TSTP Solution File: SWW473_2 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SWW473_2 : TPTP v8.1.2. Released v5.3.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n003.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 00:50:17 EDT 2023
% Result : Theorem 80.77s 11.91s
% Output : Proof 178.32s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.13 % Problem : SWW473_2 : TPTP v8.1.2. Released v5.3.0.
% 0.06/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.12/0.34 % Computer : n003.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Sun Aug 27 22:36:40 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.17/0.62 ________ _____
% 0.17/0.62 ___ __ \_________(_)________________________________
% 0.17/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.17/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.17/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.17/0.62
% 0.17/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.17/0.62 (2023-06-19)
% 0.17/0.62
% 0.17/0.62 (c) Philipp Rümmer, 2009-2023
% 0.17/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.17/0.62 Amanda Stjerna.
% 0.17/0.62 Free software under BSD-3-Clause.
% 0.17/0.62
% 0.17/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.17/0.62
% 0.17/0.62 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.17/0.64 Running up to 7 provers in parallel.
% 0.17/0.65 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.17/0.65 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.17/0.65 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.17/0.65 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.17/0.65 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.17/0.65 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.17/0.65 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 24.83/4.28 Prover 1: Preprocessing ...
% 25.57/4.41 Prover 0: Preprocessing ...
% 25.57/4.41 Prover 6: Preprocessing ...
% 25.57/4.41 Prover 3: Preprocessing ...
% 26.81/4.53 Prover 5: Preprocessing ...
% 27.27/4.57 Prover 4: Preprocessing ...
% 27.81/4.61 Prover 2: Preprocessing ...
% 62.04/9.47 Prover 3: Warning: ignoring some quantifiers
% 65.42/9.66 Prover 3: Constructing countermodel ...
% 65.42/9.67 Prover 1: Warning: ignoring some quantifiers
% 67.72/9.98 Prover 1: Constructing countermodel ...
% 68.15/10.18 Prover 6: Proving ...
% 72.42/10.62 Prover 0: Proving ...
% 74.22/11.03 Prover 4: Warning: ignoring some quantifiers
% 78.46/11.40 Prover 4: Constructing countermodel ...
% 80.77/11.90 Prover 3: proved (11253ms)
% 80.77/11.90
% 80.77/11.91 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 80.77/11.91
% 80.77/11.91 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 80.77/11.92 Prover 0: stopped
% 80.77/11.94 Prover 6: stopped
% 82.55/11.94 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 82.55/11.94 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 84.23/12.15 Prover 5: Proving ...
% 84.23/12.16 Prover 5: stopped
% 84.23/12.17 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 92.14/13.33 Prover 10: Preprocessing ...
% 92.14/13.39 Prover 7: Preprocessing ...
% 94.78/13.59 Prover 8: Preprocessing ...
% 100.28/14.30 Prover 11: Preprocessing ...
% 108.22/15.34 Prover 2: Proving ...
% 108.22/15.34 Prover 2: stopped
% 108.22/15.35 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 108.75/15.43 Prover 10: Warning: ignoring some quantifiers
% 109.27/15.49 Prover 8: Warning: ignoring some quantifiers
% 111.54/15.80 Prover 8: Constructing countermodel ...
% 111.54/15.81 Prover 10: Constructing countermodel ...
% 112.81/16.00 Prover 1: stopped
% 112.81/16.01 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 117.75/16.63 Prover 7: Warning: ignoring some quantifiers
% 118.77/16.79 Prover 13: Preprocessing ...
% 120.12/16.95 Prover 7: Constructing countermodel ...
% 123.05/17.32 Prover 16: Preprocessing ...
% 126.71/17.82 Prover 11: Warning: ignoring some quantifiers
% 129.53/18.18 Prover 11: Constructing countermodel ...
% 137.32/19.22 Prover 16: Warning: ignoring some quantifiers
% 137.32/19.27 Prover 13: Warning: ignoring some quantifiers
% 139.49/19.52 Prover 13: Constructing countermodel ...
% 140.42/19.62 Prover 16: Constructing countermodel ...
% 149.68/20.87 Prover 16: stopped
% 150.13/20.89 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085
% 164.05/22.97 Prover 19: Preprocessing ...
% 169.94/23.73 Prover 13: stopped
% 175.30/24.26 Prover 10: Found proof (size 111)
% 175.30/24.26 Prover 10: proved (12312ms)
% 175.30/24.26 Prover 7: stopped
% 175.30/24.26 Prover 11: stopped
% 175.30/24.26 Prover 4: stopped
% 175.30/24.26 Prover 8: stopped
% 176.68/24.62 Prover 19: Warning: ignoring some quantifiers
% 177.30/24.73 Prover 19: Constructing countermodel ...
% 177.30/24.73 Prover 19: stopped
% 177.30/24.73
% 177.30/24.73 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 177.30/24.73
% 177.51/24.77 % SZS output start Proof for theBenchmark
% 177.51/24.80 Assumptions after simplification:
% 177.51/24.80 ---------------------------------
% 177.51/24.80
% 177.51/24.80 (conj_0)
% 177.51/24.83 fun_fu1430349052l_bool(finite_finite_pname) & fun_pname_bool(u) & ? [v0:
% 177.51/24.83 bool] : (hAPP_f1664156314l_bool(finite_finite_pname, u) = v0 & bool(v0) &
% 177.51/24.83 hBOOL(v0))
% 177.51/24.83
% 177.51/24.83 (conj_1)
% 177.51/24.83 fun_fu1471507361l_bool(ord_le1311769555a_bool) & fun_pname_bool(u) &
% 177.51/24.83 fun_pname_a(mgt_call) & fun_a_bool(g) & ? [v0: fun_fun_a_bool_bool] : ? [v1:
% 177.51/24.83 fun_a_bool] : ? [v2: bool] : (image_pname_a(mgt_call, u) = v1 &
% 177.51/24.83 hAPP_f1631501043l_bool(ord_le1311769555a_bool, g) = v0 &
% 177.51/24.83 hAPP_fun_a_bool_bool(v0, v1) = v2 & fun_fun_a_bool_bool(v0) & fun_a_bool(v1)
% 177.51/24.83 & bool(v2) & hBOOL(v2))
% 177.51/24.83
% 177.51/24.83 (conj_2)
% 177.51/24.83 fun_fun_a_bool_nat(finite_card_a) & fun_nat_fun_nat_bool(ord_less_eq_nat) &
% 177.51/24.83 fun_nat_nat(suc) & fun_pname_bool(u) & fun_pname_a(mgt_call) & nat(na) & ?
% 177.51/24.83 [v0: nat] : ? [v1: fun_nat_bool] : ? [v2: fun_a_bool] : ? [v3: nat] : ?
% 177.51/24.83 [v4: bool] : (hAPP_nat_nat(suc, na) = v0 & hAPP_fun_a_bool_nat(finite_card_a,
% 177.51/24.83 v2) = v3 & hAPP_n1699378549t_bool(ord_less_eq_nat, v0) = v1 &
% 177.51/24.83 hAPP_nat_bool(v1, v3) = v4 & image_pname_a(mgt_call, u) = v2 &
% 177.51/24.83 fun_nat_bool(v1) & fun_a_bool(v2) & nat(v3) & nat(v0) & bool(v4) &
% 177.51/24.83 hBOOL(v4))
% 177.51/24.83
% 177.51/24.83 (conj_3)
% 177.51/24.84 fun_fun_a_bool_nat(finite_card_a) & fun_nat_nat(suc) & fun_pname_bool(u) &
% 177.51/24.84 fun_pname_a(mgt_call) & fun_a_bool(g) & nat(na) & ? [v0: nat] : ? [v1:
% 177.51/24.84 fun_a_bool] : ? [v2: nat] : ? [v3: fun_nat_nat] : ? [v4: nat] :
% 177.51/24.84 (minus_minus_nat(v2) = v3 & hAPP_nat_nat(v3, v4) = v0 & hAPP_nat_nat(suc, na)
% 177.51/24.84 = v4 & hAPP_fun_a_bool_nat(finite_card_a, v1) = v2 &
% 177.51/24.84 hAPP_fun_a_bool_nat(finite_card_a, g) = v0 & image_pname_a(mgt_call, u) = v1
% 177.51/24.84 & fun_nat_nat(v3) & fun_a_bool(v1) & nat(v4) & nat(v2) & nat(v0))
% 177.51/24.84
% 177.51/24.84 (conj_4)
% 177.51/24.84 fun_pn422929397l_bool(member_pname) & fun_pname_bool(u) & pname(pn) & ? [v0:
% 177.51/24.84 fun_fu1430349052l_bool] : ? [v1: bool] :
% 177.51/24.84 (hAPP_p338031245l_bool(member_pname, pn) = v0 & hAPP_f1664156314l_bool(v0, u)
% 177.51/24.84 = v1 & fun_fu1430349052l_bool(v0) & bool(v1) & hBOOL(v1))
% 177.51/24.84
% 177.51/24.84 (conj_5)
% 177.51/24.84 fun_pname_a(mgt_call) & fun_a_1255737515l_bool(member_a) & fun_a_bool(g) &
% 177.51/24.84 pname(pn) & ? [v0: x_a] : ? [v1: fun_fun_a_bool_bool] : ? [v2: bool] :
% 177.51/24.84 (hAPP_pname_a(mgt_call, pn) = v0 & hAPP_a85458249l_bool(member_a, v0) = v1 &
% 177.51/24.84 hAPP_fun_a_bool_bool(v1, g) = v2 & fun_fun_a_bool_bool(v1) & bool(v2) &
% 177.51/24.84 x_a(v0) & ~ hBOOL(v2))
% 177.51/24.84
% 177.51/24.84 (conj_6)
% 177.51/24.84 fun_fu1471507361l_bool(ord_le1311769555a_bool) & fun_pname_bool(u) &
% 177.51/24.84 fun_pname_a(mgt_call) & fun_a_bool(g) & pname(pn) & ? [v0: x_a] : ? [v1:
% 177.51/24.84 fun_a_bool] : ? [v2: fun_fun_a_bool_bool] : ? [v3: fun_a_bool] : ? [v4:
% 177.51/24.84 bool] : (hAPP_pname_a(mgt_call, pn) = v0 & insert_a(v0, g) = v1 &
% 177.51/24.84 image_pname_a(mgt_call, u) = v3 &
% 177.51/24.84 hAPP_f1631501043l_bool(ord_le1311769555a_bool, v1) = v2 &
% 177.51/24.84 hAPP_fun_a_bool_bool(v2, v3) = v4 & fun_fun_a_bool_bool(v2) & fun_a_bool(v3)
% 177.51/24.84 & fun_a_bool(v1) & bool(v4) & x_a(v0) & ~ hBOOL(v4))
% 177.51/24.84
% 177.51/24.84 (fact_106_finite__subset)
% 177.87/24.84 fun_fu1471507361l_bool(ord_le1311769555a_bool) &
% 177.87/24.84 fun_fun_a_bool_bool(finite_finite_a) & ! [v0: fun_a_bool] : ! [v1:
% 177.87/24.84 fun_a_bool] : ! [v2: fun_fun_a_bool_bool] : ! [v3: bool] : ( ~
% 177.87/24.84 (hAPP_f1631501043l_bool(ord_le1311769555a_bool, v0) = v2) | ~
% 177.87/24.84 (hAPP_fun_a_bool_bool(v2, v1) = v3) | ~ fun_a_bool(v1) | ~ fun_a_bool(v0)
% 177.87/24.84 | ~ hBOOL(v3) | ? [v4: bool] : ? [v5: bool] :
% 177.87/24.84 ((hAPP_fun_a_bool_bool(finite_finite_a, v1) = v4 & bool(v4) & ~ hBOOL(v4))
% 177.87/24.84 | (hAPP_fun_a_bool_bool(finite_finite_a, v0) = v5 & bool(v5) &
% 177.87/24.84 hBOOL(v5))))
% 177.87/24.84
% 177.87/24.84 (fact_112_rev__finite__subset)
% 177.87/24.85 fun_fu1471507361l_bool(ord_le1311769555a_bool) &
% 177.87/24.85 fun_fun_a_bool_bool(finite_finite_a) & ! [v0: fun_a_bool] : ! [v1:
% 177.87/24.85 fun_a_bool] : ! [v2: fun_fun_a_bool_bool] : ! [v3: bool] : ( ~
% 177.87/24.85 (hAPP_f1631501043l_bool(ord_le1311769555a_bool, v0) = v2) | ~
% 177.87/24.85 (hAPP_fun_a_bool_bool(v2, v1) = v3) | ~ fun_a_bool(v1) | ~ fun_a_bool(v0)
% 177.87/24.85 | ~ hBOOL(v3) | ? [v4: bool] : ? [v5: bool] :
% 177.87/24.85 ((hAPP_fun_a_bool_bool(finite_finite_a, v1) = v4 & bool(v4) & ~ hBOOL(v4))
% 177.87/24.85 | (hAPP_fun_a_bool_bool(finite_finite_a, v0) = v5 & bool(v5) &
% 177.87/24.85 hBOOL(v5))))
% 177.87/24.85
% 177.87/24.85 (fact_215_image__eqI)
% 177.87/24.85 fun_pn422929397l_bool(member_pname) & fun_a_1255737515l_bool(member_a) & !
% 177.87/24.85 [v0: fun_pname_bool] : ! [v1: x_a] : ! [v2: fun_pname_a] : ! [v3: pname] :
% 177.87/24.85 ! [v4: fun_fu1430349052l_bool] : ! [v5: bool] : ! [v6: fun_fun_a_bool_bool]
% 177.87/24.85 : ! [v7: fun_a_bool] : ! [v8: bool] : ( ~ (hAPP_a85458249l_bool(member_a,
% 177.87/24.85 v1) = v6) | ~ (hAPP_p338031245l_bool(member_pname, v3) = v4) | ~
% 177.87/24.85 (image_pname_a(v2, v0) = v7) | ~ (hAPP_f1664156314l_bool(v4, v0) = v5) | ~
% 177.87/24.85 (hAPP_fun_a_bool_bool(v6, v7) = v8) | ~ fun_pname_bool(v0) | ~
% 177.87/24.85 fun_pname_a(v2) | ~ pname(v3) | ~ x_a(v1) | ~ hBOOL(v5) | hBOOL(v8) | ?
% 177.87/24.85 [v9: x_a] : ( ~ (v9 = v1) & hAPP_pname_a(v2, v3) = v9 & x_a(v9)))
% 177.87/24.85
% 177.87/24.85 (fact_22_finite__imageI)
% 177.87/24.85 fun_fu1430349052l_bool(finite_finite_pname) &
% 177.87/24.85 fun_fun_a_bool_bool(finite_finite_a) & ! [v0: fun_pname_a] : ! [v1:
% 177.87/24.85 fun_pname_bool] : ! [v2: fun_a_bool] : ( ~ (image_pname_a(v0, v1) = v2) |
% 177.87/24.85 ~ fun_pname_bool(v1) | ~ fun_pname_a(v0) | ? [v3: bool] : ? [v4: bool] :
% 177.87/24.85 ((hAPP_f1664156314l_bool(finite_finite_pname, v1) = v3 & bool(v3) & ~
% 177.87/24.85 hBOOL(v3)) | (hAPP_fun_a_bool_bool(finite_finite_a, v2) = v4 & bool(v4)
% 177.87/24.85 & hBOOL(v4))))
% 177.87/24.85
% 177.87/24.85 (fact_264_insert__absorb)
% 177.87/24.85 fun_pn422929397l_bool(member_pname) & ! [v0: pname] : ! [v1: fun_pname_bool]
% 177.87/24.85 : ! [v2: fun_fu1430349052l_bool] : ! [v3: bool] : ( ~
% 177.87/24.85 (hAPP_p338031245l_bool(member_pname, v0) = v2) | ~
% 177.87/24.85 (hAPP_f1664156314l_bool(v2, v1) = v3) | ~ fun_pname_bool(v1) | ~ pname(v0)
% 177.87/24.85 | ~ hBOOL(v3) | insert_pname(v0, v1) = v1)
% 177.87/24.85
% 177.87/24.85 (fact_324_insert__subset)
% 177.87/24.86 fun_fu1471507361l_bool(ord_le1311769555a_bool) &
% 177.87/24.86 fun_a_1255737515l_bool(member_a) & ! [v0: x_a] : ! [v1: fun_a_bool] : !
% 177.87/24.86 [v2: fun_a_bool] : ! [v3: fun_a_bool] : ! [v4: fun_fun_a_bool_bool] : !
% 177.87/24.86 [v5: bool] : ( ~ (insert_a(v0, v1) = v3) | ~
% 177.87/24.86 (hAPP_f1631501043l_bool(ord_le1311769555a_bool, v3) = v4) | ~
% 177.87/24.86 (hAPP_fun_a_bool_bool(v4, v2) = v5) | ~ fun_a_bool(v2) | ~ fun_a_bool(v1)
% 177.87/24.86 | ~ x_a(v0) | ~ hBOOL(v5) | ? [v6: fun_fun_a_bool_bool] : ? [v7: bool] :
% 177.87/24.86 ? [v8: fun_fun_a_bool_bool] : ? [v9: bool] :
% 177.87/24.86 (hAPP_a85458249l_bool(member_a, v0) = v6 &
% 177.87/24.86 hAPP_f1631501043l_bool(ord_le1311769555a_bool, v1) = v8 &
% 177.87/24.86 hAPP_fun_a_bool_bool(v8, v2) = v9 & hAPP_fun_a_bool_bool(v6, v2) = v7 &
% 177.87/24.86 fun_fun_a_bool_bool(v8) & fun_fun_a_bool_bool(v6) & bool(v9) & bool(v7) &
% 177.87/24.86 hBOOL(v9) & hBOOL(v7))) & ! [v0: x_a] : ! [v1: fun_a_bool] : ! [v2:
% 177.87/24.86 fun_a_bool] : ! [v3: fun_a_bool] : ! [v4: fun_fun_a_bool_bool] : ! [v5:
% 177.87/24.86 bool] : ( ~ (insert_a(v0, v1) = v3) | ~
% 177.87/24.86 (hAPP_f1631501043l_bool(ord_le1311769555a_bool, v3) = v4) | ~
% 177.87/24.86 (hAPP_fun_a_bool_bool(v4, v2) = v5) | ~ fun_a_bool(v2) | ~ fun_a_bool(v1)
% 177.87/24.86 | ~ x_a(v0) | hBOOL(v5) | ? [v6: fun_fun_a_bool_bool] : ? [v7: bool] : ?
% 177.87/24.86 [v8: fun_fun_a_bool_bool] : ? [v9: bool] : ((hAPP_a85458249l_bool(member_a,
% 177.87/24.86 v0) = v6 & hAPP_fun_a_bool_bool(v6, v2) = v7 & fun_fun_a_bool_bool(v6)
% 177.87/24.86 & bool(v7) & ~ hBOOL(v7)) |
% 177.87/24.86 (hAPP_f1631501043l_bool(ord_le1311769555a_bool, v1) = v8 &
% 177.87/24.86 hAPP_fun_a_bool_bool(v8, v2) = v9 & fun_fun_a_bool_bool(v8) & bool(v9) &
% 177.87/24.86 ~ hBOOL(v9))))
% 177.87/24.86
% 177.87/24.86 (fact_359_subsetI)
% 177.87/24.86 fun_fu1471507361l_bool(ord_le1311769555a_bool) &
% 177.87/24.86 fun_a_1255737515l_bool(member_a) & ! [v0: fun_a_bool] : ! [v1: fun_a_bool] :
% 177.87/24.86 ! [v2: fun_fun_a_bool_bool] : ! [v3: bool] : ( ~
% 177.87/24.86 (hAPP_f1631501043l_bool(ord_le1311769555a_bool, v1) = v2) | ~
% 177.87/24.86 (hAPP_fun_a_bool_bool(v2, v0) = v3) | ~ fun_a_bool(v1) | ~ fun_a_bool(v0)
% 177.87/24.86 | hBOOL(v3) | ? [v4: x_a] : ? [v5: fun_fun_a_bool_bool] : ? [v6: bool] :
% 177.87/24.86 ? [v7: bool] : (hAPP_a85458249l_bool(member_a, v4) = v5 &
% 177.87/24.86 hAPP_fun_a_bool_bool(v5, v1) = v6 & hAPP_fun_a_bool_bool(v5, v0) = v7 &
% 177.87/24.86 fun_fun_a_bool_bool(v5) & bool(v7) & bool(v6) & x_a(v4) & hBOOL(v6) & ~
% 177.87/24.86 hBOOL(v7)))
% 177.87/24.86
% 177.87/24.86 (fact_64_card__insert__if)
% 177.87/24.87 fun_fu1668467777ol_nat(finite_card_pname) &
% 177.87/24.87 fun_fu1430349052l_bool(finite_finite_pname) & fun_nat_nat(suc) &
% 177.87/24.87 fun_pn422929397l_bool(member_pname) & ! [v0: pname] : ! [v1: fun_pname_bool]
% 177.87/24.87 : ! [v2: fun_fu1430349052l_bool] : ! [v3: bool] : ( ~
% 177.87/24.87 (hAPP_p338031245l_bool(member_pname, v0) = v2) | ~
% 177.87/24.87 (hAPP_f1664156314l_bool(v2, v1) = v3) | ~ fun_pname_bool(v1) | ~ pname(v0)
% 177.87/24.87 | ? [v4: bool] : ? [v5: fun_pname_bool] : ? [v6: nat] : ? [v7: nat] : ?
% 177.87/24.87 [v8: nat] : ((hAPP_f1664156314l_bool(finite_finite_pname, v1) = v4 &
% 177.87/24.87 bool(v4) & ~ hBOOL(v4)) | (( ~ hBOOL(v3) | (v7 = v6 &
% 177.87/24.87 hAPP_f921600141ol_nat(finite_card_pname, v5) = v6 &
% 177.87/24.87 hAPP_f921600141ol_nat(finite_card_pname, v1) = v6 & insert_pname(v0,
% 177.87/24.87 v1) = v5 & fun_pname_bool(v5) & nat(v6))) & (hBOOL(v3) | (v8 = v6
% 177.87/24.87 & hAPP_nat_nat(suc, v7) = v6 &
% 177.87/24.87 hAPP_f921600141ol_nat(finite_card_pname, v5) = v6 &
% 177.87/24.87 hAPP_f921600141ol_nat(finite_card_pname, v1) = v7 & insert_pname(v0,
% 177.87/24.87 v1) = v5 & fun_pname_bool(v5) & nat(v7) & nat(v6))))))
% 177.87/24.87
% 177.87/24.87 (function-axioms)
% 178.06/24.93 ! [v0: fun_bool_bool] : ! [v1: fun_bool_bool] : ! [v2: fun_pname_bool] : !
% 178.06/24.93 [v3: fun_fu31783638l_bool] : (v1 = v0 | ~ (hAPP_f1476298914l_bool(v3, v2) =
% 178.06/24.93 v1) | ~ (hAPP_f1476298914l_bool(v3, v2) = v0)) & ! [v0: fun_bool_bool] :
% 178.06/24.93 ! [v1: fun_bool_bool] : ! [v2: fun_nat_bool] : ! [v3:
% 178.06/24.93 fun_fu1016514960l_bool] : (v1 = v0 | ~ (hAPP_f1748468828l_bool(v3, v2) =
% 178.06/24.93 v1) | ~ (hAPP_f1748468828l_bool(v3, v2) = v0)) & ! [v0:
% 178.06/24.93 fun_fu1430349052l_bool] : ! [v1: fun_fu1430349052l_bool] : ! [v2: x_a] :
% 178.06/24.93 ! [v3: fun_a_968466022l_bool] : (v1 = v0 | ~ (hAPP_a217006258l_bool(v3, v2) =
% 178.06/24.93 v1) | ~ (hAPP_a217006258l_bool(v3, v2) = v0)) & ! [v0: fun_bool_bool] :
% 178.06/24.93 ! [v1: fun_bool_bool] : ! [v2: fun_a_bool] : ! [v3: fun_fu554186387l_bool] :
% 178.06/24.93 (v1 = v0 | ~ (hAPP_f198738859l_bool(v3, v2) = v1) | ~
% 178.06/24.93 (hAPP_f198738859l_bool(v3, v2) = v0)) & ! [v0: fun_fu425979586l_bool] : !
% 178.06/24.93 [v1: fun_fu425979586l_bool] : ! [v2: x_a] : ! [v3: fun_a_762926252l_bool] :
% 178.06/24.93 (v1 = v0 | ~ (hAPP_a1392362872l_bool(v3, v2) = v1) | ~
% 178.06/24.93 (hAPP_a1392362872l_bool(v3, v2) = v0)) & ! [v0: fun_bool_bool] : ! [v1:
% 178.06/24.93 fun_bool_bool] : ! [v2: pname] : ! [v3: fun_pn250273176l_bool] : (v1 = v0
% 178.06/24.93 | ~ (hAPP_p393069232l_bool(v3, v2) = v1) | ~ (hAPP_p393069232l_bool(v3,
% 178.06/24.93 v2) = v0)) & ! [v0: fun_bool_bool] : ! [v1: fun_bool_bool] : ! [v2:
% 178.06/24.93 nat] : ! [v3: fun_na1469252690l_bool] : (v1 = v0 | ~
% 178.06/24.93 (hAPP_n1006566506l_bool(v3, v2) = v1) | ~ (hAPP_n1006566506l_bool(v3, v2) =
% 178.06/24.93 v0)) & ! [v0: fun_bool_bool] : ! [v1: fun_bool_bool] : ! [v2: x_a] : !
% 178.06/24.93 [v3: fun_a_fun_bool_bool] : (v1 = v0 | ~ (hAPP_a_fun_bool_bool(v3, v2) = v1)
% 178.32/24.93 | ~ (hAPP_a_fun_bool_bool(v3, v2) = v0)) & ! [v0: fun_nat_bool] : ! [v1:
% 178.32/24.93 fun_nat_bool] : ! [v2: fun_nat_bool] : ! [v3: bool] : (v1 = v0 | ~
% 178.32/24.93 (nat_case_bool(v3, v2) = v1) | ~ (nat_case_bool(v3, v2) = v0)) & ! [v0:
% 178.32/24.93 bool] : ! [v1: bool] : ! [v2: x_a] : ! [v3: fun_a_bool] : (v1 = v0 | ~
% 178.32/24.93 (hAPP_a_bool(v3, v2) = v1) | ~ (hAPP_a_bool(v3, v2) = v0)) & ! [v0: bool]
% 178.32/24.93 : ! [v1: bool] : ! [v2: pname] : ! [v3: fun_pname_bool] : (v1 = v0 | ~
% 178.32/24.93 (hAPP_pname_bool(v3, v2) = v1) | ~ (hAPP_pname_bool(v3, v2) = v0)) & !
% 178.32/24.93 [v0: fun_a_bool] : ! [v1: fun_a_bool] : ! [v2: fun_a_bool] : ! [v3:
% 178.32/24.93 fun_bool_bool] : (v1 = v0 | ~ (cOMBB_bool_bool_a(v3, v2) = v1) | ~
% 178.32/24.93 (cOMBB_bool_bool_a(v3, v2) = v0)) & ! [v0: fun_nat_bool] : ! [v1:
% 178.32/24.93 fun_nat_bool] : ! [v2: fun_nat_bool] : ! [v3: fun_bool_bool] : (v1 = v0 |
% 178.32/24.93 ~ (cOMBB_bool_bool_nat(v3, v2) = v1) | ~ (cOMBB_bool_bool_nat(v3, v2) =
% 178.32/24.93 v0)) & ! [v0: fun_fun_a_bool_bool] : ! [v1: fun_fun_a_bool_bool] : !
% 178.32/24.93 [v2: fun_fun_a_bool_bool] : ! [v3: fun_bool_bool] : (v1 = v0 | ~
% 178.32/24.93 (cOMBB_2140588453a_bool(v3, v2) = v1) | ~ (cOMBB_2140588453a_bool(v3, v2) =
% 178.32/24.93 v0)) & ! [v0: fun_fu1430349052l_bool] : ! [v1: fun_fu1430349052l_bool] :
% 178.32/24.93 ! [v2: fun_fu1430349052l_bool] : ! [v3: fun_bool_bool] : (v1 = v0 | ~
% 178.32/24.93 (cOMBB_307249310e_bool(v3, v2) = v1) | ~ (cOMBB_307249310e_bool(v3, v2) =
% 178.32/24.93 v0)) & ! [v0: fun_fu425979586l_bool] : ! [v1: fun_fu425979586l_bool] :
% 178.32/24.93 ! [v2: fun_fu425979586l_bool] : ! [v3: fun_bool_bool] : (v1 = v0 | ~
% 178.32/24.93 (cOMBB_238756964t_bool(v3, v2) = v1) | ~ (cOMBB_238756964t_bool(v3, v2) =
% 178.32/24.93 v0)) & ! [v0: fun_pname_bool] : ! [v1: fun_pname_bool] : ! [v2:
% 178.32/24.93 fun_pname_bool] : ! [v3: fun_bool_bool] : (v1 = v0 | ~
% 178.32/24.93 (cOMBB_647938656_pname(v3, v2) = v1) | ~ (cOMBB_647938656_pname(v3, v2) =
% 178.32/24.93 v0)) & ! [v0: fun_pname_fun_a_bool] : ! [v1: fun_pname_fun_a_bool] : !
% 178.32/24.93 [v2: fun_pname_a] : ! [v3: fun_a_fun_a_bool] : (v1 = v0 | ~
% 178.32/24.93 (cOMBB_1897541054_pname(v3, v2) = v1) | ~ (cOMBB_1897541054_pname(v3, v2) =
% 178.32/24.93 v0)) & ! [v0: x_a] : ! [v1: x_a] : ! [v2: pname] : ! [v3: fun_pname_a]
% 178.32/24.93 : (v1 = v0 | ~ (hAPP_pname_a(v3, v2) = v1) | ~ (hAPP_pname_a(v3, v2) = v0))
% 178.32/24.93 & ! [v0: fun_a_1255737515l_bool] : ! [v1: fun_a_1255737515l_bool] : ! [v2:
% 178.32/24.93 fun_a_fun_a_bool] : ! [v3: fun_fu1471507361l_bool] : (v1 = v0 | ~
% 178.32/24.93 (cOMBB_472261505bool_a(v3, v2) = v1) | ~ (cOMBB_472261505bool_a(v3, v2) =
% 178.32/24.93 v0)) & ! [v0: fun_a_968466022l_bool] : ! [v1: fun_a_968466022l_bool] :
% 178.32/24.93 ! [v2: fun_a_fun_pname_bool] : ! [v3: fun_fu802393907l_bool] : (v1 = v0 | ~
% 178.32/24.93 (cOMBB_1137537805bool_a(v3, v2) = v1) | ~ (cOMBB_1137537805bool_a(v3, v2) =
% 178.32/24.93 v0)) & ! [v0: fun_pname_bool] : ! [v1: fun_pname_bool] : ! [v2: x_a] :
% 178.32/24.93 ! [v3: fun_a_fun_pname_bool] : (v1 = v0 | ~ (hAPP_a93125764e_bool(v3, v2) =
% 178.32/24.93 v1) | ~ (hAPP_a93125764e_bool(v3, v2) = v0)) & ! [v0: fun_a_bool] : !
% 178.32/24.93 [v1: fun_a_bool] : ! [v2: fun_pname_bool] : ! [v3: fun_fu923319872a_bool] :
% 178.32/24.93 (v1 = v0 | ~ (hAPP_f1051908748a_bool(v3, v2) = v1) | ~
% 178.32/24.93 (hAPP_f1051908748a_bool(v3, v2) = v0)) & ! [v0: fun_a_762926252l_bool] : !
% 178.32/24.93 [v1: fun_a_762926252l_bool] : ! [v2: fun_a_fun_nat_bool] : ! [v3:
% 178.32/24.93 fun_fu1217155507l_bool] : (v1 = v0 | ~ (cOMBB_743407885bool_a(v3, v2) = v1)
% 178.32/24.93 | ~ (cOMBB_743407885bool_a(v3, v2) = v0)) & ! [v0: fun_a_bool] : ! [v1:
% 178.32/24.93 fun_a_bool] : ! [v2: fun_nat_bool] : ! [v3: fun_fu277003770a_bool] : (v1 =
% 178.32/24.93 v0 | ~ (hAPP_f1549043526a_bool(v3, v2) = v1) | ~
% 178.32/24.93 (hAPP_f1549043526a_bool(v3, v2) = v0)) & ! [v0: fun_a_fun_a_bool] : ! [v1:
% 178.32/24.93 fun_a_fun_a_bool] : ! [v2: fun_a_a] : ! [v3: fun_a_fun_a_bool] : (v1 = v0
% 178.32/24.93 | ~ (cOMBB_a_fun_a_bool_a(v3, v2) = v1) | ~ (cOMBB_a_fun_a_bool_a(v3, v2)
% 178.32/24.93 = v0)) & ! [v0: x_a] : ! [v1: x_a] : ! [v2: x_a] : ! [v3: fun_a_a] :
% 178.32/24.93 (v1 = v0 | ~ (hAPP_a_a(v3, v2) = v1) | ~ (hAPP_a_a(v3, v2) = v0)) & ! [v0:
% 178.32/24.93 fun_a_bool] : ! [v1: fun_a_bool] : ! [v2: x_a] : ! [v3: fun_a_fun_a_bool]
% 178.32/24.93 : (v1 = v0 | ~ (hAPP_a_fun_a_bool(v3, v2) = v1) | ~ (hAPP_a_fun_a_bool(v3,
% 178.32/24.93 v2) = v0)) & ! [v0: fun_pn1038293468l_bool] : ! [v1:
% 178.32/24.93 fun_pn1038293468l_bool] : ! [v2: fun_pname_fun_a_bool] : ! [v3:
% 178.32/24.93 fun_fu1471507361l_bool] : (v1 = v0 | ~ (cOMBB_392435466_pname(v3, v2) = v1)
% 178.32/24.93 | ~ (cOMBB_392435466_pname(v3, v2) = v0)) & ! [v0: fun_pname_bool] : !
% 178.32/24.94 [v1: fun_pname_bool] : ! [v2: fun_a_bool] : ! [v3: fun_fu2112074076e_bool] :
% 178.32/24.94 (v1 = v0 | ~ (hAPP_f1794073134e_bool(v3, v2) = v1) | ~
% 178.32/24.94 (hAPP_f1794073134e_bool(v3, v2) = v0)) & ! [v0: fun_pn422929397l_bool] : !
% 178.32/24.94 [v1: fun_pn422929397l_bool] : ! [v2: fun_pn800050071e_bool] : ! [v3:
% 178.32/24.94 fun_fu802393907l_bool] : (v1 = v0 | ~ (cOMBB_408569982_pname(v3, v2) = v1)
% 178.32/24.94 | ~ (cOMBB_408569982_pname(v3, v2) = v0)) & ! [v0: fun_pn1165013435l_bool]
% 178.32/24.94 : ! [v1: fun_pn1165013435l_bool] : ! [v2: fun_pn406123357t_bool] : ! [v3:
% 178.32/24.94 fun_fu1217155507l_bool] : (v1 = v0 | ~ (cOMBB_928955006_pname(v3, v2) = v1)
% 178.32/24.94 | ~ (cOMBB_928955006_pname(v3, v2) = v0)) & ! [v0: fun_pname_bool] : !
% 178.32/24.94 [v1: fun_pname_bool] : ! [v2: fun_nat_bool] : ! [v3: fun_fu1492573599e_bool]
% 178.32/24.94 : (v1 = v0 | ~ (hAPP_f654413245e_bool(v3, v2) = v1) | ~
% 178.32/24.94 (hAPP_f654413245e_bool(v3, v2) = v0)) & ! [v0: fun_na1632405922l_bool] : !
% 178.32/24.94 [v1: fun_na1632405922l_bool] : ! [v2: fun_nat_fun_a_bool] : ! [v3:
% 178.32/24.94 fun_fu1471507361l_bool] : (v1 = v0 | ~ (cOMBB_1823939024ol_nat(v3, v2) =
% 178.32/24.94 v1) | ~ (cOMBB_1823939024ol_nat(v3, v2) = v0)) & ! [v0: fun_nat_bool] :
% 178.32/24.94 ! [v1: fun_nat_bool] : ! [v2: fun_a_bool] : ! [v3: fun_fu600484770t_bool] :
% 178.32/24.94 (v1 = v0 | ~ (hAPP_f282463732t_bool(v3, v2) = v1) | ~
% 178.32/24.94 (hAPP_f282463732t_bool(v3, v2) = v0)) & ! [v0: fun_na2122364079l_bool] : !
% 178.32/24.94 [v1: fun_na2122364079l_bool] : ! [v2: fun_na936072029e_bool] : ! [v3:
% 178.32/24.94 fun_fu802393907l_bool] : (v1 = v0 | ~ (cOMBB_2117322052ol_nat(v3, v2) = v1)
% 178.32/24.94 | ~ (cOMBB_2117322052ol_nat(v3, v2) = v0)) & ! [v0: fun_nat_bool] : !
% 178.32/24.94 [v1: fun_nat_bool] : ! [v2: fun_pname_bool] : ! [v3: fun_fu900310687t_bool]
% 178.32/24.94 : (v1 = v0 | ~ (hAPP_f1066163005t_bool(v3, v2) = v1) | ~
% 178.32/24.94 (hAPP_f1066163005t_bool(v3, v2) = v0)) & ! [v0: fun_na1436237685l_bool] :
% 178.32/24.94 ! [v1: fun_na1436237685l_bool] : ! [v2: fun_nat_fun_nat_bool] : ! [v3:
% 178.32/24.94 fun_fu1217155507l_bool] : (v1 = v0 | ~ (cOMBB_2026977092ol_nat(v3, v2) =
% 178.32/24.94 v1) | ~ (cOMBB_2026977092ol_nat(v3, v2) = v0)) & ! [v0:
% 178.32/24.94 fun_nat_fun_a_bool] : ! [v1: fun_nat_fun_a_bool] : ! [v2: fun_nat_a] : !
% 178.32/24.94 [v3: fun_a_fun_a_bool] : (v1 = v0 | ~ (cOMBB_1885489796ol_nat(v3, v2) = v1) |
% 178.32/24.94 ~ (cOMBB_1885489796ol_nat(v3, v2) = v0)) & ! [v0: x_a] : ! [v1: x_a] : !
% 178.32/24.94 [v2: nat] : ! [v3: fun_nat_a] : (v1 = v0 | ~ (hAPP_nat_a(v3, v2) = v1) | ~
% 178.32/24.94 (hAPP_nat_a(v3, v2) = v0)) & ! [v0: fun_nat_bool] : ! [v1: fun_nat_bool] :
% 178.32/24.94 ! [v2: x_a] : ! [v3: fun_a_fun_nat_bool] : (v1 = v0 | ~
% 178.32/24.94 (hAPP_a_fun_nat_bool(v3, v2) = v1) | ~ (hAPP_a_fun_nat_bool(v3, v2) = v0))
% 178.32/24.94 & ! [v0: fun_fu600484770t_bool] : ! [v1: fun_fu600484770t_bool] : ! [v2:
% 178.32/24.94 fun_fun_a_bool_nat] : ! [v3: fun_nat_fun_nat_bool] : (v1 = v0 | ~
% 178.32/24.94 (cOMBB_164527437a_bool(v3, v2) = v1) | ~ (cOMBB_164527437a_bool(v3, v2) =
% 178.32/24.94 v0)) & ! [v0: fun_fun_a_bool_bool] : ! [v1: fun_fun_a_bool_bool] : !
% 178.32/24.94 [v2: nat] : ! [v3: fun_na1632405922l_bool] : (v1 = v0 | ~
% 178.32/24.94 (hAPP_n1414589940l_bool(v3, v2) = v1) | ~ (hAPP_n1414589940l_bool(v3, v2) =
% 178.32/24.94 v0)) & ! [v0: fun_fu900310687t_bool] : ! [v1: fun_fu900310687t_bool] :
% 178.32/24.94 ! [v2: fun_fu1668467777ol_nat] : ! [v3: fun_nat_fun_nat_bool] : (v1 = v0 | ~
% 178.32/24.94 (cOMBB_1896684278e_bool(v3, v2) = v1) | ~ (cOMBB_1896684278e_bool(v3, v2) =
% 178.32/24.94 v0)) & ! [v0: fun_fu1430349052l_bool] : ! [v1: fun_fu1430349052l_bool] :
% 178.32/24.94 ! [v2: nat] : ! [v3: fun_na2122364079l_bool] : (v1 = v0 | ~
% 178.32/24.94 (hAPP_n850744903l_bool(v3, v2) = v1) | ~ (hAPP_n850744903l_bool(v3, v2) =
% 178.32/24.94 v0)) & ! [v0: fun_fu821463397t_bool] : ! [v1: fun_fu821463397t_bool] :
% 178.32/24.94 ! [v2: fun_fun_nat_bool_nat] : ! [v3: fun_nat_fun_nat_bool] : (v1 = v0 | ~
% 178.32/24.94 (cOMBB_1250273980t_bool(v3, v2) = v1) | ~ (cOMBB_1250273980t_bool(v3, v2) =
% 178.32/24.94 v0)) & ! [v0: fun_pn406123357t_bool] : ! [v1: fun_pn406123357t_bool] :
% 178.32/24.94 ! [v2: fun_pname_nat] : ! [v3: fun_nat_fun_nat_bool] : (v1 = v0 | ~
% 178.32/24.94 (cOMBB_523834888_pname(v3, v2) = v1) | ~ (cOMBB_523834888_pname(v3, v2) =
% 178.32/24.94 v0)) & ! [v0: nat] : ! [v1: nat] : ! [v2: pname] : ! [v3:
% 178.32/24.94 fun_pname_nat] : (v1 = v0 | ~ (hAPP_pname_nat(v3, v2) = v1) | ~
% 178.32/24.94 (hAPP_pname_nat(v3, v2) = v0)) & ! [v0: fun_a_fun_nat_bool] : ! [v1:
% 178.32/24.94 fun_a_fun_nat_bool] : ! [v2: fun_a_nat] : ! [v3: fun_nat_fun_nat_bool] :
% 178.32/24.94 (v1 = v0 | ~ (cOMBB_1321347587bool_a(v3, v2) = v1) | ~
% 178.32/24.94 (cOMBB_1321347587bool_a(v3, v2) = v0)) & ! [v0: nat] : ! [v1: nat] : !
% 178.32/24.94 [v2: x_a] : ! [v3: fun_a_nat] : (v1 = v0 | ~ (hAPP_a_nat(v3, v2) = v1) | ~
% 178.32/24.94 (hAPP_a_nat(v3, v2) = v0)) & ! [v0: fun_nat_fun_nat_bool] : ! [v1:
% 178.32/24.94 fun_nat_fun_nat_bool] : ! [v2: fun_nat_nat] : ! [v3: fun_nat_fun_nat_bool]
% 178.32/24.94 : (v1 = v0 | ~ (cOMBB_800536526ol_nat(v3, v2) = v1) | ~
% 178.32/24.94 (cOMBB_800536526ol_nat(v3, v2) = v0)) & ! [v0: fun_fun_a_bool_bool] : !
% 178.32/24.94 [v1: fun_fun_a_bool_bool] : ! [v2: fun_fun_a_bool_bool] : ! [v3:
% 178.32/24.94 fun_fu911136611l_bool] : (v1 = v0 | ~ (hAPP_f2117159681l_bool(v3, v2) = v1)
% 178.32/24.94 | ~ (hAPP_f2117159681l_bool(v3, v2) = v0)) & ! [v0:
% 178.32/24.94 fun_fu2112074076e_bool] : ! [v1: fun_fu2112074076e_bool] : ! [v2:
% 178.32/24.94 fun_fun_a_bool_pname] : ! [v3: fun_pn800050071e_bool] : (v1 = v0 | ~
% 178.32/24.94 (cOMBB_1693087065a_bool(v3, v2) = v1) | ~ (cOMBB_1693087065a_bool(v3, v2) =
% 178.32/24.94 v0)) & ! [v0: pname] : ! [v1: pname] : ! [v2: fun_a_bool] : ! [v3:
% 178.32/24.94 fun_fun_a_bool_pname] : (v1 = v0 | ~ (hAPP_f1128469712_pname(v3, v2) = v1)
% 178.32/24.94 | ~ (hAPP_f1128469712_pname(v3, v2) = v0)) & ! [v0: fun_fun_a_bool_bool] :
% 178.32/24.94 ! [v1: fun_fun_a_bool_bool] : ! [v2: pname] : ! [v3:
% 178.32/24.94 fun_pn1038293468l_bool] : (v1 = v0 | ~ (hAPP_p1824510254l_bool(v3, v2) =
% 178.32/24.94 v1) | ~ (hAPP_p1824510254l_bool(v3, v2) = v0)) & ! [v0:
% 178.32/24.94 fun_fu1430349052l_bool] : ! [v1: fun_fu1430349052l_bool] : ! [v2:
% 178.32/24.94 fun_fu1430349052l_bool] : ! [v3: fun_fu2087345469l_bool] : (v1 = v0 | ~
% 178.32/24.94 (hAPP_f559147733l_bool(v3, v2) = v1) | ~ (hAPP_f559147733l_bool(v3, v2) =
% 178.32/24.94 v0)) & ! [v0: fun_fu410713561e_bool] : ! [v1: fun_fu410713561e_bool] :
% 178.32/24.94 ! [v2: fun_fu1499449723_pname] : ! [v3: fun_pn800050071e_bool] : (v1 = v0 |
% 178.32/24.94 ~ (cOMBB_598082538e_bool(v3, v2) = v1) | ~ (cOMBB_598082538e_bool(v3, v2) =
% 178.32/24.94 v0)) & ! [v0: pname] : ! [v1: pname] : ! [v2: fun_pname_bool] : ! [v3:
% 178.32/24.94 fun_fu1499449723_pname] : (v1 = v0 | ~ (hAPP_f1297739591_pname(v3, v2) =
% 178.32/24.94 v1) | ~ (hAPP_f1297739591_pname(v3, v2) = v0)) & ! [v0:
% 178.32/24.94 fun_fu425979586l_bool] : ! [v1: fun_fu425979586l_bool] : ! [v2:
% 178.32/24.94 fun_fu425979586l_bool] : ! [v3: fun_fu616551101l_bool] : (v1 = v0 | ~
% 178.32/24.94 (hAPP_f1246832597l_bool(v3, v2) = v1) | ~ (hAPP_f1246832597l_bool(v3, v2) =
% 178.32/24.94 v0)) & ! [v0: fun_fu1492573599e_bool] : ! [v1: fun_fu1492573599e_bool] :
% 178.32/24.94 ! [v2: fun_fu665170229_pname] : ! [v3: fun_pn800050071e_bool] : (v1 = v0 |
% 178.32/24.94 ~ (cOMBB_141086128t_bool(v3, v2) = v1) | ~ (cOMBB_141086128t_bool(v3, v2) =
% 178.32/24.94 v0)) & ! [v0: pname] : ! [v1: pname] : ! [v2: fun_nat_bool] : ! [v3:
% 178.32/24.94 fun_fu665170229_pname] : (v1 = v0 | ~ (hAPP_f1291551745_pname(v3, v2) = v1)
% 178.32/24.94 | ~ (hAPP_f1291551745_pname(v3, v2) = v0)) & ! [v0: fun_fu425979586l_bool]
% 178.32/24.94 : ! [v1: fun_fu425979586l_bool] : ! [v2: pname] : ! [v3:
% 178.32/24.94 fun_pn1165013435l_bool] : (v1 = v0 | ~ (hAPP_p130839763l_bool(v3, v2) = v1)
% 178.32/24.94 | ~ (hAPP_p130839763l_bool(v3, v2) = v0)) & ! [v0: fun_pname_bool] : !
% 178.32/24.94 [v1: fun_pname_bool] : ! [v2: fun_pname_bool] : ! [v3:
% 178.32/24.94 fun_fu410713561e_bool] : (v1 = v0 | ~ (hAPP_f759274231e_bool(v3, v2) = v1)
% 178.32/24.94 | ~ (hAPP_f759274231e_bool(v3, v2) = v0)) & ! [v0: fun_pn800050071e_bool]
% 178.32/24.94 : ! [v1: fun_pn800050071e_bool] : ! [v2: fun_pname_pname] : ! [v3:
% 178.32/24.94 fun_pn800050071e_bool] : (v1 = v0 | ~ (cOMBB_542850580_pname(v3, v2) = v1)
% 178.32/24.94 | ~ (cOMBB_542850580_pname(v3, v2) = v0)) & ! [v0: pname] : ! [v1: pname]
% 178.32/24.94 : ! [v2: pname] : ! [v3: fun_pname_pname] : (v1 = v0 | ~
% 178.32/24.94 (hAPP_pname_pname(v3, v2) = v1) | ~ (hAPP_pname_pname(v3, v2) = v0)) & !
% 178.32/24.94 [v0: fun_pname_bool] : ! [v1: fun_pname_bool] : ! [v2: pname] : ! [v3:
% 178.32/24.94 fun_pn800050071e_bool] : (v1 = v0 | ~ (hAPP_p61793385e_bool(v3, v2) = v1) |
% 178.32/24.94 ~ (hAPP_p61793385e_bool(v3, v2) = v0)) & ! [v0: fun_a_bool] : ! [v1:
% 178.32/24.94 fun_a_bool] : ! [v2: fun_a_bool] : ! [v3: fun_fu1731003005a_bool] : (v1 =
% 178.32/24.94 v0 | ~ (hAPP_f2050579477a_bool(v3, v2) = v1) | ~
% 178.32/24.94 (hAPP_f2050579477a_bool(v3, v2) = v0)) & ! [v0: fun_a_fun_pname_bool] : !
% 178.32/24.94 [v1: fun_a_fun_pname_bool] : ! [v2: fun_a_pname] : ! [v3:
% 178.32/24.94 fun_pn800050071e_bool] : (v1 = v0 | ~ (cOMBB_610033911bool_a(v3, v2) = v1)
% 178.32/24.94 | ~ (cOMBB_610033911bool_a(v3, v2) = v0)) & ! [v0: pname] : ! [v1: pname]
% 178.32/24.94 : ! [v2: x_a] : ! [v3: fun_a_pname] : (v1 = v0 | ~ (hAPP_a_pname(v3, v2) =
% 178.32/24.94 v1) | ~ (hAPP_a_pname(v3, v2) = v0)) & ! [v0: fun_a_bool] : ! [v1:
% 178.32/24.94 fun_a_bool] : ! [v2: pname] : ! [v3: fun_pname_fun_a_bool] : (v1 = v0 | ~
% 178.32/24.94 (hAPP_p1534023578a_bool(v3, v2) = v1) | ~ (hAPP_p1534023578a_bool(v3, v2) =
% 178.32/24.94 v0)) & ! [v0: fun_nat_bool] : ! [v1: fun_nat_bool] : ! [v2:
% 178.32/24.94 fun_nat_bool] : ! [v3: fun_fu821463397t_bool] : (v1 = v0 | ~
% 178.32/24.94 (hAPP_f800510211t_bool(v3, v2) = v1) | ~ (hAPP_f800510211t_bool(v3, v2) =
% 178.32/24.94 v0)) & ! [v0: fun_na936072029e_bool] : ! [v1: fun_na936072029e_bool] :
% 178.32/24.94 ! [v2: fun_nat_pname] : ! [v3: fun_pn800050071e_bool] : (v1 = v0 | ~
% 178.32/24.94 (cOMBB_1212655066ol_nat(v3, v2) = v1) | ~ (cOMBB_1212655066ol_nat(v3, v2) =
% 178.32/24.94 v0)) & ! [v0: pname] : ! [v1: pname] : ! [v2: nat] : ! [v3:
% 178.32/24.94 fun_nat_pname] : (v1 = v0 | ~ (hAPP_nat_pname(v3, v2) = v1) | ~
% 178.32/24.94 (hAPP_nat_pname(v3, v2) = v0)) & ! [v0: fun_nat_bool] : ! [v1:
% 178.32/24.94 fun_nat_bool] : ! [v2: pname] : ! [v3: fun_pn406123357t_bool] : (v1 = v0 |
% 178.32/24.94 ~ (hAPP_p1499970991t_bool(v3, v2) = v1) | ~ (hAPP_p1499970991t_bool(v3,
% 178.32/24.94 v2) = v0)) & ! [v0: fun_a_bool] : ! [v1: fun_a_bool] : ! [v2: nat] :
% 178.32/24.94 ! [v3: fun_nat_fun_a_bool] : (v1 = v0 | ~ (hAPP_nat_fun_a_bool(v3, v2) = v1)
% 178.32/24.94 | ~ (hAPP_nat_fun_a_bool(v3, v2) = v0)) & ! [v0: fun_pname_bool] : ! [v1:
% 178.32/24.94 fun_pname_bool] : ! [v2: nat] : ! [v3: fun_na936072029e_bool] : (v1 = v0 |
% 178.32/24.94 ~ (hAPP_n1025906991e_bool(v3, v2) = v1) | ~ (hAPP_n1025906991e_bool(v3,
% 178.32/24.94 v2) = v0)) & ! [v0: fun_bool_bool] : ! [v1: fun_bool_bool] : ! [v2:
% 178.32/24.94 bool] : ! [v3: fun_bo1549164019l_bool] : (v1 = v0 | ~
% 178.32/24.94 (hAPP_b589554111l_bool(v3, v2) = v1) | ~ (hAPP_b589554111l_bool(v3, v2) =
% 178.32/24.94 v0)) & ! [v0: bool] : ! [v1: bool] : ! [v2: bool] : ! [v3:
% 178.32/24.94 fun_bool_bool] : (v1 = v0 | ~ (hAPP_bool_bool(v3, v2) = v1) | ~
% 178.32/24.94 (hAPP_bool_bool(v3, v2) = v0)) & ! [v0: fun_fun_a_bool_bool] : ! [v1:
% 178.32/24.94 fun_fun_a_bool_bool] : ! [v2: fun_a_bool] : ! [v3: fun_a_fun_a_bool] : (v1
% 178.32/24.94 = v0 | ~ (image_a_fun_a_bool(v3, v2) = v1) | ~ (image_a_fun_a_bool(v3, v2)
% 178.32/24.94 = v0)) & ! [v0: fun_fu1430349052l_bool] : ! [v1: fun_fu1430349052l_bool]
% 178.32/24.94 : ! [v2: fun_a_bool] : ! [v3: fun_a_fun_pname_bool] : (v1 = v0 | ~
% 178.32/24.94 (image_819518260e_bool(v3, v2) = v1) | ~ (image_819518260e_bool(v3, v2) =
% 178.32/24.94 v0)) & ! [v0: fun_fu425979586l_bool] : ! [v1: fun_fu425979586l_bool] :
% 178.32/24.94 ! [v2: fun_a_bool] : ! [v3: fun_a_fun_nat_bool] : (v1 = v0 | ~
% 178.32/24.94 (image_a_fun_nat_bool(v3, v2) = v1) | ~ (image_a_fun_nat_bool(v3, v2) =
% 178.32/24.94 v0)) & ! [v0: fun_nat_bool] : ! [v1: fun_nat_bool] : ! [v2:
% 178.32/24.94 fun_nat_bool] : ! [v3: fun_nat_nat] : (v1 = v0 | ~ (image_nat_nat(v3, v2)
% 178.32/24.94 = v1) | ~ (image_nat_nat(v3, v2) = v0)) & ! [v0: fun_na1469252690l_bool]
% 178.32/24.94 : ! [v1: fun_na1469252690l_bool] : ! [v2: fun_nat_bool] : ! [v3:
% 178.32/24.94 fun_bo1549164019l_bool] : (v1 = v0 | ~ (cOMBB_1015721476ol_nat(v3, v2) =
% 178.32/24.94 v1) | ~ (cOMBB_1015721476ol_nat(v3, v2) = v0)) & ! [v0: fun_nat_bool] :
% 178.32/24.94 ! [v1: fun_nat_bool] : ! [v2: fun_nat_bool] : ! [v3: fun_na1469252690l_bool]
% 178.32/24.94 : (v1 = v0 | ~ (cOMBS_nat_bool_bool(v3, v2) = v1) | ~
% 178.32/24.94 (cOMBS_nat_bool_bool(v3, v2) = v0)) & ! [v0: fun_pn250273176l_bool] : !
% 178.32/24.94 [v1: fun_pn250273176l_bool] : ! [v2: fun_pname_bool] : ! [v3:
% 178.32/24.94 fun_bo1549164019l_bool] : (v1 = v0 | ~ (cOMBB_675860798_pname(v3, v2) = v1)
% 178.32/24.94 | ~ (cOMBB_675860798_pname(v3, v2) = v0)) & ! [v0: fun_pname_bool] : !
% 178.32/24.94 [v1: fun_pname_bool] : ! [v2: fun_pname_bool] : ! [v3:
% 178.32/24.94 fun_pn250273176l_bool] : (v1 = v0 | ~ (cOMBS_568398431l_bool(v3, v2) = v1)
% 178.32/24.94 | ~ (cOMBS_568398431l_bool(v3, v2) = v0)) & ! [v0: fun_fu554186387l_bool]
% 178.32/24.94 : ! [v1: fun_fu554186387l_bool] : ! [v2: fun_fun_a_bool_bool] : ! [v3:
% 178.32/24.94 fun_bo1549164019l_bool] : (v1 = v0 | ~ (cOMBB_338059395a_bool(v3, v2) = v1)
% 178.32/24.94 | ~ (cOMBB_338059395a_bool(v3, v2) = v0)) & ! [v0: fun_fun_a_bool_bool] :
% 178.32/24.94 ! [v1: fun_fun_a_bool_bool] : ! [v2: fun_fun_a_bool_bool] : ! [v3:
% 178.32/24.94 fun_fu554186387l_bool] : (v1 = v0 | ~ (cOMBS_1035972772l_bool(v3, v2) = v1)
% 178.32/24.94 | ~ (cOMBS_1035972772l_bool(v3, v2) = v0)) & ! [v0: fun_fu31783638l_bool]
% 178.32/24.94 : ! [v1: fun_fu31783638l_bool] : ! [v2: fun_fu1430349052l_bool] : ! [v3:
% 178.32/24.94 fun_bo1549164019l_bool] : (v1 = v0 | ~ (cOMBB_2095475776e_bool(v3, v2) =
% 178.32/24.94 v1) | ~ (cOMBB_2095475776e_bool(v3, v2) = v0)) & ! [v0:
% 178.32/24.94 fun_fu1430349052l_bool] : ! [v1: fun_fu1430349052l_bool] : ! [v2:
% 178.32/24.94 fun_fu1430349052l_bool] : ! [v3: fun_fu31783638l_bool] : (v1 = v0 | ~
% 178.32/24.94 (cOMBS_350070575l_bool(v3, v2) = v1) | ~ (cOMBS_350070575l_bool(v3, v2) =
% 178.32/24.94 v0)) & ! [v0: fun_fu1016514960l_bool] : ! [v1: fun_fu1016514960l_bool] :
% 178.32/24.94 ! [v2: fun_fu425979586l_bool] : ! [v3: fun_bo1549164019l_bool] : (v1 = v0 |
% 178.32/24.94 ~ (cOMBB_444170502t_bool(v3, v2) = v1) | ~ (cOMBB_444170502t_bool(v3, v2) =
% 178.32/24.94 v0)) & ! [v0: fun_fu425979586l_bool] : ! [v1: fun_fu425979586l_bool] :
% 178.32/24.94 ! [v2: fun_fu425979586l_bool] : ! [v3: fun_fu1016514960l_bool] : (v1 = v0 |
% 178.32/24.94 ~ (cOMBS_1187019125l_bool(v3, v2) = v1) | ~ (cOMBS_1187019125l_bool(v3, v2)
% 178.32/24.94 = v0)) & ! [v0: fun_a_fun_bool_bool] : ! [v1: fun_a_fun_bool_bool] : !
% 178.32/24.94 [v2: fun_a_bool] : ! [v3: fun_bo1549164019l_bool] : (v1 = v0 | ~
% 178.32/24.94 (cOMBB_1972296269bool_a(v3, v2) = v1) | ~ (cOMBB_1972296269bool_a(v3, v2) =
% 178.32/24.94 v0)) & ! [v0: fun_a_bool] : ! [v1: fun_a_bool] : ! [v2: fun_a_bool] :
% 178.32/24.94 ! [v3: fun_a_fun_bool_bool] : (v1 = v0 | ~ (cOMBS_a_bool_bool(v3, v2) = v1) |
% 178.32/24.94 ~ (cOMBS_a_bool_bool(v3, v2) = v0)) & ! [v0: fun_fun_a_bool_bool] : !
% 178.32/24.94 [v1: fun_fun_a_bool_bool] : ! [v2: x_a] : ! [v3: fun_a_1255737515l_bool] :
% 178.32/24.94 (v1 = v0 | ~ (hAPP_a85458249l_bool(v3, v2) = v1) | ~
% 178.32/24.94 (hAPP_a85458249l_bool(v3, v2) = v0)) & ! [v0: fun_fu1430349052l_bool] : !
% 178.32/24.94 [v1: fun_fu1430349052l_bool] : ! [v2: pname] : ! [v3: fun_pn422929397l_bool]
% 178.32/24.94 : (v1 = v0 | ~ (hAPP_p338031245l_bool(v3, v2) = v1) | ~
% 178.32/24.94 (hAPP_p338031245l_bool(v3, v2) = v0)) & ! [v0: fun_fu425979586l_bool] : !
% 178.32/24.94 [v1: fun_fu425979586l_bool] : ! [v2: nat] : ! [v3: fun_na1436237685l_bool] :
% 178.32/24.94 (v1 = v0 | ~ (hAPP_n215258509l_bool(v3, v2) = v1) | ~
% 178.32/24.94 (hAPP_n215258509l_bool(v3, v2) = v0)) & ! [v0: fun_fu885608257l_bool] : !
% 178.32/24.94 [v1: fun_fu885608257l_bool] : ! [v2: fun_a_bool] : ! [v3:
% 178.32/24.94 fun_fu386216885l_bool] : (v1 = v0 | ~ (hAPP_f285962445l_bool(v3, v2) = v1)
% 178.32/24.94 | ~ (hAPP_f285962445l_bool(v3, v2) = v0)) & ! [v0: fun_fu399576434l_bool]
% 178.32/24.94 : ! [v1: fun_fu399576434l_bool] : ! [v2: fun_pname_bool] : ! [v3:
% 178.32/24.94 fun_fu931343505l_bool] : (v1 = v0 | ~ (hAPP_f556039215l_bool(v3, v2) = v1)
% 178.32/24.94 | ~ (hAPP_f556039215l_bool(v3, v2) = v0)) & ! [v0: fun_fu814369080l_bool]
% 178.32/24.94 : ! [v1: fun_fu814369080l_bool] : ! [v2: fun_nat_bool] : ! [v3:
% 178.32/24.94 fun_fu1436348701l_bool] : (v1 = v0 | ~ (hAPP_f1951378235l_bool(v3, v2) =
% 178.32/24.94 v1) | ~ (hAPP_f1951378235l_bool(v3, v2) = v0)) & ! [v0: nat] : ! [v1:
% 178.32/24.94 nat] : ! [v2: nat] : ! [v3: fun_nat_nat] : (v1 = v0 | ~ (hAPP_nat_nat(v3,
% 178.32/24.94 v2) = v1) | ~ (hAPP_nat_nat(v3, v2) = v0)) & ! [v0: fun_pname_bool] :
% 178.32/24.94 ! [v1: fun_pname_bool] : ! [v2: fun_nat_bool] : ! [v3: fun_nat_pname] : (v1
% 178.32/24.94 = v0 | ~ (image_nat_pname(v3, v2) = v1) | ~ (image_nat_pname(v3, v2) =
% 178.32/24.94 v0)) & ! [v0: fun_nat_bool] : ! [v1: fun_nat_bool] : ! [v2:
% 178.32/24.94 fun_pname_bool] : ! [v3: fun_pname_nat] : (v1 = v0 | ~
% 178.32/24.94 (image_pname_nat(v3, v2) = v1) | ~ (image_pname_nat(v3, v2) = v0)) & !
% 178.32/24.94 [v0: nat] : ! [v1: nat] : ! [v2: fun_nat_bool] : ! [v3:
% 178.32/24.94 fun_fun_nat_bool_nat] : (v1 = v0 | ~ (hAPP_f22106695ol_nat(v3, v2) = v1) |
% 178.32/24.94 ~ (hAPP_f22106695ol_nat(v3, v2) = v0)) & ! [v0: fun_a_bool] : ! [v1:
% 178.32/24.94 fun_a_bool] : ! [v2: fun_fun_a_bool_bool] : ! [v3: fun_fun_a_bool_a] : (v1
% 178.32/24.94 = v0 | ~ (image_fun_a_bool_a(v3, v2) = v1) | ~ (image_fun_a_bool_a(v3, v2)
% 178.32/24.94 = v0)) & ! [v0: nat] : ! [v1: nat] : ! [v2: fun_fun_a_bool_bool] : !
% 178.32/24.94 [v3: fun_fu2020802748ol_nat] : (v1 = v0 | ~ (hAPP_f2009550088ol_nat(v3, v2) =
% 178.32/24.94 v1) | ~ (hAPP_f2009550088ol_nat(v3, v2) = v0)) & ! [v0: fun_a_bool] : !
% 178.32/24.94 [v1: fun_a_bool] : ! [v2: fun_fu1430349052l_bool] : ! [v3:
% 178.32/24.94 fun_fun_pname_bool_a] : (v1 = v0 | ~ (image_876012084bool_a(v3, v2) = v1) |
% 178.32/24.94 ~ (image_876012084bool_a(v3, v2) = v0)) & ! [v0: nat] : ! [v1: nat] : !
% 178.32/24.94 [v2: fun_fu1430349052l_bool] : ! [v3: fun_fu1730389579ol_nat] : (v1 = v0 | ~
% 178.32/24.94 (hAPP_f55526627ol_nat(v3, v2) = v1) | ~ (hAPP_f55526627ol_nat(v3, v2) =
% 178.32/24.94 v0)) & ! [v0: fun_a_bool] : ! [v1: fun_a_bool] : ! [v2:
% 178.32/24.94 fun_fu425979586l_bool] : ! [v3: fun_fun_nat_bool_a] : (v1 = v0 | ~
% 178.32/24.94 (image_fun_nat_bool_a(v3, v2) = v1) | ~ (image_fun_nat_bool_a(v3, v2) =
% 178.32/24.94 v0)) & ! [v0: nat] : ! [v1: nat] : ! [v2: fun_fu425979586l_bool] : !
% 178.32/24.94 [v3: fun_fu411113733ol_nat] : (v1 = v0 | ~ (hAPP_f696928925ol_nat(v3, v2) =
% 178.32/24.94 v1) | ~ (hAPP_f696928925ol_nat(v3, v2) = v0)) & ! [v0: fun_a_bool] : !
% 178.32/24.94 [v1: fun_a_bool] : ! [v2: fun_a_bool] : ! [v3: fun_a_a] : (v1 = v0 | ~
% 178.32/24.94 (image_a_a(v3, v2) = v1) | ~ (image_a_a(v3, v2) = v0)) & ! [v0: nat] : !
% 178.32/24.94 [v1: nat] : ! [v2: fun_a_bool] : ! [v3: fun_fun_a_bool_nat] : (v1 = v0 | ~
% 178.32/24.94 (hAPP_fun_a_bool_nat(v3, v2) = v1) | ~ (hAPP_fun_a_bool_nat(v3, v2) = v0))
% 178.32/24.94 & ! [v0: fun_pname_bool] : ! [v1: fun_pname_bool] : ! [v2: fun_pname_bool]
% 178.32/24.94 : ! [v3: fun_pname_pname] : (v1 = v0 | ~ (image_pname_pname(v3, v2) = v1) |
% 178.32/24.94 ~ (image_pname_pname(v3, v2) = v0)) & ! [v0: fun_nat_bool] : ! [v1:
% 178.32/24.94 fun_nat_bool] : ! [v2: nat] : ! [v3: fun_nat_fun_nat_bool] : (v1 = v0 | ~
% 178.32/24.94 (hAPP_n1699378549t_bool(v3, v2) = v1) | ~ (hAPP_n1699378549t_bool(v3, v2) =
% 178.32/24.94 v0)) & ! [v0: nat] : ! [v1: nat] : ! [v2: fun_pname_bool] : ! [v3:
% 178.32/24.94 fun_fu1668467777ol_nat] : (v1 = v0 | ~ (hAPP_f921600141ol_nat(v3, v2) = v1)
% 178.32/24.94 | ~ (hAPP_f921600141ol_nat(v3, v2) = v0)) & ! [v0: bool] : ! [v1: bool] :
% 178.32/24.94 ! [v2: nat] : ! [v3: fun_nat_bool] : (v1 = v0 | ~ (hAPP_nat_bool(v3, v2) =
% 178.32/24.94 v1) | ~ (hAPP_nat_bool(v3, v2) = v0)) & ! [v0: fun_a_bool] : ! [v1:
% 178.32/24.94 fun_a_bool] : ! [v2: fun_a_bool] : ! [v3: x_a] : (v1 = v0 | ~
% 178.32/24.94 (insert_a(v3, v2) = v1) | ~ (insert_a(v3, v2) = v0)) & ! [v0:
% 178.32/24.94 fun_nat_bool] : ! [v1: fun_nat_bool] : ! [v2: fun_nat_bool] : ! [v3: nat]
% 178.32/24.94 : (v1 = v0 | ~ (insert_nat(v3, v2) = v1) | ~ (insert_nat(v3, v2) = v0)) & !
% 178.32/24.94 [v0: fun_pname_bool] : ! [v1: fun_pname_bool] : ! [v2: fun_pname_bool] : !
% 178.32/24.94 [v3: pname] : (v1 = v0 | ~ (insert_pname(v3, v2) = v1) | ~ (insert_pname(v3,
% 178.32/24.94 v2) = v0)) & ! [v0: fun_fun_a_bool_bool] : ! [v1: fun_fun_a_bool_bool]
% 178.32/24.94 : ! [v2: fun_fun_a_bool_bool] : ! [v3: fun_a_bool] : (v1 = v0 | ~
% 178.32/24.94 (insert_fun_a_bool(v3, v2) = v1) | ~ (insert_fun_a_bool(v3, v2) = v0)) & !
% 178.32/24.94 [v0: fun_fu1430349052l_bool] : ! [v1: fun_fu1430349052l_bool] : ! [v2:
% 178.32/24.94 fun_fu1430349052l_bool] : ! [v3: fun_pname_bool] : (v1 = v0 | ~
% 178.32/24.94 (insert1325755072e_bool(v3, v2) = v1) | ~ (insert1325755072e_bool(v3, v2) =
% 178.32/24.94 v0)) & ! [v0: fun_fu425979586l_bool] : ! [v1: fun_fu425979586l_bool] :
% 178.32/24.94 ! [v2: fun_fu425979586l_bool] : ! [v3: fun_nat_bool] : (v1 = v0 | ~
% 178.32/24.94 (insert_fun_nat_bool(v3, v2) = v1) | ~ (insert_fun_nat_bool(v3, v2) = v0))
% 178.32/24.94 & ! [v0: fun_a_bool] : ! [v1: fun_a_bool] : ! [v2: fun_pname_bool] : !
% 178.32/24.94 [v3: fun_pname_a] : (v1 = v0 | ~ (image_pname_a(v3, v2) = v1) | ~
% 178.32/24.94 (image_pname_a(v3, v2) = v0)) & ! [v0: fun_nat_bool] : ! [v1:
% 178.32/24.94 fun_nat_bool] : ! [v2: fun_fun_a_bool_bool] : ! [v3: fun_fun_a_bool_nat] :
% 178.32/24.94 (v1 = v0 | ~ (image_fun_a_bool_nat(v3, v2) = v1) | ~
% 178.32/24.94 (image_fun_a_bool_nat(v3, v2) = v0)) & ! [v0: fun_nat_bool] : ! [v1:
% 178.32/24.94 fun_nat_bool] : ! [v2: fun_fu1430349052l_bool] : ! [v3:
% 178.32/24.94 fun_fu1668467777ol_nat] : (v1 = v0 | ~ (image_1551609309ol_nat(v3, v2) =
% 178.32/24.94 v1) | ~ (image_1551609309ol_nat(v3, v2) = v0)) & ! [v0: fun_nat_bool] :
% 178.32/24.94 ! [v1: fun_nat_bool] : ! [v2: fun_fu425979586l_bool] : ! [v3:
% 178.32/24.94 fun_fun_nat_bool_nat] : (v1 = v0 | ~ (image_496248727ol_nat(v3, v2) = v1) |
% 178.32/24.94 ~ (image_496248727ol_nat(v3, v2) = v0)) & ! [v0: fun_nat_bool] : ! [v1:
% 178.32/24.94 fun_nat_bool] : ! [v2: fun_a_bool] : ! [v3: fun_a_nat] : (v1 = v0 | ~
% 178.32/24.94 (image_a_nat(v3, v2) = v1) | ~ (image_a_nat(v3, v2) = v0)) & ! [v0:
% 178.32/24.94 fun_pname_bool] : ! [v1: fun_pname_bool] : ! [v2: fun_fun_a_bool_bool] :
% 178.32/24.94 ! [v3: fun_fun_a_bool_pname] : (v1 = v0 | ~ (image_1854862208_pname(v3, v2) =
% 178.32/24.94 v1) | ~ (image_1854862208_pname(v3, v2) = v0)) & ! [v0: fun_pname_bool]
% 178.32/24.94 : ! [v1: fun_pname_bool] : ! [v2: fun_fu1430349052l_bool] : ! [v3:
% 178.32/24.94 fun_fu1499449723_pname] : (v1 = v0 | ~ (image_1283814551_pname(v3, v2) =
% 178.32/24.94 v1) | ~ (image_1283814551_pname(v3, v2) = v0)) & ! [v0: fun_pname_bool]
% 178.32/24.94 : ! [v1: fun_pname_bool] : ! [v2: fun_fu425979586l_bool] : ! [v3:
% 178.32/24.94 fun_fu665170229_pname] : (v1 = v0 | ~ (image_1921560913_pname(v3, v2) = v1)
% 178.32/24.94 | ~ (image_1921560913_pname(v3, v2) = v0)) & ! [v0: fun_pname_bool] : !
% 178.32/24.94 [v1: fun_pname_bool] : ! [v2: fun_a_bool] : ! [v3: fun_a_pname] : (v1 = v0 |
% 178.32/24.94 ~ (image_a_pname(v3, v2) = v1) | ~ (image_a_pname(v3, v2) = v0)) & ! [v0:
% 178.32/24.94 fun_fun_a_bool_bool] : ! [v1: fun_fun_a_bool_bool] : ! [v2: fun_nat_bool]
% 178.32/24.94 : ! [v3: fun_nat_fun_a_bool] : (v1 = v0 | ~ (image_nat_fun_a_bool(v3, v2) =
% 178.32/24.94 v1) | ~ (image_nat_fun_a_bool(v3, v2) = v0)) & ! [v0:
% 178.32/24.94 fun_fu1430349052l_bool] : ! [v1: fun_fu1430349052l_bool] : ! [v2:
% 178.32/24.94 fun_nat_bool] : ! [v3: fun_na936072029e_bool] : (v1 = v0 | ~
% 178.32/24.94 (image_1655916159e_bool(v3, v2) = v1) | ~ (image_1655916159e_bool(v3, v2) =
% 178.32/24.94 v0)) & ! [v0: fun_fu425979586l_bool] : ! [v1: fun_fu425979586l_bool] :
% 178.32/24.94 ! [v2: fun_nat_bool] : ! [v3: fun_nat_fun_nat_bool] : (v1 = v0 | ~
% 178.32/24.94 (image_26036933t_bool(v3, v2) = v1) | ~ (image_26036933t_bool(v3, v2) =
% 178.32/24.94 v0)) & ! [v0: fun_a_bool] : ! [v1: fun_a_bool] : ! [v2: fun_nat_bool] :
% 178.32/24.94 ! [v3: fun_nat_a] : (v1 = v0 | ~ (image_nat_a(v3, v2) = v1) | ~
% 178.32/24.94 (image_nat_a(v3, v2) = v0)) & ! [v0: fun_fun_a_bool_bool] : ! [v1:
% 178.32/24.94 fun_fun_a_bool_bool] : ! [v2: fun_pname_bool] : ! [v3:
% 178.32/24.94 fun_pname_fun_a_bool] : (v1 = v0 | ~ (image_112932426a_bool(v3, v2) = v1) |
% 178.32/24.94 ~ (image_112932426a_bool(v3, v2) = v0)) & ! [v0: fun_fu1430349052l_bool] :
% 178.32/24.94 ! [v1: fun_fu1430349052l_bool] : ! [v2: fun_pname_bool] : ! [v3:
% 178.32/24.94 fun_pn800050071e_bool] : (v1 = v0 | ~ (image_47868345e_bool(v3, v2) = v1) |
% 178.32/24.94 ~ (image_47868345e_bool(v3, v2) = v0)) & ! [v0: fun_fu425979586l_bool] :
% 178.32/24.94 ! [v1: fun_fu425979586l_bool] : ! [v2: fun_pname_bool] : ! [v3:
% 178.32/24.94 fun_pn406123357t_bool] : (v1 = v0 | ~ (image_2129980159t_bool(v3, v2) = v1)
% 178.32/24.94 | ~ (image_2129980159t_bool(v3, v2) = v0)) & ! [v0: fun_fu425979586l_bool]
% 178.32/24.94 : ! [v1: fun_fu425979586l_bool] : ! [v2: fun_nat_bool] : ! [v3:
% 178.32/24.94 fun_fu1217155507l_bool] : (v1 = v0 | ~ (hAPP_f103356543l_bool(v3, v2) = v1)
% 178.32/24.94 | ~ (hAPP_f103356543l_bool(v3, v2) = v0)) & ! [v0: bool] : ! [v1: bool] :
% 178.32/24.94 ! [v2: fun_nat_bool] : ! [v3: fun_fu425979586l_bool] : (v1 = v0 | ~
% 178.32/24.94 (hAPP_f54304608l_bool(v3, v2) = v1) | ~ (hAPP_f54304608l_bool(v3, v2) =
% 178.32/24.94 v0)) & ! [v0: fun_fu1430349052l_bool] : ! [v1: fun_fu1430349052l_bool] :
% 178.32/24.94 ! [v2: fun_pname_bool] : ! [v3: fun_fu802393907l_bool] : (v1 = v0 | ~
% 178.32/24.94 (hAPP_f434788991l_bool(v3, v2) = v1) | ~ (hAPP_f434788991l_bool(v3, v2) =
% 178.32/24.94 v0)) & ! [v0: bool] : ! [v1: bool] : ! [v2: fun_pname_bool] : ! [v3:
% 178.32/24.94 fun_fu1430349052l_bool] : (v1 = v0 | ~ (hAPP_f1664156314l_bool(v3, v2) =
% 178.32/24.94 v1) | ~ (hAPP_f1664156314l_bool(v3, v2) = v0)) & ! [v0:
% 178.32/24.94 fun_fu885608257l_bool] : ! [v1: fun_fu885608257l_bool] : ! [v2:
% 178.32/24.94 fun_fun_a_bool_bool] : ! [v3: fun_fu418465139l_bool] : (v1 = v0 | ~
% 178.32/24.94 (hAPP_f1434722111l_bool(v3, v2) = v1) | ~ (hAPP_f1434722111l_bool(v3, v2) =
% 178.32/24.94 v0)) & ! [v0: bool] : ! [v1: bool] : ! [v2: fun_fun_a_bool_bool] : !
% 178.32/24.94 [v3: fun_fu885608257l_bool] : (v1 = v0 | ~ (hAPP_f621171935l_bool(v3, v2) =
% 178.32/24.94 v1) | ~ (hAPP_f621171935l_bool(v3, v2) = v0)) & ! [v0: bool] : ! [v1:
% 178.32/24.94 bool] : ! [v2: fun_fu885608257l_bool] : ! [v3: fun_fu255076663l_bool] :
% 178.32/24.94 (v1 = v0 | ~ (hAPP_f292226953l_bool(v3, v2) = v1) | ~
% 178.32/24.94 (hAPP_f292226953l_bool(v3, v2) = v0)) & ! [v0: fun_fu399576434l_bool] : !
% 178.32/24.94 [v1: fun_fu399576434l_bool] : ! [v2: fun_fu1430349052l_bool] : ! [v3:
% 178.32/24.94 fun_fu1911931399l_bool] : (v1 = v0 | ~ (hAPP_f510955609l_bool(v3, v2) = v1)
% 178.32/24.94 | ~ (hAPP_f510955609l_bool(v3, v2) = v0)) & ! [v0: bool] : ! [v1: bool] :
% 178.32/24.94 ! [v2: fun_fu1430349052l_bool] : ! [v3: fun_fu399576434l_bool] : (v1 = v0 |
% 178.32/24.94 ~ (hAPP_f1935102916l_bool(v3, v2) = v1) | ~ (hAPP_f1935102916l_bool(v3, v2)
% 178.32/24.94 = v0)) & ! [v0: bool] : ! [v1: bool] : ! [v2: fun_fu399576434l_bool] :
% 178.32/24.94 ! [v3: fun_fu1438281908l_bool] : (v1 = v0 | ~ (hAPP_f389811538l_bool(v3, v2)
% 178.32/24.94 = v1) | ~ (hAPP_f389811538l_bool(v3, v2) = v0)) & ! [v0:
% 178.32/24.94 fun_fu814369080l_bool] : ! [v1: fun_fu814369080l_bool] : ! [v2:
% 178.32/24.94 fun_fu425979586l_bool] : ! [v3: fun_fu140186515l_bool] : (v1 = v0 | ~
% 178.32/24.94 (hAPP_f1772781669l_bool(v3, v2) = v1) | ~ (hAPP_f1772781669l_bool(v3, v2) =
% 178.32/24.94 v0)) & ! [v0: bool] : ! [v1: bool] : ! [v2: fun_fu425979586l_bool] : !
% 178.32/24.94 [v3: fun_fu814369080l_bool] : (v1 = v0 | ~ (hAPP_f1637334154l_bool(v3, v2) =
% 178.32/24.94 v1) | ~ (hAPP_f1637334154l_bool(v3, v2) = v0)) & ! [v0: bool] : ! [v1:
% 178.32/24.94 bool] : ! [v2: fun_fu814369080l_bool] : ! [v3: fun_fu61768826l_bool] : (v1
% 178.32/24.94 = v0 | ~ (hAPP_f937997336l_bool(v3, v2) = v1) | ~
% 178.32/24.94 (hAPP_f937997336l_bool(v3, v2) = v0)) & ! [v0: fun_fun_a_bool_bool] : !
% 178.32/24.94 [v1: fun_fun_a_bool_bool] : ! [v2: fun_a_bool] : ! [v3:
% 178.32/24.94 fun_fu1471507361l_bool] : (v1 = v0 | ~ (hAPP_f1631501043l_bool(v3, v2) =
% 178.32/24.94 v1) | ~ (hAPP_f1631501043l_bool(v3, v2) = v0)) & ! [v0: bool] : ! [v1:
% 178.32/24.94 bool] : ! [v2: fun_a_bool] : ! [v3: fun_fun_a_bool_bool] : (v1 = v0 | ~
% 178.32/24.94 (hAPP_fun_a_bool_bool(v3, v2) = v1) | ~ (hAPP_fun_a_bool_bool(v3, v2) =
% 178.32/24.94 v0)) & ! [v0: fun_nat_nat] : ! [v1: fun_nat_nat] : ! [v2: nat] : (v1 =
% 178.32/24.94 v0 | ~ (plus_plus_nat(v2) = v1) | ~ (plus_plus_nat(v2) = v0)) & ! [v0:
% 178.32/24.94 option_com] : ! [v1: option_com] : ! [v2: pname] : (v1 = v0 | ~ (body(v2)
% 178.32/24.94 = v1) | ~ (body(v2) = v0)) & ! [v0: com] : ! [v1: com] : ! [v2:
% 178.32/24.94 option_com] : (v1 = v0 | ~ (the_com(v2) = v1) | ~ (the_com(v2) = v0)) & !
% 178.32/24.94 [v0: fun_pname_a] : ! [v1: fun_pname_a] : ! [v2: x_a] : (v1 = v0 | ~
% 178.32/24.94 (cOMBK_a_pname(v2) = v1) | ~ (cOMBK_a_pname(v2) = v0)) & ! [v0:
% 178.32/24.94 fun_nat_bool] : ! [v1: fun_nat_bool] : ! [v2: bool] : (v1 = v0 | ~
% 178.32/24.94 (cOMBK_bool_nat(v2) = v1) | ~ (cOMBK_bool_nat(v2) = v0)) & ! [v0:
% 178.32/24.94 fun_a_bool] : ! [v1: fun_a_bool] : ! [v2: bool] : (v1 = v0 | ~
% 178.32/24.94 (cOMBK_bool_a(v2) = v1) | ~ (cOMBK_bool_a(v2) = v0)) & ! [v0:
% 178.32/24.94 fun_fun_a_bool_bool] : ! [v1: fun_fun_a_bool_bool] : ! [v2: bool] : (v1 =
% 178.32/24.94 v0 | ~ (cOMBK_324466864a_bool(v2) = v1) | ~ (cOMBK_324466864a_bool(v2) =
% 178.32/24.94 v0)) & ! [v0: fun_fu1430349052l_bool] : ! [v1: fun_fu1430349052l_bool] :
% 178.32/24.94 ! [v2: bool] : (v1 = v0 | ~ (cOMBK_1857069011e_bool(v2) = v1) | ~
% 178.32/24.95 (cOMBK_1857069011e_bool(v2) = v0)) & ! [v0: fun_fu425979586l_bool] : !
% 178.32/24.95 [v1: fun_fu425979586l_bool] : ! [v2: bool] : (v1 = v0 | ~
% 178.32/24.95 (cOMBK_1994329625t_bool(v2) = v1) | ~ (cOMBK_1994329625t_bool(v2) = v0)) &
% 178.32/24.95 ! [v0: fun_pname_bool] : ! [v1: fun_pname_bool] : ! [v2: bool] : (v1 = v0 |
% 178.32/24.95 ~ (cOMBK_bool_pname(v2) = v1) | ~ (cOMBK_bool_pname(v2) = v0)) & ! [v0:
% 178.32/24.95 x_a] : ! [v1: x_a] : ! [v2: com] : (v1 = v0 | ~ (mgt(v2) = v1) | ~
% 178.32/24.95 (mgt(v2) = v0)) & ! [v0: bool] : ! [v1: bool] : ! [v2: com] : (v1 = v0 |
% 178.32/24.95 ~ (wt(v2) = v1) | ~ (wt(v2) = v0)) & ! [v0: fun_a_fun_pname_bool] : !
% 178.32/24.95 [v1: fun_a_fun_pname_bool] : ! [v2: fun_pname_fun_a_bool] : (v1 = v0 | ~
% 178.32/24.95 (cOMBC_pname_a_bool(v2) = v1) | ~ (cOMBC_pname_a_bool(v2) = v0)) & ! [v0:
% 178.32/24.95 fun_fu923319872a_bool] : ! [v1: fun_fu923319872a_bool] : ! [v2:
% 178.32/24.95 fun_a_968466022l_bool] : (v1 = v0 | ~ (cOMBC_1834145417l_bool(v2) = v1) |
% 178.32/24.95 ~ (cOMBC_1834145417l_bool(v2) = v0)) & ! [v0: fun_fu277003770a_bool] : !
% 178.32/24.95 [v1: fun_fu277003770a_bool] : ! [v2: fun_a_762926252l_bool] : (v1 = v0 | ~
% 178.32/24.95 (cOMBC_777206479l_bool(v2) = v1) | ~ (cOMBC_777206479l_bool(v2) = v0)) & !
% 178.32/24.95 [v0: fun_a_fun_a_bool] : ! [v1: fun_a_fun_a_bool] : ! [v2: fun_a_fun_a_bool]
% 178.32/24.95 : (v1 = v0 | ~ (cOMBC_a_a_bool(v2) = v1) | ~ (cOMBC_a_a_bool(v2) = v0)) & !
% 178.32/24.95 [v0: fun_fu2112074076e_bool] : ! [v1: fun_fu2112074076e_bool] : ! [v2:
% 178.32/24.95 fun_pn1038293468l_bool] : (v1 = v0 | ~ (cOMBC_445755039l_bool(v2) = v1) |
% 178.32/24.95 ~ (cOMBC_445755039l_bool(v2) = v0)) & ! [v0: fun_fu1492573599e_bool] : !
% 178.32/24.95 [v1: fun_fu1492573599e_bool] : ! [v2: fun_pn1165013435l_bool] : (v1 = v0 | ~
% 178.32/24.95 (cOMBC_267053842l_bool(v2) = v1) | ~ (cOMBC_267053842l_bool(v2) = v0)) & !
% 178.32/24.95 [v0: fun_fu600484770t_bool] : ! [v1: fun_fu600484770t_bool] : ! [v2:
% 178.32/24.95 fun_na1632405922l_bool] : (v1 = v0 | ~ (cOMBC_1928494297l_bool(v2) = v1) |
% 178.32/24.95 ~ (cOMBC_1928494297l_bool(v2) = v0)) & ! [v0: fun_fu900310687t_bool] : !
% 178.32/24.95 [v1: fun_fu900310687t_bool] : ! [v2: fun_na2122364079l_bool] : (v1 = v0 | ~
% 178.32/24.95 (cOMBC_386238098l_bool(v2) = v1) | ~ (cOMBC_386238098l_bool(v2) = v0)) & !
% 178.32/24.95 [v0: fun_a_fun_nat_bool] : ! [v1: fun_a_fun_nat_bool] : ! [v2:
% 178.32/24.95 fun_nat_fun_a_bool] : (v1 = v0 | ~ (cOMBC_nat_a_bool(v2) = v1) | ~
% 178.32/24.95 (cOMBC_nat_a_bool(v2) = v0)) & ! [v0: fun_na1632405922l_bool] : ! [v1:
% 178.32/24.95 fun_na1632405922l_bool] : ! [v2: fun_fu600484770t_bool] : (v1 = v0 | ~
% 178.32/24.95 (cOMBC_619334683t_bool(v2) = v1) | ~ (cOMBC_619334683t_bool(v2) = v0)) & !
% 178.32/24.95 [v0: fun_na2122364079l_bool] : ! [v1: fun_na2122364079l_bool] : ! [v2:
% 178.32/24.95 fun_fu900310687t_bool] : (v1 = v0 | ~ (cOMBC_1666426608t_bool(v2) = v1) |
% 178.32/24.95 ~ (cOMBC_1666426608t_bool(v2) = v0)) & ! [v0: fun_na1436237685l_bool] : !
% 178.32/24.95 [v1: fun_na1436237685l_bool] : ! [v2: fun_fu821463397t_bool] : (v1 = v0 | ~
% 178.32/24.95 (cOMBC_385542954t_bool(v2) = v1) | ~ (cOMBC_385542954t_bool(v2) = v0)) & !
% 178.32/24.95 [v0: fun_na936072029e_bool] : ! [v1: fun_na936072029e_bool] : ! [v2:
% 178.32/24.95 fun_pn406123357t_bool] : (v1 = v0 | ~ (cOMBC_pname_nat_bool(v2) = v1) | ~
% 178.32/24.95 (cOMBC_pname_nat_bool(v2) = v0)) & ! [v0: fun_nat_fun_a_bool] : ! [v1:
% 178.32/24.95 fun_nat_fun_a_bool] : ! [v2: fun_a_fun_nat_bool] : (v1 = v0 | ~
% 178.32/24.95 (cOMBC_a_nat_bool(v2) = v1) | ~ (cOMBC_a_nat_bool(v2) = v0)) & ! [v0:
% 178.32/24.95 fun_fu911136611l_bool] : ! [v1: fun_fu911136611l_bool] : ! [v2:
% 178.32/24.95 fun_fu386216885l_bool] : (v1 = v0 | ~ (cOMBC_1880041174l_bool(v2) = v1) |
% 178.32/24.95 ~ (cOMBC_1880041174l_bool(v2) = v0)) & ! [v0: fun_pn1038293468l_bool] : !
% 178.32/24.95 [v1: fun_pn1038293468l_bool] : ! [v2: fun_fu2112074076e_bool] : (v1 = v0 | ~
% 178.32/24.95 (cOMBC_1738168533e_bool(v2) = v1) | ~ (cOMBC_1738168533e_bool(v2) = v0)) &
% 178.32/24.95 ! [v0: fun_fu2087345469l_bool] : ! [v1: fun_fu2087345469l_bool] : ! [v2:
% 178.32/24.95 fun_fu931343505l_bool] : (v1 = v0 | ~ (cOMBC_1988546018l_bool(v2) = v1) |
% 178.32/24.95 ~ (cOMBC_1988546018l_bool(v2) = v0)) & ! [v0: fun_pn422929397l_bool] : !
% 178.32/24.95 [v1: fun_pn422929397l_bool] : ! [v2: fun_fu410713561e_bool] : (v1 = v0 | ~
% 178.32/24.95 (cOMBC_1004116266e_bool(v2) = v1) | ~ (cOMBC_1004116266e_bool(v2) = v0)) &
% 178.32/24.95 ! [v0: fun_fu616551101l_bool] : ! [v1: fun_fu616551101l_bool] : ! [v2:
% 178.32/24.95 fun_fu1436348701l_bool] : (v1 = v0 | ~ (cOMBC_1245412066l_bool(v2) = v1) |
% 178.32/24.95 ~ (cOMBC_1245412066l_bool(v2) = v0)) & ! [v0: fun_pn1165013435l_bool] : !
% 178.32/24.95 [v1: fun_pn1165013435l_bool] : ! [v2: fun_fu1492573599e_bool] : (v1 = v0 | ~
% 178.32/24.95 (cOMBC_615407716e_bool(v2) = v1) | ~ (cOMBC_615407716e_bool(v2) = v0)) & !
% 178.32/24.95 [v0: fun_fu410713561e_bool] : ! [v1: fun_fu410713561e_bool] : ! [v2:
% 178.32/24.95 fun_pn422929397l_bool] : (v1 = v0 | ~ (cOMBC_1058051404l_bool(v2) = v1) |
% 178.32/24.95 ~ (cOMBC_1058051404l_bool(v2) = v0)) & ! [v0: fun_pn800050071e_bool] : !
% 178.32/24.95 [v1: fun_pn800050071e_bool] : ! [v2: fun_pn800050071e_bool] : (v1 = v0 | ~
% 178.32/24.95 (cOMBC_1149511130e_bool(v2) = v1) | ~ (cOMBC_1149511130e_bool(v2) = v0)) &
% 178.32/24.95 ! [v0: fun_fu1731003005a_bool] : ! [v1: fun_fu1731003005a_bool] : ! [v2:
% 178.32/24.95 fun_a_1255737515l_bool] : (v1 = v0 | ~ (cOMBC_1355376034l_bool(v2) = v1) |
% 178.32/24.95 ~ (cOMBC_1355376034l_bool(v2) = v0)) & ! [v0: fun_pname_fun_a_bool] : !
% 178.32/24.95 [v1: fun_pname_fun_a_bool] : ! [v2: fun_a_fun_pname_bool] : (v1 = v0 | ~
% 178.32/24.95 (cOMBC_a_pname_bool(v2) = v1) | ~ (cOMBC_a_pname_bool(v2) = v0)) & ! [v0:
% 178.32/24.95 fun_fu821463397t_bool] : ! [v1: fun_fu821463397t_bool] : ! [v2:
% 178.32/24.95 fun_na1436237685l_bool] : (v1 = v0 | ~ (cOMBC_226598744l_bool(v2) = v1) |
% 178.32/24.95 ~ (cOMBC_226598744l_bool(v2) = v0)) & ! [v0: fun_pn406123357t_bool] : !
% 178.32/24.95 [v1: fun_pn406123357t_bool] : ! [v2: fun_na936072029e_bool] : (v1 = v0 | ~
% 178.32/24.95 (cOMBC_nat_pname_bool(v2) = v1) | ~ (cOMBC_nat_pname_bool(v2) = v0)) & !
% 178.32/24.95 [v0: fun_nat_fun_nat_bool] : ! [v1: fun_nat_fun_nat_bool] : ! [v2:
% 178.32/24.95 fun_nat_fun_nat_bool] : (v1 = v0 | ~ (cOMBC_nat_nat_bool(v2) = v1) | ~
% 178.32/24.95 (cOMBC_nat_nat_bool(v2) = v0)) & ! [v0: fun_nat_nat] : ! [v1: fun_nat_nat]
% 178.32/24.95 : ! [v2: nat] : (v1 = v0 | ~ (minus_minus_nat(v2) = v1) | ~
% 178.32/24.95 (minus_minus_nat(v2) = v0)) & ! [v0: fun_nat_bool] : ! [v1: fun_nat_bool]
% 178.32/24.95 : ! [v2: fun_nat_bool] : (v1 = v0 | ~ (collect_nat(v2) = v1) | ~
% 178.32/24.95 (collect_nat(v2) = v0)) & ! [v0: fun_pname_bool] : ! [v1: fun_pname_bool]
% 178.32/24.95 : ! [v2: fun_pname_bool] : (v1 = v0 | ~ (collect_pname(v2) = v1) | ~
% 178.32/24.95 (collect_pname(v2) = v0)) & ! [v0: fun_a_bool] : ! [v1: fun_a_bool] : !
% 178.32/24.95 [v2: fun_a_bool] : (v1 = v0 | ~ (collect_a(v2) = v1) | ~ (collect_a(v2) =
% 178.32/24.95 v0)) & ! [v0: fun_fu1217155507l_bool] : ! [v1: fun_fu1217155507l_bool] :
% 178.32/24.95 ! [v2: fun_fu1217155507l_bool] : (v1 = v0 | ~ (cOMBC_1693257480l_bool(v2) =
% 178.32/24.95 v1) | ~ (cOMBC_1693257480l_bool(v2) = v0)) & ! [v0:
% 178.32/24.95 fun_fu425979586l_bool] : ! [v1: fun_fu425979586l_bool] : ! [v2:
% 178.32/24.95 fun_fu425979586l_bool] : (v1 = v0 | ~ (collect_fun_nat_bool(v2) = v1) | ~
% 178.32/24.95 (collect_fun_nat_bool(v2) = v0)) & ! [v0: fun_fu802393907l_bool] : ! [v1:
% 178.32/24.95 fun_fu802393907l_bool] : ! [v2: fun_fu802393907l_bool] : (v1 = v0 | ~
% 178.32/24.95 (cOMBC_1284144636l_bool(v2) = v1) | ~ (cOMBC_1284144636l_bool(v2) = v0)) &
% 178.32/24.95 ! [v0: fun_fu1430349052l_bool] : ! [v1: fun_fu1430349052l_bool] : ! [v2:
% 178.32/24.95 fun_fu1430349052l_bool] : (v1 = v0 | ~ (collec1974731493e_bool(v2) = v1) |
% 178.32/24.95 ~ (collec1974731493e_bool(v2) = v0)) & ! [v0: fun_fu1471507361l_bool] : !
% 178.32/24.95 [v1: fun_fu1471507361l_bool] : ! [v2: fun_fu1471507361l_bool] : (v1 = v0 | ~
% 178.32/24.95 (cOMBC_1732670874l_bool(v2) = v1) | ~ (cOMBC_1732670874l_bool(v2) = v0)) &
% 178.32/24.95 ! [v0: fun_fun_a_bool_bool] : ! [v1: fun_fun_a_bool_bool] : ! [v2:
% 178.32/24.95 fun_fun_a_bool_bool] : (v1 = v0 | ~ (collect_fun_a_bool(v2) = v1) | ~
% 178.32/24.95 (collect_fun_a_bool(v2) = v0)) & ! [v0: fun_fu418465139l_bool] : ! [v1:
% 178.32/24.95 fun_fu418465139l_bool] : ! [v2: fun_fu418465139l_bool] : (v1 = v0 | ~
% 178.32/24.95 (cOMBC_331553030l_bool(v2) = v1) | ~ (cOMBC_331553030l_bool(v2) = v0)) & !
% 178.32/24.95 [v0: fun_fu885608257l_bool] : ! [v1: fun_fu885608257l_bool] : ! [v2:
% 178.32/24.95 fun_fu885608257l_bool] : (v1 = v0 | ~ (collec707592106l_bool(v2) = v1) | ~
% 178.32/24.95 (collec707592106l_bool(v2) = v0)) & ! [v0: fun_fu1911931399l_bool] : !
% 178.32/24.95 [v1: fun_fu1911931399l_bool] : ! [v2: fun_fu1911931399l_bool] : (v1 = v0 | ~
% 178.32/24.95 (cOMBC_7971162l_bool(v2) = v1) | ~ (cOMBC_7971162l_bool(v2) = v0)) & !
% 178.32/24.95 [v0: fun_fu399576434l_bool] : ! [v1: fun_fu399576434l_bool] : ! [v2:
% 178.32/24.95 fun_fu399576434l_bool] : (v1 = v0 | ~ (collec1613912337l_bool(v2) = v1) |
% 178.32/24.95 ~ (collec1613912337l_bool(v2) = v0)) & ! [v0: fun_fu140186515l_bool] : !
% 178.32/24.95 [v1: fun_fu140186515l_bool] : ! [v2: fun_fu140186515l_bool] : (v1 = v0 | ~
% 178.32/24.95 (cOMBC_595898202l_bool(v2) = v1) | ~ (cOMBC_595898202l_bool(v2) = v0)) & !
% 178.32/24.95 [v0: fun_fu814369080l_bool] : ! [v1: fun_fu814369080l_bool] : ! [v2:
% 178.32/24.95 fun_fu814369080l_bool] : (v1 = v0 | ~ (collec1015864663l_bool(v2) = v1) |
% 178.32/24.95 ~ (collec1015864663l_bool(v2) = v0)) & ! [v0: fun_fun_a_bool_bool] : !
% 178.32/24.95 [v1: fun_fun_a_bool_bool] : ! [v2: fun_a_bool] : (v1 = v0 | ~ (p(v2) = v1) |
% 178.32/24.95 ~ (p(v2) = v0))
% 178.32/24.95
% 178.32/24.95 Further assumptions not needed in the proof:
% 178.32/24.95 --------------------------------------------
% 178.32/24.95 fact_0_assms_I1_J, fact_100_finite__insert, fact_101_finite__insert,
% 178.32/24.95 fact_102_finite__insert, fact_103_finite__subset, fact_104_finite__subset,
% 178.32/24.95 fact_105_finite__subset, fact_107_finite__subset, fact_108_finite__subset,
% 178.32/24.95 fact_109_rev__finite__subset, fact_10_finite__imageI,
% 178.32/24.95 fact_110_rev__finite__subset, fact_111_rev__finite__subset,
% 178.32/24.95 fact_113_rev__finite__subset, fact_114_rev__finite__subset, fact_115_Suc__leD,
% 178.32/24.95 fact_116_le__SucE, fact_117_le__SucI, fact_118_Suc__le__mono,
% 178.32/24.95 fact_119_le__Suc__eq, fact_11_finite__imageI, fact_120_not__less__eq__eq,
% 178.32/24.95 fact_121_Suc__n__not__le__n, fact_122_Suc__diff__diff, fact_123_diff__Suc__Suc,
% 178.32/24.95 fact_124_le__diff__iff, fact_125_Nat_Odiff__diff__eq, fact_126_eq__diff__iff,
% 178.32/24.95 fact_127_diff__diff__cancel, fact_128_diff__le__mono, fact_129_diff__le__mono2,
% 178.32/24.95 fact_12_finite__imageI, fact_130_diff__le__self, fact_131_finite__surj,
% 178.32/24.95 fact_132_finite__surj, fact_133_finite__surj, fact_134_finite__surj,
% 178.32/24.95 fact_135_finite__surj, fact_136_finite__surj, fact_137_finite__surj,
% 178.32/24.95 fact_138_finite__surj, fact_139_finite__surj, fact_13_finite__imageI,
% 178.32/24.95 fact_140_finite__surj, fact_141_finite__surj, fact_142_finite__surj,
% 178.32/24.95 fact_143_finite__surj, fact_144_finite__surj, fact_145_finite__surj,
% 178.32/24.95 fact_146_finite__surj, fact_147_finite__surj, fact_148_finite__surj,
% 178.32/24.95 fact_149_finite__surj, fact_14_finite__imageI, fact_150_finite__surj,
% 178.32/24.95 fact_151_finite__surj, fact_152_finite__surj, fact_153_finite__surj,
% 178.32/24.95 fact_154_finite__surj, fact_155_finite__subset__image,
% 178.32/24.95 fact_156_finite__subset__image, fact_157_finite__subset__image,
% 178.32/24.95 fact_158_finite__subset__image, fact_159_finite__subset__image,
% 178.32/24.95 fact_15_finite__imageI, fact_160_finite__subset__image,
% 178.32/24.95 fact_161_finite__subset__image, fact_162_finite__subset__image,
% 178.32/24.95 fact_163_finite__subset__image, fact_164_finite__subset__image,
% 178.32/24.95 fact_165_finite__subset__image, fact_166_finite__subset__image,
% 178.32/24.95 fact_167_finite__subset__image, fact_168_finite__subset__image,
% 178.32/24.95 fact_169_finite__subset__image, fact_16_finite__imageI,
% 178.32/24.95 fact_170_finite__subset__image, fact_171_finite__subset__image,
% 178.32/24.95 fact_172_finite__subset__image, fact_173_finite__subset__image,
% 178.32/24.95 fact_174_finite__subset__image, fact_175_finite__subset__image,
% 178.32/24.95 fact_176_finite__subset__image, fact_177_finite__subset__image,
% 178.32/24.95 fact_178_finite__subset__image, fact_179_finite__subset__image,
% 178.32/24.95 fact_17_finite__imageI, fact_180_finite__subset__image,
% 178.32/24.95 fact_181_finite__subset__image, fact_182_lift__Suc__mono__le,
% 178.32/24.95 fact_183_lift__Suc__mono__le, fact_184_lift__Suc__mono__le,
% 178.32/24.95 fact_185_lift__Suc__mono__le, fact_186_lift__Suc__mono__le,
% 178.32/24.95 fact_187_pigeonhole__infinite, fact_188_pigeonhole__infinite,
% 178.32/24.95 fact_189_pigeonhole__infinite, fact_18_finite__imageI,
% 178.32/24.95 fact_190_pigeonhole__infinite, fact_191_pigeonhole__infinite,
% 178.32/24.95 fact_192_pigeonhole__infinite, fact_193_pigeonhole__infinite,
% 178.32/24.95 fact_194_pigeonhole__infinite, fact_195_pigeonhole__infinite,
% 178.32/24.95 fact_196_pigeonhole__infinite, fact_197_pigeonhole__infinite,
% 178.32/24.95 fact_198_pigeonhole__infinite, fact_199_pigeonhole__infinite,
% 178.32/24.95 fact_19_finite__imageI, fact_1_finite__Collect__subsets,
% 178.32/24.95 fact_200_pigeonhole__infinite, fact_201_pigeonhole__infinite,
% 178.32/24.95 fact_202_pigeonhole__infinite, fact_203_pigeonhole__infinite,
% 178.32/24.95 fact_204_pigeonhole__infinite, fact_205_pigeonhole__infinite,
% 178.32/24.95 fact_206_pigeonhole__infinite, fact_207_pigeonhole__infinite,
% 178.32/24.95 fact_208_pigeonhole__infinite, fact_209_pigeonhole__infinite,
% 178.32/24.95 fact_20_finite__imageI, fact_210_pigeonhole__infinite, fact_211_image__eqI,
% 178.32/24.95 fact_212_image__eqI, fact_213_image__eqI, fact_214_image__eqI,
% 178.32/24.95 fact_216_equalityI, fact_217_equalityI, fact_218_equalityI, fact_219_subsetD,
% 178.32/24.95 fact_21_finite__imageI, fact_220_subsetD, fact_221_subsetD, fact_222_insertCI,
% 178.32/24.95 fact_223_insertCI, fact_224_insertCI, fact_225_insertE, fact_226_insertE,
% 178.32/24.95 fact_227_insertE, fact_228_zero__induct__lemma, fact_229_Suc__le__D,
% 178.32/24.95 fact_230_insertI1, fact_231_insertI1, fact_232_insertI1, fact_233_insert__compr,
% 178.32/24.95 fact_234_insert__compr, fact_235_insert__compr, fact_236_insert__compr,
% 178.32/24.95 fact_237_insert__compr, fact_238_insert__compr, fact_239_insert__Collect,
% 178.32/24.95 fact_23_finite_OinsertI, fact_240_insert__Collect, fact_241_insert__Collect,
% 178.32/24.95 fact_242_insert__Collect, fact_243_insert__Collect, fact_244_insert__Collect,
% 178.32/24.95 fact_245_insert__absorb2, fact_246_insert__absorb2, fact_247_insert__absorb2,
% 178.32/24.95 fact_248_insert__commute, fact_249_insert__commute, fact_24_finite_OinsertI,
% 178.32/24.95 fact_250_insert__commute, fact_251_insert__iff, fact_252_insert__iff,
% 178.32/24.95 fact_253_insert__iff, fact_254_insert__code, fact_255_insert__code,
% 178.32/24.95 fact_256_insert__code, fact_257_insert__ident, fact_258_insert__ident,
% 178.32/24.95 fact_259_insert__ident, fact_25_finite_OinsertI, fact_260_insertI2,
% 178.32/24.95 fact_261_insertI2, fact_262_insertI2, fact_263_insert__absorb,
% 178.32/24.95 fact_265_insert__absorb, fact_266_subset__refl, fact_267_subset__refl,
% 178.32/24.95 fact_268_subset__refl, fact_269_set__eq__subset, fact_26_finite_OinsertI,
% 178.32/24.95 fact_270_set__eq__subset, fact_271_set__eq__subset, fact_272_equalityD1,
% 178.32/24.95 fact_273_equalityD1, fact_274_equalityD1, fact_275_equalityD2,
% 178.32/24.95 fact_276_equalityD2, fact_277_equalityD2, fact_278_in__mono, fact_279_in__mono,
% 178.32/24.95 fact_27_finite_OinsertI, fact_280_in__mono, fact_281_set__rev__mp,
% 178.32/24.95 fact_282_set__rev__mp, fact_283_set__rev__mp, fact_284_set__mp,
% 178.32/24.95 fact_285_set__mp, fact_286_set__mp, fact_287_mem__def, fact_288_mem__def,
% 178.32/24.95 fact_289_mem__def, fact_28_finite_OinsertI, fact_290_Collect__def,
% 178.32/24.95 fact_291_Collect__def, fact_292_Collect__def, fact_293_Collect__def,
% 178.32/24.95 fact_294_Collect__def, fact_295_Collect__def, fact_296_subset__trans,
% 178.32/24.95 fact_297_subset__trans, fact_298_subset__trans, fact_299_equalityE,
% 178.32/24.95 fact_29_card__image__le, fact_2_finite__Collect__subsets, fact_300_equalityE,
% 178.32/24.95 fact_301_equalityE, fact_302_image__iff, fact_303_imageI, fact_304_imageI,
% 178.32/24.95 fact_305_imageI, fact_306_imageI, fact_307_imageI, fact_308_rev__image__eqI,
% 178.32/24.95 fact_309_rev__image__eqI, fact_30_card__image__le, fact_310_rev__image__eqI,
% 178.32/24.95 fact_311_rev__image__eqI, fact_312_rev__image__eqI, fact_313_insert__compr__raw,
% 178.32/24.95 fact_314_insert__compr__raw, fact_315_insert__compr__raw,
% 178.32/24.95 fact_316_insert__compr__raw, fact_317_insert__compr__raw,
% 178.32/24.95 fact_318_insert__compr__raw, fact_319_subset__insertI, fact_31_card__image__le,
% 178.32/24.95 fact_320_subset__insertI, fact_321_subset__insertI, fact_322_insert__subset,
% 178.32/24.95 fact_323_insert__subset, fact_325_subset__insert, fact_326_subset__insert,
% 178.32/24.95 fact_327_subset__insert, fact_328_subset__insertI2, fact_329_subset__insertI2,
% 178.32/24.95 fact_32_card__image__le, fact_330_subset__insertI2, fact_331_insert__mono,
% 178.32/24.95 fact_332_insert__mono, fact_333_insert__mono, fact_334_image__insert,
% 178.32/24.95 fact_335_image__insert, fact_336_image__insert, fact_337_image__insert,
% 178.32/24.95 fact_338_insert__image, fact_339_insert__image, fact_33_card__image__le,
% 178.32/24.95 fact_340_insert__image, fact_341_insert__image, fact_342_insert__image,
% 178.32/24.95 fact_343_insert__image, fact_344_subset__image__iff,
% 178.32/24.95 fact_345_subset__image__iff, fact_346_subset__image__iff,
% 178.32/24.95 fact_347_subset__image__iff, fact_348_image__mono, fact_349_image__mono,
% 178.32/24.95 fact_34_card__image__le, fact_350_image__mono, fact_351_image__mono,
% 178.32/24.95 fact_352_imageE, fact_353_imageE, fact_354_imageE, fact_355_imageE,
% 178.32/24.95 fact_356_imageE, fact_357_subsetI, fact_358_subsetI, fact_35_card__image__le,
% 178.32/24.95 fact_360_image__subsetI, fact_361_image__subsetI, fact_362_image__subsetI,
% 178.32/24.95 fact_363_image__subsetI, fact_364_image__subsetI, fact_365_image__subsetI,
% 178.32/24.95 fact_366_image__subsetI, fact_367_order__refl, fact_368_order__refl,
% 178.32/24.95 fact_369_order__refl, fact_36_card__image__le, fact_370_order__refl,
% 178.32/24.95 fact_371_order__refl, fact_372_finite__nat__set__iff__bounded__le,
% 178.32/24.95 fact_373_assms_I3_J, fact_374_le__fun__def, fact_375_le__fun__def,
% 178.32/24.95 fact_376_le__fun__def, fact_377_le__funD, fact_378_le__funD, fact_379_le__funD,
% 178.32/24.95 fact_37_card__image__le, fact_380_le__funE, fact_381_le__funE,
% 178.32/24.95 fact_382_le__funE, fact_383_emptyE, fact_384_emptyE, fact_385_emptyE,
% 178.32/24.95 fact_386_finite_OemptyI, fact_387_finite_OemptyI, fact_388_finite_OemptyI,
% 178.32/24.95 fact_389_finite_OemptyI, fact_38_card__image__le, fact_390_finite_OemptyI,
% 178.32/24.95 fact_391_finite_OemptyI, fact_392_empty__subsetI, fact_393_empty__subsetI,
% 178.32/24.95 fact_394_empty__subsetI, fact_395_equals0D, fact_396_equals0D,
% 178.32/24.95 fact_397_equals0D, fact_398_Collect__empty__eq, fact_399_Collect__empty__eq,
% 178.32/24.95 fact_39_card__image__le, fact_3_finite__Collect__subsets,
% 178.32/24.95 fact_400_Collect__empty__eq, fact_401_Collect__empty__eq,
% 178.32/24.95 fact_402_Collect__empty__eq, fact_403_Collect__empty__eq, fact_404_empty__iff,
% 178.32/24.95 fact_405_empty__iff, fact_406_empty__iff, fact_407_empty__Collect__eq,
% 178.32/24.95 fact_408_empty__Collect__eq, fact_409_empty__Collect__eq,
% 178.32/24.95 fact_40_card__image__le, fact_410_empty__Collect__eq,
% 178.32/24.95 fact_411_empty__Collect__eq, fact_412_empty__Collect__eq, fact_413_ex__in__conv,
% 178.32/24.95 fact_414_ex__in__conv, fact_415_ex__in__conv, fact_416_all__not__in__conv,
% 178.32/24.95 fact_417_all__not__in__conv, fact_418_all__not__in__conv, fact_419_empty__def,
% 178.32/24.95 fact_41_card__image__le, fact_420_empty__def, fact_421_empty__def,
% 178.32/24.95 fact_422_empty__def, fact_423_empty__def, fact_424_empty__def,
% 178.32/24.95 fact_425_bot__fun__def, fact_426_bot__fun__def, fact_427_bot__fun__def,
% 178.32/24.95 fact_428_bot__apply, fact_429_bot__apply, fact_42_card__mono,
% 178.32/24.95 fact_430_bot__apply, fact_431_le__bot, fact_432_le__bot, fact_433_le__bot,
% 178.32/24.95 fact_434_le__bot, fact_435_le__bot, fact_436_bot__unique, fact_437_bot__unique,
% 178.32/24.95 fact_438_bot__unique, fact_439_bot__unique, fact_43_card__mono,
% 178.32/24.95 fact_440_bot__unique, fact_441_bot__least, fact_442_bot__least,
% 178.32/24.95 fact_443_bot__least, fact_444_bot__least, fact_445_bot__least,
% 178.32/24.95 fact_446_singleton__inject, fact_447_singleton__inject,
% 178.32/24.95 fact_448_singleton__inject, fact_449_singletonE, fact_44_card__mono,
% 178.32/24.95 fact_450_singletonE, fact_451_singletonE, fact_452_doubleton__eq__iff,
% 178.32/24.95 fact_453_doubleton__eq__iff, fact_454_doubleton__eq__iff,
% 178.32/24.95 fact_455_singleton__iff, fact_456_singleton__iff, fact_457_singleton__iff,
% 178.32/24.95 fact_458_insert__not__empty, fact_459_insert__not__empty, fact_45_card__mono,
% 178.32/24.95 fact_460_insert__not__empty, fact_461_empty__not__insert,
% 178.32/24.95 fact_462_empty__not__insert, fact_463_empty__not__insert,
% 178.32/24.95 fact_464_subset__empty, fact_465_subset__empty, fact_466_subset__empty,
% 178.32/24.95 fact_467_image__is__empty, fact_468_image__empty, fact_469_empty__is__image,
% 178.32/24.95 fact_46_card__mono, fact_470_Collect__conv__if, fact_471_Collect__conv__if,
% 178.32/24.95 fact_472_Collect__conv__if, fact_473_Collect__conv__if,
% 178.32/24.95 fact_474_Collect__conv__if, fact_475_Collect__conv__if,
% 178.32/24.95 fact_476_Collect__conv__if2, fact_477_Collect__conv__if2,
% 178.32/24.95 fact_478_Collect__conv__if2, fact_479_Collect__conv__if2, fact_47_card__mono,
% 178.32/24.95 fact_480_Collect__conv__if2, fact_481_Collect__conv__if2,
% 178.32/24.95 fact_482_singleton__conv, fact_483_singleton__conv, fact_484_singleton__conv,
% 178.32/24.95 fact_485_singleton__conv, fact_486_singleton__conv, fact_487_singleton__conv,
% 178.32/24.95 fact_488_singleton__conv2, fact_489_singleton__conv2, fact_48_card__seteq,
% 178.32/24.95 fact_490_singleton__conv2, fact_491_singleton__conv2, fact_492_singleton__conv2,
% 178.32/24.95 fact_493_singleton__conv2, fact_494_subset__singletonD,
% 178.32/24.95 fact_495_subset__singletonD, fact_496_subset__singletonD,
% 178.32/24.95 fact_497_image__constant, fact_498_image__constant__conv,
% 178.32/24.95 fact_499_linorder__le__cases, fact_49_card__seteq,
% 178.32/24.95 fact_4_finite__Collect__subsets, fact_500_xt1_I6_J, fact_501_xt1_I6_J,
% 178.32/24.95 fact_502_xt1_I6_J, fact_503_xt1_I6_J, fact_504_xt1_I6_J, fact_505_xt1_I5_J,
% 178.32/24.95 fact_506_xt1_I5_J, fact_507_xt1_I5_J, fact_508_xt1_I5_J, fact_509_xt1_I5_J,
% 178.32/24.95 fact_50_card__seteq, fact_510_order__trans, fact_511_order__trans,
% 178.32/24.95 fact_512_order__trans, fact_513_order__trans, fact_514_order__trans,
% 178.32/24.95 fact_515_order__antisym, fact_516_order__antisym, fact_517_order__antisym,
% 178.32/24.95 fact_518_order__antisym, fact_519_order__antisym, fact_51_card__seteq,
% 178.32/24.95 fact_520_xt1_I4_J, fact_521_xt1_I4_J, fact_522_xt1_I4_J, fact_523_xt1_I4_J,
% 178.32/24.95 fact_524_xt1_I4_J, fact_525_ord__le__eq__trans, fact_526_ord__le__eq__trans,
% 178.32/24.95 fact_527_ord__le__eq__trans, fact_528_ord__le__eq__trans,
% 178.32/24.95 fact_529_ord__le__eq__trans, fact_52_card__seteq, fact_530_xt1_I3_J,
% 178.32/24.95 fact_531_xt1_I3_J, fact_532_xt1_I3_J, fact_533_xt1_I3_J, fact_534_xt1_I3_J,
% 178.32/24.95 fact_535_ord__eq__le__trans, fact_536_ord__eq__le__trans,
% 178.32/24.95 fact_537_ord__eq__le__trans, fact_538_ord__eq__le__trans,
% 178.32/24.95 fact_539_ord__eq__le__trans, fact_53_card__seteq, fact_540_order__antisym__conv,
% 178.32/24.95 fact_541_order__antisym__conv, fact_542_order__antisym__conv,
% 178.32/24.95 fact_543_order__antisym__conv, fact_544_order__antisym__conv,
% 178.32/24.95 fact_545_order__eq__refl, fact_546_order__eq__refl, fact_547_order__eq__refl,
% 178.32/24.95 fact_548_order__eq__refl, fact_549_order__eq__refl, fact_54_card__insert__le,
% 178.32/24.95 fact_550_order__eq__iff, fact_551_order__eq__iff, fact_552_order__eq__iff,
% 178.32/24.95 fact_553_order__eq__iff, fact_554_order__eq__iff, fact_555_linorder__linear,
% 178.32/24.95 fact_556_finite__subset__induct, fact_557_finite__subset__induct,
% 178.32/24.95 fact_558_finite__subset__induct, fact_559_finite__subset__induct,
% 178.32/24.95 fact_55_card__insert__le, fact_560_finite__subset__induct,
% 178.32/24.95 fact_561_finite__subset__induct, fact_562_assms_I2_J, fact_563_finite__induct,
% 178.32/24.95 fact_564_finite__induct, fact_565_finite__induct, fact_566_finite__less__ub,
% 178.32/24.95 fact_567_assms_I4_J, fact_568_diff__Suc__eq__diff__pred, fact_569_diff__Suc__1,
% 178.32/24.95 fact_56_card__insert__le, fact_570_less__eq__nat_Osimps_I2_J,
% 178.32/24.95 fact_571_add__Suc__right, fact_572_add__Suc, fact_573_add__Suc__shift,
% 178.32/24.95 fact_574_nat__add__right__cancel, fact_575_nat__add__left__cancel,
% 178.32/24.95 fact_576_nat__add__assoc, fact_577_nat__add__left__commute,
% 178.32/24.95 fact_578_nat__add__commute, fact_579_diff__add__inverse2,
% 178.32/24.95 fact_57_card__insert__le, fact_580_diff__add__inverse,
% 178.32/24.95 fact_581_diff__diff__left, fact_582_diff__cancel, fact_583_diff__cancel2,
% 178.32/24.95 fact_584_le__add2, fact_585_le__add1, fact_586_le__iff__add,
% 178.32/24.95 fact_587_nat__add__left__cancel__le, fact_588_trans__le__add1,
% 178.32/24.95 fact_589_trans__le__add2, fact_58_card__insert__le, fact_590_add__le__mono1,
% 178.32/24.95 fact_591_add__le__mono, fact_592_add__leD2, fact_593_add__leD1,
% 178.32/24.95 fact_594_add__leE, fact_595_diff__add__assoc2, fact_596_add__diff__assoc2,
% 178.32/24.95 fact_597_diff__add__assoc, fact_598_le__imp__diff__is__add,
% 178.32/24.95 fact_599_le__add__diff__inverse2, fact_59_card__insert__le,
% 178.32/24.95 fact_5_finite__Collect__subsets, fact_600_le__diff__conv2,
% 178.32/24.95 fact_601_add__diff__assoc, fact_602_le__add__diff__inverse,
% 178.32/24.95 fact_603_le__add__diff, fact_604_le__diff__conv, fact_605_diff__diff__right,
% 178.32/24.95 fact_606_Suc__eq__plus1, fact_607_Suc__eq__plus1__left,
% 178.32/24.95 fact_608_diff__Suc__diff__eq2, fact_609_diff__Suc__diff__eq1,
% 178.32/24.95 fact_60_card__insert__if, fact_610_termination__basic__simps_I3_J,
% 178.32/24.95 fact_611_termination__basic__simps_I4_J, fact_612_lessI, fact_613_Suc__mono,
% 178.32/24.95 fact_614_finite__Collect__less__nat, fact_615_termination__basic__simps_I1_J,
% 178.32/24.95 fact_616_termination__basic__simps_I2_J, fact_617_add__lessD1,
% 178.32/24.95 fact_618_less__add__eq__less, fact_619_add__less__mono,
% 178.32/24.95 fact_61_card__insert__if, fact_620_add__less__mono1, fact_621_trans__less__add2,
% 178.32/24.95 fact_622_trans__less__add1, fact_623_nat__add__left__cancel__less,
% 178.32/24.95 fact_624_not__add__less2, fact_625_not__add__less1, fact_626_Suc__less__SucD,
% 178.32/24.95 fact_627_Suc__lessD, fact_628_less__SucE, fact_629_less__trans__Suc,
% 178.32/24.95 fact_62_card__insert__if, fact_630_Suc__lessI, fact_631_less__SucI,
% 178.32/24.95 fact_632_less__antisym, fact_633_not__less__less__Suc__eq,
% 178.32/24.95 fact_634_Suc__less__eq, fact_635_less__Suc__eq, fact_636_not__less__eq,
% 178.32/24.95 fact_637_less__or__eq__imp__le, fact_638_le__neq__implies__less,
% 178.32/24.95 fact_639_less__imp__le__nat, fact_63_card__insert__if,
% 178.32/24.95 fact_640_le__eq__less__or__eq, fact_641_nat__less__le,
% 178.32/24.95 fact_642_diff__less__mono2, fact_643_less__imp__diff__less,
% 178.32/24.95 fact_644_termination__basic__simps_I5_J, fact_645_less__not__refl,
% 178.32/24.95 fact_646_nat__neq__iff, fact_647_linorder__neqE__nat,
% 178.32/24.95 fact_648_less__irrefl__nat, fact_649_less__not__refl2,
% 178.32/24.95 fact_650_less__not__refl3, fact_651_nat__less__cases,
% 178.32/24.95 fact_652_finite__nat__set__iff__bounded, fact_653_card__Collect__less__nat,
% 178.32/24.95 fact_654_finite__M__bounded__by__nat, fact_655_less__add__Suc1,
% 178.32/24.95 fact_656_less__add__Suc2, fact_657_less__iff__Suc__add,
% 178.32/24.95 fact_658_less__eq__Suc__le, fact_659_less__Suc__eq__le,
% 178.32/24.95 fact_65_card__insert__if, fact_660_Suc__le__eq, fact_661_le__imp__less__Suc,
% 178.32/24.95 fact_662_Suc__leI, fact_663_le__less__Suc__eq, fact_664_Suc__le__lessD,
% 178.32/24.95 fact_665_diff__less__Suc, fact_666_add__diff__inverse,
% 178.32/24.95 fact_667_less__diff__conv, fact_668_diff__less__mono, fact_669_less__diff__iff,
% 178.32/24.95 fact_66_card__insert__disjoint, fact_670_less__eq__Suc__le__raw,
% 178.32/24.95 fact_671_mono__nat__linear__lb, fact_672_inc__induct,
% 178.32/24.95 fact_673_less__imp__Suc__add, fact_674_bounded__nat__set__is__finite,
% 178.32/24.95 fact_675_less__mono__imp__le__mono, fact_676_Suc__lessE, fact_677_lessE,
% 178.32/24.95 fact_678_less__zeroE, fact_679_le0, fact_67_card__insert__disjoint,
% 178.32/24.95 fact_680_zero__less__Suc, fact_681_add__is__1, fact_682_one__is__add,
% 178.32/24.95 fact_683_diff__add__0, fact_684_diff__is__0__eq_H, fact_685_diff__is__0__eq,
% 178.32/24.95 fact_686_One__nat__def, fact_687_diffs0__imp__equal, fact_688_diff__self__eq__0,
% 178.32/24.95 fact_689_minus__nat_Odiff__0, fact_68_card__insert__disjoint,
% 178.32/24.95 fact_690_diff__0__eq__0, fact_691_Suc__neq__Zero, fact_692_Zero__neq__Suc,
% 178.32/24.95 fact_693_nat_Osimps_I3_J, fact_694_Suc__not__Zero, fact_695_nat_Osimps_I2_J,
% 178.32/24.95 fact_696_Zero__not__Suc, fact_697_bot__nat__def, fact_698_le__0__eq,
% 178.32/24.95 fact_699_less__eq__nat_Osimps_I1_J, fact_69_card__insert__disjoint,
% 178.32/24.95 fact_6_finite__Collect__subsets, fact_70_card__insert__disjoint,
% 178.32/24.95 fact_71_card__insert__disjoint, fact_72_finite__Collect__conjI,
% 178.32/24.95 fact_73_finite__Collect__conjI, fact_74_finite__Collect__conjI,
% 178.32/24.95 fact_75_finite__Collect__conjI, fact_76_finite__Collect__conjI,
% 178.32/24.95 fact_77_finite__Collect__conjI, fact_78_Suc__diff__le,
% 178.32/24.95 fact_79_finite__Collect__le__nat, fact_7_finite__imageI,
% 178.32/24.95 fact_80_card__Collect__le__nat, fact_81_Suc__inject, fact_82_nat_Oinject,
% 178.32/24.95 fact_83_Suc__n__not__n, fact_84_n__not__Suc__n, fact_85_le__antisym,
% 178.32/24.95 fact_86_le__trans, fact_87_eq__imp__le, fact_88_nat__le__linear,
% 178.32/24.95 fact_89_le__refl, fact_8_finite__imageI, fact_90_diff__commute,
% 178.32/24.95 fact_91_finite__Collect__disjI, fact_92_finite__Collect__disjI,
% 178.32/24.95 fact_93_finite__Collect__disjI, fact_94_finite__Collect__disjI,
% 178.32/24.95 fact_95_finite__Collect__disjI, fact_96_finite__Collect__disjI,
% 178.32/24.95 fact_97_finite__insert, fact_98_finite__insert, fact_99_finite__insert,
% 178.32/24.95 fact_9_finite__imageI,
% 178.32/24.95 help_COMBB_1_1_COMBB_000t__a_000tc__fun_It__a_Mtc__HOL__Obool_J_000t__a_U,
% 178.32/24.95 help_COMBB_1_1_COMBB_000t__a_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__Com__Opna,
% 178.32/24.95 help_COMBB_1_1_COMBB_000t__a_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__Nat__Onat,
% 178.32/24.95 help_COMBB_1_1_COMBB_000tc__Com__Opname_000tc__fun_Itc__Com__Opname_Mtc__HOL__Ob,
% 178.32/24.95 help_COMBB_1_1_COMBB_000tc__Com__Opname_000tc__fun_Itc__Com__Opname_Mtc__HOL__Ob_037,
% 178.32/24.95 help_COMBB_1_1_COMBB_000tc__Com__Opname_000tc__fun_Itc__Com__Opname_Mtc__HOL__Ob_039,
% 178.32/24.95 help_COMBB_1_1_COMBB_000tc__Com__Opname_000tc__fun_Itc__Com__Opname_Mtc__HOL__Ob_042,
% 178.32/24.95 help_COMBB_1_1_COMBB_000tc__Com__Opname_000tc__fun_Itc__Com__Opname_Mtc__HOL__Ob_046,
% 178.32/24.95 help_COMBB_1_1_COMBB_000tc__Com__Opname_000tc__fun_Itc__Com__Opname_Mtc__HOL__Ob_048,
% 178.32/24.95 help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000t__a_U,
% 178.32/24.95 help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__Com__Opname_U,
% 178.32/24.95 help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__Nat__Onat_U,
% 178.32/24.95 help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__fun_It__a_Mtc__H,
% 178.32/24.95 help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__fun_Itc__Com__Op,
% 178.32/24.95 help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__fun_Itc__Nat__On,
% 178.32/24.95 help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo,
% 178.32/24.95 help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_035,
% 178.32/24.95 help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_038,
% 178.32/24.95 help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_041,
% 178.32/24.95 help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_044,
% 178.32/24.95 help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_047,
% 178.32/24.95 help_COMBB_1_1_COMBB_000tc__Nat__Onat_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_,
% 178.32/24.95 help_COMBB_1_1_COMBB_000tc__Nat__Onat_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool__034,
% 178.32/24.95 help_COMBB_1_1_COMBB_000tc__Nat__Onat_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool__036,
% 178.32/24.95 help_COMBB_1_1_COMBB_000tc__Nat__Onat_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool__040,
% 178.32/24.95 help_COMBB_1_1_COMBB_000tc__Nat__Onat_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool__043,
% 178.32/24.95 help_COMBB_1_1_COMBB_000tc__Nat__Onat_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool__045,
% 178.32/24.95 help_COMBB_1_1_COMBB_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__fun_Itc__fun_It__,
% 178.32/24.95 help_COMBB_1_1_COMBB_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__fun_Itc__fun_It___049,
% 178.32/24.95 help_COMBB_1_1_COMBB_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__fun_Itc__fun_It___050,
% 178.32/24.95 help_COMBB_1_1_COMBB_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__fun_It,
% 178.32/24.95 help_COMBB_1_1_COMBB_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__fun_It_054,
% 178.32/24.95 help_COMBB_1_1_COMBB_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__fun_It_056,
% 178.32/24.95 help_COMBB_1_1_COMBB_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__fun_Itc_,
% 178.32/24.95 help_COMBB_1_1_COMBB_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__fun_Itc__051,
% 178.32/24.95 help_COMBB_1_1_COMBB_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__fun_Itc__053,
% 178.32/24.95 help_COMBC_1_1_COMBC_000t__a_000t__a_000tc__HOL__Obool_U,
% 178.32/24.95 help_COMBC_1_1_COMBC_000t__a_000tc__Com__Opname_000tc__HOL__Obool_U,
% 178.32/24.95 help_COMBC_1_1_COMBC_000t__a_000tc__Nat__Onat_000tc__HOL__Obool_U,
% 178.32/24.95 help_COMBC_1_1_COMBC_000t__a_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__HOL__Oboo,
% 178.32/24.95 help_COMBC_1_1_COMBC_000t__a_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc,
% 178.32/24.95 help_COMBC_1_1_COMBC_000t__a_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__,
% 178.32/24.95 help_COMBC_1_1_COMBC_000tc__Com__Opname_000t__a_000tc__HOL__Obool_U,
% 178.32/24.95 help_COMBC_1_1_COMBC_000tc__Com__Opname_000tc__Com__Opname_000tc__HOL__Obool_U,
% 178.32/24.95 help_COMBC_1_1_COMBC_000tc__Com__Opname_000tc__Nat__Onat_000tc__HOL__Obool_U,
% 178.32/24.95 help_COMBC_1_1_COMBC_000tc__Com__Opname_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc,
% 178.32/24.95 help_COMBC_1_1_COMBC_000tc__Com__Opname_000tc__fun_Itc__Com__Opname_Mtc__HOL__Ob,
% 178.32/24.95 help_COMBC_1_1_COMBC_000tc__Com__Opname_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Oboo,
% 178.32/24.95 help_COMBC_1_1_COMBC_000tc__Nat__Onat_000t__a_000tc__HOL__Obool_U,
% 178.32/24.95 help_COMBC_1_1_COMBC_000tc__Nat__Onat_000tc__Com__Opname_000tc__HOL__Obool_U,
% 178.32/24.95 help_COMBC_1_1_COMBC_000tc__Nat__Onat_000tc__Nat__Onat_000tc__HOL__Obool_U,
% 178.32/24.95 help_COMBC_1_1_COMBC_000tc__Nat__Onat_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__,
% 178.32/24.95 help_COMBC_1_1_COMBC_000tc__Nat__Onat_000tc__fun_Itc__Com__Opname_Mtc__HOL__Oboo,
% 178.32/24.95 help_COMBC_1_1_COMBC_000tc__Nat__Onat_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_,
% 178.32/24.95 help_COMBC_1_1_COMBC_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__Com__Opname_000tc,
% 178.32/24.95 help_COMBC_1_1_COMBC_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__Nat__Onat_000tc__,
% 178.32/24.95 help_COMBC_1_1_COMBC_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__fun_It__a_Mtc__HO,
% 178.32/24.95 help_COMBC_1_1_COMBC_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__fun_Itc__fun_It__,
% 178.32/24.95 help_COMBC_1_1_COMBC_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__Com__O,
% 178.32/24.95 help_COMBC_1_1_COMBC_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__Nat__O,
% 178.32/24.95 help_COMBC_1_1_COMBC_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__fun_It,
% 178.32/24.95 help_COMBC_1_1_COMBC_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__fun_It_055,
% 178.32/24.95 help_COMBC_1_1_COMBC_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__Com__Opn,
% 178.32/24.95 help_COMBC_1_1_COMBC_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__Nat__Ona,
% 178.32/24.95 help_COMBC_1_1_COMBC_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__fun_Itc_,
% 178.32/24.95 help_COMBC_1_1_COMBC_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__fun_Itc__052,
% 178.32/24.95 help_COMBC_1_1_COMBC_000tc__fun_Itc__fun_It__a_Mtc__HOL__Obool_J_Mtc__HOL__Obool,
% 178.32/24.95 help_COMBC_1_1_COMBC_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_Mtc_,
% 178.32/24.95 help_COMBC_1_1_COMBC_000tc__fun_Itc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_Mtc__H,
% 178.32/24.95 help_COMBK_1_1_COMBK_000t__a_000tc__Com__Opname_U,
% 178.32/24.95 help_COMBK_1_1_COMBK_000tc__HOL__Obool_000t__a_U,
% 178.32/24.95 help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__Com__Opname_U,
% 178.32/24.95 help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__Nat__Onat_U,
% 178.32/24.95 help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__fun_It__a_Mtc__HOL__Obool_J_U,
% 178.32/24.95 help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obo,
% 178.32/24.95 help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool,
% 178.32/24.95 help_COMBS_1_1_COMBS_000t__a_000tc__HOL__Obool_000tc__HOL__Obool_U,
% 178.32/24.95 help_COMBS_1_1_COMBS_000tc__Com__Opname_000tc__HOL__Obool_000tc__HOL__Obool_U,
% 178.32/24.95 help_COMBS_1_1_COMBS_000tc__Nat__Onat_000tc__HOL__Obool_000tc__HOL__Obool_U,
% 178.32/24.95 help_COMBS_1_1_COMBS_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__HOL__Obool_000tc_,
% 178.32/24.95 help_COMBS_1_1_COMBS_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__HOL__O,
% 178.32/24.95 help_COMBS_1_1_COMBS_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__HOL__Obo,
% 178.32/24.95 help_fFalse_1_1_T, help_fFalse_1_1_U, help_fNot_1_1_U, help_fNot_2_1_U,
% 178.32/24.95 help_fconj_1_1_U, help_fconj_2_1_U, help_fconj_3_1_U, help_fdisj_1_1_U,
% 178.32/24.95 help_fdisj_2_1_U, help_fdisj_3_1_U, help_fequal_1_1_fequal_000t__a_T,
% 178.32/24.95 help_fequal_1_1_fequal_000tc__Com__Opname_T,
% 178.32/24.95 help_fequal_1_1_fequal_000tc__Nat__Onat_T,
% 178.32/24.95 help_fequal_1_1_fequal_000tc__fun_It__a_Mtc__HOL__Obool_J_T,
% 178.32/24.95 help_fequal_1_1_fequal_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_T,
% 178.32/24.95 help_fequal_1_1_fequal_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_T,
% 178.32/24.95 help_fequal_2_1_fequal_000t__a_T, help_fequal_2_1_fequal_000tc__Com__Opname_T,
% 178.32/24.95 help_fequal_2_1_fequal_000tc__Nat__Onat_T,
% 178.32/24.95 help_fequal_2_1_fequal_000tc__fun_It__a_Mtc__HOL__Obool_J_T,
% 178.32/24.95 help_fequal_2_1_fequal_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_T,
% 178.32/24.95 help_fequal_2_1_fequal_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_T,
% 178.32/24.95 help_fimplies_1_1_U, help_fimplies_2_1_U, help_fimplies_3_1_U
% 178.32/24.95
% 178.32/24.95 Those formulas are unsatisfiable:
% 178.32/24.95 ---------------------------------
% 178.32/24.95
% 178.32/24.95 Begin of proof
% 178.32/24.95 |
% 178.32/24.96 | ALPHA: (fact_22_finite__imageI) implies:
% 178.32/24.96 | (1) ! [v0: fun_pname_a] : ! [v1: fun_pname_bool] : ! [v2: fun_a_bool] :
% 178.32/24.96 | ( ~ (image_pname_a(v0, v1) = v2) | ~ fun_pname_bool(v1) | ~
% 178.32/24.96 | fun_pname_a(v0) | ? [v3: bool] : ? [v4: bool] :
% 178.32/24.96 | ((hAPP_f1664156314l_bool(finite_finite_pname, v1) = v3 & bool(v3) &
% 178.32/24.96 | ~ hBOOL(v3)) | (hAPP_fun_a_bool_bool(finite_finite_a, v2) = v4 &
% 178.32/24.96 | bool(v4) & hBOOL(v4))))
% 178.32/24.96 |
% 178.32/24.96 | ALPHA: (fact_64_card__insert__if) implies:
% 178.32/24.96 | (2) ! [v0: pname] : ! [v1: fun_pname_bool] : ! [v2:
% 178.32/24.96 | fun_fu1430349052l_bool] : ! [v3: bool] : ( ~
% 178.32/24.96 | (hAPP_p338031245l_bool(member_pname, v0) = v2) | ~
% 178.32/24.96 | (hAPP_f1664156314l_bool(v2, v1) = v3) | ~ fun_pname_bool(v1) | ~
% 178.32/24.96 | pname(v0) | ? [v4: bool] : ? [v5: fun_pname_bool] : ? [v6: nat] :
% 178.32/24.96 | ? [v7: nat] : ? [v8: nat] :
% 178.32/24.96 | ((hAPP_f1664156314l_bool(finite_finite_pname, v1) = v4 & bool(v4) &
% 178.32/24.96 | ~ hBOOL(v4)) | (( ~ hBOOL(v3) | (v7 = v6 &
% 178.32/24.96 | hAPP_f921600141ol_nat(finite_card_pname, v5) = v6 &
% 178.32/24.96 | hAPP_f921600141ol_nat(finite_card_pname, v1) = v6 &
% 178.32/24.96 | insert_pname(v0, v1) = v5 & fun_pname_bool(v5) & nat(v6))) &
% 178.32/24.96 | (hBOOL(v3) | (v8 = v6 & hAPP_nat_nat(suc, v7) = v6 &
% 178.32/24.96 | hAPP_f921600141ol_nat(finite_card_pname, v5) = v6 &
% 178.32/24.96 | hAPP_f921600141ol_nat(finite_card_pname, v1) = v7 &
% 178.32/24.96 | insert_pname(v0, v1) = v5 & fun_pname_bool(v5) & nat(v7) &
% 178.32/24.96 | nat(v6))))))
% 178.32/24.96 |
% 178.32/24.96 | ALPHA: (fact_112_rev__finite__subset) implies:
% 178.32/24.96 | (3) ! [v0: fun_a_bool] : ! [v1: fun_a_bool] : ! [v2:
% 178.32/24.96 | fun_fun_a_bool_bool] : ! [v3: bool] : ( ~
% 178.32/24.96 | (hAPP_f1631501043l_bool(ord_le1311769555a_bool, v0) = v2) | ~
% 178.32/24.96 | (hAPP_fun_a_bool_bool(v2, v1) = v3) | ~ fun_a_bool(v1) | ~
% 178.32/24.96 | fun_a_bool(v0) | ~ hBOOL(v3) | ? [v4: bool] : ? [v5: bool] :
% 178.32/24.96 | ((hAPP_fun_a_bool_bool(finite_finite_a, v1) = v4 & bool(v4) & ~
% 178.32/24.96 | hBOOL(v4)) | (hAPP_fun_a_bool_bool(finite_finite_a, v0) = v5 &
% 178.32/24.96 | bool(v5) & hBOOL(v5))))
% 178.32/24.96 |
% 178.32/24.96 | ALPHA: (fact_215_image__eqI) implies:
% 178.32/24.96 | (4) ! [v0: fun_pname_bool] : ! [v1: x_a] : ! [v2: fun_pname_a] : ! [v3:
% 178.32/24.96 | pname] : ! [v4: fun_fu1430349052l_bool] : ! [v5: bool] : ! [v6:
% 178.32/24.96 | fun_fun_a_bool_bool] : ! [v7: fun_a_bool] : ! [v8: bool] : ( ~
% 178.32/24.96 | (hAPP_a85458249l_bool(member_a, v1) = v6) | ~
% 178.32/24.96 | (hAPP_p338031245l_bool(member_pname, v3) = v4) | ~
% 178.32/24.96 | (image_pname_a(v2, v0) = v7) | ~ (hAPP_f1664156314l_bool(v4, v0) =
% 178.32/24.96 | v5) | ~ (hAPP_fun_a_bool_bool(v6, v7) = v8) | ~
% 178.32/24.96 | fun_pname_bool(v0) | ~ fun_pname_a(v2) | ~ pname(v3) | ~ x_a(v1) |
% 178.32/24.96 | ~ hBOOL(v5) | hBOOL(v8) | ? [v9: x_a] : ( ~ (v9 = v1) &
% 178.32/24.96 | hAPP_pname_a(v2, v3) = v9 & x_a(v9)))
% 178.32/24.96 |
% 178.32/24.96 | ALPHA: (fact_264_insert__absorb) implies:
% 178.32/24.96 | (5) ! [v0: pname] : ! [v1: fun_pname_bool] : ! [v2:
% 178.32/24.96 | fun_fu1430349052l_bool] : ! [v3: bool] : ( ~
% 178.32/24.96 | (hAPP_p338031245l_bool(member_pname, v0) = v2) | ~
% 178.32/24.96 | (hAPP_f1664156314l_bool(v2, v1) = v3) | ~ fun_pname_bool(v1) | ~
% 178.32/24.96 | pname(v0) | ~ hBOOL(v3) | insert_pname(v0, v1) = v1)
% 178.32/24.96 |
% 178.32/24.96 | ALPHA: (fact_324_insert__subset) implies:
% 178.32/24.96 | (6) ! [v0: x_a] : ! [v1: fun_a_bool] : ! [v2: fun_a_bool] : ! [v3:
% 178.32/24.96 | fun_a_bool] : ! [v4: fun_fun_a_bool_bool] : ! [v5: bool] : ( ~
% 178.32/24.96 | (insert_a(v0, v1) = v3) | ~
% 178.32/24.96 | (hAPP_f1631501043l_bool(ord_le1311769555a_bool, v3) = v4) | ~
% 178.32/24.96 | (hAPP_fun_a_bool_bool(v4, v2) = v5) | ~ fun_a_bool(v2) | ~
% 178.32/24.96 | fun_a_bool(v1) | ~ x_a(v0) | hBOOL(v5) | ? [v6:
% 178.32/24.96 | fun_fun_a_bool_bool] : ? [v7: bool] : ? [v8: fun_fun_a_bool_bool]
% 178.32/24.96 | : ? [v9: bool] : ((hAPP_a85458249l_bool(member_a, v0) = v6 &
% 178.32/24.96 | hAPP_fun_a_bool_bool(v6, v2) = v7 & fun_fun_a_bool_bool(v6) &
% 178.32/24.96 | bool(v7) & ~ hBOOL(v7)) |
% 178.32/24.96 | (hAPP_f1631501043l_bool(ord_le1311769555a_bool, v1) = v8 &
% 178.32/24.96 | hAPP_fun_a_bool_bool(v8, v2) = v9 & fun_fun_a_bool_bool(v8) &
% 178.32/24.96 | bool(v9) & ~ hBOOL(v9))))
% 178.32/24.96 |
% 178.32/24.96 | ALPHA: (fact_359_subsetI) implies:
% 178.32/24.96 | (7) ! [v0: fun_a_bool] : ! [v1: fun_a_bool] : ! [v2:
% 178.32/24.96 | fun_fun_a_bool_bool] : ! [v3: bool] : ( ~
% 178.32/24.96 | (hAPP_f1631501043l_bool(ord_le1311769555a_bool, v1) = v2) | ~
% 178.32/24.96 | (hAPP_fun_a_bool_bool(v2, v0) = v3) | ~ fun_a_bool(v1) | ~
% 178.32/24.96 | fun_a_bool(v0) | hBOOL(v3) | ? [v4: x_a] : ? [v5:
% 178.32/24.96 | fun_fun_a_bool_bool] : ? [v6: bool] : ? [v7: bool] :
% 178.32/24.96 | (hAPP_a85458249l_bool(member_a, v4) = v5 & hAPP_fun_a_bool_bool(v5,
% 178.32/24.96 | v1) = v6 & hAPP_fun_a_bool_bool(v5, v0) = v7 &
% 178.32/24.96 | fun_fun_a_bool_bool(v5) & bool(v7) & bool(v6) & x_a(v4) & hBOOL(v6)
% 178.32/24.96 | & ~ hBOOL(v7)))
% 178.32/24.96 |
% 178.32/24.96 | ALPHA: (conj_0) implies:
% 178.32/24.96 | (8) ? [v0: bool] : (hAPP_f1664156314l_bool(finite_finite_pname, u) = v0 &
% 178.32/24.96 | bool(v0) & hBOOL(v0))
% 178.32/24.96 |
% 178.32/24.96 | ALPHA: (conj_1) implies:
% 178.32/24.97 | (9) ? [v0: fun_fun_a_bool_bool] : ? [v1: fun_a_bool] : ? [v2: bool] :
% 178.32/24.97 | (image_pname_a(mgt_call, u) = v1 &
% 178.32/24.97 | hAPP_f1631501043l_bool(ord_le1311769555a_bool, g) = v0 &
% 178.32/24.97 | hAPP_fun_a_bool_bool(v0, v1) = v2 & fun_fun_a_bool_bool(v0) &
% 178.32/24.97 | fun_a_bool(v1) & bool(v2) & hBOOL(v2))
% 178.32/24.97 |
% 178.32/24.97 | ALPHA: (conj_2) implies:
% 178.32/24.97 | (10) ? [v0: nat] : ? [v1: fun_nat_bool] : ? [v2: fun_a_bool] : ? [v3:
% 178.32/24.97 | nat] : ? [v4: bool] : (hAPP_nat_nat(suc, na) = v0 &
% 178.32/24.97 | hAPP_fun_a_bool_nat(finite_card_a, v2) = v3 &
% 178.32/24.97 | hAPP_n1699378549t_bool(ord_less_eq_nat, v0) = v1 & hAPP_nat_bool(v1,
% 178.32/24.97 | v3) = v4 & image_pname_a(mgt_call, u) = v2 & fun_nat_bool(v1) &
% 178.32/24.97 | fun_a_bool(v2) & nat(v3) & nat(v0) & bool(v4) & hBOOL(v4))
% 178.32/24.97 |
% 178.32/24.97 | ALPHA: (conj_3) implies:
% 178.32/24.97 | (11) ? [v0: nat] : ? [v1: fun_a_bool] : ? [v2: nat] : ? [v3:
% 178.32/24.97 | fun_nat_nat] : ? [v4: nat] : (minus_minus_nat(v2) = v3 &
% 178.32/24.97 | hAPP_nat_nat(v3, v4) = v0 & hAPP_nat_nat(suc, na) = v4 &
% 178.32/24.97 | hAPP_fun_a_bool_nat(finite_card_a, v1) = v2 &
% 178.32/24.97 | hAPP_fun_a_bool_nat(finite_card_a, g) = v0 & image_pname_a(mgt_call,
% 178.32/24.97 | u) = v1 & fun_nat_nat(v3) & fun_a_bool(v1) & nat(v4) & nat(v2) &
% 178.32/24.97 | nat(v0))
% 178.32/24.97 |
% 178.32/24.97 | ALPHA: (conj_4) implies:
% 178.32/24.97 | (12) ? [v0: fun_fu1430349052l_bool] : ? [v1: bool] :
% 178.32/24.97 | (hAPP_p338031245l_bool(member_pname, pn) = v0 &
% 178.32/24.97 | hAPP_f1664156314l_bool(v0, u) = v1 & fun_fu1430349052l_bool(v0) &
% 178.32/24.97 | bool(v1) & hBOOL(v1))
% 178.32/24.97 |
% 178.32/24.97 | ALPHA: (conj_5) implies:
% 178.32/24.97 | (13) ? [v0: x_a] : ? [v1: fun_fun_a_bool_bool] : ? [v2: bool] :
% 178.32/24.97 | (hAPP_pname_a(mgt_call, pn) = v0 & hAPP_a85458249l_bool(member_a, v0)
% 178.32/24.97 | = v1 & hAPP_fun_a_bool_bool(v1, g) = v2 & fun_fun_a_bool_bool(v1) &
% 178.32/24.97 | bool(v2) & x_a(v0) & ~ hBOOL(v2))
% 178.32/24.97 |
% 178.32/24.97 | ALPHA: (conj_6) implies:
% 178.32/24.97 | (14) pname(pn)
% 178.32/24.97 | (15) fun_a_bool(g)
% 178.32/24.97 | (16) fun_pname_a(mgt_call)
% 178.32/24.97 | (17) fun_pname_bool(u)
% 178.32/24.97 | (18) ? [v0: x_a] : ? [v1: fun_a_bool] : ? [v2: fun_fun_a_bool_bool] : ?
% 178.32/24.97 | [v3: fun_a_bool] : ? [v4: bool] : (hAPP_pname_a(mgt_call, pn) = v0 &
% 178.32/24.97 | insert_a(v0, g) = v1 & image_pname_a(mgt_call, u) = v3 &
% 178.32/24.97 | hAPP_f1631501043l_bool(ord_le1311769555a_bool, v1) = v2 &
% 178.32/24.97 | hAPP_fun_a_bool_bool(v2, v3) = v4 & fun_fun_a_bool_bool(v2) &
% 178.32/24.97 | fun_a_bool(v3) & fun_a_bool(v1) & bool(v4) & x_a(v0) & ~ hBOOL(v4))
% 178.32/24.97 |
% 178.32/24.97 | ALPHA: (function-axioms) implies:
% 178.32/24.97 | (19) ! [v0: bool] : ! [v1: bool] : ! [v2: fun_a_bool] : ! [v3:
% 178.32/24.97 | fun_fun_a_bool_bool] : (v1 = v0 | ~ (hAPP_fun_a_bool_bool(v3, v2) =
% 178.32/24.97 | v1) | ~ (hAPP_fun_a_bool_bool(v3, v2) = v0))
% 178.32/24.97 | (20) ! [v0: fun_fun_a_bool_bool] : ! [v1: fun_fun_a_bool_bool] : ! [v2:
% 178.32/24.97 | fun_a_bool] : ! [v3: fun_fu1471507361l_bool] : (v1 = v0 | ~
% 178.32/24.97 | (hAPP_f1631501043l_bool(v3, v2) = v1) | ~
% 178.32/24.97 | (hAPP_f1631501043l_bool(v3, v2) = v0))
% 178.32/24.97 | (21) ! [v0: bool] : ! [v1: bool] : ! [v2: fun_pname_bool] : ! [v3:
% 178.32/24.97 | fun_fu1430349052l_bool] : (v1 = v0 | ~ (hAPP_f1664156314l_bool(v3,
% 178.32/24.97 | v2) = v1) | ~ (hAPP_f1664156314l_bool(v3, v2) = v0))
% 178.32/24.97 | (22) ! [v0: fun_a_bool] : ! [v1: fun_a_bool] : ! [v2: fun_pname_bool] :
% 178.32/24.97 | ! [v3: fun_pname_a] : (v1 = v0 | ~ (image_pname_a(v3, v2) = v1) | ~
% 178.32/24.97 | (image_pname_a(v3, v2) = v0))
% 178.32/24.97 | (23) ! [v0: fun_pname_bool] : ! [v1: fun_pname_bool] : ! [v2:
% 178.32/24.97 | fun_pname_bool] : ! [v3: pname] : (v1 = v0 | ~ (insert_pname(v3,
% 178.32/24.97 | v2) = v1) | ~ (insert_pname(v3, v2) = v0))
% 178.32/24.97 | (24) ! [v0: fun_fun_a_bool_bool] : ! [v1: fun_fun_a_bool_bool] : ! [v2:
% 178.32/24.97 | x_a] : ! [v3: fun_a_1255737515l_bool] : (v1 = v0 | ~
% 178.32/24.97 | (hAPP_a85458249l_bool(v3, v2) = v1) | ~ (hAPP_a85458249l_bool(v3,
% 178.32/24.97 | v2) = v0))
% 178.32/24.97 | (25) ! [v0: x_a] : ! [v1: x_a] : ! [v2: pname] : ! [v3: fun_pname_a] :
% 178.32/24.97 | (v1 = v0 | ~ (hAPP_pname_a(v3, v2) = v1) | ~ (hAPP_pname_a(v3, v2) =
% 178.32/24.97 | v0))
% 178.32/24.97 |
% 178.32/24.97 | DELTA: instantiating (8) with fresh symbol all_870_0 gives:
% 178.32/24.97 | (26) hAPP_f1664156314l_bool(finite_finite_pname, u) = all_870_0 &
% 178.32/24.97 | bool(all_870_0) & hBOOL(all_870_0)
% 178.32/24.97 |
% 178.32/24.97 | ALPHA: (26) implies:
% 178.32/24.97 | (27) hBOOL(all_870_0)
% 178.32/24.97 | (28) hAPP_f1664156314l_bool(finite_finite_pname, u) = all_870_0
% 178.32/24.97 |
% 178.32/24.97 | DELTA: instantiating (12) with fresh symbols all_912_0, all_912_1 gives:
% 178.32/24.97 | (29) hAPP_p338031245l_bool(member_pname, pn) = all_912_1 &
% 178.32/24.97 | hAPP_f1664156314l_bool(all_912_1, u) = all_912_0 &
% 178.32/24.97 | fun_fu1430349052l_bool(all_912_1) & bool(all_912_0) & hBOOL(all_912_0)
% 178.32/24.97 |
% 178.32/24.97 | ALPHA: (29) implies:
% 178.32/24.98 | (30) hBOOL(all_912_0)
% 178.32/24.98 | (31) hAPP_f1664156314l_bool(all_912_1, u) = all_912_0
% 178.32/24.98 | (32) hAPP_p338031245l_bool(member_pname, pn) = all_912_1
% 178.32/24.98 |
% 178.32/24.98 | DELTA: instantiating (9) with fresh symbols all_950_0, all_950_1, all_950_2
% 178.32/24.98 | gives:
% 178.32/24.98 | (33) image_pname_a(mgt_call, u) = all_950_1 &
% 178.32/24.98 | hAPP_f1631501043l_bool(ord_le1311769555a_bool, g) = all_950_2 &
% 178.32/24.98 | hAPP_fun_a_bool_bool(all_950_2, all_950_1) = all_950_0 &
% 178.32/24.98 | fun_fun_a_bool_bool(all_950_2) & fun_a_bool(all_950_1) &
% 178.32/24.98 | bool(all_950_0) & hBOOL(all_950_0)
% 178.32/24.98 |
% 178.32/24.98 | ALPHA: (33) implies:
% 178.32/24.98 | (34) hBOOL(all_950_0)
% 178.32/24.98 | (35) hAPP_fun_a_bool_bool(all_950_2, all_950_1) = all_950_0
% 178.32/24.98 | (36) hAPP_f1631501043l_bool(ord_le1311769555a_bool, g) = all_950_2
% 178.32/24.98 | (37) image_pname_a(mgt_call, u) = all_950_1
% 178.32/24.98 |
% 178.32/24.98 | DELTA: instantiating (13) with fresh symbols all_955_0, all_955_1, all_955_2
% 178.32/24.98 | gives:
% 178.32/24.98 | (38) hAPP_pname_a(mgt_call, pn) = all_955_2 &
% 178.32/24.98 | hAPP_a85458249l_bool(member_a, all_955_2) = all_955_1 &
% 178.32/24.98 | hAPP_fun_a_bool_bool(all_955_1, g) = all_955_0 &
% 178.32/24.98 | fun_fun_a_bool_bool(all_955_1) & bool(all_955_0) & x_a(all_955_2) & ~
% 178.32/24.98 | hBOOL(all_955_0)
% 178.32/24.98 |
% 178.32/24.98 | ALPHA: (38) implies:
% 178.32/24.98 | (39) hAPP_a85458249l_bool(member_a, all_955_2) = all_955_1
% 178.32/24.98 | (40) hAPP_pname_a(mgt_call, pn) = all_955_2
% 178.32/24.98 |
% 178.32/24.98 | DELTA: instantiating (11) with fresh symbols all_978_0, all_978_1, all_978_2,
% 178.32/24.98 | all_978_3, all_978_4 gives:
% 178.32/24.98 | (41) minus_minus_nat(all_978_2) = all_978_1 & hAPP_nat_nat(all_978_1,
% 178.32/24.98 | all_978_0) = all_978_4 & hAPP_nat_nat(suc, na) = all_978_0 &
% 178.32/24.98 | hAPP_fun_a_bool_nat(finite_card_a, all_978_3) = all_978_2 &
% 178.32/24.98 | hAPP_fun_a_bool_nat(finite_card_a, g) = all_978_4 &
% 178.32/24.98 | image_pname_a(mgt_call, u) = all_978_3 & fun_nat_nat(all_978_1) &
% 178.32/24.98 | fun_a_bool(all_978_3) & nat(all_978_0) & nat(all_978_2) &
% 178.32/24.98 | nat(all_978_4)
% 178.32/24.98 |
% 178.32/24.98 | ALPHA: (41) implies:
% 178.32/24.98 | (42) fun_a_bool(all_978_3)
% 178.32/24.98 | (43) image_pname_a(mgt_call, u) = all_978_3
% 178.32/24.98 |
% 178.32/24.98 | DELTA: instantiating (18) with fresh symbols all_980_0, all_980_1, all_980_2,
% 178.32/24.98 | all_980_3, all_980_4 gives:
% 178.32/24.98 | (44) hAPP_pname_a(mgt_call, pn) = all_980_4 & insert_a(all_980_4, g) =
% 178.32/24.98 | all_980_3 & image_pname_a(mgt_call, u) = all_980_1 &
% 178.32/24.98 | hAPP_f1631501043l_bool(ord_le1311769555a_bool, all_980_3) = all_980_2
% 178.32/24.98 | & hAPP_fun_a_bool_bool(all_980_2, all_980_1) = all_980_0 &
% 178.32/24.98 | fun_fun_a_bool_bool(all_980_2) & fun_a_bool(all_980_1) &
% 178.32/24.98 | fun_a_bool(all_980_3) & bool(all_980_0) & x_a(all_980_4) & ~
% 178.32/24.98 | hBOOL(all_980_0)
% 178.32/24.98 |
% 178.32/24.98 | ALPHA: (44) implies:
% 178.32/24.98 | (45) ~ hBOOL(all_980_0)
% 178.32/24.98 | (46) x_a(all_980_4)
% 178.32/24.98 | (47) fun_a_bool(all_980_3)
% 178.32/24.98 | (48) hAPP_fun_a_bool_bool(all_980_2, all_980_1) = all_980_0
% 178.32/24.98 | (49) hAPP_f1631501043l_bool(ord_le1311769555a_bool, all_980_3) = all_980_2
% 178.32/24.98 | (50) image_pname_a(mgt_call, u) = all_980_1
% 178.32/24.98 | (51) insert_a(all_980_4, g) = all_980_3
% 178.32/24.98 | (52) hAPP_pname_a(mgt_call, pn) = all_980_4
% 178.32/24.98 |
% 178.32/24.98 | DELTA: instantiating (10) with fresh symbols all_982_0, all_982_1, all_982_2,
% 178.32/24.98 | all_982_3, all_982_4 gives:
% 178.32/24.98 | (53) hAPP_nat_nat(suc, na) = all_982_4 & hAPP_fun_a_bool_nat(finite_card_a,
% 178.32/24.98 | all_982_2) = all_982_1 & hAPP_n1699378549t_bool(ord_less_eq_nat,
% 178.32/24.98 | all_982_4) = all_982_3 & hAPP_nat_bool(all_982_3, all_982_1) =
% 178.32/24.98 | all_982_0 & image_pname_a(mgt_call, u) = all_982_2 &
% 178.32/24.98 | fun_nat_bool(all_982_3) & fun_a_bool(all_982_2) & nat(all_982_1) &
% 178.32/24.98 | nat(all_982_4) & bool(all_982_0) & hBOOL(all_982_0)
% 178.32/24.98 |
% 178.32/24.98 | ALPHA: (53) implies:
% 178.32/24.98 | (54) image_pname_a(mgt_call, u) = all_982_2
% 178.32/24.98 |
% 178.32/24.98 | GROUND_INST: instantiating (22) with all_978_3, all_980_1, u, mgt_call,
% 178.32/24.98 | simplifying with (43), (50) gives:
% 178.32/24.98 | (55) all_980_1 = all_978_3
% 178.32/24.98 |
% 178.32/24.98 | GROUND_INST: instantiating (22) with all_980_1, all_982_2, u, mgt_call,
% 178.32/24.98 | simplifying with (50), (54) gives:
% 178.32/24.98 | (56) all_982_2 = all_980_1
% 178.32/24.98 |
% 178.32/24.98 | GROUND_INST: instantiating (22) with all_950_1, all_982_2, u, mgt_call,
% 178.32/24.98 | simplifying with (37), (54) gives:
% 178.32/24.98 | (57) all_982_2 = all_950_1
% 178.32/24.98 |
% 178.32/24.98 | GROUND_INST: instantiating (25) with all_955_2, all_980_4, pn, mgt_call,
% 178.32/24.98 | simplifying with (40), (52) gives:
% 178.32/24.98 | (58) all_980_4 = all_955_2
% 178.32/24.98 |
% 178.32/24.98 | COMBINE_EQS: (56), (57) imply:
% 178.32/24.98 | (59) all_980_1 = all_950_1
% 178.32/24.98 |
% 178.32/24.98 | SIMP: (59) implies:
% 178.32/24.98 | (60) all_980_1 = all_950_1
% 178.32/24.98 |
% 178.32/24.98 | COMBINE_EQS: (55), (60) imply:
% 178.32/24.98 | (61) all_978_3 = all_950_1
% 178.32/24.98 |
% 178.32/24.98 | REDUCE: (51), (58) imply:
% 178.32/24.98 | (62) insert_a(all_955_2, g) = all_980_3
% 178.32/24.98 |
% 178.32/24.98 | REDUCE: (48), (60) imply:
% 178.32/24.98 | (63) hAPP_fun_a_bool_bool(all_980_2, all_950_1) = all_980_0
% 178.32/24.98 |
% 178.32/24.98 | REDUCE: (42), (61) imply:
% 178.32/24.98 | (64) fun_a_bool(all_950_1)
% 178.32/24.98 |
% 178.32/24.98 | REDUCE: (46), (58) imply:
% 178.32/24.98 | (65) x_a(all_955_2)
% 178.32/24.98 |
% 178.32/24.98 | GROUND_INST: instantiating (3) with g, all_950_1, all_950_2, all_950_0,
% 178.32/24.98 | simplifying with (15), (34), (35), (36), (64) gives:
% 178.32/24.98 | (66) ? [v0: bool] : ? [v1: bool] :
% 178.32/24.98 | ((hAPP_fun_a_bool_bool(finite_finite_a, all_950_1) = v0 & bool(v0) &
% 178.32/24.98 | ~ hBOOL(v0)) | (hAPP_fun_a_bool_bool(finite_finite_a, g) = v1 &
% 178.32/24.98 | bool(v1) & hBOOL(v1)))
% 178.32/24.98 |
% 178.32/24.98 | GROUND_INST: instantiating (7) with all_950_1, all_980_3, all_980_2,
% 178.32/24.98 | all_980_0, simplifying with (45), (47), (49), (63), (64) gives:
% 178.32/24.99 | (67) ? [v0: x_a] : ? [v1: fun_fun_a_bool_bool] : ? [v2: bool] : ? [v3:
% 178.32/24.99 | bool] : (hAPP_a85458249l_bool(member_a, v0) = v1 &
% 178.32/24.99 | hAPP_fun_a_bool_bool(v1, all_980_3) = v2 & hAPP_fun_a_bool_bool(v1,
% 178.32/24.99 | all_950_1) = v3 & fun_fun_a_bool_bool(v1) & bool(v3) & bool(v2) &
% 178.32/24.99 | x_a(v0) & hBOOL(v2) & ~ hBOOL(v3))
% 178.32/24.99 |
% 178.32/24.99 | GROUND_INST: instantiating (1) with mgt_call, u, all_950_1, simplifying with
% 178.32/24.99 | (16), (17), (37) gives:
% 178.32/24.99 | (68) ? [v0: bool] : ? [v1: bool] :
% 178.32/24.99 | ((hAPP_f1664156314l_bool(finite_finite_pname, u) = v0 & bool(v0) & ~
% 178.32/24.99 | hBOOL(v0)) | (hAPP_fun_a_bool_bool(finite_finite_a, all_950_1) =
% 178.32/24.99 | v1 & bool(v1) & hBOOL(v1)))
% 178.32/24.99 |
% 178.32/24.99 | GROUND_INST: instantiating (6) with all_955_2, g, all_950_1, all_980_3,
% 178.32/24.99 | all_980_2, all_980_0, simplifying with (15), (45), (49), (62),
% 178.32/24.99 | (63), (64), (65) gives:
% 178.32/24.99 | (69) ? [v0: fun_fun_a_bool_bool] : ? [v1: bool] : ? [v2:
% 178.32/24.99 | fun_fun_a_bool_bool] : ? [v3: bool] :
% 178.32/24.99 | ((hAPP_a85458249l_bool(member_a, all_955_2) = v0 &
% 178.32/24.99 | hAPP_fun_a_bool_bool(v0, all_950_1) = v1 & fun_fun_a_bool_bool(v0)
% 178.32/24.99 | & bool(v1) & ~ hBOOL(v1)) |
% 178.32/24.99 | (hAPP_f1631501043l_bool(ord_le1311769555a_bool, g) = v2 &
% 178.32/24.99 | hAPP_fun_a_bool_bool(v2, all_950_1) = v3 & fun_fun_a_bool_bool(v2)
% 178.32/24.99 | & bool(v3) & ~ hBOOL(v3)))
% 178.32/24.99 |
% 178.32/24.99 | GROUND_INST: instantiating (5) with pn, u, all_912_1, all_912_0, simplifying
% 178.32/24.99 | with (14), (17), (30), (31), (32) gives:
% 178.32/24.99 | (70) insert_pname(pn, u) = u
% 178.32/24.99 |
% 178.32/24.99 | GROUND_INST: instantiating (2) with pn, u, all_912_1, all_912_0, simplifying
% 178.32/24.99 | with (14), (17), (31), (32) gives:
% 178.32/24.99 | (71) ? [v0: bool] : ? [v1: fun_pname_bool] : ? [v2: nat] : ? [v3: nat]
% 178.32/24.99 | : ? [v4: nat] : ((hAPP_f1664156314l_bool(finite_finite_pname, u) = v0
% 178.32/24.99 | & bool(v0) & ~ hBOOL(v0)) | (( ~ hBOOL(all_912_0) | (v3 = v2 &
% 178.32/24.99 | hAPP_f921600141ol_nat(finite_card_pname, v1) = v2 &
% 178.32/24.99 | hAPP_f921600141ol_nat(finite_card_pname, u) = v2 &
% 178.32/24.99 | insert_pname(pn, u) = v1 & fun_pname_bool(v1) & nat(v2))) &
% 178.32/24.99 | (hBOOL(all_912_0) | (v4 = v2 & hAPP_nat_nat(suc, v3) = v2 &
% 178.32/24.99 | hAPP_f921600141ol_nat(finite_card_pname, v1) = v2 &
% 178.32/24.99 | hAPP_f921600141ol_nat(finite_card_pname, u) = v3 &
% 178.32/24.99 | insert_pname(pn, u) = v1 & fun_pname_bool(v1) & nat(v3) &
% 178.32/24.99 | nat(v2)))))
% 178.32/24.99 |
% 178.32/24.99 | DELTA: instantiating (68) with fresh symbols all_1223_0, all_1223_1 gives:
% 178.32/24.99 | (72) (hAPP_f1664156314l_bool(finite_finite_pname, u) = all_1223_1 &
% 178.32/24.99 | bool(all_1223_1) & ~ hBOOL(all_1223_1)) |
% 178.32/24.99 | (hAPP_fun_a_bool_bool(finite_finite_a, all_950_1) = all_1223_0 &
% 178.32/24.99 | bool(all_1223_0) & hBOOL(all_1223_0))
% 178.32/24.99 |
% 178.32/24.99 | DELTA: instantiating (66) with fresh symbols all_1227_0, all_1227_1 gives:
% 178.32/24.99 | (73) (hAPP_fun_a_bool_bool(finite_finite_a, all_950_1) = all_1227_1 &
% 178.32/24.99 | bool(all_1227_1) & ~ hBOOL(all_1227_1)) |
% 178.32/24.99 | (hAPP_fun_a_bool_bool(finite_finite_a, g) = all_1227_0 &
% 178.32/24.99 | bool(all_1227_0) & hBOOL(all_1227_0))
% 178.32/24.99 |
% 178.32/24.99 | DELTA: instantiating (67) with fresh symbols all_1230_0, all_1230_1,
% 178.32/24.99 | all_1230_2, all_1230_3 gives:
% 178.32/24.99 | (74) hAPP_a85458249l_bool(member_a, all_1230_3) = all_1230_2 &
% 178.32/24.99 | hAPP_fun_a_bool_bool(all_1230_2, all_980_3) = all_1230_1 &
% 178.32/24.99 | hAPP_fun_a_bool_bool(all_1230_2, all_950_1) = all_1230_0 &
% 178.32/24.99 | fun_fun_a_bool_bool(all_1230_2) & bool(all_1230_0) & bool(all_1230_1)
% 178.32/24.99 | & x_a(all_1230_3) & hBOOL(all_1230_1) & ~ hBOOL(all_1230_0)
% 178.32/24.99 |
% 178.32/24.99 | ALPHA: (74) implies:
% 178.32/24.99 | (75) ~ hBOOL(all_1230_0)
% 178.32/24.99 | (76) x_a(all_1230_3)
% 178.32/24.99 | (77) hAPP_fun_a_bool_bool(all_1230_2, all_950_1) = all_1230_0
% 178.32/24.99 | (78) hAPP_a85458249l_bool(member_a, all_1230_3) = all_1230_2
% 178.32/24.99 |
% 178.32/24.99 | DELTA: instantiating (69) with fresh symbols all_1241_0, all_1241_1,
% 178.32/24.99 | all_1241_2, all_1241_3 gives:
% 178.32/24.99 | (79) (hAPP_a85458249l_bool(member_a, all_955_2) = all_1241_3 &
% 178.32/24.99 | hAPP_fun_a_bool_bool(all_1241_3, all_950_1) = all_1241_2 &
% 178.32/24.99 | fun_fun_a_bool_bool(all_1241_3) & bool(all_1241_2) & ~
% 178.32/24.99 | hBOOL(all_1241_2)) | (hAPP_f1631501043l_bool(ord_le1311769555a_bool,
% 178.32/24.99 | g) = all_1241_1 & hAPP_fun_a_bool_bool(all_1241_1, all_950_1) =
% 178.32/24.99 | all_1241_0 & fun_fun_a_bool_bool(all_1241_1) & bool(all_1241_0) & ~
% 178.32/24.99 | hBOOL(all_1241_0))
% 178.32/24.99 |
% 178.32/24.99 | DELTA: instantiating (71) with fresh symbols all_1248_0, all_1248_1,
% 178.32/24.99 | all_1248_2, all_1248_3, all_1248_4 gives:
% 178.32/24.99 | (80) (hAPP_f1664156314l_bool(finite_finite_pname, u) = all_1248_4 &
% 178.32/24.99 | bool(all_1248_4) & ~ hBOOL(all_1248_4)) | (( ~ hBOOL(all_912_0) |
% 178.32/24.99 | (all_1248_1 = all_1248_2 &
% 178.32/24.99 | hAPP_f921600141ol_nat(finite_card_pname, all_1248_3) =
% 178.32/24.99 | all_1248_2 & hAPP_f921600141ol_nat(finite_card_pname, u) =
% 178.32/24.99 | all_1248_2 & insert_pname(pn, u) = all_1248_3 &
% 178.32/24.99 | fun_pname_bool(all_1248_3) & nat(all_1248_2))) &
% 178.32/24.99 | (hBOOL(all_912_0) | (all_1248_0 = all_1248_2 & hAPP_nat_nat(suc,
% 178.32/24.99 | all_1248_1) = all_1248_2 &
% 178.32/24.99 | hAPP_f921600141ol_nat(finite_card_pname, all_1248_3) =
% 178.32/24.99 | all_1248_2 & hAPP_f921600141ol_nat(finite_card_pname, u) =
% 178.32/24.99 | all_1248_1 & insert_pname(pn, u) = all_1248_3 &
% 178.32/24.99 | fun_pname_bool(all_1248_3) & nat(all_1248_1) &
% 178.32/24.99 | nat(all_1248_2))))
% 178.32/24.99 |
% 178.32/24.99 | BETA: splitting (79) gives:
% 178.32/24.99 |
% 178.32/24.99 | Case 1:
% 178.32/24.99 | |
% 178.32/24.99 | | (81) hAPP_a85458249l_bool(member_a, all_955_2) = all_1241_3 &
% 178.32/24.99 | | hAPP_fun_a_bool_bool(all_1241_3, all_950_1) = all_1241_2 &
% 178.32/24.99 | | fun_fun_a_bool_bool(all_1241_3) & bool(all_1241_2) & ~
% 178.32/24.99 | | hBOOL(all_1241_2)
% 178.32/24.99 | |
% 178.32/24.99 | | ALPHA: (81) implies:
% 178.32/24.99 | | (82) ~ hBOOL(all_1241_2)
% 178.32/24.99 | | (83) hAPP_fun_a_bool_bool(all_1241_3, all_950_1) = all_1241_2
% 178.32/24.99 | | (84) hAPP_a85458249l_bool(member_a, all_955_2) = all_1241_3
% 178.32/24.99 | |
% 178.32/24.99 | | BETA: splitting (80) gives:
% 178.32/24.99 | |
% 178.32/24.99 | | Case 1:
% 178.32/24.99 | | |
% 178.32/24.99 | | | (85) hAPP_f1664156314l_bool(finite_finite_pname, u) = all_1248_4 &
% 178.32/24.99 | | | bool(all_1248_4) & ~ hBOOL(all_1248_4)
% 178.32/24.99 | | |
% 178.32/24.99 | | | ALPHA: (85) implies:
% 178.32/24.99 | | | (86) ~ hBOOL(all_1248_4)
% 178.32/24.99 | | | (87) hAPP_f1664156314l_bool(finite_finite_pname, u) = all_1248_4
% 178.32/24.99 | | |
% 178.32/24.99 | | | GROUND_INST: instantiating (21) with all_870_0, all_1248_4, u,
% 178.32/24.99 | | | finite_finite_pname, simplifying with (28), (87) gives:
% 178.32/24.99 | | | (88) all_1248_4 = all_870_0
% 178.32/24.99 | | |
% 178.32/24.99 | | | REDUCE: (86), (88) imply:
% 178.32/24.99 | | | (89) ~ hBOOL(all_870_0)
% 178.32/24.99 | | |
% 178.32/24.99 | | | PRED_UNIFY: (27), (89) imply:
% 178.32/24.99 | | | (90) $false
% 178.32/25.00 | | |
% 178.32/25.00 | | | CLOSE: (90) is inconsistent.
% 178.32/25.00 | | |
% 178.32/25.00 | | Case 2:
% 178.32/25.00 | | |
% 178.32/25.00 | | | (91) ( ~ hBOOL(all_912_0) | (all_1248_1 = all_1248_2 &
% 178.32/25.00 | | | hAPP_f921600141ol_nat(finite_card_pname, all_1248_3) =
% 178.32/25.00 | | | all_1248_2 & hAPP_f921600141ol_nat(finite_card_pname, u) =
% 178.32/25.00 | | | all_1248_2 & insert_pname(pn, u) = all_1248_3 &
% 178.32/25.00 | | | fun_pname_bool(all_1248_3) & nat(all_1248_2))) &
% 178.32/25.00 | | | (hBOOL(all_912_0) | (all_1248_0 = all_1248_2 & hAPP_nat_nat(suc,
% 178.32/25.00 | | | all_1248_1) = all_1248_2 &
% 178.32/25.00 | | | hAPP_f921600141ol_nat(finite_card_pname, all_1248_3) =
% 178.32/25.00 | | | all_1248_2 & hAPP_f921600141ol_nat(finite_card_pname, u) =
% 178.32/25.00 | | | all_1248_1 & insert_pname(pn, u) = all_1248_3 &
% 178.32/25.00 | | | fun_pname_bool(all_1248_3) & nat(all_1248_1) &
% 178.32/25.00 | | | nat(all_1248_2)))
% 178.32/25.00 | | |
% 178.32/25.00 | | | ALPHA: (91) implies:
% 178.32/25.00 | | | (92) ~ hBOOL(all_912_0) | (all_1248_1 = all_1248_2 &
% 178.32/25.00 | | | hAPP_f921600141ol_nat(finite_card_pname, all_1248_3) =
% 178.32/25.00 | | | all_1248_2 & hAPP_f921600141ol_nat(finite_card_pname, u) =
% 178.32/25.00 | | | all_1248_2 & insert_pname(pn, u) = all_1248_3 &
% 178.32/25.00 | | | fun_pname_bool(all_1248_3) & nat(all_1248_2))
% 178.32/25.00 | | |
% 178.32/25.00 | | | BETA: splitting (92) gives:
% 178.32/25.00 | | |
% 178.32/25.00 | | | Case 1:
% 178.32/25.00 | | | |
% 178.32/25.00 | | | | (93) ~ hBOOL(all_912_0)
% 178.32/25.00 | | | |
% 178.32/25.00 | | | | PRED_UNIFY: (30), (93) imply:
% 178.32/25.00 | | | | (94) $false
% 178.32/25.00 | | | |
% 178.32/25.00 | | | | CLOSE: (94) is inconsistent.
% 178.32/25.00 | | | |
% 178.32/25.00 | | | Case 2:
% 178.32/25.00 | | | |
% 178.32/25.00 | | | | (95) all_1248_1 = all_1248_2 &
% 178.32/25.00 | | | | hAPP_f921600141ol_nat(finite_card_pname, all_1248_3) =
% 178.32/25.00 | | | | all_1248_2 & hAPP_f921600141ol_nat(finite_card_pname, u) =
% 178.32/25.00 | | | | all_1248_2 & insert_pname(pn, u) = all_1248_3 &
% 178.32/25.00 | | | | fun_pname_bool(all_1248_3) & nat(all_1248_2)
% 178.32/25.00 | | | |
% 178.32/25.00 | | | | ALPHA: (95) implies:
% 178.32/25.00 | | | | (96) fun_pname_bool(all_1248_3)
% 178.32/25.00 | | | | (97) insert_pname(pn, u) = all_1248_3
% 178.32/25.00 | | | |
% 178.32/25.00 | | | | BETA: splitting (72) gives:
% 178.32/25.00 | | | |
% 178.32/25.00 | | | | Case 1:
% 178.32/25.00 | | | | |
% 178.32/25.00 | | | | | (98) hAPP_f1664156314l_bool(finite_finite_pname, u) = all_1223_1 &
% 178.32/25.00 | | | | | bool(all_1223_1) & ~ hBOOL(all_1223_1)
% 178.32/25.00 | | | | |
% 178.32/25.00 | | | | | ALPHA: (98) implies:
% 178.32/25.00 | | | | | (99) ~ hBOOL(all_1223_1)
% 178.32/25.00 | | | | | (100) hAPP_f1664156314l_bool(finite_finite_pname, u) = all_1223_1
% 178.32/25.00 | | | | |
% 178.32/25.00 | | | | | GROUND_INST: instantiating (21) with all_870_0, all_1223_1, u,
% 178.32/25.00 | | | | | finite_finite_pname, simplifying with (28), (100) gives:
% 178.32/25.00 | | | | | (101) all_1223_1 = all_870_0
% 178.32/25.00 | | | | |
% 178.32/25.00 | | | | | REDUCE: (99), (101) imply:
% 178.32/25.00 | | | | | (102) ~ hBOOL(all_870_0)
% 178.32/25.00 | | | | |
% 178.32/25.00 | | | | | PRED_UNIFY: (27), (102) imply:
% 178.32/25.00 | | | | | (103) $false
% 178.32/25.00 | | | | |
% 178.32/25.00 | | | | | CLOSE: (103) is inconsistent.
% 178.32/25.00 | | | | |
% 178.32/25.00 | | | | Case 2:
% 178.32/25.00 | | | | |
% 178.32/25.00 | | | | | (104) hAPP_fun_a_bool_bool(finite_finite_a, all_950_1) = all_1223_0
% 178.32/25.00 | | | | | & bool(all_1223_0) & hBOOL(all_1223_0)
% 178.32/25.00 | | | | |
% 178.32/25.00 | | | | | ALPHA: (104) implies:
% 178.32/25.00 | | | | | (105) hBOOL(all_1223_0)
% 178.32/25.00 | | | | | (106) hAPP_fun_a_bool_bool(finite_finite_a, all_950_1) = all_1223_0
% 178.32/25.00 | | | | |
% 178.32/25.00 | | | | | BETA: splitting (73) gives:
% 178.32/25.00 | | | | |
% 178.32/25.00 | | | | | Case 1:
% 178.32/25.00 | | | | | |
% 178.32/25.00 | | | | | | (107) hAPP_fun_a_bool_bool(finite_finite_a, all_950_1) =
% 178.32/25.00 | | | | | | all_1227_1 & bool(all_1227_1) & ~ hBOOL(all_1227_1)
% 178.32/25.00 | | | | | |
% 178.32/25.00 | | | | | | ALPHA: (107) implies:
% 178.32/25.00 | | | | | | (108) ~ hBOOL(all_1227_1)
% 178.32/25.00 | | | | | | (109) hAPP_fun_a_bool_bool(finite_finite_a, all_950_1) =
% 178.32/25.00 | | | | | | all_1227_1
% 178.32/25.00 | | | | | |
% 178.32/25.00 | | | | | | GROUND_INST: instantiating (19) with all_1223_0, all_1227_1,
% 178.32/25.00 | | | | | | all_950_1, finite_finite_a, simplifying with (106),
% 178.32/25.00 | | | | | | (109) gives:
% 178.32/25.00 | | | | | | (110) all_1227_1 = all_1223_0
% 178.32/25.00 | | | | | |
% 178.32/25.00 | | | | | | REDUCE: (108), (110) imply:
% 178.32/25.00 | | | | | | (111) ~ hBOOL(all_1223_0)
% 178.32/25.00 | | | | | |
% 178.32/25.00 | | | | | | PRED_UNIFY: (105), (111) imply:
% 178.32/25.00 | | | | | | (112) $false
% 178.32/25.00 | | | | | |
% 178.32/25.00 | | | | | | CLOSE: (112) is inconsistent.
% 178.32/25.00 | | | | | |
% 178.32/25.00 | | | | | Case 2:
% 178.32/25.00 | | | | | |
% 178.32/25.00 | | | | | |
% 178.32/25.00 | | | | | | GROUND_INST: instantiating (23) with u, all_1248_3, u, pn,
% 178.32/25.00 | | | | | | simplifying with (70), (97) gives:
% 178.32/25.00 | | | | | | (113) all_1248_3 = u
% 178.32/25.00 | | | | | |
% 178.32/25.00 | | | | | | GROUND_INST: instantiating (24) with all_955_1, all_1241_3,
% 178.32/25.00 | | | | | | all_955_2, member_a, simplifying with (39), (84) gives:
% 178.32/25.00 | | | | | | (114) all_1241_3 = all_955_1
% 178.32/25.00 | | | | | |
% 178.32/25.00 | | | | | | REDUCE: (83), (114) imply:
% 178.32/25.00 | | | | | | (115) hAPP_fun_a_bool_bool(all_955_1, all_950_1) = all_1241_2
% 178.32/25.00 | | | | | |
% 178.32/25.00 | | | | | | GROUND_INST: instantiating (4) with u, all_955_2, mgt_call, pn,
% 178.32/25.00 | | | | | | all_912_1, all_912_0, all_955_1, all_950_1, all_1241_2,
% 178.32/25.00 | | | | | | simplifying with (14), (16), (17), (30), (31), (32),
% 178.32/25.00 | | | | | | (37), (39), (65), (82), (115) gives:
% 178.32/25.00 | | | | | | (116) ? [v0: any] : ( ~ (v0 = all_955_2) &
% 178.32/25.00 | | | | | | hAPP_pname_a(mgt_call, pn) = v0 & x_a(v0))
% 178.32/25.00 | | | | | |
% 178.32/25.00 | | | | | | GROUND_INST: instantiating (4) with u, all_1230_3, mgt_call, pn,
% 178.32/25.00 | | | | | | all_912_1, all_912_0, all_1230_2, all_950_1,
% 178.32/25.00 | | | | | | all_1230_0, simplifying with (14), (16), (17), (30),
% 178.32/25.00 | | | | | | (31), (32), (37), (75), (76), (77), (78) gives:
% 178.32/25.00 | | | | | | (117) ? [v0: any] : ( ~ (v0 = all_1230_3) &
% 178.32/25.00 | | | | | | hAPP_pname_a(mgt_call, pn) = v0 & x_a(v0))
% 178.32/25.00 | | | | | |
% 178.32/25.00 | | | | | | DELTA: instantiating (116) with fresh symbol all_1387_0 gives:
% 178.32/25.01 | | | | | | (118) ~ (all_1387_0 = all_955_2) & hAPP_pname_a(mgt_call, pn) =
% 178.32/25.01 | | | | | | all_1387_0 & x_a(all_1387_0)
% 178.32/25.01 | | | | | |
% 178.32/25.01 | | | | | | ALPHA: (118) implies:
% 178.32/25.01 | | | | | | (119) ~ (all_1387_0 = all_955_2)
% 178.32/25.01 | | | | | | (120) hAPP_pname_a(mgt_call, pn) = all_1387_0
% 178.32/25.01 | | | | | |
% 178.32/25.01 | | | | | | DELTA: instantiating (117) with fresh symbol all_1397_0 gives:
% 178.32/25.01 | | | | | | (121) ~ (all_1397_0 = all_1230_3) & hAPP_pname_a(mgt_call, pn) =
% 178.32/25.01 | | | | | | all_1397_0 & x_a(all_1397_0)
% 178.32/25.01 | | | | | |
% 178.32/25.01 | | | | | | ALPHA: (121) implies:
% 178.32/25.01 | | | | | | (122) hAPP_pname_a(mgt_call, pn) = all_1397_0
% 178.32/25.01 | | | | | |
% 178.32/25.01 | | | | | | GROUND_INST: instantiating (25) with all_955_2, all_1397_0, pn,
% 178.32/25.01 | | | | | | mgt_call, simplifying with (40), (122) gives:
% 178.32/25.01 | | | | | | (123) all_1397_0 = all_955_2
% 178.32/25.01 | | | | | |
% 178.32/25.01 | | | | | | GROUND_INST: instantiating (25) with all_1387_0, all_1397_0, pn,
% 178.32/25.01 | | | | | | mgt_call, simplifying with (120), (122) gives:
% 178.32/25.01 | | | | | | (124) all_1397_0 = all_1387_0
% 178.32/25.01 | | | | | |
% 178.32/25.01 | | | | | | COMBINE_EQS: (123), (124) imply:
% 178.32/25.01 | | | | | | (125) all_1387_0 = all_955_2
% 178.32/25.01 | | | | | |
% 178.32/25.01 | | | | | | REDUCE: (119), (125) imply:
% 178.32/25.01 | | | | | | (126) $false
% 178.32/25.01 | | | | | |
% 178.32/25.01 | | | | | | CLOSE: (126) is inconsistent.
% 178.32/25.01 | | | | | |
% 178.32/25.01 | | | | | End of split
% 178.32/25.01 | | | | |
% 178.32/25.01 | | | | End of split
% 178.32/25.01 | | | |
% 178.32/25.01 | | | End of split
% 178.32/25.01 | | |
% 178.32/25.01 | | End of split
% 178.32/25.01 | |
% 178.32/25.01 | Case 2:
% 178.32/25.01 | |
% 178.32/25.01 | | (127) hAPP_f1631501043l_bool(ord_le1311769555a_bool, g) = all_1241_1 &
% 178.32/25.01 | | hAPP_fun_a_bool_bool(all_1241_1, all_950_1) = all_1241_0 &
% 178.32/25.01 | | fun_fun_a_bool_bool(all_1241_1) & bool(all_1241_0) & ~
% 178.32/25.01 | | hBOOL(all_1241_0)
% 178.32/25.01 | |
% 178.32/25.01 | | ALPHA: (127) implies:
% 178.32/25.01 | | (128) ~ hBOOL(all_1241_0)
% 178.32/25.01 | | (129) hAPP_fun_a_bool_bool(all_1241_1, all_950_1) = all_1241_0
% 178.32/25.01 | | (130) hAPP_f1631501043l_bool(ord_le1311769555a_bool, g) = all_1241_1
% 178.32/25.01 | |
% 178.32/25.01 | | GROUND_INST: instantiating (20) with all_950_2, all_1241_1, g,
% 178.32/25.01 | | ord_le1311769555a_bool, simplifying with (36), (130) gives:
% 178.32/25.01 | | (131) all_1241_1 = all_950_2
% 178.32/25.01 | |
% 178.32/25.01 | | REDUCE: (129), (131) imply:
% 178.32/25.01 | | (132) hAPP_fun_a_bool_bool(all_950_2, all_950_1) = all_1241_0
% 178.32/25.01 | |
% 178.32/25.01 | | GROUND_INST: instantiating (19) with all_950_0, all_1241_0, all_950_1,
% 178.32/25.01 | | all_950_2, simplifying with (35), (132) gives:
% 178.32/25.01 | | (133) all_1241_0 = all_950_0
% 178.32/25.01 | |
% 178.32/25.01 | | REDUCE: (128), (133) imply:
% 178.32/25.01 | | (134) ~ hBOOL(all_950_0)
% 178.32/25.01 | |
% 178.32/25.01 | | PRED_UNIFY: (34), (134) imply:
% 178.32/25.01 | | (135) $false
% 178.32/25.01 | |
% 178.32/25.01 | | CLOSE: (135) is inconsistent.
% 178.32/25.01 | |
% 178.32/25.01 | End of split
% 178.32/25.01 |
% 178.32/25.01 End of proof
% 178.32/25.01 % SZS output end Proof for theBenchmark
% 178.32/25.01
% 178.32/25.01 24388ms
%------------------------------------------------------------------------------