | | | |
% 287.84/41.07 | | | | Case 1:
% 287.84/41.07 | | | | |
% 287.84/41.07 | | | | | (579) number_number_of_int(all_1182_0) = all_1970_3 &
% 287.84/41.07 | | | | | hAPP_int_bool(nat_neg, all_1970_3) = all_1970_0 &
% 287.84/41.07 | | | | | $i(all_1970_0) & $i(all_1970_3) & ~ hBOOL(all_1970_0)
% 287.84/41.07 | | | | |
% 287.84/41.07 | | | | | ALPHA: (579) implies:
% 287.84/41.07 | | | | | (580) number_number_of_int(all_1182_0) = all_1970_3
% 287.84/41.07 | | | | |
% 287.84/41.07 | | | | | REDUCE: (543), (580) imply:
% 287.84/41.07 | | | | | (581) number_number_of_int(one_one_int) = all_1970_3
% 287.84/41.07 | | | | |
% 287.84/41.07 | | | | | BETA: splitting (555) gives:
% 287.84/41.07 | | | | |
% 287.84/41.07 | | | | | Case 1:
% 287.84/41.07 | | | | | |
% 287.84/41.07 | | | | | | (582) zero_zero_int = one_one_int
% 287.84/41.07 | | | | | |
% 287.84/41.07 | | | | | | REDUCE: (22), (582) imply:
% 287.84/41.07 | | | | | | (583) $false
% 287.84/41.07 | | | | | |
% 287.84/41.07 | | | | | | CLOSE: (583) is inconsistent.
% 287.84/41.07 | | | | | |
% 287.84/41.07 | | | | | Case 2:
% 287.84/41.07 | | | | | |
% 287.84/41.07 | | | | | | (584) hAPP_i1948725293t_bool(ord_less_eq_int, one_one_int) =
% 287.84/41.07 | | | | | | all_1934_1 & hAPP_int_bool(all_1934_1, zero_zero_int) =
% 287.84/41.07 | | | | | | all_1934_0 & $i(all_1934_0) & $i(all_1934_1) & ~
% 287.84/41.07 | | | | | | hBOOL(all_1934_0)
% 287.84/41.07 | | | | | |
% 287.84/41.07 | | | | | | ALPHA: (584) implies:
% 287.84/41.07 | | | | | | (585) hAPP_int_bool(all_1934_1, zero_zero_int) = all_1934_0
% 287.84/41.07 | | | | | | (586) hAPP_i1948725293t_bool(ord_less_eq_int, one_one_int) =
% 287.84/41.07 | | | | | | all_1934_1
% 287.84/41.07 | | | | | |
% 287.84/41.07 | | | | | | BETA: splitting (553) gives:
% 287.84/41.07 | | | | | |
% 287.84/41.07 | | | | | | Case 1:
% 287.84/41.07 | | | | | | |
% 287.84/41.07 | | | | | | | (587) hAPP_f1631501043l_bool(ord_le1311769555a_bool, g) =
% 287.84/41.07 | | | | | | | all_1928_1 & hAPP_fun_a_bool_bool(all_1928_1, all_1330_1)
% 287.84/41.07 | | | | | | | = all_1928_0 & $i(all_1928_0) & $i(all_1928_1) & ~
% 287.84/41.07 | | | | | | | hBOOL(all_1928_0)
% 287.84/41.07 | | | | | | |
% 287.84/41.07 | | | | | | | ALPHA: (587) implies:
% 287.84/41.07 | | | | | | | (588) ~ hBOOL(all_1928_0)
% 287.84/41.07 | | | | | | | (589) hAPP_fun_a_bool_bool(all_1928_1, all_1330_1) = all_1928_0
% 287.84/41.07 | | | | | | | (590) hAPP_f1631501043l_bool(ord_le1311769555a_bool, g) =
% 287.84/41.07 | | | | | | | all_1928_1
% 287.84/41.07 | | | | | | |
% 287.84/41.07 | | | | | | | BETA: splitting (551) gives:
% 287.84/41.07 | | | | | | |
% 287.84/41.07 | | | | | | | Case 1:
% 287.84/41.07 | | | | | | | |
% 287.84/41.07 | | | | | | | |
% 287.84/41.07 | | | | | | | | GROUND_INST: instantiating (91) with all_1330_2, all_1928_1, g,
% 287.84/41.07 | | | | | | | | ord_le1311769555a_bool, simplifying with (153),
% 287.84/41.07 | | | | | | | | (590) gives:
% 287.84/41.07 | | | | | | | | (591) all_1928_1 = all_1330_2
% 287.84/41.07 | | | | | | | |
% 287.84/41.07 | | | | | | | | REDUCE: (589), (591) imply:
% 287.84/41.07 | | | | | | | | (592) hAPP_fun_a_bool_bool(all_1330_2, all_1330_1) =
% 287.84/41.07 | | | | | | | | all_1928_0
% 287.84/41.08 | | | | | | | |
% 287.84/41.08 | | | | | | | | GROUND_INST: instantiating (90) with all_1330_0, all_1928_0,
% 287.84/41.08 | | | | | | | | all_1330_1, all_1330_2, simplifying with (152),
% 287.84/41.08 | | | | | | | | (592) gives:
% 287.84/41.08 | | | | | | | | (593) all_1928_0 = all_1330_0
% 287.84/41.08 | | | | | | | |
% 287.84/41.08 | | | | | | | | REDUCE: (588), (593) imply:
% 287.84/41.08 | | | | | | | | (594) ~ hBOOL(all_1330_0)
% 287.84/41.08 | | | | | | | |
% 287.84/41.08 | | | | | | | | PRED_UNIFY: (150), (594) imply:
% 287.84/41.08 | | | | | | | | (595) $false
% 287.84/41.08 | | | | | | | |
% 287.84/41.08 | | | | | | | | CLOSE: (595) is inconsistent.
% 287.84/41.08 | | | | | | | |
% 287.84/41.08 | | | | | | | Case 2:
% 287.84/41.08 | | | | | | | |
% 287.84/41.08 | | | | | | | | (596) hAPP_int_bool(nat_neg, one_one_int) = all_1919_0 &
% 287.84/41.08 | | | | | | | | $i(all_1919_0) & hBOOL(all_1919_0)
% 287.84/41.08 | | | | | | | |
% 287.84/41.08 | | | | | | | | ALPHA: (596) implies:
% 287.84/41.08 | | | | | | | | (597) hBOOL(all_1919_0)
% 287.84/41.08 | | | | | | | | (598) hAPP_int_bool(nat_neg, one_one_int) = all_1919_0
% 287.84/41.08 | | | | | | | |
% 287.84/41.08 | | | | | | | | GROUND_INST: instantiating (89) with all_1200_0, all_1919_0,
% 287.84/41.08 | | | | | | | | one_one_int, nat_neg, simplifying with (114), (598)
% 287.84/41.08 | | | | | | | | gives:
% 287.84/41.08 | | | | | | | | (599) all_1919_0 = all_1200_0
% 287.84/41.08 | | | | | | | |
% 287.84/41.08 | | | | | | | | REDUCE: (597), (599) imply:
% 287.84/41.08 | | | | | | | | (600) hBOOL(all_1200_0)
% 287.84/41.08 | | | | | | | |
% 287.84/41.08 | | | | | | | | PRED_UNIFY: (113), (600) imply:
% 287.84/41.08 | | | | | | | | (601) $false
% 287.84/41.08 | | | | | | | |
% 287.84/41.08 | | | | | | | | CLOSE: (601) is inconsistent.
% 287.84/41.08 | | | | | | | |
% 287.84/41.08 | | | | | | | End of split
% 287.84/41.08 | | | | | | |
% 287.84/41.08 | | | | | | Case 2:
% 287.84/41.08 | | | | | | |
% 287.84/41.08 | | | | | | | (602) hAPP_fun_a_bool_bool(all_1928_3, all_1330_1) = all_1928_2
% 287.84/41.08 | | | | | | | & hAPP_a85458249l_bool(member_a, all_1328_2) = all_1928_3
% 287.84/41.08 | | | | | | | & $i(all_1928_2) & $i(all_1928_3) & ~ hBOOL(all_1928_2)
% 287.84/41.08 | | | | | | |
% 287.84/41.08 | | | | | | | ALPHA: (602) implies:
% 287.84/41.08 | | | | | | | (603) ~ hBOOL(all_1928_2)
% 287.84/41.08 | | | | | | | (604) hAPP_a85458249l_bool(member_a, all_1328_2) = all_1928_3
% 287.84/41.08 | | | | | | | (605) hAPP_fun_a_bool_bool(all_1928_3, all_1330_1) = all_1928_2
% 287.84/41.08 | | | | | | |
% 287.84/41.08 | | | | | | | GROUND_INST: instantiating (87) with all_1328_1, all_1928_3,
% 287.84/41.08 | | | | | | | all_1328_2, member_a, simplifying with (147), (604)
% 287.84/41.08 | | | | | | | gives:
% 287.84/41.08 | | | | | | | (606) all_1928_3 = all_1328_1
% 287.84/41.08 | | | | | | |
% 287.84/41.08 | | | | | | | GROUND_INST: instantiating (94) with all_1534_1, all_2007_1,
% 287.84/41.08 | | | | | | | one_one_int, ord_less_eq_int, simplifying with (203),
% 287.84/41.08 | | | | | | | (567) gives:
% 287.84/41.08 | | | | | | | (607) all_2007_1 = all_1534_1
% 287.84/41.08 | | | | | | |
% 287.84/41.08 | | | | | | | GROUND_INST: instantiating (94) with all_1934_1, all_2007_1,
% 287.84/41.08 | | | | | | | one_one_int, ord_less_eq_int, simplifying with (567),
% 287.84/41.08 | | | | | | | (586) gives:
% 287.84/41.08 | | | | | | | (608) all_2007_1 = all_1934_1
% 287.84/41.08 | | | | | | |
% 287.84/41.08 | | | | | | | GROUND_INST: instantiating (84) with one_one_int, all_1970_3,
% 287.84/41.08 | | | | | | | one_one_int, simplifying with (560), (581) gives:
% 287.84/41.08 | | | | | | | (609) all_1970_3 = one_one_int
% 287.84/41.08 | | | | | | |
% 287.84/41.08 | | | | | | | GROUND_INST: instantiating (85) with one_one_int, all_1917_3,
% 287.84/41.08 | | | | | | | zero_zero_int, simplifying with (559), (571) gives:
% 287.84/41.08 | | | | | | | (610) all_1917_3 = one_one_int
% 287.84/41.08 | | | | | | |
% 287.84/41.08 | | | | | | | COMBINE_EQS: (607), (608) imply:
% 287.84/41.08 | | | | | | | (611) all_1934_1 = all_1534_1
% 287.84/41.08 | | | | | | |
% 287.84/41.08 | | | | | | | REDUCE: (570), (610) imply:
% 287.84/41.08 | | | | | | | (612) hAPP_i1948725293t_bool(ord_less_eq_int, one_one_int) =
% 287.84/41.08 | | | | | | | all_1917_2
% 287.84/41.08 | | | | | | |
% 287.84/41.08 | | | | | | | REDUCE: (605), (606) imply:
% 287.84/41.08 | | | | | | | (613) hAPP_fun_a_bool_bool(all_1328_1, all_1330_1) = all_1928_2
% 287.84/41.08 | | | | | | |
% 287.84/41.08 | | | | | | | REDUCE: (566), (607) imply:
% 287.84/41.08 | | | | | | | (614) hAPP_int_bool(all_1534_1, zero_zero_int) = all_2007_0
% 287.84/41.08 | | | | | | |
% 287.84/41.08 | | | | | | | REDUCE: (585), (611) imply:
% 287.84/41.08 | | | | | | | (615) hAPP_int_bool(all_1534_1, zero_zero_int) = all_1934_0
% 287.84/41.08 | | | | | | |
% 287.84/41.08 | | | | | | | GROUND_INST: instantiating (89) with all_1934_0, all_2007_0,
% 287.84/41.08 | | | | | | | zero_zero_int, all_1534_1, simplifying with (614),
% 287.84/41.08 | | | | | | | (615) gives:
% 287.84/41.08 | | | | | | | (616) all_2007_0 = all_1934_0
% 287.84/41.08 | | | | | | |
% 287.84/41.08 | | | | | | | GROUND_INST: instantiating (94) with all_1534_1, all_1917_2,
% 287.84/41.08 | | | | | | | one_one_int, ord_less_eq_int, simplifying with (203),
% 287.84/41.08 | | | | | | | (612) gives:
% 287.84/41.08 | | | | | | | (617) all_1917_2 = all_1534_1
% 287.84/41.08 | | | | | | |
% 287.84/41.08 | | | | | | | REDUCE: (572), (617) imply:
% 287.84/41.08 | | | | | | | (618) hAPP_int_bool(all_1534_1, zero_zero_int) = all_1917_1
% 287.84/41.08 | | | | | | |
% 287.84/41.08 | | | | | | | REDUCE: (565), (616) imply:
% 287.84/41.08 | | | | | | | (619) ~ hBOOL(all_1934_0)
% 287.84/41.08 | | | | | | |
% 287.84/41.08 | | | | | | | BETA: splitting (557) gives:
% 287.84/41.08 | | | | | | |
% 287.84/41.08 | | | | | | | Case 1:
% 287.84/41.08 | | | | | | | |
% 287.84/41.08 | | | | | | | | (620) number_number_of_int(all_1182_0) = all_1970_3 &
% 287.84/41.08 | | | | | | | | hAPP_i1948725293t_bool(ord_less_eq_int, all_1970_3) =
% 287.84/41.08 | | | | | | | | all_1970_2 & hAPP_int_bool(all_1970_2, zero_zero_int) =
% 287.84/41.08 | | | | | | | | all_1970_1 & $i(all_1970_1) & $i(all_1970_2) &
% 287.84/41.08 | | | | | | | | $i(all_1970_3) & hBOOL(all_1970_1)
% 287.84/41.08 | | | | | | | |
% 287.84/41.08 | | | | | | | | ALPHA: (620) implies:
% 287.84/41.08 | | | | | | | | (621) hBOOL(all_1970_1)
% 287.84/41.08 | | | | | | | | (622) hAPP_int_bool(all_1970_2, zero_zero_int) = all_1970_1
% 287.84/41.08 | | | | | | | | (623) hAPP_i1948725293t_bool(ord_less_eq_int, all_1970_3) =
% 287.84/41.08 | | | | | | | | all_1970_2
% 287.84/41.08 | | | | | | | |
% 287.84/41.08 | | | | | | | | REDUCE: (609), (623) imply:
% 287.84/41.08 | | | | | | | | (624) hAPP_i1948725293t_bool(ord_less_eq_int, one_one_int) =
% 287.84/41.08 | | | | | | | | all_1970_2
% 287.84/41.08 | | | | | | | |
% 287.84/41.08 | | | | | | | | GROUND_INST: instantiating (89) with all_1934_0, all_1917_1,
% 287.84/41.08 | | | | | | | | zero_zero_int, all_1534_1, simplifying with (615),
% 287.84/41.08 | | | | | | | | (618) gives:
% 287.84/41.08 | | | | | | | | (625) all_1934_0 = all_1917_1
% 287.84/41.08 | | | | | | | |
% 287.84/41.08 | | | | | | | | GROUND_INST: instantiating (94) with all_1534_1, all_1970_2,
% 287.84/41.08 | | | | | | | | one_one_int, ord_less_eq_int, simplifying with
% 287.84/41.08 | | | | | | | | (203), (624) gives:
% 287.84/41.08 | | | | | | | | (626) all_1970_2 = all_1534_1
% 287.84/41.08 | | | | | | | |
% 287.84/41.08 | | | | | | | | REDUCE: (622), (626) imply:
% 287.84/41.08 | | | | | | | | (627) hAPP_int_bool(all_1534_1, zero_zero_int) = all_1970_1
% 287.84/41.08 | | | | | | | |
% 287.84/41.08 | | | | | | | | REDUCE: (619), (625) imply:
% 287.84/41.08 | | | | | | | | (628) ~ hBOOL(all_1917_1)
% 287.84/41.08 | | | | | | | |
% 287.84/41.08 | | | | | | | | GROUND_INST: instantiating (89) with all_1917_1, all_1970_1,
% 287.84/41.08 | | | | | | | | zero_zero_int, all_1534_1, simplifying with (618),
% 287.84/41.08 | | | | | | | | (627) gives:
% 287.84/41.08 | | | | | | | | (629) all_1970_1 = all_1917_1
% 287.84/41.08 | | | | | | | |
% 287.84/41.08 | | | | | | | | REDUCE: (621), (629) imply:
% 287.84/41.08 | | | | | | | | (630) hBOOL(all_1917_1)
% 287.84/41.08 | | | | | | | |
% 287.84/41.08 | | | | | | | | PRED_UNIFY: (628), (630) imply:
% 287.84/41.08 | | | | | | | | (631) $false
% 287.84/41.08 | | | | | | | |
% 287.84/41.08 | | | | | | | | CLOSE: (631) is inconsistent.
% 287.84/41.08 | | | | | | | |
% 287.84/41.08 | | | | | | | Case 2:
% 287.84/41.08 | | | | | | | |
% 287.84/41.08 | | | | | | | |
% 287.84/41.08 | | | | | | | | GROUND_INST: instantiating (2) with all_1328_2, mgt_call, pn, u,
% 287.84/41.08 | | | | | | | | all_1235_1, all_1235_0, all_1328_1, all_1330_1,
% 287.84/41.08 | | | | | | | | all_1928_2, simplifying with (80), (81), (82),
% 287.84/41.08 | | | | | | | | (124), (125), (126), (147), (151), (527), (603),
% 287.84/41.08 | | | | | | | | (613) gives:
% 287.84/41.08 | | | | | | | | (632) ? [v0: any] : ( ~ (v0 = all_1328_2) &
% 287.84/41.08 | | | | | | | | hAPP_pname_a(mgt_call, pn) = v0 & $i(v0))
% 287.84/41.08 | | | | | | | |
% 287.84/41.08 | | | | | | | | GROUND_INST: instantiating (2) with all_1910_3, mgt_call, pn, u,
% 287.84/41.08 | | | | | | | | all_1235_1, all_1235_0, all_1910_2, all_1330_1,
% 287.84/41.08 | | | | | | | | all_1910_0, simplifying with (80), (81), (82),
% 287.84/41.08 | | | | | | | | (124), (125), (126), (151), (546), (547), (548),
% 287.84/41.08 | | | | | | | | (549) gives:
% 287.84/41.08 | | | | | | | | (633) ? [v0: any] : ( ~ (v0 = all_1910_3) &
% 287.84/41.08 | | | | | | | | hAPP_pname_a(mgt_call, pn) = v0 & $i(v0))
% 287.84/41.08 | | | | | | | |
% 287.84/41.08 | | | | | | | | DELTA: instantiating (632) with fresh symbol all_2219_0 gives:
% 287.84/41.08 | | | | | | | | (634) ~ (all_2219_0 = all_1328_2) & hAPP_pname_a(mgt_call,
% 287.84/41.08 | | | | | | | | pn) = all_2219_0 & $i(all_2219_0)
% 287.84/41.08 | | | | | | | |
% 287.84/41.08 | | | | | | | | ALPHA: (634) implies:
% 287.84/41.08 | | | | | | | | (635) ~ (all_2219_0 = all_1328_2)
% 287.84/41.08 | | | | | | | | (636) hAPP_pname_a(mgt_call, pn) = all_2219_0
% 287.84/41.08 | | | | | | | |
% 287.84/41.08 | | | | | | | | DELTA: instantiating (633) with fresh symbol all_2253_0 gives:
% 287.84/41.08 | | | | | | | | (637) ~ (all_2253_0 = all_1910_3) & hAPP_pname_a(mgt_call,
% 287.84/41.08 | | | | | | | | pn) = all_2253_0 & $i(all_2253_0)
% 287.84/41.08 | | | | | | | |
% 287.84/41.08 | | | | | | | | ALPHA: (637) implies:
% 287.84/41.08 | | | | | | | | (638) hAPP_pname_a(mgt_call, pn) = all_2253_0
% 287.84/41.08 | | | | | | | |
% 287.84/41.08 | | | | | | | | GROUND_INST: instantiating (88) with all_1328_2, all_2253_0, pn,
% 287.84/41.08 | | | | | | | | mgt_call, simplifying with (148), (638) gives:
% 287.84/41.08 | | | | | | | | (639) all_2253_0 = all_1328_2
% 287.84/41.08 | | | | | | | |
% 287.84/41.08 | | | | | | | | GROUND_INST: instantiating (88) with all_2219_0, all_2253_0, pn,
% 287.84/41.08 | | | | | | | | mgt_call, simplifying with (636), (638) gives:
% 287.84/41.08 | | | | | | | | (640) all_2253_0 = all_2219_0
% 287.84/41.08 | | | | | | | |
% 287.84/41.08 | | | | | | | | COMBINE_EQS: (639), (640) imply:
% 287.84/41.08 | | | | | | | | (641) all_2219_0 = all_1328_2
% 287.84/41.08 | | | | | | | |
% 287.84/41.08 | | | | | | | | REDUCE: (635), (641) imply:
% 287.84/41.08 | | | | | | | | (642) $false
% 287.84/41.08 | | | | | | | |
% 287.84/41.08 | | | | | | | | CLOSE: (642) is inconsistent.
% 287.84/41.08 | | | | | | | |
% 287.84/41.08 | | | | | | | End of split
% 287.84/41.08 | | | | | | |
% 287.84/41.09 | | | | | | End of split
% 287.84/41.09 | | | | | |
% 287.84/41.09 | | | | | End of split
% 287.84/41.09 | | | | |
% 287.84/41.09 | | | | Case 2:
% 287.84/41.09 | | | | |
% 287.84/41.09 | | | | | (643) number_number_of_int(all_1182_0) = all_1970_5 &
% 287.84/41.09 | | | | | hAPP_int_bool(nat_neg, all_1970_5) = all_1970_4 &
% 287.84/41.09 | | | | | $i(all_1970_4) & $i(all_1970_5) & hBOOL(all_1970_4)
% 287.84/41.09 | | | | |
% 287.84/41.09 | | | | | ALPHA: (643) implies:
% 287.84/41.09 | | | | | (644) hBOOL(all_1970_4)
% 287.84/41.09 | | | | | (645) hAPP_int_bool(nat_neg, all_1970_5) = all_1970_4
% 287.84/41.09 | | | | | (646) number_number_of_int(all_1182_0) = all_1970_5
% 287.84/41.09 | | | | |
% 287.84/41.09 | | | | | REDUCE: (543), (646) imply:
% 287.84/41.09 | | | | | (647) number_number_of_int(one_one_int) = all_1970_5
% 287.84/41.09 | | | | |
% 287.84/41.09 | | | | | BETA: splitting (542) gives:
% 287.84/41.09 | | | | |
% 287.84/41.09 | | | | | Case 1:
% 287.84/41.09 | | | | | |
% 287.84/41.09 | | | | | | (648) one_one_nat = bot_bot_nat
% 287.84/41.09 | | | | | |
% 287.84/41.09 | | | | | | REDUCE: (523), (648) imply:
% 287.84/41.09 | | | | | | (649) hAPP_nat_int(semiri1621563631at_int, bot_bot_nat) =
% 287.84/41.09 | | | | | | one_one_int
% 287.84/41.09 | | | | | |
% 287.84/41.09 | | | | | | GROUND_INST: instantiating (93) with zero_zero_int, one_one_int,
% 287.84/41.09 | | | | | | bot_bot_nat, semiri1621563631at_int, simplifying with
% 287.84/41.09 | | | | | | (283), (649) gives:
% 287.84/41.09 | | | | | | (650) zero_zero_int = one_one_int
% 287.84/41.09 | | | | | |
% 287.84/41.09 | | | | | | REDUCE: (22), (650) imply:
% 287.84/41.09 | | | | | | (651) $false
% 287.84/41.09 | | | | | |
% 287.84/41.09 | | | | | | CLOSE: (651) is inconsistent.
% 287.84/41.09 | | | | | |
% 287.84/41.09 | | | | | Case 2:
% 287.84/41.09 | | | | | |
% 287.84/41.09 | | | | | | (652) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ?
% 287.84/41.09 | | | | | | [v4: $i] : ? [v5: $i] : (number_number_of_int(all_1182_0)
% 287.84/41.09 | | | | | | = v2 & number_number_of_int(zero_zero_int) = v0 &
% 287.84/41.09 | | | | | | hAPP_int_bool(nat_neg, v0) = v1 & $i(v2) & $i(v1) &
% 287.84/41.09 | | | | | | $i(v0) & ((hAPP_i1948725293t_bool(ord_less_eq_int, v2) =
% 287.84/41.09 | | | | | | v3 & hAPP_int_bool(v3, zero_zero_int) = v4 & $i(v4) &
% 287.84/41.09 | | | | | | $i(v3) & hBOOL(v1) & ~ hBOOL(v4)) |
% 287.84/41.09 | | | | | | (hAPP_int_bool(nat_neg, v2) = v5 & $i(v5) & ~
% 287.84/41.09 | | | | | | hBOOL(v1) & (( ~ (v0 = zero_zero_int) & hBOOL(v5)) |
% 287.84/41.09 | | | | | | ( ~ (all_1182_0 = zero_zero_int) & ~
% 287.84/41.09 | | | | | | hBOOL(v5))))))
% 287.84/41.09 | | | | | |
% 287.84/41.09 | | | | | | DELTA: instantiating (652) with fresh symbols all_2053_0,
% 287.84/41.09 | | | | | | all_2053_1, all_2053_2, all_2053_3, all_2053_4, all_2053_5
% 287.84/41.09 | | | | | | gives:
% 288.29/41.09 | | | | | | (653) number_number_of_int(all_1182_0) = all_2053_3 &
% 288.29/41.09 | | | | | | number_number_of_int(zero_zero_int) = all_2053_5 &
% 288.29/41.09 | | | | | | hAPP_int_bool(nat_neg, all_2053_5) = all_2053_4 &
% 288.29/41.09 | | | | | | $i(all_2053_3) & $i(all_2053_4) & $i(all_2053_5) &
% 288.29/41.09 | | | | | | ((hAPP_i1948725293t_bool(ord_less_eq_int, all_2053_3) =
% 288.29/41.09 | | | | | | all_2053_2 & hAPP_int_bool(all_2053_2, zero_zero_int) =
% 288.29/41.09 | | | | | | all_2053_1 & $i(all_2053_1) & $i(all_2053_2) &
% 288.29/41.09 | | | | | | hBOOL(all_2053_4) & ~ hBOOL(all_2053_1)) |
% 288.29/41.09 | | | | | | (hAPP_int_bool(nat_neg, all_2053_3) = all_2053_0 &
% 288.29/41.09 | | | | | | $i(all_2053_0) & ~ hBOOL(all_2053_4) & (( ~
% 288.29/41.09 | | | | | | (all_2053_5 = zero_zero_int) & hBOOL(all_2053_0)) |
% 288.29/41.09 | | | | | | ( ~ (all_1182_0 = zero_zero_int) & ~
% 288.29/41.09 | | | | | | hBOOL(all_2053_0)))))
% 288.29/41.09 | | | | | |
% 288.29/41.09 | | | | | | ALPHA: (653) implies:
% 288.29/41.09 | | | | | | (654) number_number_of_int(all_1182_0) = all_2053_3
% 288.29/41.09 | | | | | |
% 288.29/41.09 | | | | | | REDUCE: (543), (654) imply:
% 288.29/41.09 | | | | | | (655) number_number_of_int(one_one_int) = all_2053_3
% 288.29/41.09 | | | | | |
% 288.29/41.09 | | | | | | BETA: splitting (552) gives:
% 288.29/41.09 | | | | | |
% 288.29/41.09 | | | | | | Case 1:
% 288.29/41.09 | | | | | | |
% 288.29/41.09 | | | | | | |
% 288.29/41.09 | | | | | | | GROUND_INST: instantiating (84) with all_1970_5, all_2053_3,
% 288.29/41.09 | | | | | | | one_one_int, simplifying with (647), (655) gives:
% 288.29/41.09 | | | | | | | (656) all_2053_3 = all_1970_5
% 288.29/41.09 | | | | | | |
% 288.29/41.09 | | | | | | | GROUND_INST: instantiating (84) with one_one_int, all_2053_3,
% 288.29/41.09 | | | | | | | one_one_int, simplifying with (560), (655) gives:
% 288.29/41.09 | | | | | | | (657) all_2053_3 = one_one_int
% 288.29/41.09 | | | | | | |
% 288.29/41.09 | | | | | | | COMBINE_EQS: (656), (657) imply:
% 288.29/41.09 | | | | | | | (658) all_1970_5 = one_one_int
% 288.29/41.09 | | | | | | |
% 288.29/41.09 | | | | | | | SIMP: (658) implies:
% 288.29/41.09 | | | | | | | (659) all_1970_5 = one_one_int
% 288.29/41.09 | | | | | | |
% 288.29/41.09 | | | | | | | REDUCE: (645), (659) imply:
% 288.29/41.09 | | | | | | | (660) hAPP_int_bool(nat_neg, one_one_int) = all_1970_4
% 288.29/41.09 | | | | | | |
% 288.29/41.09 | | | | | | | GROUND_INST: instantiating (89) with all_1200_0, all_1970_4,
% 288.29/41.09 | | | | | | | one_one_int, nat_neg, simplifying with (114), (660)
% 288.29/41.09 | | | | | | | gives:
% 288.29/41.09 | | | | | | | (661) all_1970_4 = all_1200_0
% 288.29/41.09 | | | | | | |
% 288.29/41.09 | | | | | | | REDUCE: (644), (661) imply:
% 288.29/41.09 | | | | | | | (662) hBOOL(all_1200_0)
% 288.29/41.09 | | | | | | |
% 288.29/41.09 | | | | | | | PRED_UNIFY: (113), (662) imply:
% 288.29/41.09 | | | | | | | (663) $false
% 288.29/41.09 | | | | | | |
% 288.29/41.09 | | | | | | | CLOSE: (663) is inconsistent.
% 288.29/41.09 | | | | | | |
% 288.29/41.09 | | | | | | Case 2:
% 288.29/41.09 | | | | | | |
% 288.29/41.09 | | | | | | | (664) hAPP_int_bool(all_1245_1, pls) = all_1926_0 &
% 288.29/41.09 | | | | | | | $i(all_1926_0) & hBOOL(all_1926_0)
% 288.29/41.09 | | | | | | |
% 288.29/41.09 | | | | | | | ALPHA: (664) implies:
% 288.29/41.09 | | | | | | | (665) hBOOL(all_1926_0)
% 288.29/41.09 | | | | | | | (666) hAPP_int_bool(all_1245_1, pls) = all_1926_0
% 288.29/41.09 | | | | | | |
% 288.29/41.09 | | | | | | | REDUCE: (66), (666) imply:
% 288.29/41.09 | | | | | | | (667) hAPP_int_bool(all_1245_1, zero_zero_int) = all_1926_0
% 288.29/41.09 | | | | | | |
% 288.29/41.09 | | | | | | | GROUND_INST: instantiating (89) with all_1245_0, all_1926_0,
% 288.29/41.09 | | | | | | | zero_zero_int, all_1245_1, simplifying with (297),
% 288.29/41.09 | | | | | | | (667) gives:
% 288.29/41.09 | | | | | | | (668) all_1926_0 = all_1245_0
% 288.29/41.09 | | | | | | |
% 288.29/41.09 | | | | | | | REDUCE: (665), (668) imply:
% 288.29/41.09 | | | | | | | (669) hBOOL(all_1245_0)
% 288.29/41.09 | | | | | | |
% 288.29/41.09 | | | | | | | PRED_UNIFY: (128), (669) imply:
% 288.29/41.09 | | | | | | | (670) $false
% 288.29/41.09 | | | | | | |
% 288.29/41.09 | | | | | | | CLOSE: (670) is inconsistent.
% 288.29/41.09 | | | | | | |
% 288.29/41.09 | | | | | | End of split
% 288.29/41.09 | | | | | |
% 288.29/41.09 | | | | | End of split
% 288.29/41.09 | | | | |
% 288.29/41.09 | | | | End of split
% 288.29/41.09 | | | |
% 288.29/41.09 | | | End of split
% 288.29/41.09 | | |
% 288.29/41.09 | | Case 2:
% 288.29/41.09 | | |
% 288.29/41.09 | | | (671) hAPP_int_bool(all_1245_1, pls) = all_1917_0 & $i(all_1917_0) &
% 288.29/41.09 | | | hBOOL(all_1917_0)
% 288.29/41.09 | | |
% 288.29/41.09 | | | ALPHA: (671) implies:
% 288.29/41.09 | | | (672) hBOOL(all_1917_0)
% 288.29/41.09 | | | (673) hAPP_int_bool(all_1245_1, pls) = all_1917_0
% 288.29/41.09 | | |
% 288.29/41.09 | | | REDUCE: (66), (673) imply:
% 288.29/41.09 | | | (674) hAPP_int_bool(all_1245_1, zero_zero_int) = all_1917_0
% 288.29/41.09 | | |
% 288.29/41.09 | | | GROUND_INST: instantiating (89) with all_1245_0, all_1917_0,
% 288.29/41.09 | | | zero_zero_int, all_1245_1, simplifying with (297), (674)
% 288.29/41.09 | | | gives:
% 288.29/41.09 | | | (675) all_1917_0 = all_1245_0
% 288.29/41.09 | | |
% 288.29/41.09 | | | REDUCE: (672), (675) imply:
% 288.29/41.09 | | | (676) hBOOL(all_1245_0)
% 288.29/41.09 | | |
% 288.29/41.09 | | | PRED_UNIFY: (128), (676) imply:
% 288.29/41.09 | | | (677) $false
% 288.29/41.09 | | |
% 288.29/41.09 | | | CLOSE: (677) is inconsistent.
% 288.29/41.09 | | |
% 288.29/41.09 | | End of split
% 288.29/41.09 | |
% 288.29/41.09 | End of split
% 288.29/41.09 |
% 288.29/41.09 End of proof
% 288.29/41.09 % SZS output end Proof for theBenchmark
% 288.29/41.09
% 288.29/41.09 40477ms
%------------------------------------------------------------------------------